LMFDB - Embedded newform 87.2.k.a.8.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] 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("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			8.6
Character	$\chi$	$=$	87.8
Dual form			87.2.k.a.11.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.454505 - 1.29890i) q^{2} +(0.337040 + 1.69894i) q^{3} +(0.0830922 + 0.0662638i) q^{4} +(-0.181368 + 0.0873422i) q^{5} +(2.35995 + 0.334396i) q^{6} +(-0.770934 - 0.966720i) q^{7} +(2.45423 - 1.54210i) q^{8} +(-2.77281 + 1.14522i) q^{9} +(0.0310162 + 0.275277i) q^{10} +(-4.24536 - 2.66753i) q^{11} +(-0.0845730 + 0.163502i) q^{12} +(0.0513081 - 0.0117107i) q^{13} +(-1.60607 + 0.561988i) q^{14} +(-0.209518 - 0.278696i) q^{15} +(-0.840272 - 3.68147i) q^{16} +(-3.02679 + 3.02679i) q^{17} +(0.227277 + 4.12212i) q^{18} +(5.19364 - 0.585183i) q^{19} +(-0.0208579 - 0.00476068i) q^{20} +(1.38257 - 1.63560i) q^{21} +(-5.39440 + 4.30189i) q^{22} +(0.708287 - 1.47077i) q^{23} +(3.44711 + 3.64985i) q^{24} +(-3.09218 + 3.87748i) q^{25} +(0.00810871 - 0.0719668i) q^{26} +(-2.88022 - 4.32485i) q^{27} -0.131412i q^{28} +(0.690188 + 5.34075i) q^{29} +(-0.457225 + 0.145474i) q^{30} +(1.57922 + 0.552592i) q^{31} +(0.596780 + 0.0672409i) q^{32} +(3.10113 - 8.11168i) q^{33} +(2.55581 + 5.30719i) q^{34} +(0.224258 + 0.107997i) q^{35} +(-0.306286 - 0.0885777i) q^{36} +(-2.96911 - 4.72531i) q^{37} +(1.60044 - 7.01200i) q^{38} +(0.0371888 + 0.0832225i) q^{39} +(-0.310429 + 0.494045i) q^{40} +(2.80557 + 2.80557i) q^{41} +(-1.49609 - 2.53920i) q^{42} +(-0.771632 - 2.20520i) q^{43} +(-0.175995 - 0.502965i) q^{44} +(0.402872 - 0.449890i) q^{45} +(-1.58847 - 1.58847i) q^{46} +(6.13509 - 9.76394i) q^{47} +(5.97140 - 2.66838i) q^{48} +(1.21744 - 5.33394i) q^{49} +(3.63105 + 5.77878i) q^{50} +(-6.16248 - 4.12219i) q^{51} +(0.00503930 + 0.00242680i) q^{52} +(3.63041 + 7.53862i) q^{53} +(-6.92663 + 1.77545i) q^{54} +(1.00296 + 0.113006i) q^{55} +(-3.38283 - 1.18370i) q^{56} +(2.74466 + 8.62646i) q^{57} +(7.25081 + 1.53091i) q^{58} +10.1765i q^{59} +(0.00105817 - 0.0370409i) q^{60} +(-1.51909 + 13.4823i) q^{61} +(1.43552 - 1.80009i) q^{62} +(3.24476 + 1.79764i) q^{63} +(3.63540 - 7.54898i) q^{64} +(-0.00828281 + 0.00660532i) q^{65} +(-9.12680 - 7.71487i) q^{66} +(-5.24543 - 1.19723i) q^{67} +(-0.452069 + 0.0509359i) q^{68} +(2.73748 + 0.707629i) q^{69} +(0.242204 - 0.242204i) q^{70} +(1.05188 + 4.60860i) q^{71} +(-5.03907 + 7.08658i) q^{72} +(11.0856 - 3.87901i) q^{73} +(-7.48719 + 1.70890i) q^{74} +(-7.62980 - 3.94657i) q^{75} +(0.470327 + 0.295526i) q^{76} +(0.694129 + 6.16056i) q^{77} +(0.125000 - 0.0104795i) q^{78} +(-2.54600 + 1.59976i) q^{79} +(0.473946 + 0.594310i) q^{80} +(6.37693 - 6.35097i) q^{81} +(4.91931 - 2.36901i) q^{82} +(-9.70654 - 7.74070i) q^{83} +(0.223261 - 0.0442911i) q^{84} +(0.284596 - 0.813329i) q^{85} -3.21505 q^{86} +(-8.84101 + 2.97264i) q^{87} -14.5327 q^{88} +(-0.741261 + 2.11840i) q^{89} +(-0.401255 - 0.727769i) q^{90} +(-0.0508762 - 0.0405724i) q^{91} +(0.156312 - 0.0752760i) q^{92} +(-0.406562 + 2.86924i) q^{93} +(-9.89397 - 12.4066i) q^{94} +(-0.890849 + 0.559758i) q^{95} +(0.0869004 + 1.03656i) q^{96} +(-1.07237 - 9.51752i) q^{97} +(-6.37493 - 4.00564i) q^{98} +(14.8265 + 2.53468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$-1$

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 $

$2$	0.454505	−	1.29890i	0.321384	−	0.918462i	−0.663943	−	0.747783i	$-0.731118\pi$
$2$	0.454505	−	1.29890i	0.321384	−	0.918462i	0.985327	−	0.170679i	$-0.0545961\pi$
$3$	0.337040	+	1.69894i	0.194590	+	0.980885i
$3$	0.337040	+	1.69894i	0.194590	+	0.980885i
$4$	0.0830922	+	0.0662638i	0.0415461	+	0.0331319i
$5$	−0.181368	+	0.0873422i	−0.0811102	+	0.0390606i	−0.473999	−	0.880525i	$-0.657190\pi$
$5$	−0.181368	+	0.0873422i	−0.0811102	+	0.0390606i	0.392889	+	0.919586i	$0.371476\pi$
$6$	2.35995	+	0.334396i	0.963444	+	0.136517i
$7$	−0.770934	−	0.966720i	−0.291386	−	0.365386i	0.614494	−	0.788922i	$-0.289360\pi$
$7$	−0.770934	−	0.966720i	−0.291386	−	0.365386i	−0.905879	+	0.423536i	$0.860789\pi$
$8$	2.45423	−	1.54210i	0.867703	−	0.545214i
$9$	−2.77281	+	1.14522i	−0.924269	+	0.381741i
$10$	0.0310162	+	0.275277i	0.00980820	+	0.0870501i
$11$	−4.24536	−	2.66753i	−1.28002	−	0.804292i	−0.291677	−	0.956517i	$-0.594213\pi$
$11$	−4.24536	−	2.66753i	−1.28002	−	0.804292i	−0.988346	+	0.152225i	$0.951356\pi$
$12$	−0.0845730	+	0.163502i	−0.0244141	+	0.0471991i
$13$	0.0513081	−	0.0117107i	0.0142303	−	0.00324798i	−0.215400	−	0.976526i	$-0.569105\pi$
$13$	0.0513081	−	0.0117107i	0.0142303	−	0.00324798i	0.229630	+	0.973278i	$0.426248\pi$
$14$	−1.60607	+	0.561988i	−0.429240	+	0.150198i
$15$	−0.209518	−	0.278696i	−0.0540972	−	0.0719590i
$16$	−0.840272	−	3.68147i	−0.210068	−	0.920368i
$17$	−3.02679	+	3.02679i	−0.734104	+	0.734104i	−0.971430	−	0.237326i	$-0.923729\pi$
$17$	−3.02679	+	3.02679i	−0.734104	+	0.734104i	0.237326	+	0.971430i	$0.423729\pi$
$18$	0.227277	+	4.12212i	0.0535697	+	0.971592i
$19$	5.19364	−	0.585183i	1.19150	−	0.134250i	0.506140	−	0.862452i	$-0.331072\pi$
$19$	5.19364	−	0.585183i	1.19150	−	0.134250i	0.685363	+	0.728201i	$0.259643\pi$
$20$	−0.0208579	−	0.00476068i	−0.00466397	−	0.00106452i
$21$	1.38257	−	1.63560i	0.301701	−	0.356916i
$22$	−5.39440	+	4.30189i	−1.15009	+	0.917167i
$23$	0.708287	−	1.47077i	0.147688	−	0.306677i	−0.813980	−	0.580892i	$-0.802704\pi$
$23$	0.708287	−	1.47077i	0.147688	−	0.306677i	0.961668	+	0.274215i	$0.0884180\pi$
$24$	3.44711	+	3.64985i	0.703638	+	0.745023i
$25$	−3.09218	+	3.87748i	−0.618437	+	0.775495i
$26$	0.00810871	−	0.0719668i	0.00159025	−	0.0141139i
$27$	−2.88022	−	4.32485i	−0.554298	−	0.832318i
$28$		−	0.131412i		−	0.0248345i
$29$	0.690188	+	5.34075i	0.128165	+	0.991753i
$29$	0.690188	+	5.34075i	0.128165	+	0.991753i
$30$	−0.457225	+	0.145474i	−0.0834776	+	0.0265598i
$31$	1.57922	+	0.552592i	0.283636	+	0.0992484i	0.468348	−	0.883544i	$-0.344850\pi$
$31$	1.57922	+	0.552592i	0.283636	+	0.0992484i	−0.184712	+	0.982793i	$0.559135\pi$
$32$	0.596780	+	0.0672409i	0.105497	+	0.0118866i
$33$	3.10113	−	8.11168i	0.539838	−	1.41206i
$34$	2.55581	+	5.30719i	0.438317	+	0.910176i
$35$	0.224258	+	0.107997i	0.0379066	+	0.0182548i
$36$	−0.306286	−	0.0885777i	−0.0510476	−	0.0147629i
$37$	−2.96911	−	4.72531i	−0.488119	−	0.776837i	0.508319	−	0.861169i	$-0.330267\pi$
$37$	−2.96911	−	4.72531i	−0.488119	−	0.776837i	−0.996438	+	0.0843323i	$0.973124\pi$
$38$	1.60044	−	7.01200i	0.259626	−	1.13750i
$39$	0.0371888	+	0.0832225i	0.00595497	+	0.0133263i
$40$	−0.310429	+	0.494045i	−0.0490832	+	0.0781154i
$41$	2.80557	+	2.80557i	0.438157	+	0.438157i	0.891391	−	0.453235i	$-0.149730\pi$
$41$	2.80557	+	2.80557i	0.438157	+	0.438157i	−0.453235	+	0.891391i	$0.649730\pi$
$42$	−1.49609	−	2.53920i	−0.230852	−	0.391808i
$43$	−0.771632	−	2.20520i	−0.117673	−	0.336289i	0.869949	−	0.493141i	$-0.164151\pi$
$43$	−0.771632	−	2.20520i	−0.117673	−	0.336289i	−0.987622	+	0.156852i	$0.949866\pi$
$44$	−0.175995	−	0.502965i	−0.0265322	−	0.0758248i
$45$	0.402872	−	0.449890i	0.0600566	−	0.0670657i
$46$	−1.58847	−	1.58847i	−0.234207	−	0.234207i
$47$	6.13509	−	9.76394i	0.894895	−	1.42422i	−0.0106389	−	0.999943i	$-0.503387\pi$
$47$	6.13509	−	9.76394i	0.894895	−	1.42422i	0.905534	−	0.424274i	$-0.139471\pi$
$48$	5.97140	−	2.66838i	0.861897	−	0.385147i
$49$	1.21744	−	5.33394i	0.173920	−	0.761992i
$50$	3.63105	+	5.77878i	0.513507	+	0.817242i
$51$	−6.16248	−	4.12219i	−0.862920	−	0.577222i
$52$	0.00503930	+	0.00242680i	0.000698825	+	0.000336537i
$53$	3.63041	+	7.53862i	0.498675	+	1.03551i	0.986681	+	0.162668i	$0.0520100\pi$
$53$	3.63041	+	7.53862i	0.498675	+	1.03551i	−0.488006	+	0.872840i	$0.662276\pi$
$54$	−6.92663	+	1.77545i	−0.942595	+	0.241608i
$55$	1.00296	+	0.113006i	0.135239	+	0.0152378i
$56$	−3.38283	−	1.18370i	−0.452049	−	0.158179i
$57$	2.74466	+	8.62646i	0.363539	+	1.14260i
$58$	7.25081	+	1.53091i	0.952078	+	0.201019i
$59$			10.1765i			1.32487i	0.749119	+	0.662435i	$0.230477\pi$
$59$			10.1765i			1.32487i	−0.749119	+	0.662435i	$0.769523\pi$
$60$	0.00105817	−	0.0370409i	0.000136609	−	0.00478196i
$61$	−1.51909	+	13.4823i	−0.194500	+	1.72623i	0.395188	+	0.918600i	$0.370680\pi$
$61$	−1.51909	+	13.4823i	−0.194500	+	1.72623i	−0.589687	+	0.807632i	$0.700749\pi$
$62$	1.43552	−	1.80009i	0.182312	−	0.228612i
$63$	3.24476	+	1.79764i	0.408802	+	0.226481i
$64$	3.63540	−	7.54898i	0.454425	−	0.943622i
$65$	−0.00828281	+	0.00660532i	−0.00102736	+	0.000819289i
$66$	−9.12680	−	7.71487i	−1.12343	−	0.949634i
$67$	−5.24543	−	1.19723i	−0.640831	−	0.146265i	−0.110255	−	0.993903i	$-0.535167\pi$
$67$	−5.24543	−	1.19723i	−0.640831	−	0.146265i	−0.530575	+	0.847638i	$0.678024\pi$
$68$	−0.452069	+	0.0509359i	−0.0548214	+	0.00617689i
$69$	2.73748	+	0.707629i	0.329554	+	0.0851885i
$70$	0.242204	−	0.242204i	0.0289489	−	0.0289489i
$71$	1.05188	+	4.60860i	0.124835	+	0.546940i	0.998205	+	0.0598824i	$0.0190726\pi$
$71$	1.05188	+	4.60860i	0.124835	+	0.546940i	−0.873370	+	0.487057i	$0.838070\pi$
$72$	−5.03907	+	7.08658i	−0.593860	+	0.835162i
$73$	11.0856	−	3.87901i	1.29747	−	0.454004i	0.408829	−	0.912611i	$-0.365937\pi$
$73$	11.0856	−	3.87901i	1.29747	−	0.454004i	0.888639	+	0.458607i	$0.151651\pi$
$74$	−7.48719	+	1.70890i	−0.870369	+	0.198656i
$75$	−7.62980	−	3.94657i	−0.881013	−	0.455711i
$76$	0.470327	+	0.295526i	0.0539503	+	0.0338992i
$77$	0.694129	+	6.16056i	0.0791033	+	0.702062i
