LMFDB - Embedded newform 87.2.k.a.8.3

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			8.3
Character	$\chi$	$=$	87.8
Dual form			87.2.k.a.11.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.454505 + 1.29890i) q^{2} +(-0.706640 + 1.58135i) q^{3} +(0.0830922 + 0.0662638i) q^{4} +(0.181368 - 0.0873422i) q^{5} +(-1.73284 - 1.63659i) q^{6} +(-0.770934 - 0.966720i) q^{7} +(-2.45423 + 1.54210i) q^{8} +(-2.00132 - 2.23489i) q^{9} +(0.0310162 + 0.275277i) q^{10} +(4.24536 + 2.66753i) q^{11} +(-0.163502 + 0.0845730i) q^{12} +(0.0513081 - 0.0117107i) q^{13} +(1.60607 - 0.561988i) q^{14} +(0.00995651 + 0.348525i) q^{15} +(-0.840272 - 3.68147i) q^{16} +(3.02679 - 3.02679i) q^{17} +(3.81251 - 1.58375i) q^{18} +(5.19364 - 0.585183i) q^{19} +(0.0208579 + 0.00476068i) q^{20} +(2.07349 - 0.535991i) q^{21} +(-5.39440 + 4.30189i) q^{22} +(-0.708287 + 1.47077i) q^{23} +(-0.704332 - 4.97070i) q^{24} +(-3.09218 + 3.87748i) q^{25} +(-0.00810871 + 0.0719668i) q^{26} +(4.94835 - 1.58552i) 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} +(-7.21824 + 4.82840i) q^{33} +(2.55581 + 5.30719i) q^{34} +(-0.224258 - 0.107997i) q^{35} +(-0.0182019 - 0.318317i) q^{36} +(-2.96911 - 4.72531i) q^{37} +(-1.60044 + 7.01200i) q^{38} +(-0.0177376 + 0.0894112i) q^{39} +(-0.310429 + 0.494045i) q^{40} +(-2.80557 - 2.80557i) q^{41} +(-0.246215 + 2.93687i) q^{42} +(-0.771632 - 2.20520i) q^{43} +(0.175995 + 0.502965i) q^{44} +(-0.558175 - 0.230537i) q^{45} +(-1.58847 - 1.58847i) q^{46} +(-6.13509 + 9.76394i) q^{47} +(6.41545 + 1.27271i) q^{48} +(1.21744 - 5.33394i) q^{49} +(-3.63105 - 5.77878i) q^{50} +(2.64755 + 6.92525i) q^{51} +(0.00503930 + 0.00242680i) q^{52} +(-3.63041 - 7.53862i) q^{53} +(-0.189614 + 7.14804i) 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} +(-0.0222673 + 0.0296195i) q^{60} +(-1.51909 + 13.4823i) q^{61} +(-1.43552 + 1.80009i) q^{62} +(-0.617626 + 3.65767i) q^{63} +(3.63540 - 7.54898i) q^{64} +(0.00828281 - 0.00660532i) q^{65} +(-2.99089 - 11.5703i) q^{66} +(-5.24543 - 1.19723i) q^{67} +(0.452069 - 0.0509359i) q^{68} +(-1.82530 - 2.15936i) q^{69} +(0.242204 - 0.242204i) q^{70} +(-1.05188 - 4.60860i) q^{71} +(8.35812 + 2.39871i) q^{72} +(11.0856 - 3.87901i) q^{73} +(7.48719 - 1.70890i) q^{74} +(-3.94657 - 7.62980i) q^{75} +(0.470327 + 0.295526i) q^{76} +(-0.694129 - 6.16056i) q^{77} +(-0.108075 - 0.0636773i) q^{78} +(-2.54600 + 1.59976i) q^{79} +(-0.473946 - 0.594310i) q^{80} +(-0.989440 + 8.94545i) q^{81} +(4.91931 - 2.36901i) q^{82} +(9.70654 + 7.74070i) q^{83} +(0.207808 + 0.0928609i) q^{84} +(0.284596 - 0.813329i) q^{85} +3.21505 q^{86} +(8.93330 + 2.68256i) q^{87} -14.5327 q^{88} +(0.741261 - 2.11840i) q^{89} +(0.553139 - 0.620234i) q^{90} +(-0.0508762 - 0.0405724i) q^{91} +(-0.156312 + 0.0752760i) q^{92} +(-1.98978 + 2.10681i) q^{93} +(-9.89397 - 12.4066i) q^{94} +(0.890849 - 0.559758i) q^{95} +(0.528040 - 0.896201i) q^{96} +(-1.07237 - 9.51752i) q^{97} +(6.37493 + 4.00564i) q^{98} +(-2.53468 - 14.8265i) 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	$0.268882\pi$
$2$	−0.454505	+	1.29890i	−0.321384	+	0.918462i	−0.985327	+	0.170679i	$0.945404\pi$
$3$	−0.706640	+	1.58135i	−0.407979	+	0.912991i
$3$	−0.706640	+	1.58135i	−0.407979	+	0.912991i
$4$	0.0830922	+	0.0662638i	0.0415461	+	0.0331319i
$5$	0.181368	−	0.0873422i	0.0811102	−	0.0390606i	−0.392889	−	0.919586i	$-0.628524\pi$
$5$	0.181368	−	0.0873422i	0.0811102	−	0.0390606i	0.473999	+	0.880525i	$0.342810\pi$
$6$	−1.73284	−	1.63659i	−0.707430	−	0.668134i
$7$	−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
$9$	−2.00132	−	2.23489i	−0.667107	−	0.744962i
$10$	0.0310162	+	0.275277i	0.00980820	+	0.0870501i
$11$	4.24536	+	2.66753i	1.28002	+	0.804292i	0.988346	−	0.152225i	$-0.0486438\pi$
$11$	4.24536	+	2.66753i	1.28002	+	0.804292i	0.291677	+	0.956517i	$0.405787\pi$
$12$	−0.163502	+	0.0845730i	−0.0471991	+	0.0244141i
$13$	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
$15$	0.00995651	+	0.348525i	0.00257076	+	0.0899889i
$16$	−0.840272	−	3.68147i	−0.210068	−	0.920368i
$17$	3.02679	−	3.02679i	0.734104	−	0.734104i	−0.237326	−	0.971430i	$-0.576271\pi$
$17$	3.02679	−	3.02679i	0.734104	−	0.734104i	0.971430	+	0.237326i	$0.0762711\pi$
$18$	3.81251	−	1.58375i	0.898617	−	0.373293i
$19$	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
$21$	2.07349	−	0.535991i	0.452473	−	0.116963i
$22$	−5.39440	+	4.30189i	−1.15009	+	0.917167i
$23$	−0.708287	+	1.47077i	−0.147688	+	0.306677i	−0.961668	−	0.274215i	$-0.911582\pi$
$23$	−0.708287	+	1.47077i	−0.147688	+	0.306677i	0.813980	+	0.580892i	$0.197296\pi$
$24$	−0.704332	−	4.97070i	−0.143771	−	1.01464i
$25$	−3.09218	+	3.87748i	−0.618437	+	0.775495i
$26$	−0.00810871	+	0.0719668i	−0.00159025	+	0.0141139i
$27$	4.94835	−	1.58552i	0.952310	−	0.305134i
$28$		−	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
$33$	−7.21824	+	4.82840i	−1.25653	+	0.840516i
$34$	2.55581	+	5.30719i	0.438317	+	0.910176i
$35$	−0.224258	−	0.107997i	−0.0379066	−	0.0182548i
$36$	−0.0182019	−	0.318317i	−0.00303365	−	0.0530528i
$37$	−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
$39$	−0.0177376	+	0.0894112i	−0.00284029	+	0.0143173i
$40$	−0.310429	+	0.494045i	−0.0490832	+	0.0781154i
$41$	−2.80557	−	2.80557i	−0.438157	−	0.438157i	0.453235	−	0.891391i	$-0.350270\pi$
$41$	−2.80557	−	2.80557i	−0.438157	−	0.438157i	−0.891391	+	0.453235i	$0.850270\pi$
$42$	−0.246215	+	2.93687i	−0.0379917	+	0.453170i
$43$	−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
$45$	−0.558175	−	0.230537i	−0.0832079	−	0.0343665i
$46$	−1.58847	−	1.58847i	−0.234207	−	0.234207i
$47$	−6.13509	+	9.76394i	−0.894895	+	1.42422i	0.0106389	+	0.999943i	$0.496613\pi$
$47$	−6.13509	+	9.76394i	−0.894895	+	1.42422i	−0.905534	+	0.424274i	$0.860529\pi$
$48$	6.41545	+	1.27271i	0.925991	+	0.183700i
$49$	1.21744	−	5.33394i	0.173920	−	0.761992i
$50$	−3.63105	−	5.77878i	−0.513507	−	0.817242i
$51$	2.64755	+	6.92525i	0.370732	+	0.969729i
$52$	0.00503930	+	0.00242680i	0.000698825	+	0.000336537i
$53$	−3.63041	−	7.53862i	−0.498675	−	1.03551i	−0.986681	−	0.162668i	$-0.947990\pi$
$53$	−3.63041	−	7.53862i	−0.498675	−	1.03551i	0.488006	−	0.872840i	$-0.337724\pi$
$54$	−0.189614	+	7.14804i	−0.0258032	+	0.972725i
$55$	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	$-0.769523\pi$
$59$		−	10.1765i		−	1.32487i	0.749119	−	0.662435i	$-0.230477\pi$
$60$	−0.0222673	+	0.0296195i	−0.00287470	+	0.00382386i
$61$	−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
$63$	−0.617626	+	3.65767i	−0.0778135	+	0.460823i
$64$	3.63540	−	7.54898i	0.454425	−	0.943622i
$65$	0.00828281	−	0.00660532i	0.00102736	−	0.000819289i
$66$	−2.99089	−	11.5703i	−0.368153	−	1.42421i
$67$	−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
$69$	−1.82530	−	2.15936i	−0.219740	−	0.259956i
$70$	0.242204	−	0.242204i	0.0289489	−	0.0289489i
$71$	−1.05188	−	4.60860i	−0.124835	−	0.546940i	−0.998205	−	0.0598824i	$-0.980927\pi$
$71$	−1.05188	−	4.60860i	−0.124835	−	0.546940i	0.873370	−	0.487057i	$-0.161930\pi$
$72$	8.35812	+	2.39871i	0.985014	+	0.282690i
$73$	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
$75$	−3.94657	−	7.62980i	−0.455711	−	0.881013i
$76$	0.470327	+	0.295526i	0.0539503	+	0.0338992i
$77$	−0.694129	−	6.16056i	−0.0791033	−	0.702062i
$78$	−0.108075	−	0.0636773i	−0.0122370	−	0.00721004i
$79$	−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
