LMFDB - Embedded newform 216.2.d.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(109,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("216.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.d (of order $2$, degree $1$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 3x^{2} + 4 $ x^4 - 3*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.1
Root			$-1.32288 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	216.109
Dual form			216.2.d.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32288 - 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} +1.00000i q^{5} +1.00000 q^{7} +(-1.32288 - 2.50000i) q^{8} +O(q^{10})$	\(q+(-1.32288 - 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} +1.00000i q^{5} +1.00000 q^{7} +(-1.32288 - 2.50000i) q^{8} +(0.500000 - 1.32288i) q^{10} +3.00000i q^{11} +5.29150i q^{13} +(-1.32288 - 0.500000i) q^{14} +(0.500000 + 3.96863i) q^{16} +5.29150 q^{17} -5.29150i q^{19} +(-1.32288 + 1.50000i) q^{20} +(1.50000 - 3.96863i) q^{22} +5.29150 q^{23} +4.00000 q^{25} +(2.64575 - 7.00000i) q^{26} +(1.50000 + 1.32288i) q^{28} +6.00000i q^{29} -7.00000 q^{31} +(1.32288 - 5.50000i) q^{32} +(-7.00000 - 2.64575i) q^{34} +1.00000i q^{35} +5.29150i q^{37} +(-2.64575 + 7.00000i) q^{38} +(2.50000 - 1.32288i) q^{40} -5.29150 q^{41} -10.5830i q^{43} +(-3.96863 + 4.50000i) q^{44} +(-7.00000 - 2.64575i) q^{46} -6.00000 q^{49} +(-5.29150 - 2.00000i) q^{50} +(-7.00000 + 7.93725i) q^{52} -9.00000i q^{53} -3.00000 q^{55} +(-1.32288 - 2.50000i) q^{56} +(3.00000 - 7.93725i) q^{58} -4.00000i q^{59} +(9.26013 + 3.50000i) q^{62} +(-4.50000 + 6.61438i) q^{64} -5.29150 q^{65} +(7.93725 + 7.00000i) q^{68} +(0.500000 - 1.32288i) q^{70} -15.8745 q^{71} +3.00000 q^{73} +(2.64575 - 7.00000i) q^{74} +(7.00000 - 7.93725i) q^{76} +3.00000i q^{77} +4.00000 q^{79} +(-3.96863 + 0.500000i) q^{80} +(7.00000 + 2.64575i) q^{82} -7.00000i q^{83} +5.29150i q^{85} +(-5.29150 + 14.0000i) q^{86} +(7.50000 - 3.96863i) q^{88} +10.5830 q^{89} +5.29150i q^{91} +(7.93725 + 7.00000i) q^{92} +5.29150 q^{95} +7.00000 q^{97} +(7.93725 + 3.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} + 4 q^{7}+O(q^{10}) $ 4 * q + 6 * q^4 + 4 * q^7	$ 4 q + 6 q^{4} + 4 q^{7} + 2 q^{10} + 2 q^{16} + 6 q^{22} + 16 q^{25} + 6 q^{28} - 28 q^{31} - 28 q^{34} + 10 q^{40} - 28 q^{46} - 24 q^{49} - 28 q^{52} - 12 q^{55} + 12 q^{58} - 18 q^{64} + 2 q^{70} + 12 q^{73} + 28 q^{76} + 16 q^{79} + 28 q^{82} + 30 q^{88} + 28 q^{97}+O(q^{100}) $ 4 * q + 6 * q^4 + 4 * q^7 + 2 * q^10 + 2 * q^16 + 6 * q^22 + 16 * q^25 + 6 * q^28 - 28 * q^31 - 28 * q^34 + 10 * q^40 - 28 * q^46 - 24 * q^49 - 28 * q^52 - 12 * q^55 + 12 * q^58 - 18 * q^64 + 2 * q^70 + 12 * q^73 + 28 * q^76 + 16 * q^79 + 28 * q^82 + 30 * q^88 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32288	−	0.500000i	−0.935414	−	0.353553i
$2$	−1.32288	−	0.500000i	−0.935414	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.50000	+	1.32288i	0.750000	+	0.661438i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$		0			0
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.32288	−	2.50000i	−0.467707	−	0.883883i
$9$		0			0
$10$	0.500000	−	1.32288i	0.158114	−	0.418330i
$11$			3.00000i			0.904534i	0.891883	+	0.452267i	$0.149385\pi$
$11$			3.00000i			0.904534i	−0.891883	+	0.452267i	$0.850615\pi$
$12$		0			0
$13$			5.29150i			1.46760i	0.679366	+	0.733799i	$0.262255\pi$
$13$			5.29150i			1.46760i	−0.679366	+	0.733799i	$0.737745\pi$
$14$	−1.32288	−	0.500000i	−0.353553	−	0.133631i
$15$		0			0
$16$	0.500000	+	3.96863i	0.125000	+	0.992157i
$17$	5.29150			1.28338			0.641689	−	0.766965i	$-0.278234\pi$
$17$	5.29150			1.28338			0.641689	+	0.766965i	$0.278234\pi$
$18$		0			0
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	−1.32288	+	1.50000i	−0.295804	+	0.335410i
$21$		0			0
$22$	1.50000	−	3.96863i	0.319801	−	0.846114i
$23$	5.29150			1.10335			0.551677	−	0.834058i	$-0.313988\pi$
$23$	5.29150			1.10335			0.551677	+	0.834058i	$0.313988\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	2.64575	−	7.00000i	0.518875	−	1.37281i
$27$		0			0
$28$	1.50000	+	1.32288i	0.283473	+	0.250000i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.32288	−	5.50000i	0.233854	−	0.972272i
$33$		0			0
$34$	−7.00000	−	2.64575i	−1.20049	−	0.453743i
$35$			1.00000i			0.169031i
$36$		0			0
$37$			5.29150i			0.869918i	0.900450	+	0.434959i	$0.143237\pi$
$37$			5.29150i			0.869918i	−0.900450	+	0.434959i	$0.856763\pi$
$38$	−2.64575	+	7.00000i	−0.429198	+	1.13555i
$39$		0			0
$40$	2.50000	−	1.32288i	0.395285	−	0.209165i
$41$	−5.29150			−0.826394			−0.413197	−	0.910642i	$-0.635588\pi$
$41$	−5.29150			−0.826394			−0.413197	+	0.910642i	$0.635588\pi$
$42$		0			0
$43$		−	10.5830i		−	1.61389i	−0.590624	−	0.806947i	$-0.701119\pi$
$43$		−	10.5830i		−	1.61389i	0.590624	−	0.806947i	$-0.298881\pi$
$44$	−3.96863	+	4.50000i	−0.598293	+	0.678401i
$45$		0			0
$46$	−7.00000	−	2.64575i	−1.03209	−	0.390095i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	−5.29150	−	2.00000i	−0.748331	−	0.282843i
$51$		0			0
$52$	−7.00000	+	7.93725i	−0.970725	+	1.10070i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$	−1.32288	−	2.50000i	−0.176777	−	0.334077i
$57$		0			0
$58$	3.00000	−	7.93725i	0.393919	−	1.04221i
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	9.26013	+	3.50000i	1.17604	+	0.444500i
$63$		0			0
$64$	−4.50000	+	6.61438i	−0.562500	+	0.826797i
$65$	−5.29150			−0.656330
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	7.93725	+	7.00000i	0.962533	+	0.848875i
$69$		0			0
$70$	0.500000	−	1.32288i	0.0597614	−	0.158114i
$71$	−15.8745			−1.88396			−0.941979	−	0.335673i	$-0.891036\pi$
$71$	−15.8745			−1.88396			−0.941979	+	0.335673i	$0.891036\pi$
$72$		0			0
$73$	3.00000			0.351123			0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000			0.351123			0.175562	+	0.984468i	$0.443826\pi$
$74$	2.64575	−	7.00000i	0.307562	−	0.813733i
$75$		0			0
$76$	7.00000	−	7.93725i	0.802955	−	0.910465i
$77$			3.00000i			0.341882i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−3.96863	+	0.500000i	−0.443706	+	0.0559017i
$81$		0			0
$82$	7.00000	+	2.64575i	0.773021	+	0.292174i
