LMFDB - Embedded newform 1248.2.bb.c.463.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(463,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("1248.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (of order $4$, 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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1248.463
Dual form			1248.2.bb.c.655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(-2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +(-2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{9} +(2.00000 - 2.00000i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(-2.00000 + 2.00000i) q^{15} -6.00000i q^{17} +(3.00000 + 3.00000i) q^{19} +(-1.00000 - 1.00000i) q^{21} +8.00000 q^{23} -3.00000i q^{25} +1.00000 q^{27} -2.00000i q^{29} +(1.00000 - 1.00000i) q^{31} +(2.00000 - 2.00000i) q^{33} +4.00000 q^{35} +(-1.00000 - 1.00000i) q^{37} +(-2.00000 - 3.00000i) q^{39} +(8.00000 + 8.00000i) q^{41} -4.00000i q^{43} +(-2.00000 + 2.00000i) q^{45} +(8.00000 + 8.00000i) q^{47} -5.00000i q^{49} -6.00000i q^{51} -2.00000i q^{53} +8.00000i q^{55} +(3.00000 + 3.00000i) q^{57} +(4.00000 - 4.00000i) q^{59} +2.00000i q^{61} +(-1.00000 - 1.00000i) q^{63} +(10.0000 + 2.00000i) q^{65} +(1.00000 + 1.00000i) q^{67} +8.00000 q^{69} +(6.00000 - 6.00000i) q^{71} +(-9.00000 + 9.00000i) q^{73} -3.00000i q^{75} -4.00000 q^{77} -10.0000i q^{79} +1.00000 q^{81} +(-8.00000 - 8.00000i) q^{83} +(12.0000 + 12.0000i) q^{85} -2.00000i q^{87} +(10.0000 - 10.0000i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(1.00000 - 1.00000i) q^{93} -12.0000 q^{95} +(-5.00000 - 5.00000i) q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 2 q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{15} + 6 q^{19} - 2 q^{21} + 16 q^{23} + 2 q^{27} + 2 q^{31} + 4 q^{33} + 8 q^{35} - 2 q^{37} - 4 q^{39} + 16 q^{41} - 4 q^{45} + 16 q^{47} + 6 q^{57} + 8 q^{59} - 2 q^{63} + 20 q^{65} + 2 q^{67} + 16 q^{69} + 12 q^{71} - 18 q^{73} - 8 q^{77} + 2 q^{81} - 16 q^{83} + 24 q^{85} + 20 q^{89} - 2 q^{91} + 2 q^{93} - 24 q^{95} - 10 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 2 * q^9 + 4 * q^11 - 4 * q^13 - 4 * q^15 + 6 * q^19 - 2 * q^21 + 16 * q^23 + 2 * q^27 + 2 * q^31 + 4 * q^33 + 8 * q^35 - 2 * q^37 - 4 * q^39 + 16 * q^41 - 4 * q^45 + 16 * q^47 + 6 * q^57 + 8 * q^59 - 2 * q^63 + 20 * q^65 + 2 * q^67 + 16 * q^69 + 12 * q^71 - 18 * q^73 - 8 * q^77 + 2 * q^81 - 16 * q^83 + 24 * q^85 + 20 * q^89 - 2 * q^91 + 2 * q^93 - 24 * q^95 - 10 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	−0.994936	−	0.100509i	$-0.967953\pi$
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	0.100509	+	0.994936i	$0.467953\pi$
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	0.941113	+	0.338091i	$0.109781\pi$
$12$		0			0
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		0			0
$15$	−2.00000	+	2.00000i	−0.516398	+	0.516398i
$16$		0			0
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		0			0
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$		0			0
$21$	−1.00000	−	1.00000i	−0.218218	−	0.218218i
$22$		0			0
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	4.00000			0.676123
$36$		0			0
$37$	−1.00000	−	1.00000i	−0.164399	−	0.164399i	0.620113	−	0.784512i	$-0.287087\pi$
$37$	−1.00000	−	1.00000i	−0.164399	−	0.164399i	−0.784512	+	0.620113i	$0.787087\pi$
$38$		0			0
$39$	−2.00000	−	3.00000i	−0.320256	−	0.480384i
$40$		0			0
$41$	8.00000	+	8.00000i	1.24939	+	1.24939i	0.955990	+	0.293400i	$0.0947869\pi$
$41$	8.00000	+	8.00000i	1.24939	+	1.24939i	0.293400	+	0.955990i	$0.405213\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	−2.00000	+	2.00000i	−0.298142	+	0.298142i
$46$		0			0
$47$	8.00000	+	8.00000i	1.16692	+	1.16692i	0.982928	+	0.183992i	$0.0589021\pi$
$47$	8.00000	+	8.00000i	1.16692	+	1.16692i	0.183992	+	0.982928i	$0.441098\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$		−	6.00000i		−	0.840168i
$52$		0			0
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$		0			0
$55$			8.00000i			1.07872i
$56$		0			0
$57$	3.00000	+	3.00000i	0.397360	+	0.397360i
$58$		0			0
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	−0.397044	−	0.917800i	$-0.629964\pi$
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	0.917800	+	0.397044i	$0.129964\pi$
$60$		0			0
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$		0			0
$63$	−1.00000	−	1.00000i	−0.125988	−	0.125988i
$64$		0			0
$65$	10.0000	+	2.00000i	1.24035	+	0.248069i
$66$		0			0
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	0.765548	−	0.643379i	$-0.222468\pi$
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	−0.643379	+	0.765548i	$0.722468\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	−0.254899	−	0.966968i	$-0.582042\pi$
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	0.966968	+	0.254899i	$0.0820421\pi$
$72$		0			0
$73$	−9.00000	+	9.00000i	−1.05337	+	1.05337i	−0.0548772	+	0.998493i	$0.517477\pi$
$73$	−9.00000	+	9.00000i	−1.05337	+	1.05337i	−0.998493	+	0.0548772i	$0.982523\pi$
$74$		0			0
$75$		−	3.00000i		−	0.346410i
$76$		0			0
$77$	−4.00000			−0.455842
$78$		0			0
$79$		−	10.0000i		−	1.12509i	−0.826767	−	0.562544i	$-0.809823\pi$
$79$		−	10.0000i		−	1.12509i	0.826767	−	0.562544i	$-0.190177\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−8.00000	−	8.00000i	−0.878114	−	0.878114i	0.115225	−	0.993339i	$-0.463241\pi$
$83$	−8.00000	−	8.00000i	−0.878114	−	0.878114i	−0.993339	+	0.115225i	$0.963241\pi$
$84$		0			0
$85$	12.0000	+	12.0000i	1.30158	+	1.30158i
$86$		0			0
$87$		−	2.00000i		−	0.214423i
