LMFDB - Embedded newform 960.2.y.c.943.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(847,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.847"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.66563859404$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	960.943
Dual form			960.2.y.c.847.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +(1.00000 + 1.00000i) q^{11} +(1.00000 + 2.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +(1.00000 + 1.00000i) q^{19} +(-3.00000 + 3.00000i) q^{21} +(-5.00000 - 5.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +1.00000 q^{27} +(-5.00000 + 5.00000i) q^{29} +6.00000i q^{31} +(1.00000 + 1.00000i) q^{33} +(-9.00000 - 3.00000i) q^{35} +4.00000i q^{37} +12.0000i q^{41} -10.0000i q^{43} +(1.00000 + 2.00000i) q^{45} +(3.00000 + 3.00000i) q^{47} -11.0000i q^{49} +(1.00000 - 1.00000i) q^{51} +6.00000 q^{53} +(-1.00000 + 3.00000i) q^{55} +(1.00000 + 1.00000i) q^{57} +(-5.00000 + 5.00000i) q^{59} +(-5.00000 - 5.00000i) q^{61} +(-3.00000 + 3.00000i) q^{63} -2.00000i q^{67} +(-5.00000 - 5.00000i) q^{69} +16.0000 q^{71} +(9.00000 - 9.00000i) q^{73} +(-3.00000 + 4.00000i) q^{75} -6.00000 q^{77} +16.0000 q^{79} +1.00000 q^{81} -4.00000 q^{83} +(3.00000 + 1.00000i) q^{85} +(-5.00000 + 5.00000i) q^{87} +6.00000 q^{89} +6.00000i q^{93} +(-1.00000 + 3.00000i) q^{95} +(1.00000 - 1.00000i) q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{5} - 6 q^{7} + 2 q^{9} + 2 q^{11} + 2 q^{15} + 2 q^{17} + 2 q^{19} - 6 q^{21} - 10 q^{23} - 6 q^{25} + 2 q^{27} - 10 q^{29} + 2 q^{33} - 18 q^{35} + 2 q^{45} + 6 q^{47} + 2 q^{51} + 12 q^{53}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^5 - 6 * q^7 + 2 * q^9 + 2 * q^11 + 2 * q^15 + 2 * q^17 + 2 * q^19 - 6 * q^21 - 10 * q^23 - 6 * q^25 + 2 * q^27 - 10 * q^29 + 2 * q^33 - 18 * q^35 + 2 * q^45 + 6 * q^47 + 2 * q^51 + 12 * q^53 - 2 * q^55 + 2 * q^57 - 10 * q^59 - 10 * q^61 - 6 * q^63 - 10 * q^69 + 32 * q^71 + 18 * q^73 - 6 * q^75 - 12 * q^77 + 32 * q^79 + 2 * q^81 - 8 * q^83 + 6 * q^85 - 10 * q^87 + 12 * q^89 - 2 * q^95 + 2 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		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
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$		0			0
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		0			0
$19$	1.00000	+	1.00000i	0.229416	+	0.229416i	0.812449	−	0.583033i	$-0.198134\pi$
$19$	1.00000	+	1.00000i	0.229416	+	0.229416i	−0.583033	+	0.812449i	$0.698134\pi$
$20$		0			0
$21$	−3.00000	+	3.00000i	−0.654654	+	0.654654i
$22$		0			0
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.999053	−	0.0435195i	$-0.986143\pi$
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.0435195	−	0.999053i	$-0.513857\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.00000	+	5.00000i	−0.928477	+	0.928477i	−0.997608	−	0.0691309i	$-0.977977\pi$
$29$	−5.00000	+	5.00000i	−0.928477	+	0.928477i	0.0691309	+	0.997608i	$0.477977\pi$
$30$		0			0
$31$			6.00000i			1.07763i	0.842424	+	0.538816i	$0.181128\pi$
$31$			6.00000i			1.07763i	−0.842424	+	0.538816i	$0.818872\pi$
$32$		0			0
$33$	1.00000	+	1.00000i	0.174078	+	0.174078i
$34$		0			0
$35$	−9.00000	−	3.00000i	−1.52128	−	0.507093i
$36$		0			0
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			12.0000i			1.87409i	0.349215	+	0.937043i	$0.386448\pi$
$41$			12.0000i			1.87409i	−0.349215	+	0.937043i	$0.613552\pi$
$42$		0			0
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$		0			0
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$		0			0
$47$	3.00000	+	3.00000i	0.437595	+	0.437595i	0.891202	−	0.453607i	$-0.149863\pi$
$47$	3.00000	+	3.00000i	0.437595	+	0.437595i	−0.453607	+	0.891202i	$0.649863\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$	1.00000	−	1.00000i	0.140028	−	0.140028i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−1.00000	+	3.00000i	−0.134840	+	0.404520i
$56$		0			0
$57$	1.00000	+	1.00000i	0.132453	+	0.132453i
$58$		0			0
$59$	−5.00000	+	5.00000i	−0.650945	+	0.650945i	−0.953220	−	0.302276i	$-0.902254\pi$
$59$	−5.00000	+	5.00000i	−0.650945	+	0.650945i	0.302276	+	0.953220i	$0.402254\pi$
$60$		0			0
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	0.310416	−	0.950601i	$-0.399532\pi$
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	−0.950601	+	0.310416i	$0.899532\pi$
$62$		0			0
$63$	−3.00000	+	3.00000i	−0.377964	+	0.377964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	2.00000i		−	0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$		−	2.00000i		−	0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$		0			0
$69$	−5.00000	−	5.00000i	−0.601929	−	0.601929i
$70$		0			0
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$		0			0
$73$	9.00000	−	9.00000i	1.05337	−	1.05337i	0.0548772	−	0.998493i	$-0.482523\pi$
$73$	9.00000	−	9.00000i	1.05337	−	1.05337i	0.998493	−	0.0548772i	$-0.0174767\pi$
$74$		0			0
$75$	−3.00000	+	4.00000i	−0.346410	+	0.461880i
$76$		0			0
$77$	−6.00000			−0.683763
$78$		0			0
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	3.00000	+	1.00000i	0.325396	+	0.108465i
$86$		0			0
$87$	−5.00000	+	5.00000i	−0.536056	+	0.536056i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			6.00000i			0.622171i
$94$		0			0
$95$	−1.00000	+	3.00000i	−0.102598	+	0.307794i
$96$		0			0
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$98$		0			0
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$		0			0
$101$	−9.00000	+	9.00000i	−0.895533	+	0.895533i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$	−9.00000	+	9.00000i	−0.895533	+	0.895533i	0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$	3.00000	+	3.00000i	0.295599	+	0.295599i	0.839287	−	0.543688i	$-0.182973\pi$
