LMFDB - Embedded newform 387.2.f.d.259.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, 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("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			259.4
Character	$\chi$	$=$	387.259
Dual form			387.2.f.d.130.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.911404 + 1.57860i) q^{2} +(-0.100359 - 1.72914i) q^{3} +(-0.661315 - 1.14543i) q^{4} +(0.216442 + 0.374888i) q^{5} +(2.82109 + 1.41752i) q^{6} +(0.345529 - 0.598473i) q^{7} -1.23472 q^{8} +(-2.97986 + 0.347069i) q^{9} +O(q^{10})$	\(q+(-0.911404 + 1.57860i) q^{2} +(-0.100359 - 1.72914i) q^{3} +(-0.661315 - 1.14543i) q^{4} +(0.216442 + 0.374888i) q^{5} +(2.82109 + 1.41752i) q^{6} +(0.345529 - 0.598473i) q^{7} -1.23472 q^{8} +(-2.97986 + 0.347069i) q^{9} -0.789063 q^{10} +(-1.26780 + 2.19589i) q^{11} +(-1.91424 + 1.25846i) q^{12} +(3.60136 + 6.23773i) q^{13} +(0.629833 + 1.09090i) q^{14} +(0.626512 - 0.411881i) q^{15} +(2.44795 - 4.23998i) q^{16} +4.46895 q^{17} +(2.16797 - 5.02032i) q^{18} +6.05843 q^{19} +(0.286272 - 0.495838i) q^{20} +(-1.06952 - 0.537406i) q^{21} +(-2.31095 - 4.00268i) q^{22} +(2.05578 + 3.56072i) q^{23} +(0.123914 + 2.13500i) q^{24} +(2.40631 - 4.16784i) q^{25} -13.1292 q^{26} +(0.899185 + 5.11776i) q^{27} -0.914014 q^{28} +(-3.23074 + 5.59581i) q^{29} +(0.0791893 + 1.36440i) q^{30} +(1.26948 + 2.19881i) q^{31} +(3.22744 + 5.59009i) q^{32} +(3.92423 + 1.97182i) q^{33} +(-4.07302 + 7.05468i) q^{34} +0.299147 q^{35} +(2.36817 + 3.18370i) q^{36} -9.14340 q^{37} +(-5.52168 + 9.56383i) q^{38} +(10.4245 - 6.85327i) q^{39} +(-0.267244 - 0.462880i) q^{40} +(-0.455380 - 0.788741i) q^{41} +(1.82311 - 1.19855i) q^{42} +(0.500000 - 0.866025i) q^{43} +3.35365 q^{44} +(-0.775077 - 1.04199i) q^{45} -7.49459 q^{46} +(4.79713 - 8.30887i) q^{47} +(-7.57720 - 3.80734i) q^{48} +(3.26122 + 5.64860i) q^{49} +(4.38623 + 7.59718i) q^{50} +(-0.448498 - 7.72745i) q^{51} +(4.76326 - 8.25022i) q^{52} -8.85806 q^{53} +(-8.89841 - 3.24490i) q^{54} -1.09761 q^{55} +(-0.426630 + 0.738944i) q^{56} +(-0.608016 - 10.4759i) q^{57} +(-5.88902 - 10.2001i) q^{58} +(6.51130 + 11.2779i) q^{59} +(-0.886104 - 0.445243i) q^{60} +(-0.396746 + 0.687184i) q^{61} -4.62805 q^{62} +(-0.821915 + 1.90329i) q^{63} -1.97418 q^{64} +(-1.55897 + 2.70021i) q^{65} +(-6.68927 + 4.39766i) q^{66} +(-5.69986 - 9.87245i) q^{67} +(-2.95539 - 5.11888i) q^{68} +(5.95066 - 3.91208i) q^{69} +(-0.272644 + 0.472233i) q^{70} -13.2707 q^{71} +(3.67927 - 0.428531i) q^{72} -4.01445 q^{73} +(8.33334 - 14.4338i) q^{74} +(-7.44828 - 3.74256i) q^{75} +(-4.00653 - 6.93952i) q^{76} +(0.876120 + 1.51748i) q^{77} +(1.31763 + 22.7022i) q^{78} +(5.94290 - 10.2934i) q^{79} +2.11936 q^{80} +(8.75909 - 2.06843i) q^{81} +1.66014 q^{82} +(4.88090 - 8.45396i) q^{83} +(0.0917292 + 1.58046i) q^{84} +(0.967268 + 1.67536i) q^{85} +(0.911404 + 1.57860i) q^{86} +(10.0002 + 5.02482i) q^{87} +(1.56537 - 2.71129i) q^{88} +8.04947 q^{89} +(2.35130 - 0.273859i) q^{90} +4.97749 q^{91} +(2.71904 - 4.70951i) q^{92} +(3.67465 - 2.41578i) q^{93} +(8.74425 + 15.1455i) q^{94} +(1.31130 + 2.27123i) q^{95} +(9.34214 - 6.14171i) q^{96} +(-7.49445 + 12.9808i) q^{97} -11.8892 q^{98} +(3.01572 - 6.98344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) $ 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.911404	+	1.57860i	−0.644460	+	1.11624i	0.339966	+	0.940438i	$0.389584\pi$
$2$	−0.911404	+	1.57860i	−0.644460	+	1.11624i	−0.984426	+	0.175800i	$0.943749\pi$
$3$	−0.100359	−	1.72914i	−0.0579421	−	0.998320i
$3$	−0.100359	−	1.72914i	−0.0579421	−	0.998320i
$4$	−0.661315	−	1.14543i	−0.330658	−	0.572716i
$5$	0.216442	+	0.374888i	0.0967957	+	0.167655i	0.910357	−	0.413825i	$-0.135807\pi$
$5$	0.216442	+	0.374888i	0.0967957	+	0.167655i	−0.813561	+	0.581480i	$0.802474\pi$
$6$	2.82109	+	1.41752i	1.15170	+	0.578700i
$7$	0.345529	−	0.598473i	0.130598	−	0.226202i	−0.793309	−	0.608819i	$-0.791644\pi$
$7$	0.345529	−	0.598473i	0.130598	−	0.226202i	0.923907	+	0.382617i	$0.124977\pi$
$8$	−1.23472			−0.436538
$9$	−2.97986	+	0.347069i	−0.993285	+	0.115690i
$10$	−0.789063			−0.249524
$11$	−1.26780	+	2.19589i	−0.382255	+	0.662084i	−0.991384	−	0.130986i	$-0.958186\pi$
$11$	−1.26780	+	2.19589i	−0.382255	+	0.662084i	0.609130	+	0.793071i	$0.291519\pi$
$12$	−1.91424	+	1.25846i	−0.552595	+	0.363286i
$13$	3.60136	+	6.23773i	0.998837	+	1.73004i	0.541176	+	0.840909i	$0.317979\pi$
$13$	3.60136	+	6.23773i	0.998837	+	1.73004i	0.457661	+	0.889127i	$0.348687\pi$
$14$	0.629833	+	1.09090i	0.168330	+	0.291556i
$15$	0.626512	−	0.411881i	0.161765	−	0.106347i
$16$	2.44795	−	4.23998i	0.611989	−	1.06000i
$17$	4.46895			1.08388			0.541940	−	0.840417i	$-0.317690\pi$
$17$	4.46895			1.08388			0.541940	+	0.840417i	$0.317690\pi$
$18$	2.16797	−	5.02032i	0.510996	−	1.18330i
$19$	6.05843			1.38990			0.694950	−	0.719058i	$-0.255427\pi$
$19$	6.05843			1.38990			0.694950	+	0.719058i	$0.255427\pi$
$20$	0.286272	−	0.495838i	0.0640124	−	0.110873i
$21$	−1.06952	−	0.537406i	−0.233389	−	0.117272i
$22$	−2.31095	−	4.00268i	−0.492696	−	0.853374i
$23$	2.05578	+	3.56072i	0.428660	+	0.742460i	0.996754	−	0.0805028i	$-0.0256526\pi$
$23$	2.05578	+	3.56072i	0.428660	+	0.742460i	−0.568095	+	0.822963i	$0.692319\pi$
$24$	0.123914	+	2.13500i	0.0252939	+	0.435804i
$25$	2.40631	−	4.16784i	0.481261	−	0.833569i
$26$	−13.1292			−2.57484
$27$	0.899185	+	5.11776i	0.173048	+	0.984913i
$28$	−0.914014			−0.172732
$29$	−3.23074	+	5.59581i	−0.599933	+	1.03912i	0.392897	+	0.919583i	$0.371473\pi$
$29$	−3.23074	+	5.59581i	−0.599933	+	1.03912i	−0.992830	+	0.119533i	$0.961860\pi$
$30$	0.0791893	+	1.36440i	0.0144579	+	0.249105i
$31$	1.26948	+	2.19881i	0.228006	+	0.394918i	0.957217	−	0.289371i	$-0.0934461\pi$
$31$	1.26948	+	2.19881i	0.228006	+	0.394918i	−0.729211	+	0.684289i	$0.760113\pi$
$32$	3.22744	+	5.59009i	0.570536	+	0.988197i
$33$	3.92423	+	1.97182i	0.683121	+	0.343250i
$34$	−4.07302	+	7.05468i	−0.698518	+	1.20987i
$35$	0.299147			0.0505651
$36$	2.36817	+	3.18370i	0.394695	+	0.530617i
$37$	−9.14340			−1.50317			−0.751583	−	0.659638i	$-0.770709\pi$
$37$	−9.14340			−1.50317			−0.751583	+	0.659638i	$0.770709\pi$
$38$	−5.52168	+	9.56383i	−0.895735	+	1.55146i
$39$	10.4245	−	6.85327i	1.66925	−	1.09740i
$40$	−0.267244	−	0.462880i	−0.0422550	−	0.0731877i
$41$	−0.455380	−	0.788741i	−0.0711184	−	0.123181i	0.828273	−	0.560324i	$-0.189323\pi$
$41$	−0.455380	−	0.788741i	−0.0711184	−	0.123181i	−0.899392	+	0.437144i	$0.855990\pi$
$42$	1.82311	−	1.19855i	0.281313	−	0.184940i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$44$	3.35365			0.505582
$45$	−0.775077	−	1.04199i	−0.115542	−	0.155331i
$46$	−7.49459			−1.10502
$47$	4.79713	−	8.30887i	0.699733	−	1.21197i	−0.268826	−	0.963189i	$-0.586636\pi$
$47$	4.79713	−	8.30887i	0.699733	−	1.21197i	0.968559	−	0.248785i	$-0.0800311\pi$
$48$	−7.57720	−	3.80734i	−1.09367	−	0.549542i
$49$	3.26122	+	5.64860i	0.465889	+	0.806943i
$50$	4.38623	+	7.59718i	0.620307	+	1.07440i
$51$	−0.448498	−	7.72745i	−0.0628023	−	1.08206i
$52$	4.76326	−	8.25022i	0.660546	−	1.14410i
$53$	−8.85806			−1.21675			−0.608374	−	0.793650i	$-0.708178\pi$
$53$	−8.85806			−1.21675			−0.608374	+	0.793650i	$0.708178\pi$
$54$	−8.89841	−	3.24490i	−1.21092	−	0.441574i
$55$	−1.09761			−0.148002
$56$	−0.426630	+	0.738944i	−0.0570108	+	0.0987456i
$57$	−0.608016	−	10.4759i	−0.0805337	−	1.38756i
$58$	−5.88902	−	10.2001i	−0.773266	−	1.33934i
$59$	6.51130	+	11.2779i	0.847699	+	1.46826i	0.883257	+	0.468890i	$0.155346\pi$
$59$	6.51130	+	11.2779i	0.847699	+	1.46826i	−0.0355576	+	0.999368i	$0.511321\pi$
$60$	−0.886104	−	0.445243i	−0.114396	−	0.0574807i
$61$	−0.396746	+	0.687184i	−0.0507981	+	0.0879849i	−0.890306	−	0.455362i	$-0.849510\pi$
$61$	−0.396746	+	0.687184i	−0.0507981	+	0.0879849i	0.839508	+	0.543347i	$0.182843\pi$
$62$	−4.62805			−0.587763
$63$	−0.821915	+	1.90329i	−0.103552	+	0.239792i
$64$	−1.97418			−0.246772
$65$	−1.55897	+	2.70021i	−0.193366	+	0.334920i
$66$	−6.68927	+	4.39766i	−0.823392	+	0.541314i
$67$	−5.69986	−	9.87245i	−0.696349	−	1.20611i	−0.969724	−	0.244204i	$-0.921473\pi$
$67$	−5.69986	−	9.87245i	−0.696349	−	1.20611i	0.273375	−	0.961908i	$-0.411860\pi$
$68$	−2.95539	−	5.11888i	−0.358393	−	0.620755i
$69$	5.95066	−	3.91208i	0.716376	−	0.470959i
$70$	−0.272644	+	0.472233i	−0.0325872	+	0.0564427i
$71$	−13.2707			−1.57495			−0.787473	−	0.616349i	$-0.788611\pi$
$71$	−13.2707			−1.57495			−0.787473	+	0.616349i	$0.788611\pi$
$72$	3.67927	−	0.428531i	0.433607	−	0.0505028i
$73$	−4.01445			−0.469856			−0.234928	−	0.972013i	$-0.575485\pi$
$73$	−4.01445			−0.469856			−0.234928	+	0.972013i	$0.575485\pi$
$74$	8.33334	−	14.4338i	0.968731	−	1.67789i
