LMFDB - Embedded newform 143.2.h.c.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.4
Character	$\chi$	$=$	143.27
Dual form			143.2.h.c.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.211960 - 0.652345i) q^{2} +(-1.08207 - 0.786167i) q^{3} +(1.23741 - 0.899029i) q^{4} +(-0.482614 + 1.48533i) q^{5} +(-0.283498 + 0.872516i) q^{6} +(3.09041 - 2.24531i) q^{7} +(-1.95859 - 1.42300i) q^{8} +(-0.374242 - 1.15180i) q^{9} +O(q^{10})$	\(q+(-0.211960 - 0.652345i) q^{2} +(-1.08207 - 0.786167i) q^{3} +(1.23741 - 0.899029i) q^{4} +(-0.482614 + 1.48533i) q^{5} +(-0.283498 + 0.872516i) q^{6} +(3.09041 - 2.24531i) q^{7} +(-1.95859 - 1.42300i) q^{8} +(-0.374242 - 1.15180i) q^{9} +1.07124 q^{10} +(-2.71184 - 1.90943i) q^{11} -2.04574 q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.11976 - 1.54010i) q^{14} +(1.68994 - 1.22781i) q^{15} +(0.432150 - 1.33002i) q^{16} +(-1.31827 + 4.05722i) q^{17} +(-0.672046 + 0.488270i) q^{18} +(0.707832 + 0.514270i) q^{19} +(0.738167 + 2.27185i) q^{20} -5.10922 q^{21} +(-0.670806 + 2.17378i) q^{22} +9.35137 q^{23} +(1.00061 + 3.07956i) q^{24} +(2.07179 + 1.50524i) q^{25} +(0.554918 - 0.403171i) q^{26} +(-1.74049 + 5.35668i) q^{27} +(1.80549 - 5.55673i) q^{28} +(3.21737 - 2.33755i) q^{29} +(-1.15916 - 0.842177i) q^{30} +(1.62761 + 5.00927i) q^{31} -5.80114 q^{32} +(1.43326 + 4.19809i) q^{33} +2.92612 q^{34} +(1.84356 + 5.67390i) q^{35} +(-1.49859 - 1.08879i) q^{36} +(-7.65297 + 5.56021i) q^{37} +(0.185450 - 0.570755i) q^{38} +(0.413313 - 1.27205i) q^{39} +(3.05887 - 2.22240i) q^{40} +(-2.81191 - 2.04297i) q^{41} +(1.08295 + 3.33297i) q^{42} -5.58990 q^{43} +(-5.07228 + 0.0752792i) q^{44} +1.89142 q^{45} +(-1.98211 - 6.10031i) q^{46} +(4.99933 + 3.63222i) q^{47} +(-1.51324 + 1.09943i) q^{48} +(2.34607 - 7.22047i) q^{49} +(0.542801 - 1.67057i) q^{50} +(4.61611 - 3.35380i) q^{51} +(1.23741 + 0.899029i) q^{52} +(2.04846 + 6.30452i) q^{53} +3.86331 q^{54} +(4.14491 - 3.10647i) q^{55} -9.24793 q^{56} +(-0.361619 - 1.11295i) q^{57} +(-2.20684 - 1.60336i) q^{58} +(-3.90166 + 2.83472i) q^{59} +(0.987305 - 3.03861i) q^{60} +(3.97139 - 12.2227i) q^{61} +(2.92278 - 2.12353i) q^{62} +(-3.74271 - 2.71924i) q^{63} +(0.365306 + 1.12430i) q^{64} -1.56177 q^{65} +(2.43481 - 1.82481i) q^{66} +9.01185 q^{67} +(2.01632 + 6.20559i) q^{68} +(-10.1188 - 7.35174i) q^{69} +(3.31058 - 2.40528i) q^{70} +(1.20998 - 3.72395i) q^{71} +(-0.906023 + 2.78845i) q^{72} +(-9.89371 + 7.18820i) q^{73} +(5.24930 + 3.81384i) q^{74} +(-1.05844 - 3.25754i) q^{75} +1.33822 q^{76} +(-12.6680 + 0.188009i) q^{77} -0.917418 q^{78} +(-0.350447 - 1.07856i) q^{79} +(1.76696 + 1.28377i) q^{80} +(3.15524 - 2.29241i) q^{81} +(-0.736710 + 2.26736i) q^{82} +(1.33940 - 4.12224i) q^{83} +(-6.32218 + 4.59334i) q^{84} +(-5.39010 - 3.91614i) q^{85} +(1.18483 + 3.64654i) q^{86} -5.31911 q^{87} +(2.59427 + 7.59875i) q^{88} -0.384917 q^{89} +(-0.400904 - 1.23386i) q^{90} +(3.09041 + 2.24531i) q^{91} +(11.5714 - 8.40715i) q^{92} +(2.17694 - 6.69994i) q^{93} +(1.30981 - 4.03117i) q^{94} +(-1.10547 + 0.803172i) q^{95} +(6.27722 + 4.56067i) q^{96} +(1.62118 + 4.98949i) q^{97} -5.20751 q^{98} +(-1.18439 + 3.83808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.211960	−	0.652345i	−0.149878	−	0.461277i	0.847728	−	0.530431i	$-0.177970\pi$
$2$	−0.211960	−	0.652345i	−0.149878	−	0.461277i	−0.997606	+	0.0691540i	$0.977970\pi$
$3$	−1.08207	−	0.786167i	−0.624731	−	0.453894i	0.229840	−	0.973229i	$-0.426180\pi$
$3$	−1.08207	−	0.786167i	−0.624731	−	0.453894i	−0.854571	+	0.519335i	$0.826180\pi$
$4$	1.23741	−	0.899029i	0.618704	−	0.449514i
$5$	−0.482614	+	1.48533i	−0.215831	+	0.664261i	0.783262	+	0.621692i	$0.213554\pi$
$5$	−0.482614	+	1.48533i	−0.215831	+	0.664261i	−0.999094	+	0.0425693i	$0.986446\pi$
$6$	−0.283498	+	0.872516i	−0.115737	+	0.356203i
$7$	3.09041	−	2.24531i	1.16806	−	0.848648i	0.177289	−	0.984159i	$-0.443267\pi$
$7$	3.09041	−	2.24531i	1.16806	−	0.848648i	0.990776	+	0.135510i	$0.0432674\pi$
$8$	−1.95859	−	1.42300i	−0.692467	−	0.503107i
$9$	−0.374242	−	1.15180i	−0.124747	−	0.383933i
$10$	1.07124			0.338757
$11$	−2.71184	−	1.90943i	−0.817650	−	0.575715i
$11$	−2.71184	−	1.90943i	−0.817650	−	0.575715i
$12$	−2.04574			−0.590555
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−2.11976	−	1.54010i	−0.566530	−	0.411608i
$15$	1.68994	−	1.22781i	0.436341	−	0.317020i
$16$	0.432150	−	1.33002i	0.108038	−	0.332506i
$17$	−1.31827	+	4.05722i	−0.319727	+	0.984019i	0.654037	+	0.756462i	$0.273074\pi$
$17$	−1.31827	+	4.05722i	−0.319727	+	0.984019i	−0.973765	+	0.227557i	$0.926926\pi$
$18$	−0.672046	+	0.488270i	−0.158403	+	0.115086i
$19$	0.707832	+	0.514270i	0.162388	+	0.117982i	0.666011	−	0.745942i	$-0.268000\pi$
$19$	0.707832	+	0.514270i	0.162388	+	0.117982i	−0.503624	+	0.863923i	$0.668000\pi$
$20$	0.738167	+	2.27185i	0.165059	+	0.508000i
$21$	−5.10922			−1.11492
$22$	−0.670806	+	2.17378i	−0.143016	+	0.463451i
$23$	9.35137			1.94989			0.974947	−	0.222436i	$-0.0714008\pi$
$23$	9.35137			1.94989			0.974947	+	0.222436i	$0.0714008\pi$
$24$	1.00061	+	3.07956i	0.204249	+	0.628613i
$25$	2.07179	+	1.50524i	0.414358	+	0.301048i
$26$	0.554918	−	0.403171i	0.108828	−	0.0790684i
$27$	−1.74049	+	5.35668i	−0.334957	+	1.03089i
$28$	1.80549	−	5.55673i	0.341206	−	1.05012i
$29$	3.21737	−	2.33755i	0.597450	−	0.434073i	−0.247523	−	0.968882i	$-0.579617\pi$
$29$	3.21737	−	2.33755i	0.597450	−	0.434073i	0.844973	+	0.534809i	$0.179617\pi$
$30$	−1.15916	−	0.842177i	−0.211632	−	0.153760i
$31$	1.62761	+	5.00927i	0.292328	+	0.899692i	0.984106	+	0.177582i	$0.0568275\pi$
$31$	1.62761	+	5.00927i	0.292328	+	0.899692i	−0.691778	+	0.722110i	$0.743173\pi$
$32$	−5.80114			−1.02551
$33$	1.43326	+	4.19809i	0.249498	+	0.730794i
$34$	2.92612			0.501826
$35$	1.84356	+	5.67390i	0.311619	+	0.959065i
$36$	−1.49859	−	1.08879i	−0.249765	−	0.181465i
$37$	−7.65297	+	5.56021i	−1.25814	+	0.914093i	−0.998665	−	0.0516565i	$-0.983550\pi$
$37$	−7.65297	+	5.56021i	−1.25814	+	0.914093i	−0.259476	+	0.965750i	$0.583550\pi$
$38$	0.185450	−	0.570755i	0.0300839	−	0.0925887i
$39$	0.413313	−	1.27205i	0.0661830	−	0.203690i
$40$	3.05887	−	2.22240i	0.483650	−	0.351393i
$41$	−2.81191	−	2.04297i	−0.439146	−	0.319058i	0.346149	−	0.938179i	$-0.387489\pi$
$41$	−2.81191	−	2.04297i	−0.439146	−	0.319058i	−0.785296	+	0.619121i	$0.787489\pi$
$42$	1.08295	+	3.33297i	0.167103	+	0.514289i
$43$	−5.58990			−0.852452			−0.426226	−	0.904617i	$-0.640157\pi$
$43$	−5.58990			−0.852452			−0.426226	+	0.904617i	$0.640157\pi$
$44$	−5.07228	+	0.0752792i	−0.764675	+	0.0113488i
$45$	1.89142			0.281956
$46$	−1.98211	−	6.10031i	−0.292247	−	0.899442i
$47$	4.99933	+	3.63222i	0.729227	+	0.529814i	0.889319	−	0.457288i	$-0.151179\pi$
$47$	4.99933	+	3.63222i	0.729227	+	0.529814i	−0.160092	+	0.987102i	$0.551179\pi$
$48$	−1.51324	+	1.09943i	−0.218417	+	0.158689i
$49$	2.34607	−	7.22047i	0.335153	−	1.03150i
$50$	0.542801	−	1.67057i	0.0767637	−	0.236254i
$51$	4.61611	−	3.35380i	0.646384	−	0.469626i
$52$	1.23741	+	0.899029i	0.171598	+	0.124673i
$53$	2.04846	+	6.30452i	0.281378	+	0.865993i	0.987461	+	0.157863i	$0.0504606\pi$
$53$	2.04846	+	6.30452i	0.281378	+	0.865993i	−0.706083	+	0.708129i	$0.749539\pi$
$54$	3.86331			0.525730
$55$	4.14491	−	3.10647i	0.558900	−	0.418876i
$56$	−9.24793			−1.23581
$57$	−0.361619	−	1.11295i	−0.0478976	−	0.147414i
$58$	−2.20684	−	1.60336i	−0.289773	−	0.210532i
$59$	−3.90166	+	2.83472i	−0.507953	+	0.369049i	−0.812046	−	0.583593i	$-0.801646\pi$
$59$	−3.90166	+	2.83472i	−0.507953	+	0.369049i	0.304094	+	0.952642i	$0.401646\pi$
$60$	0.987305	−	3.03861i	0.127460	−	0.392283i
$61$	3.97139	−	12.2227i	0.508484	−	1.56495i	−0.286348	−	0.958126i	$-0.592441\pi$
$61$	3.97139	−	12.2227i	0.508484	−	1.56495i	0.794833	−	0.606829i	$-0.207559\pi$
$62$	2.92278	−	2.12353i	0.371194	−	0.269688i
$63$	−3.74271	−	2.71924i	−0.471537	−	0.342592i
$64$	0.365306	+	1.12430i	0.0456633	+	0.140537i
$65$	−1.56177			−0.193714
$66$	2.43481	−	1.82481i	0.299704	−	0.224618i
$67$	9.01185			1.10097			0.550486	−	0.834844i	$-0.314442\pi$
$67$	9.01185			1.10097			0.550486	+	0.834844i	$0.314442\pi$
$68$	2.01632	+	6.20559i	0.244515	+	0.752538i
$69$	−10.1188	−	7.35174i	−1.21816	−	0.885045i
$70$	3.31058	−	2.40528i	0.395690	−	0.287486i
$71$	1.20998	−	3.72395i	0.143599	−	0.441951i	−0.853229	−	0.521536i	$-0.825359\pi$
$71$	1.20998	−	3.72395i	0.143599	−	0.441951i	0.996828	+	0.0795844i	$0.0253593\pi$
$72$	−0.906023	+	2.78845i	−0.106776	+	0.328622i
$73$	−9.89371	+	7.18820i	−1.15797	+	0.841315i	−0.989520	−	0.144395i	$-0.953877\pi$
$73$	−9.89371	+	7.18820i	−1.15797	+	0.841315i	−0.168451	+	0.985710i	$0.553877\pi$
$74$	5.24930	+	3.81384i	0.610218	+	0.443350i
$75$	−1.05844	−	3.25754i	−0.122218	−	0.376149i
$76$	1.33822			0.153504
$77$	−12.6680	+	0.188009i	−1.44365	+	0.0214256i
$78$	−0.917418			−0.103877
