LMFDB - Embedded newform 140.2.w.b.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(23,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34754 - 0.429119i) q^{2} +(-2.71477 - 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(-2.01971 + 0.959579i) q^{5} +(3.34610 + 2.14518i) q^{6} +(2.59868 + 0.496852i) q^{7} +(-1.70252 - 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(3.13340 - 0.426375i) q^{10} +(2.75736 - 1.59196i) q^{11} +(-3.58846 - 4.32659i) q^{12} +(2.41925 + 2.41925i) q^{13} +(-3.28861 - 1.78467i) q^{14} +(6.18105 - 1.13586i) q^{15} +(1.32498 + 3.77418i) q^{16} +(2.24094 + 0.600458i) q^{17} +(-4.66612 - 5.12151i) q^{18} +(-1.39787 + 2.42118i) q^{19} +(-4.40534 - 0.770044i) q^{20} +(-6.69340 - 3.23917i) q^{21} +(-4.39878 + 0.961994i) q^{22} +(1.39288 + 5.19830i) q^{23} +(2.97897 + 7.37012i) q^{24} +(3.15842 - 3.87613i) q^{25} +(-2.22189 - 4.29818i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(3.66569 + 3.81611i) q^{28} +1.72334i q^{29} +(-8.81662 - 1.12179i) q^{30} +(-3.01685 + 1.74178i) q^{31} +(-0.165897 - 5.65442i) q^{32} +(-8.64362 + 2.31605i) q^{33} +(-2.76208 - 1.77077i) q^{34} +(-5.72534 + 1.49014i) q^{35} +(4.09004 + 8.90375i) q^{36} +(-0.623610 - 2.32734i) q^{37} +(2.92265 - 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +(5.60592 + 2.92808i) q^{40} +2.72503 q^{41} +(7.62961 + 7.23716i) q^{42} +(3.96477 - 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(-10.9197 - 0.876123i) q^{45} +(0.353728 - 7.60261i) q^{46} +(6.10452 - 1.63570i) q^{47} +(-0.851615 - 11.2098i) q^{48} +(6.50628 + 2.58232i) q^{49} +(-5.91941 + 3.86790i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(1.14965 + 6.74541i) q^{52} +(-3.37866 + 12.6093i) q^{53} +(3.46629 + 6.70545i) q^{54} +(-4.04144 + 5.86120i) q^{55} +(-3.30209 - 6.71537i) q^{56} +(5.55610 - 5.55610i) q^{57} +(0.739519 - 2.32227i) q^{58} +(-0.951402 - 1.64788i) q^{59} +(11.3993 + 5.29503i) q^{60} +(5.83980 - 10.1148i) q^{61} +(4.81275 - 1.05253i) q^{62} +(9.80850 + 8.47363i) q^{63} +(-2.20286 + 7.69073i) q^{64} +(-7.20764 - 2.56471i) q^{65} +(12.6415 + 0.588172i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(2.96214 + 3.57144i) q^{68} -15.1254i q^{69} +(8.35455 + 0.448823i) q^{70} +0.562181i q^{71} +(-1.69071 - 13.7532i) q^{72} +(0.866554 - 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(-11.3940 + 8.22531i) q^{75} +(-5.08103 + 2.33403i) q^{76} +(7.95646 - 2.76700i) q^{77} +(2.90533 + 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(-6.29770 - 6.35130i) q^{80} +(0.151981 + 0.263239i) q^{81} +(-3.67208 - 1.16936i) q^{82} +(4.38250 - 4.38250i) q^{83} +(-7.17559 - 13.0264i) q^{84} +(-5.10222 + 0.937610i) q^{85} +(-7.04404 + 3.64132i) q^{86} +(1.25360 - 4.67848i) q^{87} +(-8.29011 - 3.51752i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(14.3387 + 5.86644i) q^{90} +(5.08485 + 7.48887i) q^{91} +(-3.73908 + 10.0930i) q^{92} +(9.45706 - 2.53401i) q^{93} +(-8.92798 - 0.415394i) q^{94} +(0.499970 - 6.23143i) q^{95} +(-3.66277 + 15.4711i) q^{96} +(-10.9216 + 10.9216i) q^{97} +(-7.65933 - 6.27174i) q^{98} +15.5984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.34754	−	0.429119i	−0.952853	−	0.303433i
$2$	−1.34754	−	0.429119i	−0.952853	−	0.303433i
$3$	−2.71477	−	0.727420i	−1.56737	−	0.419976i	−0.632384	−	0.774655i	$-0.717924\pi$
$3$	−2.71477	−	0.727420i	−1.56737	−	0.419976i	−0.934988	+	0.354678i	$0.884590\pi$
$4$	1.63171	+	1.15651i	0.815857	+	0.578253i
$5$	−2.01971	+	0.959579i	−0.903240	+	0.429137i
$5$	−2.01971	+	0.959579i	−0.903240	+	0.429137i
$6$	3.34610	+	2.14518i	1.36604	+	0.875768i
$7$	2.59868	+	0.496852i	0.982209	+	0.187792i
$7$	2.59868	+	0.496852i	0.982209	+	0.187792i
$8$	−1.70252	−	2.25864i	−0.601931	−	0.798548i
$9$	4.24276	+	2.44956i	1.41425	+	0.816519i
$10$	3.13340	−	0.426375i	0.990869	−	0.134832i
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	−0.0229484	−	0.999737i	$-0.507305\pi$
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	0.854323	+	0.519742i	$0.173972\pi$
$12$	−3.58846	−	4.32659i	−1.03590	−	1.24898i
$13$	2.41925	+	2.41925i	0.670980	+	0.670980i	0.957942	−	0.286962i	$-0.0926455\pi$
$13$	2.41925	+	2.41925i	0.670980	+	0.670980i	−0.286962	+	0.957942i	$0.592645\pi$
$14$	−3.28861	−	1.78467i	−0.878918	−	0.476973i
$15$	6.18105	−	1.13586i	1.59594	−	0.293278i
$16$	1.32498	+	3.77418i	0.331246	+	0.943544i
$17$	2.24094	+	0.600458i	0.543508	+	0.145632i	0.520119	−	0.854094i	$-0.325888\pi$
$17$	2.24094	+	0.600458i	0.543508	+	0.145632i	0.0233890	+	0.999726i	$0.492554\pi$
$18$	−4.66612	−	5.12151i	−1.09982	−	1.20715i
$19$	−1.39787	+	2.42118i	−0.320693	+	0.555456i	−0.980631	−	0.195863i	$-0.937249\pi$
$19$	−1.39787	+	2.42118i	−0.320693	+	0.555456i	0.659938	+	0.751320i	$0.270582\pi$
$20$	−4.40534	−	0.770044i	−0.985064	−	0.172187i
$21$	−6.69340	−	3.23917i	−1.46062	−	0.706845i
$22$	−4.39878	+	0.961994i	−0.937824	+	0.205098i
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	0.944775	+	0.327719i	$0.106280\pi$
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	−0.654340	+	0.756201i	$0.727053\pi$
$24$	2.97897	+	7.37012i	0.608079	+	1.50442i
$25$	3.15842	−	3.87613i	0.631683	−	0.775226i
$26$	−2.22189	−	4.29818i	−0.435748	−	0.842942i
$27$	−3.77420	−	3.77420i	−0.726345	−	0.726345i
$28$	3.66569	+	3.81611i	0.692751	+	0.721177i
$29$			1.72334i			0.320017i	0.987116	+	0.160009i	$0.0511522\pi$
$29$			1.72334i			0.320017i	−0.987116	+	0.160009i	$0.948848\pi$
$30$	−8.81662	−	1.12179i	−1.60969	−	0.204810i
$31$	−3.01685	+	1.74178i	−0.541843	+	0.312833i	−0.745825	−	0.666141i	$-0.767945\pi$
$31$	−3.01685	+	1.74178i	−0.541843	+	0.312833i	0.203983	+	0.978974i	$0.434611\pi$
$32$	−0.165897	−	5.65442i	−0.0293267	−	0.999570i
$33$	−8.64362	+	2.31605i	−1.50466	+	0.403173i
$34$	−2.76208	−	1.77077i	−0.473693	−	0.303684i
$35$	−5.72534	+	1.49014i	−0.967758	+	0.251880i
$36$	4.09004	+	8.90375i	0.681673	+	1.48396i
$37$	−0.623610	−	2.32734i	−0.102521	−	0.382613i	0.895531	−	0.444999i	$-0.146796\pi$
$37$	−0.623610	−	2.32734i	−0.102521	−	0.382613i	−0.998052	+	0.0623856i	$0.980129\pi$
$38$	2.92265	−	2.66278i	0.474117	−	0.431959i
$39$	−4.80790	−	8.32752i	−0.769880	−	1.33347i
$40$	5.60592	+	2.92808i	0.886374	+	0.462970i
$41$	2.72503			0.425578			0.212789	−	0.977098i	$-0.431745\pi$
$41$	2.72503			0.425578			0.212789	+	0.977098i	$0.431745\pi$
$42$	7.62961	+	7.23716i	1.17728	+	1.11672i
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	−0.336914	−	0.941536i	$-0.609383\pi$
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	0.941536	+	0.336914i	$0.109383\pi$
$44$	6.34034	+	0.591276i	0.955842	+	0.0891383i
$45$	−10.9197	−	0.876123i	−1.62781	−	0.130605i
$46$	0.353728	−	7.60261i	0.0521544	−	1.12094i
$47$	6.10452	−	1.63570i	0.890435	−	0.238591i	0.215531	−	0.976497i	$-0.430852\pi$
$47$	6.10452	−	1.63570i	0.890435	−	0.238591i	0.674904	+	0.737905i	$0.264185\pi$
$48$	−0.851615	−	11.2098i	−0.122920	−	1.61800i
$49$	6.50628	+	2.58232i	0.929468	+	0.368903i
$50$	−5.91941	+	3.86790i	−0.837130	+	0.547003i
$51$	−5.64685	−	3.26021i	−0.790717	−	0.456521i
$52$	1.14965	+	6.74541i	0.159427	+	0.935420i
$53$	−3.37866	+	12.6093i	−0.464094	+	1.73202i	0.195780	+	0.980648i	$0.437276\pi$
$53$	−3.37866	+	12.6093i	−0.464094	+	1.73202i	−0.659874	+	0.751376i	$0.729390\pi$
$54$	3.46629	+	6.70545i	0.471703	+	0.912496i
$55$	−4.04144	+	5.86120i	−0.544947	+	0.790323i
$56$	−3.30209	−	6.71537i	−0.441261	−	0.897379i
$57$	5.55610	−	5.55610i	0.735924	−	0.735924i
$58$	0.739519	−	2.32227i	0.0971036	−	0.304929i
$59$	−0.951402	−	1.64788i	−0.123862	−	0.214535i	0.797426	−	0.603417i	$-0.206195\pi$
$59$	−0.951402	−	1.64788i	−0.123862	−	0.214535i	−0.921288	+	0.388882i	$0.872861\pi$
$60$	11.3993	+	5.29503i	1.47165	+	0.683585i
$61$	5.83980	−	10.1148i	0.747709	−	1.29507i	−0.201209	−	0.979548i	$-0.564487\pi$
$61$	5.83980	−	10.1148i	0.747709	−	1.29507i	0.948918	−	0.315522i	$-0.102180\pi$
$62$	4.81275	−	1.05253i	0.611220	−	0.133671i
$63$	9.80850	+	8.47363i	1.23575	+	1.06758i
$64$	−2.20286	+	7.69073i	−0.275358	+	0.961342i
$65$	−7.20764	−	2.56471i	−0.893997	−	0.318113i
$66$	12.6415	+	0.588172i	1.55606	+	0.0723990i
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	0.808875	+	0.587980i	$0.200077\pi$
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	−0.994497	+	0.104768i	$0.966590\pi$
$68$	2.96214	+	3.57144i	0.359212	+	0.433100i
$69$		−	15.1254i		−	1.82088i
$70$	8.35455	+	0.448823i	0.998560	+	0.0536446i
$71$			0.562181i			0.0667186i	0.999443	+	0.0333593i	$0.0106206\pi$
$71$			0.562181i			0.0667186i	−0.999443	+	0.0333593i	$0.989379\pi$
$72$	−1.69071	−	13.7532i	−0.199253	−	1.62084i
$73$	0.866554	−	3.23402i	0.101423	−	0.378514i	−0.896492	−	0.443059i	$-0.853893\pi$
$73$	0.866554	−	3.23402i	0.101423	−	0.378514i	0.997915	+	0.0645454i	$0.0205597\pi$
$74$	−0.158369	+	3.40378i	−0.0184100	+	0.395682i
$75$	−11.3940	+	8.22531i	−1.31566	+	0.949777i
$76$	−5.08103	+	2.33403i	−0.582834	+	0.267731i
$77$	7.95646	−	2.76700i	0.906723	−	0.315329i
$78$	2.90533	+	13.2848i	0.328963	+	1.50421i
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	−0.999213	−	0.0396596i	$-0.987373\pi$
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	0.533953	+	0.845514i	$0.320706\pi$
$80$	−6.29770	−	6.35130i	−0.704104	−	0.710097i
$81$	0.151981	+	0.263239i	0.0168868	+	0.0292487i
$82$	−3.67208	−	1.16936i	−0.405513	−	0.129134i
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	−0.424423	−	0.905464i	$-0.639523\pi$
