LMFDB - Embedded newform 1040.2.q.c.321.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(81,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2,0,-2,0,-1,0,-1,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1040.321
Dual form			1040.2.q.c.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +(2.50000 - 2.59808i) q^{13} +(1.00000 - 1.73205i) q^{15} +(3.00000 + 5.19615i) q^{17} +(2.50000 + 4.33013i) q^{19} +2.00000 q^{21} +1.00000 q^{25} -4.00000 q^{27} +4.00000 q^{31} +(3.00000 + 5.19615i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(2.00000 + 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(0.500000 + 0.866025i) q^{45} +3.00000 q^{47} +(3.00000 - 5.19615i) q^{49} -12.0000 q^{51} -9.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} -10.0000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-2.50000 + 2.59808i) q^{65} +(-8.00000 + 13.8564i) q^{67} +(3.00000 + 5.19615i) q^{71} +14.0000 q^{73} +(-1.00000 + 1.73205i) q^{75} -3.00000 q^{77} +16.0000 q^{79} +(5.50000 - 9.52628i) q^{81} +6.00000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(-4.50000 + 7.79423i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(5.00000 + 8.66025i) q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{5} - q^{7} - q^{9} + 3 q^{11} + 5 q^{13} + 2 q^{15} + 6 q^{17} + 5 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 8 q^{31} + 6 q^{33} + q^{35} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 2 q^{43}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^5 - q^7 - q^9 + 3 * q^11 + 5 * q^13 + 2 * q^15 + 6 * q^17 + 5 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 8 * q^31 + 6 * q^33 + q^35 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 2 * q^43 + q^45 + 6 * q^47 + 6 * q^49 - 24 * q^51 - 18 * q^53 - 3 * q^55 - 20 * q^57 - 8 * q^61 - q^63 - 5 * q^65 - 16 * q^67 + 6 * q^71 + 28 * q^73 - 2 * q^75 - 6 * q^77 + 32 * q^79 + 11 * q^81 + 12 * q^83 - 6 * q^85 - 9 * q^89 - 7 * q^91 - 8 * q^93 - 5 * q^95 + 10 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$		0			0
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	2.00000	+	6.92820i	0.320256	+	1.10940i
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	−12.0000			−1.68034
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$	−10.0000			−1.32453
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$		0			0
$65$	−2.50000	+	2.59808i	−0.310087	+	0.322252i
$66$		0			0
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.305424	+	0.952217i	$0.598798\pi$
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$		0			0
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	−3.50000	−	0.866025i	−0.366900	−	0.0907841i
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	−5.00000			−0.492665			−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000			−0.492665			−0.246332	+	0.969185i	$0.579225\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−11.0000	−	19.0526i	−1.04407	−	1.80839i
$112$		0			0
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	0.997102	+	0.0760733i	$0.0242383\pi$
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	−0.432670	+	0.901553i	$0.642428\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	−4.00000			−0.352180
$130$		0			0
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$		0			0
$133$	2.50000	−	4.33013i	0.216777	−	0.375470i
$134$		0			0
$135$	4.00000			0.344265
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	−0.915764	−	0.401718i	$-0.868413\pi$
$139$	−9.50000	−	16.4545i	−0.805779	−	1.39565i	0.109984	−	0.993933i	$-0.464920\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		0			0
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.00000	+	10.3923i	0.494872	+	0.857143i
$148$		0			0
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	17.0000			1.35675			0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000			1.35675			0.678374	+	0.734717i	$0.262685\pi$
$158$		0			0
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$		0			0
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$		0			0
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	2.50000	−	4.33013i	0.191180	−	0.331133i
$172$		0			0
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.0655145	+	0.997852i	$0.520869\pi$
