LMFDB - Embedded newform 735.2.d.f.589.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(589,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.589"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.7
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.f.589.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +(-1.41421 - 1.73205i) q^{5} +1.93185 q^{6} +0.517638i q^{8} -1.00000 q^{9} +(3.34607 - 2.73205i) q^{10} -3.46410 q^{11} +1.73205i q^{12} +4.00000i q^{13} +(-1.73205 + 1.41421i) q^{15} -4.46410 q^{16} -4.00000i q^{17} -1.93185i q^{18} +0.378937 q^{19} +(2.44949 + 3.00000i) q^{20} -6.69213i q^{22} +6.31319i q^{23} +0.517638 q^{24} +(-1.00000 + 4.89898i) q^{25} -7.72741 q^{26} +1.00000i q^{27} -8.92820 q^{29} +(-2.73205 - 3.34607i) q^{30} -7.34847 q^{31} -7.58871i q^{32} +3.46410i q^{33} +7.72741 q^{34} +1.73205 q^{36} +0.757875i q^{37} +0.732051i q^{38} +4.00000 q^{39} +(0.896575 - 0.732051i) q^{40} -8.48528 q^{41} +6.00000 q^{44} +(1.41421 + 1.73205i) q^{45} -12.1962 q^{46} -6.00000i q^{47} +4.46410i q^{48} +(-9.46410 - 1.93185i) q^{50} -4.00000 q^{51} -6.92820i q^{52} -7.34847i q^{53} -1.93185 q^{54} +(4.89898 + 6.00000i) q^{55} -0.378937i q^{57} -17.2480i q^{58} -10.5558 q^{59} +(3.00000 - 2.44949i) q^{60} +9.14162 q^{61} -14.1962i q^{62} +5.73205 q^{64} +(6.92820 - 5.65685i) q^{65} -6.69213 q^{66} +6.96953i q^{67} +6.92820i q^{68} +6.31319 q^{69} +14.3923 q^{71} -0.517638i q^{72} +10.9282i q^{73} -1.46410 q^{74} +(4.89898 + 1.00000i) q^{75} -0.656339 q^{76} +7.72741i q^{78} +11.4641 q^{79} +(6.31319 + 7.73205i) q^{80} +1.00000 q^{81} -16.3923i q^{82} +6.00000i q^{83} +(-6.92820 + 5.65685i) q^{85} +8.92820i q^{87} -1.79315i q^{88} +4.14110 q^{89} +(-3.34607 + 2.73205i) q^{90} -10.9348i q^{92} +7.34847i q^{93} +11.5911 q^{94} +(-0.535898 - 0.656339i) q^{95} -7.58871 q^{96} -5.07180i q^{97} +3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9} - 8 q^{16} - 8 q^{25} - 16 q^{29} - 8 q^{30} + 32 q^{39} + 48 q^{44} - 56 q^{46} - 48 q^{50} - 32 q^{51} + 24 q^{60} + 32 q^{64} + 32 q^{71} + 16 q^{74} + 64 q^{79} + 8 q^{81} - 32 q^{95}+O(q^{100}) $ 8 * q - 8 * q^9 - 8 * q^16 - 8 * q^25 - 16 * q^29 - 8 * q^30 + 32 * q^39 + 48 * q^44 - 56 * q^46 - 48 * q^50 - 32 * q^51 + 24 * q^60 + 32 * q^64 + 32 * q^71 + 16 * q^74 + 64 * q^79 + 8 * q^81 - 32 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.93185i			1.36603i	0.730406	+	0.683013i	$0.239331\pi$
$2$			1.93185i			1.36603i	−0.730406	+	0.683013i	$0.760669\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.73205			−0.866025
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$6$	1.93185			0.788675
$7$		0			0
$7$		0			0
$8$			0.517638i			0.183013i
$9$	−1.00000			−0.333333
$10$	3.34607	−	2.73205i	1.05812	−	0.863950i
$11$	−3.46410			−1.04447			−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410			−1.04447			−0.522233	+	0.852803i	$0.674901\pi$
$12$			1.73205i			0.500000i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	−1.73205	+	1.41421i	−0.447214	+	0.365148i
$16$	−4.46410			−1.11603
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		−	1.93185i		−	0.455342i
$19$	0.378937			0.0869342			0.0434671	−	0.999055i	$-0.486160\pi$
$19$	0.378937			0.0869342			0.0434671	+	0.999055i	$0.486160\pi$
$20$	2.44949	+	3.00000i	0.547723	+	0.670820i
$21$		0			0
$22$		−	6.69213i		−	1.42677i
$23$			6.31319i			1.31639i	0.752847	+	0.658196i	$0.228680\pi$
$23$			6.31319i			1.31639i	−0.752847	+	0.658196i	$0.771320\pi$
$24$	0.517638			0.105662
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$	−7.72741			−1.51547
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−8.92820			−1.65793			−0.828963	−	0.559304i	$-0.811069\pi$
$29$	−8.92820			−1.65793			−0.828963	+	0.559304i	$0.811069\pi$
$30$	−2.73205	−	3.34607i	−0.498802	−	0.610905i
$31$	−7.34847			−1.31982			−0.659912	−	0.751343i	$-0.729406\pi$
$31$	−7.34847			−1.31982			−0.659912	+	0.751343i	$0.729406\pi$
$32$		−	7.58871i		−	1.34151i
$33$			3.46410i			0.603023i
$34$	7.72741			1.32524
$35$		0			0
$36$	1.73205			0.288675
$37$			0.757875i			0.124594i	0.998058	+	0.0622969i	$0.0198426\pi$
$37$			0.757875i			0.124594i	−0.998058	+	0.0622969i	$0.980157\pi$
$38$			0.732051i			0.118754i
$39$	4.00000			0.640513
$40$	0.896575	−	0.732051i	0.141761	−	0.115747i
$41$	−8.48528			−1.32518			−0.662589	−	0.748983i	$-0.730542\pi$
$41$	−8.48528			−1.32518			−0.662589	+	0.748983i	$0.730542\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	6.00000			0.904534
$45$	1.41421	+	1.73205i	0.210819	+	0.258199i
$46$	−12.1962			−1.79822
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$			4.46410i			0.644338i
$49$		0			0
$50$	−9.46410	−	1.93185i	−1.33843	−	0.273205i
$51$	−4.00000			−0.560112
$52$		−	6.92820i		−	0.960769i
$53$		−	7.34847i		−	1.00939i	−0.863298	−	0.504695i	$-0.831605\pi$
$53$		−	7.34847i		−	1.00939i	0.863298	−	0.504695i	$-0.168395\pi$
$54$	−1.93185			−0.262892
$55$	4.89898	+	6.00000i	0.660578	+	0.809040i
$56$		0			0
$57$		−	0.378937i		−	0.0501915i
$58$		−	17.2480i		−	2.26477i
$59$	−10.5558			−1.37425			−0.687126	−	0.726538i	$-0.741128\pi$
$59$	−10.5558			−1.37425			−0.687126	+	0.726538i	$0.741128\pi$
$60$	3.00000	−	2.44949i	0.387298	−	0.316228i
$61$	9.14162			1.17046			0.585232	−	0.810866i	$-0.301003\pi$
$61$	9.14162			1.17046			0.585232	+	0.810866i	$0.301003\pi$
$62$		−	14.1962i		−	1.80291i
$63$		0			0
$64$	5.73205			0.716506
$65$	6.92820	−	5.65685i	0.859338	−	0.701646i
$66$	−6.69213			−0.823744
$67$			6.96953i			0.851464i	0.904849	+	0.425732i	$0.139983\pi$
$67$			6.96953i			0.851464i	−0.904849	+	0.425732i	$0.860017\pi$
$68$			6.92820i			0.840168i
$69$	6.31319			0.760019
$70$		0			0
$71$	14.3923			1.70805			0.854026	−	0.520230i	$-0.174154\pi$
$71$	14.3923			1.70805			0.854026	+	0.520230i	$0.174154\pi$
$72$		−	0.517638i		−	0.0610042i
$73$			10.9282i			1.27905i	0.768771	+	0.639525i	$0.220869\pi$
$73$			10.9282i			1.27905i	−0.768771	+	0.639525i	$0.779131\pi$
$74$	−1.46410			−0.170198
$75$	4.89898	+	1.00000i	0.565685	+	0.115470i
$76$	−0.656339			−0.0752872
$77$		0			0
$78$			7.72741i			0.874957i
$79$	11.4641			1.28981			0.644906	−	0.764262i	$-0.276896\pi$
$79$	11.4641			1.28981			0.644906	+	0.764262i	$0.276896\pi$
$80$	6.31319	+	7.73205i	0.705836	+	0.864470i
$81$	1.00000			0.111111
$82$		−	16.3923i		−	1.81023i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	−6.92820	+	5.65685i	−0.751469	+	0.613572i
