LMFDB - Embedded newform 108.4.i.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	108.13
Dual form			108.4.i.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +O(q^{10})$	\(q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +(-39.5319 + 33.1712i) q^{11} +(-10.2025 + 57.8615i) q^{13} +(31.1578 + 96.4258i) q^{15} +(-3.52013 + 6.09704i) q^{17} +(-42.6669 - 73.9012i) q^{19} +(-79.9157 - 102.630i) q^{21} +(32.2883 - 11.7520i) q^{23} +(44.3365 + 251.445i) q^{25} +(15.3437 - 139.455i) q^{27} +(37.0590 + 210.172i) q^{29} +(-133.967 + 48.7600i) q^{31} +(265.599 - 36.8883i) q^{33} +(-244.095 - 422.784i) q^{35} +(-65.2996 + 113.102i) q^{37} +(204.650 - 226.547i) q^{39} +(-8.52460 + 48.3454i) q^{41} +(126.716 - 106.327i) q^{43} +(129.041 - 510.494i) q^{45} +(-470.489 - 171.244i) q^{47} +(217.287 + 182.325i) q^{49} +(32.3280 - 17.1219i) q^{51} -347.277 q^{53} +1006.40 q^{55} +(-16.1935 + 443.112i) q^{57} +(-172.501 - 144.746i) q^{59} +(-577.795 - 210.300i) q^{61} +(68.4686 + 672.412i) q^{63} +(877.746 - 736.517i) q^{65} +(-162.166 + 919.690i) q^{67} +(-174.580 - 37.4043i) q^{69} +(46.7209 - 80.9229i) q^{71} +(-133.977 - 232.055i) q^{73} +(498.985 - 1229.29i) q^{75} +(-1213.92 + 441.832i) q^{77} +(-155.815 - 883.669i) q^{79} +(-452.535 + 571.536i) q^{81} +(6.17283 + 35.0079i) q^{83} +(129.018 - 46.9588i) q^{85} +(417.081 - 1027.51i) q^{87} +(361.721 + 626.519i) q^{89} +(-735.394 + 1273.74i) q^{91} +(724.350 + 155.194i) q^{93} +(-288.980 + 1638.89i) q^{95} +(-1214.37 + 1018.98i) q^{97} +(-1271.04 - 570.850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	−4.40211	−	2.76069i	−0.847187	−	0.531294i
$3$	−4.40211	−	2.76069i	−0.847187	−	0.531294i
$4$		0			0
$5$	−14.9393	−	12.5356i	−1.33621	−	1.12122i	−0.982582	−	0.185831i	$-0.940502\pi$
$5$	−14.9393	−	12.5356i	−1.33621	−	1.12122i	−0.353631	−	0.935385i	$-0.615053\pi$
$6$		0			0
$7$	23.5233	+	8.56177i	1.27014	+	0.462292i	0.887158	−	0.461465i	$-0.152676\pi$
$7$	23.5233	+	8.56177i	1.27014	+	0.462292i	0.382978	+	0.923757i	$0.374898\pi$
$8$		0			0
$9$	11.7572	+	24.3057i	0.435453	+	0.900211i
$10$		0			0
$11$	−39.5319	+	33.1712i	−1.08358	+	0.909227i	−0.996213	−	0.0869492i	$-0.972288\pi$
$11$	−39.5319	+	33.1712i	−1.08358	+	0.909227i	−0.0873623	+	0.996177i	$0.527844\pi$
$12$		0			0
$13$	−10.2025	+	57.8615i	−0.217668	+	1.23445i	0.658550	+	0.752537i	$0.271170\pi$
$13$	−10.2025	+	57.8615i	−0.217668	+	1.23445i	−0.876217	+	0.481917i	$0.839941\pi$
$14$		0			0
$15$	31.1578	+	96.4258i	0.536327	+	1.65980i
$16$		0			0
$17$	−3.52013	+	6.09704i	−0.0502210	+	0.0869853i	−0.890043	−	0.455876i	$-0.849326\pi$
$17$	−3.52013	+	6.09704i	−0.0502210	+	0.0869853i	0.839822	+	0.542862i	$0.182659\pi$
$18$		0			0
$19$	−42.6669	−	73.9012i	−0.515182	−	0.892321i	−0.999845	−	0.0176203i	$-0.994391\pi$
$19$	−42.6669	−	73.9012i	−0.515182	−	0.892321i	0.484663	−	0.874701i	$-0.338942\pi$
$20$		0			0
$21$	−79.9157	−	102.630i	−0.830431	−	1.06646i
$22$		0			0
$23$	32.2883	−	11.7520i	0.292721	−	0.106542i	−0.191486	−	0.981495i	$-0.561331\pi$
$23$	32.2883	−	11.7520i	0.292721	−	0.106542i	0.484206	+	0.874954i	$0.339108\pi$
$24$		0			0
$25$	44.3365	+	251.445i	0.354692	+	2.01156i
$26$		0			0
$27$	15.3437	−	139.455i	0.109367	−	0.994001i
$28$		0			0
$29$	37.0590	+	210.172i	0.237300	+	1.34579i	0.837717	+	0.546105i	$0.183890\pi$
$29$	37.0590	+	210.172i	0.237300	+	1.34579i	−0.600417	+	0.799687i	$0.704999\pi$
$30$		0			0
$31$	−133.967	+	48.7600i	−0.776168	+	0.282502i	−0.699574	−	0.714560i	$-0.746627\pi$
$31$	−133.967	+	48.7600i	−0.776168	+	0.282502i	−0.0765940	+	0.997062i	$0.524405\pi$
$32$		0			0
$33$	265.599	−	36.8883i	1.40106	−	0.194589i
$34$		0			0
$35$	−244.095	−	422.784i	−1.17884	−	2.04182i
$36$		0			0
$37$	−65.2996	+	113.102i	−0.290140	+	0.502538i	−0.973843	−	0.227223i	$-0.927035\pi$
$37$	−65.2996	+	113.102i	−0.290140	+	0.502538i	0.683702	+	0.729761i	$0.260369\pi$
$38$		0			0
$39$	204.650	−	226.547i	0.840263	−	0.930168i
$40$		0			0
$41$	−8.52460	+	48.3454i	−0.0324712	+	0.184153i	−0.996729	−	0.0808109i	$-0.974249\pi$
$41$	−8.52460	+	48.3454i	−0.0324712	+	0.184153i	0.964258	+	0.264964i	$0.0853601\pi$
$42$		0			0
$43$	126.716	−	106.327i	0.449394	−	0.377086i	−0.389817	−	0.920892i	$-0.627462\pi$
$43$	126.716	−	106.327i	0.449394	−	0.377086i	0.839211	+	0.543806i	$0.183017\pi$
$44$		0			0
$45$	129.041	−	510.494i	0.427473	−	1.69111i
$46$		0			0
$47$	−470.489	−	171.244i	−1.46017	−	0.531458i	−0.514757	−	0.857336i	$-0.672118\pi$
$47$	−470.489	−	171.244i	−1.46017	−	0.531458i	−0.945412	+	0.325878i	$0.894340\pi$
$48$		0			0
$49$	217.287	+	182.325i	0.633489	+	0.531560i
$50$		0			0
$51$	32.3280	−	17.1219i	0.0887613	−	0.0470107i
$52$		0			0
$53$	−347.277			−0.900042			−0.450021	−	0.893018i	$-0.648584\pi$
$53$	−347.277			−0.900042			−0.450021	+	0.893018i	$0.648584\pi$
$54$		0			0
$55$	1006.40			2.46733
$56$		0			0
$57$	−16.1935	+	443.112i	−0.0376295	+	1.02968i
$58$		0			0
$59$	−172.501	−	144.746i	−0.380640	−	0.319395i	0.432314	−	0.901723i	$-0.357697\pi$
$59$	−172.501	−	144.746i	−0.380640	−	0.319395i	−0.812954	+	0.582329i	$0.802142\pi$
$60$		0			0
$61$	−577.795	−	210.300i	−1.21277	−	0.441413i	−0.345107	−	0.938563i	$-0.612158\pi$
$61$	−577.795	−	210.300i	−1.21277	−	0.441413i	−0.867664	+	0.497150i	$0.834380\pi$
$62$		0			0
$63$	68.4686	+	672.412i	0.136924	+	1.34470i
$64$		0			0
$65$	877.746	−	736.517i	1.67494	−	1.40544i
$66$		0			0
$67$	−162.166	+	919.690i	−0.295698	+	1.67698i	0.368656	+	0.929566i	$0.379818\pi$
$67$	−162.166	+	919.690i	−0.295698	+	1.67698i	−0.664353	+	0.747419i	$0.731293\pi$
$68$		0			0
$69$	−174.580	−	37.4043i	−0.304594	−	0.0652601i
$70$		0			0
$71$	46.7209	−	80.9229i	0.0780950	−	0.135265i	−0.824333	−	0.566105i	$-0.808450\pi$
$71$	46.7209	−	80.9229i	0.0780950	−	0.135265i	0.902428	+	0.430841i	$0.141783\pi$
$72$		0			0
$73$	−133.977	−	232.055i	−0.214806	−	0.372055i	0.738406	−	0.674356i	$-0.235579\pi$
$73$	−133.977	−	232.055i	−0.214806	−	0.372055i	−0.953213	+	0.302301i	$0.902245\pi$
$74$		0			0
$75$	498.985	−	1229.29i	0.768238	−	1.89261i
$76$		0			0
$77$	−1213.92	+	441.832i	−1.79662	+	0.653915i
$78$		0			0
$79$	−155.815	−	883.669i	−0.221905	−	1.25849i	−0.868514	−	0.495665i	$-0.834924\pi$
$79$	−155.815	−	883.669i	−0.221905	−	1.25849i	0.646608	−	0.762822i	$-0.276187\pi$
$80$		0			0
$81$	−452.535	+	571.536i	−0.620761	+	0.784000i
$82$		0			0
$83$	6.17283	+	35.0079i	0.00816333	+	0.0462966i	0.988617	−	0.150452i	$-0.0480729\pi$
$83$	6.17283	+	35.0079i	0.00816333	+	0.0462966i	−0.980454	+	0.196748i	$0.936962\pi$
$84$		0			0
$85$	129.018	−	46.9588i	0.164635	−	0.0599223i
$86$		0			0