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.831408	+	0.555663i	$0.812464\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$	16.0000			1.18275
$184$		0			0
$185$	5.50000	−	9.52628i	0.404368	−	0.700386i
$186$		0			0
$187$	18.0000			1.31629
$188$		0			0
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$	−2.00000	−	6.92820i	−0.143223	−	0.496139i
$196$		0			0
$197$	13.5000	−	23.3827i	0.961835	−	1.66595i	0.243947	−	0.969788i	$-0.421558\pi$
$197$	13.5000	−	23.3827i	0.961835	−	1.66595i	0.717888	−	0.696159i	$-0.245109\pi$
$198$		0			0
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$		0			0
$201$	−16.0000	−	27.7128i	−1.12855	−	1.95471i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	−0.133226	−	0.991086i	$-0.542533\pi$
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	0.924918	−	0.380166i	$-0.124133\pi$
$212$		0			0
$213$	−12.0000			−0.822226
$214$		0			0
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$		0			0
$219$	−14.0000	+	24.2487i	−0.946032	+	1.63858i
$220$		0			0
$221$	21.0000	+	5.19615i	1.41261	+	0.349531i
$222$		0			0
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		0			0
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$		0			0
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$		0			0
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$		0			0
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$		0			0
$237$	−16.0000	+	27.7128i	−1.03931	+	1.80014i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	17.5000	+	4.33013i	1.11350	+	0.275519i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	0.526140	−	0.850398i	$-0.323639\pi$
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	−0.999536	+	0.0304521i	$0.990305\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	12.0000			0.751469
$256$		0			0
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	11.0000			0.683507
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$		0			0
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$		0			0
$273$	5.00000	−	5.19615i	0.302614	−	0.314485i
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		0			0
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	10.0000			0.592349
$286$		0			0
$287$	6.00000			0.354169
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−20.0000			−1.17242
$292$		0			0
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.00000	+	10.3923i	−0.348155	+	0.603023i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$		0			0
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$		0			0
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	5.00000	−	8.66025i	0.284440	−	0.492665i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	15.0000			0.842484			0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000			0.842484			0.421242	+	0.906948i	$0.361594\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$		0			0
$323$	−15.0000	+	25.9808i	−0.834622	+	1.44561i
$324$		0			0
$325$	2.50000	−	2.59808i	0.138675	−	0.144115i
$326$		0			0
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$		0			0
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	11.0000			0.602796
$334$		0			0
$335$	8.00000	−	13.8564i	0.437087	−	0.757056i
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$		0			0
$339$	−24.0000			−1.30350
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	−0.774197	+	0.632945i	$0.781846\pi$
$348$		0			0
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$		0			0
$351$	−10.0000	+	10.3923i	−0.533761	+	0.554700i
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$		0			0
$357$	6.00000	+	10.3923i	0.317554	+	0.550019i
$358$		0			0
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$	−4.00000			−0.209946
$364$		0			0
$365$	−14.0000			−0.732793
$366$		0			0
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	4.50000	+	7.79423i	0.233628	+	0.404656i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−9.50000	+	16.4545i	−0.487982	+	0.845210i	−0.999904	−	0.0138218i	$-0.995600\pi$
$379$	−9.50000	+	16.4545i	−0.487982	+	0.845210i	0.511922	+	0.859032i	$0.328934\pi$
$380$		0			0
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	3.00000			0.152894
$386$		0			0
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$		0			0
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−9.00000	+	15.5885i	−0.453990	+	0.786334i
