LMFDB - Embedded newform 2301.1.z.c.818.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			818.2
Root			$-0.883512 - 0.468408i$ of defining polynomial
Character	$\chi$	$=$	2301.818
Dual form			2301.1.z.c.1910.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0695567 - 0.424277i) q^{2} +(-0.267528 + 0.963550i) q^{3} +(0.772480 + 0.260279i) q^{4} +(-0.771856 - 1.13840i) q^{5} +(0.390204 + 0.180527i) q^{6} +(0.365549 - 0.689499i) q^{8} +(-0.856857 - 0.515554i) q^{9} +(-0.536686 + 0.248297i) q^{10} +(-0.172146 + 0.130862i) q^{11} +(-0.457452 + 0.674691i) q^{12} +(0.856857 - 0.515554i) q^{13} +(1.30340 - 0.439167i) q^{15} +(0.381824 + 0.290255i) q^{16} +(-0.278338 + 0.327685i) q^{18} +(-0.299941 - 1.08029i) q^{20} +(0.0435477 + 0.0821397i) q^{22} +(0.566572 + 0.536686i) q^{24} +(-0.330060 + 0.828389i) q^{25} +(-0.159138 - 0.399405i) q^{26} +(0.725995 - 0.687699i) q^{27} +(-0.0956682 - 0.583550i) q^{30} +(0.716279 - 0.678496i) q^{32} +(-0.0800379 - 0.200880i) q^{33} +(-0.527717 - 0.621277i) q^{36} +(0.267528 + 0.963550i) q^{39} +(-1.06708 + 0.116052i) q^{40} +(1.27772 - 1.50424i) q^{41} +(-1.15592 - 0.878708i) q^{43} +(-0.167040 + 0.0562822i) q^{44} +(0.0744626 + 1.37338i) q^{45} +(0.471273 - 0.695075i) q^{47} +(-0.381824 + 0.290255i) q^{48} +(0.907575 - 0.419889i) q^{49} +(0.328509 + 0.197657i) q^{50} +(0.796093 - 0.175233i) q^{52} +(-0.241277 - 0.355857i) q^{54} +(0.281845 + 0.0949646i) q^{55} +(0.108119 + 0.994138i) q^{59} +1.12116 q^{60} +(0.315999 - 1.92751i) q^{61} +(0.0311094 + 0.0458829i) q^{64} +(-1.24828 - 0.577515i) q^{65} +(-0.0907960 + 0.0199857i) q^{66} +(-1.08146 + 1.59504i) q^{71} +(-0.668698 + 0.402342i) q^{72} +(-0.709894 - 0.539647i) q^{75} +(0.427421 - 0.0464848i) q^{78} +(0.0865625 + 0.311770i) q^{79} +(0.0357139 - 0.658704i) q^{80} +(0.468408 + 0.883512i) q^{81} +(-0.549342 - 0.646736i) q^{82} +(1.34887 + 1.27771i) q^{83} +(-0.453217 + 0.429310i) q^{86} +(0.0273013 + 0.166531i) q^{88} +(0.246608 + 1.50424i) q^{89} +(0.587874 + 0.0639351i) q^{90} +(-0.262124 - 0.248297i) q^{94} +(0.462140 + 0.871688i) q^{96} +(-0.115021 - 0.414270i) q^{98} +(0.214970 - 0.0233794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{12} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 2 q^{39} - 58 q^{40} - 4 q^{43} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 4 q^{61} + 2 q^{64} - 2 q^{75} + 4 q^{79}+ \cdots - 2 q^{81}+O(q^{100}) $ 56 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^12 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^27 + 2 * q^36 - 2 * q^39 - 58 * q^40 - 4 * q^43 + 2 * q^48 - 2 * q^49 - 2 * q^52 + 4 * q^61 + 2 * q^64 - 2 * q^75 + 4 * q^79 - 2 * q^81

Character values

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

$n$	$886$	$1535$	$2185$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{16}{29}\right)$

Coefficient data

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

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

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

$2$	0.0695567	−	0.424277i	0.0695567	−	0.424277i	−0.928977	−	0.370138i	$-0.879310\pi$
$2$	0.0695567	−	0.424277i	0.0695567	−	0.424277i	0.998533	−	0.0541389i	$-0.0172414\pi$
$3$	−0.267528	+	0.963550i	−0.267528	+	0.963550i
$3$	−0.267528	+	0.963550i	−0.267528	+	0.963550i
$4$	0.772480	+	0.260279i	0.772480	+	0.260279i
$5$	−0.771856	−	1.13840i	−0.771856	−	1.13840i	−0.986827	−	0.161782i	$-0.948276\pi$
$5$	−0.771856	−	1.13840i	−0.771856	−	1.13840i	0.214970	−	0.976621i	$-0.431034\pi$
$6$	0.390204	+	0.180527i	0.390204	+	0.180527i
$7$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$7$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$8$	0.365549	−	0.689499i	0.365549	−	0.689499i
$9$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$10$	−0.536686	+	0.248297i	−0.536686	+	0.248297i
$11$	−0.172146	+	0.130862i	−0.172146	+	0.130862i	−0.687699	−	0.725995i	$-0.741379\pi$
$11$	−0.172146	+	0.130862i	−0.172146	+	0.130862i	0.515554	+	0.856857i	$0.327586\pi$
$12$	−0.457452	+	0.674691i	−0.457452	+	0.674691i
$13$	0.856857	−	0.515554i	0.856857	−	0.515554i
$13$	0.856857	−	0.515554i	0.856857	−	0.515554i
$14$		0			0
$15$	1.30340	−	0.439167i	1.30340	−	0.439167i
$16$	0.381824	+	0.290255i	0.381824	+	0.290255i
$17$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$17$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$18$	−0.278338	+	0.327685i	−0.278338	+	0.327685i
$19$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$19$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$20$	−0.299941	−	1.08029i	−0.299941	−	1.08029i
$21$		0			0
$22$	0.0435477	+	0.0821397i	0.0435477	+	0.0821397i
$23$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$23$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$24$	0.566572	+	0.536686i	0.566572	+	0.536686i
$25$	−0.330060	+	0.828389i	−0.330060	+	0.828389i
$26$	−0.159138	−	0.399405i	−0.159138	−	0.399405i
$27$	0.725995	−	0.687699i	0.725995	−	0.687699i
$28$		0			0
$29$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$29$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$30$	−0.0956682	−	0.583550i	−0.0956682	−	0.583550i
$31$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$31$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$32$	0.716279	−	0.678496i	0.716279	−	0.678496i
$33$	−0.0800379	−	0.200880i	−0.0800379	−	0.200880i
$34$		0			0
$35$		0			0
$36$	−0.527717	−	0.621277i	−0.527717	−	0.621277i
$37$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$37$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$38$		0			0
$39$	0.267528	+	0.963550i	0.267528	+	0.963550i
$40$	−1.06708	+	0.116052i	−1.06708	+	0.116052i
$41$	1.27772	−	1.50424i	1.27772	−	1.50424i	0.515554	−	0.856857i	$-0.327586\pi$
$41$	1.27772	−	1.50424i	1.27772	−	1.50424i	0.762162	−	0.647386i	$-0.224138\pi$
$42$		0			0
$43$	−1.15592	−	0.878708i	−1.15592	−	0.878708i	−0.161782	−	0.986827i	$-0.551724\pi$
$43$	−1.15592	−	0.878708i	−1.15592	−	0.878708i	−0.994138	+	0.108119i	$0.965517\pi$
$44$	−0.167040	+	0.0562822i	−0.167040	+	0.0562822i
$45$	0.0744626	+	1.37338i	0.0744626	+	1.37338i
$46$		0			0
$47$	0.471273	−	0.695075i	0.471273	−	0.695075i	−0.515554	−	0.856857i	$-0.672414\pi$
$47$	0.471273	−	0.695075i	0.471273	−	0.695075i	0.986827	+	0.161782i	$0.0517241\pi$
$48$	−0.381824	+	0.290255i	−0.381824	+	0.290255i
$49$	0.907575	−	0.419889i	0.907575	−	0.419889i
$50$	0.328509	+	0.197657i	0.328509	+	0.197657i
$51$		0			0
$52$	0.796093	−	0.175233i	0.796093	−	0.175233i
$53$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$53$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$54$	−0.241277	−	0.355857i	−0.241277	−	0.355857i
