LMFDB - Embedded newform 128.4.g.a.113.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.10
Character	$\chi$	$=$	128.113
Dual form			128.4.g.a.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.21198 + 7.75440i) q^{3} +(-13.6472 - 5.65283i) q^{5} +(-9.07689 - 9.07689i) q^{7} +(-30.7220 + 30.7220i) q^{9} +O(q^{10})$	\(q+(3.21198 + 7.75440i) q^{3} +(-13.6472 - 5.65283i) q^{5} +(-9.07689 - 9.07689i) q^{7} +(-30.7220 + 30.7220i) q^{9} +(-16.7195 + 40.3646i) q^{11} +(-38.4266 + 15.9168i) q^{13} -123.982i q^{15} -92.5038i q^{17} +(16.6799 - 6.90905i) q^{19} +(41.2311 - 99.5406i) q^{21} +(-95.6008 + 95.6008i) q^{23} +(65.9018 + 65.9018i) q^{25} +(-127.540 - 52.8290i) q^{27} +(19.3621 + 46.7443i) q^{29} +38.1477 q^{31} -366.706 q^{33} +(72.5636 + 175.184i) q^{35} +(227.529 + 94.2456i) q^{37} +(-246.851 - 246.851i) q^{39} +(-279.334 + 279.334i) q^{41} +(-112.235 + 270.960i) q^{43} +(592.935 - 245.602i) q^{45} +321.955i q^{47} -178.220i q^{49} +(717.312 - 297.120i) q^{51} +(-52.5056 + 126.760i) q^{53} +(456.348 - 456.348i) q^{55} +(107.151 + 107.151i) q^{57} +(332.587 + 137.762i) q^{59} +(33.6815 + 81.3143i) q^{61} +557.721 q^{63} +614.389 q^{65} +(-108.572 - 262.117i) q^{67} +(-1048.39 - 434.259i) q^{69} +(-272.246 - 272.246i) q^{71} +(372.955 - 372.955i) q^{73} +(-299.354 + 722.704i) q^{75} +(518.146 - 214.623i) q^{77} +244.410i q^{79} +14.3973i q^{81} +(-1230.52 + 509.697i) q^{83} +(-522.909 + 1262.41i) q^{85} +(-300.283 + 300.283i) q^{87} +(216.134 + 216.134i) q^{89} +(493.270 + 204.319i) q^{91} +(122.529 + 295.812i) q^{93} -266.689 q^{95} +779.862 q^{97} +(-726.422 - 1753.74i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	3.21198	+	7.75440i	0.618145	+	1.49233i	0.853855	+	0.520511i	$0.174259\pi$
$3$	3.21198	+	7.75440i	0.618145	+	1.49233i	−0.235710	+	0.971824i	$0.575741\pi$
$4$		0			0
$5$	−13.6472	−	5.65283i	−1.22064	−	0.505605i	−0.323026	−	0.946390i	$-0.604700\pi$
$5$	−13.6472	−	5.65283i	−1.22064	−	0.505605i	−0.897613	+	0.440785i	$0.854700\pi$
$6$		0			0
$7$	−9.07689	−	9.07689i	−0.490106	−	0.490106i	0.418233	−	0.908340i	$-0.362649\pi$
$7$	−9.07689	−	9.07689i	−0.490106	−	0.490106i	−0.908340	+	0.418233i	$0.862649\pi$
$8$		0			0
$9$	−30.7220	+	30.7220i	−1.13785	+	1.13785i
$10$		0			0
$11$	−16.7195	+	40.3646i	−0.458285	+	1.10640i	0.510807	+	0.859696i	$0.329347\pi$
$11$	−16.7195	+	40.3646i	−0.458285	+	1.10640i	−0.969091	+	0.246702i	$0.920653\pi$
$12$		0			0
$13$	−38.4266	+	15.9168i	−0.819817	+	0.339580i	−0.752864	−	0.658177i	$-0.771328\pi$
$13$	−38.4266	+	15.9168i	−0.819817	+	0.339580i	−0.0669538	+	0.997756i	$0.521328\pi$
$14$		0			0
$15$		−	123.982i		−	2.13414i
$16$		0			0
$17$		−	92.5038i		−	1.31973i	−0.751383	−	0.659867i	$-0.770613\pi$
$17$		−	92.5038i		−	1.31973i	0.751383	−	0.659867i	$-0.229387\pi$
$18$		0			0
$19$	16.6799	−	6.90905i	0.201402	−	0.0834235i	−0.279702	−	0.960087i	$-0.590236\pi$
$19$	16.6799	−	6.90905i	0.201402	−	0.0834235i	0.481104	+	0.876663i	$0.340236\pi$
$20$		0			0
$21$	41.2311	−	99.5406i	0.428446	−	1.03436i
$22$		0			0
$23$	−95.6008	+	95.6008i	−0.866702	+	0.866702i	−0.992106	−	0.125404i	$-0.959977\pi$
$23$	−95.6008	+	95.6008i	−0.866702	+	0.866702i	0.125404	+	0.992106i	$0.459977\pi$
$24$		0			0
$25$	65.9018	+	65.9018i	0.527215	+	0.527215i
$26$		0			0
$27$	−127.540	−	52.8290i	−0.909081	−	0.376553i
$28$		0			0
$29$	19.3621	+	46.7443i	0.123981	+	0.299317i	0.973668	−	0.227971i	$-0.0732090\pi$
$29$	19.3621	+	46.7443i	0.123981	+	0.299317i	−0.849687	+	0.527288i	$0.823209\pi$
$30$		0			0
$31$	38.1477			0.221017			0.110508	−	0.993875i	$-0.464752\pi$
$31$	38.1477			0.221017			0.110508	+	0.993875i	$0.464752\pi$
$32$		0			0
$33$	−366.706			−1.93440
$34$		0			0
$35$	72.5636	+	175.184i	0.350442	+	0.846042i
$36$		0			0
$37$	227.529	+	94.2456i	1.01096	+	0.418754i	0.825805	−	0.563955i	$-0.190721\pi$
$37$	227.529	+	94.2456i	1.01096	+	0.418754i	0.185156	+	0.982709i	$0.440721\pi$
$38$		0			0
$39$	−246.851	−	246.851i	−1.01353	−	1.01353i
$40$		0			0
$41$	−279.334	+	279.334i	−1.06401	+	1.06401i	−0.0662081	+	0.997806i	$0.521090\pi$
$41$	−279.334	+	279.334i	−1.06401	+	1.06401i	−0.997806	+	0.0662081i	$0.978910\pi$
$42$		0			0
$43$	−112.235	+	270.960i	−0.398039	+	0.960952i	0.590091	+	0.807337i	$0.299092\pi$
$43$	−112.235	+	270.960i	−0.398039	+	0.960952i	−0.988131	+	0.153616i	$0.950908\pi$
$44$		0			0
$45$	592.935	−	245.602i	1.96421	−	0.813603i
$46$		0			0
$47$			321.955i			0.999191i	0.866259	+	0.499596i	$0.166518\pi$
$47$			321.955i			0.999191i	−0.866259	+	0.499596i	$0.833482\pi$
$48$		0			0
$49$		−	178.220i		−	0.519592i
$50$		0			0
$51$	717.312	−	297.120i	1.96948	−	0.815787i
$52$		0			0
$53$	−52.5056	+	126.760i	−0.136079	+	0.328524i	−0.977199	−	0.212324i	$-0.931897\pi$
$53$	−52.5056	+	126.760i	−0.136079	+	0.328524i	0.841120	+	0.540848i	$0.181897\pi$
$54$		0			0
$55$	456.348	−	456.348i	1.11880	−	1.11880i
$56$		0			0
$57$	107.151	+	107.151i	0.248991	+	0.248991i
$58$		0			0
$59$	332.587	+	137.762i	0.733884	+	0.303985i	0.718147	−	0.695892i	$-0.244991\pi$
$59$	332.587	+	137.762i	0.733884	+	0.303985i	0.0157369	+	0.999876i	$0.494991\pi$
$60$		0			0
$61$	33.6815	+	81.3143i	0.0706963	+	0.170676i	0.955278	−	0.295709i	$-0.0955560\pi$
$61$	33.6815	+	81.3143i	0.0706963	+	0.170676i	−0.884582	+	0.466385i	$0.845556\pi$
$62$		0			0
$63$	557.721			1.11534
$64$		0			0
$65$	614.389			1.17239
$66$		0			0
$67$	−108.572	−	262.117i	−0.197974	−	0.477951i	0.793450	−	0.608635i	$-0.208283\pi$
$67$	−108.572	−	262.117i	−0.197974	−	0.477951i	−0.991424	+	0.130684i	$0.958283\pi$
$68$		0			0
$69$	−1048.39	−	434.259i	−1.82916	−	0.757661i
$70$		0			0
$71$	−272.246	−	272.246i	−0.455066	−	0.455066i	0.441966	−	0.897032i	$-0.354281\pi$
$71$	−272.246	−	272.246i	−0.455066	−	0.455066i	−0.897032	+	0.441966i	$0.854281\pi$
$72$		0			0
$73$	372.955	−	372.955i	0.597960	−	0.597960i	−0.341809	−	0.939769i	$-0.611040\pi$
$73$	372.955	−	372.955i	0.597960	−	0.597960i	0.939769	+	0.341809i	$0.111040\pi$
$74$		0			0
$75$	−299.354	+	722.704i	−0.460885	+	1.11268i
$76$		0			0
$77$	518.146	−	214.623i	0.766860	−	0.317644i
$78$		0			0
$79$			244.410i			0.348080i	0.984739	+	0.174040i	$0.0556822\pi$
$79$			244.410i			0.348080i	−0.984739	+	0.174040i	$0.944318\pi$
$80$		0			0
$81$			14.3973i			0.0197494i
$82$		0			0
$83$	−1230.52	+	509.697i	−1.62731	+	0.674054i	−0.994927	−	0.100600i	$-0.967924\pi$
$83$	−1230.52	+	509.697i	−1.62731	+	0.674054i	−0.632384	+	0.774655i	$0.717924\pi$
