LMFDB - Embedded newform 40.3.i.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(13,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.i (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:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$1.39859 + 0.209644i$ of defining polynomial
Character	$\chi$	$=$	40.13
Dual form			40.3.i.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60823 - 1.18894i) q^{2} +(-2.52630 + 2.52630i) q^{3} +(1.17282 + 3.82420i) q^{4} +(3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 + 5.20520i) q^{7} +(2.66059 - 7.54462i) q^{8} -3.76437i q^{9} +(-0.299408 - 9.99552i) q^{10} -2.49236i q^{11} +(-12.6240 - 6.69817i) q^{12} +(-6.65988 + 6.65988i) q^{13} +(14.5599 - 2.18248i) q^{14} +(-17.7376 - 2.11798i) q^{15} +(-13.2490 + 8.97020i) q^{16} +(21.9428 - 21.9428i) q^{17} +(-4.47563 + 6.05398i) q^{18} +17.5567 q^{19} +(-11.4026 + 16.4311i) q^{20} -26.2998i q^{21} +(-2.96328 + 4.00830i) q^{22} +(20.1791 + 20.1791i) q^{23} +(12.3385 + 25.7814i) q^{24} +(-5.88639 + 24.2971i) q^{25} +(18.6289 - 2.79240i) q^{26} +(-13.2268 - 13.2268i) q^{27} +(-26.0105 - 13.8010i) q^{28} +1.04754 q^{29} +(26.0081 + 24.4953i) q^{30} -2.47263 q^{31} +(31.9725 + 1.32614i) q^{32} +(6.29646 + 6.29646i) q^{33} +(-61.3780 + 9.20035i) q^{34} +(-36.5467 - 4.36391i) q^{35} +(14.3957 - 4.41493i) q^{36} +(19.2786 + 19.2786i) q^{37} +(-28.2353 - 20.8740i) q^{38} -33.6497i q^{39} +(37.8737 - 12.8680i) q^{40} -43.9414 q^{41} +(-31.2690 + 42.2962i) q^{42} +(32.9394 - 32.9394i) q^{43} +(9.53129 - 2.92310i) q^{44} +(14.7932 - 11.6372i) q^{45} +(-8.46086 - 56.4446i) q^{46} +(33.7079 - 33.7079i) q^{47} +(10.8095 - 56.1323i) q^{48} -5.18827i q^{49} +(38.3546 - 32.0768i) q^{50} +110.868i q^{51} +(-33.2795 - 17.6578i) q^{52} +(-36.4034 + 36.4034i) q^{53} +(5.54582 + 36.9976i) q^{54} +(9.79445 - 7.70491i) q^{55} +(25.4224 + 53.1202i) q^{56} +(-44.3536 + 44.3536i) q^{57} +(-1.68469 - 1.24547i) q^{58} +30.5963 q^{59} +(-12.7035 - 70.3162i) q^{60} -23.8366i q^{61} +(3.97657 + 2.93982i) q^{62} +(19.5943 + 19.5943i) q^{63} +(-49.8425 - 40.1463i) q^{64} +(-46.7603 - 5.58347i) q^{65} +(-2.64003 - 17.6123i) q^{66} +(19.9932 + 19.9932i) q^{67} +(109.649 + 58.1787i) q^{68} -101.957 q^{69} +(53.5872 + 50.4702i) q^{70} -21.8350 q^{71} +(-28.4007 - 10.0154i) q^{72} +(32.6450 + 32.6450i) q^{73} +(-8.08328 - 53.9257i) q^{74} +(-46.5110 - 76.2526i) q^{75} +(20.5909 + 67.1405i) q^{76} +(12.9733 + 12.9733i) q^{77} +(-40.0076 + 54.1165i) q^{78} +16.4124i q^{79} +(-76.2090 - 24.3351i) q^{80} +100.709 q^{81} +(70.6680 + 52.2439i) q^{82} +(-0.343799 + 0.343799i) q^{83} +(100.576 - 30.8450i) q^{84} +(154.065 + 18.3963i) q^{85} +(-92.1373 + 13.8111i) q^{86} +(-2.64640 + 2.64640i) q^{87} +(-18.8039 - 6.63116i) q^{88} -84.4631i q^{89} +(-37.6268 + 1.12708i) q^{90} -69.3320i q^{91} +(-53.5025 + 100.836i) q^{92} +(6.24661 - 6.24661i) q^{93} +(-94.2869 + 14.1333i) q^{94} +(54.2751 + 68.9942i) q^{95} +(-84.1223 + 77.4219i) q^{96} +(-24.1311 + 24.1311i) q^{97} +(-6.16856 + 8.34394i) q^{98} -9.38218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.60823	−	1.18894i	−0.804116	−	0.594472i
$2$	−1.60823	−	1.18894i	−0.804116	−	0.594472i
$3$	−2.52630	+	2.52630i	−0.842100	+	0.842100i	−0.989132	−	0.147032i	$-0.953028\pi$
$3$	−2.52630	+	2.52630i	−0.842100	+	0.842100i	0.147032	+	0.989132i	$0.453028\pi$
$4$	1.17282	+	3.82420i	0.293205	+	0.956049i
$5$	3.09141	+	3.92978i	0.618282	+	0.785957i
$5$	3.09141	+	3.92978i	0.618282	+	0.785957i
$6$	7.06650	−	1.05925i	1.17775	−	0.176541i
$7$	−5.20520	+	5.20520i	−0.743600	+	0.743600i	−0.973269	−	0.229669i	$-0.926236\pi$
$7$	−5.20520	+	5.20520i	−0.743600	+	0.743600i	0.229669	+	0.973269i	$0.426236\pi$
$8$	2.66059	−	7.54462i	0.332574	−	0.943077i
$9$		−	3.76437i		−	0.418263i
$10$	−0.299408	−	9.99552i	−0.0299408	−	0.999552i
$11$		−	2.49236i		−	0.226579i	−0.993562	−	0.113289i	$-0.963861\pi$
$11$		−	2.49236i		−	0.226579i	0.993562	−	0.113289i	$-0.0361387\pi$
$12$	−12.6240	−	6.69817i	−1.05200	−	0.558181i
$13$	−6.65988	+	6.65988i	−0.512298	+	0.512298i	−0.915230	−	0.402932i	$-0.867991\pi$
$13$	−6.65988	+	6.65988i	−0.512298	+	0.512298i	0.402932	+	0.915230i	$0.367991\pi$
$14$	14.5599	−	2.18248i	1.03999	−	0.155891i
$15$	−17.7376	−	2.11798i	−1.18251	−	0.141199i
$16$	−13.2490	+	8.97020i	−0.828061	+	0.560638i
$17$	21.9428	−	21.9428i	1.29075	−	1.29075i	0.356434	−	0.934320i	$-0.383992\pi$
$17$	21.9428	−	21.9428i	1.29075	−	1.29075i	0.934320	−	0.356434i	$-0.116008\pi$
$18$	−4.47563	+	6.05398i	−0.248646	+	0.336332i
$19$	17.5567			0.924039			0.462020	−	0.886870i	$-0.347125\pi$
$19$	17.5567			0.924039			0.462020	+	0.886870i	$0.347125\pi$
$20$	−11.4026	+	16.4311i	−0.570130	+	0.821555i
$21$		−	26.2998i		−	1.25237i
$22$	−2.96328	+	4.00830i	−0.134695	+	0.182195i
$23$	20.1791	+	20.1791i	0.877354	+	0.877354i	0.993260	−	0.115906i	$-0.0369772\pi$
$23$	20.1791	+	20.1791i	0.877354	+	0.877354i	−0.115906	+	0.993260i	$0.536977\pi$
$24$	12.3385	+	25.7814i	0.514105	+	1.07423i
$25$	−5.88639	+	24.2971i	−0.235455	+	0.971885i
$26$	18.6289	−	2.79240i	0.716495	−	0.107400i
$27$	−13.2268	−	13.2268i	−0.489880	−	0.489880i
$28$	−26.0105	−	13.8010i	−0.928946	−	0.492891i
$29$	1.04754			0.0361220			0.0180610	−	0.999837i	$-0.494251\pi$
$29$	1.04754			0.0361220			0.0180610	+	0.999837i	$0.494251\pi$
$30$	26.0081	+	24.4953i	0.866935	+	0.816509i
$31$	−2.47263			−0.0797623			−0.0398812	−	0.999204i	$-0.512698\pi$
$31$	−2.47263			−0.0797623			−0.0398812	+	0.999204i	$0.512698\pi$
$32$	31.9725	+	1.32614i	0.999141	+	0.0414418i
$33$	6.29646	+	6.29646i	0.190802	+	0.190802i
$34$	−61.3780	+	9.20035i	−1.80523	+	0.270599i
$35$	−36.5467	−	4.36391i	−1.04419	−	0.124683i
$36$	14.3957	−	4.41493i	0.399880	−	0.122637i
$37$	19.2786	+	19.2786i	0.521043	+	0.521043i	0.917886	−	0.396843i	$-0.129894\pi$
$37$	19.2786	+	19.2786i	0.521043	+	0.521043i	−0.396843	+	0.917886i	$0.629894\pi$
$38$	−28.2353	−	20.8740i	−0.743035	−	0.549316i
$39$		−	33.6497i		−	0.862813i
$40$	37.8737	−	12.8680i	0.946842	−	0.321699i
$41$	−43.9414			−1.07174			−0.535871	−	0.844300i	$-0.680017\pi$
$41$	−43.9414			−1.07174			−0.535871	+	0.844300i	$0.680017\pi$
$42$	−31.2690	+	42.2962i	−0.744500	+	1.00705i
$43$	32.9394	−	32.9394i	0.766032	−	0.766032i	−0.211373	−	0.977405i	$-0.567794\pi$
$43$	32.9394	−	32.9394i	0.766032	−	0.766032i	0.977405	+	0.211373i	$0.0677936\pi$
$44$	9.53129	−	2.92310i	0.216620	−	0.0664340i
$45$	14.7932	−	11.6372i	0.328737	−	0.258604i
$46$	−8.46086	−	56.4446i	−0.183932	−	1.22706i
$47$	33.7079	−	33.7079i	0.717189	−	0.717189i	−0.250840	−	0.968029i	$-0.580707\pi$
$47$	33.7079	−	33.7079i	0.717189	−	0.717189i	0.968029	+	0.250840i	$0.0807067\pi$
$48$	10.8095	−	56.1323i	0.225197	−	1.16942i
$49$		−	5.18827i		−	0.105883i
$50$	38.3546	−	32.0768i	0.767092	−	0.641537i
$51$			110.868i			2.17389i
$52$	−33.2795	−	17.6578i	−0.639991	−	0.339574i
$53$	−36.4034	+	36.4034i	−0.686856	+	0.686856i	−0.961536	−	0.274679i	$-0.911428\pi$
$53$	−36.4034	+	36.4034i	−0.686856	+	0.686856i	0.274679	+	0.961536i	$0.411428\pi$
$54$	5.54582	+	36.9976i	0.102700	+	0.685141i
$55$	9.79445	−	7.70491i	0.178081	−	0.140089i
$56$	25.4224	+	53.1202i	0.453971	+	0.948575i
$57$	−44.3536	+	44.3536i	−0.778133	+	0.778133i
$58$	−1.68469	−	1.24547i	−0.0290463	−	0.0214736i
$59$	30.5963			0.518581			0.259291	−	0.965799i	$-0.416511\pi$
$59$	30.5963			0.518581			0.259291	+	0.965799i	$0.416511\pi$
$60$	−12.7035	−	70.3162i	−0.211725	−	1.17194i
$61$		−	23.8366i		−	0.390764i	−0.980727	−	0.195382i	$-0.937405\pi$
$61$		−	23.8366i		−	0.390764i	0.980727	−	0.195382i	$-0.0625947\pi$
$62$	3.97657	+	2.93982i	0.0641382	+	0.0474165i
$63$	19.5943	+	19.5943i	0.311021	+	0.311021i
$64$	−49.8425	−	40.1463i	−0.778789	−	0.627286i
$65$	−46.7603	−	5.58347i	−0.719389	−	0.0858996i
$66$	−2.64003	−	17.6123i	−0.0400004	−	0.266853i
$67$	19.9932	+	19.9932i	0.298407	+	0.298407i	0.840390	−	0.541983i	$-0.182326\pi$
$67$	19.9932	+	19.9932i	0.298407	+	0.298407i	−0.541983	+	0.840390i	$0.682326\pi$
$68$	109.649	+	58.1787i	1.61248	+	0.855569i
$69$	−101.957			−1.47764
$70$	53.5872	+	50.4702i	0.765531	+	0.721003i
$71$	−21.8350			−0.307535			−0.153767	−	0.988107i	$-0.549141\pi$
$71$	−21.8350			−0.307535			−0.153767	+	0.988107i	$0.549141\pi$
$72$	−28.4007	−	10.0154i	−0.394454	−	0.139103i
$73$	32.6450	+	32.6450i	0.447191	+	0.447191i	0.894420	−	0.447228i	$-0.147589\pi$
$73$	32.6450	+	32.6450i	0.447191	+	0.447191i	−0.447228	+	0.894420i	$0.647589\pi$
$74$	−8.08328	−	53.9257i	−0.109233	−	0.728725i
$75$	−46.5110	−	76.2526i	−0.620147	−	1.01670i
$76$	20.5909	+	67.1405i	0.270933	+	0.883427i
$77$	12.9733	+	12.9733i	0.168484	+	0.168484i
$78$	−40.0076	+	54.1165i	−0.512918	+	0.693801i
$79$			16.4124i			0.207753i	0.994590	+	0.103876i	$0.0331246\pi$
