LMFDB - Embedded newform 128.4.g.a.17.9

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			17.9
Character	$\chi$	$=$	128.17
Dual form			128.4.g.a.113.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +O(q^{10})$	\(q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +(-18.6604 - 45.0502i) q^{11} +(18.9369 + 7.84392i) q^{13} -1.01558i q^{15} -85.7028i q^{17} +(-110.749 - 45.8739i) q^{19} +(-30.6868 - 74.0844i) q^{21} +(74.2331 + 74.2331i) q^{23} +(-88.3588 + 88.3588i) q^{25} +(134.544 - 55.7299i) q^{27} +(64.4881 - 155.688i) q^{29} -36.6720 q^{31} -242.316 q^{33} +(1.26201 - 3.04676i) q^{35} +(313.271 - 129.761i) q^{37} +(72.0243 - 72.0243i) q^{39} +(196.689 + 196.689i) q^{41} +(20.8770 + 50.4016i) q^{43} +(0.435291 + 0.180303i) q^{45} +508.601i q^{47} +82.6118i q^{49} +(-393.469 - 162.980i) q^{51} +(73.8289 + 178.239i) q^{53} +(-7.04657 - 7.04657i) q^{55} +(-421.223 + 421.223i) q^{57} +(-40.9489 + 16.9616i) q^{59} +(-324.831 + 784.211i) q^{61} +37.2017 q^{63} +4.18895 q^{65} +(49.4427 - 119.365i) q^{67} +(481.979 - 199.642i) q^{69} +(362.308 - 362.308i) q^{71} +(239.192 + 239.192i) q^{73} +(237.632 + 573.695i) q^{75} +(-726.954 - 301.114i) q^{77} +1018.36i q^{79} -661.438i q^{81} +(-231.267 - 95.7940i) q^{83} +(-6.70265 - 16.1816i) q^{85} +(-592.141 - 592.141i) q^{87} +(1103.08 - 1103.08i) q^{89} +(305.576 - 126.574i) q^{91} +(-69.7388 + 168.364i) q^{93} -24.4984 q^{95} -74.0528 q^{97} +(43.0203 - 103.860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.90169	−	4.59109i	0.365981	−	0.883556i	−0.628419	−	0.777875i	$-0.716298\pi$
$3$	1.90169	−	4.59109i	0.365981	−	0.883556i	0.994400	−	0.105681i	$-0.0337023\pi$
$4$		0			0
$5$	0.188811	−	0.0782080i	0.0168878	−	0.00699514i	−0.374224	−	0.927339i	$-0.622091\pi$
$5$	0.188811	−	0.0782080i	0.0168878	−	0.00699514i	0.391111	+	0.920343i	$0.372091\pi$
$6$		0			0
$7$	11.4103	−	11.4103i	0.616096	−	0.616096i	−0.328432	−	0.944528i	$-0.606520\pi$
$7$	11.4103	−	11.4103i	0.616096	−	0.616096i	0.944528	+	0.328432i	$0.106520\pi$
$8$		0			0
$9$	1.63019	+	1.63019i	0.0603773	+	0.0603773i
$10$		0			0
$11$	−18.6604	−	45.0502i	−0.511483	−	1.23483i	−0.943020	−	0.332735i	$-0.892029\pi$
$11$	−18.6604	−	45.0502i	−0.511483	−	1.23483i	0.431537	−	0.902095i	$-0.357971\pi$
$12$		0			0
$13$	18.9369	+	7.84392i	0.404011	+	0.167347i	0.575430	−	0.817851i	$-0.304835\pi$
$13$	18.9369	+	7.84392i	0.404011	+	0.167347i	−0.171418	+	0.985198i	$0.554835\pi$
$14$		0			0
$15$		−	1.01558i		−	0.0174814i
$16$		0			0
$17$		−	85.7028i		−	1.22270i	−0.791359	−	0.611352i	$-0.790626\pi$
$17$		−	85.7028i		−	1.22270i	0.791359	−	0.611352i	$-0.209374\pi$
$18$		0			0
$19$	−110.749	−	45.8739i	−1.33725	−	0.553905i	−0.404532	−	0.914524i	$-0.632566\pi$
$19$	−110.749	−	45.8739i	−1.33725	−	0.553905i	−0.932713	+	0.360619i	$0.882566\pi$
$20$		0			0
$21$	−30.6868	−	74.0844i	−0.318876	−	0.769835i
$22$		0			0
$23$	74.2331	+	74.2331i	0.672985	+	0.672985i	0.958403	−	0.285418i	$-0.0921324\pi$
$23$	74.2331	+	74.2331i	0.672985	+	0.672985i	−0.285418	+	0.958403i	$0.592132\pi$
$24$		0			0
$25$	−88.3588	+	88.3588i	−0.706871	+	0.706871i
$26$		0			0
$27$	134.544	−	55.7299i	0.959000	−	0.397231i
$28$		0			0
$29$	64.4881	−	155.688i	0.412936	−	0.996915i	−0.571410	−	0.820665i	$-0.693603\pi$
$29$	64.4881	−	155.688i	0.412936	−	0.996915i	0.984345	−	0.176250i	$-0.0563967\pi$
$30$		0			0
$31$	−36.6720			−0.212467			−0.106234	−	0.994341i	$-0.533879\pi$
$31$	−36.6720			−0.212467			−0.106234	+	0.994341i	$0.533879\pi$
$32$		0			0
$33$	−242.316			−1.27824
$34$		0			0
$35$	1.26201	−	3.04676i	0.00609481	−	0.0147142i
$36$		0			0
$37$	313.271	−	129.761i	1.39193	−	0.576557i	0.444287	−	0.895884i	$-0.353457\pi$
$37$	313.271	−	129.761i	1.39193	−	0.576557i	0.947644	+	0.319328i	$0.103457\pi$
$38$		0			0
$39$	72.0243	−	72.0243i	0.295721	−	0.295721i
$40$		0			0
$41$	196.689	+	196.689i	0.749211	+	0.749211i	0.974331	−	0.225120i	$-0.0722773\pi$
$41$	196.689	+	196.689i	0.749211	+	0.749211i	−0.225120	+	0.974331i	$0.572277\pi$
$42$		0			0
$43$	20.8770	+	50.4016i	0.0740400	+	0.178748i	0.956566	−	0.291514i	$-0.0941591\pi$
$43$	20.8770	+	50.4016i	0.0740400	+	0.178748i	−0.882526	+	0.470263i	$0.844159\pi$
$44$		0			0
$45$	0.435291	+	0.180303i	0.00144198	+	0.000597290i
$46$		0			0
$47$			508.601i			1.57845i	0.614106	+	0.789224i	$0.289517\pi$
$47$			508.601i			1.57845i	−0.614106	+	0.789224i	$0.710483\pi$
$48$		0			0
$49$			82.6118i			0.240851i
$50$		0			0
$51$	−393.469	−	162.980i	−1.08033	−	0.447487i
$52$		0			0
$53$	73.8289	+	178.239i	0.191343	+	0.461943i	0.990214	−	0.139560i	$-0.0445689\pi$
$53$	73.8289	+	178.239i	0.191343	+	0.461943i	−0.798871	+	0.601503i	$0.794569\pi$
$54$		0			0
$55$	−7.04657	−	7.04657i	−0.0172756	−	0.0172756i
$56$		0			0
$57$	−421.223	+	421.223i	−0.978813	+	0.978813i
$58$		0			0
$59$	−40.9489	+	16.9616i	−0.0903576	+	0.0374273i	−0.427404	−	0.904061i	$-0.640572\pi$
$59$	−40.9489	+	16.9616i	−0.0903576	+	0.0374273i	0.337047	+	0.941488i	$0.390572\pi$
$60$		0			0
$61$	−324.831	+	784.211i	−0.681809	+	1.64603i	0.0788549	+	0.996886i	$0.474874\pi$
$61$	−324.831	+	784.211i	−0.681809	+	1.64603i	−0.760664	+	0.649146i	$0.775126\pi$
$62$		0			0
$63$	37.2017			0.0743964
$64$		0			0
$65$	4.18895			0.00799346
$66$		0			0
$67$	49.4427	−	119.365i	0.0901550	−	0.217654i	−0.872370	−	0.488846i	$-0.837418\pi$
$67$	49.4427	−	119.365i	0.0901550	−	0.217654i	0.962525	+	0.271192i	$0.0874180\pi$
$68$		0			0
$69$	481.979	−	199.642i	0.840920	−	0.348321i
$70$		0			0
$71$	362.308	−	362.308i	0.605606	−	0.605606i	−0.336189	−	0.941795i	$-0.609138\pi$
$71$	362.308	−	362.308i	0.605606	−	0.605606i	0.941795	+	0.336189i	$0.109138\pi$
$72$		0			0
$73$	239.192	+	239.192i	0.383498	+	0.383498i	0.872361	−	0.488863i	$-0.162588\pi$
$73$	239.192	+	239.192i	0.383498	+	0.383498i	−0.488863	+	0.872361i	$0.662588\pi$
$74$		0			0
$75$	237.632	+	573.695i	0.365859	+	0.883261i
$76$		0			0
$77$	−726.954	−	301.114i	−1.07590	−	0.445651i
$78$		0			0
$79$			1018.36i			1.45030i	0.688589	+	0.725152i	$0.258231\pi$
$79$			1018.36i			1.45030i	−0.688589	+	0.725152i	$0.741769\pi$
$80$		0			0
$81$		−	661.438i		−	0.907323i
$82$		0			0
$83$	−231.267	−	95.7940i	−0.305842	−	0.126684i	0.224484	−	0.974478i	$-0.427930\pi$
$83$	−231.267	−	95.7940i	−0.305842	−	0.126684i	−0.530326	+	0.847794i	$0.677930\pi$
$84$		0			0
$85$	−6.70265	−	16.1816i	−0.00855299	−	0.0206487i
$86$		0			0
$87$	−592.141	−	592.141i	−0.729704	−	0.729704i
