LMFDB - Embedded newform 1280.2.l.c.321.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(321,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1280.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.l (of order $4$, 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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.349241344.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 81x^{4} - 100x^{3} + 96x^{2} - 52x + 17 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 81x^4 - 100x^3 + 96x^2 - 52*x + 17
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			321.3
Root			$0.500000 - 0.535026i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.c.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.742133 + 0.742133i) q^{3} +(-0.707107 + 0.707107i) q^{5} +0.463747i q^{7} -1.89848i q^{9} +O(q^{10})$	\(q+(0.742133 + 0.742133i) q^{3} +(-0.707107 + 0.707107i) q^{5} +0.463747i q^{7} -1.89848i q^{9} +(2.04953 - 2.04953i) q^{11} +(-3.94801 - 3.94801i) q^{13} -1.04953 q^{15} +1.34416 q^{17} +(-4.94801 - 4.94801i) q^{19} +(-0.344162 + 0.344162i) q^{21} -3.84894i q^{23} -1.00000i q^{25} +(3.63532 - 3.63532i) q^{27} +(1.09907 + 1.09907i) q^{29} +3.17157 q^{31} +3.04205 q^{33} +(-0.327919 - 0.327919i) q^{35} +(-6.89848 + 6.89848i) q^{37} -5.85990i q^{39} -2.89848i q^{41} +(1.62255 - 1.62255i) q^{43} +(1.34243 + 1.34243i) q^{45} +3.29217 q^{47} +6.78494 q^{49} +(0.997546 + 0.997546i) q^{51} +(-3.29217 + 3.29217i) q^{53} +2.89848i q^{55} -7.34416i q^{57} +(6.84894 - 6.84894i) q^{59} +(-3.44323 - 3.44323i) q^{61} +0.880415 q^{63} +5.58333 q^{65} +(5.93524 + 5.93524i) q^{67} +(2.85643 - 2.85643i) q^{69} -15.8960i q^{71} +0.556770i q^{73} +(0.742133 - 0.742133i) q^{75} +(0.950466 + 0.950466i) q^{77} +4.23917 q^{79} -0.299657 q^{81} +(-7.06578 - 7.06578i) q^{83} +(-0.950466 + 0.950466i) q^{85} +1.63131i q^{87} +17.3068i q^{89} +(1.83088 - 1.83088i) q^{91} +(2.35373 + 2.35373i) q^{93} +6.99755 q^{95} +9.04205 q^{97} +(-3.89100 - 3.89100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3}+O(q^{10}) $ 8 * q - 4 * q^3	$ 8 q - 4 q^{3} + 8 q^{11} + 8 q^{13} + 8 q^{17} + 32 q^{27} - 8 q^{29} + 48 q^{31} - 24 q^{33} - 4 q^{35} - 24 q^{37} + 20 q^{43} + 8 q^{45} - 16 q^{47} - 16 q^{49} - 40 q^{51} + 16 q^{53} + 32 q^{59} - 8 q^{61} + 24 q^{63} + 8 q^{65} + 12 q^{67} + 40 q^{69} - 4 q^{75} + 16 q^{77} - 44 q^{83} - 16 q^{85} + 40 q^{91} - 24 q^{93} + 8 q^{95} + 24 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 8 * q^11 + 8 * q^13 + 8 * q^17 + 32 * q^27 - 8 * q^29 + 48 * q^31 - 24 * q^33 - 4 * q^35 - 24 * q^37 + 20 * q^43 + 8 * q^45 - 16 * q^47 - 16 * q^49 - 40 * q^51 + 16 * q^53 + 32 * q^59 - 8 * q^61 + 24 * q^63 + 8 * q^65 + 12 * q^67 + 40 * q^69 - 4 * q^75 + 16 * q^77 - 44 * q^83 - 16 * q^85 + 40 * q^91 - 24 * q^93 + 8 * q^95 + 24 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	0.742133	+	0.742133i	0.428470	+	0.428470i	0.888107	−	0.459637i	$-0.152020\pi$
$3$	0.742133	+	0.742133i	0.428470	+	0.428470i	−0.459637	+	0.888107i	$0.652020\pi$
$4$		0			0
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$			0.463747i			0.175280i	0.996152	+	0.0876400i	$0.0279325\pi$
$7$			0.463747i			0.175280i	−0.996152	+	0.0876400i	$0.972067\pi$
$8$		0			0
$9$		−	1.89848i		−	0.632826i
$10$		0			0
$11$	2.04953	−	2.04953i	0.617958	−	0.617958i	−0.327049	−	0.945007i	$-0.606054\pi$
$11$	2.04953	−	2.04953i	0.617958	−	0.617958i	0.945007	+	0.327049i	$0.106054\pi$
$12$		0			0
$13$	−3.94801	−	3.94801i	−1.09498	−	1.09498i	−0.994988	−	0.0999936i	$-0.968118\pi$
$13$	−3.94801	−	3.94801i	−1.09498	−	1.09498i	−0.0999936	−	0.994988i	$-0.531882\pi$
$14$		0			0
$15$	−1.04953			−0.270988
$16$		0			0
$17$	1.34416			0.326007			0.163004	−	0.986625i	$-0.447882\pi$
$17$	1.34416			0.326007			0.163004	+	0.986625i	$0.447882\pi$
$18$		0			0
$19$	−4.94801	−	4.94801i	−1.13515	−	1.13515i	−0.989308	−	0.145844i	$-0.953410\pi$
$19$	−4.94801	−	4.94801i	−1.13515	−	1.13515i	−0.145844	−	0.989308i	$-0.546590\pi$
$20$		0			0
$21$	−0.344162	+	0.344162i	−0.0751023	+	0.0751023i
$22$		0			0
$23$		−	3.84894i		−	0.802560i	−0.915955	−	0.401280i	$-0.868565\pi$
$23$		−	3.84894i		−	0.802560i	0.915955	−	0.401280i	$-0.131435\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	3.63532	−	3.63532i	0.699618	−	0.699618i
$28$		0			0
$29$	1.09907	+	1.09907i	0.204092	+	0.204092i	0.801751	−	0.597659i	$-0.203902\pi$
$29$	1.09907	+	1.09907i	0.204092	+	0.204092i	−0.597659	+	0.801751i	$0.703902\pi$
$30$		0			0
$31$	3.17157			0.569631			0.284816	−	0.958582i	$-0.408068\pi$
$31$	3.17157			0.569631			0.284816	+	0.958582i	$0.408068\pi$
$32$		0			0
$33$	3.04205			0.529553
$34$		0			0
$35$	−0.327919	−	0.327919i	−0.0554284	−	0.0554284i
$36$		0			0
$37$	−6.89848	+	6.89848i	−1.13410	+	1.13410i	−0.144615	+	0.989488i	$0.546194\pi$
$37$	−6.89848	+	6.89848i	−1.13410	+	1.13410i	−0.989488	+	0.144615i	$0.953806\pi$
$38$		0			0
$39$		−	5.85990i		−	0.938334i
$40$		0			0
$41$		−	2.89848i		−	0.452666i	−0.974050	−	0.226333i	$-0.927326\pi$
$41$		−	2.89848i		−	0.452666i	0.974050	−	0.226333i	$-0.0726738\pi$
$42$		0			0
$43$	1.62255	−	1.62255i	0.247436	−	0.247436i	−0.572482	−	0.819918i	$-0.694019\pi$
$43$	1.62255	−	1.62255i	0.247436	−	0.247436i	0.819918	+	0.572482i	$0.194019\pi$
$44$		0			0
$45$	1.34243	+	1.34243i	0.200117	+	0.200117i
$46$		0			0
$47$	3.29217			0.480213			0.240107	−	0.970747i	$-0.422818\pi$
$47$	3.29217			0.480213			0.240107	+	0.970747i	$0.422818\pi$
$48$		0			0
$49$	6.78494			0.969277
$50$		0			0
$51$	0.997546	+	0.997546i	0.139684	+	0.139684i
$52$		0			0
$53$	−3.29217	+	3.29217i	−0.452215	+	0.452215i	−0.896089	−	0.443874i	$-0.853604\pi$
$53$	−3.29217	+	3.29217i	−0.452215	+	0.452215i	0.443874	+	0.896089i	$0.353604\pi$
$54$		0			0
$55$			2.89848i			0.390831i
$56$		0			0
$57$		−	7.34416i		−	0.972758i
$58$		0			0
$59$	6.84894	−	6.84894i	0.891657	−	0.891657i	−0.103022	−	0.994679i	$-0.532851\pi$
$59$	6.84894	−	6.84894i	0.891657	−	0.891657i	0.994679	+	0.103022i	$0.0328513\pi$
$60$		0			0
$61$	−3.44323	−	3.44323i	−0.440860	−	0.440860i	0.451441	−	0.892301i	$-0.350910\pi$
$61$	−3.44323	−	3.44323i	−0.440860	−	0.440860i	−0.892301	+	0.451441i	$0.850910\pi$
$62$		0			0
$63$	0.880415			0.110922
$64$		0			0
$65$	5.58333			0.692527
$66$		0			0
