LMFDB - Embedded newform 1920.2.bc.l.1183.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(607,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.607"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bc (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,-8,0,4,0,-20,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1183.8
Root			$0.356677 - 1.36850i$ of defining polynomial
Character	$\chi$	$=$	1920.1183
Dual form			1920.2.bc.l.607.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{3} +(1.09619 - 1.94894i) q^{5} +(2.09269 - 2.09269i) q^{7} -1.00000 q^{9} +(-2.58551 + 2.58551i) q^{11} -5.56694 q^{13} +(-1.94894 - 1.09619i) q^{15} +(-1.85127 + 1.85127i) q^{17} +(-2.23993 + 2.23993i) q^{19} +(-2.09269 - 2.09269i) q^{21} +(-2.74910 - 2.74910i) q^{23} +(-2.59675 - 4.27281i) q^{25} +1.00000i q^{27} +(-2.52646 - 2.52646i) q^{29} +8.08076i q^{31} +(2.58551 + 2.58551i) q^{33} +(-1.78455 - 6.37250i) q^{35} -11.3539 q^{37} +5.56694i q^{39} -1.77121i q^{41} -2.48260 q^{43} +(-1.09619 + 1.94894i) q^{45} +(-0.525736 - 0.525736i) q^{47} -1.75866i q^{49} +(1.85127 + 1.85127i) q^{51} -10.9352i q^{53} +(2.20481 + 7.87321i) q^{55} +(2.23993 + 2.23993i) q^{57} +(1.09168 + 1.09168i) q^{59} +(6.18650 - 6.18650i) q^{61} +(-2.09269 + 2.09269i) q^{63} +(-6.10241 + 10.8496i) q^{65} +12.3904 q^{67} +(-2.74910 + 2.74910i) q^{69} +4.46143 q^{71} +(4.11339 - 4.11339i) q^{73} +(-4.27281 + 2.59675i) q^{75} +10.8213i q^{77} +13.3425 q^{79} +1.00000 q^{81} -0.335336i q^{83} +(1.57868 + 5.63735i) q^{85} +(-2.52646 + 2.52646i) q^{87} -1.91559 q^{89} +(-11.6499 + 11.6499i) q^{91} +8.08076 q^{93} +(1.91011 + 6.82087i) q^{95} +(2.86143 - 2.86143i) q^{97} +(2.58551 - 2.58551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{5} + 4 q^{7} - 20 q^{9} + 8 q^{11} - 8 q^{13} + 12 q^{17} - 16 q^{19} - 4 q^{21} + 16 q^{23} - 4 q^{25} - 8 q^{33} - 12 q^{35} - 24 q^{37} - 8 q^{43} + 8 q^{45} - 12 q^{51} + 4 q^{55} + 16 q^{57}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q - 8 * q^5 + 4 * q^7 - 20 * q^9 + 8 * q^11 - 8 * q^13 + 12 * q^17 - 16 * q^19 - 4 * q^21 + 16 * q^23 - 4 * q^25 - 8 * q^33 - 12 * q^35 - 24 * q^37 - 8 * q^43 + 8 * q^45 - 12 * q^51 + 4 * q^55 + 16 * q^57 + 16 * q^59 + 12 * q^61 - 4 * q^63 + 4 * q^65 - 16 * q^67 + 16 * q^69 + 20 * q^73 - 8 * q^75 + 48 * q^79 + 20 * q^81 - 4 * q^85 - 40 * q^89 - 24 * q^91 - 72 * q^95 - 28 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$	1.09619	−	1.94894i	0.490230	−	0.871593i
$5$	1.09619	−	1.94894i	0.490230	−	0.871593i
$6$		0			0
$7$	2.09269	−	2.09269i	0.790961	−	0.790961i	−0.190690	−	0.981650i	$-0.561072\pi$
$7$	2.09269	−	2.09269i	0.790961	−	0.790961i	0.981650	+	0.190690i	$0.0610724\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−2.58551	+	2.58551i	−0.779561	+	0.779561i	−0.979756	−	0.200195i	$-0.935842\pi$
$11$	−2.58551	+	2.58551i	−0.779561	+	0.779561i	0.200195	+	0.979756i	$0.435842\pi$
$12$		0			0
$13$	−5.56694			−1.54399			−0.771996	−	0.635628i	$-0.780741\pi$
$13$	−5.56694			−1.54399			−0.771996	+	0.635628i	$0.780741\pi$
$14$		0			0
$15$	−1.94894	−	1.09619i	−0.503215	−	0.283034i
$16$		0			0
$17$	−1.85127	+	1.85127i	−0.448999	+	0.448999i	−0.895022	−	0.446023i	$-0.852840\pi$
$17$	−1.85127	+	1.85127i	−0.448999	+	0.448999i	0.446023	+	0.895022i	$0.352840\pi$
$18$		0			0
$19$	−2.23993	+	2.23993i	−0.513875	+	0.513875i	−0.915711	−	0.401836i	$-0.868372\pi$
$19$	−2.23993	+	2.23993i	−0.513875	+	0.513875i	0.401836	+	0.915711i	$0.368372\pi$
$20$		0			0
$21$	−2.09269	−	2.09269i	−0.456661	−	0.456661i
$22$		0			0
$23$	−2.74910	−	2.74910i	−0.573227	−	0.573227i	0.359802	−	0.933029i	$-0.382844\pi$
$23$	−2.74910	−	2.74910i	−0.573227	−	0.573227i	−0.933029	+	0.359802i	$0.882844\pi$
$24$		0			0
$25$	−2.59675	−	4.27281i	−0.519350	−	0.854562i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−2.52646	−	2.52646i	−0.469152	−	0.469152i	0.432488	−	0.901640i	$-0.357636\pi$
$29$	−2.52646	−	2.52646i	−0.469152	−	0.469152i	−0.901640	+	0.432488i	$0.857636\pi$
$30$		0			0
$31$			8.08076i			1.45135i	0.688039	+	0.725674i	$0.258472\pi$
$31$			8.08076i			1.45135i	−0.688039	+	0.725674i	$0.741528\pi$
$32$		0			0
$33$	2.58551	+	2.58551i	0.450079	+	0.450079i
$34$		0			0
$35$	−1.78455	−	6.37250i	−0.301644	−	1.07715i
$36$		0			0
$37$	−11.3539			−1.86657			−0.933284	−	0.359138i	$-0.883071\pi$
$37$	−11.3539			−1.86657			−0.933284	+	0.359138i	$0.883071\pi$
$38$		0			0
$39$			5.56694i			0.891424i
$40$		0			0
$41$		−	1.77121i		−	0.276617i	−0.990389	−	0.138309i	$-0.955833\pi$
$41$		−	1.77121i		−	0.276617i	0.990389	−	0.138309i	$-0.0441666\pi$
$42$		0			0
$43$	−2.48260			−0.378593			−0.189296	−	0.981920i	$-0.560621\pi$
$43$	−2.48260			−0.378593			−0.189296	+	0.981920i	$0.560621\pi$
$44$		0			0
$45$	−1.09619	+	1.94894i	−0.163410	+	0.290531i
$46$		0			0
$47$	−0.525736	−	0.525736i	−0.0766865	−	0.0766865i	0.667723	−	0.744410i	$-0.267269\pi$
$47$	−0.525736	−	0.525736i	−0.0766865	−	0.0766865i	−0.744410	+	0.667723i	$0.767269\pi$
$48$		0			0
$49$		−	1.75866i		−	0.251238i
$50$		0			0
$51$	1.85127	+	1.85127i	0.259230	+	0.259230i
$52$		0			0
$53$		−	10.9352i		−	1.50207i	−0.660263	−	0.751035i	$-0.729555\pi$
$53$		−	10.9352i		−	1.50207i	0.660263	−	0.751035i	$-0.270445\pi$
$54$		0			0
$55$	2.20481	+	7.87321i	0.297296	+	1.06162i
$56$		0			0
$57$	2.23993	+	2.23993i	0.296686	+	0.296686i
$58$		0			0
$59$	1.09168	+	1.09168i	0.142124	+	0.142124i	0.774589	−	0.632465i	$-0.217957\pi$
$59$	1.09168	+	1.09168i	0.142124	+	0.142124i	−0.632465	+	0.774589i	$0.717957\pi$
$60$		0			0
$61$	6.18650	−	6.18650i	0.792100	−	0.792100i	−0.189735	−	0.981835i	$-0.560763\pi$
$61$	6.18650	−	6.18650i	0.792100	−	0.792100i	0.981835	+	0.189735i	$0.0607630\pi$
$62$		0			0
$63$	−2.09269	+	2.09269i	−0.263654	+	0.263654i
$64$		0			0
$65$	−6.10241	+	10.8496i	−0.756910	+	1.34573i
$66$		0			0
$67$	12.3904			1.51373			0.756865	−	0.653571i	$-0.226730\pi$
$67$	12.3904			1.51373			0.756865	+	0.653571i	$0.226730\pi$
$68$		0			0
$69$	−2.74910	+	2.74910i	−0.330953	+	0.330953i
$70$		0			0
$71$	4.46143			0.529475			0.264737	−	0.964321i	$-0.414715\pi$
$71$	4.46143			0.529475			0.264737	+	0.964321i	$0.414715\pi$
$72$		0			0
$73$	4.11339	−	4.11339i	0.481436	−	0.481436i	−0.424154	−	0.905590i	$-0.639428\pi$
$73$	4.11339	−	4.11339i	0.481436	−	0.481436i	0.905590	+	0.424154i	$0.139428\pi$
$74$		0			0
$75$	−4.27281	+	2.59675i	−0.493381	+	0.299847i
