LMFDB - Embedded newform 128.4.g.a.113.9

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			113.9
Character	$\chi$	$=$	128.113
Dual form			128.4.g.a.17.9

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.90169	+	4.59109i	0.365981	+	0.883556i	0.994400	+	0.105681i	$0.0337023\pi$
$3$	1.90169	+	4.59109i	0.365981	+	0.883556i	−0.628419	+	0.777875i	$0.716298\pi$
$4$		0			0
$5$	0.188811	+	0.0782080i	0.0168878	+	0.00699514i	0.391111	−	0.920343i	$-0.372091\pi$
$5$	0.188811	+	0.0782080i	0.0168878	+	0.00699514i	−0.374224	+	0.927339i	$0.622091\pi$
$6$		0			0
$7$	11.4103	+	11.4103i	0.616096	+	0.616096i	0.944528	−	0.328432i	$-0.106520\pi$
$7$	11.4103	+	11.4103i	0.616096	+	0.616096i	−0.328432	+	0.944528i	$0.606520\pi$
$8$		0			0
$9$	1.63019	−	1.63019i	0.0603773	−	0.0603773i
$10$		0			0
$11$	−18.6604	+	45.0502i	−0.511483	+	1.23483i	0.431537	+	0.902095i	$0.357971\pi$
$11$	−18.6604	+	45.0502i	−0.511483	+	1.23483i	−0.943020	+	0.332735i	$0.892029\pi$
$12$		0			0
$13$	18.9369	−	7.84392i	0.404011	−	0.167347i	−0.171418	−	0.985198i	$-0.554835\pi$
$13$	18.9369	−	7.84392i	0.404011	−	0.167347i	0.575430	+	0.817851i	$0.304835\pi$
$14$		0			0
$15$			1.01558i			0.0174814i
$16$		0			0
$17$			85.7028i			1.22270i	0.791359	+	0.611352i	$0.209374\pi$
$17$			85.7028i			1.22270i	−0.791359	+	0.611352i	$0.790626\pi$
$18$		0			0
$19$	−110.749	+	45.8739i	−1.33725	+	0.553905i	−0.932713	−	0.360619i	$-0.882566\pi$
$19$	−110.749	+	45.8739i	−1.33725	+	0.553905i	−0.404532	+	0.914524i	$0.632566\pi$
$20$		0			0
$21$	−30.6868	+	74.0844i	−0.318876	+	0.769835i
$22$		0			0
$23$	74.2331	−	74.2331i	0.672985	−	0.672985i	−0.285418	−	0.958403i	$-0.592132\pi$
$23$	74.2331	−	74.2331i	0.672985	−	0.672985i	0.958403	+	0.285418i	$0.0921324\pi$
$24$		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	0.984345	+	0.176250i	$0.0563967\pi$
$29$	64.4881	+	155.688i	0.412936	+	0.996915i	−0.571410	+	0.820665i	$0.693603\pi$
$30$		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	0.947644	−	0.319328i	$-0.103457\pi$
$37$	313.271	+	129.761i	1.39193	+	0.576557i	0.444287	+	0.895884i	$0.353457\pi$
$38$		0			0
$39$	72.0243	+	72.0243i	0.295721	+	0.295721i
$40$		0			0
$41$	196.689	−	196.689i	0.749211	−	0.749211i	−0.225120	−	0.974331i	$-0.572277\pi$
$41$	196.689	−	196.689i	0.749211	−	0.749211i	0.974331	+	0.225120i	$0.0722773\pi$
$42$		0			0
$43$	20.8770	−	50.4016i	0.0740400	−	0.178748i	−0.882526	−	0.470263i	$-0.844159\pi$
$43$	20.8770	−	50.4016i	0.0740400	−	0.178748i	0.956566	+	0.291514i	$0.0941591\pi$
$44$		0			0
$45$	0.435291	−	0.180303i	0.00144198	−	0.000597290i
$46$		0			0
$47$		−	508.601i		−	1.57845i	−0.614106	−	0.789224i	$-0.710483\pi$
$47$		−	508.601i		−	1.57845i	0.614106	−	0.789224i	$-0.289517\pi$
$48$		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	−0.798871	−	0.601503i	$-0.794569\pi$
$53$	73.8289	−	178.239i	0.191343	−	0.461943i	0.990214	+	0.139560i	$0.0445689\pi$
$54$		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	0.337047	−	0.941488i	$-0.390572\pi$
$59$	−40.9489	−	16.9616i	−0.0903576	−	0.0374273i	−0.427404	+	0.904061i	$0.640572\pi$
$60$		0			0
$61$	−324.831	−	784.211i	−0.681809	−	1.64603i	−0.760664	−	0.649146i	$-0.775126\pi$
$61$	−324.831	−	784.211i	−0.681809	−	1.64603i	0.0788549	−	0.996886i	$-0.474874\pi$
$62$		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	0.962525	−	0.271192i	$-0.0874180\pi$
$67$	49.4427	+	119.365i	0.0901550	+	0.217654i	−0.872370	+	0.488846i	$0.837418\pi$
$68$		0			0
$69$	481.979	+	199.642i	0.840920	+	0.348321i
$70$		0			0
$71$	362.308	+	362.308i	0.605606	+	0.605606i	0.941795	−	0.336189i	$-0.109138\pi$
