LMFDB - Embedded newform 128.4.g.a.17.10

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			17.10
Character	$\chi$	$=$	128.17
Dual form			128.4.g.a.113.10

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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	−0.235710	−	0.971824i	$-0.575741\pi$
$3$	3.21198	−	7.75440i	0.618145	−	1.49233i	0.853855	−	0.520511i	$-0.174259\pi$
$4$		0			0
$5$	−13.6472	+	5.65283i	−1.22064	+	0.505605i	−0.897613	−	0.440785i	$-0.854700\pi$
$5$	−13.6472	+	5.65283i	−1.22064	+	0.505605i	−0.323026	+	0.946390i	$0.604700\pi$
$6$		0			0
$7$	−9.07689	+	9.07689i	−0.490106	+	0.490106i	−0.908340	−	0.418233i	$-0.862649\pi$
$7$	−9.07689	+	9.07689i	−0.490106	+	0.490106i	0.418233	+	0.908340i	$0.362649\pi$
$8$		0			0
$9$	−30.7220	−	30.7220i	−1.13785	−	1.13785i
$10$		0			0
$11$	−16.7195	−	40.3646i	−0.458285	−	1.10640i	−0.969091	−	0.246702i	$-0.920653\pi$
$11$	−16.7195	−	40.3646i	−0.458285	−	1.10640i	0.510807	−	0.859696i	$-0.329347\pi$
$12$		0			0
$13$	−38.4266	−	15.9168i	−0.819817	−	0.339580i	−0.0669538	−	0.997756i	$-0.521328\pi$
$13$	−38.4266	−	15.9168i	−0.819817	−	0.339580i	−0.752864	+	0.658177i	$0.771328\pi$
$14$		0			0
$15$			123.982i			2.13414i
$16$		0			0
$17$			92.5038i			1.31973i	0.751383	+	0.659867i	$0.229387\pi$
$17$			92.5038i			1.31973i	−0.751383	+	0.659867i	$0.770613\pi$
$18$		0			0
$19$	16.6799	+	6.90905i	0.201402	+	0.0834235i	0.481104	−	0.876663i	$-0.340236\pi$
$19$	16.6799	+	6.90905i	0.201402	+	0.0834235i	−0.279702	+	0.960087i	$0.590236\pi$
$20$		0			0
$21$	41.2311	+	99.5406i	0.428446	+	1.03436i
$22$		0			0
$23$	−95.6008	−	95.6008i	−0.866702	−	0.866702i	0.125404	−	0.992106i	$-0.459977\pi$
$23$	−95.6008	−	95.6008i	−0.866702	−	0.866702i	−0.992106	+	0.125404i	$0.959977\pi$
$24$		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	−0.849687	−	0.527288i	$-0.823209\pi$
$29$	19.3621	−	46.7443i	0.123981	−	0.299317i	0.973668	+	0.227971i	$0.0732090\pi$
$30$		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	0.185156	−	0.982709i	$-0.440721\pi$
$37$	227.529	−	94.2456i	1.01096	−	0.418754i	0.825805	+	0.563955i	$0.190721\pi$
$38$		0			0
$39$	−246.851	+	246.851i	−1.01353	+	1.01353i
$40$		0			0
$41$	−279.334	−	279.334i	−1.06401	−	1.06401i	−0.997806	−	0.0662081i	$-0.978910\pi$
$41$	−279.334	−	279.334i	−1.06401	−	1.06401i	−0.0662081	−	0.997806i	$-0.521090\pi$
$42$		0			0
$43$	−112.235	−	270.960i	−0.398039	−	0.960952i	−0.988131	−	0.153616i	$-0.950908\pi$
$43$	−112.235	−	270.960i	−0.398039	−	0.960952i	0.590091	−	0.807337i	$-0.299092\pi$
$44$		0			0
$45$	592.935	+	245.602i	1.96421	+	0.813603i
$46$		0			0
$47$		−	321.955i		−	0.999191i	−0.866259	−	0.499596i	$-0.833482\pi$
$47$		−	321.955i		−	0.999191i	0.866259	−	0.499596i	$-0.166518\pi$
$48$		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	0.841120	−	0.540848i	$-0.181897\pi$
$53$	−52.5056	−	126.760i	−0.136079	−	0.328524i	−0.977199	+	0.212324i	$0.931897\pi$
$54$		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	0.0157369	−	0.999876i	$-0.494991\pi$
$59$	332.587	−	137.762i	0.733884	−	0.303985i	0.718147	+	0.695892i	$0.244991\pi$
$60$		0			0
$61$	33.6815	−	81.3143i	0.0706963	−	0.170676i	−0.884582	−	0.466385i	$-0.845556\pi$
$61$	33.6815	−	81.3143i	0.0706963	−	0.170676i	0.955278	+	0.295709i	$0.0955560\pi$
$62$		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	−0.991424	−	0.130684i	$-0.958283\pi$
$67$	−108.572	+	262.117i	−0.197974	+	0.477951i	0.793450	+	0.608635i	$0.208283\pi$
$68$		0			0
$69$	−1048.39	+	434.259i	−1.82916	+	0.757661i
$70$		0			0
$71$	−272.246	+	272.246i	−0.455066	+	0.455066i	−0.897032	−	0.441966i	$-0.854281\pi$
