LMFDB - Embedded newform 483.2.j.a.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.1
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34482 + 2.32929i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-2.61707 - 4.53290i) q^{4} +(-0.428287 + 0.741815i) q^{5} -2.68964i q^{6} +(-2.40961 + 1.09260i) q^{7} +8.69868 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34482 + 2.32929i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-2.61707 - 4.53290i) q^{4} +(-0.428287 + 0.741815i) q^{5} -2.68964i q^{6} +(-2.40961 + 1.09260i) q^{7} +8.69868 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.15194 - 1.99521i) q^{10} +(5.56473 - 3.21280i) q^{11} +(4.53290 + 2.61707i) q^{12} -2.00159i q^{13} +(0.695512 - 7.08204i) q^{14} -0.856574i q^{15} +(-6.46400 + 11.1960i) q^{16} +(-2.77202 - 4.80127i) q^{17} +(1.34482 + 2.32929i) q^{18} +(1.67908 - 2.90825i) q^{19} +4.48344 q^{20} +(1.54049 - 2.15102i) q^{21} +17.2825i q^{22} +(0.364334 + 4.78197i) q^{23} +(-7.53328 + 4.34934i) q^{24} +(2.13314 + 3.69471i) q^{25} +(4.66229 + 2.69177i) q^{26} +1.00000i q^{27} +(11.2588 + 8.06314i) q^{28} +3.76096 q^{29} +(1.99521 + 1.15194i) q^{30} +(-4.66600 + 2.69392i) q^{31} +(-8.68714 - 15.0466i) q^{32} +(-3.21280 + 5.56473i) q^{33} +14.9114 q^{34} +(0.221501 - 2.25543i) q^{35} -5.23415 q^{36} +(-0.267976 - 0.154716i) q^{37} +(4.51611 + 7.82213i) q^{38} +(1.00079 + 1.73343i) q^{39} +(-3.72554 + 6.45282i) q^{40} +3.19695i q^{41} +(2.93869 + 6.48098i) q^{42} -3.46741i q^{43} +(-29.1266 - 16.8163i) q^{44} +(0.428287 + 0.741815i) q^{45} +(-11.6286 - 5.58224i) q^{46} +(4.53700 + 2.61944i) q^{47} -12.9280i q^{48} +(4.61246 - 5.26547i) q^{49} -11.4747 q^{50} +(4.80127 + 2.77202i) q^{51} +(-9.07301 + 5.23831i) q^{52} +(5.95288 - 3.43689i) q^{53} +(-2.32929 - 1.34482i) q^{54} +5.50400i q^{55} +(-20.9605 + 9.50415i) q^{56} +3.35816i q^{57} +(-5.05781 + 8.76038i) q^{58} +(11.7229 - 6.76821i) q^{59} +(-3.88277 + 2.24172i) q^{60} +(4.26569 - 7.38839i) q^{61} -14.4913i q^{62} +(-0.258590 + 2.63308i) q^{63} +20.8745 q^{64} +(1.48481 + 0.857255i) q^{65} +(-8.64126 - 14.9671i) q^{66} +(-1.18387 + 0.683508i) q^{67} +(-14.5091 + 25.1306i) q^{68} +(-2.70651 - 3.95914i) q^{69} +(4.95569 + 3.54909i) q^{70} -0.438423 q^{71} +(4.34934 - 7.53328i) q^{72} +(-5.98401 + 3.45487i) q^{73} +(0.720758 - 0.416130i) q^{74} +(-3.69471 - 2.13314i) q^{75} -17.5771 q^{76} +(-9.89855 + 13.8216i) q^{77} -5.38355 q^{78} +(1.26227 + 0.728773i) q^{79} +(-5.53690 - 9.59019i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.44663 - 4.29931i) q^{82} +15.2598 q^{83} +(-13.7820 - 1.35350i) q^{84} +4.74888 q^{85} +(8.07661 + 4.66303i) q^{86} +(-3.25709 + 1.88048i) q^{87} +(48.4058 - 27.9471i) q^{88} +(7.13532 - 12.3587i) q^{89} -2.30387 q^{90} +(2.18693 + 4.82305i) q^{91} +(20.7227 - 14.1663i) q^{92} +(2.69392 - 4.66600i) q^{93} +(-12.2029 + 7.04534i) q^{94} +(1.43826 + 2.49113i) q^{95} +(15.0466 + 8.68714i) q^{96} -10.3453 q^{97} +(6.06190 + 17.8249i) q^{98} -6.42560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34482	+	2.32929i	−0.950930	+	1.64706i	−0.207512	+	0.978232i	$0.566537\pi$
$2$	−1.34482	+	2.32929i	−0.950930	+	1.64706i	−0.743418	+	0.668827i	$0.766797\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−2.61707	−	4.53290i	−1.30854	−	2.26645i
$5$	−0.428287	+	0.741815i	−0.191536	+	0.331750i	−0.945759	−	0.324868i	$-0.894680\pi$
$5$	−0.428287	+	0.741815i	−0.191536	+	0.331750i	0.754224	+	0.656618i	$0.228013\pi$
$6$		−	2.68964i		−	1.09804i
$7$	−2.40961	+	1.09260i	−0.910748	+	0.412963i
$7$	−2.40961	+	1.09260i	−0.910748	+	0.412963i
$8$	8.69868			3.07545
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.15194	−	1.99521i	−0.364275	−	0.630942i
$11$	5.56473	−	3.21280i	1.67783	−	0.968695i	0.714787	−	0.699342i	$-0.246523\pi$
$11$	5.56473	−	3.21280i	1.67783	−	0.968695i	0.963042	−	0.269353i	$-0.0868098\pi$
$12$	4.53290	+	2.61707i	1.30854	+	0.755484i
$13$		−	2.00159i		−	0.555141i	−0.960705	−	0.277570i	$-0.910471\pi$
$13$		−	2.00159i		−	0.555141i	0.960705	−	0.277570i	$-0.0895292\pi$
$14$	0.695512	−	7.08204i	0.185883	−	1.89275i
$15$		−	0.856574i		−	0.221167i
$16$	−6.46400	+	11.1960i	−1.61600	+	2.79900i
$17$	−2.77202	−	4.80127i	−0.672313	−	1.16448i	−0.977247	−	0.212106i	$-0.931968\pi$
$17$	−2.77202	−	4.80127i	−0.672313	−	1.16448i	0.304934	−	0.952373i	$-0.401366\pi$
$18$	1.34482	+	2.32929i	0.316977	+	0.549020i
$19$	1.67908	−	2.90825i	0.385207	−	0.667198i	−0.606591	−	0.795014i	$-0.707463\pi$
$19$	1.67908	−	2.90825i	0.385207	−	0.667198i	0.991798	+	0.127816i	$0.0407968\pi$
$20$	4.48344			1.00253
$21$	1.54049	−	2.15102i	0.336162	−	0.469392i
$22$			17.2825i			3.68465i
$23$	0.364334	+	4.78197i	0.0759689	+	0.997110i
$23$	0.364334	+	4.78197i	0.0759689	+	0.997110i
$24$	−7.53328	+	4.34934i	−1.53772	+	0.887806i
$25$	2.13314	+	3.69471i	0.426628	+	0.738941i
$26$	4.66229	+	2.69177i	0.914350	+	0.527900i
$27$			1.00000i			0.192450i
$28$	11.2588	+	8.06314i	2.12771	+	1.52379i
$29$	3.76096			0.698393			0.349196	−	0.937050i	$-0.386455\pi$
$29$	3.76096			0.698393			0.349196	+	0.937050i	$0.386455\pi$
$30$	1.99521	+	1.15194i	0.364275	+	0.210314i
$31$	−4.66600	+	2.69392i	−0.838039	+	0.483842i	−0.856597	−	0.515986i	$-0.827426\pi$
$31$	−4.66600	+	2.69392i	−0.838039	+	0.483842i	0.0185581	+	0.999828i	$0.494092\pi$
$32$	−8.68714	−	15.0466i	−1.53568	−	2.65988i
$33$	−3.21280	+	5.56473i	−0.559276	+	0.968695i
$34$	14.9114			2.55729
$35$	0.221501	−	2.25543i	0.0374405	−	0.381238i
$36$	−5.23415			−0.872358
$37$	−0.267976	−	0.154716i	−0.0440550	−	0.0254352i	0.477811	−	0.878463i	$-0.341430\pi$
$37$	−0.267976	−	0.154716i	−0.0440550	−	0.0254352i	−0.521866	+	0.853028i	$0.674764\pi$
$38$	4.51611	+	7.82213i	0.732610	+	1.26892i
$39$	1.00079	+	1.73343i	0.160255	+	0.277570i
$40$	−3.72554	+	6.45282i	−0.589059	+	1.02028i
$41$			3.19695i			0.499279i	0.968339	+	0.249640i	$0.0803122\pi$
$41$			3.19695i			0.499279i	−0.968339	+	0.249640i	$0.919688\pi$
$42$	2.93869	+	6.48098i	0.453450	+	1.00004i
$43$		−	3.46741i		−	0.528775i	−0.964417	−	0.264387i	$-0.914830\pi$
$43$		−	3.46741i		−	0.528775i	0.964417	−	0.264387i	$-0.0851697\pi$
$44$	−29.1266	−	16.8163i	−4.39100	−	2.53515i
$45$	0.428287	+	0.741815i	0.0638453	+	0.110583i
$46$	−11.6286	−	5.58224i	−1.71454	−	0.823057i
$47$	4.53700	+	2.61944i	0.661790	+	0.382085i	0.792959	−	0.609275i	$-0.208540\pi$
$47$	4.53700	+	2.61944i	0.661790	+	0.382085i	−0.131169	+	0.991360i	$0.541873\pi$
$48$		−	12.9280i		−	1.86600i
$49$	4.61246	−	5.26547i	0.658923	−	0.752210i
$50$	−11.4747			−1.62277
$51$	4.80127	+	2.77202i	0.672313	+	0.388160i
$52$	−9.07301	+	5.23831i	−1.25820	+	0.726422i
$53$	5.95288	−	3.43689i	0.817690	−	0.472094i	−0.0319290	−	0.999490i	$-0.510165\pi$
$53$	5.95288	−	3.43689i	0.817690	−	0.472094i	0.849619	+	0.527396i	$0.176832\pi$
$54$	−2.32929	−	1.34482i	−0.316977	−	0.183007i
$55$			5.50400i			0.742159i
$56$	−20.9605	+	9.50415i	−2.80096	+	1.27005i
$57$			3.35816i			0.444799i
$58$	−5.05781	+	8.76038i	−0.664123	+	1.15029i
$59$	11.7229	−	6.76821i	1.52619	−	0.881146i	0.526672	−	0.850069i	$-0.323440\pi$
$59$	11.7229	−	6.76821i	1.52619	−	0.881146i	0.999517	−	0.0310769i	$-0.00989368\pi$
$60$	−3.88277	+	2.24172i	−0.501264	+	0.289405i
$61$	4.26569	−	7.38839i	0.546165	−	0.945986i	−0.452367	−	0.891832i	$-0.649420\pi$
$61$	4.26569	−	7.38839i	0.546165	−	0.945986i	0.998533	−	0.0541543i	$-0.0172463\pi$
$62$		−	14.4913i		−	1.84040i
$63$	−0.258590	+	2.63308i	−0.0325792	+	0.331737i
$64$	20.8745			2.60931
$65$	1.48481	+	0.857255i	0.184168	+	0.106329i
$66$	−8.64126	−	14.9671i	−1.06367	−	1.84232i
$67$	−1.18387	+	0.683508i	−0.144633	+	0.0835037i	−0.570570	−	0.821249i	$-0.693278\pi$
$67$	−1.18387	+	0.683508i	−0.144633	+	0.0835037i	0.425937	+	0.904753i	$0.359944\pi$
$68$	−14.5091	+	25.1306i	−1.75949	+	3.04753i
$69$	−2.70651	−	3.95914i	−0.325825	−	0.476625i
$70$	4.95569	+	3.54909i	0.592318	+	0.424197i
$71$	−0.438423			−0.0520312			−0.0260156	−	0.999662i	$-0.508282\pi$
$71$	−0.438423			−0.0520312			−0.0260156	+	0.999662i	$0.508282\pi$
$72$	4.34934	−	7.53328i	0.512575	−	0.887806i
$73$	−5.98401	+	3.45487i	−0.700375	+	0.404362i	−0.807487	−	0.589885i	$-0.799173\pi$
$73$	−5.98401	+	3.45487i	−0.700375	+	0.404362i	0.107112	+	0.994247i	$0.465840\pi$
$74$	0.720758	−	0.416130i	0.0837864	−	0.0483741i
$75$	−3.69471	−	2.13314i	−0.426628	−	0.246314i
$76$	−17.5771			−2.01623
$77$	−9.89855	+	13.8216i	−1.12804	+	1.57512i
$78$	−5.38355			−0.609567
$79$	1.26227	+	0.728773i	0.142017	+	0.0819934i	0.569325	−	0.822113i	$-0.307205\pi$
