LMFDB - Embedded newform 1008.2.df.e.689.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (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			689.17
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.e.929.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03050 - 1.39215i) q^{3} +2.20884 q^{5} +(-2.16520 - 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} +0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(2.27620 - 3.07503i) q^{15} +(1.98511 - 3.43832i) q^{17} +(-0.867067 + 0.500601i) q^{19} +(-4.34798 + 1.44743i) q^{21} -5.61313i q^{23} -0.121025 q^{25} +(-4.89724 - 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} +(6.89908 - 3.98319i) q^{31} +(0.253250 + 0.187461i) q^{33} +(-4.78259 - 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(4.59341 - 1.99636i) q^{39} +(-0.612906 + 1.06158i) q^{41} +(-5.47716 - 9.48671i) q^{43} +(-1.93528 - 6.33762i) q^{45} +(-3.57551 + 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(-2.74100 - 6.30675i) q^{51} +(-1.75586 - 1.01374i) q^{53} +0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +(3.27911 + 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(-2.46555 + 7.54460i) q^{63} +(5.53147 + 3.19359i) q^{65} +(3.44505 + 5.96701i) q^{67} +(-7.81431 - 5.78431i) q^{69} +11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(-0.124716 + 0.168485i) q^{75} +(0.276597 - 0.393879i) q^{77} +(6.35501 - 11.0072i) q^{79} +(-7.46471 + 5.02773i) q^{81} +(7.19085 + 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(0.159468 - 1.39755i) q^{87} +(-7.11375 - 12.3214i) q^{89} +(-3.22383 - 6.93818i) q^{91} +(1.56429 - 13.7092i) q^{93} +(-1.91521 + 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +(0.521946 - 0.159384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Character values

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

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

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
$3$	1.03050	−	1.39215i	0.594958	−	0.803757i
$3$	1.03050	−	1.39215i	0.594958	−	0.803757i
$4$		0			0
$5$	2.20884			0.987823			0.493912	−	0.869512i	$-0.335567\pi$
$5$	2.20884			0.987823			0.493912	+	0.869512i	$0.335567\pi$
$6$		0			0
$7$	−2.16520	−	1.52049i	−0.818370	−	0.574691i
$7$	−2.16520	−	1.52049i	−0.818370	−	0.574691i
$8$		0			0
$9$	−0.876153	−	2.86921i	−0.292051	−	0.956403i
$10$		0			0
$11$			0.181913i			0.0548488i	0.999624	+	0.0274244i	$0.00873056\pi$
$11$			0.181913i			0.0548488i	−0.999624	+	0.0274244i	$0.991269\pi$
$12$		0			0
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	0.805315	−	0.592847i	$-0.201996\pi$
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	−0.110763	+	0.993847i	$0.535330\pi$
$14$		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	$-0.673440\pi$
$17$	1.98511	−	3.43832i	0.481461	−	0.833915i	0.999774	+	0.0212765i	$0.00677302\pi$
$18$		0			0
$19$	−0.867067	+	0.500601i	−0.198919	+	0.114846i	−0.596151	−	0.802872i	$-0.703304\pi$
$19$	−0.867067	+	0.500601i	−0.198919	+	0.114846i	0.397232	+	0.917718i	$0.369971\pi$
$20$		0			0
$21$	−4.34798	+	1.44743i	−0.948808	+	0.315854i
$22$		0			0
$23$		−	5.61313i		−	1.17042i	−0.810882	−	0.585210i	$-0.801012\pi$
$23$		−	5.61313i		−	1.17042i	0.810882	−	0.585210i	$-0.198988\pi$
$24$		0			0
$25$	−0.121025			−0.0242050
$26$		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
$31$	6.89908	−	3.98319i	1.23911	−	0.715401i	0.270199	−	0.962805i	$-0.412911\pi$
$31$	6.89908	−	3.98319i	1.23911	−	0.715401i	0.968913	+	0.247403i	$0.0795772\pi$
$32$		0			0
$33$	0.253250	+	0.187461i	0.0440851	+	0.0326327i
$34$		0			0
$35$	−4.78259	−	3.35852i	−0.808405	−	0.567693i
$36$		0			0
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	0.950612	−	0.310382i	$-0.100457\pi$
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	−0.744105	+	0.668063i	$0.767124\pi$
$38$		0			0
$39$	4.59341	−	1.99636i	0.735535	−	0.319673i
$40$		0			0
$41$	−0.612906	+	1.06158i	−0.0957198	+	0.165792i	−0.909909	−	0.414808i	$-0.863849\pi$
$41$	−0.612906	+	1.06158i	−0.0957198	+	0.165792i	0.814189	+	0.580600i	$0.197182\pi$
$42$		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
$45$	−1.93528	−	6.33762i	−0.288495	−	0.944757i
$46$		0			0
$47$	−3.57551	+	6.19296i	−0.521542	+	0.903336i	0.478145	+	0.878281i	$0.341309\pi$
$47$	−3.57551	+	6.19296i	−0.521542	+	0.903336i	−0.999686	+	0.0250552i	$0.992024\pi$
$48$		0			0
$49$	2.37622	+	6.58434i	0.339460	+	0.940620i
$50$		0			0
$51$	−2.74100	−	6.30675i	−0.383816	−	0.883121i
$52$		0			0
$53$	−1.75586	−	1.01374i	−0.241186	−	0.139249i	0.374536	−	0.927212i	$-0.377802\pi$
$53$	−1.75586	−	1.01374i	−0.241186	−	0.139249i	−0.615722	+	0.787964i	$0.711135\pi$
$54$		0			0
$55$			0.401817i			0.0541810i
$56$		0			0
$57$	−0.196598	+	1.72295i	−0.0260401	+	0.228211i
$58$		0			0
$59$	3.27911	+	5.67958i	0.426903	+	0.739418i	0.996596	−	0.0824396i	$-0.0262712\pi$
$59$	3.27911	+	5.67958i	0.426903	+	0.739418i	−0.569693	+	0.821858i	$0.692938\pi$
$60$		0			0
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.874847	−	0.484399i	$-0.160962\pi$
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.0179215	+	0.999839i	$0.494295\pi$
$62$		0			0
$63$	−2.46555	+	7.54460i	−0.310630	+	0.950531i
$64$		0			0
$65$	5.53147	+	3.19359i	0.686094	+	0.396117i
$66$		0			0
$67$	3.44505	+	5.96701i	0.420880	+	0.728986i	0.996026	−	0.0890650i	$-0.0283879\pi$
$67$	3.44505	+	5.96701i	0.420880	+	0.728986i	−0.575145	+	0.818051i	$0.695055\pi$
$68$		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	−0.233388	−	0.972384i	$-0.574981\pi$
$73$	−10.1861	−	5.88094i	−1.19219	−	0.688312i	−0.958803	+	0.284072i	$0.908315\pi$
$74$		0			0
