LMFDB - Embedded newform 2301.1.z.c.194.2

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			194.2
Root			$-0.214970 + 0.976621i$ of defining polynomial
Character	$\chi$	$=$	2301.194
Dual form			2301.1.z.c.1364.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08146 - 1.59504i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-1.00445 - 2.52098i) q^{4} +(1.79124 + 0.828715i) q^{5} +(-1.65125 - 0.993524i) q^{6} +(-3.22529 - 0.709940i) q^{8} +(-0.994138 + 0.108119i) q^{9} +(3.25899 - 1.96087i) q^{10} +(-0.878708 - 0.832356i) q^{11} +(-2.46290 + 1.13946i) q^{12} +(0.994138 + 0.108119i) q^{13} +(0.730524 - 1.83348i) q^{15} +(-2.65027 + 2.51047i) q^{16} +(-0.902670 + 1.70262i) q^{18} +(0.289964 - 5.34808i) q^{20} +(-2.27793 + 0.501410i) q^{22} +(-0.534285 + 3.25899i) q^{24} +(1.87438 + 2.20669i) q^{25} +(1.24758 - 1.46876i) q^{26} +(0.161782 + 0.986827i) q^{27} +(-2.13443 - 3.14805i) q^{30} +(0.603842 + 3.68327i) q^{32} +(-0.783563 + 0.922482i) q^{33} +(1.27113 + 2.39760i) q^{36} +(0.0541389 - 0.998533i) q^{39} +(-5.18892 - 3.94452i) q^{40} +(-0.775393 + 1.46255i) q^{41} +(0.234906 - 0.222515i) q^{43} +(-1.21573 + 3.05126i) q^{44} +(-1.87034 - 0.630190i) q^{45} +(-0.935808 + 0.432951i) q^{47} +(2.65027 + 2.51047i) q^{48} +(-0.856857 + 0.515554i) q^{49} +(5.54684 - 0.603255i) q^{50} +(-0.725995 - 2.61480i) q^{52} +(1.74899 + 0.809168i) q^{54} +(-0.884189 - 2.21915i) q^{55} +(-0.605174 + 0.796093i) q^{59} -5.35593 q^{60} +(0.300267 - 0.442861i) q^{61} +(3.21486 + 1.48735i) q^{64} +(1.69114 + 1.01752i) q^{65} +(0.624000 + 2.24744i) q^{66} +(1.81249 - 0.838547i) q^{71} +(3.28314 + 0.357063i) q^{72} +(2.10198 - 1.99110i) q^{75} +(-1.53415 - 1.16623i) q^{78} +(0.0607641 - 1.12073i) q^{79} +(-6.82773 + 2.30053i) q^{80} +(0.976621 - 0.214970i) q^{81} +(1.49426 + 2.81847i) q^{82} +(-0.246608 + 1.50424i) q^{83} +(-0.100878 - 0.615326i) q^{86} +(2.24316 + 3.30842i) q^{88} +(-0.991631 - 1.46255i) q^{89} +(-3.02788 + 2.30174i) q^{90} +(-0.321469 + 1.96087i) q^{94} +(3.64518 - 0.802364i) q^{96} +(-0.104331 + 1.92427i) q^{98} +(0.963550 + 0.732472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2301\mathbb{Z}\right)^\times$.

$n$	$886$	$1535$	$2185$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{20}{29}\right)$

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 $

$2$	1.08146	−	1.59504i	1.08146	−	1.59504i	0.319302	−	0.947653i	$-0.396552\pi$
$2$	1.08146	−	1.59504i	1.08146	−	1.59504i	0.762162	−	0.647386i	$-0.224138\pi$
$3$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$3$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$4$	−1.00445	−	2.52098i	−1.00445	−	2.52098i
$5$	1.79124	+	0.828715i	1.79124	+	0.828715i	0.963550	+	0.267528i	$0.0862069\pi$
$5$	1.79124	+	0.828715i	1.79124	+	0.828715i	0.827689	+	0.561187i	$0.189655\pi$
$6$	−1.65125	−	0.993524i	−1.65125	−	0.993524i
$7$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$7$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$8$	−3.22529	−	0.709940i	−3.22529	−	0.709940i
$9$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$10$	3.25899	−	1.96087i	3.25899	−	1.96087i
$11$	−0.878708	−	0.832356i	−0.878708	−	0.832356i	0.108119	−	0.994138i	$-0.465517\pi$
$11$	−0.878708	−	0.832356i	−0.878708	−	0.832356i	−0.986827	+	0.161782i	$0.948276\pi$
$12$	−2.46290	+	1.13946i	−2.46290	+	1.13946i
$13$	0.994138	+	0.108119i	0.994138	+	0.108119i
$13$	0.994138	+	0.108119i	0.994138	+	0.108119i
$14$		0			0
$15$	0.730524	−	1.83348i	0.730524	−	1.83348i
$16$	−2.65027	+	2.51047i	−2.65027	+	2.51047i
$17$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$17$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$18$	−0.902670	+	1.70262i	−0.902670	+	1.70262i
$19$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$19$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$20$	0.289964	−	5.34808i	0.289964	−	5.34808i
$21$		0			0
$22$	−2.27793	+	0.501410i	−2.27793	+	0.501410i
$23$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$23$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$24$	−0.534285	+	3.25899i	−0.534285	+	3.25899i
$25$	1.87438	+	2.20669i	1.87438	+	2.20669i
$26$	1.24758	−	1.46876i	1.24758	−	1.46876i
$27$	0.161782	+	0.986827i	0.161782	+	0.986827i
$28$		0			0
$29$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$29$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$30$	−2.13443	−	3.14805i	−2.13443	−	3.14805i
$31$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$31$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$32$	0.603842	+	3.68327i	0.603842	+	3.68327i
$33$	−0.783563	+	0.922482i	−0.783563	+	0.922482i
$34$		0			0
$35$		0			0
$36$	1.27113	+	2.39760i	1.27113	+	2.39760i
$37$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$37$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$38$		0			0
$39$	0.0541389	−	0.998533i	0.0541389	−	0.998533i
$40$	−5.18892	−	3.94452i	−5.18892	−	3.94452i
$41$	−0.775393	+	1.46255i	−0.775393	+	1.46255i	0.108119	+	0.994138i	$0.465517\pi$
$41$	−0.775393	+	1.46255i	−0.775393	+	1.46255i	−0.883512	+	0.468408i	$0.844828\pi$
$42$		0			0
$43$	0.234906	−	0.222515i	0.234906	−	0.222515i	−0.561187	−	0.827689i	$-0.689655\pi$
$43$	0.234906	−	0.222515i	0.234906	−	0.222515i	0.796093	+	0.605174i	$0.206897\pi$
$44$	−1.21573	+	3.05126i	−1.21573	+	3.05126i
$45$	−1.87034	−	0.630190i	−1.87034	−	0.630190i
$46$		0			0
$47$	−0.935808	+	0.432951i	−0.935808	+	0.432951i	−0.827689	−	0.561187i	$-0.810345\pi$
$47$	−0.935808	+	0.432951i	−0.935808	+	0.432951i	−0.108119	+	0.994138i	$0.534483\pi$
$48$	2.65027	+	2.51047i	2.65027	+	2.51047i
$49$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$50$	5.54684	−	0.603255i	5.54684	−	0.603255i
$51$		0			0
$52$	−0.725995	−	2.61480i	−0.725995	−	2.61480i
$53$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$53$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$54$	1.74899	+	0.809168i	1.74899	+	0.809168i
$55$	−0.884189	−	2.21915i	−0.884189	−	2.21915i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.605174	+	0.796093i	−0.605174	+	0.796093i
$59$	−0.605174	+	0.796093i	−0.605174	+	0.796093i
$60$	−5.35593			−5.35593
$61$	0.300267	−	0.442861i	0.300267	−	0.442861i	−0.647386	−	0.762162i	$-0.724138\pi$
$61$	0.300267	−	0.442861i	0.300267	−	0.442861i	0.947653	+	0.319302i	$0.103448\pi$
$62$		0			0
$63$		0			0
$64$	3.21486	+	1.48735i	3.21486	+	1.48735i