$79$	1.26227	+	0.728773i	0.142017	+	0.0819934i	−0.427308	+	0.904106i	$0.640538\pi$
$80$	−5.53690	−	9.59019i	−0.619044	−	1.07222i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.44663	−	4.29931i	−0.822343	−	0.474780i
$83$	15.2598			1.67498			0.837488	−	0.546455i	$-0.184023\pi$
$83$	15.2598			1.67498			0.837488	+	0.546455i	$0.184023\pi$
$84$	−13.7820	−	1.35350i	−1.50373	−	0.147679i
$85$	4.74888			0.515088
$86$	8.07661	+	4.66303i	0.870923	+	0.502828i
$87$	−3.25709	+	1.88048i	−0.349196	+	0.201609i
$88$	48.4058	−	27.9471i	5.16008	−	2.97917i
$89$	7.13532	−	12.3587i	0.756343	−	1.31002i	−0.188361	−	0.982100i	$-0.560318\pi$
$89$	7.13532	−	12.3587i	0.756343	−	1.31002i	0.944704	−	0.327924i	$-0.106349\pi$
$90$	−2.30387			−0.242850
$91$	2.18693	+	4.82305i	0.229253	+	0.505593i
$92$	20.7227	−	14.1663i	2.16049	−	1.47694i
$93$	2.69392	−	4.66600i	0.279346	−	0.483842i
$94$	−12.2029	+	7.04534i	−1.25863	+	0.726672i
$95$	1.43826	+	2.49113i	0.147562	+	0.255585i
$96$	15.0466	+	8.68714i	1.53568	+	0.886628i
$97$	−10.3453			−1.05040			−0.525202	−	0.850978i	$-0.676010\pi$
$97$	−10.3453			−1.05040			−0.525202	+	0.850978i	$0.676010\pi$
$98$	6.06190	+	17.8249i	0.612344	+	1.80059i
$99$		−	6.42560i		−	0.645797i
$100$	11.1652	−	19.3386i	1.11652	−	1.93386i
$101$	−3.67853	+	2.12380i	−0.366028	+	0.211326i	−0.671722	−	0.740804i	$-0.734445\pi$
$101$	−3.67853	+	2.12380i	−0.366028	+	0.211326i	0.305694	+	0.952130i	$0.401112\pi$
$102$	−12.9137	+	7.45572i	−1.27864	+	0.738226i
$103$	6.91055	−	11.9694i	0.680917	−	1.17938i	−0.293784	−	0.955872i	$-0.594915\pi$
$103$	6.91055	−	11.9694i	0.680917	−	1.17938i	0.974701	−	0.223511i	$-0.0717520\pi$
$104$		−	17.4112i		−	1.70731i
$105$	0.935891	+	2.06401i	0.0913336	+	0.201427i
$106$			18.4880i			1.79571i
$107$	15.3942	+	8.88785i	1.48821	+	0.859221i	0.999910	−	0.0134517i	$-0.00428195\pi$
$107$	15.3942	+	8.88785i	1.48821	+	0.859221i	0.488305	+	0.872673i	$0.337615\pi$
$108$	4.53290	−	2.61707i	0.436179	−	0.251828i
$109$	−3.82475	+	2.20822i	−0.366344	+	0.211509i	−0.671860	−	0.740678i	$-0.734504\pi$
$109$	−3.82475	+	2.20822i	−0.366344	+	0.211509i	0.305516	+	0.952187i	$0.401171\pi$
$110$	−12.8204	−	7.40188i	−1.22238	−	0.705742i
$111$	0.309432			0.0293700
$112$	3.34305	−	34.0405i	0.315888	−	3.21653i
$113$		−	0.107402i		−	0.0101035i	−0.999987	−	0.00505177i	$-0.998392\pi$
$113$		−	0.107402i		−	0.0101035i	0.999987	−	0.00505177i	$-0.00160804\pi$
$114$	−7.82213	−	4.51611i	−0.732610	−	0.422972i
$115$	−3.70338	−	1.77779i	−0.345342	−	0.165780i
$116$	−9.84271	−	17.0481i	−0.913873	−	1.58287i
$117$	−1.73343	−	1.00079i	−0.160255	−	0.0925235i
$118$			36.4080i			3.35163i
$119$	11.9253	+	8.54051i	1.09319	+	0.782907i
$120$		−	7.45107i		−	0.680187i
$121$	15.1441	−	26.2304i	1.37674	−	2.38458i
$122$	11.4732	+	19.8721i	1.03873	+	1.79913i
$123$	−1.59847	−	2.76864i	−0.144130	−	0.249640i
$124$	24.4226	+	14.1004i	2.19321	+	1.26625i
$125$	−7.93726			−0.709930
$126$	−5.78547	−	4.14335i	−0.515411	−	0.369119i
$127$	15.9539			1.41568			0.707839	−	0.706374i	$-0.249670\pi$
$127$	15.9539			1.41568			0.707839	+	0.706374i	$0.249670\pi$
$128$	−10.6981	+	18.5297i	−0.945590	+	1.63781i
$129$	1.73370	+	3.00286i	0.152644	+	0.264387i
$130$	−3.99360	+	2.30570i	−0.350262	+	0.202224i
$131$	−0.394349	−	0.227677i	−0.0344544	−	0.0198923i	0.482674	−	0.875800i	$-0.339666\pi$
$131$	−0.394349	−	0.227677i	−0.0344544	−	0.0198923i	−0.517128	+	0.855908i	$0.672999\pi$
$132$	33.6325			2.92733
$133$	−0.868384	+	8.84231i	−0.0752985	+	0.766725i
$134$		−	3.67677i		−	0.317625i
$135$	−0.741815	−	0.428287i	−0.0638453	−	0.0368611i
$136$	−24.1129	−	41.7647i	−2.06766	−	3.58130i
$137$	−12.5191	+	7.22791i	−1.06958	+	0.617522i	−0.928067	−	0.372414i	$-0.878530\pi$
$137$	−12.5191	+	7.22791i	−1.06958	+	0.617522i	−0.141513	+	0.989936i	$0.545197\pi$
$138$	12.8618	−	0.979926i	1.09487	−	0.0834169i
$139$		−	6.22401i		−	0.527914i	−0.964534	−	0.263957i	$-0.914972\pi$
$139$		−	6.22401i		−	0.527914i	0.964534	−	0.263957i	$-0.0850277\pi$
$140$	−10.8033	+	4.89859i	−0.913049	+	0.414006i
$141$	−5.23888			−0.441193
$142$	0.589599	−	1.02122i	0.0494780	−	0.0856985i
$143$	−6.43070	−	11.1383i	−0.537762	−	0.931431i
$144$	6.46400	+	11.1960i	0.538667	+	0.932999i
$145$	−1.61077	+	2.78994i	−0.133767	+	0.231692i
$146$		−	18.5847i		−	1.53808i
$147$	−1.36178	+	6.86626i	−0.112317	+	0.566320i
$148$			1.61961i			0.133131i
$149$	−9.87233	−	5.69979i	−0.808773	−	0.466945i	0.0377567	−	0.999287i	$-0.487979\pi$
$149$	−9.87233	−	5.69979i	−0.808773	−	0.466945i	−0.846530	+	0.532342i	$0.821312\pi$
$150$	9.93742	−	5.73737i	0.811387	−	0.468455i
$151$	5.69605	+	9.86585i	0.463538	+	0.802871i	0.999134	−	0.0416029i	$-0.0132464\pi$
$151$	5.69605	+	9.86585i	0.463538	+	0.802871i	−0.535596	+	0.844474i	$0.679913\pi$
$152$	14.6058	−	25.2979i	1.18468	−	2.05193i
$153$	−5.54403			−0.448208
$154$	−18.8828	−	41.6442i	−1.52162	−	3.35578i
$155$		−	4.61508i		−	0.370692i
$156$	5.23831	−	9.07301i	0.419400	−	0.726422i
$157$	3.74418	+	6.48510i	0.298818	+	0.517567i	0.975866	−	0.218371i	$-0.0700744\pi$
$157$	3.74418	+	6.48510i	0.298818	+	0.517567i	−0.677048	+	0.735939i	$0.736741\pi$
$158$	−3.39505	+	1.96013i	−0.270096	+	0.155940i
$159$	−3.43689	+	5.95288i	−0.272563	+	0.472094i
$160$	14.8824			1.17655
$161$	−6.10267	−	11.1246i	−0.480958	−	0.876744i
$162$	2.68964			0.211318
$163$	3.03991	−	5.26527i	0.238104	−	0.412408i	−0.722066	−	0.691824i	$-0.756808\pi$
$163$	3.03991	−	5.26527i	0.238104	−	0.412408i	0.960170	+	0.279416i	$0.0901408\pi$
$164$	14.4915	−	8.36665i	1.13159	−	0.653326i
$165$	−2.75200	−	4.76660i	−0.214243	−	0.371080i
$166$	−20.5216	+	35.5445i	−1.59279	+	2.75879i
$167$			18.3356i			1.41885i	0.704779	+	0.709427i	$0.251046\pi$
$167$			18.3356i			1.41885i	−0.704779	+	0.709427i	$0.748954\pi$
$168$	13.4002	−	18.7111i	1.03385	−	1.44359i
$169$	8.99364			0.691819
$170$	−6.38638	+	11.0615i	−0.489813	+	0.848380i
$171$	−1.67908	−	2.90825i	−0.128402	−	0.222399i
$172$	−15.7174	+	9.07446i	−1.19844	+	0.691921i
$173$	−16.7467	−	9.66874i	−1.27323	−	0.735100i	−0.297636	−	0.954679i	$-0.596198\pi$
$173$	−16.7467	−	9.66874i	−1.27323	−	0.735100i	−0.975595	+	0.219579i	$0.929532\pi$
$174$		−	10.1156i		−	0.766863i
$175$	−9.17687	−	6.57215i	−0.693706	−	0.496808i
$176$			83.0701i			6.26165i
$177$	−6.76821	+	11.7229i	−0.508730	+	0.881146i
$178$	19.1914	+	33.2405i	1.43846	+	2.49148i
$179$	5.58052	+	9.66575i	0.417108	+	0.722452i	0.995647	−	0.0932024i	$-0.0297104\pi$
$179$	5.58052	+	9.66575i	0.417108	+	0.722452i	−0.578539	+	0.815655i	$0.696377\pi$
$180$	2.24172	−	3.88277i	0.167088	−	0.289405i
$181$	−18.7106			−1.39075			−0.695374	−	0.718648i	$-0.744761\pi$
$181$	−18.7106			−1.39075			−0.695374	+	0.718648i	$0.744761\pi$
$182$	−14.1753	−	1.39213i	−1.05075	−	0.103191i
$183$			8.53137i			0.630657i
$184$	3.16923	+	41.5969i	0.233639	+	3.06656i
$185$	0.229541	−	0.132526i	0.0168762	−	0.00974349i
$186$	7.24566	+	12.5499i	0.531278	+	0.920200i
$187$	−30.8510	−	17.8118i	−2.25605	−	1.30253i
$188$		−	27.4211i		−	1.99989i
$189$	−1.09260	−	2.40961i	−0.0794747	−	0.175274i
$190$	−7.73677			−0.561284
$191$	4.07900	+	2.35501i	0.295146	+	0.170403i	0.640260	−	0.768158i	$-0.278827\pi$
$191$	4.07900	+	2.35501i	0.295146	+	0.170403i	−0.345114	+	0.938561i	$0.612160\pi$
$192$	−18.0778	+	10.4372i	−1.30466	+	0.753243i
$193$	−8.44076	−	14.6198i	−0.607579	−	1.05236i	−0.991638	−	0.129050i	$-0.958807\pi$
$193$	−8.44076	−	14.6198i	−0.607579	−	1.05236i	0.384059	−	0.923309i	$-0.374526\pi$
$194$	13.9125	−	24.0972i	0.998861	−	1.73008i
$195$	−1.71451			−0.122779
$196$	−35.9390	−	7.12774i	−2.56707	−	0.509124i
$197$	2.45088			0.174618			0.0873088	−	0.996181i	$-0.472173\pi$
$197$	2.45088			0.174618			0.0873088	+	0.996181i	$0.472173\pi$
$198$	14.9671	+	8.64126i	1.06367	+	0.614108i
$199$	−1.62746	−	2.81885i	−0.115368	−	0.199823i	0.802559	−	0.596573i	$-0.203471\pi$
$199$	−1.62746	−	2.81885i	−0.115368	−	0.199823i	−0.917927	+	0.396750i	$0.870138\pi$
$200$	18.5555	+	32.1391i	1.31207	+	2.27258i
$201$	0.683508	−	1.18387i	0.0482109	−	0.0835037i
$202$		−	11.4245i		−	0.803826i
$203$	−9.06246	+	4.10921i	−0.636060	+	0.288410i
$204$		−	29.0183i		−	2.03169i
$205$	−2.37154	−	1.36921i	−0.165636	−	0.0956299i
$206$	18.5869	+	32.1934i	1.29501	+	2.24302i
$207$	4.32348	+	2.07546i	0.300502	+	0.144255i
$208$	22.4098	+	12.9383i	1.55384	+	0.897108i
$209$		−	21.5781i		−	1.49259i
$210$	−6.06629	−	0.595758i	−0.418614	−	0.0411112i
$211$	−7.20636			−0.496106			−0.248053	−	0.968746i	$-0.579791\pi$