$394$		0			0
$395$	−16.0000			−0.805047
$396$		0			0
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$		0			0
$399$	5.00000	+	8.66025i	0.250313	+	0.433555i
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	10.0000	−	10.3923i	0.498135	−	0.517678i
$404$		0			0
$405$	−5.50000	+	9.52628i	−0.273297	+	0.473365i
$406$		0			0
$407$	16.5000	+	28.5788i	0.817875	+	1.41660i
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000			−0.294528
$416$		0			0
$417$	38.0000			1.86087
$418$		0			0
$419$	−18.0000	+	31.1769i	−0.879358	+	1.52309i	−0.0273103	+	0.999627i	$0.508694\pi$
$419$	−18.0000	+	31.1769i	−0.879358	+	1.52309i	−0.852047	+	0.523465i	$0.824639\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$		0			0
$429$	21.0000	+	5.19615i	1.01389	+	0.250873i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		0			0
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	−0.522387	−	0.852709i	$-0.674958\pi$
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	0.999661	+	0.0260459i	$0.00829161\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$		0			0
$447$	−36.0000			−1.70274
$448$		0			0
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	0.740087	−	0.672511i	$-0.234784\pi$
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	−0.952455	+	0.304679i	$0.901451\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$		0			0
$453$	−16.0000	+	27.7128i	−0.751746	+	1.30206i
$454$		0			0
$455$	3.50000	+	0.866025i	0.164083	+	0.0405999i
$456$		0			0
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	−0.815449	−	0.578829i	$-0.803510\pi$
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	0.909005	+	0.416785i	$0.136843\pi$
$458$		0			0
$459$	−12.0000	−	20.7846i	−0.560112	−	0.970143i
$460$		0			0
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.669417	+	0.742887i	$0.266544\pi$
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.308651	+	0.951175i	$0.400123\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$		0			0
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$		0			0
$471$	−17.0000	+	29.4449i	−0.783319	+	1.35675i
$472$		0			0
$473$	6.00000			0.275880
$474$		0			0
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$		0			0
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$		0			0
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	11.0000	+	38.1051i	0.501557	+	1.73744i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	0.566429	−	0.824110i	$-0.308325\pi$
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	−0.382118	−	0.924113i	$-0.624805\pi$
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	0.991365	−	0.131132i	$-0.0418613\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	3.00000			0.134840
$496$		0			0
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	−15.0000	−	25.9808i	−0.670151	−	1.16073i
$502$		0			0
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	0.948736	−	0.316068i	$-0.102363\pi$
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	−0.748091	+	0.663596i	$0.769030\pi$
$504$		0			0
$505$	−3.00000	+	5.19615i	−0.133498	+	0.231226i
$506$		0			0
$507$	23.0000	+	12.1244i	1.02147	+	0.538462i
$508$		0			0
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$		0			0
$513$	−10.0000	−	17.3205i	−0.441511	−	0.764719i
$514$		0			0
$515$	5.00000			0.220326
$516$		0			0
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$		0			0
$519$	30.0000			1.31685
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	−0.671414	−	0.741082i	$-0.734313\pi$
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	0.977503	+	0.210921i	$0.0676463\pi$
$524$		0			0
$525$	2.00000			0.0872872
$526$		0			0
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.00000	+	20.7846i	0.259889	+	0.900281i
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$	−24.0000	−	41.5692i	−1.03568	−	1.79384i
$538$		0			0
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$		0			0
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$		0			0
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$		0			0
$555$	11.0000	+	19.0526i	0.466924	+	0.808736i
$556$		0			0
$557$	−10.5000	+	18.1865i	−0.444899	+	0.770588i	−0.998045	−	0.0624962i	$-0.980094\pi$
$557$	−10.5000	+	18.1865i	−0.444899	+	0.770588i	0.553146	+	0.833084i	$0.313427\pi$
