LMFDB - Embedded newform 1280.2.n.r.767.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(767,1280)] 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("1280.767"); 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, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-4,0,0,0,0,0,0,0,20] 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.125772815663104.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 27x^{8} + 107x^{4} + 1 $ x^12 + 27x^8 + 107x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			767.5
Root			$1.53448 + 1.53448i$ of defining polynomial
Character	$\chi$	$=$	1280.767
Dual form			1280.2.n.r.1023.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20864 + 1.20864i) q^{3} +(-2.17009 - 0.539189i) q^{5} +(-0.446112 + 0.446112i) q^{7} -0.0783777i q^{9} -3.72065i q^{11} +(-0.709275 + 0.709275i) q^{13} +(-1.97117 - 3.27454i) q^{15} +(3.34017 + 3.34017i) q^{17} +4.35348 q^{19} -1.07838 q^{21} +(5.69182 + 5.69182i) q^{23} +(4.41855 + 2.34017i) q^{25} +(3.72065 - 3.72065i) q^{27} -1.41855i q^{29} -5.72678i q^{31} +(4.49693 - 4.49693i) q^{33} +(1.20864 - 0.727563i) q^{35} +(3.78765 + 3.78765i) q^{37} -1.71452 q^{39} +9.75872 q^{41} +(-1.20864 - 1.20864i) q^{43} +(-0.0422604 + 0.170086i) q^{45} +(-4.79960 + 4.79960i) q^{47} +6.60197i q^{49} +8.07413i q^{51} +(9.04945 - 9.04945i) q^{53} +(-2.00613 + 8.07413i) q^{55} +(5.26180 + 5.26180i) q^{57} -11.7948 q^{59} +0.340173 q^{61} +(0.0349653 + 0.0349653i) q^{63} +(1.92162 - 1.15676i) q^{65} +(-4.44821 + 4.44821i) q^{67} +13.7587i q^{69} -14.4338i q^{71} +(-0.261795 + 0.261795i) q^{73} +(2.51201 + 8.16887i) q^{75} +(1.65983 + 1.65983i) q^{77} +16.1483 q^{79} +8.75872 q^{81} +(-5.56212 - 5.56212i) q^{83} +(-5.44748 - 9.04945i) q^{85} +(1.71452 - 1.71452i) q^{87} -2.15676i q^{89} -0.632832i q^{91} +(6.92162 - 6.92162i) q^{93} +(-9.44744 - 2.34735i) q^{95} +(6.41855 + 6.41855i) q^{97} -0.291616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 20 q^{13} - 4 q^{17} - 4 q^{25} - 16 q^{33} + 4 q^{37} + 16 q^{41} - 64 q^{45} + 36 q^{53} + 32 q^{57} - 40 q^{61} + 36 q^{65} + 28 q^{73} + 64 q^{77} + 4 q^{81} - 68 q^{85} + 96 q^{93}+ \cdots + 20 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 20 * q^13 - 4 * q^17 - 4 * q^25 - 16 * q^33 + 4 * q^37 + 16 * q^41 - 64 * q^45 + 36 * q^53 + 32 * q^57 - 40 * q^61 + 36 * q^65 + 28 * q^73 + 64 * q^77 + 4 * q^81 - 68 * q^85 + 96 * q^93 + 20 * q^97

Character values

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

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

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
$3$	1.20864	+	1.20864i	0.697809	+	0.697809i	0.963937	−	0.266129i	$-0.0857446\pi$
$3$	1.20864	+	1.20864i	0.697809	+	0.697809i	−0.266129	+	0.963937i	$0.585745\pi$
$4$		0			0
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$6$		0			0
$7$	−0.446112	+	0.446112i	−0.168614	+	0.168614i	−0.786370	−	0.617756i	$-0.788042\pi$
$7$	−0.446112	+	0.446112i	−0.168614	+	0.168614i	0.617756	+	0.786370i	$0.288042\pi$
$8$		0			0
$9$		−	0.0783777i		−	0.0261259i
$10$		0			0
$11$		−	3.72065i		−	1.12182i	−0.827877	−	0.560909i	$-0.810452\pi$
$11$		−	3.72065i		−	1.12182i	0.827877	−	0.560909i	$-0.189548\pi$
$12$		0			0
$13$	−0.709275	+	0.709275i	−0.196718	+	0.196718i	−0.798591	−	0.601874i	$-0.794421\pi$
$13$	−0.709275	+	0.709275i	−0.196718	+	0.196718i	0.601874	+	0.798591i	$0.294421\pi$
$14$		0			0
$15$	−1.97117	−	3.27454i	−0.508953	−	0.845482i
$16$		0			0
$17$	3.34017	+	3.34017i	0.810111	+	0.810111i	0.984650	−	0.174539i	$-0.0558436\pi$
$17$	3.34017	+	3.34017i	0.810111	+	0.810111i	−0.174539	+	0.984650i	$0.555844\pi$
$18$		0			0
$19$	4.35348			0.998758			0.499379	−	0.866384i	$-0.333562\pi$
$19$	4.35348			0.998758			0.499379	+	0.866384i	$0.333562\pi$
$20$		0			0
$21$	−1.07838			−0.235321
$22$		0			0
$23$	5.69182	+	5.69182i	1.18683	+	1.18683i	0.977940	+	0.208887i	$0.0669839\pi$
$23$	5.69182	+	5.69182i	1.18683	+	1.18683i	0.208887	+	0.977940i	$0.433016\pi$
$24$		0			0
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$		0			0
$27$	3.72065	−	3.72065i	0.716040	−	0.716040i
$28$		0			0
$29$		−	1.41855i		−	0.263418i	−0.991288	−	0.131709i	$-0.957954\pi$
$29$		−	1.41855i		−	0.263418i	0.991288	−	0.131709i	$-0.0420465\pi$
$30$		0			0
$31$		−	5.72678i		−	1.02856i	−0.857622	−	0.514280i	$-0.828059\pi$
$31$		−	5.72678i		−	1.02856i	0.857622	−	0.514280i	$-0.171941\pi$
$32$		0			0
$33$	4.49693	−	4.49693i	0.782815	−	0.782815i
$34$		0			0
$35$	1.20864	−	0.727563i	0.204297	−	0.122981i
$36$		0			0
$37$	3.78765	+	3.78765i	0.622686	+	0.622686i	0.946218	−	0.323531i	$-0.104870\pi$
$37$	3.78765	+	3.78765i	0.622686	+	0.622686i	−0.323531	+	0.946218i	$0.604870\pi$
$38$		0			0
$39$	−1.71452			−0.274543
$40$		0			0
$41$	9.75872			1.52406			0.762028	−	0.647544i	$-0.224204\pi$
$41$	9.75872			1.52406			0.762028	+	0.647544i	$0.224204\pi$
$42$		0			0
$43$	−1.20864	−	1.20864i	−0.184316	−	0.184316i	0.608918	−	0.793233i	$-0.291604\pi$
$43$	−1.20864	−	1.20864i	−0.184316	−	0.184316i	−0.793233	+	0.608918i	$0.791604\pi$
$44$		0			0
$45$	−0.0422604	+	0.170086i	−0.00629981	+	0.0253550i
$46$		0			0
$47$	−4.79960	+	4.79960i	−0.700093	+	0.700093i	−0.964430	−	0.264337i	$-0.914847\pi$
$47$	−4.79960	+	4.79960i	−0.700093	+	0.700093i	0.264337	+	0.964430i	$0.414847\pi$
$48$		0			0
$49$			6.60197i			0.943138i
$50$		0			0
$51$			8.07413i			1.13060i
$52$		0			0
$53$	9.04945	−	9.04945i	1.24304	−	1.24304i	0.284303	−	0.958735i	$-0.408238\pi$
$53$	9.04945	−	9.04945i	1.24304	−	1.24304i	0.958735	−	0.284303i	$-0.0917621\pi$
$54$		0			0
$55$	−2.00613	+	8.07413i	−0.270507	+	1.08872i
$56$		0			0
$57$	5.26180	+	5.26180i	0.696942	+	0.696942i
$58$		0			0
$59$	−11.7948			−1.53555			−0.767775	−	0.640719i	$-0.778636\pi$
$59$	−11.7948			−1.53555			−0.767775	+	0.640719i	$0.778636\pi$
$60$		0			0
$61$	0.340173			0.0435547			0.0217773	−	0.999763i	$-0.493068\pi$
$61$	0.340173			0.0435547			0.0217773	+	0.999763i	$0.493068\pi$
$62$		0			0
$63$	0.0349653	+	0.0349653i	0.00440521	+	0.00440521i
$64$		0			0
$65$	1.92162	−	1.15676i	0.238348	−	0.143478i
$66$		0			0
$67$	−4.44821	+	4.44821i	−0.543436	+	0.543436i	−0.924534	−	0.381099i	$-0.875546\pi$
$67$	−4.44821	+	4.44821i	−0.543436	+	0.543436i	0.381099	+	0.924534i	$0.375546\pi$
$68$		0			0
$69$			13.7587i			1.65636i
$70$		0			0
$71$		−	14.4338i		−	1.71297i	−0.516171	−	0.856486i	$-0.672643\pi$
