LMFDB - Embedded newform 726.2.e.o.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(487,726)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("726.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.511
Dual form			726.2.e.o.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.618034 - 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-3.23607 + 2.35114i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.618034 - 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-3.23607 + 2.35114i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -2.00000 q^{10} -1.00000 q^{12} +(1.85410 + 5.70634i) q^{13} +(3.23607 + 2.35114i) q^{14} +(1.61803 - 1.17557i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.618034 + 1.90211i) q^{17} +(0.809017 - 0.587785i) q^{18} +(3.23607 + 2.35114i) q^{19} +(0.618034 + 1.90211i) q^{20} -4.00000 q^{21} +4.00000 q^{23} +(0.309017 + 0.951057i) q^{24} +(0.809017 + 0.587785i) q^{25} +(4.85410 - 3.52671i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.23607 - 3.80423i) q^{28} +(4.85410 - 3.52671i) q^{29} +(-1.61803 - 1.17557i) q^{30} -1.00000 q^{32} +2.00000 q^{34} +(2.47214 + 7.60845i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(1.23607 - 3.80423i) q^{38} +(-1.85410 + 5.70634i) q^{39} +(1.61803 - 1.17557i) q^{40} +(-4.85410 - 3.52671i) q^{41} +(1.23607 + 3.80423i) q^{42} -4.00000 q^{43} +2.00000 q^{45} +(-1.23607 - 3.80423i) q^{46} +(9.70820 + 7.05342i) q^{47} +(0.809017 - 0.587785i) q^{48} +(2.78115 - 8.55951i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-1.61803 + 1.17557i) q^{51} +(-4.85410 - 3.52671i) q^{52} +(0.618034 + 1.90211i) q^{53} +1.00000 q^{54} -4.00000 q^{56} +(1.23607 + 3.80423i) q^{57} +(-4.85410 - 3.52671i) q^{58} +(-9.70820 + 7.05342i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(4.32624 - 13.3148i) q^{61} +(-3.23607 - 2.35114i) q^{63} +(0.309017 + 0.951057i) q^{64} +12.0000 q^{65} +4.00000 q^{67} +(-0.618034 - 1.90211i) q^{68} +(3.23607 + 2.35114i) q^{69} +(6.47214 - 4.70228i) q^{70} +(-3.70820 + 11.4127i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-4.85410 + 3.52671i) q^{73} +(4.85410 + 3.52671i) q^{74} +(0.309017 + 0.951057i) q^{75} -4.00000 q^{76} +6.00000 q^{78} +(1.23607 + 3.80423i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.85410 + 5.70634i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(3.23607 - 2.35114i) q^{84} +(3.23607 + 2.35114i) q^{85} +(1.23607 + 3.80423i) q^{86} +6.00000 q^{87} +10.0000 q^{89} +(-0.618034 - 1.90211i) q^{90} +(-19.4164 - 14.1068i) q^{91} +(-3.23607 + 2.35114i) q^{92} +(3.70820 - 11.4127i) q^{94} +(6.47214 - 4.70228i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-4.32624 - 13.3148i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 - q^9	$ 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9} - 8 q^{10} - 4 q^{12} - 6 q^{13} + 4 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} - 16 q^{21} + 16 q^{23} - q^{24} + q^{25} + 6 q^{26} + q^{27} - 4 q^{28} + 6 q^{29} - 2 q^{30} - 4 q^{32} + 8 q^{34} - 8 q^{35} - q^{36} - 6 q^{37} - 4 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} - 4 q^{42} - 16 q^{43} + 8 q^{45} + 4 q^{46} + 12 q^{47} + q^{48} - 9 q^{49} - q^{50} - 2 q^{51} - 6 q^{52} - 2 q^{53} + 4 q^{54} - 16 q^{56} - 4 q^{57} - 6 q^{58} - 12 q^{59} + 2 q^{60} - 14 q^{61} - 4 q^{63} - q^{64} + 48 q^{65} + 16 q^{67} + 2 q^{68} + 4 q^{69} + 8 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} + 6 q^{74} - q^{75} - 16 q^{76} + 24 q^{78} - 4 q^{79} - 2 q^{80} - q^{81} + 6 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{85} - 4 q^{86} + 24 q^{87} + 40 q^{89} + 2 q^{90} - 24 q^{91} - 4 q^{92} - 12 q^{94} + 8 q^{95} - q^{96} + 14 q^{97} - 36 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 - q^9 - 8 * q^10 - 4 * q^12 - 6 * q^13 + 4 * q^14 + 2 * q^15 - q^16 + 2 * q^17 + q^18 + 4 * q^19 - 2 * q^20 - 16 * q^21 + 16 * q^23 - q^24 + q^25 + 6 * q^26 + q^27 - 4 * q^28 + 6 * q^29 - 2 * q^30 - 4 * q^32 + 8 * q^34 - 8 * q^35 - q^36 - 6 * q^37 - 4 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 - 4 * q^42 - 16 * q^43 + 8 * q^45 + 4 * q^46 + 12 * q^47 + q^48 - 9 * q^49 - q^50 - 2 * q^51 - 6 * q^52 - 2 * q^53 + 4 * q^54 - 16 * q^56 - 4 * q^57 - 6 * q^58 - 12 * q^59 + 2 * q^60 - 14 * q^61 - 4 * q^63 - q^64 + 48 * q^65 + 16 * q^67 + 2 * q^68 + 4 * q^69 + 8 * q^70 + 12 * q^71 + q^72 - 6 * q^73 + 6 * q^74 - q^75 - 16 * q^76 + 24 * q^78 - 4 * q^79 - 2 * q^80 - q^81 + 6 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^85 - 4 * q^86 + 24 * q^87 + 40 * q^89 + 2 * q^90 - 24 * q^91 - 4 * q^92 - 12 * q^94 + 8 * q^95 - q^96 + 14 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.618034	−	1.90211i	0.276393	−	0.850651i	−0.712454	−	0.701719i	$-0.752416\pi$
$5$	0.618034	−	1.90211i	0.276393	−	0.850651i	0.988847	−	0.148932i	$-0.0475836\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−3.23607	+	2.35114i	−1.22312	+	0.888648i	−0.996355	−	0.0853021i	$-0.972814\pi$
$7$	−3.23607	+	2.35114i	−1.22312	+	0.888648i	−0.226764	+	0.973950i	$0.572814\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−2.00000			−0.632456
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	1.85410	+	5.70634i	0.514235	+	1.58265i	0.784669	+	0.619915i	$0.212833\pi$
$13$	1.85410	+	5.70634i	0.514235	+	1.58265i	−0.270434	+	0.962739i	$0.587167\pi$
$14$	3.23607	+	2.35114i	0.864876	+	0.628369i
$15$	1.61803	−	1.17557i	0.417775	−	0.303531i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	−0.997608	−	0.0691254i	$-0.977979\pi$
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	0.847713	+	0.530456i	$0.177979\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	0.893463	−	0.449136i	$-0.148268\pi$
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	−0.151058	+	0.988525i	$0.548268\pi$
$20$	0.618034	+	1.90211i	0.138197	+	0.425325i
$21$	−4.00000			−0.872872
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	0.809017	+	0.587785i	0.161803	+	0.117557i
$26$	4.85410	−	3.52671i	0.951968	−	0.691645i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.23607	−	3.80423i	0.233595	−	0.718931i
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	−0.0374370	−	0.999299i	$-0.511919\pi$
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	0.938821	+	0.344405i	$0.111919\pi$
$30$	−1.61803	−	1.17557i	−0.295411	−	0.214629i
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	2.00000			0.342997
$35$	2.47214	+	7.60845i	0.417867	+	1.28606i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	−0.910330	−	0.413884i	$-0.864172\pi$
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	0.112320	+	0.993672i	$0.464172\pi$
$38$	1.23607	−	3.80423i	0.200517	−	0.617127i
$39$	−1.85410	+	5.70634i	−0.296894	+	0.913746i
$40$	1.61803	−	1.17557i	0.255834	−	0.185874i
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	0.140238	−	0.990118i	$-0.455213\pi$
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	−0.898322	+	0.439338i	$0.855213\pi$
$42$	1.23607	+	3.80423i	0.190729	+	0.587005i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$	−1.23607	−	3.80423i	−0.182248	−	0.560903i
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.992402	+	0.123038i	$0.0392637\pi$
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.423685	+	0.905810i	$0.360736\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	2.78115	−	8.55951i	0.397308	−	1.22279i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	−1.61803	+	1.17557i	−0.226570	+	0.164613i
$52$	−4.85410	−	3.52671i	−0.673143	−	0.489067i
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	0.984488	−	0.175450i	$-0.0561381\pi$
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	−0.899595	+	0.436726i	$0.856138\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−4.00000			−0.534522
$57$	1.23607	+	3.80423i	0.163721	+	0.503882i
$58$	−4.85410	−	3.52671i	−0.637375	−	0.463080i
$59$	−9.70820	+	7.05342i	−1.26390	+	0.918277i	−0.998942	−	0.0459824i	$-0.985358\pi$
$59$	−9.70820	+	7.05342i	−1.26390	+	0.918277i	−0.264958	+	0.964260i	$0.585358\pi$
$60$	−0.618034	+	1.90211i	−0.0797878	+	0.245562i
$61$	4.32624	−	13.3148i	0.553918	−	1.70478i	−0.144866	−	0.989451i	$-0.546275\pi$
$61$	4.32624	−	13.3148i	0.553918	−	1.70478i	0.698784	−	0.715333i	$-0.253725\pi$
