LMFDB - Embedded newform 1008.2.df.e.689.14

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			689.14
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.e.929.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.498607 + 1.65873i) q^{3} -0.623597 q^{5} +(0.996837 - 2.45078i) q^{7} +(-2.50278 + 1.65411i) q^{9} -5.19907i q^{11} +(-2.74023 - 1.58207i) q^{13} +(-0.310929 - 1.03438i) q^{15} +(0.437594 - 0.757935i) q^{17} +(1.41874 - 0.819107i) q^{19} +(4.56221 + 0.431510i) q^{21} -8.25480i q^{23} -4.61113 q^{25} +(-3.99163 - 3.32670i) q^{27} +(4.96435 - 2.86617i) q^{29} +(-4.02256 + 2.32243i) q^{31} +(8.62387 - 2.59229i) q^{33} +(-0.621624 + 1.52830i) q^{35} +(1.24291 + 2.15278i) q^{37} +(1.25794 - 5.33415i) q^{39} +(-3.52382 + 6.10344i) q^{41} +(1.56398 + 2.70890i) q^{43} +(1.56073 - 1.03150i) q^{45} +(4.73384 - 8.19925i) q^{47} +(-5.01263 - 4.88605i) q^{49} +(1.47540 + 0.347940i) q^{51} +(-1.15189 - 0.665044i) q^{53} +3.24212i q^{55} +(2.06607 + 1.94489i) q^{57} +(3.18334 + 5.51370i) q^{59} +(9.65975 + 5.57706i) q^{61} +(1.55899 + 7.78264i) q^{63} +(1.70880 + 0.986576i) q^{65} +(6.04951 + 10.4781i) q^{67} +(13.6925 - 4.11590i) q^{69} -10.5861i q^{71} +(-11.6719 - 6.73878i) q^{73} +(-2.29914 - 7.64862i) q^{75} +(-12.7418 - 5.18263i) q^{77} +(4.84840 - 8.39767i) q^{79} +(3.52785 - 8.27975i) q^{81} +(0.192030 + 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(7.22946 + 6.80543i) q^{87} +(0.0198983 + 0.0344648i) q^{89} +(-6.60888 + 5.13864i) q^{91} +(-5.85796 - 5.51438i) q^{93} +(-0.884719 + 0.510793i) q^{95} +(5.94681 - 3.43339i) q^{97} +(8.59984 + 13.0122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.498607	+	1.65873i	0.287871	+	0.957669i
$3$	0.498607	+	1.65873i	0.287871	+	0.957669i
$4$		0			0
$5$	−0.623597			−0.278881			−0.139440	−	0.990230i	$-0.544530\pi$
$5$	−0.623597			−0.278881			−0.139440	+	0.990230i	$0.544530\pi$
$6$		0			0
$7$	0.996837	−	2.45078i	0.376769	−	0.926307i
$7$	0.996837	−	2.45078i	0.376769	−	0.926307i
$8$		0			0
$9$	−2.50278	+	1.65411i	−0.834261	+	0.551370i
$10$		0			0
$11$		−	5.19907i		−	1.56758i	−0.621026	−	0.783790i	$-0.713284\pi$
$11$		−	5.19907i		−	1.56758i	0.621026	−	0.783790i	$-0.286716\pi$
$12$		0			0
$13$	−2.74023	−	1.58207i	−0.760004	−	0.438788i	0.0692932	−	0.997596i	$-0.477926\pi$
$13$	−2.74023	−	1.58207i	−0.760004	−	0.438788i	−0.829297	+	0.558808i	$0.811259\pi$
$14$		0			0
$15$	−0.310929	−	1.03438i	−0.0802816	−	0.267076i
$16$		0			0
$17$	0.437594	−	0.757935i	0.106132	−	0.183826i	−0.808068	−	0.589089i	$-0.799487\pi$
$17$	0.437594	−	0.757935i	0.106132	−	0.183826i	0.914200	+	0.405263i	$0.132820\pi$
$18$		0			0
$19$	1.41874	−	0.819107i	0.325480	−	0.187916i	−0.328352	−	0.944555i	$-0.606493\pi$
$19$	1.41874	−	0.819107i	0.325480	−	0.187916i	0.653833	+	0.756639i	$0.273160\pi$
$20$		0			0
$21$	4.56221	+	0.431510i	0.995557	+	0.0941633i
$22$		0			0
$23$		−	8.25480i		−	1.72124i	−0.509245	−	0.860622i	$-0.670075\pi$
$23$		−	8.25480i		−	1.72124i	0.509245	−	0.860622i	$-0.329925\pi$
$24$		0			0
$25$	−4.61113			−0.922225
$26$		0			0
$27$	−3.99163	−	3.32670i	−0.768189	−	0.640223i
$28$		0			0
$29$	4.96435	−	2.86617i	0.921856	−	0.532234i	0.0376295	−	0.999292i	$-0.488019\pi$
$29$	4.96435	−	2.86617i	0.921856	−	0.532234i	0.884227	+	0.467058i	$0.154686\pi$
$30$		0			0
$31$	−4.02256	+	2.32243i	−0.722474	+	0.417120i	−0.815662	−	0.578528i	$-0.803627\pi$
$31$	−4.02256	+	2.32243i	−0.722474	+	0.417120i	0.0931888	+	0.995648i	$0.470294\pi$
$32$		0			0
$33$	8.62387	−	2.59229i	1.50122	−	0.451260i
$34$		0			0
$35$	−0.621624	+	1.52830i	−0.105074	+	0.258329i
$36$		0			0
$37$	1.24291	+	2.15278i	0.204333	+	0.353916i	0.949920	−	0.312493i	$-0.101164\pi$
$37$	1.24291	+	2.15278i	0.204333	+	0.353916i	−0.745587	+	0.666408i	$0.767831\pi$
$38$		0			0
$39$	1.25794	−	5.33415i	0.201431	−	0.854147i
$40$		0			0
$41$	−3.52382	+	6.10344i	−0.550329	+	0.953198i	0.447922	+	0.894073i	$0.352164\pi$
$41$	−3.52382	+	6.10344i	−0.550329	+	0.953198i	−0.998251	+	0.0591249i	$0.981169\pi$
$42$		0			0
$43$	1.56398	+	2.70890i	0.238505	+	0.413103i	0.960286	−	0.279019i	$-0.0900093\pi$
$43$	1.56398	+	2.70890i	0.238505	+	0.413103i	−0.721780	+	0.692122i	$0.756676\pi$
$44$		0			0
$45$	1.56073	−	1.03150i	0.232659	−	0.153766i
$46$		0			0
$47$	4.73384	−	8.19925i	0.690502	−	1.19598i	−0.281172	−	0.959657i	$-0.590723\pi$
$47$	4.73384	−	8.19925i	0.690502	−	1.19598i	0.971674	−	0.236327i	$-0.0759435\pi$
$48$		0			0
$49$	−5.01263	−	4.88605i	−0.716090	−	0.698007i
$50$		0			0
$51$	1.47540	+	0.347940i	0.206597	+	0.0487213i
$52$		0			0
$53$	−1.15189	−	0.665044i	−0.158224	−	0.0913508i	0.418797	−	0.908080i	$-0.362452\pi$
$53$	−1.15189	−	0.665044i	−0.158224	−	0.0913508i	−0.577021	+	0.816729i	$0.695785\pi$
$54$		0			0
$55$			3.24212i			0.437168i
$56$		0			0
$57$	2.06607	+	1.94489i	0.273658	+	0.257607i
$58$		0			0
$59$	3.18334	+	5.51370i	0.414435	+	0.717823i	0.995369	−	0.0961281i	$-0.0306459\pi$
$59$	3.18334	+	5.51370i	0.414435	+	0.717823i	−0.580934	+	0.813951i	$0.697313\pi$
$60$		0			0
$61$	9.65975	+	5.57706i	1.23680	+	0.714069i	0.968440	−	0.249248i	$-0.0801835\pi$
$61$	9.65975	+	5.57706i	1.23680	+	0.714069i	0.268365	+	0.963317i	$0.413517\pi$
$62$		0			0
$63$	1.55899	+	7.78264i	0.196414	+	0.980521i
$64$		0			0
$65$	1.70880	+	0.986576i	0.211951	+	0.122370i
$66$		0			0
$67$	6.04951	+	10.4781i	0.739065	+	1.28010i	0.952917	+	0.303232i	$0.0980659\pi$
$67$	6.04951	+	10.4781i	0.739065	+	1.28010i	−0.213851	+	0.976866i	$0.568601\pi$
$68$		0			0
$69$	13.6925	−	4.11590i	1.64838	−	0.495496i
$70$		0			0
$71$		−	10.5861i		−	1.25634i	−0.778076	−	0.628171i	$-0.783804\pi$
$71$		−	10.5861i		−	1.25634i	0.778076	−	0.628171i	$-0.216196\pi$
$72$		0			0
$73$	−11.6719	−	6.73878i	−1.36609	−	0.788714i	−0.375666	−	0.926755i	$-0.622586\pi$
$73$	−11.6719	−	6.73878i	−1.36609	−	0.788714i	−0.990427	+	0.138041i	$0.955920\pi$
$74$		0			0
$75$	−2.29914	−	7.64862i	−0.265482	−	0.883187i
$76$		0			0
$77$	−12.7418	−	5.18263i	−1.45206	−	0.590615i
$78$		0			0
$79$	4.84840	−	8.39767i	0.545487	−	0.944811i	−0.453089	−	0.891465i	$-0.649678\pi$
$79$	4.84840	−	8.39767i	0.545487	−	0.944811i	0.998576	−	0.0533461i	$-0.0169886\pi$
$80$		0			0
$81$	3.52785	−	8.27975i	0.391983	−	0.919973i
$82$		0			0
$83$	0.192030	+	0.332606i	0.0210781	+	0.0365083i	0.876372	−	0.481635i	$-0.159957\pi$
$83$	0.192030	+	0.332606i	0.0210781	+	0.0365083i	−0.855294	+	0.518143i	$0.826623\pi$
$84$		0			0
$85$	−0.272882	+	0.472646i	−0.0295982	+	0.0512656i
$86$		0			0
$87$	7.22946	+	6.80543i	0.775079	+	0.729619i
$88$		0			0