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	0.905464	+	0.424423i	$0.139523\pi$
$84$	−7.17559	−	13.0264i	−0.782921	−	1.42129i
$85$	−5.10222	+	0.937610i	−0.553414	+	0.101698i
$86$	−7.04404	+	3.64132i	−0.759578	+	0.392654i
$87$	1.25360	−	4.67848i	0.134400	−	0.501586i
$88$	−8.29011	−	3.51752i	−0.883729	−	0.374969i
$89$	−2.51180	−	1.45019i	−0.266250	−	0.153720i	0.360932	−	0.932592i	$-0.382459\pi$
$89$	−2.51180	−	1.45019i	−0.266250	−	0.153720i	−0.627182	+	0.778872i	$0.715792\pi$
$90$	14.3387	+	5.86644i	1.51143	+	0.618377i
$91$	5.08485	+	7.48887i	0.533037	+	0.785047i
$92$	−3.73908	+	10.0930i	−0.389826	+	1.05227i
$93$	9.45706	−	2.53401i	0.980652	−	0.262765i
$94$	−8.92798	−	0.415394i	−0.920850	−	0.0428446i
$95$	0.499970	−	6.23143i	0.0512958	−	0.639331i
$96$	−3.66277	+	15.4711i	−0.373830	+	1.57902i
$97$	−10.9216	+	10.9216i	−1.10892	+	1.10892i	−0.115629	+	0.993292i	$0.536889\pi$
$97$	−10.9216	+	10.9216i	−1.10892	+	1.10892i	−0.993292	+	0.115629i	$0.963111\pi$
$98$	−7.65933	−	6.27174i	−0.773709	−	0.633541i
$99$	15.5984			1.56770
$100$	9.63641	−	2.67201i	0.963641	−	0.267201i
$101$	5.73271	+	9.92934i	0.570426	+	0.988007i	0.996522	+	0.0833288i	$0.0265552\pi$
$101$	5.73271	+	9.92934i	0.570426	+	0.988007i	−0.426096	+	0.904678i	$0.640111\pi$
$102$	6.21032	+	6.81642i	0.614914	+	0.674926i
$103$	−3.39107	−	12.6556i	−0.334132	−	1.24700i	−0.904807	−	0.425821i	$-0.859985\pi$
$103$	−3.39107	−	12.6556i	−0.334132	−	1.24700i	0.570676	−	0.821176i	$-0.306681\pi$
$104$	1.34539	−	9.58302i	0.131926	−	0.939693i
$105$	16.6269	+	0.119329i	1.62262	+	0.0116453i
$106$	9.96376	−	15.5417i	0.967766	−	1.50954i
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	−0.277959	−	0.960593i	$-0.589658\pi$
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	0.239577	+	0.970877i	$0.422991\pi$
$108$	−1.79353	−	10.5233i	−0.172582	−	1.01260i
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	−0.165505	−	0.986209i	$-0.552926\pi$
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	0.771329	+	0.636436i	$0.219592\pi$
$110$	7.96114	−	6.16392i	0.759065	−	0.587707i
$111$			6.77183i			0.642753i
$112$	1.56800	+	10.4662i	0.148162	+	0.988963i
$113$	−11.6304	−	11.6304i	−1.09410	−	1.09410i	−0.995086	−	0.0990127i	$-0.968432\pi$
$113$	−11.6304	−	11.6304i	−1.09410	−	1.09410i	−0.0990127	−	0.995086i	$-0.531568\pi$
$114$	−9.87128	+	5.10283i	−0.924530	+	0.477924i
$115$	−7.80138	−	9.16245i	−0.727482	−	0.854402i
$116$	−1.99306	+	2.81201i	−0.185051	+	0.261088i
$117$	4.33820	+	16.1904i	0.401067	+	1.49680i
$118$	0.574915	+	2.62884i	0.0529252	+	0.242004i
$119$	5.52515	+	2.67381i	0.506489	+	0.245108i
$120$	−13.0888	−	12.0269i	−1.19484	−	1.09790i
$121$	−0.431317	+	0.747063i	−0.0392106	+	0.0679148i
$122$	−12.2098	+	11.1241i	−1.10542	+	1.00713i
$123$	−7.39783	−	1.98224i	−0.667040	−	0.178733i
$124$	−6.93702	−	0.646921i	−0.622963	−	0.0580952i
$125$	−2.65962	+	10.8594i	−0.237883	+	0.971294i
$126$	−9.58112	−	15.6275i	−0.853554	−	1.39221i
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	0.763302	−	0.646042i	$-0.223577\pi$
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	−0.646042	+	0.763302i	$0.723577\pi$
$128$	6.26868	−	9.41826i	0.554078	−	0.832465i
$129$	−13.6475	+	7.87939i	−1.20159	+	0.693741i
$130$	8.61199	+	6.54898i	0.755322	+	0.574383i
$131$	−3.52422	−	2.03471i	−0.307912	−	0.177773i	0.338080	−	0.941118i	$-0.390223\pi$
$131$	−3.52422	−	2.03471i	−0.307912	−	0.177773i	−0.645992	+	0.763344i	$0.723556\pi$
$132$	−16.7824	−	6.21727i	−1.46072	−	0.541144i
$133$	−4.83558	+	5.59733i	−0.419298	+	0.485350i
$134$	4.48068	−	6.98907i	0.387072	−	0.603764i
$135$	11.2444	+	4.00113i	0.967765	+	0.344362i
$136$	−2.45903	−	6.08376i	−0.210860	−	0.521678i
$137$	−15.5676	−	4.17132i	−1.33003	−	0.356380i	−0.477303	−	0.878739i	$-0.658385\pi$
$137$	−15.5676	−	4.17132i	−1.33003	−	0.356380i	−0.852726	+	0.522359i	$0.825052\pi$
$138$	−6.49058	+	20.3820i	−0.552515	+	1.73503i
$139$	−17.0814			−1.44882			−0.724411	−	0.689369i	$-0.757888\pi$
$139$	−17.0814			−1.44882			−0.724411	+	0.689369i	$0.757888\pi$
$140$	−11.0655	−	4.18990i	−0.935203	−	0.354111i
$141$	−17.7622			−1.49585
$142$	0.241242	−	0.757560i	0.0202446	−	0.0635730i
$143$	10.5221	+	2.81939i	0.879902	+	0.235769i
$144$	−3.62347	+	19.2585i	−0.301956	+	1.60488i
$145$	−1.65369	−	3.48065i	−0.137331	−	0.289052i
$146$	−2.55549	+	3.98611i	−0.211494	+	0.329893i
$147$	−15.7846	−	11.7432i	−1.30189	−	0.968562i
$148$	1.67403	−	4.51877i	0.137605	−	0.371441i
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	0.782905	−	0.622141i	$-0.213737\pi$
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	−0.147337	+	0.989086i	$0.547070\pi$
$150$	18.8834	−	6.19456i	1.54182	−	0.505783i
$151$	5.83274	−	3.36754i	0.474662	−	0.274046i	−0.243527	−	0.969894i	$-0.578305\pi$
$151$	5.83274	−	3.36754i	0.474662	−	0.274046i	0.718189	+	0.695848i	$0.244971\pi$
$152$	7.84845	−	0.964826i	0.636593	−	0.0782577i
$153$	8.03690	+	8.03690i	0.649745	+	0.649745i
$154$	−11.9090	+	0.314371i	−0.959655	+	0.0253327i
$155$	4.42178	−	6.41279i	0.355166	−	0.515088i
$156$	1.78572	−	19.1485i	0.142972	−	1.53311i
$157$	10.9964	+	2.94647i	0.877606	+	0.235154i	0.669374	−	0.742926i	$-0.266563\pi$
$157$	10.9964	+	2.94647i	0.877606	+	0.235154i	0.208232	+	0.978080i	$0.433229\pi$
$158$	8.64611	−	7.87732i	0.687847	−	0.626686i
$159$	18.3446	−	31.7737i	1.45482	−	2.51982i
$160$	5.76093	+	11.2611i	0.455441	+	0.890266i
$161$	1.03686	+	14.2008i	0.0817163	+	1.11918i
$162$	−0.0918394	−	0.419942i	−0.00721558	−	0.0329937i
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	0.965897	−	0.258926i	$-0.0833686\pi$
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	−0.965954	+	0.258712i	$0.916702\pi$
$164$	4.44647	+	3.15152i	0.347211	+	0.246092i
$165$	15.2351	−	12.9720i	1.18605	−	1.00987i
$166$	−7.78619	+	4.02497i	−0.604326	+	0.312398i
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	0.791312	−	0.611412i	$-0.209398\pi$
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	−0.611412	+	0.791312i	$0.709398\pi$
$168$	4.07952	+	20.6327i	0.314742	+	1.59185i
$169$		−	1.29445i		−	0.0995729i
$170$	7.27778	+	0.925994i	0.558181	+	0.0710205i
$171$	−11.8616	+	6.84831i	−0.907081	+	0.523703i
$172$	11.0547	−	1.88409i	0.842910	−	0.143661i
$173$	15.5233	−	4.15945i	1.18021	−	0.316237i	0.385201	−	0.922833i	$-0.374132\pi$
$173$	15.5233	−	4.15945i	1.18021	−	0.316237i	0.795010	+	0.606596i	$0.207465\pi$
$174$	−3.69689	+	5.76649i	−0.280261	+	0.437157i
$175$	10.1336	−	8.50356i	0.766027	−	0.642809i
$176$	9.66180	+	8.29743i	0.728286	+	0.625443i
$177$	1.38414	+	5.16567i	0.104038	+	0.388276i
$178$	2.76244	+	3.03204i	0.207054	+	0.227261i
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	0.975221	+	0.221235i	$0.0710086\pi$
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	−0.296016	+	0.955183i	$0.595658\pi$
$180$	−16.8045	−	14.0582i	−1.25254	−	1.04784i
$181$	−4.28458			−0.318471			−0.159235	−	0.987241i	$-0.550903\pi$
$181$	−4.28458			−0.318471			−0.159235	+	0.987241i	$0.550903\pi$
$182$	−3.63841	−	12.2735i	−0.269697	−	0.909775i
$183$	−23.2114	+	23.2114i	−1.71584	+	1.71584i
$184$	9.36965	−	11.9962i	0.690740	−	0.884371i
$185$	3.49278	+	4.10214i	0.256794	+	0.301596i
$186$	−13.8311	−	0.643525i	−1.01415	−	0.0471855i
$187$	7.13498	−	1.91181i	0.521761	−	0.139806i
$188$	11.8525	+	4.39092i	0.864434	+	0.320241i
$189$	−7.93272	−	11.6832i	−0.577020	−	0.849824i
$190$	−3.34775	+	8.18254i	−0.242871	+	0.593624i
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	0.816341	−	0.577570i	$-0.195999\pi$
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	−0.0920200	+	0.995757i	$0.529332\pi$
$192$	11.5747	−	19.2762i	0.835329	−	1.39114i
$193$	1.19666	−	4.46599i	0.0861374	−	0.321469i	−0.909390	−	0.415945i	$-0.863451\pi$
$193$	1.19666	−	4.46599i	0.0861374	−	0.321469i	0.995527	+	0.0944758i	$0.0301175\pi$
$194$	19.4040	−	10.0306i	1.39312	−	0.720156i
$195$	17.7014	+	12.2056i	1.26763	+	0.874060i
$196$	7.62992	+	11.7382i	0.544994	+	0.838440i
$197$	6.77330	−	6.77330i	0.482578	−	0.482578i	−0.423376	−	0.905954i	$-0.639155\pi$
$197$	6.77330	−	6.77330i	0.482578	−	0.482578i	0.905954	+	0.423376i	$0.139155\pi$
$198$	−21.0194	−	6.69356i	−1.49379	−	0.475691i
$199$	0.869824	+	1.50658i	0.0616602	+	0.106799i	0.895208	−	0.445649i	$-0.147027\pi$
$199$	0.869824	+	1.50658i	0.0616602	+	0.106799i	−0.833547	+	0.552448i	$0.813694\pi$
$200$	−14.1320	−	0.534527i	−0.999285	−	0.0377967i
$201$	8.24951	−	14.2886i	0.581876	−	1.00784i
$202$	−3.46418	−	15.8402i	−0.243739	−	1.11451i
$203$	−0.856247	+	4.47842i	−0.0600968	+	0.314324i
$204$	−5.44359	−	11.8504i	−0.381128	−	0.829691i
$205$	−5.50376	+	2.61488i	−0.384399	+	0.182631i
$206$	−0.861178	+	18.5091i	−0.0600011	+	1.28959i
$207$	−6.82387	+	25.4670i	−0.474292	+	1.77008i
$208$	−5.92521	+	12.3362i	−0.410840	+	0.855358i
$209$			8.90141i			0.615723i
$210$	−22.3542	−	7.29572i	−1.54259	−	0.503453i
$211$		−	23.7584i		−	1.63560i	−0.575506	−	0.817798i	$-0.695195\pi$
$211$		−	23.7584i		−	1.63560i	0.575506	−	0.817798i	$-0.304805\pi$
$212$	−20.0958	+	16.6674i	−1.38018	+	1.14472i
$213$	0.408942	−	1.52619i	0.0280202	−	0.104573i
$214$	0.580647	+	0.0270159i	0.0396922	+	0.00184677i
$215$	−4.20316	+	11.8122i	−0.286653	+	0.805584i
$216$	−2.09890	+	14.9502i	−0.142812	+	1.01723i
$217$	−8.70524	+	3.02740i	−0.590950	+	0.205513i
$218$	−10.0902	+	2.20668i	−0.683393	+	0.149455i
$219$	−4.70499	+	8.14928i	−0.317934	+	0.550677i
$220$	−13.3730	+	4.88985i	−0.901606	+	0.329673i
$221$	3.96874	+	6.87406i	0.266966	+	0.462399i
