LMFDB - Embedded newform 140.2.k.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(43,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.k (of order $4$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	140.43
Dual form			140.2.k.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36728 + 0.361308i) q^{2} +(-1.26588 + 1.26588i) q^{3} +(1.73891 - 0.988019i) q^{4} +(1.96164 - 1.07330i) q^{5} +(1.27344 - 2.18818i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.02060 + 1.97918i) q^{8} -0.204893i q^{9} +O(q^{10})$	\(q+(-1.36728 + 0.361308i) q^{2} +(-1.26588 + 1.26588i) q^{3} +(1.73891 - 0.988019i) q^{4} +(1.96164 - 1.07330i) q^{5} +(1.27344 - 2.18818i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.02060 + 1.97918i) q^{8} -0.204893i q^{9} +(-2.29431 + 2.17626i) q^{10} +2.11327i q^{11} +(-0.950539 + 3.45196i) q^{12} +(2.86476 + 2.86476i) q^{13} +(-1.22230 - 0.711330i) q^{14} +(-1.12452 + 3.84186i) q^{15} +(2.04764 - 3.43616i) q^{16} +(-4.47034 + 4.47034i) q^{17} +(0.0740296 + 0.280147i) q^{18} +2.95246 q^{19} +(2.35067 - 3.80452i) q^{20} -1.79022 q^{21} +(-0.763541 - 2.88943i) q^{22} +(3.94312 - 3.94312i) q^{23} +(0.0524318 - 5.06324i) q^{24} +(2.69604 - 4.21087i) q^{25} +(-4.95199 - 2.88187i) q^{26} +(-3.53826 - 3.53826i) q^{27} +(1.92823 + 0.530962i) q^{28} -2.86818i q^{29} +(0.149438 - 5.65920i) q^{30} +6.01364i q^{31} +(-1.55818 + 5.43802i) q^{32} +(-2.67514 - 2.67514i) q^{33} +(4.49704 - 7.72739i) q^{34} +(2.14603 + 0.628146i) q^{35} +(-0.202439 - 0.356292i) q^{36} +(3.91444 - 3.91444i) q^{37} +(-4.03684 + 1.06675i) q^{38} -7.25287 q^{39} +(-1.83942 + 6.05116i) q^{40} -7.98984 q^{41} +(2.44774 - 0.646822i) q^{42} +(5.64967 - 5.64967i) q^{43} +(2.08795 + 3.67479i) q^{44} +(-0.219913 - 0.401926i) q^{45} +(-3.96667 + 6.81603i) q^{46} +(-4.30339 - 4.30339i) q^{47} +(1.75770 + 6.94181i) q^{48} +1.00000i q^{49} +(-2.16482 + 6.73153i) q^{50} -11.3178i q^{51} +(7.81201 + 2.15113i) q^{52} +(-0.561181 - 0.561181i) q^{53} +(6.11620 + 3.55940i) q^{54} +(2.26818 + 4.14546i) q^{55} +(-2.82828 - 0.0292879i) q^{56} +(-3.73746 + 3.73746i) q^{57} +(1.03630 + 3.92160i) q^{58} +4.97819 q^{59} +(1.84039 + 7.79171i) q^{60} +1.68732 q^{61} +(-2.17278 - 8.22233i) q^{62} +(0.144881 - 0.144881i) q^{63} +(0.165668 - 7.99828i) q^{64} +(8.69438 + 2.54486i) q^{65} +(4.62422 + 2.69112i) q^{66} +(-8.06148 - 8.06148i) q^{67} +(-3.35675 + 12.1903i) q^{68} +9.98301i q^{69} +(-3.16118 - 0.0834748i) q^{70} -0.610925i q^{71} +(0.405521 + 0.414008i) q^{72} +(-3.23236 - 3.23236i) q^{73} +(-3.93782 + 6.76645i) q^{74} +(1.91759 + 8.74329i) q^{75} +(5.13407 - 2.91709i) q^{76} +(-1.49431 + 1.49431i) q^{77} +(9.91671 - 2.62052i) q^{78} -14.2539 q^{79} +(0.328674 - 8.93823i) q^{80} +9.57270 q^{81} +(10.9244 - 2.88679i) q^{82} +(5.51624 - 5.51624i) q^{83} +(-3.11304 + 1.76877i) q^{84} +(-3.97115 + 13.5672i) q^{85} +(-5.68341 + 9.76596i) q^{86} +(3.63076 + 3.63076i) q^{87} +(-4.18254 - 4.27008i) q^{88} -2.07881i q^{89} +(0.445902 + 0.470090i) q^{90} +4.05138i q^{91} +(2.96086 - 10.7526i) q^{92} +(-7.61253 - 7.61253i) q^{93} +(7.43879 + 4.32909i) q^{94} +(5.79166 - 3.16889i) q^{95} +(-4.91140 - 8.85634i) q^{96} +(-1.95542 + 1.95542i) q^{97} +(-0.361308 - 1.36728i) q^{98} +0.432994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 - 16 * q^10 - 16 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 28 * q^18 + 20 * q^20 + 4 * q^22 - 20 * q^25 - 32 * q^26 - 4 * q^30 + 20 * q^37 - 36 * q^40 - 20 * q^42 + 20 * q^45 + 16 * q^46 - 24 * q^48 + 40 * q^50 + 16 * q^52 - 44 * q^53 - 24 * q^56 - 16 * q^57 - 4 * q^58 + 40 * q^60 - 64 * q^61 + 40 * q^62 + 4 * q^65 + 32 * q^66 + 80 * q^68 + 80 * q^72 + 52 * q^73 + 8 * q^76 - 76 * q^78 - 20 * q^80 - 36 * q^81 + 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 - 16 * q^90 - 56 * q^92 + 32 * q^93 + 120 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.36728	+	0.361308i	−0.966813	+	0.255483i
$2$	−1.36728	+	0.361308i	−0.966813	+	0.255483i
$3$	−1.26588	+	1.26588i	−0.730855	+	0.730855i	−0.970789	−	0.239934i	$-0.922874\pi$
$3$	−1.26588	+	1.26588i	−0.730855	+	0.730855i	0.239934	+	0.970789i	$0.422874\pi$
$4$	1.73891	−	0.988019i	0.869456	−	0.494010i
$5$	1.96164	−	1.07330i	0.877271	−	0.479996i
$5$	1.96164	−	1.07330i	0.877271	−	0.479996i
$6$	1.27344	−	2.18818i	0.519879	−	0.893322i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−2.02060	+	1.97918i	−0.714391	+	0.699747i
$9$		−	0.204893i		−	0.0682978i
$10$	−2.29431	+	2.17626i	−0.725526	+	0.688195i
$11$			2.11327i			0.637174i	0.947894	+	0.318587i	$0.103208\pi$
$11$			2.11327i			0.637174i	−0.947894	+	0.318587i	$0.896792\pi$
$12$	−0.950539	+	3.45196i	−0.274397	+	0.996496i
$13$	2.86476	+	2.86476i	0.794542	+	0.794542i	0.982229	−	0.187687i	$-0.0600992\pi$
$13$	2.86476	+	2.86476i	0.794542	+	0.794542i	−0.187687	+	0.982229i	$0.560099\pi$
$14$	−1.22230	−	0.711330i	−0.326673	−	0.190111i
$15$	−1.12452	+	3.84186i	−0.290350	+	0.991965i
$16$	2.04764	−	3.43616i	0.511909	−	0.859040i
$17$	−4.47034	+	4.47034i	−1.08422	+	1.08422i	−0.0881069	+	0.996111i	$0.528082\pi$
$17$	−4.47034	+	4.47034i	−1.08422	+	1.08422i	−0.996111	+	0.0881069i	$0.971918\pi$
$18$	0.0740296	+	0.280147i	0.0174489	+	0.0660312i
$19$	2.95246			0.677341			0.338671	−	0.940905i	$-0.390023\pi$
$19$	2.95246			0.677341			0.338671	+	0.940905i	$0.390023\pi$
$20$	2.35067	−	3.80452i	0.525626	−	0.850716i
$21$	−1.79022			−0.390658
$22$	−0.763541	−	2.88943i	−0.162788	−	0.616029i
$23$	3.94312	−	3.94312i	0.822197	−	0.822197i	−0.164226	−	0.986423i	$-0.552513\pi$
$23$	3.94312	−	3.94312i	0.822197	−	0.822197i	0.986423	+	0.164226i	$0.0525126\pi$
$24$	0.0524318	−	5.06324i	0.0107026	−	1.03353i
$25$	2.69604	−	4.21087i	0.539207	−	0.842173i
$26$	−4.95199	−	2.88187i	−0.971166	−	0.565181i
$27$	−3.53826	−	3.53826i	−0.680939	−	0.680939i
$28$	1.92823	+	0.530962i	0.364402	+	0.100342i
$29$		−	2.86818i		−	0.532607i	−0.963889	−	0.266303i	$-0.914198\pi$
$29$		−	2.86818i		−	0.532607i	0.963889	−	0.266303i	$-0.0858023\pi$
$30$	0.149438	−	5.65920i	0.0272836	−	1.03322i
$31$			6.01364i			1.08008i	0.841639	+	0.540041i	$0.181591\pi$
$31$			6.01364i			1.08008i	−0.841639	+	0.540041i	$0.818409\pi$
$32$	−1.55818	+	5.43802i	−0.275450	+	0.961315i
$33$	−2.67514	−	2.67514i	−0.465682	−	0.465682i
$34$	4.49704	−	7.72739i	0.771237	−	1.32524i
$35$	2.14603	+	0.628146i	0.362745	+	0.106176i
$36$	−0.202439	−	0.356292i	−0.0337398	−	0.0593819i
$37$	3.91444	−	3.91444i	0.643530	−	0.643530i	−0.307892	−	0.951421i	$-0.599623\pi$
$37$	3.91444	−	3.91444i	0.643530	−	0.643530i	0.951421	+	0.307892i	$0.0996235\pi$
$38$	−4.03684	+	1.06675i	−0.654863	+	0.173049i
$39$	−7.25287			−1.16139
$40$	−1.83942	+	6.05116i	−0.290838	+	0.956772i
$41$	−7.98984			−1.24780			−0.623902	−	0.781503i	$-0.714453\pi$
$41$	−7.98984			−1.24780			−0.623902	+	0.781503i	$0.714453\pi$
$42$	2.44774	−	0.646822i	0.377694	−	0.0998067i
$43$	5.64967	−	5.64967i	0.861567	−	0.861567i	−0.129954	−	0.991520i	$-0.541483\pi$
$43$	5.64967	−	5.64967i	0.861567	−	0.861567i	0.991520	+	0.129954i	$0.0414828\pi$
$44$	2.08795	+	3.67479i	0.314770	+	0.553995i
$45$	−0.219913	−	0.401926i	−0.0327827	−	0.0599156i
$46$	−3.96667	+	6.81603i	−0.584853	+	1.00497i
$47$	−4.30339	−	4.30339i	−0.627713	−	0.627713i	0.319779	−	0.947492i	$-0.396391\pi$
$47$	−4.30339	−	4.30339i	−0.627713	−	0.627713i	−0.947492	+	0.319779i	$0.896391\pi$
$48$	1.75770	+	6.94181i	0.253702	+	1.00196i
$49$			1.00000i			0.142857i
$50$	−2.16482	+	6.73153i	−0.306152	+	0.951983i
$51$		−	11.3178i		−	1.58481i
$52$	7.81201	+	2.15113i	1.08333	+	0.298308i
$53$	−0.561181	−	0.561181i	−0.0770841	−	0.0770841i	0.667514	−	0.744598i	$-0.267359\pi$
$53$	−0.561181	−	0.561181i	−0.0770841	−	0.0770841i	−0.744598	+	0.667514i	$0.767359\pi$
$54$	6.11620	+	3.55940i	0.832310	+	0.484372i
$55$	2.26818	+	4.14546i	0.305841	+	0.558974i
$56$	−2.82828	−	0.0292879i	−0.377944	−	0.00391376i
$57$	−3.73746	+	3.73746i	−0.495038	+	0.495038i
$58$	1.03630	+	3.92160i	0.136072	+	0.514931i
$59$	4.97819			0.648105			0.324053	−	0.946039i	$-0.394955\pi$
$59$	4.97819			0.648105			0.324053	+	0.946039i	$0.394955\pi$
$60$	1.84039	+	7.79171i	0.237594	+	1.00591i
$61$	1.68732			0.216040			0.108020	−	0.994149i	$-0.465549\pi$
$61$	1.68732			0.216040			0.108020	+	0.994149i	$0.465549\pi$
$62$	−2.17278	−	8.22233i	−0.275943	−	1.04424i
$63$	0.144881	−	0.144881i	0.0182533	−	0.0182533i
$64$	0.165668	−	7.99828i	0.0207085	−	0.999786i
$65$	8.69438	+	2.54486i	1.07840	+	0.315651i
$66$	4.62422	+	2.69112i	0.569202	+	0.331254i
$67$	−8.06148	−	8.06148i	−0.984867	−	0.984867i	0.0150206	−	0.999887i	$-0.495219\pi$
$67$	−8.06148	−	8.06148i	−0.984867	−	0.984867i	−0.999887	+	0.0150206i	$0.995219\pi$
$68$	−3.35675	+	12.1903i	−0.407066	+	1.47829i
$69$			9.98301i			1.20181i
$70$	−3.16118	−	0.0834748i	−0.377833	−	0.00997715i
$71$		−	0.610925i		−	0.0725035i	−0.999343	−	0.0362518i	$-0.988458\pi$
$71$		−	0.610925i		−	0.0725035i	0.999343	−	0.0362518i	$-0.0115418\pi$
$72$	0.405521	+	0.414008i	0.0477911	+	0.0487913i
$73$	−3.23236	−	3.23236i	−0.378319	−	0.378319i	0.492177	−	0.870495i	$-0.336201\pi$
