LMFDB - Embedded newform 1024.2.e.m.769.2

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:	$4$
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			769.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1024.769
Dual form			1024.2.e.m.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(-1.41421 - 1.41421i) q^{11} +(1.41421 - 1.41421i) q^{13} +4.00000 q^{15} +2.00000 q^{17} +(-1.41421 + 1.41421i) q^{19} +(5.65685 + 5.65685i) q^{21} +4.00000i q^{23} -1.00000i q^{25} +(2.82843 + 2.82843i) q^{27} +(4.24264 - 4.24264i) q^{29} -4.00000 q^{33} +(-5.65685 + 5.65685i) q^{35} +(7.07107 + 7.07107i) q^{37} -4.00000i q^{39} +6.00000i q^{41} +(4.24264 + 4.24264i) q^{43} +(1.41421 - 1.41421i) q^{45} -8.00000 q^{47} -9.00000 q^{49} +(2.82843 - 2.82843i) q^{51} +(4.24264 + 4.24264i) q^{53} -4.00000i q^{55} +4.00000i q^{57} +(-9.89949 - 9.89949i) q^{59} +(-1.41421 + 1.41421i) q^{61} +4.00000 q^{63} +4.00000 q^{65} +(7.07107 - 7.07107i) q^{67} +(5.65685 + 5.65685i) q^{69} -12.0000i q^{71} -14.0000i q^{73} +(-1.41421 - 1.41421i) q^{75} +(5.65685 - 5.65685i) q^{77} -8.00000 q^{79} +11.0000 q^{81} +(4.24264 - 4.24264i) q^{83} +(2.82843 + 2.82843i) q^{85} -12.0000i q^{87} -2.00000i q^{89} +(5.65685 + 5.65685i) q^{91} -4.00000 q^{95} -2.00000 q^{97} +(-1.41421 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	1.41421	−	1.41421i	0.816497	−	0.816497i	0.985599	+	0.169102i	$0.0540867\pi$
$4$		0			0
$5$	1.41421	+	1.41421i	0.632456	+	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$5$	1.41421	+	1.41421i	0.632456	+	0.632456i	−0.316228	+	0.948683i	$0.602416\pi$
$6$		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	0.460999	−	0.887401i	$-0.347491\pi$
$11$	−1.41421	−	1.41421i	−0.426401	−	0.426401i	−0.887401	+	0.460999i	$0.847491\pi$
$12$		0			0
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	−0.483250	−	0.875482i	$-0.660544\pi$
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	0.875482	+	0.483250i	$0.160544\pi$
$14$		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	−0.850469	−	0.526026i	$-0.823682\pi$
$19$	−1.41421	+	1.41421i	−0.324443	+	0.324443i	0.526026	+	0.850469i	$0.323682\pi$
$20$		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	−0.193301	−	0.981140i	$-0.561919\pi$
$29$	4.24264	−	4.24264i	0.787839	−	0.787839i	0.981140	+	0.193301i	$0.0619194\pi$
$30$		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	$0.0571389\pi$
$37$	7.07107	+	7.07107i	1.16248	+	1.16248i	0.178545	+	0.983932i	$0.442861\pi$
$38$		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	0.952266	−	0.305269i	$-0.0987465\pi$
$43$	4.24264	+	4.24264i	0.646997	+	0.646997i	−0.305269	+	0.952266i	$0.598747\pi$
$44$		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	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		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	$-0.885063\pi$
$59$	−9.89949	−	9.89949i	−1.28880	−	1.28880i	−0.353291	−	0.935513i	$-0.614937\pi$
$60$		0			0
$61$	−1.41421	+	1.41421i	−0.181071	+	0.181071i	−0.791823	−	0.610751i	$-0.790868\pi$
$61$	−1.41421	+	1.41421i	−0.181071	+	0.181071i	0.610751	+	0.791823i	$0.290868\pi$
$62$		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	−0.127917	−	0.991785i	$-0.540829\pi$