$55$	0.281845	+	0.0949646i	0.281845	+	0.0949646i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.108119	+	0.994138i	0.108119	+	0.994138i
$59$	0.108119	+	0.994138i	0.108119	+	0.994138i
$60$	1.12116			1.12116
$61$	0.315999	−	1.92751i	0.315999	−	1.92751i	−0.0541389	−	0.998533i	$-0.517241\pi$
$61$	0.315999	−	1.92751i	0.315999	−	1.92751i	0.370138	−	0.928977i	$-0.379310\pi$
$62$		0			0
$63$		0			0
$64$	0.0311094	+	0.0458829i	0.0311094	+	0.0458829i
$65$	−1.24828	−	0.577515i	−1.24828	−	0.577515i
$66$	−0.0907960	+	0.0199857i	−0.0907960	+	0.0199857i
$67$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$67$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.08146	+	1.59504i	−1.08146	+	1.59504i	−0.319302	+	0.947653i	$0.603448\pi$
$71$	−1.08146	+	1.59504i	−1.08146	+	1.59504i	−0.762162	+	0.647386i	$0.775862\pi$
$72$	−0.668698	+	0.402342i	−0.668698	+	0.402342i
$73$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$73$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$74$		0			0
$75$	−0.709894	−	0.539647i	−0.709894	−	0.539647i
$76$		0			0
$77$		0			0
$78$	0.427421	−	0.0464848i	0.427421	−	0.0464848i
$79$	0.0865625	+	0.311770i	0.0865625	+	0.311770i	0.994138	−	0.108119i	$-0.0344828\pi$
$79$	0.0865625	+	0.311770i	0.0865625	+	0.311770i	−0.907575	+	0.419889i	$0.862069\pi$
$80$	0.0357139	−	0.658704i	0.0357139	−	0.658704i
$81$	0.468408	+	0.883512i	0.468408	+	0.883512i
$82$	−0.549342	−	0.646736i	−0.549342	−	0.646736i
$83$	1.34887	+	1.27771i	1.34887	+	1.27771i	0.928977	+	0.370138i	$0.120690\pi$
$83$	1.34887	+	1.27771i	1.34887	+	1.27771i	0.419889	+	0.907575i	$0.362069\pi$
$84$		0			0
$85$		0			0
$86$	−0.453217	+	0.429310i	−0.453217	+	0.429310i
$87$		0			0
$88$	0.0273013	+	0.166531i	0.0273013	+	0.166531i
$89$	0.246608	+	1.50424i	0.246608	+	1.50424i	0.762162	+	0.647386i	$0.224138\pi$
$89$	0.246608	+	1.50424i	0.246608	+	1.50424i	−0.515554	+	0.856857i	$0.672414\pi$
$90$	0.587874	+	0.0639351i	0.587874	+	0.0639351i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.262124	−	0.248297i	−0.262124	−	0.248297i
$95$		0			0
$96$	0.462140	+	0.871688i	0.462140	+	0.871688i
$97$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$97$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$98$	−0.115021	−	0.414270i	−0.115021	−	0.414270i
$99$	0.214970	−	0.0233794i	0.214970	−	0.0233794i
$100$	−0.470577	+	0.554007i	−0.470577	+	0.554007i
$101$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$101$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$102$		0			0
$103$	−0.507048	+	0.170844i	−0.507048	+	0.170844i	−0.561187	−	0.827689i	$-0.689655\pi$
$103$	−0.507048	+	0.170844i	−0.507048	+	0.170844i	0.0541389	+	0.998533i	$0.482759\pi$
$104$	−0.0422504	−	0.779263i	−0.0422504	−	0.779263i
$105$		0			0
$106$		0			0
$107$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$107$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$108$	0.739811	−	0.342273i	0.739811	−	0.342273i
$109$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$109$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$110$	0.0598955	−	0.112975i	0.0598955	−	0.112975i
$111$		0			0
$112$		0			0
$113$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$113$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000			−1.00000
$118$	0.429310	+	0.0232765i	0.429310	+	0.0232765i
$119$		0			0
$120$	0.173652	−	1.05923i	0.173652	−	1.05923i
$121$	−0.255019	+	0.918495i	−0.255019	+	0.918495i
$122$	−0.795818	−	0.268142i	−0.795818	−	0.268142i
$123$	1.10759	+	1.63357i	1.10759	+	1.63357i
$124$		0			0
$125$	−0.145443	+	0.0320145i	−0.145443	+	0.0320145i
$126$		0			0
$127$	−0.634311	−	0.381652i	−0.634311	−	0.381652i	0.161782	−	0.986827i	$-0.448276\pi$
$127$	−0.634311	−	0.381652i	−0.634311	−	0.381652i	−0.796093	+	0.605174i	$0.793103\pi$
$128$	0.917060	−	0.424277i	0.917060	−	0.424277i
$129$	1.15592	−	0.878708i	1.15592	−	0.878708i
$130$	−0.331852	+	0.489446i	−0.331852	+	0.489446i
$131$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$131$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$132$	−0.00954288	−	0.176008i	−0.00954288	−	0.176008i
$133$		0			0
$134$		0			0
$135$	−1.34324	−	0.295670i	−1.34324	−	0.295670i
$136$		0			0
$137$	−1.02506	+	0.111482i	−1.02506	+	0.111482i	−0.605174	−	0.796093i	$-0.706897\pi$
$137$	−1.02506	+	0.111482i	−1.02506	+	0.111482i	−0.419889	+	0.907575i	$0.637931\pi$
$138$		0			0
$139$	−0.0786092	+	1.44986i	−0.0786092	+	1.44986i	0.647386	+	0.762162i	$0.275862\pi$
$139$	−0.0786092	+	1.44986i	−0.0786092	+	1.44986i	−0.725995	+	0.687699i	$0.758621\pi$
$140$		0			0
$141$	0.543661	+	0.640047i	0.543661	+	0.640047i
$142$	0.601516	+	0.569786i	0.601516	+	0.569786i
$143$	−0.0800379	+	0.200880i	−0.0800379	+	0.200880i
$144$	−0.177526	−	0.445557i	−0.177526	−	0.445557i
$145$		0			0
$146$		0			0
$147$	0.161782	+	0.986827i	0.161782	+	0.986827i
$148$		0			0
$149$	−1.64567	−	0.178978i	−1.64567	−	0.178978i	−0.762162	−	0.647386i	$-0.775862\pi$
$149$	−1.64567	−	0.178978i	−1.64567	−	0.178978i	−0.883512	+	0.468408i	$0.844828\pi$
$150$	−0.278338	+	0.263656i	−0.278338	+	0.263656i
$151$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$151$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.0441314	+	0.813955i	−0.0441314	+	0.813955i
$157$	0.250625	+	0.902670i	0.250625	+	0.902670i	0.976621	+	0.214970i	$0.0689655\pi$
$157$	0.250625	+	0.902670i	0.250625	+	0.902670i	−0.725995	+	0.687699i	$0.758621\pi$
$158$	0.138298	−	0.0150408i	0.138298	−	0.0150408i
$159$		0			0
$160$	−1.32527	−	0.291713i	−1.32527	−	0.291713i
$161$		0			0
$162$	0.407435	−	0.137281i	0.407435	−	0.137281i
$163$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$163$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$164$	1.37853	−	0.829436i	1.37853	−	0.829436i
$165$	−0.166905	+	0.246166i	−0.166905	+	0.246166i
$166$	0.635927	−	0.483419i	0.635927	−	0.483419i
$167$	1.60371	−	0.741954i	1.60371	−	0.741954i	0.605174	−	0.796093i	$-0.293103\pi$
$167$	1.60371	−	0.741954i	1.60371	−	0.741954i	0.998533	+	0.0541389i	$0.0172414\pi$
$168$		0			0
$169$	0.468408	−	0.883512i	0.468408	−	0.883512i
$170$		0			0
$171$		0			0
$172$	−0.664216	−	0.979646i	−0.664216	−	0.979646i
$173$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$173$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$174$		0			0
$175$		0			0
$176$	−0.103712			−0.103712
$177$	−0.986827	−	0.161782i	−0.986827	−	0.161782i
$178$	0.655369			0.655369
$179$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$179$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$180$	−0.299941	+	1.08029i	−0.299941	+	1.08029i
