LMFDB - Embedded newform 483.2.h.c.160.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 $ x^12 + 17x^10 + 92x^8 + 180x^6 + 92x^4 + 17*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.9
Root			$-0.562016i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.c.160.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.51820 q^{2} -1.00000i q^{3} +4.34132 q^{4} -1.21729 q^{5} -2.51820i q^{6} +(2.34908 + 1.21729i) q^{7} +5.89592 q^{8} -1.00000 q^{9} -3.06538 q^{10} -1.13179i q^{11} -4.34132i q^{12} +0.518199i q^{13} +(5.91546 + 3.06538i) q^{14} +1.21729i q^{15} +6.16445 q^{16} -3.06538 q^{17} -2.51820 q^{18} +1.13179 q^{19} -5.28466 q^{20} +(1.21729 - 2.34908i) q^{21} -2.85008i q^{22} +(-0.341325 - 4.78367i) q^{23} -5.89592i q^{24} -3.51820 q^{25} +1.30493i q^{26} +1.00000i q^{27} +(10.1981 + 5.28466i) q^{28} -2.17687 q^{29} +3.06538i q^{30} +6.85952i q^{31} +3.73147 q^{32} -1.13179 q^{33} -7.71925 q^{34} +(-2.85952 - 1.48180i) q^{35} -4.34132 q^{36} +10.1981i q^{37} +2.85008 q^{38} +0.518199 q^{39} -7.17706 q^{40} -5.00000i q^{41} +(3.06538 - 5.91546i) q^{42} -6.71726i q^{43} -4.91348i q^{44} +1.21729 q^{45} +(-0.859523 - 12.0462i) q^{46} +4.21327i q^{47} -6.16445i q^{48} +(4.03640 + 5.71905i) q^{49} -8.85952 q^{50} +3.06538i q^{51} +2.24967i q^{52} +5.41447i q^{53} +2.51820i q^{54} +1.37772i q^{55} +(13.8500 + 7.17706i) q^{56} -1.13179i q^{57} -5.48180 q^{58} -0.200848i q^{59} +5.28466i q^{60} -6.21627 q^{61} +17.2736i q^{62} +(-2.34908 - 1.21729i) q^{63} -2.93232 q^{64} -0.630799i q^{65} -2.85008 q^{66} -3.65188i q^{67} -13.3078 q^{68} +(-4.78367 + 0.341325i) q^{69} +(-7.20085 - 3.73147i) q^{70} +2.16445 q^{71} -5.89592 q^{72} -10.2248i q^{73} +25.6809i q^{74} +3.51820i q^{75} +4.91348 q^{76} +(1.37772 - 2.65868i) q^{77} +1.30493 q^{78} +8.59454i q^{79} -7.50394 q^{80} +1.00000 q^{81} -12.5910i q^{82} +11.6307 q^{83} +(5.28466 - 10.1981i) q^{84} +3.73147 q^{85} -16.9154i q^{86} +2.17687i q^{87} -6.67296i q^{88} -5.11366 q^{89} +3.06538 q^{90} +(-0.630799 + 1.21729i) q^{91} +(-1.48180 - 20.7675i) q^{92} +6.85952 q^{93} +10.6099i q^{94} -1.37772 q^{95} -3.73147i q^{96} +18.1619 q^{97} +(10.1645 + 14.4017i) q^{98} +1.13179i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64}+ \cdots + 116 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	2.51820			1.78064			0.890318	−	0.455340i	$-0.150482\pi$
$2$	2.51820			1.78064			0.890318	+	0.455340i	$0.150482\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	4.34132			2.17066
$5$	−1.21729			−0.544390			−0.272195	−	0.962242i	$-0.587750\pi$
$5$	−1.21729			−0.544390			−0.272195	+	0.962242i	$0.587750\pi$
$6$		−	2.51820i		−	1.02805i
$7$	2.34908	+	1.21729i	0.887871	+	0.460093i
$7$	2.34908	+	1.21729i	0.887871	+	0.460093i
$8$	5.89592			2.08452
$9$	−1.00000			−0.333333
$10$	−3.06538			−0.969360
$11$		−	1.13179i		−	0.341248i	−0.985336	−	0.170624i	$-0.945422\pi$
$11$		−	1.13179i		−	0.341248i	0.985336	−	0.170624i	$-0.0545784\pi$
$12$		−	4.34132i		−	1.25323i
$13$			0.518199i			0.143722i	0.997415	+	0.0718612i	$0.0228939\pi$
$13$			0.518199i			0.143722i	−0.997415	+	0.0718612i	$0.977106\pi$
$14$	5.91546	+	3.06538i	1.58097	+	0.819259i
$15$			1.21729i			0.314304i
$16$	6.16445			1.54111
$17$	−3.06538			−0.743465			−0.371732	−	0.928340i	$-0.621236\pi$
$17$	−3.06538			−0.743465			−0.371732	+	0.928340i	$0.621236\pi$
$18$	−2.51820			−0.593545
$19$	1.13179			0.259651			0.129825	−	0.991537i	$-0.458558\pi$
$19$	1.13179			0.259651			0.129825	+	0.991537i	$0.458558\pi$
$20$	−5.28466			−1.18169
$21$	1.21729	−	2.34908i	0.265635	−	0.512612i
$22$		−	2.85008i		−	0.607639i
$23$	−0.341325	−	4.78367i	−0.0711711	−	0.997464i
$23$	−0.341325	−	4.78367i	−0.0711711	−	0.997464i
$24$		−	5.89592i		−	1.20350i
$25$	−3.51820			−0.703640
$26$			1.30493i			0.255917i
$27$			1.00000i			0.192450i
$28$	10.1981	+	5.28466i	1.92727	+	0.998707i
$29$	−2.17687			−0.404235			−0.202118	−	0.979361i	$-0.564782\pi$
$29$	−2.17687			−0.404235			−0.202118	+	0.979361i	$0.564782\pi$
$30$			3.06538i			0.559660i
$31$			6.85952i			1.23201i	0.787744	+	0.616003i	$0.211249\pi$
$31$			6.85952i			1.23201i	−0.787744	+	0.616003i	$0.788751\pi$
$32$	3.73147			0.659637
$33$	−1.13179			−0.197020
$34$	−7.71925			−1.32384
$35$	−2.85952	−	1.48180i	−0.483348	−	0.250470i
$36$	−4.34132			−0.723554
$37$			10.1981i			1.67656i	0.545237	+	0.838282i	$0.316440\pi$
$37$			10.1981i			1.67656i	−0.545237	+	0.838282i	$0.683560\pi$
$38$	2.85008			0.462344
$39$	0.518199			0.0829782
$40$	−7.17706			−1.13479
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$	3.06538	−	5.91546i	0.472999	−	0.912776i
$43$		−	6.71726i		−	1.02437i	−0.858874	−	0.512186i	$-0.828836\pi$
$43$		−	6.71726i		−	1.02437i	0.858874	−	0.512186i	$-0.171164\pi$
$44$		−	4.91348i		−	0.740734i
$45$	1.21729			0.181463
$46$	−0.859523	−	12.0462i	−0.126730	−	1.77612i
$47$			4.21327i			0.614569i	0.951618	+	0.307284i	$0.0994203\pi$
$47$			4.21327i			0.614569i	−0.951618	+	0.307284i	$0.900580\pi$
$48$		−	6.16445i		−	0.889762i
$49$	4.03640	+	5.71905i	0.576628	+	0.817007i
$50$	−8.85952			−1.25293
$51$			3.06538i			0.429240i
$52$			2.24967i			0.311973i
$53$			5.41447i			0.743735i	0.928286	+	0.371867i	$0.121282\pi$
$53$			5.41447i			0.743735i	−0.928286	+	0.371867i	$0.878718\pi$
$54$			2.51820i			0.342683i
$55$			1.37772i			0.185772i
$56$	13.8500	+	7.17706i	1.85079	+	0.959075i
$57$		−	1.13179i		−	0.149910i
$58$	−5.48180			−0.719796
$59$		−	0.200848i		−	0.0261482i	−0.999915	−	0.0130741i	$-0.995838\pi$
$59$		−	0.200848i		−	0.0261482i	0.999915	−	0.0130741i	$-0.00416173\pi$
$60$			5.28466i			0.682247i
$61$	−6.21627			−0.795912			−0.397956	−	0.917405i	$-0.630280\pi$
$61$	−6.21627			−0.795912			−0.397956	+	0.917405i	$0.630280\pi$
$62$			17.2736i			2.19375i
$63$	−2.34908	−	1.21729i	−0.295957	−	0.153364i
$64$	−2.93232			−0.366540
$65$		−	0.630799i		−	0.0782410i
$66$	−2.85008			−0.350820
$67$		−	3.65188i		−	0.446148i	−0.974802	−	0.223074i	$-0.928391\pi$
$67$		−	3.65188i		−	0.446148i	0.974802	−	0.223074i	$-0.0716091\pi$
$68$	−13.3078			−1.61381
$69$	−4.78367	+	0.341325i	−0.575886	+	0.0410907i
$70$	−7.20085	−	3.73147i	−0.860666	−	0.445996i
$71$	2.16445			0.256873			0.128437	−	0.991718i	$-0.459004\pi$
$71$	2.16445			0.256873			0.128437	+	0.991718i	$0.459004\pi$
$72$	−5.89592			−0.694841
$73$		−	10.2248i		−	1.19672i	−0.801226	−	0.598362i	$-0.795818\pi$
$73$		−	10.2248i		−	1.19672i	0.801226	−	0.598362i	$-0.204182\pi$
$74$			25.6809i			2.98535i
$75$			3.51820i			0.406247i
$76$	4.91348			0.563614
$77$	1.37772	−	2.65868i	0.157006	−	0.302984i
$78$	1.30493			0.147754
$79$			8.59454i			0.966961i	0.875355	+	0.483481i	$0.160628\pi$
$79$			8.59454i			0.966961i	−0.875355	+	0.483481i	$0.839372\pi$
$80$	−7.50394			−0.838966
