LMFDB - Embedded newform 1216.2.i.g.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.70980888579$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1216.577
Dual form			1216.2.i.g.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} -4.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(2.50000 - 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(3.50000 - 6.06218i) q^{29} -4.00000 q^{31} +(-2.00000 - 3.46410i) q^{33} -10.0000 q^{37} -1.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(2.50000 + 4.33013i) q^{43} -2.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} -7.00000 q^{49} +(1.50000 - 2.59808i) q^{51} +(5.50000 - 9.52628i) q^{53} +(2.00000 + 3.46410i) q^{55} +(-0.500000 - 4.33013i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(5.50000 - 9.52628i) q^{61} +1.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +5.00000 q^{69} +(5.50000 + 9.52628i) q^{71} +(-7.50000 - 12.9904i) q^{73} +4.00000 q^{75} +(-6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{85} +7.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(0.500000 + 4.33013i) q^{95} +(2.50000 + 4.33013i) q^{97} +(-4.00000 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 - q^5 + 2 * q^9	$ 2 q + q^{3} - q^{5} + 2 q^{9} - 8 q^{11} - q^{13} + q^{15} - 3 q^{17} - 8 q^{19} + 5 q^{23} + 4 q^{25} + 10 q^{27} + 7 q^{29} - 8 q^{31} - 4 q^{33} - 20 q^{37} - 2 q^{39} + 5 q^{41} + 5 q^{43} - 4 q^{45} - 7 q^{47} - 14 q^{49} + 3 q^{51} + 11 q^{53} + 4 q^{55} - q^{57} - 3 q^{59} + 11 q^{61} + 2 q^{65} + 3 q^{67} + 10 q^{69} + 11 q^{71} - 15 q^{73} + 8 q^{75} - 13 q^{79} - q^{81} - 3 q^{85} + 14 q^{87} - 3 q^{89} - 4 q^{93} + q^{95} + 5 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^5 + 2 * q^9 - 8 * q^11 - q^13 + q^15 - 3 * q^17 - 8 * q^19 + 5 * q^23 + 4 * q^25 + 10 * q^27 + 7 * q^29 - 8 * q^31 - 4 * q^33 - 20 * q^37 - 2 * q^39 + 5 * q^41 + 5 * q^43 - 4 * q^45 - 7 * q^47 - 14 * q^49 + 3 * q^51 + 11 * q^53 + 4 * q^55 - q^57 - 3 * q^59 + 11 * q^61 + 2 * q^65 + 3 * q^67 + 10 * q^69 + 11 * q^71 - 15 * q^73 + 8 * q^75 - 13 * q^79 - q^81 - 3 * q^85 + 14 * q^87 - 3 * q^89 - 4 * q^93 + q^95 + 5 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	−0.478407	−	0.878138i	$-0.658786\pi$
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	0.999694	−	0.0247559i	$-0.00788087\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	−2.00000	−	3.46410i	−0.348155	−	0.603023i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−1.00000			−0.160128
$40$		0			0
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$		0			0
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	0.489398	+	0.872060i	$0.337217\pi$
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	−0.999926	+	0.0121990i	$0.996117\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$		0			0
$53$	5.50000	−	9.52628i	0.755483	−	1.30854i	−0.189651	−	0.981852i	$-0.560736\pi$
$53$	5.50000	−	9.52628i	0.755483	−	1.30854i	0.945134	−	0.326683i	$-0.105931\pi$
$54$		0			0
$55$	2.00000	+	3.46410i	0.269680	+	0.467099i
$56$		0			0
$57$	−0.500000	−	4.33013i	−0.0662266	−	0.573539i
$58$		0			0
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000			0.124035
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$		0			0
$69$	5.00000			0.601929
$70$		0			0
$71$	5.50000	+	9.52628i	0.652730	+	1.13056i	0.982458	+	0.186485i	$0.0597097\pi$
$71$	5.50000	+	9.52628i	0.652730	+	1.13056i	−0.329728	+	0.944076i	$0.606957\pi$
$72$		0			0
$73$	−7.50000	−	12.9904i	−0.877809	−	1.52041i	−0.853740	−	0.520699i	$-0.825671\pi$
$73$	−7.50000	−	12.9904i	−0.877809	−	1.52041i	−0.0240681	−	0.999710i	$-0.507662\pi$
$74$		0			0
$75$	4.00000			0.461880
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.50000	−	11.2583i	−0.731307	−	1.26666i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−6.50000	−	11.2583i	−0.731307	−	1.26666i	0.225018	−	0.974355i	$-0.427756\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$		0			0
$87$	7.00000			0.750479
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$		0			0
$95$	0.500000	+	4.33013i	0.0512989	+	0.444262i
$96$		0			0
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	−4.00000	+	6.92820i	−0.402015	+	0.696311i
$100$		0			0
$101$	−0.500000	+	0.866025i	−0.0497519	+	0.0861727i	−0.889829	−	0.456294i	$-0.849176\pi$
$101$	−0.500000	+	0.866025i	−0.0497519	+	0.0861727i	0.840077	+	0.542467i	$0.182510\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	20.0000			1.93347			0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000			1.93347			0.966736	+	0.255774i	$0.0823304\pi$
$108$		0			0
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	0.928877	−	0.370387i	$-0.120775\pi$
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	−0.785203	+	0.619238i	$0.787442\pi$
$110$		0			0
$111$	−5.00000	−	8.66025i	−0.474579	−	0.821995i
$112$		0			0
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	−5.00000			−0.466252
