LMFDB - Embedded newform 140.2.c.b.139.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(139,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.6
Root			$0.328458 - 1.49331i$ of defining polynomial
Character	$\chi$	$=$	140.139
Dual form			140.2.c.b.139.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.331077 - 1.37491i) q^{2} +2.13578i q^{3} +(-1.78078 + 0.910404i) q^{4} +(-1.94442 + 1.10418i) q^{5} +(2.93651 - 0.707107i) q^{6} +(-2.35829 + 1.19935i) q^{7} +(1.84130 + 2.14700i) q^{8} -1.56155 q^{9} +(2.16191 + 2.30784i) q^{10} +2.33205i q^{11} +(-1.94442 - 3.80335i) q^{12} -1.09190 q^{13} +(2.42978 + 2.84537i) q^{14} +(-2.35829 - 4.15286i) q^{15} +(2.34233 - 3.24245i) q^{16} +4.98074 q^{17} +(0.516994 + 2.14700i) q^{18} -2.57501 q^{19} +(2.45733 - 3.73652i) q^{20} +(-2.56155 - 5.03680i) q^{21} +(3.20636 - 0.772087i) q^{22} +6.04090 q^{23} +(-4.58552 + 3.93261i) q^{24} +(2.56155 - 4.29400i) q^{25} +(0.361501 + 1.50126i) q^{26} +3.07221i q^{27} +(3.10770 - 4.28278i) q^{28} +0.561553 q^{29} +(-4.92904 + 4.61737i) q^{30} -6.59603 q^{31} +(-5.23358 - 2.14700i) q^{32} -4.98074 q^{33} +(-1.64901 - 6.84809i) q^{34} +(3.26121 - 4.93604i) q^{35} +(2.78078 - 1.42164i) q^{36} +5.49966i q^{37} +(0.852526 + 3.54042i) q^{38} -2.33205i q^{39} +(-5.95095 - 2.14154i) q^{40} +8.48528i q^{41} +(-6.07709 + 5.18948i) q^{42} -1.32431 q^{43} +(-2.12311 - 4.15286i) q^{44} +(3.03632 - 1.72424i) q^{45} +(-2.00000 - 8.30571i) q^{46} -9.74247i q^{47} +(6.92516 + 5.00270i) q^{48} +(4.12311 - 5.65685i) q^{49} +(-6.75195 - 2.10027i) q^{50} +10.6378i q^{51} +(1.94442 - 0.994066i) q^{52} +8.58800i q^{53} +(4.22402 - 1.01714i) q^{54} +(-2.57501 - 4.53448i) q^{55} +(-6.91734 - 2.85489i) q^{56} -5.49966i q^{57} +(-0.185917 - 0.772087i) q^{58} +14.3211 q^{59} +(7.98037 + 5.24831i) q^{60} +0.620058i q^{61} +(2.18379 + 9.06897i) q^{62} +(3.68260 - 1.87285i) q^{63} +(-1.21922 + 7.90655i) q^{64} +(2.12311 - 1.20565i) q^{65} +(1.64901 + 6.84809i) q^{66} +4.71659 q^{67} +(-8.86958 + 4.53448i) q^{68} +12.9020i q^{69} +(-7.86634 - 2.84968i) q^{70} +11.9473i q^{71} +(-2.87529 - 3.35265i) q^{72} +9.96148 q^{73} +(7.56155 - 1.82081i) q^{74} +(9.17104 + 5.47091i) q^{75} +(4.58552 - 2.34430i) q^{76} +(-2.79695 - 5.49966i) q^{77} +(-3.20636 + 0.772087i) q^{78} -10.6378i q^{79} +(-0.974211 + 8.89106i) q^{80} -11.2462 q^{81} +(11.6665 - 2.80928i) q^{82} -3.86098i q^{83} +(9.14707 + 6.63736i) q^{84} +(-9.68466 + 5.49966i) q^{85} +(0.438447 + 1.82081i) q^{86} +1.19935i q^{87} +(-5.00691 + 4.29400i) q^{88} -2.82843i q^{89} +(-3.37594 - 3.60382i) q^{90} +(2.57501 - 1.30957i) q^{91} +(-10.7575 + 5.49966i) q^{92} -14.0877i q^{93} +(-13.3951 + 3.22550i) q^{94} +(5.00691 - 2.84329i) q^{95} +(4.58552 - 11.1778i) q^{96} -14.9422 q^{97} +(-9.14275 - 3.79606i) q^{98} -3.64162i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 8 q^{9} - 4 q^{14} - 12 q^{16} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 4 q^{30} + 28 q^{36} + 32 q^{44} - 32 q^{46} - 12 q^{50} - 20 q^{56} + 44 q^{60} - 36 q^{64} - 32 q^{65} + 40 q^{70}+ \cdots + 40 q^{86}+O(q^{100}) $ 16 * q - 12 * q^4 + 8 * q^9 - 4 * q^14 - 12 * q^16 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 4 * q^30 + 28 * q^36 + 32 * q^44 - 32 * q^46 - 12 * q^50 - 20 * q^56 + 44 * q^60 - 36 * q^64 - 32 * q^65 + 40 * q^70 + 88 * q^74 - 48 * q^81 + 40 * q^84 - 56 * q^85 + 40 * q^86

Character values

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

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.331077	−	1.37491i	−0.234107	−	0.972211i
$2$	−0.331077	−	1.37491i	−0.234107	−	0.972211i
$3$			2.13578i			1.23309i	0.787319	+	0.616546i	$0.211469\pi$
$3$			2.13578i			1.23309i	−0.787319	+	0.616546i	$0.788531\pi$
$4$	−1.78078	+	0.910404i	−0.890388	+	0.455202i
$5$	−1.94442	+	1.10418i	−0.869572	+	0.493806i
$5$	−1.94442	+	1.10418i	−0.869572	+	0.493806i
$6$	2.93651	−	0.707107i	1.19883	−	0.288675i
$7$	−2.35829	+	1.19935i	−0.891352	+	0.453313i
$7$	−2.35829	+	1.19935i	−0.891352	+	0.453313i
$8$	1.84130	+	2.14700i	0.650998	+	0.759079i
$9$	−1.56155			−0.520518
$10$	2.16191	+	2.30784i	0.683656	+	0.729804i
$11$			2.33205i			0.703139i	0.936162	+	0.351569i	$0.114352\pi$
$11$			2.33205i			0.703139i	−0.936162	+	0.351569i	$0.885648\pi$
$12$	−1.94442	−	3.80335i	−0.561306	−	1.09793i
$13$	−1.09190			−0.302837			−0.151419	−	0.988470i	$-0.548384\pi$
$13$	−1.09190			−0.302837			−0.151419	+	0.988470i	$0.548384\pi$
$14$	2.42978	+	2.84537i	0.649387	+	0.760458i
$15$	−2.35829	−	4.15286i	−0.608909	−	1.07226i
$16$	2.34233	−	3.24245i	0.585582	−	0.810613i
$17$	4.98074			1.20801			0.604003	−	0.796982i	$-0.293571\pi$
$17$	4.98074			1.20801			0.604003	+	0.796982i	$0.293571\pi$
$18$	0.516994	+	2.14700i	0.121857	+	0.506053i
$19$	−2.57501			−0.590748			−0.295374	−	0.955382i	$-0.595444\pi$
$19$	−2.57501			−0.590748			−0.295374	+	0.955382i	$0.595444\pi$
$20$	2.45733	−	3.73652i	0.549475	−	0.835510i
$21$	−2.56155	−	5.03680i	−0.558977	−	1.09912i
$22$	3.20636	−	0.772087i	0.683599	−	0.164609i
$23$	6.04090			1.25961			0.629807	−	0.776752i	$-0.283134\pi$
$23$	6.04090			1.25961			0.629807	+	0.776752i	$0.283134\pi$
$24$	−4.58552	+	3.93261i	−0.936015	+	0.802741i
$25$	2.56155	−	4.29400i	0.512311	−	0.858800i
$26$	0.361501	+	1.50126i	0.0708962	+	0.294422i
$27$			3.07221i			0.591246i
$28$	3.10770	−	4.28278i	0.587300	−	0.809369i
$29$	0.561553			0.104278			0.0521389	−	0.998640i	$-0.483396\pi$
$29$	0.561553			0.104278			0.0521389	+	0.998640i	$0.483396\pi$
$30$	−4.92904	+	4.61737i	−0.899916	+	0.843012i
$31$	−6.59603			−1.18468			−0.592341	−	0.805688i	$-0.701796\pi$
$31$	−6.59603			−1.18468			−0.592341	+	0.805688i	$0.701796\pi$
$32$	−5.23358	−	2.14700i	−0.925175	−	0.379540i
$33$	−4.98074			−0.867035
$34$	−1.64901	−	6.84809i	−0.282802	−	1.17444i
$35$	3.26121	−	4.93604i	0.551246	−	0.834343i
$36$	2.78078	−	1.42164i	0.463463	−	0.236941i
$37$			5.49966i			0.904138i	0.891983	+	0.452069i	$0.149314\pi$
$37$			5.49966i			0.904138i	−0.891983	+	0.452069i	$0.850686\pi$
$38$	0.852526	+	3.54042i	0.138298	+	0.574332i
$39$		−	2.33205i		−	0.373427i
$40$	−5.95095	−	2.14154i	−0.940928	−	0.338607i
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	−6.07709	+	5.18948i	−0.937715	+	0.800754i
$43$	−1.32431			−0.201955			−0.100977	−	0.994889i	$-0.532197\pi$
$43$	−1.32431			−0.201955			−0.100977	+	0.994889i	$0.532197\pi$
$44$	−2.12311	−	4.15286i	−0.320070	−	0.626067i
$45$	3.03632	−	1.72424i	0.452627	−	0.257035i
$46$	−2.00000	−	8.30571i	−0.294884	−	1.22461i
$47$		−	9.74247i		−	1.42109i	−0.703654	−	0.710543i	$-0.748450\pi$
$47$		−	9.74247i		−	1.42109i	0.703654	−	0.710543i	$-0.251550\pi$
$48$	6.92516	+	5.00270i	0.999561	+	0.722077i
$49$	4.12311	−	5.65685i	0.589015	−	0.808122i
$50$	−6.75195	−	2.10027i	−0.954870	−	0.297023i
$51$			10.6378i			1.48958i
$52$	1.94442	−	0.994066i	0.269643	−	0.137852i
$53$			8.58800i			1.17965i	0.807530	+	0.589826i	$0.200804\pi$
$53$			8.58800i			1.17965i	−0.807530	+	0.589826i	$0.799196\pi$
$54$	4.22402	−	1.01714i	0.574816	−	0.138415i
$55$	−2.57501	−	4.53448i	−0.347214	−	0.611430i
$56$	−6.91734	−	2.85489i	−0.924369	−	0.381501i
$57$		−	5.49966i		−	0.728447i
$58$	−0.185917	−	0.772087i	−0.0244121	−	0.101380i
$59$	14.3211			1.86444			0.932222	−	0.361888i	$-0.117868\pi$
$59$	14.3211			1.86444			0.932222	+	0.361888i	$0.117868\pi$
$60$	7.98037	+	5.24831i	1.03026	+	0.677554i
$61$			0.620058i			0.0793903i	0.999212	+	0.0396951i	$0.0126387\pi$
$61$			0.620058i			0.0793903i	−0.999212	+	0.0396951i	$0.987361\pi$
$62$	2.18379	+	9.06897i	0.277342	+	1.15176i
$63$	3.68260	−	1.87285i	0.463964	−	0.235957i
$64$	−1.21922	+	7.90655i	−0.152403	+	0.988318i
$65$	2.12311	−	1.20565i	0.263339	−	0.149543i
$66$	1.64901	+	6.84809i	0.202979	+	0.842941i
$67$	4.71659			0.576223			0.288112	−	0.957597i	$-0.406973\pi$
$67$	4.71659			0.576223			0.288112	+	0.957597i	$0.406973\pi$
$68$	−8.86958	+	4.53448i	−1.07559	+	0.549887i
$69$			12.9020i			1.55322i
$70$	−7.86634	−	2.84968i	−0.940208	−	0.340602i
$71$			11.9473i			1.41789i	0.705265	+	0.708943i	$0.250828\pi$
$71$			11.9473i			1.41789i	−0.705265	+	0.708943i	$0.749172\pi$
$72$	−2.87529	−	3.35265i	−0.338856	−	0.395114i
$73$	9.96148			1.16590			0.582951	−	0.812507i	$-0.301898\pi$
$73$	9.96148			1.16590			0.582951	+	0.812507i	$0.301898\pi$
$74$	7.56155	−	1.82081i	0.879013	−	0.211665i
$75$	9.17104	+	5.47091i	1.05898	+	0.631726i
$76$	4.58552	−	2.34430i	0.525995	−	0.268910i
$77$	−2.79695	−	5.49966i	−0.318742	−	0.626744i
