LMFDB - Embedded newform 441.4.p.d.80.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not 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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.20
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16408 - 1.82678i) q^{2} +(2.67425 - 4.63194i) q^{4} +(8.69951 + 15.0680i) q^{5} +9.68739i q^{8} +O(q^{10})$	\(q+(3.16408 - 1.82678i) q^{2} +(2.67425 - 4.63194i) q^{4} +(8.69951 + 15.0680i) q^{5} +9.68739i q^{8} +(55.0518 + 31.7842i) q^{10} +(-28.2021 - 16.2825i) q^{11} +42.4779i q^{13} +(39.0908 + 67.7072i) q^{16} +(42.8181 - 74.1631i) q^{17} +(-59.9133 + 34.5910i) q^{19} +93.0588 q^{20} -118.978 q^{22} +(-144.644 + 83.5101i) q^{23} +(-88.8629 + 153.915i) q^{25} +(77.5978 + 134.403i) q^{26} +254.270i q^{29} +(281.837 + 162.719i) q^{31} +(180.256 + 104.071i) q^{32} -312.877i q^{34} +(-172.833 - 299.355i) q^{37} +(-126.380 + 218.897i) q^{38} +(-145.970 + 84.2756i) q^{40} +182.210 q^{41} +140.292 q^{43} +(-150.839 + 87.0871i) q^{44} +(-305.109 + 528.464i) q^{46} +(-21.5007 - 37.2404i) q^{47} +649.332i q^{50} +(196.755 + 113.597i) q^{52} +(167.182 + 96.5223i) q^{53} -566.600i q^{55} +(464.496 + 804.531i) q^{58} +(55.6370 - 96.3662i) q^{59} +(-78.4101 + 45.2701i) q^{61} +1189.00 q^{62} +135.007 q^{64} +(-640.057 + 369.537i) q^{65} +(524.458 - 908.388i) q^{67} +(-229.013 - 396.662i) q^{68} -464.023i q^{71} +(158.297 + 91.3925i) q^{73} +(-1093.71 - 631.456i) q^{74} +370.020i q^{76} +(119.473 + 206.934i) q^{79} +(-680.141 + 1178.04i) q^{80} +(576.526 - 332.857i) q^{82} +375.260 q^{83} +1489.99 q^{85} +(443.894 - 256.282i) q^{86} +(157.735 - 273.205i) q^{88} +(719.823 + 1246.77i) q^{89} +893.308i q^{92} +(-136.060 - 78.5542i) q^{94} +(-1042.43 - 601.849i) q^{95} -638.698i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4}+O(q^{10}) $ 48 * q + 96 * q^4	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.16408	−	1.82678i	1.11867	−	0.645864i	0.177609	−	0.984101i	$-0.443164\pi$
$2$	3.16408	−	1.82678i	1.11867	−	0.645864i	0.941061	+	0.338237i	$0.109830\pi$
$3$		0			0
$3$		0			0
$4$	2.67425	−	4.63194i	0.334282	−	0.578993i
$5$	8.69951	+	15.0680i	0.778108	+	1.34772i	0.933031	+	0.359796i	$0.117154\pi$
$5$	8.69951	+	15.0680i	0.778108	+	1.34772i	−0.154923	+	0.987926i	$0.549513\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			9.68739i			0.428126i
$9$		0			0
$10$	55.0518	+	31.7842i	1.74089	+	1.00510i
$11$	−28.2021	−	16.2825i	−0.773024	−	0.446306i	0.0609281	−	0.998142i	$-0.480594\pi$
$11$	−28.2021	−	16.2825i	−0.773024	−	0.446306i	−0.833952	+	0.551836i	$0.813927\pi$
$12$		0			0
$13$			42.4779i			0.906250i	0.891447	+	0.453125i	$0.149691\pi$
$13$			42.4779i			0.906250i	−0.891447	+	0.453125i	$0.850309\pi$
$14$		0			0
$15$		0			0
$16$	39.0908	+	67.7072i	0.610793	+	1.05792i
$17$	42.8181	−	74.1631i	0.610878	−	1.05807i	−0.380215	−	0.924898i	$-0.624150\pi$
$17$	42.8181	−	74.1631i	0.610878	−	1.05807i	0.991093	−	0.133173i	$-0.0425166\pi$
$18$		0			0
$19$	−59.9133	+	34.5910i	−0.723424	+	0.417669i	−0.816012	−	0.578035i	$-0.803820\pi$
$19$	−59.9133	+	34.5910i	−0.723424	+	0.417669i	0.0925874	+	0.995705i	$0.470486\pi$
$20$	93.0588			1.04043
$21$		0			0
$22$	−118.978			−1.15301
$23$	−144.644	+	83.5101i	−1.31132	+	0.757089i	−0.982314	−	0.187240i	$-0.940046\pi$
$23$	−144.644	+	83.5101i	−1.31132	+	0.757089i	−0.329003	+	0.944329i	$0.606713\pi$
$24$		0			0
$25$	−88.8629	+	153.915i	−0.710903	+	1.23132i
$26$	77.5978	+	134.403i	0.585315	+	1.01379i
$27$		0			0
$28$		0			0
$29$			254.270i			1.62817i	0.580748	+	0.814083i	$0.302760\pi$
$29$			254.270i			1.62817i	−0.580748	+	0.814083i	$0.697240\pi$
$30$		0			0
$31$	281.837	+	162.719i	1.63288	+	0.942745i	0.983198	+	0.182542i	$0.0584324\pi$
$31$	281.837	+	162.719i	1.63288	+	0.942745i	0.649685	+	0.760204i	$0.274901\pi$
$32$	180.256	+	104.071i	0.995784	+	0.574916i
$33$		0			0
$34$		−	312.877i		−	1.57818i
$35$		0			0
$36$		0			0
$37$	−172.833	−	299.355i	−0.767934	−	1.33010i	−0.938681	−	0.344786i	$-0.887951\pi$
$37$	−172.833	−	299.355i	−0.767934	−	1.33010i	0.170747	−	0.985315i	$-0.445382\pi$
$38$	−126.380	+	218.897i	−0.539515	+	0.934468i
$39$		0			0
$40$	−145.970	+	84.2756i	−0.576995	+	0.333128i
$41$	182.210			0.694058			0.347029	−	0.937854i	$-0.387191\pi$
$41$	182.210			0.694058			0.347029	+	0.937854i	$0.387191\pi$
$42$		0			0
$43$	140.292			0.497542			0.248771	−	0.968562i	$-0.419973\pi$
$43$	140.292			0.497542			0.248771	+	0.968562i	$0.419973\pi$
$44$	−150.839	+	87.0871i	−0.516816	+	0.298384i
$45$		0			0
$46$	−305.109	+	528.464i	−0.977954	+	1.69387i
$47$	−21.5007	−	37.2404i	−0.0667278	−	0.115576i	0.830731	−	0.556674i	$-0.187923\pi$
$47$	−21.5007	−	37.2404i	−0.0667278	−	0.115576i	−0.897459	+	0.441098i	$0.854589\pi$
$48$		0			0
$49$		0			0
$50$			649.332i			1.83659i
$51$		0			0
$52$	196.755	+	113.597i	0.524712	+	0.302943i
$53$	167.182	+	96.5223i	0.433286	+	0.250158i	0.700745	−	0.713411i	$-0.252851\pi$
$53$	167.182	+	96.5223i	0.433286	+	0.250158i	−0.267460	+	0.963569i	$0.586184\pi$
$54$		0			0
$55$		−	566.600i		−	1.38910i
$56$		0			0
$57$		0			0
$58$	464.496	+	804.531i	1.05157	+	1.82138i
$59$	55.6370	−	96.3662i	0.122768	−	0.212641i	−0.798090	−	0.602538i	$-0.794156\pi$
$59$	55.6370	−	96.3662i	0.122768	−	0.212641i	0.920858	+	0.389897i	$0.127489\pi$
$60$		0			0
$61$	−78.4101	+	45.2701i	−0.164580	+	0.0950204i	−0.580028	−	0.814597i	$-0.696958\pi$
$61$	−78.4101	+	45.2701i	−0.164580	+	0.0950204i	0.415448	+	0.909617i	$0.363625\pi$
$62$	1189.00			2.43554
$63$		0			0
$64$	135.007			0.263685
$65$	−640.057	+	369.537i	−1.22137	+	0.705160i
$66$		0			0
$67$	524.458	−	908.388i	0.956310	−	1.65638i	0.224968	−	0.974366i	$-0.427772\pi$
$67$	524.458	−	908.388i	0.956310	−	1.65638i	0.731342	−	0.682011i	$-0.238895\pi$
$68$	−229.013	−	396.662i	−0.408410	−	0.707387i
$69$		0			0
$70$		0			0
$71$		−	464.023i		−	0.775626i	−0.921738	−	0.387813i	$-0.873231\pi$
$71$		−	464.023i		−	0.775626i	0.921738	−	0.387813i	$-0.126769\pi$
$72$		0			0
$73$	158.297	+	91.3925i	0.253797	+	0.146530i	0.621502	−	0.783413i	$-0.286523\pi$
$73$	158.297	+	91.3925i	0.253797	+	0.146530i	−0.367704	+	0.929943i	$0.619856\pi$
$74$	−1093.71	−	631.456i	−1.71813	−	0.991963i
$75$		0			0
$76$			370.020i			0.558477i
$77$		0			0
$78$		0			0
$79$	119.473	+	206.934i	0.170149	+	0.294707i	0.938472	−	0.345356i	$-0.112242\pi$
$79$	119.473	+	206.934i	0.170149	+	0.294707i	−0.768323	+	0.640063i	$0.778908\pi$
$80$	−680.141	+	1178.04i	−0.950526	+	1.64636i
$81$		0			0
$82$	576.526	−	332.857i	0.776422	−	0.448267i
$83$	375.260			0.496267			0.248134	−	0.968726i	$-0.420183\pi$