$103$	3.00000	+	3.00000i	0.295599	+	0.295599i	−0.543688	+	0.839287i	$0.682973\pi$
$104$		0			0
$105$	−9.00000	−	3.00000i	−0.878310	−	0.292770i
$106$		0			0
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	7.00000	−	7.00000i	0.670478	−	0.670478i	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	7.00000	−	7.00000i	0.670478	−	0.670478i	0.957826	+	0.287348i	$0.0927736\pi$
$110$		0			0
$111$			4.00000i			0.379663i
$112$		0			0
$113$	1.00000	+	1.00000i	0.0940721	+	0.0940721i	0.752577	−	0.658505i	$-0.228811\pi$
$113$	1.00000	+	1.00000i	0.0940721	+	0.0940721i	−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	5.00000	−	15.0000i	0.466252	−	1.39876i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			6.00000i			0.550019i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$			12.0000i			1.08200i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	−1.00000	−	1.00000i	−0.0887357	−	0.0887357i	0.661346	−	0.750081i	$-0.269986\pi$
$127$	−1.00000	−	1.00000i	−0.0887357	−	0.0887357i	−0.750081	+	0.661346i	$0.769986\pi$
$128$		0			0
$129$		−	10.0000i		−	0.880451i
$130$		0			0
$131$	−1.00000	+	1.00000i	−0.0873704	+	0.0873704i	−0.749441	−	0.662071i	$-0.769678\pi$
$131$	−1.00000	+	1.00000i	−0.0873704	+	0.0873704i	0.662071	+	0.749441i	$0.269678\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$		0			0
$135$	1.00000	+	2.00000i	0.0860663	+	0.172133i
$136$		0			0
$137$	5.00000	+	5.00000i	0.427179	+	0.427179i	0.887666	−	0.460487i	$-0.152325\pi$
$137$	5.00000	+	5.00000i	0.427179	+	0.427179i	−0.460487	+	0.887666i	$0.652325\pi$
$138$		0			0
$139$	−5.00000	+	5.00000i	−0.424094	+	0.424094i	−0.886611	−	0.462516i	$-0.846947\pi$
$139$	−5.00000	+	5.00000i	−0.424094	+	0.424094i	0.462516	+	0.886611i	$0.346947\pi$
$140$		0			0
$141$	3.00000	+	3.00000i	0.252646	+	0.252646i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−15.0000	−	5.00000i	−1.24568	−	0.415227i
$146$		0			0
$147$		−	11.0000i		−	0.907265i
$148$		0			0
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	0.664958	−	0.746881i	$-0.268450\pi$
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	−0.746881	+	0.664958i	$0.768450\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		0			0
$153$	1.00000	−	1.00000i	0.0808452	−	0.0808452i
$154$		0			0
$155$	−12.0000	+	6.00000i	−0.963863	+	0.481932i
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	30.0000			2.36433
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	−1.00000	+	3.00000i	−0.0778499	+	0.233550i
$166$		0			0
$167$	−7.00000	+	7.00000i	−0.541676	+	0.541676i	−0.924020	−	0.382344i	$-0.875117\pi$
$167$	−7.00000	+	7.00000i	−0.541676	+	0.541676i	0.382344	+	0.924020i	$0.375117\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	1.00000	+	1.00000i	0.0764719	+	0.0764719i
$172$		0			0
$173$		−	20.0000i		−	1.52057i	−0.649589	−	0.760286i	$-0.725059\pi$
$173$		−	20.0000i		−	1.52057i	0.649589	−	0.760286i	$-0.274941\pi$
$174$		0			0
$175$	−3.00000	−	21.0000i	−0.226779	−	1.58745i
$176$		0			0
$177$	−5.00000	+	5.00000i	−0.375823	+	0.375823i
$178$		0			0
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	0.868829	−	0.495112i	$-0.164873\pi$
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	−0.495112	+	0.868829i	$0.664873\pi$
$180$		0			0
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	−0.586767	−	0.809756i	$-0.699600\pi$
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	0.809756	+	0.586767i	$0.199600\pi$
$182$		0			0
$183$	−5.00000	−	5.00000i	−0.369611	−	0.369611i
$184$		0			0
$185$	−8.00000	+	4.00000i	−0.588172	+	0.294086i
$186$		0			0
$187$	2.00000			0.146254
$188$		0			0
$189$	−3.00000	+	3.00000i	−0.218218	+	0.218218i
$190$		0			0
$191$			6.00000i			0.434145i	0.976156	+	0.217072i	$0.0696508\pi$
$191$			6.00000i			0.434145i	−0.976156	+	0.217072i	$0.930349\pi$
$192$		0			0
$193$	13.0000	+	13.0000i	0.935760	+	0.935760i	0.998058	−	0.0622972i	$-0.0198427\pi$
$193$	13.0000	+	13.0000i	0.935760	+	0.935760i	−0.0622972	+	0.998058i	$0.519843\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	24.0000i		−	1.70993i	−0.518686	−	0.854965i	$-0.673579\pi$
$197$		−	24.0000i		−	1.70993i	0.518686	−	0.854965i	$-0.326421\pi$
$198$		0			0
$199$		−	26.0000i		−	1.84309i	−0.388270	−	0.921546i	$-0.626927\pi$
$199$		−	26.0000i		−	1.84309i	0.388270	−	0.921546i	$-0.373073\pi$
$200$		0			0
$201$		−	2.00000i		−	0.141069i
$202$		0			0
$203$		−	30.0000i		−	2.10559i
$204$		0			0
$205$	−24.0000	+	12.0000i	−1.67623	+	0.838116i
$206$		0			0
$207$	−5.00000	−	5.00000i	−0.347524	−	0.347524i
$208$		0			0
$209$			2.00000i			0.138343i
$210$		0			0
$211$	15.0000	−	15.0000i	1.03264	−	1.03264i	0.0331936	−	0.999449i	$-0.489432\pi$
$211$	15.0000	−	15.0000i	1.03264	−	1.03264i	0.999449	−	0.0331936i	$-0.0105678\pi$
$212$		0			0
$213$	16.0000			1.09630
$214$		0			0
$215$	20.0000	−	10.0000i	1.36399	−	0.681994i
$216$		0			0
$217$	−18.0000	−	18.0000i	−1.22192	−	1.22192i
$218$		0			0
$219$	9.00000	−	9.00000i	0.608164	−	0.608164i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	−0.338340	−	0.941024i	$-0.609865\pi$
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	0.941024	+	0.338340i	$0.109865\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$		0			0
$227$			14.0000i			0.929213i	0.885517	+	0.464606i	$0.153804\pi$
$227$			14.0000i			0.929213i	−0.885517	+	0.464606i	$0.846196\pi$
$228$		0			0
$229$	15.0000	+	15.0000i	0.991228	+	0.991228i	0.999962	−	0.00873396i	$-0.00278014\pi$