$71$	−272.246	+	272.246i	−0.455066	+	0.455066i	0.441966	+	0.897032i	$0.354281\pi$
$72$		0			0
$73$	372.955	+	372.955i	0.597960	+	0.597960i	0.939769	−	0.341809i	$-0.111040\pi$
$73$	372.955	+	372.955i	0.597960	+	0.597960i	−0.341809	+	0.939769i	$0.611040\pi$
$74$		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	$-0.944318\pi$
$79$		−	244.410i		−	0.348080i	0.984739	−	0.174040i	$-0.0556822\pi$
$80$		0			0
$81$		−	14.3973i		−	0.0197494i
$82$		0			0
$83$	−1230.52	−	509.697i	−1.62731	−	0.674054i	−0.632384	−	0.774655i	$-0.717924\pi$
$83$	−1230.52	−	509.697i	−1.62731	−	0.674054i	−0.994927	+	0.100600i	$0.967924\pi$
$84$		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	−0.566586	−	0.824003i	$-0.691736\pi$
$89$	216.134	−	216.134i	0.257417	−	0.257417i	0.824003	+	0.566586i	$0.191736\pi$
$90$		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	−0.833106	−	0.553113i	$-0.813440\pi$
$101$	−1046.60	+	433.515i	−1.03109	+	0.427092i	−0.197985	+	0.980205i	$0.563440\pi$
$102$		0			0
$103$	−683.721	+	683.721i	−0.654069	+	0.654069i	−0.953970	−	0.299901i	$-0.903046\pi$
$103$	−683.721	+	683.721i	−0.654069	+	0.654069i	0.299901	+	0.953970i	$0.403046\pi$
$104$		0			0
$105$	−1125.37	−	1125.37i	−1.04595	−	1.04595i
$106$		0			0
$107$	289.555	+	699.048i	0.261611	+	0.631584i	0.999038	−	0.0438418i	$-0.0139598\pi$
$107$	289.555	+	699.048i	0.261611	+	0.631584i	−0.737428	+	0.675426i	$0.763960\pi$
$108$		0			0
$109$	56.3510	+	23.3413i	0.0495179	+	0.0205110i	0.407305	−	0.913292i	$-0.366469\pi$
$109$	56.3510	+	23.3413i	0.0495179	+	0.0205110i	−0.357787	+	0.933803i	$0.616469\pi$
$110$		0			0
$111$		−	2067.07i		−	1.76754i
$112$		0			0
$113$			1567.46i			1.30491i	0.757828	+	0.652454i	$0.226260\pi$
$113$			1567.46i			1.30491i	−0.757828	+	0.652454i	$0.773740\pi$
$114$		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	−0.777096	−	0.629382i	$-0.783308\pi$
$131$	326.012	−	787.064i	0.217434	−	0.524932i	0.994530	+	0.104450i	$0.0333082\pi$
$132$		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	0.998908	−	0.0467305i	$-0.0148802\pi$
$137$	1526.86	+	1526.86i	0.952177	+	0.952177i	−0.0467305	+	0.998908i	$0.514880\pi$
$138$		0			0
$139$	181.169	+	437.382i	0.110551	+	0.266894i	0.969467	−	0.245224i	$-0.0788614\pi$
$139$	181.169	+	437.382i	0.110551	+	0.266894i	−0.858916	+	0.512117i	$0.828861\pi$
$140$		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	−0.828008	−	0.560716i	$-0.810526\pi$
$149$	−1162.21	−	2805.81i	−0.639004	−	1.54269i	0.189004	−	0.981976i	$-0.439474\pi$
$150$		0			0
$151$	262.518	+	262.518i	0.141479	+	0.141479i	0.774299	−	0.632820i	$-0.218103\pi$
$151$	262.518	+	262.518i	0.141479	+	0.141479i	−0.632820	+	0.774299i	$0.718103\pi$
$152$		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	0.363575	+	0.931565i	$0.381556\pi$
$157$	−1086.34	+	2622.67i	−0.552227	+	1.33319i	−0.915802	+	0.401630i	$0.868444\pi$
$158$		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	−0.805878	−	0.592081i	$-0.798307\pi$
$163$	380.057	−	917.540i	0.182628	−	0.440903i	0.988507	+	0.151178i	$0.0483065\pi$
$164$		0			0
$165$	5004.49	−	2072.93i	2.36120	−	0.978043i
$166$		0			0
$167$	1515.61	−	1515.61i	0.702283	−	0.702283i	−0.262617	−	0.964900i	$-0.584586\pi$
$167$	1515.61	−	1515.61i	0.702283	−	0.702283i	0.964900	+	0.262617i	$0.0845857\pi$
$168$		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	−0.0594515	−	0.998231i	$-0.518935\pi$
$173$	−1837.08	−	760.945i	−0.807346	−	0.334414i	−0.747895	+	0.663817i	$0.768935\pi$
$174$		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	−0.337930	−	0.941171i	$-0.609727\pi$