$181$	−0.507048	−	0.170844i	−0.507048	−	0.170844i	0.0541389	−	0.998533i	$-0.482759\pi$
$181$	−0.507048	−	0.170844i	−0.507048	−	0.170844i	−0.561187	+	0.827689i	$0.689655\pi$
$182$		0			0
$183$	1.77271	+	0.820145i	1.77271	+	0.820145i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.544962	−	0.414270i	0.544962	−	0.414270i
$189$		0			0
$190$		0			0
$191$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$191$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$192$	−0.0525331	+	0.0177005i	−0.0525331	+	0.0177005i
$193$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$193$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$194$		0			0
$195$	0.890414	−	1.04828i	0.890414	−	1.04828i
$196$	0.810372	−	0.0881333i	0.810372	−	0.0881333i
$197$	−0.534272	−	1.92427i	−0.534272	−	1.92427i	−0.319302	−	0.947653i	$-0.603448\pi$
$197$	−0.534272	−	1.92427i	−0.534272	−	1.92427i	−0.214970	−	0.976621i	$-0.568966\pi$
$198$	0.00503327	−	0.0928332i	0.00503327	−	0.0928332i
$199$	−0.438813	−	0.827689i	−0.438813	−	0.827689i	0.561187	−	0.827689i	$-0.310345\pi$
$199$	−0.438813	−	0.827689i	−0.438813	−	0.827689i	−1.00000			$\pi$
$200$	0.450520	+	0.530394i	0.450520	+	0.530394i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.69865	−	0.293496i	−2.69865	−	0.293496i
$206$	0.0372168	+	0.227012i	0.0372168	+	0.227012i
$207$		0			0
$208$	0.476810	+	0.0518562i	0.476810	+	0.0518562i
$209$		0			0
$210$		0			0
$211$	−0.701525	+	1.76070i	−0.701525	+	1.76070i	−0.0541389	+	0.998533i	$0.517241\pi$
$211$	−0.701525	+	1.76070i	−0.701525	+	1.76070i	−0.647386	+	0.762162i	$0.724138\pi$
$212$		0			0
$213$	−1.24758	−	1.46876i	−1.24758	−	1.46876i
$214$		0			0
$215$	−0.108119	+	1.99414i	−0.108119	+	1.99414i
$216$	−0.208781	−	0.751962i	−0.208781	−	0.751962i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.193002	+	0.146717i	0.193002	+	0.146717i
$221$		0			0
$222$		0			0
$223$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$223$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$224$		0			0
$225$	0.709894	−	0.539647i	0.709894	−	0.539647i
$226$		0			0
$227$	−1.65125	−	0.993524i	−1.65125	−	0.993524i	−0.963550	−	0.267528i	$-0.913793\pi$
$227$	−1.65125	−	0.993524i	−1.65125	−	0.993524i	−0.687699	−	0.725995i	$-0.741379\pi$
$228$		0			0
$229$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$229$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$233$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$234$	−0.0695567	+	0.424277i	−0.0695567	+	0.424277i
$235$	−1.15503			−1.15503
$236$	−0.175233	+	0.796093i	−0.175233	+	0.796093i
$237$	−0.323564			−0.323564
$238$		0			0
$239$	−0.442861	+	1.59504i	−0.442861	+	1.59504i	0.319302	+	0.947653i	$0.396552\pi$
$239$	−0.442861	+	1.59504i	−0.442861	+	1.59504i	−0.762162	+	0.647386i	$0.775862\pi$
$240$	0.625140	+	0.210634i	0.625140	+	0.210634i
$241$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$241$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$242$	0.371958	+	0.172086i	0.371958	+	0.172086i
$243$	−0.976621	+	0.214970i	−0.976621	+	0.214970i
$244$	0.745793	−	1.40672i	0.745793	−	1.40672i
$245$	−1.17852	−	0.709092i	−1.17852	−	0.709092i
$246$	0.770127	−	0.356299i	0.770127	−	0.356299i
$247$		0			0
$248$		0			0
$249$	−1.59200	+	0.957875i	−1.59200	+	0.957875i
$250$	0.00346646	+	0.0639351i	0.00346646	+	0.0639351i
$251$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$251$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$252$		0			0
$253$		0			0
$254$	−0.206047	+	0.242577i	−0.206047	+	0.242577i
$255$		0			0
$256$	−0.101393	−	0.365184i	−0.101393	−	0.365184i
$257$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$257$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$258$	−0.292413	−	0.551550i	−0.292413	−	0.551550i
$259$		0			0
$260$	−0.813955	−	0.771019i	−0.813955	−	0.771019i
$261$		0			0
$262$		0			0
$263$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$263$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$264$	−0.167765	−	0.0182455i	−0.167765	−	0.0182455i
$265$		0			0
$266$		0			0
$267$	−1.51539	−	0.164808i	−1.51539	−	0.164808i
$268$		0			0
$269$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$269$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$270$	−0.218878	+	0.549341i	−0.218878	+	0.549341i
$271$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$271$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$272$		0			0
$273$		0			0
$274$	−0.0240006	+	0.442665i	−0.0240006	+	0.442665i
$275$	−0.0515860	−	0.185796i	−0.0515860	−	0.185796i
$276$		0			0
$277$	−0.726610	+	0.855431i	−0.726610	+	0.855431i	−0.994138	−	0.108119i	$-0.965517\pi$
$277$	−0.726610	+	0.855431i	−0.726610	+	0.855431i	0.267528	+	0.963550i	$0.413793\pi$
$278$	0.609675	+	0.134200i	0.609675	+	0.134200i
$279$		0			0
$280$		0			0
$281$		0			0		0.998533	−	0.0541389i	$-0.0172414\pi$
$281$		0			0		−0.998533	+	0.0541389i	$0.982759\pi$
$282$	0.309373	−	0.186143i	0.309373	−	0.186143i
$283$	−0.181580	+	0.267810i	−0.181580	+	0.267810i	−0.907575	−	0.419889i	$-0.862069\pi$
$283$	−0.181580	+	0.267810i	−0.181580	+	0.267810i	0.725995	+	0.687699i	$0.241379\pi$
$284$	−1.25056	+	0.950654i	−1.25056	+	0.950654i
$285$		0			0
$286$	0.0796616	+	0.0479308i	0.0796616	+	0.0479308i
$287$		0			0
$288$	−0.963550	+	0.212093i	−0.963550	+	0.212093i
$289$	0.907575	+	0.419889i	0.907575	+	0.419889i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.135861	+	0.828715i	−0.135861	+	0.828715i	0.827689	+	0.561187i	$0.189655\pi$
$293$	−0.135861	+	0.828715i	−0.135861	+	0.828715i	−0.963550	+	0.267528i	$0.913793\pi$
$294$	0.429941			0.429941
$295$	1.04828	−	0.890414i	1.04828	−	0.890414i
$296$		0			0
$297$	−0.0349834	+	0.213389i	−0.0349834	+	0.213389i
$298$	−0.190404	+	0.685773i	−0.190404	+	0.685773i
$299$		0			0
$300$	−0.407920	−	0.601637i	−0.407920	−	0.601637i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.43819	+	1.12803i	−2.43819	+	1.12803i
$306$		0			0
$307$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$307$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$308$		0			0
$309$	−0.0289674	−	0.534272i	−0.0289674	−	0.534272i
$310$		0			0
$311$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$311$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$312$	0.762162	+	0.167765i	0.762162	+	0.167765i
$313$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	−0.976621	−	0.214970i	$-0.931034\pi$
$313$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	0.370138	+	0.928977i	$0.379310\pi$
$314$	0.400415	−	0.0435477i	0.400415	−	0.0435477i
$315$		0			0
$316$	−0.0142793	+	0.263367i	−0.0142793	+	0.263367i