$62$		0			0
$63$	−3.23607	−	2.35114i	−0.407706	−	0.296216i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	12.0000			1.48842
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−0.618034	−	1.90211i	−0.0749476	−	0.230665i
$69$	3.23607	+	2.35114i	0.389577	+	0.283044i
$70$	6.47214	−	4.70228i	0.773568	−	0.562030i
$71$	−3.70820	+	11.4127i	−0.440083	+	1.35444i	0.447704	+	0.894182i	$0.352242\pi$
$71$	−3.70820	+	11.4127i	−0.440083	+	1.35444i	−0.887787	+	0.460254i	$0.847758\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−4.85410	+	3.52671i	−0.568130	+	0.412770i	−0.834425	−	0.551121i	$-0.814200\pi$
$73$	−4.85410	+	3.52671i	−0.568130	+	0.412770i	0.266296	+	0.963891i	$0.414200\pi$
$74$	4.85410	+	3.52671i	0.564278	+	0.409972i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	6.00000			0.679366
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	0.996201	−	0.0870877i	$-0.0277560\pi$
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	−0.857132	+	0.515097i	$0.827756\pi$
$80$	−1.61803	−	1.17557i	−0.180902	−	0.131433i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.85410	+	5.70634i	−0.204751	+	0.630160i
$83$	−1.23607	+	3.80423i	−0.135676	+	0.417568i	−0.995695	−	0.0926948i	$-0.970452\pi$
$83$	−1.23607	+	3.80423i	−0.135676	+	0.417568i	0.860018	+	0.510263i	$0.170452\pi$
$84$	3.23607	−	2.35114i	0.353084	−	0.256531i
$85$	3.23607	+	2.35114i	0.351001	+	0.255017i
$86$	1.23607	+	3.80423i	0.133289	+	0.410220i
$87$	6.00000			0.643268
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−0.618034	−	1.90211i	−0.0651465	−	0.200500i
$91$	−19.4164	−	14.1068i	−2.03539	−	1.47880i
$92$	−3.23607	+	2.35114i	−0.337383	+	0.245123i
$93$		0			0
$94$	3.70820	−	11.4127i	0.382472	−	1.17713i
$95$	6.47214	−	4.70228i	0.664027	−	0.482444i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−4.32624	−	13.3148i	−0.439263	−	1.35191i	−0.888654	−	0.458577i	$-0.848359\pi$
$97$	−4.32624	−	13.3148i	−0.439263	−	1.35191i	0.449392	−	0.893335i	$-0.351641\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−4.32624	−	13.3148i	−0.430477	−	1.32487i	−0.897651	−	0.440706i	$-0.854728\pi$
$101$	−4.32624	−	13.3148i	−0.430477	−	1.32487i	0.467175	−	0.884165i	$-0.345272\pi$
$102$	1.61803	+	1.17557i	0.160209	+	0.116399i
$103$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$103$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$104$	−1.85410	+	5.70634i	−0.181810	+	0.559553i
$105$	−2.47214	+	7.60845i	−0.241256	+	0.742509i
$106$	1.61803	−	1.17557i	0.157157	−	0.114182i
$107$	3.23607	+	2.35114i	0.312842	+	0.227293i	0.733115	−	0.680104i	$-0.238066\pi$
$107$	3.23607	+	2.35114i	0.312842	+	0.227293i	−0.420273	+	0.907398i	$0.638066\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	1.23607	+	3.80423i	0.116797	+	0.359466i
$113$	−1.61803	−	1.17557i	−0.152212	−	0.110588i	0.509073	−	0.860724i	$-0.329988\pi$
$113$	−1.61803	−	1.17557i	−0.152212	−	0.110588i	−0.661285	+	0.750135i	$0.729988\pi$
$114$	3.23607	−	2.35114i	0.303086	−	0.220205i
$115$	2.47214	−	7.60845i	0.230528	−	0.709492i
$116$	−1.85410	+	5.70634i	−0.172149	+	0.529820i
$117$	−4.85410	+	3.52671i	−0.448762	+	0.326045i
$118$	9.70820	+	7.05342i	0.893713	+	0.649320i
$119$	−2.47214	−	7.60845i	−0.226620	−	0.697466i
$120$	2.00000			0.182574
$121$		0			0
$122$	−14.0000			−1.26750
$123$	−1.85410	−	5.70634i	−0.167179	−	0.514523i
$124$		0			0
$125$	9.70820	−	7.05342i	0.868328	−	0.630877i
$126$	−1.23607	+	3.80423i	−0.110118	+	0.338907i
$127$	−3.70820	+	11.4127i	−0.329050	+	1.01271i	0.640529	+	0.767934i	$0.278715\pi$
$127$	−3.70820	+	11.4127i	−0.329050	+	1.01271i	−0.969579	+	0.244778i	$0.921285\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−3.23607	−	2.35114i	−0.284920	−	0.207006i
$130$	−3.70820	−	11.4127i	−0.325231	−	1.00096i
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−16.0000			−1.38738
$134$	−1.23607	−	3.80423i	−0.106780	−	0.328635i
$135$	1.61803	+	1.17557i	0.139258	+	0.101177i
$136$	−1.61803	+	1.17557i	−0.138745	+	0.100804i
$137$	0.618034	−	1.90211i	0.0528022	−	0.162508i	−0.921178	−	0.389141i	$-0.872772\pi$
$137$	0.618034	−	1.90211i	0.0528022	−	0.162508i	0.973980	+	0.226633i	$0.0727718\pi$
$138$	1.23607	−	3.80423i	0.105221	−	0.323837i
$139$	−3.23607	+	2.35114i	−0.274480	+	0.199421i	−0.716506	−	0.697581i	$-0.754260\pi$
$139$	−3.23607	+	2.35114i	−0.274480	+	0.199421i	0.442026	+	0.897002i	$0.354260\pi$
$140$	−6.47214	−	4.70228i	−0.546995	−	0.397415i
$141$	3.70820	+	11.4127i	0.312287	+	0.961121i
$142$	12.0000			1.00702
$143$		0			0
$144$	1.00000			0.0833333
$145$	−3.70820	−	11.4127i	−0.307950	−	0.947771i
$146$	4.85410	+	3.52671i	0.401728	+	0.291873i
$147$	7.28115	−	5.29007i	0.600539	−	0.436317i
$148$	1.85410	−	5.70634i	0.152406	−	0.469058i
$149$	3.09017	−	9.51057i	0.253157	−	0.779136i	−0.741031	−	0.671471i	$-0.765663\pi$
$149$	3.09017	−	9.51057i	0.253157	−	0.779136i	0.994187	−	0.107665i	$-0.0343373\pi$
$150$	0.809017	−	0.587785i	0.0660560	−	0.0479925i
$151$	3.23607	+	2.35114i	0.263347	+	0.191333i	0.711622	−	0.702563i	$-0.247961\pi$
$151$	3.23607	+	2.35114i	0.263347	+	0.191333i	−0.448274	+	0.893896i	$0.647961\pi$
$152$	1.23607	+	3.80423i	0.100258	+	0.308563i
$153$	−2.00000			−0.161690
$154$		0			0
$155$		0			0
$156$	−1.85410	−	5.70634i	−0.148447	−	0.456873i
$157$	8.09017	+	5.87785i	0.645666	+	0.469104i	0.861792	−	0.507262i	$-0.169342\pi$
$157$	8.09017	+	5.87785i	0.645666	+	0.469104i	−0.216126	+	0.976365i	$0.569342\pi$
$158$	3.23607	−	2.35114i	0.257448	−	0.187047i
$159$	−0.618034	+	1.90211i	−0.0490133	+	0.150847i
$160$	−0.618034	+	1.90211i	−0.0488599	+	0.150375i
$161$	−12.9443	+	9.40456i	−1.02015	+	0.741183i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	−6.18034	−	19.0211i	−0.484082	−	1.48985i	−0.833307	−	0.552811i	$-0.813555\pi$
$163$	−6.18034	−	19.0211i	−0.484082	−	1.48985i	0.349225	−	0.937039i	$-0.386445\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	4.00000			0.310460
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$	−3.23607	−	2.35114i	−0.249668	−	0.181394i
$169$	−18.6074	+	13.5191i	−1.43134	+	1.03993i
$170$	1.23607	−	3.80423i	0.0948021	−	0.291771i
$171$	−1.23607	+	3.80423i	−0.0945245	+	0.290916i
$172$	3.23607	−	2.35114i	0.246748	−	0.179273i
$173$	−8.09017	−	5.87785i	−0.615084	−	0.446885i	0.236117	−	0.971725i	$-0.424125\pi$
$173$	−8.09017	−	5.87785i	−0.615084	−	0.446885i	−0.851201	+	0.524840i	$0.824125\pi$
$174$	−1.85410	−	5.70634i	−0.140559	−	0.432596i
$175$	−4.00000			−0.302372
$176$		0			0
$177$	−12.0000			−0.901975
$178$	−3.09017	−	9.51057i	−0.231618	−	0.712847i
$179$	−16.1803	−	11.7557i	−1.20938	−	0.878663i	−0.214201	−	0.976790i	$-0.568715\pi$
$179$	−16.1803	−	11.7557i	−1.20938	−	0.878663i	−0.995174	+	0.0981269i	$0.968715\pi$
$180$	−1.61803	+	1.17557i	−0.120601	+	0.0876219i
$181$	−0.618034	+	1.90211i	−0.0459381	+	0.141383i	−0.971395	−	0.237471i	$-0.923682\pi$
$181$	−0.618034	+	1.90211i	−0.0459381	+	0.141383i	0.925457	+	0.378854i	$0.123682\pi$
$182$	−7.41641	+	22.8254i	−0.549741	+	1.69193i
$183$	11.3262	−	8.22899i	0.837260	−	0.608305i
$184$	3.23607	+	2.35114i	0.238566	+	0.173328i
$185$	3.70820	+	11.4127i	0.272633	+	0.839077i
$186$		0			0
$187$		0			0
$188$	−12.0000			−0.875190
$189$	−1.23607	−	3.80423i	−0.0899107	−	0.276717i
$190$	−6.47214	−	4.70228i	−0.469538	−	0.341139i
$191$	9.70820	−	7.05342i	0.702461	−	0.510368i	−0.178272	−	0.983981i	$-0.557051\pi$
$191$	9.70820	−	7.05342i	0.702461	−	0.510368i	0.880733	+	0.473614i	$0.157051\pi$
$192$	−0.309017	+	0.951057i	−0.0223014	+	0.0686366i
$193$	−3.09017	+	9.51057i	−0.222435	+	0.684585i	0.776107	+	0.630602i	$0.217192\pi$
$193$	−3.09017	+	9.51057i	−0.222435	+	0.684585i	−0.998542	+	0.0539836i	$0.982808\pi$
$194$	−11.3262	+	8.22899i	−0.813176	+	0.590807i
$195$	9.70820	+	7.05342i	0.695219	+	0.505106i
$196$	2.78115	+	8.55951i	0.198654	+	0.611393i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	3.23607	+	2.35114i	0.228255	+	0.165837i
$202$	−11.3262	+	8.22899i	−0.796911	+	0.578990i
$203$	−7.41641	+	22.8254i	−0.520530	+	1.60203i
$204$	0.618034	−	1.90211i	0.0432710	−	0.133175i
$205$	−9.70820	+	7.05342i	−0.678050	+	0.492632i
$206$		0			0
$207$	1.23607	+	3.80423i	0.0859127	+	0.264412i
$208$	6.00000			0.416025