$88$		0			0
$89$	10.0000	−	10.0000i	1.06000	−	1.06000i	0.0619166	−	0.998081i	$-0.480279\pi$
$89$	10.0000	−	10.0000i	1.06000	−	1.06000i	0.998081	−	0.0619166i	$-0.0197213\pi$
$90$		0			0
$91$	−1.00000	+	5.00000i	−0.104828	+	0.524142i
$92$		0			0
$93$	1.00000	−	1.00000i	0.103695	−	0.103695i
$94$		0			0
$95$	−12.0000			−1.23117
$96$		0			0
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	0.406138	−	0.913812i	$-0.366875\pi$
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$	2.00000	−	2.00000i	0.201008	−	0.201008i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$		0			0
$105$	4.00000			0.390360
$106$		0			0
$107$	16.0000			1.54678			0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000			1.54678			0.773389	+	0.633932i	$0.218560\pi$
$108$		0			0
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$		0			0
$111$	−1.00000	−	1.00000i	−0.0949158	−	0.0949158i
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−16.0000	+	16.0000i	−1.49201	+	1.49201i
$116$		0			0
$117$	−2.00000	−	3.00000i	−0.184900	−	0.277350i
$118$		0			0
$119$	−6.00000	+	6.00000i	−0.550019	+	0.550019i
$120$		0			0
$121$			3.00000i			0.272727i
$122$		0			0
$123$	8.00000	+	8.00000i	0.721336	+	0.721336i
$124$		0			0
$125$	−4.00000	−	4.00000i	−0.357771	−	0.357771i
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$		−	4.00000i		−	0.352180i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		−	6.00000i		−	0.520266i
$134$		0			0
$135$	−2.00000	+	2.00000i	−0.172133	+	0.172133i
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	8.00000	+	8.00000i	0.673722	+	0.673722i
$142$		0			0
$143$	−10.0000	−	2.00000i	−0.836242	−	0.167248i
$144$		0			0
$145$	4.00000	+	4.00000i	0.332182	+	0.332182i
$146$		0			0
$147$		−	5.00000i		−	0.412393i
$148$		0			0
$149$	8.00000	−	8.00000i	0.655386	−	0.655386i	−0.298899	−	0.954285i	$-0.596619\pi$
$149$	8.00000	−	8.00000i	0.655386	−	0.655386i	0.954285	+	0.298899i	$0.0966194\pi$
$150$		0			0
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	0.665246	−	0.746625i	$-0.268327\pi$
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	−0.746625	+	0.665246i	$0.768327\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$			4.00000i			0.321288i
$156$		0			0
$157$		−	4.00000i		−	0.319235i	−0.987179	−	0.159617i	$-0.948974\pi$
$157$		−	4.00000i		−	0.319235i	0.987179	−	0.159617i	$-0.0510260\pi$
$158$		0			0
$159$		−	2.00000i		−	0.158610i
$160$		0			0
$161$	−8.00000	−	8.00000i	−0.630488	−	0.630488i
$162$		0			0
$163$	9.00000	−	9.00000i	0.704934	−	0.704934i	−0.260531	−	0.965465i	$-0.583898\pi$
$163$	9.00000	−	9.00000i	0.704934	−	0.704934i	0.965465	+	0.260531i	$0.0838976\pi$
$164$		0			0
$165$			8.00000i			0.622799i
$166$		0			0
$167$	4.00000	+	4.00000i	0.309529	+	0.309529i	0.844727	−	0.535198i	$-0.179763\pi$
$167$	4.00000	+	4.00000i	0.309529	+	0.309529i	−0.535198	+	0.844727i	$0.679763\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$		0			0
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	−3.00000	+	3.00000i	−0.226779	+	0.226779i
$176$		0			0
$177$	4.00000	−	4.00000i	0.300658	−	0.300658i
$178$		0			0
$179$			8.00000i			0.597948i	0.954261	+	0.298974i	$0.0966444\pi$
$179$			8.00000i			0.597948i	−0.954261	+	0.298974i	$0.903356\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$		0			0
$185$	4.00000			0.294086
$186$		0			0
$187$	−12.0000	−	12.0000i	−0.877527	−	0.877527i
$188$		0			0
$189$	−1.00000	−	1.00000i	−0.0727393	−	0.0727393i
$190$		0			0
$191$		−	24.0000i		−	1.73658i	−0.496058	−	0.868290i	$-0.665220\pi$
$191$		−	24.0000i		−	1.73658i	0.496058	−	0.868290i	$-0.334780\pi$
$192$		0			0
$193$	−9.00000	+	9.00000i	−0.647834	+	0.647834i	−0.952469	−	0.304635i	$-0.901466\pi$
$193$	−9.00000	+	9.00000i	−0.647834	+	0.647834i	0.304635	+	0.952469i	$0.401466\pi$
$194$		0			0
$195$	10.0000	+	2.00000i	0.716115	+	0.143223i
$196$		0			0
$197$	2.00000	−	2.00000i	0.142494	−	0.142494i	−0.632261	−	0.774755i	$-0.717873\pi$
$197$	2.00000	−	2.00000i	0.142494	−	0.142494i	0.774755	+	0.632261i	$0.217873\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		0			0
$201$	1.00000	+	1.00000i	0.0705346	+	0.0705346i
$202$		0			0
$203$	−2.00000	+	2.00000i	−0.140372	+	0.140372i
$204$		0			0
$205$	−32.0000			−2.23498
$206$		0			0
$207$	8.00000			0.556038
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	6.00000	−	6.00000i	0.411113	−	0.411113i
$214$		0			0
$215$	8.00000	+	8.00000i	0.545595	+	0.545595i
$216$		0			0
$217$	−2.00000			−0.135769
$218$		0			0
$219$	−9.00000	+	9.00000i	−0.608164	+	0.608164i
$220$		0			0
$221$	−18.0000	+	12.0000i	−1.21081	+	0.807207i
$222$		0			0
$223$	−3.00000	+	3.00000i	−0.200895	+	0.200895i	−0.800383	−	0.599489i	$-0.795371\pi$
$223$	−3.00000	+	3.00000i	−0.200895	+	0.200895i	0.599489	+	0.800383i	$0.295371\pi$
$224$		0			0
$225$		−	3.00000i		−	0.200000i
$226$		0			0
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	0.770357	−	0.637613i	$-0.220078\pi$
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	−0.637613	+	0.770357i	$0.720078\pi$
$228$		0			0
$229$	15.0000	+	15.0000i	0.991228	+	0.991228i	0.999962	−	0.00873396i	$-0.00278014\pi$
$229$	15.0000	+	15.0000i	0.991228	+	0.991228i	−0.00873396	+	0.999962i	$0.502780\pi$
$230$		0			0
$231$	−4.00000			−0.263181
$232$		0			0
$233$		−	14.0000i		−	0.917170i	−0.888650	−	0.458585i	$-0.848356\pi$
$233$		−	14.0000i		−	0.917170i	0.888650	−	0.458585i	$-0.151644\pi$
$234$		0			0
$235$	−32.0000			−2.08745
$236$		0			0
$237$		−	10.0000i		−	0.649570i
$238$		0			0
$239$	−10.0000	+	10.0000i	−0.646846	+	0.646846i	−0.952230	−	0.305383i	$-0.901215\pi$
