LMFDB - Embedded newform 714.2.bl.a.367.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(31,714)] 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("714.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,0,0,0,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			367.10
Character	$\chi$	$=$	714.367
Dual form			714.2.bl.a.607.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.991445 - 0.130526i) q^{2} +(0.442289 + 0.896873i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-0.0230463 + 0.0202111i) q^{5} +(0.555570 + 0.831470i) q^{6} +(2.52228 + 0.798818i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-0.0202111 + 0.0230463i) q^{10} +(5.42090 - 0.355304i) q^{11} +(0.659346 + 0.751840i) q^{12} +(-3.14185 - 3.14185i) q^{13} +(2.60497 + 0.462760i) q^{14} +(-0.0283199 - 0.0117305i) q^{15} +(0.866025 - 0.500000i) q^{16} +(-4.10791 + 0.353644i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.144830 + 1.10009i) q^{19} +(-0.0170300 + 0.0254872i) q^{20} +(0.399138 + 2.61547i) q^{21} +(5.32815 - 1.05983i) q^{22} +(0.342192 + 0.168751i) q^{23} +(0.751840 + 0.659346i) q^{24} +(-0.652508 + 4.95629i) q^{25} +(-3.52507 - 2.70488i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(2.64308 + 0.118785i) q^{28} +(0.0711851 + 0.357872i) q^{29} +(-0.0296087 - 0.00793363i) q^{30} +(4.12321 - 2.03334i) q^{31} +(0.793353 - 0.608761i) q^{32} +(2.71626 + 4.70471i) q^{33} +(-4.02661 + 0.886808i) q^{34} +(-0.0742741 + 0.0325681i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(-0.475852 + 7.26009i) q^{37} +(0.287181 + 1.07177i) q^{38} +(1.42824 - 4.20745i) q^{39} +(-0.0135576 + 0.0274920i) q^{40} +(1.28774 - 6.47393i) q^{41} +(0.737110 + 2.54100i) q^{42} +(2.03175 + 4.90507i) q^{43} +(5.14423 - 1.74623i) q^{44} +(-0.00200481 - 0.0305876i) q^{45} +(0.361291 + 0.122642i) q^{46} +(1.27072 - 4.74238i) q^{47} +(0.831470 + 0.555570i) q^{48} +(5.72378 + 4.02968i) q^{49} +4.99906i q^{50} +(-2.13406 - 3.52786i) q^{51} +(-3.84797 - 2.22162i) q^{52} +(-4.84240 - 6.31074i) q^{53} +(-0.997859 - 0.0654031i) q^{54} +(-0.117751 + 0.117751i) q^{55} +(2.63598 - 0.227223i) q^{56} +(-0.922584 + 0.616451i) q^{57} +(0.117288 + 0.345518i) q^{58} +(-2.90666 - 0.382669i) q^{59} +(-0.0303909 - 0.00400104i) q^{60} +(-0.993828 - 2.92772i) q^{61} +(3.82253 - 2.55413i) q^{62} +(-2.16921 + 1.51477i) q^{63} +(0.707107 - 0.707107i) q^{64} +(0.135908 + 0.00890789i) q^{65} +(3.30711 + 4.30992i) q^{66} +(-5.88057 - 3.39515i) q^{67} +(-3.87641 + 1.40480i) q^{68} +0.381539i q^{69} +(-0.0693877 + 0.0419842i) q^{70} +(-9.52895 - 6.36704i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-6.75624 - 2.29343i) q^{73} +(0.475852 + 7.26009i) q^{74} +(-4.73376 + 1.60690i) q^{75} +(0.424619 + 1.02512i) q^{76} +(13.9568 + 3.43413i) q^{77} +(0.866835 - 4.35787i) q^{78} +(-1.70456 + 3.45651i) q^{79} +(-0.00985314 + 0.0290264i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.431710 - 6.58662i) q^{82} +(-4.70478 + 11.3583i) q^{83} +(1.06247 + 2.42305i) q^{84} +(0.0875246 - 0.0911754i) q^{85} +(2.65460 + 4.59791i) q^{86} +(-0.289481 + 0.222127i) q^{87} +(4.87229 - 2.40275i) q^{88} +(-10.0570 - 2.69477i) q^{89} +(-0.00598014 - 0.0300642i) q^{90} +(-5.41486 - 10.4344i) q^{91} +(0.374208 + 0.0744347i) q^{92} +(3.64730 + 2.79867i) q^{93} +(0.640841 - 4.86767i) q^{94} +(-0.0255717 - 0.0224258i) q^{95} +(0.896873 + 0.442289i) q^{96} +(-4.61391 + 0.917763i) q^{97} +(6.20079 + 3.24810i) q^{98} +(-3.01815 + 4.51698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) $ 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$

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 $

$2$	0.991445	−	0.130526i	0.701057	−	0.0922960i
$2$	0.991445	−	0.130526i	0.701057	−	0.0922960i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	0.965926	−	0.258819i	0.482963	−	0.129410i
$5$	−0.0230463	+	0.0202111i	−0.0103066	+	0.00903866i	−0.664484	−	0.747303i	$-0.731348\pi$
$5$	−0.0230463	+	0.0202111i	−0.0103066	+	0.00903866i	0.654177	+	0.756341i	$0.273015\pi$
$6$	0.555570	+	0.831470i	0.226811	+	0.339446i
$7$	2.52228	+	0.798818i	0.953332	+	0.301925i
$7$	2.52228	+	0.798818i	0.953332	+	0.301925i
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−0.0202111	+	0.0230463i	−0.00639130	+	0.00728788i
$11$	5.42090	−	0.355304i	1.63446	−	0.107128i	0.779702	−	0.626151i	$-0.215371\pi$
$11$	5.42090	−	0.355304i	1.63446	−	0.107128i	0.854761	+	0.519023i	$0.173704\pi$
$12$	0.659346	+	0.751840i	0.190337	+	0.217037i
$13$	−3.14185	−	3.14185i	−0.871393	−	0.871393i	0.121232	−	0.992624i	$-0.461316\pi$
$13$	−3.14185	−	3.14185i	−0.871393	−	0.871393i	−0.992624	+	0.121232i	$0.961316\pi$
$14$	2.60497	+	0.462760i	0.696207	+	0.123678i
$15$	−0.0283199	−	0.0117305i	−0.00731215	−	0.00302879i
$16$	0.866025	−	0.500000i	0.216506	−	0.125000i
$17$	−4.10791	+	0.353644i	−0.996315	+	0.0857712i
$17$	−4.10791	+	0.353644i	−0.996315	+	0.0857712i
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.144830	+	1.10009i	0.0332262	+	0.252378i	0.999995	−	0.00327571i	$-0.00104269\pi$
$19$	0.144830	+	1.10009i	0.0332262	+	0.252378i	−0.966768	+	0.255654i	$0.917709\pi$
$20$	−0.0170300	+	0.0254872i	−0.00380802	+	0.00569911i
$21$	0.399138	+	2.61547i	0.0870989	+	0.570743i
$22$	5.32815	−	1.05983i	1.13596	−	0.225957i
$23$	0.342192	+	0.168751i	0.0713520	+	0.0351869i	0.477615	−	0.878569i	$-0.341502\pi$
$23$	0.342192	+	0.168751i	0.0713520	+	0.0351869i	−0.406263	+	0.913756i	$0.633168\pi$
$24$	0.751840	+	0.659346i	0.153469	+	0.134588i
$25$	−0.652508	+	4.95629i	−0.130502	+	0.991259i
$26$	−3.52507	−	2.70488i	−0.691322	−	0.530470i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	2.64308	+	0.118785i	0.499496	+	0.0224482i
$29$	0.0711851	+	0.357872i	0.0132187	+	0.0664551i	0.986832	−	0.161751i	$-0.0517141\pi$
$29$	0.0711851	+	0.357872i	0.0132187	+	0.0664551i	−0.973613	+	0.228206i	$0.926714\pi$
$30$	−0.0296087	−	0.00793363i	−0.00540579	−	0.00144848i
$31$	4.12321	−	2.03334i	0.740550	−	0.365199i	−0.0325609	−	0.999470i	$-0.510366\pi$
$31$	4.12321	−	2.03334i	0.740550	−	0.365199i	0.773111	+	0.634271i	$0.218700\pi$
$32$	0.793353	−	0.608761i	0.140246	−	0.107615i
$33$	2.71626	+	4.70471i	0.472841	+	0.818985i
$34$	−4.02661	+	0.886808i	−0.690558	+	0.152086i
$35$	−0.0742741	+	0.0325681i	−0.0125546	+	0.00550502i
$36$	−0.382683	+	0.923880i	−0.0637806	+	0.153980i
$37$	−0.475852	+	7.26009i	−0.0782295	+	1.19355i	0.760623	+	0.649194i	$0.224893\pi$
$37$	−0.475852	+	7.26009i	−0.0782295	+	1.19355i	−0.838853	+	0.544358i	$0.816773\pi$
$38$	0.287181	+	1.07177i	0.0465869	+	0.173865i
$39$	1.42824	−	4.20745i	0.228701	−	0.673731i
$40$	−0.0135576	+	0.0274920i	−0.00214364	+	0.00434687i
$41$	1.28774	−	6.47393i	0.201112	−	1.01106i	−0.739909	−	0.672707i	$-0.765131\pi$
$41$	1.28774	−	6.47393i	0.201112	−	1.01106i	0.941020	−	0.338350i	$-0.109869\pi$
$42$	0.737110	+	2.54100i	0.113739	+	0.392084i
$43$	2.03175	+	4.90507i	0.309838	+	0.748016i	0.999710	+	0.0240842i	$0.00766698\pi$
$43$	2.03175	+	4.90507i	0.309838	+	0.748016i	−0.689872	+	0.723932i	$0.742333\pi$
$44$	5.14423	−	1.74623i	0.775521	−	0.263254i
$45$	−0.00200481	−	0.0305876i	−0.000298860	−	0.00455972i
$46$	0.361291	+	0.122642i	0.0532695	+	0.0180826i
$47$	1.27072	−	4.74238i	0.185353	−	0.691748i	−0.809201	−	0.587531i	$-0.800100\pi$
$47$	1.27072	−	4.74238i	0.185353	−	0.691748i	0.994555	−	0.104216i	$-0.0332334\pi$
$48$	0.831470	+	0.555570i	0.120012	+	0.0801897i
$49$	5.72378	+	4.02968i	0.817683	+	0.575669i
$50$			4.99906i			0.706974i
$51$	−2.13406	−	3.52786i	−0.298828	−	0.493999i
$52$	−3.84797	−	2.22162i	−0.533617	−	0.308084i
$53$	−4.84240	−	6.31074i	−0.665155	−	0.866847i	0.331917	−	0.943309i	$-0.392305\pi$
$53$	−4.84240	−	6.31074i	−0.665155	−	0.866847i	−0.997073	+	0.0764612i	$0.975638\pi$
$54$	−0.997859	−	0.0654031i	−0.135791	−	0.00890024i
$55$	−0.117751	+	0.117751i	−0.0158775	+	0.0158775i
$56$	2.63598	−	0.227223i	0.352247	−	0.0303639i
$57$	−0.922584	+	0.616451i	−0.122199	+	0.0816509i
$58$	0.117288	+	0.345518i	0.0154006	+	0.0453688i
$59$	−2.90666	−	0.382669i	−0.378415	−	0.0498192i	−0.0610800	−	0.998133i	$-0.519454\pi$
$59$	−2.90666	−	0.382669i	−0.378415	−	0.0498192i	−0.317335	+	0.948314i	$0.602788\pi$
$60$	−0.0303909	−	0.00400104i	−0.00392345	−	0.000516533i
$61$	−0.993828	−	2.92772i	−0.127247	−	0.374856i	0.864572	−	0.502508i	$-0.167589\pi$
$61$	−0.993828	−	2.92772i	−0.127247	−	0.374856i	−0.991819	+	0.127652i	$0.959256\pi$
$62$	3.82253	−	2.55413i	0.485462	−	0.324375i
$63$	−2.16921	+	1.51477i	−0.273295	+	0.190843i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	0.135908	+	0.00890789i	0.0168573	+	0.00110489i
$66$	3.30711	+	4.30992i	0.407078	+	0.530514i
$67$	−5.88057	−	3.39515i	−0.718426	−	0.414784i	0.0957469	−	0.995406i	$-0.469476\pi$
$67$	−5.88057	−	3.39515i	−0.718426	−	0.414784i	−0.814173	+	0.580622i	$0.802809\pi$
$68$	−3.87641	+	1.40480i	−0.470084	+	0.170357i
$69$			0.381539i			0.0459320i
$70$	−0.0693877	+	0.0419842i	−0.00829342	+	0.00501807i
$71$	−9.52895	−	6.36704i	−1.13088	−	0.755629i	−0.158113	−	0.987421i	$-0.550541\pi$
$71$	−9.52895	−	6.36704i	−1.13088	−	0.755629i	−0.972765	+	0.231793i	$0.925541\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−6.75624	−	2.29343i	−0.790758	−	0.268426i	−0.103300	−	0.994650i	$-0.532940\pi$
$73$	−6.75624	−	2.29343i	−0.790758	−	0.268426i	−0.687458	+	0.726224i	$0.741273\pi$
$74$	0.475852	+	7.26009i	0.0553166	+	0.843969i
$75$	−4.73376	+	1.60690i	−0.546608	+	0.185548i
$76$	0.424619	+	1.02512i	0.0487071	+	0.117589i
$77$	13.9568	+	3.43413i	1.59053	+	0.391356i
$78$	0.866835	−	4.35787i	0.0981497	−	0.493432i