$81$	−0.989440	+	8.94545i	−0.109938	+	0.993938i
$82$	4.91931	−	2.36901i	0.543247	−	0.261614i
$83$	9.70654	+	7.74070i	1.06543	+	0.849653i	0.989073	−	0.147428i	$-0.0470994\pi$
$83$	9.70654	+	7.74070i	1.06543	+	0.849653i	0.0763579	+	0.997080i	$0.475671\pi$
$84$	0.207808	+	0.0928609i	0.0226737	+	0.0101320i
$85$	0.284596	−	0.813329i	0.0308688	−	0.0882179i
$86$	3.21505			0.346687
$87$	8.93330	+	2.68256i	0.957750	+	0.287601i
$88$	−14.5327			−1.54919
$89$	0.741261	−	2.11840i	0.0785736	−	0.224550i	−0.897895	−	0.440209i	$-0.854904\pi$
$89$	0.741261	−	2.11840i	0.0785736	−	0.224550i	0.976469	+	0.215659i	$0.0691900\pi$
$90$	0.553139	−	0.620234i	0.0583060	−	0.0653785i
$91$	−0.0508762	−	0.0405724i	−0.00533327	−	0.00425314i
$92$	−0.156312	+	0.0752760i	−0.0162967	+	0.00784806i
$93$	−1.98978	+	2.10681i	−0.206330	+	0.218466i
$94$	−9.89397	−	12.4066i	−1.02049	−	1.27965i
$95$	0.890849	−	0.559758i	0.0913992	−	0.0574299i
$96$	0.528040	−	0.896201i	0.0538928	−	0.0914681i
$97$	−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
$99$	−2.53468	−	14.8265i	−0.254745	−	1.49012i
$100$	−0.513873	+	0.117288i	−0.0513873	+	0.0117288i
$101$	−9.66361	+	3.38144i	−0.961565	+	0.336466i	−0.765004	−	0.644025i	$-0.777263\pi$
$101$	−9.66361	+	3.38144i	−0.961565	+	0.336466i	−0.196561	+	0.980492i	$0.562977\pi$
$102$	−10.1985	+	0.291347i	−1.00981	+	0.0288477i
$103$	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
$105$	0.329251	−	0.278315i	0.0321316	−	0.0271608i
$106$	11.4420	−	1.28920i	1.11134	−	0.125218i
$107$	−0.568054	−	0.129655i	−0.0549159	−	0.0125342i	0.194975	−	0.980808i	$-0.437538\pi$
$107$	−0.568054	−	0.129655i	−0.0549159	−	0.0125342i	−0.249891	+	0.968274i	$0.580395\pi$
$108$	0.516232	+	0.196152i	0.0496744	+	0.0188747i
$109$	−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
$111$	9.57045	−	1.35610i	0.908387	−	0.128715i
$112$	−2.91116	+	3.65048i	−0.275079	+	0.344938i
$113$	−1.04913	+	9.31130i	−0.0986940	+	0.875934i	0.842645	+	0.538470i	$0.180998\pi$
$113$	−1.04913	+	9.31130i	−0.0986940	+	0.875934i	−0.941339	+	0.337463i	$0.890431\pi$
$114$	−9.95747	−	7.48582i	−0.932602	−	0.701111i
$115$			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
$120$	−0.561895	−	0.840009i	−0.0512938	−	0.0766819i
$121$	6.13459	+	12.7386i	0.557690	+	1.15806i
$122$	−16.8218	−	8.10093i	−1.52297	−	0.733424i
$123$	6.41911	−	2.45405i	0.578792	−	0.221275i
$124$	0.0946037	+	0.150561i	0.00849566	+	0.0135208i
$125$	−0.446127	+	1.95461i	−0.0399028	+	0.174826i
$126$	−4.47023	−	2.46466i	−0.398240	−	0.219570i
$127$	−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
$129$	4.03245	+	0.338063i	0.355037	+	0.0297648i
$130$	0.00481508	+	0.0137607i	0.000422310	+	0.00120689i
$131$	5.29192	+	15.1234i	0.462357	+	1.32134i	0.905293	+	0.424787i	$0.139651\pi$
$131$	5.29192	+	15.1234i	0.462357	+	1.32134i	−0.442936	+	0.896553i	$0.646063\pi$
$132$	−0.919727	−	0.0771059i	−0.0800520	−	0.00671120i
$133$	−4.56966	−	4.56966i	−0.396240	−	0.396240i
$134$	3.93916	−	6.26914i	0.340292	−	0.541571i
$135$	0.758989	−	0.719762i	0.0653233	−	0.0619473i
$136$	−2.76084	+	12.0960i	−0.236740	+	1.03723i
$137$	7.23413	+	11.5131i	0.618053	+	0.983626i	0.998274	+	0.0587306i	$0.0187053\pi$
$137$	7.23413	+	11.5131i	0.618053	+	0.983626i	−0.380220	+	0.924896i	$0.624152\pi$
$138$	3.63440	−	1.38945i	0.309381	−	0.118278i
$139$	−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
$141$	−11.1049	−	16.6013i	−0.935200	−	1.39808i
$142$	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
$147$	7.57452	+	5.69437i	0.624736	+	0.469664i
$148$	0.0664073	−	0.589381i	0.00545865	−	0.0484468i
$149$	8.12844	−	10.1927i	0.665908	−	0.835022i	−0.328065	−	0.944655i	$-0.606396\pi$
$149$	8.12844	−	10.1927i	0.665908	−	0.835022i	0.993972	+	0.109634i	$0.0349678\pi$
$150$	11.7041	−	1.65843i	0.955635	−	0.135410i
$151$	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
$153$	−12.8221	−	0.706959i	−1.03660	−	0.0571542i
$154$	8.31745	+	1.89840i	0.670240	+	0.152978i
$155$	0.334684	−	0.0377098i	0.0268824	−	0.00302892i
$156$	−0.00739859	+	0.00625401i	−0.000592361	+	0.000500722i
$157$	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
$159$	14.4866	−	0.413845i	1.14886	−	0.0328201i
$160$	−0.114110	+	0.0399287i	−0.00902117	+	0.00315664i
$161$	1.96787	−	0.449153i	0.155090	−	0.0353982i
$162$	−11.1696	−	5.35094i	−0.877563	−	0.420409i
$163$	−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
$165$	−0.887434	+	1.50617i	−0.0690867	+	0.117255i
$166$	−14.4661	+	9.08965i	−1.12279	+	0.705493i
$167$	−5.12646	−	6.42838i	−0.396697	−	0.497443i	0.542865	−	0.839820i	$-0.317339\pi$
$167$	−5.12646	−	6.42838i	−0.396697	−	0.497443i	−0.939563	+	0.342377i	$0.888768\pi$
$168$	−4.26229	+	4.51297i	−0.328843	+	0.348184i
$169$	−11.7101	+	5.63929i	−0.900777	+	0.433791i
$170$	0.927083	+	0.739324i	0.0711041	+	0.0567036i
$171$	−11.7020	−	10.4361i	−0.894871	−	0.798066i
$172$	0.0820082	−	0.234366i	0.00625307	−	0.0178702i
$173$	10.0124			0.761230			0.380615	−	0.924734i	$-0.375712\pi$
$173$	10.0124			0.761230			0.380615	+	0.924734i	$0.375712\pi$
$174$	−7.54462	+	10.3842i	−0.571956	+	0.787227i
$175$	6.13230			0.463558
$176$	6.25320	−	17.8706i	0.471353	−	1.34705i
$177$	16.0926	+	7.19114i	1.20960	+	0.540519i
$178$	2.41469	+	1.92565i	0.180989	+	0.144334i
$179$	−0.0976933	+	0.0470466i	−0.00730194	+	0.00351643i	−0.437531	−	0.899203i	$-0.644147\pi$
$179$	−0.0976933	+	0.0470466i	−0.00730194	+	0.00351643i	0.430229	+	0.902720i	$0.358433\pi$
$180$	−0.0311037	−	0.0561427i	−0.00231834	−	0.00418463i
$181$	−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
$183$	−20.2468	−	11.9293i	−1.49668	−	0.881843i
$184$	−0.529773	−	4.70187i	−0.0390554	−	0.346626i
$185$	−0.951221	−	0.597692i	−0.0699352	−	0.0439432i
$186$	−1.83217	−	3.54208i	−0.134341	−	0.259718i
$187$	20.9238	−	4.77573i	1.53010	−	0.349236i
$188$	−1.15677	+	0.404773i	−0.0843664	+	0.0295211i
$189$	−5.34760	−	3.56133i	−0.388981	−	0.259049i
$190$	0.322174	+	1.41154i	0.0233730	+	0.102404i
$191$	−13.7084	+	13.7084i	−0.991903	+	0.991903i	−0.999967	−	0.00806476i	$-0.997433\pi$
$191$	−13.7084	+	13.7084i	−0.991903	+	0.991903i	0.00806476	+	0.999967i	$0.497433\pi$
$192$	9.36864	+	11.0832i	0.676123	+	0.799864i
$193$	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
$195$	0.00459234	+	0.0177656i	0.000328864	+	0.00127222i
$196$	0.454607	−	0.362537i	0.0324719	−	0.0258955i
$197$	11.6702	−	24.2333i	0.831465	−	1.72655i	0.157861	−	0.987461i	$-0.449540\pi$
$197$	11.6702	−	24.2333i	0.831465	−	1.72655i	0.673604	−	0.739093i	$-0.264745\pi$
$198$	20.4102	+	3.44642i	1.45049	+	0.244926i
$199$	−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
$201$	5.59987	−	7.44883i	0.394984	−	0.525400i
$202$		−	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
$207$	4.70452	−	1.36055i	0.326987	−	0.0945645i
$208$	−0.0862255	−	0.179049i	−0.00597866	−	0.0124148i
$209$	23.6099	+	11.3699i	1.63313	+	0.786473i
$210$	0.211858	+	0.554160i	0.0146196	+	0.0382407i
$211$	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
$213$	8.03109	+	1.59323i	0.550281	+	0.109166i
$214$	0.426592	−	0.678918i	0.0291612	−	0.0464099i
$215$	−0.332556	−	0.332556i	−0.0226801	−	0.0226801i
$216$	−9.69937	+	11.5221i	−0.659958	+	0.783977i
$217$	−0.683269	−	1.95267i	−0.0463833	−	0.132556i
$218$	−7.70206	−	22.0112i	−0.521649	−	1.49079i
$219$	−1.69945	+	20.2712i	−0.114838	+	1.36980i