$239$	−10.0000	+	10.0000i	−0.646846	+	0.646846i	0.305383	+	0.952230i	$0.401215\pi$
$240$		0			0
$241$	−15.0000	+	15.0000i	−0.966235	+	0.966235i	−0.999448	−	0.0332133i	$-0.989426\pi$
$241$	−15.0000	+	15.0000i	−0.966235	+	0.966235i	0.0332133	+	0.999448i	$0.489426\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	10.0000	+	10.0000i	0.638877	+	0.638877i
$246$		0			0
$247$	3.00000	−	15.0000i	0.190885	−	0.954427i
$248$		0			0
$249$	−8.00000	−	8.00000i	−0.506979	−	0.506979i
$250$		0			0
$251$			24.0000i			1.51487i	0.652913	+	0.757433i	$0.273547\pi$
$251$			24.0000i			1.51487i	−0.652913	+	0.757433i	$0.726453\pi$
$252$		0			0
$253$	16.0000	−	16.0000i	1.00591	−	1.00591i
$254$		0			0
$255$	12.0000	+	12.0000i	0.751469	+	0.751469i
$256$		0			0
$257$			10.0000i			0.623783i	0.950118	+	0.311891i	$0.100963\pi$
$257$			10.0000i			0.623783i	−0.950118	+	0.311891i	$0.899037\pi$
$258$		0			0
$259$			2.00000i			0.124274i
$260$		0			0
$261$		−	2.00000i		−	0.123797i
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	4.00000	+	4.00000i	0.245718	+	0.245718i
$266$		0			0
$267$	10.0000	−	10.0000i	0.611990	−	0.611990i
$268$		0			0
$269$			2.00000i			0.121942i	0.998140	+	0.0609711i	$0.0194197\pi$
$269$			2.00000i			0.121942i	−0.998140	+	0.0609711i	$0.980580\pi$
$270$		0			0
$271$	13.0000	+	13.0000i	0.789694	+	0.789694i	0.981444	−	0.191750i	$-0.0614163\pi$
$271$	13.0000	+	13.0000i	0.789694	+	0.789694i	−0.191750	+	0.981444i	$0.561416\pi$
$272$		0			0
$273$	−1.00000	+	5.00000i	−0.0605228	+	0.302614i
$274$		0			0
$275$	−6.00000	−	6.00000i	−0.361814	−	0.361814i
$276$		0			0
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$		0			0
$279$	1.00000	−	1.00000i	0.0598684	−	0.0598684i
$280$		0			0
$281$	−20.0000	+	20.0000i	−1.19310	+	1.19310i	−0.216908	+	0.976192i	$0.569597\pi$
$281$	−20.0000	+	20.0000i	−1.19310	+	1.19310i	−0.976192	+	0.216908i	$0.930403\pi$
$282$		0			0
$283$		−	6.00000i		−	0.356663i	−0.983970	−	0.178331i	$-0.942930\pi$
$283$		−	6.00000i		−	0.356663i	0.983970	−	0.178331i	$-0.0570699\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$		−	16.0000i		−	0.944450i
$288$		0			0
$289$	−19.0000			−1.11765
$290$		0			0
$291$	−5.00000	−	5.00000i	−0.293105	−	0.293105i
$292$		0			0
$293$	16.0000	+	16.0000i	0.934730	+	0.934730i	0.997997	−	0.0632667i	$-0.0201519\pi$
$293$	16.0000	+	16.0000i	0.934730	+	0.934730i	−0.0632667	+	0.997997i	$0.520152\pi$
$294$		0			0
$295$			16.0000i			0.931556i
$296$		0			0
$297$	2.00000	−	2.00000i	0.116052	−	0.116052i
$298$		0			0
$299$	−16.0000	−	24.0000i	−0.925304	−	1.38796i
$300$		0			0
$301$	−4.00000	+	4.00000i	−0.230556	+	0.230556i
$302$		0			0
$303$	−6.00000			−0.344691
$304$		0			0
$305$	−4.00000	−	4.00000i	−0.229039	−	0.229039i
$306$		0			0
$307$	−21.0000	+	21.0000i	−1.19853	+	1.19853i	−0.223928	+	0.974606i	$0.571888\pi$
$307$	−21.0000	+	21.0000i	−1.19853	+	1.19853i	−0.974606	+	0.223928i	$0.928112\pi$
$308$		0			0
$309$	−10.0000			−0.568880
$310$		0			0
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	4.00000			0.225374
$316$		0			0
$317$	2.00000	−	2.00000i	0.112331	−	0.112331i	−0.648707	−	0.761038i	$-0.724690\pi$
$317$	2.00000	−	2.00000i	0.112331	−	0.112331i	0.761038	+	0.648707i	$0.224690\pi$
$318$		0			0
$319$	−4.00000	−	4.00000i	−0.223957	−	0.223957i
$320$		0			0
$321$	16.0000			0.893033
$322$		0			0
$323$	18.0000	−	18.0000i	1.00155	−	1.00155i
$324$		0			0
$325$	−9.00000	+	6.00000i	−0.499230	+	0.332820i
$326$		0			0
$327$	−1.00000	+	1.00000i	−0.0553001	+	0.0553001i
$328$		0			0
$329$		−	16.0000i		−	0.882109i
$330$		0			0
$331$	11.0000	+	11.0000i	0.604615	+	0.604615i	0.941534	−	0.336919i	$-0.109385\pi$
$331$	11.0000	+	11.0000i	0.604615	+	0.604615i	−0.336919	+	0.941534i	$0.609385\pi$
$332$		0			0
$333$	−1.00000	−	1.00000i	−0.0547997	−	0.0547997i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$		0			0
$339$	−18.0000			−0.977626
$340$		0			0
$341$		−	4.00000i		−	0.216612i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	−16.0000	+	16.0000i	−0.861411	+	0.861411i
$346$		0			0
$347$	−20.0000			−1.07366			−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000			−1.07366			−0.536828	+	0.843692i	$0.680378\pi$
$348$		0			0
$349$	−21.0000	−	21.0000i	−1.12410	−	1.12410i	−0.991118	−	0.132986i	$-0.957543\pi$
$349$	−21.0000	−	21.0000i	−1.12410	−	1.12410i	−0.132986	−	0.991118i	$-0.542457\pi$
$350$		0			0
$351$	−2.00000	−	3.00000i	−0.106752	−	0.160128i
$352$		0			0
$353$	24.0000	+	24.0000i	1.27739	+	1.27739i	0.942123	+	0.335268i	$0.108827\pi$
$353$	24.0000	+	24.0000i	1.27739	+	1.27739i	0.335268	+	0.942123i	$0.391173\pi$
$354$		0			0
$355$			24.0000i			1.27379i
$356$		0			0
$357$	−6.00000	+	6.00000i	−0.317554	+	0.317554i
$358$		0			0
$359$	8.00000	+	8.00000i	0.422224	+	0.422224i	0.885969	−	0.463745i	$-0.153495\pi$
$359$	8.00000	+	8.00000i	0.422224	+	0.422224i	−0.463745	+	0.885969i	$0.653495\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$			3.00000i			0.157459i
$364$		0			0
$365$		−	36.0000i		−	1.88433i
$366$		0			0
$367$			8.00000i			0.417597i	0.977959	+	0.208798i	$0.0669552\pi$
$367$			8.00000i			0.417597i	−0.977959	+	0.208798i	$0.933045\pi$
$368$		0			0
$369$	8.00000	+	8.00000i	0.416463	+	0.416463i
$370$		0			0
$371$	−2.00000	+	2.00000i	−0.103835	+	0.103835i
$372$		0			0
$373$		−	22.0000i		−	1.13912i	−0.821951	−	0.569558i	$-0.807114\pi$
$373$		−	22.0000i		−	1.13912i	0.821951	−	0.569558i	$-0.192886\pi$
$374$		0			0
$375$	−4.00000	−	4.00000i	−0.206559	−	0.206559i
$376$		0			0
$377$	−6.00000	+	4.00000i	−0.309016	+	0.206010i
$378$		0			0
