LMFDB - Embedded newform 1008.2.r.l.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.2
Root			$1.65525 - 0.510048i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.l.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385911 + 1.68851i) q^{3} +(1.15525 - 2.00095i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.70215 - 1.30323i) q^{9} +O(q^{10})$	\(q+(-0.385911 + 1.68851i) q^{3} +(1.15525 - 2.00095i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.70215 - 1.30323i) q^{9} +(0.655250 + 1.13493i) q^{11} +(1.93281 - 3.34772i) q^{13} +(2.93281 + 2.72284i) q^{15} -0.326936 q^{17} -3.08232 q^{19} +(1.65525 - 0.510048i) q^{21} +(1.81872 - 3.15011i) q^{23} +(-0.169204 - 0.293069i) q^{25} +(3.24331 - 4.05968i) q^{27} +(-4.75152 - 8.22988i) q^{29} +(3.24904 - 5.62751i) q^{31} +(-2.16920 + 0.668417i) q^{33} -2.31050 q^{35} -2.31050 q^{37} +(4.90677 + 4.55549i) q^{39} +(4.74904 - 8.22558i) q^{41} +(0.0493786 + 0.0855263i) q^{43} +(-5.72935 + 3.90131i) q^{45} +(0.108354 + 0.187674i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.126168 - 0.552035i) q^{51} +13.7921 q^{53} +3.02791 q^{55} +(1.18950 - 5.20454i) q^{57} +(-1.22493 + 2.12163i) q^{59} +(7.68433 + 13.3097i) q^{61} +(0.222443 + 2.99174i) q^{63} +(-4.46575 - 7.73490i) q^{65} +(-2.93529 + 5.08407i) q^{67} +(4.61714 + 4.28659i) q^{69} +1.77182 q^{71} -5.99504 q^{73} +(0.560149 - 0.172604i) q^{75} +(0.655250 - 1.13493i) q^{77} +(-7.29594 - 12.6369i) q^{79} +(5.60318 + 7.04303i) q^{81} +(-3.04116 - 5.26744i) q^{83} +(-0.377692 + 0.654183i) q^{85} +(15.7299 - 4.84701i) q^{87} +5.52224 q^{89} -3.86561 q^{91} +(8.24827 + 7.65776i) q^{93} +(-3.56085 + 6.16757i) q^{95} +(2.99178 + 5.18192i) q^{97} +(-0.291511 - 3.92068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9	$ 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9} - 7 q^{11} + 3 q^{13} + 11 q^{15} + 6 q^{17} + 8 q^{19} + q^{21} - 2 q^{23} - 5 q^{25} - 11 q^{27} - 9 q^{29} - 3 q^{31} - 21 q^{33} + 6 q^{35} + 6 q^{37} - 2 q^{39} + 9 q^{41} - 8 q^{43} + 7 q^{45} - 3 q^{47} - 4 q^{49} + 18 q^{51} + 12 q^{53} + 56 q^{55} + 34 q^{57} - 10 q^{59} + 20 q^{61} + 2 q^{63} + q^{65} - 11 q^{67} - 17 q^{69} + 6 q^{71} - 48 q^{73} - 52 q^{75} - 7 q^{77} - 21 q^{79} - 25 q^{81} - 8 q^{83} + 9 q^{85} + 15 q^{87} + 12 q^{89} - 6 q^{91} + 29 q^{93} - 36 q^{95} + 16 q^{97} - 18 q^{99}+O(q^{100}) $ 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9 - 7 * q^11 + 3 * q^13 + 11 * q^15 + 6 * q^17 + 8 * q^19 + q^21 - 2 * q^23 - 5 * q^25 - 11 * q^27 - 9 * q^29 - 3 * q^31 - 21 * q^33 + 6 * q^35 + 6 * q^37 - 2 * q^39 + 9 * q^41 - 8 * q^43 + 7 * q^45 - 3 * q^47 - 4 * q^49 + 18 * q^51 + 12 * q^53 + 56 * q^55 + 34 * q^57 - 10 * q^59 + 20 * q^61 + 2 * q^63 + q^65 - 11 * q^67 - 17 * q^69 + 6 * q^71 - 48 * q^73 - 52 * q^75 - 7 * q^77 - 21 * q^79 - 25 * q^81 - 8 * q^83 + 9 * q^85 + 15 * q^87 + 12 * q^89 - 6 * q^91 + 29 * q^93 - 36 * q^95 + 16 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.385911	+	1.68851i	−0.222806	+	0.974863i
$3$	−0.385911	+	1.68851i	−0.222806	+	0.974863i
$4$		0			0
$5$	1.15525	−	2.00095i	0.516643	−	0.894853i	−0.483170	−	0.875527i	$-0.660515\pi$
$5$	1.15525	−	2.00095i	0.516643	−	0.894853i	0.999813	−	0.0193259i	$-0.00615202\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	−2.70215	−	1.30323i	−0.900715	−	0.434410i
$10$		0			0
$11$	0.655250	+	1.13493i	0.197565	+	0.342193i	0.947738	−	0.319048i	$-0.103363\pi$
$11$	0.655250	+	1.13493i	0.197565	+	0.342193i	−0.750173	+	0.661241i	$0.770030\pi$
$12$		0			0
$13$	1.93281	−	3.34772i	0.536064	−	0.928490i	−0.463047	−	0.886334i	$-0.653244\pi$
$13$	1.93281	−	3.34772i	0.536064	−	0.928490i	0.999111	−	0.0421566i	$-0.0134228\pi$
$14$		0			0
$15$	2.93281	+	2.72284i	0.757247	+	0.703035i
$16$		0			0
$17$	−0.326936			−0.0792936			−0.0396468	−	0.999214i	$-0.512623\pi$
$17$	−0.326936			−0.0792936			−0.0396468	+	0.999214i	$0.512623\pi$
$18$		0			0
$19$	−3.08232			−0.707133			−0.353566	−	0.935409i	$-0.615031\pi$
$19$	−3.08232			−0.707133			−0.353566	+	0.935409i	$0.615031\pi$
$20$		0			0
$21$	1.65525	−	0.510048i	0.361205	−	0.111301i
$22$		0			0
$23$	1.81872	−	3.15011i	0.379229	−	0.656844i	−0.611721	−	0.791073i	$-0.709523\pi$
$23$	1.81872	−	3.15011i	0.379229	−	0.656844i	0.990950	+	0.134230i	$0.0428560\pi$
$24$		0			0
$25$	−0.169204	−	0.293069i	−0.0338407	−	0.0586139i
$26$		0			0
$27$	3.24331	−	4.05968i	0.624175	−	0.781285i
$28$		0			0
$29$	−4.75152	−	8.22988i	−0.882336	−	1.52825i	−0.848737	−	0.528815i	$-0.822636\pi$
$29$	−4.75152	−	8.22988i	−0.882336	−	1.52825i	−0.0335990	−	0.999435i	$-0.510697\pi$
$30$		0			0
$31$	3.24904	−	5.62751i	0.583545	−	1.01073i	−0.411510	−	0.911405i	$-0.634998\pi$
$31$	3.24904	−	5.62751i	0.583545	−	1.01073i	0.995055	−	0.0993246i	$-0.0316682\pi$
$32$		0			0
$33$	−2.16920	+	0.668417i	−0.377610	+	0.116356i
$34$		0			0
$35$	−2.31050			−0.390546
$36$		0			0
$37$	−2.31050			−0.379844			−0.189922	−	0.981799i	$-0.560823\pi$
$37$	−2.31050			−0.379844			−0.189922	+	0.981799i	$0.560823\pi$
$38$		0			0
$39$	4.90677	+	4.55549i	0.785713	+	0.729462i
$40$		0			0
$41$	4.74904	−	8.22558i	0.741676	−	1.28462i	−0.210056	−	0.977689i	$-0.567365\pi$
$41$	4.74904	−	8.22558i	0.741676	−	1.28462i	0.951732	−	0.306931i	$-0.0993020\pi$
$42$		0			0
$43$	0.0493786	+	0.0855263i	0.00753017	+	0.0130426i	0.869766	−	0.493465i	$-0.164270\pi$
$43$	0.0493786	+	0.0855263i	0.00753017	+	0.0130426i	−0.862236	+	0.506507i	$0.830936\pi$
$44$		0			0
$45$	−5.72935	+	3.90131i	−0.854081	+	0.581572i
$46$		0			0
$47$	0.108354	+	0.187674i	0.0158050	+	0.0273750i	0.873820	−	0.486250i	$-0.161636\pi$
$47$	0.108354	+	0.187674i	0.0158050	+	0.0273750i	−0.858015	+	0.513625i	$0.828302\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	0.126168	−	0.552035i	0.0176671	−	0.0773004i
$52$		0			0
$53$	13.7921			1.89450			0.947249	−	0.320500i	$-0.103851\pi$
$53$	13.7921			1.89450			0.947249	+	0.320500i	$0.103851\pi$
$54$		0			0
$55$	3.02791			0.408283
$56$		0			0
$57$	1.18950	−	5.20454i	0.157553	−	0.689358i
$58$		0			0
$59$	−1.22493	+	2.12163i	−0.159472	+	0.276213i	−0.934678	−	0.355495i	$-0.884312\pi$
$59$	−1.22493	+	2.12163i	−0.159472	+	0.276213i	0.775207	+	0.631708i	$0.217646\pi$
$60$		0			0
$61$	7.68433	+	13.3097i	0.983878	+	1.70413i	0.646821	+	0.762642i	$0.276098\pi$
$61$	7.68433	+	13.3097i	0.983878	+	1.70413i	0.337057	+	0.941484i	$0.390568\pi$
$62$		0			0
$63$	0.222443	+	2.99174i	0.0280252	+	0.376924i
$64$		0			0
$65$	−4.46575	−	7.73490i	−0.553908	−	0.959397i
$66$		0			0
$67$	−2.93529	+	5.08407i	−0.358603	+	0.621118i	−0.987728	−	0.156186i	$-0.950080\pi$
$67$	−2.93529	+	5.08407i	−0.358603	+	0.621118i	0.629125	+	0.777304i	$0.283413\pi$
$68$		0			0
$69$	4.61714	+	4.28659i	0.555838	+	0.516045i
$70$		0			0