$67$	5.93524	+	5.93524i	0.725105	+	0.725105i	0.969640	−	0.244535i	$-0.0786355\pi$
$67$	5.93524	+	5.93524i	0.725105	+	0.725105i	−0.244535	+	0.969640i	$0.578635\pi$
$68$		0			0
$69$	2.85643	−	2.85643i	0.343873	−	0.343873i
$70$		0			0
$71$		−	15.8960i		−	1.88651i	−0.332068	−	0.943256i	$-0.607746\pi$
$71$		−	15.8960i		−	1.88651i	0.332068	−	0.943256i	$-0.392254\pi$
$72$		0			0
$73$			0.556770i			0.0651650i	0.999469	+	0.0325825i	$0.0103732\pi$
$73$			0.556770i			0.0651650i	−0.999469	+	0.0325825i	$0.989627\pi$
$74$		0			0
$75$	0.742133	−	0.742133i	0.0856941	−	0.0856941i
$76$		0			0
$77$	0.950466	+	0.950466i	0.108316	+	0.108316i
$78$		0			0
$79$	4.23917			0.476944			0.238472	−	0.971149i	$-0.423353\pi$
$79$	4.23917			0.476944			0.238472	+	0.971149i	$0.423353\pi$
$80$		0			0
$81$	−0.299657			−0.0332952
$82$		0			0
$83$	−7.06578	−	7.06578i	−0.775570	−	0.775570i	0.203504	−	0.979074i	$-0.434767\pi$
$83$	−7.06578	−	7.06578i	−0.775570	−	0.775570i	−0.979074	+	0.203504i	$0.934767\pi$
$84$		0			0
$85$	−0.950466	+	0.950466i	−0.103093	+	0.103093i
$86$		0			0
$87$			1.63131i			0.174895i
$88$		0			0
$89$			17.3068i			1.83451i	0.398296	+	0.917257i	$0.369602\pi$
$89$			17.3068i			1.83451i	−0.398296	+	0.917257i	$0.630398\pi$
$90$		0			0
$91$	1.83088	−	1.83088i	0.191928	−	0.191928i
$92$		0			0
$93$	2.35373	+	2.35373i	0.244070	+	0.244070i
$94$		0			0
$95$	6.99755			0.717933
$96$		0			0
$97$	9.04205			0.918081			0.459041	−	0.888415i	$-0.348193\pi$
$97$	9.04205			0.918081			0.459041	+	0.888415i	$0.348193\pi$
$98$		0			0
$99$	−3.89100	−	3.89100i	−0.391060	−	0.391060i
$100$		0			0
$101$	−6.89603	+	6.89603i	−0.686180	+	0.686180i	−0.961385	−	0.275205i	$-0.911254\pi$
$101$	−6.89603	+	6.89603i	−0.686180	+	0.686180i	0.275205	+	0.961385i	$0.411254\pi$
$102$		0			0
$103$		−	15.0156i		−	1.47953i	−0.672864	−	0.739766i	$-0.734936\pi$
$103$		−	15.0156i		−	1.47953i	0.672864	−	0.739766i	$-0.265064\pi$
$104$		0			0
$105$		−	0.486719i		−	0.0474989i
$106$		0			0
$107$	−11.7687	+	11.7687i	−1.13772	+	1.13772i	−0.148865	+	0.988857i	$0.547562\pi$
$107$	−11.7687	+	11.7687i	−1.13772	+	1.13772i	−0.988857	+	0.148865i	$0.952438\pi$
$108$		0			0
$109$	−4.14357	−	4.14357i	−0.396882	−	0.396882i	0.480250	−	0.877132i	$-0.340546\pi$
$109$	−4.14357	−	4.14357i	−0.396882	−	0.396882i	−0.877132	+	0.480250i	$0.840546\pi$
$110$		0			0
$111$	−10.2392			−0.971859
$112$		0			0
$113$	−7.99509			−0.752115			−0.376058	−	0.926596i	$-0.622720\pi$
$113$	−7.99509			−0.752115			−0.376058	+	0.926596i	$0.622720\pi$
$114$		0			0
$115$	2.72161	+	2.72161i	0.253792	+	0.253792i
$116$		0			0
$117$	−7.49522	+	7.49522i	−0.692933	+	0.692933i
$118$		0			0
$119$			0.623352i			0.0571426i
$120$		0			0
$121$			2.59882i			0.236257i
$122$		0			0
$123$	2.15106	−	2.15106i	0.193954	−	0.193954i
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	10.9795			0.974272			0.487136	−	0.873326i	$-0.338042\pi$
$127$	10.9795			0.974272			0.487136	+	0.873326i	$0.338042\pi$
$128$		0			0
$129$	2.40829			0.212038
$130$		0			0
$131$	−4.39124	−	4.39124i	−0.383665	−	0.383665i	0.488756	−	0.872421i	$-0.337451\pi$
$131$	−4.39124	−	4.39124i	−0.383665	−	0.383665i	−0.872421	+	0.488756i	$0.837451\pi$
$132$		0			0
$133$	2.29463	−	2.29463i	0.198969	−	0.198969i
$134$		0			0
$135$			5.14112i			0.442477i
$136$		0			0
$137$		−	21.8960i		−	1.87070i	−0.353719	−	0.935352i	$-0.615083\pi$
$137$		−	21.8960i		−	1.87070i	0.353719	−	0.935352i	$-0.384917\pi$
$138$		0			0
$139$	4.46129	−	4.46129i	0.378402	−	0.378402i	−0.492123	−	0.870525i	$-0.663779\pi$
$139$	4.46129	−	4.46129i	0.378402	−	0.378402i	0.870525	+	0.492123i	$0.163779\pi$
$140$		0			0
$141$	2.44323	+	2.44323i	0.205757	+	0.205757i
$142$		0			0
$143$	−16.1832			−1.35330
$144$		0			0
$145$	−1.55432			−0.129079
$146$		0			0
$147$	5.03532	+	5.03532i	0.415306	+	0.415306i
$148$		0			0
$149$	7.34416	−	7.34416i	0.601657	−	0.601657i	−0.339095	−	0.940752i	$-0.610121\pi$
$149$	7.34416	−	7.34416i	0.601657	−	0.601657i	0.940752	+	0.339095i	$0.110121\pi$
$150$		0			0
$151$			17.0266i			1.38560i	0.721129	+	0.692801i	$0.243624\pi$
$151$			17.0266i			1.38560i	−0.721129	+	0.692801i	$0.756376\pi$
$152$		0			0
$153$		−	2.55186i		−	0.206306i
$154$		0			0
$155$	−2.24264	+	2.24264i	−0.180133	+	0.180133i
$156$		0			0
$157$	3.85643	+	3.85643i	0.307776	+	0.307776i	0.844046	−	0.536270i	$-0.180167\pi$
$157$	3.85643	+	3.85643i	0.307776	+	0.307776i	−0.536270	+	0.844046i	$0.680167\pi$
$158$		0			0
$159$	−4.88646			−0.387521
$160$		0			0
$161$	1.78494			0.140673
$162$		0			0
$163$	12.3255	+	12.3255i	0.965405	+	0.965405i	0.999421	−	0.0340163i	$-0.0108298\pi$
$163$	12.3255	+	12.3255i	0.965405	+	0.965405i	−0.0340163	+	0.999421i	$0.510830\pi$
$164$		0			0
$165$	−2.15106	+	2.15106i	−0.167459	+	0.167459i
$166$		0			0
$167$			18.6314i			1.44174i	0.693069	+	0.720872i	$0.256258\pi$
$167$			18.6314i			1.44174i	−0.693069	+	0.720872i	$0.743742\pi$
$168$		0			0
$169$			18.1736i			1.39797i
$170$		0			0
$171$	−9.39370	+	9.39370i	−0.718354	+	0.718354i
$172$		0			0
$173$	−4.51227	−	4.51227i	−0.343061	−	0.343061i	0.514456	−	0.857517i	$-0.327994\pi$
$173$	−4.51227	−	4.51227i	−0.343061	−	0.343061i	−0.857517	+	0.514456i	$0.827994\pi$
$174$		0			0
$175$	0.463747			0.0350560
$176$		0			0
$177$	10.1656			0.764097
$178$		0			0
$179$	−15.1907	−	15.1907i	−1.13540	−	1.13540i	−0.989264	−	0.146139i	$-0.953315\pi$
$179$	−15.1907	−	15.1907i	−1.13540	−	1.13540i	−0.146139	−	0.989264i	$-0.546685\pi$
$180$		0			0
$181$	11.6834	−	11.6834i	0.868422	−	0.868422i	−0.123876	−	0.992298i	$-0.539533\pi$
$181$	11.6834	−	11.6834i	0.868422	−	0.868422i	0.992298	+	0.123876i	$0.0395326\pi$
$182$		0			0
$183$		−	5.11067i		−	0.377791i
$184$		0			0
$185$		−	9.75592i		−	0.717270i
$186$		0			0
$187$	2.75491	−	2.75491i	0.201459	−	0.201459i
$188$		0			0
$189$	1.68587	+	1.68587i	0.122629	+	0.122629i
$190$		0			0
$191$	3.89603			0.281906			0.140953	−	0.990016i	$-0.454983\pi$
$191$	3.89603			0.281906			0.140953	+	0.990016i	$0.454983\pi$
$192$		0			0
$193$	−19.0371			−1.37032			−0.685162	−	0.728391i	$-0.740269\pi$
$193$	−19.0371			−1.37032			−0.685162	+	0.728391i	$0.740269\pi$
$194$		0			0
$195$	4.14357	+	4.14357i	0.296727	+	0.296727i
$196$		0			0
$197$	0.0470803	−	0.0470803i	0.00335433	−	0.00335433i	−0.705428	−	0.708782i	$-0.749245\pi$