$87$	417.081	−	1027.51i	0.513975	−	1.26621i
$88$		0			0
$89$	361.721	+	626.519i	0.430813	+	0.746189i	0.996943	−	0.0781261i	$-0.0248937\pi$
$89$	361.721	+	626.519i	0.430813	+	0.746189i	−0.566131	+	0.824315i	$0.691560\pi$
$90$		0			0
$91$	−735.394	+	1273.74i	−0.847146	+	1.46730i
$92$		0			0
$93$	724.350	+	155.194i	0.807651	+	0.173041i
$94$		0			0
$95$	−288.980	+	1638.89i	−0.312092	+	1.76996i
$96$		0			0
$97$	−1214.37	+	1018.98i	−1.27114	+	1.06662i	−0.276744	+	0.960944i	$0.589255\pi$
$97$	−1214.37	+	1018.98i	−1.27114	+	1.06662i	−0.994401	+	0.105673i	$0.966300\pi$
$98$		0			0
$99$	−1271.04	−	570.850i	−1.29034	−	0.579521i
$100$		0			0
$101$	1643.15	+	598.056i	1.61880	+	0.589196i	0.983153	−	0.182782i	$-0.0585103\pi$
$101$	1643.15	+	598.056i	1.61880	+	0.589196i	0.635649	+	0.771978i	$0.280732\pi$
$102$		0			0
$103$	717.798	+	602.304i	0.686667	+	0.576182i	0.917946	−	0.396705i	$-0.129846\pi$
$103$	717.798	+	602.304i	0.686667	+	0.576182i	−0.231279	+	0.972888i	$0.574291\pi$
$104$		0			0
$105$	−92.6420	+	2535.01i	−0.0861041	+	2.35611i
$106$		0			0
$107$	−16.1019			−0.0145480			−0.00727398	−	0.999974i	$-0.502315\pi$
$107$	−16.1019			−0.0145480			−0.00727398	+	0.999974i	$0.502315\pi$
$108$		0			0
$109$	1665.12			1.46321			0.731603	−	0.681731i	$-0.238772\pi$
$109$	1665.12			1.46321			0.731603	+	0.681731i	$0.238772\pi$
$110$		0			0
$111$	599.696	−	317.617i	0.512799	−	0.271594i
$112$		0			0
$113$	−632.247	−	530.518i	−0.526343	−	0.441654i	0.340493	−	0.940247i	$-0.389406\pi$
$113$	−632.247	−	530.518i	−0.526343	−	0.441654i	−0.866836	+	0.498593i	$0.833850\pi$
$114$		0			0
$115$	−629.683	−	229.186i	−0.510593	−	0.185841i
$116$		0			0
$117$	−1526.32	+	432.311i	−1.20605	+	0.341600i
$118$		0			0
$119$	−135.006	+	113.284i	−0.104000	+	0.0872664i
$120$		0			0
$121$	231.317	−	1311.87i	0.173792	−	0.985625i
$122$		0			0
$123$	170.993	−	189.288i	0.125349	−	0.138761i
$124$		0			0
$125$	1270.78	−	2201.05i	0.909295	−	1.57495i
$126$		0			0
$127$	−1130.88	−	1958.74i	−0.790151	−	1.36858i	−0.925873	−	0.377835i	$-0.876669\pi$
$127$	−1130.88	−	1958.74i	−0.790151	−	1.36858i	0.135722	−	0.990747i	$-0.456665\pi$
$128$		0			0
$129$	−851.352	+	118.242i	−0.581065	+	0.0807024i
$130$		0			0
$131$	1343.42	−	488.966i	0.895996	−	0.326116i	0.147349	−	0.989085i	$-0.452926\pi$
$131$	1343.42	−	488.966i	0.895996	−	0.326116i	0.748647	+	0.662969i	$0.230704\pi$
$132$		0			0
$133$	−370.939	−	2103.70i	−0.241839	−	1.37153i
$134$		0			0
$135$	−1977.37	+	1891.01i	−1.26063	+	1.20557i
$136$		0			0
$137$	260.376	+	1476.67i	0.162375	+	0.920877i	0.951729	+	0.306938i	$0.0993046\pi$
$137$	260.376	+	1476.67i	0.162375	+	0.920877i	−0.789354	+	0.613938i	$0.789584\pi$
$138$		0			0
$139$	−54.1508	+	19.7093i	−0.0330433	+	0.0120268i	−0.358489	−	0.933534i	$-0.616708\pi$
$139$	−54.1508	+	19.7093i	−0.0330433	+	0.0120268i	0.325446	+	0.945561i	$0.394486\pi$
$140$		0			0
$141$	1598.40	+	2052.71i	0.954676	+	1.22602i
$142$		0			0
$143$	−1516.01	−	2625.81i	−0.886540	−	1.53553i
$144$		0			0
$145$	2080.99	−	3604.38i	1.19184	−	2.06433i
$146$		0			0
$147$	−453.178	−	1402.48i	−0.254269	−	0.786900i
$148$		0			0
$149$	−236.688	+	1342.32i	−0.130136	+	0.738037i	0.847988	+	0.530015i	$0.177814\pi$
$149$	−236.688	+	1342.32i	−0.130136	+	0.738037i	−0.978124	+	0.208022i	$0.933297\pi$
$150$		0			0
$151$	897.782	−	753.329i	0.483844	−	0.405993i	−0.367970	−	0.929838i	$-0.619947\pi$
$151$	897.782	−	753.329i	0.483844	−	0.405993i	0.851814	+	0.523844i	$0.175503\pi$
$152$		0			0
$153$	−189.580	−	13.8749i	−0.100174	−	0.00733150i
$154$		0			0
$155$	2612.61	+	950.913i	1.35387	+	0.492769i
$156$		0			0
$157$	−977.108	−	819.891i	−0.496699	−	0.416780i	0.359721	−	0.933060i	$-0.382872\pi$
$157$	−977.108	−	819.891i	−0.496699	−	0.416780i	−0.856420	+	0.516280i	$0.827316\pi$
$158$		0			0
$159$	1528.76	+	958.724i	0.762504	+	0.478187i
$160$		0			0
$161$	860.144			0.421049
$162$		0			0
$163$	1616.42			0.776736			0.388368	−	0.921504i	$-0.373039\pi$
$163$	1616.42			0.776736			0.388368	+	0.921504i	$0.373039\pi$
$164$		0			0
$165$	−4430.29	−	2778.35i	−2.09029	−	1.31088i
$166$		0			0
$167$	424.273	+	356.007i	0.196594	+	0.164962i	0.735771	−	0.677231i	$-0.236820\pi$
$167$	424.273	+	356.007i	0.196594	+	0.164962i	−0.539177	+	0.842193i	$0.681264\pi$
$168$		0			0
$169$	−1179.36	−	429.252i	−0.536805	−	0.195381i
$170$		0			0
$171$	1294.58	−	1905.92i	0.578940	−	0.852337i
$172$		0			0
$173$	539.141	−	452.393i	0.236937	−	0.198814i	−0.516586	−	0.856235i	$-0.672797\pi$
$173$	539.141	−	452.393i	0.236937	−	0.198814i	0.753523	+	0.657421i	$0.228353\pi$
$174$		0			0
$175$	−1109.87	+	6294.40i	−0.479420	+	2.71892i
$176$		0			0
$177$	359.773	+	1113.41i	0.152781	+	0.472819i
$178$		0			0
$179$	−585.812	+	1014.66i	−0.244612	+	0.423681i	−0.962023	−	0.272970i	$-0.911994\pi$
$179$	−585.812	+	1014.66i	−0.244612	+	0.423681i	0.717410	+	0.696651i	$0.245327\pi$
$180$		0			0
$181$	−386.512	−	669.458i	−0.158725	−	0.274919i	0.775684	−	0.631121i	$-0.217405\pi$
$181$	−386.512	−	669.458i	−0.158725	−	0.274919i	−0.934409	+	0.356202i	$0.884072\pi$
$182$		0			0
$183$	1962.95	+	2520.88i	0.792925	+	1.01830i
$184$		0			0
$185$	2393.33	−	871.102i	0.951143	−	0.346188i
$186$		0			0
$187$	−63.0889	−	357.795i	−0.0246712	−	0.139917i
$188$		0			0
$189$	1554.91	−	3149.06i	0.598430	−	1.21196i
$190$		0			0
$191$	−98.8386	−	560.541i	−0.0374435	−	0.212353i	0.960346	−	0.278812i	$-0.0899407\pi$
$191$	−98.8386	−	560.541i	−0.0374435	−	0.212353i	−0.997789	+	0.0664597i	$0.978830\pi$
$192$		0			0
$193$	−4565.75	+	1661.80i	−1.70285	+	0.619787i	−0.996145	−	0.0877221i	$-0.972041\pi$
$193$	−4565.75	+	1661.80i	−1.70285	+	0.619787i	−0.706705	+	0.707509i	$0.749819\pi$
$194$		0			0
$195$	−5897.23	+	819.049i	−2.16569	+	0.300786i
$196$		0			0
$197$	−946.267	−	1638.98i	−0.342227	−	0.592754i	0.642619	−	0.766186i	$-0.277848\pi$
$197$	−946.267	−	1638.98i	−0.342227	−	0.592754i	−0.984846	+	0.173431i	$0.944514\pi$
$198$		0			0
$199$	1950.36	−	3378.12i	0.694759	−	1.20336i	−0.275502	−	0.961300i	$-0.588844\pi$
$199$	1950.36	−	3378.12i	0.694759	−	1.20336i	0.970262	−	0.242058i	$-0.0778225\pi$
$200$		0			0
$201$	3252.85	−	3600.89i	1.14148	−	1.26362i
$202$		0			0
$203$	−927.696	+	5261.22i	−0.320746	+	1.81904i
$204$		0			0
$205$	733.389	−	615.386i	0.249864	−	0.209661i
$206$		0			0
$207$	665.261	+	646.619i	0.223376	+	0.217117i
$208$		0			0
$209$	4138.10	+	1506.15i	1.36956	+	0.498480i
$210$		0			0
$211$	1142.91	+	959.011i	0.372895	+	0.312896i	0.809906	−	0.586560i	$-0.199518\pi$
$211$	1142.91	+	959.011i	0.372895	+	0.312896i	−0.437011	+	0.899456i	$0.643963\pi$
$212$		0			0
$213$	−429.073	+	227.250i	−0.138026	+	0.0731030i
