LMFDB - Embedded newform 1024.2.e.d.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(257,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("1024.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.e (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:	$8.17668116698$
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 512)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1024.257
Dual form			1024.2.e.d.769.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{13} -4.00000 q^{15} +4.00000 q^{17} +(5.00000 + 5.00000i) q^{19} +(4.00000 - 4.00000i) q^{21} +4.00000i q^{23} -3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(-6.00000 - 6.00000i) q^{29} +8.00000 q^{31} +2.00000 q^{33} +(8.00000 + 8.00000i) q^{35} +(2.00000 - 2.00000i) q^{37} +4.00000i q^{39} +2.00000i q^{41} +(3.00000 - 3.00000i) q^{43} +(2.00000 + 2.00000i) q^{45} -9.00000 q^{49} +(4.00000 + 4.00000i) q^{51} +(-2.00000 + 2.00000i) q^{53} +4.00000i q^{55} +10.0000i q^{57} +(-3.00000 + 3.00000i) q^{59} +(6.00000 + 6.00000i) q^{61} -4.00000 q^{63} -8.00000 q^{65} +(3.00000 + 3.00000i) q^{67} +(-4.00000 + 4.00000i) q^{69} +4.00000i q^{71} -4.00000i q^{73} +(3.00000 - 3.00000i) q^{75} +(-4.00000 - 4.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(7.00000 + 7.00000i) q^{83} +(-8.00000 + 8.00000i) q^{85} -12.0000i q^{87} -12.0000i q^{89} +(8.00000 - 8.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} -20.0000 q^{95} -4.00000 q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{5}+O(q^{10}) $ 2 * q + 2 * q^3 - 4 * q^5	$ 2 q + 2 q^{3} - 4 q^{5} + 2 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 10 q^{19} + 8 q^{21} + 8 q^{27} - 12 q^{29} + 16 q^{31} + 4 q^{33} + 16 q^{35} + 4 q^{37} + 6 q^{43} + 4 q^{45} - 18 q^{49} + 8 q^{51} - 4 q^{53} - 6 q^{59} + 12 q^{61} - 8 q^{63} - 16 q^{65} + 6 q^{67} - 8 q^{69} + 6 q^{75} - 8 q^{77} + 16 q^{79} + 10 q^{81} + 14 q^{83} - 16 q^{85} + 16 q^{91} + 16 q^{93} - 40 q^{95} - 8 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^5 + 2 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 10 * q^19 + 8 * q^21 + 8 * q^27 - 12 * q^29 + 16 * q^31 + 4 * q^33 + 16 * q^35 + 4 * q^37 + 6 * q^43 + 4 * q^45 - 18 * q^49 + 8 * q^51 - 4 * q^53 - 6 * q^59 + 12 * q^61 - 8 * q^63 - 16 * q^65 + 6 * q^67 - 8 * q^69 + 6 * q^75 - 8 * q^77 + 16 * q^79 + 10 * q^81 + 14 * q^83 - 16 * q^85 + 16 * q^91 + 16 * q^93 - 40 * q^95 - 8 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$		0			0
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	−0.994936	−	0.100509i	$-0.967953\pi$
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	0.100509	+	0.994936i	$0.467953\pi$
$6$		0			0
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$		0			0
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$		0			0
$15$	−4.00000			−1.03280
$16$		0			0
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$		0			0
$21$	4.00000	−	4.00000i	0.872872	−	0.872872i
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$		0			0
$29$	−6.00000	−	6.00000i	−1.11417	−	1.11417i	−0.992580	−	0.121592i	$-0.961200\pi$
$29$	−6.00000	−	6.00000i	−1.11417	−	1.11417i	−0.121592	−	0.992580i	$-0.538800\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	2.00000			0.348155
$34$		0			0
$35$	8.00000	+	8.00000i	1.35225	+	1.35225i
$36$		0			0
$37$	2.00000	−	2.00000i	0.328798	−	0.328798i	−0.523331	−	0.852129i	$-0.675311\pi$
$37$	2.00000	−	2.00000i	0.328798	−	0.328798i	0.852129	+	0.523331i	$0.175311\pi$
$38$		0			0
$39$			4.00000i			0.640513i
$40$		0			0
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$		0			0
$45$	2.00000	+	2.00000i	0.298142	+	0.298142i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	−9.00000			−1.28571
$50$		0			0
$51$	4.00000	+	4.00000i	0.560112	+	0.560112i
$52$		0			0
$53$	−2.00000	+	2.00000i	−0.274721	+	0.274721i	−0.830997	−	0.556276i	$-0.812230\pi$
$53$	−2.00000	+	2.00000i	−0.274721	+	0.274721i	0.556276	+	0.830997i	$0.312230\pi$
$54$		0			0
$55$			4.00000i			0.539360i
$56$		0			0
$57$			10.0000i			1.32453i
$58$		0			0
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	−0.874889	−	0.484323i	$-0.839066\pi$
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	0.484323	+	0.874889i	$0.339066\pi$
$60$		0			0
$61$	6.00000	+	6.00000i	0.768221	+	0.768221i	0.977793	−	0.209572i	$-0.0672070\pi$
$61$	6.00000	+	6.00000i	0.768221	+	0.768221i	−0.209572	+	0.977793i	$0.567207\pi$
$62$		0			0
$63$	−4.00000			−0.503953
$64$		0			0
$65$	−8.00000			−0.992278
$66$		0			0
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	0.866202	−	0.499694i	$-0.166554\pi$
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	−0.499694	+	0.866202i	$0.666554\pi$
$68$		0			0
$69$	−4.00000	+	4.00000i	−0.481543	+	0.481543i
$70$		0			0
$71$			4.00000i			0.474713i	0.971423	+	0.237356i	$0.0762809\pi$
$71$			4.00000i			0.474713i	−0.971423	+	0.237356i	$0.923719\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$	3.00000	−	3.00000i	0.346410	−	0.346410i
$76$		0			0
$77$	−4.00000	−	4.00000i	−0.455842	−	0.455842i
$78$		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
$83$	7.00000	+	7.00000i	0.768350	+	0.768350i	0.977816	−	0.209466i	$-0.0671726\pi$
$83$	7.00000	+	7.00000i	0.768350	+	0.768350i	−0.209466	+	0.977816i	$0.567173\pi$
$84$		0			0
$85$	−8.00000	+	8.00000i	−0.867722	+	0.867722i
$86$		0			0
$87$		−	12.0000i		−	1.28654i
$88$		0			0
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$	8.00000	−	8.00000i	0.838628	−	0.838628i
$92$		0			0
$93$	8.00000	+	8.00000i	0.829561	+	0.829561i
$94$		0			0
$95$	−20.0000			−2.05196
$96$		0			0
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$		0			0
