LMFDB - Embedded newform 140.2.w.b.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			107.11
Character	$\chi$	$=$	140.107
Dual form			140.2.w.b.123.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.429119 - 1.34754i) q^{2} +(-0.727420 + 2.71477i) q^{3} +(-1.63171 - 1.15651i) q^{4} +(0.178833 + 2.22891i) q^{5} +(3.34610 + 2.14518i) q^{6} +(-0.496852 + 2.59868i) q^{7} +(-2.25864 + 1.70252i) q^{8} +(-4.24276 - 2.44956i) q^{9} +O(q^{10})$	\(q+(0.429119 - 1.34754i) q^{2} +(-0.727420 + 2.71477i) q^{3} +(-1.63171 - 1.15651i) q^{4} +(0.178833 + 2.22891i) q^{5} +(3.34610 + 2.14518i) q^{6} +(-0.496852 + 2.59868i) q^{7} +(-2.25864 + 1.70252i) q^{8} +(-4.24276 - 2.44956i) q^{9} +(3.08027 + 0.715481i) q^{10} +(2.75736 - 1.59196i) q^{11} +(4.32659 - 3.58846i) 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} +(-0.600458 + 2.24094i) q^{17} +(-5.12151 + 4.66612i) q^{18} +(1.39787 - 2.42118i) q^{19} +(2.28594 - 3.84376i) q^{20} +(-6.69340 - 3.23917i) q^{21} +(-0.961994 - 4.39878i) q^{22} +(5.19830 - 1.39288i) q^{23} +(-2.97897 - 7.37012i) q^{24} +(-4.93604 + 0.797203i) q^{25} +(-2.22189 - 4.29818i) q^{26} +(3.77420 - 3.77420i) q^{27} +(3.81611 - 3.66569i) q^{28} -1.72334i q^{29} +(-4.18302 + 7.84178i) q^{30} +(-3.01685 + 1.74178i) q^{31} +(5.65442 - 0.165897i) q^{32} +(2.31605 + 8.64362i) q^{33} +(2.76208 + 1.77077i) q^{34} +(-5.88107 - 0.642706i) q^{35} +(4.09004 + 8.90375i) q^{36} +(2.32734 - 0.623610i) q^{37} +(-2.66278 - 2.92265i) q^{38} +(4.80790 + 8.32752i) q^{39} +(-4.19867 - 4.72982i) q^{40} +2.72503 q^{41} +(-7.23716 + 7.62961i) q^{42} +(-3.96477 - 3.96477i) q^{43} +(-6.34034 - 0.591276i) q^{44} +(4.70108 - 9.89476i) q^{45} +(0.353728 - 7.60261i) q^{46} +(1.63570 + 6.10452i) q^{47} +(-11.2098 + 0.851615i) q^{48} +(-6.50628 - 2.58232i) q^{49} +(-1.04388 + 6.99359i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(-6.74541 + 1.14965i) q^{52} +(12.6093 + 3.37866i) 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} +(-2.32227 - 0.739519i) q^{58} +(0.951402 + 1.64788i) q^{59} +(8.77208 + 9.00183i) q^{60} +(5.83980 - 10.1148i) q^{61} +(1.05253 + 4.81275i) q^{62} +(8.47363 - 9.80850i) q^{63} +(2.20286 - 7.69073i) q^{64} +(5.82492 + 4.95964i) q^{65} +(12.6415 + 0.588172i) q^{66} +(-5.67039 - 1.51938i) q^{67} +(3.57144 - 2.96214i) q^{68} +15.1254i q^{69} +(-3.38975 + 7.64916i) q^{70} +0.562181i q^{71} +(13.7532 - 1.69071i) q^{72} +(-3.23402 - 0.866554i) q^{73} +(0.158369 - 3.40378i) q^{74} +(1.42635 - 13.9801i) q^{75} +(-5.08103 + 2.33403i) q^{76} +(2.76700 + 7.95646i) q^{77} +(13.2848 - 2.90533i) q^{78} +(4.13532 - 7.16259i) q^{79} +(-8.17533 + 3.62821i) q^{80} +(0.151981 + 0.263239i) q^{81} +(1.16936 - 3.67208i) 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} +(4.67848 + 1.25360i) q^{87} +(-3.51752 + 8.29011i) q^{88} +(2.51180 + 1.45019i) q^{89} +(-11.3162 - 10.5809i) q^{90} +(5.08485 + 7.48887i) q^{91} +(-10.0930 - 3.73908i) q^{92} +(-2.53401 - 9.45706i) q^{93} +(8.92798 + 0.415394i) q^{94} +(5.64656 + 2.68273i) q^{95} +(-3.66277 + 15.4711i) q^{96} +(-10.9216 - 10.9216i) q^{97} +(-6.27174 + 7.65933i) 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}+O(q^{10}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.429119	−	1.34754i	0.303433	−	0.952853i
$2$	0.429119	−	1.34754i	0.303433	−	0.952853i
$3$	−0.727420	+	2.71477i	−0.419976	+	1.56737i	0.354678	+	0.934988i	$0.384590\pi$
$3$	−0.727420	+	2.71477i	−0.419976	+	1.56737i	−0.774655	+	0.632384i	$0.782076\pi$
$4$	−1.63171	−	1.15651i	−0.815857	−	0.578253i
$5$	0.178833	+	2.22891i	0.0799765	+	0.996797i
$5$	0.178833	+	2.22891i	0.0799765	+	0.996797i
$6$	3.34610	+	2.14518i	1.36604	+	0.875768i
$7$	−0.496852	+	2.59868i	−0.187792	+	0.982209i
$7$	−0.496852	+	2.59868i	−0.187792	+	0.982209i
$8$	−2.25864	+	1.70252i	−0.798548	+	0.601931i
$9$	−4.24276	−	2.44956i	−1.41425	−	0.816519i
$10$	3.08027	+	0.715481i	0.974068	+	0.226255i
$11$	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	$0.173972\pi$
$12$	4.32659	−	3.58846i	1.24898	−	1.03590i
$13$	2.41925	−	2.41925i	0.670980	−	0.670980i	−0.286962	−	0.957942i	$-0.592645\pi$
$13$	2.41925	−	2.41925i	0.670980	−	0.670980i	0.957942	+	0.286962i	$0.0926455\pi$
$14$	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
$17$	−0.600458	+	2.24094i	−0.145632	+	0.543508i	0.854094	+	0.520119i	$0.174112\pi$
$17$	−0.600458	+	2.24094i	−0.145632	+	0.543508i	−0.999726	+	0.0233890i	$0.992554\pi$
$18$	−5.12151	+	4.66612i	−1.20715	+	1.09982i
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	−0.659938	−	0.751320i	$-0.729418\pi$
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	0.980631	+	0.195863i	$0.0627510\pi$
$20$	2.28594	−	3.84376i	0.511152	−	0.859491i
$21$	−6.69340	−	3.23917i	−1.46062	−	0.706845i
$22$	−0.961994	−	4.39878i	−0.205098	−	0.937824i
$23$	5.19830	−	1.39288i	1.08392	−	0.290435i	0.327719	−	0.944775i	$-0.393720\pi$
$23$	5.19830	−	1.39288i	1.08392	−	0.290435i	0.756201	+	0.654340i	$0.227053\pi$
$24$	−2.97897	−	7.37012i	−0.608079	−	1.50442i
$25$	−4.93604	+	0.797203i	−0.987208	+	0.159441i
$26$	−2.22189	−	4.29818i	−0.435748	−	0.842942i
$27$	3.77420	−	3.77420i	0.726345	−	0.726345i
$28$	3.81611	−	3.66569i	0.721177	−	0.692751i
$29$		−	1.72334i		−	0.320017i	−0.987116	−	0.160009i	$-0.948848\pi$
$29$		−	1.72334i		−	0.320017i	0.987116	−	0.160009i	$-0.0511522\pi$
$30$	−4.18302	+	7.84178i	−0.763711	+	1.43171i
$31$	−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	$0.434611\pi$
$32$	5.65442	−	0.165897i	0.999570	−	0.0293267i
$33$	2.31605	+	8.64362i	0.403173	+	1.50466i
$34$	2.76208	+	1.77077i	0.473693	+	0.303684i
$35$	−5.88107	−	0.642706i	−0.994081	−	0.108637i
$36$	4.09004	+	8.90375i	0.681673	+	1.48396i
$37$	2.32734	−	0.623610i	0.382613	−	0.102521i	−0.0623856	−	0.998052i	$-0.519871\pi$
$37$	2.32734	−	0.623610i	0.382613	−	0.102521i	0.444999	+	0.895531i	$0.353204\pi$
$38$	−2.66278	−	2.92265i	−0.431959	−	0.474117i
$39$	4.80790	+	8.32752i	0.769880	+	1.33347i
$40$	−4.19867	−	4.72982i	−0.663868	−	0.747850i
$41$	2.72503			0.425578			0.212789	−	0.977098i	$-0.431745\pi$
$41$	2.72503			0.425578			0.212789	+	0.977098i	$0.431745\pi$
$42$	−7.23716	+	7.62961i	−1.11672	+	1.17728i
$43$	−3.96477	−	3.96477i	−0.604622	−	0.604622i	0.336914	−	0.941536i	$-0.390617\pi$
$43$	−3.96477	−	3.96477i	−0.604622	−	0.604622i	−0.941536	+	0.336914i	$0.890617\pi$
$44$	−6.34034	−	0.591276i	−0.955842	−	0.0891383i
$45$	4.70108	−	9.89476i	0.700796	−	1.47502i
$46$	0.353728	−	7.60261i	0.0521544	−	1.12094i
$47$	1.63570	+	6.10452i	0.238591	+	0.890435i	0.976497	+	0.215531i	$0.0691483\pi$
$47$	1.63570	+	6.10452i	0.238591	+	0.890435i	−0.737905	+	0.674904i	$0.764185\pi$
$48$	−11.2098	+	0.851615i	−1.61800	+	0.122920i
$49$	−6.50628	−	2.58232i	−0.929468	−	0.368903i
$50$	−1.04388	+	6.99359i	−0.147627	+	0.989043i
$51$	−5.64685	−	3.26021i	−0.790717	−	0.456521i
$52$	−6.74541	+	1.14965i	−0.935420	+	0.159427i
$53$	12.6093	+	3.37866i	1.73202	+	0.464094i	0.980648	−	0.195780i	$-0.0627238\pi$
$53$	12.6093	+	3.37866i	1.73202	+	0.464094i	0.751376	+	0.659874i	$0.229390\pi$
$54$	−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
$58$	−2.32227	−	0.739519i	−0.304929	−	0.0971036i
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	0.921288	−	0.388882i	$-0.127139\pi$
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	−0.797426	+	0.603417i	$0.793805\pi$
$60$	8.77208	+	9.00183i	1.13247	+	1.16213i
$61$	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	$-0.102180\pi$
$62$	1.05253	+	4.81275i	0.133671	+	0.611220i
$63$	8.47363	−	9.80850i	1.06758	−	1.23575i
$64$	2.20286	−	7.69073i	0.275358	−	0.961342i
$65$	5.82492	+	4.95964i	0.722493	+	0.615168i
$66$	12.6415	+	0.588172i	1.55606	+	0.0723990i
$67$	−5.67039	−	1.51938i	−0.692748	−	0.185621i	−0.104768	−	0.994497i	$-0.533410\pi$
$67$	−5.67039	−	1.51938i	−0.692748	−	0.185621i	−0.587980	+	0.808875i	$0.700077\pi$
$68$	3.57144	−	2.96214i	0.433100	−	0.359212i
$69$			15.1254i			1.82088i
$70$	−3.38975	+	7.64916i	−0.405152	+	0.914249i
$71$			0.562181i			0.0667186i	0.999443	+	0.0333593i	$0.0106206\pi$
$71$			0.562181i			0.0667186i	−0.999443	+	0.0333593i	$0.989379\pi$
$72$	13.7532	−	1.69071i	1.62084	−	0.199253i
$73$	−3.23402	−	0.866554i	−0.378514	−	0.101423i	0.0645454	−	0.997915i	$-0.479440\pi$
$73$	−3.23402	−	0.866554i	−0.378514	−	0.101423i	−0.443059	+	0.896492i	$0.646107\pi$
$74$	0.158369	−	3.40378i	0.0184100	−	0.395682i
$75$	1.42635	−	13.9801i	0.164701	−	1.61428i
$76$	−5.08103	+	2.33403i	−0.582834	+	0.267731i
$77$	2.76700	+	7.95646i	0.315329	+	0.906723i
$78$	13.2848	−	2.90533i	1.50421	−	0.328963i
$79$	4.13532	−	7.16259i	0.465260	−	0.805855i	−0.533953	−	0.845514i	$-0.679294\pi$