$220$	0.0758499	+	0.0758499i	0.00511380	+	0.00511380i
$221$	0.119853	−	0.190745i	0.00806217	−	0.0128309i
$222$	−2.58838	+	13.0474i	−0.173721	+	0.875686i
$223$	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
$225$	14.8542	−	0.849387i	0.990278	−	0.0566258i
$226$	−11.6176	−	5.59476i	−0.772793	−	0.372158i
$227$	−1.98535	−	4.12262i	−0.131772	−	0.273628i	0.824634	−	0.565666i	$-0.191381\pi$
$227$	−1.98535	−	4.12262i	−0.131772	−	0.273628i	−0.956407	+	0.292038i	$0.905667\pi$
$228$	−0.799682	+	0.534920i	−0.0529602	+	0.0354260i
$229$	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	$0.157279\pi$
$233$			14.4781i			0.948490i	−0.880393	+	0.474245i	$0.842721\pi$
$234$	0.177066	−	0.125907i	0.0115752	−	0.00823077i
$235$	−0.259905	+	2.30672i	−0.0169543	+	0.150474i
$236$	0.674335	−	0.845590i	0.0438955	−	0.0550432i
$237$	−0.730666	−	5.15656i	−0.0474619	−	0.334954i
$238$	3.16021	−	6.56224i	0.204846	−	0.425367i
$239$	−14.4057	+	11.4882i	−0.931829	+	0.743109i	−0.966601	−	0.256286i	$-0.917501\pi$
$239$	−14.4057	+	11.4882i	−0.931829	+	0.743109i	0.0347715	+	0.999395i	$0.488930\pi$
$240$	1.27472	−	0.329511i	0.0822828	−	0.0212698i
$241$	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
$243$	−13.4467	−	7.88586i	−0.862605	−	0.505878i
$244$	−1.01961	+	1.01961i	−0.0652741	+	0.0652741i
$245$	−0.245074	−	1.07374i	−0.0156572	−	0.0685987i
$246$	0.270054	+	9.45318i	0.0172180	+	0.602712i
$247$	0.259623	−	0.0908460i	0.0165194	−	0.00578039i
$248$	−4.72791	+	1.07912i	−0.300223	+	0.0685239i
$249$	−19.0998	+	9.87951i	−1.21040	+	0.626089i
$250$	−2.33608	−	1.46786i	−0.147747	−	0.0928353i
$251$	−1.83184	−	16.2580i	−0.115624	−	1.02620i	−0.908808	−	0.417214i	$-0.863007\pi$
$251$	−1.83184	−	16.2580i	−0.115624	−	1.02620i	0.793184	−	0.608982i	$-0.208422\pi$
$252$	−0.293691	+	0.262997i	−0.0185008	+	0.0165673i
$253$	−6.93027	+	4.35458i	−0.435702	+	0.273770i
$254$	−5.12315	−	6.42422i	−0.321455	−	0.403092i
$255$	1.08505	+	1.02478i	0.0679483	+	0.0641739i
$256$	2.29149	−	1.10352i	0.143218	−	0.0689703i
$257$	−4.38813	−	3.49942i	−0.273724	−	0.218288i	0.477000	−	0.878903i	$-0.341724\pi$
$257$	−4.38813	−	3.49942i	−0.273724	−	0.218288i	−0.750725	+	0.660615i	$0.770295\pi$
$258$	−2.27188	+	5.08410i	−0.141441	+	0.316522i
$259$	−2.27907	+	6.51320i	−0.141614	+	0.404711i
$260$	0.00112593			6.98272e−5
$261$	−10.5547	+	12.2310i	−0.653319	+	0.757083i
$262$	−22.0491			−1.36220
$263$	−3.08739	+	8.82326i	−0.190377	+	0.544066i	−0.999021	−	0.0442319i	$-0.985916\pi$
$263$	−3.08739	+	8.82326i	−0.190377	+	0.544066i	0.808644	+	0.588298i	$0.200202\pi$
$264$	10.2694	−	22.9812i	0.632037	−	1.41440i
$265$	−1.31688	−	1.05018i	−0.0808952	−	0.0645118i
$266$	8.01248	−	3.85861i	0.491276	−	0.236586i
$267$	2.82613	+	2.66914i	0.172956	+	0.163349i
$268$	−0.356521	−	0.447063i	−0.0217780	−	0.0273087i
$269$	−2.32570	+	1.46133i	−0.141800	+	0.0890991i	−0.601064	−	0.799201i	$-0.705256\pi$
$269$	−2.32570	+	1.46133i	−0.141800	+	0.0890991i	0.459263	+	0.888300i	$0.348113\pi$
$270$	0.589936	+	1.31299i	0.0359024	+	0.0799059i
$271$	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
$273$	0.100110	−	0.0517828i	0.00605894	−	0.00313404i
$274$	−18.2423	+	4.16368i	−1.10206	+	0.251537i
$275$	−23.4707	+	8.21276i	−1.41534	+	0.495248i
$276$	−0.00858103	−	0.300377i	−0.000516517	−	0.0180806i
$277$	−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
$279$	−1.92554	−	4.63528i	−0.115279	−	0.277507i
$280$	0.716924	−	0.0807779i	0.0428444	−	0.00482740i
$281$	−12.8065	−	2.92299i	−0.763970	−	0.174371i	−0.177255	−	0.984165i	$-0.556722\pi$
$281$	−12.8065	−	2.92299i	−0.763970	−	0.174371i	−0.586715	+	0.809794i	$0.699579\pi$
$282$	26.6107	−	6.87877i	1.58464	−	0.409625i
$283$	−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
$285$	0.255662	+	1.80429i	0.0151441	+	0.106877i
$286$	−0.226398	+	0.283894i	−0.0133872	+	0.0167870i
$287$	−0.549293	+	4.87511i	−0.0324237	+	0.287769i
$288$	1.04407	+	1.46831i	0.0615225	+	0.0865208i
$289$		−	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	0.707637	−	0.706576i	$-0.249761\pi$
$293$	21.2306	+	2.39211i	1.24030	+	0.139749i	0.532668	+	0.846325i	$0.321190\pi$
$294$	−10.8391	+	7.25044i	−0.632148	+	0.422854i
$295$	−0.888840	−	1.84570i	−0.0517503	−	0.107461i
$296$	14.5738	+	7.01836i	0.847084	+	0.407934i
$297$	25.2369	+	6.46878i	1.46439	+	0.375357i
$298$	9.54495	+	15.1907i	0.552924	+	0.879973i
$299$	−0.0191170	+	0.0837572i	−0.00110557	+	0.00484380i
$300$	0.177650	−	0.895492i	0.0102566	−	0.0517012i
$301$	−1.53693	+	2.44601i	−0.0885873	+	0.140986i
$302$	15.3213	+	15.3213i	0.881644	+	0.881644i
$303$	1.48146	−	17.6710i	0.0851075	−	1.01517i
$304$	−6.51840	−	18.6285i	−0.373856	−	1.06842i
$305$	0.902060	+	2.57794i	0.0516518	+	0.147612i
$306$	6.74598	−	16.3333i	0.385642	−	0.933714i
$307$	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
$309$	−15.2788	−	3.03105i	−0.869182	−	0.172430i
$310$	−0.103134	+	0.451861i	−0.00585763	+	0.0256640i
$311$	−7.03200	−	11.1914i	−0.398748	−	0.634604i	0.585649	−	0.810565i	$-0.300840\pi$
$311$	−7.03200	−	11.1914i	−0.398748	−	0.634604i	−0.984397	+	0.175961i	$0.943697\pi$
$312$	−0.0943485	−	0.246789i	−0.00534143	−	0.0139717i
$313$	−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
$315$	0.207451	+	0.717328i	0.0116885	+	0.0404169i
$316$	−0.317558	−	0.0357802i	−0.0178640	−	0.00201279i
$317$	−21.4655	−	7.51112i	−1.20562	−	0.421866i	−0.348664	−	0.937248i	$-0.613365\pi$
$317$	−21.4655	−	7.51112i	−1.20562	−	0.421866i	−0.856961	+	0.515381i	$0.827650\pi$
$318$	−6.04668	+	19.0047i	−0.339081	+	1.06573i
$319$	11.3165	−	24.5145i	0.633605	−	1.37255i
$320$		−	1.68667i		−	0.0942875i
$321$	0.606439	−	0.806672i	0.0338481	−	0.0450240i
$322$	−0.311001	+	2.76021i	−0.0173314	+	0.153821i
$323$	13.9488	−	17.4913i	0.776133	−	0.973240i
$324$	−0.674974	+	0.677733i	−0.0374986	+	0.0376518i
$325$	−0.113246	+	0.235158i	−0.00628176	+	0.0130442i
$326$	26.0003	−	20.7345i	1.44002	−	1.14838i
$327$	−7.34577	−	28.4173i	−0.406222	−	1.57148i
$328$	11.2120	+	2.55906i	0.619078	+	0.141301i
$329$	14.1687	−	1.59643i	0.781148	−	0.0880143i
$330$	−1.55303	−	1.83725i	−0.0854914	−	0.101138i
$331$	−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
$333$	−4.61840	+	16.0925i	−0.253087	+	0.881863i
$334$	10.6798	−	3.73703i	0.584374	−	0.204481i
$335$	−1.05592	+	0.241007i	−0.0576911	+	0.0131676i
$336$	−3.71553	−	7.18313i	−0.202699	−	0.391872i
$337$	−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
$339$	−13.9830	−	8.23878i	−0.759455	−	0.447469i
$340$	0.0775419	−	0.0487228i	0.00420530	−	0.00264237i
$341$	5.23028	+	6.55856i	0.283235	+	0.355166i
$342$	18.8740	−	10.4564i	1.02059	−	0.565420i
$343$	−13.8932	+	6.69062i	−0.750163	+	0.361259i
$344$	5.29439	+	4.22214i	0.285455	+	0.227642i
$345$	−0.519654	−	0.232212i	−0.0279772	−	0.0125019i
$346$	−4.55070	+	13.0051i	−0.244647	+	0.699161i
$347$	−3.88166			−0.208378			−0.104189	−	0.994557i	$-0.533225\pi$
$347$	−3.88166			−0.208378			−0.104189	+	0.994557i	$0.533225\pi$
$348$	0.564531	+	0.814855i	0.0302620	+	0.0436808i
$349$	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
$351$	0.235323	−	0.139299i	0.0125606	−	0.00743522i
$352$	−2.35418	−	1.87739i	−0.125478	−	0.100065i
$353$	−4.64426	+	2.23656i	−0.247189	+	0.119040i	−0.553376	−	0.832931i	$-0.686661\pi$
$353$	−4.64426	+	2.23656i	−0.247189	+	0.119040i	0.306187	+	0.951971i	$0.400947\pi$
$354$	−16.6548	+	17.6343i	−0.885191	+	0.937254i