$229$	15.0000	+	15.0000i	0.991228	+	0.991228i	−0.00873396	+	0.999962i	$0.502780\pi$
$230$		0			0
$231$	−6.00000			−0.394771
$232$		0			0
$233$	−7.00000	+	7.00000i	−0.458585	+	0.458585i	−0.898191	−	0.439606i	$-0.855118\pi$
$233$	−7.00000	+	7.00000i	−0.458585	+	0.458585i	0.439606	+	0.898191i	$0.355118\pi$
$234$		0			0
$235$	−3.00000	+	9.00000i	−0.195698	+	0.587095i
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	22.0000	−	11.0000i	1.40553	−	0.702764i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−4.00000			−0.253490
$250$		0			0
$251$	−3.00000	−	3.00000i	−0.189358	−	0.189358i	0.606060	−	0.795419i	$-0.292749\pi$
$251$	−3.00000	−	3.00000i	−0.189358	−	0.189358i	−0.795419	+	0.606060i	$0.792749\pi$
$252$		0			0
$253$		−	10.0000i		−	0.628695i
$254$		0			0
$255$	3.00000	+	1.00000i	0.187867	+	0.0626224i
$256$		0			0
$257$	−7.00000	+	7.00000i	−0.436648	+	0.436648i	−0.890882	−	0.454234i	$-0.849913\pi$
$257$	−7.00000	+	7.00000i	−0.436648	+	0.436648i	0.454234	+	0.890882i	$0.349913\pi$
$258$		0			0
$259$	−12.0000	−	12.0000i	−0.745644	−	0.745644i
$260$		0			0
$261$	−5.00000	+	5.00000i	−0.309492	+	0.309492i
$262$		0			0
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	0.959613	−	0.281324i	$-0.0907735\pi$
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	−0.281324	+	0.959613i	$0.590774\pi$
$264$		0			0
$265$	6.00000	+	12.0000i	0.368577	+	0.737154i
$266$		0			0
$267$	6.00000			0.367194
$268$		0			0
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	−0.736935	−	0.675964i	$-0.763728\pi$
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	0.675964	+	0.736935i	$0.263728\pi$
$270$		0			0
$271$			22.0000i			1.33640i	0.743980	+	0.668202i	$0.232936\pi$
$271$			22.0000i			1.33640i	−0.743980	+	0.668202i	$0.767064\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.00000	+	1.00000i	−0.422116	+	0.0603023i
$276$		0			0
$277$		−	28.0000i		−	1.68236i	−0.540758	−	0.841178i	$-0.681862\pi$
$277$		−	28.0000i		−	1.68236i	0.540758	−	0.841178i	$-0.318138\pi$
$278$		0			0
$279$			6.00000i			0.359211i
$280$		0			0
$281$			8.00000i			0.477240i	0.971113	+	0.238620i	$0.0766950\pi$
$281$			8.00000i			0.477240i	−0.971113	+	0.238620i	$0.923305\pi$
$282$		0			0
$283$		−	18.0000i		−	1.06999i	−0.844856	−	0.534994i	$-0.820314\pi$
$283$		−	18.0000i		−	1.06999i	0.844856	−	0.534994i	$-0.179686\pi$
$284$		0			0
$285$	−1.00000	+	3.00000i	−0.0592349	+	0.177705i
$286$		0			0
$287$	−36.0000	−	36.0000i	−2.12501	−	2.12501i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$	1.00000	−	1.00000i	0.0586210	−	0.0586210i
$292$		0			0
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	−15.0000	−	5.00000i	−0.873334	−	0.291111i
$296$		0			0
$297$	1.00000	+	1.00000i	0.0580259	+	0.0580259i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	30.0000	+	30.0000i	1.72917	+	1.72917i
$302$		0			0
$303$	−9.00000	+	9.00000i	−0.517036	+	0.517036i
$304$		0			0
$305$	5.00000	−	15.0000i	0.286299	−	0.858898i
$306$		0			0
$307$			22.0000i			1.25561i	0.778372	+	0.627803i	$0.216046\pi$
$307$			22.0000i			1.25561i	−0.778372	+	0.627803i	$0.783954\pi$
$308$		0			0
$309$	3.00000	+	3.00000i	0.170664	+	0.170664i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	−0.236764	−	0.971567i	$-0.576087\pi$
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	0.971567	+	0.236764i	$0.0760868\pi$
$314$		0			0
$315$	−9.00000	−	3.00000i	−0.507093	−	0.169031i
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	−10.0000			−0.559893
$320$		0			0
$321$	4.00000			0.223258
$322$		0			0
$323$	2.00000			0.111283
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.00000	−	7.00000i	0.387101	−	0.387101i
$328$		0			0
$329$	−18.0000			−0.992372
$330$		0			0
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	0.909779	−	0.415094i	$-0.136251\pi$
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	−0.415094	+	0.909779i	$0.636251\pi$
$332$		0			0
$333$			4.00000i			0.219199i
$334$		0			0
$335$	4.00000	−	2.00000i	0.218543	−	0.109272i
$336$		0			0
$337$	−3.00000	+	3.00000i	−0.163420	+	0.163420i	−0.784080	−	0.620660i	$-0.786865\pi$
$337$	−3.00000	+	3.00000i	−0.163420	+	0.163420i	0.620660	+	0.784080i	$0.286865\pi$
$338$		0			0
$339$	1.00000	+	1.00000i	0.0543125	+	0.0543125i
$340$		0			0
$341$	−6.00000	+	6.00000i	−0.324918	+	0.324918i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$		0			0
$345$	5.00000	−	15.0000i	0.269191	−	0.807573i
$346$		0			0
$347$	−4.00000			−0.214731			−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000			−0.214731			−0.107366	+	0.994220i	$0.534242\pi$
$348$		0			0
$349$	19.0000	−	19.0000i	1.01705	−	1.01705i	0.0171945	−	0.999852i	$-0.494527\pi$
$349$	19.0000	−	19.0000i	1.01705	−	1.01705i	0.999852	−	0.0171945i	$-0.00547346\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	0.184469	−	0.982838i	$-0.440943\pi$
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	−0.982838	+	0.184469i	$0.940943\pi$
$354$		0			0
$355$	16.0000	+	32.0000i	0.849192	+	1.69838i
$356$		0			0
$357$			6.00000i			0.317554i
$358$		0			0
$359$		−	2.00000i		−	0.105556i	−0.998606	−	0.0527780i	$-0.983192\pi$
$359$		−	2.00000i		−	0.105556i	0.998606	−	0.0527780i	$-0.0168076\pi$
$360$		0			0
$361$		−	17.0000i		−	0.894737i
$362$		0			0
$363$		−	9.00000i		−	0.472377i
$364$		0			0
$365$	27.0000	+	9.00000i	1.41324	+	0.471082i
$366$		0			0
$367$	−13.0000	−	13.0000i	−0.678594	−	0.678594i	0.281088	−	0.959682i	$-0.409305\pi$
$367$	−13.0000	−	13.0000i	−0.678594	−	0.678594i	−0.959682	+	0.281088i	$0.909305\pi$
$368$		0			0
$369$			12.0000i			0.624695i
$370$		0			0
