LMFDB - Embedded newform 483.2.r.a.475.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			475.3
Character	$\chi$	$=$	483.475
Dual form			483.2.r.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.351125 + 2.44213i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-3.92172 - 1.15152i) q^{4} +(-2.70553 - 3.12235i) q^{5} +(-0.695102 - 2.36730i) q^{6} +(-0.374078 + 2.61917i) q^{7} +(2.13932 - 4.68445i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.351125 + 2.44213i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-3.92172 - 1.15152i) q^{4} +(-2.70553 - 3.12235i) q^{5} +(-0.695102 - 2.36730i) q^{6} +(-0.374078 + 2.61917i) q^{7} +(2.13932 - 4.68445i) q^{8} +(0.654861 - 0.755750i) q^{9} +(8.57515 - 5.51091i) q^{10} +(2.25862 - 0.324741i) q^{11} +(4.04568 - 0.581681i) q^{12} +(-0.473459 - 0.736717i) q^{13} +(-6.26501 - 1.83320i) q^{14} +(3.75810 + 1.71627i) q^{15} +(3.81199 + 2.44982i) q^{16} +(4.80417 - 1.41063i) q^{17} +(1.61570 + 1.86462i) q^{18} +(-3.12666 - 0.918069i) q^{19} +(7.01488 + 15.3604i) q^{20} +(-0.747770 - 2.53788i) q^{21} +5.62987i q^{22} +(4.44843 - 1.79207i) q^{23} +5.14983i q^{24} +(-1.71759 + 11.9461i) q^{25} +(1.96540 - 0.897569i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(4.48306 - 9.84090i) q^{28} +(-0.842253 + 0.247308i) q^{29} +(-5.51091 + 8.57515i) q^{30} +(6.39027 + 2.91834i) q^{31} +(-0.576407 + 0.665210i) q^{32} +(-1.91961 + 1.23366i) q^{33} +(1.75808 + 12.2277i) q^{34} +(9.19004 - 5.91824i) q^{35} +(-3.43844 + 2.20975i) q^{36} +(-5.73937 - 4.97320i) q^{37} +(3.33989 - 7.31334i) q^{38} +(0.736717 + 0.473459i) q^{39} +(-20.4145 + 5.99423i) q^{40} +(1.97330 - 1.70987i) q^{41} +(6.46039 - 0.935038i) q^{42} +(7.21274 - 3.29395i) q^{43} +(-9.23163 - 1.32731i) q^{44} -4.13145 q^{45} +(2.81451 + 11.4929i) q^{46} -7.08348i q^{47} +(-4.48520 - 0.644874i) q^{48} +(-6.72013 - 1.95955i) q^{49} +(-28.5708 - 8.38914i) q^{50} +(-3.78403 + 3.27888i) q^{51} +(1.00843 + 3.43440i) q^{52} +(4.26125 - 6.63063i) q^{53} +(-2.24428 - 1.02493i) q^{54} +(-7.12472 - 6.17360i) q^{55} +(11.4691 + 7.35560i) q^{56} +(3.22549 - 0.463755i) q^{57} +(-0.308221 - 2.14373i) q^{58} +(-3.91379 - 6.08998i) q^{59} +(-12.7619 - 11.0583i) q^{60} +(0.502761 - 1.10089i) q^{61} +(-9.37075 + 14.5812i) q^{62} +(1.73447 + 1.99790i) q^{63} +(4.51263 + 5.20786i) q^{64} +(-1.01933 + 3.47151i) q^{65} +(-2.33873 - 5.12111i) q^{66} +(10.3660 + 1.49040i) q^{67} -20.4650 q^{68} +(-3.30198 + 3.47807i) q^{69} +(11.2263 + 24.5213i) q^{70} +(1.86558 - 12.9754i) q^{71} +(-2.13932 - 4.68445i) q^{72} +(0.659386 - 2.24566i) q^{73} +(14.1604 - 12.2701i) q^{74} +(-3.40021 - 11.5800i) q^{75} +(11.2047 + 7.20082i) q^{76} +(0.00565131 + 6.03720i) q^{77} +(-1.41493 + 1.63292i) q^{78} +(5.50409 + 8.56453i) q^{79} +(-2.66427 - 18.5304i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.48286 + 5.41944i) q^{82} +(-1.88668 + 2.17735i) q^{83} +(0.0101227 + 10.8139i) q^{84} +(-17.4023 - 11.1838i) q^{85} +(5.51167 + 18.7710i) q^{86} +(0.663405 - 0.574844i) q^{87} +(3.31068 - 11.2751i) q^{88} +(5.95488 + 13.0394i) q^{89} +(1.45066 - 10.0895i) q^{90} +(2.10670 - 0.964482i) q^{91} +(-19.5091 + 1.90554i) q^{92} -7.02512 q^{93} +(17.2988 + 2.48719i) q^{94} +(5.59273 + 12.2464i) q^{95} +(0.247981 - 0.844544i) q^{96} +(-6.42254 - 7.41201i) q^{97} +(7.14508 - 15.7234i) q^{98} +(1.23366 - 1.91961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.351125	+	2.44213i	−0.248283	+	1.72685i	0.359849	+	0.933010i	$0.382828\pi$
$2$	−0.351125	+	2.44213i	−0.248283	+	1.72685i	−0.608132	+	0.793836i	$0.708081\pi$
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	−3.92172	−	1.15152i	−1.96086	−	0.575760i
$5$	−2.70553	−	3.12235i	−1.20995	−	1.39636i	−0.894293	−	0.447481i	$-0.852321\pi$
$5$	−2.70553	−	3.12235i	−1.20995	−	1.39636i	−0.315655	−	0.948874i	$-0.602224\pi$
$6$	−0.695102	−	2.36730i	−0.283774	−	0.966447i
$7$	−0.374078	+	2.61917i	−0.141388	+	0.989954i
$7$	−0.374078	+	2.61917i	−0.141388	+	0.989954i
$8$	2.13932	−	4.68445i	0.756363	−	1.65620i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	8.57515	−	5.51091i	2.71170	−	1.74270i
$11$	2.25862	−	0.324741i	0.681000	−	0.0979130i	0.206871	−	0.978368i	$-0.433672\pi$
$11$	2.25862	−	0.324741i	0.681000	−	0.0979130i	0.474129	+	0.880455i	$0.342763\pi$
$12$	4.04568	−	0.581681i	1.16789	−	0.167917i
$13$	−0.473459	−	0.736717i	−0.131314	−	0.204329i	0.769370	−	0.638804i	$-0.220570\pi$
$13$	−0.473459	−	0.736717i	−0.131314	−	0.204329i	−0.900684	+	0.434475i	$0.856934\pi$
$14$	−6.26501	−	1.83320i	−1.67439	−	0.489944i
$15$	3.75810	+	1.71627i	0.970338	+	0.443139i
$16$	3.81199	+	2.44982i	0.952998	+	0.612454i
$17$	4.80417	−	1.41063i	1.16518	−	0.342128i	0.358737	−	0.933439i	$-0.383207\pi$
$17$	4.80417	−	1.41063i	1.16518	−	0.342128i	0.806444	+	0.591310i	$0.201389\pi$
$18$	1.61570	+	1.86462i	0.380824	+	0.439494i
$19$	−3.12666	−	0.918069i	−0.717304	−	0.210620i	−0.0973419	−	0.995251i	$-0.531034\pi$
$19$	−3.12666	−	0.918069i	−0.717304	−	0.210620i	−0.619963	+	0.784631i	$0.712852\pi$
$20$	7.01488	+	15.3604i	1.56857	+	3.43470i
$21$	−0.747770	−	2.53788i	−0.163177	−	0.553811i
$22$			5.62987i			1.20029i
$23$	4.44843	−	1.79207i	0.927561	−	0.373672i
$23$	4.44843	−	1.79207i	0.927561	−	0.373672i
$24$			5.14983i			1.05121i
$25$	−1.71759	+	11.9461i	−0.343517	+	2.38922i
$26$	1.96540	−	0.897569i	0.385447	−	0.176028i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	4.48306	−	9.84090i	0.847219	−	1.85976i
$29$	−0.842253	+	0.247308i	−0.156402	+	0.0459239i	−0.358997	−	0.933339i	$-0.616881\pi$
$29$	−0.842253	+	0.247308i	−0.156402	+	0.0459239i	0.202594	+	0.979263i	$0.435063\pi$
$30$	−5.51091	+	8.57515i	−1.00615	+	1.56560i
$31$	6.39027	+	2.91834i	1.14773	+	0.524149i	0.896178	−	0.443695i	$-0.146333\pi$
$31$	6.39027	+	2.91834i	1.14773	+	0.524149i	0.251549	+	0.967844i	$0.419060\pi$
$32$	−0.576407	+	0.665210i	−0.101895	+	0.117594i
$33$	−1.91961	+	1.23366i	−0.334162	+	0.214753i
$34$	1.75808	+	12.2277i	0.301508	+	2.09703i
$35$	9.19004	−	5.91824i	1.55340	−	1.00037i
$36$	−3.43844	+	2.20975i	−0.573074	+	0.368292i
$37$	−5.73937	−	4.97320i	−0.943547	−	0.817588i	0.0398218	−	0.999207i	$-0.487321\pi$
$37$	−5.73937	−	4.97320i	−0.943547	−	0.817588i	−0.983369	+	0.181618i	$0.941866\pi$
$38$	3.33989	−	7.31334i	0.541802	−	1.18638i
$39$	0.736717	+	0.473459i	0.117969	+	0.0758142i
$40$	−20.4145	+	5.99423i	−3.22781	+	0.947771i
$41$	1.97330	−	1.70987i	0.308178	−	0.267038i	−0.487016	−	0.873393i	$-0.661915\pi$
$41$	1.97330	−	1.70987i	0.308178	−	0.267038i	0.795194	+	0.606356i	$0.207369\pi$
$42$	6.46039	−	0.935038i	0.996860	−	0.144279i
$43$	7.21274	−	3.29395i	1.09993	−	0.502322i	0.219077	−	0.975708i	$-0.429695\pi$
$43$	7.21274	−	3.29395i	1.09993	−	0.502322i	0.880855	+	0.473385i	$0.156968\pi$
$44$	−9.23163	−	1.32731i	−1.39172	−	0.200099i
$45$	−4.13145			−0.615881
$46$	2.81451	+	11.4929i	0.414977	+	1.69453i
$47$		−	7.08348i		−	1.03323i	−0.856217	−	0.516616i	$-0.827191\pi$
$47$		−	7.08348i		−	1.03323i	0.856217	−	0.516616i	$-0.172809\pi$
$48$	−4.48520	−	0.644874i	−0.647383	−	0.0930796i
$49$	−6.72013	−	1.95955i	−0.960019	−	0.279936i
$50$	−28.5708	−	8.38914i	−4.04052	−	1.18640i
$51$	−3.78403	+	3.27888i	−0.529870	+	0.459135i
$52$	1.00843	+	3.43440i	0.139844	+	0.476265i
$53$	4.26125	−	6.63063i	0.585327	−	0.910787i	−0.414673	−	0.909971i	$-0.636104\pi$
$53$	4.26125	−	6.63063i	0.585327	−	0.910787i	1.00000		0.000816111i	$-0.000259776\pi$
$54$	−2.24428	−	1.02493i	−0.305408	−	0.139475i
$55$	−7.12472	−	6.17360i	−0.960696	−	0.832448i
$56$	11.4691	+	7.35560i	1.53263	+	0.982933i
$57$	3.22549	−	0.463755i	0.427226	−	0.0614259i
$58$	−0.308221	−	2.14373i	−0.0404715	−	0.281485i
$59$	−3.91379	−	6.08998i	−0.509533	−	0.792848i	0.487228	−	0.873275i	$-0.338008\pi$
$59$	−3.91379	−	6.08998i	−0.509533	−	0.792848i	−0.996761	+	0.0804267i	$0.974372\pi$
$60$	−12.7619	−	11.0583i	−1.64756	−	1.42762i
$61$	0.502761	−	1.10089i	0.0643720	−	0.140955i	−0.874712	−	0.484644i	$-0.838949\pi$
$61$	0.502761	−	1.10089i	0.0643720	−	0.140955i	0.939084	+	0.343689i	$0.111677\pi$
$62$	−9.37075	+	14.5812i	−1.19009	+	1.85181i
$63$	1.73447	+	1.99790i	0.218523	+	0.251712i
$64$	4.51263	+	5.20786i	0.564079	+	0.650982i
$65$	−1.01933	+	3.47151i	−0.126432	+	0.430588i
$66$	−2.33873	−	5.12111i	−0.287878	−	0.630365i
$67$	10.3660	+	1.49040i	1.26640	+	0.182081i	0.742587	−	0.669749i	$-0.233598\pi$
$67$	10.3660	+	1.49040i	1.26640	+	0.182081i	0.523817	+	0.851831i	$0.324508\pi$
$68$	−20.4650			−2.48174
$69$	−3.30198	+	3.47807i	−0.397511	+	0.418710i
$70$	11.2263	+	24.5213i	1.34179	+	2.93086i
$71$	1.86558	−	12.9754i	0.221403	−	1.53989i	−0.511333	−	0.859383i	$-0.670848\pi$
$71$	1.86558	−	12.9754i	0.221403	−	1.53989i	0.732737	−	0.680512i	$-0.238243\pi$
$72$	−2.13932	−	4.68445i	−0.252121	−	0.552068i
$73$	0.659386	−	2.24566i	0.0771752	−	0.262835i	−0.911863	−	0.410495i	$-0.865356\pi$
$73$	0.659386	−	2.24566i	0.0771752	−	0.262835i	0.989038	+	0.147660i	$0.0471742\pi$
$74$	14.1604	−	12.2701i	1.64612	−	1.42637i
$75$	−3.40021	−	11.5800i	−0.392622	−	1.33715i
$76$	11.2047	+	7.20082i	1.28527	+	0.825991i
$77$	0.00565131	+	6.03720i	0.000644026	+	0.688003i
$78$	−1.41493	+	1.63292i	−0.160209	+	0.184891i
