LMFDB - Embedded newform 1280.2.o.a.127.1

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:	$1$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.127
Dual form			1280.2.o.a.383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} -5.00000i q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} -5.00000i q^{9} +(1.00000 + 1.00000i) q^{13} +(6.00000 + 2.00000i) q^{15} +(-5.00000 - 5.00000i) q^{17} +4.00000i q^{19} +8.00000i q^{21} +(2.00000 + 2.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -4.00000 q^{29} +4.00000i q^{31} +(-6.00000 - 2.00000i) q^{35} +(-1.00000 + 1.00000i) q^{37} -4.00000 q^{39} +(-6.00000 + 6.00000i) q^{43} +(-10.0000 + 5.00000i) q^{45} +(2.00000 - 2.00000i) q^{47} -1.00000i q^{49} +20.0000 q^{51} +(-7.00000 - 7.00000i) q^{53} +(-8.00000 - 8.00000i) q^{57} -4.00000i q^{59} +4.00000i q^{61} +(-10.0000 - 10.0000i) q^{63} +(1.00000 - 3.00000i) q^{65} +(-10.0000 - 10.0000i) q^{67} -8.00000 q^{69} +12.0000i q^{71} +(3.00000 - 3.00000i) q^{73} +(-2.00000 - 14.0000i) q^{75} -16.0000 q^{79} -1.00000 q^{81} +(2.00000 - 2.00000i) q^{83} +(-5.00000 + 15.0000i) q^{85} +(8.00000 - 8.00000i) q^{87} +4.00000 q^{91} +(-8.00000 - 8.00000i) q^{93} +(8.00000 - 4.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) $ 2 * q - 4 * q^3 - 2 * q^5 + 4 * q^7	$ 2 q - 4 q^{3} - 2 q^{5} + 4 q^{7} + 2 q^{13} + 12 q^{15} - 10 q^{17} + 4 q^{23} - 6 q^{25} + 8 q^{27} - 8 q^{29} - 12 q^{35} - 2 q^{37} - 8 q^{39} - 12 q^{43} - 20 q^{45} + 4 q^{47} + 40 q^{51} - 14 q^{53} - 16 q^{57} - 20 q^{63} + 2 q^{65} - 20 q^{67} - 16 q^{69} + 6 q^{73} - 4 q^{75} - 32 q^{79} - 2 q^{81} + 4 q^{83} - 10 q^{85} + 16 q^{87} + 8 q^{91} - 16 q^{93} + 16 q^{95} - 6 q^{97}+O(q^{100}) $ 2 * q - 4 * q^3 - 2 * q^5 + 4 * q^7 + 2 * q^13 + 12 * q^15 - 10 * q^17 + 4 * q^23 - 6 * q^25 + 8 * q^27 - 8 * q^29 - 12 * q^35 - 2 * q^37 - 8 * q^39 - 12 * q^43 - 20 * q^45 + 4 * q^47 + 40 * q^51 - 14 * q^53 - 16 * q^57 - 20 * q^63 + 2 * q^65 - 20 * q^67 - 16 * q^69 + 6 * q^73 - 4 * q^75 - 32 * q^79 - 2 * q^81 + 4 * q^83 - 10 * q^85 + 16 * q^87 + 8 * q^91 - 16 * q^93 + 16 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.00000	+	2.00000i	−1.15470	+	1.15470i	−0.169102	+	0.985599i	$0.554087\pi$
$3$	−2.00000	+	2.00000i	−1.15470	+	1.15470i	−0.985599	+	0.169102i	$0.945913\pi$
$4$		0			0
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	−0.219650	−	0.975579i	$-0.570491\pi$
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	0.975579	+	0.219650i	$0.0704915\pi$
$8$		0			0
$9$		−	5.00000i		−	1.66667i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	0.832050	−	0.554700i	$-0.187167\pi$
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	6.00000	+	2.00000i	1.54919	+	0.516398i
$16$		0			0
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.242536	−	0.970143i	$-0.577979\pi$
$18$		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
$21$			8.00000i			1.74574i
$22$		0			0
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	0.884178	−	0.467150i	$-0.154719\pi$
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	−0.467150	+	0.884178i	$0.654719\pi$
$24$		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
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000	−	2.00000i	−1.01419	−	0.338062i
$36$		0			0
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	−0.784512	−	0.620113i	$-0.787087\pi$
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	0.620113	+	0.784512i	$0.287087\pi$
$38$		0			0
$39$	−4.00000			−0.640513
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−6.00000	+	6.00000i	−0.914991	+	0.914991i	−0.996660	−	0.0816682i	$-0.973975\pi$
$43$	−6.00000	+	6.00000i	−0.914991	+	0.914991i	0.0816682	+	0.996660i	$0.473975\pi$
$44$		0			0
$45$	−10.0000	+	5.00000i	−1.49071	+	0.745356i
$46$		0			0
$47$	2.00000	−	2.00000i	0.291730	−	0.291730i	−0.546033	−	0.837763i	$-0.683863\pi$
$47$	2.00000	−	2.00000i	0.291730	−	0.291730i	0.837763	+	0.546033i	$0.183863\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	20.0000			2.80056
$52$		0			0
$53$	−7.00000	−	7.00000i	−0.961524	−	0.961524i	0.0377628	−	0.999287i	$-0.487977\pi$
$53$	−7.00000	−	7.00000i	−0.961524	−	0.961524i	−0.999287	+	0.0377628i	$0.987977\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.00000	−	8.00000i	−1.05963	−	1.05963i
$58$		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
$61$			4.00000i			0.512148i	0.966657	+	0.256074i	$0.0824290\pi$
$61$			4.00000i			0.512148i	−0.966657	+	0.256074i	$0.917571\pi$
$62$		0			0
$63$	−10.0000	−	10.0000i	−1.25988	−	1.25988i
$64$		0			0
$65$	1.00000	−	3.00000i	0.124035	−	0.372104i
$66$		0			0
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.967029	−	0.254665i	$-0.918035\pi$
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.254665	−	0.967029i	$-0.581965\pi$
$68$		0			0
$69$	−8.00000			−0.963087
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$		0			0
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	−0.509404	−	0.860527i	$-0.670134\pi$
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	0.860527	+	0.509404i	$0.170134\pi$
$74$		0			0
$75$	−2.00000	−	14.0000i	−0.230940	−	1.61658i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.00000	−	2.00000i	0.219529	−	0.219529i	−0.588771	−	0.808300i	$-0.700388\pi$
$83$	2.00000	−	2.00000i	0.219529	−	0.219529i	0.808300	+	0.588771i	$0.200388\pi$
$84$		0			0
$85$	−5.00000	+	15.0000i	−0.542326	+	1.62698i
$86$		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
$91$	4.00000			0.419314
$92$		0			0