$84$		0			0
$85$	−522.909	+	1262.41i	−0.667264	+	1.61092i
$86$		0			0
$87$	−300.283	+	300.283i	−0.370043	+	0.370043i
$88$		0			0
$89$	216.134	+	216.134i	0.257417	+	0.257417i	0.824003	−	0.566586i	$-0.191736\pi$
$89$	216.134	+	216.134i	0.257417	+	0.257417i	−0.566586	+	0.824003i	$0.691736\pi$
$90$		0			0
$91$	493.270	+	204.319i	0.568228	+	0.235368i
$92$		0			0
$93$	122.529	+	295.812i	0.136621	+	0.329831i
$94$		0			0
$95$	−266.689			−0.288018
$96$		0			0
$97$	779.862			0.816319			0.408160	−	0.912911i	$-0.366171\pi$
$97$	779.862			0.816319			0.408160	+	0.912911i	$0.366171\pi$
$98$		0			0
$99$	−726.422	−	1753.74i	−0.737457	−	1.78038i
$100$		0			0
$101$	−1046.60	−	433.515i	−1.03109	−	0.427092i	−0.197985	−	0.980205i	$-0.563440\pi$
$101$	−1046.60	−	433.515i	−1.03109	−	0.427092i	−0.833106	+	0.553113i	$0.813440\pi$
$102$		0			0
$103$	−683.721	−	683.721i	−0.654069	−	0.654069i	0.299901	−	0.953970i	$-0.403046\pi$
$103$	−683.721	−	683.721i	−0.654069	−	0.654069i	−0.953970	+	0.299901i	$0.903046\pi$
$104$		0			0
$105$	−1125.37	+	1125.37i	−1.04595	+	1.04595i
$106$		0			0
$107$	289.555	−	699.048i	0.261611	−	0.631584i	−0.737428	−	0.675426i	$-0.763960\pi$
$107$	289.555	−	699.048i	0.261611	−	0.631584i	0.999038	+	0.0438418i	$0.0139598\pi$
$108$		0			0
$109$	56.3510	−	23.3413i	0.0495179	−	0.0205110i	−0.357787	−	0.933803i	$-0.616469\pi$
$109$	56.3510	−	23.3413i	0.0495179	−	0.0205110i	0.407305	+	0.913292i	$0.366469\pi$
$110$		0			0
$111$			2067.07i			1.76754i
$112$		0			0
$113$		−	1567.46i		−	1.30491i	−0.757828	−	0.652454i	$-0.773740\pi$
$113$		−	1567.46i		−	1.30491i	0.757828	−	0.652454i	$-0.226260\pi$
$114$		0			0
$115$	1845.09	−	764.263i	1.49614	−	0.619720i
$116$		0			0
$117$	691.546	−	1669.54i	0.546440	−	1.31922i
$118$		0			0
$119$	−839.647	+	839.647i	−0.646810	+	0.646810i
$120$		0			0
$121$	−408.595	−	408.595i	−0.306983	−	0.306983i
$122$		0			0
$123$	−3063.28	−	1268.85i	−2.24558	−	0.930150i
$124$		0			0
$125$	179.764	+	433.989i	0.128629	+	0.310538i
$126$		0			0
$127$	1291.26			0.902209			0.451105	−	0.892471i	$-0.351030\pi$
$127$	1291.26			0.902209			0.451105	+	0.892471i	$0.351030\pi$
$128$		0			0
$129$	−2461.63			−1.68011
$130$		0			0
$131$	326.012	+	787.064i	0.217434	+	0.524932i	0.994530	−	0.104450i	$-0.0333082\pi$
$131$	326.012	+	787.064i	0.217434	+	0.524932i	−0.777096	+	0.629382i	$0.783308\pi$
$132$		0			0
$133$	−214.115	−	88.6892i	−0.139595	−	0.0578220i
$134$		0			0
$135$	1441.93	+	1441.93i	0.919271	+	0.919271i
$136$		0			0
$137$	1526.86	−	1526.86i	0.952177	−	0.952177i	−0.0467305	−	0.998908i	$-0.514880\pi$
$137$	1526.86	−	1526.86i	0.952177	−	0.952177i	0.998908	+	0.0467305i	$0.0148802\pi$
$138$		0			0
$139$	181.169	−	437.382i	0.110551	−	0.266894i	−0.858916	−	0.512117i	$-0.828861\pi$
$139$	181.169	−	437.382i	0.110551	−	0.266894i	0.969467	+	0.245224i	$0.0788614\pi$
$140$		0			0
$141$	−2496.57	+	1034.11i	−1.49113	+	0.617645i
$142$		0			0
$143$		−	1817.20i		−	1.06267i
$144$		0			0
$145$		−	747.377i		−	0.428043i
$146$		0			0
$147$	1381.99	−	572.439i	0.775405	−	0.321183i
$148$		0			0
$149$	−1162.21	+	2805.81i	−0.639004	+	1.54269i	0.189004	+	0.981976i	$0.439474\pi$
$149$	−1162.21	+	2805.81i	−0.639004	+	1.54269i	−0.828008	+	0.560716i	$0.810526\pi$
$150$		0			0
$151$	262.518	−	262.518i	0.141479	−	0.141479i	−0.632820	−	0.774299i	$-0.718103\pi$
$151$	262.518	−	262.518i	0.141479	−	0.141479i	0.774299	+	0.632820i	$0.218103\pi$
$152$		0			0
$153$	2841.90	+	2841.90i	1.50166	+	1.50166i
$154$		0			0
$155$	−520.607	−	215.642i	−0.269782	−	0.111747i
$156$		0			0
$157$	−1086.34	−	2622.67i	−0.552227	−	1.33319i	−0.915802	−	0.401630i	$-0.868444\pi$
$157$	−1086.34	−	2622.67i	−0.552227	−	1.33319i	0.363575	−	0.931565i	$-0.381556\pi$
$158$		0			0
$159$	−1151.59			−0.574385
$160$		0			0
$161$	1735.52			0.849552
$162$		0			0
$163$	380.057	+	917.540i	0.182628	+	0.440903i	0.988507	−	0.151178i	$-0.0483065\pi$
$163$	380.057	+	917.540i	0.182628	+	0.440903i	−0.805878	+	0.592081i	$0.798307\pi$
$164$		0			0
$165$	5004.49	+	2072.93i	2.36120	+	0.978043i
$166$		0			0
$167$	1515.61	+	1515.61i	0.702283	+	0.702283i	0.964900	−	0.262617i	$-0.0845857\pi$
$167$	1515.61	+	1515.61i	0.702283	+	0.702283i	−0.262617	+	0.964900i	$0.584586\pi$
$168$		0			0
$169$	−330.254	+	330.254i	−0.150320	+	0.150320i
$170$		0			0
$171$	−300.181	+	724.701i	−0.134242	+	0.324089i
$172$		0			0
$173$	−1837.08	+	760.945i	−0.807346	+	0.334414i	−0.747895	−	0.663817i	$-0.768935\pi$
$173$	−1837.08	+	760.945i	−0.807346	+	0.334414i	−0.0594515	+	0.998231i	$0.518935\pi$
$174$		0			0
$175$		−	1196.37i		−	0.516782i
$176$		0			0
$177$			3021.50i			1.28311i
$178$		0			0
$179$	−2975.35	+	1232.43i	−1.24239	+	0.514615i	−0.904461	−	0.426556i	$-0.859727\pi$
$179$	−2975.35	+	1232.43i	−1.24239	+	0.514615i	−0.337930	+	0.941171i	$0.609727\pi$
$180$		0			0
$181$	1619.10	−	3908.85i	0.664899	−	1.60521i	−0.125132	−	0.992140i	$-0.539935\pi$
$181$	1619.10	−	3908.85i	0.664899	−	1.60521i	0.790030	−	0.613068i	$-0.210065\pi$
$182$		0			0
$183$	−522.359	+	522.359i	−0.211005	+	0.211005i
$184$		0			0
$185$	−2572.37	−	2572.37i	−1.02229	−	1.02229i
$186$		0			0
$187$	3733.88	+	1546.62i	1.46015	+	0.604814i
$188$		0			0
$189$	678.148	+	1637.19i	0.260995	+	0.630097i
$190$		0			0
$191$	−697.265			−0.264148			−0.132074	−	0.991240i	$-0.542164\pi$
$191$	−697.265			−0.264148			−0.132074	+	0.991240i	$0.542164\pi$
$192$		0			0
$193$	2386.61			0.890114			0.445057	−	0.895502i	$-0.353183\pi$
$193$	2386.61			0.890114			0.445057	+	0.895502i	$0.353183\pi$
$194$		0			0
$195$	1973.40	+	4764.22i	0.724710	+	1.74960i
$196$		0			0
$197$	−2583.07	−	1069.94i	−0.934194	−	0.386956i	−0.136926	−	0.990581i	$-0.543722\pi$
$197$	−2583.07	−	1069.94i	−0.934194	−	0.386956i	−0.797268	+	0.603625i	$0.793722\pi$
$198$		0			0
$199$	−2940.81	−	2940.81i	−1.04758	−	1.04758i	−0.998810	−	0.0487695i	$-0.984470\pi$
$199$	−2940.81	−	2940.81i	−1.04758	−	1.04758i	−0.0487695	−	0.998810i	$-0.515530\pi$
$200$		0			0
$201$	1683.83	−	1683.83i	0.590886	−	0.590886i
$202$		0			0
$203$	248.545	−	600.041i	0.0859332	−	0.207461i
$204$		0			0
$205$	5391.13	−	2233.08i	1.83675	−	0.760805i
$206$		0			0
$207$		−	5874.10i		−	1.97236i
$208$		0			0
$209$			788.794i			0.261062i
$210$		0			0
$211$	−1399.25	+	579.589i	−0.456533	+	0.189102i	−0.599085	−	0.800685i	$-0.704469\pi$
$211$	−1399.25	+	579.589i	−0.456533	+	0.189102i	0.142552	+	0.989787i	$0.454469\pi$