$73$	−3.23236	−	3.23236i	−0.378319	−	0.378319i	−0.870495	+	0.492177i	$0.836201\pi$
$74$	−3.93782	+	6.76645i	−0.457762	+	0.786584i
$75$	1.91759	+	8.74329i	0.221424	+	1.00959i
$76$	5.13407	−	2.91709i	0.588919	−	0.334613i
$77$	−1.49431	+	1.49431i	−0.170292	+	0.170292i
$78$	9.91671	−	2.62052i	1.12285	−	0.296716i
$79$	−14.2539			−1.60369			−0.801843	−	0.597534i	$-0.796147\pi$
$79$	−14.2539			−1.60369			−0.801843	+	0.597534i	$0.796147\pi$
$80$	0.328674	−	8.93823i	0.0367469	−	0.999325i
$81$	9.57270			1.06363
$82$	10.9244	−	2.88679i	1.20639	−	0.318793i
$83$	5.51624	−	5.51624i	0.605486	−	0.605486i	−0.336277	−	0.941763i	$-0.609168\pi$
$83$	5.51624	−	5.51624i	0.605486	−	0.605486i	0.941763	+	0.336277i	$0.109168\pi$
$84$	−3.11304	+	1.76877i	−0.339660	+	0.192989i
$85$	−3.97115	+	13.5672i	−0.430732	+	1.47157i
$86$	−5.68341	+	9.76596i	−0.612858	+	1.05309i
$87$	3.63076	+	3.63076i	0.389258	+	0.389258i
$88$	−4.18254	−	4.27008i	−0.445861	−	0.455192i
$89$		−	2.07881i		−	0.220353i	−0.993912	−	0.110176i	$-0.964858\pi$
$89$		−	2.07881i		−	0.220353i	0.993912	−	0.110176i	$-0.0351416\pi$
$90$	0.445902	+	0.470090i	0.0470022	+	0.0495518i
$91$			4.05138i			0.424700i
$92$	2.96086	−	10.7526i	0.308691	−	1.12104i
$93$	−7.61253	−	7.61253i	−0.789383	−	0.789383i
$94$	7.43879	+	4.32909i	0.767252	+	0.446511i
$95$	5.79166	−	3.16889i	0.594212	−	0.325121i
$96$	−4.91140	−	8.85634i	−0.501268	−	0.903896i
$97$	−1.95542	+	1.95542i	−0.198543	+	0.198543i	−0.799375	−	0.600832i	$-0.794836\pi$
$97$	−1.95542	+	1.95542i	−0.198543	+	0.198543i	0.600832	+	0.799375i	$0.294836\pi$
$98$	−0.361308	−	1.36728i	−0.0364976	−	0.138116i
$99$	0.432994			0.0435176
$100$	0.527757	−	9.98606i	0.0527757	−	0.998606i
$101$	1.26314			0.125687			0.0628434	−	0.998023i	$-0.479983\pi$
$101$	1.26314			0.125687			0.0628434	+	0.998023i	$0.479983\pi$
$102$	4.08922	+	15.4746i	0.404893	+	1.53222i
$103$	−9.18908	+	9.18908i	−0.905427	+	0.905427i	−0.995899	−	0.0904719i	$-0.971162\pi$
$103$	−9.18908	+	9.18908i	−0.905427	+	0.905427i	0.0904719	+	0.995899i	$0.471162\pi$
$104$	−11.4584	−	0.118656i	−1.12359	−	0.0116352i
$105$	−3.51176	+	1.92145i	−0.342713	+	0.187515i
$106$	0.970051	+	0.564533i	0.0942197	+	0.0548322i
$107$	13.6605	+	13.6605i	1.32061	+	1.32061i	0.913279	+	0.407335i	$0.133542\pi$
$107$	13.6605	+	13.6605i	1.32061	+	1.32061i	0.407335	+	0.913279i	$0.366458\pi$
$108$	−9.64860	−	2.65686i	−0.928437	−	0.255656i
$109$		−	13.6058i		−	1.30320i	−0.758563	−	0.651600i	$-0.774098\pi$
$109$		−	13.6058i		−	1.30320i	0.758563	−	0.651600i	$-0.225902\pi$
$110$	−4.59903	−	4.84850i	−0.438500	−	0.462287i
$111$			9.91040i			0.940654i
$112$	3.87763	−	0.981834i	0.366401	−	0.0927746i
$113$	−7.72607	−	7.72607i	−0.726807	−	0.726807i	0.243175	−	0.969982i	$-0.421811\pi$
$113$	−7.72607	−	7.72607i	−0.726807	−	0.726807i	−0.969982	+	0.243175i	$0.921811\pi$
$114$	3.75978	−	6.46053i	0.352135	−	0.605084i
$115$	3.50280	−	11.9671i	0.326638	−	1.11594i
$116$	−2.83381	−	4.98751i	−0.263113	−	0.463078i
$117$	0.586970	−	0.586970i	0.0542654	−	0.0542654i
$118$	−6.80658	+	1.79866i	−0.626597	+	0.165580i
$119$	−6.32202			−0.579539
$120$	−5.33154	−	9.98851i	−0.486701	−	0.911822i
$121$	6.53410			0.594009
$122$	−2.30705	+	0.609644i	−0.208870	+	0.0551946i
$123$	10.1142	−	10.1142i	0.911963	−	0.911963i
$124$	5.94159	+	10.4572i	0.533571	+	0.939084i
$125$	0.769107	−	11.1539i	0.0687910	−	0.997631i
$126$	−0.145747	+	0.250440i	−0.0129841	+	0.0223110i
$127$	−3.84193	−	3.84193i	−0.340917	−	0.340917i	0.515795	−	0.856712i	$-0.327496\pi$
$127$	−3.84193	−	3.84193i	−0.340917	−	0.340917i	−0.856712	+	0.515795i	$0.827496\pi$
$128$	2.66333	+	10.9958i	0.235407	+	0.971897i
$129$			14.3036i			1.25936i
$130$	−12.8071	−	0.338188i	−1.12326	−	0.0296611i
$131$		−	11.6259i		−	1.01576i	−0.861428	−	0.507880i	$-0.830429\pi$
$131$		−	11.6259i		−	1.01576i	0.861428	−	0.507880i	$-0.169571\pi$
$132$	−7.29492	−	2.00874i	−0.634942	−	0.174839i
$133$	2.08771	+	2.08771i	0.181027	+	0.181027i
$134$	13.9350	+	8.10963i	1.20380	+	0.700565i
$135$	−10.7384	−	3.14316i	−0.924216	−	0.270520i
$136$	0.185159	−	17.8804i	0.0158772	−	1.53323i
$137$	15.0891	−	15.0891i	1.28915	−	1.28915i	0.353839	−	0.935306i	$-0.384876\pi$
$137$	15.0891	−	15.0891i	1.28915	−	1.28915i	0.935306	−	0.353839i	$-0.115124\pi$
$138$	−3.60694	−	13.6496i	−0.307043	−	1.16193i
$139$	5.05787			0.429003			0.214501	−	0.976724i	$-0.431187\pi$
$139$	5.05787			0.429003			0.214501	+	0.976724i	$0.431187\pi$
$140$	4.35237	−	1.02803i	0.367843	−	0.0868840i
$141$	10.8951			0.917535
$142$	0.220732	+	0.835306i	0.0185234	+	0.0700974i
$143$	−6.05401	+	6.05401i	−0.506261	+	0.506261i
$144$	−0.704046	−	0.419547i	−0.0586705	−	0.0349622i
$145$	−3.07842	−	5.62632i	−0.255649	−	0.467240i
$146$	5.58741	+	3.25166i	0.462418	+	0.269109i
$147$	−1.26588	−	1.26588i	−0.104408	−	0.104408i
$148$	2.93933	−	10.6744i	0.241611	−	0.877431i
$149$			7.54249i			0.617905i	0.951078	+	0.308952i	$0.0999784\pi$
$149$			7.54249i			0.617905i	−0.951078	+	0.308952i	$0.900022\pi$
$150$	−5.78090	−	11.2617i	−0.472009	−	0.919514i
$151$			13.9342i			1.13395i	0.823735	+	0.566975i	$0.191887\pi$
$151$			13.9342i			1.13395i	−0.823735	+	0.566975i	$0.808113\pi$
$152$	−5.96575	+	5.84346i	−0.483886	+	0.473967i
$153$	0.915944	+	0.915944i	0.0740496	+	0.0740496i
$154$	1.50323	−	2.58304i	0.121134	−	0.208147i
$155$	6.45446	+	11.7966i	0.518435	+	0.947524i
$156$	−12.6121	+	7.16598i	−1.00978	+	0.573737i
$157$	−5.64257	+	5.64257i	−0.450326	+	0.450326i	−0.895463	−	0.445137i	$-0.853155\pi$
$157$	−5.64257	+	5.64257i	−0.450326	+	0.450326i	0.445137	+	0.895463i	$0.353155\pi$
$158$	19.4891	−	5.15004i	1.55047	−	0.409715i
$159$	1.42077			0.112675
$160$	2.78007	+	12.3398i	0.219784	+	0.975549i
$161$	5.57641			0.439483
$162$	−13.0886	+	3.45869i	−1.02833	+	0.271741i
$163$	−9.85026	+	9.85026i	−0.771532	+	0.771532i	−0.978374	−	0.206842i	$-0.933681\pi$
$163$	−9.85026	+	9.85026i	−0.771532	+	0.771532i	0.206842	+	0.978374i	$0.433681\pi$
$164$	−13.8936	+	7.89412i	−1.08491	+	0.616427i
$165$	−8.11889	−	2.37641i	−0.632055	−	0.185004i
$166$	−5.54919	+	9.53531i	−0.430700	+	0.740084i
$167$	14.0288	+	14.0288i	1.08558	+	1.08558i	0.995977	+	0.0896054i	$0.0285606\pi$
$167$	14.0288	+	14.0288i	1.08558	+	1.08558i	0.0896054	+	0.995977i	$0.471439\pi$
$168$	3.61733	−	3.54318i	0.279083	−	0.273362i
$169$			3.41370i			0.262592i
$170$	0.527730	−	19.9850i	0.0404750	−	1.53278i
$171$		−	0.604940i		−	0.0462609i
$172$	4.24230	−	15.4063i	0.323472	−	1.17472i
$173$	8.87742	+	8.87742i	0.674938	+	0.674938i	0.958850	−	0.283912i	$-0.0916325\pi$
$173$	8.87742	+	8.87742i	0.674938	+	0.674938i	−0.283912	+	0.958850i	$0.591632\pi$
$174$	−6.27609	−	3.65244i	−0.475789	−	0.276891i
$175$	4.88392	−	1.07115i	0.369189	−	0.0809710i
$176$	7.26153	+	4.32720i	0.547358	+	0.326175i
$177$	−6.30178	+	6.30178i	−0.473671	+	0.473671i
$178$	0.751089	+	2.84231i	0.0562965	+	0.213040i
$179$	−3.45733			−0.258413			−0.129207	−	0.991618i	$-0.541243\pi$
$179$	−3.45733			−0.258413			−0.129207	+	0.991618i	$0.541243\pi$
$180$	−0.779520	−	0.481636i	−0.0581020	−	0.0358991i
$181$	−16.0960			−1.19640			−0.598202	−	0.801345i	$-0.704118\pi$
$181$	−16.0960			−1.19640			−0.598202	+	0.801345i	$0.704118\pi$
$182$	−1.46380	−	5.53938i	−0.108504	−	0.410606i
$183$	−2.13595	+	2.13595i	−0.157894	+	0.157894i
$184$	−0.163321	+	15.7716i	−0.0120402	+	1.16270i
$185$	3.47732	−	11.8801i	0.255658	−	0.873441i
$186$	13.1589	+	7.65800i	0.964860	+	0.561512i
$187$	−9.44704	−	9.44704i	−0.690836	−	0.690836i
$188$	−11.7350	−	3.23138i	−0.855866	−	0.235673i
$189$		−	5.00386i		−	0.363977i
$190$	−6.77388	+	6.42533i	−0.491429	+	0.466143i
$191$			5.30310i			0.383719i	0.981422	+	0.191860i	$0.0614518\pi$
$191$			5.30310i			0.383719i	−0.981422	+	0.191860i	$0.938548\pi$
$192$	9.91513	+	10.3346i	0.715563	+	0.745833i
$193$	15.8240	+	15.8240i	1.13904	+	1.13904i	0.988623	+	0.150416i	$0.0480614\pi$
$193$	15.8240	+	15.8240i	1.13904	+	1.13904i	0.150416	+	0.988623i	$0.451939\pi$
$194$	1.96710	−	3.38011i	0.141229	−	0.242678i
$195$	−14.2275	+	7.78454i	−1.01885	+	0.557462i
$196$	0.988019	+	1.73891i	0.0705728	+	0.124208i
$197$	5.33556	−	5.33556i	0.380143	−	0.380143i	−0.491011	−	0.871154i	$-0.663372\pi$
$197$	5.33556	−	5.33556i	0.380143	−	0.380143i	0.871154	+	0.491011i	$0.163372\pi$
$198$	−0.592025	+	0.156444i	−0.0420734	+	0.0111180i
$199$	11.8858			0.842561			0.421280	−	0.906930i	$-0.361581\pi$
$199$	11.8858			0.842561			0.421280	+	0.906930i	$0.361581\pi$
$200$	2.88645	+	13.8444i	0.204103	+	0.978949i
$201$	20.4097			1.43959
$202$	−1.72706	+	0.456381i	−0.121516	+	0.0321109i
$203$	2.02811	−	2.02811i	0.142345	−	0.142345i
$204$	−11.1822	−	19.6807i	−0.782912	−	1.37792i
$205$	−15.6732	+	8.57553i	−1.09466	+	0.598941i
$206$	9.24396	−	15.8841i	0.644057	−	1.10670i
$207$	−0.807918	−	0.807918i	−0.0561542	−	0.0561542i
$208$	15.7098	−	3.97779i	1.08928	−	0.275810i
$209$			6.23934i			0.431584i
$210$	4.10733	−	3.89599i	0.283433	−	0.268849i
$211$			2.04430i			0.140735i	0.997521	+	0.0703677i	$0.0224173\pi$
$211$			2.04430i			0.140735i	−0.997521	+	0.0703677i	$0.977583\pi$