$75$	−7.44828	−	3.74256i	−0.860054	−	0.432154i
$76$	−4.00653	−	6.93952i	−0.459581	−	0.796017i
$77$	0.876120	+	1.51748i	0.0998431	+	0.172933i
$78$	1.31763	+	22.7022i	0.149192	+	2.57052i
$79$	5.94290	−	10.2934i	0.668628	−	1.15810i	−0.309659	−	0.950848i	$-0.600215\pi$
$79$	5.94290	−	10.2934i	0.668628	−	1.15810i	0.978288	−	0.207251i	$-0.0664516\pi$
$80$	2.11936			0.236951
$81$	8.75909	−	2.06843i	0.973232	−	0.229825i
$82$	1.66014			0.183332
$83$	4.88090	−	8.45396i	0.535748	−	0.927943i	−0.463379	−	0.886160i	$-0.653363\pi$
$83$	4.88090	−	8.45396i	0.535748	−	0.927943i	0.999127	−	0.0417825i	$-0.0133036\pi$
$84$	0.0917292	+	1.58046i	0.0100085	+	0.172442i
$85$	0.967268	+	1.67536i	0.104915	+	0.181718i
$86$	0.911404	+	1.57860i	0.0982792	+	0.170225i
$87$	10.0002	+	5.02482i	1.07213	+	0.538717i
$88$	1.56537	−	2.71129i	0.166869	−	0.289025i
$89$	8.04947			0.853242			0.426621	−	0.904431i	$-0.359704\pi$
$89$	8.04947			0.853242			0.426621	+	0.904431i	$0.359704\pi$
$90$	2.35130	−	0.273859i	0.247848	−	0.0288673i
$91$	4.97749			0.521783
$92$	2.71904	−	4.70951i	0.283479	−	0.491000i
$93$	3.67465	−	2.41578i	0.381043	−	0.250505i
$94$	8.74425	+	15.1455i	0.901900	+	1.56214i
$95$	1.31130	+	2.27123i	0.134536	+	0.233024i
$96$	9.34214	−	6.14171i	0.953479	−	0.626835i
$97$	−7.49445	+	12.9808i	−0.760947	+	1.31800i	0.181417	+	0.983406i	$0.441932\pi$
$97$	−7.49445	+	12.9808i	−0.760947	+	1.31800i	−0.942363	+	0.334592i	$0.891402\pi$
$98$	−11.8892			−1.20099
$99$	3.01572	−	6.98344i	0.303092	−	0.701862i
$100$	−6.36531			−0.636531
$101$	1.55310	−	2.69005i	0.154539	−	0.267670i	−0.778352	−	0.627828i	$-0.783944\pi$
$101$	1.55310	−	2.69005i	0.154539	−	0.267670i	0.932891	+	0.360159i	$0.117277\pi$
$102$	12.6073	+	6.33483i	1.24831	+	0.627242i
$103$	−3.48129	−	6.02977i	−0.343022	−	0.594131i	0.641970	−	0.766729i	$-0.278117\pi$
$103$	−3.48129	−	6.02977i	−0.343022	−	0.594131i	−0.984992	+	0.172598i	$0.944784\pi$
$104$	−4.44665	−	7.70183i	−0.436030	−	0.755226i
$105$	−0.0300220	−	0.517268i	−0.00292985	−	0.0504802i
$106$	8.07328	−	13.9833i	0.784146	−	1.35818i
$107$	8.10561			0.783599			0.391800	−	0.920051i	$-0.371853\pi$
$107$	8.10561			0.783599			0.391800	+	0.920051i	$0.371853\pi$
$108$	5.26740	−	4.41441i	0.506856	−	0.424776i
$109$	−0.0751888			−0.00720178			−0.00360089	−	0.999994i	$-0.501146\pi$
$109$	−0.0751888			−0.00720178			−0.00360089	+	0.999994i	$0.501146\pi$
$110$	1.00037	−	1.73269i	0.0953816	−	0.165206i
$111$	0.917620	+	15.8102i	0.0870966	+	1.50064i
$112$	−1.69168	−	2.93007i	−0.159849	−	0.276866i
$113$	−3.84430	−	6.65852i	−0.361641	−	0.626380i	0.626590	−	0.779349i	$-0.284450\pi$
$113$	−3.84430	−	6.65852i	−0.361641	−	0.626380i	−0.988231	+	0.152969i	$0.951117\pi$
$114$	17.0914	+	8.58795i	1.60075	+	0.804335i
$115$	−0.889913	+	1.54137i	−0.0829848	+	0.143734i
$116$	8.54615			0.793490
$117$	−12.8964	−	17.3376i	−1.19228	−	1.60286i
$118$	−23.7377			−2.18523
$119$	1.54415	−	2.67455i	0.141552	−	0.245176i
$120$	−0.773564	+	0.508556i	−0.0706164	+	0.0464246i
$121$	2.28539	+	3.95841i	0.207763	+	0.359856i
$122$	−0.723192	−	1.25260i	−0.0654747	−	0.113405i
$123$	−1.31814	+	0.866573i	−0.118853	+	0.0781363i
$124$	1.67906	−	2.90821i	0.150784	−	0.261165i
$125$	4.24772			0.379927
$126$	−2.25543	−	3.03214i	−0.200930	−	0.270124i
$127$	0.411999			0.0365590			0.0182795	−	0.999833i	$-0.494181\pi$
$127$	0.411999			0.0365590			0.0182795	+	0.999833i	$0.494181\pi$
$128$	−4.65560	+	8.06373i	−0.411501	+	0.712740i
$129$	−1.54766	−	0.777657i	−0.136264	−	0.0684689i
$130$	−2.84170	−	4.92197i	−0.249234	−	0.431685i
$131$	−1.51555	−	2.62501i	−0.132414	−	0.229348i	0.792193	−	0.610271i	$-0.208940\pi$
$131$	−1.51555	−	2.62501i	−0.132414	−	0.229348i	−0.924607	+	0.380923i	$0.875606\pi$
$132$	−0.336568	−	5.79893i	−0.0292945	−	0.504732i
$133$	2.09336	−	3.62581i	0.181518	−	0.314398i
$134$	20.7795			1.79508
$135$	−1.72397	+	1.44479i	−0.148375	+	0.124348i
$136$	−5.51788			−0.473155
$137$	5.34442	−	9.25680i	0.456604	−	0.790862i	−0.542174	−	0.840266i	$-0.682399\pi$
$137$	5.34442	−	9.25680i	0.456604	−	0.790862i	0.998779	+	0.0494039i	$0.0157321\pi$
$138$	0.752146	+	12.9592i	0.0640270	+	1.10316i
$139$	11.3648	+	19.6844i	0.963951	+	1.66961i	0.712408	+	0.701766i	$0.247605\pi$
$139$	11.3648	+	19.6844i	0.963951	+	1.66961i	0.251543	+	0.967846i	$0.419062\pi$
$140$	−0.197831	−	0.342653i	−0.0167197	−	0.0289594i
$141$	−14.8486	−	7.46105i	−1.25048	−	0.628333i
$142$	12.0950	−	20.9492i	1.01499	−	1.75801i
$143$	−18.2631			−1.52724
$144$	−5.82299	+	13.4841i	−0.485249	+	1.12368i
$145$	−2.79707			−0.232284
$146$	3.65879	−	6.33720i	0.302803	−	0.524471i
$147$	9.43993	−	6.20599i	0.778592	−	0.511862i
$148$	6.04667	+	10.4731i	0.497033	+	0.860887i
$149$	−7.49268	−	12.9777i	−0.613824	−	1.06317i	−0.990590	−	0.136866i	$-0.956297\pi$
$149$	−7.49268	−	12.9777i	−0.613824	−	1.06317i	0.376766	−	0.926309i	$-0.377036\pi$
$150$	12.6964	−	8.34686i	1.03666	−	0.681518i
$151$	−4.01750	+	6.95851i	−0.326939	+	0.566276i	−0.981903	−	0.189385i	$-0.939351\pi$
$151$	−4.01750	+	6.95851i	−0.326939	+	0.566276i	0.654964	+	0.755660i	$0.272684\pi$
$152$	−7.48044			−0.606744
$153$	−13.3168	+	1.55103i	−1.07660	+	0.125394i
$154$	−3.19400			−0.257380
$155$	−0.549538	+	0.951828i	−0.0441399	+	0.0764526i
$156$	−14.7438	−	7.40837i	−1.18045	−	0.593145i
$157$	−3.44630	−	5.96916i	−0.275045	−	0.476391i	0.695102	−	0.718911i	$-0.255359\pi$
$157$	−3.44630	−	5.96916i	−0.275045	−	0.476391i	−0.970146	+	0.242520i	$0.922026\pi$
$158$	10.8328	+	18.7629i	0.861809	+	1.49270i
$159$	0.888983	+	15.3168i	0.0705010	+	1.21470i
$160$	−1.39710	+	2.41985i	−0.110451	+	0.191306i
$161$	2.84132			0.223928
$162$	−4.71785	+	15.7123i	−0.370669	+	1.23447i
$163$	6.87193			0.538251			0.269125	−	0.963105i	$-0.413265\pi$
$163$	6.87193			0.538251			0.269125	+	0.963105i	$0.413265\pi$
$164$	−0.602299	+	1.04321i	−0.0470317	+	0.0814613i
$165$	0.110155	+	1.89793i	0.00857557	+	0.147754i
$166$	8.89694	+	15.4100i	0.690536	+	1.19604i
$167$	−7.79562	−	13.5024i	−0.603243	−	1.04485i	−0.992327	−	0.123645i	$-0.960542\pi$
$167$	−7.79562	−	13.5024i	−0.603243	−	1.04485i	0.389083	−	0.921203i	$-0.372792\pi$
$168$	1.32055	+	0.663543i	0.101883	+	0.0511935i
$169$	−19.4396	+	33.6703i	−1.49535	+	2.59002i
$170$	−3.52629			−0.270454
$171$	−18.0533	+	2.10269i	−1.38057	+	0.160797i
$172$	−1.32263			−0.100850
$173$	1.53573	−	2.65997i	0.116760	−	0.202234i	−0.801722	−	0.597697i	$-0.796083\pi$
$173$	1.53573	−	2.65997i	0.116760	−	0.202234i	0.918482	+	0.395463i	$0.129416\pi$
$174$	−17.0464	+	11.2066i	−1.29228	+	0.849571i
$175$	−1.66290	−	2.88022i	−0.125703	−	0.217724i
$176$	6.20701	+	10.7509i	0.467871	+	0.810376i
$177$	18.8476	−	12.3908i	1.41667	−	0.931349i
$178$	−7.33632	+	12.7069i	−0.549880	+	0.952420i
$179$	6.81694			0.509522			0.254761	−	0.967004i	$-0.418003\pi$
$179$	6.81694			0.509522			0.254761	+	0.967004i	$0.418003\pi$
$180$	−0.680961	+	1.57688i	−0.0507558	+	0.117534i
$181$	−6.26156			−0.465418			−0.232709	−	0.972546i	$-0.574759\pi$
$181$	−6.26156			−0.465418			−0.232709	+	0.972546i	$0.574759\pi$
$182$	−4.53651	+	7.85746i	−0.336268	+	0.582434i
$183$	1.22805	+	0.617065i	0.0907804	+	0.0456147i
$184$	−2.53830	−	4.39647i	−0.187126	−	0.324112i
$185$	−1.97901	−	3.42775i	−0.145500	−	0.252013i
$186$	0.464465	+	8.00254i	0.0340562	+	0.586775i
$187$	−5.66572	+	9.81331i	−0.414318	+	0.717620i
$188$	−12.6897			−0.925488
$189$	3.37354	+	1.23020i	0.245389	+	0.0894835i
$190$	−4.78049			−0.346813
$191$	4.89485	−	8.47813i	0.354179	−	0.613456i	−0.632798	−	0.774317i	$-0.718094\pi$
$191$	4.89485	−	8.47813i	0.354179	−	0.613456i	0.986977	+	0.160861i	$0.0514270\pi$
$192$	0.198126	+	3.41364i	0.0142985	+	0.246358i
$193$	−3.22778	−	5.59068i	−0.232341	−	0.402426i	0.726156	−	0.687530i	$-0.241305\pi$
$193$	−3.22778	−	5.59068i	−0.232341	−	0.402426i	−0.958496	+	0.285104i	$0.907972\pi$
$194$	−13.6610	−	23.6615i	−0.980799	−	1.69879i
$195$	4.82550	+	2.42469i	0.345561	+	0.173635i
$196$	4.31339	−	7.47101i	0.308099	−	0.533643i
$197$	−9.52049			−0.678307			−0.339154	−	0.940731i	$-0.610141\pi$
$197$	−9.52049			−0.678307			−0.339154	+	0.940731i	$0.610141\pi$
$198$	8.27550	+	11.1254i	0.588114	+	0.790644i
$199$	16.8531			1.19469			0.597344	−	0.801985i	$-0.296223\pi$
$199$	16.8531			1.19469			0.597344	+	0.801985i	$0.296223\pi$
$200$	−2.97110	+	5.14610i	−0.210089	+	0.363884i
$201$	−16.4988	+	10.8466i	−1.16374	+	0.765063i
$202$	2.83100	+	4.90344i	0.199189	+	0.345005i
$203$	2.23263	+	3.86702i	0.156700	+	0.271412i
$204$	−8.55466	+	5.62400i	−0.598946	+	0.393759i
$205$	0.197126	−	0.341433i	0.0137679	−	0.0238467i
$206$	12.6915			0.884256
$207$	−7.36174	−	9.89692i	−0.511676	−	0.687884i
$208$	35.2638			2.44511