$116$		0			0
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.00000			0.454545
$122$		0			0
$123$	−2.50000	+	4.33013i	−0.225417	+	0.390434i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−1.50000	+	2.59808i	−0.133103	+	0.230542i	−0.924871	−	0.380280i	$-0.875828\pi$
$127$	−1.50000	+	2.59808i	−0.133103	+	0.230542i	0.791768	+	0.610822i	$0.209161\pi$
$128$		0			0
$129$	−2.50000	+	4.33013i	−0.220113	+	0.381246i
$130$		0			0
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$		0			0
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	−0.739246	−	0.673436i	$-0.764818\pi$
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	0.952835	+	0.303488i	$0.0981512\pi$
$138$		0			0
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	−0.991303	−	0.131597i	$-0.957989\pi$
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	0.609618	+	0.792695i	$0.291323\pi$
$140$		0			0
$141$	−7.00000			−0.589506
$142$		0			0
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$		0			0
$145$	−7.00000			−0.581318
$146$		0			0
$147$	−3.50000	−	6.06218i	−0.288675	−	0.500000i
$148$		0			0
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		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
$153$	−6.00000			−0.485071
$154$		0			0
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$		0			0
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$		0			0
$159$	11.0000			0.872357
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$		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
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−7.00000	+	5.19615i	−0.535303	+	0.397360i
$172$		0			0
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.50000	−	2.59808i	0.112747	−	0.195283i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	−0.943854	−	0.330364i	$-0.892829\pi$
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	0.758030	+	0.652219i	$0.226162\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$		0			0
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$		0			0
$187$	6.00000	+	10.3923i	0.438763	+	0.759961i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		0			0
$193$	−7.50000	−	12.9904i	−0.539862	−	0.935068i	−0.998911	−	0.0466572i	$-0.985143\pi$
$193$	−7.50000	−	12.9904i	−0.539862	−	0.935068i	0.459049	−	0.888411i	$-0.348190\pi$
$194$		0			0
$195$	0.500000	+	0.866025i	0.0358057	+	0.0620174i
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	−0.963001	−	0.269498i	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$		0			0
$201$	3.00000			0.211604
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.50000	−	4.33013i	0.174608	−	0.302429i
$206$		0			0
$207$	−5.00000	−	8.66025i	−0.347524	−	0.601929i
$208$		0			0
$209$	16.0000	+	6.92820i	1.10674	+	0.479234i
$210$		0			0
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	0.978317	−	0.207114i	$-0.0664070\pi$
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	−0.668524	+	0.743690i	$0.733074\pi$
$212$		0			0
$213$	−5.50000	+	9.52628i	−0.376854	+	0.652730i
$214$		0			0
$215$	2.50000	−	4.33013i	0.170499	−	0.295312i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.50000	−	12.9904i	0.506803	−	0.877809i
$220$		0			0
$221$	3.00000			0.201802
$222$		0			0
$223$	−12.5000	−	21.6506i	−0.837062	−	1.44983i	−0.892341	−	0.451363i	$-0.850938\pi$
$223$	−12.5000	−	21.6506i	−0.837062	−	1.44983i	0.0552786	−	0.998471i	$-0.482395\pi$
$224$		0			0
$225$	−4.00000	−	6.92820i	−0.266667	−	0.461880i
$226$		0			0
$227$	−20.0000			−1.32745			−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000			−1.32745			−0.663723	+	0.747978i	$0.731025\pi$
$228$		0			0
$229$	−2.00000			−0.132164			−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000			−0.132164			−0.0660819	+	0.997814i	$0.521050\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$		0			0
$235$	7.00000			0.456630
$236$		0			0
$237$	6.50000	−	11.2583i	0.422220	−	0.731307i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$	3.50000	+	6.06218i	0.223607	+	0.387298i
$246$		0			0
$247$	3.50000	−	2.59808i	0.222700	−	0.165312i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.5000	−	26.8468i	0.978351	−	1.69455i	0.309951	−	0.950753i	$-0.399687\pi$
$251$	15.5000	−	26.8468i	0.978351	−	1.69455i	0.668400	−	0.743802i	$-0.266979\pi$
$252$		0			0
$253$	−10.0000	+	17.3205i	−0.628695	+	1.08893i
$254$		0			0
$255$	−3.00000			−0.187867
$256$		0			0
$257$	−11.5000	+	19.9186i	−0.717350	+	1.24249i	0.244696	+	0.969600i	$0.421312\pi$
$257$	−11.5000	+	19.9186i	−0.717350	+	1.24249i	−0.962046	+	0.272887i	$0.912021\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.00000	−	12.1244i	−0.433289	−	0.750479i
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$		0			0
$267$	−3.00000			−0.183597
$268$		0			0
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	0.903356	+	0.428892i	$0.141096\pi$
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	−0.0802460	+	0.996775i	$0.525571\pi$
