LMFDB - Embedded newform 1008.2.ca.e.257.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.10
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690387 - 1.58851i) q^{3} +(1.10442 + 1.91291i) q^{5} +(-0.234181 - 2.63537i) q^{7} +(-2.04673 + 2.19337i) q^{9} +(-0.157541 - 0.0909565i) q^{11} +(-2.50424 - 1.44582i) q^{13} +(2.27620 - 3.07503i) q^{15} +(-1.98511 - 3.43832i) q^{17} +(-0.867067 - 0.500601i) q^{19} +(-4.02463 + 2.19142i) q^{21} +(-4.86112 + 2.80657i) q^{23} +(0.0605124 - 0.104811i) q^{25} +(4.89724 + 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} -7.96637i q^{31} +(-0.0357208 + 0.313051i) q^{33} +(4.78259 - 3.35852i) q^{35} +(1.25614 - 2.17569i) q^{37} +(-0.567810 + 4.97619i) q^{39} +(0.612906 - 1.06158i) q^{41} +(-5.47716 - 9.48671i) q^{43} +(-6.45618 - 1.49281i) q^{45} -7.15102 q^{47} +(-6.89032 + 1.23430i) q^{49} +(-4.09131 + 5.52715i) q^{51} +(1.75586 - 1.01374i) q^{53} -0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +6.55821 q^{59} +8.05143i q^{61} +(6.25965 + 4.88024i) q^{63} -6.38719i q^{65} -6.89011 q^{67} +(7.81431 + 5.78431i) q^{69} +11.4168i q^{71} +(-10.1861 + 5.88094i) q^{73} +(-0.208270 - 0.0237647i) q^{75} +(-0.202811 + 0.436479i) q^{77} -12.7100 q^{79} +(-0.621788 - 8.97850i) q^{81} +(-7.19085 - 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(-1.13058 - 0.836880i) q^{87} +(7.11375 - 12.3214i) q^{89} +(-3.22383 + 6.93818i) q^{91} +(-12.6547 + 5.49988i) q^{93} -2.21150i q^{95} +(3.01040 - 1.73805i) q^{97} +(0.521946 - 0.159384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.690387	−	1.58851i	−0.398595	−	0.917127i
$3$	−0.690387	−	1.58851i	−0.398595	−	0.917127i
$4$		0			0
$5$	1.10442	+	1.91291i	0.493912	+	0.855480i	0.999975	−	0.00701597i	$-0.00223327\pi$
$5$	1.10442	+	1.91291i	0.493912	+	0.855480i	−0.506064	+	0.862496i	$0.668900\pi$
$6$		0			0
$7$	−0.234181	−	2.63537i	−0.0885120	−	0.996075i
$7$	−0.234181	−	2.63537i	−0.0885120	−	0.996075i
$8$		0			0
$9$	−2.04673	+	2.19337i	−0.682244	+	0.731125i
$10$		0			0
$11$	−0.157541	−	0.0909565i	−0.0475005	−	0.0274244i	0.476062	−	0.879412i	$-0.342064\pi$
$11$	−0.157541	−	0.0909565i	−0.0475005	−	0.0274244i	−0.523562	+	0.851987i	$0.675397\pi$
$12$		0			0
$13$	−2.50424	−	1.44582i	−0.694551	−	0.400999i	0.110763	−	0.993847i	$-0.464670\pi$
$13$	−2.50424	−	1.44582i	−0.694551	−	0.400999i	−0.805315	+	0.592847i	$0.798004\pi$
$14$		0			0
$15$	2.27620	−	3.07503i	0.587713	−	0.793970i
$16$		0			0
$17$	−1.98511	−	3.43832i	−0.481461	−	0.833915i	0.518313	−	0.855191i	$-0.326560\pi$
$17$	−1.98511	−	3.43832i	−0.481461	−	0.833915i	−0.999774	+	0.0212765i	$0.993227\pi$
$18$		0			0
$19$	−0.867067	−	0.500601i	−0.198919	−	0.114846i	0.397232	−	0.917718i	$-0.369971\pi$
$19$	−0.867067	−	0.500601i	−0.198919	−	0.114846i	−0.596151	+	0.802872i	$0.703304\pi$
$20$		0			0
$21$	−4.02463	+	2.19142i	−0.878247	+	0.478208i
$22$		0			0
$23$	−4.86112	+	2.80657i	−1.01361	+	0.585210i	−0.912247	−	0.409640i	$-0.865654\pi$
$23$	−4.86112	+	2.80657i	−1.01361	+	0.585210i	−0.101365	+	0.994849i	$0.532321\pi$
$24$		0			0
$25$	0.0605124	−	0.104811i	0.0121025	−	0.0209621i
$26$		0			0
$27$	4.89724	+	1.73697i	0.942473	+	0.334281i
$28$		0			0
$29$	0.703311	−	0.406057i	0.130602	−	0.0754028i	−0.433276	−	0.901261i	$-0.642642\pi$
$29$	0.703311	−	0.406057i	0.130602	−	0.0754028i	0.563877	+	0.825859i	$0.309309\pi$
$30$		0			0
$31$		−	7.96637i		−	1.43080i	−0.698714	−	0.715401i	$-0.746244\pi$
$31$		−	7.96637i		−	1.43080i	0.698714	−	0.715401i	$-0.253756\pi$
$32$		0			0
$33$	−0.0357208	+	0.313051i	−0.00621820	+	0.0544952i
$34$		0			0
$35$	4.78259	−	3.35852i	0.808405	−	0.567693i
$36$		0			0
$37$	1.25614	−	2.17569i	0.206507	−	0.357681i	−0.744105	−	0.668063i	$-0.767124\pi$
$37$	1.25614	−	2.17569i	0.206507	−	0.357681i	0.950612	+	0.310382i	$0.100457\pi$
$38$		0			0
$39$	−0.567810	+	4.97619i	−0.0909224	+	0.796828i
$40$		0			0
$41$	0.612906	−	1.06158i	0.0957198	−	0.165792i	−0.814189	−	0.580600i	$-0.802818\pi$
$41$	0.612906	−	1.06158i	0.0957198	−	0.165792i	0.909909	+	0.414808i	$0.136151\pi$
$42$		0			0
$43$	−5.47716	−	9.48671i	−0.835259	−	1.44671i	−0.893820	−	0.448426i	$-0.851985\pi$
$43$	−5.47716	−	9.48671i	−0.835259	−	1.44671i	0.0585613	−	0.998284i	$-0.481349\pi$
$44$		0			0
$45$	−6.45618	−	1.49281i	−0.962431	−	0.222535i
$46$		0			0
$47$	−7.15102			−1.04308			−0.521542	−	0.853226i	$-0.674643\pi$
$47$	−7.15102			−1.04308			−0.521542	+	0.853226i	$0.674643\pi$
$48$		0			0
$49$	−6.89032	+	1.23430i	−0.984331	+	0.176329i
$50$		0			0
$51$	−4.09131	+	5.52715i	−0.572898	+	0.773955i
$52$		0			0
$53$	1.75586	−	1.01374i	0.241186	−	0.139249i	−0.374536	−	0.927212i	$-0.622198\pi$
$53$	1.75586	−	1.01374i	0.241186	−	0.139249i	0.615722	+	0.787964i	$0.288865\pi$
$54$		0			0
$55$		−	0.401817i		−	0.0541810i
$56$		0			0
$57$	−0.196598	+	1.72295i	−0.0260401	+	0.228211i
$58$		0			0
$59$	6.55821			0.853806			0.426903	−	0.904297i	$-0.359604\pi$
$59$	6.55821			0.853806			0.426903	+	0.904297i	$0.359604\pi$
$60$		0			0
$61$			8.05143i			1.03088i	0.856926	+	0.515440i	$0.172372\pi$
$61$			8.05143i			1.03088i	−0.856926	+	0.515440i	$0.827628\pi$
$62$		0			0
$63$	6.25965	+	4.88024i	0.788642	+	0.614852i
$64$		0			0
$65$		−	6.38719i		−	0.792233i
$66$		0			0
$67$	−6.89011			−0.841761			−0.420880	−	0.907116i	$-0.638279\pi$
$67$	−6.89011			−0.841761			−0.420880	+	0.907116i	$0.638279\pi$
$68$		0			0
$69$	7.81431	+	5.78431i	0.940733	+	0.696350i
$70$		0			0
$71$			11.4168i			1.35492i	0.735560	+	0.677460i	$0.236919\pi$
$71$			11.4168i			1.35492i	−0.735560	+	0.677460i	$0.763081\pi$
$72$		0			0
$73$	−10.1861	+	5.88094i	−1.19219	+	0.688312i	−0.958803	−	0.284072i	$-0.908315\pi$
$73$	−10.1861	+	5.88094i	−1.19219	+	0.688312i	−0.233388	+	0.972384i	$0.574981\pi$
$74$		0			0
$75$	−0.208270	−	0.0237647i	−0.0240489	−	0.00274411i
$76$		0			0
$77$	−0.202811	+	0.436479i	−0.0231124	+	0.0497414i
$78$		0			0
$79$	−12.7100			−1.42999			−0.714994	−	0.699130i	$-0.753571\pi$
$79$	−12.7100			−1.42999			−0.714994	+	0.699130i	$0.753571\pi$
$80$		0			0
$81$	−0.621788	−	8.97850i	−0.0690875	−	0.997611i
$82$		0			0
$83$	−7.19085	−	12.4549i	−0.789298	−	1.36710i	−0.926397	−	0.376547i	$-0.877111\pi$
$83$	−7.19085	−	12.4549i	−0.789298	−	1.36710i	0.137099	−	0.990557i	$-0.456222\pi$
$84$		0			0
$85$	4.38480	−	7.59470i	0.475598	−	0.823760i
$86$		0			0
$87$	−1.13058	−	0.836880i	−0.121211	−	0.0897230i
$88$		0			0
$89$	7.11375	−	12.3214i	0.754055	−	1.30606i	−0.191787	−	0.981437i	$-0.561428\pi$
$89$	7.11375	−	12.3214i	0.754055	−	1.30606i	0.945843	−	0.324626i	$-0.105238\pi$
