LMFDB - Embedded newform 585.2.i.g.196.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.8
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.238506 - 0.413105i) q^{2} +(1.59029 + 0.686267i) q^{3} +(0.886230 + 1.53499i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.662795 - 0.493279i) q^{6} +(0.335964 - 0.581906i) q^{7} +1.79951 q^{8} +(2.05807 + 2.18273i) q^{9} +O(q^{10})$	\(q+(0.238506 - 0.413105i) q^{2} +(1.59029 + 0.686267i) q^{3} +(0.886230 + 1.53499i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.662795 - 0.493279i) q^{6} +(0.335964 - 0.581906i) q^{7} +1.79951 q^{8} +(2.05807 + 2.18273i) q^{9} -0.477012 q^{10} +(-1.85231 + 3.20829i) q^{11} +(0.355950 + 3.04928i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.160259 - 0.277576i) q^{14} +(-0.200823 - 1.72037i) q^{15} +(-1.34327 + 2.32660i) q^{16} +6.76009 q^{17} +(1.39256 - 0.329605i) q^{18} -4.86376 q^{19} +(0.886230 - 1.53499i) q^{20} +(0.933625 - 0.694842i) q^{21} +(0.883574 + 1.53039i) q^{22} +(-4.21102 - 7.29370i) q^{23} +(2.86175 + 1.23494i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.477012 q^{26} +(1.77501 + 4.88358i) q^{27} +1.19096 q^{28} +(4.84813 - 8.39721i) q^{29} +(-0.758590 - 0.327358i) q^{30} +(1.02820 + 1.78089i) q^{31} +(2.44026 + 4.22666i) q^{32} +(-5.14746 + 3.83095i) q^{33} +(1.61232 - 2.79262i) q^{34} -0.671928 q^{35} +(-1.52656 + 5.09354i) q^{36} +3.15079 q^{37} +(-1.16004 + 2.00924i) q^{38} +(0.200823 + 1.72037i) q^{39} +(-0.899754 - 1.55842i) q^{40} +(-3.83107 - 6.63561i) q^{41} +(-0.0643672 - 0.551409i) q^{42} +(-3.41131 + 5.90856i) q^{43} -6.56628 q^{44} +(0.861266 - 2.87371i) q^{45} -4.01741 q^{46} +(-1.77468 + 3.07383i) q^{47} +(-3.73286 + 2.77815i) q^{48} +(3.27426 + 5.67118i) q^{49} +(0.238506 + 0.413105i) q^{50} +(10.7505 + 4.63923i) q^{51} +(-0.886230 + 1.53499i) q^{52} +5.30936 q^{53} +(2.44078 + 0.431500i) q^{54} +3.70462 q^{55} +(0.604570 - 1.04715i) q^{56} +(-7.73481 - 3.33784i) q^{57} +(-2.31262 - 4.00557i) q^{58} +(-3.16134 - 5.47561i) q^{59} +(2.46278 - 1.83290i) q^{60} +(-1.37355 + 2.37907i) q^{61} +0.980925 q^{62} +(1.96159 - 0.464287i) q^{63} -3.04499 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.354883 + 3.04015i) q^{66} +(-5.88093 - 10.1861i) q^{67} +(5.99099 + 10.3767i) q^{68} +(-1.69134 - 14.4890i) q^{69} +(-0.160259 + 0.277576i) q^{70} -5.06552 q^{71} +(3.70352 + 3.92785i) q^{72} -9.39507 q^{73} +(0.751483 - 1.30161i) q^{74} +(-1.38947 + 1.03410i) q^{75} +(-4.31041 - 7.46585i) q^{76} +(1.24462 + 2.15574i) q^{77} +(0.758590 + 0.327358i) q^{78} +(7.13987 - 12.3666i) q^{79} +2.68653 q^{80} +(-0.528656 + 8.98446i) q^{81} -3.65494 q^{82} +(8.34140 - 14.4477i) q^{83} +(1.89398 + 0.817320i) q^{84} +(-3.38004 - 5.85441i) q^{85} +(1.62724 + 2.81845i) q^{86} +(13.4727 - 10.0269i) q^{87} +(-3.33325 + 5.77335i) q^{88} -4.23971 q^{89} +(-0.981727 - 1.04119i) q^{90} +0.671928 q^{91} +(7.46386 - 12.9278i) q^{92} +(0.412970 + 3.53776i) q^{93} +(0.846542 + 1.46625i) q^{94} +(2.43188 + 4.21214i) q^{95} +(0.980120 + 8.39631i) q^{96} +(-0.471471 + 0.816612i) q^{97} +3.12372 q^{98} +(-10.8150 + 2.55981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.238506	−	0.413105i	0.168649	−	0.292109i	−0.769296	−	0.638893i	$-0.779393\pi$
$2$	0.238506	−	0.413105i	0.168649	−	0.292109i	0.937945	+	0.346784i	$0.112726\pi$
$3$	1.59029	+	0.686267i	0.918157	+	0.396217i
$3$	1.59029	+	0.686267i	0.918157	+	0.396217i
$4$	0.886230	+	1.53499i	0.443115	+	0.767497i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.662795	−	0.493279i	0.270585	−	0.201380i
$7$	0.335964	−	0.581906i	0.126982	−	0.219940i	−0.795524	−	0.605922i	$-0.792804\pi$
$7$	0.335964	−	0.581906i	0.126982	−	0.219940i	0.922506	+	0.385983i	$0.126138\pi$
$8$	1.79951			0.636222
$9$	2.05807	+	2.18273i	0.686025	+	0.727578i
$10$	−0.477012			−0.150844
$11$	−1.85231	+	3.20829i	−0.558492	+	0.967337i	0.439131	+	0.898423i	$0.355287\pi$
$11$	−1.85231	+	3.20829i	−0.558492	+	0.967337i	−0.997623	+	0.0689135i	$0.978047\pi$
$12$	0.355950	+	3.04928i	0.102754	+	0.880253i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−0.160259	−	0.277576i	−0.0428310	−	0.0741854i
$15$	−0.200823	−	1.72037i	−0.0518522	−	0.444197i
$16$	−1.34327	+	2.32660i	−0.335816	+	0.581651i
$17$	6.76009			1.63956			0.819781	−	0.572677i	$-0.194095\pi$
$17$	6.76009			1.63956			0.819781	+	0.572677i	$0.194095\pi$
$18$	1.39256	−	0.329605i	0.328230	−	0.0776886i
$19$	−4.86376			−1.11582			−0.557912	−	0.829900i	$-0.688397\pi$
$19$	−4.86376			−1.11582			−0.557912	+	0.829900i	$0.688397\pi$
$20$	0.886230	−	1.53499i	0.198167	−	0.343235i
$21$	0.933625	−	0.694842i	0.203734	−	0.151627i
$22$	0.883574	+	1.53039i	0.188379	+	0.326281i
$23$	−4.21102	−	7.29370i	−0.878058	−	1.52084i	−0.853469	−	0.521143i	$-0.825506\pi$
$23$	−4.21102	−	7.29370i	−0.878058	−	1.52084i	−0.0245888	−	0.999698i	$-0.507828\pi$
$24$	2.86175	+	1.23494i	0.584152	+	0.252082i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.477012			0.0935498
$27$	1.77501	+	4.88358i	0.341600	+	0.939845i
$28$	1.19096			0.225071
$29$	4.84813	−	8.39721i	0.900276	−	1.55932i	0.0731393	−	0.997322i	$-0.476698\pi$
$29$	4.84813	−	8.39721i	0.900276	−	1.55932i	0.827136	−	0.562001i	$-0.189968\pi$
$30$	−0.758590	−	0.327358i	−0.138499	−	0.0597671i
$31$	1.02820	+	1.78089i	0.184670	+	0.319857i	0.943465	−	0.331472i	$-0.107545\pi$
$31$	1.02820	+	1.78089i	0.184670	+	0.319857i	−0.758796	+	0.651329i	$0.774212\pi$
$32$	2.44026	+	4.22666i	0.431382	+	0.747175i
$33$	−5.14746	+	3.83095i	−0.896058	+	0.666883i
$34$	1.61232	−	2.79262i	0.276511	−	0.478931i
$35$	−0.671928			−0.113576
$36$	−1.52656	+	5.09354i	−0.254426	+	0.848923i
$37$	3.15079			0.517987			0.258994	−	0.965879i	$-0.416609\pi$
$37$	3.15079			0.517987			0.258994	+	0.965879i	$0.416609\pi$
$38$	−1.16004	+	2.00924i	−0.188183	+	0.325942i
$39$	0.200823	+	1.72037i	0.0321574	+	0.275480i
$40$	−0.899754	−	1.55842i	−0.142264	−	0.246408i
$41$	−3.83107	−	6.63561i	−0.598313	−	1.03631i	−0.993070	−	0.117523i	$-0.962505\pi$
$41$	−3.83107	−	6.63561i	−0.598313	−	1.03631i	0.394757	−	0.918785i	$-0.370829\pi$
$42$	−0.0643672	−	0.551409i	−0.00993207	−	0.0850842i
$43$	−3.41131	+	5.90856i	−0.520220	+	0.901047i	0.479504	+	0.877540i	$0.340817\pi$
$43$	−3.41131	+	5.90856i	−0.520220	+	0.901047i	−0.999724	+	0.0235074i	$0.992517\pi$
$44$	−6.56628			−0.989905
$45$	0.861266	−	2.87371i	0.128390	−	0.428388i
$46$	−4.01741			−0.592335
$47$	−1.77468	+	3.07383i	−0.258863	+	0.448364i	−0.965938	−	0.258775i	$-0.916681\pi$
$47$	−1.77468	+	3.07383i	−0.258863	+	0.448364i	0.707074	+	0.707139i	$0.250015\pi$
$48$	−3.73286	+	2.77815i	−0.538792	+	0.400991i
$49$	3.27426	+	5.67118i	0.467751	+	0.810168i
$50$	0.238506	+	0.413105i	0.0337298	+	0.0584218i
$51$	10.7505	+	4.63923i	1.50538	+	0.649622i
$52$	−0.886230	+	1.53499i	−0.122898	+	0.212866i
$53$	5.30936			0.729297			0.364648	−	0.931145i	$-0.381189\pi$
$53$	5.30936			0.729297			0.364648	+	0.931145i	$0.381189\pi$
$54$	2.44078	+	0.431500i	0.332148	+	0.0587197i
$55$	3.70462			0.499531
$56$	0.604570	−	1.04715i	0.0807890	−	0.139931i
$57$	−7.73481	−	3.33784i	−1.02450	−	0.442108i
$58$	−2.31262	−	4.00557i	−0.303662	−	0.525957i
$59$	−3.16134	−	5.47561i	−0.411572	−	0.712863i	0.583490	−	0.812120i	$-0.301687\pi$
$59$	−3.16134	−	5.47561i	−0.411572	−	0.712863i	−0.995062	+	0.0992570i	$0.968353\pi$
$60$	2.46278	−	1.83290i	0.317944	−	0.236627i
$61$	−1.37355	+	2.37907i	−0.175866	+	0.304608i	−0.940461	−	0.339903i	$-0.889606\pi$
$61$	−1.37355	+	2.37907i	−0.175866	+	0.304608i	0.764595	+	0.644511i	$0.222939\pi$
$62$	0.980925			0.124578
$63$	1.96159	−	0.464287i	0.247137	−	0.0584947i
$64$	−3.04499			−0.380624
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	0.354883	+	3.04015i	0.0436831	+	0.374216i
$67$	−5.88093	−	10.1861i	−0.718471	−	1.24443i	−0.961606	−	0.274435i	$-0.911509\pi$
$67$	−5.88093	−	10.1861i	−0.718471	−	1.24443i	0.243135	−	0.969992i	$-0.421824\pi$
$68$	5.99099	+	10.3767i	0.726515	+	1.25836i
$69$	−1.69134	−	14.4890i	−0.203613	−	1.74427i
$70$	−0.160259	+	0.277576i	−0.0191546	+	0.0331767i
$71$	−5.06552			−0.601167			−0.300583	−	0.953756i	$-0.597181\pi$
$71$	−5.06552			−0.601167			−0.300583	+	0.953756i	$0.597181\pi$
$72$	3.70352	+	3.92785i	0.436464	+	0.462901i
$73$	−9.39507			−1.09961			−0.549805	−	0.835293i	$-0.685298\pi$
$73$	−9.39507			−1.09961			−0.549805	+	0.835293i	$0.685298\pi$
$74$	0.751483	−	1.30161i	0.0873582	−	0.151309i
$75$	−1.38947	+	1.03410i	−0.160442	+	0.119408i
$76$	−4.31041	−	7.46585i	−0.494438	−	0.856392i
$77$	1.24462	+	2.15574i	0.141837	+	0.245669i
$78$	0.758590	+	0.327358i	0.0858934	+	0.0370660i
$79$	7.13987	−	12.3666i	0.803298	−	1.39135i	−0.114136	−	0.993465i	$-0.536410\pi$