$76$		0			0
$77$			10.8213i			1.23320i
$78$		0			0
$79$	13.3425			1.50115			0.750573	−	0.660788i	$-0.229778\pi$
$79$	13.3425			1.50115			0.750573	+	0.660788i	$0.229778\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$		−	0.335336i		−	0.0368079i	−0.999831	−	0.0184039i	$-0.994142\pi$
$83$		−	0.335336i		−	0.0368079i	0.999831	−	0.0184039i	$-0.00585848\pi$
$84$		0			0
$85$	1.57868	+	5.63735i	0.171232	+	0.611457i
$86$		0			0
$87$	−2.52646	+	2.52646i	−0.270865	+	0.270865i
$88$		0			0
$89$	−1.91559			−0.203052			−0.101526	−	0.994833i	$-0.532372\pi$
$89$	−1.91559			−0.203052			−0.101526	+	0.994833i	$0.532372\pi$
$90$		0			0
$91$	−11.6499	+	11.6499i	−1.22124	+	1.22124i
$92$		0			0
$93$	8.08076			0.837936
$94$		0			0
$95$	1.91011	+	6.82087i	0.195973	+	0.699807i
$96$		0			0
$97$	2.86143	−	2.86143i	0.290534	−	0.290534i	−0.546757	−	0.837291i	$-0.684138\pi$
$97$	2.86143	−	2.86143i	0.290534	−	0.290534i	0.837291	+	0.546757i	$0.184138\pi$
$98$		0			0
$99$	2.58551	−	2.58551i	0.259854	−	0.259854i
$100$		0			0
$101$	−9.70834	−	9.70834i	−0.966016	−	0.966016i	0.0334254	−	0.999441i	$-0.489358\pi$
$101$	−9.70834	−	9.70834i	−0.966016	−	0.966016i	−0.999441	+	0.0334254i	$0.989358\pi$
$102$		0			0
$103$	−9.93641	−	9.93641i	−0.979064	−	0.979064i	0.0207213	−	0.999785i	$-0.493404\pi$
$103$	−9.93641	−	9.93641i	−0.979064	−	0.979064i	−0.999785	+	0.0207213i	$0.993404\pi$
$104$		0			0
$105$	−6.37250	+	1.78455i	−0.621892	+	0.174154i
$106$		0			0
$107$			2.36442i			0.228577i	0.993448	+	0.114289i	$0.0364589\pi$
$107$			2.36442i			0.228577i	−0.993448	+	0.114289i	$0.963541\pi$
$108$		0			0
$109$	8.64138	+	8.64138i	0.827694	+	0.827694i	0.987197	−	0.159503i	$-0.0509893\pi$
$109$	8.64138	+	8.64138i	0.827694	+	0.827694i	−0.159503	+	0.987197i	$0.550989\pi$
$110$		0			0
$111$			11.3539i			1.07766i
$112$		0			0
$113$	−11.3091	−	11.3091i	−1.06387	−	1.06387i	−0.997816	−	0.0660567i	$-0.978958\pi$
$113$	−11.3091	−	11.3091i	−1.06387	−	1.06387i	−0.0660567	−	0.997816i	$-0.521042\pi$
$114$		0			0
$115$	−8.37136	+	2.34431i	−0.780633	+	0.218608i
$116$		0			0
$117$	5.56694			0.514664
$118$		0			0
$119$			7.74825i			0.710281i
$120$		0			0
$121$		−	2.36972i		−	0.215429i
$122$		0			0
$123$	−1.77121			−0.159705
$124$		0			0
$125$	−11.1740	+	0.377121i	−0.999431	+	0.0337308i
$126$		0			0
$127$	0.566200	+	0.566200i	0.0502421	+	0.0502421i	0.731781	−	0.681539i	$-0.238689\pi$
$127$	0.566200	+	0.566200i	0.0502421	+	0.0502421i	−0.681539	+	0.731781i	$0.738689\pi$
$128$		0			0
$129$			2.48260i			0.218581i
$130$		0			0
$131$	−12.6717	−	12.6717i	−1.10713	−	1.10713i	−0.993526	−	0.113601i	$-0.963761\pi$
$131$	−12.6717	−	12.6717i	−1.10713	−	1.10713i	−0.113601	−	0.993526i	$-0.536239\pi$
$132$		0			0
$133$			9.37494i			0.812910i
$134$		0			0
$135$	1.94894	+	1.09619i	0.167738	+	0.0943447i
$136$		0			0
$137$	−9.38260	−	9.38260i	−0.801610	−	0.801610i	0.181737	−	0.983347i	$-0.441828\pi$
$137$	−9.38260	−	9.38260i	−0.801610	−	0.801610i	−0.983347	+	0.181737i	$0.941828\pi$
$138$		0			0
$139$	1.90899	+	1.90899i	0.161918	+	0.161918i	0.783416	−	0.621498i	$-0.213476\pi$
$139$	1.90899	+	1.90899i	0.161918	+	0.161918i	−0.621498	+	0.783416i	$0.713476\pi$
$140$		0			0
$141$	−0.525736	+	0.525736i	−0.0442750	+	0.0442750i
$142$		0			0
$143$	14.3934	−	14.3934i	1.20364	−	1.20364i
$144$		0			0
$145$	−7.69340	+	2.15445i	−0.638902	+	0.178918i
$146$		0			0
$147$	−1.75866			−0.145052
$148$		0			0
$149$	−5.52485	+	5.52485i	−0.452613	+	0.452613i	−0.896221	−	0.443608i	$-0.853698\pi$
$149$	−5.52485	+	5.52485i	−0.452613	+	0.452613i	0.443608	+	0.896221i	$0.353698\pi$
$150$		0			0
$151$	−15.6530			−1.27383			−0.636914	−	0.770935i	$-0.719789\pi$
$151$	−15.6530			−1.27383			−0.636914	+	0.770935i	$0.719789\pi$
$152$		0			0
$153$	1.85127	−	1.85127i	0.149666	−	0.149666i
$154$		0			0
$155$	15.7489	+	8.85802i	1.26498	+	0.711493i
$156$		0			0
$157$		−	3.75134i		−	0.299390i	−0.988732	−	0.149695i	$-0.952171\pi$
$157$		−	3.75134i		−	0.299390i	0.988732	−	0.149695i	$-0.0478291\pi$
$158$		0			0
$159$	−10.9352			−0.867220
$160$		0			0
$161$	−11.5060			−0.906800
$162$		0			0
$163$			24.0013i			1.87993i	0.341277	+	0.939963i	$0.389141\pi$
$163$			24.0013i			1.87993i	−0.341277	+	0.939963i	$0.610859\pi$
$164$		0			0
$165$	7.87321	−	2.20481i	0.612929	−	0.171644i
$166$		0			0
$167$	−4.52747	+	4.52747i	−0.350346	+	0.350346i	−0.860238	−	0.509892i	$-0.829685\pi$
$167$	−4.52747	+	4.52747i	−0.350346	+	0.350346i	0.509892	+	0.860238i	$0.329685\pi$
$168$		0			0
$169$	17.9908			1.38391
$170$		0			0
$171$	2.23993	−	2.23993i	0.171292	−	0.171292i
$172$		0			0
$173$	−11.4102			−0.867501			−0.433751	−	0.901033i	$-0.642810\pi$
$173$	−11.4102			−0.867501			−0.433751	+	0.901033i	$0.642810\pi$
$174$		0			0
$175$	−14.3758	−	3.50746i	−1.08671	−	0.265139i
$176$		0			0
$177$	1.09168	−	1.09168i	0.0820553	−	0.0820553i
$178$		0			0
$179$	−0.636317	+	0.636317i	−0.0475605	+	0.0475605i	−0.730487	−	0.682927i	$-0.760707\pi$
$179$	−0.636317	+	0.636317i	−0.0475605	+	0.0475605i	0.682927	+	0.730487i	$0.260707\pi$
$180$		0			0
$181$	−7.26171	−	7.26171i	−0.539759	−	0.539759i	0.383699	−	0.923458i	$-0.374650\pi$
$181$	−7.26171	−	7.26171i	−0.539759	−	0.539759i	−0.923458	+	0.383699i	$0.874650\pi$
$182$		0			0
$183$	−6.18650	−	6.18650i	−0.457319	−	0.457319i
$184$		0			0
$185$	−12.4460	+	22.1281i	−0.915047	+	1.62689i
$186$		0			0
$187$		−	9.57295i		−	0.700043i
$188$		0			0
$189$	2.09269	+	2.09269i	0.152220	+	0.152220i
$190$		0			0
$191$		−	2.60235i		−	0.188300i	−0.995558	−	0.0941498i	$-0.969987\pi$
$191$		−	2.60235i		−	0.188300i	0.995558	−	0.0941498i	$-0.0300133\pi$
$192$		0			0
$193$	−7.12141	−	7.12141i	−0.512610	−	0.512610i	0.402715	−	0.915325i	$-0.368066\pi$
$193$	−7.12141	−	7.12141i	−0.512610	−	0.512610i	−0.915325	+	0.402715i	$0.868066\pi$
$194$		0			0
$195$	10.8496	+	6.10241i	0.776959	+	0.437002i
$196$		0			0
$197$	20.6396			1.47051			0.735255	−	0.677791i	$-0.237062\pi$
$197$	20.6396			1.47051			0.735255	+	0.677791i	$0.237062\pi$
$198$		0			0
$199$		−	2.57987i		−	0.182882i	−0.995810	−	0.0914412i	$-0.970853\pi$
$199$		−	2.57987i		−	0.182882i	0.995810	−	0.0914412i	$-0.0291473\pi$
$200$		0			0
$201$		−	12.3904i		−	0.873952i
$202$		0			0
$203$	−10.5742			−0.742161
$204$		0			0
$205$	−3.45199	−	1.94158i	−0.241098	−	0.135606i
$206$		0			0
$207$	2.74910	+	2.74910i	0.191076	+	0.191076i
$208$		0			0
