LMFDB - Embedded newform 483.2.j.a.229.2

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			229.2
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.2

$q$-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} +(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} +(-4.32348 + 2.07546i) 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} +(0.979926 - 12.8618i) 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} - 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}+ \cdots + 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

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	−0.754224	−	0.656618i	$-0.771987\pi$
$5$	0.428287	−	0.741815i	0.191536	−	0.331750i	0.945759	+	0.324868i	$0.105320\pi$
$6$		−	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	$0.753477\pi$
$11$	−5.56473	+	3.21280i	−1.67783	+	0.968695i	−0.963042	+	0.269353i	$0.913190\pi$
$12$	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	$0.0680322\pi$
$17$	2.77202	+	4.80127i	0.672313	+	1.16448i	−0.304934	+	0.952373i	$0.598634\pi$
$18$	1.34482	+	2.32929i	0.316977	+	0.549020i
$19$	−1.67908	+	2.90825i	−0.385207	+	0.667198i	−0.991798	−	0.127816i	$-0.959203\pi$
$19$	−1.67908	+	2.90825i	−0.385207	+	0.667198i	0.606591	+	0.795014i	$0.292537\pi$
$20$	−4.48344			−1.00253
$21$	−1.54049	+	2.15102i	−0.336162	+	0.469392i
$22$		−	17.2825i		−	3.68465i
$23$	−4.32348	+	2.07546i	−0.901507	+	0.432764i
$23$	−4.32348	+	2.07546i	−0.901507	+	0.432764i
$24$	−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	0.521866	−	0.853028i	$-0.325236\pi$
$37$	0.267976	+	0.154716i	0.0440550	+	0.0254352i	−0.477811	+	0.878463i	$0.658570\pi$
$38$	−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	$0.0851697\pi$
$43$			3.46741i			0.528775i	−0.964417	+	0.264387i	$0.914830\pi$
$44$	29.1266	+	16.8163i	4.39100	+	2.53515i
$45$	−0.428287	−	0.741815i	−0.0638453	−	0.110583i
$46$	0.979926	−	12.8618i	0.144482	−	1.89636i
$47$	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	−0.849619	−	0.527396i	$-0.823168\pi$
$53$	−5.95288	+	3.43689i	−0.817690	+	0.472094i	0.0319290	+	0.999490i	$0.489835\pi$
$54$	−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	$0.350580\pi$
$61$	−4.26569	+	7.38839i	−0.546165	+	0.945986i	−0.998533	+	0.0541543i	$0.982754\pi$
$62$		−	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	−0.425937	−	0.904753i	$-0.640056\pi$
$67$	1.18387	−	0.683508i	0.144633	−	0.0835037i	0.570570	+	0.821249i	$0.306722\pi$
$68$	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	0.427308	−	0.904106i	$-0.359462\pi$
$79$	−1.26227	−	0.728773i	−0.142017	−	0.0819934i	−0.569325	+	0.822113i	$0.692795\pi$
$80$	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	$-0.815977\pi$
$83$	−15.2598			−1.67498			−0.837488	+	0.546455i	$0.815977\pi$
$84$	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	$0.439682\pi$
$89$	−7.13532	+	12.3587i	−0.756343	+	1.31002i	−0.944704	+	0.327924i	$0.893651\pi$
$90$	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	$-0.323990\pi$
$97$	10.3453			1.05040			0.525202	+	0.850978i	$0.323990\pi$
$98$	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	$0.405085\pi$
$103$	−6.91055	+	11.9694i	−0.680917	+	1.17938i	−0.974701	+	0.223511i	$0.928248\pi$
$104$		−	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	−0.488305	−	0.872673i	$-0.662385\pi$
$107$	−15.3942	−	8.88785i	−1.48821	−	0.859221i	−0.999910	+	0.0134517i	$0.995718\pi$
$108$	4.53290	−	2.61707i	0.436179	−	0.251828i
$109$	3.82475	−	2.20822i	0.366344	−	0.211509i	−0.305516	−	0.952187i	$-0.598829\pi$
$109$	3.82475	−	2.20822i	0.366344	−	0.211509i	0.671860	+	0.740678i	$0.265496\pi$
$110$	−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	$0.00160804\pi$
$113$			0.107402i			0.0101035i	−0.999987	+	0.00505177i	$0.998392\pi$
$114$	7.82213	+	4.51611i	0.732610	+	0.422972i
$115$	−0.312079	+	4.09612i	−0.0291015	+	0.381965i
$116$	−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	0.141513	−	0.989936i	$-0.454803\pi$