$83$		−	7.00000i		−	0.768350i	−0.923260	−	0.384175i	$-0.874486\pi$
$83$		−	7.00000i		−	0.768350i	0.923260	−	0.384175i	$-0.125514\pi$
$84$		0			0
$85$			5.29150i			0.573944i
$86$	−5.29150	+	14.0000i	−0.570597	+	1.50966i
$87$		0			0
$88$	7.50000	−	3.96863i	0.799503	−	0.423057i
$89$	10.5830			1.12180			0.560898	−	0.827885i	$-0.310456\pi$
$89$	10.5830			1.12180			0.560898	+	0.827885i	$0.310456\pi$
$90$		0			0
$91$			5.29150i			0.554700i
$92$	7.93725	+	7.00000i	0.827516	+	0.729800i
$93$		0			0
$94$		0			0
$95$	5.29150			0.542897
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	7.93725	+	3.00000i	0.801784	+	0.303046i
$99$		0			0
$100$	6.00000	+	5.29150i	0.600000	+	0.529150i
$101$		−	17.0000i		−	1.69156i	−0.533529	−	0.845782i	$-0.679135\pi$
$101$		−	17.0000i		−	1.69156i	0.533529	−	0.845782i	$-0.320865\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	13.2288	−	7.00000i	1.29719	−	0.686406i
$105$		0			0
$106$	−4.50000	+	11.9059i	−0.437079	+	1.15640i
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$		0			0
$109$		−	5.29150i		−	0.506834i	−0.967357	−	0.253417i	$-0.918446\pi$
$109$		−	5.29150i		−	0.506834i	0.967357	−	0.253417i	$-0.0815545\pi$
$110$	3.96863	+	1.50000i	0.378394	+	0.143019i
$111$		0			0
$112$	0.500000	+	3.96863i	0.0472456	+	0.375000i
$113$	−15.8745			−1.49335			−0.746674	−	0.665190i	$-0.768350\pi$
$113$	−15.8745			−1.49335			−0.746674	+	0.665190i	$0.768350\pi$
$114$		0			0
$115$			5.29150i			0.493435i
$116$	−7.93725	+	9.00000i	−0.736956	+	0.835629i
$117$		0			0
$118$	−2.00000	+	5.29150i	−0.184115	+	0.487122i
$119$	5.29150			0.485071
$120$		0			0
$121$	2.00000			0.181818
$122$		0			0
$123$		0			0
$124$	−10.5000	−	9.26013i	−0.942928	−	0.831584i
$125$			9.00000i			0.804984i
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	9.26013	−	6.50000i	0.818488	−	0.574524i
$129$		0			0
$130$	7.00000	+	2.64575i	0.613941	+	0.232048i
$131$		−	7.00000i		−	0.611593i	−0.952097	−	0.305796i	$-0.901077\pi$
$131$		−	7.00000i		−	0.611593i	0.952097	−	0.305796i	$-0.0989227\pi$
$132$		0			0
$133$		−	5.29150i		−	0.458831i
$134$		0			0
$135$		0			0
$136$	−7.00000	−	13.2288i	−0.600245	−	1.13436i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$			10.5830i			0.897639i	0.893622	+	0.448819i	$0.148155\pi$
$139$			10.5830i			0.897639i	−0.893622	+	0.448819i	$0.851845\pi$
$140$	−1.32288	+	1.50000i	−0.111803	+	0.126773i
$141$		0			0
$142$	21.0000	+	7.93725i	1.76228	+	0.666080i
$143$	−15.8745			−1.32749
$144$		0			0
$145$	−6.00000			−0.498273
$146$	−3.96863	−	1.50000i	−0.328446	−	0.124141i
$147$		0			0
$148$	−7.00000	+	7.93725i	−0.575396	+	0.652438i
$149$		−	3.00000i		−	0.245770i	−0.992421	−	0.122885i	$-0.960785\pi$
$149$		−	3.00000i		−	0.245770i	0.992421	−	0.122885i	$-0.0392146\pi$
$150$		0			0
$151$	3.00000			0.244137			0.122068	−	0.992522i	$-0.461047\pi$
$151$	3.00000			0.244137			0.122068	+	0.992522i	$0.461047\pi$
$152$	−13.2288	+	7.00000i	−1.07299	+	0.567775i
$153$		0			0
$154$	1.50000	−	3.96863i	0.120873	−	0.319801i
$155$		−	7.00000i		−	0.562254i
$156$		0			0
$157$		−	10.5830i		−	0.844616i	−0.906452	−	0.422308i	$-0.861220\pi$
$157$		−	10.5830i		−	0.844616i	0.906452	−	0.422308i	$-0.138780\pi$
$158$	−5.29150	−	2.00000i	−0.420969	−	0.159111i
$159$		0			0
$160$	5.50000	+	1.32288i	0.434813	+	0.104583i
$161$	5.29150			0.417029
$162$		0			0
$163$			5.29150i			0.414462i	0.978292	+	0.207231i	$0.0664452\pi$
$163$			5.29150i			0.414462i	−0.978292	+	0.207231i	$0.933555\pi$
$164$	−7.93725	−	7.00000i	−0.619795	−	0.546608i
$165$		0			0
$166$	−3.50000	+	9.26013i	−0.271653	+	0.718725i
$167$	10.5830			0.818938			0.409469	−	0.912324i	$-0.365714\pi$
$167$	10.5830			0.818938			0.409469	+	0.912324i	$0.365714\pi$
$168$		0			0
$169$	−15.0000			−1.15385
$170$	2.64575	−	7.00000i	0.202920	−	0.536875i
$171$		0			0
$172$	14.0000	−	15.8745i	1.06749	−	1.21042i
$173$			15.0000i			1.14043i	0.821496	+	0.570214i	$0.193140\pi$
$173$			15.0000i			1.14043i	−0.821496	+	0.570214i	$0.806860\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$	−11.9059	+	1.50000i	−0.897440	+	0.113067i
$177$		0			0
$178$	−14.0000	−	5.29150i	−1.04934	−	0.396615i
$179$			23.0000i			1.71910i	0.511051	+	0.859550i	$0.329256\pi$
$179$			23.0000i			1.71910i	−0.511051	+	0.859550i	$0.670744\pi$
$180$		0			0
$181$		−	21.1660i		−	1.57326i	−0.617426	−	0.786629i	$-0.711825\pi$
$181$		−	21.1660i		−	1.57326i	0.617426	−	0.786629i	$-0.288175\pi$
$182$	2.64575	−	7.00000i	0.196116	−	0.518875i
$183$		0			0
$184$	−7.00000	−	13.2288i	−0.516047	−	0.975237i
$185$	−5.29150			−0.389039
$186$		0			0
$187$			15.8745i			1.16086i
$188$		0			0
$189$		0			0
$190$	−7.00000	−	2.64575i	−0.507833	−	0.191943i
$191$	5.29150			0.382880			0.191440	−	0.981504i	$-0.438684\pi$
$191$	5.29150			0.382880			0.191440	+	0.981504i	$0.438684\pi$
$192$		0			0
$193$	−3.00000			−0.215945			−0.107972	−	0.994154i	$-0.534436\pi$
$193$	−3.00000			−0.215945			−0.107972	+	0.994154i	$0.534436\pi$
$194$	−9.26013	−	3.50000i	−0.664839	−	0.251285i
$195$		0			0
$196$	−9.00000	−	7.93725i	−0.642857	−	0.566947i
$197$		−	13.0000i		−	0.926212i	−0.886303	−	0.463106i	$-0.846735\pi$
$197$		−	13.0000i		−	0.926212i	0.886303	−	0.463106i	$-0.153265\pi$
$198$		0			0
$199$	−17.0000			−1.20510			−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000			−1.20510			−0.602549	+	0.798082i	$0.705848\pi$
$200$	−5.29150	−	10.0000i	−0.374166	−	0.707107i
$201$		0			0
$202$	−8.50000	+	22.4889i	−0.598058	+	1.58231i
$203$			6.00000i			0.421117i
$204$		0			0
$205$		−	5.29150i		−	0.369575i
$206$		0			0
$207$		0			0
$208$	−21.0000	+	2.64575i	−1.45609	+	0.183450i
$209$	15.8745			1.09806
$210$		0			0
$211$			5.29150i			0.364282i	0.983272	+	0.182141i	$0.0583027\pi$
$211$			5.29150i			0.364282i	−0.983272	+	0.182141i	$0.941697\pi$
$212$	11.9059	−	13.5000i	0.817699	−	0.927184i
$213$		0			0
$214$	1.50000	−	3.96863i	0.102538	−	0.271290i
$215$	10.5830			0.721755
$216$		0			0
$217$	−7.00000			−0.475191
$218$	−2.64575	+	7.00000i	−0.179193	+	0.474100i
$219$		0			0
$220$	−4.50000	−	3.96863i	−0.303390	−	0.267565i
$221$			28.0000i			1.88348i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	1.32288	−	5.50000i	0.0883883	−	0.367484i
