LMFDB - Embedded newform 591.1.d.a.590.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [591,1,Mod(590,591)] 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("591.590"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(591, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 591 = 3 \cdot 197 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	591.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$0.294947422466$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{11}$
Projective field:	Galois closure of 11.1.72100355223951.1

Embedding invariants

Embedding label			590.4
Root			$1.91899$ of defining polynomial
Character	$\chi$	$=$	591.590

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.830830 q^{2} +1.00000 q^{3} -0.309721 q^{4} +1.68251 q^{5} +0.830830 q^{6} -1.91899 q^{7} -1.08816 q^{8} +1.00000 q^{9} +1.39788 q^{10} -0.284630 q^{11} -0.309721 q^{12} -1.59435 q^{14} +1.68251 q^{15} -0.594351 q^{16} -1.30972 q^{17} +0.830830 q^{18} -0.284630 q^{19} -0.521109 q^{20} -1.91899 q^{21} -0.236479 q^{22} -1.08816 q^{24} +1.83083 q^{25} +1.00000 q^{27} +0.594351 q^{28} +1.39788 q^{30} +0.594351 q^{32} -0.284630 q^{33} -1.08816 q^{34} -3.22871 q^{35} -0.309721 q^{36} -1.30972 q^{37} -0.236479 q^{38} -1.83083 q^{40} -1.59435 q^{42} +0.830830 q^{43} +0.0881559 q^{44} +1.68251 q^{45} -0.594351 q^{48} +2.68251 q^{49} +1.52111 q^{50} -1.30972 q^{51} +0.830830 q^{54} -0.478891 q^{55} +2.08816 q^{56} -0.284630 q^{57} -0.521109 q^{60} +1.68251 q^{61} -1.91899 q^{63} +1.08816 q^{64} -0.236479 q^{66} +0.405649 q^{68} -2.68251 q^{70} -1.91899 q^{71} -1.08816 q^{72} -1.08816 q^{74} +1.83083 q^{75} +0.0881559 q^{76} +0.546200 q^{77} -1.00000 q^{80} +1.00000 q^{81} +0.594351 q^{84} -2.20362 q^{85} +0.690279 q^{86} +0.309721 q^{88} +0.830830 q^{89} +1.39788 q^{90} -0.478891 q^{95} +0.594351 q^{96} -1.30972 q^{97} +2.22871 q^{98} -0.284630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 5 q^{3} + 4 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} + 5 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 2 q^{14} - q^{15} + 3 q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - q^{21} - 2 q^{22}+ \cdots - q^{99}+O(q^{100}) $ 5 * q - q^2 + 5 * q^3 + 4 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 + 5 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 2 * q^14 - q^15 + 3 * q^16 - q^17 - q^18 - q^19 - 3 * q^20 - q^21 - 2 * q^22 - 2 * q^24 + 4 * q^25 + 5 * q^27 - 3 * q^28 - 2 * q^30 - 3 * q^32 - q^33 - 2 * q^34 - 2 * q^35 + 4 * q^36 - q^37 - 2 * q^38 - 4 * q^40 - 2 * q^42 - q^43 - 3 * q^44 - q^45 + 3 * q^48 + 4 * q^49 + 8 * q^50 - q^51 - q^54 - 2 * q^55 + 7 * q^56 - q^57 - 3 * q^60 - q^61 - q^63 + 2 * q^64 - 2 * q^66 + 8 * q^68 - 4 * q^70 - q^71 - 2 * q^72 - 2 * q^74 + 4 * q^75 - 3 * q^76 - 2 * q^77 - 5 * q^80 + 5 * q^81 - 3 * q^84 - 2 * q^85 + 9 * q^86 - 4 * q^88 - q^89 - 2 * q^90 - 2 * q^95 - 3 * q^96 - q^97 - 3 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/591\mathbb{Z}\right)^\times$.

