LMFDB - Embedded newform 1024.2.e.m.769.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1024,2,Mod(257,1024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,0,0,0,0,0,0,0,0,0,0,0,0,16,0,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			769.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1024.769
Dual form			1024.2.e.m.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 + 1.41421i) q^{3} +(-1.41421 - 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(1.41421 + 1.41421i) q^{11} +(-1.41421 + 1.41421i) q^{13} +4.00000 q^{15} +2.00000 q^{17} +(1.41421 - 1.41421i) q^{19} +(-5.65685 - 5.65685i) q^{21} +4.00000i q^{23} -1.00000i q^{25} +(-2.82843 - 2.82843i) q^{27} +(-4.24264 + 4.24264i) q^{29} -4.00000 q^{33} +(5.65685 - 5.65685i) q^{35} +(-7.07107 - 7.07107i) q^{37} -4.00000i q^{39} +6.00000i q^{41} +(-4.24264 - 4.24264i) q^{43} +(-1.41421 + 1.41421i) q^{45} -8.00000 q^{47} -9.00000 q^{49} +(-2.82843 + 2.82843i) q^{51} +(-4.24264 - 4.24264i) q^{53} -4.00000i q^{55} +4.00000i q^{57} +(9.89949 + 9.89949i) q^{59} +(1.41421 - 1.41421i) q^{61} +4.00000 q^{63} +4.00000 q^{65} +(-7.07107 + 7.07107i) q^{67} +(-5.65685 - 5.65685i) q^{69} -12.0000i q^{71} -14.0000i q^{73} +(1.41421 + 1.41421i) q^{75} +(-5.65685 + 5.65685i) q^{77} -8.00000 q^{79} +11.0000 q^{81} +(-4.24264 + 4.24264i) q^{83} +(-2.82843 - 2.82843i) q^{85} -12.0000i q^{87} -2.00000i q^{89} +(-5.65685 - 5.65685i) q^{91} -4.00000 q^{95} -2.00000 q^{97} +(1.41421 - 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{15} + 8 q^{17} - 16 q^{33} - 32 q^{47} - 36 q^{49} + 16 q^{63} + 16 q^{65} - 32 q^{79} + 44 q^{81} - 16 q^{95} - 8 q^{97}+O(q^{100}) $ 4 * q + 16 * q^15 + 8 * q^17 - 16 * q^33 - 32 * q^47 - 36 * q^49 + 16 * q^63 + 16 * q^65 - 32 * q^79 + 44 * q^81 - 16 * q^95 - 8 * q^97

Character values

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

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

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
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	0.169102	+	0.985599i	$0.445913\pi$
$4$		0			0
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	0.316228	−	0.948683i	$-0.397584\pi$
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$		0			0
$7$			4.00000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			4.00000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	0.887401	−	0.460999i	$-0.152509\pi$
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	−0.460999	+	0.887401i	$0.652509\pi$
$12$		0			0
$13$	−1.41421	+	1.41421i	−0.392232	+	0.392232i	−0.875482	−	0.483250i	$-0.839456\pi$
$13$	−1.41421	+	1.41421i	−0.392232	+	0.392232i	0.483250	+	0.875482i	$0.339456\pi$
$14$		0			0
$15$	4.00000			1.03280
$16$		0			0
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	1.41421	−	1.41421i	0.324443	−	0.324443i	−0.526026	−	0.850469i	$-0.676318\pi$
$19$	1.41421	−	1.41421i	0.324443	−	0.324443i	0.850469	+	0.526026i	$0.176318\pi$
$20$		0			0
$21$	−5.65685	−	5.65685i	−1.23443	−	1.23443i
$22$		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
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−2.82843	−	2.82843i	−0.544331	−	0.544331i
$28$		0			0
$29$	−4.24264	+	4.24264i	−0.787839	+	0.787839i	−0.981140	−	0.193301i	$-0.938081\pi$
$29$	−4.24264	+	4.24264i	−0.787839	+	0.787839i	0.193301	+	0.981140i	$0.438081\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$	−4.00000			−0.696311
$34$		0			0
$35$	5.65685	−	5.65685i	0.956183	−	0.956183i
$36$		0			0
$37$	−7.07107	−	7.07107i	−1.16248	−	1.16248i	−0.983932	−	0.178545i	$-0.942861\pi$
$37$	−7.07107	−	7.07107i	−1.16248	−	1.16248i	−0.178545	−	0.983932i	$-0.557139\pi$
$38$		0			0
$39$		−	4.00000i		−	0.640513i
$40$		0			0
$41$			6.00000i			0.937043i	0.883452	+	0.468521i	$0.155213\pi$
$41$			6.00000i			0.937043i	−0.883452	+	0.468521i	$0.844787\pi$
$42$		0			0
$43$	−4.24264	−	4.24264i	−0.646997	−	0.646997i	0.305269	−	0.952266i	$-0.401253\pi$
$43$	−4.24264	−	4.24264i	−0.646997	−	0.646997i	−0.952266	+	0.305269i	$0.901253\pi$
$44$		0			0
$45$	−1.41421	+	1.41421i	−0.210819	+	0.210819i
$46$		0			0
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	−9.00000			−1.28571
$50$		0			0
$51$	−2.82843	+	2.82843i	−0.396059	+	0.396059i
$52$		0			0
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$		−	4.00000i		−	0.539360i
$56$		0			0
$57$			4.00000i			0.529813i
$58$		0			0
$59$	9.89949	+	9.89949i	1.28880	+	1.28880i	0.935513	+	0.353291i	$0.114937\pi$
$59$	9.89949	+	9.89949i	1.28880	+	1.28880i	0.353291	+	0.935513i	$0.385063\pi$
$60$		0			0
$61$	1.41421	−	1.41421i	0.181071	−	0.181071i	−0.610751	−	0.791823i	$-0.709132\pi$
$61$	1.41421	−	1.41421i	0.181071	−	0.181071i	0.791823	+	0.610751i	$0.209132\pi$
$62$		0			0
$63$	4.00000			0.503953
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	−7.07107	+	7.07107i	−0.863868	+	0.863868i	−0.991785	−	0.127917i	$-0.959171\pi$
$67$	−7.07107	+	7.07107i	−0.863868	+	0.863868i	0.127917	+	0.991785i	$0.459171\pi$
$68$		0			0
$69$	−5.65685	−	5.65685i	−0.681005	−	0.681005i
$70$		0			0
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$		0			0
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$		0			0
$75$	1.41421	+	1.41421i	0.163299	+	0.163299i
$76$		0			0
$77$	−5.65685	+	5.65685i	−0.644658	+	0.644658i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$		0			0
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$		0			0
$85$	−2.82843	−	2.82843i	−0.306786	−	0.306786i
$86$		0			0
$87$		−	12.0000i		−	1.28654i
$88$		0			0
$89$		−	2.00000i		−	0.212000i	−0.994366	−	0.106000i	$-0.966196\pi$
$89$		−	2.00000i		−	0.212000i	0.994366	−	0.106000i	$-0.0338043\pi$
