LMFDB - Embedded newform 403.2.k.d.66.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.4
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.365564 - 1.12509i) q^{2} +(-0.709225 + 2.18277i) q^{3} +(0.485840 - 0.352983i) q^{4} +3.83735 q^{5} +2.71508 q^{6} +(3.69636 - 2.68556i) q^{7} +(-2.48886 - 1.80827i) q^{8} +(-1.83443 - 1.33279i) q^{9} +O(q^{10})$	\(q+(-0.365564 - 1.12509i) q^{2} +(-0.709225 + 2.18277i) q^{3} +(0.485840 - 0.352983i) q^{4} +3.83735 q^{5} +2.71508 q^{6} +(3.69636 - 2.68556i) q^{7} +(-2.48886 - 1.80827i) q^{8} +(-1.83443 - 1.33279i) q^{9} +(-1.40280 - 4.31737i) q^{10} +(-2.22162 + 1.61410i) q^{11} +(0.425911 + 1.31082i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-4.37276 - 3.17700i) q^{14} +(-2.72154 + 8.37605i) q^{15} +(-0.753476 + 2.31896i) q^{16} +(-3.58469 - 2.60443i) q^{17} +(-0.828910 + 2.55112i) q^{18} +(-0.987268 - 3.03850i) q^{19} +(1.86434 - 1.35452i) q^{20} +(3.24041 + 9.97297i) q^{21} +(2.62816 + 1.90947i) q^{22} +(3.54452 + 2.57524i) q^{23} +(5.71219 - 4.15015i) q^{24} +9.72526 q^{25} +1.18299 q^{26} +(-1.36012 + 0.988187i) q^{27} +(0.847880 - 2.60951i) q^{28} +(-2.47236 - 7.60913i) q^{29} +10.4187 q^{30} +(-2.67458 + 4.88330i) q^{31} -3.26832 q^{32} +(-1.94759 - 5.99405i) q^{33} +(-1.61979 + 4.98520i) q^{34} +(14.1842 - 10.3054i) q^{35} -1.36169 q^{36} +2.91823 q^{37} +(-3.05768 + 2.22153i) q^{38} +(-1.85677 - 1.34903i) q^{39} +(-9.55065 - 6.93895i) q^{40} +(3.88239 + 11.9488i) q^{41} +(10.0359 - 7.29153i) q^{42} +(1.32629 + 4.08190i) q^{43} +(-0.509602 + 1.56839i) q^{44} +(-7.03935 - 5.11439i) q^{45} +(1.60163 - 4.92932i) q^{46} +(-1.73995 + 5.35502i) q^{47} +(-4.52737 - 3.28933i) q^{48} +(4.28772 - 13.1962i) q^{49} +(-3.55521 - 10.9418i) q^{50} +(8.22723 - 5.97743i) q^{51} +(0.185574 + 0.571139i) q^{52} +(-1.60139 - 1.16348i) q^{53} +(1.60901 + 1.16902i) q^{54} +(-8.52515 + 6.19388i) q^{55} -14.0560 q^{56} +7.33254 q^{57} +(-7.65717 + 5.56326i) q^{58} +(-2.68018 + 8.24874i) q^{59} +(1.63437 + 5.03008i) q^{60} +0.710650 q^{61} +(6.47189 + 1.22398i) q^{62} -10.3600 q^{63} +(2.70174 + 8.31509i) q^{64} +(-1.18581 + 3.64954i) q^{65} +(-6.03189 + 4.38243i) q^{66} -7.83185 q^{67} -2.66091 q^{68} +(-8.13502 + 5.91044i) q^{69} +(-16.7798 - 12.1913i) q^{70} +(-4.48499 - 3.25854i) q^{71} +(2.15561 + 6.63428i) q^{72} +(8.50131 - 6.17657i) q^{73} +(-1.06680 - 3.28327i) q^{74} +(-6.89739 + 21.2280i) q^{75} +(-1.55219 - 1.12773i) q^{76} +(-3.87714 + 11.9326i) q^{77} +(-0.839007 + 2.58220i) q^{78} +(0.126322 + 0.0917780i) q^{79} +(-2.89135 + 8.89867i) q^{80} +(-3.29442 - 10.1392i) q^{81} +(12.0242 - 8.73610i) q^{82} +(-1.04452 - 3.21471i) q^{83} +(5.09461 + 3.70145i) q^{84} +(-13.7557 - 9.99412i) q^{85} +(4.10767 - 2.98439i) q^{86} +18.3624 q^{87} +8.44805 q^{88} +(-7.33423 + 5.32863i) q^{89} +(-3.18082 + 9.78956i) q^{90} +(1.41188 + 4.34533i) q^{91} +2.63109 q^{92} +(-8.76225 - 9.30134i) q^{93} +6.66095 q^{94} +(-3.78849 - 11.6598i) q^{95} +(2.31798 - 7.13400i) q^{96} +(0.528744 - 0.384155i) q^{97} -16.4144 q^{98} +6.22668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.365564	−	1.12509i	−0.258493	−	0.795560i	−0.993121	−	0.117090i	$-0.962643\pi$
$2$	−0.365564	−	1.12509i	−0.258493	−	0.795560i	0.734628	−	0.678470i	$-0.237357\pi$
$3$	−0.709225	+	2.18277i	−0.409471	+	1.26022i	0.507633	+	0.861574i	$0.330521\pi$
$3$	−0.709225	+	2.18277i	−0.409471	+	1.26022i	−0.917104	+	0.398649i	$0.869479\pi$
$4$	0.485840	−	0.352983i	0.242920	−	0.176492i
$5$	3.83735			1.71612			0.858058	−	0.513553i	$-0.171671\pi$
$5$	3.83735			1.71612			0.858058	+	0.513553i	$0.171671\pi$
$6$	2.71508			1.10843
$7$	3.69636	−	2.68556i	1.39709	−	1.01505i	0.402049	−	0.915618i	$-0.368298\pi$
$7$	3.69636	−	2.68556i	1.39709	−	1.01505i	0.995045	−	0.0994294i	$-0.0317017\pi$
$8$	−2.48886	−	1.80827i	−0.879947	−	0.639319i
$9$	−1.83443	−	1.33279i	−0.611477	−	0.444264i
$10$	−1.40280	−	4.31737i	−0.443604	−	1.36527i
$11$	−2.22162	+	1.61410i	−0.669845	+	0.486671i	−0.869973	−	0.493099i	$-0.835864\pi$
$11$	−2.22162	+	1.61410i	−0.669845	+	0.486671i	0.200128	+	0.979770i	$0.435864\pi$
$12$	0.425911	+	1.31082i	0.122950	+	0.378401i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−4.37276	−	3.17700i	−1.16867	−	0.849089i
$15$	−2.72154	+	8.37605i	−0.702700	+	2.16269i
$16$	−0.753476	+	2.31896i	−0.188369	+	0.579740i
$17$	−3.58469	−	2.60443i	−0.869416	−	0.631668i	0.0610143	−	0.998137i	$-0.480566\pi$
$17$	−3.58469	−	2.60443i	−0.869416	−	0.631668i	−0.930430	+	0.366469i	$0.880566\pi$
$18$	−0.828910	+	2.55112i	−0.195376	+	0.601306i
$19$	−0.987268	−	3.03850i	−0.226495	−	0.697079i	−0.998136	−	0.0610218i	$-0.980564\pi$
$19$	−0.987268	−	3.03850i	−0.226495	−	0.697079i	0.771642	−	0.636058i	$-0.219436\pi$
$20$	1.86434	−	1.35452i	0.416879	−	0.302880i
$21$	3.24041	+	9.97297i	0.707117	+	2.17628i
$22$	2.62816	+	1.90947i	0.560326	+	0.407101i
$23$	3.54452	+	2.57524i	0.739083	+	0.536975i	0.892424	−	0.451198i	$-0.149003\pi$
$23$	3.54452	+	2.57524i	0.739083	+	0.536975i	−0.153341	+	0.988173i	$0.549003\pi$
$24$	5.71219	−	4.15015i	1.16600	−	0.847146i
$25$	9.72526			1.94505
$26$	1.18299			0.232004
$27$	−1.36012	+	0.988187i	−0.261756	+	0.190177i
$28$	0.847880	−	2.60951i	0.160234	−	0.493151i
$29$	−2.47236	−	7.60913i	−0.459105	−	1.41298i	−0.866247	−	0.499615i	$-0.833475\pi$
$29$	−2.47236	−	7.60913i	−0.459105	−	1.41298i	0.407142	−	0.913365i	$-0.366525\pi$
$30$	10.4187			1.90219
$31$	−2.67458	+	4.88330i	−0.480368	+	0.877067i
$31$	−2.67458	+	4.88330i	−0.480368	+	0.877067i
$32$	−3.26832			−0.577763
$33$	−1.94759	−	5.99405i	−0.339031	−	1.04343i
$34$	−1.61979	+	4.98520i	−0.277791	+	0.854954i
$35$	14.1842	−	10.3054i	2.39757	−	1.74194i
$36$	−1.36169			−0.226949
$37$	2.91823			0.479754			0.239877	−	0.970803i	$-0.422893\pi$
$37$	2.91823			0.479754			0.239877	+	0.970803i	$0.422893\pi$
$38$	−3.05768	+	2.22153i	−0.496021	+	0.360380i
$39$	−1.85677	−	1.34903i	−0.297322	−	0.216017i
$40$	−9.55065	−	6.93895i	−1.51009	−	1.09714i
$41$	3.88239	+	11.9488i	0.606328	+	1.86609i	0.487390	+	0.873185i	$0.337949\pi$
$41$	3.88239	+	11.9488i	0.606328	+	1.86609i	0.118939	+	0.992902i	$0.462051\pi$
$42$	10.0359	−	7.29153i	1.54858	−	1.12511i
$43$	1.32629	+	4.08190i	0.202257	+	0.622484i	0.999815	+	0.0192409i	$0.00612494\pi$
$43$	1.32629	+	4.08190i	0.202257	+	0.622484i	−0.797558	+	0.603243i	$0.793875\pi$
$44$	−0.509602	+	1.56839i	−0.0768253	+	0.236444i
$45$	−7.03935	−	5.11439i	−1.04936	−	0.762408i
$46$	1.60163	−	4.92932i	0.236148	−	0.726789i
$47$	−1.73995	+	5.35502i	−0.253798	+	0.781110i	0.740266	+	0.672314i	$0.234699\pi$
$47$	−1.73995	+	5.35502i	−0.253798	+	0.781110i	−0.994064	+	0.108796i	$0.965301\pi$
$48$	−4.52737	−	3.28933i	−0.653470	−	0.474774i
$49$	4.28772	−	13.1962i	0.612531	−	1.88518i
$50$	−3.55521	−	10.9418i	−0.502783	−	1.54741i
$51$	8.22723	−	5.97743i	1.15204	−	0.837008i
$52$	0.185574	+	0.571139i	0.0257345	+	0.0792027i
$53$	−1.60139	−	1.16348i	−0.219968	−	0.159816i	0.472344	−	0.881414i	$-0.343408\pi$
$53$	−1.60139	−	1.16348i	−0.219968	−	0.159816i	−0.692312	+	0.721598i	$0.743408\pi$
$54$	1.60901	+	1.16902i	0.218959	+	0.159083i
$55$	−8.52515	+	6.19388i	−1.14953	+	0.835183i
$56$	−14.0560			−1.87831
$57$	7.33254			0.971218
$58$	−7.65717	+	5.56326i	−1.00544	+	0.730491i
$59$	−2.68018	+	8.24874i	−0.348929	+	1.07389i	0.610517	+	0.792003i	$0.290962\pi$
$59$	−2.68018	+	8.24874i	−0.348929	+	1.07389i	−0.959446	+	0.281891i	$0.909038\pi$
$60$	1.63437	+	5.03008i	0.210996	+	0.649380i
$61$	0.710650			0.0909894			0.0454947	−	0.998965i	$-0.485514\pi$
$61$	0.710650			0.0909894			0.0454947	+	0.998965i	$0.485514\pi$
$62$	6.47189	+	1.22398i	0.821931	+	0.155446i
$63$	−10.3600			−1.30524
$64$	2.70174	+	8.31509i	0.337717	+	1.03939i
$65$	−1.18581	+	3.64954i	−0.147081	+	0.452669i
$66$	−6.03189	+	4.38243i	−0.742475	+	0.539439i
$67$	−7.83185			−0.956812			−0.478406	−	0.878139i	$-0.658785\pi$
$67$	−7.83185			−0.956812			−0.478406	+	0.878139i	$0.658785\pi$
$68$	−2.66091			−0.322682
$69$	−8.13502	+	5.91044i	−0.979341	+	0.711533i
$70$	−16.7798	−	12.1913i	−2.00557	−	1.45713i
$71$	−4.48499	−	3.25854i	−0.532271	−	0.386717i	0.288936	−	0.957348i	$-0.406699\pi$
$71$	−4.48499	−	3.25854i	−0.532271	−	0.386717i	−0.821206	+	0.570631i	$0.806699\pi$
$72$	2.15561	+	6.63428i	0.254041	+	0.781857i
$73$	8.50131	−	6.17657i	0.995003	−	0.722912i	0.0339923	−	0.999422i	$-0.489178\pi$
$73$	8.50131	−	6.17657i	0.995003	−	0.722912i	0.961011	+	0.276510i	$0.0891778\pi$
$74$	−1.06680	−	3.28327i	−0.124013	−	0.381673i
$75$	−6.89739	+	21.2280i	−0.796442	+	2.45120i
$76$	−1.55219	−	1.12773i	−0.178049	−	0.129360i
$77$	−3.87714	+	11.9326i	−0.441842	+	1.35985i
$78$	−0.839007	+	2.58220i	−0.0949988	+	0.292376i