$67$	7.07107	−	7.07107i	0.863868	−	0.863868i	0.991785	+	0.127917i	$0.0408290\pi$
$68$		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	−0.434825	−	0.900515i	$-0.643190\pi$
$83$	4.24264	−	4.24264i	0.465690	−	0.465690i	0.900515	+	0.434825i	$0.143190\pi$
$84$		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	0.463788	−	0.885946i	$-0.346490\pi$
$101$	−4.24264	−	4.24264i	−0.422159	−	0.422159i	−0.885946	+	0.463788i	$0.846490\pi$
$102$		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	0.635436	−	0.772153i	$-0.280820\pi$
$107$	−1.41421	−	1.41421i	−0.136717	−	0.136717i	−0.772153	+	0.635436i	$0.780820\pi$
$108$		0			0
$109$	−4.24264	+	4.24264i	−0.406371	+	0.406371i	−0.880471	−	0.474100i	$-0.842774\pi$
$109$	−4.24264	+	4.24264i	−0.406371	+	0.406371i	0.474100	+	0.880471i	$0.342774\pi$
$110$		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	−0.867725	−	0.497044i	$-0.834419\pi$
$131$	−4.24264	+	4.24264i	−0.370681	+	0.370681i	0.497044	+	0.867725i	$0.334419\pi$
$132$		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	0.340489	−	0.940249i	$-0.389408\pi$
$139$	−7.07107	−	7.07107i	−0.599760	−	0.599760i	−0.940249	+	0.340489i	$0.889408\pi$
$140$		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	$-0.986096\pi$
$149$	−12.7279	−	12.7279i	−1.04271	−	1.04271i	−0.0436658	−	0.999046i	$-0.513904\pi$
$150$		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	$0.505069\pi$
$157$	−12.7279	+	12.7279i	−1.01580	+	1.01580i	−0.999873	+	0.0159256i	$0.994931\pi$
$158$		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	−0.649550	−	0.760319i	$-0.725042\pi$
$163$	1.41421	−	1.41421i	0.110770	−	0.110770i	0.760319	+	0.649550i	$0.225042\pi$
$164$		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	−0.0318080	−	0.999494i	$-0.510127\pi$
$173$	12.7279	−	12.7279i	0.967686	−	0.967686i	0.999494	+	0.0318080i	$0.0101265\pi$
$174$		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	−0.530546	−	0.847656i	$-0.678013\pi$
$179$	4.24264	−	4.24264i	0.317110	−	0.317110i	0.847656	+	0.530546i	$0.178013\pi$
$180$		0			0
$181$	−1.41421	−	1.41421i	−0.105118	−	0.105118i	0.652592	−	0.757710i	$-0.273682\pi$
$181$	−1.41421	−	1.41421i	−0.105118	−	0.105118i	−0.757710	+	0.652592i	$0.773682\pi$
$182$		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	0.260235	−	0.965545i	$-0.416200\pi$
$197$	−9.89949	−	9.89949i	−0.705310	−	0.705310i	−0.965545	+	0.260235i	$0.916200\pi$
$198$		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	$-0.476532\pi$
$211$	15.5563	−	15.5563i	1.07094	−	1.07094i	0.997283	−	0.0736598i	$-0.0234679\pi$
$212$		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	−0.144695	−	0.989476i	$-0.546220\pi$
$227$	12.7279	−	12.7279i	0.844782	−	0.844782i	0.989476	+	0.144695i	$0.0462199\pi$
$228$		0			0
$229$	−9.89949	−	9.89949i	−0.654177	−	0.654177i	0.299819	−	0.953996i	$-0.403074\pi$
$229$	−9.89949	−	9.89949i	−0.654177	−	0.654177i	−0.953996	+	0.299819i	$0.903074\pi$
$230$		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	0.983622	−	0.180243i	$-0.0576884\pi$
$251$	12.7279	+	12.7279i	0.803379	+	0.803379i	−0.180243	+	0.983622i	$0.557688\pi$
$252$		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	−0.457882	−	0.889013i	$-0.651392\pi$
