LMFDB - Embedded newform 504.2.r.e.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, degree $2$, 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:	$4.02446026187$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.3
Root			$1.65525 - 0.510048i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.e.337.3

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.999813	+	0.0193259i	$0.00615202\pi$
$5$	1.15525	+	2.00095i	0.516643	+	0.894853i	−0.483170	+	0.875527i	$0.660515\pi$
$6$		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	$-0.896637\pi$
$11$	−0.655250	+	1.13493i	−0.197565	+	0.342193i	0.750173	+	0.661241i	$0.229970\pi$
$12$		0			0
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	0.999111	+	0.0421566i	$0.0134228\pi$
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	−0.463047	+	0.886334i	$0.653244\pi$
$14$		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	$-0.384969\pi$
$19$	3.08232			0.707133			0.353566	+	0.935409i	$0.384969\pi$
$20$		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	$-0.290477\pi$
$23$	−1.81872	−	3.15011i	−0.379229	−	0.656844i	−0.990950	+	0.134230i	$0.957144\pi$
$24$		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	−0.0335990	+	0.999435i	$0.510697\pi$
$29$	−4.75152	+	8.22988i	−0.882336	+	1.52825i	−0.848737	+	0.528815i	$0.822636\pi$
$30$		0			0
$31$	−3.24904	−	5.62751i	−0.583545	−	1.01073i	−0.995055	−	0.0993246i	$-0.968332\pi$
$31$	−3.24904	−	5.62751i	−0.583545	−	1.01073i	0.411510	−	0.911405i	$-0.365002\pi$
$32$		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	0.951732	+	0.306931i	$0.0993020\pi$
$41$	4.74904	+	8.22558i	0.741676	+	1.28462i	−0.210056	+	0.977689i	$0.567365\pi$
$42$		0			0
$43$	−0.0493786	+	0.0855263i	−0.00753017	+	0.0130426i	−0.869766	−	0.493465i	$-0.835730\pi$
$43$	−0.0493786	+	0.0855263i	−0.00753017	+	0.0130426i	0.862236	+	0.506507i	$0.169064\pi$
$44$		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	$-0.838364\pi$
$47$	−0.108354	+	0.187674i	−0.0158050	+	0.0273750i	0.858015	+	0.513625i	$0.171698\pi$
$48$		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	$-0.115688\pi$
$59$	1.22493	+	2.12163i	0.159472	+	0.276213i	−0.775207	+	0.631708i	$0.782354\pi$
$60$		0			0
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.337057	−	0.941484i	$-0.390568\pi$
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.646821	−	0.762642i	$-0.276098\pi$
$62$		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	$-0.0499200\pi$
$67$	2.93529	+	5.08407i	0.358603	+	0.621118i	−0.629125	+	0.777304i	$0.716587\pi$
$68$		0			0
$69$	4.61714	−	4.28659i	0.555838	−	0.516045i
$70$		0			0
$71$	−1.77182			−0.210277			−0.105138	−	0.994458i	$-0.533529\pi$
$71$	−1.77182			−0.210277			−0.105138	+	0.994458i	$0.533529\pi$
$72$		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	−0.0841876	−	0.996450i	$-0.526829\pi$
$79$	7.29594	−	12.6369i	0.820857	−	1.42177i	0.905045	−	0.425316i	$-0.139837\pi$
$80$		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	$-0.724999\pi$
$83$	3.04116	−	5.26744i	0.333811	−	0.578177i	0.983256	+	0.182231i	$0.0583320\pi$
$84$		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	−0.673217	−	0.739445i	$-0.735088\pi$
$97$	2.99178	−	5.18192i	0.303769	−	0.526144i	0.976987	+	0.213301i	$0.0684214\pi$
$98$		0			0
$99$	0.291511	−	3.92068i	0.0292980	−	0.394043i
$100$		0			0
$101$	3.85105	−	6.67022i	0.383194	−	0.663712i	−0.608323	−	0.793690i	$-0.708157\pi$
$101$	3.85105	−	6.67022i	0.383194	−	0.663712i	0.991517	+	0.129978i	$0.0414907\pi$
$102$		0			0
$103$	−2.03046	−	3.51686i	−0.200067	−	0.346526i	0.748483	−	0.663154i	$-0.230783\pi$
