LMFDB - Embedded newform 1280.2.o.d.383.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(127,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1280.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.o (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:	$10.2208514587$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			383.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.383
Dual form			1280.2.o.d.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +6.00000 q^{11} +(-1.00000 + 1.00000i) q^{13} +(3.00000 + 1.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +4.00000i q^{19} +2.00000i q^{21} +(5.00000 - 5.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} -8.00000 q^{29} +2.00000i q^{31} +(-6.00000 - 6.00000i) q^{33} +(3.00000 + 1.00000i) q^{35} +(-5.00000 - 5.00000i) q^{37} +2.00000 q^{39} -6.00000 q^{41} +(-3.00000 - 3.00000i) q^{43} +(1.00000 + 2.00000i) q^{45} +(-7.00000 - 7.00000i) q^{47} -5.00000i q^{49} -2.00000 q^{51} +(1.00000 - 1.00000i) q^{53} +(-12.0000 + 6.00000i) q^{55} +(4.00000 - 4.00000i) q^{57} -4.00000i q^{59} -2.00000i q^{61} +(-1.00000 + 1.00000i) q^{63} +(1.00000 - 3.00000i) q^{65} +(7.00000 - 7.00000i) q^{67} -10.0000 q^{69} +6.00000i q^{71} +(-9.00000 - 9.00000i) q^{73} +(-7.00000 + 1.00000i) q^{75} +(-6.00000 - 6.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(-5.00000 - 5.00000i) q^{83} +(-1.00000 + 3.00000i) q^{85} +(8.00000 + 8.00000i) q^{87} +2.00000 q^{91} +(2.00000 - 2.00000i) q^{93} +(-4.00000 - 8.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} -6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{5} - 2 q^{7}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^5 - 2 * q^7	$ 2 q - 2 q^{3} - 4 q^{5} - 2 q^{7} + 12 q^{11} - 2 q^{13} + 6 q^{15} + 2 q^{17} + 10 q^{23} + 6 q^{25} - 8 q^{27} - 16 q^{29} - 12 q^{33} + 6 q^{35} - 10 q^{37} + 4 q^{39} - 12 q^{41} - 6 q^{43} + 2 q^{45} - 14 q^{47} - 4 q^{51} + 2 q^{53} - 24 q^{55} + 8 q^{57} - 2 q^{63} + 2 q^{65} + 14 q^{67} - 20 q^{69} - 18 q^{73} - 14 q^{75} - 12 q^{77} + 16 q^{79} + 10 q^{81} - 10 q^{83} - 2 q^{85} + 16 q^{87} + 4 q^{91} + 4 q^{93} - 8 q^{95} - 6 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^5 - 2 * q^7 + 12 * q^11 - 2 * q^13 + 6 * q^15 + 2 * q^17 + 10 * q^23 + 6 * q^25 - 8 * q^27 - 16 * q^29 - 12 * q^33 + 6 * q^35 - 10 * q^37 + 4 * q^39 - 12 * q^41 - 6 * q^43 + 2 * q^45 - 14 * q^47 - 4 * q^51 + 2 * q^53 - 24 * q^55 + 8 * q^57 - 2 * q^63 + 2 * q^65 + 14 * q^67 - 20 * q^69 - 18 * q^73 - 14 * q^75 - 12 * q^77 + 16 * q^79 + 10 * q^81 - 10 * q^83 - 2 * q^85 + 16 * q^87 + 4 * q^91 + 4 * q^93 - 8 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$		0			0
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		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
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$	−1.00000	+	1.00000i	−0.277350	+	0.277350i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−1.00000	+	1.00000i	−0.277350	+	0.277350i	0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	3.00000	+	1.00000i	0.774597	+	0.258199i
$16$		0			0
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$			2.00000i			0.436436i
$22$		0			0
$23$	5.00000	−	5.00000i	1.04257	−	1.04257i	0.0435195	−	0.999053i	$-0.486143\pi$
$23$	5.00000	−	5.00000i	1.04257	−	1.04257i	0.999053	−	0.0435195i	$-0.0138571\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$			2.00000i			0.359211i	0.983739	+	0.179605i	$0.0574821\pi$
$31$			2.00000i			0.359211i	−0.983739	+	0.179605i	$0.942518\pi$
$32$		0			0
$33$	−6.00000	−	6.00000i	−1.04447	−	1.04447i
$34$		0			0
$35$	3.00000	+	1.00000i	0.507093	+	0.169031i
$36$		0			0
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	0.440337	−	0.897833i	$-0.354859\pi$
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	−0.897833	+	0.440337i	$0.854859\pi$
$44$		0			0
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$		0			0
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.999774	−	0.0212814i	$-0.993225\pi$
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.0212814	−	0.999774i	$-0.506775\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$		0			0
$55$	−12.0000	+	6.00000i	−1.61808	+	0.809040i
$56$		0			0
$57$	4.00000	−	4.00000i	0.529813	−	0.529813i
$58$		0			0
$59$		−	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
$61$		−	2.00000i		−	0.256074i	−0.991769	−	0.128037i	$-0.959132\pi$
$61$		−	2.00000i		−	0.256074i	0.991769	−	0.128037i	$-0.0408676\pi$
$62$		0			0
$63$	−1.00000	+	1.00000i	−0.125988	+	0.125988i
$64$		0			0
$65$	1.00000	−	3.00000i	0.124035	−	0.372104i
$66$		0			0
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	−0.135580	−	0.990766i	$-0.543290\pi$
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	0.990766	+	0.135580i	$0.0432899\pi$
$68$		0			0
$69$	−10.0000			−1.20386
$70$		0			0
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$		0			0
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.998493	−	0.0548772i	$-0.982523\pi$
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.0548772	−	0.998493i	$-0.517477\pi$
$74$		0			0
$75$	−7.00000	+	1.00000i	−0.808290	+	0.115470i
$76$		0			0
$77$	−6.00000	−	6.00000i	−0.683763	−	0.683763i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	0.377279	−	0.926100i	$-0.376860\pi$
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	−0.926100	+	0.377279i	$0.876860\pi$
$84$		0			0
$85$	−1.00000	+	3.00000i	−0.108465	+	0.325396i
$86$		0			0
$87$	8.00000	+	8.00000i	0.857690	+	0.857690i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$		0			0
$93$	2.00000	−	2.00000i	0.207390	−	0.207390i
$94$		0			0
$95$	−4.00000	−	8.00000i	−0.410391	−	0.820783i
$96$		0			0
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$		0			0
$99$		−	6.00000i		−	0.603023i
$100$		0			0