$209$	−7.68085	+	13.3036i	−0.531296	+	0.920231i
$210$	0.843920	+	0.424047i	0.0582360	+	0.0292621i
$211$	−0.656265	−	1.13668i	−0.0451792	−	0.0782526i	0.842552	−	0.538616i	$-0.181053\pi$
$211$	−0.656265	−	1.13668i	−0.0451792	−	0.0782526i	−0.887731	+	0.460363i	$0.847719\pi$
$212$	5.85797	+	10.1463i	0.402327	+	0.696851i
$213$	1.33183	+	22.9470i	0.0912557	+	1.57230i
$214$	−7.38749	+	12.7955i	−0.504998	+	0.874683i
$215$	0.432883			0.0295224
$216$	−1.11024	−	6.31898i	−0.0755421	−	0.429952i
$217$	1.75457			0.119108
$218$	0.0685274	−	0.118693i	0.00464126	−	0.00803890i
$219$	0.402885	+	6.94155i	0.0272244	+	0.469067i
$220$	0.725869	+	1.25724i	0.0489381	+	0.0847633i
$221$	16.0943	+	27.8761i	1.08262	+	1.87515i
$222$	−25.7943	−	12.9610i	−1.73120	−	0.869883i
$223$	0.949986	−	1.64542i	0.0636157	−	0.110186i	−0.832463	−	0.554080i	$-0.813070\pi$
$223$	0.949986	−	1.64542i	0.0636157	−	0.110186i	0.896079	+	0.443894i	$0.146403\pi$
$224$	4.46069			0.298042
$225$	−5.72392	+	13.2547i	−0.381595	+	0.883649i
$226$	14.0148			0.932252
$227$	6.36963	−	11.0325i	0.422767	−	0.732254i	−0.573442	−	0.819246i	$-0.694392\pi$
$227$	6.36963	−	11.0325i	0.422767	−	0.732254i	0.996209	+	0.0869919i	$0.0277254\pi$
$228$	−11.5973	+	7.62430i	−0.768051	+	0.504932i
$229$	−11.8720	−	20.5630i	−0.784526	−	1.35884i	−0.929282	−	0.369371i	$-0.879573\pi$
$229$	−11.8720	−	20.5630i	−0.784526	−	1.35884i	0.144756	−	0.989467i	$-0.453760\pi$
$230$	−1.62214	−	2.80963i	−0.106961	−	0.185262i
$231$	2.53602	−	1.66723i	0.166858	−	0.109695i
$232$	3.98904	−	6.90923i	0.261894	−	0.453613i
$233$	−7.78814			−0.510218			−0.255109	−	0.966912i	$-0.582111\pi$
$233$	−7.78814			−0.510218			−0.255109	+	0.966912i	$0.582111\pi$
$234$	39.1230	−	4.55672i	2.55755	−	0.297882i
$235$	4.15319			0.270925
$236$	8.61204	−	14.9165i	0.560596	−	0.970981i
$237$	−18.3952	−	9.24308i	−1.19489	−	0.600402i
$238$	2.81469	+	4.87519i	0.182449	+	0.316012i
$239$	1.70650	+	2.95575i	0.110385	+	0.191192i	0.915925	−	0.401349i	$-0.131458\pi$
$239$	1.70650	+	2.95575i	0.110385	+	0.191192i	−0.805541	+	0.592540i	$0.798125\pi$
$240$	−0.212696	−	3.66467i	−0.0137295	−	0.236553i
$241$	6.16770	−	10.6828i	0.397296	−	0.688137i	−0.596095	−	0.802914i	$-0.703282\pi$
$241$	6.16770	−	10.6828i	0.397296	−	0.688137i	0.993391	+	0.114777i	$0.0366152\pi$
$242$	−8.33166			−0.535579
$243$	−4.45565	−	14.9381i	−0.285830	−	0.958280i
$244$	1.04950			0.0671871
$245$	−1.41173	+	2.44518i	−0.0901920	+	0.156217i
$246$	−0.166610	−	2.87062i	−0.0106226	−	0.183024i
$247$	21.8186	+	37.7909i	1.38828	+	2.40458i
$248$	−1.56745	−	2.71490i	−0.0995331	−	0.172396i
$249$	−15.1079	−	7.59133i	−0.957426	−	0.481081i
$250$	−3.87139	+	6.70544i	−0.244848	+	0.424089i
$251$	7.32241			0.462186			0.231093	−	0.972932i	$-0.425770\pi$
$251$	7.32241			0.462186			0.231093	+	0.972932i	$0.425770\pi$
$252$	2.72363	−	0.317225i	0.171573	−	0.0199833i
$253$	−10.4252			−0.655429
$254$	−0.375498	+	0.650381i	−0.0235608	+	0.0408086i
$255$	2.79985	−	1.84068i	0.175334	−	0.115268i
$256$	−10.4604	−	18.1180i	−0.653778	−	1.13238i
$257$	−2.49747	−	4.32575i	−0.155788	−	0.269833i	0.777558	−	0.628812i	$-0.216458\pi$
$257$	−2.49747	−	4.32575i	−0.155788	−	0.269833i	−0.933346	+	0.358979i	$0.883125\pi$
$258$	2.63815	−	1.73437i	0.164244	−	0.107977i
$259$	−3.15931	+	5.47208i	−0.196310	+	0.340019i
$260$	4.12388			0.255752
$261$	7.68501	−	17.7960i	0.475690	−	1.10154i
$262$	5.52511			0.341342
$263$	9.05500	−	15.6837i	0.558355	−	0.967099i	−0.439279	−	0.898351i	$-0.644766\pi$
$263$	9.05500	−	15.6837i	0.558355	−	0.967099i	0.997634	−	0.0687485i	$-0.0219006\pi$
$264$	−4.84531	−	2.43464i	−0.298208	−	0.149842i
$265$	−1.91725	−	3.32078i	−0.117776	−	0.203994i
$266$	3.81580	+	6.60916i	0.233962	+	0.405234i
$267$	−0.807834	−	13.9187i	−0.0494386	−	0.851808i
$268$	−7.53881	+	13.0576i	−0.460506	+	0.797620i
$269$	12.3502			0.753004			0.376502	−	0.926416i	$-0.377127\pi$
$269$	12.3502			0.753004			0.376502	+	0.926416i	$0.377127\pi$
$270$	−0.709514	−	4.03824i	−0.0431796	−	0.245759i
$271$	−11.1352			−0.676418			−0.338209	−	0.941071i	$-0.609821\pi$
$271$	−11.1352			−0.676418			−0.338209	+	0.941071i	$0.609821\pi$
$272$	10.9398	−	18.9483i	0.663322	−	1.14891i
$273$	−0.499534	−	8.60678i	−0.0302332	−	0.520906i
$274$	9.74185	+	16.8734i	0.588527	+	1.01936i
$275$	6.10141	+	10.5679i	0.367929	+	0.637271i
$276$	−8.41628	−	4.22896i	−0.506601	−	0.254553i
$277$	−7.92554	+	13.7274i	−0.476200	+	0.824802i	−0.999628	−	0.0272677i	$-0.991319\pi$
$277$	−7.92554	+	13.7274i	−0.476200	+	0.824802i	0.523429	+	0.852070i	$0.324653\pi$
$278$	−41.4318			−2.48491
$279$	−4.54601	−	6.11154i	−0.272163	−	0.365888i
$280$	−0.369362			−0.0220736
$281$	4.44576	−	7.70028i	0.265212	−	0.459360i	−0.702407	−	0.711775i	$-0.747891\pi$
$281$	4.44576	−	7.70028i	0.265212	−	0.459360i	0.967619	+	0.252415i	$0.0812248\pi$
$282$	25.3111	−	16.6400i	1.50725	−	0.990899i
$283$	3.93496	+	6.81556i	0.233909	+	0.405143i	0.958955	−	0.283558i	$-0.0915148\pi$
$283$	3.93496	+	6.81556i	0.233909	+	0.405143i	−0.725046	+	0.688701i	$0.758181\pi$
$284$	8.77614	+	15.2007i	0.520768	+	0.901997i
$285$	3.79568	−	2.49536i	0.224837	−	0.147812i
$286$	16.6451	−	28.8302i	0.984245	−	1.70476i
$287$	−0.629388			−0.0371516
$288$	−11.5574	−	15.5375i	−0.681029	−	0.915557i
$289$	2.97154			0.174796
$290$	2.54926	−	4.41545i	0.149698	−	0.259284i
$291$	23.1977	+	11.6562i	1.35987	+	0.683301i
$292$	2.65482	+	4.59828i	0.155361	+	0.269094i
$293$	16.7554	+	29.0212i	0.978859	+	1.69543i	0.666561	+	0.745450i	$0.267765\pi$
$293$	16.7554	+	29.0212i	0.978859	+	1.69543i	0.312298	+	0.949984i	$0.398901\pi$
$294$	1.19318	+	20.5580i	0.0695877	+	1.19897i
$295$	−2.81863	+	4.88202i	−0.164107	+	0.284242i
$296$	11.2895			0.656189
$297$	−12.3780	−	4.51376i	−0.718244	−	0.261915i
$298$	27.3154			1.58234
$299$	−14.8072	+	25.6468i	−0.856322	+	1.48319i
$300$	0.638814	+	11.0065i	0.0368819	+	0.635461i
$301$	−0.345529	−	0.598473i	−0.0199160	−	0.0344954i
$302$	−7.32313	−	12.6840i	−0.421399	−	0.729884i
$303$	−4.80734	−	2.41556i	−0.276174	−	0.138770i
$304$	14.8308	−	25.6876i	0.850603	−	1.47329i
$305$	−0.343489			−0.0196681
$306$	9.68856	−	22.4356i	0.553858	−	1.28256i
$307$	12.9225			0.737524			0.368762	−	0.929524i	$-0.379782\pi$
$307$	12.9225			0.737524			0.368762	+	0.929524i	$0.379782\pi$
$308$	1.15878	−	2.00707i	0.0660277	−	0.114363i
$309$	−10.0770	+	6.62478i	−0.573258	+	0.376871i
$310$	−1.00170	−	1.73500i	−0.0568929	−	0.0985413i
$311$	6.78105	+	11.7451i	0.384518	+	0.666005i	0.991702	−	0.128556i	$-0.0410343\pi$
$311$	6.78105	+	11.7451i	0.384518	+	0.666005i	−0.607184	+	0.794561i	$0.707701\pi$
$312$	−12.8713	+	8.46183i	−0.728693	+	0.479057i
$313$	11.6910	−	20.2493i	0.660812	−	1.14456i	−0.319591	−	0.947556i	$-0.603546\pi$
$313$	11.6910	−	20.2493i	0.660812	−	1.14456i	0.980403	−	0.197004i	$-0.0631211\pi$
$314$	12.5639			0.709021
$315$	−0.891416	+	0.103825i	−0.0502256	+	0.00584985i
$316$	−15.7205			−0.884348
$317$	−0.805713	+	1.39554i	−0.0452533	+	0.0783811i	−0.887765	−	0.460297i	$-0.847743\pi$
$317$	−0.805713	+	1.39554i	−0.0452533	+	0.0783811i	0.842512	+	0.538678i	$0.181076\pi$
$318$	−24.9894	−	12.5565i	−1.40133	−	0.704133i
$319$	−8.19183	−	14.1887i	−0.458655	−	0.794413i
$320$	−0.427295	−	0.740096i	−0.0238865	−	0.0413726i
$321$	−0.813468	−	14.0157i	−0.0454034	−	0.782283i
$322$	−2.58960	+	4.48531i	−0.144312	+	0.249957i
$323$	27.0748			1.50648
$324$	−8.16176	−	8.66505i	−0.453431	−	0.481392i
$325$	34.6639			1.92281
$326$	−6.26310	+	10.8480i	−0.346881	+	0.600816i
$327$	0.00754585	+	0.130012i	0.000417286	+	0.00718968i
$328$	0.562265	+	0.973871i	0.0310459	+	0.0537730i
$329$	−3.31509	−	5.74191i	−0.182767	−	0.316562i
$330$	−3.09647	−	1.55589i	−0.170455	−	0.0856490i
$331$	−17.1277	+	29.6660i	−0.941422	+	1.63059i	−0.178660	+	0.983911i	$0.557176\pi$
$331$	−17.1277	+	29.6660i	−0.941422	+	1.63059i	−0.762762	+	0.646679i	$0.776157\pi$
$332$	−12.9112			−0.708597
$333$	27.2460	−	3.17339i	1.49307	−	0.173901i
$334$	28.4198			1.55506
$335$	2.46737	−	4.27362i	0.134807	−	0.233493i
$336$	−4.89673	+	3.21921i	−0.267139	+	0.175622i
$337$	−7.67840	−	13.2994i	−0.418269	−	0.724464i	0.577496	−	0.816393i	$-0.304030\pi$
$337$	−7.67840	−	13.2994i	−0.418269	−	0.724464i	−0.995766	+	0.0919297i	$0.970697\pi$
$338$	−35.4346	−	61.3745i	−1.92739	−	3.33833i
$339$	−11.1277	+	7.31557i	−0.604374	+	0.397327i
$340$	1.27934	−	2.21588i	0.0693818	−	0.120173i
$341$	−6.43778			−0.348625
$342$	13.1345	−	30.4152i	0.710233	−	1.64467i
$343$	9.34478			0.504571
$344$	−0.617358	+	1.06929i	−0.0332857	+	0.0576525i
$345$	2.75456	+	1.38409i	0.148301	+	0.0745171i
$346$	2.79935	+	4.84861i	0.150494	+	0.260663i
$347$	0.967222	+	1.67528i	0.0519232	+	0.0899336i	0.890819	−	0.454359i	$-0.150132\pi$