$90$		0			0
$91$	−3.22383	+	6.93818i	−0.337949	+	0.727319i
$92$		0			0
$93$	−12.6547	+	5.49988i	−1.31223	+	0.570311i
$94$		0			0
$95$		−	2.21150i		−	0.226895i
$96$		0			0
$97$	3.01040	−	1.73805i	0.305659	−	0.176473i	−0.339323	−	0.940670i	$-0.610198\pi$
$97$	3.01040	−	1.73805i	0.305659	−	0.176473i	0.644982	+	0.764197i	$0.276865\pi$
$98$		0			0
$99$	0.521946	−	0.159384i	0.0524576	−	0.0160187i
$100$		0			0
$101$	4.75282	−	8.23212i	0.472923	−	0.819126i	−0.526597	−	0.850115i	$-0.676532\pi$
$101$	4.75282	−	8.23212i	0.472923	−	0.819126i	0.999520	+	0.0309887i	$0.00986560\pi$
$102$		0			0
$103$	−7.26167	+	4.19253i	−0.715514	+	0.413102i	−0.813099	−	0.582125i	$-0.802221\pi$
$103$	−7.26167	+	4.19253i	−0.715514	+	0.413102i	0.0975856	+	0.995227i	$0.468888\pi$
$104$		0			0
$105$	−8.63688	−	5.27852i	−0.842873	−	0.515130i
$106$		0			0
$107$	12.7310	+	7.35026i	1.23075	+	0.710576i	0.967187	−	0.254065i	$-0.0817677\pi$
$107$	12.7310	+	7.35026i	1.23075	+	0.710576i	0.263567	+	0.964641i	$0.415101\pi$
$108$		0			0
$109$	8.35648	+	14.4738i	0.800405	+	1.38634i	0.919350	+	0.393442i	$0.128716\pi$
$109$	8.35648	+	14.4738i	0.800405	+	1.38634i	−0.118944	+	0.992901i	$0.537951\pi$
$110$		0			0
$111$	−4.32333	−	0.493315i	−0.410352	−	0.0468234i
$112$		0			0
$113$	−1.19493	−	0.689894i	−0.112410	−	0.0648998i	0.442741	−	0.896650i	$-0.354006\pi$
$113$	−1.19493	−	0.689894i	−0.112410	−	0.0648998i	−0.555151	+	0.831750i	$0.687339\pi$
$114$		0			0
$115$	−10.7374	−	6.19926i	−1.00127	−	0.578084i
$116$		0			0
$117$	8.29674	−	2.53353i	0.767034	−	0.234225i
$118$		0			0
$119$	−8.59636	+	6.03669i	−0.788027	+	0.553383i
$120$		0			0
$121$	−5.48345	−	9.49762i	−0.498496	−	0.863420i
$122$		0			0
$123$	−2.10948	−	0.240703i	−0.190205	−	0.0217035i
$124$		0			0
$125$	11.3115			1.01173
$126$		0			0
$127$	11.9684			1.06202			0.531012	−	0.847364i	$-0.321812\pi$
$127$	11.9684			1.06202			0.531012	+	0.847364i	$0.321812\pi$
$128$		0			0
$129$	−11.2884	+	15.2500i	−0.993887	+	1.34269i
$130$		0			0
$131$	3.67698	+	6.36872i	0.321259	+	0.556438i	0.980748	−	0.195277i	$-0.0625605\pi$
$131$	3.67698	+	6.36872i	0.321259	+	0.556438i	−0.659489	+	0.751714i	$0.729227\pi$
$132$		0			0
$133$	−1.11622	+	2.40227i	−0.0967884	+	0.208303i
$134$		0			0
$135$	2.08593	+	11.2863i	0.179528	+	0.971373i
$136$		0			0
$137$	−14.2302	−	8.21582i	−1.21577	−	0.701925i	−0.251760	−	0.967790i	$-0.581009\pi$
$137$	−14.2302	−	8.21582i	−1.21577	−	0.701925i	−0.964010	+	0.265865i	$0.914343\pi$
$138$		0			0
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.893361	−	0.449339i	$-0.148340\pi$
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.0575417	+	0.998343i	$0.481674\pi$
$140$		0			0
$141$	4.93697	+	11.3595i	0.415768	+	0.956639i
$142$		0			0
$143$	0.263014	+	0.455554i	0.0219944	+	0.0380953i
$144$		0			0
$145$	1.55350	+	0.896914i	0.129011	+	0.0744847i
$146$		0			0
$147$	6.71769	+	10.0932i	0.554066	+	0.832473i
$148$		0			0
$149$	13.1947	−	7.61797i	1.08095	−	0.624088i	0.149799	−	0.988716i	$-0.452137\pi$
$149$	13.1947	−	7.61797i	1.08095	−	0.624088i	0.931153	+	0.364628i	$0.118804\pi$
$150$		0			0
$151$	−6.83125	+	11.8321i	−0.555919	+	0.962880i	0.441912	+	0.897058i	$0.354300\pi$
$151$	−6.83125	+	11.8321i	−0.555919	+	0.962880i	−0.997831	+	0.0658217i	$0.979033\pi$
$152$		0			0
$153$	11.6045	+	2.68321i	0.938169	+	0.216925i
$154$		0			0
$155$	15.2390	−	8.79822i	1.22402	−	0.706690i
$156$		0			0
$157$		−	11.8151i		−	0.942951i	−0.881879	−	0.471475i	$-0.843722\pi$
$157$		−	11.8151i		−	0.942951i	0.881879	−	0.471475i	$-0.156278\pi$
$158$		0			0
$159$	−2.82257	−	2.08932i	−0.223844	−	0.165694i
$160$		0			0
$161$	8.53471	+	12.1536i	0.672630	+	0.957836i
$162$		0			0
$163$	4.35998	−	7.55170i	0.341500	−	0.591495i	−0.643212	−	0.765688i	$-0.722399\pi$
$163$	4.35998	−	7.55170i	0.341500	−	0.591495i	0.984711	+	0.174194i	$0.0557319\pi$
$164$		0			0
$165$	−0.638290	+	0.277409i	−0.0496908	+	0.0215963i
$166$		0			0
$167$	8.89862	−	15.4129i	0.688596	−	1.19268i	−0.283696	−	0.958914i	$-0.591561\pi$
$167$	8.89862	−	15.4129i	0.688596	−	1.19268i	0.972292	−	0.233769i	$-0.0751059\pi$
$168$		0			0
$169$	−2.31918	−	4.01695i	−0.178399	−	0.308996i
$170$		0			0
$171$	2.87266	−	0.877207i	0.219678	−	0.0670817i
$172$		0			0
$173$	19.1203			1.45369			0.726845	−	0.686802i	$-0.240986\pi$
$173$	19.1203			1.45369			0.726845	+	0.686802i	$0.240986\pi$
$174$		0			0
$175$	−0.290385	−	0.134928i	−0.0219511	−	0.0101996i
$176$		0			0
$177$	−4.52771	−	10.4178i	−0.340323	−	0.783049i
$178$		0			0
$179$	−5.31891	+	3.07088i	−0.397554	+	0.229528i	−0.685428	−	0.728140i	$-0.740385\pi$
$179$	−5.31891	+	3.07088i	−0.397554	+	0.229528i	0.287874	+	0.957668i	$0.407052\pi$
$180$		0			0
$181$		−	11.1208i		−	0.826604i	−0.910594	−	0.413302i	$-0.864375\pi$
$181$		−	11.1208i		−	0.826604i	0.910594	−	0.413302i	$-0.135625\pi$
$182$		0			0
$183$	12.7898	−	5.55861i	0.945448	−	0.410904i
$184$		0			0
$185$	5.54920			0.407986
$186$		0			0
$187$			0.722236i			0.0528151i
$188$		0			0
$189$	3.43073	−	13.3128i	0.249549	−	0.968362i
$190$		0			0
$191$			14.9352i			1.08067i	0.841450	+	0.540336i	$0.181703\pi$
$191$			14.9352i			1.08067i	−0.841450	+	0.540336i	$0.818297\pi$
$192$		0			0
$193$	−12.4277			−0.894569			−0.447284	−	0.894392i	$-0.647609\pi$
$193$	−12.4277			−0.894569			−0.447284	+	0.894392i	$0.647609\pi$
$194$		0			0
$195$	−10.1461	+	4.40963i	−0.726578	+	0.315780i
$196$		0			0
$197$			16.1512i			1.15073i	0.817897	+	0.575364i	$0.195140\pi$
$197$			16.1512i			1.15073i	−0.817897	+	0.575364i	$0.804860\pi$
$198$		0			0
$199$	21.5762	−	12.4571i	1.52950	−	0.883057i	0.530117	−	0.847925i	$-0.322148\pi$
$199$	21.5762	−	12.4571i	1.52950	−	0.883057i	0.999383	−	0.0351325i	$-0.0111853\pi$
$200$		0			0
$201$	4.75684	+	10.9450i	0.335522	+	0.772001i
$202$		0			0
$203$	−1.23481	−	1.75839i	−0.0866667	−	0.123415i
$204$		0			0
$205$	2.70762			0.189108
$206$		0			0
$207$	3.79354	−	16.4065i	0.263669	−	1.14033i
$208$		0			0
$209$	0.0910659	+	0.157731i	0.00629916	+	0.0109105i
$210$		0			0
$211$	−5.78631	+	10.0222i	−0.398346	+	0.689955i	−0.993522	−	0.113640i	$-0.963749\pi$
$211$	−5.78631	+	10.0222i	−0.398346	+	0.689955i	0.595176	+	0.803595i	$0.297082\pi$
$212$		0			0
$213$	18.1356	−	7.88198i	1.24263	−	0.540065i
$214$		0			0
$215$	12.0982	−	20.9546i	0.825088	−	1.42909i
$216$		0			0
$217$	−20.9943	+	1.86557i	−1.42519	+	0.126643i
$218$		0			0
$219$	16.3743	+	12.1206i	1.10647	+	0.819033i
$220$		0			0
$221$			11.4805i			0.772262i
$222$		0			0
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.0467358	−	0.998907i	$-0.485118\pi$