$71$	1.77182			0.210277			0.105138	−	0.994458i	$-0.466471\pi$
$71$	1.77182			0.210277			0.105138	+	0.994458i	$0.466471\pi$
$72$		0			0
$73$	−5.99504			−0.701666			−0.350833	−	0.936438i	$-0.614101\pi$
$73$	−5.99504			−0.701666			−0.350833	+	0.936438i	$0.614101\pi$
$74$		0			0
$75$	0.560149	−	0.172604i	0.0646804	−	0.0199306i
$76$		0			0
$77$	0.655250	−	1.13493i	0.0746726	−	0.129337i
$78$		0			0
$79$	−7.29594	−	12.6369i	−0.820857	−	1.42177i	−0.905045	−	0.425316i	$-0.860163\pi$
$79$	−7.29594	−	12.6369i	−0.820857	−	1.42177i	0.0841876	−	0.996450i	$-0.473171\pi$
$80$		0			0
$81$	5.60318	+	7.04303i	0.622576	+	0.782559i
$82$		0			0
$83$	−3.04116	−	5.26744i	−0.333811	−	0.578177i	0.649445	−	0.760409i	$-0.275001\pi$
$83$	−3.04116	−	5.26744i	−0.333811	−	0.578177i	−0.983256	+	0.182231i	$0.941668\pi$
$84$		0			0
$85$	−0.377692	+	0.654183i	−0.0409665	+	0.0709561i
$86$		0			0
$87$	15.7299	−	4.84701i	1.68642	−	0.519654i
$88$		0			0
$89$	5.52224			0.585356			0.292678	−	0.956211i	$-0.405454\pi$
$89$	5.52224			0.585356			0.292678	+	0.956211i	$0.405454\pi$
$90$		0			0
$91$	−3.86561			−0.405226
$92$		0			0
$93$	8.24827	+	7.65776i	0.855306	+	0.794073i
$94$		0			0
$95$	−3.56085	+	6.16757i	−0.365336	+	0.632780i
$96$		0			0
$97$	2.99178	+	5.18192i	0.303769	+	0.526144i	0.976987	−	0.213301i	$-0.0684214\pi$
$97$	2.99178	+	5.18192i	0.303769	+	0.526144i	−0.673217	+	0.739445i	$0.735088\pi$
$98$		0			0
$99$	−0.291511	−	3.92068i	−0.0292980	−	0.394043i
$100$		0			0
$101$	3.85105	+	6.67022i	0.383194	+	0.663712i	0.991517	−	0.129978i	$-0.0414907\pi$
$101$	3.85105	+	6.67022i	0.383194	+	0.663712i	−0.608323	+	0.793690i	$0.708157\pi$
$102$		0			0
$103$	2.03046	−	3.51686i	0.200067	−	0.346526i	−0.748483	−	0.663154i	$-0.769217\pi$
$103$	2.03046	−	3.51686i	0.200067	−	0.346526i	0.948550	+	0.316628i	$0.102551\pi$
$104$		0			0
$105$	0.891646	−	3.90131i	0.0870158	−	0.380728i
$106$		0			0
$107$	14.0774			1.36091			0.680455	−	0.732790i	$-0.261782\pi$
$107$	14.0774			1.36091			0.680455	+	0.732790i	$0.261782\pi$
$108$		0			0
$109$	−6.67306			−0.639164			−0.319582	−	0.947559i	$-0.603542\pi$
$109$	−6.67306			−0.639164			−0.319582	+	0.947559i	$0.603542\pi$
$110$		0			0
$111$	0.891646	−	3.90131i	0.0846313	−	0.370296i
$112$		0			0
$113$	3.84918	−	6.66697i	0.362100	−	0.627176i	−0.626206	−	0.779658i	$-0.715393\pi$
$113$	3.84918	−	6.66697i	0.362100	−	0.627176i	0.988306	+	0.152482i	$0.0487265\pi$
$114$		0			0
$115$	−4.20215	−	7.27833i	−0.391852	−	0.678708i
$116$		0			0
$117$	−9.58557	+	6.52714i	−0.886187	+	0.603434i
$118$		0			0
$119$	0.163468	+	0.283135i	0.0149851	+	0.0259549i
$120$		0			0
$121$	4.64130	−	8.03896i	0.421936	−	0.730815i
$122$		0			0
$123$	12.0563	+	11.1932i	1.08708	+	1.00925i
$124$		0			0
$125$	10.7706			0.963352
$126$		0			0
$127$	−14.9847			−1.32968			−0.664838	−	0.746987i	$-0.731500\pi$
$127$	−14.9847			−1.32968			−0.664838	+	0.746987i	$0.731500\pi$
$128$		0			0
$129$	−0.163468	+	0.0503709i	−0.0143925	+	0.00443491i
$130$		0			0
$131$	5.20788	−	9.02032i	0.455015	−	0.788109i	−0.543674	−	0.839296i	$-0.682967\pi$
$131$	5.20788	−	9.02032i	0.455015	−	0.788109i	0.998689	+	0.0511876i	$0.0163007\pi$
$132$		0			0
$133$	1.54116	+	2.66937i	0.133636	+	0.231464i
$134$		0			0
$135$	−4.37638	−	11.1796i	−0.376659	−	0.962190i
$136$		0			0
$137$	−3.13170	−	5.42426i	−0.267559	−	0.463426i	0.700672	−	0.713484i	$-0.252884\pi$
$137$	−3.13170	−	5.42426i	−0.267559	−	0.463426i	−0.968231	+	0.250058i	$0.919550\pi$
$138$		0			0
$139$	−10.0798	+	17.4588i	−0.854961	+	1.48084i	0.0217207	+	0.999764i	$0.493086\pi$
$139$	−10.0798	+	17.4588i	−0.854961	+	1.48084i	−0.876681	+	0.481071i	$0.840248\pi$
$140$		0			0
$141$	−0.358704	+	0.110531i	−0.0302084	+	0.00930838i
$142$		0			0
$143$	5.06588			0.423631
$144$		0			0
$145$	−21.9568			−1.82341
$146$		0			0
$147$	−1.26934	−	1.17846i	−0.104693	−	0.0971981i
$148$		0			0
$149$	−8.50878	+	14.7376i	−0.697067	+	1.20736i	0.272412	+	0.962181i	$0.412179\pi$
$149$	−8.50878	+	14.7376i	−0.697067	+	1.20736i	−0.969479	+	0.245174i	$0.921155\pi$
$150$		0			0
$151$	−8.19641	−	14.1966i	−0.667014	−	1.15530i	−0.978735	−	0.205129i	$-0.934239\pi$
$151$	−8.19641	−	14.1966i	−0.667014	−	1.15530i	0.311721	−	0.950174i	$-0.399095\pi$
$152$		0			0
$153$	0.883428	+	0.426072i	0.0714209	+	0.0344459i
$154$		0			0
$155$	−7.50691	−	13.0023i	−0.602969	−	1.04437i
$156$		0			0
$157$	−10.2274	+	17.7144i	−0.816238	+	1.41377i	0.0921971	+	0.995741i	$0.470611\pi$
$157$	−10.2274	+	17.7144i	−0.816238	+	1.41377i	−0.908435	+	0.418025i	$0.862722\pi$
$158$		0			0
$159$	−5.32254	+	23.2882i	−0.422105	+	1.84687i
$160$		0			0
$161$	−3.63744			−0.286670
$162$		0			0
$163$	−16.8810			−1.32222			−0.661110	−	0.750289i	$-0.729914\pi$
$163$	−16.8810			−1.32222			−0.661110	+	0.750289i	$0.729914\pi$
$164$		0			0
$165$	−1.16850	+	5.11266i	−0.0909678	+	0.398020i
$166$		0			0
$167$	−1.60587	+	2.78145i	−0.124266	+	0.215235i	−0.921446	−	0.388507i	$-0.872991\pi$
$167$	−1.60587	+	2.78145i	−0.124266	+	0.215235i	0.797180	+	0.603742i	$0.206324\pi$
$168$		0			0
$169$	−0.971485	−	1.68266i	−0.0747296	−	0.129435i
$170$		0			0
$171$	8.32888	+	4.01697i	0.636925	+	0.307186i
$172$		0			0
$173$	−0.306072	−	0.530133i	−0.0232703	−	0.0403053i	0.854156	−	0.520017i	$-0.174074\pi$
$173$	−0.306072	−	0.530133i	−0.0232703	−	0.0403053i	−0.877426	+	0.479712i	$0.840741\pi$
$174$		0			0
$175$	−0.169204	+	0.293069i	−0.0127906	+	0.0221540i
$176$		0			0
$177$	−3.10969	−	2.88706i	−0.233739	−	0.217005i
$178$		0			0
$179$	−4.38135			−0.327477			−0.163739	−	0.986504i	$-0.552355\pi$
$179$	−4.38135			−0.327477			−0.163739	+	0.986504i	$0.552355\pi$
$180$		0			0
$181$	−3.50192			−0.260295			−0.130148	−	0.991495i	$-0.541545\pi$
$181$	−3.50192			−0.260295			−0.130148	+	0.991495i	$0.541545\pi$
$182$		0			0
$183$	−25.4390	+	7.83875i	−1.88050	+	0.579457i
$184$		0			0
$185$	−2.66920	+	4.62320i	−0.196244	+	0.339904i
$186$		0			0
$187$	−0.214225	−	0.371048i	−0.0156657	−	0.0271337i
$188$		0			0
$189$	−5.13744	−	0.778948i	−0.373693	−	0.0566601i
$190$		0			0
$191$	−2.71533	−	4.70309i	−0.196474	−	0.340303i	0.750909	−	0.660406i	$-0.229616\pi$
$191$	−2.71533	−	4.70309i	−0.196474	−	0.340303i	−0.947383	+	0.320103i	$0.896283\pi$
$192$		0			0
$193$	4.54193	−	7.86686i	0.326935	−	0.566269i	−0.654967	−	0.755658i	$-0.727317\pi$
$193$	4.54193	−	7.86686i	0.326935	−	0.566269i	0.981902	+	0.189389i	$0.0606507\pi$
$194$		0			0
$195$	14.7839	−	4.55549i	1.05869	−	0.326225i
$196$		0			0
$197$	−8.58040			−0.611329			−0.305664	−	0.952139i	$-0.598879\pi$
$197$	−8.58040			−0.611329			−0.305664	+	0.952139i	$0.598879\pi$
$198$		0			0
$199$	25.4905			1.80697			0.903487	−	0.428616i	$-0.140999\pi$
$199$	25.4905			1.80697			0.903487	+	0.428616i	$0.140999\pi$
$200$		0			0