$212$	−1.53030	−	0.421387i	−0.105102	−	0.0289410i
$213$	0.773357	+	0.773357i	0.0529895	+	0.0529895i
$214$	−23.6135	−	13.7421i	−1.61418	−	0.939392i
$215$	5.01879	−	17.1464i	0.342278	−	1.16938i
$216$	14.1523	+	0.146552i	0.962942	+	0.00997163i
$217$	−4.25228	+	4.25228i	−0.288664	+	0.288664i
$218$	4.91589	+	18.6030i	0.332946	+	1.25995i
$219$	8.18354			0.552992
$220$	8.03997	+	4.96760i	0.542054	+	0.334915i
$221$	−25.6129			−1.72291
$222$	−3.58071	−	13.5503i	−0.240321	−	0.909437i
$223$	13.1600	−	13.1600i	0.881261	−	0.881261i	−0.112402	−	0.993663i	$-0.535854\pi$
$223$	13.1600	−	13.1600i	0.881261	−	0.881261i	0.993663	+	0.112402i	$0.0358544\pi$
$224$	−4.94706	+	2.74346i	−0.330539	+	0.183305i
$225$	−0.862778	−	0.552400i	−0.0575185	−	0.0368267i
$226$	13.3552	+	7.77221i	0.888374	+	0.517000i
$227$	−3.93549	−	3.93549i	−0.261207	−	0.261207i	0.564337	−	0.825544i	$-0.309132\pi$
$227$	−3.93549	−	3.93549i	−0.261207	−	0.261207i	−0.825544	+	0.564337i	$0.809132\pi$
$228$	−2.80643	+	10.1918i	−0.185860	+	0.674968i
$229$		−	8.21070i		−	0.542579i	−0.962498	−	0.271289i	$-0.912550\pi$
$229$		−	8.21070i		−	0.542579i	0.962498	−	0.271289i	$-0.0874500\pi$
$230$	−0.465490	+	17.6280i	−0.0306935	+	1.16236i
$231$		−	3.78322i		−	0.248917i
$232$	5.67664	+	5.79544i	0.372690	+	0.380489i
$233$	−8.47827	−	8.47827i	−0.555430	−	0.555430i	0.372573	−	0.928003i	$-0.378476\pi$
$233$	−8.47827	−	8.47827i	−0.555430	−	0.555430i	−0.928003	+	0.372573i	$0.878476\pi$
$234$	−0.590476	+	1.01463i	−0.0386006	+	0.0663284i
$235$	−13.0605	−	3.82284i	−0.851974	−	0.249374i
$236$	8.65664	−	4.91855i	0.563499	−	0.320170i
$237$	18.0437	−	18.0437i	1.17206	−	1.17206i
$238$	8.64398	−	2.28420i	0.560306	−	0.148063i
$239$	−18.5038			−1.19691			−0.598456	−	0.801155i	$-0.704219\pi$
$239$	−18.5038			−1.19691			−0.598456	+	0.801155i	$0.704219\pi$
$240$	10.8986	+	11.7308i	0.703505	+	0.757218i
$241$	0.0823683			0.00530581			0.00265290	−	0.999996i	$-0.499156\pi$
$241$	0.0823683			0.00530581			0.00265290	+	0.999996i	$0.499156\pi$
$242$	−8.93394	+	2.36082i	−0.574296	+	0.151759i
$243$	−1.50308	+	1.50308i	−0.0964224	+	0.0964224i
$244$	2.93411	−	1.66711i	0.187837	−	0.106726i
$245$	1.07330	+	1.96164i	0.0685709	+	0.125324i
$246$	−10.1746	+	17.4832i	−0.648707	+	1.11469i
$247$	8.45810	+	8.45810i	0.538176	+	0.538176i
$248$	−11.9021	−	12.1512i	−0.755784	−	0.771600i
$249$			13.9658i			0.885045i
$250$	2.97839	+	15.5283i	0.188370	+	0.982098i
$251$		−	9.07743i		−	0.572963i	−0.958086	−	0.286481i	$-0.907514\pi$
$251$		−	9.07743i		−	0.572963i	0.958086	−	0.286481i	$-0.0924856\pi$
$252$	0.108791	−	0.395082i	0.00685316	−	0.0248878i
$253$	8.33287	+	8.33287i	0.523883	+	0.523883i
$254$	6.64112	+	3.86488i	0.416701	+	0.242504i
$255$	−12.1475	−	22.2015i	−0.760704	−	1.39031i
$256$	−7.61438	−	14.0720i	−0.475899	−	0.879500i
$257$	−5.15309	+	5.15309i	−0.321441	+	0.321441i	−0.849320	−	0.527879i	$-0.822988\pi$
$257$	−5.15309	+	5.15309i	−0.321441	+	0.321441i	0.527879	+	0.849320i	$0.322988\pi$
$258$	−5.16800	−	19.5570i	−0.321746	−	1.21757i
$259$	5.53585			0.343981
$260$	17.6331	−	4.16492i	1.09356	−	0.258298i
$261$	−0.587670			−0.0363758
$262$	4.20054	+	15.8959i	0.259510	+	0.982051i
$263$	3.79458	−	3.79458i	0.233984	−	0.233984i	−0.580369	−	0.814353i	$-0.697092\pi$
$263$	3.79458	−	3.79458i	0.233984	−	0.233984i	0.814353	+	0.580369i	$0.197092\pi$
$264$	10.7000	+	0.110802i	0.658538	+	0.00681942i
$265$	−1.70315	−	0.498515i	−0.104624	−	0.0306236i
$266$	−3.60879	−	2.10017i	−0.221269	−	0.128770i
$267$	2.63151	+	2.63151i	0.161046	+	0.161046i
$268$	−21.9831	−	6.05331i	−1.34283	−	0.369765i
$269$		−	5.41769i		−	0.330323i	−0.986267	−	0.165161i	$-0.947186\pi$
$269$		−	5.41769i		−	0.330323i	0.986267	−	0.165161i	$-0.0528145\pi$
$270$	15.8181	+	0.417696i	0.962658	+	0.0254202i
$271$		−	8.20258i		−	0.498271i	−0.968469	−	0.249136i	$-0.919853\pi$
$271$		−	8.20258i		−	0.498271i	0.968469	−	0.249136i	$-0.0801465\pi$
$272$	6.20718	+	24.5145i	0.376365	+	1.48641i
$273$	−5.12856	−	5.12856i	−0.310394	−	0.310394i
$274$	−15.1792	+	26.0828i	−0.917008	+	1.57572i
$275$	8.89869	+	5.69745i	0.536611	+	0.343569i
$276$	9.86341	+	17.3596i	0.593707	+	1.04492i
$277$	−10.7214	+	10.7214i	−0.644189	+	0.644189i	−0.951583	−	0.307393i	$-0.900543\pi$
$277$	−10.7214	+	10.7214i	−0.644189	+	0.644189i	0.307393	+	0.951583i	$0.400543\pi$
$278$	−6.91553	+	1.82745i	−0.414766	+	0.109603i
$279$	1.23215			0.0737671
$280$	−5.57948	+	2.97815i	−0.333438	+	0.177978i
$281$	−23.7586			−1.41732			−0.708659	−	0.705551i	$-0.750700\pi$
$281$	−23.7586			−1.41732			−0.708659	+	0.705551i	$0.750700\pi$
$282$	−14.8967	+	3.93650i	−0.887085	+	0.234415i
$283$	−16.7507	+	16.7507i	−0.995723	+	0.995723i	−0.999991	−	0.00426748i	$-0.998642\pi$
$283$	−16.7507	+	16.7507i	−0.995723	+	0.995723i	0.00426748	+	0.999991i	$0.498642\pi$
$284$	−0.603606	−	1.06235i	−0.0358174	−	0.0630386i
$285$	−3.32010	+	11.3430i	−0.196666	+	0.671899i
$286$	6.09016	−	10.4649i	0.360119	−	0.618802i
$287$	−5.64967	−	5.64967i	−0.333489	−	0.333489i
$288$	1.11421	+	0.319261i	0.0656557	+	0.0188126i
$289$		−	22.9680i		−	1.35106i
$290$	6.24190	+	6.58050i	0.366537	+	0.386420i
$291$		−	4.95064i		−	0.290212i
$292$	−8.81442	−	2.42716i	−0.515825	−	0.142039i
$293$	18.6078	+	18.6078i	1.08708	+	1.08708i	0.995828	+	0.0912527i	$0.0290871\pi$
$293$	18.6078	+	18.6078i	1.08708	+	1.08708i	0.0912527	+	0.995828i	$0.470913\pi$
$294$	2.18818	+	1.27344i	0.127617	+	0.0742684i
$295$	9.76540	−	5.34311i	0.568564	−	0.311088i
$296$	−0.162133	+	15.6569i	−0.00942381	+	0.910040i
$297$	7.47730	−	7.47730i	0.433877	−	0.433877i
$298$	−2.72516	−	10.3127i	−0.157864	−	0.597399i
$299$	22.5922			1.30654
$300$	11.9731	+	13.3092i	0.691265	+	0.768408i
$301$	7.98984			0.460527
$302$	−5.03455	−	19.0520i	−0.289706	−	1.09632i
$303$	−1.59898	+	1.59898i	−0.0918587	+	0.0918587i
$304$	6.04557	−	10.1451i	0.346737	−	0.581863i
$305$	3.30992	−	1.81101i	0.189525	−	0.103698i
$306$	−1.58329	−	0.921414i	−0.0905107	−	0.0526737i
$307$	−19.1930	−	19.1930i	−1.09540	−	1.09540i	−0.994941	−	0.100459i	$-0.967969\pi$
$307$	−19.1930	−	19.1930i	−1.09540	−	1.09540i	−0.100459	−	0.994941i	$-0.532031\pi$
$308$	−1.12206	+	4.07487i	−0.0639356	+	0.232187i
$309$		−	23.2645i		−	1.32347i
$310$	−13.0873	−	13.7972i	−0.743306	−	0.783627i
$311$		−	13.8475i		−	0.785218i	−0.919706	−	0.392609i	$-0.871573\pi$
$311$		−	13.8475i		−	0.785218i	0.919706	−	0.392609i	$-0.128427\pi$
$312$	14.6552	−	14.3548i	0.829686	−	0.812678i
$313$	−16.6316	−	16.6316i	−0.940074	−	0.940074i	0.0582290	−	0.998303i	$-0.481455\pi$
$313$	−16.6316	−	16.6316i	−0.940074	−	0.940074i	−0.998303	+	0.0582290i	$0.981455\pi$
$314$	5.67627	−	9.75368i	0.320331	−	0.550432i
$315$	0.128703	−	0.439707i	0.00725159	−	0.0247747i
$316$	−24.7863	+	14.0831i	−1.39434	+	0.792237i
$317$	−0.583141	+	0.583141i	−0.0327525	+	0.0327525i	−0.723293	−	0.690541i	$-0.757373\pi$
$317$	−0.583141	+	0.583141i	−0.0327525	+	0.0327525i	0.690541	+	0.723293i	$0.257373\pi$
$318$	−1.94260	+	0.513337i	−0.108935	+	0.0287865i
$319$	6.06122			0.339363
$320$	−8.25961	−	15.8675i	−0.461726	−	0.887022i
$321$	−34.5851			−1.93035
$322$	−7.62452	+	2.01480i	−0.424898	+	0.112281i
$323$	−13.1985	+	13.1985i	−0.734386	+	0.734386i
$324$	16.6461	−	9.45801i	0.924783	−	0.525445i
$325$	19.7866	−	4.33962i	1.09756	−	0.240719i
$326$	9.90909	−	17.0271i	0.548814	−	0.943041i
$327$	17.2233	+	17.2233i	0.952451	+	0.952451i
$328$	16.1443	−	15.8134i	0.891419	−	0.873146i
$329$		−	6.08591i		−	0.335527i
$330$	11.9594	+	0.315804i	0.658344	+	0.0173844i
$331$		−	14.3496i		−	0.788726i	−0.918955	−	0.394363i	$-0.870965\pi$
$331$		−	14.3496i		−	0.788726i	0.918955	−	0.394363i	$-0.129035\pi$
$332$	4.14211	−	15.0424i	0.227328	−	0.825560i
$333$	−0.802042	−	0.802042i	−0.0439516	−	0.0439516i
$334$	−24.2501	−	14.1126i	−1.32690	−	0.772208i
$335$	−24.4661	−	7.16128i	−1.33673	−	0.391262i
$336$	−3.66572	+	6.15149i	−0.199982	+	0.335591i
$337$	0.0624771	−	0.0624771i	0.00340335	−	0.00340335i	−0.705403	−	0.708806i	$-0.749234\pi$
$337$	0.0624771	−	0.0624771i	0.00340335	−	0.00340335i	0.708806	+	0.705403i	$0.249234\pi$
$338$	−1.23340	−	4.66749i	−0.0670880	−	0.253878i
$339$	19.5605			1.06238
$340$	6.49920	+	27.5158i	0.352468	+	1.49225i
$341$	−12.7084			−0.688200
$342$	0.218570	+	0.827122i	0.0118189	+	0.0447256i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−0.234005	+	22.5975i	−0.0126167	+	1.21837i
$345$	10.7148	+	19.5830i	0.576866	+	1.05432i
$346$	−15.3454	−	8.93044i	−0.824974	−	0.480104i
$347$	6.23825	+	6.23825i	0.334887	+	0.334887i	0.854439	−	0.519552i	$-0.173901\pi$
$347$	6.23825	+	6.23825i	0.334887	+	0.334887i	−0.519552	+	0.854439i	$0.673901\pi$
$348$	9.90083	+	2.72631i	0.530740	+	0.146146i
$349$			3.77799i			0.202231i	0.994875	+	0.101116i	$0.0322412\pi$
$349$			3.77799i			0.202231i	−0.994875	+	0.101116i	$0.967759\pi$
$350$	−6.29067	+	3.22916i	−0.336251	+	0.172606i
$351$		−	20.2726i		−	1.08207i
$352$	−11.4920	−	3.29285i	−0.612526	−	0.175510i
$353$	−0.878862	−	0.878862i	−0.0467771	−	0.0467771i	0.683331	−	0.730108i	$-0.260530\pi$
$353$	−0.878862	−	0.878862i	−0.0467771	−	0.0467771i	−0.730108	+	0.683331i	$0.760530\pi$
