LMFDB - Embedded newform 361.2.e.m.62.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,24,0,0,0,30,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			62.3
Character	$\chi$	$=$	361.62
Dual form			361.2.e.m.99.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10467 - 0.402069i) q^{2} +(0.204136 - 1.15771i) q^{3} +(-0.473442 + 0.397265i) q^{4} +(0.946883 + 0.794529i) q^{5} +(-0.239976 - 1.36097i) q^{6} +(2.11803 + 3.66854i) q^{7} +(-1.53884 + 2.66535i) q^{8} +(1.52045 + 0.553400i) q^{9} +(1.36545 + 0.496984i) q^{10} +(1.80902 - 3.13331i) q^{11} +(0.363271 + 0.629204i) q^{12} +(-0.534434 - 3.03093i) q^{13} +(3.81475 + 3.20095i) q^{14} +(1.11313 - 0.934025i) q^{15} +(-0.413624 + 2.34578i) q^{16} +(-2.32305 + 0.845520i) q^{17} +1.90211 q^{18} -0.763932 q^{20} +(4.67948 - 1.70319i) q^{21} +(0.738570 - 4.18864i) q^{22} +(-2.00553 + 1.68284i) q^{23} +(2.77157 + 2.32563i) q^{24} +(-0.602930 - 3.41939i) q^{25} +(-1.80902 - 3.13331i) q^{26} +(2.71441 - 4.70150i) q^{27} +(-2.46015 - 0.895420i) q^{28} +(-2.47013 - 0.899053i) q^{29} +(0.854102 - 1.47935i) q^{30} +(-0.587785 - 1.01807i) q^{31} +(-0.582624 - 3.30423i) q^{32} +(-3.25818 - 2.73394i) q^{33} +(-2.22626 + 1.86805i) q^{34} +(-0.909234 + 5.15652i) q^{35} +(-0.939693 + 0.342020i) q^{36} +6.43288 q^{37} -3.61803 q^{39} +(-3.57480 + 1.30112i) q^{40} +(-1.60330 + 9.09278i) q^{41} +(4.48450 - 3.76294i) q^{42} +(-4.84618 - 4.06643i) q^{43} +(0.388289 + 2.20210i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.53884 + 2.66535i) q^{46} +(2.37542 + 0.864580i) q^{47} +(2.63130 + 0.957714i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-2.04087 - 3.53489i) q^{50} +(0.504651 + 2.86202i) q^{51} +(1.45710 + 1.22265i) q^{52} +(-0.343975 + 0.288630i) q^{53} +(1.10822 - 6.28501i) q^{54} +(4.20243 - 1.52956i) q^{55} -13.0373 q^{56} -3.09017 q^{58} +(-2.63130 + 0.957714i) q^{59} +(-0.155946 + 0.884412i) q^{60} +(-0.404367 + 0.339304i) q^{61} +(-1.05865 - 0.888311i) q^{62} +(1.19020 + 6.74997i) q^{63} +(-4.35410 - 7.54153i) q^{64} +(1.90211 - 3.29456i) q^{65} +(-4.69846 - 1.71010i) q^{66} +(-0.161170 - 0.0586610i) q^{67} +(0.763932 - 1.32317i) q^{68} +(1.53884 + 2.66535i) q^{69} +(1.06887 + 6.06185i) q^{70} +(-9.29918 - 7.80294i) q^{71} +(-3.81475 + 3.20095i) q^{72} +(1.56283 - 8.86327i) q^{73} +(7.10624 - 2.58646i) q^{74} -4.08174 q^{75} +15.3262 q^{77} +(-3.99675 + 1.45470i) q^{78} +(1.32119 - 7.49286i) q^{79} +(-2.25544 + 1.89254i) q^{80} +(-1.17041 - 0.982092i) q^{81} +(1.88480 + 10.6892i) q^{82} +(-0.618034 - 1.07047i) q^{83} +(-1.53884 + 2.66535i) q^{84} +(-2.87145 - 1.04512i) q^{85} +(-6.98844 - 2.54358i) q^{86} +(-1.54508 + 2.67617i) q^{87} +(5.56758 + 9.64333i) q^{88} +(3.08044 + 17.4701i) q^{89} +(1.80108 + 1.51128i) q^{90} +(9.98713 - 8.38020i) q^{91} +(0.280969 - 1.59345i) q^{92} +(-1.29862 + 0.472660i) q^{93} +2.97168 q^{94} -3.94427 q^{96} +(-14.7212 + 5.35806i) q^{97} +(-2.23412 + 12.6703i) q^{98} +(4.48450 - 3.76294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) $ 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	1.10467	−	0.402069i	0.781123	−	0.284306i	0.0794822	−	0.996836i	$-0.474673\pi$
$2$	1.10467	−	0.402069i	0.781123	−	0.284306i	0.701641	+	0.712531i	$0.252451\pi$
$3$	0.204136	−	1.15771i	0.117858	−	0.668405i	−0.867438	−	0.497546i	$-0.834235\pi$
$3$	0.204136	−	1.15771i	0.117858	−	0.668405i	0.985296	−	0.170859i	$-0.0546542\pi$
$4$	−0.473442	+	0.397265i	−0.236721	+	0.198632i
$5$	0.946883	+	0.794529i	0.423459	+	0.355324i	0.829477	−	0.558541i	$-0.188639\pi$
$5$	0.946883	+	0.794529i	0.423459	+	0.355324i	−0.406018	+	0.913865i	$0.633083\pi$
$6$	−0.239976	−	1.36097i	−0.0979697	−	0.555614i
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	0.919260	+	0.393651i	$0.128788\pi$
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	−0.118718	+	0.992928i	$0.537879\pi$
$8$	−1.53884	+	2.66535i	−0.544063	+	0.942344i
$9$	1.52045	+	0.553400i	0.506818	+	0.184467i
$10$	1.36545	+	0.496984i	0.431794	+	0.157160i
$11$	1.80902	−	3.13331i	0.545439	−	0.944728i	−0.453140	−	0.891439i	$-0.649696\pi$
$11$	1.80902	−	3.13331i	0.545439	−	0.944728i	0.998579	−	0.0532889i	$-0.0169704\pi$
$12$	0.363271	+	0.629204i	0.104867	+	0.181636i
$13$	−0.534434	−	3.03093i	−0.148225	−	0.840628i	−0.964721	−	0.263276i	$-0.915197\pi$
$13$	−0.534434	−	3.03093i	−0.148225	−	0.840628i	0.816495	−	0.577352i	$-0.195914\pi$
$14$	3.81475	+	3.20095i	1.01953	+	0.855490i
$15$	1.11313	−	0.934025i	0.287408	−	0.241164i
$16$	−0.413624	+	2.34578i	−0.103406	+	0.586445i
$17$	−2.32305	+	0.845520i	−0.563422	+	0.205069i	−0.608000	−	0.793937i	$-0.708028\pi$
$17$	−2.32305	+	0.845520i	−0.563422	+	0.205069i	0.0445780	+	0.999006i	$0.485806\pi$
$18$	1.90211			0.448332
$19$		0			0
$19$		0			0
$20$	−0.763932			−0.170820
$21$	4.67948	−	1.70319i	1.02115	−	0.371667i
$22$	0.738570	−	4.18864i	0.157464	−	0.893021i
$23$	−2.00553	+	1.68284i	−0.418182	+	0.350896i	−0.827471	−	0.561508i	$-0.810221\pi$
$23$	−2.00553	+	1.68284i	−0.418182	+	0.350896i	0.409289	+	0.912405i	$0.365777\pi$
$24$	2.77157	+	2.32563i	0.565745	+	0.474717i
$25$	−0.602930	−	3.41939i	−0.120586	−	0.683877i
$26$	−1.80902	−	3.13331i	−0.354777	−	0.614493i
$27$	2.71441	−	4.70150i	0.522389	−	0.904804i
$28$	−2.46015	−	0.895420i	−0.464924	−	0.169219i
$29$	−2.47013	−	0.899053i	−0.458691	−	0.166950i	0.102331	−	0.994750i	$-0.467370\pi$
$29$	−2.47013	−	0.899053i	−0.458691	−	0.166950i	−0.561023	+	0.827800i	$0.689592\pi$
$30$	0.854102	−	1.47935i	0.155937	−	0.270091i
$31$	−0.587785	−	1.01807i	−0.105569	−	0.182851i	0.808401	−	0.588632i	$-0.200333\pi$
$31$	−0.587785	−	1.01807i	−0.105569	−	0.182851i	−0.913971	+	0.405780i	$0.867000\pi$
$32$	−0.582624	−	3.30423i	−0.102994	−	0.584110i
$33$	−3.25818	−	2.73394i	−0.567177	−	0.475918i
$34$	−2.22626	+	1.86805i	−0.381800	+	0.320368i
$35$	−0.909234	+	5.15652i	−0.153689	+	0.871611i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	6.43288			1.05756			0.528780	−	0.848759i	$-0.322650\pi$
$37$	6.43288			1.05756			0.528780	+	0.848759i	$0.322650\pi$
$38$		0			0
$39$	−3.61803			−0.579349
$40$	−3.57480	+	1.30112i	−0.565226	+	0.205725i
$41$	−1.60330	+	9.09278i	−0.250394	+	1.42005i	0.557231	+	0.830357i	$0.311864\pi$
$41$	−1.60330	+	9.09278i	−0.250394	+	1.42005i	−0.807625	+	0.589696i	$0.799247\pi$
$42$	4.48450	−	3.76294i	0.691974	−	0.580635i
$43$	−4.84618	−	4.06643i	−0.739035	−	0.620124i	0.193543	−	0.981092i	$-0.438002\pi$
$43$	−4.84618	−	4.06643i	−0.739035	−	0.620124i	−0.932578	+	0.360967i	$0.882447\pi$
$44$	0.388289	+	2.20210i	0.0585368	+	0.331979i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−1.53884	+	2.66535i	−0.226890	+	0.392985i
$47$	2.37542	+	0.864580i	0.346490	+	0.126112i	0.509402	−	0.860529i	$-0.329867\pi$
$47$	2.37542	+	0.864580i	0.346490	+	0.126112i	−0.162912	+	0.986641i	$0.552089\pi$
$48$	2.63130	+	0.957714i	0.379795	+	0.138234i
$49$	−5.47214	+	9.47802i	−0.781734	+	1.35400i
$50$	−2.04087	−	3.53489i	−0.288623	−	0.499909i
$51$	0.504651	+	2.86202i	0.0706653	+	0.400763i
$52$	1.45710	+	1.22265i	0.202064	+	0.169552i
$53$	−0.343975	+	0.288630i	−0.0472487	+	0.0396463i	−0.666106	−	0.745857i	$-0.732040\pi$
$53$	−0.343975	+	0.288630i	−0.0472487	+	0.0396463i	0.618858	+	0.785503i	$0.287596\pi$
$54$	1.10822	−	6.28501i	0.150809	−	0.855281i
$55$	4.20243	−	1.52956i	0.566656	−	0.206246i
$56$	−13.0373			−1.74218
$57$		0			0
$58$	−3.09017			−0.405759
$59$	−2.63130	+	0.957714i	−0.342566	+	0.124684i	−0.507573	−	0.861609i	$-0.669457\pi$
$59$	−2.63130	+	0.957714i	−0.342566	+	0.124684i	0.165008	+	0.986292i	$0.447235\pi$
$60$	−0.155946	+	0.884412i	−0.0201325	+	0.114177i
$61$	−0.404367	+	0.339304i	−0.0517739	+	0.0434435i	−0.668307	−	0.743885i	$-0.732981\pi$
$61$	−0.404367	+	0.339304i	−0.0517739	+	0.0434435i	0.616534	+	0.787329i	$0.288536\pi$
$62$	−1.05865	−	0.888311i	−0.134448	−	0.112816i
$63$	1.19020	+	6.74997i	0.149951	+	0.850417i
$64$	−4.35410	−	7.54153i	−0.544263	−	0.942691i
$65$	1.90211	−	3.29456i	0.235928	−	0.408639i
$66$	−4.69846	−	1.71010i	−0.578341	−	0.210499i
$67$	−0.161170	−	0.0586610i	−0.0196900	−	0.00716659i	0.332156	−	0.943224i	$-0.392224\pi$
$67$	−0.161170	−	0.0586610i	−0.0196900	−	0.00716659i	−0.351846	+	0.936058i	$0.614446\pi$
$68$	0.763932	−	1.32317i	0.0926404	−	0.160458i
$69$	1.53884	+	2.66535i	0.185255	+	0.320871i
$70$	1.06887	+	6.06185i	0.127754	+	0.724530i
$71$	−9.29918	−	7.80294i	−1.10361	−	0.926039i	−0.105947	−	0.994372i	$-0.533788\pi$
$71$	−9.29918	−	7.80294i	−1.10361	−	0.926039i	−0.997663	+	0.0683331i	$0.978232\pi$
$72$	−3.81475	+	3.20095i	−0.449572	+	0.377236i
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	−0.745688	−	0.666295i	$-0.767879\pi$
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	0.928604	−	0.371072i	$-0.121010\pi$
$74$	7.10624	−	2.58646i	0.826084	−	0.300670i
$75$	−4.08174			−0.471319
$76$		0			0
$77$	15.3262			1.74659
$78$	−3.99675	+	1.45470i	−0.452543	+	0.164712i
$79$	1.32119	−	7.49286i	0.148646	−	0.843013i	−0.815721	−	0.578445i	$-0.803660\pi$