$347$	0.967222	+	1.67528i	0.0519232	+	0.0899336i	−0.838896	+	0.544292i	$0.816798\pi$
$348$	−0.857680	−	14.7775i	−0.0459765	−	0.792157i
$349$	−2.79439	+	4.84003i	−0.149580	+	0.259081i	−0.931072	−	0.364834i	$-0.881126\pi$
$349$	−2.79439	+	4.84003i	−0.149580	+	0.259081i	0.781492	+	0.623915i	$0.214459\pi$
$350$	6.06228			0.324043
$351$	−28.6849	+	24.0398i	−1.53109	+	1.28315i
$352$	−16.3669			−0.872360
$353$	2.26919	−	3.93036i	0.120777	−	0.209192i	−0.799297	−	0.600936i	$-0.794795\pi$
$353$	2.26919	−	3.93036i	0.120777	−	0.209192i	0.920074	+	0.391744i	$0.128128\pi$
$354$	2.38228	+	41.0458i	0.126617	+	2.18156i
$355$	−2.87234	−	4.97504i	−0.152448	−	0.264048i
$356$	−5.32323	−	9.22011i	−0.282131	−	0.488665i
$357$	−4.77964	−	2.40164i	−0.252965	−	0.127108i
$358$	−6.21298	+	10.7612i	−0.328366	+	0.568747i
$359$	−11.5921			−0.611809			−0.305904	−	0.952062i	$-0.598959\pi$
$359$	−11.5921			−0.611809			−0.305904	+	0.952062i	$0.598959\pi$
$360$	0.956999	+	1.28656i	0.0504383	+	0.0678079i
$361$	17.7046			0.931821
$362$	5.70681	−	9.88449i	0.299943	−	0.519517i
$363$	6.61529	−	4.34902i	0.347213	−	0.228265i
$364$	−3.29169	−	5.70137i	−0.172531	−	0.298833i
$365$	−0.868894	−	1.50497i	−0.0454800	−	0.0787737i
$366$	−2.09335	+	1.37621i	−0.109421	+	0.0719356i
$367$	3.61750	−	6.26569i	0.188832	−	0.327066i	−0.756029	−	0.654538i	$-0.772863\pi$
$367$	3.61750	−	6.26569i	0.188832	−	0.327066i	0.944861	+	0.327472i	$0.106197\pi$
$368$	20.1298			1.04934
$369$	1.63071	+	2.19229i	0.0848916	+	0.114126i
$370$	7.21472			0.375076
$371$	−3.06072	+	5.30132i	−0.158904	+	0.275231i
$372$	−5.19721	−	2.61146i	−0.269463	−	0.135398i
$373$	−5.87996	−	10.1844i	−0.304453	−	0.527328i	0.672686	−	0.739928i	$-0.265140\pi$
$373$	−5.87996	−	10.1844i	−0.304453	−	0.527328i	−0.977139	+	0.212600i	$0.931807\pi$
$374$	−10.3275	−	17.8878i	−0.534023	−	0.924955i
$375$	−0.426295	−	7.34490i	−0.0220138	−	0.379289i
$376$	−5.92309	+	10.2591i	−0.305460	+	0.529072i
$377$	−46.5402			−2.39694
$378$	−5.01664	+	4.20426i	−0.258028	+	0.216244i
$379$	−5.11108			−0.262539			−0.131269	−	0.991347i	$-0.541905\pi$
$379$	−5.11108			−0.262539			−0.131269	+	0.991347i	$0.541905\pi$
$380$	1.73436	−	3.00400i	0.0889709	−	0.154102i
$381$	−0.0413477	−	0.712405i	−0.00211831	−	0.0364976i
$382$	8.92237	+	15.4540i	0.456508	+	0.790696i
$383$	−8.07593	−	13.9879i	−0.412661	−	0.714749i	0.582519	−	0.812817i	$-0.302067\pi$
$383$	−8.07593	−	13.9879i	−0.412661	−	0.714749i	−0.995180	+	0.0980678i	$0.968734\pi$
$384$	14.4106	+	7.24092i	0.735386	+	0.369512i
$385$	−0.379258	+	0.656893i	−0.0193288	+	0.0334784i
$386$	11.7672			0.598937
$387$	−1.18936	+	2.75417i	−0.0604585	+	0.140002i
$388$	19.8248			1.00645
$389$	−8.61616	+	14.9236i	−0.436857	+	0.756658i	−0.997445	−	0.0714365i	$-0.977242\pi$
$389$	−8.61616	+	14.9236i	−0.436857	+	0.756658i	0.560588	+	0.828095i	$0.310575\pi$
$390$	−8.22559	+	5.40766i	−0.416519	+	0.273828i
$391$	9.18718	+	15.9127i	0.464616	+	0.804738i
$392$	−4.02668	−	6.97441i	−0.203378	−	0.352261i
$393$	−4.38691	+	2.88404i	−0.221290	+	0.145480i
$394$	8.67702	−	15.0290i	0.437142	−	0.757152i
$395$	5.14516			0.258881
$396$	−9.99339	+	1.16395i	−0.502187	+	0.0584905i
$397$	−29.6151			−1.48634			−0.743170	−	0.669103i	$-0.766679\pi$
$397$	−29.6151			−1.48634			−0.743170	+	0.669103i	$0.766679\pi$
$398$	−15.3600	+	26.6043i	−0.769929	+	1.33356i
$399$	−6.47963	−	3.25584i	−0.324387	−	0.162996i
$400$	−11.7811	−	20.4054i	−0.589053	−	1.02027i
$401$	7.15251	+	12.3885i	0.357179	+	0.618653i	0.987488	−	0.157692i	$-0.0504052\pi$
$401$	7.15251	+	12.3885i	0.357179	+	0.618653i	−0.630309	+	0.776344i	$0.717072\pi$
$402$	−2.08540	−	35.9307i	−0.104010	−	1.79206i
$403$	−9.14372	+	15.8374i	−0.455481	+	0.788917i
$404$	−4.10835			−0.204398
$405$	2.67126	+	2.83598i	0.132736	+	0.140921i
$406$	−8.13931			−0.403947
$407$	11.5920	−	20.0779i	0.574592	−	0.995223i
$408$	0.553767	+	9.54120i	0.0274156	+	0.472360i
$409$	−8.43314	−	14.6066i	−0.416992	−	0.722251i	0.578644	−	0.815581i	$-0.303582\pi$
$409$	−8.43314	−	14.6066i	−0.416992	−	0.722251i	−0.995635	+	0.0933297i	$0.970249\pi$
$410$	0.359324	+	0.622367i	0.0177457	+	0.0307365i
$411$	−16.5427	−	8.31225i	−0.815990	−	0.410013i
$412$	−4.60446	+	7.97516i	−0.226846	+	0.392908i
$413$	8.99937			0.442830
$414$	22.3328	−	2.60113i	1.09760	−	0.127839i
$415$	4.22572			0.207432
$416$	−23.2463	+	40.2638i	−1.13974	+	1.97409i
$417$	32.8966	−	21.6269i	1.61095	−	1.05907i
$418$	−14.0007	−	24.2500i	−0.684798	−	1.18610i
$419$	0.720706	+	1.24830i	0.0352088	+	0.0609835i	0.883093	−	0.469198i	$-0.155457\pi$
$419$	0.720706	+	1.24830i	0.0352088	+	0.0609835i	−0.847884	+	0.530182i	$0.822124\pi$
$420$	−0.572641	+	0.376465i	−0.0279420	+	0.0183696i
$421$	0.693490	−	1.20116i	0.0337986	−	0.0585409i	−0.848631	−	0.528985i	$-0.822573\pi$
$421$	0.693490	−	1.20116i	0.0337986	−	0.0585409i	0.882430	+	0.470444i	$0.155906\pi$
$422$	2.39249			0.116465
$423$	−11.4110	+	26.4242i	−0.554822	+	1.28479i
$424$	10.9372			0.531157
$425$	10.7537	−	18.6259i	0.521630	−	0.903489i
$426$	−37.4379	−	18.8115i	−1.81387	−	0.911422i
$427$	0.274174	+	0.474884i	0.0132682	+	0.0229812i
$428$	−5.36036	−	9.28442i	−0.259103	−	0.448780i
$429$	1.83286	+	31.5795i	0.0884915	+	1.52467i
$430$	−0.394532	+	0.683349i	−0.0190260	+	0.0329540i
$431$	−19.8758			−0.957383			−0.478692	−	0.877983i	$-0.658889\pi$
$431$	−19.8758			−0.957383			−0.478692	+	0.877983i	$0.658889\pi$
$432$	23.9004	+	8.71552i	1.14991	+	0.419326i
$433$	−3.09155			−0.148570			−0.0742851	−	0.997237i	$-0.523667\pi$
$433$	−3.09155			−0.148570			−0.0742851	+	0.997237i	$0.523667\pi$
$434$	−1.59912	+	2.76976i	−0.0767604	+	0.132953i
$435$	0.280710	+	4.83652i	0.0134590	+	0.231894i
$436$	0.0497235	+	0.0861236i	0.00238132	+	0.00412457i
$437$	12.4548	+	21.5724i	0.595794	+	1.03195i
$438$	−11.3251	−	5.69056i	−0.541135	−	0.271906i
$439$	−4.45099	+	7.70933i	−0.212434	+	0.367946i	−0.952476	−	0.304614i	$-0.901472\pi$
$439$	−4.45099	+	7.70933i	−0.212434	+	0.367946i	0.740042	+	0.672561i	$0.234806\pi$
$440$	1.35524			0.0646086
$441$	−11.6784	−	15.7001i	−0.556115	−	0.747626i
$442$	−58.6736			−2.79082
$443$	5.48826	−	9.50594i	0.260755	−	0.451641i	−0.705688	−	0.708523i	$-0.749362\pi$
$443$	5.48826	−	9.50594i	0.260755	−	0.451641i	0.966443	+	0.256882i	$0.0826952\pi$
$444$	17.5027	−	11.5066i	0.830641	−	0.546080i
$445$	1.74224	+	3.01765i	0.0825901	+	0.143050i
$446$	1.73164	+	2.99929i	0.0819956	+	0.142021i
$447$	−21.6883	+	14.2583i	−1.02582	+	0.674395i
$448$	−0.682136	+	1.18149i	−0.0322279	+	0.0558204i
$449$	18.7937			0.886931			0.443465	−	0.896292i	$-0.353749\pi$
$449$	18.7937			0.886931			0.443465	+	0.896292i	$0.353749\pi$
$450$	−15.7071	−	21.1162i	−0.740439	−	0.995426i
$451$	2.30931			0.108741
$452$	−5.08458	+	8.80675i	−0.239159	+	0.414235i
$453$	12.4354	+	6.24847i	0.584268	+	0.293579i
$454$	11.6106	+	20.1102i	0.544913	+	0.943818i
$455$	1.07734	+	1.86600i	0.0505063	+	0.0874795i
$456$	0.750727	+	12.9347i	0.0351560	+	0.605724i
$457$	−9.85804	+	17.0746i	−0.461140	+	0.798717i	−0.999018	−	0.0443053i	$-0.985893\pi$
$457$	−9.85804	+	17.0746i	−0.461140	+	0.798717i	0.537879	+	0.843022i	$0.319226\pi$
$458$	43.2809			2.02238
$459$	4.01841	+	22.8710i	0.187564	+	1.06753i
$460$	2.35405			0.109758
$461$	20.0872	−	34.7921i	0.935556	−	1.62043i	0.161918	−	0.986804i	$-0.448232\pi$
$461$	20.0872	−	34.7921i	0.935556	−	1.62043i	0.773639	−	0.633627i	$-0.218435\pi$
$462$	0.320545	+	5.52287i	0.0149131	+	0.256947i
$463$	−11.1465	−	19.3064i	−0.518024	−	0.897243i	−0.999781	−	0.0209385i	$-0.993335\pi$
$463$	−11.1465	−	19.3064i	−0.518024	−	0.897243i	0.481757	−	0.876305i	$-0.339999\pi$
$464$	15.8174	+	27.3966i	0.734305	+	1.27185i
$465$	1.70099	+	0.854704i	0.0788817	+	0.0396360i
$466$	7.09814	−	12.2943i	0.328815	−	0.569524i
$467$	2.81433			0.130232			0.0651158	−	0.997878i	$-0.479258\pi$
$467$	2.81433			0.130232			0.0651158	+	0.997878i	$0.479258\pi$
$468$	−11.3305	+	26.2376i	−0.523750	+	1.21284i
$469$	−7.87786			−0.363766
$470$	−3.78524	+	6.55623i	−0.174600	+	0.302416i
$471$	−9.97566	+	6.55819i	−0.459654	+	0.302186i
$472$	−8.03960	−	13.9250i	−0.370053	−	0.640950i
$473$	1.26780	+	2.19589i	0.0582933	+	0.100967i
$474$	31.3565	−	20.6144i	1.44025	−	0.946851i
$475$	14.5784	−	25.2506i	0.668905	−	1.15858i
$476$	−4.08468			−0.187221
$477$	26.3958	−	3.07436i	1.20858	−	0.140765i
$478$	−6.22126			−0.284554
$479$	−7.84457	+	13.5872i	−0.358428	+	0.620815i	−0.987698	−	0.156371i	$-0.950020\pi$
$479$	−7.84457	+	13.5872i	−0.358428	+	0.620815i	0.629271	+	0.777186i	$0.283354\pi$
$480$	4.32448	+	2.17294i	0.197385	+	0.0991805i
$481$	−32.9287	−	57.0341i	−1.50142	−	2.60053i
$482$	11.2425	+	19.4726i	0.512083	+	0.886954i
$483$	−0.285152	−	4.91305i	−0.0129748	−	0.223552i
