LMFDB - Embedded newform 119.5.h.a.101.41

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(33,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.41
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.41

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.21912 + 5.57567i) q^{2} +(-6.37245 + 11.0374i) q^{3} +(-12.7254 + 22.0411i) q^{4} +(12.0871 + 20.9355i) q^{5} -82.0546 q^{6} +(1.73482 + 48.9693i) q^{7} -60.8466 q^{8} +(-40.7162 - 70.5225i) q^{9} +(-77.8195 + 134.787i) q^{10} +(110.347 + 63.7089i) q^{11} +(-162.184 - 280.911i) q^{12} -173.407i q^{13} +(-267.452 + 167.311i) q^{14} -308.098 q^{15} +(7.73430 + 13.3962i) q^{16} +(280.853 - 68.1383i) q^{17} +(262.140 - 454.040i) q^{18} +(401.436 - 231.769i) q^{19} -615.253 q^{20} +(-551.549 - 292.906i) q^{21} +820.345i q^{22} +(77.4845 - 44.7357i) q^{23} +(387.742 - 671.589i) q^{24} +(20.3041 - 35.1677i) q^{25} +(966.863 - 558.218i) q^{26} +5.51108 q^{27} +(-1101.41 - 584.917i) q^{28} +7.79645i q^{29} +(-991.802 - 1717.85i) q^{30} +(545.098 - 944.137i) q^{31} +(-536.568 + 929.363i) q^{32} +(-1406.36 + 811.963i) q^{33} +(1284.01 + 1346.60i) q^{34} +(-1004.23 + 628.216i) q^{35} +2072.52 q^{36} +(101.759 - 58.7505i) q^{37} +(2584.54 + 1492.18i) q^{38} +(1913.97 + 1105.03i) q^{39} +(-735.459 - 1273.85i) q^{40} -2278.14 q^{41} +(-142.350 - 4018.15i) q^{42} +3069.29 q^{43} +(-2808.42 + 1621.44i) q^{44} +(984.282 - 1704.83i) q^{45} +(498.863 + 288.019i) q^{46} +(-1034.86 + 597.477i) q^{47} -197.146 q^{48} +(-2394.98 + 169.906i) q^{49} +261.445 q^{50} +(-1037.65 + 3534.09i) q^{51} +(3822.08 + 2206.68i) q^{52} +(-603.165 + 1044.71i) q^{53} +(17.7408 + 30.7280i) q^{54} +3080.22i q^{55} +(-105.558 - 2979.62i) q^{56} +5907.75i q^{57} +(-43.4705 + 25.0977i) q^{58} +(-4777.05 - 2758.03i) q^{59} +(3920.67 - 6790.80i) q^{60} +(-2297.66 - 3979.66i) q^{61} +7018.93 q^{62} +(3382.80 - 2116.19i) q^{63} -6661.60 q^{64} +(3630.36 - 2095.99i) q^{65} +(-9054.48 - 5227.61i) q^{66} +(726.810 - 1258.87i) q^{67} +(-2072.12 + 7057.38i) q^{68} +1140.30i q^{69} +(-6735.45 - 3576.94i) q^{70} +5808.00i q^{71} +(2477.44 + 4291.06i) q^{72} +(-1509.73 + 2614.93i) q^{73} +(655.147 + 378.249i) q^{74} +(258.773 + 448.209i) q^{75} +11797.4i q^{76} +(-2928.35 + 5514.14i) q^{77} +14228.9i q^{78} +(2835.48 - 1637.07i) q^{79} +(-186.970 + 323.842i) q^{80} +(3262.89 - 5651.50i) q^{81} +(-7333.60 - 12702.2i) q^{82} -5697.38i q^{83} +(13474.7 - 8429.37i) q^{84} +(4821.20 + 5056.19i) q^{85} +(9880.41 + 17113.4i) q^{86} +(-86.0526 - 49.6825i) q^{87} +(-6714.24 - 3876.47i) q^{88} +(3073.97 - 1774.76i) q^{89} +12674.1 q^{90} +(8491.63 - 300.831i) q^{91} +2277.12i q^{92} +(6947.22 + 12032.9i) q^{93} +(-6662.67 - 3846.69i) q^{94} +(9704.39 + 5602.83i) q^{95} +(-6838.51 - 11844.6i) q^{96} +3854.51 q^{97} +(-8657.06 - 12806.7i) q^{98} -10375.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) $ 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	3.21912	+	5.57567i	0.804779	+	1.39392i	0.916440	+	0.400172i	$0.131050\pi$
$2$	3.21912	+	5.57567i	0.804779	+	1.39392i	−0.111661	+	0.993746i	$0.535617\pi$
$3$	−6.37245	+	11.0374i	−0.708050	+	1.22638i	0.257530	+	0.966270i	$0.417091\pi$
$3$	−6.37245	+	11.0374i	−0.708050	+	1.22638i	−0.965580	+	0.260108i	$0.916242\pi$
$4$	−12.7254	+	22.0411i	−0.795338	+	1.37757i
$5$	12.0871	+	20.9355i	0.483484	+	0.837419i	0.999820	−	0.0189672i	$-0.00603782\pi$
$5$	12.0871	+	20.9355i	0.483484	+	0.837419i	−0.516336	+	0.856386i	$0.672704\pi$
$6$	−82.0546			−2.27929
$7$	1.73482	+	48.9693i	0.0354045	+	0.999373i
$7$	1.73482	+	48.9693i	0.0354045	+	0.999373i
$8$	−60.8466			−0.950728
$9$	−40.7162	−	70.5225i	−0.502669	−	0.870649i
$10$	−77.8195	+	134.787i	−0.778195	+	1.34787i
$11$	110.347	+	63.7089i	0.911959	+	0.526520i	0.881061	−	0.473003i	$-0.156830\pi$
$11$	110.347	+	63.7089i	0.911959	+	0.526520i	0.0308979	+	0.999523i	$0.490163\pi$
$12$	−162.184	−	280.911i	−1.12628	−	1.95077i
$13$		−	173.407i		−	1.02608i	−0.858365	−	0.513039i	$-0.828519\pi$
$13$		−	173.407i		−	1.02608i	0.858365	−	0.513039i	$-0.171481\pi$
$14$	−267.452	+	167.311i	−1.36455	+	0.853625i
$15$	−308.098			−1.36932
$16$	7.73430	+	13.3962i	0.0302121	+	0.0523289i
$17$	280.853	−	68.1383i	0.971808	−	0.235773i
$17$	280.853	−	68.1383i	0.971808	−	0.235773i
$18$	262.140	−	454.040i	0.809075	−	1.40136i
$19$	401.436	−	231.769i	1.11201	−	0.642020i	0.172661	−	0.984981i	$-0.444763\pi$
$19$	401.436	−	231.769i	1.11201	−	0.642020i	0.939349	+	0.342962i	$0.111430\pi$
$20$	−615.253			−1.53813
$21$	−551.549	−	292.906i	−1.25068	−	0.664187i
$22$			820.345i			1.69493i
$23$	77.4845	−	44.7357i	0.146474	−	0.0845665i	−0.424972	−	0.905206i	$-0.639716\pi$
$23$	77.4845	−	44.7357i	0.146474	−	0.0845665i	0.571446	+	0.820640i	$0.306383\pi$
$24$	387.742	−	671.589i	0.673163	−	1.16595i
$25$	20.3041	−	35.1677i	0.0324865	−	0.0562683i
$26$	966.863	−	558.218i	1.43027	−	0.825767i
$27$	5.51108			0.00755978
$28$	−1101.41	−	584.917i	−1.40486	−	0.746068i
$29$			7.79645i			0.00927046i	0.999989	+	0.00463523i	$0.00147544\pi$
$29$			7.79645i			0.00927046i	−0.999989	+	0.00463523i	$0.998525\pi$
$30$	−991.802	−	1717.85i	−1.10200	−	1.90872i
$31$	545.098	−	944.137i	0.567220	−	0.982453i	−0.429620	−	0.903010i	$-0.641352\pi$
$31$	545.098	−	944.137i	0.567220	−	0.982453i	0.996839	−	0.0794432i	$-0.0253142\pi$
$32$	−536.568	+	929.363i	−0.523992	+	0.907581i
$33$	−1406.36	+	811.963i	−1.29142	+	0.745604i
$34$	1284.01	+	1346.60i	1.11074	+	1.16488i
$35$	−1004.23	+	628.216i	−0.819776	+	0.512829i
$36$	2072.52			1.59917
$37$	101.759	−	58.7505i	0.0743308	−	0.0429149i	−0.462374	−	0.886685i	$-0.653002\pi$
$37$	101.759	−	58.7505i	0.0743308	−	0.0429149i	0.536705	+	0.843770i	$0.319669\pi$
$38$	2584.54	+	1492.18i	1.78985	+	1.03337i
$39$	1913.97	+	1105.03i	1.25836	+	0.726515i
$40$	−735.459	−	1273.85i	−0.459662	−	0.796158i
$41$	−2278.14			−1.35523			−0.677615	−	0.735417i	$-0.736987\pi$
$41$	−2278.14			−1.35523			−0.677615	+	0.735417i	$0.736987\pi$
$42$	−142.350	−	4018.15i	−0.0806973	−	2.27787i
$43$	3069.29			1.65997			0.829987	−	0.557782i	$-0.188348\pi$
$43$	3069.29			1.65997			0.829987	+	0.557782i	$0.188348\pi$
$44$	−2808.42	+	1621.44i	−1.45063	+	0.837523i
$45$	984.282	−	1704.83i	0.486065	−	0.841889i
$46$	498.863	+	288.019i	0.235758	+	0.136115i
$47$	−1034.86	+	597.477i	−0.468475	+	0.270474i	−0.715601	−	0.698509i	$-0.753847\pi$
$47$	−1034.86	+	597.477i	−0.468475	+	0.270474i	0.247126	+	0.968983i	$0.420514\pi$
$48$	−197.146			−0.0855667
$49$	−2394.98	+	169.906i	−0.997493	+	0.0707646i
$50$	261.445			0.104578
$51$	−1037.65	+	3534.09i	−0.398942	+	1.35874i
$52$	3822.08	+	2206.68i	1.41349	+	0.816080i
$53$	−603.165	+	1044.71i	−0.214726	+	0.371916i	−0.953188	−	0.302379i	$-0.902219\pi$
$53$	−603.165	+	1044.71i	−0.214726	+	0.371916i	0.738462	+	0.674295i	$0.235553\pi$
$54$	17.7408	+	30.7280i	0.00608396	+	0.0105377i
$55$			3080.22i			1.01826i
$56$	−105.558	−	2979.62i	−0.0336601	−	0.950132i
$57$			5907.75i			1.81833i
$58$	−43.4705	+	25.0977i	−0.0129223	+	0.00746067i
$59$	−4777.05	−	2758.03i	−1.37232	−	0.792310i	−0.381101	−	0.924533i	$-0.624455\pi$
$59$	−4777.05	−	2758.03i	−1.37232	−	0.792310i	−0.991220	+	0.132223i	$0.957788\pi$
$60$	3920.67	−	6790.80i	1.08908	−	1.88633i
$61$	−2297.66	−	3979.66i	−0.617483	−	1.06951i	−0.989943	−	0.141464i	$-0.954819\pi$
$61$	−2297.66	−	3979.66i	−0.617483	−	1.06951i	0.372460	−	0.928048i	$-0.378514\pi$
$62$	7018.93			1.82595
$63$	3382.80	−	2116.19i	0.852306	−	0.533179i
$64$	−6661.60			−1.62637
$65$	3630.36	−	2095.99i	0.859258	−	0.496093i
$66$	−9054.48	−	5227.61i	−2.07862	−	1.20009i
$67$	726.810	−	1258.87i	0.161909	−	0.280435i	−0.773644	−	0.633620i	$-0.781568\pi$
$67$	726.810	−	1258.87i	0.161909	−	0.280435i	0.935553	+	0.353185i	$0.114901\pi$
$68$	−2072.12	+	7057.38i	−0.448124	+	1.52625i
$69$			1140.30i			0.239509i
$70$	−6735.45	−	3576.94i	−1.37458	−	0.729987i
$71$			5808.00i			1.15215i	0.817396	+	0.576076i	$0.195417\pi$
$71$			5808.00i			1.15215i	−0.817396	+	0.576076i	$0.804583\pi$
$72$	2477.44	+	4291.06i	0.477902	+	0.827750i
$73$	−1509.73	+	2614.93i	−0.283305	+	0.490699i	−0.972197	−	0.234166i	$-0.924764\pi$
$73$	−1509.73	+	2614.93i	−0.283305	+	0.490699i	0.688892	+	0.724864i	$0.258098\pi$
$74$	655.147	+	378.249i	0.119640	+	0.0690740i
$75$	258.773	+	448.209i	0.0460042	+	0.0796816i
$76$			11797.4i			2.04249i
$77$	−2928.35	+	5514.14i	−0.493902	+	0.930028i
$78$			14228.9i			2.33874i
$79$	2835.48	−	1637.07i	0.454331	−	0.262308i	−0.255327	−	0.966855i	$-0.582183\pi$