$79$	1.32119	−	7.49286i	0.148646	−	0.843013i	0.964367	−	0.264568i	$-0.0852292\pi$
$80$	−2.25544	+	1.89254i	−0.252166	+	0.211593i
$81$	−1.17041	−	0.982092i	−0.130046	−	0.109121i
$82$	1.88480	+	10.6892i	0.208141	+	1.18043i
$83$	−0.618034	−	1.07047i	−0.0678380	−	0.117499i	0.830111	−	0.557598i	$-0.188277\pi$
$83$	−0.618034	−	1.07047i	−0.0678380	−	0.117499i	−0.897949	+	0.440099i	$0.854943\pi$
$84$	−1.53884	+	2.66535i	−0.167901	+	0.290814i
$85$	−2.87145	−	1.04512i	−0.311452	−	0.113359i
$86$	−6.98844	−	2.54358i	−0.753582	−	0.274282i
$87$	−1.54508	+	2.67617i	−0.165650	+	0.286915i
$88$	5.56758	+	9.64333i	0.593506	+	1.02798i
$89$	3.08044	+	17.4701i	0.326526	+	1.85182i	0.498725	+	0.866760i	$0.333802\pi$
$89$	3.08044	+	17.4701i	0.326526	+	1.85182i	−0.172199	+	0.985062i	$0.555087\pi$
$90$	1.80108	+	1.51128i	0.189850	+	0.159303i
$91$	9.98713	−	8.38020i	1.04694	−	0.878484i
$92$	0.280969	−	1.59345i	0.0292930	−	0.166129i
$93$	−1.29862	+	0.472660i	−0.134661	+	0.0490126i
$94$	2.97168			0.306506
$95$		0			0
$96$	−3.94427			−0.402561
$97$	−14.7212	+	5.35806i	−1.49471	+	0.544029i	−0.954684	−	0.297621i	$-0.903807\pi$
$97$	−14.7212	+	5.35806i	−1.49471	+	0.544029i	−0.540023	+	0.841650i	$0.681585\pi$
$98$	−2.23412	+	12.6703i	−0.225680	+	1.27989i
$99$	4.48450	−	3.76294i	0.450709	−	0.378190i
$100$	1.64385	+	1.37936i	0.164385	+	0.137936i
$101$	−2.42140	−	13.7324i	−0.240938	−	1.36643i	−0.829740	−	0.558150i	$-0.811511\pi$
$101$	−2.42140	−	13.7324i	−0.240938	−	1.36643i	0.588802	−	0.808277i	$-0.299600\pi$
$102$	1.70820	+	2.95870i	0.169137	+	0.292955i
$103$	0.502029	−	0.869539i	0.0494663	−	0.0856782i	−0.840232	−	0.542227i	$-0.817581\pi$
$103$	0.502029	−	0.869539i	0.0494663	−	0.0856782i	0.889698	+	0.456549i	$0.150915\pi$
$104$	8.90090	+	3.23966i	0.872805	+	0.317675i
$105$	5.78415	+	2.10526i	0.564476	+	0.205452i
$106$	−0.263932	+	0.457144i	−0.0256353	+	0.0444017i
$107$	−5.79210	−	10.0322i	−0.559943	−	0.969850i	−0.997501	−	0.0706593i	$-0.977490\pi$
$107$	−5.79210	−	10.0322i	−0.559943	−	0.969850i	0.437557	−	0.899190i	$-0.355844\pi$
$108$	0.582624	+	3.30423i	0.0560630	+	0.317949i
$109$	0.556564	+	0.467013i	0.0533092	+	0.0447317i	0.669053	−	0.743215i	$-0.266700\pi$
$109$	0.556564	+	0.467013i	0.0533092	+	0.0447317i	−0.615744	+	0.787946i	$0.711144\pi$
$110$	4.02733	−	3.37933i	0.383991	−	0.322207i
$111$	1.31318	−	7.44742i	0.124642	−	0.706878i
$112$	−9.48166	+	3.45104i	−0.895932	+	0.326093i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−3.23607			−0.301765
$116$	1.52662	−	0.555645i	0.141743	−	0.0515904i
$117$	0.864733	−	4.90414i	0.0799446	−	0.453388i
$118$	−2.52166	+	2.11593i	−0.232138	+	0.194787i
$119$	−8.02212	−	6.73136i	−0.735387	−	0.617063i
$120$	0.776578	+	4.40419i	0.0708916	+	0.402046i
$121$	−1.04508	−	1.81014i	−0.0950077	−	0.164558i
$122$	−0.310271	+	0.537405i	−0.0280906	+	0.0486543i
$123$	10.1995	+	3.71232i	0.919660	+	0.334729i
$124$	0.682727	+	0.248492i	0.0613107	+	0.0223153i
$125$	5.23607	−	9.06914i	0.468328	−	0.811168i
$126$	4.02874	+	6.97798i	0.358909	+	0.621648i
$127$	−2.76855	−	15.7012i	−0.245669	−	1.39326i	−0.818934	−	0.573888i	$-0.805434\pi$
$127$	−2.76855	−	15.7012i	−0.245669	−	1.39326i	0.573264	−	0.819370i	$-0.305677\pi$
$128$	−2.70162	−	2.26693i	−0.238792	−	0.200370i
$129$	−5.69703	+	4.78037i	−0.501595	+	0.420888i
$130$	0.776578	−	4.40419i	0.0681104	−	0.386273i
$131$	4.78320	−	1.74094i	0.417910	−	0.152107i	−0.124502	−	0.992219i	$-0.539733\pi$
$131$	4.78320	−	1.74094i	0.417910	−	0.152107i	0.542412	+	0.840113i	$0.317511\pi$
$132$	2.62866			0.228795
$133$		0			0
$134$	−0.201626			−0.0174178
$135$	6.30571	−	2.29509i	0.542709	−	0.197530i
$136$	1.32119	−	7.49286i	0.113291	−	0.642508i
$137$	−3.60669	+	3.02638i	−0.308141	+	0.258561i	−0.783723	−	0.621111i	$-0.786682\pi$
$137$	−3.60669	+	3.02638i	−0.308141	+	0.258561i	0.475582	+	0.879671i	$0.342237\pi$
$138$	2.77157	+	2.32563i	0.235932	+	0.197971i
$139$	−0.157990	−	0.896008i	−0.0134006	−	0.0759984i	0.977374	−	0.211518i	$-0.0678407\pi$
$139$	−0.157990	−	0.896008i	−0.0134006	−	0.0759984i	−0.990775	+	0.135520i	$0.956730\pi$
$140$	−1.61803	−	2.80252i	−0.136749	−	0.236856i
$141$	1.48584	−	2.57355i	0.125130	−	0.216732i
$142$	−13.4099	−	4.88080i	−1.12533	−	0.409588i
$143$	−10.4636	−	3.80845i	−0.875013	−	0.318479i
$144$	−1.92705	+	3.33775i	−0.160588	+	0.278146i
$145$	−1.62460	−	2.81389i	−0.134916	−	0.233681i
$146$	−1.83722	−	10.4194i	−0.152049	−	0.862316i
$147$	9.85575	+	8.26995i	0.812888	+	0.682094i
$148$	−3.04559	+	2.55556i	−0.250346	+	0.210065i
$149$	−3.99989	+	22.6845i	−0.327684	+	1.85839i	0.162419	+	0.986722i	$0.448070\pi$
$149$	−3.99989	+	22.6845i	−0.327684	+	1.85839i	−0.490103	+	0.871665i	$0.663041\pi$
$150$	−4.50900	+	1.64114i	−0.368158	+	0.133999i
$151$	2.45714			0.199959			0.0999797	−	0.994989i	$-0.468122\pi$
$151$	2.45714			0.199959			0.0999797	+	0.994989i	$0.468122\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	16.9305	−	6.16220i	1.36430	−	0.496564i
$155$	0.252326	−	1.43101i	0.0202673	−	0.114941i
$156$	1.71293	−	1.43732i	0.137144	−	0.115077i
$157$	11.9214	+	10.0033i	0.951433	+	0.798347i	0.979538	−	0.201258i	$-0.0645030\pi$
$157$	11.9214	+	10.0033i	0.951433	+	0.798347i	−0.0281055	+	0.999605i	$0.508947\pi$
$158$	−1.55316	−	8.80839i	−0.123562	−	0.700758i
$159$	0.263932	+	0.457144i	0.0209312	+	0.0362539i
$160$	2.07363	−	3.59163i	0.163935	−	0.283943i
$161$	−10.4214	−	3.79306i	−0.821318	−	0.298935i
$162$	−1.68779	−	0.614306i	−0.132606	−	0.0482645i
$163$	−3.26393	+	5.65330i	−0.255651	+	0.442800i	−0.965072	−	0.261984i	$-0.915623\pi$
$163$	−3.26393	+	5.65330i	−0.255651	+	0.442800i	0.709421	+	0.704785i	$0.248956\pi$
$164$	−2.85317	−	4.94183i	−0.222795	−	0.385892i
$165$	−0.912922	−	5.17744i	−0.0710709	−	0.403063i
$166$	−1.11313	−	0.934025i	−0.0863955	−	0.0724944i
$167$	−5.27185	+	4.42361i	−0.407948	+	0.342309i	−0.823556	−	0.567235i	$-0.808013\pi$
$167$	−5.27185	+	4.42361i	−0.407948	+	0.342309i	0.415608	+	0.909544i	$0.363569\pi$
$168$	−2.66137	+	15.0934i	−0.205329	+	1.16448i
$169$	3.31511	−	1.20660i	0.255008	−	0.0928154i
$170$	−3.59222			−0.275511
$171$		0			0
$172$	3.90983			0.298122
$173$	14.6216	−	5.32181i	1.11166	−	0.404610i	0.280055	−	0.959984i	$-0.409647\pi$
$173$	14.6216	−	5.32181i	1.11166	−	0.404610i	0.831601	+	0.555374i	$0.187425\pi$
$174$	−0.630814	+	3.57752i	−0.0478219	+	0.271211i
$175$	11.2671	−	9.45425i	0.851716	−	0.714674i
$176$	6.60180	+	5.53957i	0.497629	+	0.417560i
$177$	0.571614	+	3.24179i	0.0429652	+	0.243668i
$178$	10.4271	+	18.0602i	0.781541	+	1.35367i
$179$	−9.14729	+	15.8436i	−0.683701	+	1.18420i	0.290142	+	0.956983i	$0.406297\pi$
$179$	−9.14729	+	15.8436i	−0.683701	+	1.18420i	−0.973843	+	0.227221i	$0.927036\pi$
$180$	−1.16152	−	0.422760i	−0.0865749	−	0.0315107i
$181$	23.1366	+	8.42104i	1.71973	+	0.625931i	0.997816	−	0.0660513i	$-0.0210401\pi$
$181$	23.1366	+	8.42104i	1.71973	+	0.625931i	0.721915	+	0.691982i	$0.243262\pi$
$182$	7.66312	−	13.2729i	0.568028	−	0.983854i
$183$	0.310271	+	0.537405i	0.0229359	+	0.0397261i
$184$	−1.39917	−	7.93507i	−0.103148	−	0.584981i
$185$	6.09119	+	5.11111i	0.447833	+	0.375776i
$186$	−1.24451	+	1.04427i	−0.0912522	+	0.0765697i
$187$	−1.55316	+	8.80839i	−0.113578	+	0.644133i
$188$	−1.46809	+	0.534340i	−0.107071	+	0.0389708i
$189$	22.9969			1.67278
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	−9.61973	+	3.50130i	−0.694245	+	0.252684i
$193$	−0.912922	+	5.17744i	−0.0657136	+	0.372680i	0.934161	+	0.356852i	$0.116150\pi$
$193$	−0.912922	+	5.17744i	−0.0657136	+	0.372680i	−0.999875	+	0.0158288i	$0.994961\pi$
$194$	−14.1078	+	11.8378i	−1.01288	+	0.849907i
$195$	−3.42585	−	2.87463i	−0.245331	−	0.205857i
$196$	−1.17454	−	6.66117i	−0.0838960	−	0.475798i
$197$	−1.26393	−	2.18919i	−0.0900514	−	0.155974i	0.817481	−	0.575955i	$-0.195370\pi$
$197$	−1.26393	−	2.18919i	−0.0900514	−	0.155974i	−0.907533	+	0.419982i	$0.862036\pi$
$198$	3.44095	−	5.95991i	0.244538	−	0.423552i
$199$	17.8018	+	6.47932i	1.26194	+	0.459307i	0.884418	−	0.466695i	$-0.154556\pi$
$199$	17.8018	+	6.47932i	1.26194	+	0.459307i	0.377518	+	0.926002i	$0.376778\pi$
$200$	10.0417	+	3.65487i	0.710054	+	0.258439i
$201$	−0.100813	+	0.174613i	−0.00711081	+	0.0123163i
$202$	−8.19624	−	14.1963i	−0.576685	−	0.998848i
$203$	−1.93360	−	10.9660i	−0.135712	−	0.769662i
$204$	−1.37590	−	1.15452i	−0.0963324	−	0.0808325i
$205$	−8.74262	+	7.33593i	−0.610611	+	0.512363i
$206$	0.204964	−	1.16241i	0.0142805	−	0.0809888i
$207$	−3.98060	+	1.44882i	−0.276671	+	0.100700i
$208$	7.33094			0.508309
$209$		0			0
$210$	7.23607			0.499336
$211$	16.9305	−	6.16220i	1.16554	−	0.424223i	0.314469	−	0.949268i	$-0.398173\pi$
$211$	16.9305	−	6.16220i	1.16554	−	0.424223i	0.851075	+	0.525044i	$0.175951\pi$
$212$	0.0481899	−	0.273298i	0.00330970	−	0.0187702i
$213$	−10.9318	+	9.17291i	−0.749038	+	0.628517i
$214$	−10.4320	−	8.75350i	−0.713118	−	0.598377i
$215$	−1.35787	−	7.70086i	−0.0926059	−	0.525194i