$201$	−7.45175	−	6.91827i	−0.525606	−	0.487977i
$202$		0			0
$203$	−4.75152	+	8.22988i	−0.333492	+	0.577624i
$204$		0			0
$205$	−10.9727	−	19.0052i	−0.766364	−	1.32738i
$206$		0			0
$207$	−9.01976	+	6.14185i	−0.626917	+	0.426888i
$208$		0			0
$209$	−2.01969	−	3.49821i	−0.139705	−	0.241976i
$210$		0			0
$211$	−8.32066	+	14.4118i	−0.572818	+	0.992150i	0.423457	+	0.905916i	$0.360816\pi$
$211$	−8.32066	+	14.4118i	−0.572818	+	0.992150i	−0.996275	+	0.0862336i	$0.972517\pi$
$212$		0			0
$213$	−0.683765	+	2.99174i	−0.0468508	+	0.204991i
$214$		0			0
$215$	0.228179			0.0155616
$216$		0			0
$217$	−6.49808			−0.441119
$218$		0			0
$219$	2.31355	−	10.1227i	0.156335	−	0.684028i
$220$		0			0
$221$	−0.631904	+	1.09449i	−0.0425064	+	0.0736233i
$222$		0			0
$223$	9.28503	+	16.0821i	0.621772	+	1.07694i	0.989156	+	0.146871i	$0.0469202\pi$
$223$	9.28503	+	16.0821i	0.621772	+	1.07694i	−0.367384	+	0.930069i	$0.619746\pi$
$224$		0			0
$225$	0.0752763	+	1.01243i	0.00501842	+	0.0674952i
$226$		0			0
$227$	−7.84096	−	13.5809i	−0.520423	−	0.901399i	−0.999718	−	0.0237449i	$-0.992441\pi$
$227$	−7.84096	−	13.5809i	−0.520423	−	0.901399i	0.479295	−	0.877654i	$-0.340892\pi$
$228$		0			0
$229$	−5.57024	+	9.64794i	−0.368092	+	0.637554i	−0.989267	−	0.146118i	$-0.953322\pi$
$229$	−5.57024	+	9.64794i	−0.368092	+	0.637554i	0.621175	+	0.783672i	$0.286656\pi$
$230$		0			0
$231$	1.66347	+	1.54438i	0.109448	+	0.101613i
$232$		0			0
$233$	−21.6831			−1.42050			−0.710252	−	0.703948i	$-0.751419\pi$
$233$	−21.6831			−1.42050			−0.710252	+	0.703948i	$0.751419\pi$
$234$		0			0
$235$	0.500702			0.0326622
$236$		0			0
$237$	24.1532	−	7.44255i	1.56892	−	0.483446i
$238$		0			0
$239$	−6.20271	+	10.7434i	−0.401220	+	0.694934i	−0.993873	−	0.110524i	$-0.964747\pi$
$239$	−6.20271	+	10.7434i	−0.401220	+	0.694934i	0.592653	+	0.805458i	$0.298080\pi$
$240$		0			0
$241$	8.35028	+	14.4631i	0.537889	+	0.931651i	0.999017	+	0.0443176i	$0.0141114\pi$
$241$	8.35028	+	14.4631i	0.537889	+	0.931651i	−0.461129	+	0.887333i	$0.652555\pi$
$242$		0			0
$243$	−14.0546	+	6.74306i	−0.901601	+	0.432568i
$244$		0			0
$245$	1.15525	+	2.00095i	0.0738062	+	0.127836i
$246$		0			0
$247$	−5.95753	+	10.3187i	−0.379069	+	0.656566i
$248$		0			0
$249$	10.0678	−	3.10227i	0.638018	−	0.196599i
$250$		0			0
$251$	27.0215			1.70558			0.852790	−	0.522255i	$-0.174909\pi$
$251$	27.0215			1.70558			0.852790	+	0.522255i	$0.174909\pi$
$252$		0			0
$253$	4.76686			0.299690
$254$		0			0
$255$	−0.958840	−	0.890194i	−0.0600449	−	0.0557461i
$256$		0			0
$257$	9.97645	−	17.2797i	0.622314	−	1.07788i	−0.366740	−	0.930324i	$-0.619526\pi$
$257$	9.97645	−	17.2797i	0.622314	−	1.07788i	0.989054	−	0.147556i	$-0.0471406\pi$
$258$		0			0
$259$	1.15525	+	2.00095i	0.0717837	+	0.124333i
$260$		0			0
$261$	2.11388	+	28.4307i	0.130846	+	1.75981i
$262$		0			0
$263$	7.92841	+	13.7324i	0.488887	+	0.846776i	0.999918	−	0.0127855i	$-0.00406985\pi$
$263$	7.92841	+	13.7324i	0.488887	+	0.846776i	−0.511032	+	0.859562i	$0.670737\pi$
$264$		0			0
$265$	15.9334	−	27.5974i	0.978779	−	1.69530i
$266$		0			0
$267$	−2.13109	+	9.32437i	−0.130421	+	0.570642i
$268$		0			0
$269$	0.694466			0.0423423			0.0211712	−	0.999776i	$-0.493261\pi$
$269$	0.694466			0.0423423			0.0211712	+	0.999776i	$0.493261\pi$
$270$		0			0
$271$	9.08883			0.552107			0.276053	−	0.961142i	$-0.410973\pi$
$271$	9.08883			0.552107			0.276053	+	0.961142i	$0.410973\pi$
$272$		0			0
$273$	1.49178	−	6.52714i	0.0902867	−	0.395040i
$274$		0			0
$275$	0.221741	−	0.384067i	0.0133715	−	0.0231601i
$276$		0			0
$277$	−7.20084	−	12.4722i	−0.432656	−	0.749383i	0.564445	−	0.825471i	$-0.309090\pi$
$277$	−7.20084	−	12.4722i	−0.432656	−	0.749383i	−0.997101	+	0.0760880i	$0.975757\pi$
$278$		0			0
$279$	−16.1133	+	10.9721i	−0.964679	+	0.656882i
$280$		0			0
$281$	4.68356	+	8.11216i	0.279398	+	0.483931i	0.971235	−	0.238122i	$-0.0765319\pi$
$281$	4.68356	+	8.11216i	0.279398	+	0.483931i	−0.691837	+	0.722053i	$0.743199\pi$
$282$		0			0
$283$	−9.54310	+	16.5291i	−0.567279	+	0.982556i	0.429555	+	0.903041i	$0.358670\pi$
$283$	−9.54310	+	16.5291i	−0.567279	+	0.982556i	−0.996834	+	0.0795148i	$0.974663\pi$
$284$		0			0
$285$	−9.03985	−	8.39267i	−0.535475	−	0.497139i
$286$		0			0
$287$	−9.49808			−0.560654
$288$		0			0
$289$	−16.8931			−0.993713
$290$		0			0
$291$	−9.90429	+	3.05190i	−0.580600	+	0.178906i
$292$		0			0
$293$	−9.10262	+	15.7662i	−0.531781	+	0.921071i	0.467531	+	0.883977i	$0.345144\pi$
$293$	−9.10262	+	15.7662i	−0.531781	+	0.921071i	−0.999312	+	0.0370944i	$0.988190\pi$
$294$		0			0
$295$	2.83019	+	4.90203i	0.164780	+	0.285407i
$296$		0			0
$297$	6.73261	+	1.02081i	0.390665	+	0.0592334i
$298$		0			0
$299$	−7.03046	−	12.1771i	−0.406582	−	0.704221i
$300$		0			0
$301$	0.0493786	−	0.0855263i	0.00284614	−	0.00492965i
$302$		0			0
$303$	−12.7489	+	3.92844i	−0.732406	+	0.225683i
$304$		0			0
$305$	35.5093			2.03326
$306$		0			0
$307$	26.8537			1.53262			0.766312	−	0.642469i	$-0.222090\pi$
$307$	26.8537			1.53262			0.766312	+	0.642469i	$0.222090\pi$
$308$		0			0
$309$	5.15468	+	4.78565i	0.293240	+	0.272246i
$310$		0			0
$311$	−0.790243	+	1.36874i	−0.0448106	+	0.0776142i	−0.887561	−	0.460691i	$-0.847602\pi$
$311$	−0.790243	+	1.36874i	−0.0448106	+	0.0776142i	0.842750	+	0.538305i	$0.180935\pi$
$312$		0			0
$313$	−10.2617	−	17.7738i	−0.580025	−	1.00463i	−0.995476	−	0.0950169i	$-0.969709\pi$
$313$	−10.2617	−	17.7738i	−0.580025	−	1.00463i	0.415451	−	0.909616i	$-0.363624\pi$
$314$		0			0
$315$	6.24331	+	3.01111i	0.351770	+	0.169657i
$316$		0			0
$317$	−15.9323	−	27.5955i	−0.894845	−	1.54992i	−0.833996	−	0.551771i	$-0.813952\pi$
$317$	−15.9323	−	27.5955i	−0.894845	−	1.54992i	−0.0608495	−	0.998147i	$-0.519381\pi$
$318$		0			0
$319$	6.22687	−	10.7853i	0.348638	−	0.603858i
$320$		0			0
$321$	−5.43260	+	23.7698i	−0.303218	+	1.32670i
$322$		0			0
$323$	1.00772			0.0560711
$324$		0			0
$325$	−1.30815			−0.0725632
$326$		0			0
$327$	2.57521	−	11.2675i	0.142409	−	0.623097i
$328$		0			0
$329$	0.108354	−	0.187674i	0.00597372	−	0.0103468i
$330$		0			0
$331$	17.0714	+	29.5686i	0.938330	+	1.62524i	0.768586	+	0.639747i	$0.220961\pi$
$331$	17.0714	+	29.5686i	0.938330	+	1.62524i	0.169744	+	0.985488i	$0.445706\pi$
$332$		0			0
$333$	6.24331	+	3.01111i	0.342131	+	0.165008i
$334$		0			0
$335$	6.78198	+	11.7467i	0.370539	+	0.641793i
$336$		0			0
$337$	−0.252833	+	0.437920i	−0.0137727	+	0.0238550i	−0.872830	−	0.488025i	$-0.837717\pi$
$337$	−0.252833	+	0.437920i	−0.0137727	+	0.0238550i	0.859057	+	0.511880i	$0.171051\pi$
$338$		0			0
$339$	9.77182	+	9.07224i	0.530732	+	0.492736i
$340$		0			0
$341$	8.51573			0.461153
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	13.9112	−	4.28659i	0.748954	−	0.230782i
$346$		0			0