$270$		0			0
$271$	15.5000	+	26.8468i	0.941558	+	1.63083i	0.762501	+	0.646988i	$0.223971\pi$
$271$	15.5000	+	26.8468i	0.941558	+	1.63083i	0.179057	+	0.983839i	$0.442695\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.00000	+	13.8564i	−0.482418	+	0.835573i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$		0			0
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$		0			0
$281$	−3.50000	+	6.06218i	−0.208792	+	0.361639i	−0.951334	−	0.308160i	$-0.900287\pi$
$281$	−3.50000	+	6.06218i	−0.208792	+	0.361639i	0.742542	+	0.669800i	$0.233620\pi$
$282$		0			0
$283$	4.50000	+	7.79423i	0.267497	+	0.463319i	0.968215	−	0.250120i	$-0.0804700\pi$
$283$	4.50000	+	7.79423i	0.267497	+	0.463319i	−0.700718	+	0.713439i	$0.747137\pi$
$284$		0			0
$285$	−3.50000	+	2.59808i	−0.207322	+	0.153897i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−2.50000	+	4.33013i	−0.146553	+	0.253837i
$292$		0			0
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$	−1.50000	+	2.59808i	−0.0873334	+	0.151266i
$296$		0			0
$297$	−20.0000			−1.16052
$298$		0			0
$299$	2.50000	+	4.33013i	0.144579	+	0.250418i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.00000			−0.0574485
$304$		0			0
$305$	−11.0000			−0.629858
$306$		0			0
$307$	−13.5000	−	23.3827i	−0.770486	−	1.33452i	−0.937297	−	0.348532i	$-0.886680\pi$
$307$	−13.5000	−	23.3827i	−0.770486	−	1.33452i	0.166811	−	0.985989i	$-0.446653\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		0			0
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.50000	−	12.9904i	0.421242	−	0.729612i	−0.574819	−	0.818280i	$-0.694928\pi$
$317$	7.50000	−	12.9904i	0.421242	−	0.729612i	0.996061	+	0.0886679i	$0.0282610\pi$
$318$		0			0
$319$	−14.0000	+	24.2487i	−0.783850	+	1.35767i
$320$		0			0
$321$	10.0000	+	17.3205i	0.558146	+	0.966736i
$322$		0			0
$323$	1.50000	+	12.9904i	0.0834622	+	0.722804i
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$		0			0
$327$	−1.50000	+	2.59808i	−0.0829502	+	0.143674i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$		0			0
$333$	−10.0000	+	17.3205i	−0.547997	+	0.949158i
$334$		0			0
$335$	−3.00000			−0.163908
$336$		0			0
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$		0			0
$339$	7.00000	+	12.1244i	0.380188	+	0.658505i
$340$		0			0
$341$	16.0000			0.866449
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.50000	−	4.33013i	−0.134595	−	0.233126i
$346$		0			0
$347$	2.50000	+	4.33013i	0.134207	+	0.232453i	0.925294	−	0.379250i	$-0.123818\pi$
$347$	2.50000	+	4.33013i	0.134207	+	0.232453i	−0.791087	+	0.611703i	$0.790485\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	−2.50000	+	4.33013i	−0.133440	+	0.231125i
$352$		0			0
$353$	30.0000			1.59674			0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000			1.59674			0.798369	+	0.602168i	$0.205696\pi$
$354$		0			0
$355$	5.50000	−	9.52628i	0.291910	−	0.505602i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	0.993207	−	0.116358i	$-0.0371219\pi$
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	−0.597372	+	0.801964i	$0.703789\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	2.50000	+	4.33013i	0.131216	+	0.227273i
$364$		0			0
$365$	−7.50000	+	12.9904i	−0.392568	+	0.679948i
$366$		0			0
$367$	12.5000	−	21.6506i	0.652495	−	1.13015i	−0.330021	−	0.943974i	$-0.607056\pi$
$367$	12.5000	−	21.6506i	0.652495	−	1.13015i	0.982516	−	0.186180i	$-0.0596109\pi$
$368$		0			0
$369$	10.0000			0.520579
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$		0			0
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$		0			0
$377$	3.50000	+	6.06218i	0.180259	+	0.312218i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$	−3.00000			−0.153695
$382$		0			0
$383$	−14.5000	−	25.1147i	−0.740915	−	1.28330i	−0.952079	−	0.305852i	$-0.901059\pi$
$383$	−14.5000	−	25.1147i	−0.740915	−	1.28330i	0.211164	−	0.977451i	$-0.432275\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.0000			0.508329
$388$		0			0
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		0			0
$391$	−15.0000			−0.758583
$392$		0			0
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$		0			0
$395$	−6.50000	+	11.2583i	−0.327050	+	0.566468i
$396$		0			0
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	−0.988080	−	0.153941i	$-0.950803\pi$
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	0.360723	−	0.932673i	$-0.382530\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.50000	−	16.4545i	−0.474407	−	0.821698i	0.525163	−	0.851002i	$-0.324004\pi$
$401$	−9.50000	−	16.4545i	−0.474407	−	0.821698i	−0.999571	+	0.0293039i	$0.990671\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$		0			0
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$		0			0
$407$	40.0000			1.98273
$408$		0			0
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	−0.575670	−	0.817682i	$-0.695259\pi$
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	0.995968	+	0.0897044i	$0.0285922\pi$