$89$	0.0198983	+	0.0344648i	0.00210921	+	0.00365326i	0.867078	−	0.498172i	$-0.165995\pi$
$89$	0.0198983	+	0.0344648i	0.00210921	+	0.00365326i	−0.864969	+	0.501826i	$0.832662\pi$
$90$		0			0
$91$	−6.60888	+	5.13864i	−0.692799	+	0.538675i
$92$		0			0
$93$	−5.85796	−	5.51438i	−0.607442	−	0.571814i
$94$		0			0
$95$	−0.884719	+	0.510793i	−0.0907702	+	0.0524062i
$96$		0			0
$97$	5.94681	−	3.43339i	0.603807	−	0.348608i	−0.166731	−	0.986002i	$-0.553321\pi$
$97$	5.94681	−	3.43339i	0.603807	−	0.348608i	0.770538	+	0.637394i	$0.219988\pi$
$98$		0			0
$99$	8.59984	+	13.0122i	0.864316	+	1.30777i
$100$		0			0
$101$	8.92598			0.888168			0.444084	−	0.895985i	$-0.353529\pi$
$101$	8.92598			0.888168			0.444084	+	0.895985i	$0.353529\pi$
$102$		0			0
$103$			8.86879i			0.873868i	0.899494	+	0.436934i	$0.143936\pi$
$103$			8.86879i			0.873868i	−0.899494	+	0.436934i	$0.856064\pi$
$104$		0			0
$105$	−2.84498	−	0.269088i	−0.277642	−	0.0262603i
$106$		0			0
$107$	2.64326	−	1.52609i	0.255534	−	0.147532i	−0.366762	−	0.930315i	$-0.619534\pi$
$107$	2.64326	−	1.52609i	0.255534	−	0.147532i	0.622295	+	0.782782i	$0.286200\pi$
$108$		0			0
$109$	−5.55069	+	9.61408i	−0.531660	+	0.920862i	0.467657	+	0.883910i	$0.345098\pi$
$109$	−5.55069	+	9.61408i	−0.531660	+	0.920862i	−0.999317	+	0.0369519i	$0.988235\pi$
$110$		0			0
$111$	−2.95117	+	3.13505i	−0.280113	+	0.297566i
$112$		0			0
$113$	−3.13836	−	1.81193i	−0.295232	−	0.170452i	0.345067	−	0.938578i	$-0.387856\pi$
$113$	−3.13836	−	1.81193i	−0.295232	−	0.170452i	−0.640299	+	0.768126i	$0.721190\pi$
$114$		0			0
$115$			5.14766i			0.480022i
$116$		0			0
$117$	9.47513	−	0.573056i	0.875976	−	0.0529791i
$118$		0			0
$119$	−1.42132	−	1.82798i	−0.130292	−	0.167571i
$120$		0			0
$121$	−16.0304			−1.45731
$122$		0			0
$123$	−11.8810	−	2.80186i	−1.07127	−	0.252636i
$124$		0			0
$125$	5.99347			0.536072
$126$		0			0
$127$	10.1408			0.899852			0.449926	−	0.893066i	$-0.351450\pi$
$127$	10.1408			0.899852			0.449926	+	0.893066i	$0.351450\pi$
$128$		0			0
$129$	−3.71352	+	3.94490i	−0.326957	+	0.347329i
$130$		0			0
$131$	−21.7576			−1.90097			−0.950484	−	0.310774i	$-0.899412\pi$
$131$	−21.7576			−1.90097			−0.950484	+	0.310774i	$0.899412\pi$
$132$		0			0
$133$	−0.593203	−	4.29352i	−0.0514372	−	0.372296i
$134$		0			0
$135$	2.48917	+	2.07452i	0.214233	+	0.178546i
$136$		0			0
$137$			0.393118i			0.0335863i	0.999859	+	0.0167932i	$0.00534568\pi$
$137$			0.393118i			0.0335863i	−0.999859	+	0.0167932i	$0.994654\pi$
$138$		0			0
$139$	15.6647	+	9.04400i	1.32866	+	0.767102i	0.985092	−	0.172026i	$-0.0550312\pi$
$139$	15.6647	+	9.04400i	1.32866	+	0.767102i	0.343568	+	0.939128i	$0.388365\pi$
$140$		0			0
$141$	15.9607	+	3.76397i	1.34413	+	0.316984i
$142$		0			0
$143$	−8.22532	+	14.2467i	−0.687836	+	1.19137i
$144$		0			0
$145$	−3.09575	+	1.78733i	−0.257088	+	0.148430i
$146$		0			0
$147$	5.60532	−	10.7508i	0.462319	−	0.886714i
$148$		0			0
$149$		−	10.2508i		−	0.839781i	−0.907575	−	0.419891i	$-0.862068\pi$
$149$		−	10.2508i		−	0.839781i	0.907575	−	0.419891i	$-0.137932\pi$
$150$		0			0
$151$	−23.8012			−1.93691			−0.968457	−	0.249181i	$-0.919839\pi$
$151$	−23.8012			−1.93691			−0.968457	+	0.249181i	$0.919839\pi$
$152$		0			0
$153$	0.158505	+	2.62078i	0.0128143	+	0.211877i
$154$		0			0
$155$	2.50846	−	1.44826i	0.201484	−	0.116327i
$156$		0			0
$157$	9.96626	−	5.75402i	0.795394	−	0.459221i	−0.0464641	−	0.998920i	$-0.514795\pi$
$157$	9.96626	−	5.75402i	0.795394	−	0.459221i	0.841858	+	0.539699i	$0.181462\pi$
$158$		0			0
$159$	0.528789	−	2.24227i	0.0419357	−	0.177824i
$160$		0			0
$161$	−20.2307	−	8.22868i	−1.59440	−	0.648511i
$162$		0			0
$163$	−10.4614	−	18.1197i	−0.819399	−	1.41924i	−0.906125	−	0.423009i	$-0.860974\pi$
$163$	−10.4614	−	18.1197i	−0.819399	−	1.41924i	0.0867261	−	0.996232i	$-0.472360\pi$
$164$		0			0
$165$	−5.37782	+	1.61654i	−0.418662	+	0.125848i
$166$		0			0
$167$	6.69358	−	11.5936i	0.517965	−	0.897141i	−0.481817	−	0.876272i	$-0.660023\pi$
$167$	6.69358	−	11.5936i	0.517965	−	0.897141i	0.999782	−	0.0208697i	$-0.00664350\pi$
$168$		0			0
$169$	−1.49408	−	2.58782i	−0.114929	−	0.199063i
$170$		0			0
$171$	−2.19589	+	4.39679i	−0.167924	+	0.336231i
$172$		0			0
$173$	−2.94433	+	5.09972i	−0.223853	+	0.387725i	−0.955975	−	0.293449i	$-0.905197\pi$
$173$	−2.94433	+	5.09972i	−0.223853	+	0.387725i	0.732122	+	0.681174i	$0.238530\pi$
$174$		0			0
$175$	−4.59654	+	11.3009i	−0.347466	+	0.854264i
$176$		0			0
$177$	−7.55852	+	8.02947i	−0.568133	+	0.603532i
$178$		0			0
$179$	−14.4333	−	8.33310i	−1.07880	−	0.622845i	−0.148227	−	0.988953i	$-0.547357\pi$
$179$	−14.4333	−	8.33310i	−1.07880	−	0.622845i	−0.930572	+	0.366109i	$0.880690\pi$
$180$		0			0
$181$			0.462705i			0.0343926i	0.999852	+	0.0171963i	$0.00547402\pi$
$181$			0.462705i			0.0343926i	−0.999852	+	0.0171963i	$0.994526\pi$
$182$		0			0
$183$	−4.43443	+	18.8037i	−0.327803	+	1.39001i
$184$		0			0
$185$	−0.775075	−	1.34247i	−0.0569846	−	0.0987003i
$186$		0			0
$187$	−3.94056	−	2.27508i	−0.288162	−	0.166371i
$188$		0			0
$189$	−12.1320	+	6.46642i	−0.882473	+	0.470363i
$190$		0			0
$191$	11.8113	+	6.81927i	0.854637	+	0.493425i	0.862213	−	0.506546i	$-0.169078\pi$
$191$	11.8113	+	6.81927i	0.854637	+	0.493425i	−0.00757544	+	0.999971i	$0.502411\pi$
$192$		0			0
$193$	5.73933	+	9.94080i	0.413126	+	0.715555i	0.995230	−	0.0975597i	$-0.0311037\pi$
$193$	5.73933	+	9.94080i	0.413126	+	0.715555i	−0.582104	+	0.813114i	$0.697770\pi$
$194$		0			0
$195$	−0.784447	+	3.32636i	−0.0561754	+	0.238205i
$196$		0			0
$197$			4.78184i			0.340692i	0.985384	+	0.170346i	$0.0544885\pi$
$197$			4.78184i			0.340692i	−0.985384	+	0.170346i	$0.945511\pi$
$198$		0			0
$199$	−7.87833	−	4.54856i	−0.558480	−	0.322439i	0.194055	−	0.980991i	$-0.437836\pi$
$199$	−7.87833	−	4.54856i	−0.558480	−	0.322439i	−0.752535	+	0.658552i	$0.771169\pi$
$200$		0			0
$201$	−14.3640	+	15.2589i	−1.01316	+	1.07628i
$202$		0			0
$203$	−2.07570	−	15.0236i	−0.145685	−	1.05445i
$204$		0			0
$205$	2.19745	−	3.80609i	0.153476	−	0.265829i
$206$		0			0
$207$	13.6543	+	20.6600i	0.949042	+	1.43597i
$208$		0			0
$209$	−4.25860	−	7.37611i	−0.294573	−	0.510216i
$210$		0			0
$211$	−1.47477	+	2.55437i	−0.101527	+	0.175850i	−0.912314	−	0.409491i	$-0.865706\pi$
$211$	−1.47477	+	2.55437i	−0.101527	+	0.175850i	0.810787	+	0.585341i	$0.199040\pi$
$212$		0			0
$213$	17.5595	−	5.27831i	1.20316	−	0.361664i
$214$		0			0
$215$	−0.975294	−	1.68926i	−0.0665145	−	0.115207i
$216$		0			0
$217$	1.68192	+	12.1735i	0.114176	+	0.826391i
$218$		0			0
$219$	5.35814	−	22.7206i	0.362069	−	1.53531i