$78$	0.125000	−	0.0104795i	0.0141535	−	0.00118657i
$79$	−2.54600	+	1.59976i	−0.286447	+	0.179987i	−0.667589	−	0.744530i	$-0.732674\pi$
$79$	−2.54600	+	1.59976i	−0.286447	+	0.179987i	0.381142	+	0.924516i	$0.375531\pi$
$80$	0.473946	+	0.594310i	0.0529888	+	0.0664459i
$81$	6.37693	−	6.35097i	0.708547	−	0.705663i
$82$	4.91931	−	2.36901i	0.543247	−	0.261614i
$83$	−9.70654	−	7.74070i	−1.06543	−	0.849653i	−0.0763579	−	0.997080i	$-0.524329\pi$
$83$	−9.70654	−	7.74070i	−1.06543	−	0.849653i	−0.989073	+	0.147428i	$0.952901\pi$
$84$	0.223261	−	0.0442911i	0.0243598	−	0.00483256i
$85$	0.284596	−	0.813329i	0.0308688	−	0.0882179i
$86$	−3.21505			−0.346687
$87$	−8.84101	+	2.97264i	−0.947856	+	0.318700i
$88$	−14.5327			−1.54919
$89$	−0.741261	+	2.11840i	−0.0785736	+	0.224550i	−0.976469	−	0.215659i	$-0.930810\pi$
$89$	−0.741261	+	2.11840i	−0.0785736	+	0.224550i	0.897895	+	0.440209i	$0.145096\pi$
$90$	−0.401255	−	0.727769i	−0.0422960	−	0.0767136i
$91$	−0.0508762	−	0.0405724i	−0.00533327	−	0.00425314i
$92$	0.156312	−	0.0752760i	0.0162967	−	0.00784806i
$93$	−0.406562	+	2.86924i	−0.0421585	+	0.297526i
$94$	−9.89397	−	12.4066i	−1.02049	−	1.27965i
$95$	−0.890849	+	0.559758i	−0.0913992	+	0.0574299i
$96$	0.0869004	+	1.03656i	0.00886923	+	0.105793i
$97$	−1.07237	−	9.51752i	−0.108882	−	0.966358i	−0.922774	−	0.385341i	$-0.874084\pi$
$97$	−1.07237	−	9.51752i	−0.108882	−	0.966358i	0.813892	−	0.581016i	$-0.197345\pi$
$98$	−6.37493	−	4.00564i	−0.643966	−	0.404630i
$99$	14.8265	+	2.53468i	1.49012	+	0.254745i
$100$	−0.513873	+	0.117288i	−0.0513873	+	0.0117288i
$101$	9.66361	−	3.38144i	0.961565	−	0.336466i	0.196561	−	0.980492i	$-0.437023\pi$
$101$	9.66361	−	3.38144i	0.961565	−	0.336466i	0.765004	+	0.644025i	$0.222737\pi$
$102$	−8.15520	+	6.13091i	−0.807485	+	0.607050i
$103$	2.00116	+	8.76766i	0.197180	+	0.863903i	0.972605	+	0.232463i	$0.0746786\pi$
$103$	2.00116	+	8.76766i	0.197180	+	0.863903i	−0.775425	+	0.631440i	$0.782464\pi$
$104$	0.107863	−	0.107863i	0.0105768	−	0.0105768i
$105$	−0.107897	+	0.417401i	−0.0105296	+	0.0407342i
$106$	11.4420	−	1.28920i	1.11134	−	0.125218i
$107$	0.568054	+	0.129655i	0.0549159	+	0.0125342i	0.249891	−	0.968274i	$-0.419605\pi$
$107$	0.568054	+	0.129655i	0.0549159	+	0.0125342i	−0.194975	+	0.980808i	$0.562462\pi$
$108$	0.0472578	−	0.550216i	0.00454738	−	0.0529445i
$109$	−13.2489	+	10.5657i	−1.26902	+	1.01201i	−0.270229	+	0.962796i	$0.587100\pi$
$109$	−13.2489	+	10.5657i	−1.26902	+	1.01201i	−0.998788	+	0.0492120i	$0.984329\pi$
$110$	0.602635	−	1.25138i	0.0574590	−	0.119315i
$111$	7.02732	−	6.63697i	0.667004	−	0.629953i
$112$	−2.91116	+	3.65048i	−0.275079	+	0.344938i
$113$	1.04913	−	9.31130i	0.0986940	−	0.875934i	−0.842645	−	0.538470i	$-0.819002\pi$
$113$	1.04913	−	9.31130i	0.0986940	−	0.875934i	0.941339	−	0.337463i	$-0.109569\pi$
$114$	12.4524	+	0.355734i	1.16627	+	0.0333176i
$115$			0.328615i			0.0306435i
$116$	−0.296549	+	0.489509i	−0.0275339	+	0.0454498i
$117$	−0.128856	+	0.0912309i	−0.0119128	+	0.00843430i
$118$	13.2183	+	4.62529i	1.21684	+	0.425792i
$119$	5.25951	+	0.592604i	0.482138	+	0.0543239i
$120$	−0.943981	−	0.360888i	−0.0861733	−	0.0329444i
$121$	6.13459	+	12.7386i	0.557690	+	1.15806i
$122$	16.8218	+	8.10093i	1.52297	+	0.733424i
$123$	−3.82091	+	5.71209i	−0.344520	+	0.515042i
$124$	0.0946037	+	0.150561i	0.00849566	+	0.0135208i
$125$	0.446127	−	1.95461i	0.0399028	−	0.174826i
$126$	3.80972	−	3.39759i	0.339397	−	0.302681i
$127$	−3.17678	+	5.05582i	−0.281894	+	0.448631i	−0.957418	−	0.288707i	$-0.906775\pi$
$127$	−3.17678	+	5.05582i	−0.281894	+	0.448631i	0.675524	+	0.737338i	$0.263918\pi$
$128$	−7.30376	−	7.30376i	−0.645567	−	0.645567i
$129$	3.48643	−	2.05420i	0.306963	−	0.180862i
$130$	0.00481508	+	0.0137607i	0.000422310	+	0.00120689i
$131$	−5.29192	−	15.1234i	−0.462357	−	1.32134i	−0.905293	−	0.424787i	$-0.860349\pi$
$131$	−5.29192	−	15.1234i	−0.462357	−	1.32134i	0.442936	−	0.896553i	$-0.353937\pi$
$132$	0.795191	−	0.468525i	0.0692125	−	0.0407798i
$133$	−4.56966	−	4.56966i	−0.396240	−	0.396240i
$134$	−3.93916	+	6.26914i	−0.340292	+	0.541571i
$135$	0.900121	+	0.532825i	0.0774701	+	0.0458583i
$136$	−2.76084	+	12.0960i	−0.236740	+	1.03723i
$137$	−7.23413	−	11.5131i	−0.618053	−	0.983626i	−0.998274	−	0.0587306i	$-0.981295\pi$
$137$	−7.23413	−	11.5131i	−0.618053	−	0.983626i	0.380220	−	0.924896i	$-0.375848\pi$
$138$	2.16334	−	3.23410i	0.184156	−	0.275305i
$139$	−5.51087	−	2.65389i	−0.467426	−	0.225100i	0.185319	−	0.982678i	$-0.440668\pi$
$139$	−5.51087	−	2.65389i	−0.467426	−	0.225100i	−0.652745	+	0.757578i	$0.726383\pi$
$140$	0.0114778	+	0.0238339i	0.000970052	+	0.00201433i
$141$	18.6561	+	7.13232i	1.57113	+	0.600650i
$142$	6.46420	+	0.728340i	0.542463	+	0.0611210i
$143$	−0.249060	−	0.0871499i	−0.0208274	−	0.00728784i
$144$	6.54602	+	9.24571i	0.545502	+	0.770476i
$145$	−0.591651	−	0.908359i	−0.0491340	−	0.0754351i
$146$		−	16.1621i		−	1.33759i
$147$	9.47238	+	0.270603i	0.781269	+	0.0223189i
$148$	0.0664073	−	0.589381i	0.00545865	−	0.0484468i
$149$	−8.12844	+	10.1927i	−0.665908	+	0.835022i	−0.993972	−	0.109634i	$-0.965032\pi$
$149$	−8.12844	+	10.1927i	−0.665908	+	0.835022i	0.328065	+	0.944655i	$0.393604\pi$
$150$	−8.59400	+	8.11662i	−0.701697	+	0.662719i
$151$	6.83167	−	14.1861i	0.555954	−	1.15445i	−0.413801	−	0.910368i	$-0.635799\pi$
$151$	6.83167	−	14.1861i	0.555954	−	1.15445i	0.969754	−	0.244082i	$-0.0784868\pi$
$152$	11.8440	−	9.44527i	0.960675	−	0.766113i
$153$	4.92635	−	11.8590i	0.398272	−	0.958747i
$154$	8.31745	+	1.89840i	0.670240	+	0.152978i
$155$	−0.334684	+	0.0377098i	−0.0268824	+	0.00302892i
$156$	−0.00242454	+	0.00937941i	−0.000194119	+	0.000750954i
$157$	10.9712	−	10.9712i	0.875601	−	0.875601i	−0.117475	−	0.993076i	$-0.537480\pi$
$157$	10.9712	−	10.9712i	0.875601	−	0.875601i	0.993076	+	0.117475i	$0.0374800\pi$
$158$	0.920756	+	4.03410i	0.0732514	+	0.320935i
$159$	−11.5841	+	8.70867i	−0.918677	+	0.690642i
$160$	−0.114110	+	0.0399287i	−0.00902117	+	0.00315664i
$161$	−1.96787	+	0.449153i	−0.155090	+	0.0353982i
$162$	−5.35094	−	11.1696i	−0.420409	−	0.877563i
$163$	−20.4620	−	12.8571i	−1.60271	−	1.00705i	−0.973172	−	0.230078i	$-0.926102\pi$
$163$	−20.4620	−	12.8571i	−1.60271	−	1.00705i	−0.629537	−	0.776971i	$-0.716755\pi$
$164$	0.0472132	+	0.419029i	0.00368673	+	0.0327207i
$165$	0.146046	+	1.74206i	0.0113697	+	0.135619i
$166$	−14.4661	+	9.08965i	−1.12279	+	0.705493i
$167$	5.12646	+	6.42838i	0.396697	+	0.497443i	0.939563	−	0.342377i	$-0.111232\pi$
$167$	5.12646	+	6.42838i	0.396697	+	0.497443i	−0.542865	+	0.839820i	$0.682661\pi$
$168$	0.870893	−	6.14618i	0.0671909	−	0.474188i
$169$	−11.7101	+	5.63929i	−0.900777	+	0.433791i
$170$	−0.927083	−	0.739324i	−0.0711041	−	0.0567036i
$171$	−13.7308	+	7.57048i	−1.05002	+	0.578929i
$172$	0.0820082	−	0.234366i	0.00625307	−	0.0178702i
$173$	−10.0124			−0.761230			−0.380615	−	0.924734i	$-0.624288\pi$
$173$	−10.0124			−0.761230			−0.380615	+	0.924734i	$0.624288\pi$
$174$	−0.157120	+	12.8347i	−0.0119112	+	0.972995i
$175$	6.13230			0.463558
$176$	−6.25320	+	17.8706i	−0.471353	+	1.34705i
$177$	−17.2893	+	3.42990i	−1.29955	+	0.257807i
$178$	2.41469	+	1.92565i	0.180989	+	0.144334i
$179$	0.0976933	−	0.0470466i	0.00730194	−	0.00351643i	−0.430229	−	0.902720i	$-0.641567\pi$
$179$	0.0976933	−	0.0470466i	0.00730194	−	0.00351643i	0.437531	+	0.899203i	$0.355853\pi$
$180$	0.0632870	−	0.0106865i	0.00471713	−	0.000796525i
$181$	−4.95770	−	6.21675i	−0.368503	−	0.462088i	0.562662	−	0.826687i	$-0.309777\pi$
$181$	−4.95770	−	6.21675i	−0.368503	−	0.462088i	−0.931164	+	0.364599i	$0.881206\pi$
$182$	−0.0758230	+	0.0476428i	−0.00562038	+	0.00353152i
$183$	−23.4176	+	1.96323i	−1.73108	+	0.145126i
$184$	−0.529773	−	4.70187i	−0.0390554	−	0.346626i
$185$	0.951221	+	0.597692i	0.0699352	+	0.0439432i
$186$	3.54208	+	1.83217i	0.259718	+	0.134341i
$187$	20.9238	−	4.77573i	1.53010	−	0.349236i
$188$	1.15677	−	0.404773i	0.0843664	−	0.0295211i
$189$	−1.96047	+	6.11854i	−0.142603	+	0.445058i
$190$	0.322174	+	1.41154i	0.0233730	+	0.102404i
$191$	13.7084	−	13.7084i	0.991903	−	0.991903i	−0.00806476	−	0.999967i	$-0.502567\pi$
$191$	13.7084	−	13.7084i	0.991903	−	0.991903i	0.999967	+	0.00806476i	$0.00256712\pi$
$192$	14.0506	+	3.63202i	1.01401	+	0.262118i
$193$	7.87198	−	0.886959i	0.566637	−	0.0638447i	0.176001	−	0.984390i	$-0.443684\pi$
$193$	7.87198	−	0.886959i	0.566637	−	0.0638447i	0.390636	+	0.920545i	$0.372255\pi$
$194$	−12.8497	−	2.93286i	−0.922556	−	0.210567i
$195$	−0.0140137	−	0.0118458i	−0.00100354	−	0.000848292i
$196$	0.454607	−	0.362537i	0.0324719	−	0.0258955i
$197$	−11.6702	+	24.2333i	−0.831465	+	1.72655i	−0.157861	+	0.987461i	$0.550460\pi$
$197$	−11.6702	+	24.2333i	−0.831465	+	1.72655i	−0.673604	+	0.739093i	$0.735255\pi$
$198$	10.0310	−	18.1061i	0.712873	−	1.28675i
$199$	−4.21341	+	5.28345i	−0.298681	+	0.374534i	−0.908413	−	0.418074i	$-0.862705\pi$
$199$	−4.21341	+	5.28345i	−0.298681	+	0.374534i	0.609733	+	0.792607i	$0.291277\pi$
$200$	−1.60950	+	14.2847i	−0.113809	+	1.01008i
$201$	0.266112	−	9.31519i	0.0187701	−	0.657043i
$202$		−	14.0890i		−	0.991296i
$203$	4.63092	−	4.78459i	0.325027	−	0.335812i
$204$	−0.238903	−	0.750871i	−0.0167265	−	0.0525715i
$205$	−0.753885	−	0.263796i	−0.0526536	−	0.0184243i
$206$	12.2979	+	1.38564i	0.856833	+	0.0965419i
$207$	−0.279580	+	4.88932i	−0.0194321	+	0.339831i
$208$	−0.0862255	−	0.179049i	−0.00597866	−	0.0124148i
$209$	−23.6099	−	11.3699i	−1.63313	−	0.786473i
