LMFDB - Embedded newform 726.2.h.e.239.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(161,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,2,-2,0,2,0,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.1
Root			$0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	726.239
Dual form			726.2.h.e.161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.65401 - 0.514040i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.831254 - 1.14412i) q^{5} +(1.64027 - 0.556338i) q^{6} +(-4.03499 - 1.31105i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.47152 + 1.70046i) q^{9} +1.41421i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 - 3.43237i) q^{13} +(4.03499 - 1.31105i) q^{14} +(-1.96303 + 1.46510i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.99901 + 0.0770245i) q^{18} +(-0.831254 - 1.14412i) q^{20} +(6.00000 + 4.24264i) q^{21} +1.41421i q^{23} +(-0.0222369 - 1.73191i) q^{24} +(0.927051 + 2.85317i) q^{25} +(4.03499 + 1.31105i) q^{26} +(-3.21383 - 4.08305i) q^{27} +(-2.49376 + 3.43237i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(0.726963 - 2.33913i) q^{30} +(3.23607 - 2.35114i) q^{31} +1.00000 q^{32} +(-4.85410 + 3.52671i) q^{35} +(2.38098 - 1.82509i) q^{36} +(0.618034 - 1.90211i) q^{37} +(2.36034 + 6.95908i) q^{39} +(1.34500 + 0.437016i) q^{40} +(1.85410 + 5.70634i) q^{41} +(-7.34786 + 0.0943431i) q^{42} +8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} +(-0.831254 - 1.14412i) q^{46} +(-9.41498 + 3.05911i) q^{47} +(1.03598 + 1.38807i) q^{48} +(8.89919 + 6.46564i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(-4.03499 + 1.31105i) q^{52} +(4.15627 + 5.72061i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(-1.85410 - 5.70634i) q^{58} +(-10.7600 - 3.49613i) q^{59} +(0.786780 + 2.31969i) q^{60} +(-2.49376 + 3.43237i) q^{61} +(-1.23607 + 3.80423i) q^{62} +(-7.74320 - 10.1016i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.00000 q^{65} -4.00000 q^{67} +(0.726963 - 2.33913i) q^{69} +(1.85410 - 5.70634i) q^{70} +(-4.15627 + 5.72061i) q^{71} +(-0.853491 + 2.87603i) q^{72} +(0.618034 + 1.90211i) q^{74} +(-0.0667106 - 5.19572i) q^{75} +(-6.00000 - 4.24264i) q^{78} +(2.49376 + 3.43237i) q^{79} +(-1.34500 + 0.437016i) q^{80} +(3.21687 + 8.40546i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(5.88909 - 4.39529i) q^{84} +(-4.98752 - 6.86474i) q^{86} +(6.00000 - 8.48528i) q^{87} +5.65685i q^{89} +(-2.40481 + 3.49526i) q^{90} +(5.56231 + 17.1190i) q^{91} +(1.34500 + 0.437016i) q^{92} +(-6.56108 + 2.22535i) q^{93} +(5.81878 - 8.00886i) q^{94} +(-1.65401 - 0.514040i) q^{96} +(-6.47214 + 4.70228i) q^{97} -11.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 8 q^{12} + 4 q^{15} - 2 q^{16} + 2 q^{18} + 48 q^{21} + 2 q^{24} - 6 q^{25} - 10 q^{27} + 12 q^{29} + 4 q^{30} + 8 q^{31} + 8 q^{32} - 12 q^{35}+ \cdots - 88 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 8 * q^12 + 4 * q^15 - 2 * q^16 + 2 * q^18 + 48 * q^21 + 2 * q^24 - 6 * q^25 - 10 * q^27 + 12 * q^29 + 4 * q^30 + 8 * q^31 + 8 * q^32 - 12 * q^35 + 2 * q^36 - 4 * q^37 + 12 * q^39 - 12 * q^41 - 12 * q^42 + 32 * q^45 + 2 * q^48 + 22 * q^49 - 6 * q^50 + 40 * q^54 + 12 * q^58 + 4 * q^60 + 8 * q^62 + 24 * q^63 - 2 * q^64 - 48 * q^65 - 32 * q^67 + 4 * q^69 - 12 * q^70 + 2 * q^72 - 4 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 - 24 * q^83 - 12 * q^84 + 48 * q^87 - 8 * q^90 - 36 * q^91 - 8 * q^93 + 2 * q^96 - 16 * q^97 - 88 * q^98

Character values

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

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−1.65401	−	0.514040i	−0.954945	−	0.296781i
$3$	−1.65401	−	0.514040i	−0.954945	−	0.296781i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.831254	−	1.14412i	0.371748	−	0.511667i	−0.581627	−	0.813456i	$-0.697584\pi$
$5$	0.831254	−	1.14412i	0.371748	−	0.511667i	0.953375	+	0.301788i	$0.0975836\pi$
$6$	1.64027	−	0.556338i	0.669638	−	0.227124i
$7$	−4.03499	−	1.31105i	−1.52508	−	0.495530i	−0.577869	−	0.816130i	$-0.696115\pi$
$7$	−4.03499	−	1.31105i	−1.52508	−	0.495530i	−0.947215	+	0.320600i	$0.896115\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.47152	+	1.70046i	0.823842	+	0.566820i
$10$			1.41421i			0.447214i
$11$		0			0
$11$		0			0
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−2.49376	−	3.43237i	−0.691645	−	0.951968i	−1.00000		0.000696272i	$-0.999778\pi$
$13$	−2.49376	−	3.43237i	−0.691645	−	0.951968i	0.308355	−	0.951271i	$-0.400222\pi$
$14$	4.03499	−	1.31105i	1.07840	−	0.350392i
$15$	−1.96303	+	1.46510i	−0.506852	+	0.378286i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$	−2.99901	+	0.0770245i	−0.706874	+	0.0181548i
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$	−0.831254	−	1.14412i	−0.185874	−	0.255834i
$21$	6.00000	+	4.24264i	1.30931	+	0.925820i
$22$		0			0
$23$			1.41421i			0.294884i	0.989071	+	0.147442i	$0.0471040\pi$
$23$			1.41421i			0.294884i	−0.989071	+	0.147442i	$0.952896\pi$
$24$	−0.0222369	−	1.73191i	−0.00453908	−	0.353524i
$25$	0.927051	+	2.85317i	0.185410	+	0.570634i
$26$	4.03499	+	1.31105i	0.791327	+	0.257118i
$27$	−3.21383	−	4.08305i	−0.618502	−	0.785783i
$28$	−2.49376	+	3.43237i	−0.471277	+	0.648657i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$	0.726963	−	2.33913i	0.132725	−	0.427065i
$31$	3.23607	−	2.35114i	0.581215	−	0.422277i	−0.257947	−	0.966159i	$-0.583046\pi$
$31$	3.23607	−	2.35114i	0.581215	−	0.422277i	0.839162	+	0.543882i	$0.183046\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		0			0
$35$	−4.85410	+	3.52671i	−0.820493	+	0.596123i
$36$	2.38098	−	1.82509i	0.396830	−	0.304181i
$37$	0.618034	−	1.90211i	0.101604	−	0.312705i	−0.887314	−	0.461165i	$-0.847432\pi$
$37$	0.618034	−	1.90211i	0.101604	−	0.312705i	0.988918	+	0.148460i	$0.0474315\pi$
$38$		0			0
$39$	2.36034	+	6.95908i	0.377957	+	1.11434i
$40$	1.34500	+	0.437016i	0.212663	+	0.0690983i
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	0.984994	+	0.172588i	$0.0552131\pi$
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	−0.695432	+	0.718592i	$0.744787\pi$
$42$	−7.34786	+	0.0943431i	−1.13380	+	0.0145575i
$43$			8.48528i			1.29399i	0.762493	+	0.646997i	$0.223975\pi$
$43$			8.48528i			1.29399i	−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$	−0.831254	−	1.14412i	−0.122562	−	0.168692i
$47$	−9.41498	+	3.05911i	−1.37332	+	0.446217i	−0.900466	−	0.434926i	$-0.856775\pi$
$47$	−9.41498	+	3.05911i	−1.37332	+	0.446217i	−0.472850	+	0.881143i	$0.656775\pi$
$48$	1.03598	+	1.38807i	0.149531	+	0.200351i
$49$	8.89919	+	6.46564i	1.27131	+	0.923663i
$50$	−2.42705	−	1.76336i	−0.343237	−	0.249376i
$51$		0			0
$52$	−4.03499	+	1.31105i	−0.559553	+	0.181810i
$53$	4.15627	+	5.72061i	0.570908	+	0.785787i	0.992662	−	0.120923i	$-0.0385855\pi$
$53$	4.15627	+	5.72061i	0.570908	+	0.785787i	−0.421754	+	0.906710i	$0.638586\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$		0			0
$58$	−1.85410	−	5.70634i	−0.243456	−	0.749279i
$59$	−10.7600	−	3.49613i	−1.40083	−	0.455157i	−0.491371	−	0.870951i	$-0.663504\pi$
$59$	−10.7600	−	3.49613i	−1.40083	−	0.455157i	−0.909459	+	0.415794i	$0.863504\pi$
$60$	0.786780	+	2.31969i	0.101573	+	0.299471i
$61$	−2.49376	+	3.43237i	−0.319293	+	0.439470i	−0.938251	−	0.345954i	$-0.887555\pi$
$61$	−2.49376	+	3.43237i	−0.319293	+	0.439470i	0.618958	+	0.785424i	$0.287555\pi$
$62$	−1.23607	+	3.80423i	−0.156981	+	0.483137i
$63$	−7.74320	−	10.1016i	−0.975551	−	1.27269i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.00000			−0.744208
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	0.726963	−	2.33913i	0.0875161	−	0.281598i
$70$	1.85410	−	5.70634i	0.221608	−	0.682038i
$71$	−4.15627	+	5.72061i	−0.493258	+	0.678912i	−0.980985	−	0.194085i	$-0.937826\pi$
$71$	−4.15627	+	5.72061i	−0.493258	+	0.678912i	0.487726	+	0.872997i	$0.337826\pi$
$72$	−0.853491	+	2.87603i	−0.100585	+	0.338943i
$73$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$73$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$74$	0.618034	+	1.90211i	0.0718450	+	0.221116i
$75$	−0.0667106	−	5.19572i	−0.00770308	−	0.599951i
$76$		0			0
$77$		0			0
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$	2.49376	+	3.43237i	0.280570	+	0.386172i	0.925923	−	0.377713i	$-0.123290\pi$
$79$	2.49376	+	3.43237i	0.280570	+	0.386172i	−0.645353	+	0.763885i	$0.723290\pi$