$79$	−0.350447	−	1.07856i	−0.0394284	−	0.121348i	0.929405	−	0.369062i	$-0.120321\pi$
$79$	−0.350447	−	1.07856i	−0.0394284	−	0.121348i	−0.968833	+	0.247714i	$0.920321\pi$
$80$	1.76696	+	1.28377i	0.197553	+	0.143530i
$81$	3.15524	−	2.29241i	0.350582	−	0.254713i
$82$	−0.736710	+	2.26736i	−0.0813560	+	0.250388i
$83$	1.33940	−	4.12224i	0.147018	−	0.452474i	−0.850247	−	0.526384i	$-0.823548\pi$
$83$	1.33940	−	4.12224i	0.147018	−	0.452474i	0.997265	+	0.0739094i	$0.0235476\pi$
$84$	−6.32218	+	4.59334i	−0.689807	+	0.501174i
$85$	−5.39010	−	3.91614i	−0.584638	−	0.424765i
$86$	1.18483	+	3.64654i	0.127764	+	0.393217i
$87$	−5.31911			−0.570269
$88$	2.59427	+	7.59875i	0.276550	+	0.810029i
$89$	−0.384917			−0.0408012			−0.0204006	−	0.999792i	$-0.506494\pi$
$89$	−0.384917			−0.0408012			−0.0204006	+	0.999792i	$0.506494\pi$
$90$	−0.400904	−	1.23386i	−0.0422590	−	0.130060i
$91$	3.09041	+	2.24531i	0.323963	+	0.235373i
$92$	11.5714	−	8.40715i	1.20641	−	0.876506i
$93$	2.17694	−	6.69994i	0.225738	−	0.694751i
$94$	1.30981	−	4.03117i	0.135096	−	0.415784i
$95$	−1.10547	+	0.803172i	−0.113419	+	0.0824037i
$96$	6.27722	+	4.56067i	0.640666	+	0.465471i
$97$	1.62118	+	4.98949i	0.164606	+	0.506606i	0.999007	−	0.0445522i	$-0.0141861\pi$
$97$	1.62118	+	4.98949i	0.164606	+	0.506606i	−0.834401	+	0.551158i	$0.814186\pi$
$98$	−5.20751			−0.526038
$99$	−1.18439	+	3.83808i	−0.119036	+	0.385742i
$100$	3.91690			0.391690
$101$	−3.52731	−	10.8559i	−0.350980	−	1.08021i	−0.958304	−	0.285751i	$-0.907757\pi$
$101$	−3.52731	−	10.8559i	−0.350980	−	1.08021i	0.607324	−	0.794455i	$-0.292243\pi$
$102$	−3.16626	−	2.30042i	−0.313506	−	0.227776i
$103$	11.7390	−	8.52885i	1.15667	−	0.840372i	0.167319	−	0.985903i	$-0.446489\pi$
$103$	11.7390	−	8.52885i	1.15667	−	0.840372i	0.989354	+	0.145530i	$0.0464889\pi$
$104$	0.748116	−	2.30246i	0.0733588	−	0.225775i
$105$	2.46578	−	7.58889i	0.240635	−	0.740600i
$106$	3.67853	−	2.67261i	0.357290	−	0.259587i
$107$	−1.89499	−	1.37679i	−0.183195	−	0.133099i	0.492408	−	0.870364i	$-0.336117\pi$
$107$	−1.89499	−	1.37679i	−0.183195	−	0.133099i	−0.675603	+	0.737265i	$0.736117\pi$
$108$	2.66211	+	8.19314i	0.256162	+	0.788385i
$109$	−6.05518			−0.579981			−0.289990	−	0.957030i	$-0.593652\pi$
$109$	−6.05518			−0.579981			−0.289990	+	0.957030i	$0.593652\pi$
$110$	−2.90504	−	2.04547i	−0.276985	−	0.195027i
$111$	12.6523			1.20090
$112$	−1.65080	−	5.08062i	−0.155985	−	0.480074i
$113$	−11.1116	−	8.07308i	−1.04530	−	0.759452i	−0.0739833	−	0.997259i	$-0.523571\pi$
$113$	−11.1116	−	8.07308i	−1.04530	−	0.759452i	−0.971312	+	0.237808i	$0.923571\pi$
$114$	−0.649378	+	0.471800i	−0.0608198	+	0.0441882i
$115$	−4.51310	+	13.8899i	−0.420849	+	1.29524i
$116$	1.87966	−	5.78501i	0.174522	−	0.537125i
$117$	0.979778	−	0.711851i	0.0905805	−	0.0658106i
$118$	2.67621	+	1.94438i	0.246365	+	0.178995i
$119$	5.03573	+	15.4984i	0.461624	+	1.42073i
$120$	−5.05708			−0.461647
$121$	3.70815	+	10.3561i	0.337104	+	0.941467i
$122$	−8.81518			−0.798089
$123$	1.43655	+	4.42126i	0.129530	+	0.398652i
$124$	6.51750	+	4.73524i	0.585289	+	0.425237i
$125$	−9.55316	+	6.94077i	−0.854460	+	0.620802i
$126$	−0.980577	+	3.01790i	−0.0873567	+	0.268856i
$127$	−5.72606	+	17.6230i	−0.508106	+	1.56379i	0.287380	+	0.957817i	$0.407216\pi$
$127$	−5.72606	+	17.6230i	−0.508106	+	1.56379i	−0.795486	+	0.605972i	$0.792784\pi$
$128$	−8.73044	+	6.34304i	−0.771669	+	0.560650i
$129$	6.04865	+	4.39460i	0.532554	+	0.386923i
$130$	0.331033	+	1.01881i	0.0290335	+	0.0893558i
$131$	13.0069			1.13641			0.568207	−	0.822886i	$-0.307637\pi$
$131$	13.0069			1.13641			0.568207	+	0.822886i	$0.307637\pi$
$132$	5.54773	+	3.90621i	0.482868	+	0.339992i
$133$	3.34219			0.289804
$134$	−1.91015	−	5.87883i	−0.165012	−	0.507854i
$135$	−7.11646	−	5.17041i	−0.612488	−	0.444998i
$136$	8.35537	−	6.07053i	0.716467	−	0.520544i
$137$	0.0669614	−	0.206086i	0.00572090	−	0.0176071i	−0.948155	−	0.317807i	$-0.897053\pi$
$137$	0.0669614	−	0.206086i	0.00572090	−	0.0176071i	0.953876	+	0.300200i	$0.0970535\pi$
$138$	−2.65109	+	8.15922i	−0.225676	+	0.694559i
$139$	−4.09969	+	2.97860i	−0.347731	+	0.252642i	−0.747917	−	0.663793i	$-0.768946\pi$
$139$	−4.09969	+	2.97860i	−0.347731	+	0.252642i	0.400185	+	0.916434i	$0.368946\pi$
$140$	7.38224	+	5.36351i	0.623913	+	0.453300i
$141$	−2.55407	−	7.86062i	−0.215091	−	0.661983i
$142$	−2.68577			−0.225384
$143$	0.977972	−	3.16916i	0.0817821	−	0.265018i
$144$	−1.69365			−0.141137
$145$	1.91930	+	5.90699i	0.159389	+	0.490549i
$146$	6.78625	+	4.93050i	0.561634	+	0.408051i
$147$	−8.21511	+	5.96862i	−0.677571	+	0.492284i
$148$	−4.47105	+	13.7605i	−0.367518	+	1.13111i
$149$	−2.42201	+	7.45418i	−0.198419	+	0.610671i	0.801501	+	0.597994i	$0.204035\pi$
$149$	−2.42201	+	7.45418i	−0.198419	+	0.610671i	−0.999920	+	0.0126768i	$0.995965\pi$
$150$	−1.90070	+	1.38094i	−0.155191	+	0.112753i
$151$	−15.8577	−	11.5213i	−1.29048	−	0.937590i	−0.290667	−	0.956824i	$-0.593877\pi$
$151$	−15.8577	−	11.5213i	−1.29048	−	0.937590i	−0.999815	+	0.0192344i	$0.993877\pi$
$152$	−0.654548	−	2.01449i	−0.0530908	−	0.163397i
$153$	5.16645			0.417682
$154$	2.80774	+	8.22403i	0.226254	+	0.662711i
$155$	−8.22594			−0.660724
$156$	−0.632170	−	1.94562i	−0.0506141	−	0.155774i
$157$	−0.737409	−	0.535759i	−0.0588516	−	0.0427582i	0.557970	−	0.829861i	$-0.311580\pi$
$157$	−0.737409	−	0.535759i	−0.0588516	−	0.0427582i	−0.616822	+	0.787103i	$0.711580\pi$
$158$	−0.629315	+	0.457224i	−0.0500656	+	0.0363748i
$159$	2.73984	−	8.43235i	0.217283	−	0.668729i
$160$	2.79971	−	8.61662i	0.221337	−	0.681204i
$161$	28.8995	−	20.9967i	2.27760	−	1.65478i
$162$	−2.16423	−	1.57240i	−0.170038	−	0.123540i
$163$	−6.63719	−	20.4272i	−0.519865	−	1.59998i	−0.774253	−	0.632877i	$-0.781874\pi$
$163$	−6.63719	−	20.4272i	−0.519865	−	1.59998i	0.254388	−	0.967102i	$-0.418126\pi$
$164$	−5.31617			−0.415123
$165$	−6.92727	+	0.102810i	−0.539287	+	0.00800372i
$166$	−2.97302			−0.230751
$167$	−1.04482	−	3.21561i	−0.0808503	−	0.248832i	0.902458	−	0.430777i	$-0.141761\pi$
$167$	−1.04482	−	3.21561i	−0.0808503	−	0.248832i	−0.983309	+	0.181946i	$0.941761\pi$
$168$	10.0069	+	7.27042i	0.772047	+	0.560925i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−1.41219	+	4.34627i	−0.108310	+	0.333343i
$171$	0.327435	−	1.00774i	0.0250396	−	0.0770639i
$172$	−6.91699	+	5.02549i	−0.527415	+	0.383190i
$173$	9.07635	+	6.59435i	0.690062	+	0.501360i	0.876681	−	0.481073i	$-0.159753\pi$
$173$	9.07635	+	6.59435i	0.690062	+	0.501360i	−0.186618	+	0.982432i	$0.559753\pi$
$174$	1.12744	+	3.46989i	0.0854708	+	0.263052i
$175$	9.78241			0.739481
$176$	−3.71151	+	2.78165i	−0.279765	+	0.209674i
$177$	6.45042			0.484843
$178$	0.0815870	+	0.251099i	0.00611520	+	0.0188207i
$179$	−3.17528	−	2.30698i	−0.237332	−	0.172431i	0.462762	−	0.886483i	$-0.346858\pi$
$179$	−3.17528	−	2.30698i	−0.237332	−	0.172431i	−0.700094	+	0.714051i	$0.746858\pi$
$180$	2.34045	−	1.70044i	0.174447	−	0.126743i
$181$	−4.47371	+	13.7687i	−0.332528	+	1.02342i	0.635399	+	0.772184i	$0.280836\pi$
$181$	−4.47371	+	13.7687i	−0.332528	+	1.02342i	−0.967927	+	0.251232i	$0.919164\pi$
$182$	0.809676	−	2.49193i	0.0600172	−	0.184714i
$183$	−13.9064	+	10.1036i	−1.02799	+	0.746878i
$184$	−18.3155	−	13.3070i	−1.35024	−	0.981005i
$185$	−4.56533	−	14.0506i	−0.335650	−	1.03302i
$186$	−4.83210			−0.354306
$187$	11.3219	−	8.48537i	0.827940	−	0.620512i
$188$	9.45168			0.689335
$189$	6.64859	+	20.4623i	0.483614	+	1.48841i
$190$	0.758260	+	0.550908i	0.0550100	+	0.0399671i
$191$	4.24806	−	3.08640i	0.307379	−	0.223324i	−0.423392	−	0.905947i	$-0.639161\pi$
$191$	4.24806	−	3.08640i	0.307379	−	0.223324i	0.730771	+	0.682623i	$0.239161\pi$
$192$	0.488600	−	1.50376i	0.0352617	−	0.108524i
$193$	5.00924	−	15.4168i	0.360573	−	1.10973i	−0.592135	−	0.805839i	$-0.701715\pi$
$193$	5.00924	−	15.4168i	0.360573	−	1.10973i	0.952707	−	0.303890i	$-0.0982854\pi$
$194$	2.91124	−	2.11514i	0.209015	−	0.151858i
$195$	1.68994	+	1.22781i	0.121019	+	0.0879256i
$196$	−3.58836	−	11.0438i	−0.256312	−	0.788846i
$197$	−0.509998			−0.0363358			−0.0181679	−	0.999835i	$-0.505783\pi$
$197$	−0.509998			−0.0363358			−0.0181679	+	0.999835i	$0.505783\pi$
$198$	2.75480	−	0.0408847i	0.195775	−	0.00290555i
$199$	−9.17221			−0.650201			−0.325100	−	0.945680i	$-0.605398\pi$
$199$	−9.17221			−0.650201			−0.325100	+	0.945680i	$0.605398\pi$
$200$	−1.91583	−	5.89631i	−0.135469	−	0.416932i
$201$	−9.75142	−	7.08482i	−0.687812	−	0.499725i
$202$	−6.33417	+	4.60204i	−0.445670	+	0.323798i
$203$	4.69443	−	14.4480i	0.329485	−	1.01405i
$204$	2.69684	−	8.30003i	0.188817	−	0.581118i
$205$	4.39156	−	3.19065i	0.306720	−	0.222845i
$206$	−8.05193	−	5.85007i	−0.561005	−	0.407594i
$207$	−3.49967	−	10.7709i	−0.243244	−	0.748629i
$208$	1.39847			0.0969663
$209$	−0.937564	−	2.74617i	−0.0648526	−	0.189957i
$210$	−5.47322			−0.377688
