LMFDB - Embedded newform 1280.2.j.d.63.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(63,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,-32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.14
Character	$\chi$	$=$	1280.63
Dual form			1280.2.j.d.447.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.41944i q^{3} +(-2.21185 + 0.328182i) q^{5} +(0.988699 - 0.988699i) q^{7} -2.85370 q^{9} +(3.82960 - 3.82960i) q^{11} -1.72421 q^{13} +(-0.794018 - 5.35145i) q^{15} +(5.54452 - 5.54452i) q^{17} +(0.392303 - 0.392303i) q^{19} +(2.39210 + 2.39210i) q^{21} +(-4.28678 - 4.28678i) q^{23} +(4.78459 - 1.45178i) q^{25} +0.353970i q^{27} +(4.24211 + 4.24211i) q^{29} -6.43503i q^{31} +(9.26549 + 9.26549i) q^{33} +(-1.86238 + 2.51133i) q^{35} -0.399068 q^{37} -4.17163i q^{39} -2.41844i q^{41} -1.73814 q^{43} +(6.31196 - 0.936533i) q^{45} +(2.36373 + 2.36373i) q^{47} +5.04495i q^{49} +(13.4146 + 13.4146i) q^{51} +6.63925i q^{53} +(-7.21370 + 9.72732i) q^{55} +(0.949154 + 0.949154i) q^{57} +(-6.32477 - 6.32477i) q^{59} +(7.89676 - 7.89676i) q^{61} +(-2.82145 + 2.82145i) q^{63} +(3.81371 - 0.565856i) q^{65} -0.547191 q^{67} +(10.3716 - 10.3716i) q^{69} +2.49249 q^{71} +(-5.30061 + 5.30061i) q^{73} +(3.51250 + 11.5760i) q^{75} -7.57264i q^{77} +14.1666 q^{79} -9.41750 q^{81} -9.94637i q^{83} +(-10.4440 + 14.0833i) q^{85} +(-10.2635 + 10.2635i) q^{87} +8.69135 q^{89} +(-1.70473 + 1.70473i) q^{91} +15.5692 q^{93} +(-0.738970 + 0.996463i) q^{95} +(-3.81410 + 3.81410i) q^{97} +(-10.9285 + 10.9285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) $ 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Character values

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

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

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
$3$			2.41944i			1.39687i	0.715676	+	0.698433i	$0.246119\pi$
$3$			2.41944i			1.39687i	−0.715676	+	0.698433i	$0.753881\pi$
$4$		0			0
$5$	−2.21185	+	0.328182i	−0.989171	+	0.146768i
$5$	−2.21185	+	0.328182i	−0.989171	+	0.146768i
$6$		0			0
$7$	0.988699	−	0.988699i	0.373693	−	0.373693i	−0.495127	−	0.868820i	$-0.664879\pi$
$7$	0.988699	−	0.988699i	0.373693	−	0.373693i	0.868820	+	0.495127i	$0.164879\pi$
$8$		0			0
$9$	−2.85370			−0.951232
$10$		0			0
$11$	3.82960	−	3.82960i	1.15467	−	1.15467i	0.169062	−	0.985605i	$-0.445926\pi$
$11$	3.82960	−	3.82960i	1.15467	−	1.15467i	0.985605	−	0.169062i	$-0.0540737\pi$
$12$		0			0
$13$	−1.72421			−0.478211			−0.239105	−	0.970994i	$-0.576854\pi$
$13$	−1.72421			−0.478211			−0.239105	+	0.970994i	$0.576854\pi$
$14$		0			0
$15$	−0.794018	−	5.35145i	−0.205014	−	1.38174i
$16$		0			0
$17$	5.54452	−	5.54452i	1.34474	−	1.34474i	0.453473	−	0.891270i	$-0.350185\pi$
$17$	5.54452	−	5.54452i	1.34474	−	1.34474i	0.891270	−	0.453473i	$-0.149815\pi$
$18$		0			0
$19$	0.392303	−	0.392303i	0.0900004	−	0.0900004i	−0.660673	−	0.750674i	$-0.729729\pi$
$19$	0.392303	−	0.392303i	0.0900004	−	0.0900004i	0.750674	+	0.660673i	$0.229729\pi$
$20$		0			0
$21$	2.39210	+	2.39210i	0.521999	+	0.521999i
$22$		0			0
$23$	−4.28678	−	4.28678i	−0.893855	−	0.893855i	0.101029	−	0.994883i	$-0.467787\pi$
$23$	−4.28678	−	4.28678i	−0.893855	−	0.893855i	−0.994883	+	0.101029i	$0.967787\pi$
$24$		0			0
$25$	4.78459	−	1.45178i	0.956919	−	0.290356i
$26$		0			0
$27$			0.353970i			0.0681216i
$28$		0			0
$29$	4.24211	+	4.24211i	0.787741	+	0.787741i	0.981123	−	0.193383i	$-0.0619459\pi$
$29$	4.24211	+	4.24211i	0.787741	+	0.787741i	−0.193383	+	0.981123i	$0.561946\pi$
$30$		0			0
$31$		−	6.43503i		−	1.15577i	−0.816120	−	0.577883i	$-0.803879\pi$
$31$		−	6.43503i		−	1.15577i	0.816120	−	0.577883i	$-0.196121\pi$
$32$		0			0
$33$	9.26549	+	9.26549i	1.61291	+	1.61291i
$34$		0			0
$35$	−1.86238	+	2.51133i	−0.314800	+	0.424492i
$36$		0			0
$37$	−0.399068			−0.0656063			−0.0328032	−	0.999462i	$-0.510443\pi$
$37$	−0.399068			−0.0656063			−0.0328032	+	0.999462i	$0.510443\pi$
$38$		0			0
$39$		−	4.17163i		−	0.667996i
$40$		0			0
$41$		−	2.41844i		−	0.377696i	−0.982006	−	0.188848i	$-0.939525\pi$
$41$		−	2.41844i		−	0.377696i	0.982006	−	0.188848i	$-0.0604754\pi$
$42$		0			0
$43$	−1.73814			−0.265063			−0.132532	−	0.991179i	$-0.542311\pi$
$43$	−1.73814			−0.265063			−0.132532	+	0.991179i	$0.542311\pi$
$44$		0			0
$45$	6.31196	−	0.936533i	0.940932	−	0.139610i
$46$		0			0
$47$	2.36373	+	2.36373i	0.344786	+	0.344786i	0.858163	−	0.513377i	$-0.171606\pi$
$47$	2.36373	+	2.36373i	0.344786	+	0.344786i	−0.513377	+	0.858163i	$0.671606\pi$
$48$		0			0
$49$			5.04495i			0.720707i
$50$		0			0
$51$	13.4146	+	13.4146i	1.87842	+	1.87842i
$52$		0			0
$53$			6.63925i			0.911971i	0.889987	+	0.455986i	$0.150713\pi$
$53$			6.63925i			0.911971i	−0.889987	+	0.455986i	$0.849287\pi$
$54$		0			0
$55$	−7.21370	+	9.72732i	−0.972696	+	1.31163i
$56$		0			0
$57$	0.949154	+	0.949154i	0.125718	+	0.125718i
$58$		0			0
$59$	−6.32477	−	6.32477i	−0.823415	−	0.823415i	0.163181	−	0.986596i	$-0.447825\pi$
$59$	−6.32477	−	6.32477i	−0.823415	−	0.823415i	−0.986596	+	0.163181i	$0.947825\pi$
$60$		0			0
$61$	7.89676	−	7.89676i	1.01108	−	1.01108i	0.0111391	−	0.999938i	$-0.496454\pi$
$61$	7.89676	−	7.89676i	1.01108	−	1.01108i	0.999938	−	0.0111391i	$-0.00354577\pi$
$62$		0			0
$63$	−2.82145	+	2.82145i	−0.355469	+	0.355469i
$64$		0			0
$65$	3.81371	−	0.565856i	0.473032	−	0.0701858i
$66$		0			0
$67$	−0.547191			−0.0668500			−0.0334250	−	0.999441i	$-0.510641\pi$
$67$	−0.547191			−0.0668500			−0.0334250	+	0.999441i	$0.510641\pi$
$68$		0			0
$69$	10.3716	−	10.3716i	1.24859	−	1.24859i
$70$		0			0
$71$	2.49249			0.295804			0.147902	−	0.989002i	$-0.452748\pi$
$71$	2.49249			0.295804			0.147902	+	0.989002i	$0.452748\pi$
$72$		0			0
$73$	−5.30061	+	5.30061i	−0.620390	+	0.620390i	−0.945631	−	0.325241i	$-0.894554\pi$
$73$	−5.30061	+	5.30061i	−0.620390	+	0.620390i	0.325241	+	0.945631i	$0.394554\pi$
$74$		0			0
$75$	3.51250	+	11.5760i	0.405589	+	1.33669i
$76$		0			0
$77$		−	7.57264i		−	0.862982i
$78$		0			0
$79$	14.1666			1.59387			0.796933	−	0.604068i	$-0.206454\pi$
$79$	14.1666			1.59387			0.796933	+	0.604068i	$0.206454\pi$
$80$		0			0
$81$	−9.41750			−1.04639
$82$		0			0
$83$		−	9.94637i		−	1.09176i	−0.837865	−	0.545878i	$-0.816196\pi$