$354$	6.33942	−	10.8932i	0.336936	−	0.578966i
$355$	−0.655709	−	1.19841i	−0.0348014	−	0.0636052i
$356$	−2.05390	−	3.61486i	−0.108856	−	0.191587i
$357$	8.00291	−	8.00291i	0.423559	−	0.423559i
$358$	4.72714	−	1.24916i	0.249837	−	0.0660203i
$359$	17.5043			0.923843			0.461922	−	0.886921i	$-0.347160\pi$
$359$	17.5043			0.923843			0.461922	+	0.886921i	$0.347160\pi$
$360$	1.23984	+	0.376885i	0.0653454	+	0.0198636i
$361$	−10.2830			−0.541209
$362$	22.0077	−	5.81561i	1.15670	−	0.305662i
$363$	−8.27137	+	8.27137i	−0.434134	+	0.434134i
$364$	4.00284	+	7.04500i	0.209806	+	0.369258i
$365$	−9.81001	−	2.87141i	−0.513479	−	0.150296i
$366$	2.14870	−	3.69217i	0.112315	−	0.192993i
$367$	11.0087	+	11.0087i	0.574651	+	0.574651i	0.933425	−	0.358773i	$-0.116805\pi$
$367$	11.0087	+	11.0087i	0.574651	+	0.574651i	−0.358773	+	0.933425i	$0.616805\pi$
$368$	−5.47511	−	21.6232i	−0.285410	−	1.12719i
$369$			1.63706i			0.0852222i
$370$	−0.462104	+	17.4998i	−0.0240237	+	0.909771i
$371$		−	0.793630i		−	0.0412032i
$372$	−20.7589	−	5.71620i	−1.07630	−	0.296371i
$373$	0.556354	+	0.556354i	0.0288069	+	0.0288069i	0.721364	−	0.692557i	$-0.243516\pi$
$373$	0.556354	+	0.556354i	0.0288069	+	0.0288069i	−0.692557	+	0.721364i	$0.743516\pi$
$374$	16.3300	+	9.50346i	0.844407	+	0.491412i
$375$	13.1458	+	15.0930i	0.678847	+	0.779400i
$376$	17.2126	+	0.178243i	0.887673	+	0.00919220i
$377$	8.21663	−	8.21663i	0.423178	−	0.423178i
$378$	1.80794	+	6.84168i	0.0929902	+	0.351898i
$379$	9.14995			0.470001			0.235001	−	0.971995i	$-0.424491\pi$
$379$	9.14995			0.470001			0.235001	+	0.971995i	$0.424491\pi$
$380$	6.94026	−	11.2327i	0.356028	−	0.576225i
$381$	9.72684			0.498321
$382$	−1.91605	−	7.25083i	−0.0980339	−	0.370985i
$383$	−5.96998	+	5.96998i	−0.305052	+	0.305052i	−0.842987	−	0.537935i	$-0.819205\pi$
$383$	−5.96998	+	5.96998i	−0.305052	+	0.305052i	0.537935	+	0.842987i	$0.319205\pi$
$384$	−17.2907	−	10.5478i	−0.882364	−	0.538267i
$385$	−1.32744	+	4.53513i	−0.0676527	+	0.231132i
$386$	−27.3533	−	15.9185i	−1.39224	−	0.810233i
$387$	−1.15758	−	1.15758i	−0.0588431	−	0.0588431i
$388$	−1.46831	+	5.33229i	−0.0745422	+	0.270706i
$389$			28.7326i			1.45680i	0.685152	+	0.728400i	$0.259736\pi$
$389$			28.7326i			1.45680i	−0.685152	+	0.728400i	$0.740264\pi$
$390$	16.6404	−	15.7842i	0.842618	−	0.799262i
$391$			35.2542i			1.78288i
$392$	−1.97918	−	2.02060i	−0.0999638	−	0.102056i
$393$	14.7170	+	14.7170i	0.742373	+	0.742373i
$394$	−5.36743	+	9.22299i	−0.270407	+	0.464648i
$395$	−27.9609	+	15.2987i	−1.40687	+	0.769764i
$396$	0.752940	−	0.427807i	0.0378366	−	0.0214981i
$397$	−18.0493	+	18.0493i	−0.905871	+	0.905871i	−0.995936	−	0.0900652i	$-0.971292\pi$
$397$	−18.0493	+	18.0493i	−0.905871	+	0.905871i	0.0900652	+	0.995936i	$0.471292\pi$
$398$	−16.2512	+	4.29443i	−0.814599	+	0.215260i
$399$	−5.28556			−0.264609
$400$	−8.94870	−	17.8863i	−0.447435	−	0.894316i
$401$	26.1679			1.30676			0.653380	−	0.757030i	$-0.273350\pi$
$401$	26.1679			1.30676			0.653380	+	0.757030i	$0.273350\pi$
$402$	−27.9058	+	7.37419i	−1.39181	+	0.367791i
$403$	−17.2276	+	17.2276i	−0.858169	+	0.858169i
$404$	2.19648	−	1.24800i	0.109279	−	0.0620904i
$405$	18.7782	−	10.2744i	0.933094	−	0.510540i
$406$	−2.04022	+	3.50576i	−0.101254	+	0.173988i
$407$	8.27226	+	8.27226i	0.410041	+	0.410041i
$408$	22.4000	+	22.8688i	1.10897	+	1.13218i
$409$		−	0.985101i		−	0.0487101i	−0.999703	−	0.0243550i	$-0.992247\pi$
$409$		−	0.985101i		−	0.0487101i	0.999703	−	0.0243550i	$-0.00775322\pi$
$410$	18.3312	−	17.3880i	0.905314	−	0.858732i
$411$			38.2018i			1.88436i
$412$	−6.90002	+	25.0580i	−0.339940	+	1.23452i
$413$	3.52011	+	3.52011i	0.173213	+	0.173213i
$414$	1.39656	+	0.812743i	0.0686371	+	0.0399442i
$415$	4.90026	−	16.7415i	0.240544	−	0.821806i
$416$	−20.0424	+	11.1148i	−0.982661	+	0.544949i
$417$	−6.40264	+	6.40264i	−0.313539	+	0.313539i
$418$	−2.25433	−	8.53094i	−0.110263	−	0.417262i
$419$	−16.7317			−0.817399			−0.408699	−	0.912669i	$-0.634018\pi$
$419$	−16.7317			−0.817399			−0.408699	+	0.912669i	$0.634018\pi$
$420$	−4.20822	+	6.81093i	−0.205340	+	0.332339i
$421$	35.5024			1.73028			0.865140	−	0.501530i	$-0.167229\pi$
$421$	35.5024			1.73028			0.865140	+	0.501530i	$0.167229\pi$
$422$	−0.738622	−	2.79513i	−0.0359556	−	0.136065i
$423$	−0.881735	+	0.881735i	−0.0428714	+	0.0428714i
$424$	2.24460	+	0.0232437i	0.109008	+	0.00112882i
$425$	6.77180	+	30.8762i	0.328481	+	1.49772i
$426$	−1.33682	−	0.777976i	−0.0647689	−	0.0376930i
$427$	1.19312	+	1.19312i	0.0577391	+	0.0577391i
$428$	37.2514	+	10.2576i	1.80061	+	0.495820i
$429$		−	15.3273i		−	0.740007i
$430$	−0.666950	+	25.2573i	−0.0321632	+	1.21801i
$431$			1.04633i			0.0504002i	0.999682	+	0.0252001i	$0.00802229\pi$
$431$			1.04633i			0.0504002i	−0.999682	+	0.0252001i	$0.991978\pi$
$432$	−19.4031	+	4.91296i	−0.933533	+	0.236375i
$433$	9.24591	+	9.24591i	0.444330	+	0.444330i	0.893464	−	0.449134i	$-0.148267\pi$
$433$	9.24591	+	9.24591i	0.444330	+	0.444330i	−0.449134	+	0.893464i	$0.648267\pi$
$434$	4.27768	−	7.35045i	0.205335	−	0.352833i
$435$	11.0191	+	3.22532i	0.528327	+	0.154642i
$436$	−13.4428	−	23.6593i	−0.643794	−	1.13308i
$437$	11.6419	−	11.6419i	0.556908	−	0.556908i
$438$	−11.1892	+	2.95678i	−0.534640	+	0.141280i
$439$	−22.7314			−1.08491			−0.542455	−	0.840085i	$-0.682505\pi$
$439$	−22.7314			−1.08491			−0.542455	+	0.840085i	$0.682505\pi$
$440$	−12.7877	−	3.88719i	−0.609631	−	0.185315i
$441$	0.204893			0.00975682
$442$	35.0201	−	9.25416i	1.66573	−	0.440176i
$443$	−16.5056	+	16.5056i	−0.784207	+	0.784207i	−0.980538	−	0.196331i	$-0.937097\pi$
$443$	−16.5056	+	16.5056i	−0.784207	+	0.784207i	0.196331	+	0.980538i	$0.437097\pi$
$444$	9.79167	+	17.2333i	0.464692	+	0.817857i
$445$	−2.23119	−	4.07786i	−0.105769	−	0.193309i
$446$	−13.2386	+	22.7483i	−0.626867	+	1.07716i
$447$	−9.54787	−	9.54787i	−0.451599	−	0.451599i
$448$	5.77279	−	5.53850i	0.272739	−	0.261669i
$449$		−	18.0937i		−	0.853895i	−0.904276	−	0.426947i	$-0.859589\pi$
$449$		−	18.0937i		−	0.853895i	0.904276	−	0.426947i	$-0.140411\pi$
$450$	1.37925	+	0.443557i	0.0650183	+	0.0209095i
$451$		−	16.8847i		−	0.795068i
$452$	−21.0685	−	5.80145i	−0.990977	−	0.272877i
$453$	−17.6390	−	17.6390i	−0.828754	−	0.828754i
$454$	6.80284	+	3.95899i	0.319273	+	0.185805i
$455$	4.34837	+	7.94734i	0.203855	+	0.372577i
$456$	0.154803	−	14.9490i	0.00724931	−	0.700052i
$457$	−12.8567	+	12.8567i	−0.601409	+	0.601409i	−0.940686	−	0.339277i	$-0.889817\pi$
$457$	−12.8567	+	12.8567i	−0.601409	+	0.601409i	0.339277	+	0.940686i	$0.389817\pi$
$458$	2.96659	+	11.2263i	0.138620	+	0.524572i
$459$	31.6345			1.47657
$460$	−5.73269	−	24.2706i	−0.267288	−	1.13162i
$461$	30.3805			1.41496			0.707481	−	0.706733i	$-0.249832\pi$
$461$	30.3805			1.41496			0.707481	+	0.706733i	$0.249832\pi$
$462$	1.36691	+	5.17272i	0.0635943	+	0.240657i
$463$	20.1652	−	20.1652i	0.937156	−	0.937156i	−0.0609833	−	0.998139i	$-0.519424\pi$
$463$	20.1652	−	20.1652i	0.937156	−	0.937156i	0.998139	+	0.0609833i	$0.0194236\pi$
$464$	−9.85551	−	5.87298i	−0.457530	−	0.272646i
$465$	−23.1036	−	6.76246i	−1.07140	−	0.313602i
$466$	14.6555	+	8.52891i	0.678901	+	0.395094i
$467$	14.8295	+	14.8295i	0.686228	+	0.686228i	0.961396	−	0.275168i	$-0.0887335\pi$
$467$	14.8295	+	14.8295i	0.686228	+	0.686228i	−0.275168	+	0.961396i	$0.588733\pi$
$468$	0.440752	−	1.60063i	0.0203738	−	0.0739890i
$469$		−	11.4007i		−	0.526433i
$470$	19.2386	+	0.508020i	0.887411	+	0.0234332i
$471$		−	14.2856i		−	0.658246i
$472$	−10.0589	+	9.85275i	−0.463000	+	0.453510i
$473$	11.9393	+	11.9393i	0.548968	+	0.548968i
$474$	−18.1514	+	31.1901i	−0.833723	+	1.43261i
$475$	7.95995	−	12.4324i	0.365227	−	0.570439i
$476$	−10.9934	+	6.24628i	−0.503884	+	0.286298i
$477$	−0.114982	+	0.114982i	−0.00526467	+	0.00526467i
$478$	25.2999	−	6.68558i	1.15719	−	0.305791i
$479$	−27.8904			−1.27434			−0.637172	−	0.770722i	$-0.719896\pi$
$479$	−27.8904			−1.27434			−0.637172	+	0.770722i	$0.719896\pi$
$480$	−19.1399	−	12.1015i	−0.873614	−	0.552355i
$481$	22.4279			1.02262
$482$	−0.112621	+	0.0297603i	−0.00512972	+	0.00135555i
$483$	−7.05905	+	7.05905i	−0.321198	+	0.321198i
$484$	11.3622	−	6.45581i	0.516465	−	0.293446i
$485$	−1.73706	+	5.93458i	−0.0788759	+	0.269475i
$486$	1.51205	−	2.59820i	0.0685881	−	0.117857i
$487$	2.75176	+	2.75176i	0.124694	+	0.124694i	0.766700	−	0.642006i	$-0.221897\pi$
$487$	2.75176	+	2.75176i	0.124694	+	0.124694i	−0.642006	+	0.766700i	$0.721897\pi$
$488$	−3.40941	+	3.33952i	−0.154337	+	0.151173i
$489$		−	24.9385i		−	1.12776i
$490$	−2.17626	−	2.29431i	−0.0983135	−	0.103647i
$491$		−	14.4151i		−	0.650544i	−0.945620	−	0.325272i	$-0.894544\pi$
$491$		−	14.4151i		−	0.650544i	0.945620	−	0.325272i	$-0.105456\pi$
$492$	7.59466	−	27.5806i	0.342394	−	1.24343i
$493$	12.8217	+	12.8217i	0.577462	+	0.577462i
$494$	−14.6206	−	8.50861i	−0.657811	−	0.382821i
$495$	0.849378	−	0.464735i	0.0381767	−	0.0208883i
$496$	20.6638	+	12.3137i	0.927833	+	0.552903i
$497$	0.431989	−	0.431989i	0.0193774	−	0.0193774i
$498$	−5.04595	−	19.0951i	−0.226114	−	0.855673i