$88$		0			0
$89$	1103.08	−	1103.08i	1.31378	−	1.31378i	0.395174	−	0.918606i	$-0.370684\pi$
$89$	1103.08	−	1103.08i	1.31378	−	1.31378i	0.918606	−	0.395174i	$-0.129316\pi$
$90$		0			0
$91$	305.576	−	126.574i	0.352012	−	0.145808i
$92$		0			0
$93$	−69.7388	+	168.364i	−0.0777589	+	0.187727i
$94$		0			0
$95$	−24.4984			−0.0264577
$96$		0			0
$97$	−74.0528			−0.0775147			−0.0387573	−	0.999249i	$-0.512340\pi$
$97$	−74.0528			−0.0775147			−0.0387573	+	0.999249i	$0.512340\pi$
$98$		0			0
$99$	43.0203	−	103.860i	0.0436737	−	0.105438i
$100$		0			0
$101$	564.281	−	233.733i	0.555922	−	0.230270i	−0.0869918	−	0.996209i	$-0.527725\pi$
$101$	564.281	−	233.733i	0.555922	−	0.230270i	0.642914	+	0.765939i	$0.277725\pi$
$102$		0			0
$103$	504.784	−	504.784i	0.482892	−	0.482892i	−0.423162	−	0.906054i	$-0.639080\pi$
$103$	504.784	−	504.784i	0.482892	−	0.482892i	0.906054	+	0.423162i	$0.139080\pi$
$104$		0			0
$105$	−11.5880	−	11.5880i	−0.0107702	−	0.0107702i
$106$		0			0
$107$	399.644	+	964.826i	0.361075	+	0.871713i	0.995143	+	0.0984356i	$0.0313839\pi$
$107$	399.644	+	964.826i	0.361075	+	0.871713i	−0.634068	+	0.773277i	$0.718616\pi$
$108$		0			0
$109$	−1362.55	−	564.385i	−1.19732	−	0.495948i	−0.307191	−	0.951648i	$-0.599389\pi$
$109$	−1362.55	−	564.385i	−1.19732	−	0.495948i	−0.890133	+	0.455700i	$0.849389\pi$
$110$		0			0
$111$		−	1685.02i		−	1.44086i
$112$		0			0
$113$		−	1171.99i		−	0.975681i	−0.872933	−	0.487840i	$-0.837785\pi$
$113$		−	1171.99i		−	0.975681i	0.872933	−	0.487840i	$-0.162215\pi$
$114$		0			0
$115$	19.8216	+	8.21039i	0.0160728	+	0.00665759i
$116$		0			0
$117$	18.0836	+	43.6577i	0.0142892	+	0.0344971i
$118$		0			0
$119$	−977.891	−	977.891i	−0.753304	−	0.753304i
$120$		0			0
$121$	−740.147	+	740.147i	−0.556084	+	0.556084i
$122$		0			0
$123$	1277.06	−	528.976i	0.936168	−	0.387773i
$124$		0			0
$125$	−19.5487	+	47.1948i	−0.0139879	+	0.0337699i
$126$		0			0
$127$	−2033.56			−1.42086			−0.710432	−	0.703766i	$-0.751500\pi$
$127$	−2033.56			−1.42086			−0.710432	+	0.703766i	$0.751500\pi$
$128$		0			0
$129$	271.100			0.185031
$130$		0			0
$131$	−268.953	+	649.310i	−0.179378	+	0.433057i	−0.987836	−	0.155496i	$-0.950302\pi$
$131$	−268.953	+	649.310i	−0.179378	+	0.433057i	0.808458	+	0.588553i	$0.200302\pi$
$132$		0			0
$133$	−1787.11	+	740.247i	−1.16513	+	0.482613i
$134$		0			0
$135$	21.0448	−	21.0448i	0.0134167	−	0.0134167i
$136$		0			0
$137$	1077.41	+	1077.41i	0.671894	+	0.671894i	0.958152	−	0.286259i	$-0.0924116\pi$
$137$	1077.41	+	1077.41i	0.671894	+	0.671894i	−0.286259	+	0.958152i	$0.592412\pi$
$138$		0			0
$139$	−285.862	−	690.132i	−0.174435	−	0.421124i	0.812347	−	0.583174i	$-0.198189\pi$
$139$	−285.862	−	690.132i	−0.174435	−	0.421124i	−0.986783	+	0.162050i	$0.948189\pi$
$140$		0			0
$141$	2335.03	+	967.202i	1.39465	+	0.577682i
$142$		0			0
$143$		−	999.480i		−	0.584481i
$144$		0			0
$145$		−	34.4391i		−	0.0197242i
$146$		0			0
$147$	379.278	+	157.102i	0.212805	+	0.0881468i
$148$		0			0
$149$	−634.226	−	1531.16i	−0.348710	−	0.841860i	−0.996773	−	0.0802736i	$-0.974421\pi$
$149$	−634.226	−	1531.16i	−0.348710	−	0.841860i	0.648063	−	0.761587i	$-0.275579\pi$
$150$		0			0
$151$	805.847	+	805.847i	0.434297	+	0.434297i	0.890087	−	0.455790i	$-0.150643\pi$
$151$	805.847	+	805.847i	0.434297	+	0.434297i	−0.455790	+	0.890087i	$0.650643\pi$
$152$		0			0
$153$	139.712	−	139.712i	0.0738236	−	0.0738236i
$154$		0			0
$155$	−6.92407	+	2.86804i	−0.00358809	+	0.00148624i
$156$		0			0
$157$	−308.064	+	743.733i	−0.156600	+	0.378066i	−0.982634	−	0.185554i	$-0.940592\pi$
$157$	−308.064	+	743.733i	−0.156600	+	0.378066i	0.826034	+	0.563620i	$0.190592\pi$
$158$		0			0
$159$	958.710			0.478180
$160$		0			0
$161$	1694.04			0.829248
$162$		0			0
$163$	−396.959	+	958.344i	−0.190750	+	0.460511i	−0.990102	−	0.140353i	$-0.955176\pi$
$163$	−396.959	+	958.344i	−0.190750	+	0.460511i	0.799352	+	0.600863i	$0.205176\pi$
$164$		0			0
$165$	−45.7519	+	18.9510i	−0.0215865	+	0.00894143i
$166$		0			0
$167$	−307.489	+	307.489i	−0.142480	+	0.142480i	−0.774749	−	0.632269i	$-0.782124\pi$
$167$	−307.489	+	307.489i	−0.142480	+	0.142480i	0.632269	+	0.774749i	$0.282124\pi$
$168$		0			0
$169$	−1256.43	−	1256.43i	−0.571887	−	0.571887i
$170$		0			0
$171$	−105.759	−	255.325i	−0.0472960	−	0.114183i
$172$		0			0
$173$	328.204	+	135.946i	0.144236	+	0.0597446i	0.453634	−	0.891188i	$-0.350127\pi$
$173$	328.204	+	135.946i	0.144236	+	0.0597446i	−0.309398	+	0.950933i	$0.600127\pi$
$174$		0			0
$175$			2016.39i			0.871001i
$176$		0			0
$177$			220.256i			0.0935337i
$178$		0			0
$179$	1270.86	+	526.407i	0.530662	+	0.219807i	0.631893	−	0.775056i	$-0.282278\pi$
$179$	1270.86	+	526.407i	0.530662	+	0.219807i	−0.101231	+	0.994863i	$0.532278\pi$
$180$		0			0
$181$	1449.19	+	3498.66i	0.595125	+	1.43676i	0.878496	+	0.477749i	$0.158547\pi$
$181$	1449.19	+	3498.66i	0.595125	+	1.43676i	−0.283371	+	0.959010i	$0.591453\pi$
$182$		0			0
$183$	2982.66	+	2982.66i	1.20483	+	1.20483i
$184$		0			0
$185$	49.0007	−	49.0007i	0.0194735	−	0.0194735i
$186$		0			0
$187$	−3860.92	+	1599.25i	−1.50983	+	0.625393i
$188$		0			0
$189$	899.289	−	2171.08i	0.346104	−	0.835569i
$190$		0			0
$191$	2124.08			0.804677			0.402338	−	0.915491i	$-0.368197\pi$
$191$	2124.08			0.804677			0.402338	+	0.915491i	$0.368197\pi$
$192$		0			0
$193$	−2384.50			−0.889328			−0.444664	−	0.895697i	$-0.646677\pi$
$193$	−2384.50			−0.889328			−0.444664	+	0.895697i	$0.646677\pi$
$194$		0			0
$195$	7.96609	−	19.2319i	0.00292546	−	0.00706268i
$196$		0			0
$197$	−3010.53	+	1247.00i	−1.08879	+	0.450990i	−0.853584	−	0.520956i	$-0.825576\pi$
$197$	−3010.53	+	1247.00i	−1.08879	+	0.450990i	−0.235204	+	0.971946i	$0.575576\pi$
$198$		0			0
$199$	−2542.97	+	2542.97i	−0.905862	+	0.905862i	−0.995935	−	0.0900734i	$-0.971290\pi$
$199$	−2542.97	+	2542.97i	−0.905862	+	0.905862i	0.0900734	+	0.995935i	$0.471290\pi$
$200$		0			0
$201$	−453.992	−	453.992i	−0.159314	−	0.159314i
$202$		0			0
$203$	−1040.61	−	2512.27i	−0.359787	−	0.868604i
$204$		0			0
$205$	52.5197	+	21.7544i	0.0178933	+	0.00741167i
$206$		0			0
$207$			242.028i			0.0812661i
$208$		0			0
$209$			5845.30i			1.93458i
$210$		0			0
$211$	−411.497	−	170.448i	−0.134259	−	0.0556118i	0.314543	−	0.949243i	$-0.398149\pi$
$211$	−411.497	−	170.448i	−0.134259	−	0.0556118i	−0.448801	+	0.893632i	$0.648149\pi$
$212$		0			0
$213$	−974.390	−	2352.39i	−0.313447	−	0.756727i
$214$		0			0
