LMFDB - Embedded newform 357.2.bl.a.250.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			250.14
Character	$\chi$	$=$	357.250
Dual form			357.2.bl.a.10.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.235499 + 0.0310041i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(-1.87735 - 0.503035i) q^{4} +(-0.00654072 - 0.00573606i) q^{5} +(-0.131965 + 0.197500i) q^{6} +(1.26448 - 2.32402i) q^{7} +(-0.865421 - 0.358469i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(-0.00136250 - 0.00155363i) q^{10} +(1.05308 + 0.0690224i) q^{11} +(1.28149 - 1.46126i) q^{12} +(3.83168 - 3.83168i) q^{13} +(0.369839 - 0.508102i) q^{14} +(0.00803740 - 0.00332920i) q^{15} +(3.17368 + 1.83233i) q^{16} +(-1.69172 - 3.76006i) q^{17} +(-0.118766 - 0.205708i) q^{18} +(-0.347810 + 2.64188i) q^{19} +(0.00939381 + 0.0140588i) q^{20} +(1.52509 + 2.16197i) q^{21} +(0.245859 + 0.0489044i) q^{22} +(7.58370 - 3.73987i) q^{23} +(0.704267 - 0.617625i) q^{24} +(-0.652621 - 4.95715i) q^{25} +(1.02116 - 0.783561i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-3.54295 + 3.72693i) q^{28} +(-1.00808 + 5.06794i) q^{29} +(0.00199602 - 0.000534833i) q^{30} +(-4.84339 - 2.38850i) q^{31} +(2.17690 + 1.67039i) q^{32} +(-0.527669 + 0.913949i) q^{33} +(-0.281822 - 0.937944i) q^{34} +(-0.0216014 + 0.00794765i) q^{35} +(0.743775 + 1.79563i) q^{36} +(-0.412260 - 6.28987i) q^{37} +(-0.163818 + 0.611378i) q^{38} +(1.74182 + 5.13124i) q^{39} +(0.00360428 + 0.00730875i) q^{40} +(1.22485 + 6.15774i) q^{41} +(0.292127 + 0.556427i) q^{42} +(1.72205 - 4.15739i) q^{43} +(-1.94228 - 0.659314i) q^{44} +(-0.000568983 + 0.00868100i) q^{45} +(1.90191 - 0.645611i) q^{46} +(0.355382 + 1.32630i) q^{47} +(-3.04705 + 2.03597i) q^{48} +(-3.80217 - 5.87737i) q^{49} -1.18764i q^{50} +(4.12053 + 0.145777i) q^{51} +(-9.12088 + 5.26595i) q^{52} +(-5.95550 + 7.76136i) q^{53} +(0.237023 - 0.0155353i) q^{54} +(-0.00649197 - 0.00649197i) q^{55} +(-1.92740 + 1.55798i) q^{56} +(-2.21560 - 1.48041i) q^{57} +(-0.394528 + 1.16224i) q^{58} +(-12.2413 + 1.61160i) q^{59} +(-0.0167637 + 0.00220699i) q^{60} +(-1.55873 + 4.59188i) q^{61} +(-1.06656 - 0.712655i) q^{62} +(-2.61354 + 0.411595i) q^{63} +(-4.72174 - 4.72174i) q^{64} +(-0.0470407 + 0.00308321i) q^{65} +(-0.152602 + 0.198875i) q^{66} +(0.347577 - 0.200674i) q^{67} +(1.28451 + 7.90996i) q^{68} +8.45572i q^{69} +(-0.00533352 + 0.00120194i) q^{70} +(11.1814 - 7.47114i) q^{71} +(0.242442 + 0.904806i) q^{72} +(3.43863 - 1.16726i) q^{73} +(0.0979247 - 1.49404i) q^{74} +(4.73458 + 1.60717i) q^{75} +(1.98192 - 4.78478i) q^{76} +(1.49201 - 2.36010i) q^{77} +(0.251108 + 1.26241i) q^{78} +(-0.399476 - 0.810057i) q^{79} +(-0.0102479 - 0.0301892i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(0.0975366 + 1.48812i) q^{82} +(5.10769 + 12.3311i) q^{83} +(-1.77558 - 4.82595i) q^{84} +(-0.0105029 + 0.0342973i) q^{85} +(0.534437 - 0.925672i) q^{86} +(-4.09944 - 3.14561i) q^{87} +(-0.886613 - 0.437229i) q^{88} +(9.34042 - 2.50276i) q^{89} +(-0.000403142 + 0.00202673i) q^{90} +(-4.05982 - 13.7500i) q^{91} +(-16.1186 + 3.20618i) q^{92} +(4.28436 - 3.28750i) q^{93} +(0.0425714 + 0.323362i) q^{94} +(0.0174289 - 0.0152847i) q^{95} +(-2.46095 + 1.21361i) q^{96} +(-16.8354 - 3.34876i) q^{97} +(-0.713186 - 1.50200i) q^{98} +(-0.586314 - 0.877481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	0.235499	+	0.0310041i	0.166523	+	0.0219232i	0.213327	−	0.976981i	$-0.431570\pi$
$2$	0.235499	+	0.0310041i	0.166523	+	0.0219232i	−0.0468035	+	0.998904i	$0.514903\pi$
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$4$	−1.87735	−	0.503035i	−0.938676	−	0.251518i
$5$	−0.00654072	−	0.00573606i	−0.00292510	−	0.00256524i	0.657882	−	0.753121i	$-0.271453\pi$
$5$	−0.00654072	−	0.00573606i	−0.00292510	−	0.00256524i	−0.660807	+	0.750556i	$0.729786\pi$
$6$	−0.131965	+	0.197500i	−0.0538747	+	0.0806292i
$7$	1.26448	−	2.32402i	0.477929	−	0.878398i
$7$	1.26448	−	2.32402i	0.477929	−	0.878398i
$8$	−0.865421	−	0.358469i	−0.305972	−	0.126738i
$9$	−0.608761	−	0.793353i	−0.202920	−	0.264451i
$10$	−0.00136250	−	0.00155363i	−0.000430859	−	0.000491300i
$11$	1.05308	+	0.0690224i	0.317515	+	0.0208110i	0.223327	−	0.974743i	$-0.428308\pi$
$11$	1.05308	+	0.0690224i	0.317515	+	0.0208110i	0.0941873	+	0.995554i	$0.469975\pi$
$12$	1.28149	−	1.46126i	0.369934	−	0.421829i
$13$	3.83168	−	3.83168i	1.06272	−	1.06272i	0.0648197	−	0.997897i	$-0.479353\pi$
$13$	3.83168	−	3.83168i	1.06272	−	1.06272i	0.997897	−	0.0648197i	$-0.0206472\pi$
$14$	0.369839	−	0.508102i	0.0988437	−	0.135796i
$15$	0.00803740	−	0.00332920i	0.00207525	−	0.000859596i
$16$	3.17368	+	1.83233i	0.793421	+	0.458082i
$17$	−1.69172	−	3.76006i	−0.410302	−	0.911950i
$17$	−1.69172	−	3.76006i	−0.410302	−	0.911950i
$18$	−0.118766	−	0.205708i	−0.0279934	−	0.0484859i
$19$	−0.347810	+	2.64188i	−0.0797931	+	0.606089i	0.904099	+	0.427324i	$0.140544\pi$
$19$	−0.347810	+	2.64188i	−0.0797931	+	0.606089i	−0.983892	+	0.178765i	$0.942790\pi$
$20$	0.00939381	+	0.0140588i	0.00210052	+	0.00314365i
$21$	1.52509	+	2.16197i	0.332801	+	0.471780i
$22$	0.245859	+	0.0489044i	0.0524174	+	0.0104265i
$23$	7.58370	−	3.73987i	1.58131	−	0.779816i	0.581871	−	0.813281i	$-0.302321\pi$
$23$	7.58370	−	3.73987i	1.58131	−	0.779816i	0.999440	+	0.0334643i	$0.0106540\pi$
$24$	0.704267	−	0.617625i	0.143758	−	0.126072i
$25$	−0.652621	−	4.95715i	−0.130524	−	0.991430i
$26$	1.02116	−	0.783561i	0.200265	−	0.153669i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	−3.54295	+	3.72693i	−0.669554	+	0.704324i
$29$	−1.00808	+	5.06794i	−0.187195	+	0.941093i	0.766940	+	0.641718i	$0.221778\pi$
$29$	−1.00808	+	5.06794i	−0.187195	+	0.941093i	−0.954136	+	0.299375i	$0.903222\pi$
$30$	0.00199602		0.000534833i	0.000364422		9.76467e-5i
$31$	−4.84339	−	2.38850i	−0.869899	−	0.428987i	−0.0481526	−	0.998840i	$-0.515333\pi$
$31$	−4.84339	−	2.38850i	−0.869899	−	0.428987i	−0.821746	+	0.569853i	$0.807000\pi$
$32$	2.17690	+	1.67039i	0.384825	+	0.295287i
$33$	−0.527669	+	0.913949i	−0.0918553	+	0.159098i
$34$	−0.281822	−	0.937944i	−0.0483320	−	0.160856i
$35$	−0.0216014	+	0.00794765i	−0.00365130	+	0.00134340i
$36$	0.743775	+	1.79563i	0.123963	+	0.299272i
$37$	−0.412260	−	6.28987i	−0.0677751	−	1.03405i	−0.887356	−	0.461085i	$-0.847460\pi$
$37$	−0.412260	−	6.28987i	−0.0677751	−	1.03405i	0.819581	−	0.572963i	$-0.194206\pi$
$38$	−0.163818	+	0.611378i	−0.0265748	+	0.0991786i
$39$	1.74182	+	5.13124i	0.278914	+	0.821656i
$40$	0.00360428	+	0.00730875i	0.000569886	+	0.00115562i
$41$	1.22485	+	6.15774i	0.191290	+	0.961678i	0.950474	+	0.310803i	$0.100598\pi$
$41$	1.22485	+	6.15774i	0.191290	+	0.961678i	−0.759185	+	0.650875i	$0.774402\pi$
$42$	0.292127	+	0.556427i	0.0450762	+	0.0858585i
$43$	1.72205	−	4.15739i	0.262610	−	0.633995i	−0.736489	−	0.676450i	$-0.763518\pi$
$43$	1.72205	−	4.15739i	0.262610	−	0.633995i	0.999098	+	0.0424542i	$0.0135176\pi$
$44$	−1.94228	−	0.659314i	−0.292809	−	0.0993954i
$45$	−0.000568983		0.00868100i	−8.48189e−5		0.00129409i
$46$	1.90191	−	0.645611i	0.280421	−	0.0951902i
$47$	0.355382	+	1.32630i	0.0518378	+	0.193461i	0.986989	−	0.160787i	$-0.0514033\pi$
$47$	0.355382	+	1.32630i	0.0518378	+	0.193461i	−0.935151	+	0.354249i	$0.884737\pi$
$48$	−3.04705	+	2.03597i	−0.439804	+	0.293867i
$49$	−3.80217	−	5.87737i	−0.543167	−	0.839625i
$50$		−	1.18764i		−	0.167958i
$51$	4.12053	+	0.145777i	0.576989	+	0.0204129i
$52$	−9.12088	+	5.26595i	−1.26484	+	0.730255i
$53$	−5.95550	+	7.76136i	−0.818051	+	1.06611i	0.178567	+	0.983928i	$0.442854\pi$
$53$	−5.95550	+	7.76136i	−0.818051	+	1.06611i	−0.996618	+	0.0821772i	$0.973813\pi$
$54$	0.237023	−	0.0155353i	0.0322547	−	0.00211409i
$55$	−0.00649197	−	0.00649197i	−0.000875377	−	0.000875377i
$56$	−1.92740	+	1.55798i	−0.257560	+	0.208194i
$57$	−2.21560	−	1.48041i	−0.293463	−	0.196086i
$58$	−0.394528	+	1.16224i	−0.0518041	+	0.152610i
$59$	−12.2413	+	1.61160i	−1.59368	+	0.209812i	−0.874506	−	0.485015i	$-0.838814\pi$
$59$	−12.2413	+	1.61160i	−1.59368	+	0.209812i	−0.719176	+	0.694828i	$0.755481\pi$
$60$	−0.0167637	+	0.00220699i	−0.00216419	+	0.000284921i
$61$	−1.55873	+	4.59188i	−0.199575	+	0.587930i	−0.999933	−	0.0115929i	$-0.996310\pi$
$61$	−1.55873	+	4.59188i	−0.199575	+	0.587930i	0.800357	+	0.599523i	$0.204643\pi$
$62$	−1.06656	−	0.712655i	−0.135454	−	0.0905073i
$63$	−2.61354	+	0.411595i	−0.329275	+	0.0518560i
$64$	−4.72174	−	4.72174i	−0.590217	−	0.590217i
$65$	−0.0470407	+	0.00308321i	−0.00583468	+	0.000382425i
$66$	−0.152602	+	0.198875i	−0.0187840	+	0.0244798i
$67$	0.347577	−	0.200674i	0.0424633	−	0.0245162i	−0.478618	−	0.878023i	$-0.658862\pi$
$67$	0.347577	−	0.200674i	0.0424633	−	0.0245162i	0.521081	+	0.853507i	$0.325529\pi$
$68$	1.28451	+	7.90996i	0.155770	+	0.959224i
$69$			8.45572i			1.01795i
$70$	−0.00533352	+	0.00120194i	−0.000637478	+	0.000143659i
$71$	11.1814	−	7.47114i	1.32698	−	0.886661i	0.328654	−	0.944450i	$-0.393405\pi$
$71$	11.1814	−	7.47114i	1.32698	−	0.886661i	0.998329	+	0.0577891i	$0.0184051\pi$
$72$	0.242442	+	0.904806i	0.0285721	+	0.106632i
$73$	3.43863	−	1.16726i	0.402462	−	0.136617i	−0.112867	−	0.993610i	$-0.536003\pi$
$73$	3.43863	−	1.16726i	0.402462	−	0.136617i	0.515328	+	0.856993i	$0.327670\pi$
$74$	0.0979247	−	1.49404i	0.0113835	−	0.173679i
$75$	4.73458	+	1.60717i	0.546702	+	0.185580i
$76$	1.98192	−	4.78478i	0.227342	−	0.548852i
$77$	1.49201	−	2.36010i	0.170030	−	0.268958i
$78$	0.251108	+	1.26241i	0.0284324	+	0.142939i
$79$	−0.399476	−	0.810057i	−0.0449445	−	0.0911385i	0.873242	−	0.487287i	$-0.162013\pi$
$79$	−0.399476	−	0.810057i	−0.0449445	−	0.0911385i	−0.918187	+	0.396148i	$0.870347\pi$