$90$		0			0
$91$	−5.65685	−	5.65685i	−0.592999	−	0.592999i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000			−0.410391
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	1.41421	−	1.41421i	0.142134	−	0.142134i
$100$		0			0
$101$	4.24264	+	4.24264i	0.422159	+	0.422159i	0.885946	−	0.463788i	$-0.153510\pi$
$101$	4.24264	+	4.24264i	0.422159	+	0.422159i	−0.463788	+	0.885946i	$0.653510\pi$
$102$		0			0
$103$			4.00000i			0.394132i	0.980390	+	0.197066i	$0.0631413\pi$
$103$			4.00000i			0.394132i	−0.980390	+	0.197066i	$0.936859\pi$
$104$		0			0
$105$			16.0000i			1.56144i
$106$		0			0
$107$	1.41421	+	1.41421i	0.136717	+	0.136717i	0.772153	−	0.635436i	$-0.219180\pi$
$107$	1.41421	+	1.41421i	0.136717	+	0.136717i	−0.635436	+	0.772153i	$0.719180\pi$
$108$		0			0
$109$	4.24264	−	4.24264i	0.406371	−	0.406371i	−0.474100	−	0.880471i	$-0.657226\pi$
$109$	4.24264	−	4.24264i	0.406371	−	0.406371i	0.880471	+	0.474100i	$0.157226\pi$
$110$		0			0
$111$	20.0000			1.89832
$112$		0			0
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	5.65685	−	5.65685i	0.527504	−	0.527504i
$116$		0			0
$117$	1.41421	+	1.41421i	0.130744	+	0.130744i
$118$		0			0
$119$			8.00000i			0.733359i
$120$		0			0
$121$		−	7.00000i		−	0.636364i
$122$		0			0
$123$	−8.48528	−	8.48528i	−0.765092	−	0.765092i
$124$		0			0
$125$	−8.48528	+	8.48528i	−0.758947	+	0.758947i
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	12.0000			1.05654
$130$		0			0
$131$	4.24264	−	4.24264i	0.370681	−	0.370681i	−0.497044	−	0.867725i	$-0.665581\pi$
$131$	4.24264	−	4.24264i	0.370681	−	0.370681i	0.867725	+	0.497044i	$0.165581\pi$
$132$		0			0
$133$	5.65685	+	5.65685i	0.490511	+	0.490511i
$134$		0			0
$135$			8.00000i			0.688530i
$136$		0			0
$137$		−	10.0000i		−	0.854358i	−0.904167	−	0.427179i	$-0.859507\pi$
$137$		−	10.0000i		−	0.854358i	0.904167	−	0.427179i	$-0.140493\pi$
$138$		0			0
$139$	7.07107	+	7.07107i	0.599760	+	0.599760i	0.940249	−	0.340489i	$-0.110592\pi$
$139$	7.07107	+	7.07107i	0.599760	+	0.599760i	−0.340489	+	0.940249i	$0.610592\pi$
$140$		0			0
$141$	11.3137	−	11.3137i	0.952786	−	0.952786i
$142$		0			0
$143$	−4.00000			−0.334497
$144$		0			0
$145$	12.0000			0.996546
$146$		0			0
$147$	12.7279	−	12.7279i	1.04978	−	1.04978i
$148$		0			0
$149$	12.7279	+	12.7279i	1.04271	+	1.04271i	0.999046	+	0.0436658i	$0.0139037\pi$
$149$	12.7279	+	12.7279i	1.04271	+	1.04271i	0.0436658	+	0.999046i	$0.486096\pi$
$150$		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
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.7279	−	12.7279i	1.01580	−	1.01580i	0.0159256	−	0.999873i	$-0.494931\pi$
$157$	12.7279	−	12.7279i	1.01580	−	1.01580i	0.999873	−	0.0159256i	$-0.00506949\pi$
$158$		0			0
$159$	12.0000			0.951662
$160$		0			0
$161$	−16.0000			−1.26098
$162$		0			0
$163$	−1.41421	+	1.41421i	−0.110770	+	0.110770i	−0.760319	−	0.649550i	$-0.774958\pi$
$163$	−1.41421	+	1.41421i	−0.110770	+	0.110770i	0.649550	+	0.760319i	$0.274958\pi$
$164$		0			0
$165$	5.65685	+	5.65685i	0.440386	+	0.440386i
$166$		0			0
$167$			20.0000i			1.54765i	0.633402	+	0.773823i	$0.281658\pi$
$167$			20.0000i			1.54765i	−0.633402	+	0.773823i	$0.718342\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$		0			0
$171$	−1.41421	−	1.41421i	−0.108148	−	0.108148i
$172$		0			0
$173$	−12.7279	+	12.7279i	−0.967686	+	0.967686i	−0.999494	−	0.0318080i	$-0.989873\pi$
$173$	−12.7279	+	12.7279i	−0.967686	+	0.967686i	0.0318080	+	0.999494i	$0.489873\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$		0			0
$177$	−28.0000			−2.10461
$178$		0			0
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	−0.847656	−	0.530546i	$-0.821987\pi$
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	0.530546	+	0.847656i	$0.321987\pi$
$180$		0			0
$181$	1.41421	+	1.41421i	0.105118	+	0.105118i	0.757710	−	0.652592i	$-0.226318\pi$
$181$	1.41421	+	1.41421i	0.105118	+	0.105118i	−0.652592	+	0.757710i	$0.726318\pi$
$182$		0			0
$183$			4.00000i			0.295689i
$184$		0			0
$185$			20.0000i			1.47043i
$186$		0			0
$187$	2.82843	+	2.82843i	0.206835	+	0.206835i
$188$		0			0
$189$	11.3137	−	11.3137i	0.822951	−	0.822951i
$190$		0			0
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$		0			0
$195$	−5.65685	+	5.65685i	−0.405096	+	0.405096i
$196$		0			0
$197$	9.89949	+	9.89949i	0.705310	+	0.705310i	0.965545	−	0.260235i	$-0.0838002\pi$
$197$	9.89949	+	9.89949i	0.705310	+	0.705310i	−0.260235	+	0.965545i	$0.583800\pi$
$198$		0			0
$199$			4.00000i			0.283552i	0.989899	+	0.141776i	$0.0452813\pi$
$199$			4.00000i			0.283552i	−0.989899	+	0.141776i	$0.954719\pi$
$200$		0			0
$201$		−	20.0000i		−	1.41069i
$202$		0			0
$203$	−16.9706	−	16.9706i	−1.19110	−	1.19110i
$204$		0			0
$205$	8.48528	−	8.48528i	0.592638	−	0.592638i
$206$		0			0
$207$	4.00000			0.278019
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	−15.5563	+	15.5563i	−1.07094	+	1.07094i	−0.0736598	+	0.997283i	$0.523468\pi$
$211$	−15.5563	+	15.5563i	−1.07094	+	1.07094i	−0.997283	+	0.0736598i	$0.976532\pi$
$212$		0			0
$213$	16.9706	+	16.9706i	1.16280	+	1.16280i
$214$		0			0
$215$			12.0000i			0.818393i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	19.7990	+	19.7990i	1.33789	+	1.33789i
$220$		0			0
$221$	−2.82843	+	2.82843i	−0.190261	+	0.190261i
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−12.7279	+	12.7279i	−0.844782	+	0.844782i	−0.989476	−	0.144695i	$-0.953780\pi$
$227$	−12.7279	+	12.7279i	−0.844782	+	0.844782i	0.144695	+	0.989476i	$0.453780\pi$
$228$		0			0
$229$	9.89949	+	9.89949i	0.654177	+	0.654177i	0.953996	−	0.299819i	$-0.0969263\pi$