$75$	−0.124716	+	0.168485i	−0.0144009	+	0.0194549i
$76$		0			0
$77$	0.276597	−	0.393879i	0.0315211	−	0.0448867i
$78$		0			0
$79$	6.35501	−	11.0072i	0.714994	−	1.23841i	−0.247968	−	0.968768i	$-0.579763\pi$
$79$	6.35501	−	11.0072i	0.714994	−	1.23841i	0.962962	−	0.269638i	$-0.0869040\pi$
$80$		0			0
$81$	−7.46471	+	5.02773i	−0.829412	+	0.558637i
$82$		0			0
$83$	7.19085	+	12.4549i	0.789298	+	1.36710i	0.926397	+	0.376547i	$0.122889\pi$
$83$	7.19085	+	12.4549i	0.789298	+	1.36710i	−0.137099	+	0.990557i	$0.543778\pi$
$84$		0			0
$85$	4.38480	−	7.59470i	0.475598	−	0.823760i
$86$		0			0
$87$	0.159468	−	1.39755i	0.0170968	−	0.149833i
$88$		0			0
$89$	−7.11375	−	12.3214i	−0.754055	−	1.30606i	−0.945843	−	0.324626i	$-0.894762\pi$
$89$	−7.11375	−	12.3214i	−0.754055	−	1.30606i	0.191787	−	0.981437i	$-0.438572\pi$
$90$		0			0
$91$	−3.22383	−	6.93818i	−0.337949	−	0.727319i
$92$		0			0
$93$	1.56429	−	13.7092i	0.162210	−	1.42158i
$94$		0			0
$95$	−1.91521	+	1.10575i	−0.196497	+	0.113447i
$96$		0			0
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	−0.644982	−	0.764197i	$-0.723135\pi$
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	0.339323	+	0.940670i	$0.389802\pi$
$98$		0			0
$99$	0.521946	−	0.159384i	0.0524576	−	0.0160187i
$100$		0			0
$101$	9.50563			0.945846			0.472923	−	0.881104i	$-0.343199\pi$
$101$	9.50563			0.945846			0.472923	+	0.881104i	$0.343199\pi$
$102$		0			0
$103$			8.38505i			0.826204i	0.910685	+	0.413102i	$0.135555\pi$
$103$			8.38505i			0.826204i	−0.910685	+	0.413102i	$0.864445\pi$
$104$		0			0
$105$	−9.60400	+	3.19713i	−0.937254	+	0.312008i
$106$		0			0
$107$	−12.7310	+	7.35026i	−1.23075	+	0.710576i	−0.967187	−	0.254065i	$-0.918232\pi$
$107$	−12.7310	+	7.35026i	−1.23075	+	0.710576i	−0.263567	+	0.964641i	$0.584899\pi$
$108$		0			0
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	−0.118944	−	0.992901i	$-0.537951\pi$
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	0.919350	−	0.393442i	$-0.128716\pi$
$110$		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
$115$		−	12.3985i		−	1.15617i
$116$		0			0
$117$	1.95427	−	8.45195i	0.180673	−	0.781383i
$118$		0			0
$119$	−9.52611	+	4.42632i	−0.873257	+	0.405760i
$120$		0			0
$121$	10.9669			0.996992
$122$		0			0
$123$	0.846285	+	1.94721i	0.0763069	+	0.175574i
$124$		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
$129$	−18.8511	−	2.15101i	−1.65975	−	0.189386i
$130$		0			0
$131$	7.35396			0.642519			0.321259	−	0.946991i	$-0.395894\pi$
$131$	7.35396			0.642519			0.321259	+	0.946991i	$0.395894\pi$
$132$		0			0
$133$	2.63854	+	0.234462i	0.228790	+	0.0203305i
$134$		0			0
$135$	−10.8172	−	3.83670i	−0.930997	−	0.330210i
$136$		0			0
$137$			16.4316i			1.40385i	0.712251	+	0.701925i	$0.247676\pi$
$137$			16.4316i			1.40385i	−0.712251	+	0.701925i	$0.752324\pi$
$138$		0			0
$139$	−11.2110	−	6.47266i	−0.950903	−	0.549004i	−0.0575417	−	0.998343i	$-0.518326\pi$
$139$	−11.2110	−	6.47266i	−0.950903	−	0.549004i	−0.893361	+	0.449339i	$0.851660\pi$
$140$		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
$147$	11.6151	+	3.47709i	0.957995	+	0.286786i
$148$		0			0
$149$			15.2359i			1.24818i	0.781354	+	0.624088i	$0.214529\pi$
$149$			15.2359i			1.24818i	−0.781354	+	0.624088i	$0.785471\pi$
$150$		0			0
$151$	13.6625			1.11184			0.555919	−	0.831236i	$-0.312366\pi$
$151$	13.6625			1.11184			0.555919	+	0.831236i	$0.312366\pi$
$152$		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
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	−0.0326299	−	0.999468i	$-0.510388\pi$
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	0.849249	+	0.527992i	$0.177055\pi$
$158$		0			0
$159$	−3.22069	+	1.39975i	−0.255417	+	0.111008i
$160$		0			0
$161$	−8.53471	+	12.1536i	−0.672630	+	0.957836i
$162$		0			0
$163$	4.35998	+	7.55170i	0.341500	+	0.591495i	0.984711	−	0.174194i	$-0.0557319\pi$
$163$	4.35998	+	7.55170i	0.341500	+	0.591495i	−0.643212	+	0.765688i	$0.722399\pi$
$164$		0			0
$165$	0.559389	+	0.414071i	0.0435483	+	0.0322354i
$166$		0			0
$167$	−8.89862	+	15.4129i	−0.688596	+	1.19268i	0.283696	+	0.958914i	$0.408439\pi$
$167$	−8.89862	+	15.4129i	−0.688596	+	1.19268i	−0.972292	+	0.233769i	$0.924894\pi$
$168$		0			0
$169$	−2.31918	−	4.01695i	−0.178399	−	0.308996i
$170$		0			0
$171$	2.19601	+	2.04919i	0.167933	+	0.156706i
$172$		0			0
$173$	9.56015	−	16.5587i	0.726845	−	1.25893i	−0.231366	−	0.972867i	$-0.574319\pi$
$173$	9.56015	−	16.5587i	0.726845	−	1.25893i	0.958210	−	0.286065i	$-0.0923473\pi$
$174$		0			0
$175$	0.262044	+	0.184017i	0.0198086	+	0.0139104i
$176$		0			0
$177$	11.2859	+	1.28779i	0.848302	+	0.0967959i
$178$		0			0
$179$	5.31891	+	3.07088i	0.397554	+	0.229528i	0.685428	−	0.728140i	$-0.259615\pi$
$179$	5.31891	+	3.07088i	0.397554	+	0.229528i	−0.287874	+	0.957668i	$0.592948\pi$
$180$		0			0
$181$			11.1208i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$181$			11.1208i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$182$		0			0
$183$	12.7898	−	5.55861i	0.945448	−	0.410904i
$184$		0			0
$185$	2.77460	+	4.80575i	0.203993	+	0.353326i
$186$		0			0
$187$	0.625475	+	0.361118i	0.0457393	+	0.0264076i
$188$		0			0
$189$	7.96246	+	11.2071i	0.579184	+	0.815197i
$190$		0			0
$191$	−12.9342	−	7.46759i	−0.935889	−	0.540336i	−0.0472195	−	0.998885i	$-0.515036\pi$
$191$	−12.9342	−	7.46759i	−0.935889	−	0.540336i	−0.888669	+	0.458549i	$0.848369\pi$
$192$		0			0
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	0.998208	−	0.0598363i	$-0.0190579\pi$
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	−0.550924	+	0.834556i	$0.685725\pi$
$194$		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	0.999383	+	0.0351325i	$0.0111853\pi$
