LMFDB - Embedded newform 1547.2.a.g.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1547,2,Mod(1,1547)] 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("1547.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1547, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1547 = 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1547.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,-3] 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:	$12.3528571927$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 21x^{6} + 6x^{5} - 34x^{4} - 2x^{3} + 13x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 21x^6 + 6x^5 - 34x^4 - 2x^3 + 13*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.310487$ of defining polynomial
Character	$\chi$	$=$	1547.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.310487 q^{2} -1.20477 q^{3} -1.90360 q^{4} +1.91026 q^{5} -0.374064 q^{6} +1.00000 q^{7} -1.21202 q^{8} -1.54854 q^{9} +0.593111 q^{10} +0.933608 q^{11} +2.29339 q^{12} -1.00000 q^{13} +0.310487 q^{14} -2.30142 q^{15} +3.43088 q^{16} +1.00000 q^{17} -0.480800 q^{18} -2.56036 q^{19} -3.63637 q^{20} -1.20477 q^{21} +0.289873 q^{22} -0.142760 q^{23} +1.46020 q^{24} -1.35090 q^{25} -0.310487 q^{26} +5.47993 q^{27} -1.90360 q^{28} -4.09227 q^{29} -0.714561 q^{30} -1.16994 q^{31} +3.48927 q^{32} -1.12478 q^{33} +0.310487 q^{34} +1.91026 q^{35} +2.94779 q^{36} +7.10312 q^{37} -0.794958 q^{38} +1.20477 q^{39} -2.31527 q^{40} -10.4590 q^{41} -0.374064 q^{42} -6.62646 q^{43} -1.77721 q^{44} -2.95811 q^{45} -0.0443252 q^{46} +1.67934 q^{47} -4.13341 q^{48} +1.00000 q^{49} -0.419437 q^{50} -1.20477 q^{51} +1.90360 q^{52} +7.52913 q^{53} +1.70145 q^{54} +1.78343 q^{55} -1.21202 q^{56} +3.08464 q^{57} -1.27060 q^{58} -5.82899 q^{59} +4.38098 q^{60} -9.38495 q^{61} -0.363250 q^{62} -1.54854 q^{63} -5.77839 q^{64} -1.91026 q^{65} -0.349229 q^{66} +1.15178 q^{67} -1.90360 q^{68} +0.171993 q^{69} +0.593111 q^{70} -9.83677 q^{71} +1.87685 q^{72} -15.2483 q^{73} +2.20543 q^{74} +1.62752 q^{75} +4.87389 q^{76} +0.933608 q^{77} +0.374064 q^{78} -16.3320 q^{79} +6.55388 q^{80} -1.95643 q^{81} -3.24737 q^{82} -9.69241 q^{83} +2.29339 q^{84} +1.91026 q^{85} -2.05743 q^{86} +4.93023 q^{87} -1.13155 q^{88} -11.5419 q^{89} -0.918454 q^{90} -1.00000 q^{91} +0.271758 q^{92} +1.40950 q^{93} +0.521413 q^{94} -4.89096 q^{95} -4.20376 q^{96} +7.09254 q^{97} +0.310487 q^{98} -1.44572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 6 q^{8} + 5 q^{9} - 9 q^{10} - 7 q^{11} + 2 q^{12} - 9 q^{13} - 3 q^{14} - 5 q^{15} + 3 q^{16} + 9 q^{17} - 9 q^{18} - 6 q^{19} + 6 q^{20}+ \cdots - 25 q^{99}+O(q^{100}) $ 9 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 6 * q^8 + 5 * q^9 - 9 * q^10 - 7 * q^11 + 2 * q^12 - 9 * q^13 - 3 * q^14 - 5 * q^15 + 3 * q^16 + 9 * q^17 - 9 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 - 4 * q^22 - 3 * q^23 + 8 * q^24 - 13 * q^25 + 3 * q^26 - 13 * q^27 + 3 * q^28 - 4 * q^29 + 10 * q^32 - 12 * q^33 - 3 * q^34 - 6 * q^35 - 17 * q^36 - 31 * q^37 - 3 * q^38 + 4 * q^39 - 18 * q^40 + 3 * q^41 + 2 * q^42 - 24 * q^43 - 20 * q^44 + 3 * q^45 + 5 * q^46 + 7 * q^47 + 2 * q^48 + 9 * q^49 + 24 * q^50 - 4 * q^51 - 3 * q^52 - 18 * q^53 + 6 * q^55 - 6 * q^56 - 35 * q^57 + 2 * q^58 - 9 * q^59 + 2 * q^60 - 22 * q^61 + 30 * q^62 + 5 * q^63 - 36 * q^64 + 6 * q^65 + 22 * q^66 - 32 * q^67 + 3 * q^68 - 2 * q^69 - 9 * q^70 + 18 * q^71 - 10 * q^72 - 14 * q^73 + 12 * q^74 + 11 * q^75 - 27 * q^76 - 7 * q^77 - 2 * q^78 - 46 * q^79 - q^80 + 29 * q^81 + 3 * q^82 - 16 * q^83 + 2 * q^84 - 6 * q^85 - 34 * q^86 + 3 * q^87 - 10 * q^89 + 21 * q^90 - 9 * q^91 + 14 * q^92 - 83 * q^93 + q^94 - 55 * q^96 - 15 * q^97 - 3 * q^98 - 25 * q^99

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 $

$2$	0.310487	0.219547	0.109774	−	0.993957i	$-0.464987\pi$
$2$	0.310487	0.219547	0.109774	+	0.993957i	$0.464987\pi$
$3$	−1.20477	−0.695573	−0.347786	−	0.937574i	$-0.613067\pi$
$3$	−1.20477	−0.695573	−0.347786	+	0.937574i	$0.613067\pi$
$4$	−1.90360	−0.951799
$5$	1.91026	0.854295	0.427148	−	0.904182i	$-0.359519\pi$
$5$	1.91026	0.854295	0.427148	+	0.904182i	$0.359519\pi$
$6$	−0.374064	−0.152711
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.21202	−0.428512
$9$	−1.54854	−0.516179
$10$	0.593111	0.187558
$11$	0.933608	0.281493	0.140747	−	0.990046i	$-0.455050\pi$
$11$	0.933608	0.281493	0.140747	+	0.990046i	$0.455050\pi$
$12$	2.29339	0.662045
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.310487	0.0829811
$15$	−2.30142	−0.594224
$16$	3.43088	0.857720
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.480800	−0.113326
$19$	−2.56036	−0.587387	−0.293693	−	0.955900i	$-0.594884\pi$
$19$	−2.56036	−0.587387	−0.293693	+	0.955900i	$0.594884\pi$
$20$	−3.63637	−0.813117
$21$	−1.20477	−0.262902
$22$	0.289873	0.0618011
$23$	−0.142760	−0.0297676	−0.0148838	−	0.999889i	$-0.504738\pi$
$23$	−0.142760	−0.0297676	−0.0148838	+	0.999889i	$0.504738\pi$
$24$	1.46020	0.298061
$25$	−1.35090	−0.270180
$26$	−0.310487	−0.0608915
$27$	5.47993	1.05461
$28$	−1.90360	−0.359746
$29$	−4.09227	−0.759915	−0.379958	−	0.925004i	$-0.624061\pi$
$29$	−4.09227	−0.759915	−0.379958	+	0.925004i	$0.624061\pi$
$30$	−0.714561	−0.130460
$31$	−1.16994	−0.210127	−0.105063	−	0.994466i	$-0.533505\pi$
$31$	−1.16994	−0.210127	−0.105063	+	0.994466i	$0.533505\pi$
$32$	3.48927	0.616822
$33$	−1.12478	−0.195799
$34$	0.310487	0.0532481
$35$	1.91026	0.322893
$36$	2.94779	0.491298
$37$	7.10312	1.16775	0.583873	−	0.811845i	$-0.301537\pi$
$37$	7.10312	1.16775	0.583873	+	0.811845i	$0.301537\pi$
$38$	−0.794958	−0.128959
$39$	1.20477	0.192917
$40$	−2.31527	−0.366076
$41$	−10.4590	−1.63341	−0.816707	−	0.577053i	$-0.804203\pi$
$41$	−10.4590	−1.63341	−0.816707	+	0.577053i	$0.804203\pi$
$42$	−0.374064	−0.0577194
$43$	−6.62646	−1.01053	−0.505263	−	0.862966i	$-0.668604\pi$
$43$	−6.62646	−1.01053	−0.505263	+	0.862966i	$0.668604\pi$
$44$	−1.77721	−0.267925
$45$	−2.95811	−0.440969