$410$		0			0
$411$	5.00000			0.246632
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.00000			−0.440732
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−0.500000	−	0.866025i	−0.0243685	−	0.0422075i	0.853584	−	0.520955i	$-0.174424\pi$
$421$	−0.500000	−	0.866025i	−0.0243685	−	0.0422075i	−0.877952	+	0.478748i	$0.841091\pi$
$422$		0			0
$423$	7.00000	+	12.1244i	0.340352	+	0.589506i
$424$		0			0
$425$	−12.0000			−0.582086
$426$		0			0
$427$		0			0
$428$		0			0
$429$	4.00000			0.193122
$430$		0			0
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	−0.494211	−	0.869342i	$-0.664543\pi$
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	0.999978	−	0.00667224i	$-0.00212386\pi$
$432$		0			0
$433$	12.5000	−	21.6506i	0.600712	−	1.04046i	−0.392002	−	0.919964i	$-0.628217\pi$
$433$	12.5000	−	21.6506i	0.600712	−	1.04046i	0.992713	−	0.120499i	$-0.0384494\pi$
$434$		0			0
$435$	−3.50000	−	6.06218i	−0.167812	−	0.290659i
$436$		0			0
$437$	−17.5000	+	12.9904i	−0.837139	+	0.621414i
$438$		0			0
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	0.668184	−	0.743996i	$-0.267072\pi$
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	−7.00000	+	12.1244i	−0.333333	+	0.577350i
$442$		0			0
$443$	−12.5000	+	21.6506i	−0.593893	+	1.02865i	0.399809	+	0.916598i	$0.369076\pi$
$443$	−12.5000	+	21.6506i	−0.593893	+	1.02865i	−0.993702	+	0.112054i	$0.964257\pi$
$444$		0			0
$445$	3.00000			0.142214
$446$		0			0
$447$	−1.50000	+	2.59808i	−0.0709476	+	0.122885i
$448$		0			0
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	−10.0000	−	17.3205i	−0.470882	−	0.815591i
$452$		0			0
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	5.50000	+	9.52628i	0.256161	+	0.443683i	0.965210	−	0.261476i	$-0.0842091\pi$
$461$	5.50000	+	9.52628i	0.256161	+	0.443683i	−0.709050	+	0.705159i	$0.750876\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$		0			0
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$		0			0
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$		0			0
$475$	−14.0000	+	10.3923i	−0.642364	+	0.476832i
$476$		0			0
$477$	−11.0000	−	19.0526i	−0.503655	−	0.872357i
$478$		0			0
$479$	−11.5000	+	19.9186i	−0.525448	+	0.910103i	0.474112	+	0.880464i	$0.342769\pi$
$479$	−11.5000	+	19.9186i	−0.525448	+	0.910103i	−0.999561	+	0.0296389i	$0.990564\pi$
$480$		0			0
$481$	5.00000	−	8.66025i	0.227980	−	0.394874i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.50000	−	4.33013i	0.113519	−	0.196621i
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		0			0
$489$	−2.00000	−	3.46410i	−0.0904431	−	0.156652i
$490$		0			0
$491$	0.500000	+	0.866025i	0.0225647	+	0.0390832i	0.877087	−	0.480331i	$-0.159483\pi$
$491$	0.500000	+	0.866025i	0.0225647	+	0.0390832i	−0.854523	+	0.519414i	$0.826150\pi$
$492$		0			0
$493$	−21.0000			−0.945792
$494$		0			0
$495$	8.00000			0.359573
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	0.916542	−	0.399937i	$-0.130968\pi$
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	−0.804627	+	0.593780i	$0.797635\pi$
$500$		0			0
$501$	−15.0000			−0.670151
$502$		0			0
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	−0.531167	−	0.847267i	$-0.678246\pi$
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	0.999338	+	0.0363700i	$0.0115795\pi$
$504$		0			0
$505$	1.00000			0.0444994
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−20.0000	−	8.66025i	−0.883022	−	0.382360i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	14.0000	−	24.2487i	0.615719	−	1.06646i
$518$		0			0
$519$	−7.50000	+	12.9904i	−0.329213	+	0.570214i
$520$		0			0
$521$	26.0000			1.13908			0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000			1.13908			0.569540	+	0.821963i	$0.307121\pi$
$522$		0			0
$523$	9.50000	−	16.4545i	0.415406	−	0.719504i	−0.580065	−	0.814570i	$-0.696973\pi$
$523$	9.50000	−	16.4545i	0.415406	−	0.719504i	0.995471	+	0.0950659i	$0.0303062\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	−5.00000			−0.216574
$534$		0			0
$535$	−10.0000	−	17.3205i	−0.432338	−	0.748831i
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	28.0000			1.20605
$540$		0			0
$541$	−0.500000	+	0.866025i	−0.0214967	+	0.0372333i	−0.876574	−	0.481268i	$-0.840176\pi$
$541$	−0.500000	+	0.866025i	−0.0214967	+	0.0372333i	0.855077	+	0.518501i	$0.173510\pi$
$542$		0			0
$543$	−5.00000			−0.214571
$544$		0			0
$545$	1.50000	−	2.59808i	0.0642529	−	0.111289i
$546$		0			0
$547$	−12.5000	+	21.6506i	−0.534461	+	0.925714i	0.464728	+	0.885454i	$0.346152\pi$
$547$	−12.5000	+	21.6506i	−0.534461	+	0.925714i	−0.999189	+	0.0402607i	$0.987181\pi$
$548$		0			0
$549$	−11.0000	−	19.0526i	−0.469469	−	0.813143i
$550$		0			0
$551$	−24.5000	+	18.1865i	−1.04374	+	0.774772i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5.00000	+	8.66025i	−0.212238	+	0.367607i
$556$		0			0
$557$	−2.50000	+	4.33013i	−0.105928	+	0.183473i	−0.914117	−	0.405450i	$-0.867115\pi$