$214$		0			0
$215$	−3225.91			−1.02328
$216$		0			0
$217$	−3568.81			−1.11644
$218$		0			0
$219$	−50.8488	+	1391.40i	−0.0156897	+	0.429326i
$220$		0			0
$221$	−316.870	−	265.885i	−0.0964478	−	0.0809293i
$222$		0			0
$223$	−1925.56	−	700.848i	−0.578230	−	0.210459i	0.0363147	−	0.999340i	$-0.488438\pi$
$223$	−1925.56	−	700.848i	−0.578230	−	0.210459i	−0.614545	+	0.788882i	$0.710660\pi$
$224$		0			0
$225$	−5590.27	+	4033.92i	−1.65638	+	1.19524i
$226$		0			0
$227$	−1243.19	+	1043.16i	−0.363496	+	0.305009i	−0.806182	−	0.591667i	$-0.798470\pi$
$227$	−1243.19	+	1043.16i	−0.363496	+	0.305009i	0.442686	+	0.896677i	$0.354026\pi$
$228$		0			0
$229$	651.857	−	3696.86i	0.188104	−	1.06679i	−0.733797	−	0.679369i	$-0.762254\pi$
$229$	651.857	−	3696.86i	0.188104	−	1.06679i	0.921901	−	0.387425i	$-0.126635\pi$
$230$		0			0
$231$	6563.59	+	1406.27i	1.86949	+	0.400544i
$232$		0			0
$233$	−48.1965	+	83.4788i	−0.0135513	+	0.0234716i	−0.872722	−	0.488218i	$-0.837647\pi$
$233$	−48.1965	+	83.4788i	−0.0135513	+	0.0234716i	0.859170	+	0.511690i	$0.170980\pi$
$234$		0			0
$235$	4882.15	+	8456.12i	1.35522	+	2.34731i
$236$		0			0
$237$	−1753.62	+	4320.17i	−0.480632	+	1.18407i
$238$		0			0
$239$	−4215.25	+	1534.22i	−1.14084	+	0.415233i	−0.842218	−	0.539137i	$-0.818751\pi$
$239$	−4215.25	+	1534.22i	−1.14084	+	0.415233i	−0.298626	+	0.954370i	$0.596528\pi$
$240$		0			0
$241$	420.948	+	2387.32i	0.112513	+	0.638093i	0.987952	+	0.154764i	$0.0494616\pi$
$241$	420.948	+	2387.32i	0.112513	+	0.638093i	−0.875438	+	0.483330i	$0.839427\pi$
$242$		0			0
$243$	3569.94	−	1266.66i	0.942436	−	0.334388i
$244$		0			0
$245$	−960.563	−	5447.62i	−0.250482	−	1.42055i
$246$		0			0
$247$	4711.35	−	1714.79i	1.21367	−	0.441739i
$248$		0			0
$249$	69.4722	−	171.150i	0.0176812	−	0.0435590i
$250$		0			0
$251$	−1200.00	−	2078.47i	−0.301767	−	0.522677i	0.674769	−	0.738029i	$-0.264243\pi$
$251$	−1200.00	−	2078.47i	−0.301767	−	0.522677i	−0.976536	+	0.215352i	$0.930910\pi$
$252$		0			0
$253$	−886.591	+	1535.62i	−0.220314	+	0.381595i
$254$		0			0
$255$	−697.591	−	149.461i	−0.171313	−	0.0367043i
$256$		0			0
$257$	−65.0046	+	368.659i	−0.0157777	+	0.0894799i	−0.991680	−	0.128729i	$-0.958910\pi$
$257$	−65.0046	+	368.659i	−0.0157777	+	0.0894799i	0.975902	+	0.218209i	$0.0700214\pi$
$258$		0			0
$259$	−2504.42	+	2101.45i	−0.600837	+	0.504162i
$260$		0			0
$261$	−4672.67	+	3371.79i	−1.10816	+	0.799649i
$262$		0			0
$263$	−3775.09	−	1374.02i	−0.885102	−	0.322151i	−0.140835	−	0.990033i	$-0.544979\pi$
$263$	−3775.09	−	1374.02i	−0.885102	−	0.322151i	−0.744267	+	0.667882i	$0.767201\pi$
$264$		0			0
$265$	5188.09	+	4353.32i	1.20265	+	1.00914i
$266$		0			0
$267$	137.285	−	3756.60i	0.0314670	−	0.861050i
$268$		0			0
$269$	3102.46			0.703198			0.351599	−	0.936151i	$-0.385638\pi$
$269$	3102.46			0.703198			0.351599	+	0.936151i	$0.385638\pi$
$270$		0			0
$271$	−146.797			−0.0329050			−0.0164525	−	0.999865i	$-0.505237\pi$
$271$	−146.797			−0.0329050			−0.0164525	+	0.999865i	$0.505237\pi$
$272$		0			0
$273$	6753.69	−	3576.96i	1.49726	−	0.792994i
$274$		0			0
$275$	−10093.4	−	8469.40i	−2.21330	−	1.85718i
$276$		0			0
$277$	−4020.61	−	1463.38i	−0.872111	−	0.317423i	−0.133090	−	0.991104i	$-0.542490\pi$
$277$	−4020.61	−	1463.38i	−0.872111	−	0.317423i	−0.739022	+	0.673681i	$0.764712\pi$
$278$		0			0
$279$	−2760.23	−	2682.88i	−0.592296	−	0.575699i
$280$		0			0
$281$	−3809.81	+	3196.81i	−0.808805	+	0.678668i	−0.950322	−	0.311268i	$-0.899246\pi$
$281$	−3809.81	+	3196.81i	−0.808805	+	0.678668i	0.141517	+	0.989936i	$0.454802\pi$
$282$		0			0
$283$	−185.085	+	1049.67i	−0.0388770	+	0.220482i	−0.998056	−	0.0623156i	$-0.980151\pi$
$283$	−185.085	+	1049.67i	−0.0388770	+	0.220482i	0.959180	+	0.282798i	$0.0912626\pi$
$284$		0			0
$285$	5796.58	−	6416.79i	1.20477	−	1.33368i
$286$		0			0
$287$	−614.448	+	1064.26i	−0.126375	+	0.218889i
$288$		0			0
$289$	2431.72	+	4211.86i	0.494956	+	0.857288i
$290$		0			0
$291$	8158.90	−	1133.17i	1.64358	−	0.228273i
$292$		0			0
$293$	6323.47	−	2301.56i	1.26082	−	0.458902i	0.376778	−	0.926304i	$-0.377032\pi$
$293$	6323.47	−	2301.56i	1.26082	−	0.458902i	0.884045	+	0.467402i	$0.154810\pi$
$294$		0			0
$295$	762.579	+	4324.80i	0.150505	+	0.853559i
$296$		0			0
$297$	4019.31	+	6021.88i	0.785266	+	1.17651i
$298$		0			0
$299$	350.565	+	1988.15i	0.0678049	+	0.384541i
$300$		0			0
$301$	3891.11	−	1416.25i	0.745116	−	0.271200i
$302$		0			0
$303$	−5582.27	−	7168.92i	−1.05839	−	1.35922i
$304$		0			0
$305$	5995.63	+	10384.7i	1.12560	+	1.94960i
$306$		0			0
$307$	−419.639	+	726.835i	−0.0780132	+	0.135123i	−0.902393	−	0.430915i	$-0.858191\pi$
$307$	−419.639	+	726.835i	−0.0780132	+	0.135123i	0.824379	+	0.566038i	$0.191524\pi$
$308$		0			0
$309$	−1497.06	−	4633.03i	−0.275614	−	0.852957i
$310$		0			0
$311$	−782.999	+	4440.61i	−0.142765	+	0.809658i	0.826370	+	0.563127i	$0.190402\pi$
$311$	−782.999	+	4440.61i	−0.142765	+	0.809658i	−0.969135	+	0.246531i	$0.920709\pi$
$312$		0			0
$313$	3326.13	−	2790.96i	0.600652	−	0.504007i	−0.291003	−	0.956722i	$-0.593989\pi$
$313$	3326.13	−	2790.96i	0.600652	−	0.504007i	0.891655	+	0.452715i	$0.149545\pi$
$314$		0			0
$315$	7406.20	−	10903.7i	1.32474	−	1.95032i
$316$		0			0
$317$	−8805.07	−	3204.78i	−1.56007	−	0.567819i	−0.589317	−	0.807902i	$-0.700603\pi$
$317$	−8805.07	−	3204.78i	−1.56007	−	0.567819i	−0.970752	+	0.240083i	$0.922825\pi$
$318$		0			0
$319$	−8436.68	−	7079.22i	−1.48076	−	1.24251i
$320$		0			0
$321$	70.8825	+	44.4524i	0.0123249	+	0.00772925i
$322$		0			0
$323$	600.772			0.103492
$324$		0			0
$325$	−15001.3			−2.56038
$326$		0			0
$327$	−7330.05	−	4596.87i	−1.23961	−	0.777393i
$328$		0			0
$329$	−9601.29	−	8056.44i	−1.60893	−	1.35005i
$330$		0			0
$331$	7052.64	+	2566.95i	1.17114	+	0.426261i	0.853066	−	0.521804i	$-0.174741\pi$
$331$	7052.64	+	2566.95i	1.17114	+	0.426261i	0.318077	+	0.948065i	$0.396963\pi$
$332$		0			0
$333$	−3516.77	−	257.384i	−0.578733	−	0.0423561i
$334$		0			0
$335$	13951.5	−	11706.7i	2.27538	−	1.90927i
$336$		0			0
$337$	595.457	−	3377.01i	0.0962511	−	0.545867i	−0.898106	−	0.439780i	$-0.855057\pi$
$337$	595.457	−	3377.01i	0.0962511	−	0.545867i	0.994357	−	0.106087i	$-0.0338323\pi$
$338$		0			0
$339$	1318.63	+	4080.84i	0.211263	+	0.653807i
$340$		0			0
$341$	3678.55	−	6371.43i	0.584178	−	1.01183i
$342$		0			0
$343$	−742.883	−	1286.71i	−0.116944	−	0.202553i
$344$		0			0
$345$	2139.23	+	2747.26i	0.333832	+	0.428717i
$346$		0			0
$347$	10147.3	−	3693.32i	1.56984	−	0.571377i	0.596880	−	0.802331i	$-0.296407\pi$
$347$	10147.3	−	3693.32i	1.56984	−	0.571377i	0.972965	+	0.230954i	$0.0741848\pi$
$348$		0			0