$79$	−1.70456	+	3.45651i	−0.191778	+	0.388888i	−0.971430	−	0.237325i	$-0.923729\pi$
$79$	−1.70456	+	3.45651i	−0.191778	+	0.388888i	0.779652	+	0.626213i	$0.215396\pi$
$80$	−0.00985314	+	0.0290264i	−0.00110162	+	0.00324525i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	0.431710	−	6.58662i	0.0476744	−	0.727371i
$83$	−4.70478	+	11.3583i	−0.516417	+	1.24674i	0.423674	+	0.905815i	$0.360740\pi$
$83$	−4.70478	+	11.3583i	−0.516417	+	1.24674i	−0.940090	+	0.340925i	$0.889260\pi$
$84$	1.06247	+	2.42305i	0.115925	+	0.264376i
$85$	0.0875246	−	0.0911754i	0.00949338	−	0.00988936i
$86$	2.65460	+	4.59791i	0.286253	+	0.495805i
$87$	−0.289481	+	0.222127i	−0.0310356	+	0.0238145i
$88$	4.87229	−	2.40275i	0.519388	−	0.256134i
$89$	−10.0570	−	2.69477i	−1.06604	−	0.285645i	−0.317176	−	0.948367i	$-0.602735\pi$
$89$	−10.0570	−	2.69477i	−1.06604	−	0.285645i	−0.748866	+	0.662721i	$0.769401\pi$
$90$	−0.00598014	−	0.0300642i	−0.000630362	−	0.00316904i
$91$	−5.41486	−	10.4344i	−0.567631	−	1.09382i
$92$	0.374208	+	0.0744347i	0.0390139	+	0.00776035i
$93$	3.64730	+	2.79867i	0.378207	+	0.290208i
$94$	0.640841	−	4.86767i	0.0660977	−	0.502062i
$95$	−0.0255717	−	0.0224258i	−0.00262361	−	0.00230084i
$96$	0.896873	+	0.442289i	0.0915367	+	0.0451409i
$97$	−4.61391	+	0.917763i	−0.468471	+	0.0931847i	−0.423681	−	0.905812i	$-0.639262\pi$
$97$	−4.61391	+	0.917763i	−0.468471	+	0.0931847i	−0.0447906	+	0.998996i	$0.514262\pi$
$98$	6.20079	+	3.24810i	0.626375	+	0.328108i
$99$	−3.01815	+	4.51698i	−0.303336	+	0.453974i
$100$	0.652508	+	4.95629i	0.0652508	+	0.495629i
$101$	7.24343	−	12.5460i	0.720749	−	1.24837i	−0.239951	−	0.970785i	$-0.577132\pi$
$101$	7.24343	−	12.5460i	0.720749	−	1.24837i	0.960700	−	0.277588i	$-0.0895351\pi$
$102$	−2.57628	−	3.21913i	−0.255089	−	0.318741i
$103$	1.58375	−	0.914379i	0.156052	−	0.0900965i	−0.419941	−	0.907552i	$-0.637949\pi$
$103$	1.58375	−	0.914379i	0.156052	−	0.0900965i	0.575992	+	0.817455i	$0.304616\pi$
$104$	−4.10503	−	1.70036i	−0.402531	−	0.166734i
$105$	−0.0620601	−	0.0522099i	−0.00605644	−	0.00509517i
$106$	−5.62469	−	5.62469i	−0.546319	−	0.546319i
$107$	0.125457	+	0.143057i	0.0121284	+	0.0138298i	0.757872	−	0.652403i	$-0.226239\pi$
$107$	0.125457	+	0.143057i	0.0121284	+	0.0138298i	−0.745744	+	0.666233i	$0.767906\pi$
$108$	−0.997859	+	0.0654031i	−0.0960190	+	0.00629342i
$109$	−0.173116	+	0.197401i	−0.0165815	+	0.0189076i	−0.760071	−	0.649840i	$-0.774836\pi$
$109$	−0.173116	+	0.197401i	−0.0165815	+	0.0189076i	0.743490	+	0.668747i	$0.233169\pi$
$110$	−0.101374	+	0.132113i	−0.00966559	+	0.0125964i
$111$	−6.72184	+	2.78428i	−0.638009	+	0.264272i
$112$	2.58377	−	0.569343i	0.244143	−	0.0537979i
$113$	−0.679494	−	1.01694i	−0.0639215	−	0.0956652i	0.798132	−	0.602483i	$-0.205822\pi$
$113$	−0.679494	−	1.01694i	−0.0639215	−	0.0956652i	−0.862053	+	0.506818i	$0.830822\pi$
$114$	−0.834228	+	0.731598i	−0.0781326	+	0.0685205i
$115$	−0.0112969	+	0.00302699i	−0.00105344	+	0.000282269i
$116$	0.161384	+	0.327253i	0.0149841	+	0.0303847i
$117$	4.40524	−	0.579960i	0.407264	−	0.0536173i
$118$	−2.93174			−0.269888
$119$	−10.6438	−	2.38948i	−0.975715	−	0.219044i
$120$	−0.0306532			−0.00279824
$121$	18.3540	−	2.41635i	1.66855	−	0.219668i
$122$	−1.36747	−	2.77295i	−0.123805	−	0.251052i
$123$	6.37584	−	1.70840i	0.574890	−	0.154041i
$124$	3.45645	−	3.03122i	0.310398	−	0.272212i
$125$	−0.170284	−	0.254848i	−0.0152307	−	0.0227943i
$126$	−1.95294	+	1.78495i	−0.173981	+	0.159016i
$127$	−20.3963	+	8.44844i	−1.80988	+	0.749678i	−0.827854	+	0.560944i	$0.810438\pi$
$127$	−20.3963	+	8.44844i	−1.80988	+	0.749678i	−0.982028	+	0.188734i	$0.939562\pi$
$128$	0.608761	−	0.793353i	0.0538074	−	0.0701232i
$129$	−3.50060	+	3.99167i	−0.308211	+	0.351447i
$130$	0.135908	−	0.00890789i	0.0119199	−	0.000781274i
$131$	−9.11049	−	10.3885i	−0.795987	−	0.907650i	0.201428	−	0.979503i	$-0.435442\pi$
$131$	−9.11049	−	10.3885i	−0.795987	−	0.907650i	−0.997415	+	0.0718538i	$0.977108\pi$
$132$	3.84138	+	3.84138i	0.334349	+	0.334349i
$133$	−0.513471	+	2.89042i	−0.0445235	+	0.250632i
$134$	−6.27342	−	2.59854i	−0.541941	−	0.224479i
$135$	0.0265464	−	0.0153266i	0.00228475	−	0.00131910i
$136$	−3.65988	+	1.89875i	−0.313832	+	0.162817i
$137$	7.86871	−	13.6290i	0.672270	−	1.16441i	−0.304989	−	0.952356i	$-0.598653\pi$
$137$	7.86871	−	13.6290i	0.672270	−	1.16441i	0.977259	−	0.212049i	$-0.0680138\pi$
$138$	0.0498009	+	0.378275i	0.00423933	+	0.0322009i
$139$	−4.22008	+	6.31580i	−0.357943	+	0.535699i	−0.966117	−	0.258104i	$-0.916902\pi$
$139$	−4.22008	+	6.31580i	−0.357943	+	0.535699i	0.608174	+	0.793804i	$0.291902\pi$
$140$	−0.0633140	+	0.0506819i	−0.00535101	+	0.00428341i
$141$	4.81534	−	0.957830i	0.405525	−	0.0806639i
$142$	−10.2785	−	5.06879i	−0.862552	−	0.425363i
$143$	−18.1480	−	15.9153i	−1.51761	−	1.33091i
$144$	−0.130526	+	0.991445i	−0.0108772	+	0.0826204i
$145$	−0.00887351	−	0.00680889i	−0.000736905	−	0.000565447i
$146$	−6.99779	−	1.39195i	−0.579141	−	0.115198i
$147$	−1.08255	+	6.91579i	−0.0892871	+	0.570404i
$148$	1.41941	+	7.13587i	0.116675	+	0.586565i
$149$	1.15632	+	0.309835i	0.0947294	+	0.0253827i	0.305872	−	0.952073i	$-0.401052\pi$
$149$	1.15632	+	0.309835i	0.0947294	+	0.0253827i	−0.211143	+	0.977455i	$0.567719\pi$
$150$	−4.48352	+	2.21103i	−0.366078	+	0.180530i
$151$	14.5989	−	11.2021i	1.18804	−	0.911617i	0.190501	−	0.981687i	$-0.438989\pi$
$151$	14.5989	−	11.2021i	1.18804	−	0.911617i	0.997542	+	0.0700698i	$0.0223222\pi$
$152$	0.554791	+	0.960926i	0.0449995	+	0.0779414i
$153$	2.22017	−	3.47431i	0.179490	−	0.280881i
$154$	14.2857	+	1.58302i	1.15117	+	0.127563i
$155$	−0.0539287	+	0.130195i	−0.00433165	+	0.0104575i
$156$	0.290602	−	4.43374i	0.0232668	−	0.354983i
$157$	2.87420	+	10.7267i	0.229386	+	0.856080i	0.980600	+	0.196021i	$0.0628021\pi$
$157$	2.87420	+	10.7267i	0.229386	+	0.856080i	−0.751214	+	0.660059i	$0.770531\pi$
$158$	−1.23881	+	3.64943i	−0.0985547	+	0.290333i
$159$	3.51819	−	7.13419i	0.279011	−	0.565778i
$160$	−0.00598014	+	0.0300642i	−0.000472772	+	0.00237678i
$161$	0.728304	+	0.698985i	0.0573984	+	0.0550878i
$162$	−0.382683	−	0.923880i	−0.0300665	−	0.0725868i
$163$	18.4160	−	6.25137i	1.44245	−	0.489645i	0.512933	−	0.858428i	$-0.328559\pi$
$163$	18.4160	−	6.25137i	1.44245	−	0.489645i	0.929516	+	0.368783i	$0.120225\pi$
$164$	−0.431710	−	6.58662i	−0.0337109	−	0.514329i
$165$	−0.157687	−	0.0535275i	−0.0122759	−	0.00416711i
$166$	−3.18197	+	11.8753i	−0.246969	+	0.921699i
$167$	10.5368	+	7.04048i	0.815363	+	0.544808i	0.891886	−	0.452259i	$-0.149382\pi$
$167$	10.5368	+	7.04048i	0.815363	+	0.544808i	−0.0765231	+	0.997068i	$0.524382\pi$
$168$	1.36965	+	2.26364i	0.105671	+	0.174643i
$169$			6.74246i			0.518651i
$170$	0.0748750	−	0.101820i	0.00574265	−	0.00780921i
$171$	−0.960926	−	0.554791i	−0.0734839	−	0.0424259i
$172$	3.23204	+	4.21208i	0.246441	+	0.321168i
$173$	−3.52823	−	0.231252i	−0.268246	−	0.0175818i	−0.0693135	−	0.997595i	$-0.522081\pi$
$173$	−3.52823	−	0.231252i	−0.268246	−	0.0175818i	−0.198933	+	0.980013i	$0.563748\pi$
$174$	−0.258011	+	0.258011i	−0.0195598	+	0.0195598i
$175$	−5.60498	+	11.9799i	−0.423697	+	0.905597i
$176$	4.51698	−	3.01815i	0.340480	−	0.227502i
$177$	−0.942377	−	2.77615i	−0.0708334	−	0.208668i
$178$	−10.3227	−	1.35901i	−0.773721	−	0.101862i
$179$	3.36716	+	0.443295i	0.251673	+	0.0331334i	0.255307	−	0.966860i	$-0.417823\pi$
$179$	3.36716	+	0.443295i	0.251673	+	0.0331334i	−0.00363403	+	0.999993i	$0.501157\pi$
$180$	−0.00985314	−	0.0290264i	−0.000734410	−	0.00216350i
$181$	−10.1774	+	6.80031i	−0.756479	+	0.505463i	−0.872997	−	0.487726i	$-0.837827\pi$
$181$	−10.1774	+	6.80031i	−0.756479	+	0.505463i	0.116518	+	0.993189i	$0.462827\pi$
$182$	−6.73049	−	9.63834i	−0.498897	−	0.714441i
$183$	2.18624	−	2.18624i	0.161611	−	0.161611i
$184$	0.380723	+	0.0249539i	0.0280672	+	0.00183962i
$185$	−0.135767	−	0.176936i	−0.00998182	−	0.0130086i
$186$	3.98139	+	2.29866i	0.291930	+	0.168546i
$187$	−22.1429	+	3.37663i	−1.61925	+	0.246923i
$188$		−	4.90968i		−	0.358075i
$189$	−2.31797	−	1.27554i	−0.168608	−	0.0927819i
$190$	−0.0282801	−	0.0188962i	−0.00205166	−	0.00137087i
$191$	4.32994	−	16.1596i	0.313304	−	1.16926i	−0.612255	−	0.790660i	$-0.709737\pi$
$191$	4.32994	−	16.1596i	0.313304	−	1.16926i	0.925559	−	0.378605i	$-0.123596\pi$
$192$	0.946930	+	0.321439i	0.0683388	+	0.0231979i
$193$	0.996252	+	15.1999i	0.0717118	+	1.09411i	0.870394	+	0.492357i	$0.163864\pi$
$193$	0.996252	+	15.1999i	0.0717118	+	1.09411i	−0.798682	+	0.601754i	$0.794469\pi$
$194$	−4.45464	+	1.51215i	−0.319825	+	0.108566i
$195$	0.0521214	+	0.125832i	0.00373249	+	0.00901103i
$196$	6.57171	+	2.41095i	0.469408	+	0.172211i
$197$	1.75670	−	8.83153i	0.125160	−	0.629221i	−0.866377	−	0.499391i	$-0.833557\pi$
$197$	1.75670	−	8.83153i	0.125160	−	0.629221i	0.991536	−	0.129829i	$-0.0414430\pi$
$198$	−2.40275	+	4.87229i	−0.170756	+	0.346258i
$199$	−2.02334	+	5.96056i	−0.143431	+	0.422533i	−0.994777	−	0.102071i	$-0.967453\pi$
$199$	−2.02334	+	5.96056i	−0.143431	+	0.422533i	0.851346	+	0.524604i	$0.175787\pi$
$200$	1.29385	+	4.82872i	0.0914892	+	0.341442i
$201$	0.444107	−	6.77576i	0.0313249	−	0.477925i
$202$	5.54388	−	13.3841i	0.390066	−	0.941703i
$203$	−0.106326	+	0.959516i	−0.00746259	+	0.0673448i
$204$	−2.97442	−	2.85532i	−0.208251	−	0.199912i
$205$	0.101167	+	0.175227i	0.00706582	+	0.0122384i
$206$	1.45085	−	1.11328i	0.101086	−	0.0775657i
$207$	−0.342192	+	0.168751i	−0.0237840	+	0.0117290i
$208$	−4.29185	−	1.15000i	−0.297586	−	0.0797380i
$209$	1.17597	+	5.91202i	0.0813437	+	0.408943i
$210$	−0.0683439	−	0.0436628i	−0.00471618	−	0.00301302i
