LMFDB - Embedded newform 510.2.z.c.53.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(53,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 6, 7]))

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

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

chi := DirichletCharacter("510.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$510 = 2 \cdot 3 \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	510.z (of order $8$ , degree $4$ , 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.16
Character	$\chi$	$=$	510.53
Dual form			510.2.z.c.77.16

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.57925 - 0.711306i) q^{3} -1.00000 q^{4} +(0.396495 + 2.20063i) q^{5} +(-0.711306 - 1.57925i) q^{6} +(-1.80461 - 4.35672i) q^{7} +1.00000i q^{8} +(1.98809 - 2.24667i) q^{9} +(2.20063 - 0.396495i) q^{10} +(-0.688912 + 1.66318i) q^{11} +(-1.57925 + 0.711306i) q^{12} +(3.54409 - 3.54409i) q^{13} +(-4.35672 + 1.80461i) q^{14} +(2.19149 + 3.19333i) q^{15} +1.00000 q^{16} +(-2.12054 - 3.53600i) q^{17} +(-2.24667 - 1.98809i) q^{18} +(2.50785 - 2.50785i) q^{19} +(-0.396495 - 2.20063i) q^{20} +(-5.94891 - 5.59674i) q^{21} +(1.66318 + 0.688912i) q^{22} +(1.64310 - 0.680595i) q^{23} +(0.711306 + 1.57925i) q^{24} +(-4.68558 + 1.74508i) q^{25} +(-3.54409 - 3.54409i) q^{26} +(1.54163 - 4.96220i) q^{27} +(1.80461 + 4.35672i) q^{28} +(2.16978 + 5.23832i) q^{29} +(3.19333 - 2.19149i) q^{30} +(-0.226741 + 0.0939194i) q^{31} -1.00000i q^{32} +(0.0950631 + 3.11661i) q^{33} +(-3.53600 + 2.12054i) q^{34} +(8.87203 - 5.69871i) q^{35} +(-1.98809 + 2.24667i) q^{36} +(-0.215061 + 0.519203i) q^{37} +(-2.50785 - 2.50785i) q^{38} +(3.07608 - 8.11795i) q^{39} +(-2.20063 + 0.396495i) q^{40} +(10.5597 + 4.37395i) q^{41} +(-5.59674 + 5.94891i) q^{42} +3.98590 q^{43} +(0.688912 - 1.66318i) q^{44} +(5.73236 + 3.48426i) q^{45} +(-0.680595 - 1.64310i) q^{46} +(-3.45581 + 3.45581i) q^{47} +(1.57925 - 0.711306i) q^{48} +(-10.7746 + 10.7746i) q^{49} +(1.74508 + 4.68558i) q^{50} +(-5.86405 - 4.07589i) q^{51} +(-3.54409 + 3.54409i) q^{52} -11.3147 q^{53} +(-4.96220 - 1.54163i) q^{54} +(-3.93320 - 0.856600i) q^{55} +(4.35672 - 1.80461i) q^{56} +(2.17668 - 5.74437i) q^{57} +(5.23832 - 2.16978i) q^{58} +(-6.94726 + 6.94726i) q^{59} +(-2.19149 - 3.19333i) q^{60} +(-4.54890 + 10.9820i) q^{61} +(0.0939194 + 0.226741i) q^{62} +(-13.3758 - 4.60718i) q^{63} -1.00000 q^{64} +(9.20445 + 6.39403i) q^{65} +(3.11661 - 0.0950631i) q^{66} +(9.46678 - 9.46678i) q^{67} +(2.12054 + 3.53600i) q^{68} +(2.11076 - 2.24358i) q^{69} +(-5.69871 - 8.87203i) q^{70} +(0.247313 + 0.597066i) q^{71} +(2.24667 + 1.98809i) q^{72} +(-5.67525 + 13.7013i) q^{73} +(0.519203 + 0.215061i) q^{74} +(-6.15844 + 6.08881i) q^{75} +(-2.50785 + 2.50785i) q^{76} +8.48923 q^{77} +(-8.11795 - 3.07608i) q^{78} +(2.72004 - 6.56677i) q^{79} +(0.396495 + 2.20063i) q^{80} +(-1.09501 - 8.93314i) q^{81} +(4.37395 - 10.5597i) q^{82} -0.153600 q^{83} +(5.94891 + 5.59674i) q^{84} +(6.94066 - 6.06854i) q^{85} -3.98590i q^{86} +(7.15268 + 6.72926i) q^{87} +(-1.66318 - 0.688912i) q^{88} +2.45518i q^{89} +(3.48426 - 5.73236i) q^{90} +(-21.8363 - 9.04490i) q^{91} +(-1.64310 + 0.680595i) q^{92} +(-0.291277 + 0.309605i) q^{93} +(3.45581 + 3.45581i) q^{94} +(6.51320 + 4.52451i) q^{95} +(-0.711306 - 1.57925i) q^{96} +(6.26511 + 2.59509i) q^{97} +(10.7746 + 10.7746i) q^{98} +(2.36699 + 4.85430i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{3} - 68 q^{4} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 8 q^{14} + 20 q^{15} + 68 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 8 q^{20} - 32 q^{21} + 8 q^{22} + 4 q^{23}+ \cdots - 44 q^{98}+O(q^{100})$ 68 * q - 4 * q^3 - 68 * q^4 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 8 * q^14 + 20 * q^15 + 68 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 8 * q^20 - 32 * q^21 + 8 * q^22 + 4 * q^23 - 4 * q^24 - 8 * q^25 + 4 * q^26 - 4 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^30 + 8 * q^31 + 12 * q^33 - 12 * q^34 + 36 * q^35 + 4 * q^37 + 4 * q^38 - 44 * q^41 - 12 * q^42 + 24 * q^43 - 4 * q^44 + 56 * q^45 + 8 * q^46 + 12 * q^47 - 4 * q^48 + 44 * q^49 + 20 * q^50 - 60 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 + 32 * q^55 + 8 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 - 20 * q^60 - 24 * q^61 - 4 * q^62 - 32 * q^63 - 68 * q^64 - 16 * q^65 - 24 * q^66 + 4 * q^67 - 8 * q^68 + 104 * q^69 - 8 * q^70 - 24 * q^71 - 4 * q^72 - 64 * q^73 + 24 * q^74 - 4 * q^75 + 4 * q^76 + 24 * q^77 + 8 * q^79 - 8 * q^80 - 92 * q^81 - 32 * q^82 + 24 * q^83 + 32 * q^84 - 16 * q^85 - 36 * q^87 - 8 * q^88 + 24 * q^90 - 100 * q^91 - 4 * q^92 - 60 * q^93 - 12 * q^94 + 4 * q^96 - 8 * q^97 - 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$ .

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.57925	−	0.711306i	0.911783	−	0.410673i
$3$	1.57925	−	0.711306i	0.911783	−	0.410673i
$4$	−1.00000			−0.500000
$5$	0.396495	+	2.20063i	0.177318	+	0.984154i
$5$	0.396495	+	2.20063i	0.177318	+	0.984154i
$6$	−0.711306	−	1.57925i	−0.290389	−	0.644728i
$7$	−1.80461	−	4.35672i	−0.682080	−	1.64669i	−0.760158	−	0.649739i	$-0.774878\pi$
$7$	−1.80461	−	4.35672i	−0.682080	−	1.64669i	0.0780778	−	0.996947i	$-0.475122\pi$
$8$			1.00000i			0.353553i
$9$	1.98809	−	2.24667i	0.662696	−	0.748889i
$10$	2.20063	−	0.396495i	0.695902	−	0.125383i
$11$	−0.688912	+	1.66318i	−0.207715	+	0.501468i	−0.993063	−	0.117587i	$-0.962484\pi$
$11$	−0.688912	+	1.66318i	−0.207715	+	0.501468i	0.785348	+	0.619055i	$0.212484\pi$
$12$	−1.57925	+	0.711306i	−0.455891	+	0.205336i
$13$	3.54409	−	3.54409i	0.982953	−	0.982953i	−0.0169041	−	0.999857i	$-0.505381\pi$
$13$	3.54409	−	3.54409i	0.982953	−	0.982953i	0.999857	+	0.0169041i	$0.00538099\pi$
$14$	−4.35672	+	1.80461i	−1.16438	+	0.482303i
$15$	2.19149	+	3.19333i	0.565840	+	0.824515i
$16$	1.00000			0.250000
$17$	−2.12054	−	3.53600i	−0.514307	−	0.857606i
$17$	−2.12054	−	3.53600i	−0.514307	−	0.857606i
$18$	−2.24667	−	1.98809i	−0.529544	−	0.468597i
$19$	2.50785	−	2.50785i	0.575340	−	0.575340i	−0.358276	−	0.933616i	$-0.616635\pi$
$19$	2.50785	−	2.50785i	0.575340	−	0.575340i	0.933616	+	0.358276i	$0.116635\pi$
$20$	−0.396495	−	2.20063i	−0.0886590	−	0.492077i
$21$	−5.94891	−	5.59674i	−1.29816	−	1.22131i
$22$	1.66318	+	0.688912i	0.354591	+	0.146876i
$23$	1.64310	−	0.680595i	0.342610	−	0.141914i	−0.204742	−	0.978816i	$-0.565636\pi$
$23$	1.64310	−	0.680595i	0.342610	−	0.141914i	0.547353	+	0.836902i	$0.315636\pi$
$24$	0.711306	+	1.57925i	0.145195	+	0.322364i
$25$	−4.68558	+	1.74508i	−0.937117	+	0.349016i
$26$	−3.54409	−	3.54409i	−0.695053	−	0.695053i
$27$	1.54163	−	4.96220i	0.296687	−	0.954975i
$28$	1.80461	+	4.35672i	0.341040	+	0.823343i
$29$	2.16978	+	5.23832i	0.402918	+	0.972731i	0.986954	+	0.161003i	$0.0514729\pi$
$29$	2.16978	+	5.23832i	0.402918	+	0.972731i	−0.584036	+	0.811728i	$0.698527\pi$
$30$	3.19333	−	2.19149i	0.583020	−	0.400110i
$31$	−0.226741	+	0.0939194i	−0.0407240	+	0.0168684i	−0.402952	−	0.915221i	$-0.632016\pi$
$31$	−0.226741	+	0.0939194i	−0.0407240	+	0.0168684i	0.362228	+	0.932089i	$0.382016\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.0950631	+	3.11661i	0.0165484	+	0.542532i
$34$	−3.53600	+	2.12054i	−0.606419	+	0.363670i
$35$	8.87203	−	5.69871i	1.49965	−	0.963258i
$36$	−1.98809	+	2.24667i	−0.331348	+	0.374444i
$37$	−0.215061	+	0.519203i	−0.0353558	+	0.0853565i	−0.940571	−	0.339597i	$-0.889709\pi$
$37$	−0.215061	+	0.519203i	−0.0353558	+	0.0853565i	0.905215	+	0.424953i	$0.139709\pi$
$38$	−2.50785	−	2.50785i	−0.406826	−	0.406826i
$39$	3.07608	−	8.11795i	0.492568	−	1.29991i
$40$	−2.20063	+	0.396495i	−0.347951	+	0.0626914i
$41$	10.5597	+	4.37395i	1.64914	+	0.683097i	0.997172	−	0.0751490i	$-0.0239432\pi$
$41$	10.5597	+	4.37395i	1.64914	+	0.683097i	0.651969	+	0.758246i	$0.273943\pi$
$42$	−5.59674	+	5.94891i	−0.863596	+	0.917936i
$43$	3.98590			0.607843			0.303922	−	0.952697i	$-0.401704\pi$
$43$	3.98590			0.607843			0.303922	+	0.952697i	$0.401704\pi$
$44$	0.688912	−	1.66318i	0.103857	−	0.250734i
$45$	5.73236	+	3.48426i	0.854529	+	0.519403i
$46$	−0.680595	−	1.64310i	−0.100348	−	0.242262i
$47$	−3.45581	+	3.45581i	−0.504081	+	0.504081i	−0.912704	−	0.408622i	$-0.866009\pi$
$47$	−3.45581	+	3.45581i	−0.504081	+	0.504081i	0.408622	+	0.912704i	$0.366009\pi$
$48$	1.57925	−	0.711306i	0.227946	−	0.102668i
$49$	−10.7746	+	10.7746i	−1.53924	+	1.53924i
$50$	1.74508	+	4.68558i	0.246792	+	0.662642i
$51$	−5.86405	−	4.07589i	−0.821131	−	0.570739i
$52$	−3.54409	+	3.54409i	−0.491477	+	0.491477i
$53$	−11.3147			−1.55419			−0.777097	−	0.629381i	$-0.783309\pi$
$53$	−11.3147			−1.55419			−0.777097	+	0.629381i	$0.783309\pi$
$54$	−4.96220	−	1.54163i	−0.675269	−	0.209789i
$55$	−3.93320	−	0.856600i	−0.530353	−	0.115504i
$56$	4.35672	−	1.80461i	0.582191	−	0.241152i
$57$	2.17668	−	5.74437i	0.288308	−	0.760861i