$65$	1.69114	+	1.01752i	1.69114	+	1.01752i
$66$	0.624000	+	2.24744i	0.624000	+	2.24744i
$67$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$67$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.81249	−	0.838547i	1.81249	−	0.838547i	0.883512	−	0.468408i	$-0.155172\pi$
$71$	1.81249	−	0.838547i	1.81249	−	0.838547i	0.928977	−	0.370138i	$-0.120690\pi$
$72$	3.28314	+	0.357063i	3.28314	+	0.357063i
$73$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$73$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$74$		0			0
$75$	2.10198	−	1.99110i	2.10198	−	1.99110i
$76$		0			0
$77$		0			0
$78$	−1.53415	−	1.16623i	−1.53415	−	1.16623i
$79$	0.0607641	−	1.12073i	0.0607641	−	1.12073i	−0.796093	−	0.605174i	$-0.793103\pi$
$79$	0.0607641	−	1.12073i	0.0607641	−	1.12073i	0.856857	−	0.515554i	$-0.172414\pi$
$80$	−6.82773	+	2.30053i	−6.82773	+	2.30053i
$81$	0.976621	−	0.214970i	0.976621	−	0.214970i
$82$	1.49426	+	2.81847i	1.49426	+	2.81847i
$83$	−0.246608	+	1.50424i	−0.246608	+	1.50424i	0.515554	+	0.856857i	$0.327586\pi$
$83$	−0.246608	+	1.50424i	−0.246608	+	1.50424i	−0.762162	+	0.647386i	$0.775862\pi$
$84$		0			0
$85$		0			0
$86$	−0.100878	−	0.615326i	−0.100878	−	0.615326i
$87$		0			0
$88$	2.24316	+	3.30842i	2.24316	+	3.30842i
$89$	−0.991631	−	1.46255i	−0.991631	−	1.46255i	−0.883512	−	0.468408i	$-0.844828\pi$
$89$	−0.991631	−	1.46255i	−0.991631	−	1.46255i	−0.108119	−	0.994138i	$-0.534483\pi$
$90$	−3.02788	+	2.30174i	−3.02788	+	2.30174i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.321469	+	1.96087i	−0.321469	+	1.96087i
$95$		0			0
$96$	3.64518	−	0.802364i	3.64518	−	0.802364i
$97$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$97$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$98$	−0.104331	+	1.92427i	−0.104331	+	1.92427i
$99$	0.963550	+	0.732472i	0.963550	+	0.732472i
$100$	3.68030	−	6.94178i	3.68030	−	6.94178i
$101$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$101$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$102$		0			0
$103$	−0.0400778	+	0.100588i	−0.0400778	+	0.100588i	−0.947653	−	0.319302i	$-0.896552\pi$
$103$	−0.0400778	+	0.100588i	−0.0400778	+	0.100588i	0.907575	+	0.419889i	$0.137931\pi$
$104$	−3.12962	−	1.05449i	−3.12962	−	1.05449i
$105$		0			0
$106$		0			0
$107$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$107$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$108$	2.32527	−	1.39907i	2.32527	−	1.39907i
$109$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$109$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$110$	−4.49584	−	0.989610i	−4.49584	−	0.989610i
$111$		0			0
$112$		0			0
$113$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$113$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000			−1.00000
$118$	0.615326	+	1.82622i	0.615326	+	1.82622i
$119$		0			0
$120$	−3.65781	+	5.39487i	−3.65781	+	5.39487i
$121$	0.0251715	+	0.464261i	0.0251715	+	0.464261i
$122$	−0.381652	−	0.957875i	−0.381652	−	0.957875i
$123$	1.50238	+	0.695075i	1.50238	+	0.695075i
$124$		0			0
$125$	1.00074	+	3.60433i	1.00074	+	3.60433i
$126$		0			0
$127$	1.28718	−	0.139990i	1.28718	−	0.139990i	0.561187	−	0.827689i	$-0.310345\pi$
$127$	1.28718	−	0.139990i	1.28718	−	0.139990i	0.725995	+	0.687699i	$0.241379\pi$
$128$	2.65098	−	1.59504i	2.65098	−	1.59504i
$129$	−0.234906	−	0.222515i	−0.234906	−	0.222515i
$130$	3.45190	−	1.59702i	3.45190	−	1.59702i
$131$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$131$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$132$	3.11260	+	1.04876i	3.11260	+	1.04876i
$133$		0			0
$134$		0			0
$135$	−0.528008	+	1.90171i	−0.528008	+	1.90171i
$136$		0			0
$137$	0.172146	+	0.130862i	0.172146	+	0.130862i	0.687699	−	0.725995i	$-0.258621\pi$
$137$	0.172146	+	0.130862i	0.172146	+	0.130862i	−0.515554	+	0.856857i	$0.672414\pi$
$138$		0			0
$139$	0.306626	−	0.103314i	0.306626	−	0.103314i	−0.161782	−	0.986827i	$-0.551724\pi$
$139$	0.306626	−	0.103314i	0.306626	−	0.103314i	0.468408	+	0.883512i	$0.344828\pi$
$140$		0			0
$141$	0.482980	+	0.910996i	0.482980	+	0.910996i
$142$	0.622626	−	3.79785i	0.622626	−	3.79785i
$143$	−0.783563	−	0.922482i	−0.783563	−	0.922482i
$144$	2.36330	−	2.78230i	2.36330	−	2.78230i
$145$		0			0
$146$		0			0
$147$	0.561187	+	0.827689i	0.561187	+	0.827689i
$148$		0			0
$149$	0.668542	−	0.508212i	0.668542	−	0.508212i	−0.214970	−	0.976621i	$-0.568966\pi$
$149$	0.668542	−	0.508212i	0.668542	−	0.508212i	0.883512	+	0.468408i	$0.155172\pi$
$150$	−0.902670	−	5.50604i	−0.902670	−	5.50604i
$151$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$151$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−2.57166	+	0.866493i	−2.57166	+	0.866493i
$157$	0.105746	−	1.95038i	0.105746	−	1.95038i	−0.161782	−	0.986827i	$-0.551724\pi$
$157$	0.105746	−	1.95038i	0.105746	−	1.95038i	0.267528	−	0.963550i	$-0.413793\pi$
$158$	−1.72189	−	1.30895i	−1.72189	−	1.30895i
$159$		0			0
$160$	−1.97076	+	7.09803i	−1.97076	+	7.09803i
$161$		0			0
$162$	0.713293	−	1.79023i	0.713293	−	1.79023i
$163$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$163$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$164$	4.46589	+	0.485695i	4.46589	+	0.485695i
$165$	−2.16802	+	1.00303i	−2.16802	+	1.00303i
$166$	2.13263	+	2.02013i	2.13263	+	2.02013i
$167$	−0.368398	+	0.221658i	−0.368398	+	0.221658i	−0.687699	−	0.725995i	$-0.741379\pi$
$167$	−0.368398	+	0.221658i	−0.368398	+	0.221658i	0.319302	+	0.947653i	$0.396552\pi$
$168$		0			0
$169$	0.976621	+	0.214970i	0.976621	+	0.214970i
$170$		0			0
$171$		0			0
$172$	−0.796906	−	0.368688i	−0.796906	−	0.368688i
$173$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$173$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$174$		0			0
$175$		0			0
$176$	4.41841			4.41841
$177$	0.827689	+	0.561187i	0.827689	+	0.561187i
$178$	−3.40523			−3.40523
$179$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$179$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$180$	0.289964	+	5.34808i	0.289964	+	5.34808i
$181$	−0.0400778	−	0.100588i	−0.0400778	−	0.100588i	0.907575	−	0.419889i	$-0.137931\pi$
$181$	−0.0400778	−	0.100588i	−0.0400778	−	0.100588i	−0.947653	+	0.319302i	$0.896552\pi$
$182$		0			0
$183$	−0.458467	−	0.275851i	−0.458467	−	0.275851i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	2.03143	+	1.92427i	2.03143	+	1.92427i
$189$		0			0
$190$		0			0