$222$	2.90592	−	9.12529i	0.195032	−	0.612449i
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	−0.108108	−	0.994139i	$-0.534479\pi$
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	0.994139	+	0.108108i	$0.0344793\pi$
$224$	2.37830	−	14.7765i	0.158907	−	0.987294i
$225$	22.8952	−	8.70876i	1.52635	−	0.580584i
$226$	10.6816	+	20.6633i	0.710530	+	1.37450i
$227$	5.38070	−	20.0810i	0.357130	−	1.33283i	−0.520654	−	0.853768i	$-0.674312\pi$
$227$	5.38070	−	20.0810i	0.357130	−	1.33283i	0.877783	−	0.479058i	$-0.159022\pi$
$228$	15.4916	−	2.64030i	1.02596	−	0.174858i
$229$	−15.4800	−	8.93740i	−1.02295	−	0.590600i	−0.107992	−	0.994152i	$-0.534442\pi$
$229$	−15.4800	−	8.93740i	−1.02295	−	0.590600i	−0.914957	+	0.403552i	$0.867776\pi$
$230$	6.58087	+	15.6945i	0.433930	+	1.03486i
$231$	−23.6127	+	1.72408i	−1.55360	+	0.113436i
$232$	3.89241	−	2.93403i	0.255549	−	0.192628i
$233$	0.340822	−	0.0913229i	0.0223280	−	0.00598276i	−0.247638	−	0.968853i	$-0.579654\pi$
$233$	0.340822	−	0.0913229i	0.0223280	−	0.00598276i	0.269966	+	0.962870i	$0.412988\pi$
$234$	1.10171	−	23.6787i	0.0720208	−	1.54793i
$235$	−10.7597	+	9.16140i	−0.701888	+	0.597624i
$236$	0.353364	−	3.78917i	0.0230020	−	0.246654i
$237$	16.4367	−	16.4367i	1.06768	−	1.06768i
$238$	−6.29796	−	5.97401i	−0.408236	−	0.387237i
$239$	−24.1080			−1.55941			−0.779707	−	0.626145i	$-0.784632\pi$
$239$	−24.1080			−1.55941			−0.779707	+	0.626145i	$0.784632\pi$
$240$	12.4767	+	21.8234i	0.805370	+	1.40869i
$241$	−2.17712	−	3.77087i	−0.140240	−	0.242903i	0.787347	−	0.616510i	$-0.211454\pi$
$241$	−2.17712	−	3.77087i	−0.140240	−	0.242903i	−0.927587	+	0.373607i	$0.878121\pi$
$242$	0.901794	−	0.821609i	0.0579695	−	0.0528150i
$243$	3.92325	+	14.6418i	0.251677	+	0.939270i
$244$	21.2267	−	9.75074i	1.35890	−	0.624227i
$245$	−15.6187	+	1.02776i	−0.997842	+	0.0656613i
$246$	9.11823	+	5.84569i	0.581357	+	0.372708i
$247$	−9.23923	+	2.47564i	−0.587878	+	0.157521i
$248$	9.07029	+	3.84856i	0.575964	+	0.244384i
$249$	−15.0854	+	8.70955i	−0.955998	+	0.551945i
$250$	8.24390	−	13.4921i	0.521390	−	0.853318i
$251$		−	13.3373i		−	0.841841i	−0.907098	−	0.420920i	$-0.861707\pi$
$251$		−	13.3373i		−	0.841841i	0.907098	−	0.420920i	$-0.138293\pi$
$252$	6.20485	+	25.1701i	0.390869	+	1.58557i
$253$	12.1162	+	12.1162i	0.761736	+	0.761736i
$254$	−1.21365	−	2.34778i	−0.0761514	−	0.147313i
$255$	14.5334	+	1.16607i	0.910117	+	0.0730219i
$256$	−12.4888	+	10.0015i	−0.780552	+	0.625091i
$257$	2.60327	+	9.71554i	0.162388	+	0.606039i	0.998359	+	0.0572656i	$0.0182382\pi$
$257$	2.60327	+	9.71554i	0.162388	+	0.606039i	−0.835971	+	0.548773i	$0.815095\pi$
$258$	21.7717	−	4.76137i	1.35545	−	0.296430i
$259$	−0.464217	−	6.35786i	−0.0288450	−	0.395058i
$260$	−8.79470	−	12.5206i	−0.545424	−	0.776492i
$261$	−4.22143	+	7.31173i	−0.261300	+	0.452585i
$262$	3.87589	+	4.25415i	0.239453	+	0.262822i
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.0760347	−	0.997105i	$-0.524226\pi$
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.564401	+	0.825501i	$0.690893\pi$
$264$	19.9470	+	15.5797i	1.22765	+	0.958862i
$265$	−5.27575	−	28.7092i	−0.324087	−	1.76359i
$266$	8.91804	−	5.46758i	0.546800	−	0.335239i
$267$	5.76406	+	5.76406i	0.352755	+	0.352755i
$268$	−9.03703	+	7.49529i	−0.552024	+	0.457848i
$269$	8.18828	−	4.72750i	0.499248	−	0.288241i	−0.229155	−	0.973390i	$-0.573596\pi$
$269$	8.18828	−	4.72750i	0.499248	−	0.288241i	0.728403	+	0.685149i	$0.240263\pi$
$270$	−13.4353	−	10.2169i	−0.817646	−	0.621778i
$271$	12.4949	+	7.21392i	0.759010	+	0.438214i	0.828940	−	0.559337i	$-0.188944\pi$
$271$	12.4949	+	7.21392i	0.759010	+	0.438214i	−0.0699304	+	0.997552i	$0.522278\pi$
$272$	0.702976	+	9.25330i	0.0426242	+	0.561064i
$273$	−8.35664	−	24.0294i	−0.505767	−	1.45432i
$274$	19.1879	+	12.3013i	1.15918	+	0.743152i
$275$	2.53823	−	15.7160i	0.153061	−	0.947708i
$276$	17.4926	−	24.6803i	1.05293	−	1.48558i
$277$	−31.9620	−	8.56419i	−1.92041	−	0.514572i	−0.988332	−	0.152314i	$-0.951328\pi$
$277$	−31.9620	−	8.56419i	−1.92041	−	0.514572i	−0.932078	−	0.362259i	$-0.882006\pi$
$278$	23.0178	+	7.32993i	1.38051	+	0.439620i
$279$	−17.0664			−1.02174
$280$	13.1132	+	10.3944i	0.783662	+	0.621187i
$281$	−10.1670			−0.606514			−0.303257	−	0.952909i	$-0.598074\pi$
$281$	−10.1670			−0.606514			−0.303257	+	0.952909i	$0.598074\pi$
$282$	23.9352	+	7.62209i	1.42532	+	0.453889i
$283$	−26.7548	−	7.16893i	−1.59041	−	0.426148i	−0.648280	−	0.761402i	$-0.724511\pi$
$283$	−26.7548	−	7.16893i	−1.59041	−	0.426148i	−0.942128	+	0.335254i	$0.891178\pi$
$284$	−0.650166	+	0.917319i	−0.0385803	+	0.0544329i
$285$	−5.89017	+	16.5532i	−0.348904	+	0.980527i
$286$	−12.9691	−	8.31446i	−0.766877	−	0.491644i
$287$	7.08148	+	1.35394i	0.418007	+	0.0799204i
$288$	13.1470	−	24.3967i	0.774692	−	1.43759i
$289$	−10.0612	−	5.80882i	−0.591834	−	0.341695i
$290$	0.734792	+	5.39993i	0.0431485	+	0.317095i
$291$	37.5943	−	21.7051i	2.20381	−	1.27237i
$292$	5.15414	−	4.27483i	0.301623	−	0.250165i
$293$	−3.07964	−	3.07964i	−0.179914	−	0.179914i	0.611404	−	0.791318i	$-0.290605\pi$
$293$	−3.07964	−	3.07964i	−0.179914	−	0.179914i	−0.791318	+	0.611404i	$0.790605\pi$
$294$	16.2311	+	22.5979i	0.946619	+	1.31793i
$295$	3.50282	+	2.41528i	0.203942	+	0.140623i
$296$	−4.19491	+	5.37085i	−0.243824	+	0.312174i
$297$	−16.4152	−	4.39844i	−0.952506	−	0.255223i
$298$	−8.53225	−	9.36496i	−0.494260	−	0.542498i
$299$	−9.20626	+	15.9457i	−0.532412	+	0.922164i
$300$	−28.1043	+	0.244175i	−1.62260	+	0.0140974i
$301$	12.2731	−	8.33327i	0.707408	−	0.480322i
$302$	−9.30491	+	2.03494i	−0.535437	+	0.117098i
$303$	−8.34018	−	31.1260i	−0.479131	−	1.78814i
$304$	−10.9901	−	2.06778i	−0.630326	−	0.118595i
$305$	−2.08870	+	26.0327i	−0.119598	+	1.49063i
$306$	−7.38124	−	14.2788i	−0.421958	−	0.816265i
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	0.976511	−	0.215469i	$-0.0691280\pi$
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	−0.215469	+	0.976511i	$0.569128\pi$
$308$	16.1827	+	4.68675i	0.922096	+	0.267052i
$309$			36.8239i			2.09484i
$310$	−8.71036	+	6.74401i	−0.494715	+	0.383034i
$311$	1.35454	−	0.782046i	0.0768091	−	0.0443457i	−0.461104	−	0.887346i	$-0.652546\pi$
$311$	1.35454	−	0.782046i	0.0768091	−	0.0443457i	0.537913	+	0.843001i	$0.319213\pi$
$312$	−10.6233	+	25.0370i	−0.601426	+	1.41744i
$313$	−11.7632	+	3.15193i	−0.664893	+	0.178157i	−0.575453	−	0.817835i	$-0.695174\pi$
$313$	−11.7632	+	3.15193i	−0.664893	+	0.178157i	−0.0894395	+	0.995992i	$0.528508\pi$
$314$	−13.5536	−	8.68922i	−0.764876	−	0.490361i
$315$	−27.9414	−	7.70222i	−1.57432	−	0.433971i
$316$	−15.0313	+	6.90478i	−0.845574	+	0.388424i
$317$	−7.08901	−	26.4565i	−0.398158	−	1.48595i	−0.816334	−	0.577581i	$-0.803997\pi$
$317$	−7.08901	−	26.4565i	−0.398158	−	1.48595i	0.418175	−	0.908366i	$-0.362670\pi$
$318$	−38.3547	+	34.9443i	−2.15082	+	1.95958i
$319$	2.74350	+	4.75188i	0.153606	+	0.266054i
$320$	−2.93073	−	17.6468i	−0.163833	−	0.986488i
$321$	1.15520			0.0644768
$322$	4.69660	−	19.5810i	0.261731	−	1.09121i
$323$	−4.58635	+	4.58635i	−0.255191	+	0.255191i
$324$	−0.0564478	+	0.605297i	−0.00313599	+	0.0336276i
$325$	17.0183	−	1.73633i	0.944008	−	0.0963144i
$326$	−0.000185973		0.00399709i	−1.03001e−5		0.000221378i
$327$	−19.8272	+	5.31269i	−1.09645	+	0.293792i
$328$	−4.63941	−	6.15485i	−0.256169	−	0.339845i
$329$	16.6764	−	1.21762i	0.919399	−	0.0671296i
$330$	−26.0964	+	10.9425i	−1.43656	+	0.602367i
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	0.403988	−	0.914764i	$-0.367624\pi$
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	−0.590215	+	0.807246i	$0.700957\pi$
$332$	12.2194	−	2.08260i	0.670625	−	0.114297i
$333$	3.05513	−	11.4019i	0.167420	−	0.624821i
$334$	−2.13515	−	4.13040i	−0.116830	−	0.226005i
$335$	−2.37249	−	12.9105i	−0.129623	−	0.705374i
$336$	3.35656	−	29.5539i	0.183115	−	1.61230i
$337$	12.6447	−	12.6447i	0.688801	−	0.688801i	−0.273166	−	0.961967i	$-0.588071\pi$
$337$	12.6447	−	12.6447i	0.688801	−	0.688801i	0.961967	+	0.273166i	$0.0880709\pi$
$338$	−0.555471	+	1.74432i	−0.0302137	+	0.0948783i
$339$	23.1137	+	40.0341i	1.25537	+	2.17436i
$340$	−9.40973	−	4.37084i	−0.510314	−	0.237042i
$341$	−5.54569	+	9.60542i	−0.300316	+	0.520163i
$342$	18.9227	−	4.13831i	1.02322	−	0.223774i
$343$	15.6247	+	9.94328i	0.843655	+	0.536886i
$344$	−15.7051	−	2.20488i	−0.846761	−	0.118879i
$345$	14.5140	+	30.5488i	0.781407	+	1.64469i
$346$	−22.7031	−	1.05631i	−1.22052	−	0.0567876i
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	−0.994998	−	0.0998921i	$-0.968150\pi$
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	0.911640	+	0.410990i	$0.134817\pi$
$348$	7.45621	−	6.18416i	0.399695	−	0.331506i
$349$			15.1860i			0.812888i	0.913676	+	0.406444i	$0.133231\pi$
$349$			15.1860i			0.812888i	−0.913676	+	0.406444i	$0.866769\pi$
$350$	−17.3044	+	7.11036i	−0.924960	+	0.380065i
$351$		−	18.2615i		−	0.974725i
$352$	−9.45906	−	15.3272i	−0.504169	−	0.816941i
$353$	8.90620	−	33.2384i	0.474029	−	1.76910i	−0.151035	−	0.988528i	$-0.548261\pi$
$353$	8.90620	−	33.2384i	0.474029	−	1.76910i	0.625065	−	0.780573i	$-0.285073\pi$
$354$	0.351508	−	7.55490i	0.0186825	−	0.401538i
$355$	−0.539457	−	1.13544i	−0.0286314	−	0.0602629i
$356$	−2.42139	−	5.27121i	−0.128333	−	0.279373i
$357$	−13.0545	−	11.2779i	−0.690918	−	0.596889i
$358$	−5.49120	−	25.1089i	−0.290219	−	1.32705i
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	−0.733558	−	0.679626i	$-0.762142\pi$