$58$	5.23832	−	2.16978i	0.687825	−	0.284906i
$59$	−6.94726	+	6.94726i	−0.904456	+	0.904456i	−0.995818	−	0.0913616i	$-0.970878\pi$
$59$	−6.94726	+	6.94726i	−0.904456	+	0.904456i	0.0913616	+	0.995818i	$0.470878\pi$
$60$	−2.19149	−	3.19333i	−0.282920	−	0.412257i
$61$	−4.54890	+	10.9820i	−0.582427	+	1.40610i	0.308179	+	0.951328i	$0.400280\pi$
$61$	−4.54890	+	10.9820i	−0.582427	+	1.40610i	−0.890606	+	0.454775i	$0.849720\pi$
$62$	0.0939194	+	0.226741i	0.0119278	+	0.0287962i
$63$	−13.3758	−	4.60718i	−1.68520	−	0.580450i
$64$	−1.00000			−0.125000
$65$	9.20445	+	6.39403i	1.14167	+	0.793082i
$66$	3.11661	−	0.0950631i	0.383628	−	0.0117015i
$67$	9.46678	−	9.46678i	1.15655	−	1.15655i	0.171340	−	0.985212i	$-0.445190\pi$
$67$	9.46678	−	9.46678i	1.15655	−	1.15655i	0.985212	−	0.171340i	$-0.0548096\pi$
$68$	2.12054	+	3.53600i	0.257153	+	0.428803i
$69$	2.11076	−	2.24358i	0.254106	−	0.270095i
$70$	−5.69871	−	8.87203i	−0.681126	−	1.06041i
$71$	0.247313	+	0.597066i	0.0293506	+	0.0708587i	0.937875	−	0.346973i	$-0.112790\pi$
$71$	0.247313	+	0.597066i	0.0293506	+	0.0708587i	−0.908525	+	0.417831i	$0.862790\pi$
$72$	2.24667	+	1.98809i	0.264772	+	0.234298i
$73$	−5.67525	+	13.7013i	−0.664237	+	1.60361i	0.126860	+	0.991921i	$0.459510\pi$
$73$	−5.67525	+	13.7013i	−0.664237	+	1.60361i	−0.791098	+	0.611690i	$0.790490\pi$
$74$	0.519203	+	0.215061i	0.0603562	+	0.0250003i
$75$	−6.15844	+	6.08881i	−0.711115	+	0.703075i
$76$	−2.50785	+	2.50785i	−0.287670	+	0.287670i
$77$	8.48923			0.967438
$78$	−8.11795	−	3.07608i	−0.919176	−	0.348298i
$79$	2.72004	−	6.56677i	0.306029	−	0.738819i	−0.693797	−	0.720170i	$-0.744064\pi$
$79$	2.72004	−	6.56677i	0.306029	−	0.738819i	0.999826	−	0.0186487i	$-0.00593640\pi$
$80$	0.396495	+	2.20063i	0.0443295	+	0.246038i
$81$	−1.09501	−	8.93314i	−0.121668	−	0.992571i
$82$	4.37395	−	10.5597i	0.483022	−	1.16612i
$83$	−0.153600			−0.0168598			−0.00842990	−	0.999964i	$-0.502683\pi$
$83$	−0.153600			−0.0168598			−0.00842990	+	0.999964i	$0.502683\pi$
$84$	5.94891	+	5.59674i	0.649079	+	0.610654i
$85$	6.94066	−	6.06854i	0.752821	−	0.658226i
$86$		−	3.98590i		−	0.429810i
$87$	7.15268	+	6.72926i	0.766848	+	0.721452i
$88$	−1.66318	−	0.688912i	−0.177296	−	0.0734382i
$89$			2.45518i			0.260248i	0.991498	+	0.130124i	$0.0415376\pi$
$89$			2.45518i			0.260248i	−0.991498	+	0.130124i	$0.958462\pi$
$90$	3.48426	−	5.73236i	0.367274	−	0.604243i
$91$	−21.8363	−	9.04490i	−2.28907	−	0.948163i
$92$	−1.64310	+	0.680595i	−0.171305	+	0.0709569i
$93$	−0.291277	+	0.309605i	−0.0302040	+	0.0321046i
$94$	3.45581	+	3.45581i	0.356439	+	0.356439i
$95$	6.51320	+	4.52451i	0.668241	+	0.464204i
$96$	−0.711306	−	1.57925i	−0.0725974	−	0.161182i
$97$	6.26511	+	2.59509i	0.636125	+	0.263492i	0.677353	−	0.735658i	$-0.263127\pi$
$97$	6.26511	+	2.59509i	0.636125	+	0.263492i	−0.0412280	+	0.999150i	$0.513127\pi$
$98$	10.7746	+	10.7746i	1.08840	+	1.08840i
$99$	2.36699	+	4.85430i	0.237892	+	0.487876i
$100$	4.68558	−	1.74508i	0.468558	−	0.174508i
$101$		−	5.10513i		−	0.507980i	−0.967207	−	0.253990i	$-0.918257\pi$
$101$		−	5.10513i		−	0.507980i	0.967207	−	0.253990i	$-0.0817430\pi$
$102$	−4.07589	+	5.86405i	−0.403574	+	0.580628i
$103$	9.30742	+	9.30742i	0.917087	+	0.917087i	0.996817	−	0.0797292i	$-0.0254056\pi$
$103$	9.30742	+	9.30742i	0.917087	+	0.917087i	−0.0797292	+	0.996817i	$0.525406\pi$
$104$	3.54409	+	3.54409i	0.347526	+	0.347526i
$105$	9.95767	−	15.3104i	0.971769	−	1.49415i
$106$			11.3147i			1.09898i
$107$	1.44561	−	3.49002i	0.139753	−	0.337393i	−0.838471	−	0.544946i	$-0.816550\pi$
$107$	1.44561	−	3.49002i	0.139753	−	0.337393i	0.978224	+	0.207553i	$0.0665501\pi$
$108$	−1.54163	+	4.96220i	−0.148343	+	0.477487i
$109$	1.76725	+	0.732020i	0.169272	+	0.0701148i	0.465710	−	0.884937i	$-0.345799\pi$
$109$	1.76725	+	0.732020i	0.169272	+	0.0701148i	−0.296438	+	0.955052i	$0.595799\pi$
$110$	−0.856600	+	3.93320i	−0.0816736	+	0.375016i
$111$	0.0296763	+	0.972928i	0.00281675	+	0.0923463i
$112$	−1.80461	−	4.35672i	−0.170520	−	0.411672i
$113$	−0.503618	+	0.208605i	−0.0473764	+	0.0196240i	−0.406246	−	0.913764i	$-0.633162\pi$
$113$	−0.503618	+	0.208605i	−0.0473764	+	0.0196240i	0.358869	+	0.933388i	$0.383162\pi$
$114$	−5.74437	−	2.17668i	−0.538010	−	0.203865i
$115$	2.14922	+	3.34601i	0.200416	+	0.312017i
$116$	−2.16978	−	5.23832i	−0.201459	−	0.486366i
$117$	−0.916423	−	15.0083i	−0.0847234	−	1.38752i
$118$	6.94726	+	6.94726i	0.639547	+	0.639547i
$119$	−11.5786	+	15.6197i	−1.06141	+	1.43186i
$120$	−3.19333	+	2.19149i	−0.291510	+	0.200055i
$121$	5.48661	+	5.48661i	0.498782	+	0.498782i
$122$	10.9820	+	4.54890i	0.994266	+	0.411838i
$123$	19.7876	−	0.603563i	1.78419	−	0.0544214i
$124$	0.226741	−	0.0939194i	0.0203620	−	0.00843421i
$125$	−5.69810	−	9.61934i	−0.509653	−	0.860380i
$126$	−4.60718	+	13.3758i	−0.410440	+	1.19161i
$127$			13.8656i			1.23037i	0.788383	+	0.615185i	$0.210919\pi$
$127$			13.8656i			1.23037i	−0.788383	+	0.615185i	$0.789081\pi$
$128$			1.00000i			0.0883883i
$129$	6.29474	−	2.83519i	0.554221	−	0.249625i
$130$	6.39403	−	9.20445i	0.560793	−	0.807284i
$131$	14.0591	−	5.82346i	1.22835	−	0.508798i	0.328293	−	0.944576i	$-0.393527\pi$
$131$	14.0591	−	5.82346i	1.22835	−	0.508798i	0.900054	+	0.435778i	$0.143527\pi$
$132$	−0.0950631	−	3.11661i	−0.00827418	−	0.271266i
$133$	−15.4517	−	6.40030i	−1.33983	−	0.554976i
$134$	−9.46678	−	9.46678i	−0.817806	−	0.817806i
$135$	11.5312	+	1.42508i	0.992450	+	0.122651i
$136$	3.53600	−	2.12054i	0.303210	−	0.181835i
$137$	5.81893	+	5.81893i	0.497145	+	0.497145i	0.910548	−	0.413403i	$-0.135660\pi$
$137$	5.81893	+	5.81893i	0.497145	+	0.497145i	−0.413403	+	0.910548i	$0.635660\pi$
$138$	−2.24358	−	2.11076i	−0.190986	−	0.179680i
$139$	−0.247325	−	0.597095i	−0.0209778	−	0.0506450i	0.913044	−	0.407862i	$-0.133726\pi$
$139$	−0.247325	−	0.597095i	−0.0209778	−	0.0506450i	−0.934021	+	0.357217i	$0.883726\pi$
$140$	−8.87203	+	5.69871i	−0.749824	+	0.481629i
$141$	−2.99946	+	7.91573i	−0.252600	+	0.666625i
$142$	0.597066	−	0.247313i	0.0501046	−	0.0207540i
$143$	3.45289	+	8.33602i	0.288745	+	0.697093i
$144$	1.98809	−	2.24667i	0.165674	−	0.187222i
$145$	−10.6673	+	6.85186i	−0.885872	+	0.569016i
$146$	13.7013	+	5.67525i	1.13392	+	0.469687i
$147$	−9.35184	+	24.6800i	−0.771327	+	2.03557i
$148$	0.215061	−	0.519203i	0.0176779	−	0.0426782i
$149$		−	6.12063i		−	0.501422i	−0.968062	−	0.250711i	$-0.919336\pi$
$149$		−	6.12063i		−	0.501422i	0.968062	−	0.250711i	$-0.0806643\pi$
$150$	6.08881	+	6.15844i	0.497149	+	0.502835i
$151$	−12.3630	−	12.3630i	−1.00609	−	1.00609i	−0.999981	−	0.00610518i	$-0.998057\pi$
$151$	−12.3630	−	12.3630i	−1.00609	−	1.00609i	−0.00610518	−	0.999981i	$-0.501943\pi$
$152$	2.50785	+	2.50785i	0.203413	+	0.203413i
$153$	−12.1600	−	2.26574i	−0.983081	−	0.183174i
$154$		−	8.48923i		−	0.684082i
$155$	−0.296584	−	0.461736i	−0.0238222	−	0.0370876i
$156$	−3.07608	+	8.11795i	−0.246284	+	0.649956i
$157$	−1.29489	−	1.29489i	−0.103344	−	0.103344i	0.653544	−	0.756888i	$-0.273281\pi$
$157$	−1.29489	−	1.29489i	−0.103344	−	0.103344i	−0.756888	+	0.653544i	$0.773281\pi$
$158$	−6.56677	−	2.72004i	−0.522424	−	0.216395i
$159$	−17.8688	+	8.04822i	−1.41709	+	0.638265i
$160$	2.20063	−	0.396495i	0.173975	−	0.0313457i
$161$	−5.93032	−	5.93032i	−0.467375	−	0.467375i
$162$	−8.93314	+	1.09501i	−0.701854	+	0.0860325i
$163$	13.2094	−	5.47150i	1.03464	−	0.428561i	0.200253	−	0.979744i	$-0.435824\pi$
$163$	13.2094	−	5.47150i	1.03464	−	0.428561i	0.834384	+	0.551183i	$0.185824\pi$
$164$	−10.5597	−	4.37395i	−0.824571	−	0.341548i
$165$	−6.82083	+	1.44492i	−0.531001	+	0.112487i
$166$			0.153600i			0.0119217i
$167$	−0.937606	−	0.388369i	−0.0725541	−	0.0300529i	0.346111	−	0.938193i	$-0.387502\pi$
$167$	−0.937606	−	0.388369i	−0.0725541	−	0.0300529i	−0.418665	+	0.908141i	$0.637502\pi$
$168$	5.59674	−	5.94891i	0.431798	−	0.458968i
$169$		−	12.1211i		−	0.932393i
$170$	−6.06854	−	6.94066i	−0.465436	−	0.532325i
$171$	−0.648474	−	10.6201i	−0.0495901	−	0.812140i
$172$	−3.98590			−0.303922
$173$	−3.20143	+	7.72893i	−0.243400	+	0.587620i	−0.997616	−	0.0690063i	$-0.978017\pi$
$173$	−3.20143	+	7.72893i	−0.243400	+	0.587620i	0.754216	+	0.656626i	$0.228017\pi$
$174$	6.72926	−	7.15268i	0.510144	−	0.542244i
$175$	16.0585	+	17.2646i	1.21391	+	1.30508i
$176$	−0.688912	+	1.66318i	−0.0519287	+	0.125367i
$177$	−6.02986	+	15.9131i	−0.453232	+	1.19610i
$178$	2.45518			0.184023
$179$	13.6209	−	13.6209i	1.01807	−	1.01807i	0.0182368	−	0.999834i	$-0.494195\pi$
$179$	13.6209	−	13.6209i	1.01807	−	1.01807i	0.999834	−	0.0182368i	$-0.00580526\pi$
$180$	−5.73236	−	3.48426i	−0.427265	−	0.259702i
$181$	−13.8816	−	5.74993i	−1.03181	−	0.427389i	−0.198443	−	0.980112i	$-0.563589\pi$
$181$	−13.8816	−	5.74993i	−1.03181	−	0.427389i	−0.833365	+	0.552723i	$0.813589\pi$
$182$	−9.04490	+	21.8363i	−0.670452	+	1.61862i
$183$	0.627704	+	20.5791i	0.0464012	+	1.52125i