$79$	4.13532	−	7.16259i	0.465260	−	0.805855i	0.999213	+	0.0396596i	$0.0126274\pi$
$80$	−8.17533	+	3.62821i	−0.914030	+	0.405646i
$81$	0.151981	+	0.263239i	0.0168868	+	0.0292487i
$82$	1.16936	−	3.67208i	0.129134	−	0.405513i
$83$	−4.38250	−	4.38250i	−0.481042	−	0.481042i	0.424423	−	0.905464i	$-0.360477\pi$
$83$	−4.38250	−	4.38250i	−0.481042	−	0.481042i	−0.905464	+	0.424423i	$0.860477\pi$
$84$	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
$87$	4.67848	+	1.25360i	0.501586	+	0.134400i
$88$	−3.51752	+	8.29011i	−0.374969	+	0.883729i
$89$	2.51180	+	1.45019i	0.266250	+	0.153720i	0.627182	−	0.778872i	$-0.284208\pi$
$89$	2.51180	+	1.45019i	0.266250	+	0.153720i	−0.360932	+	0.932592i	$0.617541\pi$
$90$	−11.3162	−	10.5809i	−1.19284	−	1.11533i
$91$	5.08485	+	7.48887i	0.533037	+	0.785047i
$92$	−10.0930	−	3.73908i	−1.05227	−	0.389826i
$93$	−2.53401	−	9.45706i	−0.262765	−	0.980652i
$94$	8.92798	+	0.415394i	0.920850	+	0.0428446i
$95$	5.64656	+	2.68273i	0.579325	+	0.275242i
$96$	−3.66277	+	15.4711i	−0.373830	+	1.57902i
$97$	−10.9216	−	10.9216i	−1.10892	−	1.10892i	−0.993292	−	0.115629i	$-0.963111\pi$
$97$	−10.9216	−	10.9216i	−1.10892	−	1.10892i	−0.115629	−	0.993292i	$-0.536889\pi$
$98$	−6.27174	+	7.65933i	−0.633541	+	0.773709i
$99$	−15.5984			−1.56770
$100$	8.97618	+	4.40775i	0.897618	+	0.440775i
$101$	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	$0.640111\pi$
$102$	−6.81642	+	6.21032i	−0.674926	+	0.614914i
$103$	−12.6556	+	3.39107i	−1.24700	+	0.334132i	−0.821176	−	0.570676i	$-0.806681\pi$
$103$	−12.6556	+	3.39107i	−1.24700	+	0.334132i	−0.425821	+	0.904807i	$0.640015\pi$
$104$	−1.34539	+	9.58302i	−0.131926	+	0.939693i
$105$	6.02281	−	15.4982i	0.587766	−	1.51247i
$106$	9.96376	−	15.5417i	0.967766	−	1.50954i
$107$	−0.106381	−	0.397018i	−0.0102842	−	0.0383812i	0.960593	−	0.277959i	$-0.0896578\pi$
$107$	−0.106381	−	0.397018i	−0.0102842	−	0.0383812i	−0.970877	+	0.239577i	$0.922991\pi$
$108$	−10.5233	+	1.79353i	−1.01260	+	0.172582i
$109$	−6.32499	+	3.65173i	−0.605824	+	0.349773i	−0.771329	−	0.636436i	$-0.780408\pi$
$109$	−6.32499	+	3.65173i	−0.605824	+	0.349773i	0.165505	+	0.986209i	$0.447074\pi$
$110$	9.63244	−	2.93084i	0.918417	−	0.279445i
$111$			6.77183i			0.642753i
$112$	−10.4662	+	1.56800i	−0.988963	+	0.148162i
$113$	−11.6304	+	11.6304i	−1.09410	+	1.09410i	−0.0990127	+	0.995086i	$0.531568\pi$
$113$	−11.6304	+	11.6304i	−1.09410	+	1.09410i	−0.995086	+	0.0990127i	$0.968432\pi$
$114$	9.87128	−	5.10283i	0.924530	−	0.477924i
$115$	4.03422	+	11.3374i	0.376193	+	1.05722i
$116$	−1.99306	+	2.81201i	−0.185051	+	0.261088i
$117$	−16.1904	+	4.33820i	−1.49680	+	0.401067i
$118$	2.62884	−	0.574915i	0.242004	−	0.0529252i
$119$	−5.52515	−	2.67381i	−0.506489	−	0.245108i
$120$	15.8946	−	7.95785i	1.45097	−	0.726449i
$121$	−0.431317	+	0.747063i	−0.0392106	+	0.0679148i
$122$	−11.1241	−	12.2098i	−1.00713	−	1.10542i
$123$	−1.98224	+	7.39783i	−0.178733	+	0.667040i
$124$	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	$-0.776423\pi$
$127$	−1.32146	+	1.32146i	−0.117261	+	0.117261i	0.646042	+	0.763302i	$0.276423\pi$
$128$	−9.41826	−	6.26868i	−0.832465	−	0.554078i
$129$	13.6475	−	7.87939i	1.20159	−	0.693741i
$130$	9.18288	−	5.72103i	0.805392	−	0.501767i
$131$	−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	$0.723556\pi$
$132$	6.21727	−	16.7824i	0.541144	−	1.46072i
$133$	5.59733	+	4.83558i	0.485350	+	0.419298i
$134$	−4.48068	+	6.98907i	−0.387072	+	0.603764i
$135$	9.08728	+	7.73738i	0.782109	+	0.665928i
$136$	−2.45903	−	6.08376i	−0.210860	−	0.521678i
$137$	4.17132	−	15.5676i	0.356380	−	1.33003i	−0.522359	−	0.852726i	$-0.674948\pi$
$137$	4.17132	−	15.5676i	0.356380	−	1.33003i	0.878739	−	0.477303i	$-0.158385\pi$
$138$	20.3820	+	6.49058i	1.73503	+	0.552515i
$139$	17.0814			1.44882			0.724411	−	0.689369i	$-0.242112\pi$
$139$	17.0814			1.44882			0.724411	+	0.689369i	$0.242112\pi$
$140$	8.85293	+	7.85020i	0.748209	+	0.663463i
$141$	−17.7622			−1.49585
$142$	0.757560	+	0.241242i	0.0635730	+	0.0202446i
$143$	2.81939	−	10.5221i	0.235769	−	0.879902i
$144$	3.62347	−	19.2585i	0.301956	−	1.60488i
$145$	3.84117	−	0.308191i	0.318992	−	0.0255939i
$146$	−2.55549	+	3.98611i	−0.211494	+	0.329893i
$147$	11.7432	−	15.7846i	0.968562	−	1.30189i
$148$	−4.51877	−	1.67403i	−0.371441	−	0.137605i
$149$	−7.75810	−	4.47914i	−0.635569	−	0.366946i	0.147337	−	0.989086i	$-0.452930\pi$
$149$	−7.75810	−	4.47914i	−0.635569	−	0.366946i	−0.782905	+	0.622141i	$0.786263\pi$
$150$	−18.2266	−	7.92118i	−1.48820	−	0.646762i
$151$	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	$0.244971\pi$
$152$	0.964826	+	7.84845i	0.0782577	+	0.636593i
$153$	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
$157$	−2.94647	+	10.9964i	−0.235154	+	0.877606i	0.742926	+	0.669374i	$0.233437\pi$
$157$	−2.94647	+	10.9964i	−0.235154	+	0.877606i	−0.978080	+	0.208232i	$0.933229\pi$
$158$	−7.87732	−	8.64611i	−0.626686	−	0.687847i
$159$	−18.3446	+	31.7737i	−1.45482	+	2.51982i
$160$	1.38097	+	12.5735i	0.109175	+	0.994023i
$161$	1.03686	+	14.2008i	0.0817163	+	1.11918i
$162$	0.419942	−	0.0918394i	0.0329937	−	0.00721558i
$163$	−0.00273302		0.000732309i	−0.000214066		5.73589e-5i	−0.258926	−	0.965897i	$-0.583369\pi$
$163$	−0.00273302		0.000732309i	−0.000214066		5.73589e-5i	0.258712	+	0.965954i	$0.416702\pi$
$164$	−4.44647	−	3.15152i	−0.347211	−	0.246092i
$165$	−18.8516	+	6.70802i	−1.46760	+	0.522219i
$166$	−7.78619	+	4.02497i	−0.604326	+	0.312398i
$167$	−2.32482	+	2.32482i	−0.179900	+	0.179900i	−0.791312	−	0.611412i	$-0.790602\pi$
$167$	−2.32482	+	2.32482i	−0.179900	+	0.179900i	0.611412	+	0.791312i	$0.290602\pi$
$168$	20.6327	−	4.07952i	1.59185	−	0.314742i
$169$			1.29445i			0.0995729i
$170$	−3.45292	+	6.47309i	−0.264827	+	0.496464i
$171$	−11.8616	+	6.84831i	−0.907081	+	0.523703i
$172$	1.88409	+	11.0547i	0.143661	+	0.842910i
$173$	−4.15945	−	15.5233i	−0.316237	−	1.18021i	−0.922833	−	0.385201i	$-0.874132\pi$
$173$	−4.15945	−	15.5233i	−0.316237	−	1.18021i	0.606596	−	0.795010i	$-0.292535\pi$
$174$	3.69689	−	5.76649i	0.280261	−	0.437157i
$175$	0.380804	−	13.2233i	0.0287860	−	0.999586i
$176$	9.66180	+	8.29743i	0.728286	+	0.625443i
$177$	−5.16567	+	1.38414i	−0.388276	+	0.104038i
$178$	3.03204	−	2.76244i	0.227261	−	0.207054i
$179$	−9.08714	−	15.7394i	−0.679205	−	1.17642i	−0.975221	−	0.221235i	$-0.928991\pi$
$179$	−9.08714	−	15.7394i	−0.679205	−	1.17642i	0.296016	−	0.955183i	$-0.404342\pi$
$180$	−19.1142	+	10.7086i	−1.42469	+	0.798171i
$181$	−4.28458			−0.318471			−0.159235	−	0.987241i	$-0.550903\pi$
$181$	−4.28458			−0.318471			−0.159235	+	0.987241i	$0.550903\pi$
$182$	12.2735	−	3.63841i	0.909775	−	0.269697i
$183$	23.2114	+	23.2114i	1.71584	+	1.71584i
$184$	−9.36965	+	11.9962i	−0.690740	+	0.884371i
$185$	1.80617	+	5.07591i	0.132792	+	0.373188i
$186$	−13.8311	−	0.643525i	−1.01415	−	0.0471855i
$187$	1.91181	+	7.13498i	0.139806	+	0.521761i
$188$	4.39092	−	11.8525i	0.320241	−	0.864434i
$189$	7.93272	+	11.6832i	0.577020	+	0.849824i
$190$	6.03812	−	6.45774i	0.438051	−	0.468494i
$191$	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	$0.529332\pi$
$192$	19.2762	+	11.5747i	1.39114	+	0.835329i
$193$	−4.46599	−	1.19666i	−0.321469	−	0.0861374i	0.0944758	−	0.995527i	$-0.469882\pi$
$193$	−4.46599	−	1.19666i	−0.321469	−	0.0861374i	−0.415945	+	0.909390i	$0.636549\pi$
$194$	−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	0.905954	−	0.423376i	$-0.139155\pi$
$197$	6.77330	+	6.77330i	0.482578	+	0.482578i	−0.423376	+	0.905954i	$0.639155\pi$
$198$	−6.69356	+	21.0194i	−0.475691	+	1.49379i
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	0.833547	−	0.552448i	$-0.186306\pi$
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	−0.895208	+	0.445649i	$0.852973\pi$
$200$	9.79145	−	10.2043i	0.692360	−	0.721552i
$201$	8.24951	−	14.2886i	0.581876	−	1.00784i
$202$	15.8402	−	3.46418i	1.11451	−	0.243739i
$203$	4.47842	+	0.856247i	0.314324	+	0.0600968i
$204$	5.44359	+	11.8504i	0.381128	+	0.829691i
$205$	0.487325	+	6.07383i	0.0340363	+	0.424215i
$206$	−0.861178	+	18.5091i	−0.0600011	+	1.28959i
$207$	−25.4670	−	6.82387i	−1.77008	−	0.474292i
$208$	12.3362	+	5.92521i	0.855358	+	0.410840i
$209$		−	8.90141i		−	0.615723i
$210$	−18.2999	−	14.7665i	−1.26282	−	1.01899i
$211$		−	23.7584i		−	1.63560i	−0.575506	−	0.817798i	$-0.695195\pi$
$211$		−	23.7584i		−	1.63560i	0.575506	−	0.817798i	$-0.304805\pi$
$212$	−16.6674	−	20.0958i	−1.14472	−	1.38018i
$213$	−1.52619	−	0.408942i	−0.104573	−	0.0280202i
$214$	−0.580647	−	0.0270159i	−0.0396922	−	0.00184677i
$215$	8.12807	−	9.54613i	0.554330	−	0.651041i
$216$	−2.09890	+	14.9502i	−0.142812	+	1.01723i
$217$	−3.02740	−	8.70524i	−0.205513	−	0.590950i
$218$	2.20668	+	10.0902i	0.149455	+	0.683393i