$71$	362.308	+	362.308i	0.605606	+	0.605606i	−0.336189	+	0.941795i	$0.609138\pi$
$72$		0			0
$73$	239.192	−	239.192i	0.383498	−	0.383498i	−0.488863	−	0.872361i	$-0.662588\pi$
$73$	239.192	−	239.192i	0.383498	−	0.383498i	0.872361	+	0.488863i	$0.162588\pi$
$74$		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	$-0.741769\pi$
$79$		−	1018.36i		−	1.45030i	0.688589	−	0.725152i	$-0.258231\pi$
$80$		0			0
$81$			661.438i			0.907323i
$82$		0			0
$83$	−231.267	+	95.7940i	−0.305842	+	0.126684i	−0.530326	−	0.847794i	$-0.677930\pi$
$83$	−231.267	+	95.7940i	−0.305842	+	0.126684i	0.224484	+	0.974478i	$0.427930\pi$
$84$		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	0.918606	+	0.395174i	$0.129316\pi$
$89$	1103.08	+	1103.08i	1.31378	+	1.31378i	0.395174	+	0.918606i	$0.370684\pi$
$90$		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	0.642914	−	0.765939i	$-0.277725\pi$
$101$	564.281	+	233.733i	0.555922	+	0.230270i	−0.0869918	+	0.996209i	$0.527725\pi$
$102$		0			0
$103$	504.784	+	504.784i	0.482892	+	0.482892i	0.906054	−	0.423162i	$-0.139080\pi$
$103$	504.784	+	504.784i	0.482892	+	0.482892i	−0.423162	+	0.906054i	$0.639080\pi$
$104$		0			0
$105$	−11.5880	+	11.5880i	−0.0107702	+	0.0107702i
$106$		0			0
$107$	399.644	−	964.826i	0.361075	−	0.871713i	−0.634068	−	0.773277i	$-0.718616\pi$
$107$	399.644	−	964.826i	0.361075	−	0.871713i	0.995143	−	0.0984356i	$-0.0313839\pi$
$108$		0			0
$109$	−1362.55	+	564.385i	−1.19732	+	0.495948i	−0.890133	−	0.455700i	$-0.849389\pi$
$109$	−1362.55	+	564.385i	−1.19732	+	0.495948i	−0.307191	+	0.951648i	$0.599389\pi$
$110$		0			0
$111$			1685.02i			1.44086i
$112$		0			0
$113$			1171.99i			0.975681i	0.872933	+	0.487840i	$0.162215\pi$
$113$			1171.99i			0.975681i	−0.872933	+	0.487840i	$0.837785\pi$
$114$		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	0.808458	−	0.588553i	$-0.200302\pi$
$131$	−268.953	−	649.310i	−0.179378	−	0.433057i	−0.987836	+	0.155496i	$0.950302\pi$
$132$		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	−0.286259	−	0.958152i	$-0.592412\pi$
$137$	1077.41	−	1077.41i	0.671894	−	0.671894i	0.958152	+	0.286259i	$0.0924116\pi$
$138$		0			0
$139$	−285.862	+	690.132i	−0.174435	+	0.421124i	−0.986783	−	0.162050i	$-0.948189\pi$
$139$	−285.862	+	690.132i	−0.174435	+	0.421124i	0.812347	+	0.583174i	$0.198189\pi$
$140$		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	0.648063	+	0.761587i	$0.275579\pi$
$149$	−634.226	+	1531.16i	−0.348710	+	0.841860i	−0.996773	+	0.0802736i	$0.974421\pi$
$150$		0			0
$151$	805.847	−	805.847i	0.434297	−	0.434297i	−0.455790	−	0.890087i	$-0.650643\pi$
$151$	805.847	−	805.847i	0.434297	−	0.434297i	0.890087	+	0.455790i	$0.150643\pi$
$152$		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	0.826034	−	0.563620i	$-0.190592\pi$
$157$	−308.064	−	743.733i	−0.156600	−	0.378066i	−0.982634	+	0.185554i	$0.940592\pi$
$158$		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	0.799352	−	0.600863i	$-0.205176\pi$
$163$	−396.959	−	958.344i	−0.190750	−	0.460511i	−0.990102	+	0.140353i	$0.955176\pi$
$164$		0			0
$165$	−45.7519	−	18.9510i	−0.0215865	−	0.00894143i
$166$		0			0
$167$	−307.489	−	307.489i	−0.142480	−	0.142480i	0.632269	−	0.774749i	$-0.282124\pi$
$167$	−307.489	−	307.489i	−0.142480	−	0.142480i	−0.774749	+	0.632269i	$0.782124\pi$
$168$		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	−0.309398	−	0.950933i	$-0.600127\pi$
$173$	328.204	−	135.946i	0.144236	−	0.0597446i	0.453634	+	0.891188i	$0.350127\pi$
$174$		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	−0.101231	−	0.994863i	$-0.532278\pi$
$179$	1270.86	−	526.407i	0.530662	−	0.219807i	0.631893	+	0.775056i	$0.282278\pi$