$349$	−221.987	−	1258.95i	−0.0340479	−	0.193095i	0.963040	−	0.269359i	$-0.0868119\pi$
$349$	−221.987	−	1258.95i	−0.0340479	−	0.193095i	−0.997088	+	0.0762641i	$0.975701\pi$
$350$		0			0
$351$	7912.51	+	2310.60i	1.20324	+	0.351370i
$352$		0			0
$353$	1599.06	+	9068.74i	0.241104	+	1.36737i	0.829370	+	0.558700i	$0.188699\pi$
$353$	1599.06	+	9068.74i	0.241104	+	1.36737i	−0.588267	+	0.808667i	$0.700189\pi$
$354$		0			0
$355$	−1712.39	+	623.260i	−0.256012	+	0.0931809i
$356$		0			0
$357$	907.054	−	125.978i	0.134472	−	0.0186764i
$358$		0			0
$359$	−331.332	−	573.884i	−0.0487104	−	0.0843689i	0.840642	−	0.541591i	$-0.182178\pi$
$359$	−331.332	−	573.884i	−0.0487104	−	0.0843689i	−0.889353	+	0.457222i	$0.848844\pi$
$360$		0			0
$361$	−211.429	+	366.206i	−0.0308250	+	0.0533905i
$362$		0			0
$363$	−4639.94	+	5136.39i	−0.670891	+	0.742674i
$364$		0			0
$365$	−907.419	+	5146.23i	−0.130127	+	0.737989i
$366$		0			0
$367$	−4961.59	+	4163.27i	−0.705702	+	0.592155i	−0.923390	−	0.383864i	$-0.874593\pi$
$367$	−4961.59	+	4163.27i	−0.705702	+	0.592155i	0.217687	+	0.976019i	$0.430149\pi$
$368$		0			0
$369$	−1275.29	+	361.211i	−0.179916	+	0.0509591i
$370$		0			0
$371$	−8169.10	−	2973.31i	−1.14318	−	0.416082i
$372$		0			0
$373$	5459.75	+	4581.27i	0.757896	+	0.635950i	0.937578	−	0.347775i	$-0.113063\pi$
$373$	5459.75	+	4581.27i	0.757896	+	0.635950i	−0.179682	+	0.983725i	$0.557507\pi$
$374$		0			0
$375$	−11670.5	+	6181.07i	−1.60710	+	0.851170i
$376$		0			0
$377$	−12539.0			−1.71297
$378$		0			0
$379$	7451.59			1.00993			0.504964	−	0.863140i	$-0.331506\pi$
$379$	7451.59			1.00993			0.504964	+	0.863140i	$0.331506\pi$
$380$		0			0
$381$	−429.205	+	11744.6i	−0.0577135	+	1.57925i
$382$		0			0
$383$	10198.1	+	8557.21i	1.36057	+	1.14165i	0.975806	+	0.218637i	$0.0701610\pi$
$383$	10198.1	+	8557.21i	1.36057	+	1.14165i	0.384762	+	0.923016i	$0.374283\pi$
$384$		0			0
$385$	23673.8	+	8616.56i	3.13384	+	1.14063i
$386$		0			0
$387$	4074.18	+	1829.80i	0.535148	+	0.240346i
$388$		0			0
$389$	−10703.4	+	8981.22i	−1.39508	+	1.17061i	−0.431839	+	0.901951i	$0.642135\pi$
$389$	−10703.4	+	8981.22i	−1.39508	+	1.17061i	−0.963236	+	0.268656i	$0.913420\pi$
$390$		0			0
$391$	−42.0066	+	238.232i	−0.00543316	+	0.0308130i
$392$		0			0
$393$	−7263.79	−	1556.29i	−0.932340	−	0.199756i
$394$		0			0
$395$	−8749.53	+	15154.6i	−1.11452	+	1.93041i
$396$		0			0
$397$	−4359.70	−	7551.22i	−0.551151	−	0.954622i	−0.998192	−	0.0601082i	$-0.980855\pi$
$397$	−4359.70	−	7551.22i	−0.551151	−	0.954622i	0.447041	−	0.894514i	$-0.352478\pi$
$398$		0			0
$399$	−4174.74	+	10284.8i	−0.523806	+	1.29043i
$400$		0			0
$401$	12751.4	−	4641.12i	1.58796	−	0.577971i	0.611046	−	0.791595i	$-0.290749\pi$
$401$	12751.4	−	4641.12i	1.58796	−	0.577971i	0.976916	+	0.213624i	$0.0685267\pi$
$402$		0			0
$403$	−1454.52	−	8249.02i	−0.179789	−	1.01963i
$404$		0			0
$405$	13925.1	−	2865.56i	1.70850	−	0.351583i
$406$		0			0
$407$	−1170.32	−	6637.22i	−0.142532	−	0.808341i
$408$		0			0
$409$	−8465.11	+	3081.05i	−1.02341	+	0.372489i	−0.798566	−	0.601907i	$-0.794408\pi$
$409$	−8465.11	+	3081.05i	−1.02341	+	0.372489i	−0.224839	+	0.974396i	$0.572186\pi$
$410$		0			0
$411$	2930.41	−	7219.27i	0.351694	−	0.866424i
$412$		0			0
$413$	−2818.51	−	4881.81i	−0.335811	−	0.581642i
$414$		0			0
$415$	346.626	−	600.374i	0.0410005	−	0.0710149i
$416$		0			0
$417$	292.789	+	62.7309i	0.0343836	+	0.00736677i
$418$		0			0
$419$	769.338	−	4363.13i	0.0897008	−	0.508718i	−0.906542	−	0.422115i	$-0.861288\pi$
$419$	769.338	−	4363.13i	0.0897008	−	0.508718i	0.996243	−	0.0866031i	$-0.0276012\pi$
$420$		0			0
$421$	−472.103	+	396.141i	−0.0546529	+	0.0458592i	−0.669705	−	0.742627i	$-0.733579\pi$
$421$	−472.103	+	396.141i	−0.0546529	+	0.0458592i	0.615052	+	0.788487i	$0.289135\pi$
$422$		0			0
$423$	−1369.44	−	13448.9i	−0.157410	−	1.54589i
$424$		0			0
$425$	−1689.14	−	614.796i	−0.192789	−	0.0701694i
$426$		0			0
$427$	−11791.1	−	9893.89i	−1.33632	−	1.12131i
$428$		0			0
$429$	−575.376	+	15744.3i	−0.0647539	+	1.77190i
$430$		0			0
$431$	9458.47			1.05707			0.528537	−	0.848910i	$-0.322741\pi$
$431$	9458.47			1.05707			0.528537	+	0.848910i	$0.322741\pi$
$432$		0			0
$433$	5691.49			0.631676			0.315838	−	0.948813i	$-0.397714\pi$
$433$	5691.49			0.631676			0.315838	+	0.948813i	$0.397714\pi$
$434$		0			0
$435$	−19111.3	+	10121.9i	−2.10648	+	1.11566i
$436$		0			0
$437$	−2246.13	−	1884.72i	−0.245874	−	0.206313i
$438$		0			0
$439$	−12777.3	−	4650.57i	−1.38913	−	0.505602i	−0.464198	−	0.885732i	$-0.653657\pi$
$439$	−12777.3	−	4650.57i	−1.38913	−	0.505602i	−0.924933	+	0.380129i	$0.875880\pi$
$440$		0			0
$441$	−1876.85	+	7424.94i	−0.202662	+	0.801743i
$442$		0			0
$443$	−8689.72	+	7291.54i	−0.931966	+	0.782013i	−0.976169	−	0.217010i	$-0.930370\pi$
$443$	−8689.72	+	7291.54i	−0.931966	+	0.782013i	0.0442031	+	0.999023i	$0.485925\pi$
$444$		0			0
$445$	2449.91	−	13894.1i	0.260982	−	1.48010i
$446$		0			0
$447$	4747.67	−	5255.65i	0.502364	−	0.556115i
$448$		0			0
$449$	2603.29	−	4509.03i	0.273623	−	0.473930i	−0.696163	−	0.717883i	$-0.745111\pi$
$449$	2603.29	−	4509.03i	0.273623	−	0.473930i	0.969787	+	0.243954i	$0.0784444\pi$
$450$		0			0
$451$	−1266.68	−	2193.96i	−0.132252	−	0.229067i
$452$		0			0
$453$	−6031.84	+	837.745i	−0.625609	+	0.0868889i
$454$		0			0
$455$	26953.3	−	9810.21i	2.77713	−	1.01079i
$456$		0			0
$457$	2794.59	+	15848.9i	0.286051	+	1.62228i	0.701506	+	0.712664i	$0.252512\pi$
$457$	2794.59	+	15848.9i	0.286051	+	1.62228i	−0.415454	+	0.909614i	$0.636377\pi$
$458$		0			0
$459$	796.248	+	584.449i	0.0809710	+	0.0594330i
$460$		0			0
$461$	2417.98	+	13713.0i	0.244287	+	1.38542i	0.822143	+	0.569282i	$0.192779\pi$
$461$	2417.98	+	13713.0i	0.244287	+	1.38542i	−0.577855	+	0.816139i	$0.696110\pi$
$462$		0			0
$463$	−683.331	+	248.712i	−0.0685898	+	0.0249646i	−0.376087	−	0.926584i	$-0.622731\pi$
$463$	−683.331	+	248.712i	−0.0685898	+	0.0249646i	0.307497	+	0.951549i	$0.400508\pi$
$464$		0			0
$465$	−8875.84	−	11398.6i	−0.885177	−	1.13677i
$466$		0			0
$467$	6275.96	+	10870.3i	0.621877	+	1.07712i	0.989136	+	0.147004i	$0.0469630\pi$
$467$	6275.96	+	10870.3i	0.621877	+	1.07712i	−0.367259	+	0.930119i	$0.619704\pi$
$468$		0			0
$469$	−11688.8	+	20245.7i	−1.15083	+	1.99330i
$470$		0			0
$471$	2037.88	+	6306.74i	0.199364	+	0.616984i
$472$		0			0
$473$	−1482.31	+	8406.62i	−0.144095	+	0.817203i
$474$		0			0
$475$	16690.4	−	14004.9i	1.61222	−	1.35282i
$476$		0			0
$477$	−4083.02	−	8440.83i	−0.391926	−	0.810228i
$478$		0			0
$479$	8706.20	+	3168.80i	0.830472	+	0.302267i	0.722053	−	0.691838i	$-0.243199\pi$