$379$	−9.00000	−	9.00000i	−0.462299	−	0.462299i	0.437109	−	0.899408i	$-0.356002\pi$
$379$	−9.00000	−	9.00000i	−0.462299	−	0.462299i	−0.899408	+	0.437109i	$0.856002\pi$
$380$		0			0
$381$	−8.00000			−0.409852
$382$		0			0
$383$	−8.00000	+	8.00000i	−0.408781	+	0.408781i	−0.881313	−	0.472532i	$-0.843340\pi$
$383$	−8.00000	+	8.00000i	−0.408781	+	0.408781i	0.472532	+	0.881313i	$0.343340\pi$
$384$		0			0
$385$	8.00000	−	8.00000i	0.407718	−	0.407718i
$386$		0			0
$387$		−	4.00000i		−	0.203331i
$388$		0			0
$389$	26.0000			1.31825			0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000			1.31825			0.659126	+	0.752032i	$0.270926\pi$
$390$		0			0
$391$		−	48.0000i		−	2.42746i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.0000	+	20.0000i	1.00631	+	1.00631i
$396$		0			0
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	0.222178	−	0.975006i	$-0.428683\pi$
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	−0.975006	+	0.222178i	$0.928683\pi$
$398$		0			0
$399$		−	6.00000i		−	0.300376i
$400$		0			0
$401$	−6.00000	+	6.00000i	−0.299626	+	0.299626i	−0.840867	−	0.541241i	$-0.817954\pi$
$401$	−6.00000	+	6.00000i	−0.299626	+	0.299626i	0.541241	+	0.840867i	$0.317954\pi$
$402$		0			0
$403$	−5.00000	−	1.00000i	−0.249068	−	0.0498135i
$404$		0			0
$405$	−2.00000	+	2.00000i	−0.0993808	+	0.0993808i
$406$		0			0
$407$	−4.00000			−0.198273
$408$		0			0
$409$	−13.0000	−	13.0000i	−0.642809	−	0.642809i	0.308436	−	0.951245i	$-0.400194\pi$
$409$	−13.0000	−	13.0000i	−0.642809	−	0.642809i	−0.951245	+	0.308436i	$0.900194\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.00000			−0.393654
$414$		0			0
$415$	32.0000			1.57082
$416$		0			0
$417$	−10.0000			−0.489702
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−15.0000	+	15.0000i	−0.731055	+	0.731055i	−0.970829	−	0.239774i	$-0.922927\pi$
$421$	−15.0000	+	15.0000i	−0.731055	+	0.731055i	0.239774	+	0.970829i	$0.422927\pi$
$422$		0			0
$423$	8.00000	+	8.00000i	0.388973	+	0.388973i
$424$		0			0
$425$	−18.0000			−0.873128
$426$		0			0
$427$	2.00000	−	2.00000i	0.0967868	−	0.0967868i
$428$		0			0
$429$	−10.0000	−	2.00000i	−0.482805	−	0.0965609i
$430$		0			0
$431$	−12.0000	+	12.0000i	−0.578020	+	0.578020i	−0.934357	−	0.356338i	$-0.884025\pi$
$431$	−12.0000	+	12.0000i	−0.578020	+	0.578020i	0.356338	+	0.934357i	$0.384025\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$		0			0
$435$	4.00000	+	4.00000i	0.191785	+	0.191785i
$436$		0			0
$437$	24.0000	+	24.0000i	1.14808	+	1.14808i
$438$		0			0
$439$	−26.0000			−1.24091			−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000			−1.24091			−0.620456	+	0.784241i	$0.713053\pi$
$440$		0			0
$441$		−	5.00000i		−	0.238095i
$442$		0			0
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$		0			0
$445$			40.0000i			1.89618i
$446$		0			0
$447$	8.00000	−	8.00000i	0.378387	−	0.378387i
$448$		0			0
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	−0.658337	−	0.752723i	$-0.728740\pi$
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	0.752723	+	0.658337i	$0.228740\pi$
$450$		0			0
$451$	32.0000			1.50682
$452$		0			0
$453$	−1.00000	−	1.00000i	−0.0469841	−	0.0469841i
$454$		0			0
$455$	−8.00000	−	12.0000i	−0.375046	−	0.562569i
$456$		0			0
$457$	−19.0000	−	19.0000i	−0.888783	−	0.888783i	0.105624	−	0.994406i	$-0.466316\pi$
$457$	−19.0000	−	19.0000i	−0.888783	−	0.888783i	−0.994406	+	0.105624i	$0.966316\pi$
$458$		0			0
$459$		−	6.00000i		−	0.280056i
$460$		0			0
$461$	−6.00000	+	6.00000i	−0.279448	+	0.279448i	−0.832889	−	0.553441i	$-0.813315\pi$
$461$	−6.00000	+	6.00000i	−0.279448	+	0.279448i	0.553441	+	0.832889i	$0.313315\pi$
$462$		0			0
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	0.884606	−	0.466340i	$-0.154428\pi$
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	−0.466340	+	0.884606i	$0.654428\pi$
$464$		0			0
$465$			4.00000i			0.185496i
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$		−	2.00000i		−	0.0923514i
$470$		0			0
$471$		−	4.00000i		−	0.184310i
$472$		0			0
$473$	−8.00000	−	8.00000i	−0.367840	−	0.367840i
$474$		0			0
$475$	9.00000	−	9.00000i	0.412948	−	0.412948i
$476$		0			0
$477$		−	2.00000i		−	0.0915737i
$478$		0			0
$479$	−2.00000	−	2.00000i	−0.0913823	−	0.0913823i	0.659938	−	0.751320i	$-0.270583\pi$
$479$	−2.00000	−	2.00000i	−0.0913823	−	0.0913823i	−0.751320	+	0.659938i	$0.770583\pi$
$480$		0			0
$481$	−1.00000	+	5.00000i	−0.0455961	+	0.227980i
$482$		0			0
$483$	−8.00000	−	8.00000i	−0.364013	−	0.364013i
$484$		0			0
$485$	20.0000			0.908153
$486$		0			0
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	−0.280221	−	0.959936i	$-0.590408\pi$
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	0.959936	+	0.280221i	$0.0904077\pi$
$488$		0			0
$489$	9.00000	−	9.00000i	0.406994	−	0.406994i
$490$		0			0
$491$			28.0000i			1.26362i	0.775122	+	0.631811i	$0.217688\pi$
$491$			28.0000i			1.26362i	−0.775122	+	0.631811i	$0.782312\pi$
$492$		0			0
$493$	−12.0000			−0.540453
$494$		0			0
$495$			8.00000i			0.359573i
$496$		0			0
$497$	−12.0000			−0.538274
$498$		0			0
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	0.771060	−	0.636762i	$-0.219727\pi$
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	−0.636762	+	0.771060i	$0.719727\pi$
$500$		0			0
$501$	4.00000	+	4.00000i	0.178707	+	0.178707i
$502$		0			0
$503$			28.0000i			1.24846i	0.781241	+	0.624229i	$0.214587\pi$
$503$			28.0000i			1.24846i	−0.781241	+	0.624229i	$0.785413\pi$
$504$		0			0
$505$	12.0000	−	12.0000i	0.533993	−	0.533993i
$506$		0			0
$507$	−5.00000	+	12.0000i	−0.222058	+	0.532939i
$508$		0			0