$80$	−0.0102479	−	0.0301892i	−0.00114574	−	0.00337525i
$81$	−0.258819	+	0.965926i	−0.0287577	+	0.107325i
$82$	0.0975366	+	1.48812i	0.0107711	+	0.164335i
$83$	5.10769	+	12.3311i	0.560642	+	1.35351i	0.909254	+	0.416242i	$0.136653\pi$
$83$	5.10769	+	12.3311i	0.560642	+	1.35351i	−0.348612	+	0.937267i	$0.613347\pi$
$84$	−1.77558	−	4.82595i	−0.193732	−	0.526554i
$85$	−0.0105029	+	0.0342973i	−0.00113920	+	0.00372007i
$86$	0.534437	−	0.925672i	0.0576298	−	0.0998178i
$87$	−4.09944	−	3.14561i	−0.439506	−	0.337245i
$88$	−0.886613	−	0.437229i	−0.0945132	−	0.0466088i
$89$	9.34042	−	2.50276i	0.990083	−	0.265292i	0.272798	−	0.962071i	$-0.412051\pi$
$89$	9.34042	−	2.50276i	0.990083	−	0.265292i	0.717285	+	0.696779i	$0.245384\pi$
$90$	−0.000403142		0.00202673i	−4.24949e−5		0.000213636i
$91$	−4.05982	−	13.7500i	−0.425585	−	1.44139i
$92$	−16.1186	+	3.20618i	−1.68048	+	0.334268i
$93$	4.28436	−	3.28750i	0.444267	−	0.340898i
$94$	0.0425714	+	0.323362i	0.00439091	+	0.0333523i
$95$	0.0174289	−	0.0152847i	0.00178817	−	0.00156818i
$96$	−2.46095	+	1.21361i	−0.251169	+	0.123863i
$97$	−16.8354	−	3.34876i	−1.70937	−	0.340015i	−0.758990	−	0.651103i	$-0.774307\pi$
$97$	−16.8354	−	3.34876i	−1.70937	−	0.340015i	−0.950381	+	0.311088i	$0.899307\pi$
$98$	−0.713186	−	1.50200i	−0.0720427	−	0.151725i
$99$	−0.586314	−	0.877481i	−0.0589268	−	0.0881901i
$100$	−1.26842	+	9.63461i	−0.126842	+	0.963461i
$101$	5.47075	+	9.47562i	0.544360	+	0.942859i	0.998647	+	0.0520039i	$0.0165608\pi$
$101$	5.47075	+	9.47562i	0.544360	+	0.942859i	−0.454287	+	0.890856i	$0.650106\pi$
$102$	0.965862	+	0.162084i	0.0956346	+	0.0160487i
$103$	15.8165	+	9.13164i	1.55844	+	0.899767i	0.997406	+	0.0719760i	$0.0229305\pi$
$103$	15.8165	+	9.13164i	1.55844	+	0.899767i	0.561036	+	0.827791i	$0.310403\pi$
$104$	−4.68955	+	1.94248i	−0.459849	+	0.190475i
$105$	0.00242601	−	0.0228888i	0.000236755	−	0.00223372i
$106$	−1.64315	+	1.64315i	−0.159597	+	0.159597i
$107$	5.37160	−	6.12514i	0.519292	−	0.592139i	−0.431444	−	0.902140i	$-0.641996\pi$
$107$	5.37160	−	6.12514i	0.519292	−	0.592139i	0.950736	+	0.310000i	$0.100329\pi$
$108$	−1.93942	−	0.127116i	−0.186621	−	0.0122318i
$109$	0.465916	+	0.531276i	0.0446267	+	0.0508870i	0.773723	−	0.633525i	$-0.218392\pi$
$109$	0.465916	+	0.531276i	0.0446267	+	0.0508870i	−0.729096	+	0.684412i	$0.760059\pi$
$110$	−0.00132758	−	0.00173013i	−0.000126580	−	0.000164962i
$111$	5.82355	+	2.41219i	0.552747	+	0.228955i
$112$	8.27144	−	5.05877i	0.781578	−	0.478009i
$113$	−4.53416	+	6.78584i	−0.426538	+	0.638359i	−0.981036	−	0.193826i	$-0.937910\pi$
$113$	−4.53416	+	6.78584i	−0.426538	+	0.638359i	0.554498	+	0.832185i	$0.312910\pi$
$114$	−0.475873	−	0.417330i	−0.0445696	−	0.0390865i
$115$	−0.0710550	−	0.0190391i	−0.00662591	−	0.00177541i
$116$	4.44187	−	9.00722i	0.412417	−	0.836299i
$117$	−5.37245	−	0.707297i	−0.496684	−	0.0653896i
$118$	−2.93279			−0.269985
$119$	−10.8776	−	0.822941i	−0.997150	−	0.0754388i
$120$	−0.00814915			−0.000743912
$121$	−9.80169	−	1.29042i	−0.891062	−	0.117311i
$122$	−0.509448	+	1.03306i	−0.0461233	+	0.0935288i
$123$	−6.06445	−	1.62496i	−0.546813	−	0.146518i
$124$	7.89126	+	6.92045i	0.708656	+	0.621475i
$125$	−0.0483322	+	0.0723342i	−0.00432296	+	0.00646977i
$126$	−0.628248	+	0.0158999i	−0.0559688	+	0.00141647i
$127$	8.82787	+	3.65662i	0.783347	+	0.324473i	0.738265	−	0.674510i	$-0.235645\pi$
$127$	8.82787	+	3.65662i	0.783347	+	0.324473i	0.0450815	+	0.998983i	$0.485645\pi$
$128$	−4.30636	−	5.61216i	−0.380632	−	0.496049i
$129$	2.96701	+	3.38322i	0.261230	+	0.297876i
$130$	−0.0111737		0.000732360i	−0.000979994		6.42322e-5i
$131$	−2.98083	+	3.39899i	−0.260437	+	0.296971i	−0.867250	−	0.497874i	$-0.834114\pi$
$131$	−2.98083	+	3.39899i	−0.260437	+	0.296971i	0.606813	+	0.794845i	$0.292448\pi$
$132$	1.45037	−	1.45037i	0.126238	−	0.126238i
$133$	5.69999	+	4.14893i	0.494252	+	0.359758i
$134$	0.0880760	−	0.0364823i	0.00760860	−	0.00315159i
$135$	−0.00753409	−	0.00434981i	−0.000648432	−	0.000374372i
$136$	0.116182	+	3.86047i	0.00996254	+	0.331032i
$137$	−0.301278	−	0.521829i	−0.0257399	−	0.0445829i	0.852869	−	0.522126i	$-0.174861\pi$
$137$	−0.301278	−	0.521829i	−0.0257399	−	0.0445829i	−0.878608	+	0.477543i	$0.841528\pi$
$138$	−0.262162	+	1.99132i	−0.0223167	+	0.169512i
$139$	0.0963923	+	0.144261i	0.00817589	+	0.0122361i	0.835535	−	0.549437i	$-0.185158\pi$
$139$	0.0963923	+	0.144261i	0.00817589	+	0.0122361i	−0.827359	+	0.561673i	$0.810158\pi$
$140$	0.0445513	−	0.00405429i	0.00376527	−	0.000342650i
$141$	−1.34671	−	0.267877i	−0.113413	−	0.0225593i
$142$	2.86484	−	1.41278i	0.240412	−	0.118558i
$143$	4.29953	−	3.77058i	0.359545	−	0.315312i
$144$	−0.478334	−	3.63330i	−0.0398611	−	0.302775i
$145$	0.0356636	−	0.0273656i	0.00296170	−	0.00227259i
$146$	0.845986	−	0.168277i	0.0700143	−	0.0139267i
$147$	6.95291	−	0.810566i	0.573466	−	0.0668544i
$148$	−2.39007	+	12.0157i	−0.196462	+	0.987683i
$149$	12.7766	−	3.42348i	1.04670	−	0.280463i	0.305813	−	0.952092i	$-0.401072\pi$
$149$	12.7766	−	3.42348i	1.04670	−	0.280463i	0.740888	+	0.671629i	$0.234405\pi$
$150$	1.06516	+	0.525280i	0.0869701	+	0.0428889i
$151$	11.6708	+	8.95532i	0.949756	+	0.728774i	0.962539	−	0.271145i	$-0.0874022\pi$
$151$	11.6708	+	8.95532i	0.949756	+	0.728774i	−0.0127822	+	0.999918i	$0.504069\pi$
$152$	1.24803	−	2.16166i	0.101229	−	0.175334i
$153$	−1.95321	+	3.63111i	−0.157907	+	0.293558i
$154$	0.424540	−	0.509544i	0.0342104	−	0.0410602i
$155$	0.0179787	+	0.0434045i	0.00144409	+	0.00348633i
$156$	−0.688819	−	10.5093i	−0.0551496	−	0.841421i
$157$	−2.80320	+	10.4617i	−0.223719	+	0.834932i	0.759194	+	0.650864i	$0.225593\pi$
$157$	−2.80320	+	10.4617i	−0.223719	+	0.834932i	−0.982914	+	0.184068i	$0.941073\pi$
$158$	−0.0689613	−	0.203153i	−0.00548626	−	0.0161620i
$159$	−4.32690	−	8.77409i	−0.343146	−	0.695831i
$160$	−0.00465702	−	0.0234124i	−0.000368169	−	0.00185091i
$161$	0.897917	−	22.3537i	0.0707658	−	1.76172i
$162$	−0.0908994	+	0.219451i	−0.00714173	+	0.0172417i
$163$	13.0790	+	4.43973i	1.02443	+	0.347746i	0.782568	−	0.622565i	$-0.213909\pi$
$163$	13.0790	+	4.43973i	1.02443	+	0.347746i	0.241860	+	0.970311i	$0.422243\pi$
$164$	0.798083	−	12.1764i	0.0623198	−	0.950817i
$165$	0.00869380	−	0.00295115i	0.000676811	−	0.000229746i
$166$	0.820545	+	3.06232i	0.0636866	+	0.237682i
$167$	−3.54198	+	2.36668i	−0.274087	+	0.183139i	−0.685015	−	0.728529i	$-0.740205\pi$
$167$	−3.54198	+	2.36668i	−0.274087	+	0.183139i	0.410929	+	0.911668i	$0.365205\pi$
$168$	−0.544843	−	2.41771i	−0.0420355	−	0.186530i
$169$		−	16.3635i		−	1.25873i
$170$	−0.00353678	+	0.00775137i	−0.000271259	+	0.000594503i
$171$	2.30768	−	1.33234i	0.176473	−	0.101886i
$172$	−5.32420	+	6.93863i	−0.405966	+	0.529066i
$173$	−21.1572	+	1.38671i	−1.60855	+	0.105430i	−0.842988	−	0.537932i	$-0.819206\pi$
$173$	−21.1572	+	1.38671i	−1.60855	+	0.105430i	−0.765562	+	0.643362i	$0.777539\pi$
$174$	−0.867889	−	0.867889i	−0.0657945	−	0.0657945i
$175$	−12.3458	−	4.75152i	−0.933252	−	0.359181i
$176$	3.21566	+	2.14864i	0.242390	+	0.161960i
$177$	3.96879	−	11.6917i	0.298313	−	0.878801i
$178$	2.27726	−	0.299807i	0.170688	−	0.0224715i
$179$	21.0971	−	2.77749i	1.57687	−	0.207599i	0.709299	−	0.704907i	$-0.249011\pi$
$179$	21.0971	−	2.77749i	1.57687	−	0.207599i	0.867574	+	0.497308i	$0.165678\pi$
$180$	0.00543503	−	0.0160111i	0.000405103	−	0.00119340i
$181$	−8.89479	−	5.94331i	−0.661145	−	0.441763i	0.179202	−	0.983812i	$-0.442648\pi$
$181$	−8.89479	−	5.94331i	−0.661145	−	0.441763i	−0.840346	+	0.542050i	$0.817648\pi$
$182$	−0.529780	−	3.36399i	−0.0392699	−	0.249356i
$183$	−3.42892	−	3.42892i	−0.253473	−	0.253473i
$184$	−7.90372	+	0.518037i	−0.582670	+	0.0381902i
$185$	−0.0333826	+	0.0435050i	−0.00245434	+	0.00319855i
$186$	1.11089	−	0.641372i	0.0814544	−	0.0470277i
$187$	−1.52198	−	4.07641i	−0.111298	−	0.298096i
$188$		−	2.66871i		−	0.194636i
$189$	0.786791	−	2.52606i	0.0572306	−	0.183744i
$190$	0.00457839	−	0.00305918i	0.000332151	−	0.000221936i
$191$	2.55426	+	9.53263i	0.184820	+	0.689757i	0.994669	+	0.103119i	$0.0328823\pi$
$191$	2.55426	+	9.53263i	0.184820	+	0.689757i	−0.809849	+	0.586638i	$0.800451\pi$
$192$	6.32317	−	2.14643i	0.456335	−	0.154905i
$193$	0.432341	−	6.59626i	0.0311206	−	0.474809i	−0.953646	−	0.300930i	$-0.902703\pi$
$193$	0.432341	−	6.59626i	0.0311206	−	0.474809i	0.984767	−	0.173879i	$-0.0556303\pi$
$194$	−3.86089	−	1.31060i	−0.277196	−	0.0940953i
$195$	0.0180403	−	0.0435532i	0.00129189	−	0.00311891i
$196$	4.18149	+	12.9465i	0.298678	+	0.924752i
$197$	−2.59299	−	13.0358i	−0.184743	−	0.928765i	−0.956251	−	0.292546i	$-0.905497\pi$
$197$	−2.59299	−	13.0358i	−0.184743	−	0.928765i	0.771508	−	0.636219i	$-0.219503\pi$
$198$	−0.110871	−	0.224824i	−0.00787927	−	0.0159776i
$199$	−1.67387	−	4.93108i	−0.118658	−	0.349555i	0.871332	−	0.490694i	$-0.163257\pi$
$199$	−1.67387	−	4.93108i	−0.118658	−	0.349555i	−0.989990	+	0.141139i	$0.954923\pi$
$200$	−1.21219	+	4.52396i	−0.0857150	+	0.319893i
$201$	0.0262494	+	0.400488i	0.00185149	+	0.0282483i
$202$	0.994576	+	2.40112i	0.0699781	+	0.168942i
$203$	10.5033	+	8.75112i	0.737189	+	0.614208i
$204$	−7.66235	−	2.34645i	−0.536472	−	0.164284i
$205$	0.0273098	−	0.0473019i	0.00190740	−	0.00330371i
$206$	3.44165	+	2.64087i	0.239791	+	0.183998i
$207$	−7.58370	−	3.73987i	−0.527104	−	0.259939i
$208$	19.1814	−	5.13965i	1.32999	−	0.356371i
$209$	−0.548620	+	2.75810i	−0.0379488	+	0.190782i
$210$	0.00128097	−	0.00531509i	8.83955e−5	−	0.000366776i
$211$	23.7543	−	4.72503i	1.63532	−	0.325285i	0.709919	−	0.704283i	$-0.248732\pi$