$210$	0.493123	+	0.329858i	0.0340287	+	0.0227624i
$211$	8.24251	+	13.1179i	0.567438	+	0.903072i	0.999999	+	0.00146754i	$0.000467133\pi$
$211$	8.24251	+	13.1179i	0.567438	+	0.903072i	−0.432561	+	0.901605i	$0.642390\pi$
$212$	−0.197879	+	0.866965i	−0.0135904	+	0.0595434i
$213$	−7.47521	+	3.34037i	−0.512193	+	0.228878i
$214$	0.426592	−	0.678918i	0.0291612	−	0.0464099i
$215$	0.332556	+	0.332556i	0.0226801	+	0.0226801i
$216$	−13.7381	−	6.17263i	−0.934757	−	0.419994i
$217$	−0.683269	−	1.95267i	−0.0463833	−	0.132556i
$218$	7.70206	+	22.0112i	0.521649	+	1.49079i
$219$	10.3265	+	17.5264i	0.697800	+	1.18432i
$220$	0.0758499	+	0.0758499i	0.00511380	+	0.00511380i
$221$	−0.119853	+	0.190745i	−0.00806217	+	0.0128309i
$222$	−5.42681	−	12.1443i	−0.364224	−	0.815075i
$223$	0.726163	−	3.18153i	0.0486275	−	0.213051i	−0.944777	−	0.327714i	$-0.893722\pi$
$223$	0.726163	−	3.18153i	0.0486275	−	0.213051i	0.993404	+	0.114663i	$0.0365789\pi$
$224$	−0.395075	−	0.628757i	−0.0263970	−	0.0420106i
$225$	4.13345	−	14.2927i	0.275564	−	0.952849i
$226$	−11.6176	−	5.59476i	−0.772793	−	0.372158i
$227$	1.98535	+	4.12262i	0.131772	+	0.273628i	0.956407	−	0.292038i	$-0.0943334\pi$
$227$	1.98535	+	4.12262i	0.131772	+	0.273628i	−0.824634	+	0.565666i	$0.808619\pi$
$228$	−0.343563	+	0.898663i	−0.0227530	+	0.0595154i
$229$	8.89396	+	1.00211i	0.587730	+	0.0662212i	0.400822	−	0.916156i	$-0.368725\pi$
$229$	8.89396	+	1.00211i	0.587730	+	0.0662212i	0.186908	+	0.982377i	$0.440153\pi$
$230$	0.426838	+	0.149357i	0.0281449	+	0.00984831i
$231$	−10.2325	+	3.25564i	−0.673249	+	0.214206i
$232$	9.92984	+	12.0431i	0.651926	+	0.790669i
$233$		−	14.4781i		−	0.948490i	−0.880393	−	0.474245i	$-0.842721\pi$
$233$		−	14.4781i		−	0.948490i	0.880393	−	0.474245i	$-0.157279\pi$
$234$	0.0599342	+	0.208836i	0.00391802	+	0.0136521i
$235$	−0.259905	+	2.30672i	−0.0169543	+	0.150474i
$236$	−0.674335	+	0.845590i	−0.0438955	+	0.0550432i
$237$	−3.57599	−	3.78632i	−0.232286	−	0.245948i
$238$	3.16021	−	6.56224i	0.204846	−	0.425367i
$239$	14.4057	−	11.4882i	0.931829	−	0.743109i	−0.0347715	−	0.999395i	$-0.511070\pi$
$239$	14.4057	−	11.4882i	0.931829	−	0.743109i	0.966601	+	0.256286i	$0.0824989\pi$
$240$	−0.849959	+	1.00551i	−0.0548646	+	0.0649056i
$241$	5.50128	+	1.25563i	0.354369	+	0.0808823i	0.396000	−	0.918251i	$-0.370398\pi$
$241$	5.50128	+	1.25563i	0.354369	+	0.0808823i	−0.0416308	+	0.999133i	$0.513255\pi$
$242$	19.3344	−	2.17847i	1.24286	−	0.140037i
$243$	12.9392	+	8.69349i	0.830051	+	0.557688i
$244$	−1.01961	+	1.01961i	−0.0652741	+	0.0652741i
$245$	0.245074	+	1.07374i	0.0156572	+	0.0685987i
$246$	5.68282	+	7.55917i	0.362323	+	0.481955i
$247$	0.259623	−	0.0908460i	0.0165194	−	0.00578039i
$248$	4.72791	−	1.07912i	0.300223	−	0.0685239i
$249$	9.87951	−	19.0998i	0.626089	−	1.21040i
$250$	−2.33608	−	1.46786i	−0.147747	−	0.0928353i
$251$	1.83184	+	16.2580i	0.115624	+	1.02620i	0.908808	+	0.417214i	$0.136993\pi$
$251$	1.83184	+	16.2580i	0.115624	+	1.02620i	−0.793184	+	0.608982i	$0.791578\pi$
$252$	0.150496	+	0.364380i	0.00948036	+	0.0229538i
$253$	−6.93027	+	4.35458i	−0.435702	+	0.273770i
$254$	5.12315	+	6.42422i	0.321455	+	0.403092i
$255$	1.47772	+	0.209388i	0.0925383	+	0.0131124i
$256$	2.29149	−	1.10352i	0.143218	−	0.0689703i
$257$	4.38813	+	3.49942i	0.273724	+	0.218288i	0.750725	−	0.660615i	$-0.229705\pi$
$257$	4.38813	+	3.49942i	0.273724	+	0.218288i	−0.477000	+	0.878903i	$0.658276\pi$
$258$	−1.08360	−	5.46218i	−0.0674620	−	0.340060i
$259$	−2.27907	+	6.51320i	−0.141614	+	0.404711i
$260$	−0.00112593			−6.98272e−5
$261$	−8.03012	−	14.0185i	−0.497052	−	0.867721i
$262$	−22.0491			−1.36220
$263$	3.08739	−	8.82326i	0.190377	−	0.544066i	−0.808644	−	0.588298i	$-0.799798\pi$
$263$	3.08739	−	8.82326i	0.190377	−	0.544066i	0.999021	+	0.0442319i	$0.0140841\pi$
$264$	−4.89810	−	24.6902i	−0.301457	−	1.51958i
$265$	−1.31688	−	1.05018i	−0.0808952	−	0.0645118i
$266$	−8.01248	+	3.85861i	−0.491276	+	0.236586i
$267$	−3.84888	−	0.545373i	−0.235548	−	0.0333763i
$268$	−0.356521	−	0.447063i	−0.0217780	−	0.0273087i
$269$	2.32570	−	1.46133i	0.141800	−	0.0890991i	−0.459263	−	0.888300i	$-0.651887\pi$
$269$	2.32570	−	1.46133i	0.141800	−	0.0890991i	0.601064	+	0.799201i	$0.294744\pi$
$270$	1.10120	−	0.926997i	0.0670168	−	0.0564152i
$271$	1.04025	+	9.23248i	0.0631907	+	0.560833i	0.984921	+	0.173003i	$0.0553469\pi$
$271$	1.04025	+	9.23248i	0.0631907	+	0.560833i	−0.921731	+	0.387831i	$0.873225\pi$
$272$	13.6864	+	8.59970i	0.829857	+	0.521434i
$273$	0.0517828	−	0.100110i	0.00313404	−	0.00605894i
$274$	−18.2423	+	4.16368i	−1.10206	+	0.251537i
$275$	23.4707	−	8.21276i	1.41534	−	0.495248i
$276$	0.180573	+	0.240194i	0.0108692	+	0.0144580i
$277$	−0.281476	−	1.23323i	−0.0169123	−	0.0740974i	0.965768	−	0.259409i	$-0.0835277\pi$
$277$	−0.281476	−	1.23323i	−0.0169123	−	0.0740974i	−0.982680	+	0.185311i	$0.940671\pi$
$278$	−5.95187	+	5.95187i	−0.356969	+	0.356969i
$279$	−5.01170	+	0.276325i	−0.300043	+	0.0165432i
$280$	0.716924	−	0.0807779i	0.0428444	−	0.00482740i
$281$	12.8065	+	2.92299i	0.763970	+	0.174371i	0.586715	−	0.809794i	$-0.300421\pi$
$281$	12.8065	+	2.92299i	0.763970	+	0.174371i	0.177255	+	0.984165i	$0.443278\pi$
$282$	17.7435	−	20.9908i	1.05661	−	1.24999i
$283$	−4.26666	+	3.40255i	−0.253627	+	0.202261i	−0.742047	−	0.670348i	$-0.766145\pi$
$283$	−4.26666	+	3.40255i	−0.253627	+	0.202261i	0.488420	+	0.872609i	$0.337573\pi$
$284$	−0.217980	+	0.452640i	−0.0129347	+	0.0268592i
$285$	−1.25125	−	1.32484i	−0.0741175	−	0.0784767i
$286$	−0.226398	+	0.283894i	−0.0133872	+	0.0167870i
$287$	0.549293	−	4.87511i	0.0324237	−	0.287769i
$288$	−1.73176	+	0.497000i	−0.102045	+	0.0292860i
$289$		−	1.32288i		−	0.0778163i
$290$	−1.44878	+	0.355643i	−0.0850752	+	0.0208841i
$291$	15.8083	−	5.02968i	0.926698	−	0.294845i
$292$	1.17816	+	0.412257i	0.0689468	+	0.0241255i
$293$	−21.2306	−	2.39211i	−1.24030	−	0.139749i	−0.532668	−	0.846325i	$-0.678810\pi$
$293$	−21.2306	−	2.39211i	−1.24030	−	0.139749i	−0.707637	+	0.706576i	$0.750239\pi$
$294$	4.65673	−	12.1807i	0.271586	−	0.710393i
$295$	−0.888840	−	1.84570i	−0.0517503	−	0.107461i
$296$	−14.5738	−	7.01836i	−0.847084	−	0.407934i
$297$	0.690850	+	26.0436i	0.0400872	+	1.51120i
$298$	9.54495	+	15.1907i	0.552924	+	0.879973i
$299$	0.0191170	−	0.0837572i	0.00110557	−	0.00484380i
$300$	−0.372461	−	0.833509i	−0.0215041	−	0.0481227i
$301$	−1.53693	+	2.44601i	−0.0885873	+	0.140986i
$302$	−15.3213	−	15.3213i	−0.881644	−	0.881644i
$303$	9.00190	+	15.2782i	0.517146	+	0.877712i
$304$	−6.51840	−	18.6285i	−0.373856	−	1.06842i
$305$	−0.902060	−	2.57794i	−0.0516518	−	0.147612i
$306$	−13.1647	−	11.7888i	−0.752575	−	0.673923i
$307$	18.2981	+	18.2981i	1.04433	+	1.04433i	0.998971	+	0.0453595i	$0.0144433\pi$
$307$	18.2981	+	18.2981i	1.04433	+	1.04433i	0.0453595	+	0.998971i	$0.485557\pi$
$308$	−0.350546	+	0.557890i	−0.0199742	+	0.0317888i
$309$	−14.2213	+	6.35491i	−0.809020	+	0.361518i
$310$	−0.103134	+	0.451861i	−0.00585763	+	0.0256640i
$311$	7.03200	+	11.1914i	0.398748	+	0.634604i	0.984397	−	0.175961i	$-0.0563032\pi$
$311$	7.03200	+	11.1914i	0.398748	+	0.634604i	−0.585649	+	0.810565i	$0.699160\pi$
$312$	0.219607	+	0.146899i	0.0124328	+	0.00831651i
$313$	−3.18504	−	1.53384i	−0.180029	−	0.0866975i	0.341698	−	0.939810i	$-0.388998\pi$
$313$	−3.18504	−	1.53384i	−0.180029	−	0.0866975i	−0.521727	+	0.853112i	$0.674712\pi$
$314$	−9.26408	−	19.2371i	−0.522802	−	1.08561i
$315$	−0.745506	−	0.0426293i	−0.0420045	−	0.00240189i
$316$	−0.317558	−	0.0357802i	−0.0178640	−	0.00201279i
$317$	21.4655	+	7.51112i	1.20562	+	0.421866i	0.856961	−	0.515381i	$-0.172350\pi$
$317$	21.4655	+	7.51112i	1.20562	+	0.421866i	0.348664	+	0.937248i	$0.386635\pi$
$318$	6.04668	+	19.0047i	0.339081	+	1.06573i
$319$	11.3165	−	24.5145i	0.633605	−	1.37255i
$320$			1.68667i			0.0942875i
$321$	−0.0288186	+	1.00879i	−0.00160850	+	0.0563051i
$322$	−0.311001	+	2.76021i	−0.0173314	+	0.153821i
$323$	−13.9488	+	17.4913i	−0.776133	+	0.973240i
$324$	0.950712	−	0.105157i	0.0528173	−	0.00584203i
$325$	−0.113246	+	0.235158i	−0.00628176	+	0.0130442i
$326$	−26.0003	+	20.7345i	−1.44002	+	1.14838i
$327$	−22.4159	−	18.9481i	−1.23960	−	1.04783i
$328$	11.2120	+	2.55906i	0.619078	+	0.141301i
$329$	−14.1687	+	1.59643i	−0.781148	+	0.0880143i
$330$	2.32914	+	0.602075i	0.128215	+	0.0331431i
$331$	−3.09917	+	3.09917i	−0.170346	+	0.170346i	−0.787131	−	0.616785i	$-0.788435\pi$
$331$	−3.09917	+	3.09917i	−0.170346	+	0.170346i	0.616785	+	0.787131i	$0.288435\pi$
$332$	−0.293609	−	1.28638i	−0.0161139	−	0.0705995i
$333$	13.6443	+	9.70209i	0.747704	+	0.531671i
$334$	10.6798	−	3.73703i	0.584374	−	0.204481i
$335$	1.05592	−	0.241007i	0.0576911	−	0.0131676i
$336$	−7.18313	−	3.71553i	−0.391872	−	0.202699i
$337$	−9.67987	−	6.08226i	−0.527296	−	0.331322i	0.241935	−	0.970292i	$-0.422218\pi$
$337$	−9.67987	−	6.08226i	−0.527296	−	0.331322i	−0.769231	+	0.638970i	$0.779361\pi$
$338$	2.00258	+	17.7734i	0.108926	+	0.966743i
$339$	16.1730	−	1.35587i	0.878395	−	0.0736407i
$340$	0.0775419	−	0.0487228i	0.00420530	−	0.00264237i
$341$	−5.23028	−	6.55856i	−0.283235	−	0.355166i
$342$	3.59259	+	21.2758i	0.194265	+	1.15046i
$343$	−13.8932	+	6.69062i	−0.750163	+	0.361259i
$344$	−5.29439	−	4.22214i	−0.285455	−	0.227642i
$345$	−0.558297	+	0.110756i	−0.0300577	+	0.00596292i
$346$	−4.55070	+	13.0051i	−0.244647	+	0.699161i
$347$	3.88166			0.208378			0.104189	−	0.994557i	$-0.466775\pi$
$347$	3.88166			0.208378			0.104189	+	0.994557i	$0.466775\pi$