$371$	−18.0000	+	18.0000i	−0.934513	+	0.934513i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−11.0000	−	2.00000i	−0.568038	−	0.103280i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	3.00000	−	3.00000i	0.154100	−	0.154100i	−0.625847	−	0.779946i	$-0.715246\pi$
$379$	3.00000	−	3.00000i	0.154100	−	0.154100i	0.779946	+	0.625847i	$0.215246\pi$
$380$		0			0
$381$	−1.00000	−	1.00000i	−0.0512316	−	0.0512316i
$382$		0			0
$383$	9.00000	−	9.00000i	0.459879	−	0.459879i	−0.438737	−	0.898616i	$-0.644574\pi$
$383$	9.00000	−	9.00000i	0.459879	−	0.459879i	0.898616	+	0.438737i	$0.144574\pi$
$384$		0			0
$385$	−6.00000	−	12.0000i	−0.305788	−	0.611577i
$386$		0			0
$387$		−	10.0000i		−	0.508329i
$388$		0			0
$389$	7.00000	+	7.00000i	0.354914	+	0.354914i	0.861934	−	0.507020i	$-0.169253\pi$
$389$	7.00000	+	7.00000i	0.354914	+	0.354914i	−0.507020	+	0.861934i	$0.669253\pi$
$390$		0			0
$391$	−10.0000			−0.505722
$392$		0			0
$393$	−1.00000	+	1.00000i	−0.0504433	+	0.0504433i
$394$		0			0
$395$	16.0000	+	32.0000i	0.805047	+	1.61009i
$396$		0			0
$397$	14.0000			0.702640			0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000			0.702640			0.351320	+	0.936255i	$0.385733\pi$
$398$		0			0
$399$	−6.00000			−0.300376
$400$		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
$403$		0			0
$404$		0			0
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$	−4.00000	+	4.00000i	−0.198273	+	0.198273i
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$		0			0
$411$	5.00000	+	5.00000i	0.246632	+	0.246632i
$412$		0			0
$413$		−	30.0000i		−	1.47620i
$414$		0			0
$415$	−4.00000	−	8.00000i	−0.196352	−	0.392705i
$416$		0			0
$417$	−5.00000	+	5.00000i	−0.244851	+	0.244851i
$418$		0			0
$419$	9.00000	+	9.00000i	0.439679	+	0.439679i	0.891904	−	0.452225i	$-0.149370\pi$
$419$	9.00000	+	9.00000i	0.439679	+	0.439679i	−0.452225	+	0.891904i	$0.649370\pi$
$420$		0			0
$421$	−17.0000	+	17.0000i	−0.828529	+	0.828529i	−0.987313	−	0.158784i	$-0.949243\pi$
$421$	−17.0000	+	17.0000i	−0.828529	+	0.828529i	0.158784	+	0.987313i	$0.449243\pi$
$422$		0			0
$423$	3.00000	+	3.00000i	0.145865	+	0.145865i
$424$		0			0
$425$	1.00000	+	7.00000i	0.0485071	+	0.339550i
$426$		0			0
$427$	30.0000			1.45180
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	2.00000i		−	0.0963366i	−0.998839	−	0.0481683i	$-0.984662\pi$
$431$		−	2.00000i		−	0.0963366i	0.998839	−	0.0481683i	$-0.0153384\pi$
$432$		0			0
$433$	1.00000	+	1.00000i	0.0480569	+	0.0480569i	0.730727	−	0.682670i	$-0.239181\pi$
$433$	1.00000	+	1.00000i	0.0480569	+	0.0480569i	−0.682670	+	0.730727i	$0.739181\pi$
$434$		0			0
$435$	−15.0000	−	5.00000i	−0.719195	−	0.239732i
$436$		0			0
$437$		−	10.0000i		−	0.478365i
$438$		0			0
$439$			14.0000i			0.668184i	0.942541	+	0.334092i	$0.108430\pi$
$439$			14.0000i			0.668184i	−0.942541	+	0.334092i	$0.891570\pi$
$440$		0			0
$441$		−	11.0000i		−	0.523810i
$442$		0			0
$443$			6.00000i			0.285069i	0.989790	+	0.142534i	$0.0455251\pi$
$443$			6.00000i			0.285069i	−0.989790	+	0.142534i	$0.954475\pi$
$444$		0			0
$445$	6.00000	+	12.0000i	0.284427	+	0.568855i
$446$		0			0
$447$	−1.00000	−	1.00000i	−0.0472984	−	0.0472984i
$448$		0			0
$449$		−	16.0000i		−	0.755087i	−0.925992	−	0.377543i	$-0.876769\pi$
$449$		−	16.0000i		−	0.755087i	0.925992	−	0.377543i	$-0.123231\pi$
$450$		0			0
$451$	−12.0000	+	12.0000i	−0.565058	+	0.565058i
$452$		0			0
$453$	−16.0000			−0.751746
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000	+	17.0000i	0.795226	+	0.795226i	0.982339	−	0.187112i	$-0.0599128\pi$
$457$	17.0000	+	17.0000i	0.795226	+	0.795226i	−0.187112	+	0.982339i	$0.559913\pi$
$458$		0			0
$459$	1.00000	−	1.00000i	0.0466760	−	0.0466760i
$460$		0			0
$461$	−1.00000	−	1.00000i	−0.0465746	−	0.0465746i	0.683436	−	0.730011i	$-0.260485\pi$
$461$	−1.00000	−	1.00000i	−0.0465746	−	0.0465746i	−0.730011	+	0.683436i	$0.760485\pi$
$462$		0			0
$463$	−19.0000	+	19.0000i	−0.883005	+	0.883005i	−0.993839	−	0.110834i	$-0.964648\pi$
$463$	−19.0000	+	19.0000i	−0.883005	+	0.883005i	0.110834	+	0.993839i	$0.464648\pi$
$464$		0			0
$465$	−12.0000	+	6.00000i	−0.556487	+	0.278243i
$466$		0			0
$467$			30.0000i			1.38823i	0.719862	+	0.694117i	$0.244205\pi$
$467$			30.0000i			1.38823i	−0.719862	+	0.694117i	$0.755795\pi$
$468$		0			0
$469$	6.00000	+	6.00000i	0.277054	+	0.277054i
$470$		0			0
$471$	2.00000			0.0921551
$472$		0			0
$473$	10.0000	−	10.0000i	0.459800	−	0.459800i
$474$		0			0
$475$	−7.00000	+	1.00000i	−0.321182	+	0.0458831i
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	30.0000			1.36505
$484$		0			0
$485$	3.00000	+	1.00000i	0.136223	+	0.0454077i
$486$		0			0
$487$	9.00000	−	9.00000i	0.407829	−	0.407829i	−0.473152	−	0.880981i	$-0.656884\pi$
$487$	9.00000	−	9.00000i	0.407829	−	0.407829i	0.880981	+	0.473152i	$0.156884\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	1.00000	+	1.00000i	0.0451294	+	0.0451294i	0.729311	−	0.684182i	$-0.239841\pi$
$491$	1.00000	+	1.00000i	0.0451294	+	0.0451294i	−0.684182	+	0.729311i	$0.739841\pi$
$492$		0			0
$493$			10.0000i			0.450377i
$494$		0			0
$495$	−1.00000	+	3.00000i	−0.0449467	+	0.134840i
$496$		0			0
$497$	−48.0000	+	48.0000i	−2.15309	+	2.15309i
$498$		0			0
$499$	−15.0000	−	15.0000i	−0.671492	−	0.671492i	0.286568	−	0.958060i	$-0.407486\pi$
$499$	−15.0000	−	15.0000i	−0.671492	−	0.671492i	−0.958060	+	0.286568i	$0.907486\pi$
$500$		0			0
$501$	−7.00000	+	7.00000i	−0.312737	+	0.312737i
$502$		0			0
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	0.217964	−	0.975957i	$-0.430058\pi$
$503$	−17.0000	−	17.0000i	−0.757993	−	0.757993i	−0.975957	+	0.217964i	$0.930058\pi$