$80$	−1.34500	+	0.437016i	−0.150375	+	0.0488599i
$81$	3.21687	+	8.40546i	0.357430	+	0.933940i
$82$	−4.85410	−	3.52671i	−0.536046	−	0.389460i
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.0904951	−	0.995897i	$-0.528845\pi$
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.975119	+	0.221683i	$0.928845\pi$
$84$	5.88909	−	4.39529i	0.642553	−	0.479566i
$85$		0			0
$86$	−4.98752	−	6.86474i	−0.537818	−	0.740244i
$87$	6.00000	−	8.48528i	0.643268	−	0.909718i
$88$		0			0
$89$			5.65685i			0.599625i	0.953998	+	0.299813i	$0.0969242\pi$
$89$			5.65685i			0.599625i	−0.953998	+	0.299813i	$0.903076\pi$
$90$	−2.40481	+	3.49526i	−0.253490	+	0.368433i
$91$	5.56231	+	17.1190i	0.583088	+	1.79456i
$92$	1.34500	+	0.437016i	0.140226	+	0.0455621i
$93$	−6.56108	+	2.22535i	−0.680353	+	0.230758i
$94$	5.81878	−	8.00886i	0.600161	−	0.826051i
$95$		0			0
$96$	−1.65401	−	0.514040i	−0.168812	−	0.0524640i
$97$	−6.47214	+	4.70228i	−0.657146	+	0.477444i	−0.865698	−	0.500567i	$-0.833125\pi$
$97$	−6.47214	+	4.70228i	−0.657146	+	0.477444i	0.208552	+	0.978011i	$0.433125\pi$
$98$	−11.0000			−1.11117
$99$		0			0
$100$	3.00000			0.300000
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	−0.319485	−	0.947591i	$-0.603510\pi$
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	0.802486	+	0.596670i	$0.203510\pi$
$102$		0			0
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	−0.993303	−	0.115536i	$-0.963141\pi$
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	0.871510	+	0.490378i	$0.163141\pi$
$104$	2.49376	−	3.43237i	0.244533	−	0.336571i
$105$	9.84163	−	3.33803i	0.960444	−	0.325758i
$106$	−6.72499	−	2.18508i	−0.653188	−	0.212234i
$107$	5.56231	+	17.1190i	0.537728	+	1.65496i	0.737679	+	0.675152i	$0.235922\pi$
$107$	5.56231	+	17.1190i	0.537728	+	1.65496i	−0.199950	+	0.979806i	$0.564078\pi$
$108$	−4.87634	+	1.79480i	−0.469226	+	0.172705i
$109$		−	12.7279i		−	1.21911i	−0.792742	−	0.609557i	$-0.791347\pi$
$109$		−	12.7279i		−	1.21911i	0.792742	−	0.609557i	$-0.208653\pi$
$110$		0			0
$111$	−2.00000	+	2.82843i	−0.189832	+	0.268462i
$112$	2.49376	+	3.43237i	0.235638	+	0.324328i
$113$	10.7600	−	3.49613i	1.01221	−	0.328888i	0.244478	−	0.969655i	$-0.421383\pi$
$113$	10.7600	−	3.49613i	1.01221	−	0.328888i	0.767736	+	0.640767i	$0.221383\pi$
$114$		0			0
$115$	1.61803	+	1.17557i	0.150882	+	0.109623i
$116$	4.85410	+	3.52671i	0.450692	+	0.327447i
$117$	−0.326787	−	12.7237i	−0.0302115	−	1.17631i
$118$	10.7600	−	3.49613i	0.990536	−	0.321845i
$119$		0			0
$120$	−2.00000	−	1.41421i	−0.182574	−	0.129099i
$121$		0			0
$122$		−	4.24264i		−	0.384111i
$123$	−0.133421	−	10.3914i	−0.0120302	−	0.936965i
$124$	−1.23607	−	3.80423i	−0.111002	−	0.341630i
$125$	10.7600	+	3.49613i	0.962402	+	0.312703i
$126$	12.2020	+	3.62105i	1.08704	+	0.322589i
$127$	7.48128	−	10.2971i	0.663857	−	0.913720i	−0.335745	−	0.941953i	$-0.608988\pi$
$127$	7.48128	−	10.2971i	0.663857	−	0.913720i	0.999601	+	0.0282327i	$0.00898794\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.36178	−	14.0348i	0.384033	−	1.23569i
$130$	4.85410	−	3.52671i	0.425733	−	0.309313i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	3.23607	−	2.35114i	0.279554	−	0.203108i
$135$	−7.34302	+	0.282967i	−0.631986	+	0.0243539i
$136$		0			0
$137$	−1.66251	+	2.28825i	−0.142038	+	0.195498i	−0.874109	−	0.485730i	$-0.838554\pi$
$137$	−1.66251	+	2.28825i	−0.142038	+	0.195498i	0.732071	+	0.681228i	$0.238554\pi$
$138$	0.786780	+	2.31969i	0.0669752	+	0.197465i
$139$	16.1400	+	5.24419i	1.36897	+	0.444807i	0.899029	−	0.437889i	$-0.144274\pi$
$139$	16.1400	+	5.24419i	1.36897	+	0.444807i	0.469945	+	0.882696i	$0.344274\pi$
$140$	1.85410	+	5.70634i	0.156700	+	0.482274i
$141$	17.1450	−	0.220134i	1.44387	−	0.0185386i
$142$		−	7.07107i		−	0.593391i
$143$		0			0
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	4.98752	+	6.86474i	0.414191	+	0.570085i
$146$		0			0
$147$	−11.3958	−	15.2688i	−0.939908	−	1.25935i
$148$	−1.61803	−	1.17557i	−0.133002	−	0.0966313i
$149$	−4.85410	−	3.52671i	−0.397664	−	0.288919i	0.370925	−	0.928663i	$-0.379041\pi$
$149$	−4.85410	−	3.52671i	−0.397664	−	0.288919i	−0.768589	+	0.639743i	$0.779041\pi$
$150$	3.10794	+	4.16422i	0.253762	+	0.340007i
$151$	4.03499	−	1.31105i	0.328363	−	0.106692i	−0.140196	−	0.990124i	$-0.544773\pi$
$151$	4.03499	−	1.31105i	0.328363	−	0.106692i	0.468559	+	0.883432i	$0.344773\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	5.65685i		−	0.454369i
$156$	7.34786	−	0.0943431i	0.588300	−	0.00755349i
$157$	−6.79837	−	20.9232i	−0.542569	−	1.66986i	−0.726700	−	0.686955i	$-0.758947\pi$
$157$	−6.79837	−	20.9232i	−0.542569	−	1.66986i	0.184131	−	0.982902i	$-0.441053\pi$
$158$	−4.03499	−	1.31105i	−0.321007	−	0.104301i
$159$	−3.93390	−	11.5985i	−0.311979	−	0.919818i
$160$	0.831254	−	1.14412i	0.0657164	−	0.0904508i
$161$	1.85410	−	5.70634i	0.146124	−	0.449723i
$162$	−7.54311	−	4.90933i	−0.592642	−	0.385714i
$163$	−1.61803	+	1.17557i	−0.126734	+	0.0920778i	−0.649347	−	0.760493i	$-0.724958\pi$
$163$	−1.61803	+	1.17557i	−0.126734	+	0.0920778i	0.522612	+	0.852570i	$0.324958\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	12.0000			0.931381
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	−0.144969	−	0.989436i	$-0.546308\pi$
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	0.896212	+	0.443626i	$0.146308\pi$
$168$	−2.18089	+	7.01739i	−0.168259	+	0.541403i
$169$	−1.54508	+	4.75528i	−0.118853	+	0.365791i
$170$		0			0
$171$		0			0
$172$	8.06998	+	2.62210i	0.615330	+	0.199933i
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	0.855505	−	0.517794i	$-0.173247\pi$
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	−0.996470	+	0.0839492i	$0.973247\pi$
$174$	0.133421	+	10.3914i	0.0101146	+	0.787774i
$175$		−	12.7279i		−	0.962140i
$176$		0			0
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$	−3.32502	−	4.57649i	−0.249220	−	0.343023i
$179$	−5.37999	+	1.74806i	−0.402119	+	0.130656i	−0.503092	−	0.864233i	$-0.667804\pi$
$179$	−5.37999	+	1.74806i	−0.402119	+	0.130656i	0.100973	+	0.994889i	$0.467804\pi$
$180$	−0.108929	−	4.24124i	−0.00811909	−	0.316124i
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	0.526026	−	0.850469i	$-0.323682\pi$
$181$	−1.61803	−	1.17557i	−0.120268	−	0.0873795i	−0.646293	+	0.763089i	$0.723682\pi$
$182$	−14.5623	−	10.5801i	−1.07943	−	0.784252i
$183$	5.88909	−	4.39529i	0.435334	−	0.324909i
$184$	−1.34500	+	0.437016i	−0.0991545	+	0.0322172i
$185$	−1.66251	−	2.28825i	−0.122230	−	0.168235i
$186$	4.00000	−	5.65685i	0.293294	−	0.414781i
$187$		0			0
$188$			9.89949i			0.721995i
$189$	7.61471	+	20.6886i	0.553888	+	1.50487i
$190$		0			0
$191$	9.41498	+	3.05911i	0.681244	+	0.221350i	0.629140	−	0.777292i	$-0.283407\pi$
$191$	9.41498	+	3.05911i	0.681244	+	0.221350i	0.0521041	+	0.998642i	$0.483407\pi$
$192$	1.64027	−	0.556338i	0.118376	−	0.0401502i
$193$	−4.98752	+	6.86474i	−0.359010	+	0.494135i	−0.949872	−	0.312638i	$-0.898787\pi$
$193$	−4.98752	+	6.86474i	−0.359010	+	0.494135i	0.590863	+	0.806772i	$0.298787\pi$
$194$	2.47214	−	7.60845i	0.177489	−	0.546255i
$195$	9.92408	+	3.08424i	0.710678	+	0.220867i
$196$	8.89919	−	6.46564i	0.635656	−	0.461831i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−2.42705	+	1.76336i	−0.171618	+	0.124688i
$201$	6.61606	+	2.05616i	0.466661	+	0.145030i
$202$	−1.85410	+	5.70634i	−0.130454	+	0.401497i
$203$	14.9626	−	20.5942i	1.05017	−	1.44543i
$204$		0			0
$205$	8.06998	+	2.62210i	0.563632	+	0.183135i
$206$	−1.23607	−	3.80423i	−0.0861209	−	0.265053i
$207$	−2.40481	+	3.49526i	−0.167146	+	0.242938i
$208$			4.24264i			0.294174i
$209$		0			0
$210$	−6.00000	+	8.48528i	−0.414039	+	0.585540i
$211$	4.98752	+	6.86474i	0.343355	+	0.472588i	0.945418	−	0.325861i	$-0.105654\pi$
$211$	4.98752	+	6.86474i	0.343355	+	0.472588i	−0.602062	+	0.798449i	$0.705654\pi$
$212$	6.72499	−	2.18508i	0.461874	−	0.150072i
$213$	9.81516	−	7.32549i	0.672523	−	0.501934i
$214$	−14.5623	−	10.5801i	−0.995459	−	0.723243i
$215$	9.70820	+	7.05342i	0.662094	+	0.481039i
$216$	2.89008	−	4.31827i	0.196645	−	0.293821i
$217$	−16.1400	+	5.24419i	−1.09565	+	0.355999i
$218$	7.48128	+	10.2971i	0.506697	+	0.697408i
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−0.0444738	−	3.46382i	−0.00298488	−	0.232476i