$71$		−	14.4338i		−	1.71297i	0.516171	−	0.856486i	$-0.327357\pi$
$72$		0			0
$73$	−0.261795	+	0.261795i	−0.0306408	+	0.0306408i	−0.722261	−	0.691620i	$-0.756897\pi$
$73$	−0.261795	+	0.261795i	−0.0306408	+	0.0306408i	0.691620	+	0.722261i	$0.256897\pi$
$74$		0			0
$75$	2.51201	+	8.16887i	0.290062	+	0.943259i
$76$		0			0
$77$	1.65983	+	1.65983i	0.189155	+	0.189155i
$78$		0			0
$79$	16.1483			1.81682			0.908411	−	0.418078i	$-0.137296\pi$
$79$	16.1483			1.81682			0.908411	+	0.418078i	$0.137296\pi$
$80$		0			0
$81$	8.75872			0.973192
$82$		0			0
$83$	−5.56212	−	5.56212i	−0.610522	−	0.610522i	0.332560	−	0.943082i	$-0.392088\pi$
$83$	−5.56212	−	5.56212i	−0.610522	−	0.610522i	−0.943082	+	0.332560i	$0.892088\pi$
$84$		0			0
$85$	−5.44748	−	9.04945i	−0.590862	−	0.981550i
$86$		0			0
$87$	1.71452	−	1.71452i	0.183816	−	0.183816i
$88$		0			0
$89$		−	2.15676i		−	0.228616i	−0.993445	−	0.114308i	$-0.963535\pi$
$89$		−	2.15676i		−	0.228616i	0.993445	−	0.114308i	$-0.0364650\pi$
$90$		0			0
$91$		−	0.632832i		−	0.0663389i
$92$		0			0
$93$	6.92162	−	6.92162i	0.717739	−	0.717739i
$94$		0			0
$95$	−9.44744	−	2.34735i	−0.969286	−	0.240833i
$96$		0			0
$97$	6.41855	+	6.41855i	0.651705	+	0.651705i	0.953403	−	0.301698i	$-0.0975535\pi$
$97$	6.41855	+	6.41855i	0.651705	+	0.651705i	−0.301698	+	0.953403i	$0.597554\pi$
$98$		0			0
$99$	−0.291616			−0.0293085
$100$		0			0
$101$	−10.5236			−1.04714			−0.523568	−	0.851984i	$-0.675399\pi$
$101$	−10.5236			−1.04714			−0.523568	+	0.851984i	$0.675399\pi$
$102$		0			0
$103$	−1.74948	−	1.74948i	−0.172382	−	0.172382i	0.615643	−	0.788025i	$-0.288896\pi$
$103$	−1.74948	−	1.74948i	−0.172382	−	0.172382i	−0.788025	+	0.615643i	$0.788896\pi$
$104$		0			0
$105$	2.34017	+	0.581449i	0.228377	+	0.0567436i
$106$		0			0
$107$	−2.99309	+	2.99309i	−0.289353	+	0.289353i	−0.836824	−	0.547472i	$-0.815590\pi$
$107$	−2.99309	+	2.99309i	−0.289353	+	0.289353i	0.547472	+	0.836824i	$0.315590\pi$
$108$		0			0
$109$			13.7587i			1.31785i	0.752210	+	0.658923i	$0.228988\pi$
$109$			13.7587i			1.31785i	−0.752210	+	0.658923i	$0.771012\pi$
$110$		0			0
$111$			9.15582i			0.869032i
$112$		0			0
$113$	1.92162	−	1.92162i	0.180771	−	0.180771i	−0.610921	−	0.791692i	$-0.709201\pi$
$113$	1.92162	−	1.92162i	0.180771	−	0.180771i	0.791692	+	0.610921i	$0.209201\pi$
$114$		0			0
$115$	−9.28277	−	15.4207i	−0.865623	−	1.43799i
$116$		0			0
$117$	0.0555914	+	0.0555914i	0.00513943	+	0.00513943i
$118$		0			0
$119$	−2.98018			−0.273193
$120$		0			0
$121$	−2.84324			−0.258477
$122$		0			0
$123$	11.7948	+	11.7948i	1.06350	+	1.06350i
$124$		0			0
$125$	−8.32684	−	7.46081i	−0.744775	−	0.667315i
$126$		0			0
$127$	−6.99519	+	6.99519i	−0.620723	+	0.620723i	−0.945716	−	0.324993i	$-0.894638\pi$
$127$	−6.99519	+	6.99519i	−0.620723	+	0.620723i	0.324993	+	0.945716i	$0.394638\pi$
$128$		0			0
$129$		−	2.92162i		−	0.257234i
$130$		0			0
$131$		−	7.73292i		−	0.675628i	−0.941213	−	0.337814i	$-0.890312\pi$
$131$		−	7.73292i		−	0.675628i	0.941213	−	0.337814i	$-0.109688\pi$
$132$		0			0
$133$	−1.94214	+	1.94214i	−0.168405	+	0.168405i
$134$		0			0
$135$	−10.0803	+	6.06800i	−0.867571	+	0.522250i
$136$		0			0
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	0.460487	−	0.887666i	$-0.347675\pi$
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	−0.887666	+	0.460487i	$0.847675\pi$
$138$		0			0
$139$	−0.341216			−0.0289416			−0.0144708	−	0.999895i	$-0.504606\pi$
$139$	−0.341216			−0.0289416			−0.0144708	+	0.999895i	$0.504606\pi$
$140$		0			0
$141$	−11.6020			−0.977062
$142$		0			0
$143$	2.63897	+	2.63897i	0.220681	+	0.220681i
$144$		0			0
$145$	−0.764867	+	3.07838i	−0.0635187	+	0.255645i
$146$		0			0
$147$	−7.97940	+	7.97940i	−0.658130	+	0.658130i
$148$		0			0
$149$		−	10.4391i		−	0.855202i	−0.903968	−	0.427601i	$-0.859359\pi$
$149$		−	10.4391i		−	0.855202i	0.903968	−	0.427601i	$-0.140641\pi$
$150$		0			0
$151$		−	13.1681i		−	1.07160i	−0.844344	−	0.535802i	$-0.820009\pi$
$151$		−	13.1681i		−	1.07160i	0.844344	−	0.535802i	$-0.179991\pi$
$152$		0			0
$153$	0.261795	−	0.261795i	0.0211649	−	0.0211649i
$154$		0			0
$155$	−3.08782	+	12.4276i	−0.248020	+	0.998210i
$156$		0			0
$157$	4.55252	+	4.55252i	0.363331	+	0.363331i	0.865038	−	0.501707i	$-0.167294\pi$
$157$	4.55252	+	4.55252i	0.363331	+	0.363331i	−0.501707	+	0.865038i	$0.667294\pi$
$158$		0			0
$159$	21.8751			1.73480
$160$		0			0
$161$	−5.07838			−0.400232
$162$		0			0
$163$	−6.23266	−	6.23266i	−0.488180	−	0.488180i	0.419552	−	0.907731i	$-0.362187\pi$
$163$	−6.23266	−	6.23266i	−0.488180	−	0.488180i	−0.907731	+	0.419552i	$0.862187\pi$
$164$		0			0
$165$	−12.1834	+	7.33403i	−0.948478	+	0.570953i
$166$		0			0
$167$	12.2409	−	12.2409i	0.947229	−	0.947229i	−0.0514466	−	0.998676i	$-0.516383\pi$
$167$	12.2409	−	12.2409i	0.947229	−	0.947229i	0.998676	+	0.0514466i	$0.0163832\pi$
$168$		0			0
$169$			11.9939i			0.922604i
$170$		0			0
$171$		−	0.341216i		−	0.0260935i
$172$		0			0
$173$	9.94441	−	9.94441i	0.756059	−	0.756059i	−0.219543	−	0.975603i	$-0.570457\pi$
$173$	9.94441	−	9.94441i	0.756059	−	0.756059i	0.975603	+	0.219543i	$0.0704567\pi$
$174$		0			0
$175$	−3.01515	+	0.927189i	−0.227924	+	0.0700889i
$176$		0			0
$177$	−14.2557	−	14.2557i	−1.07152	−	1.07152i
$178$		0			0
$179$	23.2484			1.73766			0.868832	−	0.495107i	$-0.164871\pi$
$179$	23.2484			1.73766			0.868832	+	0.495107i	$0.164871\pi$
$180$		0			0
$181$	7.20394			0.535464			0.267732	−	0.963493i	$-0.413726\pi$
$181$	7.20394			0.535464			0.267732	+	0.963493i	$0.413726\pi$
$182$		0			0
$183$	0.411147	+	0.411147i	0.0303928	+	0.0303928i
$184$		0			0
$185$	−6.17727	−	10.2618i	−0.454162	−	0.754462i
$186$		0			0
$187$	12.4276	−	12.4276i	0.908797	−	0.908797i
$188$		0			0
$189$			3.31965i			0.241469i
$190$		0			0
$191$			10.4215i			0.754072i	0.926199	+	0.377036i	$0.123057\pi$
$191$			10.4215i			0.754072i	−0.926199	+	0.377036i	$0.876943\pi$
$192$		0			0
$193$	−16.1773	+	16.1773i	−1.16447	+	1.16447i	−0.180979	+	0.983487i	$0.557926\pi$
$193$	−16.1773	+	16.1773i	−1.16447	+	1.16447i	−0.983487	+	0.180979i	$0.942074\pi$
$194$		0			0
$195$	3.72065	+	0.924449i	0.266441	+	0.0662011i
$196$		0			0
$197$	13.7877	+	13.7877i	0.982330	+	0.982330i	0.999847	−	0.0175170i	$-0.00557611\pi$
$197$	13.7877	+	13.7877i	0.982330	+	0.982330i	−0.0175170	+	0.999847i	$0.505576\pi$
$198$		0			0
$199$	−16.1483			−1.14472			−0.572360	−	0.820002i	$-0.693972\pi$
$199$	−16.1483			−1.14472			−0.572360	+	0.820002i	$0.693972\pi$