$79$	5.50409	+	8.56453i	0.619259	+	0.963585i	0.999255	+	0.0385971i	$0.0122889\pi$
$79$	5.50409	+	8.56453i	0.619259	+	0.963585i	−0.379996	+	0.924988i	$0.624075\pi$
$80$	−2.66427	−	18.5304i	−0.297874	−	2.07176i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	3.48286	+	5.41944i	0.384618	+	0.598477i
$83$	−1.88668	+	2.17735i	−0.207090	+	0.238995i	−0.849788	−	0.527125i	$-0.823270\pi$
$83$	−1.88668	+	2.17735i	−0.207090	+	0.238995i	0.642697	+	0.766120i	$0.277815\pi$
$84$	0.0101227	+	10.8139i	0.00110448	+	1.17990i
$85$	−17.4023	−	11.1838i	−1.88754	−	1.21305i
$86$	5.51167	+	18.7710i	0.594339	+	2.02413i
$87$	0.663405	−	0.574844i	0.0711245	−	0.0616297i
$88$	3.31068	−	11.2751i	0.352919	−	1.20193i
$89$	5.95488	+	13.0394i	0.631216	+	1.38217i	0.907074	+	0.420972i	$0.138311\pi$
$89$	5.95488	+	13.0394i	0.631216	+	1.38217i	−0.275857	+	0.961199i	$0.588962\pi$
$90$	1.45066	−	10.0895i	0.152913	−	1.06353i
$91$	2.10670	−	0.964482i	0.220842	−	0.101105i
$92$	−19.5091	+	1.90554i	−2.03396	+	0.198666i
$93$	−7.02512			−0.728471
$94$	17.2988	+	2.48719i	1.78423	+	0.256534i
$95$	5.59273	+	12.2464i	0.573802	+	1.25645i
$96$	0.247981	−	0.844544i	0.0253094	−	0.0861959i
$97$	−6.42254	−	7.41201i	−0.652110	−	0.752575i	0.329357	−	0.944206i	$-0.393168\pi$
$97$	−6.42254	−	7.41201i	−0.652110	−	0.752575i	−0.981467	+	0.191630i	$0.938623\pi$
$98$	7.14508	−	15.7234i	0.721762	−	1.58830i
$99$	1.23366	−	1.91961i	0.123987	−	0.192928i
$100$	20.4920	−	44.8713i	2.04920	−	4.48713i
$101$	−5.47005	−	4.73982i	−0.544290	−	0.471630i	0.338784	−	0.940864i	$-0.389984\pi$
$101$	−5.47005	−	4.73982i	−0.544290	−	0.471630i	−0.883074	+	0.469234i	$0.844530\pi$
$102$	−6.67878	−	10.3924i	−0.661297	−	1.02900i
$103$	−2.01933	−	14.0447i	−0.198970	−	1.38387i	−0.807279	−	0.590170i	$-0.799061\pi$
$103$	−2.01933	−	14.0447i	−0.198970	−	1.38387i	0.608309	−	0.793700i	$-0.291848\pi$
$104$	−4.46400	+	0.641826i	−0.437731	+	0.0629362i
$105$	−5.90103	+	9.20110i	−0.575881	+	0.897936i
$106$	14.6966	+	12.7347i	1.42746	+	1.23690i
$107$	−2.08946	−	0.954227i	−0.201996	−	0.0922486i	0.311848	−	0.950132i	$-0.399052\pi$
$107$	−2.08946	−	0.954227i	−0.201996	−	0.0922486i	−0.513845	+	0.857883i	$0.671779\pi$
$108$	2.20975	−	3.43844i	0.212634	−	0.330864i
$109$	−0.872951	−	2.97300i	−0.0836135	−	0.284762i	0.907063	−	0.420994i	$-0.138319\pi$
$109$	−0.872951	−	2.97300i	−0.0836135	−	0.284762i	−0.990677	+	0.136233i	$0.956501\pi$
$110$	17.5784	−	15.2318i	1.67603	−	1.45229i
$111$	7.28666	+	2.13956i	0.691619	+	0.203078i
$112$	−7.84248	+	9.06784i	−0.741044	+	0.856830i
$113$	13.6062	+	1.95628i	1.27996	+	0.184031i	0.748548	−	0.663081i	$-0.230751\pi$
$113$	13.6062	+	1.95628i	1.27996	+	0.184031i	0.531415	+	0.847112i	$0.321660\pi$
$114$			8.03989i			0.753005i
$115$	−17.6308	−	9.04103i	−1.64408	−	0.843080i
$116$	3.58786			0.333125
$117$	−0.866824	−	0.124630i	−0.0801379	−	0.0115221i
$118$	16.2468	−	7.41964i	1.49563	−	0.683034i
$119$	1.89755	+	13.1106i	0.173948	+	1.20185i
$120$	16.0796	−	13.9330i	1.46786	−	1.27190i
$121$	−5.55851	+	1.63213i	−0.505319	+	0.148375i
$122$	2.51199	+	1.61436i	0.227425	+	0.146157i
$123$	−1.08467	+	2.37510i	−0.0978014	+	0.214155i
$124$	−21.7003	−	18.8035i	−1.94875	−	1.68860i
$125$	24.5687	−	15.7894i	2.19750	−	1.41224i
$126$	−5.48815	+	3.53428i	−0.488923	+	0.314859i
$127$	2.75000	+	19.1267i	0.244023	+	1.69722i	0.631531	+	0.775351i	$0.282427\pi$
$127$	2.75000	+	19.1267i	0.244023	+	1.69722i	−0.387508	+	0.921866i	$0.626664\pi$
$128$	−15.7837	+	10.1436i	−1.39509	+	0.896573i
$129$	−5.19258	+	5.99256i	−0.457181	+	0.527615i
$130$	−8.11997	−	3.70827i	−0.712169	−	0.325237i
$131$	−8.13556	+	12.6592i	−0.710808	+	1.10604i	0.278534	+	0.960426i	$0.410151\pi$
$131$	−8.13556	+	12.6592i	−0.710808	+	1.10604i	−0.989342	+	0.145612i	$0.953485\pi$
$132$	8.94877	−	2.62760i	0.778890	−	0.228703i
$133$	3.57420	−	7.84583i	0.309922	−	0.680319i
$134$	−7.27950	+	24.7917i	−0.628853	+	2.14168i
$135$	3.75810	−	1.71627i	0.323446	−	0.147713i
$136$	3.66961	−	25.5227i	0.314666	−	2.18855i
$137$		−	1.86310i		−	0.159175i	−0.996828	−	0.0795877i	$-0.974640\pi$
$137$		−	1.86310i		−	0.159175i	0.996828	−	0.0795877i	$-0.0253604\pi$
$138$	−7.33448	−	9.28509i	−0.624352	−	0.790400i
$139$			1.52350i			0.129222i	0.997911	+	0.0646110i	$0.0205807\pi$
$139$			1.52350i			0.129222i	−0.997911	+	0.0646110i	$0.979419\pi$
$140$	−42.8557	+	12.6272i	−3.62197	+	1.06719i
$141$	2.94258	+	6.44336i	0.247810	+	0.542629i
$142$	31.0325	+	9.11197i	2.60419	+	0.764659i
$143$	−1.30861	−	1.51021i	−0.109431	−	0.126290i
$144$	4.34777	−	1.27662i	0.362314	−	0.106385i
$145$	3.05092	+	1.96071i	0.253365	+	0.162828i
$146$	5.25267	+	2.39881i	0.434714	+	0.198527i
$147$	6.92687	−	1.00917i	0.571319	−	0.0832353i
$148$	16.7815	+	26.1125i	1.37943	+	2.14643i
$149$	−13.4840	+	1.93870i	−1.10465	+	0.158825i	−0.670423	−	0.741979i	$-0.733887\pi$
$149$	−13.4840	+	1.93870i	−1.10465	+	0.158825i	−0.434226	+	0.900804i	$0.642978\pi$
$150$	29.4739	−	4.23770i	2.40653	−	0.346007i
$151$	−4.82845	+	3.10306i	−0.392934	+	0.252523i	−0.722157	−	0.691729i	$-0.756849\pi$
$151$	−4.82845	+	3.10306i	−0.392934	+	0.252523i	0.329223	+	0.944252i	$0.393213\pi$
$152$	−10.9896	+	12.6826i	−0.891372	+	1.02870i
$153$	2.07998	−	4.55451i	0.168156	−	0.368211i
$154$	−14.7456	−	2.10601i	−1.18823	−	0.169707i
$155$	−8.17700	−	27.8483i	−0.656792	−	2.23683i
$156$	−2.34400	−	2.70512i	−0.187670	−	0.216583i
$157$	11.3987	+	3.34697i	0.909717	+	0.267117i	0.702922	−	0.711267i	$-0.251878\pi$
$157$	11.3987	+	3.34697i	0.909717	+	0.267117i	0.206795	+	0.978384i	$0.433697\pi$
$158$	−22.8483	+	10.4345i	−1.81771	+	0.830122i
$159$	−1.12170	+	7.80162i	−0.0889569	+	0.618708i
$160$	3.63650			0.287491
$161$	3.02968	+	12.3216i	0.238772	+	0.971076i
$162$	2.46724			0.193845
$163$	2.65011	−	18.4319i	0.207573	−	1.44370i	−0.573471	−	0.819226i	$-0.694404\pi$
$163$	2.65011	−	18.4319i	0.207573	−	1.44370i	0.781044	−	0.624476i	$-0.214687\pi$
$164$	−9.70769	+	4.43335i	−0.758043	+	0.346187i
$165$	9.04548	+	2.65599i	0.704189	+	0.206769i
$166$	−4.65490	−	5.37205i	−0.361291	−	0.416952i
$167$	−4.19939	−	14.3018i	−0.324959	−	1.10671i	−0.946333	−	0.323194i	$-0.895243\pi$
$167$	−4.19939	−	14.3018i	−0.324959	−	1.10671i	0.621374	−	0.783514i	$-0.286575\pi$
$168$	−13.4883	−	1.92644i	−1.04065	−	0.148628i
$169$	5.08181	−	11.1276i	0.390908	−	0.855970i
$170$	33.4226	−	38.5717i	2.56339	−	2.95832i
$171$	−2.74136	+	1.76176i	−0.209637	+	0.134725i
$172$	−32.0794	+	4.61232i	−2.44603	+	0.351686i
$173$	−22.2829	+	3.20379i	−1.69413	+	0.243580i	−0.920693	−	0.390288i	$-0.872375\pi$
$173$	−22.2829	+	3.20379i	−1.69413	+	0.243580i	−0.773441	+	0.633868i	$0.781466\pi$
$174$	1.17090	+	1.82196i	0.0887660	+	0.138123i
$175$	−30.6463	−	8.96742i	−2.31664	−	0.677873i
$176$	9.40540	+	4.29530i	0.708959	+	0.323771i
$177$	6.08998	+	3.91379i	0.457751	+	0.294179i
$178$	−33.9347	+	9.96414i	−2.54352	+	0.746844i
$179$	−7.90021	−	9.11733i	−0.590490	−	0.681461i	0.379336	−	0.925259i	$-0.376152\pi$
$179$	−7.90021	−	9.11733i	−0.590490	−	0.681461i	−0.969826	+	0.243797i	$0.921607\pi$
$180$	16.2024	+	4.75746i	1.20766	+	0.354600i
$181$	−1.52036	−	3.32912i	−0.113007	−	0.247451i	0.844675	−	0.535280i	$-0.179794\pi$
$181$	−1.52036	−	3.32912i	−0.113007	−	0.247451i	−0.957682	+	0.287829i	$0.907067\pi$
$182$	1.61567	+	5.48349i	0.119762	+	0.406463i
$183$			1.21026i			0.0894652i
$184$	1.12173	−	24.6723i	0.0826954	−	1.81886i
$185$			31.3754i			2.30677i
$186$	2.46670	−	17.1563i	0.180867	−	1.25796i
$187$	10.3927	−	4.74619i	0.759990	−	0.347076i
$188$	−8.15678	+	27.7794i	−0.594894	+	2.02602i
$189$	−2.40769	−	1.09683i	−0.175134	−	0.0797828i
$190$	−31.8710	+	9.35816i	−2.31216	+	0.678912i
$191$	13.7412	−	21.3817i	0.994276	−	1.54712i	0.166518	−	0.986038i	$-0.446748\pi$
$191$	13.7412	−	21.3817i	0.994276	−	1.54712i	0.827758	−	0.561085i	$-0.189616\pi$
$192$	−6.26826	−	2.86262i	−0.452372	−	0.206592i
$193$	0.784522	−	0.905386i	0.0564711	−	0.0651711i	−0.726811	−	0.686837i	$-0.758998\pi$
$193$	0.784522	−	0.905386i	0.0564711	−	0.0651711i	0.783282	+	0.621666i	$0.213544\pi$
$194$	20.3562	−	13.0821i	1.46149	−	0.939243i
$195$	−0.514905	−	3.58124i	−0.0368731	−	0.256458i
$196$	24.0980	+	15.4232i	1.72129	+	1.10166i
$197$	6.45937	−	4.15118i	0.460211	−	0.295759i	−0.289918	−	0.957052i	$-0.593628\pi$
$197$	6.45937	−	4.15118i	0.460211	−	0.295759i	0.750129	+	0.661292i	$0.229992\pi$
$198$	4.25477	+	3.68678i	0.302373	+	0.262008i
$199$	−7.17188	+	15.7042i	−0.508401	+	1.11324i	0.465246	+	0.885182i	$0.345966\pi$
$199$	−7.17188	+	15.7042i	−0.508401	+	1.11324i	−0.973647	+	0.228062i	$0.926761\pi$
$200$	52.2864	+	33.6024i	3.69721	+	2.37605i
$201$	−10.0483	+	2.95046i	−0.708756	+	0.208109i
$202$	13.4959	−	11.6943i	0.949570	−	0.822807i
$203$	−0.332673	−	2.29852i	−0.0233491	−	0.161324i
$204$	18.6156	−	8.50145i	1.30335	−	0.595221i
$205$	−10.6776	−	1.53521i	−0.745759	−	0.107224i
$206$	35.0081			2.43913
$207$	1.55874	−	4.53545i	0.108340	−	0.315236i
$208$		−	3.96825i		−	0.275149i
$209$	−7.36007	−	1.05822i	−0.509107	−	0.0731985i
$210$	−20.3983	−	17.6418i	−1.40762	−	1.21740i
$211$	−5.80016	−	1.70308i	−0.399300	−	0.117245i	0.0759162	−	0.997114i	$-0.475812\pi$