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.888447	+	0.458979i	$0.151785\pi$
$224$		0			0
$225$	0.106036	+	0.347246i	0.00706909	+	0.0231497i
$226$		0			0
$227$	9.90180	−	17.1504i	0.657206	−	1.13831i	−0.324130	−	0.946012i	$-0.605072\pi$
$227$	9.90180	−	17.1504i	0.657206	−	1.13831i	0.981336	−	0.192301i	$-0.0615950\pi$
$228$		0			0
$229$	13.5101	−	7.80006i	0.892772	−	0.515442i	0.0179241	−	0.999839i	$-0.494294\pi$
$229$	13.5101	−	7.80006i	0.892772	−	0.515442i	0.874848	+	0.484397i	$0.160961\pi$
$230$		0			0
$231$	0.833370	+	0.0208270i	0.0548317	+	0.00137031i
$232$		0			0
$233$	10.6450	+	6.14590i	0.697378	+	0.402631i	0.806370	−	0.591411i	$-0.201429\pi$
$233$	10.6450	+	6.14590i	0.697378	+	0.402631i	−0.108992	+	0.994043i	$0.534762\pi$
$234$		0			0
$235$	−7.89773	−	13.6793i	−0.515191	−	0.892337i
$236$		0			0
$237$	8.77483	+	20.1900i	0.569987	+	1.31148i
$238$		0			0
$239$	13.8058	+	7.97079i	0.893024	+	0.515588i	0.874930	−	0.484249i	$-0.160907\pi$
$239$	13.8058	+	7.97079i	0.893024	+	0.515588i	0.0180934	+	0.999836i	$0.494240\pi$
$240$		0			0
$241$	17.9156	+	10.3436i	1.15405	+	0.666290i	0.949870	−	0.312644i	$-0.101215\pi$
$241$	17.9156	+	10.3436i	1.15405	+	0.666290i	0.204178	+	0.978934i	$0.434548\pi$
$242$		0			0
$243$	−13.8332	+	7.18636i	−0.887398	+	0.461005i
$244$		0			0
$245$	−9.97092	−	11.8174i	−0.637019	−	0.754985i
$246$		0			0
$247$	1.44756	+	2.50725i	0.0921062	+	0.159533i
$248$		0			0
$249$	−14.8203	+	20.0215i	−0.939198	+	1.26881i
$250$		0			0
$251$	7.66566			0.483852			0.241926	−	0.970295i	$-0.422221\pi$
$251$	7.66566			0.483852			0.241926	+	0.970295i	$0.422221\pi$
$252$		0			0
$253$	1.02110			0.0641961
$254$		0			0
$255$	−15.0915	−	1.72202i	−0.945064	−	0.107837i
$256$		0			0
$257$	−5.96487	−	10.3315i	−0.372078	−	0.644459i	0.617807	−	0.786330i	$-0.288021\pi$
$257$	−5.96487	−	10.3315i	−0.372078	−	0.644459i	−0.989885	+	0.141871i	$0.954688\pi$
$258$		0			0
$259$	−6.02791	−	2.80087i	−0.374556	−	0.174038i
$260$		0			0
$261$	−0.548853	+	2.37371i	−0.0339732	+	0.146929i
$262$		0			0
$263$	−6.69006	−	3.86251i	−0.412527	−	0.238172i	0.279348	−	0.960190i	$-0.409882\pi$
$263$	−6.69006	−	3.86251i	−0.412527	−	0.238172i	−0.691875	+	0.722018i	$0.743215\pi$
$264$		0			0
$265$	3.87841	+	2.23920i	0.238249	+	0.137553i
$266$		0			0
$267$	−24.4839	−	2.79374i	−1.49839	−	0.170974i
$268$		0			0
$269$	4.98739	+	8.63841i	0.304086	+	0.526693i	0.977058	−	0.212976i	$-0.0683155\pi$
$269$	4.98739	+	8.63841i	0.304086	+	0.526693i	−0.672971	+	0.739669i	$0.734982\pi$
$270$		0			0
$271$	−3.61508	−	2.08717i	−0.219600	−	0.126786i	0.386165	−	0.922430i	$-0.373800\pi$
$271$	−3.61508	−	2.08717i	−0.219600	−	0.126786i	−0.605765	+	0.795643i	$0.707133\pi$
$272$		0			0
$273$	13.2471	+	0.331061i	0.801749	+	0.0200367i
$274$		0			0
$275$	−0.0190664	+	0.0110080i	−0.00114975	+	0.000663807i
$276$		0			0
$277$	−2.22504	+	3.85387i	−0.133689	+	0.231557i	−0.925096	−	0.379733i	$-0.876016\pi$
$277$	−2.22504	+	3.85387i	−0.133689	+	0.231557i	0.791407	+	0.611290i	$0.209349\pi$
$278$		0			0
$279$	17.4732	+	16.3050i	1.04610	+	0.976156i
$280$		0			0
$281$	−24.5472	+	14.1723i	−1.46436	+	0.845451i	−0.999209	−	0.0397785i	$-0.987335\pi$
$281$	−24.5472	+	14.1723i	−1.46436	+	0.845451i	−0.465155	+	0.885229i	$0.654001\pi$
$282$		0			0
$283$		−	11.5963i		−	0.689329i	−0.938726	−	0.344664i	$-0.887993\pi$
$283$		−	11.5963i		−	0.689329i	0.938726	−	0.344664i	$-0.112007\pi$
$284$		0			0
$285$	−3.51299	+	1.52679i	−0.208091	+	0.0904392i
$286$		0			0
$287$	−2.94119	−	1.36663i	−0.173613	−	0.0806696i
$288$		0			0
$289$	0.618645	−	1.07152i	0.0363909	−	0.0630308i
$290$		0			0
$291$	−4.83925	−	3.58212i	−0.283682	−	0.209987i
$292$		0			0
$293$	−14.4199	+	24.9760i	−0.842418	+	1.45911i	0.0454266	+	0.998968i	$0.485535\pi$
$293$	−14.4199	+	24.9760i	−0.842418	+	1.45911i	−0.887845	+	0.460143i	$0.847798\pi$
$294$		0			0
$295$	7.24302	+	12.5453i	0.421705	+	0.730414i
$296$		0			0
$297$	−0.613528	−	0.719081i	−0.0356005	−	0.0417253i
$298$		0			0
$299$	16.2312			0.938675
$300$		0			0
$301$	−23.7183	+	16.6559i	−1.36710	+	0.960031i
$302$		0			0
$303$	−16.3581	−	1.86655i	−0.939748	−	0.107230i
$304$		0			0
$305$	−15.4017	+	8.89216i	−0.881898	+	0.509164i
$306$		0			0
$307$			10.8117i			0.617059i	0.951215	+	0.308529i	$0.0998368\pi$
$307$			10.8117i			0.617059i	−0.951215	+	0.308529i	$0.900163\pi$
$308$		0			0
$309$	11.6732	+	8.64077i	0.664067	+	0.491556i
$310$		0			0
$311$	−17.1832			−0.974370			−0.487185	−	0.873299i	$-0.661976\pi$
$311$	−17.1832			−0.974370			−0.487185	+	0.873299i	$0.661976\pi$
$312$		0			0
$313$		−	9.14399i		−	0.516849i	−0.966031	−	0.258425i	$-0.916797\pi$
$313$		−	9.14399i		−	0.516849i	0.966031	−	0.258425i	$-0.0832033\pi$
$314$		0			0
$315$	−2.42218	+	17.3640i	−0.136474	+	0.978351i
$316$		0			0
$317$		−	1.13698i		−	0.0638589i	−0.999490	−	0.0319295i	$-0.989835\pi$
$317$		−	1.13698i		−	0.0638589i	0.999490	−	0.0319295i	$-0.0101652\pi$
$318$		0			0
$319$	−0.147734			−0.00827152
$320$		0			0
$321$	2.88663	−	25.2979i	0.161116	−	1.41199i
$322$		0			0
$323$			3.97500i			0.221175i
$324$		0			0
$325$	−0.303075	+	0.174981i	−0.0168116	+	0.00970618i
$326$		0			0
$327$	17.2226	−	23.2669i	0.952414	−	1.28666i
$328$		0			0
$329$	1.67463	+	18.8456i	0.0923254	+	1.03899i
$330$		0			0
$331$	6.04788			0.332421			0.166211	−	0.986090i	$-0.446847\pi$
$331$	6.04788			0.332421			0.166211	+	0.986090i	$0.446847\pi$
$332$		0			0
$333$	2.20113	+	7.20823i	0.120621	+	0.395008i
$334$		0			0
$335$	−7.60957	−	13.1802i	−0.415755	−	0.720110i
$336$		0			0
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.249871	−	0.968279i	$-0.419612\pi$
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.713619	−	0.700534i	$-0.247055\pi$
$338$		0			0
$339$	−0.270938	+	2.37446i	−0.0147153	+	0.128963i
$340$		0			0
$341$	−0.724593	+	1.25503i	−0.0392389	+	0.0679638i
$342$		0			0
$343$	4.86643	+	17.8695i	0.262762	+	0.964861i
$344$		0			0
$345$	−2.43460	+	21.3364i	−0.131074	+	1.14871i
$346$		0			0
$347$			23.2102i			1.24599i	0.782225	+	0.622995i	$0.214084\pi$
$347$			23.2102i			1.24599i	−0.782225	+	0.622995i	$0.785916\pi$
$348$		0			0
$349$	−12.7248	+	7.34667i	−0.681144	+	0.393258i	−0.800286	−	0.599619i	$-0.795319\pi$
$349$	−12.7248	+	7.34667i	−0.681144	+	0.393258i	0.119142	+	0.992877i	$0.461986\pi$
$350$		0			0
$351$	−9.75250	−	11.4303i	−0.520550	−	0.610107i
$352$		0			0
$353$	−6.73122	+	11.6588i	−0.358267	+	0.620536i	−0.987671	−	0.156542i	$-0.949965\pi$
$353$	−6.73122	+	11.6588i	−0.358267	+	0.620536i	0.629405	+	0.777078i	$0.283299\pi$
$354$		0			0