$211$	−25.5414	−	5.08050i	−1.75834	−	0.349756i	−0.792695	−	0.609618i	$-0.791323\pi$
$211$	−25.5414	−	5.08050i	−1.75834	−	0.349756i	−0.965646	+	0.259862i	$0.916323\pi$
$212$	−6.31074	−	4.84240i	−0.433424	−	0.332578i
$213$	1.49588	−	11.3623i	0.102496	−	0.778534i
$214$	0.143057	+	0.125457i	0.00977914	+	0.00857608i
$215$	−0.145961	−	0.0719799i	−0.00995444	−	0.00490899i
$216$	−0.980785	+	0.195090i	−0.0667340	+	0.0132742i
$217$	12.0241	−	1.83496i	0.816252	−	0.124565i
$218$	−0.145869	+	0.218308i	−0.00987948	+	0.0147857i
$219$	−0.931290	−	7.07385i	−0.0629307	−	0.478006i
$220$	−0.0832622	+	0.144214i	−0.00561354	+	0.00972293i
$221$	14.0175	+	11.7954i	0.942922	+	0.793441i
$222$	−6.30092	+	3.63784i	−0.422890	+	0.244156i
$223$	8.28668	+	3.43246i	0.554917	+	0.229854i	0.642477	−	0.766305i	$-0.277907\pi$
$223$	8.28668	+	3.43246i	0.554917	+	0.229854i	−0.0875597	+	0.996159i	$0.527907\pi$
$224$	2.48735	−	0.901721i	0.166193	−	0.0602488i
$225$	−3.53487	−	3.53487i	−0.235658	−	0.235658i
$226$	−0.806418	−	0.919543i	−0.0536421	−	0.0611671i
$227$	−25.2278	+	1.65351i	−1.67443	+	0.109748i	−0.872800	−	0.488079i	$-0.837698\pi$
$227$	−25.2278	+	1.65351i	−1.67443	+	0.109748i	−0.801626	+	0.597826i	$0.796031\pi$
$228$	−0.731598	+	0.834228i	−0.0484513	+	0.0552481i
$229$	0.305146	−	0.397674i	0.0201646	−	0.0262790i	−0.783162	−	0.621817i	$-0.786395\pi$
$229$	0.305146	−	0.397674i	0.0201646	−	0.0262790i	0.803327	+	0.595538i	$0.203061\pi$
$230$	−0.0108051	+	0.00447564i	−0.000712470	+	0.000295115i
$231$	3.09297	+	14.0364i	0.203503	+	0.923527i
$232$	0.202718	+	0.303389i	0.0133091	+	0.0199185i
$233$	−12.7891	+	11.2157i	−0.837841	+	0.734767i	−0.966430	−	0.256931i	$-0.917289\pi$
$233$	−12.7891	+	11.2157i	−0.837841	+	0.734767i	0.128588	+	0.991698i	$0.458955\pi$
$234$	4.29185	−	1.15000i	0.280567	−	0.0751777i
$235$	0.0665632	+	0.134977i	0.00434211	+	0.00880492i
$236$	−2.90666	+	0.382669i	−0.189207	+	0.0249096i
$237$	−3.85396			−0.250341
$238$	−10.8646	−	0.979748i	−0.704249	−	0.0635076i
$239$	21.0609			1.36231			0.681157	−	0.732137i	$-0.261477\pi$
$239$	21.0609			1.36231			0.681157	+	0.732137i	$0.261477\pi$
$240$	−0.0303909	+	0.00400104i	−0.00196173	+	0.000258266i
$241$	10.1784	+	20.6397i	0.655645	+	1.32952i	0.929883	+	0.367855i	$0.119908\pi$
$241$	10.1784	+	20.6397i	0.655645	+	1.32952i	−0.274238	+	0.961662i	$0.588425\pi$
$242$	17.8816	−	4.79136i	1.14947	−	0.308000i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	−1.71771	−	2.57074i	−0.109965	−	0.164575i
$245$	−0.213356	+	0.0228144i	−0.0136308	+	0.00145756i
$246$	6.09830	−	2.52600i	0.388814	−	0.161052i
$247$	3.00128	−	3.91135i	0.190967	−	0.248873i
$248$	3.03122	−	3.45645i	0.192483	−	0.219484i
$249$	−12.2679	+	0.804078i	−0.777444	+	0.0509564i
$250$	−0.202092	−	0.230441i	−0.0127814	−	0.0145744i
$251$	14.7925	+	14.7925i	0.933695	+	0.933695i	0.997935	−	0.0642395i	$-0.0204622\pi$
$251$	14.7925	+	14.7925i	0.933695	+	0.933695i	−0.0642395	+	0.997935i	$0.520462\pi$
$252$	−1.70325	+	2.02459i	−0.107294	+	0.127537i
$253$	1.91495	+	0.793197i	0.120392	+	0.0498679i
$254$	−19.1191	+	11.0384i	−1.19964	+	0.692612i
$255$	0.120484	+	0.0381726i	0.00754499	+	0.00239046i
$256$	0.500000	−	0.866025i	0.0312500	−	0.0541266i
$257$	−1.14833	−	8.72242i	−0.0716307	−	0.544090i	−0.989206	−	0.146528i	$-0.953190\pi$
$257$	−1.14833	−	8.72242i	−0.0716307	−	0.544090i	0.917576	−	0.397561i	$-0.130143\pi$
$258$	−2.94964	+	4.41445i	−0.183636	+	0.274831i
$259$	−6.99972	+	17.9319i	−0.434942	+	1.11423i
$260$	0.133583	−	0.0265712i	0.00828445	−	0.00164788i
$261$	−0.327253	−	0.161384i	−0.0202565	−	0.00998939i
$262$	−10.3885	−	9.11049i	−0.641805	−	0.562848i
$263$	0.723774	−	5.49761i	0.0446298	−	0.338997i	−0.954534	−	0.298103i	$-0.903646\pi$
$263$	0.723774	−	5.49761i	0.0446298	−	0.338997i	0.999163	−	0.0408939i	$-0.0130206\pi$
$264$	4.30992	+	3.30711i	0.265257	+	0.203539i
$265$	0.239146	+	0.0475691i	0.0146906	+	0.00292215i
$266$	−0.131802	+	2.93272i	−0.00808128	+	0.179816i
$267$	−2.03124	−	10.2117i	−0.124310	−	0.624948i
$268$	−6.55893	−	1.75746i	−0.400650	−	0.107354i
$269$	1.34405	−	0.662812i	0.0819481	−	0.0404123i	−0.400853	−	0.916142i	$-0.631286\pi$
$269$	1.34405	−	0.662812i	0.0819481	−	0.0404123i	0.482801	+	0.875730i	$0.339619\pi$
$270$	0.0243188	−	0.0186605i	0.00148000	−	0.00113564i
$271$	10.7827	+	18.6761i	0.655000	+	1.13449i	0.981894	+	0.189433i	$0.0606649\pi$
$271$	10.7827	+	18.6761i	0.655000	+	1.13449i	−0.326893	+	0.945061i	$0.606002\pi$
$272$	−3.38073	+	2.36022i	−0.204987	+	0.143109i
$273$	6.96339	−	9.47145i	0.421444	−	0.573238i
$274$	6.02245	−	14.5395i	0.363830	−	0.878363i
$275$	−1.77619	+	27.0994i	−0.107108	+	1.63416i
$276$	0.0987497	+	0.368539i	0.00594403	+	0.0221834i
$277$	9.04670	−	26.6507i	0.543564	−	1.60129i	−0.233833	−	0.972277i	$-0.575127\pi$
$277$	9.04670	−	26.6507i	0.543564	−	1.60129i	0.777397	−	0.629010i	$-0.216540\pi$
$278$	−3.35960	+	6.81260i	−0.201496	+	0.408593i
$279$	−0.896892	+	4.50898i	−0.0536955	+	0.269946i
$280$	−0.0561570	+	0.0585125i	−0.00335603	+	0.00349679i
$281$	6.97238	+	16.8328i	0.415937	+	1.00416i	0.983512	+	0.180840i	$0.0578817\pi$
$281$	6.97238	+	16.8328i	0.415937	+	1.00416i	−0.567575	+	0.823322i	$0.692118\pi$
$282$	4.64912	−	1.57816i	0.276851	−	0.0939783i
$283$	−1.87175	−	28.5574i	−0.111264	−	1.69756i	−0.580317	−	0.814391i	$-0.697071\pi$
$283$	−1.87175	−	28.5574i	−0.111264	−	1.69756i	0.469053	−	0.883170i	$-0.344595\pi$
$284$	−10.8522	−	3.68381i	−0.643958	−	0.218594i
$285$	0.00880301	−	0.0328533i	0.000521445	−	0.00194606i
$286$	−20.0701	−	13.4104i	−1.18677	−	0.792974i
$287$	8.41954	−	15.3004i	0.496989	−	0.903152i
$288$			1.00000i			0.0589256i
$289$	16.7499	−	2.90547i	0.985287	−	0.170910i
$290$	−0.00968634	−	0.00559241i	−0.000568801	−	0.000328398i
$291$	−2.86379	−	3.73217i	−0.167879	−	0.218784i
$292$	−7.11961	−	0.466644i	−0.416644	−	0.0273083i
$293$	−9.66848	+	9.66848i	−0.564839	+	0.564839i	−0.930678	−	0.365839i	$-0.880782\pi$
$293$	−9.66848	+	9.66848i	−0.564839	+	0.564839i	0.365839	+	0.930678i	$0.380782\pi$
$294$	−0.170596	+	6.99792i	−0.00994937	+	0.408127i
$295$	0.0747218	−	0.0499275i	0.00435047	−	0.00290689i
$296$	2.33869	+	6.88955i	0.135933	+	0.400447i
$297$	−5.38605	−	0.709087i	−0.312531	−	0.0411454i
$298$	1.18687	+	0.156254i	0.0687535	+	0.00905156i
$299$	−0.544928	−	1.60531i	−0.0315140	−	0.0928373i
$300$	−4.15657	+	2.77733i	−0.239979	+	0.160349i
$301$	1.20637	+	13.9949i	0.0695342	+	0.806655i
$302$	13.0118	−	13.0118i	0.748748	−	0.748748i
$303$	14.4559	+	0.947486i	0.830467	+	0.0544317i
$304$	0.675471	+	0.880291i	0.0387409	+	0.0504881i
$305$	0.0820764	+	0.0473868i	0.00469968	+	0.00271336i
$306$	1.74769	−	3.73438i	0.0999089	−	0.213480i
$307$			27.1098i			1.54724i	0.633652	+	0.773618i	$0.281555\pi$
$307$			27.1098i			1.54724i	−0.633652	+	0.773618i	$0.718445\pi$
$308$	14.3701	−	0.295178i	0.818812	−	0.0168194i
$309$	1.52056	+	1.01600i	0.0865015	+	0.0577984i
$310$	−0.0364734	+	0.136121i	−0.00207155	+	0.00773113i
$311$	11.5347	+	3.91552i	0.654075	+	0.222029i	0.628698	−	0.777649i	$-0.283588\pi$
$311$	11.5347	+	3.91552i	0.654075	+	0.222029i	0.0253769	+	0.999678i	$0.491921\pi$
$312$	−0.290602	−	4.43374i	−0.0164521	−	0.251011i
$313$	17.4157	−	5.91183i	0.984393	−	0.334156i	0.217591	−	0.976040i	$-0.430180\pi$
$313$	17.4157	−	5.91183i	0.984393	−	0.334156i	0.766802	+	0.641884i	$0.221847\pi$
$314$	4.24972	+	10.2597i	0.239825	+	0.578990i
$315$	0.0193772	−	0.0787518i	0.00109178	−	0.00443716i
$316$	−0.751869	+	3.77990i	−0.0422960	+	0.212636i
$317$	−6.52257	+	13.2265i	−0.366344	+	0.742872i	−0.999515	−	0.0311399i	$-0.990086\pi$
$317$	−6.52257	+	13.2265i	−0.366344	+	0.742872i	0.633171	+	0.774012i	$0.281753\pi$
$318$	2.55690	−	7.53237i	0.143384	−	0.422395i
$319$	0.513041	+	1.91469i	0.0287248	+	0.107202i
$320$	−0.00200481	+	0.0305876i	−0.000112073	+	0.00170990i
$321$	−0.0728152	+	0.175791i	−0.00406415	+	0.00981172i
$322$	0.813309	+	0.597943i	0.0453239	+	0.0333220i
$323$	−0.983987	−	4.46785i	−0.0547505	−	0.248598i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	17.6220	−	13.5218i	0.977494	−	0.750057i
$326$	17.4424	−	8.60166i	0.966047	−	0.476402i
$327$	−0.253610	−	0.0679547i	−0.0140247	−	0.00375790i
$328$	−1.28774	−	6.47393i	−0.0711038	−	0.357463i
$329$	6.99340	−	10.9465i	0.385559	−	0.603502i
$330$	−0.163325	−	0.0324873i	−0.00899073	−	0.00178837i
$331$	−5.09191	−	3.90716i	−0.279877	−	0.214757i	0.459278	−	0.888292i	$-0.348108\pi$
$331$	−5.09191	−	3.90716i	−0.279877	−	0.214757i	−0.739155	+	0.673536i	$0.764775\pi$
$332$	−1.60471	+	12.1890i	−0.0880700	+	0.668958i
$333$	−5.47014	−	4.79718i	−0.299762	−	0.262884i
$334$	11.3656	+	5.60491i	0.621900	+	0.306687i
$335$	0.204145	−	0.0406069i	0.0111536	−	0.00221859i
$336$	1.65340	+	2.06550i	0.0902003	+	0.112682i
$337$	−4.22457	+	6.32251i	−0.230127	+	0.344409i	−0.928505	−	0.371320i	$-0.878905\pi$
$337$	−4.22457	+	6.32251i	−0.230127	+	0.344409i	0.698378	+	0.715729i	$0.253905\pi$
$338$	0.880067	+	6.68477i	0.0478693	+	0.363604i
$339$	0.611529	−	1.05920i	0.0332137	−	0.0575278i
$340$	0.0609443	−	0.110722i	0.00330517	−	0.00600473i
$341$	21.6290	−	12.4875i	1.17128	−	0.676238i
$342$	−1.02512	−	0.424619i	−0.0554322	−	0.0229607i
$343$	11.2180	+	14.7362i	0.605714	+	0.795682i
$344$	3.75418	+	3.75418i	0.202412	+	0.202412i
$345$	−0.00771131	−	0.00879307i	−0.000415163	−	0.000473403i
$346$	−3.52823	+	0.231252i	−0.189679	+	0.0124322i
$347$	14.4250	−	16.4486i	0.774376	−	0.883007i	−0.221366	−	0.975191i	$-0.571051\pi$
$347$	14.4250	−	16.4486i	0.774376	−	0.883007i	0.995742	+	0.0921839i	$0.0293848\pi$
