LMFDB - Embedded newform 128.2.e.a.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	128.97
Dual form			128.2.e.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{13} -2.00000 q^{15} -2.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} -6.00000i q^{23} -3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +8.00000 q^{31} -2.00000 q^{33} +(-2.00000 + 2.00000i) q^{35} +(-3.00000 - 3.00000i) q^{37} +2.00000i q^{39} +(5.00000 + 5.00000i) q^{43} +(-1.00000 + 1.00000i) q^{45} -8.00000 q^{47} +3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(5.00000 + 5.00000i) q^{53} +2.00000i q^{55} +6.00000i q^{57} +(-3.00000 - 3.00000i) q^{59} +(9.00000 - 9.00000i) q^{61} -2.00000 q^{63} +2.00000 q^{65} +(-5.00000 + 5.00000i) q^{67} +(6.00000 + 6.00000i) q^{69} +10.0000i q^{71} -4.00000i q^{73} +(3.00000 + 3.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +5.00000 q^{81} +(-1.00000 + 1.00000i) q^{83} +(-2.00000 - 2.00000i) q^{85} -6.00000i q^{87} +4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +(-8.00000 + 8.00000i) q^{93} +6.00000 q^{95} -2.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^5	$ 2 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 2 q^{13} - 4 q^{15} - 4 q^{17} + 6 q^{19} - 4 q^{21} - 8 q^{27} - 6 q^{29} + 16 q^{31} - 4 q^{33} - 4 q^{35} - 6 q^{37} + 10 q^{43} - 2 q^{45} - 16 q^{47} + 6 q^{49} + 4 q^{51} + 10 q^{53} - 6 q^{59} + 18 q^{61} - 4 q^{63} + 4 q^{65} - 10 q^{67} + 12 q^{69} + 6 q^{75} - 4 q^{77} + 10 q^{81} - 2 q^{83} - 4 q^{85} + 4 q^{91} - 16 q^{93} + 12 q^{95} - 4 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 2 * q^13 - 4 * q^15 - 4 * q^17 + 6 * q^19 - 4 * q^21 - 8 * q^27 - 6 * q^29 + 16 * q^31 - 4 * q^33 - 4 * q^35 - 6 * q^37 + 10 * q^43 - 2 * q^45 - 16 * q^47 + 6 * q^49 + 4 * q^51 + 10 * q^53 - 6 * q^59 + 18 * q^61 - 4 * q^63 + 4 * q^65 - 10 * q^67 + 12 * q^69 + 6 * q^75 - 4 * q^77 + 10 * q^81 - 2 * q^83 - 4 * q^85 + 4 * q^91 - 16 * q^93 + 12 * q^95 - 4 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		0			0
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	−2.00000	−	2.00000i	−0.436436	−	0.436436i
$22$		0			0
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	−2.00000			−0.348155
$34$		0			0
$35$	−2.00000	+	2.00000i	−0.338062	+	0.338062i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$			2.00000i			0.320256i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	0.976772	−	0.214280i	$-0.0687403\pi$
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	−0.214280	+	0.976772i	$0.568740\pi$
$44$		0			0
$45$	−1.00000	+	1.00000i	−0.149071	+	0.149071i
$46$		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
$49$	3.00000			0.428571
$50$		0			0
$51$	2.00000	−	2.00000i	0.280056	−	0.280056i
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$			2.00000i			0.269680i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	0.484323	−	0.874889i	$-0.339066\pi$
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	−0.874889	+	0.484323i	$0.839066\pi$
$60$		0			0
$61$	9.00000	−	9.00000i	1.15233	−	1.15233i	0.166248	−	0.986084i	$-0.446835\pi$
$61$	9.00000	−	9.00000i	1.15233	−	1.15233i	0.986084	−	0.166248i	$-0.0531652\pi$
$62$		0			0
$63$	−2.00000			−0.251976
$64$		0			0
$65$	2.00000			0.248069
$66$		0			0
$67$	−5.00000	+	5.00000i	−0.610847	+	0.610847i	−0.943167	−	0.332320i	$-0.892169\pi$
$67$	−5.00000	+	5.00000i	−0.610847	+	0.610847i	0.332320	+	0.943167i	$0.392169\pi$
$68$		0			0
$69$	6.00000	+	6.00000i	0.722315	+	0.722315i
$70$		0			0
$71$			10.0000i			1.18678i	0.804914	+	0.593391i	$0.202211\pi$
$71$			10.0000i			1.18678i	−0.804914	+	0.593391i	$0.797789\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$	3.00000	+	3.00000i	0.346410	+	0.346410i
$76$		0			0
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	−0.759856	−	0.650092i	$-0.774731\pi$
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	0.650092	+	0.759856i	$0.274731\pi$
$84$		0			0
$85$	−2.00000	−	2.00000i	−0.216930	−	0.216930i
$86$		0			0
$87$		−	6.00000i		−	0.643268i
$88$		0			0
$89$			4.00000i			0.423999i	0.977270	+	0.212000i	$0.0679975\pi$
$89$			4.00000i			0.423999i	−0.977270	+	0.212000i	$0.932002\pi$
$90$		0			0
$91$	2.00000	+	2.00000i	0.209657	+	0.209657i
$92$		0			0
$93$	−8.00000	+	8.00000i	−0.829561	+	0.829561i
$94$		0			0
$95$	6.00000			0.615587
$96$		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
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		0			0
$101$	−11.0000	−	11.0000i	−1.09454	−	1.09454i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$	−11.0000	−	11.0000i	−1.09454	−	1.09454i	−0.0995037	−	0.995037i	$-0.531726\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$		0			0
$105$		−	4.00000i		−	0.390360i
$106$		0			0
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	0.282540	−	0.959256i	$-0.408823\pi$
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	−0.959256	+	0.282540i	$0.908823\pi$
$108$		0			0
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	−0.836031	−	0.548683i	$-0.815129\pi$
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	0.548683	+	0.836031i	$0.315129\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	6.00000	−	6.00000i	0.559503	−	0.559503i
$116$		0			0
$117$	1.00000	+	1.00000i	0.0924500	+	0.0924500i
$118$		0			0
$119$		−	4.00000i		−	0.366679i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$	−10.0000			−0.880451
$130$		0			0
