LMFDB - Embedded newform 289.4.a.h.1.10

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			1.10
Root			$-4.28857$ 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)

$f(q)$	$=$	$q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +O(q^{10})$	\(q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +27.3023 q^{10} -61.3595 q^{11} -29.6207 q^{12} +18.5582 q^{13} -126.216 q^{14} -18.1464 q^{15} -39.1446 q^{16} -80.9480 q^{18} +115.793 q^{19} +66.1574 q^{20} +83.8892 q^{21} -263.144 q^{22} +7.38352 q^{23} -29.2379 q^{24} -84.4703 q^{25} +79.5883 q^{26} +130.762 q^{27} -305.840 q^{28} -164.974 q^{29} -77.8221 q^{30} +127.132 q^{31} -249.934 q^{32} +174.898 q^{33} -187.365 q^{35} -196.149 q^{36} +158.120 q^{37} +496.588 q^{38} -52.8982 q^{39} +65.3022 q^{40} +31.3736 q^{41} +359.764 q^{42} +157.708 q^{43} -637.637 q^{44} -120.166 q^{45} +31.6647 q^{46} -460.704 q^{47} +111.577 q^{48} +523.171 q^{49} -362.257 q^{50} +192.854 q^{52} -166.846 q^{53} +560.783 q^{54} -390.632 q^{55} -301.886 q^{56} -330.056 q^{57} -707.502 q^{58} -343.136 q^{59} -188.574 q^{60} -112.359 q^{61} +545.216 q^{62} +555.515 q^{63} -758.704 q^{64} +118.147 q^{65} +750.063 q^{66} -984.209 q^{67} -21.0459 q^{69} -803.528 q^{70} -524.337 q^{71} -193.613 q^{72} +852.636 q^{73} +678.106 q^{74} +240.773 q^{75} +1203.30 q^{76} +1805.86 q^{77} -226.858 q^{78} -201.021 q^{79} -249.206 q^{80} +136.909 q^{81} +134.548 q^{82} -22.5351 q^{83} +871.761 q^{84} +676.342 q^{86} +470.240 q^{87} -629.395 q^{88} +502.230 q^{89} -515.338 q^{90} -546.184 q^{91} +76.7282 q^{92} -362.377 q^{93} -1975.76 q^{94} +737.175 q^{95} +712.410 q^{96} +680.691 q^{97} +2243.65 q^{98} +1158.18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.28857	1.51624	0.758119	−	0.652116i	$-0.226119\pi$
$2$	4.28857	1.51624	0.758119	+	0.652116i	$0.226119\pi$
$3$	−2.85039	−0.548557	−0.274279	−	0.961650i	$-0.588439\pi$
$3$	−2.85039	−0.548557	−0.274279	+	0.961650i	$0.588439\pi$
$4$	10.3918	1.29898
$5$	6.36629	0.569418	0.284709	−	0.958614i	$-0.408103\pi$
$5$	6.36629	0.569418	0.284709	+	0.958614i	$0.408103\pi$
$6$	−12.2241	−0.831744
$7$	−29.4308	−1.58911	−0.794556	−	0.607190i	$-0.792297\pi$
$7$	−29.4308	−1.58911	−0.794556	+	0.607190i	$0.792297\pi$
$8$	10.2575	0.453322
$9$	−18.8753	−0.699085
$10$	27.3023	0.863374
$11$	−61.3595	−1.68187	−0.840935	−	0.541136i	$-0.817995\pi$
$11$	−61.3595	−1.68187	−0.840935	+	0.541136i	$0.817995\pi$
$12$	−29.6207	−0.712564
$13$	18.5582	0.395933	0.197967	−	0.980209i	$-0.436566\pi$
$13$	18.5582	0.395933	0.197967	+	0.980209i	$0.436566\pi$
$14$	−126.216	−2.40947
$15$	−18.1464	−0.312359
$16$	−39.1446	−0.611634
$17$	0	0
$17$	0	0
$18$	−80.9480	−1.05998
$19$	115.793	1.39815	0.699075	−	0.715049i	$-0.253596\pi$
$19$	115.793	1.39815	0.699075	+	0.715049i	$0.253596\pi$
$20$	66.1574	0.739662
$21$	83.8892	0.871720
$22$	−263.144	−2.55012
$23$	7.38352	0.0669378	0.0334689	−	0.999440i	$-0.489345\pi$
$23$	7.38352	0.0669378	0.0334689	+	0.999440i	$0.489345\pi$
$24$	−29.2379	−0.248673
$25$	−84.4703	−0.675763
$26$	79.5883	0.600329
$27$	130.762	0.932046
$28$	−305.840	−2.06422
$29$	−164.974	−1.05638	−0.528188	−	0.849127i	$-0.677128\pi$
$29$	−164.974	−1.05638	−0.528188	+	0.849127i	$0.677128\pi$
$30$	−77.8221	−0.473610
$31$	127.132	0.736570	0.368285	−	0.929713i	$-0.379945\pi$
$31$	127.132	0.736570	0.368285	+	0.929713i	$0.379945\pi$
$32$	−249.934	−1.38070
$33$	174.898	0.922603
$34$	0	0
$35$	−187.365	−0.904870
$36$	−196.149	−0.908096
$37$	158.120	0.702559	0.351280	−	0.936271i	$-0.385747\pi$
$37$	158.120	0.702559	0.351280	+	0.936271i	$0.385747\pi$
$38$	496.588	2.11993
$39$	−52.8982	−0.217192
$40$	65.3022	0.258130
$41$	31.3736	0.119506	0.0597528	−	0.998213i	$-0.480969\pi$
$41$	31.3736	0.119506	0.0597528	+	0.998213i	$0.480969\pi$
$42$	359.764	1.32173
$43$	157.708	0.559309	0.279654	−	0.960101i	$-0.409780\pi$
$43$	157.708	0.559309	0.279654	+	0.960101i	$0.409780\pi$
$44$	−637.637	−2.18471
$45$	−120.166	−0.398072
$46$	31.6647	0.101494
$47$	−460.704	−1.42980	−0.714900	−	0.699227i	$-0.753528\pi$
