LMFDB - Embedded newform 1600.2.l.a.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (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:	$12.7760643234$
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			1201.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.a.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$		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
$15$		0			0
$16$		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
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$		0			0
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$		0			0
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	0.928477	+	0.371391i	$0.121119\pi$
$30$		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
$35$		0			0
$36$		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
$45$		0			0
$46$		0			0
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		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
$55$		0			0
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$		0			0
$59$	3.00000	+	3.00000i	0.390567	+	0.390567i	0.874889	−	0.484323i	$-0.160934\pi$
$59$	3.00000	+	3.00000i	0.390567	+	0.390567i	−0.484323	+	0.874889i	$0.660934\pi$
$60$		0			0
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.166248	+	0.986084i	$0.553165\pi$
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.986084	+	0.166248i	$0.946835\pi$
$62$		0			0
$63$	2.00000			0.251976
$64$		0			0
$65$		0			0
$66$		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	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$		0			0
$75$		0			0
$76$		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
$85$		0			0
$86$		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
$95$		0			0
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		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	$0.0317255\pi$
$101$	11.0000	+	11.0000i	1.09454	+	1.09454i	0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$		0			0
$106$		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	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$		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
$125$		0			0
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−10.0000			−0.880451
$130$		0			0
$131$	−11.0000	+	11.0000i	−0.961074	+	0.961074i	−0.999270	−	0.0381958i	$-0.987839\pi$
$131$	−11.0000	+	11.0000i	−0.961074	+	0.961074i	0.0381958	+	0.999270i	$0.487839\pi$
$132$		0			0
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	8.00000i		−	0.683486i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$		−	8.00000i		−	0.683486i	0.939793	−	0.341743i	$-0.111017\pi$
$138$		0			0
$139$	3.00000	+	3.00000i	0.254457	+	0.254457i	0.822795	−	0.568338i	$-0.192414\pi$
$139$	3.00000	+	3.00000i	0.254457	+	0.254457i	−0.568338	+	0.822795i	$0.692414\pi$
$140$		0			0
$141$	−8.00000	+	8.00000i	−0.673722	+	0.673722i
$142$		0			0
$143$	−2.00000			−0.167248
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$		0			0
$149$	7.00000	+	7.00000i	0.573462	+	0.573462i	0.933094	−	0.359632i	$-0.117098\pi$
$149$	7.00000	+	7.00000i	0.573462	+	0.573462i	−0.359632	+	0.933094i	$0.617098\pi$
$150$		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
$155$		0			0
$156$		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
$165$		0			0
$166$		0			0
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		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
$175$		0			0
$176$		0			0
$177$	−6.00000			−0.450988
$178$		0			0
$179$	17.0000	−	17.0000i	1.27064	−	1.27064i	0.324887	−	0.945753i	$-0.394674\pi$
$179$	17.0000	−	17.0000i	1.27064	−	1.27064i	0.945753	−	0.324887i	$-0.105326\pi$
$180$		0			0
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	0.288512	−	0.957476i	$-0.406840\pi$
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	−0.957476	+	0.288512i	$0.906840\pi$
$182$		0			0
$183$		−	18.0000i		−	1.33060i
$184$		0			0
$185$		0			0
$186$		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	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$		0			0
$195$		0			0
$196$		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	−0.325840	−	0.945425i	$-0.605647\pi$
$211$	9.00000	−	9.00000i	0.619586	−	0.619586i	0.945425	+	0.325840i	$0.105647\pi$
$212$		0			0
$213$	−10.0000	−	10.0000i	−0.685189	−	0.685189i
$214$		0			0
$215$		0			0
$216$		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	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$		0			0