$101$			6.00000i			0.597022i	0.954406	+	0.298511i	$0.0964900\pi$
$101$			6.00000i			0.597022i	−0.954406	+	0.298511i	$0.903510\pi$
$102$		0			0
$103$	−3.00000	+	3.00000i	−0.295599	+	0.295599i	−0.839287	−	0.543688i	$-0.817027\pi$
$103$	−3.00000	+	3.00000i	−0.295599	+	0.295599i	0.543688	+	0.839287i	$0.317027\pi$
$104$		0			0
$105$	−2.00000	−	4.00000i	−0.195180	−	0.390360i
$106$		0			0
$107$	−3.00000	+	3.00000i	−0.290021	+	0.290021i	−0.837088	−	0.547068i	$-0.815744\pi$
$107$	−3.00000	+	3.00000i	−0.290021	+	0.290021i	0.547068	+	0.837088i	$0.315744\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$			10.0000i			0.949158i
$112$		0			0
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	0.551776	−	0.833992i	$-0.313950\pi$
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	−0.833992	+	0.551776i	$0.813950\pi$
$114$		0			0
$115$	−5.00000	+	15.0000i	−0.466252	+	1.39876i
$116$		0			0
$117$	1.00000	+	1.00000i	0.0924500	+	0.0924500i
$118$		0			0
$119$	−2.00000			−0.183340
$120$		0			0
$121$	25.0000			2.27273
$122$		0			0
$123$	6.00000	+	6.00000i	0.541002	+	0.541002i
$124$		0			0
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	5.00000	+	5.00000i	0.443678	+	0.443678i	0.893246	−	0.449568i	$-0.148422\pi$
$127$	5.00000	+	5.00000i	0.443678	+	0.443678i	−0.449568	+	0.893246i	$0.648422\pi$
$128$		0			0
$129$			6.00000i			0.528271i
$130$		0			0
$131$	2.00000			0.174741			0.0873704	−	0.996176i	$-0.472154\pi$
$131$	2.00000			0.174741			0.0873704	+	0.996176i	$0.472154\pi$
$132$		0			0
$133$	4.00000	−	4.00000i	0.346844	−	0.346844i
$134$		0			0
$135$	4.00000	−	12.0000i	0.344265	−	1.03280i
$136$		0			0
$137$	−13.0000	+	13.0000i	−1.11066	+	1.11066i	−0.117604	+	0.993061i	$0.537521\pi$
$137$	−13.0000	+	13.0000i	−1.11066	+	1.11066i	−0.993061	+	0.117604i	$0.962479\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$			14.0000i			1.17901i
$142$		0			0
$143$	−6.00000	+	6.00000i	−0.501745	+	0.501745i
$144$		0			0
$145$	16.0000	−	8.00000i	1.32873	−	0.664364i
$146$		0			0
$147$	−5.00000	+	5.00000i	−0.412393	+	0.412393i
$148$		0			0
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$		0			0
$151$		−	18.0000i		−	1.46482i	−0.680864	−	0.732410i	$-0.738396\pi$
$151$		−	18.0000i		−	1.46482i	0.680864	−	0.732410i	$-0.261604\pi$
$152$		0			0
$153$	−1.00000	−	1.00000i	−0.0808452	−	0.0808452i
$154$		0			0
$155$	−2.00000	−	4.00000i	−0.160644	−	0.321288i
$156$		0			0
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	0.577186	−	0.816612i	$-0.304151\pi$
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	−0.816612	+	0.577186i	$0.804151\pi$
$158$		0			0
$159$	−2.00000			−0.158610
$160$		0			0
$161$	−10.0000			−0.788110
$162$		0			0
$163$	−1.00000	−	1.00000i	−0.0783260	−	0.0783260i	0.666858	−	0.745184i	$-0.267639\pi$
$163$	−1.00000	−	1.00000i	−0.0783260	−	0.0783260i	−0.745184	+	0.666858i	$0.767639\pi$
$164$		0			0
$165$	18.0000	+	6.00000i	1.40130	+	0.467099i
$166$		0			0
$167$	−5.00000	−	5.00000i	−0.386912	−	0.386912i	0.486673	−	0.873584i	$-0.338210\pi$
$167$	−5.00000	−	5.00000i	−0.386912	−	0.386912i	−0.873584	+	0.486673i	$0.838210\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$		0			0
$171$	4.00000			0.305888
$172$		0			0
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	−0.389026	−	0.921227i	$-0.627189\pi$
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	0.921227	+	0.389026i	$0.127189\pi$
$174$		0			0
$175$	−7.00000	+	1.00000i	−0.529150	+	0.0755929i
$176$		0			0
$177$	−4.00000	+	4.00000i	−0.300658	+	0.300658i
$178$		0			0
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$		0			0
$181$		−	10.0000i		−	0.743294i	−0.928374	−	0.371647i	$-0.878793\pi$
$181$		−	10.0000i		−	0.743294i	0.928374	−	0.371647i	$-0.121207\pi$
$182$		0			0
$183$	−2.00000	+	2.00000i	−0.147844	+	0.147844i
$184$		0			0
$185$	15.0000	+	5.00000i	1.10282	+	0.367607i
$186$		0			0
$187$	6.00000	−	6.00000i	0.438763	−	0.438763i
$188$		0			0
$189$	8.00000			0.581914
$190$		0			0
$191$			10.0000i			0.723575i	0.932261	+	0.361787i	$0.117833\pi$
$191$			10.0000i			0.723575i	−0.932261	+	0.361787i	$0.882167\pi$
$192$		0			0
$193$	1.00000	+	1.00000i	0.0719816	+	0.0719816i	0.742181	−	0.670199i	$-0.233791\pi$
$193$	1.00000	+	1.00000i	0.0719816	+	0.0719816i	−0.670199	+	0.742181i	$0.733791\pi$
$194$		0			0
$195$	−4.00000	+	2.00000i	−0.286446	+	0.143223i
$196$		0			0
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	0.670585	−	0.741832i	$-0.266043\pi$
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	−0.741832	+	0.670585i	$0.766043\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	−14.0000			−0.987484
$202$		0			0
$203$	8.00000	+	8.00000i	0.561490	+	0.561490i
$204$		0			0
$205$	12.0000	−	6.00000i	0.838116	−	0.419058i
$206$		0			0
$207$	−5.00000	−	5.00000i	−0.347524	−	0.347524i
$208$		0			0
$209$			24.0000i			1.66011i
$210$		0			0
$211$	10.0000			0.688428			0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000			0.688428			0.344214	+	0.938891i	$0.388145\pi$
$212$		0			0
$213$	6.00000	−	6.00000i	0.411113	−	0.411113i
$214$		0			0
$215$	9.00000	+	3.00000i	0.613795	+	0.204598i
$216$		0			0
$217$	2.00000	−	2.00000i	0.135769	−	0.135769i
$218$		0			0
$219$			18.0000i			1.21633i
$220$		0			0
$221$			2.00000i			0.134535i
$222$		0			0
$223$	19.0000	−	19.0000i	1.27233	−	1.27233i	0.327474	−	0.944860i	$-0.393803\pi$
$223$	19.0000	−	19.0000i	1.27233	−	1.27233i	0.944860	−	0.327474i	$-0.106197\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$		0			0
$227$	−13.0000	+	13.0000i	−0.862840	+	0.862840i	−0.991667	−	0.128827i	$-0.958879\pi$
$227$	−13.0000	+	13.0000i	−0.862840	+	0.862840i	0.128827	+	0.991667i	$0.458879\pi$
$228$		0			0
$229$	16.0000			1.05731			0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000			1.05731			0.528655	+	0.848837i	$0.322697\pi$