$211$	−7.20636			−0.496106			−0.248053	+	0.968746i	$0.579791\pi$
$212$	−31.1582	−	17.9892i	−2.13996	−	1.23550i
$213$	0.379685	−	0.219211i	0.0260156	−	0.0150201i
$214$	−41.4048	+	23.9051i	−2.83038	+	1.63412i
$215$	2.57218	+	1.48505i	0.175421	+	0.101279i
$216$			8.69868i			0.591870i
$217$	8.29990	−	11.5894i	0.563434	−	0.786737i
$218$		−	11.8786i		−	0.804521i
$219$	3.45487	−	5.98401i	0.233458	−	0.404362i
$220$	24.9491	−	14.4044i	1.68207	−	0.971143i
$221$	−9.61017	+	5.54844i	−0.646450	+	0.373228i
$222$	−0.416130	+	0.720758i	−0.0279288	+	0.0483741i
$223$			8.78847i			0.588519i	0.955726	+	0.294260i	$0.0950730\pi$
$223$			8.78847i			0.588519i	−0.955726	+	0.294260i	$0.904927\pi$
$224$	37.3725	+	26.7649i	2.49705	+	1.78830i
$225$	4.26628			0.284419
$226$	0.250171	+	0.144436i	0.0166411	+	0.00960777i
$227$	0.760880	+	1.31788i	0.0505014	+	0.0874710i	0.890171	−	0.455626i	$-0.150585\pi$
$227$	0.760880	+	1.31788i	0.0505014	+	0.0874710i	−0.839670	+	0.543097i	$0.817251\pi$
$228$	15.2222	−	8.78854i	1.00811	−	0.582035i
$229$	0.936409	−	1.62191i	0.0618796	−	0.107179i	−0.833426	−	0.552631i	$-0.813624\pi$
$229$	0.936409	−	1.62191i	0.0618796	−	0.107179i	0.895306	+	0.445452i	$0.146957\pi$
$230$	9.12137	−	6.23546i	0.601445	−	0.411154i
$231$	1.66159	−	16.9191i	0.109325	−	1.11320i
$232$	32.7154			2.14787
$233$	14.4340	−	25.0005i	0.945606	−	1.63784i	0.191072	−	0.981576i	$-0.438804\pi$
$233$	14.4340	−	25.0005i	0.945606	−	1.63784i	0.754534	−	0.656261i	$-0.227863\pi$
$234$	4.66229	−	2.69177i	0.304783	−	0.175967i
$235$	−3.88628	+	2.24375i	−0.253513	+	0.146366i
$236$	−61.3593	−	35.4258i	−3.99415	−	2.30602i
$237$	−1.45755			−0.0946778
$238$	−35.9308	+	16.2922i	−2.32905	+	1.05607i
$239$	−3.89261			−0.251792			−0.125896	−	0.992043i	$-0.540181\pi$
$239$	−3.89261			−0.251792			−0.125896	+	0.992043i	$0.540181\pi$
$240$	9.59019	+	5.53690i	0.619044	+	0.357405i
$241$	−2.50834	−	4.34458i	−0.161576	−	0.279859i	0.773858	−	0.633359i	$-0.218325\pi$
$241$	−2.50834	−	4.34458i	−0.161576	−	0.279859i	−0.935434	+	0.353501i	$0.884991\pi$
$242$	40.7322	+	70.5503i	2.61837	+	4.53514i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−44.6545			−2.85871
$245$	1.93055	+	5.67673i	0.123338	+	0.362673i
$246$	8.59863			0.548229
$247$	−5.82112	−	3.36082i	−0.370389	−	0.213844i
$248$	−40.5881	+	23.4336i	−2.57735	+	1.48803i
$249$	−13.2153	+	7.62988i	−0.837488	+	0.483524i
$250$	10.6742	−	18.4882i	0.675094	−	1.16930i
$251$	11.2564			0.710498			0.355249	−	0.934772i	$-0.384396\pi$
$251$	11.2564			0.710498			0.355249	+	0.934772i	$0.384396\pi$
$252$	12.6123	−	5.71881i	0.794498	−	0.360251i
$253$	17.3909	+	25.4398i	1.09336	+	1.59939i
$254$	−21.4551	+	37.1613i	−1.34621	+	2.33171i
$255$	−4.11265	+	2.37444i	−0.257544	+	0.148693i
$256$	−7.89959	−	13.6825i	−0.493724	−	0.855155i
$257$	1.56882	+	0.905758i	0.0978602	+	0.0564996i	0.548131	−	0.836392i	$-0.315339\pi$
$257$	1.56882	+	0.905758i	0.0978602	+	0.0564996i	−0.450271	+	0.892892i	$0.648673\pi$
$258$	−9.32607			−0.580616
$259$	0.814761	+	0.0800159i	0.0506268	+	0.00497195i
$260$		−	8.97400i		−	0.556544i
$261$	1.88048	−	3.25709i	0.116399	−	0.201609i
$262$	1.06065	−	0.612369i	0.0655275	−	0.0378323i
$263$	−7.09833	+	4.09822i	−0.437702	+	0.252707i	−0.702622	−	0.711563i	$-0.747988\pi$
$263$	−7.09833	+	4.09822i	−0.437702	+	0.252707i	0.264921	+	0.964270i	$0.414654\pi$
$264$	−27.9471	+	48.4058i	−1.72003	+	2.97917i
$265$			5.88791i			0.361692i
$266$	−19.4285	−	13.9140i	−1.19124	−	0.853123i
$267$			14.2706i			0.873349i
$268$	6.19655	+	3.57758i	0.378515	+	0.218535i
$269$	−2.55256	+	1.47372i	−0.155633	+	0.0898545i	−0.575794	−	0.817595i	$-0.695307\pi$
$269$	−2.55256	+	1.47372i	−0.155633	+	0.0898545i	0.420161	+	0.907450i	$0.361974\pi$
$270$	1.99521	−	1.15194i	0.121425	−	0.0701047i
$271$	−7.65236	−	4.41809i	−0.464848	−	0.268380i	0.249233	−	0.968444i	$-0.419822\pi$
$271$	−7.65236	−	4.41809i	−0.464848	−	0.268380i	−0.714080	+	0.700064i	$0.753155\pi$
$272$	71.6733			4.34583
$273$	−4.30546	−	3.08342i	−0.260579	−	0.186617i
$274$		−	38.8809i		−	2.34888i
$275$	23.7407	+	13.7067i	1.43162	+	0.826545i
$276$	−10.8633	+	22.6297i	−0.653893	+	1.36215i
$277$	−2.58409	−	4.47577i	−0.155263	−	0.268923i	0.777892	−	0.628398i	$-0.216289\pi$
$277$	−2.58409	−	4.47577i	−0.155263	−	0.268923i	−0.933155	+	0.359475i	$0.882956\pi$
$278$	14.4976	+	8.37017i	0.869506	+	0.502009i
$279$			5.38784i			0.322561i
$280$	1.92677	−	19.6193i	0.115146	−	1.17248i
$281$			17.1229i			1.02147i	0.859739	+	0.510734i	$0.170626\pi$
$281$			17.1229i			1.02147i	−0.859739	+	0.510734i	$0.829374\pi$
$282$	7.04534	−	12.2029i	0.419544	−	0.726672i
$283$	−10.1703	−	17.6154i	−0.604559	−	1.04713i	−0.992121	−	0.125283i	$-0.960016\pi$
$283$	−10.1703	−	17.6154i	−0.604559	−	1.04713i	0.387562	−	0.921844i	$-0.373317\pi$
$284$	1.14738	+	1.98733i	0.0680847	+	0.117926i
$285$	−2.49113	−	1.43826i	−0.147562	−	0.0851949i
$286$	34.5925			2.04550
$287$	−3.49298	−	7.70341i	−0.206184	−	0.454718i
$288$	−17.3743			−1.02379
$289$	−6.86814	+	11.8960i	−0.404008	+	0.699763i
$290$	−4.33239	−	7.50392i	−0.254407	−	0.440645i
$291$	8.95927	−	5.17264i	0.525202	−	0.303225i
$292$	31.3212	+	18.0833i	1.83293	+	1.05824i
$293$	23.9010			1.39631			0.698156	−	0.715946i	$-0.254004\pi$
$293$	23.9010			1.39631			0.698156	+	0.715946i	$0.254004\pi$
$294$	−14.1622	−	12.4059i	−0.825956	−	0.723524i
$295$			11.5949i			0.675084i
$296$	−2.33104	−	1.34583i	−0.135489	−	0.0782245i
$297$	3.21280	+	5.56473i	0.186425	+	0.322898i
$298$	26.5530	−	15.3304i	1.53817	−	0.888065i
$299$	9.57154	−	0.729247i	0.553537	−	0.0421734i
$300$			22.3303i			1.28924i
$301$	3.78848	+	8.35511i	0.218364	+	0.481580i
$302$	−30.6406			−1.76317
$303$	2.12380	−	3.67853i	0.122009	−	0.211326i
$304$	21.7071	+	37.5979i	1.24499	+	2.15638i
$305$	3.65388	+	6.32870i	0.209220	+	0.362380i
$306$	7.45572	−	12.9137i	0.426215	−	0.738226i
$307$		−	2.80653i		−	0.160177i	−0.996788	−	0.0800884i	$-0.974480\pi$
$307$		−	2.80653i		−	0.160177i	0.996788	−	0.0800884i	$-0.0255203\pi$
$308$	88.5572	+	8.69702i	5.04602	+	0.495559i
$309$			13.8211i			0.786255i
$310$	10.7499	+	6.20645i	0.610553	+	0.352503i
$311$	0.721295	−	0.416440i	0.0409009	−	0.0236142i	−0.479410	−	0.877591i	$-0.659149\pi$
$311$	0.721295	−	0.416440i	0.0409009	−	0.0236142i	0.520311	+	0.853977i	$0.325816\pi$
$312$	8.70559	+	15.0785i	0.492857	+	0.853654i
$313$	−4.04501	+	7.00617i	−0.228638	+	0.396012i	−0.957405	−	0.288750i	$-0.906760\pi$
$313$	−4.04501	+	7.00617i	−0.228638	+	0.396012i	0.728767	+	0.684762i	$0.240094\pi$
$314$	−20.1409			−1.13662
$315$	−1.84251	−	1.31954i	−0.103814	−	0.0743478i
$316$		−	7.62901i		−	0.429165i
$317$	11.0513	−	19.1415i	0.620704	−	1.07509i	−0.368650	−	0.929568i	$-0.620180\pi$
$317$	11.0513	−	19.1415i	0.620704	−	1.07509i	0.989355	−	0.145523i	$-0.0464866\pi$
$318$	−9.24400	−	16.0111i	−0.518378	−	0.897857i
$319$	20.9287	−	12.0832i	1.17178	−	0.676529i
$320$	−8.94028	+	15.4850i	−0.499777	+	0.865639i
$321$	−17.7757			−0.992143
$322$	34.1195	+	0.745691i	1.90141	+	0.0415557i
$323$	−18.6177			−1.03592
$324$	−2.61707	+	4.53290i	−0.145393	+	0.251828i
$325$	7.39528	−	4.26967i	0.410217	−	0.236839i
$326$	8.17624	+	14.1617i	0.452840	+	0.784342i
$327$	2.20822	−	3.82475i	0.122115	−	0.211509i
$328$			27.8092i			1.53551i
$329$	−13.7944	−	1.35472i	−0.760511	−	0.0746881i
$330$	14.8038			0.814920
$331$	1.05716	−	1.83105i	0.0581068	−	0.100644i	−0.835509	−	0.549477i	$-0.814827\pi$
$331$	1.05716	−	1.83105i	0.0581068	−	0.100644i	0.893616	+	0.448833i	$0.148160\pi$
$332$	−39.9359	−	69.1710i	−2.19177	−	3.79625i
$333$	−0.267976	+	0.154716i	−0.0146850	+	0.00847839i
$334$	−42.7091	−	24.6581i	−2.33694	−	1.34923i
$335$		−	1.17095i		−	0.0639758i
$336$	14.1251	+	31.1515i	0.770587	+	1.69945i
$337$		−	30.2288i		−	1.64667i	−0.567559	−	0.823333i	$-0.692112\pi$
$337$		−	30.2288i		−	1.64667i	0.567559	−	0.823333i	$-0.307888\pi$
$338$	−12.0948	+	20.9488i	−0.657871	+	1.13947i
$339$	0.0537011	+	0.0930130i	0.00291664	+	0.00505177i
$340$	−12.4282	−	21.5262i	−0.674011	−	1.16742i
$341$	−17.3100	+	29.9819i	−0.937391	+	1.62361i
$342$	9.03222			0.488407
$343$	−5.36122	+	17.7273i	−0.289478	+	0.957185i
$344$		−	30.1619i		−	1.62622i
$345$	4.09612	−	0.312079i	0.220527	−	0.0168018i
$346$	45.0427	−	26.0054i	2.42151	−	1.39806i
$347$	−14.0341	−	24.3077i	−0.753388	−	1.30491i	−0.946172	−	0.323665i	$-0.895085\pi$
$347$	−14.0341	−	24.3077i	−0.753388	−	1.30491i	0.192784	−	0.981241i	$-0.438248\pi$
$348$	17.0481	+	9.84271i	0.913873	+	0.527625i