$215$	7.88363	+	7.88363i	0.00250074	+	0.00250074i
$216$		0			0
$217$	−418.437	+	418.437i	−0.130900	+	0.130900i
$218$		0			0
$219$	1553.02	−	643.284i	0.479195	−	0.198489i
$220$		0			0
$221$	672.246	−	1622.94i	0.204616	−	0.493987i
$222$		0			0
$223$	1847.81			0.554880			0.277440	−	0.960743i	$-0.410514\pi$
$223$	1847.81			0.554880			0.277440	+	0.960743i	$0.410514\pi$
$224$		0			0
$225$	−288.083			−0.0853579
$226$		0			0
$227$	904.304	−	2183.18i	0.264409	−	0.638339i	−0.734793	−	0.678291i	$-0.762721\pi$
$227$	904.304	−	2183.18i	0.264409	−	0.638339i	0.999202	+	0.0399527i	$0.0127207\pi$
$228$		0			0
$229$	4319.52	−	1789.20i	1.24647	−	0.516305i	0.340740	−	0.940158i	$-0.389322\pi$
$229$	4319.52	−	1789.20i	1.24647	−	0.516305i	0.905731	+	0.423852i	$0.139322\pi$
$230$		0			0
$231$	−2764.89	+	2764.89i	−0.787516	+	0.787516i
$232$		0			0
$233$	−3523.28	−	3523.28i	−0.990634	−	0.990634i	0.00932269	−	0.999957i	$-0.497032\pi$
$233$	−3523.28	−	3523.28i	−0.990634	−	0.990634i	−0.999957	+	0.00932269i	$0.997032\pi$
$234$		0			0
$235$	39.7767	+	96.0294i	0.0110415	+	0.0266564i
$236$		0			0
$237$	4675.37	+	1936.60i	1.28143	+	0.530784i
$238$		0			0
$239$		−	6222.79i		−	1.68418i	−0.539337	−	0.842090i	$-0.681325\pi$
$239$		−	6222.79i		−	1.68418i	0.539337	−	0.842090i	$-0.318675\pi$
$240$		0			0
$241$			4271.08i			1.14160i	0.821091	+	0.570798i	$0.193366\pi$
$241$			4271.08i			1.14160i	−0.821091	+	0.570798i	$0.806634\pi$
$242$		0			0
$243$	595.962	+	246.856i	0.157329	+	0.0651679i
$244$		0			0
$245$	6.46091	+	15.5980i	0.00168478	+	0.00406743i
$246$		0			0
$247$	−1737.42	−	1737.42i	−0.447568	−	0.447568i
$248$		0			0
$249$	−879.598	+	879.598i	−0.223864	+	0.223864i
$250$		0			0
$251$	−4861.21	+	2013.58i	−1.22246	+	0.506358i	−0.898190	−	0.439608i	$-0.855117\pi$
$251$	−4861.21	+	2013.58i	−1.22246	+	0.506358i	−0.324267	+	0.945966i	$0.605117\pi$
$252$		0			0
$253$	1958.99	−	4729.43i	0.486802	−	1.17524i
$254$		0			0
$255$	−87.0377			−0.0213746
$256$		0			0
$257$	2043.19			0.495917			0.247958	−	0.968771i	$-0.420240\pi$
$257$	2043.19			0.495917			0.247958	+	0.968771i	$0.420240\pi$
$258$		0			0
$259$	2093.90	−	5055.12i	0.502349	−	1.21278i
$260$		0			0
$261$	358.928	−	148.673i	0.0851230	−	0.0352591i
$262$		0			0
$263$	3376.45	−	3376.45i	0.791638	−	0.791638i	−0.190123	−	0.981760i	$-0.560889\pi$
$263$	3376.45	−	3376.45i	0.791638	−	0.791638i	0.981760	+	0.190123i	$0.0608886\pi$
$264$		0			0
$265$	27.8794	+	27.8794i	0.00646271	+	0.00646271i
$266$		0			0
$267$	−2966.63	−	7162.07i	−0.679980	−	1.64162i
$268$		0			0
$269$	−3758.60	−	1556.86i	−0.851917	−	0.352876i	−0.0863762	−	0.996263i	$-0.527529\pi$
$269$	−3758.60	−	1556.86i	−0.851917	−	0.352876i	−0.765541	+	0.643387i	$0.777529\pi$
$270$		0			0
$271$			4182.58i			0.937540i	0.883320	+	0.468770i	$0.155303\pi$
$271$			4182.58i			0.937540i	−0.883320	+	0.468770i	$0.844697\pi$
$272$		0			0
$273$		−	1643.63i		−	0.364385i
$274$		0			0
$275$	5629.39	+	2331.77i	1.23442	+	0.511313i
$276$		0			0
$277$	−26.8731	−	64.8775i	−0.00582906	−	0.0140726i	0.920938	−	0.389709i	$-0.127424\pi$
$277$	−26.8731	−	64.8775i	−0.00582906	−	0.0140726i	−0.926767	+	0.375636i	$0.877424\pi$
$278$		0			0
$279$	−59.7822	−	59.7822i	−0.0128282	−	0.0128282i
$280$		0			0
$281$	3756.73	−	3756.73i	0.797536	−	0.797536i	−0.185171	−	0.982706i	$-0.559284\pi$
$281$	3756.73	−	3756.73i	0.797536	−	0.797536i	0.982706	+	0.185171i	$0.0592837\pi$
$282$		0			0
$283$	−47.8634	+	19.8257i	−0.0100536	+	0.00416436i	−0.387705	−	0.921784i	$-0.626732\pi$
$283$	−47.8634	+	19.8257i	−0.0100536	+	0.00416436i	0.377651	+	0.925948i	$0.376732\pi$
$284$		0			0
$285$	−46.5885	+	112.474i	−0.00968303	+	0.0233769i
$286$		0			0
$287$	4488.55			0.923173
$288$		0			0
$289$	−2431.97			−0.495007
$290$		0			0
$291$	−140.826	+	339.983i	−0.0283689	+	0.0684886i
$292$		0			0
$293$	−3659.53	+	1515.83i	−0.729666	+	0.302238i	−0.716415	−	0.697674i	$-0.754218\pi$
$293$	−3659.53	+	1515.83i	−0.729666	+	0.302238i	−0.0132515	+	0.999912i	$0.504218\pi$
$294$		0			0
$295$	−6.40507	+	6.40507i	−0.00126413	+	0.00126413i
$296$		0			0
$297$	−5021.28	−	5021.28i	−0.981025	−	0.981025i
$298$		0			0
$299$	823.465	+	1988.02i	0.159272	+	0.384516i
$300$		0			0
$301$	813.309	+	336.883i	0.155742	+	0.0645104i
$302$		0			0
$303$		−	3035.16i		−	0.575463i
$304$		0			0
$305$			173.472i			0.0325671i
$306$		0			0
$307$	−1166.44	−	483.155i	−0.216847	−	0.0898211i	0.271615	−	0.962406i	$-0.412442\pi$
$307$	−1166.44	−	483.155i	−0.216847	−	0.0898211i	−0.488463	+	0.872585i	$0.662442\pi$
$308$		0			0
$309$	−1357.57	−	3277.46i	−0.249933	−	0.603391i
$310$		0			0
$311$	−811.491	−	811.491i	−0.147960	−	0.147960i	0.629246	−	0.777206i	$-0.283364\pi$
$311$	−811.491	−	811.491i	−0.147960	−	0.147960i	−0.777206	+	0.629246i	$0.783364\pi$
$312$		0			0
$313$	−748.416	+	748.416i	−0.135153	+	0.135153i	−0.771447	−	0.636294i	$-0.780467\pi$
$313$	−748.416	+	748.416i	−0.135153	+	0.135153i	0.636294	+	0.771447i	$0.280467\pi$
$314$		0			0
$315$	7.02409	−	2.90947i	0.00125639	−	0.000520414i
$316$		0			0
$317$	−1647.93	+	3978.45i	−0.291977	+	0.704896i	−0.999999	−	0.00129494i	$-0.999588\pi$
$317$	−1647.93	+	3978.45i	−0.291977	+	0.704896i	0.708022	+	0.706191i	$0.249588\pi$
$318$		0			0
$319$	−8217.14			−1.44223
$320$		0			0
$321$	5189.61			0.902354
$322$		0			0
$323$	−3931.52	+	9491.54i	−0.677263	+	1.63506i
$324$		0			0
$325$	−2366.32	+	980.162i	−0.403876	+	0.167291i
$326$		0			0
$327$	−5182.29	+	5182.29i	−0.876395	+	0.876395i
$328$		0			0
$329$	5803.27	+	5803.27i	0.972476	+	0.972476i
$330$		0			0
$331$	2379.90	+	5745.58i	0.395199	+	0.954095i	0.988788	+	0.149327i	$0.0477106\pi$
$331$	2379.90	+	5745.58i	0.395199	+	0.954095i	−0.593589	+	0.804769i	$0.702289\pi$
$332$		0			0
$333$	722.225	+	299.156i	0.118852	+	0.0492301i
$334$		0			0
$335$		−	26.4043i		−	0.00430633i
$336$		0			0
$337$		−	10731.5i		−	1.73466i	−0.497730	−	0.867332i	$-0.665833\pi$
$337$		−	10731.5i		−	1.73466i	0.497730	−	0.867332i	$-0.334167\pi$
$338$		0			0
$339$	−5380.73	−	2228.77i	−0.862069	−	0.357081i
$340$		0			0
$341$	684.313	+	1652.08i	0.108673	+	0.262361i
$342$		0			0
$343$	4856.34	+	4856.34i	0.764484	+	0.764484i
$344$		0			0
$345$	75.3893	−	75.3893i	0.0117647	−	0.0117647i
$346$		0			0
$347$	5414.63	−	2242.81i	0.837673	−	0.346976i	0.0777376	−	0.996974i	$-0.475230\pi$
$347$	5414.63	−	2242.81i	0.837673	−	0.346976i	0.759936	+	0.649998i	$0.225230\pi$
$348$		0			0
