LMFDB - Embedded newform 289.4.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 $ x^12 - 72x^10 - 17x^9 + 1872x^8 + 627x^7 - 20922x^6 - 5163x^5 + 93255x^4 - 4607x^3 - 117822x^2 + 21960x + 29352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.26162$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} +O(q^{10})$	\(q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} -16.7325 q^{10} -45.5149 q^{11} -39.0610 q^{12} -52.5379 q^{13} +34.3910 q^{14} -80.8409 q^{15} +28.3328 q^{16} +12.8100 q^{18} +3.08418 q^{19} +84.9911 q^{20} +166.156 q^{21} -57.4227 q^{22} -112.369 q^{23} -110.801 q^{24} +50.8981 q^{25} -66.2831 q^{26} -102.685 q^{27} -174.686 q^{28} +18.6294 q^{29} -101.991 q^{30} -238.763 q^{31} +181.168 q^{32} -277.430 q^{33} -361.531 q^{35} -65.0674 q^{36} +162.717 q^{37} +3.89108 q^{38} -320.238 q^{39} +241.087 q^{40} -383.816 q^{41} +209.626 q^{42} +468.761 q^{43} +291.673 q^{44} -134.664 q^{45} -141.767 q^{46} -199.727 q^{47} +172.699 q^{48} +400.071 q^{49} +64.2142 q^{50} +336.679 q^{52} -105.679 q^{53} -129.550 q^{54} +603.649 q^{55} -495.516 q^{56} +18.7993 q^{57} +23.5033 q^{58} +207.142 q^{59} +518.053 q^{60} -586.101 q^{61} -301.230 q^{62} +276.780 q^{63} +1.90375 q^{64} +696.792 q^{65} -350.013 q^{66} +401.953 q^{67} -684.930 q^{69} -456.116 q^{70} +481.559 q^{71} -184.571 q^{72} +725.281 q^{73} +205.287 q^{74} +310.243 q^{75} -19.7644 q^{76} -1240.71 q^{77} -404.020 q^{78} +382.621 q^{79} -375.768 q^{80} -900.052 q^{81} -484.231 q^{82} -182.391 q^{83} -1064.78 q^{84} +591.401 q^{86} +113.553 q^{87} +827.364 q^{88} -623.009 q^{89} -169.895 q^{90} -1432.15 q^{91} +720.094 q^{92} -1455.35 q^{93} -251.981 q^{94} -40.9045 q^{95} +1104.29 q^{96} +369.544 q^{97} +504.739 q^{98} -462.140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.26162	0.446051	0.223026	−	0.974813i	$-0.428407\pi$
$2$	1.26162	0.446051	0.223026	+	0.974813i	$0.428407\pi$
$3$	6.09538	1.17306	0.586528	−	0.809929i	$-0.300494\pi$
$3$	6.09538	1.17306	0.586528	+	0.809929i	$0.300494\pi$
$4$	−6.40830	−0.801038
$5$	−13.2627	−1.18625	−0.593124	−	0.805111i	$-0.702106\pi$
$5$	−13.2627	−1.18625	−0.593124	+	0.805111i	$0.702106\pi$
$6$	7.69007	0.523243
$7$	27.2593	1.47186	0.735932	−	0.677055i	$-0.236744\pi$
$7$	27.2593	1.47186	0.735932	+	0.677055i	$0.236744\pi$
$8$	−18.1779	−0.803356
$9$	10.1536	0.376059
$10$	−16.7325	−0.529128
$11$	−45.5149	−1.24757	−0.623785	−	0.781596i	$-0.714406\pi$
$11$	−45.5149	−1.24757	−0.623785	+	0.781596i	$0.714406\pi$
$12$	−39.0610	−0.939662
$13$	−52.5379	−1.12088	−0.560438	−	0.828196i	$-0.689367\pi$
$13$	−52.5379	−1.12088	−0.560438	+	0.828196i	$0.689367\pi$
$14$	34.3910	0.656527
$15$	−80.8409	−1.39153
$16$	28.3328	0.442700
$17$	0	0
$17$	0	0
$18$	12.8100	0.167742
$19$	3.08418	0.0372400	0.0186200	−	0.999827i	$-0.494073\pi$
$19$	3.08418	0.0372400	0.0186200	+	0.999827i	$0.494073\pi$
$20$	84.9911	0.950230
$21$	166.156	1.72658
$22$	−57.4227	−0.556480
$23$	−112.369	−1.01872	−0.509359	−	0.860554i	$-0.670118\pi$
$23$	−112.369	−1.01872	−0.509359	+	0.860554i	$0.670118\pi$
$24$	−110.801	−0.942381
$25$	50.8981	0.407185
$26$	−66.2831	−0.499968
$27$	−102.685	−0.731917
$28$	−174.686	−1.17902
$29$	18.6294	0.119290	0.0596448	−	0.998220i	$-0.481003\pi$
$29$	18.6294	0.119290	0.0596448	+	0.998220i	$0.481003\pi$
$30$	−101.991	−0.620696
$31$	−238.763	−1.38333	−0.691664	−	0.722219i	$-0.743122\pi$
$31$	−238.763	−1.38333	−0.691664	+	0.722219i	$0.743122\pi$
$32$	181.168	1.00082
$33$	−277.430	−1.46347
$34$	0	0
$35$	−361.531	−1.74600
$36$	−65.0674	−0.301238
$37$	162.717	0.722986	0.361493	−	0.932375i	$-0.382267\pi$
$37$	162.717	0.722986	0.361493	+	0.932375i	$0.382267\pi$
$38$	3.89108	0.0166110
$39$	−320.238	−1.31485
$40$	241.087	0.952979
$41$	−383.816	−1.46200	−0.730999	−	0.682378i	$-0.760946\pi$
$41$	−383.816	−1.46200	−0.730999	+	0.682378i	$0.760946\pi$
$42$	209.626	0.770143
$43$	468.761	1.66245	0.831226	−	0.555935i	$-0.187640\pi$
$43$	468.761	1.66245	0.831226	+	0.555935i	$0.187640\pi$
$44$	291.673	0.999350
$45$	−134.664	−0.446100
$46$	−141.767	−0.454401
$47$	−199.727	−0.619856	−0.309928	−	0.950760i	$-0.600305\pi$
$47$	−199.727	−0.619856	−0.309928	+	0.950760i	$0.600305\pi$
$48$	172.699	0.519312
$49$	400.071	1.16639
$50$	64.2142	0.181625
$51$	0	0
$52$	336.679	0.897864
$53$	−105.679	−0.273889	−0.136944	−	0.990579i	$-0.543728\pi$
$53$	−105.679	−0.273889	−0.136944	+	0.990579i	$0.543728\pi$
$54$	−129.550	−0.326473
$55$	603.649	1.47993
$56$	−495.516	−1.18243
$57$	18.7993	0.0436846
$58$	23.5033	0.0532093
$59$	207.142	0.457078	0.228539	−	0.973535i	$-0.426605\pi$
$59$	207.142	0.457078	0.228539	+	0.973535i	$0.426605\pi$
$60$	518.053	1.11467
$61$	−586.101	−1.23021	−0.615103	−	0.788447i	$-0.710886\pi$
$61$	−586.101	−1.23021	−0.615103	+	0.788447i	$0.710886\pi$
$62$	−301.230	−0.617036
$63$	276.780	0.553508
$64$	1.90375	0.00371826
$65$	696.792	1.32964
$66$	−350.013	−0.652782
$67$	401.953	0.732931	0.366466	−	0.930432i	$-0.380568\pi$
$67$	401.953	0.732931	0.366466	+	0.930432i	$0.380568\pi$
$68$	0	0
$69$	−684.930	−1.19501
$70$	−456.116	−0.778805
$71$	481.559	0.804937	0.402468	−	0.915434i	$-0.368152\pi$
$71$	481.559	0.804937	0.402468	+	0.915434i	$0.368152\pi$
$72$	−184.571	−0.302109
$73$	725.281	1.16285	0.581423	−	0.813602i	$-0.302496\pi$
$73$	725.281	1.16285	0.581423	+	0.813602i	$0.302496\pi$
$74$	205.287	0.322489
$75$	310.243	0.477650
$76$	−19.7644	−0.0298307