$348$	−0.222127	+	0.289481i	−0.0119072	+	0.0155178i
$349$	−11.8635	+	4.91402i	−0.635038	+	0.263041i	−0.676892	−	0.736082i	$-0.736674\pi$
$349$	−11.8635	+	4.91402i	−0.635038	+	0.263041i	0.0418540	+	0.999124i	$0.486674\pi$
$350$	−3.99334	+	12.6090i	−0.213453	+	0.673981i
$351$	2.46854	+	3.69443i	0.131761	+	0.197194i
$352$	4.08439	−	3.58192i	0.217699	−	0.190917i
$353$	29.3923	−	7.87564i	1.56439	−	0.419178i	0.630342	−	0.776317i	$-0.282915\pi$
$353$	29.3923	−	7.87564i	1.56439	−	0.419178i	0.934051	+	0.357140i	$0.116248\pi$
$354$	−1.29668	−	2.62940i	−0.0689175	−	0.139751i
$355$	0.348291	−	0.0458534i	0.0184854	−	0.00243365i
$356$	−10.4118			−0.551824
$357$	−2.56457	−	10.6030i	−0.135731	−	0.561169i
$358$	3.39621			0.179495
$359$	−32.4884	+	4.27718i	−1.71467	+	0.225741i	−0.922891	−	0.385061i	$-0.874180\pi$
$359$	−32.4884	+	4.27718i	−1.71467	+	0.225741i	−0.791783	+	0.610802i	$0.790847\pi$
$360$	−0.0135576	−	0.0274920i	−0.000714546	−	0.00144896i
$361$	17.1634	−	4.59891i	0.903335	−	0.242048i
$362$	−9.20270	+	8.07055i	−0.483683	+	0.424179i
$363$	10.2849	+	15.3925i	0.539819	+	0.807896i
$364$	−7.93097	−	8.67738i	−0.415696	−	0.454818i
$365$	0.202059	−	0.0836956i	0.0105762	−	0.00438083i
$366$	1.88217	−	2.45289i	0.0983827	−	0.128215i
$367$	16.3641	−	18.6597i	0.854201	−	0.974030i	−0.145682	−	0.989331i	$-0.546538\pi$
$367$	16.3641	−	18.6597i	0.854201	−	0.974030i	0.999883	+	0.0153018i	$0.00487091\pi$
$368$	0.380723	−	0.0249539i	0.0198465	−	0.00130081i
$369$	4.35218	+	4.96271i	0.226566	+	0.258348i
$370$	−0.157701	−	0.157701i	−0.00819847	−	0.00819847i
$371$	−7.17276	−	19.7857i	−0.372391	−	1.02722i
$372$	4.24737	+	1.75932i	0.220216	+	0.0912163i
$373$	−1.44145	+	0.832222i	−0.0746355	+	0.0430908i	−0.536853	−	0.843676i	$-0.680387\pi$
$373$	−1.44145	+	0.832222i	−0.0746355	+	0.0430908i	0.462218	+	0.886766i	$0.347054\pi$
$374$	−21.5127	+	6.23797i	−1.11240	+	0.322558i
$375$	0.153252	−	0.265439i	0.00791388	−	0.0137072i
$376$	−0.640841	−	4.86767i	−0.0330489	−	0.251031i
$377$	0.900726	−	1.34803i	0.0463898	−	0.0694272i
$378$	−2.46463	−	0.962072i	−0.126767	−	0.0494837i
$379$	−16.0541	+	3.19336i	−0.824643	+	0.164032i	−0.589334	−	0.807889i	$-0.700610\pi$
$379$	−16.0541	+	3.19336i	−0.824643	+	0.164032i	−0.235308	+	0.971921i	$0.575610\pi$
$380$	−0.0305046	−	0.0150432i	−0.00156486	−	0.000771701i
$381$	−16.5982	−	14.5563i	−0.850354	−	0.745740i
$382$	2.18365	−	16.5865i	0.111725	−	0.848638i
$383$	−21.0372	−	16.1424i	−1.07495	−	0.824837i	−0.0897002	−	0.995969i	$-0.528591\pi$
$383$	−21.0372	−	16.1424i	−1.07495	−	0.824837i	−0.985248	+	0.171132i	$0.945258\pi$
$384$	0.980785	+	0.195090i	0.0500505	+	0.00995566i
$385$	−0.391061	+	0.202938i	−0.0199303	+	0.0103427i
$386$	2.97171	+	14.9398i	0.151256	+	0.760415i
$387$	−5.12830	−	1.37412i	−0.260686	−	0.0698507i
$388$	−4.21916	+	2.08066i	−0.214195	+	0.105629i
$389$	5.05808	−	3.88120i	0.256455	−	0.196785i	−0.472530	−	0.881315i	$-0.656659\pi$
$389$	5.05808	−	3.88120i	0.256455	−	0.196785i	0.728985	+	0.684530i	$0.239992\pi$
$390$	0.0680999	+	0.117952i	0.00344837	+	0.00597275i
$391$	−1.46537	−	0.572198i	−0.0741071	−	0.0289373i
$392$	6.83018	+	1.53254i	0.344976	+	0.0774052i
$393$	5.28772	−	12.7657i	0.266730	−	0.643943i
$394$	0.588926	−	8.98527i	0.0296697	−	0.452671i
$395$	−0.0305759	−	0.114111i	−0.00153844	−	0.00574153i
$396$	−1.74623	+	5.14423i	−0.0877513	+	0.258507i
$397$	−8.16571	+	16.5584i	−0.409825	+	0.831044i	0.589897	+	0.807479i	$0.299168\pi$
$397$	−8.16571	+	16.5584i	−0.409825	+	0.831044i	−0.999722	+	0.0235652i	$0.992498\pi$
$398$	−1.22802	+	6.17367i	−0.0615550	+	0.309458i
$399$	−2.81945	+	0.817884i	−0.141149	+	0.0409454i
$400$	1.91306	+	4.61853i	0.0956529	+	0.230926i
$401$	−10.8967	+	3.69892i	−0.544154	+	0.184715i	−0.579962	−	0.814643i	$-0.696933\pi$
$401$	−10.8967	+	3.69892i	−0.544154	+	0.184715i	0.0358085	+	0.999359i	$0.488599\pi$
$402$	−0.444107	−	6.77576i	−0.0221500	−	0.337944i
$403$	−19.3430	−	6.56605i	−0.963541	−	0.327078i
$404$	3.74948	−	13.9932i	0.186543	−	0.696190i
$405$	0.0254872	+	0.0170300i	0.00126647	+	0.000846227i
$406$	0.0198260	+	0.965185i	0.000983949	+	0.0479013i
$407$			39.5253i			1.95920i
$408$	−3.32166	−	2.44265i	−0.164447	−	0.120929i
$409$	26.0683	+	15.0506i	1.28900	+	0.744202i	0.978475	−	0.206364i	$-0.0661632\pi$
$409$	26.0683	+	15.0506i	1.28900	+	0.744202i	0.310521	+	0.950567i	$0.399497\pi$
$410$	0.123173	+	0.160523i	0.00608310	+	0.00792764i
$411$	15.7037	+	1.02928i	0.774608	+	0.0507705i
$412$	1.29313	−	1.29313i	0.0637078	−	0.0637078i
$413$	−7.02572	−	3.28709i	−0.345713	−	0.161747i
$414$	−0.317238	+	0.211972i	−0.0155914	+	0.0104179i
$415$	−0.121136	−	0.356856i	−0.00594635	−	0.0175174i
$416$	−4.40524	−	0.579960i	−0.215984	−	0.0284349i
$417$	−7.53097	−	0.991470i	−0.368793	−	0.0485525i
$418$	1.93759	+	5.70794i	0.0947704	+	0.279185i
$419$	−0.445814	+	0.297883i	−0.0217794	+	0.0145526i	−0.566412	−	0.824122i	$-0.691669\pi$
$419$	−0.445814	+	0.297883i	−0.0217794	+	0.0145526i	0.544633	+	0.838675i	$0.316669\pi$
$420$	−0.0734583	−	0.0343686i	−0.00358440	−	0.00167701i
$421$	0.0889224	−	0.0889224i	0.00433381	−	0.00433381i	−0.704937	−	0.709270i	$-0.749025\pi$
$421$	0.0889224	−	0.0889224i	0.00433381	−	0.00433381i	0.709270	+	0.704937i	$0.249025\pi$
$422$	−25.9860	−	1.70321i	−1.26498	−	0.0829111i
$423$	2.98882	+	3.89511i	0.145321	+	0.189387i
$424$	−6.88881	−	3.97726i	−0.334550	−	0.193153i
$425$	0.927685	−	20.5908i	0.0449993	−	0.998799i
$426$		−	11.4604i		−	0.555257i
$427$	−0.167994	−	8.17842i	−0.00812981	−	0.395781i
$428$	0.158208	+	0.105711i	0.00764728	+	0.00510975i
$429$	6.24739	−	23.3156i	0.301627	−	1.12569i
$430$	−0.154107	−	0.0523124i	−0.00743172	−	0.00252273i
$431$	1.46609	+	22.3682i	0.0706191	+	1.07744i	0.875252	+	0.483667i	$0.160695\pi$
$431$	1.46609	+	22.3682i	0.0706191	+	1.07744i	−0.804633	+	0.593772i	$0.797638\pi$
$432$	−0.946930	+	0.321439i	−0.0455592	+	0.0154653i
$433$	11.0067	+	26.5725i	0.528947	+	1.27699i	0.932214	+	0.361909i	$0.117875\pi$
$433$	11.0067	+	26.5725i	0.528947	+	1.27699i	−0.403266	+	0.915083i	$0.632125\pi$
$434$	11.6818	−	3.38873i	0.560743	−	0.162664i
$435$	0.00218205	−	0.0109699i	0.000104621	−	0.000525967i
$436$	−0.116126	+	0.235480i	−0.00556142	+	0.0112774i
$437$	−0.136081	+	0.400882i	−0.00650965	+	0.0191768i
$438$	−1.84664	−	6.89177i	−0.0882361	−	0.329302i
$439$	0.266585	−	4.06731i	0.0127234	−	0.194122i	−0.986765	−	0.162154i	$-0.948156\pi$
$439$	0.266585	−	4.06731i	0.0127234	−	0.194122i	0.999489	−	0.0319680i	$-0.0101775\pi$
$440$	−0.0637261	+	0.153848i	−0.00303802	+	0.00733444i
$441$	−6.68138	+	2.08787i	−0.318161	+	0.0994222i
$442$	15.4372	+	9.86478i	0.734274	+	0.469220i
$443$	19.1271	+	33.1290i	0.908754	+	1.57401i	0.815797	+	0.578338i	$0.196299\pi$
$443$	19.1271	+	33.1290i	0.908754	+	1.57401i	0.0929572	+	0.995670i	$0.470368\pi$
$444$	−5.77218	+	4.42915i	−0.273935	+	0.210198i
$445$	0.286241	−	0.141159i	0.0135691	−	0.00669156i
$446$	8.66381	+	2.32146i	0.410243	+	0.109924i
$447$	0.233545	+	1.17411i	0.0110463	+	0.0555334i
$448$	2.34837	−	1.21867i	0.110950	−	0.0575768i
$449$	−0.0232962	−	0.00463391i	−0.00109942	−	0.000218688i	0.194541	−	0.980894i	$-0.437678\pi$
$449$	−0.0232962	−	0.00463391i	−0.00109942	−	0.000218688i	−0.195640	+	0.980676i	$0.562678\pi$
$450$	−3.96602	−	3.04324i	−0.186960	−	0.143459i
$451$	4.68051	−	35.5520i	0.220397	−	1.67408i
$452$	−0.919543	−	0.806418i	−0.0432517	−	0.0379307i
$453$	16.5038	+	8.13879i	0.775418	+	0.382394i
$454$	−24.7961	+	4.93225i	−1.16374	+	0.231482i
$455$	0.335682	+	0.131034i	0.0157370	+	0.00614297i
$456$	−0.616451	+	0.922584i	−0.0288680	+	0.0432039i
$457$	1.94455	+	14.7703i	0.0909620	+	0.690925i	0.974792	+	0.223117i	$0.0716230\pi$
$457$	1.94455	+	14.7703i	0.0909620	+	0.690925i	−0.883830	+	0.467809i	$0.845044\pi$
$458$	0.250628	−	0.434101i	0.0117111	−	0.0202842i
$459$	4.09797	+	0.454565i	0.191277	+	0.0212173i
$460$	−0.0101285	+	0.00584770i	−0.000472244	+	0.000272650i
$461$	19.8762	+	8.23297i	0.925725	+	0.383448i	0.794055	−	0.607846i	$-0.207966\pi$
$461$	19.8762	+	8.23297i	0.925725	+	0.383448i	0.131670	+	0.991294i	$0.457966\pi$
$462$	4.89863	+	13.5126i	0.227905	+	0.628663i
$463$	−14.1325	−	14.1325i	−0.656795	−	0.656795i	0.297825	−	0.954620i	$-0.403739\pi$
$463$	−14.1325	−	14.1325i	−0.656795	−	0.656795i	−0.954620	+	0.297825i	$0.903739\pi$
$464$	0.240584	+	0.274333i	0.0111688	+	0.0127356i
$465$	−0.140621	+	0.00921677i	−0.00652113	+	0.000427417i
$466$	−11.2157	+	12.7891i	−0.519559	+	0.592443i
$467$	−9.07143	+	11.8221i	−0.419776	+	0.547062i	−0.954596	−	0.297903i	$-0.903713\pi$
$467$	−9.07143	+	11.8221i	−0.419776	+	0.547062i	0.534820	+	0.844966i	$0.320379\pi$
$468$	4.10503	−	1.70036i	0.189755	−	0.0785991i
$469$	−12.1203	−	13.2610i	−0.559665	−	0.612337i
$470$	0.0836118	+	0.125134i	0.00385672	+	0.00577199i
$471$	−8.34922	+	7.32207i	−0.384712	+	0.337383i
$472$	−2.83184	+	0.758790i	−0.130346	+	0.0349261i
$473$	12.7567	+	25.8680i	0.586553	+	1.18941i
$474$	−3.82098	+	0.503042i	−0.175504	+	0.0231055i
$475$	−5.54687			−0.254508
$476$	−10.8996	+	0.446752i	−0.499581	+	0.0204768i
$477$	7.95452			0.364212
$478$	20.8807	−	2.74900i	0.955061	−	0.125736i
$479$	6.77670	+	13.7418i	0.309635	+	0.627878i	0.994950	−	0.100369i	$-0.0320022\pi$
$479$	6.77670	+	13.7418i	0.309635	+	0.627878i	−0.685315	+	0.728247i	$0.740336\pi$
$480$	−0.0296087	+	0.00793363i	−0.00135145	+	0.000362119i
$481$	24.3052	−	21.3151i	1.10822	−	0.971884i
$482$	12.7853	+	19.1345i	0.582354	+	0.871555i
$483$	−0.304780	+	0.962349i	−0.0138680	+	0.0437884i
$484$	17.1032	−	7.08438i	0.777419	−	0.322017i