$220$		0			0
$221$	−2.39822	+	1.38461i	−0.161322	+	0.0931391i
$222$		0			0
$223$	−20.4564	+	11.8105i	−1.36986	+	0.790891i	−0.990910	−	0.134524i	$-0.957049\pi$
$223$	−20.4564	+	11.8105i	−1.36986	+	0.790891i	−0.378954	+	0.925416i	$0.623716\pi$
$224$		0			0
$225$	11.5407	−	7.62731i	0.769377	−	0.508487i
$226$		0			0
$227$	18.0507			1.19807			0.599033	−	0.800725i	$-0.295552\pi$
$227$	18.0507			1.19807			0.599033	+	0.800725i	$0.295552\pi$
$228$		0			0
$229$			12.1488i			0.802815i	0.915900	+	0.401407i	$0.131479\pi$
$229$			12.1488i			0.802815i	−0.915900	+	0.401407i	$0.868521\pi$
$230$		0			0
$231$	2.24345	−	23.7193i	0.147608	−	1.56061i
$232$		0			0
$233$	3.39111	−	1.95786i	0.222159	−	0.128264i	−0.384791	−	0.923004i	$-0.625726\pi$
$233$	3.39111	−	1.95786i	0.222159	−	0.128264i	0.606950	+	0.794740i	$0.292393\pi$
$234$		0			0
$235$	−2.95201	+	5.11303i	−0.192568	+	0.333537i
$236$		0			0
$237$	16.3469	+	3.85506i	1.06185	+	0.250413i
$238$		0			0
$239$	−10.3996	−	6.00423i	−0.672696	−	0.388381i	0.124401	−	0.992232i	$-0.460299\pi$
$239$	−10.3996	−	6.00423i	−0.672696	−	0.388381i	−0.797097	+	0.603851i	$0.793632\pi$
$240$		0			0
$241$			28.2853i			1.82202i	0.412385	+	0.911010i	$0.364696\pi$
$241$			28.2853i			1.82202i	−0.412385	+	0.911010i	$0.635304\pi$
$242$		0			0
$243$	15.4929	+	1.72341i	0.993870	+	0.110557i
$244$		0			0
$245$	3.12586	+	3.04693i	0.199704	+	0.194661i
$246$		0			0
$247$	−5.18355			−0.329822
$248$		0			0
$249$	−0.455957	+	0.484367i	−0.0288951	+	0.0306955i
$250$		0			0
$251$	12.0425			0.760117			0.380059	−	0.924962i	$-0.375904\pi$
$251$	12.0425			0.760117			0.380059	+	0.924962i	$0.375904\pi$
$252$		0			0
$253$	−42.9173			−2.69819
$254$		0			0
$255$	−0.920054	−	0.216974i	−0.0576160	−	0.0135874i
$256$		0			0
$257$	14.6504			0.913868			0.456934	−	0.889501i	$-0.348948\pi$
$257$	14.6504			0.913868			0.456934	+	0.889501i	$0.348948\pi$
$258$		0			0
$259$	6.51498	−	0.900125i	0.404821	−	0.0559310i
$260$		0			0
$261$	−7.68373	+	15.3850i	−0.475611	+	0.952306i
$262$		0			0
$263$			5.73134i			0.353410i	0.984264	+	0.176705i	$0.0565438\pi$
$263$			5.73134i			0.353410i	−0.984264	+	0.176705i	$0.943456\pi$
$264$		0			0
$265$	0.718314	+	0.414719i	0.0441257	+	0.0254760i
$266$		0			0
$267$	−0.0472464	+	0.0501902i	−0.00289144	+	0.00307159i
$268$		0			0
$269$	1.61724	−	2.80114i	0.0986047	−	0.170788i	−0.812503	−	0.582957i	$-0.801895\pi$
$269$	1.61724	−	2.80114i	0.0986047	−	0.170788i	0.911107	+	0.412169i	$0.135229\pi$
$270$		0			0
$271$	20.6677	−	11.9325i	1.25548	−	0.724849i	0.283284	−	0.959036i	$-0.408576\pi$
$271$	20.6677	−	11.9325i	1.25548	−	0.724849i	0.972192	+	0.234187i	$0.0752428\pi$
$272$		0			0
$273$	−11.8188	−	8.40020i	−0.715309	−	0.508403i
$274$		0			0
$275$			23.9736i			1.44566i
$276$		0			0
$277$	−7.66845			−0.460753			−0.230376	−	0.973102i	$-0.573996\pi$
$277$	−7.66845			−0.460753			−0.230376	+	0.973102i	$0.573996\pi$
$278$		0			0
$279$	6.22605	−	12.4663i	0.372744	−	0.746337i
$280$		0			0
$281$	8.78880	−	5.07422i	0.524296	−	0.302702i	−0.214395	−	0.976747i	$-0.568778\pi$
$281$	8.78880	−	5.07422i	0.524296	−	0.302702i	0.738690	+	0.674045i	$0.235445\pi$
$282$		0			0
$283$	−11.8373	+	6.83427i	−0.703654	+	0.406255i	−0.808707	−	0.588212i	$-0.799832\pi$
$283$	−11.8373	+	6.83427i	−0.703654	+	0.406255i	0.105053	+	0.994467i	$0.466499\pi$
$284$		0			0
$285$	−1.28839	−	1.21283i	−0.0763179	−	0.0718417i
$286$		0			0
$287$	11.4455	+	14.7203i	0.675607	+	0.868909i
$288$		0			0
$289$	8.11702	+	14.0591i	0.477472	+	0.827006i
$290$		0			0
$291$	8.66019	+	8.15225i	0.507669	+	0.477893i
$292$		0			0
$293$	−2.70903	+	4.69218i	−0.158263	+	0.274120i	−0.934242	−	0.356639i	$-0.883923\pi$
$293$	−2.70903	+	4.69218i	−0.158263	+	0.274120i	0.775979	+	0.630758i	$0.217256\pi$
$294$		0			0
$295$	−1.98512	−	3.43833i	−0.115578	−	0.200187i
$296$		0			0
$297$	−17.2957	+	20.7528i	−1.00360	+	1.20420i
$298$		0			0
$299$	−13.0597	+	22.6201i	−0.755262	+	1.30815i
$300$		0			0
$301$	8.19794	−	1.13265i	0.472522	−	0.0652847i
$302$		0			0
$303$	4.45055	+	14.8058i	0.255677	+	0.850571i
$304$		0			0
$305$	−6.02379	−	3.47784i	−0.344921	−	0.199140i
$306$		0			0
$307$		−	3.56336i		−	0.203372i	−0.994817	−	0.101686i	$-0.967576\pi$
$307$		−	3.56336i		−	0.203372i	0.994817	−	0.101686i	$-0.0324236\pi$
$308$		0			0
$309$	−14.7109	+	4.42204i	−0.836876	+	0.251561i
$310$		0			0
$311$	−5.63234	−	9.75550i	−0.319381	−	0.553184i	0.660978	−	0.750405i	$-0.270142\pi$
$311$	−5.63234	−	9.75550i	−0.319381	−	0.553184i	−0.980359	+	0.197221i	$0.936808\pi$
$312$		0			0
$313$	9.89696	+	5.71401i	0.559409	+	0.322975i	0.752908	−	0.658125i	$-0.228650\pi$
$313$	9.89696	+	5.71401i	0.559409	+	0.322975i	−0.193499	+	0.981100i	$0.561984\pi$
$314$		0			0
$315$	−0.972181	−	4.85323i	−0.0547762	−	0.273449i
$316$		0			0
$317$	16.8604	+	9.73436i	0.946975	+	0.546736i	0.892140	−	0.451759i	$-0.149203\pi$
$317$	16.8604	+	9.73436i	0.946975	+	0.546736i	0.0548352	+	0.998495i	$0.482537\pi$
$318$		0			0
$319$	−14.9014	−	25.8100i	−0.834319	−	1.44508i
$320$		0			0
$321$	3.84932	+	3.62354i	0.214848	+	0.202247i
$322$		0			0
$323$		−	1.43375i		−	0.0797758i
$324$		0			0
$325$	12.6356	+	7.29515i	0.700895	+	0.404662i
$326$		0			0
$327$	−18.7148	−	4.41347i	−1.03493	−	0.244065i
$328$		0			0
$329$	−15.3757	−	19.7749i	−0.847689	−	1.09023i
$330$		0			0
$331$	13.4838	−	23.3546i	0.741135	−	1.28368i	−0.210844	−	0.977520i	$-0.567621\pi$
$331$	13.4838	−	23.3546i	0.741135	−	1.28368i	0.951979	−	0.306164i	$-0.0990454\pi$
$332$		0			0
$333$	−6.67168	−	3.33204i	−0.365606	−	0.182595i
$334$		0			0
$335$	−3.77245	−	6.53408i	−0.206111	−	0.356995i
$336$		0			0
$337$	0.993296	−	1.72044i	0.0541083	−	0.0937183i	−0.837703	−	0.546127i	$-0.816102\pi$
$337$	0.993296	−	1.72044i	0.0541083	−	0.0937183i	0.891811	+	0.452408i	$0.149435\pi$
$338$		0			0
$339$	1.44070	−	6.10914i	0.0782483	−	0.331803i
$340$		0			0
$341$	12.0745	+	20.9136i	0.653869	+	1.13254i
$342$		0			0
$343$	−16.9714	+	7.41426i	−0.916370	+	0.400332i
$344$		0			0
$345$	−8.53859	+	2.56666i	−0.459702	+	0.138184i
$346$		0			0
$347$	−29.7673	+	17.1862i	−1.59799	+	0.922603i	−0.606122	+	0.795372i	$0.707276\pi$
$347$	−29.7673	+	17.1862i	−1.59799	+	0.922603i	−0.991873	+	0.127231i	$0.959391\pi$
$348$		0			0
$349$	25.3935	−	14.6609i	1.35928	−	0.784781i	0.369754	−	0.929130i	$-0.379442\pi$
$349$	25.3935	−	14.6609i	1.35928	−	0.784781i	0.989527	+	0.144348i	$0.0461085\pi$
$350$		0			0
$351$	5.67491	+	15.4310i	0.302904	+	0.823645i
$352$		0			0
$353$	1.17305			0.0624353			0.0312177	−	0.999513i	$-0.490061\pi$