$225$		0			0
$226$	21.0000	+	7.93725i	1.39690	+	0.527978i
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$		0			0
$229$		−	21.1660i		−	1.39869i	−0.714785	−	0.699345i	$-0.753475\pi$
$229$		−	21.1660i		−	1.39869i	0.714785	−	0.699345i	$-0.246525\pi$
$230$	2.64575	−	7.00000i	0.174456	−	0.461566i
$231$		0			0
$232$	15.0000	−	7.93725i	0.984798	−	0.521106i
$233$	10.5830			0.693316			0.346658	−	0.937992i	$-0.387316\pi$
$233$	10.5830			0.693316			0.346658	+	0.937992i	$0.387316\pi$
$234$		0			0
$235$		0			0
$236$	5.29150	−	6.00000i	0.344447	−	0.390567i
$237$		0			0
$238$	−7.00000	−	2.64575i	−0.453743	−	0.171499i
$239$	15.8745			1.02684			0.513418	−	0.858138i	$-0.328379\pi$
$239$	15.8745			1.02684			0.513418	+	0.858138i	$0.328379\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	−2.64575	−	1.00000i	−0.170075	−	0.0642824i
$243$		0			0
$244$		0			0
$245$		−	6.00000i		−	0.383326i
$246$		0			0
$247$	28.0000			1.78160
$248$	9.26013	+	17.5000i	0.588019	+	1.11125i
$249$		0			0
$250$	4.50000	−	11.9059i	0.284605	−	0.752994i
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$		0			0
$253$			15.8745i			0.998022i
$254$	−17.1974	−	6.50000i	−1.07906	−	0.407846i
$255$		0			0
$256$	−15.5000	+	3.96863i	−0.968750	+	0.248039i
$257$	15.8745			0.990225			0.495112	−	0.868829i	$-0.335127\pi$
$257$	15.8745			0.990225			0.495112	+	0.868829i	$0.335127\pi$
$258$		0			0
$259$			5.29150i			0.328798i
$260$	−7.93725	−	7.00000i	−0.492248	−	0.434122i
$261$		0			0
$262$	−3.50000	+	9.26013i	−0.216231	+	0.572093i
$263$	−5.29150			−0.326288			−0.163144	−	0.986602i	$-0.552164\pi$
$263$	−5.29150			−0.326288			−0.163144	+	0.986602i	$0.552164\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	−2.64575	+	7.00000i	−0.162221	+	0.429198i
$267$		0			0
$268$		0			0
$269$			18.0000i			1.09748i	0.835993	+	0.548740i	$0.184892\pi$
$269$			18.0000i			1.09748i	−0.835993	+	0.548740i	$0.815108\pi$
$270$		0			0
$271$	15.0000			0.911185			0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000			0.911185			0.455593	+	0.890188i	$0.349427\pi$
$272$	2.64575	+	21.0000i	0.160422	+	1.27331i
$273$		0			0
$274$		0			0
$275$			12.0000i			0.723627i
$276$		0			0
$277$			10.5830i			0.635871i	0.948112	+	0.317936i	$0.102990\pi$
$277$			10.5830i			0.635871i	−0.948112	+	0.317936i	$0.897010\pi$
$278$	5.29150	−	14.0000i	0.317363	−	0.839664i
$279$		0			0
$280$	2.50000	−	1.32288i	0.149404	−	0.0790569i
$281$	−15.8745			−0.946994			−0.473497	−	0.880795i	$-0.657008\pi$
$281$	−15.8745			−0.946994			−0.473497	+	0.880795i	$0.657008\pi$
$282$		0			0
$283$		−	26.4575i		−	1.57274i	−0.617758	−	0.786368i	$-0.711959\pi$
$283$		−	26.4575i		−	1.57274i	0.617758	−	0.786368i	$-0.288041\pi$
$284$	−23.8118	−	21.0000i	−1.41297	−	1.24612i
$285$		0			0
$286$	21.0000	+	7.93725i	1.24176	+	0.469340i
$287$	−5.29150			−0.312348
$288$		0			0
$289$	11.0000			0.647059
$290$	7.93725	+	3.00000i	0.466092	+	0.176166i
$291$		0			0
$292$	4.50000	+	3.96863i	0.263343	+	0.232246i
$293$		−	30.0000i		−	1.75262i	−0.481749	−	0.876309i	$-0.659998\pi$
$293$		−	30.0000i		−	1.75262i	0.481749	−	0.876309i	$-0.340002\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$	13.2288	−	7.00000i	0.768906	−	0.406867i
$297$		0			0
$298$	−1.50000	+	3.96863i	−0.0868927	+	0.229896i
$299$			28.0000i			1.61928i
$300$		0			0
$301$		−	10.5830i		−	0.609994i
$302$	−3.96863	−	1.50000i	−0.228369	−	0.0863153i
$303$		0			0
$304$	21.0000	−	2.64575i	1.20443	−	0.151744i
$305$		0			0
$306$		0			0
$307$			15.8745i			0.906006i	0.891509	+	0.453003i	$0.149647\pi$
$307$			15.8745i			0.906006i	−0.891509	+	0.453003i	$0.850353\pi$
$308$	−3.96863	+	4.50000i	−0.226134	+	0.256411i
$309$		0			0
$310$	−3.50000	+	9.26013i	−0.198787	+	0.525940i
$311$	−26.4575			−1.50027			−0.750134	−	0.661286i	$-0.770011\pi$
$311$	−26.4575			−1.50027			−0.750134	+	0.661286i	$0.770011\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	−5.29150	+	14.0000i	−0.298617	+	0.790066i
$315$		0			0
$316$	6.00000	+	5.29150i	0.337526	+	0.297670i
$317$			13.0000i			0.730153i	0.930978	+	0.365076i	$0.118957\pi$
$317$			13.0000i			0.730153i	−0.930978	+	0.365076i	$0.881043\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	−6.61438	−	4.50000i	−0.369755	−	0.251558i
$321$		0			0
$322$	−7.00000	−	2.64575i	−0.390095	−	0.147442i
$323$		−	28.0000i		−	1.55796i
$324$		0			0
$325$			21.1660i			1.17408i
$326$	2.64575	−	7.00000i	0.146535	−	0.387694i
$327$		0			0
$328$	7.00000	+	13.2288i	0.386510	+	0.730436i
$329$		0			0
$330$		0			0
$331$			21.1660i			1.16339i	0.813407	+	0.581695i	$0.197610\pi$
$331$			21.1660i			1.16339i	−0.813407	+	0.581695i	$0.802390\pi$
$332$	9.26013	−	10.5000i	0.508216	−	0.576262i
$333$		0			0
$334$	−14.0000	−	5.29150i	−0.766046	−	0.289538i
$335$		0			0
$336$		0			0
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$	19.8431	+	7.50000i	1.07932	+	0.407946i
$339$		0			0
$340$	−7.00000	+	7.93725i	−0.379628	+	0.430458i
$341$		−	21.0000i		−	1.13721i
$342$		0			0
$343$	−13.0000			−0.701934
$344$	−26.4575	+	14.0000i	−1.42649	+	0.754829i
$345$		0			0
$346$	7.50000	−	19.8431i	0.403202	−	1.06677i
$347$		−	23.0000i		−	1.23470i	−0.786687	−	0.617352i	$-0.788205\pi$
$347$		−	23.0000i		−	1.23470i	0.786687	−	0.617352i	$-0.211795\pi$
$348$		0			0
$349$			5.29150i			0.283248i	0.989921	+	0.141624i	$0.0452323\pi$
$349$			5.29150i			0.283248i	−0.989921	+	0.141624i	$0.954768\pi$
$350$	−5.29150	−	2.00000i	−0.282843	−	0.106904i
$351$		0			0
$352$	16.5000	+	3.96863i	0.879453	+	0.211529i
$353$	−15.8745			−0.844915			−0.422457	−	0.906383i	$-0.638832\pi$
$353$	−15.8745			−0.844915			−0.422457	+	0.906383i	$0.638832\pi$
$354$		0			0
$355$		−	15.8745i		−	0.842531i
$356$	15.8745	+	14.0000i	0.841347	+	0.741999i
$357$		0			0
$358$	11.5000	−	30.4261i	0.607794	−	1.60807i
$359$	21.1660			1.11710			0.558550	−	0.829471i	$-0.311358\pi$
$359$	21.1660			1.11710			0.558550	+	0.829471i	$0.311358\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	−10.5830	+	28.0000i	−0.556230	+	1.47165i
$363$		0			0
$364$	−7.00000	+	7.93725i	−0.366900	+	0.416025i
$365$			3.00000i			0.157027i
$366$		0			0
$367$	−3.00000			−0.156599			−0.0782994	−	0.996930i	$-0.524949\pi$