$355$	−0.593303	−	0.743978i	−0.0314892	−	0.0394862i
$356$	0.201967	−	0.126904i	0.0107042	−	0.00672590i
$357$	4.65369	−	7.89835i	0.246300	−	0.418025i
$358$	−0.0167068	−	0.148277i	−0.000882981	−	0.00783668i
$359$	4.17006	+	2.62022i	0.220087	+	0.138290i	0.637563	−	0.770398i	$-0.279942\pi$
$359$	4.17006	+	2.62022i	0.220087	+	0.138290i	−0.417476	+	0.908688i	$0.637085\pi$
$360$	1.72540	−	0.294968i	0.0909367	−	0.0155462i
$361$	8.10784	−	1.85056i	0.426728	−	0.0973979i
$362$	10.3283	−	3.61401i	0.542841	−	0.189948i
$363$	−24.4791	+	0.699308i	−1.28482	+	0.0367042i
$364$	−0.00153893	−	0.00674250i	−8.06619e−5	−	0.000353403i
$365$	1.67177	−	1.67177i	0.0875043	−	0.0875043i
$366$	24.6973	−	20.8766i	1.29095	−	1.09124i
$367$	−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
$369$	−0.655290	+	11.8850i	−0.0341130	+	0.618707i
$370$	1.20868	−	0.963888i	0.0628362	−	0.0501102i
$371$	−4.48893	+	9.32136i	−0.233054	+	0.483941i
$372$	−0.304940	+	0.0432089i	−0.0158104	+	0.00224028i
$373$	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
$375$	−2.77566	−	2.08669i	−0.143335	−	0.107756i
$376$		−	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
$381$	−5.75016	−	8.59624i	−0.294590	−	0.440399i
$382$	−11.5753	−	24.0364i	−0.592244	−	1.22981i
$383$	−9.87708	−	4.75655i	−0.504695	−	0.243048i	0.164170	−	0.986432i	$-0.447505\pi$
$383$	−9.87708	−	4.75655i	−0.504695	−	0.243048i	−0.668865	+	0.743384i	$0.733220\pi$
$384$	−16.7109	+	6.38865i	−0.852775	+	0.326020i
$385$	−0.663970	−	1.05670i	−0.0338391	−	0.0538545i
$386$	−2.42578	+	10.6281i	−0.123469	+	0.540954i
$387$	−3.38408	+	6.13781i	−0.172023	+	0.312003i
$388$	0.541562	−	0.861891i	0.0274936	−	0.0437559i
$389$	0.0567524	+	0.0567524i	0.00287746	+	0.00287746i	0.708544	−	0.705667i	$-0.249352\pi$
$389$	0.0567524	+	0.0567524i	0.00287746	+	0.00287746i	−0.705667	+	0.708544i	$0.749352\pi$
$390$	−0.0251630	−	0.00210955i	−0.00127418	−	0.000106821i
$391$	2.30788	+	6.59555i	0.116715	+	0.333551i
$392$	5.23758	+	14.9681i	0.264538	+	0.756005i
$393$	−27.6549	−	2.31846i	−1.39500	−	0.116951i
$394$	26.1726	+	26.1726i	1.31856	+	1.31856i
$395$	−0.322036	+	0.512517i	−0.0162034	+	0.0257875i
$396$	0.771847	−	1.39992i	0.0387868	−	0.0703487i
$397$	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
$399$	10.4553	−	3.99712i	0.523421	−	0.200106i
$400$	16.8731	+	8.12565i	0.843654	+	0.406283i
$401$	13.8274	+	28.7129i	0.690507	+	1.43385i	0.890929	+	0.454143i	$0.150055\pi$
$401$	13.8274	+	28.7129i	0.690507	+	1.43385i	−0.200421	+	0.979710i	$0.564231\pi$
$402$	7.13012	+	10.6592i	0.355618	+	0.531633i
$403$	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
$408$	−17.1771	−	12.9134i	−0.850394	−	0.639308i
$409$	−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
$411$	−23.3181	+	3.30409i	−1.15020	+	0.162979i
$412$	−0.414698	+	0.861129i	−0.0204307	+	0.0424248i
$413$	−9.83785	+	7.84543i	−0.484089	+	0.386048i
$414$	−0.371015	+	6.72909i	−0.0182344	+	0.330717i
$415$	2.43655	+	0.556126i	0.119605	+	0.0272991i
$416$	−0.0314071	+	0.00353873i	−0.00153986	+	0.000173500i
$417$	8.09093	−	6.83925i	0.396215	−	0.334920i
$418$	−25.4992	+	25.4992i	−1.24721	+	1.24721i
$419$	4.65946	+	20.4144i	0.227630	+	0.997311i	0.951566	+	0.307444i	$0.0994737\pi$
$419$	4.65946	+	20.4144i	0.227630	+	0.997311i	−0.723936	+	0.689867i	$0.757669\pi$
$420$	0.0458004	−	0.00130840i	0.00223483	−	6.38436e-5i
$421$	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
$423$	34.0996	−	5.82953i	1.65798	−	0.283442i
$424$	20.5351	+	12.9031i	0.997274	+	0.626629i
$425$	2.37691	+	21.0957i	0.115297	+	1.02329i
$426$	−5.71962	+	9.70747i	−0.277117	+	0.470328i
$427$	14.2047	−	8.92543i	0.687415	−	0.431932i
$428$	−0.0386094	−	0.0484147i	−0.00186626	−	0.00234021i
$429$	−0.313810	+	0.332267i	−0.0151509	+	0.0160420i
$430$	0.583106	−	0.280809i	0.0281199	−	0.0135418i
$431$	−9.40806	−	7.50268i	−0.453170	−	0.361391i	0.370147	−	0.928973i	$-0.379307\pi$
$431$	−9.40806	−	7.50268i	−0.453170	−	0.361391i	−0.823317	+	0.567582i	$0.807879\pi$
$432$	−9.99500	−	16.8849i	−0.480885	−	0.812376i
$433$	−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
$435$	1.85452	−	0.293723i	0.0889172	−	0.0140830i
$436$	−1.80100			−0.0862525
$437$	−2.81792	+	8.05315i	−0.134799	+	0.385234i
$438$	−25.5579	−	11.4208i	−1.22120	−	0.545707i
$439$	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
$441$	−14.3572	+	7.95409i	−0.683678	+	0.378766i
$442$	0.193285	+	0.242371i	0.00919362	+	0.0115284i
$443$	−3.01520	+	1.89458i	−0.143257	+	0.0900141i	−0.601753	−	0.798682i	$-0.705531\pi$
$443$	−3.01520	+	1.89458i	−0.143257	+	0.0900141i	0.458497	+	0.888696i	$0.348388\pi$
$444$	0.885090	+	0.521493i	0.0420045	+	0.0247490i
$445$	−0.0505850	−	0.448954i	−0.00239796	−	0.0212825i
$446$	3.80245	+	2.38924i	0.180051	+	0.113134i
$447$	10.3744	+	20.0565i	0.490691	+	0.948639i
$448$	−10.1004	+	2.30535i	−0.477199	+	0.108918i
$449$	11.1011	−	3.88445i	0.523894	−	0.183319i	−0.0553585	−	0.998467i	$-0.517630\pi$
$449$	11.1011	−	3.88445i	0.523894	−	0.183319i	0.579253	+	0.815148i	$0.303344\pi$
$450$	−5.64803	+	19.6802i	−0.266251	+	0.927731i
$451$	−4.42669	−	19.3946i	−0.208445	−	0.913256i
$452$	−0.704177	+	0.704177i	−0.0331217	+	0.0331217i
$453$	17.6056	+	20.8277i	0.827185	+	0.978572i
$454$	6.25723	−	0.705020i	0.293666	−	0.0330882i
$455$	−0.0127710	−	0.00291490i	−0.000598713	−	0.000136652i
$456$	−6.56682	−	25.4039i	−0.307519	−	1.18965i
$457$	−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
$459$	10.1786	−	19.7766i	0.475094	−	0.923094i
$460$	−0.0217753	+	0.0273053i	−0.00101528	+	0.00127312i
$461$	4.28290	−	38.0118i	0.199475	−	1.77039i	−0.351813	−	0.936070i	$-0.614435\pi$
$461$	4.28290	−	38.0118i	0.199475	−	1.77039i	0.551288	−	0.834315i	$-0.314137\pi$
$462$	−8.87948	+	11.8113i	−0.413111	+	0.549511i
$463$		−	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	0.131033	−	0.991378i	$-0.458171\pi$
$467$	0.825034	+	0.0929590i	0.0381780	+	0.00430163i	−0.0928548	+	0.995680i	$0.529599\pi$
$468$	−0.00466163	−	0.0161191i	−0.000215484	−	0.000745104i
$469$	2.88648	+	5.99385i	0.133285	+	0.276770i
$470$	−2.87807	−	1.38601i	−0.132756	−	0.0639317i
$471$	9.59663	+	25.1021i	0.442189	+	1.15664i
$472$	15.6932	+	24.9756i	0.722338	+	1.14959i
$473$	2.60659	−	11.4202i	0.119851	−	0.525102i
$474$	7.02995	+	1.39462i	0.322896	+	0.0640570i
$475$	−13.7907	+	21.9477i	−0.632759	+	1.00703i
$476$	−0.397756	−	0.397756i	−0.0182311	−	0.0182311i
$477$	−9.58235	+	23.2007i	−0.438746	+	1.06229i
$478$	−8.37455	−	23.9331i	−0.383043	−	1.09467i
$479$	−2.08653	−	5.96295i	−0.0953358	−	0.272454i	0.886333	−	0.463048i	$-0.153244\pi$
$479$	−2.08653	−	5.96295i	−0.0953358	−	0.272454i	−0.981669	+	0.190594i	$0.938959\pi$
$480$	0.0174933	−	0.208662i	0.000798457	−	0.00952409i
$481$	−0.207676	−	0.207676i	−0.00946923	−	0.00946923i
$482$	−4.13130	+	6.57493i	−0.188176	+	0.299480i
$483$	−0.680308	+	3.42927i	−0.0309551	+	0.156037i
$484$	−0.334372	+	1.46498i	−0.0151987	+	0.0665900i
$485$	−1.02577	−	1.63251i	−0.0465780	−	0.0741285i
$486$	16.3545	−	13.8818i	0.741857	−	0.629689i
$487$	−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
$489$	34.7909	−	23.2722i	1.57330	−	1.05240i
$490$	1.50607	+	0.169693i	0.0680373	+	0.00766596i
$491$	28.5759	+	9.99916i	1.28961	+	0.451256i	0.886005	−	0.463676i	$-0.153470\pi$
$491$	28.5759	+	9.99916i	1.28961	+	0.451256i	0.403610	+	0.914931i	$0.367755\pi$