$353$	1.17305			0.0624353			0.0312177	+	0.999513i	$0.490061\pi$
$354$		0			0
$355$			6.60147i			0.350370i
$356$		0			0
$357$	2.32345	−	3.26904i	0.122970	−	0.173016i
$358$		0			0
$359$	−5.69591	+	3.28854i	−0.300619	+	0.173562i	−0.642721	−	0.766101i	$-0.722194\pi$
$359$	−5.69591	+	3.28854i	−0.300619	+	0.173562i	0.342102	+	0.939663i	$0.388861\pi$
$360$		0			0
$361$	−8.15813	+	14.1303i	−0.429375	+	0.743699i
$362$		0			0
$363$	−7.99285	−	26.5901i	−0.419516	−	1.39562i
$364$		0			0
$365$	7.27856	+	4.20228i	0.380977	+	0.219957i
$366$		0			0
$367$			9.51617i			0.496740i	0.968665	+	0.248370i	$0.0798948\pi$
$367$			9.51617i			0.496740i	−0.968665	+	0.248370i	$0.920105\pi$
$368$		0			0
$369$	−1.27639	−	21.1044i	−0.0664464	−	1.09865i
$370$		0			0
$371$	−2.77812	+	2.16009i	−0.144233	+	0.112146i
$372$		0			0
$373$	20.6303			1.06820			0.534098	−	0.845422i	$-0.320651\pi$
$373$	20.6303			1.06820			0.534098	+	0.845422i	$0.320651\pi$
$374$		0			0
$375$	2.98838	+	9.94155i	0.154319	+	0.513380i
$376$		0			0
$377$	−18.1380			−0.934153
$378$		0			0
$379$	7.98265			0.410041			0.205020	−	0.978758i	$-0.434274\pi$
$379$	7.98265			0.410041			0.205020	+	0.978758i	$0.434274\pi$
$380$		0			0
$381$	5.05628	+	16.8209i	0.259041	+	0.861761i
$382$		0			0
$383$	28.0968			1.43568			0.717840	−	0.696208i	$-0.245131\pi$
$383$	28.0968			1.43568			0.717840	+	0.696208i	$0.245131\pi$
$384$		0			0
$385$	7.94573	+	3.23187i	0.404952	+	0.164711i
$386$		0			0
$387$	−8.39512	−	4.19278i	−0.426748	−	0.213131i
$388$		0			0
$389$		−	32.8397i		−	1.66504i	−0.553997	−	0.832519i	$-0.686898\pi$
$389$		−	32.8397i		−	1.66504i	0.553997	−	0.832519i	$-0.313102\pi$
$390$		0			0
$391$	−6.25660	−	3.61225i	−0.316410	−	0.182679i
$392$		0			0
$393$	−10.8485	−	36.0900i	−0.547233	−	1.82050i
$394$		0			0
$395$	−3.02344	+	5.23676i	−0.152126	+	0.263490i
$396$		0			0
$397$	9.24672	−	5.33859i	0.464079	−	0.267936i	−0.249679	−	0.968329i	$-0.580325\pi$
$397$	9.24672	−	5.33859i	0.464079	−	0.267936i	0.713758	+	0.700392i	$0.246992\pi$
$398$		0			0
$399$	6.82603	−	3.12474i	0.341729	−	0.156433i
$400$		0			0
$401$		−	14.2789i		−	0.713052i	−0.934285	−	0.356526i	$-0.883961\pi$
$401$		−	14.2789i		−	0.713052i	0.934285	−	0.356526i	$-0.116039\pi$
$402$		0			0
$403$	14.6970			0.732111
$404$		0			0
$405$	−2.19995	+	5.16323i	−0.109317	+	0.256563i
$406$		0			0
$407$	11.1925	−	6.46198i	0.554791	−	0.320309i
$408$		0			0
$409$	7.04206	−	4.06574i	0.348208	−	0.201038i	−0.315688	−	0.948863i	$-0.602235\pi$
$409$	7.04206	−	4.06574i	0.348208	−	0.201038i	0.663896	+	0.747825i	$0.268902\pi$
$410$		0			0
$411$	−0.652077	+	0.196011i	−0.0321646	+	0.00966852i
$412$		0			0
$413$	16.6861	−	2.30539i	0.821071	−	0.113441i
$414$		0			0
$415$	−0.119750	−	0.207412i	−0.00587827	−	0.0101815i
$416$		0			0
$417$	−7.19107	+	30.4929i	−0.352148	+	1.49324i
$418$		0			0
$419$	−1.53415	+	2.65723i	−0.0749481	+	0.129814i	−0.901064	−	0.433687i	$-0.857212\pi$
$419$	−1.53415	+	2.65723i	−0.0749481	+	0.129814i	0.826116	+	0.563501i	$0.190546\pi$
$420$		0			0
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	0.950926	−	0.309418i	$-0.100134\pi$
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	−0.743427	+	0.668817i	$0.766801\pi$
$422$		0			0
$423$	1.71468	+	28.3512i	0.0833708	+	1.37848i
$424$		0			0
$425$	−2.01780	+	3.49494i	−0.0978778	+	0.169529i
$426$		0			0
$427$	23.2973	−	18.1145i	1.12744	−	0.876622i
$428$		0			0
$429$	−27.7326	−	6.54012i	−1.33894	−	0.315760i
$430$		0			0
$431$	−19.8414	−	11.4554i	−0.955727	−	0.551789i	−0.0608716	−	0.998146i	$-0.519388\pi$
$431$	−19.8414	−	11.4554i	−0.955727	−	0.551789i	−0.894855	+	0.446356i	$0.852721\pi$
$432$		0			0
$433$		−	32.7273i		−	1.57278i	−0.617733	−	0.786388i	$-0.711949\pi$
$433$		−	32.7273i		−	1.57278i	0.617733	−	0.786388i	$-0.288051\pi$
$434$		0			0
$435$	−4.50827	−	4.24384i	−0.216155	−	0.203477i
$436$		0			0
$437$	−6.76156	−	11.7114i	−0.323449	−	0.560231i
$438$		0			0
$439$	−5.57285	−	3.21749i	−0.265978	−	0.153562i	0.361081	−	0.932535i	$-0.382408\pi$
$439$	−5.57285	−	3.21749i	−0.265978	−	0.153562i	−0.627058	+	0.778972i	$0.715741\pi$
$440$		0			0
$441$	20.6276	+	3.93729i	0.982267	+	0.187490i
$442$		0			0
$443$	22.1159	+	12.7686i	1.05076	+	0.606656i	0.922862	−	0.385131i	$-0.125844\pi$
$443$	22.1159	+	12.7686i	1.05076	+	0.606656i	0.127898	+	0.991787i	$0.459177\pi$
$444$		0			0
$445$	−0.0124085	−	0.0214921i	−0.000588219	−	0.00101882i
$446$		0			0
$447$	17.0034	−	5.11113i	0.804233	−	0.241748i
$448$		0			0
$449$			40.1008i			1.89247i	0.323474	+	0.946237i	$0.395149\pi$
$449$			40.1008i			1.89247i	−0.323474	+	0.946237i	$0.604851\pi$
$450$		0			0
$451$	31.7322	+	18.3206i	1.49421	+	0.862684i
$452$		0			0
$453$	−11.8674	−	39.4798i	−0.557581	−	1.85492i
$454$		0			0
$455$	4.12128	−	3.20444i	0.193208	−	0.150226i
$456$		0			0
$457$	19.2357	−	33.3173i	0.899810	−	1.55852i	0.0720726	−	0.997399i	$-0.477039\pi$
$457$	19.2357	−	33.3173i	0.899810	−	1.55852i	0.827737	−	0.561116i	$-0.189628\pi$
$458$		0			0
$459$	−4.26813	+	1.56965i	−0.199219	+	0.0732651i
$460$		0			0
$461$	−12.0830	−	20.9283i	−0.562759	−	0.974728i	−0.997254	−	0.0740533i	$-0.976407\pi$
$461$	−12.0830	−	20.9283i	−0.562759	−	0.974728i	0.434495	−	0.900674i	$-0.356927\pi$
$462$		0			0
$463$	8.65455	−	14.9901i	0.402211	−	0.696650i	−0.591781	−	0.806098i	$-0.701575\pi$
$463$	8.65455	−	14.9901i	0.402211	−	0.696650i	0.993992	+	0.109449i	$0.0349085\pi$
$464$		0			0
$465$	3.65301	+	3.43875i	0.169404	+	0.159468i
$466$		0			0
$467$	5.46858	+	9.47185i	0.253056	+	0.438305i	0.964366	−	0.264573i	$-0.0852311\pi$
$467$	5.46858	+	9.47185i	0.253056	+	0.438305i	−0.711310	+	0.702878i	$0.751898\pi$
$468$		0			0
$469$	31.7098	−	4.38110i	1.46422	−	0.202300i
$470$		0			0
$471$	14.5136	+	13.6624i	0.668752	+	0.629528i
$472$		0			0
$473$	14.0838	−	8.13126i	0.647572	−	0.373876i
$474$		0			0
$475$	−6.54197	+	3.77701i	−0.300166	+	0.173301i
$476$		0			0
$477$	3.98298	−	0.240891i	0.182368	−	0.0110296i
$478$		0			0
$479$	−1.51349			−0.0691531			−0.0345765	−	0.999402i	$-0.511008\pi$
$479$	−1.51349			−0.0691531			−0.0345765	+	0.999402i	$0.511008\pi$
$480$		0			0
$481$		−	7.86551i		−	0.358636i
$482$		0			0
$483$	3.56203	−	37.6601i	0.162078	−	1.71360i
$484$		0			0
$485$	−3.70841	+	2.14105i	−0.168390	+	0.0972201i
$486$		0			0
$487$	0.0853077	−	0.147757i	0.00386566	−	0.00669552i	−0.864086	−	0.503344i	$-0.832103\pi$
$487$	0.0853077	−	0.147757i	0.00386566	−	0.00669552i	0.867952	+	0.496649i	$0.165436\pi$
$488$		0			0
$489$	24.8395	−	26.3872i	1.12328	−	1.19327i
$490$		0			0
