LMFDB - Embedded newform 117.2.e.b.40.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(40,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("117.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.487558322307.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 43x^{6} + 48x^{4} + 21x^{2} + 3 $ x^10 + 13x^8 + 43x^6 + 48x^4 + 21x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.5
Root			$-1.65737i$ of defining polynomial
Character	$\chi$	$=$	117.40
Dual form			117.2.e.b.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.786226 + 1.36178i) q^{2} +(-0.557959 - 1.63972i) q^{3} +(-0.236304 + 0.409291i) q^{4} +(0.557959 - 0.966413i) q^{5} +(1.79426 - 2.04901i) q^{6} +(1.93532 + 3.35208i) q^{7} +2.40175 q^{8} +(-2.37736 + 1.82979i) q^{9} +1.75473 q^{10} +(-2.48935 - 4.31168i) q^{11} +(0.802970 + 0.159105i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-3.04320 + 5.27098i) q^{14} +(-1.89596 - 0.375678i) q^{15} +(2.36093 + 4.08925i) q^{16} -4.37224 q^{17} +(-4.36093 - 1.79883i) q^{18} -6.30588 q^{19} +(0.263696 + 0.456735i) q^{20} +(4.41664 - 5.04371i) q^{21} +(3.91439 - 6.77992i) q^{22} +(-0.977469 + 1.69303i) q^{23} +(-1.34008 - 3.93820i) q^{24} +(1.87736 + 3.25169i) q^{25} -1.57245 q^{26} +(4.32682 + 2.87726i) q^{27} -1.82930 q^{28} +(1.08049 + 1.87146i) q^{29} +(-0.979066 - 2.87726i) q^{30} +(1.25490 - 2.17356i) q^{31} +(-1.31070 + 2.27020i) q^{32} +(-5.68100 + 6.48758i) q^{33} +(-3.43757 - 5.95405i) q^{34} +4.31932 q^{35} +(-0.187136 - 1.40542i) q^{36} +7.10248 q^{37} +(-4.95785 - 8.58725i) q^{38} +(1.69902 + 0.336654i) q^{39} +(1.34008 - 2.32108i) q^{40} +(-2.75305 + 4.76842i) q^{41} +(10.3409 + 2.04901i) q^{42} +(-3.94721 - 6.83676i) q^{43} +2.35298 q^{44} +(0.441864 + 3.31846i) q^{45} -3.07405 q^{46} +(-3.99982 - 6.92790i) q^{47} +(5.38792 - 6.15290i) q^{48} +(-3.99095 + 6.91253i) q^{49} +(-2.95207 + 5.11313i) q^{50} +(2.43953 + 7.16925i) q^{51} +(-0.236304 - 0.409291i) q^{52} +5.68016 q^{53} +(-0.516351 + 8.15437i) q^{54} -5.55582 q^{55} +(4.64816 + 8.05086i) q^{56} +(3.51842 + 10.3399i) q^{57} +(-1.69902 + 2.94279i) q^{58} +(2.34811 - 4.06705i) q^{59} +(0.601786 - 0.687227i) q^{60} +(-1.06675 - 1.84766i) q^{61} +3.94656 q^{62} +(-10.7346 - 4.42787i) q^{63} +5.32169 q^{64} +(0.557959 + 0.966413i) q^{65} +(-13.3012 - 2.63559i) q^{66} +(-1.16845 + 2.02382i) q^{67} +(1.03318 - 1.78952i) q^{68} +(3.32148 + 0.658137i) q^{69} +(3.39596 + 5.88198i) q^{70} +4.31876 q^{71} +(-5.70984 + 4.39471i) q^{72} +7.66241 q^{73} +(5.58416 + 9.67205i) q^{74} +(4.28437 - 4.89266i) q^{75} +(1.49011 - 2.58094i) q^{76} +(9.63540 - 16.6890i) q^{77} +(0.877364 + 2.57838i) q^{78} +(1.49553 + 2.59034i) q^{79} +5.26920 q^{80} +(2.30372 - 8.70017i) q^{81} -8.65808 q^{82} +(-6.98114 - 12.0917i) q^{83} +(1.02067 + 2.99954i) q^{84} +(-2.43953 + 4.22539i) q^{85} +(6.20679 - 10.7505i) q^{86} +(2.46581 - 2.81590i) q^{87} +(-5.97881 - 10.3556i) q^{88} +7.98729 q^{89} +(-4.17163 + 3.21079i) q^{90} -3.87065 q^{91} +(-0.461960 - 0.800138i) q^{92} +(-4.26421 - 0.844936i) q^{93} +(6.28953 - 10.8938i) q^{94} +(-3.51842 + 6.09409i) q^{95} +(4.45380 + 0.882502i) q^{96} +(-3.82682 - 6.62824i) q^{97} -12.5512 q^{98} +(13.8076 + 5.69544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.786226	+	1.36178i	0.555946	+	0.962927i	0.997829	+	0.0658542i	$0.0209772\pi$
$2$	0.786226	+	1.36178i	0.555946	+	0.962927i	−0.441883	+	0.897073i	$0.645689\pi$
$3$	−0.557959	−	1.63972i	−0.322138	−	0.946693i
$3$	−0.557959	−	1.63972i	−0.322138	−	0.946693i
$4$	−0.236304	+	0.409291i	−0.118152	+	0.204645i
$5$	0.557959	−	0.966413i	0.249527	−	0.432193i	−0.713868	−	0.700280i	$-0.753058\pi$
$5$	0.557959	−	0.966413i	0.249527	−	0.432193i	0.963395	+	0.268087i	$0.0863916\pi$
$6$	1.79426	−	2.04901i	0.732505	−	0.836505i
$7$	1.93532	+	3.35208i	0.731483	+	1.26697i	0.956249	+	0.292553i	$0.0945049\pi$
$7$	1.93532	+	3.35208i	0.731483	+	1.26697i	−0.224766	+	0.974413i	$0.572162\pi$
$8$	2.40175			0.849147
$9$	−2.37736	+	1.82979i	−0.792455	+	0.609931i
$10$	1.75473			0.554894
$11$	−2.48935	−	4.31168i	−0.750568	−	1.30002i	−0.947548	−	0.319614i	$-0.896447\pi$
$11$	−2.48935	−	4.31168i	−0.750568	−	1.30002i	0.196980	−	0.980408i	$-0.436887\pi$
$12$	0.802970	+	0.159105i	0.231798	+	0.0459297i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−3.04320	+	5.27098i	−0.813330	+	1.40873i
$15$	−1.89596	−	0.375678i	−0.489536	−	0.0969995i
$16$	2.36093	+	4.08925i	0.590232	+	1.02231i
$17$	−4.37224			−1.06042			−0.530212	−	0.847865i	$-0.677888\pi$
$17$	−4.37224			−1.06042			−0.530212	+	0.847865i	$0.677888\pi$
$18$	−4.36093	−	1.79883i	−1.02788	−	0.423987i
$19$	−6.30588			−1.44667			−0.723335	−	0.690498i	$-0.757392\pi$
$19$	−6.30588			−1.44667			−0.723335	+	0.690498i	$0.757392\pi$
$20$	0.263696	+	0.456735i	0.0589642	+	0.102129i
$21$	4.41664	−	5.04371i	0.963789	−	1.10063i
$22$	3.91439	−	6.77992i	0.834550	−	1.44548i
$23$	−0.977469	+	1.69303i	−0.203816	+	0.353020i	−0.949755	−	0.312994i	$-0.898668\pi$
$23$	−0.977469	+	1.69303i	−0.203816	+	0.353020i	0.745939	+	0.666015i	$0.232001\pi$
$24$	−1.34008	−	3.93820i	−0.273542	−	0.803882i
$25$	1.87736	+	3.25169i	0.375473	+	0.650338i
$26$	−1.57245			−0.308383
$27$	4.32682	+	2.87726i	0.832697	+	0.553729i
$28$	−1.82930			−0.345705
$29$	1.08049	+	1.87146i	0.200642	+	0.347522i	0.948735	−	0.316071i	$-0.102364\pi$
$29$	1.08049	+	1.87146i	0.200642	+	0.347522i	−0.748094	+	0.663593i	$0.769031\pi$
$30$	−0.979066	−	2.87726i	−0.178752	−	0.525314i
$31$	1.25490	−	2.17356i	0.225388	−	0.390383i	−0.731048	−	0.682326i	$-0.760968\pi$
$31$	1.25490	−	2.17356i	0.225388	−	0.390383i	0.956436	+	0.291943i	$0.0943018\pi$
$32$	−1.31070	+	2.27020i	−0.231701	+	0.401318i
$33$	−5.68100	+	6.48758i	−0.988935	+	1.12934i
$34$	−3.43757	−	5.95405i	−0.589539	−	1.02111i
$35$	4.31932			0.730099
$36$	−0.187136	−	1.40542i	−0.0311894	−	0.234237i
$37$	7.10248			1.16764			0.583820	−	0.811883i	$-0.301557\pi$
$37$	7.10248			1.16764			0.583820	+	0.811883i	$0.301557\pi$
$38$	−4.95785	−	8.58725i	−0.804270	−	1.39304i
$39$	1.69902	+	0.336654i	0.272061	+	0.0539077i
$40$	1.34008	−	2.32108i	0.211885	−	0.366996i
$41$	−2.75305	+	4.76842i	−0.429954	+	0.744702i	−0.996869	−	0.0790745i	$-0.974803\pi$
$41$	−2.75305	+	4.76842i	−0.429954	+	0.744702i	0.566915	+	0.823776i	$0.308137\pi$
$42$	10.3409	+	2.04901i	1.59564	+	0.316169i
$43$	−3.94721	−	6.83676i	−0.601943	−	1.04260i	−0.992527	−	0.122029i	$-0.961060\pi$
$43$	−3.94721	−	6.83676i	−0.601943	−	1.04260i	0.390583	−	0.920568i	$-0.372273\pi$
$44$	2.35298			0.354725
$45$	0.441864	+	3.31846i	0.0658692	+	0.494687i
$46$	−3.07405			−0.453244
$47$	−3.99982	−	6.92790i	−0.583434	−	1.01054i	−0.995069	−	0.0991886i	$-0.968375\pi$
$47$	−3.99982	−	6.92790i	−0.583434	−	1.01054i	0.411635	−	0.911349i	$-0.364958\pi$
$48$	5.38792	−	6.15290i	0.777680	−	0.888094i
$49$	−3.99095	+	6.91253i	−0.570135	+	0.987504i
$50$	−2.95207	+	5.11313i	−0.417485	+	0.723106i
$51$	2.43953	+	7.16925i	0.341603	+	1.00390i
$52$	−0.236304	−	0.409291i	−0.0327695	−	0.0567584i
$53$	5.68016			0.780230			0.390115	−	0.920766i	$-0.372435\pi$
$53$	5.68016			0.780230			0.390115	+	0.920766i	$0.372435\pi$
$54$	−0.516351	+	8.15437i	−0.0702665	+	1.10967i
$55$	−5.55582			−0.749147
$56$	4.64816	+	8.05086i	0.621137	+	1.07584i
$57$	3.51842	+	10.3399i	0.466027	+	1.36955i
$58$	−1.69902	+	2.94279i	−0.223092	+	0.386407i
$59$	2.34811	−	4.06705i	0.305699	−	0.529485i	−0.671718	−	0.740807i	$-0.734443\pi$
$59$	2.34811	−	4.06705i	0.305699	−	0.529485i	0.977417	+	0.211321i	$0.0677767\pi$
$60$	0.601786	−	0.687227i	0.0776902	−	0.0887206i
$61$	−1.06675	−	1.84766i	−0.136583	−	0.236569i	0.789618	−	0.613599i	$-0.210279\pi$
$61$	−1.06675	−	1.84766i	−0.136583	−	0.236569i	−0.926201	+	0.377030i	$0.876945\pi$
$62$	3.94656			0.501213
$63$	−10.7346	−	4.42787i	−1.35243	−	0.557859i
$64$	5.32169			0.665212
$65$	0.557959	+	0.966413i	0.0692063	+	0.119869i
$66$	−13.3012	−	2.63559i	−1.63727	−	0.324418i
$67$	−1.16845	+	2.02382i	−0.142749	+	0.247249i	−0.928531	−	0.371255i	$-0.878928\pi$
$67$	−1.16845	+	2.02382i	−0.142749	+	0.247249i	0.785782	+	0.618504i	$0.212261\pi$
$68$	1.03318	−	1.78952i	0.125291	−	0.217011i
$69$	3.32148	+	0.658137i	0.399859	+	0.0792304i
$70$	3.39596	+	5.88198i	0.405895	+	0.703032i
$71$	4.31876			0.512543			0.256272	−	0.966605i	$-0.417506\pi$
$71$	4.31876			0.512543			0.256272	+	0.966605i	$0.417506\pi$
$72$	−5.70984	+	4.39471i	−0.672911	+	0.517921i
$73$	7.66241			0.896817			0.448408	−	0.893829i	$-0.351991\pi$
$73$	7.66241			0.896817			0.448408	+	0.893829i	$0.351991\pi$
$74$	5.58416	+	9.67205i	0.649145	+	1.12435i