$191$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$191$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$192$	1.31112	−	3.29067i	1.31112	−	3.29067i
$193$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$193$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$194$		0			0
$195$	0.924476	−	1.74375i	0.924476	−	1.74375i
$196$	2.16037	+	1.64227i	2.16037	+	1.64227i
$197$	−0.0345733	+	0.637666i	−0.0345733	+	0.637666i	0.928977	+	0.370138i	$0.120690\pi$
$197$	−0.0345733	+	0.637666i	−0.0345733	+	0.637666i	−0.963550	+	0.267528i	$0.913793\pi$
$198$	2.21037	−	0.744759i	2.21037	−	0.744759i
$199$	−1.90758	+	0.419889i	−1.90758	+	0.419889i	−0.907575	+	0.419889i	$0.862069\pi$
$199$	−1.90758	+	0.419889i	−1.90758	+	0.419889i	−1.00000			$\pi$
$200$	−4.47880	−	8.44792i	−4.47880	−	8.44792i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.60095	+	1.97719i	−2.60095	+	1.97719i
$206$	0.117099	+	0.172707i	0.117099	+	0.172707i
$207$		0			0
$208$	−2.90616	+	2.20921i	−2.90616	+	2.20921i
$209$		0			0
$210$		0			0
$211$	0.479245	+	0.564211i	0.479245	+	0.564211i	0.947653	−	0.319302i	$-0.103448\pi$
$211$	0.479245	+	0.564211i	0.479245	+	0.564211i	−0.468408	+	0.883512i	$0.655172\pi$
$212$		0			0
$213$	−0.935443	−	1.76443i	−0.935443	−	1.76443i
$214$		0			0
$215$	0.605174	−	0.203907i	0.605174	−	0.203907i
$216$	0.178794	−	3.29766i	0.178794	−	3.29766i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−4.70630	+	4.45804i	−4.70630	+	4.45804i
$221$		0			0
$222$		0			0
$223$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$223$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$224$		0			0
$225$	−2.10198	−	1.99110i	−2.10198	−	1.99110i
$226$		0			0
$227$	−1.98536	+	0.215921i	−1.98536	+	0.215921i	−0.986827	+	0.161782i	$0.948276\pi$
$227$	−1.98536	+	0.215921i	−1.98536	+	0.215921i	−0.998533	+	0.0541389i	$0.982759\pi$
$228$		0			0
$229$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$229$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$233$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$234$	−1.08146	+	1.59504i	−1.08146	+	1.59504i
$235$	−2.03505			−2.03505
$236$	2.61480	+	0.725995i	2.61480	+	0.725995i
$237$	−1.12237			−1.12237
$238$		0			0
$239$	−0.0454647	−	0.838547i	−0.0454647	−	0.838547i	−0.928977	−	0.370138i	$-0.879310\pi$
$239$	−0.0454647	−	0.838547i	−0.0454647	−	0.838547i	0.883512	−	0.468408i	$-0.155172\pi$
$240$	2.66680	+	6.69317i	2.66680	+	6.69317i
$241$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$241$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$242$	0.767737	+	0.461932i	0.767737	+	0.461932i
$243$	−0.267528	−	0.963550i	−0.267528	−	0.963550i
$244$	−1.41804	−	0.312135i	−1.41804	−	0.312135i
$245$	−1.96208	+	0.213389i	−1.96208	+	0.213389i
$246$	2.73344	−	1.64466i	2.73344	−	1.64466i
$247$		0			0
$248$		0			0
$249$	1.51539	+	0.164808i	1.51539	+	0.164808i
$250$	6.83131	+	2.30174i	6.83131	+	2.30174i
$251$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$251$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$252$		0			0
$253$		0			0
$254$	1.16875	−	2.20450i	1.16875	−	2.20450i
$255$		0			0
$256$	0.131010	−	2.41633i	0.131010	−	2.41633i
$257$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$257$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$258$	−0.608962	+	0.134043i	−0.608962	+	0.134043i
$259$		0			0
$260$	0.866493	−	5.28537i	0.866493	−	5.28537i
$261$		0			0
$262$		0			0
$263$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$263$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$264$	3.18212	−	2.41899i	3.18212	−	2.41899i
$265$		0			0
$266$		0			0
$267$	−1.40672	+	1.06936i	−1.40672	+	1.06936i
$268$		0			0
$269$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$269$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$270$	2.46229	+	2.89883i	2.46229	+	2.89883i
$271$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$271$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$272$		0			0
$273$		0			0
$274$	0.394899	−	0.133057i	0.394899	−	0.133057i
$275$	0.189721	−	3.49919i	0.189721	−	3.49919i
$276$		0			0
$277$	0.850232	−	1.60371i	0.850232	−	1.60371i	0.0541389	−	0.998533i	$-0.482759\pi$
$277$	0.850232	−	1.60371i	0.850232	−	1.60371i	0.796093	−	0.605174i	$-0.206897\pi$
$278$	0.166815	−	0.600812i	0.166815	−	0.600812i
$279$		0			0
$280$		0			0
$281$		0			0		0.319302	−	0.947653i	$-0.396552\pi$
$281$		0			0		−0.319302	+	0.947653i	$0.603448\pi$
$282$	1.97540	+	0.214838i	1.97540	+	0.214838i
$283$	1.01864	−	0.471273i	1.01864	−	0.471273i	0.161782	−	0.986827i	$-0.448276\pi$
$283$	1.01864	−	0.471273i	1.01864	−	0.471273i	0.856857	+	0.515554i	$0.172414\pi$
$284$	−3.93451	−	3.72697i	−3.93451	−	3.72697i
$285$		0			0
$286$	−2.31879	+	0.252184i	−2.31879	+	0.252184i
$287$		0			0
$288$	−0.998533	−	3.59639i	−0.998533	−	3.59639i
$289$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.578644	+	0.853437i	−0.578644	+	0.853437i	−0.998533	−	0.0541389i	$-0.982759\pi$
$293$	−0.578644	+	0.853437i	−0.578644	+	0.853437i	0.419889	+	0.907575i	$0.362069\pi$
$294$	1.92710			1.92710
$295$	−1.74375	+	0.924476i	−1.74375	+	0.924476i
$296$		0			0
$297$	0.679232	−	1.00179i	0.679232	−	1.00179i
$298$	−0.0876150	−	1.61596i	−0.0876150	−	1.61596i
$299$		0			0
$300$	−7.13085	−	3.29908i	−7.13085	−	3.29908i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.904855	−	0.544433i	0.904855	−	0.544433i
$306$		0			0
$307$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$307$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$308$		0			0
$309$	0.102610	+	0.0345733i	0.102610	+	0.0345733i
$310$		0			0
$311$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$311$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$312$	−0.883512	+	3.18212i	−0.883512	+	3.18212i
$313$	−0.914915	+	1.72571i	−0.914915	+	1.72571i	−0.267528	+	0.963550i	$0.586207\pi$
$313$	−0.914915	+	1.72571i	−0.914915	+	1.72571i	−0.647386	+	0.762162i	$0.724138\pi$
$314$	−2.99657	−	2.27793i	−2.99657	−	2.27793i
$315$		0			0
$316$	−2.88636	+	0.972529i	−2.88636	+	0.972529i
$317$	−1.00700	+	0.221658i	−1.00700	+	0.221658i	−0.687699	−	0.725995i	$-0.741379\pi$
$317$	−1.00700	+	0.221658i	−1.00700	+	0.221658i	−0.319302	+	0.947653i	$0.603448\pi$
$318$		0			0
$319$		0			0
$320$	4.52599	+	5.32841i	4.52599	+	5.32841i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.52290	−	2.24611i	−1.52290	−	2.24611i
$325$	1.62481	+	2.39641i	1.62481	+	2.39641i
$326$		0			0
$327$		0			0