$n$	$199$	$395$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$2$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$3$	1.00000	1.00000
$3$	1.00000	1.00000
$4$	−0.309721	−0.309721
$5$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$5$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$6$	0.830830	0.830830
$7$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$7$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$8$	−1.08816	−1.08816
$9$	1.00000	1.00000
$10$	1.39788	1.39788
$11$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$11$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$12$	−0.309721	−0.309721
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−1.59435	−1.59435
$15$	1.68251	1.68251
$16$	−0.594351	−0.594351
$17$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$17$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$18$	0.830830	0.830830
$19$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$19$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$20$	−0.521109	−0.521109
$21$	−1.91899	−1.91899
$22$	−0.236479	−0.236479
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−1.08816	−1.08816
$25$	1.83083	1.83083
$26$	0	0
$27$	1.00000	1.00000
$28$	0.594351	0.594351
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	1.39788	1.39788
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0.594351	0.594351
$33$	−0.284630	−0.284630
$34$	−1.08816	−1.08816
$35$	−3.22871	−3.22871
$36$	−0.309721	−0.309721
$37$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$37$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$38$	−0.236479	−0.236479
$39$	0	0
$40$	−1.83083	−1.83083
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	−1.59435	−1.59435
$43$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$43$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$44$	0.0881559	0.0881559
$45$	1.68251	1.68251
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−0.594351	−0.594351
$49$	2.68251	2.68251
$50$	1.52111	1.52111
$51$	−1.30972	−1.30972
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0.830830	0.830830
$55$	−0.478891	−0.478891
$56$	2.08816	2.08816
$57$	−0.284630	−0.284630
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−0.521109	−0.521109
$61$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$61$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$62$	0	0
$63$	−1.91899	−1.91899
$64$	1.08816	1.08816
$65$	0	0
$66$	−0.236479	−0.236479
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0.405649	0.405649
$69$	0	0
$70$	−2.68251	−2.68251
$71$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$71$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$72$	−1.08816	−1.08816
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−1.08816	−1.08816
$75$	1.83083	1.83083
$76$	0.0881559	0.0881559
$77$	0.546200	0.546200
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−1.00000	−1.00000
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0.594351	0.594351
$85$	−2.20362	−2.20362
$86$	0.690279	0.690279
$87$	0	0
$88$	0.309721	0.309721
$89$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$89$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$90$	1.39788	1.39788
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−0.478891	−0.478891
$96$	0.594351	0.594351
$97$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$97$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$98$	2.22871	2.22871
$99$	−0.284630	−0.284630
$100$	−0.567047	−0.567047
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−1.08816	−1.08816
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	−3.22871	−3.22871
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−0.309721	−0.309721
$109$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$109$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$110$	−0.397877	−0.397877
$111$	−1.30972	−1.30972
$112$	1.14055	1.14055
$113$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$113$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$114$	−0.236479	−0.236479
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	2.51334	2.51334
$120$	−1.83083	−1.83083
$121$	−0.918986	−0.918986
$122$	1.39788	1.39788
$123$	0	0
$124$	0	0
$125$	1.39788	1.39788
$126$	−1.59435	−1.59435
$127$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$127$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$128$	0.309721	0.309721
$129$	0.830830	0.830830
$130$	0	0
$131$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$131$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$132$	0.0881559	0.0881559
$133$	0.546200	0.546200
$134$	0	0
$135$	1.68251	1.68251
$136$	1.42518	1.42518
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	1.00000	1.00000
$141$	0	0
$142$	−1.59435	−1.59435
$143$	0	0
$144$	−0.594351	−0.594351
$145$	0	0
$146$	0	0
$147$	2.68251	2.68251