$509$	−14.0000	+	14.0000i	−0.620539	+	0.620539i	−0.945669	−	0.325130i	$-0.894592\pi$
$509$	−14.0000	+	14.0000i	−0.620539	+	0.620539i	0.325130	+	0.945669i	$0.394592\pi$
$510$		0			0
$511$	18.0000			0.796273
$512$		0			0
$513$	3.00000	+	3.00000i	0.132453	+	0.132453i
$514$		0			0
$515$	20.0000	−	20.0000i	0.881305	−	0.881305i
$516$		0			0
$517$	32.0000			1.40736
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	30.0000			1.31181			0.655904	−	0.754844i	$-0.272288\pi$
$523$	30.0000			1.31181			0.655904	+	0.754844i	$0.272288\pi$
$524$		0			0
$525$	−3.00000	+	3.00000i	−0.130931	+	0.130931i
$526$		0			0
$527$	−6.00000	−	6.00000i	−0.261364	−	0.261364i
$528$		0			0
$529$	41.0000			1.78261
$530$		0			0
$531$	4.00000	−	4.00000i	0.173585	−	0.173585i
$532$		0			0
$533$	8.00000	−	40.0000i	0.346518	−	1.73259i
$534$		0			0
$535$	−32.0000	+	32.0000i	−1.38348	+	1.38348i
$536$		0			0
$537$			8.00000i			0.345225i
$538$		0			0
$539$	−10.0000	−	10.0000i	−0.430730	−	0.430730i
$540$		0			0
$541$	21.0000	+	21.0000i	0.902861	+	0.902861i	0.995683	−	0.0928222i	$-0.0295888\pi$
$541$	21.0000	+	21.0000i	0.902861	+	0.902861i	−0.0928222	+	0.995683i	$0.529589\pi$
$542$		0			0
$543$	26.0000			1.11577
$544$		0			0
$545$		−	4.00000i		−	0.171341i
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$		0			0
$549$			2.00000i			0.0853579i
$550$		0			0
$551$	6.00000	−	6.00000i	0.255609	−	0.255609i
$552$		0			0
$553$	−10.0000	+	10.0000i	−0.425243	+	0.425243i
$554$		0			0
$555$	4.00000			0.169791
$556$		0			0
$557$	28.0000	+	28.0000i	1.18640	+	1.18640i	0.978056	+	0.208342i	$0.0668067\pi$
$557$	28.0000	+	28.0000i	1.18640	+	1.18640i	0.208342	+	0.978056i	$0.433193\pi$
$558$		0			0
$559$	−12.0000	+	8.00000i	−0.507546	+	0.338364i
$560$		0			0
$561$	−12.0000	−	12.0000i	−0.506640	−	0.506640i
$562$		0			0
$563$			28.0000i			1.18006i	0.807382	+	0.590030i	$0.200884\pi$
$563$			28.0000i			1.18006i	−0.807382	+	0.590030i	$0.799116\pi$
$564$		0			0
$565$	36.0000	−	36.0000i	1.51453	−	1.51453i
$566$		0			0
$567$	−1.00000	−	1.00000i	−0.0419961	−	0.0419961i
$568$		0			0
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		0			0
$571$			14.0000i			0.585882i	0.956131	+	0.292941i	$0.0946339\pi$
$571$			14.0000i			0.585882i	−0.956131	+	0.292941i	$0.905366\pi$
$572$		0			0
$573$		−	24.0000i		−	1.00261i
$574$		0			0
$575$		−	24.0000i		−	1.00087i
$576$		0			0
$577$	27.0000	+	27.0000i	1.12402	+	1.12402i	0.991130	+	0.132895i	$0.0424272\pi$
$577$	27.0000	+	27.0000i	1.12402	+	1.12402i	0.132895	+	0.991130i	$0.457573\pi$
$578$		0			0
$579$	−9.00000	+	9.00000i	−0.374027	+	0.374027i
$580$		0			0
$581$			16.0000i			0.663792i
$582$		0			0
$583$	−4.00000	−	4.00000i	−0.165663	−	0.165663i
$584$		0			0
$585$	10.0000	+	2.00000i	0.413449	+	0.0826898i
$586$		0			0
$587$	−12.0000	−	12.0000i	−0.495293	−	0.495293i	0.414676	−	0.909969i	$-0.363895\pi$
$587$	−12.0000	−	12.0000i	−0.495293	−	0.495293i	−0.909969	+	0.414676i	$0.863895\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$		0			0
$591$	2.00000	−	2.00000i	0.0822690	−	0.0822690i
$592$		0			0
$593$	14.0000	−	14.0000i	0.574911	−	0.574911i	−0.358586	−	0.933497i	$-0.616741\pi$
$593$	14.0000	−	14.0000i	0.574911	−	0.574911i	0.933497	+	0.358586i	$0.116741\pi$
$594$		0			0
$595$		−	24.0000i		−	0.983904i
$596$		0			0
$597$	24.0000			0.982255
$598$		0			0
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$		0			0
$601$	16.0000			0.652654			0.326327	−	0.945257i	$-0.394189\pi$
$601$	16.0000			0.652654			0.326327	+	0.945257i	$0.394189\pi$
$602$		0			0
$603$	1.00000	+	1.00000i	0.0407231	+	0.0407231i
$604$		0			0
$605$	−6.00000	−	6.00000i	−0.243935	−	0.243935i
$606$		0			0
$607$			16.0000i			0.649420i	0.945814	+	0.324710i	$0.105267\pi$
$607$			16.0000i			0.649420i	−0.945814	+	0.324710i	$0.894733\pi$
$608$		0			0
$609$	−2.00000	+	2.00000i	−0.0810441	+	0.0810441i
$610$		0			0
$611$	8.00000	−	40.0000i	0.323645	−	1.61823i
$612$		0			0
$613$	−17.0000	+	17.0000i	−0.686624	+	0.686624i	−0.961484	−	0.274861i	$-0.911368\pi$
$613$	−17.0000	+	17.0000i	−0.686624	+	0.686624i	0.274861	+	0.961484i	$0.411368\pi$
$614$		0			0
$615$	−32.0000			−1.29036
$616$		0			0
$617$	−8.00000	−	8.00000i	−0.322068	−	0.322068i	0.527492	−	0.849560i	$-0.323132\pi$
$617$	−8.00000	−	8.00000i	−0.322068	−	0.322068i	−0.849560	+	0.527492i	$0.823132\pi$
$618$		0			0
$619$	27.0000	−	27.0000i	1.08522	−	1.08522i	0.0892087	−	0.996013i	$-0.471566\pi$
$619$	27.0000	−	27.0000i	1.08522	−	1.08522i	0.996013	−	0.0892087i	$-0.0284338\pi$
$620$		0			0
$621$	8.00000			0.321029
$622$		0			0
$623$	−20.0000			−0.801283
$624$		0			0
$625$	31.0000			1.24000
$626$		0			0
$627$	12.0000			0.479234
$628$		0			0
$629$	−6.00000	+	6.00000i	−0.239236	+	0.239236i
$630$		0			0
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	0.453403	−	0.891306i	$-0.350210\pi$
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	−0.891306	+	0.453403i	$0.850210\pi$
$632$		0			0
$633$	4.00000			0.158986
$634$		0			0
$635$	16.0000	−	16.0000i	0.634941	−	0.634941i
$636$		0			0
$637$	−15.0000	+	10.0000i	−0.594322	+	0.396214i
$638$		0			0
$639$	6.00000	−	6.00000i	0.237356	−	0.237356i
$640$		0			0
$641$			6.00000i			0.236986i	0.992955	+	0.118493i	$0.0378063\pi$
$641$			6.00000i			0.236986i	−0.992955	+	0.118493i	$0.962194\pi$
$642$		0			0
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	0.159103	−	0.987262i	$-0.449140\pi$
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	−0.987262	+	0.159103i	$0.949140\pi$
$644$		0			0
$645$	8.00000	+	8.00000i	0.315000	+	0.315000i
$646$		0			0