$328$	3.53919	−	4.16665i	3.53919	−	4.16665i
$329$		0			0
$330$	−0.744759	+	4.54283i	−0.744759	+	4.54283i
$331$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$331$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$332$	4.03987	−	0.889242i	4.03987	−	0.889242i
$333$		0			0
$334$	−0.0448562	+	0.827324i	−0.0448562	+	0.827324i
$335$		0			0
$336$		0			0
$337$	0.458467	−	1.65125i	0.458467	−	1.65125i	−0.267528	−	0.963550i	$-0.586207\pi$
$337$	0.458467	−	1.65125i	0.458467	−	1.65125i	0.725995	−	0.687699i	$-0.241379\pi$
$338$	1.39907	−	1.32527i	1.39907	−	1.32527i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−0.915612	+	0.550905i	−0.915612	+	0.550905i
$345$		0			0
$346$		0			0
$347$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$347$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$348$		0			0
$349$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$349$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$350$		0			0
$351$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$352$	2.53519	−	3.73913i	2.53519	−	3.73913i
$353$	−1.85795			−1.85795			−0.928977	−	0.370138i	$-0.879310\pi$
$353$	−1.85795			−1.85795			−0.928977	+	0.370138i	$0.879310\pi$
$354$	1.79023	−	0.713293i	1.79023	−	0.713293i
$355$	3.94152			3.94152
$356$	−2.69100	+	3.96893i	−2.69100	+	3.96893i
$357$		0			0
$358$		0			0
$359$	−0.390204	−	0.180527i	−0.390204	−	0.180527i	0.214970	−	0.976621i	$-0.431034\pi$
$359$	−0.390204	−	0.180527i	−0.390204	−	0.180527i	−0.605174	+	0.796093i	$0.706897\pi$
$360$	5.58498	+	3.36037i	5.58498	+	3.36037i
$361$	0.267528	+	0.963550i	0.267528	+	0.963550i
$362$	−0.203784	−	0.0448562i	−0.203784	−	0.0448562i
$363$	0.462218	−	0.0502692i	0.462218	−	0.0502692i
$364$		0			0
$365$		0			0
$366$	−0.935808	+	0.432951i	−0.935808	+	0.432951i
$367$	−1.58285	−	0.172146i	−1.58285	−	0.172146i	−0.725995	−	0.687699i	$-0.758621\pi$
$367$	−1.58285	−	0.172146i	−1.58285	−	0.172146i	−0.856857	+	0.515554i	$0.827586\pi$
$368$		0			0
$369$	0.612719	−	1.53781i	0.612719	−	1.53781i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.15592	+	0.878708i	1.15592	+	0.878708i	0.994138	−	0.108119i	$-0.0344828\pi$
$373$	1.15592	+	0.878708i	1.15592	+	0.878708i	0.161782	+	0.986827i	$0.448276\pi$
$374$		0			0
$375$	3.54486	−	1.19440i	3.54486	−	1.19440i
$376$	3.32562	−	0.732024i	3.32562	−	0.732024i
$377$		0			0
$378$		0			0
$379$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$379$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$380$		0			0
$381$	−0.209471	−	1.27772i	−0.209471	−	1.27772i
$382$		0			0
$383$	0.771856	+	1.13840i	0.771856	+	1.13840i	0.986827	+	0.161782i	$0.0517241\pi$
$383$	0.771856	+	1.13840i	0.771856	+	1.13840i	−0.214970	+	0.976621i	$0.568966\pi$
$384$	−1.73622	−	2.56073i	−1.73622	−	2.56073i
$385$		0			0
$386$		0			0
$387$	−0.209471	+	0.246608i	−0.209471	+	0.246608i
$388$		0			0
$389$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$389$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$390$	−1.78156	−	3.36037i	−1.78156	−	3.36037i
$391$		0			0
$392$	3.12962	−	1.05449i	3.12962	−	1.05449i
$393$		0			0
$394$	0.979713	+	0.744759i	0.979713	+	0.744759i
$395$	1.03761	−	1.95714i	1.03761	−	1.95714i
$396$	0.878708	−	3.16482i	0.878708	−	3.16482i
$397$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$397$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$398$	−1.39323	+	3.49675i	−1.39323	+	3.49675i
$399$		0			0
$400$	−10.5074	−	1.14275i	−10.5074	−	1.14275i
$401$	0.390204	−	0.180527i	0.390204	−	0.180527i	−0.214970	−	0.976621i	$-0.568966\pi$
$401$	0.390204	−	0.180527i	0.390204	−	0.180527i	0.605174	+	0.796093i	$0.293103\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.92751	+	0.424277i	1.92751	+	0.424277i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$409$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$410$	0.340864	+	6.28688i	0.340864	+	6.28688i
$411$	0.121350	−	0.178978i	0.121350	−	0.178978i
$412$	0.293835			0.293835
$413$		0			0
$414$		0			0
$415$	−1.68832	+	2.49009i	−1.68832	+	2.49009i
$416$	0.202070	+	3.72697i	0.202070	+	3.72697i
$417$	−0.119763	−	0.300583i	−0.119763	−	0.300583i
$418$		0			0
$419$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$419$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$420$		0			0
$421$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$421$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$422$	1.41822	−	0.154241i	1.41822	−	0.154241i
$423$	0.883512	−	0.531592i	0.883512	−	0.531592i
$424$		0			0
$425$		0			0
$426$	−3.82599	−	0.416101i	−3.82599	−	0.416101i
$427$		0			0
$428$		0			0
$429$	−0.878708	+	0.832356i	−0.878708	+	0.832356i
$430$	0.329234	−	1.18579i	0.329234	−	1.18579i
$431$	−0.870281	+	1.64152i	−0.870281	+	1.64152i	−0.108119	+	0.994138i	$0.534483\pi$
$431$	−0.870281	+	1.64152i	−0.870281	+	1.64152i	−0.762162	+	0.647386i	$0.775862\pi$
$432$	−2.90616	−	2.20921i	−2.90616	−	2.20921i
$433$	0.107643	−	1.98536i	0.107643	−	1.98536i	−0.0541389	−	0.998533i	$-0.517241\pi$
$433$	0.107643	−	1.98536i	0.107643	−	1.98536i	0.161782	−	0.986827i	$-0.448276\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.28718	+	1.51539i	−1.28718	+	1.51539i	−0.561187	+	0.827689i	$0.689655\pi$
$439$	−1.28718	+	1.51539i	−1.28718	+	1.51539i	−0.725995	+	0.687699i	$0.758621\pi$
$440$	1.27630	+	7.78511i	1.27630	+	7.78511i
$441$	0.796093	−	0.605174i	0.796093	−	0.605174i
$442$		0			0
$443$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$443$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$444$		0			0
$445$	−0.564213	−	3.44155i	−0.564213	−	3.44155i
$446$		0			0
$447$	−0.543661	−	0.640047i	−0.543661	−	0.640047i
$448$		0			0
$449$	0.299127	+	0.564213i	0.299127	+	0.564213i	0.986827	−	0.161782i	$-0.0517241\pi$
$449$	0.299127	+	0.564213i	0.299127	+	0.564213i	−0.687699	+	0.725995i	$0.741379\pi$
$450$	−5.44910	+	1.19944i	−5.44910	+	1.19944i
$451$	1.89870	−	0.639747i	1.89870	−	0.639747i
$452$		0			0
$453$		0			0
$454$	−1.80269	+	3.40024i	−1.80269	+	3.40024i
$455$		0			0
$456$		0			0
$457$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$457$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.998533	+	0.945861i	0.998533	+	0.945861i	0.998533	−	0.0541389i	$-0.0172414\pi$
$461$	0.998533	+	0.945861i	0.998533	+	0.945861i			1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$463$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$467$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$468$	1.00445	+	2.52098i	1.00445	+	2.52098i