$230$		0			0
$231$			12.0000i			0.789542i
$232$		0			0
$233$	−13.0000	−	13.0000i	−0.851658	−	0.851658i	0.138679	−	0.990337i	$-0.455714\pi$
$233$	−13.0000	−	13.0000i	−0.851658	−	0.851658i	−0.990337	+	0.138679i	$0.955714\pi$
$234$		0			0
$235$	21.0000	+	7.00000i	1.36989	+	0.456630i
$236$		0			0
$237$	−8.00000	−	8.00000i	−0.519656	−	0.519656i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$		0			0
$245$	5.00000	+	10.0000i	0.319438	+	0.638877i
$246$		0			0
$247$	−4.00000	−	4.00000i	−0.254514	−	0.254514i
$248$		0			0
$249$			10.0000i			0.633724i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	30.0000	−	30.0000i	1.88608	−	1.88608i
$254$		0			0
$255$	4.00000	−	2.00000i	0.250490	−	0.125245i
$256$		0			0
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	−0.961381	−	0.275220i	$-0.911249\pi$
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	0.275220	+	0.961381i	$0.411249\pi$
$258$		0			0
$259$			10.0000i			0.621370i
$260$		0			0
$261$			8.00000i			0.495188i
$262$		0			0
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	−0.372906	−	0.927869i	$-0.621638\pi$
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	0.927869	+	0.372906i	$0.121638\pi$
$264$		0			0
$265$	−1.00000	+	3.00000i	−0.0614295	+	0.184289i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$		0			0
$271$		−	22.0000i		−	1.33640i	−0.743980	−	0.668202i	$-0.767064\pi$
$271$		−	22.0000i		−	1.33640i	0.743980	−	0.668202i	$-0.232936\pi$
$272$		0			0
$273$	−2.00000	−	2.00000i	−0.121046	−	0.121046i
$274$		0			0
$275$	18.0000	−	24.0000i	1.08544	−	1.44725i
$276$		0			0
$277$	−9.00000	−	9.00000i	−0.540758	−	0.540758i	0.382993	−	0.923751i	$-0.374893\pi$
$277$	−9.00000	−	9.00000i	−0.540758	−	0.540758i	−0.923751	+	0.382993i	$0.874893\pi$
$278$		0			0
$279$	2.00000			0.119737
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$		0			0
$285$	−4.00000	+	12.0000i	−0.236940	+	0.710819i
$286$		0			0
$287$	6.00000	+	6.00000i	0.354169	+	0.354169i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$	6.00000			0.351726
$292$		0			0
$293$	17.0000	−	17.0000i	0.993151	−	0.993151i	−0.00682610	−	0.999977i	$-0.502173\pi$
$293$	17.0000	−	17.0000i	0.993151	−	0.993151i	0.999977	+	0.00682610i	$0.00217283\pi$
$294$		0			0
$295$	4.00000	+	8.00000i	0.232889	+	0.465778i
$296$		0			0
$297$	−24.0000	+	24.0000i	−1.39262	+	1.39262i
$298$		0			0
$299$			10.0000i			0.578315i
$300$		0			0
$301$			6.00000i			0.345834i
$302$		0			0
$303$	6.00000	−	6.00000i	0.344691	−	0.344691i
$304$		0			0
$305$	2.00000	+	4.00000i	0.114520	+	0.229039i
$306$		0			0
$307$	7.00000	−	7.00000i	0.399511	−	0.399511i	−0.478549	−	0.878061i	$-0.658837\pi$
$307$	7.00000	−	7.00000i	0.399511	−	0.399511i	0.878061	+	0.478549i	$0.158837\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$		0			0
$311$			22.0000i			1.24751i	0.781622	+	0.623753i	$0.214393\pi$
$311$			22.0000i			1.24751i	−0.781622	+	0.623753i	$0.785607\pi$
$312$		0			0
$313$	15.0000	+	15.0000i	0.847850	+	0.847850i	0.989865	−	0.142014i	$-0.0453579\pi$
$313$	15.0000	+	15.0000i	0.847850	+	0.847850i	−0.142014	+	0.989865i	$0.545358\pi$
$314$		0			0
$315$	1.00000	−	3.00000i	0.0563436	−	0.169031i
$316$		0			0
$317$	25.0000	+	25.0000i	1.40414	+	1.40414i	0.786318	+	0.617822i	$0.211985\pi$
$317$	25.0000	+	25.0000i	1.40414	+	1.40414i	0.617822	+	0.786318i	$0.288015\pi$
$318$		0			0
$319$	−48.0000			−2.68748
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	4.00000	+	4.00000i	0.222566	+	0.222566i
$324$		0			0
$325$	1.00000	+	7.00000i	0.0554700	+	0.388290i
$326$		0			0
$327$	4.00000	+	4.00000i	0.221201	+	0.221201i
$328$		0			0
$329$			14.0000i			0.771845i
$330$		0			0
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$		0			0
$333$	−5.00000	+	5.00000i	−0.273998	+	0.273998i
$334$		0			0
$335$	−7.00000	+	21.0000i	−0.382451	+	1.14735i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$			6.00000i			0.325875i
$340$		0			0
$341$			12.0000i			0.649836i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	20.0000	−	10.0000i	1.07676	−	0.538382i
$346$		0			0
$347$	9.00000	−	9.00000i	0.483145	−	0.483145i	−0.422989	−	0.906135i	$-0.639019\pi$
$347$	9.00000	−	9.00000i	0.483145	−	0.483145i	0.906135	+	0.422989i	$0.139019\pi$
$348$		0			0
$349$	−32.0000			−1.71292			−0.856460	−	0.516213i	$-0.827341\pi$
$349$	−32.0000			−1.71292			−0.856460	+	0.516213i	$0.827341\pi$
$350$		0			0
$351$		−	8.00000i		−	0.427008i
$352$		0			0
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	0.184469	−	0.982838i	$-0.440943\pi$
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	−0.982838	+	0.184469i	$0.940943\pi$
$354$		0			0
$355$	−6.00000	−	12.0000i	−0.318447	−	0.636894i
$356$		0			0
$357$	2.00000	+	2.00000i	0.105851	+	0.105851i
$358$		0			0
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$	−25.0000	−	25.0000i	−1.31216	−	1.31216i
$364$		0			0
$365$	27.0000	+	9.00000i	1.41324	+	0.471082i
$366$		0			0
$367$	13.0000	+	13.0000i	0.678594	+	0.678594i	0.959682	−	0.281088i	$-0.0906952\pi$
$367$	13.0000	+	13.0000i	0.678594	+	0.678594i	−0.281088	+	0.959682i	$0.590695\pi$
$368$		0			0
$369$			6.00000i			0.312348i
$370$		0			0
$371$	−2.00000			−0.103835
$372$		0			0
$373$	21.0000	−	21.0000i	1.08734	−	1.08734i	0.0915371	−	0.995802i	$-0.470822\pi$
$373$	21.0000	−	21.0000i	1.08734	−	1.08734i	0.995802	−	0.0915371i	$-0.0291780\pi$
$374$		0			0
$375$	13.0000	−	9.00000i	0.671317	−	0.464758i
$376$		0			0
$377$	8.00000	−	8.00000i	0.412021	−	0.412021i
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$		0			0
$381$		−	10.0000i		−	0.512316i
$382$		0			0
$383$	−13.0000	+	13.0000i	−0.664269	+	0.664269i	−0.956383	−	0.292114i	$-0.905641\pi$
$383$	−13.0000	+	13.0000i	−0.664269	+	0.664269i	0.292114	+	0.956383i	$0.405641\pi$
$384$		0			0