$47$	−460.704	−1.42980	−0.714900	+	0.699227i	$0.753528\pi$
$48$	111.577	0.335517
$49$	523.171	1.52528
$50$	−362.257	−1.02462
$51$	0	0
$52$	192.854	0.514308
$53$	−166.846	−0.432417	−0.216208	−	0.976347i	$-0.569369\pi$
$53$	−166.846	−0.432417	−0.216208	+	0.976347i	$0.569369\pi$
$54$	560.783	1.41320
$55$	−390.632	−0.957688
$56$	−301.886	−0.720379
$57$	−330.056	−0.766965
$58$	−707.502	−1.60172
$59$	−343.136	−0.757161	−0.378581	−	0.925568i	$-0.623588\pi$
$59$	−343.136	−0.757161	−0.378581	+	0.925568i	$0.623588\pi$
$60$	−188.574	−0.405747
$61$	−112.359	−0.235837	−0.117918	−	0.993023i	$-0.537622\pi$
$61$	−112.359	−0.235837	−0.117918	+	0.993023i	$0.537622\pi$
$62$	545.216	1.11682
$63$	555.515	1.11092
$64$	−758.704	−1.48184
$65$	118.147	0.225452
$66$	750.063	1.39889
$67$	−984.209	−1.79463	−0.897316	−	0.441390i	$-0.854486\pi$
$67$	−984.209	−1.79463	−0.897316	+	0.441390i	$0.854486\pi$
$68$	0	0
$69$	−21.0459	−0.0367192
$70$	−803.528	−1.37200
$71$	−524.337	−0.876442	−0.438221	−	0.898867i	$-0.644391\pi$
$71$	−524.337	−0.876442	−0.438221	+	0.898867i	$0.644391\pi$
$72$	−193.613	−0.316910
$73$	852.636	1.36703	0.683517	−	0.729934i	$-0.260449\pi$
$73$	852.636	1.36703	0.683517	+	0.729934i	$0.260449\pi$
$74$	678.106	1.06525
$75$	240.773	0.370695
$76$	1203.30	1.81616
$77$	1805.86	2.67268
$78$	−226.858	−0.329315
$79$	−201.021	−0.286286	−0.143143	−	0.989702i	$-0.545721\pi$
$79$	−201.021	−0.286286	−0.143143	+	0.989702i	$0.545721\pi$
$80$	−249.206	−0.348276
$81$	136.909	0.187804
$82$	134.548	0.181199
$83$	−22.5351	−0.0298017	−0.0149009	−	0.999889i	$-0.504743\pi$
$83$	−22.5351	−0.0298017	−0.0149009	+	0.999889i	$0.504743\pi$
$84$	871.761	1.13234
$85$	0	0
$86$	676.342	0.848045
$87$	470.240	0.579483
$88$	−629.395	−0.762428
$89$	502.230	0.598161	0.299080	−	0.954228i	$-0.403320\pi$
$89$	502.230	0.598161	0.299080	+	0.954228i	$0.403320\pi$
$90$	−515.338	−0.603572
$91$	−546.184	−0.629182
$92$	76.7282	0.0869507
$93$	−362.377	−0.404051
$94$	−1975.76	−2.16792
$95$	737.175	0.796132
$96$	712.410	0.757396
$97$	680.691	0.712512	0.356256	−	0.934388i	$-0.384053\pi$
$97$	680.691	0.712512	0.356256	+	0.934388i	$0.384053\pi$
$98$	2243.65	2.31269
$99$	1158.18	1.17577
$100$	−877.801	−0.877801
$101$	1921.92	1.89345	0.946724	−	0.322045i	$-0.104370\pi$
$101$	1921.92	1.89345	0.946724	+	0.322045i	$0.104370\pi$
$102$	0	0
$103$	−1123.80	−1.07506	−0.537529	−	0.843245i	$-0.680642\pi$
$103$	−1123.80	−1.07506	−0.537529	+	0.843245i	$0.680642\pi$
$104$	190.361	0.179485
$105$	534.063	0.496373
$106$	−715.532	−0.655647
$107$	−122.786	−0.110937	−0.0554683	−	0.998460i	$-0.517665\pi$
$107$	−122.786	−0.110937	−0.0554683	+	0.998460i	$0.517665\pi$
$108$	1358.86	1.21071
$109$	791.497	0.695520	0.347760	−	0.937584i	$-0.386942\pi$
$109$	791.497	0.695520	0.347760	+	0.937584i	$0.386942\pi$
$110$	−1675.25	−1.45208
$111$	−450.702	−0.385394
$112$	1152.06	0.971956
$113$	−73.7910	−0.0614307	−0.0307154	−	0.999528i	$-0.509779\pi$
$113$	−73.7910	−0.0614307	−0.0307154	+	0.999528i	$0.509779\pi$
$114$	−1415.47	−1.16290
$115$	47.0056	0.0381156
$116$	−1714.38	−1.37221
$117$	−350.292	−0.276791
$118$	−1471.56	−1.14804
$119$	0	0
$120$	−186.137	−0.141599
$121$	2433.98	1.82869
$122$	−481.857	−0.357585
$123$	−89.4269	−0.0655557
$124$	1321.14	0.956788
$125$	−1333.55	−0.954210
$126$	2382.36	1.68443
$127$	−1475.81	−1.03115	−0.515577	−	0.856843i	$-0.672423\pi$
$127$	−1475.81	−1.03115	−0.515577	+	0.856843i	$0.672423\pi$
$128$	−1254.28	−0.866122
$129$	−449.529	−0.306813
$130$	506.682	0.341838
$131$	−1029.79	−0.686821	−0.343410	−	0.939185i	$-0.611582\pi$
$131$	−1029.79	−0.686821	−0.343410	+	0.939185i	$0.611582\pi$
$132$	1817.51	1.19844
$133$	−3407.89	−2.22182
$134$	−4220.85	−2.72109
$135$	832.471	0.530724
$136$	0	0
$137$	−1018.26	−0.635008	−0.317504	−	0.948257i	$-0.602845\pi$
$137$	−1018.26	−0.635008	−0.317504	+	0.948257i	$0.602845\pi$
$138$	−90.2567	−0.0556751
$139$	−1506.59	−0.919332	−0.459666	−	0.888092i	$-0.652031\pi$
$139$	−1506.59	−0.919332	−0.459666	+	0.888092i	$0.652031\pi$
$140$	−1947.06	−1.17541