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$		0			0
$101$	2.00000	−	2.00000i	0.199007	−	0.199007i	−0.600567	−	0.799574i	$-0.705058\pi$
$101$	2.00000	−	2.00000i	0.199007	−	0.199007i	0.799574	+	0.600567i	$0.205058\pi$
$102$		0			0
$103$		−	12.0000i		−	1.18240i	−0.806527	−	0.591198i	$-0.798655\pi$
$103$		−	12.0000i		−	1.18240i	0.806527	−	0.591198i	$-0.201345\pi$
$104$		0			0
$105$			16.0000i			1.56144i
$106$		0			0
$107$	−7.00000	+	7.00000i	−0.676716	+	0.676716i	−0.959256	−	0.282540i	$-0.908823\pi$
$107$	−7.00000	+	7.00000i	−0.676716	+	0.676716i	0.282540	+	0.959256i	$0.408823\pi$
$108$		0			0
$109$	−10.0000	−	10.0000i	−0.957826	−	0.957826i	0.0413197	−	0.999146i	$-0.486844\pi$
$109$	−10.0000	−	10.0000i	−0.957826	−	0.957826i	−0.999146	+	0.0413197i	$0.986844\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	−8.00000	−	8.00000i	−0.746004	−	0.746004i
$116$		0			0
$117$	2.00000	−	2.00000i	0.184900	−	0.184900i
$118$		0			0
$119$		−	16.0000i		−	1.46672i
$120$		0			0
$121$			9.00000i			0.818182i
$122$		0			0
$123$	−2.00000	+	2.00000i	−0.180334	+	0.180334i
$124$		0			0
$125$	−4.00000	−	4.00000i	−0.357771	−	0.357771i
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	6.00000			0.528271
$130$		0			0
$131$	−5.00000	−	5.00000i	−0.436852	−	0.436852i	0.454099	−	0.890951i	$-0.349961\pi$
$131$	−5.00000	−	5.00000i	−0.436852	−	0.436852i	−0.890951	+	0.454099i	$0.849961\pi$
$132$		0			0
$133$	20.0000	−	20.0000i	1.73422	−	1.73422i
$134$		0			0
$135$			16.0000i			1.37706i
$136$		0			0
$137$		−	18.0000i		−	1.53784i	−0.639343	−	0.768922i	$-0.720793\pi$
$137$		−	18.0000i		−	1.53784i	0.639343	−	0.768922i	$-0.279207\pi$
$138$		0			0
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	−0.568338	−	0.822795i	$-0.692414\pi$
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	0.822795	+	0.568338i	$0.192414\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00000			0.334497
$144$		0			0
$145$	24.0000			1.99309
$146$		0			0
$147$	−9.00000	−	9.00000i	−0.742307	−	0.742307i
$148$		0			0
$149$	2.00000	−	2.00000i	0.163846	−	0.163846i	−0.620422	−	0.784268i	$-0.713039\pi$
$149$	2.00000	−	2.00000i	0.163846	−	0.163846i	0.784268	+	0.620422i	$0.213039\pi$
$150$		0			0
$151$			4.00000i			0.325515i	0.986666	+	0.162758i	$0.0520389\pi$
$151$			4.00000i			0.325515i	−0.986666	+	0.162758i	$0.947961\pi$
$152$		0			0
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	−16.0000	+	16.0000i	−1.28515	+	1.28515i
$156$		0			0
$157$	6.00000	+	6.00000i	0.478852	+	0.478852i	0.904764	−	0.425912i	$-0.140047\pi$
$157$	6.00000	+	6.00000i	0.478852	+	0.478852i	−0.425912	+	0.904764i	$0.640047\pi$
$158$		0			0
$159$	−4.00000			−0.317221
$160$		0			0
$161$	16.0000			1.26098
$162$		0			0
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	0.377661	−	0.925944i	$-0.376728\pi$
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	−0.925944	+	0.377661i	$0.876728\pi$
$164$		0			0
$165$	−4.00000	+	4.00000i	−0.311400	+	0.311400i
$166$		0			0
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	5.00000	−	5.00000i	0.382360	−	0.382360i
$172$		0			0
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	0.976374	−	0.216088i	$-0.0693298\pi$
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	−0.216088	+	0.976374i	$0.569330\pi$
$174$		0			0
$175$	−12.0000			−0.907115
$176$		0			0
$177$	−6.00000			−0.450988
$178$		0			0
$179$	−1.00000	−	1.00000i	−0.0747435	−	0.0747435i	0.668747	−	0.743490i	$-0.266831\pi$
$179$	−1.00000	−	1.00000i	−0.0747435	−	0.0747435i	−0.743490	+	0.668747i	$0.766831\pi$
$180$		0			0
$181$	−6.00000	+	6.00000i	−0.445976	+	0.445976i	−0.894015	−	0.448038i	$-0.852123\pi$
$181$	−6.00000	+	6.00000i	−0.445976	+	0.445976i	0.448038	+	0.894015i	$0.352123\pi$
$182$		0			0
$183$			12.0000i			0.887066i
$184$		0			0
$185$			8.00000i			0.588172i
$186$		0			0
$187$	4.00000	−	4.00000i	0.292509	−	0.292509i
$188$		0			0
$189$	−16.0000	−	16.0000i	−1.16383	−	1.16383i
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$		0			0
$195$	−8.00000	−	8.00000i	−0.572892	−	0.572892i
$196$		0			0
$197$	−10.0000	+	10.0000i	−0.712470	+	0.712470i	−0.967051	−	0.254581i	$-0.918062\pi$
$197$	−10.0000	+	10.0000i	−0.712470	+	0.712470i	0.254581	+	0.967051i	$0.418062\pi$
$198$		0			0
$199$		−	4.00000i		−	0.283552i	−0.989899	−	0.141776i	$-0.954719\pi$
$199$		−	4.00000i		−	0.283552i	0.989899	−	0.141776i	$-0.0452813\pi$
$200$		0			0
$201$			6.00000i			0.423207i
$202$		0			0
$203$	−24.0000	+	24.0000i	−1.68447	+	1.68447i
$204$		0			0
$205$	−4.00000	−	4.00000i	−0.279372	−	0.279372i
$206$		0			0
$207$	4.00000			0.278019
$208$		0			0
$209$	10.0000			0.691714
$210$		0			0
$211$	−17.0000	−	17.0000i	−1.17033	−	1.17033i	−0.982131	−	0.188197i	$-0.939736\pi$
$211$	−17.0000	−	17.0000i	−1.17033	−	1.17033i	−0.188197	−	0.982131i	$-0.560264\pi$
$212$		0			0
$213$	−4.00000	+	4.00000i	−0.274075	+	0.274075i
$214$		0			0
$215$			12.0000i			0.818393i
$216$		0			0
$217$		−	32.0000i		−	2.17230i
$218$		0			0
$219$	4.00000	−	4.00000i	0.270295	−	0.270295i
$220$		0			0
$221$	8.00000	+	8.00000i	0.538138	+	0.538138i
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	−15.0000	−	15.0000i	−0.995585	−	0.995585i	0.00440533	−	0.999990i	$-0.498598\pi$
$227$	−15.0000	−	15.0000i	−0.995585	−	0.995585i	−0.999990	+	0.00440533i	$0.998598\pi$
$228$		0			0
$229$	−18.0000	+	18.0000i	−1.18947	+	1.18947i	−0.212260	+	0.977213i	$0.568082\pi$
$229$	−18.0000	+	18.0000i	−1.18947	+	1.18947i	−0.977213	+	0.212260i	$0.931918\pi$
$230$		0			0
$231$		−	8.00000i		−	0.526361i
$232$		0			0