$79$	2835.48	−	1637.07i	0.454331	−	0.262308i	0.709658	+	0.704547i	$0.248850\pi$
$80$	−186.970	+	323.842i	−0.0292141	+	0.0506004i
$81$	3262.89	−	5651.50i	0.497317	−	0.861377i
$82$	−7333.60	−	12702.2i	−1.09066	−	1.88908i
$83$		−	5697.38i		−	0.827025i	−0.910498	−	0.413513i	$-0.864302\pi$
$83$		−	5697.38i		−	0.827025i	0.910498	−	0.413513i	$-0.135698\pi$
$84$	13474.7	−	8429.37i	1.90967	−	1.19464i
$85$	4821.20	+	5056.19i	0.667294	+	0.699818i
$86$	9880.41	+	17113.4i	1.33591	+	2.31387i
$87$	−86.0526	−	49.6825i	−0.0113691	−	0.00656394i
$88$	−6714.24	−	3876.47i	−0.867025	−	0.500577i
$89$	3073.97	−	1774.76i	0.388078	−	0.224057i	−0.293249	−	0.956036i	$-0.594736\pi$
$89$	3073.97	−	1774.76i	0.388078	−	0.224057i	0.681327	+	0.731979i	$0.261403\pi$
$90$	12674.1			1.56470
$91$	8491.63	−	300.831i	1.02544	−	0.0363278i
$92$			2277.12i			0.269036i
$93$	6947.22	+	12032.9i	0.803239	+	1.39125i
$94$	−6662.67	−	3846.69i	−0.754037	−	0.435343i
$95$	9704.39	+	5602.83i	1.07528	+	0.620812i
$96$	−6838.51	−	11844.6i	−0.742025	−	1.28523i
$97$	3854.51			0.409662			0.204831	−	0.978797i	$-0.434336\pi$
$97$	3854.51			0.409662			0.204831	+	0.978797i	$0.434336\pi$
$98$	−8657.06	−	12806.7i	−0.901401	−	1.33347i
$99$		−	10375.9i		−	1.05866i
$100$	516.756	+	895.047i	0.0516756	+	0.0895047i
$101$	13594.2	+	7848.61i	1.33263	+	0.769396i	0.985702	−	0.168495i	$-0.0538907\pi$
$101$	13594.2	+	7848.61i	1.33263	+	0.769396i	0.346930	+	0.937891i	$0.387224\pi$
$102$	−23045.2	+	5591.06i	−2.21504	+	0.537396i
$103$	14979.9	−	8648.66i	1.41200	−	0.815219i	0.416424	−	0.909171i	$-0.363283\pi$
$103$	14979.9	−	8648.66i	1.41200	−	0.815219i	0.995577	+	0.0939519i	$0.0299500\pi$
$104$			10551.3i			0.975522i
$105$	−534.494	−	15087.3i	−0.0484802	−	1.36846i
$106$	−7766.64			−0.691228
$107$	281.346	−	162.435i	0.0245739	−	0.0141877i	−0.487663	−	0.873032i	$-0.662150\pi$
$107$	281.346	−	162.435i	0.0245739	−	0.0141877i	0.512237	+	0.858844i	$0.328817\pi$
$108$	−70.1308	+	121.470i	−0.00601259	+	0.0104141i
$109$	−10493.3	−	6058.29i	−0.883197	−	0.509914i	−0.0114858	−	0.999934i	$-0.503656\pi$
$109$	−10493.3	−	6058.29i	−0.883197	−	0.509914i	−0.871711	+	0.490020i	$0.836989\pi$
$110$	−17174.3	+	9915.59i	−1.41936	+	0.819470i
$111$			1497.54i			0.121544i
$112$	−642.584	+	401.983i	−0.0512264	+	0.0320458i
$113$		−	18266.0i		−	1.43050i	−0.698870	−	0.715249i	$-0.746313\pi$
$113$		−	18266.0i		−	1.43050i	0.698870	−	0.715249i	$-0.253687\pi$
$114$	−32939.7	+	19017.7i	−2.53460	+	1.46335i
$115$	1873.13	+	1081.45i	0.141635	+	0.0817731i
$116$	−171.842	−	99.2131i	−0.0127707	−	0.00737315i
$117$	−12229.1	+	7060.49i	−0.893354	+	0.515778i
$118$		−	35513.7i		−	2.55054i
$119$	3823.91	+	13634.9i	0.270031	+	0.962852i
$120$	18746.7			1.30185
$121$	797.143	+	1380.69i	0.0544459	+	0.0943031i
$122$	14792.8	−	25622.0i	0.993875	−	1.72144i
$123$	14517.3	−	25144.8i	0.959571	−	1.66203i
$124$	13873.2	+	24029.1i	0.902263	+	1.56277i
$125$	16090.5			1.02979
$126$	22688.8	+	12049.1i	1.42913	+	0.758954i
$127$	−10015.0			−0.620929			−0.310465	−	0.950585i	$-0.600485\pi$
$127$	−10015.0			−0.620929			−0.310465	+	0.950585i	$0.600485\pi$
$128$	−12859.4	−	22273.1i	−0.784874	−	1.35944i
$129$	−19558.9	+	33877.0i	−1.17534	+	2.03576i
$130$	23373.1	+	13494.5i	1.38303	+	0.798490i
$131$	−9595.14	−	16619.3i	−0.559125	−	0.968432i	−0.997570	−	0.0696744i	$-0.977804\pi$
$131$	−9595.14	−	16619.3i	−0.559125	−	0.968432i	0.438445	−	0.898758i	$-0.355529\pi$
$132$		−	41330.3i		−	2.37203i
$133$	12046.0	+	19255.9i	0.680987	+	1.08858i
$134$	9358.75			0.521205
$135$	66.6130	+	115.377i	0.00365503	+	0.00633071i
$136$	−17088.9	+	4145.99i	−0.923926	+	0.224156i
$137$	−17145.6	+	29697.0i	−0.913506	+	1.58224i	−0.104432	+	0.994532i	$0.533303\pi$
$137$	−17145.6	+	29697.0i	−0.913506	+	1.58224i	−0.809074	+	0.587707i	$0.800031\pi$
$138$	−6357.96	+	3670.77i	−0.333856	+	0.192752i
$139$	−36844.3			−1.90696			−0.953478	−	0.301462i	$-0.902525\pi$
$139$	−36844.3			−1.90696			−0.953478	+	0.301462i	$0.902525\pi$
$140$	−1067.35	−	30128.5i	−0.0544568	−	1.53717i
$141$		−	15229.6i		−	0.766036i
$142$	−32383.5	+	18696.6i	−1.60600	+	0.927227i
$143$	11047.6	−	19135.0i	0.540251	−	0.935742i
$144$	629.823	−	1090.88i	0.0303734	−	0.0526082i
$145$	−163.222	+	94.2365i	−0.00776325	+	0.00448212i
$146$	−19440.0			−0.911991
$147$	13386.6	−	27517.1i	0.619491	−	1.27341i
$148$			2990.50i			0.136527i
$149$	10571.9	+	18311.0i	0.476188	+	0.824782i	0.999628	−	0.0272808i	$-0.00868481\pi$
$149$	10571.9	+	18311.0i	0.476188	+	0.824782i	−0.523440	+	0.852063i	$0.675351\pi$
$150$	−1666.04	+	2885.67i	−0.0740464	+	0.128252i
$151$	−176.922	+	306.439i	−0.00775941	+	0.0134397i	−0.869879	−	0.493265i	$-0.835803\pi$
$151$	−176.922	+	306.439i	−0.00775941	+	0.0134397i	0.862120	+	0.506705i	$0.169137\pi$
$152$	−24426.0	+	14102.4i	−1.05722	+	0.610386i
$153$	−16240.5	−	17032.1i	−0.693773	−	0.727588i
$154$	−40171.7	+	1423.15i	−1.69387	+	0.0600081i
$155$	26354.6			1.09697
$156$	−48712.0	+	28123.9i	−2.00165	+	1.15565i
$157$	−34468.9	−	19900.6i	−1.39839	−	0.807360i	−0.404165	−	0.914686i	$-0.632438\pi$
$157$	−34468.9	−	19900.6i	−1.39839	−	0.807360i	−0.994224	+	0.107326i	$0.965771\pi$
$158$	18255.5	+	10539.8i	0.731272	+	0.422200i
$159$	−7687.28	−	13314.8i	−0.304073	−	0.526671i
$160$	−25942.2			−1.01337
$161$	2325.10	+	3716.75i	0.0896994	+	0.143388i
$162$	42014.5			1.60092
$163$	25733.9	−	14857.5i	0.968570	−	0.559204i	0.0697697	−	0.997563i	$-0.477774\pi$
$163$	25733.9	−	14857.5i	0.968570	−	0.559204i	0.898800	+	0.438359i	$0.144440\pi$
$164$	28990.3	−	50212.7i	1.07787	−	1.86692i
$165$	−33997.7	−	19628.6i	−1.24877	−	0.720975i
$166$	31766.7	−	18340.5i	1.15281	−	0.665573i
$167$	10133.5			0.363353			0.181676	−	0.983358i	$-0.441848\pi$
$167$	10133.5			0.363353			0.181676	+	0.983358i	$0.441848\pi$
$168$	33559.9	+	17822.4i	1.18905	+	0.631461i
$169$	−1509.11			−0.0528380
$170$	−12671.6	+	43157.9i	−0.438465	+	1.49335i
$171$	−32689.9	−	18873.5i	−1.11795	−	0.645447i
$172$	−39058.0	+	67650.5i	−1.32024	+	2.28673i
$173$	−5941.53	−	10291.0i	−0.198521	−	0.343848i	0.749528	−	0.661972i	$-0.230280\pi$
$173$	−5941.53	−	10291.0i	−0.198521	−	0.343848i	−0.948049	+	0.318124i	$0.896947\pi$
$174$		−	639.735i		−	0.0211301i
$175$	1757.36	+	933.267i	0.0573832	+	0.0304740i
$176$			1970.97i			0.0636291i
$177$	60883.0	−	35150.8i	1.94334	−	1.12199i
$178$	19790.9	+	11426.3i	0.624634	+	0.360633i
$179$	5724.70	−	9915.48i	0.178668	−	0.309462i	−0.762757	−	0.646686i	$-0.776155\pi$
$179$	5724.70	−	9915.48i	0.178668	−	0.309462i	0.941425	+	0.337224i	$0.109488\pi$
$180$	25050.8	+	43389.2i	0.773172	+	1.33917i
$181$	−20900.2			−0.637959			−0.318979	−	0.947762i	$-0.603340\pi$
$181$	−20900.2			−0.637959			−0.318979	+	0.947762i	$0.603340\pi$
$182$	29012.9	+	46378.2i	0.875887	+	1.40014i
$183$	58566.8			1.74884
$184$	−4714.67	+	2722.02i	−0.139257	+	0.0803998i
$185$	2459.94	+	1420.25i	0.0718755	+	0.0414973i
$186$	−44727.8	+	77470.8i	−1.29286	+	2.23930i
$187$	35332.3	+	10373.9i	1.01039	+	0.296661i
$188$		−	30412.6i		−	0.860473i
$189$	9.56074	+	269.874i	0.000267650	+	0.00755504i
$190$			72144.7i			1.99847i
$191$	8913.23	+	15438.2i	0.244325	+	0.423184i	0.961942	−	0.273255i	$-0.0881002\pi$
$191$	8913.23	+	15438.2i	0.244325	+	0.423184i	−0.717616	+	0.696439i	$0.754767\pi$
$192$	42450.7	−	73526.8i	1.15155	−	1.99454i
$193$	−7079.15	−	4087.15i	−0.190049	−	0.109725i	0.401956	−	0.915659i	$-0.368330\pi$
$193$	−7079.15	−	4087.15i	−0.190049	−	0.109725i	−0.592006	+	0.805934i	$0.701664\pi$
$194$	12408.1	+	21491.5i	0.329687	+	0.571035i
$195$			53426.4i			1.40503i
$196$	26732.2	−	54950.0i	0.695862	−	1.43039i
$197$			22768.7i			0.586685i	0.956007	+	0.293343i	$0.0947676\pi$
$197$			22768.7i			0.586685i	−0.956007	+	0.293343i	$0.905232\pi$
$198$	57852.8	−	33401.3i	1.47569	−	0.851988i
$199$	−68.5686	+	118.764i	−0.00173149	+	0.00299902i	−0.866890	−	0.498500i	$-0.833884\pi$
$199$	−68.5686	+	118.764i	−0.00173149	+	0.00299902i	0.865158	+	0.501499i	$0.167218\pi$
$200$	−1235.43	+	2139.84i	−0.0308859	+	0.0534959i
$201$	9263.13	+	16044.2i	0.229280	+	0.397124i
$202$			101062.i			2.47677i
$203$	−381.787	+	13.5254i	−0.00926464	+	0.000328216i
$204$	−64690.6	−	67843.7i	−1.55447	−	1.63023i
$205$	−27536.1	−	47694.0i	−0.655232	−	1.13490i
$206$	96444.1	+	55682.1i	2.27270	+	1.31214i
$207$	−6309.75	−	3642.94i	−0.147255	−	0.0850180i
$208$	2323.00	−	1341.18i	0.0536936	−	0.0310000i
$209$	59063.0			1.35214
$210$	82401.4	−	51548.0i	1.86851	−	1.16889i
$211$			84485.2i			1.89765i	0.315804	+	0.948824i	$0.397726\pi$