$46$	−0.0443252	−0.00653539
$47$	1.67934	0.244957	0.122478	−	0.992471i	$-0.460916\pi$
$47$	1.67934	0.244957	0.122478	+	0.992471i	$0.460916\pi$
$48$	−4.13341	−0.596607
$49$	1.00000	0.142857
$50$	−0.419437	−0.0593173
$51$	−1.20477	−0.168701
$52$	1.90360	0.263982
$53$	7.52913	1.03421	0.517103	−	0.855923i	$-0.327011\pi$
$53$	7.52913	1.03421	0.517103	+	0.855923i	$0.327011\pi$
$54$	1.70145	0.231537
$55$	1.78343	0.240478
$56$	−1.21202	−0.161962
$57$	3.08464	0.408570
$58$	−1.27060	−0.166837
$59$	−5.82899	−0.758869	−0.379435	−	0.925219i	$-0.623881\pi$
$59$	−5.82899	−0.758869	−0.379435	+	0.925219i	$0.623881\pi$
$60$	4.38098	0.565582
$61$	−9.38495	−1.20162	−0.600810	−	0.799392i	$-0.705155\pi$
$61$	−9.38495	−1.20162	−0.600810	+	0.799392i	$0.705155\pi$
$62$	−0.363250	−0.0461328
$63$	−1.54854	−0.195097
$64$	−5.77839	−0.722299
$65$	−1.91026	−0.236939
$66$	−0.349229	−0.0429872
$67$	1.15178	0.140712	0.0703559	−	0.997522i	$-0.477587\pi$
$67$	1.15178	0.140712	0.0703559	+	0.997522i	$0.477587\pi$
$68$	−1.90360	−0.230845
$69$	0.171993	0.0207055
$70$	0.593111	0.0708903
$71$	−9.83677	−1.16741	−0.583705	−	0.811966i	$-0.698397\pi$
$71$	−9.83677	−1.16741	−0.583705	+	0.811966i	$0.698397\pi$
$72$	1.87685	0.221189
$73$	−15.2483	−1.78467	−0.892337	−	0.451370i	$-0.850935\pi$
$73$	−15.2483	−1.78467	−0.892337	+	0.451370i	$0.850935\pi$
$74$	2.20543	0.256376
$75$	1.62752	0.187930
$76$	4.87389	0.559074
$77$	0.933608	0.106394
$78$	0.374064	0.0423544
$79$	−16.3320	−1.83749	−0.918745	−	0.394852i	$-0.870796\pi$
$79$	−16.3320	−1.83749	−0.918745	+	0.394852i	$0.870796\pi$
$80$	6.55388	0.732746
$81$	−1.95643	−0.217381
$82$	−3.24737	−0.358612
$83$	−9.69241	−1.06388	−0.531940	−	0.846782i	$-0.678537\pi$
$83$	−9.69241	−1.06388	−0.531940	+	0.846782i	$0.678537\pi$
$84$	2.29339	0.250230
$85$	1.91026	0.207197
$86$	−2.05743	−0.221858
$87$	4.93023	0.528576
$88$	−1.13155	−0.120623
$89$	−11.5419	−1.22343	−0.611717	−	0.791077i	$-0.709521\pi$
$89$	−11.5419	−1.22343	−0.611717	+	0.791077i	$0.709521\pi$
$90$	−0.918454	−0.0968135
$91$	−1.00000	−0.104828
$92$	0.271758	0.0283328
$93$	1.40950	0.146158
$94$	0.521413	0.0537797
$95$	−4.89096	−0.501801
$96$	−4.20376	−0.429045
$97$	7.09254	0.720139	0.360069	−	0.932926i	$-0.382753\pi$
$97$	7.09254	0.720139	0.360069	+	0.932926i	$0.382753\pi$
$98$	0.310487	0.0313639
$99$	−1.44572	−0.145301
$100$	2.57157	0.257157
$101$	13.6480	1.35802	0.679011	−	0.734128i	$-0.262409\pi$
$101$	13.6480	1.35802	0.679011	+	0.734128i	$0.262409\pi$
$102$	−0.374064	−0.0370379
$103$	19.3469	1.90631	0.953154	−	0.302485i	$-0.0978161\pi$
$103$	19.3469	1.90631	0.953154	+	0.302485i	$0.0978161\pi$
$104$	1.21202	0.118848
$105$	−2.30142	−0.224596
$106$	2.33769	0.227057
$107$	−8.65671	−0.836875	−0.418438	−	0.908246i	$-0.637422\pi$
$107$	−8.65671	−0.836875	−0.418438	+	0.908246i	$0.637422\pi$
$108$	−10.4316	−1.00378
$109$	12.7298	1.21930	0.609648	−	0.792673i	$-0.291311\pi$
$109$	12.7298	1.21930	0.609648	+	0.792673i	$0.291311\pi$
$110$	0.553733	0.0527964
$111$	−8.55761	−0.812252
$112$	3.43088	0.324188
$113$	−17.3759	−1.63459	−0.817294	−	0.576221i	$-0.804527\pi$
$113$	−17.3759	−1.63459	−0.817294	+	0.576221i	$0.804527\pi$
$114$	0.957739	0.0897005
$115$	−0.272710	−0.0254303
$116$	7.79003	0.723286
$117$	1.54854	0.143162
$118$	−1.80982	−0.166608
$119$	1.00000	0.0916698
$120$	2.78936	0.254632
$121$	−10.1284	−0.920762
$122$	−2.91390	−0.263812
$123$	12.6006	1.13616
$124$	2.22709	0.199998
$125$	−12.1319	−1.08511
$126$	−0.480800	−0.0428331
$127$	−12.2117	−1.08361	−0.541807	−	0.840503i	$-0.682260\pi$
$127$	−12.2117	−1.08361	−0.541807	+	0.840503i	$0.682260\pi$
$128$	−8.77266	−0.775401
$129$	7.98334	0.702894
$130$	−0.593111	−0.0520193
$131$	5.01677	0.438317	0.219159	−	0.975689i	$-0.429669\pi$
$131$	5.01677	0.438317	0.219159	+	0.975689i	$0.429669\pi$
$132$	2.14113	0.186361
$133$	−2.56036	−0.222011
$134$	0.357611	0.0308929
$135$	10.4681	0.900950
$136$	−1.21202	−0.103929
$137$	−11.9450	−1.02053	−0.510264	−	0.860018i	$-0.670452\pi$
$137$	−11.9450	−1.02053	−0.510264	+	0.860018i	$0.670452\pi$
$138$	0.0534015	0.00454584
$139$	10.3283	0.876032	0.438016	−	0.898967i	$-0.355681\pi$
$139$	10.3283	0.876032	0.438016	+	0.898967i	$0.355681\pi$
$140$	−3.63637	−0.307329
$141$	−2.02321	−0.170385
$142$	−3.05419	−0.256302
$143$	−0.933608	−0.0780722
$144$	−5.31284	−0.442737
$145$	−7.81730	−0.649192
$146$	−4.73438	−0.391820
$147$	−1.20477	−0.0993675
$148$	−13.5215	−1.11146
$149$	3.18905	0.261258	0.130629	−	0.991431i	$-0.458300\pi$
$149$	3.18905	0.261258	0.130629	+	0.991431i	$0.458300\pi$
$150$	0.505324	0.0412595
$151$	12.0435	0.980087	0.490043	−	0.871698i	$-0.336981\pi$
$151$	12.0435	0.980087	0.490043	+	0.871698i	$0.336981\pi$
$152$	3.10320	0.251702
$153$	−1.54854	−0.125192
$154$	0.289873	0.0233586
$155$	−2.23488	−0.179510
$156$	−2.29339	−0.183618
$157$	−21.5759	−1.72195	−0.860973	−	0.508650i	$-0.830145\pi$
$157$	−21.5759	−1.72195	−0.860973	+	0.508650i	$0.830145\pi$
$158$	−5.07086	−0.403416
$159$	−9.07085	−0.719365
$160$	6.66543	0.526948
$161$	−0.142760	−0.0112511
$162$	−0.607445	−0.0477254
$163$	0.538447	0.0421744	0.0210872	−	0.999778i	$-0.493287\pi$
$163$	0.538447	0.0421744	0.0210872	+	0.999778i	$0.493287\pi$
$164$	19.9096	1.55468
$165$	−2.14862	−0.167270
$166$	−3.00937	−0.233572
$167$	24.4256	1.89011	0.945054	−	0.326913i	$-0.106008\pi$
$167$	24.4256	1.89011	0.945054	+	0.326913i	$0.106008\pi$
$168$	1.46020	0.112657
$169$	1.00000	0.0769231
$170$	0.593111	0.0454895
$171$	3.96481	0.303196
$172$	12.6141	0.961817
$173$	−23.4345	−1.78169	−0.890845	−	0.454307i	$-0.849887\pi$
$173$	−23.4345	−1.78169	−0.890845	+	0.454307i	$0.849887\pi$
$174$	1.53077	0.116047
$175$	−1.35090	−0.102118
$176$	3.20310	0.241442
$177$	7.02257	0.527849
$178$	−3.58359	−0.268602
$179$	7.83894	0.585910	0.292955	−	0.956126i	$-0.405361\pi$
$179$	7.83894	0.585910	0.292955	+	0.956126i	$0.405361\pi$
$180$	5.63105	0.419714
$181$	−6.76175	−0.502597	−0.251298	−	0.967910i	$-0.580858\pi$