$197$	0.0470803	−	0.0470803i	0.00335433	−	0.00335433i	0.708782	+	0.705428i	$0.249245\pi$
$198$		0			0
$199$		−	11.3137i		−	0.802008i	−0.916076	−	0.401004i	$-0.868661\pi$
$199$		−	11.3137i		−	0.802008i	0.916076	−	0.401004i	$-0.131339\pi$
$200$		0			0
$201$			8.80947i			0.621372i
$202$		0			0
$203$	−0.509690	+	0.509690i	−0.0357732	+	0.0357732i
$204$		0			0
$205$	2.04953	+	2.04953i	0.143146	+	0.143146i
$206$		0			0
$207$	−7.30714			−0.507881
$208$		0			0
$209$	−20.2822			−1.40295
$210$		0			0
$211$	0.338117	+	0.338117i	0.0232769	+	0.0232769i	0.718649	−	0.695373i	$-0.244761\pi$
$211$	0.338117	+	0.338117i	0.0232769	+	0.0232769i	−0.695373	+	0.718649i	$0.744761\pi$
$212$		0			0
$213$	11.7970	−	11.7970i	0.808314	−	0.808314i
$214$		0			0
$215$			2.29463i			0.156492i
$216$		0			0
$217$			1.47081i			0.0998450i
$218$		0			0
$219$	−0.413197	+	0.413197i	−0.0279213	+	0.0279213i
$220$		0			0
$221$	−5.30677	−	5.30677i	−0.356972	−	0.356972i
$222$		0			0
$223$	19.6049			1.31284			0.656419	−	0.754396i	$-0.272070\pi$
$223$	19.6049			1.31284			0.656419	+	0.754396i	$0.272070\pi$
$224$		0			0
$225$	−1.89848			−0.126565
$226$		0			0
$227$	16.1549	+	16.1549i	1.07224	+	1.07224i	0.997179	+	0.0750599i	$0.0239148\pi$
$227$	16.1549	+	16.1549i	1.07224	+	1.07224i	0.0750599	+	0.997179i	$0.476085\pi$
$228$		0			0
$229$	18.7970	−	18.7970i	1.24214	−	1.24214i	0.283026	−	0.959112i	$-0.408662\pi$
$229$	18.7970	−	18.7970i	1.24214	−	1.24214i	0.959112	−	0.283026i	$-0.0913381\pi$
$230$		0			0
$231$			1.41074i			0.0928201i
$232$		0			0
$233$			17.2402i			1.12944i	0.825282	+	0.564721i	$0.191016\pi$
$233$			17.2402i			1.12944i	−0.825282	+	0.564721i	$0.808984\pi$
$234$		0			0
$235$	−2.32792	+	2.32792i	−0.151857	+	0.151857i
$236$		0			0
$237$	3.14603	+	3.14603i	0.204356	+	0.204356i
$238$		0			0
$239$	−27.6930			−1.79131			−0.895655	−	0.444749i	$-0.853293\pi$
$239$	−27.6930			−1.79131			−0.895655	+	0.444749i	$0.853293\pi$
$240$		0			0
$241$	−9.09661			−0.585964			−0.292982	−	0.956118i	$-0.594648\pi$
$241$	−9.09661			−0.585964			−0.292982	+	0.956118i	$0.594648\pi$
$242$		0			0
$243$	−11.1283	−	11.1283i	−0.713884	−	0.713884i
$244$		0			0
$245$	−4.79768	+	4.79768i	−0.306512	+	0.306512i
$246$		0			0
$247$			39.0696i			2.48594i
$248$		0			0
$249$		−	10.4875i		−	0.664617i
$250$		0			0
$251$	8.63388	−	8.63388i	0.544966	−	0.544966i	−0.380015	−	0.924980i	$-0.624081\pi$
$251$	8.63388	−	8.63388i	0.544966	−	0.544966i	0.924980	+	0.380015i	$0.124081\pi$
$252$		0			0
$253$	−7.88854	−	7.88854i	−0.495948	−	0.495948i
$254$		0			0
$255$	−1.41074			−0.0883442
$256$		0			0
$257$	−23.0647			−1.43874			−0.719369	−	0.694628i	$-0.755569\pi$
$257$	−23.0647			−1.43874			−0.719369	+	0.694628i	$0.755569\pi$
$258$		0			0
$259$	−3.19915	−	3.19915i	−0.198786	−	0.198786i
$260$		0			0
$261$	2.08656	−	2.08656i	0.129155	−	0.129155i
$262$		0			0
$263$			21.1833i			1.30622i	0.757264	+	0.653109i	$0.226536\pi$
$263$			21.1833i			1.30622i	−0.757264	+	0.653109i	$0.773464\pi$
$264$		0			0
$265$		−	4.65584i		−	0.286006i
$266$		0			0
$267$	−12.8439	+	12.8439i	−0.786035	+	0.786035i
$268$		0			0
$269$	6.35373	+	6.35373i	0.387394	+	0.387394i	0.873757	−	0.486363i	$-0.161677\pi$
$269$	6.35373	+	6.35373i	0.387394	+	0.387394i	−0.486363	+	0.873757i	$0.661677\pi$
$270$		0			0
$271$	10.8235			0.657482			0.328741	−	0.944420i	$-0.393376\pi$
$271$	10.8235			0.657482			0.328741	+	0.944420i	$0.393376\pi$
$272$		0			0
$273$	2.71751			0.164471
$274$		0			0
$275$	−2.04953	−	2.04953i	−0.123592	−	0.123592i
$276$		0			0
$277$	−16.5074	+	16.5074i	−0.991831	+	0.991831i	−0.999967	−	0.00813590i	$-0.997410\pi$
$277$	−16.5074	+	16.5074i	−0.991831	+	0.991831i	0.00813590	+	0.999967i	$0.497410\pi$
$278$		0			0
$279$		−	6.02116i		−	0.360478i
$280$		0			0
$281$		−	10.6064i		−	0.632726i	−0.948638	−	0.316363i	$-0.897538\pi$
$281$		−	10.6064i		−	0.632726i	0.948638	−	0.316363i	$-0.102462\pi$
$282$		0			0
$283$	−2.80017	+	2.80017i	−0.166453	+	0.166453i	−0.785418	−	0.618966i	$-0.787552\pi$
$283$	−2.80017	+	2.80017i	−0.166453	+	0.166453i	0.618966	+	0.785418i	$0.287552\pi$
$284$		0			0
$285$	5.19311	+	5.19311i	0.307613	+	0.307613i
$286$		0			0
$287$	1.34416			0.0793434
$288$		0			0
$289$	−15.1932			−0.893719
$290$		0			0
$291$	6.71040	+	6.71040i	0.393371	+	0.393371i
$292$		0			0
$293$	14.1387	−	14.1387i	0.825990	−	0.825990i	−0.160970	−	0.986959i	$-0.551462\pi$
$293$	14.1387	−	14.1387i	0.825990	−	0.825990i	0.986959	+	0.160970i	$0.0514621\pi$
$294$		0			0
$295$			9.68587i			0.563933i
$296$		0			0
$297$		−	14.9014i		−	0.864668i
$298$		0			0
$299$	−15.1957	+	15.1957i	−0.878789	+	0.878789i
$300$		0			0
$301$	0.752452	+	0.752452i	0.0433706	+	0.0433706i
$302$		0			0
$303$	−10.2355			−0.588016
$304$		0			0
$305$	4.86946			0.278825
$306$		0			0
$307$	21.6912	+	21.6912i	1.23798	+	1.23798i	0.960825	+	0.277155i	$0.0893914\pi$
$307$	21.6912	+	21.6912i	1.23798	+	1.23798i	0.277155	+	0.960825i	$0.410609\pi$
$308$		0			0
$309$	11.1436	−	11.1436i	0.633936	−	0.633936i
$310$		0			0
$311$			0.490189i			0.0277960i	0.999903	+	0.0138980i	$0.00442402\pi$
$311$			0.490189i			0.0277960i	−0.999903	+	0.0138980i	$0.995576\pi$
$312$		0			0
$313$			22.5794i			1.27627i	0.769926	+	0.638133i	$0.220293\pi$
$313$			22.5794i			1.27627i	−0.769926	+	0.638133i	$0.779707\pi$
$314$		0			0
$315$	−0.622547	+	0.622547i	−0.0350766	+	0.0350766i
$316$		0			0
$317$	18.6314	+	18.6314i	1.04645	+	1.04645i	0.998868	+	0.0475778i	$0.0151502\pi$
$317$	18.6314	+	18.6314i	1.04645	+	1.04645i	0.0475778	+	0.998868i	$0.484850\pi$
$318$		0			0
$319$	4.50515			0.252240
$320$		0			0
$321$	−17.4679			−0.974961
$322$		0			0
$323$	−6.65093	−	6.65093i	−0.370068	−	0.370068i
$324$		0			0
$325$	−3.94801	+	3.94801i	−0.218996	+	0.218996i
$326$		0			0
$327$		−	6.15016i		−	0.340105i
$328$		0			0
$329$			1.52674i			0.0841718i
$330$		0			0
$331$	−17.7460	+	17.7460i	−0.975408	+	0.975408i	−0.999705	−	0.0242972i	$-0.992265\pi$
$331$	−17.7460	+	17.7460i	−0.975408	+	0.975408i	0.0242972	+	0.999705i	$0.492265\pi$
$332$		0			0
$333$	13.0966	+	13.0966i	0.717690	+	0.717690i
$334$		0			0
$335$	−8.39370			−0.458597
$336$		0			0
$337$	12.2972			0.669871			0.334936	−	0.942241i	$-0.391285\pi$
$337$	12.2972			0.669871			0.334936	+	0.942241i	$0.391285\pi$
$338$		0			0
$339$	−5.93342	−	5.93342i	−0.322259	−	0.322259i