$148$	0.405649	0.405649
$149$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$149$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$150$	1.52111	1.52111
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0.309721	0.309721
$153$	−1.30972	−1.30972
$154$	0.453800	0.453800
$155$	0	0
$156$	0	0
$157$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$157$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$158$	0	0
$159$	0	0
$160$	1.00000	1.00000
$161$	0	0
$162$	0.830830	0.830830
$163$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$163$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$164$	0	0
$165$	−0.478891	−0.478891
$166$	0	0
$167$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$167$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$168$	2.08816	2.08816
$169$	1.00000	1.00000
$170$	−1.83083	−1.83083
$171$	−0.284630	−0.284630
$172$	−0.257326	−0.257326
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−3.51334	−3.51334
$176$	0.169170	0.169170
$177$	0	0
$178$	0.690279	0.690279
$179$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$179$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$180$	−0.521109	−0.521109
$181$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$181$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$182$	0	0
$183$	1.68251	1.68251
$184$	0	0
$185$	−2.20362	−2.20362
$186$	0	0
$187$	0.372786	0.372786
$188$	0	0
$189$	−1.91899	−1.91899
$190$	−0.397877	−0.397877
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	1.08816	1.08816
$193$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$193$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$194$	−1.08816	−1.08816
$195$	0	0
$196$	−0.830830	−0.830830
$197$	1.00000	1.00000
$197$	1.00000	1.00000
$198$	−0.236479	−0.236479
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.99223	−1.99223
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0.405649	0.405649
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0.0810141	0.0810141
$210$	−2.68251	−2.68251
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	−1.91899	−1.91899
$214$	0	0
$215$	1.39788	1.39788
$216$	−1.08816	−1.08816
$217$	0	0
$218$	0.690279	0.690279
$219$	0	0
$220$	0.148323	0.148323
$221$	0	0
$222$	−1.08816	−1.08816
$223$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$223$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$224$	−1.14055	−1.14055
$225$	1.83083	1.83083
$226$	−1.59435	−1.59435
$227$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$227$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$228$	0.0881559	0.0881559
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0.546200	0.546200
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	2.08816	2.08816
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−1.00000	−1.00000
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−0.763521	−0.763521
$243$	1.00000	1.00000
$244$	−0.521109	−0.521109
$245$	4.51334	4.51334
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	1.16140	1.16140
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0.594351	0.594351
$253$	0	0
$254$	−0.236479	−0.236479
$255$	−2.20362	−2.20362
$256$	−0.830830	−0.830830
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0.690279	0.690279
$259$	2.51334	2.51334
$260$	0	0
$261$	0	0
$262$	1.39788	1.39788
$263$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$263$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$264$	0.309721	0.309721
$265$	0	0
$266$	0.453800	0.453800
$267$	0.830830	0.830830
$268$	0	0
$269$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$269$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$270$	1.39788	1.39788
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0.778434	0.778434
$273$	0	0
$274$	0	0
$275$	−0.521109	−0.521109
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	3.51334	3.51334
$281$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0.594351	0.594351
$285$	−0.478891	−0.478891
$286$	0	0
$287$	0	0
$288$	0.594351	0.594351
$289$	0.715370	0.715370
$290$	0	0
$291$	−1.30972	−1.30972
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	2.22871	2.22871
$295$	0	0
$296$	1.42518	1.42518
$297$	−0.284630	−0.284630
$298$	−1.08816	−1.08816
$299$	0	0
$300$	−0.567047	−0.567047
$301$	−1.59435	−1.59435
$302$	0	0
$303$	0	0
$304$	0.169170	0.169170
$305$	2.83083	2.83083
$306$	−1.08816	−1.08816
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	−0.169170	−0.169170
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$313$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$314$	1.39788	1.39788
$315$	−3.22871	−3.22871
$316$	0	0
$317$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$317$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$318$	0	0
$319$	0	0
$320$	1.83083	1.83083
$321$	0	0
$322$	0	0
$323$	0.372786	0.372786
$324$	−0.309721	−0.309721
