LMFDB - Embedded newform 960.2.bc.f.463.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(367,960)] 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("960.367"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.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:	$7.66563859404$
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			463.3
Root			$0.356677 - 1.36850i$ of defining polynomial
Character	$\chi$	$=$	960.463
Dual form			960.2.bc.f.367.3

$q$-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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	−0.200195	−	0.979756i	$-0.564158\pi$
$11$	2.58551	−	2.58551i	0.779561	−	0.779561i	0.979756	+	0.200195i	$0.0641577\pi$
$12$		0			0
$13$	5.56694			1.54399			0.771996	−	0.635628i	$-0.219259\pi$
$13$	5.56694			1.54399			0.771996	+	0.635628i	$0.219259\pi$
$14$		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	−0.401836	−	0.915711i	$-0.631628\pi$
$19$	2.23993	−	2.23993i	0.513875	−	0.513875i	0.915711	+	0.401836i	$0.131628\pi$
$20$		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	0.901640	−	0.432488i	$-0.142364\pi$
$29$	2.52646	+	2.52646i	0.469152	+	0.469152i	−0.432488	+	0.901640i	$0.642364\pi$
$30$		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	$-0.116929\pi$
$37$	11.3539			1.86657			0.933284	+	0.359138i	$0.116929\pi$
$38$		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	$-0.439379\pi$
$43$	2.48260			0.378593			0.189296	+	0.981920i	$0.439379\pi$
$44$		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	$0.270445\pi$
$53$			10.9352i			1.50207i	−0.660263	+	0.751035i	$0.729555\pi$
$54$		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	0.632465	−	0.774589i	$-0.282043\pi$
$59$	−1.09168	−	1.09168i	−0.142124	−	0.142124i	−0.774589	+	0.632465i	$0.782043\pi$
$60$		0			0
$61$	−6.18650	+	6.18650i	−0.792100	+	0.792100i	−0.981835	−	0.189735i	$-0.939237\pi$
$61$	−6.18650	+	6.18650i	−0.792100	+	0.792100i	0.189735	+	0.981835i	$0.439237\pi$
$62$		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	$-0.773270\pi$
$67$	−12.3904			−1.51373			−0.756865	+	0.653571i	$0.773270\pi$
$68$		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	$0.00585848\pi$
$83$			0.335336i			0.0368079i	−0.999831	+	0.0184039i	$0.994142\pi$
$84$		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	0.999441	−	0.0334254i	$-0.0106416\pi$
$101$	9.70834	+	9.70834i	0.966016	+	0.966016i	−0.0334254	+	0.999441i	$0.510642\pi$
$102$		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	$-0.963541\pi$
$107$		−	2.36442i		−	0.228577i	0.993448	−	0.114289i	$-0.0364589\pi$
$108$		0			0
$109$	−8.64138	−	8.64138i	−0.827694	−	0.827694i	0.159503	−	0.987197i	$-0.449011\pi$
$109$	−8.64138	−	8.64138i	−0.827694	−	0.827694i	−0.987197	+	0.159503i	$0.949011\pi$
$110$		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	$0.0362386\pi$
$131$	12.6717	+	12.6717i	1.10713	+	1.10713i	0.113601	+	0.993526i	$0.463761\pi$
$132$		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	0.621498	−	0.783416i	$-0.286524\pi$
$139$	−1.90899	−	1.90899i	−0.161918	−	0.161918i	−0.783416	+	0.621498i	$0.786524\pi$
$140$		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	−0.443608	−	0.896221i	$-0.646302\pi$
$149$	5.52485	−	5.52485i	0.452613	−	0.452613i	0.896221	+	0.443608i	$0.146302\pi$
$150$		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	$0.0478291\pi$
$157$			3.75134i			0.299390i	−0.988732	+	0.149695i	$0.952171\pi$
$158$		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	$-0.610859\pi$
$163$		−	24.0013i		−	1.87993i	0.341277	−	0.939963i	$-0.389141\pi$
$164$		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	$-0.357190\pi$
$173$	11.4102			0.867501			0.433751	+	0.901033i	$0.357190\pi$
$174$		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	−0.682927	−	0.730487i	$-0.739293\pi$
$179$	0.636317	−	0.636317i	0.0475605	−	0.0475605i	0.730487	+	0.682927i	$0.239293\pi$
$180$		0			0