$79$			16.4124i			0.207753i	−0.994590	+	0.103876i	$0.966875\pi$
$80$	−76.2090	−	24.3351i	−0.952612	−	0.304188i
$81$	100.709			1.24332
$82$	70.6680	+	52.2439i	0.861805	+	0.637121i
$83$	−0.343799	+	0.343799i	−0.00414216	+	0.00414216i	−0.709175	−	0.705033i	$-0.750932\pi$
$83$	−0.343799	+	0.343799i	−0.00414216	+	0.00414216i	0.705033	+	0.709175i	$0.250932\pi$
$84$	100.576	−	30.8450i	1.19733	−	0.367202i
$85$	154.065	+	18.3963i	1.81253	+	0.216427i
$86$	−92.1373	+	13.8111i	−1.07136	+	0.160594i
$87$	−2.64640	+	2.64640i	−0.0304184	+	0.0304184i
$88$	−18.8039	−	6.63116i	−0.213681	−	0.0753541i
$89$		−	84.4631i		−	0.949024i	−0.880249	−	0.474512i	$-0.842625\pi$
$89$		−	84.4631i		−	0.949024i	0.880249	−	0.474512i	$-0.157375\pi$
$90$	−37.6268	+	1.12708i	−0.418076	+	0.0125232i
$91$		−	69.3320i		−	0.761891i
$92$	−53.5025	+	100.836i	−0.581549	+	1.09604i
$93$	6.24661	−	6.24661i	0.0671678	−	0.0671678i
$94$	−94.2869	+	14.1333i	−1.00305	+	0.150354i
$95$	54.2751	+	68.9942i	0.571316	+	0.726255i
$96$	−84.1223	+	77.4219i	−0.876274	+	0.806478i
$97$	−24.1311	+	24.1311i	−0.248774	+	0.248774i	−0.820467	−	0.571693i	$-0.806287\pi$
$97$	−24.1311	+	24.1311i	−0.248774	+	0.248774i	0.571693	+	0.820467i	$0.306287\pi$
$98$	−6.16856	+	8.34394i	−0.0629445	+	0.0851422i
$99$	−9.38218			−0.0947695
$100$	−99.8207	+	5.98548i	−0.998207	+	0.0598548i
$101$		−	152.095i		−	1.50589i	−0.658085	−	0.752944i	$-0.728633\pi$
$101$		−	152.095i		−	1.50589i	0.658085	−	0.752944i	$-0.271367\pi$
$102$	131.816	−	178.302i	1.29232	−	1.74806i
$103$	−120.657	−	120.657i	−1.17143	−	1.17143i	−0.981870	−	0.189558i	$-0.939295\pi$
$103$	−120.657	−	120.657i	−1.17143	−	1.17143i	−0.189558	−	0.981870i	$-0.560705\pi$
$104$	32.5270	+	67.9655i	0.312760	+	0.653514i
$105$	103.352	−	81.3034i	0.984309	−	0.774318i
$106$	101.827	−	15.2635i	0.960629	−	0.143995i
$107$	−75.2789	−	75.2789i	−0.703541	−	0.703541i	0.261628	−	0.965169i	$-0.415741\pi$
$107$	−75.2789	−	75.2789i	−0.703541	−	0.703541i	−0.965169	+	0.261628i	$0.915741\pi$
$108$	35.0691	−	66.0944i	0.324714	−	0.611985i
$109$	11.8614			0.108820			0.0544100	−	0.998519i	$-0.482672\pi$
$109$	11.8614			0.108820			0.0544100	+	0.998519i	$0.482672\pi$
$110$	−24.9125	+	0.746235i	−0.226477	+	0.00678395i
$111$	−97.4070			−0.877541
$112$	22.2719	−	115.655i	0.198856	−	1.03264i
$113$	−82.0090	−	82.0090i	−0.725743	−	0.725743i	0.244025	−	0.969769i	$-0.421532\pi$
$113$	−82.0090	−	82.0090i	−0.725743	−	0.725743i	−0.969769	+	0.244025i	$0.921532\pi$
$114$	124.065	−	18.5969i	1.08829	−	0.163131i
$115$	−16.9177	+	141.682i	−0.147110	+	1.23201i
$116$	1.22858	+	4.00600i	0.0105912	+	0.0345345i
$117$	25.0702	+	25.0702i	0.214276	+	0.214276i
$118$	−49.2059	−	36.3773i	−0.416999	−	0.308282i
$119$			228.434i			1.91961i
$120$	−63.1719	+	128.189i	−0.526433	+	1.06824i
$121$	114.788			0.948662
$122$	−28.3404	+	38.3348i	−0.232299	+	0.314220i
$123$	111.009	−	111.009i	0.902513	−	0.902513i
$124$	−2.89996	−	9.45584i	−0.0233867	−	0.0762567i
$125$	−113.680	+	51.9801i	−0.909437	+	0.415841i
$126$	−8.21565	−	54.8087i	−0.0652035	−	0.434990i
$127$	−55.8589	+	55.8589i	−0.439834	+	0.439834i	−0.891956	−	0.452122i	$-0.850667\pi$
$127$	−55.8589	+	55.8589i	−0.439834	+	0.439834i	0.452122	+	0.891956i	$0.350667\pi$
$128$	32.4266	+	123.825i	0.253333	+	0.967379i
$129$			166.429i			1.29015i
$130$	68.5630	+	64.5749i	0.527407	+	0.496730i
$131$			151.619i			1.15740i	0.815541	+	0.578700i	$0.196440\pi$
$131$			151.619i			1.15740i	−0.815541	+	0.578700i	$0.803560\pi$
$132$	−16.6943	+	31.4635i	−0.126472	+	0.238360i
$133$	−91.3864	+	91.3864i	−0.687116	+	0.687116i
$134$	−8.38292	−	55.9246i	−0.0625591	−	0.417348i
$135$	11.0890	−	92.8677i	0.0821406	−	0.687909i
$136$	−107.169	−	223.931i	−0.788010	−	1.64655i
$137$	68.2473	−	68.2473i	0.498156	−	0.498156i	−0.412708	−	0.910863i	$-0.635417\pi$
$137$	68.2473	−	68.2473i	0.498156	−	0.498156i	0.910863	+	0.412708i	$0.135417\pi$
$138$	163.971	+	121.221i	1.18819	+	0.878415i
$139$	69.7245			0.501615			0.250807	−	0.968037i	$-0.419304\pi$
$139$	69.7245			0.501615			0.250807	+	0.968037i	$0.419304\pi$
$140$	−26.1743	−	144.880i	−0.186959	−	1.03486i
$141$			170.312i			1.20789i
$142$	35.1157	+	25.9606i	0.247294	+	0.182821i
$143$	16.5988	+	16.5988i	0.116076	+	0.116076i
$144$	33.7671	+	49.8740i	0.234494	+	0.346348i
$145$	3.23837	+	4.11660i	0.0223336	+	0.0283904i
$146$	−13.6876	−	91.3138i	−0.0937509	−	0.625437i
$147$	13.1071	+	13.1071i	0.0891640	+	0.0891640i
$148$	−51.1148	+	96.3355i	−0.345370	+	0.650916i
$149$	78.9012			0.529538			0.264769	−	0.964312i	$-0.414704\pi$
$149$	78.9012			0.529538			0.264769	+	0.964312i	$0.414704\pi$
$150$	−15.8595	+	177.931i	−0.105730	+	1.18621i
$151$	197.562			1.30835			0.654177	−	0.756341i	$-0.273015\pi$
$151$	197.562			1.30835			0.654177	+	0.756341i	$0.273015\pi$
$152$	46.7113	−	132.459i	0.307311	−	0.871440i
$153$	−82.6009	−	82.6009i	−0.539875	−	0.539875i
$154$	−5.43953	−	36.2885i	−0.0353216	−	0.235640i
$155$	−7.64392	−	9.71691i	−0.0493156	−	0.0626897i
$156$	128.683	−	39.4651i	0.824891	−	0.252981i
$157$	−94.1106	−	94.1106i	−0.599431	−	0.599431i	0.340730	−	0.940161i	$-0.389326\pi$
$157$	−94.1106	−	94.1106i	−0.599431	−	0.599431i	−0.940161	+	0.340730i	$0.889326\pi$
$158$	19.5135	−	26.3950i	0.123503	−	0.167057i
$159$		−	183.932i		−	1.15680i
$160$	93.6287	+	129.745i	0.585179	+	0.810904i
$161$	−210.073			−1.30480
$162$	−161.963	−	119.737i	−0.999773	−	0.739119i
$163$	−132.980	+	132.980i	−0.815827	+	0.815827i	−0.985500	−	0.169673i	$-0.945729\pi$
$163$	−132.980	+	132.980i	−0.815827	+	0.815827i	0.169673	+	0.985500i	$0.445729\pi$
$164$	−51.5354	−	168.041i	−0.314240	−	1.02464i
$165$	−5.27879	+	44.2086i	−0.0319926	+	0.267931i
$166$	0.961668	−	0.144151i	0.00579318	−	0.000868378i
$167$	−51.4111	+	51.4111i	−0.307851	+	0.307851i	−0.844075	−	0.536225i	$-0.819850\pi$
$167$	−51.4111	+	51.4111i	−0.307851	+	0.307851i	0.536225	+	0.844075i	$0.319850\pi$
$168$	−198.422	−	69.9730i	−1.18108	−	0.416506i
$169$			80.2920i			0.475101i
$170$	−225.900	−	212.760i	−1.32882	−	1.25153i
$171$		−	66.0900i		−	0.386492i
$172$	164.599	+	87.3347i	0.956969	+	0.507760i
$173$	183.164	−	183.164i	1.05875	−	1.05875i	0.0605880	−	0.998163i	$-0.480702\pi$
$173$	183.164	−	183.164i	1.05875	−	1.05875i	0.998163	−	0.0605880i	$-0.0192976\pi$
$174$	7.40244	−	1.10960i	0.0425428	−	0.00637702i
$175$	−95.8316	−	157.111i	−0.547609	−	0.897779i
$176$	22.3570	+	33.0213i	0.127028	+	0.187621i
$177$	−77.2954	+	77.2954i	−0.436697	+	0.436697i
$178$	−100.422	+	135.836i	−0.564168	+	0.763125i
$179$	−31.3468			−0.175122			−0.0875610	−	0.996159i	$-0.527907\pi$
$179$	−31.3468			−0.175122			−0.0875610	+	0.996159i	$0.527907\pi$
$180$	61.8527	+	42.9236i	0.343626	+	0.238464i
$181$		−	57.4156i		−	0.317214i	−0.987342	−	0.158607i	$-0.949300\pi$
$181$		−	57.4156i		−	0.317214i	0.987342	−	0.158607i	$-0.0507002\pi$
$182$	−82.4320	+	111.502i	−0.452923	+	0.612648i
$183$	60.2184	+	60.2184i	0.329063	+	0.329063i
$184$	205.932	−	98.5555i	1.11920	−	0.535628i
$185$	−16.1627	+	135.359i	−0.0873659	+	0.731669i
$186$	−17.4729	+	2.61912i	−0.0939401	+	0.0140813i
$187$	−54.6895	−	54.6895i	−0.292457	−	0.292457i
$188$	168.439	+	89.3723i	0.895952	+	0.475385i
$189$	137.696			0.728550
$190$	−5.25664	−	175.489i	−0.0276665	−	0.923625i
$191$	161.923			0.847767			0.423884	−	0.905717i	$-0.360667\pi$
$191$	161.923			0.847767			0.423884	+	0.905717i	$0.360667\pi$
$192$	227.339	−	24.4956i	1.18405	−	0.127581i
$193$	63.0037	+	63.0037i	0.326444	+	0.326444i	0.851233	−	0.524789i	$-0.175856\pi$
$193$	63.0037	+	63.0037i	0.326444	+	0.326444i	−0.524789	+	0.851233i	$0.675856\pi$
$194$	67.4989	−	10.1179i	0.347933	−	0.0521540i
$195$	132.236	−	104.025i	0.678133	−	0.533461i
$196$	19.8410	−	6.08491i	0.101229	−	0.0310455i
$197$	−3.96178	−	3.96178i	−0.0201106	−	0.0201106i	0.696980	−	0.717091i	$-0.254527\pi$
$197$	−3.96178	−	3.96178i	−0.0201106	−	0.0201106i	−0.717091	+	0.696980i	$0.754527\pi$
$198$	15.0887	+	11.1549i	0.0762056	+	0.0563378i
$199$		−	123.026i		−	0.618221i	−0.951026	−	0.309110i	$-0.899969\pi$
$199$		−	123.026i		−	0.618221i	0.951026	−	0.309110i	$-0.100031\pi$
$200$	167.651	+	109.055i	0.838256	+	0.545276i
$201$	−101.018			−0.502576
$202$	−180.832	+	244.603i	−0.895208	+	1.21091i
$203$	−5.45265	+	5.45265i	−0.0268604	+	0.0268604i
$204$	−423.982	+	130.029i	−2.07834	+	0.637395i
$205$	−135.841	−	172.680i	−0.662639	−	0.842343i
$206$	50.5900	+	337.499i	0.245582	+	1.63834i
$207$	75.9617	−	75.9617i	0.366965	−	0.366965i
$208$	28.4961	−	147.977i	0.137001	−	0.711428i
$209$		−	43.7578i		−	0.209367i
$210$	−262.880	+	7.87438i	−1.25181	+	0.0374970i
$211$		−	273.854i		−	1.29789i	−0.760837	−	0.648943i	$-0.775211\pi$
$211$		−	273.854i		−	1.29789i	0.760837	−	0.648943i	$-0.224789\pi$
$212$	−181.908	−	96.5191i	−0.858059	−	0.455279i
$213$	55.1617	−	55.1617i	0.258975	−	0.258975i