$77$	−1240.71	−1.83625
$78$	−404.020	−0.586491
$79$	382.621	0.544914	0.272457	−	0.962168i	$-0.412164\pi$
$79$	382.621	0.544914	0.272457	+	0.962168i	$0.412164\pi$
$80$	−375.768	−0.525152
$81$	−900.052	−1.23464
$82$	−484.231	−0.652127
$83$	−182.391	−0.241204	−0.120602	−	0.992701i	$-0.538483\pi$
$83$	−182.391	−0.241204	−0.120602	+	0.992701i	$0.538483\pi$
$84$	−1064.78	−1.38306
$85$	0	0
$86$	591.401	0.741539
$87$	113.553	0.139933
$88$	827.364	1.00224
$89$	−623.009	−0.742010	−0.371005	−	0.928631i	$-0.620987\pi$
$89$	−623.009	−0.742010	−0.371005	+	0.928631i	$0.620987\pi$
$90$	−169.895	−0.198983
$91$	−1432.15	−1.64978
$92$	720.094	0.816032
$93$	−1455.35	−1.62272
$94$	−251.981	−0.276488
$95$	−40.9045	−0.0441759
$96$	1104.29	1.17402
$97$	369.544	0.386820	0.193410	−	0.981118i	$-0.438045\pi$
$97$	369.544	0.386820	0.193410	+	0.981118i	$0.438045\pi$
$98$	504.739	0.520268
$99$	−462.140	−0.469160
$100$	−326.170	−0.326170
$101$	810.381	0.798375	0.399188	−	0.916869i	$-0.369292\pi$
$101$	810.381	0.798375	0.399188	+	0.916869i	$0.369292\pi$
$102$	0	0
$103$	772.683	0.739172	0.369586	−	0.929197i	$-0.379500\pi$
$103$	772.683	0.739172	0.369586	+	0.929197i	$0.379500\pi$
$104$	955.026	0.900462
$105$	−2203.67	−2.04815
$106$	−133.327	−0.122169
$107$	996.966	0.900751	0.450375	−	0.892839i	$-0.351290\pi$
$107$	996.966	0.900751	0.450375	+	0.892839i	$0.351290\pi$
$108$	658.038	0.586293
$109$	−700.996	−0.615993	−0.307996	−	0.951388i	$-0.599658\pi$
$109$	−700.996	−0.615993	−0.307996	+	0.951388i	$0.599658\pi$
$110$	761.578	0.660123
$111$	991.820	0.848102
$112$	772.333	0.651595
$113$	−1459.26	−1.21483	−0.607415	−	0.794384i	$-0.707794\pi$
$113$	−1459.26	−1.21483	−0.607415	+	0.794384i	$0.707794\pi$
$114$	23.7176	0.0194856
$115$	1490.31	1.20845
$116$	−119.383	−0.0955554
$117$	−533.449	−0.421516
$118$	261.335	0.203880
$119$	0	0
$120$	1469.51	1.11790
$121$	740.607	0.556429
$122$	−739.439	−0.548735
$123$	−2339.50	−1.71501
$124$	1530.07	1.10810
$125$	982.788	0.703226
$126$	349.193	0.246893
$127$	426.418	0.297941	0.148970	−	0.988842i	$-0.452404\pi$
$127$	426.418	0.297941	0.148970	+	0.988842i	$0.452404\pi$
$128$	−1446.94	−0.999164
$129$	2857.28	1.95015
$130$	879.089	0.593086
$131$	19.9037	0.0132747	0.00663737	−	0.999978i	$-0.497887\pi$
$131$	19.9037	0.0132747	0.00663737	+	0.999978i	$0.497887\pi$
$132$	1777.86	1.17229
$133$	84.0728	0.0548123
$134$	507.114	0.326925
$135$	1361.88	0.868235
$136$	0	0
$137$	−1824.89	−1.13804	−0.569019	−	0.822324i	$-0.692677\pi$
$137$	−1824.89	−1.13804	−0.569019	+	0.822324i	$0.692677\pi$
$138$	−864.125	−0.533037
$139$	−1803.87	−1.10074	−0.550368	−	0.834922i	$-0.685512\pi$
$139$	−1803.87	−1.10074	−0.550368	+	0.834922i	$0.685512\pi$
$140$	2316.80	1.39861
$141$	−1217.41	−0.727126
$142$	607.546	0.359043
$143$	2391.26	1.39837
$144$	287.680	0.166482
$145$	−247.076	−0.141507
$146$	915.032	0.518689
$147$	2438.58	1.36824
$148$	−1042.74	−0.579139
$149$	2742.46	1.50786	0.753929	−	0.656955i	$-0.228156\pi$
$149$	2742.46	1.50786	0.753929	+	0.656955i	$0.228156\pi$
$150$	391.410	0.213057
$151$	2085.22	1.12379	0.561896	−	0.827208i	$-0.310072\pi$
$151$	2085.22	1.12379	0.561896	+	0.827208i	$0.310072\pi$
$152$	−56.0639	−0.0299170
$153$	0	0
$154$	−1565.30	−0.819063
$155$	3166.64	1.64097
$156$	2052.18	1.05324
$157$	−2703.53	−1.37430	−0.687149	−	0.726516i	$-0.741138\pi$
$157$	−2703.53	−1.37430	−0.687149	+	0.726516i	$0.741138\pi$
$158$	482.724	0.243060
$159$	−644.152	−0.321287
$160$	−2402.77	−1.18722
$161$	−3063.10	−1.49942
$162$	−1135.53	−0.550712
$163$	−2923.57	−1.40486	−0.702428	−	0.711755i	$-0.747901\pi$
$163$	−2923.57	−1.40486	−0.702428	+	0.711755i	$0.747901\pi$
$164$	2459.61	1.17112
$165$	3679.46	1.73604
$166$	−230.108	−0.107590
$167$	−2419.31	−1.12103	−0.560514	−	0.828145i	$-0.689397\pi$
$167$	−2419.31	−1.12103	−0.560514	+	0.828145i	$0.689397\pi$
$168$	−3020.36	−1.38706
$169$	563.229	0.256363
$170$	0	0
$171$	31.3156	0.0140045
$172$	−3003.97	−1.33169
$173$	−393.655	−0.173000	−0.0865000	−	0.996252i	$-0.527568\pi$
$173$	−393.655	−0.173000	−0.0865000	+	0.996252i	$0.527568\pi$
$174$	143.262	0.0624174
$175$	1387.45	0.599321
$176$	−1289.57	−0.552299
$177$	1262.61	0.536178
$178$	−786.004	−0.330975
$179$	1918.60	0.801133	0.400567	−	0.916268i	$-0.368813\pi$
$179$	1918.60	0.801133	0.400567	+	0.916268i	$0.368813\pi$
$180$	862.966	0.357343
$181$	−1677.03	−0.688688	−0.344344	−	0.938844i	$-0.611899\pi$
$181$	−1677.03	−0.688688	−0.344344	+	0.938844i	$0.611899\pi$
$182$	−1806.83	−0.735886
$183$	−3572.51	−1.44310
$184$	2042.63	0.818393
$185$	−2158.06	−0.857640
$186$	−1836.11	−0.723817
$187$	0	0
$188$	1279.91	0.496529
$189$	−2799.13	−1.07728
$190$	−51.6061	−0.0197047
$191$	2347.19	0.889196	0.444598	−	0.895730i	$-0.353347\pi$
$191$	2347.19	0.889196	0.444598	+	0.895730i	$0.353347\pi$
$192$	11.6041	0.00436173
$193$	650.982	0.242791	0.121396	−	0.992604i	$-0.461263\pi$
$193$	650.982	0.242791	0.121396	+	0.992604i	$0.461263\pi$
$194$	466.226	0.172542
$195$	4247.21	1.55974
$196$	−2563.77	−0.934320
$197$	−2681.01	−0.969614	−0.484807	−	0.874621i	$-0.661110\pi$
$197$	−2681.01	−0.969614	−0.484807	+	0.874621i	$0.661110\pi$
$198$	−583.047	−0.209269
$199$	−1784.74	−0.635762	−0.317881	−	0.948131i	$-0.602971\pi$
$199$	−1784.74	−0.635762	−0.317881	+	0.948131i	$0.602971\pi$
$200$	−925.218	−0.327114
$201$	2450.06	0.859769
$202$	1022.40	0.356116
$203$	507.825	0.175578
$204$	0	0
$205$	5090.42	1.73429