$349$			18.0571i			0.966576i	0.875461	+	0.483288i	$0.160558\pi$
$349$			18.0571i			0.966576i	−0.875461	+	0.483288i	$0.839442\pi$
$350$	27.6497	−	12.5373i	1.47794	−	0.670145i
$351$	2.00159			0.106837
$352$	−96.6832	−	55.8200i	−5.15323	−	2.97522i
$353$	−9.57512	+	5.52820i	−0.509632	+	0.294236i	−0.732682	−	0.680571i	$-0.761732\pi$
$353$	−9.57512	+	5.52820i	−0.509632	+	0.294236i	0.223050	+	0.974807i	$0.428399\pi$
$354$	−18.2040	−	31.5303i	−0.967533	−	1.67582i
$355$	0.187771	−	0.325229i	0.00996584	−	0.0172613i
$356$	−74.6947			−3.95881
$357$	−14.5979	−	1.43363i	−0.772603	−	0.0758757i
$358$	−30.0192			−1.58656
$359$	−21.7523	−	12.5587i	−1.14804	−	0.662824i	−0.199634	−	0.979870i	$-0.563975\pi$
$359$	−21.7523	−	12.5587i	−1.14804	−	0.662824i	−0.948410	+	0.317047i	$0.897309\pi$
$360$	3.72554	+	6.45282i	0.196353	+	0.340093i
$361$	3.86140	+	6.68813i	0.203231	+	0.352007i
$362$	25.1624	−	43.5825i	1.32251	−	2.29065i
$363$			30.2883i			1.58972i
$364$	16.1391	−	22.5354i	0.845918	−	1.18118i
$365$		−	5.91870i		−	0.309799i
$366$	−19.8721	−	11.4732i	−1.03873	−	0.599711i
$367$	0.238871	+	0.413736i	0.0124690	+	0.0215969i	0.872193	−	0.489163i	$-0.162698\pi$
$367$	0.238871	+	0.413736i	0.0124690	+	0.0215969i	−0.859724	+	0.510760i	$0.829364\pi$
$368$	−55.8939	−	26.8316i	−2.91367	−	1.39869i
$369$	2.76864	+	1.59847i	0.144130	+	0.0832132i
$370$			0.712893i			0.0370615i
$371$	−10.5890	+	14.7857i	−0.549753	+	0.767634i
$372$	−28.2007			−1.46214
$373$	2.98158	+	1.72142i	0.154380	+	0.0891316i	0.575200	−	0.818013i	$-0.304924\pi$
$373$	2.98158	+	1.72142i	0.154380	+	0.0891316i	−0.420820	+	0.907144i	$0.638258\pi$
$374$	82.9781	−	47.9074i	4.29069	−	2.47723i
$375$	6.87387	−	3.96863i	0.354965	−	0.204939i
$376$	39.4660	+	22.7857i	2.03530	+	1.17508i
$377$		−	7.52790i		−	0.387706i
$378$	7.08204	+	0.695512i	0.364261	+	0.0357733i
$379$			21.2746i			1.09280i	0.837524	+	0.546401i	$0.184002\pi$
$379$			21.2746i			1.09280i	−0.837524	+	0.546401i	$0.815998\pi$
$380$	7.52804	−	13.0389i	0.386180	−	0.668884i
$381$	−13.8165	+	7.97694i	−0.707839	+	0.408671i
$382$	−10.9710	+	6.33412i	−0.561326	+	0.324082i
$383$	5.10185	−	8.83667i	0.260692	−	0.451533i	−0.705734	−	0.708477i	$-0.749382\pi$
$383$	5.10185	−	8.83667i	0.260692	−	0.451533i	0.966426	+	0.256945i	$0.0827158\pi$
$384$		−	21.3963i		−	1.09187i
$385$	−6.01365	−	13.2625i	−0.306484	−	0.675920i
$386$	45.4052			2.31106
$387$	−3.00286	−	1.73370i	−0.152644	−	0.0881291i
$388$	27.0744	+	46.8942i	1.37449	+	2.38069i
$389$	−10.9438	+	6.31840i	−0.554872	+	0.320356i	−0.751085	−	0.660206i	$-0.770469\pi$
$389$	−10.9438	+	6.31840i	−0.554872	+	0.320356i	0.196213	+	0.980561i	$0.437136\pi$
$390$	2.30570	−	3.99360i	0.116754	−	0.202224i
$391$	21.9496	−	15.0050i	1.11004	−	0.758834i
$392$	40.1224	−	45.8027i	2.02649	−	2.31338i
$393$	0.455354			0.0229696
$394$	−3.29598	+	5.70881i	−0.166049	+	0.287606i
$395$	−1.08123	+	0.624248i	−0.0544026	+	0.0314093i
$396$	−29.1266	+	16.8163i	−1.46367	+	0.845049i
$397$	−22.0118	−	12.7085i	−1.10474	−	0.637821i	−0.167277	−	0.985910i	$-0.553497\pi$
$397$	−22.0118	−	12.7085i	−1.10474	−	0.637821i	−0.937461	+	0.348089i	$0.886831\pi$
$398$	8.75457			0.438827
$399$	−3.66911	−	8.09185i	−0.183685	−	0.405099i
$400$	−55.1545			−2.75773
$401$	−2.65659	−	1.53378i	−0.132664	−	0.0765933i	0.432199	−	0.901778i	$-0.357738\pi$
$401$	−2.65659	−	1.53378i	−0.132664	−	0.0765933i	−0.564863	+	0.825185i	$0.691071\pi$
$402$	1.83839	+	3.18418i	0.0916904	+	0.158812i
$403$	5.39212	+	9.33942i	0.268601	+	0.465230i
$404$	19.2540	+	11.1163i	0.957921	+	0.553056i
$405$	0.856574			0.0425635
$406$	2.61579	−	26.6353i	0.129820	−	1.32189i
$407$	−1.98829			−0.0985556
$408$	41.7647	+	24.1129i	2.06766	+	1.19377i
$409$	16.0410	−	9.26126i	0.793175	−	0.457940i	−0.0479040	−	0.998852i	$-0.515254\pi$
$409$	16.0410	−	9.26126i	0.793175	−	0.457940i	0.841079	+	0.540912i	$0.181921\pi$
$410$	6.37859	−	3.68268i	0.315016	−	0.181875i
$411$	7.22791	−	12.5191i	0.356527	−	0.617522i
$412$	−72.3417			−3.56402
$413$	−20.8527	+	29.1171i	−1.02609	+	1.43276i
$414$	−10.6487	+	7.27953i	−0.523353	+	0.357769i
$415$	−6.53556	+	11.3199i	−0.320818	+	0.555673i
$416$	−30.1170	+	17.3881i	−1.47661	+	0.852521i
$417$	3.11201	+	5.39015i	0.152396	+	0.263957i
$418$	50.2619	+	29.0187i	2.45839	+	1.41935i
$419$	−0.0577500			−0.00282127			−0.00141064	−	0.999999i	$-0.500449\pi$
$419$	−0.0577500			−0.00282127			−0.00141064	+	0.999999i	$0.500449\pi$
$420$	6.90668	−	9.64398i	0.337011	−	0.470578i
$421$		−	18.2698i		−	0.890418i	−0.895427	−	0.445209i	$-0.853129\pi$
$421$		−	18.2698i		−	0.890418i	0.895427	−	0.445209i	$-0.146871\pi$
$422$	9.69124	−	16.7857i	0.471762	−	0.817116i
$423$	4.53700	−	2.61944i	0.220597	−	0.127362i
$424$	51.7822	−	29.8965i	2.51477	−	1.45190i
$425$	11.8262	−	20.4836i	0.573655	−	0.993599i
$426$			1.17920i			0.0571323i
$427$	−2.20612	+	22.4638i	−0.106762	+	1.08710i
$428$		−	93.0407i		−	4.49729i
$429$	11.1383	+	6.43070i	0.537762	+	0.310477i
$430$	−6.91822	+	3.99423i	−0.333626	+	0.192619i
$431$	14.6332	−	8.44848i	0.704856	−	0.406949i	−0.104297	−	0.994546i	$-0.533259\pi$
$431$	14.6332	−	8.44848i	0.704856	−	0.406949i	0.809154	+	0.587597i	$0.199926\pi$
$432$	−11.1960	−	6.46400i	−0.538667	−	0.311000i
$433$	−20.1013			−0.966008			−0.483004	−	0.875618i	$-0.660454\pi$
$433$	−20.1013			−0.966008			−0.483004	+	0.875618i	$0.660454\pi$
$434$	15.8332	+	34.9185i	0.760017	+	1.67614i
$435$		−	3.22154i		−	0.154461i
$436$	20.0193	+	11.5581i	0.958750	+	0.553535i
$437$	14.5189	+	6.96973i	0.694534	+	0.333407i
$438$	9.29234	+	16.0948i	0.444005	+	0.769040i
$439$	14.6643	+	8.46645i	0.699890	+	0.404082i	0.807306	−	0.590132i	$-0.200924\pi$
$439$	14.6643	+	8.46645i	0.699890	+	0.404082i	−0.107416	+	0.994214i	$0.534258\pi$
$440$			47.8776i			2.28247i
$441$	−2.25380	−	6.62725i	−0.107324	−	0.315583i
$442$		−	29.8466i		−	1.41966i
$443$	−11.6797	+	20.2299i	−0.554921	+	0.961152i	0.442988	+	0.896527i	$0.353918\pi$
$443$	−11.6797	+	20.2299i	−0.554921	+	0.961152i	−0.997910	+	0.0646244i	$0.979415\pi$
$444$	−0.809807	−	1.40263i	−0.0384317	−	0.0665657i
$445$	6.11193	+	10.5862i	0.289733	+	0.501833i
$446$	−20.4709	−	11.8189i	−0.969326	−	0.559641i
$447$	11.3996			0.539182
$448$	−50.2994	+	22.8074i	−2.37643	+	1.07755i
$449$	−24.4885			−1.15568			−0.577841	−	0.816149i	$-0.696105\pi$
$449$	−24.4885			−1.15568			−0.577841	+	0.816149i	$0.696105\pi$
$450$	−5.73737	+	9.93742i	−0.270462	+	0.468455i
$451$	10.2711	+	17.7901i	0.483649	+	0.837705i
$452$	−0.486844	+	0.281079i	−0.0228992	+	0.0132209i
$453$	−9.86585	−	5.69605i	−0.463538	−	0.267624i
$454$	−4.09298			−0.192093
$455$	−4.51445	−	0.443354i	−0.211641	−	0.0207848i
$456$			29.2115i			1.36796i
$457$	24.2056	+	13.9751i	1.13229	+	0.653727i	0.944509	−	0.328484i	$-0.106538\pi$
$457$	24.2056	+	13.9751i	1.13229	+	0.653727i	0.187779	+	0.982211i	$0.439871\pi$
$458$	2.51860	+	4.36234i	0.117686	+	0.203839i
$459$	4.80127	−	2.77202i	0.224104	−	0.129387i
$460$	1.63347	+	21.4397i	0.0761609	+	0.999630i
$461$			31.3581i			1.46049i	0.683185	+	0.730245i	$0.260594\pi$
$461$			31.3581i			1.46049i	−0.683185	+	0.730245i	$0.739406\pi$
$462$	37.1751	+	26.6235i	1.72954	+	1.23864i
$463$	5.61859			0.261118			0.130559	−	0.991441i	$-0.458323\pi$
$463$	5.61859			0.261118			0.130559	+	0.991441i	$0.458323\pi$
$464$	−24.3109	+	42.1076i	−1.12860	+	1.95480i
$465$	2.30754	+	3.99678i	0.107010	+	0.185346i
$466$	38.8223	+	67.2423i	1.79841	+	3.11494i
$467$	−18.4349	+	31.9303i	−0.853068	+	1.47756i	0.0253587	+	0.999678i	$0.491927\pi$
$467$	−18.4349	+	31.9303i	−0.853068	+	1.47756i	−0.878426	+	0.477878i	$0.841406\pi$
$468$			10.4766i			0.484282i
$469$	2.10587	−	2.94048i	0.0972400	−	0.135779i
$470$		−	12.0697i		−	0.556735i
$471$	−6.48510	−	3.74418i	−0.298818	−	0.172522i
$472$	101.974	−	58.8745i	4.69372	−	2.70992i
$473$	−11.1401	−	19.2952i	−0.512221	−	0.887193i
$474$	1.96013	−	3.39505i	0.0900320	−	0.155940i
$475$	14.3268			0.657360
$476$	7.50382	−	76.4076i	0.343937	−	3.50213i
$477$		−	6.87379i		−	0.314729i
$478$	5.23485	−	9.06703i	0.239437	−	0.414716i
$479$	14.6458	+	25.3673i	0.669184	+	1.15906i	0.978133	+	0.207982i	$0.0666896\pi$
$479$	14.6458	+	25.3673i	0.669184	+	1.15906i	−0.308948	+	0.951079i	$0.599977\pi$
$480$	−12.8885	+	7.44118i	−0.588277	+	0.339642i
$481$	−0.309678	+	0.536378i	−0.0141201	+	0.0244567i
$482$	13.4931			0.614592
$483$	10.8474	+	6.58288i	0.493573	+	0.299531i
$484$	−158.533			−7.20606
$485$	4.43075	−	7.67428i	0.201190	−	0.348471i
$486$	−2.32929	+	1.34482i	−0.105659	+	0.0610022i