$484$	3.02273	−	5.23552i	0.137397	−	0.237978i
$485$	−6.48845			−0.294625
$486$	27.6422	+	6.58097i	1.25387	+	0.298519i
$487$	−8.31905			−0.376972			−0.188486	−	0.982076i	$-0.560358\pi$
$487$	−8.31905			−0.376972			−0.188486	+	0.982076i	$0.560358\pi$
$488$	0.489868	−	0.848476i	0.0221753	−	0.0384087i
$489$	−0.689657	−	11.8825i	−0.0311874	−	0.537347i
$490$	−2.57331	−	4.45710i	−0.116250	−	0.201351i
$491$	−10.7300	−	18.5849i	−0.484237	−	0.838723i	0.515599	−	0.856830i	$-0.327569\pi$
$491$	−10.7300	−	18.5849i	−0.484237	−	0.838723i	−0.999836	+	0.0181071i	$0.994236\pi$
$492$	1.86431	+	0.936765i	0.0840495	+	0.0422326i
$493$	−14.4380	+	25.0074i	−0.650256	+	1.12628i
$494$	−79.5422			−3.57877
$495$	3.27073	−	0.380948i	0.147009	−	0.0171223i
$496$	12.4305			0.558148
$497$	−4.58542	+	7.94218i	−0.205684	+	0.356256i
$498$	25.7531	−	16.9306i	1.15402	−	0.758678i
$499$	4.43186	+	7.67620i	0.198397	+	0.343634i	0.948009	−	0.318244i	$-0.103093\pi$
$499$	4.43186	+	7.67620i	0.198397	+	0.343634i	−0.749612	+	0.661878i	$0.769760\pi$
$500$	−2.80908	−	4.86547i	−0.125626	−	0.217590i
$501$	−22.5652	+	14.8348i	−1.00814	+	0.662770i
$502$	−6.67367	+	11.5591i	−0.297861	+	0.515910i
$503$	−18.4384			−0.822126			−0.411063	−	0.911607i	$-0.634842\pi$
$503$	−18.4384			−0.822126			−0.411063	+	0.911607i	$0.634842\pi$
$504$	1.01483	−	2.35002i	0.0452042	−	0.104678i
$505$	1.34462			0.0598349
$506$	9.50160	−	16.4573i	0.422398	−	0.731614i
$507$	60.1716	+	30.2346i	2.67231	+	1.34277i
$508$	−0.272461	−	0.471917i	−0.0120885	−	0.0209379i
$509$	2.69763	+	4.67243i	0.119570	+	0.207102i	0.919597	−	0.392862i	$-0.128515\pi$
$509$	2.69763	+	4.67243i	0.119570	+	0.207102i	−0.800027	+	0.599964i	$0.795182\pi$
$510$	0.353893	+	6.09745i	0.0156707	+	0.269999i
$511$	−1.38711	+	2.40254i	−0.0613621	+	0.106282i
$512$	19.5124			0.862333
$513$	5.44765	+	31.0056i	0.240520	+	1.36893i
$514$	9.10483			0.401597
$515$	1.50699	−	2.61019i	0.0664061	−	0.115019i
$516$	0.132737	+	2.28701i	0.00584344	+	0.100680i
$517$	12.1636	+	21.0679i	0.534953	+	0.926565i
$518$	−5.75881	−	9.97456i	−0.253028	−	0.438257i
$519$	−4.75358	−	2.38855i	−0.208659	−	0.104846i
$520$	1.92488	−	3.33399i	0.0844116	−	0.146205i
$521$	34.0231			1.49058			0.745290	−	0.666741i	$-0.232311\pi$
$521$	34.0231			1.49058			0.745290	+	0.666741i	$0.232311\pi$
$522$	21.0886	+	28.3509i	0.923021	+	1.24088i
$523$	17.5996			0.769576			0.384788	−	0.923005i	$-0.374275\pi$
$523$	17.5996			0.769576			0.384788	+	0.923005i	$0.374275\pi$
$524$	−2.00451	+	3.47191i	−0.0875674	+	0.151671i
$525$	−4.81342	+	3.16444i	−0.210075	+	0.138107i
$526$	16.5055	+	28.5884i	0.719675	+	1.24651i
$527$	5.67326	+	9.82637i	0.247131	+	0.428043i
$528$	17.9668	−	11.8117i	0.781906	−	0.514040i
$529$	3.04754	−	5.27849i	0.132502	−	0.229500i
$530$	6.98957			0.303608
$531$	−23.3169	−	31.3467i	−1.01187	−	1.36033i
$532$	−5.53749			−0.240081
$533$	3.27997	−	5.68108i	0.142071	−	0.246075i
$534$	22.7082	+	11.4103i	0.982681	+	0.493771i
$535$	1.75439	+	3.03870i	0.0758490	+	0.131374i
$536$	7.03770	+	12.1897i	0.303983	+	0.526513i
$537$	−0.684139	−	11.7874i	−0.0295228	−	0.508666i
$538$	−11.2560	+	19.4960i	−0.485281	+	0.840531i
$539$	−16.5382			−0.712352
$540$	2.79499	+	1.01922i	0.120277	+	0.0438604i
$541$	19.6744			0.845868			0.422934	−	0.906160i	$-0.361000\pi$
$541$	19.6744			0.845868			0.422934	+	0.906160i	$0.361000\pi$
$542$	10.1487	−	17.5781i	0.435924	−	0.755043i
$543$	0.628402	+	10.8271i	0.0269673	+	0.464636i
$544$	14.4233	+	24.9818i	0.618392	+	1.07109i
$545$	−0.0162740	−	0.0281874i	−0.000697101	−	0.00120741i
$546$	14.0419	+	7.05569i	0.600939	+	0.301956i
$547$	7.16166	−	12.4044i	0.306211	−	0.530372i	−0.671320	−	0.741168i	$-0.734272\pi$
$547$	7.16166	−	12.4044i	0.306211	−	0.530372i	0.977530	+	0.210796i	$0.0676055\pi$
$548$	−14.1374			−0.603919
$549$	0.943746	−	2.18541i	0.0402781	−	0.0932709i
$550$	−22.2434			−0.948461
$551$	−19.5732	+	33.9018i	−0.833847	+	1.44427i
$552$	−7.34737	+	4.83031i	−0.312725	+	0.205591i
$553$	−4.10689	−	7.11333i	−0.174643	−	0.302490i
$554$	−14.4467	−	25.0225i	−0.613783	−	1.06310i
$555$	−5.72845	+	3.76600i	−0.243159	+	0.159858i
$556$	15.0314	−	26.0352i	0.637475	−	1.10414i
$557$	1.21426			0.0514499			0.0257250	−	0.999669i	$-0.491811\pi$
$557$	1.21426			0.0514499			0.0257250	+	0.999669i	$0.491811\pi$
$558$	13.7909	−	1.60625i	0.583816	−	0.0679980i
$559$	7.20272			0.304642
$560$	0.732299	−	1.26838i	0.0309453	−	0.0535988i
$561$	17.5372	+	8.81197i	0.740421	+	0.372042i
$562$	8.10377	+	14.0361i	0.341837	+	0.592079i
$563$	−15.8136	−	27.3900i	−0.666464	−	1.15435i	−0.978886	−	0.204406i	$-0.934474\pi$
$563$	−15.8136	−	27.3900i	−0.666464	−	1.15435i	0.312422	−	0.949943i	$-0.398860\pi$
$564$	1.27352	+	21.9422i	0.0536247	+	0.923933i
$565$	1.66413	−	2.88236i	0.0700105	−	0.121262i
$566$	−14.3454			−0.602981
$567$	1.78862	−	5.95678i	0.0751149	−	0.250161i
$568$	16.3856			0.687524
$569$	23.5071	−	40.7155i	0.985468	−	1.70688i	0.345632	−	0.938370i	$-0.387664\pi$
$569$	23.5071	−	40.7155i	0.985468	−	1.70688i	0.639836	−	0.768511i	$-0.279002\pi$
$570$	0.479763	+	8.26614i	0.0200951	+	0.346230i
$571$	−15.8025	−	27.3707i	−0.661314	−	1.14543i	−0.980271	−	0.197661i	$-0.936666\pi$
$571$	−15.8025	−	27.3707i	−0.661314	−	1.14543i	0.318956	−	0.947769i	$-0.396668\pi$
$572$	12.0777	+	20.9192i	0.504993	+	0.874674i
$573$	−15.1511	−	7.61303i	−0.632947	−	0.318039i
$574$	0.573627	−	0.993550i	0.0239427	−	0.0414700i
$575$	19.7873			0.825189
$576$	5.88277	−	0.685176i	0.245116	−	0.0285490i
$577$	−35.2559			−1.46772			−0.733860	−	0.679300i	$-0.762283\pi$
$577$	−35.2559			−1.46772			−0.733860	+	0.679300i	$0.762283\pi$
$578$	−2.70827	+	4.69087i	−0.112649	+	0.195114i
$579$	−9.34313	+	6.14236i	−0.388287	+	0.255268i
$580$	1.84974	+	3.20385i	0.0768064	+	0.133033i
$581$	−3.37298	−	5.84217i	−0.139935	−	0.242374i
$582$	−39.5430	+	25.9963i	−1.63911	+	1.07758i
$583$	11.2302	−	19.4513i	0.465108	−	0.805590i
$584$	4.95670			0.205110
$585$	3.70834	−	8.58731i	0.153321	−	0.355042i
$586$	−61.0837			−2.52334
$587$	14.2400	−	24.6645i	0.587749	−	1.01801i	−0.406777	−	0.913527i	$-0.633348\pi$
$587$	14.2400	−	24.6645i	0.587749	−	1.01801i	0.994527	−	0.104484i	$-0.0333191\pi$
$588$	−13.3513	−	6.70867i	−0.550599	−	0.276661i
$589$	7.69107	+	13.3213i	0.316905	+	0.548896i
$590$	−5.13783	−	8.89898i	−0.211521	−	0.366365i
$591$	0.955464	+	16.4623i	0.0393025	+	0.677167i
$592$	−22.3826	+	38.7679i	−0.919921	+	1.59335i
$593$	−4.79696			−0.196987			−0.0984937	−	0.995138i	$-0.531402\pi$
$593$	−4.79696			−0.196987			−0.0984937	+	0.995138i	$0.531402\pi$
$594$	18.4068	−	15.4260i	0.755239	−	0.632937i
$595$	1.33688			0.0548065
$596$	−9.91004	+	17.1647i	−0.405931	+	0.703093i
$597$	−1.69136	−	29.1415i	−0.0692227	−	1.19268i
$598$	−26.9907	−	46.7492i	−1.10373	−	1.91172i
$599$	−2.53206	−	4.38566i	−0.103457	−	0.179193i	0.809650	−	0.586914i	$-0.199657\pi$
$599$	−2.53206	−	4.38566i	−0.103457	−	0.179193i	−0.913107	+	0.407720i	$0.866324\pi$
$600$	9.19651	+	4.62100i	0.375446	+	0.188652i
$601$	17.9645	−	31.1154i	0.732785	−	1.26922i	−0.222903	−	0.974841i	$-0.571553\pi$
$601$	17.9645	−	31.1154i	0.732785	−	1.26922i	0.955688	−	0.294381i	$-0.0951134\pi$
$602$	1.25967			0.0513401
$603$	20.4112	+	27.4402i	0.831208	+	1.11745i
$604$	10.6273			0.432420
$605$	−0.989308	+	1.71353i	−0.0402211	+	0.0696649i
$606$	8.19462	−	5.38730i	0.332884	−	0.218844i
$607$	2.62783	+	4.55154i	0.106660	+	0.184741i	0.914415	−	0.404777i	$-0.132651\pi$
$607$	2.62783	+	4.55154i	0.106660	+	0.184741i	−0.807755	+	0.589518i	$0.799318\pi$
$608$	19.5532	+	33.8672i	0.792987	+	1.37349i
$609$	6.46257	−	4.24862i	0.261876	−	0.172163i
$610$	0.313058	−	0.542232i	0.0126753	−	0.0219543i
$611$	69.1047			2.79568
$612$	10.5832	+	14.2278i	0.427802	+	0.575125i
$613$	−21.9713			−0.887412			−0.443706	−	0.896172i	$-0.646337\pi$
$613$	−21.9713			−0.887412			−0.443706	+	0.896172i	$0.646337\pi$
$614$	−11.7776	+	20.3994i	−0.475305	+	0.823252i
$615$	−0.610169	−	0.306594i	−0.0246044	−	0.0123630i
$616$	−1.08176	−	1.87366i	−0.0435853	−	0.0754919i
$617$	15.8691	+	27.4860i	0.638864	+	1.10654i	0.985682	+	0.168613i	$0.0539287\pi$
$617$	15.8691	+	27.4860i	0.638864	+	1.10654i	−0.346818	+	0.937932i	$0.612738\pi$
$618$	−1.27370	−	21.9453i	−0.0512356	−	0.882770i
$619$	18.2257	−	31.5679i	0.732554	−	1.26882i	−0.223235	−	0.974765i	$-0.571662\pi$
$619$	18.2257	−	31.5679i	0.732554	−	1.26882i	0.955788	−	0.294055i	$-0.0950050\pi$
$620$	1.45367			0.0583808
$621$	−16.3744	+	13.7227i	−0.657080	+	0.550674i
$622$	−24.7211			−0.991226
$623$	2.78132	−	4.81739i	0.111431	−	0.193005i
$624$	−3.53903	−	60.9762i	−0.141675	−	2.44100i
$625$	−11.1121	−	19.2468i	−0.444486	−	0.769872i