$223$	2.47214	+	7.60845i	0.165546	+	0.509500i	0.999076	−	0.0429750i	$-0.0136836\pi$
$223$	2.47214	+	7.60845i	0.165546	+	0.509500i	−0.833530	+	0.552475i	$0.813684\pi$
$224$	−4.03499	−	1.31105i	−0.269599	−	0.0875981i
$225$	−2.56047	+	8.62809i	−0.170698	+	0.575206i
$226$	−6.65003	+	9.15298i	−0.442353	+	0.608847i
$227$	−1.85410	+	5.70634i	−0.123061	+	0.378743i	−0.993543	−	0.113458i	$-0.963807\pi$
$227$	−1.85410	+	5.70634i	−0.123061	+	0.378743i	0.870482	+	0.492201i	$0.163807\pi$
$228$		0			0
$229$	−11.3262	+	8.22899i	−0.748459	+	0.543787i	−0.895349	−	0.445366i	$-0.853074\pi$
$229$	−11.3262	+	8.22899i	−0.748459	+	0.543787i	0.146890	+	0.989153i	$0.453074\pi$
$230$	−2.00000			−0.131876
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.951752	−	0.306870i	$-0.900718\pi$
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.00225687	+	0.999997i	$0.500718\pi$
$234$	7.74320	+	10.1016i	0.506188	+	0.660364i
$235$	−4.32624	+	13.3148i	−0.282213	+	0.868561i
$236$	−6.65003	+	9.15298i	−0.432880	+	0.595808i
$237$	−2.36034	−	6.95908i	−0.153321	−	0.452041i
$238$		0			0
$239$	−3.70820	−	11.4127i	−0.239864	−	0.738225i	−0.996439	−	0.0843180i	$-0.973129\pi$
$239$	−3.70820	−	11.4127i	−0.239864	−	0.738225i	0.756575	−	0.653907i	$-0.226871\pi$
$240$	2.44929	−	0.0314477i	0.158101	−	0.00202994i
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$		0			0
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$	2.49376	+	3.43237i	0.159647	+	0.219735i
$245$	14.7950	−	4.80718i	0.945216	−	0.307119i
$246$	6.21588	+	8.32844i	0.396310	+	0.531002i
$247$		0			0
$248$	3.23607	+	2.35114i	0.205491	+	0.149298i
$249$	12.4318	+	16.6569i	0.787831	+	1.05559i
$250$	−10.7600	+	3.49613i	−0.680521	+	0.221115i
$251$	−3.32502	−	4.57649i	−0.209873	−	0.288866i	0.691083	−	0.722775i	$-0.257134\pi$
$251$	−3.32502	−	4.57649i	−0.209873	−	0.288866i	−0.900956	+	0.433910i	$0.857134\pi$
$252$	−12.0000	+	4.24264i	−0.755929	+	0.267261i
$253$		0			0
$254$			12.7279i			0.798621i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−10.7600	−	3.49613i	−0.671189	−	0.218082i	−0.0464552	−	0.998920i	$-0.514792\pi$
$257$	−10.7600	−	3.49613i	−0.671189	−	0.218082i	−0.624734	+	0.780838i	$0.714792\pi$
$258$	4.72068	+	13.9182i	0.293897	+	0.866507i
$259$	−4.98752	+	6.86474i	−0.309910	+	0.426554i
$260$	−1.85410	+	5.70634i	−0.114987	+	0.353892i
$261$	−14.2859	+	10.9505i	−0.884273	+	0.677821i
$262$	9.70820	−	7.05342i	0.599775	−	0.435762i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	2.90785	−	9.35652i	0.177958	−	0.572609i
$268$	−1.23607	+	3.80423i	−0.0755049	+	0.232380i
$269$	−4.15627	+	5.72061i	−0.253412	+	0.348792i	−0.916703	−	0.399570i	$-0.869159\pi$
$269$	−4.15627	+	5.72061i	−0.253412	+	0.348792i	0.663290	+	0.748362i	$0.269159\pi$
$270$	5.77430	−	4.54504i	0.351413	−	0.276603i
$271$	−12.1050	−	3.93314i	−0.735325	−	0.238921i	−0.0826700	−	0.996577i	$-0.526345\pi$
$271$	−12.1050	−	3.93314i	−0.735325	−	0.238921i	−0.652655	+	0.757655i	$0.726345\pi$
$272$		0			0
$273$	−0.400264	−	31.1743i	−0.0242251	−	1.88676i
$274$		−	2.82843i		−	0.170872i
$275$		0			0
$276$	−2.00000	−	1.41421i	−0.120386	−	0.0851257i
$277$	−12.4688	−	17.1618i	−0.749178	−	1.03116i	−0.998038	−	0.0626156i	$-0.980056\pi$
$277$	−12.4688	−	17.1618i	−0.749178	−	1.03116i	0.248860	−	0.968540i	$-0.419944\pi$
$278$	−16.1400	+	5.24419i	−0.968011	+	0.314526i
$279$	11.9960	−	0.308098i	0.718184	−	0.0184453i
$280$	−4.85410	−	3.52671i	−0.290088	−	0.210761i
$281$	−9.70820	−	7.05342i	−0.579143	−	0.420772i	0.259272	−	0.965804i	$-0.416517\pi$
$281$	−9.70820	−	7.05342i	−0.579143	−	0.420772i	−0.838415	+	0.545032i	$0.816517\pi$
$282$	−13.7412	+	10.2557i	−0.818278	+	0.610717i
$283$	8.06998	−	2.62210i	0.479711	−	0.155867i	−0.0591728	−	0.998248i	$-0.518846\pi$
$283$	8.06998	−	2.62210i	0.479711	−	0.155867i	0.538883	+	0.842380i	$0.318846\pi$
$284$	4.15627	+	5.72061i	0.246629	+	0.339456i
$285$		0			0
$286$		0			0
$287$		−	25.4558i		−	1.50261i
$288$	2.47152	+	1.70046i	0.145636	+	0.100201i
$289$	−5.25329	−	16.1680i	−0.309017	−	0.951057i
$290$	−8.06998	−	2.62210i	−0.473886	−	0.153975i
$291$	13.1222	−	4.45070i	0.769235	−	0.260905i
$292$		0			0
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	−0.882177	−	0.470918i	$-0.843923\pi$
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	0.990495	+	0.137550i	$0.0439228\pi$
$294$	18.1942	+	5.65445i	1.06110	+	0.329774i
$295$	−12.9443	+	9.40456i	−0.753645	+	0.547555i
$296$	2.00000			0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	4.85410	−	3.52671i	0.280720	−	0.203955i
$300$	−4.96204	−	1.54212i	−0.286484	−	0.0890344i
$301$	11.1246	−	34.2380i	0.641212	−	1.97345i
$302$	−2.49376	+	3.43237i	−0.143500	+	0.197511i
$303$	−9.84163	+	3.33803i	−0.565387	+	0.191765i
$304$		0			0
$305$	1.85410	+	5.70634i	0.106166	+	0.326744i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	4.00000	−	5.65685i	0.227552	−	0.321807i
$310$	3.32502	+	4.57649i	0.188848	+	0.259927i
$311$	−25.5549	+	8.30330i	−1.44909	+	0.470837i	−0.924718	−	0.380653i	$-0.875699\pi$
$311$	−25.5549	+	8.30330i	−1.44909	+	0.470837i	−0.524370	+	0.851490i	$0.675699\pi$
$312$	−5.88909	+	4.39529i	−0.333404	+	0.248834i
$313$	8.09017	+	5.87785i	0.457283	+	0.332236i	0.792465	−	0.609918i	$-0.208798\pi$
$313$	8.09017	+	5.87785i	0.457283	+	0.332236i	−0.335181	+	0.942154i	$0.608798\pi$
$314$	17.7984	+	12.9313i	1.00442	+	0.729754i
$315$	−17.9941	+	0.462147i	−1.01385	+	0.0260390i
$316$	4.03499	−	1.31105i	0.226986	−	0.0737522i
$317$	−5.81878	−	8.00886i	−0.326815	−	0.449822i	0.613718	−	0.789526i	$-0.289673\pi$
$317$	−5.81878	−	8.00886i	−0.326815	−	0.449822i	−0.940533	+	0.339703i	$0.889673\pi$
$318$	10.0000	+	7.07107i	0.560772	+	0.396526i
$319$		0			0
$320$			1.41421i			0.0790569i
$321$	−0.400264	−	31.1743i	−0.0223406	−	1.73998i
$322$	1.85410	+	5.70634i	0.103325	+	0.318002i
$323$		0			0
$324$	8.98813	−	0.461994i	0.499341	−	0.0256664i
$325$	7.48128	−	10.2971i	0.414987	−	0.571181i
$326$	0.618034	−	1.90211i	0.0342297	−	0.105348i
$327$	−6.54267	+	21.0522i	−0.361810	+	1.16419i
$328$	−4.85410	+	3.52671i	−0.268023	+	0.194730i
$329$	42.0000			2.31553
$330$		0			0
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$	−9.70820	+	7.05342i	−0.532807	+	0.387107i
$333$	4.76195	−	3.65018i	0.260953	−	0.200028i
$334$	−3.70820	+	11.4127i	−0.202904	+	0.624474i
$335$	−3.32502	+	4.57649i	−0.181665	+	0.250040i
$336$	−2.36034	−	6.95908i	−0.128767	−	0.379649i
$337$	−32.2799	−	10.4884i	−1.75840	−	0.571339i	−0.761367	−	0.648321i	$-0.775472\pi$
$337$	−32.2799	−	10.4884i	−1.75840	−	0.571339i	−0.997032	+	0.0769821i	$0.975472\pi$
$338$	−1.54508	−	4.75528i	−0.0840415	−	0.258653i
$339$	−19.5943	+	0.251582i	−1.06422	+	0.0136640i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−9.97505	−	13.7295i	−0.538602	−	0.741322i
$344$	−8.06998	+	2.62210i	−0.435104	+	0.141374i
$345$	−2.07196	−	2.77615i	−0.111551	−	0.149463i
$346$	4.85410	+	3.52671i	0.260958	+	0.189597i
$347$	9.70820	+	7.05342i	0.521164	+	0.378648i	0.817042	−	0.576578i	$-0.195612\pi$
$347$	9.70820	+	7.05342i	0.521164	+	0.378648i	−0.295878	+	0.955226i	$0.595612\pi$
$348$	−6.21588	−	8.32844i	−0.333206	−	0.446451i
$349$	28.2449	−	9.17734i	1.51192	−	0.491252i	0.568450	−	0.822718i	$-0.307543\pi$
$349$	28.2449	−	9.17734i	1.51192	−	0.491252i	0.943467	+	0.331466i	$0.107543\pi$
$350$	7.48128	+	10.2971i	0.399891	+	0.550403i
$351$	−6.00000	+	21.2132i	−0.320256	+	1.13228i
$352$		0			0
$353$			22.6274i			1.20434i	0.798369	+	0.602168i	$0.205696\pi$
$353$			22.6274i			1.20434i	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−19.5943	+	0.251582i	−1.04143	+	0.0133714i
$355$	3.09017	+	9.51057i	0.164009	+	0.504768i
$356$	5.37999	+	1.74806i	0.285139	+	0.0926472i
$357$		0			0
$358$	3.32502	−	4.57649i	0.175733	−	0.241875i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$	2.58107	+	3.36721i	0.136034	+	0.177468i
$361$	−15.3713	+	11.1679i	−0.809017	+	0.587785i
$362$	2.00000			0.105118
$363$		0			0
$364$	18.0000			0.943456
$365$		0			0
$366$	−2.18089	+	7.01739i	−0.113997	+	0.366805i
$367$	−8.65248	+	26.6296i	−0.451656	+	1.39005i	0.423362	+	0.905961i	$0.360850\pi$
$367$	−8.65248	+	26.6296i	−0.451656	+	1.39005i	−0.875017	+	0.484092i	$0.839150\pi$
$368$	0.831254	−	1.14412i	0.0433321	−	0.0596415i
$369$	−5.12094	+	17.2562i	−0.266586	+	0.898321i