$75$	4.28437	−	4.89266i	0.494716	−	0.564956i
$76$	1.49011	−	2.58094i	0.170927	−	0.296054i
$77$	9.63540	−	16.6890i	1.09806	−	1.90189i
$78$	0.877364	+	2.57838i	0.0993419	+	0.291944i
$79$	1.49553	+	2.59034i	0.168260	+	0.291436i	0.937808	−	0.347154i	$-0.112852\pi$
$79$	1.49553	+	2.59034i	0.168260	+	0.291436i	−0.769548	+	0.638589i	$0.779518\pi$
$80$	5.26920			0.589115
$81$	2.30372	−	8.70017i	0.255969	−	0.966685i
$82$	−8.65808			−0.956125
$83$	−6.98114	−	12.0917i	−0.766279	−	1.32724i	−0.939567	−	0.342364i	$-0.888772\pi$
$83$	−6.98114	−	12.0917i	−0.766279	−	1.32724i	0.173288	−	0.984871i	$-0.444561\pi$
$84$	1.02067	+	2.99954i	0.111365	+	0.327276i
$85$	−2.43953	+	4.22539i	−0.264604	+	0.458308i
$86$	6.20679	−	10.7505i	0.669296	−	1.15925i
$87$	2.46581	−	2.81590i	0.264362	−	0.301896i
$88$	−5.97881	−	10.3556i	−0.637343	−	1.10391i
$89$	7.98729			0.846651			0.423325	−	0.905978i	$-0.360863\pi$
$89$	7.98729			0.846651			0.423325	+	0.905978i	$0.360863\pi$
$90$	−4.17163	+	3.21079i	−0.439728	+	0.338447i
$91$	−3.87065			−0.405754
$92$	−0.461960	−	0.800138i	−0.0481627	−	0.0834202i
$93$	−4.26421	−	0.844936i	−0.442178	−	0.0876158i
$94$	6.28953	−	10.8938i	0.648716	−	1.12361i
$95$	−3.51842	+	6.09409i	−0.360983	+	0.625240i
$96$	4.45380	+	0.882502i	0.454564	+	0.0900700i
$97$	−3.82682	−	6.62824i	−0.388555	−	0.672996i	0.603701	−	0.797211i	$-0.293692\pi$
$97$	−3.82682	−	6.62824i	−0.388555	−	0.672996i	−0.992255	+	0.124215i	$0.960359\pi$
$98$	−12.5512			−1.26786
$99$	13.8076	+	5.69544i	1.38771	+	0.572414i
$100$	−1.77452			−0.177452
$101$	5.50684	+	9.53813i	0.547951	+	0.949080i	0.998415	+	0.0562848i	$0.0179255\pi$
$101$	5.50684	+	9.53813i	0.547951	+	0.949080i	−0.450463	+	0.892795i	$0.648741\pi$
$102$	−7.84495	+	8.95877i	−0.776766	+	0.887051i
$103$	−2.31923	+	4.01702i	−0.228520	+	0.395809i	−0.957370	−	0.288865i	$-0.906722\pi$
$103$	−2.31923	+	4.01702i	−0.228520	+	0.395809i	0.728849	+	0.684674i	$0.240055\pi$
$104$	−1.20088	+	2.07998i	−0.117756	+	0.203959i
$105$	−2.41000	−	7.08248i	−0.235192	−	0.691179i
$106$	4.46589	+	7.73515i	0.433766	+	0.751304i
$107$	−2.23334			−0.215906			−0.107953	−	0.994156i	$-0.534430\pi$
$107$	−2.23334			−0.215906			−0.107953	+	0.994156i	$0.534430\pi$
$108$	−2.20008	+	1.09102i	−0.211703	+	0.104983i
$109$	−12.9073			−1.23630			−0.618149	−	0.786061i	$-0.712117\pi$
$109$	−12.9073			−1.23630			−0.618149	+	0.786061i	$0.712117\pi$
$110$	−4.36814	−	7.56583i	−0.416485	−	0.721374i
$111$	−3.96289	−	11.6461i	−0.376141	−	1.10540i
$112$	−9.13832	+	15.8280i	−0.863490	+	1.49561i
$113$	−2.77305	+	4.80306i	−0.260867	+	0.451834i	−0.966472	−	0.256770i	$-0.917342\pi$
$113$	−2.77305	+	4.80306i	−0.260867	+	0.451834i	0.705606	+	0.708605i	$0.250675\pi$
$114$	−11.3144	+	12.9208i	−1.05969	+	1.21015i
$115$	1.09078	+	1.88928i	0.101715	+	0.176176i
$116$	−1.02130			−0.0948250
$117$	−0.395965	−	2.97375i	−0.0366070	−	0.274924i
$118$	7.38460			0.679808
$119$	−8.46170	−	14.6561i	−0.775683	−	1.34352i
$120$	−4.55364	−	0.902284i	−0.415688	−	0.0823669i
$121$	−6.89375	+	11.9403i	−0.626704	+	1.08548i
$122$	1.67741	−	2.90537i	0.151866	−	0.263039i
$123$	9.35496	+	1.85365i	0.843508	+	0.167138i
$124$	0.593078	+	1.02724i	0.0532600	+	0.0922490i
$125$	9.76955			0.873816
$126$	−2.41000	−	18.0995i	−0.214700	−	1.61243i
$127$	11.0870			0.983809			0.491905	−	0.870649i	$-0.336301\pi$
$127$	11.0870			0.983809			0.491905	+	0.870649i	$0.336301\pi$
$128$	6.80545	+	11.7874i	0.601523	+	1.04187i
$129$	−9.00799	+	10.2869i	−0.793110	+	0.905715i
$130$	−0.877364	+	1.51964i	−0.0769499	+	0.133281i
$131$	−2.84980	+	4.93599i	−0.248988	+	0.431259i	−0.963245	−	0.268624i	$-0.913431\pi$
$131$	−2.84980	+	4.93599i	−0.248988	+	0.431259i	0.714257	+	0.699883i	$0.246765\pi$
$132$	−1.31286	−	3.85822i	−0.114270	−	0.335815i
$133$	−12.2039	−	21.1378i	−1.05821	−	1.83288i
$134$	−3.67467			−0.317443
$135$	5.19481	−	2.57610i	0.447098	−	0.221715i
$136$	−10.5010			−0.900457
$137$	−3.00702	−	5.20831i	−0.256907	−	0.444976i	0.708505	−	0.705706i	$-0.249370\pi$
$137$	−3.00702	−	5.20831i	−0.256907	−	0.444976i	−0.965412	+	0.260730i	$0.916037\pi$
$138$	1.71519	+	5.04058i	0.146007	+	0.429083i
$139$	5.99085	−	10.3765i	0.508138	−	0.880120i	−0.491818	−	0.870698i	$-0.663667\pi$
$139$	5.99085	−	10.3765i	0.508138	−	0.880120i	0.999956	−	0.00942221i	$-0.00299923\pi$
$140$	−1.02067	+	1.76786i	−0.0862626	+	0.149411i
$141$	−9.12807	+	10.4241i	−0.768723	+	0.877865i
$142$	3.39553	+	5.88123i	0.284946	+	0.493541i
$143$	4.97870			0.416340
$144$	−13.0953	−	5.40162i	−1.09127	−	0.450135i
$145$	2.41147			0.200262
$146$	6.02439	+	10.4345i	0.498582	+	0.863569i
$147$	13.5614	+	2.68713i	1.11852	+	0.221631i
$148$	−1.67835	+	2.90698i	−0.137959	+	0.238952i
$149$	−10.0766	+	17.4532i	−0.825507	+	1.42982i	0.0760235	+	0.997106i	$0.475778\pi$
$149$	−10.0766	+	17.4532i	−0.825507	+	1.42982i	−0.901531	+	0.432715i	$0.857556\pi$
$150$	10.0312	+	1.98765i	0.819047	+	0.162291i
$151$	−0.540200	−	0.935654i	−0.0439608	−	0.0761424i	0.843208	−	0.537588i	$-0.180664\pi$
$151$	−0.540200	−	0.935654i	−0.0439608	−	0.0761424i	−0.887169	+	0.461445i	$0.847331\pi$
$152$	−15.1452			−1.22844
$153$	10.3944	−	8.00030i	0.840338	−	0.646786i
$154$	30.3024			2.44184
$155$	−1.40037	−	2.42551i	−0.112480	−	0.194822i
$156$	−0.539274	+	0.615840i	−0.0431765	+	0.0493067i
$157$	10.3978	−	18.0095i	0.829833	−	1.43731i	−0.0683361	−	0.997662i	$-0.521769\pi$
$157$	10.3978	−	18.0095i	0.829833	−	1.43731i	0.898169	−	0.439650i	$-0.144898\pi$
$158$	−2.35165	+	4.07318i	−0.187087	+	0.324045i
$159$	−3.16929	−	9.31387i	−0.251341	−	0.738638i
$160$	1.46263	+	2.53335i	0.115631	+	0.200279i
$161$	−7.56688			−0.596353
$162$	13.6590	−	3.70313i	1.07315	−	0.290946i
$163$	23.3112			1.82587			0.912937	−	0.408101i	$-0.133809\pi$
$163$	23.3112			1.82587			0.912937	+	0.408101i	$0.133809\pi$
$164$	−1.30111	−	2.25359i	−0.101600	−	0.175976i
$165$	3.09992	+	9.10999i	0.241328	+	0.709212i
$166$	10.9775	−	19.0136i	0.852020	−	1.47574i
$167$	−7.88747	+	13.6615i	−0.610351	+	1.05716i	0.380830	+	0.924645i	$0.375638\pi$
$167$	−7.88747	+	13.6615i	−0.610351	+	1.05716i	−0.991181	+	0.132514i	$0.957695\pi$
$168$	10.6077	−	12.1137i	0.818399	−	0.934595i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−7.67209			−0.588423
$171$	14.9914	−	11.5385i	1.14642	−	0.882368i
$172$	3.73096			0.284483
$173$	5.16995	+	8.95461i	0.393064	+	0.680806i	0.992852	−	0.119352i	$-0.0380818\pi$
$173$	5.16995	+	8.95461i	0.393064	+	0.680806i	−0.599788	+	0.800159i	$0.704748\pi$
$174$	5.77333	+	1.14396i	0.437675	+	0.0867235i
$175$	−7.26661	+	12.5861i	−0.549304	+	0.951423i
$176$	11.7544	−	20.3592i	0.886019	−	1.53463i
$177$	−7.97898	−	1.58100i	−0.599737	−	0.118835i
$178$	6.27982	+	10.8770i	0.470692	+	0.815263i
$179$	−9.84680			−0.735984			−0.367992	−	0.929829i	$-0.619955\pi$
$179$	−9.84680			−0.735984			−0.367992	+	0.929829i	$0.619955\pi$
$180$	−1.46263	−	0.603316i	−0.109018	−	0.0449685i
$181$	−19.0799			−1.41820			−0.709098	−	0.705110i	$-0.750898\pi$
$181$	−19.0799			−1.41820			−0.709098	+	0.705110i	$0.750898\pi$
$182$	−3.04320	−	5.27098i	−0.225577	−	0.390711i
$183$	−2.43445	+	2.78009i	−0.179960	+	0.205510i
$184$	−2.34764	+	4.06623i	−0.173070	+	0.299766i
$185$	3.96289	−	6.86393i	0.291358	−	0.504646i
$186$	−2.20202	−	6.47125i	−0.161460	−	0.474495i
$187$	10.8840	+	18.8517i	0.795920	+	1.37857i
$188$	3.78070			0.275736
$189$	−1.27102	+	20.0723i	−0.0924528	+	1.46004i
$190$	−11.0651			−0.802748
$191$	2.71267	+	4.69848i	0.196282	+	0.339970i	0.947320	−	0.320289i	$-0.103780\pi$
$191$	2.71267	+	4.69848i	0.196282	+	0.339970i	−0.751038	+	0.660259i	$0.770447\pi$
$192$	−2.96929	−	8.72609i	−0.214290	−	0.629751i
$193$	8.90207	−	15.4188i	0.640785	−	1.10987i	−0.344473	−	0.938796i	$-0.611942\pi$
$193$	8.90207	−	15.4188i	0.640785	−	1.10987i	0.985258	−	0.171076i	$-0.0547243\pi$
$194$	6.01749	−	10.4226i	0.432031	−	0.748299i
$195$	1.27333	−	1.45411i	0.0911850	−	0.104131i
$196$	−1.88615	−	3.26692i	−0.134725	−	0.233351i
$197$	−9.90279			−0.705545			−0.352772	−	0.935709i	$-0.614761\pi$
$197$	−9.90279			−0.705545			−0.352772	+	0.935709i	$0.614761\pi$
$198$	3.09992	+	23.2809i	0.220302	+	1.65450i
$199$	9.39752			0.666172			0.333086	−	0.942896i	$-0.391910\pi$
$199$	9.39752			0.666172			0.333086	+	0.942896i	$0.391910\pi$
$200$	4.50896	+	7.80975i	0.318832	+	0.552233i
$201$	3.97044	+	0.786727i	0.280053	+	0.0554914i
$202$	−8.65925	+	14.9983i	−0.609263	+	1.05527i
$203$	−4.18219	+	7.24377i	−0.293532	+	0.508413i
$204$	−3.51078	−	0.695647i	−0.245804	−	0.0487050i
$205$	3.07217	+	5.32116i	0.214570	+	0.371646i
$206$	−7.29375			−0.508180
$207$	−0.774087	−	5.81351i	−0.0538028	−	0.404067i