$211$	1.74945	+	5.38426i	0.120437	+	0.370668i	0.993042	−	0.117759i	$-0.0375709\pi$
$211$	1.74945	+	5.38426i	0.120437	+	0.370668i	−0.872605	+	0.488427i	$0.837571\pi$
$212$	8.20273	+	5.95963i	0.563366	+	0.409309i
$213$	−4.23693	+	3.07831i	−0.290310	+	0.210922i
$214$	−0.496480	+	1.52801i	−0.0339387	+	0.104452i
$215$	2.69777	−	8.30287i	0.183986	−	0.566251i
$216$	11.0315	−	8.01483i	0.750596	−	0.545340i
$217$	16.2774	+	11.8262i	1.10498	+	0.802815i
$218$	1.28345	+	3.95006i	0.0869265	+	0.267532i
$219$	16.3568			1.10529
$220$	2.33614	−	7.57036i	0.157503	−	0.510394i
$221$	−4.26601			−0.286963
$222$	−2.68177	−	8.25365i	−0.179989	−	0.553949i
$223$	1.56098	+	1.13412i	0.104531	+	0.0759461i	0.638823	−	0.769354i	$-0.279422\pi$
$223$	1.56098	+	1.13412i	0.104531	+	0.0759461i	−0.534292	+	0.845300i	$0.679422\pi$
$224$	−17.9279	+	13.0254i	−1.19786	+	0.870294i
$225$	0.958385	−	2.94961i	0.0638924	−	0.196640i
$226$	−2.91121	+	8.95979i	−0.193651	+	0.595996i
$227$	−9.22346	+	6.70123i	−0.612182	+	0.444777i	−0.850182	−	0.526489i	$-0.823508\pi$
$227$	−9.22346	+	6.70123i	−0.612182	+	0.444777i	0.238000	+	0.971265i	$0.423508\pi$
$228$	−1.44804	−	1.05206i	−0.0958990	−	0.0696747i
$229$	2.09178	+	6.43785i	0.138229	+	0.425425i	0.996078	−	0.0884762i	$-0.0281997\pi$
$229$	2.09178	+	6.43785i	0.138229	+	0.425425i	−0.857849	+	0.513901i	$0.828200\pi$
$230$	10.0176			0.660540
$231$	13.8554	+	9.75570i	0.911617	+	0.641878i
$232$	−9.62785			−0.632099
$233$	3.27373	+	10.0755i	0.214469	+	0.660067i	0.999191	+	0.0402195i	$0.0128057\pi$
$233$	3.27373	+	10.0755i	0.214469	+	0.660067i	−0.784722	+	0.619848i	$0.787194\pi$
$234$	−0.672046	−	0.488270i	−0.0439330	−	0.0319192i
$235$	−7.80781	+	5.67270i	−0.509325	+	0.370046i
$236$	−2.27944	+	7.01541i	−0.148379	+	0.456664i
$237$	−0.468726	+	1.44259i	−0.0304470	+	0.0937062i
$238$	9.04291	−	6.57006i	0.586165	−	0.425874i
$239$	−12.0554	−	8.75873i	−0.779796	−	0.566555i	0.125122	−	0.992141i	$-0.460068\pi$
$239$	−12.0554	−	8.75873i	−0.779796	−	0.566555i	−0.904918	+	0.425586i	$0.860068\pi$
$240$	−0.902711	−	2.77826i	−0.0582698	−	0.179336i
$241$	−6.71327			−0.432439			−0.216220	−	0.976345i	$-0.569373\pi$
$241$	−6.71327			−0.432439			−0.216220	+	0.976345i	$0.569373\pi$
$242$	5.96980	−	4.61408i	0.383753	−	0.296604i
$243$	11.6806			0.749313
$244$	−6.07432	−	18.6948i	−0.388868	−	1.19681i
$245$	9.59255	+	6.96940i	0.612846	+	0.445259i
$246$	2.57970	−	1.87426i	0.164475	−	0.119498i
$247$	−0.270368	+	0.832106i	−0.0172031	+	0.0529457i
$248$	3.94037	−	12.1272i	0.250214	−	0.770079i
$249$	−4.69008	+	3.40755i	−0.297222	+	0.215944i
$250$	6.55266	+	4.76079i	0.414427	+	0.301099i
$251$	0.701425	+	2.15876i	0.0442736	+	0.136260i	0.970750	−	0.240093i	$-0.0771780\pi$
$251$	0.701425	+	2.15876i	0.0442736	+	0.136260i	−0.926476	+	0.376353i	$0.877178\pi$
$252$	−7.07593			−0.445742
$253$	−25.3594	−	17.8558i	−1.59433	−	1.12258i
$254$	12.7100			0.797495
$255$	2.75371	+	8.47504i	0.172444	+	0.530728i
$256$	7.90112	+	5.74050i	0.493820	+	0.358781i
$257$	−1.63978	+	1.19137i	−0.102287	+	0.0743157i	−0.637753	−	0.770241i	$-0.720136\pi$
$257$	−1.63978	+	1.19137i	−0.102287	+	0.0743157i	0.535466	+	0.844557i	$0.320136\pi$
$258$	1.58473	−	4.87728i	0.0986607	−	0.303646i
$259$	−11.1664	+	34.3666i	−0.693846	+	2.13544i
$260$	−1.93255	+	1.40408i	−0.119851	+	0.0870772i
$261$	−3.89646	−	2.83095i	−0.241185	−	0.175231i
$262$	−2.75693	−	8.48495i	−0.170324	−	0.524202i
$263$	24.0658			1.48396			0.741980	−	0.670422i	$-0.233887\pi$
$263$	24.0658			1.48396			0.741980	+	0.670422i	$0.233887\pi$
$264$	3.16672	−	10.2619i	0.194898	−	0.631575i
$265$	−10.3529			−0.635975
$266$	−0.708409	−	2.18026i	−0.0434353	−	0.133680i
$267$	0.416506	+	0.302610i	0.0254898	+	0.0185194i
$268$	11.1513	−	8.10191i	0.681176	−	0.494903i
$269$	−1.60831	+	4.94988i	−0.0980606	+	0.301799i	−0.988039	−	0.154203i	$-0.950719\pi$
$269$	−1.60831	+	4.94988i	−0.0980606	+	0.301799i	0.889979	+	0.456002i	$0.150719\pi$
$270$	−1.86449	+	5.73831i	−0.113469	+	0.349222i
$271$	−4.53742	+	3.29663i	−0.275629	+	0.200256i	−0.717009	−	0.697064i	$-0.754489\pi$
$271$	−4.53742	+	3.29663i	−0.275629	+	0.200256i	0.441380	+	0.897320i	$0.354489\pi$
$272$	4.82650	+	3.50666i	0.292649	+	0.212622i
$273$	−1.57884	−	4.85916i	−0.0955555	−	0.294090i
$274$	−0.148632			−0.00897920
$275$	−2.74420	−	8.03791i	−0.165482	−	0.484704i
$276$	−19.1305			−1.15152
$277$	−0.0968454	−	0.298060i	−0.00581888	−	0.0179087i	0.948105	−	0.317958i	$-0.102997\pi$
$277$	−0.0968454	−	0.298060i	−0.00581888	−	0.0179087i	−0.953924	+	0.300049i	$0.902997\pi$
$278$	2.81204	+	2.04307i	0.168655	+	0.122535i
$279$	5.16055	−	3.74936i	0.308954	−	0.224468i
$280$	4.46318	−	13.7363i	0.266726	−	0.820898i
$281$	−0.835562	+	2.57159i	−0.0498454	+	0.153408i	−0.972881	−	0.231306i	$-0.925700\pi$
$281$	−0.835562	+	2.57159i	−0.0498454	+	0.153408i	0.923036	+	0.384715i	$0.125700\pi$
$282$	−4.58647	+	3.33227i	−0.273121	+	0.198434i
$283$	−8.30945	−	6.03717i	−0.493945	−	0.358872i	0.312754	−	0.949834i	$-0.398748\pi$
$283$	−8.30945	−	6.03717i	−0.493945	−	0.358872i	−0.806700	+	0.590962i	$0.798748\pi$
$284$	−1.85069	−	5.69585i	−0.109818	−	0.337987i
$285$	1.82762			0.108259
$286$	−2.27468	+	0.0337591i	−0.134504	+	0.00199622i
$287$	−13.2771			−0.783720
$288$	2.17103	+	6.68174i	0.127929	+	0.393725i
$289$	−0.969874	−	0.704655i	−0.0570514	−	0.0414503i
$290$	3.44658	−	2.50409i	0.202390	−	0.147045i
$291$	2.16835	−	6.67348i	0.127111	−	0.391206i
$292$	−5.78015	+	17.7895i	−0.338258	+	1.04105i
$293$	−2.72658	+	1.98098i	−0.159289	+	0.115730i	−0.664574	−	0.747222i	$-0.731387\pi$
$293$	−2.72658	+	1.98098i	−0.159289	+	0.115730i	0.505286	+	0.862952i	$0.331387\pi$
$294$	5.63487	+	4.09397i	0.328632	+	0.238765i
$295$	−2.32751	−	7.16334i	−0.135513	−	0.417066i
$296$	22.9012			1.33111
$297$	14.9481	−	11.2031i	0.867379	−	0.650070i
$298$	5.37607			0.311427
$299$	2.88973	+	8.89368i	0.167117	+	0.514335i
$300$	−4.23835	−	3.07934i	−0.244701	−	0.177786i
$301$	−17.2751	+	12.5511i	−0.995719	+	0.723432i
$302$	−4.15466	+	12.7867i	−0.239074	+	0.735794i
$303$	−4.71780	+	14.5199i	−0.271031	+	0.834146i
$304$	0.989880	−	0.719190i	0.0567735	−	0.0412484i
$305$	16.2381	+	11.7977i	0.929791	+	0.675533i
$306$	−1.09508	−	3.37030i	−0.0626015	−	0.192667i
$307$	2.90821			0.165980			0.0829902	−	0.996550i	$-0.473553\pi$
$307$	2.90821			0.165980			0.0829902	+	0.996550i	$0.473553\pi$
$308$	−15.5064	+	11.6215i	−0.883559	+	0.662197i
$309$	−19.4074			−1.10405
$310$	1.74357	+	5.36615i	0.0990280	+	0.304777i
$311$	−18.4153	−	13.3795i	−1.04424	−	0.758682i	−0.0731281	−	0.997323i	$-0.523298\pi$
$311$	−18.4153	−	13.3795i	−1.04424	−	0.758682i	−0.971108	+	0.238641i	$0.923298\pi$
$312$	−2.61963	+	1.90327i	−0.148308	+	0.107752i
$313$	−5.03789	+	15.5050i	−0.284758	+	0.876396i	0.701713	+	0.712460i	$0.252419\pi$
$313$	−5.03789	+	15.5050i	−0.284758	+	0.876396i	−0.986471	+	0.163936i	$0.947581\pi$
$314$	−0.193199	+	0.594604i	−0.0109028	+	0.0335555i
$315$	5.84525	−	4.24683i	0.329343	−	0.239282i
$316$	−1.40331	−	1.01956i	−0.0789422	−	0.0573548i
$317$	9.06039	+	27.8850i	0.508882	+	1.56618i	0.794145	+	0.607729i	$0.207919\pi$
$317$	9.06039	+	27.8850i	0.508882	+	1.56618i	−0.285262	+	0.958449i	$0.592081\pi$
$318$	−6.08153			−0.341035
$319$	−13.1884	+	0.195732i	−0.738407	+	0.0109589i
$320$	−1.84626			−0.103209
$321$	0.968115	+	2.97955i	0.0540349	+	0.166302i
$322$	−19.8227	−	14.4020i	−1.10467	−	0.802592i
$323$	−3.01962	+	2.19388i	−0.168016	+	0.122071i
$324$	1.84337	−	5.67330i	0.102409	−	0.315183i
$325$	−0.791352	+	2.43553i	−0.0438963	+	0.135099i
$326$	−11.9187	+	8.65947i	−0.660118	+	0.479604i
$327$	6.55211	+	4.76038i	0.362332	+	0.263250i
$328$	2.60023	+	8.00270i	0.143574	+	0.441875i
$329$	23.6054			1.30141
$330$	1.53537	+	4.49718i	0.0845193	+	0.247562i
$331$	33.2880			1.82967			0.914837	−	0.403823i	$-0.132319\pi$
$331$	33.2880			1.82967			0.914837	+	0.403823i	$0.132319\pi$
$332$	−2.04863	−	6.30504i	−0.112433	−	0.346034i
$333$	9.26831	+	6.73382i	0.507900	+	0.369011i
$334$	−1.87623	+	1.36316i	−0.102663	+	0.0745888i
$335$	−4.34924	+	13.3856i	−0.237625	+	0.731333i
$336$	−2.20795	+	6.79538i	−0.120454	+	0.370718i
$337$	−8.09368	+	5.88040i	−0.440891	+	0.320326i	−0.785989	−	0.618241i	$-0.787846\pi$
$337$	−8.09368	+	5.88040i	−0.440891	+	0.320326i	0.345098	+	0.938567i	$0.387846\pi$
$338$	0.554918	+	0.403171i	0.0301835	+	0.0219296i
$339$	5.67674	+	17.4712i	0.308318	+	0.948907i
$340$	−10.1905			−0.552656
$341$	5.15104	−	16.6922i	0.278944	−	0.903931i
$342$	−0.726798			−0.0393007
$343$	−0.698876	−	2.15092i	−0.0377358	−	0.116139i
$344$	10.9483	+	7.95444i	0.590295	+	0.428875i
$345$	15.8033	−	11.4817i	0.850819	−	0.618156i
$346$	2.37797	−	7.31865i	0.127841	−	0.393453i
$347$	−1.02930	+	3.16785i	−0.0552555	+	0.170059i	−0.974876	−	0.222750i	$-0.928497\pi$
$347$	−1.02930	+	3.16785i	−0.0552555	+	0.170059i	0.919620	+	0.392809i	$0.128497\pi$