$269$	7.07107	−	7.07107i	0.431131	−	0.431131i	0.889013	+	0.457882i	$0.151392\pi$
$270$		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	0.822982	−	0.568067i	$-0.192309\pi$
$277$	4.24264	+	4.24264i	0.254916	+	0.254916i	−0.568067	+	0.822982i	$0.692309\pi$
$278$		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	0.569673	−	0.821872i	$-0.307070\pi$
$283$	−4.24264	−	4.24264i	−0.252199	−	0.252199i	−0.821872	+	0.569673i	$0.807070\pi$
$284$		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	0.356110	−	0.934444i	$-0.384103\pi$
$293$	−9.89949	−	9.89949i	−0.578335	−	0.578335i	−0.934444	+	0.356110i	$0.884103\pi$
$294$		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	−0.969905	−	0.243484i	$-0.921710\pi$
$307$	−12.7279	+	12.7279i	−0.726421	+	0.726421i	0.243484	+	0.969905i	$0.421710\pi$
$308$		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	−0.577851	−	0.816142i	$-0.696109\pi$
$317$	4.24264	−	4.24264i	0.238290	−	0.238290i	0.816142	+	0.577851i	$0.196109\pi$
$318$		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	0.924736	−	0.380610i	$-0.124286\pi$
$331$	9.89949	+	9.89949i	0.544125	+	0.544125i	−0.380610	+	0.924736i	$0.624286\pi$
$332$		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	0.960736	−	0.277465i	$-0.0894943\pi$
$347$	12.7279	+	12.7279i	0.683271	+	0.683271i	−0.277465	+	0.960736i	$0.589494\pi$
$348$		0			0
$349$	−7.07107	+	7.07107i	−0.378506	+	0.378506i	−0.870563	−	0.492057i	$-0.836245\pi$
$349$	−7.07107	+	7.07107i	−0.378506	+	0.378506i	0.492057	+	0.870563i	$0.336245\pi$
$350$		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	0.499936	−	0.866062i	$-0.333357\pi$
$373$	−7.07107	−	7.07107i	−0.366126	−	0.366126i	−0.866062	+	0.499936i	$0.833357\pi$
$374$		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	0.742495	−	0.669852i	$-0.233642\pi$
$379$	1.41421	+	1.41421i	0.0726433	+	0.0726433i	−0.669852	+	0.742495i	$0.733642\pi$
$380$		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	0.863266	−	0.504749i	$-0.168415\pi$
$389$	7.07107	+	7.07107i	0.358517	+	0.358517i	−0.504749	+	0.863266i	$0.668415\pi$
$390$		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	−0.805512	−	0.592580i	$-0.798110\pi$
$397$	−4.24264	+	4.24264i	−0.212932	+	0.212932i	0.592580	+	0.805512i	$0.298110\pi$
$398$		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	−0.0971178	−	0.995273i	$-0.530962\pi$
$419$	18.3848	−	18.3848i	0.898155	−	0.898155i	0.995273	+	0.0971178i	$0.0309624\pi$
$420$		0			0
$421$	24.0416	+	24.0416i	1.17172	+	1.17172i	0.981800	+	0.189917i	$0.0608220\pi$
$421$	24.0416	+	24.0416i	1.17172	+	1.17172i	0.189917	+	0.981800i	$0.439178\pi$
$422$		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	0.599100	−	0.800674i	$-0.295525\pi$
$443$	−4.24264	−	4.24264i	−0.201574	−	0.201574i	−0.800674	+	0.599100i	$0.795525\pi$
$444$		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	−0.523000	−	0.852333i	$-0.675187\pi$
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	0.852333	+	0.523000i	$0.175187\pi$
$462$		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	−0.439935	−	0.898029i	$-0.644999\pi$
$467$	9.89949	−	9.89949i	0.458094	−	0.458094i	0.898029	+	0.439935i	$0.144999\pi$