$216$	8.35410	+	14.4697i	0.568425	+	0.984540i
$217$	2.48990	−	4.31263i	0.169025	−	0.292760i
$218$	0.802593	+	0.292120i	0.0543585	+	0.0197849i
$219$	−9.94207	−	3.61862i	−0.671823	−	0.244524i
$220$	−1.38197	+	2.39364i	−0.0931721	+	0.161379i
$221$	3.80423	+	6.58911i	0.255900	+	0.443232i
$222$	−1.54374	−	8.75496i	−0.103609	−	0.587595i
$223$	10.4123	+	8.73697i	0.697260	+	0.585071i	0.920993	−	0.389580i	$-0.127380\pi$
$223$	10.4123	+	8.73697i	0.697260	+	0.585071i	−0.223733	+	0.974651i	$0.571824\pi$
$224$	10.8877	−	9.13584i	0.727463	−	0.610414i
$225$	0.975561	−	5.53268i	0.0650374	−	0.368846i
$226$		0			0
$227$	−29.7073			−1.97174			−0.985870	−	0.167511i	$-0.946427\pi$
$227$	−29.7073			−1.97174			−0.985870	+	0.167511i	$0.946427\pi$
$228$		0			0
$229$	4.09017			0.270286			0.135143	−	0.990826i	$-0.456851\pi$
$229$	4.09017			0.270286			0.135143	+	0.990826i	$0.456851\pi$
$230$	−3.57480	+	1.30112i	−0.235716	+	0.0857934i
$231$	3.12863	−	17.7434i	0.205849	−	1.16743i
$232$	6.19743	−	5.20026i	0.406881	−	0.341414i
$233$	10.3203	+	8.65972i	0.676102	+	0.567317i	0.914865	−	0.403761i	$-0.132297\pi$
$233$	10.3203	+	8.65972i	0.676102	+	0.567317i	−0.238762	+	0.971078i	$0.576742\pi$
$234$	−1.01655	−	5.76517i	−0.0664542	−	0.376881i
$235$	1.56231	+	2.70599i	0.101914	+	0.176520i
$236$	0.865300	−	1.49874i	0.0563262	−	0.0975599i
$237$	−8.40487	−	3.05912i	−0.545955	−	0.198711i
$238$	−11.5683	−	4.21052i	−0.749862	−	0.272927i
$239$	7.92705	−	13.7301i	0.512758	−	0.888123i	−0.487132	−	0.873328i	$-0.661957\pi$
$239$	7.92705	−	13.7301i	0.512758	−	0.888123i	0.999891	−	0.0147952i	$-0.00470963\pi$
$240$	1.73060	+	2.99749i	0.111710	+	0.193487i
$241$	3.93380	+	22.3097i	0.253398	+	1.43709i	0.800151	+	0.599799i	$0.204753\pi$
$241$	3.93380	+	22.3097i	0.253398	+	1.43709i	−0.546753	+	0.837294i	$0.684136\pi$
$242$	−1.88228	−	1.57942i	−0.120998	−	0.101529i
$243$	11.1003	−	9.31422i	0.712082	−	0.597508i
$244$	0.0566506	−	0.321282i	0.00362668	−	0.0205679i
$245$	−12.7120	+	4.62680i	−0.812142	+	0.295596i
$246$	12.7598			0.813533
$247$		0			0
$248$	3.61803			0.229745
$249$	−1.36545	+	0.496984i	−0.0865321	+	0.0314951i
$250$	2.13774	−	12.1237i	0.135202	−	0.766771i
$251$	7.97943	−	6.69554i	0.503657	−	0.422619i	−0.355233	−	0.934778i	$-0.615599\pi$
$251$	7.97943	−	6.69554i	0.503657	−	0.422619i	0.858891	+	0.512159i	$0.171154\pi$
$252$	−3.24502	−	2.72289i	−0.204417	−	0.171526i
$253$	1.64482	+	9.32823i	0.103409	+	0.586461i
$254$	−9.37132	−	16.2316i	−0.588009	−	1.01846i
$255$	−1.79611	+	3.11096i	−0.112477	+	0.194816i
$256$	12.4702	+	4.53878i	0.779388	+	0.283674i
$257$	−8.51506	−	3.09923i	−0.531155	−	0.193325i	0.0624991	−	0.998045i	$-0.480093\pi$
$257$	−8.51506	−	3.09923i	−0.531155	−	0.193325i	−0.593654	+	0.804720i	$0.702315\pi$
$258$	−4.37132	+	7.57135i	−0.272147	+	0.471372i
$259$	13.6251	+	23.5993i	0.846620	+	1.46639i
$260$	0.408271	+	2.31542i	0.0253199	+	0.143596i
$261$	−3.25818	−	2.73394i	−0.201676	−	0.169227i
$262$	4.58390	−	3.84635i	0.283194	−	0.237628i
$263$	2.06442	−	11.7079i	0.127298	−	0.721942i	−0.852619	−	0.522534i	$-0.824987\pi$
$263$	2.06442	−	11.7079i	0.127298	−	0.721942i	0.979917	−	0.199408i	$-0.0639020\pi$
$264$	12.3007	−	4.47710i	0.757058	−	0.275547i
$265$	−0.555029			−0.0340952
$266$		0			0
$267$	20.8541			1.27625
$268$	0.0996085	−	0.0362545i	0.00608456	−	0.00221460i
$269$	−1.33960	+	7.59725i	−0.0816769	+	0.463213i	0.916347	+	0.400384i	$0.131123\pi$
$269$	−1.33960	+	7.59725i	−0.0816769	+	0.463213i	−0.998024	+	0.0628287i	$0.979988\pi$
$270$	6.04298	−	5.07066i	0.367764	−	0.308590i
$271$	10.9318	+	9.17291i	0.664062	+	0.557214i	0.911301	−	0.411740i	$-0.135079\pi$
$271$	10.9318	+	9.17291i	0.664062	+	0.557214i	−0.247239	+	0.968955i	$0.579523\pi$
$272$	−1.02253	−	5.79908i	−0.0620003	−	0.351621i
$273$	−7.66312	−	13.2729i	−0.463793	−	0.803313i
$274$	−2.76741	+	4.79330i	−0.167186	+	0.289574i
$275$	−11.8047	−	4.29656i	−0.711851	−	0.259092i
$276$	−1.78740	−	0.650561i	−0.107589	−	0.0391592i
$277$	9.61803	−	16.6589i	0.577892	−	1.00094i	−0.417829	−	0.908526i	$-0.637209\pi$
$277$	9.61803	−	16.6589i	0.577892	−	1.00094i	0.995721	−	0.0924121i	$-0.0294577\pi$
$278$	−0.534785	−	0.926274i	−0.0320743	−	0.0555542i
$279$	−0.330298	−	1.87322i	−0.0197745	−	0.112146i
$280$	−12.3448	−	10.3585i	−0.737741	−	0.619039i
$281$	−3.38957	+	2.84419i	−0.202205	+	0.169670i	−0.738267	−	0.674508i	$-0.764356\pi$
$281$	−3.38957	+	2.84419i	−0.202205	+	0.169670i	0.536062	+	0.844178i	$0.319911\pi$
$282$	0.606626	−	3.44035i	0.0361241	−	0.204870i
$283$	0.854961	−	0.311180i	0.0508221	−	0.0184977i	−0.316484	−	0.948598i	$-0.602502\pi$
$283$	0.854961	−	0.311180i	0.0508221	−	0.0184977i	0.367306	+	0.930100i	$0.380280\pi$
$284$	7.50245			0.445189
$285$		0			0
$286$	−13.0902			−0.774038
$287$	−36.7531	+	13.3770i	−2.16947	+	0.789621i
$288$	0.942705	−	5.34635i	0.0555495	−	0.315037i
$289$	−8.34111	+	6.99902i	−0.490653	+	0.411707i
$290$	−2.92603	−	2.45523i	−0.171822	−	0.144176i
$291$	3.19798	+	18.1366i	0.187469	+	1.06319i
$292$	2.78115	+	4.81710i	0.162755	+	0.281899i
$293$	−12.3637	+	21.4146i	−0.722297	+	1.25106i	0.237780	+	0.971319i	$0.423580\pi$
$293$	−12.3637	+	21.4146i	−0.722297	+	1.25106i	−0.960077	+	0.279736i	$0.909753\pi$
$294$	14.2125	+	5.17292i	0.828889	+	0.301691i
$295$	−3.25246	−	1.18380i	−0.189366	−	0.0689235i
$296$	−9.89919	+	17.1459i	−0.575379	+	0.996585i
$297$	−9.82084	−	17.0102i	−0.569863	−	0.987031i
$298$	4.70215	+	26.6672i	0.272388	+	1.54479i
$299$	6.17239	+	5.17925i	0.356958	+	0.299524i
$300$	1.93247	−	1.62153i	0.111571	−	0.0936191i
$301$	4.65349	−	26.3912i	0.268223	−	1.52117i
$302$	2.71434	−	0.987940i	0.156193	−	0.0568496i
$303$	−16.3925			−0.941723
$304$		0			0
$305$	−0.652476			−0.0373607
$306$	−4.41870	+	1.60828i	−0.252600	+	0.0919390i
$307$	−4.79150	+	27.1739i	−0.273465	+	1.55090i	0.470329	+	0.882491i	$0.344135\pi$
$307$	−4.79150	+	27.1739i	−0.273465	+	1.55090i	−0.743795	+	0.668408i	$0.766976\pi$
$308$	−7.25608	+	6.08857i	−0.413453	+	0.346929i
$309$	−0.904193	−	0.758708i	−0.0514377	−	0.0431614i
$310$	−0.296626	−	1.68225i	−0.0168473	−	0.0955455i
$311$	2.76393	+	4.78727i	0.156728	+	0.271461i	0.933687	−	0.358090i	$-0.116572\pi$
$311$	2.76393	+	4.78727i	0.156728	+	0.271461i	−0.776959	+	0.629551i	$0.783239\pi$
$312$	5.56758	−	9.64333i	0.315202	−	0.545946i
$313$	−7.15861	−	2.60552i	−0.404629	−	0.147273i	0.131685	−	0.991292i	$-0.457961\pi$
$313$	−7.15861	−	2.60552i	−0.404629	−	0.147273i	−0.536313	+	0.844019i	$0.680184\pi$
$314$	17.1913	+	6.25712i	0.970161	+	0.353110i
$315$	−4.23607	+	7.33708i	−0.238675	+	0.413398i
$316$	2.35114	+	4.07230i	0.132262	+	0.229085i
$317$	1.53671	+	8.71509i	0.0863100	+	0.489488i	0.997066	+	0.0765438i	$0.0243885\pi$
$317$	1.53671	+	8.71509i	0.0863100	+	0.489488i	−0.910756	+	0.412944i	$0.864500\pi$
$318$	0.475362	+	0.398876i	0.0266570	+	0.0223679i
$319$	−7.28552	+	6.11327i	−0.407911	+	0.342278i
$320$	1.86914	−	10.6004i	0.104488	−	0.592581i
$321$	−12.7968	+	4.65764i	−0.714246	+	0.259964i
$322$	−13.0373			−0.726539
$323$		0			0
$324$	0.944272			0.0524596
$325$	−10.0417	+	3.65487i	−0.557012	+	0.202736i
$326$	−1.33257	+	7.55738i	−0.0738042	+	0.418565i
$327$	0.654280	−	0.549006i	0.0361818	−	0.0303601i
$328$	−21.7682	−	18.2657i	−1.20195	−	1.00856i
$329$	1.85946	+	10.5455i	0.102515	+	0.581393i
$330$	−3.09017	−	5.35233i	−0.170108	−	0.294636i
$331$	12.1392	−	21.0257i	0.667232	−	1.15568i	−0.311443	−	0.950265i	$-0.600812\pi$
$331$	12.1392	−	21.0257i	0.667232	−	1.15568i	0.978675	−	0.205415i	$-0.0658543\pi$
$332$	0.717861	+	0.261280i	0.0393978	+	0.0143396i
$333$	9.78090	+	3.55996i	0.535990	+	0.195085i
$334$	−4.04508	+	7.00629i	−0.221337	+	0.383367i
$335$	−0.106001	−	0.183599i	−0.00579146	−	0.0100311i
$336$	2.05976	+	11.6815i	0.112369	+	0.637278i
$337$	−12.3448	−	10.3585i	−0.672463	−	0.564263i	0.241330	−	0.970443i	$-0.422416\pi$
$337$	−12.3448	−	10.3585i	−0.672463	−	0.564263i	−0.913793	+	0.406180i	$0.866861\pi$
$338$	3.17698	−	2.66580i	0.172805	−	0.145001i
$339$		0			0
$340$	1.77465	−	0.645920i	0.0962439	−	0.0350299i
$341$	−4.25325			−0.230327
$342$		0			0
$343$	−16.7082			−0.902158
$344$	18.2960	−	6.65919i	0.986452	−	0.359039i
$345$	−0.660597	+	3.74643i	−0.0355653	+	0.201701i
$346$	14.0123	−	11.7577i	0.753307	−	0.632100i
$347$	−19.0230	−	15.9622i	−1.02121	−	0.856897i	−0.0314312	−	0.999506i	$-0.510007\pi$
$347$	−19.0230	−	15.9622i	−1.02121	−	0.856897i	−0.989779	+	0.142609i	$0.954451\pi$
$348$	−0.331639	−	1.88082i	−0.0177777	−	0.100822i
$349$	−5.69098	−	9.85707i	−0.304631	−	0.527637i	0.672548	−	0.740054i	$-0.265200\pi$
$349$	−5.69098	−	9.85707i	−0.304631	−	0.527637i	−0.977179	+	0.212417i	$0.931867\pi$
$350$	8.64527	−	14.9740i	0.462109	−	0.800396i
$351$	−15.7006	−	5.71454i	−0.838035	−	0.305020i
$352$	−11.4071	−	4.15186i	−0.608002	−	0.221295i
$353$	−13.8090	+	23.9179i	−0.734980	+	1.27302i	0.219752	+	0.975556i	$0.429475\pi$
$353$	−13.8090	+	23.9179i	−0.734980	+	1.27302i	−0.954732	+	0.297467i	$0.903858\pi$