$499$	−2.95034			−0.132075			−0.0660377	−	0.997817i	$-0.521036\pi$
$499$	−2.95034			−0.132075			−0.0660377	+	0.997817i	$0.521036\pi$
$500$	−9.68281	−	20.1555i	−0.433029	−	0.901380i
$501$	−35.5175			−1.58681
$502$	3.27975	+	12.4114i	0.146382	+	0.553948i
$503$	17.2036	−	17.2036i	0.767071	−	0.767071i	−0.210518	−	0.977590i	$-0.567515\pi$
$503$	17.2036	−	17.2036i	0.767071	−	0.767071i	0.977590	+	0.210518i	$0.0675152\pi$
$504$	−0.00600089	+	0.579495i	−0.000267301	+	0.0258127i
$505$	2.47781	−	1.35573i	0.110261	−	0.0603291i
$506$	−14.4041	−	8.38263i	−0.640340	−	0.372653i
$507$	−4.32133	−	4.32133i	−0.191917	−	0.191917i
$508$	−10.4767	−	2.88488i	−0.464828	−	0.127996i
$509$		−	2.68000i		−	0.118789i	−0.998235	−	0.0593944i	$-0.981083\pi$
$509$		−	2.68000i		−	0.118789i	0.998235	−	0.0593944i	$-0.0189170\pi$
$510$	24.6306	+	25.9666i	1.09066	+	1.14982i
$511$		−	4.57124i		−	0.202220i
$512$	15.4953	+	16.4892i	0.684803	+	0.728728i
$513$	−10.4466	−	10.4466i	−0.461228	−	0.461228i
$514$	5.18387	−	8.90758i	0.228651	−	0.392896i
$515$	−8.16296	+	27.8883i	−0.359703	+	1.22891i
$516$	14.1322	+	24.8727i	0.622136	+	1.09496i
$517$	9.09421	−	9.09421i	0.399963	−	0.399963i
$518$	−7.56906	+	2.00015i	−0.332566	+	0.0878815i
$519$	−22.4755			−0.986563
$520$	−22.6046	+	12.0656i	−0.991278	+	0.529112i
$521$	−45.0207			−1.97239			−0.986196	−	0.165580i	$-0.947050\pi$
$521$	−45.0207			−1.97239			−0.986196	+	0.165580i	$0.947050\pi$
$522$	0.803509	−	0.212330i	0.0351687	−	0.00929343i
$523$	4.47737	−	4.47737i	0.195782	−	0.195782i	−0.602407	−	0.798189i	$-0.705792\pi$
$523$	4.47737	−	4.47737i	0.195782	−	0.195782i	0.798189	+	0.602407i	$0.205792\pi$
$524$	−11.4866	−	20.2164i	−0.501795	−	0.883159i
$525$	−4.82650	+	7.53838i	−0.210646	+	0.329002i
$526$	−3.81724	+	6.55927i	−0.166440	+	0.285998i
$527$	−26.8830	−	26.8830i	−1.17104	−	1.17104i
$528$	−14.6699	+	3.71449i	−0.638426	+	0.161653i
$529$		−	8.09635i		−	0.352015i
$530$	2.50880	+	0.0662481i	0.108975	+	0.00287763i
$531$		−	1.02000i		−	0.0442641i
$532$	5.69303	+	1.56764i	0.246824	+	0.0679660i
$533$	−22.8890	−	22.8890i	−0.991432	−	0.991432i
$534$	−4.54881	−	2.64723i	−0.196846	−	0.114557i
$535$	41.4589	+	12.1351i	1.79243	+	0.524646i
$536$	32.2442	+	0.333901i	1.39274	+	0.0144223i
$537$	4.37656	−	4.37656i	0.188862	−	0.188862i
$538$	1.95746	+	7.40751i	0.0843919	+	0.319360i
$539$	−2.11327			−0.0910249
$540$	−21.7787	+	5.14409i	−0.937205	+	0.221367i
$541$	16.7537			0.720298			0.360149	−	0.932895i	$-0.382726\pi$
$541$	16.7537			0.720298			0.360149	+	0.932895i	$0.382726\pi$
$542$	2.96366	+	11.2152i	0.127300	+	0.481736i
$543$	20.3755	−	20.3755i	0.874398	−	0.874398i
$544$	−17.3442	−	31.2754i	−0.743628	−	1.34092i
$545$	−14.6032	−	26.6897i	−0.625531	−	1.14326i
$546$	8.86516	+	5.15919i	0.379394	+	0.220793i
$547$	−12.5910	−	12.5910i	−0.538352	−	0.538352i	0.384693	−	0.923045i	$-0.374307\pi$
$547$	−12.5910	−	12.5910i	−0.538352	−	0.538352i	−0.923045	+	0.384693i	$0.874307\pi$
$548$	11.3303	−	41.1468i	0.484005	−	1.75771i
$549$		−	0.345721i		−	0.0147550i
$550$	−14.2255	−	4.57484i	−0.606579	−	0.195072i
$551$		−	8.46818i		−	0.360757i
$552$	−19.7582	−	20.1717i	−0.840965	−	0.858564i
$553$	−10.0790	−	10.0790i	−0.428603	−	0.428603i
$554$	10.7855	−	18.5330i	0.458231	−	0.787391i
$555$	10.6369	+	19.4406i	0.451510	+	0.825208i
$556$	8.79519	−	4.99727i	0.372999	−	0.211932i
$557$	−23.4003	+	23.4003i	−0.991501	+	0.991501i	−0.999964	−	0.00846362i	$-0.997306\pi$
$557$	−23.4003	+	23.4003i	−0.991501	+	0.991501i	0.00846362	+	0.999964i	$0.497306\pi$
$558$	−1.68470	+	0.445187i	−0.0713190	+	0.0188463i
$559$	32.3699			1.36910
$560$	6.55269	−	6.08788i	0.276902	−	0.257260i
$561$	23.9176			1.00980
$562$	32.4846	−	8.58417i	1.37028	−	0.362101i
$563$	13.8165	−	13.8165i	0.582298	−	0.582298i	−0.353236	−	0.935534i	$-0.614919\pi$
$563$	13.8165	−	13.8165i	0.582298	−	0.582298i	0.935534	+	0.353236i	$0.114919\pi$
$564$	18.9457	−	10.7646i	0.797756	−	0.453271i
$565$	−23.4482	−	6.86332i	−0.986472	−	0.288742i
$566$	16.8507	−	28.9550i	0.708288	−	1.21707i
$567$	6.76892	+	6.76892i	0.284268	+	0.284268i
$568$	1.20913	+	1.23444i	0.0507341	+	0.0517958i
$569$			38.9280i			1.63195i	0.578088	+	0.815974i	$0.303799\pi$
$569$			38.9280i			1.63195i	−0.578088	+	0.815974i	$0.696201\pi$
$570$	0.441211	−	16.7086i	0.0184803	−	0.699846i
$571$			20.4937i			0.857634i	0.903391	+	0.428817i	$0.141069\pi$
$571$			20.4937i			0.857634i	−0.903391	+	0.428817i	$0.858931\pi$
$572$	−4.54591	+	16.5089i	−0.190074	+	0.690270i
$573$	−6.71308	−	6.71308i	−0.280443	−	0.280443i
$574$	9.76596	+	5.68341i	0.407623	+	0.237221i
$575$	−5.97315	−	27.2347i	−0.249097	−	1.13577i
$576$	−1.63879	−	0.0339443i	−0.0682831	−	0.00141435i
$577$	−4.97206	+	4.97206i	−0.206990	+	0.206990i	−0.802987	−	0.595997i	$-0.796757\pi$
$577$	−4.97206	+	4.97206i	−0.206990	+	0.206990i	0.595997	+	0.802987i	$0.296757\pi$
$578$	8.29851	+	31.4037i	0.345173	+	1.30622i
$579$	−40.0626			−1.66494
$580$	−10.9120	−	6.74213i	−0.453097	−	0.279952i
$581$	7.80114			0.323646
$582$	1.78871	+	6.76892i	0.0741443	+	0.280581i
$583$	1.18593	−	1.18593i	0.0491160	−	0.0491160i
$584$	12.9287	+	0.133882i	0.534995	+	0.00554008i
$585$	0.521425	−	1.78142i	0.0215583	−	0.0736526i
$586$	−32.1653	−	18.7190i	−1.32874	−	0.773273i
$587$	−4.00401	−	4.00401i	−0.165263	−	0.165263i	0.619631	−	0.784894i	$-0.287282\pi$
$587$	−4.00401	−	4.00401i	−0.165263	−	0.165263i	−0.784894	+	0.619631i	$0.787282\pi$
$588$	−3.45196	−	0.950539i	−0.142357	−	0.0391996i
$589$			17.7550i			0.731584i
$590$	−11.4215	+	10.8339i	−0.470217	+	0.446023i
$591$			13.5083i			0.555659i
$592$	−5.43529	−	21.4660i	−0.223389	−	0.882246i
$593$	24.8290	+	24.8290i	1.01961	+	1.01961i	0.999804	+	0.0198022i	$0.00630366\pi$
$593$	24.8290	+	24.8290i	1.01961	+	1.01961i	0.0198022	+	0.999804i	$0.493696\pi$
$594$	−7.52196	+	12.9252i	−0.308630	+	0.530326i
$595$	−12.4015	+	6.78545i	−0.508412	+	0.278176i
$596$	7.45212	+	13.1157i	0.305251	+	0.537241i
$597$	−15.0459	+	15.0459i	−0.615790	+	0.615790i
$598$	−30.8898	+	8.16274i	−1.26318	+	0.333799i
$599$	1.37498			0.0561802			0.0280901	−	0.999605i	$-0.491057\pi$
$599$	1.37498			0.0561802			0.0280901	+	0.999605i	$0.491057\pi$
$600$	−21.1793	−	13.8715i	−0.864640	−	0.566300i
$601$	−8.86739			−0.361708			−0.180854	−	0.983510i	$-0.557886\pi$
$601$	−8.86739			−0.361708			−0.180854	+	0.983510i	$0.557886\pi$
$602$	−10.9244	+	2.88679i	−0.445243	+	0.117657i
$603$	−1.65174	+	1.65174i	−0.0672642	+	0.0672642i
$604$	13.7673	+	24.2304i	0.560183	+	0.985921i
$605$	12.8175	−	7.01307i	0.521106	−	0.285122i
$606$	1.60853	−	2.76397i	0.0653419	−	0.112279i
$607$	12.0451	+	12.0451i	0.488896	+	0.488896i	0.907958	−	0.419062i	$-0.137641\pi$
$607$	12.0451	+	12.0451i	0.488896	+	0.488896i	−0.419062	+	0.907958i	$0.637641\pi$
$608$	−4.60047	+	16.0556i	−0.186574	+	0.651139i
$609$			5.13467i			0.208067i
$610$	−3.87125	+	3.67206i	−0.156742	+	0.148677i
$611$		−	24.6563i		−	0.997489i
$612$	2.49772	+	0.687776i	0.100964	+	0.0278017i
$613$	−20.1345	−	20.1345i	−0.813224	−	0.813224i	0.171892	−	0.985116i	$-0.445012\pi$
$613$	−20.1345	−	20.1345i	−0.813224	−	0.813224i	−0.985116	+	0.171892i	$0.945012\pi$
$614$	33.1767	+	19.3076i	1.33890	+	0.779191i
$615$	8.98474	−	30.6959i	0.362300	−	1.23778i
$616$	0.0618931	−	5.97690i	0.00249375	−	0.240816i
$617$	0.247352	−	0.247352i	0.00995801	−	0.00995801i	−0.702110	−	0.712068i	$-0.747759\pi$
$617$	0.247352	−	0.247352i	0.00995801	−	0.00995801i	0.712068	+	0.702110i	$0.247759\pi$
$618$	8.40566	+	31.8091i	0.338125	+	1.27955i
$619$	8.89901			0.357681			0.178841	−	0.983878i	$-0.442765\pi$
$619$	8.89901			0.357681			0.178841	+	0.983878i	$0.442765\pi$
$620$	22.8790	+	14.1361i	0.918842	+	0.567719i
$621$	−27.9036			−1.11973
$622$	5.00320	+	18.9334i	0.200610	+	0.759159i
$623$	1.46994	−	1.46994i	0.0588918	−	0.0588918i
$624$	−14.8512	+	24.9220i	−0.594525	+	0.997679i
$625$	−10.4628	−	22.7053i	−0.418511	−	0.908212i
$626$	28.7492	+	16.7309i	1.14905	+	0.668703i
$627$	−7.89825	−	7.89825i	−0.315426	−	0.315426i
$628$	−4.23697	+	15.3869i	−0.169073	+	0.614004i
$629$			34.9978i			1.39545i
$630$	−0.0171034	+	0.647704i	−0.000681417	+	0.0258051i
$631$			30.9594i			1.23248i	0.787560	+	0.616238i	$0.211344\pi$
$631$			30.9594i			1.23248i	−0.787560	+	0.616238i	$0.788656\pi$
$632$	28.8014	−	28.2110i	1.14566	−	1.12217i
$633$	−2.58783	−	2.58783i	−0.102857	−	0.102857i
$634$	0.586624	−	1.00801i	0.0232978	−	0.0400332i
$635$	−11.6600	−	3.41292i	−0.462715	−	0.135437i
$636$	2.47060	−	1.40375i	0.0979657	−	0.0556624i
$637$	−2.86476	+	2.86476i	−0.113506	+	0.113506i
$638$	−8.28739	+	2.18997i	−0.328101	+	0.0867017i
$639$	−0.125174			−0.00495183
$640$	17.0263	+	18.7111i	0.673023	+	0.739622i
$641$	12.3616			0.488253			0.244127	−	0.969743i	$-0.421499\pi$
$641$	12.3616			0.488253			0.244127	+	0.969743i	$0.421499\pi$
$642$	47.2876	−	12.4959i	1.86629	−	0.493174i
$643$	2.95024	−	2.95024i	0.116346	−	0.116346i	−0.646537	−	0.762883i	$-0.723783\pi$
$643$	2.95024	−	2.95024i	0.116346	−	0.116346i	0.762883	+	0.646537i	$0.223783\pi$
$644$	9.69689	−	5.50960i	0.382111	−	0.217109i
$645$	15.3521	+	28.0584i	0.604488	+	1.10480i