$491$	−23.5139	−	13.5757i	−1.06117	−	0.612665i	−0.135412	−	0.990789i	$-0.543236\pi$
$491$	−23.5139	−	13.5757i	−1.06117	−	0.612665i	−0.925755	+	0.378125i	$0.876569\pi$
$492$		0			0
$493$		−	5.01687i		−	0.225949i
$494$		0			0
$495$	−5.36283	−	8.11434i	−0.241041	−	0.364712i
$496$		0			0
$497$	−25.9442	−	10.5526i	−1.16376	−	0.473350i
$498$		0			0
$499$	−22.2654			−0.996738			−0.498369	−	0.866965i	$-0.666067\pi$
$499$	−22.2654			−0.996738			−0.498369	+	0.866965i	$0.666067\pi$
$500$		0			0
$501$	22.5682	+	5.32220i	1.00827	+	0.237778i
$502$		0			0
$503$	32.2005			1.43575			0.717876	−	0.696171i	$-0.245115\pi$
$503$	32.2005			1.43575			0.717876	+	0.696171i	$0.245115\pi$
$504$		0			0
$505$	−5.56621			−0.247693
$506$		0			0
$507$	3.54755	−	3.76859i	0.157552	−	0.167369i
$508$		0			0
$509$	−9.21817			−0.408588			−0.204294	−	0.978910i	$-0.565490\pi$
$509$	−9.21817			−0.408588			−0.204294	+	0.978910i	$0.565490\pi$
$510$		0			0
$511$	−28.1502	+	21.8878i	−1.24529	+	0.968259i
$512$		0			0
$513$	−8.38799	−	1.45013i	−0.370339	−	0.0640248i
$514$		0			0
$515$		−	5.53055i		−	0.243705i
$516$		0			0
$517$	−42.6285	−	24.6116i	−1.87480	−	1.08242i
$518$		0			0
$519$	−9.92714	−	2.34109i	−0.435753	−	0.102763i
$520$		0			0
$521$	−7.44581	+	12.8965i	−0.326207	+	0.565007i	−0.981756	−	0.190146i	$-0.939104\pi$
$521$	−7.44581	+	12.8965i	−0.326207	+	0.565007i	0.655549	+	0.755153i	$0.272437\pi$
$522$		0			0
$523$	29.3725	−	16.9582i	1.28437	−	0.741532i	0.306727	−	0.951798i	$-0.400766\pi$
$523$	29.3725	−	16.9582i	1.28437	−	0.741532i	0.977644	+	0.210266i	$0.0674329\pi$
$524$		0			0
$525$	−21.0370	−	1.98975i	−0.918128	−	0.0868398i
$526$		0			0
$527$			4.06512i			0.177080i
$528$		0			0
$529$	−45.1416			−1.96268
$530$		0			0
$531$	−17.0875	−	8.53401i	−0.741533	−	0.370344i
$532$		0			0
$533$	19.3122	−	11.1499i	0.836504	−	0.482956i
$534$		0			0
$535$	−1.64833	+	0.951663i	−0.0712635	+	0.0411440i
$536$		0			0
$537$	6.62581	−	28.0960i	0.285925	−	1.21243i
$538$		0			0
$539$	−25.4029	+	26.0610i	−1.09418	+	1.12253i
$540$		0			0
$541$	−2.65164	−	4.59278i	−0.114003	−	0.197459i	0.803378	−	0.595470i	$-0.203034\pi$
$541$	−2.65164	−	4.59278i	−0.114003	−	0.197459i	−0.917381	+	0.398011i	$0.869701\pi$
$542$		0			0
$543$	−0.767504	+	0.230708i	−0.0329368	+	0.00990062i
$544$		0			0
$545$	3.46139	−	5.99531i	0.148270	−	0.256811i
$546$		0			0
$547$	4.13892	+	7.16882i	0.176967	+	0.306517i	0.940840	−	0.338850i	$-0.110038\pi$
$547$	4.13892	+	7.16882i	0.176967	+	0.306517i	−0.763873	+	0.645367i	$0.776705\pi$
$548$		0			0
$549$	−33.4013	+	2.02011i	−1.42553	+	0.0862163i
$550$		0			0
$551$	4.69540	−	8.13267i	0.200031	−	0.346463i
$552$		0			0
$553$	−15.7478	−	20.2534i	−0.669663	−	0.861264i
$554$		0			0
$555$	1.84034	−	1.95501i	0.0781180	−	0.0829854i
$556$		0			0
$557$	−6.96801	−	4.02299i	−0.295244	−	0.170459i	0.345060	−	0.938581i	$-0.387858\pi$
$557$	−6.96801	−	4.02299i	−0.295244	−	0.170459i	−0.640304	+	0.768121i	$0.721192\pi$
$558$		0			0
$559$		−	9.89735i		−	0.418613i
$560$		0			0
$561$	1.80896	−	7.67070i	0.0763745	−	0.323857i
$562$		0			0
$563$	14.9578	+	25.9077i	0.630396	+	1.09188i	0.987471	+	0.157802i	$0.0504409\pi$
$563$	14.9578	+	25.9077i	0.630396	+	1.09188i	−0.357074	+	0.934076i	$0.616226\pi$
$564$		0			0
$565$	1.95707	+	1.12992i	0.0823346	+	0.0475359i
$566$		0			0
$567$	−16.7752	−	16.8995i	−0.704490	−	0.709714i
$568$		0			0
$569$	26.6942	+	15.4119i	1.11908	+	0.646101i	0.941166	−	0.337946i	$-0.109732\pi$
$569$	26.6942	+	15.4119i	1.11908	+	0.646101i	0.177913	+	0.984046i	$0.443065\pi$
$570$		0			0
$571$	−2.67347	−	4.63058i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$571$	−2.67347	−	4.63058i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$572$		0			0
$573$	−5.42214	+	22.9920i	−0.226513	+	0.960503i
$574$		0			0
$575$			38.0639i			1.58737i
$576$		0			0
$577$	16.3235	+	9.42437i	0.679556	+	0.392342i	0.799688	−	0.600416i	$-0.204998\pi$
$577$	16.3235	+	9.42437i	0.679556	+	0.392342i	−0.120132	+	0.992758i	$0.538332\pi$
$578$		0			0
$579$	−13.6275	+	14.4766i	−0.566338	+	0.601625i
$580$		0			0
$581$	1.00657	−	0.139070i	0.0417595	−	0.00576959i
$582$		0			0
$583$	−3.45761	+	5.98876i	−0.143200	+	0.248029i
$584$		0			0
$585$	−5.90866	+	0.357356i	−0.244293	+	0.0147749i
$586$		0			0
$587$	−12.3955	−	21.4697i	−0.511619	−	0.886150i	−0.999909	−	0.0134687i	$-0.995713\pi$
$587$	−12.3955	−	21.4697i	−0.511619	−	0.886150i	0.488290	−	0.872681i	$-0.337621\pi$
$588$		0			0
$589$	−3.80464	+	6.58982i	−0.156767	+	0.271529i
$590$		0			0
$591$	−7.93179	+	2.38426i	−0.326270	+	0.0980752i
$592$		0			0
$593$	1.87451	+	3.24675i	0.0769770	+	0.133328i	0.901944	−	0.431852i	$-0.142140\pi$
$593$	1.87451	+	3.24675i	0.0769770	+	0.133328i	−0.824967	+	0.565180i	$0.808807\pi$
$594$		0			0
$595$	0.886331	+	1.13992i	0.0363360	+	0.0467323i
$596$		0			0
$597$	3.61665	−	15.3360i	0.148020	−	0.627660i
$598$		0			0
$599$	27.7711	−	16.0337i	1.13470	−	0.655118i	0.189586	−	0.981864i	$-0.439286\pi$
$599$	27.7711	−	16.0337i	1.13470	−	0.655118i	0.945112	+	0.326746i	$0.105952\pi$
$600$		0			0
$601$	−5.98069	+	3.45296i	−0.243958	+	0.140849i	−0.616994	−	0.786968i	$-0.711650\pi$
$601$	−5.98069	+	3.45296i	−0.243958	+	0.140849i	0.373037	+	0.927817i	$0.378317\pi$
$602$		0			0
$603$	−32.4725	−	16.2178i	−1.32238	−	0.660438i
$604$		0			0
$605$	9.99648			0.406415
$606$		0			0
$607$		−	21.6959i		−	0.880608i	−0.897849	−	0.440304i	$-0.854871\pi$
$607$		−	21.6959i		−	0.880608i	0.897849	−	0.440304i	$-0.145129\pi$
$608$		0			0
$609$	23.8852	−	10.9339i	0.967877	−	0.443064i
$610$		0			0
$611$	−25.9437	+	14.9786i	−1.04957	+	0.605968i
$612$		0			0
$613$	8.96928	−	15.5352i	0.362266	−	0.627463i	−0.626068	−	0.779769i	$-0.715337\pi$
$613$	8.96928	−	15.5352i	0.362266	−	0.627463i	0.988333	+	0.152306i	$0.0486699\pi$
$614$		0			0
$615$	7.40894	+	1.74723i	0.298757	+	0.0704552i
$616$		0			0
$617$	32.9146	+	19.0033i	1.32509	+	0.765043i	0.984536	−	0.175181i	$-0.0560509\pi$
$617$	32.9146	+	19.0033i	1.32509	+	0.765043i	0.340557	+	0.940224i	$0.389384\pi$
$618$		0			0
$619$		−	43.3774i		−	1.74349i	−0.489964	−	0.871743i	$-0.662990\pi$
$619$		−	43.3774i		−	1.74349i	0.489964	−	0.871743i	$-0.337010\pi$
$620$		0			0
$621$	−27.4612	+	32.9501i	−1.10198	+	1.32224i
$622$		0			0
$623$	0.104301	−	0.0144105i	0.00417873	−	0.000577343i
$624$		0			0
$625$	19.3181			0.772725
$626$		0			0
$627$	10.1116	−	10.7417i	0.403819	−	0.428980i
$628$		0			0
$629$	2.17556			0.0867453
$630$		0			0
$631$	−11.2735			−0.448793			−0.224396	−	0.974498i	$-0.572041\pi$
$631$	−11.2735			−0.448793			−0.224396	+	0.974498i	$0.572041\pi$