$199$	21.5762	+	12.4571i	1.52950	+	0.883057i	0.530117	+	0.847925i	$0.322148\pi$
$200$		0			0
$201$	11.8571	+	1.35296i	0.836334	+	0.0954302i
$202$		0			0
$203$	−2.14022	−	0.190181i	−0.150214	−	0.0133481i
$204$		0			0
$205$	−1.35381	+	2.34487i	−0.0945542	+	0.163773i
$206$		0			0
$207$	−16.1052	+	4.91796i	−1.11939	+	0.341822i
$208$		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
$213$	15.8938	+	11.7649i	1.08903	+	0.806120i
$214$		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
$219$	−18.6839	+	8.12025i	−1.26254	+	0.548716i
$220$		0			0
$221$	9.94241	−	5.74025i	0.668799	−	0.386131i
$222$		0			0
$223$	−13.9653	+	8.06285i	−0.935183	+	0.539928i	−0.888447	−	0.458979i	$-0.848215\pi$
$223$	−13.9653	+	8.06285i	−0.935183	+	0.539928i	−0.0467358	+	0.998907i	$0.514882\pi$
$224$		0			0
$225$	0.106036	+	0.347246i	0.00706909	+	0.0231497i
$226$		0			0
$227$	19.8036			1.31441			0.657206	−	0.753711i	$-0.271738\pi$
$227$	19.8036			1.31441			0.657206	+	0.753711i	$0.271738\pi$
$228$		0			0
$229$		−	15.6001i		−	1.03088i	−0.856924	−	0.515442i	$-0.827628\pi$
$229$		−	15.6001i		−	1.03088i	0.856924	−	0.515442i	$-0.172372\pi$
$230$		0			0
$231$	−0.263306	−	0.790955i	−0.0173242	−	0.0520410i
$232$		0			0
$233$	−10.6450	+	6.14590i	−0.697378	+	0.402631i	−0.806370	−	0.591411i	$-0.798571\pi$
$233$	−10.6450	+	6.14590i	−0.697378	+	0.402631i	0.108992	+	0.994043i	$0.465238\pi$
$234$		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
$241$			20.6872i			1.33258i	0.745693	+	0.666290i	$0.232119\pi$
$241$			20.6872i			1.33258i	−0.745693	+	0.666290i	$0.767881\pi$
$242$		0			0
$243$	−0.693013	+	15.5730i	−0.0444568	+	0.999011i
$244$		0			0
$245$	5.24869	+	14.5438i	0.335327	+	0.929167i
$246$		0			0
$247$	−2.89513			−0.184212
$248$		0			0
$249$	24.7492	+	2.82402i	1.56842	+	0.178965i
$250$		0			0
$251$	−7.66566			−0.483852			−0.241926	−	0.970295i	$-0.577779\pi$
$251$	−7.66566			−0.483852			−0.241926	+	0.970295i	$0.577779\pi$
$252$		0			0
$253$	1.02110			0.0641961
$254$		0			0
$255$	−6.05442	−	13.9306i	−0.379143	−	0.872368i
$256$		0			0
$257$	−11.9297			−0.744157			−0.372078	−	0.928201i	$-0.621355\pi$
$257$	−11.9297			−0.744157			−0.372078	+	0.928201i	$0.621355\pi$
$258$		0			0
$259$	0.588325	−	6.62076i	0.0365568	−	0.411394i
$260$		0			0
$261$	−1.78127	−	1.66218i	−0.110258	−	0.102886i
$262$		0			0
$263$			7.72501i			0.476345i	0.971223	+	0.238172i	$0.0765483\pi$
$263$			7.72501i			0.476345i	−0.971223	+	0.238172i	$0.923452\pi$
$264$		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	$-0.931685\pi$
$269$	−4.98739	+	8.63841i	−0.304086	+	0.526693i	0.672971	+	0.739669i	$0.265018\pi$
$270$		0			0
$271$	−3.61508	+	2.08717i	−0.219600	+	0.126786i	−0.605765	−	0.795643i	$-0.707133\pi$
$271$	−3.61508	+	2.08717i	−0.219600	+	0.126786i	0.386165	+	0.922430i	$0.373800\pi$
$272$		0			0
$273$	−12.9811	−	2.66172i	−0.785653	−	0.161094i
$274$		0			0
$275$		−	0.0220160i		−	0.00132761i
$276$		0			0
$277$	4.45007			0.267379			0.133689	−	0.991023i	$-0.457318\pi$
$277$	4.45007			0.267379			0.133689	+	0.991023i	$0.457318\pi$
$278$		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
$283$	10.0427	−	5.79815i	0.596976	−	0.344664i	−0.170875	−	0.985293i	$-0.554659\pi$
$283$	10.0427	−	5.79815i	0.596976	−	0.344664i	0.767851	+	0.640628i	$0.221326\pi$
$284$		0			0
$285$	−0.434254	+	3.80573i	−0.0257230	+	0.225432i
$286$		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
$291$	−0.682576	+	5.98198i	−0.0400133	+	0.350670i
$292$		0			0
$293$	14.4199	−	24.9760i	0.842418	−	1.45911i	−0.0454266	−	0.998968i	$-0.514465\pi$
$293$	14.4199	−	24.9760i	0.842418	−	1.45911i	0.887845	−	0.460143i	$-0.152202\pi$
$294$		0			0
$295$	7.24302	+	12.5453i	0.421705	+	0.730414i
$296$		0			0
$297$	0.315978	−	0.890871i	0.0183349	−	0.0516936i
$298$		0			0
$299$	8.11560	−	14.0566i	0.469337	−	0.812916i
$300$		0			0
$301$	−2.56529	+	28.8686i	−0.147861	+	1.66396i
$302$		0			0
$303$	9.79552	−	13.2332i	0.562738	−	0.760230i
$304$		0			0
$305$	15.4017	+	8.89216i	0.881898	+	0.509164i
$306$		0			0
$307$		−	10.8117i		−	0.617059i	−0.951215	−	0.308529i	$-0.900163\pi$
$307$		−	10.8117i		−	0.617059i	0.951215	−	0.308529i	$-0.0998368\pi$
$308$		0			0
$309$	11.6732	+	8.64077i	0.664067	+	0.491556i
$310$		0			0
$311$	−8.59161	−	14.8811i	−0.487185	−	0.843830i	0.512706	−	0.858564i	$-0.328643\pi$
$311$	−8.59161	−	14.8811i	−0.487185	−	0.843830i	−0.999891	+	0.0147345i	$0.995310\pi$
$312$		0			0
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	0.259214	−	0.965820i	$-0.416537\pi$
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	−0.706818	+	0.707396i	$0.749870\pi$
$314$		0			0
$315$	−5.44601	+	16.6648i	−0.306848	+	0.938957i
$316$		0			0
$317$	0.984650	+	0.568488i	0.0553034	+	0.0319295i	0.527397	−	0.849619i	$-0.323168\pi$
$317$	0.984650	+	0.568488i	0.0553034	+	0.0319295i	−0.472093	+	0.881549i	$0.656501\pi$
$318$		0			0
$319$	0.0738670	+	0.127941i	0.00413576	+	0.00716334i
$320$		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
$327$	−11.5384	−	26.5487i	−0.638076	−	1.46815i
$328$		0			0
$329$	17.1580	−	7.97250i	0.945954	−	0.439538i
$330$		0			0
$331$	−3.02394	+	5.23761i	−0.166211	+	0.287885i	−0.937085	−	0.349102i	$-0.886487\pi$
$331$	−3.02394	+	5.23761i	−0.166211	+	0.287885i	0.770874	+	0.636988i	$0.219820\pi$
$332$		0			0
$333$	5.14194	−	5.51035i	0.281777	−	0.301965i
$334$		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
$339$	−2.19181	+	0.952588i	−0.119043	+	0.0517375i
$340$		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
$345$	−17.2606	−	12.7766i	−0.929278	−	0.687870i
$346$		0			0