$93$	−8.00000	−	8.00000i	−0.829561	−	0.829561i
$94$		0			0
$95$	8.00000	−	4.00000i	0.820783	−	0.410391i
$96$		0			0
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	6.00000i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$101$		−	6.00000i		−	0.597022i	0.954406	−	0.298511i	$-0.0964900\pi$
$102$		0			0
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	0.346757	−	0.937955i	$-0.387283\pi$
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	−0.937955	+	0.346757i	$0.887283\pi$
$104$		0			0
$105$	16.0000	−	8.00000i	1.56144	−	0.780720i
$106$		0			0
$107$	−6.00000	−	6.00000i	−0.580042	−	0.580042i	0.354873	−	0.934915i	$-0.384524\pi$
$107$	−6.00000	−	6.00000i	−0.580042	−	0.580042i	−0.934915	+	0.354873i	$0.884524\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$		−	4.00000i		−	0.379663i
$112$		0			0
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	−0.989713	−	0.143065i	$-0.954304\pi$
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	0.143065	+	0.989713i	$0.454304\pi$
$114$		0			0
$115$	2.00000	−	6.00000i	0.186501	−	0.559503i
$116$		0			0
$117$	5.00000	−	5.00000i	0.462250	−	0.462250i
$118$		0			0
$119$	−20.0000			−1.83340
$120$		0			0
$121$	−11.0000			−1.00000
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	−10.0000	+	10.0000i	−0.887357	+	0.887357i	−0.994268	−	0.106912i	$-0.965904\pi$
$127$	−10.0000	+	10.0000i	−0.887357	+	0.887357i	0.106912	+	0.994268i	$0.465904\pi$
$128$		0			0
$129$		−	24.0000i		−	2.11308i
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$	8.00000	+	8.00000i	0.693688	+	0.693688i
$134$		0			0
$135$	4.00000	−	12.0000i	0.344265	−	1.03280i
$136$		0			0
$137$	−1.00000	−	1.00000i	−0.0854358	−	0.0854358i	0.663097	−	0.748533i	$-0.269242\pi$
$137$	−1.00000	−	1.00000i	−0.0854358	−	0.0854358i	−0.748533	+	0.663097i	$0.769242\pi$
$138$		0			0
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$		0			0
$141$			8.00000i			0.673722i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	4.00000	+	8.00000i	0.332182	+	0.664364i
$146$		0			0
$147$	2.00000	+	2.00000i	0.164957	+	0.164957i
$148$		0			0
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$		0			0
$153$	−25.0000	+	25.0000i	−2.02113	+	2.02113i
$154$		0			0
$155$	8.00000	−	4.00000i	0.642575	−	0.321288i
$156$		0			0
$157$	−9.00000	+	9.00000i	−0.718278	+	0.718278i	−0.968252	−	0.249974i	$-0.919578\pi$
$157$	−9.00000	+	9.00000i	−0.718278	+	0.718278i	0.249974	+	0.968252i	$0.419578\pi$
$158$		0			0
$159$	28.0000			2.22054
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$	−2.00000	+	2.00000i	−0.156652	+	0.156652i	−0.781081	−	0.624429i	$-0.785332\pi$
$163$	−2.00000	+	2.00000i	−0.156652	+	0.156652i	0.624429	+	0.781081i	$0.285332\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.00000	+	2.00000i	−0.154765	+	0.154765i	−0.780242	−	0.625478i	$-0.784904\pi$
$167$	−2.00000	+	2.00000i	−0.154765	+	0.154765i	0.625478	+	0.780242i	$0.284904\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$		0			0
$171$	20.0000			1.52944
$172$		0			0
$173$	−13.0000	−	13.0000i	−0.988372	−	0.988372i	0.0115615	−	0.999933i	$-0.496320\pi$
$173$	−13.0000	−	13.0000i	−0.988372	−	0.988372i	−0.999933	+	0.0115615i	$0.996320\pi$
$174$		0			0
$175$	2.00000	+	14.0000i	0.151186	+	1.05830i
$176$		0			0
$177$	8.00000	+	8.00000i	0.601317	+	0.601317i
$178$		0			0
$179$			12.0000i			0.896922i	0.893802	+	0.448461i	$0.148028\pi$
$179$			12.0000i			0.896922i	−0.893802	+	0.448461i	$0.851972\pi$
$180$		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
$183$	−8.00000	−	8.00000i	−0.591377	−	0.591377i
$184$		0			0
$185$	3.00000	+	1.00000i	0.220564	+	0.0735215i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	16.0000			1.16383
$190$		0			0
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$		0			0
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$	4.00000	+	8.00000i	0.286446	+	0.572892i
$196$		0			0
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$		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
$201$	40.0000			2.82138
$202$		0			0
$203$	−8.00000	+	8.00000i	−0.561490	+	0.561490i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	10.0000	−	10.0000i	0.695048	−	0.695048i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−24.0000	−	24.0000i	−1.64445	−	1.64445i
$214$		0			0
$215$	18.0000	+	6.00000i	1.22759	+	0.409197i
$216$		0			0
$217$	8.00000	+	8.00000i	0.543075	+	0.543075i
$218$		0			0
$219$			12.0000i			0.810885i
$220$		0			0
$221$		−	10.0000i		−	0.672673i
$222$		0			0
$223$	10.0000	+	10.0000i	0.669650	+	0.669650i	0.957635	−	0.287985i	$-0.0929854\pi$
$223$	10.0000	+	10.0000i	0.669650	+	0.669650i	−0.287985	+	0.957635i	$0.592985\pi$
$224$		0			0
$225$	20.0000	+	15.0000i	1.33333	+	1.00000i
$226$		0			0
$227$	10.0000	+	10.0000i	0.663723	+	0.663723i	0.956256	−	0.292532i	$-0.0944979\pi$
$227$	10.0000	+	10.0000i	0.663723	+	0.663723i	−0.292532	+	0.956256i	$0.594498\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	0.851658	+	0.524097i	$0.175597\pi$
$234$		0			0
$235$	−6.00000	−	2.00000i	−0.391397	−	0.130466i
$236$		0			0
$237$	32.0000	−	32.0000i	2.07862	−	2.07862i
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$		0			0
$243$	−10.0000	+	10.0000i	−0.641500	+	0.641500i
$244$		0			0
$245$	−2.00000	+	1.00000i	−0.127775	+	0.0638877i
$246$		0			0
$247$	−4.00000	+	4.00000i	−0.254514	+	0.254514i
$248$		0			0
$249$			8.00000i			0.506979i
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−20.0000	−	40.0000i	−1.25245	−	2.50490i
$256$		0			0