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	0.955353	+	0.295467i	$0.0954752\pi$
$360$	16.6121	+	26.1551i	0.875533	+	1.37850i
$361$	5.59193	+	9.68551i	0.294312	+	0.509764i
$362$	5.77364	+	1.83859i	0.303456	+	0.0966344i
$363$	1.71435	−	1.71435i	0.0899803	−	0.0899803i
$364$	−0.363904	+	18.1004i	−0.0190737	+	0.948717i
$365$	1.35312	+	7.36330i	0.0708254	+	0.385413i
$366$	41.2387	−	21.3178i	2.15558	−	1.11430i
$367$	−7.95960	+	29.7056i	−0.415488	+	1.55062i	0.368369	+	0.929679i	$0.379916\pi$
$367$	−7.95960	+	29.7056i	−0.415488	+	1.55062i	−0.783857	+	0.620941i	$0.786751\pi$
$368$	−17.7737	+	12.1446i	−0.926521	+	0.633083i
$369$	11.5616	+	6.67511i	0.601875	+	0.347493i
$370$	−2.94634	−	7.02661i	−0.153173	−	0.365296i
$371$	−15.0450	+	31.0889i	−0.781099	+	1.61406i
$372$	18.3618	+	6.80237i	0.952017	+	0.352687i
$373$	−14.5253	+	3.89204i	−0.752091	+	0.201522i	−0.614446	−	0.788959i	$-0.710620\pi$
$373$	−14.5253	+	3.89204i	−0.752091	+	0.201522i	−0.137646	+	0.990482i	$0.543954\pi$
$374$	−10.4350	−	0.485514i	−0.539583	−	0.0251053i
$375$	15.1196	−	27.5461i	0.780772	−	1.42247i
$376$	−14.0875	−	11.0031i	−0.726507	−	0.567440i
$377$	−4.16920	+	4.16920i	−0.214725	+	0.214725i
$378$	5.67617	+	19.1476i	0.291951	+	0.984844i
$379$	−1.92262			−0.0987586			−0.0493793	−	0.998780i	$-0.515724\pi$
$379$	−1.92262			−0.0987586			−0.0493793	+	0.998780i	$0.515724\pi$
$380$	8.02250	−	9.58970i	0.411545	−	0.491941i
$381$	−2.62620	−	4.54871i	−0.134544	−	0.233038i
$382$	−11.0092	−	12.0836i	−0.563280	−	0.618253i
$383$	−4.13733	−	15.4407i	−0.211408	−	0.788984i	−0.987400	−	0.158242i	$-0.949417\pi$
$383$	−4.13733	−	15.4407i	−0.211408	−	0.788984i	0.775993	−	0.630742i	$-0.217249\pi$
$384$	−23.8691	+	21.0084i	−1.21806	+	1.07208i
$385$	−13.4146	+	13.2234i	−0.683669	+	0.673926i
$386$	−3.52898	+	5.50459i	−0.179621	+	0.280176i
$387$	26.5335	−	7.10963i	1.34877	−	0.361403i
$388$	−30.4519	+	5.19004i	−1.54596	+	0.263484i
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	−0.230150	−	0.973155i	$-0.573922\pi$
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	0.727702	+	0.685893i	$0.240588\pi$
$390$	−18.6157	−	24.0435i	−0.942644	−	1.21749i
$391$			12.4854i			0.631415i
$392$	−5.24454	−	19.0917i	−0.264889	−	0.964279i
$393$	8.08735	+	8.08735i	0.407953	+	0.407953i
$394$	−12.0338	+	6.22073i	−0.606255	+	0.313396i
$395$	1.47906	−	18.4345i	0.0744198	−	0.927540i
$396$	25.4521	+	18.0396i	1.27902	+	0.906526i
$397$	3.01844	+	11.2650i	0.151491	+	0.565372i	0.999380	+	0.0351987i	$0.0112064\pi$
$397$	3.01844	+	11.2650i	0.151491	+	0.565372i	−0.847889	+	0.530173i	$0.822127\pi$
$398$	−0.525620	−	2.40343i	−0.0263469	−	0.120473i
$399$	17.1991	−	11.6780i	0.861031	−	0.584630i
$400$	18.8141	+	6.78461i	0.940703	+	0.339231i
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	−0.280587	−	0.959829i	$-0.590529\pi$
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	0.971529	−	0.236919i	$-0.0761376\pi$
$402$	−17.2480	+	15.7144i	−0.860253	+	0.783761i
$403$	−11.5123	−	3.08472i	−0.573470	−	0.153661i
$404$	−2.12921	+	22.8318i	−0.105932	+	1.13592i
$405$	−0.559555	−	0.385827i	−0.0278045	−	0.0191719i
$406$	3.07560	−	5.66741i	0.152639	−	0.281269i
$407$	−5.42456	−	5.42456i	−0.268885	−	0.268885i
$408$	2.25024	+	18.3047i	0.111403	+	0.906220i
$409$	11.9780	−	6.91550i	0.592274	−	0.341950i	−0.173722	−	0.984795i	$-0.555579\pi$
$409$	11.9780	−	6.91550i	0.592274	−	0.341950i	0.765996	+	0.642845i	$0.222246\pi$
$410$	8.53861	−	1.16189i	0.421692	−	0.0573815i
$411$	39.2281	+	22.6483i	1.93498	+	1.11716i
$412$	9.10307	−	24.5722i	0.448476	−	1.21058i
$413$	−1.65364	−	4.75501i	−0.0813702	−	0.233979i
$414$	20.1238	−	31.3895i	0.989031	−	1.54271i
$415$	−4.64600	+	13.0567i	−0.228063	+	0.640928i
$416$	13.2781	−	14.0808i	0.651013	−	0.690369i
$417$	46.3719	+	12.4253i	2.27084	+	0.608471i
$418$	3.81976	−	11.9950i	0.186830	−	0.586694i
$419$	20.6976			1.01114			0.505572	−	0.862784i	$-0.331281\pi$
$419$	20.6976			1.01114			0.505572	+	0.862784i	$0.331281\pi$
$420$	26.9924	+	19.4239i	1.31709	+	0.947787i
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	−10.1952	+	32.0153i	−0.496293	+	1.55848i
$423$	29.9067	+	8.01348i	1.45411	+	0.389629i
$424$	34.2321	−	13.8364i	1.66246	−	0.671957i
$425$	9.40528	−	6.78968i	0.456223	−	0.329348i
$426$	−1.20598	+	1.88112i	−0.0584300	+	0.0911404i
$427$	20.2013	−	23.3837i	0.977611	−	1.13162i
$428$	−0.770850	−	0.285571i	−0.0372605	−	0.0138036i
$429$	−26.5142	−	15.3080i	−1.28012	−	0.739076i
$430$	10.7327	−	14.1137i	0.517579	−	0.680623i
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.722914	+	0.690937i	$0.757198\pi$
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.959827	+	0.280594i	$0.909469\pi$
$432$	9.24374	−	19.2452i	0.444740	−	0.925937i
$433$	16.5835	+	16.5835i	0.796954	+	0.796954i	0.982614	−	0.185660i	$-0.0594423\pi$
$433$	16.5835	+	16.5835i	0.796954	+	0.796954i	−0.185660	+	0.982614i	$0.559442\pi$
$434$	13.0298	−	0.343956i	0.625448	−	0.0165104i
$435$	1.95748	+	10.6521i	0.0938540	+	0.510728i
$436$	14.5438	+	1.35630i	0.696523	+	0.0649552i
$437$	−14.5331	−	3.89412i	−0.695210	−	0.186281i
$438$	9.83716	−	8.96246i	0.470038	−	0.428243i
$439$	2.87067	−	4.97215i	0.137010	−	0.237308i	−0.789354	−	0.613939i	$-0.789584\pi$
$439$	2.87067	−	4.97215i	0.137010	−	0.237308i	0.926363	+	0.376631i	$0.122918\pi$
$440$	20.1189	−	0.850657i	0.959132	−	0.0405535i
$441$	21.2790	+	26.8936i	1.01329	+	1.28065i
$442$	−2.39824	−	10.9661i	−0.114073	−	0.521604i
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	0.970988	−	0.239126i	$-0.0768610\pi$
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	−0.960464	+	0.278405i	$0.910194\pi$
$444$	−7.83166	+	11.0497i	−0.371674	+	0.524395i
$445$	6.46467	+	0.518683i	0.306455	+	0.0245879i
$446$	−23.5074	+	12.1518i	−1.11311	+	0.575407i
$447$	−17.8032	−	17.8032i	−0.842064	−	0.842064i
$448$	−9.54570	+	18.8913i	−0.450992	+	0.892528i
$449$		−	4.66158i		−	0.219993i	−0.993932	−	0.109997i	$-0.964916\pi$
$449$		−	4.66158i		−	0.219993i	0.993932	−	0.109997i	$-0.0350840\pi$
$450$	−34.5892	+	1.91063i	−1.63055	+	0.0900680i
$451$	7.51388	−	4.33814i	0.353815	−	0.204275i
$452$	−5.52687	−	32.4282i	−0.259962	−	1.52529i
$453$	−18.2842	+	4.89923i	−0.859065	+	0.230186i
$454$	−15.8678	+	24.7510i	−0.744715	+	1.16162i
$455$	−17.4561	−	10.2460i	−0.818353	−	0.480340i
$456$	−22.0086	−	3.08984i	−1.03065	−	0.144695i
$457$	8.23274	+	30.7250i	0.385111	+	1.43726i	0.837991	+	0.545684i	$0.183730\pi$
$457$	8.23274	+	30.7250i	0.385111	+	1.43726i	−0.452880	+	0.891572i	$0.649603\pi$
$458$	17.0247	+	18.6863i	0.795513	+	0.873151i
$459$	−6.19150	−	10.7240i	−0.288995	−	0.500553i
$460$	−2.13319	−	23.9728i	−0.0994606	−	1.11774i
$461$	−23.4445			−1.09192			−0.545959	−	0.837812i	$-0.683835\pi$
$461$	−23.4445			−1.09192			−0.545959	+	0.837812i	$0.683835\pi$
$462$	32.5589	+	7.80940i	1.51478	+	0.363326i
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	−0.663017	−	0.748604i	$-0.730724\pi$
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	0.748604	+	0.663017i	$0.230724\pi$
$464$	−6.50421	+	2.28341i	−0.301950	+	0.106004i
$465$	−16.6689	+	14.1928i	−0.773001	+	0.658173i
$466$	−0.498458	−	0.0231919i	−0.0230906	−	0.00107434i
$467$	−8.01462	+	2.14751i	−0.370872	+	0.0993749i	−0.439441	−	0.898271i	$-0.644823\pi$
$467$	−8.01462	+	2.14751i	−0.370872	+	0.0993749i	0.0685687	+	0.997646i	$0.478157\pi$
$468$	−11.6456	+	31.4352i	−0.538317	+	1.45309i
$469$	−6.76572	+	13.9806i	−0.312412	+	0.645565i
$470$	18.4305	−	7.72812i	0.850135	−	0.356472i
$471$	−27.7093	−	15.9980i	−1.27678	−	0.737147i
$472$	−2.10217	+	4.95441i	−0.0967603	+	0.228045i
$473$	4.62053	−	17.2441i	0.212452	−	0.792883i
$474$	−29.2023	+	15.0957i	−1.34131	+	0.693371i
$475$	4.96976	+	13.0654i	0.228028	+	0.599482i
$476$	5.92318	+	10.7528i	0.271488	+	0.492852i
$477$	−45.2221	+	45.2221i	−2.07058	+	2.07058i
$478$	32.4864	+	10.3452i	1.48589	+	0.473177i
$479$	−6.99926	−	12.1231i	−0.319805	−	0.553918i	0.660643	−	0.750701i	$-0.270284\pi$
$479$	−6.99926	−	12.1231i	−0.319805	−	0.553918i	−0.980447	+	0.196783i	$0.936951\pi$
$480$	−7.44805	−	34.7618i	−0.339955	−	1.58665i
$481$	4.12176	−	7.13910i	0.187936	−	0.325515i
$482$	1.31559	+	6.01563i	0.0599236	+	0.274005i
$483$	7.51507	−	39.3060i	0.341948	−	1.78849i
$484$	−1.56777	+	0.720172i	−0.0712622	+	0.0327351i
$485$	11.5783	−	32.5386i	0.525743	−	1.47750i
$486$	0.996328	−	21.4139i	0.0451943	−	0.971353i
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	−0.615995	−	0.787750i	$-0.711246\pi$
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	0.927342	−	0.374214i	$-0.122087\pi$
$488$	−32.7881	+	4.03070i	−1.48425	+	0.182461i
$489$			0.00795220i			0.000359611i
$490$	21.4878	+	5.31732i	0.970720	+	0.240212i
$491$			35.5868i			1.60601i	0.595973	+	0.803004i	$0.296766\pi$
$491$			35.5868i			1.60601i	−0.595973	+	0.803004i	$0.703234\pi$
$492$	−9.77867	−	11.7901i	−0.440856	−	0.531538i
$493$	−1.03480	+	3.86191i	−0.0466049	+	0.173932i
$494$	13.5126	+	0.628702i	0.607959	+	0.0282866i
$495$	−31.5042	+	14.9679i	−1.41601	+	0.672757i
$496$	−10.5711	−	9.07830i	−0.474655	−	0.407628i
$497$	−0.279321	+	1.46093i	−0.0125293	+	0.0655316i
$498$	24.0656	−	5.26303i	1.07840	−	0.235842i
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	−0.733975	−	0.679176i	$-0.762337\pi$
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	0.955172	+	0.296053i	$0.0956705\pi$
$500$	−16.8987	+	14.6436i	−0.755733	+	0.654880i
$501$	−4.62022	−	8.00245i	−0.206416	−	0.357523i
$502$	−5.72327	+	17.9725i	−0.255442	+	0.802151i