$348$	−6.58191	+	4.78204i	−0.352827	+	0.256344i
$349$	26.1112	+	18.9709i	1.39770	+	1.01549i	0.994971	+	0.100167i	$0.0319377\pi$
$349$	26.1112	+	18.9709i	1.39770	+	1.01549i	0.402727	+	0.915320i	$0.368062\pi$
$350$	−2.07348	−	6.38150i	−0.110832	−	0.341106i
$351$	−5.63234			−0.300632
$352$	15.7318	+	11.0769i	0.838506	+	0.590399i
$353$	0.0277205			0.00147541			0.000737706	−	1.00000i	$-0.499765\pi$
$353$	0.0277205			0.00147541			0.000737706		1.00000i	$0.499765\pi$
$354$	−1.36723	−	4.20790i	−0.0726674	−	0.223647i
$355$	4.94735	+	3.59446i	0.262578	+	0.190774i
$356$	−0.476300	+	0.346052i	−0.0252438	+	0.0183407i
$357$	6.73533	−	20.7292i	0.356471	−	1.09711i
$358$	−0.831912	+	2.56036i	−0.0439679	+	0.135319i
$359$	12.2819	−	8.92332i	0.648213	−	0.470955i	−0.214449	−	0.976735i	$-0.568795\pi$
$359$	12.2819	−	8.92332i	0.648213	−	0.470955i	0.862662	+	0.505781i	$0.168795\pi$
$360$	−3.70452	−	2.69149i	−0.195245	−	0.141854i
$361$	−5.63477	−	17.3420i	−0.296567	−	0.912739i
$362$	9.93015			0.521917
$363$	4.12920	−	14.1213i	0.216727	−	0.741174i
$364$	5.84269			0.306240
$365$	−5.90203	−	18.1646i	−0.308926	−	0.950777i
$366$	9.53861	+	6.93021i	0.498591	+	0.362248i
$367$	−12.6785	+	9.21148i	−0.661813	+	0.480835i	−0.867275	−	0.497830i	$-0.834130\pi$
$367$	−12.6785	+	9.21148i	−0.661813	+	0.480835i	0.205462	+	0.978665i	$0.434130\pi$
$368$	4.04120	−	12.4375i	0.210662	−	0.648351i
$369$	−1.30076	+	4.00332i	−0.0677147	+	0.208404i
$370$	−8.19820	+	5.95634i	−0.426204	+	0.309655i
$371$	20.4862	+	14.8841i	1.06359	+	0.772744i
$372$	−3.32968	−	10.2477i	−0.172636	−	0.531318i
$373$	−28.0231			−1.45098			−0.725490	−	0.688233i	$-0.758387\pi$
$373$	−28.0231			−1.45098			−0.725490	+	0.688233i	$0.758387\pi$
$374$	−7.93518	−	5.58723i	−0.410318	−	0.288909i
$375$	15.7938			0.815586
$376$	−4.62299	−	14.2281i	−0.238412	−	0.733758i
$377$	3.21737	+	2.33755i	0.165703	+	0.120390i
$378$	11.9392	−	8.67435i	0.614087	−	0.446160i
$379$	0.104950	−	0.323004i	0.00539093	−	0.0165916i	−0.948325	−	0.317301i	$-0.897223\pi$
$379$	0.104950	−	0.323004i	0.00539093	−	0.0165916i	0.953716	+	0.300709i	$0.0972234\pi$
$380$	−0.645843	+	1.98770i	−0.0331311	+	0.101967i
$381$	20.0506	−	14.5676i	1.02722	−	0.746322i
$382$	−2.91381	−	2.11701i	−0.149084	−	0.108316i
$383$	−11.8093	−	36.3454i	−0.603429	−	1.85716i	−0.507250	−	0.861799i	$-0.669338\pi$
$383$	−11.8093	−	36.3454i	−0.603429	−	1.85716i	−0.0961788	−	0.995364i	$-0.530662\pi$
$384$	14.4336			0.736562
$385$	5.83448	−	18.9069i	0.297353	−	0.963583i
$386$	−11.1189			−0.565935
$387$	2.09198	+	6.43844i	0.106341	+	0.327284i
$388$	6.49176	+	4.71654i	0.329569	+	0.239446i
$389$	−10.9511	+	7.95644i	−0.555243	+	0.403408i	−0.829715	−	0.558188i	$-0.811497\pi$
$389$	−10.9511	+	7.95644i	−0.555243	+	0.403408i	0.274472	+	0.961595i	$0.411497\pi$
$390$	0.442759	−	1.36267i	0.0224200	−	0.0690015i
$391$	−12.3276	+	37.9405i	−0.623434	+	1.91873i
$392$	−14.8697	+	10.8035i	−0.751035	+	0.545659i
$393$	−14.0743	−	10.2256i	−0.709954	−	0.515812i
$394$	0.108099	+	0.332694i	0.00544595	+	0.0167609i
$395$	1.77116			0.0891166
$396$	1.98497	+	5.81408i	0.0997484	+	0.292168i
$397$	−18.6406			−0.935544			−0.467772	−	0.883849i	$-0.654943\pi$
$397$	−18.6406			−0.935544			−0.467772	+	0.883849i	$0.654943\pi$
$398$	1.94414	+	5.98344i	0.0974509	+	0.299923i
$399$	−3.61647	−	2.62752i	−0.181050	−	0.131540i
$400$	2.89733	−	2.10503i	0.144866	−	0.105252i
$401$	1.94093	−	5.97358i	0.0969256	−	0.298306i	−0.890825	−	0.454346i	$-0.849873\pi$
$401$	1.94093	−	5.97358i	0.0969256	−	0.298306i	0.987751	+	0.156040i	$0.0498729\pi$
$402$	−2.55484	+	7.86299i	−0.127424	+	0.392170i
$403$	−4.26114	+	3.09590i	−0.212263	+	0.154218i
$404$	−14.1245	−	10.2621i	−0.702721	−	0.510557i
$405$	1.88224	+	5.79292i	0.0935290	+	0.287853i
$406$	−10.4201			−0.517141
$407$	31.3705	−	0.465578i	1.55498	−	0.0230779i
$408$	−13.8135			−0.683871
$409$	1.08671	+	3.34455i	0.0537344	+	0.165377i	0.974322	−	0.225158i	$-0.0722899\pi$
$409$	1.08671	+	3.34455i	0.0537344	+	0.165377i	−0.920588	+	0.390535i	$0.872290\pi$
$410$	−3.01224	−	2.18852i	−0.148764	−	0.108083i
$411$	−0.234475	+	0.170356i	−0.0115658	+	0.00840304i
$412$	6.85818	−	21.1073i	0.337878	−	1.03988i
$413$	−5.69288	+	17.5209i	−0.280128	+	0.862147i
$414$	−6.28454	+	4.56599i	−0.308868	+	0.224406i
$415$	5.47648	+	3.97890i	0.268830	+	0.195316i
$416$	−1.79265	−	5.51721i	−0.0878919	−	0.270504i
$417$	6.77782			0.331911
$418$	−1.59273	+	1.19369i	−0.0779028	+	0.0583854i
$419$	−27.3384			−1.33557			−0.667785	−	0.744354i	$-0.732758\pi$
$419$	−27.3384			−1.33557			−0.667785	+	0.744354i	$0.732758\pi$
$420$	−3.77146	−	11.6074i	−0.184028	−	0.566381i
$421$	2.69950	+	1.96130i	0.131566	+	0.0955881i	0.651622	−	0.758544i	$-0.274089\pi$
$421$	2.69950	+	1.96130i	0.131566	+	0.0955881i	−0.520056	+	0.854132i	$0.674089\pi$
$422$	3.14158	−	2.28249i	0.152930	−	0.111110i
$423$	2.31263	−	7.11755i	0.112444	−	0.346067i
$424$	4.95923	−	15.2630i	0.240842	−	0.741234i
$425$	−8.83826	+	6.42137i	−0.428719	+	0.311482i
$426$	2.90618	+	2.11146i	0.140805	+	0.102301i
$427$	−15.1705	−	46.6901i	−0.734153	−	2.25949i
$428$	−3.58264			−0.173174
$429$	−3.54972	+	2.66039i	−0.171382	+	0.128445i
$430$	−5.98815			−0.288774
$431$	−1.11948	−	3.44541i	−0.0539236	−	0.165960i	0.920468	−	0.390818i	$-0.127808\pi$
$431$	−1.11948	−	3.44541i	−0.0539236	−	0.165960i	−0.974391	+	0.224859i	$0.927808\pi$
$432$	6.37235	+	4.62978i	0.306590	+	0.222750i
$433$	17.3221	−	12.5853i	0.832448	−	0.604809i	−0.0878026	−	0.996138i	$-0.527984\pi$
$433$	17.3221	−	12.5853i	0.832448	−	0.604809i	0.920251	+	0.391329i	$0.127984\pi$
$434$	4.26461	−	13.1251i	0.204708	−	0.630026i
$435$	2.56708	−	7.90065i	0.123082	−	0.378807i
$436$	−7.49272	+	5.44378i	−0.358836	+	0.260710i
$437$	6.61919	+	4.80913i	0.316639	+	0.230052i
$438$	−3.46698	−	10.6703i	−0.165659	−	0.509845i
$439$	−29.5556			−1.41061			−0.705305	−	0.708904i	$-0.749190\pi$
$439$	−29.5556			−1.41061			−0.705305	+	0.708904i	$0.749190\pi$
$440$	−12.5387	+	0.186090i	−0.597759	+	0.00887151i
$441$	−9.19453			−0.437835
$442$	0.904222	+	2.78291i	0.0430094	+	0.132369i
$443$	−7.19343	−	5.22634i	−0.341770	−	0.248311i	0.403638	−	0.914919i	$-0.367746\pi$
$443$	−7.19343	−	5.22634i	−0.341770	−	0.248311i	−0.745408	+	0.666608i	$0.767746\pi$
$444$	15.6560	−	11.3748i	0.743002	−	0.539823i
$445$	0.185766	−	0.571730i	0.00880618	−	0.0271026i
$446$	0.408971	−	1.25868i	0.0193653	−	0.0596004i
$447$	8.48101	−	6.16182i	0.401138	−	0.291444i
$448$	3.65335	+	2.65431i	0.172604	+	0.125404i
$449$	5.51893	+	16.9855i	0.260454	+	0.801596i	0.992706	+	0.120562i	$0.0384695\pi$
$449$	5.51893	+	16.9855i	0.260454	+	0.801596i	−0.732252	+	0.681034i	$0.761530\pi$
$450$	−2.12730			−0.100282
$451$	3.72453	+	10.9094i	0.175381	+	0.513701i
$452$	−21.0076			−0.988113
$453$	8.10143	+	24.9336i	0.380638	+	1.17148i
$454$	6.32652	+	4.59648i	0.296918	+	0.215724i
$455$	−4.82651	+	3.50667i	−0.226270	+	0.164395i
$456$	−0.875463	+	2.69440i	−0.0409973	+	0.126177i
$457$	11.9191	−	36.6831i	0.557551	−	1.71597i	−0.131559	−	0.991308i	$-0.541998\pi$
$457$	11.9191	−	36.6831i	0.557551	−	1.71597i	0.689110	−	0.724657i	$-0.258002\pi$
$458$	3.75632	−	2.72913i	0.175521	−	0.127524i
$459$	−19.4388	−	14.1231i	−0.907323	−	0.659209i
$460$	6.90287	+	21.2449i	0.321848	+	0.990547i
$461$	22.8699			1.06516			0.532579	−	0.846380i	$-0.321223\pi$
$461$	22.8699			1.06516			0.532579	+	0.846380i	$0.321223\pi$
$462$	3.42730	−	11.1063i	0.159452	−	0.516712i
$463$	−29.9610			−1.39241			−0.696203	−	0.717845i	$-0.745129\pi$
$463$	−29.9610			−1.39241			−0.696203	+	0.717845i	$0.745129\pi$
$464$	−1.71861	−	5.28934i	−0.0797845	−	0.245552i
$465$	8.90102	+	6.46697i	0.412775	+	0.299898i
$466$	5.87880	−	4.27120i	0.272330	−	0.197859i
$467$	11.5871	−	35.6615i	0.536188	−	1.65022i	−0.204881	−	0.978787i	$-0.565681\pi$
$467$	11.5871	−	35.6615i	0.536188	−	1.65022i	0.741069	−	0.671429i	$-0.234319\pi$
$468$	0.572410	−	1.76170i	0.0264597	−	0.0814345i
$469$	27.8503	−	20.2344i	1.28601	−	0.934339i
$470$	5.35550	+	3.89100i	0.247031	+	0.179478i
$471$	0.376729	+	1.15945i	0.0173588	+	0.0534248i
$472$	11.6756			0.537412
$473$	15.1589	+	10.6735i	0.697008	+	0.490770i
$474$	1.04042			0.0477879
$475$	0.692377	+	2.13092i	0.0317684	+	0.0977731i
$476$	20.1647	+	14.6505i	0.924249	+	0.671506i
$477$	6.49492	−	4.71883i	0.297382	−	0.216061i
$478$	−3.15846	+	9.72074i	−0.144465	+	0.444616i
$479$	10.1430	−	31.2170i	0.463446	−	1.42634i	−0.397479	−	0.917611i	$-0.630115\pi$
$479$	10.1430	−	31.2170i	0.463446	−	1.42634i	0.860926	−	0.508731i	$-0.169885\pi$
$480$	−9.80358	+	7.12272i	−0.447470	+	0.325106i
$481$	−7.65297	−	5.56021i	−0.348946	−	0.253524i
$482$	1.42294	+	4.37936i	0.0648132	+	0.199475i
$483$	−47.7782			−2.17398
$484$	13.8990	+	9.48103i	0.631771	+	0.430956i
$485$	−8.19346			−0.372046
$486$	−2.47582	−	7.61980i	−0.112306	−	0.345641i