$257$	7.00000	+	7.00000i	0.436648	+	0.436648i	0.890882	−	0.454234i	$-0.150087\pi$
$257$	7.00000	+	7.00000i	0.436648	+	0.436648i	−0.454234	+	0.890882i	$0.650087\pi$
$258$		0			0
$259$			4.00000i			0.248548i
$260$		0			0
$261$			20.0000i			1.23797i
$262$		0			0
$263$	6.00000	+	6.00000i	0.369976	+	0.369976i	0.867468	−	0.497492i	$-0.165746\pi$
$263$	6.00000	+	6.00000i	0.369976	+	0.369976i	−0.497492	+	0.867468i	$0.665746\pi$
$264$		0			0
$265$	−7.00000	+	21.0000i	−0.430007	+	1.29002i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$		−	20.0000i		−	1.21491i	−0.794353	−	0.607457i	$-0.792190\pi$
$271$		−	20.0000i		−	1.21491i	0.794353	−	0.607457i	$-0.207810\pi$
$272$		0			0
$273$	−8.00000	+	8.00000i	−0.484182	+	0.484182i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.00000	−	9.00000i	0.540758	−	0.540758i	−0.382993	−	0.923751i	$-0.625107\pi$
$277$	9.00000	−	9.00000i	0.540758	−	0.540758i	0.923751	+	0.382993i	$0.125107\pi$
$278$		0			0
$279$	20.0000			1.19737
$280$		0			0
$281$	−8.00000			−0.477240			−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000			−0.477240			−0.238620	+	0.971113i	$0.576695\pi$
$282$		0			0
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	−0.505918	−	0.862581i	$-0.668846\pi$
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	0.862581	+	0.505918i	$0.168846\pi$
$284$		0			0
$285$	−8.00000	+	24.0000i	−0.473879	+	1.42164i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			33.0000i			1.94118i
$290$		0			0
$291$	12.0000			0.703452
$292$		0			0
$293$	−5.00000	−	5.00000i	−0.292103	−	0.292103i	0.545807	−	0.837911i	$-0.316223\pi$
$293$	−5.00000	−	5.00000i	−0.292103	−	0.292103i	−0.837911	+	0.545807i	$0.816223\pi$
$294$		0			0
$295$	−8.00000	+	4.00000i	−0.465778	+	0.232889i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			4.00000i			0.231326i
$300$		0			0
$301$			24.0000i			1.38334i
$302$		0			0
$303$	12.0000	+	12.0000i	0.689382	+	0.689382i
$304$		0			0
$305$	8.00000	−	4.00000i	0.458079	−	0.229039i
$306$		0			0
$307$	−10.0000	−	10.0000i	−0.570730	−	0.570730i	0.361602	−	0.932332i	$-0.382230\pi$
$307$	−10.0000	−	10.0000i	−0.570730	−	0.570730i	−0.932332	+	0.361602i	$0.882230\pi$
$308$		0			0
$309$	24.0000			1.36531
$310$		0			0
$311$		−	28.0000i		−	1.58773i	−0.608091	−	0.793867i	$-0.708065\pi$
$311$		−	28.0000i		−	1.58773i	0.608091	−	0.793867i	$-0.291935\pi$
$312$		0			0
$313$	−15.0000	+	15.0000i	−0.847850	+	0.847850i	−0.989865	−	0.142014i	$-0.954642\pi$
$313$	−15.0000	+	15.0000i	−0.847850	+	0.847850i	0.142014	+	0.989865i	$0.454642\pi$
$314$		0			0
$315$	−10.0000	+	30.0000i	−0.563436	+	1.69031i
$316$		0			0
$317$	11.0000	−	11.0000i	0.617822	−	0.617822i	−0.327151	−	0.944972i	$-0.606088\pi$
$317$	11.0000	−	11.0000i	0.617822	−	0.617822i	0.944972	+	0.327151i	$0.106088\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	20.0000	−	20.0000i	1.11283	−	1.11283i
$324$		0			0
$325$	−7.00000	+	1.00000i	−0.388290	+	0.0554700i
$326$		0			0
$327$	−20.0000	+	20.0000i	−1.10600	+	1.10600i
$328$		0			0
$329$		−	8.00000i		−	0.441054i
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$	5.00000	+	5.00000i	0.273998	+	0.273998i
$334$		0			0
$335$	−10.0000	+	30.0000i	−0.546358	+	1.63908i
$336$		0			0
$337$	−23.0000	−	23.0000i	−1.25289	−	1.25289i	−0.954419	−	0.298471i	$-0.903523\pi$
$337$	−23.0000	−	23.0000i	−1.25289	−	1.25289i	−0.298471	−	0.954419i	$-0.596477\pi$
$338$		0			0
$339$		−	36.0000i		−	1.95525i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$		0			0
$345$	8.00000	+	16.0000i	0.430706	+	0.861411i
$346$		0			0
$347$	−18.0000	−	18.0000i	−0.966291	−	0.966291i	0.0331594	−	0.999450i	$-0.489443\pi$
$347$	−18.0000	−	18.0000i	−0.966291	−	0.966291i	−0.999450	+	0.0331594i	$0.989443\pi$
$348$		0			0
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$		0			0
$351$			8.00000i			0.427008i
$352$		0			0
$353$	9.00000	−	9.00000i	0.479022	−	0.479022i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	9.00000	−	9.00000i	0.479022	−	0.479022i	0.904819	+	0.425797i	$0.140006\pi$
$354$		0			0
$355$	24.0000	−	12.0000i	1.27379	−	0.636894i
$356$		0			0
$357$	40.0000	−	40.0000i	2.11702	−	2.11702i
$358$		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
$363$	22.0000	−	22.0000i	1.15470	−	1.15470i
$364$		0			0
$365$	−9.00000	−	3.00000i	−0.471082	−	0.157027i
$366$		0			0
$367$	22.0000	−	22.0000i	1.14839	−	1.14839i	0.161521	−	0.986869i	$-0.448360\pi$
$367$	22.0000	−	22.0000i	1.14839	−	1.14839i	0.986869	−	0.161521i	$-0.0516401\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−28.0000			−1.45369
$372$		0			0
$373$	21.0000	+	21.0000i	1.08734	+	1.08734i	0.995802	+	0.0915371i	$0.0291780\pi$
$373$	21.0000	+	21.0000i	1.08734	+	1.08734i	0.0915371	+	0.995802i	$0.470822\pi$
$374$		0			0
$375$	−26.0000	+	18.0000i	−1.34263	+	0.929516i
$376$		0			0
$377$	−4.00000	−	4.00000i	−0.206010	−	0.206010i
$378$		0			0
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$		0			0
$381$		−	40.0000i		−	2.04926i
$382$		0			0
$383$	−22.0000	−	22.0000i	−1.12415	−	1.12415i	−0.991111	−	0.133036i	$-0.957527\pi$
$383$	−22.0000	−	22.0000i	−1.12415	−	1.12415i	−0.133036	−	0.991111i	$-0.542473\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	30.0000	+	30.0000i	1.52499	+	1.52499i
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$		−	20.0000i		−	1.01144i
$392$		0			0
$393$	16.0000	−	16.0000i	0.807093	−	0.807093i
$394$		0			0
$395$	16.0000	+	32.0000i	0.805047	+	1.61009i
$396$		0			0
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$		0			0
$399$	−32.0000			−1.60200
$400$		0			0