$79$	0.126322	+	0.0917780i	0.0142123	+	0.0103258i	0.594869	−	0.803823i	$-0.297204\pi$
$79$	0.126322	+	0.0917780i	0.0142123	+	0.0103258i	−0.580656	+	0.814149i	$0.697204\pi$
$80$	−2.89135	+	8.89867i	−0.323263	+	0.994901i
$81$	−3.29442	−	10.1392i	−0.366047	−	1.12658i
$82$	12.0242	−	8.73610i	1.32785	−	0.964741i
$83$	−1.04452	−	3.21471i	−0.114651	−	0.352861i	0.877223	−	0.480084i	$-0.159394\pi$
$83$	−1.04452	−	3.21471i	−0.114651	−	0.352861i	−0.991874	+	0.127223i	$0.959394\pi$
$84$	5.09461	+	3.70145i	0.555868	+	0.403862i
$85$	−13.7557	−	9.99412i	−1.49202	−	1.08401i
$86$	4.10767	−	2.98439i	0.442941	−	0.321815i
$87$	18.3624			1.96866
$88$	8.44805			0.900565
$89$	−7.33423	+	5.32863i	−0.777427	+	0.564833i	−0.904206	−	0.427098i	$-0.859536\pi$
$89$	−7.33423	+	5.32863i	−0.777427	+	0.564833i	0.126779	+	0.991931i	$0.459536\pi$
$90$	−3.18082	+	9.78956i	−0.335288	+	1.03191i
$91$	1.41188	+	4.34533i	0.148006	+	0.455515i
$92$	2.63109			0.274310
$93$	−8.76225	−	9.30134i	−0.908603	−	0.964504i
$94$	6.66095			0.687025
$95$	−3.78849	−	11.6598i	−0.388691	−	1.19627i
$96$	2.31798	−	7.13400i	0.236577	−	0.728110i
$97$	0.528744	−	0.384155i	0.0536858	−	0.0390050i	−0.560619	−	0.828074i	$-0.689437\pi$
$97$	0.528744	−	0.384155i	0.0536858	−	0.0390050i	0.614305	+	0.789069i	$0.289437\pi$
$98$	−16.4144			−1.65811
$99$	6.22668			0.625805
$100$	4.72492	−	3.43285i	0.472492	−	0.343285i
$101$	−0.499396	−	0.362832i	−0.0496918	−	0.0361032i	0.562662	−	0.826687i	$-0.309777\pi$
$101$	−0.499396	−	0.362832i	−0.0496918	−	0.0361032i	−0.612354	+	0.790584i	$0.709777\pi$
$102$	−9.73274	−	7.07125i	−0.963685	−	0.700158i
$103$	−2.29541	−	7.06453i	−0.226173	−	0.696089i	−0.998170	−	0.0604633i	$-0.980742\pi$
$103$	−2.29541	−	7.06453i	−0.226173	−	0.696089i	0.771997	−	0.635626i	$-0.219258\pi$
$104$	2.48886	−	1.80827i	0.244053	−	0.177315i
$105$	12.4346	+	38.2698i	1.21349	+	3.73475i
$106$	−0.723610	+	2.22704i	−0.0702832	+	0.216310i
$107$	11.6314	+	8.45073i	1.12445	+	0.816963i	0.984878	−	0.173249i	$-0.0554265\pi$
$107$	11.6314	+	8.45073i	1.12445	+	0.816963i	0.139574	+	0.990212i	$0.455427\pi$
$108$	−0.311988	+	0.960201i	−0.0300211	+	0.0923954i
$109$	1.67908	−	5.16769i	0.160827	−	0.494975i	−0.837877	−	0.545858i	$-0.816204\pi$
$109$	1.67908	−	5.16769i	0.160827	−	0.494975i	0.998705	+	0.0508833i	$0.0162036\pi$
$110$	10.0852	+	7.32731i	0.961584	+	0.698632i
$111$	−2.06968	+	6.36982i	−0.196445	+	0.604596i
$112$	3.44260	+	10.5952i	0.325295	+	1.00115i
$113$	−2.08312	+	1.51348i	−0.195963	+	0.142376i	−0.681440	−	0.731874i	$-0.738646\pi$
$113$	−2.08312	+	1.51348i	−0.195963	+	0.142376i	0.485477	+	0.874250i	$0.338646\pi$
$114$	−2.68051	−	8.24978i	−0.251053	−	0.772662i
$115$	13.6016	+	9.88211i	1.26835	+	0.921511i
$116$	−3.88707	−	2.82412i	−0.360905	−	0.262213i
$117$	1.83443	−	1.33279i	0.169593	−	0.123217i
$118$	10.2604			0.944543
$119$	−20.2447			−1.85583
$120$	21.9197	−	15.9256i	2.00098	−	1.45380i
$121$	−1.06891	+	3.28976i	−0.0971733	+	0.299069i
$122$	−0.259788	−	0.799547i	−0.0235201	−	0.0723875i
$123$	−28.8349			−2.59996
$124$	0.424309	+	3.31658i	0.0381040	+	0.297838i
$125$	18.1325			1.62182
$126$	3.78725	+	11.6560i	0.337395	+	1.03840i
$127$	4.09920	−	12.6160i	0.363745	−	1.11949i	−0.587018	−	0.809574i	$-0.699698\pi$
$127$	4.09920	−	12.6160i	0.363745	−	1.11949i	0.950763	−	0.309919i	$-0.100302\pi$
$128$	3.07932	−	2.23726i	0.272176	−	0.197747i
$129$	−9.85048			−0.867286
$130$	4.53955			0.398145
$131$	−14.7083	+	10.6862i	−1.28507	+	0.933657i	−0.999693	−	0.0247592i	$-0.992118\pi$
$131$	−14.7083	+	10.6862i	−1.28507	+	0.933657i	−0.285375	+	0.958416i	$0.592118\pi$
$132$	−3.06202	−	2.22468i	−0.266514	−	0.193634i
$133$	−11.8094	−	8.58002i	−1.02400	−	0.743982i
$134$	2.86304	+	8.81155i	0.247329	+	0.761202i
$135$	−5.21927	+	3.79202i	−0.449203	+	0.326365i
$136$	4.21231	+	12.9642i	0.361203	+	1.11167i
$137$	5.35313	−	16.4753i	0.457349	−	1.40758i	−0.411006	−	0.911633i	$-0.634822\pi$
$137$	5.35313	−	16.4753i	0.457349	−	1.40758i	0.868355	−	0.495943i	$-0.165178\pi$
$138$	9.62366	+	6.99200i	0.819220	+	0.595198i
$139$	−6.12756	+	18.8587i	−0.519733	+	1.59957i	0.254770	+	0.967002i	$0.418000\pi$
$139$	−6.12756	+	18.8587i	−0.519733	+	1.59957i	−0.774502	+	0.632571i	$0.782000\pi$
$140$	3.25361	−	10.0136i	0.274981	−	0.846303i
$141$	−10.4548	−	7.59582i	−0.880449	−	0.639684i
$142$	−2.02660	+	6.23723i	−0.170069	+	0.523417i
$143$	−0.848585	−	2.61168i	−0.0709622	−	0.218399i
$144$	4.47289	−	3.24975i	0.372741	−	0.270812i
$145$	−9.48730	−	29.1989i	−0.787877	−	2.42484i
$146$	−10.0570	−	7.30682i	−0.832322	−	0.604717i
$147$	25.7634	+	18.7182i	2.12493	+	1.54385i
$148$	1.41779	−	1.03009i	0.116542	−	0.0846725i
$149$	−17.7056			−1.45050			−0.725250	−	0.688485i	$-0.758276\pi$
$149$	−17.7056			−1.45050			−0.725250	+	0.688485i	$0.758276\pi$
$150$	26.4049			2.15595
$151$	−8.83563	+	6.41946i	−0.719033	+	0.522408i	−0.886075	−	0.463541i	$-0.846579\pi$
$151$	−8.83563	+	6.41946i	−0.719033	+	0.522408i	0.167042	+	0.985950i	$0.446579\pi$
$152$	−3.03724	+	9.34765i	−0.246352	+	0.758195i
$153$	3.10471	+	9.55530i	0.251001	+	0.772500i
$154$	14.8426			1.19605
$155$	−10.2633	+	18.7389i	−0.824367	+	1.50515i
$156$	−1.37828			−0.110351
$157$	−2.32651	−	7.16025i	−0.185675	−	0.571450i	0.814284	−	0.580467i	$-0.197130\pi$
$157$	−2.32651	−	7.16025i	−0.185675	−	0.571450i	−0.999959	+	0.00901667i	$0.997130\pi$
$158$	0.0570800	−	0.175674i	0.00454104	−	0.0139759i
$159$	3.67536	−	2.67030i	0.291475	−	0.211769i
$160$	−12.5417			−0.991509
$161$	20.0178			1.57762
$162$	−10.2032	+	7.41305i	−0.801639	+	0.582425i
$163$	10.8736	+	7.90015i	0.851688	+	0.618787i	0.925611	−	0.378477i	$-0.123552\pi$
$163$	10.8736	+	7.90015i	0.851688	+	0.618787i	−0.0739232	+	0.997264i	$0.523552\pi$
$164$	6.10394	+	4.43477i	0.476638	+	0.346298i
$165$	−7.47357	−	23.0013i	−0.581817	−	1.79065i
$166$	−3.23501	+	2.35037i	−0.251085	+	0.182424i
$167$	−0.264510	−	0.814079i	−0.0204684	−	0.0629953i	0.940301	−	0.340345i	$-0.110544\pi$
$167$	−0.264510	−	0.814079i	−0.0204684	−	0.0629953i	−0.960769	+	0.277350i	$0.910544\pi$
$168$	9.96883	−	30.6809i	0.769112	−	2.36708i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−6.21570	+	19.1299i	−0.476722	+	1.46720i
$171$	−2.23861	+	6.88974i	−0.171191	+	0.526871i
$172$	2.08521	+	1.51499i	0.158995	+	0.115517i
$173$	2.99485	−	9.21719i	0.227694	−	0.700770i	−0.770313	−	0.637666i	$-0.779900\pi$
$173$	2.99485	−	9.21719i	0.227694	−	0.700770i	0.998007	−	0.0631039i	$-0.0200999\pi$
$174$	−6.71265	−	20.6594i	−0.508885	−	1.56619i
$175$	35.9481	−	26.1178i	2.71742	−	1.97432i
$176$	−2.06910	−	6.36805i	−0.155965	−	0.480010i
$177$	−16.1042	−	11.7004i	−1.21047	−	0.879457i
$178$	8.67633	+	6.30372i	0.650318	+	0.472484i
$179$	−1.79028	+	1.30071i	−0.133812	+	0.0972200i	−0.652678	−	0.757636i	$-0.726354\pi$
$179$	−1.79028	+	1.30071i	−0.133812	+	0.0972200i	0.518866	+	0.854856i	$0.326354\pi$
$180$	−5.22529			−0.389470
$181$	1.05675			0.0785476			0.0392738	−	0.999228i	$-0.487496\pi$
$181$	1.05675			0.0785476			0.0392738	+	0.999228i	$0.487496\pi$
$182$	4.37276	−	3.17700i	0.324131	−	0.235495i
$183$	−0.504011	+	1.55118i	−0.0372575	+	0.114667i
$184$	−4.16510	−	12.8189i	−0.307055	−	0.945019i
$185$	11.1983			0.823313
$186$	−7.26170	+	13.2586i	−0.532453	+	0.972166i
$187$	12.1677			0.889788
$188$	1.04489	+	3.21585i	0.0762068	+	0.234540i
$189$	−2.37367	+	7.30539i	−0.172659	+	0.531389i
$190$	−11.7334	+	8.52480i	−0.851229	+	0.618454i
$191$	−12.7374			−0.921647			−0.460823	−	0.887492i	$-0.652446\pi$
$191$	−12.7374			−0.921647			−0.460823	+	0.887492i	$0.652446\pi$
$192$	−20.0661			−1.44814
$193$	16.4320	−	11.9386i	1.18280	−	0.859356i	0.190317	−	0.981723i	$-0.439048\pi$
$193$	16.4320	−	11.9386i	1.18280	−	0.859356i	0.992485	+	0.122367i	$0.0390484\pi$
$194$	−0.625500	−	0.454452i	−0.0449083	−	0.0326278i
$195$	−7.12509	−	5.17668i	−0.510239	−	0.370710i
$196$	−2.57491	−	7.92475i	−0.183922	−	0.566053i
$197$	3.51008	−	2.55023i	0.250083	−	0.181696i	−0.455681	−	0.890143i	$-0.650604\pi$
$197$	3.51008	−	2.55023i	0.250083	−	0.181696i	0.705764	+	0.708447i	$0.250604\pi$
$198$	−2.27625	−	7.00559i	−0.161766	−	0.497865i
$199$	6.33966	−	19.5115i	0.449406	−	1.38313i	−0.428172	−	0.903697i	$-0.640842\pi$
$199$	6.33966	−	19.5115i	0.449406	−	1.38313i	0.877578	−	0.479433i	$-0.159158\pi$
$200$	−24.2049	−	17.5859i	−1.71154	−	1.24351i
$201$	5.55454	−	17.0951i	0.391787	−	1.20580i
$202$	−0.225658	+	0.694505i	−0.0158773	+	0.0488652i
$203$	−29.5735	−	21.4864i	−2.07565	−	1.50805i
$204$	1.88718	−	5.80815i	0.132129	−	0.406652i
$205$	14.8981	+	45.8517i	1.04053	+	3.20242i
$206$	−7.10913	+	5.16508i	−0.495316	+	0.359868i
$207$	−3.06991	−	9.44821i	−0.213373	−	0.656696i
$208$	−1.97263	−	1.43320i	−0.136777	−	0.0993743i
