LMFDB - Embedded newform 591.1.d.b.590.5

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			590.5
Root			$-1.68251$ 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)

$f(q)$	$=$	\(q+1.91899 q^{2} -1.00000 q^{3} +2.68251 q^{4} +0.284630 q^{5} -1.91899 q^{6} -1.30972 q^{7} +3.22871 q^{8} +1.00000 q^{9} +0.546200 q^{10} -0.830830 q^{11} -2.68251 q^{12} -2.51334 q^{14} -0.284630 q^{15} +3.51334 q^{16} -1.68251 q^{17} +1.91899 q^{18} +0.830830 q^{19} +0.763521 q^{20} +1.30972 q^{21} -1.59435 q^{22} -3.22871 q^{24} -0.918986 q^{25} -1.00000 q^{27} -3.51334 q^{28} -0.546200 q^{30} +3.51334 q^{32} +0.830830 q^{33} -3.22871 q^{34} -0.372786 q^{35} +2.68251 q^{36} +1.68251 q^{37} +1.59435 q^{38} +0.918986 q^{40} +2.51334 q^{42} -1.91899 q^{43} -2.22871 q^{44} +0.284630 q^{45} -3.51334 q^{48} +0.715370 q^{49} -1.76352 q^{50} +1.68251 q^{51} -1.91899 q^{54} -0.236479 q^{55} -4.22871 q^{56} -0.830830 q^{57} -0.763521 q^{60} -0.284630 q^{61} -1.30972 q^{63} +3.22871 q^{64} +1.59435 q^{66} -4.51334 q^{68} -0.715370 q^{70} +1.30972 q^{71} +3.22871 q^{72} +3.22871 q^{74} +0.918986 q^{75} +2.22871 q^{76} +1.08816 q^{77} +1.00000 q^{80} +1.00000 q^{81} +3.51334 q^{84} -0.478891 q^{85} -3.68251 q^{86} -2.68251 q^{88} +1.91899 q^{89} +0.546200 q^{90} +0.236479 q^{95} -3.51334 q^{96} +1.68251 q^{97} +1.37279 q^{98} -0.830830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$2$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$3$	−1.00000	−1.00000
$3$	−1.00000	−1.00000
$4$	2.68251	2.68251
$5$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$5$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$6$	−1.91899	−1.91899
$7$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$7$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$8$	3.22871	3.22871
$9$	1.00000	1.00000
$10$	0.546200	0.546200
$11$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$11$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$12$	−2.68251	−2.68251
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−2.51334	−2.51334
$15$	−0.284630	−0.284630
$16$	3.51334	3.51334
$17$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$17$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$18$	1.91899	1.91899
$19$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$19$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$20$	0.763521	0.763521
$21$	1.30972	1.30972
$22$	−1.59435	−1.59435
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−3.22871	−3.22871
$25$	−0.918986	−0.918986
$26$	0	0
$27$	−1.00000	−1.00000
$28$	−3.51334	−3.51334
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	−0.546200	−0.546200
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	3.51334	3.51334
$33$	0.830830	0.830830
$34$	−3.22871	−3.22871
$35$	−0.372786	−0.372786
$36$	2.68251	2.68251
$37$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$37$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$38$	1.59435	1.59435
$39$	0	0
$40$	0.918986	0.918986
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	2.51334	2.51334
$43$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$43$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$44$	−2.22871	−2.22871
$45$	0.284630	0.284630
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−3.51334	−3.51334
$49$	0.715370	0.715370
$50$	−1.76352	−1.76352
$51$	1.68251	1.68251
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−1.91899	−1.91899
$55$	−0.236479	−0.236479
$56$	−4.22871	−4.22871
$57$	−0.830830	−0.830830
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−0.763521	−0.763521
$61$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$61$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$62$	0	0
$63$	−1.30972	−1.30972
$64$	3.22871	3.22871
$65$	0	0
$66$	1.59435	1.59435
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−4.51334	−4.51334
$69$	0	0
$70$	−0.715370	−0.715370
$71$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$71$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$72$	3.22871	3.22871
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	3.22871	3.22871
$75$	0.918986	0.918986
$76$	2.22871	2.22871
$77$	1.08816	1.08816