$214$	31.5635	+	210.568i	0.147493	+	0.983964i
$215$	231.274	+	27.6155i	1.07569	+	0.128444i
$216$	−134.982	+	64.5999i	−0.624916	+	0.299074i
$217$	12.8706	−	12.8706i	0.0593113	−	0.0593113i
$218$	−19.0759	−	14.1025i	−0.0875040	−	0.0646905i
$219$	−164.942			−0.753159
$220$	40.9523	+	28.4194i	0.186147	+	0.129179i
$221$			292.273i			1.32250i
$222$	156.653	+	115.812i	0.705644	+	0.521674i
$223$	128.870	+	128.870i	0.577894	+	0.577894i	0.934323	−	0.356429i	$-0.116006\pi$
$223$	128.870	+	128.870i	0.577894	+	0.577894i	−0.356429	+	0.934323i	$0.616006\pi$
$224$	−173.326	+	159.521i	−0.773778	+	0.712145i
$225$	91.4634	+	22.1585i	0.406504	+	0.0984824i
$226$	34.3854	+	229.394i	0.152148	+	1.01502i
$227$	242.455	+	242.455i	1.06808	+	1.06808i	0.997506	+	0.0705768i	$0.0224840\pi$
$227$	242.455	+	242.455i	1.06808	+	1.06808i	0.0705768	+	0.997506i	$0.477516\pi$
$228$	−221.636	−	117.598i	−0.972086	−	0.515781i
$229$	−385.669			−1.68414			−0.842072	−	0.539365i	$-0.818664\pi$
$229$	−385.669			−1.68414			−0.842072	+	0.539365i	$0.818664\pi$
$230$	195.659	−	207.743i	0.850692	−	0.903229i
$231$	−65.5487			−0.283760
$232$	2.78707	−	7.90328i	0.0120132	−	0.0340659i
$233$	9.90826	+	9.90826i	0.0425247	+	0.0425247i	0.728049	−	0.685525i	$-0.240427\pi$
$233$	9.90826	+	9.90826i	0.0425247	+	0.0425247i	−0.685525	+	0.728049i	$0.740427\pi$
$234$	−10.5116	−	70.1259i	−0.0449215	−	0.299683i
$235$	236.669	+	28.2598i	1.00710	+	0.120255i
$236$	35.8840	+	117.006i	0.152051	+	0.495789i
$237$	−41.4627	−	41.4627i	−0.174948	−	0.174948i
$238$	271.595	−	367.374i	1.14116	−	1.54359i
$239$		−	44.7391i		−	0.187193i	−0.995610	−	0.0935965i	$-0.970164\pi$
$239$		−	44.7391i		−	0.187193i	0.995610	−	0.0935965i	$-0.0298364\pi$
$240$	254.004	−	131.049i	1.05835	−	0.546037i
$241$	−21.4785			−0.0891223			−0.0445611	−	0.999007i	$-0.514189\pi$
$241$	−21.4785			−0.0891223			−0.0445611	+	0.999007i	$0.514189\pi$
$242$	−184.606	−	136.477i	−0.762835	−	0.563953i
$243$	−135.380	+	135.380i	−0.557118	+	0.557118i
$244$	91.1560	−	27.9561i	0.373590	−	0.114574i
$245$	20.3888	−	16.0391i	0.0832194	−	0.0654655i
$246$	−310.512	+	46.5448i	−1.26224	+	0.189206i
$247$	−116.926	+	116.926i	−0.473384	+	0.473384i
$248$	−6.57866	+	18.6551i	−0.0265269	+	0.0752220i
$249$		−	1.73708i		−	0.00697623i
$250$	244.625	+	51.5627i	0.978499	+	0.206251i
$251$		−	149.651i		−	0.596218i	−0.954532	−	0.298109i	$-0.903644\pi$
$251$		−	149.651i		−	0.596218i	0.954532	−	0.298109i	$-0.0963560\pi$
$252$	−51.9519	+	97.9131i	−0.206158	+	0.388544i
$253$	50.2938	−	50.2938i	0.198790	−	0.198790i
$254$	156.247	−	23.4209i	0.615146	−	0.0922084i
$255$	−435.688	+	342.739i	−1.70858	+	1.34407i
$256$	95.0710	−	237.692i	0.371371	−	0.928485i
$257$	244.045	−	244.045i	0.949590	−	0.949590i	−0.0491992	−	0.998789i	$-0.515667\pi$
$257$	244.045	−	244.045i	0.949590	−	0.949590i	0.998789	+	0.0491992i	$0.0156669\pi$
$258$	197.875	−	267.657i	0.766959	−	1.03743i
$259$	−200.698			−0.774896
$260$	−33.4892	−	185.369i	−0.128804	−	0.712958i
$261$		−	3.94332i		−	0.0151085i
$262$	180.267	−	243.839i	0.688042	−	0.930683i
$263$	−241.557	−	241.557i	−0.918467	−	0.918467i	0.0784512	−	0.996918i	$-0.475003\pi$
$263$	−241.557	−	241.557i	−0.918467	−	0.918467i	−0.996918	+	0.0784512i	$0.975003\pi$
$264$	64.2566	−	30.7521i	0.243396	−	0.116485i
$265$	−255.595	−	30.5197i	−0.964510	−	0.115169i
$266$	255.624	−	38.3172i	0.960992	−	0.144050i
$267$	213.379	+	213.379i	0.799172	+	0.799172i
$268$	−53.0096	+	99.9066i	−0.197797	+	0.372786i
$269$	350.619			1.30342			0.651708	−	0.758470i	$-0.274053\pi$
$269$	350.619			1.30342			0.651708	+	0.758470i	$0.274053\pi$
$270$	−128.248	+	136.169i	−0.474993	+	0.504328i
$271$	−298.610			−1.10188			−0.550940	−	0.834545i	$-0.685731\pi$
$271$	−298.610			−1.10188			−0.550940	+	0.834545i	$0.685731\pi$
$272$	−93.8885	+	487.552i	−0.345178	+	1.79247i
$273$	175.153	+	175.153i	0.641588	+	0.641588i
$274$	−190.900	+	28.6153i	−0.696715	+	0.104435i
$275$	60.5573	+	14.6710i	0.220208	+	0.0533492i
$276$	−119.577	−	389.904i	−0.433252	−	1.41270i
$277$	275.798	+	275.798i	0.995660	+	0.995660i	0.999991	−	0.00433109i	$-0.00137863\pi$
$277$	275.798	+	275.798i	0.995660	+	0.995660i	−0.00433109	+	0.999991i	$0.501379\pi$
$278$	−112.133	−	82.8985i	−0.403357	−	0.298196i
$279$			9.30790i			0.0333617i
$280$	−130.160	+	264.120i	−0.464857	+	0.943287i
$281$	13.2859			0.0472808			0.0236404	−	0.999721i	$-0.492474\pi$
$281$	13.2859			0.0472808			0.0236404	+	0.999721i	$0.492474\pi$
$282$	202.492	−	273.902i	0.718057	−	0.971283i
$283$	−253.189	+	253.189i	−0.894662	+	0.894662i	−0.994958	−	0.100296i	$-0.968021\pi$
$283$	−253.189	+	253.189i	−0.894662	+	0.894662i	0.100296	+	0.994958i	$0.468021\pi$
$284$	−25.6085	−	83.5013i	−0.0901709	−	0.294019i
$285$	−311.415	−	37.1849i	−1.09268	−	0.130473i
$286$	−6.95969	−	46.4299i	−0.0243346	−	0.162342i
$287$	228.724	−	228.724i	0.796948	−	0.796948i
$288$	4.99207	−	120.356i	0.0173336	−	0.417904i
$289$		−	673.975i		−	2.33209i
$290$	−0.313642	−	10.4707i	−0.00108152	−	0.0361058i
$291$		−	121.925i		−	0.418985i
$292$	−86.5541	+	163.128i	−0.296418	+	0.558656i
$293$	−143.408	+	143.408i	−0.489447	+	0.489447i	−0.908132	−	0.418685i	$-0.862491\pi$
$293$	−143.408	+	143.408i	−0.489447	+	0.489447i	0.418685	+	0.908132i	$0.362491\pi$
$294$	−5.49565	−	36.6629i	−0.0186927	−	0.124704i
$295$	94.5856	+	120.237i	0.320629	+	0.407582i
$296$	196.742	−	94.1572i	0.664669	−	0.318099i
$297$	−32.9659	+	32.9659i	−0.110996	+	0.110996i
$298$	−126.891	−	93.8092i	−0.425810	−	0.314796i
$299$	−268.781			−0.898934
$300$	237.056	−	267.298i	0.790186	−	0.890993i
$301$			342.912i			1.13924i
$302$	−317.725	−	234.890i	−1.05207	−	0.777781i
$303$	384.236	+	384.236i	1.26811	+	1.26811i
$304$	−232.609	+	157.488i	−0.765161	+	0.518051i
$305$	93.6728	−	73.6888i	0.307124	−	0.241602i
$306$	34.6335	+	231.049i	0.113181	+	0.755063i
$307$	−357.761	−	357.761i	−1.16535	−	1.16535i	−0.983288	−	0.182059i	$-0.941724\pi$
$307$	−357.761	−	357.761i	−1.16535	−	1.16535i	−0.182059	−	0.983288i	$-0.558276\pi$
$308$	−34.3970	+	64.8276i	−0.111679	+	0.210479i
$309$	609.631			1.97292
$310$	0.740327	+	24.7152i	0.00238815	+	0.0797266i
$311$	−380.204			−1.22252			−0.611261	−	0.791429i	$-0.709337\pi$
$311$	−380.204			−1.22252			−0.611261	+	0.791429i	$0.709337\pi$
$312$	−253.874	−	89.5280i	−0.813699	−	0.286949i
$313$	270.798	+	270.798i	0.865169	+	0.865169i	0.991933	−	0.126764i	$-0.0404591\pi$
$313$	270.798	+	270.798i	0.865169	+	0.865169i	−0.126764	+	0.991933i	$0.540459\pi$
$314$	39.4594	+	263.244i	0.125667	+	0.838357i
$315$	−16.4274	+	137.575i	−0.0521503	+	0.436747i
$316$	−62.7645	+	19.2489i	−0.198622	+	0.0609141i
$317$	−238.939	−	238.939i	−0.753752	−	0.753752i	0.221426	−	0.975177i	$-0.428929\pi$
$317$	−238.939	−	238.939i	−0.753752	−	0.753752i	−0.975177	+	0.221426i	$0.928929\pi$
$318$	−218.685	+	295.805i	−0.687687	+	0.930204i
$319$		−	2.61085i		−	0.00818448i
$320$	3.68258	−	319.979i	0.0115081	−	0.999934i
$321$	380.354			1.18490
$322$	337.846	+	249.765i	1.04921	+	0.775668i
$323$	385.245	−	385.245i	1.19271	−	1.19271i
$324$	118.113	+	385.131i	0.364548	+	1.18867i
$325$	−122.613	−	201.019i	−0.377272	−	0.618519i
$326$	371.968	−	55.7568i	1.14101	−	0.171033i
$327$	−29.9654	+	29.9654i	−0.0916373	+	0.0916373i
$328$	−116.910	+	331.521i	−0.356433	+	1.01074i
$329$			350.913i			1.06660i
$330$	61.0511	−	64.8215i	0.185003	−	0.196429i
$331$			73.0725i			0.220763i	0.993889	+	0.110381i	$0.0352072\pi$
$331$			73.0725i			0.220763i	−0.993889	+	0.110381i	$0.964793\pi$
$332$	−1.71797	−	0.911542i	−0.00517462	−	0.00274561i
$333$	72.5718	−	72.5718i	0.217933	−	0.217933i
$334$	143.806	−	21.5560i	0.430557	−	0.0645390i
$335$	−16.7618	+	140.376i	−0.0500353	+	0.419034i
$336$	235.914	+	348.445i	0.702126	+	1.03704i
$337$	−207.932	+	207.932i	−0.617008	+	0.617008i	−0.944763	−	0.327755i	$-0.893708\pi$
$337$	−207.932	+	207.932i	−0.617008	+	0.617008i	0.327755	+	0.944763i	$0.393708\pi$
$338$	95.4627	−	129.128i	0.282434	−	0.382036i
$339$	414.358			1.22230
$340$	110.339	+	610.750i	0.324528	+	1.79632i
$341$			6.16270i			0.0180724i
$342$	−78.5774	+	106.288i	−0.229759	+	0.310784i
$343$	−228.049	−	228.049i	−0.664866	−	0.664866i
$344$	−160.877	−	336.153i	−0.467665	−	0.977189i
$345$	−315.191	−	400.669i	−0.913597	−	1.16136i
$346$	−512.342	+	76.7983i	−1.48076	+	0.221961i
$347$	150.516	+	150.516i	0.433765	+	0.433765i	0.889907	−	0.456142i	$-0.150769\pi$
$347$	150.516	+	150.516i	0.433765	+	0.433765i	−0.456142	+	0.889907i	$0.650769\pi$
$348$	−13.2241	−	7.01659i	−0.0380003	−	0.0201626i
$349$	−159.797			−0.457871			−0.228935	−	0.973442i	$-0.573524\pi$
$349$	−159.797			−0.457871			−0.228935	+	0.973442i	$0.573524\pi$
$350$	−32.6771	+	366.610i	−0.0933632	+	1.04746i
$351$	176.177			0.501930
$352$	3.30521	−	79.6871i	0.00938981	−	0.226384i