$347$	20.1007	−	11.6051i	1.07906	−	0.622995i	0.148417	−	0.988925i	$-0.452582\pi$
$347$	20.1007	−	11.6051i	1.07906	−	0.622995i	0.930643	+	0.365929i	$0.119249\pi$
$348$		0			0
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	−0.119142	−	0.992877i	$-0.538014\pi$
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	0.800286	+	0.599619i	$0.204681\pi$
$350$		0			0
$351$	−9.75250	−	11.4303i	−0.520550	−	0.610107i
$352$		0			0
$353$	−13.4624			−0.716533			−0.358267	−	0.933619i	$-0.616632\pi$
$353$	−13.4624			−0.716533			−0.358267	+	0.933619i	$0.616632\pi$
$354$		0			0
$355$			25.2178i			1.33842i
$356$		0			0
$357$	−3.65453	+	17.8231i	−0.193418	+	0.943296i
$358$		0			0
$359$	−13.5004	+	7.79444i	−0.712522	+	0.411375i	−0.811994	−	0.583666i	$-0.801618\pi$
$359$	−13.5004	+	7.79444i	−0.712522	+	0.411375i	0.0994721	+	0.995040i	$0.468285\pi$
$360$		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
$367$			8.67003i			0.452572i	0.974061	+	0.226286i	$0.0726584\pi$
$367$			8.67003i			0.452572i	−0.974061	+	0.226286i	$0.927342\pi$
$368$		0			0
$369$	3.58290	+	0.828444i	0.186519	+	0.0431271i
$370$		0			0
$371$	2.26040	+	4.86473i	0.117354	+	0.252564i
$372$		0			0
$373$	−24.0978			−1.24774			−0.623868	−	0.781530i	$-0.714440\pi$
$373$	−24.0978			−1.24774			−0.623868	+	0.781530i	$0.714440\pi$
$374$		0			0
$375$	−11.6565	+	15.7473i	−0.601939	+	0.813188i
$376$		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
$381$	12.3334	−	16.6618i	0.631859	−	0.853609i
$382$		0			0
$383$	−4.70476			−0.240402			−0.120201	−	0.992750i	$-0.538354\pi$
$383$	−4.70476			−0.240402			−0.120201	+	0.992750i	$0.538354\pi$
$384$		0			0
$385$	0.610958	−	0.870015i	0.0311373	−	0.0443401i
$386$		0			0
$387$	−22.4205	+	24.0269i	−1.13970	+	1.22136i
$388$		0			0
$389$			21.5003i			1.09011i	0.838401	+	0.545055i	$0.183491\pi$
$389$			21.5003i			1.09011i	−0.838401	+	0.545055i	$0.816509\pi$
$390$		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	−0.958809	−	0.284052i	$-0.908321\pi$
$397$	−23.7548	+	13.7148i	−1.19222	+	0.688327i	−0.233408	+	0.972379i	$0.574988\pi$
$398$		0			0
$399$	3.04541	−	3.43162i	0.152461	−	0.171796i
$400$		0			0
$401$			29.2299i			1.45967i	0.683622	+	0.729836i	$0.260404\pi$
$401$			29.2299i			1.45967i	−0.683622	+	0.729836i	$0.739596\pi$
$402$		0			0
$403$	23.0359			1.14750
$404$		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
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.364061	−	0.931375i	$-0.381390\pi$
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.988625	+	0.150401i	$0.0480565\pi$
$410$		0			0
$411$	22.8753	+	16.9328i	1.12835	+	0.835231i
$412$		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
$417$	−20.5638	+	8.93729i	−1.00701	+	0.437661i
$418$		0			0
$419$	6.80176	−	11.7810i	0.332288	−	0.575539i	−0.650672	−	0.759359i	$-0.725513\pi$
$419$	6.80176	−	11.7810i	0.332288	−	0.575539i	0.982960	+	0.183819i	$0.0588462\pi$
$420$		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
$423$	20.9016	+	4.83289i	1.01627	+	0.234983i
$424$		0			0
$425$	−0.240248	+	0.416122i	−0.0116537	+	0.0201849i
$426$		0			0
$427$	−8.97636	−	19.3185i	−0.434396	−	0.934887i
$428$		0			0
$429$	0.363163	+	0.835602i	0.0175337	+	0.0403432i
$430$		0			0
$431$	21.6467	+	12.4977i	1.04268	+	0.601994i	0.920592	−	0.390525i	$-0.127707\pi$
$431$	21.6467	+	12.4977i	1.04268	+	0.601994i	0.122091	+	0.992519i	$0.461040\pi$
$432$		0			0
$433$		−	18.7778i		−	0.902401i	−0.892423	−	0.451201i	$-0.850996\pi$
$433$		−	18.7778i		−	0.902401i	0.892423	−	0.451201i	$-0.149004\pi$
$434$		0			0
$435$	0.352240	−	3.08697i	0.0168886	−	0.148009i
$436$		0			0
$437$	2.80994	+	4.86696i	0.134418	+	0.232818i
$438$		0			0
$439$	1.82363	+	1.05287i	0.0870369	+	0.0502508i	0.542887	−	0.839806i	$-0.317331\pi$
$439$	1.82363	+	1.05287i	0.0870369	+	0.0502508i	−0.455850	+	0.890057i	$0.650665\pi$
$440$		0			0
$441$	16.8099	−	12.5868i	0.800472	−	0.599370i
$442$		0			0
$443$	11.6452	+	6.72337i	0.553281	+	0.319437i	0.750444	−	0.660934i	$-0.229840\pi$
$443$	11.6452	+	6.72337i	0.553281	+	0.319437i	−0.197163	+	0.980371i	$0.563173\pi$
$444$		0			0
$445$	−15.7131	−	27.2159i	−0.744874	−	1.29016i
$446$		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
$453$	14.0792	−	19.0202i	0.661496	−	0.893648i
$454$		0			0
$455$	−7.12093	−	15.3253i	−0.333834	−	0.718462i
$456$		0			0
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	−0.862756	−	0.505621i	$-0.831263\pi$
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	0.869258	+	0.494358i	$0.164597\pi$
$458$		0			0
$459$	−15.6938	+	13.3902i	−0.732526	+	0.624999i
$460$		0			0
$461$	−3.98573	−	6.90348i	−0.185634	−	0.321527i	0.758156	−	0.652073i	$-0.226100\pi$
$461$	−3.98573	−	6.90348i	−0.185634	−	0.321527i	−0.943790	+	0.330546i	$0.892767\pi$
$462$		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
$465$	3.45528	−	30.2814i	0.160235	−	1.40427i
$466$		0			0
$467$	−18.4485	−	31.9538i	−0.853695	−	1.47864i	−0.877850	−	0.478935i	$-0.841023\pi$
$467$	−18.4485	−	31.9538i	−0.853695	−	1.47864i	0.0241548	−	0.999708i	$-0.492311\pi$
$468$		0			0
$469$	1.61353	−	18.1580i	0.0745059	−	0.838457i
$470$		0			0
$471$	2.32005	−	20.3325i	0.106902	−	0.936872i
$472$		0			0
$473$	1.72576	−	0.996366i	0.0793504	−	0.0458130i
$474$		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
$479$	−3.41169			−0.155884			−0.0779420	−	0.996958i	$-0.524835\pi$
$479$	−3.41169			−0.155884			−0.0779420	+	0.996958i	$0.524835\pi$
$480$		0			0
$481$			7.26460i			0.331237i
$482$		0			0
$483$	8.12459	+	24.4058i	0.369682	+	1.11050i
$484$		0			0
$485$	−6.64948	+	3.83908i	−0.301938	+	0.174324i
$486$		0			0
$487$	1.17122	−	2.02861i	0.0530729	−	0.0919249i	−0.838268	−	0.545258i	$-0.816432\pi$