$211$			84485.2i			1.89765i	−0.315804	+	0.948824i	$0.602274\pi$
$212$	−15351.1	−	26588.8i	−0.341560	−	0.591599i
$213$	−64105.2	−	37011.2i	−1.41297	−	0.815781i
$214$	1811.37	+	1045.80i	0.0395531	+	0.0228360i
$215$	37098.8	+	64257.1i	0.802571	+	1.39009i
$216$	−335.331			−0.00718730
$217$	47179.4	+	25055.1i	1.00192	+	0.532081i
$218$		−	78009.3i		−	1.64147i
$219$	−19241.4	−	33327.0i	−0.401188	−	0.694878i
$220$	−67891.4	−	39197.1i	−1.40271	−	0.809857i
$221$	−11815.7	−	48701.9i	−0.241921	−	0.997152i
$222$	−8349.78	+	4820.75i	−0.169422	+	0.0978157i
$223$			38714.8i			0.778516i	0.921129	+	0.389258i	$0.127268\pi$
$223$			38714.8i			0.778516i	−0.921129	+	0.389258i	$0.872732\pi$
$224$	−46441.1	−	24663.1i	−0.925564	−	0.491531i
$225$	−3306.82			−0.0653199
$226$	101845.	−	58800.5i	1.99400	−	1.15123i
$227$	6793.09	−	11766.0i	0.131830	−	0.228337i	−0.792552	−	0.609805i	$-0.791248\pi$
$227$	6793.09	−	11766.0i	0.131830	−	0.228337i	0.924382	+	0.381468i	$0.124581\pi$
$228$	−130213.	−	75178.5i	−2.50487	−	1.44619i
$229$	−76758.0	+	44316.3i	−1.46370	+	0.845069i	−0.999180	−	0.0404918i	$-0.987108\pi$
$229$	−76758.0	+	44316.3i	−1.46370	+	0.845069i	−0.464523	+	0.885561i	$0.653774\pi$
$230$			13925.2i			0.263237i
$231$	−42201.0	−	67459.9i	−0.790859	−	1.26422i
$232$		−	474.388i		−	0.00881369i
$233$	−50059.1	+	28901.6i	−0.922085	+	0.532366i	−0.884300	−	0.466920i	$-0.845364\pi$
$233$	−50059.1	+	28901.6i	−0.922085	+	0.532366i	−0.0377851	+	0.999286i	$0.512030\pi$
$234$	−78733.9	−	45457.1i	−1.43791	−	0.830175i
$235$	−25016.9	−	14443.5i	−0.453000	−	0.261540i
$236$	121580.	−	70194.2i	2.18292	−	1.26031i
$237$			41728.5i			0.742909i
$238$	−63714.3	+	65213.3i	−1.12482	+	1.15128i
$239$	−21391.3			−0.374492			−0.187246	−	0.982313i	$-0.559956\pi$
$239$	−21391.3			−0.374492			−0.187246	+	0.982313i	$0.559956\pi$
$240$	−2382.92	−	4127.34i	−0.0413701	−	0.0716552i
$241$	−13162.1	+	22797.4i	−0.226616	+	0.392510i	−0.956803	−	0.290737i	$-0.906100\pi$
$241$	−13162.1	+	22797.4i	−0.226616	+	0.392510i	0.730187	+	0.683247i	$0.239433\pi$
$242$	−5132.19	+	8889.21i	−0.0876339	+	0.151786i
$243$	41808.4	+	72414.4i	0.708030	+	1.22634i
$244$	116954.			1.96443
$245$	−32505.4	−	48086.4i	−0.541531	−	0.801106i
$246$	186932.			3.08897
$247$	−40190.5	−	69611.9i	−0.658763	−	1.14101i
$248$	−33167.4	+	57447.6i	−0.539272	+	0.934046i
$249$	62884.3	+	36306.2i	1.01425	+	0.585575i
$250$	51797.3	+	89715.6i	0.828757	+	1.43545i
$251$			59018.5i			0.936787i	0.883520	+	0.468393i	$0.155167\pi$
$251$			59018.5i			0.936787i	−0.883520	+	0.468393i	$0.844833\pi$
$252$	3595.45	+	101490.i	0.0566178	+	1.59817i
$253$	11400.2			0.178104
$254$	−32239.3	−	55840.2i	−0.499711	−	0.865525i
$255$	−86530.0	+	20993.3i	−1.33072	+	0.322849i
$256$	29498.9	−	51093.5i	0.450117	−	0.779625i
$257$	37989.9	−	21933.5i	0.575178	−	0.332079i	−0.184037	−	0.982919i	$-0.558917\pi$
$257$	37989.9	−	21933.5i	0.575178	−	0.332079i	0.759215	+	0.650840i	$0.225583\pi$
$258$	−251850.			−3.78357
$259$	3053.50	+	4881.13i	0.0455196	+	0.0727648i
$260$			106689.i			1.57825i
$261$	549.826	−	317.442i	0.00807131	−	0.00465997i
$262$	61775.7	−	106999.i	0.899944	−	1.55875i
$263$	−3252.50	+	5633.50i	−0.0470225	+	0.0814454i	−0.888579	−	0.458724i	$-0.848307\pi$
$263$	−3252.50	+	5633.50i	−0.0470225	+	0.0814454i	0.841556	+	0.540170i	$0.181640\pi$
$264$	85572.3	−	49405.2i	1.22779	−	0.708867i
$265$	−29162.1			−0.415266
$266$	−68587.4	+	129152.i	−0.969351	+	1.82531i
$267$			45238.2i			0.634574i
$268$	18497.9	+	32039.4i	0.257545	+	0.446081i
$269$	−49124.0	+	85085.3i	−0.678874	+	1.17584i	0.296446	+	0.955050i	$0.404199\pi$
$269$	−49124.0	+	85085.3i	−0.678874	+	1.17584i	−0.975320	+	0.220795i	$0.929135\pi$
$270$	−428.870	+	742.825i	−0.00588299	+	0.0101896i
$271$	107385.	−	61998.6i	1.46219	−	0.844196i	0.463078	−	0.886318i	$-0.346745\pi$
$271$	107385.	−	61998.6i	1.46219	−	0.844196i	0.999112	+	0.0421218i	$0.0134118\pi$
$272$	3084.99	+	3235.35i	0.0416981	+	0.0437305i
$273$	−50792.1	+	95642.6i	−0.681508	+	1.28329i
$274$	−220775.			−2.94068
$275$	4480.99	−	2587.10i	0.0592528	−	0.0342096i
$276$	−25133.5	−	14510.8i	−0.329940	−	0.190491i
$277$	−12378.2	−	7146.55i	−0.161323	−	0.0931401i	0.417165	−	0.908831i	$-0.363024\pi$
$277$	−12378.2	−	7146.55i	−0.161323	−	0.0931401i	−0.578488	+	0.815691i	$0.696357\pi$
$278$	−118606.	−	205432.i	−1.53468	−	2.65814i
$279$	−88777.3			−1.14050
$280$	61103.8	−	38224.8i	0.779385	−	0.487561i
$281$	−154210.			−1.95300			−0.976498	−	0.215529i	$-0.930853\pi$
$281$	−154210.			−1.95300			−0.976498	+	0.215529i	$0.930853\pi$
$282$	84915.0	−	49025.7i	1.06779	−	0.616490i
$283$	12709.6	−	22013.6i	0.158693	−	0.274864i	−0.775705	−	0.631096i	$-0.782605\pi$
$283$	12709.6	−	22013.6i	0.158693	−	0.274864i	0.934398	+	0.356232i	$0.115939\pi$
$284$	−128014.	−	73909.2i	−1.58717	−	0.916350i
$285$	−123681.	+	71407.5i	−1.52270	+	0.879132i
$286$	142254.			1.73913
$287$	−3952.17	−	111559.i	−0.0479813	−	1.35438i
$288$	87388.1			1.05358
$289$	74235.3	−	38273.6i	0.888822	−	0.458252i
$290$	−1050.86	−	606.716i	−0.0124954	−	0.00721423i
$291$	−24562.6	+	42543.7i	−0.290061	+	0.502400i
$292$	−38423.9	−	66552.2i	−0.450647	−	0.780543i
$293$		−	42248.8i		−	0.492129i	−0.969253	−	0.246065i	$-0.920862\pi$
$293$		−	42248.8i		−	0.492129i	0.969253	−	0.246065i	$-0.0791375\pi$
$294$	196519.	−	13941.6i	2.27358	−	0.161293i
$295$		−	133346.i		−	1.53228i
$296$	−6191.68	+	3574.77i	−0.0706684	+	0.0408004i
$297$	608.132	+	351.105i	0.00689421	+	0.00398037i
$298$	−68064.0	+	117890.i	−0.766452	+	1.32753i
$299$	−7757.50	−	13436.4i	−0.0867720	−	0.150293i
$300$	−13172.0			−0.146356
$301$	5324.67	+	150301.i	0.0587706	+	1.65893i
$302$	−2278.13			−0.0249785
$303$	−173257.	+	100030.i	−1.88714	+	1.08954i
$304$	6209.65	+	3585.14i	0.0671924	+	0.0387935i
$305$	55544.0	−	96205.0i	0.597087	−	1.03418i
$306$	42685.2	−	145380.i	0.455864	−	1.55261i
$307$			32924.9i			0.349339i	0.984627	+	0.174669i	$0.0558857\pi$
$307$			32924.9i			0.349339i	−0.984627	+	0.174669i	$0.944114\pi$
$308$	−84273.0	−	134714.i	−0.888356	−	1.42007i
$309$			220452.i			2.30886i
$310$	84838.5	+	146945.i	0.882815	+	1.52908i
$311$	55250.7	−	95697.1i	0.571238	−	0.989414i	−0.425201	−	0.905099i	$-0.639797\pi$
$311$	55250.7	−	95697.1i	0.571238	−	0.989414i	0.996439	−	0.0843146i	$-0.0268701\pi$
$312$	−116458.	−	67237.3i	−1.19636	−	0.690719i
$313$	75285.1	+	130398.i	0.768459	+	1.33101i	0.938399	+	0.345555i	$0.112309\pi$
$313$	75285.1	+	130398.i	0.768459	+	1.33101i	−0.169940	+	0.985454i	$0.554357\pi$
$314$		−	256250.i		−	2.59899i
$315$	85191.6	+	45242.0i	0.858570	+	0.455954i
$316$			83329.3i			0.834495i
$317$	148176.	−	85549.6i	1.47455	−	0.851333i	0.474964	−	0.880005i	$-0.342461\pi$
$317$	148176.	−	85549.6i	1.47455	−	0.851333i	0.999589	+	0.0286722i	$0.00912789\pi$
$318$	49492.5	−	85723.5i	0.489424	−	0.847707i
$319$	−496.703	+	860.315i	−0.00488108	+	0.00845427i
$320$	−80519.5	−	139464.i	−0.786323	−	1.36195i
$321$			4140.44i			0.0401825i
$322$	−13238.6	+	24928.6i	−0.127683	+	0.240429i
$323$	96951.9	−	92446.1i	0.929290	−	0.886102i
$324$	83043.3	+	143835.i	0.791070	+	1.37017i
$325$	−6098.34	−	3520.88i	−0.0577357	−	0.0333337i
$326$	165681.	+	95656.0i	1.55897	+	0.900071i
$327$	133736.	−	77212.3i	1.25070	−	0.722089i
$328$	138617.			1.28846
$329$	−31053.3	−	49639.8i	−0.286890	−	0.458605i
$330$		−	252746.i		−	2.32090i
$331$	−44472.3	−	77028.4i	−0.405914	−	0.703064i	0.588513	−	0.808487i	$-0.299713\pi$
$331$	−44472.3	−	77028.4i	−0.405914	−	0.703064i	−0.994427	+	0.105424i	$0.966380\pi$
$332$	125576.	+	72501.5i	1.13928	+	0.657765i
$333$	−8286.47	−	4784.19i	−0.0747276	−	0.0431440i
$334$	32621.0	+	56501.3i	0.292419	+	0.506484i
$335$	35140.1			0.313122
$336$	−342.012	−	9654.08i	−0.00302945	−	0.0855130i
$337$			28904.1i			0.254507i	0.991870	+	0.127253i	$0.0406161\pi$
$337$			28904.1i			0.254507i	−0.991870	+	0.127253i	$0.959384\pi$
$338$	−4857.99	−	8414.28i	−0.0425229	−	0.0736519i
$339$	201610.	+	116399.i	1.75433	+	1.01286i
$340$	−172795.	+	41922.3i	−1.49477	+	0.362650i
$341$	120300.	−	69455.2i	1.03456	−	0.597304i
$342$		−	243024.i		−	2.07777i
$343$	−12475.0	−	116986.i	−0.106036	−	0.994362i
$344$	−186756.			−1.57819
$345$	−23872.8	+	13783.0i	−0.200570	+	0.115799i
$346$	38253.0	−	66256.1i	0.319531	−	0.553444i
$347$	−68077.9	−	39304.8i	−0.565388	−	0.326427i	0.189917	−	0.981800i	$-0.439178\pi$
$347$	−68077.9	−	39304.8i	−0.565388	−	0.326427i	−0.755305	+	0.655373i	$0.772511\pi$
$348$	2190.11	−	1264.46i	0.0180845	−	0.0104411i
$349$			232649.i			1.91008i	0.296481	+	0.955039i	$0.404187\pi$