$206$	974.835	0.329709
$207$	−1140.95	−0.383099
$208$	−1488.55	−0.496212
$209$	−140.376	−0.0464595
$210$	−2780.20	−0.913581
$211$	68.5651	0.0223707	0.0111853	−	0.999937i	$-0.496440\pi$
$211$	68.5651	0.0223707	0.0111853	+	0.999937i	$0.496440\pi$
$212$	677.222	0.219395
$213$	2935.28	0.944235
$214$	1257.80	0.401781
$215$	−6217.02	−1.97208
$216$	1866.60	0.587990
$217$	−6508.53	−2.03607
$218$	−884.393	−0.274765
$219$	4420.86	1.36408
$220$	−3868.36	−1.18548
$221$	0	0
$222$	1251.30	0.378297
$223$	4734.22	1.42164	0.710822	−	0.703372i	$-0.248323\pi$
$223$	4734.22	1.42164	0.710822	+	0.703372i	$0.248323\pi$
$224$	4938.52	1.47308
$225$	516.799	0.153126
$226$	−1841.04	−0.541877
$227$	1722.86	0.503745	0.251873	−	0.967760i	$-0.418954\pi$
$227$	1722.86	0.503745	0.251873	+	0.967760i	$0.418954\pi$
$228$	−120.471	−0.0349930
$229$	−313.375	−0.0904297	−0.0452149	−	0.998977i	$-0.514397\pi$
$229$	−313.375	−0.0904297	−0.0452149	+	0.998977i	$0.514397\pi$
$230$	1880.21	0.539032
$231$	−7562.57	−2.15403
$232$	−338.643	−0.0958319
$233$	−2101.61	−0.590905	−0.295453	−	0.955357i	$-0.595470\pi$
$233$	−2101.61	−0.590905	−0.295453	+	0.955357i	$0.595470\pi$
$234$	−673.012	−0.188018
$235$	2648.92	0.735303
$236$	−1327.43	−0.366137
$237$	2332.22	0.639215
$238$	0	0
$239$	−5525.44	−1.49544	−0.747721	−	0.664013i	$-0.768852\pi$
$239$	−5525.44	−1.49544	−0.747721	+	0.664013i	$0.768852\pi$
$240$	−2290.45	−0.616033
$241$	2005.92	0.536153	0.268076	−	0.963398i	$-0.413612\pi$
$241$	2005.92	0.536153	0.268076	+	0.963398i	$0.413612\pi$
$242$	934.367	0.248196
$243$	−2713.65	−0.716383
$244$	3755.91	0.985442
$245$	−5306.00	−1.38362
$246$	−2951.57	−0.764981
$247$	−162.037	−0.0417414
$248$	4340.21	1.11130
$249$	−1111.74	−0.282946
$250$	1239.91	0.313675
$251$	4427.81	1.11347	0.556735	−	0.830690i	$-0.312054\pi$
$251$	4427.81	1.11347	0.556735	+	0.830690i	$0.312054\pi$
$252$	−1773.69	−0.443381
$253$	5114.46	1.27092
$254$	537.979	0.132897
$255$	0	0
$256$	−1840.73	−0.449397
$257$	−6198.01	−1.50436	−0.752182	−	0.658956i	$-0.770998\pi$
$257$	−6198.01	−1.50436	−0.752182	+	0.658956i	$0.770998\pi$
$258$	3604.81	0.869867
$259$	4435.55	1.06414
$260$	−4465.26	−1.06509
$261$	189.156	0.0448599
$262$	25.1109	0.00592122
$263$	477.072	0.111854	0.0559269	−	0.998435i	$-0.482189\pi$
$263$	477.072	0.111854	0.0559269	+	0.998435i	$0.482189\pi$
$264$	5043.09	1.17569
$265$	1401.58	0.324900
$266$	106.068	0.0244491
$267$	−3797.48	−0.870419
$268$	−2575.84	−0.587106
$269$	−7583.93	−1.71896	−0.859481	−	0.511168i	$-0.829213\pi$
$269$	−7583.93	−1.71896	−0.859481	+	0.511168i	$0.829213\pi$
$270$	1718.18	0.387278
$271$	−5431.92	−1.21759	−0.608793	−	0.793329i	$-0.708346\pi$
$271$	−5431.92	−1.21759	−0.608793	+	0.793329i	$0.708346\pi$
$272$	0	0
$273$	−8729.47	−1.93528
$274$	−2302.33	−0.507624
$275$	−2316.62	−0.507991
$276$	4389.24	0.957251
$277$	−4091.98	−0.887594	−0.443797	−	0.896127i	$-0.646369\pi$
$277$	−4091.98	−0.887594	−0.443797	+	0.896127i	$0.646369\pi$
$278$	−2275.81	−0.490985
$279$	−2424.31	−0.520213
$280$	6571.86	1.40266
$281$	−3410.26	−0.723983	−0.361991	−	0.932181i	$-0.617903\pi$
$281$	−3410.26	−0.723983	−0.361991	+	0.932181i	$0.617903\pi$
$282$	−1535.92	−0.324336
$283$	4322.86	0.908011	0.454006	−	0.890999i	$-0.349995\pi$
$283$	4322.86	0.908011	0.454006	+	0.890999i	$0.349995\pi$
$284$	−3085.97	−0.644785
$285$	−249.328	−0.0518208
$286$	3016.87	0.623745
$287$	−10462.6	−2.15186
$288$	1839.51	0.376369
$289$	0	0
$290$	−311.716	−0.0631194
$291$	2252.51	0.453761
$292$	−4647.82	−0.931484
$293$	3073.56	0.612831	0.306416	−	0.951898i	$-0.400870\pi$
$293$	3073.56	0.612831	0.306416	+	0.951898i	$0.400870\pi$
$294$	3076.57	0.610304
$295$	−2747.26	−0.542208
$296$	−2957.84	−0.580815
$297$	4673.70	0.913117
$298$	3459.95	0.672583
$299$	5903.62	1.14186
$300$	−1988.13	−0.382616
$301$	12778.1	2.44690
$302$	2630.76	0.501269
$303$	4939.57	0.936538
$304$	87.3836	0.0164862
$305$	7773.26	1.45933
$306$	0	0
$307$	−3954.45	−0.735154	−0.367577	−	0.929993i	$-0.619813\pi$
$307$	−3954.45	−0.735154	−0.367577	+	0.929993i	$0.619813\pi$
$308$	7950.82	1.47091
$309$	4709.79	0.867089
$310$	3995.11	0.731957
$311$	−8984.40	−1.63813	−0.819065	−	0.573701i	$-0.805507\pi$
$311$	−8984.40	−1.63813	−0.819065	+	0.573701i	$0.805507\pi$
$312$	5821.24	1.05629
$313$	−1737.01	−0.313680	−0.156840	−	0.987624i	$-0.550131\pi$
$313$	−1737.01	−0.313680	−0.156840	+	0.987624i	$0.550131\pi$
$314$	−3410.83	−0.613008
$315$	−3670.84	−0.656598
$316$	−2451.95	−0.436497
$317$	−8232.55	−1.45863	−0.729316	−	0.684177i	$-0.760162\pi$
$317$	−8232.55	−1.45863	−0.729316	+	0.684177i	$0.760162\pi$
$318$	−812.678	−0.143310
$319$	−847.916	−0.148822
$320$	−25.2488	−0.00441078
$321$	6076.88	1.05663
$322$	−3864.48	−0.668817
$323$	0	0
$324$	5767.81	0.988993
$325$	−2674.08	−0.456403
$326$	−3688.44	−0.626638
$327$	−4272.83	−0.722594
$328$	6976.95	1.17451
$329$	−5444.44	−0.912345
$330$	4642.10	0.774361
$331$	−4153.12	−0.689655	−0.344828	−	0.938666i	$-0.612063\pi$
$331$	−4153.12	−0.689655	−0.344828	+	0.938666i	$0.612063\pi$
$332$	1168.81	0.193214
$333$	1652.16	0.271885
$334$	−3052.26	−0.500037
$335$	−5330.97	−0.869439
$336$	4707.66	0.764357
$337$	−6569.49	−1.06191	−0.530954	−	0.847401i	$-0.678166\pi$
$337$	−6569.49	−1.06191	−0.530954	+	0.847401i	$0.678166\pi$
$338$	710.584	0.114351
$339$	−8894.75	−1.42506
$340$	0	0
$341$	10867.3	1.72580
$342$	39.5085	0.00624671
$343$	1555.70	0.244898