$479$	8706.20	+	3168.80i	0.830472	+	0.302267i	0.108420	+	0.994105i	$0.465421\pi$
$480$		0			0
$481$	−5878.05	−	4932.27i	−0.557206	−	0.467551i
$482$		0			0
$483$	−3786.45	−	2374.59i	−0.356707	−	0.223701i
$484$		0			0
$485$	30915.4			2.89443
$486$		0			0
$487$	−7806.10			−0.726341			−0.363170	−	0.931723i	$-0.618306\pi$
$487$	−7806.10			−0.726341			−0.363170	+	0.931723i	$0.618306\pi$
$488$		0			0
$489$	−7115.67	−	4462.43i	−0.658041	−	0.412675i
$490$		0			0
$491$	−4101.97	−	3441.96i	−0.377025	−	0.316361i	0.434508	−	0.900668i	$-0.356922\pi$
$491$	−4101.97	−	3441.96i	−0.377025	−	0.316361i	−0.811533	+	0.584306i	$0.801367\pi$
$492$		0			0
$493$	−1411.88	−	513.882i	−0.128982	−	0.0469454i
$494$		0			0
$495$	11832.5	+	24461.3i	1.07440	+	2.22112i
$496$		0			0
$497$	1791.87	−	1503.56i	0.161723	−	0.135702i
$498$		0			0
$499$	256.588	−	1455.18i	0.0230190	−	0.130547i	−0.971133	−	0.238540i	$-0.923331\pi$
$499$	256.588	−	1455.18i	0.0230190	−	0.130547i	0.994152	+	0.107993i	$0.0344423\pi$
$500$		0			0
$501$	−884.874	−	2738.47i	−0.0789087	−	0.244203i
$502$		0			0
$503$	−6261.59	+	10845.4i	−0.555051	+	0.961376i	0.442849	+	0.896596i	$0.353968\pi$
$503$	−6261.59	+	10845.4i	−0.555051	+	0.961376i	−0.997900	+	0.0647801i	$0.979365\pi$
$504$		0			0
$505$	−17050.5	−	29532.3i	−1.50245	−	2.60232i
$506$		0			0
$507$	4006.65	+	5145.46i	0.350970	+	0.450726i
$508$		0			0
$509$	980.124	−	356.736i	0.0853502	−	0.0310649i	−0.298992	−	0.954256i	$-0.596650\pi$
$509$	980.124	−	356.736i	0.0853502	−	0.0310649i	0.384342	+	0.923191i	$0.374428\pi$
$510$		0			0
$511$	−1164.78	−	6605.78i	−0.100835	−	0.571864i
$512$		0			0
$513$	−10960.5	+	4816.17i	−0.943313	+	0.414501i
$514$		0			0
$515$	−3173.18	−	17996.0i	−0.271509	−	1.53980i
$516$		0			0
$517$	24279.7	−	8837.10i	2.06542	−	0.751751i
$518$		0			0
$519$	−3622.28	+	503.088i	−0.306359	+	0.0425493i
$520$		0			0
$521$	4911.87	+	8507.61i	0.413038	+	0.715403i	0.995220	−	0.0976552i	$-0.0311342\pi$
$521$	4911.87	+	8507.61i	0.413038	+	0.715403i	−0.582182	+	0.813058i	$0.697801\pi$
$522$		0			0
$523$	−904.471	+	1566.59i	−0.0756209	+	0.130979i	−0.901356	−	0.433079i	$-0.857427\pi$
$523$	−904.471	+	1566.59i	−0.0756209	+	0.130979i	0.825735	+	0.564058i	$0.190761\pi$
$524$		0			0
$525$	22262.6	−	24644.7i	1.85071	−	2.04873i
$526$		0			0
$527$	174.289	−	988.444i	0.0144064	−	0.0817027i
$528$		0			0
$529$	−8416.04	+	7061.89i	−0.691710	+	0.580414i
$530$		0			0
$531$	1490.01	−	5894.57i	0.121772	−	0.481738i
$532$		0			0
$533$	−2710.37	−	986.492i	−0.220261	−	0.0801683i
$534$		0			0
$535$	240.552	+	201.847i	0.0194392	+	0.0163114i
$536$		0			0
$537$	5379.96	−	2849.39i	0.432332	−	0.228976i
$538$		0			0
$539$	−14637.7			−1.16974
$540$		0			0
$541$	5724.91			0.454960			0.227480	−	0.973783i	$-0.426951\pi$
$541$	5724.91			0.454960			0.227480	+	0.973783i	$0.426951\pi$
$542$		0			0
$543$	−146.694	+	4014.07i	−0.0115934	+	0.317238i
$544$		0			0
$545$	−24875.7	−	20873.2i	−1.95516	−	1.64057i
$546$		0			0
$547$	6752.26	+	2457.62i	0.527798	+	0.192103i	0.592155	−	0.805824i	$-0.298277\pi$
$547$	6752.26	+	2457.62i	0.527798	+	0.192103i	−0.0643567	+	0.997927i	$0.520500\pi$
$548$		0			0
$549$	−1681.77	−	16516.3i	−0.130740	−	1.28397i
$550$		0			0
$551$	13950.8	−	11706.1i	1.07863	−	0.905075i
$552$		0			0
$553$	3900.50	−	22120.8i	0.299939	−	1.70104i
$554$		0			0
$555$	−12940.6	−	2772.55i	−0.989723	−	0.212051i
$556$		0			0
$557$	−800.454	+	1386.43i	−0.0608910	+	0.105466i	−0.894864	−	0.446339i	$-0.852728\pi$
$557$	−800.454	+	1386.43i	−0.0608910	+	0.105466i	0.833973	+	0.551805i	$0.186061\pi$
$558$		0			0
$559$	4859.42	+	8416.77i	0.367677	+	0.636836i
$560$		0			0
$561$	−710.034	+	1749.22i	−0.0534361	+	0.131644i
$562$		0			0
$563$	−12290.5	+	4473.39i	−0.920042	+	0.334868i	−0.758255	−	0.651958i	$-0.773948\pi$
$563$	−12290.5	+	4473.39i	−0.920042	+	0.334868i	−0.161787	+	0.986826i	$0.551726\pi$
$564$		0			0
$565$	2794.98	+	15851.1i	0.208117	+	1.18029i
$566$		0			0
$567$	−15538.5	+	9569.88i	−1.15089	+	0.708813i
$568$		0			0
$569$	−3956.96	−	22441.0i	−0.291537	−	1.65339i	−0.680955	−	0.732325i	$-0.738435\pi$
$569$	−3956.96	−	22441.0i	−0.291537	−	1.65339i	0.389419	−	0.921061i	$-0.372676\pi$
$570$		0			0
$571$	10197.6	−	3711.63i	0.747386	−	0.272026i	0.0598805	−	0.998206i	$-0.480928\pi$
$571$	10197.6	−	3711.63i	0.747386	−	0.272026i	0.687505	+	0.726179i	$0.258706\pi$
$572$		0			0
$573$	−1112.38	+	2740.43i	−0.0811001	+	0.199796i
$574$		0			0
$575$	4386.52	+	7597.68i	0.318140	+	0.551035i
$576$		0			0
$577$	−10891.7	+	18865.0i	−0.785835	+	1.36111i	0.142664	+	0.989771i	$0.454433\pi$
$577$	−10891.7	+	18865.0i	−0.785835	+	1.36111i	−0.928499	+	0.371335i	$0.878900\pi$
$578$		0			0
$579$	24686.7	+	5289.18i	1.77192	+	0.379639i
$580$		0			0
$581$	−154.524	+	876.350i	−0.0110340	+	0.0625768i
$582$		0			0
$583$	13728.5	−	11519.6i	0.975263	−	0.818343i
$584$		0			0
$585$	28221.4	+	12674.9i	1.99455	+	0.895796i
$586$		0			0
$587$	−9679.74	−	3523.14i	−0.680623	−	0.247726i	−0.0215079	−	0.999769i	$-0.506847\pi$
$587$	−9679.74	−	3523.14i	−0.680623	−	0.247726i	−0.659115	+	0.752042i	$0.729069\pi$
$588$		0			0
$589$	9319.39	+	7819.90i	0.651950	+	0.547051i
$590$		0			0
$591$	−359.139	+	9827.33i	−0.0249966	+	0.683997i
$592$		0			0
$593$	4017.02			0.278178			0.139089	−	0.990280i	$-0.455583\pi$
$593$	4017.02			0.278178			0.139089	+	0.990280i	$0.455583\pi$
$594$		0			0
$595$	3436.98			0.236811
$596$		0			0
$597$	−17911.6	+	9486.54i	−1.22793	+	0.650349i
$598$		0			0
$599$	−3884.65	−	3259.61i	−0.264979	−	0.222344i	0.500611	−	0.865672i	$-0.333109\pi$
$599$	−3884.65	−	3259.61i	−0.264979	−	0.222344i	−0.765590	+	0.643328i	$0.777553\pi$
$600$		0			0
$601$	−6769.34	−	2463.84i	−0.459446	−	0.167225i	0.101919	−	0.994793i	$-0.467502\pi$
$601$	−6769.34	−	2463.84i	−0.459446	−	0.167225i	−0.561366	+	0.827568i	$0.689724\pi$
$602$		0			0
$603$	−24260.3	+	6871.44i	−1.63840	+	0.464057i
$604$		0			0
$605$	−19900.7	+	16698.7i	−1.33732	+	1.12215i
$606$		0			0
$607$	−829.608	+	4704.94i	−0.0554741	+	0.314609i	−0.999900	−	0.0141141i	$-0.995507\pi$
$607$	−829.608	+	4704.94i	−0.0554741	+	0.314609i	0.944426	+	0.328723i	$0.106618\pi$
$608$		0			0
$609$	18608.4	−	20599.4i	1.23818	−	1.37066i
$610$		0			0
$611$	14708.6	−	25476.1i	0.973892	−	1.68683i
$612$		0			0
$613$	9124.06	+	15803.3i	0.601170	+	1.04126i	0.992644	+	0.121068i	$0.0386319\pi$
$613$	9124.06	+	15803.3i	0.601170	+	1.04126i	−0.391474	+	0.920189i	$0.628035\pi$
$614$		0			0
$615$	−4927.35	+	684.345i	−0.323073	+	0.0448707i
$616$		0			0
$617$	9238.38	−	3362.50i	0.602793	−	0.219399i	−0.0225540	−	0.999746i	$-0.507180\pi$
$617$	9238.38	−	3362.50i	0.602793	−	0.219399i	0.625347	+	0.780347i	$0.284958\pi$