$229$	9.89949	+	9.89949i	0.654177	+	0.654177i	−0.299819	+	0.953996i	$0.596926\pi$
$230$		0			0
$231$		−	16.0000i		−	1.05272i
$232$		0			0
$233$			18.0000i			1.17922i	0.807688	+	0.589610i	$0.200718\pi$
$233$			18.0000i			1.17922i	−0.807688	+	0.589610i	$0.799282\pi$
$234$		0			0
$235$	11.3137	+	11.3137i	0.738025	+	0.738025i
$236$		0			0
$237$	11.3137	−	11.3137i	0.734904	−	0.734904i
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		0			0
$243$	−7.07107	+	7.07107i	−0.453609	+	0.453609i
$244$		0			0
$245$	12.7279	+	12.7279i	0.813157	+	0.813157i
$246$		0			0
$247$			4.00000i			0.254514i
$248$		0			0
$249$		−	12.0000i		−	0.760469i
$250$		0			0
$251$	−12.7279	−	12.7279i	−0.803379	−	0.803379i	0.180243	−	0.983622i	$-0.442312\pi$
$251$	−12.7279	−	12.7279i	−0.803379	−	0.803379i	−0.983622	+	0.180243i	$0.942312\pi$
$252$		0			0
$253$	−5.65685	+	5.65685i	−0.355643	+	0.355643i
$254$		0			0
$255$	8.00000			0.500979
$256$		0			0
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		0			0
$259$	28.2843	−	28.2843i	1.75750	−	1.75750i
$260$		0			0
$261$	4.24264	+	4.24264i	0.262613	+	0.262613i
$262$		0			0
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$			12.0000i			0.737154i
$266$		0			0
$267$	2.82843	+	2.82843i	0.173097	+	0.173097i
$268$		0			0
$269$	−7.07107	+	7.07107i	−0.431131	+	0.431131i	−0.889013	−	0.457882i	$-0.848608\pi$
$269$	−7.07107	+	7.07107i	−0.431131	+	0.431131i	0.457882	+	0.889013i	$0.348608\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$	16.0000			0.968364
$274$		0			0
$275$	1.41421	−	1.41421i	0.0852803	−	0.0852803i
$276$		0			0
$277$	−4.24264	−	4.24264i	−0.254916	−	0.254916i	0.568067	−	0.822982i	$-0.307691\pi$
$277$	−4.24264	−	4.24264i	−0.254916	−	0.254916i	−0.822982	+	0.568067i	$0.807691\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	18.0000i		−	1.07379i	−0.843649	−	0.536895i	$-0.819597\pi$
$281$		−	18.0000i		−	1.07379i	0.843649	−	0.536895i	$-0.180403\pi$
$282$		0			0
$283$	4.24264	+	4.24264i	0.252199	+	0.252199i	0.821872	−	0.569673i	$-0.192930\pi$
$283$	4.24264	+	4.24264i	0.252199	+	0.252199i	−0.569673	+	0.821872i	$0.692930\pi$
$284$		0			0
$285$	5.65685	−	5.65685i	0.335083	−	0.335083i
$286$		0			0
$287$	−24.0000			−1.41668
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$	2.82843	−	2.82843i	0.165805	−	0.165805i
$292$		0			0
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	0.934444	−	0.356110i	$-0.115897\pi$
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	−0.356110	+	0.934444i	$0.615897\pi$
$294$		0			0
$295$		−	28.0000i		−	1.63022i
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$		0			0
$299$	−5.65685	−	5.65685i	−0.327144	−	0.327144i
$300$		0			0
$301$	16.9706	−	16.9706i	0.978167	−	0.978167i
$302$		0			0
$303$	−12.0000			−0.689382
$304$		0			0
$305$	−4.00000			−0.229039
$306$		0			0
$307$	12.7279	−	12.7279i	0.726421	−	0.726421i	−0.243484	−	0.969905i	$-0.578290\pi$
$307$	12.7279	−	12.7279i	0.726421	−	0.726421i	0.969905	+	0.243484i	$0.0782903\pi$
$308$		0			0
$309$	−5.65685	−	5.65685i	−0.321807	−	0.321807i
$310$		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
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$		0			0
$315$	−5.65685	−	5.65685i	−0.318728	−	0.318728i
$316$		0			0
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	−0.816142	−	0.577851i	$-0.803891\pi$
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	0.577851	+	0.816142i	$0.303891\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$		0			0
$321$	−4.00000			−0.223258
$322$		0			0
$323$	2.82843	−	2.82843i	0.157378	−	0.157378i
$324$		0			0
$325$	1.41421	+	1.41421i	0.0784465	+	0.0784465i
$326$		0			0
$327$			12.0000i			0.663602i
$328$		0			0
$329$		−	32.0000i		−	1.76422i
$330$		0			0
$331$	−9.89949	−	9.89949i	−0.544125	−	0.544125i	0.380610	−	0.924736i	$-0.375714\pi$
$331$	−9.89949	−	9.89949i	−0.544125	−	0.544125i	−0.924736	+	0.380610i	$0.875714\pi$
$332$		0			0
$333$	−7.07107	+	7.07107i	−0.387492	+	0.387492i
$334$		0			0
$335$	20.0000			1.09272
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	2.82843	−	2.82843i	0.153619	−	0.153619i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	8.00000i		−	0.431959i
$344$		0			0
$345$			16.0000i			0.861411i
$346$		0			0
$347$	−12.7279	−	12.7279i	−0.683271	−	0.683271i	0.277465	−	0.960736i	$-0.410506\pi$
$347$	−12.7279	−	12.7279i	−0.683271	−	0.683271i	−0.960736	+	0.277465i	$0.910506\pi$
$348$		0			0
$349$	7.07107	−	7.07107i	0.378506	−	0.378506i	−0.492057	−	0.870563i	$-0.663755\pi$
$349$	7.07107	−	7.07107i	0.378506	−	0.378506i	0.870563	+	0.492057i	$0.163755\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$	−16.9706	+	16.9706i	−0.900704	+	0.900704i
$356$		0			0
$357$	−11.3137	−	11.3137i	−0.598785	−	0.598785i
$358$		0			0
$359$			4.00000i			0.211112i	0.994413	+	0.105556i	$0.0336622\pi$
$359$			4.00000i			0.211112i	−0.994413	+	0.105556i	$0.966338\pi$
$360$		0			0
$361$			15.0000i			0.789474i
$362$		0			0
$363$	9.89949	+	9.89949i	0.519589	+	0.519589i
$364$		0			0
$365$	−19.7990	+	19.7990i	−1.03633	+	1.03633i
$366$		0			0
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	16.9706	−	16.9706i	0.881068	−	0.881068i
$372$		0			0
$373$	7.07107	+	7.07107i	0.366126	+	0.366126i	0.866062	−	0.499936i	$-0.166643\pi$
$373$	7.07107	+	7.07107i	0.366126	+	0.366126i	−0.499936	+	0.866062i	$0.666643\pi$
$374$		0			0
$375$		−	24.0000i		−	1.23935i
$376$		0			0
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	−1.41421	−	1.41421i	−0.0726433	−	0.0726433i	0.669852	−	0.742495i	$-0.266358\pi$
$379$	−1.41421	−	1.41421i	−0.0726433	−	0.0726433i	−0.742495	+	0.669852i	$0.766358\pi$
$380$		0			0