$209$	7.09779	+	5.15685i	0.490964	+	0.356707i
$210$	38.5114	−	27.9802i	2.65754	−	1.93081i
$211$	−0.498873			−0.0343439			−0.0171719	−	0.999853i	$-0.505466\pi$
$211$	−0.498873			−0.0343439			−0.0171719	+	0.999853i	$0.505466\pi$
$212$	−1.18871			−0.0816410
$213$	10.2935	−	7.47867i	0.705299	−	0.512430i
$214$	5.25581	−	16.1757i	0.359280	−	1.10575i
$215$	5.08944	+	15.6637i	0.347097	+	1.06825i
$216$	5.17207			0.351915
$217$	3.22822	+	25.2332i	0.219146	+	1.71294i
$218$	−6.42794			−0.435355
$219$	7.45268	+	22.9370i	0.503605	+	1.54994i
$220$	−1.95552	+	6.01847i	−0.131841	+	0.405765i
$221$	3.58469	−	2.60443i	0.241133	−	0.175193i
$222$	7.92323			0.531772
$223$	10.8652			0.727589			0.363795	−	0.931479i	$-0.381481\pi$
$223$	10.8652			0.727589			0.363795	+	0.931479i	$0.381481\pi$
$224$	−12.0809	+	8.77729i	−0.807189	+	0.586457i
$225$	−17.8403	−	12.9617i	−1.18935	−	0.864116i
$226$	2.46431	+	1.79043i	0.163924	+	0.119098i
$227$	−2.66669	−	8.20723i	−0.176994	−	0.544733i	0.822725	−	0.568440i	$-0.192453\pi$
$227$	−2.66669	−	8.20723i	−0.176994	−	0.544733i	−0.999719	+	0.0237075i	$0.992453\pi$
$228$	3.56244	−	2.58826i	0.235928	−	0.171412i
$229$	3.73032	+	11.4808i	0.246507	+	0.758670i	0.995385	+	0.0959622i	$0.0305928\pi$
$229$	3.73032	+	11.4808i	0.246507	+	0.758670i	−0.748878	+	0.662708i	$0.769407\pi$
$230$	6.14603	−	18.9155i	0.405257	−	1.24725i
$231$	−23.2964	−	16.9258i	−1.53279	−	1.11364i
$232$	−7.60597	+	23.4088i	−0.499357	+	1.53686i
$233$	3.24285	−	9.98046i	0.212446	−	0.653841i	−0.786879	−	0.617107i	$-0.788304\pi$
$233$	3.24285	−	9.98046i	0.212446	−	0.653841i	0.999325	−	0.0367342i	$-0.0116955\pi$
$234$	−2.17012	−	1.57668i	−0.141865	−	0.103071i
$235$	−6.67680	+	20.5491i	−0.435546	+	1.34047i
$236$	1.60953	+	4.95362i	0.104771	+	0.322453i
$237$	−0.289921	+	0.210640i	−0.0188324	+	0.0136825i
$238$	7.40074	+	22.7771i	0.479719	+	1.47642i
$239$	−15.5240	−	11.2788i	−1.00416	−	0.729567i	−0.0411860	−	0.999151i	$-0.513114\pi$
$239$	−15.5240	−	11.2788i	−1.00416	−	0.729567i	−0.962977	+	0.269585i	$0.913114\pi$
$240$	−17.3731	−	12.6223i	−1.12143	−	0.814767i
$241$	4.31075	−	3.13194i	0.277680	−	0.201746i	−0.440225	−	0.897887i	$-0.645101\pi$
$241$	4.31075	−	3.13194i	0.277680	−	0.201746i	0.717905	+	0.696141i	$0.245101\pi$
$242$	4.09203			0.263046
$243$	19.4244			1.24607
$244$	0.345262	−	0.250848i	0.0221031	−	0.0160589i
$245$	16.4535	−	50.6386i	1.05117	−	3.23518i
$246$	10.5410	+	32.4419i	0.672071	+	2.06842i
$247$	3.19487			0.203284
$248$	15.4870	−	7.31753i	0.983424	−	0.464664i
$249$	7.75778			0.491629
$250$	−6.62859	−	20.4007i	−0.419229	−	1.29025i
$251$	−3.35920	+	10.3385i	−0.212031	+	0.652563i	0.787320	+	0.616544i	$0.211468\pi$
$251$	−3.35920	+	10.3385i	−0.212031	+	0.652563i	−0.999351	+	0.0360193i	$0.988532\pi$
$252$	−5.03331	+	3.65691i	−0.317069	+	0.230364i
$253$	−12.0313			−0.756401
$254$	−15.6927			−0.984649
$255$	31.5708	−	22.9375i	1.97704	−	1.43640i
$256$	10.5037	+	7.63136i	0.656479	+	0.476960i
$257$	10.5554	+	7.66895i	0.658428	+	0.478376i	0.866132	−	0.499816i	$-0.166599\pi$
$257$	10.5554	+	7.66895i	0.658428	+	0.478376i	−0.207704	+	0.978192i	$0.566599\pi$
$258$	3.60098	+	11.0827i	0.224188	+	0.689978i
$259$	10.7868	−	7.83709i	0.670261	−	0.486973i
$260$	0.712114	+	2.19166i	0.0441634	+	0.135921i
$261$	−5.60602	+	17.2536i	−0.347004	+	1.06797i
$262$	17.3998	+	12.6417i	1.07496	+	0.781005i
$263$	3.83840	−	11.8134i	0.236686	−	0.728444i	−0.760207	−	0.649681i	$-0.774903\pi$
$263$	3.83840	−	11.8134i	0.236686	−	0.728444i	0.996893	−	0.0787639i	$-0.0250973\pi$
$264$	−5.99157	+	18.4401i	−0.368755	+	1.13491i
$265$	−6.14511	−	4.46468i	−0.377491	−	0.274263i
$266$	−5.33622	+	16.4232i	−0.327184	+	1.00697i
$267$	−6.42955	−	19.7881i	−0.393482	−	1.21101i
$268$	−3.80502	+	2.76451i	−0.232429	+	0.168869i
$269$	−8.07067	−	24.8390i	−0.492077	−	1.51446i	−0.821462	−	0.570263i	$-0.806841\pi$
$269$	−8.07067	−	24.8390i	−0.492077	−	1.51446i	0.329385	−	0.944196i	$-0.393159\pi$
$270$	6.17435	+	4.48593i	0.375759	+	0.273005i
$271$	−11.4560	−	8.32329i	−0.695904	−	0.505604i	0.182692	−	0.983170i	$-0.441519\pi$
$271$	−11.4560	−	8.32329i	−0.695904	−	0.505604i	−0.878596	+	0.477567i	$0.841519\pi$
$272$	8.74056	−	6.35039i	0.529974	−	0.385049i
$273$	−10.4862			−0.634654
$274$	−20.4931			−1.23803
$275$	−21.6059	+	15.6976i	−1.30288	+	0.946600i
$276$	−1.86603	+	5.74305i	−0.112322	+	0.345691i
$277$	−2.70969	−	8.33956i	−0.162809	−	0.501076i	0.836059	−	0.548640i	$-0.184854\pi$
$277$	−2.70969	−	8.33956i	−0.162809	−	0.501076i	−0.998868	+	0.0475641i	$0.984854\pi$
$278$	23.4578			1.40690
$279$	11.4147	−	5.39343i	0.683383	−	0.322896i
$280$	−53.9376			−3.22339
$281$	4.71758	+	14.5192i	0.281427	+	0.866144i	0.987447	+	0.157952i	$0.0504890\pi$
$281$	4.71758	+	14.5192i	0.281427	+	0.866144i	−0.706020	+	0.708192i	$0.749511\pi$
$282$	−4.72411	+	14.5393i	−0.281317	+	0.865804i
$283$	11.3372	−	8.23692i	0.673924	−	0.489634i	−0.197413	−	0.980320i	$-0.563254\pi$
$283$	11.3372	−	8.23692i	0.673924	−	0.489634i	0.871336	+	0.490686i	$0.163254\pi$
$284$	−3.32920			−0.197552
$285$	28.1375			1.66672
$286$	−2.62816	+	1.90947i	−0.155406	+	0.112909i
$287$	46.4399	+	33.7406i	2.74126	+	1.99164i
$288$	5.99551	+	4.35599i	0.353289	+	0.256679i
$289$	0.813671	+	2.50422i	0.0478630	+	0.147307i
$290$	−29.3832	+	21.3482i	−1.72544	+	1.25361i
$291$	0.463524	+	1.42658i	0.0271722	+	0.0836275i
$292$	1.95005	−	6.00164i	0.114118	−	0.351220i
$293$	13.4292	+	9.75692i	0.784545	+	0.570005i	0.906340	−	0.422550i	$-0.138865\pi$
$293$	13.4292	+	9.75692i	0.784545	+	0.570005i	−0.121795	+	0.992555i	$0.538865\pi$
$294$	11.6415	−	35.8289i	0.678946	−	2.08958i
$295$	−10.2848	+	31.6533i	−0.598803	+	1.84293i
$296$	−7.26307	−	5.27693i	−0.422158	−	0.306715i
$297$	1.42664	−	4.39076i	0.0827823	−	0.254778i
$298$	6.47254	+	19.9204i	0.374944	+	1.15396i
$299$	−3.54452	+	2.57524i	−0.204985	+	0.148930i
$300$	4.14210	+	12.7481i	0.239144	+	0.736010i
$301$	15.8646	+	11.5263i	0.914423	+	0.664367i
$302$	10.4525	+	7.59417i	0.601472	+	0.436995i
$303$	1.14616	−	0.832736i	0.0658454	−	0.0478395i
$304$	7.79004			0.446790
$305$	2.72701			0.156148
$306$	9.61562	−	6.98616i	0.549688	−	0.399372i
$307$	−3.62147	+	11.1457i	−0.206688	+	0.636121i	0.792952	+	0.609285i	$0.208543\pi$
$307$	−3.62147	+	11.1457i	−0.206688	+	0.636121i	−0.999640	+	0.0268363i	$0.991457\pi$
$308$	2.32835	+	7.16591i	0.132670	+	0.408316i
$309$	17.0482			0.969838
$310$	24.8349	+	4.69685i	1.41053	+	0.266763i
$311$	20.4722			1.16087			0.580437	−	0.814305i	$-0.302882\pi$
$311$	20.4722			1.16087			0.580437	+	0.814305i	$0.302882\pi$
$312$	2.18186	+	6.71508i	0.123524	+	0.380167i
$313$	4.50579	−	13.8674i	0.254682	−	0.783832i	−0.739210	−	0.673475i	$-0.764801\pi$
$313$	4.50579	−	13.8674i	0.254682	−	0.783832i	0.993892	−	0.110357i	$-0.0351993\pi$
$314$	−7.20545	+	5.23507i	−0.406627	+	0.295432i
$315$	−39.7550			−2.23994
$316$	0.0937681			0.00527487
$317$	−13.3990	+	9.73495i	−0.752564	+	0.546769i	−0.896620	−	0.442800i	$-0.853985\pi$
$317$	−13.3990	+	9.73495i	−0.752564	+	0.546769i	0.144057	+	0.989569i	$0.453985\pi$
$318$	−4.34792	−	3.15895i	−0.243819	−	0.177145i
$319$	17.7746	+	12.9140i	0.995185	+	0.723044i
$320$	10.3675	+	31.9079i	0.579561	+	1.78371i
$321$	−26.6953	+	19.3953i	−1.48999	+	1.08254i
$322$	−7.31779	−	22.5219i	−0.407805	−	1.25509i
$323$	−4.37451	+	13.4634i	−0.243404	+	0.749121i
$324$	−5.17953	−	3.76315i	−0.287751	−	0.209064i
$325$	−3.00527	+	9.24927i	−0.166702	+	0.513057i
$326$	4.91338	−	15.1218i	0.272127	−	0.837521i
$327$	10.0890	+	7.33011i	0.557925	+	0.405356i
$328$	11.9438	−	36.7593i	0.659487	−	2.02969i
$329$	7.94976	+	24.4668i	0.438284	+	1.34890i
$330$	−23.1465	+	16.8169i	−1.27417	+	0.925740i
$331$	−2.91282	−	8.96473i	−0.160103	−	0.492746i	0.838539	−	0.544841i	$-0.183410\pi$
$331$	−2.91282	−	8.96473i	−0.160103	−	0.492746i	−0.998642	+	0.0520952i	$0.983410\pi$
$332$	−1.64221	−	1.19314i	−0.0901280	−	0.0654819i
$333$	−5.35329	−	3.88939i	−0.293358	−	0.213137i
$334$	−0.819218	+	0.595197i	−0.0448256	+	0.0325677i
$335$	−30.0535			−1.64200
$336$	−25.5685			−1.39488
$337$	−17.7488	+	12.8953i	−0.966839	+	0.702450i	−0.954729	−	0.297477i	$-0.903855\pi$
$337$	−17.7488	+	12.8953i	−0.966839	+	0.702450i	−0.0121101	+	0.999927i	$0.503855\pi$
$338$	−0.365564	+	1.12509i	−0.0198841	+	0.0611969i
$339$	−1.82617	−	5.62036i	−0.0991838	−	0.305256i
$340$	−10.2108			−0.553760
$341$	−1.94026	−	15.1659i	−0.105071	−	0.821280i
$342$	8.56994			0.463409
$343$	−9.70719	−	29.8756i	−0.524139	−	1.61313i
$344$	4.08020	−	12.5576i	0.219990	−	0.677059i
$345$	−31.2169	+	22.6804i	−1.68066	+	1.22107i
$346$	−11.4650			−0.616362
$347$	12.2566			0.657967			0.328984	−	0.944336i	$-0.393294\pi$
$347$	12.2566			0.657967			0.328984	+	0.944336i	$0.393294\pi$