$647$	−28.0000			−1.10079			−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000			−1.10079			−0.550397	+	0.834903i	$0.685524\pi$
$648$		0			0
$649$		−	16.0000i		−	0.628055i
$650$		0			0
$651$	−2.00000			−0.0783862
$652$		0			0
$653$		−	26.0000i		−	1.01746i	−0.860927	−	0.508729i	$-0.830115\pi$
$653$		−	26.0000i		−	1.01746i	0.860927	−	0.508729i	$-0.169885\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−9.00000	+	9.00000i	−0.351123	+	0.351123i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−3.00000	−	3.00000i	−0.116686	−	0.116686i	0.646352	−	0.763039i	$-0.276294\pi$
$661$	−3.00000	−	3.00000i	−0.116686	−	0.116686i	−0.763039	+	0.646352i	$0.776294\pi$
$662$		0			0
$663$	−18.0000	+	12.0000i	−0.699062	+	0.466041i
$664$		0			0
$665$	12.0000	+	12.0000i	0.465340	+	0.465340i
$666$		0			0
$667$		−	16.0000i		−	0.619522i
$668$		0			0
$669$	−3.00000	+	3.00000i	−0.115987	+	0.115987i
$670$		0			0
$671$	4.00000	+	4.00000i	0.154418	+	0.154418i
$672$		0			0
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$		0			0
$675$		−	3.00000i		−	0.115470i
$676$		0			0
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$		0			0
$679$			10.0000i			0.383765i
$680$		0			0
$681$	2.00000	+	2.00000i	0.0766402	+	0.0766402i
$682$		0			0
$683$	14.0000	−	14.0000i	0.535695	−	0.535695i	−0.386566	−	0.922262i	$-0.626339\pi$
$683$	14.0000	−	14.0000i	0.535695	−	0.535695i	0.922262	+	0.386566i	$0.126339\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	15.0000	+	15.0000i	0.572286	+	0.572286i
$688$		0			0
$689$	−6.00000	+	4.00000i	−0.228582	+	0.152388i
$690$		0			0
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	0.982919	−	0.184041i	$-0.0589179\pi$
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	−0.184041	+	0.982919i	$0.558918\pi$
$692$		0			0
$693$	−4.00000			−0.151947
$694$		0			0
$695$	20.0000	−	20.0000i	0.758643	−	0.758643i
$696$		0			0
$697$	48.0000	−	48.0000i	1.81813	−	1.81813i
$698$		0			0
$699$		−	14.0000i		−	0.529529i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$		−	6.00000i		−	0.226294i
$704$		0			0
$705$	−32.0000			−1.20519
$706$		0			0
$707$	6.00000	+	6.00000i	0.225653	+	0.225653i
$708$		0			0
$709$	7.00000	+	7.00000i	0.262891	+	0.262891i	0.826227	−	0.563337i	$-0.190483\pi$
$709$	7.00000	+	7.00000i	0.262891	+	0.262891i	−0.563337	+	0.826227i	$0.690483\pi$
$710$		0			0
$711$		−	10.0000i		−	0.375029i
$712$		0			0
$713$	8.00000	−	8.00000i	0.299602	−	0.299602i
$714$		0			0
$715$	24.0000	−	16.0000i	0.897549	−	0.598366i
$716$		0			0
$717$	−10.0000	+	10.0000i	−0.373457	+	0.373457i
$718$		0			0
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	10.0000	+	10.0000i	0.372419	+	0.372419i
$722$		0			0
$723$	−15.0000	+	15.0000i	−0.557856	+	0.557856i
$724$		0			0
$725$	−6.00000			−0.222834
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−24.0000			−0.887672
$732$		0			0
$733$	15.0000	−	15.0000i	0.554038	−	0.554038i	−0.373566	−	0.927604i	$-0.621865\pi$
$733$	15.0000	−	15.0000i	0.554038	−	0.554038i	0.927604	+	0.373566i	$0.121865\pi$
$734$		0			0
$735$	10.0000	+	10.0000i	0.368856	+	0.368856i
$736$		0			0
$737$	4.00000			0.147342
$738$		0			0
$739$	9.00000	−	9.00000i	0.331070	−	0.331070i	−0.521923	−	0.852993i	$-0.674785\pi$
$739$	9.00000	−	9.00000i	0.331070	−	0.331070i	0.852993	+	0.521923i	$0.174785\pi$
$740$		0			0
$741$	3.00000	−	15.0000i	0.110208	−	0.551039i
$742$		0			0
$743$	6.00000	−	6.00000i	0.220119	−	0.220119i	−0.588430	−	0.808548i	$-0.700254\pi$
$743$	6.00000	−	6.00000i	0.220119	−	0.220119i	0.808548	+	0.588430i	$0.200254\pi$
$744$		0			0
$745$			32.0000i			1.17239i
$746$		0			0
$747$	−8.00000	−	8.00000i	−0.292705	−	0.292705i
$748$		0			0
$749$	−16.0000	−	16.0000i	−0.584627	−	0.584627i
$750$		0			0
$751$	−38.0000			−1.38664			−0.693320	−	0.720630i	$-0.743853\pi$
$751$	−38.0000			−1.38664			−0.693320	+	0.720630i	$0.743853\pi$
$752$		0			0
$753$			24.0000i			0.874609i
$754$		0			0
$755$	4.00000			0.145575
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$		0			0
$759$	16.0000	−	16.0000i	0.580763	−	0.580763i
$760$		0			0
$761$	−12.0000	+	12.0000i	−0.435000	+	0.435000i	−0.890325	−	0.455325i	$-0.849523\pi$
$761$	−12.0000	+	12.0000i	−0.435000	+	0.435000i	0.455325	+	0.890325i	$0.349523\pi$
$762$		0			0
$763$	2.00000			0.0724049
$764$		0			0
$765$	12.0000	+	12.0000i	0.433861	+	0.433861i
$766$		0			0
$767$	−20.0000	−	4.00000i	−0.722158	−	0.144432i
$768$		0			0
$769$	−27.0000	−	27.0000i	−0.973645	−	0.973645i	0.0260166	−	0.999662i	$-0.491718\pi$
$769$	−27.0000	−	27.0000i	−0.973645	−	0.973645i	−0.999662	+	0.0260166i	$0.991718\pi$
$770$		0			0
$771$			10.0000i			0.360141i
$772$		0			0
$773$	−24.0000	+	24.0000i	−0.863220	+	0.863220i	−0.991711	−	0.128491i	$-0.958987\pi$
$773$	−24.0000	+	24.0000i	−0.863220	+	0.863220i	0.128491	+	0.991711i	$0.458987\pi$
$774$		0			0
$775$	−3.00000	−	3.00000i	−0.107763	−	0.107763i
$776$		0			0
$777$			2.00000i			0.0717496i
$778$		0			0
$779$			48.0000i			1.71978i
$780$		0			0
$781$		−	24.0000i		−	0.858788i
$782$		0			0
$783$		−	2.00000i		−	0.0714742i
$784$		0			0
$785$	8.00000	+	8.00000i	0.285532	+	0.285532i
$786$		0			0
$787$	13.0000	−	13.0000i	0.463400	−	0.463400i	−0.436368	−	0.899768i	$-0.643735\pi$
$787$	13.0000	−	13.0000i	0.463400	−	0.463400i	0.899768	+	0.436368i	$0.143735\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.0000	+	18.0000i	0.640006	+	0.640006i
$792$		0			0
$793$	6.00000	−	4.00000i	0.213066	−	0.142044i
$794$		0			0
$795$	4.00000	+	4.00000i	0.141865	+	0.141865i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$	48.0000	−	48.0000i	1.69812	−	1.69812i