$181$	−6.76175	−0.502597	−0.251298	+	0.967910i	$0.580858\pi$
$182$	−0.310487	−0.0230148
$183$	11.3067	0.835814
$184$	0.173028	0.0127558
$185$	13.5688	0.997600
$186$	0.437631	0.0320887
$187$	0.933608	0.0682721
$188$	−3.19679	−0.233150
$189$	5.47993	0.398606
$190$	−1.51858	−0.110169
$191$	−14.8029	−1.07110	−0.535549	−	0.844504i	$-0.679895\pi$
$191$	−14.8029	−1.07110	−0.535549	+	0.844504i	$0.679895\pi$
$192$	6.96161	0.502411
$193$	10.4202	0.750061	0.375031	−	0.927012i	$-0.377632\pi$
$193$	10.4202	0.750061	0.375031	+	0.927012i	$0.377632\pi$
$194$	2.20214	0.158105
$195$	2.30142	0.164808
$196$	−1.90360	−0.135971
$197$	−1.33454	−0.0950818	−0.0475409	−	0.998869i	$-0.515138\pi$
$197$	−1.33454	−0.0950818	−0.0475409	+	0.998869i	$0.515138\pi$
$198$	−0.448879	−0.0319004
$199$	14.8848	1.05515	0.527577	−	0.849507i	$-0.323101\pi$
$199$	14.8848	1.05515	0.527577	+	0.849507i	$0.323101\pi$
$200$	1.63731	0.115775
$201$	−1.38762	−0.0978753
$202$	4.23751	0.298150
$203$	−4.09227	−0.287221
$204$	2.29339	0.160570
$205$	−19.9793	−1.39542
$206$	6.00696	0.418525
$207$	0.221070	0.0153654
$208$	−3.43088	−0.237889
$209$	−2.39037	−0.165345
$210$	−0.714561	−0.0493094
$211$	−15.8098	−1.08839	−0.544196	−	0.838958i	$-0.683165\pi$
$211$	−15.8098	−1.08839	−0.544196	+	0.838958i	$0.683165\pi$
$212$	−14.3324	−0.984355
$213$	11.8510	0.812018
$214$	−2.68779	−0.183734
$215$	−12.6583	−0.863287
$216$	−6.64176	−0.451914
$217$	−1.16994	−0.0794204
$218$	3.95244	0.267693
$219$	18.3706	1.24137
$220$	−3.39494	−0.228887
$221$	−1.00000	−0.0672673
$222$	−2.65703	−0.178328
$223$	3.73710	0.250255	0.125127	−	0.992141i	$-0.460066\pi$
$223$	3.73710	0.250255	0.125127	+	0.992141i	$0.460066\pi$
$224$	3.48927	0.233137
$225$	2.09192	0.139461
$226$	−5.39499	−0.358869
$227$	23.1272	1.53501	0.767504	−	0.641044i	$-0.221499\pi$
$227$	23.1272	1.53501	0.767504	+	0.641044i	$0.221499\pi$
$228$	−5.87191	−0.388877
$229$	−5.69418	−0.376282	−0.188141	−	0.982142i	$-0.560246\pi$
$229$	−5.69418	−0.376282	−0.188141	+	0.982142i	$0.560246\pi$
$230$	−0.0846727	−0.00558315
$231$	−1.12478	−0.0740051
$232$	4.95989	0.325633
$233$	24.1106	1.57954	0.789770	−	0.613403i	$-0.210200\pi$
$233$	24.1106	1.57954	0.789770	+	0.613403i	$0.210200\pi$
$234$	0.480800	0.0314309
$235$	3.20798	0.209266
$236$	11.0960	0.722291
$237$	19.6762	1.27811
$238$	0.310487	0.0201259
$239$	17.0879	1.10533	0.552663	−	0.833405i	$-0.313612\pi$
$239$	17.0879	1.10533	0.552663	+	0.833405i	$0.313612\pi$
$240$	−7.89590	−0.509678
$241$	20.5081	1.32104	0.660522	−	0.750807i	$-0.270335\pi$
$241$	20.5081	1.32104	0.660522	+	0.750807i	$0.270335\pi$
$242$	−3.14473	−0.202151
$243$	−14.0827	−0.903408
$244$	17.8652	1.14370
$245$	1.91026	0.122042
$246$	3.91232	0.249440
$247$	2.56036	0.162912
$248$	1.41798	0.0900419
$249$	11.6771	0.740006
$250$	−3.76679	−0.238233
$251$	−10.0961	−0.637258	−0.318629	−	0.947880i	$-0.603222\pi$
$251$	−10.0961	−0.637258	−0.318629	+	0.947880i	$0.603222\pi$
$252$	2.94779	0.185693
$253$	−0.133282	−0.00837938
$254$	−3.79157	−0.237904
$255$	−2.30142	−0.144121
$256$	8.83298	0.552061
$257$	14.3301	0.893889	0.446945	−	0.894562i	$-0.352512\pi$
$257$	14.3301	0.893889	0.446945	+	0.894562i	$0.352512\pi$
$258$	2.47872	0.154318
$259$	7.10312	0.441367
$260$	3.63637	0.225518
$261$	6.33702	0.392252
$262$	1.55764	0.0962314
$263$	14.6691	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$263$	14.6691	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$264$	1.36325	0.0839023
$265$	14.3826	0.883516
$266$	−0.794958	−0.0487420
$267$	13.9052	0.850987
$268$	−2.19252	−0.133929
$269$	−26.9591	−1.64372	−0.821861	−	0.569688i	$-0.807064\pi$
$269$	−26.9591	−1.64372	−0.821861	+	0.569688i	$0.807064\pi$
$270$	3.25021	0.197801
$271$	24.6135	1.49516	0.747582	−	0.664170i	$-0.231215\pi$
$271$	24.6135	1.49516	0.747582	+	0.664170i	$0.231215\pi$
$272$	3.43088	0.208028
$273$	1.20477	0.0729158
$274$	−3.70876	−0.224054
$275$	−1.26121	−0.0760539
$276$	−0.327405	−0.0197075
$277$	−7.74399	−0.465291	−0.232646	−	0.972562i	$-0.574738\pi$
$277$	−7.74399	−0.465291	−0.232646	+	0.972562i	$0.574738\pi$
$278$	3.20679	0.192331
$279$	1.81169	0.108463
$280$	−2.31527	−0.138364
$281$	−18.1424	−1.08228	−0.541142	−	0.840931i	$-0.682008\pi$
$281$	−18.1424	−1.08228	−0.541142	+	0.840931i	$0.682008\pi$
$282$	−0.628181	−0.0374077
$283$	23.2152	1.38000	0.689999	−	0.723810i	$-0.257611\pi$
$283$	23.2152	1.38000	0.689999	+	0.723810i	$0.257611\pi$
$284$	18.7252	1.11114
$285$	5.89246	0.349039
$286$	−0.289873	−0.0171405
$287$	−10.4590	−0.617372
$288$	−5.40327	−0.318391
$289$	1.00000	0.0588235
$290$	−2.42717	−0.142528
$291$	−8.54487	−0.500909
$292$	29.0265	1.69865
$293$	15.7957	0.922795	0.461397	−	0.887194i	$-0.347348\pi$
$293$	15.7957	0.922795	0.461397	+	0.887194i	$0.347348\pi$
$294$	−0.374064	−0.0218159
$295$	−11.1349	−0.648298
$296$	−8.60910	−0.500394
$297$	5.11610	0.296866
$298$	0.990159	0.0573584
$299$	0.142760	0.00825604
$300$	−3.09814	−0.178871
$301$	−6.62646	−0.381943
$302$	3.73935	0.215175
$303$	−16.4426	−0.944604
$304$	−8.78429	−0.503813
$305$	−17.9277	−1.02654
$306$	−0.480800	−0.0274855
$307$	9.92143	0.566246	0.283123	−	0.959084i	$-0.408630\pi$
$307$	9.92143	0.566246	0.283123	+	0.959084i	$0.408630\pi$
$308$	−1.77721	−0.101266
$309$	−23.3085	−1.32598
$310$	−0.693902	−0.0394110
$311$	8.83335	0.500893	0.250447	−	0.968130i	$-0.419423\pi$
$311$	8.83335	0.500893	0.250447	+	0.968130i	$0.419423\pi$
$312$	−1.46020	−0.0826674
$313$	−19.2692	−1.08916	−0.544581	−	0.838708i	$-0.683311\pi$
$313$	−19.2692	−1.08916	−0.544581	+	0.838708i	$0.683311\pi$
$314$	−6.69904	−0.378049
$315$	−2.95811	−0.166671
$316$	31.0895	1.74892
$317$	14.1812	0.796497	0.398249	−	0.917277i	$-0.369618\pi$
$317$	14.1812	0.796497	0.398249	+	0.917277i	$0.369618\pi$
$318$	−2.81638	−0.157935
$319$	−3.82057	−0.213911
$320$	−11.0382	−0.617056
$321$	10.4293	0.582108
$322$	−0.0443252	−0.00247015
$323$	−2.56036	−0.142462
$324$	3.72425	0.206903
$325$	1.35090	0.0749345