$233$			12.0000i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$233$			12.0000i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.00000	+	8.00000i	0.519656	+	0.519656i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−12.0000			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$242$		0			0
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$		0			0
$245$	18.0000	−	18.0000i	1.14998	−	1.14998i
$246$		0			0
$247$			20.0000i			1.27257i
$248$		0			0
$249$			14.0000i			0.887214i
$250$		0			0
$251$	−3.00000	+	3.00000i	−0.189358	+	0.189358i	−0.795419	−	0.606060i	$-0.792749\pi$
$251$	−3.00000	+	3.00000i	−0.189358	+	0.189358i	0.606060	+	0.795419i	$0.292749\pi$
$252$		0			0
$253$	4.00000	+	4.00000i	0.251478	+	0.251478i
$254$		0			0
$255$	−16.0000			−1.00196
$256$		0			0
$257$	−2.00000			−0.124757			−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000			−0.124757			−0.0623783	+	0.998053i	$0.519869\pi$
$258$		0			0
$259$	−8.00000	−	8.00000i	−0.497096	−	0.497096i
$260$		0			0
$261$	−6.00000	+	6.00000i	−0.371391	+	0.371391i
$262$		0			0
$263$		−	28.0000i		−	1.72655i	−0.504730	−	0.863277i	$-0.668408\pi$
$263$		−	28.0000i		−	1.72655i	0.504730	−	0.863277i	$-0.331592\pi$
$264$		0			0
$265$		−	8.00000i		−	0.491436i
$266$		0			0
$267$	12.0000	−	12.0000i	0.734388	−	0.734388i
$268$		0			0
$269$	14.0000	+	14.0000i	0.853595	+	0.853595i	0.990574	−	0.136979i	$-0.0437393\pi$
$269$	14.0000	+	14.0000i	0.853595	+	0.853595i	−0.136979	+	0.990574i	$0.543739\pi$
$270$		0			0
$271$	−32.0000			−1.94386			−0.971931	−	0.235267i	$-0.924404\pi$
$271$	−32.0000			−1.94386			−0.971931	+	0.235267i	$0.924404\pi$
$272$		0			0
$273$	16.0000			0.968364
$274$		0			0
$275$	−3.00000	−	3.00000i	−0.180907	−	0.180907i
$276$		0			0
$277$	6.00000	−	6.00000i	0.360505	−	0.360505i	−0.503494	−	0.863999i	$-0.667952\pi$
$277$	6.00000	−	6.00000i	0.360505	−	0.360505i	0.863999	+	0.503494i	$0.167952\pi$
$278$		0			0
$279$		−	8.00000i		−	0.478947i
$280$		0			0
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$		0			0
$283$	−17.0000	+	17.0000i	−1.01055	+	1.01055i	−0.0106013	+	0.999944i	$0.503375\pi$
$283$	−17.0000	+	17.0000i	−1.01055	+	1.01055i	−0.999944	+	0.0106013i	$0.996625\pi$
$284$		0			0
$285$	−20.0000	−	20.0000i	−1.18470	−	1.18470i
$286$		0			0
$287$	8.00000			0.472225
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	−4.00000	−	4.00000i	−0.234484	−	0.234484i
$292$		0			0
$293$	6.00000	−	6.00000i	0.350524	−	0.350524i	−0.509781	−	0.860304i	$-0.670273\pi$
$293$	6.00000	−	6.00000i	0.350524	−	0.350524i	0.860304	+	0.509781i	$0.170273\pi$
$294$		0			0
$295$		−	12.0000i		−	0.698667i
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$		0			0
$299$	−8.00000	+	8.00000i	−0.462652	+	0.462652i
$300$		0			0
$301$	−12.0000	−	12.0000i	−0.691669	−	0.691669i
$302$		0			0
$303$	4.00000			0.229794
$304$		0			0
$305$	−24.0000			−1.37424
$306$		0			0
$307$	5.00000	+	5.00000i	0.285365	+	0.285365i	0.835244	−	0.549879i	$-0.185326\pi$
$307$	5.00000	+	5.00000i	0.285365	+	0.285365i	−0.549879	+	0.835244i	$0.685326\pi$
$308$		0			0
$309$	12.0000	−	12.0000i	0.682656	−	0.682656i
$310$		0			0
$311$		−	20.0000i		−	1.13410i	−0.823685	−	0.567048i	$-0.808085\pi$
$311$		−	20.0000i		−	1.13410i	0.823685	−	0.567048i	$-0.191915\pi$
$312$		0			0
$313$			14.0000i			0.791327i	0.918396	+	0.395663i	$0.129485\pi$
$313$			14.0000i			0.791327i	−0.918396	+	0.395663i	$0.870515\pi$
$314$		0			0
$315$	8.00000	−	8.00000i	0.450749	−	0.450749i
$316$		0			0
$317$	2.00000	+	2.00000i	0.112331	+	0.112331i	0.761038	−	0.648707i	$-0.224690\pi$
$317$	2.00000	+	2.00000i	0.112331	+	0.112331i	−0.648707	+	0.761038i	$0.724690\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$		0			0
$321$	−14.0000			−0.781404
$322$		0			0
$323$	20.0000	+	20.0000i	1.11283	+	1.11283i
$324$		0			0
$325$	6.00000	−	6.00000i	0.332820	−	0.332820i
$326$		0			0
$327$		−	20.0000i		−	1.10600i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.00000	−	9.00000i	0.494685	−	0.494685i	−0.415094	−	0.909779i	$-0.636251\pi$
$331$	9.00000	−	9.00000i	0.494685	−	0.494685i	0.909779	+	0.415094i	$0.136251\pi$
$332$		0			0
$333$	−2.00000	−	2.00000i	−0.109599	−	0.109599i
$334$		0			0
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$		0			0
$339$	−14.0000	−	14.0000i	−0.760376	−	0.760376i
$340$		0			0
$341$	8.00000	−	8.00000i	0.433224	−	0.433224i
$342$		0			0
$343$			8.00000i			0.431959i
$344$		0			0
$345$		−	16.0000i		−	0.861411i
$346$		0			0
$347$	−11.0000	+	11.0000i	−0.590511	+	0.590511i	−0.937769	−	0.347259i	$-0.887113\pi$
$347$	−11.0000	+	11.0000i	−0.590511	+	0.590511i	0.347259	+	0.937769i	$0.387113\pi$
$348$		0			0
$349$	−14.0000	−	14.0000i	−0.749403	−	0.749403i	0.224964	−	0.974367i	$-0.427773\pi$
$349$	−14.0000	−	14.0000i	−0.749403	−	0.749403i	−0.974367	+	0.224964i	$0.927773\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$		0			0
$355$	−8.00000	−	8.00000i	−0.424596	−	0.424596i
$356$		0			0
$357$	16.0000	−	16.0000i	0.846810	−	0.846810i
$358$		0			0
$359$			36.0000i			1.90001i	0.312239	+	0.950004i	$0.398921\pi$
$359$			36.0000i			1.90001i	−0.312239	+	0.950004i	$0.601079\pi$
$360$		0			0
$361$			31.0000i			1.63158i
$362$		0			0
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$		0			0
$365$	8.00000	+	8.00000i	0.418739	+	0.418739i
$366$		0			0
$367$	−16.0000			−0.835193			−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000			−0.835193			−0.417597	+	0.908633i	$0.637127\pi$
$368$		0			0
$369$	2.00000			0.104116
$370$		0			0
$371$	8.00000	+	8.00000i	0.415339	+	0.415339i
$372$		0			0
$373$	−26.0000	+	26.0000i	−1.34623	+	1.34623i	−0.456511	+	0.889718i	$0.650901\pi$
$373$	−26.0000	+	26.0000i	−1.34623	+	1.34623i	−0.889718	+	0.456511i	$0.849099\pi$
$374$		0			0
$375$		−	8.00000i		−	0.413118i
$376$		0			0
$377$		−	24.0000i		−	1.23606i
$378$		0			0