$348$	8.92120	−	6.48163i	0.478227	−	0.347452i
$349$	−12.4132	−	9.01872i	−0.664463	−	0.482761i	0.203704	−	0.979033i	$-0.434702\pi$
$349$	−12.4132	−	9.01872i	−0.664463	−	0.482761i	−0.868167	+	0.496272i	$0.834702\pi$
$350$	−42.5263	−	30.8971i	−2.27312	−	1.65152i
$351$	−0.519521	−	1.59892i	−0.0277300	−	0.0853440i
$352$	7.26099	−	5.27541i	0.387012	−	0.281181i
$353$	8.35734	+	25.7213i	0.444816	+	1.36900i	0.882685	+	0.469965i	$0.155734\pi$
$353$	8.35734	+	25.7213i	0.444816	+	1.36900i	−0.437869	+	0.899039i	$0.644266\pi$
$354$	−7.27691	+	22.3960i	−0.386763	+	1.19033i
$355$	−17.2105	−	12.5042i	−0.913438	−	0.663652i
$356$	−1.68234	+	5.17772i	−0.0891640	+	0.274419i
$357$	14.3580	−	44.1895i	0.759908	−	2.33876i
$358$	2.11789	+	1.53873i	0.111934	+	0.0813247i
$359$	7.33126	−	22.5633i	0.386929	−	1.19085i	−0.548142	−	0.836385i	$-0.684665\pi$
$359$	7.33126	−	22.5633i	0.386929	−	1.19085i	0.935071	−	0.354460i	$-0.115335\pi$
$360$	8.27182	+	25.4580i	0.435963	+	1.34176i
$361$	7.11355	−	5.16830i	0.374397	−	0.272016i
$362$	−0.386310	−	1.18894i	−0.0203040	−	0.0624893i
$363$	−6.42268	−	4.66635i	−0.337104	−	0.244920i
$364$	2.21978	+	1.61276i	0.116348	+	0.0845318i
$365$	32.6225	−	23.7016i	1.70754	−	1.24060i
$366$	1.92947			0.100855
$367$	12.1296			0.633157			0.316579	−	0.948566i	$-0.397466\pi$
$367$	12.1296			0.633157			0.316579	+	0.948566i	$0.397466\pi$
$368$	−8.64260	+	6.27921i	−0.450527	+	0.327327i
$369$	8.80326	−	27.0936i	0.458279	−	1.41044i
$370$	−4.09369	−	12.5991i	−0.212821	−	0.654995i
$371$	−9.04393			−0.469538
$372$	−7.54027	−	1.42604i	−0.390945	−	0.0739365i
$373$	−24.9740			−1.29310			−0.646551	−	0.762871i	$-0.723789\pi$
$373$	−24.9740			−1.29310			−0.646551	+	0.762871i	$0.723789\pi$
$374$	−4.44807	−	13.6897i	−0.230004	−	0.707880i
$375$	−12.8600	+	39.5790i	−0.664087	+	2.04385i
$376$	14.0138	−	10.1816i	0.722707	−	0.525077i
$377$	8.00071			0.412058
$378$	9.08697			0.467383
$379$	6.06489	−	4.40640i	0.311533	−	0.226342i	−0.421021	−	0.907051i	$-0.638328\pi$
$379$	6.06489	−	4.40640i	0.311533	−	0.226342i	0.732554	+	0.680709i	$0.238328\pi$
$380$	−5.95631	−	4.32751i	−0.305552	−	0.221997i
$381$	24.6307	+	17.8952i	1.26187	+	0.916800i
$382$	4.65634	+	14.3308i	0.238239	+	0.733225i
$383$	−20.9737	+	15.2383i	−1.07171	+	0.778639i	−0.976218	−	0.216791i	$-0.930441\pi$
$383$	−20.9737	+	15.2383i	−1.07171	+	0.778639i	−0.0954872	+	0.995431i	$0.530441\pi$
$384$	2.69948	+	8.30816i	0.137758	+	0.423974i
$385$	−14.8780	+	45.7897i	−0.758251	+	2.33366i
$386$	−19.4389	−	14.1232i	−0.989415	−	0.718852i
$387$	3.00733	−	9.25562i	0.152871	−	0.470490i
$388$	0.121285	−	0.373276i	0.00615730	−	0.0189502i
$389$	17.2253	+	12.5149i	0.873359	+	0.634533i	0.931486	−	0.363777i	$-0.118513\pi$
$389$	17.2253	+	12.5149i	0.873359	+	0.634533i	−0.0581271	+	0.998309i	$0.518513\pi$
$390$	−3.21956	+	9.90880i	−0.163029	+	0.501751i
$391$	−5.99896	−	18.4629i	−0.303381	−	0.933710i
$392$	−34.5338	+	25.0903i	−1.74422	+	1.26725i
$393$	−12.8940	−	39.6837i	−0.650417	−	2.00178i
$394$	−4.15240	−	3.01690i	−0.209195	−	0.151989i
$395$	0.484740	+	0.352184i	0.0243899	+	0.0177203i
$396$	3.02517	−	2.19791i	0.152020	−	0.110449i
$397$	−27.8182			−1.39615			−0.698077	−	0.716023i	$-0.745961\pi$
$397$	−27.8182			−1.39615			−0.698077	+	0.716023i	$0.745961\pi$
$398$	−24.2697			−1.21653
$399$	27.1037	−	19.6920i	1.35688	−	0.985833i
$400$	−7.32775	+	22.5525i	−0.366388	+	1.12763i
$401$	2.55672	+	7.86878i	0.127677	+	0.392948i	0.994379	−	0.105877i	$-0.0337650\pi$
$401$	2.55672	+	7.86878i	0.127677	+	0.392948i	−0.866703	+	0.498825i	$0.833765\pi$
$402$	−21.2641			−1.06056
$403$	−3.81781	−	4.05270i	−0.190179	−	0.201879i
$404$	−0.370700			−0.0184430
$405$	−12.6419	−	38.9076i	−0.628179	−	1.93334i
$406$	−13.3632	+	41.1276i	−0.663203	+	2.04113i
$407$	−6.48320	+	4.71032i	−0.321360	+	0.233482i
$408$	−31.2852			−1.54885
$409$	9.39635			0.464619			0.232310	−	0.972642i	$-0.425372\pi$
$409$	9.39635			0.464619			0.232310	+	0.972642i	$0.425372\pi$
$410$	46.1411	−	33.5235i	2.27875	−	1.65561i
$411$	32.1651	+	23.3693i	1.58659	+	1.15272i
$412$	−3.60886	−	2.62199i	−0.177796	−	0.129176i
$413$	12.2456	+	37.6881i	0.602567	+	1.85451i
$414$	−9.50785	+	6.90786i	−0.467285	+	0.339503i
$415$	−4.00820	−	12.3360i	−0.196755	−	0.605550i
$416$	1.00997	−	3.10836i	0.0495177	−	0.152400i
$417$	−36.8183	−	26.7501i	−1.80300	−	1.30996i
$418$	3.20723	−	9.87083i	0.156871	−	0.482798i
$419$	−0.691979	+	2.12969i	−0.0338054	+	0.104042i	−0.966535	−	0.256533i	$-0.917420\pi$
$419$	−0.691979	+	2.12969i	−0.0338054	+	0.104042i	0.932730	+	0.360576i	$0.117420\pi$
$420$	19.5498	+	14.2038i	0.953934	+	0.693073i
$421$	−7.91134	+	24.3486i	−0.385575	+	1.18668i	0.550487	+	0.834844i	$0.314442\pi$
$421$	−7.91134	+	24.3486i	−0.385575	+	1.18668i	−0.936062	+	0.351835i	$0.885558\pi$
$422$	0.182370	+	0.561278i	0.00887765	+	0.0273226i
$423$	10.3289	−	7.50442i	0.502210	−	0.364877i
$424$	1.88177	+	5.79149i	0.0913869	+	0.281260i
$425$	−34.8621	−	25.3288i	−1.69106	−	1.22863i
$426$	−12.1771	−	8.84720i	−0.589984	−	0.428648i
$427$	2.62682	−	1.90850i	0.127121	−	0.0923586i
$428$	8.63398			0.417339
$429$	6.30252			0.304289
$430$	15.7626	−	11.4522i	0.760138	−	0.552272i
$431$	8.08591	−	24.8859i	0.389485	−	1.19871i	−0.543689	−	0.839287i	$-0.682973\pi$
$431$	8.08591	−	24.8859i	0.389485	−	1.19871i	0.933174	−	0.359424i	$-0.117027\pi$
$432$	−1.26675	−	3.89865i	−0.0609464	−	0.187574i
$433$	2.51993			0.121100			0.0605500	−	0.998165i	$-0.480715\pi$
$433$	2.51993			0.121100			0.0605500	+	0.998165i	$0.480715\pi$
$434$	27.2095	−	12.8564i	1.30610	−	0.617127i
$435$	70.4631			3.37845
$436$	−1.00834	−	3.10336i	−0.0482909	−	0.148624i
$437$	4.32548	−	13.3125i	0.206916	−	0.636822i
$438$	23.0818	−	16.7699i	1.10289	−	0.801296i
$439$	1.02886			0.0491050			0.0245525	−	0.999699i	$-0.492184\pi$
$439$	1.02886			0.0491050			0.0245525	+	0.999699i	$0.492184\pi$
$440$	32.4181			1.54547
$441$	−25.4533	+	18.4929i	−1.21206	+	0.880616i
$442$	−4.24066	−	3.08102i	−0.201708	−	0.146549i
$443$	−2.54016	−	1.84553i	−0.120687	−	0.0876840i	0.525805	−	0.850605i	$-0.323764\pi$
$443$	−2.54016	−	1.84553i	−0.120687	−	0.0876840i	−0.646491	+	0.762921i	$0.723764\pi$
$444$	1.24291	+	3.82527i	0.0589857	+	0.181539i
$445$	−28.1440	+	20.4478i	−1.33415	+	0.969319i
$446$	−3.97194	−	12.2244i	−0.188077	−	0.578841i
$447$	12.5573	−	38.6473i	0.593938	−	1.82795i
$448$	32.3173	+	23.4799i	1.52685	+	1.10932i
$449$	−1.55993	+	4.80096i	−0.0736175	+	0.226571i	−0.981094	−	0.193531i	$-0.938006\pi$
$449$	−1.55993	+	4.80096i	−0.0736175	+	0.226571i	0.907477	+	0.420103i	$0.138006\pi$
$450$	−8.06137	+	24.8103i	−0.380017	+	1.16957i
$451$	−27.9118	−	20.2791i	−1.31432	−	0.954906i
$452$	−0.477831	+	1.47061i	−0.0224753	+	0.0691718i
$453$	−7.74576	−	23.8390i	−0.363927	−	1.12005i
$454$	−8.25904	+	6.00054i	−0.387616	+	0.281619i
$455$	5.41790	+	16.6746i	0.253995	+	0.781716i
$456$	−18.2497	−	13.2592i	−0.854620	−	0.620918i
$457$	9.05930	+	6.58196i	0.423776	+	0.307891i	0.779155	−	0.626831i	$-0.215648\pi$
$457$	9.05930	+	6.58196i	0.423776	+	0.307891i	−0.355379	+	0.934722i	$0.615648\pi$
$458$	11.5532	−	8.39392i	0.539847	−	0.392222i
$459$	7.44929			0.347703
$460$	10.0964			0.470747
$461$	2.47304	−	1.79677i	0.115181	−	0.0836839i	−0.528704	−	0.848807i	$-0.677322\pi$
$461$	2.47304	−	1.79677i	0.115181	−	0.0836839i	0.643885	+	0.765123i	$0.277322\pi$
$462$	−10.5268	+	32.3981i	−0.489750	+	1.50729i
$463$	5.99444	+	18.4490i	0.278585	+	0.857398i	0.988248	+	0.152856i	$0.0488472\pi$
$463$	5.99444	+	18.4490i	0.278585	+	0.857398i	−0.709663	+	0.704541i	$0.751153\pi$
$464$	19.5081			0.905643
$465$	−33.6238	−	35.6925i	−1.55927	−	1.65520i
$466$	−12.4144			−0.575086
$467$	5.65509	+	17.4046i	0.261686	+	0.805388i	0.992438	+	0.122745i	$0.0391696\pi$
$467$	5.65509	+	17.4046i	0.261686	+	0.805388i	−0.730752	+	0.682643i	$0.760830\pi$
$468$	0.420786	−	1.29505i	0.0194508	−	0.0598636i
$469$	−28.9493	+	21.0329i	−1.33676	+	0.971210i
$470$	25.5604			1.17901
$471$	17.2792			0.796183
$472$	21.5865	−	15.6835i	0.993600	−	0.721893i
$473$	−9.53512	−	6.92767i	−0.438425	−	0.318535i
$474$	0.342974	+	0.249185i	0.0157533	+	0.0114454i
$475$	−9.60144	−	29.5502i	−0.440544	−	1.35586i
$476$	−9.83568	+	7.14604i	−0.450818	+	0.327538i
$477$	1.38697	+	4.26865i	0.0635049	+	0.195448i
$478$	−7.01470	+	21.5890i	−0.320845	+	0.987460i
$479$	−8.60696	−	6.25332i	−0.393262	−	0.285722i	0.373529	−	0.927619i	$-0.378148\pi$
$479$	−8.60696	−	6.25332i	−0.393262	−	0.285722i	−0.766791	+	0.641897i	$0.778148\pi$
$480$	8.89489	−	27.3756i	0.405994	−	1.24952i
$481$	−0.901782	+	2.77540i	−0.0411177	+	0.126547i
$482$	−5.09958	−	3.70506i	−0.232279	−	0.168761i
$483$	−14.1971	+	43.6942i	−0.645991	+	1.98816i