$385$	18.0000	+	6.00000i	0.917365	+	0.305788i
$386$		0			0
$387$	−3.00000	+	3.00000i	−0.152499	+	0.152499i
$388$		0			0
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$		−	10.0000i		−	0.505722i
$392$		0			0
$393$	−2.00000	−	2.00000i	−0.100887	−	0.100887i
$394$		0			0
$395$	−16.0000	+	8.00000i	−0.805047	+	0.402524i
$396$		0			0
$397$	−19.0000	−	19.0000i	−0.953583	−	0.953583i	0.0453868	−	0.998969i	$-0.485548\pi$
$397$	−19.0000	−	19.0000i	−0.953583	−	0.953583i	−0.998969	+	0.0453868i	$0.985548\pi$
$398$		0			0
$399$	−8.00000			−0.400501
$400$		0			0
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$		0			0
$403$	−2.00000	−	2.00000i	−0.0996271	−	0.0996271i
$404$		0			0
$405$	−10.0000	+	5.00000i	−0.496904	+	0.248452i
$406$		0			0
$407$	−30.0000	−	30.0000i	−1.48704	−	1.48704i
$408$		0			0
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$		0			0
$411$	26.0000			1.28249
$412$		0			0
$413$	−4.00000	+	4.00000i	−0.196827	+	0.196827i
$414$		0			0
$415$	15.0000	+	5.00000i	0.736321	+	0.245440i
$416$		0			0
$417$	−12.0000	+	12.0000i	−0.587643	+	0.587643i
$418$		0			0
$419$			12.0000i			0.586238i	0.956076	+	0.293119i	$0.0946933\pi$
$419$			12.0000i			0.586238i	−0.956076	+	0.293119i	$0.905307\pi$
$420$		0			0
$421$			2.00000i			0.0974740i	0.998812	+	0.0487370i	$0.0155196\pi$
$421$			2.00000i			0.0974740i	−0.998812	+	0.0487370i	$0.984480\pi$
$422$		0			0
$423$	−7.00000	+	7.00000i	−0.340352	+	0.340352i
$424$		0			0
$425$	−1.00000	−	7.00000i	−0.0485071	−	0.339550i
$426$		0			0
$427$	−2.00000	+	2.00000i	−0.0967868	+	0.0967868i
$428$		0			0
$429$	12.0000			0.579365
$430$		0			0
$431$		−	38.0000i		−	1.83040i	−0.403005	−	0.915198i	$-0.632034\pi$
$431$		−	38.0000i		−	1.83040i	0.403005	−	0.915198i	$-0.367966\pi$
$432$		0			0
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	0.816968	−	0.576683i	$-0.195653\pi$
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$	−24.0000	−	8.00000i	−1.15071	−	0.383571i
$436$		0			0
$437$	20.0000	+	20.0000i	0.956730	+	0.956730i
$438$		0			0
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$		0			0
$441$	−5.00000			−0.238095
$442$		0			0
$443$	17.0000	+	17.0000i	0.807694	+	0.807694i	0.984284	−	0.176590i	$-0.0565067\pi$
$443$	17.0000	+	17.0000i	0.807694	+	0.807694i	−0.176590	+	0.984284i	$0.556507\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.0000	+	12.0000i	0.567581	+	0.567581i
$448$		0			0
$449$		−	4.00000i		−	0.188772i	−0.995536	−	0.0943858i	$-0.969911\pi$
$449$		−	4.00000i		−	0.188772i	0.995536	−	0.0943858i	$-0.0300887\pi$
$450$		0			0
$451$	−36.0000			−1.69517
$452$		0			0
$453$	−18.0000	+	18.0000i	−0.845714	+	0.845714i
$454$		0			0
$455$	−4.00000	+	2.00000i	−0.187523	+	0.0937614i
$456$		0			0
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	−0.263099	−	0.964769i	$-0.584744\pi$
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	0.964769	+	0.263099i	$0.0847444\pi$
$458$		0			0
$459$			8.00000i			0.373408i
$460$		0			0
$461$			2.00000i			0.0931493i	0.998915	+	0.0465746i	$0.0148305\pi$
$461$			2.00000i			0.0931493i	−0.998915	+	0.0465746i	$0.985169\pi$
$462$		0			0
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	−0.981503	−	0.191446i	$-0.938682\pi$
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	0.191446	+	0.981503i	$0.438682\pi$
$464$		0			0
$465$	−2.00000	+	6.00000i	−0.0927478	+	0.278243i
$466$		0			0
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$		0			0
$469$	−14.0000			−0.646460
$470$		0			0
$471$			6.00000i			0.276465i
$472$		0			0
$473$	−18.0000	−	18.0000i	−0.827641	−	0.827641i
$474$		0			0
$475$	16.0000	+	12.0000i	0.734130	+	0.550598i
$476$		0			0
$477$	−1.00000	−	1.00000i	−0.0457869	−	0.0457869i
$478$		0			0
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	10.0000			0.455961
$482$		0			0
$483$	10.0000	+	10.0000i	0.455016	+	0.455016i
$484$		0			0
$485$	3.00000	−	9.00000i	0.136223	−	0.408669i
$486$		0			0
$487$	15.0000	+	15.0000i	0.679715	+	0.679715i	0.959936	−	0.280221i	$-0.0904077\pi$
$487$	15.0000	+	15.0000i	0.679715	+	0.679715i	−0.280221	+	0.959936i	$0.590408\pi$
$488$		0			0
$489$			2.00000i			0.0904431i
$490$		0			0
$491$	−2.00000			−0.0902587			−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000			−0.0902587			−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$	−8.00000	+	8.00000i	−0.360302	+	0.360302i
$494$		0			0
$495$	6.00000	+	12.0000i	0.269680	+	0.539360i
$496$		0			0
$497$	6.00000	−	6.00000i	0.269137	−	0.269137i
$498$		0			0
$499$		−	20.0000i		−	0.895323i	−0.894203	−	0.447661i	$-0.852257\pi$
$499$		−	20.0000i		−	0.895323i	0.894203	−	0.447661i	$-0.147743\pi$
$500$		0			0
$501$			10.0000i			0.446767i
$502$		0			0
$503$	−11.0000	+	11.0000i	−0.490466	+	0.490466i	−0.908453	−	0.417987i	$-0.862736\pi$
$503$	−11.0000	+	11.0000i	−0.490466	+	0.490466i	0.417987	+	0.908453i	$0.362736\pi$
$504$		0			0
$505$	−6.00000	−	12.0000i	−0.266996	−	0.533993i
$506$		0			0
$507$	11.0000	−	11.0000i	0.488527	−	0.488527i
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$			18.0000i			0.796273i
$512$		0			0
$513$	−16.0000	−	16.0000i	−0.706417	−	0.706417i
$514$		0			0
$515$	3.00000	−	9.00000i	0.132196	−	0.396587i
$516$		0			0
$517$	−42.0000	−	42.0000i	−1.84716	−	1.84716i
$518$		0			0
$519$	−14.0000			−0.614532
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	25.0000	+	25.0000i	1.09317	+	1.09317i	0.995188	+	0.0979859i	$0.0312400\pi$
$523$	25.0000	+	25.0000i	1.09317	+	1.09317i	0.0979859	+	0.995188i	$0.468760\pi$
$524$		0			0
$525$	8.00000	+	6.00000i	0.349149	+	0.261861i
$526$		0			0
$527$	2.00000	+	2.00000i	0.0871214	+	0.0871214i
$528$		0			0
$529$		−	27.0000i		−	1.17391i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	6.00000	−	6.00000i	0.259889	−	0.259889i
$534$		0			0
$535$	3.00000	−	9.00000i	0.129701	−	0.389104i
$536$		0			0