$86$		0			0
$87$			8.92820i			0.957204i
$88$		−	1.79315i		−	0.191151i
$89$	4.14110			0.438956			0.219478	−	0.975617i	$-0.429565\pi$
$89$	4.14110			0.438956			0.219478	+	0.975617i	$0.429565\pi$
$90$	−3.34607	+	2.73205i	−0.352706	+	0.287983i
$91$		0			0
$92$		−	10.9348i		−	1.14003i
$93$			7.34847i			0.762001i
$94$	11.5911			1.19553
$95$	−0.535898	−	0.656339i	−0.0549820	−	0.0673389i
$96$	−7.58871			−0.774519
$97$		−	5.07180i		−	0.514963i	−0.966283	−	0.257481i	$-0.917107\pi$
$97$		−	5.07180i		−	0.514963i	0.966283	−	0.257481i	$-0.0828926\pi$
$98$		0			0
$99$	3.46410			0.348155
$100$	1.73205	−	8.48528i	0.173205	−	0.848528i
$101$	−12.6264			−1.25637			−0.628186	−	0.778063i	$-0.716202\pi$
$101$	−12.6264			−1.25637			−0.628186	+	0.778063i	$0.716202\pi$
$102$		−	7.72741i		−	0.765127i
$103$		−	13.8564i		−	1.36531i	−0.730740	−	0.682656i	$-0.760825\pi$
$103$		−	13.8564i		−	1.36531i	0.730740	−	0.682656i	$-0.239175\pi$
$104$	−2.07055			−0.203034
$105$		0			0
$106$	14.1962			1.37885
$107$			15.5563i			1.50389i	0.659226	+	0.751945i	$0.270884\pi$
$107$			15.5563i			1.50389i	−0.659226	+	0.751945i	$0.729116\pi$
$108$		−	1.73205i		−	0.166667i
$109$	11.8564			1.13564			0.567819	−	0.823154i	$-0.307787\pi$
$109$	11.8564			1.13564			0.567819	+	0.823154i	$0.307787\pi$
$110$	−11.5911	+	9.46410i	−1.10517	+	0.902367i
$111$	0.757875			0.0719343
$112$		0			0
$113$			0.378937i			0.0356474i	0.999841	+	0.0178237i	$0.00567377\pi$
$113$			0.378937i			0.0356474i	−0.999841	+	0.0178237i	$0.994326\pi$
$114$	0.732051			0.0685628
$115$	10.9348	−	8.92820i	1.01967	−	0.832559i
$116$	15.4641			1.43581
$117$		−	4.00000i		−	0.369800i
$118$		−	20.3923i		−	1.87726i
$119$		0			0
$120$	−0.732051	−	0.896575i	−0.0668268	−	0.0818458i
$121$	1.00000			0.0909091
$122$			17.6603i			1.59888i
$123$			8.48528i			0.765092i
$124$	12.7279			1.14300
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$		0			0
$127$			2.82843i			0.250982i	0.992095	+	0.125491i	$0.0400507\pi$
$127$			2.82843i			0.250982i	−0.992095	+	0.125491i	$0.959949\pi$
$128$		−	4.10394i		−	0.362740i
$129$		0			0
$130$	10.9282	+	13.3843i	0.958467	+	1.17388i
$131$	5.65685			0.494242			0.247121	−	0.968985i	$-0.420516\pi$
$131$	5.65685			0.494242			0.247121	+	0.968985i	$0.420516\pi$
$132$		−	6.00000i		−	0.522233i
$133$		0			0
$134$	−13.4641			−1.16312
$135$	1.73205	−	1.41421i	0.149071	−	0.121716i
$136$	2.07055			0.177548
$137$		−	4.52004i		−	0.386173i	−0.981182	−	0.193087i	$-0.938150\pi$
$137$		−	4.52004i		−	0.386173i	0.981182	−	0.193087i	$-0.0618498\pi$
$138$			12.1962i			1.03821i
$139$	−5.27792			−0.447667			−0.223834	−	0.974627i	$-0.571857\pi$
$139$	−5.27792			−0.447667			−0.223834	+	0.974627i	$0.571857\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$			27.8038i			2.33324i
$143$		−	13.8564i		−	1.15873i
$144$	4.46410			0.372008
$145$	12.6264	+	15.4641i	1.04856	+	1.28422i
$146$	−21.1117			−1.74721
$147$		0			0
$148$		−	1.31268i		−	0.107901i
$149$	−20.9282			−1.71451			−0.857253	−	0.514896i	$-0.827831\pi$
$149$	−20.9282			−1.71451			−0.857253	+	0.514896i	$0.827831\pi$
$150$	−1.93185	+	9.46410i	−0.157735	+	0.772741i
$151$	−12.5359			−1.02016			−0.510078	−	0.860128i	$-0.670384\pi$
$151$	−12.5359			−1.02016			−0.510078	+	0.860128i	$0.670384\pi$
$152$			0.196152i			0.0159101i
$153$			4.00000i			0.323381i
$154$		0			0
$155$	10.3923	+	12.7279i	0.834730	+	1.02233i
$156$	−6.92820			−0.554700
$157$		−	18.9282i		−	1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$157$		−	18.9282i		−	1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$158$			22.1469i			1.76192i
$159$	−7.34847			−0.582772
$160$	−13.1440	+	10.7321i	−1.03913	+	0.848443i
$161$		0			0
$162$			1.93185i			0.151781i
$163$		−	16.7675i		−	1.31333i	−0.754182	−	0.656666i	$-0.771966\pi$
$163$		−	16.7675i		−	1.31333i	0.754182	−	0.656666i	$-0.228034\pi$
$164$	14.6969			1.14764
$165$	6.00000	−	4.89898i	0.467099	−	0.381385i
$166$	−11.5911			−0.899645
$167$		−	5.07180i		−	0.392467i	−0.980557	−	0.196234i	$-0.937129\pi$
$167$		−	5.07180i		−	0.392467i	0.980557	−	0.196234i	$-0.0628711\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−10.9282	−	13.3843i	−0.838155	−	1.02653i
$171$	−0.378937			−0.0289781
$172$		0			0
$173$			16.0000i			1.21646i	0.793762	+	0.608229i	$0.208120\pi$
$173$			16.0000i			1.21646i	−0.793762	+	0.608229i	$0.791880\pi$
$174$	−17.2480			−1.30756
$175$		0			0
$176$	15.4641			1.16565
$177$			10.5558i			0.793425i
$178$			8.00000i			0.599625i
$179$	10.3923			0.776757			0.388379	−	0.921500i	$-0.373035\pi$
$179$	10.3923			0.776757			0.388379	+	0.921500i	$0.373035\pi$
$180$	−2.44949	−	3.00000i	−0.182574	−	0.223607i
$181$	−3.48477			−0.259021			−0.129510	−	0.991578i	$-0.541341\pi$
$181$	−3.48477			−0.259021			−0.129510	+	0.991578i	$0.541341\pi$
$182$		0			0
$183$		−	9.14162i		−	0.675768i
$184$	−3.26795			−0.240916
$185$	1.31268	−	1.07180i	0.0965100	−	0.0788001i
$186$	−14.1962			−1.04091
$187$			13.8564i			1.01328i
$188$			10.3923i			0.757937i
$189$		0			0
$190$	1.26795	−	1.03528i	0.0919867	−	0.0751068i
$191$	−0.535898			−0.0387762			−0.0193881	−	0.999812i	$-0.506172\pi$
$191$	−0.535898			−0.0387762			−0.0193881	+	0.999812i	$0.506172\pi$
$192$		−	5.73205i		−	0.413675i
$193$			16.2127i			1.16701i	0.812108	+	0.583507i	$0.198320\pi$
$193$			16.2127i			1.16701i	−0.812108	+	0.583507i	$0.801680\pi$
$194$	9.79796			0.703452
$195$	−5.65685	−	6.92820i	−0.405096	−	0.496139i
$196$		0			0
$197$			11.4896i			0.818598i	0.912400	+	0.409299i	$0.134227\pi$
$197$			11.4896i			0.818598i	−0.912400	+	0.409299i	$0.865773\pi$
$198$			6.69213i			0.475589i
$199$	3.20736			0.227364			0.113682	−	0.993517i	$-0.463735\pi$
$199$	3.20736			0.227364			0.113682	+	0.993517i	$0.463735\pi$
$200$	−2.53590	−	0.517638i	−0.179315	−	0.0366025i
$201$	6.96953			0.491593
$202$		−	24.3923i		−	1.71624i
$203$		0			0
$204$	6.92820			0.485071
$205$	12.0000	+	14.6969i	0.838116	+	1.02648i
$206$	26.7685			1.86505
$207$		−	6.31319i		−	0.438797i
$208$		−	17.8564i		−	1.23812i
$209$	−1.31268			−0.0907998
$210$		0			0
$211$	−13.0718			−0.899900			−0.449950	−	0.893054i	$-0.648558\pi$
$211$	−13.0718			−0.899900			−0.449950	+	0.893054i	$0.648558\pi$
$212$			12.7279i			0.874157i
$213$		−	14.3923i		−	0.986144i
$214$	−30.0526			−2.05435
$215$		0			0
$216$	−0.517638			−0.0352208
$217$		0			0
$218$			22.9048i			1.55131i
$219$	10.9282			0.738460
$220$	−8.48528	−	10.3923i	−0.572078	−	0.700649i