$492$	0.695993	+	0.221442i	0.0313778	+	0.00998338i
$493$	−18.2544	−	14.0763i	−0.822136	−	0.633963i
$494$			0.378515i			0.0170302i
$495$	−1.75469	−	2.46766i	−0.0788673	−	0.110913i
$496$	0.707379	−	6.27816i	0.0317623	−	0.281898i
$497$	−3.64429	+	4.56980i	−0.163469	+	0.204983i
$498$	−4.15157	−	29.2990i	−0.186036	−	1.31292i
$499$	−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
$501$	13.7881	−	3.56416i	0.616005	−	0.159235i
$502$	21.9501	+	5.00997i	0.979682	+	0.223606i
$503$	34.1679	−	3.84980i	1.52347	−	0.171654i	0.689836	−	0.723966i	$-0.257683\pi$
$503$	34.1679	−	3.84980i	1.52347	−	0.171654i	0.833638	+	0.552312i	$0.186254\pi$
$504$	−4.12468	−	9.92920i	−0.183728	−	0.442282i
$505$	−1.45733	+	1.45733i	−0.0648502	+	0.0648502i
$506$	−2.50632	−	10.9809i	−0.111420	−	0.488161i
$507$	−0.642846	−	22.5027i	−0.0285498	−	0.999379i
$508$	−0.598984	+	0.209593i	−0.0265756	+	0.00929920i
$509$	6.74522	−	1.53955i	0.298977	−	0.0682395i	−0.0704012	−	0.997519i	$-0.522428\pi$
$509$	6.74522	−	1.53955i	0.298977	−	0.0682395i	0.369378	+	0.929279i	$0.379571\pi$
$510$	−1.82424	+	0.943605i	−0.0807788	+	0.0417835i
$511$	−12.2962	−	7.72619i	−0.543950	−	0.341787i
$512$	2.70485	+	24.0062i	0.119539	+	1.06094i
$513$	24.7721	−	11.1303i	1.09372	−	0.491415i
$514$	6.53983	−	4.10925i	0.288460	−	0.181251i
$515$	1.12873	+	1.41539i	0.0497379	+	0.0623694i
$516$	0.312664	+	0.295296i	0.0137643	+	0.0129997i
$517$	−52.0913	+	25.0858i	−2.29097	+	1.10327i
$518$	−7.42416	−	5.92057i	−0.326199	−	0.260135i
$519$	−7.07518	+	15.8331i	−0.310566	+	0.694997i
$520$	−0.0101419	+	0.0289839i	−0.000444752	+	0.00127103i
$521$	−15.0161			−0.657865			−0.328933	−	0.944353i	$-0.606689\pi$
$521$	−15.0161			−0.657865			−0.328933	+	0.944353i	$0.606689\pi$
$522$	−11.0898	−	19.2686i	−0.485386	−	0.843363i
$523$	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
$525$	−4.33333	+	9.69730i	−0.189122	+	0.423225i
$526$	−10.0573	−	8.02044i	−0.438520	−	0.349708i
$527$	6.45253	−	3.10737i	0.281076	−	0.135359i
$528$	23.8409	+	22.5166i	1.03754	+	0.979908i
$529$	12.6788	+	15.8987i	0.551251	+	0.691246i
$530$	1.96260	−	1.23319i	0.0852501	−	0.0535662i
$531$	−22.7434	+	20.3665i	−0.986979	+	0.883830i
$532$	−0.0769000	−	0.682506i	−0.00333404	−	0.0295904i
$533$	−0.176804	−	0.111093i	−0.00765823	−	0.00481198i
$534$	−4.75144	+	2.45772i	−0.205615	+	0.106356i
$535$	−0.114351	+	0.0260999i	−0.00494383	+	0.00112840i
$536$	14.7197	−	5.15066i	0.635796	−	0.222475i
$537$	−0.00536304	−	0.187732i	−0.000231432	−	0.00810123i
$538$	−0.841087	−	3.68504i	−0.0362618	−	0.158873i
$539$	19.3969	−	19.3969i	0.835485	−	0.835485i
$540$	0.110760	−	0.00951315i	0.00476636	−	0.000409381i
$541$	−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
$543$	13.3342	−	3.44683i	0.572223	−	0.147918i
$544$	−2.00985	+	1.60280i	−0.0861716	+	0.0687195i
$545$	−1.48010	+	3.07347i	−0.0634007	+	0.131653i
$546$	0.0217602	+	0.153569i	0.000931250	+	0.00657214i
$547$	−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
$549$	33.1716	−	23.5874i	1.41573	−	1.00669i
$550$		−	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
$555$	1.61733	−	1.08186i	0.0686518	−	0.0459223i
$556$	−0.282053	−	0.585689i	−0.0119617	−	0.0248388i
$557$	−8.89296	−	4.28263i	−0.376807	−	0.181461i	0.235888	−	0.971780i	$-0.424200\pi$
$557$	−8.89296	−	4.28263i	−0.376807	−	0.181461i	−0.612695	+	0.790320i	$0.709914\pi$
$558$	6.89594	−	0.394322i	0.291928	−	0.0166930i
$559$	−0.0654155	−	0.104108i	−0.00276678	−	0.00440330i
$560$	−0.209150	+	0.916347i	−0.00883821	+	0.0387227i
$561$	−7.23354	+	36.4626i	−0.305400	+	1.53945i
$562$	9.61729	−	15.3058i	0.405681	−	0.645638i
$563$	−23.0783	−	23.0783i	−0.972634	−	0.972634i	0.0270013	−	0.999635i	$-0.491404\pi$
$563$	−23.0783	−	23.0783i	−0.972634	−	0.972634i	−0.999635	+	0.0270013i	$0.991404\pi$
$564$	0.177337	−	2.11529i	0.00746722	−	0.0890698i
$565$	0.622991	+	1.78041i	0.0262094	+	0.0749022i
$566$	−2.48036	−	7.08846i	−0.104257	−	0.297950i
$567$	9.41054	−	5.93983i	0.395205	−	0.249450i
$568$	9.68846	+	9.68846i	0.406519	+	0.406519i
$569$	7.94786	−	12.6489i	0.333191	−	0.530271i	−0.637547	−	0.770412i	$-0.720051\pi$
$569$	7.94786	−	12.6489i	0.333191	−	0.530271i	0.970738	+	0.240141i	$0.0771935\pi$
$570$	−2.45979	−	0.487980i	−0.103029	−	0.0204392i
$571$	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
$573$	−11.9908	−	31.3646i	−0.500923	−	1.31027i
$574$	−6.08263	−	2.92924i	−0.253884	−	0.122264i
$575$	−3.51273	−	7.29427i	−0.146491	−	0.304192i
$576$	−24.1467	+	6.98322i	−1.00611	+	0.290967i
$577$	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
$582$	−13.7180	+	18.2474i	−0.568630	+	0.756379i
$583$	4.69715	−	41.6883i	0.194536	−	1.72655i
$584$	−21.2248	+	26.6150i	−0.878288	+	1.10134i
$585$	−0.0313387	−	0.00529178i	−0.00129570	−	0.000218788i
$586$	−12.7565	+	26.4892i	−0.526968	+	1.09426i
$587$	28.2498	−	22.5284i	1.16599	−	0.929849i	0.167563	−	0.985861i	$-0.446410\pi$
$587$	28.2498	−	22.5284i	1.16599	−	0.929849i	0.998430	+	0.0560128i	$0.0178388\pi$
$588$	0.252053	+	0.975074i	0.0103945	+	0.0402114i
$589$	8.52525	+	1.94583i	0.351277	+	0.0801766i
$590$	2.80136	−	0.315637i	0.115330	−	0.0129946i
$591$	30.0747	+	35.5788i	1.23711	+	1.46352i
$592$	−14.9012	+	14.9012i	−0.612437	+	0.612437i
$593$	−3.24604	−	14.2219i	−0.133299	−	0.584021i	−0.996818	−	0.0797057i	$-0.974602\pi$
$593$	−3.24604	−	14.2219i	−0.133299	−	0.584021i	0.863519	−	0.504316i	$-0.168255\pi$
$594$	−19.8726	+	29.8402i	−0.815384	+	1.22436i
$595$	−1.00567	+	0.351898i	−0.0412283	+	0.0144264i
$596$	1.35082	−	0.308316i	0.0553317	−	0.0126291i
$597$	−5.37760	−	10.3964i	−0.220091	−	0.425495i
$598$	−0.100104	−	0.0628992i	−0.00409354	−	0.00257214i
$599$	4.16495	+	36.9649i	0.170175	+	1.51035i	0.730980	+	0.682399i	$0.239063\pi$
$599$	4.16495	+	36.9649i	0.170175	+	1.51035i	−0.560805	+	0.827948i	$0.689508\pi$
$600$	21.4517	+	12.6393i	0.875762	+	0.515997i
$601$	−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
$603$	7.82209	+	14.1190i	0.318540	+	0.574969i
$604$	1.50769	−	0.726063i	0.0613468	−	0.0295431i
$605$	2.22524	+	1.77457i	0.0904688	+	0.0721464i
$606$	22.2796	+	9.95583i	0.905045	+	0.404428i
$607$	−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
$609$	−4.29370	−	10.7041i	−0.173989	−	0.433751i
$610$	−3.75848			−0.152176
$611$	−0.200437	+	0.572816i	−0.00810881	+	0.0231737i
$612$	−1.01857	−	0.908384i	−0.0411733	−	0.0367192i
$613$	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
$615$	0.949879	−	1.00575i	0.0383028	−	0.0405556i
$616$	11.2037	+	14.0490i	0.451412	+	0.566052i
$617$	−4.71470	+	2.96244i	−0.189807	+	0.119263i	−0.623583	−	0.781757i	$-0.714324\pi$
$617$	−4.71470	+	2.96244i	−0.189807	+	0.119263i	0.433776	+	0.901021i	$0.357181\pi$
$618$	10.8813	−	18.4681i	0.437712	−	0.742894i
$619$	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
$621$	−1.17291	+	8.40090i	−0.0470671	+	0.337116i
$622$	17.7326	−	4.04734i	0.711011	−	0.162284i
$623$	−2.61937	+	0.916556i	−0.104943	+	0.0367211i
$624$	0.344069	−	0.00982921i	0.0137738	−	0.000393483i
$625$	−5.42813	−	23.7822i	−0.217125	−	0.951288i
$626$	3.43992	−	3.43992i	0.137487	−	0.137487i
$627$	−34.6634	+	29.3010i	−1.38432	+	1.17017i
$628$	1.63862	−	0.184628i	0.0653881	−	0.00736747i
$629$	−23.2894	−	5.31565i	−0.928608	−	0.211949i
$630$	−1.02603	−	0.0565710i	−0.0408779	−	0.00225384i
$631$	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
$633$	−26.5684	+	3.76465i	−1.05600	+	0.149632i