$469$		0			0
$470$	−2.20083	+	3.24598i	−2.20083	+	3.24598i
$471$	−1.95324			−1.95324
$472$	2.51704	−	2.13799i	2.51704	−	2.13799i
$473$	−0.391625			−0.391625
$474$	−1.21381	+	1.79023i	−1.21381	+	1.79023i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.38668	−	0.834340i	−1.38668	−	0.834340i
$479$	−0.515554	−	1.85686i	−0.515554	−	1.85686i	−0.515554	−	0.856857i	$-0.672414\pi$
$479$	−0.515554	−	1.85686i	−0.515554	−	1.85686i		−	1.00000i	$-0.5\pi$
$480$	7.19432	+	1.58359i	7.19432	+	1.58359i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.14511	−	0.529784i	1.14511	−	0.529784i
$485$		0			0
$486$	−1.82622	−	0.615326i	−1.82622	−	0.615326i
$487$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$487$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$488$	−1.28285	+	1.21518i	−1.28285	+	1.21518i
$489$		0			0
$490$	−1.78156	+	3.36037i	−1.78156	+	3.36037i
$491$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$491$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$492$	0.243204	−	4.48563i	0.243204	−	4.48563i
$493$		0			0
$494$		0			0
$495$	1.11894	+	2.11054i	1.11894	+	2.11054i
$496$		0			0
$497$		0			0
$498$	1.90171	−	2.23887i	1.90171	−	2.23887i
$499$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$499$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$500$	8.08124	−	6.14320i	8.08124	−	6.14320i
$501$	0.241277	+	0.355857i	0.241277	+	0.355857i
$502$		0			0
$503$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$503$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.161782	−	0.986827i	0.161782	−	0.986827i
$508$	−1.64582	−	3.10435i	−1.64582	−	3.10435i
$509$	−1.72571	+	0.379858i	−1.72571	+	0.379858i	−0.963550	−	0.267528i	$-0.913793\pi$
$509$	−1.72571	+	0.379858i	−1.72571	+	0.379858i	−0.762162	+	0.647386i	$0.775862\pi$
$510$		0			0
$511$		0			0
$512$	−1.24948	−	0.949829i	−1.24948	−	0.949829i
$513$		0			0
$514$		0			0
$515$	−0.155147	+	0.146963i	−0.155147	+	0.146963i
$516$	−0.325004	+	0.815698i	−0.325004	+	0.815698i
$517$	1.18267	+	0.398488i	1.18267	+	0.398488i
$518$		0			0
$519$		0			0
$520$	−4.73203	−	4.48242i	−4.73203	−	4.48242i
$521$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$521$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$522$		0			0
$523$	1.26450	+	0.278338i	1.26450	+	0.278338i	0.796093	−	0.605174i	$-0.206897\pi$
$523$	1.26450	+	0.278338i	1.26450	+	0.278338i	0.468408	+	0.883512i	$0.344828\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.239208	−	4.41193i	−0.239208	−	4.41193i
$529$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$530$		0			0
$531$	0.515554	−	0.856857i	0.515554	−	0.856857i
$532$		0			0
$533$	−0.928977	+	1.37014i	−0.928977	+	1.37014i
$534$	0.184356	+	3.40024i	0.184356	+	3.40024i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.18205	+	0.260189i	1.18205	+	0.260189i
$540$	5.32453	−	0.579078i	5.32453	−	0.579078i
$541$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$541$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$542$		0			0
$543$	−0.0982703	+	0.0454647i	−0.0982703	+	0.0454647i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.15592	+	1.09495i	−1.15592	+	1.09495i	−0.161782	+	0.986827i	$0.551724\pi$
$547$	−1.15592	+	1.09495i	−1.15592	+	1.09495i	−0.994138	+	0.108119i	$0.965517\pi$
$548$	0.156988	−	0.565419i	0.156988	−	0.565419i
$549$	−0.250625	+	0.472729i	−0.250625	+	0.472729i
$550$	−5.37617	−	4.08686i	−5.37617	−	4.08686i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.63848	−	3.09050i	−1.63848	−	3.09050i
$555$		0			0
$556$	−0.568444	−	0.669224i	−0.568444	−	0.669224i
$557$	−1.24758	+	1.46876i	−1.24758	+	1.46876i	−0.419889	+	0.907575i	$0.637931\pi$
$557$	−1.24758	+	1.46876i	−1.24758	+	1.46876i	−0.827689	+	0.561187i	$0.810345\pi$
$558$		0			0
$559$	0.257587	−	0.195813i	0.257587	−	0.195813i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$563$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$564$	1.81147	−	2.13263i	1.81147	−	2.13263i
$565$		0			0
$566$	0.349923	−	2.13443i	0.349923	−	2.13443i
$567$		0			0
$568$	−6.44112	+	1.41780i	−6.44112	+	1.41780i
$569$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$569$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$570$		0			0
$571$	1.50884	+	1.14699i	1.50884	+	1.14699i	0.947653	+	0.319302i	$0.103448\pi$
$571$	1.50884	+	1.14699i	1.50884	+	1.14699i	0.561187	+	0.827689i	$0.310345\pi$
$572$	−1.53851	+	2.90193i	−1.53851	+	2.90193i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−3.35683	−	1.13105i	−3.35683	−	1.13105i
$577$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$577$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$578$	−1.74899	+	0.809168i	−1.74899	+	0.809168i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1.79124	−	0.828715i	−1.79124	−	0.828715i
$586$	0.735482	+	1.84592i	0.735482	+	1.84592i
$587$	−0.0825252	−	1.52209i	−0.0825252	−	1.52209i	−0.687699	−	0.725995i	$-0.741379\pi$
$587$	−0.0825252	−	1.52209i	−0.0825252	−	1.52209i	0.605174	−	0.796093i	$-0.293103\pi$
$588$	1.52290	−	2.24611i	1.52290	−	2.24611i
$589$		0			0
$590$	−0.411223	+	3.78113i	−0.411223	+	3.78113i
$591$	0.638603			0.638603
$592$		0			0
$593$	−0.100588	−	1.85523i	−0.100588	−	1.85523i	−0.419889	−	0.907575i	$-0.637931\pi$
$593$	−0.100588	−	1.85523i	−0.100588	−	1.85523i	0.319302	−	0.947653i	$-0.396552\pi$
$594$	−0.863333	−	2.16680i	−0.863333	−	2.16680i
$595$		0			0
$596$	−1.95271	−	1.17491i	−1.95271	−	1.17491i
$597$	0.522547	+	1.88205i	0.522547	+	1.88205i
$598$		0			0
$599$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$599$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$600$	−8.19305	+	4.92960i	−8.19305	+	4.92960i
$601$	0.939999	+	0.890414i	0.939999	+	0.890414i	0.994138	−	0.108119i	$-0.0344828\pi$
$601$	0.939999	+	0.890414i	0.939999	+	0.890414i	−0.0541389	+	0.998533i	$0.517241\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.339652	+	0.852463i	−0.339652	+	0.852463i
$606$		0			0
$607$	−0.300267	+	1.08146i	−0.300267	+	1.08146i	0.647386	+	0.762162i	$0.275862\pi$
$607$	−0.300267	+	1.08146i	−0.300267	+	1.08146i	−0.947653	+	0.319302i	$0.896552\pi$
$608$		0			0
$609$		0			0
$610$	0.110175	−	2.03206i	0.110175	−	2.03206i
$611$	−0.977132	+	0.329234i	−0.977132	+	0.329234i
$612$		0			0
$613$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$613$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$614$		0			0