$326$	0.167181	0.00925928
$327$	−15.3365	−0.848108
$328$	12.6764	0.699938
$329$	1.67934	0.0925850
$330$	−0.667119	−0.0367237
$331$	−8.27011	−0.454566	−0.227283	−	0.973829i	$-0.572984\pi$
$331$	−8.27011	−0.454566	−0.227283	+	0.973829i	$0.572984\pi$
$332$	18.4505	1.01260
$333$	−10.9994	−0.602766
$334$	7.58382	0.414968
$335$	2.20019	0.120209
$336$	−4.13341	−0.225496
$337$	−26.2248	−1.42856	−0.714279	−	0.699861i	$-0.753245\pi$
$337$	−26.2248	−1.42856	−0.714279	+	0.699861i	$0.753245\pi$
$338$	0.310487	0.0168883
$339$	20.9339	1.13697
$340$	−3.63637	−0.197210
$341$	−1.09226	−0.0591493
$342$	1.23102	0.0665660
$343$	1.00000	0.0539949
$344$	8.03137	0.433023
$345$	0.328552	0.0176886
$346$	−7.27610	−0.391165
$347$	5.79589	0.311140	0.155570	−	0.987825i	$-0.450279\pi$
$347$	5.79589	0.311140	0.155570	+	0.987825i	$0.450279\pi$
$348$	−9.38518	−0.503098
$349$	2.18852	0.117149	0.0585745	−	0.998283i	$-0.481344\pi$
$349$	2.18852	0.117149	0.0585745	+	0.998283i	$0.481344\pi$
$350$	−0.419437	−0.0224198
$351$	−5.47993	−0.292497
$352$	3.25761	0.173631
$353$	−2.38672	−0.127032	−0.0635162	−	0.997981i	$-0.520231\pi$
$353$	−2.38672	−0.127032	−0.0635162	+	0.997981i	$0.520231\pi$
$354$	2.18042	0.115888
$355$	−18.7908	−0.997312
$356$	21.9711	1.16446
$357$	−1.20477	−0.0637630
$358$	2.43389	0.128635
$359$	17.3614	0.916297	0.458149	−	0.888876i	$-0.348513\pi$
$359$	17.3614	0.916297	0.458149	+	0.888876i	$0.348513\pi$
$360$	3.58527	0.188961
$361$	−12.4446	−0.654977
$362$	−2.09943	−0.110344
$363$	12.2023	0.640457
$364$	1.90360	0.0997756
$365$	−29.1282	−1.52464
$366$	3.51058	0.183501
$367$	20.8370	1.08768	0.543842	−	0.839188i	$-0.316969\pi$
$367$	20.8370	1.08768	0.543842	+	0.839188i	$0.316969\pi$
$368$	−0.489794	−0.0255323
$369$	16.1961	0.843133
$370$	4.21294	0.219020
$371$	7.52913	0.390893
$372$	−2.68312	−0.139113
$373$	−8.58674	−0.444605	−0.222302	−	0.974978i	$-0.571357\pi$
$373$	−8.58674	−0.444605	−0.222302	+	0.974978i	$0.571357\pi$
$374$	0.289873	0.0149890
$375$	14.6161	0.754772
$376$	−2.03539	−0.104967
$377$	4.09227	0.210763
$378$	1.70145	0.0875129
$379$	−21.4974	−1.10425	−0.552125	−	0.833761i	$-0.686183\pi$
$379$	−21.4974	−1.10425	−0.552125	+	0.833761i	$0.686183\pi$
$380$	9.31041	0.477614
$381$	14.7123	0.753732
$382$	−4.59610	−0.235157
$383$	15.6268	0.798492	0.399246	−	0.916844i	$-0.369272\pi$
$383$	15.6268	0.798492	0.399246	+	0.916844i	$0.369272\pi$
$384$	10.5690	0.539348
$385$	1.78343	0.0908923
$386$	3.23533	0.164674
$387$	10.2613	0.521612
$388$	−13.5014	−0.685427
$389$	13.1130	0.664858	0.332429	−	0.943128i	$-0.392132\pi$
$389$	13.1130	0.664858	0.332429	+	0.943128i	$0.392132\pi$
$390$	0.714561	0.0361832
$391$	−0.142760	−0.00721970
$392$	−1.21202	−0.0612160
$393$	−6.04404	−0.304882
$394$	−0.414356	−0.0208750
$395$	−31.1983	−1.56976
$396$	2.75208	0.138297
$397$	11.7168	0.588049	0.294025	−	0.955798i	$-0.405005\pi$
$397$	11.7168	0.588049	0.294025	+	0.955798i	$0.405005\pi$
$398$	4.62153	0.231656
$399$	3.08464	0.154425
$400$	−4.63478	−0.231739
$401$	6.14617	0.306925	0.153462	−	0.988154i	$-0.450958\pi$
$401$	6.14617	0.306925	0.153462	+	0.988154i	$0.450958\pi$
$402$	−0.430838	−0.0214883
$403$	1.16994	0.0582787
$404$	−25.9802	−1.29256
$405$	−3.73729	−0.185707
$406$	−1.27060	−0.0630586
$407$	6.63153	0.328713
$408$	1.46020	0.0722905
$409$	−25.0861	−1.24043	−0.620214	−	0.784433i	$-0.712954\pi$
$409$	−25.0861	−1.24043	−0.620214	+	0.784433i	$0.712954\pi$
$410$	−6.20332	−0.306360
$411$	14.3909	0.709851
$412$	−36.8288	−1.81442
$413$	−5.82899	−0.286826
$414$	0.0686392	0.00337343
$415$	−18.5150	−0.908868
$416$	−3.48927	−0.171076
$417$	−12.4432	−0.609344
$418$	−0.742179	−0.0363011
$419$	2.00654	0.0980257	0.0490128	−	0.998798i	$-0.484392\pi$
$419$	2.00654	0.0980257	0.0490128	+	0.998798i	$0.484392\pi$
$420$	4.38098	0.213770
$421$	−0.929827	−0.0453170	−0.0226585	−	0.999743i	$-0.507213\pi$
$421$	−0.929827	−0.0453170	−0.0226585	+	0.999743i	$0.507213\pi$
$422$	−4.90874	−0.238954
$423$	−2.60052	−0.126442
$424$	−9.12542	−0.443170
$425$	−1.35090	−0.0655283
$426$	3.67958	0.178276
$427$	−9.38495	−0.454170
$428$	16.4789	0.796537
$429$	1.12478	0.0543049
$430$	−3.93023	−0.189532
$431$	−37.7264	−1.81722	−0.908609	−	0.417647i	$-0.862855\pi$
$431$	−37.7264	−1.81722	−0.908609	+	0.417647i	$0.862855\pi$
$432$	18.8010	0.904562
$433$	12.1415	0.583485	0.291742	−	0.956497i	$-0.405765\pi$
$433$	12.1415	0.583485	0.291742	+	0.956497i	$0.405765\pi$
$434$	−0.363250	−0.0174365
$435$	9.41803	0.451560
$436$	−24.2325	−1.16052
$437$	0.365518	0.0174851
$438$	5.70383	0.272539
$439$	22.4671	1.07230	0.536148	−	0.844124i	$-0.319879\pi$
$439$	22.4671	1.07230	0.536148	+	0.844124i	$0.319879\pi$
$440$	−2.16155	−0.103048
$441$	−1.54854	−0.0737398
$442$	−0.310487	−0.0147684
$443$	−34.1303	−1.62158	−0.810791	−	0.585336i	$-0.800962\pi$
$443$	−34.1303	−1.62158	−0.810791	+	0.585336i	$0.800962\pi$
$444$	16.2902	0.773101
$445$	−22.0480	−1.04517
$446$	1.16032	0.0549427
$447$	−3.84207	−0.181724
$448$	−5.77839	−0.273003
$449$	−39.5244	−1.86527	−0.932636	−	0.360818i	$-0.882498\pi$
$449$	−39.5244	−1.86527	−0.932636	+	0.360818i	$0.882498\pi$
$450$	0.649513	0.0306183
$451$	−9.76456	−0.459795
$452$	33.0767	1.55580
$453$	−14.5096	−0.681722
$454$	7.18070	0.337007
$455$	−1.91026	−0.0895545
$456$	−3.73863	−0.175077
$457$	−23.4298	−1.09600	−0.548000	−	0.836479i	$-0.684610\pi$
$457$	−23.4298	−1.09600	−0.548000	+	0.836479i	$0.684610\pi$
$458$	−1.76797	−0.0826117
$459$	5.47993	0.255781
$460$	0.519129	0.0242045
$461$	29.1241	1.35645	0.678223	−	0.734856i	$-0.262750\pi$
$461$	29.1241	1.35645	0.678223	+	0.734856i	$0.262750\pi$
$462$	−0.349229	−0.0162476
$463$	−3.58116	−0.166431	−0.0832154	−	0.996532i	$-0.526519\pi$
$463$	−3.58116	−0.166431	−0.0832154	+	0.996532i	$0.526519\pi$
$464$	−14.0401	−0.651795
$465$	2.69252	0.124862
$466$	7.48603	0.346784
$467$	−9.23264	−0.427236	−0.213618	−	0.976917i	$-0.568525\pi$
$467$	−9.23264	−0.427236	−0.213618	+	0.976917i	$0.568525\pi$
$468$	−2.94779	−0.136262