$340$		0			0
$341$	6.50025	−	6.50025i	0.352008	−	0.352008i
$342$		0			0
$343$			6.39273i			0.345175i
$344$		0			0
$345$			4.03960i			0.217485i
$346$		0			0
$347$	−4.37745	+	4.37745i	−0.234994	+	0.234994i	−0.814773	−	0.579779i	$-0.803139\pi$
$347$	−4.37745	+	4.37745i	−0.234994	+	0.234994i	0.579779	+	0.814773i	$0.303139\pi$
$348$		0			0
$349$	−18.9951	−	18.9951i	−1.01678	−	1.01678i	−0.999857	−	0.0169273i	$-0.994612\pi$
$349$	−18.9951	−	18.9951i	−1.01678	−	1.01678i	−0.0169273	−	0.999857i	$-0.505388\pi$
$350$		0			0
$351$	−28.7046			−1.53214
$352$		0			0
$353$	24.6785			1.31350			0.656752	−	0.754106i	$-0.271930\pi$
$353$	24.6785			1.31350			0.656752	+	0.754106i	$0.271930\pi$
$354$		0			0
$355$	11.2402	+	11.2402i	0.596567	+	0.596567i
$356$		0			0
$357$	−0.462610	+	0.462610i	−0.0244839	+	0.0244839i
$358$		0			0
$359$		−	28.5745i		−	1.50811i	−0.656813	−	0.754053i	$-0.728096\pi$
$359$		−	28.5745i		−	1.50811i	0.656813	−	0.754053i	$-0.271904\pi$
$360$		0			0
$361$			29.9657i			1.57714i
$362$		0			0
$363$	−1.92867	+	1.92867i	−0.101229	+	0.101229i
$364$		0			0
$365$	−0.393696	−	0.393696i	−0.0206070	−	0.0206070i
$366$		0			0
$367$	9.86594			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$367$	9.86594			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$368$		0			0
$369$	−5.50270			−0.286459
$370$		0			0
$371$	−1.52674	−	1.52674i	−0.0792643	−	0.0792643i
$372$		0			0
$373$	7.88891	−	7.88891i	0.408472	−	0.408472i	−0.472733	−	0.881206i	$-0.656733\pi$
$373$	7.88891	−	7.88891i	0.408472	−	0.408472i	0.881206	+	0.472733i	$0.156733\pi$
$374$		0			0
$375$			1.04953i			0.0541977i
$376$		0			0
$377$		−	8.67827i		−	0.446953i
$378$		0			0
$379$	3.39370	−	3.39370i	0.174322	−	0.174322i	−0.614553	−	0.788875i	$-0.710664\pi$
$379$	3.39370	−	3.39370i	0.174322	−	0.174322i	0.788875	+	0.614553i	$0.210664\pi$
$380$		0			0
$381$	8.14823	+	8.14823i	0.417447	+	0.417447i
$382$		0			0
$383$	−6.25012			−0.319366			−0.159683	−	0.987168i	$-0.551047\pi$
$383$	−6.25012			−0.319366			−0.159683	+	0.987168i	$0.551047\pi$
$384$		0			0
$385$	−1.34416			−0.0685048
$386$		0			0
$387$	−3.08037	−	3.08037i	−0.156584	−	0.156584i
$388$		0			0
$389$	3.04205	−	3.04205i	0.154238	−	0.154238i	−0.625770	−	0.780008i	$-0.715215\pi$
$389$	3.04205	−	3.04205i	0.154238	−	0.154238i	0.780008	+	0.625770i	$0.215215\pi$
$390$		0			0
$391$		−	5.17361i		−	0.261640i
$392$		0			0
$393$		−	6.51777i		−	0.328778i
$394$		0			0
$395$	−2.99755	+	2.99755i	−0.150823	+	0.150823i
$396$		0			0
$397$	−6.93845	−	6.93845i	−0.348231	−	0.348231i	0.511220	−	0.859450i	$-0.329194\pi$
$397$	−6.93845	−	6.93845i	−0.348231	−	0.348231i	−0.859450	+	0.511220i	$0.829194\pi$
$398$		0			0
$399$	3.40584			0.170505
$400$		0			0
$401$	−11.1736			−0.557983			−0.278992	−	0.960294i	$-0.590000\pi$
$401$	−11.1736			−0.557983			−0.278992	+	0.960294i	$0.590000\pi$
$402$		0			0
$403$	−12.5214	−	12.5214i	−0.623736	−	0.623736i
$404$		0			0
$405$	0.211889	−	0.211889i	0.0105289	−	0.0105289i
$406$		0			0
$407$			28.2773i			1.40166i
$408$		0			0
$409$			39.6611i			1.96111i	0.196233	+	0.980557i	$0.437129\pi$
$409$			39.6611i			1.96111i	−0.196233	+	0.980557i	$0.562871\pi$
$410$		0			0
$411$	16.2498	−	16.2498i	0.801541	−	0.801541i
$412$		0			0
$413$	3.17618	+	3.17618i	0.156290	+	0.156290i
$414$		0			0
$415$	9.99252			0.490513
$416$		0			0
$417$	6.62174			0.324268
$418$		0			0
$419$	3.81400	+	3.81400i	0.186326	+	0.186326i	0.794106	−	0.607780i	$-0.207940\pi$
$419$	3.81400	+	3.81400i	0.186326	+	0.186326i	−0.607780	+	0.794106i	$0.707940\pi$
$420$		0			0
$421$	8.45280	−	8.45280i	0.411964	−	0.411964i	−0.470458	−	0.882422i	$-0.655911\pi$
$421$	8.45280	−	8.45280i	0.411964	−	0.411964i	0.882422	+	0.470458i	$0.155911\pi$
$422$		0			0
$423$		−	6.25012i		−	0.303891i
$424$		0			0
$425$		−	1.34416i		−	0.0652014i
$426$		0			0
$427$	1.59679	−	1.59679i	0.0772740	−	0.0772740i
$428$		0			0
$429$	−12.0101	−	12.0101i	−0.579851	−	0.579851i
$430$		0			0
$431$	23.3909			1.12670			0.563349	−	0.826219i	$-0.309513\pi$
$431$	23.3909			1.12670			0.563349	+	0.826219i	$0.309513\pi$
$432$		0			0
$433$	3.33925			0.160474			0.0802372	−	0.996776i	$-0.474432\pi$
$433$	3.33925			0.160474			0.0802372	+	0.996776i	$0.474432\pi$
$434$		0			0
$435$	−1.15351	−	1.15351i	−0.0553065	−	0.0553065i
$436$		0			0
$437$	−19.0446	+	19.0446i	−0.911028	+	0.911028i
$438$		0			0
$439$		−	1.27064i		−	0.0606444i	−0.999540	−	0.0303222i	$-0.990347\pi$
$439$		−	1.27064i		−	0.0606444i	0.999540	−	0.0303222i	$-0.00965333\pi$
$440$		0			0
$441$		−	12.8811i		−	0.613384i
$442$		0			0
$443$	−17.4991	+	17.4991i	−0.831406	+	0.831406i	−0.987709	−	0.156303i	$-0.950042\pi$
$443$	−17.4991	+	17.4991i	−0.831406	+	0.831406i	0.156303	+	0.987709i	$0.450042\pi$
$444$		0			0
$445$	−12.2377	−	12.2377i	−0.580124	−	0.580124i
$446$		0			0
$447$	10.9007			0.515585
$448$		0			0
$449$	−15.9831			−0.754288			−0.377144	−	0.926155i	$-0.623094\pi$
$449$	−15.9831			−0.754288			−0.377144	+	0.926155i	$0.623094\pi$
$450$		0			0
$451$	−5.94053	−	5.94053i	−0.279729	−	0.279729i
$452$		0			0
$453$	−12.6360	+	12.6360i	−0.593689	+	0.593689i
$454$		0			0
$455$			2.58926i			0.121386i
$456$		0			0
$457$		−	6.78739i		−	0.317501i	−0.987319	−	0.158750i	$-0.949253\pi$
$457$		−	6.78739i		−	0.317501i	0.987319	−	0.158750i	$-0.0507465\pi$
$458$		0			0
$459$	4.88646	−	4.88646i	0.228080	−	0.228080i
$460$		0			0
$461$	21.0942	+	21.0942i	0.982453	+	0.982453i	0.999849	−	0.0173957i	$-0.00553750\pi$
$461$	21.0942	+	21.0942i	0.982453	+	0.982453i	−0.0173957	+	0.999849i	$0.505537\pi$
$462$		0			0
$463$	−21.3234			−0.990982			−0.495491	−	0.868613i	$-0.665012\pi$
$463$	−21.3234			−0.990982			−0.495491	+	0.868613i	$0.665012\pi$
$464$		0			0
$465$	−3.32867			−0.154364
$466$		0			0
$467$	4.71168	+	4.71168i	0.218031	+	0.218031i	0.807668	−	0.589638i	$-0.200729\pi$
$467$	4.71168	+	4.71168i	0.218031	+	0.218031i	−0.589638	+	0.807668i	$0.700729\pi$
$468$		0			0
$469$	−2.75245	+	2.75245i	−0.127096	+	0.127096i
$470$		0			0
$471$			5.72396i			0.263746i
$472$		0			0
$473$		−	6.65093i		−	0.305810i
$474$		0			0
$475$	−4.94801	+	4.94801i	−0.227030	+	0.227030i
$476$		0			0
$477$	6.25012	+	6.25012i	0.286173	+	0.286173i
$478$		0			0
$479$	10.1932			0.465740			0.232870	−	0.972508i	$-0.425188\pi$