$81$	1.00000			0.111111
$82$		−	12.5910i		−	1.39044i
$83$	11.6307			1.27664			0.638320	−	0.769771i	$-0.279630\pi$
$83$	11.6307			1.27664			0.638320	+	0.769771i	$0.279630\pi$
$84$	5.28466	−	10.1981i	0.576604	−	1.11271i
$85$	3.73147			0.404735
$86$		−	16.9154i		−	1.82403i
$87$			2.17687i			0.233385i
$88$		−	6.67296i		−	0.711340i
$89$	−5.11366			−0.542047			−0.271024	−	0.962573i	$-0.587362\pi$
$89$	−5.11366			−0.542047			−0.271024	+	0.962573i	$0.587362\pi$
$90$	3.06538			0.323120
$91$	−0.630799	+	1.21729i	−0.0661257	+	0.127607i
$92$	−1.48180	−	20.7675i	−0.154488	−	2.16516i
$93$	6.85952			0.711299
$94$			10.6099i			1.09432i
$95$	−1.37772			−0.141351
$96$		−	3.73147i		−	0.380842i
$97$	18.1619			1.84406			0.922030	−	0.387119i	$-0.126530\pi$
$97$	18.1619			1.84406			0.922030	+	0.387119i	$0.126530\pi$
$98$	10.1645	+	14.4017i	1.02676	+	1.45479i
$99$			1.13179i			0.113749i
$100$	−15.2736			−1.52736
$101$		−	8.88350i		−	0.883941i	−0.897030	−	0.441971i	$-0.854280\pi$
$101$		−	8.88350i		−	0.883941i	0.897030	−	0.441971i	$-0.145720\pi$
$102$			7.71925i			0.764319i
$103$	−11.5009			−1.13322			−0.566610	−	0.823986i	$-0.691745\pi$
$103$	−11.5009			−1.13322			−0.566610	+	0.823986i	$0.691745\pi$
$104$			3.05526i			0.299593i
$105$	−1.48180	+	2.85952i	−0.144609	+	0.279061i
$106$			13.6347i			1.32432i
$107$		−	2.67908i		−	0.258996i	−0.991580	−	0.129498i	$-0.958663\pi$
$107$		−	2.67908i		−	0.258996i	0.991580	−	0.129498i	$-0.0413366\pi$
$108$			4.34132i			0.417744i
$109$		−	17.7464i		−	1.69980i	−0.526948	−	0.849898i	$-0.676664\pi$
$109$		−	17.7464i		−	1.69980i	0.526948	−	0.849898i	$-0.323336\pi$
$110$			3.46938i			0.330792i
$111$	10.1981			0.967965
$112$	14.4808	+	7.50394i	1.36831	+	0.709056i
$113$			2.21928i			0.208772i	0.994537	+	0.104386i	$0.0332878\pi$
$113$			2.21928i			0.208772i	−0.994537	+	0.104386i	$0.966712\pi$
$114$		−	2.85008i		−	0.266934i
$115$	0.415492	+	5.82313i	0.0387448	+	0.543009i
$116$	−9.45052			−0.877458
$117$		−	0.518199i		−	0.0479075i
$118$		−	0.505775i		−	0.0465604i
$119$	−7.20085	−	3.73147i	−0.660101	−	0.342063i
$120$			7.17706i			0.655173i
$121$	9.71905			0.883550
$122$	−15.6538			−1.41723
$123$	−5.00000			−0.450835
$124$			29.7794i			2.67427i
$125$	10.3691			0.927444
$126$	−5.91546	−	3.06538i	−0.526991	−	0.273086i
$127$	−2.73147			−0.242379			−0.121189	−	0.992629i	$-0.538671\pi$
$127$	−2.73147			−0.242379			−0.121189	+	0.992629i	$0.538671\pi$
$128$	−14.8471			−1.31231
$129$	−6.71726			−0.591422
$130$		−	1.58848i		−	0.139319i
$131$		−	18.7190i		−	1.63549i	−0.575580	−	0.817745i	$-0.695224\pi$
$131$		−	18.7190i		−	1.63549i	0.575580	−	0.817745i	$-0.304776\pi$
$132$	−4.91348			−0.427663
$133$	2.65868	+	1.37772i	0.230536	+	0.119464i
$134$		−	9.19615i		−	0.794427i
$135$		−	1.21729i		−	0.104768i
$136$	−18.0733			−1.54977
$137$			12.3027i			1.05109i	0.850765	+	0.525547i	$0.176139\pi$
$137$			12.3027i			1.05109i	−0.850765	+	0.525547i	$0.823861\pi$
$138$	−12.0462	+	0.859523i	−1.02544	+	0.0731675i
$139$			13.7794i			1.16876i	0.811482	+	0.584378i	$0.198661\pi$
$139$			13.7794i			1.16876i	−0.811482	+	0.584378i	$0.801339\pi$
$140$	−12.4141	−	6.43298i	−1.04918	−	0.543686i
$141$	4.21327			0.354821
$142$	5.45052			0.457397
$143$	0.586493			0.0490450
$144$	−6.16445			−0.513704
$145$	2.64989			0.220062
$146$		−	25.7481i		−	2.13093i
$147$	5.71905	−	4.03640i	0.471699	−	0.332916i
$148$			44.2734i			3.63925i
$149$		−	8.46473i		−	0.693458i	−0.937965	−	0.346729i	$-0.887292\pi$
$149$		−	8.46473i		−	0.693458i	0.937965	−	0.346729i	$-0.112708\pi$
$150$			8.85952i			0.723377i
$151$	17.5786			1.43052			0.715262	−	0.698857i	$-0.246307\pi$
$151$	17.5786			1.43052			0.715262	+	0.698857i	$0.246307\pi$
$152$	6.67296			0.541248
$153$	3.06538			0.247822
$154$	3.46938	−	6.69507i	0.279570	−	0.539504i
$155$		−	8.35005i		−	0.670692i
$156$	2.24967			0.180118
$157$	−18.6337			−1.48713			−0.743565	−	0.668664i	$-0.766867\pi$
$157$	−18.6337			−1.48713			−0.743565	+	0.668664i	$0.766867\pi$
$158$			21.6428i			1.72181i
$159$	5.41447			0.429395
$160$	−4.54229			−0.359100
$161$	5.02133	−	11.6527i	0.395736	−	0.918364i
$162$	2.51820			0.197848
$163$	7.23725			0.566865			0.283432	−	0.958992i	$-0.408527\pi$
$163$	7.23725			0.566865			0.283432	+	0.958992i	$0.408527\pi$
$164$		−	21.7066i		−	1.69500i
$165$	1.37772			0.107256
$166$	29.2885			2.27323
$167$		−	17.8282i		−	1.37959i	−0.724004	−	0.689795i	$-0.757701\pi$
$167$		−	17.8282i		−	1.37959i	0.724004	−	0.689795i	$-0.242299\pi$
$168$	7.17706	−	13.8500i	0.553722	−	1.06855i
$169$	12.7315			0.979344
$170$	9.39658			0.720685
$171$	−1.13179			−0.0865503
$172$		−	29.1618i		−	2.22357i
$173$		−	20.2248i		−	1.53766i	−0.639450	−	0.768832i	$-0.720838\pi$
$173$		−	20.2248i		−	1.53766i	0.639450	−	0.768832i	$-0.279162\pi$
$174$			5.48180i			0.415574i
$175$	−8.26455	−	4.28268i	−0.624741	−	0.323740i
$176$		−	6.97688i		−	0.525902i
$177$	−0.200848			−0.0150967
$178$	−12.8772			−0.965188
$179$	−10.4141			−0.778388			−0.389194	−	0.921156i	$-0.627246\pi$
$179$	−10.4141			−0.778388			−0.389194	+	0.921156i	$0.627246\pi$
$180$	5.28466			0.393895
$181$	14.0653			1.04547			0.522734	−	0.852496i	$-0.324912\pi$
$181$	14.0653			1.04547			0.522734	+	0.852496i	$0.324912\pi$
$182$	−1.58848	+	3.06538i	−0.117746	+	0.227221i
$183$			6.21627i			0.459520i
$184$	−2.01242	−	28.2041i	−0.148358	−	2.07924i
$185$		−	12.4141i		−	0.912704i
$186$	17.2736			1.26656
$187$			3.46938i			0.253706i
$188$			18.2912i			1.33402i
$189$	−1.21729	+	2.34908i	−0.0885450	+	0.170871i
$190$	−3.46938			−0.251695
$191$			12.3319i			0.892306i	0.894957	+	0.446153i	$0.147206\pi$
$191$			12.3319i			0.892306i	−0.894957	+	0.446153i	$0.852794\pi$
$192$			2.93232i			0.211622i
$193$	−3.17687			−0.228676			−0.114338	−	0.993442i	$-0.536475\pi$
$193$	−3.17687			−0.228676			−0.114338	+	0.993442i	$0.536475\pi$
$194$	45.7352			3.28360
$195$	−0.630799			−0.0451725
$196$	17.5233	+	24.8282i	1.25167	+	1.77345i
$197$	16.5661			1.18029			0.590145	−	0.807298i	$-0.299071\pi$
$197$	16.5661			1.18029			0.590145	+	0.807298i	$0.299071\pi$
$198$			2.85008i			0.202546i
$199$	−9.28165			−0.657959			−0.328980	−	0.944337i	$-0.606705\pi$
$199$	−9.28165			−0.657959			−0.328980	+	0.944337i	$0.606705\pi$
$200$	−20.7430			−1.46675
$201$	−3.65188			−0.257584
$202$		−	22.3704i		−	1.57398i
$203$	−5.11366	−	2.64989i	−0.358909	−	0.185986i
$204$			13.3078i			0.931734i
$205$			6.08646i			0.425097i
$206$	−28.9616			−2.01785
$207$	0.341325	+	4.78367i	0.0237237	+	0.332488i
$208$			3.19441i			0.221493i
$209$		−	1.28095i		−	0.0886054i
$210$	−3.73147	+	7.20085i	−0.257496	+	0.496906i
$211$	7.96360			0.548237			0.274119	−	0.961696i	$-0.411614\pi$
$211$	7.96360			0.548237			0.274119	+	0.961696i	$0.411614\pi$
