LMFDB - Embedded newform 1008.2.df.d.689.8

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 = [16,0,0,0,0,0,1] 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.8
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.d.929.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60579 + 0.649187i) q^{3} -2.96988 q^{5} +(-2.38485 - 1.14563i) q^{7} +(2.15711 + 2.08491i) q^{9} -4.72811i q^{11} +(3.54045 + 2.04408i) q^{13} +(-4.76900 - 1.92801i) q^{15} +(0.835278 - 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +(-3.08584 - 3.38786i) q^{21} -4.91090i q^{23} +3.82018 q^{25} +(2.11037 + 4.74830i) q^{27} +(0.238557 - 0.137731i) q^{29} +(1.38847 - 0.801636i) q^{31} +(3.06943 - 7.59235i) q^{33} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(4.35823 + 5.58078i) q^{39} +(3.55632 - 6.15972i) q^{41} +(-5.22930 - 9.05742i) q^{43} +(-6.40637 - 6.19194i) q^{45} +(5.49885 - 9.52430i) q^{47} +(4.37505 + 5.46433i) q^{49} +(2.28049 - 1.78091i) q^{51} +(-0.707381 - 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 - 1.18219i) q^{57} +(-1.37428 - 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(-2.75585 - 7.44347i) q^{63} +(-10.5147 - 6.07067i) q^{65} +(5.80513 + 10.0548i) q^{67} +(3.18809 - 7.88587i) q^{69} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(6.13440 + 2.48001i) q^{75} +(-5.41668 + 11.2759i) q^{77} +(-6.15163 + 10.6549i) q^{79} +(0.306275 + 8.99479i) q^{81} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(0.472485 - 0.0662987i) q^{87} +(-4.60872 - 7.98254i) q^{89} +(-6.10169 - 8.93089i) q^{91} +(2.75001 - 0.385879i) q^{93} +(-12.6332 + 7.29377i) q^{95} +(-7.00772 + 4.04591i) q^{97} +(9.85770 - 10.1991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * 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
$3$	1.60579	+	0.649187i	0.927102	+	0.374808i
$3$	1.60579	+	0.649187i	0.927102	+	0.374808i
$4$		0			0
$5$	−2.96988			−1.32817			−0.664085	−	0.747657i	$-0.731179\pi$
$5$	−2.96988			−1.32817			−0.664085	+	0.747657i	$0.731179\pi$
$6$		0			0
$7$	−2.38485	−	1.14563i	−0.901390	−	0.433009i
$7$	−2.38485	−	1.14563i	−0.901390	−	0.433009i
$8$		0			0
$9$	2.15711	+	2.08491i	0.719038	+	0.694971i
$10$		0			0
$11$		−	4.72811i		−	1.42558i	−0.701378	−	0.712790i	$-0.747431\pi$
$11$		−	4.72811i		−	1.42558i	0.701378	−	0.712790i	$-0.252569\pi$
$12$		0			0
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.902857	−	0.429942i	$-0.141466\pi$
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.0790880	+	0.996868i	$0.474799\pi$
$14$		0			0
$15$	−4.76900	−	1.92801i	−1.23135	−	0.497809i
$16$		0			0
$17$	0.835278	−	1.44674i	0.202585	−	0.350887i	−0.746776	−	0.665076i	$-0.768399\pi$
$17$	0.835278	−	1.44674i	0.202585	−	0.350887i	0.949360	+	0.314189i	$0.101733\pi$
$18$		0			0
$19$	4.25377	−	2.45592i	0.975882	−	0.563426i	0.0748577	−	0.997194i	$-0.476150\pi$
$19$	4.25377	−	2.45592i	0.975882	−	0.563426i	0.901024	+	0.433768i	$0.142816\pi$
$20$		0			0
$21$	−3.08584	−	3.38786i	−0.673385	−	0.739292i
$22$		0			0
$23$		−	4.91090i		−	1.02399i	−0.858987	−	0.511997i	$-0.828906\pi$
$23$		−	4.91090i		−	1.02399i	0.858987	−	0.511997i	$-0.171094\pi$
$24$		0			0
$25$	3.82018			0.764036
$26$		0			0
$27$	2.11037	+	4.74830i	0.406141	+	0.913811i
$28$		0			0
$29$	0.238557	−	0.137731i	0.0442989	−	0.0255760i	−0.477687	−	0.878530i	$-0.658525\pi$
$29$	0.238557	−	0.137731i	0.0442989	−	0.0255760i	0.521986	+	0.852954i	$0.325191\pi$
$30$		0			0
$31$	1.38847	−	0.801636i	0.249377	−	0.143978i	−0.370102	−	0.928991i	$-0.620677\pi$
$31$	1.38847	−	0.801636i	0.249377	−	0.143978i	0.619479	+	0.785013i	$0.287344\pi$
$32$		0			0
$33$	3.06943	−	7.59235i	0.534319	−	1.32166i
$34$		0			0
$35$	7.08273	+	3.40239i	1.19720	+	0.575109i
$36$		0			0
$37$	−1.69681	−	2.93896i	−0.278954	−	0.483162i	0.692171	−	0.721733i	$-0.256654\pi$
$37$	−1.69681	−	2.93896i	−0.278954	−	0.483162i	−0.971125	+	0.238571i	$0.923321\pi$
$38$		0			0
$39$	4.35823	+	5.58078i	0.697875	+	0.893639i
$40$		0			0
$41$	3.55632	−	6.15972i	0.555404	−	0.961987i	−0.442468	−	0.896784i	$-0.645897\pi$
$41$	3.55632	−	6.15972i	0.555404	−	0.961987i	0.997872	−	0.0652031i	$-0.0207695\pi$
$42$		0			0
$43$	−5.22930	−	9.05742i	−0.797461	−	1.38124i	−0.921265	−	0.388936i	$-0.872843\pi$
$43$	−5.22930	−	9.05742i	−0.797461	−	1.38124i	0.123804	−	0.992307i	$-0.460491\pi$
$44$		0			0
$45$	−6.40637	−	6.19194i	−0.955005	−	0.923040i
$46$		0			0
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	−0.116148	−	0.993232i	$-0.537055\pi$
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	0.918238	−	0.396029i	$-0.129612\pi$
$48$		0			0
$49$	4.37505	+	5.46433i	0.625007	+	0.780619i
$50$		0			0
$51$	2.28049	−	1.78091i	0.319332	−	0.249378i
$52$		0			0
$53$	−0.707381	−	0.408407i	−0.0971663	−	0.0560990i	0.450629	−	0.892711i	$-0.351200\pi$
$53$	−0.707381	−	0.408407i	−0.0971663	−	0.0560990i	−0.547796	+	0.836612i	$0.684533\pi$
$54$		0			0
$55$			14.0419i			1.89341i
$56$		0			0
$57$	8.42500	−	1.18219i	1.11592	−	0.156585i
$58$		0			0
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	0.762594	−	0.646878i	$-0.223926\pi$
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	−0.941509	+	0.336986i	$0.890592\pi$
$60$		0			0
$61$	−6.23807	−	3.60155i	−0.798703	−	0.461131i	0.0443147	−	0.999018i	$-0.485890\pi$
$61$	−6.23807	−	3.60155i	−0.798703	−	0.461131i	−0.843017	+	0.537886i	$0.819223\pi$
$62$		0			0
$63$	−2.75585	−	7.44347i	−0.347205	−	0.937789i
$64$		0			0
$65$	−10.5147	−	6.07067i	−1.30419	−	0.752974i
$66$		0			0
$67$	5.80513	+	10.0548i	0.709210	+	1.22839i	0.965151	+	0.261695i	$0.0842814\pi$
$67$	5.80513	+	10.0548i	0.709210	+	1.22839i	−0.255941	+	0.966692i	$0.582385\pi$
$68$		0			0
$69$	3.18809	−	7.88587i	0.383801	−	0.949347i
$70$		0			0
$71$			10.4406i			1.23907i	0.784968	+	0.619537i	$0.212680\pi$
$71$			10.4406i			1.23907i	−0.784968	+	0.619537i	$0.787320\pi$
$72$		0			0
$73$	13.6493	+	7.88042i	1.59753	+	0.922334i	0.991962	+	0.126539i	$0.0403870\pi$
$73$	13.6493	+	7.88042i	1.59753	+	0.922334i	0.605567	+	0.795794i	$0.292946\pi$
$74$		0			0
$75$	6.13440	+	2.48001i	0.708340	+	0.286367i
$76$		0			0
$77$	−5.41668	+	11.2759i	−0.617288	+	1.28500i
$78$		0			0
$79$	−6.15163	+	10.6549i	−0.692112	+	1.19877i	0.279032	+	0.960282i	$0.409986\pi$
$79$	−6.15163	+	10.6549i	−0.692112	+	1.19877i	−0.971145	+	0.238492i	$0.923347\pi$
$80$		0			0
$81$	0.306275	+	8.99479i	0.0340305	+	0.999421i
$82$		0			0
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	0.554515	−	0.832174i	$-0.312904\pi$
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	−0.997941	+	0.0641368i	$0.979571\pi$
$84$		0			0
$85$	−2.48067	+	4.29665i	−0.269067	+	0.466037i
$86$		0			0
$87$	0.472485	−	0.0662987i	0.0506557	−	0.00710797i
$88$		0			0
$89$	−4.60872	−	7.98254i	−0.488523	−	0.846147i	0.511390	−	0.859349i	$-0.329131\pi$