$487$	−11.4990	−	19.9169i	−0.521070	−	0.902519i	−0.999700	−	0.0245024i	$-0.992200\pi$
$487$	−11.4990	−	19.9169i	−0.521070	−	0.902519i	0.478630	−	0.878017i	$-0.341133\pi$
$488$	37.1059	−	64.2692i	1.67970	−	2.90933i
$489$			6.07981i			0.274939i
$490$	−15.8190	−	3.13736i	−0.714630	−	0.141732i
$491$	29.4492			1.32902			0.664511	−	0.747279i	$-0.268640\pi$
$491$	29.4492			1.32902			0.664511	+	0.747279i	$0.268640\pi$
$492$	−8.36665	+	14.4915i	−0.377198	+	0.653326i
$493$	−10.4254	−	18.0574i	−0.469538	−	0.813264i
$494$	15.6567	−	9.03940i	0.704428	−	0.406702i
$495$	4.76660	+	2.75200i	0.214243	+	0.123693i
$496$		−	69.6540i		−	3.12756i
$497$	1.05643	−	0.479019i	0.0473873	−	0.0214869i
$498$		−	41.0432i		−	1.83919i
$499$	−6.14823	+	10.6490i	−0.275233	+	0.476717i	−0.970194	−	0.242330i	$-0.922088\pi$
$499$	−6.14823	+	10.6490i	−0.275233	+	0.476717i	0.694961	+	0.719047i	$0.255422\pi$
$500$	20.7724	+	35.9788i	0.928970	+	1.60902i
$501$	−9.16781	−	15.8791i	−0.409588	−	0.709427i
$502$	−15.1378	+	26.2195i	−0.675634	+	1.17023i
$503$	−30.9546			−1.38020			−0.690099	−	0.723715i	$-0.742433\pi$
$503$	−30.9546			−1.38020			−0.690099	+	0.723715i	$0.742433\pi$
$504$	−2.24939	+	22.9044i	−0.100196	+	1.02024i
$505$		−	3.63839i		−	0.161906i
$506$	−82.6445	+	6.29661i	−3.67400	+	0.279918i
$507$	−7.78872	+	4.49682i	−0.345909	+	0.199711i
$508$	−41.7525	−	72.3174i	−1.85247	−	3.20857i
$509$	22.1312	+	12.7775i	0.980950	+	0.566352i	0.902557	−	0.430571i	$-0.141688\pi$
$509$	22.1312	+	12.7775i	0.980950	+	0.566352i	0.0783932	+	0.996923i	$0.475021\pi$
$510$		−	12.7728i		−	0.565587i
$511$	10.6444	−	14.8630i	0.470879	−	0.657500i
$512$	−0.298468			−0.0131905
$513$	2.90825	+	1.67908i	0.128402	+	0.0741331i
$514$	−4.21955	+	2.43616i	−0.186116	+	0.107454i
$515$	5.91940	+	10.2527i	0.260840	+	0.451788i
$516$	9.07446	−	15.7174i	0.399481	−	0.691921i
$517$	33.6629			1.48049
$518$	−1.28209	+	1.79021i	−0.0563316	+	0.0786573i
$519$	19.3375			0.848821
$520$	12.9159	+	7.45699i	0.566399	+	0.327011i
$521$	15.2934	+	26.4890i	0.670017	+	1.16050i	0.977899	+	0.209079i	$0.0670466\pi$
$521$	15.2934	+	26.4890i	0.670017	+	1.16050i	−0.307882	+	0.951425i	$0.599620\pi$
$522$	5.05781	+	8.76038i	0.221374	+	0.383431i
$523$	−5.93307	+	10.2764i	−0.259435	+	0.449355i	−0.966091	−	0.258203i	$-0.916870\pi$
$523$	−5.93307	+	10.2764i	−0.259435	+	0.449355i	0.706656	+	0.707558i	$0.250203\pi$
$524$			2.38339i			0.104119i
$525$	11.2335	+	1.10322i	0.490269	+	0.0481483i
$526$		−	22.0455i		−	0.961228i
$527$	25.8685	+	14.9352i	1.12685	+	0.650586i
$528$	−41.5351	−	71.9409i	−1.80758	−	3.13082i
$529$	−22.7345	+	3.48447i	−0.988457	+	0.151499i
$530$	−13.7147	−	7.91817i	−0.595728	−	0.343943i
$531$		−	13.5364i		−	0.587430i
$532$	42.3540	−	19.2047i	1.83628	−	0.832628i
$533$	6.39898			0.277170
$534$	−33.2405	−	19.1914i	−1.43846	−	0.830494i
$535$	−13.1863	+	7.61311i	−0.570093	+	0.329143i
$536$	−10.2981	+	5.94562i	−0.444811	+	0.256812i
$537$	−9.66575	−	5.58052i	−0.417108	−	0.240817i
$538$		−	7.92756i		−	0.341782i
$539$	8.75022	−	44.1198i	0.376899	−	1.90038i
$540$			4.48344i			0.192936i
$541$	−8.54879	+	14.8069i	−0.367541	+	0.636600i	−0.989180	−	0.146704i	$-0.953134\pi$
$541$	−8.54879	+	14.8069i	−0.367541	+	0.636600i	0.621639	+	0.783304i	$0.286467\pi$
$542$	20.5821	−	11.8831i	0.884075	−	0.510421i
$543$	16.2039	−	9.35530i	0.695374	−	0.401475i
$544$	−48.1618	+	83.4186i	−2.06492	+	3.57654i
$545$		−	3.78301i		−	0.162046i
$546$	12.9723	−	5.88205i	0.555162	−	0.251728i
$547$	23.7968			1.01748			0.508739	−	0.860921i	$-0.330112\pi$
$547$	23.7968			1.01748			0.508739	+	0.860921i	$0.330112\pi$
$548$	65.5269	+	37.8320i	2.79917	+	1.61610i
$549$	−4.26569	−	7.38839i	−0.182055	−	0.315329i
$550$	−63.8538	+	36.8660i	−2.72274	+	1.57197i
$551$	6.31494	−	10.9378i	0.269026	−	0.465966i
$552$	−23.5431	−	34.4393i	−1.00206	−	1.46584i
$553$	−3.83784	−	0.376906i	−0.163202	−	0.0160277i
$554$	13.9005			0.590576
$555$	−0.132526	+	0.229541i	−0.00562541	+	0.00974349i
$556$	−28.2129	+	16.2887i	−1.19649	+	0.690795i
$557$	15.4213	−	8.90346i	0.653419	−	0.377252i	−0.136346	−	0.990661i	$-0.543536\pi$
$557$	15.4213	−	8.90346i	0.653419	−	0.377252i	0.789765	+	0.613409i	$0.210202\pi$
$558$	−12.5499	−	7.24566i	−0.531278	−	0.306733i
$559$	−6.94032			−0.293544
$560$	23.8200	+	17.0590i	1.00658	+	0.720876i
$561$	35.6237			1.50403
$562$	−39.8843	−	23.0272i	−1.68242	−	0.971344i
$563$	−13.0870	−	22.6673i	−0.551551	−	0.955315i	−0.998163	−	0.0605870i	$-0.980703\pi$
$563$	−13.0870	−	22.6673i	−0.551551	−	0.955315i	0.446612	−	0.894728i	$-0.352631\pi$
$564$	13.7105	+	23.7473i	0.577318	+	0.999944i
$565$	0.0796726	+	0.0459990i	0.00335185	+	0.00193519i
$566$	54.7086			2.29957
$567$	2.15102	+	1.54049i	0.0903345	+	0.0646944i
$568$	−3.81370			−0.160019
$569$	−25.7672	−	14.8767i	−1.08022	−	0.623663i	−0.149261	−	0.988798i	$-0.547689\pi$
$569$	−25.7672	−	14.8767i	−1.08022	−	0.623663i	−0.930954	+	0.365135i	$0.881023\pi$
$570$	6.70024	−	3.86838i	0.280642	−	0.162029i
$571$	−26.7991	+	15.4725i	−1.12151	+	0.647503i	−0.941785	−	0.336214i	$-0.890853\pi$
$571$	−26.7991	+	15.4725i	−1.12151	+	0.647503i	−0.179722	+	0.983717i	$0.557520\pi$
$572$	−33.6592	+	58.2995i	−1.40736	+	2.43762i
$573$	−4.71002			−0.196764
$574$	22.6409	+	2.22352i	0.945014	+	0.0928078i
$575$	−16.8908	+	11.5467i	−0.704396	+	0.481532i
$576$	10.4372	−	18.0778i	0.434885	−	0.753243i
$577$	−26.7580	+	15.4488i	−1.11395	+	0.643140i	−0.939850	−	0.341587i	$-0.889035\pi$
$577$	−26.7580	+	15.4488i	−1.11395	+	0.643140i	−0.174102	+	0.984728i	$0.555702\pi$
$578$	−18.4728	−	31.9958i	−0.768367	−	1.33085i
$579$	14.6198	+	8.44076i	0.607579	+	0.350786i
$580$	16.8620			0.700158
$581$	−36.7701	+	16.6728i	−1.52548	+	0.691703i
$582$			27.8250i			1.15339i
$583$	22.0841	−	38.2508i	0.914630	−	1.58419i
$584$	−52.0530	+	30.0528i	−2.15397	+	1.24359i
$585$	1.48481	−	0.857255i	0.0613893	−	0.0354431i
$586$	−32.1425	+	55.6725i	−1.32780	+	2.29981i
$587$		−	21.3835i		−	0.882590i	−0.897362	−	0.441295i	$-0.854519\pi$
$587$		−	21.3835i		−	0.882590i	0.897362	−	0.441295i	$-0.145481\pi$
$588$	34.6880	−	11.7967i	1.43051	−	0.486488i
$589$			18.0932i			0.745517i
$590$	−27.0080	−	15.5931i	−1.11190	−	0.641958i
$591$	−2.12252	+	1.22544i	−0.0873088	+	0.0504078i
$592$	3.46440	−	2.00017i	0.142386	−	0.0822065i
$593$	−19.1545	−	11.0589i	−0.786582	−	0.454133i	0.0521757	−	0.998638i	$-0.483384\pi$
$593$	−19.1545	−	11.0589i	−0.786582	−	0.454133i	−0.838758	+	0.544504i	$0.816718\pi$
$594$	−17.2825			−0.709110
$595$	−11.4429	+	5.18861i	−0.469115	+	0.212712i
$596$			59.6671i			2.44406i
$597$	2.81885	+	1.62746i	0.115368	+	0.0666076i
$598$	−11.1734	+	23.2756i	−0.456913	+	0.951812i
$599$	1.75526	+	3.04020i	0.0717179	+	0.124219i	0.899654	−	0.436603i	$-0.143819\pi$
$599$	1.75526	+	3.04020i	0.0717179	+	0.124219i	−0.827936	+	0.560822i	$0.810485\pi$
$600$	−32.1391	−	18.5555i	−1.31207	−	0.757526i
$601$		−	16.1248i		−	0.657744i	−0.944375	−	0.328872i	$-0.893332\pi$
$601$		−	16.1248i		−	0.657744i	0.944375	−	0.328872i	$-0.106668\pi$
$602$	−24.5563	−	2.41162i	−1.00084	−	0.0982904i
$603$			1.36702i			0.0556692i
$604$	29.8140	−	51.6393i	1.21311	−	2.10117i
$605$	12.9721	+	22.4683i	0.527390	+	0.913466i
$606$	5.71225	+	9.89391i	0.232044	+	0.401913i
$607$	13.5859	+	7.84383i	0.551435	+	0.318371i	0.749701	−	0.661777i	$-0.230198\pi$
$607$	13.5859	+	7.84383i	0.551435	+	0.318371i	−0.198266	+	0.980148i	$0.563531\pi$
$608$	−58.3455			−2.36622
$609$	5.79371	−	8.08991i	0.234773	−	0.327820i
$610$	−19.6552			−0.795816
$611$	5.24304	−	9.08122i	0.212111	−	0.367387i
$612$	14.5091	+	25.1306i	0.586497	+	1.01584i
$613$	34.2566	−	19.7781i	1.38361	−	0.798829i	0.391028	−	0.920379i	$-0.372120\pi$
$613$	34.2566	−	19.7781i	1.38361	−	0.798829i	0.992585	+	0.121550i	$0.0387864\pi$
$614$	6.53722	+	3.77427i	0.263821	+	0.152317i
$615$	2.73842			0.110424
$616$	−86.1043	+	120.230i	−3.46924	+	4.84419i
$617$			29.2060i			1.17579i	0.808937	+	0.587895i	$0.200043\pi$
$617$			29.2060i			1.17579i	−0.808937	+	0.587895i	$0.799957\pi$
$618$	−32.1934	−	18.5869i	−1.29501	−	0.747674i
$619$	12.3676	+	21.4212i	0.497094	+	0.860992i	0.999994	−	0.00335238i	$-0.00106710\pi$
$619$	12.3676	+	21.4212i	0.497094	+	0.860992i	−0.502900	+	0.864344i	$0.667734\pi$
$620$	−20.9197	+	12.0780i	−0.840157	+	0.485065i
$621$	−4.78197	+	0.364334i	−0.191894	+	0.0146202i
$622$			2.24015i			0.0898216i
$623$	−3.69024	+	37.5758i	−0.147846	+	1.50544i
$624$	−25.8766			−1.03589
$625$	−7.26627	+	12.5856i	−0.290651	+	0.503422i
$626$	−10.8796	−	18.8440i	−0.434837	−	0.753159i