$800$		0			0
$801$	10.0000	−	10.0000i	0.353333	−	0.353333i
$802$		0			0
$803$			36.0000i			1.27041i
$804$		0			0
$805$	32.0000			1.12785
$806$		0			0
$807$			2.00000i			0.0704033i
$808$		0			0
$809$	22.0000			0.773479			0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000			0.773479			0.386739	+	0.922189i	$0.373601\pi$
$810$		0			0
$811$	1.00000	+	1.00000i	0.0351147	+	0.0351147i	0.724446	−	0.689331i	$-0.242096\pi$
$811$	1.00000	+	1.00000i	0.0351147	+	0.0351147i	−0.689331	+	0.724446i	$0.742096\pi$
$812$		0			0
$813$	13.0000	+	13.0000i	0.455930	+	0.455930i
$814$		0			0
$815$			36.0000i			1.26102i
$816$		0			0
$817$	12.0000	−	12.0000i	0.419827	−	0.419827i
$818$		0			0
$819$	−1.00000	+	5.00000i	−0.0349428	+	0.174714i
$820$		0			0
$821$	−40.0000	+	40.0000i	−1.39601	+	1.39601i	−0.584915	+	0.811095i	$0.698872\pi$
$821$	−40.0000	+	40.0000i	−1.39601	+	1.39601i	−0.811095	+	0.584915i	$0.801128\pi$
$822$		0			0
$823$	−34.0000			−1.18517			−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000			−1.18517			−0.592583	+	0.805510i	$0.701892\pi$
$824$		0			0
$825$	−6.00000	−	6.00000i	−0.208893	−	0.208893i
$826$		0			0
$827$	22.0000	−	22.0000i	0.765015	−	0.765015i	−0.212209	−	0.977224i	$-0.568066\pi$
$827$	22.0000	−	22.0000i	0.765015	−	0.765015i	0.977224	+	0.212209i	$0.0680659\pi$
$828$		0			0
$829$	−40.0000			−1.38926			−0.694629	−	0.719368i	$-0.744431\pi$
$829$	−40.0000			−1.38926			−0.694629	+	0.719368i	$0.744431\pi$
$830$		0			0
$831$	−22.0000			−0.763172
$832$		0			0
$833$	−30.0000			−1.03944
$834$		0			0
$835$	−16.0000			−0.553703
$836$		0			0
$837$	1.00000	−	1.00000i	0.0345651	−	0.0345651i
$838$		0			0
$839$	30.0000	+	30.0000i	1.03572	+	1.03572i	0.999338	+	0.0363769i	$0.0115817\pi$
$839$	30.0000	+	30.0000i	1.03572	+	1.03572i	0.0363769	+	0.999338i	$0.488418\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$		0			0
$843$	−20.0000	+	20.0000i	−0.688837	+	0.688837i
$844$		0			0
$845$	−14.0000	−	34.0000i	−0.481615	−	1.16964i
$846$		0			0
$847$	3.00000	−	3.00000i	0.103081	−	0.103081i
$848$		0			0
$849$		−	6.00000i		−	0.205919i
$850$		0			0
$851$	−8.00000	−	8.00000i	−0.274236	−	0.274236i
$852$		0			0
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	0.402034	−	0.915625i	$-0.368303\pi$
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	−0.915625	+	0.402034i	$0.868303\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$		−	2.00000i		−	0.0683187i	−0.999416	−	0.0341593i	$-0.989125\pi$
$857$		−	2.00000i		−	0.0683187i	0.999416	−	0.0341593i	$-0.0108754\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$		0			0
$861$		−	16.0000i		−	0.545279i
$862$		0			0
$863$	40.0000	−	40.0000i	1.36162	−	1.36162i	0.489757	−	0.871859i	$-0.337086\pi$
$863$	40.0000	−	40.0000i	1.36162	−	1.36162i	0.871859	−	0.489757i	$-0.162914\pi$
$864$		0			0
$865$	12.0000	−	12.0000i	0.408012	−	0.408012i
$866$		0			0
$867$	−19.0000			−0.645274
$868$		0			0
$869$	−20.0000	−	20.0000i	−0.678454	−	0.678454i
$870$		0			0
$871$	1.00000	−	5.00000i	0.0338837	−	0.169419i
$872$		0			0
$873$	−5.00000	−	5.00000i	−0.169224	−	0.169224i
$874$		0			0
$875$			8.00000i			0.270449i
$876$		0			0
$877$	15.0000	−	15.0000i	0.506514	−	0.506514i	−0.406941	−	0.913455i	$-0.633404\pi$
$877$	15.0000	−	15.0000i	0.506514	−	0.506514i	0.913455	+	0.406941i	$0.133404\pi$
$878$		0			0
$879$	16.0000	+	16.0000i	0.539667	+	0.539667i
$880$		0			0
$881$		−	10.0000i		−	0.336909i	−0.985709	−	0.168454i	$-0.946122\pi$
$881$		−	10.0000i		−	0.336909i	0.985709	−	0.168454i	$-0.0538776\pi$
$882$		0			0
$883$		−	26.0000i		−	0.874970i	−0.899226	−	0.437485i	$-0.855869\pi$
$883$		−	26.0000i		−	0.874970i	0.899226	−	0.437485i	$-0.144131\pi$
$884$		0			0
$885$			16.0000i			0.537834i
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		0			0
$889$	8.00000	+	8.00000i	0.268311	+	0.268311i
$890$		0			0
$891$	2.00000	−	2.00000i	0.0670025	−	0.0670025i
$892$		0			0
$893$			48.0000i			1.60626i
$894$		0			0
$895$	−16.0000	−	16.0000i	−0.534821	−	0.534821i
$896$		0			0
$897$	−16.0000	−	24.0000i	−0.534224	−	0.801337i
$898$		0			0
$899$	−2.00000	−	2.00000i	−0.0667037	−	0.0667037i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	−4.00000	+	4.00000i	−0.133112	+	0.133112i
$904$		0			0
$905$	−52.0000	+	52.0000i	−1.72854	+	1.72854i
$906$		0			0
$907$			26.0000i			0.863316i	0.902037	+	0.431658i	$0.142071\pi$
$907$			26.0000i			0.863316i	−0.902037	+	0.431658i	$0.857929\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$			24.0000i			0.795155i	0.917568	+	0.397578i	$0.130149\pi$
$911$			24.0000i			0.795155i	−0.917568	+	0.397578i	$0.869851\pi$
$912$		0			0
$913$	−32.0000			−1.05905
$914$		0			0
$915$	−4.00000	−	4.00000i	−0.132236	−	0.132236i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			10.0000i			0.329870i	0.986304	+	0.164935i	$0.0527414\pi$
$919$			10.0000i			0.329870i	−0.986304	+	0.164935i	$0.947259\pi$
$920$		0			0
$921$	−21.0000	+	21.0000i	−0.691974	+	0.691974i
$922$		0			0
$923$	−30.0000	−	6.00000i	−0.987462	−	0.197492i
$924$		0			0
$925$	−3.00000	+	3.00000i	−0.0986394	+	0.0986394i
$926$		0			0
$927$	−10.0000			−0.328443
$928$		0			0
$929$	−16.0000	−	16.0000i	−0.524943	−	0.524943i	0.394117	−	0.919060i	$-0.371050\pi$
$929$	−16.0000	−	16.0000i	−0.524943	−	0.524943i	−0.919060	+	0.394117i	$0.871050\pi$
$930$		0			0
$931$	15.0000	−	15.0000i	0.491605	−	0.491605i
$932$		0			0
$933$	16.0000			0.523816
$934$		0			0
$935$	48.0000			1.56977
$936$		0			0
$937$	−20.0000			−0.653372			−0.326686	−	0.945133i	$-0.605932\pi$