$78$	−3.20636	+	0.772087i	−0.363049	+	0.0874216i
$79$		−	10.6378i		−	1.19684i	−0.801182	−	0.598421i	$-0.795795\pi$
$79$		−	10.6378i		−	1.19684i	0.801182	−	0.598421i	$-0.204205\pi$
$80$	−0.974211	+	8.89106i	−0.108920	+	0.994051i
$81$	−11.2462			−1.24958
$82$	11.6665	−	2.80928i	1.28835	−	0.310233i
$83$		−	3.86098i		−	0.423798i	−0.977292	−	0.211899i	$-0.932035\pi$
$83$		−	3.86098i		−	0.423798i	0.977292	−	0.211899i	$-0.0679648\pi$
$84$	9.14707	+	6.63736i	0.998027	+	0.724195i
$85$	−9.68466	+	5.49966i	−1.05045	+	0.596521i
$86$	0.438447	+	1.82081i	0.0472790	+	0.196343i
$87$			1.19935i			0.128584i
$88$	−5.00691	+	4.29400i	−0.533738	+	0.457742i
$89$		−	2.82843i		−	0.299813i	−0.988700	−	0.149906i	$-0.952103\pi$
$89$		−	2.82843i		−	0.299813i	0.988700	−	0.149906i	$-0.0478972\pi$
$90$	−3.37594	−	3.60382i	−0.355855	−	0.379876i
$91$	2.57501	−	1.30957i	0.269935	−	0.137280i
$92$	−10.7575	+	5.49966i	−1.12155	+	0.573379i
$93$		−	14.0877i		−	1.46082i
$94$	−13.3951	+	3.22550i	−1.38159	+	0.332685i
$95$	5.00691	−	2.84329i	0.513698	−	0.291715i
$96$	4.58552	−	11.1778i	0.468008	−	1.14083i
$97$	−14.9422			−1.51715			−0.758576	−	0.651584i	$-0.774105\pi$
$97$	−14.9422			−1.51715			−0.758576	+	0.651584i	$0.774105\pi$
$98$	−9.14275	−	3.79606i	−0.923557	−	0.383460i
$99$		−	3.64162i		−	0.365996i
$100$	−0.652277	+	9.97870i	−0.0652277	+	0.997870i
$101$		−	15.1104i		−	1.50354i	−0.659425	−	0.751770i	$-0.729200\pi$
$101$		−	15.1104i		−	1.50354i	0.659425	−	0.751770i	$-0.270800\pi$
$102$	14.6260	−	3.52191i	1.44819	−	0.348722i
$103$			5.47091i			0.539065i	0.962991	+	0.269532i	$0.0868691\pi$
$103$			5.47091i			0.539065i	−0.962991	+	0.269532i	$0.913131\pi$
$104$	−2.01051	−	2.34430i	−0.197147	−	0.229878i
$105$	10.5423	+	6.96523i	1.02882	+	0.679737i
$106$	11.8078	−	2.84329i	1.14687	−	0.276165i
$107$	−10.0138			−0.968072			−0.484036	−	0.875048i	$-0.660830\pi$
$107$	−10.0138			−0.968072			−0.484036	+	0.875048i	$0.660830\pi$
$108$	−2.79695	−	5.47091i	−0.269136	−	0.526439i
$109$	4.56155			0.436918			0.218459	−	0.975846i	$-0.429897\pi$
$109$	4.56155			0.436918			0.218459	+	0.975846i	$0.429897\pi$
$110$	−5.38200	+	5.04168i	−0.513154	+	0.480705i
$111$	−11.7460			−1.11489
$112$	−1.63506	+	10.4559i	−0.154498	+	0.987993i
$113$			5.49966i			0.517364i	0.965963	+	0.258682i	$0.0832882\pi$
$113$			5.49966i			0.517364i	−0.965963	+	0.258682i	$0.916712\pi$
$114$	−7.56155	+	1.82081i	−0.708204	+	0.170534i
$115$	−11.7460	+	6.67026i	−1.09532	+	0.622005i
$116$	−1.00000	+	0.511240i	−0.0928477	+	0.0474674i
$117$	1.70505			0.157632
$118$	−4.74137	−	19.6902i	−0.436478	−	1.81263i
$119$	−11.7460	+	5.97366i	−1.07676	+	0.547605i
$120$	4.57385	−	12.7099i	0.417534	−	1.16025i
$121$	5.56155			0.505596
$122$	0.852526	−	0.205287i	0.0771841	−	0.0185858i
$123$	−18.1227			−1.63407
$124$	11.7460	−	6.00505i	1.05483	−	0.539269i
$125$	−0.239369	+	11.1778i	−0.0214098	+	0.999771i
$126$	−3.79423	−	4.44320i	−0.338017	−	0.395832i
$127$	5.29723			0.470053			0.235026	−	0.971989i	$-0.424482\pi$
$127$	5.29723			0.470053			0.235026	+	0.971989i	$0.424482\pi$
$128$	11.2745	−	0.941346i	0.996533	−	0.0832041i
$129$		−	2.82843i		−	0.249029i
$130$	−2.36058	−	2.51992i	−0.207037	−	0.221012i
$131$	2.57501			0.224980			0.112490	−	0.993653i	$-0.464117\pi$
$131$	2.57501			0.224980			0.112490	+	0.993653i	$0.464117\pi$
$132$	8.86958	−	4.53448i	0.771998	−	0.394676i
$133$	6.07263	−	3.08835i	0.526564	−	0.267794i
$134$	−1.56155	−	6.48490i	−0.134898	−	0.560210i
$135$	−3.39228	−	5.97366i	−0.291961	−	0.514131i
$136$	9.17104	+	10.6937i	0.786410	+	0.916973i
$137$		−	3.08835i		−	0.263855i	−0.991259	−	0.131928i	$-0.957883\pi$
$137$		−	3.08835i		−	0.263855i	0.991259	−	0.131928i	$-0.0421167\pi$
$138$	17.7392	−	4.27156i	1.51006	−	0.363619i
$139$	4.02102			0.341058			0.170529	−	0.985353i	$-0.445452\pi$
$139$	4.02102			0.341058			0.170529	+	0.985353i	$0.445452\pi$
$140$	−1.31370	+	11.7590i	−0.111028	+	0.993817i
$141$	20.8078			1.75233
$142$	16.4265	−	3.95548i	1.37849	−	0.331937i
$143$		−	2.54635i		−	0.212937i
$144$	−3.65767	+	5.06326i	−0.304806	+	0.421938i
$145$	−1.09190	+	0.620058i	−0.0906770	+	0.0514930i
$146$	−3.29801	−	13.6962i	−0.272946	−	1.13350i
$147$	12.0818	+	8.80604i	0.996489	+	0.726310i
$148$	−5.00691	−	9.79366i	−0.411565	−	0.805034i
$149$	−2.00000			−0.163846			−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000			−0.163846			−0.0819232	+	0.996639i	$0.526106\pi$
$150$	4.48571	−	14.4207i	0.366257	−	1.17744i
$151$		−	4.95118i		−	0.402922i	−0.979497	−	0.201461i	$-0.935431\pi$
$151$		−	4.95118i		−	0.402922i	0.979497	−	0.201461i	$-0.0645689\pi$
$152$	−4.74137	−	5.52855i	−0.384576	−	0.448425i
$153$	−7.77769			−0.628789
$154$	−6.63555	+	5.66637i	−0.534708	+	0.456609i
$155$	12.8255	−	7.28323i	1.03017	−	0.585003i
$156$	2.12311	+	4.15286i	0.169984	+	0.332495i
$157$	−3.88884			−0.310364			−0.155182	−	0.987886i	$-0.549596\pi$
$157$	−3.88884			−0.310364			−0.155182	+	0.987886i	$0.549596\pi$
$158$	−14.6260	+	3.52191i	−1.16358	+	0.280188i
$159$	−18.3421			−1.45462
$160$	12.5470	−	1.60417i	0.991926	−	0.126820i
$161$	−14.2462	+	7.24517i	−1.12276	+	0.570999i
$162$	3.72336	+	15.4626i	0.292535	+	1.21485i
$163$	−11.5012			−0.900840			−0.450420	−	0.892817i	$-0.648726\pi$
$163$	−11.5012			−0.900840			−0.450420	+	0.892817i	$0.648726\pi$
$164$	−7.72503	−	15.1104i	−0.603224	−	1.17992i
$165$	9.68466	−	5.49966i	0.753950	−	0.428148i
$166$	−5.30852	+	1.27828i	−0.412021	+	0.0992139i
$167$			0.673500i			0.0521170i	0.999660	+	0.0260585i	$0.00829562\pi$
$167$			0.673500i			0.0521170i	−0.999660	+	0.0260585i	$0.991704\pi$
$168$	6.09742	−	14.7739i	0.470426	−	1.13983i
$169$	−11.8078			−0.908290
$170$	10.7679	+	11.4948i	0.825862	+	0.881608i
$171$	4.02102			0.307495
$172$	2.35829	−	1.20565i	0.179818	−	0.0919303i
$173$	11.0534			0.840372			0.420186	−	0.907438i	$-0.361965\pi$
$173$	11.0534			0.840372			0.420186	+	0.907438i	$0.361965\pi$
$174$	1.64901	−	0.397078i	0.125011	−	0.0301024i
$175$	−0.890873	+	13.1987i	−0.0673437	+	0.997730i
$176$	7.56155	+	5.46242i	0.569973	+	0.411746i
$177$			30.5866i			2.29903i
$178$	−3.88884	+	0.936426i	−0.291481	+	0.0701881i
$179$			8.30571i			0.620798i	0.950606	+	0.310399i	$0.100463\pi$
$179$			8.30571i			0.620798i	−0.950606	+	0.310399i	$0.899537\pi$
$180$	−3.83725	+	5.83477i	−0.286011	+	0.434898i
$181$		−	3.44849i		−	0.256324i	−0.991753	−	0.128162i	$-0.959092\pi$
$181$		−	3.44849i		−	0.256324i	0.991753	−	0.128162i	$-0.0409077\pi$
$182$	−2.65307	−	3.10685i	−0.196659	−	0.230295i
$183$	−1.32431			−0.0978956
$184$	11.1231	+	12.9698i	0.820006	+	0.956147i
$185$	−6.07263	−	10.6937i	−0.446469	−	0.786213i
$186$	−19.3693	+	4.66410i	−1.42023	+	0.341988i
$187$			11.6153i			0.849396i
$188$	8.86958	+	17.3492i	0.646881	+	1.26532i
$189$	−3.68466	−	7.24517i	−0.268019	−	0.527008i
$190$	−5.56695	−	5.94272i	−0.403869	−	0.431130i
$191$		−	19.9660i		−	1.44469i	−0.691535	−	0.722343i	$-0.743065\pi$
$191$		−	19.9660i		−	1.44469i	0.691535	−	0.722343i	$-0.256935\pi$
$192$	−16.8866	−	2.60399i	−1.21869	−	0.187927i
$193$		−	5.49966i		−	0.395874i	−0.980215	−	0.197937i	$-0.936576\pi$
$193$		−	5.49966i		−	0.395874i	0.980215	−	0.197937i	$-0.0634241\pi$
$194$	4.94702	+	20.5443i	0.355175	+	1.47499i
$195$	2.57501	+	4.53448i	0.184400	+	0.324721i
$196$	−2.19231	+	13.8273i	−0.156593	+	0.987663i
$197$		−	16.4990i		−	1.17550i	−0.809042	−	0.587751i	$-0.800013\pi$
$197$		−	16.4990i		−	1.17550i	0.809042	−	0.587751i	$-0.199987\pi$
$198$	−5.00691	+	1.20565i	−0.355825	+	0.0856821i
$199$	18.3421			1.30024			0.650118	−	0.759834i	$-0.274720\pi$
$199$	18.3421			1.30024			0.650118	+	0.759834i	$0.274720\pi$
$200$	13.9358	−	2.40689i	0.985411	−	0.170193i
$201$			10.0736i			0.710536i
$202$	−20.7755	+	5.00270i	−1.46176	+	0.351989i
$203$	−1.32431	+	0.673500i	−0.0929481	+	0.0472704i
$204$	−9.68466	−	18.9435i	−0.678062	−	1.32631i
$205$	−9.36932	−	16.4990i	−0.654381	−	1.15234i
$206$	7.52203	−	1.81129i	0.524085	−	0.126199i
$207$	−9.43318			−0.655651
$208$	−2.55758	+	3.54042i	−0.177336	+	0.245484i
$209$		−	6.00505i		−	0.415378i
$210$	6.08628	−	16.8008i	0.419993	−	1.15936i
$211$			0.287088i			0.0197640i	0.999951	+	0.00988198i	$0.00314558\pi$
$211$			0.287088i			0.0197640i	−0.999951	+	0.00988198i	$0.996854\pi$
$212$	−7.81855	−	15.2933i	−0.536980	−	1.05035i
$213$	−25.5169			−1.74839
$214$	3.31534	+	13.7681i	0.226632	+	0.941170i
$215$	2.57501	−	1.46228i	0.175614	−	0.0997266i
$216$	−6.59603	+	5.65685i	−0.448803	+	0.384900i
$217$	15.5554	−	7.91096i	1.05597	−	0.537031i