$557$	−2.50000	+	4.33013i	−0.105928	+	0.183473i	0.808189	+	0.588924i	$0.200448\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$	−6.00000	+	10.3923i	−0.253320	+	0.438763i
$562$		0			0
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$		0			0
$565$	−7.00000	−	12.1244i	−0.294492	−	0.510075i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.0000			0.922288			0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000			0.922288			0.461144	+	0.887325i	$0.347439\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	−8.00000	−	13.8564i	−0.334205	−	0.578860i
$574$		0			0
$575$	−10.0000	−	17.3205i	−0.417029	−	0.722315i
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$	7.50000	−	12.9904i	0.311689	−	0.539862i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−22.0000	+	38.1051i	−0.911147	+	1.57815i
$584$		0			0
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$		0			0
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	0.668708	−	0.743525i	$-0.266848\pi$
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	−0.978266	+	0.207355i	$0.933514\pi$
$588$		0			0
$589$	16.0000	+	6.92820i	0.659269	+	0.285472i
$590$		0			0
$591$	−1.00000	−	1.73205i	−0.0411345	−	0.0712470i
$592$		0			0
$593$	2.50000	−	4.33013i	0.102663	−	0.177817i	−0.810118	−	0.586267i	$-0.800597\pi$
$593$	2.50000	−	4.33013i	0.102663	−	0.177817i	0.912781	+	0.408450i	$0.133930\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.00000			−0.286491
$598$		0			0
$599$	22.5000	−	38.9711i	0.919325	−	1.59232i	0.118882	−	0.992908i	$-0.462069\pi$
$599$	22.5000	−	38.9711i	0.919325	−	1.59232i	0.800443	−	0.599409i	$-0.204598\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	−3.00000	−	5.19615i	−0.122169	−	0.211604i
$604$		0			0
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$		0			0
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.50000	−	6.06218i	−0.141595	−	0.245249i
$612$		0			0
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$		0			0
$615$	5.00000			0.201619
$616$		0			0
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.0859976	−	0.996295i	$-0.472592\pi$
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.819818	−	0.572624i	$-0.194074\pi$
$618$		0			0
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$	12.5000	−	21.6506i	0.501608	−	0.868810i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	2.00000	+	17.3205i	0.0798723	+	0.691714i
$628$		0			0
$629$	15.0000	+	25.9808i	0.598089	+	1.03592i
$630$		0			0
$631$	20.5000	−	35.5070i	0.816092	−	1.41351i	−0.0924489	−	0.995717i	$-0.529469\pi$
$631$	20.5000	−	35.5070i	0.816092	−	1.41351i	0.908541	−	0.417796i	$-0.137197\pi$
$632$		0			0
$633$	−4.50000	+	7.79423i	−0.178859	+	0.309793i
$634$		0			0
$635$	3.00000			0.119051
$636$		0			0
$637$	3.50000	−	6.06218i	0.138675	−	0.240192i
$638$		0			0
$639$	22.0000			0.870307
$640$		0			0
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	−0.937451	−	0.348117i	$-0.886821\pi$
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	0.167247	−	0.985915i	$-0.446512\pi$
$642$		0			0
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	0.615630	−	0.788035i	$-0.288902\pi$
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	−0.990274	+	0.139134i	$0.955568\pi$
$644$		0			0
$645$	5.00000			0.196875
$646$		0			0
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$		0			0
$649$	6.00000	+	10.3923i	0.235521	+	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	30.0000			1.17399			0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000			1.17399			0.586995	+	0.809590i	$0.300311\pi$
$654$		0			0
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$		0			0
$657$	−30.0000			−1.17041
$658$		0			0
$659$	−2.50000	+	4.33013i	−0.0973862	+	0.168678i	−0.910602	−	0.413284i	$-0.864382\pi$
$659$	−2.50000	+	4.33013i	−0.0973862	+	0.168678i	0.813216	+	0.581962i	$0.197715\pi$
$660$		0			0
$661$	15.5000	−	26.8468i	0.602880	−	1.04422i	−0.389503	−	0.921025i	$-0.627353\pi$
$661$	15.5000	−	26.8468i	0.602880	−	1.04422i	0.992383	−	0.123194i	$-0.0393136\pi$
$662$		0			0
$663$	1.50000	+	2.59808i	0.0582552	+	0.100901i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−17.5000	−	30.3109i	−0.677603	−	1.17364i
$668$		0			0
$669$	12.5000	−	21.6506i	0.483278	−	0.837062i
$670$		0			0
$671$	−22.0000	+	38.1051i	−0.849301	+	1.47103i
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$		0			0
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$		0			0
$677$	−10.0000			−0.384331			−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000			−0.384331			−0.192166	+	0.981363i	$0.561551\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.0000	−	17.3205i	−0.383201	−	0.663723i
$682$		0			0
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		0			0
$685$	−5.00000			−0.191040
$686$		0			0
$687$	−1.00000	−	1.73205i	−0.0381524	−	0.0660819i
$688$		0			0
$689$	5.50000	+	9.52628i	0.209533	+	0.362922i