$221$	16.0000			1.07628
$222$			1.46410i			0.0982641i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	1.00000	−	4.89898i	0.0666667	−	0.326599i
$226$	−0.732051			−0.0486953
$227$		−	4.00000i		−	0.265489i	−0.991150	−	0.132745i	$-0.957621\pi$
$227$		−	4.00000i		−	0.265489i	0.991150	−	0.132745i	$-0.0423790\pi$
$228$			0.656339i			0.0434671i
$229$	−23.2838			−1.53863			−0.769317	−	0.638867i	$-0.779403\pi$
$229$	−23.2838			−1.53863			−0.769317	+	0.638867i	$0.779403\pi$
$230$	17.2480	+	21.1244i	1.13730	+	1.39290i
$231$		0			0
$232$		−	4.62158i		−	0.303421i
$233$			0.378937i			0.0248250i	0.999923	+	0.0124125i	$0.00395113\pi$
$233$			0.378937i			0.0248250i	−0.999923	+	0.0124125i	$0.996049\pi$
$234$	7.72741			0.505156
$235$	−10.3923	+	8.48528i	−0.677919	+	0.553519i
$236$	18.2832			1.19014
$237$		−	11.4641i		−	0.744673i
$238$		0			0
$239$	15.4641			1.00029			0.500145	−	0.865942i	$-0.333280\pi$
$239$	15.4641			1.00029			0.500145	+	0.865942i	$0.333280\pi$
$240$	7.73205	−	6.31319i	0.499102	−	0.407515i
$241$	5.55532			0.357850			0.178925	−	0.983863i	$-0.442738\pi$
$241$	5.55532			0.357850			0.178925	+	0.983863i	$0.442738\pi$
$242$			1.93185i			0.124184i
$243$		−	1.00000i		−	0.0641500i
$244$	−15.8338			−1.01365
$245$		0			0
$246$	−16.3923			−1.04514
$247$			1.51575i			0.0964448i
$248$		−	3.80385i		−	0.241545i
$249$	6.00000			0.380235
$250$	10.0382	+	19.1244i	0.634871	+	1.20953i
$251$	9.04008			0.570605			0.285303	−	0.958438i	$-0.407906\pi$
$251$	9.04008			0.570605			0.285303	+	0.958438i	$0.407906\pi$
$252$		0			0
$253$		−	21.8695i		−	1.37493i
$254$	−5.46410			−0.342848
$255$	5.65685	+	6.92820i	0.354246	+	0.433861i
$256$	19.3923			1.21202
$257$		−	3.46410i		−	0.216085i	−0.994146	−	0.108042i	$-0.965542\pi$
$257$		−	3.46410i		−	0.216085i	0.994146	−	0.108042i	$-0.0344582\pi$
$258$		0			0
$259$		0			0
$260$	−12.0000	+	9.79796i	−0.744208	+	0.607644i
$261$	8.92820			0.552642
$262$			10.9282i			0.675147i
$263$			21.7680i			1.34227i	0.741334	+	0.671136i	$0.234194\pi$
$263$			21.7680i			1.34227i	−0.741334	+	0.671136i	$0.765806\pi$
$264$	−1.79315			−0.110361
$265$	−12.7279	+	10.3923i	−0.781870	+	0.638394i
$266$		0			0
$267$		−	4.14110i		−	0.253431i
$268$		−	12.0716i		−	0.737389i
$269$	−8.28221			−0.504975			−0.252488	−	0.967600i	$-0.581249\pi$
$269$	−8.28221			−0.504975			−0.252488	+	0.967600i	$0.581249\pi$
$270$	2.73205	+	3.34607i	0.166267	+	0.203635i
$271$	−13.0053			−0.790017			−0.395009	−	0.918677i	$-0.629258\pi$
$271$	−13.0053			−0.790017			−0.395009	+	0.918677i	$0.629258\pi$
$272$			17.8564i			1.08270i
$273$		0			0
$274$	8.73205			0.527522
$275$	3.46410	−	16.9706i	0.208893	−	1.02336i
$276$	−10.9348			−0.658196
$277$		−	11.3137i		−	0.679775i	−0.940466	−	0.339887i	$-0.889611\pi$
$277$		−	11.3137i		−	0.679775i	0.940466	−	0.339887i	$-0.110389\pi$
$278$		−	10.1962i		−	0.611525i
$279$	7.34847			0.439941
$280$		0			0
$281$	0.143594			0.00856607			0.00428304	−	0.999991i	$-0.498637\pi$
$281$	0.143594			0.00856607			0.00428304	+	0.999991i	$0.498637\pi$
$282$		−	11.5911i		−	0.690241i
$283$			29.8564i			1.77478i	0.461020	+	0.887390i	$0.347484\pi$
$283$			29.8564i			1.77478i	−0.461020	+	0.887390i	$0.652516\pi$
$284$	−24.9282			−1.47922
$285$	−0.656339	+	0.535898i	−0.0388782	+	0.0317439i
$286$	26.7685			1.58286
$287$		0			0
$288$			7.58871i			0.447169i
$289$	1.00000			0.0588235
$290$	−29.8744	+	24.3923i	−1.75428	+	1.43237i
$291$	−5.07180			−0.297314
$292$		−	18.9282i		−	1.10769i
$293$			4.53590i			0.264990i	0.991184	+	0.132495i	$0.0422989\pi$
$293$			4.53590i			0.264990i	−0.991184	+	0.132495i	$0.957701\pi$
$294$		0			0
$295$	14.9282	+	18.2832i	0.869154	+	1.06449i
$296$	−0.392305			−0.0228023
$297$		−	3.46410i		−	0.201008i
$298$		−	40.4302i		−	2.34206i
$299$	−25.2528			−1.46041
$300$	−8.48528	−	1.73205i	−0.489898	−	0.100000i
$301$		0			0
$302$		−	24.2175i		−	1.39356i
$303$			12.6264i			0.725367i
$304$	−1.69161			−0.0970208
$305$	−12.9282	−	15.8338i	−0.740267	−	0.906638i
$306$	−7.72741			−0.441746
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		0			0
$309$	−13.8564			−0.788263
$310$	−24.5885	+	20.0764i	−1.39653	+	1.14026i
$311$	15.4548			0.876362			0.438181	−	0.898887i	$-0.355623\pi$
$311$	15.4548			0.876362			0.438181	+	0.898887i	$0.355623\pi$
$312$			2.07055i			0.117222i
$313$			10.9282i			0.617699i	0.951111	+	0.308849i	$0.0999439\pi$
$313$			10.9282i			0.617699i	−0.951111	+	0.308849i	$0.900056\pi$
$314$	36.5665			2.06357
$315$		0			0
$316$	−19.8564			−1.11701
$317$		−	29.2180i		−	1.64105i	−0.571613	−	0.820524i	$-0.693682\pi$
$317$		−	29.2180i		−	1.64105i	0.571613	−	0.820524i	$-0.306318\pi$
$318$		−	14.1962i		−	0.796081i
$319$	30.9282			1.73165
$320$	−8.10634	−	9.92820i	−0.453158	−	0.555003i
$321$	15.5563			0.868271
$322$		0			0
$323$		−	1.51575i		−	0.0843386i
$324$	−1.73205			−0.0962250
$325$	−19.5959	−	4.00000i	−1.08699	−	0.221880i
$326$	32.3923			1.79404
$327$		−	11.8564i		−	0.655661i
$328$		−	4.39230i		−	0.242524i
$329$		0			0
$330$	9.46410	+	11.5911i	0.520982	+	0.638070i
$331$	32.7846			1.80201			0.901003	−	0.433814i	$-0.142832\pi$
$331$	32.7846			1.80201			0.901003	+	0.433814i	$0.142832\pi$
$332$		−	10.3923i		−	0.570352i
$333$		−	0.757875i		−	0.0415313i
$334$	9.79796			0.536120
$335$	12.0716	−	9.85641i	0.659541	−	0.538513i
$336$		0			0
$337$		−	27.5264i		−	1.49946i	−0.661745	−	0.749729i	$-0.730184\pi$
$337$		−	27.5264i		−	1.49946i	0.661745	−	0.749729i	$-0.269816\pi$
$338$		−	5.79555i		−	0.315237i
$339$	0.378937			0.0205811
$340$	12.0000	−	9.79796i	0.650791	−	0.531369i
$341$	25.4558			1.37851
$342$		−	0.732051i		−	0.0395848i
$343$		0			0
$344$		0			0
$345$	−8.92820	−	10.9348i	−0.480678	−	0.588708i
$346$	−30.9096			−1.66171
$347$		−	11.4152i		−	0.612802i	−0.951902	−	0.306401i	$-0.900875\pi$
$347$		−	11.4152i		−	0.612802i	0.951902	−	0.306401i	$-0.0991249\pi$
$348$		−	15.4641i		−	0.828963i
$349$	−7.82894			−0.419074			−0.209537	−	0.977801i	$-0.567196\pi$
$349$	−7.82894			−0.419074			−0.209537	+	0.977801i	$0.567196\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$			26.2880i			1.40116i
$353$			4.53590i			0.241422i	0.992688	+	0.120711i	$0.0385174\pi$
$353$			4.53590i			0.241422i	−0.992688	+	0.120711i	$0.961483\pi$
$354$	−20.3923			−1.08384
$355$	−20.3538	−	24.9282i	−1.08027	−	1.32305i
$356$	−7.17260			−0.380147
$357$		0			0
$358$			20.0764i			1.06107i