$83$	375.260			0.496267			0.248134	+	0.968726i	$0.420183\pi$
$84$		0			0
$85$	1489.99			1.90131
$86$	443.894	−	256.282i	0.556585	−	0.321345i
$87$		0			0
$88$	157.735	−	273.205i	0.191075	−	0.330952i
$89$	719.823	+	1246.77i	0.857315	+	1.48491i	0.874480	+	0.485061i	$0.161203\pi$
$89$	719.823	+	1246.77i	0.857315	+	1.48491i	−0.0171652	+	0.999853i	$0.505464\pi$
$90$		0			0
$91$		0			0
$92$			893.308i			1.01232i
$93$		0			0
$94$	−136.060	−	78.5542i	−0.149293	−	0.0861942i
$95$	−1042.43	−	601.849i	−1.12580	−	0.649983i
$96$		0			0
$97$		−	638.698i		−	0.668556i	−0.942474	−	0.334278i	$-0.891508\pi$
$97$		−	638.698i		−	0.668556i	0.942474	−	0.334278i	$-0.108492\pi$
$98$		0			0
$99$		0			0
$100$	475.284	+	823.216i	0.475284	+	0.823216i
$101$	−525.820	+	910.748i	−0.518031	+	0.897255i	0.481750	+	0.876309i	$0.340001\pi$
$101$	−525.820	+	910.748i	−0.518031	+	0.897255i	−0.999781	+	0.0209465i	$0.993332\pi$
$102$		0			0
$103$	950.302	−	548.657i	0.909088	−	0.524862i	0.0289505	−	0.999581i	$-0.490783\pi$
$103$	950.302	−	548.657i	0.909088	−	0.524862i	0.880138	+	0.474719i	$0.157450\pi$
$104$	−411.500			−0.387989
$105$		0			0
$106$	705.300			0.646272
$107$	−498.620	+	287.878i	−0.450499	+	0.260096i	−0.708041	−	0.706171i	$-0.750421\pi$
$107$	−498.620	+	287.878i	−0.450499	+	0.260096i	0.257542	+	0.966267i	$0.417087\pi$
$108$		0			0
$109$	215.291	−	372.895i	0.189185	−	0.327677i	−0.755794	−	0.654809i	$-0.772749\pi$
$109$	215.291	−	372.895i	0.189185	−	0.327677i	0.944979	+	0.327132i	$0.106082\pi$
$110$	−1035.05	−	1792.76i	−0.897168	−	1.55394i
$111$		0			0
$112$		0			0
$113$		−	583.877i		−	0.486075i	−0.970017	−	0.243038i	$-0.921856\pi$
$113$		−	583.877i		−	0.486075i	0.970017	−	0.243038i	$-0.0781438\pi$
$114$		0			0
$115$	−2516.66	−	1452.99i	−2.04069	−	1.17819i
$116$	1177.77	+	679.983i	0.942697	+	0.544266i
$117$		0			0
$118$		−	406.546i		−	0.317166i
$119$		0			0
$120$		0			0
$121$	−135.259	−	234.276i	−0.101622	−	0.176015i
$122$	−165.397	+	286.476i	−0.122741	+	0.212593i
$123$		0			0
$124$	1507.41	−	870.301i	1.09169	−	0.630285i
$125$	−917.377			−0.656422
$126$		0			0
$127$	−499.692			−0.349138			−0.174569	−	0.984645i	$-0.555853\pi$
$127$	−499.692			−0.349138			−0.174569	+	0.984645i	$0.555853\pi$
$128$	−1014.88	+	585.940i	−0.700808	+	0.404611i
$129$		0			0
$130$	−1350.13	+	2338.49i	−0.910875	+	1.57768i
$131$	−98.3602	−	170.365i	−0.0656013	−	0.113625i	0.831359	−	0.555735i	$-0.187563\pi$
$131$	−98.3602	−	170.365i	−0.0656013	−	0.113625i	−0.896961	+	0.442111i	$0.854230\pi$
$132$		0			0
$133$		0			0
$134$		−	3832.28i		−	2.47059i
$135$		0			0
$136$	718.448	+	414.796i	0.452988	+	0.261533i
$137$	335.087	+	193.462i	0.208966	+	0.120647i	0.600831	−	0.799376i	$-0.294837\pi$
$137$	335.087	+	193.462i	0.208966	+	0.120647i	−0.391865	+	0.920023i	$0.628170\pi$
$138$		0			0
$139$		−	1507.09i		−	0.919636i	−0.888013	−	0.459818i	$-0.847915\pi$
$139$		−	1507.09i		−	0.919636i	0.888013	−	0.459818i	$-0.152085\pi$
$140$		0			0
$141$		0			0
$142$	−847.669	−	1468.21i	−0.500949	−	0.867669i
$143$	691.647	−	1197.97i	0.404465	−	0.700553i
$144$		0			0
$145$	−3831.34	+	2212.03i	−2.19432	+	1.26689i
$146$	667.816			0.378554
$147$		0			0
$148$	−1848.80			−1.02683
$149$	1282.41	−	740.402i	0.705097	−	0.407088i	−0.104146	−	0.994562i	$-0.533211\pi$
$149$	1282.41	−	740.402i	0.705097	−	0.407088i	0.809243	+	0.587474i	$0.199878\pi$
$150$		0			0
$151$	1338.67	−	2318.64i	0.721453	−	1.24959i	−0.238964	−	0.971028i	$-0.576808\pi$
$151$	1338.67	−	2318.64i	0.721453	−	1.24959i	0.960417	−	0.278565i	$-0.0898587\pi$
$152$	−335.096	−	580.404i	−0.178815	−	0.309717i
$153$		0			0
$154$		0			0
$155$			5662.28i			2.93423i
$156$		0			0
$157$	−1108.46	−	639.967i	−0.563468	−	0.325318i	0.191068	−	0.981577i	$-0.438805\pi$
$157$	−1108.46	−	639.967i	−0.563468	−	0.325318i	−0.754536	+	0.656259i	$0.772138\pi$
$158$	756.045	+	436.503i	0.380682	+	0.219787i
$159$		0			0
$160$			3621.46i			1.78939i
$161$		0			0
$162$		0			0
$163$	−897.930	−	1555.26i	−0.431481	−	0.747346i	0.565521	−	0.824734i	$-0.308675\pi$
$163$	−897.930	−	1555.26i	−0.431481	−	0.747346i	−0.997001	+	0.0773881i	$0.975342\pi$
$164$	487.275	−	843.985i	0.232011	−	0.401855i
$165$		0			0
$166$	1187.35	−	685.518i	0.555159	−	0.320521i
$167$	−3546.20			−1.64319			−0.821596	−	0.570070i	$-0.806916\pi$
$167$	−3546.20			−1.64319			−0.821596	+	0.570070i	$0.806916\pi$
$168$		0			0
$169$	392.629			0.178711
$170$	4714.43	−	2721.88i	2.12694	−	1.22799i
$171$		0			0
$172$	375.176	−	649.824i	0.166319	−	0.288073i
$173$	1928.35	+	3339.99i	0.847453	+	1.46783i	0.883474	+	0.468481i	$0.155198\pi$
$173$	1928.35	+	3339.99i	0.847453	+	1.46783i	−0.0360207	+	0.999351i	$0.511468\pi$
$174$		0			0
$175$		0			0
$176$		−	2545.98i		−	1.09040i
$177$		0			0
$178$	4555.15	+	2629.92i	1.91811	+	1.10742i
$179$	1741.04	+	1005.19i	0.726990	+	0.419728i	0.817320	−	0.576184i	$-0.195459\pi$
$179$	1741.04	+	1005.19i	0.726990	+	0.419728i	−0.0903302	+	0.995912i	$0.528792\pi$
$180$		0			0
$181$			3081.71i			1.26554i	0.774341	+	0.632768i	$0.218081\pi$
$181$			3081.71i			1.26554i	−0.774341	+	0.632768i	$0.781919\pi$
$182$		0			0
$183$		0			0
$184$	−808.995	−	1401.22i	−0.324130	−	0.561409i
$185$	3007.12	−	5208.49i	1.19507	−	2.06992i
$186$		0			0
$187$	−2415.13	+	1394.37i	−0.944446	+	0.545276i
$188$	−229.994			−0.0892234
$189$		0			0
$190$	−4397.78			−1.67920
$191$	−877.113	+	506.401i	−0.332281	+	0.191842i	−0.656853	−	0.754018i	$-0.728113\pi$
$191$	−877.113	+	506.401i	−0.332281	+	0.191842i	0.324572	+	0.945861i	$0.394780\pi$
$192$		0			0
$193$	−722.062	+	1250.65i	−0.269301	+	0.466443i	−0.968682	−	0.248306i	$-0.920126\pi$
$193$	−722.062	+	1250.65i	−0.269301	+	0.466443i	0.699380	+	0.714750i	$0.253459\pi$
$194$	−1166.76	−	2020.89i	−0.431797	−	0.747894i
$195$		0			0
$196$		0			0
$197$		−	2503.72i		−	0.905494i	−0.891639	−	0.452747i	$-0.850444\pi$
$197$		−	2503.72i		−	0.905494i	0.891639	−	0.452747i	$-0.149556\pi$
$198$		0			0
$199$	2478.52	+	1430.97i	0.882902	+	0.509744i	0.871614	−	0.490192i	$-0.163073\pi$
$199$	2478.52	+	1430.97i	0.882902	+	0.509744i	0.0112881	+	0.999936i	$0.496407\pi$
$200$	−1491.04	−	860.850i	−0.527161	−	0.304356i
$201$		0			0
$202$			3842.23i			1.33831i
$203$		0			0
$204$		0			0
$205$	1585.14	+	2745.54i	0.540052	+	0.935398i
$206$	2004.55	−	3471.99i	0.677980	−	1.17430i
$207$		0			0
$208$	−2876.06	+	1660.49i	−0.958744	+	0.553531i
$209$	2252.91			0.745633
$210$		0			0
$211$	−4118.68			−1.34380			−0.671900	−	0.740642i	$-0.734521\pi$
$211$	−4118.68			−1.34380			−0.671900	+	0.740642i	$0.734521\pi$
$212$	894.171	−	516.250i	0.289679	−	0.167246i
$213$		0			0