$141$	1313.18	0.784327
$142$	−2248.66	−1.32890
$143$	−1138.72	−0.665908
$144$	738.865	0.427584
$145$	−1050.27	−0.601520
$146$	3656.59	2.07275
$147$	−1491.24	−0.836704
$148$	1643.15	0.912609
$149$	−424.614	−0.233462	−0.116731	−	0.993164i	$-0.537241\pi$
$149$	−424.614	−0.233462	−0.116731	+	0.993164i	$0.537241\pi$
$150$	1032.57	0.562061
$151$	1566.83	0.844418	0.422209	−	0.906499i	$-0.361255\pi$
$151$	1566.83	0.844418	0.422209	+	0.906499i	$0.361255\pi$
$152$	1187.75	0.633811
$153$	0	0
$154$	7744.54	4.05242
$155$	809.362	0.419416
$156$	−549.709	−0.282128
$157$	−762.291	−0.387500	−0.193750	−	0.981051i	$-0.562065\pi$
$157$	−762.291	−0.387500	−0.193750	+	0.981051i	$0.562065\pi$
$158$	−862.092	−0.434078
$159$	475.577	0.237206
$160$	−1591.15	−0.786199
$161$	−217.303	−0.106372
$162$	587.145	0.284756
$163$	−2253.74	−1.08299	−0.541493	−	0.840705i	$-0.682141\pi$
$163$	−2253.74	−1.08299	−0.541493	+	0.840705i	$0.682141\pi$
$164$	326.029	0.155235
$165$	1113.45	0.525347
$166$	−96.6432	−0.0451865
$167$	1995.81	0.924792	0.462396	−	0.886673i	$-0.346990\pi$
$167$	1995.81	0.924792	0.462396	+	0.886673i	$0.346990\pi$
$168$	860.493	0.395169
$169$	−1852.59	−0.843237
$170$	0	0
$171$	−2185.63	−0.977425
$172$	1638.88	0.726529
$173$	−1853.93	−0.814749	−0.407375	−	0.913261i	$-0.633556\pi$
$173$	−1853.93	−0.814749	−0.407375	+	0.913261i	$0.633556\pi$
$174$	2016.66	0.878634
$175$	2486.03	1.07386
$176$	2401.89	1.02869
$177$	978.071	0.415346
$178$	2153.85	0.906954
$179$	−1623.39	−0.677865	−0.338933	−	0.940811i	$-0.610066\pi$
$179$	−1623.39	−0.677865	−0.338933	+	0.940811i	$0.610066\pi$
$180$	−1248.74	−0.517086
$181$	759.107	0.311735	0.155867	−	0.987778i	$-0.450183\pi$
$181$	759.107	0.311735	0.155867	+	0.987778i	$0.450183\pi$
$182$	−2342.35	−0.953990
$183$	320.266	0.129370
$184$	75.7364	0.0303444
$185$	1006.64	0.400050
$186$	−1554.08	−0.612637
$187$	0	0
$188$	−4787.55	−1.85728
$189$	−3848.44	−1.48113
$190$	3161.42	1.20713
$191$	−1878.32	−0.711572	−0.355786	−	0.934567i	$-0.615787\pi$
$191$	−1878.32	−0.711572	−0.355786	+	0.934567i	$0.615787\pi$
$192$	2162.60	0.812876
$193$	497.364	0.185498	0.0927489	−	0.995690i	$-0.470435\pi$
$193$	497.364	0.185498	0.0927489	+	0.995690i	$0.470435\pi$
$194$	2919.19	1.08034
$195$	−336.765	−0.123673
$196$	5436.70	1.98130
$197$	−1052.05	−0.380486	−0.190243	−	0.981737i	$-0.560928\pi$
$197$	−1052.05	−0.380486	−0.190243	+	0.981737i	$0.560928\pi$
$198$	4966.92	1.78275
$199$	1783.55	0.635338	0.317669	−	0.948202i	$-0.397100\pi$
$199$	1783.55	0.635338	0.317669	+	0.948202i	$0.397100\pi$
$200$	−866.454	−0.306338
$201$	2805.38	0.984458
$202$	8242.29	2.87092
$203$	4855.31	1.67870
$204$	0	0
$205$	199.733	0.0680487
$206$	−4819.48	−1.63004
$207$	−139.366	−0.0467952
$208$	−726.455	−0.242166
$209$	−7105.02	−2.35151
$210$	2290.37	0.752620
$211$	−3756.09	−1.22550	−0.612748	−	0.790278i	$-0.709936\pi$
$211$	−3756.09	−1.22550	−0.612748	+	0.790278i	$0.709936\pi$
$212$	−1733.84	−0.561700
$213$	1494.57	0.480779
$214$	−526.578	−0.168206
$215$	1004.02	0.318481
$216$	1341.30	0.422517
$217$	−3741.61	−1.17049
$218$	3394.39	1.05457
$219$	−2430.34	−0.749897
$220$	−4059.38	−1.24402
$221$	0	0
$222$	−1932.87	−0.584349
$223$	−3356.40	−1.00790	−0.503949	−	0.863733i	$-0.668120\pi$
$223$	−3356.40	−1.00790	−0.503949	+	0.863733i	$0.668120\pi$
$224$	7355.76	2.19410
$225$	1594.40	0.472415
$226$	−316.458	−0.0931436
$227$	−1988.64	−0.581457	−0.290728	−	0.956806i	$-0.593898\pi$
$227$	−1988.64	−0.581457	−0.290728	+	0.956806i	$0.593898\pi$
$228$	−3429.89	−0.996271
$229$	5203.50	1.50156	0.750779	−	0.660554i	$-0.229678\pi$
$229$	5203.50	1.50156	0.750779	+	0.660554i	$0.229678\pi$
$230$	201.587	0.0577924
$231$	−5147.39	−1.46612
$232$	−1692.22	−0.478878
$233$	5702.70	1.60342	0.801709	−	0.597714i	$-0.203924\pi$
$233$	5702.70	1.60342	0.801709	+	0.597714i	$0.203924\pi$
$234$	−1502.25	−0.419681
$235$	−2932.98	−0.814154
$236$	−3565.81	−0.983536
$237$	572.988	0.157045
$238$	0	0
$239$	1418.04	0.383787	0.191894	−	0.981416i	$-0.438537\pi$
$239$	1418.04	0.383787	0.191894	+	0.981416i	$0.438537\pi$