$349$	−443.942	+	1071.77i	−0.0680907	+	0.164385i	−0.954261	−	0.298973i	$-0.903356\pi$
$349$	−443.942	+	1071.77i	−0.0680907	+	0.164385i	0.886171	+	0.463359i	$0.153356\pi$
$350$		0			0
$351$	2984.99			0.453922
$352$		0			0
$353$	812.561			0.122516			0.0612582	−	0.998122i	$-0.480489\pi$
$353$	812.561			0.122516			0.0612582	+	0.998122i	$0.480489\pi$
$354$		0			0
$355$	40.0723	−	96.7430i	0.00599103	−	0.0144636i
$356$		0			0
$357$	−6349.24	+	2629.94i	−0.941281	+	0.389891i
$358$		0			0
$359$	3733.47	−	3733.47i	0.548871	−	0.548871i	−0.377243	−	0.926114i	$-0.623128\pi$
$359$	3733.47	−	3733.47i	0.548871	−	0.548871i	0.926114	+	0.377243i	$0.123128\pi$
$360$		0			0
$361$	5310.98	+	5310.98i	0.774308	+	0.774308i
$362$		0			0
$363$	1990.55	+	4805.62i	0.287815	+	0.694847i
$364$		0			0
$365$	63.8689	+	26.4554i	0.00915904	+	0.00379380i
$366$		0			0
$367$		−	6820.92i		−	0.970161i	−0.874469	−	0.485081i	$-0.838790\pi$
$367$		−	6820.92i		−	0.970161i	0.874469	−	0.485081i	$-0.161210\pi$
$368$		0			0
$369$			641.280i			0.0904707i
$370$		0			0
$371$	2876.16	+	1191.34i	0.402487	+	0.166716i
$372$		0			0
$373$	3875.45	+	9356.15i	0.537970	+	1.29878i	0.926137	+	0.377186i	$0.123108\pi$
$373$	3875.45	+	9356.15i	0.537970	+	1.29878i	−0.388167	+	0.921589i	$0.626892\pi$
$374$		0			0
$375$	179.500	+	179.500i	0.0247183	+	0.0247183i
$376$		0			0
$377$	2442.41	−	2442.41i	0.333661	−	0.333661i
$378$		0			0
$379$	4336.19	−	1796.11i	0.587692	−	0.243430i	−0.0689653	−	0.997619i	$-0.521970\pi$
$379$	4336.19	−	1796.11i	0.587692	−	0.243430i	0.656657	+	0.754189i	$0.271970\pi$
$380$		0			0
$381$	−3867.22	+	9336.29i	−0.520009	+	1.25541i
$382$		0			0
$383$	−8452.79			−1.12772			−0.563861	−	0.825870i	$-0.690685\pi$
$383$	−8452.79			−1.12772			−0.563861	+	0.825870i	$0.690685\pi$
$384$		0			0
$385$	−160.806			−0.0212869
$386$		0			0
$387$	−48.1306	+	116.198i	−0.00632201	+	0.0152627i
$388$		0			0
$389$	−468.925	+	194.235i	−0.0611194	+	0.0253165i	−0.413034	−	0.910716i	$-0.635531\pi$
$389$	−468.925	+	194.235i	−0.0611194	+	0.0253165i	0.351914	+	0.936032i	$0.385531\pi$
$390$		0			0
$391$	6361.98	−	6361.98i	0.822862	−	0.822862i
$392$		0			0
$393$	2469.58	+	2469.58i	0.316981	+	0.316981i
$394$		0			0
$395$	79.6437	+	192.277i	0.0101451	+	0.0244924i
$396$		0			0
$397$	−3306.01	−	1369.40i	−0.417945	−	0.173118i	0.163793	−	0.986495i	$-0.447627\pi$
$397$	−3306.01	−	1369.40i	−0.417945	−	0.173118i	−0.581738	+	0.813376i	$0.697627\pi$
$398$		0			0
$399$			9612.53i			1.20609i
$400$		0			0
$401$			3887.84i			0.484164i	0.970256	+	0.242082i	$0.0778303\pi$
$401$			3887.84i			0.484164i	−0.970256	+	0.242082i	$0.922170\pi$
$402$		0			0
$403$	−694.453	−	287.652i	−0.0858392	−	0.0355557i
$404$		0			0
$405$	−51.7298	−	124.887i	−0.00634685	−	0.0153227i
$406$		0			0
$407$	−11691.5	−	11691.5i	−1.42390	−	1.42390i
$408$		0			0
$409$	−7188.15	+	7188.15i	−0.869025	+	0.869025i	−0.992365	−	0.123339i	$-0.960640\pi$
$409$	−7188.15	+	7188.15i	−0.869025	+	0.869025i	0.123339	+	0.992365i	$0.460640\pi$
$410$		0			0
$411$	6995.40	−	2897.59i	0.839556	−	0.347756i
$412$		0			0
$413$	−273.702	+	660.775i	−0.0326101	+	0.0787278i
$414$		0			0
$415$	−51.1576			−0.00605115
$416$		0			0
$417$	−3712.08			−0.435927
$418$		0			0
$419$	−4190.33	+	10116.4i	−0.488571	+	1.17951i	0.466869	+	0.884327i	$0.345382\pi$
$419$	−4190.33	+	10116.4i	−0.488571	+	1.17951i	−0.955439	+	0.295187i	$0.904618\pi$
$420$		0			0
$421$	14568.6	−	6034.51i	1.68653	−	0.698584i	0.686927	−	0.726726i	$-0.258959\pi$
$421$	14568.6	−	6034.51i	1.68653	−	0.698584i	0.999604	+	0.0281419i	$0.00895901\pi$
$422$		0			0
$423$	−829.114	+	829.114i	−0.0953024	+	0.0953024i
$424$		0			0
$425$	7572.60	+	7572.60i	0.864294	+	0.864294i
$426$		0			0
$427$	5241.65	+	12654.5i	0.594054	+	1.43417i
$428$		0			0
$429$	−4588.71	−	1900.70i	−0.516422	−	0.213909i
$430$		0			0
$431$			844.040i			0.0943295i	0.998887	+	0.0471647i	$0.0150186\pi$
$431$			844.040i			0.0943295i	−0.998887	+	0.0471647i	$0.984981\pi$
$432$		0			0
$433$		−	11447.7i		−	1.27053i	−0.772293	−	0.635266i	$-0.780890\pi$
$433$		−	11447.7i		−	1.27053i	0.772293	−	0.635266i	$-0.219110\pi$
$434$		0			0
$435$	−158.113	−	65.4925i	−0.0174274	−	0.00721868i
$436$		0			0
$437$	−4815.91	−	11626.6i	−0.527177	−	1.27272i
$438$		0			0
$439$	−2040.34	−	2040.34i	−0.221823	−	0.221823i	0.587443	−	0.809266i	$-0.300135\pi$
$439$	−2040.34	−	2040.34i	−0.221823	−	0.221823i	−0.809266	+	0.587443i	$0.800135\pi$
$440$		0			0
$441$	−134.673	+	134.673i	−0.0145419	+	0.0145419i
$442$		0			0
$443$	−12477.8	+	5168.47i	−1.33823	+	0.554315i	−0.932993	−	0.359895i	$-0.882813\pi$
$443$	−12477.8	+	5168.47i	−1.33823	+	0.554315i	−0.405241	+	0.914210i	$0.632813\pi$
$444$		0			0
$445$	122.004	−	294.544i	0.0129967	−	0.0313769i
$446$		0			0
$447$	−8235.78			−0.871452
$448$		0			0
$449$	−3601.74			−0.378567			−0.189283	−	0.981922i	$-0.560616\pi$
$449$	−3601.74			−0.378567			−0.189283	+	0.981922i	$0.560616\pi$
$450$		0			0
$451$	5190.58	−	12531.2i	0.541940	−	1.30836i
$452$		0			0
$453$	5232.19	−	2167.25i	0.542671	−	0.224782i
$454$		0			0
$455$	47.7970	−	47.7970i	0.00492474	−	0.00492474i
$456$		0			0
$457$	−10018.4	−	10018.4i	−1.02547	−	1.02547i	−0.999667	−	0.0258078i	$-0.991784\pi$
$457$	−10018.4	−	10018.4i	−1.02547	−	1.02547i	−0.0258078	−	0.999667i	$-0.508216\pi$
$458$		0			0
$459$	−4776.21	−	11530.8i	−0.485696	−	1.17257i
$460$		0			0
$461$	−1495.66	−	619.524i	−0.151106	−	0.0625902i	0.305849	−	0.952080i	$-0.401060\pi$
$461$	−1495.66	−	619.524i	−0.151106	−	0.0625902i	−0.456955	+	0.889490i	$0.651060\pi$
$462$		0			0
$463$			14517.8i			1.45724i	0.684921	+	0.728618i	$0.259837\pi$
$463$			14517.8i			1.45724i	−0.684921	+	0.728618i	$0.740163\pi$
$464$		0			0
$465$			37.2432i			0.00371422i
$466$		0			0
$467$	−5649.95	−	2340.29i	−0.559847	−	0.231896i	0.0847717	−	0.996400i	$-0.472984\pi$
$467$	−5649.95	−	2340.29i	−0.559847	−	0.231896i	−0.644619	+	0.764504i	$0.722984\pi$
$468$		0			0
$469$	−797.835	−	1926.14i	−0.0785513	−	0.189640i
$470$		0			0
$471$	2828.70	+	2828.70i	0.276730	+	0.276730i
$472$		0			0
$473$	1881.03	−	1881.03i	0.182854	−	0.182854i
$474$		0			0
$475$	13839.1	−	5732.32i	1.33680	−	0.553720i
$476$		0			0
$477$	−170.207	+	410.917i	−0.0163381	+	0.0394436i
$478$		0			0
$479$	10244.1			0.977172			0.488586	−	0.872516i	$-0.337513\pi$
$479$	10244.1			0.977172			0.488586	+	0.872516i	$0.337513\pi$
$480$		0			0
$481$	6950.22			0.658841
$482$		0			0
$483$	3221.54	−	7777.48i	0.303489	−	0.732687i