$181$	7.26171	+	7.26171i	0.539759	+	0.539759i	0.923458	−	0.383699i	$-0.125350\pi$
$181$	7.26171	+	7.26171i	0.539759	+	0.539759i	−0.383699	+	0.923458i	$0.625350\pi$
$182$		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	$-0.762938\pi$
$197$	−20.6396			−1.47051			−0.735255	+	0.677791i	$0.762938\pi$
$198$		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	0.811565	−	0.584262i	$-0.198616\pi$
$211$	3.30177	+	3.30177i	0.227303	+	0.227303i	−0.584262	+	0.811565i	$0.698616\pi$
$212$		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	$-0.715186\pi$
$227$	−18.8542			−1.25140			−0.625699	+	0.780064i	$0.715186\pi$
$228$		0			0
$229$	11.8744	−	11.8744i	0.784683	−	0.784683i	−0.195934	−	0.980617i	$-0.562774\pi$
$229$	11.8744	−	11.8744i	0.784683	−	0.784683i	0.980617	+	0.195934i	$0.0627740\pi$
$230$		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	$0.654956\pi$
$251$	−21.4140	+	21.4140i	−1.35164	+	1.35164i	−0.883830	+	0.467808i	$0.845044\pi$
$252$		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	0.877940	−	0.478771i	$-0.158917\pi$
$269$	6.54686	+	6.54686i	0.399169	+	0.399169i	−0.478771	+	0.877940i	$0.658917\pi$
$270$		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	$-0.815866\pi$
$277$	−27.8708			−1.67460			−0.837299	+	0.546746i	$0.815866\pi$
$278$		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	$-0.657267\pi$
$283$	−15.9550			−0.948425			−0.474212	+	0.880410i	$0.657267\pi$
$284$		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	$-0.856617\pi$
$293$		−	14.9047i		−	0.870741i	0.900251	−	0.435371i	$-0.143383\pi$
$294$		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	$-0.582215\pi$
$307$	−8.95078			−0.510848			−0.255424	+	0.966829i	$0.582215\pi$
$308$		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	$-0.835452\pi$
$317$		−	17.5989i		−	0.988450i	0.869334	−	0.494225i	$-0.164548\pi$
$318$		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	−0.576199	−	0.817310i	$-0.695465\pi$
$331$	4.38662	−	4.38662i	0.241111	−	0.241111i	0.817310	+	0.576199i	$0.195465\pi$
$332$		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	$0.388387\pi$
$347$			34.9889i			1.87830i	−0.343501	+	0.939152i	$0.611613\pi$
$348$		0			0
$349$	7.60199	+	7.60199i	0.406925	+	0.406925i	0.880665	−	0.473740i	$-0.157096\pi$
$349$	7.60199	+	7.60199i	0.406925	+	0.406925i	−0.473740	+	0.880665i	$0.657096\pi$
$350$		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	$0.132036\pi$
$373$			15.5668i			0.806019i	−0.915196	+	0.403009i	$0.867964\pi$
$374$		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	0.873186	−	0.487387i	$-0.162050\pi$
$379$	7.51070	+	7.51070i	0.385799	+	0.385799i	−0.487387	+	0.873186i	$0.662050\pi$
$380$		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	−0.599569	−	0.800323i	$-0.704661\pi$
$389$	3.95949	−	3.95949i	0.200754	−	0.200754i	0.800323	+	0.599569i	$0.204661\pi$
$390$		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	$-0.903164\pi$
$397$		−	11.9369i		−	0.599095i	0.954081	−	0.299547i	$-0.0968357\pi$
$398$		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	−0.976331	−	0.216280i	$-0.930608\pi$
$419$	−15.5579	+	15.5579i	−0.760052	+	0.760052i	0.216280	+	0.976331i	$0.430608\pi$
$420$		0			0
$421$	−11.8886	−	11.8886i	−0.579415	−	0.579415i	0.355327	−	0.934742i	$-0.384369\pi$
$421$	−11.8886	−	11.8886i	−0.579415	−	0.579415i	−0.934742	+	0.355327i	$0.884369\pi$
$422$		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	$-0.135184\pi$
$443$	38.3556			1.82233			0.911165	+	0.412041i	$0.135184\pi$
$444$		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	$-0.410660\pi$
$461$	26.5782	−	26.5782i	1.23787	−	1.23787i	0.960870	−	0.277000i	$-0.0893403\pi$
$462$		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	$-0.504728\pi$
$467$	−0.641894			−0.0297033			−0.0148517	+	0.999890i	$0.504728\pi$
$468$		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	−0.334394	−	0.942434i	$-0.608531\pi$