$558$		0			0
$559$	7.00000	+	1.73205i	0.296068	+	0.0732579i
$560$		0			0
$561$	−18.0000	+	31.1769i	−0.759961	+	1.31629i
$562$		0			0
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$	−6.00000	−	10.3923i	−0.252422	−	0.437208i
$566$		0			0
$567$	−11.0000			−0.461957
$568$		0			0
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$		0			0
$571$	−17.0000			−0.711428			−0.355714	−	0.934595i	$-0.615762\pi$
$571$	−17.0000			−0.711428			−0.355714	+	0.934595i	$0.615762\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$		0			0
$579$	4.00000	+	6.92820i	0.166234	+	0.287926i
$580$		0			0
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$		0			0
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$		0			0
$585$	3.50000	+	0.866025i	0.144707	+	0.0358057i
$586$		0			0
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	−0.921272	−	0.388918i	$-0.872849\pi$
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	0.797449	+	0.603386i	$0.206182\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	27.0000	+	46.7654i	1.11063	+	1.92367i
$592$		0			0
$593$	24.0000			0.985562			0.492781	−	0.870153i	$-0.335980\pi$
$593$	24.0000			0.985562			0.492781	+	0.870153i	$0.335980\pi$
$594$		0			0
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$		0			0
$597$	20.0000			0.818546
$598$		0			0
$599$	18.0000			0.735460			0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000			0.735460			0.367730	+	0.929933i	$0.380135\pi$
$600$		0			0
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$		0			0
$603$	16.0000			0.651570
$604$		0			0
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.50000	−	7.79423i	0.303418	−	0.315321i
$612$		0			0
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	−0.704382	−	0.709821i	$-0.748776\pi$
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	0.966914	+	0.255102i	$0.0821090\pi$
$614$		0			0
$615$	6.00000	+	10.3923i	0.241943	+	0.419058i
$616$		0			0
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$		0			0
$619$	1.00000			0.0401934			0.0200967	−	0.999798i	$-0.493603\pi$
$619$	1.00000			0.0401934			0.0200967	+	0.999798i	$0.493603\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.00000			0.360577
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−15.0000	+	25.9808i	−0.599042	+	1.03757i
$628$		0			0
$629$	−66.0000			−2.63159
$630$		0			0
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	−0.997718	−	0.0675178i	$-0.978492\pi$
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	0.440387	−	0.897808i	$-0.354841\pi$
$632$		0			0
$633$	23.0000	+	39.8372i	0.914168	+	1.58339i
$634$		0			0
$635$	0.500000	−	0.866025i	0.0198419	−	0.0343672i
$636$		0			0
$637$	−6.00000	−	20.7846i	−0.237729	−	0.823516i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	0.885070	−	0.465458i	$-0.154110\pi$
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	−0.845634	+	0.533764i	$0.820777\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$		0			0
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	8.00000			0.313545
$652$		0			0
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	−9.00000			−0.351659
$656$		0			0
$657$	−7.00000	−	12.1244i	−0.273096	−	0.473016i
$658$		0			0
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	−0.824506	−	0.565854i	$-0.808547\pi$
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	0.902297	+	0.431116i	$0.141880\pi$
$662$		0			0
$663$	−30.0000	+	31.1769i	−1.16510	+	1.21081i
$664$		0			0
$665$	−2.50000	+	4.33013i	−0.0969458	+	0.167915i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−19.0000	−	32.9090i	−0.734582	−	1.27233i
$670$		0			0
$671$	−24.0000			−0.926510
$672$		0			0
$673$	−10.0000	+	17.3205i	−0.385472	+	0.667657i	−0.991835	−	0.127532i	$-0.959295\pi$
$673$	−10.0000	+	17.3205i	−0.385472	+	0.667657i	0.606363	+	0.795188i	$0.292628\pi$
$674$		0			0
$675$	−4.00000			−0.153960
$676$		0			0
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$		0			0
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$	48.0000			1.83936
$682$		0			0
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	0.802905	−	0.596107i	$-0.203287\pi$
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	−0.917697	+	0.397282i	$0.869953\pi$
$684$		0			0
$685$	3.00000	+	5.19615i	0.114624	+	0.198535i
$686$		0			0