$379$	21.0000	−	21.0000i	1.07870	−	1.07870i	0.0820711	−	0.996626i	$-0.473847\pi$
$379$	21.0000	−	21.0000i	1.07870	−	1.07870i	0.996626	−	0.0820711i	$-0.0261534\pi$
$380$		0			0
$381$	8.00000	+	8.00000i	0.409852	+	0.409852i
$382$		0			0
$383$	16.0000			0.817562			0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000			0.817562			0.408781	+	0.912633i	$0.365954\pi$
$384$		0			0
$385$	16.0000			0.815436
$386$		0			0
$387$	−3.00000	−	3.00000i	−0.152499	−	0.152499i
$388$		0			0
$389$	−14.0000	+	14.0000i	−0.709828	+	0.709828i	−0.966499	−	0.256671i	$-0.917374\pi$
$389$	−14.0000	+	14.0000i	−0.709828	+	0.709828i	0.256671	+	0.966499i	$0.417374\pi$
$390$		0			0
$391$			16.0000i			0.809155i
$392$		0			0
$393$		−	10.0000i		−	0.504433i
$394$		0			0
$395$	−16.0000	+	16.0000i	−0.805047	+	0.805047i
$396$		0			0
$397$	−2.00000	−	2.00000i	−0.100377	−	0.100377i	0.655135	−	0.755512i	$-0.272612\pi$
$397$	−2.00000	−	2.00000i	−0.100377	−	0.100377i	−0.755512	+	0.655135i	$0.772612\pi$
$398$		0			0
$399$	40.0000			2.00250
$400$		0			0
$401$	36.0000			1.79775			0.898877	−	0.438201i	$-0.144384\pi$
$401$	36.0000			1.79775			0.898877	+	0.438201i	$0.144384\pi$
$402$		0			0
$403$	16.0000	+	16.0000i	0.797017	+	0.797017i
$404$		0			0
$405$	−10.0000	+	10.0000i	−0.496904	+	0.496904i
$406$		0			0
$407$		−	4.00000i		−	0.198273i
$408$		0			0
$409$			14.0000i			0.692255i	0.938187	+	0.346128i	$0.112504\pi$
$409$			14.0000i			0.692255i	−0.938187	+	0.346128i	$0.887496\pi$
$410$		0			0
$411$	18.0000	−	18.0000i	0.887875	−	0.887875i
$412$		0			0
$413$	12.0000	+	12.0000i	0.590481	+	0.590481i
$414$		0			0
$415$	−28.0000			−1.37447
$416$		0			0
$417$	6.00000			0.293821
$418$		0			0
$419$	19.0000	+	19.0000i	0.928211	+	0.928211i	0.997590	−	0.0693796i	$-0.0221020\pi$
$419$	19.0000	+	19.0000i	0.928211	+	0.928211i	−0.0693796	+	0.997590i	$0.522102\pi$
$420$		0			0
$421$	6.00000	−	6.00000i	0.292422	−	0.292422i	−0.545614	−	0.838036i	$-0.683704\pi$
$421$	6.00000	−	6.00000i	0.292422	−	0.292422i	0.838036	+	0.545614i	$0.183704\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	12.0000i		−	0.582086i
$426$		0			0
$427$	24.0000	−	24.0000i	1.16144	−	1.16144i
$428$		0			0
$429$	4.00000	+	4.00000i	0.193122	+	0.193122i
$430$		0			0
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$		0			0
$435$	24.0000	+	24.0000i	1.15071	+	1.15071i
$436$		0			0
$437$	−20.0000	+	20.0000i	−0.956730	+	0.956730i
$438$		0			0
$439$		−	4.00000i		−	0.190910i	−0.995434	−	0.0954548i	$-0.969569\pi$
$439$		−	4.00000i		−	0.190910i	0.995434	−	0.0954548i	$-0.0304305\pi$
$440$		0			0
$441$			9.00000i			0.428571i
$442$		0			0
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.210108	+	0.977678i	$0.567381\pi$
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.977678	+	0.210108i	$0.932619\pi$
$444$		0			0
$445$	24.0000	+	24.0000i	1.13771	+	1.13771i
$446$		0			0
$447$	4.00000			0.189194
$448$		0			0
$449$	−20.0000			−0.943858			−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000			−0.943858			−0.471929	+	0.881636i	$0.656442\pi$
$450$		0			0
$451$	2.00000	+	2.00000i	0.0941763	+	0.0941763i
$452$		0			0
$453$	−4.00000	+	4.00000i	−0.187936	+	0.187936i
$454$		0			0
$455$			32.0000i			1.50018i
$456$		0			0
$457$			2.00000i			0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$			2.00000i			0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$		0			0
$459$	16.0000	−	16.0000i	0.746816	−	0.746816i
$460$		0			0
$461$	−10.0000	−	10.0000i	−0.465746	−	0.465746i	0.434787	−	0.900533i	$-0.356824\pi$
$461$	−10.0000	−	10.0000i	−0.465746	−	0.465746i	−0.900533	+	0.434787i	$0.856824\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$	−32.0000			−1.48396
$466$		0			0
$467$	13.0000	+	13.0000i	0.601568	+	0.601568i	0.940729	−	0.339160i	$-0.110143\pi$
$467$	13.0000	+	13.0000i	0.601568	+	0.601568i	−0.339160	+	0.940729i	$0.610143\pi$
$468$		0			0
$469$	12.0000	−	12.0000i	0.554109	−	0.554109i
$470$		0			0
$471$			12.0000i			0.552931i
$472$		0			0
$473$		−	6.00000i		−	0.275880i
$474$		0			0
$475$	15.0000	−	15.0000i	0.688247	−	0.688247i
$476$		0			0
$477$	2.00000	+	2.00000i	0.0915737	+	0.0915737i
$478$		0			0
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$		0			0
$481$	8.00000			0.364769
$482$		0			0
$483$	16.0000	+	16.0000i	0.728025	+	0.728025i
$484$		0			0
$485$	8.00000	−	8.00000i	0.363261	−	0.363261i
$486$		0			0
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$		0			0
$489$		−	14.0000i		−	0.633102i
$490$		0			0
$491$	11.0000	−	11.0000i	0.496423	−	0.496423i	−0.413900	−	0.910323i	$-0.635834\pi$
$491$	11.0000	−	11.0000i	0.496423	−	0.496423i	0.910323	+	0.413900i	$0.135834\pi$
$492$		0			0
$493$	−24.0000	−	24.0000i	−1.08091	−	1.08091i
$494$		0			0
$495$	4.00000			0.179787
$496$		0			0
$497$	16.0000			0.717698
$498$		0			0
$499$	−9.00000	−	9.00000i	−0.402895	−	0.402895i	0.476357	−	0.879252i	$-0.341957\pi$
$499$	−9.00000	−	9.00000i	−0.402895	−	0.402895i	−0.879252	+	0.476357i	$0.841957\pi$
$500$		0			0
$501$	−12.0000	+	12.0000i	−0.536120	+	0.536120i
$502$		0			0
$503$			20.0000i			0.891756i	0.895094	+	0.445878i	$0.147108\pi$
$503$			20.0000i			0.891756i	−0.895094	+	0.445878i	$0.852892\pi$
$504$		0			0
$505$			8.00000i			0.355995i
$506$		0			0
$507$	5.00000	−	5.00000i	0.222058	−	0.222058i
$508$		0			0
$509$	−2.00000	−	2.00000i	−0.0886484	−	0.0886484i	0.661392	−	0.750040i	$-0.269966\pi$
$509$	−2.00000	−	2.00000i	−0.0886484	−	0.0886484i	−0.750040	+	0.661392i	$0.769966\pi$
$510$		0			0
$511$	−16.0000			−0.707798
$512$		0			0
$513$	40.0000			1.76604
$514$		0			0
$515$	24.0000	+	24.0000i	1.05757	+	1.05757i
$516$		0			0
$517$		0			0
$518$		0			0
$519$			20.0000i			0.877903i