$209$		−	11.5827i		−	0.801194i
$210$		0			0
$211$	−3.30177	−	3.30177i	−0.227303	−	0.227303i	0.584262	−	0.811565i	$-0.301384\pi$
$211$	−3.30177	−	3.30177i	−0.227303	−	0.227303i	−0.811565	+	0.584262i	$0.801384\pi$
$212$		0			0
$213$		−	4.46143i		−	0.305692i
$214$		0			0
$215$	−2.72139	+	4.83844i	−0.185597	+	0.329979i
$216$		0			0
$217$	16.9105	+	16.9105i	1.14796	+	1.14796i
$218$		0			0
$219$	−4.11339	−	4.11339i	−0.277957	−	0.277957i
$220$		0			0
$221$	10.3059	−	10.3059i	0.693250	−	0.693250i
$222$		0			0
$223$	−1.64213	+	1.64213i	−0.109965	+	0.109965i	−0.759948	−	0.649983i	$-0.774776\pi$
$223$	−1.64213	+	1.64213i	−0.109965	+	0.109965i	0.649983	+	0.759948i	$0.274776\pi$
$224$		0			0
$225$	2.59675	+	4.27281i	0.173117	+	0.284854i
$226$		0			0
$227$	18.8542			1.25140			0.625699	−	0.780064i	$-0.284814\pi$
$227$	18.8542			1.25140			0.625699	+	0.780064i	$0.284814\pi$
$228$		0			0
$229$	−11.8744	+	11.8744i	−0.784683	+	0.784683i	−0.980617	−	0.195934i	$-0.937226\pi$
$229$	−11.8744	+	11.8744i	−0.784683	+	0.784683i	0.195934	+	0.980617i	$0.437226\pi$
$230$		0			0
$231$	10.8213			0.711990
$232$		0			0
$233$	12.9422	−	12.9422i	0.847874	−	0.847874i	−0.141994	−	0.989868i	$-0.545351\pi$
$233$	12.9422	−	12.9422i	0.847874	−	0.847874i	0.989868	+	0.141994i	$0.0453513\pi$
$234$		0			0
$235$	−1.60093	+	0.448324i	−0.104433	+	0.0292455i
$236$		0			0
$237$		−	13.3425i		−	0.866687i
$238$		0			0
$239$	−17.0514			−1.10297			−0.551483	−	0.834186i	$-0.685938\pi$
$239$	−17.0514			−1.10297			−0.551483	+	0.834186i	$0.685938\pi$
$240$		0			0
$241$	14.1921			0.914195			0.457097	−	0.889417i	$-0.348889\pi$
$241$	14.1921			0.914195			0.457097	+	0.889417i	$0.348889\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	−3.42753	−	1.92782i	−0.218977	−	0.123164i
$246$		0			0
$247$	12.4696	−	12.4696i	0.793419	−	0.793419i
$248$		0			0
$249$	−0.335336			−0.0212510
$250$		0			0
$251$	21.4140	−	21.4140i	1.35164	−	1.35164i	0.467808	−	0.883830i	$-0.345044\pi$
$251$	21.4140	−	21.4140i	1.35164	−	1.35164i	0.883830	−	0.467808i	$-0.154956\pi$
$252$		0			0
$253$	14.2156			0.893730
$254$		0			0
$255$	5.63735	−	1.57868i	0.353025	−	0.0988608i
$256$		0			0
$257$	5.47773	−	5.47773i	0.341691	−	0.341691i	−0.515312	−	0.857003i	$-0.672324\pi$
$257$	5.47773	−	5.47773i	0.341691	−	0.341691i	0.857003	+	0.515312i	$0.172324\pi$
$258$		0			0
$259$	−23.7601	+	23.7601i	−1.47638	+	1.47638i
$260$		0			0
$261$	2.52646	+	2.52646i	0.156384	+	0.156384i
$262$		0			0
$263$	−13.4067	−	13.4067i	−0.826693	−	0.826693i	0.160365	−	0.987058i	$-0.448733\pi$
$263$	−13.4067	−	13.4067i	−0.826693	−	0.826693i	−0.987058	+	0.160365i	$0.948733\pi$
$264$		0			0
$265$	−21.3121	−	11.9871i	−1.30919	−	0.736359i
$266$		0			0
$267$			1.91559i			0.117232i
$268$		0			0
$269$	−6.54686	−	6.54686i	−0.399169	−	0.399169i	0.478771	−	0.877940i	$-0.341083\pi$
$269$	−6.54686	−	6.54686i	−0.399169	−	0.399169i	−0.877940	+	0.478771i	$0.841083\pi$
$270$		0			0
$271$			8.11806i			0.493137i	0.969125	+	0.246568i	$0.0793030\pi$
$271$			8.11806i			0.493137i	−0.969125	+	0.246568i	$0.920697\pi$
$272$		0			0
$273$	11.6499	+	11.6499i	0.705081	+	0.705081i
$274$		0			0
$275$	17.7613	+	4.33346i	1.07105	+	0.261318i
$276$		0			0
$277$	27.8708			1.67460			0.837299	−	0.546746i	$-0.184134\pi$
$277$	27.8708			1.67460			0.837299	+	0.546746i	$0.184134\pi$
$278$		0			0
$279$		−	8.08076i		−	0.483782i
$280$		0			0
$281$			2.35087i			0.140241i	0.997539	+	0.0701206i	$0.0223384\pi$
$281$			2.35087i			0.140241i	−0.997539	+	0.0701206i	$0.977662\pi$
$282$		0			0
$283$	15.9550			0.948425			0.474212	−	0.880410i	$-0.342733\pi$
$283$	15.9550			0.948425			0.474212	+	0.880410i	$0.342733\pi$
$284$		0			0
$285$	6.82087	−	1.91011i	0.404034	−	0.113145i
$286$		0			0
$287$	−3.70659	−	3.70659i	−0.218793	−	0.218793i
$288$		0			0
$289$			10.1456i			0.596800i
$290$		0			0
$291$	−2.86143	−	2.86143i	−0.167740	−	0.167740i
$292$		0			0
$293$			14.9047i			0.870741i	0.900251	+	0.435371i	$0.143383\pi$
$293$			14.9047i			0.870741i	−0.900251	+	0.435371i	$0.856617\pi$
$294$		0			0
$295$	3.32429	−	0.930932i	0.193548	−	0.0542010i
$296$		0			0
$297$	−2.58551	−	2.58551i	−0.150026	−	0.150026i
$298$		0			0
$299$	15.3041	+	15.3041i	0.885058	+	0.885058i
$300$		0			0
$301$	−5.19530	+	5.19530i	−0.299452	+	0.299452i
$302$		0			0
$303$	−9.70834	+	9.70834i	−0.557729	+	0.557729i
$304$		0			0
$305$	−5.27557	−	18.8387i	−0.302078	−	1.07870i
$306$		0			0
$307$	8.95078			0.510848			0.255424	−	0.966829i	$-0.417785\pi$
$307$	8.95078			0.510848			0.255424	+	0.966829i	$0.417785\pi$
$308$		0			0
$309$	−9.93641	+	9.93641i	−0.565263	+	0.565263i
$310$		0			0
$311$	−7.32409			−0.415311			−0.207655	−	0.978202i	$-0.566583\pi$
$311$	−7.32409			−0.415311			−0.207655	+	0.978202i	$0.566583\pi$
$312$		0			0
$313$	1.98518	−	1.98518i	0.112209	−	0.112209i	−0.648773	−	0.760982i	$-0.724718\pi$
$313$	1.98518	−	1.98518i	0.112209	−	0.112209i	0.760982	+	0.648773i	$0.224718\pi$
$314$		0			0
$315$	1.78455	+	6.37250i	0.100548	+	0.359049i
$316$		0			0
$317$			17.5989i			0.988450i	0.869334	+	0.494225i	$0.164548\pi$
$317$			17.5989i			0.988450i	−0.869334	+	0.494225i	$0.835452\pi$
$318$		0			0
$319$	13.0644			0.731465
$320$		0			0
$321$	2.36442			0.131969
$322$		0			0
$323$		−	8.29343i		−	0.461459i
$324$		0			0
$325$	14.4560	+	23.7865i	0.801872	+	1.31944i
$326$		0			0
$327$	8.64138	−	8.64138i	0.477869	−	0.477869i
$328$		0			0
$329$	−2.20040			−0.121312
$330$		0			0
$331$	−4.38662	+	4.38662i	−0.241111	+	0.241111i	−0.817310	−	0.576199i	$-0.804535\pi$
$331$	−4.38662	+	4.38662i	−0.241111	+	0.241111i	0.576199	+	0.817310i	$0.304535\pi$
$332$		0			0
$333$	11.3539			0.622190
$334$		0			0
$335$	13.5822	−	24.1482i	0.742075	−	1.31936i
$336$		0			0
$337$	−12.2682	+	12.2682i	−0.668290	+	0.668290i	−0.957320	−	0.289030i	$-0.906667\pi$
$337$	−12.2682	+	12.2682i	−0.668290	+	0.668290i	0.289030	+	0.957320i	$0.406667\pi$
$338$		0			0
$339$	−11.3091	+	11.3091i	−0.614227	+	0.614227i
$340$		0			0
$341$	−20.8929	−	20.8929i	−1.13141	−	1.13141i
$342$		0			0
$343$	10.9685	+	10.9685i	0.592242	+	0.592242i
$344$		0			0
$345$	2.34431	+	8.37136i	0.126213	+	0.450699i
$346$		0			0
$347$		−	34.9889i		−	1.87830i	−0.343501	−	0.939152i	$-0.611613\pi$
$347$		−	34.9889i		−	1.87830i	0.343501	−	0.939152i	$-0.388387\pi$
$348$		0			0
$349$	−7.60199	−	7.60199i	−0.406925	−	0.406925i	0.473740	−	0.880665i	$-0.342904\pi$