$137$	12.5191	−	7.22791i	1.06958	−	0.617522i	0.928067	+	0.372414i	$0.121470\pi$
$138$	5.58224	+	11.6286i	0.475192	+	0.989891i
$139$		−	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	0.846530	−	0.532342i	$-0.178688\pi$
$149$	9.87233	+	5.69979i	0.808773	+	0.466945i	−0.0377567	+	0.999287i	$0.512021\pi$
$150$	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	0.677048	−	0.735939i	$-0.263259\pi$
$157$	−3.74418	−	6.48510i	−0.298818	−	0.517567i	−0.975866	+	0.218371i	$0.929926\pi$
$158$	3.39505	−	1.96013i	0.270096	−	0.155940i
$159$	3.43689	−	5.95288i	0.272563	−	0.472094i
$160$	−14.8824			−1.17655
$161$	−8.15026	+	9.72488i	−0.642330	+	0.766428i
$162$	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	$-0.255239\pi$
$181$	18.7106			1.39075			0.695374	+	0.718648i	$0.255239\pi$
$182$	14.1753	+	1.39213i	1.05075	+	0.103191i
$183$		−	8.53137i		−	0.630657i
$184$	−37.6086	+	18.0538i	−2.77254	+	1.33094i
$185$	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	0.345114	−	0.938561i	$-0.387840\pi$
$191$	−4.07900	−	2.35501i	−0.295146	−	0.170403i	−0.640260	+	0.768158i	$0.721173\pi$
$192$	−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	0.917927	−	0.396750i	$-0.129862\pi$
$199$	1.62746	+	2.81885i	0.115368	+	0.199823i	−0.802559	+	0.596573i	$0.796529\pi$
$200$	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
$207$	−0.364334	+	4.78197i	−0.0253230	+	0.332370i
$208$	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	0.839670	−	0.543097i	$-0.182749\pi$
$227$	−0.760880	−	1.31788i	−0.0505014	−	0.0874710i	−0.890171	+	0.455626i	$0.849415\pi$
$228$	−15.2222	+	8.78854i	−1.00811	+	0.582035i
$229$	−0.936409	+	1.62191i	−0.0618796	+	0.107179i	−0.895306	−	0.445452i	$-0.853043\pi$
$229$	−0.936409	+	1.62191i	−0.0618796	+	0.107179i	0.833426	+	0.552631i	$0.186376\pi$
$230$	−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	0.935434	−	0.353501i	$-0.115009\pi$
$241$	2.50834	+	4.34458i	0.161576	+	0.279859i	−0.773858	+	0.633359i	$0.781675\pi$
$242$	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	$-0.615604\pi$
$251$	−11.2564			−0.710498			−0.355249	+	0.934772i	$0.615604\pi$
$252$	−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	−0.264921	−	0.964270i	$-0.585346\pi$
$263$	7.09833	−	4.09822i	0.437702	−	0.252707i	0.702622	+	0.711563i	$0.252012\pi$
$264$	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
$276$	−25.0296	−	1.90698i	−1.50660	−	0.114787i
$277$	−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	$-0.829374\pi$
$281$		−	17.1229i		−	1.02147i	0.859739	−	0.510734i	$-0.170626\pi$
$282$	7.04534	−	12.2029i	0.419544	−	0.726672i
$283$	10.1703	+	17.6154i	0.604559	+	1.04713i	0.992121	+	0.125283i	$0.0399839\pi$
$283$	10.1703	+	17.6154i	0.604559	+	1.04713i	−0.387562	+	0.921844i	$0.626683\pi$
$284$	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	$-0.745996\pi$
$293$	−23.9010			−1.39631			−0.698156	+	0.715946i	$0.745996\pi$
$294$	−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
$299$	4.15423	+	8.65382i	0.240245	+	0.500464i
$300$			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	−0.728767	−	0.684762i	$-0.759906\pi$
$313$	4.04501	−	7.00617i	0.228638	−	0.396012i	0.957405	+	0.288750i	$0.0932396\pi$
$314$	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
$322$	−11.6915	−	32.0625i	−0.651541	−	1.78678i
$323$	−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	$0.307888\pi$
$337$			30.2288i			1.64667i	−0.567559	+	0.823333i	$0.692112\pi$
$338$	−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
$345$	−1.77779	−	3.70338i	−0.0957129	−	0.199383i
$346$	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	0.948410	−	0.317047i	$-0.102691\pi$
$359$	21.7523	+	12.5587i	1.14804	+	0.662824i	0.199634	+	0.979870i	$0.436025\pi$
$360$	−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	0.859724	−	0.510760i	$-0.170636\pi$
$367$	−0.238871	−	0.413736i	−0.0124690	−	0.0215969i	−0.872193	+	0.489163i	$0.837302\pi$
$368$	4.71011	−	61.8214i	0.245532	−	3.22266i