$208$	−4.72186			−0.327402
$209$	15.6976	+	27.1890i	1.08582	+	1.88070i
$210$	7.75000	−	8.85034i	0.534801	−	0.610731i
$211$	−11.3713	+	19.6957i	−0.782835	+	1.35591i	0.147448	+	0.989070i	$0.452894\pi$
$211$	−11.3713	+	19.6957i	−0.782835	+	1.35591i	−0.930284	+	0.366841i	$0.880439\pi$
$212$	−1.34224	+	2.32484i	−0.0921857	+	0.159670i
$213$	−2.40969	−	7.08157i	−0.165109	−	0.485221i
$214$	−1.75591	−	3.04133i	−0.120032	−	0.207901i
$215$	−8.80951			−0.600804
$216$	10.3919	+	6.91047i	0.707082	+	0.470198i
$217$	9.71458			0.659469
$218$	−10.1481	−	17.5770i	−0.687315	−	1.19046i
$219$	−4.27531	−	12.5642i	−0.288899	−	0.849010i
$220$	1.31286	−	2.27395i	0.0885133	−	0.153309i
$221$	2.18612	−	3.78647i	0.147054	−	0.254706i
$222$	12.7437	−	14.5531i	0.855302	−	0.976737i
$223$	−9.62529	−	16.6715i	−0.644557	−	1.11641i	−0.984404	−	0.175925i	$-0.943708\pi$
$223$	−9.62529	−	16.6715i	−0.644557	−	1.11641i	0.339847	−	0.940481i	$-0.389625\pi$
$224$	−10.1465			−0.677941
$225$	−10.4131	−	4.29526i	−0.694206	−	0.286351i
$226$	−8.72098			−0.580111
$227$	2.57312	+	4.45677i	0.170784	+	0.295806i	0.938694	−	0.344751i	$-0.112037\pi$
$227$	2.57312	+	4.45677i	0.170784	+	0.295806i	−0.767910	+	0.640557i	$0.778703\pi$
$228$	−5.06344	−	1.00330i	−0.335334	−	0.0664451i
$229$	−4.52272	+	7.83357i	−0.298869	+	0.517657i	−0.975878	−	0.218318i	$-0.929943\pi$
$229$	−4.52272	+	7.83357i	−0.298869	+	0.517657i	0.677008	+	0.735976i	$0.263276\pi$
$230$	−1.71519	+	2.97080i	−0.113096	+	0.195889i
$231$	−32.7414	−	6.48758i	−2.15423	−	0.426852i
$232$	2.59507	+	4.49479i	0.170375	+	0.295097i
$233$	5.69101			0.372830			0.186415	−	0.982471i	$-0.440313\pi$
$233$	5.69101			0.372830			0.186415	+	0.982471i	$0.440313\pi$
$234$	3.73829	−	2.87726i	0.244380	−	0.188093i
$235$	−8.92695			−0.582330
$236$	1.10974	+	1.92212i	0.0722378	+	0.125120i
$237$	3.41298	−	3.89755i	0.221697	−	0.253173i
$238$	13.3056	−	23.0460i	0.862475	−	1.49385i
$239$	5.22578	−	9.05132i	0.338028	−	0.585481i	−0.646034	−	0.763309i	$-0.723574\pi$
$239$	5.22578	−	9.05132i	0.338028	−	0.585481i	0.984062	+	0.177827i	$0.0569069\pi$
$240$	−2.94000	−	8.64002i	−0.189776	−	0.557711i
$241$	−7.45124	−	12.9059i	−0.479976	−	0.831343i	0.519760	−	0.854312i	$-0.326021\pi$
$241$	−7.45124	−	12.9059i	−0.479976	−	0.831343i	−0.999736	+	0.0229690i	$0.992688\pi$
$242$	−21.6802			−1.39365
$243$	−15.5512	+	1.07688i	−0.997611	+	0.0690819i
$244$	1.00831			0.0645504
$245$	4.45357	+	7.71381i	0.284528	+	0.492817i
$246$	4.83085	+	14.1968i	0.308004	+	0.905156i
$247$	3.15294	−	5.46106i	0.200617	−	0.347479i
$248$	3.01397	−	5.22035i	0.191387	−	0.331493i
$249$	−15.9318	+	18.1938i	−1.00964	+	1.15298i
$250$	7.68108	+	13.3040i	0.485794	+	0.841420i
$251$	7.44478			0.469910			0.234955	−	0.972006i	$-0.424506\pi$
$251$	7.44478			0.469910			0.234955	+	0.972006i	$0.424506\pi$
$252$	4.34891	−	3.34724i	0.273956	−	0.210856i
$253$	9.73306			0.611912
$254$	8.71687	+	15.0981i	0.546945	+	0.947336i
$255$	8.28962	+	1.64255i	0.519116	+	0.102861i
$256$	−5.37956	+	9.31767i	−0.336222	+	0.582354i
$257$	−3.98142	+	6.89602i	−0.248354	+	0.430162i	−0.963069	−	0.269254i	$-0.913223\pi$
$257$	−3.98142	+	6.89602i	−0.248354	+	0.430162i	0.714715	+	0.699416i	$0.246556\pi$
$258$	−21.0909	−	4.17908i	−1.31306	−	0.260178i
$259$	13.7456	+	23.8081i	0.854110	+	1.47936i
$260$	−0.527392			−0.0327075
$261$	−5.99310	−	2.47208i	−0.370964	−	0.153018i
$262$	−8.96234			−0.553695
$263$	1.72097	+	2.98080i	0.106119	+	0.183804i	0.914195	−	0.405275i	$-0.132824\pi$
$263$	1.72097	+	2.98080i	0.106119	+	0.183804i	−0.808076	+	0.589079i	$0.799491\pi$
$264$	−13.6443	+	15.5816i	−0.839752	+	0.958979i
$265$	3.16929	−	5.48938i	0.194688	−	0.337210i
$266$	19.1901	−	33.2382i	1.17662	−	2.03797i
$267$	−4.45658	−	13.0969i	−0.272738	−	0.801518i
$268$	−0.552220	−	0.956473i	−0.0337322	−	0.0584259i
$269$	9.24141			0.563458			0.281729	−	0.959494i	$-0.409092\pi$
$269$	9.24141			0.563458			0.281729	+	0.959494i	$0.409092\pi$
$270$	7.59239	+	5.04881i	0.462058	+	0.307261i
$271$	−25.6813			−1.56003			−0.780015	−	0.625761i	$-0.784788\pi$
$271$	−25.6813			−1.56003			−0.780015	+	0.625761i	$0.784788\pi$
$272$	−10.3226	−	17.8792i	−0.625897	−	1.08408i
$273$	2.15966	+	6.34678i	0.130709	+	0.384124i
$274$	4.72840	−	8.18983i	0.285653	−	0.494766i
$275$	9.34684	−	16.1892i	0.563636	−	0.976245i
$276$	−1.05425	+	1.20393i	−0.0634583	+	0.0724680i
$277$	5.10462	+	8.84145i	0.306707	+	0.531232i	0.977640	−	0.210286i	$-0.0674396\pi$
$277$	5.10462	+	8.84145i	0.306707	+	0.531232i	−0.670933	+	0.741518i	$0.734106\pi$
$278$	18.8407			1.12999
$279$	0.993796	+	7.46356i	0.0594970	+	0.446831i
$280$	10.3739			0.619961
$281$	−9.87570	−	17.1052i	−0.589135	−	1.02041i	−0.994346	−	0.106188i	$-0.966135\pi$
$281$	−9.87570	−	17.1052i	−0.589135	−	1.02041i	0.405211	−	0.914223i	$-0.367198\pi$
$282$	−21.3721	−	4.23479i	−1.27269	−	0.252178i
$283$	−10.1506	+	17.5814i	−0.603391	+	1.04510i	0.388912	+	0.921275i	$0.372851\pi$
$283$	−10.1506	+	17.5814i	−0.603391	+	1.04510i	−0.992304	+	0.123829i	$0.960482\pi$
$284$	−1.02054	+	1.76763i	−0.0605580	+	0.104890i
$285$	11.9557	+	2.36898i	0.708197	+	0.140326i
$286$	3.91439	+	6.77992i	0.231463	+	0.400905i
$287$	−21.3121			−1.25802
$288$	−1.03798	−	7.79539i	−0.0611636	−	0.459348i
$289$	2.11650			0.124500
$290$	1.89596	+	3.28391i	0.111335	+	0.192838i
$291$	−8.73326	+	9.97320i	−0.511953	+	0.584639i
$292$	−1.81066	+	3.13615i	−0.105961	+	0.183529i
$293$	4.05935	−	7.03101i	0.237150	−	0.410756i	−0.722745	−	0.691114i	$-0.757120\pi$
$293$	4.05935	−	7.03101i	0.237150	−	0.410756i	0.959895	+	0.280359i	$0.0904534\pi$
$294$	7.00303	+	20.5804i	0.408425	+	1.20027i
$295$	−2.62030	−	4.53850i	−0.152560	−	0.264242i
$296$	17.0584			0.991499
$297$	1.63487	−	25.8184i	0.0948649	−	1.49814i
$298$	−31.6900			−1.83575
$299$	−0.977469	−	1.69303i	−0.0565285	−	0.0979103i
$300$	0.990106	+	2.90971i	0.0571638	+	0.167992i
$301$	15.2782	−	26.4627i	0.880623	−	1.52528i
$302$	0.849439	−	1.47127i	0.0488797	−	0.0846621i
$303$	12.5673	−	14.3516i	0.721971	−	0.824476i
$304$	−14.8877	−	25.7863i	−0.853871	−	1.47895i
$305$	−2.38081			−0.136325
$306$	19.0670	+	7.86490i	1.08999	+	0.449606i
$307$	−14.1914			−0.809944			−0.404972	−	0.914329i	$-0.632719\pi$
$307$	−14.1914			−0.809944			−0.404972	+	0.914329i	$0.632719\pi$
$308$	4.55377	+	7.88736i	0.259475	+	0.449424i
$309$	7.88082	+	1.56155i	0.448324	+	0.0888336i
$310$	2.20202	−	3.81400i	0.125066	−	0.216621i
$311$	−13.5633	+	23.4923i	−0.769102	+	1.33212i	0.168948	+	0.985625i	$0.445963\pi$
$311$	−13.5633	+	23.4923i	−0.769102	+	1.33212i	−0.938050	+	0.346499i	$0.887370\pi$
$312$	4.08062	+	0.808558i	0.231020	+	0.0457756i
$313$	13.5933	+	23.5444i	0.768341	+	1.33081i	0.938462	+	0.345383i	$0.112251\pi$
$313$	13.5933	+	23.5444i	0.768341	+	1.33081i	−0.170121	+	0.985423i	$0.554416\pi$
$314$	32.7000			1.84537
$315$	−10.2686	+	7.90346i	−0.578570	+	0.445310i
$316$	−1.41360			−0.0795212
$317$	−12.7249	−	22.0402i	−0.714704	−	1.23790i	−0.963074	−	0.269238i	$-0.913228\pi$
$317$	−12.7249	−	22.0402i	−0.714704	−	1.23790i	0.248370	−	0.968665i	$-0.420105\pi$
$318$	10.1917	−	11.6387i	0.571522	−	0.652666i
$319$	5.37944	−	9.31746i	0.301191	−	0.521677i
$320$	2.96929	−	5.14295i	0.165988	−	0.287500i
$321$	1.24611	+	3.66206i	0.0695513	+	0.204396i
$322$	−5.94928	−	10.3045i	−0.331540	−	0.574245i
$323$	27.5709			1.53408
$324$	3.01652	+	2.99878i	0.167584	+	0.166599i
$325$	−3.75473			−0.208275
$326$	18.3279	+	31.7448i	1.01509	+	1.75818i
$327$	7.20176	+	21.1644i	0.398258	+	1.17039i
$328$	−6.61214	+	11.4526i	−0.365094	+	0.632362i
$329$	15.4819	−	26.8154i	0.853545	−	1.47838i
$330$	−9.96861	+	11.3839i	−0.548754	+	0.626665i
$331$	1.80139	+	3.12009i	0.0990131	+	0.171496i	0.911276	−	0.411795i	$-0.135098\pi$
$331$	1.80139	+	3.12009i	0.0990131	+	0.171496i	−0.812263	+	0.583291i	$0.801765\pi$
$332$	6.59869			0.362150
$333$	−16.8852	+	12.9961i	−0.925302	+	0.712180i
$334$	−24.8054			−1.35729
$335$	1.30390	+	2.25841i	0.0712394	+	0.123390i
$336$	31.0523	+	6.15290i	1.69404	+	0.335668i
$337$	2.85188	−	4.93960i	0.155352	−	0.269077i	−0.777835	−	0.628468i	$-0.783682\pi$
$337$	2.85188	−	4.93960i	0.155352	−	0.269077i	0.933187	+	0.359391i	$0.117016\pi$
$338$	0.786226	−	1.36178i	0.0427651	−	0.0740713i
$339$	9.42293	+	1.86711i	0.511783	+	0.101408i
$340$	−1.15294	−	1.99695i	−0.0625271	−	0.108300i
$341$	−12.4956			−0.676675
$342$	27.4995	+	11.3432i	1.48700	+	0.613369i
$343$	−3.80057			−0.205212
$344$	−9.48021	−	16.4202i	−0.511138	−	0.885318i
$345$	2.48928	−	2.84271i	0.134018	−	0.153046i
$346$	−8.12950	+	14.0807i	−0.437045	+	0.756983i
$347$	−17.6247	+	30.5268i	−0.946142	+	1.63877i	−0.192693	+	0.981259i	$0.561722\pi$