$226$		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	0.899498	−	0.436925i	$-0.143932\pi$
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	−0.436925	+	0.899498i	$0.643932\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$			4.00000i			0.262049i	0.991379	+	0.131024i	$0.0418266\pi$
$233$			4.00000i			0.262049i	−0.991379	+	0.131024i	$0.958173\pi$
$234$		0			0
$235$		0			0
$236$		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
$245$		0			0
$246$		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	$-0.863339\pi$
$251$	−21.0000	−	21.0000i	−1.32551	−	1.32551i	−0.416265	−	0.909243i	$-0.636661\pi$
$252$		0			0
$253$	6.00000	−	6.00000i	0.377217	−	0.377217i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$		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	$0.0592246\pi$
$263$			6.00000i			0.369976i	−0.982741	+	0.184988i	$0.940775\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.00000	−	4.00000i	−0.244796	−	0.244796i
$268$		0			0
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	0.792624	+	0.609711i	$0.208714\pi$
$270$		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
$275$		0			0
$276$		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
$285$		0			0
$286$		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
$295$		0			0
$296$		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
$305$		0			0
$306$		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	$-0.850644\pi$
$313$		−	16.0000i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$314$		0			0
$315$		0			0
$316$		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
$325$		0			0
$326$		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	0.679090	−	0.734055i	$-0.262375\pi$
$331$	−1.00000	−	1.00000i	−0.0549650	−	0.0549650i	−0.734055	+	0.679090i	$0.762375\pi$
$332$		0			0
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		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
$345$		0			0
$346$		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	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$	−8.00000			−0.427008
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$		0			0
$356$		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
$365$		0			0
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$		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
$375$		0			0
$376$		0			0
$377$		−	6.00000i		−	0.309016i
$378$		0			0
$379$	3.00000	+	3.00000i	0.154100	+	0.154100i	0.779946	−	0.625847i	$-0.215246\pi$
$379$	3.00000	+	3.00000i	0.154100	+	0.154100i	−0.625847	+	0.779946i	$0.715246\pi$
$380$		0			0
$381$	−8.00000	+	8.00000i	−0.409852	+	0.409852i
$382$		0			0
$383$	−16.0000			−0.817562			−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000			−0.817562			−0.408781	+	0.912633i	$0.634046\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.00000	+	5.00000i	−0.254164	+	0.254164i
$388$		0			0
$389$	−13.0000	−	13.0000i	−0.659126	−	0.659126i	0.296047	−	0.955173i	$-0.404331\pi$
$389$	−13.0000	−	13.0000i	−0.659126	−	0.659126i	−0.955173	+	0.296047i	$0.904331\pi$
$390$		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
$405$		0			0
$406$		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
$415$		0			0
$416$		0			0
$417$	−6.00000			−0.293821
$418$		0			0
$419$	−3.00000	+	3.00000i	−0.146560	+	0.146560i	−0.776579	−	0.630020i	$-0.783047\pi$
$419$	−3.00000	+	3.00000i	−0.146560	+	0.146560i	0.630020	+	0.776579i	$0.283047\pi$
$420$		0			0
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	0.452919	−	0.891552i	$-0.350383\pi$
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	−0.891552	+	0.452919i	$0.850383\pi$
$422$		0			0
$423$			8.00000i			0.388973i
$424$		0			0
$425$		0			0
$426$		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	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		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
$445$		0			0
$446$		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
$455$		0			0
$456$		0			0
$457$			32.0000i			1.49690i	0.663193	+	0.748448i	$0.269201\pi$
$457$			32.0000i			1.49690i	−0.663193	+	0.748448i	$0.730799\pi$
$458$		0			0
$459$	−8.00000	−	8.00000i	−0.373408	−	0.373408i
$460$		0			0
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	−0.402916	−	0.915237i	$-0.632003\pi$
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	0.915237	+	0.402916i	$0.132003\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$		0			0