$211$	−5.80016	−	1.70308i	−0.399300	−	0.117245i	−0.475216	+	0.879869i	$0.657630\pi$
$212$	−24.3467	+	21.0966i	−1.67214	+	1.44892i
$213$	3.69318	+	12.5778i	0.253052	+	0.861818i
$214$	3.06401	−	4.76769i	0.209451	−	0.325913i
$215$	−29.7991	−	13.6088i	−2.03228	−	0.928112i
$216$	3.89199	+	3.37242i	0.264816	+	0.229464i
$217$	−10.0341	+	15.6455i	−0.681159	+	1.06209i
$218$	7.56696	−	1.08796i	0.512499	−	0.0736863i
$219$	0.333083	+	2.31664i	0.0225077	+	0.156544i
$220$	20.8321	+	32.4154i	1.40450	+	2.18545i
$221$	−3.31381	−	2.87144i	−0.222911	−	0.193154i
$222$	−7.78360	+	17.0437i	−0.522401	+	1.14390i
$223$	10.9340	−	17.0137i	0.732198	−	1.13932i	−0.252928	−	0.967485i	$-0.581394\pi$
$223$	10.9340	−	17.0137i	0.732198	−	1.13932i	0.985125	−	0.171837i	$-0.0549701\pi$
$224$	−1.52668	−	1.75855i	−0.102005	−	0.117498i
$225$	7.90346	+	9.12108i	0.526897	+	0.608072i
$226$	−9.55495	+	32.5412i	−0.635586	+	2.16461i
$227$	1.16986	+	2.56163i	0.0776461	+	0.170021i	0.944474	−	0.328586i	$-0.106572\pi$
$227$	1.16986	+	2.56163i	0.0776461	+	0.170021i	−0.866828	+	0.498608i	$0.833845\pi$
$228$	−13.1835	−	1.89550i	−0.873097	−	0.125532i
$229$	27.8753			1.84205			0.921026	−	0.389501i	$-0.127353\pi$
$229$	27.8753			1.84205			0.921026	+	0.389501i	$0.127353\pi$
$230$	28.2700	−	39.8821i	1.86407	−	2.62975i
$231$	−2.51308	−	5.48928i	−0.165349	−	0.361168i
$232$	−0.643346	+	4.47457i	−0.0422377	+	0.293770i
$233$	8.35747	+	18.3003i	0.547516	+	1.19889i	0.957932	+	0.286995i	$0.0926563\pi$
$233$	8.35747	+	18.3003i	0.547516	+	1.19889i	−0.410416	+	0.911898i	$0.634616\pi$
$234$	0.608727	−	2.07313i	0.0397937	−	0.135525i
$235$	−22.1171	+	19.1646i	−1.44276	+	1.25016i
$236$	8.33606	+	28.3900i	0.542631	+	1.84803i
$237$	−8.56453	−	5.50409i	−0.556326	−	0.357529i
$238$	−32.6841	+	0.0305950i	−2.11860	+	0.00198318i
$239$	−1.21710	+	1.40461i	−0.0787276	+	0.0908565i	−0.793747	−	0.608248i	$-0.791872\pi$
$239$	−1.21710	+	1.40461i	−0.0787276	+	0.0908565i	0.715019	+	0.699105i	$0.246418\pi$
$240$	10.1213	+	15.7491i	0.653328	+	1.01660i
$241$	3.39587	+	23.6188i	0.218747	+	1.52142i	0.742673	+	0.669654i	$0.233558\pi$
$241$	3.39587	+	23.6188i	0.218747	+	1.52142i	−0.523926	+	0.851764i	$0.675533\pi$
$242$	−2.03413	−	14.1477i	−0.130759	−	0.909447i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	−3.23939	+	3.73846i	−0.207381	+	0.239330i
$245$	12.0631	+	26.2842i	0.770684	+	1.67924i
$246$	−5.41944	−	3.48286i	−0.345531	−	0.222059i
$247$	0.803988	+	2.73813i	0.0511565	+	0.174223i
$248$	27.3417	−	23.6917i	1.73620	−	1.50442i
$249$	0.811684	−	2.76434i	0.0514384	−	0.175183i
$250$	29.9330	+	65.5441i	1.89313	+	4.14537i
$251$	−3.91302	+	27.2157i	−0.246988	+	1.71784i	0.368447	+	0.929649i	$0.379890\pi$
$251$	−3.91302	+	27.2157i	−0.246988	+	1.71784i	−0.615434	+	0.788188i	$0.711019\pi$
$252$	−4.50148	−	9.83249i	−0.283566	−	0.619389i
$253$	9.46535	−	5.49219i	0.595082	−	0.345291i
$254$	−47.6754			−2.99142
$255$	20.4756	+	2.94394i	1.28223	+	0.184357i
$256$	−13.5046	−	29.5710i	−0.844038	−	1.84819i
$257$	0.319176	−	1.08701i	0.0199097	−	0.0678061i	−0.948939	−	0.315460i	$-0.897841\pi$
$257$	0.319176	−	1.08701i	0.0199097	−	0.0678061i	0.968849	+	0.247654i	$0.0796595\pi$
$258$	−12.8114	−	14.7851i	−0.797600	−	0.920480i
$259$	15.1726	−	13.1720i	0.942782	−	0.818471i
$260$	7.99504	−	12.4405i	0.495831	−	0.771529i
$261$	−0.364656	+	0.798485i	−0.0225716	+	0.0494250i
$262$	−28.0588	−	24.3131i	−1.73348	−	1.50207i
$263$	−7.03322	−	10.9439i	−0.433687	−	0.674830i	0.553779	−	0.832664i	$-0.313185\pi$
$263$	−7.03322	−	10.9439i	−0.433687	−	0.674830i	−0.987466	+	0.157834i	$0.949549\pi$
$264$	1.67236	+	11.6315i	0.102927	+	0.715871i
$265$	−32.2320	+	4.63427i	−1.98000	+	0.284681i
$266$	17.9055	+	11.4835i	1.09786	+	0.704100i
$267$	−10.8335	−	9.38728i	−0.663000	−	0.574492i
$268$	−38.9362	−	17.7816i	−2.37841	−	1.08618i
$269$	3.09136	−	4.81026i	0.188484	−	0.293287i	−0.734132	−	0.679007i	$-0.762411\pi$
$269$	3.09136	−	4.81026i	0.188484	−	0.293287i	0.922616	+	0.385720i	$0.126047\pi$
$270$	2.87178	+	9.78040i	0.174771	+	0.595216i
$271$	14.0333	−	12.1599i	0.852459	−	0.738660i	−0.114546	−	0.993418i	$-0.536541\pi$
$271$	14.0333	−	12.1599i	0.852459	−	0.738660i	0.967005	+	0.254758i	$0.0819957\pi$
$272$	21.7692	+	6.39202i	1.31995	+	0.387573i
$273$	−1.51566	+	1.75248i	−0.0917320	+	0.106065i
$274$	4.54993	+	0.654182i	0.274872	+	0.0395206i
$275$			27.5394i			1.66069i
$276$	16.9545	−	9.83770i	1.02054	−	0.592160i
$277$	−2.28660			−0.137388			−0.0686941	−	0.997638i	$-0.521883\pi$
$277$	−2.28660			−0.137388			−0.0686941	+	0.997638i	$0.521883\pi$
$278$	−3.72060	−	0.534941i	−0.223147	−	0.0320836i
$279$	6.39027	−	2.91834i	0.382576	−	0.174716i
$280$	−8.06332	−	55.7113i	−0.481875	−	3.32939i
$281$	0.908278	−	0.787027i	0.0541833	−	0.0469501i	−0.627348	−	0.778739i	$-0.715860\pi$
$281$	0.908278	−	0.787027i	0.0541833	−	0.0469501i	0.681532	+	0.731789i	$0.261314\pi$
$282$	−16.7687	+	4.92375i	−0.998564	+	0.293205i
$283$	20.3171	+	13.0570i	1.20773	+	0.776160i	0.980277	−	0.197629i	$-0.0633241\pi$
$283$	20.3171	+	13.0570i	1.20773	+	0.776160i	0.227452	+	0.973789i	$0.426960\pi$
$284$	−22.2577	+	48.7376i	−1.32075	+	2.89204i
$285$	−10.1746	−	8.81638i	−0.602694	−	0.522237i
$286$	4.14762	−	2.66552i	0.245254	−	0.157615i
$287$	3.74029	+	5.80804i	0.220782	+	0.342838i
$288$	0.125265	+	0.871239i	0.00738133	+	0.0513383i
$289$	6.78882	−	4.36291i	0.399343	−	0.256642i
$290$	−5.85955	+	6.76229i	−0.344085	+	0.397095i
$291$	8.92121	+	4.07418i	0.522971	+	0.238833i
$292$	−5.17185	+	8.04756i	−0.302660	+	0.470948i
$293$	20.0886	−	5.89856i	1.17359	−	0.344597i	0.363891	−	0.931442i	$-0.381448\pi$
$293$	20.0886	−	5.89856i	1.17359	−	0.344597i	0.809700	+	0.586844i	$0.199630\pi$
$294$	0.0323335	+	17.2707i	0.00188573	+	1.00725i
$295$	−8.42615	+	28.6968i	−0.490589	+	1.67079i
$296$	−35.5751	+	16.2466i	−2.06776	+	0.944314i
$297$	−0.324741	+	2.25862i	−0.0188434	+	0.131059i
$298$		−	33.6103i		−	1.94699i
$299$	−3.42640	−	2.42876i	−0.198154	−	0.140459i
$300$			49.3291i			2.84802i
$301$	5.92929	+	20.1236i	0.341759	+	1.15991i
$302$	−5.88268	−	12.8813i	−0.338510	−	0.741234i
$303$	6.94472	+	2.03915i	0.398964	+	0.117146i
$304$	−9.66969	−	11.1594i	−0.554595	−	0.640036i
$305$	−4.79760	+	1.40870i	−0.274710	+	0.0806621i
$306$	10.3924	+	6.67878i	0.594093	+	0.381800i
$307$	5.73703	+	2.62001i	0.327429	+	0.149532i	0.572346	−	0.820012i	$-0.306033\pi$
$307$	5.73703	+	2.62001i	0.327429	+	0.149532i	−0.244917	+	0.969544i	$0.578761\pi$
$308$	6.92980	−	23.6827i	0.394862	−	1.34945i
$309$	7.67125	+	11.9367i	0.436402	+	0.679055i
$310$	70.8803	−	10.1910i	4.02573	−	0.578813i
$311$	3.06824	−	0.441147i	0.173984	−	0.0250151i	−0.0547721	−	0.998499i	$-0.517443\pi$
$311$	3.06824	−	0.441147i	0.173984	−	0.0250151i	0.228756	+	0.973484i	$0.426534\pi$
$312$	3.79397	−	2.43824i	0.214791	−	0.138038i
$313$	−0.719029	+	0.829803i	−0.0406419	+	0.0469033i	−0.775707	−	0.631094i	$-0.782606\pi$
$313$	−0.719029	+	0.829803i	−0.0406419	+	0.0469033i	0.735065	+	0.677997i	$0.237152\pi$
$314$	−12.1761	+	26.6619i	−0.687137	+	1.50462i
$315$	1.54549	−	10.8210i	0.0870783	−	0.609694i
$316$	−11.7233	−	39.9258i	−0.659485	−	2.24600i
$317$	−7.91484	−	9.13421i	−0.444542	−	0.513029i	0.488614	−	0.872500i	$-0.337503\pi$
$317$	−7.91484	−	9.13421i	−0.444542	−	0.513029i	−0.933156	+	0.359471i	$0.882957\pi$
$318$	−18.6587	−	5.47869i	−1.04633	−	0.307230i
$319$	−1.82202	+	0.832089i	−0.102014	+	0.0465880i
$320$	4.05167	−	28.1800i	0.226495	−	1.57531i
$321$	2.29704			0.128209
$322$	−31.1547	+	3.07246i	−1.73618	+	0.171221i
$323$	−16.3160			−0.907849
$324$	−0.581681	+	4.04568i	−0.0323156	+	0.224760i
$325$	9.61409	−	4.39061i	0.533294	−	0.243547i
$326$	44.0827	+	12.9438i	2.44151	+	0.716893i
$327$	2.02909	+	2.34170i	0.112209	+	0.129496i
$328$	−3.78831	−	12.9018i	−0.209175	−	0.712383i
$329$	18.5529	+	2.64978i	1.02285	+	0.146087i
$330$	−9.66237	+	21.1576i	−0.531896	+	1.16469i
$331$	5.28161	−	6.09531i	0.290304	−	0.335028i	−0.591799	−	0.806086i	$-0.701582\pi$
$331$	5.28161	−	6.09531i	0.290304	−	0.335028i	0.882103	+	0.471057i	$0.156128\pi$
$332$	9.90631	−	6.36640i	0.543679	−	0.349401i
$333$	−7.51698	+	1.08078i	−0.411928	+	0.0592263i
$334$	36.4014	−	5.23373i	1.99180	−	0.286377i
$335$	−23.3919	−	36.3984i	−1.27803	−	1.98866i
$336$	3.36685	−	11.5063i	0.183677	−	0.627719i
$337$	−1.35549	−	0.619029i	−0.0738380	−	0.0337207i	0.378154	−	0.925743i	$-0.376559\pi$
$337$	−1.35549	−	0.619029i	−0.0738380	−	0.0337207i	−0.451992	+	0.892022i	$0.649286\pi$
$338$	25.3907	+	16.3176i	1.38107	+	0.887561i
$339$	−13.1893	+	3.87273i	−0.716344	+	0.210338i
$340$	55.3685	+	63.8987i	3.00278	+	3.46539i
$341$	15.3809	+	4.51624i	0.832923	+	0.244568i
$342$	−3.33989	−	7.31334i	−0.180601	−	0.395460i
$343$	7.64625	−	16.8682i	0.412859	−	0.910795i
$344$		−	40.8345i		−	2.20165i
$345$	19.7933	+	0.899912i	1.06564	+	0.0484496i
$346$		−	55.5425i		−	2.98598i
$347$	1.81319	−	12.6110i	0.0973370	−	0.676994i	−0.881475	−	0.472231i	$-0.843449\pi$
$347$	1.81319	−	12.6110i	0.0973370	−	0.676994i	0.978812	−	0.204762i	$-0.0656422\pi$
$348$	−3.26363	+	1.49045i	−0.174949	+	0.0798966i
$349$	−6.56811	+	22.3689i	−0.351583	+	1.19738i	0.574006	+	0.818851i	$0.305389\pi$