$344$	−8521.08	−1.33554
$345$	9084.00	1.41758
$346$	−496.644	−0.0771669
$347$	2038.58	0.315380	0.157690	−	0.987489i	$-0.449595\pi$
$347$	2038.58	0.315380	0.157690	+	0.987489i	$0.449595\pi$
$348$	−727.684	−0.112092
$349$	−1791.21	−0.274731	−0.137365	−	0.990520i	$-0.543863\pi$
$349$	−1791.21	−0.274731	−0.137365	+	0.990520i	$0.543863\pi$
$350$	1750.44	0.267328
$351$	5394.86	0.820388
$352$	−8245.86	−1.24860
$353$	−5928.71	−0.893919	−0.446959	−	0.894554i	$-0.647493\pi$
$353$	−5928.71	−0.893919	−0.446959	+	0.894554i	$0.647493\pi$
$354$	1592.94	0.239163
$355$	−6386.75	−0.954854
$356$	3992.43	0.594378
$357$	0	0
$358$	2420.55	0.357347
$359$	413.998	0.0608634	0.0304317	−	0.999537i	$-0.490312\pi$
$359$	413.998	0.0608634	0.0304317	+	0.999537i	$0.490312\pi$
$360$	2447.90	0.358377
$361$	−6849.49	−0.998613
$362$	−2115.78	−0.307190
$363$	4514.28	0.652722
$364$	9177.63	1.32154
$365$	−9619.15	−1.37942
$366$	−4507.16	−0.643697
$367$	−6979.15	−0.992667	−0.496334	−	0.868132i	$-0.665321\pi$
$367$	−6979.15	−0.992667	−0.496334	+	0.868132i	$0.665321\pi$
$368$	−3183.73	−0.450987
$369$	−3897.11	−0.549798
$370$	−2722.66	−0.382552
$371$	−2880.73	−0.403127
$372$	9326.34	1.29986
$373$	6855.64	0.951667	0.475833	−	0.879535i	$-0.342147\pi$
$373$	6855.64	0.951667	0.475833	+	0.879535i	$0.342147\pi$
$374$	0	0
$375$	5990.46	0.824923
$376$	3630.62	0.497965
$377$	−978.750	−0.133709
$378$	−3531.45	−0.480524
$379$	8206.78	1.11228	0.556140	−	0.831089i	$-0.312282\pi$
$379$	8206.78	1.11228	0.556140	+	0.831089i	$0.312282\pi$
$380$	262.128	0.0353866
$381$	2599.18	0.349501
$382$	2961.27	0.396627
$383$	−889.401	−0.118659	−0.0593293	−	0.998238i	$-0.518896\pi$
$383$	−889.401	−0.118659	−0.0593293	+	0.998238i	$0.518896\pi$
$384$	−8819.67	−1.17208
$385$	16455.1	2.17825
$386$	821.294	0.108297
$387$	4759.62	0.625180
$388$	−2368.15	−0.309857
$389$	−12992.8	−1.69347	−0.846736	−	0.532013i	$-0.821436\pi$
$389$	−12992.8	−1.69347	−0.846736	+	0.532013i	$0.821436\pi$
$390$	5358.38	0.695723
$391$	0	0
$392$	−7272.43	−0.937023
$393$	121.320	0.0155720
$394$	−3382.42	−0.432498
$395$	−5074.57	−0.646403
$396$	2961.54	0.375815
$397$	−4325.29	−0.546801	−0.273400	−	0.961900i	$-0.588148\pi$
$397$	−4325.29	−0.546801	−0.273400	+	0.961900i	$0.588148\pi$
$398$	−2251.67	−0.283583
$399$	512.455	0.0642979
$400$	1442.09	0.180261
$401$	11849.1	1.47560	0.737798	−	0.675022i	$-0.235866\pi$
$401$	11849.1	1.47560	0.737798	+	0.675022i	$0.235866\pi$
$402$	3091.05	0.383501
$403$	12544.1	1.55054
$404$	−5193.17	−0.639529
$405$	11937.1	1.46459
$406$	640.685	0.0783168
$407$	−7406.04	−0.901975
$408$	0	0
$409$	7677.24	0.928154	0.464077	−	0.885795i	$-0.346386\pi$
$409$	7677.24	0.928154	0.464077	+	0.885795i	$0.346386\pi$
$410$	6422.19	0.773584
$411$	−11123.4	−1.33498
$412$	−4951.59	−0.592105
$413$	5646.55	0.672757
$414$	−1439.45	−0.170882
$415$	2418.98	0.286128
$416$	−9518.20	−1.12180
$417$	−10995.3	−1.29122
$418$	−177.102	−0.0207233
$419$	3235.83	0.377280	0.188640	−	0.982046i	$-0.439592\pi$
$419$	3235.83	0.377280	0.188640	+	0.982046i	$0.439592\pi$
$420$	14121.8	1.64065
$421$	14496.6	1.67820	0.839100	−	0.543977i	$-0.183082\pi$
$421$	14496.6	1.67820	0.839100	+	0.543977i	$0.183082\pi$
$422$	86.5033	0.00997848
$423$	−2027.95	−0.233103
$424$	1921.02	0.220030
$425$	0	0
$426$	3703.22	0.421178
$427$	−15976.7	−1.81070
$428$	−6388.86	−0.721536
$429$	14575.6	1.64037
$430$	−7843.54	−0.879649
$431$	−7136.25	−0.797543	−0.398771	−	0.917050i	$-0.630563\pi$
$431$	−7136.25	−0.797543	−0.398771	+	0.917050i	$0.630563\pi$
$432$	−2909.36	−0.324020
$433$	11434.3	1.26904	0.634521	−	0.772905i	$-0.281197\pi$
$433$	11434.3	1.26904	0.634521	+	0.772905i	$0.281197\pi$
$434$	−8211.32	−0.908193
$435$	−1506.02	−0.165996
$436$	4492.20	0.493434
$437$	−346.566	−0.0379371
$438$	5577.46	0.608451
$439$	13308.0	1.44682	0.723412	−	0.690417i	$-0.242573\pi$
$439$	13308.0	1.44682	0.723412	+	0.690417i	$0.242573\pi$
$440$	−10973.0	−1.18891
$441$	4062.16	0.438630
$442$	0	0
$443$	−10897.9	−1.16880	−0.584398	−	0.811467i	$-0.698669\pi$
$443$	−10897.9	−1.16880	−0.584398	+	0.811467i	$0.698669\pi$
$444$	−6355.88	−0.679362
$445$	8262.76	0.880208
$446$	5972.80	0.634126
$447$	16716.3	1.76880
$448$	51.8949	0.00547278
$449$	16756.4	1.76121	0.880603	−	0.473855i	$-0.157138\pi$
$449$	16756.4	1.76121	0.880603	+	0.473855i	$0.157138\pi$
$450$	652.006	0.0683019
$451$	17469.3	1.82394
$452$	9351.40	0.973126
$453$	12710.2	1.31827
$454$	2173.60	0.224696
$455$	18994.1	1.95705
$456$	−341.730	−0.0350943
$457$	13561.8	1.38817	0.694087	−	0.719891i	$-0.255808\pi$
$457$	13561.8	1.38817	0.694087	+	0.719891i	$0.255808\pi$
$458$	−395.361	−0.0403363
$459$	0	0
$460$	−9550.36	−0.968017
$461$	15516.4	1.56762	0.783810	−	0.621000i	$-0.213273\pi$
$461$	15516.4	1.56762	0.783810	+	0.621000i	$0.213273\pi$
$462$	−9541.11	−0.960807
$463$	−15186.4	−1.52435	−0.762174	−	0.647372i	$-0.775868\pi$
$463$	−15186.4	−1.52435	−0.762174	+	0.647372i	$0.775868\pi$
$464$	527.824	0.0528095
$465$	19301.8	1.92495
$466$	−2651.44	−0.263574
$467$	10544.3	1.04482	0.522412	−	0.852693i	$-0.325032\pi$
$467$	10544.3	1.04482	0.522412	+	0.852693i	$0.325032\pi$
$468$	3418.50	0.337650
$469$	10957.0	1.07878
$470$	3341.94	0.327983
$471$	−16479.0	−1.61213
$472$	−3765.40	−0.367196
$473$	−21335.6	−2.07402
$474$	2942.38	0.285123
$475$	156.979	0.0151636
$476$	0	0
$477$	−1073.02	−0.102998
$478$	−6971.02	−0.667044