$381$	22.6274	−	22.6274i	1.15924	−	1.15924i
$382$		0			0
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$	16.0000			0.815436
$386$		0			0
$387$	−4.24264	+	4.24264i	−0.215666	+	0.215666i
$388$		0			0
$389$	−7.07107	−	7.07107i	−0.358517	−	0.358517i	0.504749	−	0.863266i	$-0.331585\pi$
$389$	−7.07107	−	7.07107i	−0.358517	−	0.358517i	−0.863266	+	0.504749i	$0.831585\pi$
$390$		0			0
$391$			8.00000i			0.404577i
$392$		0			0
$393$			12.0000i			0.605320i
$394$		0			0
$395$	11.3137	+	11.3137i	0.569254	+	0.569254i
$396$		0			0
$397$	4.24264	−	4.24264i	0.212932	−	0.212932i	−0.592580	−	0.805512i	$-0.701890\pi$
$397$	4.24264	−	4.24264i	0.212932	−	0.212932i	0.805512	+	0.592580i	$0.201890\pi$
$398$		0			0
$399$	−16.0000			−0.801002
$400$		0			0
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−15.5563	−	15.5563i	−0.773001	−	0.773001i
$406$		0			0
$407$		−	20.0000i		−	0.991363i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$	14.1421	+	14.1421i	0.697580	+	0.697580i
$412$		0			0
$413$	−39.5980	+	39.5980i	−1.94849	+	1.94849i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	−18.3848	+	18.3848i	−0.898155	+	0.898155i	−0.995273	−	0.0971178i	$-0.969038\pi$
$419$	−18.3848	+	18.3848i	−0.898155	+	0.898155i	0.0971178	+	0.995273i	$0.469038\pi$
$420$		0			0
$421$	−24.0416	−	24.0416i	−1.17172	−	1.17172i	−0.981800	−	0.189917i	$-0.939178\pi$
$421$	−24.0416	−	24.0416i	−1.17172	−	1.17172i	−0.189917	−	0.981800i	$-0.560822\pi$
$422$		0			0
$423$			8.00000i			0.388973i
$424$		0			0
$425$		−	2.00000i		−	0.0970143i
$426$		0			0
$427$	5.65685	+	5.65685i	0.273754	+	0.273754i
$428$		0			0
$429$	5.65685	−	5.65685i	0.273115	−	0.273115i
$430$		0			0
$431$	40.0000			1.92673			0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000			1.92673			0.963366	+	0.268190i	$0.0864254\pi$
$432$		0			0
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$		0			0
$435$	−16.9706	+	16.9706i	−0.813676	+	0.813676i
$436$		0			0
$437$	5.65685	+	5.65685i	0.270604	+	0.270604i
$438$		0			0
$439$			36.0000i			1.71819i	0.511819	+	0.859093i	$0.328972\pi$
$439$			36.0000i			1.71819i	−0.511819	+	0.859093i	$0.671028\pi$
$440$		0			0
$441$			9.00000i			0.428571i
$442$		0			0
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	0.800674	−	0.599100i	$-0.204475\pi$
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	−0.599100	+	0.800674i	$0.704475\pi$
$444$		0			0
$445$	−2.82843	+	2.82843i	−0.134080	+	0.134080i
$446$		0			0
$447$	−36.0000			−1.70274
$448$		0			0
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$		0			0
$451$	−8.48528	+	8.48528i	−0.399556	+	0.399556i
$452$		0			0
$453$	−5.65685	−	5.65685i	−0.265782	−	0.265782i
$454$		0			0
$455$			16.0000i			0.750092i
$456$		0			0
$457$			6.00000i			0.280668i	0.990104	+	0.140334i	$0.0448177\pi$
$457$			6.00000i			0.280668i	−0.990104	+	0.140334i	$0.955182\pi$
$458$		0			0
$459$	−5.65685	−	5.65685i	−0.264039	−	0.264039i
$460$		0			0
$461$	−7.07107	+	7.07107i	−0.329332	+	0.329332i	−0.852333	−	0.523000i	$-0.824813\pi$
$461$	−7.07107	+	7.07107i	−0.329332	+	0.329332i	0.523000	+	0.852333i	$0.324813\pi$
$462$		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
$465$		0			0
$466$		0			0
$467$	−9.89949	+	9.89949i	−0.458094	+	0.458094i	−0.898029	−	0.439935i	$-0.855001\pi$
$467$	−9.89949	+	9.89949i	−0.458094	+	0.458094i	0.439935	+	0.898029i	$0.355001\pi$
$468$		0			0
$469$	−28.2843	−	28.2843i	−1.30605	−	1.30605i
$470$		0			0
$471$			36.0000i			1.65879i
$472$		0			0
$473$		−	12.0000i		−	0.551761i
$474$		0			0
$475$	−1.41421	−	1.41421i	−0.0648886	−	0.0648886i
$476$		0			0
$477$	−4.24264	+	4.24264i	−0.194257	+	0.194257i
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$	20.0000			0.911922
$482$		0			0
$483$	22.6274	−	22.6274i	1.02958	−	1.02958i
$484$		0			0
$485$	2.82843	+	2.82843i	0.128432	+	0.128432i
$486$		0			0
$487$			20.0000i			0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$			20.0000i			0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$		0			0
$489$		−	4.00000i		−	0.180886i
$490$		0			0
$491$	7.07107	+	7.07107i	0.319113	+	0.319113i	0.848426	−	0.529313i	$-0.177550\pi$
$491$	7.07107	+	7.07107i	0.319113	+	0.319113i	−0.529313	+	0.848426i	$0.677550\pi$
$492$		0			0
$493$	−8.48528	+	8.48528i	−0.382158	+	0.382158i
$494$		0			0
$495$	−4.00000			−0.179787
$496$		0			0
$497$	48.0000			2.15309
$498$		0			0
$499$	−15.5563	+	15.5563i	−0.696398	+	0.696398i	−0.963632	−	0.267234i	$-0.913890\pi$
$499$	−15.5563	+	15.5563i	−0.696398	+	0.696398i	0.267234	+	0.963632i	$0.413890\pi$
$500$		0			0
$501$	−28.2843	−	28.2843i	−1.26365	−	1.26365i
$502$		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
$505$		−	12.0000i		−	0.533993i
$506$		0			0
$507$	−12.7279	−	12.7279i	−0.565267	−	0.565267i
$508$		0			0
$509$	−9.89949	+	9.89949i	−0.438787	+	0.438787i	−0.891604	−	0.452816i	$-0.850419\pi$
$509$	−9.89949	+	9.89949i	−0.438787	+	0.438787i	0.452816	+	0.891604i	$0.350419\pi$
$510$		0			0
$511$	56.0000			2.47729
$512$		0			0
$513$	−8.00000			−0.353209
$514$		0			0
$515$	5.65685	−	5.65685i	0.249271	−	0.249271i
$516$		0			0
$517$	−11.3137	−	11.3137i	−0.497576	−	0.497576i
$518$		0			0
$519$		−	36.0000i		−	1.58022i
$520$		0			0
$521$			22.0000i			0.963837i	0.876216	+	0.481919i	$0.160060\pi$
$521$			22.0000i			0.963837i	−0.876216	+	0.481919i	$0.839940\pi$
$522$		0			0
$523$	−9.89949	−	9.89949i	−0.432875	−	0.432875i	0.456730	−	0.889605i	$-0.349020\pi$
$523$	−9.89949	−	9.89949i	−0.432875	−	0.432875i	−0.889605	+	0.456730i	$0.849020\pi$
$524$		0			0
$525$	−5.65685	+	5.65685i	−0.246885	+	0.246885i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	9.89949	−	9.89949i	0.429601	−	0.429601i