$484$	0.641912	+	1.97560i	0.0291778	+	0.0898001i
$485$	2.02898	−	1.47414i	0.0921311	−	0.0669372i
$486$	−7.10086	−	21.8542i	−0.322102	−	0.991327i
$487$	−22.8474	−	16.5996i	−1.03531	−	0.752200i	−0.0659486	−	0.997823i	$-0.521007\pi$
$487$	−22.8474	−	16.5996i	−1.03531	−	0.752200i	−0.969365	+	0.245623i	$0.921007\pi$
$488$	−1.76871	−	1.28504i	−0.0800658	−	0.0581712i
$489$	−24.9560	+	18.1316i	−1.12855	+	0.819940i
$490$	−62.9878			−2.84550
$491$	30.5706			1.37963			0.689816	−	0.723984i	$-0.257691\pi$
$491$	30.5706			1.37963			0.689816	+	0.723984i	$0.257691\pi$
$492$	−14.0092	+	10.1782i	−0.631581	+	0.458871i
$493$	−10.9548	+	33.7155i	−0.493381	+	1.51847i
$494$	−1.16793	−	3.59452i	−0.0525476	−	0.161725i
$495$	23.8940			1.07395
$496$	−9.30896	−	9.88169i	−0.417985	−	0.443701i
$497$	−25.3292			−1.13617
$498$	−2.83597	−	8.72821i	−0.127083	−	0.391121i
$499$	−8.23117	+	25.3329i	−0.368478	+	1.13406i	0.579297	+	0.815117i	$0.303327\pi$
$499$	−8.23117	+	25.3329i	−0.368478	+	1.13406i	−0.947775	+	0.318941i	$0.896673\pi$
$500$	8.80948	−	6.40046i	0.393972	−	0.286237i
$501$	1.96454			0.0877694
$502$	12.8598			0.573962
$503$	13.9417	−	10.1293i	0.621631	−	0.451642i	−0.231860	−	0.972749i	$-0.574481\pi$
$503$	13.9417	−	10.1293i	0.621631	−	0.451642i	0.853491	+	0.521108i	$0.174481\pi$
$504$	25.7847	+	18.7337i	1.14854	+	0.834464i
$505$	−1.91636	−	1.39232i	−0.0852768	−	0.0619572i
$506$	4.39821	+	13.5363i	0.195524	+	0.601762i
$507$	1.85677	−	1.34903i	0.0824622	−	0.0599123i
$508$	−2.46170	−	7.57633i	−0.109220	−	0.336145i
$509$	−2.04333	+	6.28871i	−0.0905688	+	0.278742i	−0.986074	−	0.166310i	$-0.946815\pi$
$509$	−2.04333	+	6.28871i	−0.0905688	+	0.278742i	0.895505	+	0.445052i	$0.146815\pi$
$510$	−37.3479	−	27.1349i	−1.65379	−	1.20155i
$511$	14.8364	−	45.6616i	0.656322	−	2.01995i
$512$	7.09860	−	21.8473i	0.313717	−	0.965521i
$513$	4.34541	+	3.15713i	0.191855	+	0.139390i
$514$	4.76959	−	14.6793i	0.210378	−	0.647476i
$515$	−8.80827	−	27.1091i	−0.388139	−	1.19457i
$516$	−4.78575	+	3.47705i	−0.210681	+	0.153069i
$517$	−4.77804	−	14.7053i	−0.210138	−	0.646738i
$518$	−12.7607	−	9.27121i	−0.560674	−	0.407353i
$519$	17.9950	+	13.0741i	0.789892	+	0.573890i
$520$	9.55065	−	6.93895i	0.418824	−	0.304293i
$521$	17.5368			0.768300			0.384150	−	0.923271i	$-0.374494\pi$
$521$	17.5368			0.768300			0.384150	+	0.923271i	$0.374494\pi$
$522$	21.4612			0.939331
$523$	1.21691	−	0.884135i	0.0532117	−	0.0386605i	−0.560861	−	0.827910i	$-0.689530\pi$
$523$	1.21691	−	0.884135i	0.0532117	−	0.0386605i	0.614073	+	0.789249i	$0.289530\pi$
$524$	−3.37382	+	10.3836i	−0.147386	+	0.453608i
$525$	31.5139	+	96.9897i	1.37538	+	4.23298i
$526$	−14.6943			−0.640703
$527$	22.3058	−	10.5394i	0.971654	−	0.459103i
$528$	15.3674			0.668782
$529$	−1.17566	−	3.61832i	−0.0511158	−	0.157318i
$530$	−2.77675	+	8.54594i	−0.120614	+	0.371212i
$531$	15.9105	−	11.5596i	0.690455	−	0.501645i
$532$	−8.76607			−0.380057
$533$	−12.5637			−0.544194
$534$	−19.9130	+	14.4677i	−0.861721	+	0.626077i
$535$	44.6339	+	32.4284i	1.92969	+	1.40200i
$536$	19.4924	+	14.1621i	0.841944	+	0.611708i
$537$	−1.56945	−	4.83027i	−0.0677267	−	0.208441i
$538$	−24.9958	+	18.1605i	−1.07764	+	0.782954i
$539$	11.7744	+	36.2379i	0.507159	+	1.56088i
$540$	−1.19721	+	3.68463i	−0.0515196	+	0.158561i
$541$	13.1200	+	9.53223i	0.564073	+	0.409823i	0.832947	−	0.553352i	$-0.186652\pi$
$541$	13.1200	+	9.53223i	0.564073	+	0.409823i	−0.268875	+	0.963175i	$0.586652\pi$
$542$	−5.17655	+	15.9318i	−0.222352	+	0.684328i
$543$	−0.749473	+	2.30664i	−0.0321630	+	0.0989874i
$544$	11.7159	+	8.51213i	0.502317	+	0.364954i
$545$	6.44324	−	19.8302i	0.275998	−	0.849434i
$546$	3.83338	+	11.7979i	0.164054	+	0.504905i
$547$	15.0662	−	10.9462i	0.644182	−	0.468026i	−0.217102	−	0.976149i	$-0.569661\pi$
$547$	15.0662	−	10.9462i	0.644182	−	0.468026i	0.861284	+	0.508123i	$0.169661\pi$
$548$	−3.21472	−	9.89390i	−0.137326	−	0.422647i
$549$	−1.30364	−	0.947149i	−0.0556379	−	0.0404233i
$550$	25.5596	+	18.5701i	1.08986	+	0.791832i
$551$	−20.6795	+	15.0245i	−0.880974	+	0.640065i
$552$	30.9346			1.31666
$553$	0.713406			0.0303371
$554$	−8.39221	+	6.09730i	−0.356551	+	0.259049i
$555$	−7.94208	+	24.4432i	−0.337123	+	1.03756i
$556$	3.67979	+	11.3252i	0.156058	+	0.480297i
$557$	9.08992			0.385152			0.192576	−	0.981282i	$-0.438316\pi$
$557$	9.08992			0.385152			0.192576	+	0.981282i	$0.438316\pi$
$558$	−10.2409	−	10.8710i	−0.433533	−	0.460206i
$559$	−4.29196			−0.181531
$560$	13.2105	+	40.6576i	0.558244	+	1.71810i
$561$	−8.62961	+	26.5592i	−0.364342	+	1.12133i
$562$	14.6109	−	10.6154i	0.616322	−	0.447784i
$563$	42.3906			1.78655			0.893276	−	0.449509i	$-0.148401\pi$
$563$	42.3906			1.78655			0.893276	+	0.449509i	$0.148401\pi$
$564$	−7.76053			−0.326777
$565$	−7.99366	+	5.80774i	−0.336296	+	0.244333i
$566$	−13.4118	−	9.74421i	−0.563738	−	0.409580i
$567$	−39.4068	−	28.6307i	−1.65493	−	1.20238i
$568$	5.27024	+	16.2201i	0.221134	+	0.680581i
$569$	34.7651	−	25.2584i	1.45743	−	1.05889i	0.473408	−	0.880843i	$-0.343024\pi$
$569$	34.7651	−	25.2584i	1.45743	−	1.05889i	0.984023	−	0.178042i	$-0.0569762\pi$
$570$	−10.2861	−	31.6573i	−0.430836	−	1.32598i
$571$	7.32454	−	22.5426i	0.306523	−	0.943380i	−0.672582	−	0.740023i	$-0.734815\pi$
$571$	7.32454	−	22.5426i	0.306523	−	0.943380i	0.979105	−	0.203357i	$-0.0651852\pi$
$572$	−1.33415	−	0.969320i	−0.0557838	−	0.0405293i
$573$	9.03369	−	27.8028i	0.377388	−	1.16148i
$574$	20.9845	−	64.5836i	0.875875	−	2.69567i
$575$	34.4713	+	25.0449i	1.43755	+	1.04444i
$576$	6.12613	−	18.8543i	0.255256	−	0.785596i
$577$	−2.17267	−	6.68680i	−0.0904496	−	0.278375i	0.895592	−	0.444877i	$-0.146753\pi$
$577$	−2.17267	−	6.68680i	−0.0904496	−	0.278375i	−0.986041	+	0.166502i	$0.946753\pi$
$578$	2.52003	−	1.83091i	0.104819	−	0.0761558i
$579$	14.4051	+	44.3344i	0.598656	+	1.84247i
$580$	−14.9160	−	10.8371i	−0.619355	−	0.449987i
$581$	−12.4943	−	9.07761i	−0.518349	−	0.376603i
$582$	1.43558	−	1.04301i	0.0595069	−	0.0432343i
$583$	5.43567			0.225123
$584$	−32.3275			−1.33772
$585$	7.03935	−	5.11439i	0.291041	−	0.211454i
$586$	6.06817	−	18.6759i	0.250674	−	0.771495i
$587$	−8.68487	−	26.7293i	−0.358463	−	1.10324i	−0.953974	−	0.299889i	$-0.903050\pi$
$587$	−8.68487	−	26.7293i	−0.358463	−	1.10324i	0.595511	−	0.803347i	$-0.296950\pi$
$588$	19.1241			0.788664
$589$	17.4784	+	3.30557i	0.720186	+	0.136204i
$590$	39.3726			1.62095
$591$	3.07711	+	9.47039i	0.126576	+	0.389560i
$592$	−2.19882	+	6.76726i	−0.0903708	+	0.278133i
$593$	1.04695	−	0.760652i	0.0429930	−	0.0312362i	−0.566081	−	0.824349i	$-0.691541\pi$
$593$	1.04695	−	0.760652i	0.0429930	−	0.0312362i	0.609074	+	0.793113i	$0.291541\pi$
$594$	−5.46154			−0.224090
$595$	−77.6860			−3.18481
$596$	−8.60209	+	6.24979i	−0.352355	+	0.256001i
$597$	38.0928	+	27.6760i	1.55903	+	1.13270i
$598$	4.19313	+	3.04649i	0.171470	+	0.124580i
$599$	−12.7549	−	39.2555i	−0.521151	−	1.60394i	−0.771804	−	0.635860i	$-0.780645\pi$
$599$	−12.7549	−	39.2555i	−0.521151	−	1.60394i	0.250653	−	0.968077i	$-0.419355\pi$
$600$	55.5525	−	40.3613i	2.26792	−	1.64774i
$601$	7.41584	+	22.8236i	0.302499	+	0.930995i	0.980599	+	0.196026i	$0.0628035\pi$
$601$	7.41584	+	22.8236i	0.302499	+	0.930995i	−0.678100	+	0.734969i	$0.737196\pi$
$602$	7.16864	−	22.0628i	0.292172	−	0.899212i
$603$	14.3670	+	10.4382i	0.585069	+	0.425077i
$604$	−2.02674	+	6.23766i	−0.0824668	+	0.253807i
$605$	−4.10177	+	12.6240i	−0.166761	+	0.513237i
$606$	−1.35590	−	0.985120i	−0.0550797	−	0.0400178i
$607$	−3.41155	+	10.4997i	−0.138471	+	0.426169i	−0.996114	−	0.0880767i	$-0.971928\pi$
$607$	−3.41155	+	10.4997i	−0.138471	+	0.426169i	0.857643	+	0.514245i	$0.171928\pi$
$608$	3.22671	+	9.93080i	0.130860	+	0.402747i
$609$	67.8742	−	49.3135i	2.75040	−	1.99828i
$610$	−0.996899	−	3.06814i	−0.0403633	−	0.124225i
$611$	−4.55525	−	3.30958i	−0.184286	−	0.133891i
$612$	4.88125	+	3.54644i	0.197313	+	0.143356i
$613$	−33.7371	+	24.5115i	−1.36263	+	0.990009i	−0.364357	+	0.931259i	$0.618711\pi$
$613$	−33.7371	+	24.5115i	−1.36263	+	0.990009i	−0.998273	+	0.0587492i	$0.981289\pi$
$614$	13.8639			0.559500
$615$	−110.650			−4.46183
$616$	31.2271	−	22.6878i	1.25817	−	0.914117i
$617$	11.7685	−	36.2198i	0.473784	−	1.45816i	−0.373807	−	0.927506i	$-0.621948\pi$
$617$	11.7685	−	36.2198i	0.473784	−	1.45816i	0.847591	−	0.530650i	$-0.178052\pi$
$618$	−6.23222	−	19.1808i	−0.250697	−	0.771565i
$619$	−19.2160			−0.772357			−0.386178	−	0.922424i	$-0.626205\pi$
$619$	−19.2160			−0.772357			−0.386178	+	0.922424i	$0.626205\pi$
$620$	1.62822	+	12.7269i	0.0653909	+	0.511124i
$621$	−7.36580			−0.295579
$622$	−7.48393	−	23.0332i	−0.300078	−	0.923546i
$623$	−12.7996	+	39.3931i	−0.512805	+	1.57825i