$79$	7.13987	−	12.3666i	0.803298	−	1.39135i	0.917434	−	0.397888i	$-0.130257\pi$
$80$	2.68653			0.300363
$81$	−0.528656	+	8.98446i	−0.0587395	+	0.998273i
$82$	−3.65494			−0.403620
$83$	8.34140	−	14.4477i	0.915588	−	1.58584i	0.109549	−	0.993981i	$-0.465059\pi$
$83$	8.34140	−	14.4477i	0.915588	−	1.58584i	0.806038	−	0.591863i	$-0.201607\pi$
$84$	1.89398	+	0.817320i	0.206651	+	0.0891769i
$85$	−3.38004	−	5.85441i	−0.366617	−	0.635000i
$86$	1.62724	+	2.81845i	0.175469	+	0.303922i
$87$	13.4727	−	10.0269i	1.44442	−	1.07500i
$88$	−3.33325	+	5.77335i	−0.355325	+	0.615441i
$89$	−4.23971			−0.449408			−0.224704	−	0.974427i	$-0.572142\pi$
$89$	−4.23971			−0.449408			−0.224704	+	0.974427i	$0.572142\pi$
$90$	−0.981727	−	1.04119i	−0.103483	−	0.109751i
$91$	0.671928			0.0704371
$92$	7.46386	−	12.9278i	0.778161	−	1.34781i
$93$	0.412970	+	3.53776i	0.0428230	+	0.366848i
$94$	0.846542	+	1.46625i	0.0873142	+	0.151233i
$95$	2.43188	+	4.21214i	0.249506	+	0.432156i
$96$	0.980120	+	8.39631i	0.100033	+	0.856944i
$97$	−0.471471	+	0.816612i	−0.0478706	+	0.0829144i	−0.888968	−	0.457970i	$-0.848577\pi$
$97$	−0.471471	+	0.816612i	−0.0478706	+	0.0829144i	0.841097	+	0.540884i	$0.181910\pi$
$98$	3.12372			0.315543
$99$	−10.8150	+	2.55981i	−1.08695	+	0.257271i
$100$	−1.77246			−0.177246
$101$	−0.650724	+	1.12709i	−0.0647495	+	0.112149i	−0.896583	−	0.442876i	$-0.853958\pi$
$101$	−0.650724	+	1.12709i	−0.0647495	+	0.112149i	0.831833	+	0.555025i	$0.187291\pi$
$102$	4.48055	−	3.33461i	0.443641	−	0.330176i
$103$	0.791776	+	1.37140i	0.0780160	+	0.135128i	0.902394	−	0.430912i	$-0.141808\pi$
$103$	0.791776	+	1.37140i	0.0780160	+	0.135128i	−0.824378	+	0.566040i	$0.808475\pi$
$104$	0.899754	+	1.55842i	0.0882282	+	0.152816i
$105$	−1.06856	−	0.461122i	−0.104281	−	0.0450009i
$106$	1.26631	−	2.19332i	0.122995	−	0.213034i
$107$	−12.0179			−1.16181			−0.580907	−	0.813970i	$-0.697302\pi$
$107$	−12.0179			−1.16181			−0.580907	+	0.813970i	$0.697302\pi$
$108$	−5.92321	+	7.05260i	−0.569961	+	0.678637i
$109$	10.8392			1.03820			0.519102	−	0.854712i	$-0.326266\pi$
$109$	10.8392			1.03820			0.519102	+	0.854712i	$0.326266\pi$
$110$	0.883574	−	1.53039i	0.0842454	−	0.145917i
$111$	5.01069	+	2.16229i	0.475594	+	0.205235i
$112$	0.902577	+	1.56331i	0.0852855	+	0.147719i
$113$	2.52260	+	4.36928i	0.237307	+	0.411027i	0.959941	−	0.280204i	$-0.0904021\pi$
$113$	2.52260	+	4.36928i	0.237307	+	0.411027i	−0.722634	+	0.691231i	$0.757069\pi$
$114$	−3.22368	+	2.39919i	−0.301925	+	0.224705i
$115$	−4.21102	+	7.29370i	−0.392679	+	0.680141i
$116$	17.1862			1.59570
$117$	−0.861266	+	2.87371i	−0.0796240	+	0.265675i
$118$	−3.01600			−0.277645
$119$	2.27115	−	3.93374i	0.208196	−	0.360605i
$120$	−0.361382	−	3.09582i	−0.0329895	−	0.282608i
$121$	−1.36210	−	2.35922i	−0.123827	−	0.214475i
$122$	0.655202	+	1.13484i	0.0593192	+	0.102744i
$123$	−1.53873	−	13.1817i	−0.138743	−	1.18856i
$124$	−1.82244	+	3.15655i	−0.163660	+	0.283467i
$125$	1.00000			0.0894427
$126$	0.276051	−	0.921075i	0.0245926	−	0.0820559i
$127$	−9.87765			−0.876499			−0.438250	−	0.898853i	$-0.644401\pi$
$127$	−9.87765			−0.876499			−0.438250	+	0.898853i	$0.644401\pi$
$128$	−5.60677	+	9.71122i	−0.495574	+	0.858359i
$129$	−9.47984	+	7.05528i	−0.834653	+	0.621183i
$130$	−0.238506	−	0.413105i	−0.0209184	−	0.0362317i
$131$	−6.12856	−	10.6150i	−0.535455	−	0.927436i	−0.999141	−	0.0414360i	$-0.986807\pi$
$131$	−6.12856	−	10.6150i	−0.535455	−	0.927436i	0.463686	−	0.886000i	$-0.346527\pi$
$132$	−10.4423	−	4.50623i	−0.908888	−	0.392217i
$133$	−1.63405	+	2.83025i	−0.141690	+	0.245414i
$134$	−5.61055			−0.484678
$135$	3.34180	−	3.97899i	0.287616	−	0.342457i
$136$	12.1648			1.04313
$137$	−6.38780	+	11.0640i	−0.545746	+	0.945261i	0.452813	+	0.891605i	$0.350420\pi$
$137$	−6.38780	+	11.0640i	−0.545746	+	0.945261i	−0.998560	+	0.0536551i	$0.982913\pi$
$138$	−6.38887	−	2.75702i	−0.543857	−	0.234693i
$139$	−10.4617	−	18.1201i	−0.887346	−	1.53693i	−0.843001	−	0.537913i	$-0.819213\pi$
$139$	−10.4617	−	18.1201i	−0.887346	−	1.53693i	−0.0443458	−	0.999016i	$-0.514120\pi$
$140$	−0.595482	−	1.03141i	−0.0503274	−	0.0871697i
$141$	−4.93173	+	3.67039i	−0.415326	+	0.309103i
$142$	−1.20816	+	2.09259i	−0.101386	+	0.175606i
$143$	−3.70462			−0.309796
$144$	−7.84290	+	1.85633i	−0.653575	+	0.154695i
$145$	−9.69626			−0.805231
$146$	−2.24078	+	3.88115i	−0.185448	+	0.321206i
$147$	1.31509	+	11.2659i	0.108467	+	0.929193i
$148$	2.79233	+	4.83645i	0.229528	+	0.397554i
$149$	−8.00033	−	13.8570i	−0.655412	−	1.13521i	−0.981790	−	0.189968i	$-0.939162\pi$
$149$	−8.00033	−	13.8570i	−0.655412	−	1.13521i	0.326378	−	0.945239i	$-0.394172\pi$
$150$	0.0957948	+	0.820637i	0.00782161	+	0.0670047i
$151$	1.19426	−	2.06853i	0.0971879	−	0.168334i	−0.813332	−	0.581800i	$-0.802349\pi$
$151$	1.19426	−	2.06853i	0.0971879	−	0.168334i	0.910520	+	0.413466i	$0.135682\pi$
$152$	−8.75238			−0.709912
$153$	13.9128	+	14.7555i	1.12478	+	1.19291i
$154$	1.18739			0.0956830
$155$	1.02820	−	1.78089i	0.0825868	−	0.143044i
$156$	−2.46278	+	1.83290i	−0.197180	+	0.146750i
$157$	−5.32413	−	9.22167i	−0.424912	−	0.735969i	0.571500	−	0.820602i	$-0.306362\pi$
$157$	−5.32413	−	9.22167i	−0.424912	−	0.735969i	−0.996412	+	0.0846328i	$0.973028\pi$
$158$	−3.40580	−	5.89903i	−0.270951	−	0.469301i
$159$	8.44345	+	3.64364i	0.669609	+	0.288959i
$160$	2.44026	−	4.22666i	0.192920	−	0.334147i
$161$	−5.65900			−0.445992
$162$	3.58543	+	2.36124i	0.281698	+	0.185516i
$163$	13.0677			1.02354			0.511771	−	0.859122i	$-0.328990\pi$
$163$	13.0677			1.02354			0.511771	+	0.859122i	$0.328990\pi$
$164$	6.79042	−	11.7614i	0.530243	−	0.918407i
$165$	5.89143	+	2.54236i	0.458648	+	0.197922i
$166$	−3.97895	−	6.89174i	−0.308826	−	0.534903i
$167$	6.15146	+	10.6546i	0.476014	+	0.824480i	0.999622	−	0.0274788i	$-0.00874786\pi$
$167$	6.15146	+	10.6546i	0.476014	+	0.824480i	−0.523609	+	0.851959i	$0.675415\pi$
$168$	1.68007	−	1.25037i	0.129620	−	0.0964684i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−3.22464			−0.247319
$171$	−10.0100	−	10.6163i	−0.765483	−	0.811848i
$172$	−12.0928			−0.922069
$173$	−4.10829	+	7.11577i	−0.312348	+	0.541002i	−0.978870	−	0.204483i	$-0.934449\pi$
$173$	−4.10829	+	7.11577i	−0.312348	+	0.541002i	0.666523	+	0.745485i	$0.267782\pi$
$174$	−0.928852	−	7.95711i	−0.0704161	−	0.603227i
$175$	0.335964	+	0.581906i	0.0253965	+	0.0439880i
$176$	−4.97629	−	8.61918i	−0.375102	−	0.649695i
$177$	−1.26974	−	10.8774i	−0.0954394	−	0.817592i
$178$	−1.01120	+	1.75144i	−0.0757923	+	0.131276i
$179$	0.0872515			0.00652148			0.00326074	−	0.999995i	$-0.498962\pi$
$179$	0.0872515			0.00652148			0.00326074	+	0.999995i	$0.498962\pi$
$180$	5.17441	−	1.22473i	0.385678	−	0.0912860i
$181$	−10.5494			−0.784127			−0.392064	−	0.919938i	$-0.628239\pi$
$181$	−10.5494			−0.784127			−0.392064	+	0.919938i	$0.628239\pi$
$182$	0.160259	−	0.277576i	0.0118792	−	0.0205753i
$183$	−3.81703	+	2.84079i	−0.282163	+	0.209997i
$184$	−7.57776	−	13.1251i	−0.558640	−	0.967593i
$185$	−1.57540	−	2.72867i	−0.115826	−	0.200616i
$186$	1.55996	+	0.673176i	0.114382	+	0.0493597i
$187$	−12.5218	+	21.6883i	−0.915683	+	1.58601i
$188$	−6.29109			−0.458825
$189$	3.43812	+	0.607818i	0.250087	+	0.0442123i
$190$	2.32007			0.168316
$191$	−4.86310	+	8.42313i	−0.351881	+	0.609476i	−0.986579	−	0.163284i	$-0.947791\pi$
$191$	−4.86310	+	8.42313i	−0.351881	+	0.609476i	0.634698	+	0.772760i	$0.281125\pi$
$192$	−4.84244	−	2.08968i	−0.349473	−	0.150810i
$193$	10.7517	+	18.6225i	0.773923	+	1.34047i	0.935398	+	0.353597i	$0.115042\pi$
$193$	10.7517	+	18.6225i	0.773923	+	1.34047i	−0.161475	+	0.986877i	$0.551625\pi$
$194$	0.224897	+	0.389534i	0.0161467	+	0.0279669i
$195$	1.38947	−	1.03410i	0.0995022	−	0.0740536i
$196$	−5.80349	+	10.0519i	−0.414535	+	0.717995i
$197$	13.4912			0.961207			0.480604	−	0.876938i	$-0.340418\pi$
$197$	13.4912			0.961207			0.480604	+	0.876938i	$0.340418\pi$
$198$	−1.52198	+	5.07827i	−0.108163	+	0.360897i
$199$	23.0015			1.63053			0.815267	−	0.579086i	$-0.196590\pi$
$199$	23.0015			1.63053			0.815267	+	0.579086i	$0.196590\pi$
$200$	−0.899754	+	1.55842i	−0.0636222	+	0.110197i
$201$	−2.36205	−	20.2348i	−0.166606	−	1.42725i
$202$	0.310403	+	0.537634i	0.0218399	+	0.0378278i
$203$	−3.25759	−	5.64232i	−0.228638	−	0.396013i
$204$	2.40625	+	20.6134i	0.168471	+	1.44323i
$205$	−3.83107	+	6.63561i	−0.267574	+	0.463451i
$206$	0.755373			0.0526293
$207$	7.25361	−	24.2025i	0.504161	−	1.68219i
$208$	−2.68653			−0.186277
$209$	9.00919	−	15.6044i	0.623179	−	1.07938i
$210$	−0.445350	+	0.331448i	−0.0307321	+	0.0228721i
$211$	7.66516	+	13.2764i	0.527691	+	0.913988i	0.999479	+	0.0322756i	$0.0102754\pi$