$347$	14.2154	−	24.6217i	0.763120	−	1.32176i	−0.178114	−	0.984010i	$-0.557000\pi$
$347$	14.2154	−	24.6217i	0.763120	−	1.32176i	0.941235	−	0.337753i	$-0.109667\pi$
$348$		0			0
$349$	17.5804	+	30.4502i	0.941057	+	1.62996i	0.763459	+	0.645856i	$0.223500\pi$
$349$	17.5804	+	30.4502i	0.941057	+	1.62996i	0.177599	+	0.984103i	$0.443167\pi$
$350$		0			0
$351$	−7.32197	−	18.7042i	−0.390818	−	0.998359i
$352$		0			0
$353$	−0.496139	−	0.859339i	−0.0264068	−	0.0457380i	0.852520	−	0.522695i	$-0.175073\pi$
$353$	−0.496139	−	0.859339i	−0.0264068	−	0.0457380i	−0.878927	+	0.476957i	$0.841740\pi$
$354$		0			0
$355$	2.04690	−	3.54533i	0.108638	−	0.188166i
$356$		0			0
$357$	−0.541160	+	0.166753i	−0.0286412	+	0.00882549i
$358$		0			0
$359$	23.2914			1.22928			0.614638	−	0.788810i	$-0.289302\pi$
$359$	23.2914			1.22928			0.614638	+	0.788810i	$0.289302\pi$
$360$		0			0
$361$	−9.49930			−0.499963
$362$		0			0
$363$	11.7828	+	10.9392i	0.618434	+	0.574159i
$364$		0			0
$365$	−6.92576	+	11.9958i	−0.362511	+	0.627887i
$366$		0			0
$367$	−5.89144	−	10.2043i	−0.307531	−	0.532659i	0.670291	−	0.742099i	$-0.266169\pi$
$367$	−5.89144	−	10.2043i	−0.307531	−	0.532659i	−0.977822	+	0.209440i	$0.932836\pi$
$368$		0			0
$369$	−23.5524	+	16.0376i	−1.22609	+	0.834886i
$370$		0			0
$371$	−6.89607	−	11.9443i	−0.358026	−	0.620120i
$372$		0			0
$373$	6.91714	−	11.9808i	0.358156	−	0.620344i	−0.629497	−	0.777003i	$-0.716739\pi$
$373$	6.91714	−	11.9808i	0.358156	−	0.620344i	0.987653	+	0.156659i	$0.0500723\pi$
$374$		0			0
$375$	−4.15649	+	18.1863i	−0.214640	+	0.939136i
$376$		0			0
$377$	−36.7351			−1.89195
$378$		0			0
$379$	21.5877			1.10889			0.554443	−	0.832222i	$-0.312931\pi$
$379$	21.5877			1.10889			0.554443	+	0.832222i	$0.312931\pi$
$380$		0			0
$381$	5.78275	−	25.3018i	0.296260	−	1.29625i
$382$		0			0
$383$	8.31989	−	14.4105i	0.425127	−	0.736341i	−0.571306	−	0.820737i	$-0.693563\pi$
$383$	8.31989	−	14.4105i	0.425127	−	0.736341i	0.996432	+	0.0843965i	$0.0268962\pi$
$384$		0			0
$385$	−1.51395	−	2.62225i	−0.0771582	−	0.133642i
$386$		0			0
$387$	−0.0219678	−	0.295456i	−0.00111669	−	0.0150189i
$388$		0			0
$389$	9.46709	+	16.3975i	0.480000	+	0.831385i	0.999737	−	0.0229417i	$-0.00730320\pi$
$389$	9.46709	+	16.3975i	0.480000	+	0.831385i	−0.519736	+	0.854327i	$0.673970\pi$
$390$		0			0
$391$	−0.594604	+	1.02988i	−0.0300704	+	0.0520835i
$392$		0			0
$393$	13.2211	+	12.2746i	0.666918	+	0.619172i
$394$		0			0
$395$	−33.7145			−1.69636
$396$		0			0
$397$	16.0746			0.806761			0.403381	−	0.915032i	$-0.367835\pi$
$397$	16.0746			0.806761			0.403381	+	0.915032i	$0.367835\pi$
$398$		0			0
$399$	−5.10201	+	1.57213i	−0.255420	+	0.0787049i
$400$		0			0
$401$	−19.4409	+	33.6726i	−0.970832	+	1.68153i	−0.277776	+	0.960646i	$0.589597\pi$
$401$	−19.4409	+	33.6726i	−0.970832	+	1.68153i	−0.693056	+	0.720884i	$0.743736\pi$
$402$		0			0
$403$	−12.5595	−	21.7538i	−0.625635	−	1.08363i
$404$		0			0
$405$	20.5658	−	3.07524i	1.02192	−	0.152810i
$406$		0			0
$407$	−1.51395	−	2.62225i	−0.0750439	−	0.129980i
$408$		0			0
$409$	−6.39993	+	11.0850i	−0.316456	+	0.548119i	−0.979746	−	0.200244i	$-0.935826\pi$
$409$	−6.39993	+	11.0850i	−0.316456	+	0.548119i	0.663290	+	0.748363i	$0.269160\pi$
$410$		0			0
$411$	10.3675	−	3.19463i	0.511391	−	0.157580i
$412$		0			0
$413$	2.44985			0.120549
$414$		0			0
$415$	−14.0532			−0.689844
$416$		0			0
$417$	−25.5895	−	23.7575i	−1.25312	−	1.16341i
$418$		0			0
$419$	0.597046	−	1.03411i	0.0291676	−	0.0505197i	−0.851073	−	0.525047i	$-0.824048\pi$
$419$	0.597046	−	1.03411i	0.0291676	−	0.0505197i	0.880241	+	0.474527i	$0.157381\pi$
$420$		0			0
$421$	−8.19067	−	14.1867i	−0.399189	−	0.691416i	0.594437	−	0.804142i	$-0.297375\pi$
$421$	−8.19067	−	14.1867i	−0.399189	−	0.691416i	−0.993626	+	0.112726i	$0.964042\pi$
$422$		0			0
$423$	−0.0482049	−	0.648332i	−0.00234380	−	0.0315230i
$424$		0			0
$425$	0.0553187	+	0.0958149i	0.00268335	+	0.00464770i
$426$		0			0
$427$	7.68433	−	13.3097i	0.371871	−	0.644099i
$428$		0			0
$429$	−1.95498	+	8.55381i	−0.0943873	+	0.412982i
$430$		0			0
$431$	26.3928			1.27130			0.635649	−	0.771978i	$-0.280733\pi$
$431$	26.3928			1.27130			0.635649	+	0.771978i	$0.280733\pi$
$432$		0			0
$433$	23.7503			1.14137			0.570684	−	0.821170i	$-0.306678\pi$
$433$	23.7503			1.14137			0.570684	+	0.821170i	$0.306678\pi$
$434$		0			0
$435$	8.47336	−	37.0743i	0.406267	−	1.77758i
$436$		0			0
$437$	−5.60587	+	9.70965i	−0.268165	+	0.464476i
$438$		0			0
$439$	−10.2431	−	17.7416i	−0.488877	−	0.846759i	0.511042	−	0.859556i	$-0.329260\pi$
$439$	−10.2431	−	17.7416i	−0.488877	−	0.846759i	−0.999918	+	0.0127969i	$0.995926\pi$
$440$		0			0
$441$	2.47970	−	1.68851i	0.118081	−	0.0804053i
$442$		0			0
$443$	−3.89909	−	6.75343i	−0.185252	−	0.320865i	0.758410	−	0.651778i	$-0.225977\pi$
$443$	−3.89909	−	6.75343i	−0.185252	−	0.320865i	−0.943661	+	0.330913i	$0.892643\pi$
$444$		0			0
$445$	6.37957	−	11.0497i	0.302421	−	0.523808i
$446$		0			0
$447$	−21.6011	−	20.0546i	−1.02170	−	0.948550i
$448$		0			0
$449$	2.35981			0.111366			0.0556831	−	0.998448i	$-0.482266\pi$
$449$	2.35981			0.111366			0.0556831	+	0.998448i	$0.482266\pi$
$450$		0			0
$451$	12.4472			0.586117
$452$		0			0
$453$	27.1342	−	8.36112i	1.27488	−	0.392840i
$454$		0			0
$455$	−4.46575	+	7.73490i	−0.209358	+	0.362618i
$456$		0			0
$457$	−10.1012	−	17.4959i	−0.472516	−	0.818422i	0.526989	−	0.849872i	$-0.323321\pi$
$457$	−10.1012	−	17.4959i	−0.472516	−	0.818422i	−0.999505	+	0.0314501i	$0.989987\pi$
$458$		0			0
$459$	−1.06035	+	1.32725i	−0.0494930	+	0.0619509i
$460$		0			0
$461$	6.02197	+	10.4304i	0.280471	+	0.485790i	0.971501	−	0.237036i	$-0.0761760\pi$
$461$	6.02197	+	10.4304i	0.280471	+	0.485790i	−0.691030	+	0.722826i	$0.742843\pi$
$462$		0			0
$463$	−11.6437	+	20.1675i	−0.541130	+	0.937265i	0.457709	+	0.889102i	$0.348670\pi$
$463$	−11.6437	+	20.1675i	−0.541130	+	0.937265i	−0.998839	+	0.0481633i	$0.984663\pi$
$464$		0			0
$465$	24.8516	−	7.65776i	1.15247	−	0.355120i
$466$		0			0
$467$	−34.0682			−1.57649			−0.788243	−	0.615364i	$-0.789009\pi$
$467$	−34.0682			−1.57649			−0.788243	+	0.615364i	$0.789009\pi$
$468$		0			0
$469$	5.87058			0.271078
$470$		0			0
$471$	−25.9642	−	24.1053i	−1.19637	−	1.11072i
$472$		0			0
$473$	−0.0647107	+	0.112082i	−0.00297540	+	0.00515354i
$474$		0			0
$475$	0.521540	+	0.903334i	0.0239299	+	0.0414478i
$476$		0			0
$477$	−37.2684	−	17.9743i	−1.70640	−	0.822988i
$478$		0			0
$479$	−9.38477	−	16.2549i	−0.428801	−	0.742705i	0.567966	−	0.823052i	$-0.307730\pi$
$479$	−9.38477	−	16.2549i	−0.428801	−	0.742705i	−0.996767	+	0.0803471i	$0.974397\pi$
$480$		0			0
$481$	−4.46575	+	7.73490i	−0.203621	+	0.352681i
$482$		0			0
$483$	1.40373	−	6.14185i	0.0638717	−	0.279464i
$484$		0			0
$485$	13.8250			0.627762
$486$		0			0