$646$	13.2774	−	22.8148i	0.522390	−	0.897637i
$647$	−3.37363	−	3.37363i	−0.132631	−	0.132631i	0.637675	−	0.770306i	$-0.279896\pi$
$647$	−3.37363	−	3.37363i	−0.132631	−	0.132631i	−0.770306	+	0.637675i	$0.779896\pi$
$648$	−19.3426	+	18.9461i	−0.759850	+	0.744274i
$649$			10.5203i			0.412956i
$650$	−25.4859	+	13.0825i	−0.999640	+	0.513140i
$651$		−	10.7657i		−	0.421943i
$652$	−7.39650	+	26.8610i	−0.289669	+	1.05196i
$653$	5.92468	+	5.92468i	0.231851	+	0.231851i	0.813465	−	0.581614i	$-0.197579\pi$
$653$	5.92468	+	5.92468i	0.231851	+	0.231851i	−0.581614	+	0.813465i	$0.697579\pi$
$654$	−29.7720	−	17.3262i	−1.16418	−	0.677507i
$655$	−12.4781	−	22.8058i	−0.487561	−	0.891097i
$656$	−16.3603	+	27.4544i	−0.638762	+	1.07191i
$657$	−0.662288	+	0.662288i	−0.0258383	+	0.0258383i
$658$	2.19889	+	8.32114i	0.0857216	+	0.324392i
$659$	−35.0426			−1.36507			−0.682534	−	0.730854i	$-0.739122\pi$
$659$	−35.0426			−1.36507			−0.682534	+	0.730854i	$0.739122\pi$
$660$	−16.4660	+	3.88924i	−0.640938	+	0.151389i
$661$	19.0422			0.740655			0.370328	−	0.928901i	$-0.379245\pi$
$661$	19.0422			0.740655			0.370328	+	0.928901i	$0.379245\pi$
$662$	5.18463	+	19.6199i	0.201506	+	0.762550i
$663$	32.4228	−	32.4228i	1.25920	−	1.25920i
$664$	−0.228479	+	22.0638i	−0.00886670	+	0.856241i
$665$	6.33606	+	1.85458i	0.245702	+	0.0719174i
$666$	1.38640	+	0.806832i	0.0537219	+	0.0312641i
$667$	−11.3096	−	11.3096i	−0.437908	−	0.437908i
$668$	38.2556	+	10.5341i	1.48016	+	0.407579i
$669$			33.3180i			1.28815i
$670$	36.0395	+	0.951668i	1.39233	+	0.0367661i
$671$			3.56577i			0.137655i
$672$	2.78949	−	9.73526i	0.107607	−	0.375546i
$673$	−25.9196	−	25.9196i	−0.999127	−	0.999127i	0.000872915	−	1.00000i	$-0.499722\pi$
$673$	−25.9196	−	25.9196i	−0.999127	−	0.999127i	−1.00000		0.000872915i	$0.999722\pi$
$674$	−0.0628503	+	0.107997i	−0.00242090	+	0.00415990i
$675$	−24.4384	+	5.35986i	−0.940636	+	0.206301i
$676$	3.37280	+	5.93613i	0.129723	+	0.228313i
$677$	9.73014	−	9.73014i	0.373960	−	0.373960i	−0.494958	−	0.868917i	$-0.664816\pi$
$677$	9.73014	−	9.73014i	0.373960	−	0.373960i	0.868917	+	0.494958i	$0.164816\pi$
$678$	−26.7447	+	7.06737i	−1.02712	+	0.271421i
$679$	−2.76538			−0.106125
$680$	−18.8279	−	35.2736i	−0.722018	−	1.35268i
$681$	9.96369			0.381809
$682$	17.3760	−	4.59166i	0.665361	−	0.175824i
$683$	5.87319	−	5.87319i	0.224731	−	0.224731i	−0.585756	−	0.810487i	$-0.699202\pi$
$683$	5.87319	−	5.87319i	0.224731	−	0.224731i	0.810487	+	0.585756i	$0.199202\pi$
$684$	−0.597692	−	1.05194i	−0.0228533	−	0.0402218i
$685$	13.4041	−	45.7944i	0.512145	−	1.74971i
$686$	0.711330	−	1.22230i	0.0271587	−	0.0466675i
$687$	10.3937	+	10.3937i	0.396546	+	0.396546i
$688$	−7.84470	−	30.9816i	−0.299076	−	1.18116i
$689$		−	3.21530i		−	0.122493i
$690$	−21.7257	−	22.9042i	−0.827082	−	0.871947i
$691$		−	8.26699i		−	0.314491i	−0.987560	−	0.157246i	$-0.949739\pi$
$691$		−	8.26699i		−	0.314491i	0.987560	−	0.157246i	$-0.0502614\pi$
$692$	24.2081	+	6.66600i	0.920255	+	0.253403i
$693$	0.306173	+	0.306173i	0.0116306	+	0.0116306i
$694$	−10.7834	−	6.27551i	−0.409331	−	0.238215i
$695$	9.92170	−	5.42863i	0.376352	−	0.205920i
$696$	−14.5223	−	0.150384i	−0.550465	−	0.00570027i
$697$	35.7173	−	35.7173i	1.35289	−	1.35289i
$698$	−1.36502	−	5.16558i	−0.0516668	−	0.195520i
$699$	21.4649			0.811878
$700$	7.43439	−	6.68803i	0.280994	−	0.252784i
$701$	−14.1462			−0.534296			−0.267148	−	0.963656i	$-0.586081\pi$
$701$	−14.1462			−0.534296			−0.267148	+	0.963656i	$0.586081\pi$
$702$	7.32464	+	27.7183i	0.276451	+	1.04616i
$703$	11.5572	−	11.5572i	0.435889	−	0.435889i
$704$	16.9025	+	0.350102i	0.637038	+	0.0131950i
$705$	21.3723	−	11.6938i	0.804926	−	0.440413i
$706$	1.51919	+	0.884111i	0.0571755	+	0.0332740i
$707$	0.893172	+	0.893172i	0.0335912	+	0.0335912i
$708$	−4.73197	+	17.1845i	−0.177838	+	0.645834i
$709$		−	11.7846i		−	0.442579i	−0.975208	−	0.221289i	$-0.928973\pi$
$709$		−	11.7846i		−	0.442579i	0.975208	−	0.221289i	$-0.0710265\pi$
$710$	1.32953	+	1.40165i	0.0498965	+	0.0526032i
$711$			2.92052i			0.109528i
$712$	4.11434	+	4.20044i	0.154191	+	0.157418i
$713$	23.7125	+	23.7125i	0.888039	+	0.888039i
$714$	−8.05071	+	13.8337i	−0.301290	+	0.517715i
$715$	−5.37797	+	18.3736i	−0.201125	+	0.687132i
$716$	−6.01200	+	3.41591i	−0.224679	+	0.127659i
$717$	23.4236	−	23.4236i	0.874769	−	0.874769i
$718$	−23.9333	+	6.32446i	−0.893184	+	0.236027i
$719$	−19.4887			−0.726806			−0.363403	−	0.931632i	$-0.618385\pi$
$719$	−19.4887			−0.726806			−0.363403	+	0.931632i	$0.618385\pi$
$720$	−1.83138	−	0.0673431i	−0.0682516	−	0.00250973i
$721$	−12.9953			−0.483971
$722$	14.0597	−	3.71532i	0.523248	−	0.138270i
$723$	−0.104268	+	0.104268i	−0.00387777	+	0.00387777i
$724$	−27.9895	+	15.9031i	−1.04022	+	0.591036i
$725$	−12.0775	−	7.73271i	−0.448547	−	0.287185i
$726$	8.32077	−	14.2978i	0.308813	−	0.530641i
$727$	−21.7062	−	21.7062i	−0.805039	−	0.805039i	0.178839	−	0.983878i	$-0.442766\pi$
$727$	−21.7062	−	21.7062i	−0.805039	−	0.805039i	−0.983878	+	0.178839i	$0.942766\pi$
$728$	−8.01843	−	8.18623i	−0.297183	−	0.303402i
$729$			24.9127i			0.922692i
$730$	14.4505	+	0.381584i	0.534837	+	0.0141230i
$731$			50.5119i			1.86825i
$732$	−1.60387	+	5.82458i	−0.0592807	+	0.215283i
$733$	−16.5285	−	16.5285i	−0.610493	−	0.610493i	0.332582	−	0.943074i	$-0.392080\pi$
$733$	−16.5285	−	16.5285i	−0.610493	−	0.610493i	−0.943074	+	0.332582i	$0.892080\pi$
$734$	−19.0296	−	11.0745i	−0.702395	−	0.408767i
$735$	−3.84186	−	1.12452i	−0.141709	−	0.0414786i
$736$	15.2987	+	27.5868i	0.563916	+	1.01686i
$737$	17.0361	−	17.0361i	0.627532	−	0.627532i
$738$	−0.591485	−	2.23833i	−0.0217729	−	0.0823939i
$739$	9.64520			0.354805			0.177402	−	0.984138i	$-0.443231\pi$
$739$	9.64520			0.354805			0.177402	+	0.984138i	$0.443231\pi$
$740$	−5.69099	−	24.0941i	−0.209205	−	0.885717i
$741$	−21.4138			−0.786657
$742$	0.286745	+	1.08511i	0.0105267	+	0.0398358i
$743$	−24.5711	+	24.5711i	−0.901426	+	0.901426i	−0.995560	−	0.0941337i	$-0.969992\pi$
$743$	−24.5711	+	24.5711i	−0.901426	+	0.901426i	0.0941337	+	0.995560i	$0.469992\pi$
$744$	30.4485	+	0.315306i	1.11630	+	0.0115597i
$745$	8.09538	+	14.7956i	0.296592	+	0.542070i
$746$	−0.961708	−	0.559677i	−0.0352106	−	0.0204912i
$747$	−1.13024	−	1.13024i	−0.0413533	−	0.0413533i
$748$	−25.7614	−	7.09372i	−0.941931	−	0.259372i
$749$			19.3189i			0.705898i
$750$	−23.4273	−	15.8867i	−0.855442	−	0.580100i
$751$			52.7628i			1.92534i	0.270676	+	0.962671i	$0.412753\pi$
$751$			52.7628i			1.92534i	−0.270676	+	0.962671i	$0.587247\pi$
$752$	−23.5989	+	5.97535i	−0.860563	+	0.217899i
$753$	11.4909	+	11.4909i	0.418752	+	0.418752i
$754$	−8.26571	+	14.2032i	−0.301019	+	0.517249i
$755$	14.9557	+	27.3339i	0.544292	+	0.994782i
$756$	−4.94391	−	8.70128i	−0.179808	−	0.316462i
$757$	−4.54052	+	4.54052i	−0.165028	+	0.165028i	−0.784790	−	0.619762i	$-0.787229\pi$
$757$	−4.54052	+	4.54052i	−0.165028	+	0.165028i	0.619762	+	0.784790i	$0.287229\pi$
$758$	−12.5106	+	3.30595i	−0.454404	+	0.120078i
$759$	−21.0968			−0.765765
$760$	−5.43083	+	17.8658i	−0.196997	+	0.648061i
$761$	11.9323			0.432545			0.216272	−	0.976333i	$-0.430610\pi$
$761$	11.9323			0.432545			0.216272	+	0.976333i	$0.430610\pi$
$762$	−13.2993	+	3.51439i	−0.481783	+	0.127313i
$763$	9.62076	−	9.62076i	0.348295	−	0.348295i
$764$	5.23957	+	9.22163i	0.189561	+	0.333627i
$765$	2.77983	+	0.813663i	0.100505	+	0.0294180i
$766$	6.00564	−	10.3196i	0.216993	−	0.372864i
$767$	14.2613	+	14.2613i	0.514947	+	0.514947i
$768$	27.4523	+	8.17457i	0.990600	+	0.294974i
$769$			29.2063i			1.05321i	0.850111	+	0.526603i	$0.176535\pi$
$769$			29.2063i			1.05321i	−0.850111	+	0.526603i	$0.823465\pi$
$770$	0.176405	−	6.68041i	0.00635718	−	0.240745i
$771$		−	13.0464i		−	0.469854i
$772$	43.1511	+	11.8822i	1.55304	+	0.427649i
$773$	−25.4449	−	25.4449i	−0.915189	−	0.915189i	0.0814855	−	0.996675i	$-0.474034\pi$
$773$	−25.4449	−	25.4449i	−0.915189	−	0.915189i	−0.996675	+	0.0814855i	$0.974034\pi$
$774$	2.00098	+	1.16449i	0.0719237	+	0.0418568i
$775$	25.3226	+	16.2130i	0.909615	+	0.582388i
$776$	0.0809921	−	7.82125i	0.00290745	−	0.280767i
$777$	−7.00771	+	7.00771i	−0.251400	+	0.251400i
$778$	−10.3813	−	39.2855i	−0.372188	−	1.40845i
$779$	−23.5897			−0.845189
$780$	−17.0491	+	27.5937i	−0.610456	+	0.988012i
$781$	1.29105			0.0461974
$782$	−12.7376	−	48.2024i	−0.455497	−	1.72371i
$783$	−10.1484	+	10.1484i	−0.362673	+	0.362673i
$784$	3.43616	+	2.04764i	0.122720	+	0.0731298i
$785$	−5.01248	+	17.1249i	−0.178903	+	0.611213i
$786$	−25.4396	−	14.8049i	−0.907401	−	0.528072i
$787$	−12.7260	−	12.7260i	−0.453634	−	0.453634i	0.442925	−	0.896559i	$-0.353941\pi$
$787$	−12.7260	−	12.7260i	−0.453634	−	0.453634i	−0.896559	+	0.442925i	$0.853941\pi$
$788$	4.00644	−	14.5497i	0.142724	−	0.518312i
$789$			9.60695i			0.342017i
$790$	32.7029	−	31.0202i	1.16352	−	1.10365i
$791$		−	10.9263i		−	0.388495i
$792$	−0.874910	+	0.856975i	−0.0310886	+	0.0304513i
$793$	4.83378	+	4.83378i	0.171653	+	0.171653i
$794$	18.1571	−	31.1999i	0.644373	−	1.10724i
$795$	2.78704	−	1.52492i	0.0988461	−	0.0540834i