$180$		0			0
$181$	1449.19	−	3498.66i	0.595125	−	1.43676i	−0.283371	−	0.959010i	$-0.591453\pi$
$181$	1449.19	−	3498.66i	0.595125	−	1.43676i	0.878496	−	0.477749i	$-0.158547\pi$
$182$		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	−0.235204	−	0.971946i	$-0.575576\pi$
$197$	−3010.53	−	1247.00i	−1.08879	−	0.450990i	−0.853584	+	0.520956i	$0.825576\pi$
$198$		0			0
$199$	−2542.97	−	2542.97i	−0.905862	−	0.905862i	0.0900734	−	0.995935i	$-0.471290\pi$
$199$	−2542.97	−	2542.97i	−0.905862	−	0.905862i	−0.995935	+	0.0900734i	$0.971290\pi$
$200$		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	−0.448801	−	0.893632i	$-0.648149\pi$
$211$	−411.497	+	170.448i	−0.134259	+	0.0556118i	0.314543	+	0.949243i	$0.398149\pi$
$212$		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	0.999202	−	0.0399527i	$-0.0127207\pi$
$227$	904.304	+	2183.18i	0.264409	+	0.638339i	−0.734793	+	0.678291i	$0.762721\pi$
$228$		0			0
$229$	4319.52	+	1789.20i	1.24647	+	0.516305i	0.905731	−	0.423852i	$-0.139322\pi$
$229$	4319.52	+	1789.20i	1.24647	+	0.516305i	0.340740	+	0.940158i	$0.389322\pi$
$230$		0			0
$231$	−2764.89	−	2764.89i	−0.787516	−	0.787516i
$232$		0			0
$233$	−3523.28	+	3523.28i	−0.990634	+	0.990634i	−0.999957	−	0.00932269i	$-0.997032\pi$
$233$	−3523.28	+	3523.28i	−0.990634	+	0.990634i	0.00932269	+	0.999957i	$0.497032\pi$
$234$		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	$0.318675\pi$
$239$			6222.79i			1.68418i	−0.539337	+	0.842090i	$0.681325\pi$
$240$		0			0
$241$		−	4271.08i		−	1.14160i	−0.821091	−	0.570798i	$-0.806634\pi$
$241$		−	4271.08i		−	1.14160i	0.821091	−	0.570798i	$-0.193366\pi$
$242$		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	−0.324267	−	0.945966i	$-0.605117\pi$
$251$	−4861.21	−	2013.58i	−1.22246	−	0.506358i	−0.898190	+	0.439608i	$0.855117\pi$
$252$		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	0.981760	−	0.190123i	$-0.0608886\pi$
$263$	3376.45	+	3376.45i	0.791638	+	0.791638i	−0.190123	+	0.981760i	$0.560889\pi$
$264$		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	−0.765541	−	0.643387i	$-0.777529\pi$
$269$	−3758.60	+	1556.86i	−0.851917	+	0.352876i	−0.0863762	+	0.996263i	$0.527529\pi$
$270$		0			0
$271$		−	4182.58i		−	0.937540i	−0.883320	−	0.468770i	$-0.844697\pi$
$271$		−	4182.58i		−	0.937540i	0.883320	−	0.468770i	$-0.155303\pi$
$272$		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	−0.926767	−	0.375636i	$-0.877424\pi$
$277$	−26.8731	+	64.8775i	−0.00582906	+	0.0140726i	0.920938	+	0.389709i	$0.127424\pi$
$278$		0			0
$279$	−59.7822	+	59.7822i	−0.0128282	+	0.0128282i
$280$		0			0
$281$	3756.73	+	3756.73i	0.797536	+	0.797536i	0.982706	−	0.185171i	$-0.0592837\pi$
$281$	3756.73	+	3756.73i	0.797536	+	0.797536i	−0.185171	+	0.982706i	$0.559284\pi$
$282$		0			0
$283$	−47.8634	−	19.8257i	−0.0100536	−	0.00416436i	0.377651	−	0.925948i	$-0.376732\pi$
$283$	−47.8634	−	19.8257i	−0.0100536	−	0.00416436i	−0.387705	+	0.921784i	$0.626732\pi$
$284$		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	−0.0132515	−	0.999912i	$-0.504218\pi$
$293$	−3659.53	−	1515.83i	−0.729666	−	0.302238i	−0.716415	+	0.697674i	$0.754218\pi$
$294$		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	−0.488463	−	0.872585i	$-0.662442\pi$
$307$	−1166.44	+	483.155i	−0.216847	+	0.0898211i	0.271615	+	0.962406i	$0.412442\pi$
$308$		0			0
$309$	−1357.57	+	3277.46i	−0.249933	+	0.603391i
$310$		0			0
$311$	−811.491	+	811.491i	−0.147960	+	0.147960i	−0.777206	−	0.629246i	$-0.783364\pi$
$311$	−811.491	+	811.491i	−0.147960	+	0.147960i	0.629246	+	0.777206i	$0.283364\pi$
$312$		0			0