$184$	0.680595	+	1.64310i	0.0501741	+	0.121131i
$185$	−1.22785	−	0.267409i	−0.0902731	−	0.0196603i
$186$	0.309605	+	0.291277i	0.0227013	+	0.0213575i
$187$	7.34187	−	1.09085i	0.536891	−	0.0797707i
$188$	3.45581	−	3.45581i	0.252041	−	0.252041i
$189$	−24.4009	+	2.23839i	−1.77491	+	0.162819i
$190$	4.52451	−	6.51320i	0.328242	−	0.472517i
$191$	−14.5916			−1.05581			−0.527904	−	0.849304i	$-0.677022\pi$
$191$	−14.5916			−1.05581			−0.527904	+	0.849304i	$0.677022\pi$
$192$	−1.57925	+	0.711306i	−0.113973	+	0.0513341i
$193$	6.68863	+	16.1478i	0.481458	+	1.16234i	0.958917	+	0.283688i	$0.0915581\pi$
$193$	6.68863	+	16.1478i	0.481458	+	1.16234i	−0.477459	+	0.878654i	$0.658442\pi$
$194$	2.59509	−	6.26511i	0.186317	−	0.449808i
$195$	19.0843	+	3.55061i	1.36665	+	0.254265i
$196$	10.7746	−	10.7746i	0.769618	−	0.769618i
$197$	4.28102	−	1.77326i	0.305010	−	0.126339i	−0.224929	−	0.974375i	$-0.572215\pi$
$197$	4.28102	−	1.77326i	0.305010	−	0.126339i	0.529939	+	0.848036i	$0.322215\pi$
$198$	4.85430	−	2.36699i	0.344980	−	0.168215i
$199$	8.69686	−	3.60236i	0.616504	−	0.255364i	−0.0525026	−	0.998621i	$-0.516720\pi$
$199$	8.69686	−	3.60236i	0.616504	−	0.255364i	0.669007	+	0.743256i	$0.266720\pi$
$200$	−1.74508	−	4.68558i	−0.123396	−	0.331321i
$201$	8.21668	−	21.6842i	0.579560	−	1.52949i
$202$	−5.10513			−0.359196
$203$	18.9063	−	18.9063i	1.32696	−	1.32696i
$204$	5.86405	+	4.07589i	0.410566	+	0.285370i
$205$	−5.43862	+	24.9722i	−0.379850	+	1.74413i
$206$	9.30742	−	9.30742i	0.648479	−	0.648479i
$207$	1.73756	−	5.04458i	0.120769	−	0.350623i
$208$	3.54409	−	3.54409i	0.245738	−	0.245738i
$209$	2.44332	+	5.89868i	0.169008	+	0.408021i
$210$	−15.3104	−	9.95767i	−1.05652	−	0.687144i
$211$	−6.57236	+	15.8671i	−0.452460	+	1.09234i	0.518924	+	0.854820i	$0.326333\pi$
$211$	−6.57236	+	15.8671i	−0.452460	+	1.09234i	−0.971384	+	0.237515i	$0.923667\pi$
$212$	11.3147			0.777097
$213$	0.815266	+	0.767004i	0.0558611	+	0.0525542i
$214$	−3.49002	−	1.44561i	−0.238573	−	0.0988201i
$215$	1.58039	+	8.77150i	0.107782	+	0.598211i
$216$	4.96220	+	1.54163i	0.337635	+	0.104895i
$217$	0.818361	+	0.818361i	0.0555540	+	0.0555540i
$218$	0.732020	−	1.76725i	0.0495787	−	0.119694i
$219$	0.783128	+	25.6746i	0.0529189	+	1.73493i
$220$	3.93320	+	0.856600i	0.265176	+	0.0577520i
$221$	−20.0473	−	5.01652i	−1.34853	−	0.337448i
$222$	0.972928	−	0.0296763i	0.0652987	−	0.00199174i
$223$		−	22.4751i		−	1.50505i	−0.658565	−	0.752524i	$-0.728836\pi$
$223$		−	22.4751i		−	1.50505i	0.658565	−	0.752524i	$-0.271164\pi$
$224$	−4.35672	+	1.80461i	−0.291096	+	0.120576i
$225$	−5.39474	+	13.9963i	−0.359649	+	0.933088i
$226$	0.208605	+	0.503618i	0.0138762	+	0.0335002i
$227$	0.129873	+	0.313542i	0.00862000	+	0.0208105i	0.928131	−	0.372254i	$-0.121415\pi$
$227$	0.129873	+	0.313542i	0.00862000	+	0.0208105i	−0.919511	+	0.393064i	$0.871415\pi$
$228$	−2.17668	+	5.74437i	−0.144154	+	0.380430i
$229$	−3.02183	−	3.02183i	−0.199688	−	0.199688i	0.600178	−	0.799866i	$-0.295096\pi$
$229$	−3.02183	−	3.02183i	−0.199688	−	0.199688i	−0.799866	+	0.600178i	$0.795096\pi$
$230$	3.34601	−	2.14922i	0.220630	−	0.141715i
$231$	13.4067	−	6.03844i	0.882093	−	0.397300i
$232$	−5.23832	+	2.16978i	−0.343912	+	0.142453i
$233$	−11.5367	−	4.77864i	−0.755791	−	0.313059i	−0.0286893	−	0.999588i	$-0.509133\pi$
$233$	−11.5367	−	4.77864i	−0.755791	−	0.313059i	−0.727102	+	0.686529i	$0.759133\pi$
$234$	−15.0083	+	0.916423i	−0.981126	+	0.0599085i
$235$	−8.97518	−	6.23476i	−0.585476	−	0.406711i
$236$	6.94726	−	6.94726i	0.452228	−	0.452228i
$237$	−0.375340	−	12.3054i	−0.0243809	−	0.799320i
$238$	15.6197	+	11.5786i	1.01248	+	0.750531i
$239$	−12.7713			−0.826109			−0.413054	−	0.910706i	$-0.635538\pi$
$239$	−12.7713			−0.826109			−0.413054	+	0.910706i	$0.635538\pi$
$240$	2.19149	+	3.19333i	0.141460	+	0.206129i
$241$	23.4226	−	9.70195i	1.50878	−	0.624958i	0.533475	−	0.845816i	$-0.320886\pi$
$241$	23.4226	−	9.70195i	1.50878	−	0.624958i	0.975306	+	0.220858i	$0.0708857\pi$
$242$	5.48661	−	5.48661i	0.352692	−	0.352692i
$243$	−8.08350	−	13.3288i	−0.518557	−	0.855043i
$244$	4.54890	−	10.9820i	0.291214	−	0.703052i
$245$	−27.9832	−	19.4390i	−1.78778	−	1.24191i
$246$	−0.603563	−	19.7876i	−0.0384818	−	1.26161i
$247$		−	17.7761i		−	1.13106i
$248$	−0.0939194	−	0.226741i	−0.00596389	−	0.0143981i
$249$	−0.242574	+	0.109257i	−0.0153725	+	0.00692386i
$250$	−9.61934	+	5.69810i	−0.608380	+	0.360379i
$251$	−1.40103			−0.0884321			−0.0442161	−	0.999022i	$-0.514079\pi$
$251$	−1.40103			−0.0884321			−0.0442161	+	0.999022i	$0.514079\pi$
$252$	13.3758	+	4.60718i	0.842598	+	0.290225i
$253$			3.20164i			0.201286i
$254$	13.8656			0.870003
$255$	6.64448	−	14.5207i	0.416094	−	0.909322i
$256$	1.00000			0.0625000
$257$			8.61957i			0.537674i	0.963186	+	0.268837i	$0.0866393\pi$
$257$			8.61957i			0.537674i	−0.963186	+	0.268837i	$0.913361\pi$
$258$	−2.83519	−	6.29474i	−0.176511	−	0.391894i
$259$	2.65013			0.164671
$260$	−9.20445	−	6.39403i	−0.570836	−	0.396541i
$261$	16.0825	+	5.53946i	0.995480	+	0.342884i
$262$	−5.82346	−	14.0591i	−0.359774	−	0.868572i
$263$			9.63543i			0.594146i	0.954855	+	0.297073i	$0.0960104\pi$
$263$			9.63543i			0.594146i	−0.954855	+	0.297073i	$0.903990\pi$
$264$	−3.11661	+	0.0950631i	−0.191814	+	0.00585073i
$265$	−4.48622	−	24.8995i	−0.275587	−	1.52957i
$266$	−6.40030	+	15.4517i	−0.392427	+	0.947404i
$267$	1.74638	+	3.87735i	0.106877	+	0.237290i
$268$	−9.46678	+	9.46678i	−0.578276	+	0.578276i
$269$	−13.2764	+	5.49928i	−0.809478	+	0.335297i	−0.748746	−	0.662857i	$-0.769344\pi$
$269$	−13.2764	+	5.49928i	−0.809478	+	0.335297i	−0.0607325	+	0.998154i	$0.519344\pi$
$270$	1.42508	−	11.5312i	0.0867274	−	0.701768i
$271$	−11.0494			−0.671202			−0.335601	−	0.942004i	$-0.608939\pi$
$271$	−11.0494			−0.671202			−0.335601	+	0.942004i	$0.608939\pi$
$272$	−2.12054	−	3.53600i	−0.128577	−	0.214402i
$273$	−40.9188	+	1.24811i	−2.47652	+	0.0755389i
$274$	5.81893	−	5.81893i	0.351534	−	0.351534i
$275$	0.325569	−	8.99517i	0.0196326	−	0.542429i
$276$	−2.11076	+	2.24358i	−0.127053	+	0.135048i
$277$	2.34448	+	0.971115i	0.140866	+	0.0583486i	0.452003	−	0.892017i	$-0.350710\pi$
$277$	2.34448	+	0.971115i	0.140866	+	0.0583486i	−0.311137	+	0.950365i	$0.600710\pi$
$278$	−0.597095	+	0.247325i	−0.0358114	+	0.0148336i
$279$	−0.239776	+	0.696132i	−0.0143550	+	0.0416763i
$280$	5.69871	+	8.87203i	0.340563	+	0.530205i
$281$	−0.485574	−	0.485574i	−0.0289669	−	0.0289669i	0.692475	−	0.721442i	$-0.256520\pi$
$281$	−0.485574	−	0.485574i	−0.0289669	−	0.0289669i	−0.721442	+	0.692475i	$0.756520\pi$
$282$	7.91573	+	2.99946i	0.471375	+	0.178615i
$283$	−0.602379	−	1.45427i	−0.0358077	−	0.0864474i	0.904964	−	0.425488i	$-0.139898\pi$
$283$	−0.602379	−	1.45427i	−0.0358077	−	0.0864474i	−0.940772	+	0.339041i	$0.889898\pi$
$284$	−0.247313	−	0.597066i	−0.0146753	−	0.0354293i
$285$	13.5043	+	2.51246i	0.799926	+	0.148826i
$286$	8.33602	−	3.45289i	0.492919	−	0.204174i
$287$		−	53.8988i		−	3.18154i
$288$	−2.24667	−	1.98809i	−0.132386	−	0.117149i
$289$	−8.00662	+	14.9965i	−0.470977	+	0.882145i
$290$	6.85186	+	10.6673i	0.402355	+	0.626406i
$291$	11.7401	−	0.358097i	0.688217	−	0.0209920i
$292$	5.67525	−	13.7013i	0.332119	−	0.801805i
$293$	−15.6880	−	15.6880i	−0.916505	−	0.916505i	0.0802686	−	0.996773i	$-0.474422\pi$
$293$	−15.6880	−	15.6880i	−0.916505	−	0.916505i	−0.996773	+	0.0802686i	$0.974422\pi$
$294$	24.6800	+	9.35184i	1.43937	+	0.545410i
$295$	−18.0429	−	12.5338i	−1.05050	−	0.729748i
$296$	−0.519203	−	0.215061i	−0.0301781	−	0.0125002i
$297$	7.19098	+	5.98252i	0.417263	+	0.347141i
$298$	−6.12063			−0.354559
$299$	3.41121	−	8.23538i	0.197275	−	0.476264i
$300$	6.15844	−	6.08881i	0.355558	−	0.351538i
$301$	−7.19300	−	17.3654i	−0.414598	−	1.00093i
$302$	−12.3630	+	12.3630i	−0.711411	+	0.711411i
$303$	−3.63131	−	8.06230i	−0.208613	−	0.463167i
$304$	2.50785	−	2.50785i	0.143835	−	0.143835i
$305$	−25.9710	−	5.65615i	−1.48710	−	0.323870i
$306$	−2.26574	+	12.1600i	−0.129523	+	0.695143i
$307$	−8.38184	+	8.38184i	−0.478377	+	0.478377i	−0.904612	−	0.426235i	$-0.859840\pi$
$307$	−8.38184	+	8.38184i	−0.478377	+	0.478377i	0.426235	+	0.904612i	$0.359840\pi$
$308$	−8.48923			−0.483719
$309$	21.3192	+	8.07836i	1.21281	+	0.459562i
$310$	−0.461736	+	0.296584i	−0.0262249	+	0.0168448i
$311$	−24.7850	+	10.2663i	−1.40543	+	0.582149i	−0.951155	−	0.308713i	$-0.900102\pi$
$311$	−24.7850	+	10.2663i	−1.40543	+	0.582149i	−0.454276	+	0.890861i	$0.650102\pi$
$312$	8.11795	+	3.07608i	0.459588	+	0.174149i
$313$	0.145636	−	0.0603242i	0.00823181	−	0.00340973i	−0.378564	−	0.925575i	$-0.623582\pi$
$313$	0.145636	−	0.0603242i	0.00823181	−	0.00340973i	0.386796	+	0.922166i	$0.373582\pi$
$314$	−1.29489	+	1.29489i	−0.0730751	+	0.0730751i
$315$	4.83527	−	31.2620i	0.272437	−	1.76142i
$316$	−2.72004	+	6.56677i	−0.153014	+	0.369410i
$317$	−3.32277	−	8.02188i	−0.186625	−	0.450554i	0.802680	−	0.596409i	$-0.203406\pi$