$78$	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			$\pi$
$84$	3.51334	3.51334
$85$	−0.478891	−0.478891
$86$	−3.68251	−3.68251
$87$	0	0
$88$	−2.68251	−2.68251
$89$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$89$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$90$	0.546200	0.546200
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0.236479	0.236479
$96$	−3.51334	−3.51334
$97$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$97$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$98$	1.37279	1.37279
$99$	−0.830830	−0.830830
$100$	−2.46519	−2.46519
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	3.22871	3.22871
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0.372786	0.372786
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−2.68251	−2.68251
$109$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$109$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$110$	−0.453800	−0.453800
$111$	−1.68251	−1.68251
$112$	−4.60149	−4.60149
$113$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$113$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$114$	−1.59435	−1.59435
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	2.20362	2.20362
$120$	−0.918986	−0.918986
$121$	−0.309721	−0.309721
$122$	−0.546200	−0.546200
$123$	0	0
$124$	0	0
$125$	−0.546200	−0.546200
$126$	−2.51334	−2.51334
$127$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$127$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$128$	2.68251	2.68251
$129$	1.91899	1.91899
$130$	0	0
$131$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$131$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$132$	2.22871	2.22871
$133$	−1.08816	−1.08816
$134$	0	0
$135$	−0.284630	−0.284630
$136$	−5.43232	−5.43232
$137$	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
$142$	2.51334	2.51334
$143$	0	0
$144$	3.51334	3.51334
$145$	0	0
$146$	0	0
$147$	−0.715370	−0.715370
$148$	4.51334	4.51334
$149$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$149$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$150$	1.76352	1.76352
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	2.68251	2.68251
$153$	−1.68251	−1.68251
$154$	2.08816	2.08816
$155$	0	0
$156$	0	0
$157$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$157$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$158$	0	0
$159$	0	0
$160$	1.00000	1.00000
$161$	0	0
$162$	1.91899	1.91899
$163$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$163$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$164$	0	0
$165$	0.236479	0.236479
$166$	0	0
$167$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$167$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$168$	4.22871	4.22871
$169$	1.00000	1.00000
$170$	−0.918986	−0.918986
$171$	0.830830	0.830830
$172$	−5.14769	−5.14769
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	1.20362	1.20362
$176$	−2.91899	−2.91899
$177$	0	0
$178$	3.68251	3.68251
$179$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$179$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$180$	0.763521	0.763521
$181$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$181$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$182$	0	0
$183$	0.284630	0.284630
$184$	0	0
$185$	0.478891	0.478891
$186$	0	0
$187$	1.39788	1.39788
$188$	0	0
$189$	1.30972	1.30972
$190$	0.453800	0.453800
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−3.22871	−3.22871
$193$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$193$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$194$	3.22871	3.22871
$195$	0	0
$196$	1.91899	1.91899
$197$	−1.00000	−1.00000
$197$	−1.00000	−1.00000
$198$	−1.59435	−1.59435
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−2.96714	−2.96714
$201$	0	0
$202$	0	0
$203$	0	0
$204$	4.51334	4.51334
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−0.690279	−0.690279
$210$	0.715370	0.715370
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	−1.30972	−1.30972
$214$	0	0
$215$	−0.546200	−0.546200
$216$	−3.22871	−3.22871
$217$	0	0
$218$	−3.68251	−3.68251
$219$	0	0
$220$	−0.634356	−0.634356
$221$	0	0
$222$	−3.22871	−3.22871
$223$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$224$	−4.60149	−4.60149