$618$		0			0
$619$	−2028.41	−	11503.7i	−0.131710	−	0.746966i	−0.977094	−	0.212807i	$-0.931739\pi$
$619$	−2028.41	−	11503.7i	−0.131710	−	0.746966i	0.845384	−	0.534159i	$-0.179372\pi$
$620$		0			0
$621$	−1143.44	−	4683.07i	−0.0738886	−	0.302617i
$622$		0			0
$623$	3144.74	+	17834.7i	0.202234	+	1.14692i
$624$		0			0
$625$	−16585.3	+	6036.55i	−1.06146	+	0.386339i
$626$		0			0
$627$	−14058.4	−	18054.2i	−0.895436	−	1.14995i
$628$		0			0
$629$	−459.726	−	796.269i	−0.0291423	−	0.0504759i
$630$		0			0
$631$	−5452.85	+	9444.62i	−0.344017	+	0.595855i	−0.985175	−	0.171554i	$-0.945121\pi$
$631$	−5452.85	+	9444.62i	−0.344017	+	0.595855i	0.641158	+	0.767409i	$0.278454\pi$
$632$		0			0
$633$	−2383.67	−	7376.88i	−0.149672	−	0.463199i
$634$		0			0
$635$	−7659.36	+	43438.4i	−0.478665	+	2.71465i
$636$		0			0
$637$	−12766.5	+	10712.4i	−0.794077	+	0.666309i
$638$		0			0
$639$	2516.20	+	184.155i	0.155773	+	0.0114007i
$640$		0			0
$641$	19546.8	+	7114.47i	1.20445	+	0.438385i	0.864776	−	0.502158i	$-0.167460\pi$
$641$	19546.8	+	7114.47i	1.20445	+	0.438385i	0.339676	+	0.940542i	$0.389682\pi$
$642$		0			0
$643$	6541.99	+	5489.38i	0.401230	+	0.336672i	0.820969	−	0.570973i	$-0.193434\pi$
$643$	6541.99	+	5489.38i	0.401230	+	0.336672i	−0.419739	+	0.907645i	$0.637878\pi$
$644$		0			0
$645$	14200.8	+	8905.73i	0.866911	+	0.543663i
$646$		0			0
$647$	−17690.0			−1.07491			−0.537454	−	0.843293i	$-0.680614\pi$
$647$	−17690.0			−1.07491			−0.537454	+	0.843293i	$0.680614\pi$
$648$		0			0
$649$	11620.7			0.702854
$650$		0			0
$651$	15710.3	+	9852.38i	0.945832	+	0.593157i
$652$		0			0
$653$	−10827.1	−	9085.01i	−0.648847	−	0.544447i	0.257874	−	0.966179i	$-0.416978\pi$
$653$	−10827.1	−	9085.01i	−0.648847	−	0.544447i	−0.906721	+	0.421732i	$0.861422\pi$
$654$		0			0
$655$	−26199.3	−	9535.77i	−1.56289	−	0.568845i
$656$		0			0
$657$	4065.07	−	5984.74i	0.241390	−	0.355383i
$658$		0			0
$659$	−7705.44	+	6465.63i	−0.455480	+	0.382193i	−0.841465	−	0.540312i	$-0.818306\pi$
$659$	−7705.44	+	6465.63i	−0.455480	+	0.382193i	0.385985	+	0.922505i	$0.373862\pi$
$660$		0			0
$661$	−3544.49	+	20101.8i	−0.208570	+	1.18286i	0.683153	+	0.730275i	$0.260608\pi$
$661$	−3544.49	+	20101.8i	−0.208570	+	1.18286i	−0.891723	+	0.452582i	$0.850503\pi$
$662$		0			0
$663$	660.872	+	2045.24i	0.0387121	+	0.119805i
$664$		0			0
$665$	−20829.5	+	36077.8i	−1.21464	+	2.10382i
$666$		0			0
$667$	3666.51	+	6350.58i	0.212845	+	0.368659i
$668$		0			0
$669$	6541.74	+	8401.09i	0.378054	+	0.485508i
$670$		0			0
$671$	29817.3	−	10852.6i	1.71547	−	0.624381i
$672$		0			0
$673$	2017.24	+	11440.4i	0.115541	+	0.655265i	0.986481	+	0.163876i	$0.0523996\pi$
$673$	2017.24	+	11440.4i	0.115541	+	0.655265i	−0.870940	+	0.491389i	$0.836489\pi$
$674$		0			0
$675$	35745.4	−	2324.82i	2.03828	−	0.132566i
$676$		0			0
$677$	−3453.35	−	19584.9i	−0.196046	−	1.11183i	−0.910921	−	0.412580i	$-0.864628\pi$
$677$	−3453.35	−	19584.9i	−0.196046	−	1.11183i	0.714876	−	0.699252i	$-0.246483\pi$
$678$		0			0
$679$	−37290.3	+	13572.6i	−2.10762	+	0.767109i
$680$		0			0
$681$	8352.52	−	1160.06i	0.469999	−	0.0652768i
$682$		0			0
$683$	−5188.26	−	8986.33i	−0.290664	−	0.503444i	0.683303	−	0.730135i	$-0.260543\pi$
$683$	−5188.26	−	8986.33i	−0.290664	−	0.503444i	−0.973967	+	0.226690i	$0.927209\pi$
$684$		0			0
$685$	14621.0	−	25324.3i	0.815533	−	1.41255i
$686$		0			0
$687$	−13075.4	+	14474.4i	−0.726141	+	0.803835i
$688$		0			0
$689$	3543.12	−	20094.0i	0.195910	−	1.11106i
$690$		0			0
$691$	−23664.3	+	19856.7i	−1.30279	+	1.09317i	−0.313140	+	0.949707i	$0.601381\pi$
$691$	−23664.3	+	19856.7i	−1.30279	+	1.09317i	−0.989655	+	0.143468i	$0.954175\pi$
$692$		0			0
$693$	−25011.4	−	24310.6i	−1.37100	−	1.33259i
$694$		0			0
$695$	1056.04	+	384.368i	0.0576374	+	0.0209783i
$696$		0			0
$697$	−264.756	−	222.157i	−0.0143879	−	0.0120729i
$698$		0			0
$699$	442.625	−	234.428i	0.0239508	−	0.0126851i
$700$		0			0
$701$	−28142.8			−1.51632			−0.758158	−	0.652071i	$-0.773901\pi$
$701$	−28142.8			−1.51632			−0.758158	+	0.652071i	$0.773901\pi$
$702$		0			0
$703$	11144.5			0.597900
$704$		0			0
$705$	1852.94	−	50702.9i	0.0989866	−	2.70863i
$706$		0			0
$707$	33531.7	+	28136.5i	1.78372	+	1.49672i
$708$		0			0
$709$	20208.5	+	7355.30i	1.07045	+	0.389611i	0.816344	−	0.577566i	$-0.195997\pi$
$709$	20208.5	+	7355.30i	1.07045	+	0.389611i	0.254103	+	0.967177i	$0.418220\pi$
$710$		0			0
$711$	19646.3	−	14176.7i	1.03628	−	0.747774i
$712$		0			0
$713$	−3752.54	+	3148.76i	−0.197102	+	0.165388i
$714$		0			0
$715$	−10267.8	+	58231.9i	−0.537057	+	3.04580i
$716$		0			0
$717$	22791.5	+	4883.14i	1.18712	+	0.254343i
$718$		0			0
$719$	18578.1	−	32178.3i	0.963626	−	1.66905i	0.250366	−	0.968151i	$-0.419449\pi$
$719$	18578.1	−	32178.3i	0.963626	−	1.66905i	0.713261	−	0.700899i	$-0.247217\pi$
$720$		0			0
$721$	11728.2	+	20313.8i	0.605797	+	1.04927i
$722$		0			0
$723$	4737.57	−	11671.3i	0.243696	−	0.600362i
$724$		0			0
$725$	−51203.6	+	18636.6i	−2.62297	+	0.954683i
$726$		0			0
$727$	−2772.11	−	15721.4i	−0.141419	−	0.802029i	−0.970173	−	0.242415i	$-0.922060\pi$
$727$	−2772.11	−	15721.4i	−0.141419	−	0.802029i	0.828753	−	0.559614i	$-0.189051\pi$
$728$		0			0
$729$	−19212.1	−	4279.51i	−0.976078	−	0.217422i
$730$		0			0
$731$	202.225	+	1146.87i	0.0102320	+	0.0580283i
$732$		0			0
$733$	31627.8	−	11511.6i	1.59372	−	0.580067i	0.615592	−	0.788065i	$-0.288917\pi$
$733$	31627.8	−	11511.6i	1.59372	−	0.580067i	0.978129	+	0.207998i	$0.0666948\pi$
$734$		0			0
$735$	−10810.7	+	26632.9i	−0.542527	+	1.33656i
$736$		0			0
$737$	−24096.5	−	41736.4i	−1.20435	−	2.08600i
$738$		0			0
$739$	14420.2	−	24976.5i	0.717801	−	1.24327i	−0.244068	−	0.969758i	$-0.578482\pi$
$739$	14420.2	−	24976.5i	0.717801	−	1.24327i	0.961869	−	0.273510i	$-0.0881845\pi$
$740$		0			0
$741$	−25473.9	−	5457.85i	−1.26290	−	0.270579i
$742$		0			0
$743$	−1573.69	+	8924.86i	−0.0777028	+	0.440675i	0.920991	+	0.389583i	$0.127381\pi$
$743$	−1573.69	+	8924.86i	−0.0777028	+	0.440675i	−0.998694	+	0.0510912i	$0.983730\pi$
$744$		0			0
$745$	20362.8	−	17086.4i	1.00139	−	0.840264i
$746$		0			0
$747$	−778.316	+	561.631i	−0.0381219	+	0.0275087i
$748$		0			0
$749$	−378.770	−	137.861i	−0.0184779	−	0.00672541i
$750$		0			0
$751$	4600.11	+	3859.95i	0.223516	+	0.187552i	0.747668	−	0.664072i	$-0.231173\pi$
$751$	4600.11	+	3859.95i	0.223516	+	0.187552i	−0.524152	+	0.851625i	$0.675618\pi$
$752$		0			0
$753$	−455.441	+	12462.5i	−0.0220414	+	0.603132i
$754$		0			0
$755$	−22855.7			−1.10172
$756$		0			0
$757$	−25006.2			−1.20061			−0.600307	−	0.799770i	$-0.704955\pi$