$209$		0			0
$210$	8.00000			0.552052
$211$	1.23607	+	3.80423i	0.0850944	+	0.261894i	0.984546	−	0.175127i	$-0.0560336\pi$
$211$	1.23607	+	3.80423i	0.0850944	+	0.261894i	−0.899451	+	0.437021i	$0.856034\pi$
$212$	−1.61803	−	1.17557i	−0.111127	−	0.0807385i
$213$	−9.70820	+	7.05342i	−0.665195	+	0.483293i
$214$	1.23607	−	3.80423i	0.0844959	−	0.260052i
$215$	−2.47214	+	7.60845i	−0.168598	+	0.518892i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$		0			0
$218$	−1.85410	−	5.70634i	−0.125576	−	0.386482i
$219$	−6.00000			−0.405442
$220$		0			0
$221$	−12.0000			−0.807207
$222$	1.85410	+	5.70634i	0.124439	+	0.382984i
$223$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$223$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$224$	3.23607	−	2.35114i	0.216219	−	0.157092i
$225$	−0.309017	+	0.951057i	−0.0206011	+	0.0634038i
$226$	−0.618034	+	1.90211i	−0.0411110	+	0.126527i
$227$	9.70820	−	7.05342i	0.644356	−	0.468152i	−0.216988	−	0.976174i	$-0.569623\pi$
$227$	9.70820	−	7.05342i	0.644356	−	0.468152i	0.861344	+	0.508022i	$0.169623\pi$
$228$	−3.23607	−	2.35114i	−0.214314	−	0.155708i
$229$	4.32624	+	13.3148i	0.285886	+	0.879866i	0.986132	+	0.165964i	$0.0530737\pi$
$229$	4.32624	+	13.3148i	0.285886	+	0.879866i	−0.700246	+	0.713902i	$0.746926\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	6.00000			0.393919
$233$	−3.09017	−	9.51057i	−0.202444	−	0.623058i	−0.999809	−	0.0195604i	$-0.993773\pi$
$233$	−3.09017	−	9.51057i	−0.202444	−	0.623058i	0.797365	−	0.603497i	$-0.206227\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$	19.4164	−	14.1068i	1.26659	−	0.920229i
$236$	3.70820	−	11.4127i	0.241384	−	0.742902i
$237$	−1.23607	+	3.80423i	−0.0802912	+	0.247111i
$238$	−6.47214	+	4.70228i	−0.419526	+	0.304804i
$239$	6.47214	+	4.70228i	0.418648	+	0.304165i	0.777093	−	0.629385i	$-0.216693\pi$
$239$	6.47214	+	4.70228i	0.418648	+	0.304165i	−0.358446	+	0.933551i	$0.616693\pi$
$240$	−0.618034	−	1.90211i	−0.0398939	−	0.122781i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	4.32624	+	13.3148i	0.276959	+	0.852392i
$245$	−14.5623	−	10.5801i	−0.930352	−	0.675940i
$246$	−4.85410	+	3.52671i	−0.309486	+	0.224855i
$247$	−7.41641	+	22.8254i	−0.471895	+	1.45234i
$248$		0			0
$249$	−3.23607	+	2.35114i	−0.205077	+	0.148998i
$250$	−9.70820	−	7.05342i	−0.614001	−	0.446098i
$251$	−1.23607	−	3.80423i	−0.0780199	−	0.240121i	0.904438	−	0.426605i	$-0.140291\pi$
$251$	−1.23607	−	3.80423i	−0.0780199	−	0.240121i	−0.982458	+	0.186485i	$0.940291\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$	12.0000			0.752947
$255$	1.23607	+	3.80423i	0.0774056	+	0.238230i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.61803	+	1.17557i	−0.100930	+	0.0733301i	−0.637106	−	0.770776i	$-0.719869\pi$
$257$	−1.61803	+	1.17557i	−0.100930	+	0.0733301i	0.536175	+	0.844107i	$0.319869\pi$
$258$	−1.23607	+	3.80423i	−0.0769542	+	0.236841i
$259$	7.41641	−	22.8254i	0.460833	−	1.41830i
$260$	−9.70820	+	7.05342i	−0.602077	+	0.437435i
$261$	4.85410	+	3.52671i	0.300461	+	0.218298i
$262$	1.23607	+	3.80423i	0.0763645	+	0.235026i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$	4.94427	+	15.2169i	0.303153	+	0.933008i
$267$	8.09017	+	5.87785i	0.495110	+	0.359719i
$268$	−3.23607	+	2.35114i	−0.197674	+	0.143619i
$269$	8.03444	−	24.7275i	0.489869	−	1.50766i	−0.334935	−	0.942241i	$-0.608714\pi$
$269$	8.03444	−	24.7275i	0.489869	−	1.50766i	0.824804	−	0.565419i	$-0.191286\pi$
$270$	0.618034	−	1.90211i	0.0376124	−	0.115759i
$271$	16.1803	−	11.7557i	0.982886	−	0.714108i	0.0245340	−	0.999699i	$-0.492190\pi$
$271$	16.1803	−	11.7557i	0.982886	−	0.714108i	0.958352	+	0.285591i	$0.0921898\pi$
$272$	1.61803	+	1.17557i	0.0981077	+	0.0712794i
$273$	−7.41641	−	22.8254i	−0.448861	−	1.38145i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	−4.00000			−0.240772
$277$	−8.03444	−	24.7275i	−0.482743	−	1.48573i	−0.835224	−	0.549911i	$-0.814662\pi$
$277$	−8.03444	−	24.7275i	−0.482743	−	1.48573i	0.352481	−	0.935819i	$-0.385338\pi$
$278$	3.23607	+	2.35114i	0.194086	+	0.141012i
$279$		0			0
$280$	−2.47214	+	7.60845i	−0.147738	+	0.454692i
$281$	6.79837	−	20.9232i	0.405557	−	1.24818i	−0.514872	−	0.857267i	$-0.672161\pi$
$281$	6.79837	−	20.9232i	0.405557	−	1.24818i	0.920429	−	0.390909i	$-0.127839\pi$
$282$	9.70820	−	7.05342i	0.578115	−	0.420025i
$283$	3.23607	+	2.35114i	0.192364	+	0.139761i	0.679799	−	0.733399i	$-0.262067\pi$
$283$	3.23607	+	2.35114i	0.192364	+	0.139761i	−0.487434	+	0.873160i	$0.662067\pi$
$284$	−3.70820	−	11.4127i	−0.220041	−	0.677218i
$285$	8.00000			0.473879
$286$		0			0
$287$	24.0000			1.41668
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	10.5172	+	7.64121i	0.618660	+	0.449483i
$290$	−9.70820	+	7.05342i	−0.570085	+	0.414191i
$291$	4.32624	−	13.3148i	0.253609	−	0.780527i
$292$	1.85410	−	5.70634i	0.108503	−	0.333938i
$293$	17.7984	−	12.9313i	1.03979	−	0.755453i	0.0695472	−	0.997579i	$-0.477845\pi$
$293$	17.7984	−	12.9313i	1.03979	−	0.755453i	0.970245	+	0.242125i	$0.0778446\pi$
$294$	−7.28115	−	5.29007i	−0.424645	−	0.308523i
$295$	7.41641	+	22.8254i	0.431800	+	1.32894i
$296$	−6.00000			−0.348743
$297$		0			0
$298$	−10.0000			−0.579284
$299$	7.41641	+	22.8254i	0.428902	+	1.32002i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	12.9443	−	9.40456i	0.746095	−	0.542070i
$302$	1.23607	−	3.80423i	0.0711277	−	0.218909i
$303$	4.32624	−	13.3148i	0.248536	−	0.764915i
$304$	3.23607	−	2.35114i	0.185601	−	0.134847i
$305$	−22.6525	−	16.4580i	−1.29708	−	0.942382i
$306$	0.618034	+	1.90211i	0.0353307	+	0.108737i
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.23607	−	2.35114i	−0.183501	−	0.133321i	0.492243	−	0.870458i	$-0.336177\pi$
$311$	−3.23607	−	2.35114i	−0.183501	−	0.133321i	−0.675743	+	0.737137i	$0.736177\pi$
$312$	−4.85410	+	3.52671i	−0.274809	+	0.199661i
$313$	8.03444	−	24.7275i	0.454134	−	1.39768i	−0.418016	−	0.908440i	$-0.637274\pi$
$313$	8.03444	−	24.7275i	0.454134	−	1.39768i	0.872149	−	0.489240i	$-0.162726\pi$
$314$	3.09017	−	9.51057i	0.174388	−	0.536712i
$315$	−6.47214	+	4.70228i	−0.364664	+	0.264944i
$316$	−3.23607	−	2.35114i	−0.182043	−	0.132262i
$317$	5.56231	+	17.1190i	0.312410	+	0.961500i	0.976807	+	0.214120i	$0.0686884\pi$
$317$	5.56231	+	17.1190i	0.312410	+	0.961500i	−0.664397	+	0.747380i	$0.731312\pi$
$318$	2.00000			0.112154
$319$		0			0
$320$	2.00000			0.111803
$321$	1.23607	+	3.80423i	0.0689906	+	0.212331i
$322$	12.9443	+	9.40456i	0.721356	+	0.524096i
$323$	−6.47214	+	4.70228i	−0.360119	+	0.261642i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−1.85410	+	5.70634i	−0.102847	+	0.316531i
$326$	−16.1803	+	11.7557i	−0.896146	+	0.651088i
$327$	4.85410	+	3.52671i	0.268432	+	0.195028i
$328$	−1.85410	−	5.70634i	−0.102376	−	0.315080i
$329$	−48.0000			−2.64633
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−1.23607	−	3.80423i	−0.0678380	−	0.208784i
$333$	−4.85410	−	3.52671i	−0.266003	−	0.193263i
$334$		0			0
$335$	2.47214	−	7.60845i	0.135067	−	0.415694i
$336$	−1.23607	+	3.80423i	−0.0674330	+	0.207538i
$337$	14.5623	−	10.5801i	0.793259	−	0.576337i	−0.115670	−	0.993288i	$-0.536901\pi$
$337$	14.5623	−	10.5801i	0.793259	−	0.576337i	0.908929	+	0.416951i	$0.136901\pi$
$338$	18.6074	+	13.5191i	1.01211	+	0.735340i
$339$	−0.618034	−	1.90211i	−0.0335670	−	0.103309i
$340$	−4.00000			−0.216930
$341$		0			0
$342$	4.00000			0.216295
$343$	2.47214	+	7.60845i	0.133483	+	0.410818i
$344$	−3.23607	−	2.35114i	−0.174477	−	0.126765i
$345$	6.47214	−	4.70228i	0.348448	−	0.253162i
$346$	−3.09017	+	9.51057i	−0.166129	+	0.511291i
$347$	1.23607	−	3.80423i	0.0663556	−	0.204222i	−0.912381	−	0.409342i	$-0.865758\pi$
$347$	1.23607	−	3.80423i	0.0663556	−	0.204222i	0.978737	+	0.205120i	$0.0657585\pi$
$348$	−4.85410	+	3.52671i	−0.260207	+	0.189052i
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	0.450240	−	0.892908i	$-0.351338\pi$
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	−0.710074	+	0.704127i	$0.751338\pi$
$350$	1.23607	+	3.80423i	0.0660706	+	0.203344i
$351$	−6.00000			−0.320256
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	3.70820	+	11.4127i	0.197089	+	0.606577i
$355$	19.4164	+	14.1068i	1.03052	+	0.748714i
$356$	−8.09017	+	5.87785i	−0.428778	+	0.311526i
$357$	2.47214	−	7.60845i	0.130839	−	0.402682i