$484$		0			0
$485$	−13.9820	+	5.79153i	−0.00130905	+	0.000542226i
$486$		0			0
$487$	12510.0	−	12510.0i	1.16403	−	1.16403i	0.180446	−	0.983585i	$-0.442246\pi$
$487$	12510.0	−	12510.0i	1.16403	−	1.16403i	0.983585	−	0.180446i	$-0.0577542\pi$
$488$		0			0
$489$	3644.95	+	3644.95i	0.337076	+	0.337076i
$490$		0			0
$491$	4847.78	+	11703.6i	0.445575	+	1.07571i	0.973962	+	0.226710i	$0.0727970\pi$
$491$	4847.78	+	11703.6i	0.445575	+	1.07571i	−0.528387	+	0.849004i	$0.677203\pi$
$492$		0			0
$493$	−13342.9	−	5526.81i	−1.21893	−	0.504898i
$494$		0			0
$495$		−	22.9744i		−	0.00208611i
$496$		0			0
$497$		−	8268.05i		−	0.746223i
$498$		0			0
$499$	−18011.3	−	7460.51i	−1.61582	−	0.669295i	−0.622282	−	0.782793i	$-0.713794\pi$
$499$	−18011.3	−	7460.51i	−1.61582	−	0.669295i	−0.993538	+	0.113498i	$0.963794\pi$
$500$		0			0
$501$	826.961	+	1996.46i	0.0737443	+	0.178034i
$502$		0			0
$503$	3687.97	+	3687.97i	0.326915	+	0.326915i	0.851412	−	0.524497i	$-0.175747\pi$
$503$	3687.97	+	3687.97i	0.326915	+	0.326915i	−0.524497	+	0.851412i	$0.675747\pi$
$504$		0			0
$505$	88.2627	−	88.2627i	0.00777750	−	0.00777750i
$506$		0			0
$507$	−8157.76	+	3379.06i	−0.714594	+	0.295994i
$508$		0			0
$509$	1071.88	−	2587.76i	0.0933407	−	0.225344i	−0.870313	−	0.492499i	$-0.836083\pi$
$509$	1071.88	−	2587.76i	0.0933407	−	0.225344i	0.963654	+	0.267155i	$0.0860835\pi$
$510$		0			0
$511$	5458.49			0.472543
$512$		0			0
$513$	−17457.2			−1.50245
$514$		0			0
$515$	55.8306	−	134.787i	0.00477707	−	0.0115329i
$516$		0			0
$517$	22912.5	−	9490.68i	1.94911	−	0.807350i
$518$		0			0
$519$	1248.29	−	1248.29i	0.105575	−	0.105575i
$520$		0			0
$521$	−8038.89	−	8038.89i	−0.675988	−	0.675988i	0.283102	−	0.959090i	$-0.408637\pi$
$521$	−8038.89	−	8038.89i	−0.675988	−	0.675988i	−0.959090	+	0.283102i	$0.908637\pi$
$522$		0			0
$523$	−7860.76	−	18977.6i	−0.657222	−	1.58667i	−0.802076	−	0.597222i	$-0.796271\pi$
$523$	−7860.76	−	18977.6i	−0.657222	−	1.58667i	0.144854	−	0.989453i	$-0.453729\pi$
$524$		0			0
$525$	9257.45	+	3834.56i	0.769578	+	0.318770i
$526$		0			0
$527$			3142.89i			0.259785i
$528$		0			0
$529$		−	1145.90i		−	0.0941813i
$530$		0			0
$531$	−94.4050	−	39.1038i	−0.00771531	−	0.00319579i
$532$		0			0
$533$	2181.87	+	5267.49i	0.177312	+	0.428068i
$534$		0			0
$535$	150.914	+	150.914i	0.0121955	+	0.0121955i
$536$		0			0
$537$	4833.57	−	4833.57i	0.388424	−	0.388424i
$538$		0			0
$539$	3721.67	−	1541.57i	0.297410	−	0.123191i
$540$		0			0
$541$	−1316.22	+	3177.63i	−0.104600	+	0.252527i	−0.967511	−	0.252829i	$-0.918639\pi$
$541$	−1316.22	+	3177.63i	−0.104600	+	0.252527i	0.862911	+	0.505356i	$0.168639\pi$
$542$		0			0
$543$	18818.6			1.48726
$544$		0			0
$545$	−301.403			−0.0236893
$546$		0			0
$547$	6431.02	−	15525.9i	0.502689	−	1.21360i	−0.445325	−	0.895369i	$-0.646912\pi$
$547$	6431.02	−	15525.9i	0.502689	−	1.21360i	0.948014	−	0.318229i	$-0.103088\pi$
$548$		0			0
$549$	−1807.95	+	748.876i	−0.140549	+	0.0582172i
$550$		0			0
$551$	−14284.0	+	14284.0i	−1.10439	+	1.10439i
$552$		0			0
$553$	11619.7	+	11619.7i	0.893527	+	0.893527i
$554$		0			0
$555$	−131.782	−	318.151i	−0.0100790	−	0.0243329i
$556$		0			0
$557$	−5335.11	−	2209.88i	−0.405846	−	0.168107i	0.170416	−	0.985372i	$-0.445489\pi$
$557$	−5335.11	−	2209.88i	−0.405846	−	0.168107i	−0.576261	+	0.817266i	$0.695489\pi$
$558$		0			0
$559$			1118.21i			0.0846068i
$560$		0			0
$561$			20767.1i			1.56290i
$562$		0			0
$563$	−5228.46	−	2165.70i	−0.391391	−	0.162120i	0.178304	−	0.983975i	$-0.442939\pi$
$563$	−5228.46	−	2165.70i	−0.391391	−	0.162120i	−0.569696	+	0.821856i	$0.692939\pi$
$564$		0			0
$565$	−91.6594	−	221.285i	−0.00682502	−	0.0164771i
$566$		0			0
$567$	−7547.18	−	7547.18i	−0.558998	−	0.558998i
$568$		0			0
$569$	−4183.25	+	4183.25i	−0.308209	+	0.308209i	−0.844215	−	0.536005i	$-0.819933\pi$
$569$	−4183.25	+	4183.25i	−0.308209	+	0.308209i	0.536005	+	0.844215i	$0.319933\pi$
$570$		0			0
$571$	−7441.94	+	3082.55i	−0.545421	+	0.225921i	−0.638342	−	0.769753i	$-0.720380\pi$
$571$	−7441.94	+	3082.55i	−0.545421	+	0.225921i	0.0929211	+	0.995673i	$0.470380\pi$
$572$		0			0
$573$	4039.35	−	9751.87i	0.294496	−	0.710977i
$574$		0			0
$575$	−13118.3			−0.951427
$576$		0			0
$577$	2828.16			0.204052			0.102026	−	0.994782i	$-0.467468\pi$
$577$	2828.16			0.204052			0.102026	+	0.994782i	$0.467468\pi$
$578$		0			0
$579$	−4534.59	+	10947.5i	−0.325477	+	0.785771i
$580$		0			0
$581$	−3731.85	+	1545.78i	−0.266477	+	0.110379i
$582$		0			0
$583$	6652.00	−	6652.00i	0.472552	−	0.472552i
$584$		0			0
$585$	6.82877	+	6.82877i	0.000482624	+	0.000482624i
$586$		0			0
$587$	−1835.52	−	4431.34i	−0.129063	−	0.311586i	0.846118	−	0.532996i	$-0.178934\pi$
$587$	−1835.52	−	4431.34i	−0.129063	−	0.311586i	−0.975181	+	0.221410i	$0.928934\pi$
$588$		0			0
$589$	4061.40	+	1682.29i	0.284121	+	0.117687i
$590$		0			0
$591$			16193.0i			1.12706i
$592$		0			0
$593$			13545.0i			0.937989i	0.883201	+	0.468995i	$0.155384\pi$
$593$			13545.0i			0.937989i	−0.883201	+	0.468995i	$0.844616\pi$
$594$		0			0
$595$	−261.116	−	108.158i	−0.0179911	−	0.00745215i
$596$		0			0
$597$	6839.07	+	16511.0i	0.468852	+	1.13191i
$598$		0			0
$599$	12379.3	+	12379.3i	0.844414	+	0.844414i	0.989429	−	0.145015i	$-0.0463231\pi$
$599$	12379.3	+	12379.3i	0.844414	+	0.844414i	−0.145015	+	0.989429i	$0.546323\pi$
$600$		0			0
$601$	−17513.1	+	17513.1i	−1.18864	+	1.18864i	−0.211202	+	0.977442i	$0.567738\pi$
$601$	−17513.1	+	17513.1i	−1.18864	+	1.18864i	−0.977442	+	0.211202i	$0.932262\pi$
$602$		0			0
$603$	275.189	−	113.987i	0.0185846	−	0.00769801i
$604$		0			0
$605$	−81.8624	+	197.633i	−0.00550112	+	0.0132809i
$606$		0			0
$607$	−21984.1			−1.47003			−0.735013	−	0.678053i	$-0.762824\pi$
$607$	−21984.1			−1.47003			−0.735013	+	0.678053i	$0.762824\pi$
$608$		0			0
$609$	−13513.0			−0.899135
$610$		0			0
$611$	−3989.42	+	9631.31i	−0.264148	+	0.637711i
$612$		0			0
$613$	−13582.2	+	5625.93i	−0.894910	+	0.370684i	−0.782261	−	0.622951i	$-0.785934\pi$
$613$	−13582.2	+	5625.93i	−0.894910	+	0.370684i	−0.112649	+	0.993635i	$0.535934\pi$
$614$		0			0
$615$	199.753	−	199.753i	0.0130972	−	0.0130972i
$616$		0			0
$617$	−4045.14	−	4045.14i	−0.263941	−	0.263941i	0.562712	−	0.826653i	$-0.309758\pi$
$617$	−4045.14	−	4045.14i	−0.263941	−	0.263941i	−0.826653	+	0.562712i	$0.809758\pi$
$618$		0			0
$619$	4901.51	+	11833.3i	0.318268	+	0.768368i	0.999346	+	0.0361568i	$0.0115116\pi$