$240$	710.334	0.191049
$241$	−6215.71	−1.66137	−0.830683	−	0.556746i	$-0.812050\pi$
$241$	−6215.71	−1.66137	−0.830683	+	0.556746i	$0.812050\pi$
$242$	10438.3	2.77273
$243$	−3920.83	−1.03507
$244$	−1167.61	−0.306347
$245$	3330.66	0.868523
$246$	−383.514	−0.0993981
$247$	2148.92	0.553573
$248$	1304.06	0.333903
$249$	64.2337	0.0163480
$250$	−5719.02	−1.44681
$251$	1547.45	0.389139	0.194570	−	0.980889i	$-0.437669\pi$
$251$	1547.45	0.389139	0.194570	+	0.980889i	$0.437669\pi$
$252$	5772.81	1.44307
$253$	−453.049	−0.112581
$254$	−6329.10	−1.56348
$255$	0	0
$256$	690.569	0.168596
$257$	7251.45	1.76005	0.880025	−	0.474928i	$-0.157526\pi$
$257$	7251.45	1.76005	0.880025	+	0.474928i	$0.157526\pi$
$258$	−1927.84	−0.465201
$259$	−4653.58	−1.11645
$260$	1227.76	0.292857
$261$	3113.93	0.738496
$262$	−4416.34	−1.04138
$263$	4635.13	1.08675	0.543373	−	0.839491i	$-0.317147\pi$
$263$	4635.13	1.08675	0.543373	+	0.839491i	$0.317147\pi$
$264$	1794.02	0.418236
$265$	−1062.19	−0.246226
$266$	−14615.0	−3.36880
$267$	−1431.55	−0.328126
$268$	−10227.7	−2.33119
$269$	−7116.95	−1.61311	−0.806557	−	0.591156i	$-0.798672\pi$
$269$	−7116.95	−1.61311	−0.806557	+	0.591156i	$0.798672\pi$
$270$	3570.11	0.804704
$271$	163.713	0.0366970	0.0183485	−	0.999832i	$-0.494159\pi$
$271$	163.713	0.0366970	0.0183485	+	0.999832i	$0.494159\pi$
$272$	0	0
$273$	1556.83	0.345143
$274$	−4366.89	−0.962823
$275$	5183.05	1.13655
$276$	−218.705	−0.0476975
$277$	4174.84	0.905567	0.452784	−	0.891620i	$-0.350431\pi$
$277$	4174.84	0.905567	0.452784	+	0.891620i	$0.350431\pi$
$278$	−6461.11	−1.39393
$279$	−2399.66	−0.514925
$280$	−1921.90	−0.410197
$281$	−6920.09	−1.46910	−0.734551	−	0.678553i	$-0.762607\pi$
$281$	−6920.09	−1.46910	−0.734551	+	0.678553i	$0.762607\pi$
$282$	5631.68	1.18923
$283$	−6292.91	−1.32182	−0.660909	−	0.750466i	$-0.729829\pi$
$283$	−6292.91	−1.32182	−0.660909	+	0.750466i	$0.729829\pi$
$284$	−5448.82	−1.13848
$285$	−2101.23	−0.436724
$286$	−4883.50	−1.00968
$287$	−923.350	−0.189908
$288$	4717.58	0.965230
$289$	0	0
$290$	−4504.17	−0.912048
$291$	−1940.23	−0.390854
$292$	8860.45	1.77575
$293$	2292.96	0.457189	0.228595	−	0.973522i	$-0.426587\pi$
$293$	2292.96	0.457189	0.228595	+	0.973522i	$0.426587\pi$
$294$	−6395.29	−1.26864
$295$	−2184.50	−0.431142
$296$	1621.91	0.318485
$297$	−8023.51	−1.56758
$298$	−1820.99	−0.353983
$299$	137.025	0.0265029
$300$	2502.07	0.481524
$301$	−4641.47	−0.888804
$302$	6719.47	1.28034
$303$	−5478.22	−1.03867
$304$	−4532.69	−0.855156
$305$	−715.308	−0.134290
$306$	0	0
$307$	2300.11	0.427604	0.213802	−	0.976877i	$-0.431415\pi$
$307$	2300.11	0.427604	0.213802	+	0.976877i	$0.431415\pi$
$308$	18766.1	3.47176
$309$	3203.26	0.589731
$310$	3471.01	0.635935
$311$	−5775.22	−1.05300	−0.526499	−	0.850175i	$-0.676496\pi$
$311$	−5775.22	−1.05300	−0.526499	+	0.850175i	$0.676496\pi$
$312$	−542.603	−0.0984579
$313$	−2799.69	−0.505585	−0.252792	−	0.967521i	$-0.581349\pi$
$313$	−2799.69	−0.505585	−0.252792	+	0.967521i	$0.581349\pi$
$314$	−3269.14	−0.587542
$315$	3536.57	0.632581
$316$	−2088.97	−0.371880
$317$	−5140.47	−0.910781	−0.455390	−	0.890292i	$-0.650500\pi$
$317$	−5140.47	−0.910781	−0.455390	+	0.890292i	$0.650500\pi$
$318$	2039.54	0.359660
$319$	10122.7	1.77669
$320$	−4830.13	−0.843789
$321$	349.989	0.0608550
$322$	−931.917	−0.161285
$323$	0	0
$324$	1422.74	0.243954
$325$	−1567.62	−0.267557
$326$	−9665.33	−1.64206
$327$	−2256.07	−0.381533
$328$	321.815	0.0541745
$329$	13558.9	2.27211
$330$	4775.12	0.796551
$331$	459.510	0.0763050	0.0381525	−	0.999272i	$-0.487853\pi$
$331$	459.510	0.0763050	0.0381525	+	0.999272i	$0.487853\pi$
$332$	−234.180	−0.0387118
$333$	−2984.55	−0.491148
$334$	8559.16	1.40221
$335$	−6265.76	−1.02190
$336$	−3283.81	−0.533174
$337$	6233.46	1.00759	0.503796	−	0.863823i	$-0.331937\pi$
$337$	6233.46	1.00759	0.503796	+	0.863823i	$0.331937\pi$
$338$	−7944.97	−1.27855
$339$	210.333	0.0336983
$340$	0	0
$341$	−7800.78	−1.23882
$342$	−9373.24	−1.48201
$343$	−5302.57	−0.834729
$344$	1617.69	0.253547