$358$	−6.18034	+	19.0211i	−0.326641	+	1.00530i
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	1.61803	+	1.17557i	0.0852779	+	0.0619580i
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$	2.00000			0.105118
$363$		0			0
$364$	24.0000			1.25794
$365$	3.70820	+	11.4127i	0.194096	+	0.597367i
$366$	−11.3262	−	8.22899i	−0.592032	−	0.430136i
$367$	12.9443	−	9.40456i	0.675685	−	0.490914i	−0.196238	−	0.980556i	$-0.562873\pi$
$367$	12.9443	−	9.40456i	0.675685	−	0.490914i	0.871924	+	0.489642i	$0.162873\pi$
$368$	1.23607	−	3.80423i	0.0644345	−	0.198309i
$369$	1.85410	−	5.70634i	0.0965207	−	0.297060i
$370$	9.70820	−	7.05342i	0.504705	−	0.366690i
$371$	−6.47214	−	4.70228i	−0.336017	−	0.244130i
$372$		0			0
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$	3.70820	+	11.4127i	0.191236	+	0.588564i
$377$	29.1246	+	21.1603i	1.49999	+	1.08981i
$378$	−3.23607	+	2.35114i	−0.166445	+	0.120930i
$379$	−8.65248	+	26.6296i	−0.444448	+	1.36787i	0.438640	+	0.898663i	$0.355460\pi$
$379$	−8.65248	+	26.6296i	−0.444448	+	1.36787i	−0.883088	+	0.469207i	$0.844540\pi$
$380$	−2.47214	+	7.60845i	−0.126818	+	0.390305i
$381$	−9.70820	+	7.05342i	−0.497366	+	0.361358i
$382$	−9.70820	−	7.05342i	−0.496715	−	0.360885i
$383$	−1.23607	−	3.80423i	−0.0631601	−	0.194387i	0.914497	−	0.404593i	$-0.132587\pi$
$383$	−1.23607	−	3.80423i	−0.0631601	−	0.194387i	−0.977657	+	0.210206i	$0.932587\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	10.0000			0.508987
$387$	−1.23607	−	3.80423i	−0.0628329	−	0.193380i
$388$	11.3262	+	8.22899i	0.575003	+	0.417764i
$389$	24.2705	−	17.6336i	1.23056	−	0.894057i	0.233631	−	0.972325i	$-0.424939\pi$
$389$	24.2705	−	17.6336i	1.23056	−	0.894057i	0.996932	+	0.0782684i	$0.0249391\pi$
$390$	3.70820	−	11.4127i	0.187772	−	0.577903i
$391$	−2.47214	+	7.60845i	−0.125021	+	0.384776i
$392$	7.28115	−	5.29007i	0.367754	−	0.267189i
$393$	−3.23607	−	2.35114i	−0.163238	−	0.118599i
$394$	−0.618034	−	1.90211i	−0.0311361	−	0.0958271i
$395$	8.00000			0.402524
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	4.94427	+	15.2169i	0.247834	+	0.762754i
$399$	−12.9443	−	9.40456i	−0.648024	−	0.470817i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−11.7426	+	36.1401i	−0.586400	+	1.80475i	0.00717537	+	0.999974i	$0.497716\pi$
$401$	−11.7426	+	36.1401i	−0.586400	+	1.80475i	−0.593575	+	0.804779i	$0.702284\pi$
$402$	1.23607	−	3.80423i	0.0616495	−	0.189738i
$403$		0			0
$404$	11.3262	+	8.22899i	0.563501	+	0.409408i
$405$	0.618034	+	1.90211i	0.0307104	+	0.0945168i
$406$	24.0000			1.19110
$407$		0			0
$408$	−2.00000			−0.0990148
$409$	4.32624	+	13.3148i	0.213919	+	0.658374i	0.999229	+	0.0392712i	$0.0125036\pi$
$409$	4.32624	+	13.3148i	0.213919	+	0.658374i	−0.785310	+	0.619103i	$0.787496\pi$
$410$	9.70820	+	7.05342i	0.479454	+	0.348344i
$411$	1.61803	−	1.17557i	0.0798117	−	0.0579866i
$412$		0			0
$413$	14.8328	−	45.6507i	0.729875	−	2.24632i
$414$	3.23607	−	2.35114i	0.159044	−	0.115552i
$415$	6.47214	+	4.70228i	0.317705	+	0.230826i
$416$	−1.85410	−	5.70634i	−0.0909048	−	0.279776i
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	−2.47214	−	7.60845i	−0.120628	−	0.371254i
$421$	8.09017	+	5.87785i	0.394291	+	0.286469i	0.767211	−	0.641394i	$-0.221644\pi$
$421$	8.09017	+	5.87785i	0.394291	+	0.286469i	−0.372921	+	0.927863i	$0.621644\pi$
$422$	3.23607	−	2.35114i	0.157529	−	0.114452i
$423$	−3.70820	+	11.4127i	−0.180299	+	0.554903i
$424$	−0.618034	+	1.90211i	−0.0300144	+	0.0923748i
$425$	−1.61803	+	1.17557i	−0.0784862	+	0.0570235i
$426$	9.70820	+	7.05342i	0.470364	+	0.341739i
$427$	17.3050	+	53.2592i	0.837445	+	2.57739i
$428$	−4.00000			−0.193347
$429$		0			0
$430$	8.00000			0.385794
$431$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$431$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−1.61803	+	1.17557i	−0.0777578	+	0.0564943i	−0.625985	−	0.779835i	$-0.715303\pi$
$433$	−1.61803	+	1.17557i	−0.0777578	+	0.0564943i	0.548227	+	0.836329i	$0.315303\pi$
$434$		0			0
$435$	3.70820	−	11.4127i	0.177795	−	0.547196i
$436$	−4.85410	+	3.52671i	−0.232469	+	0.168899i
$437$	12.9443	+	9.40456i	0.619208	+	0.449881i
$438$	1.85410	+	5.70634i	0.0885924	+	0.272659i
$439$	−4.00000			−0.190910			−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000			−0.190910			−0.0954548	+	0.995434i	$0.530431\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	3.70820	+	11.4127i	0.176381	+	0.542846i
$443$	−22.6525	−	16.4580i	−1.07625	−	0.781943i	−0.0992261	−	0.995065i	$-0.531637\pi$
$443$	−22.6525	−	16.4580i	−1.07625	−	0.781943i	−0.977026	+	0.213122i	$0.931637\pi$
$444$	4.85410	−	3.52671i	0.230365	−	0.167370i
$445$	6.18034	−	19.0211i	0.292976	−	0.901688i
$446$		0			0
$447$	8.09017	−	5.87785i	0.382652	−	0.278013i
$448$	−3.23607	−	2.35114i	−0.152890	−	0.111081i
$449$	−6.79837	−	20.9232i	−0.320835	−	0.987429i	−0.973286	−	0.229598i	$-0.926259\pi$
$449$	−6.79837	−	20.9232i	−0.320835	−	0.987429i	0.652451	−	0.757831i	$-0.273741\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	2.00000			0.0940721
$453$	1.23607	+	3.80423i	0.0580755	+	0.178738i
$454$	−9.70820	−	7.05342i	−0.455629	−	0.331034i
$455$	−38.8328	+	28.2137i	−1.82051	+	1.32268i
$456$	−1.23607	+	3.80423i	−0.0578842	+	0.178149i
$457$	−10.5066	+	32.3359i	−0.491477	+	1.51261i	0.330899	+	0.943666i	$0.392648\pi$
$457$	−10.5066	+	32.3359i	−0.491477	+	1.51261i	−0.822376	+	0.568944i	$0.807352\pi$
$458$	11.3262	−	8.22899i	0.529240	−	0.384516i
$459$	−1.61803	−	1.17557i	−0.0755234	−	0.0548709i
$460$	2.47214	+	7.60845i	0.115264	+	0.354746i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	−1.85410	−	5.70634i	−0.0860745	−	0.264910i
$465$		0			0
$466$	−8.09017	+	5.87785i	−0.374770	+	0.272286i
$467$	3.70820	−	11.4127i	0.171595	−	0.528116i	−0.827866	−	0.560925i	$-0.810445\pi$
$467$	3.70820	−	11.4127i	0.171595	−	0.528116i	0.999462	+	0.0328096i	$0.0104455\pi$
$468$	1.85410	−	5.70634i	0.0857059	−	0.263776i
$469$	−12.9443	+	9.40456i	−0.597711	+	0.434262i
$470$	−19.4164	−	14.1068i	−0.895612	−	0.650700i
$471$	3.09017	+	9.51057i	0.142388	+	0.438224i
$472$	−12.0000			−0.552345
$473$		0			0
$474$	4.00000			0.183726
$475$	1.23607	+	3.80423i	0.0567147	+	0.174550i
$476$	6.47214	+	4.70228i	0.296650	+	0.215529i
$477$	−1.61803	+	1.17557i	−0.0740847	+	0.0538257i
$478$	2.47214	−	7.60845i	0.113073	−	0.348003i
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$	−1.61803	+	1.17557i	−0.0738528	+	0.0536572i
$481$	−29.1246	−	21.1603i	−1.32797	−	0.964825i
$482$	3.09017	+	9.51057i	0.140753	+	0.433194i
$483$	−16.0000			−0.728025
$484$		0			0
$485$	−28.0000			−1.27141
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	12.9443	+	9.40456i	0.586561	+	0.426161i	0.841083	−	0.540905i	$-0.181918\pi$
$487$	12.9443	+	9.40456i	0.586561	+	0.426161i	−0.254523	+	0.967067i	$0.581918\pi$
$488$	11.3262	−	8.22899i	0.512715	−	0.372509i
$489$	6.18034	−	19.0211i	0.279485	−	0.860165i
$490$	−5.56231	+	17.1190i	−0.251279	+	0.773358i
$491$	−22.6525	+	16.4580i	−1.02229	+	0.742739i	−0.966751	−	0.255718i	$-0.917688\pi$
$491$	−22.6525	+	16.4580i	−1.02229	+	0.742739i	−0.0555405	+	0.998456i	$0.517688\pi$
$492$	4.85410	+	3.52671i	0.218840	+	0.158996i
$493$	3.70820	+	11.4127i	0.167009	+	0.514001i
$494$	24.0000			1.07981
$495$		0			0
$496$		0			0
$497$	−14.8328	−	45.6507i	−0.665343	−	2.04771i
$498$	3.23607	+	2.35114i	0.145012	+	0.105357i
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	−0.512992	−	0.858394i	$-0.671463\pi$
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	0.657858	+	0.753142i	$0.271463\pi$
$500$	−3.70820	+	11.4127i	−0.165836	+	0.510390i
$501$		0			0
$502$	−3.23607	+	2.35114i	−0.144433	+	0.104937i
$503$	25.8885	+	18.8091i	1.15431	+	0.838658i	0.989048	−	0.147592i	$-0.0471521\pi$
$503$	25.8885	+	18.8091i	1.15431	+	0.838658i	0.165265	+	0.986249i	$0.447152\pi$
$504$	−1.23607	−	3.80423i	−0.0550588	−	0.169454i
$505$	−28.0000			−1.24598
$506$		0			0
$507$	−23.0000			−1.02147
$508$	−3.70820	−	11.4127i	−0.164525	−	0.506356i
$509$	17.7984	+	12.9313i	0.788899	+	0.573169i	0.907637	−	0.419757i	$-0.137885\pi$
$509$	17.7984	+	12.9313i	0.788899	+	0.573169i	−0.118737	+	0.992926i	$0.537885\pi$
$510$	3.23607	−	2.35114i	0.143295	−	0.104110i