$211$	7.66516	+	13.2764i	0.527691	+	0.913988i	−0.471788	+	0.881712i	$0.656391\pi$
$212$	4.70531	+	8.14984i	0.323162	+	0.559733i
$213$	−8.05567	−	3.47630i	−0.551965	−	0.238192i
$214$	−2.86634	+	4.96465i	−0.195939	+	0.339376i
$215$	6.82262			0.465299
$216$	3.19414	+	8.78804i	0.217334	+	0.597951i
$217$	1.38175			0.0937991
$218$	2.58521	−	4.47771i	0.175092	−	0.303269i
$219$	−14.9409	−	6.44753i	−1.00961	−	0.435684i
$220$	3.28314	+	5.68657i	0.221349	+	0.383388i
$221$	3.38004	+	5.85441i	0.227366	+	0.393810i
$222$	2.08833	−	1.55422i	0.140160	−	0.104313i
$223$	−11.3279	+	19.6205i	−0.758572	+	1.31388i	0.185007	+	0.982737i	$0.440769\pi$
$223$	−11.3279	+	19.6205i	−0.758572	+	1.31388i	−0.943579	+	0.331148i	$0.892564\pi$
$224$	3.27936			0.219111
$225$	−2.91934	+	0.690978i	−0.194623	+	0.0460652i
$226$	2.40662			0.160086
$227$	7.94535	−	13.7617i	0.527351	−	0.913399i	−0.472141	−	0.881523i	$-0.656519\pi$
$227$	7.94535	−	13.7617i	0.527351	−	0.913399i	0.999492	−	0.0318758i	$-0.0101481\pi$
$228$	−1.73126	−	14.8310i	−0.114655	−	0.982206i
$229$	−11.5027	−	19.9232i	−0.760117	−	1.31656i	−0.942790	−	0.333388i	$-0.891808\pi$
$229$	−11.5027	−	19.9232i	−0.760117	−	1.31656i	0.182673	−	0.983174i	$-0.441525\pi$
$230$	2.00871	+	3.47918i	0.132450	+	0.229410i
$231$	0.499895	+	4.28240i	0.0328907	+	0.281761i
$232$	8.72426	−	15.1109i	0.572775	−	0.992076i
$233$	18.0519			1.18262			0.591310	−	0.806444i	$-0.298611\pi$
$233$	18.0519			1.18262			0.591310	+	0.806444i	$0.298611\pi$
$234$	0.981727	+	1.04119i	0.0641775	+	0.0680647i
$235$	3.54935			0.231534
$236$	5.60335	−	9.70529i	0.364747	−	0.631761i
$237$	19.8413	−	14.7667i	1.28883	−	0.959201i
$238$	−1.08336	−	1.87644i	−0.0702240	−	0.121632i
$239$	8.47673	+	14.6821i	0.548314	+	0.949708i	0.998390	+	0.0567180i	$0.0180636\pi$
$239$	8.47673	+	14.6821i	0.548314	+	0.949708i	−0.450076	+	0.892990i	$0.648603\pi$
$240$	4.27238	+	1.84368i	0.275781	+	0.119009i
$241$	−10.0408	+	17.3912i	−0.646784	+	1.12026i	0.337103	+	0.941468i	$0.390553\pi$
$241$	−10.0408	+	17.3912i	−0.646784	+	1.12026i	−0.983886	+	0.178795i	$0.942780\pi$
$242$	−1.29947			−0.0835333
$243$	−7.00646	+	13.9251i	−0.449464	+	0.893298i
$244$	−4.86914			−0.311715
$245$	3.27426	−	5.67118i	0.209185	−	0.362318i
$246$	−5.81242	−	2.50826i	−0.370587	−	0.159921i
$247$	−2.43188	−	4.21214i	−0.154737	−	0.268012i
$248$	1.85025	+	3.20473i	0.117491	+	0.203500i
$249$	23.1803	−	17.2517i	1.46899	−	1.09328i
$250$	0.238506	−	0.413105i	0.0150844	−	0.0261270i
$251$	−13.4125			−0.846587			−0.423293	−	0.905993i	$-0.639126\pi$
$251$	−13.4125			−0.846587			−0.423293	+	0.905993i	$0.639126\pi$
$252$	2.45109	+	2.59956i	0.154404	+	0.163757i
$253$	31.2004			1.96155
$254$	−2.35588	+	4.08050i	−0.147821	+	0.256033i
$255$	−1.35758	−	11.6298i	−0.0850149	−	0.728289i
$256$	−0.370495	−	0.641716i	−0.0231559	−	0.0401073i
$257$	9.04927	+	15.6738i	0.564478	+	0.977705i	0.997098	+	0.0761283i	$0.0242558\pi$
$257$	9.04927	+	15.6738i	0.564478	+	0.977705i	−0.432620	+	0.901576i	$0.642411\pi$
$258$	0.653572	+	5.59889i	0.0406896	+	0.348572i
$259$	1.05855	−	1.83347i	0.0657753	−	0.113926i
$260$	1.77246			0.109923
$261$	28.3067	−	6.69991i	1.75214	−	0.414714i
$262$	−5.84680			−0.361216
$263$	−10.5213	+	18.2234i	−0.648772	+	1.12371i	0.334644	+	0.942344i	$0.391384\pi$
$263$	−10.5213	+	18.2234i	−0.648772	+	1.12371i	−0.983416	+	0.181362i	$0.941950\pi$
$264$	−9.26290	+	6.89383i	−0.570092	+	0.424286i
$265$	−2.65468	−	4.59804i	−0.163076	−	0.282455i
$266$	0.779460	+	1.35006i	0.0477918	+	0.0827778i
$267$	−6.74239	−	2.90957i	−0.412627	−	0.178063i
$268$	10.4237	−	18.0544i	0.636730	−	1.10285i
$269$	−9.84439			−0.600223			−0.300111	−	0.953904i	$-0.597024\pi$
$269$	−9.84439			−0.600223			−0.300111	+	0.953904i	$0.597024\pi$
$270$	−0.846700	−	2.32953i	−0.0515285	−	0.141770i
$271$	16.9936			1.03229			0.516144	−	0.856502i	$-0.327367\pi$
$271$	16.9936			1.03229			0.516144	+	0.856502i	$0.327367\pi$
$272$	−9.08060	+	15.7281i	−0.550592	+	0.953653i
$273$	1.06856	+	0.461122i	0.0646724	+	0.0279084i
$274$	3.04706	+	5.27766i	0.184079	+	0.318835i
$275$	−1.85231	−	3.20829i	−0.111698	−	0.193467i
$276$	20.7416	−	15.4368i	1.24850	−	0.929185i
$277$	−4.86623	+	8.42856i	−0.292383	+	0.506423i	−0.974373	−	0.224939i	$-0.927782\pi$
$277$	−4.86623	+	8.42856i	−0.292383	+	0.506423i	0.681989	+	0.731362i	$0.261115\pi$
$278$	−9.98068			−0.598601
$279$	−1.77110	+	5.90948i	−0.106033	+	0.353792i
$280$	−1.20914			−0.0722599
$281$	−9.33260	+	16.1645i	−0.556736	+	0.964296i	0.441030	+	0.897493i	$0.354613\pi$
$281$	−9.33260	+	16.1645i	−0.556736	+	0.964296i	−0.997766	+	0.0668034i	$0.978720\pi$
$282$	0.340010	+	2.91273i	0.0202473	+	0.173451i
$283$	1.92406	+	3.33257i	0.114374	+	0.198101i	0.917529	−	0.397669i	$-0.130181\pi$
$283$	1.92406	+	3.33257i	0.114374	+	0.198101i	−0.803156	+	0.595769i	$0.796847\pi$
$284$	−4.48921	−	7.77555i	−0.266386	−	0.461394i
$285$	0.976753	+	8.36746i	0.0578579	+	0.495646i
$286$	−0.883574	+	1.53039i	−0.0522468	+	0.0904941i
$287$	−5.14841			−0.303901
$288$	−4.20343	+	14.0252i	−0.247689	+	0.826444i
$289$	28.6988			1.68817
$290$	−2.31262	+	4.00557i	−0.135802	+	0.235215i
$291$	−1.31019	+	0.975098i	−0.0768048	+	0.0571613i
$292$	−8.32619	−	14.4214i	−0.487253	−	0.843948i
$293$	9.54406	+	16.5308i	0.557570	+	0.965739i	0.997699	+	0.0678045i	$0.0215994\pi$
$293$	9.54406	+	16.5308i	0.557570	+	0.965739i	−0.440129	+	0.897935i	$0.645067\pi$
$294$	4.96764	+	2.14371i	0.289718	+	0.125023i
$295$	−3.16134	+	5.47561i	−0.184061	+	0.318802i
$296$	5.66988			0.329555
$297$	−18.9558	−	3.35115i	−1.09993	−	0.194454i
$298$	−7.63251			−0.442139
$299$	4.21102	−	7.29370i	0.243529	−	0.421805i
$300$	−2.81873	−	1.21638i	−0.162740	−	0.0702278i
$301$	2.29215	+	3.97013i	0.132117	+	0.228834i
$302$	−0.569679	−	0.986712i	−0.0327813	−	0.0567789i
$303$	−1.80833	+	1.34583i	−0.103886	+	0.0773159i
$304$	6.53332	−	11.3160i	0.374712	−	0.649020i
$305$	2.74711			0.157299
$306$	9.41383	−	2.22816i	0.538153	−	0.127375i
$307$	16.8238			0.960186			0.480093	−	0.877218i	$-0.340603\pi$
$307$	16.8238			0.960186			0.480093	+	0.877218i	$0.340603\pi$
$308$	−2.20603	+	3.82096i	−0.125700	+	0.217720i
$309$	0.318013	+	2.72429i	0.0180911	+	0.154980i
$310$	−0.490462	−	0.849506i	−0.0278564	−	0.0482487i
$311$	−6.44769	−	11.1677i	−0.365615	−	0.633264i	0.623260	−	0.782015i	$-0.285808\pi$
$311$	−6.44769	−	11.1677i	−0.365615	−	0.633264i	−0.988875	+	0.148751i	$0.952475\pi$
$312$	0.361382	+	3.09582i	0.0204592	+	0.175266i
$313$	14.9727	−	25.9334i	0.846306	−	1.46584i	−0.0381770	−	0.999271i	$-0.512155\pi$
$313$	14.9727	−	25.9334i	0.846306	−	1.46584i	0.884483	−	0.466573i	$-0.154512\pi$
$314$	−5.07935			−0.286644
$315$	−1.38288	−	1.46664i	−0.0779163	−	0.0826358i
$316$	25.3103			1.42381
$317$	−8.83334	+	15.2998i	−0.496130	+	0.859322i	−0.999990	−	0.00446330i	$-0.998579\pi$
$317$	−8.83334	+	15.2998i	−0.496130	+	0.859322i	0.503860	+	0.863785i	$0.331913\pi$
$318$	3.51902	−	2.61900i	0.197337	−	0.146866i
$319$	17.9605	+	31.1085i	1.00559	+	1.74174i
$320$	1.52250	+	2.63704i	0.0851102	+	0.147415i
$321$	−19.1120	−	8.24749i	−1.06673	−	0.460330i
$322$	−1.34971	+	2.33776i	−0.0752161	+	0.130278i
$323$	−32.8795			−1.82946
$324$	−14.2596	+	7.15081i	−0.792201	+	0.397267i
$325$	−1.00000			−0.0554700
$326$	3.11672	−	5.39833i	0.172619	−	0.298986i
$327$	17.2375	+	7.43857i	0.953235	+	0.411354i
$328$	−6.89405	−	11.9408i	−0.380660	−	0.659323i
$329$	1.19245	+	2.06539i	0.0657421	+	0.113869i
$330$	2.45540	−	1.82741i	0.135165	−	0.100596i
$331$	−5.34761	+	9.26234i	−0.293931	+	0.509104i	−0.974736	−	0.223361i	$-0.928297\pi$
$331$	−5.34761	+	9.26234i	−0.293931	+	0.509104i	0.680804	+	0.732465i	$0.261630\pi$
$332$	29.5696			1.62284
$333$	6.48457	+	6.87735i	0.355352	+	0.376876i
$334$	5.86864			0.321117
$335$	−5.88093	+	10.1861i	−0.321310	+	0.556525i
$336$	0.362516	+	3.10553i	0.0197769	+	0.169421i
$337$	−3.88441	−	6.72799i	−0.211597	−	0.366497i	0.740617	−	0.671927i	$-0.234533\pi$
$337$	−3.88441	−	6.72799i	−0.211597	−	0.366497i	−0.952215	+	0.305430i	$0.901200\pi$
$338$	0.238506	+	0.413105i	0.0129730	+	0.0224699i
$339$	1.01319	+	8.67962i	0.0550290	+	0.471412i
$340$	5.99099	−	10.3767i	0.324907	−	0.562756i
$341$	−7.61815			−0.412546
$342$	−6.77308	+	1.60312i	−0.366246	+	0.0866868i
$343$	9.10362			0.491549
$344$	−6.13868	+	10.6325i	−0.330975	+	0.573266i
$345$	−11.7022	+	8.70925i	−0.630024	+	0.468890i
$346$	1.95970	+	3.39431i	0.105354	+	0.182479i
$347$	3.38866	+	5.86933i	0.181913	+	0.315082i	0.942532	−	0.334116i	$-0.108438\pi$
$347$	3.38866	+	5.86933i	0.181913	+	0.315082i	−0.760619	+	0.649198i	$0.775104\pi$
$348$	27.3312	+	11.7943i	1.46511	+	0.632243i
$349$	8.50569	−	14.7323i	0.455299	−	0.788602i	−0.543406	−	0.839470i	$-0.682866\pi$