$225$	−0.918986	−0.918986
$226$	2.51334	2.51334
$227$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$227$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$228$	−2.22871	−2.22871
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−1.08816	−1.08816
$232$	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
$238$	4.22871	4.22871
$239$	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			$\pi$
$242$	−0.594351	−0.594351
$243$	−1.00000	−1.00000
$244$	−0.763521	−0.763521
$245$	0.203616	0.203616
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	−1.04815	−1.04815
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−3.51334	−3.51334
$253$	0	0
$254$	1.59435	1.59435
$255$	0.478891	0.478891
$256$	1.91899	1.91899
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	3.68251	3.68251
$259$	−2.20362	−2.20362
$260$	0	0
$261$	0	0
$262$	0.546200	0.546200
$263$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$263$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$264$	2.68251	2.68251
$265$	0	0
$266$	−2.08816	−2.08816
$267$	−1.91899	−1.91899
$268$	0	0
$269$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$269$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$270$	−0.546200	−0.546200
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−5.91121	−5.91121
$273$	0	0
$274$	0	0
$275$	0.763521	0.763521
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	−1.20362	−1.20362
$281$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$281$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	3.51334	3.51334
$285$	−0.236479	−0.236479
$286$	0	0
$287$	0	0
$288$	3.51334	3.51334
$289$	1.83083	1.83083
$290$	0	0
$291$	−1.68251	−1.68251
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	−1.37279	−1.37279
$295$	0	0
$296$	5.43232	5.43232
$297$	0.830830	0.830830
$298$	−3.22871	−3.22871
$299$	0	0
$300$	2.46519	2.46519
$301$	2.51334	2.51334
$302$	0	0
$303$	0	0
$304$	2.91899	2.91899
$305$	−0.0810141	−0.0810141
$306$	−3.22871	−3.22871
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	2.91899	2.91899
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$313$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$314$	−0.546200	−0.546200
$315$	−0.372786	−0.372786
$316$	0	0
$317$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$317$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$318$	0	0
$319$	0	0
$320$	0.918986	0.918986
$321$	0	0
$322$	0	0
$323$	−1.39788	−1.39788
$324$	2.68251	2.68251
$325$	0	0
$326$	−0.546200	−0.546200
$327$	1.91899	1.91899
$328$	0	0
$329$	0	0
$330$	0.453800	0.453800
$331$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$331$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$332$	0	0
$333$	1.68251	1.68251
$334$	2.51334	2.51334
$335$	0	0
$336$	4.60149	4.60149
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	1.91899	1.91899
$339$	−1.30972	−1.30972
$340$	−1.28463	−1.28463
$341$	0	0
$342$	1.59435	1.59435
$343$	0.372786	0.372786
$344$	−6.19584	−6.19584
$345$	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			$\pi$
$350$	2.30972	2.30972
$351$	0	0
$352$	−2.91899	−2.91899
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0.372786	0.372786
$356$	5.14769	5.14769
$357$	−2.20362	−2.20362
$358$	3.68251	3.68251
$359$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$359$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$360$	0.918986	0.918986
$361$	−0.309721	−0.309721
$362$	−2.51334	−2.51334
$363$	0.309721	0.309721
$364$	0	0
$365$	0	0
$366$	0.546200	0.546200
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0.918986	0.918986
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	2.68251	2.68251
$375$	0.546200	0.546200
$376$	0	0
$377$	0	0
$378$	2.51334	2.51334
$379$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$379$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$380$	0.634356	0.634356
$381$	−0.830830	−0.830830
$382$	0	0
$383$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$383$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$384$	−2.68251	−2.68251
$385$	0.309721	0.309721
$386$	−0.546200	−0.546200
$387$	−1.91899	−1.91899
$388$	4.51334	4.51334
$389$	−2.00000	−2.00000	−1.00000			$\pi$