$487$	16.9257	+	12.2972i	0.766976	+	0.557241i	0.901042	−	0.433731i	$-0.142803\pi$
$487$	16.9257	+	12.2972i	0.766976	+	0.557241i	−0.134066	+	0.990972i	$0.542803\pi$
$488$	−25.1712	+	18.2880i	−1.13945	+	0.827857i
$489$	−8.87729	+	27.3215i	−0.401445	+	1.23552i
$490$	2.51322	−	7.73488i	0.113536	−	0.349426i
$491$	4.82833	−	3.50799i	0.217899	−	0.158313i	−0.473481	−	0.880804i	$-0.657003\pi$
$491$	4.82833	−	3.50799i	0.217899	−	0.158313i	0.691381	+	0.722491i	$0.257003\pi$
$492$	5.75245	+	4.17940i	0.259340	+	0.188422i
$493$	5.24260	+	16.1351i	0.236115	+	0.726687i
$494$	0.600127			0.0270010
$495$	−5.12922	−	3.61153i	−0.230541	−	0.162326i
$496$	7.36582			0.330735
$497$	−4.62208	−	14.2253i	−0.207329	−	0.638093i
$498$	3.21700	+	2.33729i	0.144157	+	0.104736i
$499$	9.69543	−	7.04414i	0.434027	−	0.315339i	−0.349230	−	0.937037i	$-0.613557\pi$
$499$	9.69543	−	7.04414i	0.434027	−	0.315339i	0.783257	+	0.621698i	$0.213557\pi$
$500$	−5.58119	+	17.1771i	−0.249598	+	0.768184i
$501$	−1.39745	+	4.30091i	−0.0624335	+	0.192150i
$502$	1.25958	−	0.915142i	0.0562180	−	0.0408448i
$503$	−22.5341	−	16.3720i	−1.00475	−	0.729991i	−0.0416455	−	0.999132i	$-0.513260\pi$
$503$	−22.5341	−	16.3720i	−1.00475	−	0.729991i	−0.963101	+	0.269142i	$0.913260\pi$
$504$	3.46096	+	10.6518i	0.154164	+	0.474467i
$505$	17.8270			0.793291
$506$	−6.27296	+	20.3278i	−0.278867	+	0.903680i
$507$	1.33751			0.0594008
$508$	8.75812	+	26.9547i	0.388579	+	1.19592i
$509$	−0.0116945	−	0.00849657i	−0.000518351	−	0.000376604i	0.587526	−	0.809205i	$-0.300102\pi$
$509$	−0.0116945	−	0.00849657i	−0.000518351	−	0.000376604i	−0.588044	+	0.808829i	$0.700102\pi$
$510$	4.94497	−	3.59273i	0.218967	−	0.159089i
$511$	−14.4358	+	44.4290i	−0.638604	+	1.96542i
$512$	−4.59940	+	14.1555i	−0.203267	+	0.625590i
$513$	−3.98675	+	2.89654i	−0.176019	+	0.127886i
$514$	1.12475	+	0.817181i	0.0496107	+	0.0360443i
$515$	7.00280	+	21.5524i	0.308580	+	0.949712i
$516$	11.4355			0.503420
$517$	−6.62190	−	19.3959i	−0.291231	−	0.853030i
$518$	24.7857			1.08902
$519$	−4.63695	−	14.2711i	−0.203539	−	0.626430i
$520$	3.05887	+	2.22240i	0.134140	+	0.0974588i
$521$	−30.1475	+	21.9035i	−1.32079	+	0.959608i	−0.320865	+	0.947125i	$0.603973\pi$
$521$	−30.1475	+	21.9035i	−1.32079	+	0.959608i	−0.999922	+	0.0124827i	$0.996027\pi$
$522$	−1.02086	+	3.14188i	−0.0446818	+	0.137517i
$523$	−5.17703	+	15.9332i	−0.226376	+	0.696712i	0.771774	+	0.635898i	$0.219370\pi$
$523$	−5.17703	+	15.9332i	−0.226376	+	0.696712i	−0.998149	+	0.0608148i	$0.980630\pi$
$524$	16.0948	−	11.6935i	0.703104	−	0.510835i
$525$	−10.5852	−	7.69061i	−0.461977	−	0.335646i
$526$	−5.10098	−	15.6992i	−0.222413	−	0.684517i
$527$	−22.4693			−0.978779
$528$	6.20294	−	0.0920596i	0.269948	−	0.00400638i
$529$	64.4480			2.80209
$530$	2.19440	+	6.75368i	0.0953188	+	0.293361i
$531$	4.72519	+	3.43305i	0.205056	+	0.148982i
$532$	4.13564	−	3.00472i	0.179303	−	0.130271i
$533$	1.07405	−	3.30560i	0.0465224	−	0.143181i
$534$	0.109123	−	0.335847i	0.00472222	−	0.0145335i
$535$	2.95954	−	2.15023i	0.127952	−	0.0929625i
$536$	−17.6505	−	12.8239i	−0.762387	−	0.553907i
$537$	1.62219	+	4.99260i	0.0700029	+	0.215447i
$538$	3.56992			0.153910
$539$	−20.1492	+	15.1011i	−0.867886	+	0.650450i
$540$	−13.4543			−0.578981
$541$	0.366047	+	1.12658i	0.0157376	+	0.0484353i	0.958617	−	0.284699i	$-0.0918937\pi$
$541$	0.366047	+	1.12658i	0.0157376	+	0.0484353i	−0.942879	+	0.333134i	$0.891894\pi$
$542$	3.11229	+	2.26121i	0.133684	+	0.0971273i
$543$	15.6653	−	11.3815i	0.672263	−	0.488428i
$544$	7.64746	−	23.5365i	0.327882	−	1.00912i
$545$	2.92231	−	8.99396i	0.125178	−	0.385259i
$546$	−2.83520	+	2.05989i	−0.121335	+	0.0881552i
$547$	9.70249	+	7.04927i	0.414848	+	0.301405i	0.775562	−	0.631272i	$-0.217467\pi$
$547$	9.70249	+	7.04927i	0.414848	+	0.301405i	−0.360713	+	0.932677i	$0.617467\pi$
$548$	−0.102419	−	0.315213i	−0.00437511	−	0.0134652i
$549$	−15.5643			−0.664269
$550$	−4.66183	+	3.49388i	−0.198781	+	0.148979i
$551$	3.47949			0.148231
$552$	9.35708	+	28.7981i	0.398264	+	1.22573i
$553$	−3.50474	−	2.54634i	−0.149037	−	0.108281i
$554$	−0.173910	+	0.126353i	−0.00738874	+	0.00536823i
$555$	−6.10617	+	18.7929i	−0.259192	+	0.797712i
$556$	−2.39514	+	7.37148i	−0.101577	+	0.312620i
$557$	−34.5558	+	25.1063i	−1.46418	+	1.06379i	−0.481928	+	0.876211i	$0.660063\pi$
$557$	−34.5558	+	25.1063i	−1.46418	+	1.06379i	−0.982250	+	0.187577i	$0.939937\pi$
$558$	−3.53970	−	2.57175i	−0.149848	−	0.108871i
$559$	−1.72738	−	5.31631i	−0.0730602	−	0.224856i
$560$	8.34312			0.352561
$561$	−18.9220	+	0.280827i	−0.798887	+	0.0118565i
$562$	1.85467			0.0782346
$563$	−14.3253	−	44.0888i	−0.603741	−	1.85812i	−0.505225	−	0.862988i	$-0.668590\pi$
$563$	−14.3253	−	44.0888i	−0.603741	−	1.85812i	−0.0985162	−	0.995135i	$-0.531410\pi$
$564$	−10.2273	−	7.43060i	−0.430649	−	0.312885i
$565$	17.3538	−	12.6083i	0.730082	−	0.530435i
$566$	−2.17705	+	6.70026i	−0.0915081	+	0.281633i
$567$	4.60378	−	14.1690i	0.193341	−	0.595041i
$568$	−7.66905	+	5.57189i	−0.321786	+	0.233791i
$569$	26.5471	+	19.2876i	1.11291	+	0.808579i	0.983120	−	0.182962i	$-0.0585686\pi$
$569$	26.5471	+	19.2876i	1.11291	+	0.808579i	0.129793	+	0.991541i	$0.458569\pi$
$570$	−0.387382	−	1.19224i	−0.0162256	−	0.0499374i
$571$	16.9439			0.709082			0.354541	−	0.935041i	$-0.384637\pi$
$571$	16.9439			0.709082			0.354541	+	0.935041i	$0.384637\pi$
$572$	−1.63902	−	4.80077i	−0.0685307	−	0.200730i
$573$	−7.02312			−0.293395
$574$	2.81420	+	8.66122i	0.117462	+	0.361512i
$575$	19.3740	+	14.0761i	0.807954	+	0.587013i
$576$	1.15825	−	0.841519i	0.0482605	−	0.0350633i
$577$	−0.572075	+	1.76067i	−0.0238158	+	0.0732975i	−0.962258	−	0.272139i	$-0.912269\pi$
$577$	−0.572075	+	1.76067i	−0.0238158	+	0.0732975i	0.938442	+	0.345436i	$0.112269\pi$
$578$	−0.254104	+	0.782051i	−0.0105693	+	0.0325290i
$579$	−17.5405	+	12.7440i	−0.728960	+	0.529621i
$580$	7.68551	+	5.58385i	0.319124	+	0.231857i
$581$	−5.11643	−	15.7468i	−0.212265	−	0.653286i
$582$	−4.81301			−0.199506
$583$	6.48294	−	21.0082i	0.268496	−	0.870073i
$584$	29.6066			1.22513
$585$	0.584480	+	1.79885i	0.0241653	+	0.0743731i
$586$	1.87021	+	1.35879i	0.0772576	+	0.0561309i
$587$	−11.8457	+	8.60639i	−0.488923	+	0.355224i	−0.804770	−	0.593587i	$-0.797711\pi$
$587$	−11.8457	+	8.60639i	−0.488923	+	0.355224i	0.315847	+	0.948810i	$0.397711\pi$
$588$	−4.79947	+	14.7712i	−0.197927	+	0.609155i
$589$	−1.42404	+	4.38275i	−0.0586767	+	0.180588i
$590$	−4.17963	+	3.03668i	−0.172073	+	0.125018i
$591$	0.551852	+	0.400944i	0.0227001	+	0.0164926i
$592$	4.08797	+	12.5815i	0.168014	+	0.517095i
$593$	33.3874			1.37106			0.685529	−	0.728046i	$-0.259571\pi$
$593$	33.3874			1.37106			0.685529	+	0.728046i	$0.259571\pi$
$594$	−10.4767	−	7.37673i	−0.429864	−	0.302671i
$595$	−25.4506			−1.04337
$596$	3.70451	+	11.4013i	0.151743	+	0.467016i
$597$	9.92494	+	7.21089i	0.406201	+	0.295122i
$598$	5.18924	−	3.77020i	0.212204	−	0.154175i
$599$	9.87255	−	30.3846i	0.403381	−	1.24148i	−0.518858	−	0.854861i	$-0.673643\pi$
$599$	9.87255	−	30.3846i	0.403381	−	1.24148i	0.922239	−	0.386620i	$-0.126357\pi$
$600$	−2.56243	+	7.88636i	−0.104611	+	0.321959i
$601$	4.67594	−	3.39727i	0.190735	−	0.138577i	−0.488319	−	0.872665i	$-0.662390\pi$
$601$	4.67594	−	3.39727i	0.190735	−	0.138577i	0.679055	+	0.734088i	$0.262390\pi$
$602$	11.8493	+	8.60899i	0.482940	+	0.350876i
$603$	−3.37261	−	10.3798i	−0.137343	−	0.422700i
$604$	−29.9804			−1.21989
$605$	−17.1719	+	0.509819i	−0.698138	+	0.0207271i
$606$	10.4720			0.425394
$607$	14.9449	+	45.9955i	0.606593	+	1.86690i	0.485447	+	0.874266i	$0.338657\pi$
$607$	14.9449	+	45.9955i	0.606593	+	1.86690i	0.121146	+	0.992635i	$0.461343\pi$
$608$	−4.10623	−	2.98335i	−0.166530	−	0.120991i
$609$	−16.4382	+	11.9431i	−0.666111	+	0.483958i
$610$	4.25433	−	13.0935i	0.172253	−	0.530139i
$611$	−1.90957	+	5.87706i	−0.0772531	+	0.237761i
$612$	6.39300	−	4.64478i	0.258422	−	0.187754i
$613$	−23.4567	−	17.0423i	−0.947407	−	0.688332i	0.00278502	−	0.999996i	$-0.499113\pi$
$613$	−23.4567	−	17.0423i	−0.947407	−	0.688332i	−0.950192	+	0.311665i	$0.899113\pi$
$614$	−0.616424	−	1.89716i	−0.0248768	−	0.0765630i
$615$	−7.26035			−0.292765
$616$	25.0789	+	17.6583i	1.01046	+	0.711473i
$617$	−9.12126			−0.367208			−0.183604	−	0.983000i	$-0.558776\pi$
$617$	−9.12126			−0.367208			−0.183604	+	0.983000i	$0.558776\pi$
$618$	4.11359	+	12.6603i	0.165473	+	0.509273i
$619$	−19.7915	−	14.3794i	−0.795490	−	0.577957i	0.114098	−	0.993470i	$-0.463602\pi$
$619$	−19.7915	−	14.3794i	−0.795490	−	0.577957i	−0.909587	+	0.415513i	$0.863602\pi$
$620$	−10.1788	+	7.39536i	−0.408792	+	0.297005i
$621$	−16.2760	+	50.0922i	−0.653132	+	2.01013i
$622$	−4.82475	+	14.8490i	−0.193455	+	0.595392i
$623$	−1.18955	+	0.864260i	−0.0476584	+	0.0346258i
$624$	−1.51324	−	1.09943i	−0.0605779	−	0.0440124i
$625$	−1.74211	−	5.36167i	−0.0696844	−	0.214467i