$367$	−3.00000			−0.156599			−0.0782994	+	0.996930i	$0.524949\pi$
$368$	2.64575	+	21.0000i	0.137919	+	1.09470i
$369$		0			0
$370$	7.00000	+	2.64575i	0.363913	+	0.137546i
$371$		−	9.00000i		−	0.467257i
$372$		0			0
$373$			26.4575i			1.36992i	0.728582	+	0.684959i	$0.240180\pi$
$373$			26.4575i			1.36992i	−0.728582	+	0.684959i	$0.759820\pi$
$374$	7.93725	−	21.0000i	0.410426	−	1.08588i
$375$		0			0
$376$		0			0
$377$	−31.7490			−1.63516
$378$		0			0
$379$		−	21.1660i		−	1.08722i	−0.839336	−	0.543612i	$-0.817056\pi$
$379$		−	21.1660i		−	1.08722i	0.839336	−	0.543612i	$-0.182944\pi$
$380$	7.93725	+	7.00000i	0.407173	+	0.359092i
$381$		0			0
$382$	−7.00000	−	2.64575i	−0.358151	−	0.135368i
$383$	−15.8745			−0.811149			−0.405575	−	0.914062i	$-0.632929\pi$
$383$	−15.8745			−0.811149			−0.405575	+	0.914062i	$0.632929\pi$
$384$		0			0
$385$	−3.00000			−0.152894
$386$	3.96863	+	1.50000i	0.201998	+	0.0763480i
$387$		0			0
$388$	10.5000	+	9.26013i	0.533057	+	0.470112i
$389$			5.00000i			0.253510i	0.991934	+	0.126755i	$0.0404562\pi$
$389$			5.00000i			0.253510i	−0.991934	+	0.126755i	$0.959544\pi$
$390$		0			0
$391$	28.0000			1.41602
$392$	7.93725	+	15.0000i	0.400892	+	0.757614i
$393$		0			0
$394$	−6.50000	+	17.1974i	−0.327465	+	0.866392i
$395$			4.00000i			0.201262i
$396$		0			0
$397$		−	5.29150i		−	0.265573i	−0.991145	−	0.132786i	$-0.957608\pi$
$397$		−	5.29150i		−	0.265573i	0.991145	−	0.132786i	$-0.0423924\pi$
$398$	22.4889	+	8.50000i	1.12727	+	0.426067i
$399$		0			0
$400$	2.00000	+	15.8745i	0.100000	+	0.793725i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		−	37.0405i		−	1.84512i
$404$	22.4889	−	25.5000i	1.11886	−	1.26867i
$405$		0			0
$406$	3.00000	−	7.93725i	0.148888	−	0.393919i
$407$	−15.8745			−0.786870
$408$		0			0
$409$	−11.0000			−0.543915			−0.271957	−	0.962309i	$-0.587671\pi$
$409$	−11.0000			−0.543915			−0.271957	+	0.962309i	$0.587671\pi$
$410$	−2.64575	+	7.00000i	−0.130664	+	0.345705i
$411$		0			0
$412$		0			0
$413$		−	4.00000i		−	0.196827i
$414$		0			0
$415$	7.00000			0.343616
$416$	29.1033	+	7.00000i	1.42690	+	0.343203i
$417$		0			0
$418$	−21.0000	−	7.93725i	−1.02714	−	0.388224i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$			10.5830i			0.515784i	0.966174	+	0.257892i	$0.0830279\pi$
$421$			10.5830i			0.515784i	−0.966174	+	0.257892i	$0.916972\pi$
$422$	2.64575	−	7.00000i	0.128793	−	0.340755i
$423$		0			0
$424$	−22.5000	+	11.9059i	−1.09270	+	0.578201i
$425$	21.1660			1.02670
$426$		0			0
$427$		0			0
$428$	−3.96863	+	4.50000i	−0.191831	+	0.217516i
$429$		0			0
$430$	−14.0000	−	5.29150i	−0.675140	−	0.255179i
$431$	31.7490			1.52930			0.764648	−	0.644448i	$-0.222913\pi$
$431$	31.7490			1.52930			0.764648	+	0.644448i	$0.222913\pi$
$432$		0			0
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	9.26013	+	3.50000i	0.444500	+	0.168005i
$435$		0			0
$436$	7.00000	−	7.93725i	0.335239	−	0.380126i
$437$		−	28.0000i		−	1.33942i
$438$		0			0
$439$	−21.0000			−1.00228			−0.501138	−	0.865368i	$-0.667085\pi$
$439$	−21.0000			−1.00228			−0.501138	+	0.865368i	$0.667085\pi$
$440$	3.96863	+	7.50000i	0.189197	+	0.357548i
$441$		0			0
$442$	14.0000	−	37.0405i	0.665912	−	1.76184i
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$			10.5830i			0.501683i
$446$	21.1660	+	8.00000i	1.00224	+	0.378811i
$447$		0			0
$448$	−4.50000	+	6.61438i	−0.212605	+	0.312500i
$449$	−15.8745			−0.749164			−0.374582	−	0.927194i	$-0.622214\pi$
$449$	−15.8745			−0.749164			−0.374582	+	0.927194i	$0.622214\pi$
$450$		0			0
$451$		−	15.8745i		−	0.747501i
$452$	−23.8118	−	21.0000i	−1.12001	−	0.987757i
$453$		0			0
$454$	2.00000	−	5.29150i	0.0938647	−	0.248343i
$455$	−5.29150			−0.248069
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	−10.5830	+	28.0000i	−0.494511	+	1.30835i
$459$		0			0
$460$	−7.00000	+	7.93725i	−0.326377	+	0.370076i
$461$		−	9.00000i		−	0.419172i	−0.977790	−	0.209586i	$-0.932788\pi$
$461$		−	9.00000i		−	0.419172i	0.977790	−	0.209586i	$-0.0672116\pi$
$462$		0			0
$463$	−41.0000			−1.90543			−0.952716	−	0.303863i	$-0.901724\pi$
$463$	−41.0000			−1.90543			−0.952716	+	0.303863i	$0.901724\pi$
$464$	−23.8118	+	3.00000i	−1.10543	+	0.139272i
$465$		0			0
$466$	−14.0000	−	5.29150i	−0.648537	−	0.245124i
$467$			1.00000i			0.0462745i	0.999732	+	0.0231372i	$0.00736547\pi$
$467$			1.00000i			0.0462745i	−0.999732	+	0.0231372i	$0.992635\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−10.0000	+	5.29150i	−0.460287	+	0.243561i
$473$	31.7490			1.45982
$474$		0			0
$475$		−	21.1660i		−	0.971163i
$476$	7.93725	+	7.00000i	0.363803	+	0.320844i
$477$		0			0
$478$	−21.0000	−	7.93725i	−0.960518	−	0.363042i
$479$	−21.1660			−0.967100			−0.483550	−	0.875317i	$-0.660653\pi$
$479$	−21.1660			−0.967100			−0.483550	+	0.875317i	$0.660653\pi$
$480$		0			0
$481$	−28.0000			−1.27669
$482$	13.2288	+	5.00000i	0.602553	+	0.227744i
$483$		0			0
$484$	3.00000	+	2.64575i	0.136364	+	0.120261i
$485$			7.00000i			0.317854i
$486$		0			0
$487$	−40.0000			−1.81257			−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000			−1.81257			−0.906287	+	0.422664i	$0.861095\pi$
$488$		0			0
$489$		0			0
$490$	−3.00000	+	7.93725i	−0.135526	+	0.358569i
$491$			29.0000i			1.30875i	0.756169	+	0.654376i	$0.227069\pi$
$491$			29.0000i			1.30875i	−0.756169	+	0.654376i	$0.772931\pi$
$492$		0			0
$493$			31.7490i			1.42990i
$494$	−37.0405	−	14.0000i	−1.66653	−	0.629890i
$495$		0			0
$496$	−3.50000	−	27.7804i	−0.157155	−	1.24738i
$497$	−15.8745			−0.712069
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−11.9059	+	13.5000i	−0.532447	+	0.603738i
$501$		0			0
$502$	−6.00000	+	15.8745i	−0.267793	+	0.708514i
$503$	−15.8745			−0.707809			−0.353905	−	0.935282i	$-0.615146\pi$
$503$	−15.8745			−0.707809			−0.353905	+	0.935282i	$0.615146\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$	7.93725	−	21.0000i	0.352854	−	0.933564i
$507$		0			0
$508$	19.5000	+	17.1974i	0.865173	+	0.763011i
$509$			21.0000i			0.930809i	0.885098	+	0.465404i	$0.154091\pi$
$509$			21.0000i			0.930809i	−0.885098	+	0.465404i	$0.845909\pi$
$510$		0			0
$511$	3.00000			0.132712
$512$	22.4889	+	2.50000i	0.993878	+	0.110485i