$626$	21.3104	+	36.9106i	0.851734	+	1.47525i
$627$	23.7747	+	11.9461i	0.949469	+	0.477083i
$628$	−4.55818	+	7.89500i	−0.181891	+	0.315045i
$629$	−40.8614			−1.62925
$630$	0.648543	−	1.50181i	0.0258386	−	0.0598337i
$631$	−6.25533			−0.249021			−0.124510	−	0.992218i	$-0.539736\pi$
$631$	−6.25533			−0.249021			−0.124510	+	0.992218i	$0.539736\pi$
$632$	−7.33779	+	12.7094i	−0.291882	+	0.505554i
$633$	−1.89963	+	1.24885i	−0.0755033	+	0.0496374i
$634$	−1.46866	−	2.54379i	−0.0583279	−	0.101027i
$635$	0.0891738	+	0.154454i	0.00353876	+	0.00612930i
$636$	16.9565	−	11.1475i	0.672369	−	0.442028i
$637$	−23.4896	+	40.6852i	−0.930693	+	1.61201i
$638$	29.8643			1.18234
$639$	39.5449	−	4.60586i	1.56437	−	0.182205i
$640$	−4.03066			−0.159326
$641$	−19.6607	+	34.0533i	−0.776550	+	1.34502i	0.157370	+	0.987540i	$0.449699\pi$
$641$	−19.6607	+	34.0533i	−0.776550	+	1.34502i	−0.933919	+	0.357484i	$0.883635\pi$
$642$	22.8666	+	11.4899i	0.902474	+	0.453469i
$643$	−4.50051	−	7.79512i	−0.177483	−	0.307410i	0.763535	−	0.645767i	$-0.223462\pi$
$643$	−4.50051	−	7.79512i	−0.177483	−	0.307410i	−0.941018	+	0.338357i	$0.890129\pi$
$644$	−1.87901	−	3.25454i	−0.0740434	−	0.128247i
$645$	−0.0434436	−	0.748516i	−0.00171059	−	0.0294728i
$646$	−24.6761	+	42.7403i	−0.970869	+	1.68160i
$647$	49.7161			1.95454			0.977271	−	0.211996i	$-0.0679964\pi$
$647$	49.7161			1.95454			0.977271	+	0.211996i	$0.0679964\pi$
$648$	−10.8150	+	2.55392i	−0.424852	+	0.100327i
$649$	−33.0200			−1.29615
$650$	−31.5928	+	54.7203i	−1.23917	+	2.14631i
$651$	−0.176086	−	3.03390i	−0.00690137	−	0.118908i
$652$	−4.54451	−	7.87132i	−0.177977	−	0.308265i
$653$	13.9053	+	24.0846i	0.544155	+	0.942504i	0.998660	+	0.0517595i	$0.0164829\pi$
$653$	13.9053	+	24.0846i	0.544155	+	0.942504i	−0.454505	+	0.890744i	$0.650184\pi$
$654$	−0.212114	−	0.106582i	−0.00829432	−	0.00416767i
$655$	0.656055	−	1.13632i	0.0256342	−	0.0443998i
$656$	−4.45900			−0.174095
$657$	11.9625	−	1.39329i	0.466701	−	0.0543574i
$658$	12.0856			0.471144
$659$	−4.38026	+	7.58682i	−0.170631	+	0.295541i	−0.938640	−	0.344897i	$-0.887914\pi$
$659$	−4.38026	+	7.58682i	−0.170631	+	0.295541i	0.768010	+	0.640438i	$0.221247\pi$
$660$	2.10110	−	1.38131i	0.0817853	−	0.0537672i
$661$	2.31545	+	4.01048i	0.0900606	+	0.155990i	0.907536	−	0.419973i	$-0.137961\pi$
$661$	2.31545	+	4.01048i	0.0900606	+	0.155990i	−0.817476	+	0.575963i	$0.804627\pi$
$662$	−31.2205	−	54.0754i	−1.21342	−	2.10170i
$663$	46.5866	−	30.6269i	1.80927	−	1.18945i
$664$	−6.02652	+	10.4382i	−0.233874	+	0.405082i
$665$	1.81236			0.0702805
$666$	−19.8226	+	45.9028i	−0.768112	+	1.77870i
$667$	−26.5668			−1.02867
$668$	−10.3107	+	17.8587i	−0.398934	+	0.690974i
$669$	−2.94051	−	1.47753i	−0.113687	−	0.0571245i
$670$	4.49755	+	7.78999i	0.173756	+	0.300953i
$671$	−1.00598	−	1.74242i	−0.0388356	−	0.0672653i
$672$	−0.447669	−	7.71316i	−0.0172692	−	0.297542i
$673$	−5.26726	+	9.12317i	−0.203038	+	0.351672i	−0.949506	−	0.313749i	$-0.898415\pi$
$673$	−5.26726	+	9.12317i	−0.203038	+	0.351672i	0.746468	+	0.665422i	$0.231748\pi$
$674$	27.9925			1.07823
$675$	23.4937	+	8.56723i	0.904274	+	0.329753i
$676$	51.4227			1.97780
$677$	1.01209	−	1.75299i	0.0388978	−	0.0673730i	−0.845921	−	0.533308i	$-0.820949\pi$
$677$	1.01209	−	1.75299i	0.0388978	−	0.0673730i	0.884819	+	0.465935i	$0.154282\pi$
$678$	−1.40651	−	24.2336i	−0.0540167	−	0.930686i
$679$	5.17910	+	8.97046i	0.198756	+	0.344255i
$680$	−1.19430	−	2.06859i	−0.0457993	−	0.0793267i
$681$	−19.7160	−	9.90678i	−0.755520	−	0.379629i
$682$	5.86742	−	10.1627i	0.224675	−	0.389148i
$683$	−30.3719			−1.16215			−0.581075	−	0.813850i	$-0.697368\pi$
$683$	−30.3719			−1.16215			−0.581075	+	0.813850i	$0.697368\pi$
$684$	14.3474	+	19.2882i	0.548586	+	0.737504i
$685$	4.62702			0.176789
$686$	−8.51688	+	14.7517i	−0.325176	+	0.563221i
$687$	−34.3648	+	22.5921i	−1.31110	+	0.861942i
$688$	−2.44795	−	4.23998i	−0.0933274	−	0.161648i
$689$	−31.9011	−	55.2543i	−1.21533	−	2.10502i
$690$	−4.69545	+	3.08688i	−0.178753	+	0.117516i
$691$	9.17681	−	15.8947i	0.349102	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$691$	9.17681	−	15.8947i	0.349102	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$692$	−4.06241			−0.154430
$693$	−3.13738	−	4.21781i	−0.119179	−	0.160221i
$694$	−3.52612			−0.133850
$695$	−4.91964	+	8.52106i	−0.186613	+	0.323222i
$696$	−12.3474	−	6.20422i	−0.468026	−	0.235170i
$697$	−2.03507	−	3.52485i	−0.0770838	−	0.133513i
$698$	−5.09364	−	8.82245i	−0.192797	−	0.333935i
$699$	0.781607	+	13.4668i	0.0295631	+	0.509361i
$700$	−2.19940	+	3.80947i	−0.0831294	+	0.143984i
$701$	−4.98491			−0.188277			−0.0941387	−	0.995559i	$-0.530010\pi$
$701$	−4.98491			−0.188277			−0.0941387	+	0.995559i	$0.530010\pi$
$702$	−11.8055	−	67.1919i	−0.445572	−	2.53600i
$703$	−55.3947			−2.08925
$704$	2.50286	−	4.33507i	0.0943299	−	0.163384i
$705$	−0.416809	−	7.18146i	−0.0156979	−	0.270469i
$706$	4.13630	+	7.16429i	0.155672	+	0.269632i
$707$	−1.07328	−	1.85898i	−0.0403649	−	0.0699140i
$708$	−26.6570	−	13.3944i	−1.00183	−	0.503394i
$709$	−13.9418	+	24.1480i	−0.523597	+	0.906896i	0.476026	+	0.879431i	$0.342077\pi$
$709$	−13.9418	+	24.1480i	−0.523597	+	0.906896i	−0.999623	+	0.0274647i	$0.991257\pi$
$710$	10.4715			0.392987
$711$	−14.1365	+	32.7355i	−0.530159	+	1.22768i
$712$	−9.93880			−0.372472
$713$	−5.21955	+	9.04053i	−0.195474	+	0.338571i
$714$	8.14741	−	5.35627i	0.304909	−	0.200453i
$715$	−3.95290	−	6.84663i	−0.147830	−	0.256049i
$716$	−4.50814	−	7.80833i	−0.168477	−	0.291811i
$717$	4.93965	−	3.24742i	0.184474	−	0.121277i
$718$	10.5651	−	18.2993i	0.394286	−	0.682924i
$719$	−10.7704			−0.401668			−0.200834	−	0.979625i	$-0.564365\pi$
$719$	−10.7704			−0.401668			−0.200834	+	0.979625i	$0.564365\pi$
$720$	−6.31538	+	0.735562i	−0.235360	+	0.0274128i
$721$	−4.81155			−0.179191
$722$	−16.1361	+	27.9485i	−0.600522	+	1.04013i
$723$	−19.0910	−	9.59271i	−0.710001	−	0.356757i
$724$	4.14087	+	7.17219i	0.153894	+	0.266552i
$725$	15.5483	+	26.9304i	0.577449	+	1.00017i
$726$	0.836154	+	14.4066i	0.0310326	+	0.534679i
$727$	−1.23443	+	2.13810i	−0.0457826	+	0.0792977i	−0.888009	−	0.459827i	$-0.847911\pi$
$727$	−1.23443	+	2.13810i	−0.0457826	+	0.0792977i	0.842226	+	0.539125i	$0.181245\pi$
$728$	−6.14578			−0.227778
$729$	−25.3829	+	9.20362i	−0.940109	+	0.340875i
$730$	3.16766			0.117240
$731$	2.23448	−	3.87023i	0.0826451	−	0.143146i
$732$	−0.105326	−	1.81473i	−0.00389296	−	0.0670742i
$733$	6.20513	+	10.7476i	0.229192	+	0.396972i	0.957569	−	0.288205i	$-0.0930584\pi$
$733$	6.20513	+	10.7476i	0.229192	+	0.396972i	−0.728377	+	0.685177i	$0.759725\pi$
$734$	6.59400	+	11.4211i	0.243389	+	0.421562i
$735$	4.36975	+	2.19568i	0.161181	+	0.0809889i
$736$	−13.2698	+	22.9840i	−0.489131	+	0.847200i
$737$	28.9050			1.06473
$738$	−4.94698	+	0.576183i	−0.182101	+	0.0212096i
$739$	38.5237			1.41712			0.708559	−	0.705651i	$-0.249346\pi$
$739$	38.5237			1.41712			0.708559	+	0.705651i	$0.249346\pi$
$740$	−2.61750	+	4.53365i	−0.0962213	+	0.166660i
$741$	63.1561	−	41.5200i	2.32010	−	1.52528i
$742$	−5.57910	−	9.66328i	−0.204815	−	0.354750i
$743$	−18.4038	−	31.8762i	−0.675168	−	1.16943i	−0.976420	−	0.215881i	$-0.930738\pi$
$743$	−18.4038	−	31.8762i	−0.675168	−	1.16943i	0.301251	−	0.953545i	$-0.402596\pi$
$744$	−4.53714	+	2.98280i	−0.166340	+	0.109355i
$745$	3.24345	−	5.61783i	0.118831	−	0.205821i
$746$	21.4361			0.784831
$747$	−11.6103	+	26.8856i	−0.424797	+	0.983693i
$748$	14.9873			0.547990
$749$	2.80072	−	4.85099i	0.102336	−	0.177251i
$750$	11.9832	+	6.02122i	0.437564	+	0.219864i
$751$	−7.09925	−	12.2963i	−0.259055	−	0.448697i	0.706934	−	0.707280i	$-0.250078\pi$
$751$	−7.09925	−	12.2963i	−0.259055	−	0.448697i	−0.965989	+	0.258583i	$0.916745\pi$
$752$	−23.4863	−	40.6795i	−0.856458	−	1.48343i
$753$	−0.734867	−	12.6615i	−0.0267800	−	0.461410i
$754$	42.4169	−	73.4683i	1.54473	−	2.67556i
$755$	−3.47822			−0.126585
$756$	−0.821867	−	4.67770i	−0.0298910	−	0.170126i
$757$	10.5676			0.384085			0.192042	−	0.981387i	$-0.438489\pi$
$757$	10.5676			0.384085			0.192042	+	0.981387i	$0.438489\pi$
$758$	4.65826	−	8.06835i	0.169196	−	0.293056i
$759$	1.04626	+	18.0267i	0.0379769	+	0.654327i
$760$	−1.61908	−	2.80433i	−0.0587302	−	0.101724i
$761$	−13.7421	−	23.8020i	−0.498151	−	0.862823i	0.501847	−	0.864957i	$-0.332654\pi$
$761$	−13.7421	−	23.8020i	−0.498151	−	0.862823i	−0.999998	+	0.00213360i	$0.999321\pi$
$762$	1.16229	+	0.584017i	0.0421052	+	0.0211567i
$763$	−0.0259799	+	0.0449985i	−0.000940535	+	0.00162906i
$764$	−12.9482			−0.468448
$765$	−3.46378	−	4.65661i	−0.125233	−	0.168360i
$766$	29.4417			1.06377
$767$	−46.8990	+	81.2315i	−1.69343	+	2.93310i
$768$	−30.2788	+	19.9059i	−1.09259	+	0.718292i