$317$	−0.393359	−	0.741954i	−0.393359	−	0.741954i	0.605174	−	0.796093i	$-0.293103\pi$
$317$	−0.393359	−	0.741954i	−0.393359	−	0.741954i	−0.998533	+	0.0541389i	$0.982759\pi$
$318$		0			0
$319$		0			0
$320$	0.0282212	−	0.0708300i	0.0282212	−	0.0708300i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.131877	+	0.804412i	0.131877	+	0.804412i
$325$	0.144265	+	0.879975i	0.144265	+	0.879975i
$326$		0			0
$327$		0			0
$328$	−0.570107	−	1.43086i	−0.570107	−	1.43086i
$329$		0			0
$330$	0.0928332	+	0.0879363i	0.0928332	+	0.0879363i
$331$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$331$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$332$	0.709410	+	1.33809i	0.709410	+	1.33809i
$333$		0			0
$334$	−0.203246	−	0.732024i	−0.203246	−	0.732024i
$335$		0			0
$336$		0			0
$337$	−1.77271	−	0.390204i	−1.77271	−	0.390204i	−0.796093	−	0.605174i	$-0.793103\pi$
$337$	−1.77271	−	0.390204i	−1.77271	−	0.390204i	−0.976621	+	0.214970i	$0.931034\pi$
$338$	−0.342273	−	0.260189i	−0.342273	−	0.260189i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−1.02841	+	0.475795i	−1.02841	+	0.475795i
$345$		0			0
$346$		0			0
$347$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$347$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$348$		0			0
$349$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$349$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$350$		0			0
$351$	0.267528	−	0.963550i	0.267528	−	0.963550i
$352$	−0.0345152	+	0.210534i	−0.0345152	+	0.210534i
$353$	0.638603			0.638603			0.319302	−	0.947653i	$-0.396552\pi$
$353$	0.638603			0.638603			0.319302	+	0.947653i	$0.396552\pi$
$354$	−0.137281	+	0.407435i	−0.137281	+	0.407435i
$355$	2.65053			2.65053
$356$	−0.201023	+	1.22619i	−0.201023	+	1.22619i
$357$		0			0
$358$		0			0
$359$	0.991631	+	1.46255i	0.991631	+	1.46255i	0.883512	+	0.468408i	$0.155172\pi$
$359$	0.991631	+	1.46255i	0.991631	+	1.46255i	0.108119	+	0.994138i	$0.465517\pi$
$360$	0.974166	+	0.450697i	0.974166	+	0.450697i
$361$	0.976621	−	0.214970i	0.976621	−	0.214970i
$362$	−0.107754	+	0.203246i	−0.107754	+	0.203246i
$363$	−0.816791	−	0.491447i	−0.816791	−	0.491447i
$364$		0			0
$365$		0			0
$366$	0.471273	−	0.695075i	0.471273	−	0.695075i
$367$	1.70367	−	1.02506i	1.70367	−	1.02506i	0.796093	−	0.605174i	$-0.206897\pi$
$367$	1.70367	−	1.02506i	1.70367	−	1.02506i	0.907575	−	0.419889i	$-0.137931\pi$
$368$		0			0
$369$	−1.87034	+	0.630190i	−1.87034	+	0.630190i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.58285	−	0.172146i	1.58285	−	0.172146i	0.725995	−	0.687699i	$-0.241379\pi$
$373$	1.58285	−	0.172146i	1.58285	−	0.172146i	0.856857	+	0.515554i	$0.172414\pi$
$374$		0			0
$375$	0.00806265	−	0.148707i	0.00806265	−	0.148707i
$376$	−0.306980	−	0.579027i	−0.306980	−	0.579027i
$377$		0			0
$378$		0			0
$379$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$379$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$380$		0			0
$381$	0.537437	−	0.509088i	0.537437	−	0.509088i
$382$		0			0
$383$	−0.195813	−	1.19440i	−0.195813	−	1.19440i	−0.883512	−	0.468408i	$-0.844828\pi$
$383$	−0.195813	−	1.19440i	−0.195813	−	1.19440i	0.687699	−	0.725995i	$-0.258621\pi$
$384$	0.163473	+	0.997139i	0.163473	+	0.997139i
$385$		0			0
$386$		0			0
$387$	0.537437	+	1.34887i	0.537437	+	1.34887i
$388$		0			0
$389$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$389$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$390$	−0.382826	−	0.450697i	−0.382826	−	0.450697i
$391$		0			0
$392$	0.0422504	−	0.779263i	0.0422504	−	0.779263i
$393$		0			0
$394$	−0.853587	+	0.0928332i	−0.853587	+	0.0928332i
$395$	0.288106	−	0.339185i	0.288106	−	0.339185i
$396$	0.172146	+	0.0378921i	0.172146	+	0.0378921i
$397$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$397$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$398$	−0.381692	+	0.128607i	−0.381692	+	0.128607i
$399$		0			0
$400$	−0.366469	+	0.220497i	−0.366469	+	0.220497i
$401$	−0.991631	+	1.46255i	−0.991631	+	1.46255i	−0.108119	+	0.994138i	$0.534483\pi$
$401$	−0.991631	+	1.46255i	−0.991631	+	1.46255i	−0.883512	+	0.468408i	$0.844828\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.644248	−	1.21518i	0.644248	−	1.21518i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$409$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$410$	−0.312232	+	1.12456i	−0.312232	+	1.12456i
$411$	0.166815	−	1.01752i	0.166815	−	1.01752i
$412$	−0.436152			−0.436152
$413$		0			0
$414$		0			0
$415$	0.413422	−	2.52176i	0.413422	−	2.52176i
$416$	0.263948	−	0.950654i	0.263948	−	0.950654i
$417$	−1.37598	−	0.463623i	−1.37598	−	0.463623i
$418$		0			0
$419$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$419$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$420$		0			0
$421$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$421$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$422$	0.698227	+	0.420109i	0.698227	+	0.420109i
$423$	−0.762162	+	0.352614i	−0.762162	+	0.352614i
$424$		0			0
$425$		0			0
$426$	−0.709940	+	0.427157i	−0.709940	+	0.427157i
$427$		0			0
$428$		0			0
$429$	−0.172146	−	0.130862i	−0.172146	−	0.130862i
$430$	0.838547	+	0.184578i	0.838547	+	0.184578i
$431$	0.413423	−	0.486719i	0.413423	−	0.486719i	−0.515554	−	0.856857i	$-0.672414\pi$
$431$	0.413423	−	0.486719i	0.413423	−	0.486719i	0.928977	+	0.370138i	$0.120690\pi$
$432$	0.476810	−	0.0518562i	0.476810	−	0.0518562i
$433$	0.458467	+	1.65125i	0.458467	+	1.65125i	0.725995	+	0.687699i	$0.241379\pi$
$433$	0.458467	+	1.65125i	0.458467	+	1.65125i	−0.267528	+	0.963550i	$0.586207\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.634311	+	1.59200i	0.634311	+	1.59200i	0.796093	+	0.605174i	$0.206897\pi$
$439$	0.634311	+	1.59200i	0.634311	+	1.59200i	−0.161782	+	0.986827i	$0.551724\pi$
$440$	0.168506	−	0.159618i	0.168506	−	0.159618i
$441$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$442$		0			0
$443$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$443$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$444$		0			0
$445$	1.52209	−	1.44180i	1.52209	−	1.44180i
$446$		0			0
$447$	0.612719	−	1.53781i	0.612719	−	1.53781i
$448$		0			0
$449$	1.29287	+	1.52209i	1.29287	+	1.52209i	0.687699	+	0.725995i	$0.258621\pi$
$449$	1.29287	+	1.52209i	1.29287	+	1.52209i	0.605174	+	0.796093i	$0.293103\pi$
$450$	−0.179582	−	0.338728i	−0.179582	−	0.338728i
$451$	−0.0231053	+	0.426153i	−0.0231053	+	0.426153i
$452$		0			0
$453$		0			0
$454$	−0.536385	+	0.631481i	−0.536385	+	0.631481i
$455$		0			0
$456$		0			0
$457$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$457$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.963550	−	0.732472i	0.963550	−	0.732472i		−	1.00000i	$-0.5\pi$