$211$	23.7543	−	4.72503i	1.63532	−	0.325285i	0.925397	+	0.378999i	$0.123732\pi$
$212$	15.0848	−	11.5750i	1.03603	−	0.794973i
$213$	1.75528	+	13.3327i	0.120270	+	0.913538i
$214$	1.45491	−	1.27593i	0.0994559	−	0.0872205i
$215$	−0.0351104	+	0.0173146i	−0.00239451	+	0.00118084i
$216$	−0.918726	−	0.182746i	−0.0625114	−	0.0124343i
$217$	−11.6753	+	8.23595i	−0.792572	+	0.559092i
$218$	0.0932514	+	0.139561i	0.00631578	+	0.00945223i
$219$	−0.473986	+	3.60028i	−0.0320290	+	0.243285i
$220$	0.00892203	+	0.0154534i	0.000601523	+	0.00104187i
$221$	−20.8895	−	7.92524i	−1.40518	−	0.533109i
$222$	1.29666	+	0.748624i	0.0870258	+	0.0502444i
$223$	15.0077	−	6.21641i	1.00499	−	0.416282i	0.181367	−	0.983415i	$-0.441948\pi$
$223$	15.0077	−	6.21641i	1.00499	−	0.416282i	0.823626	+	0.567134i	$0.191948\pi$
$224$	6.63468	−	2.94698i	0.443298	−	0.196903i
$225$	−3.53548	+	3.53548i	−0.235699	+	0.235699i
$226$	−1.27818	+	1.45749i	−0.0850233	+	0.0969505i
$227$	3.78729	+	0.248232i	0.251371	+	0.0164758i	0.190568	−	0.981674i	$-0.438967\pi$
$227$	3.78729	+	0.248232i	0.251371	+	0.0164758i	0.0608035	+	0.998150i	$0.480634\pi$
$228$	3.41476	+	3.89378i	0.226148	+	0.257872i
$229$	−5.61147	−	7.31301i	−0.370817	−	0.483258i	0.570254	−	0.821469i	$-0.306845\pi$
$229$	−5.61147	−	7.31301i	−0.370817	−	0.483258i	−0.941070	+	0.338211i	$0.890178\pi$
$230$	−0.0161431	−	0.00668670i	−0.00106445	−	0.000440908i
$231$	1.45681	+	2.38199i	0.0958511	+	0.156723i
$232$	2.68911	−	4.02454i	0.176549	−	0.264224i
$233$	−15.1455	−	13.2823i	−0.992217	−	0.870151i	−0.000683189	−	1.00000i	$-0.500217\pi$
$233$	−15.1455	−	13.2823i	−0.992217	−	0.870151i	−0.991534	+	0.129849i	$0.958551\pi$
$234$	−1.24328	−	0.333136i	−0.0812758	−	0.0217778i
$235$	0.00528330	−	0.0107135i	0.000344645	−	0.000698870i
$236$	23.7919	+	3.13227i	1.54872	+	0.203893i
$237$	0.903201			0.0586692
$238$	−2.53616	−	0.531053i	−0.164395	−	0.0344231i
$239$	−23.3228			−1.50863			−0.754314	−	0.656513i	$-0.772031\pi$
$239$	−23.3228			−1.50863			−0.754314	+	0.656513i	$0.772031\pi$
$240$	0.0316084	+	0.00416132i	0.00204031	+	0.000268612i
$241$	−2.56466	+	5.20061i	−0.165204	+	0.335001i	−0.963695	−	0.267007i	$-0.913965\pi$
$241$	−2.56466	+	5.20061i	−0.165204	+	0.335001i	0.798491	+	0.602007i	$0.205632\pi$
$242$	−2.26828	−	0.607785i	−0.145811	−	0.0390699i
$243$	−0.751840	−	0.659346i	−0.0482305	−	0.0422971i
$244$	5.23617	−	7.83649i	0.335212	−	0.501680i
$245$	−0.00884403	+	0.0602517i	−0.000565024	+	0.00384934i
$246$	−1.37779	−	0.570701i	−0.0878449	−	0.0363866i
$247$	8.79014	+	11.4555i	0.559303	+	0.728898i
$248$	3.33537	+	3.80326i	0.211796	+	0.241507i
$249$	−13.3185	−	0.872938i	−0.844023	−	0.0553202i
$250$	−0.0136249	+	0.0155362i	−0.000861711	+	0.000982593i
$251$	2.29598	−	2.29598i	0.144921	−	0.144921i	−0.630924	−	0.775845i	$-0.717324\pi$
$251$	2.29598	−	2.29598i	0.144921	−	0.144921i	0.775845	+	0.630924i	$0.217324\pi$
$252$	5.11358	+	0.541994i	0.322125	+	0.0341424i
$253$	8.24436	−	3.41493i	0.518319	−	0.214695i
$254$	1.96559	+	1.13483i	0.123332	+	0.0712058i
$255$	−0.0261150	−	0.0245891i	−0.00163539	−	0.00153983i
$256$	5.83740	+	10.1107i	0.364837	+	0.631917i
$257$	−3.86635	+	29.3678i	−0.241176	+	1.83191i	0.258866	+	0.965913i	$0.416651\pi$
$257$	−3.86635	+	29.3678i	−0.241176	+	1.83191i	−0.500043	+	0.866001i	$0.666682\pi$
$258$	0.593835	+	0.888736i	0.0369705	+	0.0553303i
$259$	−15.1391	−	6.99533i	−0.940698	−	0.434668i
$260$	0.0898630	+	0.0178749i	0.00557306	+	0.00110855i
$261$	4.63435	−	2.28541i	0.286859	−	0.141463i
$262$	−0.807368	+	0.708042i	−0.0498793	+	0.0437430i
$263$	0.608237	+	4.62002i	0.0375055	+	0.284883i	0.999912	+	0.0132692i	$0.00422385\pi$
$263$	0.608237	+	4.62002i	0.0375055	+	0.284883i	−0.962406	+	0.271613i	$0.912443\pi$
$264$	0.784278	−	0.601797i	0.0482689	−	0.0370381i
$265$	0.0834729	−	0.0166038i	0.00512770	−	0.00101996i
$266$	1.21371	+	1.15379i	0.0744174	+	0.0707436i
$267$	−1.88651	+	9.48411i	−0.115452	+	0.580418i
$268$	−0.753471	+	0.201892i	−0.0460256	+	0.0123325i
$269$	−7.00955	−	3.45673i	−0.427380	−	0.210760i	0.215861	−	0.976424i	$-0.430744\pi$
$269$	−7.00955	−	3.45673i	−0.427380	−	0.210760i	−0.643241	+	0.765664i	$0.722411\pi$
$270$	−0.00163941	−	0.00125797i	−9.97715e−5	−	7.65574e-5i
$271$	−4.16087	+	7.20684i	−0.252755	+	0.437784i	−0.964283	−	0.264873i	$-0.914670\pi$
$271$	−4.16087	+	7.20684i	−0.252755	+	0.437784i	0.711528	+	0.702657i	$0.248003\pi$
$272$	1.52069	−	15.0330i	0.0922052	−	0.911512i
$273$	14.1276	+	2.44033i	0.855042	+	0.147695i
$274$	−0.0547720	−	0.132231i	−0.00330890	−	0.00798839i
$275$	−0.345107	−	5.26531i	−0.0208107	−	0.317510i
$276$	4.25352	−	15.8744i	0.256032	−	0.955525i
$277$	10.0611	+	29.6390i	0.604512	+	1.78083i	0.624489	+	0.781034i	$0.285307\pi$
$277$	10.0611	+	29.6390i	0.604512	+	1.78083i	−0.0199773	+	0.999800i	$0.506359\pi$
$278$	0.0182276	+	0.0369620i	0.00109322	+	0.00221683i
$279$	1.05355	+	5.29655i	0.0630743	+	0.317096i
$280$	0.0215433		0.000865362i	0.00128746		5.17153e-5i
$281$	−6.22995	+	15.0404i	−0.371648	+	0.897237i	0.621824	+	0.783157i	$0.286392\pi$
$281$	−6.22995	+	15.0404i	−0.371648	+	0.897237i	−0.993472	+	0.114080i	$0.963608\pi$
$282$	−0.308844	−	0.104838i	−0.0183914	−	0.00624303i
$283$	−0.0343392	+	0.523915i	−0.00204125	+	0.0311435i	−0.998758	−	0.0498234i	$-0.984134\pi$
$283$	−0.0343392	+	0.523915i	−0.00204125	+	0.0311435i	0.996717	+	0.0809669i	$0.0258008\pi$
$284$	−24.7496	+	8.40135i	−1.46862	+	0.498529i
$285$	0.00599986	+	0.0223918i	0.000355401	+	0.00132637i
$286$	1.12944	−	0.754668i	0.0667852	−	0.0446244i
$287$	15.8595	+	4.93977i	0.936159	+	0.291586i
$288$		−	2.74392i		−	0.161687i
$289$	−11.2762	+	12.7219i	−0.663304	+	0.748350i
$290$	0.00924720	−	0.00533887i	0.000543014	−	0.000313509i
$291$	10.4495	−	13.6180i	0.612560	−	0.798304i
$292$	−7.04270	+	0.461603i	−0.412143	+	0.0270133i
$293$	1.39493	+	1.39493i	0.0814925	+	0.0814925i	0.746678	−	0.665186i	$-0.231648\pi$
$293$	1.39493	+	1.39493i	0.0814925	+	0.0814925i	−0.665186	+	0.746678i	$0.731648\pi$
$294$	1.66254	+	0.0246808i	0.0969612	+	0.00143941i
$295$	0.0893112	+	0.0596758i	0.00519990	+	0.00347446i
$296$	−1.89794	+	5.59117i	−0.110316	+	0.324980i
$297$	1.04631	−	0.137749i	0.0607130	−	0.00799302i
$298$	3.11503	−	0.410101i	0.180449	−	0.0237565i
$299$	14.7283	−	43.3883i	0.851762	−	2.50921i
$300$	−8.08001	−	5.39889i	−0.466500	−	0.311705i
$301$	−7.48437	−	9.25902i	−0.431392	−	0.533681i
$302$	2.47082	+	2.47082i	0.142180	+	0.142180i
$303$	−10.9181	+	0.715609i	−0.627227	+	0.0411106i
$304$	−5.94463	+	7.74719i	−0.340948	+	0.444332i
$305$	0.0365346	−	0.0210932i	0.00209196	−	0.00120780i
$306$	−0.572559	+	0.794568i	−0.0327310	+	0.0454224i
$307$			29.3064i			1.67260i	0.548268	+	0.836302i	$0.315287\pi$
$307$			29.3064i			1.67260i	−0.548268	+	0.836302i	$0.684713\pi$
$308$	−3.98824	+	3.68021i	−0.227251	+	0.209699i
$309$	−15.1854	+	10.1465i	−0.863865	+	0.577216i
$310$	0.00288826	+	0.0107791i	0.000164042	+	0.000612215i
$311$	−21.3817	+	7.25810i	−1.21244	+	0.411569i	−0.853155	−	0.521658i	$-0.825314\pi$
$311$	−21.3817	+	7.25810i	−1.21244	+	0.411569i	−0.359288	+	0.933227i	$0.616981\pi$
$312$	0.331982	−	5.06507i	0.0187948	−	0.286753i
$313$	−5.49738	−	1.86611i	−0.310730	−	0.105479i	0.161718	−	0.986837i	$-0.448296\pi$
$313$	−5.49738	−	1.86611i	−0.310730	−	0.105479i	−0.472449	+	0.881358i	$0.656630\pi$
$314$	−0.984506	+	2.37681i	−0.0555589	+	0.134131i
$315$	0.0194554	+	0.0122993i	0.00109619	+	0.000692987i
$316$	0.342470	+	1.72171i	0.0192654	+	0.0968539i
$317$	7.71763	+	15.6498i	0.433465	+	0.878980i	0.998544	+	0.0539433i	$0.0171790\pi$
$317$	7.71763	+	15.6498i	0.433465	+	0.878980i	−0.565079	+	0.825037i	$0.691154\pi$
$318$	−0.746951	−	2.20045i	−0.0418869	−	0.123395i
$319$	−1.41138	+	5.26736i	−0.0790223	+	0.294915i
$320$	0.00379941	+	0.0579677i	0.000212393	+	0.00324049i
$321$	3.11767	+	7.52672i	0.174011	+	0.420101i
$322$	0.904515	−	5.23645i	0.0504067	−	0.291816i
$323$	10.5220	−	3.16153i	0.585462	−	0.175912i
$324$	0.971789	−	1.68319i	0.0539883	−	0.0935105i
$325$	−21.4948	−	16.4936i	−1.19232	−	0.914899i
$326$	2.94245	+	1.45106i	0.162967	+	0.0803666i
$327$	−0.682556	+	0.182890i	−0.0377455	+	0.0101139i
$328$	1.14735	−	5.76811i	0.0633517	−	0.318490i
$329$	3.53173	+	0.851171i	0.194711	+	0.0469266i
$330$	0.00213888		0.000425450i	0.000117742		2.34203e-5i
$331$	−17.7199	+	13.5970i	−0.973974	+	0.747357i	−0.967565	−	0.252623i	$-0.918707\pi$
$331$	−17.7199	+	13.5970i	−0.973974	+	0.747357i	−0.00640955	+	0.999979i	$0.502040\pi$
$332$	−3.38598	−	25.7191i	−0.185830	−	1.41152i
$333$	−4.73912	+	4.15610i	−0.259702	+	0.227753i
$334$	−0.907512	+	0.447535i	−0.0496568	+	0.0244880i
$335$	−0.00342448		0.000681172i	−0.000187099		3.72164e-5i
$336$	0.878710	+	9.65587i	0.0479375	+	0.526771i
$337$	−0.194249	−	0.290715i	−0.0105814	−	0.0158362i	0.826141	−	0.563463i	$-0.190531\pi$
$337$	−0.194249	−	0.290715i	−0.0105814	−	0.0158362i	−0.836723	+	0.547627i	$0.815531\pi$
$338$	0.507337	−	3.85360i	0.0275955	−	0.209608i
$339$	−4.08063	−	7.06786i	−0.221630	−	0.383874i
$340$	0.0369704	−	0.0591049i	0.00200500	−	0.00320541i
$341$	−4.93561	−	2.84958i	−0.267278	−	0.154313i
$342$	0.584765	−	0.242218i	0.0316205	−	0.0130976i
$343$	−18.4669	+	1.40450i	−0.997120	+	0.0758356i
$344$	−2.98059	+	2.98059i	−0.160703	+	0.160703i
$345$	0.0485025	−	0.0553065i	0.00261129	−	0.00297760i
$346$	−5.02550	−	0.329388i	−0.270172	−	0.0177080i
$347$	−17.1761	−	19.5856i	−0.922064	−	1.05141i	−0.998523	−	0.0543396i	$-0.982695\pi$
$347$	−17.1761	−	19.5856i	−0.922064	−	1.05141i	0.0764586	−	0.997073i	$-0.475639\pi$
$348$	6.11374	+	7.96758i	0.327731	+	0.427107i
$349$	7.87803	+	3.26319i	0.421701	+	0.174674i	0.583435	−	0.812160i	$-0.301708\pi$