$345$	−133.984	−0.0209086
$346$	−7950.70	−1.23535
$347$	6370.01	0.985476	0.492738	−	0.870178i	$-0.335996\pi$
$347$	6370.01	0.985476	0.492738	+	0.870178i	$0.335996\pi$
$348$	4886.65	0.752735
$349$	−6494.79	−0.996155	−0.498078	−	0.867132i	$-0.665961\pi$
$349$	−6494.79	−0.996155	−0.498078	+	0.867132i	$0.665961\pi$
$350$	10661.5	1.62823
$351$	2426.72	0.369028
$352$	15335.8	2.32217
$353$	502.630	0.0757856	0.0378928	−	0.999282i	$-0.487935\pi$
$353$	502.630	0.0757856	0.0378928	+	0.999282i	$0.487935\pi$
$354$	4194.53	0.629764
$355$	−3338.09	−0.499062
$356$	5219.09	0.776998
$357$	0	0
$358$	−6962.02	−1.02781
$359$	−974.431	−0.143255	−0.0716275	−	0.997431i	$-0.522819\pi$
$359$	−974.431	−0.143255	−0.0716275	+	0.997431i	$0.522819\pi$
$360$	−1232.60	−0.180455
$361$	6549.11	0.954821
$362$	3255.48	0.472664
$363$	−6937.80	−1.00314
$364$	−5675.84	−0.817294
$365$	5428.13	0.778415
$366$	1373.48	0.196156
$367$	4693.11	0.667515	0.333758	−	0.942659i	$-0.391683\pi$
$367$	4693.11	0.667515	0.333758	+	0.942659i	$0.391683\pi$
$368$	−289.025	−0.0409415
$369$	−592.186	−0.0835446
$370$	4317.02	0.606571
$371$	4910.42	0.687159
$372$	−3765.76	−0.524853
$373$	8651.16	1.20091	0.600456	−	0.799658i	$-0.294986\pi$
$373$	8651.16	1.20091	0.600456	+	0.799658i	$0.294986\pi$
$374$	0	0
$375$	3801.13	0.523439
$376$	−4725.67	−0.648159
$377$	−3061.63	−0.418254
$378$	−16504.3	−2.24574
$379$	3490.01	0.473007	0.236503	−	0.971631i	$-0.423999\pi$
$379$	3490.01	0.473007	0.236503	+	0.971631i	$0.423999\pi$
$380$	7660.59	1.03416
$381$	4206.62	0.565648
$382$	−8055.29	−1.07891
$383$	3928.41	0.524105	0.262052	−	0.965054i	$-0.415601\pi$
$383$	3928.41	0.524105	0.262052	+	0.965054i	$0.415601\pi$
$384$	3575.18	0.475118
$385$	11496.6	1.52187
$386$	2132.98	0.281259
$387$	−2976.79	−0.391004
$388$	7073.62	0.925537
$389$	6961.15	0.907312	0.453656	−	0.891177i	$-0.350120\pi$
$389$	6961.15	0.907312	0.453656	+	0.891177i	$0.350120\pi$
$390$	−1444.24	−0.187518
$391$	0	0
$392$	5366.43	0.691443
$393$	2935.31	0.376761
$394$	−4511.81	−0.576908
$395$	−1279.76	−0.163017
$396$	12035.6	1.52730
$397$	5331.94	0.674062	0.337031	−	0.941494i	$-0.390577\pi$
$397$	5331.94	0.674062	0.337031	+	0.941494i	$0.390577\pi$
$398$	7648.86	0.963323
$399$	9713.81	1.21879
$400$	3306.56	0.413320
$401$	546.021	0.0679975	0.0339988	−	0.999422i	$-0.489176\pi$
$401$	546.021	0.0679975	0.0339988	+	0.999422i	$0.489176\pi$
$402$	12031.1	1.49267
$403$	2359.35	0.291632
$404$	19972.3	2.45955
$405$	871.604	0.106939
$406$	20822.3	2.54531
$407$	−9702.13	−1.18161
$408$	0	0
$409$	15964.6	1.93007	0.965037	−	0.262114i	$-0.0844196\pi$
$409$	15964.6	1.93007	0.965037	+	0.262114i	$0.0844196\pi$
$410$	856.571	0.103178
$411$	2902.44	0.348338
$412$	−11678.3	−1.39648
$413$	10098.8	1.20321
$414$	−597.681	−0.0709527
$415$	−143.465	−0.0169697
$416$	−4638.34	−0.546667
$417$	4294.36	0.504306
$418$	−30470.4	−3.56544
$419$	7643.91	0.891240	0.445620	−	0.895222i	$-0.352983\pi$
$419$	7643.91	0.891240	0.445620	+	0.895222i	$0.352983\pi$
$420$	5549.89	0.644778
$421$	−7524.14	−0.871031	−0.435516	−	0.900181i	$-0.643434\pi$
$421$	−7524.14	−0.871031	−0.435516	+	0.900181i	$0.643434\pi$
$422$	−16108.2	−1.85814
$423$	8695.92	0.999551
$424$	−1711.43	−0.196024
$425$	0	0
$426$	6409.55	0.728975
$427$	3306.80	0.374771
$428$	−1275.97	−0.144104
$429$	3245.80	0.365289
$430$	4305.79	0.482892
$431$	−12222.4	−1.36597	−0.682986	−	0.730431i	$-0.739319\pi$
$431$	−12222.4	−1.36597	−0.682986	+	0.730431i	$0.739319\pi$
$432$	−5118.64	−0.570071
$433$	−15420.3	−1.71144	−0.855719	−	0.517440i	$-0.826885\pi$
$433$	−15420.3	−1.71144	−0.855719	+	0.517440i	$0.826885\pi$
$434$	−16046.1	−1.77475
$435$	2993.68	0.329968
$436$	8225.10	0.903465
$437$	854.963	0.0935890
$438$	−10422.7	−1.13702
$439$	17832.7	1.93874	0.969369	−	0.245607i	$-0.0789874\pi$
$439$	17832.7	1.93874	0.969369	+	0.245607i	$0.0789874\pi$
$440$	−4006.91	−0.434141
$441$	−9875.00	−1.06630
$442$	0	0
$443$	241.629	0.0259145	0.0129573	−	0.999916i	$-0.495875\pi$
$443$	241.629	0.0259145	0.0129573	+	0.999916i	$0.495875\pi$