$200$		0			0
$201$	−10.7526			−0.758429
$202$		0			0
$203$	0.632832	+	0.632832i	0.0444161	+	0.0444161i
$204$		0			0
$205$	−21.1773	−	5.26180i	−1.47909	−	0.367500i
$206$		0			0
$207$	0.446112	−	0.446112i	0.0310069	−	0.0310069i
$208$		0			0
$209$		−	16.1978i		−	1.12042i
$210$		0			0
$211$			7.73292i			0.532356i	0.963924	+	0.266178i	$0.0857609\pi$
$211$			7.73292i			0.532356i	−0.963924	+	0.266178i	$0.914239\pi$
$212$		0			0
$213$	17.4452	−	17.4452i	1.19533	−	1.19533i
$214$		0			0
$215$	1.97117	+	3.27454i	0.134433	+	0.223322i
$216$		0			0
$217$	2.55479	+	2.55479i	0.173430	+	0.173430i
$218$		0			0
$219$	−0.632832			−0.0427629
$220$		0			0
$221$	−4.73820			−0.318726
$222$		0			0
$223$	1.33834	+	1.33834i	0.0896216	+	0.0896216i	0.750496	−	0.660875i	$-0.229815\pi$
$223$	1.33834	+	1.33834i	0.0896216	+	0.0896216i	−0.660875	+	0.750496i	$0.729815\pi$
$224$		0			0
$225$	0.183417	−	0.346316i	0.0122278	−	0.0230877i
$226$		0			0
$227$	12.8140	−	12.8140i	0.850493	−	0.850493i	−0.139701	−	0.990194i	$-0.544614\pi$
$227$	12.8140	−	12.8140i	0.850493	−	0.850493i	0.990194	+	0.139701i	$0.0446141\pi$
$228$		0			0
$229$			21.4186i			1.41538i	0.706524	+	0.707689i	$0.250262\pi$
$229$			21.4186i			1.41538i	−0.706524	+	0.707689i	$0.749738\pi$
$230$		0			0
$231$			4.01227i			0.263988i
$232$		0			0
$233$	10.0205	−	10.0205i	0.656466	−	0.656466i	−0.298076	−	0.954542i	$-0.596345\pi$
$233$	10.0205	−	10.0205i	0.656466	−	0.656466i	0.954542	+	0.298076i	$0.0963449\pi$
$234$		0			0
$235$	13.0034	−	7.82765i	0.848250	−	0.510620i
$236$		0			0
$237$	19.5174	+	19.5174i	1.26779	+	1.26779i
$238$		0			0
$239$	−18.8949			−1.22221			−0.611104	−	0.791550i	$-0.709274\pi$
$239$	−18.8949			−1.22221			−0.611104	+	0.791550i	$0.709274\pi$
$240$		0			0
$241$	−16.9627			−1.09266			−0.546330	−	0.837570i	$-0.683976\pi$
$241$	−16.9627			−1.09266			−0.546330	+	0.837570i	$0.683976\pi$
$242$		0			0
$243$	−0.575808	−	0.575808i	−0.0369381	−	0.0369381i
$244$		0			0
$245$	3.55971	−	14.3268i	0.227421	−	0.915308i
$246$		0			0
$247$	−3.08782	+	3.08782i	−0.196473	+	0.196473i
$248$		0			0
$249$		−	13.4452i		−	0.852056i
$250$		0			0
$251$		−	11.1620i		−	0.704536i	−0.935899	−	0.352268i	$-0.885411\pi$
$251$		−	11.1620i		−	0.704536i	0.935899	−	0.352268i	$-0.114589\pi$
$252$		0			0
$253$	21.1773	−	21.1773i	1.33140	−	1.33140i
$254$		0			0
$255$	4.35348	−	17.5216i	0.272626	−	1.09724i
$256$		0			0
$257$	−8.60197	−	8.60197i	−0.536576	−	0.536576i	0.385946	−	0.922522i	$-0.373875\pi$
$257$	−8.60197	−	8.60197i	−0.536576	−	0.536576i	−0.922522	+	0.385946i	$0.873875\pi$
$258$		0			0
$259$	−3.37943			−0.209988
$260$		0			0
$261$	−0.111183			−0.00688204
$262$		0			0
$263$	13.5443	+	13.5443i	0.835175	+	0.835175i	0.988219	−	0.153044i	$-0.0489076\pi$
$263$	13.5443	+	13.5443i	0.835175	+	0.835175i	−0.153044	+	0.988219i	$0.548908\pi$
$264$		0			0
$265$	−24.5174	+	14.7587i	−1.50609	+	0.906621i
$266$		0			0
$267$	2.60674	−	2.60674i	0.159530	−	0.159530i
$268$		0			0
$269$			18.0722i			1.10188i	0.834544	+	0.550942i	$0.185731\pi$
$269$			18.0722i			1.10188i	−0.834544	+	0.550942i	$0.814269\pi$
$270$		0			0
$271$		−	17.8628i		−	1.08509i	−0.840028	−	0.542544i	$-0.817461\pi$
$271$		−	17.8628i		−	1.08509i	0.840028	−	0.542544i	$-0.182539\pi$
$272$		0			0
$273$	0.764867	−	0.764867i	0.0462918	−	0.0462918i
$274$		0			0
$275$	8.70697	−	16.4399i	0.525050	−	0.991362i
$276$		0			0
$277$	−7.38962	−	7.38962i	−0.443999	−	0.443999i	0.449354	−	0.893354i	$-0.351654\pi$
$277$	−7.38962	−	7.38962i	−0.443999	−	0.443999i	−0.893354	+	0.449354i	$0.851654\pi$
$278$		0			0
$279$	−0.448852			−0.0268721
$280$		0			0
$281$	−22.0722			−1.31672			−0.658360	−	0.752704i	$-0.728749\pi$
$281$	−22.0722			−1.31672			−0.658360	+	0.752704i	$0.728749\pi$
$282$		0			0
$283$	−10.5861	−	10.5861i	−0.629281	−	0.629281i	0.318606	−	0.947887i	$-0.396785\pi$
$283$	−10.5861	−	10.5861i	−0.629281	−	0.629281i	−0.947887	+	0.318606i	$0.896785\pi$
$284$		0			0
$285$	−8.58145	−	14.2557i	−0.508321	−	0.844432i
$286$		0			0
$287$	−4.35348	+	4.35348i	−0.256978	+	0.256978i
$288$		0			0
$289$			5.31351i			0.312559i
$290$		0			0
$291$			15.5154i			0.909531i
$292$		0			0
$293$	−8.80817	+	8.80817i	−0.514579	+	0.514579i	−0.915926	−	0.401347i	$-0.868542\pi$
$293$	−8.80817	+	8.80817i	−0.514579	+	0.514579i	0.401347	+	0.915926i	$0.368542\pi$
$294$		0			0
$295$	25.5957	+	6.35962i	1.49024	+	0.370271i
$296$		0			0
$297$	−13.8432	−	13.8432i	−0.803267	−	0.803267i
$298$		0			0
$299$	−8.07413			−0.466939
$300$		0			0
$301$	1.07838			0.0621567
$302$		0			0
$303$	−12.7192	−	12.7192i	−0.730701	−	0.730701i
$304$		0			0
$305$	−0.738205	−	0.183417i	−0.0422695	−	0.0105025i
$306$		0			0
$307$	−15.9018	+	15.9018i	−0.907563	+	0.907563i	−0.996075	−	0.0885124i	$-0.971789\pi$
$307$	−15.9018	+	15.9018i	−0.907563	+	0.907563i	0.0885124	+	0.996075i	$0.471789\pi$
$308$		0			0
$309$		−	4.22899i		−	0.240579i
$310$		0			0
$311$			4.46112i			0.252967i	0.991969	+	0.126483i	$0.0403691\pi$
$311$			4.46112i			0.252967i	−0.991969	+	0.126483i	$0.959631\pi$
$312$		0			0
$313$	−18.6020	+	18.6020i	−1.05145	+	1.05145i	−0.0528426	+	0.998603i	$0.516828\pi$
$313$	−18.6020	+	18.6020i	−1.05145	+	1.05145i	−0.998603	+	0.0528426i	$0.983172\pi$
$314$		0			0
$315$	−0.0570247	−	0.0947305i	−0.00321298	−	0.00533746i
$316$		0			0
$317$	4.02893	+	4.02893i	0.226287	+	0.226287i	0.811140	−	0.584852i	$-0.198848\pi$
$317$	4.02893	+	4.02893i	0.226287	+	0.226287i	−0.584852	+	0.811140i	$0.698848\pi$
$318$		0			0
$319$	−5.27793			−0.295507
$320$		0			0
$321$	−7.23513			−0.403826
$322$		0			0
$323$	14.5414	+	14.5414i	0.809104	+	0.809104i
$324$		0			0
$325$	−4.79380	+	1.47414i	−0.265912	+	0.0817707i
$326$		0			0
$327$	−16.6293	+	16.6293i	−0.919605	+	0.919605i
$328$		0			0
$329$		−	4.28231i		−	0.236092i
$330$		0			0
$331$		−	0.291616i		−	0.0160287i	−0.999968	−	0.00801434i	$-0.997449\pi$
$331$		−	0.291616i		−	0.0160287i	0.999968	−	0.00801434i	$-0.00255107\pi$
$332$		0			0
$333$	0.296868	−	0.296868i	0.0162683	−	0.0162683i
$334$		0			0
$335$	12.0514	−	7.25458i	0.658440	−	0.396360i
$336$		0			0
$337$	−2.68649	−	2.68649i	−0.146342	−	0.146342i	0.630140	−	0.776482i	$-0.282998\pi$
$337$	−2.68649	−	2.68649i	−0.146342	−	0.146342i	−0.776482	+	0.630140i	$0.782998\pi$
$338$		0			0
$339$	4.64510			0.252287
$340$		0			0
$341$	−21.3074			−1.15386
$342$		0			0
$343$	−6.06800	−	6.06800i	−0.327641	−	0.327641i
$344$		0			0