$634$	19.5124	−	24.4678i	0.774937	−	0.971740i
$635$	−0.134580	+	1.19443i	−0.00534065	+	0.0473995i
$636$	1.23114	+	0.925547i	0.0488180	+	0.0367003i
$637$		−	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	−0.477926	−	0.878400i	$-0.658611\pi$
$641$	−28.8456	−	3.25011i	−1.13933	−	0.128372i	−0.661406	+	0.750028i	$0.730040\pi$
$642$	0.772157	+	1.15434i	0.0304746	+	0.0455582i
$643$	−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
$645$	0.760884	−	0.290889i	0.0299598	−	0.0114538i
$646$	16.3796	+	26.0680i	0.644448	+	1.02563i
$647$	1.25790	−	5.51123i	0.0494532	−	0.216669i	−0.944164	−	0.329477i	$-0.893128\pi$
$647$	1.25790	−	5.51123i	0.0494532	−	0.216669i	0.993617	+	0.112809i	$0.0359847\pi$
$648$	−11.3664	−	23.4800i	−0.446516	−	0.922382i
$649$	27.1462	−	43.2030i	1.06558	−	1.69587i
$650$	−0.253976	−	0.253976i	−0.00996175	−	0.00996175i
$651$	3.57068	+	0.299350i	0.139946	+	0.0117324i
$652$	−0.848271	−	2.42422i	−0.0332209	−	0.0949397i
$653$	−2.41775	−	6.90953i	−0.0946138	−	0.270391i	0.886844	−	0.462069i	$-0.152893\pi$
$653$	−2.41775	−	6.90953i	−0.0946138	−	0.270391i	−0.981458	+	0.191678i	$0.938607\pi$
$654$	40.2500	+	3.37438i	1.57390	+	0.131949i
$655$	2.28070	+	2.28070i	0.0891143	+	0.0891143i
$656$	−7.97119	+	12.6861i	−0.311223	+	0.495308i
$657$	−30.8549	−	17.0119i	−1.20377	−	0.663696i
$658$	−4.36616	+	19.1294i	−0.170211	+	0.745742i
$659$	17.7469	+	28.2441i	0.691322	+	1.10023i	0.989333	+	0.145670i	$0.0465337\pi$
$659$	17.7469	+	28.2441i	0.691322	+	1.10023i	−0.298012	+	0.954562i	$0.596323\pi$
$660$	−0.173544	+	0.0663465i	−0.00675518	+	0.00258253i
$661$	−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
$663$	0.216941	+	0.324317i	0.00842528	+	0.0125954i
$664$	−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
$669$	4.51797	+	3.39651i	0.174675	+	0.131317i
$670$	0.166877	−	1.48108i	0.00644703	−	0.0572190i
$671$	−42.4136	+	53.1850i	−1.63736	+	2.05318i
$672$	−1.27346	+	0.180445i	−0.0491248	+	0.00696081i
$673$	−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
$675$	−9.15337	+	24.0898i	−0.352314	+	0.927217i
$676$	−1.34670	−	0.307375i	−0.0517961	−	0.0118221i
$677$	−40.8511	+	4.60281i	−1.57003	+	0.176900i	−0.853666	−	0.520821i	$-0.825626\pi$
$677$	−40.8511	+	4.60281i	−1.57003	+	0.176900i	−0.716369	+	0.697722i	$0.754197\pi$
$678$	17.0567	−	14.4180i	0.655060	−	0.553721i
$679$	−8.37405	+	8.37405i	−0.321367	+	0.321367i
$680$	0.555767	+	2.43497i	0.0213127	+	0.0933769i
$681$	7.92222	−	0.226318i	0.303580	−	0.00867253i
$682$	−10.8961	+	3.81272i	−0.417234	+	0.145996i
$683$	41.7646	−	9.53251i	1.59808	−	0.364751i	0.671546	−	0.740963i	$-0.265631\pi$
$683$	41.7646	−	9.53251i	1.59808	−	0.364751i	0.926534	+	0.376212i	$0.122773\pi$
$684$	−0.280808	−	1.64257i	−0.0107369	−	0.0628053i
$685$	2.31762	+	1.45625i	0.0885515	+	0.0556406i
$686$	−2.37592	−	21.0868i	−0.0907129	−	0.805099i
$687$	−7.86951	+	13.3563i	−0.300241	+	0.509575i
$688$	−7.46999	+	4.69371i	−0.284791	+	0.178946i
$689$	−0.274552	−	0.344277i	−0.0104596	−	0.0131159i
$690$	0.537806	−	0.569438i	0.0204739	−	0.0216781i
$691$	−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
$693$	−12.3790	+	13.8806i	−0.470239	+	0.527279i
$694$	1.76424	−	5.04190i	0.0669695	−	0.191388i
$695$	−1.23129			−0.0467056
$696$	−26.0612	+	7.19238i	−0.987846	+	0.272627i
$697$	−16.9837			−0.643305
$698$	−7.54274	+	21.5559i	−0.285497	+	0.815903i
$699$	−22.8949	−	10.2308i	−0.865964	−	0.386964i
$700$	0.509546	+	0.406350i	0.0192590	+	0.0153586i
$701$	−0.235454	+	0.113389i	−0.00889297	+	0.00428263i	−0.438325	−	0.898817i	$-0.644428\pi$
$701$	−0.235454	+	0.113389i	−0.00889297	+	0.00428263i	0.429432	+	0.903099i	$0.358714\pi$
$702$	0.0739802	+	0.368973i	0.00279220	+	0.0139260i
$703$	−18.1857	−	22.8041i	−0.685885	−	0.860073i
$704$	35.5707	−	22.3506i	1.34062	−	0.842369i
$705$	−3.46406	−	2.04102i	−0.130464	−	0.0768693i
$706$	−0.794228	−	7.04897i	−0.0298912	−	0.265291i
$707$	10.7189	+	6.73514i	0.403126	+	0.253301i
$708$	0.860659	+	1.66389i	0.0323455	+	0.0625327i
$709$	−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
$711$	8.67062	+	2.48839i	0.325174	+	0.0933220i
$712$	1.44756	+	6.34215i	0.0542494	+	0.237682i
$713$	−1.93127	+	1.93127i	−0.0723268	+	0.0723268i
$714$	8.14406	+	9.63453i	0.304784	+	0.360563i
$715$	0.0527834	−	0.00594726i	0.00197399	−	0.000222415i
$716$	−0.0112350	−	0.00256432i	−0.000419873	−	9.58333e-5i
$717$	−7.98715	−	30.8985i	−0.298286	−	1.15393i
$718$	−5.29873	+	4.22560i	−0.197747	+	0.157698i
$719$	−7.14279	+	14.8321i	−0.266381	+	0.553146i	−0.990659	−	0.136362i	$-0.956459\pi$
$719$	−7.14279	+	14.8321i	−0.266381	+	0.553146i	0.724278	+	0.689508i	$0.242173\pi$
$720$	−0.379697	+	2.24862i	−0.0141505	+	0.0838011i
$721$	6.93311	−	8.69385i	0.258203	−	0.323776i
$722$	−1.28136	+	11.3724i	−0.0476872	+	0.423236i
$723$	−5.87302	+	7.81216i	−0.218420	+	0.290537i
$724$		−	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
$729$	21.9722	−	15.6914i	0.813787	−	0.581163i
$730$	1.41163	+	2.93129i	0.0522469	+	0.108492i
$731$	−9.01023	−	4.33910i	−0.333255	−	0.160487i
$732$	−0.891863	−	2.33286i	−0.0329642	−	0.0862251i
$733$	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
$735$	1.87113	+	0.371200i	0.0690178	+	0.0136919i
$736$	0.521588	−	0.830102i	0.0192260	−	0.0305980i
$737$	−19.0750	−	19.0750i	−0.702638	−	0.702638i
$738$	−15.1396	−	6.25294i	−0.557296	−	0.230174i
$739$	−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
$741$	−0.0398009	+	0.474750i	−0.00146212	+	0.0174404i
$742$	−10.0673	−	10.0673i	−0.369582	−	0.369582i
$743$	7.07352	−	11.2574i	0.259502	−	0.412995i	−0.691407	−	0.722465i	$-0.743009\pi$
$743$	7.07352	−	11.2574i	0.259502	−	0.412995i	0.950909	+	0.309470i	$0.100152\pi$
$744$	1.63448	−	8.23902i	0.0599228	−	0.302057i
$745$	0.583982	−	2.55859i	0.0213954	−	0.0937396i
$746$	11.8212	+	18.8133i	0.432805	+	0.688805i
$747$	−2.12628	−	37.1846i	−0.0777966	−	1.36051i
$748$	2.05507	+	0.989668i	0.0751407	+	0.0361858i
$749$	0.312592	+	0.649104i	0.0114219	+	0.0237178i
$750$	3.97196	−	2.65691i	0.145035	−	0.0970165i
$751$	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
$756$	−0.208356	−	0.650272i	−0.00757785	−	0.0236501i
$757$	−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
$759$	−1.98889	−	14.0363i	−0.0721922	−	0.509485i
$760$	−1.32315	+	2.74755i	−0.0479957	+	0.0996642i
$761$	−1.48985	+	1.18812i	−0.0540070	+	0.0430692i	−0.650121	−	0.759830i	$-0.725282\pi$
$761$	−1.48985	+	1.18812i	−0.0540070	+	0.0430692i	0.596114	+	0.802900i	$0.296711\pi$
$762$	13.7792	−	3.56186i	0.499166	−	0.129033i
$763$	20.4281	+	4.66258i	0.739547	+	0.168797i
$764$	−2.04743	+	0.230690i	−0.0740733	+	0.00834606i
$765$	−2.38726	+	0.991690i	−0.0863117	+	0.0358546i
$766$	10.6675	−	10.6675i	0.385432	−	0.385432i
$767$	−0.119175	−	0.522138i	−0.00430315	−	0.0188533i
$768$	0.125795	+	4.40344i	0.00453925	+	0.158895i
$769$	−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
$771$	8.63463	−	4.46633i	0.310969	−	0.160851i
$772$	0.712873	+	0.447928i	0.0256569	+	0.0161213i
$773$	5.01650	+	44.5226i	0.180431	+	1.60137i	0.678747	+	0.734372i	$0.262523\pi$
$773$	5.01650	+	44.5226i	0.180431	+	1.60137i	−0.498316	+	0.866995i	$0.666048\pi$
$774$	−6.43433	−	7.18526i	−0.231277	−	0.258269i
$775$	−7.02588	+	4.41466i	−0.252377	+	0.158579i
$776$	17.3088	+	21.7045i	0.621349	+	0.779147i
$777$	−8.68916	−	8.20649i	−0.311722	−	0.294406i