$513$		0			0
$514$	−21.0000	−	7.93725i	−0.926270	−	0.350097i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	2.64575	−	7.00000i	0.116248	−	0.307562i
$519$		0			0
$520$	7.00000	+	13.2288i	0.306970	+	0.580119i
$521$	−15.8745			−0.695475			−0.347737	−	0.937592i	$-0.613050\pi$
$521$	−15.8745			−0.695475			−0.347737	+	0.937592i	$0.613050\pi$
$522$		0			0
$523$		−	15.8745i		−	0.694144i	−0.937839	−	0.347072i	$-0.887176\pi$
$523$		−	15.8745i		−	0.694144i	0.937839	−	0.347072i	$-0.112824\pi$
$524$	9.26013	−	10.5000i	0.404531	−	0.458695i
$525$		0			0
$526$	7.00000	+	2.64575i	0.305215	+	0.115360i
$527$	−37.0405			−1.61351
$528$		0			0
$529$	5.00000			0.217391
$530$	−11.9059	−	4.50000i	−0.517158	−	0.195468i
$531$		0			0
$532$	7.00000	−	7.93725i	0.303488	−	0.344124i
$533$		−	28.0000i		−	1.21281i
$534$		0			0
$535$	−3.00000			−0.129701
$536$		0			0
$537$		0			0
$538$	9.00000	−	23.8118i	0.388018	−	1.02660i
$539$		−	18.0000i		−	0.775315i
$540$		0			0
$541$		−	10.5830i		−	0.454999i	−0.973778	−	0.227499i	$-0.926945\pi$
$541$		−	10.5830i		−	0.454999i	0.973778	−	0.227499i	$-0.0730550\pi$
$542$	−19.8431	−	7.50000i	−0.852336	−	0.322153i
$543$		0			0
$544$	7.00000	−	29.1033i	0.300123	−	1.24779i
$545$	5.29150			0.226663
$546$		0			0
$547$		−	5.29150i		−	0.226248i	−0.993581	−	0.113124i	$-0.963914\pi$
$547$		−	5.29150i		−	0.226248i	0.993581	−	0.113124i	$-0.0360858\pi$
$548$		0			0
$549$		0			0
$550$	6.00000	−	15.8745i	0.255841	−	0.676891i
$551$	31.7490			1.35255
$552$		0			0
$553$	4.00000			0.170097
$554$	5.29150	−	14.0000i	0.224814	−	0.594803i
$555$		0			0
$556$	−14.0000	+	15.8745i	−0.593732	+	0.673229i
$557$			39.0000i			1.65248i	0.563316	+	0.826242i	$0.309525\pi$
$557$			39.0000i			1.65248i	−0.563316	+	0.826242i	$0.690475\pi$
$558$		0			0
$559$	56.0000			2.36855
$560$	−3.96863	+	0.500000i	−0.167705	+	0.0211289i
$561$		0			0
$562$	21.0000	+	7.93725i	0.885832	+	0.334813i
$563$			3.00000i			0.126435i	0.998000	+	0.0632175i	$0.0201362\pi$
$563$			3.00000i			0.126435i	−0.998000	+	0.0632175i	$0.979864\pi$
$564$		0			0
$565$		−	15.8745i		−	0.667846i
$566$	−13.2288	+	35.0000i	−0.556046	+	1.47116i
$567$		0			0
$568$	21.0000	+	39.6863i	0.881140	+	1.66520i
$569$	31.7490			1.33099			0.665494	−	0.746403i	$-0.268221\pi$
$569$	31.7490			1.33099			0.665494	+	0.746403i	$0.268221\pi$
$570$		0			0
$571$			26.4575i			1.10721i	0.832779	+	0.553606i	$0.186749\pi$
$571$			26.4575i			1.10721i	−0.832779	+	0.553606i	$0.813251\pi$
$572$	−23.8118	−	21.0000i	−0.995620	−	0.878054i
$573$		0			0
$574$	7.00000	+	2.64575i	0.292174	+	0.110432i
$575$	21.1660			0.882684
$576$		0			0
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	−14.5516	−	5.50000i	−0.605268	−	0.228770i
$579$		0			0
$580$	−9.00000	−	7.93725i	−0.373705	−	0.329577i
$581$		−	7.00000i		−	0.290409i
$582$		0			0
$583$	27.0000			1.11823
$584$	−3.96863	−	7.50000i	−0.164223	−	0.310352i
$585$		0			0
$586$	−15.0000	+	39.6863i	−0.619644	+	1.63942i
$587$			23.0000i			0.949312i	0.880172	+	0.474656i	$0.157427\pi$
$587$			23.0000i			0.949312i	−0.880172	+	0.474656i	$0.842573\pi$
$588$		0			0
$589$			37.0405i			1.52623i
$590$	−5.29150	−	2.00000i	−0.217848	−	0.0823387i
$591$		0			0
$592$	−21.0000	+	2.64575i	−0.863095	+	0.108740i
$593$	−31.7490			−1.30378			−0.651888	−	0.758315i	$-0.726023\pi$
$593$	−31.7490			−1.30378			−0.651888	+	0.758315i	$0.726023\pi$
$594$		0			0
$595$			5.29150i			0.216930i
$596$	3.96863	−	4.50000i	0.162561	−	0.184327i
$597$		0			0
$598$	14.0000	−	37.0405i	0.572503	−	1.51470i
$599$	21.1660			0.864820			0.432410	−	0.901677i	$-0.357663\pi$
$599$	21.1660			0.864820			0.432410	+	0.901677i	$0.357663\pi$
$600$		0			0
$601$	5.00000			0.203954			0.101977	−	0.994787i	$-0.467483\pi$
$601$	5.00000			0.203954			0.101977	+	0.994787i	$0.467483\pi$
$602$	−5.29150	+	14.0000i	−0.215666	+	0.570597i
$603$		0			0
$604$	4.50000	+	3.96863i	0.183102	+	0.161481i
$605$			2.00000i			0.0813116i
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$	−29.1033	−	7.00000i	−1.18029	−	0.283887i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$			10.5830i			0.427444i	0.976895	+	0.213722i	$0.0685586\pi$
$613$			10.5830i			0.427444i	−0.976895	+	0.213722i	$0.931441\pi$
$614$	7.93725	−	21.0000i	0.320321	−	0.847491i
$615$		0			0
$616$	7.50000	−	3.96863i	0.302184	−	0.159901i
$617$	5.29150			0.213028			0.106514	−	0.994311i	$-0.466031\pi$
$617$	5.29150			0.213028			0.106514	+	0.994311i	$0.466031\pi$
$618$		0			0
$619$		−	15.8745i		−	0.638050i	−0.947746	−	0.319025i	$-0.896645\pi$
$619$		−	15.8745i		−	0.638050i	0.947746	−	0.319025i	$-0.103355\pi$
$620$	9.26013	−	10.5000i	0.371896	−	0.421690i
$621$		0			0
$622$	35.0000	+	13.2288i	1.40337	+	0.530425i
$623$	10.5830			0.423999
$624$		0			0
$625$	11.0000			0.440000
$626$	1.32288	+	0.500000i	0.0528727	+	0.0199840i
$627$		0			0
$628$	14.0000	−	15.8745i	0.558661	−	0.633462i
$629$			28.0000i			1.11643i
$630$		0			0
$631$	−23.0000			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$632$	−5.29150	−	10.0000i	−0.210485	−	0.397779i
$633$		0			0
$634$	6.50000	−	17.1974i	0.258148	−	0.682995i
$635$			13.0000i			0.515889i
$636$		0			0
$637$		−	31.7490i		−	1.25794i
$638$	23.8118	+	9.00000i	0.942717	+	0.356313i
$639$		0			0
$640$	6.50000	+	9.26013i	0.256935	+	0.366039i
$641$	37.0405			1.46301			0.731506	−	0.681835i	$-0.238818\pi$
$641$	37.0405			1.46301			0.731506	+	0.681835i	$0.238818\pi$
$642$		0			0
$643$			21.1660i			0.834706i	0.908744	+	0.417353i	$0.137042\pi$
$643$			21.1660i			0.834706i	−0.908744	+	0.417353i	$0.862958\pi$
$644$	7.93725	+	7.00000i	0.312772	+	0.275839i
$645$		0			0
$646$	−14.0000	+	37.0405i	−0.550823	+	1.45734i
$647$	31.7490			1.24818			0.624091	−	0.781351i	$-0.285469\pi$
$647$	31.7490			1.24818			0.624091	+	0.781351i	$0.285469\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$	10.5830	−	28.0000i	0.415100	−	1.09825i
$651$		0			0
$652$	−7.00000	+	7.93725i	−0.274141	+	0.310847i
$653$			3.00000i			0.117399i	0.998276	+	0.0586995i	$0.0186954\pi$
$653$			3.00000i			0.117399i	−0.998276	+	0.0586995i	$0.981305\pi$
$654$		0			0
$655$	7.00000			0.273513
$656$	−2.64575	−	21.0000i	−0.103299	−	0.819912i
$657$		0			0