$349$			232649.i			1.91008i	−0.296481	+	0.955039i	$0.595813\pi$
$350$	453.560	+	12802.8i	0.00370253	+	0.104512i
$351$		−	955.662i		−	0.00775694i
$352$	−118417.	+	68368.3i	−0.955719	+	0.551785i
$353$	−30205.8	−	17439.4i	−0.242405	−	0.139953i	0.373877	−	0.927478i	$-0.378028\pi$
$353$	−30205.8	−	17439.4i	−0.242405	−	0.139953i	−0.616282	+	0.787526i	$0.711362\pi$
$354$	391979.	+	226309.i	3.12792	+	1.80591i
$355$	−121593.	+	70201.8i	−0.964833	+	0.557047i
$356$			90338.0i			0.712805i
$357$	−174862.	−	44681.9i	−1.37202	−	0.350586i
$358$	73713.9			0.575153
$359$	−55882.9	−	96792.0i	−0.433601	−	0.751018i	0.563580	−	0.826062i	$-0.309424\pi$
$359$	−55882.9	−	96792.0i	−0.433601	−	0.751018i	−0.997180	+	0.0750433i	$0.976090\pi$
$360$	−59890.2	+	103733.i	−0.462116	+	0.800408i
$361$	42273.3	−	73219.5i	0.324378	−	0.561840i
$362$	−67280.1	−	116532.i	−0.513416	−	0.889262i
$363$	−20319.0			−0.154202
$364$	−101429.	+	190993.i	−0.765524	+	1.44150i
$365$	−72993.1			−0.547894
$366$	188533.	+	326549.i	1.40743	+	2.43773i
$367$	107866.	−	186829.i	0.800850	−	1.38711i	−0.118208	−	0.992989i	$-0.537715\pi$
$367$	107866.	−	186829.i	0.800850	−	1.38711i	0.919058	−	0.394123i	$-0.128952\pi$
$368$	1198.58	+	691.998i	0.00885055	+	0.00510987i
$369$	92757.3	+	160660.i	0.681233	+	1.17993i
$370$			18287.7i			0.133585i
$371$	−52205.2	−	27724.2i	−0.379285	−	0.201424i
$372$	−353625.			−2.55539
$373$	−94698.9	−	164023.i	−0.680655	−	1.17893i	−0.974781	−	0.223163i	$-0.928362\pi$
$373$	−94698.9	−	164023.i	−0.680655	−	1.17893i	0.294126	−	0.955767i	$-0.404971\pi$
$374$	55896.9	+	230396.i	0.399618	+	1.64714i
$375$	−102536.	+	177598.i	−0.729146	+	1.26292i
$376$	62967.7	−	36354.4i	0.445392	−	0.257147i
$377$	1351.96			0.00951222
$378$	−1473.95	+	922.062i	−0.0103157	+	0.00645322i
$379$			118819.i			0.827195i	0.910460	+	0.413598i	$0.135728\pi$
$379$			118819.i			0.827195i	−0.910460	+	0.413598i	$0.864272\pi$
$380$	−246985.	+	142597.i	−1.71042	+	0.987512i
$381$	63819.9	−	110539.i	0.439649	−	0.761494i
$382$	−57385.4	+	99394.5i	−0.393256	+	0.681139i
$383$	−150955.	+	87154.0i	−1.02908	+	0.594142i	−0.916722	−	0.399526i	$-0.869175\pi$
$383$	−150955.	+	87154.0i	−1.02908	+	0.594142i	−0.112362	+	0.993667i	$0.535841\pi$
$384$	327783.			2.22292
$385$	−150836.	+	5343.63i	−1.01762	+	0.0360508i
$386$		−	52628.1i		−	0.353218i
$387$	−124970.	−	216454.i	−0.834418	−	1.44525i
$388$	−49050.2	+	84957.4i	−0.325820	+	0.564336i
$389$	−76634.6	+	132735.i	−0.506437	+	0.877175i	0.493535	+	0.869726i	$0.335705\pi$
$389$	−76634.6	+	132735.i	−0.506437	+	0.877175i	−0.999972	+	0.00744931i	$0.997629\pi$
$390$	−297888.	+	171986.i	−1.95850	+	1.13074i
$391$	18713.5	−	17843.8i	0.122406	−	0.116717i
$392$	145726.	−	10338.2i	0.948345	−	0.0672779i
$393$	244578.			1.58355
$394$	−126951.	+	73295.0i	−0.817791	+	0.472152i
$395$	68545.4	+	39574.7i	0.439323	+	0.253644i
$396$	228697.	+	132038.i	1.45838	+	0.841994i
$397$	49441.2	+	85634.7i	0.313695	+	0.543336i	0.979159	−	0.203094i	$-0.0650996\pi$
$397$	49441.2	+	85634.7i	0.313695	+	0.543336i	−0.665464	+	0.746430i	$0.731766\pi$
$398$	−882.921			−0.00557386
$399$	−289298.	+	10248.9i	−1.81719	+	0.0643770i
$400$	628.151			0.00392595
$401$	32168.6	−	18572.6i	0.200052	−	0.115500i	−0.396628	−	0.917980i	$-0.629820\pi$
$401$	32168.6	−	18572.6i	0.200052	−	0.115500i	0.596680	+	0.802479i	$0.296486\pi$
$402$	−59638.1	+	103296.i	−0.369039	+	0.639194i
$403$	−163720.	−	94524.0i	−1.00807	−	0.582012i
$404$	−345983.	+	199754.i	−2.11979	+	1.22386i
$405$	157756.			0.961778
$406$	−1304.43	−	2085.18i	−0.00791350	−	0.0126500i
$407$	14971.7			0.0903821
$408$	63137.4	−	215038.i	0.379286	−	1.29180i
$409$	−62946.0	−	36341.9i	−0.376289	−	0.217251i	0.299913	−	0.953966i	$-0.403042\pi$
$409$	−62946.0	−	36341.9i	−0.376289	−	0.217251i	−0.676203	+	0.736716i	$0.736376\pi$
$410$	177284.	−	307065.i	1.05463	−	1.82668i
$411$	−218519.	−	378486.i	−1.29362	−	2.24061i
$412$			440231.i			2.59350i
$413$	126771.	−	238713.i	0.743227	−	1.39951i
$414$		−	46908.1i		−	0.273683i
$415$	119277.	−	68864.8i	0.692567	−	0.399854i
$416$	161158.	+	93044.9i	0.931250	+	0.537658i
$417$	234788.	−	406666.i	1.35022	−	2.33865i
$418$	190131.	+	329316.i	1.08818	+	1.88478i
$419$	−155942.			−0.888250			−0.444125	−	0.895965i	$-0.646485\pi$
$419$	−155942.			−0.888250			−0.444125	+	0.895965i	$0.646485\pi$
$420$	339342.	+	180212.i	1.92371	+	1.02161i
$421$	44984.9			0.253807			0.126903	−	0.991915i	$-0.459496\pi$
$421$	44984.9			0.253807			0.126903	+	0.991915i	$0.459496\pi$
$422$	−471062.	+	271968.i	−2.64517	+	1.52719i
$423$	84271.2	+	48654.0i	0.470975	+	0.271918i
$424$	36700.6	−	63567.2i	0.204146	−	0.353591i
$425$	3306.19	−	11260.4i	0.0183041	−	0.0623415i
$426$		−	476573.i		−	2.62609i
$427$	190895.	−	119419.i	1.04698	−	0.654962i
$428$			8268.23i			0.0451362i
$429$	140800.	+	243873.i	0.765049	+	1.32510i
$430$	−238851.	+	413702.i	−1.29178	+	2.23744i
$431$	87068.5	+	50269.0i	0.468712	+	0.270611i	0.715701	−	0.698407i	$-0.246108\pi$
$431$	87068.5	+	50269.0i	0.468712	+	0.270611i	−0.246988	+	0.969018i	$0.579441\pi$
$432$	42.6244	+	73.8275i	0.000228397	+	0.000395595i
$433$		−	230742.i		−	1.23070i	−0.788255	−	0.615349i	$-0.789015\pi$
$433$		−	230742.i		−	1.23070i	0.788255	−	0.615349i	$-0.210985\pi$
$434$	12176.6	+	343712.i	0.0646467	+	1.82480i
$435$		−	2402.07i		−	0.0126942i
$436$	267062.	−	154188.i	1.40488	−	0.811108i
$437$	20736.7	−	35917.0i	0.108587	−	0.188078i
$438$	123880.	−	214567.i	0.645735	−	1.11845i
$439$	−68957.7	−	119438.i	−0.357811	−	0.619747i	0.629784	−	0.776771i	$-0.283144\pi$
$439$	−68957.7	−	119438.i	−0.357811	−	0.619747i	−0.987595	+	0.157023i	$0.949810\pi$
$440$		−	187421.i		−	0.968084i
$441$	109497.	+	161982.i	0.563020	+	0.832895i
$442$	233510.	−	222657.i	1.19525	−	1.13971i
$443$	189048.	+	327440.i	0.963305	+	1.66849i	0.714102	+	0.700042i	$0.246835\pi$
$443$	189048.	+	327440.i	0.963305	+	1.66849i	0.249203	+	0.968451i	$0.419831\pi$
$444$	−33007.3	−	19056.8i	−0.167434	−	0.0966682i
$445$	74310.7	+	42903.3i	0.375259	+	0.216656i
$446$	−215861.	+	124627.i	−1.08519	+	0.626533i
$447$	−269474.			−1.34866
$448$	−11556.7	−	326214.i	−0.0575807	−	1.62535i
$449$		−	185194.i		−	0.918615i	−0.888277	−	0.459307i	$-0.848098\pi$
$449$		−	185194.i		−	0.918615i	0.888277	−	0.459307i	$-0.151902\pi$
$450$	−10645.0	−	18437.7i	−0.0525681	−	0.0910506i
$451$	−251386.	−	145138.i	−1.23591	−	0.713556i
$452$	402603.	+	232443.i	1.97061	+	1.13773i
$453$	−2254.86	−	3905.53i	−0.0109881	−	0.0190320i
$454$	87471.0			0.424377
$455$	108937.	+	174140.i	0.526203	+	0.841155i
$456$		−	359466.i		−	1.72874i
$457$	−173049.	−	299730.i	−0.828585	−	1.43515i	−0.899148	−	0.437645i	$-0.855813\pi$
$457$	−173049.	−	299730.i	−0.828585	−	1.43515i	0.0705625	−	0.997507i	$-0.477521\pi$
$458$	−494186.	−	285318.i	−2.35591	−	1.36019i
$459$	1547.80	−	375.516i	0.00734666	−	0.00178239i
$460$	−47672.6	+	27523.8i	−0.225296	+	0.130075i
$461$			405523.i			1.90815i	0.299562	+	0.954077i	$0.403160\pi$
$461$			405523.i			1.90815i	−0.299562	+	0.954077i	$0.596840\pi$
$462$	240284.	−	452460.i	1.12575	−	2.11981i
$463$	−70717.1			−0.329885			−0.164942	−	0.986303i	$-0.552744\pi$
$463$	−70717.1			−0.329885			−0.164942	+	0.986303i	$0.552744\pi$
$464$	−104.443	+	60.3001i	−0.000485113	+	0.000280080i
$465$	−167943.	+	290887.i	−0.776707	+	1.34530i
$466$	−322292.	−	186075.i	−1.48415	−	0.856874i
$467$	86123.7	−	49723.5i	0.394902	−	0.227996i	−0.289380	−	0.957214i	$-0.593449\pi$
$467$	86123.7	−	49723.5i	0.394902	−	0.227996i	0.684282	+	0.729218i	$0.260116\pi$
$468$		−	359391.i		−	1.64087i
$469$	62907.0	+	33407.5i	0.285991	+	0.151879i
$470$		−	185981.i		−	0.841926i
$471$	439302.	−	253631.i	1.98026	−	1.14330i
$472$	290667.	+	167817.i	1.30470	+	0.753272i
$473$	338687.	+	195541.i	1.51383	+	0.874009i
$474$	−232664.	+	134329.i	−1.03555	+	0.597877i
$475$		−	18823.4i		−	0.0834280i
$476$	−349189.	−	89227.1i	−1.54116	−	0.393807i
$477$	98234.4			0.431745
$478$	−68861.2	−	119271.i	−0.301383	−	0.522011i
$479$	138380.	−	239681.i	0.603116	−	1.04463i	−0.389230	−	0.921141i	$-0.627259\pi$
$479$	138380.	−	239681.i	0.603116	−	1.04463i	0.992346	−	0.123488i	$-0.0394079\pi$
$480$	165315.	−	286335.i	0.717515	−	1.24277i
$481$	−10187.8	−	17645.7i	−0.0440341	−	0.0762692i
$482$	−169481.			−0.729503
$483$	−55839.9	+	1978.22i	−0.239359	+	0.00847971i
$484$	−40575.9			−0.173212
$485$	46589.8	+	80695.9i	0.198065	+	0.343058i
$486$	−269172.	+	466220.i	−1.13961	+	1.97387i