$687$	4.00000	−	6.92820i	0.152610	−	0.264327i
$688$		0			0
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	−0.962768	−	0.270330i	$-0.912867\pi$
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	0.715496	+	0.698617i	$0.246201\pi$
$692$		0			0
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$		0			0
$695$	9.50000	+	16.4545i	0.360356	+	0.624154i
$696$		0			0
$697$	−36.0000			−1.36360
$698$		0			0
$699$	24.0000	−	41.5692i	0.907763	−	1.57229i
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	−55.0000			−2.07436
$704$		0			0
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$		0			0
$707$	−6.00000			−0.225653
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	−8.00000	−	13.8564i	−0.300023	−	0.519656i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	3.00000	+	10.3923i	0.112194	+	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	2.50000	+	4.33013i	0.0931049	+	0.161262i
$722$		0			0
$723$	46.0000			1.71076
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	−25.0000			−0.923396			−0.461698	−	0.887037i	$-0.652760\pi$
$733$	−25.0000			−0.923396			−0.461698	+	0.887037i	$0.652760\pi$
$734$		0			0
$735$	−6.00000	−	10.3923i	−0.221313	−	0.383326i
$736$		0			0
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$		0			0
$739$	−3.50000	+	6.06218i	−0.128750	+	0.223001i	−0.923192	−	0.384338i	$-0.874430\pi$
$739$	−3.50000	+	6.06218i	−0.128750	+	0.223001i	0.794443	+	0.607339i	$0.207763\pi$
$740$		0			0
$741$	−25.0000	+	25.9808i	−0.918398	+	0.954427i
$742$		0			0
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$		0			0
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$		0			0
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$	12.0000			0.438470
$750$		0			0
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	0.227153	+	0.973859i	$0.427058\pi$
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	−0.956963	+	0.290209i	$0.906275\pi$
$752$		0			0
$753$	30.0000			1.09326
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	−0.995736	−	0.0922527i	$-0.970593\pi$
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	0.577761	+	0.816206i	$0.303927\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50000	+	2.59808i	0.0543750	+	0.0941802i	0.891932	−	0.452170i	$-0.149350\pi$
$761$	1.50000	+	2.59808i	0.0543750	+	0.0941802i	−0.837557	+	0.546350i	$0.816017\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$		0			0
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$		0			0
$771$	−12.0000	−	20.7846i	−0.432169	−	0.748539i
$772$		0			0
$773$	−19.5000	−	33.7750i	−0.701366	−	1.21480i	−0.967987	−	0.251000i	$-0.919240\pi$
$773$	−19.5000	−	33.7750i	−0.701366	−	1.21480i	0.266621	−	0.963802i	$-0.414093\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$	−11.0000	+	19.0526i	−0.394623	+	0.683507i
$778$		0			0
$779$	−30.0000			−1.07486
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−17.0000			−0.606756
$786$		0			0
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$		0			0
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$		0			0
$791$	6.00000	−	10.3923i	0.213335	−	0.369508i
$792$		0			0
$793$	−28.0000	−	6.92820i	−0.994309	−	0.246028i
$794$		0			0
$795$	−9.00000	+	15.5885i	−0.319197	+	0.552866i
$796$		0			0
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$		0			0
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$		0			0
$801$	9.00000			0.317999
$802$		0			0
$803$	21.0000	−	36.3731i	0.741074	−	1.28358i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.0000			0.422420
$808$		0			0
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	−0.663316	−	0.748340i	$-0.730851\pi$
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	0.979739	+	0.200279i	$0.0641847\pi$
$810$		0			0
$811$	49.0000			1.72062			0.860311	−	0.509769i	$-0.170269\pi$
$811$	49.0000			1.72062			0.860311	+	0.509769i	$0.170269\pi$
$812$		0			0
$813$	20.0000	+	34.6410i	0.701431	+	1.21491i
$814$		0			0
$815$	−1.00000	−	1.73205i	−0.0350285	−	0.0606711i
$816$		0			0
$817$	−5.00000	+	8.66025i	−0.174928	+	0.302984i
$818$		0			0
$819$	1.00000	+	3.46410i	0.0349428	+	0.121046i
$820$		0			0
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	0.359708	+	0.933065i	$0.382876\pi$
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	−0.987912	+	0.155017i	$0.950457\pi$