$131$	11.0000	−	11.0000i	0.961074	−	0.961074i	−0.0381958	−	0.999270i	$-0.512161\pi$
$131$	11.0000	−	11.0000i	0.961074	−	0.961074i	0.999270	+	0.0381958i	$0.0121611\pi$
$132$		0			0
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$		0			0
$135$		−	8.00000i		−	0.688530i
$136$		0			0
$137$			8.00000i			0.683486i	0.939793	+	0.341743i	$0.111017\pi$
$137$			8.00000i			0.683486i	−0.939793	+	0.341743i	$0.888983\pi$
$138$		0			0
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	0.568338	−	0.822795i	$-0.307586\pi$
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	−0.822795	+	0.568338i	$0.807586\pi$
$140$		0			0
$141$	8.00000	−	8.00000i	0.673722	−	0.673722i
$142$		0			0
$143$	2.00000			0.167248
$144$		0			0
$145$	−6.00000			−0.498273
$146$		0			0
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$		0			0
$149$	−7.00000	−	7.00000i	−0.573462	−	0.573462i	0.359632	−	0.933094i	$-0.382902\pi$
$149$	−7.00000	−	7.00000i	−0.573462	−	0.573462i	−0.933094	+	0.359632i	$0.882902\pi$
$150$		0			0
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	8.00000	+	8.00000i	0.642575	+	0.642575i
$156$		0			0
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$		0			0
$159$	−10.0000			−0.793052
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	−0.745184	−	0.666858i	$-0.767639\pi$
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	0.666858	+	0.745184i	$0.267639\pi$
$164$		0			0
$165$	−2.00000	−	2.00000i	−0.155700	−	0.155700i
$166$		0			0
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$		0			0
$173$	1.00000	−	1.00000i	0.0760286	−	0.0760286i	−0.668070	−	0.744099i	$-0.732879\pi$
$173$	1.00000	−	1.00000i	0.0760286	−	0.0760286i	0.744099	+	0.668070i	$0.232879\pi$
$174$		0			0
$175$	6.00000			0.453557
$176$		0			0
$177$	6.00000			0.450988
$178$		0			0
$179$	−17.0000	+	17.0000i	−1.27064	+	1.27064i	−0.324887	+	0.945753i	$0.605326\pi$
$179$	−17.0000	+	17.0000i	−1.27064	+	1.27064i	−0.945753	+	0.324887i	$0.894674\pi$
$180$		0			0
$181$	9.00000	+	9.00000i	0.668965	+	0.668965i	0.957476	−	0.288512i	$-0.0931604\pi$
$181$	9.00000	+	9.00000i	0.668965	+	0.668965i	−0.288512	+	0.957476i	$0.593160\pi$
$182$		0			0
$183$			18.0000i			1.33060i
$184$		0			0
$185$		−	6.00000i		−	0.441129i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$	8.00000	−	8.00000i	0.581914	−	0.581914i
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$	−2.00000	+	2.00000i	−0.143223	+	0.143223i
$196$		0			0
$197$	17.0000	+	17.0000i	1.21120	+	1.21120i	0.970632	+	0.240567i	$0.0773335\pi$
$197$	17.0000	+	17.0000i	1.21120	+	1.21120i	0.240567	+	0.970632i	$0.422666\pi$
$198$		0			0
$199$		−	14.0000i		−	0.992434i	−0.868199	−	0.496217i	$-0.834722\pi$
$199$		−	14.0000i		−	0.992434i	0.868199	−	0.496217i	$-0.165278\pi$
$200$		0			0
$201$		−	10.0000i		−	0.705346i
$202$		0			0
$203$	−6.00000	−	6.00000i	−0.421117	−	0.421117i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−9.00000	+	9.00000i	−0.619586	+	0.619586i	−0.945425	−	0.325840i	$-0.894353\pi$
$211$	−9.00000	+	9.00000i	−0.619586	+	0.619586i	0.325840	+	0.945425i	$0.394353\pi$
$212$		0			0
$213$	−10.0000	−	10.0000i	−0.685189	−	0.685189i
$214$		0			0
$215$			10.0000i			0.681994i
$216$		0			0
$217$			16.0000i			1.08615i
$218$		0			0
$219$	4.00000	+	4.00000i	0.270295	+	0.270295i
$220$		0			0
$221$	−2.00000	+	2.00000i	−0.134535	+	0.134535i
$222$		0			0
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$		0			0
$227$	15.0000	−	15.0000i	0.995585	−	0.995585i	−0.00440533	−	0.999990i	$-0.501402\pi$
$227$	15.0000	−	15.0000i	0.995585	−	0.995585i	0.999990	+	0.00440533i	$0.00140226\pi$
$228$		0			0
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	0.436925	−	0.899498i	$-0.356068\pi$
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	−0.899498	+	0.436925i	$0.856068\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$		−	4.00000i		−	0.262049i	−0.991379	−	0.131024i	$-0.958173\pi$
$233$		−	4.00000i		−	0.262049i	0.991379	−	0.131024i	$-0.0418266\pi$
$234$		0			0
$235$	−8.00000	−	8.00000i	−0.521862	−	0.521862i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	3.00000	+	3.00000i	0.191663	+	0.191663i
$246$		0			0
$247$		−	6.00000i		−	0.381771i
$248$		0			0
$249$		−	2.00000i		−	0.126745i
$250$		0			0
$251$	21.0000	+	21.0000i	1.32551	+	1.32551i	0.909243	+	0.416265i	$0.136661\pi$
$251$	21.0000	+	21.0000i	1.32551	+	1.32551i	0.416265	+	0.909243i	$0.363339\pi$
$252$		0			0
$253$	6.00000	−	6.00000i	0.377217	−	0.377217i
$254$		0			0
$255$	4.00000			0.250490
$256$		0			0
$257$	−22.0000			−1.37232			−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000			−1.37232			−0.686161	+	0.727450i	$0.740706\pi$
$258$		0			0
$259$	6.00000	−	6.00000i	0.372822	−	0.372822i
$260$		0			0
$261$	−3.00000	−	3.00000i	−0.185695	−	0.185695i
$262$		0			0
$263$		−	6.00000i		−	0.369976i	−0.982741	−	0.184988i	$-0.940775\pi$
$263$		−	6.00000i		−	0.369976i	0.982741	−	0.184988i	$-0.0592246\pi$
$264$		0			0
$265$			10.0000i			0.614295i
$266$		0			0
$267$	−4.00000	−	4.00000i	−0.244796	−	0.244796i
$268$		0			0
$269$	−3.00000	+	3.00000i	−0.182913	+	0.182913i	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−3.00000	+	3.00000i	−0.182913	+	0.182913i	0.609711	+	0.792624i	$0.291286\pi$
$270$		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
$273$	−4.00000			−0.242091
$274$		0			0
$275$	3.00000	−	3.00000i	0.180907	−	0.180907i
$276$		0			0