$658$		0			0
$659$			15.0000i			0.584317i	0.956370	+	0.292159i	$0.0943735\pi$
$659$			15.0000i			0.584317i	−0.956370	+	0.292159i	$0.905627\pi$
$660$		0			0
$661$		−	26.4575i		−	1.02908i	−0.857467	−	0.514539i	$-0.827963\pi$
$661$		−	26.4575i		−	1.02908i	0.857467	−	0.514539i	$-0.172037\pi$
$662$	10.5830	−	28.0000i	0.411320	−	1.08825i
$663$		0			0
$664$	−17.5000	+	9.26013i	−0.679132	+	0.359363i
$665$	5.29150			0.205196
$666$		0			0
$667$			31.7490i			1.22933i
$668$	15.8745	+	14.0000i	0.614203	+	0.541676i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	29.0000			1.11787			0.558934	−	0.829212i	$-0.311211\pi$
$673$	29.0000			1.11787			0.558934	+	0.829212i	$0.311211\pi$
$674$	−44.9778	−	17.0000i	−1.73248	−	0.654816i
$675$		0			0
$676$	−22.5000	−	19.8431i	−0.865385	−	0.763197i
$677$			6.00000i			0.230599i	0.993331	+	0.115299i	$0.0367827\pi$
$677$			6.00000i			0.230599i	−0.993331	+	0.115299i	$0.963217\pi$
$678$		0			0
$679$	7.00000			0.268635
$680$	13.2288	−	7.00000i	0.507300	−	0.268438i
$681$		0			0
$682$	−10.5000	+	27.7804i	−0.402066	+	1.06377i
$683$			44.0000i			1.68361i	0.539779	+	0.841807i	$0.318508\pi$
$683$			44.0000i			1.68361i	−0.539779	+	0.841807i	$0.681492\pi$
$684$		0			0
$685$		0			0
$686$	17.1974	+	6.50000i	0.656599	+	0.248171i
$687$		0			0
$688$	42.0000	−	5.29150i	1.60123	−	0.201737i
$689$	47.6235			1.81431
$690$		0			0
$691$			42.3320i			1.61039i	0.593013	+	0.805193i	$0.297938\pi$
$691$			42.3320i			1.61039i	−0.593013	+	0.805193i	$0.702062\pi$
$692$	−19.8431	+	22.5000i	−0.754323	+	0.855322i
$693$		0			0
$694$	−11.5000	+	30.4261i	−0.436534	+	1.15496i
$695$	−10.5830			−0.401436
$696$		0			0
$697$	−28.0000			−1.06058
$698$	2.64575	−	7.00000i	0.100143	−	0.264954i
$699$		0			0
$700$	6.00000	+	5.29150i	0.226779	+	0.200000i
$701$			1.00000i			0.0377695i	0.999822	+	0.0188847i	$0.00601156\pi$
$701$			1.00000i			0.0377695i	−0.999822	+	0.0188847i	$0.993988\pi$
$702$		0			0
$703$	28.0000			1.05604
$704$	−19.8431	−	13.5000i	−0.747866	−	0.508800i
$705$		0			0
$706$	21.0000	+	7.93725i	0.790345	+	0.298722i
$707$		−	17.0000i		−	0.639351i
$708$		0			0
$709$		−	21.1660i		−	0.794906i	−0.917622	−	0.397453i	$-0.869894\pi$
$709$		−	21.1660i		−	0.794906i	0.917622	−	0.397453i	$-0.130106\pi$
$710$	−7.93725	+	21.0000i	−0.297880	+	0.788116i
$711$		0			0
$712$	−14.0000	−	26.4575i	−0.524672	−	0.991537i
$713$	−37.0405			−1.38718
$714$		0			0
$715$		−	15.8745i		−	0.593673i
$716$	−30.4261	+	34.5000i	−1.13708	+	1.28933i
$717$		0			0
$718$	−28.0000	−	10.5830i	−1.04495	−	0.394954i
$719$	21.1660			0.789359			0.394679	−	0.918819i	$-0.370856\pi$
$719$	21.1660			0.789359			0.394679	+	0.918819i	$0.370856\pi$
$720$		0			0
$721$		0			0
$722$	11.9059	+	4.50000i	0.443091	+	0.167473i
$723$		0			0
$724$	28.0000	−	31.7490i	1.04061	−	1.17994i
$725$			24.0000i			0.891338i
$726$		0			0
$727$	33.0000			1.22390			0.611951	−	0.790896i	$-0.290385\pi$
$727$	33.0000			1.22390			0.611951	+	0.790896i	$0.290385\pi$
$728$	13.2288	−	7.00000i	0.490290	−	0.259437i
$729$		0			0
$730$	1.50000	−	3.96863i	0.0555175	−	0.146885i
$731$		−	56.0000i		−	2.07123i
$732$		0			0
$733$			5.29150i			0.195446i	0.995214	+	0.0977231i	$0.0311559\pi$
$733$			5.29150i			0.195446i	−0.995214	+	0.0977231i	$0.968844\pi$
$734$	3.96863	+	1.50000i	0.146485	+	0.0553660i
$735$		0			0
$736$	7.00000	−	29.1033i	0.258023	−	1.07276i
$737$		0			0
$738$		0			0
$739$			5.29150i			0.194651i	0.995253	+	0.0973255i	$0.0310288\pi$
$739$			5.29150i			0.194651i	−0.995253	+	0.0973255i	$0.968971\pi$
$740$	−7.93725	−	7.00000i	−0.291779	−	0.257325i
$741$		0			0
$742$	−4.50000	+	11.9059i	−0.165200	+	0.437079i
$743$	−37.0405			−1.35888			−0.679442	−	0.733729i	$-0.737778\pi$
$743$	−37.0405			−1.35888			−0.679442	+	0.733729i	$0.737778\pi$
$744$		0			0
$745$	3.00000			0.109911
$746$	13.2288	−	35.0000i	0.484339	−	1.28144i
$747$		0			0
$748$	−21.0000	+	23.8118i	−0.767836	+	0.870644i
$749$			3.00000i			0.109618i
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$		0			0
$753$		0			0
$754$	42.0000	+	15.8745i	1.52955	+	0.578115i
$755$			3.00000i			0.109181i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	−10.5830	+	28.0000i	−0.384392	+	1.01701i
$759$		0			0
$760$	−7.00000	−	13.2288i	−0.253917	−	0.479857i
$761$	−10.5830			−0.383634			−0.191817	−	0.981431i	$-0.561438\pi$
$761$	−10.5830			−0.383634			−0.191817	+	0.981431i	$0.561438\pi$
$762$		0			0
$763$		−	5.29150i		−	0.191565i
$764$	7.93725	+	7.00000i	0.287160	+	0.253251i
$765$		0			0
$766$	21.0000	+	7.93725i	0.758761	+	0.286785i
$767$	21.1660			0.764260
$768$		0			0
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$	3.96863	+	1.50000i	0.143019	+	0.0540562i
$771$		0			0
$772$	−4.50000	−	3.96863i	−0.161959	−	0.142834i
$773$		−	14.0000i		−	0.503545i	−0.967786	−	0.251773i	$-0.918987\pi$
$773$		−	14.0000i		−	0.503545i	0.967786	−	0.251773i	$-0.0810135\pi$
$774$		0			0
$775$	−28.0000			−1.00579
$776$	−9.26013	−	17.5000i	−0.332419	−	0.628213i
$777$		0			0
$778$	2.50000	−	6.61438i	0.0896293	−	0.237137i
$779$			28.0000i			1.00320i
$780$		0			0
$781$		−	47.6235i		−	1.70410i
$782$	−37.0405	−	14.0000i	−1.32457	−	0.500639i
$783$		0			0
$784$	−3.00000	−	23.8118i	−0.107143	−	0.850420i
$785$	10.5830			0.377724
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	17.1974	−	19.5000i	0.612631	−	0.694659i
$789$		0			0
$790$	2.00000	−	5.29150i	0.0711568	−	0.188263i
$791$	−15.8745			−0.564433
$792$		0			0
$793$		0			0
$794$	−2.64575	+	7.00000i	−0.0938942	+	0.248421i
$795$		0			0
$796$	−25.5000	−	22.4889i	−0.903824	−	0.797097i
$797$		−	49.0000i		−	1.73567i	−0.496853	−	0.867835i	$-0.665511\pi$
$797$		−	49.0000i		−	1.73567i	0.496853	−	0.867835i	$-0.334489\pi$
$798$		0			0
$799$		0			0
$800$	5.29150	−	22.0000i	0.187083	−	0.777817i
$801$		0			0
$802$		0			0
$803$			9.00000i			0.317603i
$804$		0			0
$805$			5.29150i			0.186501i
$806$	−18.5203	+	49.0000i	−0.652348	+	1.72595i
$807$		0			0
$808$	−42.5000	+	22.4889i	−1.49514	+	0.791156i
$809$	−31.7490			−1.11624			−0.558118	−	0.829762i	$-0.688476\pi$
$809$	−31.7490			−1.11624			−0.558118	+	0.829762i	$0.688476\pi$
$810$		0			0
$811$			37.0405i			1.30067i	0.759648	+	0.650334i	$0.225371\pi$