$504$		0			0
$505$	−27.0000	−	9.00000i	−1.20148	−	0.400495i
$506$		0			0
$507$	13.0000			0.577350
$508$		0			0
$509$	−5.00000	+	5.00000i	−0.221621	+	0.221621i	−0.809181	−	0.587560i	$-0.800089\pi$
$509$	−5.00000	+	5.00000i	−0.221621	+	0.221621i	0.587560	+	0.809181i	$0.300089\pi$
$510$		0			0
$511$			54.0000i			2.38882i
$512$		0			0
$513$	1.00000	+	1.00000i	0.0441511	+	0.0441511i
$514$		0			0
$515$	−3.00000	+	9.00000i	−0.132196	+	0.396587i
$516$		0			0
$517$			6.00000i			0.263880i
$518$		0			0
$519$		−	20.0000i		−	0.877903i
$520$		0			0
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$		0			0
$523$			38.0000i			1.66162i	0.556553	+	0.830812i	$0.312124\pi$
$523$			38.0000i			1.66162i	−0.556553	+	0.830812i	$0.687876\pi$
$524$		0			0
$525$	−3.00000	−	21.0000i	−0.130931	−	0.916515i
$526$		0			0
$527$	6.00000	+	6.00000i	0.261364	+	0.261364i
$528$		0			0
$529$			27.0000i			1.17391i
$530$		0			0
$531$	−5.00000	+	5.00000i	−0.216982	+	0.216982i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$		0			0
$537$	5.00000	+	5.00000i	0.215766	+	0.215766i
$538$		0			0
$539$	11.0000	−	11.0000i	0.473804	−	0.473804i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$		0			0
$543$	3.00000	−	3.00000i	0.128742	−	0.128742i
$544$		0			0
$545$	21.0000	+	7.00000i	0.899541	+	0.299847i
$546$		0			0
$547$		−	2.00000i		−	0.0855138i	−0.999086	−	0.0427569i	$-0.986386\pi$
$547$		−	2.00000i		−	0.0855138i	0.999086	−	0.0427569i	$-0.0136141\pi$
$548$		0			0
$549$	−5.00000	−	5.00000i	−0.213395	−	0.213395i
$550$		0			0
$551$	−10.0000			−0.426014
$552$		0			0
$553$	−48.0000	+	48.0000i	−2.04117	+	2.04117i
$554$		0			0
$555$	−8.00000	+	4.00000i	−0.339581	+	0.169791i
$556$		0			0
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.00000			0.0844401
$562$		0			0
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$		0			0
$565$	−1.00000	+	3.00000i	−0.0420703	+	0.126211i
$566$		0			0
$567$	−3.00000	+	3.00000i	−0.125988	+	0.125988i
$568$		0			0
$569$	22.0000			0.922288			0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000			0.922288			0.461144	+	0.887325i	$0.347439\pi$
$570$		0			0
$571$	−27.0000	−	27.0000i	−1.12991	−	1.12991i	−0.990190	−	0.139724i	$-0.955378\pi$
$571$	−27.0000	−	27.0000i	−1.12991	−	1.12991i	−0.139724	−	0.990190i	$-0.544622\pi$
$572$		0			0
$573$			6.00000i			0.250654i
$574$		0			0
$575$	35.0000	−	5.00000i	1.45960	−	0.208514i
$576$		0			0
$577$	−15.0000	+	15.0000i	−0.624458	+	0.624458i	−0.946668	−	0.322210i	$-0.895574\pi$
$577$	−15.0000	+	15.0000i	−0.624458	+	0.624458i	0.322210	+	0.946668i	$0.395574\pi$
$578$		0			0
$579$	13.0000	+	13.0000i	0.540262	+	0.540262i
$580$		0			0
$581$	12.0000	−	12.0000i	0.497844	−	0.497844i
$582$		0			0
$583$	6.00000	+	6.00000i	0.248495	+	0.248495i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−6.00000	+	6.00000i	−0.247226	+	0.247226i
$590$		0			0
$591$		−	24.0000i		−	0.987228i
$592$		0			0
$593$	5.00000	+	5.00000i	0.205325	+	0.205325i	0.802277	−	0.596952i	$-0.203622\pi$
$593$	5.00000	+	5.00000i	0.205325	+	0.205325i	−0.596952	+	0.802277i	$0.703622\pi$
$594$		0			0
$595$	−12.0000	+	6.00000i	−0.491952	+	0.245976i
$596$		0			0
$597$		−	26.0000i		−	1.06411i
$598$		0			0
$599$		−	10.0000i		−	0.408589i	−0.978909	−	0.204294i	$-0.934510\pi$
$599$		−	10.0000i		−	0.408589i	0.978909	−	0.204294i	$-0.0654900\pi$
$600$		0			0
$601$			16.0000i			0.652654i	0.945257	+	0.326327i	$0.105811\pi$
$601$			16.0000i			0.652654i	−0.945257	+	0.326327i	$0.894189\pi$
$602$		0			0
$603$		−	2.00000i		−	0.0814463i
$604$		0			0
$605$	18.0000	−	9.00000i	0.731804	−	0.365902i
$606$		0			0
$607$	−17.0000	−	17.0000i	−0.690009	−	0.690009i	0.272225	−	0.962234i	$-0.412241\pi$
$607$	−17.0000	−	17.0000i	−0.690009	−	0.690009i	−0.962234	+	0.272225i	$0.912241\pi$
$608$		0			0
$609$		−	30.0000i		−	1.21566i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$		0			0
$615$	−24.0000	+	12.0000i	−0.967773	+	0.483887i
$616$		0			0
$617$	17.0000	+	17.0000i	0.684394	+	0.684394i	0.960987	−	0.276593i	$-0.0892054\pi$
$617$	17.0000	+	17.0000i	0.684394	+	0.684394i	−0.276593	+	0.960987i	$0.589205\pi$
$618$		0			0
$619$	−21.0000	+	21.0000i	−0.844061	+	0.844061i	−0.989384	−	0.145323i	$-0.953578\pi$
$619$	−21.0000	+	21.0000i	−0.844061	+	0.844061i	0.145323	+	0.989384i	$0.453578\pi$
$620$		0			0
$621$	−5.00000	−	5.00000i	−0.200643	−	0.200643i
$622$		0			0
$623$	−18.0000	+	18.0000i	−0.721155	+	0.721155i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$			2.00000i			0.0798723i
$628$		0			0
$629$	4.00000	+	4.00000i	0.159490	+	0.159490i
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$	15.0000	−	15.0000i	0.596196	−	0.596196i
$634$		0			0
$635$	1.00000	−	3.00000i	0.0396838	−	0.119051i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	16.0000			0.632950
$640$		0			0
$641$	42.0000			1.65890			0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000			1.65890			0.829450	+	0.558581i	$0.188654\pi$
$642$		0			0
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	20.0000	−	10.0000i	0.787499	−	0.393750i
$646$		0			0
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	−0.403775	−	0.914858i	$-0.632302\pi$
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	0.914858	+	0.403775i	$0.132302\pi$
$648$		0			0
$649$	−10.0000			−0.392534
$650$		0			0
$651$	−18.0000	−	18.0000i	−0.705476	−	0.705476i
$652$		0			0
$653$			24.0000i			0.939193i	0.882881	+	0.469596i	$0.155601\pi$
$653$			24.0000i			0.939193i	−0.882881	+	0.469596i	$0.844399\pi$
$654$		0			0
$655$	−3.00000	−	1.00000i	−0.117220	−	0.0390732i