$485$	0.0877844	−	0.114403i	0.00398609	−	0.00519477i
$486$	0.659346	−	0.751840i	0.0299085	−	0.0341041i
$487$	43.3447	−	2.84096i	1.96414	−	0.128736i	0.970480	−	0.241183i	$-0.0775354\pi$
$487$	43.3447	−	2.84096i	1.96414	−	0.128736i	0.993658	+	0.112447i	$0.0358687\pi$
$488$	−2.03857	−	2.32454i	−0.0922816	−	0.105227i
$489$	13.7519	+	13.7519i	0.621880	+	0.621880i
$490$	−0.208553	+	0.0504678i	−0.00942146	+	0.00227990i
$491$	33.9761	+	14.0734i	1.53332	+	0.635122i	0.980206	−	0.197982i	$-0.0634388\pi$
$491$	33.9761	+	14.0734i	1.53332	+	0.635122i	0.553115	+	0.833105i	$0.313439\pi$
$492$	5.71642	−	3.30038i	0.257716	−	0.148793i
$493$	−0.418981	−	1.44493i	−0.0188700	−	0.0650764i
$494$	2.46507	−	4.26963i	0.110909	−	0.192100i
$495$	−0.0217358	−	0.165100i	−0.000976951	−	0.00742068i
$496$	2.55413	−	3.82253i	0.114684	−	0.171637i
$497$	−18.9486	−	23.6713i	−0.849959	−	1.06180i
$498$	−12.0580	+	2.39848i	−0.540330	+	0.107478i
$499$	−20.9998	−	10.3560i	−0.940080	−	0.463596i	−0.0933586	−	0.995633i	$-0.529760\pi$
$499$	−20.9998	−	10.3560i	−0.940080	−	0.463596i	−0.846722	+	0.532036i	$0.821427\pi$
$500$	−0.230441	−	0.202092i	−0.0103056	−	0.00903781i
$501$	−1.65410	+	12.5641i	−0.0738996	+	0.561323i
$502$	16.5968	+	12.7351i	0.740750	+	0.568397i
$503$	34.8910	+	6.94025i	1.55571	+	0.309451i	0.896685	−	0.442668i	$-0.145968\pi$
$503$	34.8910	+	6.94025i	1.55571	+	0.309451i	0.659027	+	0.752119i	$0.270968\pi$
$504$	−1.42441	+	2.22958i	−0.0634484	+	0.0993136i
$505$	0.0866335	+	0.435536i	0.00385514	+	0.0193811i
$506$	2.00210	+	0.536461i	0.0890041	+	0.0238486i
$507$	−6.04713	+	2.98211i	−0.268562	+	0.132440i
$508$	−17.5147	+	13.4395i	−0.777091	+	0.596283i
$509$	17.6452	+	30.5623i	0.782109	+	1.35465i	0.930711	+	0.365755i	$0.119189\pi$
$509$	17.6452	+	30.5623i	0.782109	+	1.35465i	−0.148602	+	0.988897i	$0.547477\pi$
$510$	0.124436	+	0.0221197i	0.00551010	+	0.000979477i
$511$	−15.2091	−	11.1817i	−0.672810	−	0.494649i
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	0.0725701	−	1.10721i	0.00320405	−	0.0488844i
$514$	−2.27701	−	8.49791i	−0.100435	−	0.374827i
$515$	−0.0180190	+	0.0530823i	−0.000794013	+	0.00233909i
$516$	−2.34820	+	4.76168i	−0.103374	+	0.209621i
$517$	5.20344	−	26.1595i	0.228847	−	1.15049i
$518$	−4.59926	+	18.6921i	−0.202080	+	0.821284i
$519$	−1.35309	−	3.26665i	−0.0593941	−	0.143390i
$520$	0.128972	−	0.0437800i	0.00565578	−	0.00191988i
$521$	0.0533025	+	0.813238i	0.00233522	+	0.0356286i	0.998868	−	0.0475784i	$-0.0151504\pi$
$521$	0.0533025	+	0.813238i	0.00233522	+	0.0356286i	−0.996532	+	0.0832070i	$0.973484\pi$
$522$	−0.345518	−	0.117288i	−0.0151229	−	0.00513354i
$523$	−0.688014	+	2.56770i	−0.0300848	+	0.112278i	−0.979335	−	0.202243i	$-0.935177\pi$
$523$	−0.688014	+	2.56770i	−0.0300848	+	0.112278i	0.949251	+	0.314520i	$0.101844\pi$
$524$	−11.4888	−	7.67657i	−0.501891	−	0.335353i
$525$	−13.2235	+	0.271626i	−0.577120	+	0.0118547i
$526$		−	5.54504i		−	0.241775i
$527$	−16.2187	+	9.81093i	−0.706497	+	0.427371i
$528$	4.70471	+	2.71626i	0.204746	+	0.118210i
$529$	−13.9129	−	18.1316i	−0.604908	−	0.788332i
$530$	0.243309	+	0.0159473i	0.0105687	+	0.000692708i
$531$	2.07305	−	2.07305i	0.0899628	−	0.0899628i
$532$	0.252123	+	2.92483i	0.0109309	+	0.126808i
$533$	−24.3860	+	16.2942i	−1.05628	+	0.705781i
$534$	−3.34676	−	9.85924i	−0.144829	−	0.426651i
$535$	−0.00578264		0.000761300i	−0.000250006		3.29139e-5i
$536$	−6.73221	−	0.886312i	−0.290787	−	0.0382828i
$537$	1.09168	+	3.21598i	0.0471093	+	0.138780i
$538$	1.24604	−	0.832575i	0.0537204	−	0.0358949i
$539$	32.4598	+	19.8108i	1.39814	+	0.853312i
$540$	0.0216751	−	0.0216751i	0.000932747	−	0.000932747i
$541$	35.8311	+	2.34850i	1.54050	+	0.100970i	0.811829	−	0.583895i	$-0.198472\pi$
$541$	35.8311	+	2.34850i	1.54050	+	0.100970i	0.728670	+	0.684864i	$0.240139\pi$
$542$	13.1281	+	17.1089i	0.563902	+	0.734891i
$543$	−10.6004	−	6.12012i	−0.454905	−	0.262639i
$544$	−3.04374	+	2.78130i	−0.130499	+	0.119247i
$545$		−	0.00804820i		−	0.000344747i
$546$	5.66754	−	10.2993i	0.242549	−	0.440770i
$547$	−24.9602	−	16.6779i	−1.06722	−	0.713095i	−0.107545	−	0.994200i	$-0.534299\pi$
$547$	−24.9602	−	16.6779i	−1.06722	−	0.713095i	−0.959677	+	0.281105i	$0.909299\pi$
$548$	4.07315	−	15.2012i	0.173996	−	0.649363i
$549$	2.92772	+	0.993828i	0.124952	+	0.0424155i
$550$	1.77619	+	27.0994i	0.0757369	+	1.15552i
$551$	−0.383381	+	0.130140i	−0.0163326	+	0.00554417i
$552$	0.146009	+	0.352497i	0.00621455	+	0.0150032i
$553$	−7.06050	+	7.35664i	−0.300243	+	0.312836i
$554$	5.49069	−	27.6036i	0.233277	−	1.17276i
$555$	0.0986403	−	0.200023i	0.00418705	−	0.00849049i
$556$	−2.44164	+	7.19283i	−0.103549	+	0.305044i
$557$	−6.55683	−	24.4704i	−0.277822	−	1.03684i	−0.953927	−	0.300040i	$-0.903000\pi$
$557$	−6.55683	−	24.4704i	−0.277822	−	1.03684i	0.676105	−	0.736805i	$-0.263667\pi$
$558$	−0.300679	+	4.58747i	−0.0127288	+	0.194203i
$559$	9.02755	−	21.7944i	0.381825	−	0.921807i
$560$	−0.0480392	+	0.0653419i	−0.00203003	+	0.00276120i
$561$	−12.8220	−	18.3659i	−0.541344	−	0.775411i
$562$	9.10986	+	15.7787i	0.384276	+	0.665586i
$563$	−26.1005	+	20.0276i	−1.10000	+	0.844063i	−0.988728	−	0.149726i	$-0.952161\pi$
$563$	−26.1005	+	20.0276i	−1.10000	+	0.844063i	−0.111277	+	0.993789i	$0.535494\pi$
$564$	4.40335	−	2.17149i	0.185415	−	0.0914364i
$565$	0.0362132	+	0.00970328i	0.00152350	+	0.000408220i
$566$	−5.58323	−	28.0688i	−0.234680	−	1.17982i
$567$	0.118785	−	2.64308i	0.00498850	−	0.110999i
$568$	−11.2402	−	2.23581i	−0.471627	−	0.0938124i
$569$	27.9532	+	21.4492i	1.17186	+	0.899199i	0.996357	−	0.0852806i	$-0.0271787\pi$
$569$	27.9532	+	21.4492i	1.17186	+	0.899199i	0.175501	+	0.984479i	$0.443845\pi$
$570$	0.00443949	−	0.0337213i	0.000185950	−	0.00141243i
$571$	−11.0330	−	9.67572i	−0.461718	−	0.404916i	0.396634	−	0.917977i	$-0.370178\pi$
$571$	−11.0330	−	9.67572i	−0.461718	−	0.404916i	−0.858352	+	0.513061i	$0.828512\pi$
$572$	−21.6488	−	10.6760i	−0.905181	−	0.446386i
$573$	16.4082	−	3.26379i	0.685461	−	0.136347i
$574$	6.35041	−	16.2684i	0.265061	−	0.679032i
$575$	−1.05966	+	1.58589i	−0.0441909	+	0.0661364i
$576$	0.130526	+	0.991445i	0.00543859	+	0.0413102i
$577$	−8.63010	+	14.9478i	−0.359276	+	0.622284i	−0.987840	−	0.155474i	$-0.950310\pi$
$577$	−8.63010	+	14.9478i	−0.359276	+	0.622284i	0.628564	+	0.777758i	$0.283643\pi$
$578$	16.2273	−	5.06691i	0.674968	−	0.210756i
$579$	−13.1917	+	7.61624i	−0.548229	+	0.316520i
$580$	−0.0103334	−	0.00428025i	−0.000429072	−	0.000177728i
$581$	−20.9400	+	24.8906i	−0.868738	+	1.03264i
$582$	−3.32644	−	3.32644i	−0.137885	−	0.137885i
$583$	−28.4924	−	32.4894i	−1.18004	−	1.34557i
$584$	−7.11961	+	0.466644i	−0.294612	+	0.0193099i
$585$	−0.0898027	+	0.102400i	−0.00371289	+	0.00423373i
$586$	−8.32377	+	10.8478i	−0.343852	+	0.448117i
$587$	−43.4295	+	17.9891i	−1.79253	+	0.742490i	−0.803400	+	0.595440i	$0.796978\pi$
$587$	−43.4295	+	17.9891i	−1.79253	+	0.742490i	−0.989129	+	0.147050i	$0.953022\pi$
$588$	0.744275	+	6.96032i	0.0306934	+	0.287039i
$589$	2.83402	+	4.24141i	0.116774	+	0.174764i
$590$	0.0675657	−	0.0592535i	0.00278164	−	0.00243943i
$591$	8.69773	−	2.33055i	0.357777	−	0.0958660i
$592$	3.21795	+	6.52535i	0.132257	+	0.268190i
$593$	−44.0948	+	5.80519i	−1.81076	+	0.238391i	−0.958572	−	0.284851i	$-0.908056\pi$
$593$	−44.0948	+	5.80519i	−1.81076	+	0.238391i	−0.852185	+	0.523241i	$0.824723\pi$
$594$	−5.43253			−0.222899
$595$	0.293594	−	0.160054i	0.0120362	−	0.00656155i
$596$	1.19711			0.0490355
$597$	−6.24077	+	0.821613i	−0.255418	+	0.0336264i
$598$	−0.749801	−	1.52045i	−0.0306616	−	0.0621756i
$599$	8.98770	−	2.40825i	0.367227	−	0.0983983i	−0.0704862	−	0.997513i	$-0.522455\pi$
$599$	8.98770	−	2.40825i	0.367227	−	0.0983983i	0.437714	+	0.899114i	$0.355788\pi$
$600$	−3.75849	+	3.29611i	−0.153440	+	0.134563i
$601$	−18.9072	−	28.2966i	−0.771241	−	1.15424i	−0.984179	−	0.177178i	$-0.943303\pi$
$601$	−18.9072	−	28.2966i	−0.771241	−	1.15424i	0.212937	−	0.977066i	$-0.431697\pi$
$602$	3.02276	+	13.7178i	0.123199	+	0.559094i
$603$	6.27342	−	2.59854i	0.255473	−	0.105821i
$604$	11.2021	−	14.5989i	0.455809	−	0.594021i
$605$	−0.374155	+	0.426642i	−0.0152116	+	0.0173455i
$606$	14.4559	−	0.947486i	0.587229	−	0.0384890i
$607$	10.5307	+	12.0079i	0.427427	+	0.487387i	0.924963	−	0.380056i	$-0.124095\pi$
$607$	10.5307	+	12.0079i	0.427427	+	0.487387i	−0.497537	+	0.867443i	$0.665762\pi$
$608$	0.784593	+	0.784593i	0.0318195	+	0.0318195i
$609$	−0.907590	+	0.329023i	−0.0367774	+	0.0133327i
$610$	0.0875594	+	0.0362683i	0.00354518	+	0.00146846i
$611$	−18.8923	+	10.9075i	−0.764299	+	0.441268i
$612$	1.24531	−	3.93055i	0.0503385	−	0.158883i
$613$	−16.8471	+	29.1800i	−0.680446	+	1.17857i	0.294398	+	0.955683i	$0.404881\pi$
$613$	−16.8471	+	29.1800i	−0.680446	+	1.17857i	−0.974845	+	0.222885i	$0.928453\pi$
$614$	3.53854	+	26.8778i	0.142804	+	1.08470i
$615$	−0.112411	+	0.168235i	−0.00453284	+	0.00678388i
$616$	14.2086	−	2.16833i	0.572482	−	0.0873644i
$617$	−10.6900	+	2.12637i	−0.430363	+	0.0856046i	−0.405519	−	0.914087i	$-0.632909\pi$
$617$	−10.6900	+	2.12637i	−0.430363	+	0.0856046i	−0.0248446	+	0.999691i	$0.507909\pi$
$618$	1.64016	+	0.808839i	0.0659771	+	0.0325363i
$619$	−34.4801	−	30.2382i	−1.38587	−	1.21538i	−0.948771	−	0.315965i	$-0.897672\pi$
$619$	−34.4801	−	30.2382i	−1.38587	−	1.21538i	−0.437101	−	0.899412i	$-0.643995\pi$
$620$	−0.0183941	+	0.139717i	−0.000738723	+	0.00561116i
$621$	−0.302696	−	0.232267i	−0.0121468	−	0.00932053i
$622$	11.9471	+	2.37643i	0.479037	+	0.0952863i
$623$	−23.2140	−	14.8307i	−0.930049	−	0.594179i
$624$	−0.866835	−	4.35787i	−0.0347012	−	0.174455i