$345$	7.41855	−	29.8576i	0.399401	−	1.60748i
$346$		0			0
$347$	−8.80170	+	8.80170i	−0.472500	+	0.472500i	−0.902723	−	0.430223i	$-0.858435\pi$
$347$	−8.80170	+	8.80170i	−0.472500	+	0.472500i	0.430223	+	0.902723i	$0.358435\pi$
$348$		0			0
$349$			11.9421i			0.639248i	0.947544	+	0.319624i	$0.103557\pi$
$349$			11.9421i			0.639248i	−0.947544	+	0.319624i	$0.896443\pi$
$350$		0			0
$351$			5.27793i			0.281715i
$352$		0			0
$353$	−1.15676	+	1.15676i	−0.0615679	+	0.0615679i	−0.737220	−	0.675652i	$-0.763862\pi$
$353$	−1.15676	+	1.15676i	−0.0615679	+	0.0615679i	0.675652	+	0.737220i	$0.263862\pi$
$354$		0			0
$355$	−7.78252	+	31.3225i	−0.413053	+	1.66243i
$356$		0			0
$357$	−3.60197	−	3.60197i	−0.190636	−	0.190636i
$358$		0			0
$359$	12.1360			0.640514			0.320257	−	0.947331i	$-0.396231\pi$
$359$	12.1360			0.640514			0.320257	+	0.947331i	$0.396231\pi$
$360$		0			0
$361$	−0.0471809			−0.00248321
$362$		0			0
$363$	−3.43646	−	3.43646i	−0.180367	−	0.180367i
$364$		0			0
$365$	0.709275	−	0.426961i	0.0371252	−	0.0223482i
$366$		0			0
$367$	4.45838	−	4.45838i	0.232726	−	0.232726i	−0.581104	−	0.813829i	$-0.697379\pi$
$367$	4.45838	−	4.45838i	0.232726	−	0.232726i	0.813829	+	0.581104i	$0.197379\pi$
$368$		0			0
$369$		−	0.764867i		−	0.0398174i
$370$		0			0
$371$			8.07413i			0.419188i
$372$		0			0
$373$	19.0494	−	19.0494i	0.986343	−	0.986343i	−0.0135649	−	0.999908i	$-0.504318\pi$
$373$	19.0494	−	19.0494i	0.986343	−	0.986343i	0.999908	+	0.0135649i	$0.00431799\pi$
$374$		0			0
$375$	−1.04672	−	19.0816i	−0.0540524	−	0.985369i
$376$		0			0
$377$	1.00614	+	1.00614i	0.0518190	+	0.0518190i
$378$		0			0
$379$	−15.8071			−0.811954			−0.405977	−	0.913883i	$-0.633069\pi$
$379$	−15.8071			−0.811954			−0.405977	+	0.913883i	$0.633069\pi$
$380$		0			0
$381$	−16.9093			−0.866292
$382$		0			0
$383$	−10.1152	−	10.1152i	−0.516864	−	0.516864i	0.399757	−	0.916621i	$-0.369095\pi$
$383$	−10.1152	−	10.1152i	−0.516864	−	0.516864i	−0.916621	+	0.399757i	$0.869095\pi$
$384$		0			0
$385$	−2.70701	−	4.49693i	−0.137962	−	0.229185i
$386$		0			0
$387$	−0.0947305	+	0.0947305i	−0.00481542	+	0.00481542i
$388$		0			0
$389$			25.2762i			1.28155i	0.767728	+	0.640776i	$0.221387\pi$
$389$			25.2762i			1.28155i	−0.767728	+	0.640776i	$0.778613\pi$
$390$		0			0
$391$			38.0233i			1.92292i
$392$		0			0
$393$	9.34632	−	9.34632i	0.471459	−	0.471459i
$394$		0			0
$395$	−35.0431	−	8.70697i	−1.76321	−	0.438095i
$396$		0			0
$397$	−14.8348	−	14.8348i	−0.744539	−	0.744539i	0.228909	−	0.973448i	$-0.426484\pi$
$397$	−14.8348	−	14.8348i	−0.744539	−	0.744539i	−0.973448	+	0.228909i	$0.926484\pi$
$398$		0			0
$399$	−4.69470			−0.235029
$400$		0			0
$401$	6.36683			0.317945			0.158972	−	0.987283i	$-0.449182\pi$
$401$	6.36683			0.317945			0.158972	+	0.987283i	$0.449182\pi$
$402$		0			0
$403$	4.06187	+	4.06187i	0.202336	+	0.202336i
$404$		0			0
$405$	−19.0072	−	4.72261i	−0.944475	−	0.234668i
$406$		0			0
$407$	14.0925	−	14.0925i	0.698541	−	0.698541i
$408$		0			0
$409$			19.2762i			0.953145i	0.879135	+	0.476573i	$0.158121\pi$
$409$			19.2762i			0.953145i	−0.879135	+	0.476573i	$0.841879\pi$
$410$		0			0
$411$		−	12.0864i		−	0.596178i
$412$		0			0
$413$	5.26180	−	5.26180i	0.258916	−	0.258916i
$414$		0			0
$415$	9.07125	+	15.0693i	0.445290	+	0.739724i
$416$		0			0
$417$	−0.412408	−	0.412408i	−0.0201957	−	0.0201957i
$418$		0			0
$419$	−24.5140			−1.19759			−0.598794	−	0.800903i	$-0.704353\pi$
$419$	−24.5140			−1.19759			−0.598794	+	0.800903i	$0.704353\pi$
$420$		0			0
$421$	−18.6947			−0.911125			−0.455562	−	0.890204i	$-0.650562\pi$
$421$	−18.6947			−0.911125			−0.455562	+	0.890204i	$0.650562\pi$
$422$		0			0
$423$	0.376181	+	0.376181i	0.0182906	+	0.0182906i
$424$		0			0
$425$	6.94214	+	22.5753i	0.336743	+	1.09506i
$426$		0			0
$427$	−0.151755	+	0.151755i	−0.00734395	+	0.00734395i
$428$		0			0
$429$			6.37912i			0.307987i
$430$		0			0
$431$			14.4338i			0.695249i	0.937634	+	0.347625i	$0.113012\pi$
$431$			14.4338i			0.695249i	−0.937634	+	0.347625i	$0.886988\pi$
$432$		0			0
$433$	−4.10504	+	4.10504i	−0.197276	+	0.197276i	−0.798831	−	0.601555i	$-0.794548\pi$
$433$	−4.10504	+	4.10504i	−0.197276	+	0.197276i	0.601555	+	0.798831i	$0.294548\pi$
$434$		0			0
$435$	−4.64510	+	2.79620i	−0.222715	+	0.134068i
$436$		0			0
$437$	24.7792	+	24.7792i	1.18535	+	1.18535i
$438$		0			0
$439$	−20.1605			−0.962210			−0.481105	−	0.876663i	$-0.659764\pi$
$439$	−20.1605			−0.962210			−0.481105	+	0.876663i	$0.659764\pi$
$440$		0			0
$441$	0.517447			0.0246404
$442$		0			0
$443$	−3.14484	−	3.14484i	−0.149416	−	0.149416i	0.628441	−	0.777857i	$-0.283693\pi$
$443$	−3.14484	−	3.14484i	−0.149416	−	0.149416i	−0.777857	+	0.628441i	$0.783693\pi$
$444$		0			0
$445$	−1.16290	+	4.68035i	−0.0551267	+	0.221870i
$446$		0			0
$447$	12.6171	−	12.6171i	0.596767	−	0.596767i
$448$		0			0
$449$		−	15.3919i		−	0.726388i	−0.931714	−	0.363194i	$-0.881686\pi$
$449$		−	15.3919i		−	0.726388i	0.931714	−	0.363194i	$-0.118314\pi$
$450$		0			0
$451$		−	36.3088i		−	1.70971i
$452$		0			0
$453$	15.9155	−	15.9155i	0.747774	−	0.747774i
$454$		0			0
$455$	−0.341216	+	1.37330i	−0.0159965	+	0.0643814i
$456$		0			0
$457$	−8.07838	−	8.07838i	−0.377891	−	0.377891i	0.492450	−	0.870341i	$-0.336101\pi$
$457$	−8.07838	−	8.07838i	−0.377891	−	0.377891i	−0.870341	+	0.492450i	$0.836101\pi$
$458$		0			0
$459$	24.8552			1.16014
$460$		0			0
$461$	−17.1629			−0.799356			−0.399678	−	0.916656i	$-0.630878\pi$
$461$	−17.1629			−0.799356			−0.399678	+	0.916656i	$0.630878\pi$
$462$		0			0
$463$	3.01515	+	3.01515i	0.140126	+	0.140126i	0.773690	−	0.633564i	$-0.218409\pi$
$463$	3.01515	+	3.01515i	0.140126	+	0.140126i	−0.633564	+	0.773690i	$0.718409\pi$
$464$		0			0
$465$	−18.7526	+	11.2885i	−0.869630	+	0.523490i
$466$		0			0
$467$	0.0947305	−	0.0947305i	0.00438360	−	0.00438360i	−0.704912	−	0.709295i	$-0.749013\pi$
$467$	0.0947305	−	0.0947305i	0.00438360	−	0.00438360i	0.709295	+	0.704912i	$0.249013\pi$
$468$		0			0
$469$		−	3.96880i		−	0.183262i
$470$		0			0
$471$			11.0047i			0.507071i
$472$		0			0
$473$	−4.49693	+	4.49693i	−0.206769	+	0.206769i
$474$		0			0
$475$	19.2361	+	10.1879i	0.882612	+	0.467453i
$476$		0			0
$477$	−0.709275	−	0.709275i	−0.0324755	−	0.0324755i
$478$		0			0
$479$	−35.0431			−1.60116			−0.800581	−	0.599225i	$-0.795476\pi$
$479$	−35.0431			−1.60116			−0.800581	+	0.599225i	$0.795476\pi$
$480$		0			0
$481$	−5.37298			−0.244987