$444$	−4683.62	−0.500618
$445$	3197.35	0.340604
$446$	−14394.2	−1.52821
$447$	1210.32	0.128067
$448$	22329.2	2.35482
$449$	−14481.4	−1.52209	−0.761046	−	0.648698i	$-0.775314\pi$
$449$	−14481.4	−1.52209	−0.761046	+	0.648698i	$0.775314\pi$
$450$	6837.70	0.716294
$451$	−1925.07	−0.200993
$452$	−766.823	−0.0797971
$453$	−4466.08	−0.463211
$454$	−8528.42	−0.881627
$455$	−3477.16	−0.358268
$456$	−3385.55	−0.347682
$457$	−1814.51	−0.185731	−0.0928654	−	0.995679i	$-0.529603\pi$
$457$	−1814.51	−0.185731	−0.0928654	+	0.995679i	$0.529603\pi$
$458$	22315.6	2.27672
$459$	0	0
$460$	488.474	0.0495114
$461$	−13434.1	−1.35724	−0.678621	−	0.734489i	$-0.737422\pi$
$461$	−13434.1	−1.35724	−0.678621	+	0.734489i	$0.737422\pi$
$462$	−22075.0	−2.22299
$463$	−16593.9	−1.66562	−0.832810	−	0.553559i	$-0.813269\pi$
$463$	−16593.9	−1.66562	−0.832810	+	0.553559i	$0.813269\pi$
$464$	6457.84	0.646116
$465$	−2307.00	−0.230074
$466$	24456.4	2.43116
$467$	−3944.12	−0.390818	−0.195409	−	0.980722i	$-0.562603\pi$
$467$	−3944.12	−0.390818	−0.195409	+	0.980722i	$0.562603\pi$
$468$	−3640.17	−0.359545
$469$	28966.0	2.85187
$470$	−12578.3	−1.23445
$471$	2172.83	0.212566
$472$	−3519.72	−0.343238
$473$	−9676.89	−0.940685
$474$	2457.30	0.238117
$475$	−9781.11	−0.944817
$476$	0	0
$477$	3149.27	0.302296
$478$	6081.35	0.581913
$479$	11162.8	1.06480	0.532401	−	0.846492i	$-0.321290\pi$
$479$	11162.8	1.06480	0.532401	+	0.846492i	$0.321290\pi$
$480$	4535.41	0.431275
$481$	2934.42	0.278166
$482$	−26656.5	−2.51903
$483$	619.397	0.0583510
$484$	25293.5	2.37543
$485$	4333.48	0.405717
$486$	−16814.7	−1.56941
$487$	9984.01	0.928991	0.464496	−	0.885575i	$-0.346236\pi$
$487$	9984.01	0.928991	0.464496	+	0.885575i	$0.346236\pi$
$488$	−1152.52	−0.106910
$489$	6424.04	0.594080
$490$	14283.8	1.31689
$491$	−19639.7	−1.80514	−0.902572	−	0.430540i	$-0.858323\pi$
$491$	−19639.7	−1.80514	−0.902572	+	0.430540i	$0.858323\pi$
$492$	−929.309	−0.0851554
$493$	0	0
$494$	9215.80	0.839349
$495$	7373.30	0.669505
$496$	−4976.55	−0.450511
$497$	15431.7	1.39277
$498$	275.470	0.0247874
$499$	5764.32	0.517127	0.258564	−	0.965994i	$-0.416751\pi$
$499$	5764.32	0.517127	0.258564	+	0.965994i	$0.416751\pi$
$500$	−13858.0	−1.23950
$501$	−5688.83	−0.507302
$502$	6636.33	0.590027
$503$	−1747.34	−0.154890	−0.0774452	−	0.996997i	$-0.524676\pi$
$503$	−1747.34	−0.154890	−0.0774452	+	0.996997i	$0.524676\pi$
$504$	5698.19	0.503606
$505$	12235.5	1.07816
$506$	−1942.93	−0.170699
$507$	5280.61	0.462564
$508$	−15336.3	−1.33945
$509$	−9110.89	−0.793385	−0.396693	−	0.917952i	$-0.629842\pi$
$509$	−9110.89	−0.793385	−0.396693	+	0.917952i	$0.629842\pi$
$510$	0	0
$511$	−25093.8	−2.17237
$512$	12995.8	1.12175
$513$	15141.4	1.30314
$514$	31098.3	2.66865
$515$	−7154.42	−0.612158
$516$	−4671.43	−0.398543
$517$	28268.5	2.40474
$518$	−19957.2	−1.69280
$519$	5284.42	0.446937
$520$	1211.89	0.102202
$521$	−9231.61	−0.776285	−0.388142	−	0.921599i	$-0.626883\pi$
$521$	−9231.61	−0.776285	−0.388142	+	0.921599i	$0.626883\pi$
$522$	13354.3	1.11974
$523$	14927.5	1.24806	0.624028	−	0.781402i	$-0.285495\pi$
$523$	14927.5	1.24806	0.624028	+	0.781402i	$0.285495\pi$
$524$	−10701.4	−0.892165
$525$	−7086.14	−0.589076
$526$	19878.1	1.64777
$527$	0	0
$528$	−6846.32	−0.564295
$529$	−12112.5	−0.995519
$530$	−4555.28	−0.373338
$531$	6476.79	0.529320
$532$	−35414.2	−2.88609
$533$	582.239	0.0473162
$534$	−6139.31	−0.497516
$535$	−781.694	−0.0631693
$536$	−10095.5	−0.813545
$537$	4627.29	0.371848
$538$	−30521.5	−2.44587
$539$	−32101.5	−2.56532
$540$	8650.90	0.689399
$541$	−9005.10	−0.715637	−0.357818	−	0.933791i	$-0.616479\pi$
$541$	−9005.10	−0.715637	−0.357818	+	0.933791i	$0.616479\pi$
$542$	702.096	0.0556413
$543$	−2163.75	−0.171004
$544$	0	0
$545$	5038.90	0.396042
$546$	6676.59	0.523318
$547$	6774.33	0.529524	0.264762	−	0.964314i	$-0.414707\pi$
$547$	6774.33	0.529524	0.264762	+	0.964314i	$0.414707\pi$
$548$	−10581.6	−0.824861
$549$	2120.80	0.164870
$550$	22227.9	1.72327
$551$	−19102.9	−1.47697
$552$	−215.878	−0.0166456
$553$	5916.20	0.454941