$83$		−	9.94637i		−	1.09176i	0.837865	−	0.545878i	$-0.183804\pi$
$84$		0			0
$85$	−10.4440	+	14.0833i	−1.13282	+	1.52755i
$86$		0			0
$87$	−10.2635	+	10.2635i	−1.10037	+	1.10037i
$88$		0			0
$89$	8.69135			0.921281			0.460640	−	0.887587i	$-0.347620\pi$
$89$	8.69135			0.921281			0.460640	+	0.887587i	$0.347620\pi$
$90$		0			0
$91$	−1.70473	+	1.70473i	−0.178704	+	0.178704i
$92$		0			0
$93$	15.5692			1.61445
$94$		0			0
$95$	−0.738970	+	0.996463i	−0.0758167	+	0.102235i
$96$		0			0
$97$	−3.81410	+	3.81410i	−0.387263	+	0.387263i	−0.873710	−	0.486447i	$-0.838293\pi$
$97$	−3.81410	+	3.81410i	−0.387263	+	0.387263i	0.486447	+	0.873710i	$0.338293\pi$
$98$		0			0
$99$	−10.9285	+	10.9285i	−1.09836	+	1.09836i
$100$		0			0
$101$	12.8267	+	12.8267i	1.27630	+	1.27630i	0.942723	+	0.333577i	$0.108256\pi$
$101$	12.8267	+	12.8267i	1.27630	+	1.27630i	0.333577	+	0.942723i	$0.391744\pi$
$102$		0			0
$103$	−12.2361	−	12.2361i	−1.20566	−	1.20566i	−0.972418	−	0.233243i	$-0.925066\pi$
$103$	−12.2361	−	12.2361i	−1.20566	−	1.20566i	−0.233243	−	0.972418i	$-0.574934\pi$
$104$		0			0
$105$	−6.07602	−	4.50593i	−0.592959	−	0.439734i
$106$		0			0
$107$			10.3616i			1.00170i	0.865535	+	0.500848i	$0.166978\pi$
$107$			10.3616i			1.00170i	−0.865535	+	0.500848i	$0.833022\pi$
$108$		0			0
$109$	−10.6838	−	10.6838i	−1.02332	−	1.02332i	−0.999722	−	0.0235966i	$-0.992488\pi$
$109$	−10.6838	−	10.6838i	−1.02332	−	1.02332i	−0.0235966	−	0.999722i	$-0.507512\pi$
$110$		0			0
$111$		−	0.965521i		−	0.0916432i
$112$		0			0
$113$	6.22637	+	6.22637i	0.585728	+	0.585728i	0.936472	−	0.350744i	$-0.114071\pi$
$113$	6.22637	+	6.22637i	0.585728	+	0.585728i	−0.350744	+	0.936472i	$0.614071\pi$
$114$		0			0
$115$	10.8886	+	8.07488i	1.01536	+	0.752986i
$116$		0			0
$117$	4.92038			0.454889
$118$		0			0
$119$		−	10.9637i		−	1.00504i
$120$		0			0
$121$		−	18.3316i		−	1.66651i
$122$		0			0
$123$	5.85126			0.527591
$124$		0			0
$125$	−10.1064	+	4.78135i	−0.903941	+	0.427657i
$126$		0			0
$127$	1.51284	+	1.51284i	0.134242	+	0.134242i	0.771035	−	0.636793i	$-0.219739\pi$
$127$	1.51284	+	1.51284i	0.134242	+	0.134242i	−0.636793	+	0.771035i	$0.719739\pi$
$128$		0			0
$129$		−	4.20532i		−	0.370258i
$130$		0			0
$131$	2.48069	+	2.48069i	0.216739	+	0.216739i	0.807123	−	0.590384i	$-0.201024\pi$
$131$	2.48069	+	2.48069i	0.216739	+	0.216739i	−0.590384	+	0.807123i	$0.701024\pi$
$132$		0			0
$133$		−	0.775739i		−	0.0672651i
$134$		0			0
$135$	−0.116167	−	0.782931i	−0.00999805	−	0.0673840i
$136$		0			0
$137$	14.5773	+	14.5773i	1.24543	+	1.24543i	0.957718	+	0.287709i	$0.0928936\pi$
$137$	14.5773	+	14.5773i	1.24543	+	1.24543i	0.287709	+	0.957718i	$0.407106\pi$
$138$		0			0
$139$	−1.22127	−	1.22127i	−0.103587	−	0.103587i	0.653414	−	0.757001i	$-0.273336\pi$
$139$	−1.22127	−	1.22127i	−0.103587	−	0.103587i	−0.757001	+	0.653414i	$0.773336\pi$
$140$		0			0
$141$	−5.71892	+	5.71892i	−0.481620	+	0.481620i
$142$		0			0
$143$	−6.60304	+	6.60304i	−0.552174	+	0.552174i
$144$		0			0
$145$	−10.7751	−	7.99075i	−0.894825	−	0.663595i
$146$		0			0
$147$	−12.2060			−1.00673
$148$		0			0
$149$	8.19719	−	8.19719i	0.671540	−	0.671540i	−0.286531	−	0.958071i	$-0.592502\pi$
$149$	8.19719	−	8.19719i	0.671540	−	0.671540i	0.958071	+	0.286531i	$0.0925021\pi$
$150$		0			0
$151$	10.3301			0.840652			0.420326	−	0.907373i	$-0.361916\pi$
$151$	10.3301			0.840652			0.420326	+	0.907373i	$0.361916\pi$
$152$		0			0
$153$	−15.8224	+	15.8224i	−1.27916	+	1.27916i
$154$		0			0
$155$	2.11186	+	14.2334i	0.169629	+	1.14325i
$156$		0			0
$157$			0.493020i			0.0393473i	0.999806	+	0.0196737i	$0.00626272\pi$
$157$			0.493020i			0.0393473i	−0.999806	+	0.0196737i	$0.993737\pi$
$158$		0			0
$159$	−16.0633			−1.27390
$160$		0			0
$161$	−8.47666			−0.668055
$162$		0			0
$163$		−	16.9807i		−	1.33003i	−0.746831	−	0.665014i	$-0.768426\pi$
$163$		−	16.9807i		−	1.33003i	0.746831	−	0.665014i	$-0.231574\pi$
$164$		0			0
$165$	−23.5347	−	17.4531i	−1.83217	−	1.35872i
$166$		0			0
$167$	3.95546	−	3.95546i	0.306083	−	0.306083i	−0.537305	−	0.843388i	$-0.680558\pi$
$167$	3.95546	−	3.95546i	0.306083	−	0.306083i	0.843388	+	0.537305i	$0.180558\pi$
$168$		0			0
$169$	−10.0271			−0.771315
$170$		0			0
$171$	−1.11951	+	1.11951i	−0.0856113	+	0.0856113i
$172$		0			0
$173$	0.380124			0.0289003			0.0144501	−	0.999896i	$-0.495400\pi$
$173$	0.380124			0.0289003			0.0144501	+	0.999896i	$0.495400\pi$
$174$		0			0
$175$	3.29515	−	6.16590i	0.249090	−	0.466098i
$176$		0			0
$177$	15.3024	−	15.3024i	1.15020	−	1.15020i
$178$		0			0
$179$	10.6632	−	10.6632i	0.797007	−	0.797007i	−0.185615	−	0.982622i	$-0.559428\pi$
$179$	10.6632	−	10.6632i	0.797007	−	0.797007i	0.982622	+	0.185615i	$0.0594279\pi$
$180$		0			0
$181$	−13.1021	−	13.1021i	−0.973875	−	0.973875i	0.0257926	−	0.999667i	$-0.491789\pi$
$181$	−13.1021	−	13.1021i	−0.973875	−	0.973875i	−0.999667	+	0.0257926i	$0.991789\pi$
$182$		0			0
$183$	19.1058	+	19.1058i	1.41234	+	1.41234i
$184$		0			0
$185$	0.882680	−	0.130967i	0.0648959	−	0.00962888i
$186$		0			0
$187$		−	42.4665i		−	3.10546i
$188$		0			0
$189$	0.349970	+	0.349970i	0.0254566	+	0.0254566i
$190$		0			0
$191$		−	11.2575i		−	0.814565i	−0.913302	−	0.407282i	$-0.866477\pi$
$191$		−	11.2575i		−	0.814565i	0.913302	−	0.407282i	$-0.133523\pi$
$192$		0			0
$193$	8.11178	+	8.11178i	0.583898	+	0.583898i	0.935972	−	0.352074i	$-0.114523\pi$
$193$	8.11178	+	8.11178i	0.583898	+	0.583898i	−0.352074	+	0.935972i	$0.614523\pi$
$194$		0			0
$195$	1.36906	+	9.22704i	0.0980401	+	0.660762i
$196$		0			0
$197$	9.56913			0.681772			0.340886	−	0.940105i	$-0.389273\pi$
$197$	9.56913			0.681772			0.340886	+	0.940105i	$0.389273\pi$
$198$		0			0
$199$		−	3.28634i		−	0.232962i	−0.993193	−	0.116481i	$-0.962839\pi$
$199$		−	3.28634i		−	0.232962i	0.993193	−	0.116481i	$-0.0371615\pi$
$200$		0			0
$201$		−	1.32390i		−	0.0933804i
$202$		0			0
$203$	8.38834			0.588746
$204$		0			0
$205$	0.793687	+	5.34923i	0.0554335	+	0.373606i
$206$		0			0
$207$	12.2332	+	12.2332i	0.850264	+	0.850264i
$208$		0			0
$209$		−	3.00472i		−	0.207841i
$210$		0			0
$211$	−12.0755	−	12.0755i	−0.831309	−	0.831309i	0.156387	−	0.987696i	$-0.450015\pi$
$211$	−12.0755	−	12.0755i	−0.831309	−	0.831309i	−0.987696	+	0.156387i	$0.950015\pi$