$313$	−748.416	−	748.416i	−0.135153	−	0.135153i	0.636294	−	0.771447i	$-0.280467\pi$
$313$	−748.416	−	748.416i	−0.135153	−	0.135153i	−0.771447	+	0.636294i	$0.780467\pi$
$314$		0			0
$315$	7.02409	+	2.90947i	0.00125639	+	0.000520414i
$316$		0			0
$317$	−1647.93	−	3978.45i	−0.291977	−	0.704896i	0.708022	−	0.706191i	$-0.249588\pi$
$317$	−1647.93	−	3978.45i	−0.291977	−	0.704896i	−0.999999	+	0.00129494i	$0.999588\pi$
$318$		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	−0.593589	−	0.804769i	$-0.702289\pi$
$331$	2379.90	−	5745.58i	0.395199	−	0.954095i	0.988788	−	0.149327i	$-0.0477106\pi$
$332$		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	$0.334167\pi$
$337$			10731.5i			1.73466i	−0.497730	+	0.867332i	$0.665833\pi$
$338$		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	0.759936	−	0.649998i	$-0.225230\pi$
$347$	5414.63	+	2242.81i	0.837673	+	0.346976i	0.0777376	+	0.996974i	$0.475230\pi$
$348$		0			0
$349$	−443.942	−	1071.77i	−0.0680907	−	0.164385i	0.886171	−	0.463359i	$-0.153356\pi$
$349$	−443.942	−	1071.77i	−0.0680907	−	0.164385i	−0.954261	+	0.298973i	$0.903356\pi$
$350$		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	0.926114	−	0.377243i	$-0.123128\pi$
$359$	3733.47	+	3733.47i	0.548871	+	0.548871i	−0.377243	+	0.926114i	$0.623128\pi$
$360$		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	$0.161210\pi$
$367$			6820.92i			0.970161i	−0.874469	+	0.485081i	$0.838790\pi$
$368$		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	−0.388167	−	0.921589i	$-0.626892\pi$
$373$	3875.45	−	9356.15i	0.537970	−	1.29878i	0.926137	−	0.377186i	$-0.123108\pi$
$374$		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	0.656657	−	0.754189i	$-0.271970\pi$
$379$	4336.19	+	1796.11i	0.587692	+	0.243430i	−0.0689653	+	0.997619i	$0.521970\pi$
$380$		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	0.351914	−	0.936032i	$-0.385531\pi$
$389$	−468.925	−	194.235i	−0.0611194	−	0.0253165i	−0.413034	+	0.910716i	$0.635531\pi$
$390$		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	−0.581738	−	0.813376i	$-0.697627\pi$
$397$	−3306.01	+	1369.40i	−0.417945	+	0.173118i	0.163793	+	0.986495i	$0.447627\pi$
$398$		0			0
$399$		−	9612.53i		−	1.20609i
$400$		0			0
$401$		−	3887.84i		−	0.484164i	−0.970256	−	0.242082i	$-0.922170\pi$
$401$		−	3887.84i		−	0.484164i	0.970256	−	0.242082i	$-0.0778303\pi$
$402$		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	0.123339	−	0.992365i	$-0.460640\pi$
$409$	−7188.15	−	7188.15i	−0.869025	−	0.869025i	−0.992365	+	0.123339i	$0.960640\pi$
$410$		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	−0.955439	−	0.295187i	$-0.904618\pi$
$419$	−4190.33	−	10116.4i	−0.488571	−	1.17951i	0.466869	−	0.884327i	$-0.345382\pi$
$420$		0			0
$421$	14568.6	+	6034.51i	1.68653	+	0.698584i	0.999604	−	0.0281419i	$-0.00895901\pi$
$421$	14568.6	+	6034.51i	1.68653	+	0.698584i	0.686927	+	0.726726i	$0.258959\pi$
$422$		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	$-0.984981\pi$
$431$		−	844.040i		−	0.0943295i	0.998887	−	0.0471647i	$-0.0150186\pi$
$432$		0			0
$433$			11447.7i			1.27053i	0.772293	+	0.635266i	$0.219110\pi$
$433$			11447.7i			1.27053i	−0.772293	+	0.635266i	$0.780890\pi$
$434$		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	−0.809266	−	0.587443i	$-0.800135\pi$
$439$	−2040.34	+	2040.34i	−0.221823	+	0.221823i	0.587443	+	0.809266i	$0.300135\pi$
$440$		0			0
$441$	−134.673	−	134.673i	−0.0145419	−	0.0145419i
$442$		0			0
$443$	−12477.8	−	5168.47i	−1.33823	−	0.554315i	−0.405241	−	0.914210i	$-0.632813\pi$
$443$	−12477.8	−	5168.47i	−1.33823	−	0.554315i	−0.932993	+	0.359895i	$0.882813\pi$