$468$		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	0.529313	−	0.848426i	$-0.322450\pi$
$491$	−7.07107	−	7.07107i	−0.319113	−	0.319113i	−0.848426	+	0.529313i	$0.822450\pi$
$492$		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	−0.267234	−	0.963632i	$-0.586110\pi$
$499$	15.5563	−	15.5563i	0.696398	−	0.696398i	0.963632	+	0.267234i	$0.0861096\pi$
$500$		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	−0.452816	−	0.891604i	$-0.649581\pi$
$509$	9.89949	−	9.89949i	0.438787	−	0.438787i	0.891604	+	0.452816i	$0.149581\pi$
$510$		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	0.889605	−	0.456730i	$-0.150980\pi$
$523$	9.89949	+	9.89949i	0.432875	+	0.432875i	−0.456730	+	0.889605i	$0.650980\pi$
$524$		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	$0.510893\pi$
$541$	−24.0416	+	24.0416i	−1.03363	+	1.03363i	−0.999414	+	0.0342160i	$0.989107\pi$
$542$		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	$0.551829\pi$
$547$	−26.8701	+	26.8701i	−1.14888	+	1.14888i	−0.986773	+	0.162108i	$0.948171\pi$
$548$		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	−0.676511	−	0.736433i	$-0.736509\pi$
$557$	1.41421	−	1.41421i	0.0599222	−	0.0599222i	0.736433	+	0.676511i	$0.236509\pi$
$558$		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	−0.922475	−	0.386057i	$-0.873837\pi$
$563$	−12.7279	+	12.7279i	−0.536418	+	0.536418i	0.386057	+	0.922475i	$0.373837\pi$
$564$		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	$-0.957405\pi$
$571$	−26.8701	−	26.8701i	−1.12448	−	1.12448i	−0.133417	−	0.991060i	$-0.542595\pi$
$572$		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	0.00766632	−	0.999971i	$-0.497560\pi$
$587$	−24.0416	−	24.0416i	−0.992304	−	0.992304i	−0.999971	+	0.00766632i	$0.997560\pi$
$588$		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	0.999592	−	0.0285598i	$-0.00909209\pi$
$613$	24.0416	+	24.0416i	0.971032	+	0.971032i	−0.0285598	+	0.999592i	$0.509092\pi$
$614$		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	$0.125474\pi$
$619$	32.5269	+	32.5269i	1.30737	+	1.30737i	0.384058	+	0.923309i	$0.374526\pi$
$620$		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	$-0.439388\pi$
$643$	29.6985	−	29.6985i	1.17119	−	1.17119i	0.981925	−	0.189269i	$-0.0606117\pi$
$644$		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	$-0.442974\pi$
$653$	29.6985	−	29.6985i	1.16219	−	1.16219i	0.983995	−	0.178197i	$-0.0570263\pi$
$654$		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	−0.619627	−	0.784897i	$-0.712716\pi$
$659$	4.24264	−	4.24264i	0.165270	−	0.165270i	0.784897	+	0.619627i	$0.212716\pi$
$660$		0			0
$661$	−24.0416	−	24.0416i	−0.935111	−	0.935111i	0.0629083	−	0.998019i	$-0.479962\pi$
$661$	−24.0416	−	24.0416i	−0.935111	−	0.935111i	−0.998019	+	0.0629083i	$0.979962\pi$
$662$		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	0.341869	−	0.939748i	$-0.388940\pi$
$677$	−15.5563	−	15.5563i	−0.597879	−	0.597879i	−0.939748	+	0.341869i	$0.888940\pi$
$678$		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	$-0.952946\pi$
$683$	−29.6985	−	29.6985i	−1.13638	−	1.13638i	−0.147287	−	0.989094i	$-0.547054\pi$
$684$		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	−0.621788	−	0.783186i	$-0.713593\pi$