$212$			23.5060i			1.61440i
$213$		−	2.16445i		−	0.148306i
$214$		−	6.74645i		−	0.461178i
$215$			8.17687i			0.557658i
$216$			5.89592i			0.401167i
$217$	−8.35005	+	16.1136i	−0.566838	+	1.09386i
$218$		−	44.6889i		−	3.02672i
$219$	−10.2248			−0.690929
$220$			5.98114i			0.403248i
$221$		−	1.58848i		−	0.106853i
$222$	25.6809			1.72359
$223$			21.0968i			1.41274i	0.707841	+	0.706372i	$0.249669\pi$
$223$			21.0968i			1.41274i	−0.707841	+	0.706372i	$0.750331\pi$
$224$	8.76554	+	4.54229i	0.585672	+	0.303495i
$225$	3.51820			0.234547
$226$			5.58858i			0.371747i
$227$	−24.8791			−1.65129			−0.825643	−	0.564193i	$-0.809188\pi$
$227$	−24.8791			−1.65129			−0.825643	+	0.564193i	$0.809188\pi$
$228$		−	4.91348i		−	0.325403i
$229$	19.5090			1.28919			0.644595	−	0.764524i	$-0.277026\pi$
$229$	19.5090			1.28919			0.644595	+	0.764524i	$0.277026\pi$
$230$	1.04629	+	14.6638i	0.0689904	+	0.966902i
$231$	−2.65868	−	1.37772i	−0.174928	−	0.0906475i
$232$	−12.8347			−0.842638
$233$	−8.34132			−0.546458			−0.273229	−	0.961949i	$-0.588092\pi$
$233$	−8.34132			−0.546458			−0.273229	+	0.961949i	$0.588092\pi$
$234$		−	1.30493i		−	0.0853058i
$235$		−	5.12878i		−	0.334565i
$236$		−	0.871947i		−	0.0567589i
$237$	8.59454			0.558275
$238$	−18.1332	−	9.39658i	−1.17540	−	0.609090i
$239$	−21.3777			−1.38281			−0.691405	−	0.722467i	$-0.743008\pi$
$239$	−21.3777			−1.38281			−0.691405	+	0.722467i	$0.743008\pi$
$240$			7.50394i			0.484377i
$241$	−8.86616			−0.571120			−0.285560	−	0.958361i	$-0.592180\pi$
$241$	−8.86616			−0.571120			−0.285560	+	0.958361i	$0.592180\pi$
$242$	24.4745			1.57328
$243$		−	1.00000i		−	0.0641500i
$244$	−26.9868			−1.72766
$245$	−4.91348	−	6.96175i	−0.313911	−	0.444770i
$246$	−12.5910			−0.802772
$247$			0.586493i			0.0373177i
$248$			40.4432i			2.56815i
$249$		−	11.6307i		−	0.737068i
$250$	26.1116			1.65144
$251$	13.0925			0.826393			0.413196	−	0.910642i	$-0.364412\pi$
$251$	13.0925			0.826393			0.413196	+	0.910642i	$0.364412\pi$
$252$	−10.1981	−	5.28466i	−0.642422	−	0.332902i
$253$	−5.41412	+	0.386309i	−0.340383	+	0.0242870i
$254$	−6.87838			−0.431588
$255$		−	3.73147i		−	0.233674i
$256$	−31.5233			−1.97021
$257$			13.9075i			0.867524i	0.901027	+	0.433762i	$0.142814\pi$
$257$			13.9075i			0.867524i	−0.901027	+	0.433762i	$0.857186\pi$
$258$	−16.9154			−1.05311
$259$	−12.4141	+	23.9563i	−0.771376	+	1.48857i
$260$		−	2.73851i		−	0.169835i
$261$	2.17687			0.134745
$262$		−	47.1383i		−	2.91221i
$263$			23.7917i			1.46706i	0.679659	+	0.733528i	$0.262128\pi$
$263$			23.7917i			1.46706i	−0.679659	+	0.733528i	$0.737872\pi$
$264$	−6.67296			−0.410692
$265$		−	6.59099i		−	0.404882i
$266$	6.69507	+	3.46938i	0.410501	+	0.212721i
$267$			5.11366i			0.312951i
$268$		−	15.8540i		−	0.968436i
$269$			5.76275i			0.351361i	0.984447	+	0.175681i	$0.0562126\pi$
$269$			5.76275i			0.351361i	−0.984447	+	0.175681i	$0.943787\pi$
$270$		−	3.06538i		−	0.186553i
$271$			11.5422i			0.701137i	0.936537	+	0.350569i	$0.114012\pi$
$271$			11.5422i			0.701137i	−0.936537	+	0.350569i	$0.885988\pi$
$272$	−18.8964			−1.14576
$273$	1.21729	+	0.630799i	0.0736739	+	0.0381777i
$274$			30.9807i			1.87161i
$275$			3.98187i			0.240116i
$276$	−20.7675	+	1.48180i	−1.25005	+	0.0891940i
$277$	24.5713			1.47634			0.738172	−	0.674613i	$-0.235689\pi$
$277$	24.5713			1.47634			0.738172	+	0.674613i	$0.235689\pi$
$278$			34.6993i			2.08113i
$279$		−	6.85952i		−	0.410669i
$280$	−16.8595	−	8.73658i	−1.00755	−	0.522111i
$281$		−	16.7001i		−	0.996244i	−0.867107	−	0.498122i	$-0.834023\pi$
$281$		−	16.7001i		−	0.996244i	0.867107	−	0.498122i	$-0.165977\pi$
$282$	10.6099			0.631808
$283$	12.2172			0.726239			0.363120	−	0.931743i	$-0.381712\pi$
$283$	12.2172			0.726239			0.363120	+	0.931743i	$0.381712\pi$
$284$	9.39658			0.557585
$285$			1.37772i			0.0816092i
$286$	1.47691			0.0873313
$287$	6.08646	−	11.7454i	0.359273	−	0.693310i
$288$	−3.73147			−0.219879
$289$	−7.60342			−0.447260
$290$	6.67296			0.391849
$291$		−	18.1619i		−	1.06467i
$292$		−	44.3893i		−	2.59769i
$293$	22.0582			1.28866			0.644328	−	0.764749i	$-0.277137\pi$
$293$	22.0582			1.28866			0.644328	+	0.764749i	$0.277137\pi$
$294$	14.4017	−	10.1645i	0.839924	−	0.592803i
$295$			0.244491i			0.0142348i
$296$			60.1274i			3.49484i
$297$	1.13179			0.0656732
$298$		−	21.3159i		−	1.23480i
$299$	2.47889	−	0.176874i	0.143358	−	0.0102289i
$300$			15.2736i			0.881824i
$301$	8.17687	−	15.7794i	0.471307	−	0.909511i
$302$	44.2663			2.54724
$303$	−8.88350			−0.510344
$304$	6.97688			0.400151
$305$	7.56702			0.433286
$306$	7.71925			0.441280
$307$		−	20.0167i		−	1.14241i	−0.820807	−	0.571206i	$-0.806476\pi$
$307$		−	20.0167i		−	1.14241i	0.820807	−	0.571206i	$-0.193524\pi$
$308$	5.98114	−	11.5422i	0.340807	−	0.657676i
$309$			11.5009i			0.654265i
$310$		−	21.0271i		−	1.19426i
$311$			15.7430i			0.892705i	0.894857	+	0.446352i	$0.147277\pi$
$311$			15.7430i			0.892705i	−0.894857	+	0.446352i	$0.852723\pi$
$312$	3.05526			0.172970
$313$	−8.46473			−0.478455			−0.239227	−	0.970964i	$-0.576894\pi$
$313$	−8.46473			−0.478455			−0.239227	+	0.970964i	$0.576894\pi$
$314$	−46.9233			−2.64804
$315$	2.85952	+	1.48180i	0.161116	+	0.0834900i
$316$			37.3117i			2.09895i
$317$	28.1083			1.57872			0.789360	−	0.613930i	$-0.210412\pi$
$317$	28.1083			1.57872			0.789360	+	0.613930i	$0.210412\pi$
$318$	13.6347			0.764597
$319$			2.46377i			0.137945i
$320$	3.56949			0.199541
$321$	−2.67908			−0.149531
$322$	12.6447	−	29.3439i	0.704661	−	1.63527i
$323$	−3.46938			−0.193041
$324$	4.34132			0.241185
$325$		−	1.82313i		−	0.101129i
$326$	18.2248			1.00938
$327$	−17.7464			−0.981377
$328$		−	29.4796i		−	1.62774i
$329$	−5.12878	+	9.89733i	−0.282759	+	0.545658i
$330$	3.46938			0.190983
$331$	−9.22482			−0.507042			−0.253521	−	0.967330i	$-0.581589\pi$
$331$	−9.22482			−0.507042			−0.253521	+	0.967330i	$0.581589\pi$
$332$	50.4928			2.77115
$333$		−	10.1981i		−	0.558855i
$334$		−	44.8950i		−	2.45655i
$335$			4.44540i			0.242878i
$336$	7.50394	−	14.4808i	0.409374	−	0.789993i
$337$		−	14.0794i		−	0.766953i	−0.923551	−	0.383476i	$-0.874727\pi$
$337$		−	14.0794i		−	0.766953i	0.923551	−	0.383476i	$-0.125273\pi$
$338$	32.0604			1.74385
$339$	2.21928			0.120535
$340$	16.1995			0.878543
$341$	7.76355			0.420420
$342$	−2.85008			−0.154115
$343$	2.52009	+	18.3480i	0.136072	+	0.990699i
$344$		−	39.6044i		−	2.13533i
$345$	5.82313	−	0.415492i	0.313507	−	0.0223693i
$346$		−	50.9301i		−	2.73802i
$347$	−4.50578			−0.241883			−0.120941	−	0.992660i	$-0.538591\pi$
$347$	−4.50578			−0.241883			−0.120941	+	0.992660i	$0.538591\pi$
$348$			9.45052i			0.506601i
$349$			11.8522i			0.634434i	0.948353	+	0.317217i	$0.102748\pi$
$349$			11.8522i			0.634434i	−0.948353	+	0.317217i	$0.897252\pi$