$532$		0			0
$533$	−8.48528	−	8.48528i	−0.367538	−	0.367538i
$534$		0			0
$535$		−	4.00000i		−	0.172935i
$536$		0			0
$537$		−	12.0000i		−	0.517838i
$538$		0			0
$539$	−12.7279	−	12.7279i	−0.548230	−	0.548230i
$540$		0			0
$541$	24.0416	−	24.0416i	1.03363	−	1.03363i	0.0342160	−	0.999414i	$-0.489107\pi$
$541$	24.0416	−	24.0416i	1.03363	−	1.03363i	0.999414	−	0.0342160i	$-0.0108934\pi$
$542$		0			0
$543$	−4.00000			−0.171656
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	26.8701	−	26.8701i	1.14888	−	1.14888i	0.162108	−	0.986773i	$-0.448171\pi$
$547$	26.8701	−	26.8701i	1.14888	−	1.14888i	0.986773	−	0.162108i	$-0.0518292\pi$
$548$		0			0
$549$	−1.41421	−	1.41421i	−0.0603572	−	0.0603572i
$550$		0			0
$551$			12.0000i			0.511217i
$552$		0			0
$553$		−	32.0000i		−	1.36078i
$554$		0			0
$555$	−28.2843	−	28.2843i	−1.20060	−	1.20060i
$556$		0			0
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	−0.736433	−	0.676511i	$-0.763491\pi$
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	0.676511	+	0.736433i	$0.263491\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	12.7279	−	12.7279i	0.536418	−	0.536418i	−0.386057	−	0.922475i	$-0.626163\pi$
$563$	12.7279	−	12.7279i	0.536418	−	0.536418i	0.922475	+	0.386057i	$0.126163\pi$
$564$		0			0
$565$	2.82843	+	2.82843i	0.118993	+	0.118993i
$566$		0			0
$567$			44.0000i			1.84783i
$568$		0			0
$569$			26.0000i			1.08998i	0.838444	+	0.544988i	$0.183466\pi$
$569$			26.0000i			1.08998i	−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	26.8701	+	26.8701i	1.12448	+	1.12448i	0.991060	+	0.133417i	$0.0425949\pi$
$571$	26.8701	+	26.8701i	1.12448	+	1.12448i	0.133417	+	0.991060i	$0.457405\pi$
$572$		0			0
$573$	−22.6274	+	22.6274i	−0.945274	+	0.945274i
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	2.82843	−	2.82843i	0.117545	−	0.117545i
$580$		0			0
$581$	−16.9706	−	16.9706i	−0.704058	−	0.704058i
$582$		0			0
$583$		−	12.0000i		−	0.496989i
$584$		0			0
$585$		−	4.00000i		−	0.165380i
$586$		0			0
$587$	24.0416	+	24.0416i	0.992304	+	0.992304i	0.999971	−	0.00766632i	$-0.00244029\pi$
$587$	24.0416	+	24.0416i	0.992304	+	0.992304i	−0.00766632	+	0.999971i	$0.502440\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−28.0000			−1.15177
$592$		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
$595$	11.3137	−	11.3137i	0.463817	−	0.463817i
$596$		0			0
$597$	−5.65685	−	5.65685i	−0.231520	−	0.231520i
$598$		0			0
$599$		−	12.0000i		−	0.490307i	−0.969484	−	0.245153i	$-0.921162\pi$
$599$		−	12.0000i		−	0.490307i	0.969484	−	0.245153i	$-0.0788383\pi$
$600$		0			0
$601$			30.0000i			1.22373i	0.790964	+	0.611863i	$0.209580\pi$
$601$			30.0000i			1.22373i	−0.790964	+	0.611863i	$0.790420\pi$
$602$		0			0
$603$	7.07107	+	7.07107i	0.287956	+	0.287956i
$604$		0			0
$605$	−9.89949	+	9.89949i	−0.402472	+	0.402472i
$606$		0			0
$607$	16.0000			0.649420			0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000			0.649420			0.324710	+	0.945814i	$0.394733\pi$
$608$		0			0
$609$	48.0000			1.94506
$610$		0			0
$611$	11.3137	−	11.3137i	0.457704	−	0.457704i
$612$		0			0
$613$	−24.0416	−	24.0416i	−0.971032	−	0.971032i	0.0285598	−	0.999592i	$-0.490908\pi$
$613$	−24.0416	−	24.0416i	−0.971032	−	0.971032i	−0.999592	+	0.0285598i	$0.990908\pi$
$614$		0			0
$615$			24.0000i			0.967773i
$616$		0			0
$617$			2.00000i			0.0805170i	0.999189	+	0.0402585i	$0.0128181\pi$
$617$			2.00000i			0.0805170i	−0.999189	+	0.0402585i	$0.987182\pi$
$618$		0			0
$619$	−32.5269	−	32.5269i	−1.30737	−	1.30737i	−0.923309	−	0.384058i	$-0.874526\pi$
$619$	−32.5269	−	32.5269i	−1.30737	−	1.30737i	−0.384058	−	0.923309i	$-0.625474\pi$
$620$		0			0
$621$	11.3137	−	11.3137i	0.454003	−	0.454003i
$622$		0			0
$623$	8.00000			0.320513
$624$		0			0
$625$	19.0000			0.760000
$626$		0			0
$627$	−5.65685	+	5.65685i	−0.225913	+	0.225913i
$628$		0			0
$629$	−14.1421	−	14.1421i	−0.563884	−	0.563884i
$630$		0			0
$631$		−	44.0000i		−	1.75161i	−0.482663	−	0.875806i	$-0.660330\pi$
$631$		−	44.0000i		−	1.75161i	0.482663	−	0.875806i	$-0.339670\pi$
$632$		0			0
$633$		−	44.0000i		−	1.74884i
$634$		0			0
$635$	22.6274	+	22.6274i	0.897942	+	0.897942i
$636$		0			0
$637$	12.7279	−	12.7279i	0.504299	−	0.504299i
$638$		0			0
$639$	−12.0000			−0.474713
$640$		0			0
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	−29.6985	+	29.6985i	−1.17119	+	1.17119i	−0.189269	+	0.981925i	$0.560612\pi$
$643$	−29.6985	+	29.6985i	−1.17119	+	1.17119i	−0.981925	+	0.189269i	$0.939388\pi$
$644$		0			0
$645$	−16.9706	−	16.9706i	−0.668215	−	0.668215i
$646$		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
$649$			28.0000i			1.09910i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−29.6985	+	29.6985i	−1.16219	+	1.16219i	−0.178197	+	0.983995i	$0.557026\pi$
$653$	−29.6985	+	29.6985i	−1.16219	+	1.16219i	−0.983995	+	0.178197i	$0.942974\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$		0			0
$657$	−14.0000			−0.546192
$658$		0			0
$659$	−4.24264	+	4.24264i	−0.165270	+	0.165270i	−0.784897	−	0.619627i	$-0.787284\pi$
$659$	−4.24264	+	4.24264i	−0.165270	+	0.165270i	0.619627	+	0.784897i	$0.287284\pi$
$660$		0			0
$661$	24.0416	+	24.0416i	0.935111	+	0.935111i	0.998019	−	0.0629083i	$-0.0200376\pi$
$661$	24.0416	+	24.0416i	0.935111	+	0.935111i	−0.0629083	+	0.998019i	$0.520038\pi$
$662$		0			0
$663$		−	8.00000i		−	0.310694i
$664$		0			0
$665$		−	16.0000i		−	0.620453i
$666$		0			0
$667$	−16.9706	−	16.9706i	−0.657103	−	0.657103i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.00000			0.154418
$672$		0			0