$625$	−24.1345	−	6.46683i	−0.965381	−	0.258673i
$626$	16.4950	−	8.13445i	0.659274	−	0.325118i
$627$	−4.78221	+	3.66952i	−0.190983	+	0.146546i
$628$	5.55252	+	9.61725i	0.221570	+	0.383770i
$629$	−0.612729	−	29.9921i	−0.0244311	−	1.19586i
$630$	0.00893223	−	0.0806073i	0.000355869	−	0.00321147i
$631$	17.8324	−	43.0511i	0.709895	−	1.71384i	0.00963123	−	0.999954i	$-0.496934\pi$
$631$	17.8324	−	43.0511i	0.709895	−	1.71384i	0.700264	−	0.713884i	$-0.253066\pi$
$632$	−0.252061	+	3.84570i	−0.0100264	+	0.152974i
$633$	−6.74011	−	25.1544i	−0.267895	−	0.999798i
$634$	−4.74037	+	13.9647i	−0.188264	+	0.554608i
$635$	0.299308	−	0.606937i	0.0118777	−	0.0240855i
$636$	1.55185	−	7.80167i	0.0615348	−	0.309357i
$637$	−5.32260	−	30.6439i	−0.210889	−	1.21416i
$638$	0.758569	+	1.83135i	0.0300320	+	0.0725037i
$639$	10.8522	−	3.68381i	0.429305	−	0.145729i
$640$	0.00200481	+	0.0305876i	7.92472e−5	+	0.00120908i
$641$	15.5253	+	5.27012i	0.613211	+	0.208157i	0.610729	−	0.791840i	$-0.290877\pi$
$641$	15.5253	+	5.27012i	0.613211	+	0.208157i	0.00248230	+	0.999997i	$0.499210\pi$
$642$	−0.0492469	+	0.183792i	−0.00194362	+	0.00725368i
$643$	26.0429	+	17.4013i	1.02703	+	0.686242i	0.950468	−	0.310823i	$-0.100605\pi$
$643$	26.0429	+	17.4013i	1.02703	+	0.686242i	0.0765654	+	0.997065i	$0.475605\pi$
$644$	0.884398	+	0.486669i	0.0348502	+	0.0191775i
$645$		−	0.162744i		−	0.00640805i
$646$	−1.55874	−	4.30119i	−0.0613278	−	0.169228i
$647$	8.60113	+	4.96586i	0.338145	+	0.195228i	0.659452	−	0.751747i	$-0.270789\pi$
$647$	8.60113	+	4.96586i	0.338145	+	0.195228i	−0.321306	+	0.946975i	$0.604122\pi$
$648$	−0.608761	−	0.793353i	−0.0239144	−	0.0311659i
$649$	−15.8927	−	1.04166i	−0.623842	−	0.0408887i
$650$	15.7063	−	15.7063i	0.616052	−	0.616052i
$651$	6.96387	+	9.97255i	0.272936	+	0.390855i
$652$	16.1705	−	10.8048i	0.633285	−	0.423147i
$653$	−8.20837	−	24.1811i	−0.321218	−	0.946278i	−0.980863	−	0.194701i	$-0.937627\pi$
$653$	−8.20837	−	24.1811i	−0.321218	−	0.946278i	0.659645	−	0.751578i	$-0.270707\pi$
$654$	−0.260311	−	0.0342705i	−0.0101789	−	0.00134008i
$655$	0.419926	+	0.0552843i	0.0164079	+	0.00216014i
$656$	−2.12174	−	6.25046i	−0.0828402	−	0.244039i
$657$	5.93244	−	3.96393i	0.231447	−	0.154648i
$658$	5.50476	−	11.7657i	0.214598	−	0.458675i
$659$	−3.23190	+	3.23190i	−0.125897	+	0.125897i	−0.767248	−	0.641351i	$-0.778374\pi$
$659$	−3.23190	+	3.23190i	−0.125897	+	0.125897i	0.641351	+	0.767248i	$0.278374\pi$
$660$	−0.166168	−	0.0108912i	−0.00646807	−	0.000423940i
$661$	4.00000	+	5.21290i	0.155582	+	0.202758i	0.864640	−	0.502391i	$-0.167546\pi$
$661$	4.00000	+	5.21290i	0.155582	+	0.202758i	−0.709058	+	0.705150i	$0.750880\pi$
$662$	−5.55833	−	3.20910i	−0.216031	−	0.124725i
$663$	−4.37913	+	17.7889i	−0.170071	+	0.690864i
$664$			12.2942i			0.477107i
$665$	−0.0465849	−	0.0769913i	−0.00180649	−	0.00298560i
$666$	−6.04950	−	4.04215i	−0.234413	−	0.156630i
$667$	−0.0360321	+	0.134473i	−0.00139517	+	0.00520683i
$668$	12.0000	+	4.07345i	0.464294	+	0.157606i
$669$	0.586629	+	8.95023i	0.0226804	+	0.346036i
$670$	0.197098	−	0.0669058i	0.00761457	−	0.00258480i
$671$	−6.42767	−	15.5178i	−0.248138	−	0.599057i
$672$	1.90886	+	1.83201i	0.0736357	+	0.0706714i
$673$	−5.62216	+	28.2645i	−0.216718	+	1.08952i	0.707225	+	0.706988i	$0.249947\pi$
$673$	−5.62216	+	28.2645i	−0.216718	+	1.08952i	−0.923944	+	0.382529i	$0.875053\pi$
$674$	−3.36317	+	6.81984i	−0.129545	+	0.262690i
$675$	1.60690	−	4.73376i	0.0618494	−	0.182203i
$676$	1.74508	+	6.51271i	0.0671183	+	0.250489i
$677$	0.483656	−	7.37916i	0.0185884	−	0.283604i	−0.978438	−	0.206541i	$-0.933779\pi$
$677$	0.483656	−	7.37916i	0.0185884	−	0.283604i	0.997026	−	0.0770627i	$-0.0245542\pi$
$678$	0.468044	−	1.12996i	0.0179751	−	0.0433958i
$679$	−12.3707	−	1.37082i	−0.474743	−	0.0526071i
$680$	0.0459709	−	0.117729i	0.00176290	−	0.00451471i
$681$	−12.6409	−	21.8948i	−0.484402	−	0.839009i
$682$	19.8140	−	15.2039i	0.758719	−	0.582186i
$683$	−17.0900	+	8.42787i	−0.653932	+	0.322484i	−0.738816	−	0.673907i	$-0.764615\pi$
$683$	−17.0900	+	8.42787i	−0.653932	+	0.322484i	0.0848839	+	0.996391i	$0.472948\pi$
$684$	−1.07177	−	0.287181i	−0.0409803	−	0.0109806i
$685$	0.0941120	+	0.473133i	0.00359584	+	0.0180775i
$686$	13.0455	+	13.1459i	0.498079	+	0.501914i
$687$	0.491625	+	0.0977904i	0.0187567	+	0.00373094i
$688$	4.21208	+	3.23204i	0.160584	+	0.123220i
$689$	−4.61330	+	35.0415i	−0.175753	+	1.33498i
$690$	−0.00879307	−	0.00771131i	−0.000334746	−	0.000293565i
$691$	−7.90214	−	3.89691i	−0.300612	−	0.148245i	0.285728	−	0.958311i	$-0.407765\pi$
$691$	−7.90214	−	3.89691i	−0.300612	−	0.148245i	−0.586339	+	0.810066i	$0.699431\pi$
$692$	−3.46786	+	0.689800i	−0.131828	+	0.0262223i
$693$	−11.2209	+	8.98214i	−0.426246	+	0.341203i
$694$	12.1547	−	18.1907i	0.461384	−	0.690510i
$695$	−0.0303917	−	0.230848i	−0.00115282	−	0.00875657i
$696$	−0.182441	+	0.315998i	−0.00691542	+	0.0119779i
$697$	−3.00048	+	27.0497i	−0.113651	+	1.02458i
$698$	−11.1206	+	6.42047i	−0.420920	+	0.243018i
$699$	−15.7156	−	6.50960i	−0.594417	−	0.246216i
$700$	−2.31337	+	13.0224i	−0.0874370	+	0.492200i
$701$	−9.93364	−	9.93364i	−0.375188	−	0.375188i	0.494174	−	0.869363i	$-0.335470\pi$
$701$	−9.93364	−	9.93364i	−0.375188	−	0.375188i	−0.869363	+	0.494174i	$0.835470\pi$
$702$	2.92964	+	3.34061i	0.110572	+	0.126083i
$703$	−8.05567	+	0.527996i	−0.303825	+	0.0199138i
$704$	3.58192	−	4.08439i	0.134999	−	0.153936i
$705$	−0.0916169	+	0.119397i	−0.00345049	+	0.00449677i
$706$	28.1128	−	11.6447i	1.05804	−	0.438255i
$707$	28.2919	−	25.8583i	1.06403	−	0.972502i
$708$	−1.62879	−	2.43765i	−0.0612136	−	0.0916126i
$709$	−23.8872	+	20.9485i	−0.897102	+	0.786738i	−0.977699	−	0.210009i	$-0.932651\pi$
$709$	−23.8872	+	20.9485i	−0.897102	+	0.786738i	0.0805970	+	0.996747i	$0.474317\pi$
$710$	0.339327	−	0.0909223i	0.0127347	−	0.00341225i
$711$	−1.70456	−	3.45651i	−0.0639260	−	0.129629i
$712$	−10.3227	+	1.35901i	−0.386860	+	0.0509311i
$713$	1.75406			0.0656900
$714$	−3.92659	−	10.1775i	−0.146949	−	0.380884i
$715$	0.739909			0.0276710
$716$	3.36716	−	0.443295i	0.125837	−	0.0165667i
$717$	9.31499	+	18.8889i	0.347875	+	0.705420i
$718$	−31.6522	+	8.48118i	−1.18125	+	0.316515i
$719$	10.5106	−	9.21759i	0.391981	−	0.343758i	−0.440558	−	0.897724i	$-0.645220\pi$
$719$	10.5106	−	9.21759i	0.391981	−	0.343758i	0.832539	+	0.553966i	$0.186886\pi$
$720$	−0.0170300	−	0.0254872i	−0.000634671	−	0.000949852i
$721$	4.72508	−	1.04119i	0.175971	−	0.0387760i
$722$	16.4163	−	6.79984i	0.610950	−	0.253064i
$723$	−14.0094	+	18.2574i	−0.521014	+	0.678999i
$724$	−8.07055	+	9.20270i	−0.299940	+	0.342015i
$725$	−1.82017	+	0.119300i	−0.0675992	+	0.00443069i
$726$	12.2061	+	13.9183i	0.453009	+	0.516558i
$727$	−18.7527	−	18.7527i	−0.695498	−	0.695498i	0.267938	−	0.963436i	$-0.413658\pi$
$727$	−18.7527	−	18.7527i	−0.695498	−	0.695498i	−0.963436	+	0.267938i	$0.913658\pi$
$728$	−8.99574	−	7.56794i	−0.333404	−	0.280487i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	0.189406	−	0.109354i	0.00701022	−	0.00404736i
$731$	−10.0809	−	19.4311i	−0.372855	−	0.718684i
$732$	1.54590	−	2.67758i	0.0571382	−	0.0989662i
$733$	−3.42201	−	25.9927i	−0.126395	−	0.960063i	−0.930684	−	0.365825i	$-0.880787\pi$
$733$	−3.42201	−	25.9927i	−0.126395	−	0.960063i	0.804289	−	0.594238i	$-0.202546\pi$
$734$	13.7886	−	20.6360i	0.508945	−	0.761690i
$735$	−0.114827	−	0.181263i	−0.00423544	−	0.00668597i
$736$	0.374208	−	0.0744347i	0.0137935	−	0.00274370i
$737$	−33.0843	−	16.3154i	−1.21868	−	0.600984i
$738$	4.96271	+	4.35218i	0.182680	+	0.160206i
$739$	1.54513	−	11.7364i	0.0568385	−	0.431731i	−0.939240	−	0.343260i	$-0.888469\pi$
$739$	1.54513	−	11.7364i	0.0568385	−	0.431731i	0.996079	−	0.0884708i	$-0.0281980\pi$
$740$	−0.176936	−	0.135767i	−0.00650428	−	0.00499091i
$741$	4.83542	+	0.961824i	0.177634	+	0.0353335i
$742$	−9.69394	−	18.6802i	−0.355876	−	0.685770i
$743$	5.12087	+	25.7443i	0.187866	+	0.944468i	0.953546	+	0.301247i	$0.0974027\pi$
$743$	5.12087	+	25.7443i	0.187866	+	0.944468i	−0.765680	+	0.643222i	$0.777597\pi$
$744$	4.44067	+	1.18987i	0.162803	+	0.0436229i
$745$	−0.0329110	+	0.0162299i	−0.00120576	+	0.000594617i
$746$	−1.32049	+	1.01325i	−0.0483466	+	0.0370977i
$747$	−6.14709	−	10.6471i	−0.224910	−	0.389556i
$748$	−20.5145	+	8.99258i	−0.750084	+	0.328801i
$749$	0.202162	+	0.461046i	0.00738684	+	0.0168462i
$750$	0.117294	−	0.283172i	0.00428296	−	0.0103400i
$751$	1.53450	−	23.4120i	0.0559948	−	0.854316i	−0.873811	−	0.486266i	$-0.838359\pi$
$751$	1.53450	−	23.4120i	0.0559948	−	0.854316i	0.929806	−	0.368050i	$-0.119975\pi$
$752$	−1.27072	−	4.74238i	−0.0463383	−	0.172937i
$753$	−6.72444	+	19.8096i	−0.245052	+	0.721900i
$754$	0.717067	−	1.45407i	0.0261140	−	0.0529540i
$755$	−0.110044	+	0.553227i	−0.00400490	+	0.0201340i
$756$	−2.56912	−	0.632142i	−0.0934381	−	0.0229908i
$757$	3.51245	+	8.47980i	0.127662	+	0.308204i	0.974768	−	0.223221i	$-0.0716570\pi$
$757$	3.51245	+	8.47980i	0.127662	+	0.308204i	−0.847106	+	0.531424i	$0.821657\pi$
$758$	−15.4999	+	5.26151i	−0.562982	+	0.191107i
$759$	0.135563	+	2.06829i	0.00492061	+	0.0750741i
$760$	−0.0322072	−	0.0109329i	−0.00116828	−	0.000396577i
$761$	8.38895	−	31.3080i	0.304099	−	1.13491i	−0.629619	−	0.776904i	$-0.716789\pi$
$761$	8.38895	−	31.3080i	0.304099	−	1.13491i	0.933718	−	0.358010i	$-0.116544\pi$
$762$	−18.3562	−	12.2652i	−0.664976	−	0.444322i
$763$	−0.594333	+	0.359612i	−0.0215163	+	0.0130188i
$764$		−	16.7296i		−	0.605256i
$765$	0.0190527	+	0.124942i	0.000688852	+	0.00451729i
$766$	−22.9642	−	13.2584i	−0.829730	−	0.479045i
$767$	7.93000	+	10.3346i	0.286336	+	0.373160i