$349$	8.50569	−	14.7323i	0.455299	−	0.788602i	0.998705	+	0.0508684i	$0.0161989\pi$
$350$	0.320518			0.0171324
$351$	−3.34180	+	3.97899i	−0.178372	+	0.212383i
$352$	−18.0805			−0.963693
$353$	1.82671	−	3.16396i	0.0972260	−	0.168400i	−0.813309	−	0.581831i	$-0.802336\pi$
$353$	1.82671	−	3.16396i	0.0972260	−	0.168400i	0.910535	+	0.413431i	$0.135670\pi$
$354$	−4.79633	−	2.06978i	−0.254922	−	0.110008i
$355$	2.53276	+	4.38687i	0.134425	+	0.232831i
$356$	−3.75736	−	6.50793i	−0.199139	−	0.344920i
$357$	6.31139	−	4.69719i	0.334034	−	0.248602i
$358$	0.0208100	−	0.0360440i	0.00109984	−	0.00190498i
$359$	8.25771			0.435825			0.217913	−	0.975968i	$-0.430075\pi$
$359$	8.25771			0.435825			0.217913	+	0.975968i	$0.430075\pi$
$360$	1.54986	−	5.17127i	0.0816845	−	0.272550i
$361$	4.65617			0.245062
$362$	−2.51608	+	4.35799i	−0.132242	+	0.229051i
$363$	−0.547079	−	4.68662i	−0.0287142	−	0.245984i
$364$	0.595482	+	1.03141i	0.0312117	+	0.0540603i
$365$	4.69753	+	8.13637i	0.245880	+	0.425877i
$366$	0.263159	+	2.25438i	0.0137555	+	0.117838i
$367$	−11.4892	+	19.8999i	−0.599733	+	1.03877i	0.393127	+	0.919484i	$0.371393\pi$
$367$	−11.4892	+	19.8999i	−0.599733	+	1.03877i	−0.992860	+	0.119284i	$0.961940\pi$
$368$	22.6261			1.17947
$369$	6.59914	−	22.0188i	0.343538	−	1.14625i
$370$	−1.50297			−0.0781355
$371$	1.78375	−	3.08955i	0.0926078	−	0.160401i
$372$	−5.06445	+	3.76917i	−0.262580	+	0.195422i
$373$	7.24168	+	12.5430i	0.374960	+	0.649450i	0.990321	−	0.138796i	$-0.0443231\pi$
$373$	7.24168	+	12.5430i	0.374960	+	0.649450i	−0.615361	+	0.788245i	$0.710990\pi$
$374$	5.97304	+	10.3456i	0.308858	+	0.534958i
$375$	1.59029	+	0.686267i	0.0821225	+	0.0354387i
$376$	−3.19355	+	5.53138i	−0.164695	+	0.285259i
$377$	9.69626			0.499383
$378$	1.07111	−	1.27534i	0.0550917	−	0.0655962i
$379$	17.4080			0.894188			0.447094	−	0.894487i	$-0.352459\pi$
$379$	17.4080			0.894188			0.447094	+	0.894487i	$0.352459\pi$
$380$	−4.31041	+	7.46585i	−0.221119	+	0.382990i
$381$	−15.7084	−	6.77870i	−0.804764	−	0.347284i
$382$	2.31976	+	4.01793i	0.118689	+	0.205575i
$383$	−13.9153	−	24.1020i	−0.711038	−	1.23155i	−0.964468	−	0.264200i	$-0.914892\pi$
$383$	−13.9153	−	24.1020i	−0.711038	−	1.23155i	0.253430	−	0.967354i	$-0.418441\pi$
$384$	−15.5809	+	11.5960i	−0.795110	+	0.591754i
$385$	1.24462	−	2.15574i	0.0634316	−	0.109867i
$386$	10.2574			0.522086
$387$	−19.9175	+	4.71428i	−1.01247	+	0.239640i
$388$	−1.67133			−0.0848488
$389$	−5.90180	+	10.2222i	−0.299233	+	0.518287i	−0.975961	−	0.217946i	$-0.930064\pi$
$389$	−5.90180	+	10.2222i	−0.299233	+	0.518287i	0.676728	+	0.736234i	$0.263398\pi$
$390$	−0.0957948	−	0.820637i	−0.00485076	−	0.0415546i
$391$	−28.4669	−	49.3060i	−1.43963	−	2.49351i
$392$	5.89205	+	10.2053i	0.297594	+	0.515447i
$393$	−2.46151	−	21.0868i	−0.124167	−	1.06369i
$394$	3.21773	−	5.57327i	0.162107	−	0.280777i
$395$	−14.2797			−0.718492
$396$	−13.5139	−	14.3325i	−0.679099	−	0.720233i
$397$	19.1467			0.960944			0.480472	−	0.877010i	$-0.340465\pi$
$397$	19.1467			0.960944			0.480472	+	0.877010i	$0.340465\pi$
$398$	5.48600	−	9.50203i	0.274988	−	0.476294i
$399$	−4.54093	+	3.37954i	−0.227331	+	0.169189i
$400$	−1.34327	−	2.32660i	−0.0671633	−	0.116330i
$401$	−2.05036	−	3.55132i	−0.102390	−	0.177345i	0.810279	−	0.586044i	$-0.199316\pi$
$401$	−2.05036	−	3.55132i	−0.102390	−	0.177345i	−0.912669	+	0.408700i	$0.865982\pi$
$402$	−8.92243	−	3.85034i	−0.445011	−	0.192037i
$403$	−1.02820	+	1.78089i	−0.0512181	+	0.0887124i
$404$	−2.30676			−0.114766
$405$	8.04510	−	4.03440i	0.399764	−	0.200471i
$406$	−3.10782			−0.154239
$407$	−5.83624	+	10.1087i	−0.289292	+	0.501068i
$408$	19.3457	+	8.34833i	0.957754	+	0.413304i
$409$	10.8415	+	18.7780i	0.536076	+	0.928510i	0.999110	+	0.0421700i	$0.0134271\pi$
$409$	10.8415	+	18.7780i	0.536076	+	0.928510i	−0.463035	+	0.886340i	$0.653240\pi$
$410$	1.82747	+	3.16527i	0.0902522	+	0.156321i
$411$	−17.7513	+	13.2113i	−0.875609	+	0.651664i
$412$	−1.40339	+	2.43074i	−0.0691401	+	0.119754i
$413$	−4.24839			−0.209049
$414$	−8.26814	−	8.76894i	−0.406357	−	0.430970i
$415$	−16.6828			−0.818927
$416$	−2.44026	+	4.22666i	−0.119644	+	0.207229i
$417$	−4.20188	−	35.9958i	−0.205767	−	1.76272i
$418$	−4.29749	−	7.44347i	−0.210197	−	0.364072i
$419$	−13.5621	−	23.4902i	−0.662551	−	1.14757i	−0.979943	−	0.199277i	$-0.936141\pi$
$419$	−13.5621	−	23.4902i	−0.662551	−	1.14757i	0.317393	−	0.948294i	$-0.397193\pi$
$420$	−0.239173	−	2.04890i	−0.0116704	−	0.0999760i
$421$	3.20272	−	5.54727i	0.156091	−	0.270357i	−0.777365	−	0.629050i	$-0.783444\pi$
$421$	3.20272	−	5.54727i	0.156091	−	0.270357i	0.933456	+	0.358693i	$0.116777\pi$
$422$	7.31274			0.355979
$423$	−10.3618	+	2.45253i	−0.503807	+	0.119246i
$424$	9.55424			0.463995
$425$	−3.38004	+	5.85441i	−0.163956	+	0.283981i
$426$	−3.35740	+	2.49872i	−0.162667	+	0.121063i
$427$	0.922929	+	1.59856i	0.0446637	+	0.0773597i
$428$	−10.6506	−	18.4474i	−0.514817	−	0.891690i
$429$	−5.89143	−	2.54236i	−0.284441	−	0.122746i
$430$	1.62724	−	2.81845i	0.0784723	−	0.135918i
$431$	15.7173			0.757077			0.378539	−	0.925586i	$-0.376427\pi$
$431$	15.7173			0.757077			0.378539	+	0.925586i	$0.376427\pi$
$432$	−13.7465	−	2.43021i	−0.661377	−	0.116923i
$433$	2.63189			0.126481			0.0632403	−	0.997998i	$-0.479857\pi$
$433$	2.63189			0.126481			0.0632403	+	0.997998i	$0.479857\pi$
$434$	0.329555	−	0.570806i	0.0158192	−	0.0273996i
$435$	−15.4199	−	6.65423i	−0.739329	−	0.319046i
$436$	9.60600	+	16.6381i	0.460044	+	0.796820i
$437$	20.4814	+	35.4748i	0.979757	+	1.69699i
$438$	−6.22700	+	4.63439i	−0.297538	+	0.221440i
$439$	−10.2903	+	17.8233i	−0.491128	+	0.850658i	−0.999948	−	0.0102146i	$-0.996749\pi$
$439$	−10.2903	+	17.8233i	−0.491128	+	0.850658i	0.508820	+	0.860873i	$0.330082\pi$
$440$	6.66649			0.317813
$441$	−5.64001	+	18.8185i	−0.268572	+	0.896121i
$442$	3.22464			0.153381
$443$	0.0211107	−	0.0365649i	0.00100300	−	0.00173725i	−0.865523	−	0.500868i	$-0.833014\pi$
$443$	0.0211107	−	0.0365649i	0.00100300	−	0.00173725i	0.866526	+	0.499131i	$0.166347\pi$
$444$	1.12153	+	9.60767i	0.0532252	+	0.455960i
$445$	2.11985	+	3.67170i	0.100491	+	0.174055i
$446$	5.40354	+	9.35921i	0.255865	+	0.443171i
$447$	−3.21329	−	27.5270i	−0.151984	−	1.30198i
$448$	−1.02301	+	1.77190i	−0.0483326	+	0.0837145i
$449$	−39.2995			−1.85466			−0.927328	−	0.374249i	$-0.877900\pi$
$449$	−39.2995			−1.85466			−0.927328	+	0.374249i	$0.877900\pi$
$450$	−0.410834	+	1.37080i	−0.0193669	+	0.0646199i
$451$	28.3853			1.33661
$452$	−4.47121	+	7.74437i	−0.210308	+	0.364264i
$453$	3.31879	−	2.46998i	0.155931	−	0.116050i
$454$	−3.79003	−	6.56452i	−0.177875	−	0.308088i
$455$	−0.335964	−	0.581906i	−0.0157502	−	0.0272802i
$456$	−13.9189	−	6.00647i	−0.651811	−	0.281279i
$457$	6.63091	−	11.4851i	0.310181	−	0.537249i	−0.668220	−	0.743963i	$-0.732944\pi$
$457$	6.63091	−	11.4851i	0.310181	−	0.537249i	0.978401	+	0.206714i	$0.0662770\pi$
$458$	−10.9738			−0.512773
$459$	11.9992	+	33.0134i	0.560075	+	1.54094i
$460$	−14.9277			−0.696008
$461$	−6.07831	+	10.5279i	−0.283095	+	0.490335i	−0.972145	−	0.234378i	$-0.924695\pi$
$461$	−6.07831	+	10.5279i	−0.283095	+	0.490335i	0.689050	+	0.724713i	$0.258028\pi$
$462$	1.88831	+	0.814870i	0.0878520	+	0.0379112i
$463$	−0.875642	−	1.51666i	−0.0406945	−	0.0704850i	0.844961	−	0.534828i	$-0.179624\pi$
$463$	−0.875642	−	1.51666i	−0.0406945	−	0.0704850i	−0.885655	+	0.464343i	$0.846290\pi$
$464$	13.0247	+	22.5594i	0.604655	+	1.04729i
$465$	2.85730	−	2.12652i	0.132504	−	0.0986151i
$466$	4.30549	−	7.45733i	0.199448	−	0.345454i
$467$	3.59625			0.166414			0.0832072	−	0.996532i	$-0.473484\pi$
$467$	3.59625			0.166414			0.0832072	+	0.996532i	$0.473484\pi$
$468$	−5.17441	+	1.22473i	−0.239187	+	0.0566132i
$469$	−7.90312			−0.364932
$470$	0.846542	−	1.46625i	0.0390481	−	0.0676333i
$471$	−2.13841	−	18.3189i	−0.0985328	−	0.844092i
$472$	−5.68886	−	9.85340i	−0.261851	−	0.453540i
$473$	−12.6376	−	21.8890i	−0.581077	−	1.00646i
$474$	−1.36793	−	11.7185i	−0.0628309	−	0.538248i
$475$	2.43188	−	4.21214i	0.111582	−	0.193266i
$476$	8.05103			0.369018
$477$	10.9271	+	11.5889i	0.500316	+	0.530620i
$478$	8.08701			0.369891
$479$	−1.37107	+	2.37477i	−0.0626458	+	0.108506i	−0.895647	−	0.444765i	$-0.853287\pi$
$479$	−1.37107	+	2.37477i	−0.0626458	+	0.108506i	0.833001	+	0.553271i	$0.186621\pi$
$480$	6.78135	−	5.04696i	0.309525	−	0.230361i
$481$	1.57540	+	2.72867i	0.0718319	+	0.124417i
$482$	4.78958	+	8.29579i	0.218159	+	0.377863i
$483$	−8.99948	−	3.88358i	−0.409490	−	0.176709i
$484$	2.41426	−	4.18162i	0.109739	−	0.190074i
$485$	0.942942			0.0428168
$486$	4.08146	+	6.21563i	0.185139	+	0.281947i
$487$	12.6161			0.571689			0.285844	−	0.958276i	$-0.407726\pi$