$624$	4.52737	−	3.28933i	0.181240	−	0.131679i
$625$	20.9544			0.838175
$626$	−17.2493			−0.689419
$627$	−16.2901	+	11.8355i	−0.650565	+	0.472663i
$628$	−3.65776	−	2.65752i	−0.145960	−	0.106046i
$629$	−10.4610	−	7.60033i	−0.417105	−	0.303045i
$630$	14.5330	+	44.7280i	0.579009	+	1.78201i
$631$	28.4560	−	20.6745i	1.13282	−	0.823040i	0.146715	−	0.989179i	$-0.453130\pi$
$631$	28.4560	−	20.6745i	1.13282	−	0.823040i	0.986102	+	0.166139i	$0.0531300\pi$
$632$	−0.148438	−	0.456846i	−0.00590456	−	0.0181724i
$633$	0.353813	−	1.08893i	0.0140628	−	0.0432809i
$634$	15.8509	+	11.5164i	0.629520	+	0.457373i
$635$	15.7301	−	48.4122i	0.624229	−	1.92118i
$636$	0.843063	−	2.59468i	0.0334296	−	0.102886i
$637$	11.2254	+	8.15572i	0.444766	+	0.323141i
$638$	8.03167	−	24.7189i	0.317977	−	0.978632i
$639$	3.88446	+	11.9551i	0.153667	+	0.472937i
$640$	11.8164	−	8.58514i	0.467085	−	0.339357i
$641$	4.84730	+	14.9185i	0.191457	+	0.589244i	1.00000		0.000806461i	$0.000256705\pi$
$641$	4.84730	+	14.9185i	0.191457	+	0.589244i	−0.808543	+	0.588438i	$0.799743\pi$
$642$	31.5803	+	22.9444i	1.24637	+	0.905544i
$643$	31.8732	+	23.1573i	1.25696	+	0.913233i	0.998604	−	0.0528176i	$-0.0168202\pi$
$643$	31.8732	+	23.1573i	1.25696	+	0.913233i	0.258353	+	0.966051i	$0.416820\pi$
$644$	9.72544	−	7.06595i	0.383236	−	0.278437i
$645$	−37.7997			−1.48836
$646$	16.7467			0.658889
$647$	10.1058	−	7.34226i	0.397298	−	0.288654i	−0.371141	−	0.928576i	$-0.621033\pi$
$647$	10.1058	−	7.34226i	0.397298	−	0.288654i	0.768440	+	0.639922i	$0.221033\pi$
$648$	−10.1350	+	31.1923i	−0.398140	+	1.22535i
$649$	−7.35998	−	22.6517i	−0.288904	−	0.889156i
$650$	11.5049			0.451259
$651$	−57.3678	−	10.8495i	−2.24842	−	0.425227i
$652$	8.07146			0.316103
$653$	−7.74392	−	23.8333i	−0.303043	−	0.932670i	−0.980400	−	0.197016i	$-0.936875\pi$
$653$	−7.74392	−	23.8333i	−0.303043	−	0.932670i	0.677357	−	0.735654i	$-0.263125\pi$
$654$	4.55885	−	14.0307i	0.178265	−	0.548644i
$655$	−56.4408	+	41.0067i	−2.20533	+	1.60226i
$656$	−30.6341			−1.19606
$657$	−23.8271			−0.929585
$658$	24.6213	−	17.8884i	0.959838	−	0.697363i
$659$	−29.8157	−	21.6624i	−1.16146	−	0.843847i	−0.171494	−	0.985185i	$-0.554859\pi$
$659$	−29.8157	−	21.6624i	−1.16146	−	0.843847i	−0.989961	+	0.141338i	$0.954859\pi$
$660$	−11.7500	−	8.53690i	−0.457369	−	0.332298i
$661$	9.52280	+	29.3082i	0.370394	+	1.13996i	0.946534	+	0.322604i	$0.104558\pi$
$661$	9.52280	+	29.3082i	0.370394	+	1.13996i	−0.576140	+	0.817351i	$0.695442\pi$
$662$	−9.02132	+	6.55437i	−0.350624	+	0.254743i
$663$	3.14252	+	9.67169i	0.122045	+	0.375617i
$664$	−3.21338	+	9.88976i	−0.124703	+	0.383797i
$665$	−45.3167	−	32.9245i	−1.75731	−	1.27676i
$666$	−2.41895	+	7.44476i	−0.0937324	+	0.288479i
$667$	10.8320	−	33.3376i	0.419419	−	1.29084i
$668$	−0.415866	−	0.302144i	−0.0160903	−	0.0116903i
$669$	−7.70588	+	23.7163i	−0.297927	+	0.916924i
$670$	10.9865	+	33.8130i	0.424446	+	1.30631i
$671$	−1.57880	+	1.14706i	−0.0609488	+	0.0442819i
$672$	−10.5907	−	32.5949i	−0.408546	−	1.25738i
$673$	26.7908	+	19.4646i	1.03271	+	0.750307i	0.968849	−	0.247652i	$-0.0796589\pi$
$673$	26.7908	+	19.4646i	1.03271	+	0.750307i	0.0638598	+	0.997959i	$0.479659\pi$
$674$	20.9967	+	15.2550i	0.808762	+	0.587600i
$675$	−13.2275	+	9.61037i	−0.509128	+	0.369903i
$676$	−0.600531			−0.0230973
$677$	−14.8514			−0.570784			−0.285392	−	0.958411i	$-0.592124\pi$
$677$	−14.8514			−0.570784			−0.285392	+	0.958411i	$0.592124\pi$
$678$	−5.65584	+	4.10921i	−0.217211	+	0.157813i
$679$	0.922757	−	2.83995i	0.0354121	−	0.108987i
$680$	16.1641	+	49.7480i	0.619865	+	1.90775i
$681$	19.8058			0.758958
$682$	−16.3537	+	7.72708i	−0.626217	+	0.295885i
$683$	18.8806			0.722447			0.361223	−	0.932479i	$-0.382359\pi$
$683$	18.8806			0.722447			0.361223	+	0.932479i	$0.382359\pi$
$684$	1.34436	+	4.13750i	0.0514027	+	0.158201i
$685$	20.5419	−	63.2213i	0.784864	−	2.41556i
$686$	−30.0642	+	21.8429i	−1.14786	+	0.833968i
$687$	−27.7055			−1.05703
$688$	−10.4651			−0.398978
$689$	1.60139	−	1.16348i	0.0610083	−	0.0443251i
$690$	36.9294	+	26.8307i	1.40588	+	1.02143i
$691$	24.5937	+	17.8684i	0.935589	+	0.679745i	0.947355	−	0.320185i	$-0.103745\pi$
$691$	24.5937	+	17.8684i	0.935589	+	0.679745i	−0.0117657	+	0.999931i	$0.503745\pi$
$692$	−1.79850	−	5.53521i	−0.0683686	−	0.210417i
$693$	23.0161	−	16.7221i	0.874308	−	0.635222i
$694$	−4.48057	−	13.7898i	−0.170080	−	0.523453i
$695$	−23.5136	+	72.3674i	−0.891921	+	2.74505i
$696$	−45.7016	−	33.2042i	−1.73232	−	1.25860i
$697$	17.2026	−	52.9442i	0.651595	−	2.00540i
$698$	−5.60906	+	17.2629i	−0.212306	+	0.653411i
$699$	19.4851	+	14.1568i	0.736995	+	0.535458i
$700$	8.24586	−	25.3781i	0.311664	−	0.959203i
$701$	6.86083	+	21.1154i	0.259130	+	0.797519i	0.992988	+	0.118217i	$0.0377177\pi$
$701$	6.86083	+	21.1154i	0.259130	+	0.797519i	−0.733858	+	0.679303i	$0.762282\pi$
$702$	−1.60901	+	1.16902i	−0.0607283	+	0.0441217i
$703$	−2.88107	−	8.86703i	−0.108662	−	0.334426i
$704$	−19.4237	−	14.1121i	−0.732057	−	0.531870i
$705$	−40.1185	−	29.1478i	−1.51095	−	1.09777i
$706$	25.8836	−	18.8056i	0.974143	−	0.707756i
$707$	−2.82036			−0.106070
$708$	−11.9541			−0.449264
$709$	3.64783	−	2.65030i	0.136997	−	0.0995343i	−0.517176	−	0.855879i	$-0.673017\pi$
$709$	3.64783	−	2.65030i	0.136997	−	0.0995343i	0.654173	+	0.756345i	$0.273017\pi$
$710$	−7.77678	+	23.9345i	−0.291857	+	0.898244i
$711$	−0.109407	−	0.336721i	−0.00410309	−	0.0126280i
$712$	27.8895			1.04520
$713$	−22.0558	+	10.4213i	−0.825995	+	0.390280i
$714$	−54.9660			−2.05705
$715$	−3.25632	−	10.0219i	−0.121779	−	0.374798i
$716$	−0.410659	+	1.26388i	−0.0153470	+	0.0472333i
$717$	35.6291	−	25.8860i	1.33059	−	0.966732i
$718$	−28.0658			−1.04741
$719$	−5.06998			−0.189078			−0.0945391	−	0.995521i	$-0.530138\pi$
$719$	−5.06998			−0.189078			−0.0945391	+	0.995521i	$0.530138\pi$
$720$	17.1641	−	12.4704i	0.639667	−	0.464745i
$721$	−27.4569	−	19.9486i	−1.02255	−	0.742925i
$722$	−8.41527	−	6.11405i	−0.313184	−	0.227541i
$723$	3.77902	+	11.6306i	0.140543	+	0.432547i
$724$	0.513411	−	0.373015i	0.0190808	−	0.0138630i
$725$	−24.0443	−	74.0008i	−0.892983	−	2.74832i
$726$	−2.90217	+	8.93196i	−0.107710	+	0.331496i
$727$	1.06687	+	0.775127i	0.0395680	+	0.0287479i	0.607393	−	0.794401i	$-0.292215\pi$
$727$	1.06687	+	0.775127i	0.0395680	+	0.0287479i	−0.567825	+	0.823149i	$0.692215\pi$
$728$	4.34353	−	13.3680i	0.160982	−	0.495451i
$729$	−3.89298	+	11.9814i	−0.144185	+	0.443755i
$730$	−38.5922	−	28.0388i	−1.42836	−	1.03776i
$731$	5.87669	−	18.0866i	0.217357	−	0.668956i
$732$	0.302674	+	0.931535i	0.0111872	+	0.0344305i
$733$	23.1933	−	16.8509i	0.856665	−	0.622403i	−0.0703109	−	0.997525i	$-0.522399\pi$
$733$	23.1933	−	16.8509i	0.856665	−	0.622403i	0.926976	+	0.375122i	$0.122399\pi$
$734$	−4.43413	−	13.6469i	−0.163667	−	0.503715i
$735$	98.8631	+	71.8282i	3.64662	+	2.64942i
$736$	−11.5846	−	8.41673i	−0.427015	−	0.310245i
$737$	17.3994	−	12.6414i	0.640916	−	0.465653i
$738$	−33.7010			−1.24055
$739$	0.107878			0.00396836			0.00198418	−	0.999998i	$-0.499368\pi$
$739$	0.107878			0.00396836			0.00198418	+	0.999998i	$0.499368\pi$
$740$	5.44056	−	3.95280i	0.199999	−	0.145308i
$741$	−2.26588	+	6.97366i	−0.0832391	+	0.256184i
$742$	3.30614	+	10.1753i	0.121372	+	0.373545i
$743$	−34.0477			−1.24909			−0.624545	−	0.780989i	$-0.714716\pi$
$743$	−34.0477			−1.24909			−0.624545	+	0.780989i	$0.714716\pi$
$744$	4.98875	+	38.9943i	0.182896	+	1.42960i
$745$	−67.9426			−2.48923
$746$	9.12959	+	28.0980i	0.334258	+	1.02874i
$747$	−2.36844	+	7.28930i	−0.0866566	+	0.266702i
$748$	5.91154	−	4.29498i	0.216147	−	0.157040i
$749$	65.6889			2.40022
$750$	49.2312			1.79767
$751$	18.8019	−	13.6604i	0.686092	−	0.498475i	−0.189281	−	0.981923i	$-0.560616\pi$
$751$	18.8019	−	13.6604i	0.686092	−	0.498475i	0.875373	+	0.483448i	$0.160616\pi$
$752$	−11.1071	−	8.06976i	−0.405033	−	0.294274i
$753$	−20.1842	−	14.6647i	−0.735555	−	0.534412i
$754$	−2.92478	−	9.00154i	−0.106514	−	0.327817i
$755$	−33.9054	+	24.6337i	−1.23394	+	0.896513i
$756$	1.42546	+	4.38711i	0.0518435	+	0.159558i
$757$	−8.58693	+	26.4279i	−0.312097	+	0.960537i	0.664836	+	0.746990i	$0.268502\pi$
$757$	−8.58693	+	26.4279i	−0.312097	+	0.960537i	−0.976933	+	0.213547i	$0.931498\pi$
$758$	−7.17472	−	5.21274i	−0.260598	−	0.189335i
$759$	8.53289	−	26.2615i	0.309724	−	0.953233i
$760$	−11.6549	+	35.8702i	−0.422769	+	1.30115i
$761$	35.4857	+	25.7818i	1.28635	+	0.934591i	0.999725	−	0.0234502i	$-0.00746513\pi$
$761$	35.4857	+	25.7818i	1.28635	+	0.934591i	0.286630	+	0.958042i	$0.407465\pi$
$762$	11.1297	−	34.2536i	0.403185	−	1.24088i
$763$	−7.67166	−	23.6109i	−0.277733	−	0.854774i
$764$	−6.18834	+	4.49609i	−0.223886	+	0.162663i
$765$	11.9138	+	36.6670i	0.430746	+	1.32570i