$355$	−21.8392	+	12.6089i	−1.15911	+	0.669211i
$356$		0			0
$357$	15.5242	+	9.48774i	0.821626	+	0.502145i
$358$		0			0
$359$	13.5004	+	7.79444i	0.712522	+	0.411375i	0.811994	−	0.583666i	$-0.198382\pi$
$359$	13.5004	+	7.79444i	0.712522	+	0.411375i	−0.0994721	+	0.995040i	$0.531715\pi$
$360$		0			0
$361$	−8.99880	−	15.5864i	−0.473621	−	0.820335i
$362$		0			0
$363$	−11.3014	+	15.2676i	−0.593168	+	0.801339i
$364$		0			0
$365$	−22.4994	−	12.9901i	−1.17767	−	0.679930i
$366$		0			0
$367$	7.50847	+	4.33501i	0.391939	+	0.226286i	0.683000	−	0.730419i	$-0.260675\pi$
$367$	7.50847	+	4.33501i	0.391939	+	0.226286i	−0.291061	+	0.956704i	$0.594008\pi$
$368$		0			0
$369$	1.07400	+	3.51711i	0.0559101	+	0.183093i
$370$		0			0
$371$	−3.08278	−	4.38993i	−0.160050	−	0.227914i
$372$		0			0
$373$	12.0489	+	20.8693i	0.623868	+	1.08057i	0.988759	+	0.149521i	$0.0477730\pi$
$373$	12.0489	+	20.8693i	0.623868	+	1.08057i	−0.364891	+	0.931050i	$0.618894\pi$
$374$		0			0
$375$	−7.80933	−	17.9685i	−0.403272	−	0.927888i
$376$		0			0
$377$	−2.34835			−0.120946
$378$		0			0
$379$	−10.0778			−0.517662			−0.258831	−	0.965923i	$-0.583337\pi$
$379$	−10.0778			−0.517662			−0.258831	+	0.965923i	$0.583337\pi$
$380$		0			0
$381$	−8.26283	−	19.0119i	−0.423318	−	0.974011i
$382$		0			0
$383$	−2.35238	−	4.07444i	−0.120201	−	0.208194i	0.799646	−	0.600472i	$-0.205021\pi$
$383$	−2.35238	−	4.07444i	−0.120201	−	0.208194i	−0.919847	+	0.392278i	$0.871687\pi$
$384$		0			0
$385$	−1.05893	+	0.0940978i	−0.0539683	+	0.00479567i
$386$		0			0
$387$	32.0182	+	7.40329i	1.62758	+	0.376330i
$388$		0			0
$389$	−18.6198	−	10.7502i	−0.944062	−	0.545055i	−0.0528309	−	0.998603i	$-0.516824\pi$
$389$	−18.6198	−	10.7502i	−0.944062	−	0.545055i	−0.891231	+	0.453549i	$0.850158\pi$
$390$		0			0
$391$	19.2997	+	11.1427i	0.976030	+	0.563511i
$392$		0			0
$393$	7.57823	−	10.2378i	0.382271	−	0.516429i
$394$		0			0
$395$	−14.0372	−	24.3131i	−0.706288	−	1.22333i
$396$		0			0
$397$	−23.7548	−	13.7148i	−1.19222	−	0.688327i	−0.233408	−	0.972379i	$-0.574988\pi$
$397$	−23.7548	−	13.7148i	−1.19222	−	0.688327i	−0.958809	+	0.284052i	$0.908321\pi$
$398$		0			0
$399$	4.58666	+	0.114626i	0.229620	+	0.00573849i
$400$		0			0
$401$	25.3138	−	14.6150i	1.26411	−	0.729836i	0.290245	−	0.956952i	$-0.406263\pi$
$401$	25.3138	−	14.6150i	1.26411	−	0.729836i	0.973868	+	0.227116i	$0.0729298\pi$
$402$		0			0
$403$	−11.5180	+	19.9497i	−0.573751	+	0.993766i
$404$		0			0
$405$	16.4884	−	11.1055i	0.819313	−	0.551835i
$406$		0			0
$407$	−0.395786	+	0.228507i	−0.0196184	+	0.0113267i
$408$		0			0
$409$		−	31.5884i		−	1.56195i	−0.624564	−	0.780974i	$-0.714723\pi$
$409$		−	31.5884i		−	1.56195i	0.624564	−	0.780974i	$-0.285277\pi$
$410$		0			0
$411$	−3.22655	+	28.2770i	−0.159154	+	1.39480i
$412$		0			0
$413$	−1.53581	−	17.2833i	−0.0755721	−	0.850455i
$414$		0			0
$415$	15.8834	−	27.5109i	0.779687	−	1.35046i
$416$		0			0
$417$	2.54197	−	22.2774i	0.124481	−	1.09093i
$418$		0			0
$419$	−6.80176	+	11.7810i	−0.332288	+	0.575539i	−0.982960	−	0.183819i	$-0.941154\pi$
$419$	−6.80176	+	11.7810i	−0.332288	+	0.575539i	0.650672	+	0.759359i	$0.274487\pi$
$420$		0			0
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	−0.959232	−	0.282620i	$-0.908797\pi$
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	0.234860	−	0.972029i	$-0.424537\pi$
$422$		0			0
$423$	14.6362	−	15.6849i	0.711637	−	0.762624i
$424$		0			0
$425$	−0.480496			−0.0233075
$426$		0			0
$427$	21.2185	−	1.88549i	1.02683	−	0.0912453i
$428$		0			0
$429$	0.542071	−	0.732310i	0.0261714	−	0.0353562i
$430$		0			0
$431$	−21.6467	+	12.4977i	−1.04268	+	0.601994i	−0.920592	−	0.390525i	$-0.872293\pi$
$431$	−21.6467	+	12.4977i	−1.04268	+	0.601994i	−0.122091	+	0.992519i	$0.538960\pi$
$432$		0			0
$433$			18.7778i			0.902401i	0.892423	+	0.451201i	$0.149004\pi$
$433$			18.7778i			0.902401i	−0.892423	+	0.451201i	$0.850996\pi$
$434$		0			0
$435$	0.352240	−	3.08697i	0.0168886	−	0.148009i
$436$		0			0
$437$	5.61988			0.268836
$438$		0			0
$439$			2.10574i			0.100502i	0.998737	+	0.0502508i	$0.0160021\pi$
$439$			2.10574i			0.100502i	−0.998737	+	0.0502508i	$0.983998\pi$
$440$		0			0
$441$	11.3953	−	17.6393i	0.542635	−	0.839969i
$442$		0			0
$443$		−	13.4467i		−	0.638874i	−0.947608	−	0.319437i	$-0.896506\pi$
$443$		−	13.4467i		−	0.638874i	0.947608	−	0.319437i	$-0.103494\pi$
$444$		0			0
$445$	31.4263			1.48975
$446$		0			0
$447$	−21.2107	−	15.7006i	−1.00323	−	0.742612i
$448$		0			0
$449$		−	7.42429i		−	0.350374i	−0.984535	−	0.175187i	$-0.943947\pi$
$449$		−	7.42429i		−	0.350374i	0.984535	−	0.175187i	$-0.0560530\pi$
$450$		0			0
$451$	−0.193116	+	0.111496i	−0.00909347	+	0.00525012i
$452$		0			0
$453$	23.5116	+	2.68280i	1.10467	+	0.126049i
$454$		0			0
$455$	−16.8326	+	1.49576i	−0.789124	+	0.0701222i
$456$		0			0
$457$	−0.278018			−0.0130051			−0.00650257	−	0.999979i	$-0.502070\pi$
$457$	−0.278018			−0.0130051			−0.00650257	+	0.999979i	$0.502070\pi$
$458$		0			0
$459$	−3.74930	−	20.2863i	−0.175002	−	0.946886i
$460$		0			0
$461$	3.98573	+	6.90348i	0.185634	+	0.321527i	0.943790	−	0.330546i	$-0.107233\pi$
$461$	3.98573	+	6.90348i	0.185634	+	0.321527i	−0.758156	+	0.652073i	$0.773900\pi$
$462$		0			0
$463$	−12.4572	+	21.5765i	−0.578936	+	1.00275i	0.416666	+	0.909060i	$0.363199\pi$
$463$	−12.4572	+	21.5765i	−0.578936	+	1.00275i	−0.995602	+	0.0936870i	$0.970135\pi$
$464$		0			0
$465$	−24.4969	−	18.1331i	−1.13601	−	0.840901i
$466$		0			0
$467$	18.4485	−	31.9538i	0.853695	−	1.47864i	−0.0241548	−	0.999708i	$-0.507689\pi$
$467$	18.4485	−	31.9538i	0.853695	−	1.47864i	0.877850	−	0.478935i	$-0.158977\pi$
$468$		0			0
$469$	1.61353	+	18.1580i	0.0745059	+	0.838457i
$470$		0			0
$471$	−18.7685	+	8.15702i	−0.864806	+	0.375856i
$472$		0			0
$473$			1.99273i			0.0916259i
$474$		0			0
$475$	−0.104937	+	0.0605852i	−0.00481483	+	0.00277984i
$476$		0			0
$477$	−1.37024	+	5.92612i	−0.0627392	+	0.271338i
$478$		0			0
$479$	−1.70584	+	2.95461i	−0.0779420	+	0.135000i	−0.902362	−	0.430979i	$-0.858168\pi$
$479$	−1.70584	+	2.95461i	−0.0779420	+	0.135000i	0.824420	+	0.565979i	$0.191502\pi$
$480$		0			0
$481$	−6.29133	+	3.63230i	−0.286860	+	0.165619i
$482$		0			0
$483$	13.4138	−	21.9482i	0.610350	−	0.998676i
$484$		0			0
$485$	6.64948	+	3.83908i	0.301938	+	0.174324i
$486$		0			0
$487$	1.17122	+	2.02861i	0.0530729	+	0.0919249i	0.891341	−	0.453333i	$-0.149765\pi$
$487$	1.17122	+	2.02861i	0.0530729	+	0.0919249i	−0.838268	+	0.545258i	$0.816432\pi$
$488$		0			0
$489$	−15.0060	−	1.71227i	−0.678596	−	0.0774315i
$490$		0			0