$520$		0			0
$521$			14.0000i			0.613351i	0.951814	+	0.306676i	$0.0992167\pi$
$521$			14.0000i			0.613351i	−0.951814	+	0.306676i	$0.900783\pi$
$522$		0			0
$523$	−7.00000	+	7.00000i	−0.306089	+	0.306089i	−0.843390	−	0.537302i	$-0.819444\pi$
$523$	−7.00000	+	7.00000i	−0.306089	+	0.306089i	0.537302	+	0.843390i	$0.319444\pi$
$524$		0			0
$525$	−12.0000	−	12.0000i	−0.523723	−	0.523723i
$526$		0			0
$527$	32.0000			1.39394
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$		0			0
$533$	−4.00000	+	4.00000i	−0.173259	+	0.173259i
$534$		0			0
$535$		−	28.0000i		−	1.21055i
$536$		0			0
$537$		−	2.00000i		−	0.0863064i
$538$		0			0
$539$	−9.00000	+	9.00000i	−0.387657	+	0.387657i
$540$		0			0
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	0.824224	−	0.566264i	$-0.191612\pi$
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	−0.566264	+	0.824224i	$0.691612\pi$
$542$		0			0
$543$	−12.0000			−0.514969
$544$		0			0
$545$	40.0000			1.71341
$546$		0			0
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	0.984990	−	0.172609i	$-0.0552197\pi$
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	−0.172609	+	0.984990i	$0.555220\pi$
$548$		0			0
$549$	6.00000	−	6.00000i	0.256074	−	0.256074i
$550$		0			0
$551$		−	60.0000i		−	2.55609i
$552$		0			0
$553$		−	32.0000i		−	1.36078i
$554$		0			0
$555$	−8.00000	+	8.00000i	−0.339581	+	0.339581i
$556$		0			0
$557$	−22.0000	−	22.0000i	−0.932170	−	0.932170i	0.0656714	−	0.997841i	$-0.479081\pi$
$557$	−22.0000	−	22.0000i	−0.932170	−	0.932170i	−0.997841	+	0.0656714i	$0.979081\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$		0			0
$561$	8.00000			0.337760
$562$		0			0
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	0.804575	−	0.593851i	$-0.202393\pi$
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	−0.593851	+	0.804575i	$0.702393\pi$
$564$		0			0
$565$	28.0000	−	28.0000i	1.17797	−	1.17797i
$566$		0			0
$567$		−	20.0000i		−	0.839921i
$568$		0			0
$569$		−	30.0000i		−	1.25767i	−0.777541	−	0.628833i	$-0.783533\pi$
$569$		−	30.0000i		−	1.25767i	0.777541	−	0.628833i	$-0.216467\pi$
$570$		0			0
$571$	23.0000	−	23.0000i	0.962520	−	0.962520i	−0.0368025	−	0.999323i	$-0.511717\pi$
$571$	23.0000	−	23.0000i	0.962520	−	0.962520i	0.999323	+	0.0368025i	$0.0117173\pi$
$572$		0			0
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$		0			0
$579$	−4.00000	−	4.00000i	−0.166234	−	0.166234i
$580$		0			0
$581$	28.0000	−	28.0000i	1.16164	−	1.16164i
$582$		0			0
$583$			4.00000i			0.165663i
$584$		0			0
$585$			8.00000i			0.330759i
$586$		0			0
$587$	1.00000	−	1.00000i	0.0412744	−	0.0412744i	−0.686168	−	0.727443i	$-0.740709\pi$
$587$	1.00000	−	1.00000i	0.0412744	−	0.0412744i	0.727443	+	0.686168i	$0.240709\pi$
$588$		0			0
$589$	40.0000	+	40.0000i	1.64817	+	1.64817i
$590$		0			0
$591$	−20.0000			−0.822690
$592$		0			0
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$	32.0000	+	32.0000i	1.31187	+	1.31187i
$596$		0			0
$597$	4.00000	−	4.00000i	0.163709	−	0.163709i
$598$		0			0
$599$		−	36.0000i		−	1.47092i	−0.677568	−	0.735460i	$-0.736966\pi$
$599$		−	36.0000i		−	1.47092i	0.677568	−	0.735460i	$-0.263034\pi$
$600$		0			0
$601$			4.00000i			0.163163i	0.996667	+	0.0815817i	$0.0259972\pi$
$601$			4.00000i			0.163163i	−0.996667	+	0.0815817i	$0.974003\pi$
$602$		0			0
$603$	3.00000	−	3.00000i	0.122169	−	0.122169i
$604$		0			0
$605$	−18.0000	−	18.0000i	−0.731804	−	0.731804i
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$		0			0
$609$	−48.0000			−1.94506
$610$		0			0
$611$		0			0
$612$		0			0
$613$	6.00000	−	6.00000i	0.242338	−	0.242338i	−0.575479	−	0.817817i	$-0.695184\pi$
$613$	6.00000	−	6.00000i	0.242338	−	0.242338i	0.817817	+	0.575479i	$0.195184\pi$
$614$		0			0
$615$		−	8.00000i		−	0.322591i
$616$		0			0
$617$			28.0000i			1.12724i	0.826035	+	0.563619i	$0.190591\pi$
$617$			28.0000i			1.12724i	−0.826035	+	0.563619i	$0.809409\pi$
$618$		0			0
$619$	1.00000	−	1.00000i	0.0401934	−	0.0401934i	−0.686724	−	0.726918i	$-0.740952\pi$
$619$	1.00000	−	1.00000i	0.0401934	−	0.0401934i	0.726918	+	0.686724i	$0.240952\pi$
$620$		0			0
$621$	16.0000	+	16.0000i	0.642058	+	0.642058i
$622$		0			0
$623$	−48.0000			−1.92308
$624$		0			0
$625$	31.0000			1.24000
$626$		0			0
$627$	10.0000	+	10.0000i	0.399362	+	0.399362i
$628$		0			0
$629$	8.00000	−	8.00000i	0.318981	−	0.318981i
$630$		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
$633$		−	34.0000i		−	1.35138i
$634$		0			0
$635$	−16.0000	+	16.0000i	−0.634941	+	0.634941i
$636$		0			0
$637$	−18.0000	−	18.0000i	−0.713186	−	0.713186i
$638$		0			0
$639$	4.00000			0.158238
$640$		0			0
$641$	−4.00000			−0.157991			−0.0789953	−	0.996875i	$-0.525171\pi$
$641$	−4.00000			−0.157991			−0.0789953	+	0.996875i	$0.525171\pi$
$642$		0			0
$643$	3.00000	+	3.00000i	0.118308	+	0.118308i	0.763782	−	0.645474i	$-0.223340\pi$
$643$	3.00000	+	3.00000i	0.118308	+	0.118308i	−0.645474	+	0.763782i	$0.723340\pi$
$644$		0			0
$645$	−12.0000	+	12.0000i	−0.472500	+	0.472500i
$646$		0			0
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$		0			0
$649$			6.00000i			0.235521i
$650$		0			0
$651$	32.0000	−	32.0000i	1.25418	−	1.25418i
$652$		0			0
$653$	−34.0000	−	34.0000i	−1.33052	−	1.33052i	−0.904901	−	0.425622i	$-0.860055\pi$
$653$	−34.0000	−	34.0000i	−1.33052	−	1.33052i	−0.425622	−	0.904901i	$-0.639945\pi$
$654$		0			0
$655$	20.0000			0.781465
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	23.0000	+	23.0000i	0.895953	+	0.895953i	0.995075	−	0.0991224i	$-0.0316036\pi$
$659$	23.0000	+	23.0000i	0.895953	+	0.895953i	−0.0991224	+	0.995075i	$0.531604\pi$
$660$		0			0
$661$	−22.0000	+	22.0000i	−0.855701	+	0.855701i	−0.990828	−	0.135127i	$-0.956856\pi$