$348$	−0.931597	−	0.338836i	−0.0499388	−	0.0181635i
$349$	16.5955			0.888336			0.444168	−	0.895944i	$-0.353499\pi$
$349$	16.5955			0.888336			0.444168	+	0.895944i	$0.353499\pi$
$350$	2.78716	−	7.96526i	0.148980	−	0.425761i
$351$	−0.198426	−	0.188171i	−0.0105912	−	0.0100438i
$352$	−2.35418	−	1.87739i	−0.125478	−	0.100065i
$353$	4.64426	−	2.23656i	0.247189	−	0.119040i	−0.306187	−	0.951971i	$-0.599053\pi$
$353$	4.64426	−	2.23656i	0.247189	−	0.119040i	0.553376	+	0.832931i	$0.313339\pi$
$354$	−3.40299	+	24.0160i	−0.180867	+	1.27644i
$355$	−0.593303	−	0.743978i	−0.0314892	−	0.0394862i
$356$	−0.201967	+	0.126904i	−0.0107042	+	0.00672590i
$357$	0.765866	+	9.13533i	0.0405339	+	0.483493i
$358$	−0.0167068	−	0.148277i	−0.000882981	−	0.00783668i
$359$	−4.17006	−	2.62022i	−0.220087	−	0.138290i	0.417476	−	0.908688i	$-0.362915\pi$
$359$	−4.17006	−	2.62022i	−0.220087	−	0.138290i	−0.637563	+	0.770398i	$0.720058\pi$
$360$	0.294968	−	1.72540i	0.0155462	−	0.0909367i
$361$	8.10784	−	1.85056i	0.426728	−	0.0973979i
$362$	−10.3283	+	3.61401i	−0.542841	+	0.189948i
$363$	−19.5746	+	14.7157i	−1.02740	+	0.772376i
$364$	−0.00153893	−	0.00674250i	−8.06619e−5	−	0.000353403i
$365$	−1.67177	+	1.67177i	−0.0875043	+	0.0875043i
$366$	−8.09340	+	31.3095i	−0.423049	+	1.63657i
$367$	−26.8006	+	3.01971i	−1.39898	+	0.157627i	−0.779017	−	0.627003i	$-0.784282\pi$
$367$	−26.8006	+	3.01971i	−1.39898	+	0.157627i	−0.619964	+	0.784630i	$0.712853\pi$
$368$	−6.00976	−	1.37169i	−0.313281	−	0.0715042i
$369$	−10.9923	−	4.56630i	−0.572237	−	0.237712i
$370$	1.20868	−	0.963888i	0.0628362	−	0.0501102i
$371$	4.48893	−	9.32136i	0.233054	−	0.483941i
$372$	−0.223909	+	0.211471i	−0.0116091	+	0.0109643i
$373$	10.0669	−	12.6235i	0.521244	−	0.653619i	−0.449629	−	0.893215i	$-0.648444\pi$
$373$	10.0669	−	12.6235i	0.521244	−	0.653619i	0.970873	+	0.239597i	$0.0770152\pi$
$374$	3.30680	−	29.3486i	0.170990	−	1.51758i
$375$	3.47113	+	0.0991616i	0.179248	+	0.00512068i
$376$		−	33.4239i		−	1.72371i
$377$	0.0979564	+	0.265941i	0.00504501	+	0.0136967i
$378$	7.05634	+	5.32736i	0.362939	+	0.274010i
$379$	−23.8325	−	8.33935i	−1.22419	−	0.428364i	−0.360680	−	0.932690i	$-0.617455\pi$
$379$	−23.8325	−	8.33935i	−1.22419	−	0.428364i	−0.863513	+	0.504326i	$0.831741\pi$
$380$	−0.111114	−	0.0125196i	−0.00570004	−	0.000642240i
$381$	−9.66025	−	3.69315i	−0.494909	−	0.189206i
$382$	−11.5753	−	24.0364i	−0.592244	−	1.22981i
$383$	9.87708	+	4.75655i	0.504695	+	0.243048i	0.668865	−	0.743384i	$-0.266780\pi$
$383$	9.87708	+	4.75655i	0.504695	+	0.243048i	−0.164170	+	0.986432i	$0.552495\pi$
$384$	9.94700	−	14.8703i	0.507606	−	0.758848i
$385$	−0.663970	−	1.05670i	−0.0338391	−	0.0538545i
$386$	2.42578	−	10.6281i	0.123469	−	0.540954i
$387$	4.66503	+	5.23090i	0.237137	+	0.265901i
$388$	0.541562	−	0.861891i	0.0274936	−	0.0437559i
$389$	−0.0567524	−	0.0567524i	−0.00287746	−	0.00287746i	0.705667	−	0.708544i	$-0.250648\pi$
$389$	−0.0567524	−	0.0567524i	−0.00287746	−	0.00287746i	−0.708544	+	0.705667i	$0.750648\pi$
$390$	−0.0217558	+	0.0128185i	−0.00110165	+	0.000649088i
$391$	2.30788	+	6.59555i	0.116715	+	0.333551i
$392$	−5.23758	−	14.9681i	−0.264538	−	0.756005i
$393$	23.9102	−	14.0879i	1.20611	−	0.710639i
$394$	26.1726	+	26.1726i	1.31856	+	1.31856i
$395$	0.322036	−	0.512517i	0.0162034	−	0.0257875i
$396$	1.06401	+	1.19307i	0.0534684	+	0.0599541i
$397$	2.14567	−	9.40079i	0.107688	−	0.471812i	−0.892112	−	0.451814i	$-0.850777\pi$
$397$	2.14567	−	9.40079i	0.107688	−	0.471812i	0.999800	−	0.0199977i	$-0.00636589\pi$
$398$	4.94766	+	7.87416i	0.248004	+	0.394696i
$399$	6.22343	−	9.30375i	0.311561	−	0.465770i
$400$	16.8731	+	8.12565i	0.843654	+	0.406283i
$401$	−13.8274	−	28.7129i	−0.690507	−	1.43385i	−0.890929	−	0.454143i	$-0.849945\pi$
$401$	−13.8274	−	28.7129i	−0.690507	−	1.43385i	0.200421	−	0.979710i	$-0.435769\pi$
$402$	−11.9786	−	4.57946i	−0.597437	−	0.228403i
$403$	0.0874978	+	0.00985864i	0.00435858	+	0.000491094i
$404$	1.02704	+	0.359376i	0.0510971	+	0.0178796i
$405$	−0.601862	+	1.70884i	−0.0299068	+	0.0849128i
$406$	−4.10993	−	8.18974i	−0.203972	−	0.406450i
$407$			27.9808i			1.38696i
$408$	−21.4810	−	0.613659i	−1.06347	−	0.0303806i
$409$	−0.666295	+	5.91353i	−0.0329462	+	0.292405i	0.966425	+	0.256949i	$0.0827171\pi$
$409$	−0.666295	+	5.91353i	−0.0329462	+	0.292405i	−0.999371	+	0.0354566i	$0.988711\pi$
$410$	−0.685290	+	0.859327i	−0.0338441	+	0.0424391i
$411$	17.1218	−	16.1707i	0.844557	−	0.797643i
$412$	−0.414698	+	0.861129i	−0.0204307	+	0.0424248i
$413$	9.83785	−	7.84543i	0.484089	−	0.386048i
$414$	6.22367	+	2.58537i	0.305877	+	0.127064i
$415$	2.43655	+	0.556126i	0.119605	+	0.0272991i
$416$	0.0314071	−	0.00353873i	0.00153986	−	0.000173500i
$417$	2.65143	−	10.2571i	0.129841	−	0.502293i
$418$	−25.4992	+	25.4992i	−1.24721	+	1.24721i
$419$	−4.65946	−	20.4144i	−0.227630	−	0.997311i	−0.951566	−	0.307444i	$-0.900526\pi$
$419$	−4.65946	−	20.4144i	−0.227630	−	0.997311i	0.723936	−	0.689867i	$-0.242331\pi$
$420$	−0.0366240	+	0.0275331i	−0.00178707	+	0.00134348i
$421$	26.3272	−	9.21227i	1.28311	−	0.448979i	0.399296	−	0.916822i	$-0.369255\pi$
$421$	26.3272	−	9.21227i	1.28311	−	0.448979i	0.883811	+	0.467843i	$0.154969\pi$
$422$	20.7851	−	4.74406i	1.01180	−	0.230937i
$423$	−5.82953	+	34.0996i	−0.283442	+	1.65798i
$424$	20.5351	+	12.9031i	0.997274	+	0.626629i
$425$	−2.37691	−	21.0957i	−0.115297	−	1.02329i
$426$	0.941287	+	11.2278i	0.0456055	+	0.543988i
$427$	14.2047	−	8.92543i	0.687415	−	0.431932i
$428$	0.0386094	+	0.0484147i	0.00186626	+	0.00234021i
$429$	0.0641193	−	0.452512i	0.00309571	−	0.0218475i
$430$	0.583106	−	0.280809i	0.0281199	−	0.0135418i
$431$	9.40806	+	7.50268i	0.453170	+	0.361391i	0.823317	−	0.567582i	$-0.192121\pi$
$431$	9.40806	+	7.50268i	0.453170	+	0.361391i	−0.370147	+	0.928973i	$0.620693\pi$
$432$	−13.5017	+	14.2375i	−0.649599	+	0.685001i
$433$	−3.89898	+	11.1426i	−0.187373	+	0.535481i	−0.998800	−	0.0489727i	$-0.984405\pi$
$433$	−3.89898	+	11.1426i	−0.187373	+	0.535481i	0.811427	+	0.584453i	$0.198691\pi$
$434$	−2.84688			−0.136655
$435$	1.34384	−	1.31133i	0.0644321	−	0.0628737i
$436$	−1.80100			−0.0862525
$437$	2.81792	−	8.05315i	0.134799	−	0.385234i
$438$	27.4585	−	5.44728i	1.31202	−	0.260281i
$439$	7.90864	+	6.30693i	0.377459	+	0.301013i	0.793781	−	0.608204i	$-0.208110\pi$
$439$	7.90864	+	6.30693i	0.377459	+	0.301013i	−0.416322	+	0.909217i	$0.636681\pi$
$440$	2.63577	−	1.26932i	0.125655	−	0.0605123i
$441$	2.73284	+	16.1842i	0.130135	+	0.770678i
$442$	0.193285	+	0.242371i	0.00919362	+	0.0115284i
$443$	3.01520	−	1.89458i	0.143257	−	0.0900141i	−0.458497	−	0.888696i	$-0.651612\pi$
$443$	3.01520	−	1.89458i	0.143257	−	0.0900141i	0.601753	+	0.798682i	$0.294469\pi$
$444$	1.02371	−	0.0858230i	0.0485830	−	0.00407298i
$445$	−0.0505850	−	0.448954i	−0.00239796	−	0.0212825i
$446$	−3.80245	−	2.38924i	−0.180051	−	0.113134i
$447$	−20.0565	−	10.3744i	−0.948639	−	0.490691i
$448$	−10.1004	+	2.30535i	−0.477199	+	0.108918i
$449$	−11.1011	+	3.88445i	−0.523894	+	0.183319i	−0.579253	−	0.815148i	$-0.696656\pi$
$449$	−11.1011	+	3.88445i	−0.523894	+	0.183319i	0.0553585	+	0.998467i	$0.482370\pi$
$450$	−16.6862	−	11.8651i	−0.786594	−	0.559325i
$451$	−4.42669	−	19.3946i	−0.208445	−	0.913256i
$452$	0.704177	−	0.704177i	0.0331217	−	0.0331217i
$453$	26.4039	+	6.82533i	1.24057	+	0.320682i
$454$	6.25723	−	0.705020i	0.293666	−	0.0330882i
$455$	0.0127710	+	0.00291490i	0.000598713	+	0.000136652i
$456$	20.0389	+	16.9388i	0.938406	+	0.793233i
$457$	−4.23470	+	3.37706i	−0.198091	+	0.157972i	−0.717512	−	0.696546i	$-0.754719\pi$
$457$	−4.23470	+	3.37706i	−0.198091	+	0.157972i	0.519421	+	0.854518i	$0.326148\pi$
$458$	5.34400	−	11.0969i	0.249709	−	0.518525i
$459$	21.8082	+	4.37261i	1.01792	+	0.204096i
$460$	−0.0217753	+	0.0273053i	−0.00101528	+	0.00127312i
$461$	−4.28290	+	38.0118i	−0.199475	+	1.77039i	0.351813	+	0.936070i	$0.385565\pi$
$461$	−4.28290	+	38.0118i	−0.199475	+	1.77039i	−0.551288	+	0.834315i	$0.685863\pi$
$462$	−0.421963	+	14.7707i	−0.0196315	+	0.687196i
$463$		−	0.154960i		−	0.00720160i	−0.999994	−	0.00360080i	$-0.998854\pi$
$463$		−	0.154960i		−	0.00720160i	0.999994	−	0.00360080i	$-0.00114617\pi$
$464$	19.0819	−	7.02859i	0.885854	−	0.326294i
$465$	−0.176869	−	0.555899i	−0.00820209	−	0.0257792i
$466$	−18.8056	−	6.58037i	−0.871153	−	0.304830i
$467$	−0.825034	−	0.0929590i	−0.0381780	−	0.00430163i	0.0928548	−	0.995680i	$-0.470401\pi$
$467$	−0.825034	−	0.0929590i	−0.0381780	−	0.00430163i	−0.131033	+	0.991378i	$0.541829\pi$
$468$	−0.0167522		0.000957922i	−0.000774373		4.42800e-5i
$469$	2.88648	+	5.99385i	0.133285	+	0.276770i
$470$	2.87807	+	1.38601i	0.132756	+	0.0639317i
$471$	22.3373	+	14.9418i	1.02925	+	0.688480i
$472$	15.6932	+	24.9756i	0.722338	+	1.14959i
$473$	−2.60659	+	11.4202i	−0.119851	+	0.525102i
$474$	−6.54336	+	2.92396i	−0.300547	+	0.134302i
$475$	−13.7907	+	21.9477i	−0.632759	+	1.00703i
$476$	0.397756	+	0.397756i	0.0182311	+	0.0182311i
$477$	−18.6998	−	16.7455i	−0.856206	−	0.766724i
$478$	−8.37455	−	23.9331i	−0.383043	−	1.09467i
$479$	2.08653	+	5.96295i	0.0953358	+	0.272454i	0.981669	−	0.190594i	$-0.0610414\pi$
$479$	2.08653	+	5.96295i	0.0953358	+	0.272454i	−0.886333	+	0.463048i	$0.846756\pi$
$480$	−0.106296	−	0.180408i	−0.00485173	−	0.00823447i
$481$	−0.207676	−	0.207676i	−0.00946923	−	0.00946923i
$482$	4.13130	−	6.57493i	0.188176	−	0.299480i
$483$	−1.42634	−	3.19191i	−0.0649005	−	0.145237i