$491$	−4.65365	−	2.68678i	−0.210016	−	0.121253i	0.391303	−	0.920262i	$-0.372025\pi$
$491$	−4.65365	−	2.68678i	−0.210016	−	0.121253i	−0.601319	+	0.799009i	$0.705358\pi$
$492$		0			0
$493$	−2.79230	−	1.61214i	−0.125759	−	0.0726070i
$494$		0			0
$495$	0.881335	+	0.822411i	0.0396131	+	0.0369646i
$496$		0			0
$497$	30.0873	−	2.67358i	1.34960	−	0.119927i
$498$		0			0
$499$	−16.6906	−	28.9090i	−0.747175	−	1.29415i	−0.949171	−	0.314759i	$-0.898076\pi$
$499$	−16.6906	−	28.9090i	−0.747175	−	1.29415i	0.201996	−	0.979386i	$-0.435257\pi$
$500$		0			0
$501$	−30.6270	−	3.49471i	−1.36831	−	0.156132i
$502$		0			0
$503$	6.01630			0.268254			0.134127	−	0.990964i	$-0.457177\pi$
$503$	6.01630			0.268254			0.134127	+	0.990964i	$0.457177\pi$
$504$		0			0
$505$	20.9964			0.934328
$506$		0			0
$507$	−4.77982	+	6.45730i	−0.212279	+	0.286779i
$508$		0			0
$509$	−5.01991	−	8.69473i	−0.222503	−	0.385387i	0.733064	−	0.680160i	$-0.238090\pi$
$509$	−5.01991	−	8.69473i	−0.222503	−	0.385387i	−0.955568	+	0.294772i	$0.904756\pi$
$510$		0			0
$511$	17.8838	+	25.4669i	0.791133	+	1.12659i
$512$		0			0
$513$	−3.37670	−	3.95764i	−0.149085	−	0.174734i
$514$		0			0
$515$	−16.0399	−	9.26062i	−0.706801	−	0.408072i
$516$		0			0
$517$	1.12658	+	0.650432i	0.0495470	+	0.0286059i
$518$		0			0
$519$	−13.2004	−	30.3728i	−0.579434	−	1.33322i
$520$		0			0
$521$	−10.8007	−	18.7074i	−0.473188	−	0.819586i	0.526341	−	0.850274i	$-0.323564\pi$
$521$	−10.8007	−	18.7074i	−0.473188	−	0.819586i	−0.999529	+	0.0306875i	$0.990230\pi$
$522$		0			0
$523$	−11.6105	−	6.70332i	−0.507692	−	0.293116i	0.224193	−	0.974545i	$-0.428026\pi$
$523$	−11.6105	−	6.70332i	−0.507692	−	0.293116i	−0.731884	+	0.681429i	$0.761359\pi$
$524$		0			0
$525$	−0.0138560	+	0.554433i	−0.000604724	+	0.0241974i
$526$		0			0
$527$	−27.3909	+	15.8142i	−1.19317	+	0.688875i
$528$		0			0
$529$	4.25363	−	7.36750i	0.184940	−	0.320326i
$530$		0			0
$531$	−13.4229	+	14.3846i	−0.582504	+	0.624239i
$532$		0			0
$533$	−3.06973	+	1.77231i	−0.132965	+	0.0767672i
$534$		0			0
$535$			32.4711i			1.40385i
$536$		0			0
$537$	8.55023	+	6.32905i	0.368970	+	0.273119i
$538$		0			0
$539$	1.19778	+	0.432265i	0.0515919	+	0.0186190i
$540$		0			0
$541$	4.53805	−	7.86013i	0.195106	−	0.337933i	−0.751829	−	0.659358i	$-0.770828\pi$
$541$	4.53805	−	7.86013i	0.195106	−	0.337933i	0.946935	+	0.321424i	$0.104162\pi$
$542$		0			0
$543$	−17.6655	+	7.67767i	−0.758101	+	0.329480i
$544$		0			0
$545$	−18.4581	+	31.9704i	−0.790659	+	1.36946i
$546$		0			0
$547$	−13.5359	−	23.4448i	−0.578752	−	1.00243i	−0.995623	−	0.0934620i	$-0.970207\pi$
$547$	−13.5359	−	23.4448i	−0.578752	−	1.00243i	0.416871	−	0.908966i	$-0.363127\pi$
$548$		0			0
$549$	−17.6598	−	16.4791i	−0.753702	−	0.703311i
$550$		0			0
$551$	−0.813090			−0.0346388
$552$		0			0
$553$	2.97644	+	33.4956i	0.126571	+	1.42438i
$554$		0			0
$555$	−3.83110	−	8.81497i	−0.162621	−	0.374175i
$556$		0			0
$557$	23.8690	−	13.7808i	1.01136	−	0.583911i	0.0997727	−	0.995010i	$-0.468188\pi$
$557$	23.8690	−	13.7808i	1.01136	−	0.583911i	0.911591	+	0.411099i	$0.134855\pi$
$558$		0			0
$559$			31.6760i			1.33975i
$560$		0			0
$561$	1.14728	−	0.498623i	0.0484382	−	0.0210519i
$562$		0			0
$563$	−13.8466			−0.583563			−0.291781	−	0.956485i	$-0.594248\pi$
$563$	−13.8466			−0.583563			−0.291781	+	0.956485i	$0.594248\pi$
$564$		0			0
$565$		−	3.04773i		−	0.128219i
$566$		0			0
$567$	−23.5160	+	3.74123i	−0.987580	+	0.157117i
$568$		0			0
$569$			12.1497i			0.509342i	0.967028	+	0.254671i	$0.0819672\pi$
$569$			12.1497i			0.509342i	−0.967028	+	0.254671i	$0.918033\pi$
$570$		0			0
$571$	46.3010			1.93764			0.968819	−	0.247771i	$-0.0796981\pi$
$571$	46.3010			1.93764			0.968819	+	0.247771i	$0.0796981\pi$
$572$		0			0
$573$	23.7247	−	10.3111i	0.991113	−	0.430750i
$574$		0			0
$575$			0.679329i			0.0283300i
$576$		0			0
$577$	−10.6284	+	6.13630i	−0.442465	+	0.255457i	−0.704643	−	0.709562i	$-0.748893\pi$
$577$	−10.6284	+	6.13630i	−0.442465	+	0.255457i	0.262178	+	0.965020i	$0.415559\pi$
$578$		0			0
$579$	8.57996	+	19.7416i	0.356571	+	0.820433i
$580$		0			0
$581$	−31.1393	+	21.8672i	−1.29188	+	0.907206i
$582$		0			0
$583$	−0.368827			−0.0152752
$584$		0			0
$585$	14.0095	+	13.0729i	0.579222	+	0.540496i
$586$		0			0
$587$	11.9875	+	20.7630i	0.494778	+	0.856980i	0.999982	−	0.00601986i	$-0.00191619\pi$
$587$	11.9875	+	20.7630i	0.494778	+	0.856980i	−0.505204	+	0.863000i	$0.668583\pi$
$588$		0			0
$589$	−3.98798	+	6.90738i	−0.164322	+	0.284614i
$590$		0			0
$591$	25.6564	−	11.1506i	1.05536	−	0.458675i
$592$		0			0
$593$	15.4912	−	26.8315i	0.636146	−	1.10184i	−0.350125	−	0.936703i	$-0.613861\pi$
$593$	15.4912	−	26.8315i	0.636146	−	1.10184i	0.986271	−	0.165134i	$-0.0528056\pi$
$594$		0			0
$595$	−21.0416	−	9.77702i	−0.862623	−	0.400819i
$596$		0			0
$597$	−34.6841	−	25.6739i	−1.41953	−	1.05076i
$598$		0			0
$599$			24.7558i			1.01150i	0.862681	+	0.505748i	$0.168783\pi$
$599$			24.7558i			1.01150i	−0.862681	+	0.505748i	$0.831217\pi$
$600$		0			0
$601$	−7.67329	+	4.43017i	−0.313000	+	0.180711i	−0.648268	−	0.761412i	$-0.724506\pi$
$601$	−7.67329	+	4.43017i	−0.313000	+	0.180711i	0.335268	+	0.942123i	$0.391173\pi$
$602$		0			0
$603$	14.1022	−	15.1126i	0.574286	−	0.615432i
$604$		0			0
$605$	12.1121	−	20.9787i	0.492426	−	0.852907i
$606$		0			0
$607$	11.2943	−	6.52076i	0.458421	−	0.264670i	−0.252959	−	0.967477i	$-0.581404\pi$
$607$	11.2943	−	6.52076i	0.458421	−	0.264670i	0.711380	+	0.702807i	$0.248070\pi$
$608$		0			0
$609$	−1.94073	+	3.17548i	−0.0786422	+	0.128677i
$610$		0			0
$611$	17.9079	+	10.3391i	0.724475	+	0.418276i
$612$		0			0
$613$	5.90775	+	10.2325i	0.238612	+	0.413288i	0.960316	−	0.278914i	$-0.0899743\pi$
$613$	5.90775	+	10.2325i	0.238612	+	0.413288i	−0.721704	+	0.692201i	$0.756641\pi$
$614$		0			0
$615$	−1.86931	−	4.30108i	−0.0753778	−	0.173436i
$616$		0			0
$617$	−13.7906	−	7.96200i	−0.555188	−	0.320538i	0.196024	−	0.980599i	$-0.437197\pi$
$617$	−13.7906	−	7.96200i	−0.555188	−	0.320538i	−0.751212	+	0.660061i	$0.770530\pi$
$618$		0			0
$619$	−26.7802	−	15.4616i	−1.07639	−	0.621453i	−0.146468	−	0.989215i	$-0.546791\pi$
$619$	−26.7802	−	15.4616i	−1.07639	−	0.621453i	−0.929920	+	0.367762i	$0.880124\pi$
$620$		0			0
$621$	−28.6810	+	5.30078i	−1.15093	+	0.212713i
$622$		0			0
$623$	−34.1372	−	15.8619i	−1.36768	−	0.635494i
$624$		0			0
$625$	12.1901	+	21.1139i	0.487605	+	0.844556i
$626$		0			0
$627$	0.187686	−	0.253555i	0.00749547	−	0.0101260i
$628$		0			0
$629$	−9.97429			−0.397701
$630$		0			0
$631$	−0.925450			−0.0368416			−0.0184208	−	0.999830i	$-0.505864\pi$