$325$	0	0
$326$	1.39788	1.39788
$327$	0.830830	0.830830
$328$	0	0
$329$	0	0
$330$	−0.397877	−0.397877
$331$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$331$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$332$	0	0
$333$	−1.30972	−1.30972
$334$	−1.59435	−1.59435
$335$	0	0
$336$	1.14055	1.14055
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0.830830	0.830830
$339$	−1.91899	−1.91899
$340$	0.682507	0.682507
$341$	0	0
$342$	−0.236479	−0.236479
$343$	−3.22871	−3.22871
$344$	−0.904073	−0.904073
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−2.91899	−2.91899
$351$	0	0
$352$	−0.169170	−0.169170
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	−3.22871	−3.22871
$356$	−0.257326	−0.257326
$357$	2.51334	2.51334
$358$	0.690279	0.690279
$359$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$359$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$360$	−1.83083	−1.83083
$361$	−0.918986	−0.918986
$362$	−1.59435	−1.59435
$363$	−0.918986	−0.918986
$364$	0	0
$365$	0	0
$366$	1.39788	1.39788
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	−1.83083	−1.83083
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0.309721	0.309721
$375$	1.39788	1.39788
$376$	0	0
$377$	0	0
$378$	−1.59435	−1.59435
$379$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$379$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$380$	0.148323	0.148323
$381$	−0.284630	−0.284630
$382$	0	0
$383$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$383$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$384$	0.309721	0.309721
$385$	0.918986	0.918986
$386$	1.39788	1.39788
$387$	0.830830	0.830830
$388$	0.405649	0.405649
$389$	2.00000	2.00000	1.00000			$0$
$389$	2.00000	2.00000	1.00000			$0$
$390$	0	0
$391$	0	0
$392$	−2.91899	−2.91899
$393$	1.68251	1.68251
$394$	0.830830	0.830830
$395$	0	0
$396$	0.0881559	0.0881559
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0.546200	0.546200
$400$	−1.08816	−1.08816
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	1.68251	1.68251
$406$	0	0
$407$	0.372786	0.372786
$408$	1.42518	1.42518
$409$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$409$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0.0673089	0.0673089
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	1.00000	1.00000
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−2.39788	−2.39788
$426$	−1.59435	−1.59435
$427$	−3.22871	−3.22871
$428$	0	0
$429$	0	0
$430$	1.16140	1.16140
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−0.594351	−0.594351
$433$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$433$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$434$	0	0
$435$	0	0
$436$	−0.257326	−0.257326
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0.521109	0.521109
$441$	2.68251	2.68251
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0.405649	0.405649
$445$	1.39788	1.39788
$446$	0.690279	0.690279
$447$	−1.30972	−1.30972
$448$	−2.08816	−2.08816
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	1.52111	1.52111
$451$	0	0
$452$	0.594351	0.594351
$453$	0	0
$454$	0.690279	0.690279
$455$	0	0
$456$	0.309721	0.309721
$457$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$457$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$458$	0	0
$459$	−1.30972	−1.30972
$460$	0	0
$461$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$461$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$462$	0.453800	0.453800
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$467$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	1.68251	1.68251
$472$	0	0
$473$	−0.236479	−0.236479
$474$	0	0
$475$	−0.521109	−0.521109
$476$	−0.778434	−0.778434
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	1.00000	1.00000
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0.284630	0.284630
$485$	−2.20362	−2.20362
$486$	0.830830	0.830830
$487$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$487$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$488$	−1.83083	−1.83083
$489$	1.68251	1.68251
$490$	3.74982	3.74982
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−0.478891	−0.478891
$496$	0	0
$497$	3.68251	3.68251
$498$	0	0
$499$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$499$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$500$	−0.432953	−0.432953
$501$	−1.91899	−1.91899
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	2.08816	2.08816
$505$	0	0
$506$	0	0
$507$	1.00000	1.00000
$508$	0.0881559	0.0881559
$509$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$509$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$510$	−1.83083	−1.83083
$511$	0	0
$512$	−1.00000	−1.00000
$513$	−0.284630	−0.284630
$514$	0	0
$515$	0	0
$516$	−0.257326	−0.257326
$517$	0	0
$518$	2.08816	2.08816
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	−0.521109	−0.521109