$615$	2.11510	+	2.49009i	2.11510	+	2.49009i
$616$		0			0
$617$	0.246608	+	1.50424i	0.246608	+	1.50424i	0.762162	+	0.647386i	$0.224138\pi$
$617$	0.246608	+	1.50424i	0.246608	+	1.50424i	−0.515554	+	0.856857i	$0.672414\pi$
$618$	0.166115	−	0.126277i	0.166115	−	0.126277i
$619$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$619$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	2.36330	+	2.78230i	2.36330	+	2.78230i
$625$	−0.725995	+	4.42838i	−0.725995	+	4.42838i
$626$	1.76313	+	3.32562i	1.76313	+	3.32562i
$627$		0			0
$628$	−5.02307	+	1.69247i	−5.02307	+	1.69247i
$629$		0			0
$630$		0			0
$631$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$631$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$632$	−0.991631	+	3.57153i	−0.991631	+	3.57153i
$633$	0.537437	−	0.509088i	0.537437	−	0.509088i
$634$	−0.735482	+	1.84592i	−0.735482	+	1.84592i
$635$	2.42166	+	0.815953i	2.42166	+	0.815953i
$636$		0			0
$637$	−0.907575	+	0.419889i	−0.907575	+	0.419889i
$638$		0			0
$639$	−1.71120	+	1.02960i	−1.71120	+	1.02960i
$640$	6.07037	−	0.660192i	6.07037	−	0.660192i
$641$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$641$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$642$		0			0
$643$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$643$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$644$		0			0
$645$	−0.236371	−	0.593247i	−0.236371	−	0.593247i
$646$		0			0
$647$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$647$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$648$	−3.30250			−3.30250
$649$	1.19440	−	0.195813i	1.19440	−	0.195813i
$650$	5.57954			5.57954
$651$		0			0
$652$		0			0
$653$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$653$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$654$		0			0
$655$		0			0
$656$	−1.61668	−	5.82274i	−1.61668	−	5.82274i
$657$		0			0
$658$		0			0
$659$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$659$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$660$	4.70630	+	4.45804i	4.70630	+	4.45804i
$661$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$661$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$662$		0			0
$663$		0			0
$664$	1.86330	−	4.67654i	1.86330	−	4.67654i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.928831	+	0.706079i	0.928831	+	0.706079i
$669$		0			0
$670$		0			0
$671$	−0.632464	+	0.139216i	−0.632464	+	0.139216i
$672$		0			0
$673$	0.277248	−	1.69114i	0.277248	−	1.69114i	−0.370138	−	0.928977i	$-0.620690\pi$
$673$	0.277248	−	1.69114i	0.277248	−	1.69114i	0.647386	−	0.762162i	$-0.275862\pi$
$674$	−2.13799	−	2.51704i	−2.13799	−	2.51704i
$675$	−1.87438	+	2.20669i	−1.87438	+	2.20669i
$676$	−0.439030	−	2.67797i	−0.439030	−	2.67797i
$677$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$677$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.323089	+	1.97076i	0.323089	+	1.97076i
$682$		0			0
$683$	−1.07167	−	1.26167i	−1.07167	−	1.26167i	−0.963550	−	0.267528i	$-0.913793\pi$
$683$	−1.07167	−	1.26167i	−1.07167	−	1.26167i	−0.108119	−	0.994138i	$-0.534483\pi$
$684$		0			0
$685$	0.199907	+	0.377064i	0.199907	+	0.377064i
$686$		0			0
$687$		0			0
$688$	−0.0639478	+	1.17945i	−0.0639478	+	1.17945i
$689$		0			0
$690$		0			0
$691$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$691$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.634860	+	0.0690451i	0.634860	+	0.0690451i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$701$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$702$	1.65125	+	0.993524i	1.65125	+	0.993524i
$703$		0			0
$704$	−1.58692	−	3.98286i	−1.58692	−	3.98286i
$705$	0.110175	+	2.03206i	0.110175	+	2.03206i
$706$	−2.00931	+	2.96351i	−2.00931	+	2.96351i
$707$		0			0
$708$	0.583368	−	2.65027i	0.583368	−	2.65027i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$	4.26261	−	6.28688i	4.26261	−	6.28688i
$711$	0.0607641	+	1.12073i	0.0607641	+	1.12073i
$712$	2.15998	+	5.42113i	2.15998	+	5.42113i
$713$		0			0
$714$		0			0
$715$	−0.639074	−	2.30174i	−0.639074	−	2.30174i
$716$		0			0
$717$	−0.834855	+	0.0907960i	−0.834855	+	0.0907960i
$718$	−0.709940	+	0.427157i	−0.709940	+	0.427157i
$719$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$719$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$720$	6.53897	−	3.02525i	6.53897	−	3.02525i
$721$		0			0
$722$	1.82622	+	0.615326i	1.82622	+	0.615326i
$723$		0			0
$724$	−0.213323	+	0.202070i	−0.213323	+	0.202070i
$725$		0			0
$726$	0.419690	−	0.791620i	0.419690	−	0.791620i
$727$	0.589329	+	0.447996i	0.589329	+	0.447996i	0.856857	−	0.515554i	$-0.172414\pi$
$727$	0.589329	+	0.447996i	0.589329	+	0.447996i	−0.267528	+	0.963550i	$0.586207\pi$
$728$		0			0
$729$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$730$		0			0
$731$		0			0
$732$	−0.234906	+	1.43286i	−0.234906	+	1.43286i
$733$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$733$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$734$	−1.98638	+	2.33854i	−1.98638	+	2.33854i
$735$	0.319302	+	1.94765i	0.319302	+	1.94765i
$736$		0			0
$737$		0			0
$738$	−1.79023	−	2.64039i	−1.79023	−	2.64039i
$739$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$739$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.323089	−	1.97076i	0.323089	−	1.97076i	0.108119	−	0.994138i	$-0.465517\pi$
$743$	0.323089	−	1.97076i	0.323089	−	1.97076i	0.214970	−	0.976621i	$-0.431034\pi$
$744$		0			0
$745$	1.61868	−	0.356299i	1.61868	−	0.356299i
$746$	2.65166	−	0.893448i	2.65166	−	0.893448i
$747$	0.0825252	−	1.52209i	0.0825252	−	1.52209i
$748$		0			0
$749$		0			0
$750$	1.92852	−	6.94590i	1.92852	−	6.94590i
$751$	1.24415	−	1.17852i	1.24415	−	1.17852i	0.267528	−	0.963550i	$-0.413793\pi$
$751$	1.24415	−	1.17852i	1.24415	−	1.17852i	0.976621	−	0.214970i	$-0.0689655\pi$
$752$	1.39323	−	3.49675i	1.39323	−	3.49675i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.67365	−	1.00700i	1.67365	−	1.00700i	0.725995	−	0.687699i	$-0.241379\pi$
$757$	1.67365	−	1.00700i	1.67365	−	1.00700i	0.947653	−	0.319302i	$-0.103448\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.719570	−	0.432951i	−0.719570	−	0.432951i	0.108119	−	0.994138i	$-0.465517\pi$
$761$	−0.719570	−	0.432951i	−0.719570	−	0.432951i	−0.827689	+	0.561187i	$0.810345\pi$
$762$	−2.26454	−	1.04769i	−2.26454	−	1.04769i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	2.65053			2.65053