$349$	−6.56811	+	22.3689i	−0.351583	+	1.19738i	−0.925589	+	0.378530i	$0.876430\pi$
$350$	32.6603	−	71.6936i	1.74577	−	3.83218i
$351$	0.840264	−	0.246724i	0.0448500	−	0.0131691i
$352$	−1.08587	+	1.68964i	−0.0578768	+	0.0900581i
$353$	3.49704	+	1.59705i	0.186129	+	0.0850021i	0.506300	−	0.862358i	$-0.331013\pi$
$353$	3.49704	+	1.59705i	0.186129	+	0.0850021i	−0.320171	+	0.947360i	$0.603740\pi$
$354$	−11.6963	+	13.4983i	−0.621653	+	0.717426i
$355$	−45.5610	+	29.2803i	−2.41813	+	1.55404i
$356$	−8.33827	−	57.9939i	−0.441927	−	3.07367i
$357$	−7.17242	−	11.1376i	−0.379605	−	0.589463i
$358$	25.0397	−	16.0920i	1.32339	−	0.850490i
$359$	−6.22177	−	5.39119i	−0.328372	−	0.284536i	0.475034	−	0.879967i	$-0.342436\pi$
$359$	−6.22177	−	5.39119i	−0.328372	−	0.284536i	−0.803406	+	0.595431i	$0.796981\pi$
$360$	−8.83850	+	19.3536i	−0.465830	+	1.02002i
$361$	−7.05068	−	4.53120i	−0.371089	−	0.238484i
$362$	8.66397	−	2.54397i	0.455368	−	0.133708i
$363$	4.37819	−	3.79372i	0.229795	−	0.199119i
$364$	−9.37251	+	1.35652i	−0.491253	+	0.0711010i
$365$	−8.79572	+	4.01687i	−0.460389	+	0.210253i
$366$	−2.95562	−	0.424954i	−0.154493	−	0.0222127i
$367$	−24.3017			−1.26854			−0.634268	−	0.773113i	$-0.718699\pi$
$367$	−24.3017			−1.26854			−0.634268	+	0.773113i	$0.718699\pi$
$368$	21.3476	+	4.06648i	1.11282	+	0.211980i
$369$		−	2.61105i		−	0.135926i
$370$	−76.6228	−	11.0167i	−3.98343	−	0.572731i
$371$	15.7727	+	13.6413i	0.818879	+	0.708222i
$372$	27.5506	+	8.08957i	1.42843	+	0.419425i
$373$	−16.8043	+	14.5610i	−0.870096	+	0.753942i	−0.970525	−	0.241002i	$-0.922524\pi$
$373$	−16.8043	+	14.5610i	−0.870096	+	0.753942i	0.100429	+	0.994944i	$0.467979\pi$
$374$	7.94167	+	27.0468i	0.410654	+	1.39856i
$375$	−15.7894	+	24.5687i	−0.815360	+	1.26872i
$376$	−33.1822	−	15.1538i	−1.71124	−	0.781499i
$377$	0.580969	+	0.503412i	0.0299214	+	0.0259270i
$378$	3.52400	−	5.49476i	0.181255	−	0.282620i
$379$	−12.3795	+	1.77990i	−0.635891	+	0.0914273i	−0.452719	−	0.891653i	$-0.649546\pi$
$379$	−12.3795	+	1.77990i	−0.635891	+	0.0914273i	−0.183172	+	0.983081i	$0.558637\pi$
$380$	−7.83117	−	54.4670i	−0.401730	−	2.79410i
$381$	−10.4470	−	16.2558i	−0.535216	−	0.832812i
$382$	47.3919	+	41.0653i	2.42478	+	2.10109i
$383$	−4.50481	+	9.86415i	−0.230185	+	0.504034i	−0.989116	−	0.147136i	$-0.952994\pi$
$383$	−4.50481	+	9.86415i	−0.230185	+	0.504034i	0.758931	+	0.651171i	$0.225722\pi$
$384$	10.1436	−	15.7837i	0.517637	−	0.805458i
$385$	18.8349	−	16.3515i	0.959917	−	0.833347i
$386$	1.93561	+	2.23381i	0.0985197	+	0.113698i
$387$	2.23394	−	7.60810i	0.113558	−	0.386741i
$388$	16.6523	+	36.4635i	0.845394	+	1.85115i
$389$	−2.41419	−	0.347109i	−0.122404	−	0.0175991i	0.0808403	−	0.996727i	$-0.474240\pi$
$389$	−2.41419	−	0.347109i	−0.122404	−	0.0175991i	−0.203245	+	0.979128i	$0.565149\pi$
$390$	8.92666			0.452019
$391$	18.8430	−	14.8845i	0.952933	−	0.752741i
$392$	−23.5559	+	27.2880i	−1.18975	+	1.37825i
$393$	2.14155	−	14.8948i	0.108027	−	0.751345i
$394$	7.86968	+	17.2322i	0.396469	+	0.868145i
$395$	11.8500	−	40.3572i	0.596236	−	2.03059i
$396$	−7.04854	+	6.10760i	−0.354203	+	0.306918i
$397$	−3.15613	−	10.7488i	−0.158401	−	0.539466i	0.841598	−	0.540104i	$-0.181615\pi$
$397$	−3.15613	−	10.7488i	−0.158401	−	0.539466i	−1.00000		0.000638181i	$0.999797\pi$
$398$	−35.8335	−	23.0288i	−1.79617	−	1.15433i
$399$	0.00807051	+	8.62159i	0.000404031	+	0.431619i
$400$	−35.8131	+	41.3306i	−1.79066	+	2.06653i
$401$	−11.6580	−	18.1401i	−0.582171	−	0.905875i	0.417826	−	0.908527i	$-0.362792\pi$
$401$	−11.6580	−	18.1401i	−0.582171	−	0.905875i	−0.999996	+	0.00265204i	$0.999156\pi$
$402$	−3.67718	−	25.5753i	−0.183401	−	1.27558i
$403$	−0.875544	−	6.08954i	−0.0436140	−	0.303342i
$404$	15.9940	+	24.8871i	0.795731	+	1.23818i
$405$	−2.70553	+	3.12235i	−0.134439	+	0.155151i
$406$	5.73009	−	0.00536383i	0.284380	−	0.000266202i
$407$	−14.5781	−	9.36876i	−0.722608	−	0.464392i
$408$	7.26451	+	24.7407i	0.359647	+	1.22485i
$409$	11.0439	−	9.56956i	0.546084	−	0.473184i	−0.337586	−	0.941295i	$-0.609610\pi$
$409$	11.0439	−	9.56956i	0.546084	−	0.473184i	0.883670	+	0.468110i	$0.155065\pi$
$410$	7.49838	−	25.5371i	0.370318	−	1.26119i
$411$	0.773960	+	1.69474i	0.0381766	+	0.0835952i
$412$	−8.25357	+	57.4049i	−0.406624	+	2.82814i
$413$	17.4148	−	7.97277i	0.856925	−	0.392314i
$414$	10.5288	+	5.39917i	0.517464	+	0.265354i
$415$	11.9029			0.584291
$416$	0.762977	+	0.109700i	0.0374080	+	0.00537846i
$417$	−0.632887	−	1.38583i	−0.0309926	−	0.0678643i
$418$	5.16861	−	17.6027i	0.252805	−	0.860975i
$419$	0.354031	+	0.408573i	0.0172955	+	0.0199601i	0.764331	−	0.644824i	$-0.223069\pi$
$419$	0.354031	+	0.408573i	0.0172955	+	0.0199601i	−0.747036	+	0.664784i	$0.768524\pi$
$420$	33.7374	−	29.2890i	1.64622	−	1.42916i
$421$	−2.55694	+	3.97867i	−0.124618	+	0.193909i	−0.897957	−	0.440084i	$-0.854949\pi$
$421$	−2.55694	+	3.97867i	−0.124618	+	0.193909i	0.773339	+	0.633993i	$0.218585\pi$
$422$	6.19573	−	13.5668i	0.301603	−	0.660419i
$423$	−5.35334	−	4.63869i	−0.260288	−	0.225541i
$424$	−21.9447	−	34.1466i	−1.06573	−	1.65831i
$425$	8.59993	+	59.8138i	0.417158	+	2.90140i
$426$	−32.0134	+	4.60283i	−1.55106	+	0.223008i
$427$	2.69536	+	1.72864i	0.130438	+	0.0836547i
$428$	7.09548	+	6.14827i	0.342973	+	0.297188i
$429$	1.81772	+	0.830124i	0.0877602	+	0.0400787i
$430$	43.6976	−	67.9949i	2.10729	−	3.27900i
$431$	−0.0963122	−	0.328009i	−0.00463920	−	0.0157997i	0.957141	−	0.289623i	$-0.0935299\pi$
$431$	−0.0963122	−	0.328009i	−0.00463920	−	0.0157997i	−0.961780	+	0.273823i	$0.911712\pi$
$432$	−3.42454	+	2.96738i	−0.164763	+	0.142768i
$433$	20.5969	+	6.04779i	0.989822	+	0.290638i	0.736273	−	0.676685i	$-0.236584\pi$
$433$	20.5969	+	6.04779i	0.989822	+	0.290638i	0.253549	+	0.967323i	$0.418402\pi$
$434$	−34.6852	−	29.9981i	−1.66494	−	1.43996i
$435$	−3.58972	−	0.516124i	−0.172114	−	0.0247463i
$436$			12.6645i			0.606519i
$437$	−15.5539	+	1.51922i	−0.744046	+	0.0726742i
$438$	−5.77450			−0.275916
$439$	17.8451	+	2.56573i	0.851698	+	0.122456i	0.554320	−	0.832304i	$-0.312979\pi$
$439$	17.8451	+	2.56573i	0.851698	+	0.122456i	0.297379	+	0.954760i	$0.403888\pi$
$440$	−44.1620	+	20.1681i	−2.10534	+	0.961477i
$441$	−5.88168	+	3.79550i	−0.280080	+	0.180738i
$442$	8.17598	−	7.08453i	0.388892	−	0.336977i
$443$	30.1373	−	8.84910i	1.43187	−	0.420434i	0.528364	−	0.849018i	$-0.322806\pi$
$443$	30.1373	−	8.84910i	1.43187	−	0.420434i	0.903502	+	0.428585i	$0.140988\pi$
$444$	−26.1125	−	16.7815i	−1.23924	−	0.796414i
$445$	24.6023	−	53.8716i	1.16626	−	2.55376i
$446$	37.7104	+	32.6763i	1.78564	+	1.54727i
$447$	11.4601	−	7.36494i	0.542043	−	0.348350i
$448$	−15.3284	+	9.87122i	−0.724196	+	0.466371i
$449$	4.30126	+	29.9159i	0.202989	+	1.41182i	0.795352	+	0.606148i	$0.207286\pi$
$449$	4.30126	+	29.9159i	0.202989	+	1.41182i	−0.592363	+	0.805671i	$0.701805\pi$
$450$	−25.0500	+	16.0986i	−1.18087	+	0.758897i
$451$	3.90167	−	4.50277i	0.183723	−	0.212027i
$452$	−51.1070	−	23.3398i	−2.40387	−	1.09781i
$453$	3.10306	−	4.82845i	0.145794	−	0.226861i
$454$	−6.66660	+	1.95749i	−0.312879	+	0.0918695i
$455$	−8.71118	−	3.96841i	−0.408387	−	0.186042i
$456$	4.72791	−	16.1018i	0.221404	−	0.754034i
$457$	−32.6834	+	14.9260i	−1.52887	+	0.698210i	−0.989589	−	0.143919i	$-0.954029\pi$
$457$	−32.6834	+	14.9260i	−1.52887	+	0.698210i	−0.539276	+	0.842129i	$0.681302\pi$
$458$	−9.78772	+	68.0751i	−0.457350	+	3.18094i
$459$			5.00698i			0.233706i
$460$	58.7321	+	55.7586i	2.73840	+	2.59976i
$461$		−	15.8856i		−	0.739864i	−0.929059	−	0.369932i	$-0.879381\pi$
$461$		−	15.8856i		−	0.739864i	0.929059	−	0.369932i	$-0.120619\pi$
$462$	14.2879	−	4.20985i	0.664735	−	0.195860i
$463$	0.784513	+	1.71784i	0.0364594	+	0.0798350i	0.926985	−	0.375097i	$-0.122391\pi$
$463$	0.784513	+	1.71784i	0.0364594	+	0.0798350i	−0.890526	+	0.454932i	$0.849663\pi$
$464$	−3.81652	−	1.12063i	−0.177177	−	0.0520240i
$465$	19.0067	+	21.9349i	0.881413	+	1.01720i
$466$	−47.6262	+	13.9843i	−2.20624	+	0.647811i
$467$	11.0618	+	7.10896i	0.511877	+	0.328964i	0.770952	−	0.636894i	$-0.219781\pi$
$467$	11.0618	+	7.10896i	0.511877	+	0.328964i	−0.259074	+	0.965857i	$0.583417\pi$
$468$	3.25593	+	1.48693i	0.150505	+	0.0687334i
$469$	−7.78130	+	26.5927i	−0.359307	+	1.22794i
$470$	−39.0365	−	60.7419i	−1.80062	−	2.80182i
$471$	−11.7590	+	1.69069i	−0.541827	+	0.0779030i
$472$	−36.9011	+	5.30558i	−1.69851	+	0.244209i
$473$	15.2212	−	9.78205i	0.699870	−	0.449779i
$474$	16.4489	−	18.9831i	0.755524	−	0.871921i
$475$	16.3376	−	35.7744i	0.749622	−	1.64144i
$476$	7.65549	−	53.6013i	0.350889	−	2.45681i
$477$	−2.22057	−	7.56257i	−0.101673	−	0.346266i
$478$	−3.00288	−	3.46551i	−0.137348	−	0.158509i
$479$	−0.139679	−	0.0410135i	−0.00638211	−	0.00187396i	0.278540	−	0.960425i	$-0.410150\pi$
$479$	−0.139679	−	0.0410135i	−0.00638211	−	0.00187396i	−0.284922	+	0.958551i	$0.591968\pi$
$480$	−3.30788	+	1.51066i	−0.150983	+	0.0689517i
$481$	−0.946479	+	6.58290i	−0.0431557	+	0.300155i
$482$	−58.8724			−2.68157
$483$	−7.87446	−	9.94952i	−0.358300	−	0.452719i
$484$	23.6783			1.07629
$485$	−5.76649	+	40.1068i	−0.261843	+	1.82116i
$486$	−2.24428	+	1.02493i	−0.101803	+	0.0464917i
$487$	−5.44881	−	1.59991i	−0.246909	−	0.0724990i	0.155936	−	0.987767i	$-0.450161\pi$