$214$	−1051.78	+	1821.74i	−0.335973	+	0.581922i
$215$	1220.47	+	2113.92i	0.387141	+	0.670548i
$216$		0			0
$217$		0			0
$218$		−	1573.16i		−	0.488750i
$219$		0			0
$220$	−2624.46	−	1515.23i	−0.804276	−	0.464349i
$221$	3150.29	+	1818.82i	0.958877	+	0.553608i
$222$		0			0
$223$		−	3065.23i		−	0.920462i	−0.887799	−	0.460231i	$-0.847767\pi$
$223$		−	3065.23i		−	0.920462i	0.887799	−	0.460231i	$-0.152233\pi$
$224$		0			0
$225$		0			0
$226$	−1066.61	−	1847.43i	−0.313939	−	0.543758i
$227$	665.817	−	1153.23i	0.194678	−	0.337192i	−0.752117	−	0.659029i	$-0.770967\pi$
$227$	665.817	−	1153.23i	0.194678	−	0.337192i	0.946795	+	0.321838i	$0.104301\pi$
$228$		0			0
$229$	3480.37	−	2009.39i	1.00432	−	0.579844i	0.0947964	−	0.995497i	$-0.469780\pi$
$229$	3480.37	−	2009.39i	1.00432	−	0.579844i	0.909524	+	0.415652i	$0.136447\pi$
$230$	−10617.2			−3.04381
$231$		0			0
$232$	−2463.22			−0.697061
$233$	−1970.59	+	1137.72i	−0.554068	+	0.319891i	−0.750761	−	0.660574i	$-0.770313\pi$
$233$	−1970.59	+	1137.72i	−0.554068	+	0.319891i	0.196693	+	0.980465i	$0.436980\pi$
$234$		0			0
$235$	374.092	−	647.946i	0.103843	−	0.179861i
$236$	−297.575	−	515.415i	−0.0820783	−	0.142164i
$237$		0			0
$238$		0			0
$239$		−	1453.02i		−	0.393257i	−0.980478	−	0.196628i	$-0.937001\pi$
$239$		−	1453.02i		−	0.393257i	0.980478	−	0.196628i	$-0.0629992\pi$
$240$		0			0
$241$	−4094.00	−	2363.67i	−1.09426	−	0.631774i	−0.159556	−	0.987189i	$-0.551006\pi$
$241$	−4094.00	−	2363.67i	−1.09426	−	0.631774i	−0.934709	+	0.355415i	$0.884340\pi$
$242$	−855.942	−	494.178i	−0.227364	−	0.131268i
$243$		0			0
$244$			484.255i			0.127054i
$245$		0			0
$246$		0			0
$247$	−1469.35	−	2544.99i	−0.378513	−	0.655603i
$248$	−1576.32	+	2730.26i	−0.403614	+	0.699080i
$249$		0			0
$250$	−2902.65	+	1675.85i	−0.734319	+	0.423960i
$251$	−4674.94			−1.17562			−0.587808	−	0.809001i	$-0.700009\pi$
$251$	−4674.94			−1.17562			−0.587808	+	0.809001i	$0.700009\pi$
$252$		0			0
$253$	5439.02			1.35157
$254$	−1581.06	+	912.827i	−0.390570	+	0.225496i
$255$		0			0
$256$	−2680.79	+	4643.27i	−0.654491	+	1.13361i
$257$	2304.55	+	3991.60i	0.559354	+	0.968829i	0.997550	+	0.0699503i	$0.0222841\pi$
$257$	2304.55	+	3991.60i	0.559354	+	0.968829i	−0.438197	+	0.898879i	$0.644383\pi$
$258$		0			0
$259$		0			0
$260$			3952.94i			0.942888i
$261$		0			0
$262$	−622.438	−	359.365i	−0.146772	−	0.0847391i
$263$	2008.76	+	1159.76i	0.470971	+	0.271915i	0.716646	−	0.697437i	$-0.245676\pi$
$263$	2008.76	+	1159.76i	0.470971	+	0.271915i	−0.245675	+	0.969352i	$0.579010\pi$
$264$		0			0
$265$			3358.79i			0.778598i
$266$		0			0
$267$		0			0
$268$	−2805.07	−	4858.52i	−0.639354	−	1.10739i
$269$	−378.895	+	656.266i	−0.0858798	+	0.148748i	−0.905766	−	0.423779i	$-0.860703\pi$
$269$	−378.895	+	656.266i	−0.0858798	+	0.148748i	0.819886	+	0.572527i	$0.194037\pi$
$270$		0			0
$271$	7464.79	−	4309.80i	1.67326	−	0.966058i	0.707468	−	0.706745i	$-0.249837\pi$
$271$	7464.79	−	4309.80i	1.67326	−	0.966058i	0.965793	−	0.259312i	$-0.0834959\pi$
$272$	6695.17			1.49248
$273$		0			0
$274$	1413.65			0.311686
$275$	5012.25	−	2893.82i	1.09909	−	0.634560i
$276$		0			0
$277$	1027.82	−	1780.23i	0.222945	−	0.386151i	−0.732756	−	0.680491i	$-0.761766\pi$
$277$	1027.82	−	1780.23i	0.222945	−	0.386151i	0.955701	+	0.294340i	$0.0950998\pi$
$278$	−2753.11	−	4768.53i	−0.593960	−	1.02877i
$279$		0			0
$280$		0			0
$281$		−	235.581i		−	0.0500128i	−0.999687	−	0.0250064i	$-0.992039\pi$
$281$		−	235.581i		−	0.0500128i	0.999687	−	0.0250064i	$-0.00796062\pi$
$282$		0			0
$283$	−646.661	−	373.350i	−0.135830	−	0.0784217i	0.430545	−	0.902569i	$-0.358321\pi$
$283$	−646.661	−	373.350i	−0.135830	−	0.0784217i	−0.566375	+	0.824147i	$0.691655\pi$
$284$	−2149.33	−	1240.92i	−0.449082	−	0.259277i
$285$		0			0
$286$		−	5053.95i		−	1.04492i
$287$		0			0
$288$		0			0
$289$	−1210.28	−	2096.27i	−0.246343	−	0.426678i
$290$	−8081.78	+	13998.0i	−1.63648	+	2.83446i
$291$		0			0
$292$	846.650	−	488.814i	0.169680	−	0.0979645i
$293$	4087.13			0.814923			0.407461	−	0.913222i	$-0.366414\pi$
$293$	4087.13			0.814923			0.407461	+	0.913222i	$0.366414\pi$
$294$		0			0
$295$	1936.06			0.382108
$296$	2899.97	−	1674.30i	0.569451	−	0.328773i
$297$		0			0
$298$	2705.11	−	4685.38i	0.525847	−	0.910795i
$299$	−3547.33	−	6144.16i	−0.686112	−	1.18838i
$300$		0			0
$301$		0			0
$302$		−	9781.82i		−	1.86384i
$303$		0			0
$304$	−4684.12	−	2704.38i	−0.883725	−	0.510219i
$305$	−1364.26	−	787.655i	−0.256122	−	0.147872i
$306$		0			0
$307$		−	4572.60i		−	0.850073i	−0.905176	−	0.425036i	$-0.860261\pi$
$307$		−	4572.60i		−	0.850073i	0.905176	−	0.425036i	$-0.139739\pi$
$308$		0			0
$309$		0			0
$310$	10343.8	+	17915.9i	1.89511	+	3.28243i
$311$	4844.81	−	8391.46i	0.883357	−	1.53002i	0.0357722	−	0.999360i	$-0.488611\pi$
$311$	4844.81	−	8391.46i	0.883357	−	1.53002i	0.847585	−	0.530660i	$-0.178056\pi$
$312$		0			0
$313$	3393.45	−	1959.21i	0.612809	−	0.353805i	−0.161255	−	0.986913i	$-0.551554\pi$
$313$	3393.45	−	1959.21i	0.612809	−	0.353805i	0.774064	+	0.633108i	$0.218221\pi$
$314$	−4676.32			−0.840446
$315$		0			0
$316$	1278.01			0.227511
$317$	−7831.43	+	4521.48i	−1.38756	+	0.801109i	−0.993040	−	0.117778i	$-0.962423\pi$
$317$	−7831.43	+	4521.48i	−1.38756	+	0.801109i	−0.394522	+	0.918887i	$0.629090\pi$
$318$		0			0
$319$	4140.16	−	7170.97i	0.726660	−	1.25861i
$320$	1174.49	+	2034.28i	0.205175	+	0.355374i
$321$		0			0
$322$		0			0
$323$			5924.48i			1.02058i
$324$		0			0
$325$	−6537.99	−	3774.71i	−1.11588	−	0.644256i
$326$	−5682.24	−	3280.64i	−0.965369	−	0.557356i
$327$		0			0
$328$			1765.14i			0.297145i
$329$		0			0
$330$		0			0
$331$	1760.99	+	3050.13i	0.292426	+	0.506497i	0.974383	−	0.224896i	$-0.0722042\pi$
$331$	1760.99	+	3050.13i	0.292426	+	0.506497i	−0.681957	+	0.731392i	$0.738871\pi$
$332$	1003.54	−	1738.18i	0.165893	−	0.287335i
$333$		0			0
$334$	−11220.4	+	6478.13i	−1.83819	+	1.06128i
$335$	18250.1			2.97645
$336$		0			0
$337$	10294.0			1.66395			0.831975	−	0.554813i	$-0.187210\pi$
$337$	10294.0			1.66395			0.831975	+	0.554813i	$0.187210\pi$
$338$	1242.31	−	717.246i	0.199919	−	0.115423i
$339$		0			0
$340$	3984.60	−	6901.53i	0.635574	−	1.10085i
$341$	−5298.93	−	9178.02i	−0.841505	−	1.45753i
$342$		0			0
$343$		0			0
$344$			1359.06i			0.213011i
$345$		0			0
$346$	12202.9	+	7045.33i	1.89604	+	1.09468i
$347$	−81.7368	−	47.1908i	−0.0126451	−	0.00730067i	0.493664	−	0.869653i	$-0.335657\pi$
$347$	−81.7368	−	47.1908i	−0.0126451	−	0.00730067i	−0.506309	+	0.862352i	$0.668991\pi$
$348$		0			0
$349$			4242.54i			0.650711i	0.945592	+	0.325356i	$0.105484\pi$
$349$			4242.54i			0.650711i	−0.945592	+	0.325356i	$0.894516\pi$
