LMFDB - Embedded newform 108.5.k.a.65.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.7
Character	$\chi$	$=$	108.65
Dual form			108.5.k.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.126357 - 8.99911i) q^{3} +(-6.31102 + 17.3394i) q^{5} +(2.68521 - 15.2286i) q^{7} +(-80.9681 + 2.27420i) q^{9} +O(q^{10})$	\(q+(-0.126357 - 8.99911i) q^{3} +(-6.31102 + 17.3394i) q^{5} +(2.68521 - 15.2286i) q^{7} +(-80.9681 + 2.27420i) q^{9} +(-57.3804 - 157.651i) q^{11} +(-47.4796 + 39.8401i) q^{13} +(156.837 + 54.6026i) q^{15} +(-434.160 + 250.663i) q^{17} +(-226.022 + 391.482i) q^{19} +(-137.383 - 22.2403i) q^{21} +(-87.9439 + 15.5069i) q^{23} +(217.952 + 182.884i) q^{25} +(30.6966 + 728.353i) q^{27} +(-388.247 + 462.695i) q^{29} +(-253.555 - 1437.98i) q^{31} +(-1411.47 + 536.293i) q^{33} +(247.108 + 142.668i) q^{35} +(-743.956 - 1288.57i) q^{37} +(364.525 + 422.240i) q^{39} +(-1177.61 - 1403.43i) q^{41} +(1145.30 - 416.855i) q^{43} +(471.558 - 1418.29i) q^{45} +(-1675.90 - 295.507i) q^{47} +(2031.50 + 739.406i) q^{49} +(2310.60 + 3875.39i) q^{51} +448.959i q^{53} +3095.71 q^{55} +(3551.55 + 1984.53i) q^{57} +(519.236 - 1426.59i) q^{59} +(600.396 - 3405.01i) q^{61} +(-182.784 + 1239.14i) q^{63} +(-391.158 - 1074.70i) q^{65} +(130.770 - 109.729i) q^{67} +(150.660 + 789.458i) q^{69} +(-3379.60 + 1951.21i) q^{71} +(4207.66 - 7287.88i) q^{73} +(1618.25 - 1984.49i) q^{75} +(-2554.89 + 450.495i) q^{77} +(6492.89 + 5448.18i) q^{79} +(6550.66 - 368.274i) q^{81} +(-697.809 + 831.616i) q^{83} +(-1606.34 - 9110.01i) q^{85} +(4212.90 + 3435.42i) q^{87} +(-9947.94 - 5743.45i) q^{89} +(479.216 + 830.026i) q^{91} +(-12908.5 + 2463.47i) q^{93} +(-5361.62 - 6389.73i) q^{95} +(-1079.02 + 392.731i) q^{97} +(5004.51 + 12634.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{5} - 102 q^{9}+O(q^{10}) $ 72 * q + 9 * q^5 - 102 * q^9	$ 72 q + 9 q^{5} - 102 q^{9} + 18 q^{11} - 225 q^{15} - 282 q^{21} - 1278 q^{23} + 441 q^{25} + 54 q^{27} + 1854 q^{29} - 1665 q^{31} - 45 q^{33} - 2673 q^{35} + 6951 q^{39} - 5472 q^{41} + 1260 q^{43} + 5553 q^{45} + 5103 q^{47} - 5904 q^{49} + 1899 q^{51} + 1107 q^{57} - 10944 q^{59} + 8352 q^{61} - 11985 q^{63} + 8757 q^{65} + 378 q^{67} + 5607 q^{69} - 19764 q^{71} + 6111 q^{73} - 3453 q^{75} - 5679 q^{77} - 5652 q^{79} - 20466 q^{81} - 20061 q^{83} + 26100 q^{85} + 40545 q^{87} + 15633 q^{89} - 6039 q^{91} + 40179 q^{93} + 48024 q^{95} - 37530 q^{97} + 12177 q^{99}+O(q^{100}) $ 72 * q + 9 * q^5 - 102 * q^9 + 18 * q^11 - 225 * q^15 - 282 * q^21 - 1278 * q^23 + 441 * q^25 + 54 * q^27 + 1854 * q^29 - 1665 * q^31 - 45 * q^33 - 2673 * q^35 + 6951 * q^39 - 5472 * q^41 + 1260 * q^43 + 5553 * q^45 + 5103 * q^47 - 5904 * q^49 + 1899 * q^51 + 1107 * q^57 - 10944 * q^59 + 8352 * q^61 - 11985 * q^63 + 8757 * q^65 + 378 * q^67 + 5607 * q^69 - 19764 * q^71 + 6111 * q^73 - 3453 * q^75 - 5679 * q^77 - 5652 * q^79 - 20466 * q^81 - 20061 * q^83 + 26100 * q^85 + 40545 * q^87 + 15633 * q^89 - 6039 * q^91 + 40179 * q^93 + 48024 * q^95 - 37530 * q^97 + 12177 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.126357	−	8.99911i	−0.0140396	−	0.999901i
$3$	−0.126357	−	8.99911i	−0.0140396	−	0.999901i
$4$		0			0
$5$	−6.31102	+	17.3394i	−0.252441	+	0.693576i	0.747141	+	0.664665i	$0.231426\pi$
$5$	−6.31102	+	17.3394i	−0.252441	+	0.693576i	−0.999582	+	0.0289101i	$0.990796\pi$
$6$		0			0
$7$	2.68521	−	15.2286i	0.0548002	−	0.310788i	−0.945070	−	0.326867i	$-0.894007\pi$
$7$	2.68521	−	15.2286i	0.0548002	−	0.310788i	0.999871	+	0.0160790i	$0.00511834\pi$
$8$		0			0
$9$	−80.9681	+	2.27420i	−0.999606	+	0.0280765i
$10$		0			0
$11$	−57.3804	−	157.651i	−0.474218	−	1.30290i	−0.914334	−	0.404962i	$-0.867285\pi$
$11$	−57.3804	−	157.651i	−0.474218	−	1.30290i	0.440116	−	0.897941i	$-0.354937\pi$
$12$		0			0
$13$	−47.4796	+	39.8401i	−0.280944	+	0.235740i	−0.772360	−	0.635185i	$-0.780924\pi$
$13$	−47.4796	+	39.8401i	−0.280944	+	0.235740i	0.491416	+	0.870925i	$0.336479\pi$
$14$		0			0
$15$	156.837	+	54.6026i	0.697051	+	0.242678i
$16$		0			0
$17$	−434.160	+	250.663i	−1.50229	+	0.867345i	−0.502289	+	0.864700i	$0.667508\pi$
$17$	−434.160	+	250.663i	−1.50229	+	0.867345i	−0.999997	+	0.00264463i	$0.999158\pi$
$18$		0			0
$19$	−226.022	+	391.482i	−0.626100	+	1.08444i	0.362228	+	0.932090i	$0.382016\pi$
$19$	−226.022	+	391.482i	−0.626100	+	1.08444i	−0.988327	+	0.152347i	$0.951317\pi$
$20$		0			0
$21$	−137.383	−	22.2403i	−0.311526	−	0.0504315i
$22$		0			0
$23$	−87.9439	+	15.5069i	−0.166246	+	0.0293136i	−0.256151	−	0.966637i	$-0.582455\pi$
$23$	−87.9439	+	15.5069i	−0.166246	+	0.0293136i	0.0899058	+	0.995950i	$0.471343\pi$
$24$		0			0
$25$	217.952	+	182.884i	0.348724	+	0.292614i
$26$		0			0
$27$	30.6966	+	728.353i	0.0421078	+	0.999113i
$28$		0			0
$29$	−388.247	+	462.695i	−0.461650	+	0.550173i	−0.945773	−	0.324827i	$-0.894694\pi$
$29$	−388.247	+	462.695i	−0.461650	+	0.550173i	0.484124	+	0.874999i	$0.339138\pi$
$30$		0			0
$31$	−253.555	−	1437.98i	−0.263845	−	1.49634i	−0.772304	−	0.635253i	$-0.780896\pi$
$31$	−253.555	−	1437.98i	−0.263845	−	1.49634i	0.508460	−	0.861086i	$-0.330215\pi$
$32$		0			0
$33$	−1411.47	+	536.293i	−1.29612	+	0.492464i
$34$		0			0
$35$	247.108	+	142.668i	0.201721	+	0.116464i
$36$		0			0
$37$	−743.956	−	1288.57i	−0.543430	−	0.941249i	−0.998704	−	0.0508971i	$-0.983792\pi$
$37$	−743.956	−	1288.57i	−0.543430	−	0.941249i	0.455274	−	0.890351i	$-0.349541\pi$
$38$		0			0
$39$	364.525	+	422.240i	0.239661	+	0.277607i
$40$		0			0
$41$	−1177.61	−	1403.43i	−0.700544	−	0.834875i	0.292044	−	0.956405i	$-0.405665\pi$
$41$	−1177.61	−	1403.43i	−0.700544	−	0.834875i	−0.992588	+	0.121529i	$0.961220\pi$
$42$		0			0
$43$	1145.30	−	416.855i	0.619416	−	0.225449i	−0.0132024	−	0.999913i	$-0.504203\pi$
$43$	1145.30	−	416.855i	0.619416	−	0.225449i	0.632618	+	0.774464i	$0.281980\pi$
$44$		0			0
$45$	471.558	−	1418.29i	0.232868	−	0.700390i
$46$		0			0
$47$	−1675.90	−	295.507i	−0.758670	−	0.133774i	−0.219086	−	0.975706i	$-0.570307\pi$
$47$	−1675.90	−	295.507i	−0.758670	−	0.133774i	−0.539584	+	0.841932i	$0.681419\pi$
$48$		0			0
$49$	2031.50	+	739.406i	0.846107	+	0.307958i
$50$		0			0
$51$	2310.60	+	3875.39i	0.888351	+	1.48996i
$52$		0			0
$53$			448.959i			0.159829i	0.996802	+	0.0799144i	$0.0254647\pi$
$53$			448.959i			0.159829i	−0.996802	+	0.0799144i	$0.974535\pi$
$54$		0			0
$55$	3095.71			1.02337
$56$		0			0
$57$	3551.55	+	1984.53i	1.09312	+	0.610813i
$58$		0			0
$59$	519.236	−	1426.59i	0.149163	−	0.409821i	−0.842498	−	0.538700i	$-0.818916\pi$
$59$	519.236	−	1426.59i	0.149163	−	0.409821i	0.991660	+	0.128879i	$0.0411378\pi$
$60$		0			0
$61$	600.396	−	3405.01i	0.161353	−	0.915080i	−0.791392	−	0.611309i	$-0.790643\pi$
$61$	600.396	−	3405.01i	0.161353	−	0.915080i	0.952745	−	0.303771i	$-0.0982458\pi$
$62$		0			0
$63$	−182.784	+	1239.14i	−0.0460528	+	0.312204i
$64$		0			0
$65$	−391.158	−	1074.70i	−0.0925818	−	0.254366i
$66$		0			0
$67$	130.770	−	109.729i	0.0291311	−	0.0244439i	−0.628106	−	0.778128i	$-0.716170\pi$