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	−0.972010	−	0.234939i	$-0.924511\pi$
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	0.234939	+	0.972010i	$0.424511\pi$
$504$	2.43970	−	36.5803i	0.108673	−	1.62942i
$505$	−21.1064	−	14.5534i	−0.939221	−	0.647616i
$506$	−11.1277	−	21.5262i	−0.494687	−	0.956958i
$507$	−0.941607	+	3.51413i	−0.0418182	+	0.156068i
$508$	0.627968	+	3.68452i	0.0278616	+	0.163474i
$509$	−0.789343	−	0.455727i	−0.0349870	−	0.0201998i	0.482404	−	0.875949i	$-0.339764\pi$
$509$	−0.789343	−	0.455727i	−0.0349870	−	0.0201998i	−0.517391	+	0.855749i	$0.673097\pi$
$510$	−19.0839	−	7.80787i	−0.845050	−	0.345738i
$511$	3.85873	−	7.97365i	0.170700	−	0.352733i
$512$	21.1210	−	8.11815i	0.933424	−	0.358775i
$513$	14.4138	−	3.86218i	0.636386	−	0.170519i
$514$	0.661113	−	14.2092i	0.0291604	−	0.626739i
$515$	18.9930	+	22.3067i	0.836933	+	0.982949i
$516$	−31.3814	−	2.92651i	−1.38149	−	0.128833i
$517$	14.2284	−	14.2284i	0.625763	−	0.625763i
$518$	−2.10273	+	8.76666i	−0.0923885	+	0.385185i
$519$	−45.1677			−1.98264
$520$	6.47838	+	20.6459i	0.284096	+	0.905382i
$521$	3.24107	+	5.61370i	0.141994	+	0.245941i	0.928247	−	0.371963i	$-0.121315\pi$
$521$	3.24107	+	5.61370i	0.141994	+	0.245941i	−0.786254	+	0.617904i	$0.787982\pi$
$522$	8.82613	−	8.04134i	0.386309	−	0.351960i
$523$	1.22075	+	4.55591i	0.0533798	+	0.199216i	0.987466	−	0.157831i	$-0.0504502\pi$
$523$	1.22075	+	4.55591i	0.0533798	+	0.199216i	−0.934086	+	0.357047i	$0.883783\pi$
$524$	−3.39736	−	7.39585i	−0.148415	−	0.323089i
$525$	−33.6960	+	15.7138i	−1.47061	+	0.685808i
$526$	12.8015	+	8.20701i	0.558170	+	0.357842i
$527$	−7.80645	+	2.09173i	−0.340054	+	0.0911173i
$528$	−20.1938	−	29.5538i	−0.878824	−	1.28616i
$529$	−5.16358	+	2.98119i	−0.224503	+	0.129617i
$530$	−5.21039	+	40.9507i	−0.226325	+	1.77878i
$531$		−	9.32205i		−	0.404542i
$532$	−14.3636	+	3.54087i	−0.622743	+	0.153516i
$533$	6.59253	+	6.59253i	0.285554	+	0.285554i
$534$	−5.29382	−	10.2408i	−0.229086	−	0.443161i
$535$	0.699779	−	0.595828i	0.0302541	−	0.0257599i
$536$	15.3941	−	6.22222i	0.664924	−	0.268759i
$537$	−13.2203	−	49.3390i	−0.570500	−	2.12913i
$538$	−13.0627	+	2.85675i	−0.563172	+	0.123163i
$539$	22.0511	−	3.23736i	0.949808	−	0.139443i
$540$	13.7203	+	19.5329i	0.590429	+	0.840563i
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	−0.994399	−	0.105694i	$-0.966294\pi$
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	0.588733	+	0.808328i	$0.299627\pi$
$542$	−13.7417	−	15.0828i	−0.590256	−	0.647862i
$543$	11.6317	+	3.11669i	0.499162	+	0.133750i
$544$	3.02348	−	12.7708i	0.129631	−	0.547545i
$545$	−9.27048	+	13.4447i	−0.397104	+	0.575910i
$546$	0.949434	+	35.9665i	0.0406320	+	1.53922i
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	0.879212	−	0.476430i	$-0.158069\pi$
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	−0.476430	+	0.879212i	$0.658069\pi$
$548$	−20.5777	−	24.8104i	−0.879035	−	1.05985i
$549$	49.5537	−	28.6098i	2.11490	−	1.22104i
$550$	−10.1644	+	20.0886i	−0.433411	+	0.856583i
$551$	−4.17252	−	2.40901i	−0.177756	−	0.102627i
$552$	−34.1627	+	25.7512i	−1.45406	+	1.09605i
$553$	−14.3051	+	16.5586i	−0.608316	+	0.704145i
$554$	39.3949	+	25.2560i	1.67373	+	1.07303i
$555$	−6.49810	−	13.6771i	−0.275829	−	0.580560i
$556$	−27.8719	−	19.7547i	−1.18203	−	0.837786i
$557$	36.6573	+	9.82230i	1.55322	+	0.416184i	0.930509	−	0.366268i	$-0.119365\pi$
$557$	36.6573	+	9.82230i	1.55322	+	0.416184i	0.622711	+	0.782452i	$0.286031\pi$
$558$	22.9976	+	7.32349i	0.973564	+	0.310028i
$559$	19.1836			0.811378
$560$	−13.2100	−	19.6340i	−0.558226	−	0.829689i
$561$	−20.7605			−0.876510
$562$	13.7005	+	4.36286i	0.577919	+	0.184036i
$563$	36.6293	+	9.81479i	1.54374	+	0.413644i	0.927472	−	0.373892i	$-0.121977\pi$
$563$	36.6293	+	9.81479i	1.54374	+	0.413644i	0.616269	+	0.787536i	$0.288643\pi$
$564$	−28.9828	−	20.5421i	−1.22040	−	0.864978i
$565$	34.6504	+	12.3297i	1.45775	+	0.518715i
$566$	32.9768	+	21.1414i	1.38612	+	0.888638i
$567$	0.264159	+	0.759585i	0.0110936	+	0.0318996i
$568$	1.26976	−	0.957124i	0.0532780	−	0.0401600i
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	0.323601	−	0.946194i	$-0.395106\pi$
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	−0.657627	+	0.753344i	$0.728440\pi$
$570$	15.0405	−	19.7785i	0.629978	−	0.828429i
$571$	14.8692	−	8.58473i	0.622256	−	0.359260i	−0.155491	−	0.987837i	$-0.549696\pi$
$571$	14.8692	−	8.58473i	0.622256	−	0.359260i	0.777747	+	0.628578i	$0.216363\pi$
$572$	13.9084	+	16.7693i	0.581540	+	0.701160i
$573$	−22.9716	−	22.9716i	−0.959652	−	0.959652i
$574$	−8.96156	−	4.86328i	−0.374048	−	0.202989i
$575$	24.5486	+	11.0194i	1.02375	+	0.459541i
$576$	−28.1851	+	27.2339i	−1.17438	+	1.13474i
$577$	−29.5776	−	7.92529i	−1.23133	−	0.329934i	−0.416233	−	0.909258i	$-0.636650\pi$
$577$	−29.5776	−	7.92529i	−1.23133	−	0.329934i	−0.815097	+	0.579324i	$0.803317\pi$
$578$	11.0651	+	12.1450i	0.460249	+	0.505167i
$579$	−6.49731	+	11.2537i	−0.270019	+	0.467687i
$580$	1.32705	−	7.59192i	0.0551028	−	0.315237i
$581$	13.5662	−	9.21126i	0.562819	−	0.382147i
$582$	−59.9737	+	13.1160i	−2.48599	+	0.543675i
$583$	10.7574	+	40.1471i	0.445525	+	1.66272i
$584$	−8.77981	+	3.54876i	−0.363311	+	0.146849i
$585$	−24.2978	−	28.5370i	−1.00459	−	1.17986i
$586$	2.82840	+	5.47146i	0.116840	+	0.226024i
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.928520	−	0.371283i	$-0.878918\pi$
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.371283	−	0.928520i	$-0.621082\pi$
$588$	−12.1749	−	37.4165i	−0.502084	−	1.54303i
$589$		−	9.73911i		−	0.401293i
$590$	−3.68374	−	4.75780i	−0.151657	−	0.195876i
$591$	−23.3150	+	13.4609i	−0.959050	+	0.553708i
$592$	7.95753	−	5.43731i	0.327053	−	0.223472i
$593$	−7.35708	+	1.97132i	−0.302119	+	0.0809525i	−0.406694	−	0.913564i	$-0.633318\pi$
$593$	−7.35708	+	1.97132i	−0.302119	+	0.0809525i	0.104575	+	0.994517i	$0.466652\pi$
$594$	20.2326	+	12.9711i	0.830155	+	0.532212i
$595$	−13.7249	−	0.0985013i	−0.562666	−	0.00403816i
$596$	7.47885	+	16.2810i	0.306346	+	0.666895i
$597$	−1.26546	−	4.72275i	−0.0517917	−	0.193289i
$598$	19.2484	−	17.5369i	0.787125	−	0.717136i
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	0.864570	−	0.502513i	$-0.167591\pi$
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	−0.867474	+	0.497483i	$0.834258\pi$
$600$	37.9764	+	11.7310i	1.55038	+	0.478918i
$601$	−13.9872			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$601$	−13.9872			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$602$	−20.1144	+	5.96279i	−0.819801	+	0.243025i
$603$	−20.3363	+	20.3363i	−0.828157	+	0.828157i
$604$	13.4119	+	1.25075i	0.545724	+	0.0508923i
$605$	0.154267	−	1.92273i	0.00627186	−	0.0781701i
$606$	−2.11803	+	45.5223i	−0.0860390	+	1.84922i
$607$	−31.6805	+	8.48876i	−1.28587	+	0.344548i	−0.836091	−	0.548591i	$-0.815165\pi$
$607$	−31.6805	+	8.48876i	−1.28587	+	0.344548i	−0.449781	+	0.893139i	$0.648498\pi$
$608$	13.9223	+	7.50247i	0.564622	+	0.304265i
$609$	5.58221	−	11.5350i	0.226203	−	0.467423i
$610$	13.9857	−	34.1837i	0.566265	−	1.38406i
$611$	18.7255	+	10.8112i	0.757554	+	0.437374i
$612$	3.81920	+	22.4087i	0.154382	+	0.905817i
$613$	1.33983	−	5.00032i	0.0541153	−	0.201961i	−0.933575	−	0.358381i	$-0.883329\pi$
$613$	1.33983	−	5.00032i	0.0541153	−	0.201961i	0.987691	+	0.156420i	$0.0499955\pi$
$614$	−12.2467	−	23.6909i	−0.494236	−	0.956086i
$615$	16.8435	−	3.09525i	0.679197	−	0.124813i
$616$	−19.7957	−	13.2599i	−0.797590	−	0.534256i
$617$	18.4714	−	18.4714i	0.743630	−	0.743630i	−0.229644	−	0.973275i	$-0.573756\pi$
$617$	18.4714	−	18.4714i	0.743630	−	0.743630i	0.973275	+	0.229644i	$0.0737563\pi$
$618$	15.8018	−	49.6215i	0.635642	−	1.99607i
$619$	4.38197	+	7.58980i	0.176126	+	0.305060i	0.940551	−	0.339654i	$-0.110310\pi$
$619$	4.38197	+	7.58980i	0.176126	+	0.305060i	−0.764424	+	0.644714i	$0.776977\pi$
$620$	14.6315	−	5.35003i	0.587616	−	0.214862i
$621$	14.3624	−	24.8764i	0.576343	−	0.998255i
$622$	−2.16089	+	0.472576i	−0.0866437	+	0.0189486i
$623$	−5.80684	−	5.01657i	−0.232646	−	0.200985i
$624$	25.0592	−	29.1797i	1.00317	−	1.16812i
$625$	−5.04880	−	24.4849i	−0.201952	−	0.979395i
$626$	17.2038	+	0.800447i	0.687604	+	0.0319923i
$627$	6.47506	−	24.1653i	0.258589	−	0.965068i
$628$	14.5353	+	17.5252i	0.580022	+	0.699330i
$629$		−	5.58989i		−	0.222883i
$630$	34.3469	+	22.3692i	1.36841	+	0.891210i
$631$		−	31.2397i		−	1.24363i	−0.783164	−	0.621816i	$-0.786395\pi$
$631$		−	31.2397i		−	1.24363i	0.783164	−	0.621816i	$-0.213605\pi$
$632$	23.2181	−	2.85425i	0.923568	−	0.113536i
$633$	−17.2823	+	64.4986i	−0.686911	+	2.56359i
$634$	−1.80029	+	38.6932i	−0.0714985	+	1.53670i
$635$	−3.93700	−	1.40091i	−0.156235	−	0.0555936i
$636$	66.6796	−	30.6300i	2.64402	−	1.21456i
$637$	9.49304	+	21.9876i	0.376128	+	0.871180i
$638$	−1.65785	−	7.58062i	−0.0656348	−	0.300120i
$639$	−1.37709	+	2.38520i	−0.0544770	+	0.0943569i
$640$	−3.62332	+	25.0374i	−0.143224	+	0.989690i
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.636299	−	0.771443i	$-0.719535\pi$
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.349939	−	0.936772i	$-0.613798\pi$
$642$	−1.55667	−	0.495716i	−0.0614369	−	0.0195644i
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	−0.951376	−	0.308031i	$-0.900330\pi$
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	0.308031	+	0.951376i	$0.400330\pi$
$644$	−14.7314	+	24.3707i	−0.580499	+	0.960341i
$645$	20.0030	−	29.0099i	0.787618	−	1.14226i