$691$	4.24264	−	4.24264i	0.161398	−	0.161398i	0.783186	+	0.621788i	$0.213593\pi$
$692$		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	−0.733309	−	0.679895i	$-0.762025\pi$
$701$	−1.41421	+	1.41421i	−0.0534141	+	0.0534141i	0.679895	+	0.733309i	$0.262025\pi$
$702$		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	0.351832	−	0.936063i	$-0.385559\pi$
$709$	−15.5563	−	15.5563i	−0.584231	−	0.584231i	−0.936063	+	0.351832i	$0.885559\pi$
$710$		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	−0.624400	−	0.781105i	$-0.714656\pi$
$733$	4.24264	−	4.24264i	0.156706	−	0.156706i	0.781105	+	0.624400i	$0.214656\pi$
$734$		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	−0.433128	−	0.901332i	$-0.642590\pi$
$739$	12.7279	−	12.7279i	0.468204	−	0.468204i	0.901332	+	0.433128i	$0.142590\pi$
$740$		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	$0.0650823\pi$
$757$	32.5269	+	32.5269i	1.18221	+	1.18221i	0.203040	+	0.979170i	$0.434918\pi$
$758$		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	$-0.826682\pi$
$773$	−38.1838	−	38.1838i	−1.37337	−	1.37337i	−0.517985	−	0.855390i	$-0.673318\pi$
$774$		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	−0.373219	−	0.927743i	$-0.621746\pi$
$787$	15.5563	−	15.5563i	0.554524	−	0.554524i	0.927743	+	0.373219i	$0.121746\pi$
$788$		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	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		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	0.447397	−	0.894335i	$-0.352351\pi$
$811$	−12.7279	−	12.7279i	−0.446938	−	0.446938i	−0.894335	+	0.447397i	$0.852351\pi$
$812$		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	0.572867	−	0.819649i	$-0.305831\pi$
$821$	−7.07107	−	7.07107i	−0.246782	−	0.246782i	−0.819649	+	0.572867i	$0.805831\pi$
$822$		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	0.382859	−	0.923807i	$-0.374939\pi$
$827$	−15.5563	−	15.5563i	−0.540947	−	0.540947i	−0.923807	+	0.382859i	$0.874939\pi$
$828$		0			0
$829$	9.89949	−	9.89949i	0.343824	−	0.343824i	−0.513979	−	0.857803i	$-0.671829\pi$
$829$	9.89949	−	9.89949i	0.343824	−	0.343824i	0.857803	+	0.513979i	$0.171829\pi$
$830$		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	0.318455	−	0.947938i	$-0.396836\pi$
$853$	−18.3848	−	18.3848i	−0.629483	−	0.629483i	−0.947938	+	0.318455i	$0.896836\pi$
$854$		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	$0.0752126\pi$
$859$	35.3553	+	35.3553i	1.20631	+	1.20631i	0.234095	+	0.972214i	$0.424787\pi$
$860$		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	−0.919167	−	0.393867i	$-0.871137\pi$
$877$	−15.5563	+	15.5563i	−0.525301	+	0.525301i	0.393867	+	0.919167i	$0.371137\pi$
$878$		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	−0.984492	−	0.175427i	$-0.943869\pi$
$883$	−24.0416	+	24.0416i	−0.809065	+	0.809065i	0.175427	+	0.984492i	$0.443869\pi$
$884$		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	0.994730	−	0.102525i	$-0.0326921\pi$
$907$	26.8701	+	26.8701i	0.892206	+	0.892206i	−0.102525	+	0.994730i	$0.532692\pi$
$908$		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	−0.993112	−	0.117173i	$-0.962617\pi$
$941$	−26.8701	+	26.8701i	−0.875939	+	0.875939i	0.117173	+	0.993112i	$0.462617\pi$