$661$	−22.0000	+	22.0000i	−0.855701	+	0.855701i	0.135127	+	0.990828i	$0.456856\pi$
$662$		0			0
$663$			16.0000i			0.621389i
$664$		0			0
$665$			80.0000i			3.10227i
$666$		0			0
$667$	24.0000	−	24.0000i	0.929284	−	0.929284i
$668$		0			0
$669$	24.0000	+	24.0000i	0.927894	+	0.927894i
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$	−20.0000			−0.770943			−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000			−0.770943			−0.385472	+	0.922720i	$0.625961\pi$
$674$		0			0
$675$	−12.0000	−	12.0000i	−0.461880	−	0.461880i
$676$		0			0
$677$	−30.0000	+	30.0000i	−1.15299	+	1.15299i	−0.167044	+	0.985949i	$0.553422\pi$
$677$	−30.0000	+	30.0000i	−1.15299	+	1.15299i	−0.985949	+	0.167044i	$0.946578\pi$
$678$		0			0
$679$			16.0000i			0.614024i
$680$		0			0
$681$		−	30.0000i		−	1.14960i
$682$		0			0
$683$	−21.0000	+	21.0000i	−0.803543	+	0.803543i	−0.983647	−	0.180105i	$-0.942356\pi$
$683$	−21.0000	+	21.0000i	−0.803543	+	0.803543i	0.180105	+	0.983647i	$0.442356\pi$
$684$		0			0
$685$	36.0000	+	36.0000i	1.37549	+	1.37549i
$686$		0			0
$687$	−36.0000			−1.37349
$688$		0			0
$689$	−8.00000			−0.304776
$690$		0			0
$691$	−33.0000	−	33.0000i	−1.25538	−	1.25538i	−0.953275	−	0.302104i	$-0.902311\pi$
$691$	−33.0000	−	33.0000i	−1.25538	−	1.25538i	−0.302104	−	0.953275i	$-0.597689\pi$
$692$		0			0
$693$	−4.00000	+	4.00000i	−0.151947	+	0.151947i
$694$		0			0
$695$			12.0000i			0.455186i
$696$		0			0
$697$			8.00000i			0.303022i
$698$		0			0
$699$	−12.0000	+	12.0000i	−0.453882	+	0.453882i
$700$		0			0
$701$	−34.0000	−	34.0000i	−1.28416	−	1.28416i	−0.938277	−	0.345886i	$-0.887579\pi$
$701$	−34.0000	−	34.0000i	−1.28416	−	1.28416i	−0.345886	−	0.938277i	$-0.612421\pi$
$702$		0			0
$703$	20.0000			0.754314
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.00000	−	8.00000i	−0.300871	−	0.300871i
$708$		0			0
$709$	−6.00000	+	6.00000i	−0.225335	+	0.225335i	−0.810740	−	0.585406i	$-0.800935\pi$
$709$	−6.00000	+	6.00000i	−0.225335	+	0.225335i	0.585406	+	0.810740i	$0.300935\pi$
$710$		0			0
$711$		−	8.00000i		−	0.300023i
$712$		0			0
$713$			32.0000i			1.19841i
$714$		0			0
$715$	−8.00000	+	8.00000i	−0.299183	+	0.299183i
$716$		0			0
$717$	8.00000	+	8.00000i	0.298765	+	0.298765i
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−48.0000			−1.78761
$722$		0			0
$723$	−12.0000	−	12.0000i	−0.446285	−	0.446285i
$724$		0			0
$725$	−18.0000	+	18.0000i	−0.668503	+	0.668503i
$726$		0			0
$727$			28.0000i			1.03846i	0.854634	+	0.519231i	$0.173782\pi$
$727$			28.0000i			1.03846i	−0.854634	+	0.519231i	$0.826218\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	12.0000	−	12.0000i	0.443836	−	0.443836i
$732$		0			0
$733$	−14.0000	−	14.0000i	−0.517102	−	0.517102i	0.399592	−	0.916693i	$-0.369152\pi$
$733$	−14.0000	−	14.0000i	−0.517102	−	0.517102i	−0.916693	+	0.399592i	$0.869152\pi$
$734$		0			0
$735$	36.0000			1.32788
$736$		0			0
$737$	6.00000			0.221013
$738$		0			0
$739$	17.0000	+	17.0000i	0.625355	+	0.625355i	0.946896	−	0.321541i	$-0.104201\pi$
$739$	17.0000	+	17.0000i	0.625355	+	0.625355i	−0.321541	+	0.946896i	$0.604201\pi$
$740$		0			0
$741$	−20.0000	+	20.0000i	−0.734718	+	0.734718i
$742$		0			0
$743$		−	4.00000i		−	0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$		−	4.00000i		−	0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$		0			0
$745$			8.00000i			0.293097i
$746$		0			0
$747$	7.00000	−	7.00000i	0.256117	−	0.256117i
$748$		0			0
$749$	28.0000	+	28.0000i	1.02310	+	1.02310i
$750$		0			0
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$		0			0
$753$	−6.00000			−0.218652
$754$		0			0
$755$	−8.00000	−	8.00000i	−0.291150	−	0.291150i
$756$		0			0
$757$	18.0000	−	18.0000i	0.654221	−	0.654221i	−0.299786	−	0.954007i	$-0.596915\pi$
$757$	18.0000	−	18.0000i	0.654221	−	0.654221i	0.954007	+	0.299786i	$0.0969151\pi$
$758$		0			0
$759$			8.00000i			0.290382i
$760$		0			0
$761$		−	18.0000i		−	0.652499i	−0.945284	−	0.326250i	$-0.894215\pi$
$761$		−	18.0000i		−	0.652499i	0.945284	−	0.326250i	$-0.105785\pi$
$762$		0			0
$763$	−40.0000	+	40.0000i	−1.44810	+	1.44810i
$764$		0			0
$765$	8.00000	+	8.00000i	0.289241	+	0.289241i
$766$		0			0
$767$	−12.0000			−0.433295
$768$		0			0
$769$	44.0000			1.58668			0.793340	−	0.608778i	$-0.208340\pi$
$769$	44.0000			1.58668			0.793340	+	0.608778i	$0.208340\pi$
$770$		0			0
$771$	−2.00000	−	2.00000i	−0.0720282	−	0.0720282i
$772$		0			0
$773$	−6.00000	+	6.00000i	−0.215805	+	0.215805i	−0.806728	−	0.590923i	$-0.798764\pi$
$773$	−6.00000	+	6.00000i	−0.215805	+	0.215805i	0.590923	+	0.806728i	$0.298764\pi$
$774$		0			0
$775$		−	24.0000i		−	0.862105i
$776$		0			0
$777$		−	16.0000i		−	0.573997i
$778$		0			0
$779$	−10.0000	+	10.0000i	−0.358287	+	0.358287i
$780$		0			0
$781$	4.00000	+	4.00000i	0.143131	+	0.143131i
$782$		0			0
$783$	−48.0000			−1.71538
$784$		0			0
$785$	−24.0000			−0.856597
$786$		0			0
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.980674	−	0.195649i	$-0.937319\pi$
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.195649	−	0.980674i	$-0.562681\pi$
$788$		0			0
$789$	28.0000	−	28.0000i	0.996826	−	0.996826i
$790$		0			0
$791$			56.0000i			1.99113i
$792$		0			0
$793$			24.0000i			0.852265i
$794$		0			0
$795$	8.00000	−	8.00000i	0.283731	−	0.283731i
$796$		0			0
$797$	14.0000	+	14.0000i	0.495905	+	0.495905i	0.910161	−	0.414255i	$-0.135958\pi$
$797$	14.0000	+	14.0000i	0.495905	+	0.495905i	−0.414255	+	0.910161i	$0.635958\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−12.0000			−0.423999
$802$		0			0
$803$	−4.00000	−	4.00000i	−0.141157	−	0.141157i
$804$		0			0
$805$	−32.0000	+	32.0000i	−1.12785	+	1.12785i
$806$		0			0