$479$	10.1932			0.465740			0.232870	+	0.972508i	$0.425188\pi$
$480$		0			0
$481$	54.4706			2.48364
$482$		0			0
$483$	1.32466	+	1.32466i	0.0602742	+	0.0602742i
$484$		0			0
$485$	−6.39370	+	6.39370i	−0.290323	+	0.290323i
$486$		0			0
$487$		−	5.87940i		−	0.266421i	−0.991088	−	0.133210i	$-0.957471\pi$
$487$		−	5.87940i		−	0.266421i	0.991088	−	0.133210i	$-0.0425286\pi$
$488$		0			0
$489$			18.2943i			0.827295i
$490$		0			0
$491$	−3.01950	+	3.01950i	−0.136268	+	0.136268i	−0.771951	−	0.635682i	$-0.780719\pi$
$491$	−3.01950	+	3.01950i	−0.136268	+	0.136268i	0.635682	+	0.771951i	$0.280719\pi$
$492$		0			0
$493$	1.47733	+	1.47733i	0.0665354	+	0.0665354i
$494$		0			0
$495$	5.50270			0.247328
$496$		0			0
$497$	7.37174			0.330668
$498$		0			0
$499$	21.1837	+	21.1837i	0.948313	+	0.948313i	0.998728	−	0.0504151i	$-0.0160544\pi$
$499$	21.1837	+	21.1837i	0.948313	+	0.948313i	−0.0504151	+	0.998728i	$0.516054\pi$
$500$		0			0
$501$	−13.8270	+	13.8270i	−0.617744	+	0.617744i
$502$		0			0
$503$		−	31.7450i		−	1.41544i	−0.706494	−	0.707719i	$-0.749724\pi$
$503$		−	31.7450i		−	1.41544i	0.706494	−	0.707719i	$-0.250276\pi$
$504$		0			0
$505$		−	9.75245i		−	0.433978i
$506$		0			0
$507$	−13.4872	+	13.4872i	−0.598989	+	0.598989i
$508$		0			0
$509$	−1.68342	−	1.68342i	−0.0746161	−	0.0746161i	0.668814	−	0.743430i	$-0.266802\pi$
$509$	−1.68342	−	1.68342i	−0.0746161	−	0.0746161i	−0.743430	+	0.668814i	$0.766802\pi$
$510$		0			0
$511$	−0.258201			−0.0114221
$512$		0			0
$513$	−35.9752			−1.58834
$514$		0			0
$515$	10.6176	+	10.6176i	0.467869	+	0.467869i
$516$		0			0
$517$	6.74742	−	6.74742i	0.296751	−	0.296751i
$518$		0			0
$519$		−	6.69740i		−	0.293983i
$520$		0			0
$521$		−	23.1736i		−	1.01525i	−0.861577	−	0.507627i	$-0.830523\pi$
$521$		−	23.1736i		−	1.01525i	0.861577	−	0.507627i	$-0.169477\pi$
$522$		0			0
$523$	29.4991	−	29.4991i	1.28990	−	1.28990i	0.355061	−	0.934843i	$-0.384460\pi$
$523$	29.4991	−	29.4991i	1.28990	−	1.28990i	0.934843	−	0.355061i	$-0.115540\pi$
$524$		0			0
$525$	0.344162	+	0.344162i	0.0150205	+	0.0150205i
$526$		0			0
$527$	4.26311			0.185704
$528$		0			0
$529$	8.18562			0.355897
$530$		0			0
$531$	−13.0026	−	13.0026i	−0.564264	−	0.564264i
$532$		0			0
$533$	−11.4432	+	11.4432i	−0.495661	+	0.495661i
$534$		0			0
$535$		−	16.6434i		−	0.719559i
$536$		0			0
$537$		−	22.5470i		−	0.972973i
$538$		0			0
$539$	13.9060	−	13.9060i	0.598972	−	0.598972i
$540$		0			0
$541$	−13.3813	−	13.3813i	−0.575307	−	0.575307i	0.358299	−	0.933607i	$-0.383357\pi$
$541$	−13.3813	−	13.3813i	−0.575307	−	0.575307i	−0.933607	+	0.358299i	$0.883357\pi$
$542$		0			0
$543$	17.3413			0.744186
$544$		0			0
$545$	5.85990			0.251010
$546$		0			0
$547$	−4.71168	−	4.71168i	−0.201457	−	0.201457i	0.599167	−	0.800624i	$-0.295498\pi$
$547$	−4.71168	−	4.71168i	−0.201457	−	0.201457i	−0.800624	+	0.599167i	$0.795498\pi$
$548$		0			0
$549$	−6.53690	+	6.53690i	−0.278988	+	0.278988i
$550$		0			0
$551$		−	10.8764i		−	0.463350i
$552$		0			0
$553$			1.96590i			0.0835988i
$554$		0			0
$555$	7.24019	−	7.24019i	0.307329	−	0.307329i
$556$		0			0
$557$	10.4457	+	10.4457i	0.442598	+	0.442598i	0.892884	−	0.450286i	$-0.148678\pi$
$557$	10.4457	+	10.4457i	0.442598	+	0.442598i	−0.450286	+	0.892884i	$0.648678\pi$
$558$		0			0
$559$	−12.8117			−0.541876
$560$		0			0
$561$	4.08901			0.172638
$562$		0			0
$563$	−20.5411	−	20.5411i	−0.865705	−	0.865705i	0.126288	−	0.991994i	$-0.459694\pi$
$563$	−20.5411	−	20.5411i	−0.865705	−	0.865705i	−0.991994	+	0.126288i	$0.959694\pi$
$564$		0			0
$565$	5.65338	−	5.65338i	0.237840	−	0.237840i
$566$		0			0
$567$		−	0.138965i		−	0.00583599i
$568$		0			0
$569$		−	19.8690i		−	0.832954i	−0.909146	−	0.416477i	$-0.863265\pi$
$569$		−	19.8690i		−	0.832954i	0.909146	−	0.416477i	$-0.136735\pi$
$570$		0			0
$571$	15.7644	−	15.7644i	0.659720	−	0.659720i	−0.295593	−	0.955314i	$-0.595517\pi$
$571$	15.7644	−	15.7644i	0.659720	−	0.659720i	0.955314	+	0.295593i	$0.0955173\pi$
$572$		0			0
$573$	2.89137	+	2.89137i	0.120789	+	0.120789i
$574$		0			0
$575$	−3.84894			−0.160512
$576$		0			0
$577$	15.1927			0.632482			0.316241	−	0.948679i	$-0.397579\pi$
$577$	15.1927			0.632482			0.316241	+	0.948679i	$0.397579\pi$
$578$		0			0
$579$	−14.1281	−	14.1281i	−0.587143	−	0.587143i
$580$		0			0
$581$	3.27674	−	3.27674i	0.135942	−	0.135942i
$582$		0			0
$583$			13.4948i			0.558899i
$584$		0			0
$585$		−	10.5998i		−	0.438249i
$586$		0			0
$587$	21.7118	−	21.7118i	0.896142	−	0.896142i	−0.0989505	−	0.995092i	$-0.531549\pi$
$587$	21.7118	−	21.7118i	0.896142	−	0.896142i	0.995092	+	0.0989505i	$0.0315485\pi$
$588$		0			0
$589$	−15.6930	−	15.6930i	−0.646618	−	0.646618i
$590$		0			0
$591$	0.0698796			0.00287446
$592$		0			0
$593$	21.4757			0.881902			0.440951	−	0.897531i	$-0.354641\pi$
$593$	21.4757			0.881902			0.440951	+	0.897531i	$0.354641\pi$
$594$		0			0
$595$	−0.440776	−	0.440776i	−0.0180701	−	0.0180701i
$596$		0			0
$597$	8.39627	−	8.39627i	0.343636	−	0.343636i
$598$		0			0
$599$		−	26.7025i		−	1.09104i	−0.838099	−	0.545518i	$-0.816333\pi$
$599$		−	26.7025i		−	1.09104i	0.838099	−	0.545518i	$-0.183667\pi$
$600$		0			0
$601$			7.19053i			0.293308i	0.989188	+	0.146654i	$0.0468504\pi$
$601$			7.19053i			0.293308i	−0.989188	+	0.146654i	$0.953150\pi$
$602$		0			0
$603$	11.2679	−	11.2679i	0.458865	−	0.458865i
$604$		0			0
$605$	−1.83764	−	1.83764i	−0.0747109	−	0.0747109i
$606$		0			0
$607$	5.73930			0.232951			0.116475	−	0.993194i	$-0.462840\pi$
$607$	5.73930			0.232951			0.116475	+	0.993194i	$0.462840\pi$
$608$		0			0
$609$	−0.756515			−0.0306555
$610$		0			0
$611$	−12.9975	−	12.9975i	−0.525824	−	0.525824i
$612$		0			0
$613$	7.61342	−	7.61342i	0.307503	−	0.307503i	−0.536437	−	0.843940i	$-0.680230\pi$
$613$	7.61342	−	7.61342i	0.307503	−	0.307503i	0.843940	+	0.536437i	$0.180230\pi$
$614$		0			0
$615$			3.04205i			0.122667i
$616$		0			0
$617$			5.32012i			0.214180i	0.994249	+	0.107090i	$0.0341533\pi$
$617$			5.32012i			0.214180i	−0.994249	+	0.107090i	$0.965847\pi$
$618$		0			0
$619$	21.6774	−	21.6774i	0.871287	−	0.871287i	−0.121326	−	0.992613i	$-0.538715\pi$
$619$	21.6774	−	21.6774i	0.871287	−	0.871287i	0.992613	+	0.121326i	$0.0387145\pi$
$620$		0			0
$621$	−13.9921	−	13.9921i	−0.561486	−	0.561486i
$622$		0			0
$623$	−8.02597			−0.321554