$219$	4.70499	−	8.14928i	0.317934	−	0.550677i
$220$	0.184038	−	14.2377i	0.0124079	−	0.959909i
$221$	3.96874	+	6.87406i	0.266966	+	0.462399i
$222$	9.12529	+	2.90592i	0.612449	+	0.195032i
$223$	−13.2313	−	13.2313i	−0.886031	−	0.886031i	0.108108	−	0.994139i	$-0.465521\pi$
$223$	−13.2313	−	13.2313i	−0.886031	−	0.886031i	−0.994139	+	0.108108i	$0.965521\pi$
$224$	−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
$227$	20.0810	+	5.38070i	1.33283	+	0.357130i	0.853768	−	0.520654i	$-0.174312\pi$
$227$	20.0810	+	5.38070i	1.33283	+	0.357130i	0.479058	+	0.877783i	$0.340978\pi$
$228$	−2.64030	−	15.4916i	−0.174858	−	1.02596i
$229$	15.4800	+	8.93740i	1.02295	+	0.590600i	0.914957	−	0.403552i	$-0.132224\pi$
$229$	15.4800	+	8.93740i	1.02295	+	0.590600i	0.107992	+	0.994152i	$0.465558\pi$
$230$	17.0088	−	0.571170i	1.12152	−	0.0376618i
$231$	−23.6127	+	1.72408i	−1.55360	+	0.113436i
$232$	2.93403	+	3.89241i	0.192628	+	0.255549i
$233$	−0.0913229	−	0.340822i	−0.00598276	−	0.0223280i	0.962870	−	0.269966i	$-0.0870124\pi$
$233$	−0.0913229	−	0.340822i	−0.00598276	−	0.0223280i	−0.968853	+	0.247638i	$0.920346\pi$
$234$	−1.10171	+	23.6787i	−0.0720208	+	1.54793i
$235$	−13.3139	+	4.73751i	−0.868501	+	0.309041i
$236$	0.353364	−	3.78917i	0.0230020	−	0.246654i
$237$	16.4367	+	16.4367i	1.06768	+	1.06768i
$238$	−5.97401	+	6.29796i	−0.387237	+	0.408236i
$239$	24.1080			1.55941			0.779707	−	0.626145i	$-0.215368\pi$
$239$	24.1080			1.55941			0.779707	+	0.626145i	$0.215368\pi$
$240$	−3.90286	−	24.8334i	−0.251928	−	1.60299i
$241$	−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	$0.878121\pi$
$242$	0.821609	+	0.901794i	0.0528150	+	0.0579695i
$243$	14.6418	−	3.92325i	0.939270	−	0.251677i
$244$	−21.2267	+	9.75074i	−1.35890	+	0.624227i
$245$	4.59221	−	14.9637i	0.293385	−	0.955994i
$246$	9.11823	+	5.84569i	0.581357	+	0.372708i
$247$	−2.47564	−	9.23923i	−0.157521	−	0.587878i
$248$	3.84856	−	9.07029i	0.244384	−	0.575964i
$249$	15.0854	−	8.70955i	0.955998	−	0.551945i
$250$	−15.7747	−	1.07603i	−0.997682	−	0.0680544i
$251$		−	13.3373i		−	0.841841i	−0.907098	−	0.420920i	$-0.861707\pi$
$251$		−	13.3373i		−	0.841841i	0.907098	−	0.420920i	$-0.138293\pi$
$252$	−25.1701	+	6.20485i	−1.58557	+	0.390869i
$253$	12.1162	−	12.1162i	0.761736	−	0.761736i
$254$	1.21365	+	2.34778i	0.0761514	+	0.147313i
$255$	6.25686	−	13.1693i	0.391820	−	0.824695i
$256$	−12.4888	+	10.0015i	−0.780552	+	0.625091i
$257$	−9.71554	+	2.60327i	−0.606039	+	0.162388i	−0.548773	−	0.835971i	$-0.684905\pi$
$257$	−9.71554	+	2.60327i	−0.606039	+	0.162388i	−0.0572656	+	0.998359i	$0.518238\pi$
$258$	−4.76137	−	21.7717i	−0.296430	−	1.35545i
$259$	0.464217	+	6.35786i	0.0288450	+	0.395058i
$260$	−3.76876	−	14.8293i	−0.233728	−	0.919673i
$261$	−4.22143	+	7.31173i	−0.261300	+	0.452585i
$262$	−4.25415	+	3.87589i	−0.262822	+	0.239453i
$263$	−2.78295	+	10.3861i	−0.171604	+	0.640435i	0.825501	+	0.564401i	$0.190893\pi$
$263$	−2.78295	+	10.3861i	−0.171604	+	0.640435i	−0.997105	+	0.0760347i	$0.975774\pi$
$264$	−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
$268$	7.49529	+	9.03703i	0.457848	+	0.552024i
$269$	−8.18828	+	4.72750i	−0.499248	+	0.288241i	−0.728403	−	0.685149i	$-0.759737\pi$
$269$	−8.18828	+	4.72750i	−0.499248	+	0.288241i	0.229155	+	0.973390i	$0.426404\pi$
$270$	14.3259	−	8.92520i	0.871848	−	0.543170i
$271$	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	$0.522278\pi$
$272$	−9.25330	+	0.702976i	−0.561064	+	0.0426242i
$273$	−24.0294	+	8.35664i	−1.45432	+	0.505767i
$274$	−19.1879	−	12.3013i	−1.15918	−	0.743152i
$275$	−12.3413	+	10.0562i	−0.744209	+	0.606409i
$276$	17.4926	−	24.6803i	1.05293	−	1.48558i
$277$	8.56419	−	31.9620i	0.514572	−	1.92041i	0.152314	−	0.988332i	$-0.451328\pi$
$277$	8.56419	−	31.9620i	0.514572	−	1.92041i	0.362259	−	0.932078i	$-0.382006\pi$
$278$	7.32993	−	23.0178i	0.439620	−	1.38051i
$279$	17.0664			1.02174
$280$	14.3774	−	8.56098i	0.859214	−	0.511616i
$281$	−10.1670			−0.606514			−0.303257	−	0.952909i	$-0.598074\pi$
$281$	−10.1670			−0.606514			−0.303257	+	0.952909i	$0.598074\pi$
$282$	−7.62209	+	23.9352i	−0.453889	+	1.42532i
$283$	−7.16893	+	26.7548i	−0.426148	+	1.59041i	0.335254	+	0.942128i	$0.391178\pi$
$283$	−7.16893	+	26.7548i	−0.426148	+	1.59041i	−0.761402	+	0.648280i	$0.775489\pi$
$284$	0.650166	−	0.917319i	0.0385803	−	0.0544329i
$285$	−11.3904	+	13.3776i	−0.674710	+	0.792423i
$286$	−12.9691	−	8.31446i	−0.766877	−	0.491644i
$287$	−1.35394	+	7.08148i	−0.0799204	+	0.418007i
$288$	−24.3967	−	13.1470i	−1.43759	−	0.774692i
$289$	10.0612	+	5.80882i	0.591834	+	0.341695i
$290$	1.23302	−	5.30837i	0.0724054	−	0.311718i
$291$	37.5943	−	21.7051i	2.20381	−	1.27237i
$292$	4.27483	+	5.15414i	0.250165	+	0.301623i
$293$	−3.07964	+	3.07964i	−0.179914	+	0.179914i	−0.791318	−	0.611404i	$-0.790605\pi$
$293$	−3.07964	+	3.07964i	−0.179914	+	0.179914i	0.611404	+	0.791318i	$0.290605\pi$
$294$	−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
$297$	4.39844	−	16.4152i	0.255223	−	0.952506i
$298$	−9.36496	+	8.53225i	−0.542498	+	0.494260i
$299$	9.20626	−	15.9457i	0.532412	−	0.922164i
$300$	−18.4955	+	21.1620i	−1.06784	+	1.22179i
$301$	12.2731	−	8.33327i	0.707408	−	0.480322i
$302$	−2.03494	−	9.30491i	−0.117098	−	0.535437i
$303$	−31.1260	+	8.34018i	−1.78814	+	0.479131i
$304$	10.9901	+	2.06778i	0.630326	+	0.118595i
$305$	23.5893	+	11.2075i	1.35072	+	0.641739i
$306$	−7.38124	−	14.2788i	−0.421958	−	0.816265i
$307$	−13.3345	+	13.3345i	−0.761042	+	0.761042i	−0.976511	−	0.215469i	$-0.930872\pi$
$307$	−13.3345	+	13.3345i	−0.761042	+	0.761042i	0.215469	+	0.976511i	$0.430872\pi$
$308$	4.68675	−	16.1827i	0.267052	−	0.922096i
$309$		−	36.8239i		−	2.09484i
$310$	−10.5389	+	3.20666i	−0.598572	+	0.182126i
$311$	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	$0.319213\pi$
$312$	−25.0370	−	10.6233i	−1.41744	−	0.601426i
$313$	3.15193	+	11.7632i	0.178157	+	0.664893i	0.995992	+	0.0894395i	$0.0285076\pi$
$313$	3.15193	+	11.7632i	0.178157	+	0.664893i	−0.817835	+	0.575453i	$0.804826\pi$
$314$	13.5536	+	8.68922i	0.764876	+	0.490361i
$315$	23.3776	+	17.1328i	1.31718	+	0.965326i
$316$	−15.0313	+	6.90478i	−0.845574	+	0.388424i
$317$	26.4565	−	7.08901i	1.48595	−	0.398158i	0.577581	−	0.816334i	$-0.303997\pi$
$317$	26.4565	−	7.08901i	1.48595	−	0.398158i	0.908366	+	0.418175i	$0.137330\pi$
$318$	34.9443	+	38.3547i	1.95958	+	2.15082i
$319$	−2.74350	−	4.75188i	−0.153606	−	0.266054i
$320$	17.5359	+	3.53462i	0.980284	+	0.197591i
$321$	1.15520			0.0644768
$322$	19.5810	+	4.69660i	1.09121	+	0.261731i
$323$	4.58635	+	4.58635i	0.255191	+	0.255191i
$324$	0.0564478	−	0.605297i	0.00313599	−	0.0336276i
$325$	−10.0129	+	13.8701i	−0.555415	+	0.769377i
$326$	−0.000185973		0.00399709i	−1.03001e−5		0.000221378i
$327$	−5.31269	−	19.8272i	−0.293792	−	1.09645i
$328$	−6.15485	+	4.63941i	−0.339845	+	0.256169i
$329$	−16.6764	+	1.21762i	−0.919399	+	0.0671296i
$330$	0.949729	+	28.2818i	0.0522809	+	1.55686i
$331$	−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	$0.700957\pi$
$332$	2.08260	+	12.2194i	0.114297	+	0.670625i
$333$	−11.4019	−	3.05513i	−0.624821	−	0.167420i
$334$	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	0.961967	−	0.273166i	$-0.0880709\pi$
$337$	12.6447	+	12.6447i	0.688801	+	0.688801i	−0.273166	+	0.961967i	$0.588071\pi$
$338$	1.74432	+	0.555471i	0.0948783	+	0.0302137i
$339$	−23.1137	−	40.0341i	−1.25537	−	2.17436i
$340$	7.24102	+	7.43067i	0.392700	+	0.402985i
$341$	−5.54569	+	9.60542i	−0.300316	+	0.520163i
$342$	4.13831	+	18.9227i	0.223774	+	1.02322i
$343$	9.94328	−	15.6247i	0.536886	−	0.843655i
$344$	15.7051	+	2.20488i	0.846761	+	0.118879i
$345$	−33.7130	+	2.70492i	−1.81505	+	0.145628i
$346$	−22.7031	−	1.05631i	−1.22052	−	0.0567876i
$347$	−5.79511	−	1.55280i	−0.311098	−	0.0833585i	0.0998921	−	0.994998i	$-0.468150\pi$
$347$	−5.79511	−	1.55280i	−0.311098	−	0.0833585i	−0.410990	+	0.911640i	$0.634817\pi$
$348$	−6.18416	−	7.45621i	−0.331506	−	0.399695i
$349$		−	15.1860i		−	0.812888i	−0.913676	−	0.406444i	$-0.866769\pi$
$349$		−	15.1860i		−	0.812888i	0.913676	−	0.406444i	$-0.133231\pi$
$350$	−17.6554	−	6.18750i	−0.943723	−	0.330736i
$351$		−	18.2615i		−	0.974725i
$352$	15.3272	−	9.45906i	0.816941	−	0.504169i
$353$	−33.2384	−	8.90620i	−1.76910	−	0.474029i	−0.780573	−	0.625065i	$-0.785073\pi$
$353$	−33.2384	−	8.90620i	−1.76910	−	0.474029i	−0.988528	+	0.151035i	$0.951739\pi$
$354$	−0.351508	+	7.55490i	−0.0186825	+	0.401538i
$355$	−1.25305	+	0.100537i	−0.0665049	+	0.00533592i
$356$	−2.42139	−	5.27121i	−0.128333	−	0.279373i
$357$	11.2779	−	13.0545i	0.596889	−	0.690918i
$358$	−25.1089	+	5.49120i	−1.32705	+	0.290219i