$466$		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
$475$		0			0
$476$		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
$485$		0			0
$486$		0			0
$487$		−	2.00000i		−	0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$		−	2.00000i		−	0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$		0			0
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	19.0000	+	19.0000i	0.857458	+	0.857458i	0.991038	−	0.133580i	$-0.0426473\pi$
$491$	19.0000	+	19.0000i	0.857458	+	0.857458i	−0.133580	+	0.991038i	$0.542647\pi$
$492$		0			0
$493$	6.00000	−	6.00000i	0.270226	−	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.0000			0.897123
$498$		0			0
$499$	−23.0000	+	23.0000i	−1.02962	+	1.02962i	−0.0300737	+	0.999548i	$0.509574\pi$
$499$	−23.0000	+	23.0000i	−1.02962	+	1.02962i	−0.999548	+	0.0300737i	$0.990426\pi$
$500$		0			0
$501$	2.00000	+	2.00000i	0.0893534	+	0.0893534i
$502$		0			0
$503$			6.00000i			0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$			6.00000i			0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$		0			0
$505$		0			0
$506$		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	$-0.493745\pi$
$509$	23.0000	−	23.0000i	1.01946	−	1.01946i	0.999807	−	0.0196502i	$-0.00625524\pi$
$510$		0			0
$511$	8.00000			0.353899
$512$		0			0
$513$	24.0000			1.05963
$514$		0			0
$515$		0			0
$516$		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
$525$		0			0
$526$		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
$535$		0			0
$536$		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	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$		0			0
$543$	18.0000			0.772454
$544$		0			0
$545$		0			0
$546$		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
$555$		0			0
$556$		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
$565$		0			0
$566$		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	0.685873	−	0.727721i	$-0.259421\pi$
$571$	−1.00000	−	1.00000i	−0.0418487	−	0.0418487i	−0.727721	+	0.685873i	$0.759421\pi$
$572$		0			0
$573$	−8.00000	+	8.00000i	−0.334205	+	0.334205i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$		0			0
$579$	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
$585$		0			0
$586$		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	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$		0			0
$595$		0			0
$596$		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
$605$		0			0
$606$		0			0
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$		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	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$		0			0
$619$	−17.0000	−	17.0000i	−0.683288	−	0.683288i	0.277452	−	0.960740i	$-0.410510\pi$
$619$	−17.0000	−	17.0000i	−0.683288	−	0.683288i	−0.960740	+	0.277452i	$0.910510\pi$
$620$		0			0
$621$	24.0000	−	24.0000i	0.963087	−	0.963087i
$622$		0			0
$623$	8.00000			0.320513
$624$		0			0
$625$		0			0
$626$		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
$635$		0			0
$636$		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
$645$		0			0
$646$		0			0
$647$		−	42.0000i		−	1.65119i	−0.564263	−	0.825595i	$-0.690840\pi$
$647$		−	42.0000i		−	1.65119i	0.564263	−	0.825595i	$-0.309160\pi$
$648$		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
$655$		0			0
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	17.0000	−	17.0000i	0.662226	−	0.662226i	−0.293678	−	0.955904i	$-0.594879\pi$
$659$	17.0000	−	17.0000i	0.662226	−	0.662226i	0.955904	+	0.293678i	$0.0948794\pi$
$660$		0			0
$661$	−9.00000	−	9.00000i	−0.350059	−	0.350059i	0.510072	−	0.860132i	$-0.329619\pi$
$661$	−9.00000	−	9.00000i	−0.350059	−	0.350059i	−0.860132	+	0.510072i	$0.829619\pi$
$662$		0			0
$663$			4.00000i			0.155347i
$664$		0			0
$665$		0			0
$666$		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	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$		0			0
$675$		0			0
$676$		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
$685$		0			0
$686$		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	−0.514884	−	0.857260i	$-0.672165\pi$
$691$	9.00000	−	9.00000i	0.342376	−	0.342376i	0.857260	+	0.514884i	$0.172165\pi$
$692$		0			0
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$		0			0
$695$		0			0
$696$		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	$-0.439525\pi$