$484$	−0.334372	+	1.46498i	−0.0151987	+	0.0665900i
$485$	1.02577	+	1.63251i	0.0465780	+	0.0741285i
$486$	17.1729	−	12.8555i	0.778980	−	0.583138i
$487$	−0.501202	−	0.241366i	−0.0227116	−	0.0109373i	0.422493	−	0.906366i	$-0.361155\pi$
$487$	−0.501202	−	0.241366i	−0.0227116	−	0.0109373i	−0.445205	+	0.895429i	$0.646869\pi$
$488$	17.0628	+	35.4313i	0.772397	+	1.60390i
$489$	14.9470	−	39.0972i	0.675927	−	1.76803i
$490$	1.50607	+	0.169693i	0.0680373	+	0.00766596i
$491$	−28.5759	−	9.99916i	−1.28961	−	0.451256i	−0.403610	−	0.914931i	$-0.632245\pi$
$491$	−28.5759	−	9.99916i	−1.28961	−	0.451256i	−0.886005	+	0.463676i	$0.846530\pi$
$492$	−0.695993	+	0.221442i	−0.0313778	+	0.00998338i
$493$	−18.2544	−	14.0763i	−0.822136	−	0.633963i
$494$		−	0.378515i		−	0.0170302i
$495$	−2.91043	+	0.835268i	−0.130814	+	0.0375425i
$496$	0.707379	−	6.27816i	0.0317623	−	0.281898i
$497$	3.64429	−	4.56980i	0.163469	−	0.204983i
$498$	−20.3184	−	21.5135i	−0.910491	−	0.964042i
$499$	−3.93951	+	8.18047i	−0.176357	+	0.366208i	−0.970345	−	0.241725i	$-0.922287\pi$
$499$	−3.93951	+	8.18047i	−0.176357	+	0.366208i	0.793988	+	0.607933i	$0.208001\pi$
$500$	0.166589	−	0.132851i	0.00745011	−	0.00594126i
$501$	−9.19361	+	10.8762i	−0.410740	+	0.485912i
$502$	21.9501	+	5.00997i	0.979682	+	0.223606i
$503$	−34.1679	+	3.84980i	−1.52347	+	0.171654i	−0.833638	−	0.552312i	$-0.813746\pi$
$503$	−34.1679	+	3.84980i	−1.52347	+	0.171654i	−0.689836	+	0.723966i	$0.742317\pi$
$504$	10.7355	−	0.591914i	0.478199	−	0.0263660i
$505$	−1.45733	+	1.45733i	−0.0648502	+	0.0648502i
$506$	2.50632	+	10.9809i	0.111420	+	0.488161i
$507$	−13.5276	−	17.9941i	−0.600782	−	0.799147i
$508$	−0.598984	+	0.209593i	−0.0265756	+	0.00929920i
$509$	−6.74522	+	1.53955i	−0.298977	+	0.0682395i	−0.369378	−	0.929279i	$-0.620429\pi$
$509$	−6.74522	+	1.53955i	−0.298977	+	0.0682395i	0.0704012	+	0.997519i	$0.477572\pi$
$510$	0.943605	−	1.82424i	0.0417835	−	0.0807788i
$511$	−12.2962	−	7.72619i	−0.543950	−	0.341787i
$512$	−2.70485	−	24.0062i	−0.119539	−	1.06094i
$513$	−17.4896	−	20.7763i	−0.772186	−	0.917295i
$514$	6.53983	−	4.10925i	0.288460	−	0.181251i
$515$	−1.12873	−	1.41539i	−0.0497379	−	0.0623694i
$516$	0.425814	+	0.0603364i	0.0187454	+	0.00265616i
$517$	−52.0913	+	25.0858i	−2.29097	+	1.10327i
$518$	7.42416	+	5.92057i	0.326199	+	0.260135i
$519$	−3.37459	−	17.0105i	−0.148128	−	0.746679i
$520$	−0.0101419	+	0.0289839i	−0.000444752	+	0.00127103i
$521$	15.0161			0.657865			0.328933	−	0.944353i	$-0.393311\pi$
$521$	15.0161			0.657865			0.328933	+	0.944353i	$0.393311\pi$
$522$	−21.8583	+	4.05887i	−0.956713	+	0.177652i
$523$	29.8790			1.30652			0.653259	−	0.757135i	$-0.273401\pi$
$523$	29.8790			1.30652			0.653259	+	0.757135i	$0.273401\pi$
$524$	0.562419	−	1.60730i	0.0245694	−	0.0702153i
$525$	2.06683	+	10.4184i	0.0902040	+	0.454697i
$526$	−10.0573	−	8.02044i	−0.438520	−	0.349708i
$527$	−6.45253	+	3.10737i	−0.281076	+	0.135359i
$528$	−32.4687	−	4.60071i	−1.41302	−	0.200220i
$529$	12.6788	+	15.8987i	0.551251	+	0.691246i
$530$	−1.96260	+	1.23319i	−0.0852501	+	0.0535662i
$531$	−11.6544	−	28.2175i	−0.505758	−	1.22454i
$532$	−0.0769000	−	0.682506i	−0.00333404	−	0.0295904i
$533$	0.176804	+	0.111093i	0.00765823	+	0.00481198i
$534$	−2.45772	+	4.75144i	−0.106356	+	0.205615i
$535$	−0.114351	+	0.0260999i	−0.00494383	+	0.00112840i
$536$	−14.7197	+	5.15066i	−0.635796	+	0.222475i
$537$	0.112856	+	0.150119i	0.00487010	+	0.00647810i
$538$	−0.841087	−	3.68504i	−0.0362618	−	0.158873i
$539$	−19.3969	+	19.3969i	−0.835485	+	0.835485i
$540$	0.0394860	+	0.103919i	0.00169921	+	0.00447197i
$541$	−28.1664	+	3.17360i	−1.21097	+	0.136444i	−0.694265	−	0.719720i	$-0.744270\pi$
$541$	−28.1664	+	3.17360i	−1.21097	+	0.136444i	−0.516705	+	0.856163i	$0.672842\pi$
$542$	12.4649	+	2.84503i	0.535413	+	0.122204i
$543$	8.89096	−	10.5181i	0.381548	−	0.451376i
$544$	−2.00985	+	1.60280i	−0.0861716	+	0.0687195i
$545$	1.48010	−	3.07347i	0.0634007	−	0.131653i
$546$	−0.106498	−	0.112761i	−0.00455768	−	0.00482574i
$547$	−7.14651	+	8.96144i	−0.305563	+	0.383163i	−0.910777	−	0.412899i	$-0.864516\pi$
$547$	−7.14651	+	8.96144i	−0.305563	+	0.383163i	0.605214	+	0.796063i	$0.293088\pi$
$548$	0.161799	−	1.43601i	0.00691171	−	0.0613431i
$549$	−11.2281	−	39.1235i	−0.479204	−	1.66975i
$550$		−	34.2189i		−	1.45910i
$551$	6.70991	+	27.3341i	0.285852	+	1.16447i
$552$	7.80965	−	2.48477i	0.332401	−	0.105759i
$553$	3.50931	+	1.22796i	0.149231	+	0.0522182i
$554$	−1.72977	−	0.194899i	−0.0734910	−	0.00828045i
$555$	−0.694844	+	1.81752i	−0.0294945	+	0.0771492i
$556$	−0.282053	−	0.585689i	−0.0119617	−	0.0248388i
$557$	8.89296	+	4.28263i	0.376807	+	0.181461i	0.612695	−	0.790320i	$-0.290086\pi$
$557$	8.89296	+	4.28263i	0.376807	+	0.181461i	−0.235888	+	0.971780i	$0.575800\pi$
$558$	−1.91893	+	6.63530i	−0.0812346	+	0.280895i
$559$	−0.0654155	−	0.104108i	−0.00276678	−	0.00440330i
$560$	0.209150	−	0.916347i	0.00883821	−	0.0387227i
$561$	15.1659	+	33.9388i	0.640304	+	1.43290i
$562$	9.61729	−	15.3058i	0.405681	−	0.645638i
$563$	23.0783	+	23.0783i	0.972634	+	0.972634i	0.999635	−	0.0270013i	$-0.00859583\pi$
$563$	23.0783	+	23.0783i	0.972634	+	0.972634i	−0.0270013	+	0.999635i	$0.508596\pi$
$564$	1.07756	+	1.82887i	0.0453737	+	0.0770092i
$565$	0.622991	+	1.78041i	0.0262094	+	0.0749022i
$566$	2.48036	+	7.08846i	0.104257	+	0.297950i
$567$	−11.0558	−	1.26853i	−0.464300	−	0.0532731i
$568$	9.68846	+	9.68846i	0.406519	+	0.406519i
$569$	−7.94786	+	12.6489i	−0.333191	+	0.530271i	−0.970738	−	0.240141i	$-0.922806\pi$
$569$	−7.94786	+	12.6489i	−0.333191	+	0.530271i	0.637547	+	0.770412i	$0.279949\pi$
$570$	−2.28954	+	1.02310i	−0.0958981	+	0.0428530i
$571$	4.42756	−	19.3984i	0.185288	−	0.811798i	−0.793771	−	0.608217i	$-0.791885\pi$
$571$	4.42756	−	19.3984i	0.185288	−	0.811798i	0.979058	−	0.203581i	$-0.0652579\pi$
$572$	−0.0149201	−	0.0237451i	−0.000623839	−	0.000992834i
$573$	27.9100	+	18.6695i	1.16596	+	0.779928i
$574$	−6.08263	−	2.92924i	−0.253884	−	0.122264i
$575$	3.51273	+	7.29427i	0.146491	+	0.304192i
$576$	−1.43499	+	25.0952i	−0.0597911	+	1.04563i
$577$	22.0920	+	2.48917i	0.919701	+	0.103625i	0.559105	−	0.829097i	$-0.311145\pi$
$577$	22.0920	+	2.48917i	0.919701	+	0.103625i	0.360596	+	0.932722i	$0.382573\pi$
$578$	−1.71829	−	0.601255i	−0.0714713	−	0.0250089i
$579$	4.16007	+	13.0751i	0.172886	+	0.543382i
$580$	0.0110297	−	0.114683i	0.000457984	−	0.00476194i
$581$			15.3511i			0.636870i
$582$	0.651895	−	22.8194i	0.0270219	−	0.945895i
$583$	4.69715	−	41.6883i	0.194536	−	1.72655i
$584$	21.2248	−	26.6150i	0.878288	−	1.10134i
$585$	0.0154021	−	0.0278009i	0.000636797	−	0.00114943i
$586$	−12.7565	+	26.4892i	−0.526968	+	1.09426i
$587$	−28.2498	+	22.5284i	−1.16599	+	0.929849i	−0.998430	−	0.0560128i	$-0.982161\pi$
$587$	−28.2498	+	22.5284i	−1.16599	+	0.929849i	−0.167563	+	0.985861i	$0.553590\pi$
$588$	0.769150	+	0.650161i	0.0317192	+	0.0268122i
$589$	8.52525	+	1.94583i	0.351277	+	0.0801766i
$590$	−2.80136	+	0.315637i	−0.115330	+	0.0129946i
$591$	−45.1044	−	11.6593i	−1.85535	−	0.479600i
$592$	−14.9012	+	14.9012i	−0.612437	+	0.612437i
$593$	3.24604	+	14.2219i	0.133299	+	0.584021i	0.996818	+	0.0797057i	$0.0253981\pi$
$593$	3.24604	+	14.2219i	0.133299	+	0.584021i	−0.863519	+	0.504316i	$0.831745\pi$
$594$	34.1421	+	10.9396i	1.40087	+	0.448858i
$595$	−1.00567	+	0.351898i	−0.0412283	+	0.0144264i
$596$	−1.35082	+	0.308316i	−0.0553317	+	0.0126291i
$597$	−10.3964	−	5.37760i	−0.425495	−	0.220091i
$598$	−0.100104	−	0.0628992i	−0.00409354	−	0.00257214i
$599$	−4.16495	−	36.9649i	−0.170175	−	1.51035i	−0.730980	−	0.682399i	$-0.760937\pi$
$599$	−4.16495	−	36.9649i	−0.170175	−	1.51035i	0.560805	−	0.827948i	$-0.310492\pi$
$600$	−24.8113	+	2.08007i	−1.01292	+	0.0849185i
$601$	−21.1263	+	13.2745i	−0.861759	+	0.541479i	−0.888873	−	0.458153i	$-0.848511\pi$
$601$	−21.1263	+	13.2745i	−0.861759	+	0.541479i	0.0271140	+	0.999632i	$0.491368\pi$
$602$	2.47859	+	3.10805i	0.101020	+	0.126675i
$603$	15.9157	−	2.68748i	0.648136	−	0.109443i
$604$	1.50769	−	0.726063i	0.0613468	−	0.0295431i
$605$	−2.22524	−	1.77457i	−0.0904688	−	0.0721464i
$606$	23.9363	−	4.74855i	0.972347	−	0.192897i
$607$	−7.24533	+	20.7060i	−0.294079	+	0.840430i	0.698144	+	0.715957i	$0.254009\pi$
$607$	−7.24533	+	20.7060i	−0.294079	+	0.840430i	−0.992223	+	0.124472i	$0.960276\pi$
$608$	3.13881			0.127295
$609$	9.68954	+	6.25507i	0.392640	+	0.253468i
$610$	−3.75848			−0.152176
$611$	0.200437	−	0.572816i	0.00810881	−	0.0231737i
$612$	1.19517	−	0.658955i	0.0483118	−	0.0266367i
$613$	25.8069	+	20.5803i	1.04233	+	0.831231i	0.985927	−	0.167177i	$-0.0534651\pi$
$613$	25.8069	+	20.5803i	1.04233	+	0.831231i	0.0564041	+	0.998408i	$0.482036\pi$
$614$	32.0841	−	15.4509i	1.29481	−	0.623547i
$615$	0.194084	−	1.36972i	0.00782623	−	0.0552323i
$616$	11.2037	+	14.0490i	0.451412	+	0.566052i
$617$	4.71470	−	2.96244i	0.189807	−	0.119263i	−0.433776	−	0.901021i	$-0.642819\pi$
$617$	4.71470	−	2.96244i	0.189807	−	0.119263i	0.623583	+	0.781757i	$0.285676\pi$
$618$	1.79076	+	21.3604i	0.0720349	+	0.859241i
$619$	3.19769	+	28.3803i	0.128526	+	1.14070i	0.877998	+	0.478665i	$0.158879\pi$
$619$	3.19769	+	28.3803i	0.128526	+	1.14070i	−0.749472	+	0.662037i	$0.769692\pi$
$620$	−0.0303084	−	0.0190440i	−0.00121721	−	0.000764827i
$621$	−8.40090	+	1.17291i	−0.337116	+	0.0470671i
$622$	17.7326	−	4.04734i	0.711011	−	0.162284i
$623$	2.61937	−	0.916556i	0.104943	−	0.0367211i
$624$	0.275133	−	0.206839i	0.0110141	−	0.00828018i