$937$	−20.0000			−0.653372			−0.326686	+	0.945133i	$0.605932\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	28.0000	−	28.0000i	0.912774	−	0.912774i	−0.0837158	−	0.996490i	$-0.526679\pi$
$941$	28.0000	−	28.0000i	0.912774	−	0.912774i	0.996490	+	0.0837158i	$0.0266788\pi$
$942$		0			0
$943$	64.0000	+	64.0000i	2.08413	+	2.08413i
$944$		0			0
$945$	4.00000			0.130120
$946$		0			0
$947$	−20.0000	+	20.0000i	−0.649913	+	0.649913i	−0.952972	−	0.303059i	$-0.901992\pi$
$947$	−20.0000	+	20.0000i	−0.649913	+	0.649913i	0.303059	+	0.952972i	$0.401992\pi$
$948$		0			0
$949$	45.0000	+	9.00000i	1.46076	+	0.292152i
$950$		0			0
$951$	2.00000	−	2.00000i	0.0648544	−	0.0648544i
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$		0			0
$955$	48.0000	+	48.0000i	1.55324	+	1.55324i
$956$		0			0
$957$	−4.00000	−	4.00000i	−0.129302	−	0.129302i
$958$		0			0
$959$		0			0
$960$		0			0
$961$			29.0000i			0.935484i
$962$		0			0
$963$	16.0000			0.515593
$964$		0			0
$965$		−	36.0000i		−	1.15888i
$966$		0			0
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.0632081	+	0.998000i	$0.520133\pi$
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.998000	+	0.0632081i	$0.979867\pi$
$968$		0			0
$969$	18.0000	−	18.0000i	0.578243	−	0.578243i
$970$		0			0
$971$	40.0000			1.28366			0.641831	−	0.766846i	$-0.278175\pi$
$971$	40.0000			1.28366			0.641831	+	0.766846i	$0.278175\pi$
$972$		0			0
$973$	10.0000	+	10.0000i	0.320585	+	0.320585i
$974$		0			0
$975$	−9.00000	+	6.00000i	−0.288231	+	0.192154i
$976$		0			0
$977$	−26.0000	−	26.0000i	−0.831814	−	0.831814i	0.155951	−	0.987765i	$-0.450156\pi$
$977$	−26.0000	−	26.0000i	−0.831814	−	0.831814i	−0.987765	+	0.155951i	$0.950156\pi$
$978$		0			0
$979$		−	40.0000i		−	1.27841i
$980$		0			0
$981$	−1.00000	+	1.00000i	−0.0319275	+	0.0319275i
$982$		0			0
$983$	30.0000	+	30.0000i	0.956851	+	0.956851i	0.999107	−	0.0422554i	$-0.0134543\pi$
$983$	30.0000	+	30.0000i	0.956851	+	0.956851i	−0.0422554	+	0.999107i	$0.513454\pi$
$984$		0			0
$985$			8.00000i			0.254901i
$986$		0			0
$987$		−	16.0000i		−	0.509286i
$988$		0			0
$989$		−	32.0000i		−	1.01754i
$990$		0			0
$991$		−	40.0000i		−	1.27064i	−0.772248	−	0.635321i	$-0.780868\pi$
$991$		−	40.0000i		−	1.27064i	0.772248	−	0.635321i	$-0.219132\pi$
$992$		0			0
$993$	11.0000	+	11.0000i	0.349074	+	0.349074i
$994$		0			0
$995$	−48.0000	+	48.0000i	−1.52170	+	1.52170i
$996$		0			0
$997$			40.0000i			1.26681i	0.773819	+	0.633406i	$0.218344\pi$
$997$			40.0000i			1.26681i	−0.773819	+	0.633406i	$0.781656\pi$
$998$		0			0
$999$	−1.00000	−	1.00000i	−0.0316386	−	0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.c.463.1		2
4.3	odd	2		312.2.t.a.307.1	yes	2
8.3	odd	2		1248.2.bb.d.463.1		2
8.5	even	2		312.2.t.d.307.1	yes	2
12.11	even	2		936.2.w.d.307.1		2
13.5	odd	4		1248.2.bb.d.655.1		2
24.5	odd	2		936.2.w.a.307.1		2
52.31	even	4		312.2.t.d.187.1	yes	2
104.5	odd	4		312.2.t.a.187.1	✓	2
104.83	even	4	inner	1248.2.bb.c.655.1		2
156.83	odd	4		936.2.w.a.811.1		2
312.5	even	4		936.2.w.d.811.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.a.187.1	✓	2	104.5	odd	4
312.2.t.a.307.1	yes	2	4.3	odd	2
312.2.t.d.187.1	yes	2	52.31	even	4
312.2.t.d.307.1	yes	2	8.5	even	2
936.2.w.a.307.1		2	24.5	odd	2
936.2.w.a.811.1		2	156.83	odd	4
936.2.w.d.307.1		2	12.11	even	2
936.2.w.d.811.1		2	312.5	even	4
1248.2.bb.c.463.1		2	1.1	even	1	trivial
1248.2.bb.c.655.1		2	104.83	even	4	inner
1248.2.bb.d.463.1		2	8.3	odd	2
1248.2.bb.d.655.1		2	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +(-2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{9} +(2.00000 - 2.00000i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(-2.00000 + 2.00000i) q^{15} -6.00000i q^{17} +(3.00000 + 3.00000i) q^{19} +(-1.00000 - 1.00000i) q^{21} +8.00000 q^{23} -3.00000i q^{25} +1.00000 q^{27} -2.00000i q^{29} +(1.00000 - 1.00000i) q^{31} +(2.00000 - 2.00000i) q^{33} +4.00000 q^{35} +(-1.00000 - 1.00000i) q^{37} +(-2.00000 - 3.00000i) q^{39} +(8.00000 + 8.00000i) q^{41} -4.00000i q^{43} +(-2.00000 + 2.00000i) q^{45} +(8.00000 + 8.00000i) q^{47} -5.00000i q^{49} -6.00000i q^{51} -2.00000i q^{53} +8.00000i q^{55} +(3.00000 + 3.00000i) q^{57} +(4.00000 - 4.00000i) q^{59} +2.00000i q^{61} +(-1.00000 - 1.00000i) q^{63} +(10.0000 + 2.00000i) q^{65} +(1.00000 + 1.00000i) q^{67} +8.00000 q^{69} +(6.00000 - 6.00000i) q^{71} +(-9.00000 + 9.00000i) q^{73} -3.00000i q^{75} -4.00000 q^{77} -10.0000i q^{79} +1.00000 q^{81} +(-8.00000 - 8.00000i) q^{83} +(12.0000 + 12.0000i) q^{85} -2.00000i q^{87} +(10.0000 - 10.0000i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(1.00000 - 1.00000i) q^{93} -12.0000 q^{95} +(-5.00000 - 5.00000i) q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 2 q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{15} + 6 q^{19} - 2 q^{21} + 16 q^{23} + 2 q^{27} + 2 q^{31} + 4 q^{33} + 8 q^{35} - 2 q^{37} - 4 q^{39} + 16 q^{41} - 4 q^{45} + 16 q^{47} + 6 q^{57} + 8 q^{59} - 2 q^{63} + 20 q^{65} + 2 q^{67} + 16 q^{69} + 12 q^{71} - 18 q^{73} - 8 q^{77} + 2 q^{81} - 16 q^{83} + 24 q^{85} + 20 q^{89} - 2 q^{91} + 2 q^{93} - 24 q^{95} - 10 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 2 * q^9 + 4 * q^11 - 4 * q^13 - 4 * q^15 + 6 * q^19 - 2 * q^21 + 16 * q^23 + 2 * q^27 + 2 * q^31 + 4 * q^33 + 8 * q^35 - 2 * q^37 - 4 * q^39 + 16 * q^41 - 4 * q^45 + 16 * q^47 + 6 * q^57 + 8 * q^59 - 2 * q^63 + 20 * q^65 + 2 * q^67 + 16 * q^69 + 12 * q^71 - 18 * q^73 - 8 * q^77 + 2 * q^81 - 16 * q^83 + 24 * q^85 + 20 * q^89 - 2 * q^91 + 2 * q^93 - 24 * q^95 - 10 * q^97 + 4 * q^99

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