$554$	17904.1	1.37306
$555$	−2869.30	−0.219450
$556$	−15656.2	−1.19419
$557$	−8558.56	−0.651055	−0.325528	−	0.945533i	$-0.605542\pi$
$557$	−8558.56	−0.651055	−0.325528	+	0.945533i	$0.605542\pi$
$558$	−10291.1	−0.780748
$559$	2926.79	0.221449
$560$	7334.32	0.553450
$561$	0	0
$562$	−29677.3	−2.22751
$563$	13915.1	1.04165	0.520827	−	0.853662i	$-0.325624\pi$
$563$	13915.1	1.04165	0.520827	+	0.853662i	$0.325624\pi$
$564$	13646.4	1.01882
$565$	−469.775	−0.0349798
$566$	−26987.6	−2.00419
$567$	−4029.35	−0.298442
$568$	−5378.39	−0.397310
$569$	−12378.8	−0.912031	−0.456015	−	0.889972i	$-0.650724\pi$
$569$	−12378.8	−0.912031	−0.456015	+	0.889972i	$0.650724\pi$
$570$	−9011.29	−0.662178
$571$	785.845	0.0575947	0.0287974	−	0.999585i	$-0.490832\pi$
$571$	785.845	0.0575947	0.0287974	+	0.999585i	$0.490832\pi$
$572$	−11833.4	−0.865000
$573$	5353.93	0.390338
$574$	−3959.85	−0.287946
$575$	−623.688	−0.0452341
$576$	14320.8	1.03593
$577$	19662.8	1.41867	0.709334	−	0.704873i	$-0.248996\pi$
$577$	19662.8	1.41867	0.709334	+	0.704873i	$0.248996\pi$
$578$	0	0
$579$	−1417.68	−0.101756
$580$	−10914.2	−0.781361
$581$	663.224	0.0473583
$582$	−8320.82	−0.592627
$583$	10237.6	0.727269
$584$	8745.92	0.619707
$585$	−2230.06	−0.157610
$586$	9833.54	0.693208
$587$	−10024.7	−0.704875	−0.352438	−	0.935835i	$-0.614647\pi$
$587$	−10024.7	−0.704875	−0.352438	+	0.935835i	$0.614647\pi$
$588$	−15496.7	−1.08686
$589$	14721.1	1.02983
$590$	−9368.40	−0.653713
$591$	2998.76	0.208719
$592$	−6189.52	−0.429709
$593$	770.054	0.0533260	0.0266630	−	0.999644i	$-0.491512\pi$
$593$	770.054	0.0533260	0.0266630	+	0.999644i	$0.491512\pi$
$594$	−34409.4	−2.37682
$595$	0	0
$596$	−4412.52	−0.303261
$597$	−5083.80	−0.348519
$598$	587.641	0.0401847
$599$	20011.7	1.36503	0.682517	−	0.730870i	$-0.260885\pi$
$599$	20011.7	1.36503	0.682517	+	0.730870i	$0.260885\pi$
$600$	2469.73	0.168044
$601$	−16303.2	−1.10652	−0.553261	−	0.833008i	$-0.686617\pi$
$601$	−16303.2	−1.10652	−0.553261	+	0.833008i	$0.686617\pi$
$602$	−19905.3	−1.34764
$603$	18577.2	1.25460
$604$	16282.2	1.09688
$605$	15495.5	1.04129
$606$	−23493.7	−1.57486
$607$	−26777.6	−1.79056	−0.895279	−	0.445506i	$-0.853024\pi$
$607$	−26777.6	−1.79056	−0.895279	+	0.445506i	$0.853024\pi$
$608$	−28940.7	−1.93043
$609$	−13839.5	−0.920864
$610$	−3067.65	−0.203615
$611$	−8549.85	−0.566105
$612$	0	0
$613$	1385.13	0.0912639	0.0456320	−	0.998958i	$-0.485470\pi$
$613$	1385.13	0.0912639	0.0456320	+	0.998958i	$0.485470\pi$
$614$	9864.19	0.648349
$615$	−569.318	−0.0373286
$616$	18523.6	1.21158
$617$	818.646	0.0534156	0.0267078	−	0.999643i	$-0.491498\pi$
$617$	818.646	0.0534156	0.0267078	+	0.999643i	$0.491498\pi$
$618$	13737.4	0.894173
$619$	9468.86	0.614839	0.307420	−	0.951574i	$-0.400534\pi$
$619$	9468.86	0.614839	0.307420	+	0.951574i	$0.400534\pi$
$620$	8410.75	0.544813
$621$	965.486	0.0623891
$622$	−24767.4	−1.59660
$623$	−14781.0	−0.950545
$624$	2070.68	0.132842
$625$	2069.03	0.132418
$626$	−12006.7	−0.766587
$627$	20252.1	1.28994
$628$	−7921.60	−0.503354
$629$	0	0
$630$	15166.8	0.959143
$631$	11291.5	0.712374	0.356187	−	0.934415i	$-0.384077\pi$
$631$	11291.5	0.712374	0.356187	+	0.934415i	$0.384077\pi$
$632$	−2061.97	−0.129780
$633$	10706.3	0.672255
$634$	−22045.3	−1.38096
$635$	−9395.41	−0.587158
$636$	4942.11	0.308125
$637$	9709.13	0.603909
$638$	43412.0	2.69388
$639$	9897.02	0.612707
$640$	−7985.10	−0.493186
$641$	27604.9	1.70098	0.850489	−	0.525993i	$-0.176306\pi$
$641$	27604.9	1.70098	0.850489	+	0.525993i	$0.176306\pi$
$642$	1500.95	0.0922707
$643$	30899.1	1.89509	0.947544	−	0.319625i	$-0.103557\pi$
$643$	30899.1	1.89509	0.947544	+	0.319625i	$0.103557\pi$
$644$	−2258.17	−0.138175
$645$	−2861.84	−0.174705
$646$	0	0
$647$	26023.7	1.58129	0.790647	−	0.612272i	$-0.209744\pi$
$647$	26023.7	1.58129	0.790647	+	0.612272i	$0.209744\pi$
$648$	1404.35	0.0851357
$649$	21054.7	1.27345
$650$	−6722.85	−0.405680
$651$	10665.0	0.642082
$652$	−23420.5	−1.40677
$653$	−18446.4	−1.10546	−0.552728	−	0.833362i	$-0.686413\pi$