$631$	−0.925450			−0.0368416			−0.0184208	+	0.999830i	$0.505864\pi$
$632$		0			0
$633$	19.9151	+	2.27243i	0.791556	+	0.0903208i
$634$		0			0
$635$	13.2181	+	22.8945i	0.524546	+	0.908540i
$636$		0			0
$637$	19.0396	+	6.87119i	0.754377	+	0.272247i
$638$		0			0
$639$	−25.0412	−	23.3670i	−0.990616	−	0.924385i
$640$		0			0
$641$	−29.7464	−	17.1741i	−1.17491	−	0.678336i	−0.220080	−	0.975482i	$-0.570632\pi$
$641$	−29.7464	−	17.1741i	−1.17491	−	0.678336i	−0.954832	+	0.297146i	$0.903965\pi$
$642$		0			0
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	0.714906	−	0.699220i	$-0.246469\pi$
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	−0.248089	+	0.968737i	$0.579803\pi$
$644$		0			0
$645$	−41.6391	−	4.75124i	−1.63954	−	0.187080i
$646$		0			0
$647$	18.1075	+	31.3630i	0.711877	+	1.23301i	0.964152	+	0.265352i	$0.0854882\pi$
$647$	18.1075	+	31.3630i	0.711877	+	1.23301i	−0.252274	+	0.967656i	$0.581178\pi$
$648$		0			0
$649$	−1.03319	−	0.596512i	−0.0405562	−	0.0234151i
$650$		0			0
$651$	17.4577	+	32.0617i	0.684221	+	1.25660i
$652$		0			0
$653$	−31.6333	+	18.2635i	−1.23791	+	0.714705i	−0.968666	−	0.248368i	$-0.920106\pi$
$653$	−31.6333	+	18.2635i	−1.23791	+	0.714705i	−0.269240	+	0.963073i	$0.586773\pi$
$654$		0			0
$655$	−8.12186	+	14.0675i	−0.317347	+	0.549662i
$656$		0			0
$657$	7.94907	−	34.3786i	0.310123	−	1.34124i
$658$		0			0
$659$	19.5178	−	11.2686i	0.760305	−	0.438962i	−0.0691004	−	0.997610i	$-0.522013\pi$
$659$	19.5178	−	11.2686i	0.760305	−	0.438962i	0.829405	+	0.558648i	$0.188680\pi$
$660$		0			0
$661$		−	1.49643i		−	0.0582045i	−0.999576	−	0.0291022i	$-0.990735\pi$
$661$		−	1.49643i		−	0.0582045i	0.999576	−	0.0291022i	$-0.00926484\pi$
$662$		0			0
$663$	18.2369	−	7.92599i	0.708262	−	0.307820i
$664$		0			0
$665$	−5.82811	+	0.517890i	−0.226004	+	0.0200829i
$666$		0			0
$667$	−2.27925	+	3.94778i	−0.0882529	+	0.152859i
$668$		0			0
$669$	−22.4494	−	16.6175i	−0.867942	−	0.642469i
$670$		0			0
$671$	0.732330	−	1.26843i	0.0282713	−	0.0489673i
$672$		0			0
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	0.999053	+	0.0435197i	$0.0138571\pi$
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	−0.461837	+	0.886965i	$0.652810\pi$
$674$		0			0
$675$	0.478397	−	0.408174i	0.0184135	−	0.0157106i
$676$		0			0
$677$	−31.2688			−1.20176			−0.600880	−	0.799340i	$-0.705183\pi$
$677$	−31.2688			−1.20176			−0.600880	+	0.799340i	$0.705183\pi$
$678$		0			0
$679$	−5.28538	−	7.52648i	−0.202834	−	0.288840i
$680$		0			0
$681$	−34.0797	−	3.88868i	−1.30594	−	0.149015i
$682$		0			0
$683$	8.06769	−	4.65788i	0.308701	−	0.178229i	−0.337644	−	0.941274i	$-0.609630\pi$
$683$	8.06769	−	4.65788i	0.308701	−	0.178229i	0.646345	+	0.763045i	$0.276297\pi$
$684$		0			0
$685$		−	36.2949i		−	1.38676i
$686$		0			0
$687$	−21.7177	−	16.0759i	−0.828581	−	0.613333i
$688$		0			0
$689$	−5.86279			−0.223354
$690$		0			0
$691$		−	48.5515i		−	1.84699i	−0.383615	−	0.923493i	$-0.625321\pi$
$691$		−	48.5515i		−	1.84699i	0.383615	−	0.923493i	$-0.374679\pi$
$692$		0			0
$693$	−0.542264	−	1.33820i	−0.0205989	−	0.0508338i
$694$		0			0
$695$			28.5942i			1.08464i
$696$		0			0
$697$	−4.86675			−0.184341
$698$		0			0
$699$	2.41365	−	21.1528i	0.0912925	−	0.800071i
$700$		0			0
$701$			22.9812i			0.867987i	0.900916	+	0.433994i	$0.142896\pi$
$701$			22.9812i			0.867987i	−0.900916	+	0.433994i	$0.857104\pi$
$702$		0			0
$703$	−2.17831	+	1.25765i	−0.0821564	+	0.0474330i
$704$		0			0
$705$	−16.2772	+	21.9896i	−0.613033	+	0.828177i
$706$		0			0
$707$	−22.8077	−	10.5976i	−0.857771	−	0.398564i
$708$		0			0
$709$	30.6865			1.15246			0.576228	−	0.817289i	$-0.304524\pi$
$709$	30.6865			1.15246			0.576228	+	0.817289i	$0.304524\pi$
$710$		0			0
$711$	26.0140	−	27.8778i	0.975600	−	1.04550i
$712$		0			0
$713$	22.3582	+	38.7255i	0.837319	+	1.45028i
$714$		0			0
$715$	−0.580956	+	1.00625i	−0.0217265	+	0.0376315i
$716$		0			0
$717$	3.13032	−	27.4336i	0.116904	−	1.02453i
$718$		0			0
$719$	2.44166	−	4.22907i	0.0910584	−	0.157718i	−0.816898	−	0.576782i	$-0.804308\pi$
$719$	2.44166	−	4.22907i	0.0910584	−	0.157718i	0.907957	+	0.419064i	$0.137642\pi$
$720$		0			0
$721$	12.7494	+	18.1554i	0.474812	+	0.676141i
$722$		0			0
$723$	4.06218	−	35.6003i	0.151074	−	1.32399i
$724$		0			0
$725$		−	0.0982859i		−	0.00365025i
$726$		0			0
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.251678	−	0.967811i	$-0.419018\pi$
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.963988	+	0.265946i	$0.0856844\pi$
$728$		0			0
$729$	20.9658	+	17.0127i	0.776513	+	0.630102i
$730$		0			0
$731$	−21.7456	+	37.6644i	−0.804289	+	1.39307i
$732$		0			0
$733$	−40.1113	+	23.1583i	−1.48155	+	0.855370i	−0.999781	−	0.0209305i	$-0.993337\pi$
$733$	−40.1113	+	23.1583i	−1.48155	+	0.855370i	−0.481764	+	0.876301i	$0.660004\pi$
$734$		0			0
$735$	−11.8882	+	23.9975i	−0.438504	+	0.885161i
$736$		0			0
$737$	1.08548	+	0.626700i	0.0399840	+	0.0230848i
$738$		0			0
$739$	−5.15606	−	8.93056i	−0.189669	−	0.328516i	0.755471	−	0.655182i	$-0.227408\pi$
$739$	−5.15606	−	8.93056i	−0.189669	−	0.328516i	−0.945140	+	0.326666i	$0.894075\pi$
$740$		0			0
$741$	2.98342	−	4.03045i	0.109599	−	0.148062i
$742$		0			0
$743$	−21.9984	−	12.7008i	−0.807042	−	0.465946i	0.0388856	−	0.999244i	$-0.487619\pi$
$743$	−21.9984	−	12.7008i	−0.807042	−	0.465946i	−0.845928	+	0.533298i	$0.820953\pi$
$744$		0			0
$745$	29.1450	+	16.8269i	1.06779	+	0.616489i
$746$		0			0
$747$	42.0360	+	9.71963i	1.53802	+	0.355623i
$748$		0			0
$749$	16.3893	−	35.2722i	0.598851	−	1.28882i
$750$		0			0
$751$	−26.8653	−	46.5321i	−0.980329	−	1.69798i	−0.661091	−	0.750306i	$-0.729906\pi$
$751$	−26.8653	−	46.5321i	−0.980329	−	1.69798i	−0.319238	−	0.947675i	$-0.603427\pi$
$752$		0			0
$753$	−5.29228	−	12.1770i	−0.192861	−	0.443754i
$754$		0			0
$755$	−30.1783			−1.09830
$756$		0			0
$757$	28.3821			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$757$	28.3821			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$758$		0			0
$759$	−0.704956	−	1.62203i	−0.0255883	−	0.0588760i
$760$		0			0
$761$	11.5592	+	20.0211i	0.419021	+	0.725765i	0.995841	−	0.0911059i	$-0.0290402\pi$
$761$	11.5592	+	20.0211i	0.419021	+	0.725765i	−0.576821	+	0.816871i	$0.695707\pi$
$762$		0			0
$763$	36.1870	−	25.4119i	1.31006	−	0.919972i
$764$		0			0
$765$	7.68351	+	25.1618i	0.277798	+	0.909727i
$766$		0			0
$767$	−16.4233	−	9.48202i	−0.593013	−	0.342376i
$768$		0			0
$769$	23.1698	+	13.3771i	0.835524	+	0.482390i	0.855740	−	0.517406i	$-0.173102\pi$
$769$	23.1698	+	13.3771i	0.835524	+	0.482390i	−0.0202163	+	0.999796i	$0.506435\pi$