$511$	7.41641	−	22.8254i	0.328083	−	1.00973i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−3.23607	+	2.35114i	−0.142876	+	0.103805i
$514$	1.61803	+	1.17557i	0.0713684	+	0.0518522i
$515$		0			0
$516$	4.00000			0.176090
$517$		0			0
$518$	−24.0000			−1.05450
$519$	−3.09017	−	9.51057i	−0.135643	−	0.417467i
$520$	9.70820	+	7.05342i	0.425733	+	0.309313i
$521$	−14.5623	+	10.5801i	−0.637986	+	0.463524i	−0.859158	−	0.511711i	$-0.829012\pi$
$521$	−14.5623	+	10.5801i	−0.637986	+	0.463524i	0.221172	+	0.975235i	$0.429012\pi$
$522$	1.85410	−	5.70634i	0.0811518	−	0.249760i
$523$	−6.18034	+	19.0211i	−0.270247	+	0.831736i	0.720190	+	0.693776i	$0.244054\pi$
$523$	−6.18034	+	19.0211i	−0.270247	+	0.831736i	−0.990438	+	0.137960i	$0.955946\pi$
$524$	3.23607	−	2.35114i	0.141368	−	0.102710i
$525$	−3.23607	−	2.35114i	−0.141234	−	0.102612i
$526$	−7.41641	−	22.8254i	−0.323371	−	0.995233i
$527$		0			0
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−1.23607	−	3.80423i	−0.0536914	−	0.165245i
$531$	−9.70820	−	7.05342i	−0.421300	−	0.306092i
$532$	12.9443	−	9.40456i	0.561205	−	0.407740i
$533$	11.1246	−	34.2380i	0.481860	−	1.48301i
$534$	3.09017	−	9.51057i	0.133725	−	0.411562i
$535$	6.47214	−	4.70228i	0.279815	−	0.203297i
$536$	3.23607	+	2.35114i	0.139777	+	0.101554i
$537$	−6.18034	−	19.0211i	−0.266701	−	0.820822i
$538$	−26.0000			−1.12094
$539$		0			0
$540$	−2.00000			−0.0860663
$541$	11.7426	+	36.1401i	0.504856	+	1.55379i	0.801013	+	0.598647i	$0.204295\pi$
$541$	11.7426	+	36.1401i	0.504856	+	1.55379i	−0.296157	+	0.955139i	$0.595705\pi$
$542$	−16.1803	−	11.7557i	−0.695005	−	0.504951i
$543$	−1.61803	+	1.17557i	−0.0694365	+	0.0504486i
$544$	0.618034	−	1.90211i	0.0264980	−	0.0815524i
$545$	3.70820	−	11.4127i	0.158842	−	0.488865i
$546$	−19.4164	+	14.1068i	−0.830946	+	0.603717i
$547$	−22.6525	−	16.4580i	−0.968550	−	0.703693i	−0.0134293	−	0.999910i	$-0.504275\pi$
$547$	−22.6525	−	16.4580i	−0.968550	−	0.703693i	−0.955121	+	0.296217i	$0.904275\pi$
$548$	0.618034	+	1.90211i	0.0264011	+	0.0812542i
$549$	14.0000			0.597505
$550$		0			0
$551$	24.0000			1.02243
$552$	1.23607	+	3.80423i	0.0526105	+	0.161919i
$553$	−12.9443	−	9.40456i	−0.550446	−	0.399923i
$554$	−21.0344	+	15.2824i	−0.893668	+	0.649288i
$555$	−3.70820	+	11.4127i	−0.157404	+	0.484441i
$556$	1.23607	−	3.80423i	0.0524210	−	0.161335i
$557$	24.2705	−	17.6336i	1.02837	−	0.747158i	0.0603918	−	0.998175i	$-0.480765\pi$
$557$	24.2705	−	17.6336i	1.02837	−	0.747158i	0.967983	+	0.251017i	$0.0807650\pi$
$558$		0			0
$559$	−7.41641	−	22.8254i	−0.313681	−	0.965410i
$560$	8.00000			0.338062
$561$		0			0
$562$	−22.0000			−0.928014
$563$	6.18034	+	19.0211i	0.260470	+	0.801645i	0.992702	+	0.120590i	$0.0384786\pi$
$563$	6.18034	+	19.0211i	0.260470	+	0.801645i	−0.732232	+	0.681055i	$0.761521\pi$
$564$	−9.70820	−	7.05342i	−0.408789	−	0.297003i
$565$	−3.23607	+	2.35114i	−0.136142	+	0.0989132i
$566$	1.23607	−	3.80423i	0.0519558	−	0.159904i
$567$	1.23607	−	3.80423i	0.0519100	−	0.159762i
$568$	−9.70820	+	7.05342i	−0.407347	+	0.295955i
$569$	8.09017	+	5.87785i	0.339158	+	0.246412i	0.744306	−	0.667838i	$-0.232780\pi$
$569$	8.09017	+	5.87785i	0.339158	+	0.246412i	−0.405149	+	0.914251i	$0.632780\pi$
$570$	−2.47214	−	7.60845i	−0.103546	−	0.318683i
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$	−7.41641	−	22.8254i	−0.309555	−	0.952712i
$575$	3.23607	+	2.35114i	0.134953	+	0.0980494i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−14.2148	+	43.7486i	−0.591769	+	1.82128i	−0.0215762	+	0.999767i	$0.506868\pi$
$577$	−14.2148	+	43.7486i	−0.591769	+	1.82128i	−0.570193	+	0.821511i	$0.693132\pi$
$578$	4.01722	−	12.3637i	0.167094	−	0.514264i
$579$	−8.09017	+	5.87785i	−0.336216	+	0.244275i
$580$	9.70820	+	7.05342i	0.403111	+	0.292877i
$581$	−4.94427	−	15.2169i	−0.205123	−	0.631304i
$582$	−14.0000			−0.580319
$583$		0			0
$584$	−6.00000			−0.248282
$585$	3.70820	+	11.4127i	0.153315	+	0.471856i
$586$	−17.7984	−	12.9313i	−0.735244	−	0.534186i
$587$	29.1246	−	21.1603i	1.20210	−	0.873378i	0.207612	−	0.978211i	$-0.433431\pi$
$587$	29.1246	−	21.1603i	1.20210	−	0.873378i	0.994490	+	0.104834i	$0.0334310\pi$
$588$	−2.78115	+	8.55951i	−0.114693	+	0.352988i
$589$		0			0
$590$	19.4164	−	14.1068i	0.799361	−	0.580770i
$591$	1.61803	+	1.17557i	0.0665570	+	0.0483565i
$592$	1.85410	+	5.70634i	0.0762031	+	0.234529i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$	3.09017	+	9.51057i	0.126578	+	0.389568i
$597$	−12.9443	−	9.40456i	−0.529774	−	0.384903i
$598$	19.4164	−	14.1068i	0.793996	−	0.576872i
$599$	11.1246	−	34.2380i	0.454539	−	1.39893i	−0.417136	−	0.908844i	$-0.636966\pi$
$599$	11.1246	−	34.2380i	0.454539	−	1.39893i	0.871675	−	0.490084i	$-0.163034\pi$
$600$	−0.309017	+	0.951057i	−0.0126156	+	0.0388267i
$601$	8.09017	−	5.87785i	0.330005	−	0.239763i	−0.410428	−	0.911893i	$-0.634621\pi$
$601$	8.09017	−	5.87785i	0.330005	−	0.239763i	0.740433	+	0.672130i	$0.234621\pi$
$602$	−12.9443	−	9.40456i	−0.527569	−	0.383301i
$603$	1.23607	+	3.80423i	0.0503366	+	0.154920i
$604$	−4.00000			−0.162758
$605$		0			0
$606$	−14.0000			−0.568711
$607$	−8.65248	−	26.6296i	−0.351193	−	1.08086i	−0.958184	−	0.286153i	$-0.907624\pi$
$607$	−8.65248	−	26.6296i	−0.351193	−	1.08086i	0.606991	−	0.794709i	$-0.292376\pi$
$608$	−3.23607	−	2.35114i	−0.131240	−	0.0953514i
$609$	−19.4164	+	14.1068i	−0.786793	+	0.571638i
$610$	−8.65248	+	26.6296i	−0.350329	+	1.07820i
$611$	−22.2492	+	68.4761i	−0.900107	+	2.77025i
$612$	1.61803	−	1.17557i	0.0654051	−	0.0475196i
$613$	−4.85410	−	3.52671i	−0.196055	−	0.142443i	0.485427	−	0.874277i	$-0.338664\pi$
$613$	−4.85410	−	3.52671i	−0.196055	−	0.142443i	−0.681482	+	0.731835i	$0.738664\pi$
$614$	1.23607	+	3.80423i	0.0498836	+	0.153526i
$615$	−12.0000			−0.483887
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$		0			0
$619$	3.23607	+	2.35114i	0.130069	+	0.0945003i	0.650917	−	0.759149i	$-0.274384\pi$
$619$	3.23607	+	2.35114i	0.130069	+	0.0945003i	−0.520849	+	0.853649i	$0.674384\pi$
$620$		0			0
$621$	−1.23607	+	3.80423i	−0.0496017	+	0.152658i
$622$	−1.23607	+	3.80423i	−0.0495618	+	0.152536i
$623$	−32.3607	+	23.5114i	−1.29650	+	0.941965i
$624$	4.85410	+	3.52671i	0.194320	+	0.141181i
$625$	−5.87132	−	18.0701i	−0.234853	−	0.722803i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	−10.0000			−0.399043
$629$	−3.70820	−	11.4127i	−0.147856	−	0.455053i
$630$	6.47214	+	4.70228i	0.257856	+	0.187343i
$631$	6.47214	−	4.70228i	0.257652	−	0.187195i	−0.451459	−	0.892292i	$-0.649096\pi$
$631$	6.47214	−	4.70228i	0.257652	−	0.187195i	0.709111	+	0.705097i	$0.249096\pi$
$632$	−1.23607	+	3.80423i	−0.0491681	+	0.151324i
$633$	−1.23607	+	3.80423i	−0.0491293	+	0.151204i
$634$	14.5623	−	10.5801i	0.578343	−	0.420191i
$635$	19.4164	+	14.1068i	0.770517	+	0.559813i
$636$	−0.618034	−	1.90211i	−0.0245066	−	0.0754237i
$637$	54.0000			2.13956
$638$		0			0
$639$	−12.0000			−0.474713
$640$	−0.618034	−	1.90211i	−0.0244299	−	0.0751876i
$641$	−33.9787	−	24.6870i	−1.34208	−	0.975077i	−0.999365	−	0.0356372i	$-0.988654\pi$
$641$	−33.9787	−	24.6870i	−1.34208	−	0.975077i	−0.342714	−	0.939440i	$-0.611346\pi$
$642$	3.23607	−	2.35114i	0.127717	−	0.0927921i
$643$	−8.65248	+	26.6296i	−0.341220	+	1.05017i	0.622356	+	0.782734i	$0.286176\pi$
$643$	−8.65248	+	26.6296i	−0.341220	+	1.05017i	−0.963576	+	0.267434i	$0.913824\pi$
$644$	4.94427	−	15.2169i	0.194832	−	0.599630i
$645$	−6.47214	+	4.70228i	−0.254840	+	0.185152i
$646$	6.47214	+	4.70228i	0.254643	+	0.185009i
$647$	−8.65248	−	26.6296i	−0.340164	−	1.04692i	−0.964122	−	0.265459i	$-0.914476\pi$
$647$	−8.65248	−	26.6296i	−0.340164	−	1.04692i	0.623958	−	0.781458i	$-0.285524\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$	6.00000			0.235339
$651$		0			0
$652$	16.1803	+	11.7557i	0.633671	+	0.460389i
$653$	−14.5623	+	10.5801i	−0.569867	+	0.414033i	−0.835057	−	0.550164i	$-0.814565\pi$
$653$	−14.5623	+	10.5801i	−0.569867	+	0.414033i	0.265190	+	0.964196i	$0.414565\pi$
$654$	1.85410	−	5.70634i	0.0725011	−	0.223136i
$655$	−2.47214	+	7.60845i	−0.0965943	+	0.297287i
$656$	−4.85410	+	3.52671i	−0.189521	+	0.137695i
$657$	−4.85410	−	3.52671i	−0.189377	−	0.137590i
$658$	14.8328	+	45.6507i	0.578243	+	1.77965i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−6.18034	−	19.0211i	−0.240206	−	0.739277i