$179$	−2975.35	−	1232.43i	−1.24239	−	0.514615i	−0.904461	+	0.426556i	$0.859727\pi$
$180$		0			0
$181$	1619.10	+	3908.85i	0.664899	+	1.60521i	0.790030	+	0.613068i	$0.210065\pi$
$181$	1619.10	+	3908.85i	0.664899	+	1.60521i	−0.125132	+	0.992140i	$0.539935\pi$
$182$		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	−0.797268	−	0.603625i	$-0.793722\pi$
$197$	−2583.07	+	1069.94i	−0.934194	+	0.386956i	−0.136926	+	0.990581i	$0.543722\pi$
$198$		0			0
$199$	−2940.81	+	2940.81i	−1.04758	+	1.04758i	−0.0487695	+	0.998810i	$0.515530\pi$
$199$	−2940.81	+	2940.81i	−1.04758	+	1.04758i	−0.998810	+	0.0487695i	$0.984470\pi$
$200$		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	0.142552	−	0.989787i	$-0.454469\pi$
$211$	−1399.25	−	579.589i	−0.456533	−	0.189102i	−0.599085	+	0.800685i	$0.704469\pi$
$212$		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	0.547110	+	0.837061i	$0.315728\pi$
$227$	−1476.27	+	3564.04i	−0.431647	+	1.04209i	−0.978756	+	0.205026i	$0.934272\pi$
$228$		0			0
$229$	3573.95	−	1480.38i	1.03132	−	0.427188i	0.198134	−	0.980175i	$-0.436512\pi$
$229$	3573.95	−	1480.38i	1.03132	−	0.427188i	0.833190	+	0.552986i	$0.186512\pi$
$230$		0			0
$231$	3328.55	−	3328.55i	0.948062	−	0.948062i
$232$		0			0
$233$	−3668.67	−	3668.67i	−1.03151	−	1.03151i	−0.999487	−	0.0320257i	$-0.989804\pi$
$233$	−3668.67	−	3668.67i	−1.03151	−	1.03151i	−0.0320257	−	0.999487i	$-0.510196\pi$
$234$		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	$-0.722999\pi$
$239$		−	5649.23i		−	1.52895i	0.644656	−	0.764473i	$-0.277001\pi$
$240$		0			0
$241$		−	5059.57i		−	1.35235i	−0.736743	−	0.676173i	$-0.763637\pi$
$241$		−	5059.57i		−	1.35235i	0.736743	−	0.676173i	$-0.236363\pi$
$242$		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	−0.502601	−	0.864519i	$-0.667623\pi$
$251$	−980.968	+	406.330i	−0.246686	+	0.102181i	0.255915	+	0.966699i	$0.417623\pi$
$252$		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	−0.561437	−	0.827520i	$-0.689751\pi$
$263$	1134.88	−	1134.88i	0.266083	−	0.266083i	0.827520	+	0.561437i	$0.189751\pi$
$264$		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	0.116488	−	0.993192i	$-0.462836\pi$
$269$	−2221.12	−	920.017i	−0.503435	−	0.208530i	−0.619923	+	0.784663i	$0.712836\pi$
$270$		0			0
$271$		−	1860.26i		−	0.416984i	−0.978024	−	0.208492i	$-0.933144\pi$
$271$		−	1860.26i		−	0.416984i	0.978024	−	0.208492i	$-0.0668555\pi$
$272$		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	−0.948721	−	0.316113i	$-0.897622\pi$
$277$	−2311.55	−	5580.58i	−0.501400	−	1.21049i	0.447322	−	0.894373i	$-0.352378\pi$
$278$		0			0
$279$	−1171.97	−	1171.97i	−0.251485	−	0.251485i
$280$		0			0
$281$	−1740.45	+	1740.45i	−0.369490	+	0.369490i	−0.867291	−	0.497801i	$-0.834141\pi$
$281$	−1740.45	+	1740.45i	−0.369490	+	0.369490i	0.497801	+	0.867291i	$0.334141\pi$
$282$		0			0
$283$	2580.95	−	1069.06i	0.542125	−	0.224555i	−0.0947795	−	0.995498i	$-0.530215\pi$
$283$	2580.95	−	1069.06i	0.542125	−	0.224555i	0.636904	+	0.770943i	$0.280215\pi$
$284$		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	0.379603	−	0.925149i	$-0.376061\pi$
$293$	6531.00	−	2705.23i	1.30220	−	0.539390i	0.922599	+	0.385760i	$0.126061\pi$
$294$		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	0.384745	−	0.923023i	$-0.374289\pi$
$307$	22.1910	+	9.19181i	0.00412543	+	0.00170881i	−0.380620	+	0.924732i	$0.624289\pi$
$308$		0			0
$309$	3105.75	+	7497.95i	0.571780	+	1.38040i
$310$		0			0
$311$	4220.58	+	4220.58i	0.769540	+	0.769540i	0.978026	−	0.208485i	$-0.0668533\pi$
$311$	4220.58	+	4220.58i	0.769540	+	0.769540i	−0.208485	+	0.978026i	$0.566853\pi$
$312$		0			0