$350$	−20.8118	−	10.7846i	−1.11244	−	0.576463i
$351$	−0.518199			−0.0276594
$352$		−	4.22325i		−	0.225100i
$353$			24.0167i			1.27828i	0.769091	+	0.639139i	$0.220709\pi$
$353$			24.0167i			1.27828i	−0.769091	+	0.639139i	$0.779291\pi$
$354$	−0.505775			−0.0268817
$355$	−2.63477			−0.139839
$356$	−22.2001			−1.17660
$357$	−3.73147	+	7.20085i	−0.197490	+	0.381109i
$358$	−26.2248			−1.38602
$359$			1.21729i			0.0642462i	0.999484	+	0.0321231i	$0.0102269\pi$
$359$			1.21729i			0.0642462i	−0.999484	+	0.0321231i	$0.989773\pi$
$360$	7.17706			0.378264
$361$	−17.7190			−0.932581
$362$	35.4193			1.86160
$363$		−	9.71905i		−	0.510118i
$364$	−2.73851	+	5.28466i	−0.143537	+	0.276992i
$365$			12.4466i			0.651485i
$366$			15.6538i			0.818237i
$367$	10.7434			0.560803			0.280401	−	0.959883i	$-0.409532\pi$
$367$	10.7434			0.560803			0.280401	+	0.959883i	$0.409532\pi$
$368$	−2.10408	−	29.4887i	−0.109683	−	1.53720i
$369$			5.00000i			0.260290i
$370$		−	31.2612i		−	1.62519i
$371$	−6.59099	+	12.7190i	−0.342187	+	0.660340i
$372$	29.7794			1.54399
$373$		−	28.3308i		−	1.46691i	−0.679735	−	0.733457i	$-0.737905\pi$
$373$		−	28.3308i		−	1.46691i	0.679735	−	0.733457i	$-0.262095\pi$
$374$			8.73658i			0.451758i
$375$		−	10.3691i		−	0.535460i
$376$			24.8411i			1.28108i
$377$		−	1.12805i		−	0.0580977i
$378$	−3.06538	+	5.91546i	−0.157666	+	0.304259i
$379$		−	4.86917i		−	0.250112i	−0.992150	−	0.125056i	$-0.960089\pi$
$379$		−	4.86917i		−	0.250112i	0.992150	−	0.125056i	$-0.0399111\pi$
$380$	−5.98114			−0.306826
$381$			2.73147i			0.139937i
$382$			31.0542i			1.58887i
$383$	−34.6326			−1.76964			−0.884822	−	0.465930i	$-0.845720\pi$
$383$	−34.6326			−1.76964			−0.884822	+	0.465930i	$0.845720\pi$
$384$			14.8471i			0.757663i
$385$	−1.67709	+	3.23639i	−0.0854725	+	0.164941i
$386$	−8.00000			−0.407189
$387$			6.71726i			0.341458i
$388$	78.8466			4.00283
$389$			11.6307i			0.589702i	0.955543	+	0.294851i	$0.0952700\pi$
$389$			11.6307i			0.589702i	−0.955543	+	0.294851i	$0.904730\pi$
$390$	−1.58848			−0.0804357
$391$	1.04629	+	14.6638i	0.0529132	+	0.741580i
$392$	23.7983	+	33.7190i	1.20199	+	1.70307i
$393$	−18.7190			−0.944251
$394$	41.7168			2.10166
$395$		−	10.4621i		−	0.526404i
$396$			4.91348i			0.246911i
$397$		−	27.5109i		−	1.38073i	−0.723460	−	0.690366i	$-0.757450\pi$
$397$		−	27.5109i		−	1.38073i	0.723460	−	0.690366i	$-0.242550\pi$
$398$	−23.3731			−1.17159
$399$	1.37772	−	2.65868i	0.0689724	−	0.133100i
$400$	−21.6878			−1.08439
$401$		−	15.1679i		−	0.757450i	−0.925509	−	0.378725i	$-0.876363\pi$
$401$		−	15.1679i		−	0.757450i	0.925509	−	0.378725i	$-0.123637\pi$
$402$	−9.19615			−0.458662
$403$	−3.55460			−0.177067
$404$		−	38.5661i		−	1.91874i
$405$	−1.21729			−0.0604878
$406$	−12.8772	−	6.67296i	−0.639085	−	0.331173i
$407$	11.5422			0.572124
$408$			18.0733i			0.894760i
$409$			23.2861i			1.15142i	0.817653	+	0.575711i	$0.195275\pi$
$409$			23.2861i			1.15142i	−0.817653	+	0.575711i	$0.804725\pi$
$410$			15.3269i			0.756943i
$411$	12.3027			0.606849
$412$	−49.9293			−2.45984
$413$	0.244491	−	0.471809i	0.0120306	−	0.0232162i
$414$	0.859523	+	12.0462i	0.0422433	+	0.592040i
$415$	−14.1580			−0.694990
$416$			1.93364i			0.0948046i
$417$	13.7794			0.674781
$418$		−	3.22569i		−	0.157774i
$419$	−5.31385			−0.259598			−0.129799	−	0.991540i	$-0.541433\pi$
$419$	−5.31385			−0.259598			−0.129799	+	0.991540i	$0.541433\pi$
$420$	−6.43298	+	12.4141i	−0.313897	+	0.605747i
$421$			16.1136i			0.785329i	0.919682	+	0.392664i	$0.128447\pi$
$421$			16.1136i			0.785329i	−0.919682	+	0.392664i	$0.871553\pi$
$422$	20.0539			0.976210
$423$		−	4.21327i		−	0.204856i
$424$			31.9233i			1.55033i
$425$	10.7846			0.523132
$426$		−	5.45052i		−	0.264078i
$427$	−14.6025	−	7.56702i	−0.706667	−	0.366194i
$428$		−	11.6307i		−	0.562193i
$429$		−	0.586493i		−	0.0283162i
$430$			20.5910i			0.992986i
$431$		−	11.4274i		−	0.550441i	−0.961381	−	0.275220i	$-0.911249\pi$
$431$		−	11.4274i		−	0.550441i	0.961381	−	0.275220i	$-0.0887508\pi$
$432$			6.16445i			0.296587i
$433$	13.5351			0.650458			0.325229	−	0.945635i	$-0.394559\pi$
$433$	13.5351			0.650458			0.325229	+	0.945635i	$0.394559\pi$
$434$	−21.0271	+	40.5772i	−1.00933	+	1.94777i
$435$		−	2.64989i		−	0.127053i
$436$		−	77.0428i		−	3.68968i
$437$	−0.386309	−	5.41412i	−0.0184796	−	0.258992i
$438$	−25.7481			−1.23029
$439$			36.0415i			1.72017i	0.510153	+	0.860084i	$0.329589\pi$
$439$			36.0415i			1.72017i	−0.510153	+	0.860084i	$0.670411\pi$
$440$			8.12294i			0.387246i
$441$	−4.03640	−	5.71905i	−0.192209	−	0.272336i
$442$		−	4.00010i		−	0.190266i
$443$	−32.8034			−1.55854			−0.779268	−	0.626691i	$-0.784409\pi$
$443$	−32.8034			−1.55854			−0.779268	+	0.626691i	$0.784409\pi$
$444$	44.2734			2.10112
$445$	6.22482			0.295085
$446$			53.1259i			2.51558i
$447$	−8.46473			−0.400368
$448$	−6.88826	−	3.56949i	−0.325440	−	0.168643i
$449$	−20.7430			−0.978924			−0.489462	−	0.872025i	$-0.662807\pi$
$449$	−20.7430			−0.978924			−0.489462	+	0.872025i	$0.662807\pi$
$450$	8.85952			0.417642
$451$	−5.65896			−0.266470
$452$			9.63461i			0.453174i
$453$		−	17.5786i		−	0.825913i
$454$	−62.6506			−2.94034
$455$	0.767868	−	1.48180i	0.0359982	−	0.0694679i
$456$		−	6.67296i		−	0.312490i
$457$			3.13887i			0.146830i	0.997301	+	0.0734152i	$0.0233898\pi$
$457$			3.13887i			0.146830i	−0.997301	+	0.0734152i	$0.976610\pi$
$458$	49.1275			2.29558
$459$		−	3.06538i		−	0.143080i
$460$	1.80379	+	25.2801i	0.0841019	+	1.17869i
$461$			39.0094i			1.81685i	0.418051	+	0.908423i	$0.362713\pi$
$461$			39.0094i			1.81685i	−0.418051	+	0.908423i	$0.637287\pi$
$462$	−6.69507	−	3.46938i	−0.311483	−	0.161410i
$463$	−20.2299			−0.940165			−0.470082	−	0.882623i	$-0.655776\pi$
$463$	−20.2299			−0.940165			−0.470082	+	0.882623i	$0.655776\pi$
$464$	−13.4192			−0.622972
$465$	−8.35005			−0.387224
$466$	−21.0051			−0.973043
$467$	12.4617			0.576660			0.288330	−	0.957531i	$-0.406900\pi$
$467$	12.4617			0.576660			0.288330	+	0.957531i	$0.406900\pi$
$468$		−	2.24967i		−	0.103991i
$469$	4.44540	−	8.57857i	0.205270	−	0.396122i
$470$		−	12.9153i		−	0.595738i
$471$			18.6337i			0.858595i
$472$		−	1.18418i		−	0.0545065i
$473$	−7.60254			−0.349565
$474$	21.6428			0.994085
$475$	−3.98187			−0.182701
$476$	−31.2612	−	16.1995i	−1.43286	−	0.742504i
$477$		−	5.41447i		−	0.247912i
$478$	−53.8334			−2.46228
$479$	25.2363			1.15307			0.576537	−	0.817071i	$-0.304404\pi$
$479$	25.2363			1.15307			0.576537	+	0.817071i	$0.304404\pi$
$480$			4.54229i			0.207326i
$481$	−5.28466			−0.240960
$482$	−22.3268			−1.01696
$483$	−11.6527	−	5.02133i	−0.530218	−	0.228478i
$484$	42.1935			1.91789
$485$	−22.1083			−1.00389
$486$		−	2.51820i		−	0.114228i
$487$	−19.0531			−0.863377			−0.431688	−	0.902023i	$-0.642082\pi$