$632$		0			0
$633$	−4.97234	−	1.17262i	−0.197633	−	0.0466073i
$634$		0			0
$635$	−6.32378			−0.250952
$636$		0			0
$637$	6.00569	+	21.3193i	0.237954	+	0.844701i
$638$		0			0
$639$	17.5106	+	26.4948i	0.692709	+	1.04812i
$640$		0			0
$641$			29.7553i			1.17526i	0.809129	+	0.587631i	$0.199939\pi$
$641$			29.7553i			1.17526i	−0.809129	+	0.587631i	$0.800061\pi$
$642$		0			0
$643$	37.4271	+	21.6085i	1.47598	+	0.852158i	0.999633	−	0.0270991i	$-0.00862696\pi$
$643$	37.4271	+	21.6085i	1.47598	+	0.852158i	0.476348	+	0.879257i	$0.341960\pi$
$644$		0			0
$645$	2.31574	−	2.46003i	0.0911822	−	0.0968635i
$646$		0			0
$647$	9.42940	−	16.3322i	0.370708	−	0.642085i	−0.618967	−	0.785417i	$-0.712448\pi$
$647$	9.42940	−	16.3322i	0.370708	−	0.642085i	0.989675	+	0.143332i	$0.0457817\pi$
$648$		0			0
$649$	28.6661	−	16.5504i	1.12524	−	0.649660i
$650$		0			0
$651$	−19.3539	+	8.85964i	−0.758541	+	0.347237i
$652$		0			0
$653$			9.71777i			0.380286i	0.981756	+	0.190143i	$0.0608951\pi$
$653$			9.71777i			0.380286i	−0.981756	+	0.190143i	$0.939105\pi$
$654$		0			0
$655$	13.5679			0.530144
$656$		0			0
$657$	40.3589	−	2.44091i	1.57455	−	0.0952289i
$658$		0			0
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.172266	−	0.985050i	$-0.444891\pi$
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.939212	+	0.343338i	$0.111558\pi$
$660$		0			0
$661$	−1.08957	+	0.629061i	−0.0423792	+	0.0244677i	−0.521040	−	0.853532i	$-0.674456\pi$
$661$	−1.08957	+	0.629061i	−0.0423792	+	0.0244677i	0.478661	+	0.878000i	$0.341122\pi$
$662$		0			0
$663$	−3.49247	−	3.28763i	−0.135636	−	0.127681i
$664$		0			0
$665$	0.369920	+	2.67743i	0.0143449	+	0.103826i
$666$		0			0
$667$	−23.6596	−	40.9797i	−0.916104	−	1.58674i
$668$		0			0
$669$	−29.7902	−	28.0429i	−1.15176	−	1.08420i
$670$		0			0
$671$	28.9955	−	50.2217i	1.11936	−	1.93879i
$672$		0			0
$673$	−12.2655	−	21.2445i	−0.472800	−	0.818914i	0.526715	−	0.850042i	$-0.323423\pi$
$673$	−12.2655	−	21.2445i	−0.472800	−	0.818914i	−0.999515	+	0.0311279i	$0.990090\pi$
$674$		0			0
$675$	18.4059	+	15.3398i	0.708444	+	0.590430i
$676$		0			0
$677$	−11.5616	+	20.0253i	−0.444350	+	0.769636i	−0.998007	−	0.0631088i	$-0.979899\pi$
$677$	−11.5616	+	20.0253i	−0.444350	+	0.769636i	0.553657	+	0.832745i	$0.313232\pi$
$678$		0			0
$679$	−2.48649	−	17.9968i	−0.0954226	−	0.690655i
$680$		0			0
$681$	9.00018	+	29.9412i	0.344888	+	1.14735i
$682$		0			0
$683$	12.4945	+	7.21370i	0.478089	+	0.276025i	0.719620	−	0.694368i	$-0.244316\pi$
$683$	12.4945	+	7.21370i	0.478089	+	0.276025i	−0.241531	+	0.970393i	$0.577650\pi$
$684$		0			0
$685$		−	0.245147i		−	0.00936659i
$686$		0			0
$687$	−20.1516	+	6.05747i	−0.768831	+	0.231107i
$688$		0			0
$689$	2.10430	+	3.64475i	0.0801673	+	0.138854i
$690$		0			0
$691$	32.3993	+	18.7057i	1.23253	+	0.711599i	0.967556	−	0.252657i	$-0.0813045\pi$
$691$	32.3993	+	18.7057i	1.23253	+	0.711599i	0.264970	+	0.964257i	$0.414638\pi$
$692$		0			0
$693$	40.4625	−	8.10530i	1.53704	−	0.307895i
$694$		0			0
$695$	−9.76844	−	5.63981i	−0.370538	−	0.213930i
$696$		0			0
$697$	3.08401	+	5.34166i	0.116815	+	0.202330i
$698$		0			0
$699$	4.93839	+	4.64874i	0.186787	+	0.175832i
$700$		0			0
$701$			41.0429i			1.55017i	0.631859	+	0.775084i	$0.282292\pi$
$701$			41.0429i			1.55017i	−0.631859	+	0.775084i	$0.717708\pi$
$702$		0			0
$703$	3.52672	+	2.03615i	0.133013	+	0.0767950i
$704$		0			0
$705$	−9.95303	−	2.34720i	−0.374853	−	0.0884007i
$706$		0			0
$707$	8.89774	−	21.8756i	0.334634	−	0.822716i
$708$		0			0
$709$	−11.6623	+	20.1997i	−0.437987	+	0.758616i	−0.997534	−	0.0701829i	$-0.977642\pi$
$709$	−11.6623	+	20.1997i	−0.437987	+	0.758616i	0.559547	+	0.828798i	$0.310975\pi$
$710$		0			0
$711$	1.75618	+	29.0373i	0.0658618	+	1.08898i
$712$		0			0
$713$	19.1712	+	33.2054i	0.717966	+	1.24355i
$714$		0			0
$715$	5.12928	−	8.88418i	0.191824	−	0.332249i
$716$		0			0
$717$	4.77408	−	20.2439i	0.178291	−	0.756024i
$718$		0			0
$719$	21.7489	+	37.6701i	0.811096	+	1.40486i	0.912098	+	0.409973i	$0.134462\pi$
$719$	21.7489	+	37.6701i	0.811096	+	1.40486i	−0.101002	+	0.994886i	$0.532205\pi$
$720$		0			0
$721$	21.7354	+	8.84073i	0.809470	+	0.329246i
$722$		0			0
$723$	−46.9178	+	14.1033i	−1.74489	+	0.524506i
$724$		0			0
$725$	−22.8912	+	13.2163i	−0.850159	+	0.490840i
$726$		0			0
$727$	11.3715	−	6.56536i	0.421747	−	0.243496i	−0.274078	−	0.961708i	$-0.588373\pi$
$727$	11.3715	−	6.56536i	0.421747	−	0.243496i	0.695824	+	0.718212i	$0.255039\pi$
$728$		0			0
$729$	4.86618	+	26.5579i	0.180229	+	0.983625i
$730$		0			0
$731$	2.73756			0.101252
$732$		0			0
$733$		−	40.1795i		−	1.48406i	−0.670364	−	0.742032i	$-0.733862\pi$
$733$		−	40.1795i		−	1.48406i	0.670364	−	0.742032i	$-0.266138\pi$
$734$		0			0
$735$	−3.49546	+	6.70418i	−0.128932	+	0.247288i
$736$		0			0
$737$	54.4762	−	31.4518i	2.00666	−	1.15854i
$738$		0			0
$739$	−18.7073	+	32.4020i	−0.688158	+	1.19193i	0.284275	+	0.958743i	$0.408247\pi$
$739$	−18.7073	+	32.4020i	−0.688158	+	1.19193i	−0.972433	+	0.233182i	$0.925086\pi$
$740$		0			0
$741$	−2.58455	−	8.59813i	−0.0949460	−	0.315860i
$742$		0			0
$743$	−30.0501	−	17.3494i	−1.10243	−	0.636488i	−0.165572	−	0.986198i	$-0.552947\pi$
$743$	−30.0501	−	17.3494i	−1.10243	−	0.636488i	−0.936858	+	0.349709i	$0.886280\pi$
$744$		0			0
$745$			6.39239i			0.234199i
$746$		0			0
$747$	−1.03078	−	0.514802i	−0.0377142	−	0.0188356i
$748$		0			0
$749$	−1.10520	−	7.99931i	−0.0403833	−	0.292288i
$750$		0			0
$751$	29.0140			1.05873			0.529367	−	0.848393i	$-0.322429\pi$
$751$	29.0140			1.05873			0.529367	+	0.848393i	$0.322429\pi$
$752$		0			0
$753$	6.00448	+	19.9753i	0.218815	+	0.727941i
$754$		0			0
$755$	14.8423			0.540168
$756$		0			0
$757$	−8.62406			−0.313447			−0.156723	−	0.987643i	$-0.550093\pi$
$757$	−8.62406			−0.313447			−0.156723	+	0.987643i	$0.550093\pi$
$758$		0			0
$759$	−21.3988	−	71.1883i	−0.776729	−	2.58397i
$760$		0			0
$761$	−22.8213			−0.827272			−0.413636	−	0.910442i	$-0.635741\pi$
$761$	−22.8213			−0.827272			−0.413636	+	0.910442i	$0.635741\pi$
$762$		0			0
$763$	18.0288	+	23.1872i	0.652688	+	0.839432i
$764$		0			0
$765$	−0.0988429	−	1.63431i	−0.00357367	−	0.0590885i
$766$		0			0
$767$		−	20.1451i		−	0.727397i
$768$		0			0
$769$	27.6397	+	15.9578i	0.996714	+	0.575453i	0.907275	−	0.420539i	$-0.138159\pi$
$769$	27.6397	+	15.9578i	0.996714	+	0.575453i	0.0894399	+	0.995992i	$0.471492\pi$
$770$		0			0
$771$	7.30479	+	24.3011i	0.263076	+	0.875183i
$772$		0			0
$773$	−17.8503	+	30.9176i	−0.642030	+	1.11203i	0.342949	+	0.939354i	$0.388574\pi$