$347$	−17.6247	+	30.5268i	−0.946142	+	1.63877i	−0.753449	+	0.657506i	$0.771611\pi$
$348$	0.569841	+	1.67464i	0.0305467	+	0.0897701i
$349$	−5.45273	−	9.44440i	−0.291878	−	0.505547i	0.682376	−	0.731001i	$-0.260947\pi$
$349$	−5.45273	−	9.44440i	−0.291878	−	0.505547i	−0.974254	+	0.225454i	$0.927613\pi$
$350$	−22.8528			−1.22153
$351$	−4.65519	+	2.30850i	−0.248476	+	0.123219i
$352$	13.0512			0.695629
$353$	8.19606	+	14.1960i	0.436232	+	0.755577i	0.997395	−	0.0721287i	$-0.0229792\pi$
$353$	8.19606	+	14.1960i	0.436232	+	0.755577i	−0.561163	+	0.827705i	$0.689646\pi$
$354$	−4.12030	−	12.1087i	−0.218992	−	0.643569i
$355$	2.40969	−	4.17371i	0.127893	−	0.221518i
$356$	−1.88743	+	3.26912i	−0.100034	+	0.173263i
$357$	−19.3106	+	22.0523i	−1.02203	+	1.16713i
$358$	−7.74181	−	13.4092i	−0.409168	−	0.708699i
$359$	−1.31488			−0.0693969			−0.0346984	−	0.999398i	$-0.511047\pi$
$359$	−1.31488			−0.0693969			−0.0346984	+	0.999398i	$0.511047\pi$
$360$	1.06125	+	7.97013i	0.0559327	+	0.420063i
$361$	20.7642			1.09285
$362$	−15.0011	−	25.9827i	−0.788441	−	1.36562i
$363$	23.4252	+	4.64161i	1.22950	+	0.243621i
$364$	0.914649	−	1.58422i	0.0479407	−	0.0830356i
$365$	4.27531	−	7.40505i	0.223780	−	0.387598i
$366$	−5.69991	−	1.12941i	−0.297939	−	0.0590354i
$367$	11.5784	+	20.0543i	0.604386	+	1.04683i	0.992148	+	0.125068i	$0.0399149\pi$
$367$	11.5784	+	20.0543i	0.604386	+	1.04683i	−0.387762	+	0.921759i	$0.626752\pi$
$368$	−9.23094			−0.481196
$369$	−2.18022	−	16.3738i	−0.113498	−	0.852385i
$370$	12.4629			0.647916
$371$	10.9929	+	19.0403i	0.570725	+	0.988524i
$372$	1.35348	−	1.54564i	0.0701745	−	0.0801378i
$373$	15.1931	−	26.3152i	0.786668	−	1.36255i	−0.141330	−	0.989963i	$-0.545138\pi$
$373$	15.1931	−	26.3152i	0.786668	−	1.36255i	0.927998	−	0.372586i	$-0.121529\pi$
$374$	−17.1147	+	29.6435i	−0.884978	+	1.53283i
$375$	−5.45101	−	16.0193i	−0.281489	−	0.827235i
$376$	−9.60658	−	16.6391i	−0.495422	−	0.858095i
$377$	−2.16098			−0.111296
$378$	−28.3334	+	14.0505i	−1.45731	+	0.722679i
$379$	31.9119			1.63920			0.819602	−	0.572933i	$-0.194195\pi$
$379$	31.9119			1.63920			0.819602	+	0.572933i	$0.194195\pi$
$380$	−1.66284	−	2.88012i	−0.0853017	−	0.147747i
$381$	−6.18607	−	18.1795i	−0.316922	−	0.931365i
$382$	−4.26555	+	7.38814i	−0.218244	+	0.378010i
$383$	15.4894	−	26.8285i	0.791473	−	1.37087i	−0.133582	−	0.991038i	$-0.542648\pi$
$383$	15.4894	−	26.8285i	0.791473	−	1.37087i	0.925055	−	0.379834i	$-0.124019\pi$
$384$	15.5309	−	17.7359i	0.792556	−	0.905082i
$385$	−10.7523	−	18.6235i	−0.547989	−	0.949144i
$386$	27.9962			1.42497
$387$	21.8938	+	9.03090i	1.11292	+	0.459066i
$388$	3.61717			0.183634
$389$	10.1003	+	17.4943i	0.512108	+	0.886997i	0.999901	+	0.0140378i	$0.00446852\pi$
$389$	10.1003	+	17.4943i	0.512108	+	0.886997i	−0.487794	+	0.872959i	$0.662198\pi$
$390$	2.98132	+	0.590735i	0.150965	+	0.0299130i
$391$	4.27373	−	7.40232i	0.216132	−	0.374352i
$392$	−9.58527	+	16.6022i	−0.484129	+	0.838536i
$393$	9.68371	+	1.91879i	0.488479	+	0.0967900i
$394$	−7.78584	−	13.4855i	−0.392245	−	0.679388i
$395$	3.33778			0.167942
$396$	−5.59388	+	4.30546i	−0.281103	+	0.216357i
$397$	−24.3056			−1.21986			−0.609931	−	0.792454i	$-0.708803\pi$
$397$	−24.3056			−1.21986			−0.609931	+	0.792454i	$0.708803\pi$
$398$	7.38858	+	12.7974i	0.370356	+	0.641475i
$399$	−27.8508	+	31.8050i	−1.39428	+	1.59224i
$400$	−8.86465	+	15.3540i	−0.443232	+	0.767701i
$401$	−12.5171	+	21.6802i	−0.625073	+	1.08266i	0.363453	+	0.931612i	$0.381598\pi$
$401$	−12.5171	+	21.6802i	−0.625073	+	1.08266i	−0.988527	+	0.151046i	$0.951736\pi$
$402$	2.05031	+	6.02543i	0.102260	+	0.300521i
$403$	1.25490	+	2.17356i	0.0625113	+	0.108273i
$404$	−5.20516			−0.258966
$405$	−7.12257	−	7.08068i	−0.353923	−	0.351842i
$406$	−13.1526			−0.652752
$407$	−17.6806	−	30.6237i	−0.876393	−	1.51796i
$408$	5.85915	+	17.2188i	0.290071	+	0.852456i
$409$	9.30478	−	16.1164i	0.460092	−	0.796902i	−0.538873	−	0.842387i	$-0.681150\pi$
$409$	9.30478	−	16.1164i	0.460092	−	0.796902i	0.998965	+	0.0454844i	$0.0144831\pi$
$410$	−4.83085	+	8.36728i	−0.238579	+	0.413230i
$411$	−6.86238	+	7.83670i	−0.338496	+	0.386556i
$412$	−1.09609	−	1.89848i	−0.0540003	−	0.0935312i
$413$	18.1774			0.894453
$414$	7.30813	−	5.62487i	0.359175	−	0.276447i
$415$	−15.5808			−0.764829
$416$	−1.31070	−	2.27020i	−0.0642623	−	0.111305i
$417$	−20.3571	−	4.03369i	−0.996894	−	0.197530i
$418$	−24.6837	+	42.7534i	−1.20732	+	2.09114i
$419$	9.88439	−	17.1203i	0.482884	−	0.836379i	−0.516923	−	0.856032i	$-0.672923\pi$
$419$	9.88439	−	17.1203i	0.482884	−	0.836379i	0.999807	+	0.0196526i	$0.00625601\pi$
$420$	3.46829	+	0.687227i	0.169235	+	0.0335332i
$421$	−0.242394	−	0.419838i	−0.0118135	−	0.0204617i	0.860058	−	0.510196i	$-0.170427\pi$
$421$	−0.242394	−	0.419838i	−0.0118135	−	0.0204617i	−0.871872	+	0.489734i	$0.837094\pi$
$422$	−35.7618			−1.74086
$423$	22.1856	+	9.15129i	1.07870	+	0.444951i
$424$	13.6423			0.662530
$425$	−8.20829	−	14.2172i	−0.398161	−	0.689634i
$426$	7.74900	−	8.84920i	0.375440	−	0.428745i
$427$	4.12901	−	7.15166i	0.199817	−	0.346093i
$428$	0.527748	−	0.914087i	0.0255097	−	0.0441841i
$429$	−2.77791	−	8.16368i	−0.134119	−	0.394146i
$430$	−6.92627	−	11.9967i	−0.334014	−	0.578530i
$431$	−6.71380			−0.323392			−0.161696	−	0.986841i	$-0.551696\pi$
$431$	−6.71380			−0.323392			−0.161696	+	0.986841i	$0.551696\pi$
$432$	−1.55053	+	24.4865i	−0.0746000	+	1.17810i
$433$	1.48138			0.0711905			0.0355953	−	0.999366i	$-0.488667\pi$
$433$	1.48138			0.0711905			0.0355953	+	0.999366i	$0.488667\pi$
$434$	7.63786	+	13.2292i	0.366629	+	0.635020i
$435$	−1.34550	−	3.95414i	−0.0645119	−	0.189587i
$436$	3.05005	−	5.28285i	0.146071	−	0.253003i
$437$	6.16381	−	10.6760i	0.294855	−	0.510704i
$438$	13.7484	−	15.7004i	0.656923	−	0.750192i
$439$	−3.73596	−	6.47087i	−0.178308	−	0.308838i	0.762993	−	0.646406i	$-0.223729\pi$
$439$	−3.73596	−	6.47087i	−0.178308	−	0.308838i	−0.941301	+	0.337568i	$0.890396\pi$
$440$	−13.3437			−0.636136
$441$	−3.16055	−	23.7362i	−0.150502	−	1.13030i
$442$	6.87514			0.327017
$443$	−19.9367	−	34.5314i	−0.947221	−	1.64063i	−0.751242	−	0.660026i	$-0.770545\pi$
$443$	−19.9367	−	34.5314i	−0.947221	−	1.64063i	−0.195978	−	0.980608i	$-0.562788\pi$
$444$	5.70308	+	1.13004i	0.270656	+	0.0536294i
$445$	4.45658	−	7.71902i	0.211262	−	0.365917i
$446$	15.1353	−	26.2151i	0.716678	−	1.24132i
$447$	34.2407	+	6.78465i	1.61953	+	0.320903i
$448$	10.2992	+	17.8387i	0.486591	+	0.842801i
$449$	12.7677			0.602546			0.301273	−	0.953538i	$-0.402588\pi$
$449$	12.7677			0.602546			0.301273	+	0.953538i	$0.402588\pi$
$450$	−2.33783	−	17.5574i	−0.110206	−	0.827666i
$451$	27.4132			1.29084
$452$	−1.31057	−	2.26997i	−0.0616439	−	0.106770i
$453$	−1.23280	+	1.40783i	−0.0579220	+	0.0661458i
$454$	−4.04611	+	7.00806i	−0.189893	+	0.328905i
$455$	−2.15966	+	3.74064i	−0.101246	+	0.175364i
$456$	8.45038	+	24.8338i	0.395725	+	1.16295i
$457$	4.64821	+	8.05094i	0.217434	+	0.376607i	0.954023	−	0.299734i	$-0.0968979\pi$
$457$	4.64821	+	8.05094i	0.217434	+	0.376607i	−0.736589	+	0.676341i	$0.763565\pi$
$458$	−14.2235			−0.664621
$459$	−18.9179	−	12.5801i	−0.883012	−	0.587188i
$460$	−1.03102			−0.0480715
$461$	6.30336	+	10.9177i	0.293577	+	0.508490i	0.974653	−	0.223723i	$-0.0718210\pi$
$461$	6.30336	+	10.9177i	0.293577	+	0.508490i	−0.681076	+	0.732213i	$0.738488\pi$
$462$	−16.9075	−	49.6875i	−0.786608	−	2.31167i
$463$	−7.65035	+	13.2508i	−0.355542	+	0.615817i	−0.987211	−	0.159422i	$-0.949037\pi$
$463$	−7.65035	+	13.2508i	−0.355542	+	0.615817i	0.631669	+	0.775238i	$0.282370\pi$
$464$	−5.10192	+	8.83678i	−0.236851	+	0.410237i
$465$	−3.19581	+	3.64955i	−0.148202	+	0.169244i
$466$	4.47442	+	7.74992i	0.207273	+	0.359008i
$467$	16.9099			0.782498			0.391249	−	0.920285i	$-0.372043\pi$
$467$	16.9099			0.782498			0.391249	+	0.920285i	$0.372043\pi$
$468$	1.31070	+	0.540645i	0.0605870	+	0.0249913i
$469$	−9.04532			−0.417674
$470$	−7.01860	−	12.1566i	−0.323744	−	0.560741i
$471$	−35.3320	−	7.00090i	−1.62801	−	0.322584i
$472$	5.63959	−	9.76805i	0.259583	−	0.449611i
$473$	−19.6520	+	34.0382i	−0.903598	+	1.56508i
$474$	7.99100	+	1.58338i	0.367039	+	0.0727272i
$475$	−11.8384	−	20.5048i	−0.543185	−	0.940824i
$476$	7.99814			0.366594
$477$	−13.5038	+	10.3935i	−0.618297	+	0.475886i
$478$	16.4346			0.751701
$479$	5.06351	+	8.77026i	0.231358	+	0.400723i	0.958208	−	0.286073i	$-0.0923499\pi$
$479$	5.06351	+	8.77026i	0.231358	+	0.400723i	−0.726850	+	0.686796i	$0.759017\pi$
$480$	3.33790	−	3.81181i	0.152354	−	0.173985i
$481$	−3.55124	+	6.15093i	−0.161923	+	0.280458i