$619$	4901.51	+	11833.3i	0.318268	+	0.768368i	−0.681078	+	0.732211i	$0.738488\pi$
$620$		0			0
$621$	14124.6	+	5850.61i	0.912723	+	0.378062i
$622$		0			0
$623$		−	25172.9i		−	1.61883i
$624$		0			0
$625$		−	15609.3i		−	0.998998i
$626$		0			0
$627$	26836.3	+	11116.0i	1.70931	+	0.708021i
$628$		0			0
$629$	−11120.9	−	26848.2i	−0.704959	−	1.70192i
$630$		0			0
$631$	14073.2	+	14073.2i	0.887870	+	0.887870i	0.994318	−	0.106448i	$-0.0339478\pi$
$631$	14073.2	+	14073.2i	0.887870	+	0.887870i	−0.106448	+	0.994318i	$0.533948\pi$
$632$		0			0
$633$	−1565.08	+	1565.08i	−0.0982723	+	0.0982723i
$634$		0			0
$635$	−383.959	+	159.041i	−0.0239952	+	0.00993914i
$636$		0			0
$637$	−648.000	+	1564.41i	−0.0403057	+	0.0973065i
$638$		0			0
$639$	1181.26			0.0731297
$640$		0			0
$641$	14401.9			0.887430			0.443715	−	0.896168i	$-0.353660\pi$
$641$	14401.9			0.887430			0.443715	+	0.896168i	$0.353660\pi$
$642$		0			0
$643$	−3465.77	+	8367.12i	−0.212561	+	0.513168i	−0.993815	−	0.111045i	$-0.964580\pi$
$643$	−3465.77	+	8367.12i	−0.212561	+	0.513168i	0.781254	+	0.624213i	$0.214580\pi$
$644$		0			0
$645$	51.1867	−	21.2022i	0.00312477	−	0.00129432i
$646$		0			0
$647$	−17607.8	+	17607.8i	−1.06991	+	1.06991i	−0.0725490	+	0.997365i	$0.523113\pi$
$647$	−17607.8	+	17607.8i	−1.06991	+	1.06991i	−0.997365	+	0.0725490i	$0.976887\pi$
$648$		0			0
$649$	1528.25	+	1528.25i	0.0924328	+	0.0924328i
$650$		0			0
$651$	1125.34	+	2716.82i	0.0677507	+	0.163565i
$652$		0			0
$653$	25243.9	+	10456.4i	1.51282	+	0.626629i	0.976137	−	0.217157i	$-0.0696782\pi$
$653$	25243.9	+	10456.4i	1.51282	+	0.626629i	0.536680	+	0.843786i	$0.319678\pi$
$654$		0			0
$655$			143.631i			0.00856814i
$656$		0			0
$657$			779.856i			0.0463091i
$658$		0			0
$659$	2555.01	+	1058.32i	0.151030	+	0.0625588i	0.456918	−	0.889509i	$-0.348953\pi$
$659$	2555.01	+	1058.32i	0.151030	+	0.0625588i	−0.305888	+	0.952068i	$0.598953\pi$
$660$		0			0
$661$	−1008.92	−	2435.76i	−0.0593685	−	0.143328i	0.891412	−	0.453195i	$-0.149716\pi$
$661$	−1008.92	−	2435.76i	−0.0593685	−	0.143328i	−0.950780	+	0.309866i	$0.899716\pi$
$662$		0			0
$663$	−6172.68	−	6172.68i	−0.361579	−	0.361579i
$664$		0			0
$665$	−279.533	+	279.533i	−0.0163005	+	0.0163005i
$666$		0			0
$667$	16344.3	−	6770.05i	0.948809	−	0.393009i
$668$		0			0
$669$	3513.96	−	8483.45i	0.203076	−	0.490268i
$670$		0			0
$671$	41390.3			2.38130
$672$		0			0
$673$	23085.3			1.32225			0.661125	−	0.750276i	$-0.270079\pi$
$673$	23085.3			1.32225			0.661125	+	0.750276i	$0.270079\pi$
$674$		0			0
$675$	−6963.91	+	16812.4i	−0.397098	+	0.958679i
$676$		0			0
$677$	−29890.9	+	12381.2i	−1.69690	+	0.702879i	−0.999899	−	0.0141909i	$-0.995483\pi$
$677$	−29890.9	+	12381.2i	−1.69690	+	0.702879i	−0.697001	+	0.717070i	$0.745483\pi$
$678$		0			0
$679$	−844.962	+	844.962i	−0.0477565	+	0.0477565i
$680$		0			0
$681$	−8303.48	−	8303.48i	−0.467240	−	0.467240i
$682$		0			0
$683$	−4968.96	−	11996.1i	−0.278378	−	0.672063i	0.721413	−	0.692505i	$-0.243493\pi$
$683$	−4968.96	−	11996.1i	−0.278378	−	0.672063i	−0.999791	+	0.0204414i	$0.993493\pi$
$684$		0			0
$685$	287.689	+	119.165i	0.0160468	+	0.00664679i
$686$		0			0
$687$		−	23233.8i		−	1.29029i
$688$		0			0
$689$			3954.39i			0.218651i
$690$		0			0
$691$	7791.33	+	3227.27i	0.428938	+	0.177672i	0.586698	−	0.809805i	$-0.300427\pi$
$691$	7791.33	+	3227.27i	0.428938	+	0.177672i	−0.157760	+	0.987477i	$0.550427\pi$
$692$		0			0
$693$	−694.198	−	1675.94i	−0.0380525	−	0.0918670i
$694$		0			0
$695$	−107.948	−	107.948i	−0.00589165	−	0.00589165i
$696$		0			0
$697$	16856.8	−	16856.8i	0.916064	−	0.916064i
$698$		0			0
$699$	−22875.9	+	9475.51i	−1.23783	+	0.512728i
$700$		0			0
$701$	−3402.06	+	8213.30i	−0.183301	+	0.442528i	−0.988643	−	0.150283i	$-0.951982\pi$
$701$	−3402.06	+	8213.30i	−0.183301	+	0.442528i	0.805342	+	0.592810i	$0.201982\pi$
$702$		0			0
$703$	−40647.3			−2.18071
$704$		0			0
$705$	516.523			0.0275934
$706$		0			0
$707$	3771.64	−	9105.55i	0.200633	−	0.484370i
$708$		0			0
$709$	−6190.43	+	2564.16i	−0.327908	+	0.135824i	−0.540563	−	0.841303i	$-0.681789\pi$
$709$	−6190.43	+	2564.16i	−0.327908	+	0.135824i	0.212656	+	0.977127i	$0.431789\pi$
$710$		0			0
$711$	−1660.11	+	1660.11i	−0.0875655	+	0.0875655i
$712$		0			0
$713$	−2722.27	−	2722.27i	−0.142987	−	0.142987i
$714$		0			0
$715$	−78.1674	−	188.713i	−0.00408852	−	0.00987057i
$716$		0			0
$717$	−28569.4	−	11833.8i	−1.48807	−	0.616378i
$718$		0			0
$719$			7000.41i			0.363103i	0.983381	+	0.181552i	$0.0581120\pi$
$719$			7000.41i			0.363103i	−0.983381	+	0.181552i	$0.941888\pi$
$720$		0			0
$721$		−	11519.4i		−	0.595016i
$722$		0			0
$723$	19608.9	+	8122.29i	1.00866	+	0.417802i
$724$		0			0
$725$	8058.32	+	19454.5i	0.412798	+	0.996582i
$726$		0			0
$727$	4176.48	+	4176.48i	0.213063	+	0.213063i	0.805567	−	0.592504i	$-0.201861\pi$
$727$	4176.48	+	4176.48i	0.213063	+	0.213063i	−0.592504	+	0.805567i	$0.701861\pi$
$728$		0			0
$729$	14894.8	−	14894.8i	0.756733	−	0.756733i
$730$		0			0
$731$	4319.56	−	1789.22i	0.218556	−	0.0905291i
$732$		0			0
$733$	8727.96	−	21071.2i	0.439801	−	1.06177i	−0.536216	−	0.844081i	$-0.680147\pi$
$733$	8727.96	−	21071.2i	0.439801	−	1.06177i	0.976017	−	0.217694i	$-0.0698533\pi$
$734$		0			0
$735$	83.8986			0.00421040
$736$		0			0
$737$	−6300.04			−0.314878
$738$		0			0
$739$	1771.01	−	4275.60i	0.0881566	−	0.212829i	−0.873652	−	0.486551i	$-0.838255\pi$
$739$	1771.01	−	4275.60i	0.0881566	−	0.212829i	0.961809	+	0.273722i	$0.0882548\pi$
$740$		0			0
$741$	−11280.7	+	4672.61i	−0.559253	+	0.231650i
$742$		0			0
$743$	−331.818	+	331.818i	−0.0163839	+	0.0163839i	−0.715251	−	0.698867i	$-0.753688\pi$
$743$	−331.818	+	331.818i	−0.0163839	+	0.0163839i	0.698867	+	0.715251i	$0.253688\pi$
$744$		0			0
$745$	−239.497	−	239.497i	−0.0117779	−	0.0117779i
$746$		0			0
$747$	−220.846	−	533.171i	−0.0108171	−	0.0261147i
$748$		0			0
$749$	15569.0	+	6448.88i	0.759516	+	0.314602i
$750$		0			0
$751$		−	35952.8i		−	1.74692i	−0.486897	−	0.873459i	$-0.661871\pi$
$751$		−	35952.8i		−	1.74692i	0.486897	−	0.873459i	$-0.338129\pi$
$752$		0			0
$753$			26147.5i			1.26543i
$754$		0			0
$755$	215.177	+	89.1290i	0.0103723	+	0.00429634i
$756$		0			0
$757$	8248.62	+	19913.9i	0.396038	+	0.956121i	0.988596	+	0.150593i	$0.0481183\pi$
$757$	8248.62	+	19913.9i	0.396038	+	0.956121i	−0.592557	+	0.805528i	$0.701882\pi$
$758$		0			0
$759$	−17987.8	−	17987.8i	−0.860234	−	0.860234i
$760$		0			0