$773$	−17.8503	+	30.9176i	−0.642030	+	1.11203i	−0.984979	+	0.172675i	$0.944759\pi$
$774$		0			0
$775$	18.5486	−	10.7090i	0.666284	−	0.384679i
$776$		0			0
$777$	4.74148	+	10.3578i	0.170099	+	0.371584i
$778$		0			0
$779$			11.5456i			0.413663i
$780$		0			0
$781$	−55.0380			−1.96942
$782$		0			0
$783$	−29.3507	−	5.07420i	−1.04891	−	0.181337i
$784$		0			0
$785$	−6.21492	+	3.58819i	−0.221820	+	0.128068i
$786$		0			0
$787$	12.0233	−	6.94168i	0.428586	−	0.247444i	−0.270158	−	0.962816i	$-0.587076\pi$
$787$	12.0233	−	6.94168i	0.428586	−	0.247444i	0.698744	+	0.715372i	$0.253743\pi$
$788$		0			0
$789$	−9.50676	+	2.85768i	−0.338449	+	0.101736i
$790$		0			0
$791$	−7.56908	+	5.88522i	−0.269125	+	0.209254i
$792$		0			0
$793$	−17.6466	−	30.5649i	−0.626651	−	1.08539i
$794$		0			0
$795$	−0.329751	+	1.39827i	−0.0116951	+	0.0495916i
$796$		0			0
$797$	−14.2145	+	24.6203i	−0.503504	+	0.872094i	0.496488	+	0.868044i	$0.334623\pi$
$797$	−14.2145	+	24.6203i	−0.503504	+	0.872094i	−0.999992	+	0.00405063i	$0.998711\pi$
$798$		0			0
$799$	−4.14300	−	7.17589i	−0.146569	−	0.253865i
$800$		0			0
$801$	−0.106810	−	0.0533440i	−0.00377393	−	0.00188482i
$802$		0			0
$803$	−35.0354	+	60.6831i	−1.23637	+	2.14146i
$804$		0			0
$805$	12.6158	+	5.13138i	0.444648	+	0.180857i
$806$		0			0
$807$	5.45270	+	1.28590i	0.191944	+	0.0452657i
$808$		0			0
$809$	21.1074	+	12.1864i	0.742096	+	0.428449i	0.822831	−	0.568286i	$-0.192393\pi$
$809$	21.1074	+	12.1864i	0.742096	+	0.428449i	−0.0807348	+	0.996736i	$0.525727\pi$
$810$		0			0
$811$			35.2739i			1.23863i	0.785141	+	0.619317i	$0.212591\pi$
$811$			35.2739i			1.23863i	−0.785141	+	0.619317i	$0.787409\pi$
$812$		0			0
$813$	30.0979	+	28.3326i	1.05558	+	0.993668i
$814$		0			0
$815$	6.52369	+	11.2994i	0.228515	+	0.395799i
$816$		0			0
$817$	4.43776	+	2.56214i	0.155257	+	0.0896379i
$818$		0			0
$819$	8.04073	−	23.7927i	0.280966	−	0.831384i
$820$		0			0
$821$	−16.8999	−	9.75719i	−0.589812	−	0.340528i	0.175211	−	0.984531i	$-0.443939\pi$
$821$	−16.8999	−	9.75719i	−0.589812	−	0.340528i	−0.765023	+	0.644003i	$0.777273\pi$
$822$		0			0
$823$	−15.8285	−	27.4158i	−0.551747	−	0.955653i	−0.998149	−	0.0608208i	$-0.980628\pi$
$823$	−15.8285	−	27.4158i	−0.551747	−	0.955653i	0.446402	−	0.894833i	$-0.352705\pi$
$824$		0			0
$825$	−39.7658	+	11.9534i	−1.38447	+	0.416164i
$826$		0			0
$827$		−	24.4749i		−	0.851075i	−0.904941	−	0.425537i	$-0.860085\pi$
$827$		−	24.4749i		−	0.851075i	0.904941	−	0.425537i	$-0.139915\pi$
$828$		0			0
$829$	0.846010	+	0.488444i	0.0293831	+	0.0169644i	0.514620	−	0.857419i	$-0.327933\pi$
$829$	0.846010	+	0.488444i	0.0293831	+	0.0169644i	−0.485236	+	0.874383i	$0.661266\pi$
$830$		0			0
$831$	−3.82354	−	12.7199i	−0.132637	−	0.441249i
$832$		0			0
$833$	−5.89681	+	1.66114i	−0.204312	+	0.0575552i
$834$		0			0
$835$	−4.17409	+	7.22974i	−0.144450	+	0.250196i
$836$		0			0
$837$	23.7826	+	4.11158i	0.822047	+	0.142117i
$838$		0			0
$839$	−19.6920	−	34.1075i	−0.679843	−	1.17752i	−0.975028	−	0.222083i	$-0.928714\pi$
$839$	−19.6920	−	34.1075i	−0.679843	−	1.17752i	0.295184	−	0.955440i	$-0.404619\pi$
$840$		0			0
$841$	1.92983	−	3.34257i	0.0665459	−	0.115261i
$842$		0			0
$843$	12.7989	+	12.0482i	0.440818	+	0.414963i
$844$		0			0
$845$	0.931704	+	1.61376i	0.0320516	+	0.0555150i
$846$		0			0
$847$	−15.9797	+	39.2869i	−0.549067	+	1.34991i
$848$		0			0
$849$	−17.2384	−	16.2273i	−0.591620	−	0.556919i
$850$		0			0
$851$	17.7708	−	10.2600i	0.609175	−	0.351707i
$852$		0			0
$853$	−21.3507	+	12.3268i	−0.731033	+	0.422062i	−0.818800	−	0.574079i	$-0.805360\pi$
$853$	−21.3507	+	12.3268i	−0.731033	+	0.422062i	0.0877672	+	0.996141i	$0.472027\pi$
$854$		0			0
$855$	1.36935	−	2.74182i	0.0468309	−	0.0937684i
$856$		0			0
$857$	22.8290			0.779823			0.389911	−	0.920852i	$-0.372506\pi$
$857$	22.8290			0.779823			0.389911	+	0.920852i	$0.372506\pi$
$858$		0			0
$859$			47.7150i			1.62801i	0.580855	+	0.814007i	$0.302718\pi$
$859$			47.7150i			1.62801i	−0.580855	+	0.814007i	$0.697282\pi$
$860$		0			0
$861$	−18.7101	+	26.3246i	−0.637640	+	0.897142i
$862$		0			0
$863$	18.0645	−	10.4296i	0.614923	−	0.355026i	−0.159967	−	0.987122i	$-0.551139\pi$
$863$	18.0645	−	10.4296i	0.614923	−	0.355026i	0.774890	+	0.632096i	$0.217805\pi$
$864$		0			0
$865$	1.83607	−	3.18017i	0.0624283	−	0.108129i
$866$		0			0
$867$	−19.2731	+	20.4739i	−0.654548	+	0.695331i
$868$		0			0
$869$	−43.6601	−	25.2072i	−1.48107	−	0.855094i
$870$		0			0
$871$		−	38.2831i		−	1.29717i
$872$		0			0
$873$	−9.20437	+	18.4297i	−0.311521	+	0.623751i
$874$		0			0
$875$	5.97451	−	14.6887i	0.201975	−	0.496567i
$876$		0			0
$877$	−23.5436			−0.795011			−0.397506	−	0.917600i	$-0.630124\pi$
$877$	−23.5436			−0.795011			−0.397506	+	0.917600i	$0.630124\pi$
$878$		0			0
$879$	−9.13380	−	2.15400i	−0.308075	−	0.0726527i
$880$		0			0
$881$	−52.5975			−1.77205			−0.886027	−	0.463633i	$-0.846546\pi$
$881$	−52.5975			−1.77205			−0.886027	+	0.463633i	$0.846546\pi$
$882$		0			0
$883$	33.6815			1.13347			0.566737	−	0.823899i	$-0.308206\pi$
$883$	33.6815			1.13347			0.566737	+	0.823899i	$0.308206\pi$
$884$		0			0
$885$	4.71347	−	5.00715i	0.158441	−	0.168314i
$886$		0			0
$887$	−15.0228			−0.504415			−0.252208	−	0.967673i	$-0.581157\pi$
$887$	−15.0228			−0.504415			−0.252208	+	0.967673i	$0.581157\pi$
$888$		0			0
$889$	10.1087	−	24.8529i	0.339036	−	0.833540i
$890$		0			0
$891$	−43.0470	−	18.3415i	−1.44213	−	0.614464i
$892$		0			0
$893$		−	15.5101i		−	0.519026i
$894$		0			0
$895$	9.00059	+	5.19649i	0.300856	+	0.173700i
$896$		0			0
$897$	−44.0323	−	10.3840i	−1.47019	−	0.346713i
$898$		0			0
$899$	−13.3129	+	23.0587i	−0.444011	+	0.769050i
$900$		0			0
$901$	−1.00812	+	0.582038i	−0.0335853	+	0.0193905i
$902$		0			0
$903$	5.96631	+	13.0334i	0.198546	+	0.433726i
$904$		0			0
$905$		−	0.288542i		−	0.00959144i
$906$		0			0
$907$	11.6949			0.388324			0.194162	−	0.980969i	$-0.437801\pi$
$907$	11.6949			0.388324			0.194162	+	0.980969i	$0.437801\pi$
$908$		0			0
$909$	−22.3398	+	14.7645i	−0.740964	+	0.489709i
$910$		0			0
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	−0.251689	−	0.967808i	$-0.580986\pi$
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	0.712302	+	0.701873i	$0.247653\pi$
$912$		0			0
$913$	1.72925	−	0.998380i	0.0572297	−	0.0330416i
$914$		0			0
$915$	2.76530	−	11.7259i	0.0914179	−	0.387647i
$916$		0			0
$917$	−21.6887	+	53.3230i	−0.716225	+	1.76088i
$918$		0			0
$919$	−9.26860	−	16.0537i	−0.305743	−	0.529562i	0.671683	−	0.740838i	$-0.265572\pi$
$919$	−9.26860	−	16.0537i	−0.305743	−	0.529562i	−0.977426	+	0.211276i	$0.932238\pi$