$212$		0			0
$213$	1236.66	−	2985.55i	0.397814	−	0.960408i
$214$		0			0
$215$	3063.38	−	3063.38i	0.971724	−	0.971724i
$216$		0			0
$217$	−346.262	−	346.262i	−0.108322	−	0.108322i
$218$		0			0
$219$	4089.97	+	1694.12i	1.26198	+	0.522731i
$220$		0			0
$221$	1472.37	+	3554.61i	0.448155	+	1.08194i
$222$		0			0
$223$	1100.18			0.330374			0.165187	−	0.986262i	$-0.447177\pi$
$223$	1100.18			0.330374			0.165187	+	0.986262i	$0.447177\pi$
$224$		0			0
$225$	−4049.27			−1.19979
$226$		0			0
$227$	−1476.27	−	3564.04i	−0.431647	−	1.04209i	−0.978756	−	0.205026i	$-0.934272\pi$
$227$	−1476.27	−	3564.04i	−0.431647	−	1.04209i	0.547110	−	0.837061i	$-0.315728\pi$
$228$		0			0
$229$	3573.95	+	1480.38i	1.03132	+	0.427188i	0.833190	−	0.552986i	$-0.186512\pi$
$229$	3573.95	+	1480.38i	1.03132	+	0.427188i	0.198134	+	0.980175i	$0.436512\pi$
$230$		0			0
$231$	3328.55	+	3328.55i	0.948062	+	0.948062i
$232$		0			0
$233$	−3668.67	+	3668.67i	−1.03151	+	1.03151i	−0.0320257	+	0.999487i	$0.510196\pi$
$233$	−3668.67	+	3668.67i	−1.03151	+	1.03151i	−0.999487	+	0.0320257i	$0.989804\pi$
$234$		0			0
$235$	1819.96	−	4393.77i	0.505196	−	1.21965i
$236$		0			0
$237$	−1895.25	+	785.040i	−0.519451	+	0.215164i
$238$		0			0
$239$			5649.23i			1.52895i	0.644656	+	0.764473i	$0.277001\pi$
$239$			5649.23i			1.52895i	−0.644656	+	0.764473i	$0.722999\pi$
$240$		0			0
$241$			5059.57i			1.35235i	0.736743	+	0.676173i	$0.236363\pi$
$241$			5059.57i			1.35235i	−0.736743	+	0.676173i	$0.763637\pi$
$242$		0			0
$243$	−3555.24	+	1472.63i	−0.938553	+	0.388761i
$244$		0			0
$245$	−1007.45	+	2432.20i	−0.262708	+	0.634234i
$246$		0			0
$247$	−530.983	+	530.983i	−0.136784	+	0.136784i
$248$		0			0
$249$	−7904.79	−	7904.79i	−2.01183	−	2.01183i
$250$		0			0
$251$	−980.968	−	406.330i	−0.246686	−	0.102181i	0.255915	−	0.966699i	$-0.417623\pi$
$251$	−980.968	−	406.330i	−0.246686	−	0.102181i	−0.502601	+	0.864519i	$0.667623\pi$
$252$		0			0
$253$	−2260.48	−	5457.28i	−0.561720	−	1.35611i
$254$		0			0
$255$	−11468.8			−2.81649
$256$		0			0
$257$	−1021.29			−0.247886			−0.123943	−	0.992289i	$-0.539554\pi$
$257$	−1021.29			−0.247886			−0.123943	+	0.992289i	$0.539554\pi$
$258$		0			0
$259$	−1209.80	−	2920.72i	−0.290244	−	0.700712i
$260$		0			0
$261$	−2030.92	−	841.236i	−0.481651	−	0.199506i
$262$		0			0
$263$	1134.88	+	1134.88i	0.266083	+	0.266083i	0.827520	−	0.561437i	$-0.189751\pi$
$263$	1134.88	+	1134.88i	0.266083	+	0.266083i	−0.561437	+	0.827520i	$0.689751\pi$
$264$		0			0
$265$	1433.10	−	1433.10i	0.332207	−	0.332207i
$266$		0			0
$267$	−981.770	+	2370.20i	−0.225031	+	0.543273i
$268$		0			0
$269$	−2221.12	+	920.017i	−0.503435	+	0.208530i	−0.619923	−	0.784663i	$-0.712836\pi$
$269$	−2221.12	+	920.017i	−0.503435	+	0.208530i	0.116488	+	0.993192i	$0.462836\pi$
$270$		0			0
$271$			1860.26i			0.416984i	0.978024	+	0.208492i	$0.0668555\pi$
$271$			1860.26i			0.416984i	−0.978024	+	0.208492i	$0.933144\pi$
$272$		0			0
$273$			4481.28i			0.993477i
$274$		0			0
$275$	−3761.95	+	1558.25i	−0.824923	+	0.341694i
$276$		0			0
$277$	−2311.55	+	5580.58i	−0.501400	+	1.21049i	0.447322	+	0.894373i	$0.352378\pi$
$277$	−2311.55	+	5580.58i	−0.501400	+	1.21049i	−0.948721	+	0.316113i	$0.897622\pi$
$278$		0			0
$279$	−1171.97	+	1171.97i	−0.251485	+	0.251485i
$280$		0			0
$281$	−1740.45	−	1740.45i	−0.369490	−	0.369490i	0.497801	−	0.867291i	$-0.334141\pi$
$281$	−1740.45	−	1740.45i	−0.369490	−	0.369490i	−0.867291	+	0.497801i	$0.834141\pi$
$282$		0			0
$283$	2580.95	+	1069.06i	0.542125	+	0.224555i	0.636904	−	0.770943i	$-0.280215\pi$
$283$	2580.95	+	1069.06i	0.542125	+	0.224555i	−0.0947795	+	0.995498i	$0.530215\pi$
$284$		0			0
$285$	−856.600	−	2068.01i	−0.178037	−	0.429820i
$286$		0			0
$287$	5070.96			1.04296
$288$		0			0
$289$	−3643.96			−0.741697
$290$		0			0
$291$	2504.90	+	6047.36i	0.504604	+	1.21822i
$292$		0			0
$293$	6531.00	+	2705.23i	1.30220	+	0.539390i	0.922599	−	0.385760i	$-0.126061\pi$
$293$	6531.00	+	2705.23i	1.30220	+	0.539390i	0.379603	+	0.925149i	$0.376061\pi$
$294$		0			0
$295$	−3760.12	−	3760.12i	−0.742110	−	0.742110i
$296$		0			0
$297$	4264.84	−	4264.84i	0.833235	−	0.833235i
$298$		0			0
$299$	2151.95	−	5195.27i	0.416223	−	1.00485i
$300$		0			0
$301$	3478.22	−	1440.72i	0.666050	−	0.275887i
$302$		0			0
$303$		−	9508.17i		−	1.80274i
$304$		0			0
$305$		−	1300.10i		−	0.244078i
$306$		0			0
$307$	22.1910	−	9.19181i	0.00412543	−	0.00170881i	−0.380620	−	0.924732i	$-0.624289\pi$
$307$	22.1910	−	9.19181i	0.00412543	−	0.00170881i	0.384745	+	0.923023i	$0.374289\pi$
$308$		0			0
$309$	3105.75	−	7497.95i	0.571780	−	1.38040i
$310$		0			0
$311$	4220.58	−	4220.58i	0.769540	−	0.769540i	−0.208485	−	0.978026i	$-0.566853\pi$
$311$	4220.58	−	4220.58i	0.769540	−	0.769540i	0.978026	+	0.208485i	$0.0668533\pi$
$312$		0			0
$313$	6090.90	+	6090.90i	1.09993	+	1.09993i	0.994418	+	0.105512i	$0.0336481\pi$
$313$	6090.90	+	6090.90i	1.09993	+	1.09993i	0.105512	+	0.994418i	$0.466352\pi$
$314$		0			0
$315$	−7611.30	−	3152.71i	−1.36142	−	0.563920i
$316$		0			0
$317$	−1660.86	−	4009.67i	−0.294269	−	0.710428i	−0.999998	−	0.00194638i	$-0.999380\pi$
$317$	−1660.86	−	4009.67i	−0.294269	−	0.710428i	0.705729	−	0.708482i	$-0.250620\pi$
$318$		0			0
$319$	−2210.54			−0.387982
$320$		0			0
$321$	6350.74			1.10425
$322$		0			0
$323$	−639.114	−	1542.96i	−0.110097	−	0.265797i
$324$		0			0
$325$	−3581.33	−	1483.44i	−0.611251	−	0.253188i
$326$		0			0
$327$	361.996	+	361.996i	0.0612185	+	0.0612185i
$328$		0			0
$329$	2922.35	−	2922.35i	0.489710	−	0.489710i
$330$		0			0
$331$	−3722.12	+	8985.99i	−0.618085	+	1.49219i	0.235840	+	0.971792i	$0.424216\pi$
$331$	−3722.12	+	8985.99i	−0.618085	+	1.49219i	−0.853924	+	0.520397i	$0.825784\pi$
$332$		0			0
$333$	−9885.57	+	4094.74i	−1.62680	+	0.673845i
$334$		0			0
$335$			4190.90i			0.683502i
$336$		0			0
$337$		−	5211.97i		−	0.842475i	−0.906950	−	0.421238i	$-0.861596\pi$
$337$		−	5211.97i		−	0.842475i	0.906950	−	0.421238i	$-0.138404\pi$
$338$		0			0
$339$	12154.7	−	5034.66i	1.94736	−	0.806623i
$340$		0			0
$341$	−637.812	+	1539.81i	−0.101289	+	0.244532i
$342$		0			0
$343$	−4731.06	+	4731.06i	−0.744761	+	0.744761i
$344$		0			0
$345$	11852.8	+	11852.8i	1.84966	+	1.84966i
$346$		0			0
$347$	−4987.20	−	2065.77i	−0.771547	−	0.319585i	−0.0380483	−	0.999276i	$-0.512114\pi$
$347$	−4987.20	−	2065.77i	−0.771547	−	0.319585i	−0.733499	+	0.679691i	$0.762114\pi$