$370$	2.68999	+	0.874032i	0.139846	+	0.0454388i
$371$	−9.27051	−	28.5317i	−0.481301	−	1.48129i
$372$	0.0889475	+	6.92763i	0.00461171	+	0.359181i
$373$			29.6985i			1.53773i	0.639412	+	0.768865i	$0.279178\pi$
$373$			29.6985i			1.53773i	−0.639412	+	0.768865i	$0.720822\pi$
$374$		0			0
$375$	−16.0000	−	11.3137i	−0.826236	−	0.584237i
$376$	−5.81878	−	8.00886i	−0.300081	−	0.413025i
$377$	24.2099	−	7.86629i	1.24688	−	0.405134i
$378$	−18.3209	−	12.2616i	−0.942323	−	0.630668i
$379$	−1.61803	−	1.17557i	−0.0831128	−	0.0603850i	0.545453	−	0.838141i	$-0.316358\pi$
$379$	−1.61803	−	1.17557i	−0.0831128	−	0.0603850i	−0.628566	+	0.777756i	$0.716358\pi$
$380$		0			0
$381$	−17.6673	+	13.1859i	−0.905122	+	0.675533i
$382$	−9.41498	+	3.05911i	−0.481712	+	0.156518i
$383$	−0.831254	−	1.14412i	−0.0424751	−	0.0584619i	0.787251	−	0.616632i	$-0.211504\pi$
$383$	−0.831254	−	1.14412i	−0.0424751	−	0.0584619i	−0.829726	+	0.558170i	$0.811504\pi$
$384$	−1.00000	+	1.41421i	−0.0510310	+	0.0721688i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	−14.4289	+	20.9716i	−0.733461	+	1.06605i
$388$	2.47214	+	7.60845i	0.125504	+	0.386261i
$389$	9.41498	+	3.05911i	0.477358	+	0.155103i	0.537807	−	0.843068i	$-0.319253\pi$
$389$	9.41498	+	3.05911i	0.477358	+	0.155103i	−0.0604483	+	0.998171i	$0.519253\pi$
$390$	−9.84163	+	3.33803i	−0.498350	+	0.169027i
$391$		0			0
$392$	−3.39919	+	10.4616i	−0.171685	+	0.528392i
$393$	19.8482	+	6.16849i	1.00121	+	0.311159i
$394$	14.5623	−	10.5801i	0.733638	−	0.533019i
$395$	6.00000			0.301893
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	12.9443	−	9.40456i	0.648838	−	0.471408i
$399$		0			0
$400$	0.927051	−	2.85317i	0.0463525	−	0.142658i
$401$	−21.6126	+	29.7472i	−1.07928	+	1.48550i	−0.218973	+	0.975731i	$0.570271\pi$
$401$	−21.6126	+	29.7472i	−1.07928	+	1.48550i	−0.860309	+	0.509773i	$0.829729\pi$
$402$	−6.56108	+	2.22535i	−0.327237	+	0.110990i
$403$	−16.1400	−	5.24419i	−0.803989	−	0.261232i
$404$	−1.85410	−	5.70634i	−0.0922450	−	0.283901i
$405$	12.2909	+	3.30658i	0.610740	+	0.164305i
$406$			25.4558i			1.26335i
$407$		0			0
$408$		0			0
$409$	4.98752	+	6.86474i	0.246617	+	0.339439i	0.914323	−	0.404986i	$-0.132724\pi$
$409$	4.98752	+	6.86474i	0.246617	+	0.339439i	−0.667706	+	0.744425i	$0.732724\pi$
$410$	−8.06998	+	2.62210i	−0.398548	+	0.129496i
$411$	3.92606	−	2.93019i	0.193658	−	0.144536i
$412$	3.23607	+	2.35114i	0.159430	+	0.115832i
$413$	38.8328	+	28.2137i	1.91084	+	1.38831i
$414$	−0.108929	−	4.24124i	−0.00535357	−	0.208446i
$415$	−16.1400	+	5.24419i	−0.792280	+	0.257427i
$416$	−2.49376	−	3.43237i	−0.122267	−	0.168286i
$417$	−24.0000	−	16.9706i	−1.17529	−	0.831052i
$418$		0			0
$419$		−	11.3137i		−	0.552711i	−0.961056	−	0.276355i	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$	−0.133421	−	10.3914i	−0.00651029	−	0.507051i
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	0.847084	−	0.531460i	$-0.178356\pi$
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	−0.997689	+	0.0679432i	$0.978356\pi$
$422$	−8.06998	−	2.62210i	−0.392841	−	0.127642i
$423$	−28.4713	−	8.44913i	−1.38432	−	0.410811i
$424$	−4.15627	+	5.72061i	−0.201846	+	0.277818i
$425$		0			0
$426$	−3.63482	+	11.6956i	−0.176107	+	0.566656i
$427$	14.5623	−	10.5801i	0.704719	−	0.512009i
$428$	18.0000			0.870063
$429$		0			0
$430$	−12.0000			−0.578691
$431$	−29.1246	+	21.1603i	−1.40288	+	1.01925i	−0.408574	+	0.912725i	$0.633974\pi$
$431$	−29.1246	+	21.1603i	−1.40288	+	1.01925i	−0.994310	+	0.106529i	$0.966026\pi$
$432$	0.200088	+	5.19230i	0.00962674	+	0.249815i
$433$	0.618034	−	1.90211i	0.0297008	−	0.0914097i	−0.935107	−	0.354365i	$-0.884697\pi$
$433$	0.618034	−	1.90211i	0.0297008	−	0.0914097i	0.964808	+	0.262955i	$0.0846971\pi$
$434$	9.97505	−	13.7295i	0.478818	−	0.659036i
$435$	−4.72068	−	13.9182i	−0.226339	−	0.667325i
$436$	−12.1050	−	3.93314i	−0.579723	−	0.188363i
$437$		0			0
$438$		0			0
$439$			21.2132i			1.01245i	0.862401	+	0.506225i	$0.168960\pi$
$439$			21.2132i			1.01245i	−0.862401	+	0.506225i	$0.831040\pi$
$440$		0			0
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$		0			0
$443$	26.8999	−	8.74032i	1.27805	−	0.415265i	0.410160	−	0.912014i	$-0.365473\pi$
$443$	26.8999	−	8.74032i	1.27805	−	0.415265i	0.867895	+	0.496748i	$0.165473\pi$
$444$	2.07196	+	2.77615i	0.0983309	+	0.131750i
$445$	6.47214	+	4.70228i	0.306809	+	0.222910i
$446$	−6.47214	−	4.70228i	−0.306465	−	0.222660i
$447$	6.21588	+	8.32844i	0.294001	+	0.393921i
$448$	4.03499	−	1.31105i	0.190635	−	0.0619412i
$449$	−18.2876	−	25.1707i	−0.863045	−	1.18788i	−0.980835	−	0.194840i	$-0.937581\pi$
$449$	−18.2876	−	25.1707i	−0.863045	−	1.18788i	0.117790	−	0.993038i	$-0.462419\pi$
$450$	−3.00000	−	8.48528i	−0.141421	−	0.400000i
$451$		0			0
$452$		−	11.3137i		−	0.532152i
$453$	−7.34786	+	0.0943431i	−0.345233	+	0.00443263i
$454$	−1.85410	−	5.70634i	−0.0870173	−	0.267812i
$455$	24.2099	+	7.86629i	1.13498	+	0.368777i
$456$		0			0
$457$	4.98752	−	6.86474i	0.233306	−	0.321119i	−0.676271	−	0.736653i	$-0.736405\pi$
$457$	4.98752	−	6.86474i	0.233306	−	0.321119i	0.909578	+	0.415534i	$0.136405\pi$
$458$	4.32624	−	13.3148i	0.202152	−	0.622159i
$459$		0			0
$460$	1.61803	−	1.17557i	0.0754412	−	0.0548113i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	4.85410	−	3.52671i	0.225346	−	0.163723i
$465$	−2.90785	+	9.35652i	−0.134848	+	0.433898i
$466$	5.56231	−	17.1190i	0.257669	−	0.793023i
$467$	18.2876	−	25.1707i	0.846249	−	1.16476i	−0.138428	−	0.990372i	$-0.544205\pi$
$467$	18.2876	−	25.1707i	0.846249	−	1.16476i	0.984677	−	0.174389i	$-0.0557949\pi$
$468$	−12.2020	−	3.62105i	−0.564036	−	0.167383i
$469$	16.1400	+	5.24419i	0.745274	+	0.242154i
$470$	−4.32624	−	13.3148i	−0.199554	−	0.614166i
$471$	0.489211	+	38.1020i	0.0225417	+	1.75565i
$472$		−	11.3137i		−	0.520756i
$473$		0			0
$474$	6.00000	+	4.24264i	0.275589	+	0.194871i
$475$		0			0
$476$		0			0
$477$	0.544645	+	21.2062i	0.0249376	+	0.970966i
$478$	9.70820	+	7.05342i	0.444043	+	0.322616i
$479$	−9.70820	−	7.05342i	−0.443579	−	0.322279i	0.343476	−	0.939161i	$-0.388395\pi$
$479$	−9.70820	−	7.05342i	−0.443579	−	0.322279i	−0.787055	+	0.616882i	$0.788395\pi$
$480$	−1.96303	+	1.46510i	−0.0895997	+	0.0668722i
$481$	−8.06998	+	2.62210i	−0.367960	+	0.119557i
$482$	−4.98752	−	6.86474i	−0.227175	−	0.312680i
$483$	−6.00000	+	8.48528i	−0.273009	+	0.386094i
$484$		0			0
$485$			11.3137i			0.513729i
$486$	9.95281	+	11.9976i	0.451469	+	0.544221i
$487$	6.18034	+	19.0211i	0.280058	+	0.861930i	0.987837	+	0.155495i	$0.0496974\pi$
$487$	6.18034	+	19.0211i	0.280058	+	0.861930i	−0.707779	+	0.706434i	$0.750303\pi$
$488$	−4.03499	−	1.31105i	−0.182655	−	0.0593484i
$489$	3.28054	−	1.11268i	0.148351	−	0.0503169i
$490$	−9.14379	+	12.5854i	−0.413074	+	0.568548i
$491$	1.85410	−	5.70634i	0.0836745	−	0.257523i	−0.900463	−	0.434934i	$-0.856772\pi$
$491$	1.85410	−	5.70634i	0.0836745	−	0.257523i	0.984137	+	0.177410i	$0.0567719\pi$
$492$	−9.92408	−	3.08424i	−0.447412	−	0.139048i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	24.2705	−	17.6336i	1.08868	−	0.790973i
$498$	−19.8482	−	6.16849i	−0.889418	−	0.276416i
$499$	4.32624	−	13.3148i	0.193669	−	0.596052i	−0.806321	−	0.591479i	$-0.798544\pi$
$499$	4.32624	−	13.3148i	0.193669	−	0.596052i	0.999990	−	0.00457310i	$-0.00145567\pi$
$500$	6.65003	−	9.15298i	0.297398	−	0.409334i
$501$	−19.6833	+	6.67605i	−0.879383	+	0.298264i
$502$	5.37999	+	1.74806i	0.240121	+	0.0780199i
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$	7.21444	−	10.4858i	0.321357	−	0.467074i
$505$		−	8.48528i		−	0.377590i
$506$		0			0
$507$	5.00000	−	7.07107i	0.222058	−	0.314037i
$508$	−7.48128	−	10.2971i	−0.331928	−	0.456860i
$509$	−1.34500	+	0.437016i	−0.0596159	+	0.0193704i	−0.338673	−	0.940904i	$-0.609978\pi$
$509$	−1.34500	+	0.437016i	−0.0596159	+	0.0193704i	0.279057	+	0.960274i	$0.409978\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	10.7600	−	3.49613i	0.474602	−	0.154208i
$515$	3.32502	+	4.57649i	0.146518	+	0.201664i
$516$	−12.0000	−	8.48528i	−0.528271	−	0.373544i
$517$		0			0
$518$		−	8.48528i		−	0.372822i
$519$	0.133421	+	10.3914i	0.00585654	+	0.456134i
$520$	−1.85410	−	5.70634i	−0.0813077	−	0.250240i
$521$	−18.8300	−	6.11822i	−0.824955	−	0.268044i	−0.134036	−	0.990976i	$-0.542794\pi$