$656$		0			0
$657$	9.00000	−	9.00000i	0.351123	−	0.351123i
$658$		0			0
$659$	13.0000	+	13.0000i	0.506408	+	0.506408i	0.913422	−	0.407014i	$-0.133430\pi$
$659$	13.0000	+	13.0000i	0.506408	+	0.506408i	−0.407014	+	0.913422i	$0.633430\pi$
$660$		0			0
$661$	19.0000	−	19.0000i	0.739014	−	0.739014i	−0.233373	−	0.972387i	$-0.574976\pi$
$661$	19.0000	−	19.0000i	0.739014	−	0.739014i	0.972387	+	0.233373i	$0.0749763\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.00000	−	12.0000i	−0.232670	−	0.465340i
$666$		0			0
$667$	50.0000			1.93601
$668$		0			0
$669$	9.00000	−	9.00000i	0.347960	−	0.347960i
$670$		0			0
$671$		−	10.0000i		−	0.386046i
$672$		0			0
$673$	29.0000	+	29.0000i	1.11787	+	1.11787i	0.992054	+	0.125814i	$0.0401543\pi$
$673$	29.0000	+	29.0000i	1.11787	+	1.11787i	0.125814	+	0.992054i	$0.459846\pi$
$674$		0			0
$675$	−3.00000	+	4.00000i	−0.115470	+	0.153960i
$676$		0			0
$677$			48.0000i			1.84479i	0.386248	+	0.922395i	$0.373771\pi$
$677$			48.0000i			1.84479i	−0.386248	+	0.922395i	$0.626229\pi$
$678$		0			0
$679$			6.00000i			0.230259i
$680$		0			0
$681$			14.0000i			0.536481i
$682$		0			0
$683$		−	42.0000i		−	1.60709i	−0.595247	−	0.803543i	$-0.702946\pi$
$683$		−	42.0000i		−	1.60709i	0.595247	−	0.803543i	$-0.297054\pi$
$684$		0			0
$685$	−5.00000	+	15.0000i	−0.191040	+	0.573121i
$686$		0			0
$687$	15.0000	+	15.0000i	0.572286	+	0.572286i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	15.0000	−	15.0000i	0.570627	−	0.570627i	−0.361677	−	0.932304i	$-0.617796\pi$
$691$	15.0000	−	15.0000i	0.570627	−	0.570627i	0.932304	+	0.361677i	$0.117796\pi$
$692$		0			0
$693$	−6.00000			−0.227921
$694$		0			0
$695$	−15.0000	−	5.00000i	−0.568982	−	0.189661i
$696$		0			0
$697$	12.0000	+	12.0000i	0.454532	+	0.454532i
$698$		0			0
$699$	−7.00000	+	7.00000i	−0.264764	+	0.264764i
$700$		0			0
$701$	−37.0000	−	37.0000i	−1.39747	−	1.39747i	−0.807220	−	0.590251i	$-0.799029\pi$
$701$	−37.0000	−	37.0000i	−1.39747	−	1.39747i	−0.590251	−	0.807220i	$-0.700971\pi$
$702$		0			0
$703$	−4.00000	+	4.00000i	−0.150863	+	0.150863i
$704$		0			0
$705$	−3.00000	+	9.00000i	−0.112987	+	0.338960i
$706$		0			0
$707$		−	54.0000i		−	2.03088i
$708$		0			0
$709$	−17.0000	−	17.0000i	−0.638448	−	0.638448i	0.311724	−	0.950173i	$-0.399093\pi$
$709$	−17.0000	−	17.0000i	−0.638448	−	0.638448i	−0.950173	+	0.311724i	$0.899093\pi$
$710$		0			0
$711$	16.0000			0.600047
$712$		0			0
$713$	30.0000	−	30.0000i	1.12351	−	1.12351i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	8.00000			0.298765
$718$		0			0
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$		0			0
$723$	−6.00000			−0.223142
$724$		0			0
$725$	−5.00000	−	35.0000i	−0.185695	−	1.29987i
$726$		0			0
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	−0.824898	−	0.565282i	$-0.808767\pi$
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	0.565282	+	0.824898i	$0.308767\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−10.0000	−	10.0000i	−0.369863	−	0.369863i
$732$		0			0
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$		0			0
$735$	22.0000	−	11.0000i	0.811482	−	0.405741i
$736$		0			0
$737$	2.00000	−	2.00000i	0.0736709	−	0.0736709i
$738$		0			0
$739$	−15.0000	−	15.0000i	−0.551784	−	0.551784i	0.375171	−	0.926955i	$-0.377584\pi$
$739$	−15.0000	−	15.0000i	−0.551784	−	0.551784i	−0.926955	+	0.375171i	$0.877584\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.0000	−	13.0000i	−0.476924	−	0.476924i	0.427223	−	0.904146i	$-0.359492\pi$
$743$	−13.0000	−	13.0000i	−0.476924	−	0.476924i	−0.904146	+	0.427223i	$0.859492\pi$
$744$		0			0
$745$	1.00000	−	3.00000i	0.0366372	−	0.109911i
$746$		0			0
$747$	−4.00000			−0.146352
$748$		0			0
$749$	−12.0000	+	12.0000i	−0.438470	+	0.438470i
$750$		0			0
$751$		−	34.0000i		−	1.24068i	−0.784334	−	0.620339i	$-0.786995\pi$
$751$		−	34.0000i		−	1.24068i	0.784334	−	0.620339i	$-0.213005\pi$
$752$		0			0
$753$	−3.00000	−	3.00000i	−0.109326	−	0.109326i
$754$		0			0
$755$	−16.0000	−	32.0000i	−0.582300	−	1.16460i
$756$		0			0
$757$		−	20.0000i		−	0.726912i	−0.931611	−	0.363456i	$-0.881597\pi$
$757$		−	20.0000i		−	0.726912i	0.931611	−	0.363456i	$-0.118403\pi$
$758$		0			0
$759$		−	10.0000i		−	0.362977i
$760$		0			0
$761$		−	48.0000i		−	1.74000i	−0.493053	−	0.869999i	$-0.664119\pi$
$761$		−	48.0000i		−	1.74000i	0.493053	−	0.869999i	$-0.335881\pi$
$762$		0			0
$763$			42.0000i			1.52050i
$764$		0			0
$765$	3.00000	+	1.00000i	0.108465	+	0.0361551i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	44.0000i		−	1.58668i	−0.608778	−	0.793340i	$-0.708340\pi$
$769$		−	44.0000i		−	1.58668i	0.608778	−	0.793340i	$-0.291660\pi$
$770$		0			0
$771$	−7.00000	+	7.00000i	−0.252099	+	0.252099i
$772$		0			0
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$		0			0
$775$	−24.0000	−	18.0000i	−0.862105	−	0.646579i
$776$		0			0
$777$	−12.0000	−	12.0000i	−0.430498	−	0.430498i
$778$		0			0
$779$	−12.0000	+	12.0000i	−0.429945	+	0.429945i
$780$		0			0
$781$	16.0000	+	16.0000i	0.572525	+	0.572525i
$782$		0			0
$783$	−5.00000	+	5.00000i	−0.178685	+	0.178685i
$784$		0			0
$785$	2.00000	+	4.00000i	0.0713831	+	0.142766i
$786$		0			0
$787$			14.0000i			0.499046i	0.968369	+	0.249523i	$0.0802738\pi$
$787$			14.0000i			0.499046i	−0.968369	+	0.249523i	$0.919726\pi$
$788$		0			0
$789$	11.0000	+	11.0000i	0.391610	+	0.391610i
$790$		0			0
$791$	−6.00000			−0.213335
$792$		0			0
$793$		0			0
$794$		0			0
$795$	6.00000	+	12.0000i	0.212798	+	0.425596i
$796$		0			0
$797$	14.0000			0.495905			0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000			0.495905			0.247953	+	0.968772i	$0.420242\pi$