$313$	6090.90	−	6090.90i	1.09993	−	1.09993i	0.105512	−	0.994418i	$-0.466352\pi$
$313$	6090.90	−	6090.90i	1.09993	−	1.09993i	0.994418	−	0.105512i	$-0.0336481\pi$
$314$		0			0
$315$	−7611.30	+	3152.71i	−1.36142	+	0.563920i
$316$		0			0
$317$	−1660.86	+	4009.67i	−0.294269	+	0.710428i	0.705729	+	0.708482i	$0.250620\pi$
$317$	−1660.86	+	4009.67i	−0.294269	+	0.710428i	−0.999998	+	0.00194638i	$0.999380\pi$
$318$		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	−0.853924	−	0.520397i	$-0.825784\pi$
$331$	−3722.12	−	8985.99i	−0.618085	−	1.49219i	0.235840	−	0.971792i	$-0.424216\pi$
$332$		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	$0.138404\pi$
$337$			5211.97i			0.842475i	−0.906950	+	0.421238i	$0.861596\pi$
$338$		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	−0.733499	−	0.679691i	$-0.762114\pi$
$347$	−4987.20	+	2065.77i	−0.771547	+	0.319585i	−0.0380483	+	0.999276i	$0.512114\pi$
$348$		0			0
$349$	3137.63	−	7574.92i	0.481243	−	1.16182i	−0.477776	−	0.878481i	$-0.658557\pi$
$349$	3137.63	−	7574.92i	0.481243	−	1.16182i	0.959019	−	0.283341i	$-0.0914429\pi$
$350$		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	−0.271715	−	0.962378i	$-0.587591\pi$
$359$	4697.94	−	4697.94i	0.690662	−	0.690662i	0.962378	+	0.271715i	$0.0875909\pi$
$360$		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	$-0.861118\pi$
$367$		−	5942.35i		−	0.845199i	0.906316	−	0.422600i	$-0.138882\pi$
$368$		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	0.875780	−	0.482711i	$-0.160348\pi$
$373$	−611.014	−	1475.12i	−0.0848180	−	0.204769i	−0.960598	+	0.277942i	$0.910348\pi$
$374$		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	−0.603176	−	0.797608i	$-0.706098\pi$
$379$	−3436.04	+	1423.25i	−0.465692	+	0.192896i	0.137484	+	0.990504i	$0.456098\pi$
$380$		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	0.192123	−	0.981371i	$-0.438463\pi$
$389$	7840.37	−	3247.59i	1.02191	−	0.423288i	0.829785	+	0.558083i	$0.188463\pi$
$390$		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	0.770805	−	0.637071i	$-0.219854\pi$
$397$	6845.23	+	2835.39i	0.865370	+	0.358448i	0.0945649	+	0.995519i	$0.469854\pi$
$398$		0			0
$399$			1945.20i			0.244064i
$400$		0			0
$401$		−	5333.86i		−	0.664240i	−0.943237	−	0.332120i	$-0.892236\pi$
$401$		−	5333.86i		−	0.664240i	0.943237	−	0.332120i	$-0.107764\pi$
$402$		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	−0.902665	−	0.430343i	$-0.858393\pi$
$409$	−3906.82	+	3906.82i	−0.472322	+	0.472322i	0.430343	+	0.902665i	$0.358393\pi$
$410$		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	−0.950852	−	0.309646i	$-0.899790\pi$
$419$	−510.706	+	1232.95i	−0.0595456	+	0.143756i	0.891306	+	0.453401i	$0.149790\pi$
$420$		0			0
$421$	−9078.42	+	3760.41i	−1.05096	+	0.435323i	−0.840235	−	0.542222i	$-0.817583\pi$
$421$	−9078.42	+	3760.41i	−1.05096	+	0.435323i	−0.210727	+	0.977545i	$0.567583\pi$
$422$		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	$-0.858722\pi$
$431$		−	7684.54i		−	0.858820i	0.903110	−	0.429410i	$-0.141278\pi$
$432$		0			0
$433$			989.963i			0.109872i	0.998490	+	0.0549360i	$0.0174955\pi$
$433$			989.963i			0.109872i	−0.998490	+	0.0549360i	$0.982505\pi$
$434$		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	0.608287	−	0.793717i	$-0.291857\pi$
$439$	−1705.59	−	1705.59i	−0.185429	−	0.185429i	−0.793717	+	0.608287i	$0.791857\pi$
$440$		0			0
$441$	5475.28	−	5475.28i	0.591219	−	0.591219i
$442$		0			0
$443$	−14875.4	+	6161.58i	−1.59537	+	0.660826i	−0.990752	−	0.135687i	$-0.956676\pi$
$443$	−14875.4	+	6161.58i	−1.59537	+	0.660826i	−0.604622	+	0.796512i	$0.706676\pi$