$796$	20.6683	−	11.7434i	0.732570	−	0.416233i
$797$	−26.2293	+	26.2293i	−0.929091	+	0.929091i	−0.997647	−	0.0685567i	$-0.978161\pi$
$797$	−26.2293	+	26.2293i	−0.929091	+	0.929091i	0.0685567	+	0.997647i	$0.478161\pi$
$798$	7.22685	−	1.90972i	0.255828	−	0.0676032i
$799$	38.4752			1.36116
$800$	18.6979	+	21.2224i	0.661069	+	0.750325i
$801$	−0.425933			−0.0150496
$802$	−35.7788	+	9.45466i	−1.26339	+	0.333856i
$803$	6.83084	−	6.83084i	0.241055	−	0.241055i
$804$	35.4907	−	20.1652i	1.25166	−	0.711171i
$805$	10.9389	−	5.98518i	0.385545	−	0.210950i
$806$	17.3305	−	29.7795i	0.610442	−	1.04894i
$807$	6.85814	+	6.85814i	0.241418	+	0.241418i
$808$	−2.55230	+	2.49998i	−0.0897894	+	0.0879489i
$809$		−	33.1882i		−	1.16684i	−0.812172	−	0.583418i	$-0.801715\pi$
$809$		−	33.1882i		−	1.16684i	0.812172	−	0.583418i	$-0.198285\pi$
$810$	−21.9628	+	20.8327i	−0.771693	+	0.731987i
$811$			44.6901i			1.56928i	0.619950	+	0.784641i	$0.287153\pi$
$811$			44.6901i			1.56928i	−0.619950	+	0.784641i	$0.712847\pi$
$812$	1.52289	−	5.53051i	0.0534430	−	0.194083i
$813$	10.3835	+	10.3835i	0.364164	+	0.364164i
$814$	−14.2993	−	8.32166i	−0.501191	−	0.291674i
$815$	−8.75031	+	29.8950i	−0.306510	+	1.04717i
$816$	−38.8898	−	23.1748i	−1.36142	−	0.811279i
$817$	16.6804	−	16.6804i	0.583575	−	0.583575i
$818$	0.355925	+	1.34691i	0.0124446	+	0.0470936i
$819$	0.830101			0.0290061
$820$	−18.7815	+	30.3975i	−0.655878	+	1.06153i
$821$	−6.26110			−0.218514			−0.109257	−	0.994014i	$-0.534847\pi$
$821$	−6.26110			−0.218514			−0.109257	+	0.994014i	$0.534847\pi$
$822$	−13.8026	−	52.2326i	−0.481422	−	1.82182i
$823$	−15.2955	+	15.2955i	−0.533167	+	0.533167i	−0.921514	−	0.388346i	$-0.873047\pi$
$823$	−15.2955	+	15.2955i	−0.533167	+	0.533167i	0.388346	+	0.921514i	$0.373047\pi$
$824$	0.380605	−	36.7544i	0.0132590	−	1.28040i
$825$	−18.4769	+	4.05238i	−0.643284	+	0.141086i
$826$	−6.08483	−	3.54114i	−0.211718	−	0.123212i
$827$	−2.73070	−	2.73070i	−0.0949558	−	0.0949558i	0.658033	−	0.752989i	$-0.271389\pi$
$827$	−2.73070	−	2.73070i	−0.0949558	−	0.0949558i	−0.752989	+	0.658033i	$0.771389\pi$
$828$	−2.20314	−	0.606661i	−0.0765643	−	0.0210829i
$829$			42.2605i			1.46777i	0.679276	+	0.733883i	$0.262294\pi$
$829$			42.2605i			1.46777i	−0.679276	+	0.733883i	$0.737706\pi$
$830$	−0.651199	+	24.6608i	−0.0226034	+	0.855988i
$831$		−	27.1441i		−	0.941618i
$832$	23.3878	−	22.4386i	0.810825	−	0.777917i
$833$	−4.47034	−	4.47034i	−0.154888	−	0.154888i
$834$	6.44088	−	11.0675i	0.223030	−	0.383238i
$835$	42.5766	+	12.4623i	1.47343	+	0.431274i
$836$	6.16459	+	10.8497i	0.213207	+	0.375244i
$837$	21.2778	−	21.2778i	0.735470	−	0.735470i
$838$	22.8770	−	6.04531i	0.790272	−	0.208832i
$839$	−27.3666			−0.944801			−0.472400	−	0.881384i	$-0.656612\pi$
$839$	−27.3666			−0.944801			−0.472400	+	0.881384i	$0.656612\pi$
$840$	3.29297	−	10.8329i	0.113618	−	0.373771i
$841$	20.7736			0.716330
$842$	−48.5417	+	12.8273i	−1.67286	+	0.442058i
$843$	30.0755	−	30.0755i	1.03585	−	1.03585i
$844$	2.01981	+	3.55486i	0.0695246	+	0.122363i
$845$	3.66394	+	6.69644i	0.126043	+	0.230365i
$846$	0.887001	−	1.52416i	0.0304957	−	0.0524016i
$847$	4.62030	+	4.62030i	0.158756	+	0.158756i
$848$	−3.07740	+	0.779213i	−0.105678	+	0.0267583i
$849$		−	42.4086i		−	1.45546i
$850$	−20.4148	−	39.7698i	−0.700222	−	1.36409i
$851$		−	30.8702i		−	1.05822i
$852$	2.10889	+	0.580709i	0.0722494	+	0.0198948i
$853$	−15.4514	−	15.4514i	−0.529044	−	0.529044i	0.391243	−	0.920287i	$-0.372045\pi$
$853$	−15.4514	−	15.4514i	−0.529044	−	0.529044i	−0.920287	+	0.391243i	$0.872045\pi$
$854$	−2.06241	−	1.20024i	−0.0705743	−	0.0410715i
$855$	−0.649284	−	1.18667i	−0.0222050	−	0.0405833i
$856$	−54.6392	−	0.565810i	−1.86753	−	0.0193390i
$857$	−12.5198	+	12.5198i	−0.427668	+	0.427668i	−0.887833	−	0.460165i	$-0.847790\pi$
$857$	−12.5198	+	12.5198i	−0.427668	+	0.427668i	0.460165	+	0.887833i	$0.347790\pi$
$858$	5.53787	+	20.9567i	0.189060	+	0.715449i
$859$	8.82513			0.301109			0.150555	−	0.988602i	$-0.451894\pi$
$859$	8.82513			0.301109			0.150555	+	0.988602i	$0.451894\pi$
$860$	−8.21376	−	34.7748i	−0.280087	−	1.18581i
$861$	14.3036			0.487465
$862$	−0.378049	−	1.43063i	−0.0128764	−	0.0487276i
$863$	22.3265	−	22.3265i	0.760002	−	0.760002i	−0.216320	−	0.976322i	$-0.569406\pi$
$863$	22.3265	−	22.3265i	0.760002	−	0.760002i	0.976322	+	0.216320i	$0.0694055\pi$
$864$	24.7544	−	13.7279i	0.842162	−	0.467033i
$865$	26.9424	+	7.88610i	0.916071	+	0.268136i
$866$	−15.9824	−	9.30113i	−0.543103	−	0.316065i
$867$	29.0746	+	29.0746i	0.987427	+	0.987427i
$868$	−3.19301	+	11.5957i	−0.108378	+	0.393583i
$869$		−	30.1223i		−	1.02183i
$870$	−16.2316	−	0.428616i	−0.550302	−	0.0145314i
$871$		−	46.1884i		−	1.56503i
$872$	26.9284	+	27.4919i	0.911911	+	0.930995i
$873$	0.400652	+	0.400652i	0.0135600	+	0.0135600i
$874$	−11.7114	+	20.1241i	−0.396145	+	0.680707i
$875$	8.43081	−	7.34313i	0.285013	−	0.248243i
$876$	14.2305	−	8.08549i	0.480803	−	0.273183i
$877$	−11.2719	+	11.2719i	−0.380626	+	0.380626i	−0.871328	−	0.490702i	$-0.836741\pi$
$877$	−11.2719	+	11.2719i	−0.380626	+	0.380626i	0.490702	+	0.871328i	$0.336741\pi$
$878$	31.0802	−	8.21303i	1.04891	−	0.277176i
$879$	−47.1105			−1.58900
$880$	18.8889	+	0.694576i	0.636744	+	0.0234142i
$881$	−33.9704			−1.14449			−0.572245	−	0.820082i	$-0.693927\pi$
$881$	−33.9704			−1.14449			−0.572245	+	0.820082i	$0.693927\pi$
$882$	−0.280147	+	0.0740296i	−0.00943303	+	0.00249271i
$883$	−5.75604	+	5.75604i	−0.193706	+	0.193706i	−0.797295	−	0.603589i	$-0.793737\pi$
$883$	−5.75604	+	5.75604i	−0.193706	+	0.193706i	0.603589	+	0.797295i	$0.293737\pi$
$884$	−44.5387	+	25.3061i	−1.49800	+	0.851135i
$885$	−5.59808	+	19.1255i	−0.188177	+	0.642898i
$886$	16.6042	−	28.5315i	0.557830	−	0.958533i
$887$	12.8536	+	12.8536i	0.431581	+	0.431581i	0.889166	−	0.457585i	$-0.151285\pi$
$887$	12.8536	+	12.8536i	0.431581	+	0.431581i	−0.457585	+	0.889166i	$0.651285\pi$
$888$	−19.6145	−	20.0250i	−0.658219	−	0.671994i
$889$		−	5.43332i		−	0.182228i
$890$	4.52403	+	4.76943i	0.151646	+	0.159872i
$891$			20.2297i			0.677720i
$892$	9.88178	−	35.8865i	0.330867	−	1.20157i
$893$	−12.7056	−	12.7056i	−0.425176	−	0.425176i
$894$	16.5043	+	9.60489i	0.551988	+	0.321236i
$895$	−6.78203	+	3.71077i	−0.226698	+	0.124037i
$896$	−5.89192	+	9.65843i	−0.196835	+	0.322666i
$897$	−28.5989	+	28.5989i	−0.954890	+	0.954890i
$898$	6.53740	+	24.7392i	0.218156	+	0.825557i
$899$	17.2482			0.575259
$900$	−2.04608	−	0.108134i	−0.0682026	−	0.00360446i
$901$	5.01734			0.167152
$902$	6.10057	+	23.0861i	0.203127	+	0.768683i
$903$	−10.1142	+	10.1142i	−0.336578	+	0.336578i
$904$	30.9026	+	0.320008i	1.02781	+	0.0106433i
$905$	−31.5745	+	17.2759i	−1.04957	+	0.574270i
$906$	30.4906	+	17.7444i	1.01298	+	0.589517i
$907$	−32.0420	−	32.0420i	−1.06394	−	1.06394i	−0.997811	−	0.0661261i	$-0.978936\pi$
$907$	−32.0420	−	32.0420i	−1.06394	−	1.06394i	−0.0661261	−	0.997811i	$-0.521064\pi$
$908$	−10.7318	−	2.95513i	−0.356147	−	0.0980695i
$909$		−	0.258808i		−	0.00858412i
$910$	−8.81688	−	9.29515i	−0.292277	−	0.308131i
$911$			55.7310i			1.84645i	0.384261	+	0.923225i	$0.374456\pi$
$911$			55.7310i			1.84645i	−0.384261	+	0.923225i	$0.625544\pi$
$912$	5.18955	+	20.4954i	0.171843	+	0.678672i
$913$	11.6573	+	11.6573i	0.385800	+	0.385800i
$914$	12.9334	−	22.2239i	0.427800	−	0.735100i
$915$	−1.89743	+	6.48247i	−0.0627271	+	0.214304i
$916$	−8.11234	−	14.2777i	−0.268039	−	0.471748i
$917$	8.22076	−	8.22076i	0.271473	−	0.271473i
$918$	−43.2533	+	11.4298i	−1.42757	+	0.377240i
$919$	−2.01136			−0.0663487			−0.0331743	−	0.999450i	$-0.510562\pi$
$919$	−2.01136			−0.0663487			−0.0331743	+	0.999450i	$0.510562\pi$
$920$	16.6074	+	31.1135i	0.547529	+	1.02578i
$921$	48.5919			1.60116
$922$	−41.5387	+	10.9767i	−1.36800	+	0.361499i
$923$	1.75015	−	1.75015i	0.0576070	−	0.0576070i
$924$	−3.73789	−	6.57869i	−0.122968	−	0.216423i
$925$	−5.92970	−	27.0366i	−0.194967	−	0.888959i
$926$	−20.2856	+	34.8573i	−0.666627	+	1.14548i
$927$	1.88278	+	1.88278i	0.0618386	+	0.0618386i
$928$	15.5972	+	4.46913i	0.512003	+	0.146707i
$929$		−	13.9438i		−	0.457483i	−0.973487	−	0.228741i	$-0.926539\pi$
$929$		−	13.9438i		−	0.457483i	0.973487	−	0.228741i	$-0.0734610\pi$
$930$	34.0324	+	0.898669i	1.11597	+	0.0294685i
$931$			2.95246i			0.0967630i
$932$	−23.1197	−	6.36628i	−0.757310	−	0.208534i
$933$	17.5292	+	17.5292i	0.573880	+	0.573880i
$934$	−25.6341	−	14.9181i	−0.838775	−	0.488135i
$935$	−28.6712	−	8.39211i	−0.937649	−	0.274451i
$936$	−0.0243119	+	2.34775i	−0.000794659	+	0.0767388i
$937$	−10.0820	+	10.0820i	−0.329363	+	0.329363i	−0.852344	−	0.522981i	$-0.824820\pi$
$937$	−10.0820	+	10.0820i	−0.329363	+	0.329363i	0.522981	+	0.852344i	$0.324820\pi$
$938$	4.11915	+	15.5879i	0.134495	+	0.508963i
$939$	42.1072			1.37412
$940$	−26.4881	+	6.25646i	−0.863948	+	0.204063i
$941$	17.1561			0.559272			0.279636	−	0.960106i	$-0.409786\pi$
$941$	17.1561			0.559272			0.279636	+	0.960106i	$0.409786\pi$
$942$	5.16151	+	19.5324i	0.168171	+	0.636401i
$943$	−31.5049	+	31.5049i	−1.02594	+	1.02594i
$944$	10.1935	−	17.1059i	0.331771	−	0.556748i