$521$	−18.8300	−	6.11822i	−0.824955	−	0.268044i	−0.690919	+	0.722932i	$0.742794\pi$
$522$	5.12094	−	17.2562i	0.224138	−	0.755283i
$523$	−14.9626	+	20.5942i	−0.654267	+	0.900522i	−0.999275	−	0.0380781i	$-0.987876\pi$
$523$	−14.9626	+	20.5942i	−0.654267	+	0.900522i	0.345007	+	0.938600i	$0.387876\pi$
$524$	−3.70820	+	11.4127i	−0.161994	+	0.498565i
$525$	−6.54267	+	21.0522i	−0.285545	+	0.918792i
$526$	−9.70820	+	7.05342i	−0.423298	+	0.307544i
$527$		0			0
$528$		0			0
$529$	21.0000			0.913043
$530$	−8.09017	+	5.87785i	−0.351415	+	0.255318i
$531$	−20.6485	−	26.9377i	−0.896069	−	1.16900i
$532$		0			0
$533$	14.9626	−	20.5942i	0.648101	−	0.892034i
$534$	3.14712	+	9.27877i	0.136189	+	0.401532i
$535$	24.2099	+	7.86629i	1.04669	+	0.340089i
$536$	−1.23607	−	3.80423i	−0.0533900	−	0.164318i
$537$	9.79715	−	0.125791i	0.422778	−	0.00542827i
$538$		−	7.07107i		−	0.304855i
$539$		0			0
$540$	−2.00000	+	7.07107i	−0.0860663	+	0.304290i
$541$	7.48128	+	10.2971i	0.321646	+	0.442707i	0.938969	−	0.344003i	$-0.111783\pi$
$541$	7.48128	+	10.2971i	0.321646	+	0.442707i	−0.617323	+	0.786710i	$0.711783\pi$
$542$	12.1050	−	3.93314i	0.519953	−	0.168943i
$543$	2.07196	+	2.77615i	0.0889163	+	0.119136i
$544$		0			0
$545$	−14.5623	−	10.5801i	−0.623781	−	0.453203i
$546$	18.6476	+	24.9853i	0.798045	+	1.06927i
$547$	−32.2799	+	10.4884i	−1.38019	+	0.448451i	−0.902732	−	0.430204i	$-0.858442\pi$
$547$	−32.2799	+	10.4884i	−1.38019	+	0.448451i	−0.477458	+	0.878654i	$0.658442\pi$
$548$	1.66251	+	2.28825i	0.0710188	+	0.0977490i
$549$	−12.0000	+	4.24264i	−0.512148	+	0.181071i
$550$		0			0
$551$		0			0
$552$	2.44929	−	0.0314477i	0.104249	−	0.00133850i
$553$	−5.56231	−	17.1190i	−0.236533	−	0.727975i
$554$	20.1750	+	6.55524i	0.857152	+	0.278505i
$555$	1.57356	+	4.63939i	0.0667939	+	0.196931i
$556$	9.97505	−	13.7295i	0.423036	−	0.582259i
$557$	−5.56231	+	17.1190i	−0.235682	+	0.725356i	0.761348	+	0.648344i	$0.224538\pi$
$557$	−5.56231	+	17.1190i	−0.235682	+	0.725356i	−0.997030	+	0.0770122i	$0.975462\pi$
$558$	−9.52391	+	7.30035i	−0.403179	+	0.309049i
$559$	29.1246	−	21.1603i	1.23184	−	0.894984i
$560$	6.00000			0.253546
$561$		0			0
$562$	12.0000			0.506189
$563$	24.2705	−	17.6336i	1.02288	−	0.743166i	0.0560088	−	0.998430i	$-0.482163\pi$
$563$	24.2705	−	17.6336i	1.02288	−	0.743166i	0.966871	+	0.255264i	$0.0821625\pi$
$564$	5.08874	−	16.3739i	0.214275	−	0.689466i
$565$	4.94427	−	15.2169i	0.208007	−	0.640180i
$566$	−4.98752	+	6.86474i	−0.209641	+	0.288546i
$567$	−1.96008	−	38.1334i	−0.0823155	−	1.60145i
$568$	−6.72499	−	2.18508i	−0.282174	−	0.0916839i
$569$	−7.41641	−	22.8254i	−0.310912	−	0.956889i	−0.977405	−	0.211377i	$-0.932205\pi$
$569$	−7.41641	−	22.8254i	−0.310912	−	0.956889i	0.666493	−	0.745512i	$-0.267795\pi$
$570$		0			0
$571$		−	33.9411i		−	1.42039i	−0.704004	−	0.710196i	$-0.748606\pi$
$571$		−	33.9411i		−	1.42039i	0.704004	−	0.710196i	$-0.251394\pi$
$572$		0			0
$573$	−14.0000	−	9.89949i	−0.584858	−	0.413557i
$574$	14.9626	+	20.5942i	0.624526	+	0.859586i
$575$	−4.03499	+	1.31105i	−0.168271	+	0.0546745i
$576$	−2.99901	+	0.0770245i	−0.124959	+	0.00320935i
$577$	−16.1803	−	11.7557i	−0.673596	−	0.489396i	0.197631	−	0.980277i	$-0.436675\pi$
$577$	−16.1803	−	11.7557i	−0.673596	−	0.489396i	−0.871227	+	0.490880i	$0.836675\pi$
$578$	13.7533	+	9.99235i	0.572061	+	0.415627i
$579$	11.7782	−	8.79058i	0.489485	−	0.365324i
$580$	8.06998	−	2.62210i	0.335088	−	0.108877i
$581$	29.9251	+	41.1884i	1.24150	+	1.70878i
$582$	−8.00000	+	11.3137i	−0.331611	+	0.468968i
$583$		0			0
$584$		0			0
$585$	−14.8291	−	10.2028i	−0.613110	−	0.421832i
$586$	1.85410	+	5.70634i	0.0765922	+	0.235727i
$587$	−26.8999	−	8.74032i	−1.11028	−	0.360752i	−0.304229	−	0.952599i	$-0.598399\pi$
$587$	−26.8999	−	8.74032i	−1.11028	−	0.360752i	−0.806050	+	0.591847i	$0.798399\pi$
$588$	−18.0430	+	6.11971i	−0.744080	+	0.252373i
$589$		0			0
$590$	4.94427	−	15.2169i	0.203552	−	0.626470i
$591$	29.7723	+	9.25273i	1.22467	+	0.380606i
$592$	−1.61803	+	1.17557i	−0.0665008	+	0.0483157i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$		0			0
$596$	−4.85410	+	3.52671i	−0.198832	+	0.144460i
$597$	26.4642	+	8.22465i	1.08311	+	0.336612i
$598$	−1.85410	+	5.70634i	−0.0758199	+	0.233350i
$599$	−14.1313	+	19.4501i	−0.577390	+	0.794709i	−0.993406	−	0.114648i	$-0.963426\pi$
$599$	−14.1313	+	19.4501i	−0.577390	+	0.794709i	0.416016	+	0.909357i	$0.363426\pi$
$600$	4.92081	−	1.66901i	0.200891	−	0.0681372i
$601$	32.2799	+	10.4884i	1.31673	+	0.427830i	0.881369	−	0.472428i	$-0.156622\pi$
$601$	32.2799	+	10.4884i	1.31673	+	0.427830i	0.435356	+	0.900258i	$0.356622\pi$
$602$	11.1246	+	34.2380i	0.453405	+	1.39544i
$603$	−9.88610	−	6.80184i	−0.402593	−	0.276992i
$604$		−	4.24264i		−	0.172631i
$605$		0			0
$606$	6.00000	−	8.48528i	0.243733	−	0.344691i
$607$	−2.49376	−	3.43237i	−0.101219	−	0.139316i	0.755403	−	0.655260i	$-0.227441\pi$
$607$	−2.49376	−	3.43237i	−0.101219	−	0.139316i	−0.856622	+	0.515945i	$0.827441\pi$
$608$		0			0
$609$	−35.3346	+	26.3717i	−1.43183	+	1.06864i
$610$	−4.85410	−	3.52671i	−0.196537	−	0.142792i
$611$	33.9787	+	24.6870i	1.37463	+	0.998728i
$612$		0			0
$613$	12.1050	−	3.93314i	0.488915	−	0.158858i	−0.0541768	−	0.998531i	$-0.517253\pi$
$613$	12.1050	−	3.93314i	0.488915	−	0.158858i	0.543092	+	0.839673i	$0.317253\pi$
$614$		0			0
$615$	−12.0000	−	8.48528i	−0.483887	−	0.342160i
$616$		0			0
$617$			39.5980i			1.59415i	0.603877	+	0.797077i	$0.293622\pi$
$617$			39.5980i			1.59415i	−0.603877	+	0.797077i	$0.706378\pi$
$618$	0.0889475	+	6.92763i	0.00357799	+	0.278670i
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	0.717398	+	0.696664i	$0.245333\pi$
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	−0.170898	+	0.985289i	$0.554667\pi$
$620$	−5.37999	−	1.74806i	−0.216066	−	0.0702039i
$621$	5.77430	−	4.54504i	0.231715	−	0.182386i
$622$	15.7938	−	21.7383i	0.633275	−	0.871628i
$623$	7.41641	−	22.8254i	0.297132	−	0.914479i
$624$	2.18089	−	7.01739i	0.0873054	−	0.280920i
$625$	0.809017	−	0.587785i	0.0323607	−	0.0235114i
$626$	−10.0000			−0.399680
$627$		0			0
$628$	−22.0000			−0.877896
$629$		0			0
$630$	14.2859	−	10.9505i	0.569162	−	0.436280i
$631$	6.18034	−	19.0211i	0.246035	−	0.757219i	−0.749429	−	0.662085i	$-0.769672\pi$
$631$	6.18034	−	19.0211i	0.246035	−	0.757219i	0.995464	−	0.0951345i	$-0.0303281\pi$
$632$	−2.49376	+	3.43237i	−0.0991965	+	0.136532i
$633$	−4.72068	−	13.9182i	−0.187630	−	0.553197i
$634$	9.41498	+	3.05911i	0.373917	+	0.121493i
$635$	−5.56231	−	17.1190i	−0.220733	−	0.679347i
$636$	−12.2464	+	0.157238i	−0.485603	+	0.00623491i
$637$		−	46.6690i		−	1.84909i
$638$		0			0
$639$	−20.0000	+	7.07107i	−0.791188	+	0.279727i
$640$	−0.831254	−	1.14412i	−0.0328582	−	0.0452254i
$641$	−45.7299	+	14.8585i	−1.80622	+	0.586877i	−0.999989	−	0.00472015i	$-0.998498\pi$
$641$	−45.7299	+	14.8585i	−1.80622	+	0.586877i	−0.806234	+	0.591597i	$0.798498\pi$
$642$	18.6476	+	24.9853i	0.735964	+	0.986091i
$643$	3.23607	+	2.35114i	0.127618	+	0.0927200i	0.649763	−	0.760137i	$-0.274868\pi$
$643$	3.23607	+	2.35114i	0.127618	+	0.0927200i	−0.522145	+	0.852857i	$0.674868\pi$
$644$	−4.85410	−	3.52671i	−0.191278	−	0.138972i
$645$	−12.4318	−	16.6569i	−0.489500	−	0.655864i
$646$		0			0
$647$	4.15627	+	5.72061i	0.163400	+	0.224901i	0.882864	−	0.469629i	$-0.155612\pi$
$647$	4.15627	+	5.72061i	0.163400	+	0.224901i	−0.719464	+	0.694530i	$0.755612\pi$
$648$	−7.00000	+	5.65685i	−0.274986	+	0.222222i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	29.3915	−	0.377372i	1.15194	−	0.0147904i
$652$	0.618034	+	1.90211i	0.0242041	+	0.0744925i
$653$	25.5549	+	8.30330i	1.00004	+	0.324933i	0.762882	−	0.646537i	$-0.223784\pi$
$653$	25.5549	+	8.30330i	1.00004	+	0.324933i	0.237160	+	0.971471i	$0.423784\pi$
$654$	−7.08102	−	20.8772i	−0.276890	−	0.816365i
$655$	−9.97505	+	13.7295i	−0.389757	+	0.536455i
$656$	1.85410	−	5.70634i	0.0723905	−	0.222795i
$657$		0			0
$658$	−33.9787	+	24.6870i	−1.32463	+	0.962399i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	8.09017	−	5.87785i	0.314433	−	0.228449i
$663$		0			0
$664$	3.70820	−	11.4127i	0.143906	−	0.442898i
$665$		0			0
$666$	−1.70698	+	5.75206i	−0.0661442	+	0.222888i
$667$	−8.06998	−	2.62210i	−0.312471	−	0.101528i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	−0.177895	−	13.8553i	−0.00687782	−	0.535675i