$479$	5762.22	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$479$	5762.22	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$480$	−14645.8	−1.39268
$481$	−8548.79	−0.810377
$482$	2530.72	0.239152
$483$	−18670.7	−1.75890
$484$	−4746.03	−0.445721
$485$	−4901.14	−0.458864
$486$	−3423.61	−0.319544
$487$	−5369.36	−0.499608	−0.249804	−	0.968296i	$-0.580366\pi$
$487$	−5369.36	−0.499608	−0.249804	+	0.968296i	$0.580366\pi$
$488$	10654.1	0.988293
$489$	−17820.2	−1.64797
$490$	−6694.18	−0.617167
$491$	17878.0	1.64322	0.821611	−	0.570049i	$-0.193076\pi$
$491$	17878.0	1.64322	0.821611	+	0.570049i	$0.193076\pi$
$492$	14992.2	1.37378
$493$	0	0
$494$	−204.429	−0.0186188
$495$	6129.21	0.556540
$496$	−6764.84	−0.612400
$497$	13127.0	1.18476
$498$	−1402.60	−0.126209
$499$	3507.03	0.314622	0.157311	−	0.987549i	$-0.449718\pi$
$499$	3507.03	0.314622	0.157311	+	0.987549i	$0.449718\pi$
$500$	−6298.01	−0.563311
$501$	−14746.6	−1.31503
$502$	5586.23	0.496665
$503$	−1207.56	−0.107043	−0.0535214	−	0.998567i	$-0.517045\pi$
$503$	−1207.56	−0.107043	−0.0535214	+	0.998567i	$0.517045\pi$
$504$	−5031.27	−0.444664
$505$	−10747.8	−0.947071
$506$	6452.52	0.566897
$507$	3433.09	0.300728
$508$	−2732.62	−0.238662
$509$	−14092.1	−1.22716	−0.613578	−	0.789634i	$-0.710270\pi$
$509$	−14092.1	−1.22716	−0.613578	+	0.789634i	$0.710270\pi$
$510$	0	0
$511$	19770.7	1.71155
$512$	9253.25	0.798710
$513$	−316.700	−0.0272566
$514$	−7819.56	−0.671023
$515$	−10247.8	−0.876841
$516$	−18310.3	−1.56214
$517$	9090.58	0.773314
$518$	5595.99	0.474660
$519$	−2399.47	−0.202939
$520$	−12666.2	−1.06817
$521$	−10080.1	−0.847635	−0.423818	−	0.905748i	$-0.639310\pi$
$521$	−10080.1	−0.847635	−0.423818	+	0.905748i	$0.639310\pi$
$522$	238.643	0.0200098
$523$	12330.2	1.03090	0.515452	−	0.856919i	$-0.327624\pi$
$523$	12330.2	1.03090	0.515452	+	0.856919i	$0.327624\pi$
$524$	−127.549	−0.0106336
$525$	8457.01	0.703036
$526$	601.886	0.0498925
$527$	0	0
$528$	−7860.38	−0.647877
$529$	459.760	0.0377875
$530$	1768.27	0.144922
$531$	2103.24	0.171888
$532$	−538.764	−0.0439067
$533$	20164.9	1.63872
$534$	−4790.99	−0.388252
$535$	−13222.4	−1.06851
$536$	−7306.65	−0.588805
$537$	11694.6	0.939774
$538$	−9568.07	−0.766745
$539$	−18209.2	−1.45515
$540$	−8727.33	−0.695490
$541$	7122.72	0.566044	0.283022	−	0.959113i	$-0.408663\pi$
$541$	7122.72	0.566044	0.283022	+	0.959113i	$0.408663\pi$
$542$	−6853.04	−0.543106
$543$	−10222.1	−0.807869
$544$	0	0
$545$	9297.07	0.730720
$546$	−11013.3	−0.863235
$547$	14919.7	1.16622	0.583109	−	0.812394i	$-0.301836\pi$
$547$	14919.7	1.16622	0.583109	+	0.812394i	$0.301836\pi$
$548$	11694.5	0.911612
$549$	−5951.04	−0.462630
$550$	−2922.70	−0.226590
$551$	57.4566	0.00444234
$552$	12450.6	0.960021
$553$	10430.0	0.802040
$554$	−5162.55	−0.395913
$555$	−13154.2	−1.00606
$556$	11559.7	0.881731
$557$	−18935.0	−1.44039	−0.720197	−	0.693769i	$-0.755949\pi$
$557$	−18935.0	−1.44039	−0.720197	+	0.693769i	$0.755949\pi$
$558$	−3058.57	−0.232042
$559$	−24627.7	−1.86340
$560$	−10243.2	−0.772953
$561$	0	0
$562$	−4302.47	−0.322934
$563$	8150.42	0.610123	0.305062	−	0.952333i	$-0.401323\pi$
$563$	8150.42	0.610123	0.305062	+	0.952333i	$0.401323\pi$
$564$	7801.56	0.582456
$565$	19353.7	1.44109
$566$	5453.82	0.405020
$567$	−24534.8	−1.81722
$568$	−8753.71	−0.646650
$569$	18218.2	1.34226	0.671131	−	0.741338i	$-0.265809\pi$
$569$	18218.2	1.34226	0.671131	+	0.741338i	$0.265809\pi$
$570$	−314.558	−0.0231147
$571$	2443.35	0.179073	0.0895367	−	0.995984i	$-0.471461\pi$
$571$	2443.35	0.179073	0.0895367	+	0.995984i	$0.471461\pi$
$572$	−15323.9	−1.12015
$573$	14307.0	1.04308
$574$	−13199.8	−0.959842
$575$	−5719.36	−0.414806
$576$	19.3299	0.00139829
$577$	−852.752	−0.0615261	−0.0307630	−	0.999527i	$-0.509794\pi$
$577$	−852.752	−0.0615261	−0.0307630	+	0.999527i	$0.509794\pi$
$578$	0	0
$579$	3967.98	0.284807
$580$	1583.34	0.113352
$581$	−4971.84	−0.355020
$582$	2841.82	0.202401
$583$	4809.96	0.341695
$584$	−13184.1	−0.934179
$585$	7074.95	0.500022
$586$	3877.68	0.273354
$587$	900.272	0.0633019	0.0316509	−	0.999499i	$-0.489924\pi$
$587$	900.272	0.0633019	0.0316509	+	0.999499i	$0.489924\pi$
$588$	−15627.2	−1.09601
$589$	−736.390	−0.0515152
$590$	−3466.00	−0.241853
$591$	−16341.7	−1.13741
$592$	4610.22	0.320066
$593$	−25007.2	−1.73174	−0.865870	−	0.500268i	$-0.833235\pi$
$593$	−25007.2	−1.73174	−0.865870	+	0.500268i	$0.833235\pi$
$594$	5896.46	0.407297
$595$	0	0
$596$	−17574.5	−1.20785
$597$	−10878.6	−0.745784
$598$	7448.15	0.509327
$599$	−3448.82	−0.235251	−0.117625	−	0.993058i	$-0.537528\pi$
$599$	−3448.82	−0.235251	−0.117625	+	0.993058i	$0.537528\pi$
$600$	−5639.55	−0.383723
$601$	942.873	0.0639943	0.0319972	−	0.999488i	$-0.489813\pi$
$601$	942.873	0.0639943	0.0319972	+	0.999488i	$0.489813\pi$
$602$	16121.2	1.09145
$603$	4081.27	0.275626
$604$	−13362.7	−0.900201
$605$	−9822.41	−0.660063
$606$	6231.89	0.417744
$607$	−10173.9	−0.680306	−0.340153	−	0.940370i	$-0.610479\pi$
$607$	−10173.9	−0.680306	−0.340153	+	0.940370i	$0.610479\pi$
$608$	558.756	0.0372707
$609$	3095.39	0.205963
$610$	9806.93	0.650936
$611$	10493.3	0.694782
$612$	0	0
$613$	−17327.0	−1.14165	−0.570824	−	0.821073i	$-0.693376\pi$
$613$	−17327.0	−1.14165	−0.570824	+	0.821073i	$0.693376\pi$
$614$	−4989.03	−0.327916
$615$	31028.0	2.03442
$616$	22553.4	1.47516
$617$	−19782.8	−1.29080	−0.645401	−	0.763844i	$-0.723310\pi$
$617$	−19782.8	−1.29080	−0.645401	+	0.763844i	$0.723310\pi$