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$		0			0
$675$	−2.82843	+	2.82843i	−0.108866	+	0.108866i
$676$		0			0
$677$	15.5563	+	15.5563i	0.597879	+	0.597879i	0.939748	−	0.341869i	$-0.111060\pi$
$677$	15.5563	+	15.5563i	0.597879	+	0.597879i	−0.341869	+	0.939748i	$0.611060\pi$
$678$		0			0
$679$		−	8.00000i		−	0.307012i
$680$		0			0
$681$		−	36.0000i		−	1.37952i
$682$		0			0
$683$	29.6985	+	29.6985i	1.13638	+	1.13638i	0.989094	+	0.147287i	$0.0470541\pi$
$683$	29.6985	+	29.6985i	1.13638	+	1.13638i	0.147287	+	0.989094i	$0.452946\pi$
$684$		0			0
$685$	−14.1421	+	14.1421i	−0.540343	+	0.540343i
$686$		0			0
$687$	−28.0000			−1.06827
$688$		0			0
$689$	12.0000			0.457164
$690$		0			0
$691$	−4.24264	+	4.24264i	−0.161398	+	0.161398i	−0.783186	−	0.621788i	$-0.786407\pi$
$691$	−4.24264	+	4.24264i	−0.161398	+	0.161398i	0.621788	+	0.783186i	$0.286407\pi$
$692$		0			0
$693$	5.65685	+	5.65685i	0.214886	+	0.214886i
$694$		0			0
$695$		−	20.0000i		−	0.758643i
$696$		0			0
$697$			12.0000i			0.454532i
$698$		0			0
$699$	−25.4558	−	25.4558i	−0.962828	−	0.962828i
$700$		0			0
$701$	1.41421	−	1.41421i	0.0534141	−	0.0534141i	−0.679895	−	0.733309i	$-0.737975\pi$
$701$	1.41421	−	1.41421i	0.0534141	−	0.0534141i	0.733309	+	0.679895i	$0.237975\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$		0			0
$705$	−32.0000			−1.20519
$706$		0			0
$707$	−16.9706	+	16.9706i	−0.638244	+	0.638244i
$708$		0			0
$709$	15.5563	+	15.5563i	0.584231	+	0.584231i	0.936063	−	0.351832i	$-0.114441\pi$
$709$	15.5563	+	15.5563i	0.584231	+	0.584231i	−0.351832	+	0.936063i	$0.614441\pi$
$710$		0			0
$711$			8.00000i			0.300023i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	5.65685	+	5.65685i	0.211554	+	0.211554i
$716$		0			0
$717$	33.9411	−	33.9411i	1.26755	−	1.26755i
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	−16.0000			−0.595871
$722$		0			0
$723$	−2.82843	+	2.82843i	−0.105190	+	0.105190i
$724$		0			0
$725$	4.24264	+	4.24264i	0.157568	+	0.157568i
$726$		0			0
$727$		−	12.0000i		−	0.445055i	−0.974926	−	0.222528i	$-0.928569\pi$
$727$		−	12.0000i		−	0.445055i	0.974926	−	0.222528i	$-0.0714308\pi$
$728$		0			0
$729$			13.0000i			0.481481i
$730$		0			0
$731$	−8.48528	−	8.48528i	−0.313839	−	0.313839i
$732$		0			0
$733$	−4.24264	+	4.24264i	−0.156706	+	0.156706i	−0.781105	−	0.624400i	$-0.785344\pi$
$733$	−4.24264	+	4.24264i	−0.156706	+	0.156706i	0.624400	+	0.781105i	$0.285344\pi$
$734$		0			0
$735$	−36.0000			−1.32788
$736$		0			0
$737$	−20.0000			−0.736709
$738$		0			0
$739$	−12.7279	+	12.7279i	−0.468204	+	0.468204i	−0.901332	−	0.433128i	$-0.857410\pi$
$739$	−12.7279	+	12.7279i	−0.468204	+	0.468204i	0.433128	+	0.901332i	$0.357410\pi$
$740$		0			0
$741$	−5.65685	−	5.65685i	−0.207810	−	0.207810i
$742$		0			0
$743$		−	44.0000i		−	1.61420i	−0.590412	−	0.807102i	$-0.701035\pi$
$743$		−	44.0000i		−	1.61420i	0.590412	−	0.807102i	$-0.298965\pi$
$744$		0			0
$745$		−	36.0000i		−	1.31894i
$746$		0			0
$747$	4.24264	+	4.24264i	0.155230	+	0.155230i
$748$		0			0
$749$	−5.65685	+	5.65685i	−0.206697	+	0.206697i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$		0			0
$753$	36.0000			1.31191
$754$		0			0
$755$	5.65685	−	5.65685i	0.205874	−	0.205874i
$756$		0			0
$757$	−32.5269	−	32.5269i	−1.18221	−	1.18221i	−0.979170	−	0.203040i	$-0.934918\pi$
$757$	−32.5269	−	32.5269i	−1.18221	−	1.18221i	−0.203040	−	0.979170i	$-0.565082\pi$
$758$		0			0
$759$		−	16.0000i		−	0.580763i
$760$		0			0
$761$			10.0000i			0.362500i	0.983437	+	0.181250i	$0.0580143\pi$
$761$			10.0000i			0.362500i	−0.983437	+	0.181250i	$0.941986\pi$
$762$		0			0
$763$	16.9706	+	16.9706i	0.614376	+	0.614376i
$764$		0			0
$765$	−2.82843	+	2.82843i	−0.102262	+	0.102262i
$766$		0			0
$767$	−28.0000			−1.01102
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−25.4558	+	25.4558i	−0.916770	+	0.916770i
$772$		0			0
$773$	38.1838	+	38.1838i	1.37337	+	1.37337i	0.855390	+	0.517985i	$0.173318\pi$
$773$	38.1838	+	38.1838i	1.37337	+	1.37337i	0.517985	+	0.855390i	$0.326682\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			80.0000i			2.86998i
$778$		0			0
$779$	8.48528	+	8.48528i	0.304017	+	0.304017i
$780$		0			0
$781$	16.9706	−	16.9706i	0.607254	−	0.607254i
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	−36.0000			−1.28490
$786$		0			0
$787$	−15.5563	+	15.5563i	−0.554524	+	0.554524i	−0.927743	−	0.373219i	$-0.878254\pi$
$787$	−15.5563	+	15.5563i	−0.554524	+	0.554524i	0.373219	+	0.927743i	$0.378254\pi$
$788$		0			0
$789$	16.9706	+	16.9706i	0.604168	+	0.604168i
$790$		0			0
$791$		−	8.00000i		−	0.284447i
$792$		0			0
$793$			4.00000i			0.142044i
$794$		0			0
$795$	−16.9706	−	16.9706i	−0.601884	−	0.601884i
$796$		0			0
$797$	12.7279	−	12.7279i	0.450846	−	0.450846i	−0.444789	−	0.895635i	$-0.646721\pi$
$797$	12.7279	−	12.7279i	0.450846	−	0.450846i	0.895635	+	0.444789i	$0.146721\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$		0			0
$801$	−2.00000			−0.0706665
$802$		0			0
$803$	19.7990	−	19.7990i	0.698691	−	0.698691i
$804$		0			0
$805$	22.6274	+	22.6274i	0.797512	+	0.797512i
$806$		0			0
$807$		−	20.0000i		−	0.704033i
$808$		0			0
$809$			6.00000i			0.210949i	0.994422	+	0.105474i	$0.0336361\pi$
$809$			6.00000i			0.210949i	−0.994422	+	0.105474i	$0.966364\pi$
$810$		0			0
$811$	12.7279	+	12.7279i	0.446938	+	0.446938i	0.894335	−	0.447397i	$-0.147649\pi$
$811$	12.7279	+	12.7279i	0.446938	+	0.446938i	−0.447397	+	0.894335i	$0.647649\pi$
$812$		0			0
$813$	−11.3137	+	11.3137i	−0.396789	+	0.396789i
$814$		0			0
$815$	4.00000			0.140114
$816$		0			0
$817$	−12.0000			−0.419827
$818$		0			0
$819$	−5.65685	+	5.65685i	−0.197666	+	0.197666i