$401$	34.0000			1.69788			0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000			1.69788			0.848939	+	0.528490i	$0.177242\pi$
$402$		0			0
$403$	−4.00000	+	4.00000i	−0.199254	+	0.199254i
$404$		0			0
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		−	2.00000i		−	0.0988936i	−0.998777	−	0.0494468i	$-0.984254\pi$
$409$		−	2.00000i		−	0.0988936i	0.998777	−	0.0494468i	$-0.0157458\pi$
$410$		0			0
$411$	4.00000			0.197305
$412$		0			0
$413$	−8.00000	−	8.00000i	−0.393654	−	0.393654i
$414$		0			0
$415$	−6.00000	−	2.00000i	−0.294528	−	0.0981761i
$416$		0			0
$417$	−24.0000	−	24.0000i	−1.17529	−	1.17529i
$418$		0			0
$419$		−	12.0000i		−	0.586238i	−0.956076	−	0.293119i	$-0.905307\pi$
$419$		−	12.0000i		−	0.586238i	0.956076	−	0.293119i	$-0.0946933\pi$
$420$		0			0
$421$			20.0000i			0.974740i	0.873195	+	0.487370i	$0.162044\pi$
$421$			20.0000i			0.974740i	−0.873195	+	0.487370i	$0.837956\pi$
$422$		0			0
$423$	−10.0000	−	10.0000i	−0.486217	−	0.486217i
$424$		0			0
$425$	35.0000	−	5.00000i	1.69775	−	0.242536i
$426$		0			0
$427$	8.00000	+	8.00000i	0.387147	+	0.387147i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	4.00000i		−	0.192673i	−0.995349	−	0.0963366i	$-0.969287\pi$
$431$		−	4.00000i		−	0.192673i	0.995349	−	0.0963366i	$-0.0307125\pi$
$432$		0			0
$433$	−19.0000	+	19.0000i	−0.913082	+	0.913082i	−0.996513	−	0.0834318i	$-0.973412\pi$
$433$	−19.0000	+	19.0000i	−0.913082	+	0.913082i	0.0834318	+	0.996513i	$0.473412\pi$
$434$		0			0
$435$	−24.0000	−	8.00000i	−1.15071	−	0.383571i
$436$		0			0
$437$	−8.00000	+	8.00000i	−0.382692	+	0.382692i
$438$		0			0
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$	−5.00000			−0.238095
$442$		0			0
$443$	22.0000	−	22.0000i	1.04525	−	1.04525i	0.0463251	−	0.998926i	$-0.485249\pi$
$443$	22.0000	−	22.0000i	1.04525	−	1.04525i	0.998926	−	0.0463251i	$-0.0147510\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−36.0000	+	36.0000i	−1.70274	+	1.70274i
$448$		0			0
$449$		−	26.0000i		−	1.22702i	−0.789689	−	0.613508i	$-0.789758\pi$
$449$		−	26.0000i		−	1.22702i	0.789689	−	0.613508i	$-0.210242\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−24.0000	−	24.0000i	−1.12762	−	1.12762i
$454$		0			0
$455$	−4.00000	−	8.00000i	−0.187523	−	0.375046i
$456$		0			0
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	0.263099	−	0.964769i	$-0.415256\pi$
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	−0.964769	+	0.263099i	$0.915256\pi$
$458$		0			0
$459$		−	40.0000i		−	1.86704i
$460$		0			0
$461$			14.0000i			0.652045i	0.945362	+	0.326023i	$0.105709\pi$
$461$			14.0000i			0.652045i	−0.945362	+	0.326023i	$0.894291\pi$
$462$		0			0
$463$	22.0000	+	22.0000i	1.02243	+	1.02243i	0.999743	+	0.0226840i	$0.00722117\pi$
$463$	22.0000	+	22.0000i	1.02243	+	1.02243i	0.0226840	+	0.999743i	$0.492779\pi$
$464$		0			0
$465$	−8.00000	+	24.0000i	−0.370991	+	1.11297i
$466$		0			0
$467$	2.00000	+	2.00000i	0.0925490	+	0.0925490i	0.751865	−	0.659317i	$-0.229154\pi$
$467$	2.00000	+	2.00000i	0.0925490	+	0.0925490i	−0.659317	+	0.751865i	$0.729154\pi$
$468$		0			0
$469$	−40.0000			−1.84703
$470$		0			0
$471$		−	36.0000i		−	1.65879i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−16.0000	−	12.0000i	−0.734130	−	0.550598i
$476$		0			0
$477$	−35.0000	+	35.0000i	−1.60254	+	1.60254i
$478$		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
$481$	−2.00000			−0.0911922
$482$		0			0
$483$	−16.0000	+	16.0000i	−0.728025	+	0.728025i
$484$		0			0
$485$	−3.00000	+	9.00000i	−0.136223	+	0.408669i
$486$		0			0
$487$	−6.00000	+	6.00000i	−0.271886	+	0.271886i	−0.829859	−	0.557973i	$-0.811579\pi$
$487$	−6.00000	+	6.00000i	−0.271886	+	0.271886i	0.557973	+	0.829859i	$0.311579\pi$
$488$		0			0
$489$		−	8.00000i		−	0.361773i
$490$		0			0
$491$	−16.0000			−0.722070			−0.361035	−	0.932552i	$-0.617576\pi$
$491$	−16.0000			−0.722070			−0.361035	+	0.932552i	$0.617576\pi$
$492$		0			0
$493$	20.0000	+	20.0000i	0.900755	+	0.900755i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.0000	+	24.0000i	1.07655	+	1.07655i
$498$		0			0
$499$			4.00000i			0.179065i	0.995984	+	0.0895323i	$0.0285372\pi$
$499$			4.00000i			0.179065i	−0.995984	+	0.0895323i	$0.971463\pi$
$500$		0			0
$501$		−	8.00000i		−	0.357414i
$502$		0			0
$503$	10.0000	+	10.0000i	0.445878	+	0.445878i	0.893982	−	0.448104i	$-0.147900\pi$
$503$	10.0000	+	10.0000i	0.445878	+	0.445878i	−0.448104	+	0.893982i	$0.647900\pi$
$504$		0			0
$505$	−12.0000	+	6.00000i	−0.533993	+	0.266996i
$506$		0			0
$507$	22.0000	+	22.0000i	0.977054	+	0.977054i
$508$		0			0
$509$	36.0000			1.59567			0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000			1.59567			0.797836	+	0.602875i	$0.205978\pi$
$510$		0			0
$511$		−	12.0000i		−	0.530849i
$512$		0			0
$513$	−16.0000	+	16.0000i	−0.706417	+	0.706417i
$514$		0			0
$515$	−6.00000	+	18.0000i	−0.264392	+	0.793175i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	52.0000			2.28255
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	14.0000	−	14.0000i	0.612177	−	0.612177i	−0.331336	−	0.943513i	$-0.607499\pi$
$523$	14.0000	−	14.0000i	0.612177	−	0.612177i	0.943513	+	0.331336i	$0.107499\pi$
$524$		0			0
$525$	−32.0000	−	24.0000i	−1.39659	−	1.04745i
$526$		0			0
$527$	20.0000	−	20.0000i	0.871214	−	0.871214i
$528$		0			0
$529$		−	15.0000i		−	0.652174i
$530$		0			0
$531$	−20.0000			−0.867926
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−6.00000	+	18.0000i	−0.259403	+	0.778208i
$536$		0			0
$537$	−24.0000	−	24.0000i	−1.03568	−	1.03568i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$		0			0