$349$	−7.60199	−	7.60199i	−0.406925	−	0.406925i	−0.880665	+	0.473740i	$0.842904\pi$
$350$		0			0
$351$		−	5.56694i		−	0.297141i
$352$		0			0
$353$	13.8582	+	13.8582i	0.737596	+	0.737596i	0.972112	−	0.234516i	$-0.0753505\pi$
$353$	13.8582	+	13.8582i	0.737596	+	0.737596i	−0.234516	+	0.972112i	$0.575351\pi$
$354$		0			0
$355$	4.89056	−	8.69508i	0.259564	−	0.461487i
$356$		0			0
$357$	7.74825			0.410081
$358$		0			0
$359$		−	2.68203i		−	0.141552i	−0.997492	−	0.0707762i	$-0.977452\pi$
$359$		−	2.68203i		−	0.141552i	0.997492	−	0.0707762i	$-0.0225476\pi$
$360$		0			0
$361$			8.96543i			0.471865i
$362$		0			0
$363$	−2.36972			−0.124378
$364$		0			0
$365$	−3.50772	−	12.5258i	−0.183602	−	0.655631i
$366$		0			0
$367$	−12.0246	−	12.0246i	−0.627680	−	0.627680i	0.319804	−	0.947484i	$-0.396383\pi$
$367$	−12.0246	−	12.0246i	−0.627680	−	0.627680i	−0.947484	+	0.319804i	$0.896383\pi$
$368$		0			0
$369$			1.77121i			0.0922057i
$370$		0			0
$371$	−22.8840	−	22.8840i	−1.18808	−	1.18808i
$372$		0			0
$373$		−	15.5668i		−	0.806019i	−0.915196	−	0.403009i	$-0.867964\pi$
$373$		−	15.5668i		−	0.806019i	0.915196	−	0.403009i	$-0.132036\pi$
$374$		0			0
$375$	0.377121	+	11.1740i	0.0194745	+	0.577022i
$376$		0			0
$377$	14.0647	+	14.0647i	0.724367	+	0.724367i
$378$		0			0
$379$	−7.51070	−	7.51070i	−0.385799	−	0.385799i	0.487387	−	0.873186i	$-0.337950\pi$
$379$	−7.51070	−	7.51070i	−0.385799	−	0.385799i	−0.873186	+	0.487387i	$0.837950\pi$
$380$		0			0
$381$	0.566200	−	0.566200i	0.0290073	−	0.0290073i
$382$		0			0
$383$	21.1077	−	21.1077i	1.07855	−	1.07855i	0.0819157	−	0.996639i	$-0.473896\pi$
$383$	21.1077	−	21.1077i	1.07855	−	1.07855i	0.996639	−	0.0819157i	$-0.0261038\pi$
$384$		0			0
$385$	21.0901	+	11.8622i	1.07485	+	0.604553i
$386$		0			0
$387$	2.48260			0.126198
$388$		0			0
$389$	−3.95949	+	3.95949i	−0.200754	+	0.200754i	−0.800323	−	0.599569i	$-0.795339\pi$
$389$	−3.95949	+	3.95949i	−0.200754	+	0.200754i	0.599569	+	0.800323i	$0.295339\pi$
$390$		0			0
$391$	10.1786			0.514756
$392$		0			0
$393$	−12.6717	+	12.6717i	−0.639200	+	0.639200i
$394$		0			0
$395$	14.6258	−	26.0037i	0.735906	−	1.30839i
$396$		0			0
$397$			11.9369i			0.599095i	0.954081	+	0.299547i	$0.0968357\pi$
$397$			11.9369i			0.599095i	−0.954081	+	0.299547i	$0.903164\pi$
$398$		0			0
$399$	9.37494			0.469334
$400$		0			0
$401$	−18.6196			−0.929821			−0.464910	−	0.885358i	$-0.653913\pi$
$401$	−18.6196			−0.929821			−0.464910	+	0.885358i	$0.653913\pi$
$402$		0			0
$403$		−	44.9851i		−	2.24087i
$404$		0			0
$405$	1.09619	−	1.94894i	0.0544699	−	0.0968437i
$406$		0			0
$407$	29.3556	−	29.3556i	1.45510	−	1.45510i
$408$		0			0
$409$	−32.2590			−1.59510			−0.797552	−	0.603250i	$-0.793872\pi$
$409$	−32.2590			−1.59510			−0.797552	+	0.603250i	$0.793872\pi$
$410$		0			0
$411$	−9.38260	+	9.38260i	−0.462810	+	0.462810i
$412$		0			0
$413$	4.56907			0.224829
$414$		0			0
$415$	−0.653550	−	0.367590i	−0.0320815	−	0.0180443i
$416$		0			0
$417$	1.90899	−	1.90899i	0.0934835	−	0.0934835i
$418$		0			0
$419$	15.5579	−	15.5579i	0.760052	−	0.760052i	−0.216280	−	0.976331i	$-0.569392\pi$
$419$	15.5579	−	15.5579i	0.760052	−	0.760052i	0.976331	+	0.216280i	$0.0693924\pi$
$420$		0			0
$421$	11.8886	+	11.8886i	0.579415	+	0.579415i	0.934742	−	0.355327i	$-0.115631\pi$
$421$	11.8886	+	11.8886i	0.579415	+	0.579415i	−0.355327	+	0.934742i	$0.615631\pi$
$422$		0			0
$423$	0.525736	+	0.525736i	0.0255622	+	0.0255622i
$424$		0			0
$425$	12.7174	+	3.10283i	0.616885	+	0.150510i
$426$		0			0
$427$		−	25.8928i		−	1.25304i
$428$		0			0
$429$	−14.3934	−	14.3934i	−0.694919	−	0.694919i
$430$		0			0
$431$		−	11.2888i		−	0.543763i	−0.962331	−	0.271881i	$-0.912354\pi$
$431$		−	11.2888i		−	0.543763i	0.962331	−	0.271881i	$-0.0876458\pi$
$432$		0			0
$433$	−3.79336	−	3.79336i	−0.182297	−	0.182297i	0.610059	−	0.792356i	$-0.291146\pi$
$433$	−3.79336	−	3.79336i	−0.182297	−	0.182297i	−0.792356	+	0.610059i	$0.791146\pi$
$434$		0			0
$435$	2.15445	+	7.69340i	0.103298	+	0.368870i
$436$		0			0
$437$	12.3156			0.589134
$438$		0			0
$439$			14.6582i			0.699599i	0.936825	+	0.349799i	$0.113750\pi$
$439$			14.6582i			0.699599i	−0.936825	+	0.349799i	$0.886250\pi$
$440$		0			0
$441$			1.75866i			0.0837459i
$442$		0			0
$443$	−38.3556			−1.82233			−0.911165	−	0.412041i	$-0.864816\pi$
$443$	−38.3556			−1.82233			−0.911165	+	0.412041i	$0.864816\pi$
$444$		0			0
$445$	−2.09984	+	3.73337i	−0.0995419	+	0.176979i
$446$		0			0
$447$	5.52485	+	5.52485i	0.261316	+	0.261316i
$448$		0			0
$449$		−	15.1632i		−	0.715596i	−0.933799	−	0.357798i	$-0.883528\pi$
$449$		−	15.1632i		−	0.715596i	0.933799	−	0.357798i	$-0.116472\pi$
$450$		0			0
$451$	4.57949	+	4.57949i	0.215640	+	0.215640i
$452$		0			0
$453$			15.6530i			0.735444i
$454$		0			0
$455$	9.93448	+	35.4753i	0.465736	+	1.66311i
$456$		0			0
$457$	11.4152	+	11.4152i	0.533980	+	0.533980i	0.921754	−	0.387775i	$-0.126756\pi$
$457$	11.4152	+	11.4152i	0.533980	+	0.533980i	−0.387775	+	0.921754i	$0.626756\pi$
$458$		0			0
$459$	−1.85127	−	1.85127i	−0.0864098	−	0.0864098i
$460$		0			0
$461$	−26.5782	+	26.5782i	−1.23787	+	1.23787i	−0.277000	+	0.960870i	$0.589340\pi$
$461$	−26.5782	+	26.5782i	−1.23787	+	1.23787i	−0.960870	+	0.277000i	$0.910660\pi$
$462$		0			0
$463$	−24.9521	+	24.9521i	−1.15962	+	1.15962i	−0.175068	+	0.984556i	$0.556015\pi$
$463$	−24.9521	+	24.9521i	−1.15962	+	1.15962i	−0.984556	+	0.175068i	$0.943985\pi$
$464$		0			0
$465$	8.85802	−	15.7489i	0.410781	−	0.730339i
$466$		0			0
$467$	0.641894			0.0297033			0.0148517	−	0.999890i	$-0.495272\pi$
$467$	0.641894			0.0297033			0.0148517	+	0.999890i	$0.495272\pi$
$468$		0			0
$469$	25.9292	−	25.9292i	1.19730	−	1.19730i
$470$		0			0
$471$	−3.75134			−0.172853
$472$		0			0
$473$	6.41879	−	6.41879i	0.295136	−	0.295136i
$474$		0			0
$475$	15.3873	+	3.75425i	0.706019	+	0.172257i
$476$		0			0
$477$			10.9352i			0.500690i
$478$		0			0
$479$	−4.75189			−0.217119			−0.108560	−	0.994090i	$-0.534624\pi$
$479$	−4.75189			−0.217119			−0.108560	+	0.994090i	$0.534624\pi$
$480$		0			0
$481$	63.2065			2.88197
$482$		0			0
$483$			11.5060i			0.523541i
$484$		0			0
$485$	−2.44010	−	8.71342i	−0.110799	−	0.395656i
$486$		0			0
$487$	5.12743	−	5.12743i	0.232346	−	0.232346i	−0.581325	−	0.813671i	$-0.697466\pi$
$487$	5.12743	−	5.12743i	0.232346	−	0.232346i	0.813671	+	0.581325i	$0.197466\pi$
$488$		0			0
$489$	24.0013			1.08538
$490$		0			0