$354$	1.93487	+	3.35129i	0.102837	+	0.178119i
$355$	−2.60557	−	14.7769i	−0.138290	−	0.784279i
$356$	−8.39864	−	7.04730i	−0.445127	−	0.373506i
$357$	−9.43057	+	7.91319i	−0.499119	+	0.418810i
$358$	−3.73458	+	21.1798i	−0.197379	+	1.11939i
$359$	35.3494	−	12.8661i	1.86567	−	0.679048i	0.891589	−	0.452845i	$-0.149591\pi$
$359$	35.3494	−	12.8661i	1.86567	−	0.679048i	0.974080	−	0.226203i	$-0.0726313\pi$
$360$	−6.15537			−0.324416
$361$		0			0
$362$	28.9443			1.52128
$363$	−2.30896	+	0.840392i	−0.121189	+	0.0441091i
$364$	−1.39917	+	7.93507i	−0.0733363	+	0.415911i
$365$	8.52195	−	7.15076i	0.446059	−	0.374288i
$366$	0.558822	+	0.468907i	0.0292101	+	0.0245102i
$367$	3.72860	+	21.1459i	0.194631	+	1.10381i	0.912943	+	0.408087i	$0.133804\pi$
$367$	3.72860	+	21.1459i	0.194631	+	1.10381i	−0.718312	+	0.695721i	$0.755085\pi$
$368$	−3.11803	−	5.40059i	−0.162539	−	0.281525i
$369$	−7.46969	+	12.9379i	−0.388857	+	0.673520i
$370$	8.78380	+	3.19704i	0.456648	+	0.166206i
$371$	−1.78740	−	0.650561i	−0.0927973	−	0.0337754i
$372$	0.427051	−	0.739674i	0.0221416	−	0.0383503i
$373$	2.15938	+	3.74016i	0.111809	+	0.193658i	0.916500	−	0.400036i	$-0.131002\pi$
$373$	2.15938	+	3.74016i	0.111809	+	0.193658i	−0.804691	+	0.593694i	$0.797669\pi$
$374$	1.82584	+	10.3549i	0.0944122	+	0.535438i
$375$	−9.43057	−	7.91319i	−0.486993	−	0.408635i
$376$	−5.95980	+	5.00087i	−0.307353	+	0.257900i
$377$	−1.40484	+	7.96726i	−0.0723531	+	0.410335i
$378$	25.4041	−	9.24632i	1.30664	−	0.475580i
$379$	−7.95148			−0.408440			−0.204220	−	0.978925i	$-0.565466\pi$
$379$	−7.95148			−0.408440			−0.204220	+	0.978925i	$0.565466\pi$
$380$		0			0
$381$	−18.7426			−0.960215
$382$	−18.7795	+	6.83517i	−0.960841	+	0.349718i
$383$	2.43825	−	13.8280i	0.124589	−	0.706579i	−0.856962	−	0.515379i	$-0.827651\pi$
$383$	2.43825	−	13.8280i	0.124589	−	0.706579i	0.981551	−	0.191199i	$-0.0612377\pi$
$384$	−3.17594	+	2.66493i	−0.162072	+	0.135994i
$385$	14.5122	+	12.1771i	0.739608	+	0.620605i
$386$	1.07320	+	6.08645i	0.0546247	+	0.309792i
$387$	−5.11803	−	8.86469i	−0.260164	−	0.450618i
$388$	4.84104	−	8.38493i	0.245767	−	0.425680i
$389$	−12.3007	−	4.47710i	−0.623672	−	0.226998i	0.0108027	−	0.999942i	$-0.496561\pi$
$389$	−12.3007	−	4.47710i	−0.623672	−	0.226998i	−0.634475	+	0.772944i	$0.718784\pi$
$390$	−4.94026	−	1.79811i	−0.250160	−	0.0910507i
$391$	3.23607	−	5.60503i	0.163655	−	0.283459i
$392$	−16.8415	−	29.1703i	−0.850624	−	1.47332i
$393$	−1.03909	−	5.89295i	−0.0524149	−	0.297260i
$394$	−2.27644	−	1.91016i	−0.114685	−	0.0962325i
$395$	7.20431	−	6.04514i	0.362488	−	0.304164i
$396$	−0.628265	+	3.56307i	−0.0315715	+	0.179051i
$397$	−13.8212	+	5.03050i	−0.693666	+	0.252474i	−0.664704	−	0.747107i	$-0.731442\pi$
$397$	−13.8212	+	5.03050i	−0.693666	+	0.252474i	−0.0289617	+	0.999581i	$0.509220\pi$
$398$	22.2703			1.11631
$399$		0			0
$400$	8.27051			0.413525
$401$	7.14961	−	2.60224i	0.357034	−	0.129950i	−0.157275	−	0.987555i	$-0.550271\pi$
$401$	7.14961	−	2.60224i	0.357034	−	0.129950i	0.514309	+	0.857605i	$0.328049\pi$
$402$	−0.0411591	+	0.233425i	−0.00205283	+	0.0116422i
$403$	−2.77157	+	2.32563i	−0.138062	+	0.115848i
$404$	6.60180	+	5.53957i	0.328452	+	0.275604i
$405$	−0.327942	−	1.85985i	−0.0162956	−	0.0924168i
$406$	−6.54508	−	11.3364i	−0.324827	−	0.562617i
$407$	11.6372	−	20.1562i	0.576834	−	0.999106i
$408$	−8.40487	−	3.05912i	−0.416103	−	0.151449i
$409$	−20.6049	−	7.49958i	−1.01885	−	0.370830i	−0.222023	−	0.975041i	$-0.571266\pi$
$409$	−20.6049	−	7.49958i	−1.01885	−	0.370830i	−0.796824	+	0.604211i	$0.793488\pi$
$410$	−6.70820	+	11.6190i	−0.331295	+	0.573819i
$411$	2.76741	+	4.79330i	0.136506	+	0.236436i
$412$	0.107756	+	0.611114i	0.00530875	+	0.0301074i
$413$	−9.08659	−	7.62456i	−0.447122	−	0.375180i
$414$	−3.81475	+	3.20095i	−0.187485	+	0.157318i
$415$	0.265311	−	1.50465i	0.0130236	−	0.0738605i
$416$	−9.70349	+	3.53178i	−0.475753	+	0.173160i
$417$	−1.06957			−0.0523770
$418$		0			0
$419$	−33.4164			−1.63250			−0.816249	−	0.577700i	$-0.803950\pi$
$419$	−33.4164			−1.63250			−0.816249	+	0.577700i	$0.803950\pi$
$420$	−3.57480	+	1.30112i	−0.174433	+	0.0634883i
$421$	−2.45666	+	13.9324i	−0.119730	+	0.679024i	0.864569	+	0.502515i	$0.167592\pi$
$421$	−2.45666	+	13.9324i	−0.119730	+	0.679024i	−0.984299	+	0.176509i	$0.943519\pi$
$422$	16.2251	−	13.6145i	0.789825	−	0.662742i
$423$	3.13325	+	2.62911i	0.152344	+	0.127832i
$424$	−0.239976	−	1.36097i	−0.0116543	−	0.0660946i
$425$	4.29180	+	7.43361i	0.208183	+	0.360583i
$426$	−8.38800	+	14.5284i	−0.406400	+	0.703905i
$427$	−2.10122	−	0.764780i	−0.101685	−	0.0370103i
$428$	6.72766	+	2.44867i	0.325194	+	0.118361i
$429$	−6.54508	+	11.3364i	−0.316000	+	0.547328i
$430$	−4.59628	−	7.96099i	−0.221652	−	0.383913i
$431$	−2.76855	−	15.7012i	−0.133356	−	0.756302i	−0.975990	−	0.217815i	$-0.930107\pi$
$431$	−2.76855	−	15.7012i	−0.133356	−	0.756302i	0.842634	−	0.538487i	$-0.181004\pi$
$432$	9.90593	+	8.31206i	0.476599	+	0.399914i
$433$	−7.15413	+	6.00303i	−0.343805	+	0.288487i	−0.798297	−	0.602264i	$-0.794265\pi$
$433$	−7.15413	+	6.00303i	−0.343805	+	0.288487i	0.454491	+	0.890751i	$0.349821\pi$
$434$	1.01655	−	5.76517i	0.0487962	−	0.276737i
$435$	−3.58931	+	1.30640i	−0.172094	+	0.0626371i
$436$	−0.449028			−0.0215045
$437$		0			0
$438$	−12.4377			−0.594296
$439$	10.8856	−	3.96203i	0.519540	−	0.189097i	−0.0689217	−	0.997622i	$-0.521956\pi$
$439$	10.8856	−	3.96203i	0.519540	−	0.189097i	0.588462	+	0.808525i	$0.299734\pi$
$440$	−2.39006	+	13.5547i	−0.113942	+	0.646196i
$441$	−13.5653	+	11.3826i	−0.645965	+	0.542029i
$442$	6.85171	+	5.74927i	0.325903	+	0.273465i
$443$	−1.24685	−	7.07125i	−0.0592398	−	0.335965i	0.940755	−	0.339086i	$-0.110118\pi$
$443$	−1.24685	−	7.07125i	−0.0592398	−	0.335965i	−0.999995	+	0.00312062i	$0.999007\pi$
$444$	2.33688	+	4.04760i	0.110903	+	0.192090i
$445$	−10.9637	+	18.9896i	−0.519727	+	0.900193i
$446$	15.0151	+	5.46504i	0.710985	+	0.258777i
$447$	25.4456	+	9.26143i	1.20353	+	0.438051i
$448$	18.4443	−	31.9464i	0.871410	−	1.50933i
$449$	17.4823	+	30.2802i	0.825040	+	1.42901i	0.901889	+	0.431969i	$0.142181\pi$
$449$	17.4823	+	30.2802i	0.825040	+	1.42901i	−0.0768484	+	0.997043i	$0.524486\pi$
$450$	−1.14684	−	6.50406i	−0.0540626	−	0.306604i
$451$	25.5901	+	21.4726i	1.20499	+	1.01111i
$452$		0			0
$453$	0.501590	−	2.84466i	0.0235668	−	0.133654i
$454$	−32.8169	+	11.9444i	−1.54017	+	0.560577i
$455$	16.1150			0.755481
$456$		0			0
$457$	19.7082			0.921911			0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082			0.921911			0.460955	+	0.887423i	$0.347507\pi$
$458$	4.51831	−	1.64453i	0.211127	−	0.0768438i
$459$	−2.33050	+	13.2169i	−0.108778	+	0.616912i
$460$	1.53209	−	1.28558i	0.0714340	−	0.0599403i
$461$	−26.1837	−	21.9707i	−1.21949	−	1.02328i	−0.998851	−	0.0479230i	$-0.984740\pi$
$461$	−26.1837	−	21.9707i	−1.21949	−	1.02328i	−0.220644	−	0.975355i	$-0.570816\pi$
$462$	−3.67793	−	20.8586i	−0.171113	−	0.970428i
$463$	−8.42705	−	14.5961i	−0.391638	−	0.678337i	0.601028	−	0.799228i	$-0.294758\pi$
$463$	−8.42705	−	14.5961i	−0.391638	−	0.678337i	−0.992666	+	0.120891i	$0.961425\pi$
$464$	3.13068	−	5.42250i	0.145338	−	0.251733i
$465$	−1.60519	−	0.584240i	−0.0744387	−	0.0270935i
$466$	14.8823	+	5.41673i	0.689411	+	0.250925i
$467$	0.118034	−	0.204441i	0.00546196	−	0.00946040i	−0.863282	−	0.504723i	$-0.831595\pi$
$467$	0.118034	−	0.204441i	0.00546196	−	0.00946040i	0.868743	+	0.495262i	$0.164928\pi$
$468$	1.53884	+	2.66535i	0.0711330	+	0.123206i
$469$	−0.126163	−	0.715505i	−0.00582566	−	0.0330389i
$470$	2.81384	+	2.36109i	0.129793	+	0.108909i
$471$	14.0145	−	11.7595i	0.645753	−	0.541851i
$472$	1.49651	−	8.48711i	0.0688823	−	0.390651i
$473$	−21.5082	+	7.82834i	−0.988948	+	0.359948i
$474$	−10.5146			−0.482953
$475$		0			0
$476$	6.47214			0.296650
$477$	−0.682727	+	0.248492i	−0.0312599	+	0.0113777i
$478$	3.23639	−	18.3545i	0.148029	−	0.839514i
$479$	−20.7523	+	17.4132i	−0.948196	+	0.795631i	−0.978993	−	0.203895i	$-0.934640\pi$
$479$	−20.7523	+	17.4132i	−0.948196	+	0.795631i	0.0307971	+	0.999526i	$0.490195\pi$
$480$	−3.73476	−	3.13384i	−0.170468	−	0.143040i
$481$	−3.43795	−	19.4976i	−0.156757	−	0.889014i
$482$	13.3156	+	23.0633i	0.606509	+	1.05050i
$483$	−6.51864	+	11.2906i	−0.296608	+	0.513741i
$484$	1.21389	+	0.441820i	0.0551769	+	0.0200827i
$485$	−18.1964	−	6.62293i	−0.826254	−	0.300732i
$486$	8.51722	−	14.7523i	0.386349	−	0.669176i
$487$	−7.77997	−	13.4753i	−0.352544	−	0.610624i	0.634151	−	0.773210i	$-0.281350\pi$
$487$	−7.77997	−	13.4753i	−0.352544	−	0.610624i	−0.986694	+	0.162586i	$0.948017\pi$
$488$	−0.282109	−	1.59992i	−0.0127705	−	0.0724248i
$489$	5.87860	+	4.93273i	0.265839	+	0.223066i
$490$	−12.1824	+	10.2222i	−0.550343	+	0.461793i
$491$	−2.82534	+	16.0233i	−0.127506	+	0.723122i	0.852282	+	0.523083i	$0.175218\pi$
$491$	−2.82534	+	16.0233i	−0.127506	+	0.723122i	−0.979788	+	0.200040i	$0.935893\pi$
$492$	−6.30365	+	2.29434i	−0.284190	+	0.103437i