$543$	20.0000	+	20.0000i	0.858282	+	0.858282i
$544$		0			0
$545$	−10.0000	−	20.0000i	−0.428353	−	0.856706i
$546$		0			0
$547$	−6.00000	−	6.00000i	−0.256541	−	0.256541i	0.567104	−	0.823646i	$-0.308064\pi$
$547$	−6.00000	−	6.00000i	−0.256541	−	0.256541i	−0.823646	+	0.567104i	$0.808064\pi$
$548$		0			0
$549$	20.0000			0.853579
$550$		0			0
$551$		−	16.0000i		−	0.681623i
$552$		0			0
$553$	−32.0000	+	32.0000i	−1.36078	+	1.36078i
$554$		0			0
$555$	−8.00000	+	4.00000i	−0.339581	+	0.169791i
$556$		0			0
$557$	−15.0000	+	15.0000i	−0.635570	+	0.635570i	−0.949460	−	0.313889i	$-0.898368\pi$
$557$	−15.0000	+	15.0000i	−0.635570	+	0.635570i	0.313889	+	0.949460i	$0.398368\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.00000	−	6.00000i	0.252870	−	0.252870i	−0.569276	−	0.822146i	$-0.692777\pi$
$563$	6.00000	−	6.00000i	0.252870	−	0.252870i	0.822146	+	0.569276i	$0.192777\pi$
$564$		0			0
$565$	27.0000	+	9.00000i	1.13590	+	0.378633i
$566$		0			0
$567$	−2.00000	+	2.00000i	−0.0839921	+	0.0839921i
$568$		0			0
$569$			2.00000i			0.0838444i	0.999121	+	0.0419222i	$0.0133482\pi$
$569$			2.00000i			0.0838444i	−0.999121	+	0.0419222i	$0.986652\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$	−40.0000	−	40.0000i	−1.67102	−	1.67102i
$574$		0			0
$575$	−14.0000	+	2.00000i	−0.583840	+	0.0834058i
$576$		0			0
$577$	15.0000	+	15.0000i	0.624458	+	0.624458i	0.946668	−	0.322210i	$-0.104426\pi$
$577$	15.0000	+	15.0000i	0.624458	+	0.624458i	−0.322210	+	0.946668i	$0.604426\pi$
$578$		0			0
$579$		−	20.0000i		−	0.831172i
$580$		0			0
$581$		−	8.00000i		−	0.331896i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−15.0000	−	5.00000i	−0.620174	−	0.206725i
$586$		0			0
$587$	14.0000	+	14.0000i	0.577842	+	0.577842i	0.934308	−	0.356466i	$-0.116019\pi$
$587$	14.0000	+	14.0000i	0.577842	+	0.577842i	−0.356466	+	0.934308i	$0.616019\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$		0			0
$591$		−	20.0000i		−	0.822690i
$592$		0			0
$593$	1.00000	−	1.00000i	0.0410651	−	0.0410651i	−0.686276	−	0.727341i	$-0.740756\pi$
$593$	1.00000	−	1.00000i	0.0410651	−	0.0410651i	0.727341	+	0.686276i	$0.240756\pi$
$594$		0			0
$595$	20.0000	+	40.0000i	0.819920	+	1.63984i
$596$		0			0
$597$	−48.0000	+	48.0000i	−1.96451	+	1.96451i
$598$		0			0
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	−50.0000	+	50.0000i	−2.03616	+	2.03616i
$604$		0			0
$605$	11.0000	+	22.0000i	0.447214	+	0.894427i
$606$		0			0
$607$	18.0000	−	18.0000i	0.730597	−	0.730597i	−0.240141	−	0.970738i	$-0.577194\pi$
$607$	18.0000	−	18.0000i	0.730597	−	0.730597i	0.970738	+	0.240141i	$0.0771936\pi$
$608$		0			0
$609$		−	32.0000i		−	1.29671i
$610$		0			0
$611$	4.00000			0.161823
$612$		0			0
$613$	−9.00000	−	9.00000i	−0.363507	−	0.363507i	0.501596	−	0.865102i	$-0.332747\pi$
$613$	−9.00000	−	9.00000i	−0.363507	−	0.363507i	−0.865102	+	0.501596i	$0.832747\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	29.0000	+	29.0000i	1.16750	+	1.16750i	0.982795	+	0.184701i	$0.0591318\pi$
$617$	29.0000	+	29.0000i	1.16750	+	1.16750i	0.184701	+	0.982795i	$0.440868\pi$
$618$		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
$621$			16.0000i			0.642058i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.0000			0.398726
$630$		0			0
$631$			4.00000i			0.159237i	0.996825	+	0.0796187i	$0.0253703\pi$
$631$			4.00000i			0.159237i	−0.996825	+	0.0796187i	$0.974630\pi$
$632$		0			0
$633$	32.0000	−	32.0000i	1.27189	−	1.27189i
$634$		0			0
$635$	30.0000	+	10.0000i	1.19051	+	0.396838i
$636$		0			0
$637$	1.00000	−	1.00000i	0.0396214	−	0.0396214i
$638$		0			0
$639$	60.0000			2.37356
$640$		0			0
$641$	−48.0000			−1.89589			−0.947943	−	0.318440i	$-0.896841\pi$
$641$	−48.0000			−1.89589			−0.947943	+	0.318440i	$0.896841\pi$
$642$		0			0
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	−0.481877	−	0.876239i	$-0.660045\pi$
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	0.876239	+	0.481877i	$0.160045\pi$
$644$		0			0
$645$	−48.0000	+	24.0000i	−1.89000	+	0.944999i
$646$		0			0
$647$	10.0000	−	10.0000i	0.393141	−	0.393141i	−0.482665	−	0.875805i	$-0.660331\pi$
$647$	10.0000	−	10.0000i	0.393141	−	0.393141i	0.875805	+	0.482665i	$0.160331\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−32.0000			−1.25418
$652$		0			0
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	0.687270	−	0.726403i	$-0.258809\pi$
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	−0.726403	+	0.687270i	$0.758809\pi$
$654$		0			0
$655$	8.00000	+	16.0000i	0.312586	+	0.625172i
$656$		0			0
$657$	−15.0000	−	15.0000i	−0.585206	−	0.585206i
$658$		0			0
$659$			20.0000i			0.779089i	0.921008	+	0.389545i	$0.127368\pi$
$659$			20.0000i			0.779089i	−0.921008	+	0.389545i	$0.872632\pi$
$660$		0			0
$661$			12.0000i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$661$			12.0000i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$662$		0			0
$663$	20.0000	+	20.0000i	0.776736	+	0.776736i
$664$		0			0
$665$	8.00000	−	24.0000i	0.310227	−	0.930680i
$666$		0			0
$667$	−8.00000	−	8.00000i	−0.309761	−	0.309761i
$668$		0			0
$669$	−40.0000			−1.54649
$670$		0			0
$671$		0			0
$672$		0			0
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	−0.604141	−	0.796877i	$-0.706484\pi$
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	0.796877	+	0.604141i	$0.206484\pi$
$674$		0			0
$675$	−28.0000	+	4.00000i	−1.07772	+	0.153960i
$676$		0			0
$677$	3.00000	−	3.00000i	0.115299	−	0.115299i	−0.647103	−	0.762402i	$-0.724020\pi$