$389$	−2.00000	−2.00000	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	2.30972	2.30972
$393$	−0.284630	−0.284630
$394$	−1.91899	−1.91899
$395$	0	0
$396$	−2.22871	−2.22871
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	1.08816	1.08816
$400$	−3.22871	−3.22871
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0.284630	0.284630
$406$	0	0
$407$	−1.39788	−1.39788
$408$	5.43232	5.43232
$409$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$409$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	−1.32463	−1.32463
$419$	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
$425$	1.54620	1.54620
$426$	−2.51334	−2.51334
$427$	0.372786	0.372786
$428$	0	0
$429$	0	0
$430$	−1.04815	−1.04815
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−3.51334	−3.51334
$433$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$433$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$434$	0	0
$435$	0	0
$436$	−5.14769	−5.14769
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	−0.763521	−0.763521
$441$	0.715370	0.715370
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	−4.51334	−4.51334
$445$	0.546200	0.546200
$446$	−3.68251	−3.68251
$447$	1.68251	1.68251
$448$	−4.22871	−4.22871
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−1.76352	−1.76352
$451$	0	0
$452$	3.51334	3.51334
$453$	0	0
$454$	3.68251	3.68251
$455$	0	0
$456$	−2.68251	−2.68251
$457$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$457$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$458$	0	0
$459$	1.68251	1.68251
$460$	0	0
$461$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$461$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$462$	−2.08816	−2.08816
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$467$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0.284630	0.284630
$472$	0	0
$473$	1.59435	1.59435
$474$	0	0
$475$	−0.763521	−0.763521
$476$	5.91121	5.91121
$477$	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
$484$	−0.830830	−0.830830
$485$	0.478891	0.478891
$486$	−1.91899	−1.91899
$487$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$487$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$488$	−0.918986	−0.918986
$489$	0.284630	0.284630
$490$	0.390736	0.390736
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−0.236479	−0.236479
$496$	0	0
$497$	−1.71537	−1.71537
$498$	0	0
$499$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$499$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$500$	−1.46519	−1.46519
$501$	−1.30972	−1.30972
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	−4.22871	−4.22871
$505$	0	0
$506$	0	0
$507$	−1.00000	−1.00000
$508$	2.22871	2.22871
$509$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$509$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$510$	0.918986	0.918986
$511$	0	0
$512$	1.00000	1.00000
$513$	−0.830830	−0.830830
$514$	0	0
$515$	0	0
$516$	5.14769	5.14769
$517$	0	0
$518$	−4.22871	−4.22871
$519$	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			$\pi$
$524$	0.763521	0.763521
$525$	−1.20362	−1.20362
$526$	−1.59435	−1.59435
$527$	0	0
$528$	2.91899	2.91899
$529$	1.00000	1.00000
$530$	0	0
$531$	0	0
$532$	−2.91899	−2.91899
$533$	0	0
$534$	−3.68251	−3.68251
$535$	0	0
$536$	0	0
$537$	−1.91899	−1.91899
$538$	−3.22871	−3.22871
$539$	−0.594351	−0.594351
$540$	−0.763521	−0.763521
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	1.30972	1.30972
$544$	−5.91121	−5.91121
$545$	−0.546200	−0.546200
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	−0.284630	−0.284630
$550$	1.46519	1.46519
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−0.478891	−0.478891
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−1.30972	−1.30972
$561$	−1.39788	−1.39788
$562$	−1.59435	−1.59435
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0.372786	0.372786
$566$	0	0
$567$	−1.30972	−1.30972
$568$	4.22871	4.22871
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	−0.453800	−0.453800
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	3.22871	3.22871
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	3.51334	3.51334
$579$	0.284630	0.284630
$580$	0	0
$581$	0	0
$582$	−3.22871	−3.22871