$67$	130.770	−	109.729i	0.0291311	−	0.0244439i	0.657237	+	0.753684i	$0.271725\pi$
$68$		0			0
$69$	150.660	+	789.458i	0.0316447	+	0.165818i
$70$		0			0
$71$	−3379.60	+	1951.21i	−0.670423	+	0.387069i	−0.796237	−	0.604985i	$-0.793179\pi$
$71$	−3379.60	+	1951.21i	−0.670423	+	0.387069i	0.125814	+	0.992054i	$0.459846\pi$
$72$		0			0
$73$	4207.66	−	7287.88i	0.789578	−	1.36759i	−0.136648	−	0.990620i	$-0.543633\pi$
$73$	4207.66	−	7287.88i	0.789578	−	1.36759i	0.926226	−	0.376969i	$-0.123034\pi$
$74$		0			0
$75$	1618.25	−	1984.49i	0.287689	−	0.352798i
$76$		0			0
$77$	−2554.89	+	450.495i	−0.430913	+	0.0759816i
$78$		0			0
$79$	6492.89	+	5448.18i	1.04036	+	0.872966i	0.992047	−	0.125867i	$-0.0401712\pi$
$79$	6492.89	+	5448.18i	1.04036	+	0.872966i	0.0483127	+	0.998832i	$0.484616\pi$
$80$		0			0
$81$	6550.66	−	368.274i	0.998423	−	0.0561308i
$82$		0			0
$83$	−697.809	+	831.616i	−0.101293	+	0.120717i	−0.814309	−	0.580431i	$-0.802884\pi$
$83$	−697.809	+	831.616i	−0.101293	+	0.120717i	0.713016	+	0.701148i	$0.247329\pi$
$84$		0			0
$85$	−1606.34	−	9110.01i	−0.222331	−	1.26090i
$86$		0			0
$87$	4212.90	+	3435.42i	0.556600	+	0.453880i
$88$		0			0
$89$	−9947.94	−	5743.45i	−1.25589	−	0.725091i	−0.283621	−	0.958937i	$-0.591536\pi$
$89$	−9947.94	−	5743.45i	−1.25589	−	0.725091i	−0.972274	+	0.233846i	$0.924869\pi$
$90$		0			0
$91$	479.216	+	830.026i	0.0578693	+	0.100233i
$92$		0			0
$93$	−12908.5	+	2463.47i	−1.49249	+	0.284827i
$94$		0			0
$95$	−5361.62	−	6389.73i	−0.594085	−	0.708003i
$96$		0			0
$97$	−1079.02	+	392.731i	−0.114680	+	0.0417399i	−0.398723	−	0.917072i	$-0.630546\pi$
$97$	−1079.02	+	392.731i	−0.114680	+	0.0417399i	0.284043	+	0.958812i	$0.408324\pi$
$98$		0			0
$99$	5004.51	+	12634.2i	0.510612	+	1.28908i
$100$		0			0
$101$	6324.41	+	1115.16i	0.619979	+	0.109319i	0.474811	−	0.880088i	$-0.342516\pi$
$101$	6324.41	+	1115.16i	0.619979	+	0.109319i	0.145169	+	0.989407i	$0.453628\pi$
$102$		0			0
$103$	−6157.93	−	2241.30i	−0.580444	−	0.211264i	0.0350773	−	0.999385i	$-0.488832\pi$
$103$	−6157.93	−	2241.30i	−0.580444	−	0.211264i	−0.615521	+	0.788120i	$0.711054\pi$
$104$		0			0
$105$	1252.66	−	2241.78i	0.113620	−	0.203336i
$106$		0			0
$107$			4283.13i			0.374105i	0.982350	+	0.187052i	$0.0598934\pi$
$107$			4283.13i			0.374105i	−0.982350	+	0.187052i	$0.940107\pi$
$108$		0			0
$109$	−3812.13			−0.320859			−0.160430	−	0.987047i	$-0.551288\pi$
$109$	−3812.13			−0.320859			−0.160430	+	0.987047i	$0.551288\pi$
$110$		0			0
$111$	−11502.0	+	6857.76i	−0.933526	+	0.556591i
$112$		0			0
$113$	−2239.98	+	6154.29i	−0.175423	+	0.481971i	−0.995978	−	0.0895965i	$-0.971442\pi$
$113$	−2239.98	+	6154.29i	−0.175423	+	0.481971i	0.820555	+	0.571568i	$0.193664\pi$
$114$		0			0
$115$	286.136	−	1622.76i	0.0216360	−	0.122704i
$116$		0			0
$117$	3753.72	−	3333.75i	0.274215	−	0.243535i
$118$		0			0
$119$	2651.43	+	7284.73i	0.187234	+	0.514422i
$120$		0			0
$121$	−10345.8	+	8681.13i	−0.706630	+	0.592933i
$122$		0			0
$123$	−12480.8	+	10774.8i	−0.824958	+	0.712196i
$124$		0			0
$125$	−14534.1	+	8391.29i	−0.930185	+	0.537042i
$126$		0			0
$127$	11298.5	−	19569.6i	0.700511	−	1.21332i	−0.267777	−	0.963481i	$-0.586289\pi$
$127$	11298.5	−	19569.6i	0.700511	−	1.21332i	0.968287	−	0.249839i	$-0.0803778\pi$
$128$		0			0
$129$	−3896.04	−	10254.0i	−0.234123	−	0.616189i
$130$		0			0
$131$	−2408.04	+	424.602i	−0.140320	+	0.0247422i	−0.243367	−	0.969934i	$-0.578252\pi$
$131$	−2408.04	+	424.602i	−0.140320	+	0.0247422i	0.103047	+	0.994677i	$0.467141\pi$
$132$		0			0
$133$	5354.79	+	4493.21i	0.302719	+	0.254011i
$134$		0			0
$135$	−12822.9	−	4064.39i	−0.703590	−	0.223012i
$136$		0			0
$137$	8488.11	−	10115.7i	0.452241	−	0.538960i	−0.490960	−	0.871182i	$-0.663354\pi$
$137$	8488.11	−	10115.7i	0.452241	−	0.538960i	0.943201	+	0.332222i	$0.107798\pi$
$138$		0			0
$139$	6365.38	+	36099.8i	0.329454	+	1.86842i	0.476325	+	0.879269i	$0.341969\pi$
$139$	6365.38	+	36099.8i	0.329454	+	1.86842i	−0.146871	+	0.989156i	$0.546920\pi$
$140$		0			0
$141$	−2447.54	+	15119.0i	−0.123109	+	0.760473i
$142$		0			0
$143$	9005.23	+	5199.17i	0.440375	+	0.254251i
$144$		0			0
$145$	−5572.61	−	9652.05i	−0.265047	−	0.459075i
$146$		0			0
$147$	6397.31	−	18375.1i	0.296048	−	0.850347i
$148$		0			0
$149$	−13315.3	−	15868.5i	−0.599760	−	0.714766i	0.377691	−	0.925932i	$-0.376718\pi$
$149$	−13315.3	−	15868.5i	−0.599760	−	0.714766i	−0.977450	+	0.211166i	$0.932274\pi$
$150$		0			0
$151$	−25658.1	+	9338.77i	−1.12530	+	0.409577i	−0.836585	−	0.547837i	$-0.815451\pi$
$151$	−25658.1	+	9338.77i	−1.12530	+	0.409577i	−0.288719	+	0.957414i	$0.593229\pi$
$152$		0			0
$153$	34583.1	−	21283.0i	1.47734	−	0.909182i
$154$		0			0
$155$	26533.9	+	4678.64i	1.10443	+	0.194741i
$156$		0			0
$157$	−38577.4	−	14041.0i	−1.56507	−	0.569639i	−0.593180	−	0.805070i	$-0.702128\pi$
$157$	−38577.4	−	14041.0i	−1.56507	−	0.569639i	−0.971891	+	0.235431i	$0.924350\pi$
$158$		0			0
$159$	4040.23	−	56.7290i	0.159813	−	0.00224394i
$160$		0			0
$161$			1380.90i			0.0532734i
$162$		0			0
$163$	31743.5			1.19476			0.597378	−	0.801959i	$-0.296209\pi$
$163$	31743.5			1.19476			0.597378	+	0.801959i	$0.296209\pi$
$164$		0			0
$165$	−391.163	−	27858.6i	−0.0143678	−	1.02327i
$166$		0			0
$167$	18527.6	−	50904.2i	0.664334	−	1.82524i	0.108240	−	0.994125i	$-0.465478\pi$
$167$	18527.6	−	50904.2i	0.664334	−	1.82524i	0.556094	−	0.831119i	$-0.312299\pi$
$168$		0			0
$169$	−4292.49	+	24343.9i	−0.150292	+	0.852348i
$170$		0			0
$171$	17410.3	−	32211.5i	0.595406	−	1.10159i
$172$		0			0
$173$	16730.7	+	45967.2i	0.559012	+	1.53587i	0.821074	+	0.570822i	$0.193376\pi$
$173$	16730.7	+	45967.2i	0.559012	+	1.53587i	−0.262061	+	0.965051i	$0.584402\pi$
$174$		0			0
$175$	3370.31	−	2828.03i	0.110051	−	0.0923437i
$176$		0			0
$177$	−12903.6	−	4492.40i	−0.411875	−	0.143394i
$178$		0			0
$179$	−22709.4	+	13111.3i	−0.708761	+	0.409203i	−0.810602	−	0.585598i	$-0.800860\pi$
$179$	−22709.4	+	13111.3i	−0.708761	+	0.409203i	0.101841	+	0.994801i	$0.467527\pi$
$180$		0			0
$181$	−14057.5	+	24348.3i	−0.429092	+	0.743209i	−0.996793	−	0.0800256i	$-0.974500\pi$
$181$	−14057.5	+	24348.3i	−0.429092	+	0.743209i	0.567701	+	0.823235i	$0.307833\pi$
$182$		0			0
$183$	−30718.0	−	4972.78i	−0.917256	−	0.148490i
$184$		0			0
$185$	27038.1	−	4767.55i	0.790011	−	0.139300i
$186$		0			0
$187$	64429.6	+	54062.8i	1.84248	+	1.54602i
$188$		0			0
$189$	11174.2	+	1488.32i	0.312819	+	0.0416650i
$190$		0			0
$191$	23218.0	−	27670.2i	0.636442	−	0.758482i	−0.347362	−	0.937731i	$-0.612922\pi$
$191$	23218.0	−	27670.2i	0.636442	−	0.758482i	0.983804	+	0.179249i	$0.0573668\pi$
$192$		0			0
$193$	−3902.27	−	22130.9i	−0.104762	−	0.594133i	−0.991315	−	0.131507i	$-0.958018\pi$
$193$	−3902.27	−	22130.9i	−0.104762	−	0.594133i	0.886554	−	0.462626i	$-0.153093\pi$
$194$		0			0
$195$	−9621.90	+	3655.87i	−0.253041	+	0.0961439i
$196$		0			0
$197$	56910.6	+	32857.3i	1.46643	+	0.846642i	0.999295	−	0.0375447i	$-0.0119536\pi$
$197$	56910.6	+	32857.3i	1.46643	+	0.846642i	0.467133	+	0.884187i	$0.345287\pi$