$690$		0			0
$691$	36.0000			1.36950			0.684752	−	0.728776i	$-0.259910\pi$
$691$	36.0000			1.36950			0.684752	+	0.728776i	$0.259910\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.00000			0.341389
$696$		0			0
$697$	7.50000	−	12.9904i	0.284083	−	0.492046i
$698$		0			0
$699$	−10.5000	+	18.1865i	−0.397146	+	0.687878i
$700$		0			0
$701$	17.5000	+	30.3109i	0.660966	+	1.14483i	0.980362	+	0.197205i	$0.0631865\pi$
$701$	17.5000	+	30.3109i	0.660966	+	1.14483i	−0.319396	+	0.947621i	$0.603480\pi$
$702$		0			0
$703$	40.0000	+	17.3205i	1.50863	+	0.653255i
$704$		0			0
$705$	3.50000	+	6.06218i	0.131818	+	0.228315i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	−0.836483	−	0.547992i	$-0.815392\pi$
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	0.892817	+	0.450420i	$0.148726\pi$
$710$		0			0
$711$	−26.0000			−0.975076
$712$		0			0
$713$	−10.0000	+	17.3205i	−0.374503	+	0.648658i
$714$		0			0
$715$	−4.00000			−0.149592
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$		0			0
$719$	3.50000	+	6.06218i	0.130528	+	0.226081i	0.923880	−	0.382682i	$-0.124999\pi$
$719$	3.50000	+	6.06218i	0.130528	+	0.226081i	−0.793352	+	0.608763i	$0.791666\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−19.0000			−0.706618
$724$		0			0
$725$	−14.0000	−	24.2487i	−0.519947	−	0.900575i
$726$		0			0
$727$	3.50000	+	6.06218i	0.129808	+	0.224834i	0.923602	−	0.383353i	$-0.125231\pi$
$727$	3.50000	+	6.06218i	0.129808	+	0.224834i	−0.793794	+	0.608186i	$0.791897\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	7.50000	−	12.9904i	0.277398	−	0.480467i
$732$		0			0
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$		0			0
$735$	−3.50000	+	6.06218i	−0.129099	+	0.223607i
$736$		0			0
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$		0			0
$739$	6.50000	+	11.2583i	0.239106	+	0.414144i	0.960458	−	0.278425i	$-0.0898122\pi$
$739$	6.50000	+	11.2583i	0.239106	+	0.414144i	−0.721352	+	0.692569i	$0.756479\pi$
$740$		0			0
$741$	4.00000	+	1.73205i	0.146944	+	0.0636285i
$742$		0			0
$743$	−12.5000	−	21.6506i	−0.458581	−	0.794285i	0.540306	−	0.841469i	$-0.318309\pi$
$743$	−12.5000	−	21.6506i	−0.458581	−	0.794285i	−0.998886	+	0.0471840i	$0.984975\pi$
$744$		0			0
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$	31.0000			1.12970
$754$		0			0
$755$	−8.00000	−	13.8564i	−0.291150	−	0.504286i
$756$		0			0
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	0.669193	−	0.743089i	$-0.266640\pi$
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	−0.978130	+	0.207993i	$0.933307\pi$
$758$		0			0
$759$	−20.0000			−0.725954
$760$		0			0
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$	3.00000			0.108324
$768$		0			0
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	−0.922207	−	0.386698i	$-0.873616\pi$
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	0.795993	+	0.605305i	$0.206949\pi$
$770$		0			0
$771$	−23.0000			−0.828325
$772$		0			0
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.50000	−	21.6506i	−0.0895718	−	0.775715i
$780$		0			0
$781$	−22.0000	−	38.1051i	−0.787222	−	1.36351i
$782$		0			0
$783$	17.5000	−	30.3109i	0.625399	−	1.08322i
$784$		0			0
$785$	3.50000	−	6.06218i	0.124920	−	0.216368i
$786$		0			0
$787$	52.0000			1.85360			0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000			1.85360			0.926800	+	0.375555i	$0.122548\pi$
$788$		0			0
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.50000	+	9.52628i	0.195311	+	0.338288i
$794$		0			0
$795$	−5.50000	−	9.52628i	−0.195065	−	0.337862i
$796$		0			0
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	21.0000			0.742927
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$		0			0
$803$	30.0000	+	51.9615i	1.05868	+	1.83368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.5000	+	23.3827i	−0.475223	+	0.823110i
$808$		0			0
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$		0			0
$811$	−10.5000	+	18.1865i	−0.368705	+	0.638616i	−0.989363	−	0.145465i	$-0.953532\pi$
$811$	−10.5000	+	18.1865i	−0.368705	+	0.638616i	0.620658	+	0.784081i	$0.286865\pi$
$812$		0			0
$813$	−15.5000	+	26.8468i	−0.543609	+	0.941558i
$814$		0			0
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	−2.50000	−	21.6506i	−0.0874639	−	0.757460i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.50000	+	7.79423i	−0.157051	+	0.272020i	−0.933804	−	0.357785i	$-0.883532\pi$
$821$	−4.50000	+	7.79423i	−0.157051	+	0.272020i	0.776753	+	0.629805i	$0.216865\pi$
$822$		0			0
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	0.458591	+	0.888648i	$0.348354\pi$
$823$	−15.5000	+	26.8468i	−0.540296	+	0.935820i	−0.998887	+	0.0471726i	$0.984979\pi$
$824$		0			0
$825$	−16.0000			−0.557048
$826$		0			0
$827$	3.50000	−	6.06218i	0.121707	−	0.210803i	−0.798734	−	0.601684i	$-0.794497\pi$
$827$	3.50000	−	6.06218i	0.121707	−	0.210803i	0.920441	+	0.390882i	$0.127830\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$	−5.00000	−	8.66025i	−0.173448	−	0.300421i