$942$		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	−0.527725	−	0.849415i	$-0.676955\pi$
$947$	9.89949	−	9.89949i	0.321690	−	0.321690i	0.849415	+	0.527725i	$0.176955\pi$
$948$		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	0.991605	−	0.129304i	$-0.0412743\pi$
$971$	26.8701	+	26.8701i	0.862301	+	0.862301i	−0.129304	+	0.991605i	$0.541274\pi$
$972$		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	$-0.923497\pi$
$997$	−38.1838	−	38.1838i	−1.20929	−	1.20929i	−0.238036	−	0.971256i	$-0.576503\pi$
$998$		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.769.2		4
4.3	odd	2		1024.2.e.i.769.1		4
8.3	odd	2		1024.2.e.i.769.2		4
8.5	even	2	inner	1024.2.e.m.769.1		4
16.3	odd	4		1024.2.e.i.257.1		4
16.5	even	4	inner	1024.2.e.m.257.1		4
16.11	odd	4		1024.2.e.i.257.2		4
16.13	even	4	inner	1024.2.e.m.257.2		4
32.3	odd	8		128.2.a.a.1.1	✓	1
32.5	even	8		256.2.b.a.129.2		2
32.11	odd	8		256.2.b.c.129.2		2
32.13	even	8		128.2.a.b.1.1	yes	1
32.19	odd	8		128.2.a.d.1.1	yes	1
32.21	even	8		256.2.b.a.129.1		2
32.27	odd	8		256.2.b.c.129.1		2
32.29	even	8		128.2.a.c.1.1	yes	1
96.5	odd	8		2304.2.d.b.1153.1		2
96.11	even	8		2304.2.d.r.1153.2		2
96.29	odd	8		1152.2.a.r.1.1		1
96.35	even	8		1152.2.a.m.1.1		1
96.53	odd	8		2304.2.d.b.1153.2		2
96.59	even	8		2304.2.d.r.1153.1		2
96.77	odd	8		1152.2.a.h.1.1		1
96.83	even	8		1152.2.a.c.1.1		1
160.3	even	8		3200.2.c.l.2049.1		2
160.13	odd	8		3200.2.c.k.2049.1		2
160.19	odd	8		3200.2.a.h.1.1		1
160.29	even	8		3200.2.a.e.1.1		1
160.67	even	8		3200.2.c.l.2049.2		2
160.77	odd	8		3200.2.c.k.2049.2		2
160.83	even	8		3200.2.c.e.2049.2		2
160.93	odd	8		3200.2.c.f.2049.2		2
160.99	odd	8		3200.2.a.x.1.1		1
160.109	even	8		3200.2.a.u.1.1		1
160.147	even	8		3200.2.c.e.2049.1		2
160.157	odd	8		3200.2.c.f.2049.1		2
224.13	odd	8		6272.2.a.g.1.1		1
224.83	even	8		6272.2.a.a.1.1		1
224.125	odd	8		6272.2.a.b.1.1		1
224.195	even	8		6272.2.a.h.1.1		1

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

\(f(q)\)	\(=\)	\(q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(-1.41421 - 1.41421i) q^{11} +(1.41421 - 1.41421i) q^{13} +4.00000 q^{15} +2.00000 q^{17} +(-1.41421 + 1.41421i) q^{19} +(5.65685 + 5.65685i) q^{21} +4.00000i q^{23} -1.00000i q^{25} +(2.82843 + 2.82843i) q^{27} +(4.24264 - 4.24264i) q^{29} -4.00000 q^{33} +(-5.65685 + 5.65685i) q^{35} +(7.07107 + 7.07107i) q^{37} -4.00000i q^{39} +6.00000i q^{41} +(4.24264 + 4.24264i) q^{43} +(1.41421 - 1.41421i) q^{45} -8.00000 q^{47} -9.00000 q^{49} +(2.82843 - 2.82843i) q^{51} +(4.24264 + 4.24264i) q^{53} -4.00000i q^{55} +4.00000i q^{57} +(-9.89949 - 9.89949i) q^{59} +(-1.41421 + 1.41421i) q^{61} +4.00000 q^{63} +4.00000 q^{65} +(7.07107 - 7.07107i) q^{67} +(5.65685 + 5.65685i) q^{69} -12.0000i q^{71} -14.0000i q^{73} +(-1.41421 - 1.41421i) q^{75} +(5.65685 - 5.65685i) q^{77} -8.00000 q^{79} +11.0000 q^{81} +(4.24264 - 4.24264i) q^{83} +(2.82843 + 2.82843i) q^{85} -12.0000i q^{87} -2.00000i q^{89} +(5.65685 + 5.65685i) q^{91} -4.00000 q^{95} -2.00000 q^{97} +(-1.41421 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * 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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