$525$	−3.51334	−3.51334
$526$	−0.236479	−0.236479
$527$	0	0
$528$	0.169170	0.169170
$529$	1.00000	1.00000
$530$	0	0
$531$	0	0
$532$	−0.169170	−0.169170
$533$	0	0
$534$	0.690279	0.690279
$535$	0	0
$536$	0	0
$537$	0.830830	0.830830
$538$	−1.08816	−1.08816
$539$	−0.763521	−0.763521
$540$	−0.521109	−0.521109
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	−1.91899	−1.91899
$544$	−0.778434	−0.778434
$545$	1.39788	1.39788
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	1.68251	1.68251
$550$	−0.432953	−0.432953
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−2.20362	−2.20362
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	1.91899	1.91899
$561$	0.372786	0.372786
$562$	−0.236479	−0.236479
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	−3.22871	−3.22871
$566$	0	0
$567$	−1.91899	−1.91899
$568$	2.08816	2.08816
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	−0.397877	−0.397877
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.08816	1.08816
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0.594351	0.594351
$579$	1.68251	1.68251
$580$	0	0
$581$	0	0
$582$	−1.08816	−1.08816
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−0.830830	−0.830830
$589$	0	0
$590$	0	0
$591$	1.00000	1.00000
$592$	0.778434	0.778434
$593$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$593$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$594$	−0.236479	−0.236479
$595$	4.22871	4.22871
$596$	0.405649	0.405649
$597$	0	0
$598$	0	0
$599$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$599$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$600$	−1.99223	−1.99223
$601$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$601$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$602$	−1.32463	−1.32463
$603$	0	0
$604$	0	0
$605$	−1.54620	−1.54620
$606$	0	0
$607$	2.00000	2.00000	1.00000			$0$
$607$	2.00000	2.00000	1.00000			$0$
$608$	−0.169170	−0.169170
$609$	0	0
$610$	2.35194	2.35194
$611$	0	0
$612$	0.405649	0.405649
$613$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$613$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$614$	0	0
$615$	0	0
$616$	−0.594351	−0.594351
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$619$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−1.59435	−1.59435
$624$	0	0
$625$	0.521109	0.521109
$626$	−1.59435	−1.59435
$627$	0.0810141	0.0810141
$628$	−0.521109	−0.521109
$629$	1.71537	1.71537
$630$	−2.68251	−2.68251
$631$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$631$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$632$	0	0
$633$	0	0
$634$	−1.08816	−1.08816
$635$	−0.478891	−0.478891
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−1.91899	−1.91899
$640$	0.521109	0.521109
$641$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$641$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	1.39788	1.39788
$646$	0.309721	0.309721
$647$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$647$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$648$	−1.08816	−1.08816
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−0.521109	−0.521109
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0.690279	0.690279
$655$	2.83083	2.83083
$656$	0	0
$657$	0	0
$658$	0	0
$659$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$659$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$660$	0.148323	0.148323
$661$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$661$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$662$	1.39788	1.39788
$663$	0	0
$664$	0	0
$665$	0.918986	0.918986
$666$	−1.08816	−1.08816
$667$	0	0
$668$	0.594351	0.594351
$669$	0.830830	0.830830
$670$	0	0
$671$	−0.478891	−0.478891
$672$	−1.14055	−1.14055
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.83083	1.83083
$676$	−0.309721	−0.309721
$677$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$677$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$678$	−1.59435	−1.59435
$679$	2.51334	2.51334
$680$	2.39788	2.39788
$681$	0.830830	0.830830
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0.0881559	0.0881559
$685$	0	0
$686$	−2.68251	−2.68251
$687$	0	0
$688$	−0.493805	−0.493805
$689$	0	0
$690$	0	0
$691$	2.00000	2.00000	1.00000			$0$
$691$	2.00000	2.00000	1.00000			$0$
$692$	0	0
$693$	0.546200	0.546200
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	1.08816	1.08816
$701$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$701$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$702$	0	0
$703$	0.372786	0.372786
$704$	−0.309721	−0.309721
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	−2.68251	−2.68251
$711$	0	0
$712$	−0.904073	−0.904073
$713$	0	0
$714$	2.08816	2.08816
$715$	0	0
$716$	−0.257326	−0.257326
$717$	0	0
$718$	−1.08816	−1.08816
$719$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$719$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$720$	−1.00000	−1.00000