$487$	13.8837			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$487$	13.8837			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$488$		0			0
$489$	6.51455	−	28.5037i	0.294598	−	1.28898i
$490$		0			0
$491$	4.54250	−	7.86784i	0.205000	−	0.355071i	−0.745133	−	0.666916i	$-0.767614\pi$
$491$	4.54250	−	7.86784i	0.205000	−	0.355071i	0.950133	+	0.311846i	$0.100947\pi$
$492$		0			0
$493$	1.55344	+	2.69064i	0.0699636	+	0.121180i
$494$		0			0
$495$	−8.18185	−	3.94606i	−0.367747	−	0.177362i
$496$		0			0
$497$	−0.885911	−	1.53444i	−0.0397385	−	0.0688291i
$498$		0			0
$499$	−11.8788	+	20.5747i	−0.531769	+	0.921051i	0.467543	+	0.883970i	$0.345139\pi$
$499$	−11.8788	+	20.5747i	−0.531769	+	0.921051i	−0.999312	+	0.0370810i	$0.988194\pi$
$500$		0			0
$501$	−4.07679	−	3.78492i	−0.182138	−	0.169098i
$502$		0			0
$503$	22.5612			1.00595			0.502977	−	0.864300i	$-0.332238\pi$
$503$	22.5612			1.00595			0.502977	+	0.864300i	$0.332238\pi$
$504$		0			0
$505$	17.7957			0.791899
$506$		0			0
$507$	3.21610	−	0.991007i	0.142832	−	0.0440122i
$508$		0			0
$509$	−3.94814	+	6.83838i	−0.174998	+	0.303106i	−0.940161	−	0.340732i	$-0.889325\pi$
$509$	−3.94814	+	6.83838i	−0.174998	+	0.303106i	0.765162	+	0.643837i	$0.222659\pi$
$510$		0			0
$511$	2.99752	+	5.19185i	0.132602	+	0.229674i
$512$		0			0
$513$	−9.99691	+	12.5132i	−0.441374	+	0.552472i
$514$		0			0
$515$	−4.69138	−	8.12570i	−0.206727	−	0.358061i
$516$		0			0
$517$	−0.141997	+	0.245946i	−0.00624503	+	0.0108167i
$518$		0			0
$519$	1.01325	−	0.312223i	0.0444768	−	0.0137051i
$520$		0			0
$521$	9.86440			0.432167			0.216084	−	0.976375i	$-0.430672\pi$
$521$	9.86440			0.432167			0.216084	+	0.976375i	$0.430672\pi$
$522$		0			0
$523$	−22.9097			−1.00177			−0.500885	−	0.865514i	$-0.666992\pi$
$523$	−22.9097			−1.00177			−0.500885	+	0.865514i	$0.666992\pi$
$524$		0			0
$525$	−0.429554	−	0.398801i	−0.0187473	−	0.0174051i
$526$		0			0
$527$	−1.06223	+	1.83983i	−0.0462714	+	0.0801444i
$528$		0			0
$529$	4.88453	+	8.46026i	0.212371	+	0.367837i
$530$		0			0
$531$	6.07490	−	4.13660i	0.263628	−	0.179513i
$532$		0			0
$533$	−18.3580	−	31.7969i	−0.795172	−	1.37728i
$534$		0			0
$535$	16.2629	−	28.1681i	0.703105	−	1.21781i
$536$		0			0
$537$	1.69081	−	7.39796i	0.0729638	−	0.319246i
$538$		0			0
$539$	−1.31050			−0.0564472
$540$		0			0
$541$	29.7187			1.27771			0.638853	−	0.769329i	$-0.279409\pi$
$541$	29.7187			1.27771			0.638853	+	0.769329i	$0.279409\pi$
$542$		0			0
$543$	1.35143	−	5.91303i	0.0579953	−	0.253752i
$544$		0			0
$545$	−7.70906	+	13.3525i	−0.330220	+	0.571957i
$546$		0			0
$547$	−1.30472	−	2.25985i	−0.0557859	−	0.0966240i	0.836784	−	0.547533i	$-0.184433\pi$
$547$	−1.30472	−	2.25985i	−0.0557859	−	0.0966240i	−0.892570	+	0.450909i	$0.851100\pi$
$548$		0			0
$549$	−3.41865	−	45.9791i	−0.145904	−	1.96234i
$550$		0			0
$551$	14.6457	+	25.3671i	0.623929	+	1.08068i
$552$		0			0
$553$	−7.29594	+	12.6369i	−0.310255	+	0.537377i
$554$		0			0
$555$	−6.77625	−	6.29112i	−0.287636	−	0.267043i
$556$		0			0
$557$	26.0406			1.10338			0.551688	−	0.834051i	$-0.313984\pi$
$557$	26.0406			1.10338			0.551688	+	0.834051i	$0.313984\pi$
$558$		0			0
$559$	0.381757			0.0161466
$560$		0			0
$561$	0.709190	−	0.218529i	0.0299420	−	0.00922632i
$562$		0			0
$563$	−22.3876	+	38.7765i	−0.943525	+	1.63423i	−0.184848	+	0.982767i	$0.559179\pi$
$563$	−22.3876	+	38.7765i	−0.943525	+	1.63423i	−0.758677	+	0.651467i	$0.774154\pi$
$564$		0			0
$565$	−8.89352	−	15.4040i	−0.374153	−	0.648052i
$566$		0			0
$567$	3.29785	−	8.37402i	0.138497	−	0.351676i
$568$		0			0
$569$	14.6290	+	25.3382i	0.613280	+	1.06223i	0.990684	+	0.136183i	$0.0434836\pi$
$569$	14.6290	+	25.3382i	0.613280	+	1.06223i	−0.377404	+	0.926049i	$0.623183\pi$
$570$		0			0
$571$	18.2628	−	31.6321i	0.764275	−	1.32376i	−0.176354	−	0.984327i	$-0.556430\pi$
$571$	18.2628	−	31.6321i	0.764275	−	1.32376i	0.940629	−	0.339437i	$-0.110236\pi$
$572$		0			0
$573$	8.98909	−	2.76989i	0.375525	−	0.115714i
$574$		0			0
$575$	−1.23093			−0.0513335
$576$		0			0
$577$	9.88205			0.411395			0.205698	−	0.978616i	$-0.434054\pi$
$577$	9.88205			0.411395			0.205698	+	0.978616i	$0.434054\pi$
$578$		0			0
$579$	11.5305	+	10.7050i	0.479191	+	0.444885i
$580$		0			0
$581$	−3.04116	+	5.26744i	−0.126169	+	0.218530i
$582$		0			0
$583$	9.03730	+	15.6531i	0.374287	+	0.648284i
$584$		0			0
$585$	1.98675	+	26.7207i	0.0821419	+	1.10477i
$586$		0			0
$587$	−4.05954	−	7.03133i	−0.167555	−	0.290214i	0.770005	−	0.638038i	$-0.220254\pi$
$587$	−4.05954	−	7.03133i	−0.167555	−	0.290214i	−0.937560	+	0.347824i	$0.886921\pi$
$588$		0			0
$589$	−10.0146	+	17.3458i	−0.412644	+	0.714720i
$590$		0			0
$591$	3.31127	−	14.4881i	0.136207	−	0.595961i
$592$		0			0
$593$	29.6969			1.21950			0.609752	−	0.792592i	$-0.291269\pi$
$593$	29.6969			1.21950			0.609752	+	0.792592i	$0.291269\pi$
$594$		0			0
$595$	0.755385			0.0309678
$596$		0			0
$597$	−9.83706	+	43.0410i	−0.402604	+	1.76155i
$598$		0			0
$599$	−8.19531	+	14.1947i	−0.334851	+	0.579979i	−0.983456	−	0.181146i	$-0.942019\pi$
$599$	−8.19531	+	14.1947i	−0.334851	+	0.579979i	0.648605	+	0.761125i	$0.275353\pi$
$600$		0			0
$601$	24.4424	+	42.3355i	0.997028	+	1.72690i	0.565237	+	0.824928i	$0.308785\pi$
$601$	24.4424	+	42.3355i	0.997028	+	1.72690i	0.431790	+	0.901974i	$0.357882\pi$
$602$		0			0
$603$	14.5573	−	9.91254i	0.592819	−	0.403670i
$604$		0			0
$605$	−10.7237	−	18.5740i	−0.435981	−	0.755141i
$606$		0			0
$607$	23.6033	−	40.8820i	0.958027	−	1.65935i	0.230741	−	0.973015i	$-0.425885\pi$
$607$	23.6033	−	40.8820i	0.958027	−	1.65935i	0.727285	−	0.686335i	$-0.240782\pi$
$608$		0			0
$609$	−12.0626	−	11.1990i	−0.488801	−	0.453807i
$610$		0			0
$611$	0.837706			0.0338899
$612$		0			0
$613$	−15.6396			−0.631679			−0.315840	−	0.948813i	$-0.602286\pi$
$613$	−15.6396			−0.631679			−0.315840	+	0.948813i	$0.602286\pi$
$614$		0			0
$615$	36.3250	−	11.1932i	1.46476	−	0.451352i
$616$		0			0
$617$	−15.7793	+	27.3305i	−0.635251	+	1.10029i	0.351211	+	0.936296i	$0.385770\pi$
$617$	−15.7793	+	27.3305i	−0.635251	+	1.10029i	−0.986462	+	0.163990i	$0.947563\pi$
$618$		0			0
$619$	7.31619	+	12.6720i	0.294063	+	0.509331i	0.974766	−	0.223227i	$-0.0716592\pi$
$619$	7.31619	+	12.6720i	0.294063	+	0.509331i	−0.680704	+	0.732559i	$0.738326\pi$
$620$		0			0
$621$	−6.88977	−	17.6002i	−0.276477	−	0.706271i
$622$		0			0
$623$	−2.76112	−	4.78240i	−0.110622	−	0.191603i
$624$		0			0
$625$	13.2888	−	23.0168i	0.531550	−	0.920672i
$626$		0			0
$627$	6.68618	−	2.06028i	0.267020	−	0.0822795i
$628$		0			0
$629$	0.755385			0.0301192
$630$		0			0
$631$	36.3101			1.44548			0.722742	−	0.691118i	$-0.242881\pi$
$631$	36.3101			1.44548			0.722742	+	0.691118i	$0.242881\pi$
$632$		0			0
$633$	−21.1235	−	19.6112i	−0.839583	−	0.779476i