$537$	−12.0000	+	12.0000i	−0.517838	+	0.517838i
$538$		0			0
$539$		−	30.0000i		−	1.29219i
$540$		0			0
$541$		−	30.0000i		−	1.28980i	−0.764267	−	0.644900i	$-0.776899\pi$
$541$		−	30.0000i		−	1.28980i	0.764267	−	0.644900i	$-0.223101\pi$
$542$		0			0
$543$	−10.0000	+	10.0000i	−0.429141	+	0.429141i
$544$		0			0
$545$	8.00000	−	4.00000i	0.342682	−	0.171341i
$546$		0			0
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	−0.640057	−	0.768328i	$-0.721089\pi$
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	0.768328	+	0.640057i	$0.221089\pi$
$548$		0			0
$549$	−2.00000			−0.0853579
$550$		0			0
$551$		−	32.0000i		−	1.36325i
$552$		0			0
$553$	−8.00000	−	8.00000i	−0.340195	−	0.340195i
$554$		0			0
$555$	−10.0000	−	20.0000i	−0.424476	−	0.848953i
$556$		0			0
$557$	−15.0000	−	15.0000i	−0.635570	−	0.635570i	0.313889	−	0.949460i	$-0.398368\pi$
$557$	−15.0000	−	15.0000i	−0.635570	−	0.635570i	−0.949460	+	0.313889i	$0.898368\pi$
$558$		0			0
$559$	6.00000			0.253773
$560$		0			0
$561$	−12.0000			−0.506640
$562$		0			0
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	0.948613	−	0.316438i	$-0.102487\pi$
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	−0.316438	+	0.948613i	$0.602487\pi$
$564$		0			0
$565$	9.00000	+	3.00000i	0.378633	+	0.126211i
$566$		0			0
$567$	−5.00000	−	5.00000i	−0.209980	−	0.209980i
$568$		0			0
$569$		−	20.0000i		−	0.838444i	−0.907884	−	0.419222i	$-0.862303\pi$
$569$		−	20.0000i		−	0.838444i	0.907884	−	0.419222i	$-0.137697\pi$
$570$		0			0
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$		0			0
$573$	10.0000	−	10.0000i	0.417756	−	0.417756i
$574$		0			0
$575$	−5.00000	−	35.0000i	−0.208514	−	1.45960i
$576$		0			0
$577$	−3.00000	+	3.00000i	−0.124892	+	0.124892i	−0.766790	−	0.641898i	$-0.778147\pi$
$577$	−3.00000	+	3.00000i	−0.124892	+	0.124892i	0.641898	+	0.766790i	$0.278147\pi$
$578$		0			0
$579$		−	2.00000i		−	0.0831172i
$580$		0			0
$581$			10.0000i			0.414870i
$582$		0			0
$583$	6.00000	−	6.00000i	0.248495	−	0.248495i
$584$		0			0
$585$	−3.00000	−	1.00000i	−0.124035	−	0.0413449i
$586$		0			0
$587$	25.0000	−	25.0000i	1.03186	−	1.03186i	0.0323850	−	0.999475i	$-0.489690\pi$
$587$	25.0000	−	25.0000i	1.03186	−	1.03186i	0.999475	−	0.0323850i	$-0.0103103\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$			2.00000i			0.0822690i
$592$		0			0
$593$	−23.0000	−	23.0000i	−0.944497	−	0.944497i	0.0540419	−	0.998539i	$-0.482790\pi$
$593$	−23.0000	−	23.0000i	−0.944497	−	0.944497i	−0.998539	+	0.0540419i	$0.982790\pi$
$594$		0			0
$595$	4.00000	−	2.00000i	0.163984	−	0.0819920i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	−7.00000	−	7.00000i	−0.285062	−	0.285062i
$604$		0			0
$605$	−50.0000	+	25.0000i	−2.03279	+	1.01639i
$606$		0			0
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	0.333809	−	0.942641i	$-0.391666\pi$
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	−0.942641	+	0.333809i	$0.891666\pi$
$608$		0			0
$609$		−	16.0000i		−	0.648353i
$610$		0			0
$611$	14.0000			0.566379
$612$		0			0
$613$	−3.00000	+	3.00000i	−0.121169	+	0.121169i	−0.765091	−	0.643922i	$-0.777306\pi$
$613$	−3.00000	+	3.00000i	−0.121169	+	0.121169i	0.643922	+	0.765091i	$0.277306\pi$
$614$		0			0
$615$	−18.0000	−	6.00000i	−0.725830	−	0.241943i
$616$		0			0
$617$	11.0000	−	11.0000i	0.442843	−	0.442843i	−0.450123	−	0.892966i	$-0.648620\pi$
$617$	11.0000	−	11.0000i	0.442843	−	0.442843i	0.892966	+	0.450123i	$0.148620\pi$
$618$		0			0
$619$			28.0000i			1.12542i	0.826656	+	0.562708i	$0.190240\pi$
$619$			28.0000i			1.12542i	−0.826656	+	0.562708i	$0.809760\pi$
$620$		0			0
$621$			40.0000i			1.60514i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	24.0000	−	24.0000i	0.958468	−	0.958468i
$628$		0			0
$629$	−10.0000			−0.398726
$630$		0			0
$631$		−	10.0000i		−	0.398094i	−0.979990	−	0.199047i	$-0.936215\pi$
$631$		−	10.0000i		−	0.398094i	0.979990	−	0.199047i	$-0.0637846\pi$
$632$		0			0
$633$	−10.0000	−	10.0000i	−0.397464	−	0.397464i
$634$		0			0
$635$	−15.0000	−	5.00000i	−0.595257	−	0.198419i
$636$		0			0
$637$	5.00000	+	5.00000i	0.198107	+	0.198107i
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$		0			0
$643$	11.0000	+	11.0000i	0.433798	+	0.433798i	0.889918	−	0.456120i	$-0.150761\pi$
$643$	11.0000	+	11.0000i	0.433798	+	0.433798i	−0.456120	+	0.889918i	$0.650761\pi$
$644$		0			0
$645$	−6.00000	−	12.0000i	−0.236250	−	0.472500i
$646$		0			0
$647$	31.0000	+	31.0000i	1.21874	+	1.21874i	0.968075	+	0.250661i	$0.0806479\pi$
$647$	31.0000	+	31.0000i	1.21874	+	1.21874i	0.250661	+	0.968075i	$0.419352\pi$
$648$		0			0
$649$		−	24.0000i		−	0.942082i
$650$		0			0
$651$	−4.00000			−0.156772
$652$		0			0
$653$	−5.00000	+	5.00000i	−0.195665	+	0.195665i	−0.798139	−	0.602474i	$-0.794182\pi$
$653$	−5.00000	+	5.00000i	−0.195665	+	0.195665i	0.602474	+	0.798139i	$0.294182\pi$
$654$		0			0
$655$	−4.00000	+	2.00000i	−0.156293	+	0.0781465i
$656$		0			0
$657$	−9.00000	+	9.00000i	−0.351123	+	0.351123i
$658$		0			0
$659$			44.0000i			1.71400i	0.515319	+	0.856998i	$0.327673\pi$
$659$			44.0000i			1.71400i	−0.515319	+	0.856998i	$0.672327\pi$
$660$		0			0
$661$		−	30.0000i		−	1.16686i	−0.812162	−	0.583432i	$-0.801709\pi$
$661$		−	30.0000i		−	1.16686i	0.812162	−	0.583432i	$-0.198291\pi$
$662$		0			0
$663$	2.00000	−	2.00000i	0.0776736	−	0.0776736i
$664$		0			0
$665$	−4.00000	+	12.0000i	−0.155113	+	0.465340i
$666$		0			0
$667$	−40.0000	+	40.0000i	−1.54881	+	1.54881i
$668$		0			0
$669$	−38.0000			−1.46916
$670$		0			0
$671$		−	12.0000i		−	0.463255i
$672$		0			0
$673$	29.0000	+	29.0000i	1.11787	+	1.11787i	0.992054	+	0.125814i	$0.0401543\pi$
$673$	29.0000	+	29.0000i	1.11787	+	1.11787i	0.125814	+	0.992054i	$0.459846\pi$
$674$		0			0
$675$	4.00000	+	28.0000i	0.153960	+	1.07772i
$676$		0			0