$353$	31.8920	+	31.8920i	0.0903455	+	0.0903455i	0.750835	−	0.660490i	$-0.229651\pi$
$353$	31.8920	+	31.8920i	0.0903455	+	0.0903455i	−0.660490	+	0.750835i	$0.729651\pi$
$354$	216.209	−	32.4090i	0.610759	−	0.0915508i
$355$	−67.5008	−	85.8067i	−0.190143	−	0.241709i
$356$	323.004	−	99.0601i	0.907314	−	0.278259i
$357$	−577.092	−	577.092i	−1.61650	−	1.61650i
$358$	50.4130	+	37.2697i	0.140818	+	0.104105i
$359$			374.114i			1.04210i	0.853526	+	0.521050i	$0.174459\pi$
$359$			374.114i			1.04210i	−0.853526	+	0.521050i	$0.825541\pi$
$360$	−48.4397	−	142.571i	−0.134555	−	0.396029i
$361$	−52.7608			−0.146152
$362$	−68.2640	+	92.3377i	−0.188575	+	0.255076i
$363$	−289.989	+	289.989i	−0.798868	+	0.798868i
$364$	265.139	−	81.3141i	0.728405	−	0.223390i
$365$	−27.3687	+	229.207i	−0.0749828	+	0.627963i
$366$	−25.2488	−	168.442i	−0.0689859	−	0.460223i
$367$	195.775	−	195.775i	0.533446	−	0.533446i	−0.388150	−	0.921596i	$-0.626886\pi$
$367$	195.775	−	195.775i	0.533446	−	0.533446i	0.921596	+	0.388150i	$0.126886\pi$
$368$	−448.364	−	86.3421i	−1.21838	−	0.234625i
$369$			165.412i			0.448270i
$370$	186.927	−	198.472i	0.505209	−	0.536410i
$371$		−	378.974i		−	1.02149i
$372$	31.2144	+	16.5621i	0.0839097	+	0.0445218i
$373$	342.423	−	342.423i	0.918023	−	0.918023i	−0.0788627	−	0.996885i	$-0.525129\pi$
$373$	342.423	−	342.423i	0.918023	−	0.918023i	0.996885	+	0.0788627i	$0.0251289\pi$
$374$	22.9306	+	152.976i	0.0613118	+	0.409027i
$375$	155.871	−	418.506i	0.415657	−	1.11602i
$376$	−164.630	−	343.996i	−0.437846	−	0.914883i
$377$	−6.97649	+	6.97649i	−0.0185053	+	0.0185053i
$378$	−221.447	−	163.713i	−0.585839	−	0.433103i
$379$	607.050			1.60171			0.800857	−	0.598855i	$-0.204378\pi$
$379$	607.050			1.60171			0.800857	+	0.598855i	$0.204378\pi$
$380$	−200.192	+	288.476i	−0.526822	+	0.759148i
$381$		−	282.232i		−	0.740767i
$382$	−260.411	−	192.518i	−0.681703	−	0.503974i
$383$	−154.687	−	154.687i	−0.403882	−	0.403882i	0.475717	−	0.879599i	$-0.342189\pi$
$383$	−154.687	−	154.687i	−0.403882	−	0.403882i	−0.879599	+	0.475717i	$0.842189\pi$
$384$	−394.737	−	230.898i	−1.02796	−	0.601298i
$385$	−10.8764	+	91.0877i	−0.0282505	+	0.236592i
$386$	−26.4167	−	176.233i	−0.0684370	−	0.456561i
$387$	−123.996	−	123.996i	−0.320403	−	0.320403i
$388$	−120.584	−	63.9806i	−0.310782	−	0.164899i
$389$	−323.730			−0.832210			−0.416105	−	0.909317i	$-0.636605\pi$
$389$	−323.730			−0.832210			−0.416105	+	0.909317i	$0.636605\pi$
$390$	−336.346	+	10.0750i	−0.862426	+	0.0258333i
$391$	885.575			2.26490
$392$	−39.1435	−	13.8039i	−0.0998559	−	0.0352139i
$393$	−383.036	−	383.036i	−0.974645	−	0.974645i
$394$	1.66113	+	11.0818i	0.00421605	+	0.0281264i
$395$	−64.4974	+	50.7376i	−0.163284	+	0.128450i
$396$	−11.0036	−	35.8793i	−0.0277869	−	0.0906043i
$397$	376.174	+	376.174i	0.947543	+	0.947543i	0.998691	−	0.0511485i	$-0.0162882\pi$
$397$	376.174	+	376.174i	0.947543	+	0.947543i	−0.0511485	+	0.998691i	$0.516288\pi$
$398$	−146.271	+	197.854i	−0.367515	+	0.497121i
$399$		−	461.739i		−	1.15724i
$400$	−139.962	−	374.714i	−0.349904	−	0.936786i
$401$	−401.761			−1.00190			−0.500948	−	0.865477i	$-0.667015\pi$
$401$	−401.761			−1.00190			−0.500948	+	0.865477i	$0.667015\pi$
$402$	162.460	+	120.105i	0.404130	+	0.298768i
$403$	16.4674	−	16.4674i	0.0408621	−	0.0408621i
$404$	581.640	−	178.380i	1.43970	−	0.441534i
$405$	311.332	+	395.764i	0.768721	+	0.977195i
$406$	15.2520	−	2.28623i	0.0375666	−	0.00563111i
$407$	48.0493	−	48.0493i	0.118057	−	0.118057i
$408$	836.459	+	294.975i	2.05014	+	0.722978i
$409$			166.880i			0.408020i	0.978969	+	0.204010i	$0.0653974\pi$
$409$			166.880i			0.408020i	−0.978969	+	0.204010i	$0.934603\pi$
$410$	13.1564	+	439.217i	0.0320889	+	1.07126i
$411$			344.826i			0.838993i
$412$	319.907	−	602.925i	0.776474	−	1.46341i
$413$	−159.260	+	159.260i	−0.385617	+	0.385617i
$414$	−212.478	+	31.8498i	−0.513233	+	0.0769319i
$415$	−2.41388	−	0.288233i	−0.00581658	−	0.000694536i
$416$	−221.765	+	204.101i	−0.533089	+	0.490628i
$417$	−176.145	+	176.145i	−0.422410	+	0.422410i
$418$	−52.0256	+	70.3727i	−0.124463	+	0.168356i
$419$	−533.694			−1.27373			−0.636866	−	0.770974i	$-0.719770\pi$
$419$	−533.694			−1.27373			−0.636866	+	0.770974i	$0.719770\pi$
$420$	432.134	+	299.886i	1.02889	+	0.714014i
$421$			214.523i			0.509556i	0.967000	+	0.254778i	$0.0820023\pi$
$421$			214.523i			0.509556i	−0.967000	+	0.254778i	$0.917998\pi$
$422$	−325.597	+	440.421i	−0.771558	+	1.04365i
$423$	−126.889	−	126.889i	−0.299974	−	0.299974i
$424$	177.795	+	371.504i	0.419328	+	0.876189i
$425$	403.984	+	662.312i	0.950550	+	1.55838i
$426$	−154.297	+	23.1286i	−0.362199	+	0.0542925i
$427$	124.074	+	124.074i	0.290573	+	0.290573i
$428$	199.593	−	376.170i	0.466338	−	0.878902i
$429$	−83.8673			−0.195495
$430$	−339.108	−	319.384i	−0.788624	−	0.742753i
$431$	−525.371			−1.21896			−0.609479	−	0.792802i	$-0.708621\pi$
$431$	−525.371			−1.21896			−0.609479	+	0.792802i	$0.708621\pi$
$432$	293.888	+	56.5944i	0.680296	+	0.131006i
$433$	−262.829	−	262.829i	−0.606994	−	0.606994i	0.335165	−	0.942159i	$-0.391208\pi$
$433$	−262.829	−	262.829i	−0.606994	−	0.606994i	−0.942159	+	0.335165i	$0.891208\pi$
$434$	−36.0012	+	5.39646i	−0.0829521	+	0.0124342i
$435$	−18.5809	−	2.21867i	−0.0427146	−	0.00510039i
$436$	13.9113	+	45.3603i	0.0319066	+	0.104037i
$437$	354.280	+	354.280i	0.810709	+	0.810709i
$438$	265.265	+	196.107i	0.605627	+	0.447732i
$439$			419.145i			0.954771i	0.878694	+	0.477386i	$0.158416\pi$
$439$			419.145i			0.954771i	−0.878694	+	0.477386i	$0.841584\pi$
$440$	−32.0716	−	94.3950i	−0.0728900	−	0.214534i
$441$	−19.5306			−0.0442870
$442$	347.497	−	470.043i	0.786191	−	1.06345i
$443$	−119.234	+	119.234i	−0.269152	+	0.269152i	−0.828758	−	0.559606i	$-0.810952\pi$
$443$	−119.234	+	119.234i	−0.269152	+	0.269152i	0.559606	+	0.828758i	$0.310952\pi$
$444$	−114.241	−	372.504i	−0.257300	−	0.838972i
$445$	331.922	−	261.110i	0.745891	−	0.586764i
$446$	−54.0337	−	360.473i	−0.121152	−	0.808236i
$447$	−199.328	+	199.328i	−0.445924	+	0.445924i
$448$	468.410	−	50.4709i	1.04556	−	0.112658i
$449$			596.070i			1.32755i	0.747932	+	0.663775i	$0.231047\pi$
$449$			596.070i			1.32755i	−0.747932	+	0.663775i	$0.768953\pi$
$450$	−120.749	−	144.381i	−0.268331	−	0.320846i
$451$			109.518i			0.242834i
$452$	217.437	−	409.801i	0.481055	−	0.906639i
$453$	−499.099	+	499.099i	−1.10176	+	1.10176i
$454$	−101.658	−	678.189i	−0.223917	−	1.49381i
$455$	272.460	−	214.334i	0.598813	−	0.471063i
$456$	216.624	+	452.637i	0.475053	+	0.992626i
$457$	144.279	−	144.279i	0.315708	−	0.315708i	−0.531408	−	0.847116i	$-0.678337\pi$
$457$	144.279	−	144.279i	0.315708	−	0.315708i	0.847116	+	0.531408i	$0.178337\pi$
$458$	620.245	+	458.539i	1.35425	+	1.00118i
$459$	−580.465			−1.26463
$460$	−561.660	+	101.471i	−1.22100	+	0.220588i
$461$		−	743.994i		−	1.61387i	−0.590640	−	0.806935i	$-0.701125\pi$
$461$		−	743.994i		−	1.61387i	0.590640	−	0.806935i	$-0.298875\pi$
$462$	105.417	+	77.9337i	0.228176	+	0.168688i
$463$	446.519	+	446.519i	0.964404	+	0.964404i	0.999388	−	0.0349842i	$-0.0111381\pi$
$463$	446.519	+	446.519i	0.964404	+	0.964404i	−0.0349842	+	0.999388i	$0.511138\pi$
$464$	−13.8788	+	9.39664i	−0.0299113	+	0.0202514i
$465$	43.8586	+	5.23700i	0.0943196	+	0.0112624i
$466$	−4.15441	−	27.7152i	−0.00891504	−	0.0594746i
$467$	5.61916	+	5.61916i	0.0120325	+	0.0120325i	0.713097	−	0.701065i	$-0.247292\pi$
$467$	5.61916	+	5.61916i	0.0120325	+	0.0120325i	−0.701065	+	0.713097i	$0.747292\pi$
$468$	−66.4707	+	125.276i	−0.142031	+	0.267685i
$469$	−208.138			−0.443791
$470$	−347.020	−	326.835i	−0.738341	−	0.695394i
$471$	475.503			1.00956
$472$	81.4042	−	230.837i	0.172467	−	0.489062i
$473$	−82.0969	−	82.0969i	−0.173566	−	0.173566i
$474$	17.3848	+	115.979i	0.0366768	+	0.244681i
$475$	−103.346	+	426.578i	−0.217570	+	0.898060i
$476$	−873.576	+	267.912i	−1.83524	+	0.562840i
$477$	137.036	+	137.036i	0.287287	+	0.287287i
$478$	−53.1923	+	71.9509i	−0.111281	+	0.150525i
$479$		−	765.340i		−	1.59779i	−0.601472	−	0.798894i	$-0.705419\pi$
$479$		−	765.340i		−	1.59779i	0.601472	−	0.798894i	$-0.294581\pi$
$480$	−564.308	−	91.2398i	−1.17564	−	0.190083i
$481$	−256.786			−0.533859
$482$	34.5424	+	25.5367i	0.0716647	+	0.0529807i
$483$	530.707	−	530.707i	1.09877	−	1.09877i
$484$	134.626	+	438.973i	0.278153	+	0.906968i
$485$	−169.429	−	20.2309i	−0.349338	−	0.0417132i
$486$	378.681	−	56.7630i	0.779179	−	0.116796i
$487$	−611.323	+	611.323i	−1.25528	+	1.25528i	−0.301963	+	0.953320i	$0.597642\pi$
$487$	−611.323	+	611.323i	−1.25528	+	1.25528i	−0.953320	+	0.301963i	$0.902358\pi$
$488$	−179.838	−	63.4195i	−0.368521	−	0.129958i
$489$		−	671.893i		−	1.37402i
$490$	−51.8594	+	1.55341i	−0.105836	+	0.00317023i
$491$			899.211i			1.83139i	0.401877	+	0.915694i	$0.368358\pi$