$920$		0			0
$921$	5.91066	−	1.77671i	0.194763	−	0.0585447i
$922$		0			0
$923$	−16.7480	+	29.0084i	−0.551268	+	0.954824i
$924$		0			0
$925$	−5.73122	−	9.92676i	−0.188441	−	0.326390i
$926$		0			0
$927$	−14.6699	−	22.1967i	−0.481824	−	0.729034i
$928$		0			0
$929$	−26.8357	+	46.4808i	−0.880451	+	1.52499i	−0.0296102	+	0.999562i	$0.509427\pi$
$929$	−26.8357	+	46.4808i	−0.880451	+	1.52499i	−0.850841	+	0.525424i	$0.823907\pi$
$930$		0			0
$931$	−11.1138	−	2.82613i	−0.364240	−	0.0926227i
$932$		0			0
$933$	13.3734	−	14.2067i	0.437827	−	0.465107i
$934$		0			0
$935$	2.45732	+	1.41873i	0.0803630	+	0.0463976i
$936$		0			0
$937$			16.7752i			0.548023i	0.961726	+	0.274012i	$0.0883506\pi$
$937$			16.7752i			0.548023i	−0.961726	+	0.274012i	$0.911649\pi$
$938$		0			0
$939$	−4.54333	+	19.2655i	−0.148266	+	0.628704i
$940$		0			0
$941$	18.5343	+	32.1023i	0.604200	+	1.04651i	0.992177	+	0.124837i	$0.0398406\pi$
$941$	18.5343	+	32.1023i	0.604200	+	1.04651i	−0.387977	+	0.921669i	$0.626826\pi$
$942$		0			0
$943$	50.3827	+	29.0885i	1.64069	+	0.947250i
$944$		0			0
$945$	7.56547	−	4.03244i	0.246105	−	0.131175i
$946$		0			0
$947$	−2.73735	−	1.58041i	−0.0889520	−	0.0513565i	0.454864	−	0.890561i	$-0.349688\pi$
$947$	−2.73735	−	1.58041i	−0.0889520	−	0.0513565i	−0.543816	+	0.839204i	$0.683021\pi$
$948$		0			0
$949$	21.3225	+	36.9316i	0.692157	+	1.19885i
$950$		0			0
$951$	−7.73999	+	32.8205i	−0.250986	+	1.06428i
$952$		0			0
$953$		−	38.9680i		−	1.26230i	−0.775662	−	0.631149i	$-0.782584\pi$
$953$		−	38.9680i		−	1.26230i	0.775662	−	0.631149i	$-0.217416\pi$
$954$		0			0
$955$	−7.36550	−	4.25247i	−0.238342	−	0.137607i
$956$		0			0
$957$	35.3819	−	37.5865i	1.14374	−	1.21500i
$958$		0			0
$959$	0.963445	+	0.391874i	0.0311113	+	0.0126543i
$960$		0			0
$961$	−4.71266	+	8.16256i	−0.152021	+	0.263308i
$962$		0			0
$963$	−4.09119	+	8.19171i	−0.131837	+	0.263974i
$964$		0			0
$965$	−3.57902	−	6.19905i	−0.115213	−	0.199555i
$966$		0			0
$967$	7.29560	−	12.6363i	0.234611	−	0.406357i	−0.724549	−	0.689223i	$-0.757952\pi$
$967$	7.29560	−	12.6363i	0.234611	−	0.406357i	0.959159	+	0.282866i	$0.0912852\pi$
$968$		0			0
$969$	2.37820	−	0.714875i	0.0763988	−	0.0229651i
$970$		0			0
$971$	−11.3537	−	19.6652i	−0.364358	−	0.631086i	0.624315	−	0.781172i	$-0.285378\pi$
$971$	−11.3537	−	19.6652i	−0.364358	−	0.631086i	−0.988673	+	0.150087i	$0.952045\pi$
$972$		0			0
$973$	37.7800	−	29.3752i	1.21117	−	0.941727i
$974$		0			0
$975$	−5.80052	+	24.5964i	−0.185765	+	0.787716i
$976$		0			0
$977$	35.5426	−	20.5206i	1.13711	−	0.656511i	0.191397	−	0.981513i	$-0.438698\pi$
$977$	35.5426	−	20.5206i	1.13711	−	0.656511i	0.945713	+	0.325002i	$0.105365\pi$
$978$		0			0
$979$	0.179185	−	0.103453i	0.00572678	−	0.00330636i
$980$		0			0
$981$	−2.01056	−	33.2434i	−0.0641923	−	1.06138i
$982$		0			0
$983$	−20.9305			−0.667579			−0.333790	−	0.942648i	$-0.608328\pi$
$983$	−20.9305			−0.667579			−0.333790	+	0.942648i	$0.608328\pi$
$984$		0			0
$985$		−	2.98194i		−	0.0950125i
$986$		0			0
$987$	25.1349	−	35.3640i	0.800051	−	1.12565i
$988$		0			0
$989$	22.3614	−	12.9104i	0.711051	−	0.410525i
$990$		0			0
$991$	−26.9709	+	46.7149i	−0.856758	+	1.48395i	0.0182456	+	0.999834i	$0.494192\pi$
$991$	−26.9709	+	46.7149i	−0.856758	+	1.48395i	−0.875004	+	0.484116i	$0.839141\pi$
$992$		0			0
$993$	45.4621	+	10.7212i	1.44269	+	0.340227i
$994$		0			0
$995$	4.91290	+	2.83647i	0.155749	+	0.0899220i
$996$		0			0
$997$			3.21654i			0.101869i	0.998702	+	0.0509345i	$0.0162200\pi$
$997$			3.21654i			0.101869i	−0.998702	+	0.0509345i	$0.983780\pi$
$998$		0			0
$999$	2.20042	−	12.7279i	0.0696183	−	0.402693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.689.14		48
3.2	odd	2		3024.2.df.e.17.14		48
4.3	odd	2		504.2.cx.a.185.11	yes	48
7.5	odd	6		1008.2.ca.e.257.22		48
9.2	odd	6		1008.2.ca.e.353.22		48
9.7	even	3		3024.2.ca.e.2033.14		48
12.11	even	2		1512.2.cx.a.17.14		48
21.5	even	6		3024.2.ca.e.2609.14		48
28.19	even	6		504.2.bs.a.257.3	✓	48
36.7	odd	6		1512.2.bs.a.521.14		48
36.11	even	6		504.2.bs.a.353.3	yes	48
63.47	even	6	inner	1008.2.df.e.929.14		48
63.61	odd	6		3024.2.df.e.1601.14		48
84.47	odd	6		1512.2.bs.a.1097.14		48
252.47	odd	6		504.2.cx.a.425.11	yes	48
252.187	even	6		1512.2.cx.a.89.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.3	✓	48	28.19	even	6
504.2.bs.a.353.3	yes	48	36.11	even	6
504.2.cx.a.185.11	yes	48	4.3	odd	2
504.2.cx.a.425.11	yes	48	252.47	odd	6
1008.2.ca.e.257.22		48	7.5	odd	6
1008.2.ca.e.353.22		48	9.2	odd	6
1008.2.df.e.689.14		48	1.1	even	1	trivial
1008.2.df.e.929.14		48	63.47	even	6	inner
1512.2.bs.a.521.14		48	36.7	odd	6
1512.2.bs.a.1097.14		48	84.47	odd	6
1512.2.cx.a.17.14		48	12.11	even	2
1512.2.cx.a.89.14		48	252.187	even	6
3024.2.ca.e.2033.14		48	9.7	even	3
3024.2.ca.e.2609.14		48	21.5	even	6
3024.2.df.e.17.14		48	3.2	odd	2
3024.2.df.e.1601.14		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)

\(f(q)\)	\(=\)	\(q+(0.498607 + 1.65873i) q^{3} -0.623597 q^{5} +(0.996837 - 2.45078i) q^{7} +(-2.50278 + 1.65411i) q^{9} -5.19907i q^{11} +(-2.74023 - 1.58207i) q^{13} +(-0.310929 - 1.03438i) q^{15} +(0.437594 - 0.757935i) q^{17} +(1.41874 - 0.819107i) q^{19} +(4.56221 + 0.431510i) q^{21} -8.25480i q^{23} -4.61113 q^{25} +(-3.99163 - 3.32670i) q^{27} +(4.96435 - 2.86617i) q^{29} +(-4.02256 + 2.32243i) q^{31} +(8.62387 - 2.59229i) q^{33} +(-0.621624 + 1.52830i) q^{35} +(1.24291 + 2.15278i) q^{37} +(1.25794 - 5.33415i) q^{39} +(-3.52382 + 6.10344i) q^{41} +(1.56398 + 2.70890i) q^{43} +(1.56073 - 1.03150i) q^{45} +(4.73384 - 8.19925i) q^{47} +(-5.01263 - 4.88605i) q^{49} +(1.47540 + 0.347940i) q^{51} +(-1.15189 - 0.665044i) q^{53} +3.24212i q^{55} +(2.06607 + 1.94489i) q^{57} +(3.18334 + 5.51370i) q^{59} +(9.65975 + 5.57706i) q^{61} +(1.55899 + 7.78264i) q^{63} +(1.70880 + 0.986576i) q^{65} +(6.04951 + 10.4781i) q^{67} +(13.6925 - 4.11590i) q^{69} -10.5861i q^{71} +(-11.6719 - 6.73878i) q^{73} +(-2.29914 - 7.64862i) q^{75} +(-12.7418 - 5.18263i) q^{77} +(4.84840 - 8.39767i) q^{79} +(3.52785 - 8.27975i) q^{81} +(0.192030 + 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(7.22946 + 6.80543i) q^{87} +(0.0198983 + 0.0344648i) q^{89} +(-6.60888 + 5.13864i) q^{91} +(-5.85796 - 5.51438i) q^{93} +(-0.884719 + 0.510793i) q^{95} +(5.94681 - 3.43339i) q^{97} +(8.59984 + 13.0122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots + 64 q^{99}+O(q^{100}) \) 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

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