$627$	10.7891	+	18.6872i	0.430874	+	0.746296i
$628$	19.5976	−	33.9440i	0.782028	−	1.35451i
$629$			1.71550i			0.0684015i
$630$	5.55144	−	2.51721i	0.221175	−	0.100288i
$631$			3.81288i			0.151788i	0.997116	+	0.0758942i	$0.0241811\pi$
$631$			3.81288i			0.151788i	−0.997116	+	0.0758942i	$0.975819\pi$
$632$	10.9801	+	6.33936i	0.436765	+	0.252166i
$633$	6.24089	−	3.60318i	0.248053	−	0.143214i
$634$	29.7241	+	51.4836i	1.18049	+	2.04467i
$635$	−6.83284	+	11.8348i	−0.271153	+	0.469651i
$636$	35.9784			1.42664
$637$	−10.5393	−	9.23226i	−0.417583	−	0.365795i
$638$			64.9989i			2.57333i
$639$	−0.219211	+	0.379685i	−0.00867186	+	0.0150201i
$640$	−9.16374	−	15.8721i	−0.362229	−	0.627399i
$641$	−13.4004	+	7.73675i	−0.529286	+	0.305583i	−0.740725	−	0.671808i	$-0.765518\pi$
$641$	−13.4004	+	7.73675i	−0.529286	+	0.305583i	0.211440	+	0.977391i	$0.432185\pi$
$642$	23.9051	−	41.4048i	0.943459	−	1.63412i
$643$	−33.3852			−1.31659			−0.658293	−	0.752762i	$-0.728721\pi$
$643$	−33.3852			−1.31659			−0.658293	+	0.752762i	$0.728721\pi$
$644$	−34.4557	+	56.7768i	−1.35775	+	2.23732i
$645$	−2.97009			−0.116947
$646$	25.0375	−	43.3661i	0.985085	−	1.70622i
$647$	−22.2970	+	12.8732i	−0.876585	+	0.506097i	−0.869531	−	0.493879i	$-0.835579\pi$
$647$	−22.2970	+	12.8732i	−0.876585	+	0.506097i	−0.00705409	+	0.999975i	$0.502245\pi$
$648$	−4.34934	−	7.53328i	−0.170858	−	0.295935i
$649$	43.4898	−	75.3265i	1.70712	−	2.95682i
$650$			22.9677i			0.900868i
$651$	−1.39324	+	14.1866i	−0.0546053	+	0.556018i
$652$	−31.8226			−1.24627
$653$	7.26195	−	12.5781i	0.284182	−	0.492218i	−0.688228	−	0.725494i	$-0.741611\pi$
$653$	7.26195	−	12.5781i	0.284182	−	0.492218i	0.972411	+	0.233276i	$0.0749446\pi$
$654$	5.93931	+	10.2872i	0.232245	+	0.402261i
$655$	0.337789	−	0.195022i	0.0131985	−	0.00762016i
$656$	−35.7930	−	20.6651i	−1.39748	−	0.806836i
$657$			6.90973i			0.269574i
$658$	21.7065	−	30.3094i	0.846208	−	1.18158i
$659$		−	27.1350i		−	1.05703i	−0.848924	−	0.528515i	$-0.822749\pi$
$659$		−	27.1350i		−	1.05703i	0.848924	−	0.528515i	$-0.177251\pi$
$660$	−14.4044	+	24.9491i	−0.560690	+	0.971143i
$661$	−22.4248	−	38.8408i	−0.872222	−	1.51073i	−0.859692	−	0.510812i	$-0.829345\pi$
$661$	−22.4248	−	38.8408i	−0.872222	−	1.51073i	−0.0125301	−	0.999921i	$-0.503989\pi$
$662$	2.84338	+	4.92487i	0.110511	+	0.191411i
$663$	5.54844	−	9.61017i	0.215483	−	0.373228i
$664$	132.740			5.15130
$665$	−6.18744	−	4.43123i	−0.239939	−	0.171836i
$666$		−	0.832260i		−	0.0322494i
$667$	1.37025	+	17.9848i	0.0530561	+	0.696374i
$668$	83.1136	−	47.9857i	3.21576	−	1.85662i
$669$	−4.39423	−	7.61104i	−0.169891	−	0.294260i
$670$	2.72749	+	1.57472i	0.105372	+	0.0608366i
$671$		−	54.8192i		−	2.11627i
$672$	−45.7479	−	4.49281i	−1.76477	−	0.173314i
$673$	13.8797			0.535023			0.267512	−	0.963555i	$-0.413799\pi$
$673$	13.8797			0.535023			0.267512	+	0.963555i	$0.413799\pi$
$674$	70.4117	+	40.6522i	2.71216	+	1.56586i
$675$	−3.69471	+	2.13314i	−0.142209	+	0.0821046i
$676$	−23.5370	−	40.7673i	−0.905270	−	1.56797i
$677$	−14.2421	+	24.6681i	−0.547370	+	0.948072i	0.451084	+	0.892482i	$0.351038\pi$
$677$	−14.2421	+	24.6681i	−0.547370	+	0.948072i	−0.998454	+	0.0555906i	$0.982296\pi$
$678$	−0.288873			−0.0110941
$679$	24.9281	−	11.3032i	0.956653	−	0.433778i
$680$	41.3090			1.58413
$681$	−1.31788	−	0.760880i	−0.0505014	−	0.0291570i
$682$	−46.5577	−	80.6403i	−1.78279	−	3.08788i
$683$	5.62431	+	9.74159i	0.215208	+	0.372752i	0.953337	−	0.301908i	$-0.0976236\pi$
$683$	5.62431	+	9.74159i	0.215208	+	0.372752i	−0.738129	+	0.674660i	$0.764290\pi$
$684$	−8.78854	+	15.2222i	−0.336038	+	0.582035i
$685$		−	12.3825i		−	0.473111i
$686$	−34.0822	−	36.3279i	−1.30127	−	1.38700i
$687$			1.87282i			0.0714524i
$688$	38.8210	+	22.4133i	1.48004	+	0.854500i
$689$	−6.87925	−	11.9152i	−0.262079	−	0.453933i
$690$	−4.78161	+	9.96075i	−0.182033	+	0.379199i
$691$	33.4243	+	19.2976i	1.27152	+	0.734114i	0.975274	−	0.220997i	$-0.0709313\pi$
$691$	33.4243	+	19.2976i	1.27152	+	0.734114i	0.296248	+	0.955111i	$0.404265\pi$
$692$			101.215i			3.84762i
$693$	7.02059	+	15.4832i	0.266690	+	0.588158i
$694$	75.4931			2.86568
$695$	4.61707	+	2.66566i	0.175135	+	0.101114i
$696$	−28.3324	+	16.3577i	−1.07394	+	0.620037i
$697$	15.3494	−	8.86199i	0.581401	−	0.335672i
$698$	−42.0604	−	24.2836i	−1.59201	−	0.919146i
$699$			28.8681i			1.09189i
$700$	−5.77439	+	58.7977i	−0.218252	+	2.22234i
$701$		−	5.71290i		−	0.215773i	−0.994163	−	0.107887i	$-0.965592\pi$
$701$		−	5.71290i		−	0.215773i	0.994163	−	0.107887i	$-0.0344084\pi$
$702$	−2.69177	+	4.66229i	−0.101594	+	0.175967i
$703$	−0.899905	+	0.519561i	−0.0339406	+	0.0195956i
$704$	116.161	−	67.0655i	4.37798	−	2.52763i
$705$	2.24375	−	3.88628i	0.0845043	−	0.146366i
$706$		−	29.7377i		−	1.11919i
$707$	6.54338	−	9.13669i	0.246089	−	0.343621i
$708$	70.8516			2.66277
$709$	26.4498	+	15.2708i	0.993344	+	0.573508i	0.906272	−	0.422695i	$-0.138916\pi$
$709$	26.4498	+	15.2708i	0.993344	+	0.573508i	0.0870719	+	0.996202i	$0.472249\pi$
$710$	0.505035	+	0.874747i	0.0189536	+	0.0328287i
$711$	1.26227	−	0.728773i	0.0473389	−	0.0273311i
$712$	62.0679	−	107.505i	2.32609	−	4.02891i
$713$	−14.5822	−	21.3312i	−0.546109	−	0.798860i
$714$	22.9709	−	32.0748i	0.859663	−	1.20037i
$715$	11.0167			0.412003
$716$	29.2093	−	50.5920i	1.09160	−	1.89071i
$717$	3.37110	−	1.94630i	0.125896	−	0.0726860i
$718$	58.5059	−	33.7784i	2.18342	−	1.26060i
$719$	−10.3703	−	5.98731i	−0.386748	−	0.223289i	0.294002	−	0.955805i	$-0.405013\pi$
$719$	−10.3703	−	5.98731i	−0.386748	−	0.223289i	−0.680750	+	0.732516i	$0.738346\pi$
$720$	−11.0738			−0.412696
$721$	−3.57399	+	36.3921i	−0.133103	+	1.35531i
$722$	−20.7715			−0.773035
$723$	4.34458	+	2.50834i	0.161576	+	0.0932862i
$724$	48.9670	+	84.8134i	1.81985	+	3.15207i
$725$	8.02265	+	13.8956i	0.297954	+	0.516071i
$726$	−70.5503	−	40.7322i	−2.61837	−	1.51171i
$727$	29.2912			1.08635			0.543175	−	0.839619i	$-0.317222\pi$
$727$	29.2912			1.08635			0.543175	+	0.839619i	$0.317222\pi$
$728$	19.0234	+	41.9542i	0.705055	+	1.55493i
$729$	−1.00000			−0.0370370
$730$	13.7864	+	7.95958i	0.510257	+	0.294597i
$731$	−16.6480	+	9.61171i	−0.615747	+	0.355502i
$732$	38.6719	−	22.3272i	1.42935	−	0.825238i
$733$	1.41154	−	2.44485i	0.0521363	−	0.0903027i	−0.838779	−	0.544471i	$-0.816730\pi$
$733$	1.41154	−	2.44485i	0.0521363	−	0.0903027i	0.890916	+	0.454169i	$0.150064\pi$
$734$	−1.28495			−0.0474284
$735$	−4.51027	−	3.95092i	−0.166364	−	0.145732i
$736$	68.7873	−	47.0236i	2.53553	−	1.73331i
$737$	−4.39194	+	7.60707i	−0.161779	+	0.280210i
$738$	−7.44663	+	4.29931i	−0.274114	+	0.158260i
$739$	6.16956	+	10.6860i	0.226951	+	0.393090i	0.956903	−	0.290408i	$-0.0937910\pi$
$739$	6.16956	+	10.6860i	0.226951	+	0.393090i	−0.729952	+	0.683498i	$0.760458\pi$
$740$	−1.20145	−	0.693660i	−0.0441663	−	0.0254994i
$741$	6.72165			0.246926
$742$	−20.1999	−	44.5489i	−0.741563	−	1.63544i
$743$		−	34.9658i		−	1.28277i	−0.767219	−	0.641386i	$-0.778360\pi$
$743$		−	34.9658i		−	1.28277i	0.767219	−	0.641386i	$-0.221640\pi$
$744$	23.4336	−	40.5881i	0.859116	−	1.48803i
$745$	8.45639	−	4.88230i	0.309818	−	0.178874i
$746$	−8.01937	+	4.62999i	−0.293610	+	0.169516i
$747$	7.62988	−	13.2153i	0.279163	−	0.483524i
$748$			186.460i			6.81764i
$749$	−46.8049	−	4.59661i	−1.71021	−	0.167957i
$750$			21.3483i			0.779531i
$751$	−11.7250	−	6.76945i	−0.427852	−	0.247021i	0.270579	−	0.962698i	$-0.412785\pi$
$751$	−11.7250	−	6.76945i	−0.427852	−	0.247021i	−0.698431	+	0.715677i	$0.746118\pi$
$752$	−58.6544	+	33.8641i	−2.13891	+	1.23490i
$753$	−9.74833	+	5.62820i	−0.355249	+	0.205103i
$754$	17.5347	+	10.1237i	0.638575	+	0.368682i
$755$	−9.75818			−0.355137
$756$	−8.06314	+	11.2588i	−0.293253	+	0.409478i
$757$			39.3542i			1.43035i	0.698944	+	0.715177i	$0.253654\pi$
$757$			39.3542i			1.43035i	−0.698944	+	0.715177i	$0.746346\pi$
$758$	−49.5548	−	28.6104i	−1.79991	−	1.03918i
$759$	−27.7809	−	13.3361i	−1.00838	−	0.484069i
$760$	12.5109	+	21.6696i	0.453819	+	0.786038i
$761$	40.2811	+	23.2563i	1.46019	+	0.843040i	0.999020	−	0.0442720i	$-0.0140968\pi$
$761$	40.2811	+	23.2563i	1.46019	+	0.843040i	0.461169	+	0.887312i	$0.347430\pi$
$762$		−	42.9102i		−	1.55447i
$763$	6.80346	−	9.49986i	0.246302	−	0.343918i
$764$		−	24.6529i		−	0.891912i
$765$	2.37444	−	4.11265i	0.0858480	−	0.148693i
$766$	13.7221	+	23.7674i	0.495801	+	0.858752i
$767$	−13.5472	−	23.4644i	−0.489160	−	0.847250i
$768$	13.6825	+	7.89959i	0.493724	+	0.285052i
$769$	−14.9912			−0.540595			−0.270298	−	0.962777i	$-0.587122\pi$