$212$		0			0
$213$			6.03044i			0.413199i
$214$		0			0
$215$	3.84450	−	0.570425i	0.262193	−	0.0389027i
$216$		0			0
$217$	−6.36231	−	6.36231i	−0.431902	−	0.431902i
$218$		0			0
$219$	−12.8245	−	12.8245i	−0.866601	−	0.866601i
$220$		0			0
$221$	−9.55993	+	9.55993i	−0.643070	+	0.643070i
$222$		0			0
$223$	−8.59151	+	8.59151i	−0.575330	+	0.575330i	−0.933613	−	0.358283i	$-0.883362\pi$
$223$	−8.59151	+	8.59151i	−0.575330	+	0.575330i	0.358283	+	0.933613i	$0.383362\pi$
$224$		0			0
$225$	−13.6538	+	4.14295i	−0.910252	+	0.276196i
$226$		0			0
$227$	−20.0186			−1.32868			−0.664339	−	0.747431i	$-0.731287\pi$
$227$	−20.0186			−1.32868			−0.664339	+	0.747431i	$0.731287\pi$
$228$		0			0
$229$	−13.1114	+	13.1114i	−0.866426	+	0.866426i	−0.992075	−	0.125649i	$-0.959899\pi$
$229$	−13.1114	+	13.1114i	−0.866426	+	0.866426i	0.125649	+	0.992075i	$0.459899\pi$
$230$		0			0
$231$	18.3216			1.20547
$232$		0			0
$233$	8.96222	−	8.96222i	0.587134	−	0.587134i	−0.349720	−	0.936854i	$-0.613723\pi$
$233$	8.96222	−	8.96222i	0.587134	−	0.587134i	0.936854	+	0.349720i	$0.113723\pi$
$234$		0			0
$235$	−6.00397	−	4.45250i	−0.391656	−	0.290449i
$236$		0			0
$237$			34.2752i			2.22642i
$238$		0			0
$239$	21.6813			1.40244			0.701222	−	0.712943i	$-0.252638\pi$
$239$	21.6813			1.40244			0.701222	+	0.712943i	$0.252638\pi$
$240$		0			0
$241$	1.18683			0.0764507			0.0382254	−	0.999269i	$-0.487830\pi$
$241$	1.18683			0.0764507			0.0382254	+	0.999269i	$0.487830\pi$
$242$		0			0
$243$		−	21.7232i		−	1.39354i
$244$		0			0
$245$	−1.65566	−	11.1587i	−0.105776	−	0.712902i
$246$		0			0
$247$	−0.676414	+	0.676414i	−0.0430392	+	0.0430392i
$248$		0			0
$249$	24.0647			1.52504
$250$		0			0
$251$	8.90640	−	8.90640i	0.562167	−	0.562167i	−0.367755	−	0.929923i	$-0.619874\pi$
$251$	8.90640	−	8.90640i	0.562167	−	0.562167i	0.929923	+	0.367755i	$0.119874\pi$
$252$		0			0
$253$	−32.8333			−2.06421
$254$		0			0
$255$	−34.0737	−	25.2688i	−2.13378	−	1.58239i
$256$		0			0
$257$	1.35457	−	1.35457i	0.0844959	−	0.0844959i	−0.663596	−	0.748091i	$-0.730970\pi$
$257$	1.35457	−	1.35457i	0.0844959	−	0.0844959i	0.748091	+	0.663596i	$0.230970\pi$
$258$		0			0
$259$	−0.394558	+	0.394558i	−0.0245166	+	0.0245166i
$260$		0			0
$261$	−12.1057	−	12.1057i	−0.749324	−	0.749324i
$262$		0			0
$263$	7.07763	+	7.07763i	0.436426	+	0.436426i	0.890807	−	0.454382i	$-0.150140\pi$
$263$	7.07763	+	7.07763i	0.436426	+	0.436426i	−0.454382	+	0.890807i	$0.650140\pi$
$264$		0			0
$265$	−2.17888	−	14.6851i	−0.133848	−	0.902096i
$266$		0			0
$267$			21.0282i			1.28691i
$268$		0			0
$269$	4.60770	+	4.60770i	0.280936	+	0.280936i	0.833482	−	0.552546i	$-0.186344\pi$
$269$	4.60770	+	4.60770i	0.280936	+	0.280936i	−0.552546	+	0.833482i	$0.686344\pi$
$270$		0			0
$271$			9.23996i			0.561288i	0.959812	+	0.280644i	$0.0905480\pi$
$271$			9.23996i			0.561288i	−0.959812	+	0.280644i	$0.909452\pi$
$272$		0			0
$273$	−4.12449	−	4.12449i	−0.249625	−	0.249625i
$274$		0			0
$275$	12.7633	−	23.8828i	0.769658	−	1.44019i
$276$		0			0
$277$	−2.60749			−0.156669			−0.0783345	−	0.996927i	$-0.524960\pi$
$277$	−2.60749			−0.156669			−0.0783345	+	0.996927i	$0.524960\pi$
$278$		0			0
$279$			18.3636i			1.09940i
$280$		0			0
$281$			8.70372i			0.519220i	0.965714	+	0.259610i	$0.0835941\pi$
$281$			8.70372i			0.519220i	−0.965714	+	0.259610i	$0.916406\pi$
$282$		0			0
$283$	−12.6355			−0.751105			−0.375553	−	0.926801i	$-0.622547\pi$
$283$	−12.6355			−0.751105			−0.375553	+	0.926801i	$0.622547\pi$
$284$		0			0
$285$	−2.41088	−	1.78789i	−0.142808	−	0.105906i
$286$		0			0
$287$	−2.39110	−	2.39110i	−0.141142	−	0.141142i
$288$		0			0
$289$		−	44.4833i		−	2.61667i
$290$		0			0
$291$	−9.22799	−	9.22799i	−0.540955	−	0.540955i
$292$		0			0
$293$			12.5444i			0.732850i	0.930448	+	0.366425i	$0.119418\pi$
$293$			12.5444i			0.732850i	−0.930448	+	0.366425i	$0.880582\pi$
$294$		0			0
$295$	16.0651	+	11.9138i	0.935349	+	0.693648i
$296$		0			0
$297$	1.35556	+	1.35556i	0.0786578	+	0.0786578i
$298$		0			0
$299$	7.39131	+	7.39131i	0.427451	+	0.427451i
$300$		0			0
$301$	−1.71849	+	1.71849i	−0.0990523	+	0.0990523i
$302$		0			0
$303$	−31.0333	+	31.0333i	−1.78282	+	1.78282i
$304$		0			0
$305$	−14.8749	+	20.0581i	−0.851735	+	1.14852i
$306$		0			0
$307$	5.83167			0.332831			0.166416	−	0.986056i	$-0.446781\pi$
$307$	5.83167			0.332831			0.166416	+	0.986056i	$0.446781\pi$
$308$		0			0
$309$	29.6046	−	29.6046i	1.68415	−	1.68415i
$310$		0			0
$311$	−15.0727			−0.854697			−0.427348	−	0.904087i	$-0.640552\pi$
$311$	−15.0727			−0.854697			−0.427348	+	0.904087i	$0.640552\pi$
$312$		0			0
$313$	−5.72437	+	5.72437i	−0.323560	+	0.323560i	−0.850131	−	0.526571i	$-0.823477\pi$
$313$	−5.72437	+	5.72437i	−0.323560	+	0.323560i	0.526571	+	0.850131i	$0.323477\pi$
$314$		0			0
$315$	5.31468	−	7.16658i	0.299448	−	0.403791i
$316$		0			0
$317$		−	17.6245i		−	0.989888i	−0.868925	−	0.494944i	$-0.835189\pi$
$317$		−	17.6245i		−	0.989888i	0.868925	−	0.494944i	$-0.164811\pi$
$318$		0			0
$319$	32.4912			1.81916
$320$		0			0
$321$	−25.0693			−1.39923
$322$		0			0
$323$		−	4.35026i		−	0.242055i
$324$		0			0
$325$	−8.24966	+	2.50318i	−0.457609	+	0.138851i
$326$		0			0
$327$	25.8487	−	25.8487i	1.42944	−	1.42944i
$328$		0			0
$329$	4.67404			0.257688
$330$		0			0
$331$	−13.5768	+	13.5768i	−0.746247	+	0.746247i	−0.973772	−	0.227525i	$-0.926937\pi$
$331$	−13.5768	+	13.5768i	−0.746247	+	0.746247i	0.227525	+	0.973772i	$0.426937\pi$
$332$		0			0
$333$	1.13882			0.0624069
$334$		0			0
$335$	1.21031	−	0.179578i	0.0661261	−	0.00981141i
$336$		0			0
$337$	−13.1727	+	13.1727i	−0.717560	+	0.717560i	−0.968105	−	0.250545i	$-0.919390\pi$
$337$	−13.1727	+	13.1727i	−0.717560	+	0.717560i	0.250545	+	0.968105i	$0.419390\pi$
$338$		0			0
$339$	−15.0643	+	15.0643i	−0.818183	+	0.818183i
$340$		0			0
$341$	−24.6436	−	24.6436i	−1.33453	−	1.33453i
$342$		0			0
$343$	11.9088	+	11.9088i	0.643016	+	0.643016i
$344$		0			0
$345$	−19.5367	+	26.3442i	−1.05182	+	1.41833i
$346$		0			0
$347$			16.5605i			0.889015i	0.895775	+	0.444508i	$0.146621\pi$
$347$			16.5605i			0.889015i	−0.895775	+	0.444508i	$0.853379\pi$
$348$		0			0
$349$	0.491725	+	0.491725i	0.0263214	+	0.0263214i	0.720145	−	0.693824i	$-0.244075\pi$