$317$	−3.32277	−	8.02188i	−0.186625	−	0.450554i	−0.989306	+	0.145856i	$0.953406\pi$
$318$	8.04822	+	17.8688i	0.451322	+	1.00203i
$319$	−10.2071			−0.571485
$320$	−0.396495	−	2.20063i	−0.0221647	−	0.123019i
$321$	−0.199481	−	6.53990i	−0.0111339	−	0.365022i
$322$	−5.93032	+	5.93032i	−0.330484	+	0.330484i
$323$	−14.1857	−	3.54976i	−0.789316	−	0.197514i
$324$	1.09501	+	8.93314i	0.0608341	+	0.496285i
$325$	−10.4214	+	22.7908i	−0.578075	+	1.26421i
$326$	−5.47150	−	13.2094i	−0.303038	−	0.731599i
$327$	3.31163	−	0.101012i	0.183134	−	0.00558596i
$328$	−4.37395	+	10.5597i	−0.241511	+	0.583059i
$329$	21.2924	+	8.81959i	1.17389	+	0.486240i
$330$	1.44492	+	6.82083i	0.0795402	+	0.375474i
$331$	−0.572853	+	0.572853i	−0.0314869	+	0.0314869i	−0.722675	−	0.691188i	$-0.757088\pi$
$331$	−0.572853	+	0.572853i	−0.0314869	+	0.0314869i	0.691188	+	0.722675i	$0.257088\pi$
$332$	0.153600			0.00842990
$333$	0.738916	+	1.51539i	0.0404924	+	0.0830430i
$334$	−0.388369	+	0.937606i	−0.0212506	+	0.0513035i
$335$	24.5865	+	17.0794i	1.34330	+	0.933147i
$336$	−5.94891	−	5.59674i	−0.324539	−	0.305327i
$337$	0.925645	−	2.23470i	0.0504231	−	0.121732i	−0.896661	−	0.442718i	$-0.854014\pi$
$337$	0.925645	−	2.23470i	0.0504231	−	0.121732i	0.947084	+	0.320986i	$0.104014\pi$
$338$	−12.1211			−0.659302
$339$	−0.646959	+	0.687668i	−0.0351380	+	0.0373490i
$340$	−6.94066	+	6.06854i	−0.376410	+	0.329113i
$341$		−	0.441814i		−	0.0239256i
$342$	−10.6201	+	0.648474i	−0.574270	+	0.0350655i
$343$	35.8892	+	14.8658i	1.93783	+	0.802677i
$344$			3.98590i			0.214905i
$345$	5.77421	+	3.75545i	0.310873	+	0.202187i
$346$	7.72893	+	3.20143i	0.415510	+	0.172110i
$347$	−17.4123	+	7.21240i	−0.934739	+	0.387182i	−0.797475	−	0.603353i	$-0.793831\pi$
$347$	−17.4123	+	7.21240i	−0.934739	+	0.387182i	−0.137265	+	0.990534i	$0.543831\pi$
$348$	−7.15268	−	6.72926i	−0.383424	−	0.360726i
$349$	9.66879	+	9.66879i	0.517559	+	0.517559i	0.916832	−	0.399273i	$-0.130738\pi$
$349$	9.66879	+	9.66879i	0.517559	+	0.517559i	−0.399273	+	0.916832i	$0.630738\pi$
$350$	17.2646	−	16.0585i	0.922831	−	0.858363i
$351$	−12.1228	−	23.0501i	−0.647066	−	1.23032i
$352$	1.66318	+	0.688912i	0.0886478	+	0.0367191i
$353$	−13.3809	−	13.3809i	−0.712195	−	0.712195i	0.254799	−	0.966994i	$-0.417991\pi$
$353$	−13.3809	−	13.3809i	−0.712195	−	0.712195i	−0.966994	+	0.254799i	$0.917991\pi$
$354$	15.9131	+	6.02986i	0.845773	+	0.320484i
$355$	−1.21587	+	0.780978i	−0.0645314	+	0.0414500i
$356$		−	2.45518i		−	0.130124i
$357$	−7.17519	+	32.9035i	−0.379751	+	1.74144i
$358$	−13.6209	−	13.6209i	−0.719885	−	0.719885i
$359$	16.8764	+	16.8764i	0.890705	+	0.890705i	0.994589	−	0.103885i	$-0.0331273\pi$
$359$	16.8764	+	16.8764i	0.890705	+	0.890705i	−0.103885	+	0.994589i	$0.533127\pi$
$360$	−3.48426	+	5.73236i	−0.183637	+	0.302122i
$361$			6.42141i			0.337969i
$362$	−5.74993	+	13.8816i	−0.302210	+	0.729599i
$363$	12.5674	+	4.76209i	0.659618	+	0.249945i
$364$	21.8363	+	9.04490i	1.14453	+	0.474081i
$365$	−32.4017	−	7.05666i	−1.69598	−	0.369363i
$366$	20.5791	−	0.627704i	1.07569	−	0.0328106i
$367$	1.02966	+	2.48582i	0.0537479	+	0.129759i	0.948473	−	0.316859i	$-0.102628\pi$
$367$	1.02966	+	2.48582i	0.0537479	+	0.129759i	−0.894725	+	0.446618i	$0.852628\pi$
$368$	1.64310	−	0.680595i	0.0856526	−	0.0354785i
$369$	30.8203	−	15.0282i	1.60444	−	0.782338i
$370$	−0.267409	+	1.22785i	−0.0139019	+	0.0638327i
$371$	20.4187	+	49.2950i	1.06008	+	2.55927i
$372$	0.291277	−	0.309605i	0.0151020	−	0.0160523i
$373$	−1.09741	−	1.09741i	−0.0568215	−	0.0568215i	0.678125	−	0.734947i	$-0.262793\pi$
$373$	−1.09741	−	1.09741i	−0.0568215	−	0.0568215i	−0.734947	+	0.678125i	$0.762793\pi$
$374$	−1.09085	−	7.34187i	−0.0564064	−	0.379639i
$375$	−15.8410	−	11.1383i	−0.818028	−	0.575179i
$376$	−3.45581	−	3.45581i	−0.178220	−	0.178220i
$377$	26.2550	+	10.8752i	1.35220	+	0.560099i
$378$	2.23839	+	24.4009i	0.115131	+	1.25505i
$379$	19.8992	−	8.24250i	1.02215	−	0.423389i	0.192278	−	0.981341i	$-0.438413\pi$
$379$	19.8992	−	8.24250i	1.02215	−	0.423389i	0.829873	+	0.557952i	$0.188413\pi$
$380$	−6.51320	−	4.52451i	−0.334120	−	0.232102i
$381$	9.86266	+	21.8973i	0.505280	+	1.12183i
$382$			14.5916i			0.746569i
$383$		−	8.31418i		−	0.424835i	−0.977179	−	0.212417i	$-0.931866\pi$
$383$		−	8.31418i		−	0.424835i	0.977179	−	0.212417i	$-0.0681337\pi$
$384$	0.711306	+	1.57925i	0.0362987	+	0.0805910i
$385$	3.36594	+	18.6817i	0.171544	+	0.952107i
$386$	16.1478	−	6.68863i	0.821900	−	0.340442i
$387$	7.92431	−	8.95497i	0.402815	−	0.455207i
$388$	−6.26511	−	2.59509i	−0.318063	−	0.131746i
$389$	−9.71795	−	9.71795i	−0.492720	−	0.492720i	0.416443	−	0.909162i	$-0.363277\pi$
$389$	−9.71795	−	9.71795i	−0.492720	−	0.492720i	−0.909162	+	0.416443i	$0.863277\pi$
$390$	3.55061	−	19.0843i	0.179792	−	0.966370i
$391$	−5.89085	−	4.36678i	−0.297913	−	0.220838i
$392$	−10.7746	−	10.7746i	−0.544202	−	0.544202i
$393$	18.0606	−	19.1970i	0.911036	−	0.968362i
$394$	−1.77326	−	4.28102i	−0.0893354	−	0.215675i
$395$	15.5295	+	3.38213i	0.781376	+	0.170174i
$396$	−2.36699	−	4.85430i	−0.118946	−	0.243938i
$397$	−10.3776	+	4.29852i	−0.520834	+	0.215737i	−0.627583	−	0.778549i	$-0.715956\pi$
$397$	−10.3776	+	4.29852i	−0.520834	+	0.215737i	0.106749	+	0.994286i	$0.465956\pi$
$398$	−3.60236	−	8.69686i	−0.180570	−	0.435934i
$399$	−28.9547	+	0.883179i	−1.44955	+	0.0442142i
$400$	−4.68558	+	1.74508i	−0.234279	+	0.0872541i
$401$	7.50948	+	3.11053i	0.375005	+	0.155332i	0.562222	−	0.826986i	$-0.309947\pi$
$401$	7.50948	+	3.11053i	0.375005	+	0.155332i	−0.187217	+	0.982319i	$0.559947\pi$
$402$	−21.6842	−	8.21668i	−1.08151	−	0.409811i
$403$	−0.470733	+	1.13645i	−0.0234489	+	0.0566106i
$404$			5.10513i			0.253990i
$405$	19.2244	−	5.95167i	0.955268	−	0.295741i
$406$	−18.9063	−	18.9063i	−0.938303	−	0.938303i
$407$	−0.715370	−	0.715370i	−0.0354596	−	0.0354596i
$408$	4.07589	−	5.86405i	0.201787	−	0.290314i
$409$		−	12.8282i		−	0.634312i	−0.948373	−	0.317156i	$-0.897272\pi$
$409$		−	12.8282i		−	0.634312i	0.948373	−	0.317156i	$-0.102728\pi$
$410$	24.9722	+	5.43862i	1.23329	+	0.268594i
$411$	13.3286	+	5.05053i	0.657452	+	0.249124i
$412$	−9.30742	−	9.30742i	−0.458544	−	0.458544i
$413$	42.8044	+	17.7302i	2.10627	+	0.872444i
$414$	−5.04458	−	1.73756i	−0.247928	−	0.0853964i
$415$	−0.0609017	−	0.338018i	−0.00298955	−	0.0165926i
$416$	−3.54409	−	3.54409i	−0.173763	−	0.173763i
$417$	−0.815307	−	0.767042i	−0.0399257	−	0.0375622i
$418$	5.89868	−	2.44332i	0.288514	−	0.119506i
$419$	14.0484	+	5.81902i	0.686307	+	0.284278i	0.698461	−	0.715649i	$-0.253869\pi$
$419$	14.0484	+	5.81902i	0.686307	+	0.284278i	−0.0121537	+	0.999926i	$0.503869\pi$
$420$	−9.95767	+	15.3104i	−0.485884	+	0.747073i
$421$			25.5903i			1.24720i	0.781746	+	0.623598i	$0.214330\pi$
$421$			25.5903i			1.24720i	−0.781746	+	0.623598i	$0.785670\pi$
$422$	15.8671	+	6.57236i	0.772398	+	0.319938i
$423$	0.893596	+	14.6345i	0.0434481	+	0.711553i
$424$		−	11.3147i		−	0.549491i
$425$	16.1066	+	12.8677i	0.781284	+	0.624176i
$426$	0.767004	−	0.815266i	0.0371614	−	0.0394998i
$427$	56.0546			2.71267
$428$	−1.44561	+	3.49002i	−0.0698764	+	0.168696i
$429$	11.3825	+	10.7086i	0.549550	+	0.517017i
$430$	8.77150	−	1.58039i	0.422999	−	0.0762131i
$431$	−1.30620	+	3.15344i	−0.0629174	+	0.151896i	−0.952211	−	0.305440i	$-0.901196\pi$
$431$	−1.30620	+	3.15344i	−0.0629174	+	0.151896i	0.889294	+	0.457336i	$0.151196\pi$
$432$	1.54163	−	4.96220i	0.0741717	−	0.238744i
$433$	−10.9717			−0.527268			−0.263634	−	0.964623i	$-0.584921\pi$
$433$	−10.9717			−0.527268			−0.263634	+	0.964623i	$0.584921\pi$
$434$	0.818361	−	0.818361i	0.0392826	−	0.0392826i
$435$	−11.9726	+	18.4086i	−0.574044	+	0.882623i
$436$	−1.76725	−	0.732020i	−0.0846361	−	0.0350574i
$437$	2.41382	−	5.82747i	0.115469	−	0.278766i
$438$	25.6746	−	0.783128i	1.22678	−	0.0374193i
$439$	−7.31807	−	17.6674i	−0.349273	−	0.843218i	−0.996706	−	0.0810967i	$-0.974158\pi$
$439$	−7.31807	−	17.6674i	−0.349273	−	0.843218i	0.647434	−	0.762122i	$-0.275842\pi$
$440$	0.856600	−	3.93320i	0.0408368	−	0.187508i
$441$	2.78609	+	45.6280i	0.132671	+	2.17276i
$442$	−5.01652	+	20.0473i	−0.238611	+	0.953552i
$443$	−3.10804	+	3.10804i	−0.147667	+	0.147667i	−0.777075	−	0.629408i	$-0.783298\pi$
$443$	−3.10804	+	3.10804i	−0.147667	+	0.147667i	0.629408	+	0.777075i	$0.283298\pi$
$444$	−0.0296763	−	0.972928i	−0.00140838	−	0.0461731i
$445$	−5.40295	+	0.973465i	−0.256124	+	0.0461467i
$446$	−22.4751			−1.06423
$447$	−4.35364	−	9.66603i	−0.205920	−	0.457188i
$448$	1.80461	+	4.35672i	0.0852600	+	0.205836i
$449$	10.7281	−	25.8998i	0.506288	−	1.22229i	−0.439717	−	0.898136i	$-0.644921\pi$
$449$	10.7281	−	25.8998i	0.506288	−	1.22229i	0.946005	−	0.324152i	$-0.105079\pi$
$450$	13.9963	+	5.39474i	0.659793	+	0.254310i
$451$	−14.5493	+	14.5493i	−0.685102	+	0.685102i
$452$	0.503618	−	0.208605i	0.0236882	−	0.00981198i
$453$	−28.3182	−	10.7304i	−1.33050	−	0.504160i