$820$		0			0
$821$	7.07107	+	7.07107i	0.246782	+	0.246782i	0.819649	−	0.572867i	$-0.194169\pi$
$821$	7.07107	+	7.07107i	0.246782	+	0.246782i	−0.572867	+	0.819649i	$0.694169\pi$
$822$		0			0
$823$		−	28.0000i		−	0.976019i	−0.872838	−	0.488009i	$-0.837723\pi$
$823$		−	28.0000i		−	0.976019i	0.872838	−	0.488009i	$-0.162277\pi$
$824$		0			0
$825$			4.00000i			0.139262i
$826$		0			0
$827$	15.5563	+	15.5563i	0.540947	+	0.540947i	0.923807	−	0.382859i	$-0.125061\pi$
$827$	15.5563	+	15.5563i	0.540947	+	0.540947i	−0.382859	+	0.923807i	$0.625061\pi$
$828$		0			0
$829$	−9.89949	+	9.89949i	−0.343824	+	0.343824i	−0.857803	−	0.513979i	$-0.828171\pi$
$829$	−9.89949	+	9.89949i	−0.343824	+	0.343824i	0.513979	+	0.857803i	$0.328171\pi$
$830$		0			0
$831$	12.0000			0.416275
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	28.2843	−	28.2843i	0.978818	−	0.978818i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			36.0000i			1.24286i	0.783470	+	0.621429i	$0.213448\pi$
$839$			36.0000i			1.24286i	−0.783470	+	0.621429i	$0.786552\pi$
$840$		0			0
$841$		−	7.00000i		−	0.241379i
$842$		0			0
$843$	25.4558	+	25.4558i	0.876746	+	0.876746i
$844$		0			0
$845$	12.7279	−	12.7279i	0.437854	−	0.437854i
$846$		0			0
$847$	28.0000			0.962091
$848$		0			0
$849$	−12.0000			−0.411839
$850$		0			0
$851$	28.2843	−	28.2843i	0.969572	−	0.969572i
$852$		0			0
$853$	18.3848	+	18.3848i	0.629483	+	0.629483i	0.947938	−	0.318455i	$-0.103164\pi$
$853$	18.3848	+	18.3848i	0.629483	+	0.629483i	−0.318455	+	0.947938i	$0.603164\pi$
$854$		0			0
$855$			4.00000i			0.136797i
$856$		0			0
$857$		−	6.00000i		−	0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$		−	6.00000i		−	0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$		0			0
$859$	−35.3553	−	35.3553i	−1.20631	−	1.20631i	−0.972214	−	0.234095i	$-0.924787\pi$
$859$	−35.3553	−	35.3553i	−1.20631	−	1.20631i	−0.234095	−	0.972214i	$-0.575213\pi$
$860$		0			0
$861$	33.9411	−	33.9411i	1.15671	−	1.15671i
$862$		0			0
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$		0			0
$865$	36.0000			1.22404
$866$		0			0
$867$	18.3848	−	18.3848i	0.624380	−	0.624380i
$868$		0			0
$869$	−11.3137	−	11.3137i	−0.383791	−	0.383791i
$870$		0			0
$871$		−	20.0000i		−	0.677674i
$872$		0			0
$873$			2.00000i			0.0676897i
$874$		0			0
$875$	−33.9411	−	33.9411i	−1.14742	−	1.14742i
$876$		0			0
$877$	15.5563	−	15.5563i	0.525301	−	0.525301i	−0.393867	−	0.919167i	$-0.628863\pi$
$877$	15.5563	−	15.5563i	0.525301	−	0.525301i	0.919167	+	0.393867i	$0.128863\pi$
$878$		0			0
$879$	−28.0000			−0.944417
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	24.0416	−	24.0416i	0.809065	−	0.809065i	−0.175427	−	0.984492i	$-0.556131\pi$
$883$	24.0416	−	24.0416i	0.809065	−	0.809065i	0.984492	+	0.175427i	$0.0561306\pi$
$884$		0			0
$885$	39.5980	+	39.5980i	1.33107	+	1.33107i
$886$		0			0
$887$			36.0000i			1.20876i	0.796696	+	0.604381i	$0.206579\pi$
$887$			36.0000i			1.20876i	−0.796696	+	0.604381i	$0.793421\pi$
$888$		0			0
$889$		−	64.0000i		−	2.14649i
$890$		0			0
$891$	15.5563	+	15.5563i	0.521157	+	0.521157i
$892$		0			0
$893$	−11.3137	+	11.3137i	−0.378599	+	0.378599i
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$	16.0000			0.534224
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−8.48528	−	8.48528i	−0.282686	−	0.282686i
$902$		0			0
$903$			48.0000i			1.59734i
$904$		0			0
$905$		−	4.00000i		−	0.132964i
$906$		0			0
$907$	−26.8701	−	26.8701i	−0.892206	−	0.892206i	0.102525	−	0.994730i	$-0.467308\pi$
$907$	−26.8701	−	26.8701i	−0.892206	−	0.892206i	−0.994730	+	0.102525i	$0.967308\pi$
$908$		0			0
$909$	4.24264	−	4.24264i	0.140720	−	0.140720i
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$		0			0
$915$	5.65685	−	5.65685i	0.187010	−	0.187010i
$916$		0			0
$917$	16.9706	+	16.9706i	0.560417	+	0.560417i
$918$		0			0
$919$			36.0000i			1.18753i	0.804638	+	0.593765i	$0.202359\pi$
$919$			36.0000i			1.18753i	−0.804638	+	0.593765i	$0.797641\pi$
$920$		0			0
$921$			36.0000i			1.18624i
$922$		0			0
$923$	16.9706	+	16.9706i	0.558593	+	0.558593i
$924$		0			0
$925$	−7.07107	+	7.07107i	−0.232495	+	0.232495i
$926$		0			0
$927$	4.00000			0.131377
$928$		0			0
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	−12.7279	+	12.7279i	−0.417141	+	0.417141i
$932$		0			0
$933$	39.5980	+	39.5980i	1.29638	+	1.29638i
$934$		0			0
$935$		−	8.00000i		−	0.261628i
$936$		0			0
$937$		−	46.0000i		−	1.50275i	−0.659873	−	0.751377i	$-0.729390\pi$
$937$		−	46.0000i		−	1.50275i	0.659873	−	0.751377i	$-0.270610\pi$
$938$		0			0
$939$	−14.1421	−	14.1421i	−0.461511	−	0.461511i
$940$		0			0
$941$	26.8701	−	26.8701i	0.875939	−	0.875939i	−0.117173	−	0.993112i	$-0.537383\pi$
$941$	26.8701	−	26.8701i	0.875939	−	0.875939i	0.993112	+	0.117173i	$0.0373831\pi$
$942$		0			0
$943$	−24.0000			−0.781548
$944$		0			0
$945$	−32.0000			−1.04096
$946$		0			0
$947$	−9.89949	+	9.89949i	−0.321690	+	0.321690i	−0.849415	−	0.527725i	$-0.823045\pi$
$947$	−9.89949	+	9.89949i	−0.321690	+	0.321690i	0.527725	+	0.849415i	$0.323045\pi$
$948$		0			0
$949$	19.7990	+	19.7990i	0.642702	+	0.642702i
$950$		0			0
$951$		−	12.0000i		−	0.389127i
$952$		0			0
$953$			58.0000i			1.87880i	0.342817	+	0.939402i	$0.388619\pi$
$953$			58.0000i			1.87880i	−0.342817	+	0.939402i	$0.611381\pi$
$954$		0			0
$955$	−22.6274	−	22.6274i	−0.732206	−	0.732206i
$956$		0			0
$957$	16.9706	−	16.9706i	0.548580	−	0.548580i
$958$		0			0
$959$	40.0000			1.29167
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	1.41421	−	1.41421i	0.0455724	−	0.0455724i
$964$		0			0
$965$	2.82843	+	2.82843i	0.0910503	+	0.0910503i
$966$		0			0