$218$	−1.51022	−	6.27174i	−0.102285	−	0.424776i
$219$			21.2755i			1.43767i
$220$	8.71373	+	5.73060i	0.587480	+	0.386357i
$221$	−5.43845			−0.365830
$222$	3.88884	+	16.1498i	0.261002	+	1.08390i
$223$		−	0.147647i		−	0.00988718i	−0.999988	−	0.00494359i	$-0.998426\pi$
$223$		−	0.147647i		−	0.00988718i	0.999988	−	0.00494359i	$-0.00157360\pi$
$224$	14.9173	−	1.21365i	0.996707	−	0.0810906i
$225$	−4.00000	+	6.70531i	−0.266667	+	0.447021i
$226$	7.56155	−	1.82081i	0.502987	−	0.121118i
$227$		−	10.1530i		−	0.673881i	−0.941526	−	0.336941i	$-0.890608\pi$
$227$		−	10.1530i		−	0.673881i	0.941526	−	0.336941i	$-0.109392\pi$
$228$	5.00691	+	9.79366i	0.331591	+	0.648601i
$229$			9.45353i			0.624707i	0.949966	+	0.312354i	$0.101117\pi$
$229$			9.45353i			0.624707i	−0.949966	+	0.312354i	$0.898883\pi$
$230$	13.0599	+	13.9414i	0.861143	+	0.919271i
$231$	11.7460	−	5.97366i	0.772833	−	0.393038i
$232$	1.03399	+	1.20565i	0.0678846	+	0.0791551i
$233$		−	10.9993i		−	0.720589i	−0.932839	−	0.360294i	$-0.882676\pi$
$233$		−	10.9993i		−	0.720589i	0.932839	−	0.360294i	$-0.117324\pi$
$234$	−0.564503	−	2.34430i	−0.0369027	−	0.153252i
$235$	10.7575	+	18.9435i	0.701741	+	1.23574i
$236$	−25.5026	+	13.0380i	−1.66008	+	0.848698i
$237$	22.7199			1.47582
$238$	12.1021	+	14.1721i	0.784464	+	0.918639i
$239$			2.33205i			0.150848i	0.997152	+	0.0754238i	$0.0240310\pi$
$239$			2.33205i			0.150848i	−0.997152	+	0.0754238i	$0.975969\pi$
$240$	−18.9893	−	2.08070i	−1.22576	−	0.134309i
$241$			16.0786i			1.03572i	0.855466	+	0.517858i	$0.173271\pi$
$241$			16.0786i			1.03572i	−0.855466	+	0.517858i	$0.826729\pi$
$242$	−1.84130	−	7.64666i	−0.118363	−	0.491546i
$243$		−	14.8028i		−	0.949601i
$244$	−0.564503	−	1.10418i	−0.0361386	−	0.0706882i
$245$	−1.77085	+	15.5520i	−0.113135	+	0.993580i
$246$	6.00000	+	24.9171i	0.382546	+	1.58866i
$247$	2.81164			0.178901
$248$	−12.1453	−	14.1617i	−0.771225	−	0.899267i
$249$	8.24621			0.522582
$250$	15.4477	−	3.37159i	0.977000	−	0.213238i
$251$	9.17104			0.578871			0.289435	−	0.957198i	$-0.406532\pi$
$251$	9.17104			0.578871			0.289435	+	0.957198i	$0.406532\pi$
$252$	−4.85284	+	6.68779i	−0.305700	+	0.421291i
$253$			14.0877i			0.885683i
$254$	−1.75379	−	7.28323i	−0.110042	−	0.456991i
$255$	−11.7460	−	20.6843i	−0.735566	−	1.29530i
$256$	−5.02699	−	15.1898i	−0.314187	−	0.949361i
$257$	6.55137			0.408663			0.204332	−	0.978902i	$-0.434498\pi$
$257$	6.55137			0.408663			0.204332	+	0.978902i	$0.434498\pi$
$258$	−3.88884	+	0.936426i	−0.242109	+	0.0582994i
$259$	−6.59603	−	12.9698i	−0.409857	−	0.805905i
$260$	−2.68314	+	4.07988i	−0.166402	+	0.253024i
$261$	−0.876894			−0.0542784
$262$	−0.852526	−	3.54042i	−0.0526693	−	0.218728i
$263$	23.5829			1.45419			0.727093	−	0.686539i	$-0.240871\pi$
$263$	23.5829			1.45419			0.727093	+	0.686539i	$0.240871\pi$
$264$	−9.17104	−	10.6937i	−0.564438	−	0.658149i
$265$	−9.48274	−	16.6987i	−0.582520	−	1.02579i
$266$	−6.25672	−	7.32687i	−0.383624	−	0.449239i
$267$	6.04090			0.369697
$268$	−8.39919	+	4.29400i	−0.513062	+	0.262298i
$269$		−	0.968253i		−	0.0590354i	−0.999564	−	0.0295177i	$-0.990603\pi$
$269$		−	0.968253i		−	0.0590354i	0.999564	−	0.0295177i	$-0.00939715\pi$
$270$	−7.09017	+	6.64184i	−0.431494	+	0.404209i
$271$	6.59603			0.400680			0.200340	−	0.979726i	$-0.435795\pi$
$271$	6.59603			0.400680			0.200340	+	0.979726i	$0.435795\pi$
$272$	11.6665	−	16.1498i	0.707387	−	0.979226i
$273$	2.79695	+	5.49966i	0.169279	+	0.332854i
$274$	−4.24621	+	1.02248i	−0.256523	+	0.0617703i
$275$	10.0138	+	5.97366i	0.603856	+	0.360225i
$276$	−11.7460	−	22.9756i	−0.707029	−	1.38297i
$277$			19.5873i			1.17689i	0.808538	+	0.588444i	$0.200259\pi$
$277$			19.5873i			1.17689i	−0.808538	+	0.588444i	$0.799741\pi$
$278$	−1.33126	−	5.52855i	−0.0798440	−	0.331580i
$279$	10.3000			0.616648
$280$	16.6026	−	2.08691i	0.992192	−	0.124717i
$281$	17.0540			1.01735			0.508677	−	0.860957i	$-0.330135\pi$
$281$	17.0540			1.01735			0.508677	+	0.860957i	$0.330135\pi$
$282$	−6.88897	−	28.6089i	−0.410232	−	1.70363i
$283$		−	7.45904i		−	0.443394i	−0.975116	−	0.221697i	$-0.928840\pi$
$283$		−	7.45904i		−	0.443394i	0.975116	−	0.221697i	$-0.0711596\pi$
$284$	−10.8769	−	21.2755i	−0.645425	−	1.26247i
$285$	6.07263	+	10.6937i	0.359712	+	0.633437i
$286$	−3.50102	+	0.843038i	−0.207019	+	0.0498499i
$287$	−10.1768	−	20.0108i	−0.600720	−	1.18120i
$288$	8.17252	+	3.35265i	0.481570	+	0.197557i
$289$	7.80776			0.459280
$290$	1.21403	+	1.29598i	0.0712901	+	0.0761023i
$291$		−	31.9133i		−	1.87079i
$292$	−17.7392	+	9.06897i	−1.03811	+	0.530721i
$293$	14.4635			0.844965			0.422483	−	0.906371i	$-0.361159\pi$
$293$	14.4635			0.844965			0.422483	+	0.906371i	$0.361159\pi$
$294$	8.10755	−	19.5269i	0.472842	−	1.13883i
$295$	−27.8462	+	15.8131i	−1.62127	+	0.920674i
$296$	−11.8078	+	10.1265i	−0.686312	+	0.588592i
$297$	−7.16453			−0.415728
$298$	0.662153	+	2.74983i	0.0383575	+	0.159293i
$299$	−6.59603			−0.381458
$300$	−21.3123	−	1.39312i	−1.23047	−	0.0804318i
$301$	3.12311	−	1.58831i	0.180013	−	0.0915487i
$302$	−6.80745	+	1.63922i	−0.391725	+	0.0943266i
$303$	32.2725			1.85400
$304$	−6.03152	+	8.34935i	−0.345932	+	0.478868i
$305$	−0.684658	−	1.20565i	−0.0392034	−	0.0690356i
$306$	2.57501	+	10.6937i	0.147204	+	0.611315i
$307$		−	13.8987i		−	0.793243i	−0.917982	−	0.396622i	$-0.870182\pi$
$307$		−	13.8987i		−	0.793243i	0.917982	−	0.396622i	$-0.129818\pi$
$308$	9.98765	+	7.24730i	0.569099	+	0.412953i
$309$	−11.6847			−0.664717
$310$	−14.2600	−	15.2226i	−0.809915	−	0.864585i
$311$	1.44600			0.0819954			0.0409977	−	0.999159i	$-0.486946\pi$
$311$	1.44600			0.0819954			0.0409977	+	0.999159i	$0.486946\pi$
$312$	5.00691	−	4.29400i	0.283460	−	0.243100i
$313$	−7.16453			−0.404963			−0.202482	−	0.979286i	$-0.564901\pi$
$313$	−7.16453			−0.404963			−0.202482	+	0.979286i	$0.564901\pi$
$314$	1.28751	+	5.34683i	0.0726581	+	0.301739i
$315$	−5.09256	+	7.70789i	−0.286933	+	0.434290i
$316$	9.68466	+	18.9435i	0.544805	+	1.06565i
$317$			24.4099i			1.37100i	0.728073	+	0.685499i	$0.240416\pi$
$317$			24.4099i			1.37100i	−0.728073	+	0.685499i	$0.759584\pi$
$318$	6.07263	+	25.2188i	0.340536	+	1.41420i
$319$			1.30957i			0.0733217i
$320$	−6.35960	−	16.7199i	−0.355513	−	0.934671i
$321$		−	21.3873i		−	1.19372i
$322$	14.6781	+	17.1886i	0.817977	+	0.957884i
$323$	−12.8255			−0.713628
$324$	20.0270	−	10.2386i	1.11261	−	0.568811i
$325$	−2.79695	+	4.68860i	−0.155147	+	0.260077i
$326$	3.80776	+	15.8131i	0.210893	+	0.875806i
$327$			9.74247i			0.538760i
$328$	−18.2179	+	15.6240i	−1.00592	+	0.862689i
$329$	11.6847	+	22.9756i	0.644196	+	1.26669i
$330$	−10.7679	−	11.4948i	−0.592754	−	0.632766i
$331$			8.30571i			0.456523i	0.973600	+	0.228262i	$0.0733041\pi$
$331$			8.30571i			0.456523i	−0.973600	+	0.228262i	$0.926696\pi$
$332$	3.51506	+	6.87555i	0.192914	+	0.377345i
$333$		−	8.58800i		−	0.470620i
$334$	0.926004	−	0.222980i	0.0506687	−	0.0122009i
$335$	−9.17104	+	5.20798i	−0.501067	+	0.284543i
$336$	−22.3316	−	3.49212i	−1.21829	−	0.190511i
$337$		−	30.5866i		−	1.66616i	−0.553153	−	0.833080i	$-0.686575\pi$
$337$		−	30.5866i		−	1.66616i	0.553153	−	0.833080i	$-0.313425\pi$
$338$	3.90928	+	16.2347i	0.212637	+	0.883049i
$339$	−11.7460			−0.637958
$340$	12.2393	−	18.6106i	0.663769	−	1.00930i
$341$		−	15.3823i		−	0.832996i
$342$	−1.33126	−	5.52855i	−0.0719866	−	0.298950i
$343$	−2.93893	+	18.2856i	−0.158687	+	0.987329i
$344$	−2.43845	−	2.84329i	−0.131472	−	0.153300i
$345$	−14.2462	−	25.0870i	−0.766990	−	1.35064i
$346$	−3.65951	−	15.1974i	−0.196737	−	0.817019i
$347$	−1.32431			−0.0710925			−0.0355463	−	0.999368i	$-0.511317\pi$
$347$	−1.32431			−0.0710925			−0.0355463	+	0.999368i	$0.511317\pi$
$348$	−1.09190	−	2.13578i	−0.0585317	−	0.114490i
$349$		−	18.8307i		−	1.00799i	−0.863708	−	0.503993i	$-0.831864\pi$
$349$		−	18.8307i		−	1.00799i	0.863708	−	0.503993i	$-0.168136\pi$
$350$	18.4421	−	3.14492i	0.985769	−	0.168103i
$351$		−	3.35453i		−	0.179051i
$352$	5.00691	−	12.2050i	0.266869	−	0.650527i
$353$	16.1685			0.860564			0.430282	−	0.902694i	$-0.358414\pi$
$353$	16.1685			0.860564			0.430282	+	0.902694i	$0.358414\pi$
$354$	42.0540	−	10.1265i	2.23514	−	0.538218i
$355$	−13.1921	−	23.2306i	−0.700162	−	1.23295i
$356$	2.57501	+	5.03680i	0.136475	+	0.266950i
$357$	−12.7584	−	25.0870i	−0.675248	−	1.32774i
$358$	11.4196	−	2.74983i	0.603547	−	0.145333i
$359$			10.3507i			0.546288i	0.961973	+	0.273144i	$0.0880635\pi$
$359$			10.3507i			0.546288i	−0.961973	+	0.273144i	$0.911937\pi$