$482$		0			0
$483$	−6.13793	−	6.13793i	−0.279286	−	0.279286i
$484$		0			0
$485$	−10.4680	−	17.3896i	−0.475327	−	0.789622i
$486$		0			0
$487$	6.99519	−	6.99519i	0.316982	−	0.316982i	−0.530625	−	0.847607i	$-0.678043\pi$
$487$	6.99519	−	6.99519i	0.316982	−	0.316982i	0.847607	+	0.530625i	$0.178043\pi$
$488$		0			0
$489$		−	15.0661i		−	0.681312i
$490$		0			0
$491$			25.1469i			1.13486i	0.823421	+	0.567431i	$0.192063\pi$
$491$			25.1469i			1.13486i	−0.823421	+	0.567431i	$0.807937\pi$
$492$		0			0
$493$	4.73820	−	4.73820i	0.213398	−	0.213398i
$494$		0			0
$495$	0.632832	+	0.157236i	0.0284437	+	0.00706724i
$496$		0			0
$497$	6.43907	+	6.43907i	0.288832	+	0.288832i
$498$		0			0
$499$	0.924449			0.0413840			0.0206920	−	0.999786i	$-0.493413\pi$
$499$	0.924449			0.0413840			0.0206920	+	0.999786i	$0.493413\pi$
$500$		0			0
$501$	29.5897			1.32197
$502$		0			0
$503$	−21.9100	−	21.9100i	−0.976919	−	0.976919i	0.0228201	−	0.999740i	$-0.492736\pi$
$503$	−21.9100	−	21.9100i	−0.976919	−	0.976919i	−0.999740	+	0.0228201i	$0.992736\pi$
$504$		0			0
$505$	22.8371	+	5.67420i	1.01624	+	0.252499i
$506$		0			0
$507$	−14.4963	+	14.4963i	−0.643801	+	0.643801i
$508$		0			0
$509$		−	9.10504i		−	0.403574i	−0.979429	−	0.201787i	$-0.935325\pi$
$509$		−	9.10504i		−	0.403574i	0.979429	−	0.201787i	$-0.0646748\pi$
$510$		0			0
$511$		−	0.233580i		−	0.0103330i
$512$		0			0
$513$	16.1978	−	16.1978i	0.715150	−	0.715150i
$514$		0			0
$515$	2.85323	+	4.73983i	0.125728	+	0.208862i
$516$		0			0
$517$	17.8576	+	17.8576i	0.785377	+	0.785377i
$518$		0			0
$519$	24.0384			1.05517
$520$		0			0
$521$	43.1917			1.89226			0.946130	−	0.323786i	$-0.104956\pi$
$521$	43.1917			1.89226			0.946130	+	0.323786i	$0.104956\pi$
$522$		0			0
$523$	8.30873	+	8.30873i	0.363315	+	0.363315i	0.865032	−	0.501717i	$-0.167298\pi$
$523$	8.30873	+	8.30873i	0.363315	+	0.363315i	−0.501717	+	0.865032i	$0.667298\pi$
$524$		0			0
$525$	−4.76487	−	2.52359i	−0.207956	−	0.110139i
$526$		0			0
$527$	19.1285	−	19.1285i	0.833248	−	0.833248i
$528$		0			0
$529$			41.7936i			1.81711i
$530$		0			0
$531$			0.924449i			0.0401177i
$532$		0			0
$533$	−6.92162	+	6.92162i	−0.299809	+	0.299809i
$534$		0			0
$535$	8.10910	−	4.88142i	0.350587	−	0.211042i
$536$		0			0
$537$	28.0989	+	28.0989i	1.21256	+	1.21256i
$538$		0			0
$539$	24.5636			1.05803
$540$		0			0
$541$	28.5113			1.22580			0.612898	−	0.790162i	$-0.290004\pi$
$541$	28.5113			1.22580			0.612898	+	0.790162i	$0.290004\pi$
$542$		0			0
$543$	8.70697	+	8.70697i	0.373652	+	0.373652i
$544$		0			0
$545$	7.41855	−	29.8576i	0.317776	−	1.27896i
$546$		0			0
$547$	26.4309	−	26.4309i	1.13010	−	1.13010i	0.139945	−	0.990159i	$-0.455308\pi$
$547$	26.4309	−	26.4309i	1.13010	−	1.13010i	0.990159	−	0.139945i	$-0.0446924\pi$
$548$		0			0
$549$		−	0.0266620i		−	0.00113791i
$550$		0			0
$551$		−	6.17564i		−	0.263091i
$552$		0			0
$553$	−7.20394	+	7.20394i	−0.306343	+	0.306343i
$554$		0			0
$555$	4.93672	−	19.8689i	0.209552	−	0.843389i
$556$		0			0
$557$	23.4163	+	23.4163i	0.992180	+	0.992180i	0.999970	−	0.00778989i	$-0.00247962\pi$
$557$	23.4163	+	23.4163i	0.992180	+	0.992180i	−0.00778989	+	0.999970i	$0.502480\pi$
$558$		0			0
$559$	1.71452			0.0725164
$560$		0			0
$561$	30.0410			1.26833
$562$		0			0
$563$	−14.9396	−	14.9396i	−0.629630	−	0.629630i	0.318345	−	0.947975i	$-0.396873\pi$
$563$	−14.9396	−	14.9396i	−0.629630	−	0.629630i	−0.947975	+	0.318345i	$0.896873\pi$
$564$		0			0
$565$	−5.20620	+	3.13397i	−0.219027	+	0.131847i
$566$		0			0
$567$	−3.90737	+	3.90737i	−0.164094	+	0.164094i
$568$		0			0
$569$		−	25.9155i		−	1.08643i	−0.839593	−	0.543217i	$-0.817206\pi$
$569$		−	25.9155i		−	1.08643i	0.839593	−	0.543217i	$-0.182794\pi$
$570$		0			0
$571$			28.5759i			1.19586i	0.801547	+	0.597932i	$0.204011\pi$
$571$			28.5759i			1.19586i	−0.801547	+	0.597932i	$0.795989\pi$
$572$		0			0
$573$	−12.5958	+	12.5958i	−0.526198	+	0.526198i
$574$		0			0
$575$	11.8298	+	38.4694i	0.493335	+	1.60429i
$576$		0			0
$577$	30.4329	+	30.4329i	1.26694	+	1.26694i	0.947661	+	0.319278i	$0.103440\pi$
$577$	30.4329	+	30.4329i	1.26694	+	1.26694i	0.319278	+	0.947661i	$0.396560\pi$
$578$		0			0
$579$	−39.1050			−1.62515
$580$		0			0
$581$	4.96266			0.205886
$582$		0			0
$583$	−33.6698	−	33.6698i	−1.39446	−	1.39446i
$584$		0			0
$585$	−0.0906639	−	0.150612i	−0.00374849	−	0.00622706i
$586$		0			0
$587$	−4.10700	+	4.10700i	−0.169514	+	0.169514i	−0.786766	−	0.617252i	$-0.788246\pi$
$587$	−4.10700	+	4.10700i	−0.169514	+	0.169514i	0.617252	+	0.786766i	$0.288246\pi$
$588$		0			0
$589$		−	24.9315i		−	1.02728i
$590$		0			0
$591$			33.3286i			1.37096i
$592$		0			0
$593$	20.1506	−	20.1506i	0.827486	−	0.827486i	−0.159682	−	0.987169i	$-0.551047\pi$
$593$	20.1506	−	20.1506i	0.827486	−	0.827486i	0.987169	+	0.159682i	$0.0510469\pi$
$594$		0			0
$595$	6.46725	+	1.60688i	0.265132	+	0.0658757i
$596$		0			0
$597$	−19.5174	−	19.5174i	−0.798796	−	0.798796i
$598$		0			0
$599$	8.12373			0.331927			0.165963	−	0.986132i	$-0.446927\pi$
$599$	8.12373			0.331927			0.165963	+	0.986132i	$0.446927\pi$
$600$		0			0
$601$	−4.08452			−0.166611			−0.0833055	−	0.996524i	$-0.526548\pi$
$601$	−4.08452			−0.166611			−0.0833055	+	0.996524i	$0.526548\pi$
$602$		0			0
$603$	0.348641	+	0.348641i	0.0141978	+	0.0141978i
$604$		0			0
$605$	6.17009	+	1.53305i	0.250850	+	0.0623272i
$606$		0			0
$607$	15.3609	−	15.3609i	0.623481	−	0.623481i	−0.322939	−	0.946420i	$-0.604671\pi$
$607$	15.3609	−	15.3609i	0.623481	−	0.623481i	0.946420	+	0.322939i	$0.104671\pi$
$608$		0			0
$609$			1.52973i			0.0619879i
$610$		0			0
$611$		−	6.80847i		−	0.275441i
$612$		0			0
$613$	14.0700	−	14.0700i	0.568281	−	0.568281i	−0.363366	−	0.931647i	$-0.618373\pi$
$613$	14.0700	−	14.0700i	0.568281	−	0.568281i	0.931647	+	0.363366i	$0.118373\pi$
$614$		0			0
$615$	−19.2361	−	31.9553i	−0.775674	−	1.28856i
$616$		0			0
$617$	−21.8104	−	21.8104i	−0.878055	−	0.878055i	0.115278	−	0.993333i	$-0.463224\pi$
$617$	−21.8104	−	21.8104i	−0.878055	−	0.878055i	−0.993333	+	0.115278i	$0.963224\pi$
$618$		0			0
$619$	5.61915			0.225853			0.112926	−	0.993603i	$-0.463978\pi$
$619$	5.61915			0.225853			0.112926	+	0.993603i	$0.463978\pi$
$620$		0			0
$621$	42.3545			1.69963
$622$		0			0
$623$	0.962154	+	0.962154i	0.0385479	+	0.0385479i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$		0			0
$627$	19.5773	−	19.5773i	0.781842	−	0.781842i
$628$		0			0
$629$			25.3028i			1.00889i