$349$	7.87803	+	3.26319i	0.421701	+	0.174674i	−0.161733	+	0.986834i	$0.551708\pi$
$350$	−2.76010	−	1.50175i	−0.147534	−	0.0802719i
$351$	3.01053	−	4.50558i	0.160690	−	0.240490i
$352$	2.17715	+	1.90931i	0.116042	+	0.101766i
$353$	6.30513	+	1.68945i	0.335588	+	0.0899206i	0.422678	−	0.906280i	$-0.361090\pi$
$353$	6.30513	+	1.68945i	0.335588	+	0.0899206i	−0.0870900	+	0.996200i	$0.527757\pi$
$354$	1.29714	−	2.63034i	0.0689421	−	0.139801i
$355$	−0.115989	−	0.0152702i	−0.00615606	−	0.000810461i
$356$	−18.7942			−0.996093
$357$	5.54912	−	9.39187i	0.293691	−	0.497070i
$358$	5.05448			0.267137
$359$	−31.6692	−	4.16934i	−1.67144	−	0.220049i	−0.765494	−	0.643444i	$-0.777505\pi$
$359$	−31.6692	−	4.16934i	−1.67144	−	0.220049i	−0.905945	+	0.423394i	$0.860838\pi$
$360$	0.00360428	−	0.00730875i	0.000189962	−	0.000385205i
$361$	11.4940	+	3.07982i	0.604949	+	0.162096i
$362$	−1.91045	−	1.67542i	−0.100411	−	0.0880582i
$363$	5.49251	−	8.22013i	0.288282	−	0.431445i
$364$	0.704982	+	27.8558i	0.0369511	+	1.46004i
$365$	−0.0291866	−	0.0120895i	−0.00152770	−	0.000632793i
$366$	−0.701199	−	0.913821i	−0.0366523	−	0.0477662i
$367$	−5.83913	−	6.65825i	−0.304800	−	0.347558i	0.579081	−	0.815270i	$-0.303412\pi$
$367$	−5.83913	−	6.65825i	−0.304800	−	0.347558i	−0.883881	+	0.467713i	$0.845078\pi$
$368$	30.9209	+	2.02667i	1.61187	+	0.105647i
$369$	4.13962	−	4.72033i	0.215500	−	0.245731i
$370$	−0.00921042	+	0.00921042i	−0.000478827	+	0.000478827i
$371$	10.5070	+	23.6548i	0.545494	+	1.22810i
$372$	−9.69698	+	4.01662i	−0.502765	+	0.208252i
$373$	17.7666	+	10.2576i	0.919920	+	0.531116i	0.883610	−	0.468224i	$-0.155106\pi$
$373$	17.7666	+	10.2576i	0.919920	+	0.531116i	0.0363106	+	0.999341i	$0.488439\pi$
$374$	−0.232041	−	1.00718i	−0.0119986	−	0.0520800i
$375$	−0.0434978	−	0.0753404i	−0.00224622	−	0.00389056i
$376$	0.167884	−	1.27520i	0.00865794	−	0.0657636i
$377$	15.5561	+	23.2814i	0.801180	+	1.19905i
$378$	0.263607	−	0.570491i	0.0135585	−	0.0293429i
$379$	22.9326	+	4.56159i	1.17797	+	0.234313i	0.744981	−	0.667086i	$-0.232459\pi$
$379$	22.9326	+	4.56159i	1.17797	+	0.234313i	0.432990	+	0.901399i	$0.357459\pi$
$380$	−0.0404090	+	0.0199275i	−0.00207294	+	0.00102226i
$381$	−7.18399	+	6.30019i	−0.368047	+	0.322769i
$382$	0.305977	+	2.32412i	0.0156551	+	0.118912i
$383$	−10.5678	+	8.10897i	−0.539990	+	0.414349i	−0.842419	−	0.538823i	$-0.818869\pi$
$383$	−10.5678	+	8.10897i	−0.539990	+	0.414349i	0.302429	+	0.953172i	$0.402202\pi$
$384$	6.93804	−	1.38006i	0.354056	−	0.0704260i
$385$	−0.0232965	+	0.00687851i	−0.00118730	+	0.000350561i
$386$	0.306327	−	1.54001i	0.0155916	−	0.0783845i
$387$	−4.34659	+	1.16467i	−0.220950	+	0.0592033i
$388$	29.9214	+	14.7556i	1.51903	+	0.749101i
$389$	0.135213	+	0.103753i	0.00685559	+	0.00526048i	0.612184	−	0.790716i	$-0.290291\pi$
$389$	0.135213	+	0.103753i	0.00685559	+	0.00526048i	−0.605328	+	0.795976i	$0.706958\pi$
$390$	0.00559881	−	0.00969743i	0.000283507	−	0.000491048i
$391$	−26.8916	−	22.1884i	−1.35997	−	1.12212i
$392$	1.18362	+	6.44936i	0.0597818	+	0.325742i
$393$	−1.73007	−	4.17676i	−0.0872706	−	0.210690i
$394$	−0.206483	−	3.15033i	−0.0104025	−	0.158711i
$395$	−0.00203367	+	0.00758977i	−0.000102325	+	0.000381883i
$396$	0.659314	+	1.94228i	0.0331318	+	0.0976031i
$397$	−5.73778	−	11.6351i	−0.287971	−	0.583947i	0.704031	−	0.710169i	$-0.251382\pi$
$397$	−5.73778	−	11.6351i	−0.287971	−	0.583947i	−0.992002	+	0.126222i	$0.959715\pi$
$398$	−0.241313	−	1.21316i	−0.0120959	−	0.0608104i
$399$	−6.24210	+	3.27714i	−0.312496	+	0.164062i
$400$	7.01191	−	16.9282i	0.350595	−	0.846412i
$401$	−7.64083	−	2.59371i	−0.381565	−	0.129524i	0.124066	−	0.992274i	$-0.460407\pi$
$401$	−7.64083	−	2.59371i	−0.381565	−	0.129524i	−0.505630	+	0.862750i	$0.668740\pi$
$402$	−0.00623506	+	0.0951286i	−0.000310976	+	0.00474458i
$403$	−27.7103	+	9.40637i	−1.38035	+	0.468565i
$404$	−5.50396	−	20.5411i	−0.273832	−	1.02196i
$405$	0.00723347	−	0.00483325i	0.000359434	−	0.000240166i
$406$	2.20221	+	2.38653i	0.109294	+	0.118441i
$407$		−	6.65218i		−	0.329736i
$408$	−3.51373	−	1.60324i	−0.173956	−	0.0793722i
$409$	5.81881	−	3.35949i	0.287721	−	0.166116i	−0.349192	−	0.937051i	$-0.613544\pi$
$409$	5.81881	−	3.35949i	0.287721	−	0.166116i	0.636914	+	0.770935i	$0.280211\pi$
$410$	0.00789799	−	0.0102929i	0.000390054	−	0.000508328i
$411$	0.601266	−	0.0394091i	0.0296583	−	0.00194391i
$412$	−25.0995	−	25.0995i	−1.23657	−	1.23657i
$413$	−11.7335	+	30.4869i	−0.577369	+	1.50016i
$414$	−1.67001	−	1.11586i	−0.0820764	−	0.0548417i
$415$	0.0373237	−	0.109952i	0.00183215	−	0.00539733i
$416$	14.7416	−	1.94077i	0.722766	−	0.0951539i
$417$	−0.172017	+	0.0226465i	−0.00842372	+	0.00110900i
$418$	−0.214712	+	0.632521i	−0.0105019	+	0.0309376i
$419$	10.7126	+	7.15796i	0.523347	+	0.349689i	0.789014	−	0.614376i	$-0.210592\pi$
$419$	10.7126	+	7.15796i	0.523347	+	0.349689i	−0.265667	+	0.964065i	$0.585592\pi$
$420$	−0.0160684	+	0.0417500i	−0.000784056	+	0.00203719i
$421$	18.7564	+	18.7564i	0.914133	+	0.914133i	0.996594	−	0.0824616i	$-0.0262782\pi$
$421$	18.7564	+	18.7564i	0.914133	+	0.914133i	−0.0824616	+	0.996594i	$0.526278\pi$
$422$	5.74063	−	0.376261i	0.279449	−	0.0183161i
$423$	0.835884	−	1.08935i	0.0406421	−	0.0529658i
$424$	7.93622	−	4.58198i	0.385417	−	0.222521i
$425$	−17.5352	+	10.8400i	−0.850580	+	0.525817i
$426$			3.19425i			0.154762i
$427$	8.70065	+	9.42889i	0.421054	+	0.456296i
$428$	−13.1656	+	8.79694i	−0.636381	+	0.425216i
$429$	1.48010	+	5.52382i	0.0714600	+	0.266692i
$430$	−0.00880531	+	0.00298900i	−0.000424630	+	0.000144142i
$431$	0.162660	−	2.48171i	0.00783504	−	0.119540i	−0.992150	−	0.125056i	$-0.960089\pi$
$431$	0.162660	−	2.48171i	0.00783504	−	0.119540i	0.999985	+	0.00551588i	$0.00175577\pi$
$432$	3.47017	+	1.17796i	0.166959	+	0.0566749i
$433$	14.9851	−	36.1772i	0.720138	−	1.73857i	0.0471788	−	0.998886i	$-0.484977\pi$
$433$	14.9851	−	36.1772i	0.720138	−	1.73857i	0.672959	−	0.739680i	$-0.265023\pi$
$434$	−3.00488	+	1.57758i	−0.144239	+	0.0757262i
$435$	0.00876988	+	0.0440892i	0.000420484	+	0.00211391i
$436$	−0.607439	−	1.23176i	−0.0290911	−	0.0589908i
$437$	7.24259	+	21.3360i	0.346460	+	1.02064i
$438$	−0.223247	+	0.833169i	−0.0106672	+	0.0398104i
$439$	−0.576362	−	8.79358i	−0.0275082	−	0.419695i	−0.989298	−	0.145907i	$-0.953390\pi$
$439$	−0.576362	−	8.79358i	−0.0275082	−	0.419695i	0.961790	−	0.273788i	$-0.0882766\pi$
$440$	0.00329112	+	0.00794546i	0.000156898	+	0.000378785i
$441$	−2.34822	+	6.59438i	−0.111820	+	0.314018i
$442$	−4.67375	−	2.51405i	−0.222308	−	0.119581i
$443$	3.43186	−	5.94415i	0.163052	−	0.282415i	−0.772910	−	0.634516i	$-0.781199\pi$
$443$	3.43186	−	5.94415i	0.163052	−	0.282415i	0.935962	+	0.352101i	$0.114533\pi$
$444$	−9.71944	−	7.45799i	−0.461264	−	0.353940i
$445$	−0.0754491	−	0.0372074i	−0.00357663	−	0.00176380i
$446$	3.72705	−	0.998660i	0.176481	−	0.0472879i
$447$	−2.58052	+	12.9732i	−0.122054	+	0.613609i
$448$	−16.9440	+	5.00287i	−0.800528	+	0.236364i
$449$	−15.0512	+	2.99387i	−0.710309	+	0.141289i	−0.537005	−	0.843579i	$-0.680444\pi$
$449$	−15.0512	+	2.99387i	−0.710309	+	0.141289i	−0.173304	+	0.984868i	$0.555444\pi$
$450$	−0.942218	+	0.722989i	−0.0444166	+	0.0340821i
$451$	0.864841	+	6.56912i	0.0407238	+	0.309328i
$452$	11.9257	−	10.4586i	0.560939	−	0.491930i
$453$	−13.1936	+	6.50639i	−0.619892	+	0.305697i
$454$	0.884209	+	0.175880i	0.0414980	+	0.00825446i
$455$	−0.0523167	+	0.113222i	−0.00245264	+	0.00530795i
$456$	1.38674	+	2.07540i	0.0649401	+	0.0971897i
$457$	−1.26719	+	9.62523i	−0.0592765	+	0.450249i	0.935909	+	0.352241i	$0.114580\pi$
$457$	−1.26719	+	9.62523i	−0.0592765	+	0.450249i	−0.995186	+	0.0980079i	$0.968753\pi$
$458$	−1.09477	−	1.89619i	−0.0511550	−	0.0886031i
$459$	−2.39277	−	3.35778i	−0.111685	−	0.156728i
$460$	0.123818	+	0.0714863i	0.00577304	+	0.00333307i
$461$	3.60509	−	1.49328i	0.167906	−	0.0695488i	−0.297147	−	0.954832i	$-0.596035\pi$
$461$	3.60509	−	1.49328i	0.167906	−	0.0695488i	0.465053	+	0.885283i	$0.346035\pi$
$462$	0.269227	+	0.606124i	0.0125256	+	0.0281994i
$463$	5.75829	−	5.75829i	0.267610	−	0.267610i	−0.560526	−	0.828137i	$-0.689401\pi$
$463$	5.75829	−	5.75829i	0.267610	−	0.267610i	0.828137	+	0.560526i	$0.189401\pi$
$464$	−12.4854	+	14.2369i	−0.579622	+	0.660933i
$465$	−0.0468801	−	0.00307268i	−0.00217401	−	0.000142492i
$466$	−3.15496	−	3.59754i	−0.146151	−	0.166653i
$467$	−0.0377887	−	0.0492471i	−0.00174865	−	0.00227889i	0.792478	−	0.609900i	$-0.208791\pi$
$467$	−0.0377887	−	0.0492471i	−0.00174865	−	0.00227889i	−0.794227	+	0.607621i	$0.792124\pi$
$468$	9.73020	+	4.03038i	0.449779	+	0.186304i
$469$	−0.0268653	−	1.06153i	−0.00124053	−	0.0490167i
$470$	0.00157638	−	0.00235921i	7.27128e−5	−	0.000108822i
$471$	−8.14297	−	7.14119i	−0.375208	−	0.329049i
$472$	11.1716	+	2.99342i	0.514214	+	0.137783i
$473$	2.10040	−	4.25919i	0.0965765	−	0.195838i
$474$	0.212703	+	0.0280029i	0.00976979	+	0.00128622i
$475$	13.3232			0.611309
$476$	20.0072	+	7.01678i	0.917027	+	0.321614i
$477$	9.78298			0.447932
$478$	−5.49252	−	0.723103i	−0.251222	−	0.0330740i
$479$	11.9844	−	24.3021i	0.547583	−	1.11039i	−0.430580	−	0.902552i	$-0.641691\pi$
$479$	11.9844	−	24.3021i	0.547583	−	1.11039i	0.978163	−	0.207837i	$-0.0666423\pi$
$480$	0.0230577	+	0.00617829i	0.00105243	+	0.000281999i
$481$	−25.6804	−	22.5211i	−1.17093	−	1.02687i
$482$	−0.765215	+	1.14523i	−0.0348546	+	0.0521636i
$483$	19.6513	+	10.6921i	0.894164	+	0.486508i
$484$	17.7521	+	7.35316i	0.806914	+	0.334235i
$485$	0.0909067	+	0.118472i	0.00412786	+	0.00537953i
$486$	−0.156615	−	0.178586i	−0.00710422	−	0.00810081i