$444$		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	0.0493636	−	0.998781i	$-0.484281\pi$
$457$	−9275.37	−	9275.37i	−0.949417	−	0.949417i	−0.998781	+	0.0493636i	$0.984281\pi$
$458$		0			0
$459$	−4886.88	−	11798.0i	−0.496950	−	1.19974i
$460$		0			0
$461$	6867.75	+	2844.71i	0.693846	+	0.287400i	0.701601	−	0.712570i	$-0.252469\pi$
$461$	6867.75	+	2844.71i	0.693846	+	0.287400i	−0.00775571	+	0.999970i	$0.502469\pi$
$462$		0			0
$463$			7678.71i			0.770756i	0.922759	+	0.385378i	$0.125929\pi$
$463$			7678.71i			0.770756i	−0.922759	+	0.385378i	$0.874071\pi$
$464$		0			0
$465$			4729.63i			0.471681i
$466$		0			0
$467$	3867.05	+	1601.79i	0.383182	+	0.158719i	0.565955	−	0.824436i	$-0.308507\pi$
$467$	3867.05	+	1601.79i	0.383182	+	0.158719i	−0.182773	+	0.983155i	$0.558507\pi$
$468$		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	−0.281516	+	0.959556i	$0.590837\pi$
$487$	−13338.0	+	13338.0i	−1.24107	+	1.24107i	−0.959556	+	0.281516i	$0.909163\pi$
$488$		0			0
$489$	−5894.23	−	5894.23i	−0.545085	−	0.545085i
$490$		0			0
$491$	−6069.18	−	14652.3i	−0.557837	−	1.34674i	−0.911475	−	0.411356i	$-0.865055\pi$
$491$	−6069.18	−	14652.3i	−0.557837	−	1.34674i	0.353637	−	0.935383i	$-0.384945\pi$
$492$		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	0.238873	−	0.971051i	$-0.423222\pi$
$499$	−3108.34	−	1287.52i	−0.278855	−	0.115505i	−0.517728	+	0.855545i	$0.673222\pi$
$500$		0			0
$501$	−6884.53	−	16620.7i	−0.613928	−	1.48215i
$502$		0			0
$503$	9569.65	+	9569.65i	0.848289	+	0.848289i	0.989920	−	0.141630i	$-0.0452344\pi$
$503$	9569.65	+	9569.65i	0.848289	+	0.848289i	−0.141630	+	0.989920i	$0.545234\pi$
$504$		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	−0.544950	−	0.838469i	$-0.683451\pi$
$509$	4975.54	−	12012.0i	0.433275	−	1.04602i	0.978225	−	0.207549i	$-0.0665487\pi$
$510$		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	0.997689	−	0.0679465i	$-0.0216447\pi$
$521$	11056.5	+	11056.5i	0.929743	+	0.929743i	−0.0679465	+	0.997689i	$0.521645\pi$
$522$		0			0
$523$	−7704.74	−	18600.9i	−0.644178	−	1.55518i	−0.820993	−	0.570938i	$-0.806580\pi$
$523$	−7704.74	−	18600.9i	−0.644178	−	1.55518i	0.176815	−	0.984244i	$-0.443420\pi$
$524$		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	−0.997848	−	0.0655712i	$-0.979113\pi$
$541$	−3094.21	+	7470.07i	−0.245897	+	0.593648i	0.751951	+	0.659219i	$0.229113\pi$
$542$		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	0.440479	+	0.897763i	$0.354809\pi$
$547$	−6470.84	+	15622.0i	−0.505801	+	1.22111i	−0.946280	+	0.323349i	$0.895191\pi$
$548$		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	−0.0498238	−	0.998758i	$-0.515866\pi$
$557$	−10401.9	−	4308.63i	−0.791283	−	0.327760i	−0.741459	+	0.670998i	$0.765866\pi$
$558$		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	0.447593	−	0.894237i	$-0.352281\pi$
$563$	1760.24	+	729.116i	0.131768	+	0.0545801i	−0.315825	+	0.948817i	$0.602281\pi$
$564$		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	−0.343767	−	0.939055i	$-0.611703\pi$
$569$	8079.71	−	8079.71i	0.595288	−	0.595288i	0.939055	+	0.343767i	$0.111703\pi$
$570$		0			0
$571$	16823.9	−	6968.69i	1.23303	−	0.510737i	0.331498	−	0.943456i	$-0.392446\pi$
$571$	16823.9	−	6968.69i	1.23303	−	0.510737i	0.901529	+	0.432719i	$0.142446\pi$
$572$		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	0.938504	−	0.345268i	$-0.112212\pi$
$587$	437.187	+	1055.46i	0.0307404	+	0.0742139i	−0.907764	+	0.419482i	$0.862212\pi$
$588$		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	$0.360745\pi$
$593$			26161.0i			1.81164i	−0.423661	+	0.905821i	$0.639255\pi$