$348$		0			0
$349$	3137.63	+	7574.92i	0.481243	+	1.16182i	0.959019	+	0.283341i	$0.0914429\pi$
$349$	3137.63	+	7574.92i	0.481243	+	1.16182i	−0.477776	+	0.878481i	$0.658557\pi$
$350$		0			0
$351$	5741.82			0.873150
$352$		0			0
$353$	8999.28			1.35689			0.678446	−	0.734650i	$-0.262654\pi$
$353$	8999.28			1.35689			0.678446	+	0.734650i	$0.262654\pi$
$354$		0			0
$355$	2176.42	+	5254.35i	0.325387	+	0.785555i
$356$		0			0
$357$	−9207.89	−	3814.03i	−1.36508	−	0.565434i
$358$		0			0
$359$	4697.94	+	4697.94i	0.690662	+	0.690662i	0.962378	−	0.271715i	$-0.0875909\pi$
$359$	4697.94	+	4697.94i	0.690662	+	0.690662i	−0.271715	+	0.962378i	$0.587591\pi$
$360$		0			0
$361$	−4619.56	+	4619.56i	−0.673503	+	0.673503i
$362$		0			0
$363$	1856.01	−	4480.80i	0.268361	−	0.647882i
$364$		0			0
$365$	−7198.03	+	2981.52i	−1.03222	+	0.427561i
$366$		0			0
$367$			5942.35i			0.845199i	0.906316	+	0.422600i	$0.138882\pi$
$367$			5942.35i			0.845199i	−0.906316	+	0.422600i	$0.861118\pi$
$368$		0			0
$369$		−	17163.4i		−	2.42138i
$370$		0			0
$371$	1627.17	−	673.997i	0.227705	−	0.0943186i
$372$		0			0
$373$	−611.014	+	1475.12i	−0.0848180	+	0.204769i	−0.960598	−	0.277942i	$-0.910348\pi$
$373$	−611.014	+	1475.12i	−0.0848180	+	0.204769i	0.875780	+	0.482711i	$0.160348\pi$
$374$		0			0
$375$	−2787.93	+	2787.93i	−0.383915	+	0.383915i
$376$		0			0
$377$	−1488.04	−	1488.04i	−0.203284	−	0.203284i
$378$		0			0
$379$	−3436.04	−	1423.25i	−0.465692	−	0.192896i	0.137484	−	0.990504i	$-0.456098\pi$
$379$	−3436.04	−	1423.25i	−0.465692	−	0.192896i	−0.603176	+	0.797608i	$0.706098\pi$
$380$		0			0
$381$	4147.49	+	10012.9i	0.557697	+	1.34640i
$382$		0			0
$383$	9327.55			1.24443			0.622213	−	0.782848i	$-0.286234\pi$
$383$	9327.55			1.24443			0.622213	+	0.782848i	$0.286234\pi$
$384$		0			0
$385$	−8284.45			−1.09666
$386$		0			0
$387$	−4876.34	−	11772.5i	−0.640512	−	1.54633i
$388$		0			0
$389$	7840.37	+	3247.59i	1.02191	+	0.423288i	0.829785	−	0.558083i	$-0.188463\pi$
$389$	7840.37	+	3247.59i	1.02191	+	0.423288i	0.192123	+	0.981371i	$0.438463\pi$
$390$		0			0
$391$	8843.44	+	8843.44i	1.14382	+	1.14382i
$392$		0			0
$393$	−5056.06	+	5056.06i	−0.648968	+	0.648968i
$394$		0			0
$395$	1381.61	−	3335.50i	0.175991	−	0.424879i
$396$		0			0
$397$	6845.23	−	2835.39i	0.865370	−	0.358448i	0.0945649	−	0.995519i	$-0.469854\pi$
$397$	6845.23	−	2835.39i	0.865370	−	0.358448i	0.770805	+	0.637071i	$0.219854\pi$
$398$		0			0
$399$		−	1945.20i		−	0.244064i
$400$		0			0
$401$			5333.86i			0.664240i	0.943237	+	0.332120i	$0.107764\pi$
$401$			5333.86i			0.664240i	−0.943237	+	0.332120i	$0.892236\pi$
$402$		0			0
$403$	−1465.89	+	607.190i	−0.181193	+	0.0750528i
$404$		0			0
$405$	81.3857	−	196.482i	0.00998540	−	0.0241069i
$406$		0			0
$407$	−7608.37	+	7608.37i	−0.926616	+	0.926616i
$408$		0			0
$409$	−3906.82	−	3906.82i	−0.472322	−	0.472322i	0.430343	−	0.902665i	$-0.358393\pi$
$409$	−3906.82	−	3906.82i	−0.472322	−	0.472322i	−0.902665	+	0.430343i	$0.858393\pi$
$410$		0			0
$411$	16744.1	+	6935.63i	2.00955	+	0.832383i
$412$		0			0
$413$	−1768.41	−	4269.31i	−0.210696	−	0.508666i
$414$		0			0
$415$	19674.3			2.32716
$416$		0			0
$417$	3973.54			0.466631
$418$		0			0
$419$	−510.706	−	1232.95i	−0.0595456	−	0.143756i	0.891306	−	0.453401i	$-0.149790\pi$
$419$	−510.706	−	1232.95i	−0.0595456	−	0.143756i	−0.950852	+	0.309646i	$0.899790\pi$
$420$		0			0
$421$	−9078.42	−	3760.41i	−1.05096	−	0.435323i	−0.210727	−	0.977545i	$-0.567583\pi$
$421$	−9078.42	−	3760.41i	−1.05096	−	0.435323i	−0.840235	+	0.542222i	$0.817583\pi$
$422$		0			0
$423$	−9891.11	−	9891.11i	−1.13693	−	1.13693i
$424$		0			0
$425$	6096.17	−	6096.17i	0.695783	−	0.695783i
$426$		0			0
$427$	432.358	−	1043.80i	0.0490006	−	0.118298i
$428$		0			0
$429$	14091.3	−	5836.79i	1.58586	−	0.656883i
$430$		0			0
$431$			7684.54i			0.858820i	0.903110	+	0.429410i	$0.141278\pi$
$431$			7684.54i			0.858820i	−0.903110	+	0.429410i	$0.858722\pi$
$432$		0			0
$433$		−	989.963i		−	0.109872i	−0.998490	−	0.0549360i	$-0.982505\pi$
$433$		−	989.963i		−	0.109872i	0.998490	−	0.0549360i	$-0.0174955\pi$
$434$		0			0
$435$	5795.46	−	2400.56i	0.638784	−	0.264593i
$436$		0			0
$437$	−934.103	+	2255.12i	−0.102252	+	0.246859i
$438$		0			0
$439$	−1705.59	+	1705.59i	−0.185429	+	0.185429i	−0.793717	−	0.608287i	$-0.791857\pi$
$439$	−1705.59	+	1705.59i	−0.185429	+	0.185429i	0.608287	+	0.793717i	$0.291857\pi$
$440$		0			0
$441$	5475.28	+	5475.28i	0.591219	+	0.591219i
$442$		0			0
$443$	−14875.4	−	6161.58i	−1.59537	−	0.660826i	−0.604622	−	0.796512i	$-0.706676\pi$
$443$	−14875.4	−	6161.58i	−1.59537	−	0.660826i	−0.990752	+	0.135687i	$0.956676\pi$
$444$		0			0
$445$	−1727.84	−	4171.37i	−0.184062	−	0.444364i
$446$		0			0
$447$	−25490.4			−2.69721
$448$		0			0
$449$	1887.26			0.198364			0.0991819	−	0.995069i	$-0.468377\pi$
$449$	1887.26			0.198364			0.0991819	+	0.995069i	$0.468377\pi$
$450$		0			0
$451$	−6604.84	−	15945.5i	−0.689601	−	1.66484i
$452$		0			0
$453$	2878.87	+	1192.47i	0.298589	+	0.123680i
$454$		0			0
$455$	−5576.74	−	5576.74i	−0.574597	−	0.574597i
$456$		0			0
$457$	−9275.37	+	9275.37i	−0.949417	+	0.949417i	−0.998781	−	0.0493636i	$-0.984281\pi$
$457$	−9275.37	+	9275.37i	−0.949417	+	0.949417i	0.0493636	+	0.998781i	$0.484281\pi$
$458$		0			0
$459$	−4886.88	+	11798.0i	−0.496950	+	1.19974i
$460$		0			0
$461$	6867.75	−	2844.71i	0.693846	−	0.287400i	−0.00775571	−	0.999970i	$-0.502469\pi$
$461$	6867.75	−	2844.71i	0.693846	−	0.287400i	0.701601	+	0.712570i	$0.252469\pi$
$462$		0			0
$463$		−	7678.71i		−	0.770756i	−0.922759	−	0.385378i	$-0.874071\pi$
$463$		−	7678.71i		−	0.770756i	0.922759	−	0.385378i	$-0.125929\pi$
$464$		0			0
$465$		−	4729.63i		−	0.471681i
$466$		0			0
$467$	3867.05	−	1601.79i	0.383182	−	0.158719i	−0.182773	−	0.983155i	$-0.558507\pi$
$467$	3867.05	−	1601.79i	0.383182	−	0.158719i	0.565955	+	0.824436i	$0.308507\pi$
$468$		0			0
$469$	−1393.71	+	3364.71i	−0.137219	+	0.331275i
$470$		0			0
$471$	16847.9	−	16847.9i	1.64822	−	1.64822i
$472$		0			0
$473$	−9060.64	−	9060.64i	−0.880780	−	0.880780i
$474$		0			0
$475$	1554.56	+	643.919i	0.150164	+	0.0622000i
$476$		0			0
$477$	−2281.24	−	5507.40i	−0.218974	−	0.528651i
$478$		0			0
$479$	−5602.73			−0.534436			−0.267218	−	0.963636i	$-0.586104\pi$
$479$	−5602.73			−0.534436			−0.267218	+	0.963636i	$0.586104\pi$
$480$		0			0
$481$	−10243.3			−0.971004
$482$		0			0
$483$	5574.44	+	13457.9i	0.525146	+	1.26782i