$349$	0.491725	+	0.491725i	0.0263214	+	0.0263214i	−0.693824	+	0.720145i	$0.744075\pi$
$350$		0			0
$351$		−	0.610320i		−	0.0325765i
$352$		0			0
$353$	−15.2506	−	15.2506i	−0.811709	−	0.811709i	0.173181	−	0.984890i	$-0.444596\pi$
$353$	−15.2506	−	15.2506i	−0.811709	−	0.811709i	−0.984890	+	0.173181i	$0.944596\pi$
$354$		0			0
$355$	−5.51302	+	0.817991i	−0.292601	+	0.0434145i
$356$		0			0
$357$	26.5261			1.40391
$358$		0			0
$359$		−	4.01174i		−	0.211732i	−0.994380	−	0.105866i	$-0.966239\pi$
$359$		−	4.01174i		−	0.211732i	0.994380	−	0.105866i	$-0.0337614\pi$
$360$		0			0
$361$			18.6922i			0.983800i
$362$		0			0
$363$	44.3523			2.32789
$364$		0			0
$365$	9.98461	−	13.4637i	0.522618	−	0.704724i
$366$		0			0
$367$	15.8315	+	15.8315i	0.826398	+	0.826398i	0.987017	−	0.160618i	$-0.0513488\pi$
$367$	15.8315	+	15.8315i	0.826398	+	0.826398i	−0.160618	+	0.987017i	$0.551349\pi$
$368$		0			0
$369$			6.90148i			0.359277i
$370$		0			0
$371$	6.56422	+	6.56422i	0.340797	+	0.340797i
$372$		0			0
$373$			32.8148i			1.69908i	0.527521	+	0.849542i	$0.323122\pi$
$373$			32.8148i			1.69908i	−0.527521	+	0.849542i	$0.676878\pi$
$374$		0			0
$375$	−11.5682	−	24.4518i	−0.597379	−	1.26268i
$376$		0			0
$377$	−7.31430	−	7.31430i	−0.376706	−	0.376706i
$378$		0			0
$379$	0.167702	+	0.167702i	0.00861429	+	0.00861429i	0.711401	−	0.702787i	$-0.248061\pi$
$379$	0.167702	+	0.167702i	0.00861429	+	0.00861429i	−0.702787	+	0.711401i	$0.748061\pi$
$380$		0			0
$381$	−3.66022	+	3.66022i	−0.187519	+	0.187519i
$382$		0			0
$383$	−17.2141	+	17.2141i	−0.879597	+	0.879597i	−0.993493	−	0.113896i	$-0.963667\pi$
$383$	−17.2141	+	17.2141i	−0.879597	+	0.879597i	0.113896	+	0.993493i	$0.463667\pi$
$384$		0			0
$385$	2.48521	+	16.7496i	0.126658	+	0.853637i
$386$		0			0
$387$	4.96011			0.252137
$388$		0			0
$389$	−2.78168	+	2.78168i	−0.141037	+	0.141037i	−0.774100	−	0.633063i	$-0.781797\pi$
$389$	−2.78168	+	2.78168i	−0.141037	+	0.141037i	0.633063	+	0.774100i	$0.281797\pi$
$390$		0			0
$391$	−47.5362			−2.40401
$392$		0			0
$393$	−6.00189	+	6.00189i	−0.302755	+	0.302755i
$394$		0			0
$395$	−31.3344	+	4.64922i	−1.57661	+	0.233928i
$396$		0			0
$397$		−	25.7866i		−	1.29419i	−0.762409	−	0.647095i	$-0.775984\pi$
$397$		−	25.7866i		−	1.29419i	0.762409	−	0.647095i	$-0.224016\pi$
$398$		0			0
$399$	1.87685			0.0939603
$400$		0			0
$401$	−9.92544			−0.495653			−0.247827	−	0.968804i	$-0.579716\pi$
$401$	−9.92544			−0.495653			−0.247827	+	0.968804i	$0.579716\pi$
$402$		0			0
$403$			11.0954i			0.552700i
$404$		0			0
$405$	20.8301	−	3.09066i	1.03506	−	0.153576i
$406$		0			0
$407$	−1.52827	+	1.52827i	−0.0757535	+	0.0757535i
$408$		0			0
$409$	−16.1406			−0.798102			−0.399051	−	0.916929i	$-0.630660\pi$
$409$	−16.1406			−0.798102			−0.399051	+	0.916929i	$0.630660\pi$
$410$		0			0
$411$	−35.2690	+	35.2690i	−1.73969	+	1.73969i
$412$		0			0
$413$	−12.5066			−0.615409
$414$		0			0
$415$	3.26422	+	21.9999i	0.160234	+	1.07993i
$416$		0			0
$417$	2.95479	−	2.95479i	0.144697	−	0.144697i
$418$		0			0
$419$	−12.7442	+	12.7442i	−0.622597	+	0.622597i	−0.946195	−	0.323598i	$-0.895107\pi$
$419$	−12.7442	+	12.7442i	−0.622597	+	0.622597i	0.323598	+	0.946195i	$0.395107\pi$
$420$		0			0
$421$	−6.92756	−	6.92756i	−0.337629	−	0.337629i	0.517845	−	0.855474i	$-0.326734\pi$
$421$	−6.92756	−	6.92756i	−0.337629	−	0.337629i	−0.855474	+	0.517845i	$0.826734\pi$
$422$		0			0
$423$	−6.74538	−	6.74538i	−0.327972	−	0.327972i
$424$		0			0
$425$	18.4788	−	34.5777i	0.896355	−	1.67726i
$426$		0			0
$427$		−	15.6150i		−	0.755665i
$428$		0			0
$429$	−15.9757	−	15.9757i	−0.771313	−	0.771313i
$430$		0			0
$431$		−	11.3129i		−	0.544923i	−0.962167	−	0.272462i	$-0.912162\pi$
$431$		−	11.3129i		−	0.544923i	0.962167	−	0.272462i	$-0.0878378\pi$
$432$		0			0
$433$	14.5806	+	14.5806i	0.700700	+	0.700700i	0.964561	−	0.263861i	$-0.0849959\pi$
$433$	14.5806	+	14.5806i	0.700700	+	0.700700i	−0.263861	+	0.964561i	$0.584996\pi$
$434$		0			0
$435$	19.3331	−	26.0698i	0.926953	−	1.24995i
$436$		0			0
$437$	−3.36343			−0.160895
$438$		0			0
$439$			34.9768i			1.66935i	0.550743	+	0.834675i	$0.314344\pi$
$439$			34.9768i			1.66935i	−0.550743	+	0.834675i	$0.685656\pi$
$440$		0			0
$441$		−	14.3968i		−	0.685560i
$442$		0			0
$443$	7.23644			0.343814			0.171907	−	0.985113i	$-0.445007\pi$
$443$	7.23644			0.343814			0.171907	+	0.985113i	$0.445007\pi$
$444$		0			0
$445$	−19.2240	+	2.85234i	−0.911304	+	0.135214i
$446$		0			0
$447$	19.8326	+	19.8326i	0.938051	+	0.938051i
$448$		0			0
$449$		−	19.3556i		−	0.913445i	−0.889609	−	0.456723i	$-0.849023\pi$
$449$		−	19.3556i		−	0.913445i	0.889609	−	0.456723i	$-0.150977\pi$
$450$		0			0
$451$	−9.26164	−	9.26164i	−0.436113	−	0.436113i
$452$		0			0
$453$			24.9931i			1.17428i
$454$		0			0
$455$	3.21115	−	4.33007i	0.150541	−	0.202997i
$456$		0			0
$457$	−3.88093	−	3.88093i	−0.181542	−	0.181542i	0.610485	−	0.792028i	$-0.290974\pi$
$457$	−3.88093	−	3.88093i	−0.181542	−	0.181542i	−0.792028	+	0.610485i	$0.790974\pi$
$458$		0			0
$459$	1.96260	+	1.96260i	0.0916061	+	0.0916061i
$460$		0			0
$461$	−4.98860	+	4.98860i	−0.232342	+	0.232342i	−0.813670	−	0.581327i	$-0.802534\pi$
$461$	−4.98860	+	4.98860i	−0.232342	+	0.232342i	0.581327	+	0.813670i	$0.302534\pi$
$462$		0			0
$463$	14.2136	−	14.2136i	0.660560	−	0.660560i	−0.294952	−	0.955512i	$-0.595304\pi$
$463$	14.2136	−	14.2136i	0.660560	−	0.660560i	0.955512	+	0.294952i	$0.0953036\pi$
$464$		0			0
$465$	−34.4368	+	5.10953i	−1.59697	+	0.236949i
$466$		0			0
$467$	−8.37481			−0.387540			−0.193770	−	0.981047i	$-0.562072\pi$
$467$	−8.37481			−0.387540			−0.193770	+	0.981047i	$0.562072\pi$
$468$		0			0
$469$	−0.541007	+	0.541007i	−0.0249814	+	0.0249814i
$470$		0			0
$471$	−1.19283			−0.0549629
$472$		0			0
$473$	−6.65636	+	6.65636i	−0.306060	+	0.306060i
$474$		0			0
$475$	1.30747	−	2.44655i	0.0599909	−	0.112255i
$476$		0			0
$477$		−	18.9464i		−	0.867497i
$478$		0			0
$479$	−28.4608			−1.30041			−0.650204	−	0.759760i	$-0.725317\pi$
$479$	−28.4608			−1.30041			−0.650204	+	0.759760i	$0.725317\pi$
$480$		0			0
$481$	0.688078			0.0313736
$482$		0			0
$483$		−	20.5088i		−	0.933182i
$484$		0			0
$485$	7.18451	−	9.68795i	0.326232	−	0.439907i
$486$		0			0