$646$	8.14837	−	4.21219i	0.320593	−	0.165727i
$647$	−4.17257	+	15.5722i	−0.164041	+	0.612208i	0.834120	+	0.551583i	$0.185976\pi$
$647$	−4.17257	+	15.5722i	−0.164041	+	0.612208i	−0.998161	+	0.0606248i	$0.980691\pi$
$648$	0.335810	−	0.791438i	0.0131919	−	0.0310906i
$649$	−5.24671	−	3.02919i	−0.205951	−	0.118906i
$650$	−23.6779	−	4.96311i	−0.928725	−	0.194669i
$651$	25.8349	−	1.88633i	1.01255	−	0.0739310i
$652$	0.00196583	−	0.00530642i	7.69879e−5	−	0.000207816i
$653$	−21.8713	+	5.86041i	−0.855891	+	0.229335i	−0.659977	−	0.751286i	$-0.729434\pi$
$653$	−21.8713	+	5.86041i	−0.855891	+	0.229335i	−0.195914	+	0.980621i	$0.562767\pi$
$654$	28.9977	+	1.34918i	1.13390	+	0.0527572i
$655$	9.07034	+	0.727746i	0.354408	+	0.0284354i
$656$	3.61062	+	10.2847i	0.140971	+	0.401552i
$657$	11.5985	−	11.5985i	0.452501	−	0.452501i
$658$	−22.9946	−	5.51536i	−0.896421	−	0.215011i
$659$	−0.119381			−0.00465044			−0.00232522	−	0.999997i	$-0.500740\pi$
$659$	−0.119381			−0.00465044			−0.00232522	+	0.999997i	$0.500740\pi$
$660$	39.8615	−	3.54703i	1.55161	−	0.138068i
$661$	10.3433	+	17.9151i	0.402307	+	0.696816i	0.994004	−	0.109344i	$-0.0348751\pi$
$661$	10.3433	+	17.9151i	0.402307	+	0.696816i	−0.591697	+	0.806161i	$0.701542\pi$
$662$	3.72618	+	4.08983i	0.144822	+	0.158956i
$663$	−5.77388	−	21.5484i	−0.224239	−	0.836871i
$664$	−17.3597	−	2.43718i	−0.673689	−	0.0945810i
$665$	4.39536	−	15.9451i	0.170445	−	0.618324i
$666$	−9.00968	+	14.0535i	−0.349118	+	0.544562i
$667$	−8.95846	+	2.40041i	−0.346873	+	0.0929443i
$668$	1.10477	+	6.48210i	0.0427449	+	0.250800i
$669$	−45.5445	+	26.2951i	−1.76085	+	1.01663i
$670$	−2.34310	+	18.4154i	−0.0905219	+	0.711450i
$671$		−	37.1869i		−	1.43559i
$672$	−17.2052	+	38.3847i	−0.663706	+	1.48072i
$673$	34.9098	+	34.9098i	1.34568	+	1.34568i	0.890299	+	0.455376i	$0.150495\pi$
$673$	34.9098	+	34.9098i	1.34568	+	1.34568i	0.455376	+	0.890299i	$0.349505\pi$
$674$	−22.4653	+	11.6131i	−0.865330	+	0.447321i
$675$	−26.5498	+	2.70880i	−1.02190	+	0.104262i
$676$	1.49704	−	2.11217i	0.0575784	−	0.0812373i
$677$	−1.32612	−	4.94915i	−0.0509669	−	0.190211i	0.935749	−	0.352667i	$-0.114725\pi$
$677$	−1.32612	−	4.94915i	−0.0509669	−	0.190211i	−0.986716	+	0.162456i	$0.948059\pi$
$678$	−13.9672	−	63.8660i	−0.536408	−	2.45276i
$679$	−33.8082	+	22.9554i	−1.29744	+	0.880946i
$680$	10.8043	+	9.92776i	0.414328	+	0.380712i
$681$	−29.2147	+	50.6014i	−1.11951	+	1.93905i
$682$	11.5949	−	10.5639i	0.443992	−	0.404513i
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.619003	−	0.785389i	$-0.712463\pi$
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.928767	+	0.370665i	$0.879130\pi$
$684$	−27.2749	−	2.54356i	−1.04288	−	0.0972553i
$685$	35.4446	−	6.51348i	1.35427	−	0.248867i
$686$	−16.7880	−	20.1038i	−0.640970	−	0.767566i
$687$	35.5235	+	35.5235i	1.35530	+	1.35530i
$688$	20.2170	+	9.71049i	0.770766	+	0.370209i
$689$	−38.6789	+	22.3313i	−1.47355	+	0.850755i
$690$	−6.44909	−	47.3939i	−0.245513	−	1.80425i
$691$	−29.5825	−	17.0795i	−1.12537	−	0.649734i	−0.182606	−	0.983186i	$-0.558453\pi$
$691$	−29.5825	−	17.0795i	−1.12537	−	0.649734i	−0.942767	+	0.333452i	$0.891787\pi$
$692$	30.1400	+	11.1657i	1.14575	+	0.424457i
$693$	40.5352	+	7.75009i	1.53981	+	0.294402i
$694$	4.57924	−	7.14280i	0.173826	−	0.271137i
$695$	34.4993	−	16.3909i	1.30863	−	0.621742i
$696$	−12.7013	+	5.13379i	−0.481440	+	0.194596i
$697$	6.10663	+	1.63627i	0.231305	+	0.0619780i
$698$	6.51659	−	20.4637i	0.246657	−	0.774562i
$699$	−0.991682			−0.0375089
$700$	26.3695	−	2.15583i	0.996675	−	0.0814828i
$701$	−28.1444			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$701$	−28.1444			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$702$	−7.83633	+	24.6080i	−0.295763	+	0.928770i
$703$	6.50664	+	1.74345i	0.245402	+	0.0657554i
$704$	6.16927	+	24.7130i	0.232513	+	0.931406i
$705$	35.8744	−	17.0442i	1.35111	−	0.641923i
$706$	−26.2647	+	40.9682i	−0.988483	+	1.54186i
$707$	9.96406	+	28.6515i	0.374737	+	1.07755i
$708$	−3.71562	+	10.0297i	−0.139641	+	0.376938i
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	0.559434	−	0.828875i	$-0.311018\pi$
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	−0.438109	+	0.898922i	$0.644352\pi$
$710$	0.239700	+	1.76154i	0.00899579	+	0.0661094i
$711$	−35.0903	+	20.2594i	−1.31599	+	0.759788i
$712$	1.00094	+	8.14221i	0.0375118	+	0.305142i
$713$	−13.2564	−	13.2564i	−0.496456	−	0.496456i
$714$	12.7519	+	20.7993i	0.477228	+	0.778395i
$715$	−23.9570	+	4.40245i	−0.895939	+	0.164642i
$716$	−3.37509	+	36.1915i	−0.126133	+	1.35254i
$717$	65.4475	+	17.5366i	2.44418	+	0.654917i
$718$	−8.78636	+	8.00510i	−0.327904	+	0.298748i
$719$	14.3205	−	24.8039i	0.534066	−	0.925029i	−0.465142	−	0.885236i	$-0.653997\pi$
$719$	14.3205	−	24.8039i	0.534066	−	0.925029i	0.999208	−	0.0397933i	$-0.0126699\pi$
$720$	−11.1617	−	42.3736i	−0.415973	−	1.57917i
$721$	−2.52432	−	34.5728i	−0.0940106	−	1.28756i
$722$	−3.37911	−	15.4512i	−0.125757	−	0.575034i
$723$	3.16736	+	11.8207i	0.117795	+	0.439618i
$724$	−6.99122	−	4.95515i	−0.259827	−	0.184157i
$725$	6.67991	+	5.44304i	0.248086	+	0.202150i
$726$	−3.04582	+	1.57450i	−0.113041	+	0.0584350i
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.920429	+	0.390911i	$0.127840\pi$
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.390911	+	0.920429i	$0.372160\pi$
$728$	8.25757	−	24.2348i	0.306046	−	0.898200i
$729$		−	43.5147i		−	1.61166i
$730$	1.33635	−	10.5030i	0.0494607	−	0.388733i
$731$	11.2655	−	6.50414i	0.416669	−	0.240564i
$732$	−64.7186	+	11.0303i	−2.39207	+	0.407690i
$733$	19.8341	−	5.31453i	0.732589	−	0.196297i	0.126807	−	0.991927i	$-0.459527\pi$
$733$	19.8341	−	5.31453i	0.732589	−	0.196297i	0.605782	+	0.795631i	$0.292860\pi$
$734$	23.4731	−	36.6138i	0.866407	−	1.35144i
$735$	43.1488	+	8.57122i	1.59157	+	0.316154i
$736$	29.1623	−	8.73831i	1.07494	−	0.322098i
$737$	4.83758	+	18.0541i	0.178194	+	0.665031i
$738$	−12.7153	−	13.9563i	−0.468058	−	0.513738i
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.839576	−	0.543242i	$-0.817197\pi$
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.0506730	−	0.998715i	$-0.516137\pi$
$740$	0.955058	+	10.7329i	0.0351086	+	0.394551i
$741$	26.8832			0.987579
$742$	33.6146	−	35.4374i	1.23403	−	1.30095i
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	−0.634310	−	0.773078i	$-0.718716\pi$
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	0.773078	+	0.634310i	$0.218716\pi$
$744$	−21.8242	−	17.0459i	−0.800115	−	0.624931i
$745$	−19.9672	−	1.60204i	−0.731541	−	0.0586941i
$746$	21.2435	+	0.988403i	0.777781	+	0.0361880i
$747$	29.3290	−	7.85869i	1.07309	−	0.287535i
$748$	13.8533	+	5.13212i	0.506526	+	0.187649i
$749$	−1.08458	+	0.0791901i	−0.0396296	+	0.00289354i
$750$	−32.1948	+	30.6313i	−1.17559	+	1.11850i
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	0.188576	−	0.982059i	$-0.439613\pi$
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	−0.756200	+	0.654341i	$0.772946\pi$
$752$	14.2618	+	20.8723i	0.520075	+	0.761133i
$753$	−9.70180	+	36.2076i	−0.353553	+	1.31948i
$754$	7.40724	−	3.82908i	0.269756	−	0.139447i
$755$	−8.54900	+	12.3984i	−0.311130	+	0.451224i
$756$	0.567715	−	28.2378i	0.0206476	−	1.02700i
$757$	−35.0017	+	35.0017i	−1.27216	+	1.27216i	−0.327204	+	0.944954i	$0.606106\pi$
$757$	−35.0017	+	35.0017i	−1.27216	+	1.27216i	−0.944954	+	0.327204i	$0.893894\pi$
$758$	2.59081	+	0.825034i	0.0941024	+	0.0299666i
$759$	−24.0790	−	41.7061i	−0.874013	−	1.51384i
$760$	−14.9257	+	9.47987i	−0.541413	+	0.343871i
$761$	−18.0493	+	31.2622i	−0.654285	+	1.13325i	0.327788	+	0.944751i	$0.393697\pi$
$761$	−18.0493	+	31.2622i	−0.654285	+	1.13325i	−0.982073	+	0.188503i	$0.939636\pi$
$762$	1.58697	+	7.25651i	0.0574897	+	0.262876i
$763$	18.2510	−	6.34710i	0.660730	−	0.229781i
$764$	9.64999	+	21.0074i	0.349125	+	0.760022i
$765$	−23.9442	−	8.52013i	−0.865705	−	0.308046i
$766$	−1.05069	+	22.5824i	−0.0379631	+	0.815934i
$767$	1.68495	−	6.28831i	0.0608399	−	0.227058i
$768$	41.1796	−	18.0670i	1.48594	−	0.651937i
$769$		−	22.5137i		−	0.811865i	−0.913903	−	0.405933i	$-0.866947\pi$
$769$		−	22.5137i		−	0.811865i	0.913903	−	0.405933i	$-0.133053\pi$
$770$	23.7510	−	12.0626i	0.855927	−	0.434705i
$771$		−	28.2691i		−	1.01809i
$772$	7.11756	−	5.90328i	0.256167	−	0.212464i
$773$	5.98883	−	22.3506i	0.215403	−	0.803896i	−0.770621	−	0.637294i	$-0.780054\pi$
$773$	5.98883	−	22.3506i	0.215403	−	0.803896i	0.986024	−	0.166602i	$-0.0532796\pi$
$774$	−38.8057	−	1.80552i	−1.39484	−	0.0648982i
$775$	−2.77711	+	17.1950i	−0.0997566	+	0.617662i
$776$	43.2622	+	6.07370i	1.55302	+	0.218033i
$777$	−3.36460	+	17.5978i	−0.120704	+	0.631318i
$778$	−15.6550	+	3.42368i	−0.561259	+	0.122745i
$779$	−3.80923	+	6.59778i	−0.136480	+	0.236390i
$780$	14.7679	+	40.3879i	0.528775	+	1.44612i
$781$	0.894971	+	1.55014i	0.0320246	+	0.0554682i
$782$	5.35773	−	16.8246i	0.191592	−	0.601646i
$783$	6.50425	−	6.50425i	0.232443	−	0.232443i
$784$	−1.12541	+	27.9774i	−0.0401933	+	0.999192i
$785$	−25.0368	+	4.60088i	−0.893601	+	0.164213i
$786$	−7.42758	−	14.3684i	−0.264933	−	0.512505i
$787$	9.53044	−	35.5681i	0.339724	−	1.26787i	−0.558933	−	0.829213i	$-0.688789\pi$
$787$	9.53044	−	35.5681i	0.339724	−	1.26787i	0.898657	−	0.438653i	$-0.144544\pi$
$788$	18.8855	−	3.21873i	0.672767	−	0.114662i
$789$	26.1715	+	15.1101i	0.931731	+	0.537935i
$790$	−9.90368	+	24.2065i	−0.352357	+	0.861228i
$791$	−24.4452	−	36.0024i	−0.869170	−	1.28010i
$792$	−26.5565	−	35.2311i	−0.943646	−	1.25188i