$626$	11.1824			0.446941
$627$	−1.14445	+	3.70862i	−0.0457048	+	0.148108i
$628$	−1.39414			−0.0556322
$629$	−12.4703	−	38.3796i	−0.497223	−	1.53030i
$630$	−4.00935	−	2.91297i	−0.159736	−	0.116055i
$631$	18.2181	−	13.2363i	0.725253	−	0.526927i	−0.162805	−	0.986658i	$-0.552054\pi$
$631$	18.2181	−	13.2363i	0.725253	−	0.526927i	0.888058	+	0.459731i	$0.152054\pi$
$632$	−0.848416	+	2.61115i	−0.0337482	+	0.103866i
$633$	2.33991	−	7.20150i	0.0930030	−	0.286234i
$634$	16.2702	−	11.8210i	0.646172	−	0.469472i
$635$	−23.4126	−	17.0102i	−0.929099	−	0.675030i
$636$	−4.19063	−	12.8974i	−0.166169	−	0.511417i
$637$	7.59205			0.300808
$638$	2.92309	+	8.56188i	0.115726	+	0.338968i
$639$	−4.74207			−0.187593
$640$	−5.20809	−	16.0288i	−0.205868	−	0.633596i
$641$	−23.3904	−	16.9941i	−0.923864	−	0.671226i	0.0206188	−	0.999787i	$-0.493436\pi$
$641$	−23.3904	−	16.9941i	−0.923864	−	0.671226i	−0.944483	+	0.328561i	$0.893436\pi$
$642$	1.73849	−	1.26309i	0.0686129	−	0.0498502i
$643$	−0.322388	+	0.992208i	−0.0127137	+	0.0391289i	−0.957212	−	0.289387i	$-0.906548\pi$
$643$	−0.322388	+	0.992208i	−0.0127137	+	0.0391289i	0.944498	+	0.328516i	$0.106548\pi$
$644$	16.8838	−	51.9630i	0.665316	−	2.04763i
$645$	−9.44661	+	6.86336i	−0.371960	+	0.270245i
$646$	2.07120	+	1.50482i	0.0814904	+	0.0592062i
$647$	11.5319	+	35.4916i	0.453367	+	1.39532i	0.873042	+	0.487645i	$0.162144\pi$
$647$	11.5319	+	35.4916i	0.453367	+	1.39532i	−0.419675	+	0.907674i	$0.637856\pi$
$648$	−9.44193			−0.370914
$649$	15.9934	−	0.237362i	0.627795	−	0.00931729i
$650$	1.75654			0.0688972
$651$	−8.31582	−	25.5935i	−0.325923	−	1.00309i
$652$	−26.5775	−	19.3097i	−1.04086	−	0.756226i
$653$	23.0429	−	16.7417i	0.901740	−	0.655153i	−0.0371721	−	0.999309i	$-0.511835\pi$
$653$	23.0429	−	16.7417i	0.901740	−	0.655153i	0.938912	+	0.344156i	$0.111835\pi$
$654$	1.71663	−	5.28324i	0.0671255	−	0.206591i
$655$	−6.27729	+	19.3195i	−0.245274	+	0.754876i
$656$	−3.93236	+	2.85703i	−0.153533	+	0.111548i
$657$	11.9820	+	8.70543i	0.467462	+	0.339631i
$658$	−5.00340	−	15.3989i	−0.195053	−	0.600311i
$659$	11.1856			0.435731			0.217865	−	0.975979i	$-0.430091\pi$
$659$	11.1856			0.435731			0.217865	+	0.975979i	$0.430091\pi$
$660$	−8.47943	+	6.35504i	−0.330061	+	0.247369i
$661$	−8.49976			−0.330602			−0.165301	−	0.986243i	$-0.552860\pi$
$661$	−8.49976			−0.330602			−0.165301	+	0.986243i	$0.552860\pi$
$662$	−7.05571	−	21.7153i	−0.274228	−	0.843987i
$663$	4.61611	+	3.35380i	0.179275	+	0.130251i
$664$	−8.48928	+	6.16782i	−0.329448	+	0.239358i
$665$	−1.61299	+	4.96426i	−0.0625489	+	0.192506i
$666$	2.42826	−	7.47343i	0.0940933	−	0.289590i
$667$	30.0868	−	21.8593i	1.16496	−	0.846396i
$668$	−4.18379	−	3.03970i	−0.161876	−	0.117610i
$669$	−0.797477	−	2.45438i	−0.0308322	−	0.0948919i
$670$	9.65389			0.372962
$671$	−34.1081	+	25.5629i	−1.31673	+	0.986843i
$672$	29.6393			1.14336
$673$	−10.4425	−	32.1388i	−0.402530	−	1.23886i	−0.922940	−	0.384944i	$-0.874221\pi$
$673$	−10.4425	−	32.1388i	−0.402530	−	1.23886i	0.520409	−	0.853917i	$-0.325779\pi$
$674$	5.55158	+	4.03346i	0.213839	+	0.155363i
$675$	−11.6690	+	8.47804i	−0.449141	+	0.326320i
$676$	−0.472647	+	1.45466i	−0.0181787	+	0.0559484i
$677$	−5.09244	+	15.6729i	−0.195718	+	0.602359i	0.804249	+	0.594292i	$0.202568\pi$
$677$	−5.09244	+	15.6729i	−0.195718	+	0.602359i	−0.999967	+	0.00806675i	$0.997432\pi$
$678$	10.1940	−	7.40639i	0.391499	−	0.284441i
$679$	16.2131	+	11.7795i	0.622201	+	0.452056i
$680$	4.98434	+	15.3402i	0.191141	+	0.588271i
$681$	15.2487			0.584331
$682$	−11.9809	+	0.177811i	−0.458770	+	0.00680874i
$683$	36.7207			1.40508			0.702539	−	0.711645i	$-0.252050\pi$
$683$	36.7207			1.40508			0.702539	+	0.711645i	$0.252050\pi$
$684$	−0.500818	−	1.54136i	−0.0191493	−	0.0589354i
$685$	0.273790	+	0.198920i	0.0104610	+	0.00760034i
$686$	−1.25501	+	0.911816i	−0.0479164	+	0.0348133i
$687$	2.79778	−	8.61068i	0.106742	−	0.328518i
$688$	−2.41568	+	7.43470i	−0.0920969	+	0.283445i
$689$	−5.36295	+	3.89641i	−0.204312	+	0.148441i
$690$	−10.8397	−	7.87550i	−0.412660	−	0.299815i
$691$	3.43086	+	10.5591i	0.130516	+	0.401687i	0.994866	−	0.101205i	$-0.0322696\pi$
$691$	3.43086	+	10.5591i	0.130516	+	0.401687i	−0.864350	+	0.502891i	$0.832270\pi$
$692$	17.1597			0.652312
$693$	4.95743	+	14.5206i	0.188317	+	0.551591i
$694$	2.28470			0.0867259
$695$	−2.44564	−	7.52692i	−0.0927686	−	0.285512i
$696$	10.4180	+	7.56910i	0.394892	+	0.286906i
$697$	11.9956	−	8.71533i	0.454367	−	0.330117i
$698$	6.84103	−	21.0545i	0.258937	−	0.796926i
$699$	4.37863	−	13.4761i	0.165615	−	0.509711i
$700$	12.1048	−	8.79467i	0.457519	−	0.332407i
$701$	−1.34499	−	0.977191i	−0.0507995	−	0.0369080i	0.562096	−	0.827072i	$-0.309995\pi$
$701$	−1.34499	−	0.977191i	−0.0507995	−	0.0369080i	−0.612895	+	0.790164i	$0.709995\pi$
$702$	1.19383	+	3.67423i	0.0450582	+	0.138675i
$703$	−8.27647			−0.312153
$704$	1.15612	−	3.74644i	0.0435728	−	0.141199i
$705$	12.9083			0.486153
$706$	−0.00587562	−	0.0180833i	−0.000221132	−	0.000680574i
$707$	−35.2758	−	25.6294i	−1.32668	−	0.963891i
$708$	7.98180	−	5.79912i	0.299974	−	0.217944i
$709$	−4.50741	+	13.8724i	−0.169279	+	0.520988i	−0.999326	−	0.0367056i	$-0.988314\pi$
$709$	−4.50741	+	13.8724i	−0.169279	+	0.520988i	0.830047	+	0.557694i	$0.188314\pi$
$710$	1.29619	−	3.98926i	0.0486451	−	0.149714i
$711$	−1.11114	+	0.807288i	−0.0416709	+	0.0302757i
$712$	0.753896	+	0.547738i	0.0282535	+	0.0205273i
$713$	15.2204	+	46.8435i	0.570008	+	1.75430i
$714$	−14.9502			−0.559497
$715$	4.23527	+	2.98209i	0.158390	+	0.111524i
$716$	−6.00315			−0.224348
$717$	6.15887	+	18.9551i	0.230007	+	0.707889i
$718$	−8.42435	−	6.12064i	−0.314394	−	0.228420i
$719$	−22.5973	+	16.4179i	−0.842737	+	0.612284i	−0.923134	−	0.384479i	$-0.874381\pi$
$719$	−22.5973	+	16.4179i	−0.842737	+	0.612284i	0.0803968	+	0.996763i	$0.474381\pi$
$720$	0.817377	−	2.51563i	0.0304619	−	0.0937520i
$721$	17.1282	−	52.7152i	0.637888	−	1.96322i
$722$	−10.1186	+	7.35163i	−0.376577	+	0.273599i
$723$	7.26420	+	5.27775i	0.270159	+	0.196282i
$724$	6.84262	+	21.0594i	0.254304	+	0.782667i
$725$	10.1843			0.378235
$726$	−10.0872	+	0.299479i	−0.374369	+	0.0111147i
$727$	6.68933			0.248093			0.124047	−	0.992276i	$-0.460413\pi$
$727$	6.68933			0.248093			0.124047	+	0.992276i	$0.460413\pi$
$728$	−2.85777	−	8.79531i	−0.105916	−	0.325976i
$729$	−22.1049	−	16.0602i	−0.818701	−	0.594821i
$730$	−10.5986	+	7.70032i	−0.392271	+	0.285001i
$731$	7.36900	−	22.6794i	0.272552	−	0.838830i
$732$	−8.12445	+	25.0045i	−0.300288	+	0.924192i
$733$	35.7200	−	25.9521i	1.31935	−	0.958562i	0.319407	−	0.947618i	$-0.396516\pi$
$733$	35.7200	−	25.9521i	1.31935	−	0.958562i	0.999940	−	0.0109440i	$-0.00348365\pi$
$734$	8.69639	+	6.31830i	0.320990	+	0.233213i
$735$	−4.90067	−	15.0827i	−0.180764	−	0.556334i
$736$	−54.2486			−1.99963
$737$	−24.4387	−	17.2075i	−0.900211	−	0.633846i
$738$	2.88725			0.106281
$739$	−0.101515	−	0.312432i	−0.00373430	−	0.0114930i	0.949172	−	0.314758i	$-0.101923\pi$
$739$	−0.101515	−	0.312432i	−0.00373430	−	0.0114930i	−0.952906	+	0.303265i	$0.901923\pi$
$740$	−18.2811	−	13.2820i	−0.672027	−	0.488256i
$741$	0.946731	−	0.687840i	0.0347790	−	0.0252684i
$742$	5.36732	−	16.5189i	0.197040	−	0.606428i
$743$	7.74105	−	23.8245i	0.283992	−	0.874036i	−0.702707	−	0.711479i	$-0.748026\pi$
$743$	7.74105	−	23.8245i	0.283992	−	0.874036i	0.986699	−	0.162557i	$-0.0519743\pi$
$744$	−13.7978	+	10.0247i	−0.505851	+	0.367522i
$745$	−9.90305	−	7.19499i	−0.362820	−	0.263604i
$746$	5.93976	+	18.2807i	0.217470	+	0.669304i
$747$	−5.24924			−0.192060
$748$	6.38121	−	20.6786i	0.233320	−	0.756084i
$749$	−8.94760			−0.326938
$750$	−3.34764	−	10.3030i	−0.122239	−	0.376212i
$751$	−22.4459	−	16.3079i	−0.819062	−	0.595083i	0.0973819	−	0.995247i	$-0.468953\pi$
$751$	−22.4459	−	16.3079i	−0.819062	−	0.595083i	−0.916444	+	0.400164i	$0.868953\pi$
$752$	6.99140	−	5.07955i	0.254950	−	0.185232i
$753$	0.938162	−	2.88736i	0.0341885	−	0.105221i
$754$	0.842939	−	2.59430i	0.0306980	−	0.0944788i
$755$	24.7661	−	17.9936i	0.901331	−	0.654855i
$756$	26.6232	+	19.3429i	0.968276	+	0.703493i
$757$	−4.62222	−	14.2257i	−0.167998	−	0.517043i	0.831247	−	0.555903i	$-0.187627\pi$
$757$	−4.62222	−	14.2257i	−0.167998	−	0.517043i	−0.999245	+	0.0388597i	$0.987627\pi$
$758$	−0.232955			−0.00846131
$759$	13.4029	+	39.2579i	0.486496	+	1.42497i
$760$	3.30808			0.119997
$761$	9.96652	+	30.6738i	0.361286	+	1.11192i	0.952274	+	0.305244i	$0.0987379\pi$
$761$	9.96652	+	30.6738i	0.361286	+	1.11192i	−0.590988	+	0.806680i	$0.701262\pi$
$762$	−13.7530	−	9.99217i	−0.498220	−	0.361978i
$763$	−18.7130	+	13.5958i	−0.677455	+	0.492200i
$764$	2.48182	−	7.63827i	0.0897892	−	0.276343i
$765$	−2.49340	+	7.67389i	−0.0901490	+	0.277450i
$766$	−21.2066	+	15.4075i	−0.766227	+	0.556696i
$767$	−3.90166	−	2.83472i	−0.140881	−	0.102356i