$721$	0	0
$722$	−0.763521	−0.763521
$723$	0	0
$724$	0.594351	0.594351
$725$	0	0
$726$	−0.763521	−0.763521
$727$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$727$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	−1.08816	−1.08816
$732$	−0.521109	−0.521109
$733$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$733$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$734$	0	0
$735$	4.51334	4.51334
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$739$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$740$	0.682507	0.682507
$741$	0	0
$742$	0	0
$743$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$743$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$744$	0	0
$745$	−2.20362	−2.20362
$746$	0	0
$747$	0	0
$748$	−0.115460	−0.115460
$749$	0	0
$750$	1.16140	1.16140
$751$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$751$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0.594351	0.594351
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−1.59435	−1.59435
$759$	0	0
$760$	0.521109	0.521109
$761$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$761$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$762$	−0.236479	−0.236479
$763$	−1.59435	−1.59435
$764$	0	0
$765$	−2.20362	−2.20362
$766$	−0.236479	−0.236479
$767$	0	0
$768$	−0.830830	−0.830830
$769$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$769$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$770$	0.763521	0.763521
$771$	0	0
$772$	−0.521109	−0.521109
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0.690279	0.690279
$775$	0	0
$776$	1.42518	1.42518
$777$	2.51334	2.51334
$778$	1.66166	1.66166
$779$	0	0
$780$	0	0
$781$	0.546200	0.546200
$782$	0	0
$783$	0	0
$784$	−1.59435	−1.59435
$785$	2.83083	2.83083
$786$	1.39788	1.39788
$787$	2.00000	2.00000	1.00000			$0$
$787$	2.00000	2.00000	1.00000			$0$
$788$	−0.309721	−0.309721
$789$	−0.284630	−0.284630
$790$	0	0
$791$	3.68251	3.68251
$792$	0.309721	0.309721
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0.453800	0.453800
$799$	0	0
$800$	1.08816	1.08816
$801$	0.830830	0.830830
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−1.30972	−1.30972
$808$	0	0
$809$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$809$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$810$	1.39788	1.39788
$811$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$811$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$812$	0	0
$813$	0	0
$814$	0.309721	0.309721
$815$	2.83083	2.83083
$816$	0.778434	0.778434
$817$	−0.236479	−0.236479
$818$	−1.08816	−1.08816
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−0.521109	−0.521109
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$829$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−3.51334	−3.51334
$834$	0	0
$835$	−3.22871	−3.22871
$836$	−0.0250918	−0.0250918
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	3.51334	3.51334
$841$	1.00000	1.00000
$842$	0	0
$843$	−0.284630	−0.284630
$844$	0	0
$845$	1.68251	1.68251
$846$	0	0
$847$	1.76352	1.76352
$848$	0	0
$849$	0	0
$850$	−1.99223	−1.99223
$851$	0	0
$852$	0.594351	0.594351
$853$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$853$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$854$	−2.68251	−2.68251
$855$	−0.478891	−0.478891
$856$	0	0
$857$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$857$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	−0.432953	−0.432953
$861$	0	0
$862$	0	0
$863$	2.00000	2.00000	1.00000			$0$
$863$	2.00000	2.00000	1.00000			$0$
$864$	0.594351	0.594351
$865$	0	0
$866$	0.690279	0.690279
$867$	0.715370	0.715370
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−0.904073	−0.904073
$873$	−1.30972	−1.30972
$874$	0	0
$875$	−2.68251	−2.68251
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0.284630	0.284630
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	2.22871	2.22871
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$887$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$888$	1.42518	1.42518
$889$	0.546200	0.546200
$890$	1.16140	1.16140
$891$	−0.284630	−0.284630
$892$	−0.257326	−0.257326
$893$	0	0
$894$	−1.08816	−1.08816
$895$	1.39788	1.39788
$896$	−0.594351	−0.594351
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−0.567047	−0.567047
$901$	0	0
$902$	0	0
$903$	−1.59435	−1.59435
$904$	2.08816	2.08816
$905$	−3.22871	−3.22871
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	−0.257326	−0.257326
$909$	0	0
$910$	0	0
$911$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$911$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$912$	0.169170	0.169170
$913$	0	0
$914$	−0.236479	−0.236479
$915$	2.83083	2.83083
$916$	0	0
$917$	−3.22871	−3.22871
$918$	−1.08816	−1.08816
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	−1.59435	−1.59435