$103$	−2.03046	−	3.51686i	−0.200067	−	0.346526i	−0.948550	+	0.316628i	$0.897449\pi$
$104$		0			0
$105$	0.891646	+	3.90131i	0.0870158	+	0.380728i
$106$		0			0
$107$	−14.0774			−1.36091			−0.680455	−	0.732790i	$-0.738218\pi$
$107$	−14.0774			−1.36091			−0.680455	+	0.732790i	$0.738218\pi$
$108$		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	0.988306	−	0.152482i	$-0.0487265\pi$
$113$	3.84918	+	6.66697i	0.362100	+	0.627176i	−0.626206	+	0.779658i	$0.715393\pi$
$114$		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	$-0.268500\pi$
$127$	14.9847			1.32968			0.664838	+	0.746987i	$0.268500\pi$
$128$		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	$-0.317033\pi$
$131$	−5.20788	−	9.02032i	−0.455015	−	0.788109i	−0.998689	+	0.0511876i	$0.983699\pi$
$132$		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	−0.968231	−	0.250058i	$-0.919550\pi$
$137$	−3.13170	+	5.42426i	−0.267559	+	0.463426i	0.700672	+	0.713484i	$0.252884\pi$
$138$		0			0
$139$	10.0798	+	17.4588i	0.854961	+	1.48084i	0.876681	+	0.481071i	$0.159752\pi$
$139$	10.0798	+	17.4588i	0.854961	+	1.48084i	−0.0217207	+	0.999764i	$0.506914\pi$
$140$		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	−0.969479	−	0.245174i	$-0.921155\pi$
$149$	−8.50878	−	14.7376i	−0.697067	−	1.20736i	0.272412	−	0.962181i	$-0.412179\pi$
$150$		0			0
$151$	8.19641	−	14.1966i	0.667014	−	1.15530i	−0.311721	−	0.950174i	$-0.600905\pi$
$151$	8.19641	−	14.1966i	0.667014	−	1.15530i	0.978735	−	0.205129i	$-0.0657614\pi$
$152$		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	−0.908435	−	0.418025i	$-0.862722\pi$
$157$	−10.2274	−	17.7144i	−0.816238	−	1.41377i	0.0921971	−	0.995741i	$-0.470611\pi$
$158$		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	$-0.270086\pi$
$163$	16.8810			1.32222			0.661110	+	0.750289i	$0.270086\pi$
$164$		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	$-0.127009\pi$
$167$	1.60587	+	2.78145i	0.124266	+	0.215235i	−0.797180	+	0.603742i	$0.793676\pi$
$168$		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	−0.877426	−	0.479712i	$-0.840741\pi$
$173$	−0.306072	+	0.530133i	−0.0232703	+	0.0403053i	0.854156	+	0.520017i	$0.174074\pi$
$174$		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	$-0.447645\pi$
$179$	4.38135			0.327477			0.163739	+	0.986504i	$0.447645\pi$
$180$		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	$-0.770384\pi$
$191$	2.71533	−	4.70309i	0.196474	−	0.340303i	0.947383	+	0.320103i	$0.103717\pi$
$192$		0			0
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	0.981902	−	0.189389i	$-0.0606507\pi$
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	−0.654967	+	0.755658i	$0.727317\pi$
$194$		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	$-0.859001\pi$
$199$	−25.4905			−1.80697			−0.903487	+	0.428616i	$0.859001\pi$
$200$		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	0.996275	+	0.0862336i	$0.0274832\pi$
$211$	8.32066	+	14.4118i	0.572818	+	0.992150i	−0.423457	+	0.905916i	$0.639184\pi$
$212$		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	0.367384	+	0.930069i	$0.380254\pi$
$223$	−9.28503	+	16.0821i	−0.621772	+	1.07694i	−0.989156	+	0.146871i	$0.953080\pi$
$224$		0			0
$225$	0.0752763	−	1.01243i	0.00501842	−	0.0674952i
$226$		0			0
$227$	7.84096	−	13.5809i	0.520423	−	0.901399i	−0.479295	−	0.877654i	$-0.659108\pi$
$227$	7.84096	−	13.5809i	0.520423	−	0.901399i	0.999718	−	0.0237449i	$-0.00755895\pi$
$228$		0			0
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	0.621175	−	0.783672i	$-0.286656\pi$
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	−0.989267	+	0.146118i	$0.953322\pi$