$487$	1.17122	−	2.02861i	0.0530729	−	0.0919249i	0.891341	+	0.453333i	$0.149765\pi$
$488$		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
$493$		−	3.22428i		−	0.145214i
$494$		0			0
$495$	1.15290	−	0.352053i	0.0518188	−	0.0158236i
$496$		0			0
$497$	17.3591	−	24.7196i	0.778660	−	1.10883i
$498$		0			0
$499$	33.3813			1.49435			0.747175	−	0.664627i	$-0.231409\pi$
$499$	33.3813			1.49435			0.747175	+	0.664627i	$0.231409\pi$
$500$		0			0
$501$	12.2870	+	28.2711i	0.548942	+	1.26306i
$502$		0			0
$503$	−6.01630			−0.268254			−0.134127	−	0.990964i	$-0.542823\pi$
$503$	−6.01630			−0.268254			−0.134127	+	0.990964i	$0.542823\pi$
$504$		0			0
$505$	20.9964			0.934328
$506$		0			0
$507$	−7.98210	−	0.910801i	−0.354497	−	0.0404501i
$508$		0			0
$509$	−10.0398			−0.445007			−0.222503	−	0.974932i	$-0.571423\pi$
$509$	−10.0398			−0.445007			−0.222503	+	0.974932i	$0.571423\pi$
$510$		0			0
$511$	13.1130	+	28.2213i	0.580087	+	1.24844i
$512$		0			0
$513$	5.11576	−	0.945490i	0.225867	−	0.0417444i
$514$		0			0
$515$			18.5212i			0.816143i
$516$		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	$-0.676436\pi$
$521$	10.8007	−	18.7074i	0.473188	−	0.819586i	0.999529	+	0.0306875i	$0.00976968\pi$
$522$		0			0
$523$	−11.6105	+	6.70332i	−0.507692	+	0.293116i	−0.731884	−	0.681429i	$-0.761359\pi$
$523$	−11.6105	+	6.70332i	−0.507692	+	0.293116i	0.224193	+	0.974545i	$0.428026\pi$
$524$		0			0
$525$	0.526214	−	0.175174i	0.0229659	−	0.00764524i
$526$		0			0
$527$		−	31.6283i		−	1.37775i
$528$		0			0
$529$	−8.50726			−0.369881
$530$		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
$535$	−28.1208	+	16.2355i	−1.21577	+	0.701924i
$536$		0			0
$537$	9.75624	−	4.24019i	0.421013	−	0.182978i
$538$		0			0
$539$	−1.19778	+	0.432265i	−0.0515919	+	0.0186190i
$540$		0			0
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	0.946935	−	0.321424i	$-0.104162\pi$
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	−0.751829	+	0.659358i	$0.770828\pi$
$542$		0			0
$543$	15.4818	+	11.4600i	0.664389	+	0.491794i
$544$		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
$549$	5.44143	−	23.5334i	0.232234	−	1.00438i
$550$		0			0
$551$	−0.406545	+	0.704157i	−0.0173194	+	0.0299981i
$552$		0			0
$553$	−30.4962	+	14.1701i	−1.29683	+	0.602574i
$554$		0			0
$555$	9.54954	+	1.08965i	0.405355	+	0.0462532i
$556$		0			0
$557$	−23.8690	−	13.7808i	−1.01136	−	0.583911i	−0.0997727	−	0.995010i	$-0.531812\pi$
$557$	−23.8690	−	13.7808i	−1.01136	−	0.583911i	−0.911591	+	0.411099i	$0.865145\pi$
$558$		0			0
$559$		−	31.6760i		−	1.33975i
$560$		0			0
$561$	1.14728	−	0.498623i	0.0484382	−	0.0210519i
$562$		0			0
$563$	−6.92328	−	11.9915i	−0.291781	−	0.505380i	0.682450	−	0.730933i	$-0.260915\pi$
$563$	−6.92328	−	11.9915i	−0.291781	−	0.505380i	−0.974231	+	0.225552i	$0.927581\pi$
$564$		0			0
$565$	−2.63941	−	1.52387i	−0.111041	−	0.0641095i
$566$		0			0
$567$	23.8072	+	0.463952i	0.999810	+	0.0194842i
$568$		0			0
$569$	−10.5219	−	6.07485i	−0.441103	−	0.254671i	0.262962	−	0.964806i	$-0.415300\pi$
$569$	−10.5219	−	6.07485i	−0.441103	−	0.254671i	−0.704065	+	0.710135i	$0.748634\pi$
$570$		0			0
$571$	−23.1505	−	40.0979i	−0.968819	−	1.67804i	−0.698985	−	0.715136i	$-0.746365\pi$
$571$	−23.1505	−	40.0979i	−0.968819	−	1.67804i	−0.269833	−	0.962907i	$-0.586969\pi$
$572$		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	0.262178	−	0.965020i	$-0.415559\pi$
$577$	−10.6284	−	6.13630i	−0.442465	−	0.255457i	−0.704643	+	0.709562i	$0.748893\pi$
$578$		0			0
$579$	21.3867	+	2.44034i	0.888801	+	0.101417i
$580$		0			0
$581$	3.36792	−	37.9011i	0.139725	−	1.57240i
$582$		0			0
$583$	0.184413	−	0.319413i	0.00763762	−	0.0132287i
$584$		0			0
$585$	4.31667	−	18.6690i	0.178473	−	0.771869i
$586$		0			0
$587$	−11.9875	−	20.7630i	−0.494778	−	0.856980i	0.505204	−	0.863000i	$-0.331417\pi$
$587$	−11.9875	−	20.7630i	−0.494778	−	0.856980i	−0.999982	+	0.00601986i	$0.998084\pi$
$588$		0			0
$589$	−3.98798	+	6.90738i	−0.164322	+	0.284614i
$590$		0			0
$591$	22.4849	+	16.6438i	0.924906	+	0.684635i
$592$		0			0
$593$	−15.4912	−	26.8315i	−0.636146	−	1.10184i	−0.986271	−	0.165134i	$-0.947194\pi$
$593$	−15.4912	−	26.8315i	−0.636146	−	1.10184i	0.350125	−	0.936703i	$-0.386139\pi$
$594$		0			0
$595$	−21.0416	+	9.77702i	−0.862623	+	0.400819i
$596$		0			0
$597$	39.5763	−	17.2004i	1.61975	−	0.703965i
$598$		0			0
$599$	21.4392	−	12.3779i	0.875981	−	0.505748i	0.00665010	−	0.999978i	$-0.497883\pi$
$599$	21.4392	−	12.3779i	0.875981	−	0.505748i	0.869331	+	0.494230i	$0.164550\pi$
$600$		0			0
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	−0.335268	−	0.942123i	$-0.608827\pi$
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	0.648268	+	0.761412i	$0.275494\pi$
$602$		0			0
$603$	14.1022	−	15.1126i	0.574286	−	0.615432i
$604$		0			0
$605$	24.2241			0.984852
$606$		0			0
$607$		−	13.0415i		−	0.529339i	−0.964339	−	0.264670i	$-0.914737\pi$
$607$		−	13.0415i		−	0.529339i	0.964339	−	0.264670i	$-0.0852629\pi$
$608$		0			0
$609$	−2.47025	+	2.78352i	−0.100099	+	0.112794i
$610$		0			0
$611$	−17.9079	+	10.3391i	−0.724475	+	0.418276i
$612$		0			0
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	−0.721704	−	0.692201i	$-0.756641\pi$
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	0.960316	+	0.278914i	$0.0899743\pi$
$614$		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
$619$		−	30.9231i		−	1.24291i	−0.783452	−	0.621453i	$-0.786543\pi$
$619$		−	30.9231i		−	1.24291i	0.783452	−	0.621453i	$-0.213457\pi$
$620$		0			0
$621$	−9.74987	+	27.4888i	−0.391249	+	1.10309i
$622$		0			0
$623$	−3.33180	+	37.4947i	−0.133486	+	1.50219i