$487$	−4.43648	+	4.43648i	−0.201036	+	0.201036i	−0.800444	−	0.599408i	$-0.795403\pi$
$487$	−4.43648	+	4.43648i	−0.201036	+	0.201036i	0.599408	+	0.800444i	$0.295403\pi$
$488$		0			0
$489$	41.0837			1.85787
$490$		0			0
$491$	−4.12635	+	4.12635i	−0.186220	+	0.186220i	−0.794060	−	0.607840i	$-0.792036\pi$
$491$	−4.12635	+	4.12635i	−0.186220	+	0.186220i	0.607840	+	0.794060i	$0.292036\pi$
$492$		0			0
$493$	47.0409			2.11862
$494$		0			0
$495$	20.5857	−	27.7588i	0.925260	−	1.24767i
$496$		0			0
$497$	2.46432	−	2.46432i	0.110540	−	0.110540i
$498$		0			0
$499$	−2.20498	+	2.20498i	−0.0987087	+	0.0987087i	−0.754737	−	0.656028i	$-0.772235\pi$
$499$	−2.20498	+	2.20498i	−0.0987087	+	0.0987087i	0.656028	+	0.754737i	$0.272235\pi$
$500$		0			0
$501$	9.57001	+	9.57001i	0.427556	+	0.427556i
$502$		0			0
$503$	−2.73415	−	2.73415i	−0.121910	−	0.121910i	0.643520	−	0.765430i	$-0.277473\pi$
$503$	−2.73415	−	2.73415i	−0.121910	−	0.121910i	−0.765430	+	0.643520i	$0.777473\pi$
$504$		0			0
$505$	−32.5802	−	24.1612i	−1.44980	−	1.07516i
$506$		0			0
$507$		−	24.2600i		−	1.07742i
$508$		0			0
$509$	26.2648	+	26.2648i	1.16417	+	1.16417i	0.983554	+	0.180615i	$0.0578088\pi$
$509$	26.2648	+	26.2648i	1.16417	+	1.16417i	0.180615	+	0.983554i	$0.442191\pi$
$510$		0			0
$511$			10.4814i			0.463671i
$512$		0			0
$513$	0.138864	+	0.138864i	0.00613098	+	0.00613098i
$514$		0			0
$515$	31.0802	+	23.0488i	1.36956	+	1.01565i
$516$		0			0
$517$	18.1043			0.796226
$518$		0			0
$519$			0.919687i			0.0403698i
$520$		0			0
$521$			34.1422i			1.49579i	0.663814	+	0.747897i	$0.268936\pi$
$521$			34.1422i			1.49579i	−0.663814	+	0.747897i	$0.731064\pi$
$522$		0			0
$523$	12.7692			0.558357			0.279179	−	0.960239i	$-0.409938\pi$
$523$	12.7692			0.558357			0.279179	+	0.960239i	$0.409938\pi$
$524$		0			0
$525$	14.9180	+	7.97241i	0.651076	+	0.347945i
$526$		0			0
$527$	−35.6792	−	35.6792i	−1.55421	−	1.55421i
$528$		0			0
$529$			13.7529i			0.597952i
$530$		0			0
$531$	18.0490	+	18.0490i	0.783259	+	0.783259i
$532$		0			0
$533$			4.16990i			0.180618i
$534$		0			0
$535$	−3.40050	−	22.9184i	−0.147016	−	0.990849i
$536$		0			0
$537$	25.7991	+	25.7991i	1.11331	+	1.11331i
$538$		0			0
$539$	19.3201	+	19.3201i	0.832177	+	0.832177i
$540$		0			0
$541$	14.2769	−	14.2769i	0.613812	−	0.613812i	−0.330125	−	0.943937i	$-0.607091\pi$
$541$	14.2769	−	14.2769i	0.613812	−	0.613812i	0.943937	+	0.330125i	$0.107091\pi$
$542$		0			0
$543$	31.6999	−	31.6999i	1.36037	−	1.36037i
$544$		0			0
$545$	27.1371	+	20.1247i	1.16243	+	0.862047i
$546$		0			0
$547$	3.67734			0.157232			0.0786158	−	0.996905i	$-0.474950\pi$
$547$	3.67734			0.157232			0.0786158	+	0.996905i	$0.474950\pi$
$548$		0			0
$549$	−22.5350	+	22.5350i	−0.961769	+	0.961769i
$550$		0			0
$551$	3.32839			0.141794
$552$		0			0
$553$	14.0065	−	14.0065i	0.595617	−	0.595617i
$554$		0			0
$555$	0.316867	+	2.13559i	0.0134502	+	0.0906508i
$556$		0			0
$557$			22.6665i			0.960412i	0.877156	+	0.480206i	$0.159438\pi$
$557$			22.6665i			0.960412i	−0.877156	+	0.480206i	$0.840562\pi$
$558$		0			0
$559$	2.99692			0.126756
$560$		0			0
$561$	102.745			4.33791
$562$		0			0
$563$			36.8583i			1.55339i	0.629876	+	0.776696i	$0.283106\pi$
$563$			36.8583i			1.55339i	−0.629876	+	0.776696i	$0.716894\pi$
$564$		0			0
$565$	−15.8152	−	11.7284i	−0.665351	−	0.493419i
$566$		0			0
$567$	−9.31108	+	9.31108i	−0.391028	+	0.391028i
$568$		0			0
$569$	16.5462			0.693653			0.346826	−	0.937929i	$-0.387259\pi$
$569$	16.5462			0.693653			0.346826	+	0.937929i	$0.387259\pi$
$570$		0			0
$571$	12.7206	−	12.7206i	0.532340	−	0.532340i	−0.388928	−	0.921268i	$-0.627155\pi$
$571$	12.7206	−	12.7206i	0.532340	−	0.532340i	0.921268	+	0.388928i	$0.127155\pi$
$572$		0			0
$573$	27.2369			1.13784
$574$		0			0
$575$	−26.7339	−	14.2870i	−1.11488	−	0.595810i
$576$		0			0
$577$	0.737826	−	0.737826i	0.0307161	−	0.0307161i	−0.691582	−	0.722298i	$-0.743086\pi$
$577$	0.737826	−	0.737826i	0.0307161	−	0.0307161i	0.722298	+	0.691582i	$0.243086\pi$
$578$		0			0
$579$	−19.6260	+	19.6260i	−0.815627	+	0.815627i
$580$		0			0
$581$	−9.83397	−	9.83397i	−0.407982	−	0.407982i
$582$		0			0
$583$	25.4257	+	25.4257i	1.05302	+	1.05302i
$584$		0			0
$585$	−10.8832	+	1.61478i	−0.449963	+	0.0667630i
$586$		0			0
$587$		−	17.1246i		−	0.706808i	−0.935471	−	0.353404i	$-0.885024\pi$
$587$		−	17.1246i		−	0.706808i	0.935471	−	0.353404i	$-0.114976\pi$
$588$		0			0
$589$	−2.52448	−	2.52448i	−0.104019	−	0.104019i
$590$		0			0
$591$			23.1519i			0.952344i
$592$		0			0
$593$	−14.4485	−	14.4485i	−0.593328	−	0.593328i	0.345201	−	0.938529i	$-0.387811\pi$
$593$	−14.4485	−	14.4485i	−0.593328	−	0.593328i	−0.938529	+	0.345201i	$0.887811\pi$
$594$		0			0
$595$	3.59810	+	24.2501i	0.147508	+	0.994159i
$596$		0			0
$597$	7.95111			0.325417
$598$		0			0
$599$		−	12.3096i		−	0.502959i	−0.967863	−	0.251479i	$-0.919083\pi$
$599$		−	12.3096i		−	0.502959i	0.967863	−	0.251479i	$-0.0809170\pi$
$600$		0			0
$601$			7.19239i			0.293384i	0.989182	+	0.146692i	$0.0468625\pi$
$601$			7.19239i			0.293384i	−0.989182	+	0.146692i	$0.953137\pi$
$602$		0			0
$603$	1.56152			0.0635899
$604$		0			0
$605$	6.01612	+	40.5469i	0.244590	+	1.64847i
$606$		0			0
$607$	16.8591	+	16.8591i	0.684291	+	0.684291i	0.960964	−	0.276673i	$-0.0892320\pi$
$607$	16.8591	+	16.8591i	0.684291	+	0.684291i	−0.276673	+	0.960964i	$0.589232\pi$
$608$		0			0
$609$			20.2951i			0.822399i
$610$		0			0
$611$	−4.07558	−	4.07558i	−0.164880	−	0.164880i
$612$		0			0
$613$		−	0.985959i		−	0.0398225i	−0.999802	−	0.0199113i	$-0.993662\pi$
$613$		−	0.985959i		−	0.0398225i	0.999802	−	0.0199113i	$-0.00633837\pi$
$614$		0			0
$615$	−12.9421	+	1.92028i	−0.521877	+	0.0774332i
$616$		0			0
$617$	2.62025	+	2.62025i	0.105487	+	0.105487i	0.757881	−	0.652393i	$-0.226235\pi$
$617$	2.62025	+	2.62025i	0.105487	+	0.105487i	−0.652393	+	0.757881i	$0.726235\pi$
$618$		0			0
$619$	−32.6020	−	32.6020i	−1.31038	−	1.31038i	−0.921131	−	0.389254i	$-0.872733\pi$
$619$	−32.6020	−	32.6020i	−1.31038	−	1.31038i	−0.389254	−	0.921131i	$-0.627267\pi$
$620$		0			0
$621$	1.51739	−	1.51739i	0.0608909	−	0.0608909i
$622$		0			0
$623$	8.59312	−	8.59312i	0.344276	−	0.344276i
$624$		0			0
$625$	20.7847	−	13.8924i	0.831386	−	0.555695i
$626$		0			0
$627$	7.26976			0.290326