$444$		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	−0.0258078	+	0.999667i	$0.508216\pi$
$457$	−10018.4	+	10018.4i	−1.02547	+	1.02547i	−0.999667	+	0.0258078i	$0.991784\pi$
$458$		0			0
$459$	−4776.21	+	11530.8i	−0.485696	+	1.17257i
$460$		0			0
$461$	−1495.66	+	619.524i	−0.151106	+	0.0625902i	−0.456955	−	0.889490i	$-0.651060\pi$
$461$	−1495.66	+	619.524i	−0.151106	+	0.0625902i	0.305849	+	0.952080i	$0.401060\pi$
$462$		0			0
$463$		−	14517.8i		−	1.45724i	−0.684921	−	0.728618i	$-0.740163\pi$
$463$		−	14517.8i		−	1.45724i	0.684921	−	0.728618i	$-0.259837\pi$
$464$		0			0
$465$		−	37.2432i		−	0.00371422i
$466$		0			0
$467$	−5649.95	+	2340.29i	−0.559847	+	0.231896i	−0.644619	−	0.764504i	$-0.722984\pi$
$467$	−5649.95	+	2340.29i	−0.559847	+	0.231896i	0.0847717	+	0.996400i	$0.472984\pi$
$468$		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	0.983585	+	0.180446i	$0.0577542\pi$
$487$	12510.0	+	12510.0i	1.16403	+	1.16403i	0.180446	+	0.983585i	$0.442246\pi$
$488$		0			0
$489$	3644.95	−	3644.95i	0.337076	−	0.337076i
$490$		0			0
$491$	4847.78	−	11703.6i	0.445575	−	1.07571i	−0.528387	−	0.849004i	$-0.677203\pi$
$491$	4847.78	−	11703.6i	0.445575	−	1.07571i	0.973962	−	0.226710i	$-0.0727970\pi$
$492$		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	−0.993538	−	0.113498i	$-0.963794\pi$
$499$	−18011.3	+	7460.51i	−1.61582	+	0.669295i	−0.622282	+	0.782793i	$0.713794\pi$
$500$		0			0
$501$	826.961	−	1996.46i	0.0737443	−	0.178034i
$502$		0			0
$503$	3687.97	−	3687.97i	0.326915	−	0.326915i	−0.524497	−	0.851412i	$-0.675747\pi$
$503$	3687.97	−	3687.97i	0.326915	−	0.326915i	0.851412	+	0.524497i	$0.175747\pi$
$504$		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	0.963654	−	0.267155i	$-0.0860835\pi$
$509$	1071.88	+	2587.76i	0.0933407	+	0.225344i	−0.870313	+	0.492499i	$0.836083\pi$
$510$		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	−0.959090	−	0.283102i	$-0.908637\pi$
$521$	−8038.89	+	8038.89i	−0.675988	+	0.675988i	0.283102	+	0.959090i	$0.408637\pi$
$522$		0			0
$523$	−7860.76	+	18977.6i	−0.657222	+	1.58667i	0.144854	+	0.989453i	$0.453729\pi$
$523$	−7860.76	+	18977.6i	−0.657222	+	1.58667i	−0.802076	+	0.597222i	$0.796271\pi$
$524$		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	0.862911	−	0.505356i	$-0.168639\pi$
$541$	−1316.22	−	3177.63i	−0.104600	−	0.252527i	−0.967511	+	0.252829i	$0.918639\pi$
$542$		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	0.948014	+	0.318229i	$0.103088\pi$
$547$	6431.02	+	15525.9i	0.502689	+	1.21360i	−0.445325	+	0.895369i	$0.646912\pi$
$548$		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	−0.576261	−	0.817266i	$-0.695489\pi$
$557$	−5335.11	+	2209.88i	−0.405846	+	0.168107i	0.170416	+	0.985372i	$0.445489\pi$
$558$		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	−0.569696	−	0.821856i	$-0.692939\pi$
$563$	−5228.46	+	2165.70i	−0.391391	+	0.162120i	0.178304	+	0.983975i	$0.442939\pi$
$564$		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	0.536005	−	0.844215i	$-0.319933\pi$
$569$	−4183.25	−	4183.25i	−0.308209	−	0.308209i	−0.844215	+	0.536005i	$0.819933\pi$
$570$		0			0
$571$	−7441.94	−	3082.55i	−0.545421	−	0.225921i	0.0929211	−	0.995673i	$-0.470380\pi$
$571$	−7441.94	−	3082.55i	−0.545421	−	0.225921i	−0.638342	+	0.769753i	$0.720380\pi$
$572$		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	−0.975181	−	0.221410i	$-0.928934\pi$
$587$	−1835.52	+	4431.34i	−0.129063	+	0.311586i	0.846118	+	0.532996i	$0.178934\pi$
$588$		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	$-0.844616\pi$
$593$		−	13545.0i		−	0.937989i	0.883201	−	0.468995i	$-0.155384\pi$