$359$	−4.20241	+	7.27878i	−0.221795	+	0.384159i	−0.955353	−	0.295467i	$-0.904525\pi$
$359$	−4.20241	+	7.27878i	−0.221795	+	0.384159i	0.733558	+	0.679626i	$0.237858\pi$
$360$	6.22798	+	30.3523i	0.328243	+	1.59971i
$361$	5.59193	+	9.68551i	0.294312	+	0.509764i
$362$	−1.83859	+	5.77364i	−0.0966344	+	0.303456i
$363$	−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
$367$	−29.7056	−	7.95960i	−1.55062	−	0.415488i	−0.620941	−	0.783857i	$-0.713249\pi$
$367$	−29.7056	−	7.95960i	−1.55062	−	0.415488i	−0.929679	+	0.368369i	$0.879916\pi$
$368$	12.1446	+	17.7737i	0.633083	+	0.926521i
$369$	−11.5616	−	6.67511i	−0.601875	−	0.347493i
$370$	7.61504	−	0.255720i	0.395887	−	0.0132943i
$371$	−15.0450	+	31.0889i	−0.781099	+	1.61406i
$372$	−6.80237	+	18.3618i	−0.352687	+	0.952017i
$373$	3.89204	+	14.5253i	0.201522	+	0.752091i	0.990482	+	0.137646i	$0.0439536\pi$
$373$	3.89204	+	14.5253i	0.201522	+	0.752091i	−0.788959	+	0.614446i	$0.789380\pi$
$374$	10.4350	+	0.485514i	0.539583	+	0.0251053i
$375$	31.4154	+	0.679097i	1.62228	+	0.0350684i
$376$	−14.0875	−	11.0031i	−0.726507	−	0.567440i
$377$	−4.16920	−	4.16920i	−0.214725	−	0.214725i
$378$	19.1476	−	5.67617i	0.984844	−	0.291951i
$379$	1.92262			0.0987586			0.0493793	−	0.998780i	$-0.484276\pi$
$379$	1.92262			0.0987586			0.0493793	+	0.998780i	$0.484276\pi$
$380$	−6.11098	−	10.9077i	−0.313487	−	0.559555i
$381$	−2.62620	−	4.54871i	−0.134544	−	0.233038i
$382$	12.0836	−	11.0092i	0.618253	−	0.563280i
$383$	−15.4407	+	4.13733i	−0.788984	+	0.211408i	−0.630742	−	0.775993i	$-0.717249\pi$
$383$	−15.4407	+	4.13733i	−0.788984	+	0.211408i	−0.158242	+	0.987400i	$0.550583\pi$
$384$	23.8691	−	21.0084i	1.21806	−	1.07208i
$385$	−17.2394	+	7.59026i	−0.878600	+	0.386835i
$386$	−3.52898	+	5.50459i	−0.179621	+	0.280176i
$387$	7.10963	+	26.5335i	0.361403	+	1.34877i
$388$	5.19004	+	30.4519i	0.263484	+	1.54596i
$389$	−9.81327	+	5.66569i	−0.497552	+	0.287262i	−0.727702	−	0.685893i	$-0.759412\pi$
$389$	−9.81327	+	5.66569i	−0.497552	+	0.287262i	0.230150	+	0.973155i	$0.426078\pi$
$390$	8.85146	+	29.0910i	0.448211	+	1.47308i
$391$			12.4854i			0.631415i
$392$	19.0917	−	5.24454i	0.964279	−	0.264889i
$393$	8.08735	−	8.08735i	0.407953	−	0.407953i
$394$	12.0338	−	6.22073i	0.606255	−	0.313396i
$395$	16.7043	+	7.93634i	0.840483	+	0.399321i
$396$	25.4521	+	18.0396i	1.27902	+	0.906526i
$397$	−11.2650	+	3.01844i	−0.565372	+	0.151491i	−0.530173	−	0.847889i	$-0.677873\pi$
$397$	−11.2650	+	3.01844i	−0.565372	+	0.151491i	−0.0351987	+	0.999380i	$0.511206\pi$
$398$	−2.40343	+	0.525620i	−0.120473	+	0.0263469i
$399$	−17.1991	+	11.6780i	−0.861031	+	0.584630i
$400$	−9.54896	−	17.5732i	−0.477448	−	0.878660i
$401$	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	$-0.0761376\pi$
$402$	−15.7144	−	17.2480i	−0.783761	−	0.860253i
$403$	−3.08472	+	11.5123i	−0.153661	+	0.573470i
$404$	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
$408$	18.3047	−	2.25024i	0.906220	−	0.111403i
$409$	−11.9780	+	6.91550i	−0.592274	+	0.341950i	−0.765996	−	0.642845i	$-0.777754\pi$
$409$	−11.9780	+	6.91550i	−0.592274	+	0.341950i	0.173722	+	0.984795i	$0.444421\pi$
$410$	8.39384	+	1.94971i	0.414542	+	0.0962891i
$411$	39.2281	+	22.6483i	1.93498	+	1.11716i
$412$	24.5722	+	9.10307i	1.21058	+	0.448476i
$413$	−4.75501	+	1.65364i	−0.233979	+	0.0813702i
$414$	−20.1238	+	31.3895i	−0.989031	+	1.54271i
$415$	8.98444	−	10.5519i	0.441029	−	0.517973i
$416$	13.2781	−	14.0808i	0.651013	−	0.690369i
$417$	−12.4253	+	46.3719i	−0.608471	+	2.27084i
$418$	−11.9950	−	3.81976i	−0.586694	−	0.186830i
$419$	−20.6976			−1.01114			−0.505572	−	0.862784i	$-0.668719\pi$
$419$	−20.6976			−1.01114			−0.505572	+	0.862784i	$0.668719\pi$
$420$	−27.7513	+	18.3233i	−1.35412	+	0.894083i
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	−32.0153	−	10.1952i	−1.55848	−	0.496293i
$423$	8.01348	−	29.9067i	0.389629	−	1.45411i
$424$	−34.2321	+	13.8364i	−1.66246	+	0.671957i
$425$	1.17740	−	11.5401i	0.0571122	−	0.559775i
$426$	−1.20598	+	1.88112i	−0.0584300	+	0.0911404i
$427$	23.3837	+	20.2013i	1.13162	+	0.977611i
$428$	−0.285571	+	0.770850i	−0.0138036	+	0.0372605i
$429$	26.5142	+	15.3080i	1.28012	+	0.739076i
$430$	−9.37587	−	15.0493i	−0.452144	−	0.725742i
$431$	−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	$0.909469\pi$
$432$	19.2452	+	9.24374i	0.925937	+	0.444740i
$433$	16.5835	−	16.5835i	0.796954	−	0.796954i	−0.185660	−	0.982614i	$-0.559442\pi$
$433$	16.5835	−	16.5835i	0.796954	−	0.796954i	0.982614	+	0.185660i	$0.0594423\pi$
$434$	−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
$437$	3.89412	−	14.5331i	0.186281	−	0.695210i
$438$	−8.96246	−	9.83716i	−0.428243	−	0.470038i
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	−0.926363	−	0.376631i	$-0.877082\pi$
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	0.789354	+	0.613939i	$0.210416\pi$
$440$	−19.1069	−	6.35768i	−0.910887	−	0.303091i
$441$	21.2790	+	26.8936i	1.01329	+	1.28065i
$442$	10.9661	−	2.39824i	0.521604	−	0.114073i
$443$	0.826713	−	0.221517i	0.0392783	−	0.0105246i	−0.239126	−	0.970988i	$-0.576861\pi$
$443$	0.826713	−	0.221517i	0.0392783	−	0.0105246i	0.278405	+	0.960464i	$0.410194\pi$
$444$	7.83166	−	11.0497i	0.371674	−	0.524395i
$445$	−2.78314	+	5.85791i	−0.131934	+	0.277691i
$446$	−23.5074	+	12.1518i	−1.11311	+	0.575407i
$447$	17.8032	−	17.8032i	0.842064	−	0.842064i
$448$	18.8913	+	9.54570i	0.892528	+	0.450992i
$449$			4.66158i			0.219993i	0.993932	+	0.109997i	$0.0350840\pi$
$449$			4.66158i			0.219993i	−0.993932	+	0.109997i	$0.964916\pi$
$450$	21.5601	−	27.1150i	1.01635	−	1.27822i
$451$	7.51388	−	4.33814i	0.353815	−	0.204275i
$452$	32.4282	−	5.52687i	1.52529	−	0.259962i
$453$	4.89923	+	18.2842i	0.230186	+	0.859065i
$454$	15.8678	−	24.7510i	0.744715	−	1.16162i
$455$	−15.7826	+	12.6729i	−0.739902	+	0.594115i
$456$	−22.0086	−	3.08984i	−1.03065	−	0.144695i
$457$	−30.7250	+	8.23274i	−1.43726	+	0.385111i	−0.891572	−	0.452880i	$-0.850397\pi$
$457$	−30.7250	+	8.23274i	−1.43726	+	0.385111i	−0.545684	+	0.837991i	$0.683730\pi$
$458$	18.6863	−	17.0247i	0.873151	−	0.795513i
$459$	6.19150	+	10.7240i	0.288995	+	0.500553i
$460$	6.52910	−	23.1650i	0.304421	−	1.08008i
$461$	−23.4445			−1.09192			−0.545959	−	0.837812i	$-0.683835\pi$
$461$	−23.4445			−1.09192			−0.545959	+	0.837812i	$0.683835\pi$
$462$	−7.80940	+	32.5589i	−0.363326	+	1.51478i
$463$	−1.84160	−	1.84160i	−0.0855866	−	0.0855866i	0.663017	−	0.748604i	$-0.269276\pi$
$463$	−1.84160	−	1.84160i	−0.0855866	−	0.0855866i	−0.748604	+	0.663017i	$0.769276\pi$
$464$	6.50421	−	2.28341i	0.301950	−	0.106004i
$465$	20.6257	−	7.33931i	0.956495	−	0.340352i
$466$	−0.498458	−	0.0231919i	−0.0230906	−	0.00107434i
$467$	−2.14751	−	8.01462i	−0.0993749	−	0.370872i	0.898271	−	0.439441i	$-0.144823\pi$
$467$	−2.14751	−	8.01462i	−0.0993749	−	0.370872i	−0.997646	+	0.0685687i	$0.978157\pi$
$468$	31.4352	+	11.6456i	1.45309	+	0.538317i
$469$	6.76572	−	13.9806i	0.312412	−	0.645565i
$470$	0.670742	+	19.9739i	0.0309390	+	0.921327i
$471$	−27.7093	−	15.9980i	−1.27678	−	0.737147i
$472$	−4.95441	−	2.10217i	−0.228045	−	0.0967603i
$473$	−17.2441	−	4.62053i	−0.792883	−	0.212452i
$474$	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
$478$	10.3452	−	32.4864i	0.473177	−	1.48589i
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	0.980447	−	0.196783i	$-0.0630494\pi$
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	−0.660643	+	0.750701i	$0.729716\pi$
$480$	−35.1387	−	5.39722i	−1.60385	−	0.246348i
$481$	4.12176	−	7.13910i	0.187936	−	0.325515i
$482$	−6.01563	+	1.31559i	−0.274005	+	0.0599236i
$483$	−39.3060	−	7.51507i	−1.78849	−	0.341948i
$484$	1.56777	−	0.720172i	0.0712622	−	0.0327351i
$485$	22.3901	−	26.2964i	1.01668	−	1.19406i
$486$	0.996328	−	21.4139i	0.0451943	−	0.971353i
$487$	25.6423	+	6.87083i	1.16196	+	0.311347i	0.787750	−	0.615995i	$-0.211246\pi$
$487$	25.6423	+	6.87083i	1.16196	+	0.311347i	0.374214	+	0.927342i	$0.377913\pi$
$488$	4.03070	+	32.7881i	0.182461	+	1.48425i
$489$		−	0.00795220i		−	0.000359611i
$490$	−18.1935	−	12.6094i	−0.821899	−	0.569633i
$491$			35.5868i			1.60601i	0.595973	+	0.803004i	$0.296766\pi$
$491$			35.5868i			1.60601i	−0.595973	+	0.803004i	$0.703234\pi$
$492$	11.7901	−	9.77867i	0.531538	−	0.440856i
$493$	3.86191	+	1.03480i	0.173932	+	0.0466049i
$494$	−13.5126	−	0.628702i	−0.607959	−	0.0282866i
$495$	−2.78951	−	34.7673i	−0.125379	−	1.56268i
$496$	−10.5711	−	9.07830i	−0.474655	−	0.407628i
$497$	−1.46093	−	0.279321i	−0.0655316	−	0.0125293i
$498$	−5.26303	−	24.0656i	−0.235842	−	1.07840i
$499$	−4.94115	+	8.55833i	−0.221196	+	0.383123i	−0.955172	−	0.296053i	$-0.904330\pi$
$499$	−4.94115	+	8.55833i	−0.221196	+	0.383123i	0.733975	+	0.679176i	$0.237663\pi$