$670$		−	5.65685i		−	0.218543i
$671$		0			0
$672$	6.00000	+	4.24264i	0.231455	+	0.163663i
$673$	24.9376	+	34.3237i	0.961274	+	1.32308i	0.946333	+	0.323192i	$0.104756\pi$
$673$	24.9376	+	34.3237i	0.961274	+	1.32308i	0.0149412	+	0.999888i	$0.495244\pi$
$674$	32.2799	−	10.4884i	1.24338	−	0.403997i
$675$	8.67025	−	12.9548i	0.333718	−	0.498630i
$676$	4.04508	+	2.93893i	0.155580	+	0.113036i
$677$	−24.2705	−	17.6336i	−0.932791	−	0.677713i	0.0138832	−	0.999904i	$-0.495581\pi$
$677$	−24.2705	−	17.6336i	−0.932791	−	0.677713i	−0.946675	+	0.322191i	$0.895581\pi$
$678$	15.7042	−	11.7208i	0.603118	−	0.450134i
$679$	32.2799	−	10.4884i	1.23879	−	0.402507i
$680$		0			0
$681$	6.00000	−	8.48528i	0.229920	−	0.325157i
$682$		0			0
$683$			5.65685i			0.216454i	0.994126	+	0.108227i	$0.0345173\pi$
$683$			5.65685i			0.216454i	−0.994126	+	0.108227i	$0.965483\pi$
$684$		0			0
$685$	1.23607	+	3.80423i	0.0472277	+	0.145352i
$686$	16.1400	+	5.24419i	0.616227	+	0.200224i
$687$	22.9638	−	7.78873i	0.876123	−	0.297158i
$688$	4.98752	−	6.86474i	0.190148	−	0.261716i
$689$	9.27051	−	28.5317i	0.353178	−	1.08697i
$690$	3.30803	+	1.02808i	0.125934	+	0.0391384i
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	−0.0666172	−	0.997779i	$-0.521221\pi$
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	0.928358	+	0.371687i	$0.121221\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	19.4164	−	14.1068i	0.736506	−	0.535103i
$696$	9.92408	+	3.08424i	0.376171	+	0.116908i
$697$		0			0
$698$	−17.4563	+	24.0266i	−0.660732	+	0.909419i
$699$	29.5249	−	10.0141i	1.11673	−	0.378767i
$700$	−12.1050	−	3.93314i	−0.457525	−	0.148659i
$701$	−5.56231	−	17.1190i	−0.210085	−	0.646576i	−0.999466	−	0.0326724i	$-0.989598\pi$
$701$	−5.56231	−	17.1190i	−0.210085	−	0.646576i	0.789381	−	0.613904i	$-0.210402\pi$
$702$	−7.61471	−	20.6886i	−0.287399	−	0.780839i
$703$		0			0
$704$		0			0
$705$	14.0000	−	19.7990i	0.527271	−	0.745673i
$706$	−13.3001	−	18.3060i	−0.500554	−	0.688954i
$707$	−24.2099	+	7.86629i	−0.910509	+	0.295842i
$708$	15.7042	−	11.7208i	0.590202	−	0.440494i
$709$	8.09017	+	5.87785i	0.303833	+	0.220747i	0.729246	−	0.684252i	$-0.239871\pi$
$709$	8.09017	+	5.87785i	0.303833	+	0.220747i	−0.425413	+	0.904999i	$0.639871\pi$
$710$	−8.09017	−	5.87785i	−0.303619	−	0.220592i
$711$	0.326787	+	12.7237i	0.0122555	+	0.477177i
$712$	−5.37999	+	1.74806i	−0.201624	+	0.0655115i
$713$	3.32502	+	4.57649i	0.124523	+	0.171391i
$714$		0			0
$715$		0			0
$716$			5.65685i			0.211407i
$717$	0.266843	+	20.7829i	0.00996542	+	0.776151i
$718$		0			0
$719$	−30.9349	−	10.0514i	−1.15368	−	0.374853i	−0.331151	−	0.943578i	$-0.607437\pi$
$719$	−30.9349	−	10.0514i	−1.15368	−	0.374853i	−0.822528	+	0.568725i	$0.807437\pi$
$720$	−4.06732	−	1.20702i	−0.151580	−	0.0449829i
$721$	9.97505	−	13.7295i	0.371490	−	0.511312i
$722$	5.87132	−	18.0701i	0.218508	−	0.672499i
$723$	4.36178	−	14.0348i	0.162216	−	0.521959i
$724$	−1.61803	+	1.17557i	−0.0601338	+	0.0436897i
$725$	−18.0000			−0.668503
$726$		0			0
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$	−14.5623	+	10.5801i	−0.539715	+	0.392126i
$729$	−6.34258	+	26.2445i	−0.234910	+	0.972017i
$730$		0			0
$731$		0			0
$732$	−2.36034	−	6.95908i	−0.0872407	−	0.257215i
$733$	4.03499	+	1.31105i	0.149036	+	0.0484247i	0.382585	−	0.923920i	$-0.375034\pi$
$733$	4.03499	+	1.31105i	0.149036	+	0.0484247i	−0.233549	+	0.972345i	$0.575034\pi$
$734$	−8.65248	−	26.6296i	−0.319369	−	0.982916i
$735$	−26.9422	+	0.345925i	−0.993777	+	0.0127596i
$736$			1.41421i			0.0521286i
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$	−14.9626	−	20.5942i	−0.550407	−	0.757570i	0.439660	−	0.898164i	$-0.355099\pi$
$739$	−14.9626	−	20.5942i	−0.550407	−	0.757570i	−0.990067	+	0.140594i	$0.955099\pi$
$740$	−2.68999	+	0.874032i	−0.0988861	+	0.0321301i
$741$		0			0
$742$	24.2705	+	17.6336i	0.890998	+	0.647348i
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	0.171602	−	0.985166i	$-0.445106\pi$
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	−0.883921	+	0.467636i	$0.845106\pi$
$744$	−4.14392	−	5.55229i	−0.151923	−	0.203557i
$745$	−8.06998	+	2.62210i	−0.295661	+	0.0960662i
$746$	−17.4563	−	24.0266i	−0.639122	−	0.879676i
$747$	−12.0000	−	33.9411i	−0.439057	−	1.24184i
$748$		0			0
$749$		−	76.3675i		−	2.79041i
$750$	19.5943	−	0.251582i	0.715483	−	0.00918646i
$751$	−12.3607	−	38.0423i	−0.451048	−	1.38818i	−0.875713	−	0.482832i	$-0.839608\pi$
$751$	−12.3607	−	38.0423i	−0.451048	−	1.38818i	0.424666	−	0.905350i	$-0.360392\pi$
$752$	9.41498	+	3.05911i	0.343329	+	0.111554i
$753$	3.14712	+	9.27877i	0.114687	+	0.338137i
$754$	−14.9626	+	20.5942i	−0.544905	+	0.749997i
$755$	1.85410	−	5.70634i	0.0674777	−	0.207675i
$756$	22.0291	−	0.848901i	0.801189	−	0.0308742i
$757$	−1.61803	+	1.17557i	−0.0588084	+	0.0427268i	−0.616801	−	0.787119i	$-0.711572\pi$
$757$	−1.61803	+	1.17557i	−0.0588084	+	0.0427268i	0.557993	+	0.829846i	$0.311572\pi$
$758$	2.00000			0.0726433
$759$		0			0
$760$		0			0
$761$	−19.4164	+	14.1068i	−0.703844	+	0.511373i	−0.881182	−	0.472777i	$-0.843252\pi$
$761$	−19.4164	+	14.1068i	−0.703844	+	0.511373i	0.177338	+	0.984150i	$0.443252\pi$
$762$	6.54267	−	21.0522i	0.237016	−	0.762639i
$763$	−16.6869	+	51.3571i	−0.604107	+	1.85925i
$764$	5.81878	−	8.00886i	0.210516	−	0.289750i
$765$		0			0
$766$	1.34500	+	0.437016i	0.0485967	+	0.0157900i
$767$	14.8328	+	45.6507i	0.535582	+	1.64835i
$768$	−0.0222369	−	1.73191i	−0.000802404	−	0.0624948i
$769$			42.4264i			1.52994i	0.644069	+	0.764968i	$0.277245\pi$
$769$			42.4264i			1.52994i	−0.644069	+	0.764968i	$0.722755\pi$
$770$		0			0
$771$	16.0000	+	11.3137i	0.576226	+	0.407453i
$772$	4.98752	+	6.86474i	0.179505	+	0.247067i
$773$	−17.4850	+	5.68121i	−0.628890	+	0.204339i	−0.606083	−	0.795401i	$-0.707260\pi$
$773$	−17.4850	+	5.68121i	−0.628890	+	0.204339i	−0.0228069	+	0.999740i	$0.507260\pi$
$774$	−0.653574	−	25.4475i	−0.0234922	−	0.914690i
$775$	9.70820	+	7.05342i	0.348729	+	0.253366i
$776$	−6.47214	−	4.70228i	−0.232336	−	0.168802i
$777$	11.7782	−	8.79058i	0.422540	−	0.315360i
$778$	−9.41498	+	3.05911i	−0.337543	+	0.109674i
$779$		0			0
$780$	6.00000	−	8.48528i	0.214834	−	0.303822i
$781$		0			0
$782$		0			0
$783$	29.2580	−	10.7688i	1.04560	−	0.384846i
$784$	−3.39919	−	10.4616i	−0.121400	−	0.373629i
$785$	−29.5899	−	9.61435i	−1.05611	−	0.343151i
$786$	−19.6833	+	6.67605i	−0.702078	+	0.238127i
$787$	24.9376	−	34.3237i	0.888930	−	1.22351i	−0.0849366	−	0.996386i	$-0.527069\pi$
$787$	24.9376	−	34.3237i	0.888930	−	1.22351i	0.973867	−	0.227121i	$-0.0729312\pi$
$788$	−5.56231	+	17.1190i	−0.198149	+	0.609840i
$789$	−19.8482	−	6.16849i	−0.706613	−	0.219604i
$790$	−4.85410	+	3.52671i	−0.172701	+	0.125475i
$791$	−48.0000			−1.70668
$792$		0			0
$793$	18.0000			0.639199
$794$	27.5066	−	19.9847i	0.976172	−	0.709230i
$795$	−16.5401	−	5.14040i	−0.586618	−	0.182311i
$796$	−4.94427	+	15.2169i	−0.175245	+	0.539349i
$797$	0.831254	−	1.14412i	0.0294445	−	0.0405269i	−0.794041	−	0.607864i	$-0.792026\pi$
$797$	0.831254	−	1.14412i	0.0294445	−	0.0405269i	0.823485	+	0.567337i	$0.192026\pi$
$798$		0			0
$799$		0			0
$800$	0.927051	+	2.85317i	0.0327762	+	0.100875i
$801$	−9.61926	+	13.9811i	−0.339880	+	0.493996i
$802$		−	36.7696i		−	1.29838i
$803$		0			0
$804$	4.00000	−	5.65685i	0.141069	−	0.199502i
$805$	−4.98752	−	6.86474i	−0.175787	−	0.241950i
$806$	16.1400	−	5.24419i	0.568506	−	0.184719i
$807$	9.81516	−	7.32549i	0.345510	−	0.257869i
$808$	4.85410	+	3.52671i	0.170767	+	0.124069i
$809$	43.6869	+	31.7404i	1.53595	+	1.11593i	0.952812	+	0.303560i	$0.0981753\pi$
$809$	43.6869	+	31.7404i	1.53595	+	1.11593i	0.583138	+	0.812373i	$0.301825\pi$
$810$	−11.8871	+	4.54934i	−0.417671	+	0.159848i
$811$	24.2099	−	7.86629i	0.850126	−	0.276223i	0.148627	−	0.988893i	$-0.452515\pi$
$811$	24.2099	−	7.86629i	0.850126	−	0.276223i	0.701499	+	0.712671i	$0.252515\pi$
$812$	−14.9626	−	20.5942i	−0.525083	−	0.722715i
$813$	18.0000	+	12.7279i	0.631288	+	0.446388i
$814$		0			0
$815$			2.82843i			0.0990755i
$816$		0			0
$817$		0			0
$818$	−8.06998	−	2.62210i	−0.282160	−	0.0916794i
$819$	−15.3628	+	51.7686i	−0.536821	+	1.80894i
$820$	4.98752	−	6.86474i	0.174172	−	0.239727i
$821$	9.27051	−	28.5317i	0.323543	−	0.995763i	−0.648551	−	0.761171i	$-0.724625\pi$