$769$	5.50415	+	9.53346i	0.198485	+	0.343785i	0.948037	−	0.318159i	$-0.103065\pi$
$769$	5.50415	+	9.53346i	0.198485	+	0.343785i	−0.749553	+	0.661945i	$0.769731\pi$
$770$	−0.691314	−	1.19739i	−0.0249132	−	0.0431510i
$771$	−7.22919	+	4.75261i	−0.260353	+	0.171161i
$772$	−4.26916	+	7.39440i	−0.153650	+	0.266130i
$773$	−40.1139			−1.44280			−0.721398	−	0.692521i	$-0.756500\pi$
$773$	−40.1139			−1.44280			−0.721398	+	0.692521i	$0.756500\pi$
$774$	−3.26374	−	4.38768i	−0.117313	−	0.157712i
$775$	12.2191			0.438921
$776$	9.25352	−	16.0276i	0.332182	−	0.575356i
$777$	9.77907	+	4.91372i	0.350822	+	0.176279i
$778$	−15.7056	−	27.2029i	−0.563073	−	0.975272i
$779$	−2.75889	−	4.77854i	−0.0988475	−	0.171209i
$780$	−0.413867	−	7.13076i	−0.0148188	−	0.255322i
$781$	16.8246	−	29.1410i	0.602031	−	1.04275i
$782$	−33.4929			−1.19771
$783$	−31.5430	−	11.5025i	−1.12726	−	0.411065i
$784$	31.9333			1.14047
$785$	1.49185	−	2.58395i	0.0532462	−	0.0922252i
$786$	−0.554492	−	9.55369i	−0.0197781	−	0.340769i
$787$	7.84526	+	13.5884i	0.279653	+	0.484374i	0.971299	−	0.237864i	$-0.0764472\pi$
$787$	7.84526	+	13.5884i	0.279653	+	0.484374i	−0.691645	+	0.722237i	$0.743114\pi$
$788$	6.29605	+	10.9051i	0.224287	+	0.388477i
$789$	−28.0281	−	14.0834i	−0.997827	−	0.501381i
$790$	−4.68932	+	8.12215i	−0.166839	+	0.288973i
$791$	−5.31326			−0.188918
$792$	−3.72356	+	8.62255i	−0.132311	+	0.306389i
$793$	−5.71529			−0.202956
$794$	26.9913	−	46.7504i	0.957887	−	1.65911i
$795$	−5.54969	+	3.64847i	−0.196827	+	0.129398i
$796$	−11.1452	−	19.3041i	−0.395033	−	0.684216i
$797$	21.3861	+	37.0417i	0.757533	+	1.31209i	0.944105	+	0.329645i	$0.106929\pi$
$797$	21.3861	+	37.0417i	0.757533	+	1.31209i	−0.186572	+	0.982441i	$0.559738\pi$
$798$	11.0452	−	7.26134i	0.390996	−	0.257049i
$799$	21.4381	−	37.1320i	0.758427	−	1.31363i
$800$	31.0648			1.09831
$801$	−23.9863	+	2.79372i	−0.847512	+	0.0987111i
$802$	−26.0753			−0.920751
$803$	5.08950	−	8.81527i	0.179605	−	0.311084i
$804$	23.3350	+	11.7252i	0.822962	+	0.413517i
$805$	0.614981	+	1.06518i	0.0216752	+	0.0375426i
$806$	−16.6673	−	28.8685i	−0.587079	−	1.01685i
$807$	−1.23945	−	21.3552i	−0.0436306	−	0.751739i
$808$	−1.91764	+	3.32144i	−0.0674622	+	0.116848i
$809$	45.5750			1.60233			0.801166	−	0.598442i	$-0.204213\pi$
$809$	45.5750			1.60233			0.801166	+	0.598442i	$0.204213\pi$
$810$	−6.91147	+	1.63212i	−0.242844	+	0.0573469i
$811$	19.9527			0.700634			0.350317	−	0.936631i	$-0.386074\pi$
$811$	19.9527			0.700634			0.350317	+	0.936631i	$0.386074\pi$
$812$	2.95294	−	5.11464i	0.103628	−	0.179489i
$813$	1.11752	+	19.2544i	0.0391931	+	0.675281i
$814$	21.1299	+	36.5981i	0.740603	+	1.28276i
$815$	1.48737	+	2.57620i	0.0521003	+	0.0902404i
$816$	−33.8621	−	17.0148i	−1.18541	−	0.595638i
$817$	3.02922	−	5.24676i	0.105979	−	0.183561i
$818$	30.7440			1.07494
$819$	−14.8322	+	1.72753i	−0.518279	+	0.0603648i
$820$	−0.521451			−0.0182098
$821$	−23.5697	+	40.8238i	−0.822587	+	1.42476i	0.0811632	+	0.996701i	$0.474136\pi$
$821$	−23.5697	+	40.8238i	−0.822587	+	1.42476i	−0.903750	+	0.428061i	$0.859197\pi$
$822$	28.1988	−	18.5384i	0.983545	−	0.646602i
$823$	−11.1261	−	19.2710i	−0.387831	−	0.671744i	0.604326	−	0.796737i	$-0.293442\pi$
$823$	−11.1261	−	19.2710i	−0.387831	−	0.671744i	−0.992158	+	0.124993i	$0.960109\pi$
$824$	4.29840	+	7.44505i	0.149742	+	0.259361i
$825$	17.6611	−	11.6108i	0.614882	−	0.404235i
$826$	−8.20206	+	14.2064i	−0.285386	+	0.494303i
$827$	−46.9285			−1.63186			−0.815931	−	0.578149i	$-0.803775\pi$
$827$	−46.9285			−1.63186			−0.815931	+	0.578149i	$0.803775\pi$
$828$	−6.46782	+	14.9774i	−0.224772	+	0.520499i
$829$	48.4646			1.68324			0.841622	−	0.540067i	$-0.181601\pi$
$829$	48.4646			1.68324			0.841622	+	0.540067i	$0.181601\pi$
$830$	−3.85134	+	6.67071i	−0.133682	+	0.231544i
$831$	24.5321	+	12.3267i	0.851008	+	0.427609i
$832$	−7.10973	−	12.3144i	−0.246485	−	0.426925i
$833$	14.5742	+	25.2433i	0.504967	+	0.874629i
$834$	4.15804	+	71.6413i	0.143981	+	2.48074i
$835$	3.37459	−	5.84497i	0.116783	−	0.202273i
$836$	20.3179			0.702708
$837$	−10.1115	+	8.47404i	−0.349504	+	0.292906i
$838$	−2.62742			−0.0907627
$839$	−4.63098	+	8.02109i	−0.159879	+	0.276919i	−0.934825	−	0.355109i	$-0.884444\pi$
$839$	−4.63098	+	8.02109i	−0.159879	+	0.276919i	0.774946	+	0.632028i	$0.217777\pi$
$840$	0.0370687	+	0.638679i	0.00127899	+	0.0220365i
$841$	−6.37537	−	11.0425i	−0.219840	−	0.380775i
$842$	1.26410	+	2.18948i	0.0435637	+	0.0754546i
$843$	−13.7610	−	6.91456i	−0.473956	−	0.238150i
$844$	−0.867996	+	1.50341i	−0.0298777	+	0.0517496i
$845$	−16.8301			−0.578974
$846$	−31.3131	−	42.0965i	−1.07657	−	1.44731i
$847$	3.15867			0.108533
$848$	−21.6841	+	37.5580i	−0.744636	+	1.28975i
$849$	11.3901	−	7.48811i	0.390909	−	0.256991i
$850$	19.6019	+	33.9514i	0.672339	+	1.16452i
$851$	−18.7968	−	32.5571i	−0.644347	−	1.11604i
$852$	25.4034	−	16.7007i	0.870307	−	0.572157i
$853$	15.3881	−	26.6529i	0.526877	−	0.912578i	−0.472632	−	0.881260i	$-0.656696\pi$
$853$	15.3881	−	26.6529i	0.526877	−	0.912578i	0.999509	−	0.0313185i	$-0.00997062\pi$
$854$	−0.999534			−0.0342034
$855$	−4.69575	−	6.31284i	−0.160591	−	0.215895i
$856$	−10.0081			−0.342071
$857$	10.2118	−	17.6873i	0.348828	−	0.604188i	−0.637213	−	0.770687i	$-0.719913\pi$
$857$	10.2118	−	17.6873i	0.348828	−	0.604188i	0.986042	+	0.166499i	$0.0532464\pi$
$858$	−51.5219	−	25.8884i	−1.75893	−	0.883814i
$859$	17.8263	+	30.8761i	0.608226	+	1.05348i	0.991533	+	0.129858i	$0.0414521\pi$
$859$	17.8263	+	30.8761i	0.608226	+	1.05348i	−0.383306	+	0.923621i	$0.625215\pi$
$860$	−0.286272	−	0.495838i	−0.00976180	−	0.0169079i
$861$	0.0631645	+	1.08830i	0.00215264	+	0.0370892i
$862$	18.1149	−	31.3759i	0.616995	−	1.06867i
$863$	9.21342			0.313628			0.156814	−	0.987628i	$-0.449878\pi$
$863$	9.21342			0.313628			0.156814	+	0.987628i	$0.449878\pi$
$864$	−25.7067	+	21.5438i	−0.874558	+	0.732934i
$865$	1.32959			0.0452073
$866$	2.81765	−	4.88031i	0.0957476	−	0.165840i
$867$	−0.298220	−	5.13821i	−0.0101281	−	0.174503i
$868$	−1.16032	−	2.00974i	−0.0393840	−	0.0682151i
$869$	15.0688	+	26.0999i	0.511173	+	0.885377i
$870$	−7.89077	−	3.96490i	−0.267522	−	0.134423i
$871$	41.0545	−	71.1084i	1.39108	−	2.40942i
$872$	0.0928368			0.00314385
$873$	17.8272	−	41.2819i	0.603359	−	1.39718i
$874$	−45.4054			−1.53586
$875$	1.46771	−	2.54215i	0.0496176	−	0.0859402i
$876$	7.68464	−	5.05203i	0.259640	−	0.170692i
$877$	28.9184	+	50.0881i	0.976504	+	1.69135i	0.674881	+	0.737926i	$0.264195\pi$
$877$	28.9184	+	50.0881i	0.976504	+	1.69135i	0.301622	+	0.953428i	$0.402472\pi$
$878$	−8.11330	−	14.0526i	−0.273810	−	0.474254i
$879$	48.5001	−	31.8849i	1.63587	−	1.07545i
$880$	−2.68691	+	4.65387i	−0.0905758	+	0.156882i
$881$	−28.9309			−0.974706			−0.487353	−	0.873205i	$-0.662038\pi$
$881$	−28.9309			−0.974706			−0.487353	+	0.873205i	$0.662038\pi$
$882$	35.4280	−	4.12635i	1.19292	−	0.138941i
$883$	43.7957			1.47384			0.736922	−	0.675978i	$-0.236278\pi$
$883$	43.7957			1.47384			0.736922	+	0.675978i	$0.236278\pi$
$884$	21.2868	−	36.8698i	0.715953	−	1.24007i
$885$	8.72457	+	4.38386i	0.293273	+	0.147362i
$886$	10.0040	+	17.3275i	0.336092	+	0.582129i
$887$	15.0762	+	26.1128i	0.506210	+	0.876781i	0.999974	+	0.00718527i	$0.00228716\pi$
$887$	15.0762	+	26.1128i	0.506210	+	0.876781i	−0.493764	+	0.869596i	$0.664380\pi$
$888$	−1.13300	−	19.5211i	−0.0380210	−	0.655086i
$889$	0.142358	−	0.246571i	0.00477452	−	0.00826971i
$890$	−6.35154			−0.212904
$891$	−6.56270	+	21.8563i	−0.219859	+	0.732214i
$892$	−2.51296			−0.0841401
$893$	29.0631	−	50.3387i	0.972559	−	1.68452i
$894$	−2.74134	−	47.2322i	−0.0916841	−	1.57968i
$895$	1.47547	+	2.55559i	0.0493195	+	0.0854239i
$896$	3.21729	+	5.57250i	0.107482	+	0.186164i
$897$	45.8330	+	23.0298i	1.53032	+	0.768944i
$898$	−17.1287	+	29.6677i	−0.571591	+	0.990025i
$899$	−16.4055			−0.547153
$900$	18.9677	−	2.20920i	0.632257	−	0.0736399i
$901$	−39.5863			−1.31881
$902$	−2.10472	+	3.64548i	−0.0700795	+	0.121381i
$903$	−1.00017	+	0.657530i	−0.0332835	+	0.0218812i
$904$	4.74661	+	8.22137i	0.157870	+	0.273439i
$905$	−1.35526	−	2.34738i	−0.0450505	−	0.0780297i
$906$	−21.1975	+	13.9357i	−0.704241	+	0.462982i
$907$	20.8491	−	36.1118i	0.692284	−	1.19907i	−0.278803	−	0.960348i	$-0.589938\pi$
$907$	20.8491	−	36.1118i	0.692284	−	1.19907i	0.971088	−	0.238723i	$-0.0767289\pi$
$908$	−16.8493			−0.559165
$909$	−3.69438	+	8.55498i	−0.122535	+	0.283751i
$910$	−3.92756			−0.130197
$911$	−4.40486	+	7.62944i	−0.145939	+	0.252775i	−0.929723	−	0.368260i	$-0.879954\pi$
$911$	−4.40486	+	7.62944i	−0.145939	+	0.252775i	0.783784	+	0.621034i	$0.213287\pi$
$912$	−45.9060	−	23.0665i	−1.52010	−	0.763809i
$913$	12.3760	+	21.4358i	0.409584	+	0.709421i