$487$	−5.44881	−	1.59991i	−0.246909	−	0.0724990i	−0.402845	+	0.915268i	$0.631979\pi$
$488$	−4.08152	−	4.71032i	−0.184762	−	0.213226i
$489$	5.24628	+	17.8672i	0.237245	+	0.807982i
$490$	−68.4250	+	20.2306i	−3.09113	+	0.913927i
$491$	−1.46574	+	3.20953i	−0.0661481	+	0.144844i	−0.939818	−	0.341674i	$-0.889006\pi$
$491$	−1.46574	+	3.20953i	−0.0661481	+	0.144844i	0.873670	+	0.486518i	$0.161733\pi$
$492$	6.98874	−	8.06544i	0.315077	−	0.363618i
$493$	−3.69746	+	2.37622i	−0.166525	+	0.107019i
$494$	−6.96917	+	1.00202i	−0.313558	+	0.0450828i
$495$	−9.33139	+	1.34165i	−0.419415	+	0.0603028i
$496$	17.2103	+	26.7797i	0.772764	+	1.20244i
$497$	33.2869	+	9.74008i	1.49312	+	0.436902i
$498$	6.46588	+	2.95287i	0.289743	+	0.132321i
$499$	3.83914	+	2.46727i	0.171864	+	0.110450i	0.623745	−	0.781628i	$-0.285611\pi$
$499$	3.83914	+	2.46727i	0.171864	+	0.110450i	−0.451881	+	0.892078i	$0.649247\pi$
$500$	−114.534	+	33.6301i	−5.12210	+	1.50398i
$501$	9.76109	+	11.2649i	0.436093	+	0.503279i
$502$	−65.0902	−	19.1122i	−2.90512	−	0.853019i
$503$	0.0346005	+	0.0757646i	0.00154276	+	0.00337818i	0.910402	−	0.413725i	$-0.135773\pi$
$503$	0.0346005	+	0.0757646i	0.00154276	+	0.00337818i	−0.908859	+	0.417103i	$0.863045\pi$
$504$	13.0697	−	3.85089i	0.582169	−	0.171532i
$505$			29.9031i			1.33067i
$506$	10.0891	+	25.0441i	0.448516	+	1.11334i
$507$			12.2331i			0.543290i
$508$	11.2400	−	78.1761i	0.498696	−	3.46850i
$509$	6.43009	−	2.93652i	0.285009	−	0.130159i	−0.267781	−	0.963480i	$-0.586290\pi$
$509$	6.43009	−	2.93652i	0.285009	−	0.130159i	0.552790	+	0.833321i	$0.313563\pi$
$510$	−14.3790	+	48.9703i	−0.636712	+	2.16844i
$511$	5.63511	+	2.56710i	0.249283	+	0.113562i
$512$	40.9537	−	12.0251i	1.80992	−	0.531439i
$513$	1.76176	−	2.74136i	0.0777837	−	0.121034i
$514$	2.54256	+	1.16115i	0.112148	+	0.0512160i
$515$	−38.3892	+	44.3035i	−1.69163	+	1.95225i
$516$	27.2644	−	17.5218i	1.20025	−	0.771353i
$517$	−2.30030	−	15.9989i	−0.101167	−	0.703631i
$518$	26.8403	+	41.6786i	1.17930	+	1.83125i
$519$	18.9383	−	12.1709i	0.831299	−	0.534243i
$520$	14.0815	+	12.2017i	0.617514	+	0.535079i
$521$	14.2429	−	31.1876i	0.623992	−	1.36635i	−0.288588	−	0.957453i	$-0.593186\pi$
$521$	14.2429	−	31.1876i	0.623992	−	1.36635i	0.912580	−	0.408898i	$-0.134087\pi$
$522$	−1.82196	−	1.17090i	−0.0797451	−	0.0512491i
$523$	−34.1250	+	10.0200i	−1.49218	+	0.438144i	−0.923237	−	0.384232i	$-0.874466\pi$
$523$	−34.1250	+	10.0200i	−1.49218	+	0.438144i	−0.568945	+	0.822376i	$0.692648\pi$
$524$	46.4827	−	40.2775i	2.03061	−	1.75953i
$525$	31.6021	−	4.57389i	1.37923	−	0.199621i
$526$	29.1960	−	13.3333i	1.27300	−	0.581362i
$527$	34.8166	+	5.00588i	1.51664	+	0.218059i
$528$	−10.3398			−0.449981
$529$	16.5770	−	15.9438i	0.720738	−	0.693207i
$530$		−	80.3420i		−	3.48983i
$531$	−7.16549	−	1.03024i	−0.310956	−	0.0447087i
$532$	−23.0516	+	26.6534i	−0.999415	+	1.15557i
$533$	−2.19397	−	0.644208i	−0.0950315	−	0.0279038i
$534$	26.7289	−	23.1607i	1.15667	−	1.00226i
$535$	2.67368	+	9.10572i	0.115593	+	0.393675i
$536$	29.1578	−	45.3704i	1.25943	−	1.95970i
$537$	10.9738	+	5.01155i	0.473553	+	0.216264i
$538$	10.6618	+	9.23851i	0.459663	+	0.398301i
$539$	−15.8146	−	2.24358i	−0.681182	−	0.0966379i
$540$	−16.7145	+	2.40319i	−0.719280	+	0.103417i
$541$	−2.52033	−	17.5293i	−0.108358	−	0.753643i	−0.969467	−	0.245223i	$-0.921139\pi$
$541$	−2.52033	−	17.5293i	−0.108358	−	0.753643i	0.861109	−	0.508420i	$-0.169770\pi$
$542$	24.7686	+	38.5407i	1.06390	+	1.65546i
$543$	2.76593	+	2.39669i	0.118697	+	0.102852i
$544$	−1.83079	+	4.00888i	−0.0784946	+	0.171879i
$545$	−6.92093	+	10.7692i	−0.296460	+	0.461301i
$546$	−3.74759	−	4.31678i	−0.160382	−	0.184741i
$547$	20.3136	+	23.4431i	0.868546	+	1.00236i	0.999939	+	0.0110253i	$0.00350955\pi$
$547$	20.3136	+	23.4431i	0.868546	+	1.00236i	−0.131393	+	0.991330i	$0.541945\pi$
$548$	−2.14540	+	7.30656i	−0.0916469	+	0.312121i
$549$	−0.502761	−	1.10089i	−0.0214573	−	0.0469850i
$550$	−67.2549	−	9.66979i	−2.86776	−	0.412321i
$551$	2.86048			0.121861
$552$	9.22886	+	22.9087i	0.392806	+	0.975057i
$553$	−24.4909	+	11.2124i	−1.04146	+	0.476798i
$554$	0.802881	−	5.58416i	0.0341112	−	0.237248i
$555$	−13.0338	−	28.5401i	−0.553255	−	1.21146i
$556$	1.75435	−	5.97476i	0.0744009	−	0.253386i
$557$	8.26885	−	7.16500i	0.350362	−	0.303591i	−0.461844	−	0.886961i	$-0.652812\pi$
$557$	8.26885	−	7.16500i	0.350362	−	0.303591i	0.812206	+	0.583371i	$0.198266\pi$
$558$	4.88318	+	16.6306i	0.206721	+	0.704029i
$559$	−5.84165	−	3.75420i	−0.247075	−	0.158786i
$560$	49.5310	−	0.0463650i	2.09307	−	0.00195928i
$561$	−7.48190	+	8.63457i	−0.315886	+	0.364552i
$562$	1.60310	+	2.49448i	0.0676228	+	0.105223i
$563$	2.67917	+	18.6340i	0.112914	+	0.785331i	0.965060	+	0.262028i	$0.0843914\pi$
$563$	2.67917	+	18.6340i	0.112914	+	0.785331i	−0.852147	+	0.523303i	$0.824700\pi$
$564$	−4.12033	−	28.6575i	−0.173497	−	1.20670i
$565$	−30.7038	−	47.7760i	−1.29172	−	2.00995i
$566$	−39.0208	+	45.0324i	−1.64017	+	1.89285i
$567$	2.64575	−	0.00247664i	0.111111	−	0.000104009i
$568$	−56.7915	−	36.4977i	−2.38292	−	1.53141i
$569$	7.87243	+	26.8110i	0.330030	+	1.12398i	0.942701	+	0.333640i	$0.108277\pi$
$569$	7.87243	+	26.8110i	0.330030	+	1.12398i	−0.612671	+	0.790338i	$0.709905\pi$
$570$	25.1033	−	21.7522i	1.05146	−	0.911097i
$571$	4.01578	−	13.6765i	0.168055	−	0.572344i	−0.831796	−	0.555082i	$-0.812687\pi$
$571$	4.01578	−	13.6765i	0.168055	−	0.572344i	0.999851	−	0.0172620i	$-0.00549493\pi$
$572$	3.39295	+	7.42953i	0.141866	+	0.310644i
$573$	−3.61714	+	25.1577i	−0.151108	+	1.05098i
$574$	−15.4973	+	7.09492i	−0.646845	+	0.296136i
$575$	13.7676	+	56.2193i	0.574150	+	2.34451i
$576$	6.89098			0.287124
$577$	13.4582	+	1.93499i	0.560270	+	0.0805547i	0.416631	−	0.909075i	$-0.363211\pi$
$577$	13.4582	+	1.93499i	0.560270	+	0.0805547i	0.143639	+	0.989630i	$0.454120\pi$
$578$	8.27107	+	18.1111i	0.344031	+	0.753323i
$579$	−0.337515	+	1.14947i	−0.0140266	+	0.0477704i
$580$	−9.70706	−	11.2025i	−0.403064	−	0.465160i
$581$	−4.99709	−	5.75605i	−0.207314	−	0.238801i
$582$	−13.0821	+	20.3562i	−0.542272	+	0.843792i
$583$	7.47131	−	16.3599i	0.309430	−	0.677557i
$584$	−9.10906	−	7.89305i	−0.376936	−	0.326617i
$585$	1.95608	+	3.04371i	0.0808738	+	0.125842i
$586$	7.35141	+	51.1302i	0.303684	+	2.11217i
$587$	26.3162	−	3.78369i	1.08618	−	0.156170i	0.424112	−	0.905610i	$-0.360586\pi$
$587$	26.3162	−	3.78369i	1.08618	−	0.156170i	0.662072	+	0.749440i	$0.269677\pi$
$588$	−28.3273	−	4.01874i	−1.16820	−	0.165730i
$589$	−17.3010	−	14.9914i	−0.712874	−	0.617709i
$590$	−67.1227	−	30.6539i	−2.76340	−	1.26200i
$591$	−4.15118	+	6.45937i	−0.170757	+	0.265703i
$592$	−9.69502	−	33.0182i	−0.398463	−	1.35704i
$593$	−18.9458	+	16.4167i	−0.778012	+	0.674151i	−0.950453	−	0.310869i	$-0.899380\pi$
$593$	−18.9458	+	16.4167i	−0.778012	+	0.674151i	0.172441	+	0.985020i	$0.444835\pi$
$594$	−5.40182	−	1.58612i	−0.221639	−	0.0650792i
$595$	35.8020	−	41.3960i	1.46774	−	1.69707i
$596$	55.1128	+	7.92402i	2.25751	+	0.324580i
$597$		−	17.2644i		−	0.706584i
$598$	7.13444	−	7.51491i	0.291749	−	0.307307i
$599$	−24.3128			−0.993393			−0.496696	−	0.867924i	$-0.665454\pi$
$599$	−24.3128			−0.993393			−0.496696	+	0.867924i	$0.665454\pi$
$600$	−61.5203	−	8.84529i	−2.51156	−	0.361107i
$601$	−9.32872	+	4.26028i	−0.380526	+	0.173781i	−0.596489	−	0.802621i	$-0.703438\pi$
$601$	−9.32872	+	4.26028i	−0.380526	+	0.173781i	0.215963	+	0.976402i	$0.430711\pi$
$602$	−51.2264	+	7.41419i	−2.08783	+	0.302180i
$603$	7.91463	−	6.85807i	0.322309	−	0.279282i
$604$	22.5091	−	6.60926i	0.915882	−	0.268927i
$605$	20.1348	+	12.9398i	0.818594	+	0.526079i
$606$	−7.41835	+	16.2439i	−0.301350	+	0.659864i
$607$	4.41380	+	3.82458i	0.179151	+	0.155235i	0.739820	−	0.672805i	$-0.234911\pi$
$607$	4.41380	+	3.82458i	0.179151	+	0.155235i	−0.560669	+	0.828040i	$0.689456\pi$
$608$	2.41294	−	1.55070i	0.0978575	−	0.0628892i
$609$	1.25745	+	1.95261i	0.0509544	+	0.0791237i
$610$	−1.75568	−	12.2110i	−0.0710853	−	0.494409i
$611$	−5.21852	+	3.35374i	−0.211119	+	0.135678i
$612$	−13.4017	+	15.4664i	−0.541732	+	0.625192i
$613$	19.9357	+	9.10435i	0.805197	+	0.367721i	0.775110	−	0.631826i	$-0.217694\pi$
$613$	19.9357	+	9.10435i	0.805197	+	0.367721i	0.0300868	+	0.999547i	$0.490422\pi$
$614$	−8.41282	+	13.0906i	−0.339514	+	0.528294i
$615$	10.3505	−	3.03917i	0.417371	−	0.122551i
$616$	28.2931	+	12.8890i	1.13996	+	0.519313i
$617$	2.83028	−	9.63905i	0.113943	−	0.388054i	−0.882699	−	0.469939i	$-0.844276\pi$
$617$	2.83028	−	9.63905i	0.113943	−	0.388054i	0.996642	+	0.0818852i	$0.0260941\pi$
$618$	−31.8445	+	14.5429i	−1.28097	+	0.585001i
$619$	0.252742	−	1.75786i	0.0101586	−	0.0706544i	−0.984112	−	0.177551i	$-0.943182\pi$
$619$	0.252742	−	1.75786i	0.0101586	−	0.0706544i	0.994270	+	0.106897i	$0.0340915\pi$
$620$			118.629i			4.76426i
$621$	0.466211	+	4.77312i	0.0187084	+	0.191539i
$622$			7.64794i			0.306655i
$623$	−36.3800	+	10.7191i	−1.45753	+	0.429452i
$624$	1.64847	+	3.60965i	0.0659916	+	0.144501i
$625$	−57.8711	−	16.9925i	−2.31484	−	0.679699i
$626$	−1.77402	−	2.04733i	−0.0709040	−	0.0818276i
$627$	7.13456	−	2.09489i	0.284927	−	0.0836620i
$628$	−40.8485	−	26.2517i	−1.63003	−	1.04756i