$350$		0			0
$351$		0			0
$352$	−3389.07	−	5870.05i	−0.513177	−	0.888848i
$353$	−3689.08	+	6389.68i	−0.556232	+	0.963423i	0.441574	+	0.897225i	$0.354420\pi$
$353$	−3689.08	+	6389.68i	−0.556232	+	0.963423i	−0.997807	+	0.0661978i	$0.978913\pi$
$354$		0			0
$355$	6991.90	−	4036.77i	1.04533	−	0.603520i
$356$	7699.95			1.14634
$357$		0			0
$358$	7345.03			1.08435
$359$	342.175	−	197.555i	0.0503044	−	0.0290433i	−0.474637	−	0.880182i	$-0.657421\pi$
$359$	342.175	−	197.555i	0.0503044	−	0.0290433i	0.524941	+	0.851138i	$0.324087\pi$
$360$		0			0
$361$	−1036.43	+	1795.15i	−0.151105	+	0.261721i
$362$	5629.61	+	9750.78i	0.817365	+	1.41572i
$363$		0			0
$364$		0			0
$365$			3180.28i			0.456064i
$366$		0			0
$367$	3117.25	+	1799.75i	0.443377	+	0.255984i	0.705029	−	0.709179i	$-0.250934\pi$
$367$	3117.25	+	1799.75i	0.443377	+	0.255984i	−0.261652	+	0.965162i	$0.584267\pi$
$368$	−11308.5	−	6528.95i	−1.60189	−	0.924850i
$369$		0			0
$370$		−	21973.4i		−	3.08742i
$371$		0			0
$372$		0			0
$373$	4621.61	+	8004.86i	0.641549	+	1.11120i	0.985087	+	0.172057i	$0.0550412\pi$
$373$	4621.61	+	8004.86i	0.641549	+	1.11120i	−0.343538	+	0.939139i	$0.611625\pi$
$374$	−5094.43	+	8823.81i	−0.704349	+	1.21997i
$375$		0			0
$376$	360.762	−	208.286i	0.0494811	−	0.0285679i
$377$	−10800.9			−1.47553
$378$		0			0
$379$	5818.96			0.788654			0.394327	−	0.918970i	$-0.370978\pi$
$379$	5818.96			0.788654			0.394327	+	0.918970i	$0.370978\pi$
$380$	−5575.46	+	3218.99i	−0.752671	+	0.434555i
$381$		0			0
$382$	−1850.17	+	3204.58i	−0.247808	+	0.429217i
$383$	−461.324	−	799.036i	−0.0615471	−	0.106603i	0.833610	−	0.552353i	$-0.186270\pi$
$383$	−461.324	−	799.036i	−0.0615471	−	0.106603i	−0.895157	+	0.445751i	$0.852937\pi$
$384$		0			0
$385$		0			0
$386$			5276.19i			0.695728i
$387$		0			0
$388$	−2958.41	−	1708.04i	−0.387089	−	0.223486i
$389$	2021.94	+	1167.37i	0.263539	+	0.152154i	0.625948	−	0.779865i	$-0.284712\pi$
$389$	2021.94	+	1167.37i	0.263539	+	0.152154i	−0.362409	+	0.932019i	$0.618046\pi$
$390$		0			0
$391$			14303.0i			1.84996i
$392$		0			0
$393$		0			0
$394$	−4573.74	−	7921.95i	−0.584827	−	1.01295i
$395$	−2078.72	+	3600.44i	−0.264789	+	0.458628i
$396$		0			0
$397$	4496.41	−	2596.00i	0.568434	−	0.328186i	−0.188089	−	0.982152i	$-0.560229\pi$
$397$	4496.41	−	2596.00i	0.568434	−	0.328186i	0.756524	+	0.653966i	$0.226896\pi$
$398$	10456.3			1.31690
$399$		0			0
$400$	−13894.9			−1.73686
$401$	2755.18	−	1590.70i	0.343110	−	0.198094i	−0.318537	−	0.947911i	$-0.603191\pi$
$401$	2755.18	−	1590.70i	0.343110	−	0.198094i	0.661646	+	0.749816i	$0.269858\pi$
$402$		0			0
$403$	−6911.94	+	11971.8i	−0.854363	+	1.47980i
$404$	2812.35	+	4871.14i	0.346336	+	0.599872i
$405$		0			0
$406$		0			0
$407$			11256.6i			1.37093i
$408$		0			0
$409$	6626.29	+	3825.69i	0.801097	+	0.462514i	0.843855	−	0.536572i	$-0.180281\pi$
$409$	6626.29	+	3825.69i	0.801097	+	0.462514i	−0.0427573	+	0.999085i	$0.513614\pi$
$410$	10031.0	+	5791.39i	1.20828	+	0.697601i
$411$		0			0
$412$		−	5868.99i		−	0.701807i
$413$		0			0
$414$		0			0
$415$	3264.58	+	5654.42i	0.386149	+	0.668830i
$416$	−4420.71	+	7656.90i	−0.521018	+	0.902429i
$417$		0			0
$418$	7128.39	−	4115.58i	0.834117	−	0.481578i
$419$	1033.91			0.120548			0.0602740	−	0.998182i	$-0.480803\pi$
$419$	1033.91			0.120548			0.0602740	+	0.998182i	$0.480803\pi$
$420$		0			0
$421$	−10640.4			−1.23178			−0.615890	−	0.787832i	$-0.711204\pi$
$421$	−10640.4			−1.23178			−0.615890	+	0.787832i	$0.711204\pi$
$422$	−13031.8	+	7523.92i	−1.50327	+	0.867912i
$423$		0			0
$424$	−935.049	+	1619.55i	−0.107099	+	0.185501i
$425$	7609.88	+	13180.7i	0.868550	+	1.50437i
$426$		0			0
$427$		0			0
$428$			3079.44i			0.347781i
$429$		0			0
$430$	7723.32	+	4459.06i	0.866167	+	0.500081i
$431$	9787.74	+	5650.95i	1.09387	+	0.631547i	0.934605	−	0.355688i	$-0.115754\pi$
$431$	9787.74	+	5650.95i	1.09387	+	0.631547i	0.159267	+	0.987236i	$0.449087\pi$
$432$		0			0
$433$		−	8291.73i		−	0.920266i	−0.887850	−	0.460133i	$-0.847802\pi$
$433$		−	8291.73i		−	0.920266i	0.887850	−	0.460133i	$-0.152198\pi$
$434$		0			0
$435$		0			0
$436$	−1151.48	−	1994.43i	−0.126482	−	0.219073i
$437$	5777.39	−	10006.7i	0.632426	−	1.09539i
$438$		0			0
$439$	−12765.0	+	7369.87i	−1.38779	+	0.801241i	−0.993066	−	0.117559i	$-0.962493\pi$
$439$	−12765.0	+	7369.87i	−1.38779	+	0.801241i	−0.394724	+	0.918800i	$0.629160\pi$
$440$	5488.87			0.594709
$441$		0			0
$442$	13290.4			1.43022
$443$	−10389.7	+	5998.49i	−1.11429	+	0.643334i	−0.939936	−	0.341349i	$-0.889116\pi$
$443$	−10389.7	+	5998.49i	−1.11429	+	0.643334i	−0.174351	+	0.984684i	$0.555783\pi$
$444$		0			0
$445$	−12524.2	+	21692.6i	−1.33417	+	2.31085i
$446$	−5599.50	−	9698.62i	−0.594494	−	1.02969i
$447$		0			0
$448$		0			0
$449$			3457.16i			0.363371i	0.983357	+	0.181685i	$0.0581552\pi$
$449$			3457.16i			0.363371i	−0.983357	+	0.181685i	$0.941845\pi$
$450$		0			0
$451$	−5138.71	−	2966.83i	−0.536524	−	0.309762i
$452$	−2704.48	−	1561.43i	−0.281434	−	0.162486i
$453$		0			0
$454$		−	4865.21i		−	0.502941i
$455$		0			0
$456$		0			0
$457$	1080.86	+	1872.11i	0.110636	+	0.191627i	0.916027	−	0.401117i	$-0.131378\pi$
$457$	1080.86	+	1872.11i	0.110636	+	0.191627i	−0.805391	+	0.592744i	$0.798045\pi$
$458$	7341.44	−	12715.7i	0.749002	−	1.29731i
$459$		0			0
$460$	−13460.4	+	7771.34i	−1.36433	+	0.787697i
$461$	1097.92			0.110923			0.0554613	−	0.998461i	$-0.482337\pi$
$461$	1097.92			0.110923			0.0554613	+	0.998461i	$0.482337\pi$
$462$		0			0
$463$	−9514.27			−0.955001			−0.477501	−	0.878631i	$-0.658457\pi$
$463$	−9514.27			−0.955001			−0.477501	+	0.878631i	$0.658457\pi$
$464$	−17215.9	+	9939.62i	−1.72248	+	0.994473i
$465$		0			0
$466$	−4156.74	+	7199.68i	−0.413213	+	0.715706i
$467$	−851.569	−	1474.96i	−0.0843810	−	0.146152i	0.820746	−	0.571293i	$-0.193558\pi$
$467$	−851.569	−	1474.96i	−0.0843810	−	0.146152i	−0.905127	+	0.425141i	$0.860225\pi$
$468$		0			0
$469$		0			0
$470$		−	2733.53i		−	0.268273i
$471$		0			0
$472$	933.537	+	538.978i	0.0910371	+	0.0525603i
$473$	−3956.53	−	2284.30i	−0.384612	−	0.222056i
$474$		0			0
$475$		−	12295.4i		−	1.18769i
$476$		0			0
$477$		0			0
$478$	−2654.36	−	4597.48i	−0.253990	−	0.439924i
$479$	2077.11	−	3597.66i	0.198133	−	0.343176i	−0.749790	−	0.661676i	$-0.769846\pi$
$479$	2077.11	−	3597.66i	0.198133	−	0.343176i	0.947923	+	0.318500i	$0.103179\pi$
$480$		0			0
$481$	12716.0	−	7341.58i	1.20540	−	0.695940i
$482$	−17271.6			−1.63216
$483$		0			0
$484$	−1446.87			−0.135882
$485$	9623.90	−	5556.36i	0.901028	−	0.520209i
$486$		0			0
$487$	9593.66	−	16616.7i	0.892670	−	1.54615i	0.0560070	−	0.998430i	$-0.482163\pi$