$770$		0			0
$771$	−12.2936	+	16.6080i	−0.442742	+	0.598121i
$772$		0			0
$773$	3.97203	+	6.87976i	0.142864	+	0.247448i	0.928574	−	0.371147i	$-0.121035\pi$
$773$	3.97203	+	6.87976i	0.142864	+	0.247448i	−0.785710	+	0.618595i	$0.787702\pi$
$774$		0			0
$775$	−0.834960	−	0.482065i	−0.0299927	−	0.0173163i
$776$		0			0
$777$	−0.287626	+	11.5091i	−0.0103185	+	0.412886i
$778$		0			0
$779$	−1.06286	+	0.613643i	−0.0380809	+	0.0219860i
$780$		0			0
$781$	1.03843	−	1.79861i	0.0371579	−	0.0643593i
$782$		0			0
$783$	4.14959	−	0.766922i	0.148294	−	0.0274076i
$784$		0			0
$785$	22.6013	−	13.0489i	0.806676	−	0.465734i
$786$		0			0
$787$		−	12.1939i		−	0.434666i	−0.976097	−	0.217333i	$-0.930264\pi$
$787$		−	12.1939i		−	0.434666i	0.976097	−	0.217333i	$-0.0697358\pi$
$788$		0			0
$789$	−1.51690	+	13.2939i	−0.0540031	+	0.473274i
$790$		0			0
$791$	−1.53829	+	3.31064i	−0.0546954	+	0.117713i
$792$		0			0
$793$	11.6410	−	20.1627i	0.413382	−	0.715999i
$794$		0			0
$795$	0.879389	−	7.70681i	0.0311887	−	0.273332i
$796$		0			0
$797$	3.30173	−	5.71876i	0.116953	−	0.202569i	−0.801606	−	0.597853i	$-0.796021\pi$
$797$	3.30173	−	5.71876i	0.116953	−	0.202569i	0.918559	+	0.395284i	$0.129354\pi$
$798$		0			0
$799$	14.1956	+	24.5875i	0.502204	+	0.869842i
$800$		0			0
$801$	12.4655	+	40.8216i	0.440445	+	1.44236i
$802$		0			0
$803$	2.13964			0.0755062
$804$		0			0
$805$	−13.8228	+	29.7488i	−0.487190	+	1.04851i
$806$		0			0
$807$	10.2790	−	13.8864i	0.361837	−	0.488823i
$808$		0			0
$809$	−8.57462	+	4.95056i	−0.301468	+	0.174052i	−0.643102	−	0.765780i	$-0.722353\pi$
$809$	−8.57462	+	4.95056i	−0.301468	+	0.174052i	0.341634	+	0.939833i	$0.389020\pi$
$810$		0			0
$811$			33.1027i			1.16239i	0.813763	+	0.581197i	$0.197416\pi$
$811$			33.1027i			1.16239i	−0.813763	+	0.581197i	$0.802584\pi$
$812$		0			0
$813$	−0.819682	+	7.18355i	−0.0287475	+	0.251938i
$814$		0			0
$815$	19.2610			0.674683
$816$		0			0
$817$			10.9675i			0.383704i
$818$		0			0
$819$	−8.61971	−	21.2717i	−0.301197	−	0.743292i
$820$		0			0
$821$			11.4327i			0.399004i	0.979897	+	0.199502i	$0.0639324\pi$
$821$			11.4327i			0.399004i	−0.979897	+	0.199502i	$0.936068\pi$
$822$		0			0
$823$	38.9019			1.35603			0.678017	−	0.735047i	$-0.262840\pi$
$823$	38.9019			1.35603			0.678017	+	0.735047i	$0.262840\pi$
$824$		0			0
$825$	0.0306495	+	0.0226874i	0.00106708	+	0.000789874i
$826$		0			0
$827$			8.05228i			0.280005i	0.990151	+	0.140003i	$0.0447111\pi$
$827$			8.05228i			0.280005i	−0.990151	+	0.140003i	$0.955289\pi$
$828$		0			0
$829$	−11.3389	+	6.54652i	−0.393816	+	0.227370i	−0.683812	−	0.729658i	$-0.739679\pi$
$829$	−11.3389	+	6.54652i	−0.393816	+	0.227370i	0.289996	+	0.957028i	$0.406346\pi$
$830$		0			0
$831$	7.65806	+	0.873826i	0.265655	+	0.0303127i
$832$		0			0
$833$	17.9220	+	21.2409i	0.620960	+	0.735953i
$834$		0			0
$835$	39.3113			1.36042
$836$		0			0
$837$	13.8374	−	39.0132i	0.478290	−	1.34849i
$838$		0			0
$839$	5.51797	+	9.55740i	0.190501	+	0.329958i	0.945416	−	0.325864i	$-0.105655\pi$
$839$	5.51797	+	9.55740i	0.190501	+	0.329958i	−0.754915	+	0.655822i	$0.772322\pi$
$840$		0			0
$841$	−14.1702	+	24.5436i	−0.488629	+	0.846330i
$842$		0			0
$843$	39.4600	+	29.2091i	1.35907	+	1.00601i
$844$		0			0
$845$	5.12271	−	8.87279i	0.176227	−	0.305233i
$846$		0			0
$847$	−23.7456	+	16.6751i	−0.815908	+	0.572962i
$848$		0			0
$849$	−18.4209	+	8.00594i	−0.632202	+	0.274763i
$850$		0			0
$851$			14.1017i			0.483400i
$852$		0			0
$853$	−20.2134	+	11.6702i	−0.692092	+	0.399580i	−0.804395	−	0.594094i	$-0.797511\pi$
$853$	−20.2134	+	11.6702i	−0.692092	+	0.399580i	0.112303	+	0.993674i	$0.464177\pi$
$854$		0			0
$855$	4.85064	+	4.52634i	0.165888	+	0.154798i
$856$		0			0
$857$	9.10606	−	15.7722i	0.311057	−	0.538767i	−0.667534	−	0.744579i	$-0.732650\pi$
$857$	9.10606	−	15.7722i	0.311057	−	0.538767i	0.978592	+	0.205812i	$0.0659836\pi$
$858$		0			0
$859$	−33.9133	+	19.5799i	−1.15711	+	0.668057i	−0.950609	−	0.310390i	$-0.899540\pi$
$859$	−33.9133	+	19.5799i	−1.15711	+	0.668057i	−0.206499	+	0.978447i	$0.566207\pi$
$860$		0			0
$861$	−0.140341	+	5.61562i	−0.00478282	+	0.191380i
$862$		0			0
$863$	−22.7847	−	13.1548i	−0.775601	−	0.447793i	0.0592683	−	0.998242i	$-0.481123\pi$
$863$	−22.7847	−	13.1548i	−0.775601	−	0.447793i	−0.834869	+	0.550449i	$0.814457\pi$
$864$		0			0
$865$	21.1168	+	36.5754i	0.717994	+	1.24360i
$866$		0			0
$867$	−2.12923	−	0.242957i	−0.0723125	−	0.00825125i
$868$		0			0
$869$	2.00235	+	1.15606i	0.0679252	+	0.0392166i
$870$		0			0
$871$	17.2545	+	9.96189i	0.584646	+	0.337546i
$872$		0			0
$873$	−2.34927	+	10.1603i	−0.0795107	+	0.343872i
$874$		0			0
$875$	−2.64894	−	29.8100i	−0.0895506	−	1.00776i
$876$		0			0
$877$	−3.59833	−	6.23249i	−0.121507	−	0.210456i	0.798855	−	0.601523i	$-0.205439\pi$
$877$	−3.59833	−	6.23249i	−0.121507	−	0.210456i	−0.920362	+	0.391067i	$0.872106\pi$
$878$		0			0
$879$	49.6299	+	5.66304i	1.67397	+	0.191010i
$880$		0			0
$881$	−37.2133			−1.25375			−0.626874	−	0.779121i	$-0.715666\pi$
$881$	−37.2133			−1.25375			−0.626874	+	0.779121i	$0.715666\pi$
$882$		0			0
$883$	−9.72629			−0.327316			−0.163658	−	0.986517i	$-0.552329\pi$
$883$	−9.72629			−0.327316			−0.163658	+	0.986517i	$0.552329\pi$
$884$		0			0
$885$	14.9278	−	20.1667i	0.501793	−	0.677897i
$886$		0			0
$887$	−10.3493	−	17.9255i	−0.347496	−	0.601881i	0.638308	−	0.769781i	$-0.279635\pi$
$887$	−10.3493	−	17.9255i	−0.347496	−	0.601881i	−0.985804	+	0.167900i	$0.946301\pi$
$888$		0			0
$889$	−2.80277	−	31.5411i	−0.0940019	−	1.05786i
$890$		0			0
$891$	−0.718695	+	1.47104i	−0.0240772	+	0.0492817i
$892$		0			0
$893$	6.20041	+	3.57981i	0.207489	+	0.119794i
$894$		0			0
$895$	−11.7486	−	6.78307i	−0.392713	−	0.226733i
$896$		0			0
$897$	−11.2058	−	25.7834i	−0.374151	−	0.860884i
$898$		0			0
$899$	−3.23480	−	5.60284i	−0.107887	−	0.186865i
$900$		0			0
$901$	−6.97115	−	4.02480i	−0.232243	−	0.134085i
$902$		0			0
$903$	42.8329	+	26.1778i	1.42539	+	0.871142i
$904$		0			0
$905$	21.2731	−	12.2821i	0.707143	−	0.408269i
$906$		0			0
$907$	0.495464	−	0.858169i	0.0164516	−	0.0284950i	−0.857682	−	0.514180i	$-0.828096\pi$
$907$	0.495464	−	0.858169i	0.0164516	−	0.0284950i	0.874134	+	0.485685i	$0.161430\pi$
$908$		0			0
$909$	8.32839	+	27.2736i	0.276235	+	0.904609i
$910$		0			0
$911$	−15.2170	+	8.78552i	−0.504161	+	0.291077i	−0.730430	−	0.682987i	$-0.760680\pi$
$911$	−15.2170	+	8.78552i	−0.504161	+	0.291077i	0.226269	+	0.974065i	$0.427347\pi$
$912$		0			0
$913$			2.61622i			0.0865842i
$914$		0			0