$461$	0.963550	−	0.732472i	0.963550	−	0.732472i	0.963550	+	0.267528i	$0.0862069\pi$
$462$		0			0
$463$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$463$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$467$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$468$	−0.772480	−	0.260279i	−0.772480	−	0.260279i
$469$		0			0
$470$	−0.0803401	+	0.490053i	−0.0803401	+	0.490053i
$471$	−0.936817			−0.936817
$472$	0.724980	+	0.288859i	0.724980	+	0.288859i
$473$	0.313976			0.313976
$474$	−0.0225060	+	0.137281i	−0.0225060	+	0.137281i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.645935	+	0.298841i	0.645935	+	0.298841i
$479$	−0.419889	+	0.0924246i	−0.419889	+	0.0924246i	−0.419889	−	0.907575i	$-0.637931\pi$
$479$	−0.419889	+	0.0924246i	−0.419889	+	0.0924246i			1.00000i	$0.5\pi$
$480$	0.635626	−	1.19892i	0.635626	−	1.19892i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.436062	+	0.643144i	−0.436062	+	0.643144i
$485$		0			0
$486$	0.0232765	+	0.429310i	0.0232765	+	0.429310i
$487$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$487$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$488$	−1.21350	−	0.922482i	−1.21350	−	0.922482i
$489$		0			0
$490$	−0.382826	+	0.450697i	−0.382826	+	0.450697i
$491$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$491$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$492$	0.430406	+	1.55018i	0.430406	+	1.55018i
$493$		0			0
$494$		0			0
$495$	−0.192541	−	0.226677i	−0.192541	−	0.226677i
$496$		0			0
$497$		0			0
$498$	0.295670	+	0.742076i	0.295670	+	0.742076i
$499$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$499$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$500$	−0.120685	−	0.0131253i	−0.120685	−	0.0131253i
$501$	0.285873	+	1.74375i	0.285873	+	1.74375i
$502$		0			0
$503$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$503$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.725995	+	0.687699i	0.725995	+	0.687699i
$508$	−0.390657	−	0.459917i	−0.390657	−	0.459917i
$509$	0.714006	+	1.34676i	0.714006	+	1.34676i	0.928977	+	0.370138i	$0.120690\pi$
$509$	0.714006	+	1.34676i	0.714006	+	1.34676i	−0.214970	+	0.976621i	$0.568966\pi$
$510$		0			0
$511$		0			0
$512$	0.842535	−	0.0916312i	0.842535	−	0.0916312i
$513$		0			0
$514$		0			0
$515$	0.585858	+	0.445358i	0.585858	+	0.445358i
$516$	1.12163	−	0.377923i	1.12163	−	0.377923i
$517$	0.00983119	+	0.181326i	0.00983119	+	0.181326i
$518$		0			0
$519$		0			0
$520$	−0.854504	+	0.649577i	−0.854504	+	0.649577i
$521$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$521$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$522$		0			0
$523$	−0.346752	+	0.654043i	−0.346752	+	0.654043i	−0.994138	−	0.108119i	$-0.965517\pi$
$523$	−0.346752	+	0.654043i	−0.346752	+	0.654043i	0.647386	+	0.762162i	$0.275862\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.0277460	−	0.0999321i	0.0277460	−	0.0999321i
$529$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$530$		0			0
$531$	0.419889	−	0.907575i	0.419889	−	0.907575i
$532$		0			0
$533$	0.319302	−	1.94765i	0.319302	−	1.94765i
$534$	−0.175330	+	0.631481i	−0.175330	+	0.631481i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.101288	+	0.191049i	−0.101288	+	0.191049i
$540$	−0.960672	−	0.578017i	−0.960672	−	0.578017i
$541$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$541$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$542$		0			0
$543$	0.300267	−	0.442861i	0.300267	−	0.442861i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.58285	−	1.20325i	−1.58285	−	1.20325i	−0.856857	−	0.515554i	$-0.827586\pi$
$547$	−1.58285	−	1.20325i	−1.58285	−	1.20325i	−0.725995	−	0.687699i	$-0.758621\pi$
$548$	−0.820858	−	0.180684i	−0.820858	−	0.180684i
$549$	−1.26450	+	1.48869i	−1.26450	+	1.48869i
$550$	−0.0824170	+	0.00896339i	−0.0824170	+	0.00896339i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.312399	+	0.367785i	0.312399	+	0.367785i
$555$		0			0
$556$	−0.438092	+	1.09953i	−0.438092	+	1.09953i
$557$	0.159138	+	0.399405i	0.159138	+	0.399405i	0.986827	−	0.161782i	$-0.0517241\pi$
$557$	0.159138	+	0.399405i	0.159138	+	0.399405i	−0.827689	+	0.561187i	$0.810345\pi$
$558$		0			0
$559$	−1.44348	−	0.156988i	−1.44348	−	0.156988i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$563$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$564$	0.253377	+	0.635927i	0.253377	+	0.635927i
$565$		0			0
$566$	0.100996	+	0.0956682i	0.100996	+	0.0956682i
$567$		0			0
$568$	0.704450	+	1.32873i	0.704450	+	1.32873i
$569$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$569$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$570$		0			0
$571$	0.107643	−	0.0117069i	0.107643	−	0.0117069i	−0.0541389	−	0.998533i	$-0.517241\pi$
$571$	0.107643	−	0.0117069i	0.107643	−	0.0117069i	0.161782	+	0.986827i	$0.448276\pi$
$572$	−0.114113	+	0.134344i	−0.114113	+	0.134344i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.00300119	−	0.0553536i	−0.00300119	−	0.0553536i
$577$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$577$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$578$	0.241277	−	0.355857i	0.241277	−	0.355857i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.771856	+	1.13840i	0.771856	+	1.13840i
$586$	0.342155	+	0.115285i	0.342155	+	0.115285i
$587$	0.497055	−	1.79023i	0.497055	−	1.79023i	−0.108119	−	0.994138i	$-0.534483\pi$
$587$	0.497055	−	1.79023i	0.497055	−	1.79023i	0.605174	−	0.796093i	$-0.293103\pi$
$588$	−0.131877	+	0.804412i	−0.131877	+	0.804412i
$589$		0			0
$590$	−0.304868	−	0.506694i	−0.304868	−	0.506694i
$591$	1.99707			1.99707
$592$		0			0
$593$	0.170844	−	0.615326i	0.170844	−	0.615326i	−0.827689	−	0.561187i	$-0.810345\pi$
$593$	0.170844	−	0.615326i	0.170844	−	0.615326i	0.998533	−	0.0541389i	$-0.0172414\pi$
$594$	0.0881029	+	0.0296853i	0.0881029	+	0.0296853i
$595$		0			0
$596$	−1.22467	−	0.566591i	−1.22467	−	0.566591i
$597$	0.914915	−	0.201388i	0.914915	−	0.201388i
$598$		0			0
$599$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$599$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$600$	−0.631588	+	0.292204i	−0.631588	+	0.292204i
$601$	0.589329	−	0.447996i	0.589329	−	0.447996i	−0.267528	−	0.963550i	$-0.586207\pi$
$601$	0.589329	−	0.447996i	0.589329	−	0.447996i	0.856857	+	0.515554i	$0.172414\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.24246	−	0.418632i	1.24246	−	0.418632i
$606$		0			0
$607$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i	0.0541389	−	0.998533i	$-0.482759\pi$
$607$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i	−0.370138	+	0.928977i	$0.620690\pi$