$469$	1.15178	0.0531841
$470$	0.996036	0.0459437
$471$	25.9940	1.19774
$472$	7.06482	0.325185
$473$	−6.18651	−0.284456
$474$	6.10920	0.280605
$475$	3.45879	0.158700
$476$	−1.90360	−0.0872513
$477$	−11.6591	−0.533835
$478$	5.30558	0.242672
$479$	8.01213	0.366083	0.183042	−	0.983105i	$-0.441406\pi$
$479$	8.01213	0.366083	0.183042	+	0.983105i	$0.441406\pi$
$480$	−8.03029	−0.366531
$481$	−7.10312	−0.323875
$482$	6.36750	0.290032
$483$	0.171993	0.00782595
$484$	19.2804	0.876380
$485$	13.5486	0.615211
$486$	−4.37251	−0.198341
$487$	−27.1240	−1.22911	−0.614553	−	0.788876i	$-0.710664\pi$
$487$	−27.1240	−1.22911	−0.614553	+	0.788876i	$0.710664\pi$
$488$	11.3747	0.514909
$489$	−0.648703	−0.0293354
$490$	0.593111	0.0267940
$491$	7.39298	0.333641	0.166820	−	0.985987i	$-0.446650\pi$
$491$	7.39298	0.333641	0.166820	+	0.985987i	$0.446650\pi$
$492$	−23.9865	−1.08139
$493$	−4.09227	−0.184306
$494$	0.794958	0.0357668
$495$	−2.76171	−0.124130
$496$	−4.01391	−0.180230
$497$	−9.83677	−0.441239
$498$	3.62558	0.162466
$499$	−25.0362	−1.12077	−0.560387	−	0.828231i	$-0.689348\pi$
$499$	−25.0362	−1.12077	−0.560387	+	0.828231i	$0.689348\pi$
$500$	23.0942	1.03281
$501$	−29.4271	−1.31471
$502$	−3.13469	−0.139908
$503$	−33.7748	−1.50594	−0.752972	−	0.658053i	$-0.771380\pi$
$503$	−33.7748	−1.50594	−0.752972	+	0.658053i	$0.771380\pi$
$504$	1.87685	0.0836015
$505$	26.0712	1.16015
$506$	−0.0413823	−0.00183967
$507$	−1.20477	−0.0535056
$508$	23.2462	1.03138
$509$	10.1489	0.449842	0.224921	−	0.974377i	$-0.427788\pi$
$509$	10.1489	0.449842	0.224921	+	0.974377i	$0.427788\pi$
$510$	−0.714561	−0.0316413
$511$	−15.2483	−0.674543
$512$	20.2878	0.896605
$513$	−14.0306	−0.619465
$514$	4.44932	0.196251
$515$	36.9577	1.62855
$516$	−15.1971	−0.669014
$517$	1.56785	0.0689537
$518$	2.20543	0.0969009
$519$	28.2331	1.23929
$520$	2.31527	0.101531
$521$	14.5163	0.635972	0.317986	−	0.948095i	$-0.396993\pi$
$521$	14.5163	0.635972	0.317986	+	0.948095i	$0.396993\pi$
$522$	1.96756	0.0861179
$523$	22.2308	0.972085	0.486042	−	0.873935i	$-0.338440\pi$
$523$	22.2308	0.972085	0.486042	+	0.873935i	$0.338440\pi$
$524$	−9.54992	−0.417190
$525$	1.62752	0.0710308
$526$	4.55456	0.198588
$527$	−1.16994	−0.0509632
$528$	−3.85899	−0.167941
$529$	−22.9796	−0.999114
$530$	4.46561	0.193974
$531$	9.02640	0.391712
$532$	4.87389	0.211310
$533$	10.4590	0.453028
$534$	4.31740	0.186832
$535$	−16.5366	−0.714938
$536$	−1.39597	−0.0602967
$537$	−9.44409	−0.407543
$538$	−8.37043	−0.360875
$539$	0.933608	0.0402133
$540$	−19.9270	−0.857523
$541$	34.3278	1.47587	0.737933	−	0.674874i	$-0.235802\pi$
$541$	34.3278	1.47587	0.737933	+	0.674874i	$0.235802\pi$
$542$	7.64217	0.328259
$543$	8.14633	0.349592
$544$	3.48927	0.149601
$545$	24.3173	1.04164
$546$	0.374064	0.0160085
$547$	30.7540	1.31494	0.657472	−	0.753479i	$-0.271626\pi$
$547$	30.7540	1.31494	0.657472	+	0.753479i	$0.271626\pi$
$548$	22.7384	0.971338
$549$	14.5329	0.620251
$550$	−0.391589	−0.0166974
$551$	10.4777	0.446364
$552$	−0.208458	−0.00887257
$553$	−16.3320	−0.694506
$554$	−2.40441	−0.102153
$555$	−16.3473	−0.693903
$556$	−19.6609	−0.833807
$557$	24.4846	1.03744	0.518722	−	0.854943i	$-0.326408\pi$
$557$	24.4846	1.03744	0.518722	+	0.854943i	$0.326408\pi$
$558$	0.562505	0.0238128
$559$	6.62646	0.280269
$560$	6.55388	0.276952
$561$	−1.12478	−0.0474882
$562$	−5.63298	−0.237613
$563$	−5.16102	−0.217511	−0.108755	−	0.994069i	$-0.534687\pi$
$563$	−5.16102	−0.217511	−0.108755	+	0.994069i	$0.534687\pi$
$564$	3.85139	0.162173
$565$	−33.1925	−1.39642
$566$	7.20800	0.302975
$567$	−1.95643	−0.0821622
$568$	11.9223	0.500249
$569$	−20.7385	−0.869405	−0.434702	−	0.900574i	$-0.643146\pi$
$569$	−20.7385	−0.869405	−0.434702	+	0.900574i	$0.643146\pi$
$570$	1.82953	0.0766307
$571$	18.9847	0.794486	0.397243	−	0.917714i	$-0.369967\pi$
$571$	18.9847	0.794486	0.397243	+	0.917714i	$0.369967\pi$
$572$	1.77721	0.0743090
$573$	17.8340	0.745027
$574$	−3.24737	−0.135542
$575$	0.192855	0.00804261
$576$	8.94804	0.372835
$577$	−29.1658	−1.21419	−0.607095	−	0.794629i	$-0.707665\pi$
$577$	−29.1658	−1.21419	−0.607095	+	0.794629i	$0.707665\pi$
$578$	0.310487	0.0129145
$579$	−12.5539	−0.521722
$580$	14.8810	0.617900
$581$	−9.69241	−0.402109
$582$	−2.65307	−0.109973
$583$	7.02925	0.291122
$584$	18.4811	0.764754
$585$	2.95811	0.122303
$586$	4.90436	0.202597
$587$	28.1951	1.16374	0.581868	−	0.813283i	$-0.302322\pi$
$587$	28.1951	1.16374	0.581868	+	0.813283i	$0.302322\pi$
$588$	2.29339	0.0945779
$589$	2.99546	0.123426
$590$	−3.45724	−0.142332
$591$	1.60781	0.0661363
$592$	24.3700	1.00160
$593$	−34.3455	−1.41040	−0.705201	−	0.709008i	$-0.749143\pi$
$593$	−34.3455	−1.41040	−0.705201	+	0.709008i	$0.749143\pi$
$594$	1.58848	0.0651762
$595$	1.91026	0.0783131
$596$	−6.07068	−0.248665
$597$	−17.9327	−0.733936
$598$	0.0443252	0.00181259
$599$	−11.3102	−0.462120	−0.231060	−	0.972939i	$-0.574219\pi$
$599$	−11.3102	−0.462120	−0.231060	+	0.972939i	$0.574219\pi$
$600$	−1.97258	−0.0805302
$601$	27.3015	1.11365	0.556825	−	0.830630i	$-0.312019\pi$
$601$	27.3015	1.11365	0.556825	+	0.830630i	$0.312019\pi$
$602$	−2.05743	−0.0838545
$603$	−1.78357	−0.0726324
$604$	−22.9260	−0.932846
$605$	−19.3479	−0.786602
$606$	−5.10522	−0.207385
$607$	−18.8773	−0.766208	−0.383104	−	0.923705i	$-0.625145\pi$
$607$	−18.8773	−0.766208	−0.383104	+	0.923705i	$0.625145\pi$
$608$	−8.93380	−0.362313
$609$	4.93023	0.199783
$610$	−5.56632	−0.225374
$611$	−1.67934	−0.0679388
$612$	2.94779	0.119157
$613$	−41.4781	−1.67529	−0.837643	−	0.546218i	$-0.816067\pi$
$613$	−41.4781	−1.67529	−0.837643	+	0.546218i	$0.816067\pi$
$614$	3.08047	0.124318
$615$	24.0704	0.970614
$616$	−1.13155	−0.0455913
$617$	13.0738	0.526330	0.263165	−	0.964751i	$-0.415234\pi$
$617$	13.0738	0.526330	0.263165	+	0.964751i	$0.415234\pi$
$618$	−7.23699	−0.291115
$619$	−21.3131	−0.856644	−0.428322	−	0.903626i	$-0.640895\pi$
$619$	−21.3131	−0.856644	−0.428322	+	0.903626i	$0.640895\pi$
$620$	4.25432	0.170858