$628$		0			0
$629$	−2.21264	+	2.21264i	−0.0882237	+	0.0882237i
$630$		0			0
$631$	1.98558			0.0790447			0.0395224	−	0.999219i	$-0.487416\pi$
$631$	1.98558			0.0790447			0.0395224	+	0.999219i	$0.487416\pi$
$632$		0			0
$633$	29.2159	−	29.2159i	1.16123	−	1.16123i
$634$		0			0
$635$	−3.84266	−	2.84969i	−0.152491	−	0.113086i
$636$		0			0
$637$		−	8.69857i		−	0.344650i
$638$		0			0
$639$	−7.11281			−0.281379
$640$		0			0
$641$	32.5701			1.28644			0.643222	−	0.765680i	$-0.277597\pi$
$641$	32.5701			1.28644			0.643222	+	0.765680i	$0.277597\pi$
$642$		0			0
$643$		−	10.1509i		−	0.400314i	−0.979764	−	0.200157i	$-0.935855\pi$
$643$		−	10.1509i		−	0.400314i	0.979764	−	0.200157i	$-0.0641452\pi$
$644$		0			0
$645$	1.38011	+	9.30155i	0.0543418	+	0.366248i
$646$		0			0
$647$	27.9290	−	27.9290i	1.09800	−	1.09800i	0.103357	−	0.994644i	$-0.467042\pi$
$647$	27.9290	−	27.9290i	1.09800	−	1.09800i	0.994644	−	0.103357i	$-0.0329584\pi$
$648$		0			0
$649$	−48.4427			−1.90154
$650$		0			0
$651$	15.3932	−	15.3932i	0.603309	−	0.603309i
$652$		0			0
$653$	2.51371			0.0983691			0.0491845	−	0.998790i	$-0.484338\pi$
$653$	2.51371			0.0983691			0.0491845	+	0.998790i	$0.484338\pi$
$654$		0			0
$655$	−6.30104	−	4.67281i	−0.246202	−	0.182582i
$656$		0			0
$657$	15.1263	−	15.1263i	0.590135	−	0.590135i
$658$		0			0
$659$	11.2412	−	11.2412i	0.437894	−	0.437894i	−0.453409	−	0.891303i	$-0.649792\pi$
$659$	11.2412	−	11.2412i	0.437894	−	0.437894i	0.891303	+	0.453409i	$0.149792\pi$
$660$		0			0
$661$	−3.64849	−	3.64849i	−0.141910	−	0.141910i	0.632583	−	0.774493i	$-0.281995\pi$
$661$	−3.64849	−	3.64849i	−0.141910	−	0.141910i	−0.774493	+	0.632583i	$0.781995\pi$
$662$		0			0
$663$	−23.1297	−	23.1297i	−0.898283	−	0.898283i
$664$		0			0
$665$	0.254584	+	1.71582i	0.00987233	+	0.0665367i
$666$		0			0
$667$		−	36.3700i		−	1.40825i
$668$		0			0
$669$	−20.7867	−	20.7867i	−0.803658	−	0.803658i
$670$		0			0
$671$		−	60.4829i		−	2.33492i
$672$		0			0
$673$	24.4045	+	24.4045i	0.940724	+	0.940724i	0.998339	−	0.0576148i	$-0.0183495\pi$
$673$	24.4045	+	24.4045i	0.940724	+	0.940724i	−0.0576148	+	0.998339i	$0.518350\pi$
$674$		0			0
$675$	0.513888	+	1.69360i	0.0197796	+	0.0651869i
$676$		0			0
$677$	9.04721			0.347712			0.173856	−	0.984771i	$-0.444377\pi$
$677$	9.04721			0.347712			0.173856	+	0.984771i	$0.444377\pi$
$678$		0			0
$679$			7.54199i			0.289435i
$680$		0			0
$681$		−	48.4337i		−	1.85598i
$682$		0			0
$683$	6.95044			0.265951			0.132976	−	0.991119i	$-0.457547\pi$
$683$	6.95044			0.265951			0.132976	+	0.991119i	$0.457547\pi$
$684$		0			0
$685$	−37.0270	−	27.4589i	−1.41473	−	1.04915i
$686$		0			0
$687$	−31.7223	−	31.7223i	−1.21028	−	1.21028i
$688$		0			0
$689$		−	11.4475i		−	0.436114i
$690$		0			0
$691$	13.4279	+	13.4279i	0.510823	+	0.510823i	0.914778	−	0.403956i	$-0.132365\pi$
$691$	13.4279	+	13.4279i	0.510823	+	0.510823i	−0.403956	+	0.914778i	$0.632365\pi$
$692$		0			0
$693$			21.6100i			0.820897i
$694$		0			0
$695$	3.10207	+	2.30047i	0.117668	+	0.0872618i
$696$		0			0
$697$	−13.4091	−	13.4091i	−0.507904	−	0.507904i
$698$		0			0
$699$	21.6836	+	21.6836i	0.820148	+	0.820148i
$700$		0			0
$701$	10.8802	−	10.8802i	0.410939	−	0.410939i	−0.471127	−	0.882066i	$-0.656152\pi$
$701$	10.8802	−	10.8802i	0.410939	−	0.410939i	0.882066	+	0.471127i	$0.156152\pi$
$702$		0			0
$703$	−0.156555	+	0.156555i	−0.00590460	+	0.00590460i
$704$		0			0
$705$	10.7726	−	14.5263i	0.405718	−	0.547090i
$706$		0			0
$707$	25.3634			0.953889
$708$		0			0
$709$	−11.8967	+	11.8967i	−0.446788	+	0.446788i	−0.894285	−	0.447497i	$-0.852316\pi$
$709$	−11.8967	+	11.8967i	−0.446788	+	0.446788i	0.447497	+	0.894285i	$0.352316\pi$
$710$		0			0
$711$	−40.4272			−1.51614
$712$		0			0
$713$	−27.5855	+	27.5855i	−1.03309	+	1.03309i
$714$		0			0
$715$	12.4380	−	16.7720i	0.465153	−	0.627236i
$716$		0			0
$717$			52.4565i			1.95903i
$718$		0			0
$719$	19.3720			0.722455			0.361227	−	0.932478i	$-0.382358\pi$
$719$	19.3720			0.722455			0.361227	+	0.932478i	$0.382358\pi$
$720$		0			0
$721$	−24.1957			−0.901095
$722$		0			0
$723$			2.87148i			0.106791i
$724$		0			0
$725$	26.4554	+	14.1382i	0.982529	+	0.525078i
$726$		0			0
$727$	−31.8862	+	31.8862i	−1.18259	+	1.18259i	−0.203524	+	0.979070i	$0.565239\pi$
$727$	−31.8862	+	31.8862i	−1.18259	+	1.18259i	−0.979070	+	0.203524i	$0.934761\pi$
$728$		0			0
$729$	24.3055			0.900203
$730$		0			0
$731$	−9.63712	+	9.63712i	−0.356442	+	0.356442i
$732$		0			0
$733$	−8.22830			−0.303919			−0.151960	−	0.988387i	$-0.548558\pi$
$733$	−8.22830			−0.303919			−0.151960	+	0.988387i	$0.548558\pi$
$734$		0			0
$735$	26.9978	−	4.00578i	0.995829	−	0.147755i
$736$		0			0
$737$	−2.09552	+	2.09552i	−0.0771895	+	0.0771895i
$738$		0			0
$739$	−13.6995	+	13.6995i	−0.503945	+	0.503945i	−0.912661	−	0.408717i	$-0.865976\pi$
$739$	−13.6995	+	13.6995i	−0.503945	+	0.503945i	0.408717	+	0.912661i	$0.365976\pi$
$740$		0			0
$741$	−1.63654	−	1.63654i	−0.0601199	−	0.0601199i
$742$		0			0
$743$	−26.6385	−	26.6385i	−0.977273	−	0.977273i	0.0224740	−	0.999747i	$-0.492846\pi$
$743$	−26.6385	−	26.6385i	−0.977273	−	0.977273i	−0.999747	+	0.0224740i	$0.992846\pi$
$744$		0			0
$745$	−15.4408	+	20.8212i	−0.565708	+	0.762828i
$746$		0			0
$747$			28.3839i			1.03851i
$748$		0			0
$749$	10.2445	+	10.2445i	0.374327	+	0.374327i
$750$		0			0
$751$		−	15.0073i		−	0.547625i	−0.961783	−	0.273812i	$-0.911715\pi$
$751$		−	15.0073i		−	0.547625i	0.961783	−	0.273812i	$-0.0882847\pi$
$752$		0			0
$753$	21.5485	+	21.5485i	0.785272	+	0.785272i
$754$		0			0
$755$	−22.8487	+	3.39016i	−0.831549	+	0.123380i
$756$		0			0
$757$	−35.3800			−1.28591			−0.642953	−	0.765905i	$-0.722291\pi$
$757$	−35.3800			−1.28591			−0.642953	+	0.765905i	$0.722291\pi$
$758$		0			0
$759$		−	79.4382i		−	2.88342i
$760$		0			0
$761$		−	14.1721i		−	0.513738i	−0.966446	−	0.256869i	$-0.917309\pi$
$761$		−	14.1721i		−	0.513738i	0.966446	−	0.256869i	$-0.0826908\pi$
$762$		0			0
$763$	−21.1260			−0.764814
$764$		0			0
$765$	29.8042	−	40.1894i	1.07757	−	1.45305i
$766$		0			0
$767$	10.9053	+	10.9053i	0.393766	+	0.393766i
$768$		0			0
$769$			3.84244i			0.138562i	0.997597	+	0.0692809i	$0.0220705\pi$
$769$			3.84244i			0.138562i	−0.997597	+	0.0692809i	$0.977930\pi$
$770$		0			0