$230$		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	$-0.0352529\pi$
$239$	6.20271	+	10.7434i	0.401220	+	0.694934i	−0.592653	+	0.805458i	$0.701920\pi$
$240$		0			0
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	−0.461129	−	0.887333i	$-0.652555\pi$
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	0.999017	−	0.0443176i	$-0.0141114\pi$
$242$		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	$-0.825091\pi$
$251$	−27.0215			−1.70558			−0.852790	+	0.522255i	$0.825091\pi$
$252$		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	0.989054	+	0.147556i	$0.0471406\pi$
$257$	9.97645	+	17.2797i	0.622314	+	1.07788i	−0.366740	+	0.930324i	$0.619526\pi$
$258$		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	$-0.995930\pi$
$263$	−7.92841	+	13.7324i	−0.488887	+	0.846776i	0.511032	+	0.859562i	$0.329263\pi$
$264$		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	$-0.589027\pi$
$271$	−9.08883			−0.552107			−0.276053	+	0.961142i	$0.589027\pi$
$272$		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	−0.997101	−	0.0760880i	$-0.975757\pi$
$277$	−7.20084	+	12.4722i	−0.432656	+	0.749383i	0.564445	+	0.825471i	$0.309090\pi$
$278$		0			0
$279$	16.1133	+	10.9721i	0.964679	+	0.656882i
$280$		0			0
$281$	4.68356	−	8.11216i	0.279398	−	0.483931i	−0.691837	−	0.722053i	$-0.743199\pi$
$281$	4.68356	−	8.11216i	0.279398	−	0.483931i	0.971235	+	0.238122i	$0.0765319\pi$
$282$		0			0
$283$	9.54310	+	16.5291i	0.567279	+	0.982556i	0.996834	+	0.0795148i	$0.0253371\pi$
$283$	9.54310	+	16.5291i	0.567279	+	0.982556i	−0.429555	+	0.903041i	$0.641330\pi$
$284$		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	−0.999312	−	0.0370944i	$-0.988190\pi$
$293$	−9.10262	−	15.7662i	−0.531781	−	0.921071i	0.467531	−	0.883977i	$-0.345144\pi$
$294$		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	$-0.777910\pi$
$307$	−26.8537			−1.53262			−0.766312	+	0.642469i	$0.777910\pi$
$308$		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	$-0.152398\pi$
$311$	0.790243	+	1.36874i	0.0448106	+	0.0776142i	−0.842750	+	0.538305i	$0.819065\pi$
$312$		0			0
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	0.415451	+	0.909616i	$0.363624\pi$
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	−0.995476	+	0.0950169i	$0.969709\pi$
$314$		0			0
$315$	−6.24331	+	3.01111i	−0.351770	+	0.169657i
$316$		0			0
$317$	−15.9323	+	27.5955i	−0.894845	+	1.54992i	−0.0608495	+	0.998147i	$0.519381\pi$
$317$	−15.9323	+	27.5955i	−0.894845	+	1.54992i	−0.833996	+	0.551771i	$0.813952\pi$
$318$		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	−0.169744	+	0.985488i	$0.554294\pi$
$331$	−17.0714	+	29.5686i	−0.938330	+	1.62524i	−0.768586	+	0.639747i	$0.779039\pi$
$332$		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	0.859057	−	0.511880i	$-0.171051\pi$
$337$	−0.252833	−	0.437920i	−0.0137727	−	0.0238550i	−0.872830	+	0.488025i	$0.837717\pi$
$338$		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	−0.941235	−	0.337753i	$-0.890333\pi$
$347$	−14.2154	−	24.6217i	−0.763120	−	1.32176i	0.178114	−	0.984010i	$-0.443000\pi$
$348$		0			0
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.177599	−	0.984103i	$-0.443167\pi$
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.763459	−	0.645856i	$-0.223500\pi$
$350$		0			0
$351$	7.32197	−	18.7042i	0.390818	−	0.998359i
$352$		0			0
$353$	−0.496139	+	0.859339i	−0.0264068	+	0.0457380i	−0.878927	−	0.476957i	$-0.841740\pi$
$353$	−0.496139	+	0.859339i	−0.0264068	+	0.0457380i	0.852520	+	0.522695i	$0.175073\pi$
$354$		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	$-0.710698\pi$