$359$	−8.53590			−0.450507			−0.225254	−	0.974300i	$-0.572321\pi$
$359$	−8.53590			−0.450507			−0.225254	+	0.974300i	$0.572321\pi$
$360$	−0.896575	+	0.732051i	−0.0472537	+	0.0385825i
$361$	−18.8564			−0.992442
$362$		−	6.73205i		−	0.353829i
$363$		−	1.00000i		−	0.0524864i
$364$		0			0
$365$	18.9282	−	15.4548i	0.990747	−	0.808942i
$366$	17.6603			0.923116
$367$		−	4.00000i		−	0.208798i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$		−	4.00000i		−	0.208798i	0.994535	−	0.104399i	$-0.0332919\pi$
$368$		−	28.1827i		−	1.46913i
$369$	8.48528			0.441726
$370$	2.07055	+	2.53590i	0.107643	+	0.131835i
$371$		0			0
$372$		−	12.7279i		−	0.659912i
$373$		−	26.7685i		−	1.38602i	−0.720927	−	0.693011i	$-0.756284\pi$
$373$		−	26.7685i		−	1.38602i	0.720927	−	0.693011i	$-0.243716\pi$
$374$	−26.7685			−1.38417
$375$	−5.19615	−	9.89949i	−0.268328	−	0.511208i
$376$	3.10583			0.160171
$377$		−	35.7128i		−	1.83930i
$378$		0			0
$379$	−4.53590			−0.232993			−0.116497	−	0.993191i	$-0.537166\pi$
$379$	−4.53590			−0.232993			−0.116497	+	0.993191i	$0.537166\pi$
$380$	0.928203	+	1.13681i	0.0476158	+	0.0583172i
$381$	2.82843			0.144905
$382$		−	1.03528i		−	0.0529693i
$383$			3.85641i			0.197053i	0.995134	+	0.0985266i	$0.0314129\pi$
$383$			3.85641i			0.197053i	−0.995134	+	0.0985266i	$0.968587\pi$
$384$	−4.10394			−0.209428
$385$		0			0
$386$	−31.3205			−1.59417
$387$		0			0
$388$			8.78461i			0.445971i
$389$	−24.9282			−1.26391			−0.631955	−	0.775005i	$-0.717747\pi$
$389$	−24.9282			−1.26391			−0.631955	+	0.775005i	$0.717747\pi$
$390$	13.3843	−	10.9282i	0.677738	−	0.553371i
$391$	25.2528			1.27709
$392$		0			0
$393$		−	5.65685i		−	0.285351i
$394$	−22.1962			−1.11823
$395$	−16.2127	−	19.8564i	−0.815749	−	0.999084i
$396$	−6.00000			−0.301511
$397$			31.7128i			1.59162i	0.605546	+	0.795810i	$0.292955\pi$
$397$			31.7128i			1.59162i	−0.605546	+	0.795810i	$0.707045\pi$
$398$			6.19615i			0.310585i
$399$		0			0
$400$	4.46410	−	21.8695i	0.223205	−	1.09348i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$			13.4641i			0.671528i
$403$		−	29.3939i		−	1.46421i
$404$	21.8695			1.08805
$405$	−1.41421	−	1.73205i	−0.0702728	−	0.0860663i
$406$		0			0
$407$		−	2.62536i		−	0.130134i
$408$		−	2.07055i		−	0.102508i
$409$	−31.0112			−1.53340			−0.766702	−	0.642004i	$-0.778103\pi$
$409$	−31.0112			−1.53340			−0.766702	+	0.642004i	$0.778103\pi$
$410$	−28.3923	+	23.1822i	−1.40220	+	1.14489i
$411$	−4.52004			−0.222957
$412$			24.0000i			1.18240i
$413$		0			0
$414$	12.1962			0.599408
$415$	10.3923	−	8.48528i	0.510138	−	0.416526i
$416$	30.3548			1.48827
$417$			5.27792i			0.258461i
$418$		−	2.53590i		−	0.124035i
$419$	−1.51575			−0.0740492			−0.0370246	−	0.999314i	$-0.511788\pi$
$419$	−1.51575			−0.0740492			−0.0370246	+	0.999314i	$0.511788\pi$
$420$		0			0
$421$	−28.7846			−1.40288			−0.701438	−	0.712730i	$-0.747458\pi$
$421$	−28.7846			−1.40288			−0.701438	+	0.712730i	$0.747458\pi$
$422$		−	25.2528i		−	1.22929i
$423$			6.00000i			0.291730i
$424$	3.80385			0.184731
$425$	19.5959	+	4.00000i	0.950542	+	0.194029i
$426$	27.8038			1.34710
$427$		0			0
$428$		−	26.9444i		−	1.30241i
$429$	−13.8564			−0.668994
$430$		0			0
$431$	2.67949			0.129067			0.0645333	−	0.997916i	$-0.479444\pi$
$431$	2.67949			0.129067			0.0645333	+	0.997916i	$0.479444\pi$
$432$		−	4.46410i		−	0.214779i
$433$			9.85641i			0.473669i	0.971550	+	0.236834i	$0.0761099\pi$
$433$			9.85641i			0.473669i	−0.971550	+	0.236834i	$0.923890\pi$
$434$		0			0
$435$	15.4641	−	12.6264i	0.741447	−	0.605389i
$436$	−20.5359			−0.983491
$437$			2.39230i			0.114439i
$438$			21.1117i			1.00875i
$439$	−1.69161			−0.0807364			−0.0403682	−	0.999185i	$-0.512853\pi$
$439$	−1.69161			−0.0807364			−0.0403682	+	0.999185i	$0.512853\pi$
$440$	−3.10583	+	2.53590i	−0.148065	+	0.120894i
$441$		0			0
$442$			30.9096i			1.47022i
$443$			26.6670i			1.26699i	0.773748	+	0.633493i	$0.218380\pi$
$443$			26.6670i			1.26699i	−0.773748	+	0.633493i	$0.781620\pi$
$444$	−1.31268			−0.0622969
$445$	−5.85641	−	7.17260i	−0.277620	−	0.340014i
$446$	−15.4548			−0.731807
$447$			20.9282i			0.989870i
$448$		0			0
$449$	−8.14359			−0.384320			−0.192160	−	0.981364i	$-0.561549\pi$
$449$	−8.14359			−0.384320			−0.192160	+	0.981364i	$0.561549\pi$
$450$	9.46410	+	1.93185i	0.446142	+	0.0910684i
$451$	29.3939			1.38410
$452$		−	0.656339i		−	0.0308716i
$453$			12.5359i			0.588988i
$454$	7.72741			0.362665
$455$		0			0
$456$	0.196152			0.00918568
$457$		−	12.0716i		−	0.564685i	−0.959314	−	0.282342i	$-0.908889\pi$
$457$		−	12.0716i		−	0.564685i	0.959314	−	0.282342i	$-0.0911114\pi$
$458$		−	44.9808i		−	2.10181i
$459$	4.00000			0.186704
$460$	−18.9396	+	15.4641i	−0.883062	+	0.721017i
$461$	−12.8295			−0.597527			−0.298764	−	0.954327i	$-0.596574\pi$
$461$	−12.8295			−0.597527			−0.298764	+	0.954327i	$0.596574\pi$
$462$		0			0
$463$			16.7675i			0.779251i	0.920973	+	0.389626i	$0.127396\pi$
$463$			16.7675i			0.779251i	−0.920973	+	0.389626i	$0.872604\pi$
$464$	39.8564			1.85029
$465$	12.7279	−	10.3923i	0.590243	−	0.481932i
$466$	−0.732051			−0.0339116
$467$		−	17.8564i		−	0.826296i	−0.910664	−	0.413148i	$-0.864429\pi$
$467$		−	17.8564i		−	0.826296i	0.910664	−	0.413148i	$-0.135571\pi$
$468$			6.92820i			0.320256i
$469$		0			0
$470$	−16.3923	−	20.0764i	−0.756121	−	0.926055i
$471$	−18.9282			−0.872166
$472$		−	5.46410i		−	0.251506i
$473$		0			0
$474$	22.1469			1.01724
$475$	−0.378937	+	1.85641i	−0.0173868	+	0.0851778i
$476$		0			0
$477$			7.34847i			0.336463i
$478$			29.8744i			1.36642i
$479$	13.9391			0.636892			0.318446	−	0.947941i	$-0.396839\pi$
$479$	13.9391			0.636892			0.318446	+	0.947941i	$0.396839\pi$
$480$	10.7321	+	13.1440i	0.489849	+	0.599940i
$481$	−3.03150			−0.138224
$482$			10.7321i			0.488832i
$483$		0			0
$484$	−1.73205			−0.0787296
$485$	−8.78461	+	7.17260i	−0.398889	+	0.325691i
$486$	1.93185			0.0876306
$487$		−	4.14110i		−	0.187651i	−0.995589	−	0.0938257i	$-0.970090\pi$
$487$		−	4.14110i		−	0.187651i	0.995589	−	0.0938257i	$-0.0299096\pi$
$488$			4.73205i			0.214210i
$489$	−16.7675			−0.758252
$490$		0			0
$491$	6.67949			0.301441			0.150721	−	0.988576i	$-0.451841\pi$
$491$	6.67949			0.301441			0.150721	+	0.988576i	$0.451841\pi$
$492$		−	14.6969i		−	0.662589i
$493$			35.7128i			1.60842i
$494$	−2.92820			−0.131746
$495$	−4.89898	−	6.00000i	−0.220193	−	0.269680i
$496$	32.8043			1.47296
$497$		0			0
$498$			11.5911i			0.519410i