$630$		0			0
$631$			13.8505i			0.551380i	0.961247	+	0.275690i	$0.0889064\pi$
$631$			13.8505i			0.551380i	−0.961247	+	0.275690i	$0.911094\pi$
$632$		0			0
$633$	−9.34632	+	9.34632i	−0.371483	+	0.371483i
$634$		0			0
$635$	18.9519	−	11.4084i	0.752083	−	0.452730i
$636$		0			0
$637$	−4.68261	−	4.68261i	−0.185532	−	0.185532i
$638$		0			0
$639$	−1.13128			−0.0447529
$640$		0			0
$641$	4.08452			0.161329			0.0806644	−	0.996741i	$-0.474296\pi$
$641$	4.08452			0.161329			0.0806644	+	0.996741i	$0.474296\pi$
$642$		0			0
$643$	28.0001	+	28.0001i	1.10422	+	1.10422i	0.993896	+	0.110319i	$0.0351873\pi$
$643$	28.0001	+	28.0001i	1.10422	+	1.10422i	0.110319	+	0.993896i	$0.464813\pi$
$644$		0			0
$645$	−1.57531	+	6.34017i	−0.0620276	+	0.249644i
$646$		0			0
$647$	−5.14081	+	5.14081i	−0.202106	+	0.202106i	−0.800902	−	0.598796i	$-0.795646\pi$
$647$	−5.14081	+	5.14081i	−0.202106	+	0.202106i	0.598796	+	0.800902i	$0.295646\pi$
$648$		0			0
$649$			43.8843i			1.72261i
$650$		0			0
$651$			6.17564i			0.242042i
$652$		0			0
$653$	−15.2062	+	15.2062i	−0.595065	+	0.595065i	−0.938995	−	0.343930i	$-0.888242\pi$
$653$	−15.2062	+	15.2062i	−0.595065	+	0.595065i	0.343930	+	0.938995i	$0.388242\pi$
$654$		0			0
$655$	−4.16950	+	16.7811i	−0.162916	+	0.655692i
$656$		0			0
$657$	0.0205189	+	0.0205189i	0.000800519	+	0.000800519i
$658$		0			0
$659$	−1.60688			−0.0625952			−0.0312976	−	0.999510i	$-0.509964\pi$
$659$	−1.60688			−0.0625952			−0.0312976	+	0.999510i	$0.509964\pi$
$660$		0			0
$661$	−34.7480			−1.35154			−0.675771	−	0.737111i	$-0.736189\pi$
$661$	−34.7480			−1.35154			−0.675771	+	0.737111i	$0.736189\pi$
$662$		0			0
$663$	−5.72678	−	5.72678i	−0.222410	−	0.222410i
$664$		0			0
$665$	5.26180	−	3.16743i	0.204044	−	0.122828i
$666$		0			0
$667$	8.07413	−	8.07413i	0.312632	−	0.312632i
$668$		0			0
$669$			3.23513i			0.125077i
$670$		0			0
$671$		−	1.26566i		−	0.0488605i
$672$		0			0
$673$	−0.785386	+	0.785386i	−0.0302744	+	0.0302744i	−0.722082	−	0.691808i	$-0.756815\pi$
$673$	−0.785386	+	0.785386i	−0.0302744	+	0.0302744i	0.691808	+	0.722082i	$0.256815\pi$
$674$		0			0
$675$	25.1469	−	7.73292i	0.967903	−	0.297640i
$676$		0			0
$677$	−5.72979	−	5.72979i	−0.220214	−	0.220214i	0.588375	−	0.808588i	$-0.299768\pi$
$677$	−5.72979	−	5.72979i	−0.220214	−	0.220214i	−0.808588	+	0.588375i	$0.799768\pi$
$678$		0			0
$679$	−5.72678			−0.219774
$680$		0			0
$681$	30.9749			1.18696
$682$		0			0
$683$	6.23266	+	6.23266i	0.238486	+	0.238486i	0.816223	−	0.577737i	$-0.196064\pi$
$683$	6.23266	+	6.23266i	0.238486	+	0.238486i	−0.577737	+	0.816223i	$0.696064\pi$
$684$		0			0
$685$	8.15449	+	13.5464i	0.311567	+	0.517580i
$686$		0			0
$687$	−25.8873	+	25.8873i	−0.987663	+	0.987663i
$688$		0			0
$689$			12.8371i			0.489055i
$690$		0			0
$691$		−	39.4462i		−	1.50061i	−0.661095	−	0.750303i	$-0.729908\pi$
$691$		−	39.4462i		−	1.50061i	0.661095	−	0.750303i	$-0.270092\pi$
$692$		0			0
$693$	0.130094	−	0.130094i	0.00494184	−	0.00494184i
$694$		0			0
$695$	0.740469	+	0.183980i	0.0280876	+	0.00697876i
$696$		0			0
$697$	32.5958	+	32.5958i	1.23465	+	1.23465i
$698$		0			0
$699$	24.2224			0.916175
$700$		0			0
$701$	−21.3874			−0.807789			−0.403895	−	0.914806i	$-0.632344\pi$
$701$	−21.3874			−0.807789			−0.403895	+	0.914806i	$0.632344\pi$
$702$		0			0
$703$	16.4895	+	16.4895i	0.621913	+	0.621913i
$704$		0			0
$705$	25.1773	+	6.25565i	0.948231	+	0.235601i
$706$		0			0
$707$	4.69470	−	4.69470i	0.176562	−	0.176562i
$708$		0			0
$709$		−	28.8827i		−	1.08471i	−0.840149	−	0.542356i	$-0.817532\pi$
$709$		−	28.8827i		−	1.08471i	0.840149	−	0.542356i	$-0.182468\pi$
$710$		0			0
$711$		−	1.26566i		−	0.0474661i
$712$		0			0
$713$	32.5958	−	32.5958i	1.22072	−	1.22072i
$714$		0			0
$715$	−4.30388	−	7.14969i	−0.160956	−	0.267383i
$716$		0			0
$717$	−22.8371	−	22.8371i	−0.852867	−	0.852867i
$718$		0			0
$719$	1.48094			0.0552296			0.0276148	−	0.999619i	$-0.491209\pi$
$719$	1.48094			0.0552296			0.0276148	+	0.999619i	$0.491209\pi$
$720$		0			0
$721$	1.56093			0.0581321
$722$		0			0
$723$	−20.5018	−	20.5018i	−0.762468	−	0.762468i
$724$		0			0
$725$	3.31965	−	6.26794i	0.123289	−	0.232785i
$726$		0			0
$727$	−10.4187	+	10.4187i	−0.386410	+	0.386410i	−0.873405	−	0.486995i	$-0.838093\pi$
$727$	−10.4187	+	10.4187i	−0.386410	+	0.386410i	0.486995	+	0.873405i	$0.338093\pi$
$728$		0			0
$729$		−	27.6681i		−	1.02474i
$730$		0			0
$731$		−	8.07413i		−	0.298633i
$732$		0			0
$733$	−0.579182	+	0.579182i	−0.0213926	+	0.0213926i	−0.717722	−	0.696330i	$-0.754815\pi$
$733$	−0.579182	+	0.579182i	−0.0213926	+	0.0213926i	0.696330	+	0.717722i	$0.254815\pi$
$734$		0			0
$735$	21.6184	−	13.0136i	0.797407	−	0.480014i
$736$		0			0
$737$	16.5503	+	16.5503i	0.609636	+	0.609636i
$738$		0			0
$739$	−2.19011			−0.0805646			−0.0402823	−	0.999188i	$-0.512826\pi$
$739$	−2.19011			−0.0805646			−0.0402823	+	0.999188i	$0.512826\pi$
$740$		0			0
$741$	−7.46412			−0.274201
$742$		0			0
$743$	5.42053	+	5.42053i	0.198860	+	0.198860i	0.799511	−	0.600651i	$-0.205092\pi$
$743$	5.42053	+	5.42053i	0.198860	+	0.198860i	−0.600651	+	0.799511i	$0.705092\pi$
$744$		0			0
$745$	−5.62863	+	22.6537i	−0.206217	+	0.829967i
$746$		0			0
$747$	−0.435947	+	0.435947i	−0.0159505	+	0.0159505i
$748$		0			0
$749$		−	2.67050i		−	0.0975781i
$750$		0			0
$751$		−	51.6403i		−	1.88438i	−0.335079	−	0.942190i	$-0.608763\pi$
$751$		−	51.6403i		−	1.88438i	0.335079	−	0.942190i	$-0.391237\pi$
$752$		0			0
$753$	13.4908	−	13.4908i	0.491632	−	0.491632i
$754$		0			0
$755$	−7.10009	+	28.5759i	−0.258399	+	1.03998i
$756$		0			0
$757$	8.80817	+	8.80817i	0.320138	+	0.320138i	0.848820	−	0.528682i	$-0.177313\pi$
$757$	8.80817	+	8.80817i	0.320138	+	0.320138i	−0.528682	+	0.848820i	$0.677313\pi$
$758$		0			0
$759$	51.1914			1.85813
$760$		0			0
$761$	−14.6803			−0.532162			−0.266081	−	0.963951i	$-0.585729\pi$
$761$	−14.6803			−0.532162			−0.266081	+	0.963951i	$0.585729\pi$
$762$		0			0
$763$	−6.13793	−	6.13793i	−0.222208	−	0.222208i
$764$		0			0
$765$	−0.709275	+	0.426961i	−0.0256439	+	0.0154368i
$766$		0			0
$767$	8.36575	−	8.36575i	0.302070	−	0.302070i
$768$		0			0
$769$		−	11.1506i		−	0.402101i	−0.979581	−	0.201051i	$-0.935564\pi$
$769$		−	11.1506i		−	0.402101i	0.979581	−	0.201051i	$-0.0644356\pi$
$770$		0			0
$771$		−	20.7934i		−	0.748855i
$772$		0			0
$773$	−5.44748	+	5.44748i	−0.195932	+	0.195932i	−0.798254	−	0.602321i	$-0.794243\pi$