$359$	−23.2914			−1.22928			−0.614638	+	0.788810i	$0.710698\pi$
$360$		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	$-0.733831\pi$
$367$	5.89144	−	10.2043i	0.307531	−	0.532659i	0.977822	+	0.209440i	$0.0671640\pi$
$368$		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	0.987653	−	0.156659i	$-0.0500723\pi$
$373$	6.91714	+	11.9808i	0.358156	+	0.620344i	−0.629497	+	0.777003i	$0.716739\pi$
$374$		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	$-0.687069\pi$
$379$	−21.5877			−1.10889			−0.554443	+	0.832222i	$0.687069\pi$
$380$		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	$-0.306437\pi$
$383$	−8.31989	−	14.4105i	−0.425127	−	0.736341i	−0.996432	+	0.0843965i	$0.973104\pi$
$384$		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	−0.519736	−	0.854327i	$-0.673970\pi$
$389$	9.46709	−	16.3975i	0.480000	−	0.831385i	0.999737	+	0.0229417i	$0.00730320\pi$
$390$		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	−0.693056	−	0.720884i	$-0.743736\pi$
$401$	−19.4409	−	33.6726i	−0.970832	−	1.68153i	−0.277776	−	0.960646i	$-0.589597\pi$
$402$		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	0.663290	−	0.748363i	$-0.269160\pi$
$409$	−6.39993	−	11.0850i	−0.316456	−	0.548119i	−0.979746	+	0.200244i	$0.935826\pi$
$410$		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	$-0.175952\pi$
$419$	−0.597046	−	1.03411i	−0.0291676	−	0.0505197i	−0.880241	+	0.474527i	$0.842619\pi$
$420$		0			0
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	−0.993626	−	0.112726i	$-0.964042\pi$
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	0.594437	+	0.804142i	$0.297375\pi$
$422$		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	$-0.719267\pi$
$431$	−26.3928			−1.27130			−0.635649	+	0.771978i	$0.719267\pi$
$432$		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	$-0.670740\pi$
$439$	10.2431	−	17.7416i	0.488877	−	0.846759i	0.999918	+	0.0127969i	$0.00407350\pi$
$440$		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	$-0.774023\pi$
$443$	3.89909	−	6.75343i	0.185252	−	0.320865i	0.943661	+	0.330913i	$0.107357\pi$
$444$		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	−0.999505	−	0.0314501i	$-0.989987\pi$
$457$	−10.1012	+	17.4959i	−0.472516	+	0.818422i	0.526989	+	0.849872i	$0.323321\pi$
$458$		0			0
$459$	1.06035	+	1.32725i	0.0494930	+	0.0619509i
$460$		0			0
$461$	6.02197	−	10.4304i	0.280471	−	0.485790i	−0.691030	−	0.722826i	$-0.742843\pi$
$461$	6.02197	−	10.4304i	0.280471	−	0.485790i	0.971501	+	0.237036i	$0.0761760\pi$
$462$		0			0
$463$	11.6437	+	20.1675i	0.541130	+	0.937265i	0.998839	+	0.0481633i	$0.0153368\pi$
$463$	11.6437	+	20.1675i	0.541130	+	0.937265i	−0.457709	+	0.889102i	$0.651330\pi$
$464$		0			0
$465$	24.8516	+	7.65776i	1.15247	+	0.355120i
$466$		0			0
$467$	34.0682			1.57649			0.788243	−	0.615364i	$-0.210991\pi$
$467$	34.0682			1.57649			0.788243	+	0.615364i	$0.210991\pi$
$468$		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	$-0.692270\pi$
$479$	9.38477	−	16.2549i	0.428801	−	0.742705i	0.996767	+	0.0803471i	$0.0256029\pi$
$480$		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	$-0.601859\pi$
$487$	−13.8837			−0.629132			−0.314566	+	0.949236i	$0.601859\pi$
$488$		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	$-0.232386\pi$
$491$	−4.54250	−	7.86784i	−0.205000	−	0.355071i	−0.950133	+	0.311846i	$0.899053\pi$
$492$		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	0.999312	+	0.0370810i	$0.0118060\pi$
$499$	11.8788	+	20.5747i	0.531769	+	0.921051i	−0.467543	+	0.883970i	$0.654861\pi$
$500$		0			0
$501$	−4.07679	+	3.78492i	−0.182138	+	0.169098i