$621$	−0.782316	−0.0313933
$622$	2.74264	0.109970
$623$	−11.5419	−0.462415
$624$	4.13341	0.165469
$625$	−16.4206	−0.656823
$626$	−5.98284	−0.239122
$627$	2.87984	0.115010
$628$	41.0719	1.63895
$629$	7.10312	0.283220
$630$	−0.918454	−0.0365921
$631$	4.05886	0.161581	0.0807904	−	0.996731i	$-0.474256\pi$
$631$	4.05886	0.161581	0.0807904	+	0.996731i	$0.474256\pi$
$632$	19.7946	0.787387
$633$	19.0472	0.757056
$634$	4.40309	0.174869
$635$	−23.3276	−0.925726
$636$	17.2672	0.684691
$637$	−1.00000	−0.0396214
$638$	−1.18624	−0.0469636
$639$	15.2326	0.602592
$640$	−16.7581	−0.662421
$641$	−16.8319	−0.664820	−0.332410	−	0.943135i	$-0.607862\pi$
$641$	−16.8319	−0.664820	−0.332410	+	0.943135i	$0.607862\pi$
$642$	3.23816	0.127800
$643$	−40.3030	−1.58940	−0.794698	−	0.607005i	$-0.792371\pi$
$643$	−40.3030	−1.58940	−0.794698	+	0.607005i	$0.792371\pi$
$644$	0.271758	0.0107088
$645$	15.2503	0.600479
$646$	−0.794958	−0.0312772
$647$	28.5648	1.12300	0.561498	−	0.827478i	$-0.310225\pi$
$647$	28.5648	1.12300	0.561498	+	0.827478i	$0.310225\pi$
$648$	2.37122	0.0931504
$649$	−5.44199	−0.213617
$650$	0.419437	0.0164517
$651$	1.40950	0.0552427
$652$	−1.02499	−0.0401416
$653$	21.4136	0.837980	0.418990	−	0.907991i	$-0.362384\pi$
$653$	21.4136	0.837980	0.418990	+	0.907991i	$0.362384\pi$
$654$	−4.76177	−0.186200
$655$	9.58335	0.374452
$656$	−35.8834	−1.40101
$657$	23.6125	0.921210
$658$	0.521413	0.0203268
$659$	31.8914	1.24231	0.621156	−	0.783687i	$-0.286663\pi$
$659$	31.8914	1.24231	0.621156	+	0.783687i	$0.286663\pi$
$660$	4.09012	0.159208
$661$	−37.0536	−1.44122	−0.720609	−	0.693341i	$-0.756138\pi$
$661$	−37.0536	−1.44122	−0.720609	+	0.693341i	$0.756138\pi$
$662$	−2.56776	−0.0997988
$663$	1.20477	0.0467893
$664$	11.7474	0.455886
$665$	−4.89096	−0.189663
$666$	−3.41518	−0.132336
$667$	0.584214	0.0226208
$668$	−46.4965	−1.79900
$669$	−4.50233	−0.174070
$670$	0.683131	0.0263917
$671$	−8.76186	−0.338248
$672$	−4.20376	−0.162164
$673$	−17.6058	−0.678655	−0.339328	−	0.940668i	$-0.610200\pi$
$673$	−17.6058	−0.678655	−0.339328	+	0.940668i	$0.610200\pi$
$674$	−8.14246	−0.313636
$675$	−7.40283	−0.284935
$676$	−1.90360	−0.0732153
$677$	17.7319	0.681492	0.340746	−	0.940155i	$-0.389320\pi$
$677$	17.7319	0.681492	0.340746	+	0.940155i	$0.389320\pi$
$678$	6.49971	0.249620
$679$	7.09254	0.272187
$680$	−2.31527	−0.0887864
$681$	−27.8629	−1.06771
$682$	−0.339133	−0.0129861
$683$	29.8348	1.14160	0.570798	−	0.821090i	$-0.306634\pi$
$683$	29.8348	1.14160	0.570798	+	0.821090i	$0.306634\pi$
$684$	−7.54740	−0.288582
$685$	−22.8180	−0.871832
$686$	0.310487	0.0118544
$687$	6.86016	0.261731
$688$	−22.7346	−0.866748
$689$	−7.52913	−0.286837
$690$	0.102011	0.00388349
$691$	−1.58904	−0.0604498	−0.0302249	−	0.999543i	$-0.509622\pi$
$691$	−1.58904	−0.0604498	−0.0302249	+	0.999543i	$0.509622\pi$
$692$	44.6098	1.69581
$693$	−1.44572	−0.0549186
$694$	1.79955	0.0683099
$695$	19.7297	0.748390
$696$	−5.97552	−0.226501
$697$	−10.4590	−0.396161
$698$	0.679508	0.0257197
$699$	−29.0477	−1.09868
$700$	2.57157	0.0971962
$701$	−31.9042	−1.20500	−0.602502	−	0.798117i	$-0.705829\pi$
$701$	−31.9042	−1.20500	−0.602502	+	0.798117i	$0.705829\pi$
$702$	−1.70145	−0.0642169
$703$	−18.1865	−0.685919
$704$	−5.39475	−0.203322
$705$	−3.86487	−0.145559
$706$	−0.741045	−0.0278896
$707$	13.6480	0.513284
$708$	−13.3682	−0.502406
$709$	18.8034	0.706176	0.353088	−	0.935590i	$-0.385132\pi$
$709$	18.8034	0.706176	0.353088	+	0.935590i	$0.385132\pi$
$710$	−5.83429	−0.218957
$711$	25.2906	0.948473
$712$	13.9889	0.524257
$713$	0.167020	0.00625497
$714$	−0.374064	−0.0139990
$715$	−1.78343	−0.0666967
$716$	−14.9222	−0.557668
$717$	−20.5870	−0.768835
$718$	5.39047	0.201171
$719$	51.3849	1.91633	0.958167	−	0.286209i	$-0.0923950\pi$
$719$	51.3849	1.91633	0.958167	+	0.286209i	$0.0923950\pi$
$720$	−10.1489	−0.378228
$721$	19.3469	0.720517
$722$	−3.86387	−0.143798
$723$	−24.7075	−0.918882
$724$	12.8716	0.478371
$725$	5.52824	0.205314
$726$	3.78866	0.140611
$727$	3.61847	0.134202	0.0671008	−	0.997746i	$-0.478625\pi$
$727$	3.61847	0.134202	0.0671008	+	0.997746i	$0.478625\pi$
$728$	1.21202	0.0449203
$729$	22.8357	0.845767
$730$	−9.04391	−0.334730
$731$	−6.62646	−0.245088
$732$	−21.5234	−0.795527
$733$	−18.1873	−0.671763	−0.335882	−	0.941904i	$-0.609034\pi$
$733$	−18.1873	−0.671763	−0.335882	+	0.941904i	$0.609034\pi$
$734$	6.46962	0.238798
$735$	−2.30142	−0.0848892
$736$	−0.498130	−0.0183613
$737$	1.07531	0.0396094
$738$	5.02866	0.185108
$739$	−40.5966	−1.49337	−0.746686	−	0.665177i	$-0.768356\pi$
$739$	−40.5966	−1.49337	−0.746686	+	0.665177i	$0.768356\pi$
$740$	−25.8296	−0.949515
$741$	−3.08464	−0.113317
$742$	2.33769	0.0858195
$743$	0.150101	0.00550666	0.00275333	−	0.999996i	$-0.499124\pi$
$743$	0.150101	0.00550666	0.00275333	+	0.999996i	$0.499124\pi$
$744$	−1.70834	−0.0626307
$745$	6.09193	0.223191
$746$	−2.66607	−0.0976118
$747$	15.0090	0.549152
$748$	−1.77721	−0.0649814
$749$	−8.65671	−0.316309
$750$	4.53810	0.165708
$751$	10.7938	0.393873	0.196936	−	0.980416i	$-0.436901\pi$
$751$	10.7938	0.393873	0.196936	+	0.980416i	$0.436901\pi$
$752$	5.76162	0.210105
$753$	12.1634	0.443259
$754$	1.27060	0.0462723
$755$	23.0063	0.837283
$756$	−10.4316	−0.379393
$757$	−50.0934	−1.82068	−0.910338	−	0.413866i	$-0.864178\pi$
$757$	−50.0934	−1.82068	−0.910338	+	0.413866i	$0.864178\pi$
$758$	−6.67467	−0.242435
$759$	0.160574	0.00582846
$760$	5.92792	0.215028
$761$	34.7310	1.25900	0.629499	−	0.777002i	$-0.283260\pi$
$761$	34.7310	1.25900	0.629499	+	0.777002i	$0.283260\pi$
$762$	4.56796	0.165480
$763$	12.7298	0.460850
$764$	28.1787	1.01947
$765$	−2.95811	−0.106951
$766$	4.85191	0.175307
$767$	5.82899	0.210472
$768$	−10.6417	−0.383999
$769$	−31.6778	−1.14233	−0.571166	−	0.820835i	$-0.693509\pi$
$769$	−31.6778	−1.14233	−0.571166	+	0.820835i	$0.693509\pi$
$770$	0.553733	0.0199552
$771$	−17.2645	−0.621765
$772$	−19.8358	−0.713908
$773$	−0.916879	−0.0329778	−0.0164889	−	0.999864i	$-0.505249\pi$