$773$	−5.44748	+	5.44748i	−0.195932	+	0.195932i	0.602321	+	0.798254i	$0.294243\pi$
$774$		0			0
$775$	13.4017	−	25.3041i	0.481402	−	0.908950i
$776$		0			0
$777$	−4.08452	−	4.08452i	−0.146531	−	0.146531i
$778$		0			0
$779$	42.4844			1.52216
$780$		0			0
$781$	−53.7030			−1.92164
$782$		0			0
$783$	−5.27793	−	5.27793i	−0.188618	−	0.188618i
$784$		0			0
$785$	−7.42469	−	12.3340i	−0.264999	−	0.440220i
$786$		0			0
$787$	−10.6239	+	10.6239i	−0.378699	+	0.378699i	−0.870633	−	0.491933i	$-0.836290\pi$
$787$	−10.6239	+	10.6239i	−0.378699	+	0.378699i	0.491933	+	0.870633i	$0.336290\pi$
$788$		0			0
$789$			32.7403i			1.16559i
$790$		0			0
$791$			1.71452i			0.0609612i
$792$		0			0
$793$	−0.241276	+	0.241276i	−0.00856797	+	0.00856797i
$794$		0			0
$795$	−47.4708	−	11.7948i	−1.68361	−	0.418318i
$796$		0			0
$797$	4.02893	+	4.02893i	0.142712	+	0.142712i	0.774853	−	0.632141i	$-0.217824\pi$
$797$	4.02893	+	4.02893i	0.142712	+	0.142712i	−0.632141	+	0.774853i	$0.717824\pi$
$798$		0			0
$799$	−32.0630			−1.13431
$800$		0			0
$801$	−0.169042			−0.00597279
$802$		0			0
$803$	0.974049	+	0.974049i	0.0343734	+	0.0343734i
$804$		0			0
$805$	11.0205	+	2.73820i	0.388422	+	0.0965090i
$806$		0			0
$807$	−21.8428	+	21.8428i	−0.768904	+	0.768904i
$808$		0			0
$809$			23.0349i			0.809864i	0.914347	+	0.404932i	$0.132705\pi$
$809$			23.0349i			0.809864i	−0.914347	+	0.404932i	$0.867295\pi$
$810$		0			0
$811$			36.0172i			1.26473i	0.774669	+	0.632367i	$0.217917\pi$
$811$			36.0172i			1.26473i	−0.774669	+	0.632367i	$0.782083\pi$
$812$		0			0
$813$	21.5897	−	21.5897i	0.757183	−	0.757183i
$814$		0			0
$815$	10.1648	+	16.8860i	0.356059	+	0.591491i
$816$		0			0
$817$	−5.26180	−	5.26180i	−0.184087	−	0.184087i
$818$		0			0
$819$	−0.0496000			−0.00173316
$820$		0			0
$821$	11.9733			0.417872			0.208936	−	0.977929i	$-0.433000\pi$
$821$	11.9733			0.417872			0.208936	+	0.977929i	$0.433000\pi$
$822$		0			0
$823$	33.2937	+	33.2937i	1.16054	+	1.16054i	0.984357	+	0.176187i	$0.0563764\pi$
$823$	33.2937	+	33.2937i	1.16054	+	1.16054i	0.176187	+	0.984357i	$0.443624\pi$
$824$		0			0
$825$	30.3935	−	9.34632i	1.05817	−	0.325397i
$826$		0			0
$827$	−24.9500	+	24.9500i	−0.867595	+	0.867595i	−0.992206	−	0.124610i	$-0.960232\pi$
$827$	−24.9500	+	24.9500i	−0.867595	+	0.867595i	0.124610	+	0.992206i	$0.460232\pi$
$828$		0			0
$829$			21.1317i			0.733934i	0.930234	+	0.366967i	$0.119604\pi$
$829$			21.1317i			0.733934i	−0.930234	+	0.366967i	$0.880396\pi$
$830$		0			0
$831$		−	17.8628i		−	0.619653i
$832$		0			0
$833$	−22.0517	+	22.0517i	−0.764047	+	0.764047i
$834$		0			0
$835$	−33.1640	+	19.9637i	−1.14769	+	0.690871i
$836$		0			0
$837$	−21.3074	−	21.3074i	−0.736490	−	0.736490i
$838$		0			0
$839$	−12.3513			−0.426413			−0.213207	−	0.977007i	$-0.568391\pi$
$839$	−12.3513			−0.426413			−0.213207	+	0.977007i	$0.568391\pi$
$840$		0			0
$841$	26.9877			0.930611
$842$		0			0
$843$	−26.6774	−	26.6774i	−0.918818	−	0.918818i
$844$		0			0
$845$	6.46695	−	26.0277i	0.222470	−	0.895380i
$846$		0			0
$847$	1.26841	−	1.26841i	0.0435829	−	0.0435829i
$848$		0			0
$849$		−	25.5897i		−	0.878236i
$850$		0			0
$851$			43.1173i			1.47804i
$852$		0			0
$853$	−33.9588	+	33.9588i	−1.16273	+	1.16273i	−0.178850	+	0.983876i	$0.557238\pi$
$853$	−33.9588	+	33.9588i	−1.16273	+	1.16273i	−0.983876	+	0.178850i	$0.942762\pi$
$854$		0			0
$855$	−0.183980	+	0.740469i	−0.00629198	+	0.0253235i
$856$		0			0
$857$	21.1568	+	21.1568i	0.722701	+	0.722701i	0.969155	−	0.246454i	$-0.0792653\pi$
$857$	21.1568	+	21.1568i	0.722701	+	0.722701i	−0.246454	+	0.969155i	$0.579265\pi$
$858$		0			0
$859$	−14.3261			−0.488801			−0.244400	−	0.969674i	$-0.578591\pi$
$859$	−14.3261			−0.488801			−0.244400	+	0.969674i	$0.578591\pi$
$860$		0			0
$861$	−10.5236			−0.358643
$862$		0			0
$863$	−10.3865	−	10.3865i	−0.353561	−	0.353561i	0.507872	−	0.861433i	$-0.330432\pi$
$863$	−10.3865	−	10.3865i	−0.353561	−	0.353561i	−0.861433	+	0.507872i	$0.830432\pi$
$864$		0			0
$865$	−26.9421	+	16.2183i	−0.916060	+	0.551439i
$866$		0			0
$867$	−6.42212	+	6.42212i	−0.218107	+	0.218107i
$868$		0			0
$869$		−	60.0821i		−	2.03814i
$870$		0			0
$871$		−	6.31002i		−	0.213807i
$872$		0			0
$873$	0.503072	−	0.503072i	0.0170264	−	0.0170264i
$874$		0			0
$875$	7.04306	−	0.386347i	0.238099	−	0.0130609i
$876$		0			0
$877$	−9.29072	−	9.29072i	−0.313725	−	0.313725i	0.532626	−	0.846351i	$-0.321205\pi$
$877$	−9.29072	−	9.29072i	−0.313725	−	0.313725i	−0.846351	+	0.532626i	$0.821205\pi$
$878$		0			0
$879$	−21.2918			−0.718155
$880$		0			0
$881$	29.2762			0.986339			0.493170	−	0.869933i	$-0.335838\pi$
$881$	29.2762			0.986339			0.493170	+	0.869933i	$0.335838\pi$
$882$		0			0
$883$	39.6808	+	39.6808i	1.33537	+	1.33537i	0.900491	+	0.434875i	$0.143207\pi$
$883$	39.6808	+	39.6808i	1.33537	+	1.33537i	0.434875	+	0.900491i	$0.356793\pi$
$884$		0			0
$885$	23.2495	+	38.6225i	0.781524	+	1.29828i
$886$		0			0
$887$	−30.7946	+	30.7946i	−1.03398	+	1.03398i	−0.0345779	+	0.999402i	$0.511009\pi$
$887$	−30.7946	+	30.7946i	−1.03398	+	1.03398i	−0.999402	+	0.0345779i	$0.988991\pi$
$888$		0			0
$889$		−	6.24128i		−	0.209326i
$890$		0			0
$891$		−	32.5882i		−	1.09174i
$892$		0			0
$893$	−20.8950	+	20.8950i	−0.699223	+	0.699223i
$894$		0			0
$895$	−50.4509	−	12.5353i	−1.68639	−	0.419007i
$896$		0			0
$897$	−9.75872	−	9.75872i	−0.325834	−	0.325834i
$898$		0			0
$899$	−8.12373			−0.270942
$900$		0			0
$901$	60.4534			2.01400
$902$		0			0
$903$	1.30337	+	1.30337i	0.0433735	+	0.0433735i
$904$		0			0
$905$	−15.6332	−	3.88428i	−0.519664	−	0.129118i
$906$		0			0
$907$	−23.1536	+	23.1536i	−0.768803	+	0.768803i	−0.977896	−	0.209092i	$-0.932949\pi$
$907$	−23.1536	+	23.1536i	−0.768803	+	0.768803i	0.209092	+	0.977896i	$0.432949\pi$
$908$		0			0
$909$			0.824815i			0.0273574i
$910$		0			0
$911$		−	28.6339i		−	0.948684i	−0.880341	−	0.474342i	$-0.842686\pi$
$911$		−	28.6339i		−	0.948684i	0.880341	−	0.474342i	$-0.157314\pi$
$912$		0			0
$913$	−20.6947	+	20.6947i	−0.684895	+	0.684895i
$914$		0			0
$915$	−0.670538	−	1.11391i	−0.0221673	−	0.0368247i
$916$		0			0
$917$	3.44975	+	3.44975i	0.113921	+	0.113921i
$918$		0			0
$919$	1.26566			0.0417504			0.0208752	−	0.999782i	$-0.493355\pi$
$919$	1.26566			0.0417504			0.0208752	+	0.999782i	$0.493355\pi$
$920$		0			0
$921$	−38.4391			−1.26661
$922$		0			0
$923$	10.2375	+	10.2375i	0.336972	+	0.336972i
$924$		0			0
$925$	7.87217	+	25.5997i	0.258835	+	0.841713i