$491$			899.211i			1.83139i	−0.401877	+	0.915694i	$0.631642\pi$
$492$	554.715	+	294.327i	1.12747	+	0.598226i
$493$	22.9860	−	22.9860i	0.0466247	−	0.0466247i
$494$	327.062	−	49.0255i	0.662069	−	0.0992419i
$495$	−29.0041	−	36.8699i	−0.0585942	−	0.0744847i
$496$	32.7599	−	22.1800i	0.0660481	−	0.0447178i
$497$	113.655	−	113.655i	0.228683	−	0.228683i
$498$	−2.06529	+	2.79363i	−0.00414717	+	0.00560969i
$499$	755.350			1.51373			0.756864	−	0.653572i	$-0.226730\pi$
$499$	755.350			1.51373			0.756864	+	0.653572i	$0.226730\pi$
$500$	−332.108	−	373.770i	−0.664216	−	0.747540i
$501$		−	259.760i		−	0.518482i
$502$	−177.927	+	240.673i	−0.354435	+	0.479429i
$503$	−505.226	−	505.226i	−1.00443	−	1.00443i	−0.999990	−	0.00443600i	$-0.998588\pi$
$503$	−505.226	−	505.226i	−1.00443	−	1.00443i	−0.00443600	−	0.999990i	$-0.501412\pi$
$504$	199.964	−	95.6991i	0.396754	−	0.189879i
$505$	597.699	−	470.187i	1.18356	−	0.931063i
$506$	−140.681	+	21.0876i	−0.278025	+	0.0416750i
$507$	−202.842	−	202.842i	−0.400082	−	0.400082i
$508$	−279.128	−	148.103i	−0.549464	−	0.291541i
$509$	−594.029			−1.16705			−0.583526	−	0.812095i	$-0.698327\pi$
$509$	−594.029			−1.16705			−0.583526	+	0.812095i	$0.698327\pi$
$510$	1108.19	−	33.1949i	2.17291	−	0.0650880i
$511$	−339.847			−0.665063
$512$	−435.499	+	269.230i	−0.850584	+	0.525840i
$513$	−232.219	−	232.219i	−0.452668	−	0.452668i
$514$	−682.636	+	102.325i	−1.32809	+	0.199076i
$515$	101.156	−	847.156i	0.196419	−	1.64496i
$516$	−636.459	+	195.192i	−1.23345	+	0.378279i
$517$	−84.0123	−	84.0123i	−0.162500	−	0.162500i
$518$	322.769	+	238.619i	0.623106	+	0.460654i
$519$			925.453i			1.78315i
$520$	−166.535	+	337.933i	−0.320260	+	0.649871i
$521$	871.615			1.67297			0.836483	−	0.547993i	$-0.184608\pi$
$521$	871.615			1.67297			0.836483	+	0.547993i	$0.184608\pi$
$522$	−4.68839	+	6.34178i	−0.00898160	+	0.0121490i
$523$	601.907	−	601.907i	1.15087	−	1.15087i	0.164497	−	0.986378i	$-0.447400\pi$
$523$	601.907	−	601.907i	1.15087	−	1.15087i	0.986378	−	0.164497i	$-0.0526001\pi$
$524$	−579.822	+	177.822i	−1.10653	+	0.339356i
$525$	639.009	+	154.811i	1.21716	+	0.294878i
$526$	101.282	+	675.677i	0.192551	+	1.28456i
$527$	−54.2566	+	54.2566i	−0.102954	+	0.102954i
$528$	−139.902	−	26.9411i	−0.264966	−	0.0510249i
$529$			285.396i			0.539500i
$530$	374.770	+	352.971i	0.707114	+	0.665983i
$531$		−	115.176i		−	0.216903i
$532$	−456.660	−	242.300i	−0.858383	−	0.455451i
$533$	292.645	−	292.645i	0.549052	−	0.549052i
$534$	−89.4672	−	596.859i	−0.167542	−	1.11771i
$535$	63.1119	−	528.547i	0.117966	−	0.987939i
$536$	204.035	−	97.6475i	0.380663	−	0.182178i
$537$	79.1915	−	79.1915i	0.147470	−	0.147470i
$538$	−563.877	−	416.867i	−1.04810	−	0.774845i
$539$	−12.9311			−0.0239908
$540$	368.150	−	66.5107i	0.681759	−	0.123168i
$541$			109.548i			0.202492i	0.994861	+	0.101246i	$0.0322830\pi$
$541$			109.548i			0.202492i	−0.994861	+	0.101246i	$0.967717\pi$
$542$	480.233	+	355.030i	0.886040	+	0.655037i
$543$	145.049	+	145.049i	0.267125	+	0.267125i
$544$	730.666	−	672.468i	1.34314	−	1.23615i
$545$	36.6684	+	46.6127i	0.0672815	+	0.0855279i
$546$	−73.4397	−	489.935i	−0.134505	−	0.897317i
$547$	−330.968	−	330.968i	−0.605060	−	0.605060i	0.336591	−	0.941651i	$-0.390726\pi$
$547$	−330.968	−	330.968i	−0.605060	−	0.605060i	−0.941651	+	0.336591i	$0.890726\pi$
$548$	341.033	+	180.949i	0.622323	+	0.330200i
$549$	−89.7299			−0.163442
$550$	−79.9471	−	95.5937i	−0.145358	−	0.173807i
$551$	18.3914			0.0333782
$552$	−271.266	+	769.227i	−0.491424	+	1.39353i
$553$	−85.4301	−	85.4301i	−0.154485	−	0.154485i
$554$	−115.639	−	771.455i	−0.208734	−	1.39252i
$555$	−301.125	−	382.788i	−0.542567	−	0.689709i
$556$	81.7744	+	266.640i	0.147076	+	0.479569i
$557$	−62.7080	−	62.7080i	−0.112582	−	0.112582i	0.648572	−	0.761153i	$-0.275367\pi$
$557$	−62.7080	−	62.7080i	−0.112582	−	0.112582i	−0.761153	+	0.648572i	$0.775367\pi$
$558$	11.0666	−	14.9693i	0.0198326	−	0.0268266i
$559$			438.745i			0.784874i
$560$	523.352	−	270.014i	0.934557	−	0.482168i
$561$	276.324			0.492556
$562$	−21.3668	−	15.7962i	−0.0380193	−	0.0281071i
$563$	−116.120	+	116.120i	−0.206252	+	0.206252i	−0.802672	−	0.596420i	$-0.796589\pi$
$563$	−116.120	+	116.120i	−0.206252	+	0.206252i	0.596420	+	0.802672i	$0.296589\pi$
$564$	−651.308	+	199.746i	−1.15480	+	0.354159i
$565$	68.7543	−	575.801i	0.121689	−	1.01912i
$566$	708.215	−	106.159i	1.25126	−	0.187560i
$567$	−524.210	+	524.210i	−0.924533	+	0.924533i
$568$	−58.0939	+	164.737i	−0.102278	+	0.290029i
$569$		−	323.733i		−	0.568950i	−0.958683	−	0.284475i	$-0.908181\pi$
$569$		−	323.733i		−	0.568950i	0.958683	−	0.284475i	$-0.0918193\pi$
$570$	456.617	+	430.057i	0.801082	+	0.754486i
$571$			433.708i			0.759558i	0.925077	+	0.379779i	$0.124000\pi$
$571$			433.708i			0.759558i	−0.925077	+	0.379779i	$0.876000\pi$
$572$	−44.0098	+	82.9447i	−0.0769402	+	0.145008i
$573$	−409.067	+	409.067i	−0.713904	+	0.713904i
$574$	−639.782	+	95.9011i	−1.11460	+	0.167075i
$575$	−609.078	+	371.513i	−1.05927	+	0.646110i
$576$	−151.125	+	187.626i	−0.262370	+	0.325739i
$577$	27.1282	−	27.1282i	0.0470159	−	0.0470159i	−0.683208	−	0.730224i	$-0.739416\pi$
$577$	27.1282	−	27.1282i	0.0470159	−	0.0470159i	0.730224	+	0.683208i	$0.239416\pi$
$578$	−801.319	+	1083.91i	−1.38637	+	1.87527i
$579$	−318.332			−0.549797
$580$	−11.9447	+	17.2122i	−0.0205943	+	0.0296762i
$581$		−	3.57909i		−	0.00616023i
$582$	−144.962	+	196.083i	−0.249075	+	0.336913i
$583$	90.7305	+	90.7305i	0.155627	+	0.155627i
$584$	333.149	−	159.439i	0.570460	−	0.273012i
$585$	−21.0182	+	176.023i	−0.0359286	+	0.300894i
$586$	401.137	−	60.1291i	0.684535	−	0.102609i
$587$	−163.733	−	163.733i	−0.278932	−	0.278932i	0.553751	−	0.832682i	$-0.313196\pi$
$587$	−163.733	−	163.733i	−0.278932	−	0.278932i	−0.832682	+	0.553751i	$0.813196\pi$
$588$	−34.7519	+	65.4965i	−0.0591019	+	0.111389i
$589$	−43.4114			−0.0737035
$590$	−9.16078	−	305.826i	−0.0155268	−	0.518349i
$591$	20.0173			0.0338702
$592$	−428.355	−	82.4889i	−0.723572	−	0.139339i
$593$	280.606	+	280.606i	0.473198	+	0.473198i	0.902948	−	0.429750i	$-0.141398\pi$
$593$	280.606	+	280.606i	0.473198	+	0.473198i	−0.429750	+	0.902948i	$0.641398\pi$
$594$	92.2115	−	13.8222i	0.155238	−	0.0232697i
$595$	−897.695	+	706.182i	−1.50873	+	1.18686i
$596$	92.5370	+	301.734i	0.155263	+	0.506265i
$597$	310.800	+	310.800i	0.520603	+	0.520603i
$598$	432.263	+	319.566i	0.722848	+	0.534392i
$599$		−	639.232i		−	1.06716i	−0.845748	−	0.533582i	$-0.820845\pi$
$599$		−	639.232i		−	1.06716i	0.845748	−	0.533582i	$-0.179155\pi$
$600$	−699.043	+	148.031i	−1.16507	+	0.246718i
$601$	−332.979			−0.554041			−0.277021	−	0.960864i	$-0.589347\pi$
$601$	−332.979			−0.554041			−0.277021	+	0.960864i	$0.589347\pi$
$602$	407.704	−	551.482i	0.677249	−	0.916084i
$603$	75.2619	−	75.2619i	0.124812	−	0.124812i
$604$	231.704	+	755.514i	0.383617	+	1.25085i
$605$	354.857	+	451.092i	0.586540	+	0.745607i
$606$	−161.106	−	1074.78i	−0.265851	−	1.77356i
$607$	681.745	−	681.745i	1.12314	−	1.12314i	0.131873	−	0.991267i	$-0.457901\pi$
$607$	681.745	−	681.745i	1.12314	−	1.12314i	0.991267	−	0.131873i	$-0.0420990\pi$
$608$	561.333	+	23.2826i	0.923245	+	0.0382938i
$609$		−	27.5501i		−	0.0452382i
$610$	−238.259	+	7.13689i	−0.390589	+	0.0116998i
$611$			448.981i			0.734830i
$612$	219.006	−	412.758i	0.357853	−	0.674442i
$613$	378.926	−	378.926i	0.618150	−	0.618150i	−0.326907	−	0.945057i	$-0.606006\pi$
$613$	378.926	−	378.926i	0.618150	−	0.618150i	0.945057	+	0.326907i	$0.106006\pi$
$614$	150.005	+	1000.72i	0.244308	+	1.62984i
$615$	779.417	+	93.0672i	1.26734	+	0.151329i
$616$	132.395	−	63.3617i	0.214927	−	0.102860i
$617$	−68.3041	+	68.3041i	−0.110704	+	0.110704i	−0.760289	−	0.649585i	$-0.774943\pi$
$617$	−68.3041	+	68.3041i	−0.110704	+	0.110704i	0.649585	+	0.760289i	$0.274943\pi$
$618$	−980.429	−	724.818i	−1.58645	−	1.17284i
$619$	1009.69			1.63116			0.815580	−	0.578645i	$-0.196418\pi$
$619$	1009.69			1.63116			0.815580	+	0.578645i	$0.196418\pi$
$620$	28.1944	−	40.6281i	0.0454749	−	0.0655291i
$621$		−	533.810i		−	0.859597i
$622$	611.456	+	452.042i	0.983049	+	0.726755i
$623$	439.648	+	439.648i	0.705694	+	0.705694i
$624$	301.845	+	445.824i	0.483725	+	0.714462i
$625$	−555.701	−	286.045i	−0.889121	−	0.457671i
$626$	−113.542	−	757.470i	−0.181377	−	1.21002i
$627$	110.545	+	110.545i	0.176308	+	0.176308i
$628$	249.523	−	470.273i	0.397329	−	0.748842i
$629$	846.054			1.34508
$630$	189.988	−	201.722i	0.301569	−	0.320193i
$631$	−867.965			−1.37554			−0.687769	−	0.725929i	$-0.741410\pi$
$631$	−867.965			−1.37554			−0.687769	+	0.725929i	$0.741410\pi$
$632$	123.826	+	43.6668i	0.195927	+	0.0690930i
$633$	691.837	+	691.837i	1.09295	+	1.09295i
$634$	100.184	+	668.355i	0.158019	+	1.05419i
$635$	−392.196	−	46.8307i	−0.617631	−	0.0737491i