$915$	24.7584	+	18.3267i	0.818488	+	0.605862i
$916$		0			0
$917$	15.9228	−	11.1816i	0.525818	−	0.369250i
$918$		0			0
$919$	9.22417	−	15.9767i	0.304277	−	0.527024i	−0.672823	−	0.739804i	$-0.734918\pi$
$919$	9.22417	−	15.9767i	0.304277	−	0.527024i	0.977100	+	0.212780i	$0.0682517\pi$
$920$		0			0
$921$	17.1746	−	7.46429i	0.565921	−	0.245957i
$922$		0			0
$923$	16.5066	−	28.5903i	0.543322	−	0.941061i
$924$		0			0
$925$	−0.152024	−	0.263313i	−0.00499851	−	0.00865767i
$926$		0			0
$927$	5.66690	−	24.5085i	0.186125	−	0.804966i
$928$		0			0
$929$	−20.9425			−0.687100			−0.343550	−	0.939134i	$-0.611629\pi$
$929$	−20.9425			−0.687100			−0.343550	+	0.939134i	$0.611629\pi$
$930$		0			0
$931$	6.59226	+	2.37908i	0.216053	+	0.0779712i
$932$		0			0
$933$	11.8631	+	27.2957i	0.388380	+	0.893621i
$934$		0			0
$935$	−1.38157	+	0.797652i	−0.0451823	+	0.0260860i
$936$		0			0
$937$		−	27.1677i		−	0.887529i	−0.896143	−	0.443764i	$-0.853643\pi$
$937$		−	27.1677i		−	0.887529i	0.896143	−	0.443764i	$-0.146357\pi$
$938$		0			0
$939$	−14.5253	+	6.31290i	−0.474016	+	0.206014i
$940$		0			0
$941$	−2.85152			−0.0929569			−0.0464785	−	0.998919i	$-0.514800\pi$
$941$	−2.85152			−0.0929569			−0.0464785	+	0.998919i	$0.514800\pi$
$942$		0			0
$943$			6.88064i			0.224065i
$944$		0			0
$945$	29.2551	−	8.14022i	0.951670	−	0.264802i
$946$		0			0
$947$			17.6279i			0.572830i	0.958106	+	0.286415i	$0.0924635\pi$
$947$			17.6279i			0.572830i	−0.958106	+	0.286415i	$0.907536\pi$
$948$		0			0
$949$	34.0112			1.10405
$950$		0			0
$951$	−1.80610	+	0.784953i	−0.0585667	+	0.0254539i
$952$		0			0
$953$		−	47.1766i		−	1.52820i	−0.645097	−	0.764101i	$-0.723183\pi$
$953$		−	47.1766i		−	1.52820i	0.645097	−	0.764101i	$-0.276817\pi$
$954$		0			0
$955$	−28.5697	+	16.4947i	−0.924493	+	0.533756i
$956$		0			0
$957$	0.101994	+	0.234677i	0.00329699	+	0.00758603i
$958$		0			0
$959$	−18.3193	+	39.4259i	−0.591560	+	1.27313i
$960$		0			0
$961$	−32.4631			−1.04720
$962$		0			0
$963$	−42.1788	+	12.8799i	−1.35919	+	0.415049i
$964$		0			0
$965$	−13.7255	−	23.7732i	−0.441838	−	0.765286i
$966$		0			0
$967$	3.62809	−	6.28404i	0.116672	−	0.202081i	−0.801775	−	0.597626i	$-0.796111\pi$
$967$	3.62809	−	6.28404i	0.116672	−	0.202081i	0.918447	+	0.395545i	$0.129444\pi$
$968$		0			0
$969$	6.31433	−	2.74429i	0.202846	−	0.0881594i
$970$		0			0
$971$	−10.2653	+	17.7800i	−0.329429	+	0.570588i	−0.982399	−	0.186796i	$-0.940190\pi$
$971$	−10.2653	+	17.7800i	−0.329429	+	0.570588i	0.652970	+	0.757384i	$0.273523\pi$
$972$		0			0
$973$	14.4324	−	31.0608i	0.462683	−	0.995764i
$974$		0			0
$975$	0.487198	+	0.360634i	0.0156028	+	0.0115495i
$976$		0			0
$977$			44.7499i			1.43168i	0.698267	+	0.715838i	$0.253955\pi$
$977$			44.7499i			1.43168i	−0.698267	+	0.715838i	$0.746045\pi$
$978$		0			0
$979$	−2.24142	+	1.29408i	−0.0716360	+	0.0413591i
$980$		0			0
$981$	−48.8500	−	11.2952i	−1.55966	−	0.360627i
$982$		0			0
$983$	−13.4550	+	23.3047i	−0.429146	+	0.743303i	−0.996798	−	0.0799658i	$-0.974519\pi$
$983$	−13.4550	+	23.3047i	−0.429146	+	0.743303i	0.567651	+	0.823269i	$0.307852\pi$
$984$		0			0
$985$	−30.8959	+	17.8378i	−0.984425	+	0.568358i
$986$		0			0
$987$	28.7802	−	15.6709i	0.916084	−	0.498810i
$988$		0			0
$989$	53.2502	+	30.7440i	1.69326	+	0.977602i
$990$		0			0
$991$	−13.8668	−	24.0181i	−0.440494	−	0.762959i	0.557232	−	0.830357i	$-0.311864\pi$
$991$	−13.8668	−	24.0181i	−0.440494	−	0.762959i	−0.997726	+	0.0673982i	$0.978530\pi$
$992$		0			0
$993$	−4.17538	−	9.60711i	−0.132502	−	0.304873i
$994$		0			0
$995$	47.6585	+	27.5156i	1.51088	+	0.872304i
$996$		0			0
$997$	19.4320	+	11.2191i	0.615418	+	0.355312i	0.775083	−	0.631859i	$-0.217708\pi$
$997$	19.4320	+	11.2191i	0.615418	+	0.355312i	−0.159665	+	0.987171i	$0.551041\pi$
$998$		0			0
$999$	9.93071	−	8.47299i	0.314194	−	0.268074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.257.10		48
3.2	odd	2		3024.2.ca.e.2609.7		48
4.3	odd	2		504.2.bs.a.257.15	✓	48
7.3	odd	6		1008.2.df.e.689.17		48
9.2	odd	6		1008.2.df.e.929.17		48
9.7	even	3		3024.2.df.e.1601.7		48
12.11	even	2		1512.2.bs.a.1097.7		48
21.17	even	6		3024.2.df.e.17.7		48
28.3	even	6		504.2.cx.a.185.8	yes	48
36.7	odd	6		1512.2.cx.a.89.7		48
36.11	even	6		504.2.cx.a.425.8	yes	48
63.38	even	6	inner	1008.2.ca.e.353.10		48
63.52	odd	6		3024.2.ca.e.2033.7		48
84.59	odd	6		1512.2.cx.a.17.7		48
252.115	even	6		1512.2.bs.a.521.7		48
252.227	odd	6		504.2.bs.a.353.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.15	✓	48	4.3	odd	2
504.2.bs.a.353.15	yes	48	252.227	odd	6
504.2.cx.a.185.8	yes	48	28.3	even	6
504.2.cx.a.425.8	yes	48	36.11	even	6
1008.2.ca.e.257.10		48	1.1	even	1	trivial
1008.2.ca.e.353.10		48	63.38	even	6	inner
1008.2.df.e.689.17		48	7.3	odd	6
1008.2.df.e.929.17		48	9.2	odd	6
1512.2.bs.a.521.7		48	252.115	even	6
1512.2.bs.a.1097.7		48	12.11	even	2
1512.2.cx.a.17.7		48	84.59	odd	6
1512.2.cx.a.89.7		48	36.7	odd	6
3024.2.ca.e.2033.7		48	63.52	odd	6
3024.2.ca.e.2609.7		48	3.2	odd	2
3024.2.df.e.17.7		48	21.17	even	6
3024.2.df.e.1601.7		48	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.690387 - 1.58851i) q^{3} +(1.10442 + 1.91291i) q^{5} +(-0.234181 - 2.63537i) q^{7} +(-2.04673 + 2.19337i) q^{9} +(-0.157541 - 0.0909565i) q^{11} +(-2.50424 - 1.44582i) q^{13} +(2.27620 - 3.07503i) q^{15} +(-1.98511 - 3.43832i) q^{17} +(-0.867067 - 0.500601i) q^{19} +(-4.02463 + 2.19142i) q^{21} +(-4.86112 + 2.80657i) q^{23} +(0.0605124 - 0.104811i) q^{25} +(4.89724 + 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} -7.96637i q^{31} +(-0.0357208 + 0.313051i) q^{33} +(4.78259 - 3.35852i) q^{35} +(1.25614 - 2.17569i) q^{37} +(-0.567810 + 4.97619i) q^{39} +(0.612906 - 1.06158i) q^{41} +(-5.47716 - 9.48671i) q^{43} +(-6.45618 - 1.49281i) q^{45} -7.15102 q^{47} +(-6.89032 + 1.23430i) q^{49} +(-4.09131 + 5.52715i) q^{51} +(1.75586 - 1.01374i) q^{53} -0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +6.55821 q^{59} +8.05143i q^{61} +(6.25965 + 4.88024i) q^{63} -6.38719i q^{65} -6.89011 q^{67} +(7.81431 + 5.78431i) q^{69} +11.4168i q^{71} +(-10.1861 + 5.88094i) q^{73} +(-0.208270 - 0.0237647i) q^{75} +(-0.202811 + 0.436479i) q^{77} -12.7100 q^{79} +(-0.621788 - 8.97850i) q^{81} +(-7.19085 - 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(-1.13058 - 0.836880i) q^{87} +(7.11375 - 12.3214i) q^{89} +(-3.22383 + 6.93818i) q^{91} +(-12.6547 + 5.49988i) q^{93} -2.21150i q^{95} +(3.01040 - 1.73805i) q^{97} +(0.521946 - 0.159384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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