$923$	0	0
$924$	−0.169170	−0.169170
$925$	−2.39788	−2.39788
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$929$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$930$	0	0
$931$	−0.763521	−0.763521
$932$	0	0
$933$	0	0
$934$	−1.59435	−1.59435
$935$	0.627214	0.627214
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	−1.91899	−1.91899
$940$	0	0
$941$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$941$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$942$	1.39788	1.39788
$943$	0	0
$944$	0	0
$945$	−3.22871	−3.22871
$946$	−0.196474	−0.196474
$947$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$947$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$948$	0	0
$949$	0	0
$950$	−0.432953	−0.432953
$951$	−1.30972	−1.30972
$952$	−2.73490	−2.73490
$953$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$953$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	1.83083	1.83083
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	2.83083	2.83083
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	1.00000	1.00000
$969$	0.372786	0.372786
$970$	−1.83083	−1.83083
$971$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$971$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$972$	−0.309721	−0.309721
$973$	0	0
$974$	−0.236479	−0.236479
$975$	0	0
$976$	−1.00000	−1.00000
$977$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$977$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$978$	1.39788	1.39788
$979$	−0.236479	−0.236479
$980$	−1.39788	−1.39788
$981$	0.830830	0.830830
$982$	0	0
$983$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$983$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$984$	0	0
$985$	1.68251	1.68251
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	−0.397877	−0.397877
$991$	2.00000	2.00000	1.00000			$0$
$991$	2.00000	2.00000	1.00000			$0$
$992$	0	0
$993$	1.68251	1.68251
$994$	3.05954	3.05954
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	−0.236479	−0.236479
$999$	−1.30972	−1.30972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	591.1.d.a.590.4	✓	5
3.2	odd	2		591.1.d.b.590.2	yes	5
197.196	even	2		591.1.d.b.590.2	yes	5
591.590	odd	2	CM	591.1.d.a.590.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
591.1.d.a.590.4	✓	5	1.1	even	1	trivial
591.1.d.a.590.4	✓	5	591.590	odd	2	CM
591.1.d.b.590.2	yes	5	3.2	odd	2
591.1.d.b.590.2	yes	5	197.196	even	2

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:	\( N \)	\(=\)	\( 591 = 3 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	591.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.830830 q^{2} +1.00000 q^{3} -0.309721 q^{4} +1.68251 q^{5} +0.830830 q^{6} -1.91899 q^{7} -1.08816 q^{8} +1.00000 q^{9} +1.39788 q^{10} -0.284630 q^{11} -0.309721 q^{12} -1.59435 q^{14} +1.68251 q^{15} -0.594351 q^{16} -1.30972 q^{17} +0.830830 q^{18} -0.284630 q^{19} -0.521109 q^{20} -1.91899 q^{21} -0.236479 q^{22} -1.08816 q^{24} +1.83083 q^{25} +1.00000 q^{27} +0.594351 q^{28} +1.39788 q^{30} +0.594351 q^{32} -0.284630 q^{33} -1.08816 q^{34} -3.22871 q^{35} -0.309721 q^{36} -1.30972 q^{37} -0.236479 q^{38} -1.83083 q^{40} -1.59435 q^{42} +0.830830 q^{43} +0.0881559 q^{44} +1.68251 q^{45} -0.594351 q^{48} +2.68251 q^{49} +1.52111 q^{50} -1.30972 q^{51} +0.830830 q^{54} -0.478891 q^{55} +2.08816 q^{56} -0.284630 q^{57} -0.521109 q^{60} +1.68251 q^{61} -1.91899 q^{63} +1.08816 q^{64} -0.236479 q^{66} +0.405649 q^{68} -2.68251 q^{70} -1.91899 q^{71} -1.08816 q^{72} -1.08816 q^{74} +1.83083 q^{75} +0.0881559 q^{76} +0.546200 q^{77} -1.00000 q^{80} +1.00000 q^{81} +0.594351 q^{84} -2.20362 q^{85} +0.690279 q^{86} +0.309721 q^{88} +0.830830 q^{89} +1.39788 q^{90} -0.478891 q^{95} +0.594351 q^{96} -1.30972 q^{97} +2.22871 q^{98} -0.284630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 5 q^{3} + 4 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} + 5 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 2 q^{14} - q^{15} + 3 q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - q^{21} - 2 q^{22}+ \cdots - q^{99}+O(q^{100}) \) 5 * q - q^2 + 5 * q^3 + 4 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 + 5 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 2 * q^14 - q^15 + 3 * q^16 - q^17 - q^18 - q^19 - 3 * q^20 - q^21 - 2 * q^22 - 2 * q^24 + 4 * q^25 + 5 * q^27 - 3 * q^28 - 2 * q^30 - 3 * q^32 - q^33 - 2 * q^34 - 2 * q^35 + 4 * q^36 - q^37 - 2 * q^38 - 4 * q^40 - 2 * q^42 - q^43 - 3 * q^44 - q^45 + 3 * q^48 + 4 * q^49 + 8 * q^50 - q^51 - q^54 - 2 * q^55 + 7 * q^56 - q^57 - 3 * q^60 - q^61 - q^63 + 2 * q^64 - 2 * q^66 + 8 * q^68 - 4 * q^70 - q^71 - 2 * q^72 - 2 * q^74 + 4 * q^75 - 3 * q^76 - 2 * q^77 - 5 * q^80 + 5 * q^81 - 3 * q^84 - 2 * q^85 + 9 * q^86 - 4 * q^88 - q^89 - 2 * q^90 - 2 * q^95 - 3 * q^96 - q^97 - 3 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more