$454$	0.313542	−	0.129873i	0.0147153	−	0.00609526i
$455$	11.2465	−	51.6400i	0.527245	−	2.42092i
$456$	5.74437	+	2.17668i	0.269005	+	0.101932i
$457$	−20.3693			−0.952837			−0.476419	−	0.879219i	$-0.658065\pi$
$457$	−20.3693			−0.952837			−0.476419	+	0.879219i	$0.658065\pi$
$458$	−3.02183	+	3.02183i	−0.141201	+	0.141201i
$459$	−20.8154	+	5.07133i	−0.971580	+	0.236710i
$460$	−2.14922	−	3.34601i	−0.100208	−	0.156009i
$461$	−17.5254	+	17.5254i	−0.816240	+	0.816240i	−0.985561	−	0.169321i	$-0.945843\pi$
$461$	−17.5254	+	17.5254i	−0.816240	+	0.816240i	0.169321	+	0.985561i	$0.445843\pi$
$462$	−6.03844	−	13.4067i	−0.280934	−	0.623734i
$463$	−5.33778	+	5.33778i	−0.248068	+	0.248068i	−0.820177	−	0.572110i	$-0.806125\pi$
$463$	−5.33778	+	5.33778i	−0.248068	+	0.248068i	0.572110	+	0.820177i	$0.306125\pi$
$464$	2.16978	+	5.23832i	0.100730	+	0.243183i
$465$	−0.796818	−	0.518237i	−0.0369515	−	0.0240327i
$466$	−4.77864	+	11.5367i	−0.221366	+	0.534425i
$467$	−11.8120			−0.546595			−0.273297	−	0.961930i	$-0.588114\pi$
$467$	−11.8120			−0.546595			−0.273297	+	0.961930i	$0.588114\pi$
$468$	0.916423	+	15.0083i	0.0423617	+	0.693761i
$469$	−58.3280	−	24.1603i	−2.69334	−	1.11562i
$470$	−6.23476	+	8.97518i	−0.287588	+	0.413994i
$471$	−2.96603	−	1.12390i	−0.136668	−	0.0517866i
$472$	−6.94726	−	6.94726i	−0.319774	−	0.319774i
$473$	−2.74593	+	6.62926i	−0.126258	+	0.304814i
$474$	−12.3054	+	0.375340i	−0.565205	+	0.0172399i
$475$	−7.37433	+	16.1271i	−0.338357	+	0.739963i
$476$	11.5786	−	15.6197i	0.530705	−	0.715929i
$477$	−22.4946	+	25.4204i	−1.02996	+	1.16392i
$478$			12.7713i			0.584147i
$479$	22.5887	−	9.35654i	1.03210	−	0.427511i	0.198632	−	0.980074i	$-0.436350\pi$
$479$	22.5887	−	9.35654i	1.03210	−	0.427511i	0.833471	+	0.552563i	$0.186350\pi$
$480$	3.19333	−	2.19149i	0.145755	−	0.100027i
$481$	1.07791	+	2.60230i	0.0491483	+	0.118655i
$482$	−9.70195	−	23.4226i	−0.441912	−	1.06687i
$483$	−13.5838	−	5.14721i	−0.618083	−	0.234206i
$484$	−5.48661	−	5.48661i	−0.249391	−	0.249391i
$485$	−3.22676	+	14.8161i	−0.146520	+	0.672767i
$486$	−13.3288	+	8.08350i	−0.604607	+	0.366675i
$487$	21.8914	−	9.06770i	0.991993	−	0.410897i	0.173138	−	0.984898i	$-0.444609\pi$
$487$	21.8914	−	9.06770i	0.991993	−	0.410897i	0.818855	+	0.574001i	$0.194609\pi$
$488$	−10.9820	−	4.54890i	−0.497133	−	0.205919i
$489$	16.9690	−	18.0368i	0.767366	−	0.815652i
$490$	−19.4390	+	27.9832i	−0.878163	+	1.26415i
$491$	−13.2255	+	13.2255i	−0.596857	+	0.596857i	−0.939475	−	0.342618i	$-0.888686\pi$
$491$	−13.2255	+	13.2255i	−0.596857	+	0.596857i	0.342618	+	0.939475i	$0.388686\pi$
$492$	−19.7876	+	0.603563i	−0.892094	+	0.0272107i
$493$	13.9216	−	18.7804i	0.626997	−	0.845827i
$494$	−17.7761			−0.799783
$495$	−9.74404	+	7.13359i	−0.437962	+	0.320631i
$496$	−0.226741	+	0.0939194i	−0.0101810	+	0.00421710i
$497$	2.15495	−	2.15495i	0.0966625	−	0.0966625i
$498$	0.109257	+	0.242574i	0.00489591	+	0.0108700i
$499$	−13.8875	+	33.5273i	−0.621688	+	1.50089i	0.228032	+	0.973654i	$0.426771\pi$
$499$	−13.8875	+	33.5273i	−0.621688	+	1.50089i	−0.849720	+	0.527234i	$0.823229\pi$
$500$	5.69810	+	9.61934i	0.254827	+	0.430190i
$501$	−1.75697	+	0.0535911i	−0.0784955	+	0.00239428i
$502$			1.40103i			0.0625309i
$503$	2.01203	+	4.85748i	0.0897122	+	0.216584i	0.962367	−	0.271753i	$-0.0876035\pi$
$503$	2.01203	+	4.85748i	0.0897122	+	0.216584i	−0.872655	+	0.488338i	$0.837603\pi$
$504$	4.60718	−	13.3758i	0.205220	−	0.595807i
$505$	11.2345	−	2.02416i	0.499930	−	0.0900739i
$506$	3.20164			0.142330
$507$	−8.62182	−	19.1423i	−0.382908	−	0.850140i
$508$		−	13.8656i		−	0.615185i
$509$	1.57140			0.0696510			0.0348255	−	0.999393i	$-0.488912\pi$
$509$	1.57140			0.0696510			0.0348255	+	0.999393i	$0.488912\pi$
$510$	−14.5207	−	6.64448i	−0.642988	−	0.294223i
$511$	69.9342			3.09371
$512$		−	1.00000i		−	0.0441942i
$513$	−8.57826	−	16.3106i	−0.378739	−	0.720130i
$514$	8.61957			0.380193
$515$	−16.7919	+	24.1726i	−0.739939	+	1.06517i
$516$	−6.29474	+	2.83519i	−0.277111	+	0.124812i
$517$	−3.36688	−	8.12837i	−0.148075	−	0.357485i
$518$		−	2.65013i		−	0.116440i
$519$	0.441766	+	14.4831i	0.0193914	+	0.635740i
$520$	−6.39403	+	9.20445i	−0.280397	+	0.403642i
$521$	4.05287	−	9.78450i	0.177560	−	0.428667i	−0.809894	−	0.586576i	$-0.800475\pi$
$521$	4.05287	−	9.78450i	0.177560	−	0.428667i	0.987454	+	0.157909i	$0.0504754\pi$
$522$	5.53946	−	16.0825i	0.242456	−	0.703910i
$523$	11.8152	−	11.8152i	0.516641	−	0.516641i	−0.399913	−	0.916553i	$-0.630959\pi$
$523$	11.8152	−	11.8152i	0.516641	−	0.516641i	0.916553	+	0.399913i	$0.130959\pi$
$524$	−14.0591	+	5.82346i	−0.614173	+	0.254399i
$525$	37.6409	+	15.8427i	1.64278	+	0.691431i
$526$	9.63543			0.420125
$527$	0.812914	+	0.602598i	0.0354111	+	0.0262496i
$528$	0.0950631	+	3.11661i	0.00413709	+	0.135633i
$529$	−14.0269	+	14.0269i	−0.609865	+	0.609865i
$530$	−24.8995	+	4.48622i	−1.08157	+	0.194869i
$531$	1.79641	+	29.4199i	0.0779575	+	1.27672i
$532$	15.4517	+	6.40030i	0.669916	+	0.277488i
$533$	52.9260	−	21.9227i	2.29248	−	0.949576i
$534$	3.87735	−	1.74638i	0.167789	−	0.0755733i
$535$	8.25344	+	1.79749i	0.356827	+	0.0777123i
$536$	9.46678	+	9.46678i	0.408903	+	0.408903i
$537$	11.8222	−	31.1994i	0.510165	−	1.34635i
$538$	5.49928	+	13.2764i	0.237091	+	0.572388i
$539$	−10.4974	−	25.3430i	−0.452155	−	1.09160i
$540$	−11.5312	−	1.42508i	−0.496225	−	0.0613255i
$541$	37.3856	−	15.4856i	1.60733	−	0.665780i	0.614905	−	0.788601i	$-0.289194\pi$
$541$	37.3856	−	15.4856i	1.60733	−	0.665780i	0.992429	+	0.122821i	$0.0391942\pi$
$542$			11.0494i			0.474612i
$543$	−26.0125	+	0.793434i	−1.11630	+	0.0340495i
$544$	−3.53600	+	2.12054i	−0.151605	+	0.0909174i
$545$	−0.910202	+	4.17932i	−0.0389888	+	0.179022i
$546$	1.24811	+	40.9188i	0.0534141	+	1.75116i
$547$	8.19868	−	19.7934i	0.350550	−	0.846303i	−0.646002	−	0.763336i	$-0.723560\pi$
$547$	8.19868	−	19.7934i	0.350550	−	0.846303i	0.996552	−	0.0829672i	$-0.0264397\pi$
$548$	−5.81893	−	5.81893i	−0.248572	−	0.248572i
$549$	15.6293	+	32.0531i	0.667043	+	1.36799i
$550$	−8.99517	−	0.325569i	−0.383556	−	0.0138823i
$551$	18.5784	+	7.69542i	0.791465	+	0.327836i
$552$	2.24358	+	2.11076i	0.0954931	+	0.0898401i
$553$	−33.5182			−1.42534
$554$	0.971115	−	2.34448i	0.0412587	−	0.0996073i
$555$	−2.12929	+	0.451068i	−0.0903834	+	0.0191468i
$556$	0.247325	+	0.597095i	0.0104889	+	0.0253225i
$557$	27.5343	−	27.5343i	1.16667	−	1.16667i	0.183682	−	0.982986i	$-0.441198\pi$
$557$	27.5343	−	27.5343i	1.16667	−	1.16667i	0.982986	−	0.183682i	$-0.0588017\pi$
$558$	0.696132	+	0.239776i	0.0294696	+	0.0101505i
$559$	14.1264	−	14.1264i	0.597481	−	0.597481i
$560$	8.87203	−	5.69871i	0.374912	−	0.240815i
$561$	10.8188	−	6.94504i	0.456768	−	0.293220i
$562$	−0.485574	+	0.485574i	−0.0204827	+	0.0204827i
$563$	−8.15025			−0.343492			−0.171746	−	0.985141i	$-0.554941\pi$
$563$	−8.15025			−0.343492			−0.171746	+	0.985141i	$0.554941\pi$
$564$	2.99946	−	7.91573i	0.126300	−	0.333312i
$565$	−0.658747	−	1.02557i	−0.0277137	−	0.0431460i
$566$	−1.45427	+	0.602379i	−0.0611276	+	0.0253199i
$567$	−36.9431	+	20.8915i	−1.55147	+	0.877362i
$568$	−0.597066	+	0.247313i	−0.0250523	+	0.0103770i
$569$	29.3022	−	29.3022i	1.22841	−	1.22841i	0.263848	−	0.964564i	$-0.415008\pi$
$569$	29.3022	−	29.3022i	1.22841	−	1.22841i	0.964564	−	0.263848i	$-0.0849917\pi$
$570$	2.51246	−	13.5043i	0.105236	−	0.565633i
$571$	−10.2217	+	24.6774i	−0.427766	+	1.03272i	0.552228	+	0.833693i	$0.313778\pi$
$571$	−10.2217	+	24.6774i	−0.427766	+	1.03272i	−0.979994	+	0.199026i	$0.936222\pi$
$572$	−3.45289	−	8.33602i	−0.144373	−	0.348546i
$573$	−23.0438	+	10.3791i	−0.962668	+	0.433592i
$574$	−53.8988			−2.24969
$575$	−6.51119	+	6.05633i	−0.271536	+	0.252566i
$576$	−1.98809	+	2.24667i	−0.0828370	+	0.0936111i
$577$	18.7523	−	18.7523i	0.780668	−	0.780668i	−0.199275	−	0.979944i	$-0.563859\pi$
$577$	18.7523	−	18.7523i	0.780668	−	0.780668i	0.979944	+	0.199275i	$0.0638588\pi$
$578$	14.9965	+	8.00662i	0.623771	+	0.333031i
$579$	22.0491	+	20.7438i	0.916328	+	0.862082i
$580$	10.6673	−	6.85186i	0.442936	−	0.284508i
$581$	0.277189	+	0.669193i	0.0114997	+	0.0277628i
$582$	−0.358097	−	11.7401i	−0.0148436	−	0.486643i
$583$	7.79483	−	18.8184i	0.322829	−	0.779378i
$584$	−13.7013	−	5.67525i	−0.566962	−	0.234843i
$585$	32.6645	−	7.96744i	1.35051	−	0.329413i
$586$	−15.6880	+	15.6880i	−0.648067	+	0.648067i
$587$	−13.0808			−0.539901			−0.269951	−	0.962874i	$-0.587007\pi$
$587$	−13.0808			−0.539901			−0.269951	+	0.962874i	$0.587007\pi$
$588$	9.35184	−	24.6800i	0.385663	−	1.01779i
$589$	−0.333097	+	0.804168i	−0.0137250	+	0.0331352i
$590$	−12.5338	+	18.0429i	−0.516009	+	0.742816i
$591$	5.49949	−	5.84554i	0.226219	−	0.240453i
$592$	−0.215061	+	0.519203i	−0.00883895	+	0.0213391i
$593$	−7.47791			−0.307081			−0.153540	−	0.988142i	$-0.549068\pi$
$593$	−7.47791			−0.307081			−0.153540	+	0.988142i	$0.549068\pi$