$484$		0			0
$485$	−10642.9	−	4408.43i	−0.996431	−	0.412735i
$486$		0			0
$487$	−13338.0	−	13338.0i	−1.24107	−	1.24107i	−0.959556	−	0.281516i	$-0.909163\pi$
$487$	−13338.0	−	13338.0i	−1.24107	−	1.24107i	−0.281516	−	0.959556i	$-0.590837\pi$
$488$		0			0
$489$	−5894.23	+	5894.23i	−0.545085	+	0.545085i
$490$		0			0
$491$	−6069.18	+	14652.3i	−0.557837	+	1.34674i	0.353637	+	0.935383i	$0.384945\pi$
$491$	−6069.18	+	14652.3i	−0.557837	+	1.34674i	−0.911475	+	0.411356i	$0.865055\pi$
$492$		0			0
$493$	4324.03	−	1791.07i	0.395019	−	0.163622i
$494$		0			0
$495$			28039.9i			2.54606i
$496$		0			0
$497$			4942.30i			0.446061i
$498$		0			0
$499$	−3108.34	+	1287.52i	−0.278855	+	0.115505i	−0.517728	−	0.855545i	$-0.673222\pi$
$499$	−3108.34	+	1287.52i	−0.278855	+	0.115505i	0.238873	+	0.971051i	$0.423222\pi$
$500$		0			0
$501$	−6884.53	+	16620.7i	−0.613928	+	1.48215i
$502$		0			0
$503$	9569.65	−	9569.65i	0.848289	−	0.848289i	−0.141630	−	0.989920i	$-0.545234\pi$
$503$	9569.65	−	9569.65i	0.848289	−	0.848289i	0.989920	+	0.141630i	$0.0452344\pi$
$504$		0			0
$505$	11832.5	+	11832.5i	1.04265	+	1.04265i
$506$		0			0
$507$	−3621.69	−	1500.15i	−0.317248	−	0.131408i
$508$		0			0
$509$	4975.54	+	12012.0i	0.433275	+	1.04602i	0.978225	+	0.207549i	$0.0665487\pi$
$509$	4975.54	+	12012.0i	0.433275	+	1.04602i	−0.544950	+	0.838469i	$0.683451\pi$
$510$		0			0
$511$	−6770.55			−0.586128
$512$		0			0
$513$	−2492.36			−0.214504
$514$		0			0
$515$	5465.89	+	13195.8i	0.467681	+	1.12908i
$516$		0			0
$517$	−12995.6	−	5382.94i	−1.10550	−	0.457914i
$518$		0			0
$519$	−11801.3	−	11801.3i	−0.998114	−	0.998114i
$520$		0			0
$521$	11056.5	−	11056.5i	0.929743	−	0.929743i	−0.0679465	−	0.997689i	$-0.521645\pi$
$521$	11056.5	−	11056.5i	0.929743	−	0.929743i	0.997689	+	0.0679465i	$0.0216447\pi$
$522$		0			0
$523$	−7704.74	+	18600.9i	−0.644178	+	1.55518i	0.176815	+	0.984244i	$0.443420\pi$
$523$	−7704.74	+	18600.9i	−0.644178	+	1.55518i	−0.820993	+	0.570938i	$0.806580\pi$
$524$		0			0
$525$	9277.11	−	3842.71i	0.771212	−	0.319447i
$526$		0			0
$527$		−	3528.80i		−	0.291683i
$528$		0			0
$529$		−	6112.01i		−	0.502343i
$530$		0			0
$531$	−14450.1	+	5985.42i	−1.18094	+	0.489162i
$532$		0			0
$533$	6287.74	−	15179.9i	0.510980	−	1.23361i
$534$		0			0
$535$	−7903.20	+	7903.20i	−0.638664	+	0.638664i
$536$		0			0
$537$	−19113.5	−	19113.5i	−1.53596	−	1.53596i
$538$		0			0
$539$	7193.77	+	2979.76i	0.574875	+	0.238121i
$540$		0			0
$541$	−3094.21	−	7470.07i	−0.245897	−	0.593648i	0.751951	−	0.659219i	$-0.229113\pi$
$541$	−3094.21	−	7470.07i	−0.245897	−	0.593648i	−0.997848	+	0.0655712i	$0.979113\pi$
$542$		0			0
$543$	35511.3			2.80651
$544$		0			0
$545$	−900.975			−0.0708138
$546$		0			0
$547$	−6470.84	−	15622.0i	−0.505801	−	1.22111i	−0.946280	−	0.323349i	$-0.895191\pi$
$547$	−6470.84	−	15622.0i	−0.505801	−	1.22111i	0.440479	−	0.897763i	$-0.354809\pi$
$548$		0			0
$549$	−3532.90	−	1463.38i	−0.274646	−	0.113762i
$550$		0			0
$551$	645.918	+	645.918i	0.0499401	+	0.0499401i
$552$		0			0
$553$	2218.49	−	2218.49i	0.170596	−	0.170596i
$554$		0			0
$555$	11684.8	−	28209.6i	0.893678	−	2.15753i
$556$		0			0
$557$	−10401.9	+	4308.63i	−0.791283	+	0.327760i	−0.741459	−	0.670998i	$-0.765866\pi$
$557$	−10401.9	+	4308.63i	−0.791283	+	0.327760i	−0.0498238	+	0.998758i	$0.515866\pi$
$558$		0			0
$559$		−	12198.5i		−	0.922971i
$560$		0			0
$561$			33921.7i			2.55290i
$562$		0			0
$563$	1760.24	−	729.116i	0.131768	−	0.0545801i	−0.315825	−	0.948817i	$-0.602281\pi$
$563$	1760.24	−	729.116i	0.131768	−	0.0545801i	0.447593	+	0.894237i	$0.352281\pi$
$564$		0			0
$565$	−8860.61	+	21391.4i	−0.659768	+	1.59282i
$566$		0			0
$567$	130.683	−	130.683i	0.00967931	−	0.00967931i
$568$		0			0
$569$	8079.71	+	8079.71i	0.595288	+	0.595288i	0.939055	−	0.343767i	$-0.111703\pi$
$569$	8079.71	+	8079.71i	0.595288	+	0.595288i	−0.343767	+	0.939055i	$0.611703\pi$
$570$		0			0
$571$	16823.9	+	6968.69i	1.23303	+	0.510737i	0.901529	−	0.432719i	$-0.142446\pi$
$571$	16823.9	+	6968.69i	1.23303	+	0.510737i	0.331498	+	0.943456i	$0.392446\pi$
$572$		0			0
$573$	−2239.60	−	5406.87i	−0.163282	−	0.394198i
$574$		0			0
$575$	−12600.5			−0.913875
$576$		0			0
$577$	−4098.72			−0.295723			−0.147861	−	0.989008i	$-0.547239\pi$
$577$	−4098.72			−0.295723			−0.147861	+	0.989008i	$0.547239\pi$
$578$		0			0
$579$	7665.74	+	18506.7i	0.550220	+	1.32835i
$580$		0			0
$581$	15795.7	+	6542.81i	1.12791	+	0.467197i
$582$		0			0
$583$	−4238.73	−	4238.73i	−0.301115	−	0.301115i
$584$		0			0
$585$	−18875.3	+	18875.3i	−1.33401	+	1.33401i
$586$		0			0
$587$	437.187	−	1055.46i	0.0307404	−	0.0742139i	−0.907764	−	0.419482i	$-0.862212\pi$
$587$	437.187	−	1055.46i	0.0307404	−	0.0742139i	0.938504	+	0.345268i	$0.112212\pi$
$588$		0			0
$589$	636.300	−	263.564i	0.0445132	−	0.0184380i
$590$		0			0
$591$		−	23466.8i		−	1.63332i
$592$		0			0
$593$		−	26161.0i		−	1.81164i	−0.423661	−	0.905821i	$-0.639255\pi$
$593$		−	26161.0i		−	1.81164i	0.423661	−	0.905821i	$-0.360745\pi$
$594$		0			0
$595$	16205.2	−	6712.41i	1.11655	−	0.462491i
$596$		0			0
$597$	13358.4	−	32250.0i	0.915783	−	2.21090i
$598$		0			0
$599$	12392.1	−	12392.1i	0.845288	−	0.845288i	−0.144253	−	0.989541i	$-0.546078\pi$
$599$	12392.1	−	12392.1i	0.845288	−	0.845288i	0.989541	+	0.144253i	$0.0460778\pi$
$600$		0			0
$601$	5696.78	+	5696.78i	0.386650	+	0.386650i	0.873491	−	0.486841i	$-0.161851\pi$
$601$	5696.78	+	5696.78i	0.386650	+	0.386650i	−0.486841	+	0.873491i	$0.661851\pi$
$602$		0			0
$603$	11388.3	+	4717.20i	0.769103	+	0.318573i
$604$		0			0
$605$	3266.43	+	7885.87i	0.219503	+	0.529928i
$606$		0			0
$607$	−19674.4			−1.31559			−0.657793	−	0.753199i	$-0.728510\pi$
$607$	−19674.4			−1.31559			−0.657793	+	0.753199i	$0.728510\pi$
$608$		0			0
$609$	5451.28			0.362721
$610$		0			0
$611$	−5124.50	−	12371.6i	−0.339305	−	0.819154i
$612$		0			0
$613$	25148.3	+	10416.7i	1.65698	+	0.686343i	0.997841	−	0.0656781i	$-0.0209210\pi$
$613$	25148.3	+	10416.7i	1.65698	+	0.686343i	0.659139	+	0.752021i	$0.270921\pi$
$614$		0			0
$615$	34632.4	+	34632.4i	2.27075	+	2.27075i
$616$		0			0
$617$	5951.82	−	5951.82i	0.388349	−	0.388349i	−0.485749	−	0.874098i	$-0.661453\pi$
$617$	5951.82	−	5951.82i	0.388349	−	0.388349i	0.874098	+	0.485749i	$0.161453\pi$
$618$		0			0
$619$	−2222.03	+	5364.46i	−0.144283	+	0.348329i	−0.979456	−	0.201658i	$-0.935367\pi$