$926$		0			0
$927$	−0.137121	+	0.137121i	−0.00450363	+	0.00450363i
$928$		0			0
$929$			8.75258i			0.287163i	0.989639	+	0.143581i	$0.0458619\pi$
$929$			8.75258i			0.287163i	−0.989639	+	0.143581i	$0.954138\pi$
$930$		0			0
$931$			28.7416i			0.941967i
$932$		0			0
$933$	−5.39189	+	5.39189i	−0.176523	+	0.176523i
$934$		0			0
$935$	−33.6698	+	20.2682i	−1.10112	+	0.662840i
$936$		0			0
$937$	−26.6598	−	26.6598i	−0.870939	−	0.870939i	0.121636	−	0.992575i	$-0.461186\pi$
$937$	−26.6598	−	26.6598i	−0.870939	−	0.870939i	−0.992575	+	0.121636i	$0.961186\pi$
$938$		0			0
$939$	−44.9662			−1.46742
$940$		0			0
$941$	46.2388			1.50734			0.753671	−	0.657251i	$-0.228281\pi$
$941$	46.2388			1.50734			0.753671	+	0.657251i	$0.228281\pi$
$942$		0			0
$943$	55.5449	+	55.5449i	1.80879	+	1.80879i
$944$		0			0
$945$	1.78992	−	7.20394i	0.0582261	−	0.234344i
$946$		0			0
$947$	−8.46048	+	8.46048i	−0.274929	+	0.274929i	−0.831081	−	0.556152i	$-0.812277\pi$
$947$	−8.46048	+	8.46048i	−0.274929	+	0.274929i	0.556152	+	0.831081i	$0.312277\pi$
$948$		0			0
$949$		−	0.371370i		−	0.0120552i
$950$		0			0
$951$			9.73905i			0.315810i
$952$		0			0
$953$	−2.40417	+	2.40417i	−0.0778789	+	0.0778789i	−0.744973	−	0.667094i	$-0.767538\pi$
$953$	−2.40417	+	2.40417i	−0.0778789	+	0.0778789i	0.667094	+	0.744973i	$0.267538\pi$
$954$		0			0
$955$	5.61915	−	22.6155i	0.181831	−	0.731821i
$956$		0			0
$957$	−6.37912	−	6.37912i	−0.206208	−	0.206208i
$958$		0			0
$959$	4.46112			0.144057
$960$		0			0
$961$	−1.79606			−0.0579375
$962$		0			0
$963$	0.234591	+	0.234591i	0.00755961	+	0.00755961i
$964$		0			0
$965$	43.8287	−	26.3835i	1.41090	−	0.849314i
$966$		0			0
$967$	42.3741	−	42.3741i	1.36266	−	1.36266i	0.492145	−	0.870513i	$-0.336213\pi$
$967$	42.3741	−	42.3741i	1.36266	−	1.36266i	0.870513	−	0.492145i	$-0.163787\pi$
$968$		0			0
$969$			35.1506i			1.12920i
$970$		0			0
$971$		−	48.0540i		−	1.54213i	−0.636759	−	0.771063i	$-0.719725\pi$
$971$		−	48.0540i		−	1.54213i	0.636759	−	0.771063i	$-0.280275\pi$
$972$		0			0
$973$	0.152221	−	0.152221i	0.00487997	−	0.00487997i
$974$		0			0
$975$	−7.57568	−	4.01227i	−0.242616	−	0.128495i
$976$		0			0
$977$	−29.2967	−	29.2967i	−0.937284	−	0.937284i	0.0608620	−	0.998146i	$-0.480615\pi$
$977$	−29.2967	−	29.2967i	−0.937284	−	0.937284i	−0.998146	+	0.0608620i	$0.980615\pi$
$978$		0			0
$979$	−8.02453			−0.256465
$980$		0			0
$981$	1.07838			0.0344300
$982$		0			0
$983$	22.2512	+	22.2512i	0.709704	+	0.709704i	0.966473	−	0.256769i	$-0.0826579\pi$
$983$	22.2512	+	22.2512i	0.709704	+	0.709704i	−0.256769	+	0.966473i	$0.582658\pi$
$984$		0			0
$985$	−22.4863	−	37.3545i	−0.716472	−	1.19021i
$986$		0			0
$987$	5.17578	−	5.17578i	0.164747	−	0.164747i
$988$		0			0
$989$		−	13.7587i		−	0.437502i
$990$		0			0
$991$		−	27.1530i		−	0.862543i	−0.902222	−	0.431272i	$-0.858065\pi$
$991$		−	27.1530i		−	0.862543i	0.902222	−	0.431272i	$-0.141935\pi$
$992$		0			0
$993$	0.352459	−	0.352459i	0.0111850	−	0.0111850i
$994$		0			0
$995$	35.0431	+	8.70697i	1.11094	+	0.276029i
$996$		0			0
$997$	−33.0228	−	33.0228i	−1.04584	−	1.04584i	−0.998897	−	0.0469446i	$-0.985052\pi$
$997$	−33.0228	−	33.0228i	−1.04584	−	1.04584i	−0.0469446	−	0.998897i	$-0.514948\pi$
$998$		0			0
$999$	28.1851			0.891736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.r.767.5		12
4.3	odd	2	inner	1280.2.n.r.767.2		12
5.3	odd	4	inner	1280.2.n.r.1023.2		12
8.3	odd	2		1280.2.n.s.767.5		12
8.5	even	2		1280.2.n.s.767.2		12
16.3	odd	4		640.2.o.k.447.5	yes	12
16.5	even	4		640.2.o.j.447.5	yes	12
16.11	odd	4		640.2.o.j.447.2	yes	12
16.13	even	4		640.2.o.k.447.2	yes	12
20.3	even	4	inner	1280.2.n.r.1023.5		12
40.3	even	4		1280.2.n.s.1023.2		12
40.13	odd	4		1280.2.n.s.1023.5		12
80.3	even	4		640.2.o.j.63.5	yes	12
80.13	odd	4		640.2.o.j.63.2	✓	12
80.43	even	4		640.2.o.k.63.2	yes	12
80.53	odd	4		640.2.o.k.63.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.o.j.63.2	✓	12	80.13	odd	4
640.2.o.j.63.5	yes	12	80.3	even	4
640.2.o.j.447.2	yes	12	16.11	odd	4
640.2.o.j.447.5	yes	12	16.5	even	4
640.2.o.k.63.2	yes	12	80.43	even	4
640.2.o.k.63.5	yes	12	80.53	odd	4
640.2.o.k.447.2	yes	12	16.13	even	4
640.2.o.k.447.5	yes	12	16.3	odd	4
1280.2.n.r.767.2		12	4.3	odd	2	inner
1280.2.n.r.767.5		12	1.1	even	1	trivial
1280.2.n.r.1023.2		12	5.3	odd	4	inner
1280.2.n.r.1023.5		12	20.3	even	4	inner
1280.2.n.s.767.2		12	8.5	even	2
1280.2.n.s.767.5		12	8.3	odd	2
1280.2.n.s.1023.2		12	40.3	even	4
1280.2.n.s.1023.5		12	40.13	odd	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.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20864 + 1.20864i) q^{3} +(-2.17009 - 0.539189i) q^{5} +(-0.446112 + 0.446112i) q^{7} -0.0783777i q^{9} -3.72065i q^{11} +(-0.709275 + 0.709275i) q^{13} +(-1.97117 - 3.27454i) q^{15} +(3.34017 + 3.34017i) q^{17} +4.35348 q^{19} -1.07838 q^{21} +(5.69182 + 5.69182i) q^{23} +(4.41855 + 2.34017i) q^{25} +(3.72065 - 3.72065i) q^{27} -1.41855i q^{29} -5.72678i q^{31} +(4.49693 - 4.49693i) q^{33} +(1.20864 - 0.727563i) q^{35} +(3.78765 + 3.78765i) q^{37} -1.71452 q^{39} +9.75872 q^{41} +(-1.20864 - 1.20864i) q^{43} +(-0.0422604 + 0.170086i) q^{45} +(-4.79960 + 4.79960i) q^{47} +6.60197i q^{49} +8.07413i q^{51} +(9.04945 - 9.04945i) q^{53} +(-2.00613 + 8.07413i) q^{55} +(5.26180 + 5.26180i) q^{57} -11.7948 q^{59} +0.340173 q^{61} +(0.0349653 + 0.0349653i) q^{63} +(1.92162 - 1.15676i) q^{65} +(-4.44821 + 4.44821i) q^{67} +13.7587i q^{69} -14.4338i q^{71} +(-0.261795 + 0.261795i) q^{73} +(2.51201 + 8.16887i) q^{75} +(1.65983 + 1.65983i) q^{77} +16.1483 q^{79} +8.75872 q^{81} +(-5.56212 - 5.56212i) q^{83} +(-5.44748 - 9.04945i) q^{85} +(1.71452 - 1.71452i) q^{87} -2.15676i q^{89} -0.632832i q^{91} +(6.92162 - 6.92162i) q^{93} +(-9.44744 - 2.34735i) q^{95} +(6.41855 + 6.41855i) q^{97} -0.291616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 20 q^{13} - 4 q^{17} - 4 q^{25} - 16 q^{33} + 4 q^{37} + 16 q^{41} - 64 q^{45} + 36 q^{53} + 32 q^{57} - 40 q^{61} + 36 q^{65} + 28 q^{73} + 64 q^{77} + 4 q^{81} - 68 q^{85} + 96 q^{93}+ \cdots + 20 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 20 * q^13 - 4 * q^17 - 4 * q^25 - 16 * q^33 + 4 * q^37 + 16 * q^41 - 64 * q^45 + 36 * q^53 + 32 * q^57 - 40 * q^61 + 36 * q^65 + 28 * q^73 + 64 * q^77 + 4 * q^81 - 68 * q^85 + 96 * q^93 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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