$768$	0.997859	+	0.0654031i	0.0360071	+	0.00236003i
$769$	−2.40706	+	2.40706i	−0.0868008	+	0.0868008i	−0.749174	−	0.662373i	$-0.769549\pi$
$769$	−2.40706	+	2.40706i	−0.0868008	+	0.0868008i	0.662373	+	0.749174i	$0.269549\pi$
$770$	−0.361226	+	0.252246i	−0.0130177	+	0.00909031i
$771$	7.31501	−	4.88773i	0.263444	−	0.176027i
$772$	4.89632	+	14.4241i	0.176222	+	0.519134i
$773$	−14.6233	−	1.92520i	−0.525965	−	0.0692446i	−0.137132	−	0.990553i	$-0.543788\pi$
$773$	−14.6233	−	1.92520i	−0.525965	−	0.0692446i	−0.388833	+	0.921308i	$0.627122\pi$
$774$	−5.26379	−	0.692991i	−0.189203	−	0.0249090i
$775$	7.38741	+	21.7626i	0.265363	+	0.781735i
$776$	−3.91148	+	2.61357i	−0.140414	+	0.0938216i
$777$	−19.1785	+	1.65320i	−0.688025	+	0.0593082i
$778$	4.50821	−	4.50821i	0.161627	−	0.161627i
$779$	7.30840	+	0.479018i	0.261851	+	0.0171626i
$780$	0.0829131	+	0.108055i	0.00296877	+	0.00386897i
$781$	−53.9177	−	31.1294i	−1.92933	−	1.11390i
$782$	−1.52752	−	0.376033i	−0.0546241	−	0.0134469i
$783$		−	0.364883i		−	0.0130398i
$784$	6.97178	+	0.627917i	0.248992	+	0.0224256i
$785$	−0.283037	−	0.189119i	−0.0101020	−	0.00674995i
$786$	3.57622	−	13.3467i	0.127560	−	0.476059i
$787$	−3.40812	−	1.15690i	−0.121486	−	0.0412390i	0.260034	−	0.965599i	$-0.416266\pi$
$787$	−3.40812	−	1.15690i	−0.121486	−	0.0412390i	−0.381521	+	0.924360i	$0.624599\pi$
$788$	−0.588926	−	8.98527i	−0.0209796	−	0.320087i
$789$	5.25077	−	1.78240i	0.186932	−	0.0634550i
$790$	−0.0452087	−	0.109143i	−0.00160845	−	0.00388315i
$791$	−0.901528	−	3.10779i	−0.0320547	−	0.110500i
$792$	−1.05983	+	5.32815i	−0.0376596	+	0.189327i
$793$	−6.07601	+	12.3209i	−0.215765	+	0.437529i
$794$	−5.93455	+	17.4826i	−0.210609	+	0.620435i
$795$	0.0631082	+	0.235523i	0.00223822	+	0.00835314i
$796$	−0.411688	+	6.28114i	−0.0145919	+	0.222629i
$797$	15.8565	−	38.2809i	0.561664	−	1.35598i	−0.346770	−	0.937950i	$-0.612722\pi$
$797$	15.8565	−	38.2809i	0.561664	−	1.35598i	0.908434	−	0.418027i	$-0.137278\pi$
$798$	−2.68857	+	1.17890i	−0.0951743	+	0.0417326i
$799$	−3.54288	+	19.9307i	−0.125338	+	0.705096i
$800$	2.49953	+	4.32931i	0.0883717	+	0.153064i
$801$	8.26023	−	6.33830i	0.291861	−	0.223953i
$802$	−10.3206	+	5.08958i	−0.364435	+	0.179719i
$803$	−37.4398	−	10.0320i	−1.32122	−	0.354020i
$804$	−1.32472	−	6.65983i	−0.0467193	−	0.234874i
$805$	−0.0309119	−	0.00138924i	−0.00108950	−	4.89642e-5i
$806$	−20.0345	−	3.98511i	−0.705686	−	0.140370i
$807$	1.18892	+	0.912287i	0.0418518	+	0.0321140i
$808$	1.89092	−	14.3629i	0.0665222	−	0.505286i
$809$	11.3374	+	9.94263i	0.398602	+	0.349564i	0.835059	−	0.550161i	$-0.185434\pi$
$809$	11.3374	+	9.94263i	0.398602	+	0.349564i	−0.436457	+	0.899725i	$0.643767\pi$
$810$	0.0274920	+	0.0135576i	0.000965971	+	0.000476364i
$811$	−8.30736	+	1.65244i	−0.291711	+	0.0580249i	−0.338776	−	0.940867i	$-0.610013\pi$
$811$	−8.30736	+	1.65244i	−0.291711	+	0.0580249i	0.0470655	+	0.998892i	$0.485013\pi$
$812$	0.145638	+	0.954340i	0.00511091	+	0.0334908i
$813$	−11.9811	+	17.9309i	−0.420194	+	0.628865i
$814$	5.15909	+	39.1872i	0.180826	+	1.37351i
$815$	−0.298073	+	0.516277i	−0.0104410	+	0.0180844i
$816$	−3.61208	−	1.98819i	−0.126448	−	0.0696005i
$817$	−5.10176	+	2.94550i	−0.178488	+	0.103050i
$818$	27.8098	+	11.5192i	0.972347	+	0.402759i
$819$	11.5745	+	2.05616i	0.404446	+	0.0718480i
$820$	0.143072	+	0.143072i	0.00499629	+	0.00499629i
$821$	−26.8179	−	30.5799i	−0.935949	−	1.06725i	−0.997606	−	0.0691484i	$-0.977972\pi$
$821$	−26.8179	−	30.5799i	−0.935949	−	1.06725i	0.0616569	−	0.998097i	$-0.480362\pi$
$822$	15.7037	−	1.02928i	0.547731	−	0.0359002i
$823$	−16.7428	+	19.0915i	−0.583617	+	0.665487i	−0.966008	−	0.258513i	$-0.916767\pi$
$823$	−16.7428	+	19.0915i	−0.583617	+	0.665487i	0.382391	+	0.924001i	$0.375101\pi$
$824$	1.11328	−	1.45085i	0.0387829	−	0.0505428i
$825$	−25.0903	+	10.3927i	−0.873532	+	0.361829i
$826$	−7.39466	−	2.34193i	−0.257293	−	0.0814860i
$827$	−20.7707	−	31.0856i	−0.722269	−	1.08095i	−0.992979	−	0.118291i	$-0.962258\pi$
$827$	−20.7707	−	31.0856i	−0.722269	−	1.08095i	0.270710	−	0.962661i	$-0.412742\pi$
$828$	−0.286857	+	0.251566i	−0.00996895	+	0.00874254i
$829$	44.3305	−	11.8783i	1.53966	−	0.412551i	0.613505	−	0.789691i	$-0.289759\pi$
$829$	44.3305	−	11.8783i	1.53966	−	0.412551i	0.926156	+	0.377140i	$0.123093\pi$
$830$	−0.166679	−	0.337992i	−0.00578552	−	0.0117319i
$831$	27.9036	−	3.67357i	0.967964	−	0.127435i
$832$	−4.44325			−0.154042
$833$	−24.9379	−	14.5294i	−0.864045	−	0.503414i
$834$	−7.59595			−0.263026
$835$	−0.385130	+	0.0507033i	−0.0133280	+	0.00175466i
$836$	2.66604	+	5.40620i	0.0922071	+	0.186977i
$837$	−4.44067	+	1.18987i	−0.153492	+	0.0411280i
$838$	−0.403118	+	0.353525i	−0.0139255	+	0.0122123i
$839$	−2.80107	−	4.19209i	−0.0967035	−	0.144727i	0.779963	−	0.625826i	$-0.215238\pi$
$839$	−2.80107	−	4.19209i	−0.0967035	−	0.144727i	−0.876666	+	0.481099i	$0.840238\pi$
$840$	−0.0773159	−	0.0244863i	−0.00266765	−	0.000844858i
$841$	26.6695	−	11.0469i	0.919638	−	0.380927i
$842$	0.0765550	−	0.0997684i	0.00263826	−	0.00343825i
$843$	−12.0131	+	13.6983i	−0.413753	+	0.471795i
$844$	−25.9860	+	1.70321i	−0.894475	+	0.0586270i
$845$	−0.136272	−	0.155389i	−0.00468790	−	0.00534553i
$846$	3.47166	+	3.47166i	0.119358	+	0.119358i
$847$	48.2241	+	8.56680i	1.65700	+	0.294359i
$848$	−7.34902	−	3.04406i	−0.252366	−	0.104534i
$849$	24.7845	−	14.3093i	0.850602	−	0.491095i
$850$	−1.76789	−	20.5357i	−0.0606380	−	0.704369i
$851$	−1.38798	+	2.40405i	−0.0475793	+	0.0824097i
$852$	−1.49588	−	11.3623i	−0.0512479	−	0.389267i
$853$	20.9995	−	31.4280i	0.719010	−	1.07607i	−0.274418	−	0.961611i	$-0.588485\pi$
$853$	20.9995	−	31.4280i	0.719010	−	1.07607i	0.993427	−	0.114464i	$-0.0365150\pi$
$854$	−1.23405	−	8.08652i	−0.0422285	−	0.276715i
$855$	0.0333587	−	0.00663546i	0.00114084	−	0.000226928i
$856$	0.170653	+	0.0841566i	0.00583279	+	0.00287641i
$857$	28.2375	+	24.7636i	0.964574	+	0.845909i	0.988100	−	0.153814i	$-0.0491557\pi$
$857$	28.2375	+	24.7636i	0.964574	+	0.845909i	−0.0235254	+	0.999723i	$0.507489\pi$
$858$	3.15065	−	23.9316i	0.107561	−	0.817011i
$859$	17.9340	+	13.7612i	0.611899	+	0.469526i	0.867623	−	0.497223i	$-0.165647\pi$
$859$	17.9340	+	13.7612i	0.611899	+	0.469526i	−0.255724	+	0.966750i	$0.582314\pi$
$860$	−0.159617	−	0.0317498i	−0.00544290	−	0.00108266i
$861$	17.4464	+	0.784070i	0.594570	+	0.0267210i
$862$	4.37319	+	21.9855i	0.148951	+	0.748829i
$863$	53.5379	+	14.3454i	1.82245	+	0.488324i	0.997087	−	0.0762782i	$-0.0243037\pi$
$863$	53.5379	+	14.3454i	1.82245	+	0.488324i	0.825363	+	0.564602i	$0.190970\pi$
$864$	−0.896873	+	0.442289i	−0.0305122	+	0.0150470i
$865$	0.0859864	−	0.0659797i	0.00292363	−	0.00224338i
$866$	14.3809	+	24.9085i	0.488683	+	0.846425i
$867$	10.0141	+	13.7374i	0.340097	+	0.466548i
$868$	11.1395	−	4.88451i	0.378100	−	0.165791i
$869$	−8.01214	+	19.3430i	−0.271793	+	0.656167i
$870$	0.000731522	−	0.0111609i	2.48009e−5	−	0.000378389i
$871$	7.80883	+	29.1429i	0.264592	+	0.987471i
$872$	−0.0843961	+	0.248623i	−0.00285801	+	0.00841944i
$873$	2.08066	−	4.21916i	0.0704196	−	0.142797i
$874$	−0.0825914	+	0.415215i	−0.00279369	+	0.0140449i
$875$	−0.225927	−	0.778824i	−0.00763771	−	0.0263290i
$876$	−2.73040	−	6.59178i	−0.0922518	−	0.222715i
$877$	39.7734	−	13.5013i	1.34305	−	0.455905i	0.444897	−	0.895582i	$-0.353240\pi$
$877$	39.7734	−	13.5013i	1.34305	−	0.455905i	0.898156	+	0.439677i	$0.144907\pi$
$878$	−0.266585	−	4.06731i	−0.00899682	−	0.137265i
$879$	−12.9477	−	4.39514i	−0.436714	−	0.148244i
$880$	−0.0430997	+	0.160850i	−0.00145289	+	0.00542226i
$881$	−10.4555	−	6.98617i	−0.352256	−	0.235370i	0.366835	−	0.930286i	$-0.380442\pi$
$881$	−10.4555	−	6.98617i	−0.352256	−	0.235370i	−0.719091	+	0.694916i	$0.755442\pi$
$882$	−6.35170	+	2.94210i	−0.213873	+	0.0990656i
$883$			29.8551i			1.00470i	0.864663	+	0.502352i	$0.167532\pi$
$883$			29.8551i			1.00470i	−0.864663	+	0.502352i	$0.832468\pi$
$884$	16.5928	+	7.76543i	0.558075	+	0.261180i
$885$	0.0778272	+	0.0449336i	0.00261613	+	0.00151043i
$886$	23.2876	+	30.3490i	0.782363	+	1.01960i
$887$	29.8926	+	1.95926i	1.00369	+	0.0657856i	0.558377	−	0.829587i	$-0.311424\pi$
$887$	29.8926	+	1.95926i	1.00369	+	0.0657856i	0.445317	+	0.895373i	$0.353091\pi$
$888$	−5.14468	+	5.14468i	−0.172644	+	0.172644i
$889$	−58.1940	+	5.01636i	−1.95176	+	0.168243i
$890$	0.265368	−	0.177313i	0.00889514	−	0.00594354i
$891$	−1.74623	−	5.14423i	−0.0585009	−	0.172338i
$892$	8.89270	+	1.17075i	0.297750	+	0.0391995i
$893$	5.40108	+	0.711066i	0.180740	+	0.0237949i
$894$	0.384798	+	1.13358i	0.0128696	+	0.0379126i
$895$	−0.0865599	+	0.0578375i	−0.00289338	+	0.00193329i
$896$	2.16921	−	1.51477i	0.0724682	−	0.0506049i
$897$	1.19874	−	1.19874i	0.0400248	−	0.0400248i
$898$	−0.0237018	−	0.00155350i	−0.000790938	−	5.18408e-5i
$899$	1.02119	+	1.33084i	0.0340585	+	0.0443858i
$900$	−4.32931	−	2.49953i	−0.144310	−	0.0833177i
$901$	22.1239	+	24.2115i	0.737055	+	0.806602i
$902$		−	35.8588i		−	1.19397i
$903$	−12.0181	+	7.27177i	−0.399938	+	0.241989i
$904$	−1.01694	−	0.679494i	−0.0338228	−	0.0225996i
$905$	0.0971095	−	0.362418i	0.00322803	−	0.0120472i
$906$	17.4250	+	5.91498i	0.578906	+	0.196512i
$907$	−3.28713	−	50.1519i	−0.109147	−	1.66527i	−0.604522	−	0.796589i	$-0.706636\pi$
$907$	−3.28713	−	50.1519i	−0.109147	−	1.66527i	0.495374	−	0.868680i	$-0.335031\pi$
$908$	−23.9402	+	8.12660i	−0.794483	+	0.269691i
$909$	5.54388	+	13.3841i	0.183879	+	0.443923i
$910$	0.349914	+	0.0860976i	0.0115995	+	0.00285411i
$911$	3.90001	−	19.6067i	0.129213	−	0.649598i	−0.860837	−	0.508881i	$-0.830059\pi$