$594$		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	0.989541	−	0.144253i	$-0.0460778\pi$
$599$	12392.1	+	12392.1i	0.845288	+	0.845288i	−0.144253	+	0.989541i	$0.546078\pi$
$600$		0			0
$601$	5696.78	−	5696.78i	0.386650	−	0.386650i	−0.486841	−	0.873491i	$-0.661851\pi$
$601$	5696.78	−	5696.78i	0.386650	−	0.386650i	0.873491	+	0.486841i	$0.161851\pi$
$602$		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	0.659139	−	0.752021i	$-0.270921\pi$
$613$	25148.3	−	10416.7i	1.65698	−	0.686343i	0.997841	+	0.0656781i	$0.0209210\pi$
$614$		0			0
$615$	34632.4	−	34632.4i	2.27075	−	2.27075i
$616$		0			0
$617$	5951.82	+	5951.82i	0.388349	+	0.388349i	0.874098	−	0.485749i	$-0.161453\pi$
$617$	5951.82	+	5951.82i	0.388349	+	0.388349i	−0.485749	+	0.874098i	$0.661453\pi$
$618$		0			0
$619$	−2222.03	−	5364.46i	−0.144283	−	0.348329i	0.835173	−	0.549987i	$-0.185367\pi$
$619$	−2222.03	−	5364.46i	−0.144283	−	0.348329i	−0.979456	+	0.201658i	$0.935367\pi$
$620$		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	−0.790837	−	0.612027i	$-0.790354\pi$
$631$	−22236.1	−	22236.1i	−1.40286	−	1.40286i	−0.612027	−	0.790837i	$-0.709646\pi$
$632$		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	−0.506524	−	0.862226i	$-0.669070\pi$
$643$	7521.88	−	18159.4i	0.461328	−	1.11375i	0.967852	−	0.251519i	$-0.0809302\pi$
$644$		0			0
$645$	33594.2	−	13915.2i	2.05080	−	0.849471i
$646$		0			0
$647$	16784.8	−	16784.8i	1.01991	−	1.01991i	0.0201092	−	0.999798i	$-0.493599\pi$
$647$	16784.8	−	16784.8i	1.01991	−	1.01991i	0.999798	−	0.0201092i	$-0.00640140\pi$
$648$		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	−0.0266300	−	0.999645i	$-0.508478\pi$
$653$	−12553.7	−	5199.89i	−0.752316	−	0.311620i	−0.725686	+	0.688026i	$0.758478\pi$
$654$		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	0.600478	−	0.799642i	$-0.294977\pi$
$659$	7775.94	+	3220.90i	0.459647	+	0.190392i	−0.140830	+	0.990034i	$0.544977\pi$
$660$		0			0
$661$	1900.75	+	4588.81i	0.111847	+	0.270021i	0.969885	−	0.243564i	$-0.0783168\pi$
$661$	1900.75	+	4588.81i	0.111847	+	0.270021i	−0.858038	+	0.513586i	$0.828317\pi$
$662$		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	−0.989092	−	0.147297i	$-0.952943\pi$
$677$	−27908.0	+	11559.9i	−1.58433	+	0.656251i	−0.595239	+	0.803549i	$0.702943\pi$
$678$		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	0.779761	+	0.626077i	$0.215340\pi$
$683$	11978.8	+	28919.3i	0.671090	+	1.62015i	−0.108671	+	0.994078i	$0.534660\pi$
$684$		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	0.572941	−	0.819596i	$-0.305802\pi$
$691$	7238.99	+	2998.49i	0.398530	+	0.165076i	−0.174412	+	0.984673i	$0.555802\pi$
$692$		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	−0.796311	−	0.604888i	$-0.793218\pi$
$701$	3609.66	−	8714.49i	0.194486	−	0.469532i	0.990797	+	0.135356i	$0.0432179\pi$
$702$		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	−0.606232	−	0.795288i	$-0.707320\pi$
$709$	−8921.05	+	3695.22i	−0.472549	+	0.195736i	0.133683	+	0.991024i	$0.457320\pi$
$710$		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	$0.387531\pi$
$719$			36176.8i			1.87645i	−0.346025	+	0.938225i	$0.612469\pi$
$720$		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	0.934591	+	0.355723i	$0.115765\pi$
$727$	25292.8	+	25292.8i	1.29031	+	1.29031i	0.355723	+	0.934591i	$0.384235\pi$
$728$		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	0.338520	+	0.940959i	$0.390074\pi$
$733$	−11236.5	+	27127.4i	−0.566208	+	1.36695i	−0.904729	+	0.425989i	$0.859926\pi$
$734$		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	−0.977438	−	0.211224i	$-0.932255\pi$