$482$	11.7167	−	20.2940i	0.533682	−	0.924364i
$483$	4.22200	+	12.4076i	0.192108	+	0.564563i
$484$	−3.25804	−	5.64309i	−0.148093	−	0.256504i
$485$	−8.54083			−0.387819
$486$	−13.6933	−	20.3307i	−0.621139	−	0.922221i
$487$	0.181885			0.00824202			0.00412101	−	0.999992i	$-0.498688\pi$
$487$	0.181885			0.00824202			0.00412101	+	0.999992i	$0.498688\pi$
$488$	−2.56207	−	4.43763i	−0.115979	−	0.200882i
$489$	−13.0067	−	38.2238i	−0.588183	−	1.72854i
$490$	−7.00303	+	12.1296i	−0.316365	+	0.547960i
$491$	−3.62972	+	6.28685i	−0.163807	+	0.283722i	−0.936231	−	0.351385i	$-0.885711\pi$
$491$	−3.62972	+	6.28685i	−0.163807	+	0.283722i	0.772424	+	0.635107i	$0.219044\pi$
$492$	−2.96930	+	3.39087i	−0.133866	+	0.152872i
$493$	−4.72416	−	8.18249i	−0.212766	−	0.368521i
$494$	9.91571			0.446129
$495$	13.2082	−	10.1660i	0.593665	−	0.456928i
$496$	11.8510			0.532124
$497$	8.35820	+	14.4768i	0.374917	+	0.649375i
$498$	−37.3020	−	7.39124i	−1.67154	−	0.331209i
$499$	−5.49985	+	9.52603i	−0.246207	+	0.426443i	−0.962470	−	0.271387i	$-0.912518\pi$
$499$	−5.49985	+	9.52603i	−0.246207	+	0.426443i	0.716263	+	0.697830i	$0.245851\pi$
$500$	−2.30859	+	3.99859i	−0.103243	+	0.178822i
$501$	26.8019	+	5.31069i	1.19742	+	0.237264i
$502$	5.85328	+	10.1382i	0.261245	+	0.452489i
$503$	−29.7279			−1.32550			−0.662750	−	0.748841i	$-0.730611\pi$
$503$	−29.7279			−1.32550			−0.662750	+	0.748841i	$0.730611\pi$
$504$	−25.7818	−	10.6346i	−1.14841	−	0.473705i
$505$	12.2904			0.546914
$506$	7.65239	+	13.2543i	0.340190	+	0.589227i
$507$	−1.14106	+	1.30307i	−0.0506762	+	0.0578712i
$508$	−2.61990	+	4.53779i	−0.116239	+	0.201332i
$509$	2.41633	−	4.18521i	0.107102	−	0.185506i	−0.807493	−	0.589877i	$-0.799176\pi$
$509$	2.41633	−	4.18521i	0.107102	−	0.185506i	0.914595	+	0.404371i	$0.132510\pi$
$510$	4.28071	+	12.5801i	0.189553	+	0.557056i
$511$	14.8292	+	25.6850i	0.656007	+	1.13624i
$512$	10.3036			0.455359
$513$	−27.2844	−	18.1437i	−1.20464	−	0.801063i
$514$	−12.5212			−0.552286
$515$	2.58807	+	4.48266i	0.114044	+	0.197530i
$516$	−2.08172	−	6.11774i	−0.0916428	−	0.269318i
$517$	−19.9139	+	34.4919i	−0.875814	+	1.51695i
$518$	−21.6143	+	37.4371i	−0.949678	+	1.64489i
$519$	11.7984	−	13.4736i	0.517894	−	0.591424i
$520$	1.34008	+	2.32108i	0.0587663	+	0.101786i
$521$	−17.2295			−0.754836			−0.377418	−	0.926043i	$-0.623188\pi$
$521$	−17.2295			−0.754836			−0.377418	+	0.926043i	$0.623188\pi$
$522$	−1.34550	−	10.1049i	−0.0588911	−	0.442281i
$523$	9.49365			0.415128			0.207564	−	0.978221i	$-0.433446\pi$
$523$	9.49365			0.415128			0.207564	+	0.978221i	$0.433446\pi$
$524$	−1.34684	−	2.33279i	−0.0588368	−	0.101908i
$525$	24.6922	+	4.89266i	1.07766	+	0.213533i
$526$	−2.70614	+	4.68717i	−0.117993	+	0.204371i
$527$	−5.48675	+	9.50333i	−0.239007	+	0.413971i
$528$	−39.9418	−	7.91430i	−1.73824	−	0.344426i
$529$	9.58911	+	16.6088i	0.416918	+	0.722123i
$530$	9.96713			0.432944
$531$	1.85954	+	13.9654i	0.0806972	+	0.606048i
$532$	11.5353			0.500121
$533$	−2.75305	−	4.76842i	−0.119248	−	0.206543i
$534$	14.3313	−	16.3660i	0.620176	−	0.708228i
$535$	−1.24611	+	2.15833i	−0.0538742	+	0.0933129i
$536$	−2.80633	+	4.86071i	−0.121215	+	0.209951i
$537$	5.49411	+	16.1460i	0.237088	+	0.696751i
$538$	7.26584	+	12.5848i	0.313253	+	0.542569i
$539$	39.7395			1.71170
$540$	−0.173181	+	2.73493i	−0.00745254	+	0.117693i
$541$	−3.51263			−0.151020			−0.0755098	−	0.997145i	$-0.524058\pi$
$541$	−3.51263			−0.151020			−0.0755098	+	0.997145i	$0.524058\pi$
$542$	−20.1913	−	34.9724i	−0.867292	−	1.50219i
$543$	10.6458	+	31.2857i	0.456854	+	1.34260i
$544$	5.73069	−	9.92584i	0.245701	−	0.425567i
$545$	−7.20176	+	12.4738i	−0.308489	+	0.534319i
$546$	−6.94496	+	7.93099i	−0.297217	+	0.339415i
$547$	10.2324	+	17.7231i	0.437507	+	0.757785i	0.997497	−	0.0707152i	$-0.0225281\pi$
$547$	10.2324	+	17.7231i	0.437507	+	0.757785i	−0.559989	+	0.828500i	$0.689195\pi$
$548$	2.84229			0.121416
$549$	5.91690	+	2.44064i	0.252527	+	0.104164i
$550$	29.3949			1.25340
$551$	−6.81344	−	11.8012i	−0.290262	−	0.502749i
$552$	7.97736	+	1.58068i	0.339539	+	0.0672783i
$553$	−5.78867	+	10.0263i	−0.246159	+	0.426360i
$554$	−8.02677	+	13.9028i	−0.341025	+	0.590672i
$555$	−13.4661	−	2.66824i	−0.571602	−	0.113261i
$556$	2.83133	+	4.90400i	0.120075	+	0.207976i
$557$	37.6453			1.59508			0.797540	−	0.603266i	$-0.206134\pi$
$557$	37.6453			1.59508			0.797540	+	0.603266i	$0.206134\pi$
$558$	−9.38240	+	7.22138i	−0.397189	+	0.305705i
$559$	7.89441			0.333898
$560$	10.1976	+	17.6628i	0.430928	+	0.746389i
$561$	24.8387	−	28.3653i	1.04869	−	1.19758i
$562$	15.5291	−	26.8971i	0.655054	−	1.13459i
$563$	−19.5488	+	33.8596i	−0.823885	+	1.42701i	0.0788832	+	0.996884i	$0.474865\pi$
$563$	−19.5488	+	33.8596i	−0.823885	+	1.42701i	−0.902768	+	0.430127i	$0.858469\pi$
$564$	−2.10947	−	6.19929i	−0.0888249	−	0.261037i
$565$	3.09450	+	5.35982i	0.130186	+	0.225489i
$566$	−31.9227			−1.34181
$567$	33.6221	−	9.11539i	1.41199	−	0.382810i
$568$	10.3726			0.435225
$569$	−17.4317	−	30.1926i	−0.730774	−	1.26574i	−0.956553	−	0.291559i	$-0.905826\pi$
$569$	−17.4317	−	30.1926i	−0.730774	−	1.26574i	0.225779	−	0.974179i	$-0.427507\pi$
$570$	6.17388	+	18.1437i	0.258595	+	0.759955i
$571$	5.09367	−	8.82250i	0.213164	−	0.369210i	−0.739539	−	0.673113i	$-0.764957\pi$
$571$	5.09367	−	8.82250i	0.213164	−	0.369210i	0.952703	+	0.303903i	$0.0982899\pi$
$572$	−1.17649	+	2.03774i	−0.0491914	+	0.0852021i
$573$	6.19064	−	7.06958i	0.258618	−	0.295336i
$574$	−16.7562	−	29.0225i	−0.699389	−	1.21138i
$575$	−7.34026			−0.306110
$576$	−12.6516	+	9.73760i	−0.527150	+	0.405733i
$577$	20.5759			0.856587			0.428293	−	0.903640i	$-0.359115\pi$
$577$	20.5759			0.856587			0.428293	+	0.903640i	$0.359115\pi$
$578$	1.66405	+	2.88222i	0.0692153	+	0.119884i
$579$	−30.2496	−	5.99383i	−1.25713	−	0.249095i
$580$	−0.569841	+	0.986994i	−0.0236614	+	0.0409827i
$581$	27.0215	−	46.8026i	1.12104	−	1.94170i
$582$	−20.4477	−	4.05162i	−0.847583	−	0.167945i
$583$	−14.1399	−	24.4910i	−0.585615	−	1.01432i
$584$	18.4032			0.761530
$585$	−3.09481	−	1.27657i	−0.127954	−	0.0527795i
$586$	12.7663			0.527370
$587$	−1.25881	−	2.18032i	−0.0519567	−	0.0899916i	0.838877	−	0.544320i	$-0.183212\pi$
$587$	−1.25881	−	2.18032i	−0.0519567	−	0.0899916i	−0.890834	+	0.454329i	$0.849879\pi$
$588$	−4.30443	+	4.91557i	−0.177512	+	0.202715i
$589$	−7.91329	+	13.7062i	−0.326061	+	0.564755i
$590$	4.12030	−	7.13657i	0.169630	−	0.293808i
$591$	5.52535	+	16.2378i	0.227283	+	0.667934i
$592$	16.7685	+	29.0438i	0.689179	+	1.19369i
$593$	−1.33875			−0.0549761			−0.0274880	−	0.999622i	$-0.508751\pi$
$593$	−1.33875			−0.0549761			−0.0274880	+	0.999622i	$0.508751\pi$
$594$	36.4445	−	18.0728i	1.49533	−	0.741534i
$595$	−18.8851			−0.774214
$596$	−4.76228	−	8.24852i	−0.195071	−	0.337872i
$597$	−5.24343	−	15.4093i	−0.214599	−	0.630660i
$598$	1.53702	−	2.66220i	0.0628536	−	0.108866i
$599$	−0.143216	+	0.248057i	−0.00585165	+	0.0101354i	−0.868936	−	0.494924i	$-0.835196\pi$
$599$	−0.143216	+	0.248057i	−0.00585165	+	0.0101354i	0.863085	+	0.505059i	$0.168529\pi$
$600$	10.2900	−	11.7510i	0.420087	−	0.479731i
$601$	2.56733	+	4.44675i	0.104724	+	0.181387i	0.913625	−	0.406557i	$-0.133271\pi$
$601$	2.56733	+	4.44675i	0.104724	+	0.181387i	−0.808902	+	0.587944i	$0.799938\pi$
$602$	48.0486			1.95831
$603$	−0.925332	−	6.94938i	−0.0376824	−	0.283000i
$604$	0.510606			0.0207763
$605$	7.69285	+	13.3244i	0.312759	+	0.541714i
$606$	29.4245	+	5.83034i	1.19529	+	0.236841i
$607$	−15.8953	+	27.5316i	−0.645172	+	1.11747i	0.339089	+	0.940754i	$0.389881\pi$
$607$	−15.8953	+	27.5316i	−0.645172	+	1.11747i	−0.984262	+	0.176717i	$0.943452\pi$
$608$	8.26511	−	14.3156i	0.335194	−	0.580574i
$609$	14.2112	+	2.81590i	0.575869	+	0.114106i
$610$	−1.87186	−	3.24215i	−0.0757892	−	0.131271i
$611$	7.99965			0.323631
$612$	0.818205	+	6.14484i	0.0330740	+	0.248390i
$613$	−21.8649			−0.883116			−0.441558	−	0.897233i	$-0.645574\pi$
$613$	−21.8649			−0.883116			−0.441558	+	0.897233i	$0.645574\pi$
$614$	−11.1576	−	19.3256i	−0.450285	−	0.779916i
$615$	7.01107	−	8.00650i	0.282714	−	0.322853i
$616$	23.1418	−	40.0828i	0.932411	−	1.61498i
$617$	−4.10686	+	7.11329i	−0.165336	+	0.286370i	−0.936775	−	0.349933i	$-0.886204\pi$
$617$	−4.10686	+	7.11329i	−0.165336	+	0.286370i	0.771439	+	0.636304i	$0.219538\pi$
$618$	4.06961	+	11.9597i	0.163704	+	0.481090i
$619$	0.346345	+	0.599887i	0.0139208	+	0.0241115i	0.872902	−	0.487896i	$-0.162235\pi$
$619$	0.346345	+	0.599887i	0.0139208	+	0.0241115i	−0.858981	+	0.512007i	$0.828902\pi$
$620$	1.32365			0.0531592
$621$	−9.10062	+	4.51298i	−0.365195	+	0.181100i
$622$	−42.6552			−1.71032