$766$	24.8117	+	18.0267i	0.896483	+	0.651333i
$767$	−7.01680	−	5.09800i	−0.253362	−	0.184078i
$768$	−24.1069	+	17.5147i	−0.869885	+	0.632008i
$769$	−38.5363			−1.38966			−0.694828	−	0.719176i	$-0.744519\pi$
$769$	−38.5363			−1.38966			−0.694828	+	0.719176i	$0.744519\pi$
$770$	56.9564			2.05257
$771$	−24.2257	+	17.6010i	−0.872467	+	0.633885i
$772$	3.76921	−	11.6004i	0.135657	−	0.417509i
$773$	−16.5893	−	51.0566i	−0.596676	−	1.83638i	−0.546202	−	0.837654i	$-0.683927\pi$
$773$	−16.5893	−	51.0566i	−0.596676	−	1.83638i	−0.0504742	−	0.998725i	$-0.516073\pi$
$774$	−11.5128			−0.413819
$775$	−26.0109	+	47.4914i	−0.934341	+	1.70594i
$776$	−2.01063			−0.0721773
$777$	9.45627	+	29.1034i	0.339242	+	1.04408i
$778$	7.78348	−	23.9551i	0.279051	−	0.858832i
$779$	32.4734	−	23.5933i	1.16348	−	0.845318i
$780$	−5.28894			−0.189374
$781$	15.2236			0.544743
$782$	−18.5795	+	13.4988i	−0.664400	+	0.482715i
$783$	10.8820	+	7.90620i	0.388889	+	0.282545i
$784$	27.3709	+	19.8861i	0.977531	+	0.710218i
$785$	−8.92762	−	27.4764i	−0.318640	−	0.980674i
$786$	−39.9342	+	29.0139i	−1.42441	+	1.03489i
$787$	−9.05505	−	27.8686i	−0.322778	−	0.993407i	−0.972434	−	0.233179i	$-0.925087\pi$
$787$	−9.05505	−	27.8686i	−0.322778	−	0.993407i	0.649656	−	0.760228i	$-0.274913\pi$
$788$	0.805152	−	2.47800i	0.0286823	−	0.0882752i
$789$	23.0636	+	16.7567i	0.821086	+	0.596554i
$790$	0.219036	−	0.674123i	0.00779295	−	0.0239842i
$791$	−3.63543	+	11.1887i	−0.129261	+	0.397825i
$792$	−15.4974	−	11.2595i	−0.550675	−	0.400089i
$793$	−0.219603	+	0.675868i	−0.00779833	+	0.0240008i
$794$	10.1693	+	31.2980i	0.360896	+	1.11072i
$795$	14.1036	−	10.2469i	0.500205	−	0.363420i
$796$	−3.80716	−	11.7172i	−0.134941	−	0.415306i
$797$	3.09123	+	2.24591i	0.109497	+	0.0795543i	0.641186	−	0.767385i	$-0.278443\pi$
$797$	3.09123	+	2.24591i	0.109497	+	0.0795543i	−0.531689	+	0.846940i	$0.678443\pi$
$798$	−32.0634	−	23.2955i	−1.13503	−	0.824650i
$799$	20.1840	−	14.6645i	0.714058	−	0.518793i
$800$	−31.7853			−1.12378
$801$	20.5561			0.726313
$802$	7.91846	−	5.75310i	0.279610	−	0.203149i
$803$	−8.91710	+	27.4440i	−0.314678	+	0.968478i
$804$	−3.33567	−	10.2661i	−0.117640	−	0.362059i
$805$	76.8153			2.70738
$806$	−3.16400	+	5.77691i	−0.111447	+	0.203483i
$807$	59.9417			2.11005
$808$	0.586831	+	1.80608i	0.0206447	+	0.0635377i
$809$	−10.8066	+	33.2594i	−0.379941	+	1.16934i	0.560144	+	0.828396i	$0.310746\pi$
$809$	−10.8066	+	33.2594i	−0.379941	+	1.16934i	−0.940084	+	0.340942i	$0.889254\pi$
$810$	−39.1532	+	28.4465i	−1.37570	+	0.999508i
$811$	6.57303			0.230810			0.115405	−	0.993319i	$-0.463183\pi$
$811$	6.57303			0.230810			0.115405	+	0.993319i	$0.463183\pi$
$812$	−21.9523			−0.770376
$813$	26.2927	−	19.1028i	0.922125	−	0.669963i
$814$	7.66958	+	5.57227i	0.268818	+	0.195308i
$815$	41.7259	+	30.3156i	1.46159	+	1.06191i
$816$	7.66241	+	23.5825i	0.268238	+	0.825552i
$817$	11.0934	−	8.05985i	0.388110	−	0.281979i
$818$	−3.43497	−	10.5718i	−0.120101	−	0.369633i
$819$	3.20142	−	9.85296i	0.111867	−	0.344290i
$820$	23.4230	+	17.0178i	0.817965	+	0.594287i
$821$	−7.29190	+	22.4422i	−0.254489	+	0.783237i	0.739441	+	0.673221i	$0.235090\pi$
$821$	−7.29190	+	22.4422i	−0.254489	+	0.783237i	−0.993930	+	0.110015i	$0.964910\pi$
$822$	14.5342	−	44.7317i	0.506939	−	1.56020i
$823$	−32.5995	−	23.6849i	−1.13635	−	0.825605i	−0.149741	−	0.988725i	$-0.547844\pi$
$823$	−32.5995	−	23.6849i	−1.13635	−	0.825605i	−0.986606	+	0.163120i	$0.947844\pi$
$824$	−7.06160	+	21.7334i	−0.246002	+	0.757118i
$825$	−18.9408	−	58.2937i	−0.659433	−	2.02953i
$826$	37.9260	−	27.5549i	1.31962	−	0.958757i
$827$	−9.32629	−	28.7034i	−0.324307	−	0.998114i	−0.971752	−	0.236003i	$-0.924163\pi$
$827$	−9.32629	−	28.7034i	−0.324307	−	0.998114i	0.647445	−	0.762112i	$-0.275837\pi$
$828$	−4.82654	−	3.50669i	−0.167734	−	0.121866i
$829$	3.53401	+	2.56761i	0.122741	+	0.0891766i	0.647462	−	0.762098i	$-0.275830\pi$
$829$	3.53401	+	2.56761i	0.122741	+	0.0891766i	−0.524721	+	0.851274i	$0.675830\pi$
$830$	−12.4139	+	9.01919i	−0.430891	+	0.313061i
$831$	20.1251			0.698133
$832$	−8.74300			−0.303109
$833$	−49.7388	+	36.1374i	−1.72335	+	1.25209i
$834$	−16.6368	+	51.2029i	−0.576086	+	1.77301i
$835$	−1.01502	−	3.12391i	−0.0351262	−	0.108107i
$836$	5.26867			0.182221
$837$	−1.18786	−	9.28487i	−0.0410586	−	0.320932i
$838$	2.64906			0.0915104
$839$	8.72155	+	26.8422i	0.301101	+	0.926694i	0.981103	+	0.193484i	$0.0619788\pi$
$839$	8.72155	+	26.8422i	0.301101	+	0.926694i	−0.680002	+	0.733210i	$0.738021\pi$
$840$	38.2539	−	117.733i	1.31989	−	4.06219i
$841$	−28.3248	+	20.5792i	−0.976719	+	0.709628i
$842$	30.2865			1.04374
$843$	−35.0379			−1.20677
$844$	−0.242373	+	0.176094i	−0.00834281	+	0.00606140i
$845$	−3.10448	−	2.25554i	−0.106797	−	0.0775929i
$846$	−12.2191	−	8.87766i	−0.420100	−	0.305220i
$847$	4.88379	+	15.0307i	0.167809	+	0.516463i
$848$	3.90468	−	2.83692i	0.134087	−	0.0974201i
$849$	9.93871	+	30.5882i	0.341096	+	1.04978i
$850$	−15.7529	+	48.4823i	−0.540319	+	1.66293i
$851$	10.3437	+	7.51514i	0.354578	+	0.257616i
$852$	2.36115	−	7.26687i	0.0808916	−	0.248959i
$853$	−5.69900	+	17.5397i	−0.195130	+	0.600548i	0.804845	+	0.593485i	$0.202248\pi$
$853$	−5.69900	+	17.5397i	−0.195130	+	0.600548i	−0.999975	+	0.00706345i	$0.997752\pi$
$854$	−3.10750	−	2.25773i	−0.106337	−	0.0772581i
$855$	−8.59034	+	26.4383i	−0.293783	+	0.904172i
$856$	−13.6679	−	42.0654i	−0.467159	−	1.43777i
$857$	29.8518	−	21.6886i	1.01972	−	0.740869i	0.0534936	−	0.998568i	$-0.482964\pi$
$857$	29.8518	−	21.6886i	1.01972	−	0.740869i	0.966225	+	0.257699i	$0.0829643\pi$
$858$	−2.30398	−	7.09092i	−0.0786565	−	0.242080i
$859$	23.9021	+	17.3659i	0.815529	+	0.592517i	0.915428	−	0.402481i	$-0.131852\pi$
$859$	23.9021	+	17.3659i	0.815529	+	0.592517i	−0.0998990	+	0.994998i	$0.531852\pi$
$860$	8.00166	+	5.81355i	0.272854	+	0.198240i
$861$	−106.584	+	77.4380i	−3.63238	+	2.63908i
$862$	−30.9548			−1.05433
$863$	7.25219			0.246867			0.123434	−	0.992353i	$-0.460609\pi$
$863$	7.25219			0.246867			0.123434	+	0.992353i	$0.460609\pi$
$864$	4.44532	−	3.22971i	0.151233	−	0.109877i
$865$	11.4923	−	35.3696i	0.390749	−	1.20260i
$866$	−0.921196	−	2.83515i	−0.0313035	−	0.0963423i
$867$	−6.04322			−0.205238
$868$	10.4753	+	11.1198i	0.355555	+	0.377430i
$869$	−0.428778			−0.0145453
$870$	−25.7588	−	79.2775i	−0.873305	−	2.68776i
$871$	2.42017	−	7.44853i	0.0820045	−	0.252384i
$872$	−13.5236	+	9.82545i	−0.457966	+	0.332732i
$873$	−1.48194			−0.0501562
$874$	−16.5590			−0.560116
$875$	67.0242	−	48.6959i	2.26583	−	1.64622i
$876$	11.7172	+	8.51303i	0.395887	+	0.287628i
$877$	−12.5996	−	9.15413i	−0.425457	−	0.309113i	0.354373	−	0.935104i	$-0.384694\pi$
$877$	−12.5996	−	9.15413i	−0.425457	−	0.309113i	−0.779830	+	0.625991i	$0.784694\pi$
$878$	−0.376116	−	1.15757i	−0.0126933	−	0.0390660i
$879$	−30.8215	+	22.3931i	−1.03958	+	0.755300i
$880$	−7.93988	−	24.4364i	−0.267653	−	0.823752i
$881$	9.36327	−	28.8172i	0.315457	−	0.970876i	−0.660109	−	0.751169i	$-0.729490\pi$
$881$	9.36327	−	28.8172i	0.315457	−	0.970876i	0.975566	−	0.219706i	$-0.0705099\pi$
$882$	30.1111	+	21.8770i	1.01389	+	0.736637i
$883$	−16.6774	+	51.3278i	−0.561240	+	1.72732i	0.117628	+	0.993058i	$0.462471\pi$
$883$	−16.6774	+	51.3278i	−0.561240	+	1.72732i	−0.678868	+	0.734260i	$0.737529\pi$
$884$	0.822266	−	2.53067i	0.0276558	−	0.0851158i
$885$	−61.7976	−	44.8986i	−2.07730	−	1.50925i
$886$	−1.14780	+	3.53258i	−0.0385612	+	0.118679i
$887$	−1.85709	−	5.71555i	−0.0623551	−	0.191909i	0.915026	−	0.403395i	$-0.132170\pi$
$887$	−1.85709	−	5.71555i	−0.0623551	−	0.191909i	−0.977381	+	0.211486i	$0.932170\pi$
$888$	16.6695	−	12.1111i	0.559391	−	0.406421i
$889$	−18.7291	−	57.6421i	−0.628153	−	1.93325i
$890$	33.2941	+	24.1896i	1.11602	+	0.810837i
$891$	23.6847	+	17.2079i	0.793466	+	0.576487i
$892$	5.27876	−	3.83524i	0.176746	−	0.128413i
$893$	17.9890			0.601979
$894$	−48.0722			−1.60778
$895$	−6.86993	+	4.99130i	−0.229637	+	0.166841i
$896$	5.37398	−	16.5394i	0.179532	−	0.552543i
$897$	−3.10730	−	9.56329i	−0.103750	−	0.319309i
$898$	5.97178			0.199281
$899$	43.7702	+	8.27794i	1.45982	+	0.276085i
$900$	−13.2428			−0.441427
$901$	2.71030	+	8.34145i	0.0902932	+	0.277894i
$902$	−12.6123	+	38.8167i	−0.419944	+	1.29245i
$903$	−36.4109	+	26.4541i	−1.21168	+	0.880337i
$904$	7.92137			0.263461
$905$	4.05512			0.134797
$906$	−23.9895	+	17.4294i	−0.796997	+	0.579052i
$907$	−6.34583	−	4.61051i	−0.210710	−	0.153090i	0.477425	−	0.878673i	$-0.341570\pi$
$907$	−6.34583	−	4.61051i	−0.210710	−	0.153090i	−0.688135	+	0.725583i	$0.741570\pi$
$908$	−4.19260	−	3.04610i	−0.139136	−	0.101088i
$909$	0.432527	+	1.33118i	0.0143460	+	0.0441525i
$910$	16.7798	−	12.1913i	0.556246	−	0.404136i