$761$	20845.8	−	20845.8i	0.992983	−	0.992983i	−0.00699229	−	0.999976i	$-0.502226\pi$
$761$	20845.8	−	20845.8i	0.992983	−	0.992983i	0.999976	+	0.00699229i	$0.00222573\pi$
$762$		0			0
$763$	−21986.8	+	9107.23i	−1.04322	+	0.432115i
$764$		0			0
$765$	15.4525	−	37.3056i	0.000730309	−	0.00176312i
$766$		0			0
$767$	−908.491			−0.0427689
$768$		0			0
$769$	14131.4			0.662669			0.331335	−	0.943513i	$-0.392501\pi$
$769$	14131.4			0.662669			0.331335	+	0.943513i	$0.392501\pi$
$770$		0			0
$771$	3885.52	−	9380.46i	0.181496	−	0.438170i
$772$		0			0
$773$	−15774.0	+	6533.82i	−0.733962	+	0.304017i	−0.718179	−	0.695858i	$-0.755024\pi$
$773$	−15774.0	+	6533.82i	−0.733962	+	0.304017i	−0.0157831	+	0.999875i	$0.505024\pi$
$774$		0			0
$775$	3240.29	−	3240.29i	0.150187	−	0.150187i
$776$		0			0
$777$	−19226.6	−	19226.6i	−0.887708	−	0.887708i
$778$		0			0
$779$	−12760.3	−	30806.1i	−0.586888	−	1.41687i
$780$		0			0
$781$	−23082.8	−	9561.22i	−1.05758	−	0.438063i
$782$		0			0
$783$		−	24540.8i		−	1.12007i
$784$		0			0
$785$			164.518i			0.00748013i
$786$		0			0
$787$	−9893.89	−	4098.18i	−0.448131	−	0.185622i	0.147193	−	0.989108i	$-0.452976\pi$
$787$	−9893.89	−	4098.18i	−0.448131	−	0.185622i	−0.595324	+	0.803486i	$0.702976\pi$
$788$		0			0
$789$	−9080.62	−	21922.6i	−0.409732	−	0.989181i
$790$		0			0
$791$	−13372.8	−	13372.8i	−0.601113	−	0.601113i
$792$		0			0
$793$	−12302.6	+	12302.6i	−0.550917	+	0.550917i
$794$		0			0
$795$	181.015	−	74.9788i	0.00807539	−	0.00334494i
$796$		0			0
$797$	−10234.0	+	24707.0i	−0.454838	+	1.09807i	0.515623	+	0.856815i	$0.327560\pi$
$797$	−10234.0	+	24707.0i	−0.454838	+	1.09807i	−0.970461	+	0.241259i	$0.922440\pi$
$798$		0			0
$799$	43588.5			1.92998
$800$		0			0
$801$	3596.46			0.158645
$802$		0			0
$803$	6312.23	−	15239.1i	0.277402	−	0.669707i
$804$		0			0
$805$	319.853	−	132.487i	0.0140041	−	0.00580070i
$806$		0			0
$807$	−14295.4	+	14295.4i	−0.623571	+	0.623571i
$808$		0			0
$809$	−4366.67	−	4366.67i	−0.189770	−	0.189770i	0.605827	−	0.795597i	$-0.292843\pi$
$809$	−4366.67	−	4366.67i	−0.189770	−	0.189770i	−0.795597	+	0.605827i	$0.792843\pi$
$810$		0			0
$811$	16742.8	+	40420.6i	0.724930	+	1.75014i	0.658792	+	0.752325i	$0.271068\pi$
$811$	16742.8	+	40420.6i	0.724930	+	1.75014i	0.0661382	+	0.997810i	$0.478932\pi$
$812$		0			0
$813$	19202.6	+	7953.98i	0.828370	+	0.343122i
$814$		0			0
$815$			211.991i			0.00911132i
$816$		0			0
$817$		−	6539.67i		−	0.280042i
$818$		0			0
$819$	704.485	+	291.807i	0.0300570	+	0.0124500i
$820$		0			0
$821$	−2730.75	−	6592.63i	−0.116083	−	0.280249i	0.855150	−	0.518381i	$-0.173465\pi$
$821$	−2730.75	−	6592.63i	−0.116083	−	0.280249i	−0.971233	+	0.238132i	$0.923465\pi$
$822$		0			0
$823$	7832.94	+	7832.94i	0.331761	+	0.331761i	0.853255	−	0.521494i	$-0.174625\pi$
$823$	7832.94	+	7832.94i	0.331761	+	0.331761i	−0.521494	+	0.853255i	$0.674625\pi$
$824$		0			0
$825$	21410.7	−	21410.7i	0.903547	−	0.903547i
$826$		0			0
$827$	18116.8	−	7504.23i	0.761769	−	0.315535i	0.0322359	−	0.999480i	$-0.489737\pi$
$827$	18116.8	−	7504.23i	0.761769	−	0.315535i	0.729533	+	0.683945i	$0.239737\pi$
$828$		0			0
$829$	−3888.12	+	9386.75i	−0.162895	+	0.393264i	−0.984160	−	0.177284i	$-0.943269\pi$
$829$	−3888.12	+	9386.75i	−0.162895	+	0.393264i	0.821265	+	0.570547i	$0.193269\pi$
$830$		0			0
$831$	−348.963			−0.0145673
$832$		0			0
$833$	7080.06			0.294489
$834$		0			0
$835$	−34.0092	+	82.1054i	−0.00140950	+	0.00340284i
$836$		0			0
$837$	−4933.99	+	2043.73i	−0.203756	+	0.0843985i
$838$		0			0
$839$	4919.87	−	4919.87i	0.202447	−	0.202447i	−0.598601	−	0.801047i	$-0.704276\pi$
$839$	4919.87	−	4919.87i	0.202447	−	0.202447i	0.801047	+	0.598601i	$0.204276\pi$
$840$		0			0
$841$	−2834.41	−	2834.41i	−0.116217	−	0.116217i
$842$		0			0
$843$	−10103.3	−	24391.6i	−0.412785	−	0.996551i
$844$		0			0
$845$	−335.492	−	138.965i	−0.0136583	−	0.00565746i
$846$		0			0
$847$			16890.5i			0.685202i
$848$		0			0
$849$			257.447i			0.0104070i
$850$		0			0
$851$	32887.6	+	13622.5i	1.32476	+	0.548735i
$852$		0			0
$853$	−2809.03	−	6781.60i	−0.112754	−	0.272213i	0.857422	−	0.514614i	$-0.172065\pi$
$853$	−2809.03	−	6781.60i	−0.112754	−	0.272213i	−0.970176	+	0.242401i	$0.922065\pi$
$854$		0			0
$855$	−39.9370	−	39.9370i	−0.00159745	−	0.00159745i
$856$		0			0
$857$	−7846.03	+	7846.03i	−0.312737	+	0.312737i	−0.845969	−	0.533232i	$-0.820977\pi$
$857$	−7846.03	+	7846.03i	−0.312737	+	0.312737i	0.533232	+	0.845969i	$0.320977\pi$
$858$		0			0
$859$	−10278.4	+	4257.47i	−0.408261	+	0.169107i	−0.577356	−	0.816493i	$-0.695915\pi$
$859$	−10278.4	+	4257.47i	−0.408261	+	0.169107i	0.169095	+	0.985600i	$0.445915\pi$
$860$		0			0
$861$	8535.84	−	20607.3i	0.337864	−	0.815675i
$862$		0			0
$863$	−28549.2			−1.12610			−0.563050	−	0.826423i	$-0.690372\pi$
$863$	−28549.2			−1.12610			−0.563050	+	0.826423i	$0.690372\pi$
$864$		0			0
$865$	72.6005			0.00285375
$866$		0			0
$867$	−4624.86	+	11165.4i	−0.181163	+	0.437366i
$868$		0			0
$869$	45877.1	−	19002.9i	1.79088	−	0.741807i
$870$		0			0
$871$	1872.58	−	1872.58i	0.0728473	−	0.0728473i
$872$		0			0
$873$	−120.720	−	120.720i	−0.00468013	−	0.00468013i
$874$		0			0
$875$	315.449	+	761.562i	0.0121876	+	0.0294234i
$876$		0			0
$877$	−8149.22	−	3375.52i	−0.313774	−	0.129969i	0.220239	−	0.975446i	$-0.429316\pi$
$877$	−8149.22	−	3375.52i	−0.313774	−	0.129969i	−0.534012	+	0.845477i	$0.679316\pi$
$878$		0			0
$879$			19683.9i			0.755315i
$880$		0			0
$881$			22699.0i			0.868046i	0.900902	+	0.434023i	$0.142906\pi$
$881$			22699.0i			0.868046i	−0.900902	+	0.434023i	$0.857094\pi$
$882$		0			0
$883$	3173.59	+	1314.54i	0.120951	+	0.0500995i	0.442338	−	0.896848i	$-0.354149\pi$
$883$	3173.59	+	1314.54i	0.120951	+	0.0500995i	−0.321387	+	0.946948i	$0.604149\pi$
$884$		0			0
$885$	17.2258	+	41.5868i	0.000654282	+	0.00157958i
$886$		0			0
$887$	−389.896	−	389.896i	−0.0147592	−	0.0147592i	0.699689	−	0.714448i	$-0.253322\pi$
$887$	−389.896	−	389.896i	−0.0147592	−	0.0147592i	−0.714448	+	0.699689i	$0.753322\pi$
$888$		0			0
$889$	−23203.5	+	23203.5i	−0.875389	+	0.875389i
$890$		0			0
$891$	−29797.9	+	12342.7i	−1.12039	+	0.464081i
$892$		0			0
$893$	23331.5	−	56327.2i	0.874310	−	2.11077i
$894$		0			0
$895$	281.121			0.0104993
$896$		0			0
$897$	10693.2			0.398032
$898$		0			0
$899$	−2364.91	+	5709.39i	−0.0877353	+	0.211812i
$900$		0			0
$901$	15275.6	−	6327.34i	0.564820	−	0.233956i
$902$		0			0
$903$	3093.33	−	3093.33i	0.113997	−	0.113997i