$634$		0			0
$635$	−17.3111	+	29.9836i	−0.686969	+	1.18986i
$636$		0			0
$637$	1.93281	+	3.34772i	0.0765806	+	0.132641i
$638$		0			0
$639$	−4.78772	−	2.30909i	−0.189399	−	0.0913462i
$640$		0			0
$641$	−5.40731	−	9.36574i	−0.213576	−	0.369924i	0.739255	−	0.673425i	$-0.235178\pi$
$641$	−5.40731	−	9.36574i	−0.213576	−	0.369924i	−0.952831	+	0.303501i	$0.901844\pi$
$642$		0			0
$643$	−6.97535	+	12.0817i	−0.275081	+	0.476454i	−0.970155	−	0.242484i	$-0.922038\pi$
$643$	−6.97535	+	12.0817i	−0.275081	+	0.476454i	0.695075	+	0.718937i	$0.255371\pi$
$644$		0			0
$645$	−0.0880566	+	0.385282i	−0.00346722	+	0.0151705i
$646$		0			0
$647$	34.5634			1.35883			0.679414	−	0.733755i	$-0.262234\pi$
$647$	34.5634			1.35883			0.679414	+	0.733755i	$0.262234\pi$
$648$		0			0
$649$	−3.21053			−0.126024
$650$		0			0
$651$	2.50768	−	10.9721i	0.0982837	−	0.430030i
$652$		0			0
$653$	13.7927	−	23.8897i	0.539751	−	0.934875i	−0.459167	−	0.888350i	$-0.651852\pi$
$653$	13.7927	−	23.8897i	0.539751	−	0.934875i	0.998917	−	0.0465252i	$-0.0148148\pi$
$654$		0			0
$655$	−12.0328	−	20.8414i	−0.470161	−	0.814342i
$656$		0			0
$657$	16.1995	+	7.81291i	0.632001	+	0.304811i
$658$		0			0
$659$	10.3059	+	17.8503i	0.401460	+	0.695348i	0.993902	−	0.110264i	$-0.0351697\pi$
$659$	10.3059	+	17.8503i	0.401460	+	0.695348i	−0.592443	+	0.805613i	$0.701836\pi$
$660$		0			0
$661$	13.5815	−	23.5239i	0.528259	−	0.914972i	−0.471198	−	0.882028i	$-0.656178\pi$
$661$	13.5815	−	23.5239i	0.528259	−	0.914972i	0.999457	−	0.0329446i	$-0.0104885\pi$
$662$		0			0
$663$	−1.60420	−	1.48935i	−0.0623020	−	0.0578417i
$664$		0			0
$665$	7.12170			0.276168
$666$		0			0
$667$	−34.5667			−1.33843
$668$		0			0
$669$	−30.7381	+	9.47162i	−1.18840	+	0.366194i
$670$		0			0
$671$	−10.0703	+	17.4423i	−0.388760	+	0.673352i
$672$		0			0
$673$	−9.52644	−	16.5003i	−0.367217	−	0.636039i	0.621912	−	0.783087i	$-0.286356\pi$
$673$	−9.52644	−	16.5003i	−0.367217	−	0.636039i	−0.989129	+	0.147048i	$0.953023\pi$
$674$		0			0
$675$	−1.73855	−	0.263602i	−0.0669167	−	0.0101460i
$676$		0			0
$677$	10.8695	+	18.8265i	0.417748	+	0.723560i	0.995713	−	0.0925013i	$-0.0294862\pi$
$677$	10.8695	+	18.8265i	0.417748	+	0.723560i	−0.577965	+	0.816062i	$0.696153\pi$
$678$		0			0
$679$	2.99178	−	5.18192i	0.114814	−	0.198864i
$680$		0			0
$681$	25.9575	−	7.99852i	0.994693	−	0.306504i
$682$		0			0
$683$	41.0808			1.57191			0.785957	−	0.618281i	$-0.212171\pi$
$683$	41.0808			1.57191			0.785957	+	0.618281i	$0.212171\pi$
$684$		0			0
$685$	−14.4716			−0.552931
$686$		0			0
$687$	−14.1411	−	13.1287i	−0.539515	−	0.500890i
$688$		0			0
$689$	26.6576	−	46.1722i	1.01557	−	1.75902i
$690$		0			0
$691$	9.03599	+	15.6508i	0.343745	+	0.595384i	0.985125	−	0.171839i	$-0.0549710\pi$
$691$	9.03599	+	15.6508i	0.343745	+	0.595384i	−0.641380	+	0.767224i	$0.721638\pi$
$692$		0			0
$693$	−3.24965	+	2.21279i	−0.123444	+	0.0840571i
$694$		0			0
$695$	23.2895	+	40.3385i	0.883420	+	1.53013i
$696$		0			0
$697$	−1.55263	+	2.68924i	−0.0588101	+	0.101862i
$698$		0			0
$699$	8.36772	−	36.6121i	0.316496	−	1.38480i
$700$		0			0
$701$	−41.5130			−1.56793			−0.783963	−	0.620808i	$-0.786805\pi$
$701$	−41.5130			−1.56793			−0.783963	+	0.620808i	$0.786805\pi$
$702$		0			0
$703$	7.12170			0.268600
$704$		0			0
$705$	−0.193226	+	0.845441i	−0.00727732	+	0.0318411i
$706$		0			0
$707$	3.85105	−	6.67022i	0.144834	−	0.250859i
$708$		0			0
$709$	−0.684536	−	1.18565i	−0.0257083	−	0.0445280i	0.852885	−	0.522099i	$-0.174851\pi$
$709$	−0.684536	−	1.18565i	−0.0257083	−	0.0445280i	−0.878593	+	0.477571i	$0.841517\pi$
$710$		0			0
$711$	3.24586	+	43.6551i	0.121729	+	1.63720i
$712$		0			0
$713$	−11.8182	−	20.4697i	−0.442594	−	0.766596i
$714$		0			0
$715$	5.85236	−	10.1366i	0.218866	−	0.379087i
$716$		0			0
$717$	−15.7467	−	14.6194i	−0.588071	−	0.545970i
$718$		0			0
$719$	−20.1854			−0.752787			−0.376394	−	0.926460i	$-0.622836\pi$
$719$	−20.1854			−0.752787			−0.376394	+	0.926460i	$0.622836\pi$
$720$		0			0
$721$	−4.06092			−0.151237
$722$		0			0
$723$	−27.6436	+	8.51808i	−1.02808	+	0.316791i
$724$		0			0
$725$	−1.60795	+	2.78505i	−0.0597178	+	0.103434i
$726$		0			0
$727$	1.69393	+	2.93397i	0.0628243	+	0.108815i	0.895727	−	0.444605i	$-0.146656\pi$
$727$	1.69393	+	2.93397i	0.0628243	+	0.108815i	−0.832903	+	0.553420i	$0.813323\pi$
$728$		0			0
$729$	−5.96193	−	26.3335i	−0.220812	−	0.975316i
$730$		0			0
$731$	−0.0161436	−	0.0279616i	−0.000597094	−	0.00103420i
$732$		0			0
$733$	8.90603	−	15.4257i	0.328952	−	0.569761i	−0.653352	−	0.757054i	$-0.726638\pi$
$733$	8.90603	−	15.4257i	0.328952	−	0.569761i	0.982304	+	0.187293i	$0.0599713\pi$
$734$		0			0
$735$	−3.82445	+	1.17846i	−0.141067	+	0.0434683i
$736$		0			0
$737$	−7.69339			−0.283390
$738$		0			0
$739$	1.15512			0.0424918			0.0212459	−	0.999774i	$-0.493237\pi$
$739$	1.15512			0.0424918			0.0212459	+	0.999774i	$0.493237\pi$
$740$		0			0
$741$	−15.1243	−	14.0415i	−0.555603	−	0.515827i
$742$		0			0
$743$	−13.5863	+	23.5322i	−0.498435	+	0.863314i	−0.999998	−	0.00180657i	$-0.999425\pi$
$743$	−13.5863	+	23.5322i	−0.498435	+	0.863314i	0.501564	+	0.865121i	$0.332758\pi$
$744$		0			0
$745$	19.6595	+	34.0513i	0.720270	+	1.24754i
$746$		0			0
$747$	1.35297	+	18.1967i	0.0495025	+	0.665784i
$748$		0			0
$749$	−7.03868	−	12.1913i	−0.257188	−	0.445462i
$750$		0			0
$751$	11.2959	−	19.5651i	0.412195	−	0.713942i	−0.582935	−	0.812519i	$-0.698096\pi$
$751$	11.2959	−	19.5651i	0.412195	−	0.713942i	0.995129	+	0.0985769i	$0.0314290\pi$
$752$		0			0
$753$	−10.4279	+	45.6261i	−0.380013	+	1.66271i
$754$		0			0
$755$	−37.8756			−1.37843
$756$		0			0
$757$	13.9989			0.508797			0.254399	−	0.967099i	$-0.418122\pi$
$757$	13.9989			0.508797			0.254399	+	0.967099i	$0.418122\pi$
$758$		0			0
$759$	−1.83958	+	8.04889i	−0.0667726	+	0.292156i
$760$		0			0
$761$	0.252336	−	0.437059i	0.00914718	−	0.0158434i	−0.861416	−	0.507901i	$-0.830422\pi$
$761$	0.252336	−	0.437059i	0.00914718	−	0.0158434i	0.870563	+	0.492057i	$0.163755\pi$
$762$		0			0
$763$	3.33653	+	5.77904i	0.120791	+	0.209215i
$764$		0			0
$765$	1.87313	−	1.27548i	0.0677232	−	0.0461150i
$766$		0			0
$767$	4.73509	+	8.20141i	0.170974	+	0.296136i
$768$		0			0
$769$	4.89218	−	8.47351i	0.176417	−	0.305563i	−0.764234	−	0.644939i	$-0.776883\pi$
$769$	4.89218	−	8.47351i	0.176417	−	0.305563i	0.940651	+	0.339376i	$0.110216\pi$
$770$		0			0
$771$	25.3270	+	23.5138i	0.912129	+	0.846828i
$772$		0			0
$773$	26.5907			0.956403			0.478201	−	0.878250i	$-0.341289\pi$
$773$	26.5907			0.956403			0.478201	+	0.878250i	$0.341289\pi$
$774$		0			0
$775$	−2.19900			−0.0789904
$776$		0			0
$777$	−3.82445	+	1.17846i	−0.137201	+	0.0422772i
$778$		0			0
$779$	−14.6381	+	25.3539i	−0.524463	+	0.908397i
$780$		0			0
$781$	1.16099	+	2.01089i	0.0415433	+	0.0719551i