$798$		0			0
$799$	6.00000			0.212265
$800$		0			0
$801$	6.00000			0.212000
$802$		0			0
$803$	18.0000			0.635206
$804$		0			0
$805$	30.0000	+	60.0000i	1.05736	+	2.11472i
$806$		0			0
$807$	−1.00000	+	1.00000i	−0.0352017	+	0.0352017i
$808$		0			0
$809$	−38.0000			−1.33601			−0.668004	−	0.744157i	$-0.732851\pi$
$809$	−38.0000			−1.33601			−0.668004	+	0.744157i	$0.732851\pi$
$810$		0			0
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	0.289882	−	0.957062i	$-0.406384\pi$
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	−0.957062	+	0.289882i	$0.906384\pi$
$812$		0			0
$813$			22.0000i			0.771574i
$814$		0			0
$815$	4.00000	+	8.00000i	0.140114	+	0.280228i
$816$		0			0
$817$	10.0000	−	10.0000i	0.349856	−	0.349856i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00000	+	1.00000i	−0.0349002	+	0.0349002i	−0.724342	−	0.689441i	$-0.757856\pi$
$821$	−1.00000	+	1.00000i	−0.0349002	+	0.0349002i	0.689441	+	0.724342i	$0.257856\pi$
$822$		0			0
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	0.757458	−	0.652884i	$-0.226441\pi$
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	−0.652884	+	0.757458i	$0.726441\pi$
$824$		0			0
$825$	−7.00000	+	1.00000i	−0.243709	+	0.0348155i
$826$		0			0
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$		0			0
$829$	−17.0000	+	17.0000i	−0.590434	+	0.590434i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−17.0000	+	17.0000i	−0.590434	+	0.590434i	0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		−	28.0000i		−	0.971309i
$832$		0			0
$833$	−11.0000	−	11.0000i	−0.381127	−	0.381127i
$834$		0			0
$835$	−21.0000	−	7.00000i	−0.726735	−	0.242245i
$836$		0			0
$837$			6.00000i			0.207390i
$838$		0			0
$839$			30.0000i			1.03572i	0.855467	+	0.517858i	$0.173270\pi$
$839$			30.0000i			1.03572i	−0.855467	+	0.517858i	$0.826730\pi$
$840$		0			0
$841$		−	21.0000i		−	0.724138i
$842$		0			0
$843$			8.00000i			0.275535i
$844$		0			0
$845$	13.0000	+	26.0000i	0.447214	+	0.894427i
$846$		0			0
$847$	27.0000	+	27.0000i	0.927731	+	0.927731i
$848$		0			0
$849$		−	18.0000i		−	0.617758i
$850$		0			0
$851$	20.0000	−	20.0000i	0.685591	−	0.685591i
$852$		0			0
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$		0			0
$855$	−1.00000	+	3.00000i	−0.0341993	+	0.102598i
$856$		0			0
$857$	−23.0000	−	23.0000i	−0.785665	−	0.785665i	0.195115	−	0.980780i	$-0.437492\pi$
$857$	−23.0000	−	23.0000i	−0.785665	−	0.785665i	−0.980780	+	0.195115i	$0.937492\pi$
$858$		0			0
$859$	23.0000	−	23.0000i	0.784750	−	0.784750i	−0.195878	−	0.980628i	$-0.562756\pi$
$859$	23.0000	−	23.0000i	0.784750	−	0.784750i	0.980628	+	0.195878i	$0.0627558\pi$
$860$		0			0
$861$	−36.0000	−	36.0000i	−1.22688	−	1.22688i
$862$		0			0
$863$	−15.0000	+	15.0000i	−0.510606	+	0.510606i	−0.914712	−	0.404106i	$-0.867583\pi$
$863$	−15.0000	+	15.0000i	−0.510606	+	0.510606i	0.404106	+	0.914712i	$0.367583\pi$
$864$		0			0
$865$	40.0000	−	20.0000i	1.36004	−	0.680020i
$866$		0			0
$867$			15.0000i			0.509427i
$868$		0			0
$869$	16.0000	+	16.0000i	0.542763	+	0.542763i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.00000	−	1.00000i	0.0338449	−	0.0338449i
$874$		0			0
$875$	39.0000	−	27.0000i	1.31844	−	0.912767i
$876$		0			0
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$		0			0
$879$	−14.0000			−0.472208
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−15.0000	−	5.00000i	−0.504219	−	0.168073i
$886$		0			0
$887$	−3.00000	+	3.00000i	−0.100730	+	0.100730i	−0.755676	−	0.654946i	$-0.772691\pi$
$887$	−3.00000	+	3.00000i	−0.100730	+	0.100730i	0.654946	+	0.755676i	$0.272691\pi$
$888$		0			0
$889$	6.00000			0.201234
$890$		0			0
$891$	1.00000	+	1.00000i	0.0335013	+	0.0335013i
$892$		0			0
$893$			6.00000i			0.200782i
$894$		0			0
$895$	−5.00000	+	15.0000i	−0.167132	+	0.501395i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.0000	−	30.0000i	−1.00056	−	1.00056i
$900$		0			0
$901$	6.00000	−	6.00000i	0.199889	−	0.199889i
$902$		0			0
$903$	30.0000	+	30.0000i	0.998337	+	0.998337i
$904$		0			0
$905$	9.00000	+	3.00000i	0.299170	+	0.0997234i
$906$		0			0
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$		0			0
$909$	−9.00000	+	9.00000i	−0.298511	+	0.298511i
$910$		0			0
$911$		−	10.0000i		−	0.331315i	−0.986183	−	0.165657i	$-0.947025\pi$
$911$		−	10.0000i		−	0.331315i	0.986183	−	0.165657i	$-0.0529746\pi$
$912$		0			0
$913$	−4.00000	−	4.00000i	−0.132381	−	0.132381i
$914$		0			0
$915$	5.00000	−	15.0000i	0.165295	−	0.495885i
$916$		0			0
$917$		−	6.00000i		−	0.198137i
$918$		0			0
$919$			30.0000i			0.989609i	0.869004	+	0.494804i	$0.164760\pi$
$919$			30.0000i			0.989609i	−0.869004	+	0.494804i	$0.835240\pi$
$920$		0			0
$921$			22.0000i			0.724925i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−16.0000	−	12.0000i	−0.526077	−	0.394558i
$926$		0			0
$927$	3.00000	+	3.00000i	0.0985329	+	0.0985329i
$928$		0			0
$929$			40.0000i			1.31236i	0.754606	+	0.656179i	$0.227828\pi$
$929$			40.0000i			1.31236i	−0.754606	+	0.656179i	$0.772172\pi$
$930$		0			0
$931$	11.0000	−	11.0000i	0.360510	−	0.360510i
$932$		0			0
$933$	24.0000			0.785725
$934$		0			0
$935$	2.00000	+	4.00000i	0.0654070	+	0.130814i
$936$		0			0
$937$	25.0000	+	25.0000i	0.816714	+	0.816714i	0.985630	−	0.168916i	$-0.0540267\pi$
$937$	25.0000	+	25.0000i	0.816714	+	0.816714i	−0.168916	+	0.985630i	$0.554027\pi$
$938$		0			0
$939$	13.0000	−	13.0000i	0.424239	−	0.424239i
$940$		0			0
$941$	−5.00000	−	5.00000i	−0.162995	−	0.162995i	0.620897	−	0.783892i	$-0.286769\pi$
$941$	−5.00000	−	5.00000i	−0.162995	−	0.162995i	−0.783892	+	0.620897i	$0.786769\pi$