$807$			28.0000i			0.985647i
$808$		0			0
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		0			0
$811$	17.0000	−	17.0000i	0.596951	−	0.596951i	−0.342549	−	0.939500i	$-0.611290\pi$
$811$	17.0000	−	17.0000i	0.596951	−	0.596951i	0.939500	+	0.342549i	$0.111290\pi$
$812$		0			0
$813$	−32.0000	−	32.0000i	−1.12229	−	1.12229i
$814$		0			0
$815$	28.0000			0.980797
$816$		0			0
$817$	30.0000			1.04957
$818$		0			0
$819$	−8.00000	−	8.00000i	−0.279543	−	0.279543i
$820$		0			0
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	−0.594612	−	0.804013i	$-0.702694\pi$
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	0.804013	+	0.594612i	$0.202694\pi$
$822$		0			0
$823$		−	4.00000i		−	0.139431i	−0.997567	−	0.0697156i	$-0.977791\pi$
$823$		−	4.00000i		−	0.139431i	0.997567	−	0.0697156i	$-0.0222092\pi$
$824$		0			0
$825$		−	6.00000i		−	0.208893i
$826$		0			0
$827$	15.0000	−	15.0000i	0.521601	−	0.521601i	−0.396454	−	0.918055i	$-0.629759\pi$
$827$	15.0000	−	15.0000i	0.521601	−	0.521601i	0.918055	+	0.396454i	$0.129759\pi$
$828$		0			0
$829$	−18.0000	−	18.0000i	−0.625166	−	0.625166i	0.321682	−	0.946848i	$-0.395752\pi$
$829$	−18.0000	−	18.0000i	−0.625166	−	0.625166i	−0.946848	+	0.321682i	$0.895752\pi$
$830$		0			0
$831$	12.0000			0.416275
$832$		0			0
$833$	−36.0000			−1.24733
$834$		0			0
$835$	−24.0000	−	24.0000i	−0.830554	−	0.830554i
$836$		0			0
$837$	32.0000	−	32.0000i	1.10608	−	1.10608i
$838$		0			0
$839$		−	20.0000i		−	0.690477i	−0.938515	−	0.345238i	$-0.887798\pi$
$839$		−	20.0000i		−	0.690477i	0.938515	−	0.345238i	$-0.112202\pi$
$840$		0			0
$841$			43.0000i			1.48276i
$842$		0			0
$843$	−20.0000	+	20.0000i	−0.688837	+	0.688837i
$844$		0			0
$845$	10.0000	+	10.0000i	0.344010	+	0.344010i
$846$		0			0
$847$	36.0000			1.23697
$848$		0			0
$849$	−34.0000			−1.16688
$850$		0			0
$851$	8.00000	+	8.00000i	0.274236	+	0.274236i
$852$		0			0
$853$	30.0000	−	30.0000i	1.02718	−	1.02718i	0.0275603	−	0.999620i	$-0.491226\pi$
$853$	30.0000	−	30.0000i	1.02718	−	1.02718i	0.999620	−	0.0275603i	$-0.00877382\pi$
$854$		0			0
$855$			20.0000i			0.683986i
$856$		0			0
$857$			34.0000i			1.16142i	0.814111	+	0.580709i	$0.197225\pi$
$857$			34.0000i			1.16142i	−0.814111	+	0.580709i	$0.802775\pi$
$858$		0			0
$859$	−27.0000	+	27.0000i	−0.921228	+	0.921228i	−0.997116	−	0.0758882i	$-0.975821\pi$
$859$	−27.0000	+	27.0000i	−0.921228	+	0.921228i	0.0758882	+	0.997116i	$0.475821\pi$
$860$		0			0
$861$	8.00000	+	8.00000i	0.272639	+	0.272639i
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	−40.0000			−1.36004
$866$		0			0
$867$	−1.00000	−	1.00000i	−0.0339618	−	0.0339618i
$868$		0			0
$869$	8.00000	−	8.00000i	0.271381	−	0.271381i
$870$		0			0
$871$			12.0000i			0.406604i
$872$		0			0
$873$			4.00000i			0.135379i
$874$		0			0
$875$	−16.0000	+	16.0000i	−0.540899	+	0.540899i
$876$		0			0
$877$	6.00000	+	6.00000i	0.202606	+	0.202606i	0.801115	−	0.598510i	$-0.204240\pi$
$877$	6.00000	+	6.00000i	0.202606	+	0.202606i	−0.598510	+	0.801115i	$0.704240\pi$
$878$		0			0
$879$	12.0000			0.404750
$880$		0			0
$881$	34.0000			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$881$	34.0000			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$882$		0			0
$883$	29.0000	+	29.0000i	0.975928	+	0.975928i	0.999717	−	0.0237893i	$-0.00757308\pi$
$883$	29.0000	+	29.0000i	0.975928	+	0.975928i	−0.0237893	+	0.999717i	$0.507573\pi$
$884$		0			0
$885$	12.0000	−	12.0000i	0.403376	−	0.403376i
$886$		0			0
$887$			28.0000i			0.940148i	0.882627	+	0.470074i	$0.155773\pi$
$887$			28.0000i			0.940148i	−0.882627	+	0.470074i	$0.844227\pi$
$888$		0			0
$889$		−	32.0000i		−	1.07325i
$890$		0			0
$891$	5.00000	−	5.00000i	0.167506	−	0.167506i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	4.00000			0.133705
$896$		0			0
$897$	−16.0000			−0.534224
$898$		0			0
$899$	−48.0000	−	48.0000i	−1.60089	−	1.60089i
$900$		0			0
$901$	−8.00000	+	8.00000i	−0.266519	+	0.266519i
$902$		0			0
$903$		−	24.0000i		−	0.798670i
$904$		0			0
$905$		−	24.0000i		−	0.797787i
$906$		0			0
$907$	−5.00000	+	5.00000i	−0.166022	+	0.166022i	−0.785228	−	0.619206i	$-0.787455\pi$
$907$	−5.00000	+	5.00000i	−0.166022	+	0.166022i	0.619206	+	0.785228i	$0.287455\pi$
$908$		0			0
$909$	−2.00000	−	2.00000i	−0.0663358	−	0.0663358i
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	14.0000			0.463332
$914$		0			0
$915$	−24.0000	−	24.0000i	−0.793416	−	0.793416i
$916$		0			0
$917$	−20.0000	+	20.0000i	−0.660458	+	0.660458i
$918$		0			0
$919$		−	44.0000i		−	1.45143i	−0.687998	−	0.725713i	$-0.741510\pi$
$919$		−	44.0000i		−	1.45143i	0.687998	−	0.725713i	$-0.258490\pi$
$920$		0			0
$921$			10.0000i			0.329511i
$922$		0			0
$923$	−8.00000	+	8.00000i	−0.263323	+	0.263323i
$924$		0			0
$925$	−6.00000	−	6.00000i	−0.197279	−	0.197279i
$926$		0			0
$927$	−12.0000			−0.394132
$928$		0			0
$929$	60.0000			1.96854			0.984268	−	0.176682i	$-0.0565363\pi$
$929$	60.0000			1.96854			0.984268	+	0.176682i	$0.0565363\pi$
$930$		0			0
$931$	−45.0000	−	45.0000i	−1.47482	−	1.47482i
$932$		0			0
$933$	20.0000	−	20.0000i	0.654771	−	0.654771i
$934$		0			0
$935$			16.0000i			0.523256i
$936$		0			0
$937$		−	20.0000i		−	0.653372i	−0.945133	−	0.326686i	$-0.894068\pi$
$937$		−	20.0000i		−	0.653372i	0.945133	−	0.326686i	$-0.105932\pi$
$938$		0			0
$939$	−14.0000	+	14.0000i	−0.456873	+	0.456873i
$940$		0			0
$941$	−26.0000	−	26.0000i	−0.847576	−	0.847576i	0.142254	−	0.989830i	$-0.454565\pi$
$941$	−26.0000	−	26.0000i	−0.847576	−	0.847576i	−0.989830	+	0.142254i	$0.954565\pi$
$942$		0			0
$943$	−8.00000			−0.260516
$944$		0			0
$945$	64.0000			2.08192
$946$		0			0
$947$	−43.0000	−	43.0000i	−1.39731	−	1.39731i	−0.807650	−	0.589662i	$-0.799261\pi$