$500$	−8.21923	+	20.7953i	−0.367575	+	0.929994i
$501$	−4.62022	−	8.00245i	−0.206416	−	0.357523i
$502$	−17.9725	−	5.72327i	−0.802151	−	0.255442i
$503$	16.5308	+	16.5308i	0.737071	+	0.737071i	0.972010	−	0.234939i	$-0.0754890\pi$
$503$	16.5308	+	16.5308i	0.737071	+	0.737071i	−0.234939	+	0.972010i	$0.575489\pi$
$504$	−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
$507$	−3.51413	−	0.941607i	−0.156068	−	0.0418182i
$508$	3.68452	−	0.627968i	0.163474	−	0.0278616i
$509$	0.789343	+	0.455727i	0.0349870	+	0.0201998i	0.517391	−	0.855749i	$-0.326903\pi$
$509$	0.789343	+	0.455727i	0.0349870	+	0.0201998i	−0.482404	+	0.875949i	$0.660236\pi$
$510$	−15.0612	−	14.0826i	−0.666922	−	0.623586i
$511$	3.85873	−	7.97365i	0.170700	−	0.352733i
$512$	8.11815	+	21.1210i	0.358775	+	0.933424i
$513$	−3.86218	−	14.4138i	−0.170519	−	0.636386i
$514$	−0.661113	+	14.2092i	−0.0291604	+	0.626739i
$515$	−9.82161	−	27.6018i	−0.432792	−	1.21628i
$516$	−31.3814	−	2.92651i	−1.38149	−	0.128833i
$517$	14.2284	+	14.2284i	0.625763	+	0.625763i
$518$	8.76666	+	2.10273i	0.385185	+	0.0923885i
$519$	45.1677			1.98264
$520$	−21.6003	−	1.28498i	−0.947234	−	0.0563501i
$521$	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	$0.787982\pi$
$522$	8.04134	+	8.82613i	0.351960	+	0.386309i
$523$	4.55591	−	1.22075i	0.199216	−	0.0533798i	−0.157831	−	0.987466i	$-0.550450\pi$
$523$	4.55591	−	1.22075i	0.199216	−	0.0533798i	0.357047	+	0.934086i	$0.383783\pi$
$524$	3.39736	+	7.39585i	0.148415	+	0.323089i
$525$	35.6211	+	10.6527i	1.55463	+	0.464921i
$526$	12.8015	+	8.20701i	0.558170	+	0.357842i
$527$	−2.09173	−	7.80645i	−0.0911173	−	0.340054i
$528$	−29.5538	+	20.1938i	−1.28616	+	0.878824i
$529$	5.16358	−	2.98119i	0.224503	−	0.129617i
$530$	36.4228	+	19.4289i	1.58211	+	0.843938i
$531$		−	9.32205i		−	0.404542i
$532$	−3.54087	−	14.3636i	−0.153516	−	0.622743i
$533$	6.59253	−	6.59253i	0.285554	−	0.285554i
$534$	5.29382	+	10.2408i	0.229086	+	0.443161i
$535$	0.865891	−	0.308112i	0.0374358	−	0.0133209i
$536$	15.3941	−	6.22222i	0.664924	−	0.268759i
$537$	49.3390	−	13.2203i	2.12913	−	0.570500i
$538$	2.85675	+	13.0627i	0.123163	+	0.563172i
$539$	−22.0511	+	3.23736i	−0.949808	+	0.139443i
$540$	−5.87952	−	23.1347i	−0.253014	−	0.995559i
$541$	−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	$0.299627\pi$
$542$	15.0828	−	13.7417i	0.647862	−	0.590256i
$543$	3.11669	−	11.6317i	0.133750	−	0.499162i
$544$	−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	$-0.841931\pi$
$547$	−9.42028	+	9.42028i	−0.402782	+	0.402782i	0.476430	+	0.879212i	$0.341931\pi$
$548$	−24.8104	+	20.5777i	−1.05985	+	0.879035i
$549$	−49.5537	+	28.6098i	−2.11490	+	1.22104i
$550$	8.25517	+	20.9457i	0.352001	+	0.893126i
$551$	−4.17252	−	2.40901i	−0.177756	−	0.102627i
$552$	−25.7512	−	34.1627i	−1.09605	−	1.45406i
$553$	16.5586	+	14.3051i	0.704145	+	0.608316i
$554$	−39.3949	−	25.2560i	−1.67373	−	1.07303i
$555$	−15.0938	+	1.21103i	−0.640694	+	0.0514052i
$556$	−27.8719	−	19.7547i	−1.18203	−	0.837786i
$557$	−9.82230	+	36.6573i	−0.416184	+	1.55322i	0.366268	+	0.930509i	$0.380635\pi$
$557$	−9.82230	+	36.6573i	−0.416184	+	1.55322i	−0.782452	+	0.622711i	$0.786031\pi$
$558$	7.32349	−	22.9976i	0.310028	−	0.973564i
$559$	−19.1836			−0.811378
$560$	−5.36663	−	23.0478i	−0.226782	−	0.973946i
$561$	−20.7605			−0.876510
$562$	−4.36286	+	13.7005i	−0.184036	+	0.577919i
$563$	9.81479	−	36.6293i	0.413644	−	1.54374i	−0.373892	−	0.927472i	$-0.621977\pi$
$563$	9.81479	−	36.6293i	0.413644	−	1.54374i	0.787536	−	0.616269i	$-0.211357\pi$
$564$	28.9828	+	20.5421i	1.22040	+	0.864978i
$565$	−28.0030	−	23.8432i	−1.17810	−	1.00309i
$566$	32.9768	+	21.1414i	1.38612	+	0.888638i
$567$	−0.759585	+	0.264159i	−0.0318996	+	0.0110936i
$568$	−0.957124	−	1.26976i	−0.0401600	−	0.0532780i
$569$	7.96777	+	4.60019i	0.334026	+	0.192850i	0.657627	−	0.753344i	$-0.271560\pi$
$569$	7.96777	+	4.60019i	0.334026	+	0.192850i	−0.323601	+	0.946194i	$0.604894\pi$
$570$	13.1390	+	21.0896i	0.550333	+	0.883346i
$571$	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	$0.216363\pi$
$572$	−16.7693	+	13.9084i	−0.701160	+	0.581540i
$573$	−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
$577$	7.92529	−	29.5776i	0.329934	−	1.23133i	−0.579324	−	0.815097i	$-0.696683\pi$
$577$	7.92529	−	29.5776i	0.329934	−	1.23133i	0.909258	−	0.416233i	$-0.136650\pi$
$578$	12.1450	−	11.0651i	0.505167	−	0.460249i
$579$	6.49731	−	11.2537i	0.270019	−	0.467687i
$580$	−6.62412	−	3.93946i	−0.275052	−	0.163577i
$581$	13.5662	−	9.21126i	0.562819	−	0.382147i
$582$	−13.1160	−	59.9737i	−0.543675	−	2.48599i
$583$	40.1471	−	10.7574i	1.66272	−	0.445525i
$584$	8.77981	−	3.54876i	0.363311	−	0.146849i
$585$	−12.5648	−	35.3110i	−0.519491	−	1.45993i
$586$	2.82840	+	5.47146i	0.116840	+	0.226024i
$587$	31.4917	−	31.4917i	1.29980	−	1.29980i	0.371283	−	0.928520i	$-0.378918\pi$
$587$	31.4917	−	31.4917i	1.29980	−	1.29980i	0.928520	−	0.371283i	$-0.121082\pi$
$588$	−37.4165	+	12.1749i	−1.54303	+	0.502084i
$589$			9.73911i			0.401293i
$590$	1.75155	+	5.75662i	0.0721104	+	0.236996i
$591$	−23.3150	+	13.4609i	−0.959050	+	0.553708i
$592$	5.43731	+	7.95753i	0.223472	+	0.327053i
$593$	1.97132	+	7.35708i	0.0809525	+	0.302119i	0.994517	−	0.104575i	$-0.0333482\pi$
$593$	1.97132	+	7.35708i	0.0809525	+	0.302119i	−0.913564	+	0.406694i	$0.866682\pi$
$594$	−20.2326	−	12.9711i	−0.830155	−	0.532212i
$595$	4.97160	−	12.7932i	0.203816	−	0.524470i
$596$	7.47885	+	16.2810i	0.306346	+	0.666895i
$597$	4.72275	−	1.26546i	0.193289	−	0.0517917i
$598$	−17.5369	−	19.2484i	−0.717136	−	0.787125i
$599$	0.0710719	+	0.123100i	0.00290392	+	0.00502974i	0.867474	−	0.497483i	$-0.165742\pi$
$599$	0.0710719	+	0.123100i	0.00290392	+	0.00502974i	−0.864570	+	0.502513i	$0.832409\pi$
$600$	20.5798	+	34.0043i	0.840166	+	1.38822i
$601$	−13.9872			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$601$	−13.9872			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$602$	−5.96279	−	20.1144i	−0.243025	−	0.819801i
$603$	20.3363	+	20.3363i	0.828157	+	0.828157i
$604$	−13.4119	−	1.25075i	−0.545724	−	0.0508923i
$605$	−1.74227	−	0.827765i	−0.0708332	−	0.0336534i
$606$	−2.11803	+	45.5223i	−0.0860390	+	1.84922i
$607$	−8.48876	−	31.6805i	−0.344548	−	1.28587i	−0.893139	−	0.449781i	$-0.851502\pi$
$607$	−8.48876	−	31.6805i	−0.344548	−	1.28587i	0.548591	−	0.836091i	$-0.315165\pi$
$608$	7.50247	−	13.9223i	0.304265	−	0.564622i
$609$	−5.58221	+	11.5350i	−0.226203	+	0.467423i
$610$	25.2251	−	26.9782i	1.02134	−	1.09231i
$611$	18.7255	+	10.8112i	0.757554	+	0.437374i
$612$	−22.4087	+	3.81920i	−0.905817	+	0.154382i
$613$	−5.00032	−	1.33983i	−0.201961	−	0.0541153i	0.156420	−	0.987691i	$-0.450005\pi$
$613$	−5.00032	−	1.33983i	−0.201961	−	0.0541153i	−0.358381	+	0.933575i	$0.616671\pi$
$614$	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	0.973275	−	0.229644i	$-0.0737563\pi$
$617$	18.4714	+	18.4714i	0.743630	+	0.743630i	−0.229644	+	0.973275i	$0.573756\pi$
$618$	−49.6215	−	15.8018i	−1.99607	−	0.635642i
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	0.764424	−	0.644714i	$-0.223023\pi$
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	−0.940551	+	0.339654i	$0.889690\pi$
$620$	−0.201358	+	15.5777i	−0.00808674	+	0.625614i
$621$	14.3624	−	24.8764i	0.576343	−	0.998255i
$622$	−0.472576	−	2.16089i	−0.0189486	−	0.0866437i
$623$	−5.01657	+	5.80684i	−0.200985	+	0.232646i
$624$	−25.0592	+	29.1797i	−1.00317	+	1.16812i
$625$	23.7289	−	7.87005i	0.949157	−	0.314802i
$626$	17.2038	+	0.800447i	0.687604	+	0.0319923i
$627$	24.1653	+	6.47506i	0.965068	+	0.258589i
$628$	17.5252	−	14.5353i	0.699330	−	0.580022i
$629$			5.58989i			0.222883i
$630$	33.1189	−	24.1501i	1.31949	−	0.962165i
$631$		−	31.2397i		−	1.24363i	−0.783164	−	0.621816i	$-0.786395\pi$
$631$		−	31.2397i		−	1.24363i	0.783164	−	0.621816i	$-0.213605\pi$
$632$	2.85425	+	23.2181i	0.113536	+	0.923568i
$633$	64.4986	+	17.2823i	2.56359	+	0.686911i
$634$	1.80029	−	38.6932i	0.0714985	−	1.53670i
$635$	−3.18173	−	2.70909i	−0.126263	−	0.107507i
$636$	66.6796	−	30.6300i	2.64402	−	1.21456i
$637$	−21.9876	+	9.49304i	−0.871180	+	0.376128i
$638$	−7.58062	+	1.65785i	−0.300120	+	0.0656348i
$639$	1.37709	−	2.38520i	0.0544770	−	0.0943569i
$640$	12.2880	−	22.1135i	0.485726	−	0.874111i
$641$	−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	$-0.613798\pi$
$642$	0.495716	−	1.55667i	0.0195644	−	0.0614369i
$643$	16.3136	+	16.3136i	0.643345	+	0.643345i	0.951376	−	0.308031i	$-0.0996701\pi$
$643$	16.3136	+	16.3136i	0.643345	+	0.643345i	−0.308031	+	0.951376i	$0.599670\pi$
$644$	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
$647$	−15.5722	−	4.17257i	−0.612208	−	0.164041i	−0.0606248	−	0.998161i	$-0.519309\pi$