$487$	−19.0531			−0.863377			−0.431688	+	0.902023i	$0.642082\pi$
$488$	−36.6506			−1.65910
$489$		−	7.23725i		−	0.327280i
$490$	−12.3731	−	17.5311i	−0.558960	−	0.791973i
$491$	−12.8471			−0.579782			−0.289891	−	0.957060i	$-0.593619\pi$
$491$	−12.8471			−0.579782			−0.289891	+	0.957060i	$0.593619\pi$
$492$	−21.7066			−0.978610
$493$	6.67296			0.300535
$494$			1.47691i			0.0664492i
$495$		−	1.37772i		−	0.0619240i
$496$			42.2852i			1.89866i
$497$	5.08448	+	2.63477i	0.228070	+	0.118186i
$498$		−	29.2885i		−	1.31245i
$499$	−8.62228			−0.385986			−0.192993	−	0.981200i	$-0.561819\pi$
$499$	−8.62228			−0.385986			−0.192993	+	0.981200i	$0.561819\pi$
$500$	45.0158			2.01317
$501$	−17.8282			−0.796507
$502$	32.9696			1.47150
$503$	−3.30988			−0.147580			−0.0737900	−	0.997274i	$-0.523509\pi$
$503$	−3.30988			−0.147580			−0.0737900	+	0.997274i	$0.523509\pi$
$504$	−13.8500	−	7.17706i	−0.616929	−	0.319692i
$505$			10.8138i			0.481208i
$506$	−13.6338	+	0.972802i	−0.606098	+	0.0432463i
$507$		−	12.7315i		−	0.565424i
$508$	−11.8582			−0.526122
$509$			8.92077i			0.395406i	0.980262	+	0.197703i	$0.0633482\pi$
$509$			8.92077i			0.395406i	−0.980262	+	0.197703i	$0.936652\pi$
$510$		−	9.39658i		−	0.416088i
$511$	12.4466	−	24.0190i	0.550605	−	1.06254i
$512$	−49.6878			−2.19591
$513$			1.13179i			0.0499698i
$514$			35.0218i			1.54474i
$515$	14.0000			0.616914
$516$	−29.1618			−1.28378
$517$	4.76855			0.209720
$518$	−31.2612	+	60.3267i	−1.37354	+	2.65060i
$519$	−20.2248			−0.887771
$520$		−	3.71914i		−	0.163095i
$521$	−42.6255			−1.86746			−0.933729	−	0.357980i	$-0.883465\pi$
$521$	−42.6255			−1.86746			−0.933729	+	0.357980i	$0.883465\pi$
$522$	5.48180			0.239932
$523$	−20.5553			−0.898819			−0.449410	−	0.893326i	$-0.648366\pi$
$523$	−20.5553			−0.898819			−0.449410	+	0.893326i	$0.648366\pi$
$524$		−	81.2655i		−	3.55010i
$525$	−4.28268	+	8.26455i	−0.186911	+	0.360694i
$526$			59.9121i			2.61229i
$527$		−	21.0271i		−	0.915954i
$528$	−6.97688			−0.303630
$529$	−22.7670	+	3.26557i	−0.989869	+	0.141981i
$530$		−	16.5974i		−	0.720946i
$531$			0.200848i			0.00871606i
$532$	11.5422	+	5.98114i	0.500417	+	0.259315i
$533$	2.59099			0.112228
$534$			12.8772i			0.557252i
$535$			3.26122i			0.140995i
$536$		−	21.5312i		−	0.930005i
$537$			10.4141i			0.449402i
$538$			14.5118i			0.625646i
$539$	6.47277	−	4.56836i	0.278802	−	0.196773i
$540$		−	5.28466i		−	0.227416i
$541$	5.98027			0.257112			0.128556	−	0.991702i	$-0.458966\pi$
$541$	5.98027			0.257112			0.128556	+	0.991702i	$0.458966\pi$
$542$			29.0655i			1.24847i
$543$		−	14.0653i		−	0.603601i
$544$	−11.4384			−0.490417
$545$			21.6025i			0.925351i
$546$	3.06538	+	1.58848i	0.131186	+	0.0679806i
$547$	4.06037			0.173609			0.0868045	−	0.996225i	$-0.472334\pi$
$547$	4.06037			0.173609			0.0868045	+	0.996225i	$0.472334\pi$
$548$			53.4102i			2.28157i
$549$	6.21627			0.265304
$550$			10.0271i			0.427559i
$551$	−2.46377			−0.104960
$552$	−28.2041	+	2.01242i	−1.20045	+	0.0856544i
$553$	−10.4621	+	20.1893i	−0.444892	+	0.858536i
$554$	61.8753			2.62883
$555$	−12.4141			−0.526950
$556$			59.8209i			2.53697i
$557$		−	2.49295i		−	0.105630i	−0.998604	−	0.0528149i	$-0.983181\pi$
$557$		−	2.49295i		−	0.105630i	0.998604	−	0.0528149i	$-0.0168193\pi$
$558$		−	17.2736i		−	0.731252i
$559$	3.48088			0.147225
$560$	−17.6274	−	9.13449i	−0.744893	−	0.386003i
$561$	3.46938			0.146477
$562$		−	42.0542i		−	1.77395i
$563$	−0.846107			−0.0356592			−0.0178296	−	0.999841i	$-0.505676\pi$
$563$	−0.846107			−0.0356592			−0.0178296	+	0.999841i	$0.505676\pi$
$564$	18.2912			0.770198
$565$		−	2.70151i		−	0.113653i
$566$	30.7654			1.29317
$567$	2.34908	+	1.21729i	0.0986523	+	0.0511215i
$568$	12.7614			0.535458
$569$		−	40.2916i		−	1.68911i	−0.535469	−	0.844555i	$-0.679865\pi$
$569$		−	40.2916i		−	1.68911i	0.535469	−	0.844555i	$-0.320135\pi$
$570$			3.46938i			0.145316i
$571$			38.1275i			1.59559i	0.602930	+	0.797794i	$0.294000\pi$
$571$			38.1275i			1.59559i	−0.602930	+	0.797794i	$0.706000\pi$
$572$	2.54616			0.106460
$573$	12.3319			0.515173
$574$	15.3269	−	29.5773i	0.639733	−	1.23453i
$575$	1.20085	+	16.8299i	0.0500788	+	0.701855i
$576$	2.93232			0.122180
$577$		−	23.7918i		−	0.990467i	−0.868760	−	0.495234i	$-0.835082\pi$
$577$		−	23.7918i		−	0.990467i	0.868760	−	0.495234i	$-0.164918\pi$
$578$	−19.1469			−0.796407
$579$			3.17687i			0.132026i
$580$	11.5040			0.477679
$581$	27.3216	+	14.1580i	1.13349	+	0.587373i
$582$		−	45.7352i		−	1.89579i
$583$	6.12805			0.253798
$584$		−	60.2847i		−	2.49460i
$585$			0.630799i			0.0260803i
$586$	55.5470			2.29463
$587$			16.3049i			0.672976i	0.941688	+	0.336488i	$0.109239\pi$
$587$			16.3049i			0.672976i	−0.941688	+	0.336488i	$0.890761\pi$
$588$	24.8282	−	17.5233i	1.02390	−	0.722649i
$589$			7.76355i			0.319892i
$590$			0.615677i			0.0253470i
$591$		−	16.5661i		−	0.681440i
$592$			62.8659i			2.58377i
$593$			3.57346i			0.146744i	0.997305	+	0.0733721i	$0.0233761\pi$
$593$			3.57346i			0.146744i	−0.997305	+	0.0733721i	$0.976624\pi$
$594$	2.85008			0.116940
$595$	8.76554	+	4.54229i	0.359352	+	0.186216i
$596$		−	36.7481i		−	1.50526i
$597$			9.28165i			0.379873i
$598$	6.24234	−	0.445404i	0.255268	−	0.0182139i
$599$	−16.3100			−0.666410			−0.333205	−	0.942854i	$-0.608130\pi$
$599$	−16.3100			−0.666410			−0.333205	+	0.942854i	$0.608130\pi$
$600$			20.7430i			0.846830i
$601$		−	21.8771i		−	0.892384i	−0.894937	−	0.446192i	$-0.852780\pi$
$601$		−	21.8771i		−	0.892384i	0.894937	−	0.446192i	$-0.147220\pi$
$602$	20.5910	−	39.7357i	0.839226	−	1.61951i
$603$			3.65188i			0.148716i
$604$	76.3143			3.10518
$605$	−11.8309			−0.480995
$606$	−22.3704			−0.908736
$607$			17.8355i			0.723923i	0.932193	+	0.361961i	$0.117893\pi$
$607$			17.8355i			0.723923i	−0.932193	+	0.361961i	$0.882107\pi$
$608$	4.22325			0.171275
$609$	−2.64989	+	5.11366i	−0.107379	+	0.207216i
$610$	19.0553			0.771525
$611$	−2.18331			−0.0883273
$612$	13.3078			0.537937
$613$		−	28.6488i		−	1.15711i	−0.815642	−	0.578557i	$-0.803616\pi$
$613$		−	28.6488i		−	1.15711i	0.815642	−	0.578557i	$-0.196384\pi$
$614$		−	50.4059i		−	2.03422i
$615$	6.08646			0.245430
$616$	8.12294	−	15.6753i	0.327283	−	0.631577i
$617$			30.6387i			1.23347i	0.787171	+	0.616734i	$0.211545\pi$
$617$			30.6387i			1.23347i	−0.787171	+	0.616734i	$0.788455\pi$
$618$			28.9616i			1.16501i
$619$	−27.1135			−1.08979			−0.544893	−	0.838506i	$-0.683430\pi$
$619$	−27.1135			−1.08979			−0.544893	+	0.838506i	$0.683430\pi$
$620$		−	36.2503i		−	1.45585i
$621$	4.78367	−	0.341325i	0.191962	−	0.0136969i
$622$			39.6441i			1.58958i
$623$	−12.0124	−	6.22482i	−0.481268	−	0.249392i
$624$	3.19441			0.127879
$625$	4.96872			0.198749
$626$	−21.3159			−0.851954
$627$	−1.28095			−0.0511563