$369$	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	0.420820	−	0.907144i	$-0.361742\pi$
$373$	−2.98158	−	1.72142i	−0.154380	−	0.0891316i	−0.575200	+	0.818013i	$0.695076\pi$
$374$	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	$-0.815998\pi$
$379$		−	21.2746i		−	1.09280i	0.837524	−	0.546401i	$-0.184002\pi$
$380$	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	−0.966426	−	0.256945i	$-0.917284\pi$
$383$	−5.10185	+	8.83667i	−0.260692	+	0.451533i	0.705734	+	0.708477i	$0.250618\pi$
$384$		−	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	−0.196213	−	0.980561i	$-0.562864\pi$
$389$	10.9438	−	6.31840i	0.554872	−	0.320356i	0.751085	+	0.660206i	$0.229531\pi$
$390$	−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	0.564863	−	0.825185i	$-0.308929\pi$
$401$	2.65659	+	1.53378i	0.132664	+	0.0765933i	−0.432199	+	0.901778i	$0.642262\pi$
$402$	−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	$-0.499551\pi$
$419$	0.0577500			0.00282127			0.00141064	+	0.999999i	$0.499551\pi$
$420$	6.90668	−	9.64398i	0.337011	−	0.470578i
$421$			18.2698i			0.890418i	0.895427	+	0.445209i	$0.146871\pi$
$421$			18.2698i			0.890418i	−0.895427	+	0.445209i	$0.853129\pi$
$422$	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	−0.809154	−	0.587597i	$-0.800074\pi$
$431$	−14.6332	+	8.44848i	−0.704856	+	0.406949i	0.104297	+	0.994546i	$0.466741\pi$
$432$	−11.1960	−	6.46400i	−0.538667	−	0.311000i
$433$	20.1013			0.966008			0.483004	−	0.875618i	$-0.339546\pi$
$433$	20.1013			0.966008			0.483004	+	0.875618i	$0.339546\pi$
$434$	−15.8332	−	34.9185i	−0.760017	−	1.67614i
$435$			3.22154i			0.154461i
$436$	−20.0193	−	11.5581i	−0.958750	−	0.553535i
$437$	1.22349	−	16.0586i	0.0585275	−	0.768187i
$438$	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	−0.187779	−	0.982211i	$-0.560129\pi$
$457$	−24.2056	−	13.9751i	−1.13229	−	0.653727i	−0.944509	+	0.328484i	$0.893462\pi$
$458$	−2.51860	−	4.36234i	−0.117686	−	0.203839i
$459$	−4.80127	+	2.77202i	−0.224104	+	0.129387i
$460$	19.3840	−	9.30521i	0.903785	−	0.433858i
$461$			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	$-0.508073\pi$
$467$	18.4349	−	31.9303i	0.853068	−	1.47756i	0.878426	−	0.477878i	$-0.158594\pi$
$468$			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	$-0.933310\pi$
$479$	−14.6458	−	25.3673i	−0.669184	−	1.15906i	0.308948	−	0.951079i	$-0.400023\pi$
$480$	12.8885	−	7.44118i	0.588277	−	0.339642i
$481$	0.309678	−	0.536378i	0.0141201	−	0.0244567i
$482$	−13.4931			−0.614592
$483$	2.19589	−	12.4971i	0.0999165	−	0.568639i
$484$	−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	$-0.257567\pi$
$503$	30.9546			1.38020			0.690099	+	0.723715i	$0.257567\pi$
$504$	2.24939	−	22.9044i	0.100196	−	1.02024i
$505$			3.63839i			0.161906i
$506$	35.8692	+	74.7206i	1.59458	+	3.32173i
$507$	−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	$-0.932953\pi$
$521$	−15.2934	−	26.4890i	−0.670017	−	1.16050i	0.307882	−	0.951425i	$-0.400380\pi$
$522$	5.05781	+	8.76038i	0.221374	+	0.383431i
$523$	5.93307	−	10.2764i	0.259435	−	0.449355i	−0.706656	−	0.707558i	$-0.749797\pi$
$523$	5.93307	−	10.2764i	0.259435	−	0.449355i	0.966091	+	0.258203i	$0.0831303\pi$
$524$			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
$529$	14.3849	−	17.9464i	0.625430	−	0.780280i
$530$	−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	−0.789765	−	0.613409i	$-0.789798\pi$
$557$	−15.4213	+	8.90346i	−0.653419	+	0.377252i	0.136346	+	0.990661i	$0.456464\pi$
$558$	−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	$0.0192972\pi$
$563$	13.0870	+	22.6673i	0.551551	+	0.955315i	−0.446612	+	0.894728i	$0.647369\pi$
$564$	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	0.930954	−	0.365135i	$-0.118977\pi$
$569$	25.7672	+	14.8767i	1.08022	+	0.623663i	0.149261	+	0.988798i	$0.452311\pi$
$570$	6.70024	−	3.86838i	0.280642	−	0.162029i
$571$	26.7991	−	15.4725i	1.12151	−	0.647503i	0.179722	−	0.983717i	$-0.442480\pi$
$571$	26.7991	−	15.4725i	1.12151	−	0.647503i	0.941785	+	0.336214i	$0.109147\pi$