$832$		0			0
$833$	10.5000	+	18.1865i	0.363803	+	0.630126i
$834$		0			0
$835$	15.0000			0.519096
$836$		0			0
$837$	−20.0000			−0.691301
$838$		0			0
$839$	−12.5000	−	21.6506i	−0.431548	−	0.747463i	0.565459	−	0.824776i	$-0.308699\pi$
$839$	−12.5000	−	21.6506i	−0.431548	−	0.747463i	−0.997007	+	0.0773135i	$0.975366\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$		0			0
$843$	−7.00000			−0.241093
$844$		0			0
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.50000	+	7.79423i	−0.154440	+	0.267497i
$850$		0			0
$851$	−25.0000	+	43.3013i	−0.856989	+	1.48435i
$852$		0			0
$853$	19.5000	+	33.7750i	0.667667	+	1.15643i	0.978555	+	0.205987i	$0.0660404\pi$
$853$	19.5000	+	33.7750i	0.667667	+	1.15643i	−0.310887	+	0.950447i	$0.600626\pi$
$854$		0			0
$855$	8.00000	+	3.46410i	0.273594	+	0.118470i
$856$		0			0
$857$	−7.50000	−	12.9904i	−0.256195	−	0.443743i	0.709024	−	0.705184i	$-0.249136\pi$
$857$	−7.50000	−	12.9904i	−0.256195	−	0.443743i	−0.965219	+	0.261441i	$0.915802\pi$
$858$		0			0
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	−0.955348	−	0.295484i	$-0.904519\pi$
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	0.733571	+	0.679613i	$0.237852\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	7.50000	−	12.9904i	0.255008	−	0.441686i
$866$		0			0
$867$	8.00000			0.271694
$868$		0			0
$869$	26.0000	+	45.0333i	0.881990	+	1.52765i
$870$		0			0
$871$	1.50000	+	2.59808i	0.0508256	+	0.0880325i
$872$		0			0
$873$	10.0000			0.338449
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	0.820724	−	0.571324i	$-0.193570\pi$
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	−0.905143	+	0.425106i	$0.860237\pi$
$878$		0			0
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$		0			0
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$	−12.5000	+	21.6506i	−0.420658	+	0.728602i	−0.996004	−	0.0893086i	$-0.971534\pi$
$883$	−12.5000	+	21.6506i	−0.420658	+	0.728602i	0.575346	+	0.817910i	$0.304868\pi$
$884$		0			0
$885$	−3.00000			−0.100844
$886$		0			0
$887$	12.5000	−	21.6506i	0.419709	−	0.726957i	−0.576201	−	0.817308i	$-0.695465\pi$
$887$	12.5000	−	21.6506i	0.419709	−	0.726957i	0.995910	+	0.0903508i	$0.0287988\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$		0			0
$893$	24.5000	−	18.1865i	0.819861	−	0.608589i
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$	−2.50000	+	4.33013i	−0.0834726	+	0.144579i
$898$		0			0
$899$	−14.0000	+	24.2487i	−0.466926	+	0.808740i
$900$		0			0
$901$	−33.0000			−1.09939
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.00000			0.166206
$906$		0			0
$907$	−17.5000	−	30.3109i	−0.581078	−	1.00646i	−0.995352	−	0.0963043i	$-0.969298\pi$
$907$	−17.5000	−	30.3109i	−0.581078	−	1.00646i	0.414274	−	0.910152i	$-0.364036\pi$
$908$		0			0
$909$	1.00000	+	1.73205i	0.0331679	+	0.0574485i
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−5.50000	−	9.52628i	−0.181824	−	0.314929i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$		0			0
$921$	13.5000	−	23.3827i	0.444840	−	0.770486i
$922$		0			0
$923$	−11.0000			−0.362069
$924$		0			0
$925$	−20.0000	+	34.6410i	−0.657596	+	1.13899i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.5000	−	19.9186i	−0.377303	−	0.653508i	0.613366	−	0.789799i	$-0.289815\pi$
$929$	−11.5000	−	19.9186i	−0.377303	−	0.653508i	−0.990669	+	0.136291i	$0.956482\pi$
$930$		0			0
$931$	28.0000	+	12.1244i	0.917663	+	0.397360i
$932$		0			0
$933$	10.0000	+	17.3205i	0.327385	+	0.567048i
$934$		0			0
$935$	6.00000	−	10.3923i	0.196221	−	0.339865i
$936$		0			0
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	−0.990430	−	0.138017i	$-0.955927\pi$
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	0.614741	+	0.788729i	$0.289260\pi$
$938$		0			0
$939$	−11.0000			−0.358971
$940$		0			0
$941$	9.50000	−	16.4545i	0.309691	−	0.536401i	−0.668604	−	0.743619i	$-0.733108\pi$
$941$	9.50000	−	16.4545i	0.309691	−	0.536401i	0.978295	+	0.207218i	$0.0664410\pi$
$942$		0			0
$943$	25.0000			0.814112
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	0.558898	−	0.829237i	$-0.311224\pi$
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	−0.997589	+	0.0694014i	$0.977891\pi$
$948$		0			0
$949$	15.0000			0.486921
$950$		0			0
$951$	15.0000			0.486408
$952$		0			0
$953$	12.5000	+	21.6506i	0.404915	+	0.701333i	0.994312	−	0.106511i	$-0.0339679\pi$
$953$	12.5000	+	21.6506i	0.404915	+	0.701333i	−0.589397	+	0.807844i	$0.700635\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$		0			0
$957$	−28.0000			−0.905111
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	20.0000	−	34.6410i	0.644491	−	1.11629i
$964$		0			0
$965$	−7.50000	+	12.9904i	−0.241434	+	0.418175i
$966$		0			0
$967$	−22.5000	−	38.9711i	−0.723551	−	1.25323i	−0.959568	−	0.281478i	$-0.909175\pi$
$967$	−22.5000	−	38.9711i	−0.723551	−	1.25323i	0.236016	−	0.971749i	$-0.424158\pi$
$968$		0			0