$768$	−4.03654	−	12.4232i	−0.145656	−	0.448284i
$769$	39.5839			1.42743			0.713716	−	0.700435i	$-0.247011\pi$
$769$	39.5839			1.42743			0.713716	+	0.700435i	$0.247011\pi$
$770$	−13.5705	+	0.201403i	−0.489046	+	0.00725807i
$771$	2.71097			0.0976332
$772$	−7.66172	−	23.5804i	−0.275751	−	0.848676i
$773$	12.5442	+	9.11389i	0.451183	+	0.327804i	0.790063	−	0.613026i	$-0.210048\pi$
$773$	12.5442	+	9.11389i	0.451183	+	0.327804i	−0.338880	+	0.940830i	$0.610048\pi$
$774$	3.75667	−	2.72938i	0.135031	−	0.0981056i
$775$	−4.16810	+	12.8281i	−0.149723	+	0.460799i
$776$	3.92481	−	12.0793i	0.140892	−	0.433622i
$777$	39.1007	−	28.4083i	1.40273	−	1.01914i
$778$	7.51154	+	5.45745i	0.269302	+	0.195659i
$779$	−0.939720	−	2.89216i	−0.0336690	−	0.103622i
$780$	3.19498			0.114399
$781$	−10.3919	+	7.78837i	−0.371852	+	0.278690i
$782$	27.3632			0.978508
$783$	6.92172	+	21.3029i	0.247362	+	0.761303i
$784$	−8.58953	−	6.24066i	−0.306769	−	0.222881i
$785$	1.15166	−	0.836733i	0.0411047	−	0.0298643i
$786$	−3.68741	+	11.3487i	−0.131526	+	0.404795i
$787$	6.89985	−	21.2355i	0.245953	−	0.756965i	−0.749525	−	0.661976i	$-0.769718\pi$
$787$	6.89985	−	21.2355i	0.245953	−	0.756965i	0.995478	−	0.0949897i	$-0.0302818\pi$
$788$	−0.631075	+	0.458503i	−0.0224811	+	0.0163335i
$789$	−26.0408	−	18.9197i	−0.927076	−	0.673560i
$790$	−0.375414	−	1.15541i	−0.0133566	−	0.0411075i
$791$	−52.4661			−1.86548
$792$	7.78134	−	5.83184i	0.276498	−	0.207226i
$793$	12.8517			0.456377
$794$	3.95105	+	12.1601i	0.140218	+	0.431545i
$795$	11.2026	+	8.13914i	0.397314	+	0.288665i
$796$	−11.3498	+	8.24608i	−0.402282	+	0.292275i
$797$	1.36800	−	4.21028i	0.0484572	−	0.149136i	−0.923900	−	0.382634i	$-0.875017\pi$
$797$	1.36800	−	4.21028i	0.0484572	−	0.149136i	0.972357	+	0.233498i	$0.0750172\pi$
$798$	−0.947502	+	2.91611i	−0.0335412	+	0.103229i
$799$	−21.3272	+	15.4951i	−0.754501	+	0.548177i
$800$	−12.0187	−	8.73212i	−0.424926	−	0.308727i
$801$	0.144052	+	0.443347i	0.00508984	+	0.0156649i
$802$	−4.30823			−0.152129
$803$	40.5555	−	0.601896i	1.43117	−	0.0212405i
$804$	−18.4359			−0.650185
$805$	17.2398	+	53.0587i	0.607624	+	1.87008i
$806$	2.92278	+	2.12353i	0.102951	+	0.0747981i
$807$	5.63173	−	4.09169i	0.198246	−	0.144034i
$808$	−8.53945	+	26.2817i	−0.300417	+	0.924587i
$809$	−1.53772	+	4.73262i	−0.0540634	+	0.166390i	−0.974442	−	0.224637i	$-0.927880\pi$
$809$	−1.53772	+	4.73262i	−0.0540634	+	0.166390i	0.920379	+	0.391027i	$0.127880\pi$
$810$	3.38003	−	2.45573i	0.118762	−	0.0862857i
$811$	−8.82588	−	6.41238i	−0.309918	−	0.225169i	0.421943	−	0.906622i	$-0.361348\pi$
$811$	−8.82588	−	6.41238i	−0.309918	−	0.225169i	−0.731862	+	0.681453i	$0.761348\pi$
$812$	−7.18023	−	22.0985i	−0.251977	−	0.775504i
$813$	7.50150			0.263089
$814$	−6.95299	−	20.3657i	−0.243702	−	0.713817i
$815$	33.5443			1.17501
$816$	−2.46577	−	7.58887i	−0.0863193	−	0.265664i
$817$	−3.95671	−	2.87472i	−0.138428	−	0.100574i
$818$	1.95146	−	1.41782i	0.0682312	−	0.0495729i
$819$	1.42959	−	4.39982i	0.0499538	−	0.153742i
$820$	2.56566	−	7.89627i	0.0895966	−	0.275750i
$821$	25.2282	−	18.3293i	0.880470	−	0.639699i	−0.0529061	−	0.998599i	$-0.516848\pi$
$821$	25.2282	−	18.3293i	0.880470	−	0.639699i	0.933376	+	0.358901i	$0.116848\pi$
$822$	0.160830	+	0.116850i	0.00560959	+	0.00407561i
$823$	13.9100	+	42.8107i	0.484873	+	1.49229i	0.832164	+	0.554529i	$0.187102\pi$
$823$	13.9100	+	42.8107i	0.484873	+	1.49229i	−0.347291	+	0.937757i	$0.612898\pi$
$824$	−35.1284			−1.22375
$825$	−3.34973	+	10.8550i	−0.116623	+	0.377921i
$826$	12.6363			0.439674
$827$	8.43468	+	25.9593i	0.293303	+	0.902693i	0.983786	+	0.179345i	$0.0573977\pi$
$827$	8.43468	+	25.9593i	0.293303	+	0.902693i	−0.690484	+	0.723348i	$0.742602\pi$
$828$	−14.0139	−	10.1817i	−0.487015	−	0.353837i
$829$	21.9647	−	15.9583i	0.762867	−	0.554255i	−0.136922	−	0.990582i	$-0.543721\pi$
$829$	21.9647	−	15.9583i	0.762867	−	0.554255i	0.899788	+	0.436327i	$0.143721\pi$
$830$	1.43482	−	4.41592i	0.0498033	−	0.153279i
$831$	−0.129531	+	0.398657i	−0.00449340	+	0.0138293i
$832$	−0.956385	+	0.694854i	−0.0331567	+	0.0240897i
$833$	26.2022	+	19.0370i	0.907854	+	0.659595i
$834$	−1.43662	−	4.42147i	−0.0497462	−	0.153103i
$835$	5.28050			0.182739
$836$	−3.62904	−	2.55524i	−0.125513	−	0.0883747i
$837$	−29.6659			−1.02540
$838$	5.79465	+	17.8341i	0.200173	+	0.616069i
$839$	−15.9756	−	11.6069i	−0.551538	−	0.400716i	0.276814	−	0.960924i	$-0.410721\pi$
$839$	−15.9756	−	11.6069i	−0.551538	−	0.400716i	−0.828352	+	0.560207i	$0.810721\pi$
$840$	−15.6285	+	11.3547i	−0.539233	+	0.391776i
$841$	−4.07421	+	12.5391i	−0.140490	+	0.432383i
$842$	0.707261	−	2.17672i	0.0243738	−	0.0750149i
$843$	2.92584	−	2.12575i	0.100771	−	0.0732145i
$844$	7.00540	+	5.08972i	0.241136	+	0.175195i
$845$	−0.482614	−	1.48533i	−0.0166024	−	0.0510970i
$846$	−5.13328			−0.176486
$847$	34.7125	+	23.6787i	1.19273	+	0.813611i
$848$	9.27040			0.318347
$849$	4.24515	+	13.0652i	0.145693	+	0.448398i
$850$	6.06231	+	4.40452i	0.207935	+	0.151074i
$851$	−71.5658	+	51.9956i	−2.45324	+	1.78238i
$852$	−2.47532	+	7.61825i	−0.0848030	+	0.260997i
$853$	11.8416	−	36.4446i	0.405448	−	1.24784i	−0.515073	−	0.857146i	$-0.672235\pi$
$853$	11.8416	−	36.4446i	0.405448	−	1.24784i	0.920521	−	0.390693i	$-0.127765\pi$
$854$	−27.2425	+	19.7928i	−0.932219	+	0.677297i
$855$	1.33881	+	0.972700i	0.0457862	+	0.0332656i
$856$	1.75234	+	5.39313i	0.0598936	+	0.184334i
$857$	−11.5923			−0.395985			−0.197992	−	0.980204i	$-0.563442\pi$
$857$	−11.5923			−0.395985			−0.197992	+	0.980204i	$0.563442\pi$
$858$	2.48789	+	1.75175i	0.0849352	+	0.0598036i
$859$	49.6805			1.69508			0.847539	−	0.530734i	$-0.178084\pi$
$859$	49.6805			1.69508			0.847539	+	0.530734i	$0.178084\pi$
$860$	−4.12628	−	12.6994i	−0.140705	−	0.433046i
$861$	14.3667	+	10.4380i	0.489614	+	0.355726i
$862$	−2.01031	+	1.46058i	−0.0684715	+	0.0497474i
$863$	−4.87825	+	15.0137i	−0.166057	+	0.511072i	−0.999113	−	0.0421177i	$-0.986590\pi$
$863$	−4.87825	+	15.0137i	−0.166057	+	0.511072i	0.833055	+	0.553190i	$0.186590\pi$
$864$	10.0968	−	31.0748i	0.343501	−	1.05719i
$865$	−14.1752	+	10.2989i	−0.481971	+	0.350172i
$866$	−11.8815	−	8.63243i	−0.403751	−	0.293342i
$867$	0.495492	+	1.52497i	0.0168278	+	0.0517906i
$868$	30.7738			1.04453
$869$	−1.10909	+	3.59405i	−0.0376233	+	0.121920i
$870$	−5.69807			−0.193183
$871$	2.78481	+	8.57078i	0.0943598	+	0.290410i
$872$	11.8596	+	8.61652i	0.401618	+	0.291792i
$873$	5.14017	−	3.73455i	0.173968	−	0.126395i
$874$	1.73421	−	5.33734i	0.0586604	−	0.180538i
$875$	−13.9389	+	42.8996i	−0.471222	+	1.45027i
$876$	20.2400	−	14.7052i	0.683846	−	0.496843i
$877$	−18.2132	−	13.2327i	−0.615016	−	0.446835i	0.236161	−	0.971714i	$-0.424111\pi$
$877$	−18.2132	−	13.2327i	−0.615016	−	0.446835i	−0.851177	+	0.524879i	$0.824111\pi$
$878$	6.26459	+	19.2804i	0.211420	+	0.650683i
$879$	4.50773			0.152042
$880$	−2.34044	−	6.85529i	−0.0788964	−	0.231092i
$881$	−58.0386			−1.95537			−0.977686	−	0.210073i	$-0.932630\pi$
$881$	−58.0386			−1.95537			−0.977686	+	0.210073i	$0.932630\pi$
$882$	1.94887	+	5.99800i	0.0656218	+	0.201963i
$883$	−0.657817	−	0.477932i	−0.0221373	−	0.0160837i	0.576662	−	0.816983i	$-0.304355\pi$
$883$	−0.657817	−	0.477932i	−0.0221373	−	0.0160837i	−0.598799	+	0.800899i	$0.704355\pi$
$884$	−5.27879	+	3.83527i	−0.177545	+	0.128994i
$885$	−3.11306	+	9.58102i	−0.104644	+	0.322063i
$886$	−1.88466	+	5.80037i	−0.0633162	+	0.194867i
$887$	−31.3901	+	22.8062i	−1.05397	+	0.765758i	−0.972964	−	0.230956i	$-0.925815\pi$
$887$	−31.3901	+	22.8062i	−1.05397	+	0.765758i	−0.0810106	+	0.996713i	$0.525815\pi$
$888$	−24.7807	−	18.0042i	−0.831585	−	0.604182i
$889$	21.8733	+	67.3191i	0.733607	+	2.25781i
$890$	−0.412340			−0.0138217
$891$	−12.9337	+	0.191953i	−0.433295	+	0.00643066i
$892$	2.95117			0.0988125
$893$	1.67074	+	5.14201i	0.0559092	+	0.172071i
$894$	−5.81726	−	4.22649i	−0.194558	−	0.141355i
$895$	4.95906	−	3.60297i	0.165763	−	0.120434i
$896$	−12.7385	+	39.2051i	−0.425564	+	1.30975i
$897$	3.86504	−	11.8954i	0.129050	−	0.397175i
$898$	9.91062	−	7.20049i	0.330722	−	0.240283i
$899$	16.9461	+	12.3120i	0.565183	+	0.410629i
$900$	−1.46587	−	4.51148i	−0.0488623	−	0.150383i
$901$	−28.2792			−0.942118
$902$	6.32721	−	4.74202i	0.210673	−	0.157892i
$903$	28.5600			0.950419
$904$	10.2752	+	31.6238i	0.341747	+	1.05179i
$905$	−18.2920	−	13.2899i	−0.608045	−	0.441771i
$906$	14.5481	−	10.5698i	0.483330	−	0.351160i
$907$	13.0348	−	40.1170i	0.432813	−	1.33206i	−0.462497	−	0.886621i	$-0.653047\pi$
$907$	13.0348	−	40.1170i	0.432813	−	1.33206i	0.895311	−	0.445442i	$-0.146953\pi$
$908$	−5.38857	+	16.5843i	−0.178826	+	0.550370i
$909$	−11.1838	+	8.12549i	−0.370943	+	0.269506i
$910$	3.31058	+	2.40528i	0.109745	+	0.0797342i
$911$	1.29294	+	3.97926i	0.0428370	+	0.131839i	0.970188	−	0.242355i	$-0.0779197\pi$
$911$	1.29294	+	3.97926i	0.0428370	+	0.131839i	−0.927351	+	0.374193i	$0.877920\pi$