$769$	−14.9912			−0.540595			−0.270298	+	0.962777i	$0.587122\pi$
$770$	38.9796	+	3.82810i	1.40473	+	0.137955i
$771$	−1.81152			−0.0652401
$772$	−44.1802	+	76.5224i	−1.59008	+	2.75410i
$773$	6.01012	+	10.4098i	0.216169	+	0.374416i	0.953634	−	0.300970i	$-0.0973104\pi$
$773$	6.01012	+	10.4098i	0.216169	+	0.374416i	−0.737465	+	0.675386i	$0.763977\pi$
$774$	8.07661	−	4.66303i	0.290308	−	0.167609i
$775$	−19.9065	−	11.4930i	−0.715062	−	0.412841i
$776$	−89.9903			−3.23046
$777$	−0.745611	+	0.338085i	−0.0267487	+	0.0121287i
$778$		−	33.9884i		−	1.21854i
$779$	9.29752	+	5.36792i	0.333118	+	0.192326i
$780$	4.48700	+	7.77171i	0.160660	+	0.278272i
$781$	−2.43970	+	1.40856i	−0.0872994	+	0.0504023i
$782$	5.43274	+	71.3061i	0.194274	+	2.54990i
$783$			3.76096i			0.134406i
$784$	29.1371	+	85.6771i	1.04061	+	3.05990i
$785$	−6.41433			−0.228937
$786$	−0.612369	+	1.06065i	−0.0218425	+	0.0378323i
$787$	−5.09940	−	8.83242i	−0.181774	−	0.314842i	0.760711	−	0.649091i	$-0.224851\pi$
$787$	−5.09940	−	8.83242i	−0.181774	−	0.314842i	−0.942485	+	0.334249i	$0.891517\pi$
$788$	−6.41412	−	11.1096i	−0.228494	−	0.395763i
$789$	4.09822	−	7.09833i	0.145901	−	0.252707i
$790$		−	3.35800i		−	0.119472i
$791$	0.117347	+	0.258798i	0.00417239	+	0.00920179i
$792$		−	55.8942i		−	1.98611i
$793$	−14.7885	−	8.53815i	−0.525156	−	0.303199i
$794$	59.2036	−	34.1812i	2.10106	−	1.21305i
$795$	−2.94396	−	5.09908i	−0.104411	−	0.180846i
$796$	−8.51838	+	14.7543i	−0.301926	+	0.522951i
$797$	−0.453493			−0.0160635			−0.00803176	−	0.999968i	$-0.502557\pi$
$797$	−0.453493			−0.0160635			−0.00803176	+	0.999968i	$0.502557\pi$
$798$	23.7826	+	2.33564i	0.841895	+	0.0826807i
$799$		−	29.0445i		−	1.02752i
$800$	37.0618	−	64.1929i	1.31033	−	2.26956i
$801$	−7.13532	−	12.3587i	−0.252114	−	0.436675i
$802$	7.14525	−	4.12531i	0.252308	−	0.145670i
$803$	−22.1996	+	38.4508i	−0.783406	+	1.35690i
$804$	−7.15516			−0.252343
$805$	10.8661	+	0.237482i	0.382980	+	0.00837014i
$806$	−29.0057			−1.02168
$807$	1.47372	−	2.55256i	0.0518775	−	0.0898545i
$808$	−31.9984	+	18.4743i	−1.12570	+	0.649923i
$809$	−9.76658	−	16.9162i	−0.343375	−	0.594742i	0.641682	−	0.766970i	$-0.278237\pi$
$809$	−9.76658	−	16.9162i	−0.343375	−	0.594742i	−0.985057	+	0.172228i	$0.944903\pi$
$810$	−1.15194	+	1.99521i	−0.0404749	+	0.0701047i
$811$		−	7.35288i		−	0.258195i	−0.991632	−	0.129097i	$-0.958792\pi$
$811$		−	7.35288i		−	0.258195i	0.991632	−	0.129097i	$-0.0412080\pi$
$812$	42.3438	+	30.3251i	1.48598	+	1.06420i
$813$	8.83618			0.309898
$814$	2.67388	−	4.63130i	0.0937195	−	0.162327i
$815$	2.60391	+	4.51010i	0.0912108	+	0.157982i
$816$	−62.0709	+	35.8366i	−2.17292	+	1.25453i
$817$	−10.0841	−	5.82205i	−0.352797	−	0.203688i
$818$			49.8189i			1.74188i
$819$	5.27035	+	0.517590i	0.184161	+	0.0180861i
$820$			14.3333i			0.500541i
$821$	6.08233	−	10.5349i	0.212275	−	0.367670i	−0.740151	−	0.672440i	$-0.765246\pi$
$821$	6.08233	−	10.5349i	0.212275	−	0.367670i	0.952426	+	0.304770i	$0.0985795\pi$
$822$	19.4405	+	33.6719i	0.678064	+	1.17444i
$823$	−9.33630	−	16.1709i	−0.325443	−	0.563684i	0.656159	−	0.754623i	$-0.272180\pi$
$823$	−9.33630	−	16.1709i	−0.325443	−	0.563684i	−0.981602	+	0.190939i	$0.938847\pi$
$824$	60.1127	−	104.118i	2.09413	−	3.62713i
$825$	−27.4134			−0.954412
$826$	−39.7793	−	87.7293i	−1.38410	−	3.05249i
$827$			19.5677i			0.680436i	0.940347	+	0.340218i	$0.110501\pi$
$827$			19.5677i			0.680436i	−0.940347	+	0.340218i	$0.889499\pi$
$828$	−1.90698	−	25.0296i	−0.0662721	−	0.869837i
$829$	4.58192	−	2.64537i	0.159137	−	0.0918776i	−0.418317	−	0.908301i	$-0.637380\pi$
$829$	4.58192	−	2.64537i	0.159137	−	0.0918776i	0.577453	+	0.816424i	$0.304046\pi$
$830$	−17.5783	−	30.4465i	−0.610151	−	1.05681i
$831$	4.47577	+	2.58409i	0.155263	+	0.0896410i
$832$		−	41.7822i		−	1.44854i
$833$	−38.0668	−	7.54973i	−1.31894	−	0.261583i
$834$	−16.7403			−0.579670
$835$	−13.6016	−	7.85291i	−0.470704	−	0.271761i
$836$	−97.8117	+	56.4716i	−3.38289	+	1.95311i
$837$	−2.69392	−	4.66600i	−0.0931155	−	0.161281i
$838$	0.0776633	−	0.134517i	0.00268284	−	0.00464681i
$839$	18.0487			0.623111			0.311556	−	0.950228i	$-0.399150\pi$
$839$	18.0487			0.623111			0.311556	+	0.950228i	$0.399150\pi$
$840$	8.14102	+	17.9542i	0.280892	+	0.619478i
$841$	−14.8552			−0.512248
$842$	42.5558	+	24.5696i	1.46657	+	0.846725i
$843$	−8.56146	−	14.8289i	−0.294872	−	0.510734i
$844$	18.8596	+	32.6657i	0.649173	+	1.12440i
$845$	−3.85186	+	6.67162i	−0.132508	+	0.229511i
$846$			14.0907i			0.484448i
$847$	−7.83223	+	79.7516i	−0.269119	+	2.74030i
$848$			88.8644i			3.05162i
$849$	17.6154	+	10.1703i	0.604559	+	0.349042i
$850$	31.8082	+	55.0934i	1.09101	+	1.88969i
$851$	0.642215	−	1.33782i	0.0220148	−	0.0458600i
$852$	−1.98733	−	1.14738i	−0.0680847	−	0.0393087i
$853$			49.4603i			1.69349i	0.532000	+	0.846744i	$0.321441\pi$
$853$			49.4603i			1.69349i	−0.532000	+	0.846744i	$0.678559\pi$
$854$	−49.3580	−	35.3485i	−1.68900	−	1.20960i
$855$	2.87651			0.0983746
$856$	133.909	+	77.3126i	4.57693	+	2.64249i
$857$	43.2625	−	24.9776i	1.47782	−	0.853218i	0.478132	−	0.878288i	$-0.341314\pi$
$857$	43.2625	−	24.9776i	1.47782	−	0.853218i	0.999686	+	0.0250696i	$0.00798073\pi$
$858$	−29.9580	+	17.2962i	−1.02275	+	0.590484i
$859$	0.200180	+	0.115574i	0.00683006	+	0.00394334i	0.503411	−	0.864047i	$-0.332078\pi$
$859$	0.200180	+	0.115574i	0.00683006	+	0.00394334i	−0.496581	+	0.867990i	$0.665411\pi$
$860$		−	15.5459i		−	0.530111i
$861$	6.87671	+	4.92486i	0.234358	+	0.167839i
$862$			45.4467i			1.54792i
$863$	21.4061	−	37.0764i	0.728671	−	1.26209i	−0.228774	−	0.973480i	$-0.573472\pi$
$863$	21.4061	−	37.0764i	0.728671	−	1.26209i	0.957445	−	0.288615i	$-0.0931949\pi$
$864$	15.0466	−	8.68714i	0.511895	−	0.295543i
$865$	14.3448	−	8.28199i	0.487739	−	0.281596i
$866$	27.0326	−	46.8219i	0.918606	−	1.59107i
$867$		−	13.7363i		−	0.466509i
$868$	−74.2549	−	7.29242i	−2.52038	−	0.247521i
$869$	9.36560			0.317706
$870$	7.50392	+	4.33239i	0.254407	+	0.146882i
$871$	1.36810	+	2.36962i	0.0463563	+	0.0802915i
$872$	−33.2703	+	19.2086i	−1.12667	+	0.650485i
$873$	−5.17264	+	8.95927i	−0.175067	+	0.303225i
$874$	−35.7598	+	24.4458i	−1.20959	+	0.826891i
$875$	19.1257	−	8.67222i	0.646567	−	0.293175i
$876$	−36.1666			−1.22196
$877$	8.24042	−	14.2728i	0.278259	−	0.481959i	−0.692693	−	0.721233i	$-0.743576\pi$
$877$	8.24042	−	14.2728i	0.278259	−	0.481959i	0.970952	+	0.239273i	$0.0769093\pi$
$878$	−39.4417	+	22.7717i	−1.33109	+	0.768507i
$879$	−20.6989	+	11.9505i	−0.698156	+	0.403081i
$880$	−61.6227	−	35.5779i	−2.07730	−	1.19933i
$881$	−36.6278			−1.23402			−0.617012	−	0.786954i	$-0.711657\pi$
$881$	−36.6278			−1.23402			−0.617012	+	0.786954i	$0.711657\pi$
$882$	18.4678	+	3.66268i	0.621842	+	0.123329i
$883$	−8.94731			−0.301101			−0.150550	−	0.988602i	$-0.548105\pi$
$883$	−8.94731			−0.301101			−0.150550	+	0.988602i	$0.548105\pi$
$884$	50.3011	+	29.0413i	1.69181	+	0.976766i
$885$	−5.79747	−	10.0415i	−0.194880	−	0.337542i
$886$	−31.4143	−	54.4111i	−1.05538	−	1.82798i
$887$	40.0166	+	23.1036i	1.34362	+	0.775742i	0.987337	−	0.158635i	$-0.0507091\pi$
$887$	40.0166	+	23.1036i	1.34362	+	0.775742i	0.356287	+	0.934377i	$0.384042\pi$
$888$	2.69165			0.0903259
$889$	−38.4427	+	17.4312i	−1.28933	+	0.584622i
$890$	−32.8778			−1.10207
$891$	−5.56473	−	3.21280i	−0.186425	−	0.107633i
$892$	39.8373	−	23.0001i	1.33385	−	0.770099i
$893$	15.2360	−	8.79649i	0.509852	−	0.294363i
$894$	−15.3304	+	26.5530i	−0.512724	+	0.888065i
$895$	−9.56027			−0.319565
$896$	5.53285	−	56.3381i	0.184840	−	1.88213i
$897$	−7.92458	+	5.41732i	−0.264594	+	0.180879i
$898$	32.9326	−	57.0409i	1.09897	−	1.90348i
$899$	−17.5487	+	10.1317i	−0.585280	+	0.337912i
$900$	−11.1652	−	19.3386i	−0.372172	−	0.644621i
$901$	−33.0029	−	19.0543i	−1.09949	−	0.634789i
$902$	−55.2513			−1.83967
$903$	−7.45847	−	5.34150i	−0.248202	−	0.177754i
$904$		−	0.934258i		−	0.0310729i
$905$	8.01351	−	13.8798i	0.266378	−	0.461381i
$906$	26.5355	−	15.3203i	0.881585	−	0.508983i
$907$	−10.3771	+	5.99119i	−0.344564	+	0.198934i	−0.662289	−	0.749249i	$-0.730415\pi$
$907$	−10.3771	+	5.99119i	−0.344564	+	0.198934i	0.317724	+	0.948183i	$0.397081\pi$
$908$	3.98256	−	6.89800i	0.132166	−	0.228918i
$909$			4.24760i			0.140884i
$910$	7.10382	−	9.91925i	0.235489	−	0.328820i
$911$			27.8717i			0.923429i	0.887029	+	0.461715i	$0.152766\pi$
$911$			27.8717i			0.923429i	−0.887029	+	0.461715i	$0.847234\pi$
$912$	−37.5979	−	21.7071i	−1.24499	−	0.718795i
$913$	84.9164	−	49.0265i	2.81032	−	1.62254i