$491$	−13.4733	+	13.4733i	−0.608040	+	0.608040i	−0.942434	−	0.334394i	$-0.891469\pi$
$491$	−13.4733	+	13.4733i	−0.608040	+	0.608040i	0.334394	+	0.942434i	$0.391469\pi$
$492$		0			0
$493$	9.35432			0.421297
$494$		0			0
$495$	−2.20481	−	7.87321i	−0.0990987	−	0.353874i
$496$		0			0
$497$	9.33638	−	9.33638i	0.418794	−	0.418794i
$498$		0			0
$499$	3.98679	−	3.98679i	0.178473	−	0.178473i	−0.612217	−	0.790690i	$-0.709722\pi$
$499$	3.98679	−	3.98679i	0.178473	−	0.178473i	0.790690	+	0.612217i	$0.209722\pi$
$500$		0			0
$501$	4.52747	+	4.52747i	0.202272	+	0.202272i
$502$		0			0
$503$	8.69088	+	8.69088i	0.387507	+	0.387507i	0.873797	−	0.486290i	$-0.161650\pi$
$503$	8.69088	+	8.69088i	0.387507	+	0.387507i	−0.486290	+	0.873797i	$0.661650\pi$
$504$		0			0
$505$	−29.5631	+	8.27884i	−1.31554	+	0.368404i
$506$		0			0
$507$		−	17.9908i		−	0.799001i
$508$		0			0
$509$	15.2515	+	15.2515i	0.676010	+	0.676010i	0.959095	−	0.283085i	$-0.0913577\pi$
$509$	15.2515	+	15.2515i	0.676010	+	0.676010i	−0.283085	+	0.959095i	$0.591358\pi$
$510$		0			0
$511$		−	17.2161i		−	0.761594i
$512$		0			0
$513$	−2.23993	−	2.23993i	−0.0988953	−	0.0988953i
$514$		0			0
$515$	−30.2577	+	8.47333i	−1.33331	+	0.373380i
$516$		0			0
$517$	2.71859			0.119564
$518$		0			0
$519$			11.4102i			0.500852i
$520$		0			0
$521$			12.9907i			0.569131i	0.958657	+	0.284565i	$0.0918493\pi$
$521$			12.9907i			0.569131i	−0.958657	+	0.284565i	$0.908151\pi$
$522$		0			0
$523$	−11.0988			−0.485315			−0.242658	−	0.970112i	$-0.578019\pi$
$523$	−11.0988			−0.485315			−0.242658	+	0.970112i	$0.578019\pi$
$524$		0			0
$525$	−3.50746	+	14.3758i	−0.153078	+	0.627412i
$526$		0			0
$527$	−14.9597	−	14.9597i	−0.651653	−	0.651653i
$528$		0			0
$529$		−	7.88490i		−	0.342822i
$530$		0			0
$531$	−1.09168	−	1.09168i	−0.0473747	−	0.0473747i
$532$		0			0
$533$			9.86024i			0.427095i
$534$		0			0
$535$	4.60812	+	2.59185i	0.199227	+	0.112055i
$536$		0			0
$537$	0.636317	+	0.636317i	0.0274591	+	0.0274591i
$538$		0			0
$539$	4.54704	+	4.54704i	0.195855	+	0.195855i
$540$		0			0
$541$	30.5732	−	30.5732i	1.31444	−	1.31444i	0.396339	−	0.918104i	$-0.370280\pi$
$541$	30.5732	−	30.5732i	1.31444	−	1.31444i	0.918104	−	0.396339i	$-0.129720\pi$
$542$		0			0
$543$	−7.26171	+	7.26171i	−0.311630	+	0.311630i
$544$		0			0
$545$	26.3141	−	7.36899i	1.12717	−	0.315653i
$546$		0			0
$547$	−0.842518			−0.0360235			−0.0180117	−	0.999838i	$-0.505734\pi$
$547$	−0.842518			−0.0360235			−0.0180117	+	0.999838i	$0.505734\pi$
$548$		0			0
$549$	−6.18650	+	6.18650i	−0.264033	+	0.264033i
$550$		0			0
$551$	11.3182			0.482171
$552$		0			0
$553$	27.9216	−	27.9216i	1.18735	−	1.18735i
$554$		0			0
$555$	22.1281	+	12.4460i	0.939285	+	0.528303i
$556$		0			0
$557$		−	11.3560i		−	0.481169i	−0.970628	−	0.240584i	$-0.922661\pi$
$557$		−	11.3560i		−	0.481169i	0.970628	−	0.240584i	$-0.0773391\pi$
$558$		0			0
$559$	13.8205			0.584544
$560$		0			0
$561$	−9.57295			−0.404170
$562$		0			0
$563$			4.67224i			0.196912i	0.995141	+	0.0984558i	$0.0313903\pi$
$563$			4.67224i			0.196912i	−0.995141	+	0.0984558i	$0.968610\pi$
$564$		0			0
$565$	−34.4377	+	9.64391i	−1.44881	+	0.405723i
$566$		0			0
$567$	2.09269	−	2.09269i	0.0878845	−	0.0878845i
$568$		0			0
$569$	−29.8812			−1.25269			−0.626343	−	0.779548i	$-0.715449\pi$
$569$	−29.8812			−1.25269			−0.626343	+	0.779548i	$0.715449\pi$
$570$		0			0
$571$	−10.3941	+	10.3941i	−0.434978	+	0.434978i	−0.890318	−	0.455339i	$-0.849518\pi$
$571$	−10.3941	+	10.3941i	−0.434978	+	0.434978i	0.455339	+	0.890318i	$0.349518\pi$
$572$		0			0
$573$	−2.60235			−0.108715
$574$		0			0
$575$	−4.60765	+	18.8851i	−0.192152	+	0.787563i
$576$		0			0
$577$	9.76065	−	9.76065i	0.406341	−	0.406341i	−0.474119	−	0.880461i	$-0.657233\pi$
$577$	9.76065	−	9.76065i	0.406341	−	0.406341i	0.880461	+	0.474119i	$0.157233\pi$
$578$		0			0
$579$	−7.12141	+	7.12141i	−0.295956	+	0.295956i
$580$		0			0
$581$	−0.701752	−	0.701752i	−0.0291136	−	0.0291136i
$582$		0			0
$583$	28.2731	+	28.2731i	1.17095	+	1.17095i
$584$		0			0
$585$	6.10241	−	10.8496i	0.252303	−	0.448578i
$586$		0			0
$587$			20.8152i			0.859136i	0.903034	+	0.429568i	$0.141334\pi$
$587$			20.8152i			0.859136i	−0.903034	+	0.429568i	$0.858666\pi$
$588$		0			0
$589$	−18.1003	−	18.1003i	−0.745811	−	0.745811i
$590$		0			0
$591$		−	20.6396i		−	0.848999i
$592$		0			0
$593$	−11.1613	−	11.1613i	−0.458341	−	0.458341i	0.439770	−	0.898110i	$-0.355060\pi$
$593$	−11.1613	−	11.1613i	−0.458341	−	0.458341i	−0.898110	+	0.439770i	$0.855060\pi$
$594$		0			0
$595$	15.1009	+	8.49352i	0.619076	+	0.348201i
$596$		0			0
$597$	−2.57987			−0.105587
$598$		0			0
$599$		−	21.8308i		−	0.891983i	−0.895037	−	0.445992i	$-0.852851\pi$
$599$		−	21.8308i		−	0.891983i	0.895037	−	0.445992i	$-0.147149\pi$
$600$		0			0
$601$			7.57808i			0.309116i	0.987984	+	0.154558i	$0.0493954\pi$
$601$			7.57808i			0.309116i	−0.987984	+	0.154558i	$0.950605\pi$
$602$		0			0
$603$	−12.3904			−0.504577
$604$		0			0
$605$	−4.61845	−	2.59766i	−0.187767	−	0.105610i
$606$		0			0
$607$	−6.52513	−	6.52513i	−0.264847	−	0.264847i	0.562173	−	0.827020i	$-0.309966\pi$
$607$	−6.52513	−	6.52513i	−0.264847	−	0.264847i	−0.827020	+	0.562173i	$0.809966\pi$
$608$		0			0
$609$			10.5742i			0.428487i
$610$		0			0
$611$	2.92674	+	2.92674i	0.118403	+	0.118403i
$612$		0			0
$613$		−	31.2019i		−	1.26023i	−0.776500	−	0.630117i	$-0.783007\pi$
$613$		−	31.2019i		−	1.26023i	0.776500	−	0.630117i	$-0.216993\pi$
$614$		0			0
$615$	−1.94158	+	3.45199i	−0.0782921	+	0.139198i
$616$		0			0
$617$	12.7799	+	12.7799i	0.514501	+	0.514501i	0.915902	−	0.401401i	$-0.131477\pi$
$617$	12.7799	+	12.7799i	0.514501	+	0.514501i	−0.401401	+	0.915902i	$0.631477\pi$
$618$		0			0
$619$	7.22587	+	7.22587i	0.290432	+	0.290432i	0.837251	−	0.546819i	$-0.184161\pi$
$619$	7.22587	+	7.22587i	0.290432	+	0.290432i	−0.546819	+	0.837251i	$0.684161\pi$
$620$		0			0
$621$	2.74910	−	2.74910i	0.110318	−	0.110318i
$622$		0			0
$623$	−4.00872	+	4.00872i	−0.160606	+	0.160606i
$624$		0			0
$625$	−11.5138	+	22.1908i	−0.460551	+	0.887633i
$626$		0			0
$627$	−11.5827			−0.462569
$628$		0			0
$629$	21.0191	−	21.0191i	0.838087	−	0.838087i
$630$		0			0
$631$	−24.3757			−0.970382			−0.485191	−	0.874408i	$-0.661250\pi$
$631$	−24.3757			−0.970382			−0.485191	+	0.874408i	$0.661250\pi$
$632$		0			0
$633$	−3.30177	+	3.30177i	−0.131233	+	0.131233i
$634$		0			0