$487$	−11.7046	−	0.767158i	−0.530385	−	0.0347633i	−0.202141	−	0.979356i	$-0.564790\pi$
$487$	−11.7046	−	0.767158i	−0.530385	−	0.0347633i	−0.328244	+	0.944593i	$0.606457\pi$
$488$	2.99501	−	3.41515i	0.135578	−	0.154597i
$489$	−9.76657	+	9.76657i	−0.441660	+	0.441660i
$490$	−0.00395082	+	0.0139151i	−0.000178480	+	0.000628618i
$491$	13.2411	−	5.48464i	0.597562	−	0.247518i	−0.0633381	−	0.997992i	$-0.520175\pi$
$491$	13.2411	−	5.48464i	0.597562	−	0.247518i	0.660900	+	0.750474i	$0.270175\pi$
$492$	10.5677	+	6.10126i	0.476428	+	0.275066i
$493$	20.7612	−	4.78310i	0.935036	−	0.215420i
$494$	1.71490	+	2.97030i	0.0771572	+	0.133640i
$495$	−0.00119837	+	0.00910249i	−5.38625e−5	+	0.000409127i
$496$	−10.9949	−	16.4550i	−0.493685	−	0.738852i
$497$	−3.22448	−	35.4329i	−0.144638	−	1.58938i
$498$	−3.10943	−	0.618503i	−0.139337	−	0.0277158i
$499$	23.8719	−	11.7723i	1.06865	−	0.527001i	0.179098	−	0.983831i	$-0.442682\pi$
$499$	23.8719	−	11.7723i	1.06865	−	0.527001i	0.889554	+	0.456830i	$0.151015\pi$
$500$	0.127123	−	0.111484i	0.00568512	−	0.00498572i
$501$	−0.556029	−	4.22346i	−0.0248416	−	0.188690i
$502$	0.611886	−	0.469517i	0.0273098	−	0.0209556i
$503$	29.2781	−	5.82377i	1.30544	−	0.259669i	0.507109	−	0.861882i	$-0.330714\pi$
$503$	29.2781	−	5.82377i	1.30544	−	0.259669i	0.798335	+	0.602213i	$0.205714\pi$
$504$	2.40936	+	0.580671i	0.107321	+	0.0258651i
$505$	0.0185701	−	0.0933580i	0.000826357	−	0.00415437i
$506$	2.04742	−	0.548604i	0.0910189	−	0.0243884i
$507$	14.6760	+	7.23741i	0.651784	+	0.321425i
$508$	−14.7336	−	11.3055i	−0.653699	−	0.501601i
$509$	−3.32741	+	5.76325i	−0.147485	+	0.255452i	−0.930297	−	0.366806i	$-0.880451\pi$
$509$	−3.32741	+	5.76325i	−0.147485	+	0.255452i	0.782812	+	0.622258i	$0.213784\pi$
$510$	−0.00538772	−	0.00660039i	−0.000238572	−	0.000292270i
$511$	1.63535	−	9.46744i	0.0723438	−	0.418815i
$512$	6.47541	+	15.6330i	0.286176	+	0.690889i
$513$	0.174278	+	2.65897i	0.00769457	+	0.117396i
$514$	−1.82105	+	6.79623i	−0.0803229	+	0.299769i
$515$	−0.0510715	−	0.150452i	−0.00225048	−	0.00662970i
$516$	−3.86824	−	7.84401i	−0.170290	−	0.345313i
$517$	0.282700	+	1.42123i	0.0124331	+	0.0625056i
$518$	−3.34837	−	2.11677i	−0.147119	−	0.0930055i
$519$	8.11387	−	19.5886i	0.356159	−	0.859845i
$520$	0.0418152	+	0.0141944i	0.00183372	+	0.000622464i
$521$	1.08600	−	16.5692i	0.0475787	−	0.725911i	−0.905719	−	0.423879i	$-0.860668\pi$
$521$	1.08600	−	16.5692i	0.0475787	−	0.725911i	0.953298	−	0.302032i	$-0.0976650\pi$
$522$	1.16224	−	0.394528i	0.0508700	−	0.0172680i
$523$	−6.42539	−	23.9799i	−0.280963	−	1.04857i	−0.951739	−	0.306908i	$-0.900706\pi$
$523$	−6.42539	−	23.9799i	−0.280963	−	1.04857i	0.670776	−	0.741660i	$-0.265961\pi$
$524$	7.30589	−	4.88164i	0.319159	−	0.213255i
$525$	9.72190	−	8.97103i	0.424298	−	0.391528i
$526$			1.10687i			0.0482618i
$527$	−0.787243	+	22.2521i	−0.0342928	+	0.969318i
$528$	−3.34931	+	1.93372i	−0.145760	+	0.0841545i
$529$	29.5244	−	38.4770i	1.28367	−	1.67291i
$530$	0.0201726	−	0.00132218i	0.000876243	−	5.74320e-5i
$531$	8.73060	+	8.73060i	0.378876	+	0.378876i
$532$	−8.61384	−	10.6563i	−0.373457	−	0.462009i
$533$	28.2877	+	18.9013i	1.22528	+	0.818704i
$534$	−0.738318	+	2.17501i	−0.0319501	+	0.0941221i
$535$	−0.0702683	+	0.00925100i	−0.00303796	+	0.000399956i
$536$	−0.372736	+	0.0490716i	−0.0160997	+	0.00211957i
$537$	−6.83997	+	20.1499i	−0.295166	+	0.869532i
$538$	−1.54357	−	1.03138i	−0.0665481	−	0.0444661i
$539$	−3.59831	−	6.45176i	−0.154990	−	0.277897i
$540$	0.0119560	+	0.0119560i	0.000514506	+	0.000514506i
$541$	−8.40457	+	0.550865i	−0.361341	+	0.0236835i	−0.244993	−	0.969525i	$-0.578786\pi$
$541$	−8.40457	+	0.550865i	−0.361341	+	0.0236835i	−0.116348	+	0.993208i	$0.537119\pi$
$542$	−1.20332	+	1.56820i	−0.0516872	+	0.0673601i
$543$	9.26446	−	5.34884i	0.397576	−	0.229541i
$544$	2.59809	−	11.0111i	0.111392	−	0.472098i
$545$		−	0.00614745i		−	0.000263328i
$546$	3.25139	+	1.01271i	0.139146	+	0.0433400i
$547$	−15.4754	+	10.3404i	−0.661682	+	0.442122i	−0.840537	−	0.541754i	$-0.817761\pi$
$547$	−15.4754	+	10.3404i	−0.661682	+	0.442122i	0.178855	+	0.983875i	$0.442761\pi$
$548$	0.303107	+	1.13121i	0.0129481	+	0.0483229i
$549$	4.59188	−	1.55873i	0.195977	−	0.0665252i
$550$	0.0819737	−	1.25068i	0.00349537	−	0.0533291i
$551$	−13.0383	−	4.42590i	−0.555449	−	0.188550i
$552$	3.03111	−	7.31775i	0.129013	−	0.311464i
$553$	−2.38772	−	0.0959114i	−0.101536	−	0.00407857i
$554$	1.45045	+	7.29190i	0.0616237	+	0.309803i
$555$	−0.0242537	−	0.0491817i	−0.00102951	−	0.00208765i
$556$	−0.108394	−	0.319318i	−0.00459692	−	0.0135421i
$557$	7.94922	−	29.6669i	0.336819	−	1.25703i	−0.565064	−	0.825047i	$-0.691148\pi$
$557$	7.94922	−	29.6669i	0.336819	−	1.25703i	0.901883	−	0.431980i	$-0.142185\pi$
$558$	0.0838955	+	1.28000i	0.00355158	+	0.0541867i
$559$	−9.33144	−	22.5281i	−0.394678	−	0.952837i
$560$	−0.0831186	−	0.0143575i	−0.00351240	−	0.000606713i
$561$	4.32917	+	0.437923i	0.182778	+	0.0184891i
$562$	−1.93347	+	3.34886i	−0.0815583	+	0.141263i
$563$	34.7695	+	26.6795i	1.46536	+	1.12441i	0.966167	+	0.257917i	$0.0830360\pi$
$563$	34.7695	+	26.6795i	1.46536	+	1.12441i	0.499191	+	0.866492i	$0.333631\pi$
$564$	2.39349	+	1.18034i	0.100784	+	0.0497013i
$565$	0.0685807	−	0.0183761i	0.00288521	−	0.000773090i
$566$	−0.0243304	+	0.122317i	−0.00102268	+	0.00514137i
$567$	1.91756	+	1.82290i	0.0805300	+	0.0765545i
$568$	−12.3547	+	2.45751i	−0.518394	+	0.103115i
$569$	−19.9308	+	15.2935i	−0.835544	+	0.641135i	−0.935292	−	0.353877i	$-0.884863\pi$
$569$	−19.9308	+	15.2935i	−0.835544	+	0.641135i	0.0997481	+	0.995013i	$0.468196\pi$
$570$	0.000718727		0.00545927i	3.01042e−5		0.000228664i
$571$	−3.07137	+	2.69352i	−0.128533	+	0.112720i	−0.721199	−	0.692728i	$-0.756409\pi$
$571$	−3.07137	+	2.69352i	−0.128533	+	0.112720i	0.592666	+	0.805448i	$0.298075\pi$
$572$	−9.96847	+	4.91590i	−0.416803	+	0.205544i
$573$	−9.67928	−	1.92533i	−0.404358	−	0.0804318i
$574$	3.58176	+	1.65502i	0.149500	+	0.0690794i
$575$	−23.4884	−	35.1528i	−0.979533	−	1.46597i
$576$	−0.871594	+	6.62042i	−0.0363164	+	0.275851i
$577$	−3.85079	−	6.66977i	−0.160311	−	0.277666i	0.774670	−	0.632366i	$-0.217916\pi$
$577$	−3.85079	−	6.66977i	−0.160311	−	0.277666i	−0.934980	+	0.354700i	$0.884583\pi$
$578$	−3.04997	+	2.64640i	−0.126862	+	0.110076i
$579$	5.72478	+	3.30520i	0.237914	+	0.137360i
$580$	−0.0807190	+	0.0334349i	−0.00335167	+	0.00138831i
$581$	35.1162	+	3.72201i	1.45687	+	0.154415i
$582$	2.88307	−	2.88307i	0.119507	−	0.119507i
$583$	−6.80731	+	7.76225i	−0.281930	+	0.321480i
$584$	−3.39429	−	0.222474i	−0.140457	−	0.00920602i
$585$	0.0310826	+	0.0354430i	0.00128511	+	0.00146539i
$586$	0.285256	+	0.371753i	0.0117838	+	0.0153570i
$587$	−2.69299	−	1.11547i	−0.111152	−	0.0460405i	0.326415	−	0.945227i	$-0.394159\pi$
$587$	−2.69299	−	1.11547i	−0.111152	−	0.0460405i	−0.437566	+	0.899186i	$0.644159\pi$
$588$	−13.4608	−	1.97584i	−0.555115	−	0.0814823i
$589$	7.99470	−	11.9649i	0.329416	−	0.493006i
$590$	0.0191825	+	0.0168226i	0.000789733	+	0.000692577i
$591$	12.8383	+	3.44002i	0.528099	+	0.141504i
$592$	10.2167	−	20.7175i	0.419905	−	0.851482i
$593$	22.0820	+	2.90715i	0.906798	+	0.119382i	0.569477	−	0.822007i	$-0.307146\pi$
$593$	22.0820	+	2.90715i	0.906798	+	0.119382i	0.337321	+	0.941390i	$0.390479\pi$
$594$	0.250676			0.0102854
$595$	0.0664271	+	0.0677773i	0.00272325	+	0.00277860i
$596$	−25.7083			−1.05305
$597$	5.16288	+	0.679706i	0.211303	+	0.0278185i
$598$	4.81373	−	9.76128i	0.196848	−	0.399169i
$599$	−15.4284	−	4.13402i	−0.630386	−	0.168912i	−0.0705413	−	0.997509i	$-0.522473\pi$
$599$	−15.4284	−	4.13402i	−0.630386	−	0.168912i	−0.559845	+	0.828597i	$0.689139\pi$
$600$	−3.52128	−	3.08808i	−0.143756	−	0.126070i
$601$	9.18663	−	13.7488i	0.374731	−	0.560824i	−0.595393	−	0.803434i	$-0.703004\pi$
$601$	9.18663	−	13.7488i	0.374731	−	0.560824i	0.970124	+	0.242611i	$0.0780037\pi$
$602$	−1.47550	−	2.41254i	−0.0601368	−	0.0983278i
$603$	−0.370797	−	0.153589i	−0.0151000	−	0.00625463i
$604$	−17.4054	−	22.6831i	−0.708215	−	0.922963i
$605$	0.0567082	+	0.0646633i	0.00230552	+	0.00262894i
$606$	−2.59339	−	0.169980i	−0.105349	−	0.00690495i
$607$	5.75667	−	6.56422i	0.233656	−	0.266433i	−0.623116	−	0.782130i	$-0.714133\pi$
$607$	5.75667	−	6.56422i	0.233656	−	0.266433i	0.856771	+	0.515696i	$0.172467\pi$
$608$	−5.17012	+	5.17012i	−0.209676	+	0.209676i
$609$	−12.4941	+	5.54962i	−0.506288	+	0.224882i
$610$	0.00925785	−	0.00383473i	0.000374839	−	0.000155264i
$611$	6.44368	+	3.72026i	0.260683	+	0.150506i
$612$	5.49344	−	5.83435i	0.222059	−	0.235840i
$613$	−1.43740	−	2.48966i	−0.0580562	−	0.100556i	0.835537	−	0.549435i	$-0.185157\pi$
$613$	−1.43740	−	2.48966i	−0.0580562	−	0.100556i	−0.893593	+	0.448878i	$0.851824\pi$
$614$	−0.908619	+	6.90164i	−0.0366689	+	0.278528i
$615$	0.0303450	+	0.0454145i	0.00122363	+	0.00183129i
$616$	−2.13724	+	1.50764i	−0.0861117	+	0.0607446i
$617$	36.7469	+	7.30941i	1.47937	+	0.294266i	0.867797	−	0.496919i	$-0.165535\pi$
$617$	36.7469	+	7.30941i	1.47937	+	0.294266i	0.611577	+	0.791185i	$0.290535\pi$
$618$	−3.89073	+	1.91870i	−0.156508	+	0.0771812i
$619$	8.16556	−	7.16100i	0.328202	−	0.287825i	−0.479348	−	0.877625i	$-0.659127\pi$
$619$	8.16556	−	7.16100i	0.328202	−	0.287825i	0.807549	+	0.589800i	$0.200793\pi$
$620$	−0.0119184	−	0.0905295i	−0.000478656	−	0.00363575i
$621$	6.70837	−	5.14751i	0.269198	−	0.206563i
$622$	−5.26040	+	1.04636i	−0.210923	+	0.0419552i
$623$	5.99433	−	24.8721i	0.240158	−	0.996478i
$624$	−3.87412	+	19.4765i	−0.155089	+	0.779685i
$625$	−24.1470	+	6.47018i	−0.965882	+	0.258807i
$626$	−1.23677	−	0.609909i	−0.0494314	−	0.0243769i