$89$	−4.60872	−	7.98254i	−0.488523	−	0.846147i	−0.999913	+	0.0132019i	$0.995798\pi$
$90$		0			0
$91$	−6.10169	−	8.93089i	−0.639631	−	0.936212i
$92$		0			0
$93$	2.75001	−	0.385879i	0.285163	−	0.0400138i
$94$		0			0
$95$	−12.6332	+	7.29377i	−1.29614	+	0.748325i
$96$		0			0
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	−0.811626	−	0.584177i	$-0.801417\pi$
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	0.100099	+	0.994977i	$0.468084\pi$
$98$		0			0
$99$	9.85770	−	10.1991i	0.990736	−	1.02505i
$100$		0			0
$101$	−7.30730			−0.727103			−0.363552	−	0.931574i	$-0.618436\pi$
$101$	−7.30730			−0.727103			−0.363552	+	0.931574i	$0.618436\pi$
$102$		0			0
$103$		−	7.02530i		−	0.692224i	−0.938193	−	0.346112i	$-0.887502\pi$
$103$		−	7.02530i		−	0.692224i	0.938193	−	0.346112i	$-0.112498\pi$
$104$		0			0
$105$	9.16457	+	10.0615i	0.894371	+	0.981905i
$106$		0			0
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.957257	−	0.289239i	$-0.906598\pi$
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.228140	+	0.973628i	$0.573265\pi$
$108$		0			0
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	−0.968939	−	0.247300i	$-0.920457\pi$
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	0.698638	+	0.715476i	$0.253790\pi$
$110$		0			0
$111$	−0.816783	−	5.82089i	−0.0775256	−	0.552495i
$112$		0			0
$113$	11.6411	+	6.72099i	1.09510	+	0.632258i	0.934930	−	0.354831i	$-0.115462\pi$
$113$	11.6411	+	6.72099i	1.09510	+	0.632258i	0.160172	+	0.987089i	$0.448795\pi$
$114$		0			0
$115$			14.5848i			1.36004i
$116$		0			0
$117$	3.37542	+	11.7908i	0.312058	+	1.09006i
$118$		0			0
$119$	−3.64945	+	2.49335i	−0.334545	+	0.228565i
$120$		0			0
$121$	−11.3550			−1.03228
$122$		0			0
$123$	9.70951	−	7.58250i	0.875477	−	0.683691i
$124$		0			0
$125$	3.50392			0.313400
$126$		0			0
$127$	12.7730			1.13342			0.566712	−	0.823916i	$-0.308215\pi$
$127$	12.7730			1.13342			0.566712	+	0.823916i	$0.308215\pi$
$128$		0			0
$129$	−2.51720	−	17.9391i	−0.221627	−	1.57945i
$130$		0			0
$131$	−13.4178			−1.17232			−0.586159	−	0.810196i	$-0.699361\pi$
$131$	−13.4178			−1.17232			−0.586159	+	0.810196i	$0.699361\pi$
$132$		0			0
$133$	−12.9582	+	0.983737i	−1.12362	+	0.0853008i
$134$		0			0
$135$	−6.26754	−	14.1019i	−0.539424	−	1.21370i
$136$		0			0
$137$			9.00030i			0.768948i	0.923136	+	0.384474i	$0.125617\pi$
$137$			9.00030i			0.768948i	−0.923136	+	0.384474i	$0.874383\pi$
$138$		0			0
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	0.564252	−	0.825602i	$-0.309164\pi$
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	−0.432866	+	0.901458i	$0.642498\pi$
$140$		0			0
$141$	15.0130	−	11.7242i	1.26433	−	0.987357i
$142$		0			0
$143$	9.66464	−	16.7397i	0.808198	−	1.39984i
$144$		0			0
$145$	−0.708485	+	0.409044i	−0.0588365	+	0.0339693i
$146$		0			0
$147$	3.47803	+	11.6148i	0.286863	+	0.957972i
$148$		0			0
$149$		−	12.9072i		−	1.05740i	−0.848810	−	0.528698i	$-0.822680\pi$
$149$		−	12.9072i		−	1.05740i	0.848810	−	0.528698i	$-0.177320\pi$
$150$		0			0
$151$	12.9673			1.05526			0.527631	−	0.849473i	$-0.323080\pi$
$151$	12.9673			1.05526			0.527631	+	0.849473i	$0.323080\pi$
$152$		0			0
$153$	4.81812	−	1.37931i	0.389522	−	0.111510i
$154$		0			0
$155$	−4.12360	+	2.38076i	−0.331216	+	0.191227i
$156$		0			0
$157$	14.8720	−	8.58638i	1.18692	−	0.685268i	0.229314	−	0.973353i	$-0.426352\pi$
$157$	14.8720	−	8.58638i	1.18692	−	0.685268i	0.957605	+	0.288085i	$0.0930185\pi$
$158$		0			0
$159$	−0.870773	−	1.11504i	−0.0690568	−	0.0884282i
$160$		0			0
$161$	−5.62609	+	11.7118i	−0.443398	+	0.923017i
$162$		0			0
$163$	−2.53107	−	4.38394i	−0.198249	−	0.343377i	0.749712	−	0.661764i	$-0.230192\pi$
$163$	−2.53107	−	4.38394i	−0.198249	−	0.343377i	−0.947961	+	0.318387i	$0.896859\pi$
$164$		0			0
$165$	−9.11583	+	22.5484i	−0.709666	+	1.75539i
$166$		0			0
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	−0.998293	−	0.0584072i	$-0.981398\pi$
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	0.549729	+	0.835343i	$0.314731\pi$
$168$		0			0
$169$	1.85653	+	3.21561i	0.142810	+	0.247354i
$170$		0			0
$171$	14.2962	+	3.57105i	1.09326	+	0.273085i
$172$		0			0
$173$	3.13346	−	5.42730i	0.238232	−	0.412630i	−0.721975	−	0.691919i	$-0.756765\pi$
$173$	3.13346	−	5.42730i	0.238232	−	0.412630i	0.960207	+	0.279289i	$0.0900987\pi$
$174$		0			0
$175$	−9.11057	−	4.37653i	−0.688694	−	0.330834i
$176$		0			0
$177$	−0.661528	−	4.71446i	−0.0497235	−	0.354360i
$178$		0			0
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.0598395	−	0.998208i	$-0.519059\pi$
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.894393	+	0.447281i	$0.852392\pi$
$180$		0			0
$181$			0.0833642i			0.00619641i	0.999995	+	0.00309821i	$0.000986191\pi$
$181$			0.0833642i			0.00619641i	−0.999995	+	0.00309821i	$0.999014\pi$
$182$		0			0
$183$	−7.67894	−	9.83300i	−0.567643	−	0.726876i
$184$		0			0
$185$	5.03932	+	8.72835i	0.370498	+	0.641721i
$186$		0			0
$187$	−6.84036	−	3.94929i	−0.500217	−	0.288800i
$188$		0			0
$189$	0.406887	−	13.7417i	0.0295967	−	0.999562i
$190$		0			0
$191$	−13.3672	−	7.71754i	−0.967214	−	0.558421i	−0.0688282	−	0.997629i	$-0.521926\pi$
$191$	−13.3672	−	7.71754i	−0.967214	−	0.558421i	−0.898386	+	0.439207i	$0.855259\pi$
$192$		0			0
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	−0.934339	−	0.356385i	$-0.884009\pi$
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	0.158532	−	0.987354i	$-0.449324\pi$
$194$		0			0
$195$	−12.9434	−	16.5742i	−0.926896	−	1.18691i
$196$		0			0
$197$		−	9.88306i		−	0.704139i	−0.935974	−	0.352069i	$-0.885478\pi$
$197$		−	9.88306i		−	0.704139i	0.935974	−	0.352069i	$-0.114522\pi$
$198$		0			0
$199$	9.14623	+	5.28058i	0.648359	+	0.374330i	0.787827	−	0.615896i	$-0.211206\pi$
$199$	9.14623	+	5.28058i	0.648359	+	0.374330i	−0.139468	+	0.990227i	$0.544539\pi$
$200$		0			0
$201$	2.79438	+	19.9145i	0.197100	+	1.40466i
$202$		0			0
$203$	−0.726712	+	0.0551692i	−0.0510052	+	0.00387212i
$204$		0			0
$205$	−10.5618	+	18.2936i	−0.737670	+	1.27768i
$206$		0			0
$207$	10.2388	−	10.5934i	0.711646	−	0.736290i
$208$		0			0
$209$	−11.6118	−	20.1123i	−0.803208	−	1.39120i
$210$		0			0
$211$	−6.08453	+	10.5387i	−0.418876	+	0.725514i	−0.995827	−	0.0912645i	$-0.970909\pi$
$211$	−6.08453	+	10.5387i	−0.418876	+	0.725514i	0.576951	+	0.816779i	$0.304242\pi$
$212$		0			0
$213$	−6.77791	+	16.7654i	−0.464415	+	1.14875i
$214$		0			0
$215$	15.5304	+	26.8994i	1.05916	+	1.83453i
$216$		0			0
$217$	−4.22969	+	0.321102i	−0.287130	+	0.0217978i
$218$		0			0
$219$	16.8020	+	21.5152i	1.13537	+	1.45386i
$220$		0			0
$221$	5.91452	−	3.41475i	0.397854	−	0.229701i
$222$		0			0
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	−0.475886	−	0.879507i	$-0.657873\pi$
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	0.523732	+	0.851883i	$0.324539\pi$