$773$	−0.916879	−0.0329778	−0.0164889	+	0.999864i	$0.505249\pi$
$774$	3.18600	0.114518
$775$	1.58047	0.0567720
$776$	−8.59628	−0.308588
$777$	−8.55761	−0.307003
$778$	4.07143	0.145968
$779$	26.7787	0.959445
$780$	−4.38098	−0.156864
$781$	−9.18368	−0.328618
$782$	−0.0443252	−0.00158507
$783$	−22.4253	−0.801416
$784$	3.43088	0.122531
$785$	−41.2157	−1.47105
$786$	−1.87660	−0.0669359
$787$	−21.7066	−0.773758	−0.386879	−	0.922130i	$-0.626447\pi$
$787$	−21.7066	−0.773758	−0.386879	+	0.922130i	$0.626447\pi$
$788$	2.54042	0.0904988
$789$	−17.6728	−0.629169
$790$	−9.68667	−0.344636
$791$	−17.3759	−0.617816
$792$	1.75224	0.0622632
$793$	9.38495	0.333269
$794$	3.63791	0.129105
$795$	−17.3277	−0.614550
$796$	−28.3346	−1.00429
$797$	2.08365	0.0738068	0.0369034	−	0.999319i	$-0.488251\pi$
$797$	2.08365	0.0738068	0.0369034	+	0.999319i	$0.488251\pi$
$798$	0.957739	0.0339036
$799$	1.67934	0.0594108
$800$	−4.71366	−0.166653
$801$	17.8730	0.631511
$802$	1.90830	0.0673846
$803$	−14.2359	−0.502374
$804$	2.64147	0.0931576
$805$	−0.272710	−0.00961175
$806$	0.363250	0.0127949
$807$	32.4794	1.14333
$808$	−16.5415	−0.581930
$809$	14.6207	0.514037	0.257019	−	0.966406i	$-0.417260\pi$
$809$	14.6207	0.514037	0.257019	+	0.966406i	$0.417260\pi$
$810$	−1.16038	−0.0407716
$811$	55.6359	1.95364	0.976820	−	0.214063i	$-0.0686696\pi$
$811$	55.6359	1.95364	0.976820	+	0.214063i	$0.0686696\pi$
$812$	7.79003	0.273377
$813$	−29.6535	−1.03999
$814$	2.05900	0.0721680
$815$	1.02857	0.0360294
$816$	−4.13341	−0.144698
$817$	16.9661	0.593569
$818$	−7.78891	−0.272333
$819$	1.54854	0.0541102
$820$	38.0326	1.32816
$821$	19.8600	0.693119	0.346560	−	0.938028i	$-0.387350\pi$
$821$	19.8600	0.693119	0.346560	+	0.938028i	$0.387350\pi$
$822$	4.46819	0.155846
$823$	−1.37757	−0.0480191	−0.0240096	−	0.999712i	$-0.507643\pi$
$823$	−1.37757	−0.0480191	−0.0240096	+	0.999712i	$0.507643\pi$
$824$	−23.4488	−0.816877
$825$	1.51947	0.0529010
$826$	−1.80982	−0.0629718
$827$	−17.7767	−0.618155	−0.309078	−	0.951037i	$-0.600020\pi$
$827$	−17.7767	−0.618155	−0.309078	+	0.951037i	$0.600020\pi$
$828$	−0.420827	−0.0146248
$829$	31.6262	1.09842	0.549211	−	0.835684i	$-0.314928\pi$
$829$	31.6262	1.09842	0.549211	+	0.835684i	$0.314928\pi$
$830$	−5.74868	−0.199539
$831$	9.32970	0.323644
$832$	5.77839	0.200330
$833$	1.00000	0.0346479
$834$	−3.86344	−0.133780
$835$	46.6593	1.61471
$836$	4.55030	0.157376
$837$	−6.41117	−0.221602
$838$	0.623003	0.0215213
$839$	32.9407	1.13724	0.568619	−	0.822601i	$-0.307478\pi$
$839$	32.9407	1.13724	0.568619	+	0.822601i	$0.307478\pi$
$840$	2.78936	0.0962420
$841$	−12.2533	−0.422529
$842$	−0.288699	−0.00994923
$843$	21.8574	0.752808
$844$	30.0955	1.03593
$845$	1.91026	0.0657150
$846$	−0.807427	−0.0277599
$847$	−10.1284	−0.348015
$848$	25.8315	0.887059
$849$	−27.9689	−0.959889
$850$	−0.419437	−0.0143866
$851$	−1.01404	−0.0347610
$852$	−22.5596	−0.772878
$853$	19.7838	0.677385	0.338692	−	0.940897i	$-0.390015\pi$
$853$	19.7838	0.677385	0.338692	+	0.940897i	$0.390015\pi$
$854$	−2.91390	−0.0997117
$855$	7.57382	0.259019
$856$	10.4921	0.358611
$857$	19.2142	0.656345	0.328173	−	0.944618i	$-0.393567\pi$
$857$	19.2142	0.656345	0.328173	+	0.944618i	$0.393567\pi$
$858$	0.349229	0.0119225
$859$	−2.62517	−0.0895698	−0.0447849	−	0.998997i	$-0.514260\pi$
$859$	−2.62517	−0.0895698	−0.0447849	+	0.998997i	$0.514260\pi$
$860$	24.0963	0.821676
$861$	12.6006	0.429427
$862$	−11.7136	−0.398965
$863$	25.9186	0.882279	0.441139	−	0.897439i	$-0.354574\pi$
$863$	25.9186	0.882279	0.441139	+	0.897439i	$0.354574\pi$
$864$	19.1210	0.650509
$865$	−44.7660	−1.52209
$866$	3.76979	0.128103
$867$	−1.20477	−0.0409160
$868$	2.22709	0.0755923
$869$	−15.2476	−0.517241
$870$	2.92417	0.0991388
$871$	−1.15178	−0.0390264
$872$	−15.4287	−0.522483
$873$	−10.9831	−0.371720
$874$	0.113488	0.00383880
$875$	−12.1319	−0.410132
$876$	−34.9702	−1.18153
$877$	−26.5243	−0.895661	−0.447831	−	0.894118i	$-0.647803\pi$
$877$	−26.5243	−0.895661	−0.447831	+	0.894118i	$0.647803\pi$
$878$	6.97574	0.235420
$879$	−19.0301	−0.641871
$880$	6.11875	0.206263
$881$	−25.7113	−0.866236	−0.433118	−	0.901337i	$-0.642587\pi$
$881$	−25.7113	−0.866236	−0.433118	+	0.901337i	$0.642587\pi$
$882$	−0.480800	−0.0161894
$883$	−58.8214	−1.97950	−0.989749	−	0.142819i	$-0.954383\pi$
$883$	−58.8214	−1.97950	−0.989749	+	0.142819i	$0.954383\pi$
$884$	1.90360	0.0640249
$885$	13.4149	0.450939
$886$	−10.5970	−0.356014
$887$	−34.6852	−1.16462	−0.582308	−	0.812968i	$-0.697850\pi$
$887$	−34.6852	−1.16462	−0.582308	+	0.812968i	$0.697850\pi$
$888$	10.3720	0.348060
$889$	−12.2117	−0.409567
$890$	−6.84560	−0.229465
$891$	−1.82654	−0.0611912
$892$	−7.11393	−0.238192
$893$	−4.29971	−0.143884
$894$	−1.19291	−0.0398969
$895$	14.9744	0.500540
$896$	−8.77266	−0.293074
$897$	−0.171993	−0.00574268
$898$	−12.2718	−0.409516
$899$	4.78769	0.159678
$900$	−3.98217	−0.132739
$901$	7.52913	0.250832
$902$	−3.03177	−0.100947
$903$	7.98334	0.265669
$904$	21.0599	0.700441
$905$	−12.9167	−0.429366
$906$	−4.50505	−0.149670
$907$	−35.9075	−1.19229	−0.596145	−	0.802877i	$-0.703302\pi$
$907$	−35.9075	−1.19229	−0.596145	+	0.802877i	$0.703302\pi$
$908$	−44.0249	−1.46102
$909$	−21.1344	−0.700983
$910$	−0.593111	−0.0196614
$911$	41.2503	1.36668	0.683341	−	0.730099i	$-0.260526\pi$
$911$	41.2503	1.36668	0.683341	+	0.730099i	$0.260526\pi$
$912$	10.5830	0.350439
$913$	−9.04891	−0.299475
$914$	−7.27464	−0.240624
$915$	21.5987	0.714032
$916$	10.8394	0.358145
$917$	5.01677	0.165668
$918$	1.70145	0.0561561
$919$	−19.3066	−0.636865	−0.318432	−	0.947946i	$-0.603156\pi$
$919$	−19.3066	−0.636865	−0.318432	+	0.947946i	$0.603156\pi$
$920$	0.330528	0.0108972
$921$	−11.9530	−0.393865
$922$	9.04266	0.297804
$923$	9.83677	0.323781
$924$	2.14113	0.0704380
$925$	−9.59561	−0.315502
$926$	−1.11190	−0.0365394
$927$	−29.9594	−0.983996
$928$	−14.2790	−0.468733
$929$	41.8922	1.37444	0.687219	−	0.726450i	$-0.258831\pi$
$929$	41.8922	1.37444	0.687219	+	0.726450i	$0.258831\pi$