$914$	−65.1042	+	37.5879i	−2.15346	+	1.24330i
$915$	−6.32870	−	3.65388i	−0.209220	−	0.120793i
$916$	−9.80260			−0.323887
$917$	1.19899	+	0.117750i	0.0395940	+	0.00388844i
$918$			14.9114i			0.492151i
$919$	−29.0440	−	16.7685i	−0.958072	−	0.553143i	−0.0624926	−	0.998045i	$-0.519905\pi$
$919$	−29.0440	−	16.7685i	−0.958072	−	0.553143i	−0.895579	+	0.444903i	$0.853238\pi$
$920$	−32.2145	−	15.4644i	−1.06208	−	0.509847i
$921$	1.40326	+	2.43052i	0.0462391	+	0.0800884i
$922$	−73.0422	−	42.1709i	−2.40552	−	1.38883i
$923$			0.877542i			0.0288846i
$924$	−81.0413	+	36.7468i	−2.66606	+	1.20888i
$925$		−	1.32012i		−	0.0434054i
$926$	−7.55598	+	13.0873i	−0.248305	+	0.430077i
$927$	−6.91055	−	11.9694i	−0.226972	−	0.393128i
$928$	−32.6720	−	56.5895i	−1.07251	−	1.85764i
$929$	−6.78607	−	3.91794i	−0.222644	−	0.128543i	0.384530	−	0.923112i	$-0.374363\pi$
$929$	−6.78607	−	3.91794i	−0.222644	−	0.128543i	−0.607174	+	0.794569i	$0.707697\pi$
$930$	−12.4129			−0.407035
$931$	−7.56861	−	22.2553i	−0.248051	−	0.729389i
$932$	−151.100			−4.94944
$933$	−0.416440	+	0.721295i	−0.0136336	+	0.0236142i
$934$	−49.5833	−	85.8808i	−1.62242	−	2.81011i
$935$	26.4262	−	15.2572i	0.864229	−	0.498963i
$936$	−15.0785	−	8.70559i	−0.492857	−	0.284551i
$937$	21.2822			0.695259			0.347630	−	0.937632i	$-0.386987\pi$
$937$	21.2822			0.695259			0.347630	+	0.937632i	$0.386987\pi$
$938$	4.01723	+	8.85960i	0.131167	+	0.289276i
$939$		−	8.09002i		−	0.264008i
$940$	20.3414	+	11.7441i	0.663462	+	0.383050i
$941$	−26.4681	−	45.8441i	−0.862835	−	1.49447i	−0.869181	−	0.494494i	$-0.835353\pi$
$941$	−26.4681	−	45.8441i	−0.862835	−	1.49447i	0.00634612	−	0.999980i	$-0.497980\pi$
$942$	17.4426	−	10.0705i	0.568310	−	0.328114i
$943$	−15.2877	+	1.16476i	−0.497837	+	0.0379297i
$944$			174.999i			5.69573i
$945$	2.25543	+	0.221501i	0.0733692	+	0.00720544i
$946$	59.9255			1.94835
$947$	−9.97829	+	17.2829i	−0.324251	+	0.561619i	−0.981360	−	0.192176i	$-0.938446\pi$
$947$	−9.97829	+	17.2829i	−0.324251	+	0.561619i	0.657110	+	0.753795i	$0.271779\pi$
$948$	3.81450	+	6.60692i	0.123889	+	0.214583i
$949$	6.91522	+	11.9775i	0.224478	+	0.388807i
$950$	−19.2670	+	33.3714i	−0.625104	+	1.08271i
$951$			22.1027i			0.716728i
$952$	103.735	+	74.2912i	3.36206	+	2.40779i
$953$			6.83578i			0.221433i	0.993852	+	0.110716i	$0.0353145\pi$
$953$			6.83578i			0.221433i	−0.993852	+	0.110716i	$0.964685\pi$
$954$	16.0111	+	9.24400i	0.518378	+	0.299286i
$955$	−3.49396	+	2.01724i	−0.113062	+	0.0652764i
$956$	10.1872	+	17.6448i	0.329479	+	0.570674i
$957$	−12.0832	+	20.9287i	−0.390594	+	0.676529i
$958$	−78.7838			−2.54539
$959$	22.2690	−	31.0948i	0.719104	−	1.00410i
$960$		−	17.8806i		−	0.577093i
$961$	−0.985600	+	1.70711i	−0.0317935	+	0.0550680i
$962$	−0.832921	−	1.44266i	−0.0268545	−	0.0465133i
$963$	15.3942	−	8.88785i	0.496072	−	0.286407i
$964$	−13.1290	+	22.7401i	−0.422858	+	0.732411i
$965$	14.4603			0.465493
$966$	−29.9212	+	16.4140i	−0.962699	+	0.528111i
$967$	−19.8952			−0.639787			−0.319894	−	0.947453i	$-0.603647\pi$
$967$	−19.8952			−0.639787			−0.319894	+	0.947453i	$0.603647\pi$
$968$	131.734	−	228.170i	4.23409	−	7.33366i
$969$	16.1234	−	9.30886i	0.517959	−	0.299044i
$970$	11.9171	+	20.6410i	0.382635	+	0.662744i
$971$	−5.86183	+	10.1530i	−0.188115	+	0.325825i	−0.944622	−	0.328161i	$-0.893571\pi$
$971$	−5.86183	+	10.1530i	−0.188115	+	0.325825i	0.756507	+	0.653986i	$0.226904\pi$
$972$		−	5.23415i		−	0.167885i
$973$	6.80034	+	14.9975i	0.218009	+	0.480796i
$974$	61.8563			1.98200
$975$	−4.26967	+	7.39528i	−0.136739	+	0.236839i
$976$	55.1468	+	95.5171i	1.76521	+	3.05743i
$977$	−20.7301	+	11.9685i	−0.663213	+	0.382906i	−0.793500	−	0.608570i	$-0.791743\pi$
$977$	−20.7301	+	11.9685i	−0.663213	+	0.382906i	0.130287	+	0.991476i	$0.458410\pi$
$978$	−14.1617	−	8.17624i	−0.452840	−	0.261447i
$979$		−	91.6974i		−	2.93066i
$980$	20.6797	−	23.6074i	0.660589	−	0.754111i
$981$			4.41644i			0.141006i
$982$	−39.6038	+	68.5957i	−1.26381	+	2.18898i
$983$	−29.9774	−	51.9223i	−0.956129	−	1.65606i	−0.731763	−	0.681560i	$-0.761302\pi$
$983$	−29.9774	−	51.9223i	−0.956129	−	1.65606i	−0.224367	−	0.974505i	$-0.572031\pi$
$984$	−13.9046	−	24.0835i	−0.443263	−	0.767754i
$985$	−1.04968	+	1.81810i	−0.0334455	+	0.0579294i
$986$	56.0813			1.78599
$987$	12.6237	−	5.72398i	0.401816	−	0.182196i
$988$			35.1821i			1.11929i
$989$	16.5810	−	1.26329i	0.527247	−	0.0401704i
$990$	−12.8204	+	7.40188i	−0.407460	+	0.235247i
$991$	−15.8146	−	27.3916i	−0.502366	−	0.870124i	−0.999996	−	0.00273457i	$-0.999130\pi$
$991$	−15.8146	−	27.3916i	−0.502366	−	0.870124i	0.497630	−	0.867389i	$-0.334204\pi$
$992$	81.0685	+	46.8049i	2.57393	+	1.48606i
$993$			2.11432i			0.0670959i
$994$	−0.304928	+	3.10493i	−0.00967174	+	0.0984823i
$995$	2.78809			0.0883883
$996$	69.1710	+	39.9359i	2.19177	+	1.26542i
$997$	−49.5003	+	28.5790i	−1.56769	+	0.905107i	−0.571253	+	0.820774i	$0.693542\pi$
$997$	−49.5003	+	28.5790i	−1.56769	+	0.905107i	−0.996438	+	0.0843323i	$0.973124\pi$
$998$	−16.5365	−	28.6421i	−0.523454	−	0.906649i
$999$	0.154716	−	0.267976i	0.00489500	−	0.00847839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.j.a.229.1	✓	64
7.3	odd	6	inner	483.2.j.a.367.2	yes	64
23.22	odd	2	inner	483.2.j.a.229.2	yes	64
161.45	even	6	inner	483.2.j.a.367.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.j.a.229.1	✓	64	1.1	even	1	trivial
483.2.j.a.229.2	yes	64	23.22	odd	2	inner
483.2.j.a.367.1	yes	64	161.45	even	6	inner
483.2.j.a.367.2	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34482 + 2.32929i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-2.61707 - 4.53290i) q^{4} +(-0.428287 + 0.741815i) q^{5} -2.68964i q^{6} +(-2.40961 + 1.09260i) q^{7} +8.69868 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34482 + 2.32929i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-2.61707 - 4.53290i) q^{4} +(-0.428287 + 0.741815i) q^{5} -2.68964i q^{6} +(-2.40961 + 1.09260i) q^{7} +8.69868 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.15194 - 1.99521i) q^{10} +(5.56473 - 3.21280i) q^{11} +(4.53290 + 2.61707i) q^{12} -2.00159i q^{13} +(0.695512 - 7.08204i) q^{14} -0.856574i q^{15} +(-6.46400 + 11.1960i) q^{16} +(-2.77202 - 4.80127i) q^{17} +(1.34482 + 2.32929i) q^{18} +(1.67908 - 2.90825i) q^{19} +4.48344 q^{20} +(1.54049 - 2.15102i) q^{21} +17.2825i q^{22} +(0.364334 + 4.78197i) q^{23} +(-7.53328 + 4.34934i) q^{24} +(2.13314 + 3.69471i) q^{25} +(4.66229 + 2.69177i) q^{26} +1.00000i q^{27} +(11.2588 + 8.06314i) q^{28} +3.76096 q^{29} +(1.99521 + 1.15194i) q^{30} +(-4.66600 + 2.69392i) q^{31} +(-8.68714 - 15.0466i) q^{32} +(-3.21280 + 5.56473i) q^{33} +14.9114 q^{34} +(0.221501 - 2.25543i) q^{35} -5.23415 q^{36} +(-0.267976 - 0.154716i) q^{37} +(4.51611 + 7.82213i) q^{38} +(1.00079 + 1.73343i) q^{39} +(-3.72554 + 6.45282i) q^{40} +3.19695i q^{41} +(2.93869 + 6.48098i) q^{42} -3.46741i q^{43} +(-29.1266 - 16.8163i) q^{44} +(0.428287 + 0.741815i) q^{45} +(-11.6286 - 5.58224i) q^{46} +(4.53700 + 2.61944i) q^{47} -12.9280i q^{48} +(4.61246 - 5.26547i) q^{49} -11.4747 q^{50} +(4.80127 + 2.77202i) q^{51} +(-9.07301 + 5.23831i) q^{52} +(5.95288 - 3.43689i) q^{53} +(-2.32929 - 1.34482i) q^{54} +5.50400i q^{55} +(-20.9605 + 9.50415i) q^{56} +3.35816i q^{57} +(-5.05781 + 8.76038i) q^{58} +(11.7229 - 6.76821i) q^{59} +(-3.88277 + 2.24172i) q^{60} +(4.26569 - 7.38839i) q^{61} -14.4913i q^{62} +(-0.258590 + 2.63308i) q^{63} +20.8745 q^{64} +(1.48481 + 0.857255i) q^{65} +(-8.64126 - 14.9671i) q^{66} +(-1.18387 + 0.683508i) q^{67} +(-14.5091 + 25.1306i) q^{68} +(-2.70651 - 3.95914i) q^{69} +(4.95569 + 3.54909i) q^{70} -0.438423 q^{71} +(4.34934 - 7.53328i) q^{72} +(-5.98401 + 3.45487i) q^{73} +(0.720758 - 0.416130i) q^{74} +(-3.69471 - 2.13314i) q^{75} -17.5771 q^{76} +(-9.89855 + 13.8216i) q^{77} -5.38355 q^{78} +(1.26227 + 0.728773i) q^{79} +(-5.53690 - 9.59019i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.44663 - 4.29931i) q^{82} +15.2598 q^{83} +(-13.7820 - 1.35350i) q^{84} +4.74888 q^{85} +(8.07661 + 4.66303i) q^{86} +(-3.25709 + 1.88048i) q^{87} +(48.4058 - 27.9471i) q^{88} +(7.13532 - 12.3587i) q^{89} -2.30387 q^{90} +(2.18693 + 4.82305i) q^{91} +(20.7227 - 14.1663i) q^{92} +(2.69392 - 4.66600i) q^{93} +(-12.2029 + 7.04534i) q^{94} +(1.43826 + 2.49113i) q^{95} +(15.0466 + 8.68714i) q^{96} -10.3453 q^{97} +(6.06190 + 17.8249i) q^{98} -6.42560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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