$502$		0			0
$503$	−22.5612			−1.00595			−0.502977	−	0.864300i	$-0.667762\pi$
$503$	−22.5612			−1.00595			−0.502977	+	0.864300i	$0.667762\pi$
$504$		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	0.765162	−	0.643837i	$-0.222659\pi$
$509$	−3.94814	−	6.83838i	−0.174998	−	0.303106i	−0.940161	+	0.340732i	$0.889325\pi$
$510$		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	$-0.333008\pi$
$523$	22.9097			1.00177			0.500885	+	0.865514i	$0.333008\pi$
$524$		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	$-0.815567\pi$
$547$	1.30472	−	2.25985i	0.0557859	−	0.0966240i	0.892570	+	0.450909i	$0.148900\pi$
$548$		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	0.758677	+	0.651467i	$0.225846\pi$
$563$	22.3876	+	38.7765i	0.943525	+	1.63423i	0.184848	+	0.982767i	$0.440821\pi$
$564$		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	−0.377404	−	0.926049i	$-0.623183\pi$
$569$	14.6290	−	25.3382i	0.613280	−	1.06223i	0.990684	−	0.136183i	$-0.0434836\pi$
$570$		0			0
$571$	−18.2628	−	31.6321i	−0.764275	−	1.32376i	−0.940629	−	0.339437i	$-0.889764\pi$
$571$	−18.2628	−	31.6321i	−0.764275	−	1.32376i	0.176354	−	0.984327i	$-0.443570\pi$
$572$		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	$-0.779746\pi$
$587$	4.05954	−	7.03133i	0.167555	−	0.290214i	0.937560	+	0.347824i	$0.113079\pi$
$588$		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	$-0.0579806\pi$
$599$	8.19531	+	14.1947i	0.334851	+	0.579979i	−0.648605	+	0.761125i	$0.724647\pi$
$600$		0			0
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.431790	−	0.901974i	$-0.357882\pi$
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.565237	−	0.824928i	$-0.308785\pi$
$602$		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	−0.727285	−	0.686335i	$-0.759218\pi$
$607$	−23.6033	−	40.8820i	−0.958027	−	1.65935i	−0.230741	−	0.973015i	$-0.574115\pi$
$608$		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	−0.986462	−	0.163990i	$-0.947563\pi$
$617$	−15.7793	−	27.3305i	−0.635251	−	1.10029i	0.351211	−	0.936296i	$-0.385770\pi$
$618$		0			0
$619$	−7.31619	+	12.6720i	−0.294063	+	0.509331i	−0.974766	−	0.223227i	$-0.928341\pi$
$619$	−7.31619	+	12.6720i	−0.294063	+	0.509331i	0.680704	+	0.732559i	$0.261674\pi$
$620$		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	$-0.757119\pi$
$631$	−36.3101			−1.44548			−0.722742	+	0.691118i	$0.757119\pi$
$632$		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	−0.952831	−	0.303501i	$-0.901844\pi$
$641$	−5.40731	+	9.36574i	−0.213576	+	0.369924i	0.739255	+	0.673425i	$0.235178\pi$
$642$		0			0
$643$	6.97535	+	12.0817i	0.275081	+	0.476454i	0.970155	−	0.242484i	$-0.0779621\pi$
$643$	6.97535	+	12.0817i	0.275081	+	0.476454i	−0.695075	+	0.718937i	$0.744629\pi$
$644$		0			0
$645$	−0.0880566	−	0.385282i	−0.00346722	−	0.0151705i
$646$		0			0
$647$	−34.5634			−1.35883			−0.679414	−	0.733755i	$-0.737766\pi$
$647$	−34.5634			−1.35883			−0.679414	+	0.733755i	$0.737766\pi$
$648$		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	0.998917	+	0.0465252i	$0.0148148\pi$
$653$	13.7927	+	23.8897i	0.539751	+	0.934875i	−0.459167	+	0.888350i	$0.651852\pi$
$654$		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	$-0.964830\pi$
$659$	−10.3059	+	17.8503i	−0.401460	+	0.695348i	0.592443	+	0.805613i	$0.298164\pi$
$660$		0			0
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	0.999457	+	0.0329446i	$0.0104885\pi$
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	−0.471198	+	0.882028i	$0.656178\pi$
$662$		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	−0.989129	−	0.147048i	$-0.953023\pi$