$628$	−80.8949			−3.22806
$629$		−	31.2612i		−	1.24647i
$630$	7.20085	+	3.73147i	0.286889	+	0.148665i
$631$		−	39.5904i		−	1.57607i	−0.615631	−	0.788034i	$-0.711099\pi$
$631$		−	39.5904i		−	1.57607i	0.615631	−	0.788034i	$-0.288901\pi$
$632$			50.6727i			2.01565i
$633$		−	7.96360i		−	0.316525i
$634$	70.7823			2.81113
$635$	3.32500			0.131949
$636$	23.5060			0.932072
$637$	−2.96360	+	2.09166i	−0.117422	+	0.0828744i
$638$			6.20426i			0.245629i
$639$	−2.16445			−0.0856243
$640$	18.0733			0.714409
$641$			27.2725i			1.07720i	0.842562	+	0.538600i	$0.181047\pi$
$641$			27.2725i			1.07720i	−0.842562	+	0.538600i	$0.818953\pi$
$642$	−6.74645			−0.266261
$643$	32.3127			1.27429			0.637144	−	0.770745i	$-0.280116\pi$
$643$	32.3127			1.27429			0.637144	+	0.770745i	$0.280116\pi$
$644$	21.7992	−	50.5883i	0.859009	−	1.99346i
$645$	8.17687			0.321964
$646$	−8.73658			−0.343736
$647$		−	1.89168i		−	0.0743696i	−0.999308	−	0.0371848i	$-0.988161\pi$
$647$		−	1.89168i		−	0.0743696i	0.999308	−	0.0371848i	$-0.0118390\pi$
$648$	5.89592			0.231614
$649$	−0.227318			−0.00892302
$650$		−	4.59099i		−	0.180074i
$651$	16.1136	+	8.35005i	0.631542	+	0.327264i
$652$	31.4192			1.23047
$653$	39.2903			1.53755			0.768774	−	0.639520i	$-0.220867\pi$
$653$	39.2903			1.53755			0.768774	+	0.639520i	$0.220867\pi$
$654$	−44.6889			−1.74748
$655$			22.7866i			0.890344i
$656$		−	30.8223i		−	1.20341i
$657$			10.2248i			0.398908i
$658$	−12.9153	+	24.9234i	−0.503491	+	0.971617i
$659$		−	22.8600i		−	0.890501i	−0.895406	−	0.445251i	$-0.853115\pi$
$659$		−	22.8600i		−	0.890501i	0.895406	−	0.445251i	$-0.146885\pi$
$660$	5.98114			0.232816
$661$	−46.0209			−1.79001			−0.895003	−	0.446060i	$-0.852827\pi$
$661$	−46.0209			−1.79001			−0.895003	+	0.446060i	$0.852827\pi$
$662$	−23.2299			−0.902857
$663$	−1.58848			−0.0616914
$664$	68.5739			2.66118
$665$	−3.23639	−	1.67709i	−0.125502	−	0.0650348i
$666$		−	25.6809i		−	0.995116i
$667$	0.743021	+	10.4134i	0.0287699	+	0.403210i
$668$		−	77.3982i		−	2.99463i
$669$	21.0968			0.815648
$670$			11.1944i			0.432478i
$671$			7.03552i			0.271603i
$672$	4.54229	−	8.76554i	0.175223	−	0.338138i
$673$	−11.6347			−0.448485			−0.224242	−	0.974533i	$-0.571991\pi$
$673$	−11.6347			−0.448485			−0.224242	+	0.974533i	$0.571991\pi$
$674$		−	35.4547i		−	1.36566i
$675$		−	3.51820i		−	0.135416i
$676$	55.2714			2.12582
$677$	−36.8519			−1.41633			−0.708166	−	0.706046i	$-0.750477\pi$
$677$	−36.8519			−1.41633			−0.708166	+	0.706046i	$0.750477\pi$
$678$	5.58858			0.214628
$679$	42.6638	+	22.1083i	1.63729	+	0.848439i
$680$	22.0005			0.843679
$681$			24.8791i			0.953371i
$682$	19.5502			0.748615
$683$	−20.6034			−0.788368			−0.394184	−	0.919032i	$-0.628973\pi$
$683$	−20.6034			−0.788368			−0.394184	+	0.919032i	$0.628973\pi$
$684$	−4.91348			−0.187871
$685$		−	14.9760i		−	0.572205i
$686$	6.34608	+	46.2039i	0.242294	+	1.76407i
$687$		−	19.5090i		−	0.744314i
$688$		−	41.4082i		−	1.57867i
$689$	−2.80577			−0.106891
$690$	14.6638	−	1.04629i	0.558241	−	0.0398316i
$691$		−	27.9314i		−	1.06256i	−0.847196	−	0.531281i	$-0.821711\pi$
$691$		−	27.9314i		−	1.06256i	0.847196	−	0.531281i	$-0.178289\pi$
$692$		−	87.8025i		−	3.33775i
$693$	−1.37772	+	2.65868i	−0.0523353	+	0.100995i
$694$	−11.3464			−0.430705
$695$		−	16.7736i		−	0.636258i
$696$			12.8347i			0.486497i
$697$			15.3269i			0.580549i
$698$			29.8462i			1.12970i
$699$			8.34132i			0.315498i
$700$	−35.8791	−	18.5925i	−1.35610	−	0.702730i
$701$			45.7180i			1.72675i	0.504566	+	0.863373i	$0.331653\pi$
$701$			45.7180i			1.72675i	−0.504566	+	0.863373i	$0.668347\pi$
$702$	−1.30493			−0.0492513
$703$			11.5422i			0.435321i
$704$			3.31877i			0.125081i
$705$	−5.12878			−0.193161
$706$			60.4787i			2.27615i
$707$	10.8138	−	20.8681i	0.406695	−	0.784825i
$708$	−0.871947			−0.0327698
$709$			15.4536i			0.580373i	0.956970	+	0.290186i	$0.0937173\pi$
$709$			15.4536i			0.580373i	−0.956970	+	0.290186i	$0.906283\pi$
$710$	−6.63487			−0.249002
$711$		−	8.59454i		−	0.322320i
$712$	−30.1497			−1.12991
$713$	32.8137	−	2.34132i	1.22888	−	0.0876833i
$714$	−9.39658	+	18.1332i	−0.351658	+	0.678617i
$715$	−0.713934			−0.0266996
$716$	−45.2111			−1.68962
$717$			21.3777i			0.798366i
$718$			3.06538i			0.114399i
$719$		−	23.3820i		−	0.872000i	−0.899947	−	0.436000i	$-0.856395\pi$
$719$		−	23.3820i		−	0.872000i	0.899947	−	0.436000i	$-0.143605\pi$
$720$	7.50394			0.279655
$721$	−27.0167	−	14.0000i	−1.00615	−	0.521387i
$722$	−44.6201			−1.66059
$723$			8.86616i			0.329736i
$724$	61.0621			2.26936
$725$	7.65868			0.284436
$726$		−	24.4745i		−	0.908334i
$727$	0.447787			0.0166075			0.00830376	−	0.999966i	$-0.497357\pi$
$727$	0.447787			0.0166075			0.00830376	+	0.999966i	$0.497357\pi$
$728$	−3.71914	+	7.17706i	−0.137841	+	0.266000i
$729$	−1.00000			−0.0370370
$730$			31.3430i			1.16006i
$731$			20.5910i			0.761585i
$732$			26.9868i			0.997463i
$733$	−19.9959			−0.738566			−0.369283	−	0.929317i	$-0.620397\pi$
$733$	−19.9959			−0.738566			−0.369283	+	0.929317i	$0.620397\pi$
$734$	27.0541			0.998585
$735$	−6.96175	+	4.91348i	−0.256788	+	0.181236i
$736$	−1.27364	−	17.8501i	−0.0469471	−	0.657964i
$737$	−4.13317			−0.152247
$738$			12.5910i			0.463481i
$739$	−18.8449			−0.693221			−0.346610	−	0.938009i	$-0.612667\pi$
$739$	−18.8449			−0.693221			−0.346610	+	0.938009i	$0.612667\pi$
$740$		−	53.8937i		−	1.98117i
$741$	0.586493			0.0215454
$742$	−16.5974	+	32.0291i	−0.609311	+	1.17582i
$743$		−	4.81285i		−	0.176566i	−0.996095	−	0.0882832i	$-0.971862\pi$
$743$		−	4.81285i		−	0.176566i	0.996095	−	0.0882832i	$-0.0281381\pi$
$744$	40.4432			1.48272
$745$			10.3041i			0.377511i
$746$		−	71.3427i		−	2.61204i
$747$	−11.6307			−0.425546
$748$			15.0617i			0.550710i
$749$	3.26122	−	6.29338i	0.119162	−	0.229955i
$750$		−	26.1116i		−	0.953459i
$751$		−	40.5772i		−	1.48068i	−0.672230	−	0.740342i	$-0.734663\pi$
$751$		−	40.5772i		−	1.48068i	0.672230	−	0.740342i	$-0.265337\pi$
$752$			25.9725i			0.947120i
$753$		−	13.0925i		−	0.477118i
$754$		−	2.84066i		−	0.103451i
$755$	−21.3983			−0.778763
$756$	−5.28466	+	10.1981i	−0.192201	+	0.370903i
$757$		−	39.0471i		−	1.41919i	−0.704609	−	0.709596i	$-0.748877\pi$
$757$		−	39.0471i		−	1.41919i	0.704609	−	0.709596i	$-0.251123\pi$
$758$		−	12.2615i		−	0.445359i
$759$	0.386309	+	5.41412i	0.0140221	+	0.196520i
$760$	−8.12294			−0.294650
$761$			40.8959i			1.48248i	0.671242	+	0.741238i	$0.265761\pi$
$761$			40.8959i			1.48248i	−0.671242	+	0.741238i	$0.734239\pi$
$762$			6.87838i			0.249178i
$763$	21.6025	−	41.6878i	0.782065	−	1.50920i
$764$			53.5369i			1.93690i
$765$	−3.73147			−0.134912
$766$	−87.2118			−3.15109
$767$	0.104079			0.00375808
$768$			31.5233i			1.13750i
$769$	28.8730			1.04119			0.520594	−	0.853804i	$-0.325711\pi$