$493$	6.49839			0.292673
$494$		0			0
$495$	7.23607			0.325237
$496$	2.63130	−	0.957714i	0.118149	−	0.0430026i
$497$	8.92943	−	50.6413i	0.400540	−	2.27157i
$498$	−1.30856	+	1.09801i	−0.0586380	+	0.0492031i
$499$	16.4913	+	13.8378i	0.738252	+	0.619467i	0.932368	−	0.361512i	$-0.117739\pi$
$499$	16.4913	+	13.8378i	0.738252	+	0.619467i	−0.194116	+	0.980979i	$0.562184\pi$
$500$	1.12387	+	6.37381i	0.0502612	+	0.285045i
$501$	4.04508	+	7.00629i	0.180721	+	0.313018i
$502$	6.12261	−	10.6047i	0.273265	−	0.473310i
$503$	26.8722	+	9.78066i	1.19817	+	0.436098i	0.862585	−	0.505912i	$-0.168844\pi$
$503$	26.8722	+	9.78066i	1.19817	+	0.436098i	0.335585	+	0.942010i	$0.391066\pi$
$504$	−19.8226	−	7.21483i	−0.882968	−	0.321374i
$505$	8.61803	−	14.9269i	0.383497	−	0.664237i
$506$	5.56758	+	9.64333i	0.247509	+	0.428699i
$507$	−0.720163	−	4.08425i	−0.0319836	−	0.181388i
$508$	7.54829	+	6.33377i	0.334901	+	0.281015i
$509$	9.51177	−	7.98132i	0.421602	−	0.353766i	−0.407170	−	0.913352i	$-0.633484\pi$
$509$	9.51177	−	7.98132i	0.421602	−	0.353766i	0.828772	+	0.559586i	$0.189040\pi$
$510$	−0.733301	+	4.15876i	−0.0324711	+	0.184153i
$511$	35.8254	−	13.0394i	1.58482	−	0.576828i
$512$	22.6538			1.00117
$513$		0			0
$514$	−10.6525			−0.469861
$515$	1.16624	−	0.424475i	0.0513905	−	0.0187046i
$516$	0.798136	−	4.52645i	0.0351360	−	0.199266i
$517$	7.00616	−	5.87887i	0.308131	−	0.258552i
$518$	24.5398	+	20.5913i	1.07822	+	0.904732i
$519$	−3.17634	−	18.0139i	−0.139426	−	0.790723i
$520$	5.85410	+	10.1396i	0.256719	+	0.444651i
$521$	−1.48584	+	2.57355i	−0.0650959	+	0.112749i	−0.896737	−	0.442565i	$-0.854069\pi$
$521$	−1.48584	+	2.57355i	−0.0650959	+	0.112749i	0.831641	+	0.555314i	$0.187402\pi$
$522$	−4.69846	−	1.71010i	−0.205646	−	0.0748491i
$523$	−7.63312	−	2.77823i	−0.333773	−	0.121483i	0.169697	−	0.985496i	$-0.445721\pi$
$523$	−7.63312	−	2.77823i	−0.333773	−	0.121483i	−0.503470	+	0.864013i	$0.667943\pi$
$524$	−1.57295	+	2.72443i	−0.0687146	+	0.119017i
$525$	−8.64527	−	14.9740i	−0.377310	−	0.653521i
$526$	−2.42688	−	13.7635i	−0.105817	−	0.600117i
$527$	2.22626	+	1.86805i	0.0969772	+	0.0813735i
$528$	7.76088	−	6.51215i	0.337749	−	0.283405i
$529$	−2.80371	+	15.9006i	−0.121900	+	0.691331i
$530$	−0.613127	+	0.223160i	−0.0266325	+	0.00969345i
$531$	−4.53077			−0.196619
$532$		0			0
$533$	28.4164			1.23085
$534$	23.0370	−	8.38478i	0.996909	−	0.362845i
$535$	2.48644	−	14.1013i	0.107498	−	0.609653i
$536$	0.404367	−	0.339304i	0.0174660	−	0.0146557i
$537$	16.4750	+	13.8242i	0.710948	+	0.596557i
$538$	1.57480	+	8.93111i	0.0678942	+	0.385047i
$539$	19.7984	+	34.2918i	0.852776	+	1.47705i
$540$	−2.07363	+	3.59163i	−0.0892347	+	0.154559i
$541$	6.30365	+	2.29434i	0.271015	+	0.0986414i	0.473953	−	0.880550i	$-0.342827\pi$
$541$	6.30365	+	2.29434i	0.271015	+	0.0986414i	−0.202938	+	0.979192i	$0.565049\pi$
$542$	15.7643	+	5.73773i	0.677134	+	0.246456i
$543$	14.4721	−	25.0665i	0.621059	−	1.07571i
$544$	4.14725	+	7.18325i	0.177812	+	0.307979i
$545$	0.155946	+	0.884412i	0.00667998	+	0.0378841i
$546$	−13.8019	−	11.5812i	−0.590666	−	0.495628i
$547$	22.4131	−	18.8068i	0.958315	−	0.804122i	−0.0223628	−	0.999750i	$-0.507119\pi$
$547$	22.4131	−	18.8068i	0.958315	−	0.804122i	0.980678	+	0.195628i	$0.0626745\pi$
$548$	0.505287	−	2.86562i	0.0215848	−	0.122413i
$549$	−0.802593	+	0.292120i	−0.0342538	+	0.0124674i
$550$	−14.7679			−0.629704
$551$		0			0
$552$	−9.47214			−0.403161
$553$	30.2862	−	11.0233i	1.28790	−	0.468758i
$554$	3.92677	−	22.2698i	0.166832	−	0.946153i
$555$	7.16062	−	6.00847i	0.303951	−	0.255045i
$556$	0.430751	+	0.361443i	0.0182679	+	0.0153286i
$557$	0.930872	+	5.27924i	0.0394423	+	0.223689i	0.998157	−	0.0606804i	$-0.0193270\pi$
$557$	0.930872	+	5.27924i	0.0394423	+	0.223689i	−0.958715	+	0.284369i	$0.908216\pi$
$558$	−1.11803	−	1.93649i	−0.0473302	−	0.0819782i
$559$	−9.73508	+	16.8617i	−0.411750	+	0.713172i
$560$	−11.7200	−	4.26572i	−0.495259	−	0.180260i
$561$	9.88051	+	3.59621i	0.417156	+	0.151832i
$562$	−2.60081	+	4.50474i	−0.109709	+	0.190021i
$563$	9.06154	+	15.6950i	0.381898	+	0.661467i	0.991334	−	0.131369i	$-0.0419371\pi$
$563$	9.06154	+	15.6950i	0.381898	+	0.661467i	−0.609435	+	0.792836i	$0.708604\pi$
$564$	0.318922	+	1.80870i	0.0134291	+	0.0761600i
$565$		0			0
$566$	0.819338	−	0.687506i	0.0344393	−	0.0288980i
$567$	1.12387	−	6.37381i	0.0471983	−	0.267675i
$568$	35.1076	−	12.7781i	1.47308	−	0.536157i
$569$	18.3601			0.769695			0.384848	−	0.922980i	$-0.374254\pi$
$569$	18.3601			0.769695			0.384848	+	0.922980i	$0.374254\pi$
$570$		0			0
$571$	41.1033			1.72012			0.860060	−	0.510192i	$-0.170426\pi$
$571$	41.1033			1.72012			0.860060	+	0.510192i	$0.170426\pi$
$572$	6.46688	−	2.35375i	0.270394	−	0.0984153i
$573$	−3.47031	+	19.6811i	−0.144974	+	0.822189i
$574$	−35.2217	+	29.5545i	−1.47013	+	1.23358i
$575$	6.96347	+	5.84305i	0.290397	+	0.243672i
$576$	−2.44673	−	13.8761i	−0.101947	−	0.578171i
$577$	14.3541	+	24.8620i	0.597569	+	1.03502i	0.993179	+	0.116601i	$0.0372000\pi$
$577$	14.3541	+	24.8620i	0.597569	+	1.03502i	−0.395610	+	0.918419i	$0.629467\pi$
$578$	−6.40013	+	11.0853i	−0.266210	+	0.461089i
$579$	5.80762	+	2.11380i	0.241356	+	0.0878466i
$580$	1.88701	+	0.686815i	0.0783538	+	0.0285185i
$581$	2.61803	−	4.53457i	0.108614	−	0.188126i
$582$	10.8249	+	18.7493i	0.448706	+	0.777182i
$583$	0.282109	+	1.59992i	0.0116837	+	0.0662618i
$584$	21.2188	+	17.8047i	0.878039	+	0.736763i
$585$	4.71528	−	3.95659i	0.194953	−	0.163585i
$586$	−5.04776	+	28.6273i	−0.208521	+	1.18258i
$587$	−36.8175	+	13.4005i	−1.51962	+	0.553096i	−0.961053	−	0.276363i	$-0.910871\pi$
$587$	−36.8175	+	13.4005i	−1.51962	+	0.553096i	−0.558567	+	0.829460i	$0.688648\pi$
$588$	−7.95148			−0.327913
$589$		0			0
$590$	−4.06888			−0.167513
$591$	−2.79247	+	1.01638i	−0.114867	+	0.0418081i
$592$	−2.66079	+	15.0901i	−0.109358	+	0.620200i
$593$	23.5238	−	19.7389i	0.966009	−	0.810578i	−0.0159114	−	0.999873i	$-0.505065\pi$
$593$	23.5238	−	19.7389i	0.966009	−	0.810578i	0.981920	+	0.189296i	$0.0606205\pi$
$594$	−17.6881	−	14.8421i	−0.725751	−	0.608978i
$595$	−2.24775	−	12.7476i	−0.0921487	−	0.522601i
$596$	−7.11803	−	12.3288i	−0.291566	−	0.505007i
$597$	11.1352	−	19.2867i	0.455732	−	0.789351i
$598$	8.90090	+	3.23966i	0.363985	+	0.132480i
$599$	19.4006	+	7.06126i	0.792689	+	0.288515i	0.706453	−	0.707760i	$-0.250294\pi$
$599$	19.4006	+	7.06126i	0.792689	+	0.288515i	0.0862354	+	0.996275i	$0.472516\pi$
$600$	6.28115	−	10.8793i	0.256427	−	0.444145i
$601$	−20.6457	−	35.7595i	−0.842157	−	1.45866i	−0.888068	−	0.459713i	$-0.847952\pi$
$601$	−20.6457	−	35.7595i	−0.842157	−	1.45866i	0.0459108	−	0.998946i	$-0.485381\pi$
$602$	−5.47050	−	31.0248i	−0.222961	−	1.26448i
$603$	−0.212588	−	0.178383i	−0.00865727	−	0.00726431i
$604$	−1.16331	+	0.976136i	−0.0473345	+	0.0397184i
$605$	0.448636	−	2.54434i	0.0182396	−	0.103442i
$606$	−18.1084	+	6.59090i	−0.735602	+	0.267737i
$607$	−1.51860			−0.0616380			−0.0308190	−	0.999525i	$-0.509812\pi$
$607$	−1.51860			−0.0616380			−0.0308190	+	0.999525i	$0.509812\pi$
$608$		0			0
$609$	−13.0902			−0.530440
$610$	−0.720774	+	0.262340i	−0.0291833	+	0.0106218i
$611$	1.35098	−	7.66177i	0.0546547	−	0.309962i
$612$	1.89377	−	1.58906i	0.0765510	−	0.0642339i
$613$	−18.7894	−	15.7662i	−0.758898	−	0.636791i	0.178942	−	0.983860i	$-0.442733\pi$
$613$	−18.7894	−	15.7662i	−0.758898	−	0.636791i	−0.937840	+	0.347069i	$0.887177\pi$
$614$	5.63275	+	31.9449i	0.227319	+	1.28919i
$615$	6.70820	+	11.6190i	0.270501	+	0.468521i
$616$	−23.5847	+	40.8498i	−0.950253	+	1.64589i
$617$	−16.2290	−	5.90686i	−0.653354	−	0.237801i	−0.00598947	−	0.999982i	$-0.501907\pi$
$617$	−16.2290	−	5.90686i	−0.653354	−	0.237801i	−0.647364	+	0.762181i	$0.724129\pi$
$618$	−1.30389	−	0.474578i	−0.0524502	−	0.0190903i
$619$	−18.3885	+	31.8499i	−0.739098	+	1.28016i	0.213804	+	0.976877i	$0.431415\pi$
$619$	−18.3885	+	31.8499i	−0.739098	+	1.28016i	−0.952902	+	0.303279i	$0.901919\pi$
$620$	0.449028	+	0.777739i	0.0180334	+	0.0312348i
$621$	2.46804	+	13.9969i	0.0990388	+	0.561677i
$622$	4.97806	+	4.17709i	0.199602	+	0.167486i
$623$	−57.5652	+	48.3029i	−2.30630	+	1.93521i
$624$	1.49651	−	8.48711i	0.0599082	−	0.339756i
$625$	−4.15007	+	1.51050i	−0.166003	+	0.0604200i
$626$	−8.95554			−0.357935
$627$		0			0
$628$	−9.61803			−0.383801
$629$	−14.9439	+	5.43913i	−0.595852	+	0.216872i
$630$	−1.72947	+	9.80828i	−0.0689035	+	0.390771i
$631$	−19.1511	+	16.0697i	−0.762394	+	0.639724i	−0.938749	−	0.344602i	$-0.888014\pi$
$631$	−19.1511	+	16.0697i	−0.762394	+	0.639724i	0.176355	+	0.984327i	$0.443569\pi$
$632$	17.9380	+	15.0518i	0.713536	+	0.598728i
$633$	−3.67793	−	20.8586i	−0.146184	−	0.829053i
$634$	5.20163	+	9.00948i	0.206583	+	0.357812i
$635$	9.85359	−	17.0669i	0.391028	−	0.677280i
$636$	−0.306563	−	0.111580i	−0.0121560	−	0.00442443i
$637$	31.6517	+	11.5203i	1.25408	+	0.456450i
$638$	−5.59017	+	9.68246i	−0.221317	+	0.383332i
$639$	−9.82084	−	17.0102i	−0.388506	−	0.672913i