$224$		0			0
$225$	8.24056	+	7.96475i	0.549371	+	0.530983i
$226$		0			0
$227$	−0.333557			−0.0221390			−0.0110695	−	0.999939i	$-0.503524\pi$
$227$	−0.333557			−0.0221390			−0.0110695	+	0.999939i	$0.503524\pi$
$228$		0			0
$229$		−	14.4214i		−	0.952996i	−0.879176	−	0.476498i	$-0.841906\pi$
$229$		−	14.4214i		−	0.952996i	0.879176	−	0.476498i	$-0.158094\pi$
$230$		0			0
$231$	−16.0182	+	14.5902i	−1.05392	+	0.959964i
$232$		0			0
$233$	12.7953	−	7.38739i	0.838250	−	0.483964i	−0.0184192	−	0.999830i	$-0.505863\pi$
$233$	12.7953	−	7.38739i	0.838250	−	0.483964i	0.856669	+	0.515867i	$0.172530\pi$
$234$		0			0
$235$	−16.3309	+	28.2860i	−1.06531	+	1.84518i
$236$		0			0
$237$	−16.7953	+	13.1160i	−1.09097	+	0.851976i
$238$		0			0
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.998893	−	0.0470423i	$-0.0149795\pi$
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.458707	+	0.888588i	$0.348313\pi$
$240$		0			0
$241$			1.92021i			0.123692i	0.998086	+	0.0618458i	$0.0196987\pi$
$241$			1.92021i			0.123692i	−0.998086	+	0.0618458i	$0.980301\pi$
$242$		0			0
$243$	−5.34748	+	14.6426i	−0.343041	+	0.939320i
$244$		0			0
$245$	−12.9934	−	16.2284i	−0.830116	−	1.03680i
$246$		0			0
$247$	20.0804			1.27768
$248$		0			0
$249$	−1.94462	−	13.8585i	−0.123235	−	0.878249i
$250$		0			0
$251$	9.97663			0.629719			0.314860	−	0.949138i	$-0.398043\pi$
$251$	9.97663			0.629719			0.314860	+	0.949138i	$0.398043\pi$
$252$		0			0
$253$	−23.2193			−1.45978
$254$		0			0
$255$	−6.77277	+	5.28909i	−0.424127	+	0.331216i
$256$		0			0
$257$	15.0073			0.936129			0.468064	−	0.883694i	$-0.344952\pi$
$257$	15.0073			0.936129			0.468064	+	0.883694i	$0.344952\pi$
$258$		0			0
$259$	0.679670	+	8.95291i	0.0422327	+	0.556306i
$260$		0			0
$261$	0.801751	+	0.200269i	0.0496271	+	0.0123964i
$262$		0			0
$263$			7.05534i			0.435051i	0.976055	+	0.217525i	$0.0697985\pi$
$263$			7.05534i			0.435051i	−0.976055	+	0.217525i	$0.930202\pi$
$264$		0			0
$265$	2.10084	+	1.21292i	0.129053	+	0.0745090i
$266$		0			0
$267$	−2.21847	−	15.8102i	−0.135768	−	0.967568i
$268$		0			0
$269$	−14.8898	+	25.7898i	−0.907844	+	1.57243i	−0.0907911	+	0.995870i	$0.528940\pi$
$269$	−14.8898	+	25.7898i	−0.907844	+	1.57243i	−0.817053	+	0.576562i	$0.804394\pi$
$270$		0			0
$271$	2.41462	−	1.39408i	0.146677	−	0.0846843i	−0.424865	−	0.905257i	$-0.639679\pi$
$271$	2.41462	−	1.39408i	0.146677	−	0.0846843i	0.571543	+	0.820572i	$0.306345\pi$
$272$		0			0
$273$	−4.00021	−	18.3023i	−0.242104	−	1.10770i
$274$		0			0
$275$		−	18.0622i		−	1.08919i
$276$		0			0
$277$	13.5815			0.816032			0.408016	−	0.912975i	$-0.366221\pi$
$277$	13.5815			0.816032			0.408016	+	0.912975i	$0.366221\pi$
$278$		0			0
$279$	4.66644	+	1.16563i	0.279372	+	0.0697844i
$280$		0			0
$281$	−3.95777	+	2.28502i	−0.236101	+	0.136313i	−0.613383	−	0.789785i	$-0.710192\pi$
$281$	−3.95777	+	2.28502i	−0.236101	+	0.136313i	0.377283	+	0.926098i	$0.376859\pi$
$282$		0			0
$283$	−17.6685	+	10.2009i	−1.05029	+	0.606383i	−0.922729	−	0.385449i	$-0.874047\pi$
$283$	−17.6685	+	10.2009i	−1.05029	+	0.606383i	−0.127556	+	0.991831i	$0.540713\pi$
$284$		0			0
$285$	−25.0212	+	3.51096i	−1.48213	+	0.207971i
$286$		0			0
$287$	−15.5381	+	10.6158i	−0.917184	+	0.626631i
$288$		0			0
$289$	7.10462	+	12.3056i	0.417919	+	0.723857i
$290$		0			0
$291$	−13.8795	+	1.94756i	−0.813629	+	0.114168i
$292$		0			0
$293$	−6.41037	+	11.1031i	−0.374498	+	0.648649i	−0.990252	−	0.139289i	$-0.955518\pi$
$293$	−6.41037	+	11.1031i	−0.374498	+	0.648649i	0.615754	+	0.787939i	$0.288852\pi$
$294$		0			0
$295$	4.08144	+	7.06926i	0.237631	+	0.411589i
$296$		0			0
$297$	22.4505	−	9.97806i	1.30271	−	0.578986i
$298$		0			0
$299$	10.0383	−	17.3868i	0.580529	−	1.00551i
$300$		0			0
$301$	2.09464	+	27.5915i	0.120733	+	1.59035i
$302$		0			0
$303$	−11.7340	−	4.74380i	−0.674099	−	0.272524i
$304$		0			0
$305$	18.5263	+	10.6962i	1.06081	+	0.612461i
$306$		0			0
$307$		−	1.93411i		−	0.110386i	−0.998476	−	0.0551928i	$-0.982423\pi$
$307$		−	1.93411i		−	0.110386i	0.998476	−	0.0551928i	$-0.0175773\pi$
$308$		0			0
$309$	4.56073	−	11.2812i	0.259451	−	0.641762i
$310$		0			0
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	0.834889	−	0.550419i	$-0.185532\pi$
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	−0.894121	+	0.447825i	$0.852199\pi$
$312$		0			0
$313$	19.4066	+	11.2044i	1.09692	+	0.633309i	0.935411	−	0.353562i	$-0.115030\pi$
$313$	19.4066	+	11.2044i	1.09692	+	0.633309i	0.161512	+	0.986871i	$0.448363\pi$
$314$		0			0
$315$	8.18455	+	22.1062i	0.461147	+	1.24554i
$316$		0			0
$317$	−3.01788	−	1.74237i	−0.169501	−	0.0978614i	0.412850	−	0.910799i	$-0.364534\pi$
$317$	−3.01788	−	1.74237i	−0.169501	−	0.0978614i	−0.582350	+	0.812938i	$0.697867\pi$
$318$		0			0
$319$	−0.651207	−	1.12792i	−0.0364606	−	0.0631516i
$320$		0			0
$321$	−24.2858	+	3.40776i	−1.35550	+	0.190203i
$322$		0			0
$323$		−	8.20549i		−	0.456565i
$324$		0			0
$325$	13.5252	+	7.80876i	0.750241	+	0.433152i
$326$		0			0
$327$	−7.70473	+	6.01690i	−0.426073	+	0.332735i
$328$		0			0
$329$	−24.0253	+	16.4144i	−1.32456	+	0.904954i
$330$		0			0
$331$	−2.28857	+	3.96392i	−0.125791	+	0.217877i	−0.922042	−	0.387090i	$-0.873480\pi$
$331$	−2.28857	+	3.96392i	−0.125791	+	0.217877i	0.796251	+	0.604967i	$0.206814\pi$
$332$		0			0
$333$	2.46727	−	9.87737i	0.135205	−	0.541276i
$334$		0			0
$335$	−17.2405	−	29.8615i	−0.941951	−	1.63151i
$336$		0			0
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	0.117793	+	0.993038i	$0.462418\pi$
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	−0.918893	+	0.394508i	$0.870915\pi$
$338$		0			0
$339$	14.3300	+	18.3497i	0.778297	+	0.996621i
$340$		0			0
$341$	−3.79023	−	6.56486i	−0.205252	−	0.355507i
$342$		0			0
$343$	−4.17373	−	18.0438i	−0.225360	−	0.974276i
$344$		0			0
$345$	−9.46825	+	23.4201i	−0.509753	+	1.26089i
$346$		0			0
$347$	−17.0245	+	9.82911i	−0.913924	+	0.527654i	−0.881692	−	0.471826i	$-0.843595\pi$
$347$	−17.0245	+	9.82911i	−0.913924	+	0.527654i	−0.0322323	+	0.999480i	$0.510262\pi$
$348$		0			0
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	−0.255783	−	0.966734i	$-0.582333\pi$
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	0.709325	+	0.704882i	$0.249000\pi$
$350$		0			0
$351$	−2.23424	+	21.1249i	−0.119255	+	1.12756i
$352$		0			0
$353$	25.0645			1.33405			0.667023	−	0.745037i	$-0.267568\pi$
$353$	25.0645			1.33405			0.667023	+	0.745037i	$0.267568\pi$
$354$		0			0
$355$		−	31.0074i		−	1.64570i
$356$		0			0
$357$	−7.47890	+	1.63461i	−0.395825	+	0.0865130i
$358$		0			0
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	−0.698251	−	0.715853i	$-0.746038\pi$
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	0.270822	+	0.962629i	$0.412704\pi$
$360$		0			0
$361$	2.56305	−	4.43933i	0.134897	−	0.233649i