$782$		0			0
$783$	−48.8213	−	7.40238i	−1.74473	−	0.264539i
$784$		0			0
$785$	23.6305	+	40.9292i	0.843408	+	1.46083i
$786$		0			0
$787$	−19.1108	+	33.1009i	−0.681227	+	1.17992i	0.293379	+	0.955996i	$0.405220\pi$
$787$	−19.1108	+	33.1009i	−0.681227	+	1.17992i	−0.974607	+	0.223924i	$0.928113\pi$
$788$		0			0
$789$	−26.2470	+	8.08773i	−0.934418	+	0.287931i
$790$		0			0
$791$	−7.69835			−0.273722
$792$		0			0
$793$	59.4093			2.10969
$794$		0			0
$795$	40.4497	+	37.5538i	1.43460	+	1.33190i
$796$		0			0
$797$	−11.1866	+	19.3758i	−0.396250	+	0.686325i	−0.993260	−	0.115909i	$-0.963022\pi$
$797$	−11.1866	+	19.3758i	−0.396250	+	0.686325i	0.597010	+	0.802234i	$0.296355\pi$
$798$		0			0
$799$	−0.0354246	−	0.0613573i	−0.00125323	−	0.00217066i
$800$		0			0
$801$	−14.9219	−	7.19675i	−0.527239	−	0.254285i
$802$		0			0
$803$	−3.92824	−	6.80392i	−0.138625	−	0.240105i
$804$		0			0
$805$	−4.20215	+	7.27833i	−0.148106	+	0.256527i
$806$		0			0
$807$	−0.268002	+	1.17261i	−0.00943411	+	0.0412780i
$808$		0			0
$809$	5.50319			0.193482			0.0967409	−	0.995310i	$-0.469158\pi$
$809$	5.50319			0.193482			0.0967409	+	0.995310i	$0.469158\pi$
$810$		0			0
$811$	12.3713			0.434414			0.217207	−	0.976126i	$-0.430305\pi$
$811$	12.3713			0.434414			0.217207	+	0.976126i	$0.430305\pi$
$812$		0			0
$813$	−3.50748	+	15.3466i	−0.123013	+	0.538229i
$814$		0			0
$815$	−19.5017	+	33.7780i	−0.683116	+	1.18319i
$816$		0			0
$817$	−0.152201	−	0.263619i	−0.00532483	−	0.00922288i
$818$		0			0
$819$	10.4455	+	5.03778i	0.364994	+	0.176034i
$820$		0			0
$821$	−21.2767	−	36.8524i	−0.742564	−	1.28616i	−0.951324	−	0.308191i	$-0.900276\pi$
$821$	−21.2767	−	36.8524i	−0.742564	−	1.28616i	0.208761	−	0.977967i	$-0.433057\pi$
$822$		0			0
$823$	−8.11754	+	14.0600i	−0.282960	+	0.490101i	−0.972112	−	0.234516i	$-0.924650\pi$
$823$	−8.11754	+	14.0600i	−0.282960	+	0.490101i	0.689153	+	0.724616i	$0.257983\pi$
$824$		0			0
$825$	0.562930	+	0.522628i	0.0195987	+	0.0181956i
$826$		0			0
$827$	−34.0199			−1.18299			−0.591494	−	0.806309i	$-0.701462\pi$
$827$	−34.0199			−1.18299			−0.591494	+	0.806309i	$0.701462\pi$
$828$		0			0
$829$	38.6394			1.34200			0.671000	−	0.741457i	$-0.265865\pi$
$829$	38.6394			1.34200			0.671000	+	0.741457i	$0.265865\pi$
$830$		0			0
$831$	23.8384	−	7.34554i	0.826944	−	0.254814i
$832$		0			0
$833$	0.163468	−	0.283135i	0.00566383	−	0.00981004i
$834$		0			0
$835$	3.71036	+	6.42654i	0.128402	+	0.222400i
$836$		0			0
$837$	−12.3082	−	31.4418i	−0.425434	−	1.08679i
$838$		0			0
$839$	−3.88612	−	6.73095i	−0.134164	−	0.232378i	0.791114	−	0.611669i	$-0.209501\pi$
$839$	−3.88612	−	6.73095i	−0.134164	−	0.232378i	−0.925278	+	0.379291i	$0.876168\pi$
$840$		0			0
$841$	−30.6540	+	53.0942i	−1.05703	+	1.83084i
$842$		0			0
$843$	−15.5049	+	4.77768i	−0.534018	+	0.164552i
$844$		0			0
$845$	−4.48923			−0.154434
$846$		0			0
$847$	−9.28259			−0.318954
$848$		0			0
$849$	−24.2269	−	22.4924i	−0.831464	−	0.771938i
$850$		0			0
$851$	−4.20215	+	7.27833i	−0.144048	+	0.249498i
$852$		0			0
$853$	−10.0272	−	17.3676i	−0.343324	−	0.594654i	0.641724	−	0.766936i	$-0.278219\pi$
$853$	−10.0272	−	17.3676i	−0.343324	−	0.594654i	−0.985048	+	0.172282i	$0.944886\pi$
$854$		0			0
$855$	17.6597	−	12.0251i	0.603949	−	0.411249i
$856$		0			0
$857$	−0.837910	−	1.45130i	−0.0286225	−	0.0495756i	0.851359	−	0.524583i	$-0.175779\pi$
$857$	−0.837910	−	1.45130i	−0.0286225	−	0.0495756i	−0.879982	+	0.475007i	$0.842445\pi$
$858$		0			0
$859$	18.7256	−	32.4336i	0.638908	−	1.10662i	−0.346765	−	0.937952i	$-0.612720\pi$
$859$	18.7256	−	32.4336i	0.638908	−	1.10662i	0.985673	−	0.168669i	$-0.0539468\pi$
$860$		0			0
$861$	3.66541	−	16.0376i	0.124917	−	0.546561i
$862$		0			0
$863$	30.0265			1.02211			0.511057	−	0.859547i	$-0.329254\pi$
$863$	30.0265			1.02211			0.511057	+	0.859547i	$0.329254\pi$
$864$		0			0
$865$	−1.41436			−0.0480897
$866$		0			0
$867$	6.51923	−	28.5242i	0.221405	−	0.968733i
$868$		0			0
$869$	9.56132	−	16.5607i	0.324346	−	0.561783i
$870$		0			0
$871$	11.3467	+	19.6531i	0.384468	+	0.665918i
$872$		0			0
$873$	−1.33100	−	17.9013i	−0.0450475	−	0.605866i
$874$		0			0
$875$	−5.38530	−	9.32762i	−0.182056	−	0.315331i
$876$		0			0
$877$	−11.3517	+	19.6617i	−0.383318	+	0.663927i	−0.991534	−	0.129845i	$-0.958552\pi$
$877$	−11.3517	+	19.6617i	−0.383318	+	0.663927i	0.608216	+	0.793772i	$0.291885\pi$
$878$		0			0
$879$	−23.1086	−	21.4542i	−0.779434	−	0.723633i
$880$		0			0
$881$	−36.0266			−1.21377			−0.606883	−	0.794791i	$-0.707580\pi$
$881$	−36.0266			−1.21377			−0.606883	+	0.794791i	$0.707580\pi$
$882$		0			0
$883$	−47.7159			−1.60577			−0.802884	−	0.596135i	$-0.796702\pi$
$883$	−47.7159			−1.60577			−0.802884	+	0.596135i	$0.796702\pi$
$884$		0			0
$885$	−9.36934	+	2.88706i	−0.314947	+	0.0970475i
$886$		0			0
$887$	−5.70962	+	9.88935i	−0.191710	+	0.332052i	−0.945817	−	0.324700i	$-0.894737\pi$
$887$	−5.70962	+	9.88935i	−0.191710	+	0.332052i	0.754107	+	0.656752i	$0.228070\pi$
$888$		0			0
$889$	7.49235	+	12.9771i	0.251285	+	0.435239i
$890$		0			0
$891$	−4.32184	+	10.9741i	−0.144787	+	0.367648i
$892$		0			0
$893$	−0.333980	−	0.578471i	−0.0111762	−	0.0193578i
$894$		0			0
$895$	−5.06155	+	8.76686i	−0.169189	+	0.293044i
$896$		0			0
$897$	23.2743	−	7.17174i	0.777107	−	0.239457i
$898$		0			0
$899$	−61.7516			−2.05953
$900$		0			0
$901$	−4.50915			−0.150221
$902$		0			0
$903$	0.125356	+	0.116382i	0.00417160	+	0.00387295i
$904$		0			0
$905$	−4.04559	+	7.00716i	−0.134480	+	0.232926i
$906$		0			0
$907$	1.81546	+	3.14448i	0.0602815	+	0.104411i	0.894591	−	0.446885i	$-0.147467\pi$
$907$	1.81546	+	3.14448i	0.0602815	+	0.104411i	−0.834310	+	0.551296i	$0.814133\pi$
$908$		0			0
$909$	−1.71328	−	23.0427i	−0.0568258	−	0.764278i
$910$		0			0
$911$	1.24848	+	2.16242i	0.0413638	+	0.0716443i	0.885966	−	0.463750i	$-0.153496\pi$
$911$	1.24848	+	2.16242i	0.0413638	+	0.0716443i	−0.844602	+	0.535394i	$0.820163\pi$
$912$		0			0
$913$	3.98544	−	6.90298i	0.131899	−	0.228455i
$914$		0			0
$915$	−13.7034	+	59.9579i	−0.453021	+	1.98215i
$916$		0			0
$917$	−10.4158			−0.343959
$918$		0			0
$919$	−0.454816			−0.0150030			−0.00750149	−	0.999972i	$-0.502388\pi$
$919$	−0.454816			−0.0150030			−0.00750149	+	0.999972i	$0.502388\pi$
$920$		0			0
$921$	−10.3631	+	45.3429i	−0.341477	+	1.49410i
$922$		0			0
$923$	3.42459	−	5.93156i	0.112722	−	0.195240i
$924$		0			0
$925$	0.390945	+	0.677137i	0.0128542	+	0.0222641i
$926$		0			0
$927$	−10.0699	+	6.85691i	−0.330738	+	0.225211i
$928$		0			0
$929$	16.6846	+	28.8985i	0.547403	+	0.948129i	0.998451	+	0.0556301i	$0.0177168\pi$
$929$	16.6846	+	28.8985i	0.547403	+	0.948129i	−0.451049	+	0.892499i	$0.648950\pi$
$930$		0			0
$931$	1.54116	−	2.66937i	0.0505095	−	0.0874850i
$932$		0			0