$360$	9.29272	+	3.34413i	0.489770	+	0.176251i
$361$	−12.3693			−0.651017
$362$	−4.74137	+	1.14171i	−0.249201	+	0.0600071i
$363$			11.8782i			0.623446i
$364$	−3.39328	+	4.67635i	−0.177856	+	0.245107i
$365$	−19.3693	+	10.9993i	−1.01384	+	0.575730i
$366$	0.438447	+	1.82081i	0.0229180	+	0.0951752i
$367$			23.3783i			1.22034i	0.792272	+	0.610168i	$0.208898\pi$
$367$			23.3783i			1.22034i	−0.792272	+	0.610168i	$0.791102\pi$
$368$	14.1498	−	19.5873i	0.737608	−	1.02106i
$369$		−	13.2502i		−	0.689779i
$370$	−12.6923	+	11.8898i	−0.659843	+	0.618120i
$371$	−10.3000	−	20.2530i	−0.534752	−	1.05149i
$372$	12.8255	+	25.0870i	0.664969	+	1.30070i
$373$			11.6763i			0.604578i	0.953216	+	0.302289i	$0.0977508\pi$
$373$			11.6763i			0.604578i	−0.953216	+	0.302289i	$0.902249\pi$
$374$	15.9701	−	3.84556i	0.825793	−	0.198849i
$375$	−23.8733	−	0.511240i	−1.23281	−	0.0264003i
$376$	20.9171	−	17.9388i	1.07872	−	0.925124i
$377$	−0.613157			−0.0315792
$378$	−8.74157	+	7.46479i	−0.449618	+	0.383948i
$379$		−	24.9171i		−	1.27991i	−0.768414	−	0.639954i	$-0.778954\pi$
$379$		−	24.9171i		−	1.27991i	0.768414	−	0.639954i	$-0.221046\pi$
$380$	−6.32764	+	9.62157i	−0.324601	+	0.493576i
$381$			11.3137i			0.579619i
$382$	−27.4515	+	6.61026i	−1.40454	+	0.338210i
$383$			18.6638i			0.953675i	0.878991	+	0.476838i	$0.158217\pi$
$383$			18.6638i			0.953675i	−0.878991	+	0.476838i	$0.841783\pi$
$384$	2.01051	+	24.0798i	0.102598	+	1.22882i
$385$	11.5111	+	7.60530i	0.586659	+	0.387602i
$386$	−7.56155	+	1.82081i	−0.384873	+	0.0926767i
$387$	2.06798			0.105121
$388$	26.6087	−	13.6035i	1.35085	−	0.690611i
$389$	−11.9309			−0.604919			−0.302460	−	0.953162i	$-0.597808\pi$
$389$	−11.9309			−0.604919			−0.302460	+	0.953162i	$0.597808\pi$
$390$	5.38200	−	5.04168i	0.272528	−	0.255295i
$391$	30.0881			1.52162
$392$	19.7371	−	1.56366i	0.996876	−	0.0789767i
$393$			5.49966i			0.277421i
$394$	−22.6847	+	5.46242i	−1.14284	+	0.275193i
$395$	11.7460	+	20.6843i	0.591008	+	1.04074i
$396$	3.31534	+	6.48490i	0.166602	+	0.325879i
$397$	−21.0149			−1.05471			−0.527353	−	0.849647i	$-0.676815\pi$
$397$	−21.0149			−1.05471			−0.527353	+	0.849647i	$0.676815\pi$
$398$	−6.07263	−	25.2188i	−0.304394	−	1.26410i
$399$	6.59603	+	12.9698i	0.330214	+	0.649303i
$400$	−7.92309	−	18.3637i	−0.396155	−	0.918184i
$401$	13.4384			0.671084			0.335542	−	0.942025i	$-0.391081\pi$
$401$	13.4384			0.671084			0.335542	+	0.942025i	$0.391081\pi$
$402$	13.8503	−	3.33513i	0.690791	−	0.166341i
$403$	7.20217			0.358766
$404$	13.7566	+	26.9082i	0.684414	+	1.33873i
$405$	21.8674	−	12.4179i	1.08660	−	0.617050i
$406$	1.36445	+	1.59783i	0.0677166	+	0.0792989i
$407$	−12.8255			−0.635734
$408$	−22.8393	+	19.5873i	−1.13071	+	0.969717i
$409$			30.2208i			1.49432i	0.664643	+	0.747161i	$0.268583\pi$
$409$			30.2208i			1.49432i	−0.664643	+	0.747161i	$0.731417\pi$
$410$	−19.5827	+	18.3444i	−0.967120	+	0.905967i
$411$	6.59603			0.325358
$412$	−4.98074	−	9.74247i	−0.245383	−	0.479977i
$413$	−33.7733	+	17.1760i	−1.66187	+	0.845176i
$414$	3.12311	+	12.9698i	0.153492	+	0.637431i
$415$	4.26324	+	7.50738i	0.209274	+	0.368523i
$416$	5.71453	+	2.34430i	0.280178	+	0.114939i
$417$			8.58800i			0.420556i
$418$	−8.25643	+	1.98813i	−0.403835	+	0.0972427i
$419$	−22.3631			−1.09251			−0.546254	−	0.837619i	$-0.683947\pi$
$419$	−22.3631			−1.09251			−0.546254	+	0.837619i	$0.683947\pi$
$420$	−25.1146	−	2.80577i	−1.22547	−	0.136908i
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	0.394722	−	0.0950482i	0.0192147	−	0.00462688i
$423$			15.2134i			0.739700i
$424$	−18.4384	+	15.8131i	−0.895450	+	0.767952i
$425$	12.7584	−	21.3873i	0.618875	−	1.03744i
$426$	8.44804	+	35.0835i	0.409309	+	1.69980i
$427$	−0.743668	−	1.46228i	−0.0359886	−	0.0707647i
$428$	17.8324	−	9.11662i	0.861960	−	0.440668i
$429$	5.43845			0.262571
$430$	−2.86303	−	3.05629i	−0.138068	−	0.147387i
$431$			11.6602i			0.561654i	0.959758	+	0.280827i	$0.0906087\pi$
$431$			11.6602i			0.561654i	−0.959758	+	0.280827i	$0.909391\pi$
$432$	9.96148	+	7.19612i	0.479272	+	0.346223i
$433$	−9.00400			−0.432705			−0.216352	−	0.976315i	$-0.569416\pi$
$433$	−9.00400			−0.432705			−0.216352	+	0.976315i	$0.569416\pi$
$434$	−16.0269	−	18.7682i	−0.769317	−	0.900901i
$435$	−1.32431	−	2.33205i	−0.0634957	−	0.111813i
$436$	−8.12311	+	4.15286i	−0.389026	+	0.198886i
$437$	−15.5554			−0.744114
$438$	29.2520	−	7.04383i	1.39771	−	0.336567i
$439$	31.5341			1.50504			0.752521	−	0.658568i	$-0.228838\pi$
$439$	31.5341			1.50504			0.752521	+	0.658568i	$0.228838\pi$
$440$	4.99417	−	13.8779i	0.238088	−	0.661603i
$441$	−6.43845	+	8.83348i	−0.306593	+	0.420642i
$442$	1.80054	+	7.47740i	0.0856431	+	0.355663i
$443$	−17.5420			−0.833448			−0.416724	−	0.909033i	$-0.636822\pi$
$443$	−17.5420			−0.833448			−0.416724	+	0.909033i	$0.636822\pi$
$444$	20.9171	−	10.6937i	0.992681	−	0.507498i
$445$	3.12311	+	5.49966i	0.148049	+	0.260709i
$446$	−0.203002	+	0.0488825i	−0.00961242	+	0.00231465i
$447$		−	4.27156i		−	0.202038i
$448$	−6.60745	−	20.1082i	−0.312173	−	0.950025i
$449$	6.31534			0.298039			0.149020	−	0.988834i	$-0.452388\pi$
$449$	6.31534			0.298039			0.149020	+	0.988834i	$0.452388\pi$
$450$	10.5435	+	3.27968i	0.497027	+	0.154606i
$451$	−19.7881			−0.931784
$452$	−5.00691	−	9.79366i	−0.235505	−	0.460655i
$453$	10.5746			0.496840
$454$	−13.9596	+	3.36144i	−0.655155	+	0.157760i
$455$	−3.56090	+	5.38964i	−0.166938	+	0.252670i
$456$	11.8078	−	10.1265i	0.552949	−	0.474218i
$457$			10.3223i			0.482856i	0.970419	+	0.241428i	$0.0776157\pi$
$457$			10.3223i			0.482856i	−0.970419	+	0.241428i	$0.922384\pi$
$458$	12.9978	−	3.12985i	0.607347	−	0.146248i
$459$			15.3019i			0.714229i
$460$	14.8445	−	22.5719i	0.692126	−	1.05242i
$461$			21.1154i			0.983444i	0.870752	+	0.491722i	$0.163632\pi$
$461$			21.1154i			0.983444i	−0.870752	+	0.491722i	$0.836368\pi$
$462$	−12.1021	−	14.1721i	−0.563041	−	0.659344i
$463$	24.3266			1.13055			0.565277	−	0.824901i	$-0.308769\pi$
$463$	24.3266			1.13055			0.565277	+	0.824901i	$0.308769\pi$
$464$	1.31534	−	1.82081i	0.0610632	−	0.0845289i
$465$	15.5554	+	27.3924i	0.721363	+	1.27029i
$466$	−15.1231	+	3.64162i	−0.700564	+	0.168695i
$467$			23.1983i			1.07349i	0.843745	+	0.536744i	$0.180346\pi$
$467$			23.1983i			1.07349i	−0.843745	+	0.536744i	$0.819654\pi$
$468$	−3.03632	+	1.55229i	−0.140354	+	0.0717545i
$469$	−11.1231	+	5.65685i	−0.513617	+	0.261209i
$470$	22.4841	−	21.0624i	1.03711	−	0.971534i
$471$		−	8.30571i		−	0.382707i
$472$	26.3694	+	30.7473i	1.21375	+	1.41526i
$473$		−	3.08835i		−	0.142002i
$474$	−7.52203	−	31.2379i	−0.345498	−	1.43480i
$475$	−6.59603	+	11.0571i	−0.302646	+	0.507335i
$476$	15.4786	−	21.3314i	0.709462	−	0.977724i
$477$		−	13.4106i		−	0.614030i
$478$	3.20636	−	0.772087i	0.146656	−	0.0353144i
$479$	−30.0881			−1.37476			−0.687381	−	0.726297i	$-0.741240\pi$
$479$	−30.0881			−1.37476			−0.687381	+	0.726297i	$0.741240\pi$
$480$	3.42615	+	26.7976i	0.156381	+	1.22314i
$481$		−	6.00505i		−	0.273807i
$482$	22.1067	−	5.32326i	1.00693	−	0.242468i
$483$	−15.4741	−	30.4268i	−0.704095	−	1.38447i
$484$	−9.90388	+	5.06326i	−0.450176	+	0.230148i
$485$	29.0540	−	16.4990i	1.31927	−	0.749179i
$486$	−20.3526	+	4.90086i	−0.923212	+	0.222308i
$487$	−1.16128			−0.0526225			−0.0263112	−	0.999654i	$-0.508376\pi$
$487$	−1.16128			−0.0526225			−0.0263112	+	0.999654i	$0.508376\pi$
$488$	−1.33126	+	1.14171i	−0.0602635	+	0.0516829i
$489$		−	24.5639i		−	1.11082i
$490$	21.9689	−	2.71414i	0.992455	−	0.122612i
$491$		−	14.2794i		−	0.644419i	−0.946668	−	0.322210i	$-0.895574\pi$
$491$		−	14.2794i		−	0.644419i	0.946668	−	0.322210i	$-0.104426\pi$
$492$	32.2725	−	16.4990i	1.45495	−	0.743831i
$493$	2.79695			0.125968
$494$	−0.930870	−	3.86577i	−0.0418818	−	0.173929i
$495$	4.02102	+	7.08084i	0.180731	+	0.318260i
$496$	−15.4501	+	21.3873i	−0.693729	+	0.960318i
$497$	−14.3291	−	28.1753i	−0.642746	−	1.26384i
$498$	−2.73013	−	11.3378i	−0.122340	−	0.508060i
$499$		−	25.6525i		−	1.14836i	−0.818727	−	0.574182i	$-0.805320\pi$
$499$		−	25.6525i		−	1.14836i	0.818727	−	0.574182i	$-0.194680\pi$
$500$	−9.75003	−	20.1230i	−0.436035	−	0.899930i
$501$	−1.43845			−0.0642651
$502$	−3.03632	−	12.6094i	−0.135517	−	0.562785i
$503$			18.8114i			0.838761i	0.907811	+	0.419380i	$0.137753\pi$
$503$			18.8114i			0.838761i	−0.907811	+	0.419380i	$0.862247\pi$
$504$	10.8018	+	4.45806i	0.481150	+	0.198578i
$505$	16.6847	+	29.3810i	0.742458	+	1.30744i
$506$	19.3693	−	4.66410i	0.861071	−	0.207344i