$619$	−2222.03	+	5364.46i	−0.144283	+	0.348329i	0.835173	+	0.549987i	$0.185367\pi$
$620$		0			0
$621$	17243.5	−	7142.47i	1.11426	−	0.461542i
$622$		0			0
$623$		−	3923.64i		−	0.252323i
$624$		0			0
$625$		−	18588.8i		−	1.18968i
$626$		0			0
$627$	−6116.62	+	2533.59i	−0.389592	+	0.161374i
$628$		0			0
$629$	8718.08	−	21047.3i	0.552643	−	1.33420i
$630$		0			0
$631$	−22236.1	+	22236.1i	−1.40286	+	1.40286i	−0.612027	+	0.790837i	$0.709646\pi$
$631$	−22236.1	+	22236.1i	−1.40286	+	1.40286i	−0.790837	+	0.612027i	$0.790354\pi$
$632$		0			0
$633$	−8988.73	−	8988.73i	−0.564407	−	0.564407i
$634$		0			0
$635$	−17622.0	−	7299.27i	−1.10127	−	0.456162i
$636$		0			0
$637$	2836.70	+	6848.39i	0.176443	+	0.425970i
$638$		0			0
$639$	16727.9			1.03560
$640$		0			0
$641$	−3642.24			−0.224430			−0.112215	−	0.993684i	$-0.535795\pi$
$641$	−3642.24			−0.224430			−0.112215	+	0.993684i	$0.535795\pi$
$642$		0			0
$643$	7521.88	+	18159.4i	0.461328	+	1.11375i	0.967852	+	0.251519i	$0.0809302\pi$
$643$	7521.88	+	18159.4i	0.461328	+	1.11375i	−0.506524	+	0.862226i	$0.669070\pi$
$644$		0			0
$645$	33594.2	+	13915.2i	2.05080	+	0.849471i
$646$		0			0
$647$	16784.8	+	16784.8i	1.01991	+	1.01991i	0.999798	+	0.0201092i	$0.00640140\pi$
$647$	16784.8	+	16784.8i	1.01991	+	1.01991i	0.0201092	+	0.999798i	$0.493599\pi$
$648$		0			0
$649$	−11121.4	+	11121.4i	−0.672655	+	0.672655i
$650$		0			0
$651$	1572.87	−	3797.24i	0.0946937	−	0.228611i
$652$		0			0
$653$	−12553.7	+	5199.89i	−0.752316	+	0.311620i	−0.725686	−	0.688026i	$-0.758478\pi$
$653$	−12553.7	+	5199.89i	−0.752316	+	0.311620i	−0.0266300	+	0.999645i	$0.508478\pi$
$654$		0			0
$655$		−	12584.1i		−	0.750688i
$656$		0			0
$657$			22915.9i			1.36078i
$658$		0			0
$659$	7775.94	−	3220.90i	0.459647	−	0.190392i	−0.140830	−	0.990034i	$-0.544977\pi$
$659$	7775.94	−	3220.90i	0.459647	−	0.190392i	0.600478	+	0.799642i	$0.294977\pi$
$660$		0			0
$661$	1900.75	−	4588.81i	0.111847	−	0.270021i	−0.858038	−	0.513586i	$-0.828317\pi$
$661$	1900.75	−	4588.81i	0.111847	−	0.270021i	0.969885	+	0.243564i	$0.0783168\pi$
$662$		0			0
$663$	−22834.6	+	22834.6i	−1.33759	+	1.33759i
$664$		0			0
$665$	2420.71	+	2420.71i	0.141160	+	0.141160i
$666$		0			0
$667$	−6319.82	−	2617.76i	−0.366873	−	0.151964i
$668$		0			0
$669$	3533.75	+	8531.23i	0.204219	+	0.493029i
$670$		0			0
$671$	−3845.36			−0.221234
$672$		0			0
$673$	−9638.42			−0.552056			−0.276028	−	0.961150i	$-0.589018\pi$
$673$	−9638.42			−0.552056			−0.276028	+	0.961150i	$0.589018\pi$
$674$		0			0
$675$	−4923.62	−	11886.7i	−0.280756	−	0.677805i
$676$		0			0
$677$	−27908.0	−	11559.9i	−1.58433	−	0.656251i	−0.595239	−	0.803549i	$-0.702943\pi$
$677$	−27908.0	−	11559.9i	−1.58433	−	0.656251i	−0.989092	+	0.147297i	$0.952943\pi$
$678$		0			0
$679$	−7078.72	−	7078.72i	−0.400083	−	0.400083i
$680$		0			0
$681$	22895.2	−	22895.2i	1.28832	−	1.28832i
$682$		0			0
$683$	11978.8	−	28919.3i	0.671090	−	1.62015i	−0.108671	−	0.994078i	$-0.534660\pi$
$683$	11978.8	−	28919.3i	0.671090	−	1.62015i	0.779761	−	0.626077i	$-0.215340\pi$
$684$		0			0
$685$	−29468.3	+	12206.2i	−1.64369	+	0.680838i
$686$		0			0
$687$			32468.8i			1.80315i
$688$		0			0
$689$		−	5706.67i		−	0.315540i
$690$		0			0
$691$	7238.99	−	2998.49i	0.398530	−	0.165076i	−0.174412	−	0.984673i	$-0.555802\pi$
$691$	7238.99	−	2998.49i	0.398530	−	0.165076i	0.572941	+	0.819596i	$0.305802\pi$
$692$		0			0
$693$	−9324.84	+	22512.2i	−0.511142	+	1.23401i
$694$		0			0
$695$	−4944.89	+	4944.89i	−0.269885	+	0.269885i
$696$		0			0
$697$	25839.4	+	25839.4i	1.40422	+	1.40422i
$698$		0			0
$699$	−40232.0	−	16664.6i	−2.17699	−	0.901738i
$700$		0			0
$701$	3609.66	+	8714.49i	0.194486	+	0.469532i	0.990797	−	0.135356i	$-0.0432179\pi$
$701$	3609.66	+	8714.49i	0.194486	+	0.469532i	−0.796311	+	0.604888i	$0.793218\pi$
$702$		0			0
$703$	4446.32			0.238543
$704$		0			0
$705$	39916.7			2.13241
$706$		0			0
$707$	5564.88	+	13434.8i	0.296024	+	0.714665i
$708$		0			0
$709$	−8921.05	−	3695.22i	−0.472549	−	0.195736i	0.133683	−	0.991024i	$-0.457320\pi$
$709$	−8921.05	−	3695.22i	−0.472549	−	0.195736i	−0.606232	+	0.795288i	$0.707320\pi$
$710$		0			0
$711$	−7508.77	−	7508.77i	−0.396063	−	0.396063i
$712$		0			0
$713$	−3646.95	+	3646.95i	−0.191556	+	0.191556i
$714$		0			0
$715$	−10272.3	+	24799.5i	−0.537290	+	1.29713i
$716$		0			0
$717$	−43806.4	+	18145.2i	−2.28170	+	0.945111i
$718$		0			0
$719$		−	36176.8i		−	1.87645i	−0.346025	−	0.938225i	$-0.612469\pi$
$719$		−	36176.8i		−	1.87645i	0.346025	−	0.938225i	$-0.387531\pi$
$720$		0			0
$721$			12412.1i			0.641126i
$722$		0			0
$723$	−39233.9	+	16251.2i	−2.01815	+	0.835947i
$724$		0			0
$725$	−1804.54	+	4356.53i	−0.0924397	+	0.223169i
$726$		0			0
$727$	25292.8	−	25292.8i	1.29031	−	1.29031i	0.355723	−	0.934591i	$-0.384235\pi$
$727$	25292.8	−	25292.8i	1.29031	−	1.29031i	0.934591	−	0.355723i	$-0.115765\pi$
$728$		0			0
$729$	−22563.8	−	22563.8i	−1.14636	−	1.14636i
$730$		0			0
$731$	25064.8	+	10382.2i	1.26820	+	0.525306i
$732$		0			0
$733$	−11236.5	−	27127.4i	−0.566208	−	1.36695i	−0.904729	−	0.425989i	$-0.859926\pi$
$733$	−11236.5	−	27127.4i	−0.566208	−	1.36695i	0.338520	−	0.940959i	$-0.390074\pi$
$734$		0			0
$735$	−22096.1			−1.10888
$736$		0			0
$737$	12395.5			0.619532
$738$		0			0
$739$	−2750.78	−	6640.98i	−0.136927	−	0.330572i	0.840510	−	0.541795i	$-0.182255\pi$
$739$	−2750.78	−	6640.98i	−0.136927	−	0.330572i	−0.977438	+	0.211224i	$0.932255\pi$
$740$		0			0
$741$	−5822.96	−	2411.95i	−0.288680	−	0.119575i
$742$		0			0
$743$	21298.6	+	21298.6i	1.05164	+	1.05164i	0.998592	+	0.0530520i	$0.0168949\pi$
$743$	21298.6	+	21298.6i	1.05164	+	1.05164i	0.0530520	+	0.998592i	$0.483105\pi$
$744$		0			0
$745$	31721.6	−	31721.6i	1.55999	−	1.55999i
$746$		0			0
$747$	22145.1	−	53462.9i	1.08467	−	2.61861i
$748$		0			0
$749$	−8973.44	+	3716.92i	−0.437760	+	0.181326i
$750$		0			0
$751$			33892.3i			1.64680i	0.567462	+	0.823400i	$0.307925\pi$
$751$			33892.3i			1.64680i	−0.567462	+	0.823400i	$0.692075\pi$
$752$		0			0
$753$		−	8911.94i		−	0.431300i
$754$		0			0
$755$	−5066.59	+	2098.65i	−0.244228	+	0.101163i
$756$		0			0
$757$	1447.14	−	3493.72i	0.0694813	−	0.167743i	−0.885324	−	0.464975i	$-0.846063\pi$
$757$	1447.14	−	3493.72i	0.0694813	−	0.167743i	0.954805	+	0.297232i	$0.0960634\pi$
$758$		0			0
$759$	35057.3	−	35057.3i	1.67655	−	1.67655i
$760$		0			0
$761$	−8184.04	−	8184.04i	−0.389844	−	0.389844i	0.484788	−	0.874632i	$-0.338897\pi$