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−15.0521	−	15.0521i	−0.601123	−	0.601123i
$628$		0			0
$629$	−9.27267	+	9.27267i	−0.369726	+	0.369726i
$630$		0			0
$631$			7.43468i			0.295970i	0.988990	+	0.147985i	$0.0472787\pi$
$631$			7.43468i			0.295970i	−0.988990	+	0.147985i	$0.952721\pi$
$632$		0			0
$633$			0.501855i			0.0199470i
$634$		0			0
$635$	−7.76367	+	7.76367i	−0.308092	+	0.308092i
$636$		0			0
$637$	−26.7870	−	26.7870i	−1.06134	−	1.06134i
$638$		0			0
$639$	−30.1783			−1.19383
$640$		0			0
$641$	−18.9034			−0.746639			−0.373319	−	0.927703i	$-0.621780\pi$
$641$	−18.9034			−0.746639			−0.373319	+	0.927703i	$0.621780\pi$
$642$		0			0
$643$	19.4471	+	19.4471i	0.766918	+	0.766918i	0.977563	−	0.210645i	$-0.0675563\pi$
$643$	19.4471	+	19.4471i	0.766918	+	0.766918i	−0.210645	+	0.977563i	$0.567556\pi$
$644$		0			0
$645$	−1.70292	+	1.70292i	−0.0670523	+	0.0670523i
$646$		0			0
$647$		−	31.9756i		−	1.25709i	−0.777773	−	0.628545i	$-0.783651\pi$
$647$		−	31.9756i		−	1.25709i	0.777773	−	0.628545i	$-0.216349\pi$
$648$		0			0
$649$		−	28.0743i		−	1.10201i
$650$		0			0
$651$	−1.09154	+	1.09154i	−0.0427806	+	0.0427806i
$652$		0			0
$653$	−10.9060	−	10.9060i	−0.426783	−	0.426783i	0.460748	−	0.887531i	$-0.347581\pi$
$653$	−10.9060	−	10.9060i	−0.426783	−	0.426783i	−0.887531	+	0.460748i	$0.847581\pi$
$654$		0			0
$655$	6.21015			0.242651
$656$		0			0
$657$	1.05702			0.0412381
$658$		0			0
$659$	−4.22009	−	4.22009i	−0.164391	−	0.164391i	0.620118	−	0.784509i	$-0.287085\pi$
$659$	−4.22009	−	4.22009i	−0.164391	−	0.164391i	−0.784509	+	0.620118i	$0.787085\pi$
$660$		0			0
$661$	−11.8415	+	11.8415i	−0.460580	+	0.460580i	−0.898845	−	0.438266i	$-0.855593\pi$
$661$	−11.8415	+	11.8415i	−0.460580	+	0.460580i	0.438266	+	0.898845i	$0.355593\pi$
$662$		0			0
$663$		−	7.87665i		−	0.305904i
$664$		0			0
$665$			3.24509i			0.125839i
$666$		0			0
$667$	4.23025	−	4.23025i	0.163796	−	0.163796i
$668$		0			0
$669$	14.5494	+	14.5494i	0.562513	+	0.562513i
$670$		0			0
$671$	−14.1140			−0.544866
$672$		0			0
$673$	30.4089			1.17218			0.586088	−	0.810247i	$-0.300667\pi$
$673$	30.4089			1.17218			0.586088	+	0.810247i	$0.300667\pi$
$674$		0			0
$675$	−3.63532	−	3.63532i	−0.139924	−	0.139924i
$676$		0			0
$677$	−32.6265	+	32.6265i	−1.25394	+	1.25394i	−0.300000	+	0.953939i	$0.596987\pi$
$677$	−32.6265	+	32.6265i	−1.25394	+	1.25394i	−0.953939	+	0.300000i	$0.903013\pi$
$678$		0			0
$679$			4.19323i			0.160921i
$680$		0			0
$681$			23.9782i			0.918845i
$682$		0			0
$683$	17.7882	−	17.7882i	0.680646	−	0.680646i	−0.279499	−	0.960146i	$-0.590169\pi$
$683$	17.7882	−	17.7882i	0.680646	−	0.680646i	0.960146	+	0.279499i	$0.0901685\pi$
$684$		0			0
$685$	15.4828	+	15.4828i	0.591568	+	0.591568i
$686$		0			0
$687$	27.8997			1.06444
$688$		0			0
$689$	25.9951			0.990334
$690$		0			0
$691$	31.1737	+	31.1737i	1.18590	+	1.18590i	0.978189	+	0.207715i	$0.0666027\pi$
$691$	31.1737	+	31.1737i	1.18590	+	1.18590i	0.207715	+	0.978189i	$0.433397\pi$
$692$		0			0
$693$	1.80444	−	1.80444i	0.0685450	−	0.0685450i
$694$		0			0
$695$			6.30922i			0.239322i
$696$		0			0
$697$		−	3.89603i		−	0.147572i
$698$		0			0
$699$	−12.7945	+	12.7945i	−0.483933	+	0.483933i
$700$		0			0
$701$	0.633761	+	0.633761i	0.0239368	+	0.0239368i	0.718974	−	0.695037i	$-0.244612\pi$
$701$	0.633761	+	0.633761i	0.0239368	+	0.0239368i	−0.695037	+	0.718974i	$0.744612\pi$
$702$		0			0
$703$	68.2675			2.57476
$704$		0			0
$705$	−3.45525			−0.130132
$706$		0			0
$707$	−3.19801	−	3.19801i	−0.120274	−	0.120274i
$708$		0			0
$709$	−11.3021	+	11.3021i	−0.424460	+	0.424460i	−0.886736	−	0.462276i	$-0.847033\pi$
$709$	−11.3021	+	11.3021i	−0.424460	+	0.424460i	0.462276	+	0.886736i	$0.347033\pi$
$710$		0			0
$711$		−	8.04798i		−	0.301823i
$712$		0			0
$713$		−	12.2072i		−	0.457164i
$714$		0			0
$715$	11.4432	−	11.4432i	0.427953	−	0.427953i
$716$		0			0
$717$	−20.5519	−	20.5519i	−0.767523	−	0.767523i
$718$		0			0
$719$	19.7820			0.737744			0.368872	−	0.929480i	$-0.379744\pi$
$719$	19.7820			0.737744			0.368872	+	0.929480i	$0.379744\pi$
$720$		0			0
$721$	6.96345			0.259332
$722$		0			0
$723$	−6.75089	−	6.75089i	−0.251068	−	0.251068i
$724$		0			0
$725$	1.09907	−	1.09907i	0.0408184	−	0.0408184i
$726$		0			0
$727$		−	5.00706i		−	0.185702i	−0.995680	−	0.0928508i	$-0.970402\pi$
$727$		−	5.00706i		−	0.185702i	0.995680	−	0.0928508i	$-0.0295980\pi$
$728$		0			0
$729$		−	15.6184i		−	0.578461i
$730$		0			0
$731$	2.18097	−	2.18097i	0.0806660	−	0.0806660i
$732$		0			0
$733$	1.52183	+	1.52183i	0.0562101	+	0.0562101i	0.734653	−	0.678443i	$-0.237345\pi$
$733$	1.52183	+	1.52183i	0.0562101	+	0.0562101i	−0.678443	+	0.734653i	$0.737345\pi$
$734$		0			0
$735$	−7.12102			−0.262663
$736$		0			0
$737$	24.3289			0.896168
$738$		0			0
$739$	−15.0436	−	15.0436i	−0.553388	−	0.553388i	0.374029	−	0.927417i	$-0.377976\pi$
$739$	−15.0436	−	15.0436i	−0.553388	−	0.553388i	−0.927417	+	0.374029i	$0.877976\pi$
$740$		0			0
$741$	−28.9948	+	28.9948i	−1.06515	+	1.06515i
$742$		0			0
$743$			40.7480i			1.49490i	0.664318	+	0.747450i	$0.268722\pi$
$743$			40.7480i			1.49490i	−0.664318	+	0.747450i	$0.731278\pi$
$744$		0			0
$745$			10.3862i			0.380521i
$746$		0			0
$747$	−13.4142	+	13.4142i	−0.490801	+	0.490801i
$748$		0			0
$749$	−5.45770	−	5.45770i	−0.199420	−	0.199420i
$750$		0			0
$751$	20.8596			0.761179			0.380590	−	0.924744i	$-0.375721\pi$
$751$	20.8596			0.761179			0.380590	+	0.924744i	$0.375721\pi$
$752$		0			0
$753$	12.8150			0.467004
$754$		0			0
$755$	−12.0396	−	12.0396i	−0.438166	−	0.438166i
$756$		0			0
$757$	14.1062	−	14.1062i	0.512698	−	0.512698i	−0.402654	−	0.915352i	$-0.631912\pi$
$757$	14.1062	−	14.1062i	0.512698	−	0.512698i	0.915352	+	0.402654i	$0.131912\pi$
$758$		0			0
$759$		−	11.7087i		−	0.424998i
$760$		0			0
$761$		−	13.7778i		−	0.499446i	−0.968317	−	0.249723i	$-0.919660\pi$
$761$		−	13.7778i		−	0.499446i	0.968317	−	0.249723i	$-0.0803395\pi$
$762$		0			0
$763$	1.92157	−	1.92157i	0.0695656	−	0.0695656i
$764$		0			0
$765$	1.80444	+	1.80444i	0.0652397	+	0.0652397i
$766$		0			0
$767$	−54.0794			−1.95270
$768$		0			0
$769$	−6.89137			−0.248509			−0.124255	−	0.992250i	$-0.539654\pi$
$769$	−6.89137			−0.248509			−0.124255	+	0.992250i	$0.539654\pi$
$770$		0			0
$771$	−17.1171	−	17.1171i	−0.616457	−	0.616457i
$772$		0			0