$793$	38.5982	−	10.3424i	1.37066	−	0.367268i
$794$	0.766546	−	16.4752i	0.0272037	−	0.584684i
$795$	−6.56122	+	81.7766i	−0.232703	+	2.90032i
$796$	−0.323065	+	3.46427i	−0.0114507	+	0.122788i
$797$	−8.30328	+	8.30328i	−0.294117	+	0.294117i	−0.838704	−	0.544587i	$-0.816686\pi$
$797$	−8.30328	+	8.30328i	−0.294117	+	0.294117i	0.544587	+	0.838704i	$0.316686\pi$
$798$	−28.1877	+	8.35605i	−0.997832	+	0.295801i
$799$	14.6620			0.518705
$800$	−22.4413	−	17.2160i	−0.793418	−	0.608677i
$801$	−7.10464	−	12.3056i	−0.251030	−	0.434797i
$802$	−28.9284	+	26.3562i	−1.02150	+	0.930670i
$803$	−2.75904	−	10.2969i	−0.0973645	−	0.363369i
$804$	29.9857	−	13.7743i	1.05751	−	0.485781i
$805$	−15.7209	−	27.6864i	−0.554089	−	0.975817i
$806$	14.1896	+	9.09693i	0.499807	+	0.320426i
$807$	−25.6682	+	6.87776i	−0.903562	+	0.242109i
$808$	12.6667	−	29.8530i	0.445614	−	1.05022i
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.0600265	−	0.998197i	$-0.480881\pi$
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.894477	+	0.447114i	$0.147548\pi$
$810$	0.588456	+	0.760031i	0.0206762	+	0.0267048i
$811$			9.76550i			0.342913i	0.985192	+	0.171456i	$0.0548473\pi$
$811$			9.76550i			0.342913i	−0.985192	+	0.171456i	$0.945153\pi$
$812$	−6.57648	+	6.31725i	−0.230789	+	0.221692i
$813$	−28.6732	−	28.6732i	−1.00561	−	1.00561i
$814$	4.98202	+	9.63757i	0.174620	+	0.337797i
$815$	0.00410159	+	0.00481718i	0.000143673	+	0.000168738i
$816$	4.82262	−	25.6319i	0.168826	−	0.897297i
$817$	4.05719	+	15.1416i	0.141943	+	0.529739i
$818$	−19.1084	+	4.17892i	−0.668109	+	0.146112i
$819$	3.22937	+	44.2291i	0.112843	+	1.54549i
$820$	−12.0047	−	2.09839i	−0.419222	−	0.0732790i
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	−0.791368	−	0.611340i	$-0.790631\pi$
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	0.925120	+	0.379675i	$0.123964\pi$
$822$	−43.1425	−	47.3530i	−1.50477	−	1.65163i
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.999138	−	0.0415239i	$-0.0132213\pi$
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.844517	+	0.535530i	$0.179888\pi$
$824$	−22.8111	+	29.2056i	−0.794663	+	1.01743i
$825$	−18.3228	+	40.8189i	−0.637919	+	1.42113i
$826$	0.187877	+	7.11716i	0.00653708	+	0.247638i
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.961470	−	0.274910i	$-0.911352\pi$
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.274910	−	0.961470i	$-0.588648\pi$
$828$	−40.5874	+	33.6631i	−1.41051	+	1.16987i
$829$	23.4882	−	13.5609i	0.815780	−	0.470991i	−0.0331794	−	0.999449i	$-0.510563\pi$
$829$	23.4882	−	13.5609i	0.815780	−	0.470991i	0.848959	+	0.528459i	$0.177230\pi$
$830$	11.8635	−	15.6007i	0.411789	−	0.541509i
$831$	80.5397	+	46.4996i	2.79389	+	1.61305i
$832$	−23.9351	+	13.2765i	−0.829800	+	0.460281i
$833$	13.0296	+	9.69357i	0.451449	+	0.335862i
$834$	−57.1560	−	36.6426i	−1.97915	−	1.26883i
$835$	−6.92628	−	2.46460i	−0.239694	−	0.0852909i
$836$	−10.2945	+	14.5246i	−0.356044	+	0.502342i
$837$	17.9600	+	4.81237i	0.620789	+	0.166340i
$838$	−27.8908	−	8.88173i	−0.963472	−	0.306814i
$839$	−3.82948			−0.132208			−0.0661042	−	0.997813i	$-0.521057\pi$
$839$	−3.82948			−0.132208			−0.0661042	+	0.997813i	$0.521057\pi$
$840$	−28.0381	−	37.7573i	−0.967407	−	1.30275i
$841$	26.0301			0.897589
$842$	−36.0489	−	11.4796i	−1.24233	−	0.395614i
$843$	27.6011	+	7.39570i	0.950634	+	0.254722i
$844$	27.4767	−	38.7669i	0.945788	−	1.33441i
$845$	1.24212	+	2.61440i	0.0427304	+	0.0899382i
$846$	−36.8617	−	23.6320i	−1.26733	−	0.812485i
$847$	−1.49203	+	1.72708i	−0.0512669	+	0.0593431i
$848$	−52.0665	+	3.95551i	−1.78797	+	0.135833i
$849$	67.4183	+	38.9240i	2.31379	+	1.33587i
$850$	−15.5875	+	5.11337i	−0.534648	+	0.175387i
$851$	11.2296	−	6.48342i	0.384946	−	0.222249i
$852$	2.43233	−	2.01737i	0.0833302	−	0.0691138i
$853$	−1.20013	−	1.20013i	−0.0410916	−	0.0410916i	0.686262	−	0.727354i	$-0.259250\pi$
$853$	−1.20013	−	1.20013i	−0.0410916	−	0.0410916i	−0.727354	+	0.686262i	$0.759250\pi$
$854$	−37.2564	+	22.8416i	−1.27489	+	0.781624i
$855$	17.3855	−	25.2137i	0.594571	−	0.862291i
$856$	0.916206	+	0.715604i	0.0313153	+	0.0244588i
$857$	−25.5819	−	6.85466i	−0.873862	−	0.234151i	−0.206105	−	0.978530i	$-0.566079\pi$
$857$	−25.5819	−	6.85466i	−0.873862	−	0.234151i	−0.667757	+	0.744379i	$0.732746\pi$
$858$	29.1599	+	32.0058i	0.995503	+	1.09266i
$859$	19.8151	−	34.3208i	0.676083	−	1.17101i	−0.300068	−	0.953918i	$-0.597009\pi$
$859$	19.8151	−	34.3208i	0.676083	−	1.17101i	0.976151	−	0.217093i	$-0.0696574\pi$
$860$	−20.5192	+	14.4131i	−0.699700	+	0.491483i
$861$	−18.2397	−	8.82684i	−0.621608	−	0.300818i
$862$	55.7308	−	12.1881i	1.89820	−	0.415128i
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	0.995826	−	0.0912768i	$-0.0290948\pi$
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	−0.908049	+	0.418865i	$0.862428\pi$
$864$	−20.7148	+	21.9670i	−0.704731	+	0.747334i
$865$	−27.3611	+	23.2966i	−0.930305	+	0.792110i
$866$	−15.2306	−	29.4632i	−0.517558	−	1.00120i
$867$	23.0883	+	23.0883i	0.784120	+	0.784120i
$868$	−17.7057	−	5.12781i	−0.600970	−	0.174049i
$869$			26.3331i			0.893290i
$870$	1.93323	−	15.1941i	0.0655426	−	0.515127i
$871$	−17.3938	+	10.0423i	−0.589368	+	0.340272i
$872$	−19.0163	−	8.06870i	−0.643974	−	0.273241i
$873$	−73.0908	+	19.5846i	−2.47375	+	0.662839i
$874$	17.9128	+	11.4839i	0.605909	+	0.388448i
$875$	−12.3070	+	26.8987i	−0.416053	+	0.909341i
$876$	−17.1019	+	7.85595i	−0.577820	+	0.265428i
$877$	0.664074	+	2.47836i	0.0224242	+	0.0836882i	0.976231	−	0.216732i	$-0.0695398\pi$
$877$	0.664074	+	2.47836i	0.0224242	+	0.0836882i	−0.953807	+	0.300420i	$0.902873\pi$
$878$	−6.00198	+	5.46830i	−0.202557	+	0.184546i
$879$	6.12031	+	10.6007i	0.206433	+	0.357553i
$880$	−27.4760	−	7.48711i	−0.926217	−	0.252390i
$881$	20.5639			0.692816			0.346408	−	0.938084i	$-0.387401\pi$
$881$	20.5639			0.692816			0.346408	+	0.938084i	$0.387401\pi$
$882$	−17.1337	−	45.3714i	−0.576922	−	1.52773i
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	−0.0995985	−	0.995028i	$-0.531756\pi$
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	0.995028	+	0.0995985i	$0.0317558\pi$
$884$	−1.47404	+	15.8064i	−0.0495775	+	0.531626i
$885$	−7.75242	−	9.10495i	−0.260595	−	0.306059i
$886$	0.0562553	−	1.20908i	0.00188993	−	0.0406199i
$887$	−7.10873	+	1.90478i	−0.238688	+	0.0639562i	−0.376180	−	0.926547i	$-0.622762\pi$
$887$	−7.10873	+	1.90478i	−0.238688	+	0.0639562i	0.137492	+	0.990503i	$0.456096\pi$
$888$	15.2951	−	11.5292i	0.513269	−	0.386893i
$889$	2.77748	+	4.09062i	0.0931537	+	0.137195i
$890$	−8.48880	−	3.47305i	−0.284545	−	0.116417i
$891$	0.838132	+	0.483895i	0.0280785	+	0.0162111i
$892$	36.8917	−	6.28760i	1.23523	−	0.210524i
$893$	−4.57299	+	17.0666i	−0.153029	+	0.571112i
$894$	16.3508	+	31.6302i	0.546854	+	1.05787i
$895$	−33.4565	−	23.0691i	−1.11833	−	0.771115i
$896$	20.9698	−	21.3604i	0.700551	−	0.713602i
$897$	36.5921	−	36.5921i	1.22177	−	1.22177i
$898$	−2.00037	+	6.28165i	−0.0667532	+	0.209621i
$899$	−3.00169	−	5.19908i	−0.100112	−	0.173399i
$900$	47.4302	+	12.2682i	1.58101	+	0.408941i
$901$	−15.1427	+	26.2280i	−0.504478	+	0.873781i
$902$	−11.9868	+	2.62146i	−0.399117	+	0.0872852i
$903$	−39.3804	+	13.6952i	−1.31050	+	0.455748i
$904$	−6.46788	+	46.0699i	−0.215119	+	1.53226i
$905$	8.65360	−	4.11140i	0.287655	−	0.136667i
$906$	26.7409	+	1.24418i	0.888408	+	0.0413352i
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	−0.999597	−	0.0283786i	$-0.990966\pi$
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	0.879866	+	0.475222i	$0.157632\pi$
$908$	32.0036	−	26.5437i	1.06208	−	0.880884i
$909$			56.1704i			1.86305i
$910$	19.1259	+	21.2976i	0.634019	+	0.706008i
$911$		−	9.10653i		−	0.301713i	−0.988556	−	0.150856i	$-0.951797\pi$
$911$		−	9.10653i		−	0.301713i	0.988556	−	0.150856i	$-0.0482031\pi$
$912$	28.3315	+	13.6080i	0.938148	+	0.450605i
$913$	5.10735	−	19.0609i	0.169029	−	0.630823i
$914$	2.09074	−	44.9359i	0.0691557	−	1.48635i
$915$	24.6070	−	69.1534i	0.813484	−	2.28614i
$916$	−14.9228	−	32.4860i	−0.493064	−	1.07337i
$917$	−8.14737	−	7.03857i	−0.269050	−	0.232434i
$918$	3.74142	+	17.1079i	0.123485	+	0.564644i
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	−0.415312	−	0.909679i	$-0.636328\pi$
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	0.995461	−	0.0951683i	$-0.0303389\pi$
$920$	−7.41263	+	33.2197i	−0.244387	+	1.09522i
$921$	−26.5004	−	45.9000i	−0.873217	−	1.51246i
$922$	31.5923	+	10.0605i	1.04044	+	0.331324i
$923$	−1.36006	+	1.36006i	−0.0447668	+	0.0447668i
$924$	−40.5231	−	24.4951i	−1.33311	−	0.805829i
$925$	−10.9907	−	4.93353i	−0.361372	−	0.162213i
$926$	−3.27190	+	1.69136i	−0.107521	+	0.0555817i
$927$	16.6132	−	62.0014i	0.545650	−	2.03639i
$928$	9.74452	−	0.285898i	0.319879	−	0.00938505i
$929$	−32.5064	−	18.7676i	−1.06650	−	0.615745i	−0.139278	−	0.990253i	$-0.544478\pi$
$929$	−32.5064	−	18.7676i	−1.06650	−	0.615745i	−0.927223	+	0.374509i	$0.877811\pi$
$930$	28.5523	−	11.9723i	0.936268	−	0.392588i
$931$	−15.3472	+	12.1431i	−0.502983	+	0.397974i
$932$	0.661739	+	0.245150i	0.0216760	+	0.00803015i
$933$	−4.24615	+	1.13775i	−0.139013	+	0.0372483i
$934$	11.7215	+	0.545370i	0.383540	+	0.0178451i
$935$	−12.5760	+	10.7079i	−0.411280	+	0.350185i
$936$	29.1823	−	37.3628i	0.953853	−	1.22124i
$937$	−14.9371	+	14.9371i	−0.487973	+	0.487973i	−0.907666	−	0.419693i	$-0.862138\pi$
$937$	−14.9371	+	14.9371i	−0.487973	+	0.487973i	0.419693	+	0.907666i	$0.362138\pi$
$938$	15.1164	−	15.9361i	0.493568	−	0.520333i