$769$	28.8730			1.04119			0.520594	+	0.853804i	$0.325711\pi$
$770$	−4.22325	+	8.14986i	−0.152195	+	0.293701i
$771$	13.9075			0.500865
$772$	−13.7918			−0.496379
$773$	23.7213			0.853195			0.426598	−	0.904442i	$-0.359712\pi$
$773$	23.7213			0.853195			0.426598	+	0.904442i	$0.359712\pi$
$774$			16.9154i			0.608012i
$775$		−	24.1332i		−	0.866889i
$776$	107.081			3.84398
$777$	23.9563	+	12.4141i	0.859427	+	0.445354i
$778$			29.2885i			1.05004i
$779$		−	5.65896i		−	0.202753i
$780$	−2.73851			−0.0980542
$781$		−	2.44971i		−	0.0876574i
$782$	2.63477	+	36.9263i	0.0942192	+	1.32048i
$783$		−	2.17687i		−	0.0777951i
$784$	24.8822	+	35.2548i	0.888649	+	1.25910i
$785$	22.6826			0.809578
$786$	−47.1383			−1.68137
$787$	33.2615			1.18564			0.592822	−	0.805334i	$-0.298014\pi$
$787$	33.2615			1.18564			0.592822	+	0.805334i	$0.298014\pi$
$788$	71.9190			2.56201
$789$	23.7917			0.847005
$790$		−	26.3456i		−	0.937333i
$791$	−2.70151	+	5.21327i	−0.0960547	+	0.185363i
$792$			6.67296i			0.237113i
$793$		−	3.22126i		−	0.114390i
$794$		−	69.2779i		−	2.45858i
$795$	−6.59099			−0.233758
$796$	−40.2947			−1.42821
$797$	9.62571			0.340960			0.170480	−	0.985361i	$-0.445468\pi$
$797$	9.62571			0.340960			0.170480	+	0.985361i	$0.445468\pi$
$798$	3.46938	−	6.69507i	0.122815	−	0.237003i
$799$		−	12.9153i		−	0.456910i
$800$	−13.1281			−0.464147
$801$	5.11366			0.180682
$802$		−	38.1959i		−	1.34874i
$803$	−11.5724			−0.408380
$804$	−15.8540			−0.559127
$805$	−6.11242	+	14.1848i	−0.215435	+	0.499948i
$806$	−8.95118			−0.315292
$807$	5.76275			0.202859
$808$		−	52.3764i		−	1.84260i
$809$	20.6869			0.727312			0.363656	−	0.931533i	$-0.381528\pi$
$809$	20.6869			0.727312			0.363656	+	0.931533i	$0.381528\pi$
$810$	−3.06538			−0.107707
$811$		−	2.81158i		−	0.0987278i	−0.998781	−	0.0493639i	$-0.984281\pi$
$811$		−	2.81158i		−	0.0987278i	0.998781	−	0.0493639i	$-0.0157194\pi$
$812$	−22.2001	−	11.5040i	−0.779070	−	0.403713i
$813$	11.5422			0.404802
$814$	29.0655			1.01874
$815$	−8.80985			−0.308595
$816$			18.8964i			0.661507i
$817$		−	7.60254i		−	0.265979i
$818$			58.6389i			2.05026i
$819$	0.630799	−	1.21729i	0.0220419	−	0.0425356i
$820$			26.4233i			0.922742i
$821$	39.1092			1.36492			0.682460	−	0.730923i	$-0.260910\pi$
$821$	39.1092			1.36492			0.682460	+	0.730923i	$0.260910\pi$
$822$	30.9807			1.08058
$823$	34.8689			1.21545			0.607726	−	0.794147i	$-0.292082\pi$
$823$	34.8689			1.21545			0.607726	+	0.794147i	$0.292082\pi$
$824$	−67.8086			−2.36222
$825$	3.98187			0.138631
$826$	0.615677	−	1.18811i	0.0214221	−	0.0413396i
$827$			56.4343i			1.96241i	0.192957	+	0.981207i	$0.438192\pi$
$827$			56.4343i			1.96241i	−0.192957	+	0.981207i	$0.561808\pi$
$828$	1.48180	+	20.7675i	0.0514962	+	0.721719i
$829$		−	49.9687i		−	1.73549i	−0.497014	−	0.867743i	$-0.665570\pi$
$829$		−	49.9687i		−	1.73549i	0.497014	−	0.867743i	$-0.334430\pi$
$830$	−35.6527			−1.23752
$831$		−	24.5713i		−	0.852368i
$832$		−	1.51952i		−	0.0526800i
$833$	−12.3731	−	17.5311i	−0.428703	−	0.607416i
$834$	34.6993			1.20154
$835$			21.7022i			0.751035i
$836$		−	5.56103i		−	0.192332i
$837$	−6.85952			−0.237100
$838$	−13.3813			−0.462250
$839$	10.4958			0.362356			0.181178	−	0.983450i	$-0.442009\pi$
$839$	10.4958			0.362356			0.181178	+	0.983450i	$0.442009\pi$
$840$	−8.73658	+	16.8595i	−0.301441	+	0.581709i
$841$	−24.2612			−0.836594
$842$			40.5772i			1.39838i
$843$	−16.7001			−0.575182
$844$	34.5726			1.19004
$845$	−15.4979			−0.533145
$846$		−	10.6099i		−	0.364774i
$847$	22.8309	+	11.8309i	0.784478	+	0.406515i
$848$			33.3772i			1.14618i
$849$		−	12.2172i		−	0.419294i
$850$	27.1578			0.931506
$851$	48.7845	−	3.48088i	1.67231	−	0.119323i
$852$		−	9.39658i		−	0.321922i
$853$		−	40.7803i		−	1.39629i	−0.715956	−	0.698145i	$-0.754009\pi$
$853$		−	40.7803i		−	1.39629i	0.715956	−	0.698145i	$-0.245991\pi$
$854$	−36.7721	−	19.0553i	−1.25832	−	0.652058i
$855$	1.37772			0.0471171
$856$		−	15.7956i		−	0.539883i
$857$			22.6150i			0.772513i	0.922392	+	0.386256i	$0.126232\pi$
$857$			22.6150i			0.772513i	−0.922392	+	0.386256i	$0.873768\pi$
$858$		−	1.47691i		−	0.0504208i
$859$			35.5983i			1.21460i	0.794473	+	0.607299i	$0.207747\pi$
$859$			35.5983i			1.21460i	−0.794473	+	0.607299i	$0.792253\pi$
$860$			35.4985i			1.21049i
$861$	−11.7454	−	6.08646i	−0.400283	−	0.207426i
$862$		−	28.7766i		−	0.980134i
$863$	34.8282			1.18557			0.592784	−	0.805362i	$-0.298029\pi$
$863$	34.8282			1.18557			0.592784	+	0.805362i	$0.298029\pi$
$864$			3.73147i			0.126947i
$865$			24.6195i			0.837089i
$866$	34.0842			1.15823
$867$			7.60342i			0.258226i
$868$	−36.2503	+	69.9544i	−1.23041	+	2.37441i
$869$	9.72723			0.329974
$870$		−	6.67296i		−	0.226234i
$871$	1.89240			0.0641215
$872$		−	104.631i		−	3.54326i
$873$	−18.1619			−0.614686
$874$	−0.972802	−	13.6338i	−0.0329055	−	0.461171i
$875$	24.3580	+	12.6223i	0.823450	+	0.426711i
$876$	−44.3893			−1.49977
$877$	45.2350			1.52748			0.763740	−	0.645525i	$-0.223361\pi$
$877$	45.2350			1.52748			0.763740	+	0.645525i	$0.223361\pi$
$878$			90.7597i			3.06299i
$879$		−	22.0582i		−	0.744006i
$880$			8.49290i			0.286296i
$881$	47.2653			1.59241			0.796205	−	0.605027i	$-0.206838\pi$
$881$	47.2653			1.59241			0.796205	+	0.605027i	$0.206838\pi$
$882$	−10.1645	−	14.4017i	−0.342255	−	0.484930i
$883$	3.85865			0.129854			0.0649270	−	0.997890i	$-0.479319\pi$
$883$	3.85865			0.129854			0.0649270	+	0.997890i	$0.479319\pi$
$884$		−	6.89610i		−	0.231941i
$885$	0.244491			0.00821847
$886$	−82.6055			−2.77518
$887$		−	41.3944i		−	1.38989i	−0.719064	−	0.694944i	$-0.755429\pi$
$887$		−	41.3944i		−	1.38989i	0.719064	−	0.694944i	$-0.244571\pi$
$888$	60.1274			2.01774
$889$	−6.41645	−	3.32500i	−0.215201	−	0.111517i
$890$	15.6753			0.525439
$891$		−	1.13179i		−	0.0379165i
$892$			91.5879i			3.06659i
$893$			4.76855i			0.159573i
$894$	−21.3159			−0.712910
$895$	12.6770			0.423746
$896$	−34.8771	−	18.0733i	−1.16516	−	0.603785i
$897$	−0.176874	−	2.47889i	−0.00590565	−	0.0827678i
$898$	−52.2350			−1.74311
$899$		−	14.9323i		−	0.498021i
$900$	15.2736			0.509121
$901$		−	16.5974i		−	0.552941i
$902$	−14.2504			−0.474486
$903$	−15.7794	−	8.17687i	−0.525106	−	0.272109i
$904$			13.0847i			0.435190i
$905$	−17.1216			−0.569142
$906$		−	44.2663i		−	1.47065i
$907$		−	22.9335i		−	0.761496i	−0.924679	−	0.380748i	$-0.875667\pi$
$907$		−	22.9335i		−	0.761496i	0.924679	−	0.380748i	$-0.124333\pi$
$908$	−108.008			−3.58439
$909$			8.88350i			0.294647i
$910$	1.93364	−	3.73147i	0.0640996	−	0.123697i
$911$			7.56337i			0.250586i	0.992120	+	0.125293i	$0.0399870\pi$
$911$			7.56337i			0.250586i	−0.992120	+	0.125293i	$0.960013\pi$
$912$		−	6.97688i		−	0.231027i
$913$		−	13.1636i		−	0.435651i
$914$			7.90431i			0.261451i