$640$	−0.756977	−	4.29303i	−0.0299221	−	0.169697i
$641$	22.1503	+	18.5863i	0.874886	+	0.734116i	0.965121	−	0.261804i	$-0.0843175\pi$
$641$	22.1503	+	18.5863i	0.874886	+	0.734116i	−0.0902353	+	0.995920i	$0.528762\pi$
$642$	−12.2636	+	10.2904i	−0.484005	+	0.406128i
$643$	1.33852	−	7.59110i	0.0527859	−	0.299364i	−0.946973	−	0.321313i	$-0.895876\pi$
$643$	1.33852	−	7.59110i	0.0527859	−	0.299364i	0.999759	+	0.0219489i	$0.00698710\pi$
$644$	6.44075	−	2.34424i	0.253801	−	0.0923760i
$645$	−9.19256			−0.361957
$646$		0			0
$647$	−32.1246			−1.26295			−0.631474	−	0.775397i	$-0.717550\pi$
$647$	−32.1246			−1.26295			−0.631474	+	0.775397i	$0.717550\pi$
$648$	4.41870	−	1.60828i	0.173583	−	0.0631790i
$649$	−1.75925	+	9.97719i	−0.0690565	+	0.391639i
$650$	−9.62328	+	8.07489i	−0.377456	+	0.316723i
$651$	−4.48450	−	3.76294i	−0.175762	−	0.147481i
$652$	−0.700573	−	3.97315i	−0.0274366	−	0.155601i
$653$	−9.87132	−	17.0976i	−0.386295	−	0.669082i	0.605653	−	0.795729i	$-0.292912\pi$
$653$	−9.87132	−	17.0976i	−0.386295	−	0.669082i	−0.991948	+	0.126647i	$0.959579\pi$
$654$	0.502029	−	0.869539i	0.0196309	−	0.0340017i
$655$	5.91235	+	2.15192i	0.231015	+	0.0840825i
$656$	−20.6665	−	7.52198i	−0.806891	−	0.293684i
$657$	7.28115	−	12.6113i	0.284065	−	0.492015i
$658$	6.29412	+	10.9017i	0.245371	+	0.424994i
$659$	3.24342	+	18.3943i	0.126346	+	0.716542i	0.980500	+	0.196521i	$0.0629645\pi$
$659$	3.24342	+	18.3943i	0.126346	+	0.716542i	−0.854154	+	0.520020i	$0.825924\pi$
$660$	2.48903	+	2.08854i	0.0968853	+	0.0812964i
$661$	3.86493	−	3.24306i	0.150328	−	0.126140i	−0.564522	−	0.825418i	$-0.690939\pi$
$661$	3.86493	−	3.24306i	0.150328	−	0.126140i	0.714850	+	0.699278i	$0.246495\pi$
$662$	4.95610	−	28.1074i	0.192624	−	1.09243i
$663$	8.40487	−	3.05912i	0.326418	−	0.118806i
$664$	3.80423			0.147633
$665$		0			0
$666$	12.2361			0.474138
$667$	6.46688	−	2.35375i	0.250399	−	0.0911376i
$668$	0.738570	−	4.18864i	0.0285761	−	0.162063i
$669$	12.2404	−	10.2709i	0.473241	−	0.397097i
$670$	−0.190916	−	0.160198i	−0.00737574	−	0.00618898i
$671$	0.331639	+	1.88082i	0.0128028	+	0.0726081i
$672$	−8.35410	−	14.4697i	−0.322266	−	0.558182i
$673$	14.1271	−	24.4688i	0.544559	−	0.943204i	−0.454075	−	0.890963i	$-0.650030\pi$
$673$	14.1271	−	24.4688i	0.544559	−	0.943204i	0.998635	−	0.0522410i	$-0.0166364\pi$
$674$	−17.8018	−	6.47932i	−0.685699	−	0.249574i
$675$	−17.7128	−	6.44695i	−0.681768	−	0.248143i
$676$	−1.09017	+	1.88823i	−0.0419296	+	0.0726242i
$677$	5.84510	+	10.1240i	0.224645	+	0.389097i	0.956213	−	0.292672i	$-0.0945443\pi$
$677$	5.84510	+	10.1240i	0.224645	+	0.389097i	−0.731568	+	0.681769i	$0.761211\pi$
$678$		0			0
$679$	−50.8362	−	42.6566i	−1.95091	−	1.63701i
$680$	7.20431	−	6.04514i	0.276273	−	0.231820i
$681$	−6.06431	+	34.3924i	−0.232385	+	1.31792i
$682$	−4.69846	+	1.71010i	−0.179913	+	0.0654831i
$683$	32.7445			1.25293			0.626466	−	0.779449i	$-0.284501\pi$
$683$	32.7445			1.25293			0.626466	+	0.779449i	$0.284501\pi$
$684$		0			0
$685$	−5.81966			−0.222358
$686$	−18.4571	+	6.71785i	−0.704697	+	0.256489i
$687$	0.834950	−	4.73523i	0.0318553	−	0.180660i
$688$	11.5434	−	9.68609i	0.440089	−	0.369279i
$689$	1.05865	+	0.888311i	0.0403313	+	0.0338419i
$690$	0.776578	+	4.40419i	0.0295638	+	0.167665i
$691$	−23.1525	−	40.1013i	−0.880762	−	1.52552i	−0.850496	−	0.525982i	$-0.823698\pi$
$691$	−23.1525	−	40.1013i	−0.880762	−	1.52552i	−0.0302661	−	0.999542i	$-0.509635\pi$
$692$	−4.80828	+	8.32819i	−0.182783	+	0.316590i
$693$	23.3028	+	8.48154i	0.885202	+	0.322187i
$694$	−27.4322	−	9.98450i	−1.04131	−	0.379006i
$695$	0.562306	−	0.973942i	0.0213295	−	0.0369437i
$696$	−4.75528	−	8.23639i	−0.180249	−	0.312200i
$697$	−3.96358	−	22.4786i	−0.150131	−	0.851437i
$698$	−10.2499	−	8.60069i	−0.387965	−	0.325541i
$699$	12.1322	−	10.1801i	0.458881	−	0.385047i
$700$	−1.57849	+	8.95207i	−0.0596614	+	0.338356i
$701$	31.7077	−	11.5407i	1.19758	−	0.435885i	0.335203	−	0.942146i	$-0.391195\pi$
$701$	31.7077	−	11.5407i	1.19758	−	0.435885i	0.862380	+	0.506261i	$0.168973\pi$
$702$	−19.6417			−0.741327
$703$		0			0
$704$	−31.5066			−1.18745
$705$	3.45168	−	1.25631i	0.129998	−	0.0473153i
$706$	−5.63783	+	31.9737i	−0.212182	+	1.20335i
$707$	45.2494	−	37.9687i	1.70178	−	1.42796i
$708$	−1.55847	−	1.30771i	−0.0585710	−	0.0491469i
$709$	2.32973	+	13.2126i	0.0874950	+	0.496209i	0.996790	+	0.0800573i	$0.0255103\pi$
$709$	2.32973	+	13.2126i	0.0874950	+	0.496209i	−0.909295	+	0.416152i	$0.863379\pi$
$710$	−8.81966	−	15.2761i	−0.330996	−	0.573302i
$711$	6.15537	−	10.6614i	0.230844	−	0.399834i
$712$	−51.3042	−	18.6732i	−1.92270	−	0.699807i
$713$	2.89208	+	1.05263i	0.108309	+	0.0394213i
$714$	−7.23607	+	12.5332i	−0.270803	+	0.469045i
$715$	−6.88191	−	11.9198i	−0.257369	−	0.445776i
$716$	−1.96338	−	11.1349i	−0.0733751	−	0.416131i
$717$	−14.2772	−	11.9800i	−0.533193	−	0.447402i
$718$	33.8765	−	28.4258i	1.26426	−	1.06084i
$719$	2.15011	−	12.1939i	0.0801854	−	0.454754i	−0.918107	−	0.396333i	$-0.870282\pi$
$719$	2.15011	−	12.1939i	0.0801854	−	0.454754i	0.998292	−	0.0584207i	$-0.0186065\pi$
$720$	−4.47663	+	1.62936i	−0.166834	+	0.0607227i
$721$	4.25325			0.158399
$722$		0			0
$723$	26.6312			0.990425
$724$	−14.2992	+	5.20449i	−0.531426	+	0.193423i
$725$	−1.58490	+	8.98839i	−0.0588615	+	0.333820i
$726$	−2.21275	+	1.85672i	−0.0821230	+	0.0689093i
$727$	−14.5975	−	12.2488i	−0.541393	−	0.454282i	0.330621	−	0.943764i	$-0.392742\pi$
$727$	−14.5975	−	12.2488i	−0.541393	−	0.454282i	−0.872014	+	0.489481i	$0.837186\pi$
$728$	6.96757	+	39.5150i	0.258235	+	1.46452i
$729$	−10.8090	−	18.7218i	−0.400334	−	0.693399i
$730$	6.53888	−	11.3257i	0.242015	−	0.419182i
$731$	14.6962	+	5.34896i	0.543557	+	0.197839i
$732$	−0.360387	−	0.131170i	−0.0133203	−	0.00484819i
$733$	−17.5902	+	30.4671i	−0.649708	+	1.12533i	0.333485	+	0.942755i	$0.391775\pi$
$733$	−17.5902	+	30.4671i	−0.649708	+	1.12533i	−0.983193	+	0.182571i	$0.941558\pi$
$734$	12.6210	+	21.8602i	0.465850	+	0.806876i
$735$	2.76152	+	15.6614i	0.101860	+	0.577678i
$736$	6.72895	+	5.64626i	0.248032	+	0.208124i
$737$	−0.475362	+	0.398876i	−0.0175102	+	0.0146928i
$738$	−3.04966	+	17.2955i	−0.112260	+	0.636656i
$739$	−9.89296	+	3.60074i	−0.363918	+	0.132455i	−0.517506	−	0.855680i	$-0.673139\pi$
$739$	−9.89296	+	3.60074i	−0.363918	+	0.132455i	0.153588	+	0.988135i	$0.450917\pi$
$740$	−4.91428			−0.180653
$741$		0			0
$742$	−2.23607			−0.0820886
$743$	−4.05831	+	1.47711i	−0.148885	+	0.0541897i	−0.415388	−	0.909644i	$-0.636354\pi$
$743$	−4.05831	+	1.47711i	−0.148885	+	0.0541897i	0.266503	+	0.963834i	$0.414132\pi$
$744$	0.738570	−	4.18864i	0.0270773	−	0.153563i
$745$	−21.8109	+	18.3015i	−0.799090	+	0.670516i
$746$	3.88922	+	3.26344i	0.142394	+	0.119483i
$747$	−0.347296	−	1.96962i	−0.0127069	−	0.0720645i
$748$	−2.76393	−	4.78727i	−0.101059	−	0.175040i
$749$	24.5357	−	42.4971i	0.896515	−	1.55281i
$750$	−13.5994	−	4.94976i	−0.496578	−	0.180740i
$751$	−41.5937	−	15.1389i	−1.51778	−	0.552426i	−0.557185	−	0.830388i	$-0.688119\pi$
$751$	−41.5937	−	15.1389i	−1.51778	−	0.552426i	−0.960592	+	0.277962i	$0.910341\pi$
$752$	−3.01064	+	5.21459i	−0.109787	+	0.190156i
$753$	−6.12261	−	10.6047i	−0.223120	−	0.386456i
$754$	1.65149	+	9.36608i	0.0601438	+	0.341092i
$755$	2.32663	+	1.95227i	0.0846746	+	0.0710504i
$756$	−10.8877	+	9.13584i	−0.395981	+	0.332267i
$757$	−0.647619	+	3.67283i	−0.0235381	+	0.133491i	−0.994312	−	0.106503i	$-0.966035\pi$
$757$	−0.647619	+	3.67283i	−0.0235381	+	0.133491i	0.970774	+	0.239995i	$0.0771457\pi$
$758$	−8.78380	+	3.19704i	−0.319042	+	0.116122i
$759$	11.1352			0.404181
$760$		0			0
$761$	−6.05573			−0.219520			−0.109760	−	0.993958i	$-0.535008\pi$
$761$	−6.05573			−0.219520			−0.109760	+	0.993958i	$0.535008\pi$
$762$	−20.7045	+	7.53583i	−0.750046	+	0.272994i
$763$	−0.534434	+	3.03093i	−0.0193478	+	0.109727i
$764$	8.04851	−	6.75350i	0.291185	−	0.244333i
$765$	−3.78753	−	3.17812i	−0.136939	−	0.114905i
$766$	−2.86634	−	16.2558i	−0.103565	−	0.587346i
$767$	4.30902	+	7.46344i	0.155590	+	0.269489i
$768$	7.80021	−	13.5104i	0.281466	−	0.487513i
$769$	33.9784	+	12.3671i	1.22529	+	0.445970i	0.871983	−	0.489537i	$-0.162834\pi$
$769$	33.9784	+	12.3671i	1.22529	+	0.445970i	0.353310	+	0.935506i	$0.385056\pi$
$770$	20.9273	+	7.61690i	0.754166	+	0.274494i
$771$	−5.32624	+	9.22531i	−0.191820	+	0.332242i
$772$	−1.62460	−	2.81389i	−0.0584706	−	0.101274i
$773$	6.43162	+	36.4755i	0.231329	+	1.31193i	0.850208	+	0.526447i	$0.176476\pi$
$773$	6.43162	+	36.4755i	0.231329	+	1.31193i	−0.618879	+	0.785486i	$0.712413\pi$
$774$	−9.21798	−	7.73480i	−0.331333	−	0.278022i
$775$	−3.12679	+	2.62369i	−0.112318	+	0.0942458i
$776$	8.37241	−	47.4823i	0.300552	−	1.70451i
$777$	30.1025	−	10.9564i	1.07992	−	0.393060i
$778$	−15.3884			−0.551702
$779$		0			0
$780$	2.76393			0.0989646
$781$	−41.2714	+	15.0216i	−1.47681	+	0.537514i
$782$	1.32119	−	7.49286i	0.0472458	−	0.267944i
$783$	−10.9318	+	9.17291i	−0.390672	+	0.327813i