$761$	−8184.04	−	8184.04i	−0.389844	−	0.389844i	−0.874632	+	0.484788i	$0.838897\pi$
$762$		0			0
$763$	−723.359	−	299.625i	−0.0343216	−	0.0142165i
$764$		0			0
$765$	−22719.1	−	54848.7i	−1.07374	−	2.59223i
$766$		0			0
$767$	−14972.9			−0.704878
$768$		0			0
$769$	−29464.8			−1.38170			−0.690850	−	0.722998i	$-0.742763\pi$
$769$	−29464.8			−1.38170			−0.690850	+	0.722998i	$0.742763\pi$
$770$		0			0
$771$	−3280.38	−	7919.53i	−0.153229	−	0.369928i
$772$		0			0
$773$	24119.4	+	9990.57i	1.12227	+	0.464859i	0.865146	−	0.501520i	$-0.167226\pi$
$773$	24119.4	+	9990.57i	1.12227	+	0.464859i	0.257122	+	0.966379i	$0.417226\pi$
$774$		0			0
$775$	2514.00	+	2514.00i	0.116523	+	0.116523i
$776$		0			0
$777$	18762.5	−	18762.5i	0.866284	−	0.866284i
$778$		0			0
$779$	−2729.33	+	6589.19i	−0.125531	+	0.303058i
$780$		0			0
$781$	15540.9	−	6437.26i	0.712034	−	0.294934i
$782$		0			0
$783$		−	6984.67i		−	0.318789i
$784$		0			0
$785$			41932.8i			1.90656i
$786$		0			0
$787$	4642.61	−	1923.03i	0.210281	−	0.0871013i	−0.275057	−	0.961428i	$-0.588697\pi$
$787$	4642.61	−	1923.03i	0.210281	−	0.0871013i	0.485338	+	0.874327i	$0.338697\pi$
$788$		0			0
$789$	−5155.11	+	12445.5i	−0.232607	+	0.561562i
$790$		0			0
$791$	−14227.7	+	14227.7i	−0.639543	+	0.639543i
$792$		0			0
$793$	−2588.53	−	2588.53i	−0.115916	−	0.115916i
$794$		0			0
$795$	15716.0	+	6509.76i	0.701117	+	0.290412i
$796$		0			0
$797$	3908.47	+	9435.87i	0.173708	+	0.419367i	0.986624	−	0.163013i	$-0.0521213\pi$
$797$	3908.47	+	9435.87i	0.173708	+	0.419367i	−0.812916	+	0.582381i	$0.802121\pi$
$798$		0			0
$799$	29782.1			1.31867
$800$		0			0
$801$	−13280.1			−0.585805
$802$		0			0
$803$	8818.53	+	21289.8i	0.387545	+	0.935618i
$804$		0			0
$805$	−23684.8	−	9810.58i	−1.03700	−	0.429537i
$806$		0			0
$807$	−14268.4	−	14268.4i	−0.622392	−	0.622392i
$808$		0			0
$809$	−16382.1	+	16382.1i	−0.711945	+	0.711945i	−0.966942	−	0.254997i	$-0.917925\pi$
$809$	−16382.1	+	16382.1i	−0.711945	+	0.711945i	0.254997	+	0.966942i	$0.417925\pi$
$810$		0			0
$811$	−7236.38	+	17470.2i	−0.313322	+	0.756425i	0.686256	+	0.727360i	$0.259253\pi$
$811$	−7236.38	+	17470.2i	−0.313322	+	0.756425i	−0.999578	+	0.0290650i	$0.990747\pi$
$812$		0			0
$813$	−14425.2	+	5975.11i	−0.622280	+	0.257757i
$814$		0			0
$815$		−	14670.2i		−	0.630521i
$816$		0			0
$817$			5295.03i			0.226744i
$818$		0			0
$819$	−21431.3	+	8877.15i	−0.914373	+	0.378746i
$820$		0			0
$821$	−4916.31	+	11869.0i	−0.208990	+	0.504546i	−0.993265	−	0.115868i	$-0.963035\pi$
$821$	−4916.31	+	11869.0i	−0.208990	+	0.504546i	0.784275	+	0.620413i	$0.213035\pi$
$822$		0			0
$823$	−25989.7	+	25989.7i	−1.10078	+	1.10078i	−0.106465	+	0.994316i	$0.533953\pi$
$823$	−25989.7	+	25989.7i	−1.10078	+	1.10078i	−0.994316	+	0.106465i	$0.966047\pi$
$824$		0			0
$825$	−24166.6	−	24166.6i	−1.01984	−	1.01984i
$826$		0			0
$827$	16783.7	+	6952.03i	0.705715	+	0.292317i	0.706530	−	0.707683i	$-0.250260\pi$
$827$	16783.7	+	6952.03i	0.705715	+	0.292317i	−0.000815266		1.00000i	$0.500260\pi$
$828$		0			0
$829$	5184.19	+	12515.7i	0.217194	+	0.524354i	0.994496	−	0.104774i	$-0.0334120\pi$
$829$	5184.19	+	12515.7i	0.217194	+	0.524354i	−0.777302	+	0.629128i	$0.783412\pi$
$830$		0			0
$831$	−50698.7			−2.11639
$832$		0			0
$833$	−16486.0			−0.685723
$834$		0			0
$835$	−12116.2	−	29251.2i	−0.502155	−	1.21231i
$836$		0			0
$837$	−4865.37	−	2015.30i	−0.200922	−	0.0832247i
$838$		0			0
$839$	248.606	+	248.606i	0.0102298	+	0.0102298i	0.712203	−	0.701973i	$-0.247697\pi$
$839$	248.606	+	248.606i	0.0102298	+	0.0102298i	−0.701973	+	0.712203i	$0.747697\pi$
$840$		0			0
$841$	15435.5	−	15435.5i	0.632887	−	0.632887i
$842$		0			0
$843$	7905.88	−	19086.5i	0.323005	−	0.779802i
$844$		0			0
$845$	6373.89	−	2640.15i	0.259490	−	0.107484i
$846$		0			0
$847$			7417.54i			0.300909i
$848$		0			0
$849$			23447.5i			0.947840i
$850$		0			0
$851$	−30761.9	+	12742.0i	−1.23914	+	0.513267i
$852$		0			0
$853$	−5935.21	+	14328.9i	−0.238239	+	0.575159i	−0.997101	−	0.0760921i	$-0.975756\pi$
$853$	−5935.21	+	14328.9i	−0.238239	+	0.575159i	0.758862	+	0.651251i	$0.225756\pi$
$854$		0			0
$855$	8193.23	−	8193.23i	0.327722	−	0.327722i
$856$		0			0
$857$	6193.30	+	6193.30i	0.246860	+	0.246860i	0.819681	−	0.572821i	$-0.194151\pi$
$857$	6193.30	+	6193.30i	0.246860	+	0.246860i	−0.572821	+	0.819681i	$0.694151\pi$
$858$		0			0
$859$	−9296.87	−	3850.89i	−0.369272	−	0.152958i	0.190327	−	0.981721i	$-0.439045\pi$
$859$	−9296.87	−	3850.89i	−0.369272	−	0.152958i	−0.559600	+	0.828763i	$0.689045\pi$
$860$		0			0
$861$	16287.8	+	39322.3i	0.644701	+	1.55644i
$862$		0			0
$863$	−28317.6			−1.11697			−0.558483	−	0.829516i	$-0.688616\pi$
$863$	−28317.6			−1.11697			−0.558483	+	0.829516i	$0.688616\pi$
$864$		0			0
$865$	29372.5			1.15456
$866$		0			0
$867$	−11704.3	−	28256.7i	−0.458477	−	1.10686i
$868$		0			0
$869$	−9865.51	−	4086.43i	−0.385114	−	0.159520i
$870$		0			0
$871$	8344.15	+	8344.15i	0.324605	+	0.324605i
$872$		0			0
$873$	−23958.9	+	23958.9i	−0.928851	+	0.928851i
$874$		0			0
$875$	2307.57	−	5570.98i	0.0891546	−	0.215238i
$876$		0			0
$877$	43155.1	−	17875.4i	1.66162	−	0.688267i	0.663423	−	0.748244i	$-0.269103\pi$
$877$	43155.1	−	17875.4i	1.66162	−	0.688267i	0.998200	+	0.0599774i	$0.0191029\pi$
$878$		0			0
$879$			59333.1i			2.27674i
$880$		0			0
$881$			9845.05i			0.376491i	0.982122	+	0.188245i	$0.0602800\pi$
$881$			9845.05i			0.376491i	−0.982122	+	0.188245i	$0.939720\pi$
$882$		0			0
$883$	27587.3	−	11427.0i	1.05140	−	0.435504i	0.211008	−	0.977484i	$-0.432325\pi$
$883$	27587.3	−	11427.0i	1.05140	−	0.435504i	0.840391	+	0.541981i	$0.182325\pi$
$884$		0			0
$885$	17080.0	−	41234.9i	0.648745	−	1.56621i
$886$		0			0
$887$	−1279.94	+	1279.94i	−0.0484512	+	0.0484512i	−0.730917	−	0.682466i	$-0.760907\pi$
$887$	−1279.94	+	1279.94i	−0.0484512	+	0.0484512i	0.682466	+	0.730917i	$0.260907\pi$
$888$		0			0
$889$	−11720.6	−	11720.6i	−0.442178	−	0.442178i
$890$		0			0
$891$	−581.141	−	240.717i	−0.0218507	−	0.00905085i
$892$		0			0
$893$	2224.41	+	5370.19i	0.0833560	+	0.201239i
$894$		0			0
$895$	47571.7			1.77670
$896$		0			0
$897$	47198.3			1.75686
$898$		0			0
$899$	738.620	+	1783.19i	0.0274019	+	0.0661541i
$900$		0			0
$901$	11725.8	+	4856.97i	0.433565	+	0.179588i
$902$		0			0
$903$	22343.9	+	22343.9i	0.823432	+	0.823432i
$904$		0			0
$905$	−44192.2	+	44192.2i	−1.62320	+	1.62320i
$906$		0			0