$969$	−10.5000	+	7.79423i	−0.337309	+	0.250387i
$970$		0			0
$971$	−17.5000	−	30.3109i	−0.561602	−	0.972723i	−0.997357	−	0.0726575i	$-0.976852\pi$
$971$	−17.5000	−	30.3109i	−0.561602	−	0.972723i	0.435755	−	0.900065i	$-0.356481\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$		0			0
$977$	−10.0000			−0.319928			−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−10.0000			−0.319928			−0.159964	+	0.987123i	$0.551138\pi$
$978$		0			0
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	6.00000			0.191565
$982$		0			0
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	−0.961933	−	0.273285i	$-0.911890\pi$
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	0.244294	−	0.969701i	$-0.421444\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	25.0000			0.794954
$990$		0			0
$991$	−2.50000	−	4.33013i	−0.0794151	−	0.137551i	0.823583	−	0.567196i	$-0.191972\pi$
$991$	−2.50000	−	4.33013i	−0.0794151	−	0.137551i	−0.902998	+	0.429645i	$0.858639\pi$
$992$		0			0
$993$	10.0000	+	17.3205i	0.317340	+	0.549650i
$994$		0			0
$995$	7.00000			0.221915
$996$		0			0
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$		0			0
$999$	−50.0000			−1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.g.577.1		2
4.3	odd	2		1216.2.i.c.577.1		2
8.3	odd	2		76.2.e.a.45.1	✓	2
8.5	even	2		304.2.i.a.273.1		2
19.11	even	3	inner	1216.2.i.g.961.1		2
24.5	odd	2		2736.2.s.g.577.1		2
24.11	even	2		684.2.k.b.577.1		2
40.3	even	4		1900.2.s.a.349.1		4
40.19	odd	2		1900.2.i.a.501.1		2
40.27	even	4		1900.2.s.a.349.2		4
76.11	odd	6		1216.2.i.c.961.1		2
152.11	odd	6		76.2.e.a.49.1	yes	2
152.27	even	6		1444.2.e.b.429.1		2
152.45	even	6		5776.2.a.k.1.1		1
152.69	odd	6		5776.2.a.f.1.1		1
152.75	even	2		1444.2.e.b.653.1		2
152.83	odd	6		1444.2.a.b.1.1		1
152.107	even	6		1444.2.a.c.1.1		1
152.125	even	6		304.2.i.a.49.1		2
456.11	even	6		684.2.k.b.505.1		2
456.125	odd	6		2736.2.s.g.1873.1		2
760.163	even	12		1900.2.s.a.49.2		4
760.467	even	12		1900.2.s.a.49.1		4
760.619	odd	6		1900.2.i.a.201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.e.a.45.1	✓	2	8.3	odd	2
76.2.e.a.49.1	yes	2	152.11	odd	6
304.2.i.a.49.1		2	152.125	even	6
304.2.i.a.273.1		2	8.5	even	2
684.2.k.b.505.1		2	456.11	even	6
684.2.k.b.577.1		2	24.11	even	2
1216.2.i.c.577.1		2	4.3	odd	2
1216.2.i.c.961.1		2	76.11	odd	6
1216.2.i.g.577.1		2	1.1	even	1	trivial
1216.2.i.g.961.1		2	19.11	even	3	inner
1444.2.a.b.1.1		1	152.83	odd	6
1444.2.a.c.1.1		1	152.107	even	6
1444.2.e.b.429.1		2	152.27	even	6
1444.2.e.b.653.1		2	152.75	even	2
1900.2.i.a.201.1		2	760.619	odd	6
1900.2.i.a.501.1		2	40.19	odd	2
1900.2.s.a.49.1		4	760.467	even	12
1900.2.s.a.49.2		4	760.163	even	12
1900.2.s.a.349.1		4	40.3	even	4
1900.2.s.a.349.2		4	40.27	even	4
2736.2.s.g.577.1		2	24.5	odd	2
2736.2.s.g.1873.1		2	456.125	odd	6
5776.2.a.f.1.1		1	152.69	odd	6
5776.2.a.k.1.1		1	152.45	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} -4.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(2.50000 - 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(3.50000 - 6.06218i) q^{29} -4.00000 q^{31} +(-2.00000 - 3.46410i) q^{33} -10.0000 q^{37} -1.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(2.50000 + 4.33013i) q^{43} -2.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} -7.00000 q^{49} +(1.50000 - 2.59808i) q^{51} +(5.50000 - 9.52628i) q^{53} +(2.00000 + 3.46410i) q^{55} +(-0.500000 - 4.33013i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(5.50000 - 9.52628i) q^{61} +1.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +5.00000 q^{69} +(5.50000 + 9.52628i) q^{71} +(-7.50000 - 12.9904i) q^{73} +4.00000 q^{75} +(-6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{85} +7.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(0.500000 + 4.33013i) q^{95} +(2.50000 + 4.33013i) q^{97} +(-4.00000 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 - q^5 + 2 * q^9	\( 2 q + q^{3} - q^{5} + 2 q^{9} - 8 q^{11} - q^{13} + q^{15} - 3 q^{17} - 8 q^{19} + 5 q^{23} + 4 q^{25} + 10 q^{27} + 7 q^{29} - 8 q^{31} - 4 q^{33} - 20 q^{37} - 2 q^{39} + 5 q^{41} + 5 q^{43} - 4 q^{45} - 7 q^{47} - 14 q^{49} + 3 q^{51} + 11 q^{53} + 4 q^{55} - q^{57} - 3 q^{59} + 11 q^{61} + 2 q^{65} + 3 q^{67} + 10 q^{69} + 11 q^{71} - 15 q^{73} + 8 q^{75} - 13 q^{79} - q^{81} - 3 q^{85} + 14 q^{87} - 3 q^{89} - 4 q^{93} + q^{95} + 5 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^5 + 2 * q^9 - 8 * q^11 - q^13 + q^15 - 3 * q^17 - 8 * q^19 + 5 * q^23 + 4 * q^25 + 10 * q^27 + 7 * q^29 - 8 * q^31 - 4 * q^33 - 20 * q^37 - 2 * q^39 + 5 * q^41 + 5 * q^43 - 4 * q^45 - 7 * q^47 - 14 * q^49 + 3 * q^51 + 11 * q^53 + 4 * q^55 - q^57 - 3 * q^59 + 11 * q^61 + 2 * q^65 + 3 * q^67 + 10 * q^69 + 11 * q^71 - 15 * q^73 + 8 * q^75 - 13 * q^79 - q^81 - 3 * q^85 + 14 * q^87 - 3 * q^89 - 4 * q^93 + q^95 + 5 * q^97 - 8 * q^99

Introduction

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