$624$		0			0
$625$	−24.3802			−0.975209
$626$		0			0
$627$	−0.313428	−	0.0357638i	−0.0125171	−	0.00142827i
$628$		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
$633$	7.98959	+	18.3832i	0.317558	+	0.730668i
$634$		0			0
$635$	26.4363			1.04909
$636$		0			0
$637$	−3.56917	+	19.9244i	−0.141416	+	0.789433i
$638$		0			0
$639$	32.7571	−	10.0028i	1.29585	−	0.395706i
$640$		0			0
$641$			34.3482i			1.35667i	0.734752	+	0.678336i	$0.237298\pi$
$641$			34.3482i			1.35667i	−0.734752	+	0.678336i	$0.762702\pi$
$642$		0			0
$643$	−11.8373	−	6.83426i	−0.466817	−	0.269517i	0.248089	−	0.968737i	$-0.420197\pi$
$643$	−11.8373	−	6.83426i	−0.466817	−	0.269517i	−0.714906	+	0.699220i	$0.753531\pi$
$644$		0			0
$645$	−41.6391	−	4.75124i	−1.63954	−	0.187080i
$646$		0			0
$647$	−18.1075	+	31.3630i	−0.711877	+	1.23301i	0.252274	+	0.967656i	$0.418822\pi$
$647$	−18.1075	+	31.3630i	−0.711877	+	1.23301i	−0.964152	+	0.265352i	$0.914512\pi$
$648$		0			0
$649$	−1.03319	+	0.596512i	−0.0405562	+	0.0234151i
$650$		0			0
$651$	−24.2317	+	27.3047i	−0.949716	+	1.07016i
$652$		0			0
$653$		−	36.5270i		−	1.42941i	−0.699426	−	0.714705i	$-0.746561\pi$
$653$		−	36.5270i		−	1.42941i	0.699426	−	0.714705i	$-0.253439\pi$
$654$		0			0
$655$	16.2437			0.634695
$656$		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
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	−0.474585	−	0.880210i	$-0.657402\pi$
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	0.524991	+	0.851107i	$0.324068\pi$
$662$		0			0
$663$	2.25434	−	19.7566i	0.0875512	−	0.767283i
$664$		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
$669$	−3.16648	+	27.7504i	−0.122423	+	1.07289i
$670$		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
$675$	0.592687	+	0.210217i	0.0228125	+	0.00809126i
$676$		0			0
$677$	−15.6344	+	27.0796i	−0.600880	+	1.04075i	0.391809	+	0.920047i	$0.371850\pi$
$677$	−15.6344	+	27.0796i	−0.600880	+	1.04075i	−0.992688	+	0.120707i	$0.961484\pi$
$678$		0			0
$679$	9.16081	+	0.814037i	0.351560	+	0.0312399i
$680$		0			0
$681$	20.4075	−	27.5696i	0.782019	−	1.05647i
$682$		0			0
$683$	−8.06769	−	4.65788i	−0.308701	−	0.178229i	0.337644	−	0.941274i	$-0.390370\pi$
$683$	−8.06769	−	4.65788i	−0.308701	−	0.178229i	−0.646345	+	0.763045i	$0.723703\pi$
$684$		0			0
$685$			36.2949i			1.38676i
$686$		0			0
$687$	−21.7177	−	16.0759i	−0.828581	−	0.613333i
$688$		0			0
$689$	−2.93139	−	5.07732i	−0.111677	−	0.193431i
$690$		0			0
$691$	−42.0468	−	24.2757i	−1.59954	−	0.923493i	−0.991576	−	0.129526i	$-0.958654\pi$
$691$	−42.0468	−	24.2757i	−1.59954	−	0.923493i	−0.607961	−	0.793967i	$-0.708012\pi$
$692$		0			0
$693$	−1.37246	−	0.448516i	−0.0521355	−	0.0170377i
$694$		0			0
$695$	−24.7633	−	14.2971i	−0.939324	−	0.542319i
$696$		0			0
$697$	2.43338	+	4.21473i	0.0921707	+	0.159644i
$698$		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
$705$	10.9050	+	25.0912i	0.410705	+	0.944991i
$706$		0			0
$707$	−20.5816	−	14.4532i	−0.774052	−	0.543569i
$708$		0			0
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	0.419679	+	0.907673i	$0.362143\pi$
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	−0.995907	+	0.0903840i	$0.971191\pi$
$710$		0			0
$711$	−37.1499	−	8.58985i	−1.39323	−	0.322145i
$712$		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
$717$	25.3234	−	11.0059i	0.945718	−	0.411022i
$718$		0			0
$719$	−2.44166	−	4.22907i	−0.0910584	−	0.157718i	0.816898	−	0.576782i	$-0.195692\pi$
$719$	−2.44166	−	4.22907i	−0.0910584	−	0.157718i	−0.907957	+	0.419064i	$0.862358\pi$
$720$		0			0
$721$	12.7494	−	18.1554i	0.474812	−	0.676141i
$722$		0			0
$723$	28.7997	+	21.3181i	1.07107	+	0.792828i
$724$		0			0
$725$	−0.0851181	+	0.0491430i	−0.00316121	+	0.00182512i
$726$		0			0
$727$	−32.7779	+	18.9243i	−1.21567	+	0.701865i	−0.963988	−	0.265946i	$-0.914316\pi$
$727$	−32.7779	+	18.9243i	−1.21567	+	0.701865i	−0.251678	+	0.967811i	$0.580982\pi$
$728$		0			0
$729$	20.9658	+	17.0127i	0.776513	+	0.630102i
$730$		0			0
$731$	−43.4911			−1.60858
$732$		0			0
$733$			46.3166i			1.71074i	0.518017	+	0.855370i	$0.326670\pi$
$733$			46.3166i			1.71074i	−0.518017	+	0.855370i	$0.673330\pi$
$734$		0			0
$735$	25.6558	+	7.68034i	0.946330	+	0.283294i
$736$		0			0
$737$	−1.08548	+	0.626700i	−0.0399840	+	0.0230848i
$738$		0			0
$739$	−5.15606	+	8.93056i	−0.189669	+	0.328516i	−0.945140	−	0.326666i	$-0.894075\pi$
$739$	−5.15606	+	8.93056i	−0.189669	+	0.328516i	0.755471	+	0.655182i	$0.227408\pi$
$740$		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
$745$			33.6537i			1.23298i
$746$		0			0
$747$	29.4355	−	31.5445i	1.07699	−	1.15415i
$748$		0			0
$749$	38.7413	+	3.44258i	1.41557	+	0.125789i
$750$		0			0
$751$	53.7306			1.96066			0.980329	−	0.197369i	$-0.0632397\pi$
$751$	53.7306			1.96066			0.980329	+	0.197369i	$0.0632397\pi$
$752$		0			0
$753$	−7.89944	+	10.6717i	−0.287872	+	0.388900i
$754$		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
$759$	1.05224	−	1.42153i	0.0381940	−	0.0515981i
$760$		0			0
$761$	23.1184			0.838041			0.419021	−	0.907977i	$-0.362374\pi$
$761$	23.1184			0.838041			0.419021	+	0.907977i	$0.362374\pi$
$762$		0			0
$763$	−40.1008	+	18.6329i	−1.45175	+	0.674556i
$764$		0			0
$765$	−25.6325	−	5.92679i	−0.926746	−	0.214283i
$766$		0			0
$767$			18.9640i			0.684752i
$768$		0			0
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	0.0202163	−	0.999796i	$-0.493565\pi$
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	−0.855740	+	0.517406i	$0.826898\pi$
$770$		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	$-0.878965\pi$
$773$	−3.97203	+	6.87976i	−0.142864	+	0.247448i	0.785710	+	0.618595i	$0.212298\pi$