$677$	3.00000	−	3.00000i	0.115299	−	0.115299i	0.762402	+	0.647103i	$0.224020\pi$
$678$		0			0
$679$	−12.0000			−0.460518
$680$		0			0
$681$	−40.0000			−1.53280
$682$		0			0
$683$	−22.0000	+	22.0000i	−0.841807	+	0.841807i	−0.989094	−	0.147287i	$-0.952946\pi$
$683$	−22.0000	+	22.0000i	−0.841807	+	0.841807i	0.147287	+	0.989094i	$0.452946\pi$
$684$		0			0
$685$	−1.00000	+	3.00000i	−0.0382080	+	0.114624i
$686$		0			0
$687$	−40.0000	+	40.0000i	−1.52610	+	1.52610i
$688$		0			0
$689$		−	14.0000i		−	0.533358i
$690$		0			0
$691$	32.0000			1.21734			0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000			1.21734			0.608669	+	0.793424i	$0.291704\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	24.0000	−	12.0000i	0.910372	−	0.455186i
$696$		0			0
$697$		0			0
$698$		0			0
$699$			20.0000i			0.756469i
$700$		0			0
$701$		−	20.0000i		−	0.755390i	−0.925930	−	0.377695i	$-0.876717\pi$
$701$		−	20.0000i		−	0.755390i	0.925930	−	0.377695i	$-0.123283\pi$
$702$		0			0
$703$	−4.00000	−	4.00000i	−0.150863	−	0.150863i
$704$		0			0
$705$	16.0000	−	8.00000i	0.602595	−	0.301297i
$706$		0			0
$707$	−12.0000	−	12.0000i	−0.451306	−	0.451306i
$708$		0			0
$709$	12.0000			0.450669			0.225335	−	0.974281i	$-0.427652\pi$
$709$	12.0000			0.450669			0.225335	+	0.974281i	$0.427652\pi$
$710$		0			0
$711$			80.0000i			3.00023i
$712$		0			0
$713$	−8.00000	+	8.00000i	−0.299602	+	0.299602i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	16.0000	−	16.0000i	0.597531	−	0.597531i
$718$		0			0
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$		0			0
$723$	32.0000	−	32.0000i	1.19009	−	1.19009i
$724$		0			0
$725$	12.0000	−	16.0000i	0.445669	−	0.594225i
$726$		0			0
$727$	18.0000	−	18.0000i	0.667583	−	0.667583i	−0.289573	−	0.957156i	$-0.593513\pi$
$727$	18.0000	−	18.0000i	0.667583	−	0.667583i	0.957156	+	0.289573i	$0.0935133\pi$
$728$		0			0
$729$		−	43.0000i		−	1.59259i
$730$		0			0
$731$	60.0000			2.21918
$732$		0			0
$733$	−21.0000	−	21.0000i	−0.775653	−	0.775653i	0.203436	−	0.979088i	$-0.434789\pi$
$733$	−21.0000	−	21.0000i	−0.775653	−	0.775653i	−0.979088	+	0.203436i	$0.934789\pi$
$734$		0			0
$735$	2.00000	−	6.00000i	0.0737711	−	0.221313i
$736$		0			0
$737$		0			0
$738$		0			0
$739$			44.0000i			1.61857i	0.587419	+	0.809283i	$0.300144\pi$
$739$			44.0000i			1.61857i	−0.587419	+	0.809283i	$0.699856\pi$
$740$		0			0
$741$		−	16.0000i		−	0.587775i
$742$		0			0
$743$	30.0000	+	30.0000i	1.10059	+	1.10059i	0.994339	+	0.106254i	$0.0338857\pi$
$743$	30.0000	+	30.0000i	1.10059	+	1.10059i	0.106254	+	0.994339i	$0.466114\pi$
$744$		0			0
$745$	−18.0000	−	36.0000i	−0.659469	−	1.31894i
$746$		0			0
$747$	−10.0000	−	10.0000i	−0.365881	−	0.365881i
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$		−	44.0000i		−	1.60558i	−0.596260	−	0.802791i	$-0.703347\pi$
$751$		−	44.0000i		−	1.60558i	0.596260	−	0.802791i	$-0.296653\pi$
$752$		0			0
$753$	48.0000	−	48.0000i	1.74922	−	1.74922i
$754$		0			0
$755$	24.0000	−	12.0000i	0.873449	−	0.436725i
$756$		0			0
$757$	1.00000	−	1.00000i	0.0363456	−	0.0363456i	−0.688700	−	0.725046i	$-0.741818\pi$
$757$	1.00000	−	1.00000i	0.0363456	−	0.0363456i	0.725046	+	0.688700i	$0.241818\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$		0			0
$763$	20.0000	−	20.0000i	0.724049	−	0.724049i
$764$		0			0
$765$	75.0000	+	25.0000i	2.71163	+	0.903877i
$766$		0			0
$767$	4.00000	−	4.00000i	0.144432	−	0.144432i
$768$		0			0
$769$			40.0000i			1.44244i	0.692708	+	0.721218i	$0.256418\pi$
$769$			40.0000i			1.44244i	−0.692708	+	0.721218i	$0.743582\pi$
$770$		0			0
$771$	−28.0000			−1.00840
$772$		0			0
$773$	−1.00000	−	1.00000i	−0.0359675	−	0.0359675i	0.688894	−	0.724862i	$-0.258096\pi$
$773$	−1.00000	−	1.00000i	−0.0359675	−	0.0359675i	−0.724862	+	0.688894i	$0.758096\pi$
$774$		0			0
$775$	−16.0000	−	12.0000i	−0.574737	−	0.431053i
$776$		0			0
$777$	−8.00000	−	8.00000i	−0.286998	−	0.286998i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−16.0000	−	16.0000i	−0.571793	−	0.571793i
$784$		0			0
$785$	27.0000	+	9.00000i	0.963671	+	0.321224i
$786$		0			0
$787$	30.0000	+	30.0000i	1.06938	+	1.06938i	0.997406	+	0.0719783i	$0.0229312\pi$
$787$	30.0000	+	30.0000i	1.06938	+	1.06938i	0.0719783	+	0.997406i	$0.477069\pi$
$788$		0			0
$789$	−24.0000			−0.854423
$790$		0			0
$791$			36.0000i			1.28001i
$792$		0			0
$793$	−4.00000	+	4.00000i	−0.142044	+	0.142044i
$794$		0			0
$795$	−28.0000	−	56.0000i	−0.993058	−	1.98612i
$796$		0			0
$797$	−29.0000	+	29.0000i	−1.02723	+	1.02723i	−0.0276140	+	0.999619i	$0.508791\pi$
$797$	−29.0000	+	29.0000i	−1.02723	+	1.02723i	−0.999619	+	0.0276140i	$0.991209\pi$
$798$		0			0
$799$	−20.0000			−0.707549
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−8.00000	−	16.0000i	−0.281963	−	0.563926i
$806$		0			0
$807$	20.0000	−	20.0000i	0.704033	−	0.704033i
$808$		0			0
$809$		−	24.0000i		−	0.843795i	−0.906644	−	0.421898i	$-0.861364\pi$
$809$		−	24.0000i		−	0.843795i	0.906644	−	0.421898i	$-0.138636\pi$
$810$		0			0
$811$	−24.0000			−0.842754			−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$812$		0			0
$813$	40.0000	+	40.0000i	1.40286	+	1.40286i
$814$		0			0
$815$	6.00000	+	2.00000i	0.210171	+	0.0700569i
$816$		0			0
$817$	−24.0000	−	24.0000i	−0.839654	−	0.839654i
$818$		0			0
$819$		−	20.0000i		−	0.698857i
$820$		0			0
$821$		−	28.0000i		−	0.977207i	−0.872506	−	0.488603i	$-0.837507\pi$
$821$		−	28.0000i		−	0.977207i	0.872506	−	0.488603i	$-0.162493\pi$
$822$		0			0
$823$	−30.0000	−	30.0000i	−1.04573	−	1.04573i	−0.998903	−	0.0468315i	$-0.985088\pi$