$647$	−15.5722	−	4.17257i	−0.612208	−	0.164041i	−0.551583	+	0.834120i	$0.685976\pi$
$648$	−0.791438	−	0.335810i	−0.0310906	−	0.0131919i
$649$	5.24671	+	3.02919i	0.205951	+	0.118906i
$650$	14.3938	+	19.4447i	0.564573	+	0.762683i
$651$	25.8349	−	1.88633i	1.01255	−	0.0739310i
$652$	0.00530642	+	0.00196583i	0.000207816	+	7.69879e-5i
$653$	5.86041	+	21.8713i	0.229335	+	0.855891i	0.980621	+	0.195914i	$0.0627674\pi$
$653$	5.86041	+	21.8713i	0.229335	+	0.855891i	−0.751286	+	0.659977i	$0.770566\pi$
$654$	−28.9977	−	1.34918i	−1.13390	−	0.0527572i
$655$	3.90493	−	8.21902i	0.152578	−	0.321144i
$656$	3.61062	+	10.2847i	0.140971	+	0.401552i
$657$	11.5985	+	11.5985i	0.452501	+	0.452501i
$658$	−5.51536	+	22.9946i	−0.215011	+	0.896421i
$659$	0.119381			0.00465044			0.00232522	−	0.999997i	$-0.499260\pi$
$659$	0.119381			0.00465044			0.00232522	+	0.999997i	$0.499260\pi$
$660$	38.5183	+	10.8564i	1.49932	+	0.422587i
$661$	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	$0.701542\pi$
$662$	−4.08983	+	3.72618i	−0.158956	+	0.144822i
$663$	−21.5484	+	5.77388i	−0.836871	+	0.224239i
$664$	17.3597	+	2.43718i	0.673689	+	0.0945810i
$665$	−9.77706	+	13.3407i	−0.379138	+	0.517330i
$666$	−9.00968	+	14.0535i	−0.349118	+	0.544562i
$667$	−2.40041	−	8.95846i	−0.0929443	−	0.346873i
$668$	6.48210	−	1.10477i	0.250800	−	0.0427449i
$669$	45.5445	−	26.2951i	1.76085	−	1.01663i
$670$	−16.3793	−	8.73715i	−0.632786	−	0.337545i
$671$		−	37.1869i		−	1.43559i
$672$	−38.3847	−	17.2052i	−1.48072	−	0.663706i
$673$	34.9098	−	34.9098i	1.34568	−	1.34568i	0.455376	−	0.890299i	$-0.349505\pi$
$673$	34.9098	−	34.9098i	1.34568	−	1.34568i	0.890299	−	0.455376i	$-0.150495\pi$
$674$	22.4653	−	11.6131i	0.865330	−	0.447321i
$675$	−15.6208	+	21.6384i	−0.601244	+	0.832862i
$676$	1.49704	−	2.11217i	0.0575784	−	0.0812373i
$677$	4.94915	−	1.32612i	0.190211	−	0.0509669i	−0.162456	−	0.986716i	$-0.551941\pi$
$677$	4.94915	−	1.32612i	0.190211	−	0.0509669i	0.352667	+	0.935749i	$0.385275\pi$
$678$	−63.8660	+	13.9672i	−2.45276	+	0.536408i
$679$	33.8082	−	22.9554i	1.29744	−	0.880946i
$680$	13.1204	−	6.56891i	0.503143	−	0.251906i
$681$	−29.2147	+	50.6014i	−1.11951	+	1.93905i
$682$	10.5639	+	11.5949i	0.404513	+	0.443992i
$683$	−10.8385	+	40.4498i	−0.414724	+	1.54777i	0.370665	+	0.928767i	$0.379130\pi$
$683$	−10.8385	+	40.4498i	−0.414724	+	1.54777i	−0.785389	+	0.619003i	$0.787537\pi$
$684$	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
$688$	9.71049	−	20.2170i	0.370209	−	0.770766i
$689$	38.6789	−	22.3313i	1.47355	−	0.850755i
$690$	−10.8219	+	46.5903i	−0.411983	+	1.77366i
$691$	−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	$0.891787\pi$
$692$	−11.1657	+	30.1400i	−0.424457	+	1.14575i
$693$	7.75009	−	40.5352i	0.294402	−	1.53981i
$694$	−4.57924	+	7.14280i	−0.173826	+	0.271137i
$695$	3.05471	+	38.0727i	0.115872	+	1.44418i
$696$	−12.7013	+	5.13379i	−0.481440	+	0.194596i
$697$	−1.63627	+	6.10663i	−0.0619780	+	0.231305i
$698$	−20.4637	−	6.51659i	−0.774562	−	0.246657i
$699$	0.991682			0.0375089
$700$	−15.9142	+	21.1362i	−0.601499	+	0.798874i
$701$	−28.1444			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$701$	−28.1444			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$702$	−24.6080	−	7.83633i	−0.928770	−	0.295763i
$703$	1.74345	−	6.50664i	0.0657554	−	0.245402i
$704$	−6.16927	−	24.7130i	−0.232513	−	0.931406i
$705$	−3.17647	−	39.5903i	−0.119633	−	1.49106i
$706$	−26.2647	+	40.9682i	−0.988483	+	1.54186i
$707$	−28.6515	+	9.96406i	−1.07755	+	0.374737i
$708$	10.0297	+	3.71562i	0.376938	+	0.139641i
$709$	−3.23053	−	1.86515i	−0.121325	−	0.0700471i	0.438109	−	0.898922i	$-0.355648\pi$
$709$	−3.23053	−	1.86515i	−0.121325	−	0.0700471i	−0.559434	+	0.828875i	$0.688982\pi$
$710$	−0.402230	+	1.73167i	−0.0150954	+	0.0649885i
$711$	−35.0903	+	20.2594i	−1.31599	+	0.759788i
$712$	−8.14221	+	1.00094i	−0.305142	+	0.0375118i
$713$	−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
$717$	−17.5366	+	65.4475i	−0.654917	+	2.44418i
$718$	8.00510	+	8.78636i	0.298748	+	0.327904i
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	0.465142	+	0.885236i	$0.346003\pi$
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	−0.999208	+	0.0397933i	$0.987330\pi$
$720$	43.5734	+	4.63232i	1.62389	+	0.172636i
$721$	−2.52432	−	34.5728i	−0.0940106	−	1.28756i
$722$	15.4512	−	3.37911i	0.575034	−	0.125757i
$723$	11.8207	−	3.16736i	0.439618	−	0.117795i
$724$	6.99122	+	4.95515i	0.259827	+	0.184157i
$725$	1.37386	+	8.50650i	0.0510237	+	0.315923i
$726$	−3.04582	+	1.57450i	−0.113041	+	0.0584350i
$727$	−35.3576	+	35.3576i	−1.31134	+	1.31134i	−0.390911	+	0.920429i	$0.627840\pi$
$727$	−35.3576	+	35.3576i	−1.31134	+	1.31134i	−0.920429	+	0.390911i	$0.872160\pi$
$728$	−24.2348	−	8.25757i	−0.898200	−	0.306046i
$729$			43.5147i			1.61166i
$730$	−9.34168	−	4.98311i	−0.345751	−	0.184433i
$731$	11.2655	−	6.50414i	0.416669	−	0.240564i
$732$	−11.0303	−	64.7186i	−0.407690	−	2.39207i
$733$	−5.31453	−	19.8341i	−0.196297	−	0.732589i	−0.991927	−	0.126807i	$-0.959527\pi$
$733$	−5.31453	−	19.8341i	−0.196297	−	0.732589i	0.795631	−	0.605782i	$-0.207140\pi$
$734$	−23.4731	+	36.6138i	−0.866407	+	1.35144i
$735$	37.2825	+	23.3517i	1.37518	+	0.861339i
$736$	29.1623	−	8.73831i	1.07494	−	0.322098i
$737$	−18.0541	+	4.83758i	−0.665031	+	0.178194i
$738$	−13.9563	+	12.7153i	−0.513738	+	0.468058i
$739$	24.2010	+	41.9174i	0.890249	+	1.54196i	0.839576	+	0.543242i	$0.182803\pi$
$739$	24.2010	+	41.9174i	0.890249	+	1.54196i	0.0506730	+	0.998715i	$0.483863\pi$
$740$	2.92316	−	10.3713i	0.107458	−	0.381256i
$741$	26.8832			0.987579
$742$	35.4374	+	33.6146i	1.30095	+	1.23403i
$743$	−3.78255	−	3.78255i	−0.138768	−	0.138768i	0.634310	−	0.773078i	$-0.281284\pi$
$743$	−3.78255	−	3.78255i	−0.138768	−	0.138768i	−0.773078	+	0.634310i	$0.781284\pi$
$744$	21.8242	+	17.0459i	0.800115	+	0.624931i
$745$	8.59618	−	18.0931i	0.314940	−	0.662880i
$746$	21.2435	+	0.988403i	0.777781	+	0.0361880i
$747$	7.85869	+	29.3290i	0.287535	+	1.07309i
$748$	5.13212	−	13.8533i	0.187649	−	0.506526i
$749$	1.08458	−	0.0791901i	0.0396296	−	0.00289354i
$750$	14.3960	−	42.0420i	0.525669	−	1.53516i
$751$	−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	$0.772946\pi$
$752$	−20.8723	+	14.2618i	−0.761133	+	0.520075i
$753$	36.2076	+	9.70180i	1.31948	+	0.353553i
$754$	−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	−0.944954	−	0.327204i	$-0.893894\pi$
$757$	−35.0017	−	35.0017i	−1.27216	−	1.27216i	−0.327204	−	0.944954i	$-0.606106\pi$
$758$	0.825034	−	2.59081i	0.0299666	−	0.0941024i
$759$	24.0790	+	41.7061i	0.874013	+	1.51384i
$760$	−17.3209	+	3.55407i	−0.628296	+	0.128920i
$761$	−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	$0.939636\pi$
$762$	−7.25651	+	1.58697i	−0.262876	+	0.0574897i
$763$	−6.34710	−	18.2510i	−0.229781	−	0.660730i
$764$	−9.64999	−	21.0074i	−0.349125	−	0.760022i
$765$	19.3508	+	16.4762i	0.699628	+	0.595700i
$766$	−1.05069	+	22.5824i	−0.0379631	+	0.815934i
$767$	6.28831	+	1.68495i	0.227058	+	0.0608399i
$768$	−18.0670	−	41.1796i	−0.651937	−	1.48594i
$769$			22.5137i			0.811865i	0.913903	+	0.405933i	$0.133053\pi$
$769$			22.5137i			0.811865i	−0.913903	+	0.405933i	$0.866947\pi$
$770$	2.83042	+	26.4878i	0.102001	+	0.954555i
$771$		−	28.2691i		−	1.01809i
$772$	5.90328	+	7.11756i	0.212464	+	0.256167i
$773$	−22.3506	−	5.98883i	−0.803896	−	0.215403i	−0.166602	−	0.986024i	$-0.553280\pi$
$773$	−22.3506	−	5.98883i	−0.803896	−	0.215403i	−0.637294	+	0.770621i	$0.719946\pi$
$774$	38.8057	+	1.80552i	1.39484	+	0.0648982i
$775$	13.5027	−	11.0025i	0.485033	−	0.395223i
$776$	43.2622	+	6.07370i	1.55302	+	0.218033i
$777$	−17.5978	−	3.36460i	−0.631318	−	0.120704i
$778$	3.42368	+	15.6550i	0.122745	+	0.561259i
$779$	3.80923	−	6.59778i	0.136480	−	0.236390i
$780$	42.9995	+	0.555816i	1.53963	+	0.0199014i
$781$	0.894971	+	1.55014i	0.0320246	+	0.0554682i
$782$	16.8246	+	5.35773i	0.601646	+	0.191592i
$783$	−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
$787$	35.5681	+	9.53044i	1.26787	+	0.339724i	0.829213	−	0.558933i	$-0.188789\pi$
$787$	35.5681	+	9.53044i	1.26787	+	0.339724i	0.438653	+	0.898657i	$0.355456\pi$
$788$	−3.21873	−	18.8855i	−0.114662	−	0.672767i
$789$	−26.1715	−	15.1101i	−0.931731	−	0.537935i
$790$	17.8626	−	19.1040i	0.635524	−	0.679690i
$791$	−24.4452	−	36.0024i	−0.869170	−	1.28010i
$792$	35.2311	−	26.5565i	1.25188	−	0.943646i
$793$	−10.3424	−	38.5982i	−0.367268	−	1.37066i
$794$	−0.766546	+	16.4752i	−0.0272037	+	0.584684i
$795$	−74.1012	−	35.2061i	−2.62810	−	1.24863i
$796$	−0.323065	+	3.46427i	−0.0114507	+	0.122788i
$797$	−8.30328	−	8.30328i	−0.294117	−	0.294117i	0.544587	−	0.838704i	$-0.316686\pi$