$778$	−0.0995101	+	0.0479216i	−0.00356761	+	0.00171807i
$779$	−16.2129	−	12.9294i	−0.580887	−	0.463242i
$780$	−0.000795627		0.00178049i	−2.84880e−5		6.37517e-5i
$781$	7.82797	−	22.3711i	0.280107	−	0.800500i
$782$	−9.61592			−0.343865
$783$	−11.8832	−	25.3336i	−0.424670	−	0.905348i
$784$	−20.6597			−0.737847
$785$	1.03158	−	2.94809i	0.0368187	−	0.105222i
$786$	15.5808	−	34.8672i	0.555747	−	1.24367i
$787$	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
$789$	−11.7710	−	11.1171i	−0.419058	−	0.395780i
$790$	−0.519343	−	0.651235i	−0.0184774	−	0.0231699i
$791$	9.81024	−	6.16418i	0.348812	−	0.219173i
$792$	29.0846	+	32.4789i	1.03348	+	1.15409i
$793$	0.0799461	+	0.709541i	0.00283897	+	0.0251965i
$794$	11.2355	+	7.05972i	0.398732	+	0.250540i
$795$	2.59125	−	1.34035i	0.0919022	−	0.0475372i
$796$	−0.700203	+	0.159817i	−0.0248180	+	0.00566455i
$797$	35.3813	−	12.3804i	1.25327	−	0.438538i	0.379641	−	0.925134i	$-0.376047\pi$
$797$	35.3813	−	12.3804i	1.25327	−	0.438538i	0.873627	+	0.486596i	$0.161762\pi$
$798$	0.439859	+	15.3972i	0.0155708	+	0.545053i
$799$	10.9838	+	48.1230i	0.388577	+	1.70247i
$800$	2.10608	−	2.10608i	0.0744611	−	0.0744611i
$801$	−6.21789	+	2.58297i	−0.219698	+	0.0912647i
$802$	−43.5798	+	4.91027i	−1.53886	+	0.173388i
$803$	57.4096	+	13.1034i	2.02594	+	0.462408i
$804$	0.958893	−	0.247871i	0.0338176	−	0.00874172i
$805$	0.317678	−	0.253340i	0.0111967	−	0.00892906i
$806$	−0.0525736	+	0.109170i	−0.00185183	+	0.00384536i
$807$	−0.667444	−	4.71038i	−0.0234952	−	0.165813i
$808$	18.5022	−	23.2011i	0.650907	−	0.816211i
$809$	0.106877	−	0.948559i	0.00375759	−	0.0333496i	−0.991693	−	0.128623i	$-0.958944\pi$
$809$	0.106877	−	0.948559i	0.00375759	−	0.0333496i	0.995451	+	0.0952739i	$0.0303727\pi$
$810$	−2.49316	+	0.00508436i	−0.0876008	+	0.000178646i
$811$			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
$816$	23.2704	−	15.5660i	0.814629	−	0.544918i
$817$	−5.29802	−	11.0015i	−0.185354	−	0.384892i
$818$	−7.37826	−	3.55318i	−0.257975	−	0.124234i
$819$	0.0111448	+	0.194901i	0.000389430	+	0.00681039i
$820$	−0.0451619	−	0.0718747i	−0.00157712	−	0.00250997i
$821$	−0.733924	+	3.21553i	−0.0256141	+	0.112223i	−0.986119	−	0.166041i	$-0.946902\pi$
$821$	−0.733924	+	3.21553i	−0.0256141	+	0.112223i	0.960505	+	0.278263i	$0.0897588\pi$
$822$	6.30650	−	31.7896i	0.219964	−	1.10879i
$823$	−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
$825$	3.59812	−	42.9188i	0.125271	−	1.49424i
$826$	−5.71908	−	16.3442i	−0.198992	−	0.568687i
$827$	10.3930	+	29.7015i	0.361400	+	1.03282i	0.970786	+	0.239947i	$0.0771302\pi$
$827$	10.3930	+	29.7015i	0.361400	+	1.03282i	−0.609386	+	0.792873i	$0.708584\pi$
$828$	0.481064	+	0.198689i	0.0167181	+	0.00690491i
$829$	−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
$831$	2.14906	+	0.426336i	0.0745502	+	0.0147894i
$832$	0.0981212	−	0.429897i	0.00340174	−	0.0149040i
$833$	−12.4598	−	19.8296i	−0.431706	−	0.687056i
$834$	5.20614	+	13.6178i	0.180274	+	0.471546i
$835$	−1.49124	−	0.718145i	−0.0516066	−	0.0248524i
$836$	1.20838	+	2.50923i	0.0417927	+	0.0867835i
$837$	8.69065	+	0.230534i	0.300393	+	0.00796842i
$838$	−28.6341	−	3.22629i	−0.989149	−	0.111450i
$839$	−36.4369	−	12.7498i	−1.25794	−	0.440173i	−0.382707	−	0.923870i	$-0.625008\pi$
$839$	−36.4369	−	12.7498i	−1.25794	−	0.440173i	−0.875236	+	0.483697i	$0.839294\pi$
$840$	−0.378869	+	1.19079i	−0.0130722	+	0.0410860i
$841$	−28.0473	+	7.37225i	−0.967148	+	0.254216i
$842$			38.3834i			1.32278i
$843$	13.6718	−	18.1860i	0.470883	−	0.626358i
$844$	−0.184353	+	1.63617i	−0.00634567	+	0.0563194i
$845$	−1.63129	+	2.04557i	−0.0561181	+	0.0703698i
$846$	−7.92646	+	46.9416i	−0.272517	+	1.61388i
$847$	7.58531	−	15.7511i	0.260634	−	0.541213i
$848$	−24.7027	+	19.6997i	−0.848293	+	0.676491i
$849$	−2.36562	−	9.15146i	−0.0811879	−	0.314077i
$850$	−28.4815	−	6.50072i	−0.976908	−	0.222973i
$851$	9.05285	−	1.02001i	0.310328	−	0.0349655i
$852$	0.561748	+	0.664556i	0.0192452	+	0.0227673i
$853$	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
$855$	−3.03387	−	0.870693i	−0.103756	−	0.0297771i
$856$	1.59408	−	0.557792i	0.0544844	−	0.0190649i
$857$	−32.1563	+	7.33946i	−1.09844	+	0.250711i	−0.733071	−	0.680153i	$-0.761913\pi$
$857$	−32.1563	+	7.33946i	−1.09844	+	0.250711i	−0.365367	+	0.930864i	$0.619056\pi$
$858$	−0.288954	−	0.558626i	−0.00986472	−	0.0190712i
$859$	−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
$861$	−7.32109	−	4.31357i	−0.249502	−	0.147006i
$862$	14.0213	−	8.81014i	0.477566	−	0.300074i
$863$	−1.09868	−	1.37770i	−0.0373995	−	0.0468975i	0.762780	−	0.646658i	$-0.223834\pi$
$863$	−1.09868	−	1.37770i	−0.0373995	−	0.0468975i	−0.800180	+	0.599761i	$0.795262\pi$
$864$	−3.05968	+	0.613476i	−0.104093	+	0.0208709i
$865$	1.81593	−	0.874507i	0.0617435	−	0.0297341i
$866$	−12.7011	−	10.1288i	−0.431600	−	0.344190i
$867$	2.09193	+	0.934798i	0.0710456	+	0.0317474i
$868$	0.0726171	−	0.207528i	0.00246479	−	0.00704395i
$869$	−15.0761			−0.511420
$870$	−0.461370	+	2.54233i	−0.0156419	+	0.0861931i
$871$	−0.283153			−0.00959429
$872$	16.2227	−	46.3618i	0.549369	−	1.57001i
$873$	−19.1244	+	21.4442i	−0.647264	+	0.725777i
$874$	−9.17949	−	7.32040i	−0.310501	−	0.247616i
$875$	2.23349	−	1.07559i	0.0755059	−	0.0363617i
$876$	−1.48446	+	1.57177i	−0.0501552	+	0.0531051i
$877$	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
$879$	−18.7852	+	31.8826i	−0.633608	+	1.07537i
$880$	−0.426729	−	3.78733i	−0.0143850	−	0.127671i
$881$	−42.0226	−	26.4045i	−1.41578	−	0.889591i	−0.415972	−	0.909377i	$-0.636559\pi$
$881$	−42.0226	−	26.4045i	−1.41578	−	0.889591i	−0.999804	+	0.0197859i	$0.993702\pi$
$882$	−3.80614	−	22.2638i	−0.128159	−	0.749662i
$883$	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
$885$	3.54678	−	0.101323i	0.119224	−	0.00340592i
$886$	−1.09044	−	4.77755i	−0.0366342	−	0.160505i
$887$	−8.73289	+	8.73289i	−0.293222	+	0.293222i	−0.838352	−	0.545130i	$-0.816480\pi$
$887$	−8.73289	+	8.73289i	−0.293222	+	0.293222i	0.545130	+	0.838352i	$0.316480\pi$
$888$	−21.3969	+	18.0868i	−0.718033	+	0.606952i
$889$	7.33665	−	0.826642i	0.246063	−	0.0277247i
$890$	0.606138	+	0.138347i	0.0203178	+	0.00463741i
$891$	−28.0628	+	35.3372i	−0.940140	+	1.18384i
$892$	0.271159	−	0.216242i	0.00907907	−	0.00724031i
$893$	−26.1498	+	54.3006i	−0.875069	+	1.81710i
$894$	−30.7666	+	4.35952i	−1.02899	+	0.145804i
$895$	−0.0136093	+	0.0170655i	−0.000454908	+	0.000570437i
$896$	1.42998	−	12.6914i	0.0477722	−	0.423990i
$897$	−0.118940	−	0.0894168i	−0.00397130	−	0.00298554i
$898$			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
$903$	−2.78194	−	4.15887i	−0.0925771	−	0.138399i
$904$	−11.7841	−	24.4700i	−0.391934	−	0.813859i
$905$	−1.44215	−	0.694504i	−0.0479388	−	0.0230861i
$906$	−35.0550	+	13.4017i	−1.16463	+	0.445241i
$907$	−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
$909$	26.8971	+	14.8297i	0.892121	+	0.491871i
$910$	0.00959065	−	0.0152634i	0.000317927	−	0.000505978i
$911$	32.1348	+	32.1348i	1.06467	+	1.06467i	0.997759	+	0.0669161i	$0.0213160\pi$
$911$	32.1348	+	32.1348i	1.06467	+	1.06467i	0.0669161	+	0.997759i	$0.478684\pi$
$912$	34.0643	+	2.85580i	1.12798	+	0.0945651i
$913$	20.5591	+	58.7546i	0.680407	+	1.94449i
$914$	−2.46178	−	7.03535i	−0.0814283	−	0.232709i
$915$	−4.71405	−	0.395205i	−0.155842	−	0.0130651i
$916$	0.672615	+	0.672615i	0.0222238	+	0.0222238i
$917$	10.5404	−	16.7750i	0.348075	−	0.553958i