$939$	34.2270			1.11696
$940$	−28.1520	+	2.50507i	−0.918218	+	0.0817065i
$941$	−3.05589	−	5.29296i	−0.0996192	−	0.172546i	0.811908	−	0.583786i	$-0.198429\pi$
$941$	−3.05589	−	5.29296i	−0.0996192	−	0.172546i	−0.911527	+	0.411240i	$0.865096\pi$
$942$	30.4743	+	33.4484i	0.992905	+	1.08981i
$943$	3.79564	+	14.1655i	0.123603	+	0.461293i
$944$	4.95878	−	5.77417i	0.161395	−	0.187933i
$945$	27.2326	+	15.9845i	0.885878	+	0.519974i
$946$	−13.6261	+	21.2543i	−0.443022	+	0.691036i
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.492053	−	0.870565i	$-0.336247\pi$
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.861413	+	0.507905i	$0.169580\pi$
$948$	45.8291	−	7.81083i	1.48846	−	0.253684i
$949$	9.92033	−	5.72751i	0.322028	−	0.185923i
$950$	−1.09032	−	19.7387i	−0.0353748	−	0.640409i
$951$			76.9801i			2.49625i
$952$	−3.36749	−	17.0315i	−0.109141	−	0.551994i
$953$	26.8326	+	26.8326i	0.869193	+	0.869193i	0.992383	−	0.123190i	$-0.0393125\pi$
$953$	26.8326	+	26.8326i	0.869193	+	0.869193i	−0.123190	+	0.992383i	$0.539313\pi$
$954$	80.3441	−	41.5328i	2.60123	−	1.34467i
$955$	−25.7637	−	2.06711i	−0.833695	−	0.0668903i
$956$	−39.3373	−	27.8810i	−1.27226	−	0.901736i
$957$	−3.99135	−	14.8959i	−0.129022	−	0.481517i
$958$	4.22953	+	19.3398i	0.136650	+	0.624841i
$959$	−38.3826	−	18.5747i	−1.23944	−	0.599809i
$960$	−4.88042	+	50.0390i	−0.157515	+	1.61500i
$961$	−9.43240	+	16.3374i	−0.304271	+	0.527013i
$962$	−8.61774	+	7.85148i	−0.277847	+	0.253142i
$963$	−1.94504	−	0.521171i	−0.0626779	−	0.0167945i
$964$	0.808611	−	8.67084i	0.0260436	−	0.279269i
$965$	1.86857	+	10.1683i	0.0601515	+	0.327329i
$966$	−26.9938	+	49.7415i	−0.868511	+	1.60041i
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	0.845143	−	0.534540i	$-0.179515\pi$
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	−0.534540	+	0.845143i	$0.679515\pi$
$968$	2.42167	−	0.297700i	0.0778353	−	0.00956845i
$969$	15.7871	−	9.11468i	0.507155	−	0.292806i
$970$	−29.5651	+	38.8785i	−0.949278	+	1.24831i
$971$	−18.9435	−	10.9371i	−0.607927	−	0.350987i	0.164226	−	0.986423i	$-0.447487\pi$
$971$	−18.9435	−	10.9371i	−0.607927	−	0.350987i	−0.772154	+	0.635436i	$0.780821\pi$
$972$	−10.5317	+	28.4284i	−0.337804	+	0.911843i
$973$	−44.3890	−	8.48690i	−1.42305	−	0.272078i
$974$	−20.2623	+	31.6056i	−0.649246	+	1.01271i
$975$	−47.4639	−	7.66574i	−1.52006	−	0.245500i
$976$	45.9128	+	8.63844i	1.46963	+	0.276510i
$977$	25.1707	+	6.74446i	0.805281	+	0.215774i	0.637901	−	0.770118i	$-0.279803\pi$
$977$	25.1707	+	6.74446i	0.805281	+	0.215774i	0.167380	+	0.985893i	$0.446469\pi$
$978$	0.00341244	−	0.0107159i	0.000109118	−	0.000342657i
$979$	−9.23458			−0.295138
$980$	−26.6739	−	16.3861i	−0.852066	−	0.523435i
$981$	35.7805			1.14238
$982$	15.2709	−	47.9545i	0.487315	−	1.53029i
$983$	−46.8710	−	12.5590i	−1.49495	−	0.400571i	−0.583547	−	0.812080i	$-0.698336\pi$
$983$	−46.8710	−	12.5590i	−1.49495	−	0.400571i	−0.911406	+	0.411508i	$0.865002\pi$
$984$	8.11777	+	20.0838i	0.258785	+	0.640248i
$985$	−7.18055	+	20.1796i	−0.228791	+	0.642975i
$986$	3.05165	−	4.76002i	0.0971842	−	0.151590i
$987$	−46.1583	−	8.82518i	−1.46923	−	0.280909i
$988$	−17.9389	−	6.64569i	−0.570712	−	0.211427i
$989$	26.1325	+	15.0876i	0.830965	+	0.479758i
$990$	48.8760	−	6.65077i	1.55338	−	0.211375i
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	−0.553120	−	0.833102i	$-0.686563\pi$
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	0.444927	+	0.895567i	$0.353230\pi$
$992$	10.3492	+	16.7696i	0.328589	+	0.532435i
$993$	7.77497	+	7.77497i	0.246731	+	0.246731i
$994$	1.00331	−	1.84879i	0.0318230	−	0.0586402i
$995$	−3.20247	−	2.20818i	−0.101525	−	0.0700041i
$996$	−34.6877	−	3.23485i	−1.09912	−	0.102500i
$997$	−49.5831	−	13.2857i	−1.57031	−	0.420764i	−0.634402	−	0.773004i	$-0.718753\pi$
$997$	−49.5831	−	13.2857i	−1.57031	−	0.420764i	−0.935910	+	0.352240i	$0.885420\pi$
$998$	−10.3309	+	9.41233i	−0.327020	+	0.297942i
$999$	−6.43023	+	11.1375i	−0.203443	+	0.352374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.3	✓	72
4.3	odd	2	inner	140.2.w.b.23.13	yes	72
5.2	odd	4	inner	140.2.w.b.107.11	yes	72
5.3	odd	4		700.2.be.e.107.8		72
5.4	even	2		700.2.be.e.443.16		72
7.2	even	3		980.2.k.k.883.11		36
7.3	odd	6		980.2.x.m.263.15		72
7.4	even	3	inner	140.2.w.b.123.15	yes	72
7.5	odd	6		980.2.k.j.883.11		36
7.6	odd	2		980.2.x.m.863.3		72
20.3	even	4		700.2.be.e.107.4		72
20.7	even	4	inner	140.2.w.b.107.15	yes	72
20.19	odd	2		700.2.be.e.443.6		72
28.3	even	6		980.2.x.m.263.11		72
28.11	odd	6	inner	140.2.w.b.123.11	yes	72
28.19	even	6		980.2.k.j.883.2		36
28.23	odd	6		980.2.k.k.883.2		36
28.27	even	2		980.2.x.m.863.13		72
35.2	odd	12		980.2.k.k.687.2		36
35.4	even	6		700.2.be.e.543.4		72
35.12	even	12		980.2.k.j.687.2		36
35.17	even	12		980.2.x.m.67.13		72
35.18	odd	12		700.2.be.e.207.6		72
35.27	even	4		980.2.x.m.667.11		72
35.32	odd	12	inner	140.2.w.b.67.13	yes	72
140.27	odd	4		980.2.x.m.667.15		72
140.39	odd	6		700.2.be.e.543.8		72
140.47	odd	12		980.2.k.j.687.11		36
140.67	even	12	inner	140.2.w.b.67.3	yes	72
140.87	odd	12		980.2.x.m.67.3		72
140.107	even	12		980.2.k.k.687.11		36
140.123	even	12		700.2.be.e.207.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	1.1	even	1	trivial
140.2.w.b.23.13	yes	72	4.3	odd	2	inner
140.2.w.b.67.3	yes	72	140.67	even	12	inner
140.2.w.b.67.13	yes	72	35.32	odd	12	inner
140.2.w.b.107.11	yes	72	5.2	odd	4	inner
140.2.w.b.107.15	yes	72	20.7	even	4	inner
140.2.w.b.123.11	yes	72	28.11	odd	6	inner
140.2.w.b.123.15	yes	72	7.4	even	3	inner
700.2.be.e.107.4		72	20.3	even	4
700.2.be.e.107.8		72	5.3	odd	4
700.2.be.e.207.6		72	35.18	odd	12
700.2.be.e.207.16		72	140.123	even	12
700.2.be.e.443.6		72	20.19	odd	2
700.2.be.e.443.16		72	5.4	even	2
700.2.be.e.543.4		72	35.4	even	6
700.2.be.e.543.8		72	140.39	odd	6
980.2.k.j.687.2		36	35.12	even	12
980.2.k.j.687.11		36	140.47	odd	12
980.2.k.j.883.2		36	28.19	even	6
980.2.k.j.883.11		36	7.5	odd	6
980.2.k.k.687.2		36	35.2	odd	12
980.2.k.k.687.11		36	140.107	even	12
980.2.k.k.883.2		36	28.23	odd	6
980.2.k.k.883.11		36	7.2	even	3
980.2.x.m.67.3		72	140.87	odd	12
980.2.x.m.67.13		72	35.17	even	12
980.2.x.m.263.11		72	28.3	even	6
980.2.x.m.263.15		72	7.3	odd	6
980.2.x.m.667.11		72	35.27	even	4
980.2.x.m.667.15		72	140.27	odd	4
980.2.x.m.863.3		72	7.6	odd	2
980.2.x.m.863.13		72	28.27	even	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34754 - 0.429119i) q^{2} +(-2.71477 - 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(-2.01971 + 0.959579i) q^{5} +(3.34610 + 2.14518i) q^{6} +(2.59868 + 0.496852i) q^{7} +(-1.70252 - 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(3.13340 - 0.426375i) q^{10} +(2.75736 - 1.59196i) q^{11} +(-3.58846 - 4.32659i) q^{12} +(2.41925 + 2.41925i) q^{13} +(-3.28861 - 1.78467i) q^{14} +(6.18105 - 1.13586i) q^{15} +(1.32498 + 3.77418i) q^{16} +(2.24094 + 0.600458i) q^{17} +(-4.66612 - 5.12151i) q^{18} +(-1.39787 + 2.42118i) q^{19} +(-4.40534 - 0.770044i) q^{20} +(-6.69340 - 3.23917i) q^{21} +(-4.39878 + 0.961994i) q^{22} +(1.39288 + 5.19830i) q^{23} +(2.97897 + 7.37012i) q^{24} +(3.15842 - 3.87613i) q^{25} +(-2.22189 - 4.29818i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(3.66569 + 3.81611i) q^{28} +1.72334i q^{29} +(-8.81662 - 1.12179i) q^{30} +(-3.01685 + 1.74178i) q^{31} +(-0.165897 - 5.65442i) q^{32} +(-8.64362 + 2.31605i) q^{33} +(-2.76208 - 1.77077i) q^{34} +(-5.72534 + 1.49014i) q^{35} +(4.09004 + 8.90375i) q^{36} +(-0.623610 - 2.32734i) q^{37} +(2.92265 - 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +(5.60592 + 2.92808i) q^{40} +2.72503 q^{41} +(7.62961 + 7.23716i) q^{42} +(3.96477 - 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(-10.9197 - 0.876123i) q^{45} +(0.353728 - 7.60261i) q^{46} +(6.10452 - 1.63570i) q^{47} +(-0.851615 - 11.2098i) q^{48} +(6.50628 + 2.58232i) q^{49} +(-5.91941 + 3.86790i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(1.14965 + 6.74541i) q^{52} +(-3.37866 + 12.6093i) q^{53} +(3.46629 + 6.70545i) q^{54} +(-4.04144 + 5.86120i) q^{55} +(-3.30209 - 6.71537i) q^{56} +(5.55610 - 5.55610i) q^{57} +(0.739519 - 2.32227i) q^{58} +(-0.951402 - 1.64788i) q^{59} +(11.3993 + 5.29503i) q^{60} +(5.83980 - 10.1148i) q^{61} +(4.81275 - 1.05253i) q^{62} +(9.80850 + 8.47363i) q^{63} +(-2.20286 + 7.69073i) q^{64} +(-7.20764 - 2.56471i) q^{65} +(12.6415 + 0.588172i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(2.96214 + 3.57144i) q^{68} -15.1254i q^{69} +(8.35455 + 0.448823i) q^{70} +0.562181i q^{71} +(-1.69071 - 13.7532i) q^{72} +(0.866554 - 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(-11.3940 + 8.22531i) q^{75} +(-5.08103 + 2.33403i) q^{76} +(7.95646 - 2.76700i) q^{77} +(2.90533 + 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(-6.29770 - 6.35130i) q^{80} +(0.151981 + 0.263239i) q^{81} +(-3.67208 - 1.16936i) q^{82} +(4.38250 - 4.38250i) q^{83} +(-7.17559 - 13.0264i) q^{84} +(-5.10222 + 0.937610i) q^{85} +(-7.04404 + 3.64132i) q^{86} +(1.25360 - 4.67848i) q^{87} +(-8.29011 - 3.51752i) q^{88} +(-2.51180 - 1.45019i) q^{89} +(14.3387 + 5.86644i) q^{90} +(5.08485 + 7.48887i) q^{91} +(-3.73908 + 10.0930i) q^{92} +(9.45706 - 2.53401i) q^{93} +(-8.92798 - 0.415394i) q^{94} +(0.499970 - 6.23143i) q^{95} +(-3.66277 + 15.4711i) q^{96} +(-10.9216 + 10.9216i) q^{97} +(-7.65933 - 6.27174i) q^{98} +15.5984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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