$911$	−1.48020	−	4.55559i	−0.0490413	−	0.150934i	0.923537	−	0.383509i	$-0.125285\pi$
$911$	−1.48020	−	4.55559i	−0.0490413	−	0.150934i	−0.972578	+	0.232576i	$0.925285\pi$
$912$	−5.52489	+	17.0039i	−0.182947	+	0.563054i
$913$	7.50942	+	5.45591i	0.248526	+	0.180564i
$914$	4.09356	−	12.5987i	0.135403	−	0.416727i
$915$	−1.93407	+	5.95244i	−0.0639382	+	0.196782i
$916$	5.86486	+	4.26107i	0.193780	+	0.140790i
$917$	−25.6687	+	79.0000i	−0.847654	+	2.60881i
$918$	−2.72320	−	8.38113i	−0.0898789	−	0.276619i
$919$	−33.5358	+	24.3652i	−1.10624	+	0.803732i	−0.982068	−	0.188528i	$-0.939628\pi$
$919$	−33.5358	+	24.3652i	−1.10624	+	0.803732i	−0.124175	+	0.992260i	$0.539628\pi$
$920$	−15.9830	−	49.1905i	−0.526942	−	1.62176i
$921$	−21.7601	−	15.8097i	−0.717021	−	0.520946i
$922$	−2.92559	−	2.12556i	−0.0963490	−	0.0700017i
$923$	4.48499	−	3.25854i	0.147625	−	0.107256i
$924$	−17.2929			−0.568893
$925$	28.3805			0.933146
$926$	18.5655	−	13.4886i	0.610099	−	0.443263i
$927$	−5.20479	+	16.0187i	−0.170948	+	0.526123i
$928$	8.08046	+	24.8691i	0.265254	+	0.816368i
$929$	47.8535			1.57002			0.785011	−	0.619482i	$-0.212657\pi$
$929$	47.8535			1.57002			0.785011	+	0.619482i	$0.212657\pi$
$930$	−27.8657	+	50.8778i	−0.913751	+	1.66835i
$931$	−44.3299			−1.45285
$932$	−1.94743	−	5.99357i	−0.0637902	−	0.196326i
$933$	−14.5194	+	44.6862i	−0.475345	+	1.46296i
$934$	17.5144	−	12.7250i	0.573090	−	0.416374i
$935$	46.6916			1.52698
$936$	−6.97569			−0.228008
$937$	−19.8650	+	14.4328i	−0.648960	+	0.471497i	−0.862917	−	0.505346i	$-0.831365\pi$
$937$	−19.8650	+	14.4328i	−0.648960	+	0.471497i	0.213956	+	0.976843i	$0.431365\pi$
$938$	34.2468	+	24.8818i	1.11820	+	0.812419i
$939$	27.0737	+	19.6702i	0.883518	+	0.641913i
$940$	4.00963	+	12.3404i	0.130780	+	0.402498i
$941$	−34.8573	+	25.3253i	−1.13632	+	0.825582i	−0.986602	−	0.163147i	$-0.947835\pi$
$941$	−34.8573	+	25.3253i	−1.13632	+	0.825582i	−0.149715	+	0.988729i	$0.547835\pi$
$942$	−6.31666	−	19.4407i	−0.205808	−	0.633411i
$943$	−17.0098	+	52.3508i	−0.553915	+	1.70478i
$944$	−17.1091	−	12.4305i	−0.556852	−	0.404577i
$945$	−9.10859	+	28.0334i	−0.296302	+	0.911925i
$946$	−4.30857	+	13.2604i	−0.140084	+	0.431133i
$947$	29.0607	+	21.1138i	0.944344	+	0.686106i	0.949462	−	0.313881i	$-0.101629\pi$
$947$	29.0607	+	21.1138i	0.944344	+	0.686106i	−0.00511808	+	0.999987i	$0.501629\pi$
$948$	−0.0665027	+	0.204674i	−0.00215991	+	0.00664751i
$949$	3.24721	+	9.99389i	0.105409	+	0.324415i
$950$	−29.7367	+	21.6050i	−0.964787	+	0.700959i
$951$	−11.7462	−	36.1512i	−0.380898	−	1.17228i
$952$	50.3863	+	36.6078i	1.63303	+	1.18647i
$953$	18.5710	+	13.4926i	0.601574	+	0.437069i	0.846437	−	0.532489i	$-0.178743\pi$
$953$	18.5710	+	13.4926i	0.601574	+	0.437069i	−0.244863	+	0.969558i	$0.578743\pi$
$954$	4.29560	−	3.12093i	0.139075	−	0.101044i
$955$	−48.8779			−1.58165
$956$	−11.5234			−0.372694
$957$	−40.7944	+	29.6389i	−1.31870	+	0.958089i
$958$	−3.88916	+	11.9696i	−0.125653	+	0.386721i
$959$	−24.4582	−	75.2747i	−0.789797	−	2.43075i
$960$	−77.0005			−2.48518
$961$	−16.6933	−	26.1215i	−0.538493	−	0.842630i
$962$	3.45224			0.111305
$963$	−10.0740	−	31.0045i	−0.324630	−	0.999107i
$964$	0.988810	−	3.04324i	0.0318474	−	0.0980163i
$965$	63.0554	−	45.8124i	2.02982	−	1.47475i
$966$	54.3500			1.74868
$967$	−35.6928			−1.14780			−0.573901	−	0.818925i	$-0.694571\pi$
$967$	−35.6928			−1.14780			−0.573901	+	0.818925i	$0.694571\pi$
$968$	8.60912	−	6.25489i	0.276708	−	0.201040i
$969$	−26.2849	−	19.0971i	−0.844392	−	0.613487i
$970$	−2.40026	−	1.74389i	−0.0770678	−	0.0559930i
$971$	−8.00432	−	24.6347i	−0.256871	−	0.790567i	−0.993455	−	0.114221i	$-0.963563\pi$
$971$	−8.00432	−	24.6347i	−0.256871	−	0.790567i	0.736585	−	0.676345i	$-0.236437\pi$
$972$	9.43714	−	6.85648i	0.302696	−	0.219922i
$973$	27.9965	+	86.1645i	0.897528	+	2.76231i
$974$	−10.3239	+	31.7736i	−0.330798	+	1.01809i
$975$	−18.0576	−	13.1196i	−0.578306	−	0.420164i
$976$	−0.535458	+	1.64797i	−0.0171396	+	0.0527502i
$977$	−14.8534	+	45.7139i	−0.475201	+	1.46252i	0.370486	+	0.928838i	$0.379191\pi$
$977$	−14.8534	+	45.7139i	−0.475201	+	1.46252i	−0.845687	+	0.533680i	$0.820809\pi$
$978$	29.5228	+	21.4496i	0.944034	+	0.685881i
$979$	7.69293	−	23.6764i	0.245867	−	0.756702i
$980$	−9.88082	−	30.4100i	−0.315631	−	0.971413i
$981$	−9.96762	+	7.24190i	−0.318242	+	0.231216i
$982$	−11.1755	−	34.3948i	−0.356626	−	1.09758i
$983$	−4.22393	−	3.06886i	−0.134722	−	0.0978815i	0.518383	−	0.855149i	$-0.326534\pi$
$983$	−4.22393	−	3.06886i	−0.134722	−	0.0978815i	−0.653105	+	0.757267i	$0.726534\pi$
$984$	71.7662	+	52.1412i	2.28782	+	1.66220i
$985$	13.4694	−	9.78611i	0.429171	−	0.311811i
$986$	41.9377			1.33557
$987$	−59.0436			−1.87938
$988$	1.55219	−	1.12773i	0.0493818	−	0.0358780i
$989$	−5.81082	+	17.8839i	−0.184773	+	0.568674i
$990$	−8.73478	−	26.8829i	−0.277610	−	0.854394i
$991$	−14.6353			−0.464907			−0.232454	−	0.972608i	$-0.574675\pi$
$991$	−14.6353			−0.464907			−0.232454	+	0.972608i	$0.574675\pi$
$992$	8.74138	−	15.9602i	0.277539	−	0.506737i
$993$	21.6338			0.686527
$994$	9.25944	+	28.4976i	0.293692	+	0.903890i
$995$	24.3275	−	74.8723i	0.771233	−	2.37361i
$996$	3.76904	−	2.73837i	0.119427	−	0.0867685i
$997$	6.81927			0.215969			0.107984	−	0.994153i	$-0.465560\pi$
$997$	6.81927			0.215969			0.107984	+	0.994153i	$0.465560\pi$
$998$	31.5109			0.997460
$999$	−3.96915	+	2.88375i	−0.125578	+	0.0912380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.4	✓	48
31.8	even	5	inner	403.2.k.d.287.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.4	✓	48	1.1	even	1	trivial
403.2.k.d.287.4	yes	48	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.365564 - 1.12509i) q^{2} +(-0.709225 + 2.18277i) q^{3} +(0.485840 - 0.352983i) q^{4} +3.83735 q^{5} +2.71508 q^{6} +(3.69636 - 2.68556i) q^{7} +(-2.48886 - 1.80827i) q^{8} +(-1.83443 - 1.33279i) q^{9} +O(q^{10})\)	\(q+(-0.365564 - 1.12509i) q^{2} +(-0.709225 + 2.18277i) q^{3} +(0.485840 - 0.352983i) q^{4} +3.83735 q^{5} +2.71508 q^{6} +(3.69636 - 2.68556i) q^{7} +(-2.48886 - 1.80827i) q^{8} +(-1.83443 - 1.33279i) q^{9} +(-1.40280 - 4.31737i) q^{10} +(-2.22162 + 1.61410i) q^{11} +(0.425911 + 1.31082i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-4.37276 - 3.17700i) q^{14} +(-2.72154 + 8.37605i) q^{15} +(-0.753476 + 2.31896i) q^{16} +(-3.58469 - 2.60443i) q^{17} +(-0.828910 + 2.55112i) q^{18} +(-0.987268 - 3.03850i) q^{19} +(1.86434 - 1.35452i) q^{20} +(3.24041 + 9.97297i) q^{21} +(2.62816 + 1.90947i) q^{22} +(3.54452 + 2.57524i) q^{23} +(5.71219 - 4.15015i) q^{24} +9.72526 q^{25} +1.18299 q^{26} +(-1.36012 + 0.988187i) q^{27} +(0.847880 - 2.60951i) q^{28} +(-2.47236 - 7.60913i) q^{29} +10.4187 q^{30} +(-2.67458 + 4.88330i) q^{31} -3.26832 q^{32} +(-1.94759 - 5.99405i) q^{33} +(-1.61979 + 4.98520i) q^{34} +(14.1842 - 10.3054i) q^{35} -1.36169 q^{36} +2.91823 q^{37} +(-3.05768 + 2.22153i) q^{38} +(-1.85677 - 1.34903i) q^{39} +(-9.55065 - 6.93895i) q^{40} +(3.88239 + 11.9488i) q^{41} +(10.0359 - 7.29153i) q^{42} +(1.32629 + 4.08190i) q^{43} +(-0.509602 + 1.56839i) q^{44} +(-7.03935 - 5.11439i) q^{45} +(1.60163 - 4.92932i) q^{46} +(-1.73995 + 5.35502i) q^{47} +(-4.52737 - 3.28933i) q^{48} +(4.28772 - 13.1962i) q^{49} +(-3.55521 - 10.9418i) q^{50} +(8.22723 - 5.97743i) q^{51} +(0.185574 + 0.571139i) q^{52} +(-1.60139 - 1.16348i) q^{53} +(1.60901 + 1.16902i) q^{54} +(-8.52515 + 6.19388i) q^{55} -14.0560 q^{56} +7.33254 q^{57} +(-7.65717 + 5.56326i) q^{58} +(-2.68018 + 8.24874i) q^{59} +(1.63437 + 5.03008i) q^{60} +0.710650 q^{61} +(6.47189 + 1.22398i) q^{62} -10.3600 q^{63} +(2.70174 + 8.31509i) q^{64} +(-1.18581 + 3.64954i) q^{65} +(-6.03189 + 4.38243i) q^{66} -7.83185 q^{67} -2.66091 q^{68} +(-8.13502 + 5.91044i) q^{69} +(-16.7798 - 12.1913i) q^{70} +(-4.48499 - 3.25854i) q^{71} +(2.15561 + 6.63428i) q^{72} +(8.50131 - 6.17657i) q^{73} +(-1.06680 - 3.28327i) q^{74} +(-6.89739 + 21.2280i) q^{75} +(-1.55219 - 1.12773i) q^{76} +(-3.87714 + 11.9326i) q^{77} +(-0.839007 + 2.58220i) q^{78} +(0.126322 + 0.0917780i) q^{79} +(-2.89135 + 8.89867i) q^{80} +(-3.29442 - 10.1392i) q^{81} +(12.0242 - 8.73610i) q^{82} +(-1.04452 - 3.21471i) q^{83} +(5.09461 + 3.70145i) q^{84} +(-13.7557 - 9.99412i) q^{85} +(4.10767 - 2.98439i) q^{86} +18.3624 q^{87} +8.44805 q^{88} +(-7.33423 + 5.32863i) q^{89} +(-3.18082 + 9.78956i) q^{90} +(1.41188 + 4.34533i) q^{91} +2.63109 q^{92} +(-8.76225 - 9.30134i) q^{93} +6.66095 q^{94} +(-3.78849 - 11.6598i) q^{95} +(2.31798 - 7.13400i) q^{96} +(0.528744 - 0.384155i) q^{97} -16.4144 q^{98} +6.22668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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