$821$	9.27051	−	28.5317i	0.323543	−	0.995763i	0.972094	−	0.234592i	$-0.0753753\pi$
$822$	−1.45393	+	4.67826i	−0.0507115	+	0.163173i
$823$	32.3607	−	23.5114i	1.12802	−	0.819556i	0.142617	−	0.989778i	$-0.454448\pi$
$823$	32.3607	−	23.5114i	1.12802	−	0.819556i	0.985406	+	0.170222i	$0.0544484\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$	−48.0000			−1.67013
$827$	−29.1246	+	21.1603i	−1.01276	+	0.735815i	−0.964787	−	0.263034i	$-0.915277\pi$
$827$	−29.1246	+	21.1603i	−1.01276	+	0.735815i	−0.0479754	+	0.998849i	$0.515277\pi$
$828$	2.58107	+	3.36721i	0.0896982	+	0.117019i
$829$	0.618034	−	1.90211i	0.0214652	−	0.0660631i	−0.939750	−	0.341862i	$-0.888942\pi$
$829$	0.618034	−	1.90211i	0.0214652	−	0.0660631i	0.961215	+	0.275799i	$0.0889424\pi$
$830$	9.97505	−	13.7295i	0.346239	−	0.476557i
$831$	11.8017	+	34.7954i	0.409396	+	1.20704i
$832$	4.03499	+	1.31105i	0.139888	+	0.0454524i
$833$		0			0
$834$	29.3915	−	0.377372i	1.01774	−	0.0130673i
$835$		−	16.9706i		−	0.587291i
$836$		0			0
$837$	−20.0000	−	5.65685i	−0.691301	−	0.195529i
$838$	6.65003	+	9.15298i	0.229722	+	0.316185i
$839$	14.7950	−	4.80718i	0.510779	−	0.165962i	−0.0422775	−	0.999106i	$-0.513461\pi$
$839$	14.7950	−	4.80718i	0.510779	−	0.165962i	0.553056	+	0.833144i	$0.313461\pi$
$840$	6.21588	+	8.32844i	0.214468	+	0.287358i
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	8.09017	+	5.87785i	0.278806	+	0.202564i
$843$	12.4318	+	16.6569i	0.428173	+	0.573693i
$844$	8.06998	−	2.62210i	0.277780	−	0.0902563i
$845$	4.15627	+	5.72061i	0.142980	+	0.196795i
$846$	28.0000	−	9.89949i	0.962660	−	0.340352i
$847$		0			0
$848$		−	7.07107i		−	0.242821i
$849$	−14.6957	+	0.188686i	−0.504356	+	0.00647569i
$850$		0			0
$851$	2.68999	+	0.874032i	0.0922118	+	0.0299614i
$852$	−3.93390	−	11.5985i	−0.134773	−	0.397357i
$853$	12.4688	−	17.1618i	0.426924	−	0.587610i	−0.540320	−	0.841460i	$-0.681697\pi$
$853$	12.4688	−	17.1618i	0.426924	−	0.587610i	0.967244	+	0.253849i	$0.0816968\pi$
$854$	−5.56231	+	17.1190i	−0.190338	+	0.585801i
$855$		0			0
$856$	−14.5623	+	10.5801i	−0.497729	+	0.361622i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	9.70820	−	7.05342i	0.331047	−	0.240520i
$861$	−13.0853	+	42.1043i	−0.445947	+	1.43491i
$862$	11.1246	−	34.2380i	0.378906	−	1.16615i
$863$	−4.15627	+	5.72061i	−0.141481	+	0.194732i	−0.873877	−	0.486147i	$-0.838402\pi$
$863$	−4.15627	+	5.72061i	−0.141481	+	0.194732i	0.732396	+	0.680879i	$0.238402\pi$
$864$	−3.21383	−	4.08305i	−0.109337	−	0.138908i
$865$	−8.06998	−	2.62210i	−0.274388	−	0.0891539i
$866$	0.618034	+	1.90211i	0.0210016	+	0.0646364i
$867$	0.378027	+	29.4424i	0.0128385	+	0.999918i
$868$			16.9706i			0.576018i
$869$		0			0
$870$	12.0000	+	8.48528i	0.406838	+	0.287678i
$871$	9.97505	+	13.7295i	0.337992	+	0.465205i
$872$	12.1050	−	3.93314i	0.409926	−	0.133193i
$873$	−23.9921	+	0.616196i	−0.812009	+	0.0208551i
$874$		0			0
$875$	−38.8328	−	28.2137i	−1.31279	−	0.953797i
$876$		0			0
$877$	−28.2449	+	9.17734i	−0.953764	+	0.309897i	−0.744244	−	0.667908i	$-0.767190\pi$
$877$	−28.2449	+	9.17734i	−0.953764	+	0.309897i	−0.209520	+	0.977804i	$0.567190\pi$
$878$	−12.4688	−	17.1618i	−0.420802	−	0.579184i
$879$	−6.00000	+	8.48528i	−0.202375	+	0.286201i
$880$		0			0
$881$			5.65685i			0.190584i	0.995449	+	0.0952921i	$0.0303785\pi$
$881$			5.65685i			0.190584i	−0.995449	+	0.0952921i	$0.969621\pi$
$882$	−27.1868	−	18.7051i	−0.915426	−	0.629832i
$883$	6.18034	+	19.0211i	0.207985	+	0.640112i	0.999578	+	0.0290628i	$0.00925227\pi$
$883$	6.18034	+	19.0211i	0.207985	+	0.640112i	−0.791593	+	0.611049i	$0.790748\pi$
$884$		0			0
$885$	26.2443	−	8.90140i	0.882194	−	0.299217i
$886$	−16.6251	+	22.8825i	−0.558530	+	0.768751i
$887$	−14.8328	+	45.6507i	−0.498037	+	1.53280i	0.314132	+	0.949379i	$0.398286\pi$
$887$	−14.8328	+	45.6507i	−0.498037	+	1.53280i	−0.812169	+	0.583422i	$0.801714\pi$
$888$	−3.30803	−	1.02808i	−0.111010	−	0.0345001i
$889$	−43.6869	+	31.7404i	−1.46521	+	1.06454i
$890$	−8.00000			−0.268161
$891$		0			0
$892$	8.00000			0.267860
$893$		0			0
$894$	−9.92408	−	3.08424i	−0.331911	−	0.103153i
$895$	−2.47214	+	7.60845i	−0.0826344	+	0.254323i
$896$	−2.49376	+	3.43237i	−0.0833107	+	0.114667i
$897$	−9.84163	+	3.33803i	−0.328602	+	0.111453i
$898$	29.5899	+	9.61435i	0.987429	+	0.320835i
$899$	7.41641	+	22.8254i	0.247351	+	0.761268i
$900$	7.41457	+	5.10138i	0.247152	+	0.170046i
$901$		0			0
$902$		0			0
$903$	−36.0000	+	50.9117i	−1.19800	+	1.69423i
$904$	6.65003	+	9.15298i	0.221177	+	0.304424i
$905$	−2.68999	+	0.874032i	−0.0894184	+	0.0290538i
$906$	5.88909	−	4.39529i	0.195652	−	0.146024i
$907$	−35.5967	−	25.8626i	−1.18197	−	0.858752i	−0.189578	−	0.981866i	$-0.560712\pi$
$907$	−35.5967	−	25.8626i	−1.18197	−	0.858752i	−0.992393	+	0.123114i	$0.960712\pi$
$908$	4.85410	+	3.52671i	0.161089	+	0.117038i
$909$	17.9941	−	0.462147i	0.596826	−	0.0153284i
$910$	−24.2099	+	7.86629i	−0.802552	+	0.260765i
$911$	−5.81878	−	8.00886i	−0.192785	−	0.265345i	0.701672	−	0.712500i	$-0.252437\pi$
$911$	−5.81878	−	8.00886i	−0.192785	−	0.265345i	−0.894457	+	0.447155i	$0.852437\pi$
$912$		0			0
$913$		0			0
$914$			8.48528i			0.280668i
$915$	−0.133421	−	10.3914i	−0.00441077	−	0.343531i
$916$	4.32624	+	13.3148i	0.142943	+	0.439933i
$917$	48.4199	+	15.7326i	1.59897	+	0.519535i
$918$		0			0
$919$	−22.4439	+	30.8913i	−0.740354	+	1.01901i	0.258244	+	0.966080i	$0.416856\pi$
$919$	−22.4439	+	30.8913i	−0.740354	+	1.01901i	−0.998598	+	0.0529307i	$0.983144\pi$
$920$	−0.618034	+	1.90211i	−0.0203760	+	0.0627108i
$921$		0			0
$922$	−24.2705	+	17.6336i	−0.799307	+	0.580730i
$923$	30.0000			0.987462
$924$		0			0
$925$	6.00000			0.197279
$926$	−25.8885	+	18.8091i	−0.850750	+	0.618106i
$927$	−9.52391	+	7.30035i	−0.312806	+	0.239775i
$928$	−1.85410	+	5.70634i	−0.0608639	+	0.187320i
$929$	−1.66251	+	2.28825i	−0.0545451	+	0.0750749i	−0.835418	−	0.549615i	$-0.814775\pi$
$929$	−1.66251	+	2.28825i	−0.0545451	+	0.0750749i	0.780873	+	0.624690i	$0.214775\pi$
$930$	−3.14712	−	9.27877i	−0.103198	−	0.304263i
$931$		0			0
$932$	5.56231	+	17.1190i	0.182199	+	0.560752i
$933$	46.5365	−	0.597506i	1.52354	−	0.0195615i
$934$			31.1127i			1.01804i
$935$		0			0
$936$	12.0000	−	4.24264i	0.392232	−	0.138675i
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$	−16.1400	+	5.24419i	−0.526989	+	0.171229i
$939$	−10.3598	−	13.8807i	−0.338079	−	0.452980i
$940$	11.3262	+	8.22899i	0.369421	+	0.268400i
$941$	−33.9787	−	24.6870i	−1.10767	−	0.804773i	−0.125379	−	0.992109i	$-0.540015\pi$
$941$	−33.9787	−	24.6870i	−1.10767	−	0.804773i	−0.982296	+	0.187336i	$0.940015\pi$
$942$	−22.7916	−	30.5376i	−0.742589	−	0.994969i
$943$	−8.06998	+	2.62210i	−0.262795	+	0.0853872i
$944$	6.65003	+	9.15298i	0.216440	+	0.297904i
$945$	30.0000	+	8.48528i	0.975900	+	0.276026i
$946$		0			0
$947$			48.0833i			1.56250i	0.624221	+	0.781248i	$0.285417\pi$
$947$			48.0833i			1.56250i	−0.624221	+	0.781248i	$0.714583\pi$
$948$	−7.34786	+	0.0943431i	−0.238648	+	0.00306412i
$949$		0			0
$950$		0			0
$951$	5.50746	+	16.2379i	0.178592	+	0.526548i
$952$		0			0
$953$	−16.6869	+	51.3571i	−0.540542	+	1.66362i	0.190817	+	0.981626i	$0.438886\pi$
$953$	−16.6869	+	51.3571i	−0.540542	+	1.66362i	−0.731359	+	0.681992i	$0.761114\pi$
$954$	−12.9053	−	16.8361i	−0.417825	−	0.545087i
$955$	11.3262	−	8.22899i	0.366508	−	0.266284i
$956$	−12.0000			−0.388108
$957$		0			0
$958$	12.0000			0.387702
$959$	9.70820	−	7.05342i	0.313494	−	0.227767i
$960$	0.726963	−	2.33913i	0.0234626	−	0.0754951i
$961$	−4.63525	+	14.2658i	−0.149524	+	0.460189i
$962$	4.98752	−	6.86474i	0.160804	−	0.221328i
$963$	−15.3628	+	51.7686i	−0.495060	+	1.66822i
$964$	8.06998	+	2.62210i	0.259917	+	0.0844520i
$965$	3.70820	+	11.4127i	0.119371	+	0.367387i
$966$	−0.133421	−	10.3914i	−0.00429276	−	0.334339i
$967$			4.24264i			0.136434i	0.997671	+	0.0682171i	$0.0217310\pi$
$967$			4.24264i			0.136434i	−0.997671	+	0.0682171i	$0.978269\pi$
$968$		0			0
$969$		0			0
$970$	−6.65003	−	9.15298i	−0.213520	−	0.293885i
$971$	43.0399	−	13.9845i	1.38122	−	0.448784i	0.478147	−	0.878280i	$-0.341309\pi$
$971$	43.0399	−	13.9845i	1.38122	−	0.448784i	0.903069	+	0.429495i	$0.141309\pi$
$972$	−15.1040	−	3.85612i	−0.484461	−	0.123685i
$973$	−58.2492	−	42.3205i	−1.86738	−	1.35673i
$974$	−16.1803	−	11.7557i	−0.518452	−	0.376677i