$945$	−5.37066	−	9.81576i	−0.174708	−	0.319307i
$946$	−20.6381	−	12.0106i	−0.671002	−	0.390497i
$947$	−21.5073	−	21.5073i	−0.698894	−	0.698894i	0.265278	−	0.964172i	$-0.414536\pi$
$947$	−21.5073	−	21.5073i	−0.698894	−	0.698894i	−0.964172	+	0.265278i	$0.914536\pi$
$948$	13.5489	−	49.2039i	0.440047	−	1.59807i
$949$		−	18.5198i		−	0.601180i
$950$	−6.39155	+	19.8746i	−0.207369	+	0.644817i
$951$		−	1.47637i		−	0.0478746i
$952$	12.7743	−	12.5124i	0.414017	−	0.405531i
$953$	−36.7987	−	36.7987i	−1.19203	−	1.19203i	−0.976497	−	0.215529i	$-0.930852\pi$
$953$	−36.7987	−	36.7987i	−1.19203	−	1.19203i	−0.215529	−	0.976497i	$-0.569148\pi$
$954$	0.115669	−	0.198757i	0.00374492	−	0.00643499i
$955$	5.69184	+	10.4028i	0.184184	+	0.336625i
$956$	−32.1765	+	18.2821i	−1.04066	+	0.591286i
$957$	−7.67277	+	7.67277i	−0.248025	+	0.248025i
$958$	38.1340	−	10.0770i	1.23205	−	0.325574i
$959$	21.3392			0.689077
$960$	30.5420	+	9.63071i	0.985740	+	0.310830i
$961$	−5.16385			−0.166576
$962$	−30.6652	+	8.10337i	−0.988685	+	0.261263i
$963$	2.79895	−	2.79895i	0.0901950	−	0.0901950i
$964$	0.143231	−	0.0813814i	0.00461317	−	0.00262112i
$965$	48.0250	+	14.0570i	1.54598	+	0.452511i
$966$	7.10121	−	12.2022i	0.228478	−	0.392599i
$967$	2.22247	+	2.22247i	0.0714698	+	0.0714698i	0.741938	−	0.670468i	$-0.233907\pi$
$967$	2.22247	+	2.22247i	0.0714698	+	0.0714698i	−0.670468	+	0.741938i	$0.733907\pi$
$968$	−13.2028	+	12.9322i	−0.424354	+	0.415656i
$969$		−	33.4154i		−	1.07346i
$970$	0.230840	−	8.74185i	0.00741181	−	0.280684i
$971$		−	32.9636i		−	1.05785i	−0.848668	−	0.528926i	$-0.822595\pi$
$971$		−	32.9636i		−	1.05785i	0.848668	−	0.528926i	$-0.177405\pi$
$972$	−1.12865	+	4.09879i	−0.0362015	+	0.131469i
$973$	3.57645	+	3.57645i	0.114656	+	0.114656i
$974$	−4.75666	−	2.76820i	−0.152413	−	0.0886987i
$975$	−19.5540	+	30.5409i	−0.626230	+	0.978091i
$976$	3.45503	−	5.79792i	0.110593	−	0.185587i
$977$	5.04869	−	5.04869i	0.161522	−	0.161522i	−0.621719	−	0.783241i	$-0.713565\pi$
$977$	5.04869	−	5.04869i	0.161522	−	0.161522i	0.783241	+	0.621719i	$0.213565\pi$
$978$	9.01047	+	34.0979i	0.288123	+	1.09033i
$979$	4.39307			0.140403
$980$	3.80452	+	2.35067i	0.121531	+	0.0750894i
$981$	−2.78774			−0.0890057
$982$	5.20829	+	19.7095i	0.166203	+	0.628955i
$983$	24.1998	−	24.1998i	0.771853	−	0.771853i	−0.206577	−	0.978430i	$-0.566232\pi$
$983$	24.1998	−	24.1998i	0.771853	−	0.771853i	0.978430	+	0.206577i	$0.0662325\pi$
$984$	−0.418922	+	40.4545i	−0.0133547	+	1.28964i
$985$	4.73975	−	16.1931i	0.151021	−	0.515956i
$986$	−22.1635	−	12.8983i	−0.705830	−	0.410766i
$987$	7.70401	+	7.70401i	0.245221	+	0.245221i
$988$	23.0647	+	6.35113i	0.733784	+	0.202056i
$989$		−	44.5546i		−	1.41675i
$990$	−0.993425	+	0.942310i	−0.0315731	+	0.0299486i
$991$		−	32.2925i		−	1.02580i	−0.858447	−	0.512902i	$-0.828570\pi$
$991$		−	32.2925i		−	1.02580i	0.858447	−	0.512902i	$-0.171430\pi$
$992$	−32.7023	−	9.37033i	−1.03830	−	0.297508i
$993$	18.1648	+	18.1648i	0.576444	+	0.576444i
$994$	−0.434570	+	0.746732i	−0.0137837	+	0.0236849i
$995$	23.3156	−	12.7571i	0.739154	−	0.404426i
$996$	13.7985	+	24.2853i	0.437221	+	0.769508i
$997$	−18.6846	+	18.6846i	−0.591747	+	0.591747i	−0.938103	−	0.346356i	$-0.887419\pi$
$997$	−18.6846	+	18.6846i	−0.591747	+	0.591747i	0.346356	+	0.938103i	$0.387419\pi$
$998$	4.03394	−	1.06598i	0.127692	−	0.0337431i
$999$	−27.7006			−0.876409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.k.a.43.2	✓	36
4.3	odd	2	inner	140.2.k.a.43.9	yes	36
5.2	odd	4	inner	140.2.k.a.127.9	yes	36
5.3	odd	4		700.2.k.b.407.10		36
5.4	even	2		700.2.k.b.43.17		36
7.2	even	3		980.2.x.k.263.14		72
7.3	odd	6		980.2.x.l.863.11		72
7.4	even	3		980.2.x.k.863.11		72
7.5	odd	6		980.2.x.l.263.14		72
7.6	odd	2		980.2.k.l.883.2		36
20.3	even	4		700.2.k.b.407.17		36
20.7	even	4	inner	140.2.k.a.127.2	yes	36
20.19	odd	2		700.2.k.b.43.10		36
28.3	even	6		980.2.x.l.863.6		72
28.11	odd	6		980.2.x.k.863.6		72
28.19	even	6		980.2.x.l.263.17		72
28.23	odd	6		980.2.x.k.263.17		72
28.27	even	2		980.2.k.l.883.9		36
35.2	odd	12		980.2.x.k.67.6		72
35.12	even	12		980.2.x.l.67.6		72
35.17	even	12		980.2.x.l.667.17		72
35.27	even	4		980.2.k.l.687.9		36
35.32	odd	12		980.2.x.k.667.17		72
140.27	odd	4		980.2.k.l.687.2		36
140.47	odd	12		980.2.x.l.67.11		72
140.67	even	12		980.2.x.k.667.14		72
140.87	odd	12		980.2.x.l.667.14		72
140.107	even	12		980.2.x.k.67.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.2	✓	36	1.1	even	1	trivial
140.2.k.a.43.9	yes	36	4.3	odd	2	inner
140.2.k.a.127.2	yes	36	20.7	even	4	inner
140.2.k.a.127.9	yes	36	5.2	odd	4	inner
700.2.k.b.43.10		36	20.19	odd	2
700.2.k.b.43.17		36	5.4	even	2
700.2.k.b.407.10		36	5.3	odd	4
700.2.k.b.407.17		36	20.3	even	4
980.2.k.l.687.2		36	140.27	odd	4
980.2.k.l.687.9		36	35.27	even	4
980.2.k.l.883.2		36	7.6	odd	2
980.2.k.l.883.9		36	28.27	even	2
980.2.x.k.67.6		72	35.2	odd	12
980.2.x.k.67.11		72	140.107	even	12
980.2.x.k.263.14		72	7.2	even	3
980.2.x.k.263.17		72	28.23	odd	6
980.2.x.k.667.14		72	140.67	even	12
980.2.x.k.667.17		72	35.32	odd	12
980.2.x.k.863.6		72	28.11	odd	6
980.2.x.k.863.11		72	7.4	even	3
980.2.x.l.67.6		72	35.12	even	12
980.2.x.l.67.11		72	140.47	odd	12
980.2.x.l.263.14		72	7.5	odd	6
980.2.x.l.263.17		72	28.19	even	6
980.2.x.l.667.14		72	140.87	odd	12
980.2.x.l.667.17		72	35.17	even	12
980.2.x.l.863.6		72	28.3	even	6
980.2.x.l.863.11		72	7.3	odd	6

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36728 + 0.361308i) q^{2} +(-1.26588 + 1.26588i) q^{3} +(1.73891 - 0.988019i) q^{4} +(1.96164 - 1.07330i) q^{5} +(1.27344 - 2.18818i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.02060 + 1.97918i) q^{8} -0.204893i q^{9} +O(q^{10})\)	\(q+(-1.36728 + 0.361308i) q^{2} +(-1.26588 + 1.26588i) q^{3} +(1.73891 - 0.988019i) q^{4} +(1.96164 - 1.07330i) q^{5} +(1.27344 - 2.18818i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.02060 + 1.97918i) q^{8} -0.204893i q^{9} +(-2.29431 + 2.17626i) q^{10} +2.11327i q^{11} +(-0.950539 + 3.45196i) q^{12} +(2.86476 + 2.86476i) q^{13} +(-1.22230 - 0.711330i) q^{14} +(-1.12452 + 3.84186i) q^{15} +(2.04764 - 3.43616i) q^{16} +(-4.47034 + 4.47034i) q^{17} +(0.0740296 + 0.280147i) q^{18} +2.95246 q^{19} +(2.35067 - 3.80452i) q^{20} -1.79022 q^{21} +(-0.763541 - 2.88943i) q^{22} +(3.94312 - 3.94312i) q^{23} +(0.0524318 - 5.06324i) q^{24} +(2.69604 - 4.21087i) q^{25} +(-4.95199 - 2.88187i) q^{26} +(-3.53826 - 3.53826i) q^{27} +(1.92823 + 0.530962i) q^{28} -2.86818i q^{29} +(0.149438 - 5.65920i) q^{30} +6.01364i q^{31} +(-1.55818 + 5.43802i) q^{32} +(-2.67514 - 2.67514i) q^{33} +(4.49704 - 7.72739i) q^{34} +(2.14603 + 0.628146i) q^{35} +(-0.202439 - 0.356292i) q^{36} +(3.91444 - 3.91444i) q^{37} +(-4.03684 + 1.06675i) q^{38} -7.25287 q^{39} +(-1.83942 + 6.05116i) q^{40} -7.98984 q^{41} +(2.44774 - 0.646822i) q^{42} +(5.64967 - 5.64967i) q^{43} +(2.08795 + 3.67479i) q^{44} +(-0.219913 - 0.401926i) q^{45} +(-3.96667 + 6.81603i) q^{46} +(-4.30339 - 4.30339i) q^{47} +(1.75770 + 6.94181i) q^{48} +1.00000i q^{49} +(-2.16482 + 6.73153i) q^{50} -11.3178i q^{51} +(7.81201 + 2.15113i) q^{52} +(-0.561181 - 0.561181i) q^{53} +(6.11620 + 3.55940i) q^{54} +(2.26818 + 4.14546i) q^{55} +(-2.82828 - 0.0292879i) q^{56} +(-3.73746 + 3.73746i) q^{57} +(1.03630 + 3.92160i) q^{58} +4.97819 q^{59} +(1.84039 + 7.79171i) q^{60} +1.68732 q^{61} +(-2.17278 - 8.22233i) q^{62} +(0.144881 - 0.144881i) q^{63} +(0.165668 - 7.99828i) q^{64} +(8.69438 + 2.54486i) q^{65} +(4.62422 + 2.69112i) q^{66} +(-8.06148 - 8.06148i) q^{67} +(-3.35675 + 12.1903i) q^{68} +9.98301i q^{69} +(-3.16118 - 0.0834748i) q^{70} -0.610925i q^{71} +(0.405521 + 0.414008i) q^{72} +(-3.23236 - 3.23236i) q^{73} +(-3.93782 + 6.76645i) q^{74} +(1.91759 + 8.74329i) q^{75} +(5.13407 - 2.91709i) q^{76} +(-1.49431 + 1.49431i) q^{77} +(9.91671 - 2.62052i) q^{78} -14.2539 q^{79} +(0.328674 - 8.93823i) q^{80} +9.57270 q^{81} +(10.9244 - 2.88679i) q^{82} +(5.51624 - 5.51624i) q^{83} +(-3.11304 + 1.76877i) q^{84} +(-3.97115 + 13.5672i) q^{85} +(-5.68341 + 9.76596i) q^{86} +(3.63076 + 3.63076i) q^{87} +(-4.18254 - 4.27008i) q^{88} -2.07881i q^{89} +(0.445902 + 0.470090i) q^{90} +4.05138i q^{91} +(2.96086 - 10.7526i) q^{92} +(-7.61253 - 7.61253i) q^{93} +(7.43879 + 4.32909i) q^{94} +(5.79166 - 3.16889i) q^{95} +(-4.91140 - 8.85634i) q^{96} +(-1.95542 + 1.95542i) q^{97} +(-0.361308 - 1.36728i) q^{98} +0.432994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 - 16 * q^10 - 16 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 28 * q^18 + 20 * q^20 + 4 * q^22 - 20 * q^25 - 32 * q^26 - 4 * q^30 + 20 * q^37 - 36 * q^40 - 20 * q^42 + 20 * q^45 + 16 * q^46 - 24 * q^48 + 40 * q^50 + 16 * q^52 - 44 * q^53 - 24 * q^56 - 16 * q^57 - 4 * q^58 + 40 * q^60 - 64 * q^61 + 40 * q^62 + 4 * q^65 + 32 * q^66 + 80 * q^68 + 80 * q^72 + 52 * q^73 + 8 * q^76 - 76 * q^78 - 20 * q^80 - 36 * q^81 + 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 - 16 * q^90 - 56 * q^92 + 32 * q^93 + 120 * q^96 + 20 * q^97

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