$362$		0			0
$363$	−18.2338	−	7.37154i	−0.957026	−	0.386906i
$364$		0			0
$365$	−40.5367	−	23.4039i	−2.12179	−	1.22502i
$366$		0			0
$367$		−	21.8850i		−	1.14239i	−0.820815	−	0.571194i	$-0.806480\pi$
$367$		−	21.8850i		−	1.14239i	0.820815	−	0.571194i	$-0.193520\pi$
$368$		0			0
$369$	20.5139	−	5.87261i	1.06791	−	0.305716i
$370$		0			0
$371$	1.21912	+	1.78439i	0.0632934	+	0.0926409i
$372$		0			0
$373$	4.61644			0.239030			0.119515	−	0.992832i	$-0.461866\pi$
$373$	4.61644			0.239030			0.119515	+	0.992832i	$0.461866\pi$
$374$		0			0
$375$	5.62655	+	2.27470i	0.290554	+	0.117465i
$376$		0			0
$377$	1.12613			0.0579988
$378$		0			0
$379$	6.22396			0.319703			0.159852	−	0.987141i	$-0.448898\pi$
$379$	6.22396			0.319703			0.159852	+	0.987141i	$0.448898\pi$
$380$		0			0
$381$	20.5108	+	8.29209i	1.05080	+	0.424817i
$382$		0			0
$383$	21.9977			1.12403			0.562015	−	0.827127i	$-0.310026\pi$
$383$	21.9977			1.12403			0.562015	+	0.827127i	$0.310026\pi$
$384$		0			0
$385$	16.0869	−	33.4879i	0.819864	−	1.70670i
$386$		0			0
$387$	7.60373	−	30.4405i	0.386519	−	1.54738i
$388$		0			0
$389$			9.82776i			0.498287i	0.968467	+	0.249144i	$0.0801491\pi$
$389$			9.82776i			0.498287i	−0.968467	+	0.249144i	$0.919851\pi$
$390$		0			0
$391$	−7.10481	−	4.10197i	−0.359306	−	0.207445i
$392$		0			0
$393$	−21.5462	−	8.71066i	−1.08686	−	0.439395i
$394$		0			0
$395$	18.2696	−	31.6439i	0.919243	−	1.59218i
$396$		0			0
$397$	4.55324	−	2.62881i	0.228520	−	0.131936i	−0.381369	−	0.924423i	$-0.624547\pi$
$397$	4.55324	−	2.62881i	0.228520	−	0.131936i	0.609889	+	0.792487i	$0.291214\pi$
$398$		0			0
$399$	−21.4468	−	6.83262i	−1.07368	−	0.342059i
$400$		0			0
$401$			17.0719i			0.852529i	0.904598	+	0.426265i	$0.140171\pi$
$401$			17.0719i			0.852529i	−0.904598	+	0.426265i	$0.859829\pi$
$402$		0			0
$403$	6.55444			0.326500
$404$		0			0
$405$	−0.909599	−	26.7134i	−0.0451983	−	1.32740i
$406$		0			0
$407$	−13.8957	+	8.02270i	−0.688786	+	0.397671i
$408$		0			0
$409$	16.9484	−	9.78516i	0.838044	−	0.483845i	−0.0185546	−	0.999828i	$-0.505906\pi$
$409$	16.9484	−	9.78516i	0.838044	−	0.483845i	0.856599	+	0.515983i	$0.172573\pi$
$410$		0			0
$411$	−5.84288	+	14.4526i	−0.288208	+	0.712893i
$412$		0			0
$413$	0.550478	+	7.25114i	0.0270873	+	0.356805i
$414$		0			0
$415$	11.9977	+	20.7807i	0.588946	+	1.02008i
$416$		0			0
$417$	1.90681	+	2.44170i	0.0933769	+	0.119571i
$418$		0			0
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	−0.496445	−	0.868068i	$-0.665361\pi$
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	0.999992	−	0.00410056i	$-0.00130525\pi$
$420$		0			0
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	0.882688	−	0.469959i	$-0.155731\pi$
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	−0.848341	+	0.529451i	$0.822398\pi$
$422$		0			0
$423$	31.7190	−	9.08035i	1.54223	−	0.441502i
$424$		0			0
$425$	3.19091	−	5.52682i	0.154782	−	0.268090i
$426$		0			0
$427$	10.7508	+	15.7357i	0.520268	+	0.761504i
$428$		0			0
$429$	26.3865	−	20.6062i	1.27395	−	0.994876i
$430$		0			0
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	0.753931	−	0.656953i	$-0.228155\pi$
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	−0.191973	+	0.981400i	$0.561488\pi$
$432$		0			0
$433$			12.9356i			0.621646i	0.950468	+	0.310823i	$0.100605\pi$
$433$			12.9356i			0.621646i	−0.950468	+	0.310823i	$0.899395\pi$
$434$		0			0
$435$	−1.40322	+	0.196899i	−0.0672794	+	0.00944059i
$436$		0			0
$437$	−12.0608	−	20.8899i	−0.576944	−	0.999297i
$438$		0			0
$439$	−8.75023	−	5.05195i	−0.417626	−	0.241116i	0.276435	−	0.961033i	$-0.410847\pi$
$439$	−8.75023	−	5.05195i	−0.417626	−	0.241116i	−0.694061	+	0.719916i	$0.744180\pi$
$440$		0			0
$441$	−1.95519	+	20.9088i	−0.0931041	+	0.995656i
$442$		0			0
$443$	25.1220	+	14.5042i	1.19358	+	0.689115i	0.959117	−	0.283009i	$-0.0913326\pi$
$443$	25.1220	+	14.5042i	1.19358	+	0.689115i	0.234466	+	0.972124i	$0.424666\pi$
$444$		0			0
$445$	13.6873	+	23.7072i	0.648842	+	1.12383i
$446$		0			0
$447$	8.37916	−	20.7262i	0.396321	−	0.980314i
$448$		0			0
$449$		−	7.94881i		−	0.375127i	−0.982252	−	0.187564i	$-0.939941\pi$
$449$		−	7.94881i		−	0.375127i	0.982252	−	0.187564i	$-0.0600591\pi$
$450$		0			0
$451$	−29.1239	−	16.8147i	−1.37139	−	0.791772i
$452$		0			0
$453$	20.8227	+	8.41819i	0.978337	+	0.395521i
$454$		0			0
$455$	18.1213	+	26.5237i	0.849539	+	1.24345i
$456$		0			0
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	−0.655275	−	0.755391i	$-0.727447\pi$
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	0.981825	+	0.189789i	$0.0607805\pi$
$458$		0			0
$459$	8.63231	+	0.912985i	0.402922	+	0.0426145i
$460$		0			0
$461$	16.4030	+	28.4108i	0.763964	+	1.32322i	0.940793	+	0.338983i	$0.110083\pi$
$461$	16.4030	+	28.4108i	0.763964	+	1.32322i	−0.176829	+	0.984242i	$0.556584\pi$
$462$		0			0
$463$	13.8812	−	24.0429i	0.645112	−	1.11737i	−0.339163	−	0.940727i	$-0.610144\pi$
$463$	13.8812	−	24.0429i	0.645112	−	1.11737i	0.984276	−	0.176640i	$-0.0565227\pi$
$464$		0			0
$465$	−8.16719	+	1.14601i	−0.378744	+	0.0531451i
$466$		0			0
$467$	−11.4311	−	19.7992i	−0.528966	−	0.916196i	−0.999429	−	0.0337767i	$-0.989247\pi$
$467$	−11.4311	−	19.7992i	−0.528966	−	0.916196i	0.470463	−	0.882420i	$-0.344087\pi$
$468$		0			0
$469$	−2.32529	−	30.6297i	−0.107372	−	1.41435i
$470$		0			0
$471$	29.4555	−	4.13318i	1.35724	−	0.190447i
$472$		0			0
$473$	−42.8245	+	24.7247i	−1.96907	+	1.13684i
$474$		0			0
$475$	16.2502	−	9.38204i	0.745609	−	0.430478i
$476$		0			0
$477$	−0.674409	−	2.35581i	−0.0308791	−	0.107865i
$478$		0			0
$479$	−2.42425			−0.110767			−0.0553834	−	0.998465i	$-0.517638\pi$
$479$	−2.42425			−0.110767			−0.0553834	+	0.998465i	$0.517638\pi$
$480$		0			0
$481$		−	13.8737i		−	0.632584i
$482$		0			0
$483$	−16.6374	+	15.1543i	−0.757030	+	0.689542i
$484$		0			0
$485$	20.8121	−	12.0159i	0.945028	−	0.545612i
$486$		0			0
$487$	−5.19651	+	9.00061i	−0.235476	+	0.407857i	−0.959411	−	0.282012i	$-0.908998\pi$
$487$	−5.19651	+	9.00061i	−0.235476	+	0.407857i	0.723935	+	0.689868i	$0.242332\pi$
$488$		0			0
$489$	−1.21837	−	8.68282i	−0.0550964	−	0.392651i
$490$		0			0
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	0.564658	−	0.825325i	$-0.309008\pi$
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	−0.432423	+	0.901671i	$0.642341\pi$
$492$		0			0
$493$		−	0.460174i		−	0.0207252i
$494$		0			0
$495$	−29.2762	+	30.2900i	−1.31587	+	1.36143i
$496$		0			0
$497$	11.9611	−	24.8993i	0.536530	−	1.11689i
$498$		0			0
$499$	−39.5603			−1.77096			−0.885481	−	0.464676i	$-0.846171\pi$
$499$	−39.5603			−1.77096			−0.885481	+	0.464676i	$0.846171\pi$
$500$		0			0
$501$	−15.8263	+	12.3593i	−0.707067	+	0.552174i
$502$		0			0
$503$	14.5476			0.648645			0.324323	−	0.945947i	$-0.394864\pi$