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−1.91899	−1.91899
$589$	0	0
$590$	0	0
$591$	1.00000	1.00000
$592$	5.91121	5.91121
$593$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$593$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$594$	1.59435	1.59435
$595$	0.627214	0.627214
$596$	−4.51334	−4.51334
$597$	0	0
$598$	0	0
$599$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$599$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$600$	2.96714	2.96714
$601$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$601$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$602$	4.82306	4.82306
$603$	0	0
$604$	0	0
$605$	−0.0881559	−0.0881559
$606$	0	0
$607$	2.00000	2.00000	1.00000			$0$
$607$	2.00000	2.00000	1.00000			$0$
$608$	2.91899	2.91899
$609$	0	0
$610$	−0.155465	−0.155465
$611$	0	0
$612$	−4.51334	−4.51334
$613$	1.68251	1.68251	0.841254	−	0.540641i	$-0.181818\pi$
$613$	1.68251	1.68251	0.841254	+	0.540641i	$0.181818\pi$
$614$	0	0
$615$	0	0
$616$	3.51334	3.51334
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$619$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−2.51334	−2.51334
$624$	0	0
$625$	0.763521	0.763521
$626$	−2.51334	−2.51334
$627$	0.690279	0.690279
$628$	−0.763521	−0.763521
$629$	−2.83083	−2.83083
$630$	−0.715370	−0.715370
$631$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$631$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$632$	0	0
$633$	0	0
$634$	−3.22871	−3.22871
$635$	0.236479	0.236479
$636$	0	0
$637$	0	0
$638$	0	0
$639$	1.30972	1.30972
$640$	0.763521	0.763521
$641$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$641$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0.546200	0.546200
$646$	−2.68251	−2.68251
$647$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$647$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$648$	3.22871	3.22871
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−0.763521	−0.763521
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	3.68251	3.68251
$655$	0.0810141	0.0810141
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$659$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$660$	0.634356	0.634356
$661$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$661$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$662$	−0.546200	−0.546200
$663$	0	0
$664$	0	0
$665$	−0.309721	−0.309721
$666$	3.22871	3.22871
$667$	0	0
$668$	3.51334	3.51334
$669$	1.91899	1.91899
$670$	0	0
$671$	0.236479	0.236479
$672$	4.60149	4.60149
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0.918986	0.918986
$676$	2.68251	2.68251
$677$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$677$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$678$	−2.51334	−2.51334
$679$	−2.20362	−2.20362
$680$	−1.54620	−1.54620
$681$	−1.91899	−1.91899
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	2.22871	2.22871
$685$	0	0
$686$	0.715370	0.715370
$687$	0	0
$688$	−6.74204	−6.74204
$689$	0	0
$690$	0	0
$691$	2.00000	2.00000	1.00000			$0$
$691$	2.00000	2.00000	1.00000			$0$
$692$	0	0
$693$	1.08816	1.08816
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	3.22871	3.22871
$701$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$701$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$702$	0	0
$703$	1.39788	1.39788
$704$	−2.68251	−2.68251
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0.715370	0.715370
$711$	0	0
$712$	6.19584	6.19584
$713$	0	0
$714$	−4.22871	−4.22871
$715$	0	0
$716$	5.14769	5.14769
$717$	0	0
$718$	−3.22871	−3.22871
$719$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$719$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$720$	1.00000	1.00000
$721$	0	0
$722$	−0.594351	−0.594351
$723$	0	0
$724$	−3.51334	−3.51334
$725$	0	0
$726$	0.594351	0.594351
$727$	0.830830	0.830830	0.415415	−	0.909632i	$-0.363636\pi$
$727$	0.830830	0.830830	0.415415	+	0.909632i	$0.363636\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	3.22871	3.22871
$732$	0.763521	0.763521
$733$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$733$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$734$	0	0
$735$	−0.203616	−0.203616
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$739$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$740$	1.28463	1.28463