$739$	−2750.78	+	6640.98i	−0.136927	+	0.330572i	0.840510	+	0.541795i	$0.182255\pi$
$740$		0			0
$741$	−5822.96	+	2411.95i	−0.288680	+	0.119575i
$742$		0			0
$743$	21298.6	−	21298.6i	1.05164	−	1.05164i	0.0530520	−	0.998592i	$-0.483105\pi$
$743$	21298.6	−	21298.6i	1.05164	−	1.05164i	0.998592	−	0.0530520i	$-0.0168949\pi$
$744$		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	$-0.692075\pi$
$751$		−	33892.3i		−	1.64680i	0.567462	−	0.823400i	$-0.307925\pi$
$752$		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	0.954805	−	0.297232i	$-0.0960634\pi$
$757$	1447.14	+	3493.72i	0.0694813	+	0.167743i	−0.885324	+	0.464975i	$0.846063\pi$
$758$		0			0
$759$	35057.3	+	35057.3i	1.67655	+	1.67655i
$760$		0			0
$761$	−8184.04	+	8184.04i	−0.389844	+	0.389844i	−0.874632	−	0.484788i	$-0.838897\pi$
$761$	−8184.04	+	8184.04i	−0.389844	+	0.389844i	0.484788	+	0.874632i	$0.338897\pi$
$762$		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	0.257122	−	0.966379i	$-0.417226\pi$
$773$	24119.4	−	9990.57i	1.12227	−	0.464859i	0.865146	+	0.501520i	$0.167226\pi$
$774$		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	0.485338	−	0.874327i	$-0.338697\pi$
$787$	4642.61	+	1923.03i	0.210281	+	0.0871013i	−0.275057	+	0.961428i	$0.588697\pi$
$788$		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	−0.812916	−	0.582381i	$-0.802121\pi$
$797$	3908.47	−	9435.87i	0.173708	−	0.419367i	0.986624	+	0.163013i	$0.0521213\pi$
$798$		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	0.254997	−	0.966942i	$-0.417925\pi$
$809$	−16382.1	−	16382.1i	−0.711945	−	0.711945i	−0.966942	+	0.254997i	$0.917925\pi$
$810$		0			0
$811$	−7236.38	−	17470.2i	−0.313322	−	0.756425i	−0.999578	−	0.0290650i	$-0.990747\pi$
$811$	−7236.38	−	17470.2i	−0.313322	−	0.756425i	0.686256	−	0.727360i	$-0.259253\pi$
$812$		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	0.784275	−	0.620413i	$-0.213035\pi$
$821$	−4916.31	−	11869.0i	−0.208990	−	0.504546i	−0.993265	+	0.115868i	$0.963035\pi$
$822$		0			0
$823$	−25989.7	−	25989.7i	−1.10078	−	1.10078i	−0.994316	−	0.106465i	$-0.966047\pi$
$823$	−25989.7	−	25989.7i	−1.10078	−	1.10078i	−0.106465	−	0.994316i	$-0.533953\pi$
$824$		0			0
$825$	−24166.6	+	24166.6i	−1.01984	+	1.01984i
$826$		0			0
$827$	16783.7	−	6952.03i	0.705715	−	0.292317i	−0.000815266	−	1.00000i	$-0.500260\pi$
$827$	16783.7	−	6952.03i	0.705715	−	0.292317i	0.706530	+	0.707683i	$0.250260\pi$
$828$		0			0
$829$	5184.19	−	12515.7i	0.217194	−	0.524354i	−0.777302	−	0.629128i	$-0.783412\pi$
$829$	5184.19	−	12515.7i	0.217194	−	0.524354i	0.994496	+	0.104774i	$0.0334120\pi$
$830$		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	−0.701973	−	0.712203i	$-0.747697\pi$
$839$	248.606	−	248.606i	0.0102298	−	0.0102298i	0.712203	+	0.701973i	$0.247697\pi$
$840$		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	0.758862	−	0.651251i	$-0.225756\pi$
$853$	−5935.21	−	14328.9i	−0.238239	−	0.575159i	−0.997101	+	0.0760921i	$0.975756\pi$
$854$		0			0
$855$	8193.23	+	8193.23i	0.327722	+	0.327722i
$856$		0			0
$857$	6193.30	−	6193.30i	0.246860	−	0.246860i	−0.572821	−	0.819681i	$-0.694151\pi$
$857$	6193.30	−	6193.30i	0.246860	−	0.246860i	0.819681	+	0.572821i	$0.194151\pi$
$858$		0			0
$859$	−9296.87	+	3850.89i	−0.369272	+	0.152958i	−0.559600	−	0.828763i	$-0.689045\pi$
$859$	−9296.87	+	3850.89i	−0.369272	+	0.152958i	0.190327	+	0.981721i	$0.439045\pi$
$860$		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	0.998200	−	0.0599774i	$-0.0191029\pi$
$877$	43155.1	+	17875.4i	1.66162	+	0.688267i	0.663423	+	0.748244i	$0.269103\pi$
$878$		0			0