$487$	−171023.	−	98740.4i	−0.721104	−	0.416329i	0.0940550	−	0.995567i	$-0.470017\pi$
$487$	−171023.	−	98740.4i	−0.721104	−	0.416329i	−0.815159	+	0.579238i	$0.803350\pi$
$488$	139805.	+	242149.i	0.587059	+	1.01682i
$489$			378714.i			1.58378i
$490$	163475.	−	336035.i	0.680863	−	1.39956i
$491$	420580.			1.74456			0.872279	−	0.489009i	$-0.162642\pi$
$491$	420580.			1.74456			0.872279	+	0.489009i	$0.162642\pi$
$492$	369478.	+	639956.i	1.52637	+	2.64375i
$493$	531.237	+	2189.65i	0.00218572	+	0.00900910i
$494$	258756.	−	448178.i	1.06032	−	1.83652i
$495$	217225.	−	125415.i	0.886543	−	0.511846i
$496$	16863.8			0.0685476
$497$	−284413.	+	10075.8i	−1.15143	+	0.0407914i
$498$			467496.i			1.88503i
$499$	−326554.	+	188536.i	−1.31146	+	0.757170i	−0.982337	−	0.187118i	$-0.940085\pi$
$499$	−326554.	+	188536.i	−1.31146	+	0.757170i	−0.329120	+	0.944288i	$0.606752\pi$
$500$	−204759.	+	354653.i	−0.819035	+	1.41861i
$501$	−64575.5	+	111848.i	−0.257272	+	0.445608i
$502$	−329068.	+	189987.i	−1.30580	+	0.753906i
$503$	19740.0			0.0780210			0.0390105	−	0.999239i	$-0.487579\pi$
$503$	19740.0			0.0780210			0.0390105	+	0.999239i	$0.487579\pi$
$504$	−205832.	+	128763.i	−0.810312	+	0.506908i
$505$			379468.i			1.48796i
$506$	36698.7	+	63564.0i	0.143334	+	0.248262i
$507$	9616.70	−	16656.6i	0.0374119	−	0.0647994i
$508$	127445.	−	220741.i	0.493849	−	0.855371i
$509$	17427.2	−	10061.6i	0.0672656	−	0.0388358i	−0.465990	−	0.884790i	$-0.654302\pi$
$509$	17427.2	−	10061.6i	0.0672656	−	0.0388358i	0.533256	+	0.845954i	$0.320968\pi$
$510$	−395602.	−	414883.i	−1.52096	−	1.59509i
$511$	−130670.	−	69394.0i	−0.500421	−	0.265754i
$512$	−31659.3			−0.120771
$513$	2212.35	−	1277.30i	0.00840656	−	0.00485353i
$514$	244588.	+	141213.i	0.925783	+	0.534501i
$515$	362127.	+	209074.i	1.36536	+	0.788290i
$516$	−497791.	−	862199.i	−1.86959	−	3.23823i
$517$	−152258.			−0.569639
$518$	−17386.0	+	32738.3i	−0.0647949	+	0.122010i
$519$	151448.			0.562251
$520$	−220895.	+	127534.i	−0.816921	+	0.471649i
$521$	9379.77	−	16246.2i	0.0345555	−	0.0598518i	−0.848230	−	0.529627i	$-0.822332\pi$
$521$	9379.77	−	16246.2i	0.0345555	−	0.0598518i	0.882786	+	0.469775i	$0.155665\pi$
$522$	3539.91	+	2043.77i	0.0129912	+	0.00750050i
$523$	45823.1	−	26456.0i	0.167525	−	0.0967208i	−0.413893	−	0.910326i	$-0.635831\pi$
$523$	45823.1	−	26456.0i	0.167525	−	0.0967208i	0.581418	+	0.813605i	$0.302498\pi$
$524$	488408.			1.77877
$525$	−21499.5	+	13449.5i	−0.0780028	+	0.0487964i
$526$	−41880.7			−0.151371
$527$	88760.2	−	302305.i	0.319593	−	1.08849i
$528$	−21754.4	−	12559.9i	−0.0780333	−	0.0450525i
$529$	−135918.	+	235417.i	−0.485697	+	0.841252i
$530$	−93876.1	−	162598.i	−0.334198	−	0.578847i
$531$			449186.i			1.59308i
$532$	−577712.	+	20466.4i	−2.04121	+	0.0723134i
$533$			395047.i			1.39057i
$534$	−252233.	+	145627.i	−0.884544	+	0.510692i
$535$	6801.32	+	3926.74i	0.0237621	+	0.0137191i
$536$	−44224.0	+	76598.2i	−0.153932	+	0.266618i
$537$	72960.8	+	126372.i	0.253012	+	0.438229i
$538$	−632544.			−2.18538
$539$	−275103.	−	133833.i	−0.946932	−	0.460665i
$540$	−3390.71			−0.0116280
$541$	289173.	−	166954.i	0.988013	−	0.570430i	0.0833335	−	0.996522i	$-0.473443\pi$
$541$	289173.	−	166954.i	0.988013	−	0.570430i	0.904680	+	0.426092i	$0.140110\pi$
$542$	691368.	+	399161.i	2.35348	+	1.35878i
$543$	133185.	−	230684.i	0.451707	−	0.782379i
$544$	−87371.3	+	297575.i	−0.295237	+	1.00554i
$545$		−	292909.i		−	0.986141i
$546$	−696778.	+	24684.5i	−2.33727	+	0.0828018i
$547$		−	170311.i		−	0.569203i	−0.958646	−	0.284602i	$-0.908139\pi$
$547$		−	170311.i		−	0.569203i	0.958646	−	0.284602i	$-0.0918613\pi$
$548$	−436370.	−	755814.i	−1.45309	−	2.51683i
$549$	−187104.	+	324073.i	−0.620780	+	1.07522i
$550$	28849.6	+	16656.4i	0.0953707	+	0.0550623i
$551$	1806.98	+	3129.78i	0.00595181	+	0.0103088i
$552$		−	69383.6i		−	0.227708i
$553$	85084.9	+	136011.i	0.278229	+	0.444759i
$554$		−	92022.2i		−	0.299829i
$555$	−31351.7	+	18100.9i	−0.101783	+	0.0587643i
$556$	468859.	−	812088.i	1.51668	−	2.62696i
$557$	84985.1	−	147198.i	0.273925	−	0.474453i	−0.695938	−	0.718102i	$-0.745011\pi$
$557$	84985.1	−	147198.i	0.273925	−	0.474453i	0.969863	+	0.243649i	$0.0783446\pi$
$558$	−285784.	−	494993.i	−0.917847	−	1.58976i
$559$		−	532238.i		−	1.70327i
$560$	−16182.7	−	8594.00i	−0.0516029	−	0.0274043i
$561$	−339654.	+	323869.i	−1.07922	+	1.02907i
$562$	−496421.	−	859827.i	−1.57173	−	2.72232i
$563$	495833.	+	286269.i	1.56429	+	0.903146i	0.996814	+	0.0797585i	$0.0254149\pi$
$563$	495833.	+	286269.i	1.56429	+	0.903146i	0.567480	+	0.823387i	$0.307918\pi$
$564$	335676.	+	193802.i	1.05527	+	0.609258i
$565$	382408.	−	220783.i	1.19793	−	0.691623i
$566$	163654.			0.510851
$567$	282410.	+	149977.i	0.878445	+	0.466508i
$568$		−	353397.i		−	1.09538i
$569$	−33414.1	−	57874.9i	−0.103206	−	0.178758i	0.809798	−	0.586709i	$-0.199577\pi$
$569$	−33414.1	−	57874.9i	−0.103206	−	0.178758i	−0.913004	+	0.407951i	$0.866243\pi$
$570$	−796290.	−	459738.i	−2.45088	−	1.41501i
$571$	−42446.7	−	24506.6i	−0.130188	−	0.0751642i	0.433491	−	0.901158i	$-0.357281\pi$
$571$	−42446.7	−	24506.6i	−0.130188	−	0.0751642i	−0.563680	+	0.825993i	$0.690615\pi$
$572$	281170.	+	487001.i	0.859364	+	1.48846i
$573$	−227196.			−0.691978
$574$	609294.	−	381157.i	1.84928	−	1.15686i
$575$		−	3633.27i		−	0.0109891i
$576$	271235.	+	469793.i	0.817525	+	1.41600i
$577$	−6870.71	−	3966.80i	−0.0206371	−	0.0119149i	0.489646	−	0.871921i	$-0.337126\pi$
$577$	−6870.71	−	3966.80i	−0.0206371	−	0.0119149i	−0.510283	+	0.860006i	$0.670459\pi$
$578$	452373.	+	290705.i	1.35407	+	0.870154i
$579$	90223.1	−	52090.3i	0.269129	−	0.155382i
$580$		−	4796.79i		−	0.0142592i
$581$	278996.	−	9883.93i	0.826507	−	0.0292804i
$582$	−316280.			−0.933739
$583$	−133115.	+	76854.0i	−0.391642	+	0.226115i
$584$	91862.1	−	159110.i	0.269346	−	0.466521i
$585$	−295629.	−	170682.i	−0.863845	−	0.498741i
$586$	235565.	−	136004.i	0.685988	−	0.396055i
$587$			284079.i			0.824447i	0.911083	+	0.412223i	$0.135248\pi$
$587$			284079.i			0.824447i	−0.911083	+	0.412223i	$0.864752\pi$
$588$	436156.	+	645221.i	1.26150	+	1.86618i
$589$		−	505347.i		−	1.45666i
$590$	743496.	−	429257.i	2.13587	−	1.23314i
$591$	−251307.	−	145092.i	−0.719498	−	0.415402i
$592$	1574.07	+	908.787i	0.00449138	+	0.00259310i
$593$	−115820.	+	66868.7i	−0.329362	+	0.190157i	−0.655558	−	0.755145i	$-0.727567\pi$
$593$	−115820.	+	66868.7i	−0.329362	+	0.190157i	0.326196	+	0.945302i	$0.394233\pi$
$594$			4520.99i			0.0128133i
$595$	−239234.	+	244862.i	−0.675754	+	0.691653i
$596$	−538125.			−1.51492
$597$	−873.900	−	1513.64i	−0.00245196	−	0.00424692i
$598$	49944.6	−	86506.5i	0.139664	−	0.241906i
$599$	−36061.9	+	62461.0i	−0.100507	+	0.174082i	−0.911893	−	0.410427i	$-0.865380\pi$
$599$	−36061.9	+	62461.0i	−0.100507	+	0.174082i	0.811387	+	0.584509i	$0.198713\pi$
$600$	−15745.5	−	27272.0i	−0.0437375	−	0.0757555i
$601$	−365785.			−1.01269			−0.506345	−	0.862331i	$-0.669004\pi$
$601$	−365785.			−1.01269			−0.506345	+	0.862331i	$0.669004\pi$
$602$	−820889.	+	513525.i	−2.26512	+	1.41700i
$603$	−118372.			−0.325547
$604$	−4502.82	−	7799.12i	−0.0123427	−	0.0213782i
$605$	−19270.3	+	33377.1i	−0.0526475	+	0.0911881i
$606$	−1.11547e6	−	644014.i	−3.03746	−	1.75368i
$607$	325459.	+	563711.i	0.883321	+	1.52996i	0.847626	+	0.530595i	$0.178031\pi$
$607$	325459.	+	563711.i	0.883321	+	1.52996i	0.0356957	+	0.999363i	$0.488635\pi$
$608$			497440.i			1.34565i
$609$	2283.63	−	4300.12i	0.00615731	−	0.0115944i
$610$	715210.			1.92209
$611$	103607.	+	179452.i	0.277528	+	0.480692i
$612$	582073.	−	141218.i	1.55409	−	0.377040i
$613$	−237177.	+	410803.i	−0.631178	+	1.09323i	0.356134	+	0.934435i	$0.384095\pi$
$613$	−237177.	+	410803.i	−0.631178	+	1.09323i	−0.987311	+	0.158797i	$0.949239\pi$
$614$	−183578.	+	105989.i	−0.486950	+	0.281141i
$615$	701890.			1.85575
$616$	178180.	−	335517.i	0.469567	−	0.884204i
$617$		−	253409.i		−	0.665660i	−0.942987	−	0.332830i	$-0.891997\pi$
$617$		−	253409.i		−	0.665660i	0.942987	−	0.332830i	$-0.108003\pi$
$618$	−1.22917e6	+	709662.i	−3.21836	+	1.85812i
$619$	77838.3	−	134820.i	0.203148	−	0.351862i	−0.746393	−	0.665505i	$-0.768216\pi$
$619$	77838.3	−	134820.i	0.203148	−	0.351862i	0.949541	+	0.313643i	$0.101549\pi$
$620$	−335373.	+	580884.i	−0.872459	+	1.51114i
$621$	427.024	−	246.542i	0.00110731	−	0.000639305i
$622$	711434.			1.83888
$623$	92241.3	+	147451.i	0.237656	+	0.379902i
$624$			34186.5i			0.0877982i
$625$	181798.	+	314883.i	0.465403	+	0.806101i
$626$	−484703.	+	839530.i	−1.23688	+	2.14234i