$797$	−8.30328	−	8.30328i	−0.294117	−	0.294117i	−0.838704	+	0.544587i	$0.816686\pi$
$798$	8.35605	+	28.1877i	0.295801	+	0.997832i
$799$	−14.6620			−0.518705
$800$	−27.7782	+	5.32660i	−0.982107	+	0.188324i
$801$	−7.10464	−	12.3056i	−0.251030	−	0.434797i
$802$	−26.3562	−	28.9284i	−0.930670	−	1.02150i
$803$	−10.2969	+	2.75904i	−0.363369	+	0.0973645i
$804$	−29.9857	+	13.7743i	−1.05751	+	0.485781i
$805$	−31.4667	+	4.85063i	−1.10906	+	0.170962i
$806$	14.1896	+	9.09693i	0.499807	+	0.320426i
$807$	−6.87776	−	25.6682i	−0.242109	−	0.903562i
$808$	−29.8530	−	12.6667i	−1.05022	−	0.445614i
$809$	−27.1489	+	15.6744i	−0.954504	+	0.551083i	−0.894477	−	0.447114i	$-0.852452\pi$
$809$	−27.1489	+	15.6744i	−0.954504	+	0.551083i	−0.0600265	+	0.998197i	$0.519119\pi$
$810$	0.279801	+	0.919586i	0.00983119	+	0.0323110i
$811$			9.76550i			0.342913i	0.985192	+	0.171456i	$0.0548473\pi$
$811$			9.76550i			0.342913i	−0.985192	+	0.171456i	$0.945153\pi$
$812$	−6.31725	−	6.57648i	−0.221692	−	0.230789i
$813$	−28.6732	+	28.6732i	−1.00561	+	1.00561i
$814$	−4.98202	−	9.63757i	−0.174620	−	0.337797i
$815$	−0.00212100	−	0.00596067i	−7.42955e−5	−	0.000208793i
$816$	4.82262	−	25.6319i	0.168826	−	0.897297i
$817$	−15.1416	+	4.05719i	−0.529739	+	0.141943i
$818$	4.17892	+	19.1084i	0.146112	+	0.668109i
$819$	−3.22937	−	44.2291i	−0.112843	−	1.54549i
$820$	6.22925	−	10.4744i	0.217535	−	0.365780i
$821$	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	$0.123964\pi$
$822$	47.3530	−	43.1425i	1.65163	−	1.50477i
$823$	14.1720	−	52.8907i	0.494006	−	1.84365i	−0.0415239	−	0.999138i	$-0.513221\pi$
$823$	14.1720	−	52.8907i	0.494006	−	1.84365i	0.535530	−	0.844517i	$-0.320112\pi$
$824$	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	0.274910	−	0.961470i	$-0.411352\pi$
$827$	35.5553	−	35.5553i	1.23638	−	1.23638i	0.961470	−	0.274910i	$-0.0886479\pi$
$828$	33.6631	+	40.5874i	1.16987	+	1.41051i
$829$	−23.4882	+	13.5609i	−0.815780	+	0.470991i	−0.848959	−	0.528459i	$-0.822770\pi$
$829$	−23.4882	+	13.5609i	−0.815780	+	0.470991i	0.0331794	+	0.999449i	$0.489437\pi$
$830$	−10.3637	−	16.6349i	−0.359729	−	0.577405i
$831$	80.5397	+	46.4996i	2.79389	+	1.61305i
$832$	−13.2765	−	23.9351i	−0.460281	−	0.829800i
$833$	9.69357	−	13.0296i	0.335862	−	0.451449i
$834$	57.1560	+	36.6426i	1.97915	+	1.26883i
$835$	−5.59755	−	4.76604i	−0.193711	−	0.164936i
$836$	−10.2945	+	14.5246i	−0.356044	+	0.502342i
$837$	−4.81237	+	17.9600i	−0.166340	+	0.620789i
$838$	−8.88173	+	27.8908i	−0.306814	+	0.963472i
$839$	3.82948			0.132208			0.0661042	−	0.997813i	$-0.478943\pi$
$839$	3.82948			0.132208			0.0661042	+	0.997813i	$0.478943\pi$
$840$	12.7827	+	45.2588i	0.441044	+	1.56158i
$841$	26.0301			0.897589
$842$	11.4796	−	36.0489i	0.395614	−	1.24233i
$843$	7.39570	−	27.6011i	0.254722	−	0.950634i
$844$	−27.4767	+	38.7669i	−0.945788	+	1.33441i
$845$	−2.88520	+	0.231490i	−0.0992539	+	0.00796349i
$846$	−36.8617	−	23.6320i	−1.26733	−	0.812485i
$847$	−1.72708	−	1.49203i	−0.0593431	−	0.0512669i
$848$	3.95551	+	52.0665i	0.135833	+	1.78797i
$849$	−67.4183	−	38.9240i	−2.31379	−	1.33587i
$850$	−15.0454	−	6.53864i	−0.516053	−	0.224273i
$851$	11.2296	−	6.48342i	0.384946	−	0.222249i
$852$	2.01737	+	2.43233i	0.0691138	+	0.0833302i
$853$	−1.20013	+	1.20013i	−0.0410916	+	0.0410916i	−0.727354	−	0.686262i	$-0.759250\pi$
$853$	−1.20013	+	1.20013i	−0.0410916	+	0.0410916i	0.686262	+	0.727354i	$0.259250\pi$
$854$	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
$857$	6.85466	−	25.5819i	0.234151	−	0.873862i	−0.744379	−	0.667757i	$-0.767254\pi$
$857$	6.85466	−	25.5819i	0.234151	−	0.873862i	0.978530	−	0.206105i	$-0.0660789\pi$
$858$	32.0058	−	29.1599i	1.09266	−	0.995503i
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	0.300068	+	0.953918i	$0.402991\pi$
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	−0.976151	+	0.217093i	$0.930343\pi$
$860$	−24.3029	+	6.17640i	−0.828720	+	0.210613i
$861$	−18.2397	−	8.82684i	−0.621608	−	0.300818i
$862$	12.1881	+	55.7308i	0.415128	+	1.89820i
$863$	9.62351	−	2.57861i	0.327588	−	0.0877769i	−0.0912768	−	0.995826i	$-0.529095\pi$
$863$	9.62351	−	2.57861i	0.327588	−	0.0877769i	0.418865	+	0.908049i	$0.362428\pi$
$864$	20.7148	−	21.9670i	0.704731	−	0.747334i
$865$	33.8560	−	12.0471i	1.15114	−	0.409613i
$866$	−15.2306	−	29.4632i	−0.517558	−	1.00120i
$867$	−23.0883	+	23.0883i	−0.784120	+	0.784120i
$868$	−5.12781	+	17.7057i	−0.174049	+	0.600970i
$869$		−	26.3331i		−	0.893290i
$870$	13.5141	+	7.20878i	0.458171	+	0.244401i
$871$	−17.3938	+	10.0423i	−0.589368	+	0.340272i
$872$	8.06870	−	19.0163i	0.273241	−	0.643974i
$873$	19.5846	+	73.0908i	0.662839	+	2.47375i
$874$	−17.9128	−	11.4839i	−0.605909	−	0.388448i
$875$	29.5415	−	1.51598i	0.998686	−	0.0512495i
$876$	−17.1019	+	7.85595i	−0.577820	+	0.265428i
$877$	−2.47836	+	0.664074i	−0.0836882	+	0.0224242i	−0.300420	−	0.953807i	$-0.597127\pi$
$877$	−2.47836	+	0.664074i	−0.0836882	+	0.0224242i	0.216732	+	0.976231i	$0.430460\pi$
$878$	5.46830	+	6.00198i	0.184546	+	0.202557i
$879$	−6.12031	−	10.6007i	−0.206433	−	0.357553i
$880$	−16.7663	+	23.0191i	−0.565193	+	0.775974i
$881$	20.5639			0.692816			0.346408	−	0.938084i	$-0.387401\pi$
$881$	20.5639			0.692816			0.346408	+	0.938084i	$0.387401\pi$
$882$	45.3714	−	17.1337i	1.52773	−	0.576922i
$883$	−26.6080	−	26.6080i	−0.895429	−	0.895429i	0.0995985	−	0.995028i	$-0.468244\pi$
$883$	−26.6080	−	26.6080i	−0.895429	−	0.895429i	−0.995028	+	0.0995985i	$0.968244\pi$
$884$	1.47404	−	15.8064i	0.0495775	−	0.531626i
$885$	−4.00890	−	11.2663i	−0.134758	−	0.378711i
$886$	0.0562553	−	1.20908i	0.00188993	−	0.0406199i
$887$	−1.90478	−	7.10873i	−0.0639562	−	0.238688i	0.926547	−	0.376180i	$-0.122762\pi$
$887$	−1.90478	−	7.10873i	−0.0639562	−	0.238688i	−0.990503	+	0.137492i	$0.956096\pi$
$888$	−11.5292	−	15.2951i	−0.386893	−	0.513269i
$889$	−2.77748	−	4.09062i	−0.0931537	−	0.137195i
$890$	6.69945	+	6.26412i	0.224566	+	0.209974i
$891$	0.838132	+	0.483895i	0.0280785	+	0.0162111i
$892$	6.28760	+	36.8917i	0.210524	+	1.23523i
$893$	17.0666	+	4.57299i	0.571112	+	0.153029i
$894$	−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
$898$	6.28165	+	2.00037i	0.209621	+	0.0667532i
$899$	3.00169	+	5.19908i	0.100112	+	0.173399i
$900$	−27.2867	−	40.6887i	−0.909556	−	1.35629i
$901$	−15.1427	+	26.2280i	−0.504478	+	0.873781i
$902$	−2.62146	−	11.9868i	−0.0872852	−	0.399117i
$903$	13.6952	+	39.3804i	0.455748	+	1.31050i
$904$	6.46788	−	46.0699i	0.215119	−	1.53226i
$905$	−0.766225	−	9.54993i	−0.0254702	−	0.317450i
$906$	26.7409	+	1.24418i	0.888408	+	0.0413352i
$907$	−13.4573	−	3.60588i	−0.446843	−	0.119731i	0.0283786	−	0.999597i	$-0.490966\pi$
$907$	−13.4573	−	3.60588i	−0.446843	−	0.119731i	−0.475222	+	0.879866i	$0.657632\pi$
$908$	−26.5437	−	32.0036i	−0.880884	−	1.06208i
$909$		−	56.1704i		−	1.86305i
$910$	10.3046	+	26.7059i	0.341594	+	0.885291i
$911$		−	9.10653i		−	0.301713i	−0.988556	−	0.150856i	$-0.951797\pi$
$911$		−	9.10653i		−	0.301713i	0.988556	−	0.150856i	$-0.0482031\pi$
$912$	−13.6080	+	28.3315i	−0.450605	+	0.938148i
$913$	−19.0609	−	5.10735i	−0.630823	−	0.169029i
$914$	−2.09074	+	44.9359i	−0.0691557	+	1.48635i
$915$	−47.5851	+	55.8870i	−1.57311	+	1.84757i
$916$	−14.9228	−	32.4860i	−0.493064	−	1.07337i
$917$	7.03857	−	8.14737i	0.232434	−	0.269050i
$918$	17.1079	−	3.74142i	0.564644	−	0.123485i
$919$	−17.5872	+	30.4620i	−0.580149	+	1.00485i	0.415312	+	0.909679i	$0.363672\pi$
$919$	−17.5872	+	30.4620i	−0.580149	+	1.00485i	−0.995461	+	0.0951683i	$0.969661\pi$
$920$	−28.4140	−	18.7387i	−0.936781	−	0.617798i
$921$	−26.5004	−	45.9000i	−0.873217	−	1.51246i
$922$	−10.0605	+	31.5923i	−0.331324	+	1.04044i
$923$	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
$927$	62.0014	+	16.6132i	2.03639	+	0.545650i
$928$	−0.285898	−	9.74452i	−0.00938505	−	0.319879i
$929$	32.5064	+	18.7676i	1.06650	+	0.615745i	0.927223	−	0.374509i	$-0.122189\pi$
$929$	32.5064	+	18.7676i	1.06650	+	0.615745i	0.139278	+	0.990253i	$0.455522\pi$
$930$	−1.03911	−	30.9434i	−0.0340737	−	1.01467i
$931$	−15.3472	+	12.1431i	−0.502983	+	0.397974i
$932$	−0.245150	+	0.661739i	−0.00803015	+	0.0216760i
$933$	1.13775	+	4.24615i	0.0372483	+	0.139013i
$934$	−11.7215	−	0.545370i	−0.383540	−	0.0178451i
$935$	−15.5613	+	5.53722i	−0.508909	+	0.181086i
$936$	29.1823	−	37.3628i	0.953853	−	1.22124i
$937$	−14.9371	−	14.9371i	−0.487973	−	0.487973i	0.419693	−	0.907666i	$-0.362138\pi$
$937$	−14.9371	−	14.9371i	−0.487973	−	0.487973i	−0.907666	+	0.419693i	$0.862138\pi$
$938$	−15.9361	−	15.1164i	−0.520333	−	0.493568i
$939$	−34.2270			−1.11696
$940$	27.2034	+	7.66732i	0.887277	+	0.250080i
$941$	−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	$0.865096\pi$