$623$	15.4580	+	26.7740i	0.619311	+	1.07268i
$624$	2.63460	+	7.74253i	0.105468	+	0.309949i
$625$	−3.93581	+	6.81702i	−0.157432	+	0.272681i
$626$	−21.3749	+	37.0224i	−0.854313	+	1.47971i
$627$	35.8237	−	40.9099i	1.43066	−	1.63379i
$628$	4.91407	+	8.51143i	0.196093	+	0.339643i
$629$	−31.0538			−1.23819
$630$	−18.8363	−	7.76970i	−0.750454	−	0.309552i
$631$	3.59567			0.143141			0.0715707	−	0.997436i	$-0.477199\pi$
$631$	3.59567			0.143141			0.0715707	+	0.997436i	$0.477199\pi$
$632$	3.59189	+	6.22134i	0.142878	+	0.247472i
$633$	38.6402	+	7.65640i	1.53581	+	0.304315i
$634$	20.0094	−	34.6572i	0.794674	−	1.37641i
$635$	6.18607	−	10.7146i	0.245487	−	0.425195i
$636$	4.56100	+	0.903743i	0.180855	+	0.0358357i
$637$	−3.99095	−	6.91253i	−0.158127	−	0.273884i
$638$	16.9178			0.669783
$639$	−10.2673	+	7.90244i	−0.406167	+	0.312616i
$640$	15.1886			0.600384
$641$	−11.6855	−	20.2398i	−0.461548	−	0.799424i	0.537491	−	0.843270i	$-0.319372\pi$
$641$	−11.6855	−	20.2398i	−0.461548	−	0.799424i	−0.999038	+	0.0438456i	$0.986039\pi$
$642$	−4.00721	+	4.57615i	−0.158152	+	0.180606i
$643$	9.86171	−	17.0810i	0.388908	−	0.673608i	−0.603395	−	0.797442i	$-0.706186\pi$
$643$	9.86171	−	17.0810i	0.388908	−	0.673608i	0.992303	+	0.123834i	$0.0395191\pi$
$644$	1.78808	−	3.09705i	0.0704604	−	0.122041i
$645$	4.91534	+	14.4451i	0.193542	+	0.568777i
$646$	21.6769	+	37.5456i	0.852868	+	1.47721i
$647$	36.9338			1.45202			0.726008	−	0.687686i	$-0.241373\pi$
$647$	36.9338			1.45202			0.726008	+	0.687686i	$0.241373\pi$
$648$	5.53296	−	20.8956i	0.217355	−	0.820858i
$649$	−23.3811			−0.917790
$650$	−2.95207	−	5.11313i	−0.115790	−	0.200553i
$651$	−5.42034	−	15.9292i	−0.212440	−	0.624315i
$652$	−5.50853	+	9.54105i	−0.215731	+	0.373657i
$653$	12.0573	−	20.8839i	0.471841	−	0.817252i	−0.527640	−	0.849468i	$-0.676923\pi$
$653$	12.0573	−	20.8839i	0.471841	−	0.817252i	0.999481	+	0.0322160i	$0.0102565\pi$
$654$	−23.1591	+	26.4472i	−0.905594	+	1.03417i
$655$	3.18014	+	5.50816i	0.124258	+	0.215222i
$656$	−25.9990			−1.01509
$657$	−18.2163	+	14.0206i	−0.710687	+	0.546996i
$658$	48.6891			1.89810
$659$	−0.306111	−	0.530200i	−0.0119244	−	0.0206537i	0.860002	−	0.510291i	$-0.170462\pi$
$659$	−0.306111	−	0.530200i	−0.0119244	−	0.0206537i	−0.871926	+	0.489638i	$0.837129\pi$
$660$	−4.46116	−	0.883960i	−0.173650	−	0.0344081i
$661$	−16.5228	+	28.6183i	−0.642663	+	1.11312i	0.342173	+	0.939637i	$0.388837\pi$
$661$	−16.5228	+	28.6183i	−0.642663	+	1.11312i	−0.984836	+	0.173488i	$0.944496\pi$
$662$	−2.83259	+	4.90620i	−0.110092	+	0.190685i
$663$	−7.42852	−	1.47193i	−0.288500	−	0.0571651i
$664$	−16.7670	−	29.0412i	−0.650684	−	1.12702i
$665$	−27.2371			−1.05621
$666$	−30.9734	−	12.7761i	−1.20020	−	0.495065i
$667$	−4.22458			−0.163576
$668$	−3.72768	−	6.45654i	−0.144228	−	0.249811i
$669$	−21.9661	+	25.0848i	−0.849257	+	0.969834i
$670$	−2.05031	+	3.55125i	−0.0792106	+	0.137197i
$671$	−5.31103	+	9.19898i	−0.205030	+	0.355123i
$672$	5.66133	+	16.6374i	0.218390	+	0.641802i
$673$	−20.7180	−	35.8846i	−0.798619	−	1.38325i	−0.920516	−	0.390705i	$-0.872231\pi$
$673$	−20.7180	−	35.8846i	−0.798619	−	1.38325i	0.121897	−	0.992543i	$-0.461102\pi$
$674$	8.96889			0.345469
$675$	−1.23295	+	19.4711i	−0.0474563	+	0.749445i
$676$	0.472608			0.0181772
$677$	12.7842	+	22.1429i	0.491336	+	0.851019i	0.999950	−	0.00997530i	$-0.00317529\pi$
$677$	12.7842	+	22.1429i	0.491336	+	0.851019i	−0.508614	+	0.860995i	$0.669842\pi$
$678$	4.86595	+	14.3000i	0.186876	+	0.549187i
$679$	14.8123	−	25.6556i	0.568442	−	0.984571i
$680$	−5.85915	+	10.1483i	−0.224688	+	0.389171i
$681$	5.87216	−	6.70589i	0.225022	−	0.256970i
$682$	−9.82437	−	17.0163i	−0.376195	−	0.651588i
$683$	−24.4296			−0.934772			−0.467386	−	0.884053i	$-0.654804\pi$
$683$	−24.4296			−0.934772			−0.467386	+	0.884053i	$0.654804\pi$
$684$	1.18006	+	8.86242i	0.0451207	+	0.338863i
$685$	−6.71118			−0.256421
$686$	−2.98811	−	5.17556i	−0.114087	−	0.197604i
$687$	15.3684	+	3.04518i	0.586339	+	0.116181i
$688$	18.6381	−	32.2822i	0.710572	−	1.23075i
$689$	−2.84008	+	4.91916i	−0.108198	+	0.187405i
$690$	5.82829	+	1.15485i	0.221879	+	0.0439644i
$691$	2.50550	+	4.33966i	0.0953138	+	0.165088i	0.909740	−	0.415179i	$-0.136281\pi$
$691$	2.50550	+	4.33966i	0.0953138	+	0.165088i	−0.814426	+	0.580268i	$0.802948\pi$
$692$	−4.88672			−0.185765
$693$	7.63056	+	57.3066i	0.289861	+	2.17690i
$694$	−55.4279			−2.10401
$695$	−6.68530	−	11.5793i	−0.253588	−	0.439227i
$696$	5.92225	−	6.76309i	0.224482	−	0.256354i
$697$	12.0370	−	20.8487i	0.455934	−	0.789700i
$698$	8.57416	−	14.8509i	0.324537	−	0.562114i
$699$	−3.17535	−	9.33166i	−0.120103	−	0.352956i
$700$	−3.43426	−	5.94831i	−0.129803	−	0.224825i
$701$	−50.6694			−1.91376			−0.956879	−	0.290486i	$-0.906183\pi$
$701$	−50.6694			−1.91376			−0.956879	+	0.290486i	$0.906183\pi$
$702$	−6.80372	−	4.52436i	−0.256790	−	0.170761i
$703$	−44.7874			−1.68919
$704$	−13.2476	−	22.9455i	−0.499287	−	0.864790i
$705$	4.98087	+	14.6377i	0.187590	+	0.551287i
$706$	−12.8879	+	22.3225i	−0.485043	+	0.840120i
$707$	−21.3150	+	36.9187i	−0.801635	+	1.38847i
$708$	2.53256	−	2.89213i	0.0951793	−	0.108693i
$709$	−11.9738	−	20.7393i	−0.449686	−	0.778879i	0.548679	−	0.836033i	$-0.315131\pi$
$709$	−11.9738	−	20.7393i	−0.449686	−	0.778879i	−0.998365	+	0.0571538i	$0.981797\pi$
$710$	7.57826			0.284407
$711$	−8.29520	−	3.42166i	−0.311094	−	0.128322i
$712$	19.1835			0.718931
$713$	2.45326	+	4.24918i	0.0918754	+	0.159133i
$714$	−45.2130	−	8.95877i	−1.69205	−	0.335274i
$715$	2.77791	−	4.81148i	0.103888	−	0.179939i
$716$	2.32684	−	4.03020i	0.0869580	−	0.150616i
$717$	−17.7574	−	3.51856i	−0.663162	−	0.131403i
$718$	−1.03380	−	1.79059i	−0.0385809	−	0.0668241i
$719$	−37.9792			−1.41639			−0.708193	−	0.706019i	$-0.750489\pi$
$719$	−37.9792			−1.41639			−0.708193	+	0.706019i	$0.750489\pi$
$720$	−12.5268	+	9.64155i	−0.466847	+	0.359319i
$721$	−17.9538			−0.668635
$722$	16.3253	+	28.2763i	0.607567	+	1.05234i
$723$	−17.0046	+	19.4189i	−0.632408	+	0.722197i
$724$	4.50865	−	7.80922i	0.167563	−	0.290227i
$725$	−4.05694	+	7.02683i	−0.150671	+	0.260970i
$726$	12.0966	+	35.5494i	0.448949	+	1.31936i
$727$	−14.2552	−	24.6908i	−0.528698	−	0.915731i	−0.999440	−	0.0334607i	$-0.989347\pi$
$727$	−14.2552	−	24.6908i	−0.528698	−	0.915731i	0.470742	−	0.882271i	$-0.343986\pi$
$728$	−9.29633			−0.344545
$729$	10.4427	+	24.8988i	0.386767	+	0.922177i
$730$	13.4454			0.497638
$731$	17.2581	+	29.8920i	0.638315	+	1.10559i
$732$	−0.562595	−	1.65335i	−0.0207941	−	0.0611094i
$733$	0.489397	−	0.847661i	0.0180763	−	0.0313091i	−0.856846	−	0.515573i	$-0.827579\pi$
$733$	0.489397	−	0.847661i	0.0180763	−	0.0313091i	0.874922	+	0.484264i	$0.160912\pi$
$734$	−18.2064	+	31.5345i	−0.672012	+	1.16396i
$735$	10.1636	−	11.6066i	0.374889	−	0.428116i
$736$	−2.56233	−	4.43809i	−0.0944489	−	0.163590i
$737$	11.6347			0.428571
$738$	20.5834	−	15.8425i	0.757685	−	0.583170i
$739$	−36.9812			−1.36038			−0.680188	−	0.733038i	$-0.738102\pi$
$739$	−36.9812			−1.36038			−0.680188	+	0.733038i	$0.738102\pi$
$740$	1.87290	+	3.24395i	0.0688490	+	0.119250i
$741$	−10.7138	−	2.12290i	−0.393582	−	0.0779866i
$742$	−17.2859	+	29.9400i	−0.634584	+	1.09913i
$743$	14.1476	−	24.5043i	0.519024	−	0.898975i	−0.480732	−	0.876868i	$-0.659629\pi$
$743$	14.1476	−	24.5043i	0.519024	−	0.898975i	0.999756	−	0.0221077i	$-0.00703767\pi$
$744$	−10.2416	−	2.02933i	−0.375475	−	0.0743988i
$745$	11.2447	+	19.4763i	0.411972	+	0.713557i
$746$	47.7808			1.74938
$747$	38.7220	+	15.9723i	1.41676	+	0.584396i
$748$	−10.2878			−0.376159
$749$	−4.32224	−	7.48634i	−0.157931	−	0.273545i
$750$	17.5292	−	20.0179i	0.640074	−	0.730951i
$751$	5.30501	−	9.18854i	0.193582	−	0.335295i	−0.752852	−	0.658189i	$-0.771323\pi$
$751$	5.30501	−	9.18854i	0.193582	−	0.335295i	0.946435	+	0.322895i	$0.104656\pi$
$752$	18.8866	−	32.7125i	0.688723	−	1.19290i
$753$	−4.15388	−	12.2074i	−0.151376	−	0.444861i
$754$	−1.69902	−	2.94279i	−0.0618746	−	0.107170i
$755$	−1.20564			−0.0438776
$756$	−7.91504	−	5.26337i	−0.287867	−	0.191427i
$757$	−17.0596			−0.620040			−0.310020	−	0.950730i	$-0.600336\pi$
$757$	−17.0596			−0.620040			−0.310020	+	0.950730i	$0.600336\pi$
$758$	25.0900	+	43.4571i	0.911309	+	1.57843i
$759$	−5.43065	−	15.9595i	−0.197120	−	0.579293i
$760$	−8.45038	+	14.6365i	−0.306528	+	0.530921i
$761$	8.78193	−	15.2108i	0.318345	−	0.551389i	−0.661798	−	0.749682i	$-0.730206\pi$
$761$	8.78193	−	15.2108i	0.318345	−	0.551389i	0.980143	+	0.198293i	$0.0635397\pi$
$762$	19.8929	−	22.7173i	0.720645	−	0.822961i
$763$	−24.9798	−	43.2664i	−0.904331	−	1.56635i
$764$	−2.56406			−0.0927645