$627$	−376376.	+	651902.i	−0.957385	+	1.65824i
$628$	877262.	−	506487.i	2.22438	−	1.28425i
$629$	24576.1	−	23433.9i	0.0621171	−	0.0592302i
$630$	21987.2	+	620640.i	0.0553974	+	1.56372i
$631$	96841.8			0.243223			0.121611	−	0.992578i	$-0.461194\pi$
$631$	96841.8			0.243223			0.121611	+	0.992578i	$0.461194\pi$
$632$	−172529.	+	99609.9i	−0.431945	+	0.249384i
$633$	−932498.	−	538378.i	−2.32724	−	1.34363i
$634$	953993.	+	550788.i	2.37338	+	1.37027i
$635$	−121052.	−	209668.i	−0.300209	−	0.519978i
$636$	391295.			0.967365
$637$	29462.9	+	415307.i	0.0726101	+	1.02351i
$638$	−6395.78			−0.0157128
$639$	409595.	−	236480.i	1.00312	−	0.579151i
$640$	310865.	−	538434.i	0.758948	−	1.31454i
$641$	454318.	+	262300.i	1.10572	+	0.638385i	0.937716	−	0.347402i	$-0.112936\pi$
$641$	454318.	+	262300.i	1.10572	+	0.638385i	0.167999	+	0.985787i	$0.446269\pi$
$642$	−23085.8	+	13328.6i	−0.0560111	+	0.0323380i
$643$	−344347.			−0.832864			−0.416432	−	0.909167i	$-0.636720\pi$
$643$	−344347.			−0.832864			−0.416432	+	0.909167i	$0.636720\pi$
$644$	−111509.	+	3950.40i	−0.268867	+	0.00952509i
$645$	−945642.			−2.27304
$646$	827549.	+	242977.i	1.98303	+	0.582239i
$647$	561031.	+	323912.i	1.34023	+	0.773781i	0.986841	−	0.161696i	$-0.0516965\pi$
$647$	561031.	+	323912.i	1.34023	+	0.773781i	0.353387	+	0.935477i	$0.385030\pi$
$648$	−198536.	+	343875.i	−0.472813	+	0.818936i
$649$	−351422.	−	608681.i	−0.834334	−	1.44511i
$650$		−	45336.4i		−	0.107305i
$651$	−577192.	+	361075.i	−1.36194	+	0.851992i
$652$			756271.i			1.77903i
$653$	626257.	−	361569.i	1.46868	−	0.847940i	0.469292	−	0.883043i	$-0.344509\pi$
$653$	626257.	−	361569.i	1.46868	−	0.847940i	0.999384	+	0.0351025i	$0.0111758\pi$
$654$	861021.	+	497110.i	2.01307	+	1.16224i
$655$	231955.	−	401757.i	0.540656	−	0.936443i
$656$	−17619.8	−	30518.4i	−0.0409444	−	0.0709177i
$657$	245882.			0.569635
$658$	176811.	−	332939.i	0.408374	−	0.768977i
$659$	−157855.			−0.363487			−0.181743	−	0.983346i	$-0.558174\pi$
$659$	−157855.			−0.363487			−0.181743	+	0.983346i	$0.558174\pi$
$660$	865269.	−	499563.i	1.98638	−	1.14684i
$661$	−184374.	−	106448.i	−0.421985	−	0.243633i	0.273941	−	0.961746i	$-0.411673\pi$
$661$	−184374.	−	106448.i	−0.421985	−	0.243633i	−0.695926	+	0.718113i	$0.745006\pi$
$662$	286323.	−	495926.i	0.653342	−	1.13162i
$663$	612837.	+	179936.i	1.39418	+	0.409346i
$664$			346666.i			0.786277i
$665$	−257531.	+	484937.i	−0.582353	+	1.09658i
$666$		−	61603.5i		−	0.138885i
$667$	348.780	+	604.104i	0.000783970	+	0.00135788i
$668$	−128953.	+	223354.i	−0.288988	+	0.500542i
$669$	−427311.	−	246708.i	−0.954755	−	0.551228i
$670$	113120.	+	195930.i	0.251994	+	0.436466i
$671$		−	585524.i		−	1.30047i
$672$	568160.	−	355425.i	1.25815	−	0.787063i
$673$		−	741468.i		−	1.63705i	−0.574471	−	0.818525i	$-0.694792\pi$
$673$		−	741468.i		−	1.63705i	0.574471	−	0.818525i	$-0.305208\pi$
$674$	−161160.	+	93045.6i	−0.354761	+	0.204822i
$675$	111.897	−	193.812i	0.000245591	−	0.000425376i
$676$	19204.0	−	33262.3i	0.0420241	−	0.0727879i
$677$	−29776.2	−	51573.9i	−0.0649669	−	0.112526i	0.831712	−	0.555207i	$-0.187361\pi$
$677$	−29776.2	−	51573.9i	−0.0649669	−	0.112526i	−0.896679	+	0.442681i	$0.854028\pi$
$678$			1.49881e6i			3.26053i
$679$	6686.87	+	188752.i	0.0145039	+	0.409405i
$680$	−293354.	−	307652.i	−0.634416	−	0.665337i
$681$	86577.2	+	149956.i	0.186685	+	0.323348i
$682$	774518.	+	447168.i	1.66519	+	0.961396i
$683$	107161.	+	61869.6i	0.229719	+	0.132628i	0.610442	−	0.792061i	$-0.290992\pi$
$683$	107161.	+	61869.6i	0.229719	+	0.132628i	−0.380724	+	0.924689i	$0.624325\pi$
$684$	831985.	−	480347.i	1.77829	−	1.02670i
$685$	−828962.			−1.76666
$686$	612116.	−	446147.i	1.30072	−	0.948047i
$687$		−	1.12961e6i		−	2.39340i
$688$	23738.8	+	41116.9i	0.0501513	+	0.0868646i
$689$	181161.	+	104593.i	0.381615	+	0.220326i
$690$	−153699.	−	88737.9i	−0.322828	−	0.186385i
$691$	95837.6	+	165996.i	0.200715	+	0.347648i	0.948759	−	0.316001i	$-0.102340\pi$
$691$	95837.6	+	165996.i	0.200715	+	0.347648i	−0.748044	+	0.663649i	$0.769007\pi$
$692$	302434.			0.631565
$693$	508102.	−	18000.4i	1.05800	−	0.0374814i
$694$		−	506106.i		−	1.05081i
$695$	−445341.	−	771353.i	−0.921983	−	1.59692i
$696$	5236.01	+	3023.01i	0.0108089	+	0.00624053i
$697$	−639822.	+	155229.i	−1.31702	+	0.319526i
$698$	−1.29718e6	+	748925.i	−2.66249	+	1.53719i
$699$		−	736696.i		−	1.50777i
$700$	−42933.3	+	26857.9i	−0.0876190	+	0.0548120i
$701$	−706745.			−1.43822			−0.719112	−	0.694894i	$-0.755451\pi$
$701$	−706745.			−1.43822			−0.719112	+	0.694894i	$0.755451\pi$
$702$	5328.46	−	3076.39i	0.0108125	−	0.00624262i
$703$	27233.1	−	47169.1i	0.0551044	−	0.0954436i
$704$	−735088.	−	424403.i	−1.48318	−	0.856315i
$705$	318838.	−	184081.i	0.641493	−	0.370366i
$706$		−	224557.i		−	0.450524i
$707$	−360757.	+	679313.i	−0.721732	+	1.35904i
$708$			1.78924e6i			3.56945i
$709$	−129287.	+	74643.9i	−0.257195	+	0.148492i	−0.623054	−	0.782179i	$-0.714108\pi$
$709$	−129287.	+	74643.9i	−0.257195	+	0.148492i	0.365859	+	0.930670i	$0.380775\pi$
$710$	−782845.	−	451976.i	−1.55296	−	0.896599i
$711$	−230900.	−	133310.i	−0.456756	−	0.263708i
$712$	−187041.	+	107988.i	−0.368957	+	0.213017i
$713$		−	97541.4i		−	0.191871i
$714$	−313770.	−	1.11881e6i	−0.615481	−	2.19462i
$715$	534133.			1.04481
$716$	145698.	+	252357.i	0.284203	+	0.492254i
$717$	136315.	−	236105.i	0.265159	−	0.459268i
$718$	359787.	−	623169.i	0.697905	−	1.20881i
$719$	391696.	+	678437.i	0.757689	+	1.31236i	0.944026	+	0.329870i	$0.107005\pi$
$719$	391696.	+	678437.i	0.757689	+	1.31236i	−0.186337	+	0.982486i	$0.559662\pi$
$720$	30450.9			0.0587402
$721$	449506.	+	718552.i	0.864699	+	1.38225i
$722$	544331.			1.04421
$723$	−167749.	−	290550.i	−0.320911	−	0.555834i
$724$	265963.	−	460662.i	0.507393	−	0.878831i
$725$	274.183	+	158.300i	0.000521633	+	0.000301165i
$726$	−65409.2	−	113292.i	−0.124098	−	0.214945i
$727$		−	607720.i		−	1.14983i	−0.818212	−	0.574916i	$-0.805035\pi$
$727$		−	607720.i		−	1.14983i	0.818212	−	0.574916i	$-0.194965\pi$
$728$	−516687.	+	18304.5i	−0.974911	+	0.0345379i
$729$	−537100.			−1.01065
$730$	−234973.	−	406986.i	−0.440933	−	0.763719i
$731$	862019.	−	209137.i	1.61318	−	0.391377i
$732$	−745287.	+	1.29087e6i	−1.39092	+	2.40914i
$733$	285672.	−	164933.i	0.531691	−	0.306972i	−0.210014	−	0.977698i	$-0.567351\pi$
$733$	285672.	−	164933.i	0.531691	−	0.306972i	0.741705	+	0.670726i	$0.234018\pi$
$734$	1.38893e6			2.57803
$735$	737888.	−	52347.6i	1.36589	−	0.0968996i
$736$			96015.0i			0.177249i
$737$	160403.	−	92608.6i	0.295309	−	0.170497i
$738$	−597193.	+	1.03437e6i	−1.09648	+	1.89917i
$739$	−63186.3	+	109442.i	−0.115700	+	0.200399i	−0.918059	−	0.396443i	$-0.870245\pi$
$739$	−63186.3	+	109442.i	−0.115700	+	0.200399i	0.802359	+	0.596841i	$0.203578\pi$
$740$	−62607.5	+	36146.4i	−0.114331	+	0.0660088i
$741$	1.02445e6			1.86575
$742$	−13473.7	−	380327.i	−0.0244726	−	0.690794i
$743$			513936.i			0.930961i	0.885058	+	0.465480i	$0.154118\pi$
$743$			513936.i			0.930961i	−0.885058	+	0.465480i	$0.845882\pi$
$744$	−422715.	−	732163.i	−0.763663	−	1.32270i
$745$	−255566.	+	442653.i	−0.460459	+	0.797538i
$746$	609693.	−	1.05602e6i	1.09555	−	1.89755i
$747$	−401794.	+	231976.i	−0.720049	+	0.415720i
$748$	−678270.	+	646748.i	−1.21227	+	1.15593i
$749$	8442.43	+	13495.5i	0.0150489	+	0.0240562i
$750$	−1.32030e6			−2.34721
$751$	−417226.	+	240885.i	−0.739761	+	0.427101i	−0.821982	−	0.569513i	$-0.807132\pi$
$751$	−417226.	+	240885.i	−0.739761	+	0.427101i	0.0822215	+	0.996614i	$0.473798\pi$
$752$	−16007.8	−	9242.13i	−0.0283072	−	0.0163432i
$753$	−651411.	−	376092.i	−1.14885	−	0.663292i
$754$	4352.12	+	7538.10i	0.00765523	+	0.0132593i
$755$	−8553.91			−0.0150062
$756$	−6069.97	−	3223.53i	−0.0106204	−	0.00564011i
$757$	639723.			1.11635			0.558174	−	0.829724i	$-0.311502\pi$
$757$	639723.			1.11635			0.558174	+	0.829724i	$0.311502\pi$
$758$	−662497.	+	382493.i	−1.15304	+	0.665709i
$759$	−72647.5	+	125829.i	−0.126106	+	0.218423i
$760$	−590479.	−	340913.i	−1.02230	−	0.590224i
$761$	330613.	−	190880.i	0.570888	−	0.329602i	−0.186616	−	0.982433i	$-0.559752\pi$
$761$	330613.	−	190880.i	0.570888	−	0.329602i	0.757504	+	0.652831i	$0.226419\pi$
$762$	821774.			1.41528
$763$	278466.	−	524358.i	0.478325	−	0.900697i
$764$	−453698.			−0.777285
$765$	160274.	−	545872.i	0.273867	−	0.932756i
$766$	−971885.	−	561118.i	−1.65637	−	0.956305i
$767$	−478263.	+	828376.i	−0.812973	+	1.40811i
$768$	375960.	+	651182.i	0.637410	+	1.10403i
$769$			481944.i			0.814975i	0.913211	+	0.407487i	$0.133595\pi$