$879$		−	59333.1i		−	2.27674i
$880$		0			0
$881$		−	9845.05i		−	0.376491i	−0.982122	−	0.188245i	$-0.939720\pi$
$881$		−	9845.05i		−	0.376491i	0.982122	−	0.188245i	$-0.0602800\pi$
$882$		0			0
$883$	27587.3	+	11427.0i	1.05140	+	0.435504i	0.840391	−	0.541981i	$-0.182325\pi$
$883$	27587.3	+	11427.0i	1.05140	+	0.435504i	0.211008	+	0.977484i	$0.432325\pi$
$884$		0			0
$885$	17080.0	+	41234.9i	0.648745	+	1.56621i
$886$		0			0
$887$	−1279.94	−	1279.94i	−0.0484512	−	0.0484512i	0.682466	−	0.730917i	$-0.260907\pi$
$887$	−1279.94	−	1279.94i	−0.0484512	−	0.0484512i	−0.730917	+	0.682466i	$0.760907\pi$
$888$		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	0.932727	−	0.360583i	$-0.117422\pi$
$907$	497.655	+	1201.44i	0.0182187	+	0.0439838i	−0.914508	+	0.404567i	$0.867422\pi$
$908$		0			0
$909$	45472.0	+	18835.1i	1.65920	+	0.687262i
$910$		0			0
$911$			1357.76i			0.0493794i	0.999695	+	0.0246897i	$0.00785977\pi$
$911$			1357.76i			0.0493794i	−0.999695	+	0.0246897i	$0.992140\pi$
$912$		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	0.800453	−	0.599395i	$-0.204592\pi$
$919$	5601.39	+	5601.39i	0.201059	+	0.201059i	−0.599395	+	0.800453i	$0.704592\pi$
$920$		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	0.934145	−	0.356894i	$-0.116164\pi$
$937$	16556.7	+	16556.7i	0.577251	+	0.577251i	−0.356894	+	0.934145i	$0.616164\pi$
$938$		0			0
$939$	−27667.4	−	66795.1i	−0.961547	−	2.32138i
$940$		0			0
$941$	6945.83	+	2877.06i	0.240624	+	0.0996698i	0.499737	−	0.866177i	$-0.333430\pi$
$941$	6945.83	+	2877.06i	0.240624	+	0.0996698i	−0.259113	+	0.965847i	$0.583430\pi$
$942$		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	0.772184	−	0.635399i	$-0.219164\pi$
$947$	25322.0	+	10488.7i	0.868905	+	0.359912i	0.0967214	+	0.995311i	$0.469164\pi$
$948$		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	−0.729760	−	0.683704i	$-0.760368\pi$
$953$	−1354.94	+	1354.94i	−0.0460556	+	0.0460556i	0.683704	+	0.729760i	$0.260368\pi$
$954$		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	−0.527427	−	0.849600i	$-0.676843\pi$
$967$	9687.88	−	9687.88i	0.322173	−	0.322173i	0.849600	+	0.527427i	$0.176843\pi$
$968$		0			0
$969$	9911.89	+	9911.89i	0.328602	+	0.328602i
$970$		0			0
$971$	9092.27	+	21950.7i	0.300499	+	0.725469i	0.999942	+	0.0107805i	$0.00343162\pi$
$971$	9092.27	+	21950.7i	0.300499	+	0.725469i	−0.699443	+	0.714689i	$0.746568\pi$
$972$		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	$-0.985457\pi$
$977$		−	2789.43i		−	0.0913426i	0.998957	−	0.0456713i	$-0.0145427\pi$
$978$		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	0.516334	−	0.856388i	$-0.327297\pi$
$983$	−10480.4	−	10480.4i	−0.340054	−	0.340054i	−0.856388	+	0.516334i	$0.827297\pi$
$984$		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	0.137054	−	0.990564i	$-0.456237\pi$
$997$	29415.4	−	12184.3i	0.934399	−	0.387041i	0.797346	+	0.603523i	$0.206237\pi$
$998$		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.17.10		44
4.3	odd	2		32.4.g.a.13.5	yes	44
8.3	odd	2		256.4.g.b.33.10		44
8.5	even	2		256.4.g.a.33.2		44
32.5	even	8	inner	128.4.g.a.113.10		44
32.11	odd	8		256.4.g.b.225.10		44
32.21	even	8		256.4.g.a.225.2		44
32.27	odd	8		32.4.g.a.5.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.5	✓	44	32.27	odd	8
32.4.g.a.13.5	yes	44	4.3	odd	2
128.4.g.a.17.10		44	1.1	even	1	trivial
128.4.g.a.113.10		44	32.5	even	8	inner
256.4.g.a.33.2		44	8.5	even	2
256.4.g.a.225.2		44	32.21	even	8
256.4.g.b.33.10		44	8.3	odd	2
256.4.g.b.225.10		44	32.11	odd	8

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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