$915$		−	7.56702i		−	0.250158i
$916$	84.6948			2.79840
$917$	22.7866	−	43.9726i	0.752478	−	1.45210i
$918$		−	7.71925i		−	0.254773i
$919$			27.9586i			0.922269i	0.887330	+	0.461134i	$0.152557\pi$
$919$			27.9586i			0.922269i	−0.887330	+	0.461134i	$0.847443\pi$
$920$	2.44971	+	34.3327i	0.0807645	+	1.13192i
$921$	−20.0167			−0.659571
$922$			98.2333i			3.23514i
$923$			1.12162i			0.0369184i
$924$	−11.5422	−	5.98114i	−0.379710	−	0.196765i
$925$		−	35.8791i		−	1.17970i
$926$	−50.9430			−1.67409
$927$	11.5009			0.377740
$928$	−8.12294			−0.266649
$929$			11.3298i			0.371718i	0.982576	+	0.185859i	$0.0595067\pi$
$929$			11.3298i			0.371718i	−0.982576	+	0.185859i	$0.940493\pi$
$930$	−21.0271			−0.689505
$931$	4.56836	+	6.47277i	0.149722	+	0.212137i
$932$	−36.2124			−1.18618
$933$	15.7430			0.515403
$934$	31.3811			1.02682
$935$		−	4.22325i		−	0.138115i
$936$		−	3.05526i		−	0.0998642i
$937$	−7.75154			−0.253232			−0.126616	−	0.991952i	$-0.540412\pi$
$937$	−7.75154			−0.253232			−0.126616	+	0.991952i	$0.540412\pi$
$938$	11.1944	−	21.6025i	0.365510	−	0.705348i
$939$			8.46473i			0.276236i
$940$		−	22.2657i		−	0.726228i
$941$	−4.38019			−0.142790			−0.0713950	−	0.997448i	$-0.522745\pi$
$941$	−4.38019			−0.142790			−0.0713950	+	0.997448i	$0.522745\pi$
$942$			46.9233i			1.52884i
$943$	−23.9183	+	1.70662i	−0.778889	+	0.0555753i
$944$		−	1.23812i		−	0.0402973i
$945$	1.48180	−	2.85952i	0.0482030	−	0.0930203i
$946$	−19.1447			−0.622448
$947$	4.60985			0.149800			0.0749001	−	0.997191i	$-0.476136\pi$
$947$	4.60985			0.149800			0.0749001	+	0.997191i	$0.476136\pi$
$948$	37.3117			1.21183
$949$	5.29849			0.171996
$950$	−10.0271			−0.325323
$951$		−	28.1083i		−	0.911475i
$952$	−42.4556	−	22.0005i	−1.37599	−	0.713039i
$953$			2.26047i			0.0732239i	0.999330	+	0.0366119i	$0.0116565\pi$
$953$			2.26047i			0.0732239i	−0.999330	+	0.0366119i	$0.988343\pi$
$954$		−	13.6347i		−	0.441440i
$955$		−	15.0116i		−	0.485762i
$956$	−92.8076			−3.00161
$957$	2.46377			0.0796423
$958$	63.5499			2.05321
$959$	−14.9760	+	28.9002i	−0.483601	+	0.933235i
$960$		−	3.56949i		−	0.115205i
$961$	−16.0531			−0.517841
$962$	−13.3078			−0.429062
$963$			2.67908i			0.0863320i
$964$	−38.4909			−1.23971
$965$	3.86719			0.124489
$966$	−29.3439	−	12.6447i	−0.944125	−	0.406836i
$967$	33.1820			1.06706			0.533530	−	0.845781i	$-0.320865\pi$
$967$	33.1820			1.06706			0.533530	+	0.845781i	$0.320865\pi$
$968$	57.3027			1.84178
$969$			3.46938i			0.111452i
$970$	−55.6731			−1.78756
$971$	−13.1660			−0.422517			−0.211259	−	0.977430i	$-0.567756\pi$
$971$	−13.1660			−0.422517			−0.211259	+	0.977430i	$0.567756\pi$
$972$		−	4.34132i		−	0.139248i
$973$	−16.7736	+	32.3690i	−0.537736	+	1.03770i
$974$	−47.9794			−1.53736
$975$	−1.82313			−0.0583868
$976$	−38.3199			−1.22659
$977$		−	24.5200i		−	0.784463i	−0.919866	−	0.392232i	$-0.871703\pi$
$977$		−	24.5200i		−	0.784463i	0.919866	−	0.392232i	$-0.128297\pi$
$978$		−	18.2248i		−	0.582766i
$979$			5.78760i			0.184973i
$980$	−21.3310	−	30.2232i	−0.681394	−	0.965446i
$981$			17.7464i			0.566598i
$982$	−32.3516			−1.03238
$983$	47.6949			1.52123			0.760615	−	0.649203i	$-0.224897\pi$
$983$	47.6949			1.52123			0.760615	+	0.649203i	$0.224897\pi$
$984$	−29.4796			−0.939775
$985$	−20.1658			−0.642537
$986$	16.8038			0.535143
$987$	9.89733	+	5.12878i	0.315036	+	0.163251i
$988$			2.54616i			0.0810041i
$989$	−32.1332	+	2.29277i	−1.02178	+	0.0729058i
$990$		−	3.46938i		−	0.110264i
$991$	15.9512			0.506706			0.253353	−	0.967374i	$-0.418467\pi$
$991$	15.9512			0.506706			0.253353	+	0.967374i	$0.418467\pi$
$992$			25.5961i			0.812677i
$993$			9.22482i			0.292741i
$994$	12.8037	+	6.63487i	0.406110	+	0.210445i
$995$	11.2985			0.358186
$996$		−	50.4928i		−	1.59993i
$997$		−	27.8959i		−	0.883473i	−0.897145	−	0.441736i	$-0.854363\pi$
$997$		−	27.8959i		−	0.883473i	0.897145	−	0.441736i	$-0.145637\pi$
$998$	−21.7126			−0.687301
$999$	−10.1981			−0.322655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.c.160.9	✓	12
3.2	odd	2		1449.2.h.e.1126.4		12
7.6	odd	2	inner	483.2.h.c.160.12	yes	12
21.20	even	2		1449.2.h.e.1126.2		12
23.22	odd	2	inner	483.2.h.c.160.10	yes	12
69.68	even	2		1449.2.h.e.1126.1		12
161.160	even	2	inner	483.2.h.c.160.11	yes	12
483.482	odd	2		1449.2.h.e.1126.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.c.160.9	✓	12	1.1	even	1	trivial
483.2.h.c.160.10	yes	12	23.22	odd	2	inner
483.2.h.c.160.11	yes	12	161.160	even	2	inner
483.2.h.c.160.12	yes	12	7.6	odd	2	inner
1449.2.h.e.1126.1		12	69.68	even	2
1449.2.h.e.1126.2		12	21.20	even	2
1449.2.h.e.1126.3		12	483.482	odd	2
1449.2.h.e.1126.4		12	3.2	odd	2

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.51820 q^{2} -1.00000i q^{3} +4.34132 q^{4} -1.21729 q^{5} -2.51820i q^{6} +(2.34908 + 1.21729i) q^{7} +5.89592 q^{8} -1.00000 q^{9} -3.06538 q^{10} -1.13179i q^{11} -4.34132i q^{12} +0.518199i q^{13} +(5.91546 + 3.06538i) q^{14} +1.21729i q^{15} +6.16445 q^{16} -3.06538 q^{17} -2.51820 q^{18} +1.13179 q^{19} -5.28466 q^{20} +(1.21729 - 2.34908i) q^{21} -2.85008i q^{22} +(-0.341325 - 4.78367i) q^{23} -5.89592i q^{24} -3.51820 q^{25} +1.30493i q^{26} +1.00000i q^{27} +(10.1981 + 5.28466i) q^{28} -2.17687 q^{29} +3.06538i q^{30} +6.85952i q^{31} +3.73147 q^{32} -1.13179 q^{33} -7.71925 q^{34} +(-2.85952 - 1.48180i) q^{35} -4.34132 q^{36} +10.1981i q^{37} +2.85008 q^{38} +0.518199 q^{39} -7.17706 q^{40} -5.00000i q^{41} +(3.06538 - 5.91546i) q^{42} -6.71726i q^{43} -4.91348i q^{44} +1.21729 q^{45} +(-0.859523 - 12.0462i) q^{46} +4.21327i q^{47} -6.16445i q^{48} +(4.03640 + 5.71905i) q^{49} -8.85952 q^{50} +3.06538i q^{51} +2.24967i q^{52} +5.41447i q^{53} +2.51820i q^{54} +1.37772i q^{55} +(13.8500 + 7.17706i) q^{56} -1.13179i q^{57} -5.48180 q^{58} -0.200848i q^{59} +5.28466i q^{60} -6.21627 q^{61} +17.2736i q^{62} +(-2.34908 - 1.21729i) q^{63} -2.93232 q^{64} -0.630799i q^{65} -2.85008 q^{66} -3.65188i q^{67} -13.3078 q^{68} +(-4.78367 + 0.341325i) q^{69} +(-7.20085 - 3.73147i) q^{70} +2.16445 q^{71} -5.89592 q^{72} -10.2248i q^{73} +25.6809i q^{74} +3.51820i q^{75} +4.91348 q^{76} +(1.37772 - 2.65868i) q^{77} +1.30493 q^{78} +8.59454i q^{79} -7.50394 q^{80} +1.00000 q^{81} -12.5910i q^{82} +11.6307 q^{83} +(5.28466 - 10.1981i) q^{84} +3.73147 q^{85} -16.9154i q^{86} +2.17687i q^{87} -6.67296i q^{88} -5.11366 q^{89} +3.06538 q^{90} +(-0.630799 + 1.21729i) q^{91} +(-1.48180 - 20.7675i) q^{92} +6.85952 q^{93} +10.6099i q^{94} -1.37772 q^{95} -3.73147i q^{96} +18.1619 q^{97} +(10.1645 + 14.4017i) q^{98} +1.13179i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64}+ \cdots + 116 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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