$491$	13.4733	−	13.4733i	0.608040	−	0.608040i	0.942434	+	0.334394i	$0.108531\pi$
$492$		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	−0.790690	−	0.612217i	$-0.790278\pi$
$499$	−3.98679	+	3.98679i	−0.178473	+	0.178473i	0.612217	+	0.790690i	$0.290278\pi$
$500$		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	0.283085	−	0.959095i	$-0.408642\pi$
$509$	−15.2515	−	15.2515i	−0.676010	−	0.676010i	−0.959095	+	0.283085i	$0.908642\pi$
$510$		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	$-0.421981\pi$
$523$	11.0988			0.485315			0.242658	+	0.970112i	$0.421981\pi$
$524$		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	$0.629720\pi$
$541$	−30.5732	+	30.5732i	−1.31444	+	1.31444i	−0.918104	+	0.396339i	$0.870280\pi$
$542$		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	$-0.494266\pi$
$547$	0.842518			0.0360235			0.0180117	+	0.999838i	$0.494266\pi$
$548$		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	$0.0773391\pi$
$557$			11.3560i			0.481169i	−0.970628	+	0.240584i	$0.922661\pi$
$558$		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	$-0.968610\pi$
$563$		−	4.67224i		−	0.196912i	0.995141	−	0.0984558i	$-0.0313903\pi$
$564$		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	−0.455339	−	0.890318i	$-0.650482\pi$
$571$	10.3941	−	10.3941i	0.434978	−	0.434978i	0.890318	+	0.455339i	$0.150482\pi$
$572$		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	$-0.858666\pi$
$587$		−	20.8152i		−	0.859136i	0.903034	−	0.429568i	$-0.141334\pi$
$588$		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	$0.216993\pi$
$613$			31.2019i			1.26023i	−0.776500	+	0.630117i	$0.783007\pi$
$614$		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	0.546819	−	0.837251i	$-0.315839\pi$
$619$	−7.22587	−	7.22587i	−0.290432	−	0.290432i	−0.837251	+	0.546819i	$0.815839\pi$
$620$		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	$0.125550\pi$
$643$			19.4887i			0.768561i	−0.923216	+	0.384280i	$0.874450\pi$
$644$		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	$-0.310801\pi$
$653$	28.6204			1.12000			0.560001	+	0.828492i	$0.310801\pi$
$654$		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	−0.380820	−	0.924649i	$-0.624358\pi$
$659$	13.9606	−	13.9606i	0.543830	−	0.543830i	0.924649	+	0.380820i	$0.124358\pi$
$660$		0			0
$661$	2.74706	+	2.74706i	0.106848	+	0.106848i	0.758510	−	0.651662i	$-0.225928\pi$
$661$	2.74706	+	2.74706i	0.106848	+	0.106848i	−0.651662	+	0.758510i	$0.725928\pi$
$662$		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	$-0.801271\pi$
$677$	−42.2218			−1.62272			−0.811358	+	0.584550i	$0.801271\pi$
$678$		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	$-0.696217\pi$
$683$	−30.2180			−1.15626			−0.578130	+	0.815945i	$0.696217\pi$
$684$		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	0.443175	−	0.896435i	$-0.353852\pi$
$691$	−11.9148	−	11.9148i	−0.453260	−	0.453260i	−0.896435	+	0.443175i	$0.853852\pi$
$692$		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	−0.989822	−	0.142310i	$-0.954547\pi$
$701$	−22.4391	+	22.4391i	−0.847512	+	0.847512i	0.142310	+	0.989822i	$0.454547\pi$
$702$		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	$0.507337\pi$
$709$	−27.2337	+	27.2337i	−1.02278	+	1.02278i	−0.999734	+	0.0230475i	$0.992663\pi$
$710$		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	$-0.618085\pi$
$733$	−19.6299			−0.725046			−0.362523	+	0.931975i	$0.618085\pi$
$734$		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	−0.999372	−	0.0354261i	$-0.988721\pi$
$739$	−26.2044	+	26.2044i	−0.963946	+	0.963946i	0.0354261	+	0.999372i	$0.488721\pi$
$740$		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	$-0.313867\pi$
$757$	30.3747			1.10399			0.551994	+	0.833848i	$0.313867\pi$
$758$		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	$-0.677701\pi$
$773$		−	47.1635i		−	1.69635i	0.529715	−	0.848176i	$-0.322299\pi$
$774$		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	$-0.584345\pi$