$907$	497.655	−	1201.44i	0.0182187	−	0.0439838i	−0.914508	−	0.404567i	$-0.867422\pi$
$907$	497.655	−	1201.44i	0.0182187	−	0.0439838i	0.932727	+	0.360583i	$0.117422\pi$
$908$		0			0
$909$	45472.0	−	18835.1i	1.65920	−	0.687262i
$910$		0			0
$911$		−	1357.76i		−	0.0493794i	−0.999695	−	0.0246897i	$-0.992140\pi$
$911$		−	1357.76i		−	0.0493794i	0.999695	−	0.0246897i	$-0.00785977\pi$
$912$		0			0
$913$		−	58191.2i		−	2.10936i
$914$		0			0
$915$	10081.5	−	4175.91i	0.364246	−	0.150876i
$916$		0			0
$917$	4184.91	−	10103.3i	0.150707	−	0.363838i
$918$		0			0
$919$	5601.39	−	5601.39i	0.201059	−	0.201059i	−0.599395	−	0.800453i	$-0.704592\pi$
$919$	5601.39	−	5601.39i	0.201059	−	0.201059i	0.800453	+	0.599395i	$0.204592\pi$
$920$		0			0
$921$	142.554	+	142.554i	0.00510023	+	0.00510023i
$922$		0			0
$923$	14794.8	+	6128.21i	0.527602	+	0.218540i
$924$		0			0
$925$	8783.62	+	21205.5i	0.312220	+	0.753766i
$926$		0			0
$927$	42010.6			1.48847
$928$		0			0
$929$	22810.9			0.805598			0.402799	−	0.915288i	$-0.368037\pi$
$929$	22810.9			0.805598			0.402799	+	0.915288i	$0.368037\pi$
$930$		0			0
$931$	−1231.33	−	2972.70i	−0.0433461	−	0.104647i
$932$		0			0
$933$	46284.5	+	19171.7i	1.62410	+	0.672724i
$934$		0			0
$935$	−42214.0	−	42214.0i	−1.47652	−	1.47652i
$936$		0			0
$937$	16556.7	−	16556.7i	0.577251	−	0.577251i	−0.356894	−	0.934145i	$-0.616164\pi$
$937$	16556.7	−	16556.7i	0.577251	−	0.577251i	0.934145	+	0.356894i	$0.116164\pi$
$938$		0			0
$939$	−27667.4	+	66795.1i	−0.961547	+	2.32138i
$940$		0			0
$941$	6945.83	−	2877.06i	0.240624	−	0.0996698i	−0.259113	−	0.965847i	$-0.583430\pi$
$941$	6945.83	−	2877.06i	0.240624	−	0.0996698i	0.499737	+	0.866177i	$0.333430\pi$
$942$		0			0
$943$		−	53409.0i		−	1.84436i
$944$		0			0
$945$		−	26176.5i		−	0.901081i
$946$		0			0
$947$	25322.0	−	10488.7i	0.868905	−	0.359912i	0.0967214	−	0.995311i	$-0.469164\pi$
$947$	25322.0	−	10488.7i	0.868905	−	0.359912i	0.772184	+	0.635399i	$0.219164\pi$
$948$		0			0
$949$	−8395.14	+	20267.7i	−0.287163	+	0.693273i
$950$		0			0
$951$	25758.0	−	25758.0i	0.878296	−	0.878296i
$952$		0			0
$953$	−1354.94	−	1354.94i	−0.0460556	−	0.0460556i	0.683704	−	0.729760i	$-0.260368\pi$
$953$	−1354.94	−	1354.94i	−0.0460556	−	0.0460556i	−0.729760	+	0.683704i	$0.760368\pi$
$954$		0			0
$955$	9515.69	+	3941.53i	0.322430	+	0.133555i
$956$		0			0
$957$	−7100.20	−	17141.4i	−0.239829	−	0.579000i
$958$		0			0
$959$	−27718.3			−0.933336
$960$		0			0
$961$	−28335.8			−0.951152
$962$		0			0
$963$	12580.4	+	30371.9i	0.420975	+	1.01632i
$964$		0			0
$965$	−32570.4	−	13491.1i	−1.08651	−	0.450046i
$966$		0			0
$967$	9687.88	+	9687.88i	0.322173	+	0.322173i	0.849600	−	0.527427i	$-0.176843\pi$
$967$	9687.88	+	9687.88i	0.322173	+	0.322173i	−0.527427	+	0.849600i	$0.676843\pi$
$968$		0			0
$969$	9911.89	−	9911.89i	0.328602	−	0.328602i
$970$		0			0
$971$	9092.27	−	21950.7i	0.300499	−	0.725469i	−0.699443	−	0.714689i	$-0.746568\pi$
$971$	9092.27	−	21950.7i	0.300499	−	0.725469i	0.999942	−	0.0107805i	$-0.00343162\pi$
$972$		0			0
$973$	−5614.52	+	2325.61i	−0.184988	+	0.0766245i
$974$		0			0
$975$		−	32535.8i		−	1.06870i
$976$		0			0
$977$			2789.43i			0.0913426i	0.998957	+	0.0456713i	$0.0145427\pi$
$977$			2789.43i			0.0913426i	−0.998957	+	0.0456713i	$0.985457\pi$
$978$		0			0
$979$	−12337.8	+	5110.48i	−0.402776	+	0.166835i
$980$		0			0
$981$	−1014.12	+	2448.31i	−0.0330056	+	0.0796825i
$982$		0			0
$983$	−10480.4	+	10480.4i	−0.340054	+	0.340054i	−0.856388	−	0.516334i	$-0.827297\pi$
$983$	−10480.4	+	10480.4i	−0.340054	+	0.340054i	0.516334	+	0.856388i	$0.327297\pi$
$984$		0			0
$985$	29203.4	+	29203.4i	0.944666	+	0.944666i
$986$		0			0
$987$	32047.6	+	13274.6i	1.03352	+	0.428099i
$988$		0			0
$989$	−15174.2	−	36633.7i	−0.487877	−	1.17784i
$990$		0			0
$991$	43206.7			1.38497			0.692485	−	0.721432i	$-0.256516\pi$
$991$	43206.7			1.38497			0.692485	+	0.721432i	$0.256516\pi$
$992$		0			0
$993$	−81636.3			−2.60891
$994$		0			0
$995$	23509.7	+	56757.5i	0.749054	+	1.80838i
$996$		0			0
$997$	29415.4	+	12184.3i	0.934399	+	0.387041i	0.797346	−	0.603523i	$-0.206237\pi$
$997$	29415.4	+	12184.3i	0.934399	+	0.387041i	0.137054	+	0.990564i	$0.456237\pi$
$998$		0			0
$999$	−24040.3	−	24040.3i	−0.761362	−	0.761362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.113.10		44
4.3	odd	2		32.4.g.a.5.5	✓	44
8.3	odd	2		256.4.g.b.225.10		44
8.5	even	2		256.4.g.a.225.2		44
32.3	odd	8		256.4.g.b.33.10		44
32.13	even	8	inner	128.4.g.a.17.10		44
32.19	odd	8		32.4.g.a.13.5	yes	44
32.29	even	8		256.4.g.a.33.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.5	✓	44	4.3	odd	2
32.4.g.a.13.5	yes	44	32.19	odd	8
128.4.g.a.17.10		44	32.13	even	8	inner
128.4.g.a.113.10		44	1.1	even	1	trivial
256.4.g.a.33.2		44	32.29	even	8
256.4.g.a.225.2		44	8.5	even	2
256.4.g.b.33.10		44	32.3	odd	8
256.4.g.b.225.10		44	8.3	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.21198 + 7.75440i) q^{3} +(-13.6472 - 5.65283i) q^{5} +(-9.07689 - 9.07689i) q^{7} +(-30.7220 + 30.7220i) q^{9} +O(q^{10})\)	\(q+(3.21198 + 7.75440i) q^{3} +(-13.6472 - 5.65283i) q^{5} +(-9.07689 - 9.07689i) q^{7} +(-30.7220 + 30.7220i) q^{9} +(-16.7195 + 40.3646i) q^{11} +(-38.4266 + 15.9168i) q^{13} -123.982i q^{15} -92.5038i q^{17} +(16.6799 - 6.90905i) q^{19} +(41.2311 - 99.5406i) q^{21} +(-95.6008 + 95.6008i) q^{23} +(65.9018 + 65.9018i) q^{25} +(-127.540 - 52.8290i) q^{27} +(19.3621 + 46.7443i) q^{29} +38.1477 q^{31} -366.706 q^{33} +(72.5636 + 175.184i) q^{35} +(227.529 + 94.2456i) q^{37} +(-246.851 - 246.851i) q^{39} +(-279.334 + 279.334i) q^{41} +(-112.235 + 270.960i) q^{43} +(592.935 - 245.602i) q^{45} +321.955i q^{47} -178.220i q^{49} +(717.312 - 297.120i) q^{51} +(-52.5056 + 126.760i) q^{53} +(456.348 - 456.348i) q^{55} +(107.151 + 107.151i) q^{57} +(332.587 + 137.762i) q^{59} +(33.6815 + 81.3143i) q^{61} +557.721 q^{63} +614.389 q^{65} +(-108.572 - 262.117i) q^{67} +(-1048.39 - 434.259i) q^{69} +(-272.246 - 272.246i) q^{71} +(372.955 - 372.955i) q^{73} +(-299.354 + 722.704i) q^{75} +(518.146 - 214.623i) q^{77} +244.410i q^{79} +14.3973i q^{81} +(-1230.52 + 509.697i) q^{83} +(-522.909 + 1262.41i) q^{85} +(-300.283 + 300.283i) q^{87} +(216.134 + 216.134i) q^{89} +(493.270 + 204.319i) q^{91} +(122.529 + 295.812i) q^{93} -266.689 q^{95} +779.862 q^{97} +(-726.422 - 1753.74i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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