$625$	−5.42813	−	23.7822i	−0.217125	−	0.951288i
$626$	−3.43992	+	3.43992i	−0.137487	+	0.137487i
$627$	11.3593	−	43.9439i	0.453648	−	1.75495i
$628$	1.63862	−	0.184628i	0.0653881	−	0.00736747i
$629$	23.2894	+	5.31565i	0.928608	+	0.211949i
$630$	−0.394208	+	0.948963i	−0.0157056	+	0.0378076i
$631$	37.4582	−	29.8719i	1.49119	−	1.18918i	0.557971	−	0.829860i	$-0.311580\pi$
$631$	37.4582	−	29.8719i	1.49119	−	1.18918i	0.933214	−	0.359320i	$-0.116991\pi$
$632$	−3.78149	+	7.85235i	−0.150420	+	0.312350i
$633$	−19.5085	+	18.4248i	−0.775392	+	0.732320i
$634$	19.5124	−	24.4678i	0.774937	−	0.971740i
$635$	0.134580	−	1.19443i	0.00534065	−	0.0473995i
$636$	−1.53962	−	0.0439830i	−0.0610497	−	0.00174404i
$637$		−	0.287932i		−	0.0114083i
$638$	−26.6985	−	25.8411i	−1.05700	−	1.02306i
$639$	−8.19454	−	11.5741i	−0.324171	−	0.457865i
$640$	1.96259	+	0.686742i	0.0775784	+	0.0271458i
$641$	28.8456	+	3.25011i	1.13933	+	0.128372i	0.661406	−	0.750028i	$-0.269960\pi$
$641$	28.8456	+	3.25011i	1.13933	+	0.128372i	0.477926	+	0.878400i	$0.341389\pi$
$642$	1.29722	+	0.495933i	0.0511972	+	0.0195729i
$643$	−8.80588	−	18.2856i	−0.347270	−	0.721114i	0.652043	−	0.758182i	$-0.273912\pi$
$643$	−8.80588	−	18.2856i	−0.347270	−	0.721114i	−0.999313	+	0.0370684i	$0.988198\pi$
$644$	−0.193277	−	0.0930774i	−0.00761619	−	0.00366776i
$645$	−0.452909	+	0.677078i	−0.0178333	+	0.0266599i
$646$	16.3796	+	26.0680i	0.644448	+	1.02563i
$647$	−1.25790	+	5.51123i	−0.0494532	+	0.216669i	−0.993617	−	0.112809i	$-0.964015\pi$
$647$	−1.25790	+	5.51123i	−0.0494532	+	0.216669i	0.944164	+	0.329477i	$0.106872\pi$
$648$	5.85665	−	25.4206i	0.230071	−	0.998615i
$649$	27.1462	−	43.2030i	1.06558	−	1.69587i
$650$	0.253976	+	0.253976i	0.00996175	+	0.00996175i
$651$	3.08719	−	1.81896i	0.120996	−	0.0712908i
$652$	−0.848271	−	2.42422i	−0.0332209	−	0.0949397i
$653$	2.41775	+	6.90953i	0.0946138	+	0.270391i	0.981458	−	0.191678i	$-0.0613930\pi$
$653$	2.41775	+	6.90953i	0.0946138	+	0.270391i	−0.886844	+	0.462069i	$0.847107\pi$
$654$	−34.7999	+	20.5040i	−1.36078	+	0.801771i
$655$	2.28070	+	2.28070i	0.0891143	+	0.0891143i
$656$	7.97119	−	12.6861i	0.311223	−	0.495308i
$657$	−26.2958	+	23.4512i	−1.02590	+	0.914919i
$658$	−4.36616	+	19.1294i	−0.170211	+	0.745742i
$659$	−17.7469	−	28.2441i	−0.691322	−	1.10023i	−0.989333	−	0.145670i	$-0.953466\pi$
$659$	−17.7469	−	28.2441i	−0.691322	−	1.10023i	0.298012	−	0.954562i	$-0.403677\pi$
$660$	−0.103300	+	0.154429i	−0.00402095	+	0.00601114i
$661$	−2.90035	−	1.39673i	−0.112810	−	0.0543266i	0.376627	−	0.926365i	$-0.377084\pi$
$661$	−2.90035	−	1.39673i	−0.112810	−	0.0543266i	−0.489438	+	0.872038i	$0.662798\pi$
$662$	2.61693	+	5.43411i	0.101710	+	0.211203i
$663$	−0.364459	−	0.139334i	−0.0141544	−	0.00541130i
$664$	−35.7590	−	4.02907i	−1.38772	−	0.156358i
$665$	1.22791	+	0.429666i	0.0476165	+	0.0166617i
$666$	18.8035	−	13.3130i	0.728620	−	0.515867i
$667$	8.34389	+	2.76768i	0.323077	+	0.107165i
$668$			0.873846i			0.0338101i
$669$	5.64998	+	0.161406i	0.218441	+	0.00624032i
$670$	0.166877	−	1.48108i	0.00644703	−	0.0572190i
$671$	42.4136	−	53.1850i	1.63736	−	2.05318i
$672$	0.935066	−	0.883125i	0.0360710	−	0.0340673i
$673$	−0.243221	+	0.505053i	−0.00937547	+	0.0194684i	−0.905604	−	0.424124i	$-0.860582\pi$
$673$	−0.243221	+	0.505053i	−0.00937547	+	0.0194684i	0.896229	+	0.443593i	$0.146296\pi$
$674$	−12.2998	+	9.80878i	−0.473771	+	0.377820i
$675$	25.6757	+	2.20527i	0.988257	+	0.0848810i
$676$	−1.34670	−	0.307375i	−0.0517961	−	0.0118221i
$677$	40.8511	−	4.60281i	1.57003	−	0.176900i	0.716369	−	0.697722i	$-0.245803\pi$
$677$	40.8511	−	4.60281i	1.57003	−	0.176900i	0.853666	+	0.520821i	$0.174374\pi$
$678$	5.58956	−	21.6233i	0.214666	−	0.830439i
$679$	−8.37405	+	8.37405i	−0.321367	+	0.321367i
$680$	−0.555767	−	2.43497i	−0.0213127	−	0.0933769i
$681$	−6.33495	+	4.76248i	−0.242756	+	0.182499i
$682$	−10.8961	+	3.81272i	−0.417234	+	0.145996i
$683$	−41.7646	+	9.53251i	−1.59808	+	0.364751i	−0.926534	−	0.376212i	$-0.877227\pi$
$683$	−41.7646	+	9.53251i	−1.59808	+	0.364751i	−0.671546	+	0.740963i	$0.734369\pi$
$684$	−1.64257	−	0.280808i	−0.0628053	−	0.0107369i
$685$	2.31762	+	1.45625i	0.0885515	+	0.0556406i
$686$	2.37592	+	21.0868i	0.0907129	+	0.805099i
$687$	1.29510	+	15.4481i	0.0494111	+	0.589381i
$688$	−7.46999	+	4.69371i	−0.284791	+	0.178946i
$689$	0.274552	+	0.344277i	0.0104596	+	0.0131159i
$690$	−0.109887	+	0.775512i	−0.00418334	+	0.0295233i
$691$	−2.34491	+	1.12925i	−0.0892045	+	0.0429586i	−0.477954	−	0.878385i	$-0.658621\pi$
$691$	−2.34491	+	1.12925i	−0.0892045	+	0.0429586i	0.388750	+	0.921343i	$0.372907\pi$
$692$	−0.831954	−	0.663461i	−0.0316261	−	0.0252210i
$693$	−8.97991	−	16.2871i	−0.341119	−	0.618697i
$694$	1.76424	−	5.04190i	0.0669695	−	0.191388i
$695$	1.23129			0.0467056
$696$	−17.1138	+	20.9292i	−0.648697	+	0.793321i
$697$	−16.9837			−0.643305
$698$	7.54274	−	21.5559i	0.285497	−	0.815903i
$699$	24.5974	−	4.87969i	0.930360	−	0.184567i
$700$	0.509546	+	0.406350i	0.0192590	+	0.0153586i
$701$	0.235454	−	0.113389i	0.00889297	−	0.00428263i	−0.429432	−	0.903099i	$-0.641286\pi$
$701$	0.235454	−	0.113389i	0.00889297	−	0.00428263i	0.438325	+	0.898817i	$0.355572\pi$
$702$	−0.334601	+	0.172211i	−0.0126287	+	0.00649968i
$703$	−18.1857	−	22.8041i	−0.685885	−	0.860073i
$704$	−35.5707	+	22.3506i	−1.34062	+	0.842369i
$705$	−4.00658	+	0.335894i	−0.150897	+	0.0126505i
$706$	−0.794228	−	7.04897i	−0.0298912	−	0.265291i
$707$	−10.7189	−	6.73514i	−0.403126	−	0.253301i
$708$	−1.66389	−	0.860659i	−0.0625327	−	0.0323455i
$709$	−18.9397	+	4.32287i	−0.711296	+	0.162349i	−0.562835	−	0.826570i	$-0.690289\pi$
$709$	−18.9397	+	4.32287i	−0.711296	+	0.162349i	−0.148461	+	0.988918i	$0.547432\pi$
$710$	−1.23601	+	0.432500i	−0.0463868	+	0.0162314i
$711$	5.22748	−	7.35155i	0.196046	−	0.275705i
$712$	1.44756	+	6.34215i	0.0542494	+	0.237682i
$713$	1.93127	−	1.93127i	0.0723268	−	0.0723268i
$714$	12.2140	+	3.15727i	0.457097	+	0.118158i
$715$	0.0527834	−	0.00594726i	0.00197399	−	0.000222415i
$716$	0.0112350	+	0.00256432i	0.000419873	+	9.58333e-5i
$717$	24.3731	+	20.6025i	0.910229	+	0.769415i
$718$	−5.29873	+	4.22560i	−0.197747	+	0.157698i
$719$	7.14279	−	14.8321i	0.266381	−	0.553146i	−0.724278	−	0.689508i	$-0.757827\pi$
$719$	7.14279	−	14.8321i	0.266381	−	0.553146i	0.990659	+	0.136362i	$0.0435411\pi$
$720$	−1.99478	−	1.10513i	−0.0743410	−	0.0411859i
$721$	6.93311	−	8.69385i	0.258203	−	0.323776i
$722$	1.28136	−	11.3724i	0.0476872	−	0.423236i
$723$	−0.279092	+	9.76956i	−0.0103795	+	0.363334i
$724$		−	0.845080i		−	0.0314071i
$725$	−22.8428	−	13.8384i	−0.848361	−	0.513945i
$726$	10.2176	+	32.1138i	0.379209	+	1.19186i
$727$	−1.95140	−	0.682823i	−0.0723733	−	0.0253245i	0.293850	−	0.955852i	$-0.405064\pi$
$727$	−1.95140	−	0.682823i	−0.0723733	−	0.0253245i	−0.366223	+	0.930527i	$0.619349\pi$
$728$	−0.187429	−	0.0211181i	−0.00694656	−	0.000782690i
$729$	−10.4087	+	24.9130i	−0.385508	+	0.922705i
$730$	1.41163	+	2.93129i	0.0522469	+	0.108492i
$731$	9.01023	+	4.33910i	0.333255	+	0.160487i
$732$	−2.07591	−	1.38861i	−0.0767280	−	0.0513246i
$733$	4.16259	+	6.62472i	0.153749	+	0.244690i	0.914713	−	0.404104i	$-0.132417\pi$
$733$	4.16259	+	6.62472i	0.153749	+	0.244690i	−0.760964	+	0.648794i	$0.775274\pi$
$734$	−8.25873	+	36.1839i	−0.304835	+	1.33557i
$735$	−1.74162	+	0.778260i	−0.0642407	+	0.0287066i
$736$	0.521588	−	0.830102i	0.0192260	−	0.0305980i
$737$	19.0750	+	19.0750i	0.702638	+	0.702638i
$738$	−10.9272	+	12.2025i	−0.402237	+	0.449181i
$739$	−5.20519	−	14.8756i	−0.191476	−	0.547207i	0.807621	−	0.589702i	$-0.200755\pi$
$739$	−5.20519	−	14.8756i	−0.191476	−	0.547207i	−0.999097	+	0.0424952i	$0.986469\pi$
$740$	0.0394337	+	0.112695i	0.00144961	+	0.00414275i
$741$	0.241845	+	0.410466i	0.00888442	+	0.0150788i
$742$	−10.0673	−	10.0673i	−0.369582	−	0.369582i
$743$	−7.07352	+	11.2574i	−0.259502	+	0.412995i	−0.950909	−	0.309470i	$-0.899848\pi$
$743$	−7.07352	+	11.2574i	−0.259502	+	0.412995i	0.691407	+	0.722465i	$0.256991\pi$
$744$	3.42685	+	7.66875i	0.125634	+	0.281150i
$745$	0.583982	−	2.55859i	0.0213954	−	0.0937396i
$746$	−11.8212	−	18.8133i	−0.432805	−	0.688805i
$747$	35.7792	+	10.3473i	1.30909	+	0.378589i
$748$	2.05507	+	0.989668i	0.0751407	+	0.0361858i
$749$	−0.312592	−	0.649104i	−0.0114219	−	0.0237178i
$750$	1.70645	−	4.46359i	0.0623107	−	0.162987i
$751$	27.1878	+	3.06333i	0.992099	+	0.111783i	0.593066	−	0.805154i	$-0.297917\pi$
$751$	27.1878	+	3.06333i	0.992099	+	0.111783i	0.399033	+	0.916937i	$0.369346\pi$
$752$	−41.1008	−	14.3818i	−1.49879	−	0.524450i
$753$	−27.0040	+	8.59178i	−0.984080	+	0.313102i
$754$	0.389953	−	0.00636404i	0.0142013	−	0.000231765i
$755$			3.16960i			0.115354i
$756$	−0.568337	+	0.378495i	−0.0206702	+	0.0137657i
$757$	−3.96517	+	35.1919i	−0.144117	+	1.27907i	0.688506	+	0.725230i	$0.258267\pi$
$757$	−3.96517	+	35.1919i	−0.144117	+	1.27907i	−0.832623	+	0.553840i	$0.813162\pi$
$758$	−21.6640	+	27.1658i	−0.786872	+	0.986706i
$759$	−9.73395	−	10.3065i	−0.353320	−	0.374101i
$760$	−1.32315	+	2.74755i	−0.0479957	+	0.0996642i
$761$	1.48985	−	1.18812i	0.0540070	−	0.0430692i	−0.596114	−	0.802900i	$-0.703289\pi$
$761$	1.48985	−	1.18812i	0.0540070	−	0.0430692i	0.650121	+	0.759830i	$0.274718\pi$
$762$	−9.18768	+	10.8692i	−0.332834	+	0.393748i
$763$	20.4281	+	4.66258i	0.739547	+	0.168797i
$764$	2.04743	−	0.230690i	0.0740733	−	0.00834606i
$765$	0.142313	+	2.58113i	0.00514534	+	0.0933209i
$766$	10.6675	−	10.6675i	0.385432	−	0.385432i