$618$	5941.98	0.386766
$619$	−15033.2	−0.976147	−0.488074	−	0.872802i	$-0.662300\pi$
$619$	−15033.2	−0.976147	−0.488074	+	0.872802i	$0.662300\pi$
$620$	−20292.8	−1.31448
$621$	11538.6	0.745618
$622$	−11334.9	−0.730690
$623$	−16982.8	−1.09214
$624$	−9073.25	−0.582084
$625$	−19396.6	−1.24139
$626$	−2191.46	−0.139917
$627$	−855.647	−0.0544996
$628$	17325.0	1.10087
$629$	0	0
$630$	−4631.22	−0.292877
$631$	−24060.5	−1.51796	−0.758979	−	0.651115i	$-0.774302\pi$
$631$	−24060.5	−1.51796	−0.758979	+	0.651115i	$0.774302\pi$
$632$	−6955.23	−0.437760
$633$	417.930	0.0262421
$634$	−10386.4	−0.650625
$635$	−5655.44	−0.353432
$636$	4127.92	0.257363
$637$	−21018.9	−1.30737
$638$	−1069.75	−0.0663822
$639$	4889.55	0.302704
$640$	19190.3	1.18526
$641$	4886.07	0.301074	0.150537	−	0.988604i	$-0.451900\pi$
$641$	4886.07	0.301074	0.150537	+	0.988604i	$0.451900\pi$
$642$	7666.74	0.471312
$643$	24508.4	1.50314	0.751568	−	0.659655i	$-0.229298\pi$
$643$	24508.4	1.50314	0.751568	+	0.659655i	$0.229298\pi$
$644$	19629.3	1.20109
$645$	−37895.1	−2.31336
$646$	0	0
$647$	2932.50	0.178189	0.0890947	−	0.996023i	$-0.471603\pi$
$647$	2932.50	0.178189	0.0890947	+	0.996023i	$0.471603\pi$
$648$	16361.0	0.991854
$649$	−9428.06	−0.570237
$650$	−3373.68	−0.203579
$651$	−39671.9	−2.38843
$652$	18735.1	1.12534
$653$	−19977.8	−1.19723	−0.598617	−	0.801035i	$-0.704283\pi$
$653$	−19977.8	−1.19723	−0.598617	+	0.801035i	$0.704283\pi$
$654$	−5390.71	−0.322314
$655$	−263.975	−0.0157471
$656$	−10874.6	−0.647227
$657$	7364.21	0.437299
$658$	−6868.83	−0.406953
$659$	28222.7	1.66829	0.834143	−	0.551548i	$-0.185963\pi$
$659$	28222.7	1.66829	0.834143	+	0.551548i	$0.185963\pi$
$660$	−23579.1	−1.39063
$661$	20712.8	1.21881	0.609405	−	0.792859i	$-0.291408\pi$
$661$	20712.8	1.21881	0.609405	+	0.792859i	$0.291408\pi$
$662$	−5239.67	−0.307622
$663$	0	0
$664$	3315.47	0.193773
$665$	−1115.03	−0.0650210
$666$	2084.41	0.121275
$667$	−2093.37	−0.121522
$668$	15503.7	0.897987
$669$	28856.8	1.66767
$670$	−6725.68	−0.387814
$671$	26676.3	1.53477
$672$	30102.2	1.72800
$673$	−395.468	−0.0226511	−0.0113255	−	0.999936i	$-0.503605\pi$
$673$	−395.468	−0.0226511	−0.0113255	+	0.999936i	$0.503605\pi$
$674$	−8288.23	−0.473666
$675$	−5226.48	−0.298025
$676$	−3609.34	−0.205356
$677$	2297.47	0.130427	0.0652135	−	0.997871i	$-0.479227\pi$
$677$	2297.47	0.130427	0.0652135	+	0.997871i	$0.479227\pi$
$678$	−11221.8	−0.635652
$679$	10073.5	0.569347
$680$	0	0
$681$	10501.5	0.590921
$682$	13710.4	0.769794
$683$	28611.7	1.60292	0.801461	−	0.598048i	$-0.204057\pi$
$683$	28611.7	1.60292	0.801461	+	0.598048i	$0.204057\pi$
$684$	−200.680	−0.0112181
$685$	24202.9	1.35000
$686$	1962.71	0.109237
$687$	−1910.14	−0.106079
$688$	13281.3	0.735968
$689$	5552.14	0.306995
$690$	11460.6	0.632315
$691$	−4902.87	−0.269919	−0.134959	−	0.990851i	$-0.543090\pi$
$691$	−4902.87	−0.269919	−0.134959	+	0.990851i	$0.543090\pi$
$692$	2522.66	0.138580
$693$	−12597.6	−0.690540
$694$	2571.93	0.140676
$695$	23924.1	1.30575
$696$	−2064.16	−0.112416
$697$	0	0
$698$	−2259.83	−0.122544
$699$	−12810.1	−0.693165
$700$	−8891.18	−0.480079
$701$	1714.99	0.0924027	0.0462014	−	0.998932i	$-0.485288\pi$
$701$	1714.99	0.0924027	0.0462014	+	0.998932i	$0.485288\pi$
$702$	6806.28	0.365935
$703$	501.849	0.0269240
$704$	−86.6490	−0.00463879
$705$	16146.1	0.862552
$706$	−7479.80	−0.398734
$707$	22090.4	1.17510
$708$	−8091.18	−0.429499
$709$	13939.8	0.738393	0.369196	−	0.929351i	$-0.379633\pi$
$709$	13939.8	0.738393	0.369196	+	0.929351i	$0.379633\pi$
$710$	−8057.67	−0.425914
$711$	3884.98	0.204920
$712$	11325.0	0.596098
$713$	26829.6	1.40922
$714$	0	0
$715$	−31714.4	−1.65881
$716$	−12295.0	−0.641738
$717$	−33679.6	−1.75424
$718$	522.310	0.0271482
$719$	1779.18	0.0922839	0.0461419	−	0.998935i	$-0.485307\pi$
$719$	1779.18	0.0922839	0.0461419	+	0.998935i	$0.485307\pi$
$720$	−3815.40	−0.197488
$721$	21062.8	1.08796
$722$	−8641.48	−0.445433
$723$	12226.9	0.628937
$724$	10746.9	0.551665
$725$	948.201	0.0485729
$726$	5695.32	0.291148
$727$	9141.02	0.466330	0.233165	−	0.972437i	$-0.425092\pi$
$727$	9141.02	0.466330	0.233165	+	0.972437i	$0.425092\pi$
$728$	26033.4	1.32536
$729$	7760.65	0.394282
$730$	−12135.8	−0.615294
$731$	0	0
$732$	22893.7	1.15598
$733$	12176.0	0.613547	0.306773	−	0.951783i	$-0.400751\pi$
$733$	12176.0	0.613547	0.306773	+	0.951783i	$0.400751\pi$
$734$	−8805.07	−0.442781
$735$	−32342.1	−1.62307
$736$	−20357.7	−1.01956
$737$	−18294.9	−0.914383
$738$	−4916.69	−0.245238
$739$	25025.4	1.24570	0.622852	−	0.782339i	$-0.285974\pi$
$739$	25025.4	1.24570	0.622852	+	0.782339i	$0.285974\pi$
$740$	13829.5	0.687003
$741$	−987.673	−0.0489650
$742$	−3634.40	−0.179816
$743$	10781.3	0.532339	0.266170	−	0.963926i	$-0.414242\pi$
$743$	10781.3	0.532339	0.266170	+	0.963926i	$0.414242\pi$
$744$	26455.2	1.30362
$745$	−36372.3	−1.78869
$746$	8649.24	0.424492
$747$	−1851.92	−0.0907072
$748$	0	0
$749$	27176.6	1.32578
$750$	7557.71	0.367958
$751$	−33910.7	−1.64769	−0.823847	−	0.566812i	$-0.808177\pi$
$751$	−33910.7	−1.64769	−0.823847	+	0.566812i	$0.808177\pi$
$752$	−5658.84	−0.274410
$753$	26989.2	1.30616
$754$	−1234.81	−0.0596410
$755$	−27655.5	−1.33310
$756$	17937.7	0.862945
$757$	−31545.0	−1.51456	−0.757281	−	0.653090i	$-0.773472\pi$
$757$	−31545.0	−1.51456	−0.757281	+	0.653090i	$0.773472\pi$
$758$	10353.9	0.496134
$759$	31174.5	1.49086
$760$	743.556	0.0354890