$198$		0			0
$199$	−18862.4	−	32670.7i	−0.476312	−	0.824997i	0.523319	−	0.852137i	$-0.324693\pi$
$199$	−18862.4	−	32670.7i	−0.476312	−	0.824997i	−0.999632	+	0.0271397i	$0.991360\pi$
$200$		0			0
$201$	−1003.98	−	1162.94i	−0.0248505	−	0.0287851i
$202$		0			0
$203$	6003.67	+	7154.89i	0.145688	+	0.173625i
$204$		0			0
$205$	31766.5	−	11562.1i	0.755895	−	0.275123i
$206$		0			0
$207$	7085.38	−	1455.56i	0.165357	−	0.0339696i
$208$		0			0
$209$	74686.8	+	13169.3i	1.70982	+	0.301488i
$210$		0			0
$211$	−46853.0	−	17053.1i	−1.05238	−	0.383035i	−0.242820	−	0.970071i	$-0.578072\pi$
$211$	−46853.0	−	17053.1i	−1.05238	−	0.383035i	−0.809560	+	0.587036i	$0.800295\pi$
$212$		0			0
$213$	17986.2	+	30166.9i	0.396443	+	0.664922i
$214$		0			0
$215$			22489.6i			0.486524i
$216$		0			0
$217$	−22579.3			−0.479502
$218$		0			0
$219$	−66116.1	−	36944.3i	−1.37854	−	0.770299i
$220$		0			0
$221$	10627.3	−	29198.3i	0.217590	−	0.597824i
$222$		0			0
$223$	−9188.10	+	52108.3i	−0.184763	+	1.04784i	0.741496	+	0.670958i	$0.234117\pi$
$223$	−9188.10	+	52108.3i	−0.184763	+	1.04784i	−0.926259	+	0.376887i	$0.876994\pi$
$224$		0			0
$225$	−18063.1	−	14312.1i	−0.356802	−	0.282708i
$226$		0			0
$227$	−18336.8	−	50379.8i	−0.355853	−	0.977698i	−0.980453	−	0.196753i	$-0.936960\pi$
$227$	−18336.8	−	50379.8i	−0.355853	−	0.977698i	0.624600	−	0.780945i	$-0.285262\pi$
$228$		0			0
$229$	−72773.1	+	61063.9i	−1.38771	+	1.16443i	−0.421457	+	0.906848i	$0.638481\pi$
$229$	−72773.1	+	61063.9i	−1.38771	+	1.16443i	−0.966256	+	0.257582i	$0.917074\pi$
$230$		0			0
$231$	4376.88	+	22934.8i	0.0820240	+	0.429804i
$232$		0			0
$233$	−59397.7	+	34293.3i	−1.09410	+	0.631680i	−0.934665	−	0.355528i	$-0.884301\pi$
$233$	−59397.7	+	34293.3i	−1.09410	+	0.631680i	−0.159436	+	0.987208i	$0.550968\pi$
$234$		0			0
$235$	15700.6	−	27194.2i	0.284302	−	0.492425i
$236$		0			0
$237$	48208.4	−	59118.6i	0.858273	−	1.05251i
$238$		0			0
$239$	25378.0	−	4474.83i	0.444285	−	0.0783395i	0.0529698	−	0.998596i	$-0.483131\pi$
$239$	25378.0	−	4474.83i	0.444285	−	0.0783395i	0.391315	+	0.920257i	$0.372020\pi$
$240$		0			0
$241$	−4966.35	−	4167.26i	−0.0855073	−	0.0717492i	0.599032	−	0.800725i	$-0.295552\pi$
$241$	−4966.35	−	4167.26i	−0.0855073	−	0.0717492i	−0.684539	+	0.728976i	$0.739997\pi$
$242$		0			0
$243$	−4141.86	−	58903.6i	−0.0701428	−	0.997537i
$244$		0			0
$245$	−25641.7	+	30558.6i	−0.427184	+	0.509098i
$246$		0			0
$247$	−4865.23	−	27592.1i	−0.0797461	−	0.452263i
$248$		0			0
$249$	7571.98	+	6174.58i	0.122127	+	0.0995884i
$250$		0			0
$251$	−72828.7	−	42047.7i	−1.15599	−	0.667413i	−0.205653	−	0.978625i	$-0.565932\pi$
$251$	−72828.7	−	42047.7i	−1.15599	−	0.667413i	−0.950341	+	0.311212i	$0.899265\pi$
$252$		0			0
$253$	7490.93	+	12974.7i	0.117029	+	0.202701i
$254$		0			0
$255$	−81779.1	+	15606.8i	−1.25766	+	0.240012i
$256$		0			0
$257$	−18558.1	−	22116.7i	−0.280975	−	0.334853i	0.607037	−	0.794674i	$-0.292358\pi$
$257$	−18558.1	−	22116.7i	−0.280975	−	0.334853i	−0.888012	+	0.459821i	$0.847914\pi$
$258$		0			0
$259$	−21620.8	+	7869.32i	−0.322308	+	0.117311i
$260$		0			0
$261$	30383.4	−	38346.5i	0.446021	−	0.562917i
$262$		0			0
$263$	2552.92	+	450.148i	0.0369084	+	0.00650795i	0.192072	−	0.981381i	$-0.438479\pi$
$263$	2552.92	+	450.148i	0.0369084	+	0.00650795i	−0.155163	+	0.987889i	$0.549590\pi$
$264$		0			0
$265$	−7784.68	−	2833.39i	−0.110853	−	0.0403473i
$266$		0			0
$267$	−50428.9	+	90248.4i	−0.707387	+	1.26595i
$268$		0			0
$269$			62120.1i			0.858475i	0.903192	+	0.429238i	$0.141218\pi$
$269$			62120.1i			0.858475i	−0.903192	+	0.429238i	$0.858782\pi$
$270$		0			0
$271$	23727.3			0.323080			0.161540	−	0.986866i	$-0.448354\pi$
$271$	23727.3			0.323080			0.161540	+	0.986866i	$0.448354\pi$
$272$		0			0
$273$	7408.94	−	4417.39i	0.0994102	−	0.0592708i
$274$		0			0
$275$	16325.7	−	44854.4i	0.215877	−	0.593116i
$276$		0			0
$277$	−12397.3	+	70308.5i	−0.161572	+	0.916322i	0.790956	+	0.611873i	$0.209584\pi$
$277$	−12397.3	+	70308.5i	−0.161572	+	0.916322i	−0.952529	+	0.304449i	$0.901528\pi$
$278$		0			0
$279$	23800.1	+	115854.i	0.305753	+	1.48834i
$280$		0			0
$281$	40372.1	+	110922.i	0.511292	+	1.40476i	0.879891	+	0.475175i	$0.157615\pi$
$281$	40372.1	+	110922.i	0.511292	+	1.40476i	−0.368599	+	0.929589i	$0.620162\pi$
$282$		0			0
$283$	−67038.7	+	56252.2i	−0.837053	+	0.702371i	−0.956899	−	0.290422i	$-0.906204\pi$
$283$	−67038.7	+	56252.2i	−0.837053	+	0.702371i	0.119846	+	0.992792i	$0.461760\pi$
$284$		0			0
$285$	−56824.4	+	49057.2i	−0.699593	+	0.603967i
$286$		0			0
$287$	−24534.3	+	14164.9i	−0.297859	+	0.171969i
$288$		0			0
$289$	83903.0	−	145324.i	1.00457	−	1.73997i
$290$		0			0
$291$	3670.57	+	9660.60i	0.0433459	+	0.114082i
$292$		0			0
$293$	−147759.	+	26053.9i	−1.72115	+	0.303485i	−0.945002	−	0.327064i	$-0.893941\pi$
$293$	−147759.	+	26053.9i	−1.72115	+	0.303485i	−0.776149	+	0.630550i	$0.782830\pi$
$294$		0			0
$295$	21459.3	+	18006.5i	0.246587	+	0.206911i
$296$		0			0
$297$	113064.	−	46632.6i	1.28178	−	0.528660i
$298$		0			0
$299$	3557.74	−	4239.95i	0.0397953	−	0.0474262i
$300$		0			0
$301$	−3272.74	−	18560.6i	−0.0361226	−	0.204861i
$302$		0			0
$303$	9236.36	−	57055.0i	0.100604	−	0.621453i
$304$		0			0
$305$	55251.8	+	31899.6i	0.593945	+	0.342914i
$306$		0			0
$307$	2679.80	+	4641.56i	0.0284332	+	0.0492478i	0.879892	−	0.475174i	$-0.157615\pi$
$307$	2679.80	+	4641.56i	0.0284332	+	0.0492478i	−0.851459	+	0.524422i	$0.824282\pi$
$308$		0			0
$309$	−19391.6	+	55699.1i	−0.203094	+	0.583353i
$310$		0			0
$311$	−108484.	−	129286.i	−1.12161	−	1.33669i	−0.935161	−	0.354223i	$-0.884746\pi$
$311$	−108484.	−	129286.i	−1.12161	−	1.33669i	−0.186452	−	0.982464i	$-0.559699\pi$
$312$		0			0
$313$	57251.6	−	20837.9i	0.584385	−	0.212699i	−0.0328728	−	0.999460i	$-0.510466\pi$
$313$	57251.6	−	20837.9i	0.584385	−	0.212699i	0.617258	+	0.786761i	$0.288243\pi$
$314$		0			0
$315$	−20332.3	−	10989.6i	−0.204911	−	0.110754i
$316$		0			0
$317$	4583.45	+	808.187i	0.0456115	+	0.00804254i	0.196407	−	0.980522i	$-0.437073\pi$
$317$	4583.45	+	808.187i	0.0456115	+	0.00804254i	−0.150796	+	0.988565i	$0.548184\pi$
$318$		0			0
$319$	95222.2	+	34658.1i	0.935744	+	0.340583i
$320$		0			0
$321$	38544.4	−	541.202i	0.374068	−	0.00525229i
$322$		0			0
$323$		−	226621.i		−	2.17218i
$324$		0			0
$325$	−17634.4			−0.166953
$326$		0			0
$327$	481.688	+	34305.8i	0.00450474	+	0.320828i
$328$		0			0
$329$	−9000.30	+	24728.1i	−0.0831505	+	0.228454i
$330$		0			0
$331$	11428.8	−	64815.9i	0.104314	−	0.591596i	−0.887178	−	0.461428i	$-0.847337\pi$
$331$	11428.8	−	64815.9i	0.104314	−	0.591596i	0.991492	−	0.130168i	$-0.0415517\pi$
$332$		0			0
$333$	63167.1	+	102641.i	0.569643	+	0.925620i
$334$		0			0
$335$	1077.34	+	2959.96i	0.00959981	+	0.0263753i
$336$		0			0
$337$	97808.8	−	82071.3i	0.861228	−	0.722656i	−0.101004	−	0.994886i	$-0.532206\pi$
$337$	97808.8	−	82071.3i	0.861228	−	0.722656i	0.962232	+	0.272230i	$0.0877612\pi$
$338$		0			0
$339$	55666.2	+	19380.2i	0.484386	+	0.168639i