$635$	1.72415	−	0.482830i	0.0684208	−	0.0191605i
$636$		0			0
$637$			9.79038i			0.387909i
$638$		0			0
$639$	−4.46143			−0.176492
$640$		0			0
$641$	24.3980			0.963662			0.481831	−	0.876264i	$-0.339972\pi$
$641$	24.3980			0.963662			0.481831	+	0.876264i	$0.339972\pi$
$642$		0			0
$643$		−	19.4887i		−	0.768561i	−0.923216	−	0.384280i	$-0.874450\pi$
$643$		−	19.4887i		−	0.768561i	0.923216	−	0.384280i	$-0.125550\pi$
$644$		0			0
$645$	4.83844	+	2.72139i	0.190514	+	0.107155i
$646$		0			0
$647$	−10.7325	+	10.7325i	−0.421938	+	0.421938i	−0.885871	−	0.463932i	$-0.846438\pi$
$647$	−10.7325	+	10.7325i	−0.421938	+	0.421938i	0.463932	+	0.885871i	$0.346438\pi$
$648$		0			0
$649$	−5.64507			−0.221589
$650$		0			0
$651$	16.9105	−	16.9105i	0.662774	−	0.662774i
$652$		0			0
$653$	−28.6204			−1.12000			−0.560001	−	0.828492i	$-0.689199\pi$
$653$	−28.6204			−1.12000			−0.560001	+	0.828492i	$0.689199\pi$
$654$		0			0
$655$	−38.5868	+	10.8058i	−1.50771	+	0.422219i
$656$		0			0
$657$	−4.11339	+	4.11339i	−0.160479	+	0.160479i
$658$		0			0
$659$	−13.9606	+	13.9606i	−0.543830	+	0.543830i	−0.924649	−	0.380820i	$-0.875642\pi$
$659$	−13.9606	+	13.9606i	−0.543830	+	0.543830i	0.380820	+	0.924649i	$0.375642\pi$
$660$		0			0
$661$	−2.74706	−	2.74706i	−0.106848	−	0.106848i	0.651662	−	0.758510i	$-0.274072\pi$
$661$	−2.74706	−	2.74706i	−0.106848	−	0.106848i	−0.758510	+	0.651662i	$0.774072\pi$
$662$		0			0
$663$	−10.3059	−	10.3059i	−0.400248	−	0.400248i
$664$		0			0
$665$	18.2712	+	10.2767i	0.708527	+	0.398512i
$666$		0			0
$667$			13.8910i			0.537861i
$668$		0			0
$669$	1.64213	+	1.64213i	0.0634884	+	0.0634884i
$670$		0			0
$671$			31.9905i			1.23498i
$672$		0			0
$673$	−6.92750	−	6.92750i	−0.267036	−	0.267036i	0.560869	−	0.827905i	$-0.310467\pi$
$673$	−6.92750	−	6.92750i	−0.267036	−	0.267036i	−0.827905	+	0.560869i	$0.810467\pi$
$674$		0			0
$675$	4.27281	−	2.59675i	0.164460	−	0.0999490i
$676$		0			0
$677$	42.2218			1.62272			0.811358	−	0.584550i	$-0.198729\pi$
$677$	42.2218			1.62272			0.811358	+	0.584550i	$0.198729\pi$
$678$		0			0
$679$		−	11.9761i		−	0.459602i
$680$		0			0
$681$		−	18.8542i		−	0.722495i
$682$		0			0
$683$	30.2180			1.15626			0.578130	−	0.815945i	$-0.303783\pi$
$683$	30.2180			1.15626			0.578130	+	0.815945i	$0.303783\pi$
$684$		0			0
$685$	−28.5712	+	8.00106i	−1.09165	+	0.305705i
$686$		0			0
$687$	11.8744	+	11.8744i	0.453037	+	0.453037i
$688$		0			0
$689$			60.8758i			2.31918i
$690$		0			0
$691$	11.9148	+	11.9148i	0.453260	+	0.453260i	0.896435	−	0.443175i	$-0.146148\pi$
$691$	11.9148	+	11.9148i	0.453260	+	0.453260i	−0.443175	+	0.896435i	$0.646148\pi$
$692$		0			0
$693$		−	10.8213i		−	0.411068i
$694$		0			0
$695$	5.81311	−	1.62790i	0.220504	−	0.0617497i
$696$		0			0
$697$	3.27899	+	3.27899i	0.124201	+	0.124201i
$698$		0			0
$699$	−12.9422	−	12.9422i	−0.489520	−	0.489520i
$700$		0			0
$701$	22.4391	−	22.4391i	0.847512	−	0.847512i	−0.142310	−	0.989822i	$-0.545453\pi$
$701$	22.4391	−	22.4391i	0.847512	−	0.847512i	0.989822	+	0.142310i	$0.0454531\pi$
$702$		0			0
$703$	25.4319	−	25.4319i	0.959183	−	0.959183i
$704$		0			0
$705$	0.448324	+	1.60093i	0.0168849	+	0.0602947i
$706$		0			0
$707$	−40.6330			−1.52816
$708$		0			0
$709$	27.2337	−	27.2337i	1.02278	−	1.02278i	0.0230475	−	0.999734i	$-0.492663\pi$
$709$	27.2337	−	27.2337i	1.02278	−	1.02278i	0.999734	−	0.0230475i	$-0.00733688\pi$
$710$		0			0
$711$	−13.3425			−0.500382
$712$		0			0
$713$	22.2148	−	22.2148i	0.831951	−	0.831951i
$714$		0			0
$715$	−12.2740	−	43.8297i	−0.459023	−	1.63914i
$716$		0			0
$717$			17.0514i			0.636797i
$718$		0			0
$719$	29.3850			1.09588			0.547938	−	0.836519i	$-0.315413\pi$
$719$	29.3850			1.09588			0.547938	+	0.836519i	$0.315413\pi$
$720$		0			0
$721$	−41.5876			−1.54880
$722$		0			0
$723$		−	14.1921i		−	0.527811i
$724$		0			0
$725$	−4.23449	+	17.3557i	−0.157265	+	0.644573i
$726$		0			0
$727$	−6.54058	+	6.54058i	−0.242577	+	0.242577i	−0.817915	−	0.575339i	$-0.804870\pi$
$727$	−6.54058	+	6.54058i	−0.242577	+	0.242577i	0.575339	+	0.817915i	$0.304870\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.59596	−	4.59596i	0.169988	−	0.169988i
$732$		0			0
$733$	19.6299			0.725046			0.362523	−	0.931975i	$-0.381915\pi$
$733$	19.6299			0.725046			0.362523	+	0.931975i	$0.381915\pi$
$734$		0			0
$735$	−1.92782	+	3.42753i	−0.0711088	+	0.126426i
$736$		0			0
$737$	−32.0355	+	32.0355i	−1.18004	+	1.18004i
$738$		0			0
$739$	26.2044	−	26.2044i	0.963946	−	0.963946i	−0.0354261	−	0.999372i	$-0.511279\pi$
$739$	26.2044	−	26.2044i	0.963946	−	0.963946i	0.999372	+	0.0354261i	$0.0112788\pi$
$740$		0			0
$741$	−12.4696	−	12.4696i	−0.458081	−	0.458081i
$742$		0			0
$743$	−23.1496	−	23.1496i	−0.849278	−	0.849278i	0.140765	−	0.990043i	$-0.455044\pi$
$743$	−23.1496	−	23.1496i	−0.849278	−	0.849278i	−0.990043	+	0.140765i	$0.955044\pi$
$744$		0			0
$745$	4.71134	+	16.8239i	0.172610	+	0.616379i
$746$		0			0
$747$			0.335336i			0.0122693i
$748$		0			0
$749$	4.94799	+	4.94799i	0.180796	+	0.180796i
$750$		0			0
$751$			27.8530i			1.01637i	0.861248	+	0.508186i	$0.169684\pi$
$751$			27.8530i			1.01637i	−0.861248	+	0.508186i	$0.830316\pi$
$752$		0			0
$753$	−21.4140	−	21.4140i	−0.780369	−	0.780369i
$754$		0			0
$755$	−17.1587	+	30.5069i	−0.624468	+	1.11026i
$756$		0			0
$757$	−30.3747			−1.10399			−0.551994	−	0.833848i	$-0.686133\pi$
$757$	−30.3747			−1.10399			−0.551994	+	0.833848i	$0.686133\pi$
$758$		0			0
$759$		−	14.2156i		−	0.515995i
$760$		0			0
$761$		−	34.1288i		−	1.23717i	−0.785718	−	0.618584i	$-0.787707\pi$
$761$		−	34.1288i		−	1.23717i	0.785718	−	0.618584i	$-0.212293\pi$
$762$		0			0
$763$	36.1674			1.30935
$764$		0			0
$765$	−1.57868	−	5.63735i	−0.0570773	−	0.203819i
$766$		0			0
$767$	−6.07729	−	6.07729i	−0.219438	−	0.219438i
$768$		0			0
$769$		−	6.28579i		−	0.226671i	−0.993557	−	0.113336i	$-0.963846\pi$
$769$		−	6.28579i		−	0.226671i	0.993557	−	0.113336i	$-0.0361535\pi$
$770$		0			0
$771$	−5.47773	−	5.47773i	−0.197276	−	0.197276i
$772$		0			0
$773$			47.1635i			1.69635i	0.529715	+	0.848176i	$0.322299\pi$
$773$			47.1635i			1.69635i	−0.529715	+	0.848176i	$0.677701\pi$
$774$		0			0
$775$	34.5275	−	20.9837i	1.24027	−	0.753757i
$776$		0			0
$777$	23.7601	+	23.7601i	0.852390	+	0.852390i
$778$		0			0
$779$	3.96740	+	3.96740i	0.142147	+	0.142147i
$780$		0			0
$781$	−11.5351	+	11.5351i	−0.412758	+	0.412758i
$782$		0			0