$947$	−43.0000	−	43.0000i	−1.39731	−	1.39731i	−0.589662	−	0.807650i	$-0.700739\pi$
$948$		0			0
$949$	8.00000	−	8.00000i	0.259691	−	0.259691i
$950$		0			0
$951$			4.00000i			0.129709i
$952$		0			0
$953$		−	30.0000i		−	0.971795i	−0.874016	−	0.485898i	$-0.838493\pi$
$953$		−	30.0000i		−	0.971795i	0.874016	−	0.485898i	$-0.161507\pi$
$954$		0			0
$955$	−16.0000	+	16.0000i	−0.517748	+	0.517748i
$956$		0			0
$957$	−12.0000	−	12.0000i	−0.387905	−	0.387905i
$958$		0			0
$959$	−72.0000			−2.32500
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	7.00000	+	7.00000i	0.225572	+	0.225572i
$964$		0			0
$965$	8.00000	−	8.00000i	0.257529	−	0.257529i
$966$		0			0
$967$		−	20.0000i		−	0.643157i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$		−	20.0000i		−	0.643157i	0.946883	−	0.321578i	$-0.104213\pi$
$968$		0			0
$969$			40.0000i			1.28499i
$970$		0			0
$971$	11.0000	−	11.0000i	0.353007	−	0.353007i	−0.508220	−	0.861227i	$-0.669696\pi$
$971$	11.0000	−	11.0000i	0.353007	−	0.353007i	0.861227	+	0.508220i	$0.169696\pi$
$972$		0			0
$973$	−12.0000	−	12.0000i	−0.384702	−	0.384702i
$974$		0			0
$975$	12.0000			0.384308
$976$		0			0
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−12.0000	−	12.0000i	−0.383522	−	0.383522i
$980$		0			0
$981$	−10.0000	+	10.0000i	−0.319275	+	0.319275i
$982$		0			0
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$		−	40.0000i		−	1.27451i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000	+	12.0000i	0.381578	+	0.381578i
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	18.0000			0.571213
$994$		0			0
$995$	8.00000	+	8.00000i	0.253617	+	0.253617i
$996$		0			0
$997$	10.0000	−	10.0000i	0.316703	−	0.316703i	−0.530796	−	0.847499i	$-0.678107\pi$
$997$	10.0000	−	10.0000i	0.316703	−	0.316703i	0.847499	+	0.530796i	$0.178107\pi$
$998$		0			0
$999$		−	16.0000i		−	0.506218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.e.d.257.1		2
4.3	odd	2		1024.2.e.b.257.1		2
8.3	odd	2		1024.2.e.e.257.1		2
8.5	even	2		1024.2.e.c.257.1		2
16.3	odd	4		1024.2.e.e.769.1		2
16.5	even	4	inner	1024.2.e.d.769.1		2
16.11	odd	4		1024.2.e.b.769.1		2
16.13	even	4		1024.2.e.c.769.1		2
32.3	odd	8		512.2.b.b.257.1		2
32.5	even	8		512.2.a.d.1.1	yes	2
32.11	odd	8		512.2.a.c.1.1	✓	2
32.13	even	8		512.2.b.a.257.1		2
32.19	odd	8		512.2.b.b.257.2		2
32.21	even	8		512.2.a.d.1.2	yes	2
32.27	odd	8		512.2.a.c.1.2	yes	2
32.29	even	8		512.2.b.a.257.2		2
96.5	odd	8		4608.2.a.m.1.2		2
96.11	even	8		4608.2.a.f.1.1		2
96.29	odd	8		4608.2.d.a.2305.2		2
96.35	even	8		4608.2.d.b.2305.2		2
96.53	odd	8		4608.2.a.m.1.1		2
96.59	even	8		4608.2.a.f.1.2		2
96.77	odd	8		4608.2.d.a.2305.1		2
96.83	even	8		4608.2.d.b.2305.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.a.c.1.1	✓	2	32.11	odd	8
512.2.a.c.1.2	yes	2	32.27	odd	8
512.2.a.d.1.1	yes	2	32.5	even	8
512.2.a.d.1.2	yes	2	32.21	even	8
512.2.b.a.257.1		2	32.13	even	8
512.2.b.a.257.2		2	32.29	even	8
512.2.b.b.257.1		2	32.3	odd	8
512.2.b.b.257.2		2	32.19	odd	8
1024.2.e.b.257.1		2	4.3	odd	2
1024.2.e.b.769.1		2	16.11	odd	4
1024.2.e.c.257.1		2	8.5	even	2
1024.2.e.c.769.1		2	16.13	even	4
1024.2.e.d.257.1		2	1.1	even	1	trivial
1024.2.e.d.769.1		2	16.5	even	4	inner
1024.2.e.e.257.1		2	8.3	odd	2
1024.2.e.e.769.1		2	16.3	odd	4
4608.2.a.f.1.1		2	96.11	even	8
4608.2.a.f.1.2		2	96.59	even	8
4608.2.a.m.1.1		2	96.53	odd	8
4608.2.a.m.1.2		2	96.5	odd	8
4608.2.d.a.2305.1		2	96.77	odd	8
4608.2.d.a.2305.2		2	96.29	odd	8
4608.2.d.b.2305.1		2	96.83	even	8
4608.2.d.b.2305.2		2	96.35	even	8

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} -4.00000i q^{7} -1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{13} -4.00000 q^{15} +4.00000 q^{17} +(5.00000 + 5.00000i) q^{19} +(4.00000 - 4.00000i) q^{21} +4.00000i q^{23} -3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(-6.00000 - 6.00000i) q^{29} +8.00000 q^{31} +2.00000 q^{33} +(8.00000 + 8.00000i) q^{35} +(2.00000 - 2.00000i) q^{37} +4.00000i q^{39} +2.00000i q^{41} +(3.00000 - 3.00000i) q^{43} +(2.00000 + 2.00000i) q^{45} -9.00000 q^{49} +(4.00000 + 4.00000i) q^{51} +(-2.00000 + 2.00000i) q^{53} +4.00000i q^{55} +10.0000i q^{57} +(-3.00000 + 3.00000i) q^{59} +(6.00000 + 6.00000i) q^{61} -4.00000 q^{63} -8.00000 q^{65} +(3.00000 + 3.00000i) q^{67} +(-4.00000 + 4.00000i) q^{69} +4.00000i q^{71} -4.00000i q^{73} +(3.00000 - 3.00000i) q^{75} +(-4.00000 - 4.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(7.00000 + 7.00000i) q^{83} +(-8.00000 + 8.00000i) q^{85} -12.0000i q^{87} -12.0000i q^{89} +(8.00000 - 8.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} -20.0000 q^{95} -4.00000 q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{5}+O(q^{10}) \) 2 * q + 2 * q^3 - 4 * q^5	\( 2 q + 2 q^{3} - 4 q^{5} + 2 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 10 q^{19} + 8 q^{21} + 8 q^{27} - 12 q^{29} + 16 q^{31} + 4 q^{33} + 16 q^{35} + 4 q^{37} + 6 q^{43} + 4 q^{45} - 18 q^{49} + 8 q^{51} - 4 q^{53} - 6 q^{59} + 12 q^{61} - 8 q^{63} - 16 q^{65} + 6 q^{67} - 8 q^{69} + 6 q^{75} - 8 q^{77} + 16 q^{79} + 10 q^{81} + 14 q^{83} - 16 q^{85} + 16 q^{91} + 16 q^{93} - 40 q^{95} - 8 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^5 + 2 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 10 * q^19 + 8 * q^21 + 8 * q^27 - 12 * q^29 + 16 * q^31 + 4 * q^33 + 16 * q^35 + 4 * q^37 + 6 * q^43 + 4 * q^45 - 18 * q^49 + 8 * q^51 - 4 * q^53 - 6 * q^59 + 12 * q^61 - 8 * q^63 - 16 * q^65 + 6 * q^67 - 8 * q^69 + 6 * q^75 - 8 * q^77 + 16 * q^79 + 10 * q^81 + 14 * q^83 - 16 * q^85 + 16 * q^91 + 16 * q^93 - 40 * q^95 - 8 * q^97 - 2 * q^99

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