$741$	0	0
$742$	0	0
$743$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$743$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$744$	0	0
$745$	−0.478891	−0.478891
$746$	0	0
$747$	0	0
$748$	3.74982	3.74982
$749$	0	0
$750$	1.04815	1.04815
$751$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$751$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	3.51334	3.51334
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−2.51334	−2.51334
$759$	0	0
$760$	0.763521	0.763521
$761$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$761$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$762$	−1.59435	−1.59435
$763$	2.51334	2.51334
$764$	0	0
$765$	−0.478891	−0.478891
$766$	−1.59435	−1.59435
$767$	0	0
$768$	−1.91899	−1.91899
$769$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$769$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$770$	0.594351	0.594351
$771$	0	0
$772$	−0.763521	−0.763521
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−3.68251	−3.68251
$775$	0	0
$776$	5.43232	5.43232
$777$	2.20362	2.20362
$778$	−3.83797	−3.83797
$779$	0	0
$780$	0	0
$781$	−1.08816	−1.08816
$782$	0	0
$783$	0	0
$784$	2.51334	2.51334
$785$	−0.0810141	−0.0810141
$786$	−0.546200	−0.546200
$787$	2.00000	2.00000	1.00000			$0$
$787$	2.00000	2.00000	1.00000			$0$
$788$	−2.68251	−2.68251
$789$	0.830830	0.830830
$790$	0	0
$791$	−1.71537	−1.71537
$792$	−2.68251	−2.68251
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	2.08816	2.08816
$799$	0	0
$800$	−3.22871	−3.22871
$801$	1.91899	1.91899
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1.68251	1.68251
$808$	0	0
$809$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$809$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$810$	0.546200	0.546200
$811$	−0.284630	−0.284630	−0.142315	−	0.989821i	$-0.545455\pi$
$811$	−0.284630	−0.284630	−0.142315	+	0.989821i	$0.545455\pi$
$812$	0	0
$813$	0	0
$814$	−2.68251	−2.68251
$815$	−0.0810141	−0.0810141
$816$	5.91121	5.91121
$817$	−1.59435	−1.59435
$818$	3.22871	3.22871
$819$	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
$825$	−0.763521	−0.763521
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.30972	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$829$	−1.30972	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−1.20362	−1.20362
$834$	0	0
$835$	0.372786	0.372786
$836$	−1.85168	−1.85168
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	1.20362	1.20362
$841$	1.00000	1.00000
$842$	0	0
$843$	0.830830	0.830830
$844$	0	0
$845$	0.284630	0.284630
$846$	0	0
$847$	0.405649	0.405649
$848$	0	0
$849$	0	0
$850$	2.96714	2.96714
$851$	0	0
$852$	−3.51334	−3.51334
$853$	−1.91899	−1.91899	−0.959493	−	0.281733i	$-0.909091\pi$
$853$	−1.91899	−1.91899	−0.959493	+	0.281733i	$0.909091\pi$
$854$	0.715370	0.715370
$855$	0.236479	0.236479
$856$	0	0
$857$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$857$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	−1.46519	−1.46519
$861$	0	0
$862$	0	0
$863$	−2.00000	−2.00000	−1.00000			$\pi$
$863$	−2.00000	−2.00000	−1.00000			$\pi$
$864$	−3.51334	−3.51334
$865$	0	0
$866$	−3.68251	−3.68251
$867$	−1.83083	−1.83083
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−6.19584	−6.19584
$873$	1.68251	1.68251
$874$	0	0
$875$	0.715370	0.715370
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	−0.830830	−0.830830
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	1.37279	1.37279
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$887$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$888$	−5.43232	−5.43232
$889$	−1.08816	−1.08816
$890$	1.04815	1.04815
$891$	−0.830830	−0.830830
$892$	−5.14769	−5.14769
$893$	0	0
$894$	3.22871	3.22871
$895$	0.546200	0.546200
$896$	−3.51334	−3.51334
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−2.46519	−2.46519
$901$	0	0
$902$	0	0
$903$	−2.51334	−2.51334
$904$	4.22871	4.22871
$905$	−0.372786	−0.372786
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	5.14769	5.14769
$909$	0	0
$910$	0	0
$911$	1.30972	1.30972	0.654861	−	0.755750i	$-0.272727\pi$
$911$	1.30972	1.30972	0.654861	+	0.755750i	$0.272727\pi$