$636$	703.391	−	215.719i	1.10596	−	0.339181i
$637$	34.5532	+	34.5532i	0.0542437	+	0.0542437i
$638$	−3.10415	+	4.19885i	−0.00486545	+	0.00658127i
$639$			82.1949i			0.128631i
$640$	−386.360	+	510.222i	−0.603687	+	0.797222i
$641$	116.032			0.181017			0.0905083	−	0.995896i	$-0.471151\pi$
$641$	116.032			0.181017			0.0905083	+	0.995896i	$0.471151\pi$
$642$	−611.697	−	452.220i	−0.952799	−	0.704392i
$643$	−429.493	+	429.493i	−0.667951	+	0.667951i	−0.957241	−	0.289290i	$-0.906581\pi$
$643$	−429.493	+	429.493i	−0.667951	+	0.667951i	0.289290	+	0.957241i	$0.406581\pi$
$644$	−246.378	−	803.361i	−0.382575	−	1.24745i
$645$	−654.031	+	514.501i	−1.01400	+	0.797676i
$646$	−1077.60	+	161.528i	−1.66811	+	0.250044i
$647$	511.695	−	511.695i	0.790873	−	0.790873i	−0.190763	−	0.981636i	$-0.561096\pi$
$647$	511.695	−	511.695i	0.790873	−	0.790873i	0.981636	+	0.190763i	$0.0610963\pi$
$648$	267.945	−	759.810i	0.413495	−	1.17255i
$649$		−	76.2571i		−	0.117499i
$650$	−41.8093	+	469.065i	−0.0643220	+	0.721638i
$651$			65.0297i			0.0998920i
$652$	−664.503	−	352.580i	−1.01918	−	0.540766i
$653$	−777.556	+	777.556i	−1.19074	+	1.19074i	−0.213886	+	0.976859i	$0.568612\pi$
$653$	−777.556	+	777.556i	−1.19074	+	1.19074i	−0.976859	+	0.213886i	$0.931388\pi$
$654$	83.8186	−	12.5641i	0.128163	−	0.0192112i
$655$	−595.831	+	468.717i	−0.909666	+	0.715599i
$656$	582.179	−	394.163i	0.887468	−	0.600859i
$657$	122.888	−	122.888i	0.187044	−	0.187044i
$658$	417.216	−	564.349i	0.634067	−	0.857673i
$659$	734.265			1.11421			0.557105	−	0.830442i	$-0.311912\pi$
$659$	734.265			1.11421			0.557105	+	0.830442i	$0.311912\pi$
$660$	−175.254	+	31.6617i	−0.265536	+	0.0479723i
$661$			799.237i			1.20913i	0.796555	+	0.604567i	$0.206654\pi$
$661$			799.237i			1.20913i	−0.796555	+	0.604567i	$0.793346\pi$
$662$	86.8791	−	117.518i	0.131237	−	0.177519i
$663$	−738.369	−	738.369i	−1.11368	−	1.11368i
$664$	1.67913	+	3.50855i	0.00252880	+	0.00528395i
$665$	−641.641	−	76.6160i	−0.964874	−	0.115212i
$666$	−202.996	+	30.4284i	−0.304799	+	0.0456883i
$667$	21.1384	+	21.1384i	0.0316918	+	0.0316918i
$668$	−256.902	−	136.310i	−0.384584	−	0.204057i
$669$	−651.130			−0.973288
$670$	193.857	−	205.829i	0.289338	−	0.307207i
$671$	−59.4096			−0.0885388
$672$	34.8771	−	840.870i	0.0519005	−	1.25130i
$673$	−185.806	−	185.806i	−0.276087	−	0.276087i	0.555458	−	0.831545i	$-0.312543\pi$
$673$	−185.806	−	185.806i	−0.276087	−	0.276087i	−0.831545	+	0.555458i	$0.812543\pi$
$674$	581.622	−	87.1832i	0.862940	−	0.129352i
$675$	399.230	−	243.515i	0.591452	−	0.360762i
$676$	−307.053	+	94.1682i	−0.454220	+	0.139302i
$677$	−448.763	−	448.763i	−0.662870	−	0.662870i	0.293186	−	0.956055i	$-0.405285\pi$
$677$	−448.763	−	448.763i	−0.662870	−	0.662870i	−0.956055	+	0.293186i	$0.905285\pi$
$678$	−666.385	−	492.649i	−0.982868	−	0.726621i
$679$		−	251.214i		−	0.369977i
$680$	548.696	−	1113.41i	0.806907	−	1.63737i
$681$	−1225.03			−1.79886
$682$	7.32711	−	9.91105i	0.0107436	−	0.0145323i
$683$	−67.1358	+	67.1358i	−0.0982955	+	0.0982955i	−0.754544	−	0.656249i	$-0.772142\pi$
$683$	−67.1358	+	67.1358i	−0.0982955	+	0.0982955i	0.656249	+	0.754544i	$0.272142\pi$
$684$	252.741	−	77.5118i	0.369505	−	0.113321i
$685$	479.178	+	57.2168i	0.699529	+	0.0835282i
$686$	95.6181	+	637.893i	0.139385	+	0.929873i
$687$	974.315	−	974.315i	1.41822	−	1.41822i
$688$	−140.940	+	731.886i	−0.204855	+	1.06379i
$689$		−	484.884i		−	0.703751i
$690$	30.5268	+	1019.11i	0.0442417	+	1.47698i
$691$		−	533.282i		−	0.771753i	−0.922550	−	0.385877i	$-0.873899\pi$
$691$		−	533.282i		−	0.771753i	0.922550	−	0.385877i	$-0.126101\pi$
$692$	915.274	+	485.636i	1.32265	+	0.701787i
$693$	48.8361	−	48.8361i	0.0704706	−	0.0704706i
$694$	−63.1097	−	421.021i	−0.0909362	−	0.606659i
$695$	215.547	+	274.002i	0.310139	+	0.394248i
$696$	12.9251	+	27.0070i	0.0185705	+	0.0388032i
$697$	−964.199	+	964.199i	−1.38336	+	1.38336i
$698$	256.991	+	189.990i	0.368181	+	0.272192i
$699$	−50.0625			−0.0716201
$700$	488.431	−	550.743i	0.697759	−	0.786775i
$701$		−	1203.60i		−	1.71697i	−0.512835	−	0.858487i	$-0.671405\pi$
$701$		−	1203.60i		−	1.71697i	0.512835	−	0.858487i	$-0.328595\pi$
$702$	−283.334	−	209.465i	−0.403610	−	0.298383i
$703$	338.469	+	338.469i	0.481464	+	0.481464i
$704$	−100.059	+	124.226i	−0.142129	+	0.176457i
$705$	−669.291	+	526.505i	−0.949348	+	0.746816i
$706$	−13.3719	−	89.2075i	−0.0189404	−	0.126356i
$707$	791.683	+	791.683i	1.11978	+	1.11978i
$708$	−386.246	−	204.939i	−0.545546	−	0.289462i
$709$	−456.445			−0.643788			−0.321894	−	0.946776i	$-0.604319\pi$
$709$	−456.445			−0.643788			−0.321894	+	0.946776i	$0.604319\pi$
$710$	6.53757	+	218.252i	0.00920785	+	0.307397i
$711$	61.7825			0.0868952
$712$	−637.242	−	224.722i	−0.895003	−	0.315620i
$713$	−49.8956	−	49.8956i	−0.0699798	−	0.0699798i
$714$	241.967	+	1614.23i	0.338890	+	2.26082i
$715$	−13.9160	+	116.544i	−0.0194630	+	0.162998i
$716$	−36.7642	−	119.877i	−0.0513467	−	0.167425i
$717$	113.024	+	113.024i	0.157635	+	0.157635i
$718$	444.800	−	601.662i	0.619499	−	0.837969i
$719$			63.2841i			0.0880168i	0.999031	+	0.0440084i	$0.0140128\pi$
$719$			63.2841i			0.0880168i	−0.999031	+	0.0440084i	$0.985987\pi$
$720$	−91.6061	+	286.879i	−0.127231	+	0.398443i
$721$	1256.09			1.74215
$722$	84.8517	+	62.7297i	0.117523	+	0.0868833i
$723$	54.2610	−	54.2610i	0.0750498	−	0.0750498i
$724$	219.569	−	67.3383i	0.303272	−	0.0930087i
$725$	−6.16622	+	25.4522i	−0.00850513	+	0.0351065i
$726$	811.151	−	121.589i	1.11729	−	0.167478i
$727$	408.139	−	408.139i	0.561401	−	0.561401i	−0.368304	−	0.929705i	$-0.620061\pi$
$727$	408.139	−	408.139i	0.561401	−	0.561401i	0.929705	+	0.368304i	$0.120061\pi$
$728$	−523.084	−	184.464i	−0.718522	−	0.253385i
$729$			222.361i			0.305021i
$730$	316.529	−	336.078i	0.433602	−	0.460380i
$731$		−	1445.57i		−	1.97752i
$732$	−159.662	+	300.913i	−0.218117	+	0.411083i
$733$	−90.0317	+	90.0317i	−0.122826	+	0.122826i	−0.765848	−	0.643022i	$-0.777681\pi$
$733$	−90.0317	+	90.0317i	−0.122826	+	0.122826i	0.643022	+	0.765848i	$0.277681\pi$
$734$	−547.616	+	82.0858i	−0.746071	+	0.111834i
$735$	−10.9887	+	92.0275i	−0.0149506	+	0.125208i
$736$	618.418	+	671.938i	0.840241	+	0.912959i
$737$	49.8304	−	49.8304i	0.0676125	−	0.0676125i
$738$	196.665	−	266.020i	0.266484	−	0.360461i
$739$	−875.498			−1.18471			−0.592353	−	0.805679i	$-0.701801\pi$
$739$	−875.498			−1.18471			−0.592353	+	0.805679i	$0.701801\pi$
$740$	−536.595	+	96.9423i	−0.725128	+	0.131003i
$741$		−	590.779i		−	0.797272i
$742$	−450.579	+	609.478i	−0.607250	+	0.821399i
$743$	282.061	+	282.061i	0.379624	+	0.379624i	0.870967	−	0.491342i	$-0.163494\pi$
$743$	282.061	+	282.061i	0.379624	+	0.379624i	−0.491342	+	0.870967i	$0.663494\pi$
$744$	−30.5086	−	63.7479i	−0.0410062	−	0.0856827i
$745$	243.916	+	310.065i	0.327404	+	0.416194i
$746$	−957.816	+	143.573i	−1.28394	+	0.192458i
$747$	1.29419	+	1.29419i	0.00173251	+	0.00173251i
$748$	145.002	−	273.285i	0.193854	−	0.365354i
$749$	783.683			1.04631
$750$	−748.258	+	487.732i	−0.997677	+	0.650310i
$751$	606.986			0.808237			0.404119	−	0.914707i	$-0.367578\pi$
$751$	606.986			0.808237			0.404119	+	0.914707i	$0.367578\pi$
$752$	−144.229	+	748.962i	−0.191793	+	0.995960i
$753$	378.063	+	378.063i	0.502075	+	0.502075i
$754$	19.5145	−	2.92515i	0.0258812	−	0.00387951i
$755$	610.743	+	776.374i	0.808932	+	1.02831i
$756$	161.493	+	526.577i	0.213615	+	0.696530i
$757$	−173.075	−	173.075i	−0.228633	−	0.228633i	0.583488	−	0.812121i	$-0.301687\pi$
$757$	−173.075	−	173.075i	−0.228633	−	0.228633i	−0.812121	+	0.583488i	$0.801687\pi$
$758$	−976.277	−	721.749i	−1.28796	−	0.952175i
$759$			254.114i			0.334801i
$760$	664.938	−	225.919i	0.874919	−	0.297262i
$761$	100.678			0.132297			0.0661483	−	0.997810i	$-0.478929\pi$
$761$	100.678			0.132297			0.0661483	+	0.997810i	$0.478929\pi$
$762$	−335.559	+	453.895i	−0.440366	+	0.595663i
$763$	−61.7409	+	61.7409i	−0.0809187	+	0.0809187i
$764$	189.907	+	619.228i	0.248570	+	0.810507i
$765$	69.2505	−	579.957i	0.0905235	−	0.758113i
$766$	64.8582	+	432.686i	0.0846713	+	0.564864i
$767$	−203.768	+	203.768i	−0.265668	+	0.265668i
$768$	360.303	+	840.659i	0.469145	+	1.09461i
$769$			370.732i			0.482097i	0.970513	+	0.241048i	$0.0774913\pi$
$769$			370.732i			0.482097i	−0.970513	+	0.241048i	$0.922509\pi$
$770$	125.790	−	133.559i	0.163364	−	0.173453i
$771$			1233.06i			1.59930i
$772$	−167.047	+	314.831i	−0.216382	+	0.407812i
$773$	−319.455	+	319.455i	−0.413267	+	0.413267i	−0.882875	−	0.469608i	$-0.844395\pi$
$773$	−319.455	+	319.455i	−0.413267	+	0.413267i	0.469608	+	0.882875i	$0.344395\pi$
$774$	51.9900	+	346.839i	0.0671705	+	0.448112i
$775$	14.5549	−	60.0779i	0.0187805	−	0.0775198i
$776$	117.857	+	246.263i	0.151877	+	0.317349i
$777$	507.023	−	507.023i	0.652539	−	0.652539i