$340$		0			0
$341$	−212151.	+	122485.i	−1.82446	+	1.05335i
$342$		0			0
$343$	35279.1	−	61105.2i	0.299867	−	0.519385i
$344$		0			0
$345$	−14639.5	−	2369.92i	−0.122995	−	0.0199111i
$346$		0			0
$347$	54058.3	−	9531.94i	0.448956	−	0.0791630i	0.0554011	−	0.998464i	$-0.482356\pi$
$347$	54058.3	−	9531.94i	0.448956	−	0.0791630i	0.393555	+	0.919301i	$0.371245\pi$
$348$		0			0
$349$	−129327.	−	108518.i	−1.06179	−	0.890948i	−0.0675069	−	0.997719i	$-0.521504\pi$
$349$	−129327.	−	108518.i	−1.06179	−	0.890948i	−0.994284	+	0.106771i	$0.965949\pi$
$350$		0			0
$351$	−30475.1	−	33358.9i	−0.247361	−	0.270768i
$352$		0			0
$353$	109221.	−	130165.i	0.876512	−	1.04459i	−0.122131	−	0.992514i	$-0.538973\pi$
$353$	109221.	−	130165.i	0.876512	−	1.04459i	0.998643	−	0.0520726i	$-0.0165827\pi$
$354$		0			0
$355$	−12504.1	−	70914.4i	−0.0992193	−	0.562701i
$356$		0			0
$357$	65221.1	−	24781.0i	0.511743	−	0.194438i
$358$		0			0
$359$	96846.2	+	55914.2i	0.751439	+	0.433843i	0.826214	−	0.563357i	$-0.190490\pi$
$359$	96846.2	+	55914.2i	0.751439	+	0.433843i	−0.0747748	+	0.997200i	$0.523824\pi$
$360$		0			0
$361$	−37011.3	−	64105.5i	−0.284001	−	0.491905i
$362$		0			0
$363$	79429.7	+	92005.8i	0.602795	+	0.698235i
$364$		0			0
$365$	99812.7	+	118952.i	0.749204	+	0.892867i
$366$		0			0
$367$	224386.	−	81670.0i	1.66596	−	0.606360i	0.674677	−	0.738113i	$-0.264283\pi$
$367$	224386.	−	81670.0i	1.66596	−	0.606360i	0.991283	+	0.131753i	$0.0420605\pi$
$368$		0			0
$369$	98540.8	+	110955.i	0.723708	+	0.814877i
$370$		0			0
$371$	6837.01	+	1205.55i	0.0496728	+	0.00875865i
$372$		0			0
$373$	−59651.3	−	21711.3i	−0.428748	−	0.156052i	0.118627	−	0.992939i	$-0.462151\pi$
$373$	−59651.3	−	21711.3i	−0.428748	−	0.156052i	−0.547375	+	0.836887i	$0.684373\pi$
$374$		0			0
$375$	77350.6	+	129734.i	0.550049	+	0.922553i
$376$		0			0
$377$		−	37436.4i		−	0.263397i
$378$		0			0
$379$	259784.			1.80856			0.904281	−	0.426937i	$-0.140407\pi$
$379$	259784.			1.80856			0.904281	+	0.426937i	$0.140407\pi$
$380$		0			0
$381$	−177537.	−	99204.1i	−1.22304	−	0.683407i
$382$		0			0
$383$	−24459.2	+	67201.2i	−0.166742	+	0.458120i	−0.994718	−	0.102643i	$-0.967270\pi$
$383$	−24459.2	+	67201.2i	−0.166742	+	0.458120i	0.827976	+	0.560763i	$0.189492\pi$
$384$		0			0
$385$	8312.62	−	47143.2i	0.0560811	−	0.318052i
$386$		0			0
$387$	−91784.7	+	36356.6i	−0.612842	+	0.242751i
$388$		0			0
$389$	−68567.8	−	188389.i	−0.453128	−	1.24496i	−0.930511	−	0.366264i	$-0.880637\pi$
$389$	−68567.8	−	188389.i	−0.453128	−	1.24496i	0.477383	−	0.878696i	$-0.341586\pi$
$390$		0			0
$391$	34294.8	−	28776.7i	0.224323	−	0.188230i
$392$		0			0
$393$	4125.31	+	21616.5i	0.0267099	+	0.139959i
$394$		0			0
$395$	−135445.	+	78199.1i	−0.868097	+	0.501196i
$396$		0			0
$397$	−58749.4	+	101757.i	−0.372754	+	0.645629i	−0.989988	−	0.141151i	$-0.954920\pi$
$397$	−58749.4	+	101757.i	−0.372754	+	0.645629i	0.617234	+	0.786779i	$0.288253\pi$
$398$		0			0
$399$	39758.3	−	48756.1i	0.249736	−	0.306255i
$400$		0			0
$401$	−18914.7	+	3335.17i	−0.117628	+	0.0207410i	−0.232152	−	0.972679i	$-0.574577\pi$
$401$	−18914.7	+	3335.17i	−0.117628	+	0.0207410i	0.114524	+	0.993420i	$0.463466\pi$
$402$		0			0
$403$	69328.0	+	58173.1i	0.426873	+	0.358189i
$404$		0			0
$405$	−34955.7	+	115909.i	−0.213112	+	0.706652i
$406$		0			0
$407$	−160456.	+	191224.i	−0.968651	+	1.15439i
$408$		0			0
$409$	20337.6	+	115340.i	0.121577	+	0.689499i	0.983282	+	0.182089i	$0.0582858\pi$
$409$	20337.6	+	115340.i	0.121577	+	0.689499i	−0.861705	+	0.507410i	$0.830603\pi$
$410$		0			0
$411$	−92105.2	−	75107.3i	−0.545256	−	0.444630i
$412$		0			0
$413$	−20330.7	−	11737.9i	−0.119193	−	0.0688162i
$414$		0			0
$415$	−10015.8	−	17347.9i	−0.0581555	−	0.100728i
$416$		0			0
$417$	324062.	−	61844.2i	1.86362	−	0.355653i
$418$		0			0
$419$	−6735.90	−	8027.53i	−0.0383679	−	0.0457250i	0.746519	−	0.665364i	$-0.231724\pi$
$419$	−6735.90	−	8027.53i	−0.0383679	−	0.0457250i	−0.784887	+	0.619639i	$0.787279\pi$
$420$		0			0
$421$	−105571.	+	38424.7i	−0.595635	+	0.216794i	−0.622206	−	0.782853i	$-0.713763\pi$
$421$	−105571.	+	38424.7i	−0.595635	+	0.216794i	0.0265709	+	0.999647i	$0.491541\pi$
$422$		0			0
$423$	136367.	+	20115.3i	0.762127	+	0.112420i
$424$		0			0
$425$	−140468.	−	24768.4i	−0.777680	−	0.137126i
$426$		0			0
$427$	−50241.4	−	18286.4i	−0.275553	−	0.100293i
$428$		0			0
$429$	45650.1	−	81696.1i	0.248043	−	0.443901i
$430$		0			0
$431$		−	288726.i		−	1.55428i	−0.629325	−	0.777142i	$-0.716668\pi$
$431$		−	288726.i		−	1.55428i	0.629325	−	0.777142i	$-0.283332\pi$
$432$		0			0
$433$	−212012.			−1.13080			−0.565398	−	0.824818i	$-0.691277\pi$
$433$	−212012.			−1.13080			−0.565398	+	0.824818i	$0.691277\pi$
$434$		0			0
$435$	−86155.7	+	51368.2i	−0.455308	+	0.271466i
$436$		0			0
$437$	13806.6	−	37933.3i	0.0722976	−	0.198636i
$438$		0			0
$439$	−30463.9	+	172769.i	−0.158072	+	0.896473i	0.797851	+	0.602855i	$0.205970\pi$
$439$	−30463.9	+	172769.i	−0.158072	+	0.896473i	−0.955923	+	0.293618i	$0.905141\pi$
$440$		0			0
$441$	−166168.	−	55248.3i	−0.854420	−	0.284081i
$442$		0			0
$443$	25778.3	+	70825.2i	0.131355	+	0.360894i	0.987882	−	0.155208i	$-0.0496047\pi$
$443$	25778.3	+	70825.2i	0.131355	+	0.360894i	−0.856527	+	0.516102i	$0.827382\pi$
$444$		0			0
$445$	162370.	−	136244.i	0.819944	−	0.688015i
$446$		0			0
$447$	−141120.	+	121831.i	−0.706275	+	0.609736i
$448$		0			0
$449$	74850.4	−	43214.9i	0.371280	−	0.214359i	−0.302738	−	0.953074i	$-0.597901\pi$
$449$	74850.4	−	43214.9i	0.371280	−	0.214359i	0.674017	+	0.738715i	$0.264567\pi$
$450$		0			0
$451$	−153680.	+	266181.i	−0.755551	+	1.30865i
$452$		0			0
$453$	87282.7	+	229720.i	0.425336	+	1.11944i
$454$		0			0
$455$	−17416.5	+	3070.99i	−0.0841274	+	0.0148339i
$456$		0			0
$457$	−98203.7	−	82402.7i	−0.470214	−	0.394556i	0.376659	−	0.926352i	$-0.377073\pi$
$457$	−98203.7	−	82402.7i	−0.470214	−	0.394556i	−0.846873	+	0.531796i	$0.821517\pi$
$458$		0			0
$459$	−195898.	−	308528.i	−0.929833	−	1.46443i
$460$		0			0
$461$	−65000.0	+	77464.0i	−0.305852	+	0.364500i	−0.896975	−	0.442081i	$-0.854240\pi$
$461$	−65000.0	+	77464.0i	−0.305852	+	0.364500i	0.591123	+	0.806582i	$0.298685\pi$
$462$		0			0
$463$	−551.115	−	3125.53i	−0.00257087	−	0.0145801i	0.983495	−	0.180933i	$-0.0579119\pi$
$463$	−551.115	−	3125.53i	−0.00257087	−	0.0145801i	−0.986066	+	0.166353i	$0.946801\pi$
$464$		0			0
$465$	38750.9	−	239373.i	0.179216	−	1.10705i
$466$		0			0
$467$	350190.	+	202182.i	1.60572	+	0.927062i	0.990313	+	0.138851i	$0.0443410\pi$
$467$	350190.	+	202182.i	1.60572	+	0.927062i	0.615405	+	0.788211i	$0.288992\pi$
$468$		0			0
$469$	−1319.87	−	2286.08i	−0.00600047	−	0.0103931i
$470$		0			0
$471$	−121482.	+	348937.i	−0.547610	+	1.57291i
$472$		0			0
$473$	−131435.	−	156639.i	−0.587476	−	0.700127i
$474$		0			0
$475$	−120858.	+	43988.6i	−0.535657	+	0.194963i
$476$		0			0
$477$	−1021.02	−	36351.3i	−0.00448743	−	0.159766i
$478$		0			0
$479$	−323147.	−	56979.5i	−1.40841	−	0.248341i	−0.582815	−	0.812605i	$-0.698049\pi$