$677$	15.0000	+	15.0000i	0.576497	+	0.576497i	0.933936	−	0.357439i	$-0.116350\pi$
$677$	15.0000	+	15.0000i	0.576497	+	0.576497i	−0.357439	+	0.933936i	$0.616350\pi$
$678$		0			0
$679$	6.00000			0.230259
$680$		0			0
$681$	26.0000			0.996322
$682$		0			0
$683$	13.0000	+	13.0000i	0.497431	+	0.497431i	0.910637	−	0.413206i	$-0.135591\pi$
$683$	13.0000	+	13.0000i	0.497431	+	0.497431i	−0.413206	+	0.910637i	$0.635591\pi$
$684$		0			0
$685$	13.0000	−	39.0000i	0.496704	−	1.49011i
$686$		0			0
$687$	−16.0000	−	16.0000i	−0.610438	−	0.610438i
$688$		0			0
$689$			2.00000i			0.0761939i
$690$		0			0
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$		0			0
$693$	−6.00000	+	6.00000i	−0.227921	+	0.227921i
$694$		0			0
$695$	12.0000	+	24.0000i	0.455186	+	0.910372i
$696$		0			0
$697$	−6.00000	+	6.00000i	−0.227266	+	0.227266i
$698$		0			0
$699$			26.0000i			0.983410i
$700$		0			0
$701$		−	2.00000i		−	0.0755390i	−0.999286	−	0.0377695i	$-0.987975\pi$
$701$		−	2.00000i		−	0.0755390i	0.999286	−	0.0377695i	$-0.0120253\pi$
$702$		0			0
$703$	20.0000	−	20.0000i	0.754314	−	0.754314i
$704$		0			0
$705$	−14.0000	−	28.0000i	−0.527271	−	1.05454i
$706$		0			0
$707$	6.00000	−	6.00000i	0.225653	−	0.225653i
$708$		0			0
$709$	−24.0000			−0.901339			−0.450669	−	0.892691i	$-0.648815\pi$
$709$	−24.0000			−0.901339			−0.450669	+	0.892691i	$0.648815\pi$
$710$		0			0
$711$		−	8.00000i		−	0.300023i
$712$		0			0
$713$	10.0000	+	10.0000i	0.374503	+	0.374503i
$714$		0			0
$715$	6.00000	−	18.0000i	0.224387	−	0.673162i
$716$		0			0
$717$	−16.0000	−	16.0000i	−0.597531	−	0.597531i
$718$		0			0
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$		0			0
$723$	−14.0000	−	14.0000i	−0.520666	−	0.520666i
$724$		0			0
$725$	−24.0000	+	32.0000i	−0.891338	+	1.18845i
$726$		0			0
$727$	15.0000	+	15.0000i	0.556319	+	0.556319i	0.928257	−	0.371938i	$-0.121307\pi$
$727$	15.0000	+	15.0000i	0.556319	+	0.556319i	−0.371938	+	0.928257i	$0.621307\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−6.00000			−0.221918
$732$		0			0
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	−0.853506	−	0.521083i	$-0.825528\pi$
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	0.521083	+	0.853506i	$0.325528\pi$
$734$		0			0
$735$	5.00000	−	15.0000i	0.184428	−	0.553283i
$736$		0			0
$737$	42.0000	−	42.0000i	1.54709	−	1.54709i
$738$		0			0
$739$		−	28.0000i		−	1.03000i	−0.857191	−	0.514998i	$-0.827793\pi$
$739$		−	28.0000i		−	1.03000i	0.857191	−	0.514998i	$-0.172207\pi$
$740$		0			0
$741$			8.00000i			0.293887i
$742$		0			0
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	−0.522476	−	0.852654i	$-0.674992\pi$
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	0.852654	+	0.522476i	$0.174992\pi$
$744$		0			0
$745$	24.0000	−	12.0000i	0.879292	−	0.439646i
$746$		0			0
$747$	−5.00000	+	5.00000i	−0.182940	+	0.182940i
$748$		0			0
$749$	6.00000			0.219235
$750$		0			0
$751$			26.0000i			0.948753i	0.880322	+	0.474377i	$0.157327\pi$
$751$			26.0000i			0.948753i	−0.880322	+	0.474377i	$0.842673\pi$
$752$		0			0
$753$	18.0000	+	18.0000i	0.655956	+	0.655956i
$754$		0			0
$755$	18.0000	+	36.0000i	0.655087	+	1.31017i
$756$		0			0
$757$	−1.00000	−	1.00000i	−0.0363456	−	0.0363456i	0.688700	−	0.725046i	$-0.258182\pi$
$757$	−1.00000	−	1.00000i	−0.0363456	−	0.0363456i	−0.725046	+	0.688700i	$0.758182\pi$
$758$		0			0
$759$	−60.0000			−2.17786
$760$		0			0
$761$	−50.0000			−1.81250			−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000			−1.81250			−0.906249	+	0.422744i	$0.861067\pi$
$762$		0			0
$763$	4.00000	+	4.00000i	0.144810	+	0.144810i
$764$		0			0
$765$	3.00000	+	1.00000i	0.108465	+	0.0361551i
$766$		0			0
$767$	4.00000	+	4.00000i	0.144432	+	0.144432i
$768$		0			0
$769$			8.00000i			0.288487i	0.989542	+	0.144244i	$0.0460749\pi$
$769$			8.00000i			0.288487i	−0.989542	+	0.144244i	$0.953925\pi$
$770$		0			0
$771$	22.0000			0.792311
$772$		0			0
$773$	−35.0000	+	35.0000i	−1.25886	+	1.25886i	−0.307226	+	0.951637i	$0.599401\pi$
$773$	−35.0000	+	35.0000i	−1.25886	+	1.25886i	−0.951637	+	0.307226i	$0.900599\pi$
$774$		0			0
$775$	8.00000	+	6.00000i	0.287368	+	0.215526i
$776$		0			0
$777$	10.0000	−	10.0000i	0.358748	−	0.358748i
$778$		0			0
$779$		−	24.0000i		−	0.859889i
$780$		0			0
$781$			36.0000i			1.28818i
$782$		0			0
$783$	32.0000	−	32.0000i	1.14359	−	1.14359i
$784$		0			0
$785$	9.00000	+	3.00000i	0.321224	+	0.107075i
$786$		0			0
$787$	−9.00000	+	9.00000i	−0.320815	+	0.320815i	−0.849080	−	0.528265i	$-0.822843\pi$
$787$	−9.00000	+	9.00000i	−0.320815	+	0.320815i	0.528265	+	0.849080i	$0.322843\pi$
$788$		0			0
$789$	−18.0000			−0.640817
$790$		0			0
$791$			6.00000i			0.213335i
$792$		0			0
$793$	2.00000	+	2.00000i	0.0710221	+	0.0710221i
$794$		0			0
$795$	4.00000	−	2.00000i	0.141865	−	0.0709327i
$796$		0			0
$797$	17.0000	+	17.0000i	0.602171	+	0.602171i	0.940888	−	0.338717i	$-0.109993\pi$
$797$	17.0000	+	17.0000i	0.602171	+	0.602171i	−0.338717	+	0.940888i	$0.609993\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−54.0000	−	54.0000i	−1.90562	−	1.90562i
$804$		0			0
$805$	20.0000	−	10.0000i	0.704907	−	0.352454i
$806$		0			0
$807$	−4.00000	−	4.00000i	−0.140807	−	0.140807i
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$	30.0000			1.05344			0.526721	−	0.850038i	$-0.323421\pi$
$811$	30.0000			1.05344			0.526721	+	0.850038i	$0.323421\pi$
$812$		0			0
$813$	−22.0000	+	22.0000i	−0.771574	+	0.771574i
$814$		0			0
$815$	3.00000	+	1.00000i	0.105085	+	0.0350285i
$816$		0			0
$817$	12.0000	−	12.0000i	0.419827	−	0.419827i
$818$		0			0
$819$		−	2.00000i		−	0.0698857i
$820$		0			0
$821$		−	22.0000i		−	0.767805i	−0.923374	−	0.383903i	$-0.874580\pi$
$821$		−	22.0000i		−	0.767805i	0.923374	−	0.383903i	$-0.125420\pi$
$822$		0			0
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	−0.757458	−	0.652884i	$-0.773559\pi$