$629$	−34.5882	−	15.7959i	−1.37912	−	0.629825i
$630$	25.8836	+	7.57380i	1.03123	+	0.301747i
$631$	0.469347	+	0.730318i	0.0186844	+	0.0290735i	0.850470	−	0.526023i	$-0.176318\pi$
$631$	0.469347	+	0.730318i	0.0186844	+	0.0290735i	−0.831786	+	0.555097i	$0.812681\pi$
$632$	51.8952	−	7.46140i	2.06428	−	0.296798i
$633$	5.98350	−	0.860297i	0.237823	−	0.0341938i
$634$	25.0860	−	16.1218i	0.996293	−	0.640279i
$635$	52.2799	−	60.3342i	2.07466	−	2.39429i
$636$	13.3827	−	29.3041i	0.530660	−	1.16198i
$637$	1.73808	+	5.87860i	0.0688650	+	0.232919i
$638$	−1.39231	−	4.74178i	−0.0551221	−	0.187729i
$639$	−8.58445	−	9.90698i	−0.339595	−	0.391914i
$640$	74.3749	+	21.8385i	2.93993	+	0.863241i
$641$	20.4674	−	9.34715i	0.808414	−	0.369190i	0.0320589	−	0.999486i	$-0.489794\pi$
$641$	20.4674	−	9.34715i	0.808414	−	0.369190i	0.776355	+	0.630296i	$0.217066\pi$
$642$	−0.806550	+	5.60968i	−0.0318320	+	0.221396i
$643$	22.9633			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$643$	22.9633			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$644$	2.30699	−	51.8105i	0.0909081	−	2.04162i
$645$	32.7595			1.28990
$646$	5.72897	−	39.8459i	0.225403	−	1.56771i
$647$	−26.0075	+	11.8772i	−1.02246	+	0.466942i	−0.854830	−	0.518908i	$-0.826339\pi$
$647$	−26.0075	+	11.8772i	−1.02246	+	0.466942i	−0.167630	+	0.985850i	$0.553611\pi$
$648$	−4.94123	−	1.45088i	−0.194110	−	0.0569958i
$649$	−10.8174	−	12.4840i	−0.424622	−	0.490040i
$650$	7.34668	+	25.0205i	0.288161	+	0.981385i
$651$	2.62794	−	18.4000i	0.102997	−	0.721153i
$652$	−31.6178	+	69.2333i	−1.23825	+	2.71138i
$653$	6.67639	−	7.70496i	0.261267	−	0.301518i	−0.609926	−	0.792458i	$-0.708801\pi$
$653$	6.67639	−	7.70496i	0.261267	−	0.301518i	0.871194	+	0.490940i	$0.163346\pi$
$654$	−6.43119	+	4.13308i	−0.251480	+	0.161616i
$655$	61.5373	−	8.84773i	2.40446	−	0.345710i
$656$	11.7111	−	1.68380i	0.457241	−	0.0657413i
$657$	−1.26535	−	1.96893i	−0.0493661	−	0.0768151i
$658$	−12.9855	+	44.3781i	−0.506226	+	1.73004i
$659$	26.2323	+	11.9799i	1.02187	+	0.466671i	0.854625	−	0.519245i	$-0.173787\pi$
$659$	26.2323	+	11.9799i	1.02187	+	0.466671i	0.167241	+	0.985916i	$0.446514\pi$
$660$	−32.4154	−	20.8321i	−1.26177	−	0.810889i
$661$	−46.9303	+	13.7800i	−1.82538	+	0.535979i	−0.999607	−	0.0280256i	$-0.991078\pi$
$661$	−46.9303	+	13.7800i	−1.82538	+	0.535979i	−0.825771	+	0.564005i	$0.809260\pi$
$662$	13.0310	+	15.0386i	0.506465	+	0.584492i
$663$	4.20719	+	1.23534i	0.163394	+	0.0479767i
$664$	6.16347	+	13.4961i	0.239189	+	0.523751i
$665$	−34.1675	+	10.0672i	−1.32496	+	0.390390i
$666$		−	18.7369i		−	0.726041i
$667$	−3.30351	+	2.60951i	−0.127912	+	0.101040i
$668$			60.9234i			2.35720i
$669$	−2.87821	+	20.0184i	−0.111278	+	0.773955i
$670$	97.1032	−	44.3455i	3.75142	−	1.71322i
$671$	0.778042	−	2.64977i	0.0300360	−	0.102293i
$672$	2.11924	+	0.965429i	0.0817516	+	0.0372422i
$673$	−12.3722	+	3.63280i	−0.476913	+	0.140034i	−0.511350	−	0.859373i	$-0.670854\pi$
$673$	−12.3722	+	3.63280i	−0.476913	+	0.140034i	0.0344371	+	0.999407i	$0.489036\pi$
$674$	1.98769	−	3.09291i	0.0765631	−	0.119135i
$675$	−10.9783	−	5.01361i	−0.422554	−	0.192974i
$676$	−32.7431	+	37.7875i	−1.25935	+	1.45337i
$677$	−0.877840	+	0.564154i	−0.0337381	+	0.0216822i	−0.557401	−	0.830243i	$-0.688201\pi$
$677$	−0.877840	+	0.564154i	−0.0337381	+	0.0216822i	0.523663	+	0.851925i	$0.324565\pi$
$678$	−4.82660	−	33.5698i	−0.185365	−	1.28924i
$679$	21.8159	−	14.0491i	0.837216	−	0.539154i
$680$	−89.6189	+	57.5945i	−3.43673	+	2.20865i
$681$	−2.12828	−	1.84416i	−0.0815558	−	0.0706685i
$682$	−16.4299	+	35.9764i	−0.629133	+	1.37761i
$683$	18.9277	+	12.1641i	0.724250	+	0.465447i	0.850113	−	0.526601i	$-0.176534\pi$
$683$	18.9277	+	12.1641i	0.724250	+	0.465447i	−0.125863	+	0.992048i	$0.540170\pi$
$684$	12.7795	−	3.75241i	0.488638	−	0.143477i
$685$	−5.81725	+	5.04067i	−0.222266	+	0.192594i
$686$	38.5094	+	24.5960i	1.47030	+	0.939079i
$687$	−25.3563	+	11.5798i	−0.967402	+	0.441798i
$688$	35.5645	+	5.11340i	1.35588	+	0.194946i
$689$	−6.90243			−0.262961
$690$	−9.14763	+	48.0218i	−0.348244	+	1.82816i
$691$		−	0.113660i		−	0.00432384i	−0.999998	−	0.00216192i	$-0.999312\pi$
$691$		−	0.113660i		−	0.00432384i	0.999998	−	0.00216192i	$-0.000688161\pi$
$692$	91.0763	+	13.0948i	3.46220	+	0.497790i
$693$	4.56631	+	3.94925i	0.173460	+	0.150020i
$694$	30.1610	+	8.85607i	1.14490	+	0.336172i
$695$	4.75691	−	4.12188i	0.180440	−	0.156352i
$696$	−1.27359	−	4.33746i	−0.0482755	−	0.164411i
$697$	7.06806	−	10.9981i	0.267722	−	0.416584i
$698$	−52.3216	−	23.8945i	−1.98040	−	0.904419i
$699$	−15.2044	−	13.1747i	−0.575085	−	0.498314i
$700$	109.860	+	70.4576i	4.15232	+	2.66305i
$701$	−42.9652	+	6.17747i	−1.62277	+	0.233320i	−0.892898	−	0.450259i	$-0.851331\pi$
$701$	−42.9652	+	6.17747i	−1.62277	+	0.233320i	−0.729876	+	0.683579i	$0.760422\pi$
$702$	0.307493	+	2.13866i	0.0116056	+	0.0807187i
$703$	13.3793	+	20.8186i	0.504610	+	0.785189i
$704$	11.8835	+	10.2971i	0.447877	+	0.388088i
$705$	12.1572	−	26.6205i	0.457865	−	1.00258i
$706$	−5.12809	+	7.97946i	−0.192998	+	0.300311i
$707$	14.4606	−	12.5539i	0.543848	−	0.472139i
$708$	−19.3764	−	22.3615i	−0.728209	−	0.840398i
$709$	3.33206	−	11.3480i	0.125138	−	0.426182i	−0.872962	−	0.487788i	$-0.837804\pi$
$709$	3.33206	−	11.3480i	0.125138	−	0.426182i	0.998101	+	0.0616060i	$0.0196222\pi$
$710$	−55.5086	−	121.547i	−2.08320	−	4.56157i
$711$	10.0771	+	1.44886i	0.377919	+	0.0543366i
$712$	73.8217			2.76659
$713$	33.6565	+	1.53021i	1.26045	+	0.0573068i
$714$	29.7178	−	13.6053i	1.11216	−	0.509166i
$715$	−1.17493	+	8.17185i	−0.0439401	+	0.305610i
$716$	20.4836	+	44.8529i	0.765509	+	1.67623i
$717$	0.523617	−	1.78328i	0.0195548	−	0.0665977i
$718$	15.3506	−	13.3014i	0.572880	−	0.496403i
$719$	−8.09723	−	27.5766i	−0.301976	−	1.02844i	−0.961054	−	0.276361i	$-0.910872\pi$
$719$	−8.09723	−	27.5766i	−0.301976	−	1.02844i	0.659078	−	0.752075i	$-0.270947\pi$
$720$	−15.7491	−	10.1213i	−0.586933	−	0.377199i
$721$	37.5410	−	0.0351414i	1.39810	−	0.00130874i
$722$	13.5414	−	15.6277i	0.503960	−	0.581601i
$723$	−12.9006	−	20.0737i	−0.479778	−	0.746548i
$724$	2.12887	+	14.8066i	0.0791187	+	0.550283i
$725$	−1.50772	−	10.4864i	−0.0559951	−	0.389455i
$726$	7.72747	+	12.0242i	0.286793	+	0.446259i
$727$	14.1232	−	16.2990i	0.523801	−	0.604498i	−0.430778	−	0.902458i	$-0.641761\pi$
$727$	14.1232	−	16.2990i	0.523801	−	0.604498i	0.954578	+	0.297960i	$0.0963062\pi$
$728$	−0.0111694	−	11.9321i	−0.000413965	−	0.442232i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−6.72132	−	22.8907i	−0.248767	−	0.847223i
$731$	30.0046	−	25.9992i	1.10976	−	0.961614i
$732$	1.39364	−	4.74631i	0.0515105	−	0.175429i
$733$	4.79060	+	10.4900i	0.176945	+	0.387456i	0.977236	−	0.212157i	$-0.0680487\pi$
$733$	4.79060	+	10.4900i	0.176945	+	0.387456i	−0.800291	+	0.599612i	$0.795321\pi$
$734$	8.53293	−	59.3478i	0.314956	−	2.19057i
$735$	−21.8918	−	18.8977i	−0.807492	−	0.697054i
$736$	−1.37200	+	3.99210i	−0.0505727	+	0.147151i
$737$	23.8968			0.880249
$738$	6.37652	+	0.916806i	0.234723	+	0.0337481i
$739$	10.2564	+	22.4583i	0.377287	+	0.826143i	0.999077	+	0.0429588i	$0.0136784\pi$
$739$	10.2564	+	22.4583i	0.377287	+	0.826143i	−0.621790	+	0.783184i	$0.713594\pi$
$740$	36.1295	−	123.046i	1.32815	−	4.52325i
$741$	−1.86879	−	2.15670i	−0.0686519	−	0.0792285i
$742$	−38.8520	+	33.7292i	−1.42630	+	1.23824i
$743$	−8.51384	+	13.2478i	−0.312342	+	0.486014i	−0.961562	−	0.274586i	$-0.911459\pi$
$743$	−8.51384	+	13.2478i	−0.312342	+	0.486014i	0.649220	+	0.760601i	$0.275095\pi$
$744$	−15.0290	+	32.9089i	−0.550989	+	1.20650i
$745$	42.5345	+	36.8564i	1.55834	+	1.35031i
$746$	−29.6595	−	46.1511i	−1.08591	−	1.68971i
$747$	0.410015	+	2.85172i	0.0150017	+	0.104339i
$748$	−46.2226	+	6.64581i	−1.69007	+	0.242995i
$749$	3.28091	−	5.11571i	0.119882	−	0.186924i
$750$	−54.4560	−	47.1864i	−1.98845	−	1.72300i
$751$	30.4131	+	13.8892i	1.10979	+	0.506823i	0.884063	−	0.467367i	$-0.154797\pi$
$751$	30.4131	+	13.8892i	1.10979	+	0.506823i	0.225725	+	0.974191i	$0.427525\pi$
$752$	17.3532	−	27.0022i	0.632807	−	0.984668i
$753$	−7.74638	−	26.3818i	−0.282294	−	0.961405i
$754$	−1.43339	+	1.24204i	−0.0522010	+	0.0452324i
$755$	22.7523	+	6.68069i	0.828042	+	0.243135i
$756$	8.17925	+	7.07397i	0.297477	+	0.257278i
$757$	−16.8382	−	2.42096i	−0.611993	−	0.0879914i	−0.170653	−	0.985331i	$-0.554588\pi$
$757$	−16.8382	−	2.42096i	−0.611993	−	0.0879914i	−0.441340	+	0.897340i	$0.645497\pi$
$758$		−	30.8573i		−	1.12079i
$759$	−6.32845	+	8.92792i	−0.229708	+	0.324063i
$760$	69.3322			2.51494
$761$	−27.9574	−	4.01967i	−1.01345	−	0.145713i	−0.384476	−	0.923135i	$-0.625618\pi$
$761$	−27.9574	−	4.01967i	−1.01345	−	0.145713i	−0.628979	+	0.777422i	$0.716527\pi$
$762$	43.3671	−	19.8051i	1.57102	−	0.717462i
$763$	8.11335	−	1.17428i	0.293723	−	0.0425116i
$764$	−78.5104	+	68.0297i	−2.84041	+	2.46123i
$765$	−19.8482	+	5.82796i	−0.717613	+	0.210710i
$766$	−22.5078	−	14.4649i	−0.813239	−	0.522637i
$767$	−2.63357	+	5.76672i	−0.0950928	+	0.208224i
$768$	24.5685	+	21.2887i	0.886538	+	0.768189i
$769$	17.0143	−	10.9344i	0.613551	−	0.394305i	−0.196636	−	0.980477i	$-0.563002\pi$