$918$	21.0617	+	22.2095i	0.695139	+	0.733023i
$919$	−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
$921$	−41.8659	+	16.0055i	−1.37953	+	0.527400i
$922$	47.4270	+	22.8396i	1.56192	+	0.752183i
$923$	−0.107940	−	0.224140i	−0.00355289	−	0.00737766i
$924$	0.634509	+	0.948563i	0.0208738	+	0.0312054i
$925$	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	$-0.943660\pi$
$929$		−	10.7334i		−	0.352151i	0.984377	−	0.176075i	$-0.0563403\pi$
$930$	−0.641670	−	0.482394i	−0.0210412	−	0.0158183i
$931$	3.20160	−	28.4150i	0.104928	−	0.931264i
$932$	−0.959373	+	1.20302i	−0.0314253	+	0.0394061i
$933$	22.6665	−	3.21177i	0.742069	−	0.105149i
$934$	−0.495727	+	1.02939i	−0.0162207	+	0.0336826i
$935$	3.37779	−	2.69370i	0.110466	−	0.0880934i
$936$	0.456930	+	0.0251933i	0.0149352	+	0.000823468i
$937$	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
$939$	4.67621	−	3.95279i	0.152602	−	0.128994i
$940$	−0.174448	+	0.174448i	−0.00568987	+	0.00568987i
$941$	8.57290	+	37.5603i	0.279469	+	1.22443i	0.898467	+	0.439040i	$0.144681\pi$
$941$	8.57290	+	37.5603i	0.279469	+	1.22443i	−0.618999	+	0.785392i	$0.712461\pi$
$942$	−36.9669	+	1.05605i	−1.20445	+	0.0344080i
$943$	6.11351	−	2.13921i	0.199083	−	0.0696622i
$944$	−37.4646	+	8.55105i	−1.21937	+	0.278313i
$945$	−1.28094	−	0.178841i	−0.0416689	−	0.00581769i
$946$	13.6490	+	8.57625i	0.443768	+	0.278838i
$947$	1.70897	+	15.1675i	0.0555340	+	0.492878i	0.990436	+	0.137972i	$0.0440585\pi$
$947$	1.70897	+	15.1675i	0.0555340	+	0.492878i	−0.934902	+	0.354906i	$0.884513\pi$
$948$	0.280980	−	0.476886i	0.00912582	−	0.0154885i
$949$	0.523354	−	0.328845i	0.0169888	−	0.0106748i
$950$	−22.2400	−	27.8881i	−0.721560	−	0.904808i
$951$	27.0461	−	28.6368i	0.877030	−	0.928613i
$952$	13.8219	−	6.65628i	0.447971	−	0.215731i
$953$	10.5105	+	8.38186i	0.340469	+	0.271515i	0.778765	−	0.627316i	$-0.215846\pi$
$953$	10.5105	+	8.38186i	0.340469	+	0.271515i	−0.438296	+	0.898831i	$0.644418\pi$
$954$	−25.7802	−	22.9914i	−0.834666	−	0.744374i
$955$	−1.28894	+	3.68358i	−0.0417091	+	0.119198i
$956$	−1.95826			−0.0633345
$957$	30.7692	+	35.2183i	0.994628	+	1.13845i
$958$	8.69363			0.280878
$959$	5.55287	−	15.8692i	0.179311	−	0.512443i
$960$	2.66721	+	1.19187i	0.0860837	+	0.0384673i
$961$	−22.0482	−	17.5829i	−0.711233	−	0.567189i
$962$	0.364141	−	0.175361i	0.0117404	−	0.00565387i
$963$	0.847094	+	1.52902i	0.0272972	+	0.0492719i
$964$	0.373911	+	0.468869i	0.0120428	+	0.0151013i
$965$	1.35026	−	0.848422i	0.0434663	−	0.0273117i
$966$	−4.14509	−	2.44228i	−0.133366	−	0.0785789i
$967$	−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
$969$	17.8030	+	34.4180i	0.571914	+	1.10566i
$970$	2.58669	−	0.590395i	0.0830536	−	0.0189564i
$971$	30.5381	−	10.6858i	0.980015	−	0.342922i	0.207722	−	0.978188i	$-0.433395\pi$
$971$	30.5381	−	10.6858i	0.980015	−	0.342922i	0.772294	+	0.635266i	$0.219109\pi$
$972$	−0.594767	−	1.54628i	−0.0190772	−	0.0495970i
$973$	1.68294	+	7.37345i	0.0539526	+	0.236382i
$974$	0.541310	−	0.541310i	0.0173447	−	0.0173447i
$975$	−0.291842	−	0.345253i	−0.00934642	−	0.0110569i
$976$	50.9112	−	5.73631i	1.62963	−	0.183615i
$977$	−11.9643	−	2.73076i	−0.382770	−	0.0873648i	0.0268060	−	0.999641i	$-0.491466\pi$
$977$	−11.9643	−	2.73076i	−0.382770	−	0.0873648i	−0.409576	+	0.912276i	$0.634323\pi$
$978$	14.4156	+	55.7673i	0.460962	+	1.78324i
$979$	8.79783	−	7.01604i	0.281180	−	0.224234i
$980$	0.0507863	−	0.105459i	0.00162231	−	0.00336876i
$981$	50.1284	+	8.46458i	1.60048	+	0.270253i
$982$	−25.9758	+	32.5727i	−0.828923	+	1.03944i
$983$	0.725337	−	6.43754i	0.0231347	−	0.205326i	−0.976827	−	0.214028i	$-0.931342\pi$
$983$	0.725337	−	6.43754i	0.0231347	−	0.205326i	0.999962	+	0.00870246i	$0.00277012\pi$
$984$	−11.9696	+	15.9217i	−0.381577	+	0.507566i
$985$		−	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
$990$	4.00277	−	1.15760i	0.127216	−	0.0367909i
$991$	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
$993$	−2.71087	−	7.09087i	−0.0860269	−	0.225022i
$994$	−4.27937	−	6.81057i	−0.135733	−	0.216018i
$995$	−0.302709	+	1.32626i	−0.00959654	+	0.0420452i
$996$	−2.24170	−	0.444713i	−0.0710309	−	0.0140913i
$997$	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
$999$	−22.1843	−	18.6749i	−0.701879	−	0.590847i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.3	✓	96	1.1	even	1	trivial
87.2.k.a.8.6	yes	96	3.2	odd	2	inner
87.2.k.a.11.3	yes	96	87.11	even	28	inner
87.2.k.a.11.6	yes	96	29.11	odd	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} +(-0.706640 + 1.58135i) q^{3} +(0.0830922 + 0.0662638i) q^{4} +(0.181368 - 0.0873422i) q^{5} +(-1.73284 - 1.63659i) q^{6} +(-0.770934 - 0.966720i) q^{7} +(-2.45423 + 1.54210i) q^{8} +(-2.00132 - 2.23489i) q^{9} +(0.0310162 + 0.275277i) q^{10} +(4.24536 + 2.66753i) q^{11} +(-0.163502 + 0.0845730i) q^{12} +(0.0513081 - 0.0117107i) q^{13} +(1.60607 - 0.561988i) q^{14} +(0.00995651 + 0.348525i) q^{15} +(-0.840272 - 3.68147i) q^{16} +(3.02679 - 3.02679i) q^{17} +(3.81251 - 1.58375i) q^{18} +(5.19364 - 0.585183i) q^{19} +(0.0208579 + 0.00476068i) q^{20} +(2.07349 - 0.535991i) q^{21} +(-5.39440 + 4.30189i) q^{22} +(-0.708287 + 1.47077i) q^{23} +(-0.704332 - 4.97070i) q^{24} +(-3.09218 + 3.87748i) q^{25} +(-0.00810871 + 0.0719668i) q^{26} +(4.94835 - 1.58552i) 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} +(-7.21824 + 4.82840i) q^{33} +(2.55581 + 5.30719i) q^{34} +(-0.224258 - 0.107997i) q^{35} +(-0.0182019 - 0.318317i) q^{36} +(-2.96911 - 4.72531i) q^{37} +(-1.60044 + 7.01200i) q^{38} +(-0.0177376 + 0.0894112i) q^{39} +(-0.310429 + 0.494045i) q^{40} +(-2.80557 - 2.80557i) q^{41} +(-0.246215 + 2.93687i) q^{42} +(-0.771632 - 2.20520i) q^{43} +(0.175995 + 0.502965i) q^{44} +(-0.558175 - 0.230537i) q^{45} +(-1.58847 - 1.58847i) q^{46} +(-6.13509 + 9.76394i) q^{47} +(6.41545 + 1.27271i) q^{48} +(1.21744 - 5.33394i) q^{49} +(-3.63105 - 5.77878i) q^{50} +(2.64755 + 6.92525i) q^{51} +(0.00503930 + 0.00242680i) q^{52} +(-3.63041 - 7.53862i) q^{53} +(-0.189614 + 7.14804i) 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} +(-0.0222673 + 0.0296195i) q^{60} +(-1.51909 + 13.4823i) q^{61} +(-1.43552 + 1.80009i) q^{62} +(-0.617626 + 3.65767i) q^{63} +(3.63540 - 7.54898i) q^{64} +(0.00828281 - 0.00660532i) q^{65} +(-2.99089 - 11.5703i) q^{66} +(-5.24543 - 1.19723i) q^{67} +(0.452069 - 0.0509359i) q^{68} +(-1.82530 - 2.15936i) q^{69} +(0.242204 - 0.242204i) q^{70} +(-1.05188 - 4.60860i) q^{71} +(8.35812 + 2.39871i) q^{72} +(11.0856 - 3.87901i) q^{73} +(7.48719 - 1.70890i) q^{74} +(-3.94657 - 7.62980i) q^{75} +(0.470327 + 0.295526i) q^{76} +(-0.694129 - 6.16056i) q^{77} +(-0.108075 - 0.0636773i) q^{78} +(-2.54600 + 1.59976i) q^{79} +(-0.473946 - 0.594310i) q^{80} +(-0.989440 + 8.94545i) q^{81} +(4.91931 - 2.36901i) q^{82} +(9.70654 + 7.74070i) q^{83} +(0.207808 + 0.0928609i) q^{84} +(0.284596 - 0.813329i) q^{85} +3.21505 q^{86} +(8.93330 + 2.68256i) q^{87} -14.5327 q^{88} +(0.741261 - 2.11840i) q^{89} +(0.553139 - 0.620234i) q^{90} +(-0.0508762 - 0.0405724i) q^{91} +(-0.156312 + 0.0752760i) q^{92} +(-1.98978 + 2.10681i) q^{93} +(-9.89397 - 12.4066i) q^{94} +(0.890849 - 0.559758i) q^{95} +(0.528040 - 0.896201i) q^{96} +(-1.07237 - 9.51752i) q^{97} +(6.37493 + 4.00564i) q^{98} +(-2.53468 - 14.8265i) 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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