$487$	9593.66	−	16616.7i	0.892670	−	1.54615i	0.836663	−	0.547719i	$-0.184504\pi$
$488$	−438.549	−	759.590i	−0.0406807	−	0.0704611i
$489$		0			0
$490$		0			0
$491$		−	4090.61i		−	0.375981i	−0.982171	−	0.187990i	$-0.939803\pi$
$491$		−	4090.61i		−	0.375981i	0.982171	−	0.187990i	$-0.0601973\pi$
$492$		0			0
$493$	18857.5	+	10887.4i	1.72272	+	0.994610i
$494$	−9298.28	−	5368.37i	−0.846862	−	0.488936i
$495$		0			0
$496$			25443.2i			2.30329i
$497$		0			0
$498$		0			0
$499$	584.959	+	1013.18i	0.0524777	+	0.0908940i	0.891071	−	0.453864i	$-0.149955\pi$
$499$	584.959	+	1013.18i	0.0524777	+	0.0908940i	−0.838593	+	0.544758i	$0.816621\pi$
$500$	−2453.30	+	4249.24i	−0.219430	+	0.380064i
$501$		0			0
$502$	−14791.9	+	8540.09i	−1.31513	+	0.759288i
$503$	12774.4			1.13237			0.566187	−	0.824277i	$-0.308418\pi$
$503$	12774.4			1.13237			0.566187	+	0.824277i	$0.308418\pi$
$504$		0			0
$505$	−18297.5			−1.61233
$506$	17209.5	−	9935.89i	1.51196	−	0.872933i
$507$		0			0
$508$	−1336.30	+	2314.54i	−0.116710	+	0.202148i
$509$	6147.19	+	10647.3i	0.535304	+	0.927173i	0.999149	+	0.0412568i	$0.0131362\pi$
$509$	6147.19	+	10647.3i	0.535304	+	0.927173i	−0.463845	+	0.885916i	$0.653531\pi$
$510$		0			0
$511$		0			0
$512$			10213.8i			0.881626i
$513$		0			0
$514$	14583.6	+	8419.82i	1.25146	+	0.722534i
$515$	16534.3	+	9546.10i	1.41474	+	0.816799i
$516$		0			0
$517$			1400.34i			0.119124i
$518$		0			0
$519$		0			0
$520$	−3579.85	−	6200.48i	−0.301898	−	0.522902i
$521$	−3135.60	+	5431.01i	−0.263672	+	0.456693i	−0.967215	−	0.253960i	$-0.918267\pi$
$521$	−3135.60	+	5431.01i	−0.263672	+	0.456693i	0.703543	+	0.710653i	$0.251600\pi$
$522$		0			0
$523$	−15011.3	+	8666.77i	−1.25506	+	0.724611i	−0.972111	−	0.234523i	$-0.924647\pi$
$523$	−15011.3	+	8666.77i	−1.25506	+	0.724611i	−0.282953	+	0.959134i	$0.591314\pi$
$524$	−1052.16			−0.0877173
$525$		0			0
$526$	8474.48			0.702481
$527$	24135.4	−	13934.6i	1.99498	−	1.15180i
$528$		0			0
$529$	7864.36	−	13621.5i	0.646368	−	1.11954i
$530$	6135.76	+	10627.5i	0.502869	+	0.870995i
$531$		0			0
$532$		0			0
$533$			7739.89i			0.628990i
$534$		0			0
$535$	−8675.49	−	5008.80i	−0.701073	−	0.404765i
$536$	8799.91	+	5080.63i	0.709139	+	0.409421i
$537$		0			0
$538$			2768.63i			0.221867i
$539$		0			0
$540$		0			0
$541$	2818.70	+	4882.14i	0.224003	+	0.387984i	0.956020	−	0.293302i	$-0.0947542\pi$
$541$	2818.70	+	4882.14i	0.224003	+	0.387984i	−0.732017	+	0.681286i	$0.761421\pi$
$542$	15746.1	−	27273.1i	1.24788	−	2.16140i
$543$		0			0
$544$	15436.5	−	8912.24i	1.21660	−	0.702407i
$545$	7491.70			0.588824
$546$		0			0
$547$	12354.9			0.965733			0.482867	−	0.875694i	$-0.339596\pi$
$547$	12354.9			0.965733			0.482867	+	0.875694i	$0.339596\pi$
$548$	1792.21	−	1034.73i	0.139707	−	0.0806600i
$549$		0			0
$550$	10572.8	−	18312.6i	0.819680	−	1.41973i
$551$	−8795.46	−	15234.2i	−0.680035	−	1.17786i
$552$		0			0
$553$		0			0
$554$		−	7510.40i		−	0.575968i
$555$		0			0
$556$	−6980.73	−	4030.33i	−0.532462	−	0.307417i
$557$	−6629.06	−	3827.29i	−0.504277	−	0.291145i	0.226201	−	0.974081i	$-0.427369\pi$
$557$	−6629.06	−	3827.29i	−0.504277	−	0.291145i	−0.730478	+	0.682936i	$0.760703\pi$
$558$		0			0
$559$			5959.30i			0.450897i
$560$		0			0
$561$		0			0
$562$	−430.356	−	745.398i	−0.0323015	−	0.0559479i
$563$	−5336.69	+	9243.42i	−0.399493	+	0.691943i	−0.993663	−	0.112397i	$-0.964147\pi$
$563$	−5336.69	+	9243.42i	−0.399493	+	0.691943i	0.594170	+	0.804339i	$0.297481\pi$
$564$		0			0
$565$	8797.85	−	5079.44i	0.655094	−	0.378219i
$566$	−2728.11			−0.202599
$567$		0			0
$568$	4495.18			0.332066
$569$	−3794.92	+	2191.00i	−0.279598	+	0.161426i	−0.633241	−	0.773954i	$-0.718276\pi$
$569$	−3794.92	+	2191.00i	−0.279598	+	0.161426i	0.353643	+	0.935380i	$0.384943\pi$
$570$		0			0
$571$	−11932.5	+	20667.7i	−0.874536	+	1.51474i	−0.0172793	+	0.999851i	$0.505500\pi$
$571$	−11932.5	+	20667.7i	−0.874536	+	1.51474i	−0.857256	+	0.514890i	$0.827833\pi$
$572$	−3699.28	−	6407.34i	−0.270410	−	0.468364i
$573$		0			0
$574$		0			0
$575$		−	29683.8i		−	2.15287i
$576$		0			0
$577$	−11184.0	−	6457.10i	−0.806927	−	0.465879i	0.0389606	−	0.999241i	$-0.487595\pi$
$577$	−11184.0	−	6457.10i	−0.806927	−	0.465879i	−0.845888	+	0.533361i	$0.820929\pi$
$578$	−7658.85	−	4421.84i	−0.551152	−	0.318208i
$579$		0			0
$580$			23662.1i			1.69399i
$581$		0			0
$582$		0			0
$583$	−3143.25	−	5444.27i	−0.223294	−	0.386756i
$584$	−885.355	+	1533.48i	−0.0627333	+	0.108657i
$585$		0			0
$586$	12932.0	−	7466.28i	0.911630	−	0.526330i
$587$	−17218.9			−1.21074			−0.605368	−	0.795946i	$-0.706974\pi$
$587$	−17218.9			−1.21074			−0.605368	+	0.795946i	$0.706974\pi$
$588$		0			0
$589$	−22514.4			−1.57502
$590$	6125.84	−	3536.75i	0.427452	−	0.246790i
$591$		0			0
$592$	13512.3	−	23404.1i	0.938098	−	1.62483i
$593$	−5329.24	−	9230.51i	−0.369048	−	0.639210i	0.620369	−	0.784310i	$-0.286983\pi$
$593$	−5329.24	−	9230.51i	−0.369048	−	0.639210i	−0.989417	+	0.145100i	$0.953650\pi$
$594$		0			0
$595$		0			0
$596$		−	7920.09i		−	0.544328i
$597$		0			0
$598$	−22448.1	−	12960.4i	−1.53507	−	0.886271i
$599$	−18294.9	−	10562.6i	−1.24793	−	0.720493i	−0.277235	−	0.960802i	$-0.589418\pi$
$599$	−18294.9	−	10562.6i	−1.24793	−	0.720493i	−0.970696	+	0.240309i	$0.922751\pi$
$600$		0			0
$601$			10924.1i			0.741434i	0.928746	+	0.370717i	$0.120888\pi$
$601$			10924.1i			0.741434i	−0.928746	+	0.370717i	$0.879112\pi$
$602$		0			0
$603$		0			0
$604$	−7159.88	−	12401.3i	−0.482337	−	0.835432i
$605$	2353.38	−	4076.17i	0.158146	−	0.273917i
$606$		0			0
$607$	−16390.1	+	9462.85i	−1.09597	+	0.632760i	−0.935160	−	0.354225i	$-0.884745\pi$
$607$	−16390.1	+	9462.85i	−1.09597	+	0.632760i	−0.160812	+	0.986985i	$0.551411\pi$
$608$	−14399.7			−0.960499
$609$		0			0
$610$	−5755.49			−0.382022
$611$	1581.89	−	913.306i	0.104741	−	0.0604720i
$612$		0			0
$613$	7265.64	−	12584.5i	0.478722	−	0.829171i	−0.520980	−	0.853569i	$-0.674434\pi$
$613$	7265.64	−	12584.5i	0.478722	−	0.829171i	0.999702	+	0.0243980i	$0.00776691\pi$
$614$	−8353.14	−	14468.1i	−0.549032	−	0.950951i
$615$		0			0
$616$		0			0
$617$		−	2146.97i		−	0.140087i	−0.997544	−	0.0700435i	$-0.977686\pi$
$617$		−	2146.97i		−	0.140087i	0.997544	−	0.0700435i	$-0.0223138\pi$
$618$		0			0
$619$	−17385.5	−	10037.5i	−1.12889	−	0.651764i	−0.185233	−	0.982695i	$-0.559304\pi$
$619$	−17385.5	−	10037.5i	−1.12889	−	0.651764i	−0.943655	+	0.330930i	$0.892637\pi$
$620$	26227.4	+	15142.4i	1.69890	+	0.980859i
$621$		0			0
$622$		−	35401.6i		−	2.28212i
$623$		0			0
$624$		0			0
$625$	3127.13	+	5416.35i	0.200136	+	0.346646i