$507$		−	25.2188i		−	1.12001i
$508$	−9.43318	+	4.82262i	−0.418530	+	0.213969i
$509$		−	28.0124i		−	1.24163i	−0.783958	−	0.620814i	$-0.786802\pi$
$509$		−	28.0124i		−	1.24163i	0.783958	−	0.620814i	$-0.213198\pi$
$510$	−24.5503	+	22.9979i	−1.08710	+	1.01836i
$511$	−23.4921	+	11.9473i	−1.03923	+	0.528519i
$512$	−19.2203	+	11.9407i	−0.849426	+	0.527707i
$513$		−	7.91096i		−	0.349278i
$514$	−2.16901	−	9.00757i	−0.0956708	−	0.397307i
$515$	−6.04090	−	10.6378i	−0.266194	−	0.468756i
$516$	2.57501	+	5.03680i	0.113359	+	0.221733i
$517$	22.7199			0.999220
$518$	−15.6486	+	13.3630i	−0.687559	+	0.587135i
$519$			23.6076i			1.03626i
$520$	6.49782	+	2.33834i	0.284948	+	0.102543i
$521$			2.82843i			0.123916i	0.998079	+	0.0619578i	$0.0197344\pi$
$521$			2.82843i			0.123916i	−0.998079	+	0.0619578i	$0.980266\pi$
$522$	0.290319	+	1.20565i	0.0127069	+	0.0527701i
$523$		−	20.9472i		−	0.915958i	−0.888963	−	0.457979i	$-0.848574\pi$
$523$		−	20.9472i		−	0.915958i	0.888963	−	0.457979i	$-0.151426\pi$
$524$	−4.58552	+	2.34430i	−0.200319	+	0.102411i
$525$	−28.1896	−	1.90271i	−1.23029	−	0.0830410i
$526$	−7.80776	−	32.4245i	−0.340435	−	1.41378i
$527$	−32.8531			−1.43110
$528$	−11.6665	+	16.1498i	−0.507721	+	0.702830i
$529$	13.4924			0.586627
$530$	−19.8198	+	18.5665i	−0.860915	+	0.806477i
$531$	−22.3631			−0.970476
$532$	−8.00236	+	11.0282i	−0.346946	+	0.478133i
$533$		−	9.26504i		−	0.401313i
$534$	−2.00000	−	8.30571i	−0.0865485	−	0.359423i
$535$	19.4711	−	11.0571i	0.841808	−	0.478040i
$536$	8.68466	+	10.1265i	0.375120	+	0.437399i
$537$	−17.7392			−0.765502
$538$	−1.33126	+	0.320566i	−0.0573949	+	0.0138206i
$539$	13.1921	+	9.61528i	0.568222	+	0.414159i
$540$	11.4793	+	7.54941i	0.493992	+	0.324875i
$541$	−19.4384			−0.835724			−0.417862	−	0.908510i	$-0.637220\pi$
$541$	−19.4384			−0.835724			−0.417862	+	0.908510i	$0.637220\pi$
$542$	−2.18379	−	9.06897i	−0.0938019	−	0.389546i
$543$	7.36520			0.316071
$544$	−26.0671	−	10.6937i	−1.11762	−	0.458486i
$545$	−8.86958	+	5.03680i	−0.379931	+	0.215753i
$546$	6.63555	−	5.66637i	0.283975	−	0.242498i
$547$	33.4337			1.42952			0.714762	−	0.699368i	$-0.246535\pi$
$547$	33.4337			1.42952			0.714762	+	0.699368i	$0.246535\pi$
$548$	2.81164	+	5.49966i	0.120107	+	0.234934i
$549$		−	0.968253i		−	0.0413240i
$550$	4.89793	−	15.7459i	0.208849	−	0.671406i
$551$	−1.44600			−0.0616019
$552$	−27.7006	+	23.7565i	−1.17902	+	1.01114i
$553$	12.7584	+	25.0870i	0.542543	+	1.06681i
$554$	26.9309	−	6.48490i	1.14418	−	0.275517i
$555$	22.8393	−	12.9698i	0.969473	−	0.550538i
$556$	−7.16053	+	3.66075i	−0.303674	+	0.155250i
$557$		−	8.58800i		−	0.363885i	−0.983309	−	0.181943i	$-0.941761\pi$
$557$		−	8.58800i		−	0.363885i	0.983309	−	0.181943i	$-0.0582385\pi$
$558$	−3.41011	−	14.1617i	−0.144361	−	0.599512i
$559$	1.44600			0.0611595
$560$	−8.36604	−	22.1362i	−0.353530	−	0.935423i
$561$	−24.8078			−1.04738
$562$	−5.64617	−	23.4477i	−0.238169	−	0.989084i
$563$		−	6.78554i		−	0.285977i	−0.989724	−	0.142988i	$-0.954329\pi$
$563$		−	6.78554i		−	0.285977i	0.989724	−	0.142988i	$-0.0456711\pi$
$564$	−37.0540	+	18.9435i	−1.56025	+	0.797664i
$565$	−6.07263	−	10.6937i	−0.255478	−	0.449885i
$566$	−10.2555	+	2.46952i	−0.431073	+	0.103801i
$567$	26.5219	−	13.4882i	1.11381	−	0.566450i
$568$	−25.6509	+	21.9986i	−1.07629	+	0.923042i
$569$	−43.8617			−1.83878			−0.919390	−	0.393347i	$-0.871317\pi$
$569$	−43.8617			−1.83878			−0.919390	+	0.393347i	$0.871317\pi$
$570$	12.6923	−	11.8898i	0.531624	−	0.498008i
$571$			15.5889i			0.652377i	0.945305	+	0.326188i	$0.105764\pi$
$571$			15.5889i			0.652377i	−0.945305	+	0.326188i	$0.894236\pi$
$572$	2.31821	+	4.53448i	0.0969292	+	0.189596i
$573$	42.6429			1.78143
$574$	−24.1438	+	20.6174i	−1.00774	+	0.860553i
$575$	15.4741	−	25.9396i	0.645313	−	1.08176i
$576$	1.90388	−	12.3465i	0.0793284	−	0.514437i
$577$	36.0915			1.50251			0.751254	−	0.660013i	$-0.229449\pi$
$577$	36.0915			1.50251			0.751254	+	0.660013i	$0.229449\pi$
$578$	−2.58497	−	10.7350i	−0.107521	−	0.446517i
$579$	11.7460			0.488149
$580$	1.37992	−	2.09825i	0.0572980	−	0.0871251i
$581$	4.63068	+	9.10534i	0.192113	+	0.377753i
$582$	−43.8780	+	10.5657i	−1.81880	+	0.437964i
$583$	−20.0276			−0.829460
$584$	18.3421	+	21.3873i	0.759001	+	0.885013i
$585$	−3.31534	+	1.88269i	−0.137073	+	0.0778398i
$586$	−4.78852	−	19.8860i	−0.197812	−	0.821485i
$587$			2.80928i			0.115951i	0.998318	+	0.0579757i	$0.0184646\pi$
$587$			2.80928i			0.115951i	−0.998318	+	0.0579757i	$0.981535\pi$
$588$	−29.5320	−	4.68228i	−1.21788	−	0.193094i
$589$	16.9848			0.699848
$590$	30.9609	+	33.0508i	1.27464	+	1.36068i
$591$	35.2381			1.44950
$592$	17.8324	+	12.8820i	0.732906	+	0.529447i
$593$	−6.20705			−0.254893			−0.127447	−	0.991845i	$-0.540678\pi$
$593$	−6.20705			−0.254893			−0.127447	+	0.991845i	$0.540678\pi$
$594$	2.37201	+	9.85061i	0.0973247	+	0.404176i
$595$	16.2432	−	24.5851i	0.665908	−	1.00789i
$596$	3.56155	−	1.82081i	0.145887	−	0.0745832i
$597$			39.1746i			1.60331i
$598$	2.18379	+	9.06897i	0.0893019	+	0.370858i
$599$		−	17.9210i		−	0.732232i	−0.930569	−	0.366116i	$-0.880687\pi$
$599$		−	17.9210i		−	0.732232i	0.930569	−	0.366116i	$-0.119313\pi$
$600$	5.14059	+	29.7638i	0.209864	+	1.21510i
$601$		−	42.2309i		−	1.72263i	−0.508068	−	0.861317i	$-0.669640\pi$
$601$		−	42.2309i		−	1.72263i	0.508068	−	0.861317i	$-0.330360\pi$
$602$	−3.21778	−	3.76815i	−0.131147	−	0.153578i
$603$	−7.36520			−0.299934
$604$	4.50758	+	8.81695i	0.183411	+	0.358757i
$605$	−10.8140	+	6.14098i	−0.439652	+	0.249666i
$606$	−10.6847	−	44.3718i	−0.434035	−	1.80248i
$607$		−	44.9666i		−	1.82514i	−0.408921	−	0.912570i	$-0.634095\pi$
$607$		−	44.9666i		−	1.82514i	0.408921	−	0.912570i	$-0.365905\pi$
$608$	13.4765	+	5.52855i	0.546546	+	0.224212i
$609$	−1.43845	−	2.82843i	−0.0582888	−	0.114614i
$610$	−1.43100	+	1.34051i	−0.0579393	+	0.0542757i
$611$			10.6378i			0.430358i
$612$	13.8503	−	7.08084i	0.559866	−	0.286226i
$613$		−	47.7626i		−	1.92911i	−0.263874	−	0.964557i	$-0.585000\pi$
$613$		−	47.7626i		−	1.92911i	0.263874	−	0.964557i	$-0.415000\pi$
$614$	−19.1096	+	4.60155i	−0.771200	+	0.185704i
$615$	35.2381	−	20.0108i	1.42094	−	0.806913i
$616$	6.65774	−	16.1316i	0.268248	−	0.649959i
$617$			14.7647i			0.594404i	0.954815	+	0.297202i	$0.0960535\pi$
$617$			14.7647i			0.594404i	−0.954815	+	0.297202i	$0.903946\pi$
$618$	3.86852	+	16.0654i	0.155615	+	0.646245i
$619$	−26.0671			−1.04773			−0.523863	−	0.851803i	$-0.675510\pi$
$619$	−26.0671			−1.04773			−0.523863	+	0.851803i	$0.675510\pi$
$620$	−16.2086	+	24.6462i	−0.650953	+	0.989813i
$621$			18.5589i			0.744742i
$622$	−0.478739	−	1.98813i	−0.0191957	−	0.0797168i
$623$	3.39228	+	6.67026i	0.135909	+	0.267238i
$624$	−7.56155	−	5.46242i	−0.302704	−	0.218672i
$625$	−11.8769	−	21.9986i	−0.475076	−	0.879945i
$626$	2.37201	+	9.85061i	0.0948046	+	0.393710i
$627$	12.8255			0.512200
$628$	6.92516	−	3.54042i	0.276344	−	0.141278i
$629$			27.3924i			1.09220i
$630$	12.2837	+	4.44992i	0.489395	+	0.177289i
$631$			33.9582i			1.35186i	0.736968	+	0.675928i	$0.236257\pi$
$631$			33.9582i			1.35186i	−0.736968	+	0.675928i	$0.763743\pi$
$632$	22.8393	−	19.5873i	0.908498	−	0.779142i
$633$	−0.613157			−0.0243708
$634$	33.5616	−	8.08156i	1.33290	−	0.320960i
$635$	−10.3000	+	5.84912i	−0.408745	+	0.232115i
$636$	32.6631	−	16.6987i	1.29518	−	0.662147i
$637$	−4.50200	+	6.17669i	−0.178376	+	0.244730i
$638$	1.80054	−	0.433567i	0.0712842	−	0.0171651i
$639$		−	18.6564i		−	0.738035i
$640$	−20.8829	+	14.2795i	−0.825470	+	0.564446i
$641$	39.8617			1.57444			0.787222	−	0.616670i	$-0.211519\pi$
$641$	39.8617			1.57444			0.787222	+	0.616670i	$0.211519\pi$
$642$	−29.4057	+	7.08084i	−1.16055	+	0.279458i
$643$		−	36.8341i		−	1.45260i	−0.687380	−	0.726298i	$-0.741239\pi$
$643$		−	36.8341i		−	1.45260i	0.687380	−	0.726298i	$-0.258761\pi$
$644$	18.7733	−	25.8718i	0.739771	−	1.01949i
$645$	3.12311	+	5.49966i	0.122972	+	0.216549i
$646$	4.24621	+	17.6339i	0.167065	+	0.693797i
$647$			36.5712i			1.43776i	0.695134	+	0.718881i	$0.255345\pi$
$647$			36.5712i			1.43776i	−0.695134	+	0.718881i	$0.744655\pi$
$648$	−20.7077	−	24.1456i	−0.813474	−	0.948530i
$649$			33.3974i			1.31096i
$650$	7.37243	+	2.29328i	0.289170	+	0.0899497i
$651$	16.8961	+	33.2228i	0.662209	+	1.30211i
$652$	20.4810	−	10.4707i	0.802097	−	0.410064i
$653$		−	16.4990i		−	0.645654i	−0.946458	−	0.322827i	$-0.895367\pi$
$653$		−	16.4990i		−	0.645654i	0.946458	−	0.322827i	$-0.104633\pi$
$654$	13.3951	−	3.22550i	0.523788	−	0.126127i