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	0.611213	−	0.791466i	$-0.290682\pi$
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	−0.791466	+	0.611213i	$0.790682\pi$
$278$		0			0
$279$			8.00000i			0.478947i
$280$		0			0
$281$		−	20.0000i		−	1.19310i	−0.802576	−	0.596550i	$-0.796538\pi$
$281$		−	20.0000i		−	1.19310i	0.802576	−	0.596550i	$-0.203462\pi$
$282$		0			0
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$		0			0
$285$	−6.00000	+	6.00000i	−0.355409	+	0.355409i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$		0			0
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	0.116841	−	0.993151i	$-0.462723\pi$
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	−0.993151	+	0.116841i	$0.962723\pi$
$294$		0			0
$295$		−	6.00000i		−	0.349334i
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$		0			0
$299$	−6.00000	−	6.00000i	−0.346989	−	0.346989i
$300$		0			0
$301$	−10.0000	+	10.0000i	−0.576390	+	0.576390i
$302$		0			0
$303$	22.0000			1.26387
$304$		0			0
$305$	18.0000			1.03068
$306$		0			0
$307$	−5.00000	+	5.00000i	−0.285365	+	0.285365i	−0.835244	−	0.549879i	$-0.814674\pi$
$307$	−5.00000	+	5.00000i	−0.285365	+	0.285365i	0.549879	+	0.835244i	$0.314674\pi$
$308$		0			0
$309$	6.00000	+	6.00000i	0.341328	+	0.341328i
$310$		0			0
$311$		−	30.0000i		−	1.70114i	−0.525859	−	0.850572i	$-0.676256\pi$
$311$		−	30.0000i		−	1.70114i	0.525859	−	0.850572i	$-0.323744\pi$
$312$		0			0
$313$			16.0000i			0.904373i	0.891923	+	0.452187i	$0.149356\pi$
$313$			16.0000i			0.904373i	−0.891923	+	0.452187i	$0.850644\pi$
$314$		0			0
$315$	−2.00000	−	2.00000i	−0.112687	−	0.112687i
$316$		0			0
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	−0.552611	−	0.833439i	$-0.686369\pi$
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	0.833439	+	0.552611i	$0.186369\pi$
$318$		0			0
$319$	−6.00000			−0.335936
$320$		0			0
$321$	14.0000			0.781404
$322$		0			0
$323$	−6.00000	+	6.00000i	−0.333849	+	0.333849i
$324$		0			0
$325$	−3.00000	−	3.00000i	−0.166410	−	0.166410i
$326$		0			0
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$		−	16.0000i		−	0.882109i
$330$		0			0
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	0.734055	−	0.679090i	$-0.237625\pi$
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	−0.679090	+	0.734055i	$0.737625\pi$
$332$		0			0
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$		0			0
$335$	−10.0000			−0.546358
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	6.00000	−	6.00000i	0.325875	−	0.325875i
$340$		0			0
$341$	8.00000	+	8.00000i	0.433224	+	0.433224i
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$			12.0000i			0.646058i
$346$		0			0
$347$	13.0000	+	13.0000i	0.697877	+	0.697877i	0.963952	−	0.266076i	$-0.0857271\pi$
$347$	13.0000	+	13.0000i	0.697877	+	0.697877i	−0.266076	+	0.963952i	$0.585727\pi$
$348$		0			0
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$		0			0
$351$	−8.00000			−0.427008
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	−10.0000	+	10.0000i	−0.530745	+	0.530745i
$356$		0			0
$357$	4.00000	+	4.00000i	0.211702	+	0.211702i
$358$		0			0
$359$			26.0000i			1.37223i	0.727494	+	0.686114i	$0.240685\pi$
$359$			26.0000i			1.37223i	−0.727494	+	0.686114i	$0.759315\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$	9.00000	+	9.00000i	0.472377	+	0.472377i
$364$		0			0
$365$	4.00000	−	4.00000i	0.209370	−	0.209370i
$366$		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
$369$		0			0
$370$		0			0
$371$	−10.0000	+	10.0000i	−0.519174	+	0.519174i
$372$		0			0
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	0.824603	−	0.565712i	$-0.191399\pi$
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	−0.565712	+	0.824603i	$0.691399\pi$
$374$		0			0
$375$			16.0000i			0.826236i
$376$		0			0
$377$			6.00000i			0.309016i
$378$		0			0
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	0.625847	−	0.779946i	$-0.284754\pi$
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	−0.779946	+	0.625847i	$0.784754\pi$
$380$		0			0
$381$	8.00000	−	8.00000i	0.409852	−	0.409852i
$382$		0			0
$383$	16.0000			0.817562			0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000			0.817562			0.408781	+	0.912633i	$0.365954\pi$
$384$		0			0
$385$	−4.00000			−0.203859
$386$		0			0
$387$	−5.00000	+	5.00000i	−0.254164	+	0.254164i
$388$		0			0
$389$	13.0000	+	13.0000i	0.659126	+	0.659126i	0.955173	−	0.296047i	$-0.0956686\pi$
$389$	13.0000	+	13.0000i	0.659126	+	0.659126i	−0.296047	+	0.955173i	$0.595669\pi$
$390$		0			0
$391$			12.0000i			0.606866i
$392$		0			0
$393$			22.0000i			1.10975i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.00000	−	5.00000i	0.250943	−	0.250943i	−0.570414	−	0.821357i	$-0.693217\pi$
$397$	5.00000	−	5.00000i	0.250943	−	0.250943i	0.821357	+	0.570414i	$0.193217\pi$
$398$		0			0
$399$	−12.0000			−0.600751
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	8.00000	−	8.00000i	0.398508	−	0.398508i
$404$		0			0
$405$	5.00000	+	5.00000i	0.248452	+	0.248452i
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$		0			0
$409$		−	16.0000i		−	0.791149i	−0.918434	−	0.395575i	$-0.870545\pi$
$409$		−	16.0000i		−	0.791149i	0.918434	−	0.395575i	$-0.129455\pi$
$410$		0			0
$411$	−8.00000	−	8.00000i	−0.394611	−	0.394611i
$412$		0			0
$413$	6.00000	−	6.00000i	0.295241	−	0.295241i
$414$		0			0
$415$	−2.00000			−0.0981761
$416$		0			0
$417$	6.00000			0.293821
$418$		0			0