$572$	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
$598$	−25.7440	−	1.96141i	−1.05275	−	0.0802080i
$599$	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	−0.992585	−	0.121550i	$-0.961214\pi$
$613$	−34.2566	+	19.7781i	−1.38361	+	0.798829i	−0.391028	+	0.920379i	$0.627880\pi$
$614$	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	$-0.799957\pi$
$617$		−	29.2060i		−	1.17579i	0.808937	−	0.587895i	$-0.200043\pi$
$618$	32.1934	+	18.5869i	1.29501	+	0.747674i
$619$	−12.3676	−	21.4212i	−0.497094	−	0.860992i	0.502900	−	0.864344i	$-0.332266\pi$
$619$	−12.3676	−	21.4212i	−0.497094	−	0.860992i	−0.999994	+	0.00335238i	$0.998933\pi$
$620$	20.9197	−	12.0780i	0.840157	−	0.485065i
$621$	−2.07546	−	4.32348i	−0.0832855	−	0.173495i
$622$			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	$-0.975819\pi$
$631$		−	3.81288i		−	0.151788i	0.997116	−	0.0758942i	$-0.0241811\pi$
$632$	−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	−0.211440	−	0.977391i	$-0.567815\pi$
$641$	13.4004	−	7.73675i	0.529286	−	0.305583i	0.740725	+	0.671808i	$0.234482\pi$
$642$	−23.9051	+	41.4048i	−0.943459	+	1.63412i
$643$	33.3852			1.31659			0.658293	−	0.752762i	$-0.271279\pi$
$643$	33.3852			1.31659			0.658293	+	0.752762i	$0.271279\pi$
$644$	65.4118	+	11.4936i	2.57759	+	0.452912i
$645$	−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	$0.177251\pi$
$659$			27.1350i			1.05703i	−0.848924	+	0.528515i	$0.822749\pi$
$660$	−14.4044	+	24.9491i	−0.560690	+	0.971143i
$661$	22.4248	+	38.8408i	0.872222	+	1.51073i	0.859692	+	0.510812i	$0.170655\pi$
$661$	22.4248	+	38.8408i	0.872222	+	1.51073i	0.0125301	+	0.999921i	$0.496011\pi$
$662$	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
$667$	−16.2604	+	7.80574i	−0.629606	+	0.302239i
$668$	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	$-0.648962\pi$
$677$	14.2421	−	24.6681i	0.547370	−	0.948072i	0.998454	−	0.0555906i	$-0.0177042\pi$
$678$	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
$690$	11.0171	+	0.839380i	0.419412	+	0.0319546i
$691$	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	$0.0344084\pi$
$701$			5.71290i			0.215773i	−0.994163	+	0.107887i	$0.965592\pi$
$702$	−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	−0.0870719	−	0.996202i	$-0.527751\pi$
$709$	−26.4498	−	15.2708i	−0.993344	−	0.573508i	−0.906272	+	0.422695i	$0.861084\pi$
$710$	−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	$-0.682778\pi$
$727$	−29.2912			−1.08635			−0.543175	+	0.839619i	$0.682778\pi$
$728$	−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	−0.890916	−	0.454169i	$-0.849936\pi$
$733$	−1.41154	+	2.44485i	−0.0521363	+	0.0903027i	0.838779	+	0.544471i	$0.183270\pi$
$734$	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	$0.221640\pi$
$743$			34.9658i			1.28277i	−0.767219	+	0.641386i	$0.778360\pi$
$744$	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	0.698431	−	0.715677i	$-0.253882\pi$
$751$	11.7250	+	6.76945i	0.427852	+	0.247021i	−0.270579	+	0.962698i	$0.587215\pi$
$752$	−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	$-0.746346\pi$
$757$		−	39.3542i		−	1.43035i	0.698944	−	0.715177i	$-0.253654\pi$
$758$	49.5548	+	28.6104i	1.79991	+	1.03918i
$759$	−2.34106	+	30.7270i	−0.0849752	+	1.11532i
$760$	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	$-0.412878\pi$
$769$	14.9912			0.540595			0.270298	+	0.962777i	$0.412878\pi$
$770$	−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	0.737465	−	0.675386i	$-0.236023\pi$
$773$	−6.01012	−	10.4098i	−0.216169	−	0.374416i	−0.953634	+	0.300970i	$0.902690\pi$

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} +(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} +(-4.32348 + 2.07546i) 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} +(0.979926 - 12.8618i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 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

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