$787$	−14.6938			−0.523778			−0.261889	+	0.965098i	$0.584345\pi$
$788$		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	$-0.979281\pi$
$797$		−	3.67259i		−	0.130090i	0.997882	−	0.0650448i	$-0.0207190\pi$
$798$		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	−0.0868685	−	0.996220i	$-0.527686\pi$
$811$	25.8966	−	25.8966i	0.909351	−	0.909351i	0.996220	+	0.0868685i	$0.0276860\pi$
$812$		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	0.686614	−	0.727022i	$-0.259096\pi$
$821$	−1.15783	−	1.15783i	−0.0404085	−	0.0404085i	−0.727022	+	0.686614i	$0.759096\pi$
$822$		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	$-0.767267\pi$
$827$		−	38.4046i		−	1.33546i	0.744404	−	0.667729i	$-0.232733\pi$
$828$		0			0
$829$	14.5259	+	14.5259i	0.504506	+	0.504506i	0.912835	−	0.408329i	$-0.133888\pi$
$829$	14.5259	+	14.5259i	0.504506	+	0.504506i	−0.408329	+	0.912835i	$0.633888\pi$
$830$		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	$0.353391\pi$
$853$			52.3253i			1.79158i	−0.444474	+	0.895792i	$0.646609\pi$
$854$		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	$-0.957857\pi$
$859$	−32.9213	−	32.9213i	−1.12326	−	1.12326i	−0.132010	−	0.991248i	$-0.542143\pi$
$860$		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	$0.0407414\pi$
$877$			7.56014i			0.255288i	−0.991820	+	0.127644i	$0.959259\pi$
$878$		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	$0.101406\pi$
$883$			18.6145i			0.626428i	−0.949683	+	0.313214i	$0.898594\pi$
$884$		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	$0.0285994\pi$
$907$			5.40451i			0.179454i	−0.995966	+	0.0897270i	$0.971401\pi$
$908$		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	−0.754276	−	0.656557i	$-0.772012\pi$
$941$	−2.99760	+	2.99760i	−0.0977188	+	0.0977188i	0.656557	+	0.754276i	$0.272012\pi$
$942$		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	$-0.738362\pi$
$947$	−41.9001			−1.36157			−0.680786	+	0.732482i	$0.738362\pi$
$948$		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	−0.986449	−	0.164070i	$-0.947538\pi$
$971$	−25.6260	+	25.6260i	−0.822379	+	0.822379i	0.164070	+	0.986449i	$0.447538\pi$
$972$		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	$-0.438482\pi$
$997$	12.1289			0.384125			0.192062	+	0.981383i	$0.438482\pi$
$998$		0			0
$999$		−	11.3539i		−	0.359221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bc.f.463.3		20
4.3	odd	2		240.2.bc.f.43.7	yes	20
5.2	odd	4		960.2.y.f.847.8		20
8.3	odd	2		1920.2.bc.k.1183.8		20
8.5	even	2		1920.2.bc.l.1183.8		20
12.11	even	2		720.2.bd.h.523.4		20
16.3	odd	4		960.2.y.f.943.8		20
16.5	even	4		1920.2.y.l.223.3		20
16.11	odd	4		1920.2.y.k.223.3		20
16.13	even	4		240.2.y.f.163.2	✓	20
20.7	even	4		240.2.y.f.187.2	yes	20
40.27	even	4		1920.2.y.l.1567.3		20
40.37	odd	4		1920.2.y.k.1567.3		20
48.29	odd	4		720.2.z.h.163.9		20
60.47	odd	4		720.2.z.h.667.9		20
80.27	even	4		1920.2.bc.l.607.8		20
80.37	odd	4		1920.2.bc.k.607.8		20
80.67	even	4	inner	960.2.bc.f.367.3		20
80.77	odd	4		240.2.bc.f.67.7	yes	20
240.77	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	16.13	even	4
240.2.y.f.187.2	yes	20	20.7	even	4
240.2.bc.f.43.7	yes	20	4.3	odd	2
240.2.bc.f.67.7	yes	20	80.77	odd	4
720.2.z.h.163.9		20	48.29	odd	4
720.2.z.h.667.9		20	60.47	odd	4
720.2.bd.h.307.4		20	240.77	even	4
720.2.bd.h.523.4		20	12.11	even	2
960.2.y.f.847.8		20	5.2	odd	4
960.2.y.f.943.8		20	16.3	odd	4
960.2.bc.f.367.3		20	80.67	even	4	inner
960.2.bc.f.463.3		20	1.1	even	1	trivial
1920.2.y.k.223.3		20	16.11	odd	4
1920.2.y.k.1567.3		20	40.37	odd	4
1920.2.y.l.223.3		20	16.5	even	4
1920.2.y.l.1567.3		20	40.27	even	4
1920.2.bc.k.607.8		20	80.37	odd	4
1920.2.bc.k.1183.8		20	8.3	odd	2
1920.2.bc.l.607.8		20	80.27	even	4
1920.2.bc.l.1183.8		20	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.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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