$930$	0.835991	0.0274132
$931$	−2.56036	−0.0839124
$932$	−45.8969	−1.50340
$933$	−10.6421	−0.348408
$934$	−2.86661	−0.0937985
$935$	1.78343	0.0583246
$936$	−1.87685	−0.0613468
$937$	14.8004	0.483509	0.241755	−	0.970337i	$-0.422277\pi$
$937$	14.8004	0.483509	0.241755	+	0.970337i	$0.422277\pi$
$938$	0.357611	0.0116764
$939$	23.2149	0.757591
$940$	−6.10670	−0.199179
$941$	15.7966	0.514955	0.257477	−	0.966284i	$-0.417109\pi$
$941$	15.7966	0.514955	0.257477	+	0.966284i	$0.417109\pi$
$942$	8.07079	0.262960
$943$	1.49312	0.0486228
$944$	−19.9986	−0.650898
$945$	10.4681	0.340527
$946$	−1.92083	−0.0624516
$947$	−23.2036	−0.754017	−0.377009	−	0.926210i	$-0.623047\pi$
$947$	−23.2036	−0.754017	−0.377009	+	0.926210i	$0.623047\pi$
$948$	−37.4556	−1.21650
$949$	15.2483	0.494979
$950$	1.07391	0.0348422
$951$	−17.0851	−0.554022
$952$	−1.21202	−0.0392817
$953$	44.9816	1.45710	0.728548	−	0.684994i	$-0.240195\pi$
$953$	44.9816	1.45710	0.728548	+	0.684994i	$0.240195\pi$
$954$	−3.62001	−0.117202
$955$	−28.2774	−0.915034
$956$	−32.5286	−1.05205
$957$	4.60290	0.148791
$958$	2.48766	0.0803726
$959$	−11.9450	−0.385723
$960$	13.2985	0.429207
$961$	−29.6312	−0.955847
$962$	−2.20543	−0.0711058
$963$	13.4052	0.431977
$964$	−39.0392	−1.25737
$965$	19.9053	0.640774
$966$	0.0534015	0.00171817
$967$	−29.2472	−0.940525	−0.470263	−	0.882527i	$-0.655841\pi$
$967$	−29.2472	−0.940525	−0.470263	+	0.882527i	$0.655841\pi$
$968$	12.2758	0.394558
$969$	3.08464	0.0990928
$970$	4.20667	0.135068
$971$	−42.7010	−1.37034	−0.685169	−	0.728384i	$-0.740272\pi$
$971$	−42.7010	−1.37034	−0.685169	+	0.728384i	$0.740272\pi$
$972$	26.8079	0.859863
$973$	10.3283	0.331109
$974$	−8.42164	−0.269847
$975$	−1.62752	−0.0521224
$976$	−32.1986	−1.03065
$977$	29.9756	0.959003	0.479502	−	0.877541i	$-0.340817\pi$
$977$	29.9756	0.959003	0.479502	+	0.877541i	$0.340817\pi$
$978$	−0.201414	−0.00644050
$979$	−10.7756	−0.344389
$980$	−3.63637	−0.116160
$981$	−19.7126	−0.629374
$982$	2.29542	0.0732499
$983$	−10.1260	−0.322968	−0.161484	−	0.986875i	$-0.551628\pi$
$983$	−10.1260	−0.322968	−0.161484	+	0.986875i	$0.551628\pi$
$984$	−15.2721	−0.486858
$985$	−2.54932	−0.0812279
$986$	−1.27060	−0.0404640
$987$	−2.02321	−0.0643996
$988$	−4.87389	−0.155059
$989$	0.945995	0.0300809
$990$	−0.857476	−0.0272524
$991$	17.2851	0.549080	0.274540	−	0.961576i	$-0.411474\pi$
$991$	17.2851	0.549080	0.274540	+	0.961576i	$0.411474\pi$
$992$	−4.08223	−0.129611
$993$	9.96355	0.316184
$994$	−3.05419	−0.0968729
$995$	28.4338	0.901413
$996$	−22.2285	−0.704337
$997$	−34.8725	−1.10442	−0.552211	−	0.833705i	$-0.686216\pi$
$997$	−34.8725	−1.10442	−0.552211	+	0.833705i	$0.686216\pi$
$998$	−7.77341	−0.246063
$999$	38.9246	1.23152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1547.2.a.g.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1547.2.a.g.1.6	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1547 = 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1547.a (trivial)

\(f(q)\)	\(=\)	\(q+0.310487 q^{2} -1.20477 q^{3} -1.90360 q^{4} +1.91026 q^{5} -0.374064 q^{6} +1.00000 q^{7} -1.21202 q^{8} -1.54854 q^{9} +0.593111 q^{10} +0.933608 q^{11} +2.29339 q^{12} -1.00000 q^{13} +0.310487 q^{14} -2.30142 q^{15} +3.43088 q^{16} +1.00000 q^{17} -0.480800 q^{18} -2.56036 q^{19} -3.63637 q^{20} -1.20477 q^{21} +0.289873 q^{22} -0.142760 q^{23} +1.46020 q^{24} -1.35090 q^{25} -0.310487 q^{26} +5.47993 q^{27} -1.90360 q^{28} -4.09227 q^{29} -0.714561 q^{30} -1.16994 q^{31} +3.48927 q^{32} -1.12478 q^{33} +0.310487 q^{34} +1.91026 q^{35} +2.94779 q^{36} +7.10312 q^{37} -0.794958 q^{38} +1.20477 q^{39} -2.31527 q^{40} -10.4590 q^{41} -0.374064 q^{42} -6.62646 q^{43} -1.77721 q^{44} -2.95811 q^{45} -0.0443252 q^{46} +1.67934 q^{47} -4.13341 q^{48} +1.00000 q^{49} -0.419437 q^{50} -1.20477 q^{51} +1.90360 q^{52} +7.52913 q^{53} +1.70145 q^{54} +1.78343 q^{55} -1.21202 q^{56} +3.08464 q^{57} -1.27060 q^{58} -5.82899 q^{59} +4.38098 q^{60} -9.38495 q^{61} -0.363250 q^{62} -1.54854 q^{63} -5.77839 q^{64} -1.91026 q^{65} -0.349229 q^{66} +1.15178 q^{67} -1.90360 q^{68} +0.171993 q^{69} +0.593111 q^{70} -9.83677 q^{71} +1.87685 q^{72} -15.2483 q^{73} +2.20543 q^{74} +1.62752 q^{75} +4.87389 q^{76} +0.933608 q^{77} +0.374064 q^{78} -16.3320 q^{79} +6.55388 q^{80} -1.95643 q^{81} -3.24737 q^{82} -9.69241 q^{83} +2.29339 q^{84} +1.91026 q^{85} -2.05743 q^{86} +4.93023 q^{87} -1.13155 q^{88} -11.5419 q^{89} -0.918454 q^{90} -1.00000 q^{91} +0.271758 q^{92} +1.40950 q^{93} +0.521413 q^{94} -4.89096 q^{95} -4.20376 q^{96} +7.09254 q^{97} +0.310487 q^{98} -1.44572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 6 q^{8} + 5 q^{9} - 9 q^{10} - 7 q^{11} + 2 q^{12} - 9 q^{13} - 3 q^{14} - 5 q^{15} + 3 q^{16} + 9 q^{17} - 9 q^{18} - 6 q^{19} + 6 q^{20}+ \cdots - 25 q^{99}+O(q^{100}) \) 9 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 6 * q^8 + 5 * q^9 - 9 * q^10 - 7 * q^11 + 2 * q^12 - 9 * q^13 - 3 * q^14 - 5 * q^15 + 3 * q^16 + 9 * q^17 - 9 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 - 4 * q^22 - 3 * q^23 + 8 * q^24 - 13 * q^25 + 3 * q^26 - 13 * q^27 + 3 * q^28 - 4 * q^29 + 10 * q^32 - 12 * q^33 - 3 * q^34 - 6 * q^35 - 17 * q^36 - 31 * q^37 - 3 * q^38 + 4 * q^39 - 18 * q^40 + 3 * q^41 + 2 * q^42 - 24 * q^43 - 20 * q^44 + 3 * q^45 + 5 * q^46 + 7 * q^47 + 2 * q^48 + 9 * q^49 + 24 * q^50 - 4 * q^51 - 3 * q^52 - 18 * q^53 + 6 * q^55 - 6 * q^56 - 35 * q^57 + 2 * q^58 - 9 * q^59 + 2 * q^60 - 22 * q^61 + 30 * q^62 + 5 * q^63 - 36 * q^64 + 6 * q^65 + 22 * q^66 - 32 * q^67 + 3 * q^68 - 2 * q^69 - 9 * q^70 + 18 * q^71 - 10 * q^72 - 14 * q^73 + 12 * q^74 + 11 * q^75 - 27 * q^76 - 7 * q^77 - 2 * q^78 - 46 * q^79 - q^80 + 29 * q^81 + 3 * q^82 - 16 * q^83 + 2 * q^84 - 6 * q^85 - 34 * q^86 + 3 * q^87 - 10 * q^89 + 21 * q^90 - 9 * q^91 + 14 * q^92 - 83 * q^93 + q^94 - 55 * q^96 - 15 * q^97 - 3 * q^98 - 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more