$778$	520.633	+	384.897i	0.669194	+	0.494726i
$779$	−771.468			−0.990331
$780$	552.901	+	383.694i	0.708848	+	0.491915i
$781$			54.4207i			0.0696808i
$782$	−1424.21	−	1052.90i	−1.82124	−	1.34642i
$783$	−13.8556	−	13.8556i	−0.0176955	−	0.0176955i
$784$	46.5398	+	68.7393i	0.0593620	+	0.0876776i
$785$	78.8999	−	660.769i	0.100509	−	0.841744i
$786$	160.602	+	1071.42i	0.204328	+	1.36313i
$787$	−1104.16	−	1104.16i	−1.40300	−	1.40300i	−0.790372	−	0.612627i	$-0.790113\pi$
$787$	−1104.16	−	1104.16i	−1.40300	−	1.40300i	−0.612627	−	0.790372i	$-0.709887\pi$
$788$	10.5042	−	19.7971i	0.0133302	−	0.0251232i
$789$	1220.49			1.54688
$790$	164.051	−	4.91402i	0.207659	−	0.00622028i
$791$	853.747			1.07933
$792$	−24.9621	+	70.7849i	−0.0315178	+	0.0893749i
$793$	158.749	+	158.749i	0.200188	+	0.200188i
$794$	−157.725	−	1052.23i	−0.198646	−	1.32522i
$795$	722.811	−	568.608i	0.909197	−	0.715230i
$796$	470.476	−	144.287i	0.591050	−	0.181266i
$797$	434.605	+	434.605i	0.545301	+	0.545301i	0.925078	−	0.379777i	$-0.123999\pi$
$797$	434.605	+	434.605i	0.545301	+	0.545301i	−0.379777	+	0.925078i	$0.623999\pi$
$798$	−548.982	+	742.583i	−0.687947	+	0.930555i
$799$		−	1479.29i		−	1.85143i
$800$	−220.424	+	769.034i	−0.275530	+	0.961293i
$801$	−317.950			−0.396942
$802$	646.124	+	477.671i	0.805641	+	0.595600i
$803$	81.3631	−	81.3631i	0.101324	−	0.101324i
$804$	−118.476	−	386.312i	−0.147358	−	0.480488i
$805$	−649.422	−	825.542i	−0.806735	−	1.02552i
$806$	−46.0623	+	6.90459i	−0.0571493	+	0.00856649i
$807$	−885.768	+	885.768i	−1.09761	+	1.09761i
$808$	−1147.50	−	404.662i	−1.42017	−	0.500819i
$809$			164.175i			0.202935i	0.994839	+	0.101468i	$0.0323538\pi$
$809$			164.175i			0.202935i	−0.994839	+	0.101468i	$0.967646\pi$
$810$	−30.1531	−	1006.64i	−0.0372260	−	1.24276i
$811$		−	1283.08i		−	1.58210i	−0.611752	−	0.791049i	$-0.709535\pi$
$811$		−	1283.08i		−	1.58210i	0.611752	−	0.791049i	$-0.290465\pi$
$812$	−27.2470	−	14.4570i	−0.0335554	−	0.0178042i
$813$	754.377	−	754.377i	0.927893	−	0.927893i
$814$	−134.402	+	20.1465i	−0.165113	+	0.0247500i
$815$	−933.677	−	111.487i	−1.14562	−	0.136794i
$816$	−994.511	−	1468.89i	−1.21876	−	1.80011i
$817$	578.308	−	578.308i	0.707843	−	0.707843i
$818$	198.411	−	268.382i	0.242556	−	0.328095i
$819$	−260.991			−0.318671
$820$	501.046	−	722.006i	0.611032	−	0.880495i
$821$			1292.43i			1.57421i	0.616817	+	0.787106i	$0.288422\pi$
$821$			1292.43i			1.57421i	−0.616817	+	0.787106i	$0.711578\pi$
$822$	409.979	−	554.561i	0.498758	−	0.674648i
$823$	38.6290	+	38.6290i	0.0469368	+	0.0469368i	0.730186	−	0.683249i	$-0.239434\pi$
$823$	38.6290	+	38.6290i	0.0469368	+	0.0469368i	−0.683249	+	0.730186i	$0.739434\pi$
$824$	−1231.33	+	589.292i	−1.49433	+	0.715160i
$825$	−190.049	+	115.922i	−0.230363	+	0.140512i
$826$	445.478	−	66.7757i	0.539320	−	0.0808422i
$827$	−432.150	−	432.150i	−0.522552	−	0.522552i	0.395789	−	0.918341i	$-0.370471\pi$
$827$	−432.150	−	432.150i	−0.522552	−	0.522552i	−0.918341	+	0.395789i	$0.870471\pi$
$828$	379.582	+	201.403i	0.458433	+	0.243241i
$829$	−684.217			−0.825353			−0.412676	−	0.910878i	$-0.635406\pi$
$829$	−684.217			−0.825353			−0.412676	+	0.910878i	$0.635406\pi$
$830$	3.53939	+	3.33352i	0.00426432	+	0.00401629i
$831$	−1393.49			−1.67689
$832$	599.315	−	64.5758i	0.720330	−	0.0776151i
$833$	−113.845	−	113.845i	−0.136669	−	0.136669i
$834$	492.708	−	73.8553i	0.590777	−	0.0885556i
$835$	−360.967	−	43.1017i	−0.432296	−	0.0516189i
$836$	167.338	−	51.3201i	0.200166	−	0.0613876i
$837$	32.7049	+	32.7049i	0.0390740	+	0.0390740i
$838$	858.304	+	634.533i	1.02423	+	0.757199i
$839$			579.065i			0.690184i	0.938569	+	0.345092i	$0.112152\pi$
$839$			579.065i			0.690184i	−0.938569	+	0.345092i	$0.887848\pi$
$840$	−338.424	−	996.070i	−0.402886	−	1.18580i
$841$	−839.903			−0.998695
$842$	255.056	−	345.003i	0.302917	−	0.409742i
$843$	−33.5642	+	33.5642i	−0.0398151	+	0.0398151i
$844$	1047.27	−	321.182i	1.24084	−	0.380547i
$845$	−315.530	+	248.215i	−0.373408	+	0.293746i
$846$	53.2029	+	354.931i	0.0628876	+	0.419540i
$847$	−597.495	+	597.495i	−0.705426	+	0.705426i
$848$	155.762	−	808.854i	0.183682	−	0.953837i
$849$		−	1279.26i		−	1.50679i
$850$	137.752	−	1545.47i	0.162062	−	1.81819i
$851$			778.051i			0.914279i
$852$	275.644	+	146.254i	0.323526	+	0.171660i
$853$	89.6610	−	89.6610i	0.105113	−	0.105113i	−0.652595	−	0.757707i	$-0.726320\pi$
$853$	89.6610	−	89.6610i	0.105113	−	0.105113i	0.757707	+	0.652595i	$0.226320\pi$
$854$	−52.0229	−	347.058i	−0.0609167	−	0.406391i
$855$	259.720	−	204.311i	0.303766	−	0.238961i
$856$	−768.237	+	367.664i	−0.897473	+	0.429514i
$857$	−409.705	+	409.705i	−0.478069	+	0.478069i	−0.904514	−	0.426445i	$-0.859766\pi$
$857$	−409.705	+	409.705i	−0.478069	+	0.478069i	0.426445	+	0.904514i	$0.359766\pi$
$858$	134.878	+	99.7135i	0.157201	+	0.116216i
$859$	799.305			0.930507			0.465253	−	0.885178i	$-0.345963\pi$
$859$	799.305			0.930507			0.465253	+	0.885178i	$0.345963\pi$
$860$	165.635	+	916.824i	0.192599	+	1.06607i
$861$			1155.65i			1.34222i
$862$	844.918	+	624.637i	0.980184	+	0.724637i
$863$	1116.04	+	1116.04i	1.29321	+	1.29321i	0.932793	+	0.360414i	$0.117364\pi$
$863$	1116.04	+	1116.04i	1.29321	+	1.29321i	0.360414	+	0.932793i	$0.382636\pi$
$864$	−405.352	−	440.433i	−0.469158	−	0.509761i
$865$	1286.03	+	153.560i	1.48674	+	0.177526i
$866$	110.201	+	735.178i	0.127253	+	0.848935i
$867$	1702.66	+	1702.66i	1.96386	+	1.96386i
$868$	64.3144	+	34.1247i	0.0740949	+	0.0393142i
$869$	40.9058			0.0470723
$870$	27.2445	+	25.6598i	0.0313155	+	0.0294940i
$871$	−266.305			−0.305746
$872$	31.5583	−	89.4897i	0.0361907	−	0.102626i
$873$	90.8383	+	90.8383i	0.104053	+	0.104053i
$874$	−148.545	−	990.984i	−0.169960	−	1.13385i
$875$	321.159	−	862.293i	0.367038	−	0.985477i
$876$	−193.447	−	630.770i	−0.220830	−	0.720058i
$877$	−98.3606	−	98.3606i	−0.112156	−	0.112156i	0.648802	−	0.760957i	$-0.275270\pi$
$877$	−98.3606	−	98.3606i	−0.112156	−	0.112156i	−0.760957	+	0.648802i	$0.775270\pi$
$878$	498.340	−	674.082i	0.567585	−	0.767747i
$879$		−	724.582i		−	0.824326i
$880$	−60.6518	+	189.940i	−0.0689225	+	0.215841i
$881$	−654.962			−0.743430			−0.371715	−	0.928347i	$-0.621230\pi$
$881$	−654.962			−0.743430			−0.371715	+	0.928347i	$0.621230\pi$
$882$	31.4097	+	23.2207i	0.0356119	+	0.0263274i
$883$	−963.144	+	963.144i	−1.09076	+	1.09076i	−0.0953158	+	0.995447i	$0.530386\pi$
$883$	−963.144	+	963.144i	−1.09076	+	1.09076i	−0.995447	+	0.0953158i	$0.969614\pi$
$884$	−1117.71	+	342.784i	−1.26438	+	0.387765i
$885$	−542.705	−	64.8024i	−0.613227	−	0.0732231i
$886$	333.520	−	49.9935i	0.376433	−	0.0564260i
$887$	−588.066	+	588.066i	−0.662983	+	0.662983i	−0.956082	−	0.293099i	$-0.905313\pi$
$887$	−588.066	+	588.066i	−0.662983	+	0.662983i	0.293099	+	0.956082i	$0.405313\pi$
$888$	−259.160	+	734.899i	−0.291847	+	0.827588i
$889$		−	581.514i		−	0.654121i
$890$	−844.252	+	25.2890i	−0.948598	+	0.0284146i
$891$		−	251.003i		−	0.281709i
$892$	−341.684	+	643.968i	−0.383054	+	0.721937i
$893$	591.801	−	591.801i	0.662711	−	0.662711i
$894$	557.556	−	83.5758i	0.623664	−	0.0934852i
$895$	−96.9059	−	123.186i	−0.108275	−	0.137638i
$896$	−813.319	−	475.745i	−0.907722	−	0.530965i
$897$	679.022	−	679.022i	0.756992	−	0.756992i
$898$	708.694	−	958.619i	0.789192	−	1.06750i
$899$	−2.59018			−0.00288118
$900$	22.5316	+	375.762i	0.0250351	+	0.417513i
$901$			1597.59i			1.77313i
$902$	130.211	−	176.130i	0.144358	−	0.195267i
$903$	−866.299	−	866.299i	−0.959356	−	0.959356i
$904$	−836.919	+	400.534i	−0.925795	+	0.443069i
$905$	225.631	−	177.495i	0.249316	−	0.196127i
$906$	1396.07	−	209.266i	1.54092	−	0.230978i
$907$	692.104	+	692.104i	0.763069	+	0.763069i	0.976876	−	0.213807i	$-0.0685863\pi$
$907$	692.104	+	692.104i	0.763069	+	0.763069i	−0.213807	+	0.976876i	$0.568586\pi$
$908$	−642.839	+	1211.55i	−0.707973	+	1.33431i
$909$	−572.540			−0.629857
$910$	−693.010	+	20.7586i	−0.761549	+	0.0228116i
$911$	−45.1707			−0.0495836			−0.0247918	−	0.999693i	$-0.507892\pi$
$911$	−45.1707			−0.0495836			−0.0247918	+	0.999693i	$0.507892\pi$
$912$	189.779	−	985.500i	0.208091	−	1.08059i
$913$	0.856873	+	0.856873i	0.000938525	+	0.000938525i
$914$	−403.573	+	60.4943i	−0.441546	+	0.0661863i
$915$	−50.4856	+	422.805i	−0.0551755	+	0.462082i
$916$	−452.321	−	1474.87i	−0.493800	−	1.61013i
$917$	−789.209	−	789.209i	−0.860643	−	0.860643i
$918$	933.523	+	690.141i	1.01691	+	0.751788i
$919$			1598.45i			1.73934i	0.493637	+	0.869668i	$0.335667\pi$
$919$			1598.45i			1.73934i	−0.493637	+	0.869668i	$0.664333\pi$
$920$	1023.92	+	504.594i	1.11296	+	0.548472i
$921$	1807.62			1.96268
$922$	−884.568	+	1196.52i	−0.959402	+	1.29774i
$923$	145.418	−	145.418i	0.157550	−	0.157550i
$924$	−76.8769	−	250.671i	−0.0832001	−	0.271289i
$925$	−581.896	+	354.933i	−0.629077	+	0.383712i