$503$	14.5476			0.648645			0.324323	+	0.945947i	$0.394864\pi$
$504$		0			0
$505$	21.7018			0.965717
$506$		0			0
$507$	0.893668	+	6.36882i	0.0396892	+	0.282849i
$508$		0			0
$509$	20.3916			0.903841			0.451921	−	0.892058i	$-0.350739\pi$
$509$	20.3916			0.903841			0.451921	+	0.892058i	$0.350739\pi$
$510$		0			0
$511$	−23.5235	−	34.4307i	−1.04062	−	1.52313i
$512$		0			0
$513$	20.6385	+	15.0153i	0.911210	+	0.662941i
$514$		0			0
$515$			20.8643i			0.919391i
$516$		0			0
$517$	−45.0319	−	25.9992i	−1.98050	−	1.14344i
$518$		0			0
$519$	8.55500	−	6.68091i	0.375523	−	0.293259i
$520$		0			0
$521$	7.75122	−	13.4255i	0.339587	−	0.588182i	−0.644768	−	0.764379i	$-0.723046\pi$
$521$	7.75122	−	13.4255i	0.339587	−	0.588182i	0.984355	+	0.176196i	$0.0563793\pi$
$522$		0			0
$523$	−9.35989	+	5.40394i	−0.409280	+	0.236298i	−0.690480	−	0.723351i	$-0.742601\pi$
$523$	−9.35989	+	5.40394i	−0.409280	+	0.236298i	0.281201	+	0.959649i	$0.409267\pi$
$524$		0			0
$525$	−11.7885	−	12.9422i	−0.514491	−	0.564846i
$526$		0			0
$527$		−	2.67836i		−	0.116671i
$528$		0			0
$529$	−1.11695			−0.0485631
$530$		0			0
$531$	1.99829	−	7.99987i	0.0867183	−	0.347165i
$532$		0			0
$533$	25.1819	−	14.5388i	1.09075	−	0.629745i
$534$		0			0
$535$	36.4162	−	21.0249i	1.57441	−	0.908986i
$536$		0			0
$537$	−15.7156	−	20.1241i	−0.678180	−	0.868419i
$538$		0			0
$539$	25.8360	−	20.6857i	1.11283	−	0.890997i
$540$		0			0
$541$	−8.79357	−	15.2309i	−0.378065	−	0.654828i	0.612716	−	0.790303i	$-0.290077\pi$
$541$	−8.79357	−	15.2309i	−0.378065	−	0.654828i	−0.990781	+	0.135476i	$0.956744\pi$
$542$		0			0
$543$	−0.0541189	+	0.133865i	−0.00232247	+	0.00574471i
$544$		0			0
$545$	8.38108	−	14.5165i	0.359006	−	0.621817i
$546$		0			0
$547$	5.72451	+	9.91513i	0.244762	+	0.423940i	0.962065	−	0.272821i	$-0.0879568\pi$
$547$	5.72451	+	9.91513i	0.244762	+	0.423940i	−0.717303	+	0.696762i	$0.754623\pi$
$548$		0			0
$549$	−5.94730	−	20.7748i	−0.253824	−	0.886646i
$550$		0			0
$551$	0.676511	−	1.17175i	0.0288203	−	0.0499183i
$552$		0			0
$553$	26.8774	−	18.3629i	1.14294	−	0.780871i
$554$		0			0
$555$	2.42575	+	17.2873i	0.102967	+	0.733807i
$556$		0			0
$557$	32.9159	+	19.0040i	1.39469	+	0.805226i	0.993830	−	0.110912i	$-0.0353771\pi$
$557$	32.9159	+	19.0040i	1.39469	+	0.805226i	0.400863	+	0.916138i	$0.368710\pi$
$558$		0			0
$559$		−	42.7565i		−	1.80841i
$560$		0			0
$561$	−8.42035	−	10.7824i	−0.355508	−	0.455233i
$562$		0			0
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	0.990242	−	0.139360i	$-0.0445044\pi$
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	−0.615810	+	0.787895i	$0.711171\pi$
$564$		0			0
$565$	−34.5727	−	19.9605i	−1.45448	−	0.839746i
$566$		0			0
$567$	9.57431	−	21.8021i	0.402083	−	0.915603i
$568$		0			0
$569$	−33.7404	−	19.4801i	−1.41447	−	0.816646i	−0.418667	−	0.908140i	$-0.637503\pi$
$569$	−33.7404	−	19.4801i	−1.41447	−	0.816646i	−0.995806	+	0.0914936i	$0.970836\pi$
$570$		0			0
$571$	8.45245	+	14.6401i	0.353724	+	0.612668i	0.986899	−	0.161341i	$-0.0515818\pi$
$571$	8.45245	+	14.6401i	0.353724	+	0.612668i	−0.633175	+	0.774009i	$0.718248\pi$
$572$		0			0
$573$	−16.4547	−	21.0705i	−0.687406	−	0.880233i
$574$		0			0
$575$		−	18.7605i		−	0.782368i
$576$		0			0
$577$	−40.9329	−	23.6326i	−1.70406	−	0.983840i	−0.941555	−	0.336858i	$-0.890636\pi$
$577$	−40.9329	−	23.6326i	−1.70406	−	0.983840i	−0.762506	−	0.646982i	$-0.776031\pi$
$578$		0			0
$579$	−5.18808	−	36.9734i	−0.215609	−	1.53656i
$580$		0			0
$581$	1.61818	+	21.3153i	0.0671333	+	0.884308i
$582$		0			0
$583$	−1.93099	+	3.34458i	−0.0799736	+	0.138518i
$584$		0			0
$585$	−10.0246	−	35.0174i	−0.414466	−	1.44779i
$586$		0			0
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	0.999742	−	0.0227138i	$-0.00723065\pi$
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	−0.519542	+	0.854445i	$0.673897\pi$
$588$		0			0
$589$	3.93750	−	6.81995i	0.162242	−	0.281011i
$590$		0			0
$591$	6.41595	−	15.8701i	0.263917	−	0.652809i
$592$		0			0
$593$	18.5962	+	32.2095i	0.763654	+	1.32269i	0.940955	+	0.338530i	$0.109930\pi$
$593$	18.5962	+	32.2095i	0.763654	+	1.32269i	−0.177302	+	0.984157i	$0.556737\pi$
$594$		0			0
$595$	10.8384	−	7.40494i	0.444332	−	0.303573i
$596$		0			0
$597$	11.2588	+	14.4171i	0.460793	+	0.590053i
$598$		0			0
$599$	−27.9591	+	16.1422i	−1.14238	+	0.659552i	−0.947018	−	0.321180i	$-0.895921\pi$
$599$	−27.9591	+	16.1422i	−1.14238	+	0.659552i	−0.195359	+	0.980732i	$0.562587\pi$
$600$		0			0
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	−0.167885	−	0.985807i	$-0.553694\pi$
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	0.769791	+	0.638296i	$0.220360\pi$
$602$		0			0
$603$	−8.44102	+	33.7925i	−0.343745	+	1.37614i
$604$		0			0
$605$	33.7231			1.37104
$606$		0			0
$607$			9.75021i			0.395749i	0.980227	+	0.197874i	$0.0634038\pi$
$607$			9.75021i			0.395749i	−0.980227	+	0.197874i	$0.936596\pi$
$608$		0			0
$609$	−1.20276	−	0.383182i	−0.0487383	−	0.0155273i
$610$		0			0
$611$	38.9369	−	22.4802i	1.57522	−	0.909452i
$612$		0			0
$613$	−6.86332	+	11.8876i	−0.277207	+	0.480136i	−0.970690	−	0.240337i	$-0.922742\pi$
$613$	−6.86332	+	11.8876i	−0.277207	+	0.480136i	0.693483	+	0.720473i	$0.256075\pi$
$614$		0			0
$615$	−28.8361	+	22.5191i	−1.16278	+	0.908058i
$616$		0			0
$617$	−2.84301	−	1.64141i	−0.114455	−	0.0660807i	0.441680	−	0.897173i	$-0.354383\pi$
$617$	−2.84301	−	1.64141i	−0.114455	−	0.0660807i	−0.556135	+	0.831092i	$0.687716\pi$
$618$		0			0
$619$			17.3098i			0.695740i	0.937543	+	0.347870i	$0.113095\pi$
$619$			17.3098i			0.695740i	−0.937543	+	0.347870i	$0.886905\pi$
$620$		0			0
$621$	23.3184	−	10.3638i	0.935736	−	0.415886i
$622$		0			0
$623$	1.84606	+	24.3171i	0.0739608	+	0.974243i
$624$		0			0
$625$	−29.5071			−1.18028
$626$		0			0
$627$	−5.58952	−	39.8344i	−0.223224	−	1.59083i
$628$		0			0
$629$	−5.66923			−0.226047
$630$		0			0
$631$	6.27821			0.249932			0.124966	−	0.992161i	$-0.460118\pi$
$631$	6.27821			0.249932			0.124966	+	0.992161i	$0.460118\pi$
$632$		0			0
$633$	−16.6120	+	12.9729i	−0.660270	+	0.515628i
$634$		0			0
$635$	−37.9344			−1.50538
$636$		0			0
$637$	4.32011	+	28.2892i	0.171169	+	1.12086i
$638$		0			0
$639$	−21.7678	+	22.5216i	−0.861120	+	0.890941i
$640$		0			0
$641$			20.7601i			0.819976i	0.912091	+	0.409988i	$0.134467\pi$
$641$			20.7601i			0.819976i	−0.912091	+	0.409988i	$0.865533\pi$
$642$		0			0
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	0.119554	−	0.992828i	$-0.461854\pi$
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	−0.800037	+	0.599950i	$0.795187\pi$
$644$		0			0
$645$	7.47577	+	53.2769i	0.294358	+	2.09778i
$646$		0			0
$647$	−14.7670	+	25.5772i	−0.580551	+	1.00554i	0.414863	+	0.909884i	$0.363830\pi$
$647$	−14.7670	+	25.5772i	−0.580551	+	1.00554i	−0.995414	+	0.0956605i	$0.969504\pi$