$626$	7158.09	−	12398.2i	0.457020	−	0.791583i
$627$		0			0
$628$	−5928.58	+	3422.87i	−0.376714	+	0.217496i
$629$	−29601.5			−1.87645
$630$		0			0
$631$	22589.8			1.42518			0.712589	−	0.701582i	$-0.247523\pi$
$631$	22589.8			1.42518			0.712589	+	0.701582i	$0.247523\pi$
$632$	−2004.65	+	1157.38i	−0.126172	+	0.0728454i
$633$		0			0
$634$	−16519.5	+	28612.6i	−1.03482	+	1.79235i
$635$	−4347.07	−	7529.35i	−0.271667	−	0.470541i
$636$		0			0
$637$		0			0
$638$		−	30252.7i		−	1.87730i
$639$		0			0
$640$	−17657.9	−	10194.8i	−1.09061	−	0.629663i
$641$	−15222.1	−	8788.47i	−0.937966	−	0.541535i	−0.0486438	−	0.998816i	$-0.515490\pi$
$641$	−15222.1	−	8788.47i	−0.937966	−	0.541535i	−0.889322	+	0.457281i	$0.848823\pi$
$642$		0			0
$643$			2583.33i			0.158439i	0.996857	+	0.0792197i	$0.0252429\pi$
$643$			2583.33i			0.158439i	−0.996857	+	0.0792197i	$0.974757\pi$
$644$		0			0
$645$		0			0
$646$	10822.7	+	18745.5i	0.659156	+	1.14169i
$647$	−13426.8	+	23255.8i	−0.815859	+	1.41311i	0.0928511	+	0.995680i	$0.470402\pi$
$647$	−13426.8	+	23255.8i	−0.815859	+	1.41311i	−0.908710	+	0.417429i	$0.862931\pi$
$648$		0			0
$649$	−3138.17	+	1811.82i	−0.189806	+	0.109584i
$650$	−27582.3			−1.66441
$651$		0			0
$652$	−9605.17			−0.576944
$653$	−21952.2	+	12674.1i	−1.31555	+	0.759533i	−0.983009	−	0.183556i	$-0.941239\pi$
$653$	−21952.2	+	12674.1i	−1.31555	+	0.759533i	−0.332541	+	0.943089i	$0.607906\pi$
$654$		0			0
$655$	1711.37	−	2964.18i	0.102090	−	0.176825i
$656$	7122.72	+	12336.9i	0.423926	+	0.734261i
$657$		0			0
$658$		0			0
$659$		−	16599.6i		−	0.981225i	−0.871378	−	0.490612i	$-0.836773\pi$
$659$		−	16599.6i		−	0.981225i	0.871378	−	0.490612i	$-0.163227\pi$
$660$		0			0
$661$	−5798.26	−	3347.63i	−0.341189	−	0.196986i	0.319608	−	0.947550i	$-0.396449\pi$
$661$	−5798.26	−	3347.63i	−0.341189	−	0.196986i	−0.660798	+	0.750564i	$0.729782\pi$
$662$	11143.8	+	6433.90i	0.654256	+	0.377735i
$663$		0			0
$664$			3635.29i			0.212465i
$665$		0			0
$666$		0			0
$667$	−21234.1	−	36778.6i	−1.23267	−	2.13504i
$668$	−9483.43	+	16425.8i	−0.549289	+	0.951397i
$669$		0			0
$670$	57744.8	−	33339.0i	3.32966	−	1.92238i
$671$	2948.45			0.169633
$672$		0			0
$673$	10886.2			0.623524			0.311762	−	0.950160i	$-0.399081\pi$
$673$	10886.2			0.623524			0.311762	+	0.950160i	$0.399081\pi$
$674$	32571.1	−	18804.9i	1.86141	−	1.07469i
$675$		0			0
$676$	1049.99	−	1818.63i	0.0597399	−	0.103473i
$677$	9787.65	+	16952.7i	0.555643	+	0.962401i	0.997853	+	0.0654900i	$0.0208610\pi$
$677$	9787.65	+	16952.7i	0.555643	+	0.962401i	−0.442211	+	0.896911i	$0.645806\pi$
$678$		0			0
$679$		0			0
$680$			14434.1i			0.814003i
$681$		0			0
$682$	−33532.5	−	19360.0i	−1.88273	−	1.08700i
$683$	10304.8	+	5949.51i	0.577312	+	0.333311i	0.760064	−	0.649848i	$-0.225167\pi$
$683$	10304.8	+	5949.51i	0.577312	+	0.333311i	−0.182753	+	0.983159i	$0.558501\pi$
$684$		0			0
$685$			6732.11i			0.375505i
$686$		0			0
$687$		0			0
$688$	5484.11	+	9498.77i	0.303895	+	0.526362i
$689$	−4100.06	+	7101.52i	−0.226705	+	0.392665i
$690$		0			0
$691$	15656.8	−	9039.47i	0.861959	−	0.497652i	−0.00270894	−	0.999996i	$-0.500862\pi$
$691$	15656.8	−	9039.47i	0.861959	−	0.497652i	0.864668	+	0.502344i	$0.167529\pi$
$692$	20627.5			1.13315
$693$		0			0
$694$	−344.829			−0.0188610
$695$	22708.8	−	13110.9i	1.23941	−	0.715576i
$696$		0			0
$697$	7801.88	−	13513.2i	0.423985	−	0.734363i
$698$	7750.20	+	13423.7i	0.420271	+	0.727931i
$699$		0			0
$700$		0			0
$701$		−	11922.5i		−	0.642378i	−0.947015	−	0.321189i	$-0.895918\pi$
$701$		−	11922.5i		−	0.642378i	0.947015	−	0.321189i	$-0.104082\pi$
$702$		0			0
$703$	20710.0	+	11956.9i	1.11108	+	0.641485i
$704$	−3807.47	−	2198.25i	−0.203835	−	0.117684i
$705$		0			0
$706$			26956.6i			1.43700i
$707$		0			0
$708$		0			0
$709$	−12805.2	−	22179.3i	−0.678294	−	1.17484i	−0.975494	−	0.220024i	$-0.929386\pi$
$709$	−12805.2	−	22179.3i	−0.678294	−	1.17484i	0.297201	−	0.954815i	$-0.403947\pi$
$710$	14748.6	−	25545.3i	0.779585	−	1.35028i
$711$		0			0
$712$	−12077.9	+	6973.21i	−0.635731	+	0.367039i
$713$	−54354.5			−2.85497
$714$		0			0
$715$	24068.0			1.25887
$716$	9311.94	−	5376.25i	0.486039	−	0.280615i
$717$		0			0
$718$	721.778	−	1250.16i	0.0375160	−	0.0649797i
$719$	−6776.95	−	11738.0i	−0.351513	−	0.608838i	0.635002	−	0.772510i	$-0.280999\pi$
$719$	−6776.95	−	11738.0i	−0.351513	−	0.608838i	−0.986515	+	0.163673i	$0.947666\pi$
$720$		0			0
$721$		0			0
$722$			7573.30i			0.390373i
$723$		0			0
$724$	14274.3	+	8241.28i	0.732736	+	0.423045i
$725$	−39136.0	−	22595.2i	−2.00479	−	1.15747i
$726$		0			0
$727$		−	6238.21i		−	0.318243i	−0.987259	−	0.159121i	$-0.949134\pi$
$727$		−	6238.21i		−	0.318243i	0.987259	−	0.159121i	$-0.0508661\pi$
$728$		0			0
$729$		0			0
$730$	5809.67	+	10062.7i	0.294556	+	0.510186i
$731$	6007.03	−	10404.5i	0.303937	−	0.526435i
$732$		0			0
$733$	2753.40	−	1589.68i	0.138744	−	0.0801038i	−0.429021	−	0.903294i	$-0.641141\pi$
$733$	2753.40	−	1589.68i	0.138744	−	0.0801038i	0.567765	+	0.823191i	$0.307808\pi$
$734$	13151.0			0.661323
$735$		0			0
$736$	−34763.9			−1.74105
$737$	−29581.7	+	17079.0i	−1.47850	+	0.853613i
$738$		0			0
$739$	−1397.08	+	2419.81i	−0.0695431	+	0.120452i	−0.898700	−	0.438563i	$-0.855487\pi$
$739$	−1397.08	+	2419.81i	−0.0695431	+	0.120452i	0.829157	+	0.559016i	$0.188821\pi$
$740$	−16083.6	−	27857.6i	−0.798981	−	1.38387i
$741$		0			0
$742$		0			0
$743$			8539.68i			0.421656i	0.977523	+	0.210828i	$0.0676160\pi$
$743$			8539.68i			0.421656i	−0.977523	+	0.210828i	$0.932384\pi$
$744$		0			0
$745$	22312.8	+	12882.3i	1.09728	+	0.633517i
$746$	29246.2	+	16885.3i	1.43536	+	0.828707i
$747$		0			0
$748$			14915.6i			0.729103i
$749$		0			0
$750$		0			0
$751$	14409.2	+	24957.4i	0.700130	+	1.21266i	0.968420	+	0.249323i	$0.0802080\pi$
$751$	14409.2	+	24957.4i	0.700130	+	1.21266i	−0.268290	+	0.963338i	$0.586459\pi$
$752$	1680.96	−	2911.51i	0.0815137	−	0.141186i
$753$		0			0
$754$	−34174.8	+	19730.8i	−1.65063	+	0.952989i
$755$	46583.1			2.24547
$756$		0			0
$757$	−20086.6			−0.964413			−0.482206	−	0.876058i	$-0.660164\pi$
$757$	−20086.6			−0.964413			−0.482206	+	0.876058i	$0.660164\pi$
$758$	18411.6	−	10630.0i	0.882244	−	0.509364i
$759$		0			0
$760$	5830.35	−	10098.5i	0.278275	−	0.481986i
$761$	−9416.21	−	16309.3i	−0.448538	−	0.776890i	0.549753	−	0.835327i	$-0.314722\pi$
$761$	−9416.21	−	16309.3i	−0.448538	−	0.776890i	−0.998291	+	0.0584368i	$0.981388\pi$
$762$		0			0
$763$		0			0
$764$			5416.98i			0.256518i
$765$		0			0
$766$	−2919.33	−	1685.47i	−0.137702	−	0.0795022i
$767$	4093.43	+	2363.34i	0.192706	+	0.111259i
$768$		0			0