$767$	0.119175	+	0.522138i	0.00430315	+	0.0188533i
$768$	2.64715	+	3.52118i	0.0955207	+	0.127060i
$769$	−6.66710	+	2.33292i	−0.240422	+	0.0841273i	−0.447800	−	0.894134i	$-0.647793\pi$
$769$	−6.66710	+	2.33292i	−0.240422	+	0.0841273i	0.207379	+	0.978261i	$0.433507\pi$
$770$	−1.67433	+	0.382155i	−0.0603387	+	0.0137719i
$771$	−4.46633	+	8.63463i	−0.160851	+	0.310969i
$772$	0.712873	+	0.447928i	0.0256569	+	0.0161213i
$773$	−5.01650	−	44.5226i	−0.180431	−	1.60137i	−0.678747	−	0.734372i	$-0.737477\pi$
$773$	−5.01650	−	44.5226i	−0.180431	−	1.60137i	0.498316	−	0.866995i	$-0.333952\pi$
$774$	8.91470	−	3.68195i	0.320432	−	0.132345i
$775$	−7.02588	+	4.41466i	−0.252377	+	0.158579i
$776$	−17.3088	−	21.7045i	−0.621349	−	0.779147i
$777$	−11.8337	−	1.67679i	−0.424531	−	0.0601546i
$778$	−0.0995101	+	0.0479216i	−0.00356761	+	0.00171807i
$779$	16.2129	+	12.9294i	0.580887	+	0.463242i
$780$	−0.000379484	−	0.00191289i	−1.35877e−5	−	6.84925e-5i
$781$	7.82797	−	22.3711i	0.280107	−	0.800500i
$782$	9.61592			0.343865
$783$	21.1101	−	18.3675i	0.754413	−	0.656400i
$784$	−20.6597			−0.737847
$785$	−1.03158	+	2.94809i	−0.0368187	+	0.105222i
$786$	−7.43142	−	37.4601i	−0.265070	−	1.33616i
$787$	26.8317	+	21.3975i	0.956446	+	0.762740i	0.971474	−	0.237147i	$-0.0762122\pi$
$787$	26.8317	+	21.3975i	0.956446	+	0.762740i	−0.0150278	+	0.999887i	$0.504784\pi$
$788$	−2.57549	+	1.24029i	−0.0917481	+	0.0441836i
$789$	16.0308	+	2.27151i	0.570711	+	0.0808678i
$790$	−0.519343	−	0.651235i	−0.0184774	−	0.0231699i
$791$	−9.81024	+	6.16418i	−0.348812	+	0.219173i
$792$	40.2964	−	16.6432i	1.43187	−	0.591390i
$793$	0.0799461	+	0.709541i	0.00283897	+	0.0251965i
$794$	−11.2355	−	7.05972i	−0.398732	−	0.250540i
$795$	1.34035	−	2.59125i	0.0475372	−	0.0919022i
$796$	−0.700203	+	0.159817i	−0.0248180	+	0.00566455i
$797$	−35.3813	+	12.3804i	−1.25327	+	0.438538i	−0.873627	−	0.486596i	$-0.838238\pi$
$797$	−35.3813	+	12.3804i	−1.25327	+	0.438538i	−0.379641	+	0.925134i	$0.623953\pi$
$798$	−9.25607	−	12.3122i	−0.327661	−	0.435848i
$799$	10.9838	+	48.1230i	0.388577	+	1.70247i
$800$	−2.10608	+	2.10608i	−0.0744611	+	0.0744611i
$801$	−0.370670	−	6.72284i	−0.0130970	−	0.237540i
$802$	−43.5798	+	4.91027i	−1.53886	+	0.173388i
$803$	−57.4096	−	13.1034i	−2.02594	−	0.462408i
$804$	0.639372	−	0.756386i	0.0225489	−	0.0266757i
$805$	0.317678	−	0.253340i	0.0111967	−	0.00892906i
$806$	0.0525736	−	0.109170i	0.00185183	−	0.00384536i
$807$	3.26658	+	3.45870i	0.114989	+	0.121752i
$808$	18.5022	−	23.2011i	0.650907	−	0.816211i
$809$	−0.106877	+	0.948559i	−0.00375759	+	0.0333496i	−0.995451	−	0.0952739i	$-0.969627\pi$
$809$	−0.106877	+	0.948559i	−0.00375759	+	0.0333496i	0.991693	+	0.128623i	$0.0410559\pi$
$810$	1.94606	+	1.55844i	0.0683777	+	0.0547579i
$811$			17.4680i			0.613383i	0.951809	+	0.306692i	$0.0992220\pi$
$811$			17.4680i			0.613383i	−0.951809	+	0.306692i	$0.900778\pi$
$812$	0.701839	−	0.0906990i	0.0246297	−	0.00318291i
$813$	−15.3348	+	4.87904i	−0.537816	+	0.171115i
$814$	36.3444	+	12.7174i	1.27387	+	0.445746i
$815$	4.83413	+	0.544675i	0.169332	+	0.0190791i
$816$	−9.99755	+	26.1508i	−0.349984	+	0.915460i
$817$	−5.29802	−	11.0015i	−0.185354	−	0.384892i
$818$	7.37826	+	3.55318i	0.257975	+	0.124234i
$819$	0.187534	+	0.0542348i	0.00655298	+	0.00189512i
$820$	−0.0451619	−	0.0718747i	−0.00157712	−	0.00250997i
$821$	0.733924	−	3.21553i	0.0256141	−	0.112223i	−0.960505	−	0.278263i	$-0.910241\pi$
$821$	0.733924	−	3.21553i	0.0256141	−	0.112223i	0.986119	+	0.166041i	$0.0530983\pi$
$822$	−13.2222	−	29.5892i	−0.461178	−	1.03204i
$823$	−28.5068	+	45.3682i	−0.993683	+	1.58144i	−0.194012	+	0.980999i	$0.562150\pi$
$823$	−28.5068	+	45.3682i	−0.993683	+	1.58144i	−0.799671	+	0.600439i	$0.794993\pi$
$824$	18.4319	+	18.4319i	0.642106	+	0.642106i
$825$	21.8636	+	37.1074i	0.761192	+	1.29191i
$826$	−5.71908	−	16.3442i	−0.198992	−	0.568687i
$827$	−10.3930	−	29.7015i	−0.361400	−	1.03282i	−0.970786	−	0.239947i	$-0.922870\pi$
$827$	−10.3930	−	29.7015i	−0.361400	−	1.03282i	0.609386	−	0.792873i	$-0.291416\pi$
$828$	−0.347216	+	0.387738i	−0.0120666	+	0.0134748i
$829$	−6.52615	−	6.52615i	−0.226663	−	0.226663i	0.584634	−	0.811297i	$-0.301238\pi$
$829$	−6.52615	−	6.52615i	−0.226663	−	0.226663i	−0.811297	+	0.584634i	$0.801238\pi$
$830$	1.82978	−	2.91207i	0.0635124	−	0.101079i
$831$	2.00031	−	0.893859i	0.0693901	−	0.0310076i
$832$	0.0981212	−	0.429897i	0.00340174	−	0.0149040i
$833$	12.4598	+	19.8296i	0.431706	+	0.687056i
$834$	−12.1179	−	8.10586i	−0.419609	−	0.280683i
$835$	−1.49124	−	0.718145i	−0.0516066	−	0.0248524i
$836$	−1.20838	−	2.50923i	−0.0417927	−	0.0867835i
$837$	−2.15861	−	8.42146i	−0.0746123	−	0.291088i
$838$	−28.6341	−	3.22629i	−0.989149	−	0.111450i
$839$	36.4369	+	12.7498i	1.25794	+	0.440173i	0.875236	−	0.483697i	$-0.160706\pi$
$839$	36.4369	+	12.7498i	1.25794	+	0.440173i	0.382707	+	0.923870i	$0.374992\pi$
$840$	0.378869	+	1.19079i	0.0130722	+	0.0410860i
$841$	−28.0473	+	7.37225i	−0.967148	+	0.254216i
$842$		−	38.3834i		−	1.32278i
$843$	−0.649701	+	22.7426i	−0.0223769	+	0.783298i
$844$	−0.184353	+	1.63617i	−0.00634567	+	0.0563194i
$845$	1.63129	−	2.04557i	0.0561181	−	0.0703698i
$846$	41.6425	+	23.0704i	1.43170	+	0.793178i
$847$	7.58531	−	15.7511i	0.260634	−	0.541213i
$848$	24.7027	−	19.6997i	0.848293	−	0.676491i
$849$	−7.21877	−	6.10202i	−0.247748	−	0.209421i
$850$	−28.4815	−	6.50072i	−0.976908	−	0.222973i
$851$	−9.05285	+	1.02001i	−0.310328	+	0.0349655i
$852$	−0.842477	−	0.217777i	−0.0288628	−	0.00746093i
$853$	23.7372	−	23.7372i	0.812747	−	0.812747i	−0.172298	−	0.985045i	$-0.555119\pi$
$853$	23.7372	−	23.7372i	0.812747	−	0.812747i	0.985045	+	0.172298i	$0.0551191\pi$
$854$	−5.13712	−	22.5072i	−0.175789	−	0.770181i
$855$	1.82911	−	2.57232i	0.0625541	−	0.0879715i
$856$	1.59408	−	0.557792i	0.0544844	−	0.0190649i
$857$	32.1563	−	7.33946i	1.09844	−	0.250711i	0.365367	−	0.930864i	$-0.380944\pi$
$857$	32.1563	−	7.33946i	1.09844	−	0.250711i	0.733071	+	0.680153i	$0.238087\pi$
$858$	−0.558626	−	0.288954i	−0.0190712	−	0.00986472i
$859$	−25.6374	−	16.1091i	−0.874738	−	0.549635i	0.0181893	−	0.999835i	$-0.494210\pi$
$859$	−25.6374	−	16.1091i	−0.874738	−	0.549635i	−0.892928	+	0.450200i	$0.851353\pi$
$860$	0.00559638	+	0.0496693i	0.000190835	+	0.00169371i
$861$	8.46766	−	0.709891i	0.288577	−	0.0241930i
$862$	14.0213	−	8.81014i	0.477566	−	0.300074i
$863$	1.09868	+	1.37770i	0.0373995	+	0.0468975i	0.800180	−	0.599761i	$-0.204738\pi$
$863$	1.09868	+	1.37770i	0.0373995	+	0.0468975i	−0.762780	+	0.646658i	$0.776166\pi$
$864$	−1.42805	−	2.77465i	−0.0485832	−	0.0943956i
$865$	1.81593	−	0.874507i	0.0617435	−	0.0297341i
$866$	12.7011	+	10.1288i	0.431600	+	0.344190i
$867$	2.24749	−	0.445863i	0.0763288	−	0.0151423i
$868$	0.0726171	−	0.207528i	0.00246479	−	0.00704395i
$869$	15.0761			0.511420
$870$	−1.09251	−	2.34152i	−0.0370397	−	0.0793851i
$871$	−0.283153			−0.00959429
$872$	−16.2227	+	46.3618i	−0.549369	+	1.57001i
$873$	13.8732	+	25.1622i	0.469535	+	0.851610i
$874$	−9.17949	−	7.32040i	−0.310501	−	0.247616i
$875$	−2.23349	+	1.07559i	−0.0755059	+	0.0363617i
$876$	−0.303312	+	2.14058i	−0.0102480	+	0.0723234i
$877$	12.9858	+	16.2837i	0.438499	+	0.549861i	0.951147	−	0.308738i	$-0.0999068\pi$
$877$	12.9858	+	16.2837i	0.438499	+	0.549861i	−0.512648	+	0.858599i	$0.671335\pi$
$878$	11.7866	−	7.40601i	0.397779	−	0.249941i
$879$	−3.09150	−	36.8758i	−0.104274	−	1.24379i
$880$	−0.426729	−	3.78733i	−0.0143850	−	0.127671i
$881$	42.0226	+	26.4045i	1.41578	+	0.889591i	0.999804	−	0.0197859i	$-0.00629845\pi$
$881$	42.0226	+	26.4045i	1.41578	+	0.889591i	0.415972	+	0.909377i	$0.363441\pi$
$882$	22.2638	+	3.80614i	0.749662	+	0.128159i
$883$	15.1608	−	3.46036i	0.510202	−	0.116450i	0.0403330	−	0.999186i	$-0.487158\pi$
$883$	15.1608	−	3.46036i	0.510202	−	0.116450i	0.469869	+	0.882736i	$0.344301\pi$
$884$	−0.0225983	+	0.00790749i	−0.000760063	+	0.000265958i
$885$	2.83616	−	2.13216i	0.0953363	−	0.0716718i
$886$	−1.09044	−	4.77755i	−0.0366342	−	0.160505i
$887$	8.73289	−	8.73289i	0.293222	−	0.293222i	−0.545130	−	0.838352i	$-0.683520\pi$
$887$	8.73289	−	8.73289i	0.293222	−	0.293222i	0.838352	+	0.545130i	$0.183520\pi$
$888$	7.01184	−	27.1255i	0.235302	−	0.910271i
$889$	7.33665	−	0.826642i	0.246063	−	0.0277247i
$890$	−0.606138	−	0.138347i	−0.0203178	−	0.00463741i
$891$	−44.0138	+	9.95146i	−1.47452	+	0.333387i
$892$	0.271159	−	0.216242i	0.00907907	−	0.00724031i
$893$	26.1498	−	54.3006i	0.875069	−	1.81710i
$894$	−22.5911	+	21.3362i	−0.755559	+	0.713589i
$895$	−0.0136093	+	0.0170655i	−0.000454908	+	0.000570437i
$896$	−1.42998	+	12.6914i	−0.0477722	+	0.423990i
$897$	0.148742	+	0.00424919i	0.00496634	+	0.000141876i
$898$			16.1848i			0.540093i
$899$	−1.86130	+	8.81559i	−0.0620778	+	0.294017i
$900$	1.29055	−	0.913716i	0.0430183	−	0.0304572i
$901$	−33.8062	−	11.8293i	−1.12625	−	0.394092i
$902$	−27.2036	−	3.06511i	−0.905782	−	0.102057i
$903$	−4.67364	−	1.78675i	−0.155529	−	0.0594594i
$904$	−11.7841	−	24.4700i	−0.391934	−	0.813859i
$905$	1.44215	+	0.694504i	0.0479388	+	0.0230861i
$906$	20.8662	−	31.1940i	0.693232	−	1.03635i
$907$	−15.3060	−	24.3593i	−0.508226	−	0.808838i	0.489787	−	0.871842i	$-0.337075\pi$
$907$	−15.3060	−	24.3593i	−0.508226	−	0.808838i	−0.998013	+	0.0630046i	$0.979932\pi$
$908$	−0.108213	+	0.474114i	−0.00359119	+	0.0157340i
$909$	−22.9228	+	20.4431i	−0.760302	+	0.678055i
$910$	0.00959065	−	0.0152634i	0.000317927	−	0.000505978i