$912$	−2.91899	−2.91899
$913$	0	0
$914$	1.59435	1.59435
$915$	0.0810141	0.0810141
$916$	0	0
$917$	−0.372786	−0.372786
$918$	3.22871	3.22871
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	2.51334	2.51334
$923$	0	0
$924$	−2.91899	−2.91899
$925$	−1.54620	−1.54620
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$929$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$930$	0	0
$931$	0.594351	0.594351
$932$	0	0
$933$	0	0
$934$	2.51334	2.51334
$935$	0.397877	0.397877
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	1.30972	1.30972
$940$	0	0
$941$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$941$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$942$	0.546200	0.546200
$943$	0	0
$944$	0	0
$945$	0.372786	0.372786
$946$	3.05954	3.05954
$947$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$947$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$948$	0	0
$949$	0	0
$950$	−1.46519	−1.46519
$951$	1.68251	1.68251
$952$	7.11483	7.11483
$953$	0.284630	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$953$	0.284630	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	−0.918986	−0.918986
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	−0.0810141	−0.0810141
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−1.00000	−1.00000
$969$	1.39788	1.39788
$970$	0.918986	0.918986
$971$	−0.830830	−0.830830	−0.415415	−	0.909632i	$-0.636364\pi$
$971$	−0.830830	−0.830830	−0.415415	+	0.909632i	$0.636364\pi$
$972$	−2.68251	−2.68251
$973$	0	0
$974$	1.59435	1.59435
$975$	0	0
$976$	−1.00000	−1.00000
$977$	1.91899	1.91899	0.959493	−	0.281733i	$-0.0909091\pi$
$977$	1.91899	1.91899	0.959493	+	0.281733i	$0.0909091\pi$
$978$	0.546200	0.546200
$979$	−1.59435	−1.59435
$980$	0.546200	0.546200
$981$	−1.91899	−1.91899
$982$	0	0
$983$	−1.68251	−1.68251	−0.841254	−	0.540641i	$-0.818182\pi$
$983$	−1.68251	−1.68251	−0.841254	+	0.540641i	$0.818182\pi$
$984$	0	0
$985$	−0.284630	−0.284630
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	−0.453800	−0.453800
$991$	2.00000	2.00000	1.00000			$0$
$991$	2.00000	2.00000	1.00000			$0$
$992$	0	0
$993$	0.284630	0.284630
$994$	−3.29177	−3.29177
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.59435	1.59435
$999$	−1.68251	−1.68251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	591.1.d.b.590.5	yes	5
3.2	odd	2		591.1.d.a.590.1	✓	5
197.196	even	2		591.1.d.a.590.1	✓	5
591.590	odd	2	CM	591.1.d.b.590.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
591.1.d.a.590.1	✓	5	3.2	odd	2
591.1.d.a.590.1	✓	5	197.196	even	2
591.1.d.b.590.5	yes	5	1.1	even	1	trivial
591.1.d.b.590.5	yes	5	591.590	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+1.91899 q^{2} -1.00000 q^{3} +2.68251 q^{4} +0.284630 q^{5} -1.91899 q^{6} -1.30972 q^{7} +3.22871 q^{8} +1.00000 q^{9} +0.546200 q^{10} -0.830830 q^{11} -2.68251 q^{12} -2.51334 q^{14} -0.284630 q^{15} +3.51334 q^{16} -1.68251 q^{17} +1.91899 q^{18} +0.830830 q^{19} +0.763521 q^{20} +1.30972 q^{21} -1.59435 q^{22} -3.22871 q^{24} -0.918986 q^{25} -1.00000 q^{27} -3.51334 q^{28} -0.546200 q^{30} +3.51334 q^{32} +0.830830 q^{33} -3.22871 q^{34} -0.372786 q^{35} +2.68251 q^{36} +1.68251 q^{37} +1.59435 q^{38} +0.918986 q^{40} +2.51334 q^{42} -1.91899 q^{43} -2.22871 q^{44} +0.284630 q^{45} -3.51334 q^{48} +0.715370 q^{49} -1.76352 q^{50} +1.68251 q^{51} -1.91899 q^{54} -0.236479 q^{55} -4.22871 q^{56} -0.830830 q^{57} -0.763521 q^{60} -0.284630 q^{61} -1.30972 q^{63} +3.22871 q^{64} +1.59435 q^{66} -4.51334 q^{68} -0.715370 q^{70} +1.30972 q^{71} +3.22871 q^{72} +3.22871 q^{74} +0.918986 q^{75} +2.22871 q^{76} +1.08816 q^{77} +1.00000 q^{80} +1.00000 q^{81} +3.51334 q^{84} -0.478891 q^{85} -3.68251 q^{86} -2.68251 q^{88} +1.91899 q^{89} +0.546200 q^{90} +0.236479 q^{95} -3.51334 q^{96} +1.68251 q^{97} +1.37279 q^{98} -0.830830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 4 q^{4} + q^{5} - q^{6} - q^{7} + 2 q^{8} + 5 q^{9} - 2 q^{10} + q^{11} - 4 q^{12} + 2 q^{14} - q^{15} + 3 q^{16} + q^{17} + q^{18} - q^{19} + 3 q^{20} + q^{21} - 2 q^{22}+ \cdots + q^{99}+O(q^{100}) \) 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

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