$774$		0			0
$775$	−0.834960	+	0.482065i	−0.0299927	+	0.0173163i
$776$		0			0
$777$	−8.61081	−	7.64170i	−0.308911	−	0.274145i
$778$		0			0
$779$		−	1.22729i		−	0.0439721i
$780$		0			0
$781$	−2.07686			−0.0743158
$782$		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
$787$	10.5602	−	6.09696i	0.376432	−	0.217333i	−0.299833	−	0.953992i	$-0.596931\pi$
$787$	10.5602	−	6.09696i	0.376432	−	0.217333i	0.676265	+	0.736659i	$0.263598\pi$
$788$		0			0
$789$	10.7544	+	7.96060i	0.382866	+	0.283405i
$790$		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
$795$	−7.11399	+	3.09183i	−0.252307	+	0.109656i
$796$		0			0
$797$	−3.30173	+	5.71876i	−0.116953	+	0.202569i	−0.918559	−	0.395284i	$-0.870646\pi$
$797$	−3.30173	+	5.71876i	−0.116953	+	0.202569i	0.801606	+	0.597853i	$0.203979\pi$
$798$		0			0
$799$	14.1956	+	24.5875i	0.502204	+	0.869842i
$800$		0			0
$801$	−29.1198	+	31.2062i	−1.02890	+	1.10262i
$802$		0			0
$803$	1.06982	−	1.85298i	0.0377531	−	0.0653903i
$804$		0			0
$805$	−18.8518	+	26.8453i	−0.664439	+	0.946173i
$806$		0			0
$807$	6.88646	+	15.8450i	0.242415	+	0.557772i
$808$		0			0
$809$	8.57462	+	4.95056i	0.301468	+	0.174052i	0.643102	−	0.765780i	$-0.277647\pi$
$809$	8.57462	+	4.95056i	0.301468	+	0.174052i	−0.341634	+	0.939833i	$0.610980\pi$
$810$		0			0
$811$		−	33.1027i		−	1.16239i	−0.813763	−	0.581197i	$-0.802584\pi$
$811$		−	33.1027i		−	1.16239i	0.813763	−	0.581197i	$-0.197416\pi$
$812$		0			0
$813$	−0.819682	+	7.18355i	−0.0287475	+	0.251938i
$814$		0			0
$815$	9.63049	+	16.6805i	0.337341	+	0.584292i
$816$		0			0
$817$	9.49812	+	5.48374i	0.332297	+	0.191852i
$818$		0			0
$819$	−17.0825	+	15.3288i	−0.596911	+	0.535630i
$820$		0			0
$821$	−9.90100	−	5.71634i	−0.345547	−	0.199502i	0.317175	−	0.948367i	$-0.397266\pi$
$821$	−9.90100	−	5.71634i	−0.345547	−	0.199502i	−0.662722	+	0.748865i	$0.730599\pi$
$822$		0			0
$823$	−19.4509	−	33.6900i	−0.678017	−	1.17436i	−0.975577	−	0.219656i	$-0.929506\pi$
$823$	−19.4509	−	33.6900i	−0.678017	−	1.17436i	0.297561	−	0.954703i	$-0.403827\pi$
$824$		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	0.289996	−	0.957028i	$-0.406346\pi$
$829$	−11.3389	−	6.54652i	−0.393816	−	0.227370i	−0.683812	+	0.729658i	$0.739679\pi$
$830$		0			0
$831$	4.58578	−	6.19516i	0.159079	−	0.214908i
$832$		0			0
$833$	27.3561	+	4.90047i	0.947834	+	0.169791i
$834$		0			0
$835$	−19.6556	+	34.0445i	−0.680211	+	1.17816i
$836$		0			0
$837$	−40.7051	+	7.52307i	−1.40697	+	0.260035i
$838$		0			0
$839$	−5.51797	−	9.55740i	−0.190501	−	0.329958i	0.754915	−	0.655822i	$-0.227678\pi$
$839$	−5.51797	−	9.55740i	−0.190501	−	0.329958i	−0.945416	+	0.325864i	$0.894345\pi$
$840$		0			0
$841$	−14.1702	+	24.5436i	−0.488629	+	0.846330i
$842$		0			0
$843$	−5.56582	+	48.7779i	−0.191697	+	1.68000i
$844$		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
$849$	2.27708	−	19.9559i	0.0781491	−	0.684885i
$850$		0			0
$851$	12.2124	−	7.05085i	0.418637	−	0.241700i
$852$		0			0
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	−0.112303	−	0.993674i	$-0.535823\pi$
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	0.804395	+	0.594094i	$0.202489\pi$
$854$		0			0
$855$	4.85064	+	4.52634i	0.165888	+	0.154798i
$856$		0			0
$857$	18.2121			0.622115			0.311057	−	0.950391i	$-0.399317\pi$
$857$	18.2121			0.622115			0.311057	+	0.950391i	$0.399317\pi$
$858$		0			0
$859$			39.1597i			1.33611i	0.744111	+	0.668057i	$0.232874\pi$
$859$			39.1597i			1.33611i	−0.744111	+	0.668057i	$0.767126\pi$
$860$		0			0
$861$	1.12834	−	5.50288i	0.0384537	−	0.187538i
$862$		0			0
$863$	22.7847	−	13.1548i	0.775601	−	0.447793i	−0.0592683	−	0.998242i	$-0.518877\pi$
$863$	22.7847	−	13.1548i	0.775601	−	0.447793i	0.834869	+	0.550449i	$0.185543\pi$
$864$		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
$871$			19.9238i			0.675091i
$872$		0			0
$873$	7.62440	+	7.11465i	0.258047	+	0.240795i
$874$		0			0
$875$	24.4918	+	17.1991i	0.827973	+	0.581434i
$876$		0			0
$877$	7.19666			0.243014			0.121507	−	0.992591i	$-0.461227\pi$
$877$	7.19666			0.243014			0.121507	+	0.992591i	$0.461227\pi$
$878$		0			0
$879$	−19.9106	−	45.8122i	−0.671568	−	1.54521i
$880$		0			0
$881$	37.2133			1.25375			0.626874	−	0.779121i	$-0.284334\pi$
$881$	37.2133			1.25375			0.626874	+	0.779121i	$0.284334\pi$
$882$		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
$885$	24.9288	+	2.84451i	0.837972	+	0.0956172i
$886$		0			0
$887$	−20.6986			−0.694992			−0.347496	−	0.937681i	$-0.612968\pi$
$887$	−20.6986			−0.694992			−0.347496	+	0.937681i	$0.612968\pi$
$888$		0			0
$889$	−25.9140	−	18.1978i	−0.869129	−	0.610336i
$890$		0			0
$891$	−0.914610	−	1.35793i	−0.0306406	−	0.0454923i
$892$		0			0
$893$		−	7.15962i		−	0.239587i
$894$		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
$903$	37.5459	+	33.3203i	1.24945	+	1.10883i
$904$		0			0
$905$			24.5641i			0.816539i
$906$		0			0
$907$	−0.990928			−0.0329032			−0.0164516	−	0.999865i	$-0.505237\pi$
$907$	−0.990928			−0.0329032			−0.0164516	+	0.999865i	$0.505237\pi$
$908$		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
$913$	−2.26571	+	1.30811i	−0.0749841	+	0.0432921i
$914$		0			0
$915$	28.2506	−	12.2781i	0.933936	−	0.405901i
$916$		0			0
$917$	−15.9228	−	11.1816i	−0.525818	−	0.369250i
$918$		0			0
$919$	9.22417	+	15.9767i	0.304277	+	0.527024i	0.977100	−	0.212780i	$-0.0682517\pi$
$919$	9.22417	+	15.9767i	0.304277	+	0.527024i	−0.672823	+	0.739804i	$0.734918\pi$
$920$		0			0
$921$	−15.0515	−	11.1415i	−0.495965	−	0.367124i
$922$		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
$927$	24.0585	−	7.34659i	0.790184	−	0.241294i
$928$		0			0