$663$	−9.70820	−	7.05342i	−0.377035	−	0.273932i
$664$	−3.23607	+	2.35114i	−0.125584	+	0.0912420i
$665$	−9.88854	+	30.4338i	−0.383461	+	1.18017i
$666$	−1.85410	+	5.70634i	−0.0718450	+	0.221116i
$667$	19.4164	−	14.1068i	0.751806	−	0.546219i
$668$		0			0
$669$		0			0
$670$	−8.00000			−0.309067
$671$		0			0
$672$	4.00000			0.154303
$673$	−8.03444	−	24.7275i	−0.309705	−	0.953174i	−0.977879	−	0.209169i	$-0.932924\pi$
$673$	−8.03444	−	24.7275i	−0.309705	−	0.953174i	0.668174	−	0.744005i	$-0.267076\pi$
$674$	−14.5623	−	10.5801i	−0.560919	−	0.407532i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	7.10739	−	21.8743i	0.273361	−	0.841319i
$677$	−14.2148	+	43.7486i	−0.546318	+	1.68140i	0.171516	+	0.985181i	$0.445134\pi$
$677$	−14.2148	+	43.7486i	−0.546318	+	1.68140i	−0.717834	+	0.696214i	$0.754866\pi$
$678$	−1.61803	+	1.17557i	−0.0621402	+	0.0451475i
$679$	45.3050	+	32.9160i	1.73864	+	1.26320i
$680$	1.23607	+	3.80423i	0.0474010	+	0.145885i
$681$	12.0000			0.459841
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−1.23607	−	3.80423i	−0.0472622	−	0.145458i
$685$	−3.23607	−	2.35114i	−0.123644	−	0.0898325i
$686$	6.47214	−	4.70228i	0.247107	−	0.179534i
$687$	−4.32624	+	13.3148i	−0.165056	+	0.507991i
$688$	−1.23607	+	3.80423i	−0.0471246	+	0.145035i
$689$	−9.70820	+	7.05342i	−0.369853	+	0.268714i
$690$	−6.47214	−	4.70228i	−0.246390	−	0.179013i
$691$	−3.70820	−	11.4127i	−0.141067	−	0.434159i	0.855418	−	0.517939i	$-0.173301\pi$
$691$	−3.70820	−	11.4127i	−0.141067	−	0.434159i	−0.996484	+	0.0837803i	$0.973301\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	−4.00000			−0.151838
$695$	2.47214	+	7.60845i	0.0937735	+	0.288605i
$696$	4.85410	+	3.52671i	0.183994	+	0.133680i
$697$	9.70820	−	7.05342i	0.367724	−	0.267167i
$698$	−1.85410	+	5.70634i	−0.0701788	+	0.215988i
$699$	3.09017	−	9.51057i	0.116881	−	0.359723i
$700$	3.23607	−	2.35114i	0.122312	−	0.0888648i
$701$	24.2705	+	17.6336i	0.916685	+	0.666010i	0.942697	−	0.333651i	$-0.108281\pi$
$701$	24.2705	+	17.6336i	0.916685	+	0.666010i	−0.0260120	+	0.999662i	$0.508281\pi$
$702$	1.85410	+	5.70634i	0.0699786	+	0.215372i
$703$	−24.0000			−0.905177
$704$		0			0
$705$	24.0000			0.903892
$706$	−5.56231	−	17.1190i	−0.209340	−	0.644283i
$707$	45.3050	+	32.9160i	1.70387	+	1.23793i
$708$	9.70820	−	7.05342i	0.364857	−	0.265084i
$709$	−5.56231	+	17.1190i	−0.208897	+	0.642918i	0.790634	+	0.612289i	$0.209751\pi$
$709$	−5.56231	+	17.1190i	−0.208897	+	0.642918i	−0.999531	+	0.0306292i	$0.990249\pi$
$710$	7.41641	−	22.8254i	0.278333	−	0.856620i
$711$	−3.23607	+	2.35114i	−0.121362	+	0.0881747i
$712$	8.09017	+	5.87785i	0.303192	+	0.220282i
$713$		0			0
$714$	−8.00000			−0.299392
$715$		0			0
$716$	20.0000			0.747435
$717$	2.47214	+	7.60845i	0.0923236	+	0.284143i
$718$		0			0
$719$	−9.70820	+	7.05342i	−0.362055	+	0.263048i	−0.753909	−	0.656979i	$-0.771834\pi$
$719$	−9.70820	+	7.05342i	−0.362055	+	0.263048i	0.391854	+	0.920028i	$0.371834\pi$
$720$	0.618034	−	1.90211i	0.0230328	−	0.0708876i
$721$		0			0
$722$	−2.42705	+	1.76336i	−0.0903255	+	0.0656253i
$723$	−8.09017	−	5.87785i	−0.300877	−	0.218600i
$724$	−0.618034	−	1.90211i	−0.0229691	−	0.0706915i
$725$	6.00000			0.222834
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−7.41641	−	22.8254i	−0.274870	−	0.845964i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	9.70820	−	7.05342i	0.359317	−	0.261059i
$731$	2.47214	−	7.60845i	0.0914353	−	0.281409i
$732$	−4.32624	+	13.3148i	−0.159902	+	0.492129i
$733$	−17.7984	+	12.9313i	−0.657398	+	0.477628i	−0.865783	−	0.500419i	$-0.833179\pi$
$733$	−17.7984	+	12.9313i	−0.657398	+	0.477628i	0.208385	+	0.978047i	$0.433179\pi$
$734$	−12.9443	−	9.40456i	−0.477782	−	0.347129i
$735$	−5.56231	−	17.1190i	−0.205169	−	0.631444i
$736$	−4.00000			−0.147442
$737$		0			0
$738$	−6.00000			−0.220863
$739$	−13.5967	−	41.8465i	−0.500164	−	1.53935i	−0.808751	−	0.588152i	$-0.799856\pi$
$739$	−13.5967	−	41.8465i	−0.500164	−	1.53935i	0.308586	−	0.951196i	$-0.400144\pi$
$740$	−9.70820	−	7.05342i	−0.356881	−	0.259289i
$741$	−19.4164	+	14.1068i	−0.713280	+	0.518228i
$742$	−2.47214	+	7.60845i	−0.0907550	+	0.279315i
$743$	9.88854	−	30.4338i	0.362775	−	1.11651i	−0.588587	−	0.808434i	$-0.700316\pi$
$743$	9.88854	−	30.4338i	0.362775	−	1.11651i	0.951362	−	0.308074i	$-0.0996845\pi$
$744$		0			0
$745$	−16.1803	−	11.7557i	−0.592802	−	0.430696i
$746$	−4.32624	−	13.3148i	−0.158395	−	0.487489i
$747$	−4.00000			−0.146352
$748$		0			0
$749$	−16.0000			−0.584627
$750$	−3.70820	−	11.4127i	−0.135404	−	0.416732i
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	0.00485778	−	0.999988i	$-0.498454\pi$
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	−0.949544	+	0.313633i	$0.898454\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	1.23607	−	3.80423i	0.0450448	−	0.138634i
$754$	11.1246	−	34.2380i	0.405134	−	1.24688i
$755$	6.47214	−	4.70228i	0.235545	−	0.171134i
$756$	3.23607	+	2.35114i	0.117695	+	0.0855102i
$757$	11.7426	+	36.1401i	0.426794	+	1.31354i	0.901266	+	0.433266i	$0.142639\pi$
$757$	11.7426	+	36.1401i	0.426794	+	1.31354i	−0.474473	+	0.880270i	$0.657361\pi$
$758$	28.0000			1.01701
$759$		0			0
$760$	8.00000			0.290191
$761$	−12.9787	−	39.9444i	−0.470478	−	1.44798i	−0.851960	−	0.523606i	$-0.824586\pi$
$761$	−12.9787	−	39.9444i	−0.470478	−	1.44798i	0.381482	−	0.924376i	$-0.375414\pi$
$762$	9.70820	+	7.05342i	0.351691	+	0.255519i
$763$	−19.4164	+	14.1068i	−0.702921	+	0.510702i
$764$	−3.70820	+	11.4127i	−0.134158	+	0.412896i
$765$	−1.23607	+	3.80423i	−0.0446901	+	0.137542i
$766$	−3.23607	+	2.35114i	−0.116924	+	0.0849502i
$767$	−58.2492	−	42.3205i	−2.10326	−	1.52811i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$	−3.09017	−	9.51057i	−0.111218	−	0.342293i
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	0.294252	−	0.955728i	$-0.404929\pi$
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	−0.818022	+	0.575187i	$0.804929\pi$
$774$	−3.23607	+	2.35114i	−0.116318	+	0.0845100i
$775$		0			0
$776$	4.32624	−	13.3148i	0.155303	−	0.477973i
$777$	19.4164	−	14.1068i	0.696560	−	0.506080i
$778$	−24.2705	−	17.6336i	−0.870140	−	0.632194i
$779$	−7.41641	−	22.8254i	−0.265720	−	0.817803i
$780$	−12.0000			−0.429669
$781$		0			0
$782$	8.00000			0.286079
$783$	1.85410	+	5.70634i	0.0662602	+	0.203928i
$784$	−7.28115	−	5.29007i	−0.260041	−	0.188931i
$785$	16.1803	−	11.7557i	0.577501	−	0.419579i
$786$	−1.23607	+	3.80423i	−0.0440891	+	0.135692i
$787$	6.18034	−	19.0211i	0.220305	−	0.678030i	−0.778429	−	0.627733i	$-0.783983\pi$
$787$	6.18034	−	19.0211i	0.220305	−	0.678030i	0.998734	−	0.0502974i	$-0.0160169\pi$
$788$	−1.61803	+	1.17557i	−0.0576401	+	0.0418780i
$789$	19.4164	+	14.1068i	0.691242	+	0.502217i
$790$	−2.47214	−	7.60845i	−0.0879547	−	0.270697i
$791$	8.00000			0.284447
$792$		0			0
$793$	84.0000			2.98293
$794$	−6.79837	−	20.9232i	−0.241265	−	0.742538i
$795$	3.23607	+	2.35114i	0.114772	+	0.0833864i
$796$	12.9443	−	9.40456i	0.458798	−	0.333336i
$797$	−16.6869	+	51.3571i	−0.591081	+	1.81916i	−0.0177409	+	0.999843i	$0.505647\pi$
$797$	−16.6869	+	51.3571i	−0.591081	+	1.81916i	−0.573340	+	0.819317i	$0.694353\pi$
$798$	−4.94427	+	15.2169i	−0.175025	+	0.538673i
$799$	−19.4164	+	14.1068i	−0.686903	+	0.499064i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	3.09017	+	9.51057i	0.109186	+	0.336039i
$802$	38.0000			1.34183
$803$		0			0
$804$	−4.00000			−0.141069
$805$	9.88854	+	30.4338i	0.348525	+	1.07265i
$806$		0			0
$807$	21.0344	−	15.2824i	0.740447	−	0.537967i
$808$	4.32624	−	13.3148i	0.152197	−	0.468413i
$809$	−3.09017	+	9.51057i	−0.108645	+	0.334374i	−0.990569	−	0.137018i	$-0.956248\pi$
$809$	−3.09017	+	9.51057i	−0.108645	+	0.334374i	0.881924	+	0.471392i	$0.156248\pi$
$810$	1.61803	−	1.17557i	0.0568519	−	0.0413053i
$811$	−22.6525	−	16.4580i	−0.795436	−	0.577918i	0.114136	−	0.993465i	$-0.463590\pi$
$811$	−22.6525	−	16.4580i	−0.795436	−	0.577918i	−0.909572	+	0.415547i	$0.863590\pi$
$812$	−7.41641	−	22.8254i	−0.260265	−	0.801013i
$813$	20.0000			0.701431
$814$		0			0
$815$	−40.0000			−1.40114
$816$	0.618034	+	1.90211i	0.0216355	+	0.0665873i
$817$	−12.9443	−	9.40456i	−0.452863	−	0.329024i
$818$	11.3262	−	8.22899i	0.396013	−	0.287720i