$769$		−	5882.35i		−	0.275842i	−0.990443	−	0.137921i	$-0.955958\pi$
$769$		−	5882.35i		−	0.275842i	0.990443	−	0.137921i	$-0.0440421\pi$
$770$		0			0
$771$		0			0
$772$	3861.95	+	6689.10i	0.180045	+	0.311847i
$773$	−6060.65	+	10497.4i	−0.282001	+	0.488439i	−0.971877	−	0.235487i	$-0.924331\pi$
$773$	−6060.65	+	10497.4i	−0.282001	+	0.488439i	0.689877	+	0.723927i	$0.257665\pi$
$774$		0			0
$775$	−50089.7	+	28919.3i	−2.32164	+	1.34040i
$776$	6187.32			0.286227
$777$		0			0
$778$	8530.11			0.393084
$779$	−10916.8	+	6302.81i	−0.502099	+	0.289887i
$780$		0			0
$781$	−7555.47	+	13086.5i	−0.346166	+	0.599578i
$782$	26128.4	+	45255.7i	1.19482	+	2.06949i
$783$		0			0
$784$		0			0
$785$		−	22269.6i		−	1.01253i
$786$		0			0
$787$	13342.0	+	7703.03i	0.604310	+	0.348899i	0.770735	−	0.637155i	$-0.219889\pi$
$787$	13342.0	+	7703.03i	0.604310	+	0.348899i	−0.166425	+	0.986054i	$0.553222\pi$
$788$	−11597.1	−	6695.57i	−0.524275	−	0.302690i
$789$		0			0
$790$			15189.4i			0.684071i
$791$		0			0
$792$		0			0
$793$	−1922.98	−	3330.70i	−0.0861122	−	0.149151i
$794$	9484.66	−	16427.9i	0.423927	−	0.734263i
$795$		0			0
$796$	13256.4	−	7653.57i	0.590276	−	0.340796i
$797$	12661.3			0.562716			0.281358	−	0.959603i	$-0.409215\pi$
$797$	12661.3			0.562716			0.281358	+	0.959603i	$0.409215\pi$
$798$		0			0
$799$	−3682.48			−0.163050
$800$	−32036.2	+	18496.1i	−1.41581	+	0.817419i
$801$		0			0
$802$	5811.73	−	10066.2i	0.255884	−	0.443205i
$803$	−2976.20	−	5154.93i	−0.130794	−	0.226542i
$804$		0			0
$805$		0			0
$806$			50506.4i			2.20721i
$807$		0			0
$808$	−8822.77	−	5093.83i	−0.384139	−	0.221783i
$809$	−25369.6	−	14647.1i	−1.10253	−	0.636546i	−0.165646	−	0.986185i	$-0.552971\pi$
$809$	−25369.6	−	14647.1i	−1.10253	−	0.636546i	−0.936884	+	0.349639i	$0.886304\pi$
$810$		0			0
$811$		−	28420.8i		−	1.23057i	−0.788305	−	0.615284i	$-0.789041\pi$
$811$		−	28420.8i		−	1.23057i	0.788305	−	0.615284i	$-0.210959\pi$
$812$		0			0
$813$		0			0
$814$	20563.4	+	35616.8i	0.885437	+	1.53362i
$815$	15623.1	−	27060.0i	0.671477	−	1.16303i
$816$		0			0
$817$	−8405.35	+	4852.83i	−0.359934	+	0.207808i
$818$	27954.8			1.19488
$819$		0			0
$820$	16956.2			0.722118
$821$	22354.8	−	12906.5i	0.950288	−	0.548649i	0.0571174	−	0.998367i	$-0.481809\pi$
$821$	22354.8	−	12906.5i	0.950288	−	0.548649i	0.893170	+	0.449719i	$0.148476\pi$
$822$		0			0
$823$	16369.1	−	28352.1i	0.693306	−	1.20084i	−0.277442	−	0.960742i	$-0.589487\pi$
$823$	16369.1	−	28352.1i	0.693306	−	1.20084i	0.970748	−	0.240099i	$-0.0771799\pi$
$824$	5315.06	+	9205.95i	0.224707	+	0.389205i
$825$		0			0
$826$		0			0
$827$		−	652.139i		−	0.0274209i	−0.999906	−	0.0137105i	$-0.995636\pi$
$827$		−	652.139i		−	0.0274209i	0.999906	−	0.0137105i	$-0.00436431\pi$
$828$		0			0
$829$	26278.6	+	15172.0i	1.10096	+	0.635638i	0.936472	−	0.350742i	$-0.114070\pi$
$829$	26278.6	+	15172.0i	1.10096	+	0.635638i	0.164485	+	0.986380i	$0.447404\pi$
$830$	20658.8	+	11927.3i	0.863947	+	0.498800i
$831$		0			0
$832$			5734.79i			0.238964i
$833$		0			0
$834$		0			0
$835$	−30850.2	−	53434.1i	−1.27858	−	2.21457i
$836$	6024.86	−	10435.4i	0.249251	−	0.431716i
$837$		0			0
$838$	3271.36	−	1888.72i	0.134853	−	0.0778577i
$839$	2133.68			0.0877982			0.0438991	−	0.999036i	$-0.486022\pi$
$839$	2133.68			0.0877982			0.0438991	+	0.999036i	$0.486022\pi$
$840$		0			0
$841$	−40264.4			−1.65093
$842$	−33666.9	+	19437.6i	−1.37796	+	0.795563i
$843$		0			0
$844$	−11014.4	+	19077.5i	−0.449207	+	0.778050i
$845$	3415.68	+	5916.12i	0.139057	+	0.240853i
$846$		0			0
$847$		0			0
$848$			15092.5i			0.611178i
$849$		0			0
$850$	48156.5	+	27803.2i	1.94324	+	1.12193i
$851$	49998.4	+	28866.6i	2.01401	+	1.16279i
$852$		0			0
$853$		−	42021.1i		−	1.68672i	−0.537346	−	0.843362i	$-0.680573\pi$
$853$		−	42021.1i		−	1.68672i	0.537346	−	0.843362i	$-0.319427\pi$
$854$		0			0
$855$		0			0
$856$	−2788.79	−	4830.32i	−0.111354	−	0.192870i
$857$	7836.36	−	13573.0i	0.312351	−	0.541008i	−0.666520	−	0.745487i	$-0.732217\pi$
$857$	7836.36	−	13573.0i	0.312351	−	0.541008i	0.978871	+	0.204479i	$0.0655501\pi$
$858$		0			0
$859$	−28299.9	+	16338.9i	−1.12407	+	0.648984i	−0.942438	−	0.334381i	$-0.891473\pi$
$859$	−28299.9	+	16338.9i	−1.12407	+	0.648984i	−0.181636	+	0.983366i	$0.558139\pi$
$860$	13055.4			0.517657
$861$		0			0
$862$	41292.2			1.63158
$863$	22825.2	−	13178.1i	0.900323	−	0.519802i	0.0230181	−	0.999735i	$-0.492672\pi$
$863$	22825.2	−	13178.1i	0.900323	−	0.519802i	0.877305	+	0.479933i	$0.159339\pi$
$864$		0			0
$865$	−33551.3	+	58112.6i	−1.31882	+	2.28426i
$866$	−15147.2	−	26235.7i	−0.594367	−	1.02947i
$867$		0			0
$868$		0			0
$869$		−	7781.30i		−	0.303754i
$870$		0			0
$871$	38586.4	+	22277.9i	1.50109	+	0.866656i
$872$	3612.38	+	2085.61i	0.140287	+	0.0809949i
$873$		0			0
$874$		−	42216.1i		−	1.63385i
$875$		0			0
$876$		0			0
$877$	−1501.41	−	2600.51i	−0.0578095	−	0.100129i	0.835672	−	0.549228i	$-0.185078\pi$
$877$	−1501.41	−	2600.51i	−0.0578095	−	0.100129i	−0.893482	+	0.449099i	$0.851745\pi$
$878$	−26926.3	+	46637.7i	−1.03499	+	1.79265i
$879$		0			0
$880$	38362.9	−	22148.8i	1.46956	−	0.848450i
$881$	12329.6			0.471504			0.235752	−	0.971813i	$-0.424245\pi$
$881$	12329.6			0.471504			0.235752	+	0.971813i	$0.424245\pi$
$882$		0			0
$883$	−38324.4			−1.46061			−0.730305	−	0.683121i	$-0.760622\pi$
$883$	−38324.4			−1.46061			−0.730305	+	0.683121i	$0.760622\pi$
$884$	16849.4	−	9727.99i	0.641070	−	0.370122i
$885$		0			0
$886$	−21915.9	+	37959.4i	−0.831013	+	1.43936i
$887$	22765.8	+	39431.4i	0.861780	+	1.49265i	0.870209	+	0.492683i	$0.163984\pi$
$887$	22765.8	+	39431.4i	0.861780	+	1.49265i	−0.00842856	+	0.999964i	$0.502683\pi$
$888$		0			0
$889$		0			0
$890$			91515.9i			3.44676i
$891$		0			0
$892$	−14198.0	−	8197.20i	−0.532941	−	0.307694i
$893$	2576.36	+	1487.46i	0.0965450	+	0.0557403i
$894$		0			0
$895$			34978.6i			1.30637i
$896$		0			0
$897$		0			0
$898$	6315.47	+	10938.7i	0.234688	+	0.406492i
$899$	−41374.5	+	71662.7i	−1.53495	+	2.65861i
$900$		0			0
$901$	14316.8	−	8265.80i	0.529369	−	0.305631i
$902$	−21679.0			−0.800257
$903$		0			0
$904$	5656.24			0.208102
$905$	−46435.2	+	26809.4i	−1.70559	+	0.984723i
$906$		0			0
$907$	6321.23	−	10948.7i	0.231414	−	0.400822i	−0.726810	−	0.686838i	$-0.758998\pi$
$907$	6321.23	−	10948.7i	0.231414	−	0.400822i	0.958225	+	0.286017i	$0.0923313\pi$
$908$	−3561.13	−	6168.05i	−0.130154	−	0.225434i
$909$		0			0
$910$		0			0
$911$			4016.70i			0.146080i	0.997329	+	0.0730402i	$0.0232702\pi$
$911$			4016.70i			0.146080i	−0.997329	+	0.0730402i	$0.976730\pi$
$912$		0			0
$913$	−10583.1	−	6110.18i	−0.383627	−	0.221487i
$914$	6839.87	+	3949.00i	0.247531	+	0.142912i