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	−0.630020	−	0.776579i	$-0.716953\pi$
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	0.776579	+	0.630020i	$0.216953\pi$
$420$		0			0
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	0.891552	−	0.452919i	$-0.149617\pi$
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	−0.452919	+	0.891552i	$0.649617\pi$
$422$		0			0
$423$		−	8.00000i		−	0.388973i
$424$		0			0
$425$			6.00000i			0.291043i
$426$		0			0
$427$	18.0000	+	18.0000i	0.871081	+	0.871081i
$428$		0			0
$429$	−2.00000	+	2.00000i	−0.0965609	+	0.0965609i
$430$		0			0
$431$	−32.0000			−1.54139			−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000			−1.54139			−0.770693	+	0.637207i	$0.780090\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	6.00000	−	6.00000i	0.287678	−	0.287678i
$436$		0			0
$437$	−18.0000	−	18.0000i	−0.861057	−	0.861057i
$438$		0			0
$439$		−	14.0000i		−	0.668184i	−0.942541	−	0.334092i	$-0.891570\pi$
$439$		−	14.0000i		−	0.668184i	0.942541	−	0.334092i	$-0.108430\pi$
$440$		0			0
$441$			3.00000i			0.142857i
$442$		0			0
$443$	−15.0000	−	15.0000i	−0.712672	−	0.712672i	0.254422	−	0.967093i	$-0.418115\pi$
$443$	−15.0000	−	15.0000i	−0.712672	−	0.712672i	−0.967093	+	0.254422i	$0.918115\pi$
$444$		0			0
$445$	−4.00000	+	4.00000i	−0.189618	+	0.189618i
$446$		0			0
$447$	14.0000			0.662177
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−10.0000	−	10.0000i	−0.469841	−	0.469841i
$454$		0			0
$455$			4.00000i			0.187523i
$456$		0			0
$457$		−	32.0000i		−	1.49690i	−0.663193	−	0.748448i	$-0.730799\pi$
$457$		−	32.0000i		−	1.49690i	0.663193	−	0.748448i	$-0.269201\pi$
$458$		0			0
$459$	8.00000	+	8.00000i	0.373408	+	0.373408i
$460$		0			0
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	−0.915237	−	0.402916i	$-0.867997\pi$
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	0.402916	+	0.915237i	$0.367997\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$	−16.0000			−0.741982
$466$		0			0
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$		0			0
$469$	−10.0000	−	10.0000i	−0.461757	−	0.461757i
$470$		0			0
$471$		−	30.0000i		−	1.38233i
$472$		0			0
$473$			10.0000i			0.459800i
$474$		0			0
$475$	−9.00000	−	9.00000i	−0.412948	−	0.412948i
$476$		0			0
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	40.0000			1.82765			0.913823	−	0.406112i	$-0.133116\pi$
$479$	40.0000			1.82765			0.913823	+	0.406112i	$0.133116\pi$
$480$		0			0
$481$	−6.00000			−0.273576
$482$		0			0
$483$	−12.0000	+	12.0000i	−0.546019	+	0.546019i
$484$		0			0
$485$	−2.00000	−	2.00000i	−0.0908153	−	0.0908153i
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		0			0
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	−19.0000	−	19.0000i	−0.857458	−	0.857458i	0.133580	−	0.991038i	$-0.457353\pi$
$491$	−19.0000	−	19.0000i	−0.857458	−	0.857458i	−0.991038	+	0.133580i	$0.957353\pi$
$492$		0			0
$493$	6.00000	−	6.00000i	0.270226	−	0.270226i
$494$		0			0
$495$	−2.00000			−0.0898933
$496$		0			0
$497$	−20.0000			−0.897123
$498$		0			0
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	−2.00000	−	2.00000i	−0.0893534	−	0.0893534i
$502$		0			0
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$		0			0
$505$		−	22.0000i		−	0.978987i
$506$		0			0
$507$	−11.0000	−	11.0000i	−0.488527	−	0.488527i
$508$		0			0
$509$	−23.0000	+	23.0000i	−1.01946	+	1.01946i	−0.0196502	+	0.999807i	$0.506255\pi$
$509$	−23.0000	+	23.0000i	−1.01946	+	1.01946i	−0.999807	+	0.0196502i	$0.993745\pi$
$510$		0			0
$511$	8.00000			0.353899
$512$		0			0
$513$	−24.0000			−1.05963
$514$		0			0
$515$	6.00000	−	6.00000i	0.264392	−	0.264392i
$516$		0			0
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$		0			0
$519$			2.00000i			0.0877903i
$520$		0			0
$521$			40.0000i			1.75243i	0.481919	+	0.876216i	$0.339940\pi$
$521$			40.0000i			1.75243i	−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$	25.0000	+	25.0000i	1.09317	+	1.09317i	0.995188	+	0.0979859i	$0.0312400\pi$
$523$	25.0000	+	25.0000i	1.09317	+	1.09317i	0.0979859	+	0.995188i	$0.468760\pi$
$524$		0			0
$525$	−6.00000	+	6.00000i	−0.261861	+	0.261861i
$526$		0			0
$527$	−16.0000			−0.696971
$528$		0			0
$529$	−13.0000			−0.565217
$530$		0			0
$531$	3.00000	−	3.00000i	0.130189	−	0.130189i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		−	14.0000i		−	0.605273i
$536$		0			0
$537$		−	34.0000i		−	1.46721i
$538$		0			0
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	−0.486654	−	0.873595i	$-0.661783\pi$
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	0.873595	+	0.486654i	$0.161783\pi$
$542$		0			0
$543$	−18.0000			−0.772454
$544$		0			0
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−5.00000	+	5.00000i	−0.213785	+	0.213785i	−0.805873	−	0.592088i	$-0.798304\pi$
$547$	−5.00000	+	5.00000i	−0.213785	+	0.213785i	0.592088	+	0.805873i	$0.298304\pi$
$548$		0			0
$549$	9.00000	+	9.00000i	0.384111	+	0.384111i
$550$		0			0
$551$			18.0000i			0.766826i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.00000	+	6.00000i	0.254686	+	0.254686i
$556$		0			0
$557$	25.0000	−	25.0000i	1.05928	−	1.05928i	0.0611558	−	0.998128i	$-0.480521\pi$
$557$	25.0000	−	25.0000i	1.05928	−	1.05928i	0.998128	−	0.0611558i	$-0.0194786\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	−0.182459	−	0.983213i	$-0.558406\pi$
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	0.983213	+	0.182459i	$0.0584057\pi$
$564$		0			0