$784$	−19.9699	−	16.7568i	−0.713212	−	0.598456i
$785$	3.34031	+	18.9438i	0.119221	+	0.676134i
$786$	−3.51722	−	6.09201i	−0.125455	−	0.217295i
$787$	−7.15942	+	12.4005i	−0.255206	+	0.442030i	−0.964951	−	0.262429i	$-0.915477\pi$
$787$	−7.15942	+	12.4005i	−0.255206	+	0.442030i	0.709746	+	0.704458i	$0.248810\pi$
$788$	1.46809	+	0.534340i	0.0522984	+	0.0190351i
$789$	−13.1330	−	4.78001i	−0.467546	−	0.170173i
$790$	5.52786	−	9.57454i	0.196673	−	0.340647i
$791$		0			0
$792$	3.12863	+	17.7434i	0.111171	+	0.630483i
$793$	1.24451	+	1.04427i	0.0441940	+	0.0370832i
$794$	−13.2453	+	11.1141i	−0.470059	+	0.394426i
$795$	−0.113301	+	0.642563i	−0.00401838	+	0.0227894i
$796$	−11.0021	+	4.00444i	−0.389960	+	0.141934i
$797$	−12.8658			−0.455729			−0.227864	−	0.973693i	$-0.573174\pi$
$797$	−12.8658			−0.455729			−0.227864	+	0.973693i	$0.573174\pi$
$798$		0			0
$799$	−6.24922			−0.221082
$800$	−10.9471	+	3.98443i	−0.387040	+	0.140871i
$801$	−4.98426	+	28.2671i	−0.176110	+	0.998770i
$802$	6.85171	−	5.74927i	0.241942	−	0.203014i
$803$	−24.9442	−	20.9306i	−0.880261	−	0.738626i
$804$	−0.0216386	−	0.122719i	−0.000763135	−	0.00432795i
$805$	−6.85410	−	11.8717i	−0.241575	−	0.418421i
$806$	−2.12663	+	3.68343i	−0.0749072	+	0.129743i
$807$	8.52196	+	3.10174i	0.299987	+	0.109186i
$808$	40.3279	+	14.6782i	1.41873	+	0.516376i
$809$	0.364745	−	0.631757i	0.0128238	−	0.0222114i	−0.859542	−	0.511065i	$-0.829251\pi$
$809$	0.364745	−	0.631757i	0.0128238	−	0.0222114i	0.872366	+	0.488853i	$0.162585\pi$
$810$	−1.11006	−	1.92268i	−0.0390035	−	0.0675560i
$811$	5.57826	+	31.6359i	0.195879	+	1.11089i	0.911161	+	0.412050i	$0.135187\pi$
$811$	5.57826	+	31.6359i	0.195879	+	1.11089i	−0.715282	+	0.698836i	$0.753702\pi$
$812$	5.27185	+	4.42361i	0.185006	+	0.155238i
$813$	12.8512	−	10.7834i	0.450710	−	0.378190i
$814$	4.75113	−	26.9450i	0.166527	−	0.944422i
$815$	−7.58227	+	2.75972i	−0.265595	+	0.0966688i
$816$	−6.92240			−0.242332
$817$		0			0
$818$	−25.7771			−0.901275
$819$	19.8226	−	7.21483i	0.692657	−	0.252107i
$820$	1.22481	−	6.94627i	0.0427724	−	0.242574i
$821$	−14.5812	+	12.2351i	−0.508888	+	0.427008i	−0.860738	−	0.509049i	$-0.829997\pi$
$821$	−14.5812	+	12.2351i	−0.508888	+	0.427008i	0.351849	+	0.936057i	$0.385553\pi$
$822$	4.98433	+	4.18235i	0.173848	+	0.145876i
$823$	−6.72389	−	38.1331i	−0.234380	−	1.32924i	−0.843915	−	0.536477i	$-0.819755\pi$
$823$	−6.72389	−	38.1331i	−0.234380	−	1.32924i	0.609535	−	0.792759i	$-0.291356\pi$
$824$	1.54508	+	2.67617i	0.0538256	+	0.0932286i
$825$	−7.38394	+	12.7894i	−0.257076	+	0.445268i
$826$	−13.1033	−	4.76922i	−0.455923	−	0.165942i
$827$	14.7827	+	5.38047i	0.514046	+	0.187097i	0.586001	−	0.810311i	$-0.300702\pi$
$827$	14.7827	+	5.38047i	0.514046	+	0.187097i	−0.0719550	+	0.997408i	$0.522924\pi$
$828$	1.30902	−	2.26728i	0.0454915	−	0.0787936i
$829$	5.84510	+	10.1240i	0.203009	+	0.351621i	0.949496	−	0.313778i	$-0.101595\pi$
$829$	5.84510	+	10.1240i	0.203009	+	0.351621i	−0.746488	+	0.665399i	$0.768261\pi$
$830$	−0.311892	−	1.76882i	−0.0108259	−	0.0613968i
$831$	−17.3228	−	14.5356i	−0.600922	−	0.504234i
$832$	−20.5308	+	17.2274i	−0.711778	+	0.597253i
$833$	4.69818	−	26.6447i	0.162782	−	0.923184i
$834$	−1.18153	+	0.430040i	−0.0409129	+	0.0148911i
$835$	−8.50651			−0.294380
$836$		0			0
$837$	−6.38197			−0.220593
$838$	−36.9143	+	13.4357i	−1.27518	+	0.464128i
$839$	−4.10112	+	23.2586i	−0.141586	+	0.802976i	0.828458	+	0.560051i	$0.189218\pi$
$839$	−4.10112	+	23.2586i	−0.141586	+	0.802976i	−0.970045	+	0.242926i	$0.921893\pi$
$840$	−14.5122	+	12.1771i	−0.500717	+	0.420151i
$841$	−16.9221	−	14.1993i	−0.583519	−	0.489631i
$842$	2.88798	+	16.3785i	0.0995262	+	0.564441i
$843$	2.60081	+	4.50474i	0.0895768	+	0.155151i
$844$	−5.56758	+	9.64333i	−0.191644	+	0.331937i
$845$	4.09770	+	1.49144i	0.140965	+	0.0513071i
$846$	4.51831	+	1.64453i	0.155343	+	0.0565401i
$847$	4.42705	−	7.66788i	0.152115	−	0.263471i
$848$	−0.534785	−	0.926274i	−0.0183646	−	0.0318084i
$849$	−0.185729	−	1.05332i	−0.00637420	−	0.0361499i
$850$	7.72986	+	6.48612i	0.265132	+	0.222472i
$851$	−12.9013	+	10.8255i	−0.442252	+	0.371094i
$852$	1.53152	−	8.68567i	0.0524689	−	0.297566i
$853$	20.9598	−	7.62874i	0.717650	−	0.261203i	0.0427221	−	0.999087i	$-0.486397\pi$
$853$	20.9598	−	7.62874i	0.717650	−	0.261203i	0.674928	+	0.737884i	$0.264175\pi$
$854$	−2.62866			−0.0899507
$855$		0			0
$856$	35.6525			1.21858
$857$	19.7845	−	7.20098i	0.675827	−	0.245981i	0.0187723	−	0.999824i	$-0.494024\pi$
$857$	19.7845	−	7.20098i	0.675827	−	0.245981i	0.657055	+	0.753843i	$0.271802\pi$
$858$	−2.67217	+	15.1546i	−0.0912264	+	0.517371i
$859$	16.1296	−	13.5344i	0.550336	−	0.461786i	−0.324719	−	0.945811i	$-0.605270\pi$
$859$	16.1296	−	13.5344i	0.550336	−	0.461786i	0.875055	+	0.484024i	$0.160825\pi$
$860$	3.70215	+	3.10647i	0.126242	+	0.105930i
$861$	7.98412	+	45.2802i	0.272098	+	1.54314i
$862$	−9.37132	−	16.2316i	−0.319189	−	0.552851i
$863$	−13.5923	+	23.5426i	−0.462687	+	0.801398i	−0.999094	−	0.0425616i	$-0.986448\pi$
$863$	−13.5923	+	23.5426i	−0.462687	+	0.801398i	0.536406	+	0.843960i	$0.319781\pi$
$864$	−17.1163	−	6.22982i	−0.582308	−	0.211943i
$865$	18.0732	+	6.57812i	0.614508	+	0.223663i
$866$	−5.48936	+	9.50785i	−0.186536	+	0.323090i
$867$	6.40013	+	11.0853i	0.217360	+	0.376478i
$868$	0.534434	+	3.03093i	0.0181399	+	0.102876i
$869$	−21.0874	−	17.6944i	−0.715341	−	0.600242i
$870$	−3.43975	+	2.88630i	−0.116619	+	0.0978546i
$871$	−0.0916626	+	0.519845i	−0.00310587	+	0.0176143i
$872$	−2.10122	+	0.764780i	−0.0711562	+	0.0258987i
$873$	−25.3480			−0.857900
$874$		0			0
$875$	44.3607			1.49966
$876$	6.14454	−	2.23643i	0.207605	−	0.0755620i
$877$	7.17019	−	40.6641i	0.242120	−	1.37313i	−0.584967	−	0.811057i	$-0.698893\pi$
$877$	7.17019	−	40.6641i	0.242120	−	1.37313i	0.827087	−	0.562074i	$-0.189996\pi$
$878$	10.4320	−	8.75350i	0.352064	−	0.295416i
$879$	22.2681	+	18.6851i	0.751083	+	0.630233i
$880$	1.84978	+	10.4906i	0.0623562	+	0.353639i
$881$	27.7877	+	48.1298i	0.936192	+	1.62153i	0.772494	+	0.635022i	$0.219009\pi$
$881$	27.7877	+	48.1298i	0.936192	+	1.62153i	0.163699	+	0.986510i	$0.447657\pi$
$882$	−10.4086	+	18.0283i	−0.350477	+	0.607043i
$883$	−40.4391	−	14.7186i	−1.36089	−	0.495322i	−0.444558	−	0.895750i	$-0.646639\pi$
$883$	−40.4391	−	14.7186i	−1.36089	−	0.495322i	−0.916328	+	0.400428i	$0.868861\pi$
$884$	−4.41870	−	1.60828i	−0.148617	−	0.0540921i
$885$	−2.03444	+	3.52376i	−0.0683870	+	0.118450i
$886$	−4.22050	−	7.31012i	−0.141790	−	0.245588i
$887$	4.62418	+	26.2250i	0.155265	+	0.880550i	0.958543	+	0.284947i	$0.0919759\pi$
$887$	4.62418	+	26.2250i	0.155265	+	0.880550i	−0.803279	+	0.595603i	$0.796913\pi$
$888$	17.8292	+	14.9605i	0.598309	+	0.502041i
$889$	51.7367	−	43.4123i	1.73519	−	1.45600i
$890$	−4.47614	+	25.3855i	−0.150041	+	0.850923i
$891$	−5.19449	+	1.89064i	−0.174022	+	0.0633389i
$892$	−8.40051			−0.281270
$893$		0			0
$894$	31.8328			1.06465
$895$	−21.2496	+	7.73422i	−0.710296	+	0.258527i
$896$	2.59420	−	14.7124i	0.0866661	−	0.491508i
$897$	7.25608	−	6.08857i	0.242273	−	0.203291i
$898$	31.4870	+	26.4207i	1.05073	+	0.881670i
$899$	0.536602	+	3.04322i	0.0178967	+	0.101497i
$900$	1.73607	+	3.00696i	0.0578689	+	0.100232i
$901$	0.555029	−	0.961339i	0.0184907	−	0.0320268i
$902$	36.9022	+	13.4313i	1.22871	+	0.447214i
$903$	−29.6035	−	10.7748i	−0.985143	−	0.358563i
$904$		0			0
$905$	15.2169	+	26.3565i	0.505827	+	0.876118i
$906$	−0.589655	−	3.34410i	−0.0195900	−	0.111100i
$907$	9.69334	+	8.13368i	0.321862	+	0.270074i	0.789374	−	0.613912i	$-0.210405\pi$
$907$	9.69334	+	8.13368i	0.321862	+	0.270074i	−0.467512	+	0.883987i	$0.654850\pi$
$908$	14.0647	−	11.8016i	0.466752	−	0.391651i
$909$	3.91790	−	22.2195i	0.129949	−	0.736975i
$910$	17.8018	−	6.47932i	0.590124	−	0.214787i
$911$	18.3601			0.608297			0.304149	−	0.952625i	$-0.401628\pi$
$911$	18.3601			0.608297			0.304149	+	0.952625i	$0.401628\pi$
$912$		0			0
$913$	−4.47214			−0.148006
$914$	21.7712	−	7.92405i	0.720126	−	0.262104i
$915$	−0.133194	+	0.755378i	−0.00440324	+	0.0249720i
$916$	−1.93646	+	1.62488i	−0.0639823	+	0.0536875i
$917$	16.5177	+	13.8600i	0.545462	+	0.457697i
$918$	2.73966	+	15.5374i	0.0904223	+	0.512811i
$919$	1.31966	+	2.28572i	0.0435316	+	0.0753989i	0.886970	−	0.461827i	$-0.152806\pi$
$919$	1.31966	+	2.28572i	0.0435316	+	0.0753989i	−0.843439	+	0.537225i	$0.819472\pi$
$920$	4.97980	−	8.62526i	0.164179	−	0.284366i
$921$	30.4815	+	11.0943i	1.00440	+	0.365571i
$922$	−37.7582	−	13.7428i	−1.24350	−	0.452597i
$923$	−18.6803	+	32.3553i	−0.614871	+	1.06499i
$924$	5.56758	+	9.64333i	0.183160	+	0.317242i
$925$	−3.87858	−	21.9965i	−0.127527	−	0.723241i
$926$	−15.1778	−	12.7357i	−0.498773	−	0.418520i
$927$	1.24451	−	1.04427i	0.0408752	−	0.0342984i
$928$	−1.53152	+	8.68567i	−0.0502745	+	0.285121i
$929$	20.2096	−	7.35568i	0.663055	−	0.241332i	0.0115000	−	0.999934i	$-0.496339\pi$
$929$	20.2096	−	7.35568i	0.663055	−	0.241332i	0.651555	+	0.758602i	$0.274117\pi$