$915$		0			0
$916$		−	21494.5i		−	0.775325i
$917$		0			0
$918$		0			0
$919$	344.051	+	595.914i	0.0123495	+	0.0213900i	0.872134	−	0.489267i	$-0.162736\pi$
$919$	344.051	+	595.914i	0.0123495	+	0.0213900i	−0.859785	+	0.510657i	$0.829402\pi$
$920$	14075.7	−	24379.9i	0.504416	−	0.873674i
$921$		0			0
$922$	3473.91	−	2005.66i	0.124086	−	0.0716410i
$923$	19710.7			0.702911
$924$		0			0
$925$	61433.8			2.18371
$926$	−30103.9	+	17380.5i	−1.06833	+	0.616801i
$927$		0			0
$928$	−26462.2	+	45833.8i	−0.936059	+	1.62130i
$929$	24488.4	+	42415.1i	0.864842	+	1.49795i	0.867204	+	0.497953i	$0.165915\pi$
$929$	24488.4	+	42415.1i	0.864842	+	1.49795i	−0.00236244	+	0.999997i	$0.500752\pi$
$930$		0			0
$931$		0			0
$932$			12170.2i			0.427735i
$933$		0			0
$934$	−5388.86	−	3111.26i	−0.188789	−	0.108997i
$935$	−42020.8	−	24260.7i	−1.46976	−	0.848567i
$936$		0			0
$937$		−	1602.26i		−	0.0558629i	−0.999610	−	0.0279315i	$-0.991108\pi$
$937$		−	1602.26i		−	0.0558629i	0.999610	−	0.0279315i	$-0.00889202\pi$
$938$		0			0
$939$		0			0
$940$	−2000.83	−	3465.54i	−0.0694255	−	0.120248i
$941$	−28372.1	+	49141.9i	−0.982894	+	1.70242i	−0.331947	+	0.943298i	$0.607706\pi$
$941$	−28372.1	+	49141.9i	−0.982894	+	1.70242i	−0.650946	+	0.759124i	$0.725628\pi$
$942$		0			0
$943$	−26355.5	+	15216.4i	−0.910130	+	0.525464i
$944$	8699.58			0.299944
$945$		0			0
$946$	−16691.7			−0.573672
$947$	−25820.4	+	14907.4i	−0.886010	+	0.511538i	−0.872635	−	0.488372i	$-0.837591\pi$
$947$	−25820.4	+	14907.4i	−0.886010	+	0.511538i	−0.0133749	+	0.999911i	$0.504257\pi$
$948$		0			0
$949$	−3882.16	+	6724.10i	−0.132793	+	0.230004i
$950$	−22461.0	−	38903.7i	−0.767087	−	1.32863i
$951$		0			0
$952$		0			0
$953$		−	16073.0i		−	0.546335i	−0.961966	−	0.273167i	$-0.911929\pi$
$953$		−	16073.0i		−	0.546335i	0.961966	−	0.273167i	$-0.0880713\pi$
$954$		0			0
$955$	−15260.9	−	8810.88i	−0.517101	−	0.298548i
$956$	−6730.33	−	3885.76i	−0.227693	−	0.131458i
$957$		0			0
$958$		−	15177.7i		−	0.511868i
$959$		0			0
$960$		0			0
$961$	38059.1	+	65920.3i	1.27754	+	2.21276i
$962$	26822.9	−	46458.6i	0.898966	−	1.55705i
$963$		0			0
$964$	−21896.8	+	12642.1i	−0.731585	+	0.422381i
$965$	−25126.3			−0.838182
$966$		0			0
$967$	−4382.43			−0.145739			−0.0728694	−	0.997341i	$-0.523216\pi$
$967$	−4382.43			−0.145739			−0.0728694	+	0.997341i	$0.523216\pi$
$968$	2269.52	−	1310.31i	0.0753567	−	0.0435072i
$969$		0			0
$970$	20300.5	−	35161.5i	0.671969	−	1.16388i
$971$	−29008.1	−	50243.5i	−0.958718	−	1.66055i	−0.725622	−	0.688094i	$-0.758448\pi$
$971$	−29008.1	−	50243.5i	−0.958718	−	1.66055i	−0.233096	−	0.972454i	$-0.574886\pi$
$972$		0			0
$973$		0			0
$974$		−	70102.0i		−	2.30617i
$975$		0			0
$976$	−6130.22	−	3539.29i	−0.201049	−	0.116076i
$977$	−6030.41	−	3481.66i	−0.197472	−	0.114010i	0.398004	−	0.917384i	$-0.369703\pi$
$977$	−6030.41	−	3481.66i	−0.197472	−	0.114010i	−0.595476	+	0.803373i	$0.703036\pi$
$978$		0			0
$979$		−	46882.1i		−	1.53050i
$980$		0			0
$981$		0			0
$982$	−7472.64	−	12943.0i	−0.242832	−	0.420598i
$983$	21387.5	−	37044.3i	0.693954	−	1.20196i	−0.276578	−	0.960991i	$-0.589200\pi$
$983$	21387.5	−	37044.3i	0.693954	−	1.20196i	0.970532	−	0.240972i	$-0.0774663\pi$
$984$		0			0
$985$	37726.0	−	21781.1i	1.22035	−	0.704572i
$986$	79555.4			2.56953
$987$		0			0
$988$	−15717.7			−0.506119
$989$	−20292.3	+	11715.8i	−0.652435	+	0.376684i
$990$		0			0
$991$	9974.05	−	17275.6i	0.319714	−	0.553760i	−0.660715	−	0.750637i	$-0.729747\pi$
$991$	9974.05	−	17275.6i	0.319714	−	0.553760i	0.980428	+	0.196877i	$0.0630800\pi$
$992$	33868.5	+	58662.0i	1.08400	+	1.87754i
$993$		0			0
$994$		0			0
$995$			49795.1i			1.58654i
$996$		0			0
$997$	−35878.2	−	20714.3i	−1.13969	−	0.658001i	−0.193337	−	0.981132i	$-0.561931\pi$
$997$	−35878.2	−	20714.3i	−1.13969	−	0.658001i	−0.946354	+	0.323131i	$0.895265\pi$
$998$	3701.71	+	2137.18i	0.117410	+	0.0677870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.80.20		48
3.2	odd	2	inner	441.4.p.d.80.5		48
7.2	even	3	inner	441.4.p.d.215.6		48
7.3	odd	6		441.4.c.b.440.4	yes	24
7.4	even	3		441.4.c.b.440.22	yes	24
7.5	odd	6	inner	441.4.p.d.215.5		48
7.6	odd	2	inner	441.4.p.d.80.19		48
21.2	odd	6	inner	441.4.p.d.215.19		48
21.5	even	6	inner	441.4.p.d.215.20		48
21.11	odd	6		441.4.c.b.440.3	✓	24
21.17	even	6		441.4.c.b.440.21	yes	24
21.20	even	2	inner	441.4.p.d.80.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.3	✓	24	21.11	odd	6
441.4.c.b.440.4	yes	24	7.3	odd	6
441.4.c.b.440.21	yes	24	21.17	even	6
441.4.c.b.440.22	yes	24	7.4	even	3
441.4.p.d.80.5		48	3.2	odd	2	inner
441.4.p.d.80.6		48	21.20	even	2	inner
441.4.p.d.80.19		48	7.6	odd	2	inner
441.4.p.d.80.20		48	1.1	even	1	trivial
441.4.p.d.215.5		48	7.5	odd	6	inner
441.4.p.d.215.6		48	7.2	even	3	inner
441.4.p.d.215.19		48	21.2	odd	6	inner
441.4.p.d.215.20		48	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.16408 - 1.82678i) q^{2} +(2.67425 - 4.63194i) q^{4} +(8.69951 + 15.0680i) q^{5} +9.68739i q^{8} +O(q^{10})\)	\(q+(3.16408 - 1.82678i) q^{2} +(2.67425 - 4.63194i) q^{4} +(8.69951 + 15.0680i) q^{5} +9.68739i q^{8} +(55.0518 + 31.7842i) q^{10} +(-28.2021 - 16.2825i) q^{11} +42.4779i q^{13} +(39.0908 + 67.7072i) q^{16} +(42.8181 - 74.1631i) q^{17} +(-59.9133 + 34.5910i) q^{19} +93.0588 q^{20} -118.978 q^{22} +(-144.644 + 83.5101i) q^{23} +(-88.8629 + 153.915i) q^{25} +(77.5978 + 134.403i) q^{26} +254.270i q^{29} +(281.837 + 162.719i) q^{31} +(180.256 + 104.071i) q^{32} -312.877i q^{34} +(-172.833 - 299.355i) q^{37} +(-126.380 + 218.897i) q^{38} +(-145.970 + 84.2756i) q^{40} +182.210 q^{41} +140.292 q^{43} +(-150.839 + 87.0871i) q^{44} +(-305.109 + 528.464i) q^{46} +(-21.5007 - 37.2404i) q^{47} +649.332i q^{50} +(196.755 + 113.597i) q^{52} +(167.182 + 96.5223i) q^{53} -566.600i q^{55} +(464.496 + 804.531i) q^{58} +(55.6370 - 96.3662i) q^{59} +(-78.4101 + 45.2701i) q^{61} +1189.00 q^{62} +135.007 q^{64} +(-640.057 + 369.537i) q^{65} +(524.458 - 908.388i) q^{67} +(-229.013 - 396.662i) q^{68} -464.023i q^{71} +(158.297 + 91.3925i) q^{73} +(-1093.71 - 631.456i) q^{74} +370.020i q^{76} +(119.473 + 206.934i) q^{79} +(-680.141 + 1178.04i) q^{80} +(576.526 - 332.857i) q^{82} +375.260 q^{83} +1489.99 q^{85} +(443.894 - 256.282i) q^{86} +(157.735 - 273.205i) q^{88} +(719.823 + 1246.77i) q^{89} +893.308i q^{92} +(-136.060 - 78.5542i) q^{94} +(-1042.43 - 601.849i) q^{95} -638.698i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4}+O(q^{10}) \) 48 * q + 96 * q^4	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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