$819$	7.41641	−	22.8254i	0.259150	−	0.797582i
$820$	3.70820	−	11.4127i	0.129496	−	0.398548i
$821$	−1.61803	+	1.17557i	−0.0564698	+	0.0410277i	−0.615662	−	0.788010i	$-0.711111\pi$
$821$	−1.61803	+	1.17557i	−0.0564698	+	0.0410277i	0.559192	+	0.829038i	$0.311111\pi$
$822$	−1.61803	−	1.17557i	−0.0564354	−	0.0410027i
$823$	−12.3607	−	38.0423i	−0.430866	−	1.32607i	−0.897264	−	0.441495i	$-0.854448\pi$
$823$	−12.3607	−	38.0423i	−0.430866	−	1.32607i	0.466398	−	0.884575i	$-0.345552\pi$
$824$		0			0
$825$		0			0
$826$	−48.0000			−1.67013
$827$	16.0689	+	49.4549i	0.558770	+	1.71972i	0.685774	+	0.727815i	$0.259464\pi$
$827$	16.0689	+	49.4549i	0.558770	+	1.71972i	−0.127004	+	0.991902i	$0.540536\pi$
$828$	−3.23607	−	2.35114i	−0.112461	−	0.0817078i
$829$	−37.2148	+	27.0381i	−1.29252	+	0.939073i	−0.999853	−	0.0171408i	$-0.994544\pi$
$829$	−37.2148	+	27.0381i	−1.29252	+	0.939073i	−0.292670	+	0.956214i	$0.594544\pi$
$830$	2.47214	−	7.60845i	0.0858091	−	0.264093i
$831$	8.03444	−	24.7275i	0.278712	−	0.857786i
$832$	−4.85410	+	3.52671i	−0.168286	+	0.122267i
$833$	14.5623	+	10.5801i	0.504554	+	0.366580i
$834$	1.23607	+	3.80423i	0.0428015	+	0.131730i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	3.70820	+	11.4127i	0.128098	+	0.394244i
$839$	−9.70820	−	7.05342i	−0.335164	−	0.243511i	0.407454	−	0.913226i	$-0.366417\pi$
$839$	−9.70820	−	7.05342i	−0.335164	−	0.243511i	−0.742619	+	0.669714i	$0.766417\pi$
$840$	−6.47214	+	4.70228i	−0.223310	+	0.162244i
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	3.09017	−	9.51057i	0.106494	−	0.327756i
$843$	17.7984	−	12.9313i	0.613009	−	0.445377i
$844$	−3.23607	−	2.35114i	−0.111390	−	0.0809296i
$845$	14.2148	+	43.7486i	0.489003	+	1.50500i
$846$	12.0000			0.412568
$847$		0			0
$848$	2.00000			0.0686803
$849$	1.23607	+	3.80423i	0.0424217	+	0.130561i
$850$	1.61803	+	1.17557i	0.0554981	+	0.0403217i
$851$	−19.4164	+	14.1068i	−0.665586	+	0.483576i
$852$	3.70820	−	11.4127i	0.127041	−	0.390992i
$853$	1.85410	−	5.70634i	0.0634832	−	0.195381i	−0.914284	−	0.405073i	$-0.867246\pi$
$853$	1.85410	−	5.70634i	0.0634832	−	0.195381i	0.977768	+	0.209692i	$0.0672461\pi$
$854$	45.3050	−	32.9160i	1.55030	−	1.12636i
$855$	6.47214	+	4.70228i	0.221342	+	0.160815i
$856$	1.23607	+	3.80423i	0.0422479	+	0.130026i
$857$	−26.0000			−0.888143			−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000			−0.888143			−0.444072	+	0.895991i	$0.646466\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−2.47214	−	7.60845i	−0.0842991	−	0.259446i
$861$	19.4164	+	14.1068i	0.661709	+	0.480760i
$862$		0			0
$863$	6.18034	−	19.0211i	0.210381	−	0.647487i	−0.789068	−	0.614306i	$-0.789436\pi$
$863$	6.18034	−	19.0211i	0.210381	−	0.647487i	0.999449	−	0.0331811i	$-0.0105638\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−16.1803	+	11.7557i	−0.550148	+	0.399706i
$866$	1.61803	+	1.17557i	0.0549830	+	0.0399475i
$867$	4.01722	+	12.3637i	0.136432	+	0.419894i
$868$		0			0
$869$		0			0
$870$	−12.0000			−0.406838
$871$	7.41641	+	22.8254i	0.251295	+	0.773408i
$872$	4.85410	+	3.52671i	0.164381	+	0.119430i
$873$	11.3262	−	8.22899i	0.383335	−	0.278509i
$874$	4.94427	−	15.2169i	0.167242	−	0.514719i
$875$	−14.8328	+	45.6507i	−0.501441	+	1.54328i
$876$	4.85410	−	3.52671i	0.164005	−	0.119157i
$877$	33.9787	+	24.6870i	1.14738	+	0.833620i	0.988130	−	0.153618i	$-0.0490926\pi$
$877$	33.9787	+	24.6870i	1.14738	+	0.833620i	0.159249	+	0.987238i	$0.449093\pi$
$878$	1.23607	+	3.80423i	0.0417153	+	0.128386i
$879$	22.0000			0.742042
$880$		0			0
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$	−2.78115	−	8.55951i	−0.0936463	−	0.288214i
$883$	−3.23607	−	2.35114i	−0.108902	−	0.0791222i	0.532001	−	0.846744i	$-0.321440\pi$
$883$	−3.23607	−	2.35114i	−0.108902	−	0.0791222i	−0.640904	+	0.767621i	$0.721440\pi$
$884$	9.70820	−	7.05342i	0.326522	−	0.237232i
$885$	−7.41641	+	22.8254i	−0.249300	+	0.767266i
$886$	−8.65248	+	26.6296i	−0.290686	+	0.894638i
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$	−4.85410	−	3.52671i	−0.162893	−	0.118349i
$889$	−14.8328	−	45.6507i	−0.497477	−	1.53108i
$890$	−20.0000			−0.670402
$891$		0			0
$892$		0			0
$893$	14.8328	+	45.6507i	0.496361	+	1.52764i
$894$	−8.09017	−	5.87785i	−0.270576	−	0.196585i
$895$	−32.3607	+	23.5114i	−1.08170	+	0.785900i
$896$	−1.23607	+	3.80423i	−0.0412941	+	0.127090i
$897$	−7.41641	+	22.8254i	−0.247627	+	0.762116i
$898$	−17.7984	+	12.9313i	−0.593939	+	0.431522i
$899$		0			0
$900$	−0.309017	−	0.951057i	−0.0103006	−	0.0317019i
$901$	−4.00000			−0.133259
$902$		0			0
$903$	16.0000			0.532447
$904$	−0.618034	−	1.90211i	−0.0205555	−	0.0632633i
$905$	3.23607	+	2.35114i	0.107571	+	0.0781546i
$906$	3.23607	−	2.35114i	0.107511	−	0.0781114i
$907$	8.65248	−	26.6296i	0.287301	−	0.884221i	−0.698399	−	0.715709i	$-0.746104\pi$
$907$	8.65248	−	26.6296i	0.287301	−	0.884221i	0.985700	−	0.168512i	$-0.0538962\pi$
$908$	−3.70820	+	11.4127i	−0.123061	+	0.378743i
$909$	11.3262	−	8.22899i	0.375668	−	0.272938i
$910$	38.8328	+	28.2137i	1.28730	+	0.935275i
$911$	3.70820	+	11.4127i	0.122858	+	0.378119i	0.993505	−	0.113790i	$-0.0362992\pi$
$911$	3.70820	+	11.4127i	0.122858	+	0.378119i	−0.870647	+	0.491909i	$0.836299\pi$
$912$	4.00000			0.132453
$913$		0			0
$914$	34.0000			1.12462
$915$	−8.65248	−	26.6296i	−0.286042	−	0.880347i
$916$	−11.3262	−	8.22899i	−0.374229	−	0.271894i
$917$	12.9443	−	9.40456i	0.427458	−	0.310566i
$918$	−0.618034	+	1.90211i	−0.0203982	+	0.0627791i
$919$	1.23607	−	3.80423i	0.0407741	−	0.125490i	−0.928597	−	0.371089i	$-0.878985\pi$
$919$	1.23607	−	3.80423i	0.0407741	−	0.125490i	0.969372	+	0.245599i	$0.0789846\pi$
$920$	6.47214	−	4.70228i	0.213380	−	0.155030i
$921$	−3.23607	−	2.35114i	−0.106632	−	0.0774727i
$922$	4.32624	+	13.3148i	0.142477	+	0.438499i
$923$	−72.0000			−2.36991
$924$		0			0
$925$	−6.00000			−0.197279
$926$	7.41641	+	22.8254i	0.243718	+	0.750088i
$927$		0			0
$928$	−4.85410	+	3.52671i	−0.159344	+	0.115770i
$929$	12.9787	−	39.9444i	0.425818	−	1.31053i	−0.476391	−	0.879233i	$-0.658055\pi$
$929$	12.9787	−	39.9444i	0.425818	−	1.31053i	0.902209	−	0.431299i	$-0.141945\pi$
$930$		0			0
$931$	29.1246	−	21.1603i	0.954521	−	0.693500i
$932$	8.09017	+	5.87785i	0.265002	+	0.192535i
$933$	−1.23607	−	3.80423i	−0.0404670	−	0.124545i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	−6.00000			−0.196116
$937$	11.7426	+	36.1401i	0.383616	+	1.18065i	0.937480	+	0.348040i	$0.113153\pi$
$937$	11.7426	+	36.1401i	0.383616	+	1.18065i	−0.553864	+	0.832607i	$0.686847\pi$
$938$	12.9443	+	9.40456i	0.422645	+	0.307070i
$939$	21.0344	−	15.2824i	0.686433	−	0.498723i
$940$	−7.41641	+	22.8254i	−0.241897	+	0.744481i
$941$	12.9787	−	39.9444i	0.423094	−	1.30215i	−0.481714	−	0.876329i	$-0.659985\pi$
$941$	12.9787	−	39.9444i	0.423094	−	1.30215i	0.904808	−	0.425821i	$-0.140015\pi$
$942$	8.09017	−	5.87785i	0.263592	−	0.191511i
$943$	−19.4164	−	14.1068i	−0.632285	−	0.459382i
$944$	3.70820	+	11.4127i	0.120692	+	0.371451i
$945$	−8.00000			−0.260240
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$	−1.23607	−	3.80423i	−0.0401456	−	0.123556i
$949$	−29.1246	−	21.1603i	−0.945425	−	0.686891i
$950$	3.23607	−	2.35114i	0.104992	−	0.0762811i
$951$	−5.56231	+	17.1190i	−0.180370	+	0.555122i
$952$	2.47214	−	7.60845i	0.0801224	−	0.246591i
$953$	−4.85410	+	3.52671i	−0.157240	+	0.114241i	−0.663623	−	0.748067i	$-0.730982\pi$
$953$	−4.85410	+	3.52671i	−0.157240	+	0.114241i	0.506383	+	0.862309i	$0.330982\pi$
$954$	1.61803	+	1.17557i	0.0523858	+	0.0380605i
$955$	−7.41641	−	22.8254i	−0.239989	−	0.738611i
$956$	−8.00000			−0.258738
$957$		0			0
$958$		0			0
$959$	2.47214	+	7.60845i	0.0798294	+	0.245690i
$960$	1.61803	+	1.17557i	0.0522218	+	0.0379414i
$961$	25.0795	−	18.2213i	0.809017	−	0.587785i
$962$	−11.1246	+	34.2380i	−0.358672	+	1.10388i
$963$	−1.23607	+	3.80423i	−0.0398317	+	0.122589i
$964$	8.09017	−	5.87785i	0.260567	−	0.189313i
$965$	16.1803	+	11.7557i	0.520864	+	0.378430i
$966$	4.94427	+	15.2169i	0.159079	+	0.489596i
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$	8.65248	+	26.6296i	0.277814	+	0.855024i
$971$	−9.70820	−	7.05342i	−0.311551	−	0.226355i	0.421011	−	0.907056i	$-0.361675\pi$