$823$	−30.0000	−	30.0000i	−1.04573	−	1.04573i	−0.0468315	−	0.998903i	$-0.514912\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.00000	−	2.00000i	−0.0695468	−	0.0695468i	0.671478	−	0.741025i	$-0.265660\pi$
$827$	−2.00000	−	2.00000i	−0.0695468	−	0.0695468i	−0.741025	+	0.671478i	$0.765660\pi$
$828$		0			0
$829$	6.00000			0.208389			0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000			0.208389			0.104194	+	0.994557i	$0.466774\pi$
$830$		0			0
$831$			36.0000i			1.24883i
$832$		0			0
$833$	−5.00000	+	5.00000i	−0.173240	+	0.173240i
$834$		0			0
$835$	6.00000	+	2.00000i	0.207639	+	0.0692129i
$836$		0			0
$837$	−16.0000	+	16.0000i	−0.553041	+	0.553041i
$838$		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
$841$	−13.0000			−0.448276
$842$		0			0
$843$	16.0000	−	16.0000i	0.551069	−	0.551069i
$844$		0			0
$845$	−22.0000	+	11.0000i	−0.756823	+	0.378412i
$846$		0			0
$847$	−22.0000	+	22.0000i	−0.755929	+	0.755929i
$848$		0			0
$849$			24.0000i			0.823678i
$850$		0			0
$851$	−4.00000			−0.137118
$852$		0			0
$853$	15.0000	+	15.0000i	0.513590	+	0.513590i	0.915625	−	0.402034i	$-0.131697\pi$
$853$	15.0000	+	15.0000i	0.513590	+	0.513590i	−0.402034	+	0.915625i	$0.631697\pi$
$854$		0			0
$855$	−20.0000	−	40.0000i	−0.683986	−	1.36797i
$856$		0			0
$857$	7.00000	+	7.00000i	0.239115	+	0.239115i	0.816484	−	0.577368i	$-0.195920\pi$
$857$	7.00000	+	7.00000i	0.239115	+	0.239115i	−0.577368	+	0.816484i	$0.695920\pi$
$858$		0			0
$859$			28.0000i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$859$			28.0000i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34.0000	−	34.0000i	−1.15737	−	1.15737i	−0.985038	−	0.172335i	$-0.944869\pi$
$863$	−34.0000	−	34.0000i	−1.15737	−	1.15737i	−0.172335	−	0.985038i	$-0.555131\pi$
$864$		0			0
$865$	−13.0000	+	39.0000i	−0.442013	+	1.32604i
$866$		0			0
$867$	−66.0000	−	66.0000i	−2.24148	−	2.24148i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	20.0000i		−	0.677674i
$872$		0			0
$873$	−15.0000	+	15.0000i	−0.507673	+	0.507673i
$874$		0			0
$875$	26.0000	−	18.0000i	0.878960	−	0.608511i
$876$		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
$879$	20.0000			0.674583
$880$		0			0
$881$	−40.0000			−1.34763			−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000			−1.34763			−0.673817	+	0.738898i	$0.735346\pi$
$882$		0			0
$883$	−10.0000	+	10.0000i	−0.336527	+	0.336527i	−0.855058	−	0.518532i	$-0.826479\pi$
$883$	−10.0000	+	10.0000i	−0.336527	+	0.336527i	0.518532	+	0.855058i	$0.326479\pi$
$884$		0			0
$885$	8.00000	−	24.0000i	0.268917	−	0.806751i
$886$		0			0
$887$	10.0000	−	10.0000i	0.335767	−	0.335767i	−0.519004	−	0.854772i	$-0.673697\pi$
$887$	10.0000	−	10.0000i	0.335767	−	0.335767i	0.854772	+	0.519004i	$0.173697\pi$
$888$		0			0
$889$			40.0000i			1.34156i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.00000	+	8.00000i	0.267710	+	0.267710i
$894$		0			0
$895$	24.0000	−	12.0000i	0.802232	−	0.401116i
$896$		0			0
$897$	−8.00000	−	8.00000i	−0.267112	−	0.267112i
$898$		0			0
$899$		−	16.0000i		−	0.533630i
$900$		0			0
$901$			70.0000i			2.33204i
$902$		0			0
$903$	−48.0000	−	48.0000i	−1.59734	−	1.59734i
$904$		0			0
$905$	−20.0000	+	10.0000i	−0.664822	+	0.332411i
$906$		0			0
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	0.600442	−	0.799668i	$-0.294991\pi$
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	−0.799668	+	0.600442i	$0.794991\pi$
$908$		0			0
$909$	−30.0000			−0.995037
$910$		0			0
$911$			4.00000i			0.132526i	0.997802	+	0.0662630i	$0.0211076\pi$
$911$			4.00000i			0.132526i	−0.997802	+	0.0662630i	$0.978892\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−8.00000	+	24.0000i	−0.264472	+	0.793416i
$916$		0			0
$917$	−16.0000	+	16.0000i	−0.528367	+	0.528367i
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$		0			0
$921$	40.0000			1.31804
$922$		0			0
$923$	−12.0000	+	12.0000i	−0.394985	+	0.394985i
$924$		0			0
$925$	−1.00000	−	7.00000i	−0.0328798	−	0.230159i
$926$		0			0
$927$	−30.0000	+	30.0000i	−0.985329	+	0.985329i
$928$		0			0
$929$		−	6.00000i		−	0.196854i	−0.995144	−	0.0984268i	$-0.968619\pi$
$929$		−	6.00000i		−	0.196854i	0.995144	−	0.0984268i	$-0.0313810\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$		0			0
$933$	56.0000	+	56.0000i	1.83336	+	1.83336i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−27.0000	−	27.0000i	−0.882052	−	0.882052i	0.111691	−	0.993743i	$-0.464373\pi$
$937$	−27.0000	−	27.0000i	−0.882052	−	0.882052i	−0.993743	+	0.111691i	$0.964373\pi$
$938$		0			0
$939$		−	60.0000i		−	1.95803i
$940$		0			0
$941$		−	46.0000i		−	1.49956i	−0.661689	−	0.749779i	$-0.730160\pi$
$941$		−	46.0000i		−	1.49956i	0.661689	−	0.749779i	$-0.269840\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−16.0000	−	32.0000i	−0.520480	−	1.04096i
$946$		0			0
$947$	−10.0000	−	10.0000i	−0.324956	−	0.324956i	0.525708	−	0.850665i	$-0.323800\pi$
$947$	−10.0000	−	10.0000i	−0.324956	−	0.324956i	−0.850665	+	0.525708i	$0.823800\pi$
$948$		0			0
$949$	6.00000			0.194768
$950$		0			0
$951$			44.0000i			1.42680i
$952$		0			0
$953$	9.00000	−	9.00000i	0.291539	−	0.291539i	−0.546149	−	0.837688i	$-0.683907\pi$
$953$	9.00000	−	9.00000i	0.291539	−	0.291539i	0.837688	+	0.546149i	$0.183907\pi$
$954$		0			0
$955$	40.0000	−	20.0000i	1.29437	−	0.647185i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.00000			−0.129167
$960$		0			0
$961$	15.0000			0.483871
$962$		0			0
$963$	−30.0000	+	30.0000i	−0.966736	+	0.966736i
$964$		0			0
$965$	15.0000	+	5.00000i	0.482867	+	0.160956i