$942$		0			0
$943$	60.0000	−	60.0000i	1.95387	−	1.95387i
$944$		0			0
$945$	−9.00000	−	3.00000i	−0.292770	−	0.0975900i
$946$		0			0
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	29.0000	−	29.0000i	0.939402	−	0.939402i	−0.0588639	−	0.998266i	$-0.518748\pi$
$953$	29.0000	−	29.0000i	0.939402	−	0.939402i	0.998266	+	0.0588639i	$0.0187478\pi$
$954$		0			0
$955$	−12.0000	+	6.00000i	−0.388311	+	0.194155i
$956$		0			0
$957$	−10.0000			−0.323254
$958$		0			0
$959$	−30.0000			−0.968751
$960$		0			0
$961$	−5.00000			−0.161290
$962$		0			0
$963$	4.00000			0.128898
$964$		0			0
$965$	−13.0000	+	39.0000i	−0.418485	+	1.25545i
$966$		0			0
$967$	−15.0000	+	15.0000i	−0.482367	+	0.482367i	−0.905887	−	0.423520i	$-0.860795\pi$
$967$	−15.0000	+	15.0000i	−0.482367	+	0.482367i	0.423520	+	0.905887i	$0.360795\pi$
$968$		0			0
$969$	2.00000			0.0642493
$970$		0			0
$971$	−7.00000	−	7.00000i	−0.224641	−	0.224641i	0.585809	−	0.810449i	$-0.300777\pi$
$971$	−7.00000	−	7.00000i	−0.224641	−	0.224641i	−0.810449	+	0.585809i	$0.800777\pi$
$972$		0			0
$973$		−	30.0000i		−	0.961756i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.0000	−	17.0000i	0.543878	−	0.543878i	−0.380785	−	0.924663i	$-0.624346\pi$
$977$	17.0000	−	17.0000i	0.543878	−	0.543878i	0.924663	+	0.380785i	$0.124346\pi$
$978$		0			0
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$		0			0
$981$	7.00000	−	7.00000i	0.223493	−	0.223493i
$982$		0			0
$983$	−9.00000	−	9.00000i	−0.287055	−	0.287055i	0.548859	−	0.835915i	$-0.315062\pi$
$983$	−9.00000	−	9.00000i	−0.287055	−	0.287055i	−0.835915	+	0.548859i	$0.815062\pi$
$984$		0			0
$985$	48.0000	−	24.0000i	1.52941	−	0.764704i
$986$		0			0
$987$	−18.0000			−0.572946
$988$		0			0
$989$	−50.0000	+	50.0000i	−1.58991	+	1.58991i
$990$		0			0
$991$			22.0000i			0.698853i	0.936964	+	0.349427i	$0.113624\pi$
$991$			22.0000i			0.698853i	−0.936964	+	0.349427i	$0.886376\pi$
$992$		0			0
$993$	9.00000	+	9.00000i	0.285606	+	0.285606i
$994$		0			0
$995$	52.0000	−	26.0000i	1.64851	−	0.824255i
$996$		0			0
$997$		−	32.0000i		−	1.01345i	−0.862108	−	0.506725i	$-0.830856\pi$
$997$		−	32.0000i		−	1.01345i	0.862108	−	0.506725i	$-0.169144\pi$
$998$		0			0
$999$			4.00000i			0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.y.c.943.1		2
4.3	odd	2		240.2.y.c.163.1	✓	2
5.2	odd	4		960.2.bc.b.367.1		2
8.3	odd	2		1920.2.y.d.223.1		2
8.5	even	2		1920.2.y.a.223.1		2
12.11	even	2		720.2.z.a.163.1		2
16.3	odd	4		1920.2.bc.a.1183.1		2
16.5	even	4		240.2.bc.c.43.1	yes	2
16.11	odd	4		960.2.bc.b.463.1		2
16.13	even	4		1920.2.bc.f.1183.1		2
20.7	even	4		240.2.bc.c.67.1	yes	2
40.27	even	4		1920.2.bc.f.607.1		2
40.37	odd	4		1920.2.bc.a.607.1		2
48.5	odd	4		720.2.bd.b.523.1		2
60.47	odd	4		720.2.bd.b.307.1		2
80.27	even	4	inner	960.2.y.c.847.1		2
80.37	odd	4		240.2.y.c.187.1	yes	2
80.67	even	4		1920.2.y.a.1567.1		2
80.77	odd	4		1920.2.y.d.1567.1		2
240.197	even	4		720.2.z.a.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.c.163.1	✓	2	4.3	odd	2
240.2.y.c.187.1	yes	2	80.37	odd	4
240.2.bc.c.43.1	yes	2	16.5	even	4
240.2.bc.c.67.1	yes	2	20.7	even	4
720.2.z.a.163.1		2	12.11	even	2
720.2.z.a.667.1		2	240.197	even	4
720.2.bd.b.307.1		2	60.47	odd	4
720.2.bd.b.523.1		2	48.5	odd	4
960.2.y.c.847.1		2	80.27	even	4	inner
960.2.y.c.943.1		2	1.1	even	1	trivial
960.2.bc.b.367.1		2	5.2	odd	4
960.2.bc.b.463.1		2	16.11	odd	4
1920.2.y.a.223.1		2	8.5	even	2
1920.2.y.a.1567.1		2	80.67	even	4
1920.2.y.d.223.1		2	8.3	odd	2
1920.2.y.d.1567.1		2	80.77	odd	4
1920.2.bc.a.607.1		2	40.37	odd	4
1920.2.bc.a.1183.1		2	16.3	odd	4
1920.2.bc.f.607.1		2	40.27	even	4
1920.2.bc.f.1183.1		2	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(1.00000 + 2.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +(1.00000 + 1.00000i) q^{11} +(1.00000 + 2.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +(1.00000 + 1.00000i) q^{19} +(-3.00000 + 3.00000i) q^{21} +(-5.00000 - 5.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +1.00000 q^{27} +(-5.00000 + 5.00000i) q^{29} +6.00000i q^{31} +(1.00000 + 1.00000i) q^{33} +(-9.00000 - 3.00000i) q^{35} +4.00000i q^{37} +12.0000i q^{41} -10.0000i q^{43} +(1.00000 + 2.00000i) q^{45} +(3.00000 + 3.00000i) q^{47} -11.0000i q^{49} +(1.00000 - 1.00000i) q^{51} +6.00000 q^{53} +(-1.00000 + 3.00000i) q^{55} +(1.00000 + 1.00000i) q^{57} +(-5.00000 + 5.00000i) q^{59} +(-5.00000 - 5.00000i) q^{61} +(-3.00000 + 3.00000i) q^{63} -2.00000i q^{67} +(-5.00000 - 5.00000i) q^{69} +16.0000 q^{71} +(9.00000 - 9.00000i) q^{73} +(-3.00000 + 4.00000i) q^{75} -6.00000 q^{77} +16.0000 q^{79} +1.00000 q^{81} -4.00000 q^{83} +(3.00000 + 1.00000i) q^{85} +(-5.00000 + 5.00000i) q^{87} +6.00000 q^{89} +6.00000i q^{93} +(-1.00000 + 3.00000i) q^{95} +(1.00000 - 1.00000i) q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{5} - 6 q^{7} + 2 q^{9} + 2 q^{11} + 2 q^{15} + 2 q^{17} + 2 q^{19} - 6 q^{21} - 10 q^{23} - 6 q^{25} + 2 q^{27} - 10 q^{29} + 2 q^{33} - 18 q^{35} + 2 q^{45} + 6 q^{47} + 2 q^{51} + 12 q^{53}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^5 - 6 * q^7 + 2 * q^9 + 2 * q^11 + 2 * q^15 + 2 * q^17 + 2 * q^19 - 6 * q^21 - 10 * q^23 - 6 * q^25 + 2 * q^27 - 10 * q^29 + 2 * q^33 - 18 * q^35 + 2 * q^45 + 6 * q^47 + 2 * q^51 + 12 * q^53 - 2 * q^55 + 2 * q^57 - 10 * q^59 - 10 * q^61 - 6 * q^63 - 10 * q^69 + 32 * q^71 + 18 * q^73 - 6 * q^75 - 12 * q^77 + 32 * q^79 + 2 * q^81 - 8 * q^83 + 6 * q^85 - 10 * q^87 + 12 * q^89 - 2 * q^95 + 2 * q^97 + 2 * q^99

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