$769$			481944.i			0.814975i	−0.913211	+	0.407487i	$0.866405\pi$
$770$	−515354.	−	823812.i	−0.869209	−	1.38946i
$771$			559081.i			0.940515i
$772$	180170.	−	104021.i	0.302307	−	0.174537i
$773$	−194323.	−	112193.i	−0.325211	−	0.187761i	0.328502	−	0.944503i	$-0.393456\pi$
$773$	−194323.	−	112193.i	−0.325211	−	0.187761i	−0.653713	+	0.756743i	$0.726790\pi$
$774$	804586.	−	1.39358e6i	1.34304	−	2.32622i
$775$	−22135.4	−	38339.7i	−0.0368540	−	0.0638330i
$776$	−234534.			−0.389477
$777$	−73333.3	+	2597.96i	−0.121467	+	0.00430319i
$778$	−986783.			−1.63028
$779$	−914528.	+	528003.i	−1.50703	+	0.870085i
$780$	−1.17757e6	−	679873.i	−1.93553	−	1.11748i
$781$	−370021.	+	640895.i	−0.606630	+	1.05071i
$782$	159732.	+	46899.1i	0.261203	+	0.0766922i
$783$			42.9669i			7.00826e-5i
$784$	−20799.6	−	30769.5i	−0.0338394	−	0.0500598i
$785$		−	962163.i		−	1.56138i
$786$	787325.	+	1.36369e6i	1.27441	+	2.20734i
$787$	2932.61	−	5079.43i	0.00473483	−	0.00820097i	−0.863648	−	0.504095i	$-0.831826\pi$
$787$	2932.61	−	5079.43i	0.00473483	−	0.00820097i	0.868383	+	0.495894i	$0.165160\pi$
$788$	−501846.	−	289741.i	−0.808198	−	0.466613i
$789$	−41452.8	−	71798.4i	−0.0665886	−	0.115335i
$790$			509583.i			0.816508i
$791$	894474.	−	31688.3i	1.42960	−	0.0506461i
$792$			631341.i			1.00650i
$793$	−690102.	+	398430.i	−1.09740	+	0.633587i
$794$	−318314.	+	551336.i	−0.504911	+	0.874532i
$795$	185834.	−	321874.i	0.294029	−	0.509274i
$796$	−1745.13	−	3022.65i	−0.00275424	−	0.00477048i
$797$		−	300718.i		−	0.473416i	−0.971581	−	0.236708i	$-0.923932\pi$
$797$		−	300718.i		−	0.473416i	0.971581	−	0.236708i	$-0.0760684\pi$
$798$	−988429.	−	1.58004e6i	−1.55217	−	2.48120i
$799$	−249932.	+	238317.i	−0.391497	+	0.373302i
$800$	21789.0	+	37739.7i	0.0340454	+	0.0589683i
$801$	−250321.	−	144523.i	−0.390150	−	0.225253i
$802$	207109.	+	119574.i	0.321996	+	0.185904i
$803$	−333189.	+	192367.i	−0.516725	+	0.298331i
$804$	−471508.			−0.729419
$805$	−49708.3	+	93601.7i	−0.0767073	+	0.144442i
$806$		−	1.21713e6i		−	1.87356i
$807$	−626081.	−	1.08440e6i	−0.961354	−	1.66511i
$808$	−827160.	−	477561.i	−1.26697	−	0.731487i
$809$	−791390.	−	456909.i	−1.20919	−	0.698125i	−0.246605	−	0.969116i	$-0.579315\pi$
$809$	−791390.	−	456909.i	−1.20919	−	0.698125i	−0.962582	+	0.270991i	$0.912649\pi$
$810$	507834.	+	879594.i	0.774019	+	1.34064i
$811$	−518464.			−0.788274			−0.394137	−	0.919052i	$-0.628956\pi$
$811$	−518464.			−0.788274			−0.394137	+	0.919052i	$0.628956\pi$
$812$	4560.28	−	8587.10i	0.00691639	−	0.0130237i
$813$			1.58033e6i			2.39093i
$814$	48195.7	+	83477.3i	0.0727376	+	0.125985i
$815$	622097.	+	359168.i	0.936576	+	0.540732i
$816$	−55368.9	+	13433.2i	−0.0831544	+	0.0201743i
$817$	1.23212e6	−	711367.i	1.84591	−	1.06574i
$818$		−	467955.i		−	0.699355i
$819$	−366962.	−	586603.i	−0.547084	−	0.874533i
$820$	1.40163e6			2.08453
$821$	642189.	−	370768.i	0.952744	−	0.550067i	0.0588118	−	0.998269i	$-0.481269\pi$
$821$	642189.	−	370768.i	0.952744	−	0.550067i	0.893932	+	0.448202i	$0.147935\pi$
$822$	1.40688e6	−	2.43678e6i	2.08215	−	3.60639i
$823$	317634.	+	183386.i	0.468950	+	0.270749i	0.715800	−	0.698305i	$-0.246062\pi$
$823$	317634.	+	183386.i	0.468950	+	0.270749i	−0.246850	+	0.969054i	$0.579395\pi$
$824$	−911477.	+	526242.i	−1.34243	+	0.775052i
$825$			65944.7i			0.0968884i
$826$	1.73908e6	−	61609.9i	2.54894	−	0.0903005i
$827$		−	72282.2i		−	0.105687i	−0.998603	−	0.0528434i	$-0.983172\pi$
$827$		−	72282.2i		−	0.105687i	0.998603	−	0.0528434i	$-0.0168284\pi$
$828$	160588.	−	92715.7i	0.234236	−	0.135236i
$829$	−680828.	−	393076.i	−0.990668	−	0.571963i	−0.0851943	−	0.996364i	$-0.527151\pi$
$829$	−680828.	−	393076.i	−0.990668	−	0.571963i	−0.905474	+	0.424402i	$0.860484\pi$
$830$	767935.	+	443367.i	1.11473	+	0.643587i
$831$	157759.	−	91082.0i	0.228450	−	0.131896i
$832$			1.15517e6i			1.66878i
$833$	−661059.	+	210908.i	−0.952688	+	0.303951i
$834$	3.02324e6			4.34652
$835$	122485.	+	212150.i	0.175675	+	0.304278i
$836$	−751601.	+	1.30181e6i	−1.07541	+	1.86267i
$837$	3004.08	−	5203.22i	0.00428806	−	0.00742713i
$838$	−501996.	−	869482.i	−0.714845	−	1.23815i
$839$	−1.30541e6			−1.85448			−0.927240	−	0.374468i	$-0.877826\pi$
$839$	−1.30541e6			−1.85448			−0.927240	+	0.374468i	$0.877826\pi$
$840$	32522.2	+	918013.i	0.0460915	+	1.30104i
$841$	707220.			0.999914
$842$	144812.	+	250821.i	0.204258	+	0.353786i
$843$	982698.	−	1.70208e6i	1.38282	−	2.39511i
$844$	−1.86214e6	−	1.07511e6i	−2.61414	−	1.50927i
$845$	−18240.7	−	31593.8i	−0.0255463	−	0.0442475i
$846$			626491.i			0.875335i
$847$	−66228.6	+	41430.8i	−0.0923163	+	0.0577505i
$848$	−18660.2			−0.0259493
$849$	161982.	+	280561.i	0.224725	+	0.389235i
$850$	73427.4	−	17814.4i	0.101630	−	0.0246566i
$851$	5256.49	−	9104.50i	0.00725833	−	0.0125718i
$852$	1.63153e6	−	941965.i	2.24758	−	1.29764i
$853$	−868109.			−1.19310			−0.596549	−	0.802576i	$-0.703462\pi$
$853$	−868109.			−1.19310			−0.596549	+	0.802576i	$0.703462\pi$
$854$	1.28035e6	+	679945.i	1.75555	+	0.932306i
$855$		−	912504.i		−	1.24825i
$856$	−17119.0	+	9883.64i	−0.0233631	+	0.0134887i
$857$	−309865.	+	536701.i	−0.421901	+	0.730754i	−0.996125	−	0.0879442i	$-0.971970\pi$
$857$	−309865.	+	536701.i	−0.421901	+	0.730754i	0.574225	+	0.818698i	$0.305304\pi$
$858$	−906505.	+	1.57011e6i	−1.23139	+	2.13283i
$859$	−559159.	+	322830.i	−0.757790	+	0.437510i	−0.828502	−	0.559987i	$-0.810806\pi$
$859$	−559159.	+	322830.i	−0.757790	+	0.437510i	0.0707118	+	0.997497i	$0.477473\pi$
$860$	−1.88839e6			−2.55326
$861$	1.25651e6	+	667282.i	1.69496	+	0.900126i
$862$			647287.i			0.871129i
$863$	−167315.	−	289798.i	−0.224654	−	0.389112i	0.731562	−	0.681775i	$-0.238792\pi$
$863$	−167315.	−	289798.i	−0.224654	−	0.389112i	−0.956215	+	0.292664i	$0.905458\pi$
$864$	−2957.07	+	5121.80i	−0.00396127	+	0.00686112i
$865$	143632.	−	248777.i	0.191963	−	0.332490i
$866$	1.28654e6	−	742786.i	1.71549	−	0.990440i
$867$	−50619.1	+	1.06326e6i	−0.0673405	+	1.41450i
$868$	−1.15262e6	+	721046.i	−1.52984	+	0.957026i
$869$	417182.			0.552442
$870$	13393.1	−	7732.54i	0.0176947	−	0.0102161i
$871$	−218298.	−	126034.i	−0.287748	−	0.166132i
$872$	638480.	+	368626.i	0.839681	+	0.484790i
$873$	−156941.	−	271830.i	−0.205924	−	0.356671i
$874$	267015.			0.349553
$875$	27914.2	+	787942.i	0.0364594	+	1.02915i
$876$	979418.			1.27632
$877$	−457212.	+	263972.i	−0.594455	+	0.343209i	−0.766857	−	0.641818i	$-0.778180\pi$
$877$	−457212.	+	263972.i	−0.594455	+	0.343209i	0.172402	+	0.985027i	$0.444847\pi$
$878$	443966.	−	768972.i	0.575918	−	0.997519i
$879$	466317.	+	269228.i	0.603536	+	0.348452i
$880$	−41263.3	+	23823.4i	−0.0532842	+	0.0307636i
$881$	−522797.			−0.673568			−0.336784	−	0.941582i	$-0.609339\pi$
$881$	−522797.			−0.673568			−0.336784	+	0.941582i	$0.609339\pi$
$882$	−550677.	+	1.13196e6i	−0.707880	+	1.45510i
$883$	525087.			0.673457			0.336728	−	0.941602i	$-0.390680\pi$
$883$	525087.			0.673457			0.336728	+	0.941602i	$0.390680\pi$
$884$	1.22380e6	+	359322.i	1.56605	+	0.459810i
$885$	1.47180e6	+	849743.i	1.87915	+	1.08493i
$886$	−1.21713e6	+	2.10814e6i	−1.55049	+	2.68554i
$887$	218507.	+	378466.i	0.277727	+	0.481038i	0.970820	−	0.239811i	$-0.0770855\pi$
$887$	218507.	+	378466.i	0.277727	+	0.481038i	−0.693092	+	0.720849i	$0.743752\pi$
$888$		−	91120.1i		−	0.115555i
$889$	−17374.2	−	490426.i	−0.0219837	−	0.620540i
$890$			552443.i			0.697441i
$891$	720101.	−	415751.i	0.907064	−	0.523694i
$892$	−853315.	−	492662.i	−1.07246	−	0.619183i
$893$	−276953.	+	479697.i	−0.347299	+	0.601540i
$894$	−867469.	−	1.50250e6i	−1.08537	−	1.87992i
$895$	276780.			0.345533
$896$	1.06839e6	−	668354.i	1.33080	−	0.832513i
$897$	197737.			0.245755
$898$	1.03258e6	−	596160.i	1.28047	−	0.739282i
$899$	7360.92	+	4249.83i	0.00910779	+	0.00525838i
$900$	42080.7	−	72885.8i	0.0519514	−	0.0899825i
$901$	−98215.5	+	334509.i	−0.120985	+	0.412058i
$902$		−	1.86886e6i		−	2.29702i
$903$	−1.69287e6	−	899015.i	−2.07609	−	1.10253i
$904$			1.11143e6i			1.36001i
$905$	−252622.	−	437555.i	−0.308443	−	0.534239i
$906$	14517.3	−	25144.7i	0.0176860	−	0.0306330i
$907$	940823.	+	543185.i	1.14365	+	0.660287i	0.947332	−	0.320253i	$-0.103768\pi$
$907$	940823.	+	543185.i	1.14365	+	0.660287i	0.196319	+	0.980540i	$0.437101\pi$
$908$	172890.	+	299454.i	0.209700	+	0.363210i
$909$		−	1.27826e6i		−	1.54701i
$910$	−620267.	+	1.16798e6i	−0.749024	+	1.41043i
$911$		−	1.21775e6i		−	1.46731i	−0.679523	−	0.733654i	$-0.737813\pi$
$911$		−	1.21775e6i		−	1.46731i	0.679523	−	0.733654i	$-0.262187\pi$