$971$	−9.70820	−	7.05342i	−0.311551	−	0.226355i	−0.732562	+	0.680701i	$0.761675\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	4.94427	−	15.2169i	0.158506	−	0.487832i
$974$	4.94427	−	15.2169i	0.158425	−	0.487581i
$975$	−4.85410	+	3.52671i	−0.155456	+	0.112945i
$976$	−11.3262	−	8.22899i	−0.362544	−	0.263404i
$977$	8.03444	+	24.7275i	0.257045	+	0.791102i	0.993420	+	0.114529i	$0.0365358\pi$
$977$	8.03444	+	24.7275i	0.257045	+	0.791102i	−0.736375	+	0.676573i	$0.763464\pi$
$978$	−20.0000			−0.639529
$979$		0			0
$980$	18.0000			0.574989
$981$	1.85410	+	5.70634i	0.0591969	+	0.182189i
$982$	22.6525	+	16.4580i	0.722870	+	0.525195i
$983$	−29.1246	+	21.1603i	−0.928931	+	0.674908i	−0.945731	−	0.324951i	$-0.894652\pi$
$983$	−29.1246	+	21.1603i	−0.928931	+	0.674908i	0.0168000	+	0.999859i	$0.494652\pi$
$984$	1.85410	−	5.70634i	0.0591066	−	0.181911i
$985$	1.23607	−	3.80423i	0.0393844	−	0.121213i
$986$	9.70820	−	7.05342i	0.309172	−	0.224627i
$987$	−38.8328	−	28.2137i	−1.23606	−	0.898052i
$988$	−7.41641	−	22.8254i	−0.235947	−	0.726171i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$		0			0
$993$	16.1803	+	11.7557i	0.513468	+	0.373056i
$994$	−38.8328	+	28.2137i	−1.23170	+	0.894884i
$995$	−9.88854	+	30.4338i	−0.313488	+	0.964817i
$996$	1.23607	−	3.80423i	0.0391663	−	0.120542i
$997$	−11.3262	+	8.22899i	−0.358706	+	0.260615i	−0.752512	−	0.658579i	$-0.771158\pi$
$997$	−11.3262	+	8.22899i	−0.358706	+	0.260615i	0.393806	+	0.919193i	$0.371158\pi$
$998$	−3.23607	−	2.35114i	−0.102436	−	0.0744241i
$999$	−1.85410	−	5.70634i	−0.0586612	−	0.180541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.o.511.1		4
11.2	odd	10		726.2.e.g.493.1		4
11.3	even	5		726.2.a.c.1.1		1
11.4	even	5	inner	726.2.e.o.487.1		4
11.5	even	5	inner	726.2.e.o.565.1		4
11.6	odd	10		726.2.e.g.565.1		4
11.7	odd	10		726.2.e.g.487.1		4
11.8	odd	10		66.2.a.b.1.1	✓	1
11.9	even	5	inner	726.2.e.o.493.1		4
11.10	odd	2		726.2.e.g.511.1		4
33.8	even	10		198.2.a.a.1.1		1
33.14	odd	10		2178.2.a.g.1.1		1
44.3	odd	10		5808.2.a.bc.1.1		1
44.19	even	10		528.2.a.j.1.1		1
55.8	even	20		1650.2.c.e.199.1		2
55.19	odd	10		1650.2.a.k.1.1		1
55.52	even	20		1650.2.c.e.199.2		2
77.41	even	10		3234.2.a.t.1.1		1
88.19	even	10		2112.2.a.e.1.1		1
88.85	odd	10		2112.2.a.r.1.1		1
99.41	even	30		1782.2.e.v.1189.1		2
99.52	odd	30		1782.2.e.e.595.1		2
99.74	even	30		1782.2.e.v.595.1		2
99.85	odd	30		1782.2.e.e.1189.1		2
132.107	odd	10		1584.2.a.f.1.1		1
165.8	odd	20		4950.2.c.p.199.2		2
165.74	even	10		4950.2.a.bu.1.1		1
165.107	odd	20		4950.2.c.p.199.1		2
231.41	odd	10		9702.2.a.x.1.1		1
264.107	odd	10		6336.2.a.cj.1.1		1
264.173	even	10		6336.2.a.bw.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.b.1.1	✓	1	11.8	odd	10
198.2.a.a.1.1		1	33.8	even	10
528.2.a.j.1.1		1	44.19	even	10
726.2.a.c.1.1		1	11.3	even	5
726.2.e.g.487.1		4	11.7	odd	10
726.2.e.g.493.1		4	11.2	odd	10
726.2.e.g.511.1		4	11.10	odd	2
726.2.e.g.565.1		4	11.6	odd	10
726.2.e.o.487.1		4	11.4	even	5	inner
726.2.e.o.493.1		4	11.9	even	5	inner
726.2.e.o.511.1		4	1.1	even	1	trivial
726.2.e.o.565.1		4	11.5	even	5	inner
1584.2.a.f.1.1		1	132.107	odd	10
1650.2.a.k.1.1		1	55.19	odd	10
1650.2.c.e.199.1		2	55.8	even	20
1650.2.c.e.199.2		2	55.52	even	20
1782.2.e.e.595.1		2	99.52	odd	30
1782.2.e.e.1189.1		2	99.85	odd	30
1782.2.e.v.595.1		2	99.74	even	30
1782.2.e.v.1189.1		2	99.41	even	30
2112.2.a.e.1.1		1	88.19	even	10
2112.2.a.r.1.1		1	88.85	odd	10
2178.2.a.g.1.1		1	33.14	odd	10
3234.2.a.t.1.1		1	77.41	even	10
4950.2.a.bu.1.1		1	165.74	even	10
4950.2.c.p.199.1		2	165.107	odd	20
4950.2.c.p.199.2		2	165.8	odd	20
5808.2.a.bc.1.1		1	44.3	odd	10
6336.2.a.bw.1.1		1	264.173	even	10
6336.2.a.cj.1.1		1	264.107	odd	10
9702.2.a.x.1.1		1	231.41	odd	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.618034 - 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-3.23607 + 2.35114i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.618034 - 1.90211i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-3.23607 + 2.35114i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -2.00000 q^{10} -1.00000 q^{12} +(1.85410 + 5.70634i) q^{13} +(3.23607 + 2.35114i) q^{14} +(1.61803 - 1.17557i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.618034 + 1.90211i) q^{17} +(0.809017 - 0.587785i) q^{18} +(3.23607 + 2.35114i) q^{19} +(0.618034 + 1.90211i) q^{20} -4.00000 q^{21} +4.00000 q^{23} +(0.309017 + 0.951057i) q^{24} +(0.809017 + 0.587785i) q^{25} +(4.85410 - 3.52671i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.23607 - 3.80423i) q^{28} +(4.85410 - 3.52671i) q^{29} +(-1.61803 - 1.17557i) q^{30} -1.00000 q^{32} +2.00000 q^{34} +(2.47214 + 7.60845i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(1.23607 - 3.80423i) q^{38} +(-1.85410 + 5.70634i) q^{39} +(1.61803 - 1.17557i) q^{40} +(-4.85410 - 3.52671i) q^{41} +(1.23607 + 3.80423i) q^{42} -4.00000 q^{43} +2.00000 q^{45} +(-1.23607 - 3.80423i) q^{46} +(9.70820 + 7.05342i) q^{47} +(0.809017 - 0.587785i) q^{48} +(2.78115 - 8.55951i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-1.61803 + 1.17557i) q^{51} +(-4.85410 - 3.52671i) q^{52} +(0.618034 + 1.90211i) q^{53} +1.00000 q^{54} -4.00000 q^{56} +(1.23607 + 3.80423i) q^{57} +(-4.85410 - 3.52671i) q^{58} +(-9.70820 + 7.05342i) q^{59} +(-0.618034 + 1.90211i) q^{60} +(4.32624 - 13.3148i) q^{61} +(-3.23607 - 2.35114i) q^{63} +(0.309017 + 0.951057i) q^{64} +12.0000 q^{65} +4.00000 q^{67} +(-0.618034 - 1.90211i) q^{68} +(3.23607 + 2.35114i) q^{69} +(6.47214 - 4.70228i) q^{70} +(-3.70820 + 11.4127i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-4.85410 + 3.52671i) q^{73} +(4.85410 + 3.52671i) q^{74} +(0.309017 + 0.951057i) q^{75} -4.00000 q^{76} +6.00000 q^{78} +(1.23607 + 3.80423i) q^{79} +(-1.61803 - 1.17557i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.85410 + 5.70634i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(3.23607 - 2.35114i) q^{84} +(3.23607 + 2.35114i) q^{85} +(1.23607 + 3.80423i) q^{86} +6.00000 q^{87} +10.0000 q^{89} +(-0.618034 - 1.90211i) q^{90} +(-19.4164 - 14.1068i) q^{91} +(-3.23607 + 2.35114i) q^{92} +(3.70820 - 11.4127i) q^{94} +(6.47214 - 4.70228i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-4.32624 - 13.3148i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 - q^9	\( 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9} - 8 q^{10} - 4 q^{12} - 6 q^{13} + 4 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} - 16 q^{21} + 16 q^{23} - q^{24} + q^{25} + 6 q^{26} + q^{27} - 4 q^{28} + 6 q^{29} - 2 q^{30} - 4 q^{32} + 8 q^{34} - 8 q^{35} - q^{36} - 6 q^{37} - 4 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} - 4 q^{42} - 16 q^{43} + 8 q^{45} + 4 q^{46} + 12 q^{47} + q^{48} - 9 q^{49} - q^{50} - 2 q^{51} - 6 q^{52} - 2 q^{53} + 4 q^{54} - 16 q^{56} - 4 q^{57} - 6 q^{58} - 12 q^{59} + 2 q^{60} - 14 q^{61} - 4 q^{63} - q^{64} + 48 q^{65} + 16 q^{67} + 2 q^{68} + 4 q^{69} + 8 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} + 6 q^{74} - q^{75} - 16 q^{76} + 24 q^{78} - 4 q^{79} - 2 q^{80} - q^{81} + 6 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{85} - 4 q^{86} + 24 q^{87} + 40 q^{89} + 2 q^{90} - 24 q^{91} - 4 q^{92} - 12 q^{94} + 8 q^{95} - q^{96} + 14 q^{97} - 36 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 - q^9 - 8 * q^10 - 4 * q^12 - 6 * q^13 + 4 * q^14 + 2 * q^15 - q^16 + 2 * q^17 + q^18 + 4 * q^19 - 2 * q^20 - 16 * q^21 + 16 * q^23 - q^24 + q^25 + 6 * q^26 + q^27 - 4 * q^28 + 6 * q^29 - 2 * q^30 - 4 * q^32 + 8 * q^34 - 8 * q^35 - q^36 - 6 * q^37 - 4 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 - 4 * q^42 - 16 * q^43 + 8 * q^45 + 4 * q^46 + 12 * q^47 + q^48 - 9 * q^49 - q^50 - 2 * q^51 - 6 * q^52 - 2 * q^53 + 4 * q^54 - 16 * q^56 - 4 * q^57 - 6 * q^58 - 12 * q^59 + 2 * q^60 - 14 * q^61 - 4 * q^63 - q^64 + 48 * q^65 + 16 * q^67 + 2 * q^68 + 4 * q^69 + 8 * q^70 + 12 * q^71 + q^72 - 6 * q^73 + 6 * q^74 - q^75 - 16 * q^76 + 24 * q^78 - 4 * q^79 - 2 * q^80 - q^81 + 6 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^85 - 4 * q^86 + 24 * q^87 + 40 * q^89 + 2 * q^90 - 24 * q^91 - 4 * q^92 - 12 * q^94 + 8 * q^95 - q^96 + 14 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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