$975$	−17.6673	+	13.1859i	−0.565806	+	0.422286i
$976$	4.03499	−	1.31105i	0.129157	−	0.0419656i
$977$	−8.31254	−	11.4412i	−0.265942	−	0.366037i	0.655073	−	0.755566i	$-0.272638\pi$
$977$	−8.31254	−	11.4412i	−0.265942	−	0.366037i	−0.921014	+	0.389529i	$0.872638\pi$
$978$	−2.00000	+	2.82843i	−0.0639529	+	0.0904431i
$979$		0			0
$980$		−	15.5563i		−	0.496929i
$981$	21.6433	−	31.4574i	0.691018	−	1.00436i
$982$	1.85410	+	5.70634i	0.0591668	+	0.182097i
$983$	9.41498	+	3.05911i	0.300291	+	0.0975705i	0.455287	−	0.890345i	$-0.349537\pi$
$983$	9.41498	+	3.05911i	0.300291	+	0.0975705i	−0.154996	+	0.987915i	$0.549537\pi$
$984$	9.84163	−	3.33803i	0.313740	−	0.106412i
$985$	−14.9626	+	20.5942i	−0.476747	+	0.656186i
$986$		0			0
$987$	−69.4686	−	21.5897i	−2.21121	−	0.687208i
$988$		0			0
$989$	−12.0000			−0.381578
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	3.23607	−	2.35114i	0.102745	−	0.0746488i
$993$	16.5401	+	5.14040i	0.524885	+	0.163126i
$994$	−9.27051	+	28.5317i	−0.294043	+	0.904970i
$995$	−13.3001	+	18.3060i	−0.421640	+	0.580338i
$996$	19.6833	−	6.67605i	0.623688	−	0.211539i
$997$	−28.2449	−	9.17734i	−0.894526	−	0.290649i	−0.174550	−	0.984648i	$-0.555847\pi$
$997$	−28.2449	−	9.17734i	−0.894526	−	0.290649i	−0.719976	+	0.693999i	$0.755847\pi$
$998$	4.32624	+	13.3148i	0.136945	+	0.421472i
$999$	−9.75268	+	3.58961i	−0.308561	+	0.113570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.e.239.1		8
3.2	odd	2		726.2.h.i.239.2		8
11.2	odd	10		66.2.b.a.65.2	yes	2
11.3	even	5	inner	726.2.h.e.215.2		8
11.4	even	5	inner	726.2.h.e.161.2		8
11.5	even	5	inner	726.2.h.e.233.1		8
11.6	odd	10		726.2.h.i.233.1		8
11.7	odd	10		726.2.h.i.161.2		8
11.8	odd	10		726.2.h.i.215.2		8
11.9	even	5		66.2.b.b.65.2	yes	2
11.10	odd	2		726.2.h.i.239.1		8
33.2	even	10		66.2.b.b.65.1	yes	2
33.5	odd	10		726.2.h.i.233.2		8
33.8	even	10	inner	726.2.h.e.215.1		8
33.14	odd	10		726.2.h.i.215.1		8
33.17	even	10	inner	726.2.h.e.233.2		8
33.20	odd	10		66.2.b.a.65.1	✓	2
33.26	odd	10		726.2.h.i.161.1		8
33.29	even	10	inner	726.2.h.e.161.1		8
33.32	even	2	inner	726.2.h.e.239.2		8
44.31	odd	10		528.2.b.c.65.1		2
44.35	even	10		528.2.b.b.65.1		2
55.2	even	20		1650.2.f.b.1649.2		4
55.9	even	10		1650.2.d.a.1451.1		2
55.13	even	20		1650.2.f.b.1649.3		4
55.24	odd	10		1650.2.d.b.1451.1		2
55.42	odd	20		1650.2.f.a.1649.4		4
55.53	odd	20		1650.2.f.a.1649.1		4
88.13	odd	10		2112.2.b.g.65.1		2
88.35	even	10		2112.2.b.d.65.2		2
88.53	even	10		2112.2.b.i.65.1		2
88.75	odd	10		2112.2.b.b.65.2		2
99.2	even	30		1782.2.i.c.1187.2		4
99.13	odd	30		1782.2.i.f.593.2		4
99.20	odd	30		1782.2.i.f.1187.2		4
99.31	even	15		1782.2.i.c.593.2		4
99.68	even	30		1782.2.i.c.593.1		4
99.79	odd	30		1782.2.i.f.1187.1		4
99.86	odd	30		1782.2.i.f.593.1		4
99.97	even	15		1782.2.i.c.1187.1		4
132.35	odd	10		528.2.b.c.65.2		2
132.119	even	10		528.2.b.b.65.2		2
165.2	odd	20		1650.2.f.a.1649.3		4
165.53	even	20		1650.2.f.b.1649.4		4
165.68	odd	20		1650.2.f.a.1649.2		4
165.119	odd	10		1650.2.d.b.1451.2		2
165.134	even	10		1650.2.d.a.1451.2		2
165.152	even	20		1650.2.f.b.1649.1		4
264.35	odd	10		2112.2.b.b.65.1		2
264.53	odd	10		2112.2.b.g.65.2		2
264.101	even	10		2112.2.b.i.65.2		2
264.251	even	10		2112.2.b.d.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	33.20	odd	10
66.2.b.a.65.2	yes	2	11.2	odd	10
66.2.b.b.65.1	yes	2	33.2	even	10
66.2.b.b.65.2	yes	2	11.9	even	5
528.2.b.b.65.1		2	44.35	even	10
528.2.b.b.65.2		2	132.119	even	10
528.2.b.c.65.1		2	44.31	odd	10
528.2.b.c.65.2		2	132.35	odd	10
726.2.h.e.161.1		8	33.29	even	10	inner
726.2.h.e.161.2		8	11.4	even	5	inner
726.2.h.e.215.1		8	33.8	even	10	inner
726.2.h.e.215.2		8	11.3	even	5	inner
726.2.h.e.233.1		8	11.5	even	5	inner
726.2.h.e.233.2		8	33.17	even	10	inner
726.2.h.e.239.1		8	1.1	even	1	trivial
726.2.h.e.239.2		8	33.32	even	2	inner
726.2.h.i.161.1		8	33.26	odd	10
726.2.h.i.161.2		8	11.7	odd	10
726.2.h.i.215.1		8	33.14	odd	10
726.2.h.i.215.2		8	11.8	odd	10
726.2.h.i.233.1		8	11.6	odd	10
726.2.h.i.233.2		8	33.5	odd	10
726.2.h.i.239.1		8	11.10	odd	2
726.2.h.i.239.2		8	3.2	odd	2
1650.2.d.a.1451.1		2	55.9	even	10
1650.2.d.a.1451.2		2	165.134	even	10
1650.2.d.b.1451.1		2	55.24	odd	10
1650.2.d.b.1451.2		2	165.119	odd	10
1650.2.f.a.1649.1		4	55.53	odd	20
1650.2.f.a.1649.2		4	165.68	odd	20
1650.2.f.a.1649.3		4	165.2	odd	20
1650.2.f.a.1649.4		4	55.42	odd	20
1650.2.f.b.1649.1		4	165.152	even	20
1650.2.f.b.1649.2		4	55.2	even	20
1650.2.f.b.1649.3		4	55.13	even	20
1650.2.f.b.1649.4		4	165.53	even	20
1782.2.i.c.593.1		4	99.68	even	30
1782.2.i.c.593.2		4	99.31	even	15
1782.2.i.c.1187.1		4	99.97	even	15
1782.2.i.c.1187.2		4	99.2	even	30
1782.2.i.f.593.1		4	99.86	odd	30
1782.2.i.f.593.2		4	99.13	odd	30
1782.2.i.f.1187.1		4	99.79	odd	30
1782.2.i.f.1187.2		4	99.20	odd	30
2112.2.b.b.65.1		2	264.35	odd	10
2112.2.b.b.65.2		2	88.75	odd	10
2112.2.b.d.65.1		2	264.251	even	10
2112.2.b.d.65.2		2	88.35	even	10
2112.2.b.g.65.1		2	88.13	odd	10
2112.2.b.g.65.2		2	264.53	odd	10
2112.2.b.i.65.1		2	88.53	even	10
2112.2.b.i.65.2		2	264.101	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.65401 - 0.514040i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.831254 - 1.14412i) q^{5} +(1.64027 - 0.556338i) q^{6} +(-4.03499 - 1.31105i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.47152 + 1.70046i) q^{9} +1.41421i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 - 3.43237i) q^{13} +(4.03499 - 1.31105i) q^{14} +(-1.96303 + 1.46510i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.99901 + 0.0770245i) q^{18} +(-0.831254 - 1.14412i) q^{20} +(6.00000 + 4.24264i) q^{21} +1.41421i q^{23} +(-0.0222369 - 1.73191i) q^{24} +(0.927051 + 2.85317i) q^{25} +(4.03499 + 1.31105i) q^{26} +(-3.21383 - 4.08305i) q^{27} +(-2.49376 + 3.43237i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(0.726963 - 2.33913i) q^{30} +(3.23607 - 2.35114i) q^{31} +1.00000 q^{32} +(-4.85410 + 3.52671i) q^{35} +(2.38098 - 1.82509i) q^{36} +(0.618034 - 1.90211i) q^{37} +(2.36034 + 6.95908i) q^{39} +(1.34500 + 0.437016i) q^{40} +(1.85410 + 5.70634i) q^{41} +(-7.34786 + 0.0943431i) q^{42} +8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} +(-0.831254 - 1.14412i) q^{46} +(-9.41498 + 3.05911i) q^{47} +(1.03598 + 1.38807i) q^{48} +(8.89919 + 6.46564i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(-4.03499 + 1.31105i) q^{52} +(4.15627 + 5.72061i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(-1.85410 - 5.70634i) q^{58} +(-10.7600 - 3.49613i) q^{59} +(0.786780 + 2.31969i) q^{60} +(-2.49376 + 3.43237i) q^{61} +(-1.23607 + 3.80423i) q^{62} +(-7.74320 - 10.1016i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.00000 q^{65} -4.00000 q^{67} +(0.726963 - 2.33913i) q^{69} +(1.85410 - 5.70634i) q^{70} +(-4.15627 + 5.72061i) q^{71} +(-0.853491 + 2.87603i) q^{72} +(0.618034 + 1.90211i) q^{74} +(-0.0667106 - 5.19572i) q^{75} +(-6.00000 - 4.24264i) q^{78} +(2.49376 + 3.43237i) q^{79} +(-1.34500 + 0.437016i) q^{80} +(3.21687 + 8.40546i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(5.88909 - 4.39529i) q^{84} +(-4.98752 - 6.86474i) q^{86} +(6.00000 - 8.48528i) q^{87} +5.65685i q^{89} +(-2.40481 + 3.49526i) q^{90} +(5.56231 + 17.1190i) q^{91} +(1.34500 + 0.437016i) q^{92} +(-6.56108 + 2.22535i) q^{93} +(5.81878 - 8.00886i) q^{94} +(-1.65401 - 0.514040i) q^{96} +(-6.47214 + 4.70228i) q^{97} -11.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 8 q^{12} + 4 q^{15} - 2 q^{16} + 2 q^{18} + 48 q^{21} + 2 q^{24} - 6 q^{25} - 10 q^{27} + 12 q^{29} + 4 q^{30} + 8 q^{31} + 8 q^{32} - 12 q^{35}+ \cdots - 88 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 8 * q^12 + 4 * q^15 - 2 * q^16 + 2 * q^18 + 48 * q^21 + 2 * q^24 - 6 * q^25 - 10 * q^27 + 12 * q^29 + 4 * q^30 + 8 * q^31 + 8 * q^32 - 12 * q^35 + 2 * q^36 - 4 * q^37 + 12 * q^39 - 12 * q^41 - 12 * q^42 + 32 * q^45 + 2 * q^48 + 22 * q^49 - 6 * q^50 + 40 * q^54 + 12 * q^58 + 4 * q^60 + 8 * q^62 + 24 * q^63 - 2 * q^64 - 48 * q^65 - 32 * q^67 + 4 * q^69 - 12 * q^70 + 2 * q^72 - 4 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 - 24 * q^83 - 12 * q^84 + 48 * q^87 - 8 * q^90 - 36 * q^91 - 8 * q^93 + 2 * q^96 - 16 * q^97 - 88 * q^98

Introduction

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