$701$	31.0000	−	31.0000i	1.17085	−	1.17085i	0.982006	−	0.188847i	$-0.0604752\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$		0			0
$705$		0			0
$706$		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	$0.00449016\pi$
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.0141058	+	0.999901i	$0.495510\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			48.0000i			1.79761i
$714$		0			0
$715$		0			0
$716$		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
$725$		0			0
$726$		0			0
$727$		−	2.00000i		−	0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$		−	2.00000i		−	0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$		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
$735$		0			0
$736$		0			0
$737$	10.0000			0.368355
$738$		0			0
$739$	−23.0000	+	23.0000i	−0.846069	+	0.846069i	−0.989640	−	0.143571i	$-0.954141\pi$
$739$	−23.0000	+	23.0000i	−0.846069	+	0.846069i	0.143571	+	0.989640i	$0.454141\pi$
$740$		0			0
$741$	−6.00000	−	6.00000i	−0.220416	−	0.220416i
$742$		0			0
$743$			46.0000i			1.68758i	0.536676	+	0.843788i	$0.319680\pi$
$743$			46.0000i			1.68758i	−0.536676	+	0.843788i	$0.680320\pi$
$744$		0			0
$745$		0			0
$746$		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
$755$		0			0
$756$		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
$765$		0			0
$766$		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
$775$		0			0
$776$		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
$785$		0			0
$786$		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
$795$		0			0
$796$		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
$805$		0			0
$806$		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	$0.169722\pi$
$811$	39.0000	+	39.0000i	1.36948	+	1.36948i	0.508288	+	0.861187i	$0.330278\pi$
$812$		0			0
$813$	−8.00000	+	8.00000i	−0.280572	+	0.280572i
$814$		0			0
$815$		0			0
$816$		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	0.872506	−	0.488603i	$-0.162493\pi$
$821$	11.0000	+	11.0000i	0.383903	+	0.383903i	−0.488603	+	0.872506i	$0.662493\pi$
$822$		0			0
$823$		−	34.0000i		−	1.18517i	−0.805510	−	0.592583i	$-0.798108\pi$
$823$		−	34.0000i		−	1.18517i	0.805510	−	0.592583i	$-0.201892\pi$
$824$		0			0
$825$		0			0
$826$		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	−0.184087	−	0.982910i	$-0.558933\pi$
$829$	23.0000	−	23.0000i	0.798823	−	0.798823i	0.982910	+	0.184087i	$0.0589328\pi$
$830$		0			0
$831$	6.00000			0.208138
$832$		0			0
$833$	6.00000			0.207888
$834$		0			0
$835$		0			0
$836$		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
$845$		0			0
$846$		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
$855$		0			0
$856$		0			0
$857$		−	8.00000i		−	0.273275i	−0.990621	−	0.136637i	$-0.956370\pi$
$857$		−	8.00000i		−	0.273275i	0.990621	−	0.136637i	$-0.0436295\pi$
$858$		0			0
$859$	3.00000	+	3.00000i	0.102359	+	0.102359i	0.756432	−	0.654073i	$-0.226941\pi$
$859$	3.00000	+	3.00000i	0.102359	+	0.102359i	−0.654073	+	0.756432i	$0.726941\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$		0			0
$866$		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
$875$		0			0
$876$		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
$885$		0			0
$886$		0			0
$887$		−	2.00000i		−	0.0671534i	−0.999436	−	0.0335767i	$-0.989310\pi$
$887$		−	2.00000i		−	0.0671534i	0.999436	−	0.0335767i	$-0.0106898\pi$
$888$		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
$895$		0			0
$896$		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
$905$		0			0
$906$		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
$915$		0			0
$916$		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
$925$		0			0
$926$		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
$935$		0			0
$936$		0			0
$937$		−	28.0000i		−	0.914720i	−0.889282	−	0.457360i	$-0.848795\pi$
$937$		−	28.0000i		−	0.914720i	0.889282	−	0.457360i	$-0.151205\pi$
$938$		0			0
$939$	16.0000	+	16.0000i	0.522140	+	0.522140i
$940$		0			0
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	−0.998583	−	0.0532103i	$-0.983055\pi$
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	0.0532103	+	0.998583i	$0.483055\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		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	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$		0			0
$955$		0			0
$956$		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
$965$		0			0
$966$		0			0