$912$	−1.63652			−0.0541906
$913$	−11.5034	+	8.62136i	−0.380705	+	0.285325i
$914$	−26.4564			−0.875101
$915$	−8.29576	−	25.5317i	−0.274249	−	0.844053i
$916$	8.37620	+	6.08567i	0.276758	+	0.201076i
$917$	40.1965	−	29.2045i	1.32741	−	0.964416i
$918$	−5.09289	+	15.6743i	−0.168090	+	0.517329i
$919$	6.26223	−	19.2732i	0.206572	−	0.635763i	−0.793073	−	0.609126i	$-0.791520\pi$
$919$	6.26223	−	19.2732i	0.206572	−	0.635763i	0.999645	−	0.0266368i	$-0.00847976\pi$
$920$	28.6046	−	20.7825i	0.943067	−	0.685178i
$921$	−3.14688	−	2.28634i	−0.103693	−	0.0753375i
$922$	−4.84750	−	14.9191i	−0.159644	−	0.491334i
$923$	3.91559			0.128883
$924$	25.9154	−	0.384618i	0.852554	−	0.0126530i
$925$	−24.2248			−0.796506
$926$	6.35052	+	19.5449i	0.208691	+	0.642285i
$927$	−14.2167	−	10.3291i	−0.466938	−	0.339251i
$928$	−18.6644	+	13.5605i	−0.612688	+	0.445144i
$929$	12.0276	−	37.0173i	0.394614	−	1.21450i	−0.534648	−	0.845075i	$-0.679556\pi$
$929$	12.0276	−	37.0173i	0.394614	−	1.21450i	0.929262	−	0.369422i	$-0.120444\pi$
$930$	2.33204	−	7.17727i	0.0764705	−	0.235352i
$931$	5.37390	−	3.90436i	0.176122	−	0.127960i
$932$	13.1091	+	9.52431i	0.429403	+	0.311979i
$933$	9.40806	+	28.9550i	0.308006	+	0.947945i
$934$	−25.7196			−0.841570
$935$	7.13950	+	20.9120i	0.233486	+	0.683894i
$936$	−2.93195			−0.0958338
$937$	−4.34344	−	13.3677i	−0.141894	−	0.436705i	0.854705	−	0.519115i	$-0.173738\pi$
$937$	−4.34344	−	13.3677i	−0.141894	−	0.436705i	−0.996598	+	0.0824102i	$0.973738\pi$
$938$	−19.1030	−	13.8791i	−0.623734	−	0.453169i
$939$	17.6409	−	12.8168i	0.575688	−	0.418262i
$940$	−4.56151	+	14.0389i	−0.148780	+	0.457898i
$941$	−1.23673	+	3.80626i	−0.0403162	+	0.124080i	−0.969189	−	0.246319i	$-0.920779\pi$
$941$	−1.23673	+	3.80626i	−0.0403162	+	0.124080i	0.928873	+	0.370399i	$0.120779\pi$
$942$	0.676512	−	0.491515i	0.0220420	−	0.0160144i
$943$	−26.2952	−	19.1046i	−0.856289	−	0.622130i
$944$	2.08414	+	6.41432i	0.0678330	+	0.208768i
$945$	−33.6020			−1.09307
$946$	3.74974	−	12.1512i	0.121915	−	0.395070i
$947$	17.8840			0.581152			0.290576	−	0.956852i	$-0.406153\pi$
$947$	17.8840			0.581152			0.290576	+	0.956852i	$0.406153\pi$
$948$	0.716925	+	2.20647i	0.0232846	+	0.0716627i
$949$	−9.89371	−	7.18820i	−0.321163	−	0.233339i
$950$	1.24334	−	0.903337i	0.0403392	−	0.0293081i
$951$	12.1183	−	37.2964i	0.392964	−	1.20942i
$952$	12.1913	−	37.5209i	0.395121	−	1.21606i
$953$	−23.0339	+	16.7351i	−0.746142	+	0.542104i	−0.894629	−	0.446811i	$-0.852560\pi$
$953$	−23.0339	+	16.7351i	−0.746142	+	0.542104i	0.148487	+	0.988914i	$0.452560\pi$
$954$	−4.45497	−	3.23672i	−0.144235	−	0.104793i
$955$	2.53416	+	7.79933i	0.0820033	+	0.252380i
$956$	−22.7917			−0.737137
$957$	14.4246	+	10.1565i	0.466280	+	0.328312i
$958$	−22.5142			−0.727400
$959$	−0.255790	−	0.787239i	−0.00825988	−	0.0254213i
$960$	1.99777	+	1.45147i	0.0644779	+	0.0468459i
$961$	2.63584	−	1.91505i	0.0850271	−	0.0617758i
$962$	−2.00505	+	6.17092i	−0.0646455	+	0.198958i
$963$	−0.876599	+	2.69789i	−0.0282480	+	0.0869384i
$964$	−8.30704	+	6.03542i	−0.267552	+	0.194388i
$965$	20.4816	+	14.8808i	0.659327	+	0.479029i
$966$	10.1270	+	31.1678i	0.325832	+	1.00281i
$967$	24.0015			0.771838			0.385919	−	0.922533i	$-0.373884\pi$
$967$	24.0015			0.771838			0.385919	+	0.922533i	$0.373884\pi$
$968$	7.47404	−	25.5602i	0.240225	−	0.821535i
$969$	4.99218			0.160372
$970$	1.73668	+	5.34496i	0.0557615	+	0.171616i
$971$	42.7055	+	31.0273i	1.37048	+	0.995715i	0.997699	+	0.0677967i	$0.0215969\pi$
$971$	42.7055	+	31.0273i	1.37048	+	0.995715i	0.372784	+	0.927918i	$0.378403\pi$
$972$	14.4537	−	10.5012i	0.463603	−	0.336827i
$973$	−5.98183	+	18.4102i	−0.191769	+	0.590203i
$974$	4.43447	−	13.6479i	0.142090	−	0.437307i
$975$	2.77103	−	2.01327i	0.0887441	−	0.0644763i
$976$	−14.5402	−	10.5641i	−0.465421	−	0.338148i
$977$	3.15753	+	9.71789i	0.101018	+	0.310903i	0.988775	−	0.149410i	$-0.0477373\pi$
$977$	3.15753	+	9.71789i	0.101018	+	0.310903i	−0.887757	+	0.460313i	$0.847737\pi$
$978$	19.7047			0.630086
$979$	1.04383	+	0.734973i	0.0333611	+	0.0234898i
$980$	18.1356			0.579320
$981$	2.26610	+	6.97435i	0.0723511	+	0.222674i
$982$	−3.31183	−	2.40618i	−0.105685	−	0.0767844i
$983$	6.75997	−	4.91141i	0.215610	−	0.156650i	−0.474739	−	0.880127i	$-0.657457\pi$
$983$	6.75997	−	4.91141i	0.215610	−	0.156650i	0.690348	+	0.723477i	$0.257457\pi$
$984$	3.47783	−	10.7037i	0.110869	−	0.341220i
$985$	0.246132	−	0.757516i	0.00784242	−	0.0241365i
$986$	9.41441	−	6.83997i	0.299816	−	0.217829i
$987$	−25.5427	−	18.5578i	−0.813032	−	0.590702i
$988$	0.413533	+	1.27272i	0.0131562	+	0.0404907i
$989$	−52.2732			−1.66219
$990$	−1.26878	+	4.11152i	−0.0403243	+	0.130673i
$991$	35.5083			1.12796			0.563978	−	0.825790i	$-0.309270\pi$
$991$	35.5083			1.12796			0.563978	+	0.825790i	$0.309270\pi$
$992$	−9.44200	−	29.0595i	−0.299784	−	0.922639i
$993$	−36.0198	−	26.1699i	−1.14305	−	0.830478i
$994$	−8.30011	+	6.03039i	−0.263264	+	0.191272i
$995$	4.42664	−	13.6238i	0.140334	−	0.431903i
$996$	−2.74006	+	8.43304i	−0.0868222	+	0.267211i
$997$	−32.5408	+	23.6423i	−1.03058	+	0.748759i	−0.968424	−	0.249307i	$-0.919797\pi$
$997$	−32.5408	+	23.6423i	−1.03058	+	0.748759i	−0.0621541	+	0.998067i	$0.519797\pi$
$998$	−6.65025	−	4.83169i	−0.210510	−	0.152944i
$999$	−16.4643	−	50.6720i	−0.520908	−	1.60319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.27.4	✓	28
11.3	even	5		1573.2.a.s.1.6		14
11.8	odd	10		1573.2.a.r.1.9		14
11.9	even	5	inner	143.2.h.c.53.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.27.4	✓	28	1.1	even	1	trivial
143.2.h.c.53.4	yes	28	11.9	even	5	inner
1573.2.a.r.1.9		14	11.8	odd	10
1573.2.a.s.1.6		14	11.3	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.211960 - 0.652345i) q^{2} +(-1.08207 - 0.786167i) q^{3} +(1.23741 - 0.899029i) q^{4} +(-0.482614 + 1.48533i) q^{5} +(-0.283498 + 0.872516i) q^{6} +(3.09041 - 2.24531i) q^{7} +(-1.95859 - 1.42300i) q^{8} +(-0.374242 - 1.15180i) q^{9} +O(q^{10})\)	\(q+(-0.211960 - 0.652345i) q^{2} +(-1.08207 - 0.786167i) q^{3} +(1.23741 - 0.899029i) q^{4} +(-0.482614 + 1.48533i) q^{5} +(-0.283498 + 0.872516i) q^{6} +(3.09041 - 2.24531i) q^{7} +(-1.95859 - 1.42300i) q^{8} +(-0.374242 - 1.15180i) q^{9} +1.07124 q^{10} +(-2.71184 - 1.90943i) q^{11} -2.04574 q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.11976 - 1.54010i) q^{14} +(1.68994 - 1.22781i) q^{15} +(0.432150 - 1.33002i) q^{16} +(-1.31827 + 4.05722i) q^{17} +(-0.672046 + 0.488270i) q^{18} +(0.707832 + 0.514270i) q^{19} +(0.738167 + 2.27185i) q^{20} -5.10922 q^{21} +(-0.670806 + 2.17378i) q^{22} +9.35137 q^{23} +(1.00061 + 3.07956i) q^{24} +(2.07179 + 1.50524i) q^{25} +(0.554918 - 0.403171i) q^{26} +(-1.74049 + 5.35668i) q^{27} +(1.80549 - 5.55673i) q^{28} +(3.21737 - 2.33755i) q^{29} +(-1.15916 - 0.842177i) q^{30} +(1.62761 + 5.00927i) q^{31} -5.80114 q^{32} +(1.43326 + 4.19809i) q^{33} +2.92612 q^{34} +(1.84356 + 5.67390i) q^{35} +(-1.49859 - 1.08879i) q^{36} +(-7.65297 + 5.56021i) q^{37} +(0.185450 - 0.570755i) q^{38} +(0.413313 - 1.27205i) q^{39} +(3.05887 - 2.22240i) q^{40} +(-2.81191 - 2.04297i) q^{41} +(1.08295 + 3.33297i) q^{42} -5.58990 q^{43} +(-5.07228 + 0.0752792i) q^{44} +1.89142 q^{45} +(-1.98211 - 6.10031i) q^{46} +(4.99933 + 3.63222i) q^{47} +(-1.51324 + 1.09943i) q^{48} +(2.34607 - 7.22047i) q^{49} +(0.542801 - 1.67057i) q^{50} +(4.61611 - 3.35380i) q^{51} +(1.23741 + 0.899029i) q^{52} +(2.04846 + 6.30452i) q^{53} +3.86331 q^{54} +(4.14491 - 3.10647i) q^{55} -9.24793 q^{56} +(-0.361619 - 1.11295i) q^{57} +(-2.20684 - 1.60336i) q^{58} +(-3.90166 + 2.83472i) q^{59} +(0.987305 - 3.03861i) q^{60} +(3.97139 - 12.2227i) q^{61} +(2.92278 - 2.12353i) q^{62} +(-3.74271 - 2.71924i) q^{63} +(0.365306 + 1.12430i) q^{64} -1.56177 q^{65} +(2.43481 - 1.82481i) q^{66} +9.01185 q^{67} +(2.01632 + 6.20559i) q^{68} +(-10.1188 - 7.35174i) q^{69} +(3.31058 - 2.40528i) q^{70} +(1.20998 - 3.72395i) q^{71} +(-0.906023 + 2.78845i) q^{72} +(-9.89371 + 7.18820i) q^{73} +(5.24930 + 3.81384i) q^{74} +(-1.05844 - 3.25754i) q^{75} +1.33822 q^{76} +(-12.6680 + 0.188009i) q^{77} -0.917418 q^{78} +(-0.350447 - 1.07856i) q^{79} +(1.76696 + 1.28377i) q^{80} +(3.15524 - 2.29241i) q^{81} +(-0.736710 + 2.26736i) q^{82} +(1.33940 - 4.12224i) q^{83} +(-6.32218 + 4.59334i) q^{84} +(-5.39010 - 3.91614i) q^{85} +(1.18483 + 3.64654i) q^{86} -5.31911 q^{87} +(2.59427 + 7.59875i) q^{88} -0.384917 q^{89} +(-0.400904 - 1.23386i) q^{90} +(3.09041 + 2.24531i) q^{91} +(11.5714 - 8.40715i) q^{92} +(2.17694 - 6.69994i) q^{93} +(1.30981 - 4.03117i) q^{94} +(-1.10547 + 0.803172i) q^{95} +(6.27722 + 4.56067i) q^{96} +(1.62118 + 4.98949i) q^{97} -5.20751 q^{98} +(-1.18439 + 3.83808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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