$499$	−16.2487			−0.727392			−0.363696	−	0.931518i	$-0.618485\pi$
$499$	−16.2487			−0.727392			−0.363696	+	0.931518i	$0.618485\pi$
$500$	−17.1464	+	9.00000i	−0.766812	+	0.402492i
$501$	−5.07180			−0.226591
$502$			17.4641i			0.779461i
$503$		−	3.85641i		−	0.171949i	−0.996297	−	0.0859743i	$-0.972600\pi$
$503$		−	3.85641i		−	0.171949i	0.996297	−	0.0859743i	$-0.0274003\pi$
$504$		0			0
$505$	17.8564	+	21.8695i	0.794600	+	0.973182i
$506$	42.2487			1.87818
$507$			3.00000i			0.133235i
$508$		−	4.89898i		−	0.217357i
$509$	−42.2233			−1.87152			−0.935758	−	0.352642i	$-0.885283\pi$
$509$	−42.2233			−1.87152			−0.935758	+	0.352642i	$0.885283\pi$
$510$	−13.3843	+	10.9282i	−0.592665	+	0.483909i
$511$		0			0
$512$			29.2552i			1.29291i
$513$			0.378937i			0.0167305i
$514$	6.69213			0.295177
$515$	−24.0000	+	19.5959i	−1.05757	+	0.863499i
$516$		0			0
$517$			20.7846i			0.914106i
$518$		0			0
$519$	16.0000			0.702322
$520$	2.92820	+	3.58630i	0.128410	+	0.157270i
$521$	28.2843			1.23916			0.619578	−	0.784935i	$-0.287304\pi$
$521$	28.2843			1.23916			0.619578	+	0.784935i	$0.287304\pi$
$522$			17.2480i			0.754923i
$523$			11.7128i			0.512166i	0.966655	+	0.256083i	$0.0824320\pi$
$523$			11.7128i			0.512166i	−0.966655	+	0.256083i	$0.917568\pi$
$524$	−9.79796			−0.428026
$525$		0			0
$526$	−42.0526			−1.83358
$527$			29.3939i			1.28042i
$528$		−	15.4641i		−	0.672989i
$529$	−16.8564			−0.732887
$530$	−20.0764	−	24.5885i	−0.872063	−	1.06805i
$531$	10.5558			0.458084
$532$		0			0
$533$		−	33.9411i		−	1.47015i
$534$	8.00000			0.346194
$535$	26.9444	−	22.0000i	1.16491	−	0.951143i
$536$	−3.60770			−0.155829
$537$		−	10.3923i		−	0.448461i
$538$		−	16.0000i		−	0.689809i
$539$		0			0
$540$	−3.00000	+	2.44949i	−0.129099	+	0.105409i
$541$	−42.6410			−1.83328			−0.916640	−	0.399713i	$-0.869110\pi$
$541$	−42.6410			−1.83328			−0.916640	+	0.399713i	$0.869110\pi$
$542$		−	25.1244i		−	1.07918i
$543$			3.48477i			0.149546i
$544$	−30.3548			−1.30145
$545$	−16.7675	−	20.5359i	−0.718240	−	0.879661i
$546$		0			0
$547$			29.5969i			1.26547i	0.774367	+	0.632737i	$0.218069\pi$
$547$			29.5969i			1.26547i	−0.774367	+	0.632737i	$0.781931\pi$
$548$			7.82894i			0.334436i
$549$	−9.14162			−0.390155
$550$	32.7846	+	6.69213i	1.39794	+	0.285353i
$551$	−3.38323			−0.144130
$552$			3.26795i			0.139093i
$553$		0			0
$554$	21.8564			0.928590
$555$	−1.07180	−	1.31268i	−0.0454952	−	0.0557201i
$556$	9.14162			0.387691
$557$			13.7632i			0.583165i	0.956546	+	0.291583i	$0.0941819\pi$
$557$			13.7632i			0.583165i	−0.956546	+	0.291583i	$0.905818\pi$
$558$			14.1962i			0.600971i
$559$		0			0
$560$		0			0
$561$	13.8564			0.585018
$562$			0.277401i			0.0117015i
$563$			31.8564i			1.34259i	0.741191	+	0.671294i	$0.234261\pi$
$563$			31.8564i			1.34259i	−0.741191	+	0.671294i	$0.765739\pi$
$564$	10.3923			0.437595
$565$	0.656339	−	0.535898i	0.0276124	−	0.0225454i
$566$	−57.6781			−2.42439
$567$		0			0
$568$			7.45001i			0.312595i
$569$	−11.8564			−0.497046			−0.248523	−	0.968626i	$-0.579945\pi$
$569$	−11.8564			−0.497046			−0.248523	+	0.968626i	$0.579945\pi$
$570$	−1.03528	−	1.26795i	−0.0433629	−	0.0531085i
$571$	39.7128			1.66193			0.830965	−	0.556325i	$-0.187789\pi$
$571$	39.7128			1.66193			0.830965	+	0.556325i	$0.187789\pi$
$572$			24.0000i			1.00349i
$573$			0.535898i			0.0223875i
$574$		0			0
$575$	−30.9282	−	6.31319i	−1.28980	−	0.263278i
$576$	−5.73205			−0.238835
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$			1.93185i			0.0803544i
$579$	16.2127			0.673776
$580$	−21.8695	−	26.7846i	−0.908083	−	1.11217i
$581$		0			0
$582$		−	9.79796i		−	0.406138i
$583$			25.4558i			1.05427i
$584$	−5.65685			−0.234082
$585$	−6.92820	+	5.65685i	−0.286446	+	0.233882i
$586$	−8.76268			−0.361983
$587$			31.8564i			1.31485i	0.753518	+	0.657427i	$0.228355\pi$
$587$			31.8564i			1.31485i	−0.753518	+	0.657427i	$0.771645\pi$
$588$		0			0
$589$	−2.78461			−0.114738
$590$	−35.3205	+	28.8391i	−1.45412	+	1.18729i
$591$	11.4896			0.472618
$592$		−	3.38323i		−	0.139050i
$593$		−	9.32051i		−	0.382747i	−0.981517	−	0.191374i	$-0.938706\pi$
$593$		−	9.32051i		−	0.382747i	0.981517	−	0.191374i	$-0.0612942\pi$
$594$	6.69213			0.274581
$595$		0			0
$596$	36.2487			1.48481
$597$		−	3.20736i		−	0.131269i
$598$		−	48.7846i		−	1.99495i
$599$	5.32051			0.217390			0.108695	−	0.994075i	$-0.465333\pi$
$599$	5.32051			0.217390			0.108695	+	0.994075i	$0.465333\pi$
$600$	−0.517638	+	2.53590i	−0.0211325	+	0.103528i
$601$	−33.6365			−1.37206			−0.686031	−	0.727572i	$-0.740649\pi$
$601$	−33.6365			−1.37206			−0.686031	+	0.727572i	$0.740649\pi$
$602$		0			0
$603$		−	6.96953i		−	0.283821i
$604$	21.7128			0.883482
$605$	−1.41421	−	1.73205i	−0.0574960	−	0.0704179i
$606$	−24.3923			−0.990870
$607$			12.0000i			0.487065i	0.969893	+	0.243532i	$0.0783062\pi$
$607$			12.0000i			0.487065i	−0.969893	+	0.243532i	$0.921694\pi$
$608$		−	2.87564i		−	0.116623i
$609$		0			0
$610$	30.5885	−	24.9754i	1.23849	−	1.01122i
$611$	24.0000			0.970936
$612$		−	6.92820i		−	0.280056i
$613$			9.79796i			0.395736i	0.980229	+	0.197868i	$0.0634017\pi$
$613$			9.79796i			0.395736i	−0.980229	+	0.197868i	$0.936598\pi$
$614$	−7.72741			−0.311853
$615$	14.6969	−	12.0000i	0.592638	−	0.483887i
$616$		0			0
$617$			12.4505i			0.501239i	0.968086	+	0.250620i	$0.0806343\pi$
$617$			12.4505i			0.501239i	−0.968086	+	0.250620i	$0.919366\pi$
$618$		−	26.7685i		−	1.07679i
$619$	3.76217			0.151214			0.0756071	−	0.997138i	$-0.475911\pi$
$619$	3.76217			0.151214			0.0756071	+	0.997138i	$0.475911\pi$
$620$	−18.0000	−	22.0454i	−0.722897	−	0.885365i
$621$	−6.31319			−0.253340
$622$			29.8564i			1.19713i
$623$		0			0
$624$	−17.8564			−0.714828
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	−21.1117			−0.843792
$627$			1.31268i			0.0524233i
$628$			32.7846i			1.30825i
$629$	3.03150			0.120874
$630$		0			0
$631$	9.32051			0.371044			0.185522	−	0.982640i	$-0.440602\pi$
$631$	9.32051			0.371044			0.185522	+	0.982640i	$0.440602\pi$
$632$			5.93426i			0.236052i
$633$			13.0718i			0.519557i
$634$	56.4449			2.24171
$635$	4.89898	−	4.00000i	0.194410	−	0.158735i
$636$	12.7279			0.504695
$637$		0			0
$638$			59.7487i			2.36547i
$639$	−14.3923			−0.569351
$640$	−7.10823	+	5.80385i	−0.280978	+	0.229417i
$641$	10.0000			0.394976			0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000			0.394976			0.197488	+	0.980305i	$0.436722\pi$
$642$			30.0526i			1.18608i