$608$		0			0
$609$		0			0
$610$	0.309003	+	1.11293i	0.309003	+	1.11293i
$611$	0.0454647	−	0.838547i	0.0454647	−	0.838547i
$612$		0			0
$613$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$613$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$614$		0			0
$615$	1.00476	−	2.52176i	1.00476	−	2.52176i
$616$		0			0
$617$	−1.34887	+	1.27771i	−1.34887	+	1.27771i	−0.419889	+	0.907575i	$0.637931\pi$
$617$	−1.34887	+	1.27771i	−1.34887	+	1.27771i	−0.928977	+	0.370138i	$0.879310\pi$
$618$	−0.228694	−	0.0248720i	−0.228694	−	0.0248720i
$619$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$619$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.177526	+	0.445557i	−0.177526	+	0.445557i
$625$	0.796093	+	0.754099i	0.796093	+	0.754099i
$626$	0.260752	+	0.306980i	0.260752	+	0.306980i
$627$		0			0
$628$	−0.0413430	+	0.762527i	−0.0413430	+	0.762527i
$629$		0			0
$630$		0			0
$631$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$631$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$632$	0.246608	+	0.0542826i	0.246608	+	0.0542826i
$633$	−1.50884	−	1.14699i	−1.50884	−	1.14699i
$634$	−0.342155	+	0.115285i	−0.342155	+	0.115285i
$635$	0.0551229	+	1.01668i	0.0551229	+	1.01668i
$636$		0			0
$637$	0.561187	−	0.827689i	0.561187	−	0.827689i
$638$		0			0
$639$	1.74899	−	0.809168i	1.74899	−	0.809168i
$640$	−1.19084	−	0.716502i	−1.19084	−	0.716502i
$641$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$641$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$642$		0			0
$643$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$643$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$644$		0			0
$645$	−1.89253	−	0.637666i	−1.89253	−	0.637666i
$646$		0			0
$647$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$647$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$648$	0.780408			0.780408
$649$	−0.148707	−	0.156988i	−0.148707	−	0.156988i
$650$	0.383388			0.383388
$651$		0			0
$652$		0			0
$653$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$653$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$654$		0			0
$655$		0			0
$656$	0.924476	−	0.203492i	0.924476	−	0.203492i
$657$		0			0
$658$		0			0
$659$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$659$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$660$	−0.193002	+	0.146717i	−0.193002	+	0.146717i
$661$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$661$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$662$		0			0
$663$		0			0
$664$	1.37406	−	0.462975i	1.37406	−	0.462975i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.43195	−	0.155734i	1.43195	−	0.155734i
$669$		0			0
$670$		0			0
$671$	0.197839	+	0.373165i	0.197839	+	0.373165i
$672$		0			0
$673$	−1.31779	−	1.24828i	−1.31779	−	1.24828i	−0.947653	−	0.319302i	$-0.896552\pi$
$673$	−1.31779	−	1.24828i	−1.31779	−	1.24828i	−0.370138	−	0.928977i	$-0.620690\pi$
$674$	−0.288859	+	0.724980i	−0.288859	+	0.724980i
$675$	0.330060	+	0.828389i	0.330060	+	0.828389i
$676$	0.591796	−	0.560579i	0.591796	−	0.560579i
$677$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$677$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.39907	−	1.32527i	1.39907	−	1.32527i
$682$		0			0
$683$	−0.730524	+	1.83348i	−0.730524	+	1.83348i	−0.214970	+	0.976621i	$0.568966\pi$
$683$	−0.730524	+	1.83348i	−0.730524	+	1.83348i	−0.515554	+	0.856857i	$0.672414\pi$
$684$		0			0
$685$	0.918113	+	1.08089i	0.918113	+	1.08089i
$686$		0			0
$687$		0			0
$688$	−0.186308	−	0.671022i	−0.186308	−	0.671022i
$689$		0			0
$690$		0			0
$691$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$691$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.71120	−	1.02960i	1.71120	−	1.02960i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$701$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$702$	−0.390204	−	0.180527i	−0.390204	−	0.180527i
$703$		0			0
$704$	−0.0113597	−	0.00382751i	−0.0113597	−	0.00382751i
$705$	0.309003	−	1.11293i	0.309003	−	1.11293i
$706$	0.0444191	−	0.270945i	0.0444191	−	0.270945i
$707$		0			0
$708$	−0.720196	−	0.381824i	−0.720196	−	0.381824i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$	0.184362	−	1.12456i	0.184362	−	1.12456i
$711$	0.0865625	−	0.311770i	0.0865625	−	0.311770i
$712$	1.12732	+	0.379839i	1.12732	+	0.379839i
$713$		0			0
$714$		0			0
$715$	0.290460	−	0.0639351i	0.290460	−	0.0639351i
$716$		0			0
$717$	−1.41842	−	0.853437i	−1.41842	−	0.853437i
$718$	0.689499	−	0.318996i	0.689499	−	0.318996i
$719$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$719$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$720$	−0.370199	+	0.546003i	−0.370199	+	0.546003i
$721$		0			0
$722$	−0.0232765	−	0.429310i	−0.0232765	−	0.429310i
$723$		0			0
$724$	−0.347218	−	0.263948i	−0.347218	−	0.263948i
$725$		0			0
$726$	−0.265323	+	0.312362i	−0.265323	+	0.312362i
$727$	−1.88420	+	0.204919i	−1.88420	+	0.204919i	−0.976621	−	0.214970i	$-0.931034\pi$
$727$	−1.88420	+	0.204919i	−1.88420	+	0.204919i	−0.907575	+	0.419889i	$0.862069\pi$
$728$		0			0
$729$	0.0541389	−	0.998533i	0.0541389	−	0.998533i
$730$		0			0
$731$		0			0
$732$	1.15592	+	1.09495i	1.15592	+	1.09495i
$733$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$733$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$734$	−0.316409	−	0.794127i	−0.316409	−	0.794127i
$735$	0.998533	−	0.945861i	0.998533	−	0.945861i
$736$		0			0
$737$		0			0
$738$	0.137281	+	0.837376i	0.137281	+	0.837376i
$739$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$739$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.39907	+	1.32527i	1.39907	+	1.32527i	0.883512	+	0.468408i	$0.155172\pi$
$743$	1.39907	+	1.32527i	1.39907	+	1.32527i	0.515554	+	0.856857i	$0.327586\pi$
$744$		0			0
$745$	1.06647	+	2.01158i	1.06647	+	2.01158i
$746$	0.0370606	−	0.683542i	0.0370606	−	0.683542i
$747$	−0.497055	−	1.79023i	−0.497055	−	1.79023i
$748$		0			0
$749$		0			0
$750$	−0.0625321	−	0.0137643i	−0.0625321	−	0.0137643i
$751$	1.44503	+	1.09848i	1.44503	+	1.09848i	0.976621	+	0.214970i	$0.0689655\pi$
$751$	1.44503	+	1.09848i	1.44503	+	1.09848i	0.468408	+	0.883512i	$0.344828\pi$
$752$	0.381692	−	0.128607i	0.381692	−	0.128607i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.850232	+	0.393359i	−0.850232	+	0.393359i	−0.796093	−	0.605174i	$-0.793103\pi$
$757$	−0.850232	+	0.393359i	−0.850232	+	0.393359i	−0.0541389	+	0.998533i	$0.517241\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50238	+	0.695075i	1.50238	+	0.695075i	0.986827	−	0.161782i	$-0.0517241\pi$
$761$	1.50238	+	0.695075i	1.50238	+	0.695075i	0.515554	+	0.856857i	$0.327586\pi$