$811$			37.0405i			1.30067i	−0.759648	+	0.650334i	$0.774629\pi$
$812$	−7.93725	+	9.00000i	−0.278543	+	0.315838i
$813$		0			0
$814$	21.0000	+	7.93725i	0.736050	+	0.278201i
$815$	−5.29150			−0.185353
$816$		0			0
$817$	−56.0000			−1.95919
$818$	14.5516	+	5.50000i	0.508786	+	0.192303i
$819$		0			0
$820$	7.00000	−	7.93725i	0.244451	−	0.277181i
$821$			10.0000i			0.349002i	0.984657	+	0.174501i	$0.0558313\pi$
$821$			10.0000i			0.349002i	−0.984657	+	0.174501i	$0.944169\pi$
$822$		0			0
$823$	23.0000			0.801730			0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000			0.801730			0.400865	+	0.916137i	$0.368710\pi$
$824$		0			0
$825$		0			0
$826$	−2.00000	+	5.29150i	−0.0695889	+	0.184115i
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$		0			0
$829$		−	21.1660i		−	0.735126i	−0.929999	−	0.367563i	$-0.880192\pi$
$829$		−	21.1660i		−	0.735126i	0.929999	−	0.367563i	$-0.119808\pi$
$830$	−9.26013	−	3.50000i	−0.321424	−	0.121487i
$831$		0			0
$832$	−35.0000	−	23.8118i	−1.21341	−	0.825524i
$833$	−31.7490			−1.10004
$834$		0			0
$835$			10.5830i			0.366240i
$836$	23.8118	+	21.0000i	0.823547	+	0.726300i
$837$		0			0
$838$		0			0
$839$	−37.0405			−1.27878			−0.639390	−	0.768882i	$-0.720813\pi$
$839$	−37.0405			−1.27878			−0.639390	+	0.768882i	$0.720813\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	5.29150	−	14.0000i	0.182357	−	0.482472i
$843$		0			0
$844$	−7.00000	+	7.93725i	−0.240950	+	0.273212i
$845$		−	15.0000i		−	0.516016i
$846$		0			0
$847$	2.00000			0.0687208
$848$	35.7176	−	4.50000i	1.22655	−	0.154531i
$849$		0			0
$850$	−28.0000	−	10.5830i	−0.960392	−	0.362994i
$851$			28.0000i			0.959828i
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	7.50000	−	3.96863i	0.256345	−	0.135645i
$857$	−15.8745			−0.542263			−0.271131	−	0.962542i	$-0.587398\pi$
$857$	−15.8745			−0.542263			−0.271131	+	0.962542i	$0.587398\pi$
$858$		0			0
$859$			52.9150i			1.80544i	0.430231	+	0.902719i	$0.358432\pi$
$859$			52.9150i			1.80544i	−0.430231	+	0.902719i	$0.641568\pi$
$860$	15.8745	+	14.0000i	0.541316	+	0.477396i
$861$		0			0
$862$	−42.0000	−	15.8745i	−1.43053	−	0.540688i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−15.0000			−0.510015
$866$	−6.61438	−	2.50000i	−0.224766	−	0.0849535i
$867$		0			0
$868$	−10.5000	−	9.26013i	−0.356393	−	0.314309i
$869$			12.0000i			0.407072i
$870$		0			0
$871$		0			0
$872$	−13.2288	+	7.00000i	−0.447982	+	0.237050i
$873$		0			0
$874$	−14.0000	+	37.0405i	−0.473557	+	1.25291i
$875$			9.00000i			0.304256i
$876$		0			0
$877$		−	52.9150i		−	1.78681i	−0.449249	−	0.893407i	$-0.648308\pi$
$877$		−	52.9150i		−	1.78681i	0.449249	−	0.893407i	$-0.351692\pi$
$878$	27.7804	+	10.5000i	0.937543	+	0.354358i
$879$		0			0
$880$	−1.50000	−	11.9059i	−0.0505650	−	0.401347i
$881$	26.4575			0.891376			0.445688	−	0.895188i	$-0.352959\pi$
$881$	26.4575			0.891376			0.445688	+	0.895188i	$0.352959\pi$
$882$		0			0
$883$		−	58.2065i		−	1.95881i	−0.201916	−	0.979403i	$-0.564717\pi$
$883$		−	58.2065i		−	1.95881i	0.201916	−	0.979403i	$-0.435283\pi$
$884$	−37.0405	+	42.0000i	−1.24581	+	1.41261i
$885$		0			0
$886$	−12.0000	+	31.7490i	−0.403148	+	1.06663i
$887$	15.8745			0.533014			0.266507	−	0.963833i	$-0.414130\pi$
$887$	15.8745			0.533014			0.266507	+	0.963833i	$0.414130\pi$
$888$		0			0
$889$	13.0000			0.436006
$890$	5.29150	−	14.0000i	0.177372	−	0.469281i
$891$		0			0
$892$	−24.0000	−	21.1660i	−0.803579	−	0.708690i
$893$		0			0
$894$		0			0
$895$	−23.0000			−0.768805
$896$	9.26013	−	6.50000i	0.309359	−	0.217150i
$897$		0			0
$898$	21.0000	+	7.93725i	0.700779	+	0.264870i
$899$		−	42.0000i		−	1.40078i
$900$		0			0
$901$		−	47.6235i		−	1.58657i
$902$	−7.93725	+	21.0000i	−0.264282	+	0.699224i
$903$		0			0
$904$	21.0000	+	39.6863i	0.698450	+	1.31995i
$905$	21.1660			0.703582
$906$		0			0
$907$		−	5.29150i		−	0.175701i	−0.996134	−	0.0878507i	$-0.972000\pi$
$907$		−	5.29150i		−	0.175701i	0.996134	−	0.0878507i	$-0.0279999\pi$
$908$	−5.29150	+	6.00000i	−0.175605	+	0.199117i
$909$		0			0
$910$	7.00000	+	2.64575i	0.232048	+	0.0877058i
$911$	−31.7490			−1.05189			−0.525946	−	0.850518i	$-0.676289\pi$
$911$	−31.7490			−1.05189			−0.525946	+	0.850518i	$0.676289\pi$
$912$		0			0
$913$	21.0000			0.694999
$914$	−22.4889	−	8.50000i	−0.743866	−	0.281155i
$915$		0			0
$916$	28.0000	−	31.7490i	0.925146	−	1.04902i
$917$		−	7.00000i		−	0.231160i
$918$		0			0
$919$	3.00000			0.0989609			0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000			0.0989609			0.0494804	+	0.998775i	$0.484243\pi$
$920$	13.2288	−	7.00000i	0.436139	−	0.230783i
$921$		0			0
$922$	−4.50000	+	11.9059i	−0.148200	+	0.392099i
$923$		−	84.0000i		−	2.76489i
$924$		0			0
$925$			21.1660i			0.695934i
$926$	54.2379	+	20.5000i	1.78237	+	0.673672i
$927$		0			0
$928$	33.0000	+	7.93725i	1.08328	+	0.260553i
$929$	−10.5830			−0.347217			−0.173609	−	0.984815i	$-0.555543\pi$
$929$	−10.5830			−0.347217			−0.173609	+	0.984815i	$0.555543\pi$
$930$		0			0
$931$			31.7490i			1.04053i
$932$	15.8745	+	14.0000i	0.519987	+	0.458585i
$933$		0			0
$934$	0.500000	−	1.32288i	0.0163605	−	0.0432858i
$935$	−15.8745			−0.519152
$936$		0			0
$937$	−19.0000			−0.620703			−0.310351	−	0.950622i	$-0.600447\pi$
$937$	−19.0000			−0.620703			−0.310351	+	0.950622i	$0.600447\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	21.0000i		−	0.684580i	−0.939594	−	0.342290i	$-0.888797\pi$
$941$		−	21.0000i		−	0.684580i	0.939594	−	0.342290i	$-0.111203\pi$
$942$		0			0
$943$	−28.0000			−0.911805
$944$	15.8745	−	2.00000i	0.516671	−	0.0650945i
$945$		0			0
$946$	−42.0000	−	15.8745i	−1.36554	−	0.516125i
$947$			39.0000i			1.26733i	0.773608	+	0.633665i	$0.218450\pi$
$947$			39.0000i			1.26733i	−0.773608	+	0.633665i	$0.781550\pi$
$948$		0			0
$949$			15.8745i			0.515308i
$950$	−10.5830	+	28.0000i	−0.343358	+	0.908440i
$951$		0			0
$952$	−7.00000	−	13.2288i	−0.226871	−	0.428746i
$953$	31.7490			1.02845			0.514226	−	0.857655i	$-0.328079\pi$
$953$	31.7490			1.02845			0.514226	+	0.857655i	$0.328079\pi$
$954$		0			0
$955$			5.29150i			0.171229i
$956$	23.8118	+	21.0000i	0.770127	+	0.679189i
$957$		0			0
$958$	28.0000	+	10.5830i	0.904639	+	0.341921i