$822$		0			0
$823$	−21.5000	−	37.2391i	−0.749443	−	1.29807i	−0.948090	−	0.318002i	$-0.896988\pi$
$823$	−21.5000	−	37.2391i	−0.749443	−	1.29807i	0.198647	−	0.980071i	$-0.436345\pi$
$824$		0			0
$825$	3.00000	+	5.19615i	0.104447	+	0.180907i
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	−0.275677	−	0.961250i	$-0.588902\pi$
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	0.970306	−	0.241882i	$-0.0777647\pi$
$830$		0			0
$831$	−2.00000			−0.0693792
$832$		0			0
$833$	36.0000			1.24733
$834$		0			0
$835$	7.50000	−	12.9904i	0.259548	−	0.449551i
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$		0			0
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$		0			0
$845$	0.500000	+	12.9904i	0.0172005	+	0.446883i
$846$		0			0
$847$	1.00000	−	1.73205i	0.0343604	−	0.0595140i
$848$		0			0
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$	−2.50000	+	4.33013i	−0.0854982	+	0.148087i
$856$		0			0
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		0			0
$859$	31.0000			1.05771			0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000			1.05771			0.528853	+	0.848713i	$0.322622\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	7.50000	+	12.9904i	0.255008	+	0.441686i
$866$		0			0
$867$	−19.0000	−	32.9090i	−0.645274	−	1.11765i
$868$		0			0
$869$	24.0000	−	41.5692i	0.814144	−	1.41014i
$870$		0			0
$871$	16.0000	+	55.4256i	0.542139	+	1.87803i
$872$		0			0
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$		0			0
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$		0			0
$879$	18.0000			0.607125
$880$		0			0
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$		0			0
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	−0.998588	−	0.0531258i	$-0.983082\pi$
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	0.545302	+	0.838240i	$0.316415\pi$
$888$		0			0
$889$	1.00000			0.0335389
$890$		0			0
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$		0			0
$893$	7.50000	+	12.9904i	0.250978	+	0.434707i
$894$		0			0
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−27.0000	−	46.7654i	−0.899500	−	1.55798i
$902$		0			0
$903$	2.00000	+	3.46410i	0.0665558	+	0.115278i
$904$		0			0
$905$	−8.00000			−0.265929
$906$		0			0
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$		0			0
$915$	−16.0000			−0.528944
$916$		0			0
$917$	−4.50000	−	7.79423i	−0.148603	−	0.257388i
$918$		0			0
$919$	−17.0000	−	29.4449i	−0.560778	−	0.971296i	−0.997429	−	0.0716652i	$-0.977169\pi$
$919$	−17.0000	−	29.4449i	−0.560778	−	0.971296i	0.436650	−	0.899631i	$-0.356165\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$	21.0000	+	5.19615i	0.691223	+	0.171033i
$924$		0			0
$925$	−5.50000	+	9.52628i	−0.180839	+	0.313222i
$926$		0			0
$927$	2.50000	+	4.33013i	0.0821108	+	0.142220i
$928$		0			0
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$		0			0
$931$	30.0000			0.983210
$932$		0			0
$933$	30.0000	−	51.9615i	0.982156	−	1.70114i
$934$		0			0
$935$	−18.0000			−0.588663
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$		0			0
$939$	−14.0000	+	24.2487i	−0.456873	+	0.791327i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.00000	−	3.46410i	−0.0650600	−	0.112687i
$946$		0			0
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	−0.152106	−	0.988364i	$-0.548606\pi$
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	0.932002	−	0.362454i	$-0.118061\pi$
$948$		0			0
$949$	35.0000	−	36.3731i	1.13615	−	1.18072i
$950$		0			0
$951$	−15.0000	+	25.9808i	−0.486408	+	0.842484i
$952$		0			0
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	0.603559	−	0.797318i	$-0.293749\pi$
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	−0.992277	+	0.124039i	$0.960415\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−5.00000			−0.160789			−0.0803946	−	0.996763i	$-0.525618\pi$
$967$	−5.00000			−0.160789			−0.0803946	+	0.996763i	$0.525618\pi$
$968$		0			0
$969$	−30.0000	−	51.9615i	−0.963739	−	1.66924i
$970$		0			0
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	0.999408	+	0.0344175i	$0.0109576\pi$
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	−0.469897	+	0.882721i	$0.655709\pi$
$972$		0			0
$973$	−9.50000	+	16.4545i	−0.304556	+	0.527506i
$974$		0			0
$975$	2.00000	+	6.92820i	0.0640513	+	0.221880i
$976$		0			0