$594$		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	−0.145015	−	0.989429i	$-0.546323\pi$
$599$	12379.3	−	12379.3i	0.844414	−	0.844414i	0.989429	+	0.145015i	$0.0463231\pi$
$600$		0			0
$601$	−17513.1	−	17513.1i	−1.18864	−	1.18864i	−0.977442	−	0.211202i	$-0.932262\pi$
$601$	−17513.1	−	17513.1i	−1.18864	−	1.18864i	−0.211202	−	0.977442i	$-0.567738\pi$
$602$		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	−0.112649	−	0.993635i	$-0.535934\pi$
$613$	−13582.2	−	5625.93i	−0.894910	−	0.370684i	−0.782261	+	0.622951i	$0.785934\pi$
$614$		0			0
$615$	199.753	+	199.753i	0.0130972	+	0.0130972i
$616$		0			0
$617$	−4045.14	+	4045.14i	−0.263941	+	0.263941i	−0.826653	−	0.562712i	$-0.809758\pi$
$617$	−4045.14	+	4045.14i	−0.263941	+	0.263941i	0.562712	+	0.826653i	$0.309758\pi$
$618$		0			0
$619$	4901.51	−	11833.3i	0.318268	−	0.768368i	−0.681078	−	0.732211i	$-0.738488\pi$
$619$	4901.51	−	11833.3i	0.318268	−	0.768368i	0.999346	−	0.0361568i	$-0.0115116\pi$
$620$		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	−0.106448	−	0.994318i	$-0.533948\pi$
$631$	14073.2	−	14073.2i	0.887870	−	0.887870i	0.994318	+	0.106448i	$0.0339478\pi$
$632$		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	0.781254	−	0.624213i	$-0.214580\pi$
$643$	−3465.77	−	8367.12i	−0.212561	−	0.513168i	−0.993815	+	0.111045i	$0.964580\pi$
$644$		0			0
$645$	51.1867	+	21.2022i	0.00312477	+	0.00129432i
$646$		0			0
$647$	−17607.8	−	17607.8i	−1.06991	−	1.06991i	−0.997365	−	0.0725490i	$-0.976887\pi$
$647$	−17607.8	−	17607.8i	−1.06991	−	1.06991i	−0.0725490	−	0.997365i	$-0.523113\pi$
$648$		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	0.536680	−	0.843786i	$-0.319678\pi$
$653$	25243.9	−	10456.4i	1.51282	−	0.626629i	0.976137	+	0.217157i	$0.0696782\pi$
$654$		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	−0.305888	−	0.952068i	$-0.598953\pi$
$659$	2555.01	−	1058.32i	0.151030	−	0.0625588i	0.456918	+	0.889509i	$0.348953\pi$
$660$		0			0
$661$	−1008.92	+	2435.76i	−0.0593685	+	0.143328i	−0.950780	−	0.309866i	$-0.899716\pi$
$661$	−1008.92	+	2435.76i	−0.0593685	+	0.143328i	0.891412	+	0.453195i	$0.149716\pi$
$662$		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	−0.697001	−	0.717070i	$-0.745483\pi$
$677$	−29890.9	−	12381.2i	−1.69690	−	0.702879i	−0.999899	+	0.0141909i	$0.995483\pi$
$678$		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	−0.999791	−	0.0204414i	$-0.993493\pi$
$683$	−4968.96	+	11996.1i	−0.278378	+	0.672063i	0.721413	+	0.692505i	$0.243493\pi$
$684$		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	−0.157760	−	0.987477i	$-0.550427\pi$
$691$	7791.33	−	3227.27i	0.428938	−	0.177672i	0.586698	+	0.809805i	$0.300427\pi$
$692$		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	0.805342	−	0.592810i	$-0.201982\pi$
$701$	−3402.06	−	8213.30i	−0.183301	−	0.442528i	−0.988643	+	0.150283i	$0.951982\pi$
$702$		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	0.212656	−	0.977127i	$-0.431789\pi$
$709$	−6190.43	−	2564.16i	−0.327908	−	0.135824i	−0.540563	+	0.841303i	$0.681789\pi$
$710$		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	$-0.941888\pi$
$719$		−	7000.41i		−	0.363103i	0.983381	−	0.181552i	$-0.0581120\pi$
$720$		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	−0.592504	−	0.805567i	$-0.701861\pi$
$727$	4176.48	−	4176.48i	0.213063	−	0.213063i	0.805567	+	0.592504i	$0.201861\pi$
$728$		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	0.976017	+	0.217694i	$0.0698533\pi$
$733$	8727.96	+	21071.2i	0.439801	+	1.06177i	−0.536216	+	0.844081i	$0.680147\pi$
$734$		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	0.961809	−	0.273722i	$-0.0882548\pi$