$967$		−	2.00000i		−	0.0643157i	−0.999483	−	0.0321578i	$-0.989762\pi$
$967$		−	2.00000i		−	0.0643157i	0.999483	−	0.0321578i	$-0.0102379\pi$
$968$		0			0
$969$		−	12.0000i		−	0.385496i
$970$		0			0
$971$	19.0000	+	19.0000i	0.609739	+	0.609739i	0.942878	−	0.333139i	$-0.108108\pi$
$971$	19.0000	+	19.0000i	0.609739	+	0.609739i	−0.333139	+	0.942878i	$0.608108\pi$
$972$		0			0
$973$	6.00000	−	6.00000i	0.192351	−	0.192351i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.00000			0.0639857			0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000			0.0639857			0.0319928	+	0.999488i	$0.489815\pi$
$978$		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	$-0.817586\pi$
$983$		−	34.0000i		−	1.08443i	0.840239	−	0.542216i	$-0.182414\pi$
$984$		0			0
$985$		0			0
$986$		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
$995$		0			0
$996$		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	1600.2.l.a.1201.1		2
4.3	odd	2		400.2.l.c.101.1		2
5.2	odd	4		1600.2.q.b.49.1		2
5.3	odd	4		1600.2.q.a.49.1		2
5.4	even	2		64.2.e.a.49.1		2
15.14	odd	2		576.2.k.a.433.1		2
16.3	odd	4		400.2.l.c.301.1		2
16.13	even	4	inner	1600.2.l.a.401.1		2
20.3	even	4		400.2.q.b.149.1		2
20.7	even	4		400.2.q.a.149.1		2
20.19	odd	2		16.2.e.a.5.1	✓	2
40.19	odd	2		128.2.e.b.97.1		2
40.29	even	2		128.2.e.a.97.1		2
60.59	even	2		144.2.k.a.37.1		2
80.3	even	4		400.2.q.a.349.1		2
80.13	odd	4		1600.2.q.b.849.1		2
80.19	odd	4		16.2.e.a.13.1	yes	2
80.29	even	4		64.2.e.a.17.1		2
80.59	odd	4		128.2.e.b.33.1		2
80.67	even	4		400.2.q.b.349.1		2
80.69	even	4		128.2.e.a.33.1		2
80.77	odd	4		1600.2.q.a.849.1		2
120.29	odd	2		1152.2.k.a.865.1		2
120.59	even	2		1152.2.k.b.865.1		2
140.19	even	6		784.2.x.c.165.1		4
140.39	odd	6		784.2.x.f.373.1		4
140.59	even	6		784.2.x.c.373.1		4
140.79	odd	6		784.2.x.f.165.1		4
140.139	even	2		784.2.m.b.197.1		2
160.19	odd	8		1024.2.a.b.1.2		2
160.29	even	8		1024.2.a.e.1.2		2
160.59	odd	8		1024.2.b.e.513.1		2
160.69	even	8		1024.2.b.b.513.2		2
160.99	odd	8		1024.2.a.b.1.1		2
160.109	even	8		1024.2.a.e.1.1		2
160.139	odd	8		1024.2.b.e.513.2		2
160.149	even	8		1024.2.b.b.513.1		2
240.29	odd	4		576.2.k.a.145.1		2
240.59	even	4		1152.2.k.b.289.1		2
240.149	odd	4		1152.2.k.a.289.1		2
240.179	even	4		144.2.k.a.109.1		2
480.29	odd	8		9216.2.a.s.1.1		2
480.179	even	8		9216.2.a.d.1.2		2
480.269	odd	8		9216.2.a.s.1.2		2
480.419	even	8		9216.2.a.d.1.1		2
560.19	even	12		784.2.x.c.557.1		4
560.179	odd	12		784.2.x.f.765.1		4
560.339	even	12		784.2.x.c.765.1		4
560.419	even	4		784.2.m.b.589.1		2
560.499	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	20.19	odd	2
16.2.e.a.13.1	yes	2	80.19	odd	4
64.2.e.a.17.1		2	80.29	even	4
64.2.e.a.49.1		2	5.4	even	2
128.2.e.a.33.1		2	80.69	even	4
128.2.e.a.97.1		2	40.29	even	2
128.2.e.b.33.1		2	80.59	odd	4
128.2.e.b.97.1		2	40.19	odd	2
144.2.k.a.37.1		2	60.59	even	2
144.2.k.a.109.1		2	240.179	even	4
400.2.l.c.101.1		2	4.3	odd	2
400.2.l.c.301.1		2	16.3	odd	4
400.2.q.a.149.1		2	20.7	even	4
400.2.q.a.349.1		2	80.3	even	4
400.2.q.b.149.1		2	20.3	even	4
400.2.q.b.349.1		2	80.67	even	4
576.2.k.a.145.1		2	240.29	odd	4
576.2.k.a.433.1		2	15.14	odd	2
784.2.m.b.197.1		2	140.139	even	2
784.2.m.b.589.1		2	560.419	even	4
784.2.x.c.165.1		4	140.19	even	6
784.2.x.c.373.1		4	140.59	even	6
784.2.x.c.557.1		4	560.19	even	12
784.2.x.c.765.1		4	560.339	even	12
784.2.x.f.165.1		4	140.79	odd	6
784.2.x.f.373.1		4	140.39	odd	6
784.2.x.f.557.1		4	560.499	odd	12
784.2.x.f.765.1		4	560.179	odd	12
1024.2.a.b.1.1		2	160.99	odd	8
1024.2.a.b.1.2		2	160.19	odd	8
1024.2.a.e.1.1		2	160.109	even	8
1024.2.a.e.1.2		2	160.29	even	8
1024.2.b.b.513.1		2	160.149	even	8
1024.2.b.b.513.2		2	160.69	even	8
1024.2.b.e.513.1		2	160.59	odd	8
1024.2.b.e.513.2		2	160.139	odd	8
1152.2.k.a.289.1		2	240.149	odd	4
1152.2.k.a.865.1		2	120.29	odd	2
1152.2.k.b.289.1		2	240.59	even	4
1152.2.k.b.865.1		2	120.59	even	2
1600.2.l.a.401.1		2	16.13	even	4	inner
1600.2.l.a.1201.1		2	1.1	even	1	trivial
1600.2.q.a.49.1		2	5.3	odd	4
1600.2.q.a.849.1		2	80.77	odd	4
1600.2.q.b.49.1		2	5.2	odd	4
1600.2.q.b.849.1		2	80.13	odd	4
9216.2.a.d.1.1		2	480.419	even	8
9216.2.a.d.1.2		2	480.179	even	8
9216.2.a.s.1.1		2	480.29	odd	8
9216.2.a.s.1.2		2	480.269	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

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

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