$487$	12.6161			0.571689			0.285844	+	0.958276i	$0.407726\pi$
$488$	−2.47172	+	4.28115i	−0.111890	+	0.193799i
$489$	20.7815	+	8.96793i	0.939772	+	0.405544i
$490$	−1.56186	−	2.70522i	−0.0705576	−	0.122209i
$491$	3.84313	+	6.65650i	0.173438	+	0.300403i	0.939620	−	0.342221i	$-0.111179\pi$
$491$	3.84313	+	6.65650i	0.173438	+	0.300403i	−0.766182	+	0.642624i	$0.777846\pi$
$492$	18.8702	−	14.0440i	0.850734	−	0.633151i
$493$	32.7738	−	56.7659i	1.47606	−	2.55661i
$494$	−2.32007			−0.104385
$495$	7.62438	+	8.08620i	0.342690	+	0.363447i
$496$	−5.52457			−0.248060
$497$	−1.70183	+	2.94766i	−0.0763376	+	0.132221i
$498$	−1.59813	−	13.6905i	−0.0716137	−	0.613487i
$499$	7.45004	+	12.9038i	0.333509	+	0.577655i	0.983197	−	0.182546i	$-0.0584338\pi$
$499$	7.45004	+	12.9038i	0.333509	+	0.577655i	−0.649688	+	0.760201i	$0.725100\pi$
$500$	0.886230	+	1.53499i	0.0396334	+	0.0686471i
$501$	2.47070	+	21.1655i	0.110383	+	0.945607i
$502$	−3.19895	+	5.54075i	−0.142776	+	0.247296i
$503$	3.46526			0.154508			0.0772542	−	0.997011i	$-0.475385\pi$
$503$	3.46526			0.154508			0.0772542	+	0.997011i	$0.475385\pi$
$504$	3.52989	−	0.835489i	0.157234	−	0.0372156i
$505$	1.30145			0.0579137
$506$	7.44149	−	12.8890i	0.330815	−	0.572988i
$507$	−1.38947	+	1.03410i	−0.0617086	+	0.0459261i
$508$	−8.75386	−	15.1621i	−0.388390	−	0.672711i
$509$	−1.40892	−	2.44033i	−0.0624495	−	0.108166i	0.833110	−	0.553107i	$-0.186558\pi$
$509$	−1.40892	−	2.44033i	−0.0624495	−	0.108166i	−0.895560	+	0.444941i	$0.853225\pi$
$510$	−5.12813	−	2.21297i	−0.227078	−	0.0979918i
$511$	−3.15640	+	5.46705i	−0.139631	+	0.241848i
$512$	−22.7806			−1.00677
$513$	−8.63321	−	23.7526i	−0.381166	−	1.04870i
$514$	8.63322			0.380795
$515$	0.791776	−	1.37140i	0.0348898	−	0.0604309i
$516$	−19.2311	−	8.29890i	−0.846604	−	0.365339i
$517$	−6.57450	−	11.3874i	−0.289146	−	0.500816i
$518$	−0.504942	−	0.874586i	−0.0221859	−	0.0384271i
$519$	−11.4167	+	8.49678i	−0.501138	+	0.372967i
$520$	0.899754	−	1.55842i	0.0394568	−	0.0683412i
$521$	32.0857			1.40570			0.702851	−	0.711337i	$-0.251910\pi$
$521$	32.0857			1.40570			0.702851	+	0.711337i	$0.251910\pi$
$522$	3.98356	−	13.2916i	0.174356	−	0.581757i
$523$	−11.5163			−0.503572			−0.251786	−	0.967783i	$-0.581018\pi$
$523$	−11.5163			−0.503572			−0.251786	+	0.967783i	$0.581018\pi$
$524$	10.8626	−	18.8146i	0.474536	−	0.821921i
$525$	0.134938	+	1.15596i	0.00588919	+	0.0504504i
$526$	5.01879	+	8.69281i	0.218830	+	0.379024i
$527$	6.95070	+	12.0390i	0.302777	+	0.524426i
$528$	−1.99870	−	17.1221i	−0.0869823	−	0.745144i
$529$	−23.9653	+	41.5092i	−1.04197	+	1.80475i
$530$	−2.53263			−0.110010
$531$	5.44551	−	18.1696i	0.236315	−	0.788493i
$532$	−5.79257			−0.251140
$533$	3.83107	−	6.63561i	0.165942	−	0.287420i
$534$	−2.81006	+	2.09136i	−0.121603	+	0.0905020i
$535$	6.00895	+	10.4078i	0.259790	+	0.449969i
$536$	−10.5828	−	18.3299i	−0.457107	−	0.791733i
$537$	0.138756	+	0.0598778i	0.00598774	+	0.00258392i
$538$	−2.34795	+	4.06676i	−0.101227	+	0.175331i
$539$	−24.2597			−1.04494
$540$	9.06933	+	1.60335i	0.390282	+	0.0689970i
$541$	−39.2247			−1.68640			−0.843202	−	0.537597i	$-0.819332\pi$
$541$	−39.2247			−1.68640			−0.843202	+	0.537597i	$0.819332\pi$
$542$	4.05307	−	7.02013i	0.174094	−	0.301540i
$543$	−16.7766	−	7.23967i	−0.719952	−	0.310684i
$544$	16.4964	+	28.5726i	0.707277	+	1.22504i
$545$	−5.41959	−	9.38700i	−0.232150	−	0.402095i
$546$	0.445350	−	0.331448i	0.0190592	−	0.0141847i
$547$	−10.2674	+	17.7837i	−0.439004	+	0.760377i	−0.997613	−	0.0690541i	$-0.978002\pi$
$547$	−10.2674	+	17.7837i	−0.439004	+	0.760377i	0.558609	+	0.829431i	$0.311335\pi$
$548$	−22.6442			−0.967313
$549$	−8.01975	+	1.89819i	−0.342274	+	0.0810129i
$550$	−1.76715			−0.0753514
$551$	−23.5802	+	40.8420i	−1.00455	+	1.73993i
$552$	−3.04357	−	26.0731i	−0.129543	−	1.10974i
$553$	−4.79748	−	8.30947i	−0.204009	−	0.353355i
$554$	2.32125	+	4.02052i	0.0986205	+	0.170816i
$555$	−0.632751	−	5.42053i	−0.0268588	−	0.230089i
$556$	18.5429	−	32.1172i	0.786393	−	1.36207i
$557$	−29.5716			−1.25299			−0.626495	−	0.779426i	$-0.715511\pi$
$557$	−29.5716			−1.25299			−0.626495	+	0.779426i	$0.715511\pi$
$558$	2.01882	+	2.14110i	0.0854633	+	0.0906399i
$559$	−6.82262			−0.288566
$560$	0.902577	−	1.56331i	0.0381409	−	0.0660619i
$561$	−34.7973	+	25.8976i	−1.46914	+	1.09340i
$562$	4.45176	+	7.71068i	0.187786	+	0.325256i
$563$	4.37709	+	7.58134i	0.184472	+	0.319515i	0.943399	−	0.331661i	$-0.107609\pi$
$563$	4.37709	+	7.58134i	0.184472	+	0.319515i	−0.758926	+	0.651176i	$0.774276\pi$
$564$	−10.0047	−	4.31736i	−0.421273	−	0.181794i
$565$	2.52260	−	4.36928i	0.106127	−	0.183817i
$566$	1.83560			0.0771560
$567$	5.05051	+	3.32608i	0.212101	+	0.139682i
$568$	−9.11545			−0.382476
$569$	6.25553	−	10.8349i	0.262246	−	0.454223i	−0.704593	−	0.709612i	$-0.748870\pi$
$569$	6.25553	−	10.8349i	0.262246	−	0.454223i	0.966838	+	0.255389i	$0.0822036\pi$
$570$	3.68960	+	1.59219i	0.154540	+	0.0666895i
$571$	5.13376	+	8.89194i	0.214841	+	0.372116i	0.953223	−	0.302267i	$-0.0977433\pi$
$571$	5.13376	+	8.89194i	0.214841	+	0.372116i	−0.738382	+	0.674382i	$0.764410\pi$
$572$	−3.28314	−	5.68657i	−0.137275	−	0.237767i
$573$	−13.5143	+	10.0579i	−0.564567	+	0.420174i
$574$	−1.22793	+	2.12683i	−0.0512526	+	0.0887722i
$575$	8.42204			0.351223
$576$	−6.26683	−	6.64641i	−0.261118	−	0.276934i
$577$	11.8853			0.494792			0.247396	−	0.968914i	$-0.420425\pi$
$577$	11.8853			0.494792			0.247396	+	0.968914i	$0.420425\pi$
$578$	6.84484	−	11.8556i	0.284708	−	0.493128i
$579$	4.31836	+	36.9937i	0.179465	+	1.53741i
$580$	−8.59312	−	14.8837i	−0.356810	−	0.618013i
$581$	−5.60482	−	9.70783i	−0.232527	−	0.402749i
$582$	0.0903290	+	0.773813i	0.00374426	+	0.0320756i
$583$	−9.83457	+	17.0340i	−0.407306	+	0.705475i
$584$	−16.9065			−0.699596
$585$	2.91934	−	0.690978i	0.120700	−	0.0285684i
$586$	9.10526			0.376135
$587$	3.35253	−	5.80676i	0.138374	−	0.239671i	−0.788507	−	0.615025i	$-0.789146\pi$
$587$	3.35253	−	5.80676i	0.138374	−	0.239671i	0.926881	+	0.375355i	$0.122479\pi$
$588$	−16.1276	+	12.0028i	−0.665090	+	0.494987i
$589$	−5.00090	−	8.66182i	−0.206059	−	0.356904i
$590$	1.50800	+	2.61193i	0.0620833	+	0.107531i
$591$	21.4550	+	9.25856i	0.882539	+	0.380846i
$592$	−4.23235	+	7.33065i	−0.173949	+	0.301288i
$593$	−3.70728			−0.152240			−0.0761198	−	0.997099i	$-0.524253\pi$
$593$	−3.70728			−0.152240			−0.0761198	+	0.997099i	$0.524253\pi$
$594$	−5.90545	+	7.03146i	−0.242304	+	0.288504i
$595$	−4.54229			−0.186216
$596$	14.1803	−	24.5609i	0.580846	−	1.00605i
$597$	36.5792	+	15.7852i	1.49709	+	0.646044i
$598$	−2.00871	−	3.47918i	−0.0821421	−	0.142274i
$599$	−15.6057	−	27.0299i	−0.637633	−	1.10441i	−0.985951	−	0.167037i	$-0.946580\pi$
$599$	−15.6057	−	27.0299i	−0.637633	−	1.10441i	0.348317	−	0.937377i	$-0.386753\pi$
$600$	−2.50037	+	1.86088i	−0.102077	+	0.0759699i
$601$	−3.10338	+	5.37521i	−0.126589	+	0.219259i	−0.922353	−	0.386348i	$-0.873736\pi$
$601$	−3.10338	+	5.37521i	−0.126589	+	0.219259i	0.795764	+	0.605607i	$0.207070\pi$
$602$	2.18677			0.0891261
$603$	10.1301	−	33.8002i	0.412529	−	1.37645i
$604$	4.23357			0.172262
$605$	−1.36210	+	2.35922i	−0.0553771	+	0.0959159i
$606$	0.124672	+	1.06802i	0.00506445	+	0.0433852i
$607$	1.38498	+	2.39886i	0.0562147	+	0.0973667i	0.892763	−	0.450526i	$-0.148764\pi$
$607$	1.38498	+	2.39886i	0.0562147	+	0.0973667i	−0.836549	+	0.547893i	$0.815430\pi$
$608$	−11.8689	−	20.5575i	−0.481346	−	0.833715i
$609$	−1.30840	−	11.2085i	−0.0530189	−	0.454193i
$610$	0.655202	−	1.13484i	0.0265284	−	0.0459485i
$611$	−3.54935			−0.143591
$612$	−10.3197	+	34.4328i	−0.417148	+	1.39186i
$613$	48.3777			1.95396			0.976978	−	0.213339i	$-0.0684339\pi$
$613$	48.3777			1.95396			0.976978	+	0.213339i	$0.0684339\pi$
$614$	4.01258	−	6.95000i	0.161935	−	0.280479i
$615$	−10.6463	+	7.92344i	−0.429302	+	0.319504i
$616$	2.23970	+	3.87927i	0.0902401	+	0.156300i
$617$	−8.41349	−	14.5726i	−0.338714	−	0.586670i	0.645477	−	0.763780i	$-0.276659\pi$
$617$	−8.41349	−	14.5726i	−0.338714	−	0.586670i	−0.984191	+	0.177109i	$0.943325\pi$
$618$	1.20127	+	0.518388i	0.0483220	+	0.0208526i
$619$	−8.59571	+	14.8882i	−0.345491	+	0.598408i	−0.985443	−	0.170007i	$-0.945621\pi$
$619$	−8.59571	+	14.8882i	−0.345491	+	0.598408i	0.639952	+	0.768415i	$0.278954\pi$
$620$	3.64487			0.146382
$621$	28.1448	−	33.5112i	1.12941	−	1.34476i
$622$	−6.15125			−0.246643
$623$	−1.42439	+	2.46711i	−0.0570669	+	0.0988428i
$624$	−4.27238	−	1.84368i	−0.171032	−	0.0738062i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.14215	−	12.3706i	−0.285458	−	0.494427i
$627$	25.0360	−	18.6328i	0.999843	−	0.744124i
$628$	9.43681	−	16.3450i	0.376570	−	0.652238i