$767$	−0.687699	+	0.725995i	−0.687699	+	0.725995i
$768$	−2.41988			−2.41988
$769$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$769$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.185285	−	0.111482i	−0.185285	−	0.111482i	0.419889	−	0.907575i	$-0.362069\pi$
$773$	−0.185285	−	0.111482i	−0.185285	−	0.111482i	−0.605174	+	0.796093i	$0.706897\pi$
$774$	0.166815	+	0.600812i	0.166815	+	0.600812i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−5.32453	−	0.579078i	−5.32453	−	0.579078i
$781$	−2.29062	−	0.771799i	−2.29062	−	0.771799i
$782$		0			0
$783$		0			0
$784$	0.976621	−	3.51747i	0.976621	−	3.51747i
$785$	1.80572	−	3.40596i	1.80572	−	3.40596i
$786$		0			0
$787$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$787$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$788$	1.64227	−	0.553345i	1.64227	−	0.553345i
$789$		0			0
$790$	−1.99957	−	3.77160i	−1.99957	−	3.77160i
$791$		0			0
$792$	−2.58772	−	3.04649i	−2.58772	−	3.04649i
$793$	0.346388	−	0.407800i	0.346388	−	0.407800i
$794$		0			0
$795$		0			0
$796$	2.97459	+	4.38720i	2.97459	+	4.38720i
$797$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$797$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$798$		0			0
$799$		0			0
$800$	−6.99602	+	8.23635i	−6.99602	+	8.23635i
$801$	1.14395	+	1.34676i	1.14395	+	1.34676i
$802$	0.134043	−	0.817624i	0.134043	−	0.817624i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$809$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$810$	2.76127	−	2.61561i	2.76127	−	2.61561i
$811$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$811$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	7.59697	+	4.57095i	7.59697	+	4.57095i
$821$	1.79124	+	0.828715i	1.79124	+	0.828715i	0.963550	+	0.267528i	$0.0862069\pi$
$821$	1.79124	+	0.828715i	1.79124	+	0.828715i	0.827689	+	0.561187i	$0.189655\pi$
$822$	−0.154241	−	0.387116i	−0.154241	−	0.387116i
$823$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i	−0.725995	−	0.687699i	$-0.758621\pi$
$823$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i	0.647386	−	0.762162i	$-0.275862\pi$
$824$	0.200673	−	0.295971i	0.200673	−	0.295971i
$825$	−3.50433			−3.50433
$826$		0			0
$827$	1.21035			1.21035			0.605174	−	0.796093i	$-0.293103\pi$
$827$	1.21035			1.21035			0.605174	+	0.796093i	$0.293103\pi$
$828$		0			0
$829$	−0.0507182	−	0.935443i	−0.0507182	−	0.935443i	−0.907575	−	0.419889i	$-0.862069\pi$
$829$	−0.0507182	−	0.935443i	−0.0507182	−	0.935443i	0.856857	−	0.515554i	$-0.172414\pi$
$830$	2.14593	+	5.38589i	2.14593	+	5.38589i
$831$	−1.64739	−	0.762162i	−1.64739	−	0.762162i
$832$	3.03521	+	1.82622i	3.03521	+	1.82622i
$833$		0			0
$834$	−0.608962	−	0.134043i	−0.608962	−	0.134043i
$835$	−0.843580	+	0.0917448i	−0.843580	+	0.0917448i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.98536	+	0.215921i	1.98536	+	0.215921i	0.998533	+	0.0541389i	$0.0172414\pi$
$839$	1.98536	+	0.215921i	1.98536	+	0.215921i	0.986827	+	0.161782i	$0.0517241\pi$
$840$		0			0
$841$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$842$		0			0
$843$		0			0
$844$	0.940985	−	1.77489i	0.940985	−	1.77489i
$845$	1.57121	+	1.19440i	1.57121	+	1.19440i
$846$	0.107577	−	1.98413i	0.107577	−	1.98413i
$847$		0			0
$848$		0			0
$849$	−0.525730	−	0.991631i	−0.525730	−	0.991631i
$850$		0			0
$851$		0			0
$852$	−3.50849	+	4.13051i	−3.50849	+	4.13051i
$853$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$853$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$857$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$858$	0.377350	+	2.30174i	0.377350	+	2.30174i
$859$	−1.03076	+	1.21350i	−1.03076	+	1.21350i	−0.0541389	+	0.998533i	$0.517241\pi$
$859$	−1.03076	+	1.21350i	−1.03076	+	1.21350i	−0.976621	+	0.214970i	$0.931034\pi$
$860$	−1.12191	−	1.32082i	−1.12191	−	1.32082i
$861$		0			0
$862$	1.67712	+	3.16338i	1.67712	+	3.16338i
$863$	1.81452	−	0.399405i	1.81452	−	0.399405i	0.827689	−	0.561187i	$-0.189655\pi$
$863$	1.81452	−	0.399405i	1.81452	−	0.399405i	0.986827	+	0.161782i	$0.0517241\pi$
$864$	−3.53706	+	1.19177i	−3.53706	+	1.19177i
$865$		0			0
$866$	−3.05032	−	2.31879i	−3.05032	−	2.31879i
$867$	−0.468408	+	0.883512i	−0.468408	+	0.883512i
$868$		0			0
$869$	−0.986239	+	0.934215i	−0.986239	+	0.934215i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$877$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$878$	1.02506	+	3.69194i	1.02506	+	3.69194i
$879$	0.883512	+	0.531592i	0.883512	+	0.531592i
$880$	7.91444	+	3.66161i	7.91444	+	3.66161i
$881$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$881$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$882$	−0.104331	−	1.92427i	−0.104331	−	1.92427i
$883$	−0.814839	+	1.20180i	−0.814839	+	1.20180i	0.161782	+	0.986827i	$0.448276\pi$
$883$	−0.814839	+	1.20180i	−0.814839	+	1.20180i	−0.976621	+	0.214970i	$0.931034\pi$
$884$		0			0
$885$	1.01752	+	1.69114i	1.01752	+	1.69114i
$886$		0			0
$887$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$887$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$888$		0			0
$889$		0			0
$890$	−6.09958	−	2.82197i	−6.09958	−	2.82197i
$891$	−1.03710	−	0.624000i	−1.03710	−	0.624000i
$892$		0			0
$893$		0			0
$894$	−1.60885	+	0.174973i	−1.60885	+	0.174973i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.22344	+	0.133057i	1.22344	+	0.133057i
$899$		0			0
$900$	−2.90819	+	7.29900i	−2.90819	+	7.29900i
$901$		0			0
$902$	1.03296	−	3.72037i	1.03296	−	3.72037i
$903$		0			0
$904$		0			0
$905$	0.0115696	−	0.213389i	0.0115696	−	0.213389i
$906$		0			0
$907$	−1.77271	+	0.390204i	−1.77271	+	0.390204i	−0.976621	−	0.214970i	$-0.931034\pi$
$907$	−1.77271	+	0.390204i	−1.77271	+	0.390204i	−0.796093	+	0.605174i	$0.793103\pi$
$908$	2.53852	+	4.78817i	2.53852	+	4.78817i
$909$		0			0
$910$		0			0
$911$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$911$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$912$		0			0
$913$	1.46876	−	1.11652i	1.46876	−	1.11652i
$914$		0			0
$915$	−0.592623	−	0.874053i	−0.592623	−	0.874053i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.606482	−	0.714006i	−0.606482	−	0.714006i	0.370138	−	0.928977i	$-0.379310\pi$
$919$	−0.606482	−	0.714006i	−0.606482	−	0.714006i	−0.976621	+	0.214970i	$0.931034\pi$
$920$		0			0
$921$		0			0
$922$	2.58856	−	0.569786i	2.58856	−	0.569786i
$923$	1.89253	−	0.637666i	1.89253	−	0.637666i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.0289674	−	0.104331i	0.0289674	−	0.104331i