$762$	−0.178612	−	0.263433i	−0.178612	−	0.263433i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.520378			−0.520378
$767$	0.605174	+	0.796093i	0.605174	+	0.796093i
$768$	0.378999			0.378999
$769$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$769$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.935808	+	0.432951i	0.935808	+	0.432951i	0.827689	−	0.561187i	$-0.189655\pi$
$773$	0.935808	+	0.432951i	0.935808	+	0.432951i	0.108119	+	0.994138i	$0.465517\pi$
$774$	0.609675	−	0.134200i	0.609675	−	0.134200i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.960672	−	0.578017i	0.960672	−	0.578017i
$781$	−0.0225604	−	0.416101i	−0.0225604	−	0.416101i
$782$		0			0
$783$		0			0
$784$	0.468408	+	0.103104i	0.468408	+	0.103104i
$785$	0.834155	−	0.982043i	0.834155	−	0.982043i
$786$		0			0
$787$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$787$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$788$	0.0881333	−	1.62552i	0.0881333	−	1.62552i
$789$		0			0
$790$	−0.123869	−	0.145829i	−0.123869	−	0.145829i
$791$		0			0
$792$	0.0624622	−	0.156768i	0.0624622	−	0.156768i
$793$	−0.722969	−	1.81452i	−0.722969	−	1.81452i
$794$		0			0
$795$		0			0
$796$	−0.123544	−	0.753587i	−0.123544	−	0.753587i
$797$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$797$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$798$		0			0
$799$		0			0
$800$	0.325643	+	0.817302i	0.325643	+	0.817302i
$801$	0.564211	−	1.41606i	0.564211	−	1.41606i
$802$	0.551550	+	0.522456i	0.551550	+	0.522456i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$809$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$810$	−0.470762	−	0.357864i	−0.470762	−	0.357864i
$811$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$811$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−2.00826	−	0.929121i	−2.00826	−	0.929121i
$821$	−0.771856	−	1.13840i	−0.771856	−	1.13840i	−0.986827	−	0.161782i	$-0.948276\pi$
$821$	−0.771856	−	1.13840i	−0.771856	−	1.13840i	0.214970	−	0.976621i	$-0.431034\pi$
$822$	−0.420109	−	0.141551i	−0.420109	−	0.141551i
$823$	0.425955	−	1.53415i	0.425955	−	1.53415i	−0.370138	−	0.928977i	$-0.620690\pi$
$823$	0.425955	−	1.53415i	0.425955	−	1.53415i	0.796093	−	0.605174i	$-0.206897\pi$
$824$	−0.0675541	+	0.412062i	−0.0675541	+	0.412062i
$825$	0.192824			0.192824
$826$		0			0
$827$	−0.216238			−0.216238			−0.108119	−	0.994138i	$-0.534483\pi$
$827$	−0.216238			−0.216238			−0.108119	+	0.994138i	$0.534483\pi$
$828$		0			0
$829$	−0.346388	+	1.24758i	−0.346388	+	1.24758i	0.561187	+	0.827689i	$0.310345\pi$
$829$	−0.346388	+	1.24758i	−0.346388	+	1.24758i	−0.907575	+	0.419889i	$0.862069\pi$
$830$	−1.04117	−	0.350811i	−1.04117	−	0.350811i
$831$	−0.629862	−	0.928977i	−0.629862	−	0.928977i
$832$	0.0503114	+	0.0232765i	0.0503114	+	0.0232765i
$833$		0			0
$834$	−0.292413	+	0.551550i	−0.292413	+	0.551550i
$835$	−2.08247	−	1.25298i	−2.08247	−	1.25298i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.65125	−	0.993524i	1.65125	−	0.993524i	0.687699	−	0.725995i	$-0.258621\pi$
$839$	1.65125	−	0.993524i	1.65125	−	0.993524i	0.963550	−	0.267528i	$-0.0862069\pi$
$840$		0			0
$841$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$842$		0			0
$843$		0			0
$844$	−1.00019	+	1.17751i	−1.00019	+	1.17751i
$845$	−1.36734	+	0.148707i	−1.36734	+	0.148707i
$846$	0.0965924	+	0.347895i	0.0965924	+	0.347895i
$847$		0			0
$848$		0			0
$849$	−0.209471	−	0.246608i	−0.209471	−	0.246608i
$850$		0			0
$851$		0			0
$852$	−0.581442	−	1.45931i	−0.581442	−	1.45931i
$853$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$853$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$857$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$858$	−0.0674955	+	0.0639351i	−0.0674955	+	0.0639351i
$859$	−0.735937	−	1.84706i	−0.735937	−	1.84706i	−0.468408	−	0.883512i	$-0.655172\pi$
$859$	−0.735937	−	1.84706i	−0.735937	−	1.84706i	−0.267528	−	0.963550i	$-0.586207\pi$
$860$	−0.602552	+	1.51229i	−0.602552	+	1.51229i
$861$		0			0
$862$	−0.177747	−	0.209260i	−0.177747	−	0.209260i
$863$	−0.299127	−	0.564213i	−0.299127	−	0.564213i	0.687699	−	0.725995i	$-0.258621\pi$
$863$	−0.299127	−	0.564213i	−0.299127	−	0.564213i	−0.986827	+	0.161782i	$0.948276\pi$
$864$	0.0534143	−	0.985170i	0.0534143	−	0.985170i
$865$		0			0
$866$	0.732477	−	0.0796616i	0.732477	−	0.0796616i
$867$	−0.647386	+	0.762162i	−0.647386	+	0.762162i
$868$		0			0
$869$	−0.0557001	−	0.0423421i	−0.0557001	−	0.0423421i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$877$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$878$	0.719570	−	0.158389i	0.719570	−	0.158389i
$879$	−0.762162	−	0.352614i	−0.762162	−	0.352614i
$880$	0.0800511	+	0.118067i	0.0800511	+	0.118067i
$881$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$881$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$882$	−0.115021	+	0.414270i	−0.115021	+	0.414270i
$883$	0.257587	−	1.57121i	0.257587	−	1.57121i	−0.468408	−	0.883512i	$-0.655172\pi$
$883$	0.257587	−	1.57121i	0.257587	−	1.57121i	0.725995	−	0.687699i	$-0.241379\pi$
$884$		0			0
$885$	0.577515	+	1.24828i	0.577515	+	1.24828i
$886$		0			0
$887$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$887$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$888$		0			0
$889$		0			0
$890$	−0.505851	−	0.746074i	−0.505851	−	0.746074i
$891$	−0.196252	−	0.0907960i	−0.196252	−	0.0907960i
$892$		0			0
$893$		0			0
$894$	−0.609838	−	0.366927i	−0.609838	−	0.366927i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.735715	−	0.442665i	0.735715	−	0.442665i
$899$		0			0
$900$	0.688838	−	0.232096i	0.688838	−	0.232096i
$901$		0			0
$902$	0.179200	+	0.0394449i	0.179200	+	0.0394449i
$903$		0			0
$904$		0			0
$905$	0.196878	+	0.709092i	0.196878	+	0.709092i
$906$		0			0
$907$	0.525730	+	0.991631i	0.525730	+	0.991631i	0.994138	+	0.108119i	$0.0344828\pi$
$907$	0.525730	+	0.991631i	0.525730	+	0.991631i	−0.468408	+	0.883512i	$0.655172\pi$
$908$	−1.01696	−	1.19726i	−1.01696	−	1.19726i
$909$		0			0
$910$		0			0
$911$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$911$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$912$		0			0
$913$	−0.399405	−	0.0434379i	−0.399405	−	0.0434379i
$914$		0			0
$915$	−0.434625	−	2.65110i	−0.434625	−	2.65110i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.479245	−	1.20281i	0.479245	−	1.20281i	−0.468408	−	0.883512i	$-0.655172\pi$
$919$	0.479245	−	1.20281i	0.479245	−	1.20281i	0.947653	−	0.319302i	$-0.103448\pi$
$920$		0			0
$921$		0			0
$922$	−0.243750	−	0.459760i	−0.243750	−	0.459760i
$923$	−0.104331	+	1.92427i	−0.104331	+	1.92427i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.522547	+	0.115021i	0.522547	+	0.115021i