$942$	−33.4484	+	30.4743i	−1.08981	+	0.992905i
$943$	14.1655	−	3.79564i	0.461293	−	0.123603i
$944$	−4.95878	+	5.77417i	−0.161395	+	0.187933i
$945$	−24.6220	+	19.7706i	−0.800954	+	0.643138i
$946$	−13.6261	+	21.2543i	−0.443022	+	0.691036i
$947$	11.1603	+	41.6507i	0.362660	+	1.35347i	0.870565	+	0.492053i	$0.163753\pi$
$947$	11.1603	+	41.6507i	0.362660	+	1.35347i	−0.507905	+	0.861413i	$0.669580\pi$
$948$	−7.81083	−	45.8291i	−0.253684	−	1.48846i
$949$	−9.92033	+	5.72751i	−0.322028	+	0.185923i
$950$	15.4735	+	12.3035i	0.502027	+	0.399180i
$951$			76.9801i			2.49625i
$952$	17.0315	−	3.36749i	0.551994	−	0.109141i
$953$	26.8326	−	26.8326i	0.869193	−	0.869193i	−0.123190	−	0.992383i	$-0.539313\pi$
$953$	26.8326	−	26.8326i	0.869193	−	0.869193i	0.992383	+	0.123190i	$0.0393125\pi$
$954$	−80.3441	+	41.5328i	−2.60123	+	1.34467i
$955$	−11.0917	+	23.3456i	−0.358919	+	0.755446i
$956$	−39.3373	−	27.8810i	−1.27226	−	0.901736i
$957$	14.8959	−	3.99135i	0.481517	−	0.129022i
$958$	19.3398	−	4.22953i	0.624841	−	0.136650i
$959$	38.3826	+	18.5747i	1.23944	+	0.599809i
$960$	−22.3516	+	45.0347i	−0.721395	+	1.45349i
$961$	−9.43240	+	16.3374i	−0.304271	+	0.527013i
$962$	−7.85148	−	8.61774i	−0.253142	−	0.277847i
$963$	−0.521171	+	1.94504i	−0.0167945	+	0.0626779i
$964$	−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	$-0.820485\pi$
$967$	−9.65871	+	9.65871i	−0.310603	+	0.310603i	0.534540	+	0.845143i	$0.320485\pi$
$968$	−0.297700	−	2.42167i	−0.00956845	−	0.0778353i
$969$	−15.7871	+	9.11468i	−0.507155	+	0.292806i
$970$	−25.8274	−	41.4558i	−0.829267	−	1.33106i
$971$	−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	$0.780821\pi$
$972$	−28.4284	−	10.5317i	−0.911843	−	0.337804i
$973$	−8.48690	+	44.3890i	−0.272078	+	1.42305i
$974$	20.2623	−	31.6056i	0.649246	−	1.01271i
$975$	−30.3707	−	37.2721i	−0.972640	−	1.19366i
$976$	45.9128	+	8.63844i	1.46963	+	0.276510i
$977$	−6.74446	+	25.1707i	−0.215774	+	0.805281i	0.770118	+	0.637901i	$0.220197\pi$
$977$	−6.74446	+	25.1707i	−0.215774	+	0.805281i	−0.985893	+	0.167380i	$0.946469\pi$
$978$	−0.0107159	−	0.00341244i	−0.000342657	−	0.000109118i
$979$	9.23458			0.295138
$980$	−24.7988	+	19.1055i	−0.792167	+	0.610304i
$981$	35.7805			1.14238
$982$	47.9545	+	15.2709i	1.53029	+	0.487315i
$983$	−12.5590	+	46.8710i	−0.400571	+	1.49495i	0.411508	+	0.911406i	$0.365002\pi$
$983$	−12.5590	+	46.8710i	−0.400571	+	1.49495i	−0.812080	+	0.583547i	$0.801664\pi$
$984$	−8.11777	−	20.0838i	−0.258785	−	0.640248i
$985$	−13.8858	+	16.3083i	−0.442437	+	0.519627i
$986$	3.05165	−	4.76002i	0.0971842	−	0.151590i
$987$	8.82518	−	46.1583i	0.280909	−	1.46923i
$988$	−6.64569	+	17.9389i	−0.211427	+	0.570712i
$989$	−26.1325	−	15.0876i	−0.830965	−	0.479758i
$990$	−48.0473	−	11.1603i	−1.52704	−	0.354699i
$991$	−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	$0.353230\pi$
$992$	−16.7696	+	10.3492i	−0.532435	+	0.328589i
$993$	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
$997$	13.2857	−	49.5831i	0.420764	−	1.57031i	−0.352240	−	0.935910i	$-0.614580\pi$
$997$	13.2857	−	49.5831i	0.420764	−	1.57031i	0.773004	−	0.634402i	$-0.218753\pi$
$998$	9.41233	+	10.3309i	0.297942	+	0.327020i
$999$	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.107.11	yes	72
4.3	odd	2	inner	140.2.w.b.107.15	yes	72
5.2	odd	4		700.2.be.e.443.16		72
5.3	odd	4	inner	140.2.w.b.23.3	✓	72
5.4	even	2		700.2.be.e.107.8		72
7.2	even	3		980.2.k.k.687.2		36
7.3	odd	6		980.2.x.m.67.13		72
7.4	even	3	inner	140.2.w.b.67.13	yes	72
7.5	odd	6		980.2.k.j.687.2		36
7.6	odd	2		980.2.x.m.667.11		72
20.3	even	4	inner	140.2.w.b.23.13	yes	72
20.7	even	4		700.2.be.e.443.6		72
20.19	odd	2		700.2.be.e.107.4		72
28.3	even	6		980.2.x.m.67.3		72
28.11	odd	6	inner	140.2.w.b.67.3	yes	72
28.19	even	6		980.2.k.j.687.11		36
28.23	odd	6		980.2.k.k.687.11		36
28.27	even	2		980.2.x.m.667.15		72
35.3	even	12		980.2.x.m.263.15		72
35.4	even	6		700.2.be.e.207.6		72
35.13	even	4		980.2.x.m.863.3		72
35.18	odd	12	inner	140.2.w.b.123.15	yes	72
35.23	odd	12		980.2.k.k.883.11		36
35.32	odd	12		700.2.be.e.543.4		72
35.33	even	12		980.2.k.j.883.11		36
140.3	odd	12		980.2.x.m.263.11		72
140.23	even	12		980.2.k.k.883.2		36
140.39	odd	6		700.2.be.e.207.16		72
140.67	even	12		700.2.be.e.543.8		72
140.83	odd	4		980.2.x.m.863.13		72
140.103	odd	12		980.2.k.j.883.2		36
140.123	even	12	inner	140.2.w.b.123.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	5.3	odd	4	inner
140.2.w.b.23.13	yes	72	20.3	even	4	inner
140.2.w.b.67.3	yes	72	28.11	odd	6	inner
140.2.w.b.67.13	yes	72	7.4	even	3	inner
140.2.w.b.107.11	yes	72	1.1	even	1	trivial
140.2.w.b.107.15	yes	72	4.3	odd	2	inner
140.2.w.b.123.11	yes	72	140.123	even	12	inner
140.2.w.b.123.15	yes	72	35.18	odd	12	inner
700.2.be.e.107.4		72	20.19	odd	2
700.2.be.e.107.8		72	5.4	even	2
700.2.be.e.207.6		72	35.4	even	6
700.2.be.e.207.16		72	140.39	odd	6
700.2.be.e.443.6		72	20.7	even	4
700.2.be.e.443.16		72	5.2	odd	4
700.2.be.e.543.4		72	35.32	odd	12
700.2.be.e.543.8		72	140.67	even	12
980.2.k.j.687.2		36	7.5	odd	6
980.2.k.j.687.11		36	28.19	even	6
980.2.k.j.883.2		36	140.103	odd	12
980.2.k.j.883.11		36	35.33	even	12
980.2.k.k.687.2		36	7.2	even	3
980.2.k.k.687.11		36	28.23	odd	6
980.2.k.k.883.2		36	140.23	even	12
980.2.k.k.883.11		36	35.23	odd	12
980.2.x.m.67.3		72	28.3	even	6
980.2.x.m.67.13		72	7.3	odd	6
980.2.x.m.263.11		72	140.3	odd	12
980.2.x.m.263.15		72	35.3	even	12
980.2.x.m.667.11		72	7.6	odd	2
980.2.x.m.667.15		72	28.27	even	2
980.2.x.m.863.3		72	35.13	even	4
980.2.x.m.863.13		72	140.83	odd	4

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.429119 - 1.34754i) q^{2} +(-0.727420 + 2.71477i) q^{3} +(-1.63171 - 1.15651i) q^{4} +(0.178833 + 2.22891i) q^{5} +(3.34610 + 2.14518i) q^{6} +(-0.496852 + 2.59868i) q^{7} +(-2.25864 + 1.70252i) q^{8} +(-4.24276 - 2.44956i) q^{9} +O(q^{10})\)	\(q+(0.429119 - 1.34754i) q^{2} +(-0.727420 + 2.71477i) q^{3} +(-1.63171 - 1.15651i) q^{4} +(0.178833 + 2.22891i) q^{5} +(3.34610 + 2.14518i) q^{6} +(-0.496852 + 2.59868i) q^{7} +(-2.25864 + 1.70252i) q^{8} +(-4.24276 - 2.44956i) q^{9} +(3.08027 + 0.715481i) q^{10} +(2.75736 - 1.59196i) q^{11} +(4.32659 - 3.58846i) 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} +(-0.600458 + 2.24094i) q^{17} +(-5.12151 + 4.66612i) q^{18} +(1.39787 - 2.42118i) q^{19} +(2.28594 - 3.84376i) q^{20} +(-6.69340 - 3.23917i) q^{21} +(-0.961994 - 4.39878i) q^{22} +(5.19830 - 1.39288i) q^{23} +(-2.97897 - 7.37012i) q^{24} +(-4.93604 + 0.797203i) q^{25} +(-2.22189 - 4.29818i) q^{26} +(3.77420 - 3.77420i) q^{27} +(3.81611 - 3.66569i) q^{28} -1.72334i q^{29} +(-4.18302 + 7.84178i) q^{30} +(-3.01685 + 1.74178i) q^{31} +(5.65442 - 0.165897i) q^{32} +(2.31605 + 8.64362i) q^{33} +(2.76208 + 1.77077i) q^{34} +(-5.88107 - 0.642706i) q^{35} +(4.09004 + 8.90375i) q^{36} +(2.32734 - 0.623610i) q^{37} +(-2.66278 - 2.92265i) q^{38} +(4.80790 + 8.32752i) q^{39} +(-4.19867 - 4.72982i) q^{40} +2.72503 q^{41} +(-7.23716 + 7.62961i) q^{42} +(-3.96477 - 3.96477i) q^{43} +(-6.34034 - 0.591276i) q^{44} +(4.70108 - 9.89476i) q^{45} +(0.353728 - 7.60261i) q^{46} +(1.63570 + 6.10452i) q^{47} +(-11.2098 + 0.851615i) q^{48} +(-6.50628 - 2.58232i) q^{49} +(-1.04388 + 6.99359i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(-6.74541 + 1.14965i) q^{52} +(12.6093 + 3.37866i) 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} +(-2.32227 - 0.739519i) q^{58} +(0.951402 + 1.64788i) q^{59} +(8.77208 + 9.00183i) q^{60} +(5.83980 - 10.1148i) q^{61} +(1.05253 + 4.81275i) q^{62} +(8.47363 - 9.80850i) q^{63} +(2.20286 - 7.69073i) q^{64} +(5.82492 + 4.95964i) q^{65} +(12.6415 + 0.588172i) q^{66} +(-5.67039 - 1.51938i) q^{67} +(3.57144 - 2.96214i) q^{68} +15.1254i q^{69} +(-3.38975 + 7.64916i) q^{70} +0.562181i q^{71} +(13.7532 - 1.69071i) q^{72} +(-3.23402 - 0.866554i) q^{73} +(0.158369 - 3.40378i) q^{74} +(1.42635 - 13.9801i) q^{75} +(-5.08103 + 2.33403i) q^{76} +(2.76700 + 7.95646i) q^{77} +(13.2848 - 2.90533i) q^{78} +(4.13532 - 7.16259i) q^{79} +(-8.17533 + 3.62821i) q^{80} +(0.151981 + 0.263239i) q^{81} +(1.16936 - 3.67208i) 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} +(4.67848 + 1.25360i) q^{87} +(-3.51752 + 8.29011i) q^{88} +(2.51180 + 1.45019i) q^{89} +(-11.3162 - 10.5809i) q^{90} +(5.08485 + 7.48887i) q^{91} +(-10.0930 - 3.73908i) q^{92} +(-2.53401 - 9.45706i) q^{93} +(8.92798 + 0.415394i) q^{94} +(5.64656 + 2.68273i) q^{95} +(-3.66277 + 15.4711i) q^{96} +(-10.9216 - 10.9216i) q^{97} +(-6.27174 + 7.65933i) q^{98} -15.5984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) 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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