$929$	−10.4712	+	18.1367i	−0.343550	+	0.595046i	−0.985089	−	0.172044i	$-0.944963\pi$
$929$	−10.4712	+	18.1367i	−0.343550	+	0.595046i	0.641539	+	0.767090i	$0.278296\pi$
$930$		0			0
$931$	−5.35647	−	4.51953i	−0.175551	−	0.148122i
$932$		0			0
$933$	−29.5703	−	3.37413i	−0.968089	−	0.110464i
$934$		0			0
$935$	1.38157	+	0.797652i	0.0451823	+	0.0260860i
$936$		0			0
$937$			27.1677i			0.887529i	0.896143	+	0.443764i	$0.146357\pi$
$937$			27.1677i			0.887529i	−0.896143	+	0.443764i	$0.853643\pi$
$938$		0			0
$939$	−14.5253	+	6.31290i	−0.474016	+	0.206014i
$940$		0			0
$941$	−1.42576	−	2.46949i	−0.0464785	−	0.0805031i	0.841850	−	0.539711i	$-0.181467\pi$
$941$	−1.42576	−	2.46949i	−0.0464785	−	0.0805031i	−0.888329	+	0.459208i	$0.848133\pi$
$942$		0			0
$943$	5.95881	+	3.44032i	0.194046	+	0.112032i
$944$		0			0
$945$	17.5878	+	24.7547i	0.572132	+	0.805270i
$946$		0			0
$947$	−15.2662	−	8.81395i	−0.496085	−	0.286415i	0.231010	−	0.972951i	$-0.425797\pi$
$947$	−15.2662	−	8.81395i	−0.496085	−	0.286415i	−0.727095	+	0.686536i	$0.759130\pi$
$948$		0			0
$949$	−17.0056	−	29.4546i	−0.552025	−	0.956136i
$950$		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
$957$	0.254233	+	0.0290094i	0.00821819	+	0.000937740i
$958$		0			0
$959$	24.9842	−	35.5779i	0.806780	−	1.14887i
$960$		0			0
$961$	16.2315	−	28.1139i	0.523598	−	0.906899i
$962$		0			0
$963$	32.2437	+	30.0880i	1.03904	+	0.969572i
$964$		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
$969$	5.53379	+	4.09623i	0.177771	+	0.131590i
$970$		0			0
$971$	10.2653	+	17.7800i	0.329429	+	0.570588i	0.982399	−	0.186796i	$-0.0598104\pi$
$971$	10.2653	+	17.7800i	0.329429	+	0.570588i	−0.652970	+	0.757384i	$0.726477\pi$
$972$		0			0
$973$	14.4324	+	31.0608i	0.462683	+	0.995764i
$974$		0			0
$975$	−0.555917	+	0.241609i	−0.0178036	+	0.00773768i
$976$		0			0
$977$	38.7545	−	22.3749i	1.23987	−	0.715838i	0.270800	−	0.962636i	$-0.412712\pi$
$977$	38.7545	−	22.3749i	1.23987	−	0.715838i	0.969067	+	0.246798i	$0.0793784\pi$
$978$		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
$983$	−26.9099			−0.858293			−0.429146	−	0.903235i	$-0.641186\pi$
$983$	−26.9099			−0.858293			−0.429146	+	0.903235i	$0.641186\pi$
$984$		0			0
$985$			35.6755i			1.13672i
$986$		0			0
$987$	6.58240	−	32.1022i	0.209520	−	1.02182i
$988$		0			0
$989$	−53.2502	+	30.7440i	−1.69326	+	0.977602i
$990$		0			0
$991$	−13.8668	+	24.0181i	−0.440494	+	0.762959i	−0.997726	−	0.0673982i	$-0.978530\pi$
$991$	−13.8668	+	24.0181i	−0.440494	+	0.762959i	0.557232	+	0.830357i	$0.311864\pi$
$992$		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
$997$			22.4382i			0.710624i	0.934748	+	0.355312i	$0.115625\pi$
$997$			22.4382i			0.710624i	−0.934748	+	0.355312i	$0.884375\pi$
$998$		0			0
$999$	−2.37247	−	12.8367i	−0.0750617	−	0.406137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.689.17		48
3.2	odd	2		3024.2.df.e.17.7		48
4.3	odd	2		504.2.cx.a.185.8	yes	48
7.5	odd	6		1008.2.ca.e.257.10		48
9.2	odd	6		1008.2.ca.e.353.10		48
9.7	even	3		3024.2.ca.e.2033.7		48
12.11	even	2		1512.2.cx.a.17.7		48
21.5	even	6		3024.2.ca.e.2609.7		48
28.19	even	6		504.2.bs.a.257.15	✓	48
36.7	odd	6		1512.2.bs.a.521.7		48
36.11	even	6		504.2.bs.a.353.15	yes	48
63.47	even	6	inner	1008.2.df.e.929.17		48
63.61	odd	6		3024.2.df.e.1601.7		48
84.47	odd	6		1512.2.bs.a.1097.7		48
252.47	odd	6		504.2.cx.a.425.8	yes	48
252.187	even	6		1512.2.cx.a.89.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.15	✓	48	28.19	even	6
504.2.bs.a.353.15	yes	48	36.11	even	6
504.2.cx.a.185.8	yes	48	4.3	odd	2
504.2.cx.a.425.8	yes	48	252.47	odd	6
1008.2.ca.e.257.10		48	7.5	odd	6
1008.2.ca.e.353.10		48	9.2	odd	6
1008.2.df.e.689.17		48	1.1	even	1	trivial
1008.2.df.e.929.17		48	63.47	even	6	inner
1512.2.bs.a.521.7		48	36.7	odd	6
1512.2.bs.a.1097.7		48	84.47	odd	6
1512.2.cx.a.17.7		48	12.11	even	2
1512.2.cx.a.89.7		48	252.187	even	6
3024.2.ca.e.2033.7		48	9.7	even	3
3024.2.ca.e.2609.7		48	21.5	even	6
3024.2.df.e.17.7		48	3.2	odd	2
3024.2.df.e.1601.7		48	63.61	odd	6

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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03050 - 1.39215i) q^{3} +2.20884 q^{5} +(-2.16520 - 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} +0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(2.27620 - 3.07503i) q^{15} +(1.98511 - 3.43832i) q^{17} +(-0.867067 + 0.500601i) q^{19} +(-4.34798 + 1.44743i) q^{21} -5.61313i q^{23} -0.121025 q^{25} +(-4.89724 - 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} +(6.89908 - 3.98319i) q^{31} +(0.253250 + 0.187461i) q^{33} +(-4.78259 - 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(4.59341 - 1.99636i) q^{39} +(-0.612906 + 1.06158i) q^{41} +(-5.47716 - 9.48671i) q^{43} +(-1.93528 - 6.33762i) q^{45} +(-3.57551 + 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(-2.74100 - 6.30675i) q^{51} +(-1.75586 - 1.01374i) q^{53} +0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +(3.27911 + 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(-2.46555 + 7.54460i) q^{63} +(5.53147 + 3.19359i) q^{65} +(3.44505 + 5.96701i) q^{67} +(-7.81431 - 5.78431i) q^{69} +11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(-0.124716 + 0.168485i) q^{75} +(0.276597 - 0.393879i) q^{77} +(6.35501 - 11.0072i) q^{79} +(-7.46471 + 5.02773i) q^{81} +(7.19085 + 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(0.159468 - 1.39755i) q^{87} +(-7.11375 - 12.3214i) q^{89} +(-3.22383 - 6.93818i) q^{91} +(1.56429 - 13.7092i) q^{93} +(-1.91521 + 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +(0.521946 - 0.159384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more