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	0.652884	+	0.757458i	$0.273559\pi$
$824$		0			0
$825$	−42.0000	+	6.00000i	−1.46225	+	0.208893i
$826$		0			0
$827$	−7.00000	+	7.00000i	−0.243414	+	0.243414i	−0.818261	−	0.574847i	$-0.805062\pi$
$827$	−7.00000	+	7.00000i	−0.243414	+	0.243414i	0.574847	+	0.818261i	$0.305062\pi$
$828$		0			0
$829$	36.0000			1.25033			0.625166	−	0.780492i	$-0.285031\pi$
$829$	36.0000			1.25033			0.625166	+	0.780492i	$0.285031\pi$
$830$		0			0
$831$			18.0000i			0.624413i
$832$		0			0
$833$	−5.00000	−	5.00000i	−0.173240	−	0.173240i
$834$		0			0
$835$	15.0000	+	5.00000i	0.519096	+	0.173032i
$836$		0			0
$837$	−8.00000	−	8.00000i	−0.276520	−	0.276520i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$		0			0
$843$	−10.0000	−	10.0000i	−0.344418	−	0.344418i
$844$		0			0
$845$	−11.0000	−	22.0000i	−0.378412	−	0.756823i
$846$		0			0
$847$	−25.0000	−	25.0000i	−0.859010	−	0.859010i
$848$		0			0
$849$			30.0000i			1.02960i
$850$		0			0
$851$	−50.0000			−1.71398
$852$		0			0
$853$	−27.0000	+	27.0000i	−0.924462	+	0.924462i	−0.997341	−	0.0728784i	$-0.976781\pi$
$853$	−27.0000	+	27.0000i	−0.924462	+	0.924462i	0.0728784	+	0.997341i	$0.476781\pi$
$854$		0			0
$855$	−8.00000	+	4.00000i	−0.273594	+	0.136797i
$856$		0			0
$857$	−5.00000	+	5.00000i	−0.170797	+	0.170797i	−0.787329	−	0.616533i	$-0.788537\pi$
$857$	−5.00000	+	5.00000i	−0.170797	+	0.170797i	0.616533	+	0.787329i	$0.288537\pi$
$858$		0			0
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$		0			0
$861$		−	12.0000i		−	0.408959i
$862$		0			0
$863$	−25.0000	+	25.0000i	−0.851010	+	0.851010i	−0.990258	−	0.139248i	$-0.955532\pi$
$863$	−25.0000	+	25.0000i	−0.851010	+	0.851010i	0.139248	+	0.990258i	$0.455532\pi$
$864$		0			0
$865$	−7.00000	+	21.0000i	−0.238007	+	0.714021i
$866$		0			0
$867$	15.0000	−	15.0000i	0.509427	−	0.509427i
$868$		0			0
$869$	48.0000			1.62829
$870$		0			0
$871$			14.0000i			0.474372i
$872$		0			0
$873$	3.00000	+	3.00000i	0.101535	+	0.101535i
$874$		0			0
$875$	13.0000	−	9.00000i	0.439480	−	0.304256i
$876$		0			0
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	0.0846827	−	0.996408i	$-0.473012\pi$
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	−0.996408	+	0.0846827i	$0.973012\pi$
$878$		0			0
$879$	−34.0000			−1.14679
$880$		0			0
$881$	−34.0000			−1.14549			−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000			−1.14549			−0.572745	+	0.819734i	$0.694121\pi$
$882$		0			0
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	0.360618	−	0.932714i	$-0.382566\pi$
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	−0.932714	+	0.360618i	$0.882566\pi$
$884$		0			0
$885$	4.00000	−	12.0000i	0.134459	−	0.403376i
$886$		0			0
$887$	7.00000	+	7.00000i	0.235037	+	0.235037i	0.814791	−	0.579754i	$-0.196851\pi$
$887$	7.00000	+	7.00000i	0.235037	+	0.235037i	−0.579754	+	0.814791i	$0.696851\pi$
$888$		0			0
$889$		−	10.0000i		−	0.335389i
$890$		0			0
$891$	30.0000			1.00504
$892$		0			0
$893$	28.0000	−	28.0000i	0.936984	−	0.936984i
$894$		0			0
$895$	12.0000	+	24.0000i	0.401116	+	0.802232i
$896$		0			0
$897$	10.0000	−	10.0000i	0.333890	−	0.333890i
$898$		0			0
$899$		−	16.0000i		−	0.533630i
$900$		0			0
$901$		−	2.00000i		−	0.0666297i
$902$		0			0
$903$	6.00000	−	6.00000i	0.199667	−	0.199667i
$904$		0			0
$905$	10.0000	+	20.0000i	0.332411	+	0.664822i
$906$		0			0
$907$	−27.0000	+	27.0000i	−0.896520	+	0.896520i	−0.995127	−	0.0986062i	$-0.968562\pi$
$907$	−27.0000	+	27.0000i	−0.896520	+	0.896520i	0.0986062	+	0.995127i	$0.468562\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$			50.0000i			1.65657i	0.560304	+	0.828287i	$0.310684\pi$
$911$			50.0000i			1.65657i	−0.560304	+	0.828287i	$0.689316\pi$
$912$		0			0
$913$	−30.0000	−	30.0000i	−0.992855	−	0.992855i
$914$		0			0
$915$	2.00000	−	6.00000i	0.0661180	−	0.198354i
$916$		0			0
$917$	−2.00000	−	2.00000i	−0.0660458	−	0.0660458i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	−14.0000			−0.461316
$922$		0			0
$923$	−6.00000	−	6.00000i	−0.197492	−	0.197492i
$924$		0			0
$925$	−35.0000	+	5.00000i	−1.15079	+	0.164399i
$926$		0			0
$927$	3.00000	+	3.00000i	0.0985329	+	0.0985329i
$928$		0			0
$929$		−	12.0000i		−	0.393707i	−0.980433	−	0.196854i	$-0.936928\pi$
$929$		−	12.0000i		−	0.393707i	0.980433	−	0.196854i	$-0.0630724\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$		0			0
$933$	22.0000	−	22.0000i	0.720248	−	0.720248i
$934$		0			0
$935$	−6.00000	+	18.0000i	−0.196221	+	0.588663i
$936$		0			0
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	−0.656404	−	0.754410i	$-0.727923\pi$
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	0.754410	+	0.656404i	$0.227923\pi$
$938$		0			0
$939$		−	30.0000i		−	0.979013i
$940$		0			0
$941$			2.00000i			0.0651981i	0.999469	+	0.0325991i	$0.0103784\pi$
$941$			2.00000i			0.0651981i	−0.999469	+	0.0325991i	$0.989622\pi$
$942$		0			0
$943$	−30.0000	+	30.0000i	−0.976934	+	0.976934i
$944$		0			0
$945$	−16.0000	+	8.00000i	−0.520480	+	0.260240i
$946$		0			0
$947$	−41.0000	+	41.0000i	−1.33232	+	1.33232i	−0.429031	+	0.903290i	$0.641145\pi$
$947$	−41.0000	+	41.0000i	−1.33232	+	1.33232i	−0.903290	+	0.429031i	$0.858855\pi$
$948$		0			0
$949$	18.0000			0.584305
$950$		0			0
$951$		−	50.0000i		−	1.62136i
$952$		0			0
$953$	−9.00000	−	9.00000i	−0.291539	−	0.291539i	0.546149	−	0.837688i	$-0.316093\pi$
$953$	−9.00000	−	9.00000i	−0.291539	−	0.291539i	−0.837688	+	0.546149i	$0.816093\pi$
$954$		0			0
$955$	−10.0000	−	20.0000i	−0.323592	−	0.647185i
$956$		0			0
$957$	48.0000	+	48.0000i	1.55162	+	1.55162i
$958$		0			0
$959$	26.0000			0.839584
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$	3.00000	+	3.00000i	0.0966736	+	0.0966736i
$964$		0			0