$479$	−323147.	−	56979.5i	−1.40841	−	0.248341i	−0.825594	+	0.564264i	$0.809160\pi$
$480$		0			0
$481$	86659.4	+	31541.4i	0.374564	+	0.136330i
$482$		0			0
$483$	12426.9	−	174.486i	0.0532682	−	0.000747939i
$484$		0			0
$485$		−	21188.1i		−	0.0900758i
$486$		0			0
$487$	−115199.			−0.485727			−0.242863	−	0.970061i	$-0.578087\pi$
$487$	−115199.			−0.485727			−0.242863	+	0.970061i	$0.578087\pi$
$488$		0			0
$489$	−4011.00	−	285663.i	−0.0167739	−	1.19464i
$490$		0			0
$491$	−101982.	+	280195.i	−0.423022	+	1.16224i	0.526947	+	0.849898i	$0.323337\pi$
$491$	−101982.	+	280195.i	−0.423022	+	1.16224i	−0.949969	+	0.312344i	$0.898886\pi$
$492$		0			0
$493$	52581.2	−	298203.i	0.216340	−	1.22693i
$494$		0			0
$495$	−250653.	+	7040.24i	−1.02297	+	0.0287327i
$496$		0			0
$497$	20639.3	+	56706.0i	0.0835568	+	0.229570i
$498$		0			0
$499$	−26287.0	+	22057.4i	−0.105570	+	0.0885835i	−0.694045	−	0.719932i	$-0.744173\pi$
$499$	−26287.0	+	22057.4i	−0.105570	+	0.0885835i	0.588475	+	0.808515i	$0.299729\pi$
$500$		0			0
$501$	−460434.	−	160300.i	−1.83439	−	0.638643i
$502$		0			0
$503$	138252.	−	79820.0i	0.546432	−	0.315483i	−0.201250	−	0.979540i	$-0.564500\pi$
$503$	138252.	−	79820.0i	0.546432	−	0.315483i	0.747682	+	0.664057i	$0.231167\pi$
$504$		0			0
$505$	−59249.8	+	102624.i	−0.232329	+	0.402406i
$506$		0			0
$507$	219616.	+	35552.6i	0.854374	+	0.138311i
$508$		0			0
$509$	212619.	−	37490.4i	0.820665	−	0.144705i	0.252475	−	0.967603i	$-0.418755\pi$
$509$	212619.	−	37490.4i	0.820665	−	0.144705i	0.568189	+	0.822898i	$0.307644\pi$
$510$		0			0
$511$	−99685.7	−	83646.2i	−0.381760	−	0.320335i
$512$		0			0
$513$	−292075.	−	152607.i	−1.10984	−	0.579881i
$514$		0			0
$515$	77725.7	−	92629.8i	0.293056	−	0.349250i
$516$		0			0
$517$	49576.9	+	281164.i	0.185480	+	1.05191i
$518$		0			0
$519$	411550.	−	156370.i	1.52787	−	0.580520i
$520$		0			0
$521$	456380.	+	263491.i	1.68132	+	0.970712i	0.960785	+	0.277295i	$0.0894380\pi$
$521$	456380.	+	263491.i	1.68132	+	0.970712i	0.720537	+	0.693416i	$0.243895\pi$
$522$		0			0
$523$	121475.	+	210401.i	0.444104	+	0.769210i	0.997989	−	0.0633824i	$-0.0201888\pi$
$523$	121475.	+	210401.i	0.444104	+	0.769210i	−0.553885	+	0.832593i	$0.686855\pi$
$524$		0			0
$525$	−25875.6	−	29972.5i	−0.0938797	−	0.108744i
$526$		0			0
$527$	470532.	+	560758.i	1.69421	+	2.01908i
$528$		0			0
$529$	−255471.	+	92983.8i	−0.912914	+	0.332274i
$530$		0			0
$531$	−38797.2	+	116689.i	−0.137598	+	0.413848i
$532$		0			0
$533$	111825.	+	19717.8i	0.393627	+	0.0694071i
$534$		0			0
$535$	−74266.8	−	27030.9i	−0.259470	−	0.0944394i
$536$		0			0
$537$	120859.	+	202708.i	0.419113	+	0.702946i
$538$		0			0
$539$		−	362696.i		−	1.24843i
$540$		0			0
$541$	−293805.			−1.00384			−0.501921	−	0.864914i	$-0.667373\pi$
$541$	−293805.			−1.00384			−0.501921	+	0.864914i	$0.667373\pi$
$542$		0			0
$543$	220889.	+	123428.i	0.749161	+	0.418616i
$544$		0			0
$545$	24058.4	−	66100.0i	0.0809980	−	0.222540i
$546$		0			0
$547$	−23411.2	+	132772.i	−0.0782437	+	0.443742i	0.920367	+	0.391055i	$0.127890\pi$
$547$	−23411.2	+	132772.i	−0.0782437	+	0.443742i	−0.998611	+	0.0526871i	$0.983221\pi$
$548$		0			0
$549$	−40869.2	+	277063.i	−0.135598	+	0.919250i
$550$		0			0
$551$	−93384.2	−	256571.i	−0.307588	−	0.845092i
$552$		0			0
$553$	100403.	−	84248.0i	0.328319	−	0.275492i
$554$		0			0
$555$	−46320.2	−	242717.i	−0.150378	−	0.787977i
$556$		0			0
$557$	−184012.	+	106239.i	−0.593111	+	0.342433i	−0.766327	−	0.642451i	$-0.777918\pi$
$557$	−184012.	+	106239.i	−0.593111	+	0.342433i	0.173216	+	0.984884i	$0.444584\pi$
$558$		0			0
$559$	−37770.8	+	65420.9i	−0.120874	+	0.209360i
$560$		0			0
$561$	478376.	−	586640.i	1.52000	−	1.86400i
$562$		0			0
$563$	409414.	−	72190.7i	1.29165	−	0.227753i	0.514732	−	0.857351i	$-0.327891\pi$
$563$	409414.	−	72190.7i	1.29165	−	0.227753i	0.776921	+	0.629598i	$0.216780\pi$
$564$		0			0
$565$	−92575.1	−	77679.7i	−0.289999	−	0.243338i
$566$		0			0
$567$	11981.6	−	100746.i	0.0372691	−	0.313374i
$568$		0			0
$569$	57732.2	−	68802.6i	0.178317	−	0.212510i	−0.669481	−	0.742829i	$-0.733483\pi$
$569$	57732.2	−	68802.6i	0.178317	−	0.212510i	0.847798	+	0.530319i	$0.177928\pi$
$570$		0			0
$571$	−18272.9	−	103631.i	−0.0560449	−	0.317847i	0.943878	−	0.330295i	$-0.107148\pi$
$571$	−18272.9	−	103631.i	−0.0560449	−	0.317847i	−0.999923	+	0.0124489i	$0.996037\pi$
$572$		0			0
$573$	−251941.	−	205446.i	−0.767343	−	0.625731i
$574$		0			0
$575$	−22003.5	−	12703.7i	−0.0665513	−	0.0384234i
$576$		0			0
$577$	327443.	+	567148.i	0.983522	+	1.70351i	0.648330	+	0.761360i	$0.275468\pi$
$577$	327443.	+	567148.i	0.983522	+	1.70351i	0.335192	+	0.942150i	$0.391199\pi$
$578$		0			0
$579$	−198665.	+	37913.3i	−0.592604	+	0.113093i
$580$		0			0
$581$	10790.6	+	12859.7i	0.0319663	+	0.0380960i
$582$		0			0
$583$	70779.0	−	25761.4i	0.208241	−	0.0757937i
$584$		0			0
$585$	34115.4	+	86126.6i	0.0996870	+	0.251667i
$586$		0			0
$587$	281832.	+	49694.5i	0.817925	+	0.144222i	0.566930	−	0.823766i	$-0.308131\pi$
$587$	281832.	+	49694.5i	0.817925	+	0.144222i	0.250995	+	0.967988i	$0.419242\pi$
$588$		0			0
$589$	620252.	+	225753.i	1.78788	+	0.650734i
$590$		0			0
$591$	288496.	−	516297.i	0.825971	−	1.47817i
$592$		0			0
$593$		−	588614.i		−	1.67387i	−0.547303	−	0.836935i	$-0.684345\pi$
$593$		−	588614.i		−	1.67387i	0.547303	−	0.836935i	$-0.315655\pi$
$594$		0			0
$595$	−143046.			−0.404056
$596$		0			0
$597$	−291624.	+	173873.i	−0.818228	+	0.487848i
$598$		0			0
$599$	−87972.0	+	241701.i	−0.245183	+	0.673635i	0.754663	+	0.656112i	$0.227800\pi$
$599$	−87972.0	+	241701.i	−0.245183	+	0.673635i	−0.999846	+	0.0175230i	$0.994422\pi$
$600$		0			0
$601$	92944.8	−	527116.i	0.257321	−	1.45934i	−0.532721	−	0.846291i	$-0.678831\pi$
$601$	92944.8	−	527116.i	0.257321	−	1.45934i	0.790043	−	0.613052i	$-0.210058\pi$
$602$		0			0
$603$	−10338.6	+	9181.91i	−0.0284333	+	0.0252522i
$604$		0			0
$605$	−85233.1	−	234176.i	−0.232861	−	0.639781i
$606$		0			0
$607$	7438.44	−	6241.59i	0.0201885	−	0.0169402i	−0.632638	−	0.774448i	$-0.718028\pi$
$607$	7438.44	−	6241.59i	0.0201885	−	0.0169402i	0.652826	+	0.757508i	$0.273583\pi$
$608$		0			0
$609$	63629.1	−	54931.7i	0.171562	−	0.148112i
$610$		0			0
$611$	91344.1	−	52737.5i	0.244680	−	0.141266i
$612$		0			0
$613$	−211500.	+	366328.i	−0.562845	+	0.974876i	0.434402	+	0.900719i	$0.356960\pi$
$613$	−211500.	+	366328.i	−0.562845	+	0.974876i	−0.997247	+	0.0741567i	$0.976373\pi$
$614$		0			0
$615$	−108062.	−	284409.i	−0.285709	−	0.751958i
$616$		0			0
$617$	−276732.	+	48795.3i	−0.726923	+	0.128176i	−0.524851	−	0.851194i	$-0.675879\pi$
$617$	−276732.	+	48795.3i	−0.726923	+	0.128176i	−0.202073	+	0.979371i	$0.564768\pi$
$618$		0			0
$619$	10444.5	+	8763.96i	0.0272587	+	0.0228728i	0.656315	−	0.754487i	$-0.272114\pi$
$619$	10444.5	+	8763.96i	0.0272587	+	0.0228728i	−0.629056	+	0.777360i	$0.716559\pi$
$620$		0			0
$621$	−13994.1	−	63578.2i	−0.0362878	−	0.164864i
$622$		0			0
$623$	−114177.	+	136071.i	−0.294173	+	0.350581i
$624$		0			0