$648$		0			0
$649$	−11.2544	+	6.49774i	−0.441775	+	0.255059i
$650$		0			0
$651$	−7.00044	−	2.23024i	−0.274369	−	0.0874099i
$652$		0			0
$653$			15.9250i			0.623193i	0.950215	+	0.311596i	$0.100864\pi$
$653$			15.9250i			0.623193i	−0.950215	+	0.311596i	$0.899136\pi$
$654$		0			0
$655$	39.8493			1.55704
$656$		0			0
$657$	13.0131	+	45.4565i	0.507688	+	1.77343i
$658$		0			0
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	−0.553597	−	0.832785i	$-0.686745\pi$
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	0.444414	+	0.895821i	$0.353412\pi$
$660$		0			0
$661$	7.71194	−	4.45249i	0.299960	−	0.173182i	−0.342465	−	0.939531i	$-0.611262\pi$
$661$	7.71194	−	4.45249i	0.299960	−	0.173182i	0.642425	+	0.766349i	$0.277928\pi$
$662$		0			0
$663$	11.7143	−	1.64374i	0.454945	−	0.0638375i
$664$		0			0
$665$	38.4843	−	2.92158i	1.49236	−	0.113294i
$666$		0			0
$667$	−0.676383	−	1.17153i	−0.0261896	−	0.0453618i
$668$		0			0
$669$	1.41511	−	0.198567i	0.0547112	−	0.00767703i
$670$		0			0
$671$	−17.0285	+	29.4943i	−0.657379	+	1.13861i
$672$		0			0
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	−0.999933	−	0.0116101i	$-0.996304\pi$
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	0.489912	−	0.871772i	$-0.337029\pi$
$674$		0			0
$675$	8.06199	+	18.1394i	0.310306	+	0.698184i
$676$		0			0
$677$	4.46424	−	7.73229i	0.171575	−	0.297176i	−0.767396	−	0.641174i	$-0.778448\pi$
$677$	4.46424	−	7.73229i	0.171575	−	0.297176i	0.938971	+	0.343997i	$0.111781\pi$
$678$		0			0
$679$	21.3475	−	1.62062i	0.819243	−	0.0621938i
$680$		0			0
$681$	−0.535622	−	0.216541i	−0.0205251	−	0.00829786i
$682$		0			0
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.972035	−	0.234834i	$-0.0754547\pi$
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.282645	+	0.959225i	$0.408788\pi$
$684$		0			0
$685$		−	26.7298i		−	1.02129i
$686$		0			0
$687$	9.36221	−	23.1578i	0.357191	−	0.883525i
$688$		0			0
$689$	−1.66963	−	2.89189i	−0.0636080	−	0.110172i
$690$		0			0
$691$	4.94211	+	2.85333i	0.188007	+	0.108546i	0.591049	−	0.806636i	$-0.298714\pi$
$691$	4.94211	+	2.85333i	0.188007	+	0.108546i	−0.403042	+	0.915181i	$0.632047\pi$
$692$		0			0
$693$	−35.1936	+	13.0300i	−1.33689	+	0.494968i
$694$		0			0
$695$	−4.60039	−	2.65604i	−0.174503	−	0.100749i
$696$		0			0
$697$	−5.94103	−	10.2902i	−0.225032	−	0.389768i
$698$		0			0
$699$	25.3424	−	3.55602i	0.958537	−	0.134501i
$700$		0			0
$701$			8.19949i			0.309690i	0.987939	+	0.154845i	$0.0494879\pi$
$701$			8.19949i			0.309690i	−0.987939	+	0.154845i	$0.950512\pi$
$702$		0			0
$703$	−14.4357	−	8.33444i	−0.544452	−	0.314339i
$704$		0			0
$705$	−44.5869	+	34.8195i	−1.67924	+	1.31138i
$706$		0			0
$707$	17.4268	+	8.37148i	0.655403	+	0.314842i
$708$		0			0
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	−0.990830	−	0.135115i	$-0.956860\pi$
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	0.612428	+	0.790527i	$0.290193\pi$
$710$		0			0
$711$	−35.4844	+	10.1583i	−1.33077	+	0.380965i
$712$		0			0
$713$	−3.93676	−	6.81866i	−0.147433	−	0.255361i
$714$		0			0
$715$	−28.7028	+	49.7147i	−1.07342	+	1.85923i
$716$		0			0
$717$	27.7388	+	35.5200i	1.03593	+	1.32652i
$718$		0			0
$719$	25.5996	+	44.3397i	0.954702	+	1.65359i	0.735048	+	0.678015i	$0.237159\pi$
$719$	25.5996	+	44.3397i	0.954702	+	1.65359i	0.219654	+	0.975578i	$0.429507\pi$
$720$		0			0
$721$	−8.04842	+	16.7543i	−0.299739	+	0.623963i
$722$		0			0
$723$	−1.24657	+	3.08345i	−0.0463606	+	0.114675i
$724$		0			0
$725$	0.911330	−	0.526157i	0.0338460	−	0.0195410i
$726$		0			0
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	−0.222098	−	0.975024i	$-0.571290\pi$
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	0.733347	+	0.679854i	$0.237957\pi$
$728$		0			0
$729$	−18.0927	+	20.0413i	−0.670099	+	0.742271i
$730$		0			0
$731$	−17.4717			−0.646213
$732$		0			0
$733$		−	4.24025i		−	0.156617i	−0.996929	−	0.0783086i	$-0.975048\pi$
$733$		−	4.24025i		−	0.156617i	0.996929	−	0.0783086i	$-0.0249519\pi$
$734$		0			0
$735$	−10.3293	−	34.4945i	−0.381003	−	1.27235i
$736$		0			0
$737$	47.5401	−	27.4473i	1.75116	−	1.01103i
$738$		0			0
$739$	14.1835	−	24.5665i	0.521747	−	0.903693i	−0.477933	−	0.878397i	$-0.658614\pi$
$739$	14.1835	−	24.5665i	0.521747	−	0.903693i	0.999680	−	0.0252966i	$-0.00805300\pi$
$740$		0			0
$741$	32.2448	+	13.0359i	1.18454	+	0.478886i
$742$		0			0
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	0.0415945	−	0.999135i	$-0.486756\pi$
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	−0.844479	+	0.535589i	$0.820090\pi$
$744$		0			0
$745$			38.3327i			1.40440i
$746$		0			0
$747$	5.87413	−	23.5163i	0.214923	−	0.860416i
$748$		0			0
$749$	37.3531	−	2.83570i	1.36485	−	0.103614i
$750$		0			0
$751$	−47.5460			−1.73498			−0.867490	−	0.497455i	$-0.834268\pi$
$751$	−47.5460			−1.73498			−0.867490	+	0.497455i	$0.834268\pi$
$752$		0			0
$753$	16.0204	+	6.47670i	0.583814	+	0.236024i
$754$		0			0
$755$	−38.5113			−1.40157
$756$		0			0
$757$	37.3922			1.35904			0.679521	−	0.733656i	$-0.262188\pi$
$757$	37.3922			1.35904			0.679521	+	0.733656i	$0.262188\pi$
$758$		0			0
$759$	−37.2853	−	15.0737i	−1.35337	−	0.547139i
$760$		0			0
$761$	−8.24283			−0.298802			−0.149401	−	0.988777i	$-0.547735\pi$
$761$	−8.24283			−0.298802			−0.149401	+	0.988777i	$0.547735\pi$
$762$		0			0
$763$	12.3299	−	8.42390i	0.446371	−	0.304966i
$764$		0			0
$765$	−14.3092	+	4.09638i	−0.517352	+	0.148105i
$766$		0			0
$767$		−	11.2365i		−	0.405728i
$768$		0			0
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	0.818088	−	0.575094i	$-0.195034\pi$
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	−0.0890020	+	0.996031i	$0.528368\pi$
$770$		0			0
$771$	24.0985	+	9.74253i	0.867887	+	0.350869i
$772$		0			0
$773$	−17.2201	+	29.8261i	−0.619364	+	1.07277i	0.370238	+	0.928937i	$0.379276\pi$
$773$	−17.2201	+	29.8261i	−0.619364	+	1.07277i	−0.989602	+	0.143833i	$0.954057\pi$
$774$		0			0
$775$	5.30422	−	3.06240i	0.190533	−	0.110004i
$776$		0			0
$777$	−4.72070	+	14.8177i	−0.169354	+	0.531582i
$778$		0			0
$779$		−	34.9361i		−	1.25171i
$780$		0			0
$781$	49.3644			1.76640
$782$		0			0
$783$	1.15743	+	0.842076i	0.0413632	+	0.0300933i
$784$		0			0
$785$	−44.1682	+	25.5005i	−1.57643	+	0.910152i
$786$		0			0
$787$	7.19975	−	4.15678i	0.256643	−	0.148173i	−0.366159	−	0.930552i	$-0.619327\pi$
$787$	7.19975	−	4.15678i	0.256643	−	0.148173i	0.622802	+	0.782379i	$0.285994\pi$
$788$		0			0
$789$	−4.58023	+	11.3294i	−0.163061	+	0.403337i
$790$		0			0
$791$	−20.0625	−	29.3650i	−0.713341	−	1.04410i
$792$		0			0
$793$	−14.7237	−	25.5022i	−0.522854	−	0.905610i
$794$		0			0
$795$	2.58609	+	3.31153i	0.0917191	+	0.117448i
$796$		0			0
$797$	0.426036	−	0.737916i	0.0150910	−	0.0261383i	−0.858381	−	0.513012i	$-0.828530\pi$