$911$	−32.1348	−	32.1348i	−1.06467	−	1.06467i	−0.997759	−	0.0669161i	$-0.978684\pi$
$911$	−32.1348	−	32.1348i	−1.06467	−	1.06467i	−0.0669161	−	0.997759i	$-0.521316\pi$
$912$	29.4518	−	17.3530i	0.975247	−	0.574614i
$913$	20.5591	+	58.7546i	0.680407	+	1.94449i
$914$	2.46178	+	7.03535i	0.0814283	+	0.232709i
$915$	4.07574	−	2.40142i	0.134740	−	0.0793884i
$916$	0.672615	+	0.672615i	0.0222238	+	0.0222238i
$917$	−10.5404	+	16.7750i	−0.348075	+	0.553958i
$918$	15.5915	−	26.3393i	0.514597	−	0.869328i
$919$	−2.72385	+	11.9340i	−0.0898517	+	0.393666i	−0.999777	−	0.0211057i	$-0.993281\pi$
$919$	−2.72385	+	11.9340i	−0.0898517	+	0.393666i	0.909926	+	0.414772i	$0.136138\pi$
$920$	0.506755	+	0.806497i	0.0167072	+	0.0265894i
$921$	−24.9203	+	37.2547i	−0.821151	+	1.22758i
$922$	47.4270	+	22.8396i	1.56192	+	0.752183i
$923$	0.107940	+	0.224140i	0.00355289	+	0.00737766i
$924$	−1.06597	−	0.407525i	−0.0350679	−	0.0134066i
$925$	27.5033	+	3.09888i	0.904304	+	0.101891i
$926$	−0.201278	−	0.0704301i	−0.00661440	−	0.00231448i
$927$	−15.5898	−	22.0193i	−0.512035	−	0.723207i
$928$	0.0527733	+	3.23366i	0.00173237	+	0.106150i
$929$			10.7334i			0.352151i	0.984377	+	0.176075i	$0.0563403\pi$
$929$			10.7334i			0.352151i	−0.984377	+	0.176075i	$0.943660\pi$
$930$	−0.802445	−	0.0229239i	−0.0263132	−	0.000751704i
$931$	3.20160	−	28.4150i	0.104928	−	0.931264i
$932$	0.959373	−	1.20302i	0.0314253	−	0.0394061i
$933$	−16.6434	+	15.7189i	−0.544881	+	0.514614i
$934$	−0.495727	+	1.02939i	−0.0162207	+	0.0336826i
$935$	−3.37779	+	2.69370i	−0.110466	+	0.0880934i
$936$	−0.175556	+	0.422611i	−0.00573823	+	0.0138135i
$937$	31.8652	+	7.27303i	1.04099	+	0.237600i	0.708651	−	0.705560i	$-0.249304\pi$
$937$	31.8652	+	7.27303i	1.04099	+	0.237600i	0.332341	+	0.943159i	$0.392161\pi$
$938$	9.09734	−	1.02502i	0.297039	−	0.0334682i
$939$	1.53241	−	5.92817i	0.0500083	−	0.193458i
$940$	−0.174448	+	0.174448i	−0.00568987	+	0.00568987i
$941$	−8.57290	−	37.5603i	−0.279469	−	1.22443i	−0.898467	−	0.439040i	$-0.855319\pi$
$941$	−8.57290	−	37.5603i	−0.279469	−	1.22443i	0.618999	−	0.785392i	$-0.287539\pi$
$942$	29.5603	−	22.2228i	0.963126	−	0.724058i
$943$	6.11351	−	2.13921i	0.199083	−	0.0696622i
$944$	37.4646	−	8.55105i	1.21937	−	0.278313i
$945$	−0.178841	−	1.28094i	−0.00581769	−	0.0416689i
$946$	13.6490	+	8.57625i	0.443768	+	0.278838i
$947$	−1.70897	−	15.1675i	−0.0555340	−	0.492878i	−0.990436	−	0.137972i	$-0.955942\pi$
$947$	−1.70897	−	15.1675i	−0.0555340	−	0.492878i	0.934902	−	0.354906i	$-0.115487\pi$
$948$	−0.0462414	−	0.551572i	−0.00150185	−	0.0179142i
$949$	0.523354	−	0.328845i	0.0169888	−	0.0106748i
$950$	22.2400	+	27.8881i	0.721560	+	0.904808i
$951$	−5.52620	+	39.0003i	−0.179199	+	1.26467i
$952$	13.8219	−	6.65628i	0.447971	−	0.215731i
$953$	−10.5105	−	8.38186i	−0.340469	−	0.271515i	0.438296	−	0.898831i	$-0.355582\pi$
$953$	−10.5105	−	8.38186i	−0.340469	−	0.271515i	−0.778765	+	0.627316i	$0.784154\pi$
$954$	−30.2499	+	16.6783i	−0.979378	+	0.539980i
$955$	−1.28894	+	3.68358i	−0.0417091	+	0.119198i
$956$	1.95826			0.0633345
$957$	45.4629	+	10.9638i	1.46961	+	0.354409i
$958$	8.69363			0.280878
$959$	−5.55287	+	15.8692i	−0.179311	+	0.512443i
$960$	−2.86555	+	0.568475i	−0.0924852	+	0.0183474i
$961$	−22.0482	−	17.5829i	−0.711233	−	0.567189i
$962$	−0.364141	+	0.175361i	−0.0117404	+	0.00565387i
$963$	−1.72359	+	0.291041i	−0.0555418	+	0.00937868i
$964$	0.373911	+	0.468869i	0.0120428	+	0.0151013i
$965$	−1.35026	+	0.848422i	−0.0434663	+	0.0273117i
$966$	−4.79426	+	0.401929i	−0.154253	+	0.0129319i
$967$	−5.35846	−	47.5576i	−0.172316	−	1.52935i	−0.720773	−	0.693171i	$-0.756213\pi$
$967$	−5.35846	−	47.5576i	−0.172316	−	1.52935i	0.548457	−	0.836179i	$-0.315216\pi$
$968$	34.6999	+	21.8034i	1.11530	+	0.700788i
$969$	−34.4180	−	17.8030i	−1.10566	−	0.571914i
$970$	2.58669	−	0.590395i	0.0830536	−	0.0189564i
$971$	−30.5381	+	10.6858i	−0.980015	+	0.342922i	−0.772294	−	0.635266i	$-0.780891\pi$
$971$	−30.5381	+	10.6858i	−0.980015	+	0.342922i	−0.207722	+	0.978188i	$0.566605\pi$
$972$	0.499083	+	1.57976i	0.0160081	+	0.0506709i
$973$	1.68294	+	7.37345i	0.0539526	+	0.236382i
$974$	−0.541310	+	0.541310i	−0.0173447	+	0.0173447i
$975$	−0.437688	−	0.113141i	−0.0140172	−	0.00362340i
$976$	50.9112	−	5.73631i	1.62963	−	0.183615i
$977$	11.9643	+	2.73076i	0.382770	+	0.0873648i	0.409576	−	0.912276i	$-0.365677\pi$
$977$	11.9643	+	2.73076i	0.382770	+	0.0873648i	−0.0268060	+	0.999641i	$0.508534\pi$
$978$	−43.9899	−	37.1846i	−1.40664	−	1.18903i
$979$	8.79783	−	7.01604i	0.281180	−	0.224234i
$980$	−0.0507863	+	0.105459i	−0.00162231	+	0.00336876i
$981$	24.6367	−	44.4696i	0.786589	−	1.41980i
$982$	−25.9758	+	32.5727i	−0.828923	+	1.03944i
$983$	−0.725337	+	6.43754i	−0.0231347	+	0.205326i	−0.999962	−	0.00870246i	$-0.997230\pi$
$983$	−0.725337	+	6.43754i	−0.0231347	+	0.205326i	0.976827	+	0.214028i	$0.0686585\pi$
$984$	−0.568809	+	19.9110i	−0.0181330	+	0.634740i
$985$		−	5.41445i		−	0.172519i
$986$	−26.5804	+	17.3129i	−0.846492	+	0.551355i
$987$	−7.48769	−	23.5338i	−0.238336	−	0.749090i
$988$	0.0275924	+	0.00965501i	0.000877833	+	0.000307167i
$989$	−3.78988	−	0.427017i	−0.120511	−	0.0135784i
$990$	−0.237876	+	4.16000i	−0.00756020	+	0.132214i
$991$	22.0986	+	45.8883i	0.701986	+	1.45769i	0.880645	+	0.473777i	$0.157110\pi$
$991$	22.0986	+	45.8883i	0.701986	+	1.45769i	−0.178659	+	0.983911i	$0.557176\pi$
$992$	0.905287	+	0.435963i	0.0287429	+	0.0138419i
$993$	−6.30986	−	4.22077i	−0.200237	−	0.133942i
$994$	−4.27937	−	6.81057i	−0.135733	−	0.216018i
$995$	0.302709	−	1.32626i	0.00959654	−	0.0420452i
$996$	2.08653	−	0.932387i	0.0661144	−	0.0295438i
$997$	17.4343	−	27.7466i	0.552151	−	0.878744i	−0.447730	−	0.894169i	$-0.647767\pi$
$997$	17.4343	−	27.7466i	0.552151	−	0.878744i	0.999881	+	0.0154252i	$0.00491019\pi$
$998$	8.83510	+	8.83510i	0.279670	+	0.279670i
$999$	−11.8846	+	26.4509i	−0.376012	+	0.836869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.8.6	yes	96
3.2	odd	2	inner	87.2.k.a.8.3	✓	96
29.11	odd	28	inner	87.2.k.a.11.3	yes	96
87.11	even	28	inner	87.2.k.a.11.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.3	✓	96	3.2	odd	2	inner
87.2.k.a.8.6	yes	96	1.1	even	1	trivial
87.2.k.a.11.3	yes	96	29.11	odd	28	inner
87.2.k.a.11.6	yes	96	87.11	even	28	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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.454505 - 1.29890i) q^{2} +(0.337040 + 1.69894i) q^{3} +(0.0830922 + 0.0662638i) q^{4} +(-0.181368 + 0.0873422i) q^{5} +(2.35995 + 0.334396i) q^{6} +(-0.770934 - 0.966720i) q^{7} +(2.45423 - 1.54210i) q^{8} +(-2.77281 + 1.14522i) q^{9} +(0.0310162 + 0.275277i) q^{10} +(-4.24536 - 2.66753i) q^{11} +(-0.0845730 + 0.163502i) q^{12} +(0.0513081 - 0.0117107i) q^{13} +(-1.60607 + 0.561988i) q^{14} +(-0.209518 - 0.278696i) q^{15} +(-0.840272 - 3.68147i) q^{16} +(-3.02679 + 3.02679i) q^{17} +(0.227277 + 4.12212i) q^{18} +(5.19364 - 0.585183i) q^{19} +(-0.0208579 - 0.00476068i) q^{20} +(1.38257 - 1.63560i) q^{21} +(-5.39440 + 4.30189i) q^{22} +(0.708287 - 1.47077i) q^{23} +(3.44711 + 3.64985i) q^{24} +(-3.09218 + 3.87748i) q^{25} +(0.00810871 - 0.0719668i) q^{26} +(-2.88022 - 4.32485i) q^{27} -0.131412i q^{28} +(0.690188 + 5.34075i) q^{29} +(-0.457225 + 0.145474i) q^{30} +(1.57922 + 0.552592i) q^{31} +(0.596780 + 0.0672409i) q^{32} +(3.10113 - 8.11168i) q^{33} +(2.55581 + 5.30719i) q^{34} +(0.224258 + 0.107997i) q^{35} +(-0.306286 - 0.0885777i) q^{36} +(-2.96911 - 4.72531i) q^{37} +(1.60044 - 7.01200i) q^{38} +(0.0371888 + 0.0832225i) q^{39} +(-0.310429 + 0.494045i) q^{40} +(2.80557 + 2.80557i) q^{41} +(-1.49609 - 2.53920i) q^{42} +(-0.771632 - 2.20520i) q^{43} +(-0.175995 - 0.502965i) q^{44} +(0.402872 - 0.449890i) q^{45} +(-1.58847 - 1.58847i) q^{46} +(6.13509 - 9.76394i) q^{47} +(5.97140 - 2.66838i) q^{48} +(1.21744 - 5.33394i) q^{49} +(3.63105 + 5.77878i) q^{50} +(-6.16248 - 4.12219i) q^{51} +(0.00503930 + 0.00242680i) q^{52} +(3.63041 + 7.53862i) q^{53} +(-6.92663 + 1.77545i) q^{54} +(1.00296 + 0.113006i) q^{55} +(-3.38283 - 1.18370i) q^{56} +(2.74466 + 8.62646i) q^{57} +(7.25081 + 1.53091i) q^{58} +10.1765i q^{59} +(0.00105817 - 0.0370409i) q^{60} +(-1.51909 + 13.4823i) q^{61} +(1.43552 - 1.80009i) q^{62} +(3.24476 + 1.79764i) q^{63} +(3.63540 - 7.54898i) q^{64} +(-0.00828281 + 0.00660532i) q^{65} +(-9.12680 - 7.71487i) q^{66} +(-5.24543 - 1.19723i) q^{67} +(-0.452069 + 0.0509359i) q^{68} +(2.73748 + 0.707629i) q^{69} +(0.242204 - 0.242204i) q^{70} +(1.05188 + 4.60860i) q^{71} +(-5.03907 + 7.08658i) q^{72} +(11.0856 - 3.87901i) q^{73} +(-7.48719 + 1.70890i) q^{74} +(-7.62980 - 3.94657i) q^{75} +(0.470327 + 0.295526i) q^{76} +(0.694129 + 6.16056i) q^{77} +(0.125000 - 0.0104795i) q^{78} +(-2.54600 + 1.59976i) q^{79} +(0.473946 + 0.594310i) q^{80} +(6.37693 - 6.35097i) q^{81} +(4.91931 - 2.36901i) q^{82} +(-9.70654 - 7.74070i) q^{83} +(0.223261 - 0.0442911i) q^{84} +(0.284596 - 0.813329i) q^{85} -3.21505 q^{86} +(-8.84101 + 2.97264i) q^{87} -14.5327 q^{88} +(-0.741261 + 2.11840i) q^{89} +(-0.401255 - 0.727769i) q^{90} +(-0.0508762 - 0.0405724i) q^{91} +(0.156312 - 0.0752760i) q^{92} +(-0.406562 + 2.86924i) q^{93} +(-9.89397 - 12.4066i) q^{94} +(-0.890849 + 0.559758i) q^{95} +(0.0869004 + 1.03656i) q^{96} +(-1.07237 - 9.51752i) q^{97} +(-6.37493 - 4.00564i) q^{98} +(14.8265 + 2.53468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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