$625$	−22895.9	−	129849.i	−0.0586136	−	0.332414i
$626$		0			0
$627$	109075.	−	673779.i	0.277453	−	1.71389i
$628$		0			0
$629$	645992.	+	372964.i	1.63277	+	0.942682i
$630$		0			0
$631$	−181931.	−	315113.i	−0.456927	−	0.791421i	0.541870	−	0.840463i	$-0.317717\pi$
$631$	−181931.	−	315113.i	−0.456927	−	0.791421i	−0.998797	+	0.0490416i	$0.984383\pi$
$632$		0			0
$633$	−147543.	+	423790.i	−0.368222	+	1.05765i
$634$		0			0
$635$	268020.	+	319414.i	0.664692	+	0.792149i
$636$		0			0
$637$	−125913.	+	45828.5i	−0.310307	+	0.112942i
$638$		0			0
$639$	269202.	−	165672.i	0.659291	−	0.405739i
$640$		0			0
$641$	−182661.	−	32208.0i	−0.444559	−	0.0783877i	−0.0531122	−	0.998589i	$-0.516914\pi$
$641$	−182661.	−	32208.0i	−0.444559	−	0.0783877i	−0.391447	+	0.920201i	$0.628025\pi$
$642$		0			0
$643$	151393.	+	55102.5i	0.366170	+	0.133275i	0.518551	−	0.855047i	$-0.326472\pi$
$643$	151393.	+	55102.5i	0.366170	+	0.133275i	−0.152380	+	0.988322i	$0.548694\pi$
$644$		0			0
$645$	202386.	−	2841.71i	0.486476	−	0.00683062i
$646$		0			0
$647$		−	612652.i		−	1.46354i	−0.681551	−	0.731771i	$-0.738694\pi$
$647$		−	612652.i		−	1.46354i	0.681551	−	0.731771i	$-0.261306\pi$
$648$		0			0
$649$	−254697.			−0.604693
$650$		0			0
$651$	2853.04	+	203193.i	0.00673203	+	0.479455i
$652$		0			0
$653$	−96947.5	+	266361.i	−0.227358	+	0.624661i	−0.999948	−	0.0102448i	$-0.996739\pi$
$653$	−96947.5	+	266361.i	−0.227358	+	0.624661i	0.772589	+	0.634906i	$0.218961\pi$
$654$		0			0
$655$	7834.83	−	44433.5i	0.0182619	−	0.103569i
$656$		0			0
$657$	−324112.	+	599655.i	−0.750869	+	1.38922i
$658$		0			0
$659$	39534.0	+	108619.i	0.0910333	+	0.250112i	0.976851	−	0.213922i	$-0.0686238\pi$
$659$	39534.0	+	108619.i	0.0910333	+	0.250112i	−0.885817	+	0.464034i	$0.846402\pi$
$660$		0			0
$661$	−228769.	+	191960.i	−0.523594	+	0.439348i	−0.865883	−	0.500247i	$-0.833242\pi$
$661$	−228769.	+	191960.i	−0.523594	+	0.439348i	0.342289	+	0.939595i	$0.388798\pi$
$662$		0			0
$663$	−264102.	−	91947.1i	−0.600820	−	0.209176i
$664$		0			0
$665$	−111704.	+	64492.1i	−0.252595	+	0.145836i
$666$		0			0
$667$	26969.0	−	46711.7i	0.0606197	−	0.104996i
$668$		0			0
$669$	470089.	+	76100.5i	1.05034	+	0.170034i
$670$		0			0
$671$	−571256.	+	100728.i	−1.26878	+	0.223720i
$672$		0			0
$673$	51736.3	+	43412.0i	0.114226	+	0.0958471i	0.698112	−	0.715989i	$-0.254024\pi$
$673$	51736.3	+	43412.0i	0.114226	+	0.0958471i	−0.583886	+	0.811836i	$0.698468\pi$
$674$		0			0
$675$	−126514.	+	164360.i	−0.277670	+	0.360736i
$676$		0			0
$677$	32165.5	−	38333.3i	0.0701798	−	0.0836371i	−0.729812	−	0.683648i	$-0.760393\pi$
$677$	32165.5	−	38333.3i	0.0701798	−	0.0836371i	0.799992	+	0.600011i	$0.204837\pi$
$678$		0			0
$679$	3083.34	+	17486.5i	0.00668779	+	0.0379283i
$680$		0			0
$681$	−451057.	+	171380.i	−0.972606	+	0.369545i
$682$		0			0
$683$	356353.	+	205741.i	0.763905	+	0.441041i	0.830696	−	0.556726i	$-0.187943\pi$
$683$	356353.	+	205741.i	0.763905	+	0.441041i	−0.0667911	+	0.997767i	$0.521276\pi$
$684$		0			0
$685$	121832.	+	211019.i	0.259645	+	0.449719i
$686$		0			0
$687$	558716.	+	647178.i	1.18380	+	1.37123i
$688$		0			0
$689$	−17886.6	−	21316.4i	−0.0376781	−	0.0449030i
$690$		0			0
$691$	−869026.	+	316300.i	−1.82002	+	0.662434i	−0.824729	+	0.565529i	$0.808672\pi$
$691$	−869026.	+	316300.i	−1.82002	+	0.662434i	−0.995294	+	0.0969053i	$0.969106\pi$
$692$		0			0
$693$	205840.	−	42286.0i	0.428610	−	0.0880502i
$694$		0			0
$695$	−666121.	−	117455.i	−1.37906	−	0.243166i
$696$		0			0
$697$	863060.	+	314128.i	1.77654	+	0.646608i
$698$		0			0
$699$	316114.	+	530193.i	0.646978	+	1.08513i
$700$		0			0
$701$		−	503300.i		−	1.02421i	−0.858922	−	0.512107i	$-0.828865\pi$
$701$		−	503300.i		−	1.02421i	0.858922	−	0.512107i	$-0.171135\pi$
$702$		0			0
$703$	672601.			1.36097
$704$		0			0
$705$	−246707.	−	137855.i	−0.496368	−	0.277360i
$706$		0			0
$707$	33964.8	−	93317.4i	0.0679500	−	0.186691i
$708$		0			0
$709$	111417.	−	631875.i	0.221645	−	1.25701i	−0.647352	−	0.762192i	$-0.724123\pi$
$709$	111417.	−	631875.i	0.221645	−	1.25701i	0.868996	−	0.494819i	$-0.164765\pi$
$710$		0			0
$711$	−538107.	−	426362.i	−1.06446	−	0.843412i
$712$		0			0
$713$	44597.2	+	122530.i	0.0877261	+	0.241025i
$714$		0			0
$715$	−146983.	+	123333.i	−0.287511	+	0.241250i
$716$		0			0
$717$	−43476.2	−	227814.i	−0.0845693	−	0.443141i
$718$		0			0
$719$	−818071.	+	472314.i	−1.58246	+	0.913635i	−0.587964	+	0.808887i	$0.700070\pi$
$719$	−818071.	+	472314.i	−1.58246	+	0.913635i	−0.994499	+	0.104748i	$0.966597\pi$
$720$		0			0
$721$	−50667.2	+	87758.2i	−0.0974668	+	0.168817i
$722$		0			0
$723$	−36874.1	+	45219.3i	−0.0705416	+	0.0865062i
$724$		0			0
$725$	−169239.	+	29841.4i	−0.321976	+	0.0567731i
$726$		0			0
$727$	−670967.	−	563008.i	−1.26950	−	1.06524i	−0.994602	−	0.103762i	$-0.966912\pi$
$727$	−670967.	−	563008.i	−1.26950	−	1.06524i	−0.274896	−	0.961474i	$-0.588643\pi$
$728$		0			0
$729$	−529556.	+	44715.9i	−0.996454	+	0.0841409i
$730$		0			0
$731$	−392754.	+	468066.i	−0.734997	+	0.875935i
$732$		0			0
$733$	−33242.1	−	188525.i	−0.0618701	−	0.350883i	−0.999990	−	0.00457085i	$-0.998545\pi$
$733$	−33242.1	−	188525.i	−0.0618701	−	0.350883i	0.938119	−	0.346312i	$-0.112566\pi$
$734$		0			0
$735$	278240.	+	226891.i	0.515045	+	0.419994i
$736$		0			0
$737$	−24802.5	−	14319.7i	−0.0456625	−	0.0263633i
$738$		0			0
$739$	−463284.	−	802431.i	−0.848317	−	1.46933i	−0.882709	−	0.469920i	$-0.844283\pi$
$739$	−463284.	−	802431.i	−0.848317	−	1.46933i	0.0343917	−	0.999408i	$-0.489051\pi$
$740$		0			0
$741$	−247690.	+	47269.2i	−0.451099	+	0.0860879i
$742$		0			0
$743$	−151441.	−	180481.i	−0.274326	−	0.326929i	0.611238	−	0.791447i	$-0.290672\pi$
$743$	−151441.	−	180481.i	−0.274326	−	0.326929i	−0.885564	+	0.464518i	$0.846228\pi$
$744$		0			0
$745$	359183.	−	130732.i	0.647148	−	0.235543i
$746$		0			0
$747$	54609.0	−	68921.3i	0.0978640	−	0.123513i
$748$		0			0
$749$	65226.0	+	11501.1i	0.116267	+	0.0205010i
$750$		0			0
$751$	−975993.	−	355232.i	−1.73048	−	0.629843i	−0.731816	−	0.681503i	$-0.761327\pi$
$751$	−975993.	−	355232.i	−1.73048	−	0.629843i	−0.998665	+	0.0516592i	$0.983549\pi$
$752$		0			0
$753$	−369190.	+	660707.i	−0.651118	+	1.16525i
$754$		0			0
$755$		−	503832.i		−	0.883877i
$756$		0			0
$757$	514913.			0.898550			0.449275	−	0.893394i	$-0.351682\pi$
$757$	514913.			0.898550			0.449275	+	0.893394i	$0.351682\pi$
$758$		0			0
$759$	115814.	−	69051.2i	0.201038	−	0.119864i
$760$		0			0
$761$	38646.1	−	106179.i	0.0667323	−	0.183346i	−0.901844	−	0.432061i	$-0.857786\pi$
$761$	38646.1	−	106179.i	0.0667323	−	0.183346i	0.968576	+	0.248716i	$0.0800086\pi$
$762$		0			0
$763$	−10236.4	+	58053.3i	−0.0175832	+	0.0997190i
$764$		0			0
$765$	150780.	+	733967.i	0.257645	+	1.25416i
$766$		0			0
$767$	32182.3	+	88420.2i	0.0547049	+	0.150301i
$768$		0			0
$769$	560141.	−	470014.i	0.947206	−	0.794800i	−0.0316188	−	0.999500i	$-0.510066\pi$
$769$	560141.	−	470014.i	0.947206	−	0.794800i	0.978825	+	0.204700i	$0.0656218\pi$
$770$		0			0