$627$	−2.23101	−	1.71192i	−0.0890981	−	0.0683674i
$628$	10.5252	−	18.2301i	0.420000	−	0.727462i
$629$	−22.9529	+	12.1908i	−0.915192	+	0.486080i
$630$	0.00420040	+	0.00349967i	0.000167348	+	0.000139430i
$631$	12.3054	+	29.7077i	0.489868	+	1.18265i	0.954786	+	0.297293i	$0.0960838\pi$
$631$	12.3054	+	29.7077i	0.489868	+	1.18265i	−0.464918	+	0.885354i	$0.653916\pi$
$632$	0.0553344	+	0.844239i	0.00220108	+	0.0335820i
$633$	−6.26852	+	23.3944i	−0.249151	+	0.929846i
$634$	1.33229	+	3.92480i	0.0529120	+	0.155874i
$635$	−0.0367660	−	0.0745542i	−0.00145902	−	0.00295859i
$636$	3.70945	+	18.6486i	0.147089	+	0.739467i
$637$	−37.0889	−	7.95152i	−1.46952	−	0.315051i
$638$	−0.495690	+	1.19670i	−0.0196245	+	0.0473779i
$639$	−12.7340	−	4.32262i	−0.503751	−	0.171000i
$640$	−0.00402497	+	0.0614091i	−0.000159101	+	0.00242741i
$641$	−20.8346	+	7.07241i	−0.822919	+	0.279343i	−0.700968	−	0.713193i	$-0.747248\pi$
$641$	−20.8346	+	7.07241i	−0.822919	+	0.279343i	−0.121951	+	0.992536i	$0.538915\pi$
$642$	0.500851	+	1.86920i	0.0197670	+	0.0737714i
$643$	−5.03961	+	3.36736i	−0.198743	+	0.132796i	−0.650960	−	0.759112i	$-0.725633\pi$
$643$	−5.03961	+	3.36736i	−0.198743	+	0.132796i	0.452217	+	0.891908i	$0.350633\pi$
$644$	−12.9304	+	41.5141i	−0.509529	+	1.63588i
$645$		−	0.0391476i		−	0.00154144i
$646$	2.57595	−	0.418313i	0.101350	−	0.0164583i
$647$	12.9036	−	7.44992i	0.507294	−	0.292886i	−0.224427	−	0.974491i	$-0.572051\pi$
$647$	12.9036	−	7.44992i	0.507294	−	0.292886i	0.731721	+	0.681605i	$0.238718\pi$
$648$	0.570242	−	0.743154i	0.0224012	−	0.0291938i
$649$	−13.0023	+	0.852214i	−0.510384	+	0.0334523i
$650$	−4.55066	−	4.55066i	−0.178491	−	0.178491i
$651$	−2.22274	−	14.1139i	−0.0871160	−	0.553169i
$652$	−22.3206	−	14.9141i	−0.874142	−	0.584083i
$653$	5.77426	−	17.0104i	0.225964	−	0.665669i	−0.773527	−	0.633764i	$-0.781509\pi$
$653$	5.77426	−	17.0104i	0.225964	−	0.665669i	0.999491	−	0.0319054i	$-0.0101575\pi$
$654$	−0.166412	+	0.0219086i	−0.00650723	+	0.000856693i
$655$	0.0389936	−	0.00513361i	0.00152361	−	0.000200587i
$656$	−7.39571	+	21.7871i	−0.288754	+	0.850642i
$657$	−3.01936	−	2.01747i	−0.117796	−	0.0787090i
$658$	0.805332	+	0.309949i	0.0313951	+	0.0120831i
$659$	−2.90823	−	2.90823i	−0.113288	−	0.113288i	0.648190	−	0.761479i	$-0.275526\pi$
$659$	−2.90823	−	2.90823i	−0.113288	−	0.113288i	−0.761479	+	0.648190i	$0.775526\pi$
$660$	−0.0178059	+	0.00116706i	−0.000693092	+	4.54277e-5i
$661$	6.66344	−	8.68396i	0.259178	−	0.337767i	−0.645581	−	0.763692i	$-0.723385\pi$
$661$	6.66344	−	8.68396i	0.259178	−	0.337767i	0.904758	+	0.425925i	$0.140051\pi$
$662$	−4.59459	+	2.65269i	−0.178574	+	0.103100i
$663$	16.3471	−	15.2300i	0.634869	−	0.591483i
$664$		−	12.5025i		−	0.485191i
$665$	−0.0134836	−	0.0598325i	−0.000522870	−	0.00232020i
$666$	−1.24492	+	0.831827i	−0.0482395	+	0.0322326i
$667$	11.3085	+	42.2038i	0.437866	+	1.63414i
$668$	7.84007	−	2.66135i	0.303342	−	0.102971i
$669$	−1.06243	+	16.2095i	−0.0410758	+	0.626695i
$670$	−0.000785345	0	0.000266589i	−3.03405e−5	0	1.02992e-5i
$671$	−1.95841	+	4.72802i	−0.0756036	+	0.182523i
$672$	−0.291378	+	7.25388i	−0.0112402	+	0.279825i
$673$	0.293609	+	1.47607i	0.0113178	+	0.0568984i	0.986031	−	0.166559i	$-0.0532656\pi$
$673$	0.293609	+	1.47607i	0.0113178	+	0.0568984i	−0.974714	+	0.223457i	$0.928266\pi$
$674$	−0.0367323	−	0.0744857i	−0.00141487	−	0.00286908i
$675$	−1.60717	−	4.73458i	−0.0618601	−	0.182234i
$676$	−8.23143	+	30.7201i	−0.316594	+	1.18154i
$677$	−0.820998	−	12.5260i	−0.0315535	−	0.481414i	−0.984169	−	0.177235i	$-0.943285\pi$
$677$	−0.820998	−	12.5260i	−0.0315535	−	0.481414i	0.952615	−	0.304179i	$-0.0983820\pi$
$678$	−0.741854	−	1.79099i	−0.0284907	−	0.0687827i
$679$	−29.0706	+	34.8913i	−1.11563	+	1.33901i
$680$	0.0213840	−	0.0259167i	0.000820037	−	0.000993859i
$681$	−1.89771	+	3.28693i	−0.0727204	+	0.125955i
$682$	−1.07398	−	0.824098i	−0.0411250	−	0.0315563i
$683$	18.0097	+	8.88139i	0.689121	+	0.339837i	0.752907	−	0.658127i	$-0.228651\pi$
$683$	18.0097	+	8.88139i	0.689121	+	0.339837i	−0.0637861	+	0.997964i	$0.520318\pi$
$684$	−5.00254	+	1.34043i	−0.191277	+	0.0512525i
$685$	−0.00102267	+	0.00514129i	−3.90741e−5	+	0.000196439i
$686$	−4.39250	−	0.241792i	−0.167706	−	0.00923168i
$687$	9.04073	−	1.79831i	0.344925	−	0.0686099i
$688$	13.0829	−	10.0389i	0.498782	−	0.382729i
$689$	6.91947	+	52.5586i	0.263611	+	2.00232i
$690$	0.0131370	−	0.0115209i	0.000500119	−	0.000438592i
$691$	−40.6750	+	20.0587i	−1.54735	+	0.763069i	−0.997396	−	0.0721243i	$-0.977022\pi$
$691$	−40.6750	+	20.0587i	−1.54735	+	0.763069i	−0.549956	+	0.835194i	$0.685356\pi$
$692$	40.4170	+	8.03945i	1.53643	+	0.305614i
$693$	−2.78067	+	0.253048i	−0.105629	+	0.00961251i
$694$	−3.43774	−	5.14494i	−0.130495	−	0.195299i
$695$	0.000197016	−	0.00149648i	7.47324e−6	−	5.67649e-5i
$696$	2.42014	+	4.19180i	0.0917350	+	0.158890i
$697$	21.0814	−	15.0227i	0.798515	−	0.569025i
$698$	1.75410	+	1.01273i	0.0663936	+	0.0383324i
$699$	18.6112	−	7.70902i	0.703941	−	0.291582i
$700$	20.7872	+	15.1306i	0.785681	+	0.571884i
$701$	−1.87365	+	1.87365i	−0.0707666	+	0.0707666i	−0.741604	−	0.670838i	$-0.765935\pi$
$701$	−1.87365	+	1.87365i	−0.0707666	+	0.0707666i	0.670838	+	0.741604i	$0.265935\pi$
$702$	0.848670	−	0.967723i	0.0320310	−	0.0365243i
$703$	16.7605	+	1.09854i	0.632133	+	0.0414322i
$704$	−4.64645	−	5.29826i	−0.175120	−	0.199686i
$705$	0.00727188	+	0.00947690i	0.000273875	+	0.000356921i
$706$	1.43247	+	0.593350i	0.0539119	+	0.0223310i
$707$	28.9392	−	0.732401i	1.08837	−	0.0275448i
$708$	−13.3322	+	19.9530i	−0.501053	+	0.749879i
$709$	−20.3518	−	17.8480i	−0.764326	−	0.670296i	0.185651	−	0.982616i	$-0.440561\pi$
$709$	−20.3518	−	17.8480i	−0.764326	−	0.670296i	−0.949977	+	0.312320i	$0.898894\pi$
$710$	−0.0268419	−	0.00719227i	−0.00100736	−	0.000269921i
$711$	−0.399476	+	0.810057i	−0.0149815	+	0.0303795i
$712$	−8.98056	−	1.18231i	−0.336561	−	0.0443091i
$713$	−45.6635			−1.71011
$714$	1.59800	−	2.03973i	0.0598037	−	0.0763352i
$715$	−0.0497503			−0.00186056
$716$	−41.0039	−	5.39827i	−1.53239	−	0.201743i
$717$	10.3154	−	20.9176i	0.385237	−	0.781183i
$718$	−7.32883	−	1.96375i	−0.273509	−	0.0732866i
$719$	2.14920	+	1.88480i	0.0801517	+	0.0702912i	0.698484	−	0.715625i	$-0.253858\pi$
$719$	2.14920	+	1.88480i	0.0801517	+	0.0702912i	−0.618333	+	0.785917i	$0.712192\pi$
$720$	−0.0177122	+	0.0265082i	−0.000660095	+	0.000987902i
$721$	41.2218	−	25.2110i	1.53518	−	0.938908i
$722$	2.61135	+	1.08166i	0.0971845	+	0.0402551i
$723$	−3.52996	−	4.60034i	−0.131281	−	0.171088i
$724$	13.7090	+	15.6321i	0.509490	+	0.580962i
$725$	25.7804	+	1.68974i	0.957461	+	0.0627553i
$726$	1.54834	−	1.76555i	0.0574644	−	0.0655255i
$727$	−8.15934	+	8.15934i	−0.302613	+	0.302613i	−0.842035	−	0.539422i	$-0.818643\pi$
$727$	−8.15934	+	8.15934i	−0.302613	+	0.302613i	0.539422	+	0.842035i	$0.318643\pi$
$728$	−1.41550	+	13.3549i	−0.0524618	+	0.494964i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	−0.00649861	−	0.00375197i	−0.000240524	−	0.000138867i
$731$	−18.5453	+	0.558126i	−0.685921	+	0.0206431i
$732$	4.71243	+	8.16217i	0.174176	+	0.301682i
$733$	−1.45009	+	11.0146i	−0.0535605	+	0.406832i	0.943573	+	0.331165i	$0.107442\pi$
$733$	−1.45009	+	11.0146i	−0.0535605	+	0.406832i	−0.997133	+	0.0756667i	$0.975891\pi$
$734$	−1.16868	−	1.74905i	−0.0431367	−	0.0645586i
$735$	−0.0501265	−	0.0345806i	−0.00184894	−	0.00127553i
$736$	22.7560	+	4.52645i	0.838797	+	0.166847i
$737$	0.379877	−	0.187334i	0.0139929	−	0.00690055i
$738$	1.12123	−	0.983291i	0.0412730	−	0.0361954i
$739$	0.602231	+	4.57440i	0.0221534	+	0.168272i	0.998945	−	0.0459193i	$-0.0146217\pi$
$739$	0.602231	+	4.57440i	0.0221534	+	0.168272i	−0.976792	+	0.214191i	$0.931288\pi$
$740$	0.0845555	−	0.0648817i	0.00310832	−	0.00238510i
$741$	−14.1619	+	2.81698i	−0.520252	+	0.103484i
$742$	1.74099	+	5.89646i	0.0639136	+	0.216466i
$743$	8.24459	−	41.4484i	0.302465	−	1.52059i	−0.468356	−	0.883540i	$-0.655153\pi$
$743$	8.24459	−	41.4484i	0.302465	−	1.52059i	0.770820	−	0.637053i	$-0.219847\pi$
$744$	−4.88624	+	1.30926i	−0.179138	+	0.0479999i
$745$	−0.103206	−	0.0508953i	−0.00378116	−	0.00186466i
$746$	3.86600	+	2.96649i	0.141544	+	0.108611i
$747$	6.67352	−	11.5589i	0.244171	−	0.422917i
$748$	0.806723	+	8.41846i	0.0294967	+	0.307810i
$749$	−7.44267	−	20.2289i	−0.271949	−	0.739146i
$750$	−0.00790785	−	0.0190912i	−0.000288754	−	0.000697113i
$751$	0.330365	+	5.04040i	0.0120552	+	0.183927i	0.999640	+	0.0268386i	$0.00854400\pi$
$751$	0.330365	+	5.04040i	0.0120552	+	0.183927i	−0.987585	+	0.157088i	$0.949789\pi$
$752$	−1.30235	+	4.86045i	−0.0474919	+	0.177242i
$753$	1.04371	+	3.07468i	0.0380351	+	0.112048i
$754$	2.94164	+	5.96505i	0.107128	+	0.217234i
$755$	−0.0249672	−	0.125519i	−0.000908650	−	0.00456809i
$756$	−2.74778	+	4.34652i	−0.0999358	+	0.158081i
$757$	5.02413	−	12.1293i	0.182605	−	0.440848i	−0.805897	−	0.592056i	$-0.798316\pi$
$757$	5.02413	−	12.1293i	0.182605	−	0.440848i	0.988502	+	0.151208i	$0.0483164\pi$
$758$	5.25920	+	1.78526i	0.191023	+	0.0648434i
$759$	−0.583634	+	8.90453i	−0.0211846	+	0.323214i
$760$	−0.0205624	+	0.00698001i	−0.000745878	+	0.000253192i
$761$	−11.0927	−	41.3985i	−0.402110	−	1.50070i	−0.809324	−	0.587363i	$-0.800166\pi$
$761$	−11.0927	−	41.3985i	−0.402110	−	1.50070i	0.407213	−	0.913333i	$-0.366501\pi$
$762$	−1.88716	+	1.26096i	−0.0683645	+	0.0456797i
$763$	1.82384	−	0.411012i	0.0660275	−	0.0148796i
$764$		−	19.1810i		−	0.693944i
$765$	0.0336037	−	0.0125464i	0.00121494	−	0.000453616i
$766$	−2.74013	+	1.58201i	−0.0990048	+	0.0571604i