$966$		0			0
$967$	−10.0000	+	10.0000i	−0.321578	+	0.321578i	−0.849372	−	0.527794i	$-0.823019\pi$
$967$	−10.0000	+	10.0000i	−0.321578	+	0.321578i	0.527794	+	0.849372i	$0.323019\pi$
$968$		0			0
$969$			80.0000i			2.56997i
$970$		0			0
$971$	8.00000			0.256732			0.128366	−	0.991727i	$-0.459027\pi$
$971$	8.00000			0.256732			0.128366	+	0.991727i	$0.459027\pi$
$972$		0			0
$973$	24.0000	+	24.0000i	0.769405	+	0.769405i
$974$		0			0
$975$	12.0000	−	16.0000i	0.384308	−	0.512410i
$976$		0			0
$977$	21.0000	+	21.0000i	0.671850	+	0.671850i	0.958142	−	0.286293i	$-0.0924230\pi$
$977$	21.0000	+	21.0000i	0.671850	+	0.671850i	−0.286293	+	0.958142i	$0.592423\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		−	50.0000i		−	1.59638i
$982$		0			0
$983$	−34.0000	−	34.0000i	−1.08443	−	1.08443i	−0.996090	−	0.0883413i	$-0.971843\pi$
$983$	−34.0000	−	34.0000i	−1.08443	−	1.08443i	−0.0883413	−	0.996090i	$-0.528157\pi$
$984$		0			0
$985$	15.0000	+	5.00000i	0.477940	+	0.159313i
$986$		0			0
$987$	16.0000	+	16.0000i	0.509286	+	0.509286i
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$		−	4.00000i		−	0.127064i	−0.997980	−	0.0635321i	$-0.979763\pi$
$991$		−	4.00000i		−	0.127064i	0.997980	−	0.0635321i	$-0.0202365\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−24.0000	−	48.0000i	−0.760851	−	1.52170i
$996$		0			0
$997$	21.0000	−	21.0000i	0.665077	−	0.665077i	−0.291496	−	0.956572i	$-0.594153\pi$
$997$	21.0000	−	21.0000i	0.665077	−	0.665077i	0.956572	+	0.291496i	$0.0941528\pi$
$998$		0			0
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.o.a.127.1		2
4.3	odd	2		1280.2.o.o.127.1		2
5.3	odd	4		1280.2.o.b.383.1		2
8.3	odd	2		1280.2.o.b.127.1		2
8.5	even	2		1280.2.o.p.127.1		2
16.3	odd	4		160.2.n.f.127.1	yes	2
16.5	even	4		320.2.n.h.127.1		2
16.11	odd	4		320.2.n.a.127.1		2
16.13	even	4		160.2.n.a.127.1	yes	2
20.3	even	4		1280.2.o.p.383.1		2
40.3	even	4	inner	1280.2.o.a.383.1		2
40.13	odd	4		1280.2.o.o.383.1		2
48.29	odd	4		1440.2.x.i.127.1		2
48.35	even	4		1440.2.x.j.127.1		2
80.3	even	4		160.2.n.a.63.1	✓	2
80.13	odd	4		160.2.n.f.63.1	yes	2
80.19	odd	4		800.2.n.a.607.1		2
80.27	even	4		1600.2.n.a.1343.1		2
80.29	even	4		800.2.n.j.607.1		2
80.37	odd	4		1600.2.n.n.1343.1		2
80.43	even	4		320.2.n.h.63.1		2
80.53	odd	4		320.2.n.a.63.1		2
80.59	odd	4		1600.2.n.n.1407.1		2
80.67	even	4		800.2.n.j.543.1		2
80.69	even	4		1600.2.n.a.1407.1		2
80.77	odd	4		800.2.n.a.543.1		2
240.83	odd	4		1440.2.x.i.703.1		2
240.173	even	4		1440.2.x.j.703.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.n.a.63.1	✓	2	80.3	even	4
160.2.n.a.127.1	yes	2	16.13	even	4
160.2.n.f.63.1	yes	2	80.13	odd	4
160.2.n.f.127.1	yes	2	16.3	odd	4
320.2.n.a.63.1		2	80.53	odd	4
320.2.n.a.127.1		2	16.11	odd	4
320.2.n.h.63.1		2	80.43	even	4
320.2.n.h.127.1		2	16.5	even	4
800.2.n.a.543.1		2	80.77	odd	4
800.2.n.a.607.1		2	80.19	odd	4
800.2.n.j.543.1		2	80.67	even	4
800.2.n.j.607.1		2	80.29	even	4
1280.2.o.a.127.1		2	1.1	even	1	trivial
1280.2.o.a.383.1		2	40.3	even	4	inner
1280.2.o.b.127.1		2	8.3	odd	2
1280.2.o.b.383.1		2	5.3	odd	4
1280.2.o.o.127.1		2	4.3	odd	2
1280.2.o.o.383.1		2	40.13	odd	4
1280.2.o.p.127.1		2	8.5	even	2
1280.2.o.p.383.1		2	20.3	even	4
1440.2.x.i.127.1		2	48.29	odd	4
1440.2.x.i.703.1		2	240.83	odd	4
1440.2.x.j.127.1		2	48.35	even	4
1440.2.x.j.703.1		2	240.173	even	4
1600.2.n.a.1343.1		2	80.27	even	4
1600.2.n.a.1407.1		2	80.69	even	4
1600.2.n.n.1343.1		2	80.37	odd	4
1600.2.n.n.1407.1		2	80.59	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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} -5.00000i q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} -5.00000i q^{9} +(1.00000 + 1.00000i) q^{13} +(6.00000 + 2.00000i) q^{15} +(-5.00000 - 5.00000i) q^{17} +4.00000i q^{19} +8.00000i q^{21} +(2.00000 + 2.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -4.00000 q^{29} +4.00000i q^{31} +(-6.00000 - 2.00000i) q^{35} +(-1.00000 + 1.00000i) q^{37} -4.00000 q^{39} +(-6.00000 + 6.00000i) q^{43} +(-10.0000 + 5.00000i) q^{45} +(2.00000 - 2.00000i) q^{47} -1.00000i q^{49} +20.0000 q^{51} +(-7.00000 - 7.00000i) q^{53} +(-8.00000 - 8.00000i) q^{57} -4.00000i q^{59} +4.00000i q^{61} +(-10.0000 - 10.0000i) q^{63} +(1.00000 - 3.00000i) q^{65} +(-10.0000 - 10.0000i) q^{67} -8.00000 q^{69} +12.0000i q^{71} +(3.00000 - 3.00000i) q^{73} +(-2.00000 - 14.0000i) q^{75} -16.0000 q^{79} -1.00000 q^{81} +(2.00000 - 2.00000i) q^{83} +(-5.00000 + 15.0000i) q^{85} +(8.00000 - 8.00000i) q^{87} +4.00000 q^{91} +(-8.00000 - 8.00000i) q^{93} +(8.00000 - 4.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) \) 2 * q - 4 * q^3 - 2 * q^5 + 4 * q^7	\( 2 q - 4 q^{3} - 2 q^{5} + 4 q^{7} + 2 q^{13} + 12 q^{15} - 10 q^{17} + 4 q^{23} - 6 q^{25} + 8 q^{27} - 8 q^{29} - 12 q^{35} - 2 q^{37} - 8 q^{39} - 12 q^{43} - 20 q^{45} + 4 q^{47} + 40 q^{51} - 14 q^{53} - 16 q^{57} - 20 q^{63} + 2 q^{65} - 20 q^{67} - 16 q^{69} + 6 q^{73} - 4 q^{75} - 32 q^{79} - 2 q^{81} + 4 q^{83} - 10 q^{85} + 16 q^{87} + 8 q^{91} - 16 q^{93} + 16 q^{95} - 6 q^{97}+O(q^{100}) \) 2 * q - 4 * q^3 - 2 * q^5 + 4 * q^7 + 2 * q^13 + 12 * q^15 - 10 * q^17 + 4 * q^23 - 6 * q^25 + 8 * q^27 - 8 * q^29 - 12 * q^35 - 2 * q^37 - 8 * q^39 - 12 * q^43 - 20 * q^45 + 4 * q^47 + 40 * q^51 - 14 * q^53 - 16 * q^57 - 20 * q^63 + 2 * q^65 - 20 * q^67 - 16 * q^69 + 6 * q^73 - 4 * q^75 - 32 * q^79 - 2 * q^81 + 4 * q^83 - 10 * q^85 + 16 * q^87 + 8 * q^91 - 16 * q^93 + 16 * q^95 - 6 * q^97

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