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$		0			0
$645$		0			0
$646$	2.92820			0.115209
$647$			29.0718i			1.14293i	0.820626	+	0.571465i	$0.193625\pi$
$647$			29.0718i			1.14293i	−0.820626	+	0.571465i	$0.806375\pi$
$648$			0.517638i			0.0203347i
$649$	36.5665			1.43536
$650$	7.72741	−	37.8564i	0.303094	−	1.48485i
$651$		0			0
$652$			29.0421i			1.13738i
$653$			18.6622i			0.730307i	0.930947	+	0.365154i	$0.118984\pi$
$653$			18.6622i			0.730307i	−0.930947	+	0.365154i	$0.881016\pi$
$654$	22.9048			0.895649
$655$	−8.00000	−	9.79796i	−0.312586	−	0.382838i
$656$	37.8792			1.47893
$657$		−	10.9282i		−	0.426350i
$658$		0			0
$659$	10.3923			0.404827			0.202413	−	0.979300i	$-0.435122\pi$
$659$	10.3923			0.404827			0.202413	+	0.979300i	$0.435122\pi$
$660$	−10.3923	+	8.48528i	−0.404520	+	0.330289i
$661$	−23.2838			−0.905633			−0.452817	−	0.891604i	$-0.649581\pi$
$661$	−23.2838			−0.905633			−0.452817	+	0.891604i	$0.649581\pi$
$662$			63.3350i			2.46158i
$663$		−	16.0000i		−	0.621389i
$664$	−3.10583			−0.120530
$665$		0			0
$666$	1.46410			0.0567328
$667$		−	56.3655i		−	2.18248i
$668$			8.78461i			0.339887i
$669$	8.00000			0.309298
$670$	19.0411	+	23.3205i	0.735622	+	0.900950i
$671$	−31.6675			−1.22251
$672$		0			0
$673$		−	12.0716i		−	0.465325i	−0.972557	−	0.232663i	$-0.925256\pi$
$673$		−	12.0716i		−	0.465325i	0.972557	−	0.232663i	$-0.0747438\pi$
$674$	53.1769			2.04830
$675$	−4.89898	−	1.00000i	−0.188562	−	0.0384900i
$676$	5.19615			0.199852
$677$		−	39.1769i		−	1.50569i	−0.658197	−	0.752846i	$-0.728681\pi$
$677$		−	39.1769i		−	1.50569i	0.658197	−	0.752846i	$-0.271319\pi$
$678$			0.732051i			0.0281142i
$679$		0			0
$680$	−2.92820	−	3.58630i	−0.112291	−	0.137528i
$681$	−4.00000			−0.153280
$682$			49.1769i			1.88308i
$683$			22.7290i			0.869699i	0.900503	+	0.434850i	$0.143198\pi$
$683$			22.7290i			0.869699i	−0.900503	+	0.434850i	$0.856802\pi$
$684$	0.656339			0.0250957
$685$	−7.82894	+	6.39230i	−0.299129	+	0.244237i
$686$		0			0
$687$			23.2838i			0.888331i
$688$		0			0
$689$	29.3939			1.11982
$690$	21.1244	−	17.2480i	0.804190	−	0.656619i
$691$	−6.03579			−0.229612			−0.114806	−	0.993388i	$-0.536625\pi$
$691$	−6.03579			−0.229612			−0.114806	+	0.993388i	$0.536625\pi$
$692$		−	27.7128i		−	1.05348i
$693$		0			0
$694$	22.0526			0.837104
$695$	7.46410	+	9.14162i	0.283130	+	0.346761i
$696$	−4.62158			−0.175180
$697$			33.9411i			1.28561i
$698$		−	15.1244i		−	0.572465i
$699$	0.378937			0.0143327
$700$		0			0
$701$	−24.9282			−0.941525			−0.470763	−	0.882260i	$-0.656021\pi$
$701$	−24.9282			−0.941525			−0.470763	+	0.882260i	$0.656021\pi$
$702$		−	7.72741i		−	0.291652i
$703$			0.287187i			0.0108315i
$704$	−19.8564			−0.748366
$705$	8.48528	+	10.3923i	0.319574	+	0.391397i
$706$	−8.76268			−0.329788
$707$		0			0
$708$		−	18.2832i		−	0.687126i
$709$	−2.92820			−0.109971			−0.0549855	−	0.998487i	$-0.517511\pi$
$709$	−2.92820			−0.109971			−0.0549855	+	0.998487i	$0.517511\pi$
$710$	48.1576	−	39.3205i	1.80732	−	1.47567i
$711$	−11.4641			−0.429937
$712$			2.14359i			0.0803346i
$713$		−	46.3923i		−	1.73741i
$714$		0			0
$715$	−24.0000	+	19.5959i	−0.897549	+	0.732846i
$716$	−18.0000			−0.672692
$717$		−	15.4641i		−	0.577517i
$718$		−	16.4901i		−	0.615405i
$719$	−14.6969			−0.548103			−0.274052	−	0.961715i	$-0.588364\pi$
$719$	−14.6969			−0.548103			−0.274052	+	0.961715i	$0.588364\pi$
$720$	−6.31319	−	7.73205i	−0.235279	−	0.288157i
$721$		0			0
$722$		−	36.4278i		−	1.35570i
$723$		−	5.55532i		−	0.206605i
$724$	6.03579			0.224318
$725$	8.92820	−	43.7391i	0.331585	−	1.62443i
$726$	1.93185			0.0716977
$727$		−	31.7128i		−	1.17616i	−0.808802	−	0.588082i	$-0.799883\pi$
$727$		−	31.7128i		−	1.17616i	0.808802	−	0.588082i	$-0.200117\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	29.8564	+	36.5665i	1.10504	+	1.35339i
$731$		0			0
$732$			15.8338i			0.585232i
$733$		−	9.85641i		−	0.364055i	−0.983293	−	0.182027i	$-0.941734\pi$
$733$		−	9.85641i		−	0.364055i	0.983293	−	0.182027i	$-0.0582659\pi$
$734$	7.72741			0.285224
$735$		0			0
$736$	47.9090			1.76595
$737$		−	24.1432i		−	0.889325i
$738$			16.3923i			0.603409i
$739$	−1.85641			−0.0682890			−0.0341445	−	0.999417i	$-0.510871\pi$
$739$	−1.85641			−0.0682890			−0.0341445	+	0.999417i	$0.510871\pi$
$740$	−2.27362	+	1.85641i	−0.0835801	+	0.0682429i
$741$	1.51575			0.0556825
$742$		0			0
$743$		−	37.0197i		−	1.35812i	−0.734081	−	0.679061i	$-0.762387\pi$
$743$		−	37.0197i		−	1.35812i	0.734081	−	0.679061i	$-0.237613\pi$
$744$	−3.80385			−0.139456
$745$	29.5969	+	36.2487i	1.08435	+	1.32805i
$746$	51.7128			1.89334
$747$		−	6.00000i		−	0.219529i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	19.1244	−	10.0382i	0.698323	−	0.366543i
$751$	4.78461			0.174593			0.0872964	−	0.996182i	$-0.472177\pi$
$751$	4.78461			0.174593			0.0872964	+	0.996182i	$0.472177\pi$
$752$			26.7846i			0.976734i
$753$		−	9.04008i		−	0.329439i
$754$	68.9919			2.51254
$755$	17.7284	+	21.7128i	0.645204	+	0.790210i
$756$		0			0
$757$		−	34.2929i		−	1.24640i	−0.782064	−	0.623198i	$-0.785833\pi$
$757$		−	34.2929i		−	1.24640i	0.782064	−	0.623198i	$-0.214167\pi$
$758$		−	8.76268i		−	0.318275i
$759$	−21.8695			−0.793814
$760$	0.339746	−	0.277401i	0.0123239	−	0.0100624i
$761$	40.7076			1.47565			0.737824	−	0.674993i	$-0.235853\pi$
$761$	40.7076			1.47565			0.737824	+	0.674993i	$0.235853\pi$
$762$			5.46410i			0.197944i
$763$		0			0
$764$	0.928203			0.0335812
$765$	6.92820	−	5.65685i	0.250490	−	0.204524i
$766$	−7.45001			−0.269180
$767$		−	42.2233i		−	1.52460i
$768$		−	19.3923i		−	0.699760i
$769$	−19.4944			−0.702985			−0.351493	−	0.936191i	$-0.614326\pi$
$769$	−19.4944			−0.702985			−0.351493	+	0.936191i	$0.614326\pi$
$770$		0			0
$771$	−3.46410			−0.124757
$772$		−	28.0812i		−	1.01066i
$773$			10.1436i			0.364840i	0.983221	+	0.182420i	$0.0583930\pi$
$773$			10.1436i			0.364840i	−0.983221	+	0.182420i	$0.941607\pi$
$774$		0			0
$775$	7.34847	−	36.0000i	0.263965	−	1.29316i
$776$	2.62536			0.0942448
$777$		0			0
$778$		−	48.1576i		−	1.72653i
$779$	−3.21539			−0.115203
$780$	9.79796	+	12.0000i	0.350823	+	0.429669i
$781$	−49.8564			−1.78400
$782$			48.7846i			1.74453i
$783$		−	8.92820i		−	0.319068i
$784$		0			0
$785$	−32.7846	+	26.7685i	−1.17013	+	0.955410i
$786$	10.9282			0.389796
$787$			18.1436i			0.646749i	0.946271	+	0.323375i	$0.104817\pi$
$787$			18.1436i			0.646749i	−0.946271	+	0.323375i	$0.895183\pi$