$959$		0			0
$960$		0			0
$961$	18.0000			0.580645
$962$	37.0405	+	14.0000i	1.19423	+	0.451378i
$963$		0			0
$964$	−15.0000	−	13.2288i	−0.483117	−	0.426070i
$965$		−	3.00000i		−	0.0965734i
$966$		0			0
$967$	41.0000			1.31847			0.659236	−	0.751936i	$-0.270880\pi$
$967$	41.0000			1.31847			0.659236	+	0.751936i	$0.270880\pi$
$968$	−2.64575	−	5.00000i	−0.0850377	−	0.160706i
$969$		0			0
$970$	3.50000	−	9.26013i	0.112378	−	0.297325i
$971$			15.0000i			0.481373i	0.970603	+	0.240686i	$0.0773725\pi$
$971$			15.0000i			0.481373i	−0.970603	+	0.240686i	$0.922627\pi$
$972$		0			0
$973$			10.5830i			0.339276i
$974$	52.9150	+	20.0000i	1.69551	+	0.640841i
$975$		0			0
$976$		0			0
$977$	−10.5830			−0.338580			−0.169290	−	0.985566i	$-0.554148\pi$
$977$	−10.5830			−0.338580			−0.169290	+	0.985566i	$0.554148\pi$
$978$		0			0
$979$			31.7490i			1.01470i
$980$	7.93725	−	9.00000i	0.253546	−	0.287494i
$981$		0			0
$982$	14.5000	−	38.3634i	0.462714	−	1.22423i
$983$	42.3320			1.35018			0.675091	−	0.737735i	$-0.264104\pi$
$983$	42.3320			1.35018			0.675091	+	0.737735i	$0.264104\pi$
$984$		0			0
$985$	13.0000			0.414214
$986$	15.8745	−	42.0000i	0.505547	−	1.33755i
$987$		0			0
$988$	42.0000	+	37.0405i	1.33620	+	1.17842i
$989$		−	56.0000i		−	1.78070i
$990$		0			0
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$	−9.26013	+	38.5000i	−0.294009	+	1.22238i
$993$		0			0
$994$	21.0000	+	7.93725i	0.666080	+	0.251754i
$995$		−	17.0000i		−	0.538936i
$996$		0			0
$997$			15.8745i			0.502751i	0.967890	+	0.251375i	$0.0808829\pi$
$997$			15.8745i			0.502751i	−0.967890	+	0.251375i	$0.919117\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.d.b.109.1	✓	4
3.2	odd	2	inner	216.2.d.b.109.4	yes	4
4.3	odd	2		864.2.d.a.433.4		4
8.3	odd	2		864.2.d.a.433.1		4
8.5	even	2	inner	216.2.d.b.109.2	yes	4
9.2	odd	6		648.2.n.n.109.2		8
9.4	even	3		648.2.n.n.541.4		8
9.5	odd	6		648.2.n.n.541.1		8
9.7	even	3		648.2.n.n.109.3		8
12.11	even	2		864.2.d.a.433.2		4
16.3	odd	4		6912.2.a.bv.1.1		2
16.5	even	4		6912.2.a.bc.1.2		2
16.11	odd	4		6912.2.a.bd.1.2		2
16.13	even	4		6912.2.a.bu.1.1		2
24.5	odd	2	inner	216.2.d.b.109.3	yes	4
24.11	even	2		864.2.d.a.433.3		4
36.7	odd	6		2592.2.r.p.433.1		8
36.11	even	6		2592.2.r.p.433.3		8
36.23	even	6		2592.2.r.p.2161.2		8
36.31	odd	6		2592.2.r.p.2161.4		8
48.5	odd	4		6912.2.a.bu.1.2		2
48.11	even	4		6912.2.a.bv.1.2		2
48.29	odd	4		6912.2.a.bc.1.1		2
48.35	even	4		6912.2.a.bd.1.1		2
72.5	odd	6		648.2.n.n.541.2		8
72.11	even	6		2592.2.r.p.433.2		8
72.13	even	6		648.2.n.n.541.3		8
72.29	odd	6		648.2.n.n.109.1		8
72.43	odd	6		2592.2.r.p.433.4		8
72.59	even	6		2592.2.r.p.2161.3		8
72.61	even	6		648.2.n.n.109.4		8
72.67	odd	6		2592.2.r.p.2161.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.d.b.109.1	✓	4	1.1	even	1	trivial
216.2.d.b.109.2	yes	4	8.5	even	2	inner
216.2.d.b.109.3	yes	4	24.5	odd	2	inner
216.2.d.b.109.4	yes	4	3.2	odd	2	inner
648.2.n.n.109.1		8	72.29	odd	6
648.2.n.n.109.2		8	9.2	odd	6
648.2.n.n.109.3		8	9.7	even	3
648.2.n.n.109.4		8	72.61	even	6
648.2.n.n.541.1		8	9.5	odd	6
648.2.n.n.541.2		8	72.5	odd	6
648.2.n.n.541.3		8	72.13	even	6
648.2.n.n.541.4		8	9.4	even	3
864.2.d.a.433.1		4	8.3	odd	2
864.2.d.a.433.2		4	12.11	even	2
864.2.d.a.433.3		4	24.11	even	2
864.2.d.a.433.4		4	4.3	odd	2
2592.2.r.p.433.1		8	36.7	odd	6
2592.2.r.p.433.2		8	72.11	even	6
2592.2.r.p.433.3		8	36.11	even	6
2592.2.r.p.433.4		8	72.43	odd	6
2592.2.r.p.2161.1		8	72.67	odd	6
2592.2.r.p.2161.2		8	36.23	even	6
2592.2.r.p.2161.3		8	72.59	even	6
2592.2.r.p.2161.4		8	36.31	odd	6
6912.2.a.bc.1.1		2	48.29	odd	4
6912.2.a.bc.1.2		2	16.5	even	4
6912.2.a.bd.1.1		2	48.35	even	4
6912.2.a.bd.1.2		2	16.11	odd	4
6912.2.a.bu.1.1		2	16.13	even	4
6912.2.a.bu.1.2		2	48.5	odd	4
6912.2.a.bv.1.1		2	16.3	odd	4
6912.2.a.bv.1.2		2	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 - 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} +1.00000i q^{5} +1.00000 q^{7} +(-1.32288 - 2.50000i) q^{8} +O(q^{10})\)	\(q+(-1.32288 - 0.500000i) q^{2} +(1.50000 + 1.32288i) q^{4} +1.00000i q^{5} +1.00000 q^{7} +(-1.32288 - 2.50000i) q^{8} +(0.500000 - 1.32288i) q^{10} +3.00000i q^{11} +5.29150i q^{13} +(-1.32288 - 0.500000i) q^{14} +(0.500000 + 3.96863i) q^{16} +5.29150 q^{17} -5.29150i q^{19} +(-1.32288 + 1.50000i) q^{20} +(1.50000 - 3.96863i) q^{22} +5.29150 q^{23} +4.00000 q^{25} +(2.64575 - 7.00000i) q^{26} +(1.50000 + 1.32288i) q^{28} +6.00000i q^{29} -7.00000 q^{31} +(1.32288 - 5.50000i) q^{32} +(-7.00000 - 2.64575i) q^{34} +1.00000i q^{35} +5.29150i q^{37} +(-2.64575 + 7.00000i) q^{38} +(2.50000 - 1.32288i) q^{40} -5.29150 q^{41} -10.5830i q^{43} +(-3.96863 + 4.50000i) q^{44} +(-7.00000 - 2.64575i) q^{46} -6.00000 q^{49} +(-5.29150 - 2.00000i) q^{50} +(-7.00000 + 7.93725i) q^{52} -9.00000i q^{53} -3.00000 q^{55} +(-1.32288 - 2.50000i) q^{56} +(3.00000 - 7.93725i) q^{58} -4.00000i q^{59} +(9.26013 + 3.50000i) q^{62} +(-4.50000 + 6.61438i) q^{64} -5.29150 q^{65} +(7.93725 + 7.00000i) q^{68} +(0.500000 - 1.32288i) q^{70} -15.8745 q^{71} +3.00000 q^{73} +(2.64575 - 7.00000i) q^{74} +(7.00000 - 7.93725i) q^{76} +3.00000i q^{77} +4.00000 q^{79} +(-3.96863 + 0.500000i) q^{80} +(7.00000 + 2.64575i) q^{82} -7.00000i q^{83} +5.29150i q^{85} +(-5.29150 + 14.0000i) q^{86} +(7.50000 - 3.96863i) q^{88} +10.5830 q^{89} +5.29150i q^{91} +(7.93725 + 7.00000i) q^{92} +5.29150 q^{95} +7.00000 q^{97} +(7.93725 + 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} + 4 q^{7}+O(q^{10}) \) 4 * q + 6 * q^4 + 4 * q^7	\( 4 q + 6 q^{4} + 4 q^{7} + 2 q^{10} + 2 q^{16} + 6 q^{22} + 16 q^{25} + 6 q^{28} - 28 q^{31} - 28 q^{34} + 10 q^{40} - 28 q^{46} - 24 q^{49} - 28 q^{52} - 12 q^{55} + 12 q^{58} - 18 q^{64} + 2 q^{70} + 12 q^{73} + 28 q^{76} + 16 q^{79} + 28 q^{82} + 30 q^{88} + 28 q^{97}+O(q^{100}) \) 4 * q + 6 * q^4 + 4 * q^7 + 2 * q^10 + 2 * q^16 + 6 * q^22 + 16 * q^25 + 6 * q^28 - 28 * q^31 - 28 * q^34 + 10 * q^40 - 28 * q^46 - 24 * q^49 - 28 * q^52 - 12 * q^55 + 12 * q^58 - 18 * q^64 + 2 * q^70 + 12 * q^73 + 28 * q^76 + 16 * q^79 + 28 * q^82 + 30 * q^88 + 28 * q^97

Introduction

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