$797$	0.426036	−	0.737916i	0.0150910	−	0.0261383i	0.873472	+	0.486874i	$0.161863\pi$
$798$		0			0
$799$	−9.18614	−	15.9109i	−0.324982	−	0.562886i
$800$		0			0
$801$	6.70136	−	26.8280i	0.236781	−	0.947921i
$802$		0			0
$803$	37.2595	−	64.5354i	1.31486	−	2.27740i
$804$		0			0
$805$	16.7088	−	34.7826i	0.588908	−	1.22592i
$806$		0			0
$807$	−40.6522	+	31.7467i	−1.43102	+	1.11754i
$808$		0			0
$809$	−31.5580	−	18.2200i	−1.10952	−	0.640581i	−0.170814	−	0.985303i	$-0.554640\pi$
$809$	−31.5580	−	18.2200i	−1.10952	−	0.640581i	−0.938705	+	0.344722i	$0.887973\pi$
$810$		0			0
$811$			1.08986i			0.0382702i	0.999817	+	0.0191351i	$0.00609126\pi$
$811$			1.08986i			0.0382702i	−0.999817	+	0.0191351i	$0.993909\pi$
$812$		0			0
$813$	4.78238	−	0.671060i	0.167725	−	0.0235351i
$814$		0			0
$815$	7.51697	+	13.0198i	0.263308	+	0.456063i
$816$		0			0
$817$	−44.4885	−	25.6855i	−1.55646	−	0.898620i
$818$		0			0
$819$	5.45810	−	31.9864i	0.190721	−	1.11770i
$820$		0			0
$821$	−20.9748	−	12.1098i	−0.732025	−	0.422635i	0.0871374	−	0.996196i	$-0.472228\pi$
$821$	−20.9748	−	12.1098i	−0.732025	−	0.422635i	−0.819163	+	0.573561i	$0.805561\pi$
$822$		0			0
$823$	2.85592	+	4.94660i	0.0995512	+	0.172428i	0.911499	−	0.411302i	$-0.134926\pi$
$823$	2.85592	+	4.94660i	0.0995512	+	0.172428i	−0.811948	+	0.583730i	$0.801593\pi$
$824$		0			0
$825$	11.7258	−	29.0041i	0.408239	−	1.00979i
$826$		0			0
$827$		−	36.4579i		−	1.26777i	−0.773429	−	0.633883i	$-0.781460\pi$
$827$		−	36.4579i		−	1.26777i	0.773429	−	0.633883i	$-0.218540\pi$
$828$		0			0
$829$	−0.498269	−	0.287676i	−0.0173056	−	0.00999140i	0.491322	−	0.870978i	$-0.336514\pi$
$829$	−0.498269	−	0.287676i	−0.0173056	−	0.00999140i	−0.508628	+	0.860986i	$0.669847\pi$
$830$		0			0
$831$	21.8090	+	8.81692i	0.756545	+	0.305856i
$832$		0			0
$833$	11.5599	−	1.76534i	0.400526	−	0.0611653i
$834$		0			0
$835$	17.2156	−	29.8183i	0.595770	−	1.03190i
$836$		0			0
$837$	6.73660	+	4.90114i	0.232851	+	0.169408i
$838$		0			0
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	0.900925	+	0.433974i	$0.142889\pi$
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	−0.0746300	+	0.997211i	$0.523778\pi$
$840$		0			0
$841$	−14.4621	+	25.0490i	−0.498692	+	0.863759i
$842$		0			0
$843$	−7.83874	+	1.09993i	−0.269981	+	0.0378835i
$844$		0			0
$845$	−5.51368	−	9.54997i	−0.189676	−	0.328529i
$846$		0			0
$847$	27.0801	+	13.0087i	0.930483	+	0.446985i
$848$		0			0
$849$	−34.9943	+	4.91036i	−1.20100	+	0.168523i
$850$		0			0
$851$	−14.4329	+	8.33286i	−0.494755	+	0.285647i
$852$		0			0
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.394945	−	0.918705i	$-0.370764\pi$
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.993094	+	0.117320i	$0.0374303\pi$
$854$		0			0
$855$	−42.4581	−	10.6056i	−1.45204	−	0.362704i
$856$		0			0
$857$	9.56441			0.326714			0.163357	−	0.986567i	$-0.447768\pi$
$857$	9.56441			0.326714			0.163357	+	0.986567i	$0.447768\pi$
$858$		0			0
$859$		−	5.40759i		−	0.184505i	−0.995736	−	0.0922523i	$-0.970593\pi$
$859$		−	5.40759i		−	0.184505i	0.995736	−	0.0922523i	$-0.0294066\pi$
$860$		0			0
$861$	−31.8425	+	6.95961i	−1.08519	+	0.237183i
$862$		0			0
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.962716	−	0.270514i	$-0.912806\pi$
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.247086	+	0.968994i	$0.579473\pi$
$864$		0			0
$865$	−9.30598	+	16.1184i	−0.316413	+	0.548043i
$866$		0			0
$867$	3.41991	+	24.3724i	0.116146	+	0.827729i
$868$		0			0
$869$	50.3777	+	29.0856i	1.70895	+	0.986661i
$870$		0			0
$871$			47.4646i			1.60828i
$872$		0			0
$873$	−23.5518	−	5.88301i	−0.797109	−	0.199110i
$874$		0			0
$875$	−8.35633	−	4.01421i	−0.282496	−	0.135705i
$876$		0			0
$877$	−14.6502			−0.494701			−0.247351	−	0.968926i	$-0.579560\pi$
$877$	−14.6502			−0.494701			−0.247351	+	0.968926i	$0.579560\pi$
$878$		0			0
$879$	−17.5017	+	13.6677i	−0.590317	+	0.460999i
$880$		0			0
$881$	−44.8295			−1.51034			−0.755172	−	0.655527i	$-0.772447\pi$
$881$	−44.8295			−1.51034			−0.755172	+	0.655527i	$0.772447\pi$
$882$		0			0
$883$	−33.8527			−1.13923			−0.569617	−	0.821910i	$-0.692909\pi$
$883$	−33.8527			−1.13923			−0.569617	+	0.821910i	$0.692909\pi$
$884$		0			0
$885$	1.96466	+	14.0014i	0.0660413	+	0.470651i
$886$		0			0
$887$	26.6844			0.895973			0.447987	−	0.894040i	$-0.352141\pi$
$887$	26.6844			0.895973			0.447987	+	0.894040i	$0.352141\pi$
$888$		0			0
$889$	−30.4618	−	14.6332i	−1.02166	−	0.490783i
$890$		0			0
$891$	42.5284	−	1.44810i	1.42475	−	0.0485132i
$892$		0			0
$893$		−	54.0189i		−	1.80767i
$894$		0			0
$895$	37.9157	+	21.8907i	1.26738	+	0.731724i
$896$		0			0
$897$	27.4066	−	21.4028i	0.915081	−	0.714619i
$898$		0			0
$899$	0.220820	−	0.382472i	0.00736476	−	0.0127561i
$900$		0			0
$901$	−1.18172	+	0.682266i	−0.0393688	+	0.0227296i
$902$		0			0
$903$	−14.5485	+	45.6659i	−0.484143	+	1.51967i
$904$		0			0
$905$		−	0.247582i		−	0.00822989i
$906$		0			0
$907$	15.9442			0.529419			0.264710	−	0.964328i	$-0.414724\pi$
$907$	15.9442			0.529419			0.264710	+	0.964328i	$0.414724\pi$
$908$		0			0
$909$	−15.7627	−	15.2351i	−0.522815	−	0.505316i
$910$		0			0
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.989050	−	0.147584i	$-0.952850\pi$
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.366713	+	0.930334i	$0.619517\pi$
$912$		0			0
$913$	−33.0833	+	19.1007i	−1.09490	+	0.632140i
$914$		0			0
$915$	22.8055	+	29.2028i	0.753927	+	0.965415i
$916$		0			0
$917$	31.9995	+	15.3719i	1.05672	+	0.507624i
$918$		0			0
$919$	−14.8163	−	25.6625i	−0.488743	−	0.846528i	0.511173	−	0.859478i	$-0.329211\pi$
$919$	−14.8163	−	25.6625i	−0.488743	−	0.846528i	−0.999916	+	0.0129500i	$0.995878\pi$
$920$		0			0
$921$	1.25560	−	3.10578i	0.0413734	−	0.102339i
$922$		0			0
$923$	−21.3415	+	36.9645i	−0.702463	+	1.21670i
$924$		0			0
$925$	−6.48212	−	11.2274i	−0.213131	−	0.369153i
$926$		0			0
$927$	14.6471	−	15.1544i	0.481075	−	0.497735i
$928$		0			0
$929$	16.6186	−	28.7842i	0.545238	−	0.944380i	−0.453354	−	0.891331i	$-0.649773\pi$
$929$	16.6186	−	28.7842i	0.545238	−	0.944380i	0.998592	−	0.0530496i	$-0.0168941\pi$
$930$		0			0
$931$	32.0304	+	12.4993i	1.04975	+	0.409647i
$932$		0			0
$933$	−0.502822	−	3.58342i	−0.0164617	−	0.117316i
$934$		0			0
$935$	20.3151	+	11.7289i	0.664373	+	0.383576i
$936$		0			0
$937$		−	23.8190i		−	0.778134i	−0.921209	−	0.389067i	$-0.872797\pi$
$937$		−	23.8190i		−	0.778134i	0.921209	−	0.389067i	$-0.127203\pi$
$938$		0			0
$939$	23.8891	+	30.5903i	0.779591	+	0.998278i
$940$		0			0
$941$	−27.1201	−	46.9734i	−0.884091	−	1.53129i	−0.846752	−	0.531988i	$-0.821445\pi$
$941$	−27.1201	−	46.9734i	−0.884091	−	1.53129i	−0.0373389	−	0.999303i	$-0.511888\pi$
$942$		0			0
$943$	−30.2498	−	17.4647i	−0.985069	−	0.568730i
$944$		0			0
$945$	−1.20841	+	40.8112i	−0.0393095	+	1.32759i
$946$		0			0