$912$	−79141.3	+	45692.3i	−0.0951511	+	0.0549355i
$913$	362974.	−	628689.i	0.435445	−	0.754213i
$914$	1.11413e6	−	1.92973e6i	1.33366	−	2.30996i
$915$	707902.	+	1.22612e6i	0.845534	+	1.46451i
$916$		−	2.25577e6i		−	2.68846i
$917$	797188.	−	498698.i	0.948030	−	0.593061i
$918$	7076.31	+	7421.21i	0.00839694	+	0.00880621i
$919$	−235082.	−	407174.i	−0.278348	−	0.482114i	0.692626	−	0.721297i	$-0.256454\pi$
$919$	−235082.	−	407174.i	−0.278348	−	0.482114i	−0.970974	+	0.239183i	$0.923120\pi$
$920$	−113973.	−	65802.6i	−0.134657	−	0.0777441i
$921$	−363405.	−	209812.i	−0.428422	−	0.247349i
$922$	−2.26106e6	+	1.30542e6i	−2.65981	+	1.53564i
$923$	1.00715e6			1.18220
$924$	2.02391e6	−	71700.6i	2.37054	−	0.0839806i
$925$		−	4771.50i		−	0.00557662i
$926$	−227646.	−	394295.i	−0.265484	−	0.459832i
$927$	−1.21985e6	−	704281.i	−1.41954	−	0.819571i
$928$	−7245.74	−	4183.33i	−0.00841369	−	0.00485765i
$929$	−228173.	−	395207.i	−0.264382	−	0.457923i	0.703019	−	0.711171i	$-0.251835\pi$
$929$	−228173.	−	395207.i	−0.264382	−	0.457923i	−0.967402	+	0.253247i	$0.918501\pi$
$930$	−2.16252e6			−2.50031
$931$	−922052.	+	623289.i	−1.06379	+	0.719101i
$932$		−	1.47114e6i		−	1.69364i
$933$	704165.	+	1.21965e6i	0.808930	+	1.40111i
$934$	554484.	+	320132.i	0.635617	+	0.366974i
$935$	209881.	+	865088.i	0.240077	+	0.989549i
$936$	744101.	−	429607.i	0.849337	−	0.490365i
$937$		−	762263.i		−	0.868212i	−0.900862	−	0.434106i	$-0.857064\pi$
$937$		−	762263.i		−	0.868212i	0.900862	−	0.434106i	$-0.142936\pi$
$938$	16235.7	+	458291.i	0.0184530	+	0.520878i
$939$	−1.91900e6			−2.17643
$940$	636701.	−	367600.i	0.720576	−	0.416025i
$941$	−204007.	+	353350.i	−0.230391	+	0.399049i	−0.957923	−	0.287025i	$-0.907334\pi$
$941$	−204007.	+	353350.i	−0.230391	+	0.399049i	0.727532	+	0.686074i	$0.240667\pi$
$942$	2.82833e6	+	1.63294e6i	3.18734	+	1.84021i
$943$	−176521.	+	101914.i	−0.198505	+	0.114607i
$944$		−	85325.7i		−	0.0957494i
$945$	−5534.37	+	3462.15i	−0.00619733	+	0.00387688i
$946$			2.51788e6i			2.81354i
$947$	−1.10991e6	+	640807.i	−1.23762	+	0.714541i	−0.968607	−	0.248595i	$-0.920031\pi$
$947$	−1.10991e6	+	640807.i	−1.23762	+	0.714541i	−0.269014	+	0.963136i	$0.586698\pi$
$948$	−919739.	−	531012.i	−1.02341	−	0.590864i
$949$	453448.	+	261799.i	0.503495	+	0.290693i
$950$	104953.	−	60594.8i	0.116292	−	0.0671411i
$951$			2.18064e6i			2.41115i
$952$	−232672.	−	829640.i	−0.256726	−	0.915410i
$953$	133978.			0.147519			0.0737593	−	0.997276i	$-0.476500\pi$
$953$	133978.			0.147519			0.0737593	+	0.997276i	$0.476500\pi$
$954$	316228.	+	547723.i	0.347459	+	0.601817i
$955$	−215470.	+	373205.i	−0.236255	+	0.409205i
$956$	272214.	−	471488.i	0.297848	−	0.515887i
$957$	−6330.43	−	10964.6i	−0.00691209	−	0.0119721i
$958$	1.78184e6			1.94150
$959$	−1.48399e6	−	788089.i	−1.61359	−	0.856915i
$960$	2.05242e6			2.22702
$961$	−132503.	−	229502.i	−0.143476	−	0.248508i
$962$	65591.2	−	113607.i	0.0708754	−	0.122760i
$963$	−22910.7	−	13227.5i	−0.0247051	−	0.0142635i
$964$	−334986.	−	580212.i	−0.360473	−	0.624357i
$965$		−	197607.i		−	0.212201i
$966$	−190785.	−	304977.i	−0.204451	−	0.326823i
$967$	189133.			0.202262			0.101131	−	0.994873i	$-0.467754\pi$
$967$	189133.			0.202262			0.101131	+	0.994873i	$0.467754\pi$
$968$	−48503.4	−	84010.4i	−0.0517633	−	0.0896566i
$969$	402544.	+	1.65921e6i	0.428712	+	1.76707i
$970$	−299956.	+	519539.i	−0.318797	+	0.552172i
$971$	−1.01383e6	+	585334.i	−1.07529	+	0.620819i	−0.929622	−	0.368514i	$-0.879867\pi$
$971$	−1.01383e6	+	585334.i	−1.07529	+	0.620819i	−0.145668	+	0.989333i	$0.546533\pi$
$972$	−2.12812e6			−2.25249
$973$	−63918.3	−	1.80424e6i	−0.0675148	−	1.90576i
$974$		−	1.27143e6i		−	1.34021i
$975$	77722.7	−	44873.2i	0.0817596	−	0.0472039i
$976$	35541.5	−	61559.7i	0.0373109	−	0.0646245i
$977$	190929.	−	330699.i	0.200025	−	0.346453i	−0.748511	−	0.663122i	$-0.769231\pi$
$977$	190929.	−	330699.i	0.200025	−	0.346453i	0.948536	+	0.316669i	$0.102564\pi$
$978$	−2.11159e6	+	1.21913e6i	−2.20766	+	1.27459i
$979$	452271.			0.471882
$980$	1.47352e6	−	104535.i	1.53428	−	0.108845i
$981$			986682.i			1.02527i
$982$	1.35389e6	+	2.34501e6i	1.40398	+	2.43177i
$983$	−428192.	+	741650.i	−0.443130	+	0.767524i	−0.997920	−	0.0644669i	$-0.979465\pi$
$983$	−428192.	+	741650.i	−0.443130	+	0.767524i	0.554790	+	0.831990i	$0.312799\pi$
$984$	−883332.	+	1.52998e6i	−0.912291	+	1.58013i
$985$	−476673.	+	275207.i	−0.491301	+	0.283653i
$986$	−10498.7	+	10010.8i	−0.0107989	+	0.0102971i
$987$	745781.	−	26420.6i	0.765556	−	0.0271211i
$988$	2.04576e6			2.09576
$989$	237823.	−	137307.i	0.243142	−	0.140378i
$990$	1.39855e6	+	807451.i	1.42694	+	0.823845i
$991$	1.21292e6	+	700280.i	1.23505	+	0.713057i	0.968079	−	0.250647i	$-0.0806433\pi$
$991$	1.21292e6	+	700280.i	1.23505	+	0.713057i	0.266973	+	0.963704i	$0.413977\pi$
$992$	584964.	+	1.01319e6i	0.594437	+	1.02960i
$993$	1.13359e6			1.14963
$994$	−971739.	−	1.55336e6i	−0.983506	−	1.57217i
$995$	−3315.18			−0.00334858
$996$	−1.60046e6	+	924024.i	−1.61334	+	0.931461i
$997$	192411.	−	333266.i	0.193571	−	0.335274i	−0.752860	−	0.658180i	$-0.771326\pi$
$997$	192411.	−	333266.i	0.193571	−	0.335274i	0.946431	+	0.322906i	$0.104660\pi$
$998$	−2.10243e6	−	1.21384e6i	−2.11087	−	1.21871i
$999$	560.801	−	323.779i	0.000561925	−	0.000324427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.h.a.101.41	yes	92
7.5	odd	6	inner	119.5.h.a.33.42	yes	92
17.16	even	2	inner	119.5.h.a.101.42	yes	92
119.33	odd	6	inner	119.5.h.a.33.41	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.h.a.33.41	✓	92	119.33	odd	6	inner
119.5.h.a.33.42	yes	92	7.5	odd	6	inner
119.5.h.a.101.41	yes	92	1.1	even	1	trivial
119.5.h.a.101.42	yes	92	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.21912 + 5.57567i) q^{2} +(-6.37245 + 11.0374i) q^{3} +(-12.7254 + 22.0411i) q^{4} +(12.0871 + 20.9355i) q^{5} -82.0546 q^{6} +(1.73482 + 48.9693i) q^{7} -60.8466 q^{8} +(-40.7162 - 70.5225i) q^{9} +(-77.8195 + 134.787i) q^{10} +(110.347 + 63.7089i) q^{11} +(-162.184 - 280.911i) q^{12} -173.407i q^{13} +(-267.452 + 167.311i) q^{14} -308.098 q^{15} +(7.73430 + 13.3962i) q^{16} +(280.853 - 68.1383i) q^{17} +(262.140 - 454.040i) q^{18} +(401.436 - 231.769i) q^{19} -615.253 q^{20} +(-551.549 - 292.906i) q^{21} +820.345i q^{22} +(77.4845 - 44.7357i) q^{23} +(387.742 - 671.589i) q^{24} +(20.3041 - 35.1677i) q^{25} +(966.863 - 558.218i) q^{26} +5.51108 q^{27} +(-1101.41 - 584.917i) q^{28} +7.79645i q^{29} +(-991.802 - 1717.85i) q^{30} +(545.098 - 944.137i) q^{31} +(-536.568 + 929.363i) q^{32} +(-1406.36 + 811.963i) q^{33} +(1284.01 + 1346.60i) q^{34} +(-1004.23 + 628.216i) q^{35} +2072.52 q^{36} +(101.759 - 58.7505i) q^{37} +(2584.54 + 1492.18i) q^{38} +(1913.97 + 1105.03i) q^{39} +(-735.459 - 1273.85i) q^{40} -2278.14 q^{41} +(-142.350 - 4018.15i) q^{42} +3069.29 q^{43} +(-2808.42 + 1621.44i) q^{44} +(984.282 - 1704.83i) q^{45} +(498.863 + 288.019i) q^{46} +(-1034.86 + 597.477i) q^{47} -197.146 q^{48} +(-2394.98 + 169.906i) q^{49} +261.445 q^{50} +(-1037.65 + 3534.09i) q^{51} +(3822.08 + 2206.68i) q^{52} +(-603.165 + 1044.71i) q^{53} +(17.7408 + 30.7280i) q^{54} +3080.22i q^{55} +(-105.558 - 2979.62i) q^{56} +5907.75i q^{57} +(-43.4705 + 25.0977i) q^{58} +(-4777.05 - 2758.03i) q^{59} +(3920.67 - 6790.80i) q^{60} +(-2297.66 - 3979.66i) q^{61} +7018.93 q^{62} +(3382.80 - 2116.19i) q^{63} -6661.60 q^{64} +(3630.36 - 2095.99i) q^{65} +(-9054.48 - 5227.61i) q^{66} +(726.810 - 1258.87i) q^{67} +(-2072.12 + 7057.38i) q^{68} +1140.30i q^{69} +(-6735.45 - 3576.94i) q^{70} +5808.00i q^{71} +(2477.44 + 4291.06i) q^{72} +(-1509.73 + 2614.93i) q^{73} +(655.147 + 378.249i) q^{74} +(258.773 + 448.209i) q^{75} +11797.4i q^{76} +(-2928.35 + 5514.14i) q^{77} +14228.9i q^{78} +(2835.48 - 1637.07i) q^{79} +(-186.970 + 323.842i) q^{80} +(3262.89 - 5651.50i) q^{81} +(-7333.60 - 12702.2i) q^{82} -5697.38i q^{83} +(13474.7 - 8429.37i) q^{84} +(4821.20 + 5056.19i) q^{85} +(9880.41 + 17113.4i) q^{86} +(-86.0526 - 49.6825i) q^{87} +(-6714.24 - 3876.47i) q^{88} +(3073.97 - 1774.76i) q^{89} +12674.1 q^{90} +(8491.63 - 300.831i) q^{91} +2277.12i q^{92} +(6947.22 + 12032.9i) q^{93} +(-6662.67 - 3846.69i) q^{94} +(9704.39 + 5602.83i) q^{95} +(-6838.51 - 11844.6i) q^{96} +3854.51 q^{97} +(-8657.06 - 12806.7i) q^{98} -10375.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) \) 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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