$739$	1771.01	+	4275.60i	0.0881566	+	0.212829i	−0.873652	+	0.486551i	$0.838255\pi$
$740$		0			0
$741$	−11280.7	−	4672.61i	−0.559253	−	0.231650i
$742$		0			0
$743$	−331.818	−	331.818i	−0.0163839	−	0.0163839i	0.698867	−	0.715251i	$-0.253688\pi$
$743$	−331.818	−	331.818i	−0.0163839	−	0.0163839i	−0.715251	+	0.698867i	$0.753688\pi$
$744$		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	$0.338129\pi$
$751$			35952.8i			1.74692i	−0.486897	+	0.873459i	$0.661871\pi$
$752$		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	−0.592557	−	0.805528i	$-0.701882\pi$
$757$	8248.62	−	19913.9i	0.396038	−	0.956121i	0.988596	−	0.150593i	$-0.0481183\pi$
$758$		0			0
$759$	−17987.8	+	17987.8i	−0.860234	+	0.860234i
$760$		0			0
$761$	20845.8	+	20845.8i	0.992983	+	0.992983i	0.999976	−	0.00699229i	$-0.00222573\pi$
$761$	20845.8	+	20845.8i	0.992983	+	0.992983i	−0.00699229	+	0.999976i	$0.502226\pi$
$762$		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	−0.0157831	−	0.999875i	$-0.505024\pi$
$773$	−15774.0	−	6533.82i	−0.733962	−	0.304017i	−0.718179	+	0.695858i	$0.755024\pi$
$774$		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	−0.595324	−	0.803486i	$-0.702976\pi$
$787$	−9893.89	+	4098.18i	−0.448131	+	0.185622i	0.147193	+	0.989108i	$0.452976\pi$
$788$		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	−0.970461	−	0.241259i	$-0.922440\pi$
$797$	−10234.0	−	24707.0i	−0.454838	−	1.09807i	0.515623	−	0.856815i	$-0.327560\pi$
$798$		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	−0.795597	−	0.605827i	$-0.792843\pi$
$809$	−4366.67	+	4366.67i	−0.189770	+	0.189770i	0.605827	+	0.795597i	$0.292843\pi$
$810$		0			0
$811$	16742.8	−	40420.6i	0.724930	−	1.75014i	0.0661382	−	0.997810i	$-0.478932\pi$
$811$	16742.8	−	40420.6i	0.724930	−	1.75014i	0.658792	−	0.752325i	$-0.271068\pi$
$812$		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	−0.971233	−	0.238132i	$-0.923465\pi$
$821$	−2730.75	+	6592.63i	−0.116083	+	0.280249i	0.855150	+	0.518381i	$0.173465\pi$
$822$		0			0
$823$	7832.94	−	7832.94i	0.331761	−	0.331761i	−0.521494	−	0.853255i	$-0.674625\pi$
$823$	7832.94	−	7832.94i	0.331761	−	0.331761i	0.853255	+	0.521494i	$0.174625\pi$
$824$		0			0
$825$	21410.7	+	21410.7i	0.903547	+	0.903547i
$826$		0			0
$827$	18116.8	+	7504.23i	0.761769	+	0.315535i	0.729533	−	0.683945i	$-0.239737\pi$
$827$	18116.8	+	7504.23i	0.761769	+	0.315535i	0.0322359	+	0.999480i	$0.489737\pi$
$828$		0			0
$829$	−3888.12	−	9386.75i	−0.162895	−	0.393264i	0.821265	−	0.570547i	$-0.193269\pi$
$829$	−3888.12	−	9386.75i	−0.162895	−	0.393264i	−0.984160	+	0.177284i	$0.943269\pi$
$830$		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	0.801047	−	0.598601i	$-0.204276\pi$
$839$	4919.87	+	4919.87i	0.202447	+	0.202447i	−0.598601	+	0.801047i	$0.704276\pi$
$840$		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	−0.970176	−	0.242401i	$-0.922065\pi$
$853$	−2809.03	+	6781.60i	−0.112754	+	0.272213i	0.857422	+	0.514614i	$0.172065\pi$
$854$		0			0
$855$	−39.9370	+	39.9370i	−0.00159745	+	0.00159745i
$856$		0			0
$857$	−7846.03	−	7846.03i	−0.312737	−	0.312737i	0.533232	−	0.845969i	$-0.320977\pi$
$857$	−7846.03	−	7846.03i	−0.312737	−	0.312737i	−0.845969	+	0.533232i	$0.820977\pi$
$858$		0			0
$859$	−10278.4	−	4257.47i	−0.408261	−	0.169107i	0.169095	−	0.985600i	$-0.445915\pi$
$859$	−10278.4	−	4257.47i	−0.408261	−	0.169107i	−0.577356	+	0.816493i	$0.695915\pi$
$860$		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	−0.534012	−	0.845477i	$-0.679316\pi$
$877$	−8149.22	+	3375.52i	−0.313774	+	0.129969i	0.220239	+	0.975446i	$0.429316\pi$
$878$		0			0