$783$	2.52646	−	2.52646i	0.0902883	−	0.0902883i
$784$		0			0
$785$	−7.31115	−	4.11217i	−0.260946	−	0.146770i
$786$		0			0
$787$	14.6938			0.523778			0.261889	−	0.965098i	$-0.415655\pi$
$787$	14.6938			0.523778			0.261889	+	0.965098i	$0.415655\pi$
$788$		0			0
$789$	−13.4067	+	13.4067i	−0.477292	+	0.477292i
$790$		0			0
$791$	−47.3329			−1.68296
$792$		0			0
$793$	−34.4399	+	34.4399i	−1.22300	+	1.22300i
$794$		0			0
$795$	−11.9871	+	21.3121i	−0.425137	+	0.755863i
$796$		0			0
$797$			3.67259i			0.130090i	0.997882	+	0.0650448i	$0.0207190\pi$
$797$			3.67259i			0.130090i	−0.997882	+	0.0650448i	$0.979281\pi$
$798$		0			0
$799$	1.94656			0.0688643
$800$		0			0
$801$	1.91559			0.0676839
$802$		0			0
$803$			21.2704i			0.750617i
$804$		0			0
$805$	−12.6127	+	22.4245i	−0.444540	+	0.790361i
$806$		0			0
$807$	−6.54686	+	6.54686i	−0.230461	+	0.230461i
$808$		0			0
$809$	−33.4485			−1.17599			−0.587994	−	0.808865i	$-0.700082\pi$
$809$	−33.4485			−1.17599			−0.587994	+	0.808865i	$0.700082\pi$
$810$		0			0
$811$	−25.8966	+	25.8966i	−0.909351	+	0.909351i	−0.996220	−	0.0868685i	$-0.972314\pi$
$811$	−25.8966	+	25.8966i	−0.909351	+	0.909351i	0.0868685	+	0.996220i	$0.472314\pi$
$812$		0			0
$813$	8.11806			0.284713
$814$		0			0
$815$	46.7771	+	26.3099i	1.63853	+	0.921595i
$816$		0			0
$817$	5.56085	−	5.56085i	0.194550	−	0.194550i
$818$		0			0
$819$	11.6499	−	11.6499i	0.407079	−	0.407079i
$820$		0			0
$821$	1.15783	+	1.15783i	0.0404085	+	0.0404085i	0.727022	−	0.686614i	$-0.240904\pi$
$821$	1.15783	+	1.15783i	0.0404085	+	0.0404085i	−0.686614	+	0.727022i	$0.740904\pi$
$822$		0			0
$823$	−17.9269	−	17.9269i	−0.624891	−	0.624891i	0.321887	−	0.946778i	$-0.395683\pi$
$823$	−17.9269	−	17.9269i	−0.624891	−	0.624891i	−0.946778	+	0.321887i	$0.895683\pi$
$824$		0			0
$825$	4.33346	−	17.7613i	0.150872	−	0.618369i
$826$		0			0
$827$			38.4046i			1.33546i	0.744404	+	0.667729i	$0.232733\pi$
$827$			38.4046i			1.33546i	−0.744404	+	0.667729i	$0.767267\pi$
$828$		0			0
$829$	−14.5259	−	14.5259i	−0.504506	−	0.504506i	0.408329	−	0.912835i	$-0.366112\pi$
$829$	−14.5259	−	14.5259i	−0.504506	−	0.504506i	−0.912835	+	0.408329i	$0.866112\pi$
$830$		0			0
$831$		−	27.8708i		−	0.966829i
$832$		0			0
$833$	3.25576	+	3.25576i	0.112805	+	0.112805i
$834$		0			0
$835$	3.86082	+	13.7867i	0.133609	+	0.477109i
$836$		0			0
$837$	−8.08076			−0.279312
$838$		0			0
$839$			7.66262i			0.264543i	0.991214	+	0.132272i	$0.0422271\pi$
$839$			7.66262i			0.264543i	−0.991214	+	0.132272i	$0.957773\pi$
$840$		0			0
$841$		−	16.2340i		−	0.559793i
$842$		0			0
$843$	2.35087			0.0809683
$844$		0			0
$845$	19.7213	−	35.0631i	0.678434	−	1.20621i
$846$		0			0
$847$	−4.95908	−	4.95908i	−0.170396	−	0.170396i
$848$		0			0
$849$		−	15.9550i		−	0.547573i
$850$		0			0
$851$	31.2130	+	31.2130i	1.06997	+	1.06997i
$852$		0			0
$853$		−	52.3253i		−	1.79158i	−0.444474	−	0.895792i	$-0.646609\pi$
$853$		−	52.3253i		−	1.79158i	0.444474	−	0.895792i	$-0.353391\pi$
$854$		0			0
$855$	−1.91011	−	6.82087i	−0.0653245	−	0.233269i
$856$		0			0
$857$	−8.25252	−	8.25252i	−0.281901	−	0.281901i	0.551966	−	0.833867i	$-0.313878\pi$
$857$	−8.25252	−	8.25252i	−0.281901	−	0.281901i	−0.833867	+	0.551966i	$0.813878\pi$
$858$		0			0
$859$	32.9213	+	32.9213i	1.12326	+	1.12326i	0.991248	+	0.132010i	$0.0421432\pi$
$859$	32.9213	+	32.9213i	1.12326	+	1.12326i	0.132010	+	0.991248i	$0.457857\pi$
$860$		0			0
$861$	−3.70659	+	3.70659i	−0.126320	+	0.126320i
$862$		0			0
$863$	−18.7646	+	18.7646i	−0.638754	+	0.638754i	−0.950248	−	0.311494i	$-0.899171\pi$
$863$	−18.7646	+	18.7646i	−0.638754	+	0.638754i	0.311494	+	0.950248i	$0.399171\pi$
$864$		0			0
$865$	−12.5077	+	22.2378i	−0.425275	+	0.756108i
$866$		0			0
$867$	10.1456			0.344563
$868$		0			0
$869$	−34.4971	+	34.4971i	−1.17023	+	1.17023i
$870$		0			0
$871$	−68.9767			−2.33719
$872$		0			0
$873$	−2.86143	+	2.86143i	−0.0968447	+	0.0968447i
$874$		0			0
$875$	−22.5944	+	24.1728i	−0.763831	+	0.817190i
$876$		0			0
$877$		−	7.56014i		−	0.255288i	−0.991820	−	0.127644i	$-0.959259\pi$
$877$		−	7.56014i		−	0.255288i	0.991820	−	0.127644i	$-0.0407414\pi$
$878$		0			0
$879$	14.9047			0.502723
$880$		0			0
$881$	−49.1984			−1.65754			−0.828768	−	0.559592i	$-0.810958\pi$
$881$	−49.1984			−1.65754			−0.828768	+	0.559592i	$0.810958\pi$
$882$		0			0
$883$		−	18.6145i		−	0.626428i	−0.949683	−	0.313214i	$-0.898594\pi$
$883$		−	18.6145i		−	0.626428i	0.949683	−	0.313214i	$-0.101406\pi$
$884$		0			0
$885$	−0.930932	−	3.32429i	−0.0312929	−	0.111745i
$886$		0			0
$887$	26.7554	−	26.7554i	0.898360	−	0.898360i	−0.0969313	−	0.995291i	$-0.530903\pi$
$887$	26.7554	−	26.7554i	0.898360	−	0.898360i	0.995291	+	0.0969313i	$0.0309027\pi$
$888$		0			0
$889$	2.36976			0.0794790
$890$		0			0
$891$	−2.58551	+	2.58551i	−0.0866178	+	0.0866178i
$892$		0			0
$893$	2.35522			0.0788146
$894$		0			0
$895$	0.542622	+	1.93767i	0.0181379	+	0.0647690i
$896$		0			0
$897$	15.3041	−	15.3041i	0.510988	−	0.510988i
$898$		0			0
$899$	20.4157	−	20.4157i	0.680902	−	0.680902i
$900$		0			0
$901$	20.2441	+	20.2441i	0.674427	+	0.674427i
$902$		0			0
$903$	5.19530	+	5.19530i	0.172889	+	0.172889i
$904$		0			0
$905$	−22.1128	+	6.19246i	−0.735056	+	0.205844i
$906$		0			0
$907$		−	5.40451i		−	0.179454i	−0.995966	−	0.0897270i	$-0.971401\pi$
$907$		−	5.40451i		−	0.179454i	0.995966	−	0.0897270i	$-0.0285994\pi$
$908$		0			0
$909$	9.70834	+	9.70834i	0.322005	+	0.322005i
$910$		0			0
$911$		−	12.6467i		−	0.419003i	−0.977808	−	0.209502i	$-0.932816\pi$
$911$		−	12.6467i		−	0.419003i	0.977808	−	0.209502i	$-0.0671842\pi$
$912$		0			0
$913$	0.867013	+	0.867013i	0.0286940	+	0.0286940i
$914$		0			0
$915$	−18.8387	+	5.27557i	−0.622788	+	0.174405i
$916$		0			0
$917$	−53.0356			−1.75139
$918$		0			0
$919$			49.0361i			1.61755i	0.588117	+	0.808776i	$0.299869\pi$
$919$			49.0361i			1.61755i	−0.588117	+	0.808776i	$0.700131\pi$
$920$		0			0
$921$		−	8.95078i		−	0.294938i
$922$		0			0
$923$	−24.8365			−0.817505
$924$		0			0
$925$	29.4832	+	48.5130i	0.969403	+	1.59510i
$926$		0			0
$927$	9.93641	+	9.93641i	0.326355	+	0.326355i
$928$		0			0
$929$		−	30.2575i		−	0.992715i	−0.868118	−	0.496357i	$-0.834671\pi$
$929$		−	30.2575i		−	0.992715i	0.868118	−	0.496357i	$-0.165329\pi$
$930$		0			0
$931$	3.93928	+	3.93928i	0.129105	+	0.129105i
$932$		0			0
$933$			7.32409i			0.239780i
$934$		0			0
$935$	−18.6571	−	10.4937i	−0.610153	−	0.343182i