$565$	−6.00000	−	6.00000i	−0.252422	−	0.252422i
$566$		0			0
$567$			10.0000i			0.419961i
$568$		0			0
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	1.00000	+	1.00000i	0.0418487	+	0.0418487i	0.727721	−	0.685873i	$-0.240579\pi$
$571$	1.00000	+	1.00000i	0.0418487	+	0.0418487i	−0.685873	+	0.727721i	$0.740579\pi$
$572$		0			0
$573$	−8.00000	+	8.00000i	−0.334205	+	0.334205i
$574$		0			0
$575$	−18.0000			−0.750652
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$		0			0
$579$	−14.0000	+	14.0000i	−0.581820	+	0.581820i
$580$		0			0
$581$	−2.00000	−	2.00000i	−0.0829740	−	0.0829740i
$582$		0			0
$583$			10.0000i			0.414158i
$584$		0			0
$585$			2.00000i			0.0826898i
$586$		0			0
$587$	−7.00000	−	7.00000i	−0.288921	−	0.288921i	0.547733	−	0.836653i	$-0.315491\pi$
$587$	−7.00000	−	7.00000i	−0.288921	−	0.288921i	−0.836653	+	0.547733i	$0.815491\pi$
$588$		0			0
$589$	24.0000	−	24.0000i	0.988903	−	0.988903i
$590$		0			0
$591$	−34.0000			−1.39857
$592$		0			0
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$		0			0
$595$	4.00000	−	4.00000i	0.163984	−	0.163984i
$596$		0			0
$597$	14.0000	+	14.0000i	0.572982	+	0.572982i
$598$		0			0
$599$		−	14.0000i		−	0.572024i	−0.958226	−	0.286012i	$-0.907670\pi$
$599$		−	14.0000i		−	0.572024i	0.958226	−	0.286012i	$-0.0923298\pi$
$600$		0			0
$601$			20.0000i			0.815817i	0.913023	+	0.407909i	$0.133742\pi$
$601$			20.0000i			0.815817i	−0.913023	+	0.407909i	$0.866258\pi$
$602$		0			0
$603$	−5.00000	−	5.00000i	−0.203616	−	0.203616i
$604$		0			0
$605$	9.00000	−	9.00000i	0.365902	−	0.365902i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	−8.00000	+	8.00000i	−0.323645	+	0.323645i
$612$		0			0
$613$	25.0000	+	25.0000i	1.00974	+	1.00974i	0.999952	+	0.00978840i	$0.00311579\pi$
$613$	25.0000	+	25.0000i	1.00974	+	1.00974i	0.00978840	+	0.999952i	$0.496884\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		0			0
$619$	17.0000	+	17.0000i	0.683288	+	0.683288i	0.960740	−	0.277452i	$-0.0894899\pi$
$619$	17.0000	+	17.0000i	0.683288	+	0.683288i	−0.277452	+	0.960740i	$0.589490\pi$
$620$		0			0
$621$	−24.0000	+	24.0000i	−0.963087	+	0.963087i
$622$		0			0
$623$	−8.00000			−0.320513
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−6.00000	+	6.00000i	−0.239617	+	0.239617i
$628$		0			0
$629$	6.00000	+	6.00000i	0.239236	+	0.239236i
$630$		0			0
$631$			10.0000i			0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$631$			10.0000i			0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$632$		0			0
$633$		−	18.0000i		−	0.715436i
$634$		0			0
$635$	−8.00000	−	8.00000i	−0.317470	−	0.317470i
$636$		0			0
$637$	3.00000	−	3.00000i	0.118864	−	0.118864i
$638$		0			0
$639$	−10.0000			−0.395594
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$		0			0
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	−0.987262	−	0.159103i	$-0.949140\pi$
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	0.159103	+	0.987262i	$0.449140\pi$
$644$		0			0
$645$	−10.0000	−	10.0000i	−0.393750	−	0.393750i
$646$		0			0
$647$			42.0000i			1.65119i	0.564263	+	0.825595i	$0.309160\pi$
$647$			42.0000i			1.65119i	−0.564263	+	0.825595i	$0.690840\pi$
$648$		0			0
$649$		−	6.00000i		−	0.235521i
$650$		0			0
$651$	−16.0000	−	16.0000i	−0.627089	−	0.627089i
$652$		0			0
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	−0.973255	−	0.229728i	$-0.926216\pi$
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	0.229728	+	0.973255i	$0.426216\pi$
$654$		0			0
$655$	22.0000			0.859611
$656$		0			0
$657$	4.00000			0.156055
$658$		0			0
$659$	−17.0000	+	17.0000i	−0.662226	+	0.662226i	−0.955904	−	0.293678i	$-0.905121\pi$
$659$	−17.0000	+	17.0000i	−0.662226	+	0.662226i	0.293678	+	0.955904i	$0.405121\pi$
$660$		0			0
$661$	9.00000	+	9.00000i	0.350059	+	0.350059i	0.860132	−	0.510072i	$-0.170381\pi$
$661$	9.00000	+	9.00000i	0.350059	+	0.350059i	−0.510072	+	0.860132i	$0.670381\pi$
$662$		0			0
$663$		−	4.00000i		−	0.155347i
$664$		0			0
$665$			12.0000i			0.465340i
$666$		0			0
$667$	18.0000	+	18.0000i	0.696963	+	0.696963i
$668$		0			0
$669$	24.0000	−	24.0000i	0.927894	−	0.927894i
$670$		0			0
$671$	18.0000			0.694882
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	−12.0000	+	12.0000i	−0.461880	+	0.461880i
$676$		0			0
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	0.647103	−	0.762402i	$-0.275980\pi$
$677$	−3.00000	−	3.00000i	−0.115299	−	0.115299i	−0.762402	+	0.647103i	$0.775980\pi$
$678$		0			0
$679$		−	4.00000i		−	0.153506i
$680$		0			0
$681$			30.0000i			1.14960i
$682$		0			0
$683$	5.00000	+	5.00000i	0.191320	+	0.191320i	0.796266	−	0.604946i	$-0.206805\pi$
$683$	5.00000	+	5.00000i	0.191320	+	0.191320i	−0.604946	+	0.796266i	$0.706805\pi$
$684$		0			0
$685$	−8.00000	+	8.00000i	−0.305664	+	0.305664i
$686$		0			0
$687$	14.0000			0.534133
$688$		0			0
$689$	10.0000			0.380970
$690$		0			0
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	−0.857260	−	0.514884i	$-0.827835\pi$
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	0.514884	+	0.857260i	$0.327835\pi$
$692$		0			0
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$		0			0
$695$		−	6.00000i		−	0.227593i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	4.00000	+	4.00000i	0.151294	+	0.151294i
$700$		0			0
$701$	−31.0000	+	31.0000i	−1.17085	+	1.17085i	−0.188847	+	0.982006i	$0.560475\pi$
$701$	−31.0000	+	31.0000i	−1.17085	+	1.17085i	−0.982006	+	0.188847i	$0.939525\pi$