$788$		−	19.9005i		−	0.708927i
$789$	21.7680			0.774962
$790$	38.3596	−	31.3205i	1.36477	−	1.11433i
$791$		0			0
$792$			1.79315i			0.0637168i
$793$			36.5665i			1.29851i
$794$	−61.2645			−2.17419
$795$	10.3923	+	12.7279i	0.368577	+	0.451413i
$796$	−5.55532			−0.196903
$797$			37.8564i			1.34094i	0.741935	+	0.670471i	$0.233908\pi$
$797$			37.8564i			1.34094i	−0.741935	+	0.670471i	$0.766092\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	37.1769	+	7.58871i	1.31440	+	0.268301i
$801$	−4.14110			−0.146319
$802$			3.86370i			0.136432i
$803$		−	37.8564i		−	1.33592i
$804$	−12.0716			−0.425732
$805$		0			0
$806$	56.7846			2.00015
$807$			8.28221i			0.291548i
$808$		−	6.53590i		−	0.229932i
$809$	33.7128			1.18528			0.592640	−	0.805468i	$-0.298086\pi$
$809$	33.7128			1.18528			0.592640	+	0.805468i	$0.298086\pi$
$810$	3.34607	−	2.73205i	0.117569	−	0.0959945i
$811$	−8.66115			−0.304134			−0.152067	−	0.988370i	$-0.548593\pi$
$811$	−8.66115			−0.304134			−0.152067	+	0.988370i	$0.548593\pi$
$812$		0			0
$813$			13.0053i			0.456117i
$814$	5.07180			0.177766
$815$	−29.0421	+	23.7128i	−1.01730	+	0.830624i
$816$	17.8564			0.625099
$817$		0			0
$818$		−	59.9090i		−	2.09467i
$819$		0			0
$820$	−20.7846	−	25.4558i	−0.725830	−	0.888957i
$821$	−22.7846			−0.795188			−0.397594	−	0.917561i	$-0.630155\pi$
$821$	−22.7846			−0.795188			−0.397594	+	0.917561i	$0.630155\pi$
$822$		−	8.73205i		−	0.304565i
$823$			47.6771i			1.66192i	0.556332	+	0.830960i	$0.312208\pi$
$823$			47.6771i			1.66192i	−0.556332	+	0.830960i	$0.687792\pi$
$824$	7.17260			0.249869
$825$	−16.9706	−	3.46410i	−0.590839	−	0.120605i
$826$		0			0
$827$			50.6071i			1.75978i	0.475177	+	0.879890i	$0.342384\pi$
$827$			50.6071i			1.75978i	−0.475177	+	0.879890i	$0.657616\pi$
$828$			10.9348i			0.380010i
$829$	−35.9101			−1.24721			−0.623605	−	0.781739i	$-0.714333\pi$
$829$	−35.9101			−1.24721			−0.623605	+	0.781739i	$0.714333\pi$
$830$	16.3923	+	20.0764i	0.568985	+	0.696862i
$831$	−11.3137			−0.392468
$832$			22.9282i			0.794892i
$833$		0			0
$834$	−10.1962			−0.353064
$835$	−8.78461	+	7.17260i	−0.304004	+	0.248218i
$836$	2.27362			0.0786349
$837$		−	7.34847i		−	0.254000i
$838$		−	2.92820i		−	0.101153i
$839$	9.04008			0.312098			0.156049	−	0.987749i	$-0.450124\pi$
$839$	9.04008			0.312098			0.156049	+	0.987749i	$0.450124\pi$
$840$		0			0
$841$	50.7128			1.74872
$842$		−	55.6076i		−	1.91636i
$843$		−	0.143594i		−	0.00494562i
$844$	22.6410			0.779336
$845$	4.24264	+	5.19615i	0.145951	+	0.178753i
$846$	−11.5911			−0.398511
$847$		0			0
$848$			32.8043i			1.12650i
$849$	29.8564			1.02467
$850$	−7.72741	+	37.8564i	−0.265048	+	1.29846i
$851$	−4.78461			−0.164014
$852$			24.9282i			0.854026i
$853$			26.9282i			0.922004i	0.887399	+	0.461002i	$0.152510\pi$
$853$			26.9282i			0.922004i	−0.887399	+	0.461002i	$0.847490\pi$
$854$		0			0
$855$	0.535898	+	0.656339i	0.0183273	+	0.0224463i
$856$	−8.05256			−0.275231
$857$		−	17.8564i		−	0.609963i	−0.952358	−	0.304982i	$-0.901350\pi$
$857$		−	17.8564i		−	0.609963i	0.952358	−	0.304982i	$-0.0986503\pi$
$858$		−	26.7685i		−	0.913862i
$859$	−47.5013			−1.62072			−0.810361	−	0.585931i	$-0.800729\pi$
$859$	−47.5013			−1.62072			−0.810361	+	0.585931i	$0.800729\pi$
$860$		0			0
$861$		0			0
$862$			5.17638i			0.176308i
$863$		−	52.6776i		−	1.79317i	−0.442874	−	0.896584i	$-0.646041\pi$
$863$		−	52.6776i		−	1.79317i	0.442874	−	0.896584i	$-0.353959\pi$
$864$	7.58871			0.258173
$865$	27.7128	−	22.6274i	0.942264	−	0.769355i
$866$	−19.0411			−0.647043
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	−39.7128			−1.34716
$870$	24.3923	+	29.8744i	0.826977	+	1.01284i
$871$	−27.8781			−0.944614
$872$			6.13733i			0.207836i
$873$			5.07180i			0.171654i
$874$	−4.62158			−0.156327
$875$		0			0
$876$	−18.9282			−0.639525
$877$		−	33.9411i		−	1.14611i	−0.819517	−	0.573055i	$-0.805758\pi$
$877$		−	33.9411i		−	1.14611i	0.819517	−	0.573055i	$-0.194242\pi$
$878$		−	3.26795i		−	0.110288i
$879$	4.53590			0.152992
$880$	−21.8695	−	26.7846i	−0.737222	−	0.902909i
$881$	10.0010			0.336943			0.168472	−	0.985707i	$-0.446117\pi$
$881$	10.0010			0.336943			0.168472	+	0.985707i	$0.446117\pi$
$882$		0			0
$883$			29.3939i			0.989183i	0.869126	+	0.494591i	$0.164682\pi$
$883$			29.3939i			0.989183i	−0.869126	+	0.494591i	$0.835318\pi$
$884$	−27.7128			−0.932083
$885$	18.2832	−	14.9282i	0.614584	−	0.501806i
$886$	−51.5167			−1.73074
$887$			41.7128i			1.40058i	0.713859	+	0.700290i	$0.246946\pi$
$887$			41.7128i			1.40058i	−0.713859	+	0.700290i	$0.753054\pi$
$888$			0.392305i			0.0131649i
$889$		0			0
$890$	13.8564	−	11.3137i	0.464468	−	0.379236i
$891$	−3.46410			−0.116052
$892$		−	13.8564i		−	0.463947i
$893$		−	2.27362i		−	0.0760839i
$894$	−40.4302			−1.35219
$895$	−14.6969	−	18.0000i	−0.491264	−	0.601674i
$896$		0			0
$897$			25.2528i			0.843166i
$898$		−	15.7322i		−	0.524991i
$899$	65.6086			2.18817
$900$	−1.73205	+	8.48528i	−0.0577350	+	0.282843i
$901$	−29.3939			−0.979252
$902$			56.7846i			1.89072i
$903$		0			0
$904$	−0.196152			−0.00652393
$905$	4.92820	+	6.03579i	0.163819	+	0.200637i
$906$	−24.2175			−0.804572
$907$		−	52.0213i		−	1.72734i	−0.504059	−	0.863669i	$-0.668161\pi$
$907$		−	52.0213i		−	1.72734i	0.504059	−	0.863669i	$-0.331839\pi$
$908$			6.92820i			0.229920i
$909$	12.6264			0.418791
$910$		0			0
$911$	30.3923			1.00694			0.503471	−	0.864012i	$-0.332056\pi$
$911$	30.3923			1.00694			0.503471	+	0.864012i	$0.332056\pi$
$912$			1.69161i			0.0560150i
$913$		−	20.7846i		−	0.687870i
$914$	23.3205			0.771374
$915$	−15.8338	+	12.9282i	−0.523448	+	0.427393i
$916$	40.3286			1.33250
$917$		0			0
$918$			7.72741i			0.255042i
$919$	22.9282			0.756332			0.378166	−	0.925738i	$-0.376555\pi$
$919$	22.9282			0.756332			0.378166	+	0.925738i	$0.376555\pi$
$920$	4.62158	+	5.66025i	0.152369	+	0.186613i
$921$	4.00000			0.131804
$922$		−	24.7846i		−	0.816238i
$923$			57.5692i			1.89491i
$924$		0			0
$925$	−3.71281	−	0.757875i	−0.122077	−	0.0249188i
$926$	−32.3923			−1.06448
$927$			13.8564i			0.455104i
$928$			67.7535i			2.22412i
$929$	40.7076			1.33557			0.667786	−	0.744353i	$-0.267242\pi$
$929$	40.7076			1.33557			0.667786	+	0.744353i	$0.267242\pi$
$930$	20.0764	+	24.5885i	0.658331	+	0.806287i
$931$		0			0
$932$		−	0.656339i		−	0.0214991i
$933$		−	15.4548i		−	0.505968i
$934$	34.4959			1.12874
$935$	24.0000	−	19.5959i	0.784884	−	0.640855i