$655$	−5.00691	+	2.84329i	−0.195636	+	0.111096i
$656$	27.5131	+	19.8753i	1.07421	+	0.776001i
$657$	−15.5554			−0.606873
$658$	27.7210	−	23.6721i	1.08068	−	0.922834i
$659$			42.8381i			1.66874i	0.551207	+	0.834368i	$0.314167\pi$
$659$			42.8381i			1.66874i	−0.551207	+	0.834368i	$0.685833\pi$
$660$	−12.2393	+	18.6106i	−0.476414	+	0.724417i
$661$			1.51198i			0.0588092i	0.999568	+	0.0294046i	$0.00936112\pi$
$661$			1.51198i			0.0588092i	−0.999568	+	0.0294046i	$0.990639\pi$
$662$	11.4196	−	2.74983i	0.443837	−	0.106875i
$663$		−	11.6153i		−	0.451102i
$664$	8.28954	−	7.10923i	0.321696	−	0.275892i
$665$	−8.39766	+	12.7104i	−0.325647	+	0.492887i
$666$	−11.8078	+	2.84329i	−0.457542	+	0.110175i
$667$	3.39228			0.131350
$668$	−0.613157	−	1.19935i	−0.0237238	−	0.0464044i
$669$	0.315342			0.0121918
$670$	10.1968	+	10.8851i	0.393939	+	0.420530i
$671$	−1.44600			−0.0558224
$672$	2.59209	+	31.8601i	0.0999922	+	1.22903i
$673$		−	14.0877i		−	0.543039i	−0.962433	−	0.271520i	$-0.912474\pi$
$673$		−	14.0877i		−	0.543039i	0.962433	−	0.271520i	$-0.0875262\pi$
$674$	−42.0540	+	10.1265i	−1.61986	+	0.390059i
$675$	13.1921	+	7.86962i	0.507762	+	0.302902i
$676$	21.0270	−	10.7498i	0.808730	−	0.413455i
$677$	46.5317			1.78836			0.894179	−	0.447709i	$-0.147760\pi$
$677$	46.5317			1.78836			0.894179	+	0.447709i	$0.147760\pi$
$678$	3.88884	+	16.1498i	0.149350	+	0.620230i
$679$	35.2381	−	17.9210i	1.35232	−	0.687745i
$680$	−29.6401	−	10.6664i	−1.13665	−	0.409040i
$681$	21.6847			0.830958
$682$	−21.1493	+	5.09271i	−0.809847	+	0.195010i
$683$	−20.1907			−0.772574			−0.386287	−	0.922379i	$-0.626243\pi$
$683$	−20.1907			−0.772574			−0.386287	+	0.922379i	$0.626243\pi$
$684$	−7.16053	+	3.66075i	−0.273790	+	0.139972i
$685$	3.41011	+	6.00505i	0.130293	+	0.229441i
$686$	26.1141	−	2.01315i	0.997042	−	0.0768625i
$687$	−20.1907			−0.770322
$688$	−3.10196	+	4.29400i	−0.118261	+	0.163707i
$689$		−	9.37720i		−	0.357243i
$690$	−29.7758	+	27.8930i	−1.13355	+	1.06187i
$691$	−37.8132			−1.43848			−0.719240	−	0.694761i	$-0.755510\pi$
$691$	−37.8132			−1.43848			−0.719240	+	0.694761i	$0.755510\pi$
$692$	−19.6836	+	10.0630i	−0.748258	+	0.382539i
$693$	4.36758	+	8.58800i	0.165911	+	0.326231i
$694$	0.438447	+	1.82081i	0.0166432	+	0.0691169i
$695$	−7.81855	+	4.43994i	−0.296575	+	0.168417i
$696$	−2.57501	+	2.20837i	−0.0976056	+	0.0837080i
$697$			42.2630i			1.60082i
$698$	−25.8906	+	6.23442i	−0.979975	+	0.235976i
$699$	23.4921			0.888553
$700$	−10.4297	−	24.3150i	−0.394207	−	0.919022i
$701$	−30.6695			−1.15837			−0.579186	−	0.815196i	$-0.696629\pi$
$701$	−30.6695			−1.15837			−0.579186	+	0.815196i	$0.696629\pi$
$702$	−4.61219	+	1.11061i	−0.174076	+	0.0419171i
$703$		−	14.1617i		−	0.534118i
$704$	−18.4384	−	2.84329i	−0.694925	−	0.107160i
$705$	−40.4591	+	22.9756i	−1.52378	+	0.865312i
$706$	−5.35302	−	22.2303i	−0.201464	−	0.836650i
$707$	18.1227	+	35.6347i	0.681574	+	1.34018i
$708$	−27.8462	−	54.4679i	−1.04652	−	2.04703i
$709$	30.8078			1.15701			0.578505	−	0.815679i	$-0.303636\pi$
$709$	30.8078			1.15701			0.578505	+	0.815679i	$0.303636\pi$
$710$	−27.5726	+	25.8291i	−1.03478	+	0.969348i
$711$			16.6114i			0.622977i
$712$	6.07263	−	5.20798i	0.227582	−	0.195177i
$713$	−39.8459			−1.49224
$714$	−30.2684	+	25.8474i	−1.13277	+	0.967316i
$715$	2.81164	+	4.95118i	0.105150	+	0.185164i
$716$	−7.56155	−	14.7906i	−0.282588	−	0.552751i
$717$	−4.98074			−0.186009
$718$	14.2313	−	3.42687i	0.531107	−	0.127890i
$719$	27.1961			1.01424			0.507122	−	0.861874i	$-0.330709\pi$
$719$	27.1961			1.01424			0.507122	+	0.861874i	$0.330709\pi$
$720$	1.52128	−	13.8839i	0.0566948	−	0.517421i
$721$	−6.56155	−	12.9020i	−0.244365	−	0.480496i
$722$	4.09519	+	17.0067i	0.152407	+	0.632926i
$723$	−34.3404			−1.27713
$724$	3.13951	+	6.14098i	0.116679	+	0.228228i
$725$	1.43845	−	2.41131i	0.0534226	−	0.0895537i
$726$	16.3316	−	3.93261i	0.606121	−	0.145953i
$727$			32.8255i			1.21743i	0.793389	+	0.608715i	$0.208315\pi$
$727$			32.8255i			1.21743i	−0.793389	+	0.608715i	$0.791685\pi$
$728$	7.55301	+	3.11724i	0.279933	+	0.115533i
$729$	−2.12311			−0.0786335
$730$	21.5358	+	22.9895i	0.797077	+	0.850881i
$731$	−6.59603			−0.243963
$732$	2.35829	−	1.20565i	0.0871651	−	0.0445623i
$733$	−24.4250			−0.902156			−0.451078	−	0.892484i	$-0.648960\pi$
$733$	−24.4250			−0.902156			−0.451078	+	0.892484i	$0.648960\pi$
$734$	32.1431	−	7.74001i	1.18642	−	0.285689i
$735$	−33.2156	−	3.78213i	−1.22518	−	0.139506i
$736$	−31.6155	−	12.9698i	−1.16536	−	0.478073i
$737$			10.9993i			0.405165i
$738$	−18.2179	+	4.38684i	−0.670610	+	0.161482i
$739$		−	49.5472i		−	1.82262i	−0.411718	−	0.911311i	$-0.635071\pi$
$739$		−	49.5472i		−	1.82262i	0.411718	−	0.911311i	$-0.364929\pi$
$740$	20.5495	+	13.5144i	0.755416	+	0.496801i
$741$			6.00505i			0.220601i
$742$	−24.4361	+	20.8670i	−0.897077	+	0.766051i
$743$	9.43318			0.346070			0.173035	−	0.984916i	$-0.444643\pi$
$743$	9.43318			0.346070			0.173035	+	0.984916i	$0.444643\pi$
$744$	30.2462	−	25.9396i	1.10888	−	0.950992i
$745$	3.88884	−	2.20837i	0.142476	−	0.0809084i
$746$	16.0540	−	3.86577i	0.587778	−	0.141536i
$747$			6.02913i			0.220594i
$748$	−10.5746	−	20.6843i	−0.386647	−	0.756293i
$749$	23.6155	−	12.0101i	0.862893	−	0.438839i
$750$	7.20097	+	32.9929i	0.262942	+	1.20473i
$751$			37.5999i			1.37204i	0.727584	+	0.686019i	$0.240643\pi$
$751$			37.5999i			1.37204i	−0.727584	+	0.686019i	$0.759357\pi$
$752$	−31.5895	−	22.8201i	−1.15195	−	0.832162i
$753$			19.5873i			0.713801i
$754$	0.203002	+	0.843038i	0.00739290	+	0.0307016i
$755$	5.46702	+	9.62719i	0.198965	+	0.350369i
$756$	13.1576	+	9.54749i	0.478537	+	0.347239i
$757$		−	25.7640i		−	0.936409i	−0.883620	−	0.468204i	$-0.844901\pi$
$757$		−	25.7640i		−	0.936409i	0.883620	−	0.468204i	$-0.155099\pi$
$758$	−34.2589	+	8.24948i	−1.24434	+	0.299635i
$759$	−30.0881			−1.09213
$760$	15.3238	+	5.51449i	0.555851	+	0.200031i
$761$		−	43.1228i		−	1.56320i	−0.623780	−	0.781600i	$-0.714404\pi$
$761$		−	43.1228i		−	1.56320i	0.623780	−	0.781600i	$-0.285596\pi$
$762$	15.5554	−	3.74571i	0.563512	−	0.135693i
$763$	−10.7575	+	5.47091i	−0.389447	+	0.198060i
$764$	18.1771	+	35.5549i	0.657624	+	1.28633i
$765$	15.1231	−	8.58800i	0.546777	−	0.310500i
$766$	25.6611	−	6.17915i	0.927173	−	0.223262i
$767$	−15.6371			−0.564623
$768$	32.4420	−	10.7365i	1.17065	−	0.387421i
$769$		−	14.4903i		−	0.522535i	−0.965266	−	0.261267i	$-0.915860\pi$
$769$		−	14.4903i		−	0.522535i	0.965266	−	0.261267i	$-0.0841404\pi$
$770$	6.64559	−	18.3447i	0.239490	−	0.661097i
$771$			13.9923i			0.503920i
$772$	5.00691	+	9.79366i	0.180203	+	0.352481i
$773$	−15.6898			−0.564323			−0.282161	−	0.959367i	$-0.591051\pi$
$773$	−15.6898			−0.564323			−0.282161	+	0.959367i	$0.591051\pi$
$774$	−0.684658	−	2.84329i	−0.0246095	−	0.102200i
$775$	−16.8961	+	28.3234i	−0.606925	+	1.01740i
$776$	−27.5131	−	32.0810i	−0.987663	−	1.15164i
$777$	27.7006	−	14.0877i	0.993755	−	0.505392i
$778$	3.95003	+	16.4039i	0.141616	+	0.588109i
$779$		−	21.8497i		−	0.782847i
$780$	−8.71373	−	5.73060i	−0.312002	−	0.205189i
$781$	−27.8617			−0.996971
$782$	−9.96148	−	41.3686i	−0.356222	−	1.47934i
$783$			1.72521i			0.0616538i
$784$	−8.68441	−	26.6192i	−0.310157	−	0.950685i
$785$	7.56155	−	4.29400i	0.269883	−	0.153259i
$786$	7.56155	−	1.82081i	0.269712	−	0.0649461i
$787$		−	32.8578i		−	1.17126i	−0.810580	−	0.585628i	$-0.800848\pi$
$787$		−	32.8578i		−	1.17126i	0.810580	−	0.585628i	$-0.199152\pi$
$788$	15.0207	+	29.3810i	0.535091	+	1.04665i
$789$			50.3680i			1.79315i
$790$	24.5503	−	22.9979i	0.873460	−	0.818228i
$791$	−6.59603	−	12.9698i	−0.234528	−	0.461153i
$792$	7.81855	−	6.70531i	0.277820	−	0.238263i
$793$		−	0.677039i		−	0.0240423i
$794$	6.95753	+	28.8936i	0.246913	+	1.02540i
$795$	35.6647	−	20.2530i	1.26490	−	0.718301i
$796$	−32.6631	+	16.6987i	−1.15771	+	0.591870i
$797$	−2.04937			−0.0725925			−0.0362963	−	0.999341i	$-0.511556\pi$
$797$	−2.04937			−0.0725925			−0.0362963	+	0.999341i	$0.511556\pi$
$798$	15.6486	−	13.3630i	0.553954	−	0.473044i
$799$		−	48.5247i		−	1.71668i
$800$	−22.6253	+	16.9734i	−0.799926	+	0.600099i
$801$			4.41674i			0.156058i
$802$	−4.44916	−	18.4767i	−0.157105	−	0.652435i
$803$			23.2306i			0.819792i
$804$	−9.17104	−	17.9388i	−0.323438	−	0.632653i
$805$	19.7006	−	29.8181i	0.694356	−	1.05095i
$806$	−2.38447	−	9.90237i	−0.0839894	−	0.348796i
$807$	2.06798			0.0727962
$808$	32.4420	−	27.8228i	1.14131	−	0.978802i
$809$	−27.0540			−0.951167			−0.475584	−	0.879671i	$-0.657763\pi$