$761$	9150.51	0.435881	0.217941	−	0.975962i	$-0.430066\pi$
$761$	9150.51	0.435881	0.217941	+	0.975962i	$0.430066\pi$
$762$	3279.19	0.155895
$763$	−19108.7	−0.906658
$764$	−15041.5	−0.712280
$765$	0	0
$766$	−1122.09	−0.0529279
$767$	−10882.8	−0.512328
$768$	−11219.9	−0.527168
$769$	33797.5	1.58488	0.792438	−	0.609952i	$-0.208811\pi$
$769$	33797.5	1.58488	0.792438	+	0.609952i	$0.208811\pi$
$770$	20760.1	0.971612
$771$	−37779.2	−1.76470
$772$	−4171.69	−0.194485
$773$	−33969.4	−1.58059	−0.790295	−	0.612727i	$-0.790073\pi$
$773$	−33969.4	−1.58059	−0.790295	+	0.612727i	$0.790073\pi$
$774$	6004.85	0.278863
$775$	−12152.6	−0.563270
$776$	−6717.52	−0.310754
$777$	27036.3	1.24829
$778$	−16392.0	−0.755376
$779$	−1183.76	−0.0544449
$780$	−27217.4	−1.24941
$781$	−21918.1	−1.00421
$782$	0	0
$783$	−1912.96	−0.0873100
$784$	11335.1	0.516359
$785$	35856.0	1.63026
$786$	153.061	0.00694592
$787$	10962.7	0.496543	0.248271	−	0.968691i	$-0.420138\pi$
$787$	10962.7	0.496543	0.248271	+	0.968691i	$0.420138\pi$
$788$	17180.7	0.776698
$789$	2907.93	0.131211
$790$	−6402.20	−0.288329
$791$	−39778.5	−1.78807
$792$	8400.72	0.376902
$793$	30792.5	1.37891
$794$	−5456.89	−0.243901
$795$	8543.17	0.381126
$796$	11437.1	0.509270
$797$	−8041.29	−0.357386	−0.178693	−	0.983905i	$-0.557187\pi$
$797$	−8041.29	−0.357386	−0.178693	+	0.983905i	$0.557187\pi$
$798$	646.526	0.0286802
$799$	0	0
$800$	9221.12	0.407520
$801$	−6325.79	−0.279040
$802$	14949.1	0.658192
$803$	−33011.1	−1.45073
$804$	−15700.7	−0.688708
$805$	40624.8	1.77868
$806$	15826.0	0.691620
$807$	−46226.9	−2.01644
$808$	−14731.0	−0.641379
$809$	−36568.0	−1.58920	−0.794599	−	0.607134i	$-0.792319\pi$
$809$	−36568.0	−1.58920	−0.794599	+	0.607134i	$0.792319\pi$
$810$	15060.1	0.653282
$811$	−37315.7	−1.61570	−0.807849	−	0.589390i	$-0.799368\pi$
$811$	−37315.7	−1.61570	−0.807849	+	0.589390i	$0.799368\pi$
$812$	−3254.30	−0.140645
$813$	−33109.6	−1.42830
$814$	−9343.64	−0.402327
$815$	38774.3	1.66651
$816$	0	0
$817$	1445.75	0.0619097
$818$	9685.79	0.414005
$819$	−14541.4	−0.620414
$820$	−32620.9	−1.38924
$821$	27365.1	1.16328	0.581638	−	0.813448i	$-0.302412\pi$
$821$	27365.1	1.16328	0.581638	+	0.813448i	$0.302412\pi$
$822$	−14033.6	−0.595471
$823$	21138.4	0.895308	0.447654	−	0.894207i	$-0.352260\pi$
$823$	21138.4	0.895308	0.447654	+	0.894207i	$0.352260\pi$
$824$	−14045.7	−0.593818
$825$	−14120.7	−0.595902
$826$	7123.83	0.300084
$827$	43453.3	1.82711	0.913554	−	0.406717i	$-0.133327\pi$
$827$	43453.3	1.82711	0.913554	+	0.406717i	$0.133327\pi$
$828$	7311.55	0.306877
$829$	36460.2	1.52752	0.763760	−	0.645501i	$-0.223351\pi$
$829$	36460.2	1.52752	0.763760	+	0.645501i	$0.223351\pi$
$830$	3051.85	0.127628
$831$	−24942.2	−1.04120
$832$	−100.019	−0.00416771
$833$	0	0
$834$	−13871.9	−0.575952
$835$	32086.5	1.32982
$836$	899.575	0.0372158
$837$	24517.4	1.01248
$838$	4082.39	0.168286
$839$	−20236.0	−0.832687	−0.416344	−	0.909207i	$-0.636689\pi$
$839$	−20236.0	−0.832687	−0.416344	+	0.909207i	$0.636689\pi$
$840$	40058.0	1.64539
$841$	−24041.9	−0.985770
$842$	18289.3	0.748564
$843$	−20786.8	−0.849272
$844$	−439.386	−0.0179198
$845$	−7469.92	−0.304110
$846$	−2558.51	−0.103976
$847$	20188.4	0.818988
$848$	−2994.18	−0.121251
$849$	26349.4	1.06515
$850$	0	0
$851$	−18284.3	−0.736519
$852$	−18810.2	−0.756368
$853$	6934.19	0.278338	0.139169	−	0.990269i	$-0.455557\pi$
$853$	6934.19	0.278338	0.139169	+	0.990269i	$0.455557\pi$
$854$	−20156.6	−0.807664
$855$	−415.328	−0.0166128
$856$	−18122.7	−0.723623
$857$	19207.8	0.765607	0.382803	−	0.923830i	$-0.374959\pi$
$857$	19207.8	0.765607	0.382803	+	0.923830i	$0.374959\pi$
$858$	18388.9	0.731688
$859$	−9954.55	−0.395395	−0.197698	−	0.980263i	$-0.563346\pi$
$859$	−9954.55	−0.395395	−0.197698	+	0.980263i	$0.563346\pi$
$860$	39840.6	1.57971
$861$	−63773.2	−2.52426
$862$	−9003.26	−0.355745
$863$	−33698.0	−1.32919	−0.664596	−	0.747203i	$-0.731396\pi$
$863$	−33698.0	−1.32919	−0.664596	+	0.747203i	$0.731396\pi$
$864$	−18603.3	−0.732519
$865$	5220.91	0.205221
$866$	14425.7	0.566058
$867$	0	0
$868$	41708.6	1.63097
$869$	−17415.0	−0.679818
$870$	−1900.03	−0.0740425
$871$	−21117.8	−0.821525
$872$	12742.6	0.494861
$873$	3752.20	0.145467
$874$	−437.236	−0.0169219
$875$	26790.1	1.03505
$876$	−28330.2	−1.09268
$877$	4469.65	0.172097	0.0860487	−	0.996291i	$-0.472576\pi$
$877$	4469.65	0.172097	0.0860487	+	0.996291i	$0.472576\pi$
$878$	16789.7	0.645358
$879$	18734.5	0.718885
$880$	17103.1	0.655164
$881$	2081.32	0.0795930	0.0397965	−	0.999208i	$-0.487329\pi$
$881$	2081.32	0.0795930	0.0397965	+	0.999208i	$0.487329\pi$
$882$	5124.91	0.195652
$883$	10124.4	0.385857	0.192929	−	0.981213i	$-0.438201\pi$
$883$	10124.4	0.385857	0.192929	+	0.981213i	$0.438201\pi$
$884$	0	0
$885$	−16745.6	−0.636040
$886$	−13749.1	−0.521343
$887$	−42725.3	−1.61733	−0.808666	−	0.588268i	$-0.799810\pi$
$887$	−42725.3	−1.61733	−0.808666	+	0.588268i	$0.799810\pi$
$888$	−18029.2	−0.681328
$889$	11623.9	0.438529
$890$	10424.5	0.392618
$891$	40965.8	1.54030
$892$	−30338.3	−1.13879
$893$	−615.996	−0.0230835
$894$	21089.7	0.788977
$895$	−25445.7	−0.950343
$896$	−39442.7	−1.47063
$897$	35984.8	1.33946
$898$	21140.2	0.785588
$899$	−4448.02	−0.165017
$900$	−3311.80	−0.122659
$901$	0	0
$902$	22039.7	0.813573
$903$	77887.4	2.87036
$904$	26526.3	0.975941
$905$	22241.8	0.816954
$906$	16035.5	0.588017
$907$	−21767.6	−0.796893	−0.398446	−	0.917192i	$-0.630450\pi$