$911$	3.90001	−	19.6067i	0.129213	−	0.649598i	0.990050	−	0.140717i	$-0.0449408\pi$
$912$	−0.490756	+	0.995154i	−0.0162505	+	0.0329528i
$913$	−21.4685	+	63.2440i	−0.710502	+	2.09307i
$914$	3.85582	+	14.3901i	0.127539	+	0.475983i
$915$	−0.00619849	+	0.0945707i	−0.000204916	+	0.00312641i
$916$	0.191823	−	0.463101i	0.00633800	−	0.0153013i
$917$	−14.6807	−	33.4804i	−0.484798	−	1.10562i
$918$	4.12225	−	0.0842162i	0.136054	−	0.00277955i
$919$	−18.0761	−	31.3087i	−0.596275	−	1.03278i	−0.993366	−	0.115000i	$-0.963313\pi$
$919$	−18.0761	−	31.3087i	−0.596275	−	1.03278i	0.397090	−	0.917780i	$-0.370020\pi$
$920$	−0.00927859	+	0.00711971i	−0.000305906	+	0.000234730i
$921$	−24.3140	+	11.9903i	−0.801174	+	0.395095i
$922$	20.7807	+	5.56818i	0.684377	+	0.183378i
$923$	9.93425	+	49.9428i	0.326990	+	1.64389i
$924$	6.62047	+	12.7576i	0.217797	+	0.419694i
$925$	−35.6726	−	7.09573i	−1.17291	−	0.233306i
$926$	−15.8563	−	12.1670i	−0.521071	−	0.399832i
$927$	−0.238701	+	1.81311i	−0.00783997	+	0.0595504i
$928$	0.274333	+	0.240584i	0.00900543	+	0.00789755i
$929$	−52.7748	−	26.0256i	−1.73148	−	0.853874i	−0.981259	−	0.192691i	$-0.938278\pi$
$929$	−52.7748	−	26.0256i	−1.73148	−	0.853874i	−0.750225	−	0.661182i	$-0.770055\pi$
$930$	−0.138215	+	0.0274926i	−0.00453224	+	0.000901518i
$931$	−3.60404	+	6.88029i	−0.118118	+	0.225492i
$932$	−9.45047	+	14.1436i	−0.309560	+	0.463290i
$933$	1.58997	+	12.0770i	0.0520531	+	0.395383i
$934$	−7.45073	+	12.9050i	−0.243795	+	0.422266i
$935$	0.442067	−	0.525350i	0.0144571	−	0.0171808i
$936$	3.84797	−	2.22162i	0.125775	−	0.0726161i
$937$	42.5327	+	17.6176i	1.38948	+	0.575542i	0.946999	−	0.321235i	$-0.104098\pi$
$937$	42.5327	+	17.6176i	1.38948	+	0.575542i	0.442482	+	0.896777i	$0.354098\pi$
$938$	−13.7476	−	11.5655i	−0.448874	−	0.377629i
$939$	13.0049	+	13.0049i	0.424399	+	0.424399i
$940$	0.0992297	+	0.113150i	0.00323652	+	0.00369054i
$941$	44.8167	−	2.93744i	1.46098	−	0.0957578i	0.685936	−	0.727662i	$-0.259393\pi$
$941$	44.8167	−	2.93744i	1.46098	−	0.0957578i	0.775046	+	0.631904i	$0.217726\pi$
$942$	−7.32207	+	8.34922i	−0.238566	+	0.272032i
$943$	1.53313	−	1.99802i	0.0499257	−	0.0650645i
$944$	−2.70857	+	1.12193i	−0.0881566	+	0.0365156i
$945$	0.0792007	−	0.0174522i	0.00257640	−	0.000567719i
$946$	16.0240	+	23.9816i	0.520985	+	0.779709i
$947$	−7.63135	+	6.69251i	−0.247985	+	0.217477i	−0.774310	−	0.632806i	$-0.781903\pi$
$947$	−7.63135	+	6.69251i	−0.247985	+	0.217477i	0.526325	+	0.850284i	$0.323570\pi$
$948$	−3.72264	+	0.997477i	−0.120906	+	0.0323966i
$949$	14.0215	+	28.4327i	0.455156	+	0.922965i
$950$	−5.49941	+	0.724012i	−0.178425	+	0.0234900i
$951$	−14.7473			−0.478214
$952$	−10.7480	+	1.86561i	−0.348345	+	0.0604647i
$953$	−46.3548			−1.50158			−0.750789	−	0.660542i	$-0.770327\pi$
$953$	−46.3548			−1.50158			−0.750789	+	0.660542i	$0.770327\pi$
$954$	7.88647	−	1.03827i	0.255334	−	0.0336153i
$955$	0.226813	+	0.459931i	0.00733949	+	0.0148830i
$956$	20.3432	−	5.45096i	0.657947	−	0.176296i
$957$	−1.49032	+	1.30698i	−0.0481753	+	0.0422486i
$958$	8.51238	+	12.7397i	0.275023	+	0.411600i
$959$	30.7342	−	28.0905i	0.992459	−	0.907090i
$960$	−0.0283199	+	0.0117305i	−0.000914019	+	0.000378599i
$961$	−6.00524	+	7.82618i	−0.193717	+	0.252457i
$962$	21.3151	−	24.3052i	0.687226	−	0.783631i
$963$	−0.189868	+	0.0124446i	−0.00611841	+	0.000401022i
$964$	15.1735	+	17.3020i	0.488705	+	0.557261i
$965$	−0.330165	−	0.330165i	−0.0106284	−	0.0106284i
$966$	−0.176561	+	0.993898i	−0.00568077	+	0.0319781i
$967$	18.5798	+	7.69600i	0.597486	+	0.247487i	0.660867	−	0.750503i	$-0.270189\pi$
$967$	18.5798	+	7.69600i	0.597486	+	0.247487i	−0.0633818	+	0.997989i	$0.520189\pi$
$968$	16.0322	−	9.25619i	0.515294	−	0.297505i
$969$	3.57189	−	2.85859i	0.114746	−	0.0918312i
$970$	0.0721009	−	0.124882i	0.00231502	−	0.00400973i
$971$	−6.15534	−	46.7544i	−0.197534	−	1.50042i	−0.746955	−	0.664875i	$-0.768485\pi$
$971$	−6.15534	−	46.7544i	−0.197534	−	1.50042i	0.549421	−	0.835546i	$-0.314848\pi$
$972$	0.555570	−	0.831470i	0.0178199	−	0.0266694i
$973$	−15.6894	+	12.5591i	−0.502979	+	0.402627i
$974$	42.6031	−	8.47428i	1.36509	−	0.271534i
$975$	19.9214	+	9.82415i	0.637995	+	0.314624i
$976$	−2.32454	−	2.03857i	−0.0744068	−	0.0652530i
$977$	−1.22150	+	9.27820i	−0.0390792	+	0.296836i	0.960733	+	0.277473i	$0.0894970\pi$
$977$	−1.22150	+	9.27820i	−0.0390792	+	0.296836i	−0.999813	+	0.0193626i	$0.993836\pi$
$978$	15.4292	+	11.8392i	0.493371	+	0.378577i
$979$	−55.4756	−	11.0348i	−1.77301	−	0.352673i
$980$	−0.200181	+	0.0772576i	−0.00639456	+	0.00246790i
$981$	−0.0512223	−	0.257512i	−0.00163540	−	0.00822172i
$982$	35.5224	+	9.51820i	1.13357	+	0.303738i
$983$	14.7690	−	7.28325i	0.471057	−	0.232300i	−0.191237	−	0.981544i	$-0.561250\pi$
$983$	14.7690	−	7.28325i	0.471057	−	0.232300i	0.662294	+	0.749244i	$0.269583\pi$
$984$	5.23673	−	4.01829i	0.166941	−	0.128098i
$985$	0.138009	+	0.239039i	0.00439734	+	0.00761641i
$986$	−0.603998	−	1.37788i	−0.0192352	−	0.0438807i
$987$	12.9108	+	1.43066i	0.410954	+	0.0455385i
$988$	1.88669	−	4.55486i	0.0600235	−	0.144910i
$989$	−0.132485	+	2.02134i	−0.00421279	+	0.0642747i
$990$	−0.0430997	−	0.160850i	−0.00136980	−	0.00511215i
$991$	6.30398	−	18.5709i	0.200253	−	0.589925i	−0.799692	−	0.600410i	$-0.795004\pi$
$991$	6.30398	−	18.5709i	0.200253	−	0.589925i	0.999945	+	0.0104847i	$0.00333746\pi$
$992$	2.03334	−	4.12321i	0.0645586	−	0.130912i
$993$	1.25213	−	6.29488i	0.0397352	−	0.199762i
$994$	−21.8762	−	20.9955i	−0.693870	−	0.665938i
$995$	−0.0738388	−	0.178263i	−0.00234085	−	0.00565131i
$996$	−11.6417	+	3.95183i	−0.368882	+	0.125219i
$997$	2.70284	+	41.2374i	0.0855999	+	1.30600i	0.797327	+	0.603547i	$0.206246\pi$
$997$	2.70284	+	41.2374i	0.0855999	+	1.30600i	−0.711728	+	0.702456i	$0.752087\pi$
$998$	−22.1719	−	7.52633i	−0.701838	−	0.238242i
$999$	1.88308	−	7.02776i	0.0595781	−	0.222348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bl.a.367.10	yes	192
7.5	odd	6	inner	714.2.bl.a.61.10	✓	192
17.12	odd	16	inner	714.2.bl.a.199.10	yes	192
119.12	even	48	inner	714.2.bl.a.607.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bl.a.61.10	✓	192	7.5	odd	6	inner
714.2.bl.a.199.10	yes	192	17.12	odd	16	inner
714.2.bl.a.367.10	yes	192	1.1	even	1	trivial
714.2.bl.a.607.10	yes	192	119.12	even	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.991445 - 0.130526i) q^{2} +(0.442289 + 0.896873i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-0.0230463 + 0.0202111i) q^{5} +(0.555570 + 0.831470i) q^{6} +(2.52228 + 0.798818i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-0.0202111 + 0.0230463i) q^{10} +(5.42090 - 0.355304i) q^{11} +(0.659346 + 0.751840i) q^{12} +(-3.14185 - 3.14185i) q^{13} +(2.60497 + 0.462760i) q^{14} +(-0.0283199 - 0.0117305i) q^{15} +(0.866025 - 0.500000i) q^{16} +(-4.10791 + 0.353644i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.144830 + 1.10009i) q^{19} +(-0.0170300 + 0.0254872i) q^{20} +(0.399138 + 2.61547i) q^{21} +(5.32815 - 1.05983i) q^{22} +(0.342192 + 0.168751i) q^{23} +(0.751840 + 0.659346i) q^{24} +(-0.652508 + 4.95629i) q^{25} +(-3.52507 - 2.70488i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(2.64308 + 0.118785i) q^{28} +(0.0711851 + 0.357872i) q^{29} +(-0.0296087 - 0.00793363i) q^{30} +(4.12321 - 2.03334i) q^{31} +(0.793353 - 0.608761i) q^{32} +(2.71626 + 4.70471i) q^{33} +(-4.02661 + 0.886808i) q^{34} +(-0.0742741 + 0.0325681i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(-0.475852 + 7.26009i) q^{37} +(0.287181 + 1.07177i) q^{38} +(1.42824 - 4.20745i) q^{39} +(-0.0135576 + 0.0274920i) q^{40} +(1.28774 - 6.47393i) q^{41} +(0.737110 + 2.54100i) q^{42} +(2.03175 + 4.90507i) q^{43} +(5.14423 - 1.74623i) q^{44} +(-0.00200481 - 0.0305876i) q^{45} +(0.361291 + 0.122642i) q^{46} +(1.27072 - 4.74238i) q^{47} +(0.831470 + 0.555570i) q^{48} +(5.72378 + 4.02968i) q^{49} +4.99906i q^{50} +(-2.13406 - 3.52786i) q^{51} +(-3.84797 - 2.22162i) q^{52} +(-4.84240 - 6.31074i) q^{53} +(-0.997859 - 0.0654031i) q^{54} +(-0.117751 + 0.117751i) q^{55} +(2.63598 - 0.227223i) q^{56} +(-0.922584 + 0.616451i) q^{57} +(0.117288 + 0.345518i) q^{58} +(-2.90666 - 0.382669i) q^{59} +(-0.0303909 - 0.00400104i) q^{60} +(-0.993828 - 2.92772i) q^{61} +(3.82253 - 2.55413i) q^{62} +(-2.16921 + 1.51477i) q^{63} +(0.707107 - 0.707107i) q^{64} +(0.135908 + 0.00890789i) q^{65} +(3.30711 + 4.30992i) q^{66} +(-5.88057 - 3.39515i) q^{67} +(-3.87641 + 1.40480i) q^{68} +0.381539i q^{69} +(-0.0693877 + 0.0419842i) q^{70} +(-9.52895 - 6.36704i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-6.75624 - 2.29343i) q^{73} +(0.475852 + 7.26009i) q^{74} +(-4.73376 + 1.60690i) q^{75} +(0.424619 + 1.02512i) q^{76} +(13.9568 + 3.43413i) q^{77} +(0.866835 - 4.35787i) q^{78} +(-1.70456 + 3.45651i) q^{79} +(-0.00985314 + 0.0290264i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.431710 - 6.58662i) q^{82} +(-4.70478 + 11.3583i) q^{83} +(1.06247 + 2.42305i) q^{84} +(0.0875246 - 0.0911754i) q^{85} +(2.65460 + 4.59791i) q^{86} +(-0.289481 + 0.222127i) q^{87} +(4.87229 - 2.40275i) q^{88} +(-10.0570 - 2.69477i) q^{89} +(-0.00598014 - 0.0300642i) q^{90} +(-5.41486 - 10.4344i) q^{91} +(0.374208 + 0.0744347i) q^{92} +(3.64730 + 2.79867i) q^{93} +(0.640841 - 4.86767i) q^{94} +(-0.0255717 - 0.0224258i) q^{95} +(0.896873 + 0.442289i) q^{96} +(-4.61391 + 0.917763i) q^{97} +(6.20079 + 3.24810i) q^{98} +(-3.01815 + 4.51698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) \) 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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