$673$	−9.52644	+	16.5003i	−0.367217	+	0.636039i	0.621912	+	0.783087i	$0.286356\pi$
$674$		0			0
$675$	1.73855	−	0.263602i	0.0669167	−	0.0101460i
$676$		0			0
$677$	10.8695	−	18.8265i	0.417748	−	0.723560i	−0.577965	−	0.816062i	$-0.696153\pi$
$677$	10.8695	−	18.8265i	0.417748	−	0.723560i	0.995713	+	0.0925013i	$0.0294862\pi$
$678$		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	$-0.787829\pi$
$683$	−41.0808			−1.57191			−0.785957	+	0.618281i	$0.787829\pi$
$684$		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	$-0.945029\pi$
$691$	−9.03599	+	15.6508i	−0.343745	+	0.595384i	0.641380	+	0.767224i	$0.278362\pi$
$692$		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	−0.878593	−	0.477571i	$-0.841517\pi$
$709$	−0.684536	+	1.18565i	−0.0257083	+	0.0445280i	0.852885	+	0.522099i	$0.174851\pi$
$710$		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	$-0.377164\pi$
$719$	20.1854			0.752787			0.376394	+	0.926460i	$0.377164\pi$
$720$		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	$-0.853344\pi$
$727$	−1.69393	+	2.93397i	−0.0628243	+	0.108815i	0.832903	+	0.553420i	$0.186677\pi$
$728$		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	0.982304	−	0.187293i	$-0.0599713\pi$
$733$	8.90603	+	15.4257i	0.328952	+	0.569761i	−0.653352	+	0.757054i	$0.726638\pi$
$734$		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	$-0.506763\pi$
$739$	−1.15512			−0.0424918			−0.0212459	+	0.999774i	$0.506763\pi$
$740$		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	$-0.000575048\pi$
$743$	13.5863	+	23.5322i	0.498435	+	0.863314i	−0.501564	+	0.865121i	$0.667242\pi$
$744$		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	$-0.301904\pi$
$751$	−11.2959	−	19.5651i	−0.412195	−	0.713942i	−0.995129	+	0.0985769i	$0.968571\pi$
$752$		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	0.870563	−	0.492057i	$-0.163755\pi$
$761$	0.252336	+	0.437059i	0.00914718	+	0.0158434i	−0.861416	+	0.507901i	$0.830422\pi$
$762$		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	0.940651	−	0.339376i	$-0.110216\pi$
$769$	4.89218	+	8.47351i	0.176417	+	0.305563i	−0.764234	+	0.644939i	$0.776883\pi$
$770$		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	0.974607	+	0.223924i	$0.0718868\pi$
$787$	19.1108	+	33.1009i	0.681227	+	1.17992i	−0.293379	+	0.955996i	$0.594780\pi$
$788$		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	0.597010	−	0.802234i	$-0.296355\pi$
$797$	−11.1866	−	19.3758i	−0.396250	−	0.686325i	−0.993260	+	0.115909i	$0.963022\pi$
$798$		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	$-0.569695\pi$
$811$	−12.3713			−0.434414			−0.217207	+	0.976126i	$0.569695\pi$
$812$		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	0.208761	+	0.977967i	$0.433057\pi$
$821$	−21.2767	+	36.8524i	−0.742564	+	1.28616i	−0.951324	+	0.308191i	$0.900276\pi$
$822$		0			0
$823$	8.11754	+	14.0600i	0.282960	+	0.490101i	0.972112	−	0.234516i	$-0.0753504\pi$
$823$	8.11754	+	14.0600i	0.282960	+	0.490101i	−0.689153	+	0.724616i	$0.742017\pi$
$824$		0			0
$825$	0.562930	−	0.522628i	0.0195987	−	0.0181956i
$826$		0			0
$827$	34.0199			1.18299			0.591494	−	0.806309i	$-0.298538\pi$
$827$	34.0199			1.18299			0.591494	+	0.806309i	$0.298538\pi$
$828$		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	$-0.790499\pi$
$839$	3.88612	−	6.73095i	0.134164	−	0.232378i	0.925278	+	0.379291i	$0.123832\pi$
$840$		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	−0.985048	−	0.172282i	$-0.944886\pi$
$853$	−10.0272	+	17.3676i	−0.343324	+	0.594654i	0.641724	+	0.766936i	$0.278219\pi$
$854$		0			0
$855$	−17.6597	−	12.0251i	−0.603949	−	0.411249i
$856$		0			0