$765$	−1.93194	−	14.5091i	−0.0698493	−	0.524579i
$766$	48.7128			1.76007
$767$	2.34811	+	4.06705i	0.0847855	+	0.146853i
$768$	18.2799	+	3.62210i	0.659621	+	0.130701i
$769$	4.60704	−	7.97963i	0.166134	−	0.287753i	−0.770923	−	0.636928i	$-0.780205\pi$
$769$	4.60704	−	7.97963i	0.166134	−	0.287753i	0.937057	+	0.349175i	$0.113538\pi$
$770$	16.9075	−	29.2847i	0.609304	−	1.05535i
$771$	13.5290	+	2.68072i	0.487235	+	0.0965436i
$772$	4.20719	+	7.28707i	0.151420	+	0.262267i
$773$	27.0112			0.971525			0.485762	−	0.874091i	$-0.338542\pi$
$773$	27.0112			0.971525			0.485762	+	0.874091i	$0.338542\pi$
$774$	4.91534	+	36.9150i	0.176678	+	1.32688i
$775$	9.42365			0.338508
$776$	−9.19107	−	15.9194i	−0.329940	−	0.571473i
$777$	31.3691	−	35.8228i	1.12536	−	1.28514i
$778$	−15.8823	+	27.5090i	−0.569409	+	0.986245i
$779$	17.3604	−	30.0691i	0.622001	−	1.07734i
$780$	0.294263	+	0.864775i	0.0105363	+	0.0309639i
$781$	−10.7509	−	18.6211i	−0.384698	−	0.666317i
$782$	13.4405			0.480631
$783$	−0.709607	+	11.2063i	−0.0253593	+	0.400482i
$784$	−37.6894			−1.34605
$785$	−11.6031	−	20.0971i	−0.414131	−	0.717296i
$786$	5.00061	+	14.6957i	0.178366	+	0.524179i
$787$	−4.00528	+	6.93734i	−0.142773	+	0.247290i	−0.928540	−	0.371233i	$-0.878935\pi$
$787$	−4.00528	+	6.93734i	−0.142773	+	0.247290i	0.785767	+	0.618523i	$0.212268\pi$
$788$	2.34007	−	4.05312i	0.0833615	−	0.144386i
$789$	3.92746	−	4.48507i	0.139821	−	0.159673i
$790$	2.62425	+	4.54533i	0.0933666	+	0.161716i
$791$	−21.4670			−0.763278
$792$	33.1624	+	13.6790i	1.17837	+	0.486064i
$793$	2.13350			0.0757628
$794$	−19.1097	−	33.0990i	−0.678178	−	1.17464i
$795$	−10.7694	−	2.13391i	−0.381950	−	0.0756819i
$796$	−2.22067	+	3.84632i	−0.0787096	+	0.136329i
$797$	9.79921	−	16.9727i	0.347106	−	0.601205i	−0.638628	−	0.769515i	$-0.720498\pi$
$797$	9.79921	−	16.9727i	0.347106	−	0.601205i	0.985734	+	0.168311i	$0.0538312\pi$
$798$	−65.2087	−	12.9208i	−2.30836	−	0.457392i
$799$	17.4882	+	30.2904i	0.618688	+	1.07160i
$800$	−9.84263			−0.347989
$801$	−18.9887	+	14.6151i	−0.670932	+	0.516398i
$802$	−39.3651			−1.39003
$803$	−19.0744	−	33.0379i	−0.673122	−	1.16588i
$804$	−1.26023	+	1.43916i	−0.0444449	+	0.0507552i
$805$	−4.22200	+	7.31273i	−0.148806	+	0.257740i
$806$	−1.97328	+	3.41782i	−0.0695058	+	0.120388i
$807$	−5.15632	−	15.1533i	−0.181511	−	0.533422i
$808$	13.2261	+	22.9082i	0.465292	+	0.805909i
$809$	42.9313			1.50938			0.754691	−	0.656080i	$-0.227787\pi$
$809$	42.9313			1.50938			0.754691	+	0.656080i	$0.227787\pi$
$810$	4.04240	−	15.2664i	0.142035	−	0.536407i
$811$	21.7459			0.763600			0.381800	−	0.924245i	$-0.375304\pi$
$811$	21.7459			0.763600			0.381800	+	0.924245i	$0.375304\pi$
$812$	−1.97654	−	3.42346i	−0.0693629	−	0.120140i
$813$	14.3291	+	42.1102i	0.502544	+	1.47687i
$814$	27.8019	−	48.1543i	0.974455	−	1.68781i
$815$	13.0067	−	22.5282i	0.455604	−	0.789130i
$816$	−23.5573	+	26.9019i	−0.824670	+	0.941756i
$817$	24.8906	+	43.1118i	0.870813	+	1.50829i
$818$	29.2627			1.02315
$819$	9.20193	−	7.08248i	0.321542	−	0.247482i
$820$	−2.90387			−0.101408
$821$	4.07220	+	7.05326i	0.142121	+	0.246161i	0.928295	−	0.371844i	$-0.121274\pi$
$821$	4.07220	+	7.05326i	0.142121	+	0.246161i	−0.786174	+	0.618005i	$0.787941\pi$
$822$	−16.0673	−	3.18366i	−0.560411	−	0.111043i
$823$	−0.204811	+	0.354744i	−0.00713928	+	0.0123656i	−0.869573	−	0.493804i	$-0.835606\pi$
$823$	−0.204811	+	0.354744i	−0.00713928	+	0.0123656i	0.862434	+	0.506170i	$0.168939\pi$
$824$	−5.57021	+	9.64789i	−0.194047	+	0.336100i
$825$	−31.7609	−	6.29329i	−1.10577	−	0.219104i
$826$	14.2916	+	24.7538i	0.497268	+	0.861293i
$827$	35.2456			1.22561			0.612804	−	0.790235i	$-0.290041\pi$
$827$	35.2456			1.22561			0.612804	+	0.790235i	$0.290041\pi$
$828$	2.56233	+	1.05693i	0.0890473	+	0.0367308i
$829$	−10.9615			−0.380710			−0.190355	−	0.981715i	$-0.560964\pi$
$829$	−10.9615			−0.380710			−0.190355	+	0.981715i	$0.560964\pi$
$830$	−12.2500	−	21.2176i	−0.425204	−	0.736474i
$831$	11.6493	−	13.3033i	0.404111	−	0.461487i
$832$	−2.66085	+	4.60872i	−0.0922483	+	0.159779i
$833$	17.4494	−	30.2232i	0.604586	−	1.04717i
$834$	−10.5123	−	30.8934i	−0.364012	−	1.06975i
$835$	8.80177	+	15.2451i	0.304598	+	0.527579i
$836$	−14.8376			−0.513169
$837$	11.6836	−	5.79391i	0.403846	−	0.200267i
$838$	31.0855			1.07383
$839$	12.0475	+	20.8668i	0.415925	+	0.720403i	0.995525	−	0.0944981i	$-0.0301246\pi$
$839$	12.0475	+	20.8668i	0.415925	+	0.720403i	−0.579600	+	0.814901i	$0.696791\pi$
$840$	−5.78823	−	17.0104i	−0.199713	−	0.586913i
$841$	12.1651	−	21.0705i	0.419486	−	0.726571i
$842$	0.381153	−	0.660176i	0.0131354	−	0.0227512i
$843$	−22.5375	+	25.7374i	−0.776233	+	0.886442i
$844$	−5.37419	−	9.30837i	−0.184987	−	0.320407i
$845$	−1.11592			−0.0383887
$846$	4.98087	+	37.4070i	0.171246	+	1.28608i
$847$	−53.3665			−1.83369
$848$	13.4104	+	23.2276i	0.460517	+	0.797638i
$849$	34.4921	+	6.83448i	1.18377	+	0.234559i
$850$	12.9071	−	22.3558i	0.442712	−	0.766799i
$851$	−6.94246	+	12.0247i	−0.237984	+	0.412201i
$852$	3.46784	+	0.687138i	0.118806	+	0.0235410i
$853$	3.95635	+	6.85260i	0.135463	+	0.234629i	0.925774	−	0.378077i	$-0.123415\pi$
$853$	3.95635	+	6.85260i	0.135463	+	0.234629i	−0.790311	+	0.612705i	$0.790081\pi$
$854$	12.9853			0.444349
$855$	−2.78634	−	20.9259i	−0.0952910	−	0.715649i
$856$	−5.36394			−0.183336
$857$	6.01297	+	10.4148i	0.205399	+	0.355762i	0.950260	−	0.311458i	$-0.100817\pi$
$857$	6.01297	+	10.4148i	0.205399	+	0.355762i	−0.744861	+	0.667220i	$0.767484\pi$
$858$	8.93310	−	10.2014i	0.304971	−	0.348271i
$859$	−13.0444	+	22.5936i	−0.445070	+	0.770884i	−0.998057	−	0.0623058i	$-0.980155\pi$
$859$	−13.0444	+	22.5936i	−0.445070	+	0.770884i	0.552987	+	0.833190i	$0.313488\pi$
$860$	2.08172	−	3.60565i	0.0709862	−	0.122952i
$861$	11.8913	+	34.9460i	0.405254	+	1.19095i
$862$	−5.27857	−	9.14275i	−0.179789	−	0.311403i
$863$	29.5606			1.00625			0.503127	−	0.864213i	$-0.332183\pi$
$863$	29.5606			1.00625			0.503127	+	0.864213i	$0.332183\pi$
$864$	−12.2031	+	6.05150i	−0.415158	+	0.205876i
$865$	11.5385			0.392320
$866$	1.16470	+	2.01732i	0.0395781	+	0.0685513i
$867$	−1.18092	−	3.47047i	−0.0401061	−	0.117863i
$868$	−2.29560	+	3.97609i	−0.0779176	+	0.134957i
$869$	7.44581	−	12.8965i	0.252582	−	0.437484i
$870$	4.32682	−	4.94114i	0.146693	−	0.167520i
$871$	−1.16845	−	2.02382i	−0.0395915	−	0.0685744i
$872$	−31.0002			−1.04980
$873$	21.2261	+	8.75547i	0.718393	+	0.296328i
$874$	19.3846			0.655694
$875$	18.9072	+	32.7483i	0.639181	+	1.10709i
$876$	6.15268	+	1.21913i	0.207880	+	0.0411906i
$877$	6.96208	−	12.0587i	0.235093	−	0.407193i	−0.724207	−	0.689583i	$-0.757794\pi$
$877$	6.96208	−	12.0587i	0.235093	−	0.407193i	0.959300	+	0.282390i	$0.0911273\pi$
$878$	5.87462	−	10.1751i	0.198259	−	0.343394i
$879$	−13.7938	−	2.73319i	−0.465255	−	0.0921883i
$880$	−13.1169	−	22.7191i	−0.442171	−	0.765862i
$881$	−37.5189			−1.26404			−0.632022	−	0.774950i	$-0.717775\pi$
$881$	−37.5189			−1.26404			−0.632022	+	0.774950i	$0.717775\pi$
$882$	29.8387	−	22.9660i	1.00472	−	0.773306i
$883$	37.4210			1.25932			0.629658	−	0.776872i	$-0.283195\pi$
$883$	37.4210			1.25932			0.629658	+	0.776872i	$0.283195\pi$
$884$	1.03318	+	1.78952i	0.0347496	+	0.0601880i
$885$	−5.97984	+	6.82886i	−0.201010	+	0.229550i
$886$	31.3495	−	54.2989i	1.05321	−	1.82421i
$887$	4.27014	−	7.39609i	0.143377	−	0.248336i	−0.785389	−	0.619002i	$-0.787537\pi$
$887$	4.27014	−	7.39609i	0.143377	−	0.248336i	0.928766	+	0.370666i	$0.120870\pi$
$888$	−9.51788	−	27.9710i	−0.319399	−	0.938645i
$889$	21.4569	+	37.1644i	0.719640	+	1.24645i
$890$	14.0155			0.469801
$891$	−43.2471	+	11.7249i	−1.44883	+	0.392798i
$892$	9.09798			0.304623
$893$	25.2224	+	43.6865i	0.844036	+	1.46191i
$894$	17.6817	+	51.9627i	0.591364	+	1.73789i
$895$	−5.49411	+	9.51607i	−0.183648	+	0.318087i
$896$	−26.3415	+	45.6248i	−0.880008	+	1.52422i
$897$	−2.23070	+	2.54742i	−0.0744810	+	0.0850557i
$898$	10.0383	+	17.3869i	0.334983	+	0.580208i
$899$	5.42365			0.180889
$900$	4.21867	−	3.24699i	0.140622	−	0.108233i
$901$	−24.8350			−0.827374
$902$	21.5530	+	37.3309i	0.717636	+	1.24298i
$903$	−51.9160	−	10.2869i	−1.72766	−	0.342328i
$904$	−6.66018	+	11.5358i	−0.221514	+	0.383674i
$905$	−10.6458	+	18.4390i	−0.353878	+	0.612935i
$906$	−2.88642	−	0.571933i	−0.0958950	−	0.0190012i
$907$	8.93992	+	15.4844i	0.296845	+	0.514151i	0.975412	−	0.220388i	$-0.0707322\pi$
$907$	8.93992	+	15.4844i	0.296845	+	0.514151i	−0.678567	+	0.734538i	$0.737399\pi$
$908$	−2.43215			−0.0807138
$909$	−30.5446	−	12.5992i	−1.01310	−	0.417890i
$910$	−6.79193			−0.225150
$911$	−23.2627	−	40.2921i	−0.770727	−	1.33494i	−0.937165	−	0.348886i	$-0.886560\pi$