$757$	−25006.2			−1.20061			−0.600307	+	0.799770i	$0.704955\pi$
$758$		0			0
$759$	8142.24	−	4312.38i	0.389387	−	0.206231i
$760$		0			0
$761$	−16281.6	−	13661.8i	−0.775566	−	0.650777i	0.166562	−	0.986031i	$-0.446733\pi$
$761$	−16281.6	−	13661.8i	−0.775566	−	0.650777i	−0.942128	+	0.335254i	$0.891178\pi$
$762$		0			0
$763$	39169.0	+	14256.4i	1.85847	+	0.676429i
$764$		0			0
$765$	2658.26	+	2583.77i	0.125634	+	0.122113i
$766$		0			0
$767$	10135.2	−	8504.41i	0.477131	−	0.400360i
$768$		0			0
$769$	598.520	−	3394.38i	0.0280666	−	0.159173i	−0.967553	−	0.252667i	$-0.918692\pi$
$769$	598.520	−	3394.38i	0.0280666	−	0.159173i	0.995620	+	0.0934935i	$0.0298034\pi$
$770$		0			0
$771$	1303.91	−	1443.42i	0.0609068	−	0.0674236i
$772$		0			0
$773$	9004.85	−	15596.8i	0.418993	−	0.725718i	−0.576845	−	0.816853i	$-0.695716\pi$
$773$	9004.85	−	15596.8i	0.418993	−	0.725718i	0.995838	+	0.0911359i	$0.0290498\pi$
$774$		0			0
$775$	−18200.1	−	31523.5i	−0.843569	−	1.46110i
$776$		0			0
$777$	16826.2	−	2336.94i	0.776880	−	0.107899i
$778$		0			0
$779$	3936.50	−	1432.77i	0.181052	−	0.0658977i
$780$		0			0
$781$	837.347	+	4748.83i	0.0383644	+	0.217575i
$782$		0			0
$783$	29878.1	−	1943.22i	1.36367	−	0.0886909i
$784$		0			0
$785$	4319.52	+	24497.2i	0.196395	+	1.11381i
$786$		0			0
$787$	−16461.5	+	5991.50i	−0.745603	+	0.271377i	−0.686754	−	0.726890i	$-0.740965\pi$
$787$	−16461.5	+	5991.50i	−0.745603	+	0.271377i	−0.0588488	+	0.998267i	$0.518743\pi$
$788$		0			0
$789$	12825.1	+	16470.4i	0.578690	+	0.743172i
$790$		0			0
$791$	−10330.3	−	17892.7i	−0.464354	−	0.804285i
$792$		0			0
$793$	18063.3	−	31286.5i	0.808885	−	1.40103i
$794$		0			0
$795$	−10820.4	−	33486.5i	−0.482717	−	1.49389i
$796$		0			0
$797$	1312.20	−	7441.84i	0.0583192	−	0.330745i	−0.941664	−	0.336555i	$-0.890738\pi$
$797$	1312.20	−	7441.84i	0.0583192	−	0.330745i	0.999983	+	0.00581003i	$0.00184940\pi$
$798$		0			0
$799$	2700.27	−	2265.79i	0.119560	−	0.100323i
$800$		0			0
$801$	−10975.1	+	16158.0i	−0.484130	+	0.712753i
$802$		0			0
$803$	12993.9	+	4729.41i	0.571041	+	0.207842i
$804$		0			0
$805$	−12850.0	−	10782.4i	−0.562610	−	0.472086i
$806$		0			0
$807$	−13657.4	−	8564.91i	−0.595740	−	0.373605i
$808$		0			0
$809$	38981.7			1.69410			0.847048	−	0.531517i	$-0.178378\pi$
$809$	38981.7			1.69410			0.847048	+	0.531517i	$0.178378\pi$
$810$		0			0
$811$	−3470.10			−0.150249			−0.0751244	−	0.997174i	$-0.523935\pi$
$811$	−3470.10			−0.150249			−0.0751244	+	0.997174i	$0.523935\pi$
$812$		0			0
$813$	646.215	+	405.259i	0.0278767	+	0.0174822i
$814$		0			0
$815$	−24148.2	−	20262.8i	−1.03788	−	0.870888i
$816$		0			0
$817$	−13264.3	−	4827.80i	−0.568002	−	0.206736i
$818$		0			0
$819$	−39605.4	−	2898.62i	−1.68977	−	0.123670i
$820$		0			0
$821$	18661.9	−	15659.2i	0.793305	−	0.665662i	−0.153256	−	0.988187i	$-0.548976\pi$
$821$	18661.9	−	15659.2i	0.793305	−	0.665662i	0.946561	+	0.322524i	$0.104531\pi$
$822$		0			0
$823$	6973.29	−	39547.5i	0.295351	−	1.67502i	−0.370423	−	0.928863i	$-0.620787\pi$
$823$	6973.29	−	39547.5i	0.295351	−	1.67502i	0.665774	−	0.746154i	$-0.268102\pi$
$824$		0			0
$825$	21051.1	+	65148.1i	0.888371	+	2.74929i
$826$		0			0
$827$	−4564.78	+	7906.43i	−0.191938	+	0.332447i	−0.945893	−	0.324480i	$-0.894811\pi$
$827$	−4564.78	+	7906.43i	−0.191938	+	0.332447i	0.753954	+	0.656927i	$0.228144\pi$
$828$		0			0
$829$	11850.3	+	20525.3i	0.496475	+	0.859920i	0.999992	−	0.00406556i	$-0.00129411\pi$
$829$	11850.3	+	20525.3i	0.496475	+	0.859920i	−0.503517	+	0.863985i	$0.667961\pi$
$830$		0			0
$831$	13659.2	+	17541.6i	0.570197	+	0.732264i
$832$		0			0
$833$	−1876.52	+	682.998i	−0.0780523	+	0.0284087i
$834$		0			0
$835$	−1875.59	−	10637.0i	−0.0777336	−	0.440849i
$836$		0			0
$837$	4744.25	+	19430.5i	0.195920	+	0.802408i
$838$		0			0
$839$	5839.10	+	33115.2i	0.240272	+	1.36265i	0.831222	+	0.555941i	$0.187642\pi$
$839$	5839.10	+	33115.2i	0.240272	+	1.36265i	−0.590950	+	0.806708i	$0.701247\pi$
$840$		0			0
$841$	−19880.8	+	7236.01i	−0.815153	+	0.296692i
$842$		0			0
$843$	25596.6	−	3555.04i	1.04578	−	0.145246i
$844$		0			0
$845$	12237.9	+	21196.7i	0.498221	+	0.862945i
$846$		0			0
$847$	16673.2	−	28878.9i	0.676386	−	1.17154i
$848$		0			0
$849$	3712.58	−	4109.81i	0.150077	−	0.166135i
$850$		0			0
$851$	−779.238	+	4419.28i	−0.0313889	+	0.178015i
$852$		0			0
$853$	−20152.9	+	16910.3i	−0.808937	+	0.678778i	−0.950354	−	0.311172i	$-0.899279\pi$
$853$	−20152.9	+	16910.3i	−0.808937	+	0.678778i	0.141417	+	0.989950i	$0.454834\pi$
$854$		0			0
$855$	−43231.9	+	12244.9i	−1.72924	+	0.489786i
$856$		0			0
$857$	151.335	+	55.0813i	0.00603208	+	0.00219550i	0.345034	−	0.938590i	$-0.387867\pi$
$857$	151.335	+	55.0813i	0.00603208	+	0.00219550i	−0.339002	+	0.940786i	$0.610089\pi$
$858$		0			0
$859$	37816.0	+	31731.4i	1.50206	+	1.26038i	0.877675	+	0.479256i	$0.159094\pi$
$859$	37816.0	+	31731.4i	1.50206	+	1.26038i	0.624382	+	0.781119i	$0.285351\pi$
$860$		0			0
$861$	5642.95	−	2988.68i	0.223358	−	0.118297i
$862$		0			0
$863$	19390.7			0.764853			0.382426	−	0.923986i	$-0.375089\pi$
$863$	19390.7			0.764853			0.382426	+	0.923986i	$0.375089\pi$
$864$		0			0
$865$	−13725.4			−0.539512
$866$		0			0
$867$	922.917	−	25254.3i	0.0361521	−	0.989251i
$868$		0			0
$869$	35472.0	+	29764.6i	1.38470	+	1.16190i
$870$		0			0
$871$	−51560.1	−	18766.4i	−2.00580	−	0.730050i
$872$		0			0
$873$	−39044.7	−	17535.8i	−1.51370	−	0.679837i
$874$		0			0
$875$	48737.7	−	40895.8i	1.88301	−	1.58004i
$876$		0			0
$877$	−4605.11	+	26116.9i	−0.177313	+	1.00559i	0.758127	+	0.652107i	$0.226115\pi$
$877$	−4605.11	+	26116.9i	−0.177313	+	1.00559i	−0.935440	+	0.353486i	$0.884996\pi$
$878$		0			0
$879$	−34190.5	−	7325.40i	−1.31197	−	0.281092i
$880$		0			0
$881$	4444.25	−	7697.66i	0.169955	−	0.294371i	−0.768449	−	0.639911i	$-0.778971\pi$
$881$	4444.25	−	7697.66i	0.169955	−	0.294371i	0.938404	+	0.345540i	$0.112304\pi$
$882$		0			0
$883$	9393.58	+	16270.2i	0.358006	+	0.620084i	0.987628	−	0.156818i	$-0.0501235\pi$
$883$	9393.58	+	16270.2i	0.358006	+	0.620084i	−0.629622	+	0.776902i	$0.716790\pi$
$884$		0			0
$885$	8582.46	−	21143.5i	0.325984	−	0.803087i
$886$		0			0
$887$	−16935.5	+	6164.02i	−0.641081	+	0.233334i	−0.642047	−	0.766665i	$-0.721915\pi$
$887$	−16935.5	+	6164.02i	−0.641081	+	0.233334i	0.000966332		1.00000i	$0.499692\pi$
$888$		0			0
$889$	−9831.68	−	55758.2i	−0.370915	−	2.10357i
$890$		0			0
$891$	−1068.95	−	37605.1i	−0.0401922	−	1.41394i
$892$		0			0
$893$	7419.17	+	42076.2i	0.278021	+	1.57674i
$894$		0			0
$895$	21470.9	−	7814.77i	0.801892	−	0.291865i
$896$		0			0
$897$	3945.43	−	9719.86i	0.146861	−	0.361802i
$898$		0			0