$702$		0			0
$703$	−18.0000			−0.678883
$704$		0			0
$705$	16.0000			0.602595
$706$		0			0
$707$	22.0000	−	22.0000i	0.827395	−	0.827395i
$708$		0			0
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.999901	−	0.0141058i	$-0.995510\pi$
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.0141058	−	0.999901i	$-0.504490\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	48.0000i		−	1.79761i
$714$		0			0
$715$	2.00000	+	2.00000i	0.0747958	+	0.0747958i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$		0			0
$723$	18.0000	−	18.0000i	0.669427	−	0.669427i
$724$		0			0
$725$	9.00000	+	9.00000i	0.334252	+	0.334252i
$726$		0			0
$727$			2.00000i			0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$			2.00000i			0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	−10.0000	−	10.0000i	−0.369863	−	0.369863i
$732$		0			0
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	−0.203436	−	0.979088i	$-0.565211\pi$
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	0.979088	+	0.203436i	$0.0652108\pi$
$734$		0			0
$735$	−6.00000			−0.221313
$736$		0			0
$737$	−10.0000			−0.368355
$738$		0			0
$739$	23.0000	−	23.0000i	0.846069	−	0.846069i	−0.143571	−	0.989640i	$-0.545859\pi$
$739$	23.0000	−	23.0000i	0.846069	−	0.846069i	0.989640	+	0.143571i	$0.0458586\pi$
$740$		0			0
$741$	6.00000	+	6.00000i	0.220416	+	0.220416i
$742$		0			0
$743$		−	46.0000i		−	1.68758i	−0.536676	−	0.843788i	$-0.680320\pi$
$743$		−	46.0000i		−	1.68758i	0.536676	−	0.843788i	$-0.319680\pi$
$744$		0			0
$745$		−	14.0000i		−	0.512920i
$746$		0			0
$747$	−1.00000	−	1.00000i	−0.0365881	−	0.0365881i
$748$		0			0
$749$	14.0000	−	14.0000i	0.511549	−	0.511549i
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$		0			0
$753$	−42.0000			−1.53057
$754$		0			0
$755$	−10.0000	+	10.0000i	−0.363937	+	0.363937i
$756$		0			0
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	0.152374	−	0.988323i	$-0.451308\pi$
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	−0.988323	+	0.152374i	$0.951308\pi$
$758$		0			0
$759$			12.0000i			0.435572i
$760$		0			0
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$		0			0
$763$	−6.00000	−	6.00000i	−0.217215	−	0.217215i
$764$		0			0
$765$	2.00000	−	2.00000i	0.0723102	−	0.0723102i
$766$		0			0
$767$	−6.00000			−0.216647
$768$		0			0
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	22.0000	−	22.0000i	0.792311	−	0.792311i
$772$		0			0
$773$	5.00000	+	5.00000i	0.179838	+	0.179838i	0.791285	−	0.611448i	$-0.209412\pi$
$773$	5.00000	+	5.00000i	0.179838	+	0.179838i	−0.611448	+	0.791285i	$0.709412\pi$
$774$		0			0
$775$		−	24.0000i		−	0.862105i
$776$		0			0
$777$			12.0000i			0.430498i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−10.0000	+	10.0000i	−0.357828	+	0.357828i
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	−30.0000			−1.07075
$786$		0			0
$787$	15.0000	−	15.0000i	0.534692	−	0.534692i	−0.387273	−	0.921965i	$-0.626583\pi$
$787$	15.0000	−	15.0000i	0.534692	−	0.534692i	0.921965	+	0.387273i	$0.126583\pi$
$788$		0			0
$789$	6.00000	+	6.00000i	0.213606	+	0.213606i
$790$		0			0
$791$		−	12.0000i		−	0.426671i
$792$		0			0
$793$		−	18.0000i		−	0.639199i
$794$		0			0
$795$	−10.0000	−	10.0000i	−0.354663	−	0.354663i
$796$		0			0
$797$	25.0000	−	25.0000i	0.885545	−	0.885545i	−0.108546	−	0.994091i	$-0.534619\pi$
$797$	25.0000	−	25.0000i	0.885545	−	0.885545i	0.994091	+	0.108546i	$0.0346195\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$	−4.00000			−0.141333
$802$		0			0
$803$	4.00000	−	4.00000i	0.141157	−	0.141157i
$804$		0			0
$805$	12.0000	+	12.0000i	0.422944	+	0.422944i
$806$		0			0
$807$		−	6.00000i		−	0.211210i
$808$		0			0
$809$		−	16.0000i		−	0.562530i	−0.959630	−	0.281265i	$-0.909246\pi$
$809$		−	16.0000i		−	0.562530i	0.959630	−	0.281265i	$-0.0907540\pi$
$810$		0			0
$811$	−39.0000	−	39.0000i	−1.36948	−	1.36948i	−0.861187	−	0.508288i	$-0.830278\pi$
$811$	−39.0000	−	39.0000i	−1.36948	−	1.36948i	−0.508288	−	0.861187i	$-0.669722\pi$
$812$		0			0
$813$	−8.00000	+	8.00000i	−0.280572	+	0.280572i
$814$		0			0
$815$	−2.00000			−0.0700569
$816$		0			0
$817$	30.0000			1.04957
$818$		0			0
$819$	−2.00000	+	2.00000i	−0.0698857	+	0.0698857i
$820$		0			0
$821$	−11.0000	−	11.0000i	−0.383903	−	0.383903i	0.488603	−	0.872506i	$-0.337507\pi$
$821$	−11.0000	−	11.0000i	−0.383903	−	0.383903i	−0.872506	+	0.488603i	$0.837507\pi$
$822$		0			0
$823$			34.0000i			1.18517i	0.805510	+	0.592583i	$0.201892\pi$
$823$			34.0000i			1.18517i	−0.805510	+	0.592583i	$0.798108\pi$
$824$		0			0
$825$			6.00000i			0.208893i
$826$		0			0
$827$	33.0000	+	33.0000i	1.14752	+	1.14752i	0.987038	+	0.160484i	$0.0513055\pi$
$827$	33.0000	+	33.0000i	1.14752	+	1.14752i	0.160484	+	0.987038i	$0.448695\pi$
$828$		0			0
$829$	−23.0000	+	23.0000i	−0.798823	+	0.798823i	−0.982910	−	0.184087i	$-0.941067\pi$
$829$	−23.0000	+	23.0000i	−0.798823	+	0.798823i	0.184087	+	0.982910i	$0.441067\pi$
$830$		0			0
$831$	6.00000			0.208138
$832$		0			0
$833$	−6.00000			−0.207888
$834$		0			0
$835$	−2.00000	+	2.00000i	−0.0692129	+	0.0692129i
$836$		0			0
$837$	−32.0000	−	32.0000i	−1.10608	−	1.10608i
$838$		0			0
$839$		−	14.0000i		−	0.483334i	−0.970359	−	0.241667i	$-0.922306\pi$
$839$		−	14.0000i		−	0.483334i	0.970359	−	0.241667i	$-0.0776941\pi$
$840$		0			0
$841$			11.0000i			0.379310i
$842$		0			0
$843$	20.0000	+	20.0000i	0.688837	+	0.688837i
$844$		0			0