$771$	−196686.	+	169801.i	−0.330875	+	0.285648i
$772$		0			0
$773$	−692751.	+	399960.i	−1.15936	+	0.669357i	−0.951150	−	0.308728i	$-0.900097\pi$
$773$	−692751.	+	399960.i	−1.15936	+	0.669357i	−0.208209	+	0.978084i	$0.566763\pi$
$774$		0			0
$775$	207721.	−	359783.i	0.345841	−	0.599014i
$776$		0			0
$777$	73548.8	+	193573.i	0.121824	+	0.320630i
$778$		0			0
$779$	815582.	−	143809.i	1.34398	−	0.236980i
$780$		0			0
$781$	501534.	+	420837.i	0.822240	+	0.689941i
$782$		0			0
$783$	−348923.	−	268578.i	−0.569124	−	0.438074i
$784$		0			0
$785$	486926.	−	580296.i	0.790176	−	0.941695i
$786$		0			0
$787$	−32767.9	−	185836.i	−0.0529052	−	0.300041i	0.946861	−	0.321642i	$-0.104235\pi$
$787$	−32767.9	−	185836.i	−0.0529052	−	0.300041i	−0.999767	+	0.0216013i	$0.993124\pi$
$788$		0			0
$789$	3728.36	−	23030.9i	0.00598912	−	0.0369961i
$790$		0			0
$791$	87706.3	+	50637.3i	0.140177	+	0.0809314i
$792$		0			0
$793$	107150.	+	185588.i	0.170390	+	0.295124i
$794$		0			0
$795$	−24514.4	+	70413.2i	−0.0387870	+	0.111409i
$796$		0			0
$797$	−241745.	−	288101.i	−0.380576	−	0.453553i	0.541420	−	0.840752i	$-0.317887\pi$
$797$	−241745.	−	288101.i	−0.380576	−	0.453553i	−0.921996	+	0.387199i	$0.873442\pi$
$798$		0			0
$799$	801682.	−	291789.i	1.25577	−	0.457062i
$800$		0			0
$801$	818527.	+	442412.i	1.27576	+	0.689544i
$802$		0			0
$803$	−1.39038e6	−	245162.i	−2.15627	−	0.380208i
$804$		0			0
$805$	−23944.0	−	8714.89i	−0.0369491	−	0.0134484i
$806$		0			0
$807$	559026.	−	7849.29i	0.858390	−	0.0120527i
$808$		0			0
$809$			452460.i			0.691326i	0.938359	+	0.345663i	$0.112346\pi$
$809$			452460.i			0.691326i	−0.938359	+	0.345663i	$0.887654\pi$
$810$		0			0
$811$	−196742.			−0.299126			−0.149563	−	0.988752i	$-0.547787\pi$
$811$	−196742.			−0.299126			−0.149563	+	0.988752i	$0.547787\pi$
$812$		0			0
$813$	−2998.10	−	213525.i	−0.00453592	−	0.323048i
$814$		0			0
$815$	−200334.	+	550413.i	−0.301605	+	0.828654i
$816$		0			0
$817$	−95671.8	+	542582.i	−0.143331	+	0.812870i
$818$		0			0
$819$	−40688.8	−	66115.7i	−0.0606606	−	0.0985683i
$820$		0			0
$821$	−256330.	−	704262.i	−0.380289	−	1.04484i	−0.971235	−	0.238124i	$-0.923468\pi$
$821$	−256330.	−	704262.i	−0.380289	−	1.04484i	0.590946	−	0.806711i	$-0.298755\pi$
$822$		0			0
$823$	708768.	−	594727.i	1.04642	−	0.878047i	0.0537035	−	0.998557i	$-0.482897\pi$
$823$	708768.	−	594727.i	1.04642	−	0.878047i	0.992712	+	0.120510i	$0.0384530\pi$
$824$		0			0
$825$	−405713.	−	141249.i	−0.596089	−	0.207528i
$826$		0			0
$827$	587764.	−	339346.i	0.859394	−	0.496171i	−0.00441555	−	0.999990i	$-0.501406\pi$
$827$	587764.	−	339346.i	0.859394	−	0.496171i	0.863809	+	0.503819i	$0.168072\pi$
$828$		0			0
$829$	−350763.	+	607539.i	−0.510393	+	0.884026i	0.489535	+	0.871984i	$0.337167\pi$
$829$	−350763.	+	607539.i	−0.510393	+	0.884026i	−0.999927	+	0.0120423i	$0.996167\pi$
$830$		0			0
$831$	634280.	+	102681.i	0.918500	+	0.148692i
$832$		0			0
$833$	−1.06734e6	+	188201.i	−1.53820	+	0.271226i
$834$		0			0
$835$	765720.	+	642515.i	1.09824	+	0.921532i
$836$		0			0
$837$	1.03958e6	−	228819.i	1.48390	−	0.326618i
$838$		0			0
$839$	−533551.	+	635862.i	−0.757970	+	0.903314i	−0.997718	−	0.0675215i	$-0.978491\pi$
$839$	−533551.	+	635862.i	−0.757970	+	0.903314i	0.239748	+	0.970835i	$0.422935\pi$
$840$		0			0
$841$	59467.3	+	337256.i	0.0840787	+	0.476834i
$842$		0			0
$843$	993094.	−	377329.i	1.39745	−	0.530964i
$844$		0			0
$845$	−395019.	−	228064.i	−0.553228	−	0.319406i
$846$		0			0
$847$	104421.	+	180862.i	0.145553	+	0.252104i
$848$		0			0
$849$	514690.	+	596181.i	0.714053	+	0.827109i
$850$		0			0
$851$	85408.1	+	101785.i	0.117934	+	0.140548i
$852$		0			0
$853$	1.05186e6	−	382845.i	1.44564	−	0.526169i	0.504268	−	0.863547i	$-0.331762\pi$
$853$	1.05186e6	−	382845.i	1.44564	−	0.526169i	0.941369	+	0.337379i	$0.109540\pi$
$854$		0			0
$855$	448652.	+	505171.i	0.613729	+	0.691044i
$856$		0			0
$857$	1.22199e6	+	215469.i	1.66382	+	0.293375i	0.924840	−	0.380357i	$-0.124199\pi$
$857$	1.22199e6	+	215469.i	1.66382	+	0.293375i	0.738975	+	0.673732i	$0.235310\pi$
$858$		0			0
$859$	−706165.	−	257023.i	−0.957017	−	0.348326i	−0.184153	−	0.982898i	$-0.558954\pi$
$859$	−706165.	−	257023.i	−0.957017	−	0.348326i	−0.772864	+	0.634572i	$0.781176\pi$
$860$		0			0
$861$	130572.	+	218997.i	0.176134	+	0.295415i
$862$		0			0
$863$			13565.4i			0.0182143i	0.999959	+	0.00910714i	$0.00289893\pi$
$863$			13565.4i			0.0182143i	−0.999959	+	0.00910714i	$0.997101\pi$
$864$		0			0
$865$	−902630.			−1.20636
$866$		0			0
$867$	−1.31839e6	−	736690.i	−1.75390	−	0.980046i
$868$		0			0
$869$	486348.	−	1.33623e6i	0.644032	−	1.76946i
$870$		0			0
$871$	−1837.28	+	10419.7i	−0.00242181	+	0.0137347i
$872$		0			0
$873$	86473.0	−	34252.6i	0.113462	−	0.0449433i
$874$		0			0
$875$	88760.2	+	243867.i	0.115932	+	0.318520i
$876$		0			0
$877$	317821.	−	266683.i	0.413222	−	0.346734i	−0.412356	−	0.911023i	$-0.635294\pi$
$877$	317821.	−	266683.i	0.413222	−	0.346734i	0.825578	+	0.564289i	$0.190849\pi$
$878$		0			0
$879$	253132.	+	1.32641e6i	0.327620	+	1.71672i
$880$		0			0
$881$	−724092.	+	418055.i	−0.932914	+	0.538618i	−0.887732	−	0.460360i	$-0.847720\pi$
$881$	−724092.	+	418055.i	−0.932914	+	0.538618i	−0.0451823	+	0.998979i	$0.514387\pi$
$882$		0			0
$883$	501025.	−	867801.i	0.642596	−	1.11301i	−0.342255	−	0.939607i	$-0.611191\pi$
$883$	501025.	−	867801.i	0.642596	−	1.11301i	0.984851	−	0.173402i	$-0.0554759\pi$
$884$		0			0
$885$	159331.	−	195390.i	0.203429	−	0.249468i
$886$		0			0
$887$	298070.	−	52557.8i	0.378853	−	0.0668020i	0.0190210	−	0.999819i	$-0.493945\pi$
$887$	298070.	−	52557.8i	0.378853	−	0.0668020i	0.359832	+	0.933017i	$0.382834\pi$
$888$		0			0
$889$	−267679.	−	224609.i	−0.338697	−	0.284200i
$890$		0			0
$891$	−433938.	−	1.01159e6i	−0.546603	−	1.27423i
$892$		0			0
$893$	494476.	−	589293.i	0.620072	−	0.738973i
$894$		0			0
$895$	−84022.0	−	476513.i	−0.104893	−	0.594879i
$896$		0			0
$897$	−38605.3	−	31480.8i	−0.0479802	−	0.0391255i
$898$		0			0
$899$	763789.	+	440974.i	0.945048	+	0.545624i
$900$		0			0
$901$	−112537.	−	194920.i	−0.138627	−	0.240108i
$902$		0			0
$903$	−166616.	+	31797.0i	−0.204334	+	0.0389952i
$904$		0			0
$905$	−333467.	−	397411.i	−0.407152	−	0.485224i
$906$		0			0
$907$	7980.23	−	2904.57i	0.00970065	−	0.00353075i	−0.337165	−	0.941445i	$-0.609468\pi$
$907$	7980.23	−	2904.57i	0.00970065	−	0.00353075i	0.346866	+	0.937915i	$0.387246\pi$
$908$		0			0
$909$	−514611.	−	75909.7i	−0.622804	−	0.0918692i
$910$		0			0
$911$	1.00032e6	+	176383.i	1.20532	+	0.212530i	0.739996	−	0.672611i	$-0.234827\pi$
$911$	1.00032e6	+	176383.i	1.20532	+	0.212530i	0.465322	+	0.885141i	$0.345938\pi$
$912$		0			0
$913$	171146.	+	62292.0i	0.205317	+	0.0747293i
$914$		0			0
$915$	280087.	−	501248.i	0.334542	−	0.598701i
$916$		0			0
$917$			37811.1i			0.0449657i
$918$		0			0
$919$	485910.			0.575341			0.287670	−	0.957730i	$-0.407119\pi$
$919$	485910.			0.575341			0.287670	+	0.957730i	$0.407119\pi$
$920$		0			0
$921$	41431.3	−	24702.3i	0.0488438	−	0.0291218i