$594$	5.98252	−	7.19098i	0.245466	−	0.295049i
$595$	−38.9642	−	19.2872i	−1.59737	−	0.790697i
$596$			6.12063i			0.250711i
$597$	11.1722	−	11.8752i	0.457247	−	0.486018i
$598$	−8.23538	−	3.41121i	−0.336770	−	0.139495i
$599$			34.0167i			1.38988i	0.719066	+	0.694942i	$0.244570\pi$
$599$			34.0167i			1.38988i	−0.719066	+	0.694942i	$0.755430\pi$
$600$	−6.08881	−	6.15844i	−0.248575	−	0.251417i
$601$	5.48956	+	2.27385i	0.223924	+	0.0927524i	0.491825	−	0.870694i	$-0.336330\pi$
$601$	5.48956	+	2.27385i	0.223924	+	0.0927524i	−0.267901	+	0.963446i	$0.586330\pi$
$602$	−17.3654	+	7.19300i	−0.707762	+	0.293165i
$603$	−2.44790	−	40.0895i	−0.0996863	−	1.63257i
$604$	12.3630	+	12.3630i	0.503043	+	0.503043i
$605$	−9.89860	+	14.2494i	−0.402435	+	0.579322i
$606$	−8.06230	+	3.63131i	−0.327509	+	0.147512i
$607$	−27.8714	−	11.5447i	−1.13127	−	0.468586i	−0.263055	−	0.964781i	$-0.584730\pi$
$607$	−27.8714	−	11.5447i	−1.13127	−	0.468586i	−0.868211	+	0.496195i	$0.834730\pi$
$608$	−2.50785	−	2.50785i	−0.101707	−	0.101707i
$609$	16.4097	−	43.3060i	0.664953	−	1.75485i
$610$	−5.65615	+	25.9710i	−0.229011	+	1.05154i
$611$			24.4954i			0.990976i
$612$	12.1600	+	2.26574i	0.491540	+	0.0915869i
$613$	−9.35862	−	9.35862i	−0.377991	−	0.377991i	0.492386	−	0.870377i	$-0.336125\pi$
$613$	−9.35862	−	9.35862i	−0.377991	−	0.377991i	−0.870377	+	0.492386i	$0.836125\pi$
$614$	8.38184	+	8.38184i	0.338264	+	0.338264i
$615$	9.17391	+	43.3060i	0.369928	+	1.74627i
$616$			8.48923i			0.342041i
$617$	−7.28828	+	17.5955i	−0.293415	+	0.708367i	0.706585	+	0.707629i	$0.250235\pi$
$617$	−7.28828	+	17.5955i	−0.293415	+	0.708367i	−1.00000		0.000738150i	$0.999765\pi$
$618$	8.07836	−	21.3192i	0.324959	−	0.857584i
$619$	0.0498421	+	0.0206453i	0.00200332	+	0.000829803i	0.383685	−	0.923464i	$-0.374655\pi$
$619$	0.0498421	+	0.0206453i	0.00200332	+	0.000829803i	−0.381682	+	0.924294i	$0.624655\pi$
$620$	0.296584	+	0.461736i	0.0119111	+	0.0185438i
$621$	−0.844191	−	9.20261i	−0.0338762	−	0.369288i
$622$	10.2663	+	24.7850i	0.411641	+	0.993790i
$623$	10.6965	−	4.43064i	0.428547	−	0.177510i
$624$	3.07608	−	8.11795i	0.123142	−	0.324978i
$625$	18.9094	−	16.3534i	0.756375	−	0.654138i
$626$	−0.0603242	−	0.145636i	−0.00241104	−	0.00582077i
$627$	8.05439	+	7.57758i	0.321661	+	0.302619i
$628$	1.29489	+	1.29489i	0.0516719	+	0.0516719i
$629$	2.29195	−	0.340535i	0.0913860	−	0.0135780i
$630$	−31.2620	−	4.83527i	−1.24551	−	0.192642i
$631$	−13.4908	−	13.4908i	−0.537060	−	0.537060i	0.385605	−	0.922664i	$-0.373993\pi$
$631$	−13.4908	−	13.4908i	−0.537060	−	0.537060i	−0.922664	+	0.385605i	$0.873993\pi$
$632$	6.56677	+	2.72004i	0.261212	+	0.108198i
$633$	0.906922	+	29.7331i	0.0360469	+	1.18179i
$634$	−8.02188	+	3.32277i	−0.318590	+	0.131964i
$635$	−30.5131	+	5.49763i	−1.21087	+	0.218167i
$636$	17.8688	−	8.04822i	0.708544	−	0.319133i
$637$			76.3726i			3.02599i
$638$			10.2071i			0.404101i
$639$	1.83309	+	0.631390i	0.0725158	+	0.0249774i
$640$	−2.20063	+	0.396495i	−0.0869877	+	0.0156728i
$641$	−36.2601	+	15.0194i	−1.43219	+	0.593231i	−0.957890	−	0.287134i	$-0.907297\pi$
$641$	−36.2601	+	15.0194i	−1.43219	+	0.593231i	−0.474296	+	0.880365i	$0.657297\pi$
$642$	−6.53990	+	0.199481i	−0.258109	+	0.00787287i
$643$	27.1675	+	11.2531i	1.07138	+	0.443780i	0.847477	−	0.530831i	$-0.178120\pi$
$643$	27.1675	+	11.2531i	1.07138	+	0.443780i	0.223903	+	0.974612i	$0.428120\pi$
$644$	5.93032	+	5.93032i	0.233688	+	0.233688i
$645$	8.73505	+	12.7283i	0.343942	+	0.501176i
$646$	−3.54976	+	14.1857i	−0.139663	+	0.558131i
$647$	−35.1242	−	35.1242i	−1.38088	−	1.38088i	−0.843067	−	0.537808i	$-0.819253\pi$
$647$	−35.1242	−	35.1242i	−1.38088	−	1.38088i	−0.537808	−	0.843067i	$-0.680747\pi$
$648$	8.93314	−	1.09501i	0.350927	−	0.0430162i
$649$	−6.76849	−	16.3406i	−0.265687	−	0.641424i
$650$	22.7908	+	10.4214i	0.893930	+	0.408761i
$651$	1.87451	+	0.710295i	0.0734677	+	0.0278387i
$652$	−13.2094	+	5.47150i	−0.517319	+	0.214280i
$653$	16.2890	+	39.3252i	0.637439	+	1.53891i	0.830080	+	0.557644i	$0.188294\pi$
$653$	16.2890	+	39.3252i	0.637439	+	1.53891i	−0.192642	+	0.981269i	$0.561706\pi$
$654$	−0.101012	−	3.31163i	−0.00394987	−	0.129495i
$655$	18.3897	+	28.6299i	0.718543	+	1.11866i
$656$	10.5597	+	4.37395i	0.412285	+	0.170774i
$657$	19.4993	+	39.9897i	0.760738	+	1.56015i
$658$	8.81959	−	21.2924i	0.343824	−	0.830063i
$659$		−	4.96148i		−	0.193272i	−0.995320	−	0.0966359i	$-0.969192\pi$
$659$		−	4.96148i		−	0.193272i	0.995320	−	0.0966359i	$-0.0308082\pi$
$660$	6.82083	−	1.44492i	0.265500	−	0.0562434i
$661$	−32.3573	−	32.3573i	−1.25855	−	1.25855i	−0.951783	−	0.306771i	$-0.900751\pi$
$661$	−32.3573	−	32.3573i	−1.25855	−	1.25855i	−0.306771	−	0.951783i	$-0.599249\pi$
$662$	0.572853	+	0.572853i	0.0222646	+	0.0222646i
$663$	−35.2280	+	6.33739i	−1.36814	+	0.246124i
$664$		−	0.153600i		−	0.00596084i
$665$	7.95820	−	36.5412i	0.308606	−	1.41701i
$666$	1.51539	−	0.738916i	0.0587202	−	0.0286324i
$667$	7.13034	+	7.13034i	0.276088	+	0.276088i
$668$	0.937606	+	0.388369i	0.0362771	+	0.0150265i
$669$	−15.9867	−	35.4940i	−0.618082	−	1.37228i
$670$	17.0794	−	24.5865i	0.659835	−	0.949858i
$671$	−15.1313	−	15.1313i	−0.584137	−	0.584137i
$672$	−5.59674	+	5.94891i	−0.215899	+	0.229484i
$673$	34.0152	−	14.0896i	1.31119	−	0.543113i	0.385959	−	0.922516i	$-0.373871\pi$
$673$	34.0152	−	14.0896i	1.31119	−	0.543113i	0.925232	+	0.379403i	$0.123871\pi$
$674$	−2.23470	−	0.925645i	−0.0860776	−	0.0356545i
$675$	1.43600	+	25.9410i	0.0552717	+	0.998471i
$676$			12.1211i			0.466197i
$677$	0.392705	+	0.162664i	0.0150929	+	0.00625168i	0.390217	−	0.920723i	$-0.372400\pi$
$677$	0.392705	+	0.162664i	0.0150929	+	0.00625168i	−0.375124	+	0.926975i	$0.622400\pi$
$678$	0.687668	+	0.646959i	0.0264097	+	0.0248463i
$679$		−	31.9785i		−	1.22722i
$680$	6.06854	+	6.94066i	0.232718	+	0.266162i
$681$	0.428128	+	0.402783i	0.0164059	+	0.0154347i
$682$	−0.441814			−0.0169179
$683$	1.83272	−	4.42457i	0.0701270	−	0.169302i	−0.884930	−	0.465724i	$-0.845794\pi$
$683$	1.83272	−	4.42457i	0.0701270	−	0.169302i	0.955057	+	0.296423i	$0.0957938\pi$
$684$	0.648474	+	10.6201i	0.0247950	+	0.406070i
$685$	−10.4982	+	15.1125i	−0.401114	+	0.577419i
$686$	14.8658	−	35.8892i	0.567578	−	1.37025i
$687$	−6.92169	−	2.62279i	−0.264079	−	0.100066i
$688$	3.98590			0.151961
$689$	−40.1003	+	40.1003i	−1.52770	+	1.52770i
$690$	3.75545	−	5.77421i	0.142968	−	0.219820i
$691$	46.3444	+	19.1965i	1.76302	+	0.730268i	0.996070	+	0.0885649i	$0.0282281\pi$
$691$	46.3444	+	19.1965i	1.76302	+	0.730268i	0.766953	+	0.641703i	$0.221772\pi$
$692$	3.20143	−	7.72893i	0.121700	−	0.293810i
$693$	16.8773	−	19.0725i	0.641117	−	0.724503i
$694$	7.21240	+	17.4123i	0.273779	+	0.660961i
$695$	1.21593	−	0.781017i	0.0461227	−	0.0296257i
$696$	−6.72926	+	7.15268i	−0.255072	+	0.271122i
$697$	−6.92587	−	46.6141i	−0.262336	−	1.76564i
$698$	9.66879	−	9.66879i	0.365969	−	0.365969i
$699$	−21.6184	+	0.659406i	−0.817682	+	0.0249410i
$700$	−16.0585	−	17.2646i	−0.606954	−	0.652540i
$701$	13.8932			0.524738			0.262369	−	0.964968i	$-0.415496\pi$
$701$	13.8932			0.524738			0.262369	+	0.964968i	$0.415496\pi$
$702$	−23.0501	+	12.1228i	−0.869971	+	0.457545i
$703$	0.762742	+	1.84142i	0.0287674	+	0.0694506i
$704$	0.688912	−	1.66318i	0.0259643	−	0.0626834i
$705$	−18.6089	−	3.46217i	−0.700852	−	0.130393i
$706$	−13.3809	+	13.3809i	−0.503598	+	0.503598i
$707$	−22.2416	+	9.21279i	−0.836483	+	0.346483i
$708$	6.02986	−	15.9131i	0.226616	−	0.598052i
$709$	2.97097	−	1.23062i	0.111577	−	0.0462168i	−0.326196	−	0.945302i	$-0.605767\pi$
$709$	2.97097	−	1.23062i	0.111577	−	0.0462168i	0.437774	+	0.899085i	$0.355767\pi$
$710$	0.780978	+	1.21587i	0.0293096	+	0.0456306i
$711$	−9.34565	−	19.1663i	−0.350489	−	0.718794i
$712$	−2.45518			−0.0920116
$713$	−0.308638	+	0.308638i	−0.0115586	+	0.0115586i
$714$	32.9035	+	7.17519i	1.23138	+	0.268525i
$715$	−16.9755	+	10.9037i	−0.634847	+	0.407777i
$716$	−13.6209	+	13.6209i	−0.509035	+	0.509035i
$717$	−20.1692	+	9.08433i	−0.753232	+	0.339260i
$718$	16.8764	−	16.8764i	0.629823	−	0.629823i
$719$	0.155295	+	0.374915i	0.00579152	+	0.0139820i	0.926749	−	0.375681i	$-0.122591\pi$
$719$	0.155295	+	0.374915i	0.00579152	+	0.0139820i	−0.920957	+	0.389663i	$0.872591\pi$
$720$	5.73236	+	3.48426i	0.213632	+	0.129851i
$721$	23.7535	−	57.3461i	0.884628	−	2.13568i
$722$	6.42141			0.238980
$723$	30.0892	−	31.9825i	1.11903	−	1.18944i
$724$	13.8816	+	5.74993i	0.515904	+	0.213694i
$725$	−19.3080	−	20.7581i	−0.717080	−	0.770937i
$726$	4.76209	−	12.5674i	0.176738	−	0.466420i
$727$	1.20503	+	1.20503i	0.0446922	+	0.0446922i	0.729100	−	0.684407i	$-0.239939\pi$
$727$	1.20503	+	1.20503i	0.0446922	+	0.0446922i	−0.684407	+	0.729100i	$0.739939\pi$
$728$	9.04490	−	21.8363i	0.335226	−	0.809308i
$729$	−22.2468	−	15.2997i	−0.823954	−	0.566657i
$730$	−7.05666	+	32.4017i	−0.261179	+	1.19924i
$731$	−8.45225	−	14.0941i	−0.312618	−	0.521290i