$936$	2.07055			0.0676781
$937$		−	24.7846i		−	0.809678i	−0.914388	−	0.404839i	$-0.867328\pi$
$937$		−	24.7846i		−	0.809678i	0.914388	−	0.404839i	$-0.132672\pi$
$938$		0			0
$939$	10.9282			0.356628
$940$	18.0000	−	14.6969i	0.587095	−	0.479361i
$941$	−39.3949			−1.28424			−0.642119	−	0.766605i	$-0.721944\pi$
$941$	−39.3949			−1.28424			−0.642119	+	0.766605i	$0.721944\pi$
$942$		−	36.5665i		−	1.19140i
$943$		−	53.5692i		−	1.74445i
$944$	47.1223			1.53370
$945$		0			0
$946$		0			0
$947$			18.3848i			0.597425i	0.954343	+	0.298712i	$0.0965572\pi$
$947$			18.3848i			0.597425i	−0.954343	+	0.298712i	$0.903443\pi$
$948$			19.8564i			0.644906i
$949$	−43.7128			−1.41898
$950$	−3.58630	−	0.732051i	−0.116355	−	0.0237509i
$951$	−29.2180			−0.947459
$952$		0			0
$953$		−	19.6231i		−	0.635655i	−0.948148	−	0.317828i	$-0.897047\pi$
$953$		−	19.6231i		−	0.635655i	0.948148	−	0.317828i	$-0.102953\pi$
$954$	−14.1962			−0.459617
$955$	0.757875	+	0.928203i	0.0245243	+	0.0300360i
$956$	−26.7846			−0.866276
$957$		−	30.9282i		−	0.999767i
$958$			26.9282i			0.870011i
$959$		0			0
$960$	−9.92820	+	8.10634i	−0.320431	+	0.261631i
$961$	23.0000			0.741935
$962$		−	5.85641i		−	0.188818i
$963$		−	15.5563i		−	0.501296i
$964$	−9.62209			−0.309907
$965$	28.0812	−	22.9282i	0.903966	−	0.738085i
$966$		0			0
$967$			29.5969i			0.951774i	0.879507	+	0.475887i	$0.157873\pi$
$967$			29.5969i			0.951774i	−0.879507	+	0.475887i	$0.842127\pi$
$968$			0.517638i			0.0166375i
$969$	−1.51575			−0.0486929
$970$	−13.8564	−	16.9706i	−0.444902	−	0.544892i
$971$	−56.9203			−1.82666			−0.913329	−	0.407222i	$-0.866498\pi$
$971$	−56.9203			−1.82666			−0.913329	+	0.407222i	$0.866498\pi$
$972$			1.73205i			0.0555556i
$973$		0			0
$974$	8.00000			0.256337
$975$	−4.00000	+	19.5959i	−0.128103	+	0.627572i
$976$	−40.8091			−1.30627
$977$			50.5328i			1.61669i	0.588712	+	0.808343i	$0.299635\pi$
$977$			50.5328i			1.61669i	−0.588712	+	0.808343i	$0.700365\pi$
$978$		−	32.3923i		−	1.03579i
$979$	−14.3452			−0.458475
$980$		0			0
$981$	−11.8564			−0.378546
$982$			12.9038i			0.411776i
$983$			16.7846i			0.535346i	0.963510	+	0.267673i	$0.0862547\pi$
$983$			16.7846i			0.535346i	−0.963510	+	0.267673i	$0.913745\pi$
$984$	−4.39230			−0.140022
$985$	19.9005	−	16.2487i	0.634083	−	0.517727i
$986$	−68.9919			−2.19715
$987$		0			0
$988$		−	2.62536i		−	0.0835237i
$989$		0			0
$990$	11.5911	−	9.46410i	0.368390	−	0.300789i
$991$	−28.7846			−0.914373			−0.457187	−	0.889371i	$-0.651143\pi$
$991$	−28.7846			−0.914373			−0.457187	+	0.889371i	$0.651143\pi$
$992$			55.7654i			1.77055i
$993$		−	32.7846i		−	1.04039i
$994$		0			0
$995$	−4.53590	−	5.55532i	−0.143798	−	0.176115i
$996$	−10.3923			−0.329293
$997$		−	14.1436i		−	0.447932i	−0.974597	−	0.223966i	$-0.928100\pi$
$997$		−	14.1436i		−	0.447932i	0.974597	−	0.223966i	$-0.0719005\pi$
$998$		−	31.3901i		−	0.993636i
$999$	−0.757875			−0.0239781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.f.589.7	yes	8
3.2	odd	2		2205.2.d.t.1324.2		8
5.2	odd	4		3675.2.a.bs.1.1		4
5.3	odd	4		3675.2.a.bu.1.4		4
5.4	even	2	inner	735.2.d.f.589.2	yes	8
7.2	even	3		735.2.q.c.214.4		8
7.3	odd	6		735.2.q.c.79.1		8
7.4	even	3		735.2.q.d.79.1		8
7.5	odd	6		735.2.q.d.214.4		8
7.6	odd	2	inner	735.2.d.f.589.8	yes	8
15.14	odd	2		2205.2.d.t.1324.8		8
21.20	even	2		2205.2.d.t.1324.1		8
35.4	even	6		735.2.q.c.79.4		8
35.9	even	6		735.2.q.d.214.1		8
35.13	even	4		3675.2.a.bs.1.4		4
35.19	odd	6		735.2.q.c.214.1		8
35.24	odd	6		735.2.q.d.79.4		8
35.27	even	4		3675.2.a.bu.1.1		4
35.34	odd	2	inner	735.2.d.f.589.1	✓	8
105.104	even	2		2205.2.d.t.1324.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.f.589.1	✓	8	35.34	odd	2	inner
735.2.d.f.589.2	yes	8	5.4	even	2	inner
735.2.d.f.589.7	yes	8	1.1	even	1	trivial
735.2.d.f.589.8	yes	8	7.6	odd	2	inner
735.2.q.c.79.1		8	7.3	odd	6
735.2.q.c.79.4		8	35.4	even	6
735.2.q.c.214.1		8	35.19	odd	6
735.2.q.c.214.4		8	7.2	even	3
735.2.q.d.79.1		8	7.4	even	3
735.2.q.d.79.4		8	35.24	odd	6
735.2.q.d.214.1		8	35.9	even	6
735.2.q.d.214.4		8	7.5	odd	6
2205.2.d.t.1324.1		8	21.20	even	2
2205.2.d.t.1324.2		8	3.2	odd	2
2205.2.d.t.1324.7		8	105.104	even	2
2205.2.d.t.1324.8		8	15.14	odd	2
3675.2.a.bs.1.1		4	5.2	odd	4
3675.2.a.bs.1.4		4	35.13	even	4
3675.2.a.bu.1.1		4	35.27	even	4
3675.2.a.bu.1.4		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +(-1.41421 - 1.73205i) q^{5} +1.93185 q^{6} +0.517638i q^{8} -1.00000 q^{9} +(3.34607 - 2.73205i) q^{10} -3.46410 q^{11} +1.73205i q^{12} +4.00000i q^{13} +(-1.73205 + 1.41421i) q^{15} -4.46410 q^{16} -4.00000i q^{17} -1.93185i q^{18} +0.378937 q^{19} +(2.44949 + 3.00000i) q^{20} -6.69213i q^{22} +6.31319i q^{23} +0.517638 q^{24} +(-1.00000 + 4.89898i) q^{25} -7.72741 q^{26} +1.00000i q^{27} -8.92820 q^{29} +(-2.73205 - 3.34607i) q^{30} -7.34847 q^{31} -7.58871i q^{32} +3.46410i q^{33} +7.72741 q^{34} +1.73205 q^{36} +0.757875i q^{37} +0.732051i q^{38} +4.00000 q^{39} +(0.896575 - 0.732051i) q^{40} -8.48528 q^{41} +6.00000 q^{44} +(1.41421 + 1.73205i) q^{45} -12.1962 q^{46} -6.00000i q^{47} +4.46410i q^{48} +(-9.46410 - 1.93185i) q^{50} -4.00000 q^{51} -6.92820i q^{52} -7.34847i q^{53} -1.93185 q^{54} +(4.89898 + 6.00000i) q^{55} -0.378937i q^{57} -17.2480i q^{58} -10.5558 q^{59} +(3.00000 - 2.44949i) q^{60} +9.14162 q^{61} -14.1962i q^{62} +5.73205 q^{64} +(6.92820 - 5.65685i) q^{65} -6.69213 q^{66} +6.96953i q^{67} +6.92820i q^{68} +6.31319 q^{69} +14.3923 q^{71} -0.517638i q^{72} +10.9282i q^{73} -1.46410 q^{74} +(4.89898 + 1.00000i) q^{75} -0.656339 q^{76} +7.72741i q^{78} +11.4641 q^{79} +(6.31319 + 7.73205i) q^{80} +1.00000 q^{81} -16.3923i q^{82} +6.00000i q^{83} +(-6.92820 + 5.65685i) q^{85} +8.92820i q^{87} -1.79315i q^{88} +4.14110 q^{89} +(-3.34607 + 2.73205i) q^{90} -10.9348i q^{92} +7.34847i q^{93} +11.5911 q^{94} +(-0.535898 - 0.656339i) q^{95} -7.58871 q^{96} -5.07180i q^{97} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} - 8 q^{16} - 8 q^{25} - 16 q^{29} - 8 q^{30} + 32 q^{39} + 48 q^{44} - 56 q^{46} - 48 q^{50} - 32 q^{51} + 24 q^{60} + 32 q^{64} + 32 q^{71} + 16 q^{74} + 64 q^{79} + 8 q^{81} - 32 q^{95}+O(q^{100}) \) 8 * q - 8 * q^9 - 8 * q^16 - 8 * q^25 - 16 * q^29 - 8 * q^30 + 32 * q^39 + 48 * q^44 - 56 * q^46 - 48 * q^50 - 32 * q^51 + 24 * q^60 + 32 * q^64 + 32 * q^71 + 16 * q^74 + 64 * q^79 + 8 * q^81 - 32 * q^95

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