$769$	17.0143	−	10.9344i	0.613551	−	0.394305i	0.810187	+	0.586171i	$0.199365\pi$
$770$	33.3189	+	51.7387i	1.20073	+	1.86453i
$771$	0.161229	+	1.12137i	0.00580653	+	0.0403853i
$772$	−4.11925	+	2.64728i	−0.148255	+	0.0952776i
$773$	−10.4588	+	12.0701i	−0.376178	+	0.434133i	−0.911995	−	0.410202i	$-0.865458\pi$
$773$	−10.4588	+	12.0701i	−0.376178	+	0.434133i	0.535817	+	0.844334i	$0.320004\pi$
$774$	17.7956	+	8.12697i	0.639649	+	0.292118i
$775$	−45.8386	+	71.3262i	−1.64657	+	2.56211i
$776$	−48.4611	+	14.2295i	−1.73965	+	0.510808i
$777$	−8.32965	+	18.2847i	−0.298824	+	0.655958i
$778$	1.69537	−	5.77389i	0.0607819	−	0.207004i
$779$	−7.73962	+	3.53457i	−0.277301	+	0.126639i
$780$	−2.10456	+	14.6376i	−0.0753555	+	0.524109i
$781$		−	29.9123i		−	1.07035i
$782$	29.7336	+	51.2434i	1.06327	+	1.83246i
$783$		−	0.877811i		−	0.0313704i
$784$	−20.8165	−	23.9329i	−0.743448	−	0.854746i
$785$	−20.3892	−	44.6460i	−0.727720	−	1.59349i
$786$	35.6232	+	10.4599i	1.27064	+	0.373092i
$787$	−20.5260	−	23.6883i	−0.731674	−	0.844397i	0.260985	−	0.965343i	$-0.415953\pi$
$787$	−20.5260	−	23.6883i	−0.731674	−	0.844397i	−0.992659	+	0.120946i	$0.961407\pi$
$788$	−30.1120	+	8.84168i	−1.07270	+	0.314972i
$789$	10.9439	+	7.03322i	0.389613	+	0.250389i
$790$	94.3968	+	43.1096i	3.35849	+	1.53377i
$791$	−10.2136	+	34.9052i	−0.363154	+	1.24108i
$792$	−6.35314	−	9.88569i	−0.225749	−	0.351273i
$793$	−1.04908	+	0.150836i	−0.0372541	+	0.00535633i
$794$	27.3581	−	3.93350i	0.970903	−	0.139595i
$795$	27.3941	−	17.6051i	0.971570	−	0.624390i
$796$	46.2099	−	53.3290i	1.63786	−	1.89020i
$797$	−0.794821	+	1.74042i	−0.0281540	+	0.0616487i	−0.923187	−	0.384352i	$-0.874425\pi$
$797$	−0.794821	+	1.74042i	−0.0281540	+	0.0616487i	0.895033	+	0.446001i	$0.147152\pi$
$798$	−21.0579	−	3.00755i	−0.745440	−	0.106466i
$799$	−9.99218	−	34.0302i	−0.353498	−	1.20390i
$800$	−6.95661	−	8.02836i	−0.245953	−	0.283845i
$801$	13.7541	+	4.03857i	0.485978	+	0.142696i
$802$	48.3940	−	22.1008i	1.70885	−	0.780406i
$803$	0.760045	−	5.28623i	0.0268214	−	0.186547i
$804$	42.8043			1.50959
$805$	30.2753	−	42.7960i	1.06706	−	1.50836i
$806$	15.1789			0.534653
$807$	−0.813751	+	5.65976i	−0.0286454	+	0.199233i
$808$	−33.9057	+	15.4842i	−1.19280	+	0.544732i
$809$	−35.7458	−	10.4959i	−1.25676	−	0.369017i	−0.415470	−	0.909607i	$-0.636383\pi$
$809$	−35.7458	−	10.4959i	−1.25676	−	0.369017i	−0.841286	+	0.540590i	$0.818201\pi$
$810$	−6.67519	−	7.70358i	−0.234542	−	0.270676i
$811$	6.18981	+	21.0806i	0.217354	+	0.740239i	0.993910	+	0.110191i	$0.0351464\pi$
$811$	6.18981	+	21.0806i	0.217354	+	0.740239i	−0.776557	+	0.630047i	$0.783035\pi$
$812$	−1.34214	+	9.39723i	−0.0470999	+	0.329778i
$813$	−7.71370	+	16.8906i	−0.270531	+	0.592381i
$814$	27.9984	−	32.3119i	0.981345	−	1.13253i
$815$	−64.7208	+	41.5936i	−2.26707	+	1.45696i
$816$	−22.4573	+	3.22888i	−0.786164	+	0.113033i
$817$	−25.5758	+	3.67725i	−0.894785	+	0.128651i
$818$	19.4923	+	30.3307i	0.681533	+	1.06049i
$819$	0.650688	−	2.22374i	0.0227369	−	0.0777038i
$820$	40.1069	+	18.3162i	1.40059	+	0.639629i
$821$	−12.4533	−	8.00327i	−0.434624	−	0.279316i	0.304979	−	0.952359i	$-0.401351\pi$
$821$	−12.4533	−	8.00327i	−0.434624	−	0.279316i	−0.739603	+	0.673043i	$0.764987\pi$
$822$	−4.41052	+	1.29505i	−0.153835	+	0.0451699i
$823$	−17.0254	−	19.6483i	−0.593467	−	0.684898i	0.376977	−	0.926223i	$-0.376964\pi$
$823$	−17.0254	−	19.6483i	−0.593467	−	0.684898i	−0.970444	+	0.241325i	$0.922418\pi$
$824$	−70.1120	−	20.5867i	−2.44247	−	0.717173i
$825$	−11.4403	−	25.0507i	−0.398300	−	0.872155i
$826$	13.3558	+	45.3286i	0.464707	+	1.57718i
$827$		−	28.3970i		−	0.987462i	−0.869615	−	0.493731i	$-0.835633\pi$
$827$		−	28.3970i		−	0.987462i	0.869615	−	0.493731i	$-0.164367\pi$
$828$	−11.3356	+	15.9918i	−0.393940	+	0.555755i
$829$		−	22.1033i		−	0.767679i	−0.923400	−	0.383839i	$-0.874602\pi$
$829$		−	22.1033i		−	0.767679i	0.923400	−	0.383839i	$-0.125398\pi$
$830$	−4.17941	+	29.0684i	−0.145069	+	1.00898i
$831$	2.07996	−	0.949886i	0.0721530	−	0.0329512i
$832$	1.70017	−	5.79024i	0.0589427	−	0.200741i
$833$	−35.0488	+	0.0656172i	−1.21437	+	0.00227350i
$834$	3.60660	−	1.05899i	0.124886	−	0.0366699i
$835$	−33.2936	+	51.8059i	−1.15217	+	1.79282i
$836$	27.6456	+	12.6253i	0.956142	+	0.436656i
$837$	−4.60048	+	5.30923i	−0.159016	+	0.183514i
$838$	−1.12210	+	0.721128i	−0.0387622	+	0.0249110i
$839$	4.29032	+	29.8398i	0.148118	+	1.03019i	0.919296	+	0.393566i	$0.128759\pi$
$839$	4.29032	+	29.8398i	0.148118	+	1.03019i	−0.771178	+	0.636619i	$0.780332\pi$
$840$	30.4780	+	47.3272i	1.05159	+	1.63294i
$841$	−23.7481	+	15.2620i	−0.818901	+	0.526276i
$842$	−8.81863	−	7.64139i	−0.303910	−	0.263340i
$843$	−0.499256	+	1.09322i	−0.0171953	+	0.0376524i
$844$	20.7855	+	13.3580i	0.715466	+	0.459802i
$845$	−48.4932	+	14.2389i	−1.66822	+	0.489833i
$846$	13.2080	−	11.4448i	0.454100	−	0.393480i
$847$	−2.19550	−	15.1692i	−0.0754383	−	0.521221i
$848$	32.4877	−	14.8366i	1.11563	−	0.509491i
$849$	−23.9052	−	3.43705i	−0.820425	−	0.117959i
$850$	−149.093			−5.11384
$851$	−34.4435	−	11.8375i	−1.18071	−	0.405786i
$852$		−	53.5794i		−	1.83560i
$853$	18.9323	+	2.72205i	0.648228	+	0.0932011i	0.458583	−	0.888652i	$-0.348357\pi$
$853$	18.9323	+	2.72205i	0.648228	+	0.0932011i	0.189645	+	0.981853i	$0.439266\pi$
$854$	−5.16797	+	5.97544i	−0.176844	+	0.204476i
$855$	12.9176	+	3.79296i	0.441774	+	0.129717i
$856$	−8.94006	+	7.74661i	−0.305565	+	0.264774i
$857$	−14.1952	−	48.3443i	−0.484898	−	1.65141i	−0.731160	−	0.682206i	$-0.761021\pi$
$857$	−14.1952	−	48.3443i	−0.484898	−	1.65141i	0.246262	−	0.969203i	$-0.420798\pi$
$858$	−2.66552	+	4.14762i	−0.0909992	+	0.141598i
$859$	−8.77508	−	4.00745i	−0.299402	−	0.136732i	0.260050	−	0.965595i	$-0.416261\pi$
$859$	−8.77508	−	4.00745i	−0.299402	−	0.136732i	−0.559452	+	0.828863i	$0.688988\pi$
$860$	101.193	+	87.6842i	3.45065	+	2.99001i
$861$	−5.81503	−	3.72941i	−0.198176	−	0.127098i
$862$	0.834859	−	0.120035i	0.0284354	−	0.00408839i
$863$	2.10833	+	14.6637i	0.0717683	+	0.499159i	0.993724	+	0.111863i	$0.0356818\pi$
$863$	2.10833	+	14.6637i	0.0717683	+	0.499159i	−0.921955	+	0.387296i	$0.873409\pi$
$864$	−0.475871	−	0.740470i	−0.0161895	−	0.0251913i
$865$	70.2902	+	60.9068i	2.38994	+	2.07089i
$866$	−22.0016	+	48.1767i	−0.747643	+	1.63711i
$867$	−4.36291	+	6.78882i	−0.148172	+	0.230561i
$868$	57.3671	−	49.8030i	1.94717	−	1.69042i
$869$	15.2129	+	17.5566i	0.516063	+	0.595568i
$870$	2.52088	−	8.58534i	0.0854659	−	0.291070i
$871$	−3.80986	−	8.34243i	−0.129092	−	0.282672i
$872$	−15.7944	−	2.27089i	−0.534866	−	0.0769021i
$873$	−9.80749			−0.331933
$874$	1.75125	−	38.5182i	0.0592368	−	1.30290i
$875$	32.1645	+	70.2562i	1.08736	+	2.37509i
$876$	1.36141	−	9.46878i	0.0459976	−	0.319920i
$877$	−3.68158	−	8.06153i	−0.124318	−	0.272219i	0.837232	−	0.546847i	$-0.184172\pi$
$877$	−3.68158	−	8.06153i	−0.124318	−	0.272219i	−0.961550	+	0.274629i	$0.911445\pi$
$878$	−12.5317	+	42.6790i	−0.422924	+	1.44035i
$879$	−15.8229	+	13.7106i	−0.533694	+	0.462448i
$880$	−12.0352	−	40.9880i	−0.405705	−	1.38170i
$881$	−33.2717	−	21.3824i	−1.12095	−	0.720392i	−0.157300	−	0.987551i	$-0.550279\pi$
$881$	−33.2717	−	21.3824i	−1.12095	−	0.720392i	−0.963653	+	0.267159i	$0.913915\pi$
$882$	−7.20391	−	15.6965i	−0.242568	−	0.528529i
$883$	5.31841	−	6.13777i	0.178979	−	0.206552i	−0.659170	−	0.751994i	$-0.729092\pi$
$883$	5.31841	−	6.13777i	0.178979	−	0.206552i	0.838149	+	0.545441i	$0.183638\pi$
$884$	9.68933	+	15.0769i	0.325887	+	0.507091i
$885$	−4.25640	−	29.6039i	−0.143077	−	0.995124i
$886$	11.0287	+	76.7063i	0.370516	+	2.57700i
$887$	−16.4140	−	25.5407i	−0.551128	−	0.857573i	0.448210	−	0.893928i	$-0.352062\pi$
$887$	−16.4140	−	25.5407i	−0.551128	−	0.857573i	−0.999339	+	0.0363555i	$0.988425\pi$
$888$	25.6111	−	29.5568i	0.859453	−	0.991862i
$889$	−51.1248	+	0.0478569i	−1.71467	+	0.00160507i
$890$	122.923	+	78.9977i	4.12038	+	2.64801i
$891$	−0.642871	−	2.18942i	−0.0215370	−	0.0733482i
$892$	−62.4719	+	54.1322i	−2.09171	+	1.81248i
$893$	−6.50313	+	22.1476i	−0.217619	+	0.741142i
$894$	13.9622	+	30.5730i	0.466966	+	1.02251i
$895$	−7.09321	+	49.3344i	−0.237100	+	1.64907i
$896$	−20.6634	−	45.1347i	−0.690316	−	1.50784i
$897$	4.12570	+	0.785901i	0.137753	+	0.0262405i
$898$	−74.5688			−2.48839
$899$	−6.10396	−	0.877617i	−0.203578	−	0.0292702i
$900$	−20.4920	−	44.8713i	−0.683068	−	1.49571i
$901$	11.1184	−	37.8657i	0.370407	−	1.26149i
$902$	9.62637	+	11.1094i	0.320523	+	0.369903i
$903$	−13.7531	−	15.8420i	−0.457675	−	0.527187i
$904$	38.2721	−	59.5525i	1.27291	−	1.98069i
$905$	−6.28129	+	13.7541i	−0.208797	+	0.457202i
$906$	10.7021	+	9.27346i	0.355555	+	0.308090i
$907$	−3.10155	−	4.82610i	−0.102985	−	0.160248i	0.785937	−	0.618307i	$-0.212181\pi$
$907$	−3.10155	−	4.82610i	−0.102985	−	0.160248i	−0.888922	+	0.458059i	$0.848545\pi$
$908$	−1.63808	−	11.3931i	−0.0543617	−	0.378094i
$909$	−7.16424	+	1.03006i	−0.237623	+	0.0341650i
$910$	12.7501	−	19.8804i	0.422662	−	0.659030i
$911$	−13.9396	−	12.0787i	−0.461840	−	0.400186i	0.392623	−	0.919700i	$-0.371568\pi$
$911$	−13.9396	−	12.0787i	−0.461840	−	0.400186i	−0.854462	+	0.519513i	$0.826113\pi$
$912$	13.4316	+	6.13403i	0.444766	+	0.203118i