$965$	−3.00000	−	1.00000i	−0.0965734	−	0.0321911i
$966$		0			0
$967$	−37.0000	−	37.0000i	−1.18984	−	1.18984i	−0.977111	−	0.212728i	$-0.931765\pi$
$967$	−37.0000	−	37.0000i	−1.18984	−	1.18984i	−0.212728	−	0.977111i	$-0.568235\pi$
$968$		0			0
$969$		−	8.00000i		−	0.256997i
$970$		0			0
$971$	−26.0000			−0.834380			−0.417190	−	0.908819i	$-0.636985\pi$
$971$	−26.0000			−0.834380			−0.417190	+	0.908819i	$0.636985\pi$
$972$		0			0
$973$	−12.0000	+	12.0000i	−0.384702	+	0.384702i
$974$		0			0
$975$	6.00000	−	8.00000i	0.192154	−	0.256205i
$976$		0			0
$977$	−27.0000	+	27.0000i	−0.863807	+	0.863807i	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−27.0000	+	27.0000i	−0.863807	+	0.863807i	0.127971	+	0.991778i	$0.459153\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$			4.00000i			0.127710i
$982$		0			0
$983$	41.0000	−	41.0000i	1.30770	−	1.30770i	0.384623	−	0.923074i	$-0.374331\pi$
$983$	41.0000	−	41.0000i	1.30770	−	1.30770i	0.923074	−	0.384623i	$-0.125669\pi$
$984$		0			0
$985$	3.00000	+	1.00000i	0.0955879	+	0.0318626i
$986$		0			0
$987$	14.0000	−	14.0000i	0.445625	−	0.445625i
$988$		0			0
$989$	−30.0000			−0.953945
$990$		0			0
$991$			34.0000i			1.08005i	0.841650	+	0.540023i	$0.181584\pi$
$991$			34.0000i			1.08005i	−0.841650	+	0.540023i	$0.818416\pi$
$992$		0			0
$993$	18.0000	+	18.0000i	0.571213	+	0.571213i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	27.0000	+	27.0000i	0.855099	+	0.855099i	0.990756	−	0.135657i	$-0.0433146\pi$
$997$	27.0000	+	27.0000i	0.855099	+	0.855099i	−0.135657	+	0.990756i	$0.543315\pi$
$998$		0			0
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.o.d.383.1		2
4.3	odd	2		1280.2.o.k.383.1		2
5.2	odd	4		1280.2.o.e.127.1		2
8.3	odd	2		1280.2.o.e.383.1		2
8.5	even	2		1280.2.o.n.383.1		2
16.3	odd	4		160.2.n.b.63.1	✓	2
16.5	even	4		320.2.n.c.63.1		2
16.11	odd	4		320.2.n.f.63.1		2
16.13	even	4		160.2.n.e.63.1	yes	2
20.7	even	4		1280.2.o.n.127.1		2
40.27	even	4	inner	1280.2.o.d.127.1		2
40.37	odd	4		1280.2.o.k.127.1		2
48.29	odd	4		1440.2.x.e.703.1		2
48.35	even	4		1440.2.x.b.703.1		2
80.3	even	4		800.2.n.c.607.1		2
80.13	odd	4		800.2.n.h.607.1		2
80.19	odd	4		800.2.n.h.543.1		2
80.27	even	4		320.2.n.c.127.1		2
80.29	even	4		800.2.n.c.543.1		2
80.37	odd	4		320.2.n.f.127.1		2
80.43	even	4		1600.2.n.j.1407.1		2
80.53	odd	4		1600.2.n.e.1407.1		2
80.59	odd	4		1600.2.n.e.1343.1		2
80.67	even	4		160.2.n.e.127.1	yes	2
80.69	even	4		1600.2.n.j.1343.1		2
80.77	odd	4		160.2.n.b.127.1	yes	2
240.77	even	4		1440.2.x.b.127.1		2
240.227	odd	4		1440.2.x.e.127.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.n.b.63.1	✓	2	16.3	odd	4
160.2.n.b.127.1	yes	2	80.77	odd	4
160.2.n.e.63.1	yes	2	16.13	even	4
160.2.n.e.127.1	yes	2	80.67	even	4
320.2.n.c.63.1		2	16.5	even	4
320.2.n.c.127.1		2	80.27	even	4
320.2.n.f.63.1		2	16.11	odd	4
320.2.n.f.127.1		2	80.37	odd	4
800.2.n.c.543.1		2	80.29	even	4
800.2.n.c.607.1		2	80.3	even	4
800.2.n.h.543.1		2	80.19	odd	4
800.2.n.h.607.1		2	80.13	odd	4
1280.2.o.d.127.1		2	40.27	even	4	inner
1280.2.o.d.383.1		2	1.1	even	1	trivial
1280.2.o.e.127.1		2	5.2	odd	4
1280.2.o.e.383.1		2	8.3	odd	2
1280.2.o.k.127.1		2	40.37	odd	4
1280.2.o.k.383.1		2	4.3	odd	2
1280.2.o.n.127.1		2	20.7	even	4
1280.2.o.n.383.1		2	8.5	even	2
1440.2.x.b.127.1		2	240.77	even	4
1440.2.x.b.703.1		2	48.35	even	4
1440.2.x.e.127.1		2	240.227	odd	4
1440.2.x.e.703.1		2	48.29	odd	4
1600.2.n.e.1343.1		2	80.59	odd	4
1600.2.n.e.1407.1		2	80.53	odd	4
1600.2.n.j.1343.1		2	80.69	even	4
1600.2.n.j.1407.1		2	80.43	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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +6.00000 q^{11} +(-1.00000 + 1.00000i) q^{13} +(3.00000 + 1.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +4.00000i q^{19} +2.00000i q^{21} +(5.00000 - 5.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} -8.00000 q^{29} +2.00000i q^{31} +(-6.00000 - 6.00000i) q^{33} +(3.00000 + 1.00000i) q^{35} +(-5.00000 - 5.00000i) q^{37} +2.00000 q^{39} -6.00000 q^{41} +(-3.00000 - 3.00000i) q^{43} +(1.00000 + 2.00000i) q^{45} +(-7.00000 - 7.00000i) q^{47} -5.00000i q^{49} -2.00000 q^{51} +(1.00000 - 1.00000i) q^{53} +(-12.0000 + 6.00000i) q^{55} +(4.00000 - 4.00000i) q^{57} -4.00000i q^{59} -2.00000i q^{61} +(-1.00000 + 1.00000i) q^{63} +(1.00000 - 3.00000i) q^{65} +(7.00000 - 7.00000i) q^{67} -10.0000 q^{69} +6.00000i q^{71} +(-9.00000 - 9.00000i) q^{73} +(-7.00000 + 1.00000i) q^{75} +(-6.00000 - 6.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(-5.00000 - 5.00000i) q^{83} +(-1.00000 + 3.00000i) q^{85} +(8.00000 + 8.00000i) q^{87} +2.00000 q^{91} +(2.00000 - 2.00000i) q^{93} +(-4.00000 - 8.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{5} - 2 q^{7}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^5 - 2 * q^7	\( 2 q - 2 q^{3} - 4 q^{5} - 2 q^{7} + 12 q^{11} - 2 q^{13} + 6 q^{15} + 2 q^{17} + 10 q^{23} + 6 q^{25} - 8 q^{27} - 16 q^{29} - 12 q^{33} + 6 q^{35} - 10 q^{37} + 4 q^{39} - 12 q^{41} - 6 q^{43} + 2 q^{45} - 14 q^{47} - 4 q^{51} + 2 q^{53} - 24 q^{55} + 8 q^{57} - 2 q^{63} + 2 q^{65} + 14 q^{67} - 20 q^{69} - 18 q^{73} - 14 q^{75} - 12 q^{77} + 16 q^{79} + 10 q^{81} - 10 q^{83} - 2 q^{85} + 16 q^{87} + 4 q^{91} + 4 q^{93} - 8 q^{95} - 6 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^5 - 2 * q^7 + 12 * q^11 - 2 * q^13 + 6 * q^15 + 2 * q^17 + 10 * q^23 + 6 * q^25 - 8 * q^27 - 16 * q^29 - 12 * q^33 + 6 * q^35 - 10 * q^37 + 4 * q^39 - 12 * q^41 - 6 * q^43 + 2 * q^45 - 14 * q^47 - 4 * q^51 + 2 * q^53 - 24 * q^55 + 8 * q^57 - 2 * q^63 + 2 * q^65 + 14 * q^67 - 20 * q^69 - 18 * q^73 - 14 * q^75 - 12 * q^77 + 16 * q^79 + 10 * q^81 - 10 * q^83 - 2 * q^85 + 16 * q^87 + 4 * q^91 + 4 * q^93 - 8 * q^95 - 6 * q^97

Introduction

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