$809$	−27.0540			−0.951167			−0.475584	+	0.879671i	$0.657763\pi$
$810$	−24.3133	−	25.9545i	−0.854283	−	0.911948i
$811$	−9.17104			−0.322039			−0.161019	−	0.986951i	$-0.551478\pi$
$811$	−9.17104			−0.322039			−0.161019	+	0.986951i	$0.551478\pi$
$812$	1.74514	−	2.40501i	0.0612423	−	0.0843992i
$813$			14.0877i			0.494076i
$814$	4.24621	+	17.6339i	0.148830	+	0.618068i
$815$	22.3631	−	12.6994i	0.783345	−	0.444840i
$816$	34.4924	+	24.9171i	1.20748	+	0.872274i
$817$	3.41011			0.119304
$818$	41.5510	−	10.0054i	1.45280	−	0.349830i
$819$	−4.02102	+	2.04496i	−0.140506	+	0.0714567i
$820$	31.7054	+	20.8511i	1.10720	+	0.728152i
$821$	−35.9309			−1.25400			−0.626998	−	0.779021i	$-0.715717\pi$
$821$	−35.9309			−1.25400			−0.626998	+	0.779021i	$0.715717\pi$
$822$	−2.18379	−	9.06897i	−0.0761685	−	0.316317i
$823$	22.8393			0.796127			0.398064	−	0.917358i	$-0.369682\pi$
$823$	22.8393			0.796127			0.398064	+	0.917358i	$0.369682\pi$
$824$	−11.7460	+	10.0736i	−0.409193	+	0.350930i
$825$	−12.7584	+	21.3873i	−0.444191	+	0.744610i
$826$	34.7971	+	40.7488i	1.21075	+	1.41783i
$827$	4.71659			0.164012			0.0820059	−	0.996632i	$-0.473867\pi$
$827$	4.71659			0.164012			0.0820059	+	0.996632i	$0.473867\pi$
$828$	16.7984	−	8.58800i	0.583784	−	0.298454i
$829$		−	43.3947i		−	1.50716i	−0.657357	−	0.753579i	$-0.728326\pi$
$829$		−	43.3947i		−	1.50716i	0.657357	−	0.753579i	$-0.271674\pi$
$830$	8.91055	−	8.34711i	0.309290	−	0.289732i
$831$	−41.8342			−1.45121
$832$	1.33126	−	8.63312i	0.0461533	−	0.299300i
$833$	20.5361	−	28.1753i	0.711534	−	0.976217i
$834$	11.8078	−	2.84329i	0.408869	−	0.0984550i
$835$	−0.743668	−	1.30957i	−0.0257357	−	0.0453195i
$836$	5.46702	+	10.6937i	0.189081	+	0.369848i
$837$		−	20.2644i		−	0.700438i
$838$	7.40390	+	30.7473i	0.255763	+	1.06215i
$839$	−32.3461			−1.11671			−0.558356	−	0.829601i	$-0.688568\pi$
$839$	−32.3461			−1.11671			−0.558356	+	0.829601i	$0.688568\pi$
$840$	4.45718	+	35.4594i	0.153787	+	1.22347i
$841$	−28.6847			−0.989126
$842$	−4.15884	−	17.2711i	−0.143323	−	0.595200i
$843$			36.4235i			1.25449i
$844$	−0.261366	−	0.511240i	−0.00899660	−	0.0175976i
$845$	22.9593	−	13.0380i	0.789823	−	0.448519i
$846$	20.9171	−	5.03680i	0.719144	−	0.173169i
$847$	−13.1158	+	6.67026i	−0.450664	+	0.229193i
$848$	27.8462	+	20.1159i	0.956242	+	0.690784i
$849$	15.9309			0.546746
$850$	−33.6297	−	10.4609i	−1.15349	−	0.358806i
$851$			33.2228i			1.13886i
$852$	45.4398	−	23.2306i	1.55674	−	0.795869i
$853$	2.93137			0.100368			0.0501840	−	0.998740i	$-0.484019\pi$
$853$	2.93137			0.100368			0.0501840	+	0.998740i	$0.484019\pi$
$854$	−1.76430	+	1.50661i	−0.0603730	+	0.0515550i
$855$	−7.81855	+	4.43994i	−0.267389	+	0.151843i
$856$	−18.4384	−	21.4997i	−0.630213	−	0.734844i
$857$	−5.59390			−0.191084			−0.0955419	−	0.995425i	$-0.530458\pi$
$857$	−5.59390			−0.191084			−0.0955419	+	0.995425i	$0.530458\pi$
$858$	−1.80054	−	7.47740i	−0.0614695	−	0.255274i
$859$	9.17104			0.312912			0.156456	−	0.987685i	$-0.449993\pi$
$859$	9.17104			0.312912			0.156456	+	0.987685i	$0.449993\pi$
$860$	−3.25425	+	4.94829i	−0.110969	+	0.168735i
$861$	42.7386	−	21.7355i	1.45653	−	0.740744i
$862$	16.0318	−	3.86043i	0.546046	−	0.131487i
$863$	30.7851			1.04794			0.523969	−	0.851737i	$-0.324451\pi$
$863$	30.7851			1.04794			0.523969	+	0.851737i	$0.324451\pi$
$864$	6.59603	−	16.0786i	0.224401	−	0.547007i
$865$	−21.4924	+	12.2050i	−0.730764	+	0.414981i
$866$	2.98102	+	12.3797i	0.101299	+	0.420680i
$867$			16.6757i			0.566335i
$868$	−20.4985	+	28.2493i	−0.695763	+	0.958845i
$869$	24.8078			0.841546
$870$	−2.76792	+	2.59289i	−0.0938412	+	0.0879074i
$871$	−5.15002			−0.174502
$872$	8.39919	+	9.79366i	0.284432	+	0.331655i
$873$	23.3331			0.789705
$874$	5.15002	+	21.3873i	0.174202	+	0.723436i
$875$	−12.8416	−	26.6476i	−0.434125	−	0.900853i
$876$	−19.3693	−	37.8869i	−0.654429	−	1.28008i
$877$		−	5.49966i		−	0.185710i	−0.995680	−	0.0928551i	$-0.970401\pi$
$877$		−	5.49966i		−	0.185710i	0.995680	−	0.0928551i	$-0.0295993\pi$
$878$	−10.4402	−	43.3567i	−0.352340	−	1.46322i
$879$			30.8908i			1.04192i
$880$	−20.7344	−	2.27191i	−0.698956	−	0.0765859i
$881$			30.7645i			1.03648i	0.855234	+	0.518241i	$0.173413\pi$
$881$			30.7645i			1.03648i	−0.855234	+	0.518241i	$0.826587\pi$
$882$	14.2769	+	5.92775i	0.480728	+	0.199598i
$883$	−48.4902			−1.63183			−0.815913	−	0.578175i	$-0.803765\pi$
$883$	−48.4902			−1.63183			−0.815913	+	0.578175i	$0.803765\pi$
$884$	9.68466	−	4.95118i	0.325730	−	0.166526i
$885$	−33.7733	−	59.4733i	−1.13528	−	1.99917i
$886$	5.80776	+	24.1188i	0.195116	+	0.810287i
$887$		−	31.7738i		−	1.06686i	−0.845845	−	0.533429i	$-0.820903\pi$
$887$		−	31.7738i		−	1.06686i	0.845845	−	0.533429i	$-0.179097\pi$
$888$	−21.6280	−	25.2188i	−0.725788	−	0.846287i
$889$	−12.4924	+	6.35324i	−0.418982	+	0.213081i
$890$	6.52757	−	6.11481i	0.218804	−	0.204969i
$891$		−	26.2267i		−	0.878628i
$892$	0.134418	+	0.262926i	0.00450066	+	0.00880343i
$893$			25.0870i			0.839503i
$894$	−5.87302	+	1.41421i	−0.196423	+	0.0472984i
$895$	−9.17104	−	16.1498i	−0.306554	−	0.539829i
$896$	−25.4595	+	15.7420i	−0.850543	+	0.525905i
$897$		−	14.0877i		−	0.470373i
$898$	−2.09086	−	8.68305i	−0.0697730	−	0.289757i
$899$	−3.70402			−0.123536
$900$	1.01856	−	15.5823i	0.0339522	−	0.519409i
$901$			42.7746i			1.42503i
$902$	6.55137	+	27.2069i	0.218137	+	0.905891i
$903$	3.39228	+	6.67026i	0.112888	+	0.221972i
$904$	−11.8078	+	10.1265i	−0.392720	+	0.336803i
$905$	3.80776	+	6.70531i	0.126574	+	0.222892i
$906$	−3.50102	−	14.5392i	−0.116313	−	0.483033i
$907$	−53.7874			−1.78598			−0.892991	−	0.450074i	$-0.851397\pi$
$907$	−53.7874			−1.78598			−0.892991	+	0.450074i	$0.851397\pi$
$908$	9.24337	+	18.0803i	0.306752	+	0.600016i
$909$			23.5957i			0.782619i
$910$	8.58922	+	3.11155i	0.284730	+	0.103147i
$911$		−	56.0950i		−	1.85851i	−0.369438	−	0.929255i	$-0.620450\pi$
$911$		−	56.0950i		−	1.85851i	0.369438	−	0.929255i	$-0.379550\pi$
$912$	−17.8324	−	12.8820i	−0.590489	−	0.426566i
$913$	9.00400			0.297989
$914$	14.1922	−	3.41746i	0.469437	−	0.113040i
$915$	2.57501	−	1.46228i	0.0851272	−	0.0483415i
$916$	−8.60654	−	16.8346i	−0.284368	−	0.556232i
$917$	−6.07263	+	3.08835i	−0.200536	+	0.101986i
$918$	21.0387	−	5.06609i	0.694382	−	0.167206i
$919$			39.1965i			1.29297i	0.762925	+	0.646487i	$0.223762\pi$
$919$			39.1965i			1.29297i	−0.762925	+	0.646487i	$0.776238\pi$
$920$	−35.9491	−	12.9368i	−1.18521	−	0.426514i
$921$	29.6847			0.978143
$922$	29.0319	−	6.99083i	0.956115	−	0.230231i
$923$		−	13.0452i		−	0.429389i
$924$	−15.4786	+	21.3314i	−0.509210	+	0.701752i
$925$	23.6155	+	14.0877i	0.776474	+	0.463199i
$926$	−8.05398	−	33.4470i	−0.264670	−	1.09914i
$927$		−	8.54312i		−	0.280593i
$928$	−2.93893	−	1.20565i	−0.0964752	−	0.0395775i
$929$		−	28.9807i		−	0.950825i	−0.879763	−	0.475412i	$-0.842299\pi$
$929$		−	28.9807i		−	0.950825i	0.879763	−	0.475412i	$-0.157701\pi$
$930$	32.5121	−	30.4563i	1.06611	−	0.998700i
$931$	−10.6170	+	14.5665i	−0.347960	+	0.477397i
$932$	10.0138	+	19.5873i	0.328013	+	0.641604i
$933$			3.08835i			0.101108i
$934$	31.8956	−	7.68041i	1.04366	−	0.251311i
$935$	−12.8255	−	22.5851i	−0.419437	−	0.738611i
$936$	3.13951	+	3.66075i	0.102618	+	0.119655i
$937$	−49.4631			−1.61589			−0.807944	−	0.589259i	$-0.799420\pi$
$937$	−49.4631			−1.61589			−0.807944	+	0.589259i	$0.799420\pi$
$938$	11.4603	+	13.4205i	0.374192	+	0.438194i
$939$		−	15.3019i		−	0.499357i
$940$	−36.4029	−	23.9404i	−1.18733	−	0.780851i
$941$		−	8.75714i		−	0.285475i	−0.989761	−	0.142737i	$-0.954410\pi$
$941$		−	8.75714i		−	0.285475i	0.989761	−	0.142737i	$-0.0455904\pi$
$942$	−11.4196	+	2.74983i	−0.372072	+	0.0895942i
$943$			51.2587i			1.66921i
$944$	33.5446	−	46.4354i	1.09179	−	1.51134i
$945$	15.1645	+	10.0191i	0.493302	+	0.325922i
$946$	−4.24621	+	1.02248i	−0.138056	+	0.0332437i
$947$	52.6261			1.71012			0.855060	−	0.518529i	$-0.173520\pi$
$947$	52.6261			1.71012			0.855060	+	0.518529i	$0.173520\pi$
$948$	−40.4591	+	20.6843i	−1.31405	+	0.671795i
$949$	−10.8769			−0.353079
$950$	17.3864	+	5.40822i	0.564088	+	0.175466i
$951$	−52.1342			−1.69057
$952$	−34.4535	−	14.2195i	−1.11664	−	0.460856i
$953$			31.2637i			1.01273i	0.862319	+	0.506365i	$0.169011\pi$
$953$			31.2637i			1.01273i	−0.862319	+	0.506365i	$0.830989\pi$
$954$	−18.4384	+	4.43994i	−0.596967	+	0.143748i
$955$	22.0461	+	38.8222i	0.713395	+	1.25626i
$956$	−2.12311	−	4.15286i	−0.0686661	−	0.134313i
$957$	−2.79695			−0.0904125