$845$	−11.0000	+	11.0000i	−0.378412	+	0.378412i
$846$		0			0
$847$	18.0000			0.618487
$848$		0			0
$849$	30.0000			1.02960
$850$		0			0
$851$	−18.0000	+	18.0000i	−0.617032	+	0.617032i
$852$		0			0
$853$	5.00000	+	5.00000i	0.171197	+	0.171197i	0.787505	−	0.616308i	$-0.211372\pi$
$853$	5.00000	+	5.00000i	0.171197	+	0.171197i	−0.616308	+	0.787505i	$0.711372\pi$
$854$		0			0
$855$			6.00000i			0.205196i
$856$		0			0
$857$			8.00000i			0.273275i	0.990621	+	0.136637i	$0.0436295\pi$
$857$			8.00000i			0.273275i	−0.990621	+	0.136637i	$0.956370\pi$
$858$		0			0
$859$	−3.00000	−	3.00000i	−0.102359	−	0.102359i	0.654073	−	0.756432i	$-0.273059\pi$
$859$	−3.00000	−	3.00000i	−0.102359	−	0.102359i	−0.756432	+	0.654073i	$0.773059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	2.00000			0.0680020
$866$		0			0
$867$	13.0000	−	13.0000i	0.441503	−	0.441503i
$868$		0			0
$869$		0			0
$870$		0			0
$871$			10.0000i			0.338837i
$872$		0			0
$873$		−	2.00000i		−	0.0676897i
$874$		0			0
$875$	16.0000	+	16.0000i	0.540899	+	0.540899i
$876$		0			0
$877$	5.00000	−	5.00000i	0.168838	−	0.168838i	−0.617630	−	0.786468i	$-0.711907\pi$
$877$	5.00000	−	5.00000i	0.168838	−	0.168838i	0.786468	+	0.617630i	$0.211907\pi$
$878$		0			0
$879$	30.0000			1.01187
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−21.0000	+	21.0000i	−0.706706	+	0.706706i	−0.965841	−	0.259135i	$-0.916563\pi$
$883$	−21.0000	+	21.0000i	−0.706706	+	0.706706i	0.259135	+	0.965841i	$0.416563\pi$
$884$		0			0
$885$	6.00000	+	6.00000i	0.201688	+	0.201688i
$886$		0			0
$887$			2.00000i			0.0671534i	0.999436	+	0.0335767i	$0.0106898\pi$
$887$			2.00000i			0.0671534i	−0.999436	+	0.0335767i	$0.989310\pi$
$888$		0			0
$889$		−	16.0000i		−	0.536623i
$890$		0			0
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$		0			0
$893$	−24.0000	+	24.0000i	−0.803129	+	0.803129i
$894$		0			0
$895$	−34.0000			−1.13649
$896$		0			0
$897$	12.0000			0.400668
$898$		0			0
$899$	−24.0000	+	24.0000i	−0.800445	+	0.800445i
$900$		0			0
$901$	−10.0000	−	10.0000i	−0.333148	−	0.333148i
$902$		0			0
$903$		−	20.0000i		−	0.665558i
$904$		0			0
$905$			18.0000i			0.598340i
$906$		0			0
$907$	−27.0000	−	27.0000i	−0.896520	−	0.896520i	0.0986062	−	0.995127i	$-0.468562\pi$
$907$	−27.0000	−	27.0000i	−0.896520	−	0.896520i	−0.995127	+	0.0986062i	$0.968562\pi$
$908$		0			0
$909$	11.0000	−	11.0000i	0.364847	−	0.364847i
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	−2.00000			−0.0661903
$914$		0			0
$915$	−18.0000	+	18.0000i	−0.595062	+	0.595062i
$916$		0			0
$917$	22.0000	+	22.0000i	0.726504	+	0.726504i
$918$		0			0
$919$			26.0000i			0.857661i	0.903385	+	0.428830i	$0.141074\pi$
$919$			26.0000i			0.857661i	−0.903385	+	0.428830i	$0.858926\pi$
$920$		0			0
$921$		−	10.0000i		−	0.329511i
$922$		0			0
$923$	10.0000	+	10.0000i	0.329154	+	0.329154i
$924$		0			0
$925$	−9.00000	+	9.00000i	−0.295918	+	0.295918i
$926$		0			0
$927$	6.00000			0.197066
$928$		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
$931$	9.00000	−	9.00000i	0.294963	−	0.294963i
$932$		0			0
$933$	30.0000	+	30.0000i	0.982156	+	0.982156i
$934$		0			0
$935$		−	4.00000i		−	0.130814i
$936$		0			0
$937$			28.0000i			0.914720i	0.889282	+	0.457360i	$0.151205\pi$
$937$			28.0000i			0.914720i	−0.889282	+	0.457360i	$0.848795\pi$
$938$		0			0
$939$	−16.0000	−	16.0000i	−0.522140	−	0.522140i
$940$		0			0
$941$	29.0000	−	29.0000i	0.945373	−	0.945373i	−0.0532103	−	0.998583i	$-0.516945\pi$
$941$	29.0000	−	29.0000i	0.945373	−	0.945373i	0.998583	+	0.0532103i	$0.0169454\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	16.0000			0.520480
$946$		0			0
$947$	−5.00000	+	5.00000i	−0.162478	+	0.162478i	−0.783664	−	0.621185i	$-0.786651\pi$
$947$	−5.00000	+	5.00000i	−0.162478	+	0.162478i	0.621185	+	0.783664i	$0.286651\pi$
$948$		0			0
$949$	−4.00000	−	4.00000i	−0.129845	−	0.129845i
$950$		0			0
$951$			10.0000i			0.324272i
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	8.00000	+	8.00000i	0.258874	+	0.258874i
$956$		0			0
$957$	6.00000	−	6.00000i	0.193952	−	0.193952i
$958$		0			0
$959$	−16.0000			−0.516667
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	7.00000	−	7.00000i	0.225572	−	0.225572i
$964$		0			0
$965$	14.0000	+	14.0000i	0.450676	+	0.450676i
$966$		0			0
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$		0			0
$969$		−	12.0000i		−	0.385496i
$970$		0			0
$971$	−19.0000	−	19.0000i	−0.609739	−	0.609739i	0.333139	−	0.942878i	$-0.391892\pi$
$971$	−19.0000	−	19.0000i	−0.609739	−	0.609739i	−0.942878	+	0.333139i	$0.891892\pi$
$972$		0			0
$973$	6.00000	−	6.00000i	0.192351	−	0.192351i
$974$		0			0
$975$	6.00000			0.192154
$976$		0			0
$977$	−2.00000			−0.0639857			−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000			−0.0639857			−0.0319928	+	0.999488i	$0.510185\pi$
$978$		0			0
$979$	−4.00000	+	4.00000i	−0.127841	+	0.127841i
$980$		0			0
$981$	−3.00000	−	3.00000i	−0.0957826	−	0.0957826i
$982$		0			0
$983$			34.0000i			1.08443i	0.840239	+	0.542216i	$0.182414\pi$
$983$			34.0000i			1.08443i	−0.840239	+	0.542216i	$0.817586\pi$
$984$		0			0
$985$			34.0000i			1.08333i
$986$		0			0
$987$	16.0000	+	16.0000i	0.509286	+	0.509286i
$988$		0			0
$989$	30.0000	−	30.0000i	0.953945	−	0.953945i
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	−2.00000			−0.0634681
$994$		0			0
$995$	14.0000	−	14.0000i	0.443830	−	0.443830i
$996$		0			0