$629$	21.2997			0.849273
$630$	−0.935700	+	0.221471i	−0.0372792	+	0.00882360i
$631$	−39.5411			−1.57410			−0.787052	−	0.616886i	$-0.788394\pi$
$631$	−39.5411			−1.57410			−0.787052	+	0.616886i	$0.788394\pi$
$632$	12.8483	−	22.2538i	0.511076	−	0.885210i
$633$	3.07867	+	26.3738i	0.122366	+	1.04826i
$634$	4.21361	+	7.29818i	0.167344	+	0.289848i
$635$	4.93882	+	8.55429i	0.195991	+	0.339467i
$636$	1.88987	+	16.1897i	0.0749381	+	0.641965i
$637$	−3.27426	+	5.67118i	−0.129731	+	0.224700i
$638$	17.1347			0.678370
$639$	−10.4252	−	11.0567i	−0.412415	−	0.437396i
$640$	11.2135			0.443254
$641$	−6.28050	+	10.8781i	−0.248065	+	0.429661i	−0.962989	−	0.269541i	$-0.913128\pi$
$641$	−6.28050	+	10.8781i	−0.248065	+	0.429661i	0.714924	+	0.699202i	$0.246461\pi$
$642$	−7.96540	+	5.92818i	−0.314369	+	0.233967i
$643$	−8.28261	−	14.3459i	−0.326634	−	0.565747i	0.655208	−	0.755449i	$-0.272581\pi$
$643$	−8.28261	−	14.3459i	−0.326634	−	0.565747i	−0.981842	+	0.189702i	$0.939248\pi$
$644$	−5.01517	−	8.68653i	−0.197625	−	0.342297i
$645$	10.8500	+	4.68214i	0.427217	+	0.184359i
$646$	−7.84195	+	13.5827i	−0.308537	+	0.534402i
$647$	1.34773			0.0529846			0.0264923	−	0.999649i	$-0.491566\pi$
$647$	1.34773			0.0529846			0.0264923	+	0.999649i	$0.491566\pi$
$648$	−0.951320	+	16.1676i	−0.0373714	+	0.635124i
$649$	23.4231			0.919439
$650$	−0.238506	+	0.413105i	−0.00935498	+	0.0162033i
$651$	2.19739	+	0.948248i	0.0861224	+	0.0371648i
$652$	11.5810	+	20.0589i	0.453546	+	0.785565i
$653$	−8.63693	−	14.9596i	−0.337989	−	0.585414i	0.646065	−	0.763282i	$-0.276413\pi$
$653$	−8.63693	−	14.9596i	−0.337989	−	0.585414i	−0.984054	+	0.177868i	$0.943080\pi$
$654$	7.18415	−	5.34674i	0.280923	−	0.209074i
$655$	−6.12856	+	10.6150i	−0.239463	+	0.414762i
$656$	20.5846			0.803693
$657$	−19.3358	−	20.5069i	−0.754360	−	0.800052i
$658$	1.13763			0.0443494
$659$	−22.7594	+	39.4205i	−0.886582	+	1.53560i	−0.0426915	+	0.999088i	$0.513593\pi$
$659$	−22.7594	+	39.4205i	−0.886582	+	1.53560i	−0.843890	+	0.536516i	$0.819740\pi$
$660$	1.31866	+	11.2964i	0.0513287	+	0.439713i
$661$	2.77112	+	4.79972i	0.107784	+	0.186687i	0.914872	−	0.403744i	$-0.132291\pi$
$661$	2.77112	+	4.79972i	0.107784	+	0.186687i	−0.807088	+	0.590431i	$0.798958\pi$
$662$	2.55088	+	4.41825i	0.0991426	+	0.171720i
$663$	1.35758	+	11.6298i	0.0527240	+	0.451666i
$664$	15.0104	−	25.9988i	0.582517	−	1.00895i
$665$	3.26810			0.126731
$666$	4.38767	−	1.03852i	0.170019	−	0.0402417i
$667$	−81.6623			−3.16198
$668$	−10.9032	+	18.8849i	−0.421858	+	0.730679i
$669$	−31.4796	+	23.4284i	−1.21707	+	0.905794i
$670$	2.80528	+	4.85888i	0.108377	+	0.187715i
$671$	−5.08849	−	8.81353i	−0.196439	−	0.340243i
$672$	5.21515	+	2.25052i	0.201179	+	0.0868156i
$673$	12.8187	−	22.2027i	0.494126	−	0.855852i	−0.505851	−	0.862621i	$-0.668821\pi$
$673$	12.8187	−	22.2027i	0.494126	−	0.855852i	0.999977	+	0.00676902i	$0.00215466\pi$
$674$	−3.70582			−0.142743
$675$	−5.11681	−	0.904589i	−0.196946	−	0.0348176i
$676$	−1.77246			−0.0681715
$677$	14.9892	−	25.9621i	0.576083	−	0.997804i	−0.419840	−	0.907598i	$-0.637914\pi$
$677$	14.9892	−	25.9621i	0.576083	−	0.997804i	0.995923	−	0.0902065i	$-0.0287527\pi$
$678$	3.82724	+	1.65159i	0.146984	+	0.0634288i
$679$	0.316794	+	0.548704i	0.0121575	+	0.0210573i
$680$	−6.08242	−	10.5351i	−0.233250	−	0.404001i
$681$	22.0797	−	16.4326i	0.846095	−	0.629699i
$682$	−1.81698	+	3.14709i	−0.0695756	+	0.120508i
$683$	−7.41743			−0.283820			−0.141910	−	0.989880i	$-0.545324\pi$
$683$	−7.41743			−0.283820			−0.141910	+	0.989880i	$0.545324\pi$
$684$	7.42482	−	24.7738i	0.283895	−	0.947248i
$685$	12.7756			0.488130
$686$	2.17127	−	3.76075i	0.0828994	−	0.143586i
$687$	−4.61999	−	39.5776i	−0.176264	−	1.50998i
$688$	−9.16459	−	15.8735i	−0.349397	−	0.605173i
$689$	2.65468	+	4.59804i	0.101135	+	0.175171i
$690$	0.806787	+	6.91143i	0.0307139	+	0.263114i
$691$	−8.74238	+	15.1422i	−0.332576	+	0.576038i	−0.983016	−	0.183519i	$-0.941251\pi$
$691$	−8.74238	+	15.1422i	−0.332576	+	0.576038i	0.650440	+	0.759557i	$0.274584\pi$
$692$	−14.5636			−0.553623
$693$	−2.14389	+	7.15334i	−0.0814397	+	0.271733i
$694$	3.23286			0.122718
$695$	−10.4617	+	18.1201i	−0.396833	+	0.687336i
$696$	24.2442	−	18.0435i	0.918975	−	0.683939i
$697$	−25.8984	−	44.8573i	−0.980971	−	1.69909i
$698$	−4.05732	−	7.02748i	−0.153572	−	0.265994i
$699$	28.7079	+	12.3884i	1.08583	+	0.468574i
$700$	−0.595482	+	1.03141i	−0.0225071	+	0.0389835i
$701$	15.7242			0.593893			0.296947	−	0.954894i	$-0.404032\pi$
$701$	15.7242			0.593893			0.296947	+	0.954894i	$0.404032\pi$
$702$	0.846700	+	2.32953i	0.0319566	+	0.0879223i
$703$	−15.3247			−0.577982
$704$	5.64027	−	9.76923i	0.212576	−	0.368192i
$705$	5.64452	+	2.43580i	0.212585	+	0.0917377i
$706$	−0.871363	−	1.50924i	−0.0327942	−	0.0568012i
$707$	0.437239	+	0.757321i	0.0164441	+	0.0284820i
$708$	15.5714	−	11.5889i	0.585209	−	0.435537i
$709$	18.3149	−	31.7223i	0.687831	−	1.19136i	−0.284708	−	0.958614i	$-0.591897\pi$
$709$	18.3149	−	31.7223i	0.687831	−	1.19136i	0.972538	−	0.232743i	$-0.0747701\pi$
$710$	2.41631			0.0906827
$711$	41.6874	−	9.86699i	1.56340	−	0.370041i
$712$	−7.62939			−0.285924
$713$	8.65951	−	14.9987i	0.324301	−	0.561706i
$714$	−0.435128	−	3.72757i	−0.0162843	−	0.139501i
$715$	1.85231	+	3.20829i	0.0692724	+	0.119983i
$716$	0.0773248	+	0.133931i	0.00288977	+	0.00500522i
$717$	3.40464	+	29.1662i	0.127149	+	1.08923i
$718$	1.96951	−	3.41130i	0.0735016	−	0.127309i
$719$	26.7179			0.996408			0.498204	−	0.867060i	$-0.333993\pi$
$719$	26.7179			0.996408			0.498204	+	0.867060i	$0.333993\pi$
$720$	5.52908	+	5.86398i	0.206057	+	0.218538i
$721$	1.06403			0.0396266
$722$	1.11052	−	1.92348i	0.0413294	−	0.0715847i
$723$	−27.9028	+	20.7664i	−1.03772	+	0.772311i
$724$	−9.34915	−	16.1932i	−0.347458	−	0.601816i
$725$	4.84813	+	8.39721i	0.180055	+	0.311865i
$726$	−2.06654	−	0.891785i	−0.0766967	−	0.0330973i
$727$	5.55104	−	9.61469i	0.205877	−	0.356589i	−0.744535	−	0.667584i	$-0.767329\pi$
$727$	5.55104	−	9.61469i	0.205877	−	0.356589i	0.950412	+	0.310994i	$0.100662\pi$
$728$	1.20914			0.0448137
$729$	−20.6987	+	17.3368i	−0.766618	+	0.642103i
$730$	4.48156			0.165870
$731$	−23.0608	+	39.9424i	−0.852933	+	1.47732i
$732$	−7.74337	−	3.34153i	−0.286203	−	0.123507i
$733$	15.7102	+	27.2109i	0.580270	+	1.00506i	0.995447	+	0.0953169i	$0.0303864\pi$
$733$	15.7102	+	27.2109i	0.580270	+	1.00506i	−0.415177	+	0.909741i	$0.636280\pi$
$734$	5.48050	+	9.49250i	0.202289	+	0.350375i
$735$	9.09898	−	6.77183i	0.335621	−	0.249783i
$736$	20.5520	−	35.5971i	0.757556	−	1.31213i
$737$	43.5732			1.60504
$738$	−7.52213	−	7.97775i	−0.276893	−	0.293665i
$739$	−42.7936			−1.57419			−0.787094	−	0.616833i	$-0.788416\pi$
$739$	−42.7936			−1.57419			−0.787094	+	0.616833i	$0.788416\pi$
$740$	2.79233	−	4.83645i	0.102648	−	0.177792i
$741$	−0.976753	−	8.36746i	−0.0358819	−	0.307386i
$742$	−0.850871	−	1.47375i	−0.0312365	−	0.0541032i
$743$	−10.2467	−	17.7477i	−0.375913	−	0.651101i	0.614550	−	0.788878i	$-0.289338\pi$
$743$	−10.2467	−	17.7477i	−0.375913	−	0.651101i	−0.990463	+	0.137777i	$0.956004\pi$
$744$	0.743144	+	6.36622i	0.0272450	+	0.233397i
$745$	−8.00033	+	13.8570i	−0.293109	+	0.507680i
$746$	6.90874			0.252947
$747$	48.7028	−	11.5275i	1.78194	−	0.421767i
$748$	−44.3887			−1.62301
$749$	−4.03758	+	6.99329i	−0.147530	+	0.255529i
$750$	0.662795	−	0.493279i	0.0242018	−	0.0180120i
$751$	23.0796	+	39.9751i	0.842187	+	1.45871i	0.888042	+	0.459763i	$0.152066\pi$
$751$	23.0796	+	39.9751i	0.842187	+	1.45871i	−0.0458541	+	0.998948i	$0.514601\pi$
$752$	−4.76773	−	8.25794i	−0.173861	−	0.301136i
$753$	−21.3298	−	9.20453i	−0.777300	−	0.335432i
$754$	2.31262	−	4.00557i	0.0842206	−	0.145874i
$755$	−2.38853			−0.0869275
$756$	2.11397	+	5.81617i	0.0768844	+	0.211532i
$757$	−4.85406			−0.176424			−0.0882119	−	0.996102i	$-0.528115\pi$
$757$	−4.85406			−0.176424			−0.0882119	+	0.996102i	$0.528115\pi$
$758$	4.15191	−	7.19132i	0.150804	−	0.261200i
$759$	49.6179	+	21.4118i	1.80101	+	0.777200i
$760$	4.37619	+	7.57978i	0.158741	+	0.274948i
$761$	7.14677	+	12.3786i	0.259070	+	0.448723i	0.965993	−	0.258568i	$-0.0832505\pi$
$761$	7.14677	+	12.3786i	0.259070	+	0.448723i	−0.706923	+	0.707291i	$0.749917\pi$
$762$	−6.54685	+	4.87244i	−0.237167	+	0.176510i
$763$	3.64157	−	6.30739i	0.131834	−	0.228343i
$764$	−17.2393			−0.623695
$765$	5.82223	−	19.4266i	0.210503	−	0.702368i
$766$	−13.2755			−0.479664
$767$	3.16134	−	5.47561i	0.114149	−	0.197713i
$768$	−0.148808	−	1.27478i	−0.00536963	−	0.0459995i
$769$	0.0578415	+	0.100184i	0.00208582	+	0.00361274i	0.867066	−	0.498193i	$-0.166003\pi$
$769$	0.0578415	+	0.100184i	0.00208582	+	0.00361274i	−0.864981	+	0.501805i	$0.832669\pi$