$773$	−11.4803	+	11.4803i	−0.412916	+	0.412916i	−0.882753	−	0.469837i	$-0.844313\pi$
$773$	−11.4803	+	11.4803i	−0.412916	+	0.412916i	0.469837	+	0.882753i	$0.344313\pi$
$774$		0			0
$775$		−	3.17157i		−	0.113926i
$776$		0			0
$777$		−	4.74839i		−	0.170348i
$778$		0			0
$779$	−14.3417	+	14.3417i	−0.513845	+	0.513845i
$780$		0			0
$781$	−32.5794	−	32.5794i	−1.16578	−	1.16578i
$782$		0			0
$783$	7.99093			0.285572
$784$		0			0
$785$	−5.45381			−0.194655
$786$		0			0
$787$	15.0609	+	15.0609i	0.536862	+	0.536862i	0.922606	−	0.385744i	$-0.126055\pi$
$787$	15.0609	+	15.0609i	0.536862	+	0.536862i	−0.385744	+	0.922606i	$0.626055\pi$
$788$		0			0
$789$	−15.7208	+	15.7208i	−0.559676	+	0.559676i
$790$		0			0
$791$		−	3.70770i		−	0.131831i
$792$		0			0
$793$			27.1878i			0.965468i
$794$		0			0
$795$	3.45525	−	3.45525i	0.122545	−	0.122545i
$796$		0			0
$797$	10.4057	+	10.4057i	0.368589	+	0.368589i	0.866963	−	0.498373i	$-0.166069\pi$
$797$	10.4057	+	10.4057i	0.368589	+	0.368589i	−0.498373	+	0.866963i	$0.666069\pi$
$798$		0			0
$799$	4.42522			0.156553
$800$		0			0
$801$	32.8565			1.16093
$802$		0			0
$803$	1.14112	+	1.14112i	0.0402692	+	0.0402692i
$804$		0			0
$805$	−1.26214	+	1.26214i	−0.0444847	+	0.0444847i
$806$		0			0
$807$			9.43062i			0.331973i
$808$		0			0
$809$		−	17.7970i		−	0.625708i	−0.949801	−	0.312854i	$-0.898715\pi$
$809$		−	17.7970i		−	0.625708i	0.949801	−	0.312854i	$-0.101285\pi$
$810$		0			0
$811$	−2.13364	+	2.13364i	−0.0749221	+	0.0749221i	−0.743575	−	0.668653i	$-0.766871\pi$
$811$	−2.13364	+	2.13364i	−0.0749221	+	0.0749221i	0.668653	+	0.743575i	$0.266871\pi$
$812$		0			0
$813$	8.03249	+	8.03249i	0.281712	+	0.281712i
$814$		0			0
$815$	−17.4308			−0.610576
$816$		0			0
$817$	−16.0568			−0.561755
$818$		0			0
$819$	−3.47589	−	3.47589i	−0.121457	−	0.121457i
$820$		0			0
$821$	27.3074	−	27.3074i	0.953034	−	0.953034i	−0.0459119	−	0.998945i	$-0.514619\pi$
$821$	27.3074	−	27.3074i	0.953034	−	0.953034i	0.998945	+	0.0459119i	$0.0146194\pi$
$822$		0			0
$823$		−	41.1720i		−	1.43516i	−0.696474	−	0.717582i	$-0.745249\pi$
$823$		−	41.1720i		−	1.43516i	0.696474	−	0.717582i	$-0.254751\pi$
$824$		0			0
$825$		−	3.04205i		−	0.105911i
$826$		0			0
$827$	36.3202	−	36.3202i	1.26298	−	1.26298i	0.313334	−	0.949643i	$-0.398554\pi$
$827$	36.3202	−	36.3202i	1.26298	−	1.26298i	0.949643	−	0.313334i	$-0.101446\pi$
$828$		0			0
$829$	23.8586	+	23.8586i	0.828645	+	0.828645i	0.987329	−	0.158685i	$-0.0507254\pi$
$829$	23.8586	+	23.8586i	0.828645	+	0.828645i	−0.158685	+	0.987329i	$0.550725\pi$
$830$		0			0
$831$	−24.5013			−0.849940
$832$		0			0
$833$	9.12006			0.315991
$834$		0			0
$835$	−13.1744	−	13.1744i	−0.455919	−	0.455919i
$836$		0			0
$837$	11.5297	−	11.5297i	0.398524	−	0.398524i
$838$		0			0
$839$			17.7869i			0.614072i	0.951698	+	0.307036i	$0.0993372\pi$
$839$			17.7869i			0.614072i	−0.951698	+	0.307036i	$0.900663\pi$
$840$		0			0
$841$		−	26.5841i		−	0.916693i
$842$		0			0
$843$	7.87137	−	7.87137i	0.271105	−	0.271105i
$844$		0			0
$845$	−12.8507	−	12.8507i	−0.442077	−	0.442077i
$846$		0			0
$847$	−1.20520			−0.0414111
$848$		0			0
$849$	−4.15619			−0.142640
$850$		0			0
$851$	26.5519	+	26.5519i	0.910186	+	0.910186i
$852$		0			0
$853$	4.33423	−	4.33423i	0.148401	−	0.148401i	−0.629002	−	0.777403i	$-0.716536\pi$
$853$	4.33423	−	4.33423i	0.148401	−	0.148401i	0.777403	+	0.629002i	$0.216536\pi$
$854$		0			0
$855$		−	13.2847i		−	0.454327i
$856$		0			0
$857$			39.7072i			1.35637i	0.734890	+	0.678186i	$0.237234\pi$
$857$			39.7072i			1.35637i	−0.734890	+	0.678186i	$0.762766\pi$
$858$		0			0
$859$	−3.45317	+	3.45317i	−0.117820	+	0.117820i	−0.763559	−	0.645738i	$-0.776550\pi$
$859$	−3.45317	+	3.45317i	−0.117820	+	0.117820i	0.645738	+	0.763559i	$0.276550\pi$
$860$		0			0
$861$	0.997546	+	0.997546i	0.0339963	+	0.0339963i
$862$		0			0
$863$	−45.1975			−1.53854			−0.769271	−	0.638923i	$-0.779380\pi$
$863$	−45.1975			−1.53854			−0.769271	+	0.638923i	$0.779380\pi$
$864$		0			0
$865$	6.38131			0.216971
$866$		0			0
$867$	−11.2754	−	11.2754i	−0.382932	−	0.382932i
$868$		0			0
$869$	8.68832	−	8.68832i	0.294731	−	0.294731i
$870$		0			0
$871$		−	46.8648i		−	1.58795i
$872$		0			0
$873$		−	17.1661i		−	0.580986i
$874$		0			0
$875$	−0.327919	+	0.327919i	−0.0110857	+	0.0110857i
$876$		0			0
$877$	14.3758	+	14.3758i	0.485436	+	0.485436i	0.906863	−	0.421426i	$-0.138470\pi$
$877$	14.3758	+	14.3758i	0.485436	+	0.485436i	−0.421426	+	0.906863i	$0.638470\pi$
$878$		0			0
$879$	20.9855			0.707824
$880$		0			0
$881$	−12.2102			−0.411371			−0.205685	−	0.978618i	$-0.565942\pi$
$881$	−12.2102			−0.411371			−0.205685	+	0.978618i	$0.565942\pi$
$882$		0			0
$883$	18.6792	+	18.6792i	0.628605	+	0.628605i	0.947717	−	0.319112i	$-0.103385\pi$
$883$	18.6792	+	18.6792i	0.628605	+	0.628605i	−0.319112	+	0.947717i	$0.603385\pi$
$884$		0			0
$885$	−7.18820	+	7.18820i	−0.241629	+	0.241629i
$886$		0			0
$887$		−	42.4950i		−	1.42684i	−0.700736	−	0.713421i	$-0.747145\pi$
$887$		−	42.4950i		−	1.42684i	0.700736	−	0.713421i	$-0.252855\pi$
$888$		0			0
$889$			5.09171i			0.170770i
$890$		0			0
$891$	−0.614157	+	0.614157i	−0.0205750	+	0.0205750i
$892$		0			0
$893$	−16.2897	−	16.2897i	−0.545115	−	0.545115i
$894$		0			0
$895$	21.4828			0.718092
$896$		0			0
$897$	−22.5544			−0.753070
$898$		0			0
$899$	3.48577	+	3.48577i	0.116257	+	0.116257i
$900$		0			0
$901$	−4.42522	+	4.42522i	−0.147425	+	0.147425i
$902$		0			0
$903$			1.11684i			0.0371661i
$904$		0			0
$905$			16.5228i			0.549238i
$906$		0			0
$907$	−4.22149	+	4.22149i	−0.140172	+	0.140172i	−0.773711	−	0.633539i	$-0.781602\pi$
$907$	−4.22149	+	4.22149i	−0.140172	+	0.140172i	0.633539	+	0.773711i	$0.281602\pi$
$908$		0			0
$909$	13.0920	+	13.0920i	0.434233	+	0.434233i
$910$		0			0
$911$	33.0306			1.09435			0.547177	−	0.837017i	$-0.315703\pi$
$911$	33.0306			1.09435			0.547177	+	0.837017i	$0.315703\pi$
$912$		0			0
$913$	−28.9631			−0.958539
$914$		0			0
$915$	3.61379	+	3.61379i	0.119468	+	0.119468i
$916$		0			0
$917$	2.03643	−	2.03643i	0.0672488	−	0.0672488i
$918$		0			0
$919$			18.3501i			0.605313i	0.953100	+	0.302657i	$0.0978736\pi$
$919$			18.3501i			0.605313i	−0.953100	+	0.302657i	$0.902126\pi$
$920$		0			0
$921$			32.1954i			1.06088i
$922$		0			0
$923$	−62.7577	+	62.7577i	−2.06570	+	2.06570i