$911$	−23.2627	−	40.2921i	−0.770727	−	1.33494i	0.166438	−	0.986052i	$-0.446773\pi$
$912$	−33.9756	+	38.7994i	−1.12505	+	1.28478i
$913$	−34.7570	+	60.2009i	−1.15029	+	1.99236i
$914$	−7.30910	+	12.6597i	−0.241763	+	0.418746i
$915$	1.32839	+	3.90386i	0.0439153	+	0.129058i
$916$	−2.13747	−	3.70221i	−0.0706241	−	0.122324i
$917$	−22.0611			−0.728521
$918$	2.25761	−	35.6529i	0.0745123	−	1.17672i
$919$	7.44747			0.245669			0.122835	−	0.992427i	$-0.460802\pi$
$919$	7.44747			0.245669			0.122835	+	0.992427i	$0.460802\pi$
$920$	2.61977	+	4.53758i	0.0863713	+	0.149599i
$921$	7.91819	+	23.2699i	0.260913	+	0.766768i
$922$	−9.91174	+	17.1676i	−0.326426	+	0.565386i
$923$	−2.15938	+	3.74016i	−0.0710769	+	0.123109i
$924$	10.3922	−	11.8677i	0.341880	−	0.390420i
$925$	13.3339	+	23.0951i	0.438417	+	0.759361i
$926$	−24.0596			−0.790648
$927$	−1.83667	−	13.7936i	−0.0603240	−	0.453042i
$928$	−5.66478			−0.185956
$929$	13.0210	+	22.5530i	0.427204	+	0.739938i	0.996623	−	0.0821086i	$-0.0261654\pi$
$929$	13.0210	+	22.5530i	0.427204	+	0.739938i	−0.569420	+	0.822047i	$0.692832\pi$
$930$	−7.48254	−	1.48263i	−0.245362	−	0.0486175i
$931$	25.1665	−	43.5896i	0.824797	−	1.42859i
$932$	−1.34481	+	2.32928i	−0.0440507	+	0.0762980i
$933$	46.0885	+	9.13224i	1.50887	+	0.298976i
$934$	13.2950	+	23.0277i	0.435027	+	0.753488i
$935$	24.2914			0.794414
$936$	−0.951009	−	7.14222i	−0.0310847	−	0.233451i
$937$	38.7266			1.26514			0.632571	−	0.774502i	$-0.282000\pi$
$937$	38.7266			1.26514			0.632571	+	0.774502i	$0.282000\pi$
$938$	−7.11167	−	12.3178i	−0.232204	−	0.402190i
$939$	31.0216	−	35.4261i	1.01235	−	1.15609i
$940$	2.10947	−	3.65372i	0.0688034	−	0.119171i
$941$	15.1751	−	26.2840i	0.494693	−	0.856834i	−0.505288	−	0.862951i	$-0.668614\pi$
$941$	15.1751	−	26.2840i	0.494693	−	0.856834i	0.999981	+	0.00611707i	$0.00194713\pi$
$942$	−18.2453	−	53.6189i	−0.594463	−	1.74700i
$943$	−5.38204	−	9.32197i	−0.175263	−	0.303565i
$944$	22.1749			0.721733
$945$	18.6889	+	12.4278i	0.607951	+	0.404277i
$946$	−61.8036			−2.00941
$947$	−23.9432	−	41.4709i	−0.778050	−	1.34762i	−0.933064	−	0.359710i	$-0.882876\pi$
$947$	−23.9432	−	41.4709i	−0.778050	−	1.34762i	0.155014	−	0.987912i	$-0.450458\pi$
$948$	0.788731	+	2.31791i	0.0256168	+	0.0752822i
$949$	−3.83120	+	6.63584i	−0.124366	+	0.215408i
$950$	18.6154	−	32.2428i	0.603963	−	1.04609i
$951$	−29.0398	+	33.1629i	−0.941681	+	1.07538i
$952$	−20.3229	−	35.2003i	−0.658669	−	1.14085i
$953$	−59.0107			−1.91154			−0.955772	−	0.294109i	$-0.904977\pi$
$953$	−59.0107			−1.91154			−0.955772	+	0.294109i	$0.904977\pi$
$954$	−24.7708	−	10.2176i	−0.801983	−	0.330807i
$955$	6.05423			0.195910
$956$	2.46975	+	4.27773i	0.0798773	+	0.138352i
$957$	−18.2795	−	3.62201i	−0.590893	−	0.117083i
$958$	−7.96213	+	13.7908i	−0.257245	+	0.445561i
$959$	11.6391	−	20.1595i	0.375847	−	0.650985i
$960$	−10.0897	−	1.99924i	−0.325645	−	0.0645252i
$961$	12.3504	+	21.3916i	0.398401	+	0.690051i
$962$	−11.1683			−0.360081
$963$	5.30947	−	4.08656i	0.171095	−	0.131687i
$964$	7.04303			0.226841
$965$	−9.93397	−	17.2061i	−0.319786	−	0.553886i
$966$	−13.5770	+	15.5046i	−0.436832	+	0.498853i
$967$	−13.7859	+	23.8779i	−0.443325	+	0.767862i	−0.997934	−	0.0642496i	$-0.979535\pi$
$967$	−13.7859	+	23.8779i	−0.443325	+	0.767862i	0.554609	+	0.832111i	$0.312868\pi$
$968$	−16.5571	+	28.6777i	−0.532164	+	0.921735i
$969$	−15.3834	−	45.2085i	−0.494186	−	1.45231i
$970$	−6.71503	−	11.6308i	−0.215606	−	0.373441i
$971$	2.16029			0.0693270			0.0346635	−	0.999399i	$-0.488964\pi$
$971$	2.16029			0.0693270			0.0346635	+	0.999399i	$0.488964\pi$
$972$	3.23406	−	6.61944i	0.103732	−	0.212319i
$973$	46.3770			1.48678
$974$	0.143003	+	0.247689i	0.00458212	+	0.00793646i
$975$	2.09498	+	6.15670i	0.0670932	+	0.197172i
$976$	5.03704	−	8.72441i	0.161232	−	0.279262i
$977$	−10.1025	+	17.4980i	−0.323208	+	0.559812i	−0.981148	−	0.193258i	$-0.938095\pi$
$977$	−10.1025	+	17.4980i	−0.323208	+	0.559812i	0.657940	+	0.753070i	$0.271428\pi$
$978$	41.8264	−	47.7649i	1.33746	−	1.52735i
$979$	−19.8832	−	34.4387i	−0.635469	−	1.10066i
$980$	−4.20959			−0.134470
$981$	30.6854	−	23.6177i	0.979710	−	0.754056i
$982$	−11.4151			−0.364271
$983$	4.46476	+	7.73319i	0.142404	+	0.246650i	0.928401	−	0.371579i	$-0.121184\pi$
$983$	4.46476	+	7.73319i	0.142404	+	0.246650i	−0.785998	+	0.618229i	$0.787850\pi$
$984$	22.4683	+	4.45200i	0.716263	+	0.141925i
$985$	−5.52535	+	9.57019i	−0.176052	+	0.304931i
$986$	7.42852	−	12.8666i	0.236572	−	0.409755i
$987$	−52.6081	−	10.4241i	−1.67453	−	0.331802i
$988$	1.49011	+	2.58094i	0.0474066	+	0.0821106i
$989$	15.4331			0.490744
$990$	24.2286	+	9.99396i	0.770034	+	0.317629i
$991$	33.6950			1.07036			0.535179	−	0.844739i	$-0.320244\pi$
$991$	33.6950			1.07036			0.535179	+	0.844739i	$0.320244\pi$
$992$	3.28960	+	5.69776i	0.104445	+	0.180904i
$993$	4.11098	−	4.69465i	0.130458	−	0.148980i
$994$	−13.1429	+	22.7641i	−0.416867	+	0.722035i
$995$	5.24343	−	9.08188i	0.166228	−	0.287915i
$996$	−3.68180	−	10.8200i	−0.116662	−	0.342845i
$997$	−7.27953	−	12.6085i	−0.230545	−	0.399315i	0.727424	−	0.686189i	$-0.240718\pi$
$997$	−7.27953	−	12.6085i	−0.230545	−	0.399315i	−0.957969	+	0.286873i	$0.907384\pi$
$998$	−17.2965			−0.547512
$999$	30.7311	+	20.4357i	0.972290	+	0.646557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.b.40.5	✓	10
3.2	odd	2		351.2.e.b.118.1		10
9.2	odd	6		351.2.e.b.235.1		10
9.4	even	3		1053.2.a.k.1.1		5
9.5	odd	6		1053.2.a.j.1.5		5
9.7	even	3	inner	117.2.e.b.79.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.b.40.5	✓	10	1.1	even	1	trivial
117.2.e.b.79.5	yes	10	9.7	even	3	inner
351.2.e.b.118.1		10	3.2	odd	2
351.2.e.b.235.1		10	9.2	odd	6
1053.2.a.j.1.5		5	9.5	odd	6
1053.2.a.k.1.1		5	9.4	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.786226 + 1.36178i) q^{2} +(-0.557959 - 1.63972i) q^{3} +(-0.236304 + 0.409291i) q^{4} +(0.557959 - 0.966413i) q^{5} +(1.79426 - 2.04901i) q^{6} +(1.93532 + 3.35208i) q^{7} +2.40175 q^{8} +(-2.37736 + 1.82979i) q^{9} +1.75473 q^{10} +(-2.48935 - 4.31168i) q^{11} +(0.802970 + 0.159105i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-3.04320 + 5.27098i) q^{14} +(-1.89596 - 0.375678i) q^{15} +(2.36093 + 4.08925i) q^{16} -4.37224 q^{17} +(-4.36093 - 1.79883i) q^{18} -6.30588 q^{19} +(0.263696 + 0.456735i) q^{20} +(4.41664 - 5.04371i) q^{21} +(3.91439 - 6.77992i) q^{22} +(-0.977469 + 1.69303i) q^{23} +(-1.34008 - 3.93820i) q^{24} +(1.87736 + 3.25169i) q^{25} -1.57245 q^{26} +(4.32682 + 2.87726i) q^{27} -1.82930 q^{28} +(1.08049 + 1.87146i) q^{29} +(-0.979066 - 2.87726i) q^{30} +(1.25490 - 2.17356i) q^{31} +(-1.31070 + 2.27020i) q^{32} +(-5.68100 + 6.48758i) q^{33} +(-3.43757 - 5.95405i) q^{34} +4.31932 q^{35} +(-0.187136 - 1.40542i) q^{36} +7.10248 q^{37} +(-4.95785 - 8.58725i) q^{38} +(1.69902 + 0.336654i) q^{39} +(1.34008 - 2.32108i) q^{40} +(-2.75305 + 4.76842i) q^{41} +(10.3409 + 2.04901i) q^{42} +(-3.94721 - 6.83676i) q^{43} +2.35298 q^{44} +(0.441864 + 3.31846i) q^{45} -3.07405 q^{46} +(-3.99982 - 6.92790i) q^{47} +(5.38792 - 6.15290i) q^{48} +(-3.99095 + 6.91253i) q^{49} +(-2.95207 + 5.11313i) q^{50} +(2.43953 + 7.16925i) q^{51} +(-0.236304 - 0.409291i) q^{52} +5.68016 q^{53} +(-0.516351 + 8.15437i) q^{54} -5.55582 q^{55} +(4.64816 + 8.05086i) q^{56} +(3.51842 + 10.3399i) q^{57} +(-1.69902 + 2.94279i) q^{58} +(2.34811 - 4.06705i) q^{59} +(0.601786 - 0.687227i) q^{60} +(-1.06675 - 1.84766i) q^{61} +3.94656 q^{62} +(-10.7346 - 4.42787i) q^{63} +5.32169 q^{64} +(0.557959 + 0.966413i) q^{65} +(-13.3012 - 2.63559i) q^{66} +(-1.16845 + 2.02382i) q^{67} +(1.03318 - 1.78952i) q^{68} +(3.32148 + 0.658137i) q^{69} +(3.39596 + 5.88198i) q^{70} +4.31876 q^{71} +(-5.70984 + 4.39471i) q^{72} +7.66241 q^{73} +(5.58416 + 9.67205i) q^{74} +(4.28437 - 4.89266i) q^{75} +(1.49011 - 2.58094i) q^{76} +(9.63540 - 16.6890i) q^{77} +(0.877364 + 2.57838i) q^{78} +(1.49553 + 2.59034i) q^{79} +5.26920 q^{80} +(2.30372 - 8.70017i) q^{81} -8.65808 q^{82} +(-6.98114 - 12.0917i) q^{83} +(1.02067 + 2.99954i) q^{84} +(-2.43953 + 4.22539i) q^{85} +(6.20679 - 10.7505i) q^{86} +(2.46581 - 2.81590i) q^{87} +(-5.97881 - 10.3556i) q^{88} +7.98729 q^{89} +(-4.17163 + 3.21079i) q^{90} -3.87065 q^{91} +(-0.461960 - 0.800138i) q^{92} +(-4.26421 - 0.844936i) q^{93} +(6.28953 - 10.8938i) q^{94} +(-3.51842 + 6.09409i) q^{95} +(4.45380 + 0.882502i) q^{96} +(-3.82682 - 6.62824i) q^{97} -12.5512 q^{98} +(13.8076 + 5.69544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

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