$913$	−3.55423	+	5.53049i	−0.117628	+	0.183032i
$914$	−24.9753	−	85.0580i	−0.826109	−	2.81347i
$915$	3.77886	−	3.27440i	0.124925	−	0.108248i
$916$	−109.319	−	32.0990i	−3.61201	−	1.06058i
$917$	−30.1133	−	26.0440i	−0.994427	−	0.860048i
$918$	−12.2277	−	1.75808i	−0.403574	−	0.0580252i
$919$			10.5528i			0.348104i	0.984736	+	0.174052i	$0.0556861\pi$
$919$			10.5528i			0.348104i	−0.984736	+	0.174052i	$0.944314\pi$
$920$	−80.0702	+	63.2490i	−2.63984	+	2.08526i
$921$	−6.30698			−0.207822
$922$	38.7946	+	5.57782i	1.27763	+	0.183696i
$923$	−10.4425	+	4.76891i	−0.343718	+	0.156971i
$924$	3.53459	+	24.4213i	0.116279	+	0.803402i
$925$	69.2680	−	60.0211i	2.27752	−	1.97348i
$926$	−4.47066	+	1.31270i	−0.146915	+	0.0431381i
$927$	−11.9367	−	7.67125i	−0.392052	−	0.251957i
$928$	0.320969	−	0.702825i	0.0105363	−	0.0230714i
$929$	−12.2399	−	10.6059i	−0.401578	−	0.347969i	0.430537	−	0.902573i	$-0.358324\pi$
$929$	−12.2399	−	10.6059i	−0.401578	−	0.347969i	−0.832114	+	0.554604i	$0.812870\pi$
$930$	−60.2415	+	38.7148i	−1.97540	+	1.26951i
$931$	19.2125	+	12.2964i	0.629666	+	0.402998i
$932$	−11.7025	−	81.3925i	−0.383327	−	2.66610i
$933$	−2.60771	+	1.67588i	−0.0853727	+	0.0548657i
$934$	−21.2451	+	24.5181i	−0.695160	+	0.802257i
$935$	−42.9370	−	19.6087i	−1.40419	−	0.641272i
$936$	−2.43824	+	3.79397i	−0.0796963	+	0.124010i
$937$	27.0353	−	7.93828i	0.883205	−	0.259332i	0.191483	−	0.981496i	$-0.438670\pi$
$937$	27.0353	−	7.93828i	0.883205	−	0.259332i	0.691722	+	0.722164i	$0.256852\pi$
$938$	−62.2107	−	28.3403i	−2.03125	−	0.925344i
$939$	0.309339	−	1.05351i	0.0100949	−	0.0343800i
$940$	108.805	−	49.6897i	3.54884	−	1.62070i
$941$	0.178450	−	1.24115i	0.00581732	−	0.0404603i	−0.986706	−	0.162515i	$-0.948039\pi$
$941$	0.178450	−	1.24115i	0.00581732	−	0.0404603i	0.992523	+	0.122055i	$0.0389484\pi$
$942$		−	29.3107i		−	0.954994i
$943$	5.71387	−	11.1425i	0.186069	−	0.362851i
$944$		−	32.8030i		−	1.06765i
$945$	3.08938	+	10.4851i	0.100498	+	0.341082i
$946$	18.5445	+	40.6068i	0.602934	+	1.32024i
$947$	41.3568	+	12.1435i	1.34392	+	0.394610i	0.873065	−	0.487603i	$-0.162129\pi$
$947$	41.3568	+	12.1435i	1.34392	+	0.394610i	0.470851	+	0.882213i	$0.343947\pi$
$948$	27.2496	+	31.4477i	0.885027	+	1.02138i
$949$	−1.96661	+	0.577449i	−0.0638389	+	0.0187448i
$950$	81.6292	+	52.4599i	2.64840	+	1.70202i
$951$	10.9941	+	5.02083i	0.356508	+	0.162812i
$952$	65.4756	+	19.1588i	2.12208	+	0.620941i
$953$	19.1457	+	29.7913i	0.620191	+	0.965035i	0.999214	+	0.0396482i	$0.0126237\pi$
$953$	19.1457	+	29.7913i	0.620191	+	0.965035i	−0.379023	+	0.925387i	$0.623740\pi$
$954$	19.2485	−	2.76751i	0.623193	−	0.0896016i
$955$	−103.938	+	14.9440i	−3.36336	+	0.483578i
$956$	6.39056	−	4.10696i	0.206685	−	0.132829i
$957$	1.31171	−	1.51379i	0.0424014	−	0.0489338i
$958$	0.149205	−	0.326714i	0.00482060	−	0.0105557i
$959$	4.87978	+	0.696945i	0.157576	+	0.0225055i
$960$	8.02086	+	27.3166i	0.258872	+	0.881638i
$961$	12.0182	+	13.8698i	0.387684	+	0.447412i
$962$	−15.7440	−	4.62285i	−0.507606	−	0.149047i
$963$	−2.08946	+	0.954227i	−0.0673321	+	0.0307495i
$964$	13.8799	−	96.5366i	0.447040	−	3.10923i
$965$	−4.94947			−0.159329
$966$	27.0629	−	15.7369i	0.870735	−	0.506327i
$967$	−52.9624			−1.70316			−0.851578	−	0.524228i	$-0.824354\pi$
$967$	−52.9624			−1.70316			−0.851578	+	0.524228i	$0.824354\pi$
$968$	−4.24580	+	29.5302i	−0.136465	+	0.949137i
$969$	14.8416	−	6.77793i	0.476781	−	0.217738i
$970$	−95.9212	−	28.1650i	−3.07984	−	0.904324i
$971$	−3.52518	−	4.06828i	−0.113129	−	0.130557i	0.696361	−	0.717692i	$-0.254801\pi$
$971$	−3.52518	−	4.06828i	−0.113129	−	0.130557i	−0.809489	+	0.587135i	$0.800256\pi$
$972$	−1.15152	−	3.92172i	−0.0369351	−	0.125789i
$973$	−3.99032	−	0.569910i	−0.127924	−	0.0182705i
$974$	5.82041	−	12.7449i	0.186498	−	0.408374i
$975$	−6.92136	+	7.98767i	−0.221661	+	0.255810i
$976$	4.61351	−	2.96492i	0.147675	−	0.0949049i
$977$	4.52670	−	0.650841i	0.144822	−	0.0208223i	−0.0695225	−	0.997580i	$-0.522148\pi$
$977$	4.52670	−	0.650841i	0.144822	−	0.0208223i	0.214344	+	0.976758i	$0.431238\pi$
$978$	−45.4761	+	6.53847i	−1.45416	+	0.209077i
$979$	17.6842	+	27.5172i	0.565191	+	0.879454i
$980$	−17.0413	−	116.970i	−0.544366	−	3.73647i
$981$	−2.81850	−	1.28717i	−0.0899879	−	0.0410961i
$982$	−7.32343	−	4.70648i	−0.233700	−	0.150190i
$983$	42.1785	−	12.3847i	1.34528	−	0.395011i	0.471732	−	0.881742i	$-0.343629\pi$
$983$	42.1785	−	12.3847i	1.34528	−	0.395011i	0.873552	+	0.486731i	$0.161811\pi$
$984$	8.80557	+	10.1622i	0.280711	+	0.323958i
$985$	−30.4374	−	8.93723i	−0.969817	−	0.284764i
$986$	−4.50475	−	9.86403i	−0.143461	−	0.314135i
$987$	−17.9770	+	5.29682i	−0.572215	+	0.168600i
$988$		−	11.6640i		−	0.371081i
$989$	26.1823	−	27.5786i	0.832550	−	0.876949i
$990$		−	23.2596i		−	0.739237i
$991$	−6.64655	+	46.2277i	−0.211135	+	1.46847i	0.558242	+	0.829678i	$0.311476\pi$
$991$	−6.64655	+	46.2277i	−0.211135	+	1.46847i	−0.769377	+	0.638795i	$0.779433\pi$
$992$	−5.62471	+	2.56872i	−0.178585	+	0.0815569i
$993$	−2.27224	+	7.73855i	−0.0721074	+	0.245575i
$994$	−35.4744	+	77.8709i	−1.12518	+	2.46992i
$995$	68.4377	−	20.0951i	2.16962	−	0.637059i
$996$	−6.36640	+	9.90631i	−0.201727	+	0.313893i
$997$	−23.0298	−	10.5174i	−0.729362	−	0.333089i	0.0158876	−	0.999874i	$-0.494943\pi$
$997$	−23.0298	−	10.5174i	−0.729362	−	0.333089i	−0.745250	+	0.666785i	$0.767670\pi$
$998$	−7.37340	+	8.50936i	−0.233401	+	0.269359i
$999$	6.38871	−	4.10578i	0.202130	−	0.129901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.475.3	yes	320
7.6	odd	2	inner	483.2.r.a.475.4	yes	320
23.20	odd	22	inner	483.2.r.a.181.4	yes	320
161.20	even	22	inner	483.2.r.a.181.3	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.3	✓	320	161.20	even	22	inner
483.2.r.a.181.4	yes	320	23.20	odd	22	inner
483.2.r.a.475.3	yes	320	1.1	even	1	trivial
483.2.r.a.475.4	yes	320	7.6	odd	2	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.351125 + 2.44213i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-3.92172 - 1.15152i) q^{4} +(-2.70553 - 3.12235i) q^{5} +(-0.695102 - 2.36730i) q^{6} +(-0.374078 + 2.61917i) q^{7} +(2.13932 - 4.68445i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.351125 + 2.44213i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-3.92172 - 1.15152i) q^{4} +(-2.70553 - 3.12235i) q^{5} +(-0.695102 - 2.36730i) q^{6} +(-0.374078 + 2.61917i) q^{7} +(2.13932 - 4.68445i) q^{8} +(0.654861 - 0.755750i) q^{9} +(8.57515 - 5.51091i) q^{10} +(2.25862 - 0.324741i) q^{11} +(4.04568 - 0.581681i) q^{12} +(-0.473459 - 0.736717i) q^{13} +(-6.26501 - 1.83320i) q^{14} +(3.75810 + 1.71627i) q^{15} +(3.81199 + 2.44982i) q^{16} +(4.80417 - 1.41063i) q^{17} +(1.61570 + 1.86462i) q^{18} +(-3.12666 - 0.918069i) q^{19} +(7.01488 + 15.3604i) q^{20} +(-0.747770 - 2.53788i) q^{21} +5.62987i q^{22} +(4.44843 - 1.79207i) q^{23} +5.14983i q^{24} +(-1.71759 + 11.9461i) q^{25} +(1.96540 - 0.897569i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(4.48306 - 9.84090i) q^{28} +(-0.842253 + 0.247308i) q^{29} +(-5.51091 + 8.57515i) q^{30} +(6.39027 + 2.91834i) q^{31} +(-0.576407 + 0.665210i) q^{32} +(-1.91961 + 1.23366i) q^{33} +(1.75808 + 12.2277i) q^{34} +(9.19004 - 5.91824i) q^{35} +(-3.43844 + 2.20975i) q^{36} +(-5.73937 - 4.97320i) q^{37} +(3.33989 - 7.31334i) q^{38} +(0.736717 + 0.473459i) q^{39} +(-20.4145 + 5.99423i) q^{40} +(1.97330 - 1.70987i) q^{41} +(6.46039 - 0.935038i) q^{42} +(7.21274 - 3.29395i) q^{43} +(-9.23163 - 1.32731i) q^{44} -4.13145 q^{45} +(2.81451 + 11.4929i) q^{46} -7.08348i q^{47} +(-4.48520 - 0.644874i) q^{48} +(-6.72013 - 1.95955i) q^{49} +(-28.5708 - 8.38914i) q^{50} +(-3.78403 + 3.27888i) q^{51} +(1.00843 + 3.43440i) q^{52} +(4.26125 - 6.63063i) q^{53} +(-2.24428 - 1.02493i) q^{54} +(-7.12472 - 6.17360i) q^{55} +(11.4691 + 7.35560i) q^{56} +(3.22549 - 0.463755i) q^{57} +(-0.308221 - 2.14373i) q^{58} +(-3.91379 - 6.08998i) q^{59} +(-12.7619 - 11.0583i) q^{60} +(0.502761 - 1.10089i) q^{61} +(-9.37075 + 14.5812i) q^{62} +(1.73447 + 1.99790i) q^{63} +(4.51263 + 5.20786i) q^{64} +(-1.01933 + 3.47151i) q^{65} +(-2.33873 - 5.12111i) q^{66} +(10.3660 + 1.49040i) q^{67} -20.4650 q^{68} +(-3.30198 + 3.47807i) q^{69} +(11.2263 + 24.5213i) q^{70} +(1.86558 - 12.9754i) q^{71} +(-2.13932 - 4.68445i) q^{72} +(0.659386 - 2.24566i) q^{73} +(14.1604 - 12.2701i) q^{74} +(-3.40021 - 11.5800i) q^{75} +(11.2047 + 7.20082i) q^{76} +(0.00565131 + 6.03720i) q^{77} +(-1.41493 + 1.63292i) q^{78} +(5.50409 + 8.56453i) q^{79} +(-2.66427 - 18.5304i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.48286 + 5.41944i) q^{82} +(-1.88668 + 2.17735i) q^{83} +(0.0101227 + 10.8139i) q^{84} +(-17.4023 - 11.1838i) q^{85} +(5.51167 + 18.7710i) q^{86} +(0.663405 - 0.574844i) q^{87} +(3.31068 - 11.2751i) q^{88} +(5.95488 + 13.0394i) q^{89} +(1.45066 - 10.0895i) q^{90} +(2.10670 - 0.964482i) q^{91} +(-19.5091 + 1.90554i) q^{92} -7.02512 q^{93} +(17.2988 + 2.48719i) q^{94} +(5.59273 + 12.2464i) q^{95} +(0.247981 - 0.844544i) q^{96} +(-6.42254 - 7.41201i) q^{97} +(7.14508 - 15.7234i) q^{98} +(1.23366 - 1.91961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

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