$857$	−0.837910	+	1.45130i	−0.0286225	+	0.0495756i	−0.879982	−	0.475007i	$-0.842445\pi$
$857$	−0.837910	+	1.45130i	−0.0286225	+	0.0495756i	0.851359	+	0.524583i	$0.175779\pi$
$858$		0			0
$859$	−18.7256	−	32.4336i	−0.638908	−	1.10662i	−0.985673	−	0.168669i	$-0.946053\pi$
$859$	−18.7256	−	32.4336i	−0.638908	−	1.10662i	0.346765	−	0.937952i	$-0.387280\pi$
$860$		0			0
$861$	3.66541	+	16.0376i	0.124917	+	0.546561i
$862$		0			0
$863$	−30.0265			−1.02211			−0.511057	−	0.859547i	$-0.670746\pi$
$863$	−30.0265			−1.02211			−0.511057	+	0.859547i	$0.670746\pi$
$864$		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	0.608216	−	0.793772i	$-0.291885\pi$
$877$	−11.3517	−	19.6617i	−0.383318	−	0.663927i	−0.991534	+	0.129845i	$0.958552\pi$
$878$		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	$-0.203298\pi$
$883$	47.7159			1.60577			0.802884	+	0.596135i	$0.203298\pi$
$884$		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	$-0.105263\pi$
$887$	5.70962	+	9.88935i	0.191710	+	0.332052i	−0.754107	+	0.656752i	$0.771930\pi$
$888$		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	$-0.852533\pi$
$907$	−1.81546	+	3.14448i	−0.0602815	+	0.104411i	0.834310	+	0.551296i	$0.185867\pi$
$908$		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	$-0.846504\pi$
$911$	−1.24848	+	2.16242i	−0.0413638	+	0.0716443i	0.844602	+	0.535394i	$0.179837\pi$
$912$		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	$-0.497612\pi$
$919$	0.454816			0.0150030			0.00750149	+	0.999972i	$0.497612\pi$
$920$		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	−0.451049	−	0.892499i	$-0.648950\pi$
$929$	16.6846	−	28.8985i	0.547403	−	0.948129i	0.998451	−	0.0556301i	$-0.0177168\pi$
$930$		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	−0.958048	−	0.286608i	$-0.907472\pi$
$941$	−22.3084	−	38.6393i	−0.727234	−	1.25961i	0.230814	−	0.972998i	$-0.425861\pi$
$942$		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	$-0.678688\pi$
$947$	14.3695	−	24.8887i	0.466945	−	0.808773i	0.999287	+	0.0377568i	$0.0120212\pi$
$948$		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	−0.963916	−	0.266207i	$-0.914229\pi$
$967$	−22.1564	−	38.3759i	−0.712500	−	1.23409i	0.251415	−	0.967879i	$-0.419104\pi$
$968$		0			0
$969$	−0.388890	−	1.70155i	−0.0124930	−	0.0546616i
$970$		0			0
$971$	−49.8993			−1.60134			−0.800672	−	0.599103i	$-0.795524\pi$
$971$	−49.8993			−1.60134			−0.800672	+	0.599103i	$0.795524\pi$
$972$		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	0.999848	+	0.0174342i	$0.00554975\pi$
$977$	16.0981	+	27.8827i	0.515022	+	0.892045i	−0.484826	+	0.874611i	$0.661117\pi$
$978$		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	$-0.770244\pi$
$983$	6.17356	−	10.6929i	0.196906	−	0.341051i	0.947524	+	0.319686i	$0.103577\pi$
$984$		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	$-0.465529\pi$
$991$	6.80483			0.216163			0.108081	+	0.994142i	$0.465529\pi$
$992$		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	−0.878603	−	0.477552i	$-0.841524\pi$
$997$	−0.812415	+	1.40714i	−0.0257295	+	0.0445647i	0.852874	+	0.522117i	$0.174858\pi$
$998$		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	504.2.r.e.169.3	✓	8
3.2	odd	2		1512.2.r.e.505.1		8
4.3	odd	2		1008.2.r.l.673.2		8
9.2	odd	6		4536.2.a.y.1.4		4
9.4	even	3	inner	504.2.r.e.337.3	yes	8
9.5	odd	6		1512.2.r.e.1009.1		8
9.7	even	3		4536.2.a.z.1.1		4
12.11	even	2		3024.2.r.m.2017.1		8
36.7	odd	6		9072.2.a.cj.1.1		4
36.11	even	6		9072.2.a.cg.1.4		4
36.23	even	6		3024.2.r.m.1009.1		8
36.31	odd	6		1008.2.r.l.337.2		8

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more