$926$	−187.220	−	1248.99i	−0.202181	−	1.34880i
$927$	−454.197	+	454.197i	−0.489965	+	0.489965i
$928$	33.4925	+	1.38918i	0.0360910	+	0.00149696i
$929$			887.585i			0.955420i	0.878518	+	0.477710i	$0.158533\pi$
$929$			887.585i			0.955420i	−0.878518	+	0.477710i	$0.841467\pi$
$930$	−64.3084	−	60.5678i	−0.0691488	−	0.0651267i
$931$		−	91.0891i		−	0.0978400i
$932$	−26.2705	+	49.5118i	−0.0281873	+	0.0531242i
$933$	960.509	−	960.509i	1.02948	−	1.02948i
$934$	−2.35604	−	15.7178i	−0.00252253	−	0.0168285i
$935$	45.8503	−	383.986i	0.0490377	−	0.410680i
$936$	255.847	−	122.444i	0.273341	−	0.130816i
$937$	1241.34	−	1241.34i	1.32480	−	1.32480i	0.414958	−	0.909841i	$-0.363796\pi$
$937$	1241.34	−	1241.34i	1.32480	−	1.32480i	0.909841	−	0.414958i	$-0.136204\pi$
$938$	334.734	+	247.464i	0.356859	+	0.263821i
$939$	−1368.23			−1.45712
$940$	169.500	+	938.215i	0.180319	+	0.998101i
$941$			328.028i			0.348595i	0.984693	+	0.174298i	$0.0557654\pi$
$941$			328.028i			0.348595i	−0.984693	+	0.174298i	$0.944235\pi$
$942$	−764.719	−	565.347i	−0.811804	−	0.600156i
$943$	−886.700	−	886.700i	−0.940297	−	0.940297i
$944$	−405.370	+	274.455i	−0.429417	+	0.290736i
$945$	425.675	+	541.115i	0.450449	+	0.572609i
$946$	34.4222	+	229.640i	0.0363871	+	0.242748i
$947$	−228.351	−	228.351i	−0.241131	−	0.241131i	0.576187	−	0.817318i	$-0.304540\pi$
$947$	−228.351	−	228.351i	−0.241131	−	0.241131i	−0.817318	+	0.576187i	$0.804540\pi$
$948$	109.933	−	207.190i	0.115963	−	0.218555i
$949$	−434.823			−0.458191
$950$	673.382	−	563.165i	0.708823	−	0.592805i
$951$	1207.26			1.26947
$952$	1723.45	+	607.769i	1.81034	+	0.638412i
$953$	−1291.50	−	1291.50i	−1.35519	−	1.35519i	−0.879742	−	0.475451i	$-0.842285\pi$
$953$	−1291.50	−	1291.50i	−1.35519	−	1.35519i	−0.475451	−	0.879742i	$-0.657715\pi$
$954$	−57.4574	−	383.313i	−0.0602279	−	0.401796i
$955$	500.572	+	636.324i	0.524159	+	0.666308i
$956$	171.091	−	52.4710i	0.178966	−	0.0548860i
$957$	6.59578	+	6.59578i	0.00689215	+	0.00689215i
$958$	−909.947	+	1230.84i	−0.949840	+	1.28481i
$959$			710.482i			0.740857i
$960$	799.059	+	817.665i	0.832353	+	0.851735i
$961$	−954.886			−0.993638
$962$	412.972	+	305.305i	0.429285	+	0.317365i
$963$	−283.377	+	283.377i	−0.294265	+	0.294265i
$964$	−25.1904	−	82.1379i	−0.0261311	−	0.0852053i
$965$	−52.8207	+	442.361i	−0.0547365	+	0.458405i
$966$	−1484.48	+	222.519i	−1.53673	+	0.230351i
$967$	486.969	−	486.969i	0.503588	−	0.503588i	−0.408963	−	0.912551i	$-0.634110\pi$
$967$	486.969	−	486.969i	0.503588	−	0.503588i	0.912551	+	0.408963i	$0.134110\pi$
$968$	305.404	−	866.033i	0.315500	−	0.894662i
$969$			1946.49i			2.00876i
$970$	248.428	+	233.978i	0.256111	+	0.241214i
$971$		−	361.550i		−	0.372348i	−0.982517	−	0.186174i	$-0.940391\pi$
$971$		−	361.550i		−	0.372348i	0.982517	−	0.186174i	$-0.0596088\pi$
$972$	−676.495	−	358.943i	−0.695983	−	0.369282i
$973$	−362.930	+	362.930i	−0.373001	+	0.373001i
$974$	1709.98	−	256.320i	1.75562	−	0.263162i
$975$	817.591	+	198.075i	0.838555	+	0.203154i
$976$	213.819	+	315.811i	0.219077	+	0.323577i
$977$	−1073.65	+	1073.65i	−1.09892	+	1.09892i	−0.104387	+	0.994537i	$0.533288\pi$
$977$	−1073.65	+	1073.65i	−1.09892	+	1.09892i	−0.994537	+	0.104387i	$0.966712\pi$
$978$	−798.844	+	1080.56i	−0.816814	+	1.10487i
$979$	−210.513			−0.215028
$980$	85.2489	+	59.1597i	0.0869887	+	0.0603671i
$981$		−	44.6506i		−	0.0455154i
$982$	1069.11	−	1446.14i	1.08871	−	1.47265i
$983$	122.156	+	122.156i	0.124269	+	0.124269i	0.766506	−	0.642237i	$-0.221994\pi$
$983$	122.156	+	122.156i	0.124269	+	0.124269i	−0.642237	+	0.766506i	$0.721994\pi$
$984$	−542.172	−	1132.87i	−0.550988	−	1.15129i
$985$	3.32146	−	27.8164i	0.00337204	−	0.0282400i
$986$	−64.2958	+	9.63773i	−0.0652088	+	0.00977458i
$987$	−886.510	−	886.510i	−0.898187	−	0.898187i
$988$	−584.280	−	310.014i	−0.591377	−	0.313780i
$989$	1329.38			1.34416
$990$	2.80910	+	93.7797i	0.00283748	+	0.0947270i
$991$	324.300			0.327245			0.163623	−	0.986523i	$-0.447682\pi$
$991$	324.300			0.327245			0.163623	+	0.986523i	$0.447682\pi$
$992$	−79.0563	−	3.27905i	−0.0796938	−	0.00330549i
$993$	−184.603	−	184.603i	−0.185904	−	0.185904i
$994$	−317.914	+	47.6543i	−0.319833	+	0.0479420i
$995$	483.465	−	380.323i	0.485895	−	0.382235i
$996$	6.64294	−	2.03728i	0.00666962	−	0.00204547i
$997$	743.909	+	743.909i	0.746148	+	0.746148i	0.973753	−	0.227606i	$-0.0730897\pi$
$997$	743.909	+	743.909i	0.746148	+	0.746148i	−0.227606	+	0.973753i	$0.573090\pi$
$998$	−1214.78	−	898.070i	−1.21721	−	0.899869i
$999$		−	509.987i		−	0.510498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.13.2	✓	20
3.2	odd	2		360.3.u.b.253.9		20
4.3	odd	2		160.3.m.a.113.8		20
5.2	odd	4	inner	40.3.i.a.37.8	yes	20
5.3	odd	4		200.3.i.b.157.3		20
5.4	even	2		200.3.i.b.93.9		20
8.3	odd	2		160.3.m.a.113.3		20
8.5	even	2	inner	40.3.i.a.13.8	yes	20
15.2	even	4		360.3.u.b.37.3		20
20.3	even	4		800.3.m.b.657.8		20
20.7	even	4		160.3.m.a.17.3		20
20.19	odd	2		800.3.m.b.593.3		20
24.5	odd	2		360.3.u.b.253.3		20
40.3	even	4		800.3.m.b.657.3		20
40.13	odd	4		200.3.i.b.157.9		20
40.19	odd	2		800.3.m.b.593.8		20
40.27	even	4		160.3.m.a.17.8		20
40.29	even	2		200.3.i.b.93.3		20
40.37	odd	4	inner	40.3.i.a.37.2	yes	20
120.77	even	4		360.3.u.b.37.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.2	✓	20	1.1	even	1	trivial
40.3.i.a.13.8	yes	20	8.5	even	2	inner
40.3.i.a.37.2	yes	20	40.37	odd	4	inner
40.3.i.a.37.8	yes	20	5.2	odd	4	inner
160.3.m.a.17.3		20	20.7	even	4
160.3.m.a.17.8		20	40.27	even	4
160.3.m.a.113.3		20	8.3	odd	2
160.3.m.a.113.8		20	4.3	odd	2
200.3.i.b.93.3		20	40.29	even	2
200.3.i.b.93.9		20	5.4	even	2
200.3.i.b.157.3		20	5.3	odd	4
200.3.i.b.157.9		20	40.13	odd	4
360.3.u.b.37.3		20	15.2	even	4
360.3.u.b.37.9		20	120.77	even	4
360.3.u.b.253.3		20	24.5	odd	2
360.3.u.b.253.9		20	3.2	odd	2
800.3.m.b.593.3		20	20.19	odd	2
800.3.m.b.593.8		20	40.19	odd	2
800.3.m.b.657.3		20	40.3	even	4
800.3.m.b.657.8		20	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60823 - 1.18894i) q^{2} +(-2.52630 + 2.52630i) q^{3} +(1.17282 + 3.82420i) q^{4} +(3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 + 5.20520i) q^{7} +(2.66059 - 7.54462i) q^{8} -3.76437i q^{9} +(-0.299408 - 9.99552i) q^{10} -2.49236i q^{11} +(-12.6240 - 6.69817i) q^{12} +(-6.65988 + 6.65988i) q^{13} +(14.5599 - 2.18248i) q^{14} +(-17.7376 - 2.11798i) q^{15} +(-13.2490 + 8.97020i) q^{16} +(21.9428 - 21.9428i) q^{17} +(-4.47563 + 6.05398i) q^{18} +17.5567 q^{19} +(-11.4026 + 16.4311i) q^{20} -26.2998i q^{21} +(-2.96328 + 4.00830i) q^{22} +(20.1791 + 20.1791i) q^{23} +(12.3385 + 25.7814i) q^{24} +(-5.88639 + 24.2971i) q^{25} +(18.6289 - 2.79240i) q^{26} +(-13.2268 - 13.2268i) q^{27} +(-26.0105 - 13.8010i) q^{28} +1.04754 q^{29} +(26.0081 + 24.4953i) q^{30} -2.47263 q^{31} +(31.9725 + 1.32614i) q^{32} +(6.29646 + 6.29646i) q^{33} +(-61.3780 + 9.20035i) q^{34} +(-36.5467 - 4.36391i) q^{35} +(14.3957 - 4.41493i) q^{36} +(19.2786 + 19.2786i) q^{37} +(-28.2353 - 20.8740i) q^{38} -33.6497i q^{39} +(37.8737 - 12.8680i) q^{40} -43.9414 q^{41} +(-31.2690 + 42.2962i) q^{42} +(32.9394 - 32.9394i) q^{43} +(9.53129 - 2.92310i) q^{44} +(14.7932 - 11.6372i) q^{45} +(-8.46086 - 56.4446i) q^{46} +(33.7079 - 33.7079i) q^{47} +(10.8095 - 56.1323i) q^{48} -5.18827i q^{49} +(38.3546 - 32.0768i) q^{50} +110.868i q^{51} +(-33.2795 - 17.6578i) q^{52} +(-36.4034 + 36.4034i) q^{53} +(5.54582 + 36.9976i) q^{54} +(9.79445 - 7.70491i) q^{55} +(25.4224 + 53.1202i) q^{56} +(-44.3536 + 44.3536i) q^{57} +(-1.68469 - 1.24547i) q^{58} +30.5963 q^{59} +(-12.7035 - 70.3162i) q^{60} -23.8366i q^{61} +(3.97657 + 2.93982i) q^{62} +(19.5943 + 19.5943i) q^{63} +(-49.8425 - 40.1463i) q^{64} +(-46.7603 - 5.58347i) q^{65} +(-2.64003 - 17.6123i) q^{66} +(19.9932 + 19.9932i) q^{67} +(109.649 + 58.1787i) q^{68} -101.957 q^{69} +(53.5872 + 50.4702i) q^{70} -21.8350 q^{71} +(-28.4007 - 10.0154i) q^{72} +(32.6450 + 32.6450i) q^{73} +(-8.08328 - 53.9257i) q^{74} +(-46.5110 - 76.2526i) q^{75} +(20.5909 + 67.1405i) q^{76} +(12.9733 + 12.9733i) q^{77} +(-40.0076 + 54.1165i) q^{78} +16.4124i q^{79} +(-76.2090 - 24.3351i) q^{80} +100.709 q^{81} +(70.6680 + 52.2439i) q^{82} +(-0.343799 + 0.343799i) q^{83} +(100.576 - 30.8450i) q^{84} +(154.065 + 18.3963i) q^{85} +(-92.1373 + 13.8111i) q^{86} +(-2.64640 + 2.64640i) q^{87} +(-18.8039 - 6.63116i) q^{88} -84.4631i q^{89} +(-37.6268 + 1.12708i) q^{90} -69.3320i q^{91} +(-53.5025 + 100.836i) q^{92} +(6.24661 - 6.24661i) q^{93} +(-94.2869 + 14.1333i) q^{94} +(54.2751 + 68.9942i) q^{95} +(-84.1223 + 77.4219i) q^{96} +(-24.1311 + 24.1311i) q^{97} +(-6.16856 + 8.34394i) q^{98} -9.38218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Introduction

L-functions

Modular forms

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