$933$	−2.00617	−	1.86255i	−0.0656792	−	0.0609771i
$934$		0			0
$935$	−0.989932			−0.0323742
$936$		0			0
$937$	−5.28675			−0.172711			−0.0863553	−	0.996264i	$-0.527522\pi$
$937$	−5.28675			−0.172711			−0.0863553	+	0.996264i	$0.527522\pi$
$938$		0			0
$939$	33.9713	−	10.4679i	1.10861	−	0.341607i
$940$		0			0
$941$	−22.3084	+	38.6393i	−0.727234	+	1.25961i	0.230814	+	0.972998i	$0.425861\pi$
$941$	−22.3084	+	38.6393i	−0.727234	+	1.25961i	−0.958048	+	0.286608i	$0.907472\pi$
$942$		0			0
$943$	−17.2743	−	29.9200i	−0.562530	−	0.974330i
$944$		0			0
$945$	−7.49366	+	9.37988i	−0.243769	+	0.305127i
$946$		0			0
$947$	−14.3695	−	24.8887i	−0.466945	−	0.808773i	0.532342	−	0.846530i	$-0.321312\pi$
$947$	−14.3695	−	24.8887i	−0.466945	−	0.808773i	−0.999287	+	0.0377568i	$0.987979\pi$
$948$		0			0
$949$	−11.5872	+	20.0697i	−0.376138	+	0.651490i
$950$		0			0
$951$	52.7438	−	16.2524i	1.71033	−	0.527021i
$952$		0			0
$953$	−52.6957			−1.70698			−0.853491	−	0.521107i	$-0.825519\pi$
$953$	−52.6957			−1.70698			−0.853491	+	0.521107i	$0.825519\pi$
$954$		0			0
$955$	−12.5475			−0.406029
$956$		0			0
$957$	15.8080	+	14.6763i	0.511001	+	0.474417i
$958$		0			0
$959$	−3.13170	+	5.42426i	−0.101128	+	0.175159i
$960$		0			0
$961$	−5.61255	−	9.72122i	−0.181050	−	0.313588i
$962$		0			0
$963$	−38.0391	−	18.3460i	−1.22579	−	0.591193i
$964$		0			0
$965$	−10.4941	−	18.1764i	−0.337818	−	0.585118i
$966$		0			0
$967$	22.1564	−	38.3759i	0.712500	−	1.23409i	−0.251415	−	0.967879i	$-0.580896\pi$
$967$	22.1564	−	38.3759i	0.712500	−	1.23409i	0.963916	−	0.266207i	$-0.0857706\pi$
$968$		0			0
$969$	−0.388890	+	1.70155i	−0.0124930	+	0.0546616i
$970$		0			0
$971$	49.8993			1.60134			0.800672	−	0.599103i	$-0.204476\pi$
$971$	49.8993			1.60134			0.800672	+	0.599103i	$0.204476\pi$
$972$		0			0
$973$	20.1597			0.646290
$974$		0			0
$975$	0.504830	−	2.20883i	0.0161675	−	0.0707392i
$976$		0			0
$977$	16.0981	−	27.8827i	0.515022	−	0.892045i	−0.484826	−	0.874611i	$-0.661117\pi$
$977$	16.0981	−	27.8827i	0.515022	−	0.892045i	0.999848	−	0.0174342i	$-0.00554975\pi$
$978$		0			0
$979$	3.61845	+	6.26733i	0.115646	+	0.200305i
$980$		0			0
$981$	18.0316	+	8.69654i	0.575704	+	0.277659i
$982$		0			0
$983$	−6.17356	−	10.6929i	−0.196906	−	0.341051i	0.750618	−	0.660737i	$-0.229756\pi$
$983$	−6.17356	−	10.6929i	−0.196906	−	0.341051i	−0.947524	+	0.319686i	$0.896423\pi$
$984$		0			0
$985$	−9.91251	+	17.1690i	−0.315839	+	0.547049i
$986$		0			0
$987$	0.275075	+	0.255382i	0.00875572	+	0.00812889i
$988$		0			0
$989$	0.359223			0.0114226
$990$		0			0
$991$	−6.80483			−0.216163			−0.108081	−	0.994142i	$-0.534471\pi$
$991$	−6.80483			−0.216163			−0.108081	+	0.994142i	$0.534471\pi$
$992$		0			0
$993$	−56.5149	+	17.4145i	−1.79345	+	0.552631i
$994$		0			0
$995$	29.4479	−	51.0052i	0.933561	−	1.61698i
$996$		0			0
$997$	−0.812415	−	1.40714i	−0.0257295	−	0.0445647i	0.852874	−	0.522117i	$-0.174858\pi$
$997$	−0.812415	−	1.40714i	−0.0257295	−	0.0445647i	−0.878603	+	0.477552i	$0.841524\pi$
$998$		0			0
$999$	−7.49366	+	9.37988i	−0.237089	+	0.296766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.l.337.2		8
3.2	odd	2		3024.2.r.m.1009.1		8
4.3	odd	2		504.2.r.e.337.3	yes	8
9.2	odd	6		3024.2.r.m.2017.1		8
9.4	even	3		9072.2.a.cj.1.1		4
9.5	odd	6		9072.2.a.cg.1.4		4
9.7	even	3	inner	1008.2.r.l.673.2		8
12.11	even	2		1512.2.r.e.1009.1		8
36.7	odd	6		504.2.r.e.169.3	✓	8
36.11	even	6		1512.2.r.e.505.1		8
36.23	even	6		4536.2.a.y.1.4		4
36.31	odd	6		4536.2.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.3	✓	8	36.7	odd	6
504.2.r.e.337.3	yes	8	4.3	odd	2
1008.2.r.l.337.2		8	1.1	even	1	trivial
1008.2.r.l.673.2		8	9.7	even	3	inner
1512.2.r.e.505.1		8	36.11	even	6
1512.2.r.e.1009.1		8	12.11	even	2
3024.2.r.m.1009.1		8	3.2	odd	2
3024.2.r.m.2017.1		8	9.2	odd	6
4536.2.a.y.1.4		4	36.23	even	6
4536.2.a.z.1.1		4	36.31	odd	6
9072.2.a.cg.1.4		4	9.5	odd	6
9072.2.a.cj.1.1		4	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.385911 + 1.68851i) q^{3} +(1.15525 - 2.00095i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.70215 - 1.30323i) q^{9} +O(q^{10})\)	\(q+(-0.385911 + 1.68851i) q^{3} +(1.15525 - 2.00095i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-2.70215 - 1.30323i) q^{9} +(0.655250 + 1.13493i) q^{11} +(1.93281 - 3.34772i) q^{13} +(2.93281 + 2.72284i) q^{15} -0.326936 q^{17} -3.08232 q^{19} +(1.65525 - 0.510048i) q^{21} +(1.81872 - 3.15011i) q^{23} +(-0.169204 - 0.293069i) q^{25} +(3.24331 - 4.05968i) q^{27} +(-4.75152 - 8.22988i) q^{29} +(3.24904 - 5.62751i) q^{31} +(-2.16920 + 0.668417i) q^{33} -2.31050 q^{35} -2.31050 q^{37} +(4.90677 + 4.55549i) q^{39} +(4.74904 - 8.22558i) q^{41} +(0.0493786 + 0.0855263i) q^{43} +(-5.72935 + 3.90131i) q^{45} +(0.108354 + 0.187674i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.126168 - 0.552035i) q^{51} +13.7921 q^{53} +3.02791 q^{55} +(1.18950 - 5.20454i) q^{57} +(-1.22493 + 2.12163i) q^{59} +(7.68433 + 13.3097i) q^{61} +(0.222443 + 2.99174i) q^{63} +(-4.46575 - 7.73490i) q^{65} +(-2.93529 + 5.08407i) q^{67} +(4.61714 + 4.28659i) q^{69} +1.77182 q^{71} -5.99504 q^{73} +(0.560149 - 0.172604i) q^{75} +(0.655250 - 1.13493i) q^{77} +(-7.29594 - 12.6369i) q^{79} +(5.60318 + 7.04303i) q^{81} +(-3.04116 - 5.26744i) q^{83} +(-0.377692 + 0.654183i) q^{85} +(15.7299 - 4.84701i) q^{87} +5.52224 q^{89} -3.86561 q^{91} +(8.24827 + 7.65776i) q^{93} +(-3.56085 + 6.16757i) q^{95} +(2.99178 + 5.18192i) q^{97} +(-0.291511 - 3.92068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9	\( 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9} - 7 q^{11} + 3 q^{13} + 11 q^{15} + 6 q^{17} + 8 q^{19} + q^{21} - 2 q^{23} - 5 q^{25} - 11 q^{27} - 9 q^{29} - 3 q^{31} - 21 q^{33} + 6 q^{35} + 6 q^{37} - 2 q^{39} + 9 q^{41} - 8 q^{43} + 7 q^{45} - 3 q^{47} - 4 q^{49} + 18 q^{51} + 12 q^{53} + 56 q^{55} + 34 q^{57} - 10 q^{59} + 20 q^{61} + 2 q^{63} + q^{65} - 11 q^{67} - 17 q^{69} + 6 q^{71} - 48 q^{73} - 52 q^{75} - 7 q^{77} - 21 q^{79} - 25 q^{81} - 8 q^{83} + 9 q^{85} + 15 q^{87} + 12 q^{89} - 6 q^{91} + 29 q^{93} - 36 q^{95} + 16 q^{97} - 18 q^{99}+O(q^{100}) \) 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9 - 7 * q^11 + 3 * q^13 + 11 * q^15 + 6 * q^17 + 8 * q^19 + q^21 - 2 * q^23 - 5 * q^25 - 11 * q^27 - 9 * q^29 - 3 * q^31 - 21 * q^33 + 6 * q^35 + 6 * q^37 - 2 * q^39 + 9 * q^41 - 8 * q^43 + 7 * q^45 - 3 * q^47 - 4 * q^49 + 18 * q^51 + 12 * q^53 + 56 * q^55 + 34 * q^57 - 10 * q^59 + 20 * q^61 + 2 * q^63 + q^65 - 11 * q^67 - 17 * q^69 + 6 * q^71 - 48 * q^73 - 52 * q^75 - 7 * q^77 - 21 * q^79 - 25 * q^81 - 8 * q^83 + 9 * q^85 + 15 * q^87 + 12 * q^89 - 6 * q^91 + 29 * q^93 - 36 * q^95 + 16 * q^97 - 18 * q^99

Introduction

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