$771$	3.27731	+	3.27731i	0.118029	+	0.118029i
$772$		0			0
$773$		−	14.2733i		−	0.513373i	−0.966495	−	0.256687i	$-0.917369\pi$
$773$		−	14.2733i		−	0.513373i	0.966495	−	0.256687i	$-0.0826308\pi$
$774$		0			0
$775$	−9.34226	−	30.7890i	−0.335584	−	1.10597i
$776$		0			0
$777$	−0.954610	−	0.954610i	−0.0342464	−	0.0342464i
$778$		0			0
$779$	−0.948759	−	0.948759i	−0.0339928	−	0.0339928i
$780$		0			0
$781$	9.54524	−	9.54524i	0.341555	−	0.341555i
$782$		0			0
$783$	−1.50158	+	1.50158i	−0.0536622	+	0.0536622i
$784$		0			0
$785$	−0.161800	−	1.09049i	−0.00577491	−	0.0389212i
$786$		0			0
$787$	−42.0418			−1.49863			−0.749314	−	0.662215i	$-0.769616\pi$
$787$	−42.0418			−1.49863			−0.749314	+	0.662215i	$0.769616\pi$
$788$		0			0
$789$	−17.1239	+	17.1239i	−0.609628	+	0.609628i
$790$		0			0
$791$	12.3120			0.437765
$792$		0			0
$793$	−13.6157	+	13.6157i	−0.483508	+	0.483508i
$794$		0			0
$795$	35.5296	−	5.27168i	1.26011	−	0.186967i
$796$		0			0
$797$		−	28.3318i		−	1.00357i	−0.864994	−	0.501783i	$-0.832678\pi$
$797$		−	28.3318i		−	1.00357i	0.864994	−	0.501783i	$-0.167322\pi$
$798$		0			0
$799$	26.2115			0.927297
$800$		0			0
$801$	−24.8025			−0.876352
$802$		0			0
$803$			40.5984i			1.43269i
$804$		0			0
$805$	18.7491	−	2.78189i	0.660820	−	0.0980487i
$806$		0			0
$807$	−11.1481	+	11.1481i	−0.392430	+	0.392430i
$808$		0			0
$809$	−30.7394			−1.08074			−0.540369	−	0.841428i	$-0.681715\pi$
$809$	−30.7394			−1.08074			−0.540369	+	0.841428i	$0.681715\pi$
$810$		0			0
$811$	17.4751	−	17.4751i	0.613633	−	0.613633i	−0.330258	−	0.943891i	$-0.607136\pi$
$811$	17.4751	−	17.4751i	0.613633	−	0.613633i	0.943891	+	0.330258i	$0.107136\pi$
$812$		0			0
$813$	−22.3555			−0.784043
$814$		0			0
$815$	5.57275	+	37.5587i	0.195205	+	1.31563i
$816$		0			0
$817$	−0.681876	+	0.681876i	−0.0238558	+	0.0238558i
$818$		0			0
$819$	4.86478	−	4.86478i	0.169989	−	0.169989i
$820$		0			0
$821$	21.9558	+	21.9558i	0.766262	+	0.766262i	0.977446	−	0.211184i	$-0.0677321\pi$
$821$	21.9558	+	21.9558i	0.766262	+	0.766262i	−0.211184	+	0.977446i	$0.567732\pi$
$822$		0			0
$823$	25.2078	+	25.2078i	0.878687	+	0.878687i	0.993399	−	0.114712i	$-0.0365944\pi$
$823$	25.2078	+	25.2078i	0.878687	+	0.878687i	−0.114712	+	0.993399i	$0.536594\pi$
$824$		0			0
$825$	57.7831	+	30.8801i	2.01175	+	1.07511i
$826$		0			0
$827$			41.4211i			1.44035i	0.693791	+	0.720176i	$0.255939\pi$
$827$			41.4211i			1.44035i	−0.693791	+	0.720176i	$0.744061\pi$
$828$		0			0
$829$	30.0058	+	30.0058i	1.04215	+	1.04215i	0.999072	+	0.0430743i	$0.0137152\pi$
$829$	30.0058	+	30.0058i	1.04215	+	1.04215i	0.0430743	+	0.999072i	$0.486285\pi$
$830$		0			0
$831$		−	6.30867i		−	0.218845i
$832$		0			0
$833$	27.9718	+	27.9718i	0.969166	+	0.969166i
$834$		0			0
$835$	−7.45079	+	10.0470i	−0.257845	+	0.347691i
$836$		0			0
$837$	2.27781			0.0787327
$838$		0			0
$839$			54.1116i			1.86814i	0.357091	+	0.934070i	$0.383769\pi$
$839$			54.1116i			1.86814i	−0.357091	+	0.934070i	$0.616231\pi$
$840$		0			0
$841$			6.99104i			0.241070i
$842$		0			0
$843$	−21.0581			−0.725281
$844$		0			0
$845$	22.1785	−	3.29071i	0.762962	−	0.113204i
$846$		0			0
$847$	−18.1245	−	18.1245i	−0.622764	−	0.622764i
$848$		0			0
$849$		−	30.5710i		−	1.04919i
$850$		0			0
$851$	1.71071	+	1.71071i	0.0586425	+	0.0586425i
$852$		0			0
$853$		−	18.4025i		−	0.630090i	−0.949077	−	0.315045i	$-0.897980\pi$
$853$		−	18.4025i		−	0.630090i	0.949077	−	0.315045i	$-0.102020\pi$
$854$		0			0
$855$	2.10880	−	2.84360i	0.0721193	−	0.0972492i
$856$		0			0
$857$	−19.8161	−	19.8161i	−0.676904	−	0.676904i	0.282394	−	0.959298i	$-0.408871\pi$
$857$	−19.8161	−	19.8161i	−0.676904	−	0.676904i	−0.959298	+	0.282394i	$0.908871\pi$
$858$		0			0
$859$	8.36310	+	8.36310i	0.285345	+	0.285345i	0.835236	−	0.549891i	$-0.185331\pi$
$859$	8.36310	+	8.36310i	0.285345	+	0.285345i	−0.549891	+	0.835236i	$0.685331\pi$
$860$		0			0
$861$	5.78514	−	5.78514i	0.197157	−	0.197157i
$862$		0			0
$863$	−21.6634	+	21.6634i	−0.737431	+	0.737431i	−0.972080	−	0.234649i	$-0.924606\pi$
$863$	−21.6634	+	21.6634i	−0.737431	+	0.737431i	0.234649	+	0.972080i	$0.424606\pi$
$864$		0			0
$865$	−0.840778	+	0.124750i	−0.0285873	+	0.00424162i
$866$		0			0
$867$	107.625			3.65513
$868$		0			0
$869$	54.2524	−	54.2524i	1.84038	−	1.84038i
$870$		0			0
$871$	0.943473			0.0319684
$872$		0			0
$873$	10.8843	−	10.8843i	0.368377	−	0.368377i
$874$		0			0
$875$	−5.26484	+	14.7195i	−0.177984	+	0.497609i
$876$		0			0
$877$		−	40.1665i		−	1.35633i	−0.734911	−	0.678164i	$-0.762776\pi$
$877$		−	40.1665i		−	1.35633i	0.734911	−	0.678164i	$-0.237224\pi$
$878$		0			0
$879$	−30.3504			−1.02369
$880$		0			0
$881$	−39.2893			−1.32369			−0.661845	−	0.749641i	$-0.730226\pi$
$881$	−39.2893			−1.32369			−0.661845	+	0.749641i	$0.730226\pi$
$882$		0			0
$883$			53.3120i			1.79409i	0.441938	+	0.897046i	$0.354291\pi$
$883$			53.3120i			1.79409i	−0.441938	+	0.897046i	$0.645709\pi$
$884$		0			0
$885$	−28.8247	+	38.8687i	−0.968932	+	1.30656i
$886$		0			0
$887$	10.4732	−	10.4732i	0.351654	−	0.351654i	−0.509071	−	0.860725i	$-0.670011\pi$
$887$	10.4732	−	10.4732i	0.351654	−	0.351654i	0.860725	+	0.509071i	$0.170011\pi$
$888$		0			0
$889$	2.99148			0.100331
$890$		0			0
$891$	−36.0653	+	36.0653i	−1.20823	+	1.20823i
$892$		0			0
$893$	1.85460			0.0620618
$894$		0			0
$895$	−20.0860	+	27.0850i	−0.671402	+	0.905351i
$896$		0			0
$897$	−17.8829	+	17.8829i	−0.597091	+	0.597091i
$898$		0			0
$899$	27.2981	−	27.2981i	0.910444	−	0.910444i
$900$		0			0
$901$	36.8115	+	36.8115i	1.22637	+	1.22637i
$902$		0			0
$903$	−4.15779	−	4.15779i	−0.138363	−	0.138363i
$904$		0			0
$905$	33.2799	+	24.6801i	1.10626	+	0.820395i
$906$		0			0
$907$			36.6800i			1.21794i	0.793193	+	0.608970i	$0.208417\pi$
$907$			36.6800i			1.21794i	−0.793193	+	0.608970i	$0.791583\pi$
$908$		0			0
$909$	−36.6034	−	36.6034i	−1.21406	−	1.21406i
$910$		0			0
$911$			53.8902i			1.78546i	0.450590	+	0.892731i	$0.351214\pi$
$911$			53.8902i			1.78546i	−0.450590	+	0.892731i	$0.648786\pi$
$912$		0			0
$913$	−38.0906	−	38.0906i	−1.26062	−	1.26062i
$914$		0			0
$915$	−48.5293	−	35.9890i	−1.60433	−	1.18976i
$916$		0			0
$917$	4.90531			0.161988
$918$		0			0
$919$		−	19.3084i		−	0.636925i	−0.947935	−	0.318463i	$-0.896833\pi$