$924$		0			0
$925$	6.89848	+	6.89848i	0.226821	+	0.226821i
$926$		0			0
$927$	−28.5068			−0.936287
$928$		0			0
$929$	50.7648			1.66554			0.832770	−	0.553619i	$-0.186754\pi$
$929$	50.7648			1.66554			0.832770	+	0.553619i	$0.186754\pi$
$930$		0			0
$931$	−33.5720	−	33.5720i	−1.10028	−	1.10028i
$932$		0			0
$933$	−0.363785	+	0.363785i	−0.0119098	+	0.0119098i
$934$		0			0
$935$			3.89603i			0.127414i
$936$		0			0
$937$			57.2804i			1.87127i	0.352971	+	0.935634i	$0.385171\pi$
$937$			57.2804i			1.87127i	−0.352971	+	0.935634i	$0.614829\pi$
$938$		0			0
$939$	−16.7569	+	16.7569i	−0.546842	+	0.546842i
$940$		0			0
$941$	41.9897	+	41.9897i	1.36882	+	1.36882i	0.862119	+	0.506706i	$0.169137\pi$
$941$	41.9897	+	41.9897i	1.36882	+	1.36882i	0.506706	+	0.862119i	$0.330863\pi$
$942$		0			0
$943$	−11.1561			−0.363292
$944$		0			0
$945$	−2.38418			−0.0775574
$946$		0			0
$947$	−10.7588	−	10.7588i	−0.349613	−	0.349613i	0.510353	−	0.859965i	$-0.329515\pi$
$947$	−10.7588	−	10.7588i	−0.349613	−	0.349613i	−0.859965	+	0.510353i	$0.829515\pi$
$948$		0			0
$949$	2.19814	−	2.19814i	0.0713545	−	0.0713545i
$950$		0			0
$951$			27.6540i			0.896742i
$952$		0			0
$953$		−	33.6640i		−	1.09049i	−0.838278	−	0.545243i	$-0.816438\pi$
$953$		−	33.6640i		−	1.09049i	0.838278	−	0.545243i	$-0.183562\pi$
$954$		0			0
$955$	−2.75491	+	2.75491i	−0.0891467	+	0.0891467i
$956$		0			0
$957$	3.34342	+	3.34342i	0.108077	+	0.108077i
$958$		0			0
$959$	10.1542			0.327897
$960$		0			0
$961$	−20.9411			−0.675520
$962$		0			0
$963$	22.3426	+	22.3426i	0.719981	+	0.719981i
$964$		0			0
$965$	13.4613	−	13.4613i	0.433334	−	0.433334i
$966$		0			0
$967$			12.6075i			0.405430i	0.979238	+	0.202715i	$0.0649764\pi$
$967$			12.6075i			0.405430i	−0.979238	+	0.202715i	$0.935024\pi$
$968$		0			0
$969$		−	9.87174i		−	0.317126i
$970$		0			0
$971$	0.401057	−	0.401057i	0.0128705	−	0.0128705i	−0.700642	−	0.713513i	$-0.747103\pi$
$971$	0.401057	−	0.401057i	0.0128705	−	0.0128705i	0.713513	+	0.700642i	$0.247103\pi$
$972$		0			0
$973$	2.06891	+	2.06891i	0.0663263	+	0.0663263i
$974$		0			0
$975$	−5.85990			−0.187667
$976$		0			0
$977$	−21.1220			−0.675752			−0.337876	−	0.941191i	$-0.609708\pi$
$977$	−21.1220			−0.675752			−0.337876	+	0.941191i	$0.609708\pi$
$978$		0			0
$979$	35.4708	+	35.4708i	1.13365	+	1.13365i
$980$		0			0
$981$	−7.86648	+	7.86648i	−0.251158	+	0.251158i
$982$		0			0
$983$		−	35.2583i		−	1.12457i	−0.826945	−	0.562283i	$-0.809923\pi$
$983$		−	35.2583i		−	1.12457i	0.826945	−	0.562283i	$-0.190077\pi$
$984$		0			0
$985$			0.0665816i			0.00212147i
$986$		0			0
$987$	−1.13304	+	1.13304i	−0.0360651	+	0.0360651i
$988$		0			0
$989$	−6.24509	−	6.24509i	−0.198582	−	0.198582i
$990$		0			0
$991$	11.9471			0.379513			0.189756	−	0.981831i	$-0.439230\pi$
$991$	11.9471			0.379513			0.189756	+	0.981831i	$0.439230\pi$
$992$		0			0
$993$	−26.3397			−0.835867
$994$		0			0
$995$	8.00000	+	8.00000i	0.253617	+	0.253617i
$996$		0			0
$997$	7.49031	−	7.49031i	0.237221	−	0.237221i	−0.578478	−	0.815698i	$-0.696353\pi$
$997$	7.49031	−	7.49031i	0.237221	−	0.237221i	0.815698	+	0.578478i	$0.196353\pi$
$998$		0			0
$999$			50.1564i			1.58688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.l.c.321.3	yes	8
4.3	odd	2		1280.2.l.h.321.2	yes	8
8.3	odd	2		1280.2.l.b.321.3	✓	8
8.5	even	2		1280.2.l.e.321.2	yes	8
16.3	odd	4		1280.2.l.b.961.3	yes	8
16.5	even	4	inner	1280.2.l.c.961.3	yes	8
16.11	odd	4		1280.2.l.h.961.2	yes	8
16.13	even	4		1280.2.l.e.961.2	yes	8
32.5	even	8		5120.2.a.i.1.2		4
32.11	odd	8		5120.2.a.j.1.2		4
32.21	even	8		5120.2.a.p.1.3		4
32.27	odd	8		5120.2.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.l.b.321.3	✓	8	8.3	odd	2
1280.2.l.b.961.3	yes	8	16.3	odd	4
1280.2.l.c.321.3	yes	8	1.1	even	1	trivial
1280.2.l.c.961.3	yes	8	16.5	even	4	inner
1280.2.l.e.321.2	yes	8	8.5	even	2
1280.2.l.e.961.2	yes	8	16.13	even	4
1280.2.l.h.321.2	yes	8	4.3	odd	2
1280.2.l.h.961.2	yes	8	16.11	odd	4
5120.2.a.c.1.3		4	32.27	odd	8
5120.2.a.i.1.2		4	32.5	even	8
5120.2.a.j.1.2		4	32.11	odd	8
5120.2.a.p.1.3		4	32.21	even	8

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.742133 + 0.742133i) q^{3} +(-0.707107 + 0.707107i) q^{5} +0.463747i q^{7} -1.89848i q^{9} +O(q^{10})\)	\(q+(0.742133 + 0.742133i) q^{3} +(-0.707107 + 0.707107i) q^{5} +0.463747i q^{7} -1.89848i q^{9} +(2.04953 - 2.04953i) q^{11} +(-3.94801 - 3.94801i) q^{13} -1.04953 q^{15} +1.34416 q^{17} +(-4.94801 - 4.94801i) q^{19} +(-0.344162 + 0.344162i) q^{21} -3.84894i q^{23} -1.00000i q^{25} +(3.63532 - 3.63532i) q^{27} +(1.09907 + 1.09907i) q^{29} +3.17157 q^{31} +3.04205 q^{33} +(-0.327919 - 0.327919i) q^{35} +(-6.89848 + 6.89848i) q^{37} -5.85990i q^{39} -2.89848i q^{41} +(1.62255 - 1.62255i) q^{43} +(1.34243 + 1.34243i) q^{45} +3.29217 q^{47} +6.78494 q^{49} +(0.997546 + 0.997546i) q^{51} +(-3.29217 + 3.29217i) q^{53} +2.89848i q^{55} -7.34416i q^{57} +(6.84894 - 6.84894i) q^{59} +(-3.44323 - 3.44323i) q^{61} +0.880415 q^{63} +5.58333 q^{65} +(5.93524 + 5.93524i) q^{67} +(2.85643 - 2.85643i) q^{69} -15.8960i q^{71} +0.556770i q^{73} +(0.742133 - 0.742133i) q^{75} +(0.950466 + 0.950466i) q^{77} +4.23917 q^{79} -0.299657 q^{81} +(-7.06578 - 7.06578i) q^{83} +(-0.950466 + 0.950466i) q^{85} +1.63131i q^{87} +17.3068i q^{89} +(1.83088 - 1.83088i) q^{91} +(2.35373 + 2.35373i) q^{93} +6.99755 q^{95} +9.04205 q^{97} +(-3.89100 - 3.89100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3}+O(q^{10}) \) 8 * q - 4 * q^3	\( 8 q - 4 q^{3} + 8 q^{11} + 8 q^{13} + 8 q^{17} + 32 q^{27} - 8 q^{29} + 48 q^{31} - 24 q^{33} - 4 q^{35} - 24 q^{37} + 20 q^{43} + 8 q^{45} - 16 q^{47} - 16 q^{49} - 40 q^{51} + 16 q^{53} + 32 q^{59} - 8 q^{61} + 24 q^{63} + 8 q^{65} + 12 q^{67} + 40 q^{69} - 4 q^{75} + 16 q^{77} - 44 q^{83} - 16 q^{85} + 40 q^{91} - 24 q^{93} + 8 q^{95} + 24 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 8 * q^11 + 8 * q^13 + 8 * q^17 + 32 * q^27 - 8 * q^29 + 48 * q^31 - 24 * q^33 - 4 * q^35 - 24 * q^37 + 20 * q^43 + 8 * q^45 - 16 * q^47 - 16 * q^49 - 40 * q^51 + 16 * q^53 + 32 * q^59 - 8 * q^61 + 24 * q^63 + 8 * q^65 + 12 * q^67 + 40 * q^69 - 4 * q^75 + 16 * q^77 - 44 * q^83 - 16 * q^85 + 40 * q^91 - 24 * q^93 + 8 * q^95 + 24 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more