$967$		−	28.0000i		−	0.900419i	−0.892923	−	0.450210i	$-0.851349\pi$
$967$		−	28.0000i		−	0.900419i	0.892923	−	0.450210i	$-0.148651\pi$
$968$		0			0
$969$			8.00000i			0.256997i
$970$		0			0
$971$	−26.8701	−	26.8701i	−0.862301	−	0.862301i	0.129304	−	0.991605i	$-0.458726\pi$
$971$	−26.8701	−	26.8701i	−0.862301	−	0.862301i	−0.991605	+	0.129304i	$0.958726\pi$
$972$		0			0
$973$	−28.2843	+	28.2843i	−0.906752	+	0.906752i
$974$		0			0
$975$	−4.00000			−0.128103
$976$		0			0
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$		0			0
$979$	2.82843	−	2.82843i	0.0903969	−	0.0903969i
$980$		0			0
$981$	−4.24264	−	4.24264i	−0.135457	−	0.135457i
$982$		0			0
$983$			20.0000i			0.637901i	0.947771	+	0.318950i	$0.103330\pi$
$983$			20.0000i			0.637901i	−0.947771	+	0.318950i	$0.896670\pi$
$984$		0			0
$985$		−	28.0000i		−	0.892154i
$986$		0			0
$987$	45.2548	+	45.2548i	1.44048	+	1.44048i
$988$		0			0
$989$	16.9706	−	16.9706i	0.539633	−	0.539633i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	28.0000			0.888553
$994$		0			0
$995$	5.65685	−	5.65685i	0.179334	−	0.179334i
$996$		0			0
$997$	38.1838	+	38.1838i	1.20929	+	1.20929i	0.971256	+	0.238036i	$0.0765035\pi$
$997$	38.1838	+	38.1838i	1.20929	+	1.20929i	0.238036	+	0.971256i	$0.423497\pi$
$998$		0			0
$999$			40.0000i			1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.e.m.769.1		4
4.3	odd	2		1024.2.e.i.769.2		4
8.3	odd	2		1024.2.e.i.769.1		4
8.5	even	2	inner	1024.2.e.m.769.2		4
16.3	odd	4		1024.2.e.i.257.2		4
16.5	even	4	inner	1024.2.e.m.257.2		4
16.11	odd	4		1024.2.e.i.257.1		4
16.13	even	4	inner	1024.2.e.m.257.1		4
32.3	odd	8		128.2.a.d.1.1	yes	1
32.5	even	8		256.2.b.a.129.1		2
32.11	odd	8		256.2.b.c.129.1		2
32.13	even	8		128.2.a.c.1.1	yes	1
32.19	odd	8		128.2.a.a.1.1	✓	1
32.21	even	8		256.2.b.a.129.2		2
32.27	odd	8		256.2.b.c.129.2		2
32.29	even	8		128.2.a.b.1.1	yes	1
96.5	odd	8		2304.2.d.b.1153.2		2
96.11	even	8		2304.2.d.r.1153.1		2
96.29	odd	8		1152.2.a.h.1.1		1
96.35	even	8		1152.2.a.c.1.1		1
96.53	odd	8		2304.2.d.b.1153.1		2
96.59	even	8		2304.2.d.r.1153.2		2
96.77	odd	8		1152.2.a.r.1.1		1
96.83	even	8		1152.2.a.m.1.1		1
160.3	even	8		3200.2.c.e.2049.2		2
160.13	odd	8		3200.2.c.f.2049.2		2
160.19	odd	8		3200.2.a.x.1.1		1
160.29	even	8		3200.2.a.u.1.1		1
160.67	even	8		3200.2.c.e.2049.1		2
160.77	odd	8		3200.2.c.f.2049.1		2
160.83	even	8		3200.2.c.l.2049.1		2
160.93	odd	8		3200.2.c.k.2049.1		2
160.99	odd	8		3200.2.a.h.1.1		1
160.109	even	8		3200.2.a.e.1.1		1
160.147	even	8		3200.2.c.l.2049.2		2
160.157	odd	8		3200.2.c.k.2049.2		2
224.13	odd	8		6272.2.a.b.1.1		1
224.83	even	8		6272.2.a.h.1.1		1
224.125	odd	8		6272.2.a.g.1.1		1
224.195	even	8		6272.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.a.a.1.1	✓	1	32.19	odd	8
128.2.a.b.1.1	yes	1	32.29	even	8
128.2.a.c.1.1	yes	1	32.13	even	8
128.2.a.d.1.1	yes	1	32.3	odd	8
256.2.b.a.129.1		2	32.5	even	8
256.2.b.a.129.2		2	32.21	even	8
256.2.b.c.129.1		2	32.11	odd	8
256.2.b.c.129.2		2	32.27	odd	8
1024.2.e.i.257.1		4	16.11	odd	4
1024.2.e.i.257.2		4	16.3	odd	4
1024.2.e.i.769.1		4	8.3	odd	2
1024.2.e.i.769.2		4	4.3	odd	2
1024.2.e.m.257.1		4	16.13	even	4	inner
1024.2.e.m.257.2		4	16.5	even	4	inner
1024.2.e.m.769.1		4	1.1	even	1	trivial
1024.2.e.m.769.2		4	8.5	even	2	inner
1152.2.a.c.1.1		1	96.35	even	8
1152.2.a.h.1.1		1	96.29	odd	8
1152.2.a.m.1.1		1	96.83	even	8
1152.2.a.r.1.1		1	96.77	odd	8
2304.2.d.b.1153.1		2	96.53	odd	8
2304.2.d.b.1153.2		2	96.5	odd	8
2304.2.d.r.1153.1		2	96.11	even	8
2304.2.d.r.1153.2		2	96.59	even	8
3200.2.a.e.1.1		1	160.109	even	8
3200.2.a.h.1.1		1	160.99	odd	8
3200.2.a.u.1.1		1	160.29	even	8
3200.2.a.x.1.1		1	160.19	odd	8
3200.2.c.e.2049.1		2	160.67	even	8
3200.2.c.e.2049.2		2	160.3	even	8
3200.2.c.f.2049.1		2	160.77	odd	8
3200.2.c.f.2049.2		2	160.13	odd	8
3200.2.c.k.2049.1		2	160.93	odd	8
3200.2.c.k.2049.2		2	160.157	odd	8
3200.2.c.l.2049.1		2	160.83	even	8
3200.2.c.l.2049.2		2	160.147	even	8
6272.2.a.a.1.1		1	224.195	even	8
6272.2.a.b.1.1		1	224.13	odd	8
6272.2.a.g.1.1		1	224.125	odd	8
6272.2.a.h.1.1		1	224.83	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.41421 + 1.41421i) q^{3} +(-1.41421 - 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(1.41421 + 1.41421i) q^{11} +(-1.41421 + 1.41421i) q^{13} +4.00000 q^{15} +2.00000 q^{17} +(1.41421 - 1.41421i) q^{19} +(-5.65685 - 5.65685i) q^{21} +4.00000i q^{23} -1.00000i q^{25} +(-2.82843 - 2.82843i) q^{27} +(-4.24264 + 4.24264i) q^{29} -4.00000 q^{33} +(5.65685 - 5.65685i) q^{35} +(-7.07107 - 7.07107i) q^{37} -4.00000i q^{39} +6.00000i q^{41} +(-4.24264 - 4.24264i) q^{43} +(-1.41421 + 1.41421i) q^{45} -8.00000 q^{47} -9.00000 q^{49} +(-2.82843 + 2.82843i) q^{51} +(-4.24264 - 4.24264i) q^{53} -4.00000i q^{55} +4.00000i q^{57} +(9.89949 + 9.89949i) q^{59} +(1.41421 - 1.41421i) q^{61} +4.00000 q^{63} +4.00000 q^{65} +(-7.07107 + 7.07107i) q^{67} +(-5.65685 - 5.65685i) q^{69} -12.0000i q^{71} -14.0000i q^{73} +(1.41421 + 1.41421i) q^{75} +(-5.65685 + 5.65685i) q^{77} -8.00000 q^{79} +11.0000 q^{81} +(-4.24264 + 4.24264i) q^{83} +(-2.82843 - 2.82843i) q^{85} -12.0000i q^{87} -2.00000i q^{89} +(-5.65685 - 5.65685i) q^{91} -4.00000 q^{95} -2.00000 q^{97} +(1.41421 - 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{15} + 8 q^{17} - 16 q^{33} - 32 q^{47} - 36 q^{49} + 16 q^{63} + 16 q^{65} - 32 q^{79} + 44 q^{81} - 16 q^{95} - 8 q^{97}+O(q^{100}) \) 4 * q + 16 * q^15 + 8 * q^17 - 16 * q^33 - 32 * q^47 - 36 * q^49 + 16 * q^63 + 16 * q^65 - 32 * q^79 + 44 * q^81 - 16 * q^95 - 8 * q^97

Introduction

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