$907$	−21767.6	−0.796893	−0.398446	+	0.917192i	$0.630450\pi$
$908$	−11040.6	−0.403519
$909$	8228.28	0.300236
$910$	23963.4	0.872943
$911$	−21654.2	−0.787524	−0.393762	−	0.919212i	$-0.628827\pi$
$911$	−21654.2	−0.787524	−0.393762	+	0.919212i	$0.628827\pi$
$912$	532.636	0.0193392
$913$	8301.49	0.300919
$914$	17109.9	0.619197
$915$	47380.9	1.71187
$916$	2008.20	0.0724376
$917$	542.560	0.0195386
$918$	0	0
$919$	21445.1	0.769760	0.384880	−	0.922967i	$-0.374243\pi$
$919$	21445.1	0.769760	0.384880	+	0.922967i	$0.374243\pi$
$920$	−27090.6	−0.970818
$921$	−24103.8	−0.862376
$922$	19575.9	0.699239
$923$	−25300.1	−0.902234
$924$	48463.2	1.72546
$925$	8281.97	0.294389
$926$	−19159.6	−0.679938
$927$	7845.51	0.277972
$928$	3375.06	0.119388
$929$	24271.4	0.857177	0.428589	−	0.903500i	$-0.359011\pi$
$929$	24271.4	0.857177	0.428589	+	0.903500i	$0.359011\pi$
$930$	24351.7	0.858626
$931$	1233.89	0.0434363
$932$	13467.7	0.473338
$933$	−54763.3	−1.92162
$934$	13303.0	0.466046
$935$	0	0
$936$	9696.96	0.338627
$937$	38491.5	1.34201	0.671005	−	0.741453i	$-0.265863\pi$
$937$	38491.5	1.34201	0.671005	+	0.741453i	$0.265863\pi$
$938$	13823.6	0.481190
$939$	−10587.7	−0.367964
$940$	−16975.1	−0.589006
$941$	31323.4	1.08514	0.542568	−	0.840012i	$-0.317452\pi$
$941$	31323.4	1.08514	0.542568	+	0.840012i	$0.317452\pi$
$942$	−20790.3	−0.719092
$943$	43128.9	1.48937
$944$	5868.92	0.202349
$945$	37123.9	1.27793
$946$	−26917.5	−0.925121
$947$	32096.4	1.10136	0.550682	−	0.834715i	$-0.314368\pi$
$947$	32096.4	1.10136	0.550682	+	0.834715i	$0.314368\pi$
$948$	−14945.6	−0.512035
$949$	−38104.7	−1.30341
$950$	198.049	0.00676373
$951$	−50180.5	−1.71106
$952$	0	0
$953$	10493.3	0.356675	0.178338	−	0.983969i	$-0.442928\pi$
$953$	10493.3	0.356675	0.178338	+	0.983969i	$0.442928\pi$
$954$	−1353.75	−0.0459426
$955$	−31129.9	−1.05481
$956$	35408.7	1.19791
$957$	−5168.37	−0.174576
$958$	7269.75	0.245172
$959$	−49745.4	−1.67504
$960$	−153.901	−0.00517409
$961$	27217.0	0.913597
$962$	−10785.4	−0.361470
$963$	10122.8	0.338736
$964$	−12854.6	−0.429479
$965$	−8633.74	−0.288010
$966$	−23555.4	−0.784559
$967$	31468.2	1.04648	0.523242	−	0.852184i	$-0.324722\pi$
$967$	31468.2	1.04648	0.523242	+	0.852184i	$0.324722\pi$
$968$	−13462.6	−0.447010
$969$	0	0
$970$	−6183.39	−0.204677
$971$	−46923.8	−1.55083	−0.775415	−	0.631452i	$-0.782459\pi$
$971$	−46923.8	−1.55083	−0.775415	+	0.631452i	$0.782459\pi$
$972$	17389.9	0.573850
$973$	−49172.3	−1.62013
$974$	−6774.11	−0.222851
$975$	−16299.5	−0.535387
$976$	−16605.9	−0.544612
$977$	8666.25	0.283785	0.141893	−	0.989882i	$-0.454681\pi$
$977$	8666.25	0.283785	0.141893	+	0.989882i	$0.454681\pi$
$978$	−22482.4	−0.735081
$979$	28356.2	0.925709
$980$	34002.5	1.10834
$981$	−7117.63	−0.231650
$982$	22555.3	0.732961
$983$	−35155.3	−1.14067	−0.570336	−	0.821412i	$-0.693187\pi$
$983$	−35155.3	−1.14067	−0.570336	+	0.821412i	$0.693187\pi$
$984$	42527.1	1.37776
$985$	35557.3	1.15020
$986$	0	0
$987$	−33185.9	−1.07023
$988$	1038.38	0.0334365
$989$	−52674.2	−1.69357
$990$	7732.75	0.248246
$991$	11236.2	0.360170	0.180085	−	0.983651i	$-0.442363\pi$
$991$	11236.2	0.360170	0.180085	+	0.983651i	$0.442363\pi$
$992$	−43256.3	−1.38447
$993$	−25314.8	−0.809004
$994$	16561.3	0.528463
$995$	23670.4	0.754172
$996$	7124.36	0.226651
$997$	−18825.0	−0.597987	−0.298994	−	0.954255i	$-0.596651\pi$
$997$	−18825.0	−0.597987	−0.298994	+	0.954255i	$0.596651\pi$
$998$	4424.56	0.140338
$999$	−16708.6	−0.529166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.8	✓	12
17.4	even	4		289.4.b.f.288.10		24
17.13	even	4		289.4.b.f.288.9		24
17.16	even	2		289.4.a.i.1.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.8	✓	12	1.1	even	1	trivial
289.4.a.i.1.8	yes	12	17.16	even	2
289.4.b.f.288.9		24	17.13	even	4
289.4.b.f.288.10		24	17.4	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} +O(q^{10})\)	\(q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} -16.7325 q^{10} -45.5149 q^{11} -39.0610 q^{12} -52.5379 q^{13} +34.3910 q^{14} -80.8409 q^{15} +28.3328 q^{16} +12.8100 q^{18} +3.08418 q^{19} +84.9911 q^{20} +166.156 q^{21} -57.4227 q^{22} -112.369 q^{23} -110.801 q^{24} +50.8981 q^{25} -66.2831 q^{26} -102.685 q^{27} -174.686 q^{28} +18.6294 q^{29} -101.991 q^{30} -238.763 q^{31} +181.168 q^{32} -277.430 q^{33} -361.531 q^{35} -65.0674 q^{36} +162.717 q^{37} +3.89108 q^{38} -320.238 q^{39} +241.087 q^{40} -383.816 q^{41} +209.626 q^{42} +468.761 q^{43} +291.673 q^{44} -134.664 q^{45} -141.767 q^{46} -199.727 q^{47} +172.699 q^{48} +400.071 q^{49} +64.2142 q^{50} +336.679 q^{52} -105.679 q^{53} -129.550 q^{54} +603.649 q^{55} -495.516 q^{56} +18.7993 q^{57} +23.5033 q^{58} +207.142 q^{59} +518.053 q^{60} -586.101 q^{61} -301.230 q^{62} +276.780 q^{63} +1.90375 q^{64} +696.792 q^{65} -350.013 q^{66} +401.953 q^{67} -684.930 q^{69} -456.116 q^{70} +481.559 q^{71} -184.571 q^{72} +725.281 q^{73} +205.287 q^{74} +310.243 q^{75} -19.7644 q^{76} -1240.71 q^{77} -404.020 q^{78} +382.621 q^{79} -375.768 q^{80} -900.052 q^{81} -484.231 q^{82} -182.391 q^{83} -1064.78 q^{84} +591.401 q^{86} +113.553 q^{87} +827.364 q^{88} -623.009 q^{89} -169.895 q^{90} -1432.15 q^{91} +720.094 q^{92} -1455.35 q^{93} -251.981 q^{94} -40.9045 q^{95} +1104.29 q^{96} +369.544 q^{97} +504.739 q^{98} -462.140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * q^99

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