$928$		0			0
$929$	−1.89253	+	0.637666i	−1.89253	+	0.637666i	−0.928977	+	0.370138i	$0.879310\pi$
$929$	−1.89253	+	0.637666i	−1.89253	+	0.637666i	−0.963550	+	0.267528i	$0.913793\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.365549	+	0.689499i	−0.365549	+	0.689499i
$937$	1.94179	−	0.427421i	1.94179	−	0.427421i	0.947653	−	0.319302i	$-0.103448\pi$
$937$	1.94179	−	0.427421i	1.94179	−	0.427421i	0.994138	−	0.108119i	$-0.0344828\pi$
$938$		0			0
$939$	−0.525730	−	0.775393i	−0.525730	−	0.775393i
$940$	−0.892238	−	0.300630i	−0.892238	−	0.300630i
$941$	0.528008	−	1.90171i	0.528008	−	1.90171i	0.108119	−	0.994138i	$-0.465517\pi$
$941$	0.528008	−	1.90171i	0.528008	−	1.90171i	0.419889	−	0.907575i	$-0.362069\pi$
$942$	−0.0651619	+	0.397470i	−0.0651619	+	0.397470i
$943$		0			0
$944$	−0.247271	+	0.410967i	−0.247271	+	0.410967i
$945$		0			0
$946$	0.0218391	−	0.133213i	0.0218391	−	0.133213i
$947$	0.534272	−	1.92427i	0.534272	−	1.92427i	0.214970	−	0.976621i	$-0.431034\pi$
$947$	0.534272	−	1.92427i	0.534272	−	1.92427i	0.319302	−	0.947653i	$-0.396552\pi$
$948$	−0.249947	−	0.0842169i	−0.249947	−	0.0842169i
$949$		0			0
$950$		0			0
$951$	0.820145	−	0.180527i	0.820145	−	0.180527i
$952$		0			0
$953$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$953$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$954$		0			0
$955$		0			0
$956$	−0.757256	+	1.11687i	−0.757256	+	1.11687i
$957$		0			0
$958$	0.0100075	+	0.184578i	0.0100075	+	0.184578i
$959$		0			0
$960$	0.0606982	+	0.0461416i	0.0606982	+	0.0461416i
$961$	0.976621	+	0.214970i	0.976621	+	0.214970i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$967$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$968$	0.540080	+	0.511591i	0.540080	+	0.511591i
$969$		0			0
$970$		0			0
$971$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$971$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$972$	−0.810372	−	0.0881333i	−0.810372	−	0.0881333i
$973$		0			0
$974$		0			0
$975$	−0.886495	−	0.0964121i	−0.886495	−	0.0964121i
$976$	0.680125	−	0.644248i	0.680125	−	0.644248i
$977$	−0.509088	−	1.27771i	−0.509088	−	1.27771i	−0.928977	−	0.370138i	$-0.879310\pi$
$977$	−0.509088	−	1.27771i	−0.509088	−	1.27771i	0.419889	−	0.907575i	$-0.362069\pi$
$978$		0			0
$979$	−0.239300	−	0.226677i	−0.239300	−	0.226677i
$980$	−0.725822	−	0.854504i	−0.725822	−	0.854504i
$981$		0			0
$982$		0			0
$983$	0.275851	+	0.993524i	0.275851	+	0.993524i	0.963550	+	0.267528i	$0.0862069\pi$
$983$	0.275851	+	0.993524i	0.275851	+	0.993524i	−0.687699	+	0.725995i	$0.741379\pi$
$984$	1.53122	−	0.166531i	1.53122	−	0.166531i
$985$	−1.77822	+	2.09348i	−1.77822	+	2.09348i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.109567	+	0.0659240i	−0.109567	+	0.0659240i
$991$	0.181580	−	0.267810i	0.181580	−	0.267810i	−0.725995	−	0.687699i	$-0.758621\pi$
$991$	0.181580	−	0.267810i	0.181580	−	0.267810i	0.907575	+	0.419889i	$0.137931\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.603543	+	1.13840i	−0.603543	+	1.13840i
$996$	−1.47910	+	0.325575i	−1.47910	+	0.325575i
$997$	−1.80451	−	0.834855i	−1.80451	−	0.834855i	−0.947653	−	0.319302i	$-0.896552\pi$
$997$	−1.80451	−	0.834855i	−1.80451	−	0.834855i	−0.856857	−	0.515554i	$-0.827586\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2301.1.z.c.818.2	yes	56
3.2	odd	2	inner	2301.1.z.c.818.1	✓	56
13.12	even	2	inner	2301.1.z.c.818.1	✓	56
39.38	odd	2	CM	2301.1.z.c.818.2	yes	56
59.22	even	29	inner	2301.1.z.c.1910.2	yes	56
177.140	odd	58	inner	2301.1.z.c.1910.1	yes	56
767.376	even	58	inner	2301.1.z.c.1910.1	yes	56
2301.1910	odd	58	inner	2301.1.z.c.1910.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2301.1.z.c.818.1	✓	56	3.2	odd	2	inner
2301.1.z.c.818.1	✓	56	13.12	even	2	inner
2301.1.z.c.818.2	yes	56	1.1	even	1	trivial
2301.1.z.c.818.2	yes	56	39.38	odd	2	CM
2301.1.z.c.1910.1	yes	56	177.140	odd	58	inner
2301.1.z.c.1910.1	yes	56	767.376	even	58	inner
2301.1.z.c.1910.2	yes	56	59.22	even	29	inner
2301.1.z.c.1910.2	yes	56	2301.1910	odd	58	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.0695567 - 0.424277i) q^{2} +(-0.267528 + 0.963550i) q^{3} +(0.772480 + 0.260279i) q^{4} +(-0.771856 - 1.13840i) q^{5} +(0.390204 + 0.180527i) q^{6} +(0.365549 - 0.689499i) q^{8} +(-0.856857 - 0.515554i) q^{9} +(-0.536686 + 0.248297i) q^{10} +(-0.172146 + 0.130862i) q^{11} +(-0.457452 + 0.674691i) q^{12} +(0.856857 - 0.515554i) q^{13} +(1.30340 - 0.439167i) q^{15} +(0.381824 + 0.290255i) q^{16} +(-0.278338 + 0.327685i) q^{18} +(-0.299941 - 1.08029i) q^{20} +(0.0435477 + 0.0821397i) q^{22} +(0.566572 + 0.536686i) q^{24} +(-0.330060 + 0.828389i) q^{25} +(-0.159138 - 0.399405i) q^{26} +(0.725995 - 0.687699i) q^{27} +(-0.0956682 - 0.583550i) q^{30} +(0.716279 - 0.678496i) q^{32} +(-0.0800379 - 0.200880i) q^{33} +(-0.527717 - 0.621277i) q^{36} +(0.267528 + 0.963550i) q^{39} +(-1.06708 + 0.116052i) q^{40} +(1.27772 - 1.50424i) q^{41} +(-1.15592 - 0.878708i) q^{43} +(-0.167040 + 0.0562822i) q^{44} +(0.0744626 + 1.37338i) q^{45} +(0.471273 - 0.695075i) q^{47} +(-0.381824 + 0.290255i) q^{48} +(0.907575 - 0.419889i) q^{49} +(0.328509 + 0.197657i) q^{50} +(0.796093 - 0.175233i) q^{52} +(-0.241277 - 0.355857i) q^{54} +(0.281845 + 0.0949646i) q^{55} +(0.108119 + 0.994138i) q^{59} +1.12116 q^{60} +(0.315999 - 1.92751i) q^{61} +(0.0311094 + 0.0458829i) q^{64} +(-1.24828 - 0.577515i) q^{65} +(-0.0907960 + 0.0199857i) q^{66} +(-1.08146 + 1.59504i) q^{71} +(-0.668698 + 0.402342i) q^{72} +(-0.709894 - 0.539647i) q^{75} +(0.427421 - 0.0464848i) q^{78} +(0.0865625 + 0.311770i) q^{79} +(0.0357139 - 0.658704i) q^{80} +(0.468408 + 0.883512i) q^{81} +(-0.549342 - 0.646736i) q^{82} +(1.34887 + 1.27771i) q^{83} +(-0.453217 + 0.429310i) q^{86} +(0.0273013 + 0.166531i) q^{88} +(0.246608 + 1.50424i) q^{89} +(0.587874 + 0.0639351i) q^{90} +(-0.262124 - 0.248297i) q^{94} +(0.462140 + 0.871688i) q^{96} +(-0.115021 - 0.414270i) q^{98} +(0.214970 - 0.0233794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{12} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 2 q^{39} - 58 q^{40} - 4 q^{43} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 4 q^{61} + 2 q^{64} - 2 q^{75} + 4 q^{79}+ \cdots - 2 q^{81}+O(q^{100}) \) 56 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^12 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^27 + 2 * q^36 - 2 * q^39 - 58 * q^40 - 4 * q^43 + 2 * q^48 - 2 * q^49 - 2 * q^52 + 4 * q^61 + 2 * q^64 - 2 * q^75 + 4 * q^79 - 2 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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