$767$	−40.7296	+	53.0799i	−1.47066	+	1.91660i
$768$	−11.6498	+	0.763568i	−0.420376	+	0.0275529i
$769$	20.3920	+	20.3920i	0.735354	+	0.735354i	0.971675	−	0.236321i	$-0.0759416\pi$
$769$	20.3920	+	20.3920i	0.735354	+	0.735354i	−0.236321	+	0.971675i	$0.575942\pi$
$770$	−0.00569957		0.000897600i	−0.000205398		3.23472e-5i
$771$	−24.6292	−	16.4567i	−0.886997	−	0.592673i
$772$	−4.12981	+	12.1660i	−0.148635	+	0.437865i
$773$	−31.9841	+	4.21079i	−1.15039	+	0.151452i	−0.681509	−	0.731810i	$-0.738676\pi$
$773$	−31.9841	+	4.21079i	−1.15039	+	0.151452i	−0.468880	+	0.883262i	$0.655342\pi$
$774$	−1.05973	+	0.139516i	−0.0380912	+	0.00501480i
$775$	−8.67924	+	25.5682i	−0.311767	+	0.918437i
$776$	13.3692	+	8.93304i	0.479928	+	0.320677i
$777$	12.9698	−	10.4839i	0.465288	−	0.376107i
$778$	0.0286259	+	0.0286259i	0.00102629	+	0.00102629i
$779$	−16.6940	+	1.09418i	−0.598126	+	0.0392032i
$780$	−0.0557768	+	0.0726898i	−0.00199713	+	0.00260271i
$781$	12.2905	−	7.09593i	0.439789	−	0.253912i
$782$	−5.64504	−	6.05911i	−0.201866	−	0.216673i
$783$			5.16723i			0.184662i
$784$	−1.29761	−	25.6198i	−0.0463433	−	0.914991i
$785$	0.0783437	−	0.0523476i	0.00279621	−	0.00186837i
$786$	−0.277934	−	1.03727i	−0.00991359	−	0.0369980i
$787$	−21.2110	+	7.20016i	−0.756090	+	0.256658i	−0.672757	−	0.739864i	$-0.734890\pi$
$787$	−21.2110	+	7.20016i	−0.756090	+	0.256658i	−0.0833333	+	0.996522i	$0.526557\pi$
$788$	−1.68953	+	25.7772i	−0.0601870	+	0.918276i
$789$	−4.41259	−	1.49787i	−0.157092	−	0.0533256i
$790$	−0.000714243		0.00172434i	−2.54116e−5		6.13491e-5i
$791$	10.0371	+	19.1181i	0.356878	+	0.679760i
$792$	0.192859	+	0.969565i	0.00685293	+	0.0344520i
$793$	11.6221	+	23.5672i	0.412711	+	0.836896i
$794$	−0.990510	−	2.91795i	−0.0351519	−	0.103554i
$795$	−0.0220276	+	0.0822083i	−0.000781240	+	0.00291563i
$796$	0.661949	+	10.0994i	0.0234622	+	0.357963i
$797$	−7.15838	−	17.2819i	−0.253563	−	0.612155i	0.744924	−	0.667150i	$-0.232486\pi$
$797$	−7.15838	−	17.2819i	−0.253563	−	0.612155i	−0.998487	+	0.0549947i	$0.982486\pi$
$798$	−1.57162	+	0.578234i	−0.0556346	+	0.0204693i
$799$	4.38578	−	3.57999i	0.155158	−	0.126651i
$800$	6.85970	−	11.8813i	0.242527	−	0.420069i
$801$	−7.67166	−	5.88667i	−0.271065	−	0.207995i
$802$	−1.71900	−	0.847715i	−0.0606998	−	0.0299339i
$803$	3.70171	−	0.991871i	0.130631	−	0.0350024i
$804$	0.152180	−	0.765062i	0.00536699	−	0.0269817i
$805$	−0.134095	+	0.141059i	−0.00472623	+	0.00497167i
$806$	−6.81739	+	1.35606i	−0.240132	+	0.0477653i
$807$	6.20049	−	4.75780i	0.218268	−	0.167483i
$808$	−1.33779	−	10.1615i	−0.0470631	−	0.357480i
$809$	4.81990	−	4.22694i	0.169459	−	0.148611i	−0.570416	−	0.821356i	$-0.693218\pi$
$809$	4.81990	−	4.22694i	0.169459	−	0.148611i	0.739875	+	0.672745i	$0.234885\pi$
$810$	0.00185333		0.000913961i	6.51194e−5		3.21133e-5i
$811$	33.5365	+	6.67082i	1.17762	+	0.234244i	0.744834	−	0.667250i	$-0.232529\pi$
$811$	33.5365	+	6.67082i	1.17762	+	0.234244i	0.432791	+	0.901494i	$0.357529\pi$
$812$	−15.3163	−	21.7125i	−0.537497	−	0.761958i
$813$	−4.62331	−	6.91927i	−0.162147	−	0.242670i
$814$	0.206245	−	1.56658i	0.00722887	−	0.0549087i
$815$	−0.0600797	−	0.104061i	−0.00210450	−	0.00364510i
$816$	12.8101	+	8.01281i	0.448445	+	0.280504i
$817$	10.3844	+	5.99542i	0.363303	+	0.209753i
$818$	1.47448	−	0.610751i	0.0515541	−	0.0213544i
$819$	−8.43715	+	11.5913i	−0.294818	+	0.405034i
$820$	−0.0750646	+	0.0750646i	−0.00262137	+	0.00262137i
$821$	10.1635	−	11.5893i	0.354709	−	0.404468i	−0.546776	−	0.837279i	$-0.684145\pi$
$821$	10.1635	−	11.5893i	0.354709	−	0.404468i	0.901485	+	0.432811i	$0.142478\pi$
$822$	0.142820	+	0.00936090i	0.00498141	+	0.000326499i
$823$	18.7503	+	21.3807i	0.653596	+	0.745283i	0.979792	−	0.200019i	$-0.0641003\pi$
$823$	18.7503	+	21.3807i	0.653596	+	0.745283i	−0.326196	+	0.945302i	$0.605767\pi$
$824$	−10.4145	−	13.5724i	−0.362806	−	0.472818i
$825$	4.87495	+	2.01927i	0.169724	+	0.0703019i
$826$	−3.70846	+	6.81587i	−0.129034	+	0.237154i
$827$	21.1411	−	31.6399i	0.735148	−	1.10023i	−0.255898	−	0.966704i	$-0.582371\pi$
$827$	21.1411	−	31.6399i	0.735148	−	1.10023i	0.991046	−	0.133523i	$-0.0426290\pi$
$828$	12.3560	+	10.8359i	0.429401	+	0.376574i
$829$	−8.42042	−	2.25624i	−0.292453	−	0.0783626i	0.109610	−	0.993975i	$-0.465040\pi$
$829$	−8.42042	−	2.25624i	−0.292453	−	0.0783626i	−0.402063	+	0.915612i	$0.631707\pi$
$830$	0.0121987	−	0.0247365i	0.000423422	−	0.000858615i
$831$	−31.0323	−	4.08548i	−1.07650	−	0.141724i
$832$	−36.1844			−1.25447
$833$	−15.6671	+	24.2393i	−0.542833	+	0.839841i
$834$	−0.0412121			−0.00142706
$835$	0.0367425	+	0.00483725i	0.00127153	+	0.000167400i
$836$	2.41737	−	4.90195i	0.0836066	−	0.169537i
$837$	−5.21630	−	1.39770i	−0.180302	−	0.0483117i
$838$	2.30090	+	2.01783i	0.0794832	+	0.0697049i
$839$	−28.7984	+	43.0999i	−0.994232	+	1.48797i	−0.125868	+	0.992047i	$0.540172\pi$
$839$	−28.7984	+	43.0999i	−0.994232	+	1.48797i	−0.868364	+	0.495927i	$0.834828\pi$
$840$	−0.0103045	+	0.0189388i	−0.000355538	+	0.000653451i
$841$	2.12469	+	0.880074i	0.0732651	+	0.0303474i
$842$	3.83560	+	4.99866i	0.132184	+	0.172265i
$843$	−10.7339	−	12.2397i	−0.369696	−	0.421557i
$844$	−46.9721	−	3.07872i	−1.61685	−	0.105974i
$845$	−0.0938622	+	0.107029i	−0.00322896	+	0.00368192i
$846$	0.230625	−	0.230625i	0.00792904	−	0.00792904i
$847$	−15.3930	+	21.1476i	−0.528910	+	0.726641i
$848$	−33.1222	+	13.7197i	−1.13742	+	0.471136i
$849$	−0.454697	−	0.262520i	−0.0156052	−	0.00900965i
$850$	−4.46560	+	2.00915i	−0.153169	+	0.0689134i
$851$	−26.6497	−	46.1587i	−0.913541	−	1.58230i
$852$	3.41152	−	25.9131i	0.116877	−	0.887767i
$853$	20.7127	+	30.9988i	0.709191	+	1.06138i	0.994682	+	0.102997i	$0.0328433\pi$
$853$	20.7127	+	30.9988i	0.709191	+	1.06138i	−0.285491	+	0.958381i	$0.592157\pi$
$854$	1.75666	+	2.49025i	0.0601118	+	0.0852148i
$855$	−0.0227363	−	0.00452252i	−0.000777563	−	0.000154667i
$856$	−6.84437	+	3.37527i	−0.233936	+	0.115364i
$857$	30.1245	−	26.4185i	1.02903	−	0.902438i	0.0337484	−	0.999430i	$-0.489256\pi$
$857$	30.1245	−	26.4185i	1.02903	−	0.902438i	0.995285	+	0.0969921i	$0.0309222\pi$
$858$	0.177302	+	1.34675i	0.00605300	+	0.0459771i
$859$	18.8314	−	14.4498i	0.642519	−	0.493022i	−0.235358	−	0.971909i	$-0.575626\pi$
$859$	18.8314	−	14.4498i	0.642519	−	0.493022i	0.877877	+	0.478887i	$0.158959\pi$
$860$	0.0746245	−	0.0148437i	0.00254468	−	0.000506167i
$861$	−11.4448	+	12.0392i	−0.390039	+	0.410294i
$862$	0.115249	−	0.579398i	0.00392541	−	0.0197344i
$863$	−22.2758	+	5.96879i	−0.758278	+	0.203180i	−0.617187	−	0.786817i	$-0.711728\pi$
$863$	−22.2758	+	5.96879i	−0.758278	+	0.203180i	−0.141091	+	0.989997i	$0.545061\pi$
$864$	2.46095	+	1.21361i	0.0837231	+	0.0412877i
$865$	0.146337	+	0.112289i	0.00497562	+	0.00381793i
$866$	4.65062	−	8.05512i	0.158035	−	0.273724i
$867$	−6.42264	−	15.7401i	−0.218124	−	0.534561i
$868$	26.0616	−	9.58869i	0.884590	−	0.325461i
$869$	−0.364767	−	0.880625i	−0.0123739	−	0.0298732i
$870$	0.000698358		0.0106549i	2.36766e−5		0.000361234i
$871$	0.562887	−	2.10072i	0.0190727	−	0.0711802i
$872$	−0.212768	−	0.626794i	−0.00720523	−	0.0212259i
$873$	7.59196	+	15.3950i	0.256949	+	0.521041i
$874$	1.04412	+	5.24917i	0.0353180	+	0.177556i
$875$	0.106991	+	0.203790i	0.00361696	+	0.00688937i
$876$	2.70091	−	6.52057i	0.0912552	−	0.220310i
$877$	−44.4483	−	15.0882i	−1.50091	−	0.509491i	−0.554426	−	0.832233i	$-0.687062\pi$
$877$	−44.4483	−	15.0882i	−1.50091	−	0.509491i	−0.946487	+	0.322742i	$0.895395\pi$
$878$	0.136904	−	2.08875i	0.00462029	−	0.0704920i
$879$	−1.86803	+	0.634112i	−0.0630072	+	0.0213881i
$880$	−0.00870805	−	0.0324989i	−0.000293548	−	0.00109554i
$881$	14.7425	−	9.85060i	0.496686	−	0.331875i	−0.281867	−	0.959453i	$-0.590954\pi$
$881$	14.7425	−	9.85060i	0.496686	−	0.331875i	0.778554	+	0.627578i	$0.215954\pi$
$882$	−0.757457	+	1.48017i	−0.0255049	+	0.0498399i
$883$		−	24.2017i		−	0.814453i	−0.913327	−	0.407227i	$-0.866496\pi$
$883$		−	24.2017i		−	0.814453i	0.913327	−	0.407227i	$-0.133504\pi$
$884$	35.2303	+	25.3866i	1.18492	+	0.853844i
$885$	−0.0930230	+	0.0537068i	−0.00312693	+	0.00180534i
$886$	0.992494	−	1.29344i	0.0333435	−	0.0434541i
$887$	19.8698	−	1.30234i	0.667163	−	0.0437282i	0.271941	−	0.962314i	$-0.412334\pi$
$887$	19.8698	−	1.30234i	0.667163	−	0.0437282i	0.395222	+	0.918586i	$0.370668\pi$
$888$	−4.17512	−	4.17512i	−0.140108	−	0.140108i
$889$	19.6608	−	15.8924i	0.659401	−	0.533015i
$890$	−0.0166146	−	0.0111016i	−0.000556924	−	0.000372125i
$891$	−0.339227	+	0.999331i	−0.0113645	+	0.0334788i
$892$	−31.3019	+	4.12097i	−1.04807	+	0.137980i
$893$	−3.62754	+	0.477575i	−0.121391	+	0.0159814i
$894$	−1.00993	+	2.97517i	−0.0337772	+	0.0995044i
$895$	−0.153922	−	0.102848i	−0.00514506	−	0.00343782i
$896$	−18.4881	+	2.91161i	−0.617644	+	0.0972700i
$897$	32.3996	+	32.3996i	1.08179	+	1.08179i
$898$	−3.63737	+	0.238406i	−0.121381	+	0.00795570i
$899$	16.9873	−	22.1382i	0.566557	−	0.738352i
$900$	8.41582	−	4.85887i	0.280527	−	0.161962i
$901$	39.2583	+	9.26303i	1.30788	+	0.308596i
$902$			1.57384i			0.0524031i
$903$	11.6144	−	2.61737i	0.386503	−	0.0871005i
$904$	6.35647	−	4.24726i	0.211413	−	0.141262i
$905$	0.0240872	+	0.0898946i	0.000800685	+	0.00298820i
$906$	−3.30882	+	1.12319i	−0.109928	+	0.0373156i
$907$	−2.84655	+	43.4299i	−0.0945181	+	1.44207i	0.642547	+	0.766246i	$0.277878\pi$
$907$	−2.84655	+	43.4299i	−0.0945181	+	1.44207i	−0.737066	+	0.675821i	$0.763789\pi$
$908$	−6.98521	−	2.37116i	−0.231812	−	0.0786897i
$909$	4.18713	−	10.1086i	0.138878	−	0.335282i
$910$	−0.0158309	+	0.0250418i	−0.000524789	+	0.000830127i
$911$	10.1342	+	50.9482i	0.335762	+	1.68799i	0.667493	+	0.744616i	$0.267367\pi$