$997$	37.0000	+	37.0000i	1.17180	+	1.17180i	0.981780	+	0.190022i	$0.0608559\pi$
$997$	37.0000	+	37.0000i	1.17180	+	1.17180i	0.190022	+	0.981780i	$0.439144\pi$
$998$		0			0
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.e.a.97.1		2
3.2	odd	2		1152.2.k.a.865.1		2
4.3	odd	2		128.2.e.b.97.1		2
8.3	odd	2		16.2.e.a.5.1	✓	2
8.5	even	2		64.2.e.a.49.1		2
12.11	even	2		1152.2.k.b.865.1		2
16.3	odd	4		128.2.e.b.33.1		2
16.5	even	4		64.2.e.a.17.1		2
16.11	odd	4		16.2.e.a.13.1	yes	2
16.13	even	4	inner	128.2.e.a.33.1		2
24.5	odd	2		576.2.k.a.433.1		2
24.11	even	2		144.2.k.a.37.1		2
32.3	odd	8		1024.2.a.b.1.2		2
32.5	even	8		1024.2.b.b.513.1		2
32.11	odd	8		1024.2.b.e.513.1		2
32.13	even	8		1024.2.a.e.1.2		2
32.19	odd	8		1024.2.a.b.1.1		2
32.21	even	8		1024.2.b.b.513.2		2
32.27	odd	8		1024.2.b.e.513.2		2
32.29	even	8		1024.2.a.e.1.1		2
40.3	even	4		400.2.q.a.149.1		2
40.13	odd	4		1600.2.q.b.49.1		2
40.19	odd	2		400.2.l.c.101.1		2
40.27	even	4		400.2.q.b.149.1		2
40.29	even	2		1600.2.l.a.1201.1		2
40.37	odd	4		1600.2.q.a.49.1		2
48.5	odd	4		576.2.k.a.145.1		2
48.11	even	4		144.2.k.a.109.1		2
48.29	odd	4		1152.2.k.a.289.1		2
48.35	even	4		1152.2.k.b.289.1		2
56.3	even	6		784.2.x.c.373.1		4
56.11	odd	6		784.2.x.f.373.1		4
56.19	even	6		784.2.x.c.165.1		4
56.27	even	2		784.2.m.b.197.1		2
56.51	odd	6		784.2.x.f.165.1		4
80.27	even	4		400.2.q.a.349.1		2
80.37	odd	4		1600.2.q.b.849.1		2
80.43	even	4		400.2.q.b.349.1		2
80.53	odd	4		1600.2.q.a.849.1		2
80.59	odd	4		400.2.l.c.301.1		2
80.69	even	4		1600.2.l.a.401.1		2
96.29	odd	8		9216.2.a.s.1.2		2
96.35	even	8		9216.2.a.d.1.2		2
96.77	odd	8		9216.2.a.s.1.1		2
96.83	even	8		9216.2.a.d.1.1		2
112.11	odd	12		784.2.x.f.765.1		4
112.27	even	4		784.2.m.b.589.1		2
112.59	even	12		784.2.x.c.765.1		4
112.75	even	12		784.2.x.c.557.1		4
112.107	odd	12		784.2.x.f.557.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.2.e.a.5.1	✓	2	8.3	odd	2
16.2.e.a.13.1	yes	2	16.11	odd	4
64.2.e.a.17.1		2	16.5	even	4
64.2.e.a.49.1		2	8.5	even	2
128.2.e.a.33.1		2	16.13	even	4	inner
128.2.e.a.97.1		2	1.1	even	1	trivial
128.2.e.b.33.1		2	16.3	odd	4
128.2.e.b.97.1		2	4.3	odd	2
144.2.k.a.37.1		2	24.11	even	2
144.2.k.a.109.1		2	48.11	even	4
400.2.l.c.101.1		2	40.19	odd	2
400.2.l.c.301.1		2	80.59	odd	4
400.2.q.a.149.1		2	40.3	even	4
400.2.q.a.349.1		2	80.27	even	4
400.2.q.b.149.1		2	40.27	even	4
400.2.q.b.349.1		2	80.43	even	4
576.2.k.a.145.1		2	48.5	odd	4
576.2.k.a.433.1		2	24.5	odd	2
784.2.m.b.197.1		2	56.27	even	2
784.2.m.b.589.1		2	112.27	even	4
784.2.x.c.165.1		4	56.19	even	6
784.2.x.c.373.1		4	56.3	even	6
784.2.x.c.557.1		4	112.75	even	12
784.2.x.c.765.1		4	112.59	even	12
784.2.x.f.165.1		4	56.51	odd	6
784.2.x.f.373.1		4	56.11	odd	6
784.2.x.f.557.1		4	112.107	odd	12
784.2.x.f.765.1		4	112.11	odd	12
1024.2.a.b.1.1		2	32.19	odd	8
1024.2.a.b.1.2		2	32.3	odd	8
1024.2.a.e.1.1		2	32.29	even	8
1024.2.a.e.1.2		2	32.13	even	8
1024.2.b.b.513.1		2	32.5	even	8
1024.2.b.b.513.2		2	32.21	even	8
1024.2.b.e.513.1		2	32.11	odd	8
1024.2.b.e.513.2		2	32.27	odd	8
1152.2.k.a.289.1		2	48.29	odd	4
1152.2.k.a.865.1		2	3.2	odd	2
1152.2.k.b.289.1		2	48.35	even	4
1152.2.k.b.865.1		2	12.11	even	2
1600.2.l.a.401.1		2	80.69	even	4
1600.2.l.a.1201.1		2	40.29	even	2
1600.2.q.a.49.1		2	40.37	odd	4
1600.2.q.a.849.1		2	80.53	odd	4
1600.2.q.b.49.1		2	40.13	odd	4
1600.2.q.b.849.1		2	80.37	odd	4
9216.2.a.d.1.1		2	96.83	even	8
9216.2.a.d.1.2		2	96.35	even	8
9216.2.a.s.1.1		2	96.77	odd	8
9216.2.a.s.1.2		2	96.29	odd	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{13} -2.00000 q^{15} -2.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} -6.00000i q^{23} -3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +8.00000 q^{31} -2.00000 q^{33} +(-2.00000 + 2.00000i) q^{35} +(-3.00000 - 3.00000i) q^{37} +2.00000i q^{39} +(5.00000 + 5.00000i) q^{43} +(-1.00000 + 1.00000i) q^{45} -8.00000 q^{47} +3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(5.00000 + 5.00000i) q^{53} +2.00000i q^{55} +6.00000i q^{57} +(-3.00000 - 3.00000i) q^{59} +(9.00000 - 9.00000i) q^{61} -2.00000 q^{63} +2.00000 q^{65} +(-5.00000 + 5.00000i) q^{67} +(6.00000 + 6.00000i) q^{69} +10.0000i q^{71} -4.00000i q^{73} +(3.00000 + 3.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +5.00000 q^{81} +(-1.00000 + 1.00000i) q^{83} +(-2.00000 - 2.00000i) q^{85} -6.00000i q^{87} +4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +(-8.00000 + 8.00000i) q^{93} +6.00000 q^{95} -2.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^5	\( 2 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 2 q^{13} - 4 q^{15} - 4 q^{17} + 6 q^{19} - 4 q^{21} - 8 q^{27} - 6 q^{29} + 16 q^{31} - 4 q^{33} - 4 q^{35} - 6 q^{37} + 10 q^{43} - 2 q^{45} - 16 q^{47} + 6 q^{49} + 4 q^{51} + 10 q^{53} - 6 q^{59} + 18 q^{61} - 4 q^{63} + 4 q^{65} - 10 q^{67} + 12 q^{69} + 6 q^{75} - 4 q^{77} + 10 q^{81} - 2 q^{83} - 4 q^{85} + 4 q^{91} - 16 q^{93} + 12 q^{95} - 4 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 2 * q^13 - 4 * q^15 - 4 * q^17 + 6 * q^19 - 4 * q^21 - 8 * q^27 - 6 * q^29 + 16 * q^31 - 4 * q^33 - 4 * q^35 - 6 * q^37 + 10 * q^43 - 2 * q^45 - 16 * q^47 + 6 * q^49 + 4 * q^51 + 10 * q^53 - 6 * q^59 + 18 * q^61 - 4 * q^63 + 4 * q^65 - 10 * q^67 + 12 * q^69 + 6 * q^75 - 4 * q^77 + 10 * q^81 - 2 * q^83 - 4 * q^85 + 4 * q^91 - 16 * q^93 + 12 * q^95 - 4 * q^97 - 2 * q^99

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