$879$		−	19683.9i		−	0.755315i
$880$		0			0
$881$		−	22699.0i		−	0.868046i	−0.900902	−	0.434023i	$-0.857094\pi$
$881$		−	22699.0i		−	0.868046i	0.900902	−	0.434023i	$-0.142906\pi$
$882$		0			0
$883$	3173.59	−	1314.54i	0.120951	−	0.0500995i	−0.321387	−	0.946948i	$-0.604149\pi$
$883$	3173.59	−	1314.54i	0.120951	−	0.0500995i	0.442338	+	0.896848i	$0.354149\pi$
$884$		0			0
$885$	17.2258	−	41.5868i	0.000654282	−	0.00157958i
$886$		0			0
$887$	−389.896	+	389.896i	−0.0147592	+	0.0147592i	−0.714448	−	0.699689i	$-0.753322\pi$
$887$	−389.896	+	389.896i	−0.0147592	+	0.0147592i	0.699689	+	0.714448i	$0.253322\pi$
$888$		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	−0.382138	−	0.924105i	$-0.624812\pi$
$907$	14791.8	−	35710.6i	0.541516	−	1.30733i	0.923653	−	0.383229i	$-0.125188\pi$
$908$		0			0
$909$	1300.91	−	538.856i	0.0474682	−	0.0196620i
$910$		0			0
$911$		−	26874.8i		−	0.977388i	−0.872455	−	0.488694i	$-0.837473\pi$
$911$		−	26874.8i		−	0.977388i	0.872455	−	0.488694i	$-0.162527\pi$
$912$		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	−0.856680	−	0.515849i	$-0.827477\pi$
$919$	−9495.37	+	9495.37i	−0.340831	+	0.340831i	0.515849	+	0.856680i	$0.327477\pi$
$920$		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	−0.639578	−	0.768726i	$-0.720891\pi$
$937$	3704.24	−	3704.24i	0.129149	−	0.129149i	0.768726	+	0.639578i	$0.220891\pi$
$938$		0			0
$939$	2012.79	−	4859.30i	0.0699520	−	0.168879i
$940$		0			0
$941$	6682.02	−	2767.78i	0.231485	−	0.0958843i	−0.263926	−	0.964543i	$-0.585017\pi$
$941$	6682.02	−	2767.78i	0.231485	−	0.0958843i	0.495411	+	0.868659i	$0.335017\pi$
$942$		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	−0.391143	−	0.920330i	$-0.627920\pi$
$947$	−494.002	+	204.622i	−0.0169513	+	0.00702147i	0.374192	+	0.927351i	$0.377920\pi$
$948$		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	0.0242408	−	0.999706i	$-0.492283\pi$
$953$	−28698.0	−	28698.0i	−0.975465	−	0.975465i	−0.999706	+	0.0242408i	$0.992283\pi$
$954$		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	0.220780	−	0.975324i	$-0.429140\pi$
$967$	−22689.5	−	22689.5i	−0.754544	−	0.754544i	−0.975324	+	0.220780i	$0.929140\pi$
$968$		0			0
$969$	36100.0	−	36100.0i	1.19680	−	1.19680i
$970$		0			0
$971$	−18313.2	+	44211.9i	−0.605250	+	1.46120i	0.262861	+	0.964834i	$0.415334\pi$
$971$	−18313.2	+	44211.9i	−0.605250	+	1.46120i	−0.868111	+	0.496369i	$0.834666\pi$
$972$		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	$-0.983957\pi$
$977$		−	3076.94i		−	0.100757i	0.998730	−	0.0503787i	$-0.0160428\pi$
$978$		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	0.386722	−	0.922197i	$-0.373607\pi$
$983$	40340.6	−	40340.6i	1.30892	−	1.30892i	0.922197	−	0.386722i	$-0.126393\pi$
$984$		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	0.173043	−	0.984914i	$-0.444640\pi$
$997$	−12624.9	−	5229.39i	−0.401036	−	0.166115i	−0.574079	+	0.818800i	$0.694640\pi$
$998$		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.113.9		44
4.3	odd	2		32.4.g.a.5.6	✓	44
8.3	odd	2		256.4.g.b.225.9		44
8.5	even	2		256.4.g.a.225.3		44
32.3	odd	8		256.4.g.b.33.9		44
32.13	even	8	inner	128.4.g.a.17.9		44
32.19	odd	8		32.4.g.a.13.6	yes	44
32.29	even	8		256.4.g.a.33.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.6	✓	44	4.3	odd	2
32.4.g.a.13.6	yes	44	32.19	odd	8
128.4.g.a.17.9		44	32.13	even	8	inner
128.4.g.a.113.9		44	1.1	even	1	trivial
256.4.g.a.33.3		44	32.29	even	8
256.4.g.a.225.3		44	8.5	even	2
256.4.g.b.33.9		44	32.3	odd	8
256.4.g.b.225.9		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

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