$928$		0			0
$929$	−0.236371	+	0.593247i	−0.236371	+	0.593247i	−0.998533	−	0.0541389i	$-0.982759\pi$
$929$	−0.236371	+	0.593247i	−0.236371	+	0.593247i	0.762162	+	0.647386i	$0.224138\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	3.22529	+	0.709940i	3.22529	+	0.709940i
$937$	−0.425955	−	1.53415i	−0.425955	−	1.53415i	−0.796093	−	0.605174i	$-0.793103\pi$
$937$	−0.425955	−	1.53415i	−0.425955	−	1.53415i	0.370138	−	0.928977i	$-0.379310\pi$
$938$		0			0
$939$	1.77271	+	0.820145i	1.77271	+	0.820145i
$940$	2.04410	+	5.13031i	2.04410	+	5.13031i
$941$	−0.0896204	−	1.65295i	−0.0896204	−	1.65295i	−0.605174	−	0.796093i	$-0.706897\pi$
$941$	−0.0896204	−	1.65295i	−0.0896204	−	1.65295i	0.515554	−	0.856857i	$-0.327586\pi$
$942$	−2.11236	+	3.11550i	−2.11236	+	3.11550i
$943$		0			0
$944$	−0.394692	−	3.62913i	−0.394692	−	3.62913i
$945$		0			0
$946$	−0.423528	+	0.624658i	−0.423528	+	0.624658i
$947$	0.0345733	+	0.637666i	0.0345733	+	0.637666i	0.963550	+	0.267528i	$0.0862069\pi$
$947$	0.0345733	+	0.637666i	0.0345733	+	0.637666i	−0.928977	+	0.370138i	$0.879310\pi$
$948$	1.12737	+	2.82948i	1.12737	+	2.82948i
$949$		0			0
$950$		0			0
$951$	0.275851	+	0.993524i	0.275851	+	0.993524i
$952$		0			0
$953$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$953$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$954$		0			0
$955$		0			0
$956$	−2.06829	+	0.956893i	−2.06829	+	0.956893i
$957$		0			0
$958$	−3.51931	−	1.18579i	−3.51931	−	1.18579i
$959$		0			0
$960$	5.07556	−	4.80783i	5.07556	−	4.80783i
$961$	0.267528	−	0.963550i	0.267528	−	0.963550i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$967$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$968$	0.248412	−	1.51525i	0.248412	−	1.51525i
$969$		0			0
$970$		0			0
$971$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$971$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$972$	−2.16037	+	1.64227i	−2.16037	+	1.64227i
$973$		0			0
$974$		0			0
$975$	2.30493	−	1.75216i	2.30493	−	1.75216i
$976$	0.315999	+	1.92751i	0.315999	+	1.92751i
$977$	1.27772	−	1.50424i	1.27772	−	1.50424i	0.515554	−	0.856857i	$-0.327586\pi$
$977$	1.27772	−	1.50424i	1.27772	−	1.50424i	0.762162	−	0.647386i	$-0.224138\pi$
$978$		0			0
$979$	−0.346006	+	2.11054i	−0.346006	+	2.11054i
$980$	2.50876	+	4.73203i	2.50876	+	4.73203i
$981$		0			0
$982$		0			0
$983$	0.0117069	−	0.215921i	0.0117069	−	0.215921i	−0.986827	−	0.161782i	$-0.948276\pi$
$983$	0.0117069	−	0.215921i	0.0117069	−	0.215921i	0.998533	−	0.0541389i	$-0.0172414\pi$
$984$	−4.35215	−	3.30842i	−4.35215	−	3.30842i
$985$	−0.590373	+	1.11356i	−0.590373	+	1.11356i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	4.57649	+	0.497723i	4.57649	+	0.497723i
$991$	−1.01864	+	0.471273i	−1.01864	+	0.471273i	−0.856857	−	0.515554i	$-0.827586\pi$
$991$	−1.01864	+	0.471273i	−1.01864	+	0.471273i	−0.161782	+	0.986827i	$0.551724\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.76489	−	0.828715i	−3.76489	−	0.828715i
$996$	−1.10665	−	3.98580i	−1.10665	−	3.98580i
$997$	−1.36428	−	0.820858i	−1.36428	−	0.820858i	−0.370138	−	0.928977i	$-0.620690\pi$
$997$	−1.36428	−	0.820858i	−1.36428	−	0.820858i	−0.994138	+	0.108119i	$0.965517\pi$
$998$		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.194.2	yes	56
3.2	odd	2	inner	2301.1.z.c.194.1	✓	56
13.12	even	2	inner	2301.1.z.c.194.1	✓	56
39.38	odd	2	CM	2301.1.z.c.194.2	yes	56
59.7	even	29	inner	2301.1.z.c.1364.2	yes	56
177.125	odd	58	inner	2301.1.z.c.1364.1	yes	56
767.597	even	58	inner	2301.1.z.c.1364.1	yes	56
2301.1364	odd	58	inner	2301.1.z.c.1364.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2301.1.z.c.194.1	✓	56	3.2	odd	2	inner
2301.1.z.c.194.1	✓	56	13.12	even	2	inner
2301.1.z.c.194.2	yes	56	1.1	even	1	trivial
2301.1.z.c.194.2	yes	56	39.38	odd	2	CM
2301.1.z.c.1364.1	yes	56	177.125	odd	58	inner
2301.1.z.c.1364.1	yes	56	767.597	even	58	inner
2301.1.z.c.1364.2	yes	56	59.7	even	29	inner
2301.1.z.c.1364.2	yes	56	2301.1364	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)

\(f(q)\)	\(=\)	\(q+(1.08146 - 1.59504i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-1.00445 - 2.52098i) q^{4} +(1.79124 + 0.828715i) q^{5} +(-1.65125 - 0.993524i) q^{6} +(-3.22529 - 0.709940i) q^{8} +(-0.994138 + 0.108119i) q^{9} +(3.25899 - 1.96087i) q^{10} +(-0.878708 - 0.832356i) q^{11} +(-2.46290 + 1.13946i) q^{12} +(0.994138 + 0.108119i) q^{13} +(0.730524 - 1.83348i) q^{15} +(-2.65027 + 2.51047i) q^{16} +(-0.902670 + 1.70262i) q^{18} +(0.289964 - 5.34808i) q^{20} +(-2.27793 + 0.501410i) q^{22} +(-0.534285 + 3.25899i) q^{24} +(1.87438 + 2.20669i) q^{25} +(1.24758 - 1.46876i) q^{26} +(0.161782 + 0.986827i) q^{27} +(-2.13443 - 3.14805i) q^{30} +(0.603842 + 3.68327i) q^{32} +(-0.783563 + 0.922482i) q^{33} +(1.27113 + 2.39760i) q^{36} +(0.0541389 - 0.998533i) q^{39} +(-5.18892 - 3.94452i) q^{40} +(-0.775393 + 1.46255i) q^{41} +(0.234906 - 0.222515i) q^{43} +(-1.21573 + 3.05126i) q^{44} +(-1.87034 - 0.630190i) q^{45} +(-0.935808 + 0.432951i) q^{47} +(2.65027 + 2.51047i) q^{48} +(-0.856857 + 0.515554i) q^{49} +(5.54684 - 0.603255i) q^{50} +(-0.725995 - 2.61480i) q^{52} +(1.74899 + 0.809168i) q^{54} +(-0.884189 - 2.21915i) q^{55} +(-0.605174 + 0.796093i) q^{59} -5.35593 q^{60} +(0.300267 - 0.442861i) q^{61} +(3.21486 + 1.48735i) q^{64} +(1.69114 + 1.01752i) q^{65} +(0.624000 + 2.24744i) q^{66} +(1.81249 - 0.838547i) q^{71} +(3.28314 + 0.357063i) q^{72} +(2.10198 - 1.99110i) q^{75} +(-1.53415 - 1.16623i) q^{78} +(0.0607641 - 1.12073i) q^{79} +(-6.82773 + 2.30053i) q^{80} +(0.976621 - 0.214970i) q^{81} +(1.49426 + 2.81847i) q^{82} +(-0.246608 + 1.50424i) q^{83} +(-0.100878 - 0.615326i) q^{86} +(2.24316 + 3.30842i) q^{88} +(-0.991631 - 1.46255i) q^{89} +(-3.02788 + 2.30174i) q^{90} +(-0.321469 + 1.96087i) q^{94} +(3.64518 - 0.802364i) q^{96} +(-0.104331 + 1.92427i) q^{98} +(0.963550 + 0.732472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{12} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 2 q^{39} - 58 q^{40} - 4 q^{43} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 4 q^{61} + 2 q^{64} - 2 q^{75} + 4 q^{79}+ \cdots - 2 q^{81}+O(q^{100}) \) 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

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Database

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