$770$	−0.593697	−	1.02831i	−0.0213954	−	0.0370579i
$771$	3.63460	+	31.1362i	0.130897	+	1.12134i
$772$	−19.0569	+	33.0075i	−0.685873	+	1.18797i
$773$	13.8183			0.497010			0.248505	−	0.968631i	$-0.420061\pi$
$773$	13.8183			0.497010			0.248505	+	0.968631i	$0.420061\pi$
$774$	−2.80296	+	9.35241i	−0.100750	+	0.336166i
$775$	−2.05639			−0.0738678
$776$	−0.848416	+	1.46950i	−0.0304564	+	0.0527520i
$777$	2.94166	−	2.18930i	0.105531	−	0.0785408i
$778$	2.81523	+	4.87612i	0.100931	+	0.174817i
$779$	18.6334	+	32.2740i	0.667611	+	1.15634i
$780$	2.81873	+	1.21638i	0.100927	+	0.0435534i
$781$	9.38291	−	16.2517i	0.335747	−	0.581531i
$782$	−27.1581			−0.971171
$783$	49.6139	+	8.77113i	1.77306	+	0.313455i
$784$	−17.5928			−0.628314
$785$	−5.32413	+	9.22167i	−0.190026	+	0.329135i
$786$	−9.29813	−	4.01247i	−0.331653	−	0.143120i
$787$	9.96986	+	17.2683i	0.355387	+	0.615548i	0.987184	−	0.159585i	$-0.0510157\pi$
$787$	9.96986	+	17.2683i	0.355387	+	0.615548i	−0.631797	+	0.775134i	$0.717682\pi$
$788$	11.9563	+	20.7089i	0.425925	+	0.737724i
$789$	−29.2381	+	21.7602i	−1.04091	+	0.774685i
$790$	−3.40580	+	5.89903i	−0.121173	+	0.209878i
$791$	3.39001			0.120535
$792$	−19.4618	+	4.60640i	−0.691543	+	0.163681i
$793$	−2.74711			−0.0975527
$794$	4.56660	−	7.90958i	0.162063	−	0.280701i
$795$	−1.06624	−	9.13406i	−0.0378156	−	0.323952i
$796$	20.3846	+	35.3072i	0.722514	+	1.25143i
$797$	−10.3378	−	17.9056i	−0.366183	−	0.634248i	0.622782	−	0.782395i	$-0.286002\pi$
$797$	−10.3378	−	17.9056i	−0.366183	−	0.634248i	−0.988965	+	0.148148i	$0.952669\pi$
$798$	0.313067	+	2.68192i	0.0110824	+	0.0949389i
$799$	−11.9970	+	20.7794i	−0.424422	+	0.735121i
$800$	−4.88053			−0.172553
$801$	−8.72564	−	9.25416i	−0.308305	−	0.326980i
$802$	−1.95609			−0.0690719
$803$	17.4026	−	30.1421i	0.614123	−	1.06369i
$804$	28.9669	−	21.5584i	1.02158	−	0.760305i
$805$	2.82950	+	4.90084i	0.0997267	+	0.172732i
$806$	0.490462	+	0.849506i	0.0172758	+	0.0299226i
$807$	−15.6555	−	6.75588i	−0.551099	−	0.237818i
$808$	−1.17098	+	2.02820i	−0.0411951	+	0.0713519i
$809$	−50.3326			−1.76960			−0.884800	−	0.465971i	$-0.845705\pi$
$809$	−50.3326			−1.76960			−0.884800	+	0.465971i	$0.845705\pi$
$810$	0.252175	−	4.28570i	0.00886053	−	0.150584i
$811$	−3.52663			−0.123837			−0.0619184	−	0.998081i	$-0.519722\pi$
$811$	−3.52663			−0.123837			−0.0619184	+	0.998081i	$0.519722\pi$
$812$	5.77395	−	10.0008i	0.202626	−	0.350959i
$813$	27.0248	+	11.6621i	0.947802	+	0.409009i
$814$	2.78396	+	4.82196i	0.0975777	+	0.169010i
$815$	−6.53385	−	11.3170i	−0.228871	−	0.396416i
$816$	−25.2345	+	18.7805i	−0.883383	+	0.657450i
$817$	16.5918	−	28.7378i	0.580473	−	1.00541i
$818$	10.3430			0.361635
$819$	1.38288	+	1.46664i	0.0483216	+	0.0512485i
$820$	−13.5808			−0.474264
$821$	12.5522	−	21.7410i	0.438073	−	0.758765i	−0.559467	−	0.828852i	$-0.688994\pi$
$821$	12.5522	−	21.7410i	0.438073	−	0.758765i	0.997541	+	0.0700869i	$0.0223277\pi$
$822$	1.22384	+	10.4841i	0.0426862	+	0.365676i
$823$	−5.57308	−	9.65286i	−0.194265	−	0.336477i	0.752394	−	0.658713i	$-0.228899\pi$
$823$	−5.57308	−	9.65286i	−0.194265	−	0.336477i	−0.946659	+	0.322236i	$0.895566\pi$
$824$	1.42481	+	2.46784i	0.0496355	+	0.0859712i
$825$	−0.743971	−	6.37331i	−0.0259017	−	0.221890i
$826$	−1.01327	+	1.75503i	−0.0352560	+	0.0610652i
$827$	9.33769			0.324703			0.162352	−	0.986733i	$-0.448092\pi$
$827$	9.33769			0.324703			0.162352	+	0.986733i	$0.448092\pi$
$828$	43.5791	−	10.3147i	1.51448	−	0.358462i
$829$	−30.3972			−1.05574			−0.527869	−	0.849326i	$-0.677009\pi$
$829$	−30.3972			−1.05574			−0.527869	+	0.849326i	$0.677009\pi$
$830$	−3.97895	+	6.89174i	−0.138111	+	0.239216i
$831$	−13.5230	+	10.0644i	−0.469107	+	0.349129i
$832$	−1.52250	−	2.63704i	−0.0527831	−	0.0914230i
$833$	22.1343	+	38.3377i	0.766907	+	1.32832i
$834$	−15.8722	−	6.84941i	−0.549610	−	0.237176i
$835$	6.15146	−	10.6546i	0.212880	−	0.368719i
$836$	31.9368			1.10456
$837$	−6.87206	+	8.18237i	−0.237533	+	0.282824i
$838$	−12.9385			−0.446955
$839$	18.3196	−	31.7305i	0.632463	−	1.09546i	−0.354583	−	0.935024i	$-0.615377\pi$
$839$	18.3196	−	31.7305i	0.632463	−	1.09546i	0.987047	−	0.160434i	$-0.0512894\pi$
$840$	−1.92289	−	0.829793i	−0.0663459	−	0.0286306i
$841$	−32.5088	−	56.3069i	−1.12099	−	1.94162i
$842$	−1.52773	−	2.64611i	−0.0526492	−	0.0911911i
$843$	−25.9348	+	19.3017i	−0.893242	+	0.664787i
$844$	−13.5862	+	23.5319i	−0.467655	+	0.810003i
$845$	1.00000			0.0344010
$846$	−1.45820	+	4.86544i	−0.0501338	+	0.167277i
$847$	−1.83046			−0.0628953
$848$	−7.13188	+	12.3528i	−0.244910	+	0.424196i
$849$	0.772790	+	6.62019i	0.0265221	+	0.227204i
$850$	1.61232	+	2.79262i	0.0553022	+	0.0957862i
$851$	−13.2681	−	22.9809i	−0.454823	−	0.787777i
$852$	−1.80307	−	15.4462i	−0.0617722	−	0.529179i
$853$	−16.7937	+	29.0876i	−0.575006	+	0.995939i	0.421035	+	0.907044i	$0.361667\pi$
$853$	−16.7937	+	29.0876i	−0.575006	+	0.995939i	−0.996041	+	0.0888951i	$0.971666\pi$
$854$	0.880497			0.0301300
$855$	−4.18899	+	13.9770i	−0.143260	+	0.478005i
$856$	−21.6263			−0.739172
$857$	9.13754	−	15.8267i	0.312132	−	0.540629i	−0.666691	−	0.745334i	$-0.732290\pi$
$857$	9.13754	−	15.8267i	0.312132	−	0.540629i	0.978824	+	0.204705i	$0.0656234\pi$
$858$	−2.45540	+	1.82741i	−0.0838260	+	0.0623868i
$859$	0.398809	+	0.690757i	0.0136072	+	0.0235683i	0.872749	−	0.488170i	$-0.162335\pi$
$859$	0.398809	+	0.690757i	0.0136072	+	0.0235683i	−0.859142	+	0.511738i	$0.829002\pi$
$860$	6.04641	+	10.4727i	0.206181	+	0.357116i
$861$	−8.18748	−	3.53318i	−0.279029	−	0.120411i
$862$	3.74868	−	6.49290i	0.127680	−	0.221149i
$863$	−10.6285			−0.361800			−0.180900	−	0.983502i	$-0.557901\pi$
$863$	−10.6285			−0.361800			−0.180900	+	0.983502i	$0.557901\pi$
$864$	−16.3097	+	19.4196i	−0.554869	+	0.660667i
$865$	8.21658			0.279372
$866$	0.627722	−	1.08725i	0.0213309	−	0.0369461i
$867$	45.6396	+	19.6950i	1.55000	+	0.668879i
$868$	1.22455	+	2.12098i	0.0415638	+	0.0719906i
$869$	26.4505	+	45.8136i	0.897272	+	1.55412i
$870$	−6.42664	+	4.78297i	−0.217883	+	0.162158i
$871$	5.88093	−	10.1861i	0.199268	−	0.345142i
$872$	19.5052			0.660529
$873$	−2.75277	+	0.651552i	−0.0931671	+	0.0220517i
$874$	19.5397			0.660941
$875$	0.335964	−	0.581906i	0.0113576	−	0.0196720i
$876$	−3.34417	−	28.6482i	−0.112989	−	0.967934i
$877$	9.74913	+	16.8860i	0.329205	+	0.570200i	0.982354	−	0.187030i	$-0.0598860\pi$
$877$	9.74913	+	16.8860i	0.329205	+	0.570200i	−0.653149	+	0.757229i	$0.726553\pi$
$878$	4.90858	+	8.50192i	0.165657	+	0.286926i
$879$	3.83332	+	32.8386i	0.129295	+	1.10762i
$880$	−4.97629	+	8.61918i	−0.167751	+	0.290553i
$881$	−12.2440			−0.412511			−0.206255	−	0.978498i	$-0.566128\pi$
$881$	−12.2440			−0.412511			−0.206255	+	0.978498i	$0.566128\pi$
$882$	6.42885	+	6.81825i	0.216471	+	0.229582i
$883$	−31.3860			−1.05622			−0.528112	−	0.849175i	$-0.677100\pi$
$883$	−31.3860			−1.05622			−0.528112	+	0.849175i	$0.677100\pi$
$884$	−5.99099	+	10.3767i	−0.201499	+	0.349006i
$885$	−8.78520	+	6.53830i	−0.295311	+	0.219783i
$886$	−0.0100701	−	0.0174419i	−0.000338311	−	0.000585971i
$887$	4.13265	+	7.15797i	0.138761	+	0.240341i	0.927028	−	0.374992i	$-0.122355\pi$
$887$	4.13265	+	7.15797i	0.138761	+	0.240341i	−0.788267	+	0.615333i	$0.789021\pi$
$888$	9.01678	+	3.89105i	0.302583	+	0.130575i
$889$	−3.31853	+	5.74787i	−0.111300	+	0.192777i
$890$	2.02239			0.0677907
$891$	−27.8455	−	18.3381i	−0.932861	−	0.614349i
$892$	−40.1565			−1.34454
$893$	8.63160	−	14.9504i	0.288846	−	0.500295i
$894$	−12.1379	−	5.23794i	−0.405953	−	0.175183i
$895$	−0.0436257	−	0.0755620i	−0.00145825	−	0.00252576i
$896$	3.76735	+	6.52524i	0.125858	+	0.217993i
$897$	11.7022	−	8.70925i	0.390725	−	0.290793i
$898$	−9.37316	+	16.2348i	−0.312786	+	0.541762i
$899$	19.9393			0.665014
$900$	−3.64785	−	3.86881i	−0.121595	−	0.128960i
$901$	35.8917			1.19573
$902$	6.77007	−	11.7261i	0.225419	−	0.390437i
$903$	0.920632	+	7.88670i	0.0306367	+	0.262453i
$904$	4.53945	+	7.86255i	0.150980	+	0.261505i
$905$	5.27468	+	9.13601i	0.175336	+	0.303691i
$906$	−0.228809	−	1.96011i	−0.00760166	−	0.0651205i
$907$	6.65031	−	11.5187i	0.220820	−	0.382471i	−0.734237	−	0.678893i	$-0.762460\pi$
$907$	6.65031	−	11.5187i	0.220820	−	0.382471i	0.955057	+	0.296422i	$0.0957934\pi$
$908$	28.1656			0.934709
$909$	−3.79937	+	0.899272i	−0.126017	+	0.0298270i
$910$	−0.320518			−0.0106251
$911$	−1.53458	+	2.65797i	−0.0508429	+	0.0880625i	−0.890327	−	0.455322i	$-0.849524\pi$
$911$	−1.53458	+	2.65797i	−0.0508429	+	0.0880625i	0.839484	+	0.543385i	$0.182857\pi$
$912$	18.1557	−	13.5122i	0.601197	−	0.447435i
$913$	30.9017	+	53.5233i	1.02270	+	1.77136i
$914$	−3.16302	−	5.47852i	−0.104624	−	0.181213i