$904$		0			0
$905$	547.247	+	547.247i	0.0201007	+	0.0201007i
$906$		0			0
$907$	14791.8	+	35710.6i	0.541516	+	1.30733i	0.923653	+	0.383229i	$0.125188\pi$
$907$	14791.8	+	35710.6i	0.541516	+	1.30733i	−0.382138	+	0.924105i	$0.624812\pi$
$908$		0			0
$909$	1300.91	+	538.856i	0.0474682	+	0.0196620i
$910$		0			0
$911$			26874.8i			0.977388i	0.872455	+	0.488694i	$0.162527\pi$
$911$			26874.8i			0.977388i	−0.872455	+	0.488694i	$0.837473\pi$
$912$		0			0
$913$			12206.2i			0.442459i
$914$		0			0
$915$	796.426	+	329.891i	0.0287749	+	0.0119190i
$916$		0			0
$917$	4339.97	+	10477.6i	0.156291	+	0.377319i
$918$		0			0
$919$	−9495.37	−	9495.37i	−0.340831	−	0.340831i	0.515849	−	0.856680i	$-0.327477\pi$
$919$	−9495.37	−	9495.37i	−0.340831	−	0.340831i	−0.856680	+	0.515849i	$0.827477\pi$
$920$		0			0
$921$	−4436.42	+	4436.42i	−0.158724	+	0.158724i
$922$		0			0
$923$	9702.89	−	4019.07i	0.346018	−	0.143325i
$924$		0			0
$925$	−16214.7	+	39145.8i	−0.576364	+	1.39147i
$926$		0			0
$927$	1645.79			0.0583114
$928$		0			0
$929$	−51635.3			−1.82357			−0.911786	−	0.410665i	$-0.865297\pi$
$929$	−51635.3			−1.82357			−0.911786	+	0.410665i	$0.865297\pi$
$930$		0			0
$931$	3789.73	−	9149.21i	0.133409	−	0.322077i
$932$		0			0
$933$	−5268.84	+	2182.42i	−0.184881	+	0.0765803i
$934$		0			0
$935$	−603.911	+	603.911i	−0.0211230	+	0.0211230i
$936$		0			0
$937$	3704.24	+	3704.24i	0.129149	+	0.129149i	0.768726	−	0.639578i	$-0.220891\pi$
$937$	3704.24	+	3704.24i	0.129149	+	0.129149i	−0.639578	+	0.768726i	$0.720891\pi$
$938$		0			0
$939$	2012.79	+	4859.30i	0.0699520	+	0.168879i
$940$		0			0
$941$	6682.02	+	2767.78i	0.231485	+	0.0958843i	0.495411	−	0.868659i	$-0.335017\pi$
$941$	6682.02	+	2767.78i	0.231485	+	0.0958843i	−0.263926	+	0.964543i	$0.585017\pi$
$942$		0			0
$943$			29201.7i			1.00842i
$944$		0			0
$945$		−	480.254i		−	0.0165319i
$946$		0			0
$947$	−494.002	−	204.622i	−0.0169513	−	0.00702147i	0.374192	−	0.927351i	$-0.377920\pi$
$947$	−494.002	−	204.622i	−0.0169513	−	0.00702147i	−0.391143	+	0.920330i	$0.627920\pi$
$948$		0			0
$949$	2653.35	+	6405.76i	0.0907603	+	0.219115i
$950$		0			0
$951$	15131.6	+	15131.6i	0.515957	+	0.515957i
$952$		0			0
$953$	−28698.0	+	28698.0i	−0.975465	+	0.975465i	−0.999706	−	0.0242408i	$-0.992283\pi$
$953$	−28698.0	+	28698.0i	−0.975465	+	0.975465i	0.0242408	+	0.999706i	$0.492283\pi$
$954$		0			0
$955$	401.050	−	166.120i	0.0135892	−	0.00562883i
$956$		0			0
$957$	−15626.5	+	37725.6i	−0.527829	+	1.27429i
$958$		0			0
$959$	24587.1			0.827903
$960$		0			0
$961$	−28446.2			−0.954858
$962$		0			0
$963$	−921.352	+	2224.34i	−0.0308309	+	0.0744324i
$964$		0			0
$965$	−450.220	+	186.487i	−0.0150188	+	0.00622098i
$966$		0			0
$967$	−22689.5	+	22689.5i	−0.754544	+	0.754544i	−0.975324	−	0.220780i	$-0.929140\pi$
$967$	−22689.5	+	22689.5i	−0.754544	+	0.754544i	0.220780	+	0.975324i	$0.429140\pi$
$968$		0			0
$969$	36100.0	+	36100.0i	1.19680	+	1.19680i
$970$		0			0
$971$	−18313.2	−	44211.9i	−0.605250	−	1.46120i	−0.868111	−	0.496369i	$-0.834666\pi$
$971$	−18313.2	−	44211.9i	−0.605250	−	1.46120i	0.262861	−	0.964834i	$-0.415334\pi$
$972$		0			0
$973$	−11136.4	−	4612.83i	−0.366922	−	0.151984i
$974$		0			0
$975$			12728.0i			0.418073i
$976$		0			0
$977$			3076.94i			0.100757i	0.998730	+	0.0503787i	$0.0160428\pi$
$977$			3076.94i			0.100757i	−0.998730	+	0.0503787i	$0.983957\pi$
$978$		0			0
$979$	−70277.9	−	29110.1i	−2.29427	−	0.950319i
$980$		0			0
$981$	−1301.15	−	3141.26i	−0.0423472	−	0.102235i
$982$		0			0
$983$	40340.6	+	40340.6i	1.30892	+	1.30892i	0.922197	+	0.386722i	$0.126393\pi$
$983$	40340.6	+	40340.6i	1.30892	+	1.30892i	0.386722	+	0.922197i	$0.373607\pi$
$984$		0			0
$985$	−470.895	+	470.895i	−0.0152324	+	0.0152324i
$986$		0			0
$987$	37679.4	−	15607.3i	1.21514	−	0.503329i
$988$		0			0
$989$	−2191.70	+	5291.24i	−0.0704672	+	0.170123i
$990$		0			0
$991$	−19825.3			−0.635492			−0.317746	−	0.948176i	$-0.602926\pi$
$991$	−19825.3			−0.635492			−0.317746	+	0.948176i	$0.602926\pi$
$992$		0			0
$993$	30904.3			0.987632
$994$		0			0
$995$	−281.260	+	679.022i	−0.00896135	+	0.0216346i
$996$		0			0
$997$	−12624.9	+	5229.39i	−0.401036	+	0.166115i	−0.574079	−	0.818800i	$-0.694640\pi$
$997$	−12624.9	+	5229.39i	−0.401036	+	0.166115i	0.173043	+	0.984914i	$0.444640\pi$
$998$		0			0
$999$	34917.2	−	34917.2i	1.10584	−	1.10584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.17.9		44
4.3	odd	2		32.4.g.a.13.6	yes	44
8.3	odd	2		256.4.g.b.33.9		44
8.5	even	2		256.4.g.a.33.3		44
32.5	even	8	inner	128.4.g.a.113.9		44
32.11	odd	8		256.4.g.b.225.9		44
32.21	even	8		256.4.g.a.225.3		44
32.27	odd	8		32.4.g.a.5.6	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.6	✓	44	32.27	odd	8
32.4.g.a.13.6	yes	44	4.3	odd	2
128.4.g.a.17.9		44	1.1	even	1	trivial
128.4.g.a.113.9		44	32.5	even	8	inner
256.4.g.a.33.3		44	8.5	even	2
256.4.g.a.225.3		44	32.21	even	8
256.4.g.b.33.9		44	8.3	odd	2
256.4.g.b.225.9		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)

\(f(q)\)	\(=\)	\(q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +O(q^{10})\)	\(q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +(-18.6604 - 45.0502i) q^{11} +(18.9369 + 7.84392i) q^{13} -1.01558i q^{15} -85.7028i q^{17} +(-110.749 - 45.8739i) q^{19} +(-30.6868 - 74.0844i) q^{21} +(74.2331 + 74.2331i) q^{23} +(-88.3588 + 88.3588i) q^{25} +(134.544 - 55.7299i) q^{27} +(64.4881 - 155.688i) q^{29} -36.6720 q^{31} -242.316 q^{33} +(1.26201 - 3.04676i) q^{35} +(313.271 - 129.761i) q^{37} +(72.0243 - 72.0243i) q^{39} +(196.689 + 196.689i) q^{41} +(20.8770 + 50.4016i) q^{43} +(0.435291 + 0.180303i) q^{45} +508.601i q^{47} +82.6118i q^{49} +(-393.469 - 162.980i) q^{51} +(73.8289 + 178.239i) q^{53} +(-7.04657 - 7.04657i) q^{55} +(-421.223 + 421.223i) q^{57} +(-40.9489 + 16.9616i) q^{59} +(-324.831 + 784.211i) q^{61} +37.2017 q^{63} +4.18895 q^{65} +(49.4427 - 119.365i) q^{67} +(481.979 - 199.642i) q^{69} +(362.308 - 362.308i) q^{71} +(239.192 + 239.192i) q^{73} +(237.632 + 573.695i) q^{75} +(-726.954 - 301.114i) q^{77} +1018.36i q^{79} -661.438i q^{81} +(-231.267 - 95.7940i) q^{83} +(-6.70265 - 16.1816i) q^{85} +(-592.141 - 592.141i) q^{87} +(1103.08 - 1103.08i) q^{89} +(305.576 - 126.574i) q^{91} +(-69.7388 + 168.364i) q^{93} -24.4984 q^{95} -74.0528 q^{97} +(43.0203 - 103.860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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