$930$	−2.00811			−0.0658487
$931$		0			0
$932$	−8.32624			−0.272735
$933$	6.10649	−	2.22258i	0.199918	−	0.0727641i
$934$	0.0481899	−	0.273298i	0.00157682	−	0.00894260i
$935$	−8.46918	+	7.10649i	−0.276972	+	0.232407i
$936$	11.7406	+	9.85152i	0.383753	+	0.322007i
$937$	−7.25821	−	41.1634i	−0.237115	−	1.34475i	−0.838113	−	0.545497i	$-0.816341\pi$
$937$	−7.25821	−	41.1634i	−0.237115	−	1.34475i	0.600997	−	0.799251i	$-0.294770\pi$
$938$	−0.427051	−	0.739674i	−0.0139437	−	0.0241512i
$939$	−4.47777	+	7.75572i	−0.146126	+	0.253098i
$940$	−1.81466	−	0.660481i	−0.0591875	−	0.0215425i
$941$	−13.6780	−	4.97840i	−0.445892	−	0.162291i	0.109309	−	0.994008i	$-0.465136\pi$
$941$	−13.6780	−	4.97840i	−0.445892	−	0.162291i	−0.555200	+	0.831717i	$0.687358\pi$
$942$	10.7533	−	18.6252i	0.350361	−	0.606843i
$943$	−12.0862	−	20.9339i	−0.393581	−	0.681703i
$944$	−1.15822	−	6.56858i	−0.0376968	−	0.213789i
$945$	21.7753	+	18.2717i	0.708352	+	0.594378i
$946$	−20.6120	+	17.2955i	−0.670155	+	0.562327i
$947$	−1.01057	+	5.73125i	−0.0328392	+	0.186240i	−0.996815	−	0.0797499i	$-0.974588\pi$
$947$	−1.01057	+	5.73125i	−0.0328392	+	0.186240i	0.963976	+	0.265990i	$0.0856989\pi$
$948$	5.19449	−	1.89064i	0.168709	−	0.0614052i
$949$	−27.6992			−0.899153
$950$		0			0
$951$	10.4033			0.337349
$952$	30.2862	−	11.0233i	0.981582	−	0.357267i
$953$	6.47981	−	36.7488i	0.209902	−	1.19041i	−0.679636	−	0.733549i	$-0.737862\pi$
$953$	6.47981	−	36.7488i	0.209902	−	1.19041i	0.889538	−	0.456861i	$-0.151026\pi$
$954$	−0.654280	+	0.549006i	−0.0211831	+	0.0177747i
$955$	−16.0970	−	13.5070i	−0.520887	−	0.437076i
$956$	1.70147	+	9.64951i	0.0550295	+	0.312088i
$957$	5.59017	+	9.68246i	0.180705	+	0.312989i
$958$	−15.9232	+	27.5798i	−0.514455	+	0.891063i
$959$	−18.7415	−	6.82134i	−0.605194	−	0.220273i
$960$	−11.8906	−	4.32784i	−0.383769	−	0.139680i
$961$	14.8090	−	25.6500i	0.477710	−	0.827418i
$962$	−11.6372	−	20.1562i	−0.375198	−	0.649862i
$963$	−3.25479	−	18.4589i	−0.104884	−	0.594828i
$964$	−10.7253	−	8.99957i	−0.345438	−	0.289857i
$965$	−4.97806	+	4.17709i	−0.160249	+	0.134465i
$966$	−2.66137	+	15.0934i	−0.0856283	+	0.485622i
$967$	−31.6754	+	11.5289i	−1.01861	+	0.370744i	−0.796734	−	0.604331i	$-0.793441\pi$
$967$	−31.6754	+	11.5289i	−1.01861	+	0.370744i	−0.221877	+	0.975075i	$0.571218\pi$
$968$	6.43288			0.206761
$969$		0			0
$970$	−22.7639			−0.730906
$971$	16.0486	−	5.84120i	0.515023	−	0.187453i	−0.0714157	−	0.997447i	$-0.522752\pi$
$971$	16.0486	−	5.84120i	0.515023	−	0.187453i	0.586439	+	0.809994i	$0.300529\pi$
$972$	−1.55511	+	8.81948i	−0.0498803	+	0.282885i
$973$	2.95241	−	2.47737i	0.0946500	−	0.0794208i
$974$	−14.0123	−	11.7577i	−0.448984	−	0.376742i
$975$	2.18142	+	12.3715i	0.0698614	+	0.396204i
$976$	−0.628677	−	1.08890i	−0.0201235	−	0.0348549i
$977$	14.1271	−	24.4688i	0.451966	−	0.782827i	−0.546542	−	0.837431i	$-0.684056\pi$
$977$	14.1271	−	24.4688i	0.451966	−	0.782827i	0.998508	+	0.0546039i	$0.0173896\pi$
$978$	8.47724	+	3.08546i	0.271072	+	0.0986622i
$979$	60.3117	+	21.9516i	1.92757	+	0.701578i
$980$	4.18034	−	7.24056i	0.133536	−	0.231291i
$981$	0.587785	+	1.01807i	0.0187665	+	0.0325046i
$982$	3.32139	+	18.8365i	0.105990	+	0.601098i
$983$	−16.5537	−	13.8902i	−0.527980	−	0.443028i	0.339423	−	0.940634i	$-0.389768\pi$
$983$	−16.5537	−	13.8902i	−0.527980	−	0.443028i	−0.867403	+	0.497606i	$0.834213\pi$
$984$	−25.5901	+	21.4726i	−0.815782	+	0.684523i
$985$	0.542583	−	3.07714i	0.0172881	−	0.0980459i
$986$	7.17861	−	2.61280i	0.228614	−	0.0832085i
$987$	12.5882			0.400688
$988$		0			0
$989$	16.5623			0.526651
$990$	7.99350	−	2.90940i	0.254050	−	0.0924667i
$991$	3.65604	−	20.7344i	0.116138	−	0.658650i	−0.870043	−	0.492976i	$-0.835909\pi$
$991$	3.65604	−	20.7344i	0.116138	−	0.658650i	0.986181	−	0.165674i	$-0.0529799\pi$
$992$	−3.02149	+	2.53533i	−0.0959323	+	0.0804968i
$993$	−21.8637	−	18.3458i	−0.693823	−	0.582187i
$994$	−10.4972	−	59.5325i	−0.332950	−	1.88826i
$995$	11.7082	+	20.2792i	0.371175	+	0.642894i
$996$	0.449028	−	0.777739i	0.0142280	−	0.0246436i
$997$	−6.69495	−	2.43676i	−0.212031	−	0.0771730i	0.233821	−	0.972280i	$-0.424877\pi$
$997$	−6.69495	−	2.43676i	−0.212031	−	0.0771730i	−0.445852	+	0.895107i	$0.647099\pi$
$998$	23.7813	+	8.65568i	0.752784	+	0.273991i
$999$	17.4615	−	30.2442i	0.552457	−	0.956884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.m.62.3		24
19.2	odd	18		361.2.a.i.1.3	yes	4
19.3	odd	18		361.2.c.j.292.2		8
19.4	even	9	inner	361.2.e.m.99.3		24
19.5	even	9		361.2.c.j.68.3		8
19.6	even	9	inner	361.2.e.m.28.2		24
19.7	even	3	inner	361.2.e.m.245.2		24
19.8	odd	6	inner	361.2.e.m.54.3		24
19.9	even	9	inner	361.2.e.m.234.2		24
19.10	odd	18	inner	361.2.e.m.234.3		24
19.11	even	3	inner	361.2.e.m.54.2		24
19.12	odd	6	inner	361.2.e.m.245.3		24
19.13	odd	18	inner	361.2.e.m.28.3		24
19.14	odd	18		361.2.c.j.68.2		8
19.15	odd	18	inner	361.2.e.m.99.2		24
19.16	even	9		361.2.c.j.292.3		8
19.17	even	9		361.2.a.i.1.2	✓	4
19.18	odd	2	inner	361.2.e.m.62.2		24
57.2	even	18		3249.2.a.bc.1.2		4
57.17	odd	18		3249.2.a.bc.1.3		4
76.55	odd	18		5776.2.a.bu.1.2		4
76.59	even	18		5776.2.a.bu.1.3		4
95.59	odd	18		9025.2.a.bj.1.2		4
95.74	even	18		9025.2.a.bj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.2	✓	4	19.17	even	9
361.2.a.i.1.3	yes	4	19.2	odd	18
361.2.c.j.68.2		8	19.14	odd	18
361.2.c.j.68.3		8	19.5	even	9
361.2.c.j.292.2		8	19.3	odd	18
361.2.c.j.292.3		8	19.16	even	9
361.2.e.m.28.2		24	19.6	even	9	inner
361.2.e.m.28.3		24	19.13	odd	18	inner
361.2.e.m.54.2		24	19.11	even	3	inner
361.2.e.m.54.3		24	19.8	odd	6	inner
361.2.e.m.62.2		24	19.18	odd	2	inner
361.2.e.m.62.3		24	1.1	even	1	trivial
361.2.e.m.99.2		24	19.15	odd	18	inner
361.2.e.m.99.3		24	19.4	even	9	inner
361.2.e.m.234.2		24	19.9	even	9	inner
361.2.e.m.234.3		24	19.10	odd	18	inner
361.2.e.m.245.2		24	19.7	even	3	inner
361.2.e.m.245.3		24	19.12	odd	6	inner
3249.2.a.bc.1.2		4	57.2	even	18
3249.2.a.bc.1.3		4	57.17	odd	18
5776.2.a.bu.1.2		4	76.55	odd	18
5776.2.a.bu.1.3		4	76.59	even	18
9025.2.a.bj.1.2		4	95.59	odd	18
9025.2.a.bj.1.3		4	95.74	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10467 - 0.402069i) q^{2} +(0.204136 - 1.15771i) q^{3} +(-0.473442 + 0.397265i) q^{4} +(0.946883 + 0.794529i) q^{5} +(-0.239976 - 1.36097i) q^{6} +(2.11803 + 3.66854i) q^{7} +(-1.53884 + 2.66535i) q^{8} +(1.52045 + 0.553400i) q^{9} +(1.36545 + 0.496984i) q^{10} +(1.80902 - 3.13331i) q^{11} +(0.363271 + 0.629204i) q^{12} +(-0.534434 - 3.03093i) q^{13} +(3.81475 + 3.20095i) q^{14} +(1.11313 - 0.934025i) q^{15} +(-0.413624 + 2.34578i) q^{16} +(-2.32305 + 0.845520i) q^{17} +1.90211 q^{18} -0.763932 q^{20} +(4.67948 - 1.70319i) q^{21} +(0.738570 - 4.18864i) q^{22} +(-2.00553 + 1.68284i) q^{23} +(2.77157 + 2.32563i) q^{24} +(-0.602930 - 3.41939i) q^{25} +(-1.80902 - 3.13331i) q^{26} +(2.71441 - 4.70150i) q^{27} +(-2.46015 - 0.895420i) q^{28} +(-2.47013 - 0.899053i) q^{29} +(0.854102 - 1.47935i) q^{30} +(-0.587785 - 1.01807i) q^{31} +(-0.582624 - 3.30423i) q^{32} +(-3.25818 - 2.73394i) q^{33} +(-2.22626 + 1.86805i) q^{34} +(-0.909234 + 5.15652i) q^{35} +(-0.939693 + 0.342020i) q^{36} +6.43288 q^{37} -3.61803 q^{39} +(-3.57480 + 1.30112i) q^{40} +(-1.60330 + 9.09278i) q^{41} +(4.48450 - 3.76294i) q^{42} +(-4.84618 - 4.06643i) q^{43} +(0.388289 + 2.20210i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.53884 + 2.66535i) q^{46} +(2.37542 + 0.864580i) q^{47} +(2.63130 + 0.957714i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-2.04087 - 3.53489i) q^{50} +(0.504651 + 2.86202i) q^{51} +(1.45710 + 1.22265i) q^{52} +(-0.343975 + 0.288630i) q^{53} +(1.10822 - 6.28501i) q^{54} +(4.20243 - 1.52956i) q^{55} -13.0373 q^{56} -3.09017 q^{58} +(-2.63130 + 0.957714i) q^{59} +(-0.155946 + 0.884412i) q^{60} +(-0.404367 + 0.339304i) q^{61} +(-1.05865 - 0.888311i) q^{62} +(1.19020 + 6.74997i) q^{63} +(-4.35410 - 7.54153i) q^{64} +(1.90211 - 3.29456i) q^{65} +(-4.69846 - 1.71010i) q^{66} +(-0.161170 - 0.0586610i) q^{67} +(0.763932 - 1.32317i) q^{68} +(1.53884 + 2.66535i) q^{69} +(1.06887 + 6.06185i) q^{70} +(-9.29918 - 7.80294i) q^{71} +(-3.81475 + 3.20095i) q^{72} +(1.56283 - 8.86327i) q^{73} +(7.10624 - 2.58646i) q^{74} -4.08174 q^{75} +15.3262 q^{77} +(-3.99675 + 1.45470i) q^{78} +(1.32119 - 7.49286i) q^{79} +(-2.25544 + 1.89254i) q^{80} +(-1.17041 - 0.982092i) q^{81} +(1.88480 + 10.6892i) q^{82} +(-0.618034 - 1.07047i) q^{83} +(-1.53884 + 2.66535i) q^{84} +(-2.87145 - 1.04512i) q^{85} +(-6.98844 - 2.54358i) q^{86} +(-1.54508 + 2.67617i) q^{87} +(5.56758 + 9.64333i) q^{88} +(3.08044 + 17.4701i) q^{89} +(1.80108 + 1.51128i) q^{90} +(9.98713 - 8.38020i) q^{91} +(0.280969 - 1.59345i) q^{92} +(-1.29862 + 0.472660i) q^{93} +2.97168 q^{94} -3.94427 q^{96} +(-14.7212 + 5.35806i) q^{97} +(-2.23412 + 12.6703i) q^{98} +(4.48450 - 3.76294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) \) 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more