$936$		0			0
$937$	−24.6779	−	24.6779i	−0.806191	−	0.806191i	0.177864	−	0.984055i	$-0.443081\pi$
$937$	−24.6779	−	24.6779i	−0.806191	−	0.806191i	−0.984055	+	0.177864i	$0.943081\pi$
$938$		0			0
$939$	−1.98518	−	1.98518i	−0.0647839	−	0.0647839i
$940$		0			0
$941$	2.99760	−	2.99760i	0.0977188	−	0.0977188i	−0.656557	−	0.754276i	$-0.727988\pi$
$941$	2.99760	−	2.99760i	0.0977188	−	0.0977188i	0.754276	+	0.656557i	$0.227988\pi$
$942$		0			0
$943$	−4.86924	+	4.86924i	−0.158564	+	0.158564i
$944$		0			0
$945$	6.37250	−	1.78455i	0.207297	−	0.0580514i
$946$		0			0
$947$	41.9001			1.36157			0.680786	−	0.732482i	$-0.261638\pi$
$947$	41.9001			1.36157			0.680786	+	0.732482i	$0.261638\pi$
$948$		0			0
$949$	−22.8990	+	22.8990i	−0.743333	+	0.743333i
$950$		0			0
$951$	17.5989			0.570682
$952$		0			0
$953$	−8.63592	+	8.63592i	−0.279745	+	0.279745i	−0.833007	−	0.553262i	$-0.813383\pi$
$953$	−8.63592	+	8.63592i	−0.279745	+	0.279745i	0.553262	+	0.833007i	$0.313383\pi$
$954$		0			0
$955$	−5.07183	−	2.85266i	−0.164121	−	0.0923100i
$956$		0			0
$957$		−	13.0644i		−	0.422311i
$958$		0			0
$959$	−39.2697			−1.26808
$960$		0			0
$961$	−34.2987			−1.10641
$962$		0			0
$963$		−	2.36442i		−	0.0761925i
$964$		0			0
$965$	−21.6856	+	6.07282i	−0.698084	+	0.195491i
$966$		0			0
$967$	0.452031	−	0.452031i	0.0145363	−	0.0145363i	−0.699801	−	0.714338i	$-0.746728\pi$
$967$	0.452031	−	0.452031i	0.0145363	−	0.0145363i	0.714338	+	0.699801i	$0.246728\pi$
$968$		0			0
$969$	−8.29343			−0.266423
$970$		0			0
$971$	25.6260	−	25.6260i	0.822379	−	0.822379i	−0.164070	−	0.986449i	$-0.552462\pi$
$971$	25.6260	−	25.6260i	0.822379	−	0.822379i	0.986449	+	0.164070i	$0.0524623\pi$
$972$		0			0
$973$	7.98982			0.256142
$974$		0			0
$975$	23.7865	−	14.4560i	0.761777	−	0.462961i
$976$		0			0
$977$	15.6136	−	15.6136i	0.499524	−	0.499524i	−0.411766	−	0.911290i	$-0.635088\pi$
$977$	15.6136	−	15.6136i	0.499524	−	0.499524i	0.911290	+	0.411766i	$0.135088\pi$
$978$		0			0
$979$	4.95277	−	4.95277i	0.158291	−	0.158291i
$980$		0			0
$981$	−8.64138	−	8.64138i	−0.275898	−	0.275898i
$982$		0			0
$983$	25.8799	+	25.8799i	0.825441	+	0.825441i	0.986882	−	0.161442i	$-0.0516144\pi$
$983$	25.8799	+	25.8799i	0.825441	+	0.825441i	−0.161442	+	0.986882i	$0.551614\pi$
$984$		0			0
$985$	22.6248	−	40.2254i	0.720887	−	1.28169i
$986$		0			0
$987$			2.20040i			0.0700395i
$988$		0			0
$989$	6.82491	+	6.82491i	0.217020	+	0.217020i
$990$		0			0
$991$			1.03502i			0.0328785i	0.999865	+	0.0164393i	$0.00523301\pi$
$991$			1.03502i			0.0328785i	−0.999865	+	0.0164393i	$0.994767\pi$
$992$		0			0
$993$	4.38662	+	4.38662i	0.139205	+	0.139205i
$994$		0			0
$995$	−5.02802	−	2.82802i	−0.159399	−	0.0896543i
$996$		0			0
$997$	−12.1289			−0.384125			−0.192062	−	0.981383i	$-0.561518\pi$
$997$	−12.1289			−0.384125			−0.192062	+	0.981383i	$0.561518\pi$
$998$		0			0
$999$		−	11.3539i		−	0.359221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bc.l.1183.8		20
4.3	odd	2		1920.2.bc.k.1183.8		20
5.2	odd	4		1920.2.y.k.1567.3		20
8.3	odd	2		240.2.bc.f.43.7	yes	20
8.5	even	2		960.2.bc.f.463.3		20
16.3	odd	4		1920.2.y.k.223.3		20
16.5	even	4		240.2.y.f.163.2	✓	20
16.11	odd	4		960.2.y.f.943.8		20
16.13	even	4		1920.2.y.l.223.3		20
20.7	even	4		1920.2.y.l.1567.3		20
24.11	even	2		720.2.bd.h.523.4		20
40.27	even	4		240.2.y.f.187.2	yes	20
40.37	odd	4		960.2.y.f.847.8		20
48.5	odd	4		720.2.z.h.163.9		20
80.27	even	4		960.2.bc.f.367.3		20
80.37	odd	4		240.2.bc.f.67.7	yes	20
80.67	even	4	inner	1920.2.bc.l.607.8		20
80.77	odd	4		1920.2.bc.k.607.8		20
120.107	odd	4		720.2.z.h.667.9		20
240.197	even	4		720.2.bd.h.307.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.2	✓	20	16.5	even	4
240.2.y.f.187.2	yes	20	40.27	even	4
240.2.bc.f.43.7	yes	20	8.3	odd	2
240.2.bc.f.67.7	yes	20	80.37	odd	4
720.2.z.h.163.9		20	48.5	odd	4
720.2.z.h.667.9		20	120.107	odd	4
720.2.bd.h.307.4		20	240.197	even	4
720.2.bd.h.523.4		20	24.11	even	2
960.2.y.f.847.8		20	40.37	odd	4
960.2.y.f.943.8		20	16.11	odd	4
960.2.bc.f.367.3		20	80.27	even	4
960.2.bc.f.463.3		20	8.5	even	2
1920.2.y.k.223.3		20	16.3	odd	4
1920.2.y.k.1567.3		20	5.2	odd	4
1920.2.y.l.223.3		20	16.13	even	4
1920.2.y.l.1567.3		20	20.7	even	4
1920.2.bc.k.607.8		20	80.77	odd	4
1920.2.bc.k.1183.8		20	4.3	odd	2
1920.2.bc.l.607.8		20	80.67	even	4	inner
1920.2.bc.l.1183.8		20	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{3} +(1.09619 - 1.94894i) q^{5} +(2.09269 - 2.09269i) q^{7} -1.00000 q^{9} +(-2.58551 + 2.58551i) q^{11} -5.56694 q^{13} +(-1.94894 - 1.09619i) q^{15} +(-1.85127 + 1.85127i) q^{17} +(-2.23993 + 2.23993i) q^{19} +(-2.09269 - 2.09269i) q^{21} +(-2.74910 - 2.74910i) q^{23} +(-2.59675 - 4.27281i) q^{25} +1.00000i q^{27} +(-2.52646 - 2.52646i) q^{29} +8.08076i q^{31} +(2.58551 + 2.58551i) q^{33} +(-1.78455 - 6.37250i) q^{35} -11.3539 q^{37} +5.56694i q^{39} -1.77121i q^{41} -2.48260 q^{43} +(-1.09619 + 1.94894i) q^{45} +(-0.525736 - 0.525736i) q^{47} -1.75866i q^{49} +(1.85127 + 1.85127i) q^{51} -10.9352i q^{53} +(2.20481 + 7.87321i) q^{55} +(2.23993 + 2.23993i) q^{57} +(1.09168 + 1.09168i) q^{59} +(6.18650 - 6.18650i) q^{61} +(-2.09269 + 2.09269i) q^{63} +(-6.10241 + 10.8496i) q^{65} +12.3904 q^{67} +(-2.74910 + 2.74910i) q^{69} +4.46143 q^{71} +(4.11339 - 4.11339i) q^{73} +(-4.27281 + 2.59675i) q^{75} +10.8213i q^{77} +13.3425 q^{79} +1.00000 q^{81} -0.335336i q^{83} +(1.57868 + 5.63735i) q^{85} +(-2.52646 + 2.52646i) q^{87} -1.91559 q^{89} +(-11.6499 + 11.6499i) q^{91} +8.08076 q^{93} +(1.91011 + 6.82087i) q^{95} +(2.86143 - 2.86143i) q^{97} +(2.58551 - 2.58551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{5} + 4 q^{7} - 20 q^{9} + 8 q^{11} - 8 q^{13} + 12 q^{17} - 16 q^{19} - 4 q^{21} + 16 q^{23} - 4 q^{25} - 8 q^{33} - 12 q^{35} - 24 q^{37} - 8 q^{43} + 8 q^{45} - 12 q^{51} + 4 q^{55} + 16 q^{57}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q - 8 * q^5 + 4 * q^7 - 20 * q^9 + 8 * q^11 - 8 * q^13 + 12 * q^17 - 16 * q^19 - 4 * q^21 + 16 * q^23 - 4 * q^25 - 8 * q^33 - 12 * q^35 - 24 * q^37 - 8 * q^43 + 8 * q^45 - 12 * q^51 + 4 * q^55 + 16 * q^57 + 16 * q^59 + 12 * q^61 - 4 * q^63 + 4 * q^65 - 16 * q^67 + 16 * q^69 + 20 * q^73 - 8 * q^75 + 48 * q^79 + 20 * q^81 - 4 * q^85 - 40 * q^89 - 24 * q^91 - 72 * q^95 - 28 * q^97 - 8 * q^99

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