$915$	4.36871	+	1.88525i	0.144425	+	0.0623245i
$916$	20.3880	−	35.3130i	0.673638	−	1.16678i
$917$	−8.23590			−0.271973
$918$	16.4999	+	2.91698i	0.544577	+	0.0962746i
$919$	37.5115			1.23739			0.618694	−	0.785632i	$-0.287662\pi$
$919$	37.5115			1.23739			0.618694	+	0.785632i	$0.287662\pi$
$920$	−7.57776	+	13.1251i	−0.249831	+	0.432721i
$921$	26.7548	+	11.5456i	0.881602	+	0.380442i
$922$	2.89943	+	5.02195i	0.0954875	+	0.165389i
$923$	−2.53276	−	4.38687i	−0.0833668	−	0.144396i
$924$	−6.13045	+	4.56253i	−0.201677	+	0.150096i
$925$	−1.57540	+	2.72867i	−0.0517987	+	0.0897181i
$926$	−0.835384			−0.0274524
$927$	−1.36386	+	4.55067i	−0.0447950	+	0.149464i
$928$	47.3229			1.55345
$929$	−24.1139	+	41.7665i	−0.791151	+	1.37031i	0.134104	+	0.990967i	$0.457184\pi$
$929$	−24.1139	+	41.7665i	−0.791151	+	1.37031i	−0.925255	+	0.379346i	$0.876149\pi$
$930$	−0.196992	−	1.68755i	−0.00645962	−	0.0553370i
$931$	−15.9252	−	27.5833i	−0.521927	−	0.904005i
$932$	15.9981	+	27.7096i	0.524037	+	0.907658i
$933$	−2.58969	−	22.1848i	−0.0847825	−	0.726299i
$934$	0.857727	−	1.48563i	0.0280657	−	0.0486112i
$935$	25.0435			0.819012
$936$	−1.54986	+	5.17127i	−0.0506586	+	0.169028i
$937$	5.13410			0.167724			0.0838618	−	0.996477i	$-0.473275\pi$
$937$	5.13410			0.167724			0.0838618	+	0.996477i	$0.473275\pi$
$938$	−1.88494	+	3.26482i	−0.0615456	+	0.106600i
$939$	41.6082	−	30.9665i	1.35783	−	1.01056i
$940$	3.14554	+	5.44824i	0.102596	+	0.177702i
$941$	−16.6875	−	28.9035i	−0.543996	−	0.942229i	−0.998669	−	0.0515704i	$-0.983577\pi$
$941$	−16.6875	−	28.9035i	−0.543996	−	0.942229i	0.454673	−	0.890658i	$-0.349756\pi$
$942$	−8.07766	−	3.48579i	−0.263184	−	0.113573i
$943$	−32.2654	+	55.8854i	−1.05071	+	1.81988i
$944$	16.9861			0.552850
$945$	−1.19268	−	3.28141i	−0.0387978	−	0.106744i
$946$	−12.0566			−0.391993
$947$	23.1469	−	40.0915i	0.752172	−	1.30280i	−0.194597	−	0.980883i	$-0.562340\pi$
$947$	23.1469	−	40.0915i	0.752172	−	1.30280i	0.946768	−	0.321916i	$-0.104327\pi$
$948$	40.2508	+	17.3696i	1.30728	+	0.564139i
$949$	−4.69753	−	8.13637i	−0.152488	−	0.264118i
$950$	−1.16004	−	2.00924i	−0.0376365	−	0.0651884i
$951$	−24.5474	+	18.2691i	−0.796002	+	0.592418i
$952$	4.08695	−	7.07880i	0.132459	−	0.229425i
$953$	26.2863			0.851496			0.425748	−	0.904842i	$-0.360011\pi$
$953$	26.2863			0.851496			0.425748	+	0.904842i	$0.360011\pi$
$954$	7.39361	−	1.74999i	0.239377	−	0.0566580i
$955$	9.72619			0.314732
$956$	−15.0247	+	26.0235i	−0.485933	+	0.841660i
$957$	7.21374	+	61.7973i	0.233187	+	1.99762i
$958$	0.654018	+	1.13279i	0.0211303	+	0.0365988i
$959$	4.29214	+	7.43420i	0.138600	+	0.240063i
$960$	0.611504	+	5.23851i	0.0197362	+	0.169072i
$961$	13.3856	−	23.1846i	0.431794	−	0.747890i
$962$	1.50297			0.0484576
$963$	−24.7337	−	26.2319i	−0.797034	−	0.845311i
$964$	−35.5938			−1.14640
$965$	10.7517	−	18.6225i	0.346109	−	0.599478i
$966$	−3.75076	+	2.79147i	−0.120679	+	0.0898139i
$967$	15.7640	+	27.3040i	0.506934	+	0.878036i	0.999968	+	0.00802586i	$0.00255474\pi$
$967$	15.7640	+	27.3040i	0.506934	+	0.878036i	−0.493033	+	0.870010i	$0.664112\pi$
$968$	−2.45110	−	4.24544i	−0.0787815	−	0.136453i
$969$	−52.2880	−	22.5641i	−1.67973	−	0.724863i
$970$	0.224897	−	0.389534i	0.00722102	−	0.0125072i
$971$	−23.4949			−0.753986			−0.376993	−	0.926216i	$-0.623042\pi$
$971$	−23.4949			−0.753986			−0.376993	+	0.926216i	$0.623042\pi$
$972$	−27.5844	+	1.58600i	−0.884769	+	0.0508709i
$973$	−14.0590			−0.450709
$974$	3.00901	−	5.21176i	0.0964149	−	0.166995i
$975$	−1.59029	−	0.686267i	−0.0509302	−	0.0219781i
$976$	−3.69010	−	6.39144i	−0.118117	−	0.204585i
$977$	21.0548	+	36.4681i	0.673604	+	1.16672i	0.976875	+	0.213812i	$0.0685880\pi$
$977$	21.0548	+	36.4681i	0.673604	+	1.16672i	−0.303271	+	0.952904i	$0.598079\pi$
$978$	8.66120	−	6.44602i	0.276955	−	0.206121i
$979$	7.85325	−	13.6022i	0.250991	−	0.434729i
$980$	11.6070			0.370771
$981$	22.3078	+	23.6590i	0.712235	+	0.755375i
$982$	3.66644			0.117001
$983$	4.68728	−	8.11860i	0.149501	−	0.258943i	−0.781542	−	0.623852i	$-0.785567\pi$
$983$	4.68728	−	8.11860i	0.149501	−	0.258943i	0.931043	+	0.364909i	$0.118900\pi$
$984$	−2.76896	−	23.7206i	−0.0882713	−	0.756186i
$985$	−6.74559	−	11.6837i	−0.214933	−	0.372274i
$986$	−15.6335	−	27.0780i	−0.497872	−	0.862340i
$987$	0.478944	+	4.10292i	0.0152449	+	0.130597i
$988$	4.31041	−	7.46585i	0.137132	−	0.237520i
$989$	57.4603			1.82713
$990$	5.15890	−	1.22106i	0.163961	−	0.0388078i
$991$	4.99372			0.158631			0.0793153	−	0.996850i	$-0.474727\pi$
$991$	4.99372			0.158631			0.0793153	+	0.996850i	$0.474727\pi$
$992$	−5.01814	+	8.69167i	−0.159326	+	0.275961i
$993$	−14.8607	+	11.0600i	−0.471591	+	0.350977i
$994$	0.811794	+	1.40607i	0.0257485	+	0.0445978i
$995$	−11.5008	−	19.9199i	−0.364598	−	0.631503i
$996$	47.0244	+	20.2926i	1.49002	+	0.642997i
$997$	13.4920	−	23.3688i	0.427295	−	0.740096i	−0.569337	−	0.822104i	$-0.692800\pi$
$997$	13.4920	−	23.3688i	0.427295	−	0.740096i	0.996632	+	0.0820080i	$0.0261333\pi$
$998$	7.10751			0.224984
$999$	5.59268	+	15.3872i	0.176945	+	0.486828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.8	✓	26
3.2	odd	2		1755.2.i.g.586.6		26
9.2	odd	6		5265.2.a.bh.1.8		13
9.4	even	3	inner	585.2.i.g.391.8	yes	26
9.5	odd	6		1755.2.i.g.1171.6		26
9.7	even	3		5265.2.a.bg.1.6		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.8	✓	26	1.1	even	1	trivial
585.2.i.g.391.8	yes	26	9.4	even	3	inner
1755.2.i.g.586.6		26	3.2	odd	2
1755.2.i.g.1171.6		26	9.5	odd	6
5265.2.a.bg.1.6		13	9.7	even	3
5265.2.a.bh.1.8		13	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.238506 - 0.413105i) q^{2} +(1.59029 + 0.686267i) q^{3} +(0.886230 + 1.53499i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.662795 - 0.493279i) q^{6} +(0.335964 - 0.581906i) q^{7} +1.79951 q^{8} +(2.05807 + 2.18273i) q^{9} +O(q^{10})\)	\(q+(0.238506 - 0.413105i) q^{2} +(1.59029 + 0.686267i) q^{3} +(0.886230 + 1.53499i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.662795 - 0.493279i) q^{6} +(0.335964 - 0.581906i) q^{7} +1.79951 q^{8} +(2.05807 + 2.18273i) q^{9} -0.477012 q^{10} +(-1.85231 + 3.20829i) q^{11} +(0.355950 + 3.04928i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.160259 - 0.277576i) q^{14} +(-0.200823 - 1.72037i) q^{15} +(-1.34327 + 2.32660i) q^{16} +6.76009 q^{17} +(1.39256 - 0.329605i) q^{18} -4.86376 q^{19} +(0.886230 - 1.53499i) q^{20} +(0.933625 - 0.694842i) q^{21} +(0.883574 + 1.53039i) q^{22} +(-4.21102 - 7.29370i) q^{23} +(2.86175 + 1.23494i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.477012 q^{26} +(1.77501 + 4.88358i) q^{27} +1.19096 q^{28} +(4.84813 - 8.39721i) q^{29} +(-0.758590 - 0.327358i) q^{30} +(1.02820 + 1.78089i) q^{31} +(2.44026 + 4.22666i) q^{32} +(-5.14746 + 3.83095i) q^{33} +(1.61232 - 2.79262i) q^{34} -0.671928 q^{35} +(-1.52656 + 5.09354i) q^{36} +3.15079 q^{37} +(-1.16004 + 2.00924i) q^{38} +(0.200823 + 1.72037i) q^{39} +(-0.899754 - 1.55842i) q^{40} +(-3.83107 - 6.63561i) q^{41} +(-0.0643672 - 0.551409i) q^{42} +(-3.41131 + 5.90856i) q^{43} -6.56628 q^{44} +(0.861266 - 2.87371i) q^{45} -4.01741 q^{46} +(-1.77468 + 3.07383i) q^{47} +(-3.73286 + 2.77815i) q^{48} +(3.27426 + 5.67118i) q^{49} +(0.238506 + 0.413105i) q^{50} +(10.7505 + 4.63923i) q^{51} +(-0.886230 + 1.53499i) q^{52} +5.30936 q^{53} +(2.44078 + 0.431500i) q^{54} +3.70462 q^{55} +(0.604570 - 1.04715i) q^{56} +(-7.73481 - 3.33784i) q^{57} +(-2.31262 - 4.00557i) q^{58} +(-3.16134 - 5.47561i) q^{59} +(2.46278 - 1.83290i) q^{60} +(-1.37355 + 2.37907i) q^{61} +0.980925 q^{62} +(1.96159 - 0.464287i) q^{63} -3.04499 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.354883 + 3.04015i) q^{66} +(-5.88093 - 10.1861i) q^{67} +(5.99099 + 10.3767i) q^{68} +(-1.69134 - 14.4890i) q^{69} +(-0.160259 + 0.277576i) q^{70} -5.06552 q^{71} +(3.70352 + 3.92785i) q^{72} -9.39507 q^{73} +(0.751483 - 1.30161i) q^{74} +(-1.38947 + 1.03410i) q^{75} +(-4.31041 - 7.46585i) q^{76} +(1.24462 + 2.15574i) q^{77} +(0.758590 + 0.327358i) q^{78} +(7.13987 - 12.3666i) q^{79} +2.68653 q^{80} +(-0.528656 + 8.98446i) q^{81} -3.65494 q^{82} +(8.34140 - 14.4477i) q^{83} +(1.89398 + 0.817320i) q^{84} +(-3.38004 - 5.85441i) q^{85} +(1.62724 + 2.81845i) q^{86} +(13.4727 - 10.0269i) q^{87} +(-3.33325 + 5.77335i) q^{88} -4.23971 q^{89} +(-0.981727 - 1.04119i) q^{90} +0.671928 q^{91} +(7.46386 - 12.9278i) q^{92} +(0.412970 + 3.53776i) q^{93} +(0.846542 + 1.46625i) q^{94} +(2.43188 + 4.21214i) q^{95} +(0.980120 + 8.39631i) q^{96} +(-0.471471 + 0.816612i) q^{97} +3.12372 q^{98} +(-10.8150 + 2.55981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

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