$732$	−0.627704	−	20.5791i	−0.0232006	−	0.760624i
$733$			0.693912i			0.0256302i	0.999918	+	0.0128151i	$0.00407929\pi$
$733$			0.693912i			0.0256302i	−0.999918	+	0.0128151i	$0.995921\pi$
$734$	2.48582	−	1.02966i	0.0917534	−	0.0380055i
$735$	−58.0196	−	10.7945i	−2.14008	−	0.398161i
$736$	−0.680595	−	1.64310i	−0.0250871	−	0.0605655i
$737$	9.22319	+	22.2667i	0.339740	+	0.820206i
$738$	−15.0282	−	30.8203i	−0.553196	−	1.13451i
$739$	−29.5165	−	29.5165i	−1.08578	−	1.08578i	−0.995958	−	0.0898239i	$-0.971370\pi$
$739$	−29.5165	−	29.5165i	−1.08578	−	1.08578i	−0.0898239	−	0.995958i	$-0.528630\pi$
$740$	1.22785	+	0.267409i	0.0451366	+	0.00983016i
$741$	−12.6442	−	28.0729i	−0.464497	−	1.03128i
$742$	49.2950	−	20.4187i	1.80968	−	0.749593i
$743$	24.6431	+	10.2075i	0.904067	+	0.374477i	0.785782	−	0.618503i	$-0.212261\pi$
$743$	24.6431	+	10.2075i	0.904067	+	0.374477i	0.118284	+	0.992980i	$0.462261\pi$
$744$	−0.309605	−	0.291277i	−0.0113507	−	0.0106787i
$745$	13.4693	−	2.42680i	0.493476	−	0.0889111i
$746$	−1.09741	+	1.09741i	−0.0401789	+	0.0401789i
$747$	−0.305370	+	0.345088i	−0.0111729	+	0.0126261i
$748$	−7.34187	+	1.09085i	−0.268445	+	0.0398853i
$749$	−17.8138			−0.650903
$750$	−11.1383	+	15.8410i	−0.406713	+	0.578433i
$751$	−9.30930	+	3.85604i	−0.339701	+	0.140709i	−0.546011	−	0.837778i	$-0.683854\pi$
$751$	−9.30930	+	3.85604i	−0.339701	+	0.140709i	0.206310	+	0.978487i	$0.433854\pi$
$752$	−3.45581	+	3.45581i	−0.126020	+	0.126020i
$753$	−2.21258	+	0.996560i	−0.0806309	+	0.0363167i
$754$	10.8752	−	26.2550i	0.396050	−	0.956149i
$755$	22.3046	−	32.1083i	0.811747	−	1.16854i
$756$	24.4009	−	2.23839i	0.887454	−	0.0814096i
$757$			13.9134i			0.505693i	0.967506	+	0.252846i	$0.0813667\pi$
$757$			13.9134i			0.505693i	−0.967506	+	0.252846i	$0.918633\pi$
$758$	−8.24250	−	19.8992i	−0.299381	−	0.722770i
$759$	2.27735	+	5.05621i	0.0826625	+	0.183529i
$760$	−4.52451	+	6.51320i	−0.164121	+	0.236259i
$761$	29.4397			1.06719			0.533595	−	0.845740i	$-0.320841\pi$
$761$	29.4397			1.06719			0.533595	+	0.845740i	$0.320841\pi$
$762$	21.8973	−	9.86266i	0.793254	−	0.357287i
$763$		−	9.02045i		−	0.326562i
$764$	14.5916			0.527904
$765$	0.164663	−	27.6581i	0.00595341	−	0.999982i
$766$	−8.31418			−0.300404
$767$			49.2434i			1.77808i
$768$	1.57925	−	0.711306i	0.0569864	−	0.0256670i
$769$	48.2017			1.73820			0.869098	−	0.494639i	$-0.164700\pi$
$769$	48.2017			1.73820			0.869098	+	0.494639i	$0.164700\pi$
$770$	18.6817	−	3.36594i	0.673241	−	0.121300i
$771$	6.13115	+	13.6125i	0.220808	+	0.490242i
$772$	−6.68863	−	16.1478i	−0.240729	−	0.581171i
$773$			1.73800i			0.0625114i	0.999511	+	0.0312557i	$0.00995063\pi$
$773$			1.73800i			0.0625114i	−0.999511	+	0.0312557i	$0.990049\pi$
$774$	−8.95497	−	7.92431i	−0.321880	−	0.284833i
$775$	0.898519	−	0.835749i	0.0322758	−	0.0300210i
$776$	−2.59509	+	6.26511i	−0.0931584	+	0.224904i
$777$	4.18522	−	1.88505i	0.150144	−	0.0676258i
$778$	−9.71795	+	9.71795i	−0.348405	+	0.348405i
$779$	37.4512	−	15.5128i	1.34183	−	0.555804i
$780$	−19.0843	−	3.55061i	−0.683327	−	0.127132i
$781$	−1.16340			−0.0416299
$782$	−4.36678	+	5.89085i	−0.156156	+	0.210656i
$783$	29.3385	−	2.69134i	1.04847	−	0.0961806i
$784$	−10.7746	+	10.7746i	−0.384809	+	0.384809i
$785$	2.33617	−	3.36301i	0.0833815	−	0.120031i
$786$	−19.1970	−	18.0606i	−0.684735	−	0.644200i
$787$	−48.1280	−	19.9353i	−1.71558	−	0.710616i	−0.999926	−	0.0121609i	$-0.996129\pi$
$787$	−48.1280	−	19.9353i	−1.71558	−	0.710616i	−0.715654	−	0.698455i	$-0.753871\pi$
$788$	−4.28102	+	1.77326i	−0.152505	+	0.0631697i
$789$	6.85374	+	15.2168i	0.243999	+	0.541732i
$790$	3.38213	−	15.5295i	0.120331	−	0.552516i
$791$	1.81767	+	1.81767i	0.0646290	+	0.0646290i
$792$	−4.85430	+	2.36699i	−0.172490	+	0.0841074i
$793$	22.7995	+	55.0430i	0.809635	+	1.95463i
$794$	4.29852	+	10.3776i	0.152549	+	0.368285i
$795$	−24.7961	−	36.1316i	−0.879426	−	1.28146i
$796$	−8.69686	+	3.60236i	−0.308252	+	0.127682i
$797$			23.2450i			0.823379i	0.911324	+	0.411689i	$0.135061\pi$
$797$			23.2450i			0.823379i	−0.911324	+	0.411689i	$0.864939\pi$
$798$	0.883179	+	28.9547i	0.0312642	+	1.02499i
$799$	19.5479	+	4.89156i	0.691555	+	0.173051i
$800$	1.74508	+	4.68558i	0.0616979	+	0.165660i
$801$	5.51596	+	4.88111i	0.194897	+	0.172465i
$802$	3.11053	−	7.50948i	0.109837	−	0.265169i
$803$	−18.8779	−	18.8779i	−0.666187	−	0.666187i
$804$	−8.21668	+	21.6842i	−0.289780	+	0.764744i
$805$	10.6991	−	15.4018i	0.377095	−	0.542843i
$806$	1.13645	+	0.470733i	0.0400297	+	0.0165809i
$807$	−17.0552	+	18.1284i	−0.600371	+	0.638149i
$808$	5.10513			0.179598
$809$	−13.9756	+	33.7400i	−0.491355	+	1.18624i	0.462676	+	0.886528i	$0.346889\pi$
$809$	−13.9756	+	33.7400i	−0.491355	+	1.18624i	−0.954031	+	0.299709i	$0.903111\pi$
$810$	−5.95167	−	19.2244i	−0.209120	−	0.675477i
$811$	0.911381	+	2.20027i	0.0320029	+	0.0772618i	0.939073	−	0.343718i	$-0.111686\pi$
$811$	0.911381	+	2.20027i	0.0320029	+	0.0772618i	−0.907070	+	0.420980i	$0.861686\pi$
$812$	−18.9063	+	18.9063i	−0.663480	+	0.663480i
$813$	−17.4498	+	7.85949i	−0.611991	+	0.275644i
$814$	−0.715370	+	0.715370i	−0.0250737	+	0.0250737i
$815$	17.2782	+	26.8996i	0.605229	+	0.942251i
$816$	−5.86405	−	4.07589i	−0.205283	−	0.142685i
$817$	9.99602	−	9.99602i	0.349716	−	0.349716i
$818$	−12.8282			−0.448527
$819$	−63.7334	+	31.0768i	−2.22702	+	1.08591i
$820$	5.43862	−	24.9722i	0.189925	−	0.872067i
$821$	25.7837	−	10.6800i	0.899859	−	0.372734i	0.115693	−	0.993285i	$-0.463091\pi$
$821$	25.7837	−	10.6800i	0.899859	−	0.372734i	0.784166	+	0.620551i	$0.213091\pi$
$822$	5.05053	−	13.3286i	0.176157	−	0.464889i
$823$	−48.1202	+	19.9320i	−1.67736	+	0.694787i	−0.999195	−	0.0401178i	$-0.987227\pi$
$823$	−48.1202	+	19.9320i	−1.67736	+	0.694787i	−0.678170	+	0.734905i	$0.737227\pi$
$824$	−9.30742	+	9.30742i	−0.324239	+	0.324239i
$825$	−5.88416	−	14.4372i	−0.204860	−	0.502640i
$826$	17.7302	−	42.8044i	0.616911	−	1.48936i
$827$	−11.1516	−	26.9223i	−0.387778	−	0.936180i	−0.990410	−	0.138160i	$-0.955881\pi$
$827$	−11.1516	−	26.9223i	−0.387778	−	0.936180i	0.602632	−	0.798020i	$-0.294119\pi$
$828$	−1.73756	+	5.04458i	−0.0603844	+	0.175311i
$829$	40.4367			1.40442			0.702212	−	0.711968i	$-0.252196\pi$
$829$	40.4367			1.40442			0.702212	+	0.711968i	$0.252196\pi$
$830$	−0.338018	+	0.0609017i	−0.0117328	+	0.00211393i
$831$	4.39329	−	0.134004i	0.152401	−	0.00464856i
$832$	−3.54409	+	3.54409i	−0.122869	+	0.122869i
$833$	60.9473	+	15.2511i	2.11170	+	0.528419i
$834$	−0.767042	+	0.815307i	−0.0265605	+	0.0282318i
$835$	0.482902	−	2.21731i	0.0167115	−	0.0767333i
$836$	−2.44332	−	5.89868i	−0.0845038	−	0.204010i
$837$	0.116495	+	1.26992i	0.00402666	+	0.0438950i
$838$	5.81902	−	14.0484i	0.201015	−	0.485292i
$839$	8.18162	+	3.38894i	0.282461	+	0.116999i	0.519416	−	0.854521i	$-0.326149\pi$
$839$	8.18162	+	3.38894i	0.282461	+	0.116999i	−0.236955	+	0.971521i	$0.576149\pi$
$840$	15.3104	+	9.95767i	0.528261	+	0.343572i
$841$	−2.22591	+	2.22591i	−0.0767557	+	0.0767557i
$842$	25.5903			0.881900
$843$	−1.11224	−	0.421453i	−0.0383075	−	0.0145156i
$844$	6.57236	−	15.8671i	0.226230	−	0.546168i
$845$	26.6741	−	4.80596i	0.917618	−	0.165330i
$846$	14.6345	−	0.893596i	0.503144	−	0.0307225i
$847$	14.0024	−	33.8048i	0.481129	−	1.16155i
$848$	−11.3147			−0.388549
$849$	−1.98574	−	1.86819i	−0.0681504	−	0.0641160i
$850$	12.8677	−	16.1066i	0.441359	−	0.552451i
$851$			0.999473i			0.0342615i
$852$	−0.815266	−	0.767004i	−0.0279306	−	0.0262771i
$853$	−8.75786	−	3.62762i	−0.299863	−	0.124207i	0.227679	−	0.973736i	$-0.426886\pi$
$853$	−8.75786	−	3.62762i	−0.299863	−	0.124207i	−0.527542	+	0.849529i	$0.676886\pi$
$854$		−	56.0546i		−	1.91815i
$855$	23.1139	−	5.63788i	0.790478	−	0.192811i
$856$	3.49002	+	1.44561i	0.119286	+	0.0494100i
$857$	−42.5479	+	17.6239i	−1.45341	+	0.602021i	−0.963007	−	0.269476i	$-0.913150\pi$
$857$	−42.5479	+	17.6239i	−1.45341	+	0.602021i	−0.490401	+	0.871497i	$0.663150\pi$
$858$	10.7086	−	11.3825i	0.365587	−	0.388591i
$859$	−29.0048	−	29.0048i	−0.989629	−	0.989629i	0.0103175	−	0.999947i	$-0.496716\pi$
$859$	−29.0048	−	29.0048i	−0.989629	−	0.989629i	−0.999947	+	0.0103175i	$0.996716\pi$
$860$	−1.58039	−	8.77150i	−0.0538908	−	0.299106i
$861$	−38.3385	−	85.1199i	−1.30657	−	2.90088i
$862$	3.15344	+	1.30620i	0.107407	+	0.0444893i
$863$	−26.4550	−	26.4550i	−0.900540	−	0.900540i	0.0949428	−	0.995483i	$-0.469733\pi$
$863$	−26.4550	−	26.4550i	−0.900540	−	0.900540i	−0.995483	+	0.0949428i	$0.969733\pi$
$864$	−4.96220	−	1.54163i	−0.168817	−	0.0524473i
$865$	−18.2779	−	3.98069i	−0.621468	−	0.135348i
$866$			10.9717i			0.372835i
$867$	−1.97740	+	29.3784i	−0.0671562	+	0.997742i
$868$	−0.818361	−	0.818361i	−0.0277770	−	0.0277770i
$869$	9.04785	+	9.04785i	0.306927	+	0.306927i
$870$	18.4086	+	11.9726i	0.624109	+	0.405910i
$871$		−	67.1022i		−	2.27367i
$872$	−0.732020	+	1.76725i	−0.0247893	+	0.0598468i