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$	13.5000	+	23.3827i	0.431462	+	0.747314i
$980$		0			0
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$		0			0
$983$	−39.0000			−1.24391			−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000			−1.24391			−0.621953	+	0.783054i	$0.713661\pi$
$984$		0			0
$985$	−13.5000	+	23.3827i	−0.430146	+	0.745034i
$986$		0			0
$987$	6.00000			0.190982
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	−0.986148	−	0.165870i	$-0.946957\pi$
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	0.636721	+	0.771094i	$0.280290\pi$
$992$		0			0
$993$	−40.0000			−1.26936
$994$		0			0
$995$	5.00000	+	8.66025i	0.158511	+	0.274549i
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$		0			0
$999$	22.0000	−	38.1051i	0.696049	−	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.c.321.1		2
4.3	odd	2		130.2.e.b.61.1	✓	2
12.11	even	2		1170.2.i.f.451.1		2
13.3	even	3	inner	1040.2.q.c.81.1		2
20.3	even	4		650.2.o.b.399.1		4
20.7	even	4		650.2.o.b.399.2		4
20.19	odd	2		650.2.e.a.451.1		2
52.3	odd	6		130.2.e.b.81.1	yes	2
52.7	even	12		1690.2.d.a.1351.1		2
52.11	even	12		1690.2.l.i.361.1		4
52.15	even	12		1690.2.l.i.361.2		4
52.19	even	12		1690.2.d.a.1351.2		2
52.23	odd	6		1690.2.e.e.991.1		2
52.31	even	4		1690.2.l.i.1161.1		4
52.35	odd	6		1690.2.a.a.1.1		1
52.43	odd	6		1690.2.a.g.1.1		1
52.47	even	4		1690.2.l.i.1161.2		4
52.51	odd	2		1690.2.e.e.191.1		2
156.107	even	6		1170.2.i.f.991.1		2
260.3	even	12		650.2.o.b.549.2		4
260.107	even	12		650.2.o.b.549.1		4
260.139	odd	6		8450.2.a.w.1.1		1
260.159	odd	6		650.2.e.a.601.1		2
260.199	odd	6		8450.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.b.61.1	✓	2	4.3	odd	2
130.2.e.b.81.1	yes	2	52.3	odd	6
650.2.e.a.451.1		2	20.19	odd	2
650.2.e.a.601.1		2	260.159	odd	6
650.2.o.b.399.1		4	20.3	even	4
650.2.o.b.399.2		4	20.7	even	4
650.2.o.b.549.1		4	260.107	even	12
650.2.o.b.549.2		4	260.3	even	12
1040.2.q.c.81.1		2	13.3	even	3	inner
1040.2.q.c.321.1		2	1.1	even	1	trivial
1170.2.i.f.451.1		2	12.11	even	2
1170.2.i.f.991.1		2	156.107	even	6
1690.2.a.a.1.1		1	52.35	odd	6
1690.2.a.g.1.1		1	52.43	odd	6
1690.2.d.a.1351.1		2	52.7	even	12
1690.2.d.a.1351.2		2	52.19	even	12
1690.2.e.e.191.1		2	52.51	odd	2
1690.2.e.e.991.1		2	52.23	odd	6
1690.2.l.i.361.1		4	52.11	even	12
1690.2.l.i.361.2		4	52.15	even	12
1690.2.l.i.1161.1		4	52.31	even	4
1690.2.l.i.1161.2		4	52.47	even	4
8450.2.a.k.1.1		1	260.199	odd	6
8450.2.a.w.1.1		1	260.139	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +(2.50000 - 2.59808i) q^{13} +(1.00000 - 1.73205i) q^{15} +(3.00000 + 5.19615i) q^{17} +(2.50000 + 4.33013i) q^{19} +2.00000 q^{21} +1.00000 q^{25} -4.00000 q^{27} +4.00000 q^{31} +(3.00000 + 5.19615i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(2.00000 + 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(0.500000 + 0.866025i) q^{45} +3.00000 q^{47} +(3.00000 - 5.19615i) q^{49} -12.0000 q^{51} -9.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} -10.0000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-2.50000 + 2.59808i) q^{65} +(-8.00000 + 13.8564i) q^{67} +(3.00000 + 5.19615i) q^{71} +14.0000 q^{73} +(-1.00000 + 1.73205i) q^{75} -3.00000 q^{77} +16.0000 q^{79} +(5.50000 - 9.52628i) q^{81} +6.00000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(-4.50000 + 7.79423i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(5.00000 + 8.66025i) q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{5} - q^{7} - q^{9} + 3 q^{11} + 5 q^{13} + 2 q^{15} + 6 q^{17} + 5 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 8 q^{31} + 6 q^{33} + q^{35} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 2 q^{43}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^5 - q^7 - q^9 + 3 * q^11 + 5 * q^13 + 2 * q^15 + 6 * q^17 + 5 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 8 * q^31 + 6 * q^33 + q^35 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 2 * q^43 + q^45 + 6 * q^47 + 6 * q^49 - 24 * q^51 - 18 * q^53 - 3 * q^55 - 20 * q^57 - 8 * q^61 - q^63 - 5 * q^65 - 16 * q^67 + 6 * q^71 + 28 * q^73 - 2 * q^75 - 6 * q^77 + 32 * q^79 + 11 * q^81 + 12 * q^83 - 6 * q^85 - 9 * q^89 - 7 * q^91 - 8 * q^93 - 5 * q^95 + 10 * q^97 - 6 * q^99

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