$914$	−17.9693	−	31.1238i	−0.594372	−	1.02948i
$915$	0.0344721	+	0.593941i	0.00113961	+	0.0196351i
$916$	−15.7023	+	27.1972i	−0.518819	+	0.898621i
$917$	−2.09466			−0.0691718
$918$	−39.7666	−	14.5013i	−1.31249	−	0.478614i
$919$	−10.9520			−0.361273			−0.180636	−	0.983550i	$-0.557816\pi$
$919$	−10.9520			−0.361273			−0.180636	+	0.983550i	$0.557816\pi$
$920$	1.09879	−	1.90316i	0.0362260	−	0.0627453i
$921$	−1.29688	−	22.3448i	−0.0427337	−	0.736285i
$922$	36.6152	+	63.4194i	1.20586	+	2.08861i
$923$	−47.7927	−	82.7793i	−1.57312	−	2.72472i
$924$	−3.58680	−	1.80227i	−0.117997	−	0.0592904i
$925$	−22.0018	+	38.1083i	−0.723416	+	1.25299i
$926$	40.6360			1.33538
$927$	12.4665	+	16.7596i	0.409453	+	0.550458i
$928$	−41.7080			−1.36913
$929$	−14.1039	+	24.4287i	−0.462735	+	0.801481i	−0.999096	−	0.0425081i	$-0.986465\pi$
$929$	−14.1039	+	24.4287i	−0.462735	+	0.801481i	0.536361	+	0.843989i	$0.319799\pi$
$930$	−2.89953	+	1.90621i	−0.0950793	+	0.0625070i
$931$	19.7579	+	34.2217i	0.647538	+	1.12157i
$932$	5.15041	+	8.92078i	0.168707	+	0.292210i
$933$	19.6284	−	12.9041i	0.642606	−	0.422462i
$934$	−2.56499	+	4.44270i	−0.0839291	+	0.145369i
$935$	−4.90519			−0.160417
$936$	15.9234	+	21.4070i	0.520474	+	0.699711i
$937$	−32.3092			−1.05550			−0.527748	−	0.849401i	$-0.676963\pi$
$937$	−32.3092			−1.05550			−0.527748	+	0.849401i	$0.676963\pi$
$938$	7.17992	−	12.4360i	0.234433	−	0.406049i
$939$	−36.1872	−	18.1831i	−1.18093	−	0.593383i
$940$	−2.74657	−	4.75720i	−0.0895833	−	0.155163i
$941$	−11.5701	−	20.0400i	−0.377175	−	0.653286i	0.613475	−	0.789714i	$-0.289771\pi$
$941$	−11.5701	−	20.0400i	−0.377175	−	0.653286i	−0.990650	+	0.136428i	$0.956438\pi$
$942$	−1.26089	−	21.7247i	−0.0410822	−	0.707830i
$943$	1.87232	−	3.24296i	0.0609712	−	0.105605i
$944$	63.7575			2.07513
$945$	0.268989	+	1.53096i	0.00875020	+	0.0498023i
$946$	−4.62190			−0.150271
$947$	−13.1368	+	22.7537i	−0.426890	+	0.739396i	−0.996595	−	0.0824539i	$-0.973724\pi$
$947$	−13.1368	+	22.7537i	−0.426890	+	0.739396i	0.569705	+	0.821850i	$0.307058\pi$
$948$	1.57769	+	27.1830i	0.0512410	+	0.882862i
$949$	−14.4575	−	25.0411i	−0.469309	−	0.812868i
$950$	26.5737	+	46.0270i	0.862165	+	1.49331i
$951$	2.49394	+	1.25314i	0.0808715	+	0.0406357i
$952$	−1.90659	+	3.30231i	−0.0617929	+	0.107028i
$953$	−8.01441			−0.259612			−0.129806	−	0.991539i	$-0.541435\pi$
$953$	−8.01441			−0.259612			−0.129806	+	0.991539i	$0.541435\pi$
$954$	−19.2040	+	44.4703i	−0.621753	+	1.43978i
$955$	4.23780			0.137132
$956$	2.25707	−	3.90936i	0.0729989	−	0.126438i
$957$	−23.7121	+	15.5888i	−0.766503	+	0.503914i
$958$	−14.2991	−	24.7669i	−0.461985	−	0.800181i
$959$	−3.69330	−	6.39698i	−0.119263	−	0.206569i
$960$	−1.23685	+	0.813128i	−0.0399191	+	0.0262436i
$961$	12.2768	−	21.2641i	0.396027	−	0.685938i
$962$	120.045			3.87042
$963$	−24.1536	+	2.81320i	−0.778338	+	0.0906542i
$964$	−16.3152			−0.525476
$965$	1.39725	−	2.42011i	0.0449791	−	0.0779061i
$966$	8.01562	+	4.02764i	0.257898	+	0.129587i
$967$	−12.2344	−	21.1906i	−0.393432	−	0.681445i	0.599467	−	0.800399i	$-0.295379\pi$
$967$	−12.2344	−	21.1906i	−0.393432	−	0.681445i	−0.992900	+	0.118954i	$0.962046\pi$
$968$	−2.82181	−	4.88751i	−0.0906963	−	0.157091i
$969$	−2.71720	−	46.8162i	−0.0872889	−	1.50395i
$970$	5.91360	−	10.2427i	0.189874	−	0.328872i
$971$	−20.7426			−0.665662			−0.332831	−	0.942987i	$-0.608004\pi$
$971$	−20.7426			−0.665662			−0.332831	+	0.942987i	$0.608004\pi$
$972$	−14.1640	+	14.9824i	−0.454310	+	0.480562i
$973$	15.7075			0.503559
$974$	7.58202	−	13.1324i	0.242943	−	0.420790i
$975$	−3.47882	−	59.9387i	−0.111411	−	1.91958i
$976$	1.94243	+	3.36439i	0.0621757	+	0.107692i
$977$	2.31165	+	4.00389i	0.0739562	+	0.128096i	0.900632	−	0.434583i	$-0.143104\pi$
$977$	2.31165	+	4.00389i	0.0739562	+	0.128096i	−0.826676	+	0.562679i	$0.809771\pi$
$978$	19.3863	+	9.74109i	0.619905	+	0.311486i
$979$	−10.2051	+	17.6757i	−0.326156	+	0.564918i
$980$	3.73439			0.119291
$981$	0.224052	−	0.0260957i	0.00715342	−	0.000833170i
$982$	39.1174			1.24829
$983$	21.9604	−	38.0364i	0.700427	−	1.21317i	−0.267890	−	0.963449i	$-0.586326\pi$
$983$	21.9604	−	38.0364i	0.700427	−	1.21317i	0.968317	−	0.249725i	$-0.0803402\pi$
$984$	1.62753	−	1.06997i	0.0518838	−	0.0341094i
$985$	−2.06063	−	3.56912i	−0.0656572	−	0.113722i
$986$	−26.3178	−	45.5837i	−0.838128	−	1.45168i
$987$	−9.59587	+	6.30851i	−0.305440	+	0.200802i
$988$	28.8579	−	49.9834i	0.918093	−	1.59018i
$989$	4.11156			0.130740
$990$	−2.37960	+	5.51037i	−0.0756286	+	0.175131i
$991$	30.0775			0.955442			0.477721	−	0.878511i	$-0.341463\pi$
$991$	30.0775			0.955442			0.477721	+	0.878511i	$0.341463\pi$
$992$	−8.19435	+	14.1930i	−0.260171	+	0.450629i
$993$	53.0156	+	26.6389i	1.68240	+	0.845360i
$994$	−8.35835	−	14.4771i	−0.265111	−	0.459185i
$995$	3.64772	+	6.31804i	0.115641	+	0.200295i
$996$	1.29576	+	22.3254i	0.0410576	+	0.707406i
$997$	12.7130	−	22.0196i	0.402625	−	0.697367i	−0.591417	−	0.806366i	$-0.701431\pi$
$997$	12.7130	−	22.0196i	0.402625	−	0.697367i	0.994042	+	0.108999i	$0.0347646\pi$
$998$	−16.1568			−0.511436
$999$	−8.22161	−	46.7937i	−0.260120	−	1.48049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.d.259.4	yes	40
3.2	odd	2		1161.2.f.d.775.17		40
9.2	odd	6		3483.2.a.u.1.4		20
9.4	even	3	inner	387.2.f.d.130.4	✓	40
9.5	odd	6		1161.2.f.d.388.17		40
9.7	even	3		3483.2.a.t.1.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.4	✓	40	9.4	even	3	inner
387.2.f.d.259.4	yes	40	1.1	even	1	trivial
1161.2.f.d.388.17		40	9.5	odd	6
1161.2.f.d.775.17		40	3.2	odd	2
3483.2.a.t.1.17		20	9.7	even	3
3483.2.a.u.1.4		20	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.911404 + 1.57860i) q^{2} +(-0.100359 - 1.72914i) q^{3} +(-0.661315 - 1.14543i) q^{4} +(0.216442 + 0.374888i) q^{5} +(2.82109 + 1.41752i) q^{6} +(0.345529 - 0.598473i) q^{7} -1.23472 q^{8} +(-2.97986 + 0.347069i) q^{9} +O(q^{10})\)	\(q+(-0.911404 + 1.57860i) q^{2} +(-0.100359 - 1.72914i) q^{3} +(-0.661315 - 1.14543i) q^{4} +(0.216442 + 0.374888i) q^{5} +(2.82109 + 1.41752i) q^{6} +(0.345529 - 0.598473i) q^{7} -1.23472 q^{8} +(-2.97986 + 0.347069i) q^{9} -0.789063 q^{10} +(-1.26780 + 2.19589i) q^{11} +(-1.91424 + 1.25846i) q^{12} +(3.60136 + 6.23773i) q^{13} +(0.629833 + 1.09090i) q^{14} +(0.626512 - 0.411881i) q^{15} +(2.44795 - 4.23998i) q^{16} +4.46895 q^{17} +(2.16797 - 5.02032i) q^{18} +6.05843 q^{19} +(0.286272 - 0.495838i) q^{20} +(-1.06952 - 0.537406i) q^{21} +(-2.31095 - 4.00268i) q^{22} +(2.05578 + 3.56072i) q^{23} +(0.123914 + 2.13500i) q^{24} +(2.40631 - 4.16784i) q^{25} -13.1292 q^{26} +(0.899185 + 5.11776i) q^{27} -0.914014 q^{28} +(-3.23074 + 5.59581i) q^{29} +(0.0791893 + 1.36440i) q^{30} +(1.26948 + 2.19881i) q^{31} +(3.22744 + 5.59009i) q^{32} +(3.92423 + 1.97182i) q^{33} +(-4.07302 + 7.05468i) q^{34} +0.299147 q^{35} +(2.36817 + 3.18370i) q^{36} -9.14340 q^{37} +(-5.52168 + 9.56383i) q^{38} +(10.4245 - 6.85327i) q^{39} +(-0.267244 - 0.462880i) q^{40} +(-0.455380 - 0.788741i) q^{41} +(1.82311 - 1.19855i) q^{42} +(0.500000 - 0.866025i) q^{43} +3.35365 q^{44} +(-0.775077 - 1.04199i) q^{45} -7.49459 q^{46} +(4.79713 - 8.30887i) q^{47} +(-7.57720 - 3.80734i) q^{48} +(3.26122 + 5.64860i) q^{49} +(4.38623 + 7.59718i) q^{50} +(-0.448498 - 7.72745i) q^{51} +(4.76326 - 8.25022i) q^{52} -8.85806 q^{53} +(-8.89841 - 3.24490i) q^{54} -1.09761 q^{55} +(-0.426630 + 0.738944i) q^{56} +(-0.608016 - 10.4759i) q^{57} +(-5.88902 - 10.2001i) q^{58} +(6.51130 + 11.2779i) q^{59} +(-0.886104 - 0.445243i) q^{60} +(-0.396746 + 0.687184i) q^{61} -4.62805 q^{62} +(-0.821915 + 1.90329i) q^{63} -1.97418 q^{64} +(-1.55897 + 2.70021i) q^{65} +(-6.68927 + 4.39766i) q^{66} +(-5.69986 - 9.87245i) q^{67} +(-2.95539 - 5.11888i) q^{68} +(5.95066 - 3.91208i) q^{69} +(-0.272644 + 0.472233i) q^{70} -13.2707 q^{71} +(3.67927 - 0.428531i) q^{72} -4.01445 q^{73} +(8.33334 - 14.4338i) q^{74} +(-7.44828 - 3.74256i) q^{75} +(-4.00653 - 6.93952i) q^{76} +(0.876120 + 1.51748i) q^{77} +(1.31763 + 22.7022i) q^{78} +(5.94290 - 10.2934i) q^{79} +2.11936 q^{80} +(8.75909 - 2.06843i) q^{81} +1.66014 q^{82} +(4.88090 - 8.45396i) q^{83} +(0.0917292 + 1.58046i) q^{84} +(0.967268 + 1.67536i) q^{85} +(0.911404 + 1.57860i) q^{86} +(10.0002 + 5.02482i) q^{87} +(1.56537 - 2.71129i) q^{88} +8.04947 q^{89} +(2.35130 - 0.273859i) q^{90} +4.97749 q^{91} +(2.71904 - 4.70951i) q^{92} +(3.67465 - 2.41578i) q^{93} +(8.74425 + 15.1455i) q^{94} +(1.31130 + 2.27123i) q^{95} +(9.34214 - 6.14171i) q^{96} +(-7.49445 + 12.9808i) q^{97} -11.8892 q^{98} +(3.01572 - 6.98344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

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