$873$	18.2859	−	8.91633i	0.618883	−	0.301772i
$874$	−5.82747	−	2.41382i	−0.197117	−	0.0816486i
$875$	−31.6259	+	42.1842i	−1.06915	+	1.42609i
$876$	−0.783128	−	25.6746i	−0.0264595	−	0.867464i
$877$	−5.76942	−	13.9286i	−0.194820	−	0.470336i	0.796038	−	0.605246i	$-0.206925\pi$
$877$	−5.76942	−	13.9286i	−0.194820	−	0.470336i	−0.990858	+	0.134910i	$0.956925\pi$
$878$	−17.6674	+	7.31807i	−0.596245	+	0.246973i
$879$	−35.9344	−	13.6164i	−1.21204	−	0.459270i
$880$	−3.93320	−	0.856600i	−0.132588	−	0.0288760i
$881$	5.81274	+	14.0332i	0.195836	+	0.472790i	0.991042	−	0.133549i	$-0.0426374\pi$
$881$	5.81274	+	14.0332i	0.195836	+	0.472790i	−0.795206	+	0.606339i	$0.792637\pi$
$882$	45.6280	−	2.78609i	1.53637	−	0.0938125i
$883$	−6.98399	−	6.98399i	−0.235030	−	0.235030i	0.579758	−	0.814788i	$-0.303147\pi$
$883$	−6.98399	−	6.98399i	−0.235030	−	0.235030i	−0.814788	+	0.579758i	$0.803147\pi$
$884$	20.0473	+	5.01652i	0.674263	+	0.168724i
$885$	−37.4098	−	6.96005i	−1.25752	−	0.233960i
$886$	3.10804	+	3.10804i	0.104417	+	0.104417i
$887$	48.0097	+	19.8862i	1.61201	+	0.667715i	0.993048	−	0.117709i	$-0.0375550\pi$
$887$	48.0097	+	19.8862i	1.61201	+	0.667715i	0.618958	+	0.785424i	$0.287555\pi$
$888$	−0.972928	+	0.0296763i	−0.0326493	+	0.000995872i
$889$	60.4084	−	25.0220i	2.02603	−	0.839211i
$890$	0.973465	+	5.40295i	0.0326306	+	0.181107i
$891$	15.6118	+	4.33294i	0.523014	+	0.145159i
$892$			22.4751i			0.752524i
$893$			17.3333i			0.580036i
$894$	−9.66603	+	4.35364i	−0.323280	+	0.145608i
$895$	35.3751	+	24.5739i	1.18246	+	0.821416i
$896$	4.35672	−	1.80461i	0.145548	−	0.0602879i
$897$	−0.470713	−	15.4322i	−0.0157167	−	0.515265i
$898$	−25.8998	−	10.7281i	−0.864288	−	0.358000i
$899$	−0.983959	−	0.983959i	−0.0328169	−	0.0328169i
$900$	5.39474	−	13.9963i	0.179825	−	0.466544i
$901$	23.9933	+	40.0088i	0.799332	+	1.33289i
$902$	14.5493	+	14.5493i	0.484440	+	0.484440i
$903$	−23.7117	−	22.3080i	−0.789076	−	0.742364i
$904$	−0.208605	−	0.503618i	−0.00693812	−	0.0167501i
$905$	7.14953	−	32.8281i	0.237658	−	1.09124i
$906$	−10.7304	+	28.3182i	−0.356495	+	0.940809i
$907$	−6.06320	+	2.51146i	−0.201325	+	0.0833916i	−0.481068	−	0.876683i	$-0.659751\pi$
$907$	−6.06320	+	2.51146i	−0.201325	+	0.0833916i	0.279743	+	0.960075i	$0.409751\pi$
$908$	−0.129873	−	0.313542i	−0.00431000	−	0.0104053i
$909$	−11.4695	−	10.1494i	−0.380420	−	0.336636i
$910$	−51.6400	−	11.2465i	−1.71185	−	0.372819i
$911$	−30.3097	−	12.5547i	−1.00420	−	0.415955i	−0.180867	−	0.983508i	$-0.557890\pi$
$911$	−30.3097	−	12.5547i	−1.00420	−	0.415955i	−0.823337	+	0.567553i	$0.807890\pi$
$912$	2.17668	−	5.74437i	0.0720771	−	0.190215i
$913$	0.105817	−	0.255465i	0.00350203	−	0.00845464i
$914$			20.3693i			0.673758i
$915$	−45.0381	+	9.54084i	−1.48891	+	0.315411i
$916$	3.02183	+	3.02183i	0.0998442	+	0.0998442i
$917$	−50.7424	−	50.7424i	−1.67566	−	1.67566i
$918$	5.07133	+	20.8154i	0.167379	+	0.687011i
$919$			18.4857i			0.609788i	0.952386	+	0.304894i	$0.0986211\pi$
$919$			18.4857i			0.609788i	−0.952386	+	0.304894i	$0.901379\pi$
$920$	−3.34601	+	2.14922i	−0.110315	+	0.0708577i
$921$	−7.27501	+	19.1991i	−0.239720	+	0.632632i
$922$	17.5254	+	17.5254i	0.577169	+	0.577169i
$923$	2.99255	+	1.23956i	0.0985010	+	0.0408005i
$924$	−13.4067	+	6.03844i	−0.441047	+	0.198650i
$925$	0.101635	−	2.80807i	0.00334173	−	0.0923288i
$926$	5.33778	+	5.33778i	0.175410	+	0.175410i
$927$	39.4146	−	2.40670i	1.29455	−	0.0790462i
$928$	5.23832	−	2.16978i	0.171956	−	0.0712266i
$929$	29.3716	+	12.1661i	0.963651	+	0.399157i	0.808345	−	0.588709i	$-0.200364\pi$
$929$	29.3716	+	12.1661i	0.963651	+	0.399157i	0.155306	+	0.987866i	$0.450364\pi$
$930$	−0.518237	+	0.796818i	−0.0169937	+	0.0261287i
$931$			54.0423i			1.77117i
$932$	11.5367	+	4.77864i	0.377896	+	0.156530i
$933$	−31.8394	+	33.8428i	−1.04238	+	1.10797i
$934$			11.8120i			0.386501i
$935$	5.31157	+	15.7243i	0.173707	+	0.514238i
$936$	15.0083	−	0.916423i	0.490563	−	0.0299542i
$937$	−35.1626			−1.14871			−0.574355	−	0.818606i	$-0.694747\pi$
$937$	−35.1626			−1.14871			−0.574355	+	0.818606i	$0.694747\pi$
$938$	−24.1603	+	58.3280i	−0.788860	+	1.90448i
$939$	0.187087	−	0.198859i	0.00610534	−	0.00648951i
$940$	8.97518	+	6.23476i	0.292738	+	0.203355i
$941$	−7.53963	+	18.2023i	−0.245785	+	0.593377i	−0.997838	−	0.0657255i	$-0.979064\pi$
$941$	−7.53963	+	18.2023i	−0.245785	+	0.593377i	0.752053	+	0.659103i	$0.229064\pi$
$942$	−1.12390	+	2.96603i	−0.0366187	+	0.0966386i
$943$	20.3275			0.661954
$944$	−6.94726	+	6.94726i	−0.226114	+	0.226114i
$945$	−14.6007	−	52.8101i	−0.474962	−	1.71791i
$946$	6.62926	+	2.74593i	0.215536	+	0.0892779i
$947$	3.79703	−	9.16684i	0.123387	−	0.297882i	−0.850101	−	0.526619i	$-0.823459\pi$
$947$	3.79703	−	9.16684i	0.123387	−	0.297882i	0.973488	+	0.228737i	$0.0734595\pi$
$948$	0.375340	+	12.3054i	0.0121905	+	0.399660i
$949$	28.4449	+	68.6720i	0.923360	+	2.22919i
$950$	16.1271	+	7.37433i	0.523233	+	0.239255i
$951$	−10.9535	−	10.3051i	−0.355192	−	0.334165i
$952$	−15.6197	−	11.5786i	−0.506238	−	0.375265i
$953$	37.7986	−	37.7986i	1.22442	−	1.22442i	0.258373	−	0.966045i	$-0.416814\pi$
$953$	37.7986	−	37.7986i	1.22442	−	1.22442i	0.966045	−	0.258373i	$-0.0831863\pi$
$954$	25.4204	+	22.4946i	0.823014	+	0.728290i
$955$	−5.78548	−	32.1107i	−0.187214	−	1.03908i
$956$	12.7713			0.413054
$957$	−16.1195	+	7.26034i	−0.521070	+	0.234693i
$958$	−9.35654	−	22.5887i	−0.302296	−	0.729807i
$959$	14.8505	−	35.8524i	0.479549	−	1.15773i
$960$	−2.19149	−	3.19333i	−0.0707301	−	0.103064i
$961$	−21.8777	+	21.8777i	−0.705733	+	0.705733i
$962$	2.60230	−	1.07791i	0.0839014	−	0.0347531i
$963$	−4.96690	−	10.1863i	−0.160056	−	0.328248i
$964$	−23.4226	+	9.70195i	−0.754391	+	0.312479i
$965$	−32.8833	+	21.1217i	−1.05855	+	0.679933i
$966$	−5.14721	+	13.5838i	−0.165609	+	0.437050i
$967$	−35.6787			−1.14735			−0.573675	−	0.819083i	$-0.694483\pi$
$967$	−35.6787			−1.14735			−0.573675	+	0.819083i	$0.694483\pi$
$968$	−5.48661	+	5.48661i	−0.176346	+	0.176346i
$969$	−24.9279	+	4.48443i	−0.800798	+	0.144061i
$970$	14.8161	+	3.22676i	0.475718	+	0.103605i
$971$	33.0365	−	33.0365i	1.06019	−	1.06019i	0.0621234	−	0.998068i	$-0.480213\pi$
$971$	33.0365	−	33.0365i	1.06019	−	1.06019i	0.998068	−	0.0621234i	$-0.0197872\pi$
$972$	8.08350	+	13.3288i	0.259278	+	0.427522i
$973$	−2.15505	+	2.15505i	−0.0690878	+	0.0690878i
$974$	−9.06770	−	21.8914i	−0.290548	−	0.701445i
$975$	−0.246778	+	43.4053i	−0.00790321	+	1.39008i
$976$	−4.54890	+	10.9820i	−0.145607	+	0.351526i
$977$	22.2230			0.710976			0.355488	−	0.934681i	$-0.384315\pi$
$977$	22.2230			0.710976			0.355488	+	0.934681i	$0.384315\pi$
$978$	−18.0368	−	16.9690i	−0.576753	−	0.542610i
$979$	−4.08340	−	1.69140i	−0.130506	−	0.0540574i
$980$	27.9832	+	19.4390i	0.893889	+	0.620955i
$981$	5.15806	−	2.51511i	0.164684	−	0.0803012i
$982$	13.2255	+	13.2255i	0.422042	+	0.422042i
$983$	2.88573	−	6.96677i	0.0920406	−	0.222206i	−0.871154	−	0.491009i	$-0.836628\pi$
$983$	2.88573	−	6.96677i	0.0920406	−	0.222206i	0.963195	+	0.268803i	$0.0866282\pi$
$984$	0.603563	+	19.7876i	0.0192409	+	0.630806i
$985$	5.59969	+	8.71787i	0.178421	+	0.277775i
$986$	−18.7804	−	13.9216i	−0.598090	−	0.443354i
$987$	39.8995	−	1.21702i	1.27002	−	0.0387381i
$988$			17.7761i			0.565532i
$989$	6.54923	−	2.71278i	0.208253	−	0.0862614i
$990$	7.13359	+	9.74404i	0.226720	+	0.309686i
$991$	16.0348	+	38.7115i	0.509363	+	1.22971i	0.944251	+	0.329227i	$0.106788\pi$
$991$	16.0348	+	38.7115i	0.509363	+	1.22971i	−0.434888	+	0.900485i	$0.643212\pi$
$992$	0.0939194	+	0.226741i	0.00298194	+	0.00719905i
$993$	−0.497207	+	1.31215i	−0.0157784	+	0.0416400i
$994$	−2.15495	−	2.15495i	−0.0683507	−	0.0683507i
$995$	11.3757	+	17.7103i	0.360635	+	0.561454i
$996$	0.242574	−	0.109257i	0.00768624	−	0.00346193i
$997$	−23.3376	+	9.66674i	−0.739108	+	0.306149i	−0.720289	−	0.693674i	$-0.755991\pi$
$997$	−23.3376	+	9.66674i	−0.739108	+	0.306149i	−0.0188194	+	0.999823i	$0.505991\pi$
$998$	33.5273	+	13.8875i	1.06129	+	0.439600i
$999$	2.24484	+	1.86759i	0.0710237	+	0.0590881i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.z.c.53.16	yes	68
3.2	odd	2		510.2.z.d.53.11	yes	68
5.2	odd	4		510.2.w.d.257.8	yes	68
15.2	even	4		510.2.w.c.257.15	✓	68
17.9	even	8		510.2.w.c.383.15	yes	68
51.26	odd	8		510.2.w.d.383.8	yes	68
85.77	odd	8		510.2.z.d.77.11	yes	68
255.77	even	8	inner	510.2.z.c.77.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.w.c.257.15	✓	68	15.2	even	4
510.2.w.c.383.15	yes	68	17.9	even	8
510.2.w.d.257.8	yes	68	5.2	odd	4
510.2.w.d.383.8	yes	68	51.26	odd	8
510.2.z.c.53.16	yes	68	1.1	even	1	trivial
510.2.z.c.77.16	yes	68	255.77	even	8	inner
510.2.z.d.53.11	yes	68	3.2	odd	2
510.2.z.d.77.11	yes	68	85.77	odd	8

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	510.2.z.c.53.16

Level	$510$
Weight	$2$
Character	510.53
Analytic conductor	$4.072$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$