$947$	−18.2427	−	10.5324i	−0.592807	−	0.342257i	0.173399	−	0.984852i	$-0.444525\pi$
$947$	−18.2427	−	10.5324i	−0.592807	−	0.342257i	−0.766207	+	0.642594i	$0.777858\pi$
$948$		0			0
$949$	32.2164	+	55.8005i	1.04579	+	1.81136i
$950$		0			0
$951$	−3.71495	−	4.75705i	−0.120465	−	0.154258i
$952$		0			0
$953$			4.50028i			0.145778i	0.997340	+	0.0728892i	$0.0232219\pi$
$953$			4.50028i			0.145778i	−0.997340	+	0.0728892i	$0.976778\pi$
$954$		0			0
$955$	39.6989	+	22.9201i	1.28462	+	0.741679i
$956$		0			0
$957$	−0.313468	−	2.23396i	−0.0101330	−	0.0722137i
$958$		0			0
$959$	10.3110	−	21.4644i	0.332961	−	0.693122i
$960$		0			0
$961$	−14.2148	+	24.6207i	−0.458541	+	0.794216i
$962$		0			0
$963$	−41.2101	−	10.2939i	−1.32798	−	0.331715i
$964$		0			0
$965$	32.0090	+	55.4411i	1.03040	+	1.78471i
$966$		0			0
$967$	10.8811	−	18.8466i	0.349912	−	0.606065i	−0.636322	−	0.771424i	$-0.719545\pi$
$967$	10.8811	−	18.8466i	0.349912	−	0.606065i	0.986233	+	0.165359i	$0.0528783\pi$
$968$		0			0
$969$	5.32689	−	13.1763i	0.171124	−	0.423283i
$970$		0			0
$971$	23.5222	+	40.7416i	0.754862	+	1.30746i	0.945443	+	0.325788i	$0.105629\pi$
$971$	23.5222	+	40.7416i	0.754862	+	1.30746i	−0.190581	+	0.981671i	$0.561037\pi$
$972$		0			0
$973$	−2.66961	−	3.90744i	−0.0855838	−	0.125267i
$974$		0			0
$975$	16.6492	+	21.3196i	0.533202	+	0.682773i
$976$		0			0
$977$	−21.7766	+	12.5727i	−0.696695	+	0.402237i	−0.806115	−	0.591758i	$-0.798434\pi$
$977$	−21.7766	+	12.5727i	−0.696695	+	0.402237i	0.109420	+	0.993996i	$0.465101\pi$
$978$		0			0
$979$	−37.7423	+	21.7905i	−1.20625	+	0.696429i
$980$		0			0
$981$	−16.2783	+	4.66006i	−0.519725	+	0.148784i
$982$		0			0
$983$	36.2142			1.15505			0.577527	−	0.816372i	$-0.304018\pi$
$983$	36.2142			1.15505			0.577527	+	0.816372i	$0.304018\pi$
$984$		0			0
$985$			29.3515i			0.935216i
$986$		0			0
$987$	−49.2356	+	10.7611i	−1.56719	+	0.342530i
$988$		0			0
$989$	−44.4801	+	25.6806i	−1.41438	+	0.816595i
$990$		0			0
$991$	9.32769	−	16.1560i	0.296304	−	0.513213i	−0.678984	−	0.734153i	$-0.737579\pi$
$991$	9.32769	−	16.1560i	0.296304	−	0.513213i	0.975287	+	0.220940i	$0.0709126\pi$
$992$		0			0
$993$	−6.24829	+	4.87951i	−0.198284	+	0.154847i
$994$		0			0
$995$	−27.1632	−	15.6827i	−0.861131	−	0.497174i
$996$		0			0
$997$		−	17.4836i		−	0.553712i	−0.960911	−	0.276856i	$-0.910708\pi$
$997$		−	17.4836i		−	0.553712i	0.960911	−	0.276856i	$-0.0892925\pi$
$998$		0			0
$999$	10.3742	−	14.2592i	0.328224	−	0.451143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.d.689.8		16
3.2	odd	2		3024.2.df.d.17.7		16
4.3	odd	2		252.2.bm.a.185.1	yes	16
7.5	odd	6		1008.2.ca.d.257.6		16
9.2	odd	6		1008.2.ca.d.353.6		16
9.7	even	3		3024.2.ca.d.2033.7		16
12.11	even	2		756.2.bm.a.17.7		16
21.5	even	6		3024.2.ca.d.2609.7		16
28.3	even	6		1764.2.x.a.293.4		16
28.11	odd	6		1764.2.x.b.293.5		16
28.19	even	6		252.2.w.a.5.3	✓	16
28.23	odd	6		1764.2.w.b.509.6		16
28.27	even	2		1764.2.bm.a.1697.8		16
36.7	odd	6		756.2.w.a.521.7		16
36.11	even	6		252.2.w.a.101.3	yes	16
36.23	even	6		2268.2.t.b.1781.2		16
36.31	odd	6		2268.2.t.a.1781.7		16
63.47	even	6	inner	1008.2.df.d.929.8		16
63.61	odd	6		3024.2.df.d.1601.7		16
84.11	even	6		5292.2.x.b.881.2		16
84.23	even	6		5292.2.w.b.1097.2		16
84.47	odd	6		756.2.w.a.341.7		16
84.59	odd	6		5292.2.x.a.881.7		16
84.83	odd	2		5292.2.bm.a.2285.2		16
252.11	even	6		1764.2.x.a.1469.4		16
252.47	odd	6		252.2.bm.a.173.1	yes	16
252.79	odd	6		5292.2.bm.a.4625.2		16
252.83	odd	6		1764.2.w.b.1109.6		16
252.103	even	6		2268.2.t.b.2105.2		16
252.115	even	6		5292.2.x.b.4409.2		16
252.131	odd	6		2268.2.t.a.2105.7		16
252.151	odd	6		5292.2.x.a.4409.7		16
252.187	even	6		756.2.bm.a.89.7		16
252.191	even	6		1764.2.bm.a.1685.8		16
252.223	even	6		5292.2.w.b.521.2		16
252.227	odd	6		1764.2.x.b.1469.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	28.19	even	6
252.2.w.a.101.3	yes	16	36.11	even	6
252.2.bm.a.173.1	yes	16	252.47	odd	6
252.2.bm.a.185.1	yes	16	4.3	odd	2
756.2.w.a.341.7		16	84.47	odd	6
756.2.w.a.521.7		16	36.7	odd	6
756.2.bm.a.17.7		16	12.11	even	2
756.2.bm.a.89.7		16	252.187	even	6
1008.2.ca.d.257.6		16	7.5	odd	6
1008.2.ca.d.353.6		16	9.2	odd	6
1008.2.df.d.689.8		16	1.1	even	1	trivial
1008.2.df.d.929.8		16	63.47	even	6	inner
1764.2.w.b.509.6		16	28.23	odd	6
1764.2.w.b.1109.6		16	252.83	odd	6
1764.2.x.a.293.4		16	28.3	even	6
1764.2.x.a.1469.4		16	252.11	even	6
1764.2.x.b.293.5		16	28.11	odd	6
1764.2.x.b.1469.5		16	252.227	odd	6
1764.2.bm.a.1685.8		16	252.191	even	6
1764.2.bm.a.1697.8		16	28.27	even	2
2268.2.t.a.1781.7		16	36.31	odd	6
2268.2.t.a.2105.7		16	252.131	odd	6
2268.2.t.b.1781.2		16	36.23	even	6
2268.2.t.b.2105.2		16	252.103	even	6
3024.2.ca.d.2033.7		16	9.7	even	3
3024.2.ca.d.2609.7		16	21.5	even	6
3024.2.df.d.17.7		16	3.2	odd	2
3024.2.df.d.1601.7		16	63.61	odd	6
5292.2.w.b.521.2		16	252.223	even	6
5292.2.w.b.1097.2		16	84.23	even	6
5292.2.x.a.881.7		16	84.59	odd	6
5292.2.x.a.4409.7		16	252.151	odd	6
5292.2.x.b.881.2		16	84.11	even	6
5292.2.x.b.4409.2		16	252.115	even	6
5292.2.bm.a.2285.2		16	84.83	odd	2
5292.2.bm.a.4625.2		16	252.79	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)

\(f(q)\)	\(=\)	\(q+(1.60579 + 0.649187i) q^{3} -2.96988 q^{5} +(-2.38485 - 1.14563i) q^{7} +(2.15711 + 2.08491i) q^{9} -4.72811i q^{11} +(3.54045 + 2.04408i) q^{13} +(-4.76900 - 1.92801i) q^{15} +(0.835278 - 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +(-3.08584 - 3.38786i) q^{21} -4.91090i q^{23} +3.82018 q^{25} +(2.11037 + 4.74830i) q^{27} +(0.238557 - 0.137731i) q^{29} +(1.38847 - 0.801636i) q^{31} +(3.06943 - 7.59235i) q^{33} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(4.35823 + 5.58078i) q^{39} +(3.55632 - 6.15972i) q^{41} +(-5.22930 - 9.05742i) q^{43} +(-6.40637 - 6.19194i) q^{45} +(5.49885 - 9.52430i) q^{47} +(4.37505 + 5.46433i) q^{49} +(2.28049 - 1.78091i) q^{51} +(-0.707381 - 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 - 1.18219i) q^{57} +(-1.37428 - 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(-2.75585 - 7.44347i) q^{63} +(-10.5147 - 6.07067i) q^{65} +(5.80513 + 10.0548i) q^{67} +(3.18809 - 7.88587i) q^{69} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(6.13440 + 2.48001i) q^{75} +(-5.41668 + 11.2759i) q^{77} +(-6.15163 + 10.6549i) q^{79} +(0.306275 + 8.99479i) q^{81} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(0.472485 - 0.0662987i) q^{87} +(-4.60872 - 7.98254i) q^{89} +(-6.10169 - 8.93089i) q^{91} +(2.75001 - 0.385879i) q^{93} +(-12.6332 + 7.29377i) q^{95} +(-7.00772 + 4.04591i) q^{97} +(9.85770 - 10.1991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Introduction

L-functions

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Database

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