$911$	10.1342	+	50.9482i	0.335762	+	1.68799i	−0.331731	+	0.943374i	$0.607633\pi$
$912$	−4.31900	−	8.75807i	−0.143016	−	0.290009i
$913$	4.52767	+	13.3381i	0.149844	+	0.441427i
$914$	−0.596843	+	2.22745i	−0.0197418	+	0.0736775i
$915$	0.00275913	+	0.0420962i	9.12140e−5	+	0.00139166i
$916$	6.85601	+	16.5519i	0.226529	+	0.546889i
$917$	4.13012	+	11.2255i	0.136389	+	0.370698i
$918$	−0.459390	−	0.864941i	−0.0151621	−	0.0285473i
$919$	−4.52904	+	7.84453i	−0.149399	+	0.258767i	−0.931006	−	0.365005i	$-0.881067\pi$
$919$	−4.52904	+	7.84453i	−0.149399	+	0.258767i	0.781606	+	0.623772i	$0.214401\pi$
$920$	0.0546675	+	0.0419479i	0.00180234	+	0.00138298i
$921$	−26.2841	−	12.9619i	−0.866091	−	0.427109i
$922$	0.895294	−	0.239893i	0.0294849	−	0.00790046i
$923$	14.2163	−	71.4704i	0.467937	−	2.35248i
$924$	−1.53672	−	5.20466i	−0.0505545	−	0.171221i
$925$	−30.9108	+	6.14853i	−1.01634	+	0.202163i
$926$	1.53460	−	1.17754i	0.0504302	−	0.0386965i
$927$	−2.38384	−	18.1070i	−0.0782955	−	0.594713i
$928$	−10.6599	+	9.34851i	−0.349930	+	0.306880i
$929$	14.9002	−	7.34796i	0.488860	−	0.241079i	−0.181116	−	0.983462i	$-0.557971\pi$
$929$	14.9002	−	7.34796i	0.488860	−	0.241079i	0.669976	+	0.742383i	$0.266304\pi$
$930$	−0.0109450	−	0.00217709i	−0.000358900	−	7.13896e-5i
$931$	16.8497	−	8.00066i	0.552228	−	0.262211i
$932$	21.7521	+	32.5543i	0.712512	+	1.06635i
$933$	2.94728	−	22.3868i	0.0964896	−	0.732911i
$934$	−0.00737235	−	0.0127693i	−0.000241231	−	0.000417824i
$935$	−0.0134276	+	0.0353928i	−0.000439131	+	0.00115747i
$936$	4.39589	+	2.53797i	0.143684	+	0.0829561i
$937$	10.0733	−	4.17249i	0.329080	−	0.136309i	−0.212025	−	0.977264i	$-0.568006\pi$
$937$	10.0733	−	4.17249i	0.329080	−	0.136309i	0.541105	+	0.840955i	$0.318006\pi$
$938$	0.0265849	−	0.250822i	0.000868027	−	0.00818962i
$939$	4.10509	−	4.10509i	0.133965	−	0.133965i
$940$	−0.0153079	+	0.0174553i	−0.000499288	+	0.000569329i
$941$	−3.93906	−	0.258179i	−0.128410	−	0.00841641i	0.00106283	−	0.999999i	$-0.499662\pi$
$941$	−3.93906	−	0.258179i	−0.128410	−	0.00841641i	−0.129472	+	0.991583i	$0.541328\pi$
$942$	−1.69626	−	1.93421i	−0.0552671	−	0.0630200i
$943$	32.3180	+	42.1177i	1.05242	+	1.37154i
$944$	−41.8030	−	17.3154i	−1.36057	−	0.563568i
$945$	−0.0196358	+	0.0120092i	−0.000638752	+	0.000390658i
$946$	0.626696	−	0.937916i	0.0203756	−	0.0304943i
$947$	24.8792	+	21.8185i	0.808466	+	0.709005i	0.960169	−	0.279421i	$-0.0901424\pi$
$947$	24.8792	+	21.8185i	0.808466	+	0.709005i	−0.151703	+	0.988426i	$0.548476\pi$
$948$	−1.69563	−	0.454342i	−0.0550714	−	0.0147563i
$949$	8.70318	−	17.6483i	0.282517	−	0.572888i
$950$	3.13760	+	0.413073i	0.101797	+	0.0134019i
$951$	−17.4493			−0.565832
$952$	9.11872	+	4.61148i	0.295540	+	0.149459i
$953$	−54.9233			−1.77914			−0.889571	−	0.456797i	$-0.848996\pi$
$953$	−54.9233			−1.77914			−0.889571	+	0.456797i	$0.848996\pi$
$954$	2.30389	+	0.303313i	0.0745911	+	0.00982011i
$955$	0.0379730	−	0.0770017i	0.00122878	−	0.00249172i
$956$	43.7852	+	11.7322i	1.41611	+	0.379447i
$957$	−4.09991	−	3.59552i	−0.132531	−	0.116227i
$958$	3.57579	−	5.35155i	0.115529	−	0.172901i
$959$	−1.59370	+	0.0403338i	−0.0514634	+	0.00130245i
$960$	−0.0536701	−	0.0222309i	−0.00173220	−	0.000717499i
$961$	−1.11807	−	1.45710i	−0.0360667	−	0.0470031i
$962$	−5.34948	−	6.09991i	−0.172474	−	0.196669i
$963$	−8.12942	−	0.532831i	−0.261967	−	0.0171702i
$964$	7.43085	−	8.47326i	0.239332	−	0.272905i
$965$	−0.0406644	+	0.0406644i	−0.00130903	+	0.00130903i
$966$	4.29637	+	3.12726i	0.138233	+	0.100618i
$967$	−52.0344	+	21.5534i	−1.67331	+	0.693110i	−0.998973	−	0.0453095i	$-0.985573\pi$
$967$	−52.0344	+	21.5534i	−1.67331	+	0.693110i	−0.674342	+	0.738419i	$0.735573\pi$
$968$	8.02001	+	4.63035i	0.257773	+	0.148825i
$969$	−1.81829	+	10.8352i	−0.0584118	+	0.348078i
$970$	0.0177354	+	0.0307186i	0.000569448	+	0.000986313i
$971$	−2.56692	+	19.4977i	−0.0823764	+	0.625711i	0.899601	+	0.436713i	$0.143857\pi$
$971$	−2.56692	+	19.4977i	−0.0823764	+	0.625711i	−0.981977	+	0.188998i	$0.939476\pi$
$972$	1.07979	+	1.61603i	0.0346344	+	0.0518341i
$973$	0.457153	−	0.0416021i	0.0146556	−	0.00133370i
$974$	−2.73264	−	0.543555i	−0.0875593	−	0.0174166i
$975$	24.2996	−	11.9832i	0.778209	−	0.383770i
$976$	−13.3608	+	11.7171i	−0.427668	+	0.375055i
$977$	5.02680	+	38.1823i	0.160822	+	1.22156i	0.861378	+	0.507965i	$0.169602\pi$
$977$	5.02680	+	38.1823i	0.160822	+	1.22156i	−0.700556	+	0.713597i	$0.747065\pi$
$978$	−2.60283	+	1.99722i	−0.0832292	+	0.0638640i
$979$	10.0089	−	1.99090i	0.319887	−	0.0636295i
$980$	0.0469121	−	0.108665i	0.00149855	−	0.00347117i
$981$	0.137858	−	0.693057i	0.00440145	−	0.0221276i
$982$	3.28832	−	0.881102i	0.104934	−	0.0281171i
$983$	−34.4259	−	16.9770i	−1.09801	−	0.541481i	−0.199266	−	0.979945i	$-0.563856\pi$
$983$	−34.4259	−	16.9770i	−1.09801	−	0.541481i	−0.898748	+	0.438465i	$0.855522\pi$
$984$	4.66580	+	3.58019i	0.148740	+	0.114132i
$985$	−0.0578144	+	0.100137i	−0.00184212	+	0.00319064i
$986$	5.03754	−	0.482737i	0.160428	−	0.0153735i
$987$	−2.32544	+	2.79105i	−0.0740195	+	0.0888402i
$988$	−10.7397	−	25.9278i	−0.341674	−	0.824874i
$989$	−2.48859	−	37.9686i	−0.0791327	−	1.20733i
$990$	−0.000564429		0.00210648i	−1.79387e−5		6.69483e-5i
$991$	−5.42638	−	15.9856i	−0.172375	−	0.507799i	0.826069	−	0.563569i	$-0.190572\pi$
$991$	−5.42638	−	15.9856i	−0.172375	−	0.507799i	−0.998444	+	0.0557695i	$0.982239\pi$
$992$	−6.55385	−	13.2899i	−0.208085	−	0.421954i
$993$	−4.35743	−	21.9063i	−0.138279	−	0.695175i
$994$	0.339199	−	8.44439i	0.0107587	−	0.267840i
$995$	−0.0173366	+	0.0418542i	−0.000549607	+	0.00132687i
$996$	24.5643	+	8.33847i	0.778351	+	0.264214i
$997$	0.379640	−	5.79219i	0.0120233	−	0.183440i	−0.987623	−	0.156846i	$-0.949867\pi$
$997$	0.379640	−	5.79219i	0.0120233	−	0.183440i	0.999646	−	0.0265939i	$-0.00846610\pi$
$998$	5.98680	−	2.03225i	0.189509	−	0.0643296i
$999$	−1.63143	−	6.08858i	−0.0516162	−	0.192634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.250.14	yes	384
7.3	odd	6	inner	357.2.bl.a.199.11	yes	384
17.10	odd	16	inner	357.2.bl.a.61.11	yes	384
119.10	even	48	inner	357.2.bl.a.10.14	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.14	✓	384	119.10	even	48	inner
357.2.bl.a.61.11	yes	384	17.10	odd	16	inner
357.2.bl.a.199.11	yes	384	7.3	odd	6	inner
357.2.bl.a.250.14	yes	384	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.235499 + 0.0310041i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(-1.87735 - 0.503035i) q^{4} +(-0.00654072 - 0.00573606i) q^{5} +(-0.131965 + 0.197500i) q^{6} +(1.26448 - 2.32402i) q^{7} +(-0.865421 - 0.358469i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(-0.00136250 - 0.00155363i) q^{10} +(1.05308 + 0.0690224i) q^{11} +(1.28149 - 1.46126i) q^{12} +(3.83168 - 3.83168i) q^{13} +(0.369839 - 0.508102i) q^{14} +(0.00803740 - 0.00332920i) q^{15} +(3.17368 + 1.83233i) q^{16} +(-1.69172 - 3.76006i) q^{17} +(-0.118766 - 0.205708i) q^{18} +(-0.347810 + 2.64188i) q^{19} +(0.00939381 + 0.0140588i) q^{20} +(1.52509 + 2.16197i) q^{21} +(0.245859 + 0.0489044i) q^{22} +(7.58370 - 3.73987i) q^{23} +(0.704267 - 0.617625i) q^{24} +(-0.652621 - 4.95715i) q^{25} +(1.02116 - 0.783561i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-3.54295 + 3.72693i) q^{28} +(-1.00808 + 5.06794i) q^{29} +(0.00199602 - 0.000534833i) q^{30} +(-4.84339 - 2.38850i) q^{31} +(2.17690 + 1.67039i) q^{32} +(-0.527669 + 0.913949i) q^{33} +(-0.281822 - 0.937944i) q^{34} +(-0.0216014 + 0.00794765i) q^{35} +(0.743775 + 1.79563i) q^{36} +(-0.412260 - 6.28987i) q^{37} +(-0.163818 + 0.611378i) q^{38} +(1.74182 + 5.13124i) q^{39} +(0.00360428 + 0.00730875i) q^{40} +(1.22485 + 6.15774i) q^{41} +(0.292127 + 0.556427i) q^{42} +(1.72205 - 4.15739i) q^{43} +(-1.94228 - 0.659314i) q^{44} +(-0.000568983 + 0.00868100i) q^{45} +(1.90191 - 0.645611i) q^{46} +(0.355382 + 1.32630i) q^{47} +(-3.04705 + 2.03597i) q^{48} +(-3.80217 - 5.87737i) q^{49} -1.18764i q^{50} +(4.12053 + 0.145777i) q^{51} +(-9.12088 + 5.26595i) q^{52} +(-5.95550 + 7.76136i) q^{53} +(0.237023 - 0.0155353i) q^{54} +(-0.00649197 - 0.00649197i) q^{55} +(-1.92740 + 1.55798i) q^{56} +(-2.21560 - 1.48041i) q^{57} +(-0.394528 + 1.16224i) q^{58} +(-12.2413 + 1.61160i) q^{59} +(-0.0167637 + 0.00220699i) q^{60} +(-1.55873 + 4.59188i) q^{61} +(-1.06656 - 0.712655i) q^{62} +(-2.61354 + 0.411595i) q^{63} +(-4.72174 - 4.72174i) q^{64} +(-0.0470407 + 0.00308321i) q^{65} +(-0.152602 + 0.198875i) q^{66} +(0.347577 - 0.200674i) q^{67} +(1.28451 + 7.90996i) q^{68} +8.45572i q^{69} +(-0.00533352 + 0.00120194i) q^{70} +(11.1814 - 7.47114i) q^{71} +(0.242442 + 0.904806i) q^{72} +(3.43863 - 1.16726i) q^{73} +(0.0979247 - 1.49404i) q^{74} +(4.73458 + 1.60717i) q^{75} +(1.98192 - 4.78478i) q^{76} +(1.49201 - 2.36010i) q^{77} +(0.251108 + 1.26241i) q^{78} +(-0.399476 - 0.810057i) q^{79} +(-0.0102479 - 0.0301892i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(0.0975366 + 1.48812i) q^{82} +(5.10769 + 12.3311i) q^{83} +(-1.77558 - 4.82595i) q^{84} +(-0.0105029 + 0.0342973i) q^{85} +(0.534437 - 0.925672i) q^{86} +(-4.09944 - 3.14561i) q^{87} +(-0.886613 - 0.437229i) q^{88} +(9.34042 - 2.50276i) q^{89} +(-0.000403142 + 0.00202673i) q^{90} +(-4.05982 - 13.7500i) q^{91} +(-16.1186 + 3.20618i) q^{92} +(4.28436 - 3.28750i) q^{93} +(0.0425714 + 0.323362i) q^{94} +(0.0174289 - 0.0152847i) q^{95} +(-2.46095 + 1.21361i) q^{96} +(-16.8354 - 3.34876i) q^{97} +(-0.713186 - 1.50200i) q^{98} +(-0.586314 - 0.877481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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