$899$	−15212.7	−	26349.1i	−0.564373	−	0.977523i
$900$		0			0
$901$	1222.46	−	2117.37i	0.0452010	−	0.0782904i
$902$		0			0
$903$	−21038.9	−	4507.65i	−0.775340	−	0.166119i
$904$		0			0
$905$	−2617.82	+	14846.4i	−0.0961538	+	0.545315i
$906$		0			0
$907$	−23612.4	+	19813.2i	−0.864430	+	0.725343i	−0.962918	−	0.269795i	$-0.913044\pi$
$907$	−23612.4	+	19813.2i	−0.864430	+	0.725343i	0.0984877	+	0.995138i	$0.468599\pi$
$908$		0			0
$909$	4782.66	+	46969.3i	0.174511	+	1.71383i
$910$		0			0
$911$	−43762.2	−	15928.1i	−1.59155	−	0.579278i	−0.613878	−	0.789401i	$-0.710391\pi$
$911$	−43762.2	−	15928.1i	−1.59155	−	0.579278i	−0.977675	+	0.210123i	$0.932614\pi$
$912$		0			0
$913$	−1405.28	−	1179.17i	−0.0509397	−	0.0427435i
$914$		0			0
$915$	2275.54	−	62266.8i	0.0822153	−	2.24970i
$916$		0			0
$917$	35788.1			1.28880
$918$		0			0
$919$	3405.86			0.122251			0.0611256	−	0.998130i	$-0.480531\pi$
$919$	3405.86			0.122251			0.0611256	+	0.998130i	$0.480531\pi$
$920$		0			0
$921$	3853.86	−	2041.12i	0.137882	−	0.0730264i
$922$		0			0
$923$	4205.65	+	3528.96i	0.149979	+	0.125847i
$924$		0			0
$925$	−31334.1	−	11404.7i	−1.11379	−	0.405388i
$926$		0			0
$927$	−6200.11	+	24528.0i	−0.219675	+	0.869046i
$928$		0			0
$929$	−23801.4	+	19971.7i	−0.840580	+	0.705330i	−0.957694	−	0.287788i	$-0.907080\pi$
$929$	−23801.4	+	19971.7i	−0.840580	+	0.705330i	0.117114	+	0.993118i	$0.462636\pi$
$930$		0			0
$931$	4203.11	−	23837.0i	0.147961	−	0.839126i
$932$		0			0
$933$	15706.0	−	17386.4i	0.551115	−	0.610082i
$934$		0			0
$935$	−3542.66	+	6136.06i	−0.123912	+	0.214621i
$936$		0			0
$937$	14196.9	+	24589.8i	0.494976	+	0.857324i	0.999983	−	0.00579118i	$-0.00184340\pi$
$937$	14196.9	+	24589.8i	0.494976	+	0.857324i	−0.505007	+	0.863115i	$0.668510\pi$
$938$		0			0
$939$	−22347.0	+	3103.70i	−0.776641	+	0.107865i
$940$		0			0
$941$	−8174.57	+	2975.30i	−0.283192	+	0.103073i	−0.479711	−	0.877427i	$-0.659258\pi$
$941$	−8174.57	+	2975.30i	−0.283192	+	0.103073i	0.196519	+	0.980500i	$0.437036\pi$
$942$		0			0
$943$	292.909	+	1661.17i	0.0101150	+	0.0573650i
$944$		0			0
$945$	−62704.5	+	27553.0i	−2.15850	+	0.948465i
$946$		0			0
$947$	1821.30	+	10329.1i	0.0624967	+	0.354436i	0.999979	+	0.00640472i	$0.00203870\pi$
$947$	1821.30	+	10329.1i	0.0624967	+	0.354436i	−0.937483	+	0.348032i	$0.886850\pi$
$948$		0			0
$949$	14794.0	−	5384.57i	0.506041	−	0.184184i
$950$		0			0
$951$	29913.5	+	38415.9i	1.01999	+	1.30990i
$952$		0			0
$953$	16369.0	+	28351.9i	0.556393	+	0.963701i	0.997794	+	0.0663907i	$0.0211484\pi$
$953$	16369.0	+	28351.9i	0.556393	+	0.963701i	−0.441401	+	0.897310i	$0.645518\pi$
$954$		0			0
$955$	−5550.13	+	9613.10i	−0.188061	+	0.325731i
$956$		0			0
$957$	17595.7	+	54454.5i	0.594347	+	1.83936i
$958$		0			0
$959$	−6517.98	+	36965.3i	−0.219475	+	1.24470i
$960$		0			0
$961$	−7251.59	+	6084.80i	−0.243415	+	0.204250i
$962$		0			0
$963$	−189.314	−	391.369i	−0.00633495	−	0.0130962i
$964$		0			0
$965$	89040.8	+	32408.2i	2.97028	+	1.08109i
$966$		0			0
$967$	−12731.9	−	10683.3i	−0.423403	−	0.355277i	0.406053	−	0.913850i	$-0.366905\pi$
$967$	−12731.9	−	10683.3i	−0.423403	−	0.355277i	−0.829456	+	0.558572i	$0.811349\pi$
$968$		0			0
$969$	−2644.67	−	1658.54i	−0.0876769	−	0.0549846i
$970$		0			0
$971$	−30671.4			−1.01369			−0.506844	−	0.862038i	$-0.669188\pi$
$971$	−30671.4			−1.01369			−0.506844	+	0.862038i	$0.669188\pi$
$972$		0			0
$973$	−1442.55			−0.0475293
$974$		0			0
$975$	66037.5	+	41413.9i	2.16912	+	1.36032i
$976$		0			0
$977$	7083.39	+	5943.67i	0.231953	+	0.194631i	0.751355	−	0.659899i	$-0.229401\pi$
$977$	7083.39	+	5943.67i	0.231953	+	0.194631i	−0.519402	+	0.854530i	$0.673845\pi$
$978$		0			0
$979$	−35081.9	−	12768.8i	−1.14527	−	0.416845i
$980$		0			0
$981$	19577.2	+	40471.9i	0.637158	+	1.31720i
$982$		0			0
$983$	39119.3	−	32825.0i	1.26929	−	1.06506i	0.274662	−	0.961541i	$-0.411434\pi$
$983$	39119.3	−	32825.0i	1.26929	−	1.06506i	0.994627	−	0.103519i	$-0.0330104\pi$
$984$		0			0
$985$	−6409.00	+	36347.3i	−0.207318	+	1.17576i
$986$		0			0
$987$	20024.7	+	61971.5i	0.645788	+	1.99856i
$988$		0			0
$989$	2841.88	−	4922.28i	0.0913715	−	0.158260i
$990$		0			0
$991$	19142.6	+	33156.0i	0.613609	+	1.06280i	0.990627	+	0.136595i	$0.0436160\pi$
$991$	19142.6	+	33156.0i	0.613609	+	1.06280i	−0.377018	+	0.926206i	$0.623051\pi$
$992$		0			0
$993$	−23960.0	−	30770.1i	−0.765707	−	0.983344i
$994$		0			0
$995$	−71483.6	+	26017.9i	−2.27757	+	0.828968i
$996$		0			0
$997$	1194.72	+	6775.57i	0.0379509	+	0.215230i	0.997886	−	0.0649932i	$-0.0207026\pi$
$997$	1194.72	+	6775.57i	0.0379509	+	0.215230i	−0.959935	+	0.280223i	$0.909591\pi$
$998$		0			0
$999$	14770.7	+	10841.7i	0.467792	+	0.343361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.13.3	✓	54
3.2	odd	2		324.4.i.a.253.9		54
27.2	odd	18		324.4.i.a.73.9		54
27.25	even	9	inner	108.4.i.a.25.3	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.3	✓	54	1.1	even	1	trivial
108.4.i.a.25.3	yes	54	27.25	even	9	inner
324.4.i.a.73.9		54	27.2	odd	18
324.4.i.a.253.9		54	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +O(q^{10})\)	\(q+(-4.40211 - 2.76069i) q^{3} +(-14.9393 - 12.5356i) q^{5} +(23.5233 + 8.56177i) q^{7} +(11.7572 + 24.3057i) q^{9} +(-39.5319 + 33.1712i) q^{11} +(-10.2025 + 57.8615i) q^{13} +(31.1578 + 96.4258i) q^{15} +(-3.52013 + 6.09704i) q^{17} +(-42.6669 - 73.9012i) q^{19} +(-79.9157 - 102.630i) q^{21} +(32.2883 - 11.7520i) q^{23} +(44.3365 + 251.445i) q^{25} +(15.3437 - 139.455i) q^{27} +(37.0590 + 210.172i) q^{29} +(-133.967 + 48.7600i) q^{31} +(265.599 - 36.8883i) q^{33} +(-244.095 - 422.784i) q^{35} +(-65.2996 + 113.102i) q^{37} +(204.650 - 226.547i) q^{39} +(-8.52460 + 48.3454i) q^{41} +(126.716 - 106.327i) q^{43} +(129.041 - 510.494i) q^{45} +(-470.489 - 171.244i) q^{47} +(217.287 + 182.325i) q^{49} +(32.3280 - 17.1219i) q^{51} -347.277 q^{53} +1006.40 q^{55} +(-16.1935 + 443.112i) q^{57} +(-172.501 - 144.746i) q^{59} +(-577.795 - 210.300i) q^{61} +(68.4686 + 672.412i) q^{63} +(877.746 - 736.517i) q^{65} +(-162.166 + 919.690i) q^{67} +(-174.580 - 37.4043i) q^{69} +(46.7209 - 80.9229i) q^{71} +(-133.977 - 232.055i) q^{73} +(498.985 - 1229.29i) q^{75} +(-1213.92 + 441.832i) q^{77} +(-155.815 - 883.669i) q^{79} +(-452.535 + 571.536i) q^{81} +(6.17283 + 35.0079i) q^{83} +(129.018 - 46.9588i) q^{85} +(417.081 - 1027.51i) q^{87} +(361.721 + 626.519i) q^{89} +(-735.394 + 1273.74i) q^{91} +(724.350 + 155.194i) q^{93} +(-288.980 + 1638.89i) q^{95} +(-1214.37 + 1018.98i) q^{97} +(-1271.04 - 570.850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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