$958$	9.96148	+	41.3686i	0.321841	+	1.33656i
$959$	3.70402	+	7.28323i	0.119609	+	0.235188i
$960$	35.7100	−	13.5827i	1.15254	−	0.438380i
$961$	12.5076			0.403470
$962$	−8.25643	+	1.98813i	−0.266198	+	0.0641000i
$963$	15.6371			0.503899
$964$	−14.6381	−	28.6325i	−0.471460	−	0.922190i
$965$	6.07263	+	10.6937i	0.195485	+	0.344241i
$966$	−36.7111	+	31.3491i	−1.18116	+	1.00864i
$967$	16.2177			0.521527			0.260764	−	0.965403i	$-0.416026\pi$
$967$	16.2177			0.521527			0.260764	+	0.965403i	$0.416026\pi$
$968$	10.2405	+	11.9407i	0.329142	+	0.383787i
$969$		−	27.3924i		−	0.879969i
$970$	−32.3038	−	34.4843i	−1.03721	−	1.10722i
$971$	36.3672			1.16708			0.583539	−	0.812085i	$-0.301668\pi$
$971$	36.3672			1.16708			0.583539	+	0.812085i	$0.301668\pi$
$972$	13.4765	+	26.3605i	0.432260	+	0.845513i
$973$	−9.48274	+	4.82262i	−0.304003	+	0.154606i
$974$	0.384472	+	1.59666i	0.0123193	+	0.0511602i
$975$	−10.0138	−	5.97366i	−0.320699	−	0.191310i
$976$	2.01051	+	1.45238i	0.0643548	+	0.0464895i
$977$		−	14.0877i		−	0.450704i	−0.974277	−	0.225352i	$-0.927647\pi$
$977$		−	14.0877i		−	0.450704i	0.974277	−	0.225352i	$-0.0723532\pi$
$978$	−33.7733	+	8.13254i	−1.07995	+	0.260050i
$979$	6.59603			0.210810
$980$	−11.0051	−	29.3068i	−0.351545	−	0.936171i
$981$	−7.12311			−0.227423
$982$	−19.6329	+	4.72757i	−0.626511	+	0.150863i
$983$		−	44.7361i		−	1.42686i	−0.700727	−	0.713430i	$-0.747141\pi$
$983$		−	44.7361i		−	1.42686i	0.700727	−	0.713430i	$-0.252859\pi$
$984$	−33.3693	−	38.9094i	−1.06377	−	1.24039i
$985$	18.2179	+	32.0810i	0.580471	+	1.02218i
$986$	−0.926004	−	3.84556i	−0.0294900	−	0.122468i
$987$	−49.0708	+	24.9559i	−1.56194	+	0.794353i
$988$	−5.00691	+	2.55973i	−0.159291	+	0.0814359i
$989$	−8.00000			−0.254385
$990$	8.40428	−	7.87285i	0.267105	−	0.250216i
$991$			0.574176i			0.0182393i	0.999958	+	0.00911966i	$0.00290292\pi$
$991$			0.574176i			0.0182393i	−0.999958	+	0.00911966i	$0.997097\pi$
$992$	34.5209	+	14.1617i	1.09604	+	0.449634i
$993$	−17.7392			−0.562935
$994$	−33.9946	+	29.0294i	−1.07824	+	0.920757i
$995$	−35.6647	+	20.2530i	−1.13065	+	0.642065i
$996$	−14.6847	+	7.50738i	−0.465301	+	0.237881i
$997$	−47.7580			−1.51251			−0.756256	−	0.654276i	$-0.772973\pi$
$997$	−47.7580			−1.51251			−0.756256	+	0.654276i	$0.772973\pi$
$998$	−35.2700	+	8.49295i	−1.11645	+	0.268840i
$999$	−16.8961			−0.534568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.c.b.139.6	yes	16
4.3	odd	2	inner	140.2.c.b.139.9	yes	16
5.2	odd	4		700.2.g.l.251.14		16
5.3	odd	4		700.2.g.l.251.3		16
5.4	even	2	inner	140.2.c.b.139.11	yes	16
7.2	even	3		980.2.s.f.619.5		32
7.3	odd	6		980.2.s.f.19.15		32
7.4	even	3		980.2.s.f.19.16		32
7.5	odd	6		980.2.s.f.619.6		32
7.6	odd	2	inner	140.2.c.b.139.5	✓	16
8.3	odd	2		2240.2.e.f.2239.15		16
8.5	even	2		2240.2.e.f.2239.3		16
20.3	even	4		700.2.g.l.251.2		16
20.7	even	4		700.2.g.l.251.15		16
20.19	odd	2	inner	140.2.c.b.139.8	yes	16
28.3	even	6		980.2.s.f.19.12		32
28.11	odd	6		980.2.s.f.19.11		32
28.19	even	6		980.2.s.f.619.1		32
28.23	odd	6		980.2.s.f.619.2		32
28.27	even	2	inner	140.2.c.b.139.10	yes	16
35.4	even	6		980.2.s.f.19.1		32
35.9	even	6		980.2.s.f.619.12		32
35.13	even	4		700.2.g.l.251.4		16
35.19	odd	6		980.2.s.f.619.11		32
35.24	odd	6		980.2.s.f.19.2		32
35.27	even	4		700.2.g.l.251.13		16
35.34	odd	2	inner	140.2.c.b.139.12	yes	16
40.19	odd	2		2240.2.e.f.2239.1		16
40.29	even	2		2240.2.e.f.2239.13		16
56.13	odd	2		2240.2.e.f.2239.14		16
56.27	even	2		2240.2.e.f.2239.2		16
140.19	even	6		980.2.s.f.619.16		32
140.27	odd	4		700.2.g.l.251.16		16
140.39	odd	6		980.2.s.f.19.6		32
140.59	even	6		980.2.s.f.19.5		32
140.79	odd	6		980.2.s.f.619.15		32
140.83	odd	4		700.2.g.l.251.1		16
140.139	even	2	inner	140.2.c.b.139.7	yes	16
280.69	odd	2		2240.2.e.f.2239.4		16
280.139	even	2		2240.2.e.f.2239.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	7.6	odd	2	inner
140.2.c.b.139.6	yes	16	1.1	even	1	trivial
140.2.c.b.139.7	yes	16	140.139	even	2	inner
140.2.c.b.139.8	yes	16	20.19	odd	2	inner
140.2.c.b.139.9	yes	16	4.3	odd	2	inner
140.2.c.b.139.10	yes	16	28.27	even	2	inner
140.2.c.b.139.11	yes	16	5.4	even	2	inner
140.2.c.b.139.12	yes	16	35.34	odd	2	inner
700.2.g.l.251.1		16	140.83	odd	4
700.2.g.l.251.2		16	20.3	even	4
700.2.g.l.251.3		16	5.3	odd	4
700.2.g.l.251.4		16	35.13	even	4
700.2.g.l.251.13		16	35.27	even	4
700.2.g.l.251.14		16	5.2	odd	4
700.2.g.l.251.15		16	20.7	even	4
700.2.g.l.251.16		16	140.27	odd	4
980.2.s.f.19.1		32	35.4	even	6
980.2.s.f.19.2		32	35.24	odd	6
980.2.s.f.19.5		32	140.59	even	6
980.2.s.f.19.6		32	140.39	odd	6
980.2.s.f.19.11		32	28.11	odd	6
980.2.s.f.19.12		32	28.3	even	6
980.2.s.f.19.15		32	7.3	odd	6
980.2.s.f.19.16		32	7.4	even	3
980.2.s.f.619.1		32	28.19	even	6
980.2.s.f.619.2		32	28.23	odd	6
980.2.s.f.619.5		32	7.2	even	3
980.2.s.f.619.6		32	7.5	odd	6
980.2.s.f.619.11		32	35.19	odd	6
980.2.s.f.619.12		32	35.9	even	6
980.2.s.f.619.15		32	140.79	odd	6
980.2.s.f.619.16		32	140.19	even	6
2240.2.e.f.2239.1		16	40.19	odd	2
2240.2.e.f.2239.2		16	56.27	even	2
2240.2.e.f.2239.3		16	8.5	even	2
2240.2.e.f.2239.4		16	280.69	odd	2
2240.2.e.f.2239.13		16	40.29	even	2
2240.2.e.f.2239.14		16	56.13	odd	2
2240.2.e.f.2239.15		16	8.3	odd	2
2240.2.e.f.2239.16		16	280.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.331077 - 1.37491i) q^{2} +2.13578i q^{3} +(-1.78078 + 0.910404i) q^{4} +(-1.94442 + 1.10418i) q^{5} +(2.93651 - 0.707107i) q^{6} +(-2.35829 + 1.19935i) q^{7} +(1.84130 + 2.14700i) q^{8} -1.56155 q^{9} +(2.16191 + 2.30784i) q^{10} +2.33205i q^{11} +(-1.94442 - 3.80335i) q^{12} -1.09190 q^{13} +(2.42978 + 2.84537i) q^{14} +(-2.35829 - 4.15286i) q^{15} +(2.34233 - 3.24245i) q^{16} +4.98074 q^{17} +(0.516994 + 2.14700i) q^{18} -2.57501 q^{19} +(2.45733 - 3.73652i) q^{20} +(-2.56155 - 5.03680i) q^{21} +(3.20636 - 0.772087i) q^{22} +6.04090 q^{23} +(-4.58552 + 3.93261i) q^{24} +(2.56155 - 4.29400i) q^{25} +(0.361501 + 1.50126i) q^{26} +3.07221i q^{27} +(3.10770 - 4.28278i) q^{28} +0.561553 q^{29} +(-4.92904 + 4.61737i) q^{30} -6.59603 q^{31} +(-5.23358 - 2.14700i) q^{32} -4.98074 q^{33} +(-1.64901 - 6.84809i) q^{34} +(3.26121 - 4.93604i) q^{35} +(2.78078 - 1.42164i) q^{36} +5.49966i q^{37} +(0.852526 + 3.54042i) q^{38} -2.33205i q^{39} +(-5.95095 - 2.14154i) q^{40} +8.48528i q^{41} +(-6.07709 + 5.18948i) q^{42} -1.32431 q^{43} +(-2.12311 - 4.15286i) q^{44} +(3.03632 - 1.72424i) q^{45} +(-2.00000 - 8.30571i) q^{46} -9.74247i q^{47} +(6.92516 + 5.00270i) q^{48} +(4.12311 - 5.65685i) q^{49} +(-6.75195 - 2.10027i) q^{50} +10.6378i q^{51} +(1.94442 - 0.994066i) q^{52} +8.58800i q^{53} +(4.22402 - 1.01714i) q^{54} +(-2.57501 - 4.53448i) q^{55} +(-6.91734 - 2.85489i) q^{56} -5.49966i q^{57} +(-0.185917 - 0.772087i) q^{58} +14.3211 q^{59} +(7.98037 + 5.24831i) q^{60} +0.620058i q^{61} +(2.18379 + 9.06897i) q^{62} +(3.68260 - 1.87285i) q^{63} +(-1.21922 + 7.90655i) q^{64} +(2.12311 - 1.20565i) q^{65} +(1.64901 + 6.84809i) q^{66} +4.71659 q^{67} +(-8.86958 + 4.53448i) q^{68} +12.9020i q^{69} +(-7.86634 - 2.84968i) q^{70} +11.9473i q^{71} +(-2.87529 - 3.35265i) q^{72} +9.96148 q^{73} +(7.56155 - 1.82081i) q^{74} +(9.17104 + 5.47091i) q^{75} +(4.58552 - 2.34430i) q^{76} +(-2.79695 - 5.49966i) q^{77} +(-3.20636 + 0.772087i) q^{78} -10.6378i q^{79} +(-0.974211 + 8.89106i) q^{80} -11.2462 q^{81} +(11.6665 - 2.80928i) q^{82} -3.86098i q^{83} +(9.14707 + 6.63736i) q^{84} +(-9.68466 + 5.49966i) q^{85} +(0.438447 + 1.82081i) q^{86} +1.19935i q^{87} +(-5.00691 + 4.29400i) q^{88} -2.82843i q^{89} +(-3.37594 - 3.60382i) q^{90} +(2.57501 - 1.30957i) q^{91} +(-10.7575 + 5.49966i) q^{92} -14.0877i q^{93} +(-13.3951 + 3.22550i) q^{94} +(5.00691 - 2.84329i) q^{95} +(4.58552 - 11.1778i) q^{96} -14.9422 q^{97} +(-9.14275 - 3.79606i) q^{98} -3.64162i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 8 q^{9} - 4 q^{14} - 12 q^{16} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 4 q^{30} + 28 q^{36} + 32 q^{44} - 32 q^{46} - 12 q^{50} - 20 q^{56} + 44 q^{60} - 36 q^{64} - 32 q^{65} + 40 q^{70}+ \cdots + 40 q^{86}+O(q^{100}) \) 16 * q - 12 * q^4 + 8 * q^9 - 4 * q^14 - 12 * q^16 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 4 * q^30 + 28 * q^36 + 32 * q^44 - 32 * q^46 - 12 * q^50 - 20 * q^56 + 44 * q^60 - 36 * q^64 - 32 * q^65 + 40 * q^70 + 88 * q^74 - 48 * q^81 + 40 * q^84 - 56 * q^85 + 40 * q^86

Introduction

L-functions

Modular forms

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