$922$		0			0
$923$	82725.4	−	227286.i	0.0971037	−	0.266790i
$924$		0			0
$925$	73511.5	−	416904.i	0.0859155	−	0.487251i
$926$		0			0
$927$	503693.	+	167470.i	0.586147	+	0.194884i
$928$		0			0
$929$	67240.4	+	184742.i	0.0779111	+	0.214059i	0.972533	−	0.232765i	$-0.0747773\pi$
$929$	67240.4	+	184742.i	0.0779111	+	0.214059i	−0.894622	+	0.446824i	$0.852555\pi$
$930$		0			0
$931$	−748628.	+	628174.i	−0.863708	+	0.724737i
$932$		0			0
$933$	−1.14975e6	+	992592.i	−1.32081	+	1.14027i
$934$		0			0
$935$	−1.34403e6	+	775978.i	−1.53740	+	0.887618i
$936$		0			0
$937$	711754.	−	1.23279e6i	0.810682	−	1.40414i	−0.101705	−	0.994815i	$-0.532430\pi$
$937$	711754.	−	1.23279e6i	0.810682	−	1.40414i	0.912387	−	0.409328i	$-0.134237\pi$
$938$		0			0
$939$	−194757.	−	512581.i	−0.220882	−	0.581342i
$940$		0			0
$941$	525721.	−	92698.8i	0.593712	−	0.104688i	0.131285	−	0.991345i	$-0.458090\pi$
$941$	525721.	−	92698.8i	0.593712	−	0.104688i	0.462427	+	0.886657i	$0.346979\pi$
$942$		0			0
$943$	125327.	+	105162.i	0.140935	+	0.118259i
$944$		0			0
$945$	−96327.3	+	184361.i	−0.107866	+	0.206446i
$946$		0			0
$947$	−163880.	+	195304.i	−0.182737	+	0.217777i	−0.849634	−	0.527372i	$-0.823177\pi$
$947$	−163880.	+	195304.i	−0.182737	+	0.217777i	0.666898	+	0.745149i	$0.267622\pi$
$948$		0			0
$949$	90571.9	+	513659.i	0.100568	+	0.570351i
$950$		0			0
$951$	6693.81	−	41349.1i	0.00740138	−	0.0457199i
$952$		0			0
$953$	441492.	+	254896.i	0.486113	+	0.280657i	0.722961	−	0.690889i	$-0.242781\pi$
$953$	441492.	+	254896.i	0.486113	+	0.280657i	−0.236847	+	0.971547i	$0.576114\pi$
$954$		0			0
$955$	333255.	+	577214.i	0.365401	+	0.632893i
$956$		0			0
$957$	299860.	−	861295.i	0.327412	−	0.940433i
$958$		0			0
$959$	−131256.	−	156425.i	−0.142719	−	0.170086i
$960$		0			0
$961$	−1.13567e6	+	413352.i	−1.22972	+	0.447582i
$962$		0			0
$963$	−9740.67	−	346797.i	−0.0105036	−	0.373958i
$964$		0			0
$965$	408363.	+	72005.4i	0.438522	+	0.0773233i
$966$		0			0
$967$	−890903.	−	324262.i	−0.952746	−	0.346771i	−0.181559	−	0.983380i	$-0.558114\pi$
$967$	−890903.	−	324262.i	−0.952746	−	0.346771i	−0.771187	+	0.636609i	$0.780337\pi$
$968$		0			0
$969$	−2.03939e6	+	28635.1i	−2.17196	+	0.0304966i
$970$		0			0
$971$		−	41780.9i		−	0.0443138i	−0.999755	−	0.0221569i	$-0.992947\pi$
$971$		−	41780.9i		−	0.0443138i	0.999755	−	0.0221569i	$-0.00705335\pi$
$972$		0			0
$973$	566842.			0.598737
$974$		0			0
$975$	2228.22	+	158694.i	0.00234395	+	0.166936i
$976$		0			0
$977$	34917.5	−	95935.1i	0.0365809	−	0.100505i	−0.920058	−	0.391783i	$-0.871858\pi$
$977$	34917.5	−	95935.1i	0.0365809	−	0.100505i	0.956638	+	0.291278i	$0.0940805\pi$
$978$		0			0
$979$	−334645.	+	1.89787e6i	−0.349156	+	1.98016i
$980$		0			0
$981$	308661.	−	8669.52i	0.320733	−	0.00900860i
$982$		0			0
$983$	100237.	+	275399.i	0.103734	+	0.285007i	0.980691	−	0.195561i	$-0.0626528\pi$
$983$	100237.	+	275399.i	0.103734	+	0.285007i	−0.876958	+	0.480568i	$0.840431\pi$
$984$		0			0
$985$	−928890.	+	779432.i	−0.957397	+	0.803351i
$986$		0			0
$987$	223668.	+	77870.1i	0.229599	+	0.0799349i
$988$		0			0
$989$	−94258.0	+	54419.9i	−0.0963664	+	0.0556371i
$990$		0			0
$991$	498516.	−	863455.i	0.507612	−	0.879209i	−0.492349	−	0.870398i	$-0.663862\pi$
$991$	498516.	−	863455.i	0.507612	−	0.879209i	0.999961	−	0.00881174i	$-0.00280490\pi$
$992$		0			0
$993$	−584729.	−	94659.0i	−0.593002	−	0.0959983i
$994$		0			0
$995$	685531.	−	120878.i	0.692438	−	0.122096i
$996$		0			0
$997$	−978702.	−	821228.i	−0.984601	−	0.826178i	0.000176460	−	1.00000i	$-0.499944\pi$
$997$	−978702.	−	821228.i	−0.984601	−	0.826178i	−0.984777	+	0.173822i	$0.944388\pi$
$998$		0			0
$999$	915697.	−	581417.i	0.917531	−	0.582582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.k.a.65.7	yes	72
3.2	odd	2		324.5.k.a.197.9		72
27.5	odd	18	inner	108.5.k.a.5.7	✓	72
27.22	even	9		324.5.k.a.125.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.k.a.5.7	✓	72	27.5	odd	18	inner
108.5.k.a.65.7	yes	72	1.1	even	1	trivial
324.5.k.a.125.9		72	27.22	even	9
324.5.k.a.197.9		72	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.126357 - 8.99911i) q^{3} +(-6.31102 + 17.3394i) q^{5} +(2.68521 - 15.2286i) q^{7} +(-80.9681 + 2.27420i) q^{9} +O(q^{10})\)	\(q+(-0.126357 - 8.99911i) q^{3} +(-6.31102 + 17.3394i) q^{5} +(2.68521 - 15.2286i) q^{7} +(-80.9681 + 2.27420i) q^{9} +(-57.3804 - 157.651i) q^{11} +(-47.4796 + 39.8401i) q^{13} +(156.837 + 54.6026i) q^{15} +(-434.160 + 250.663i) q^{17} +(-226.022 + 391.482i) q^{19} +(-137.383 - 22.2403i) q^{21} +(-87.9439 + 15.5069i) q^{23} +(217.952 + 182.884i) q^{25} +(30.6966 + 728.353i) q^{27} +(-388.247 + 462.695i) q^{29} +(-253.555 - 1437.98i) q^{31} +(-1411.47 + 536.293i) q^{33} +(247.108 + 142.668i) q^{35} +(-743.956 - 1288.57i) q^{37} +(364.525 + 422.240i) q^{39} +(-1177.61 - 1403.43i) q^{41} +(1145.30 - 416.855i) q^{43} +(471.558 - 1418.29i) q^{45} +(-1675.90 - 295.507i) q^{47} +(2031.50 + 739.406i) q^{49} +(2310.60 + 3875.39i) q^{51} +448.959i q^{53} +3095.71 q^{55} +(3551.55 + 1984.53i) q^{57} +(519.236 - 1426.59i) q^{59} +(600.396 - 3405.01i) q^{61} +(-182.784 + 1239.14i) q^{63} +(-391.158 - 1074.70i) q^{65} +(130.770 - 109.729i) q^{67} +(150.660 + 789.458i) q^{69} +(-3379.60 + 1951.21i) q^{71} +(4207.66 - 7287.88i) q^{73} +(1618.25 - 1984.49i) q^{75} +(-2554.89 + 450.495i) q^{77} +(6492.89 + 5448.18i) q^{79} +(6550.66 - 368.274i) q^{81} +(-697.809 + 831.616i) q^{83} +(-1606.34 - 9110.01i) q^{85} +(4212.90 + 3435.42i) q^{87} +(-9947.94 - 5743.45i) q^{89} +(479.216 + 830.026i) q^{91} +(-12908.5 + 2463.47i) q^{93} +(-5361.62 - 6389.73i) q^{95} +(-1079.02 + 392.731i) q^{97} +(5004.51 + 12634.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{5} - 102 q^{9}+O(q^{10}) \) 72 * q + 9 * q^5 - 102 * q^9	\( 72 q + 9 q^{5} - 102 q^{9} + 18 q^{11} - 225 q^{15} - 282 q^{21} - 1278 q^{23} + 441 q^{25} + 54 q^{27} + 1854 q^{29} - 1665 q^{31} - 45 q^{33} - 2673 q^{35} + 6951 q^{39} - 5472 q^{41} + 1260 q^{43} + 5553 q^{45} + 5103 q^{47} - 5904 q^{49} + 1899 q^{51} + 1107 q^{57} - 10944 q^{59} + 8352 q^{61} - 11985 q^{63} + 8757 q^{65} + 378 q^{67} + 5607 q^{69} - 19764 q^{71} + 6111 q^{73} - 3453 q^{75} - 5679 q^{77} - 5652 q^{79} - 20466 q^{81} - 20061 q^{83} + 26100 q^{85} + 40545 q^{87} + 15633 q^{89} - 6039 q^{91} + 40179 q^{93} + 48024 q^{95} - 37530 q^{97} + 12177 q^{99}+O(q^{100}) \) 72 * q + 9 * q^5 - 102 * q^9 + 18 * q^11 - 225 * q^15 - 282 * q^21 - 1278 * q^23 + 441 * q^25 + 54 * q^27 + 1854 * q^29 - 1665 * q^31 - 45 * q^33 - 2673 * q^35 + 6951 * q^39 - 5472 * q^41 + 1260 * q^43 + 5553 * q^45 + 5103 * q^47 - 5904 * q^49 + 1899 * q^51 + 1107 * q^57 - 10944 * q^59 + 8352 * q^61 - 11985 * q^63 + 8757 * q^65 + 378 * q^67 + 5607 * q^69 - 19764 * q^71 + 6111 * q^73 - 3453 * q^75 - 5679 * q^77 - 5652 * q^79 - 20466 * q^81 - 20061 * q^83 + 26100 * q^85 + 40545 * q^87 + 15633 * q^89 - 6039 * q^91 + 40179 * q^93 + 48024 * q^95 - 37530 * q^97 + 12177 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more