$919$		−	19.3084i		−	0.636925i	0.947935	−	0.318463i	$-0.103167\pi$
$920$		0			0
$921$			14.1094i			0.464920i
$922$		0			0
$923$	−4.29758			−0.141457
$924$		0			0
$925$	−1.90938	+	0.579359i	−0.0627799	+	0.0190492i
$926$		0			0
$927$	34.9182	+	34.9182i	1.14686	+	1.14686i
$928$		0			0
$929$			33.9731i			1.11462i	0.830304	+	0.557310i	$0.188167\pi$
$929$			33.9731i			1.11462i	−0.830304	+	0.557310i	$0.811833\pi$
$930$		0			0
$931$	1.97915	+	1.97915i	0.0648640	+	0.0648640i
$932$		0			0
$933$		−	36.4676i		−	1.19390i
$934$		0			0
$935$	13.9368	+	93.9298i	0.455781	+	3.07183i
$936$		0			0
$937$	1.43767	+	1.43767i	0.0469665	+	0.0469665i	0.730200	−	0.683233i	$-0.239427\pi$
$937$	1.43767	+	1.43767i	0.0469665	+	0.0469665i	−0.683233	+	0.730200i	$0.739427\pi$
$938$		0			0
$939$	−13.8498	−	13.8498i	−0.451970	−	0.451970i
$940$		0			0
$941$	−0.637265	+	0.637265i	−0.0207742	+	0.0207742i	−0.717418	−	0.696643i	$-0.754676\pi$
$941$	−0.637265	+	0.637265i	−0.0207742	+	0.0207742i	0.696643	+	0.717418i	$0.254676\pi$
$942$		0			0
$943$	−10.3673	+	10.3673i	−0.337606	+	0.337606i
$944$		0			0
$945$	−0.888937	−	0.659229i	−0.0289171	−	0.0214447i
$946$		0			0
$947$	−59.0025			−1.91732			−0.958662	−	0.284548i	$-0.908156\pi$
$947$	−59.0025			−1.91732			−0.958662	+	0.284548i	$0.908156\pi$
$948$		0			0
$949$	9.13938	−	9.13938i	0.296677	−	0.296677i
$950$		0			0
$951$	42.6413			1.38274
$952$		0			0
$953$	28.7408	−	28.7408i	0.931007	−	0.931007i	−0.0667618	−	0.997769i	$-0.521267\pi$
$953$	28.7408	−	28.7408i	0.931007	−	0.931007i	0.997769	+	0.0667618i	$0.0212668\pi$
$954$		0			0
$955$	3.69451	+	24.9000i	0.119552	+	0.805744i
$956$		0			0
$957$			78.6105i			2.54112i
$958$		0			0
$959$	28.8252			0.930815
$960$		0			0
$961$	−10.4096			−0.335795
$962$		0			0
$963$		−	29.5689i		−	0.952846i
$964$		0			0
$965$	−20.6042	−	15.2799i	−0.663273	−	0.491878i
$966$		0			0
$967$	−30.8042	+	30.8042i	−0.990595	+	0.990595i	−0.999956	−	0.00936123i	$-0.997020\pi$
$967$	−30.8042	+	30.8042i	−0.990595	+	0.990595i	0.00936123	+	0.999956i	$0.497020\pi$
$968$		0			0
$969$	10.5252			0.338118
$970$		0			0
$971$	34.8214	−	34.8214i	1.11747	−	1.11747i	0.125362	−	0.992111i	$-0.459991\pi$
$971$	34.8214	−	34.8214i	1.11747	−	1.11747i	0.992111	−	0.125362i	$-0.0400092\pi$
$972$		0			0
$973$	−2.41494			−0.0774193
$974$		0			0
$975$	−6.05630	−	19.9596i	−0.193957	−	0.639218i
$976$		0			0
$977$	−15.4205	+	15.4205i	−0.493344	+	0.493344i	−0.909358	−	0.416014i	$-0.863427\pi$
$977$	−15.4205	+	15.4205i	−0.493344	+	0.493344i	0.416014	+	0.909358i	$0.363427\pi$
$978$		0			0
$979$	33.2844	−	33.2844i	1.06377	−	1.06377i
$980$		0			0
$981$	30.4882	+	30.4882i	0.973413	+	0.973413i
$982$		0			0
$983$	−24.3982	−	24.3982i	−0.778183	−	0.778183i	0.201339	−	0.979522i	$-0.435471\pi$
$983$	−24.3982	−	24.3982i	−0.778183	−	0.778183i	−0.979522	+	0.201339i	$0.935471\pi$
$984$		0			0
$985$	−21.1655	+	3.14042i	−0.674389	+	0.100062i
$986$		0			0
$987$			11.3086i			0.359956i
$988$		0			0
$989$	7.45100	+	7.45100i	0.236928	+	0.236928i
$990$		0			0
$991$		−	10.3612i		−	0.329136i	−0.986366	−	0.164568i	$-0.947377\pi$
$991$		−	10.3612i		−	0.329136i	0.986366	−	0.164568i	$-0.0526229\pi$
$992$		0			0
$993$	−32.8482	−	32.8482i	−1.04241	−	1.04241i
$994$		0			0
$995$	1.07852	+	7.26890i	0.0341913	+	0.230440i
$996$		0			0
$997$	−47.1143			−1.49212			−0.746062	−	0.665876i	$-0.768058\pi$
$997$	−47.1143			−1.49212			−0.746062	+	0.665876i	$0.768058\pi$
$998$		0			0
$999$		−	0.141258i		−	0.00446921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.j.d.63.14	yes	32
4.3	odd	2	inner	1280.2.j.d.63.3	yes	32
5.2	odd	4		1280.2.s.c.1087.14	yes	32
8.3	odd	2		1280.2.j.c.63.14	yes	32
8.5	even	2		1280.2.j.c.63.3	✓	32
16.3	odd	4		1280.2.s.c.703.14	yes	32
16.5	even	4		1280.2.s.d.703.14	yes	32
16.11	odd	4		1280.2.s.d.703.3	yes	32
16.13	even	4		1280.2.s.c.703.3	yes	32
20.7	even	4		1280.2.s.c.1087.3	yes	32
40.27	even	4		1280.2.s.d.1087.14	yes	32
40.37	odd	4		1280.2.s.d.1087.3	yes	32
80.27	even	4		1280.2.j.c.447.14	yes	32
80.37	odd	4		1280.2.j.c.447.3	yes	32
80.67	even	4	inner	1280.2.j.d.447.3	yes	32
80.77	odd	4	inner	1280.2.j.d.447.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.3	✓	32	8.5	even	2
1280.2.j.c.63.14	yes	32	8.3	odd	2
1280.2.j.c.447.3	yes	32	80.37	odd	4
1280.2.j.c.447.14	yes	32	80.27	even	4
1280.2.j.d.63.3	yes	32	4.3	odd	2	inner
1280.2.j.d.63.14	yes	32	1.1	even	1	trivial
1280.2.j.d.447.3	yes	32	80.67	even	4	inner
1280.2.j.d.447.14	yes	32	80.77	odd	4	inner
1280.2.s.c.703.3	yes	32	16.13	even	4
1280.2.s.c.703.14	yes	32	16.3	odd	4
1280.2.s.c.1087.3	yes	32	20.7	even	4
1280.2.s.c.1087.14	yes	32	5.2	odd	4
1280.2.s.d.703.3	yes	32	16.11	odd	4
1280.2.s.d.703.14	yes	32	16.5	even	4
1280.2.s.d.1087.3	yes	32	40.37	odd	4
1280.2.s.d.1087.14	yes	32	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.41944i q^{3} +(-2.21185 + 0.328182i) q^{5} +(0.988699 - 0.988699i) q^{7} -2.85370 q^{9} +(3.82960 - 3.82960i) q^{11} -1.72421 q^{13} +(-0.794018 - 5.35145i) q^{15} +(5.54452 - 5.54452i) q^{17} +(0.392303 - 0.392303i) q^{19} +(2.39210 + 2.39210i) q^{21} +(-4.28678 - 4.28678i) q^{23} +(4.78459 - 1.45178i) q^{25} +0.353970i q^{27} +(4.24211 + 4.24211i) q^{29} -6.43503i q^{31} +(9.26549 + 9.26549i) q^{33} +(-1.86238 + 2.51133i) q^{35} -0.399068 q^{37} -4.17163i q^{39} -2.41844i q^{41} -1.73814 q^{43} +(6.31196 - 0.936533i) q^{45} +(2.36373 + 2.36373i) q^{47} +5.04495i q^{49} +(13.4146 + 13.4146i) q^{51} +6.63925i q^{53} +(-7.21370 + 9.72732i) q^{55} +(0.949154 + 0.949154i) q^{57} +(-6.32477 - 6.32477i) q^{59} +(7.89676 - 7.89676i) q^{61} +(-2.82145 + 2.82145i) q^{63} +(3.81371 - 0.565856i) q^{65} -0.547191 q^{67} +(10.3716 - 10.3716i) q^{69} +2.49249 q^{71} +(-5.30061 + 5.30061i) q^{73} +(3.51250 + 11.5760i) q^{75} -7.57264i q^{77} +14.1666 q^{79} -9.41750 q^{81} -9.94637i q^{83} +(-10.4440 + 14.0833i) q^{85} +(-10.2635 + 10.2635i) q^{87} +8.69135 q^{89} +(-1.70473 + 1.70473i) q^{91} +15.5692 q^{93} +(-0.738970 + 0.996463i) q^{95} +(-3.81410 + 3.81410i) q^{97} +(-10.9285 + 10.9285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) \) 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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