$653$	−18446.4	−1.10546	−0.552728	+	0.833362i	$0.686413\pi$
$654$	−9675.33	−0.578494
$655$	−6555.97	−0.391088
$656$	−1228.11	−0.0730938
$657$	−16093.8	−0.955673
$658$	58148.2	3.44506
$659$	−987.581	−0.0583774	−0.0291887	−	0.999574i	$-0.509292\pi$
$659$	−987.581	−0.0583774	−0.0291887	+	0.999574i	$0.509292\pi$
$660$	11570.8	0.682414
$661$	4126.78	0.242834	0.121417	−	0.992602i	$-0.461256\pi$
$661$	4126.78	0.242834	0.121417	+	0.992602i	$0.461256\pi$
$662$	1970.64	0.115697
$663$	0	0
$664$	−231.153	−0.0135098
$665$	−21695.6	−1.26514
$666$	−12799.5	−0.744698
$667$	−1218.09	−0.0707115
$668$	20740.1	1.20128
$669$	9567.05	0.552890
$670$	−26871.2	−1.54944
$671$	6894.26	0.396647
$672$	−20966.8	−1.20359
$673$	−7788.28	−0.446086	−0.223043	−	0.974809i	$-0.571599\pi$
$673$	−7788.28	−0.446086	−0.223043	+	0.974809i	$0.571599\pi$
$674$	26732.6	1.52775
$675$	−11045.5	−0.629842
$676$	−19251.8	−1.09535
$677$	−849.049	−0.0482003	−0.0241001	−	0.999710i	$-0.507672\pi$
$677$	−849.049	−0.0482003	−0.0241001	+	0.999710i	$0.507672\pi$
$678$	902.027	0.0510946
$679$	−20033.3	−1.13226
$680$	0	0
$681$	5668.39	0.318962
$682$	−33454.2	−1.87834
$683$	−18449.2	−1.03359	−0.516793	−	0.856110i	$-0.672874\pi$
$683$	−18449.2	−1.03359	−0.516793	+	0.856110i	$0.672874\pi$
$684$	−22712.7	−1.26965
$685$	−6482.56	−0.361585
$686$	−22740.4	−1.26565
$687$	−14832.0	−0.823691
$688$	−6173.42	−0.342092
$689$	−3096.37	−0.171208
$690$	−574.601	−0.0317024
$691$	33194.1	1.82744	0.913722	−	0.406339i	$-0.133195\pi$
$691$	33194.1	1.82744	0.913722	+	0.406339i	$0.133195\pi$
$692$	−19265.7	−1.05834
$693$	−34086.1	−1.86843
$694$	27318.2	1.49422
$695$	−9591.38	−0.523484
$696$	4823.49	0.262692
$697$	0	0
$698$	−27853.4	−1.51041
$699$	−16254.9	−0.879567
$700$	25834.4	1.39492
$701$	−1102.73	−0.0594146	−0.0297073	−	0.999559i	$-0.509458\pi$
$701$	−1102.73	−0.0594146	−0.0297073	+	0.999559i	$0.509458\pi$
$702$	10407.2	0.559534
$703$	18309.2	0.982282
$704$	46553.7	2.49227
$705$	8360.12	0.446610
$706$	2155.57	0.114909
$707$	−56563.7	−3.00890
$708$	10163.9	0.539526
$709$	5881.49	0.311543	0.155771	−	0.987793i	$-0.450214\pi$
$709$	5881.49	0.311543	0.155771	+	0.987793i	$0.450214\pi$
$710$	−14315.6	−0.756697
$711$	3794.33	0.200138
$712$	5151.63	0.271159
$713$	938.685	0.0493044
$714$	0	0
$715$	−7249.45	−0.379180
$716$	−16870.0	−0.880532
$717$	−4041.95	−0.210529
$718$	−4178.92	−0.217209
$719$	−13392.6	−0.694661	−0.347330	−	0.937743i	$-0.612912\pi$
$719$	−13392.6	−0.694661	−0.347330	+	0.937743i	$0.612912\pi$
$720$	4703.83	0.243474
$721$	33074.2	1.70839
$722$	28086.3	1.44774
$723$	17717.2	0.911355
$724$	7888.51	0.404937
$725$	13935.4	0.713859
$726$	−29753.2	−1.52100
$727$	30483.7	1.55513	0.777564	−	0.628804i	$-0.216455\pi$
$727$	30483.7	1.55513	0.777564	+	0.628804i	$0.216455\pi$
$728$	−5602.48	−0.285222
$729$	7479.33	0.379989
$730$	23278.9	1.18026
$731$	0	0
$732$	3328.14	0.168049
$733$	23656.0	1.19203	0.596013	−	0.802975i	$-0.296751\pi$
$733$	23656.0	1.19203	0.596013	+	0.802975i	$0.296751\pi$
$734$	20126.7	1.01211
$735$	−9493.67	−0.476434
$736$	−1845.39	−0.0924214
$737$	60390.5	3.01834
$738$	−2539.63	−0.126674
$739$	−27884.4	−1.38801	−0.694007	−	0.719968i	$-0.744157\pi$
$739$	−27884.4	−1.38801	−0.694007	+	0.719968i	$0.744157\pi$
$740$	10460.8	0.519656
$741$	−6125.26	−0.303667
$742$	21058.7	1.04190
$743$	3391.10	0.167439	0.0837196	−	0.996489i	$-0.473320\pi$
$743$	3391.10	0.167439	0.0837196	+	0.996489i	$0.473320\pi$
$744$	−3717.08	−0.183165
$745$	−2703.22	−0.132937
$746$	37101.1	1.82087
$747$	425.356	0.0208339
$748$	0	0
$749$	3613.70	0.176291
$750$	16301.4	0.793658
$751$	−19843.5	−0.964181	−0.482091	−	0.876121i	$-0.660122\pi$
$751$	−19843.5	−0.964181	−0.482091	+	0.876121i	$0.660122\pi$
$752$	18034.1	0.874514
$753$	−4410.82	−0.213465
$754$	−13130.0	−0.634173
$755$	9974.92	0.480827
$756$	−39992.3	−1.92395
$757$	−23915.1	−1.14823	−0.574114	−	0.818775i	$-0.694653\pi$
$757$	−23915.1	−1.14823	−0.574114	+	0.818775i	$0.694653\pi$
$758$	14967.1	0.717191
$759$	1291.36	0.0617570
$760$	7561.57	0.360904
$761$	17162.3	0.817520	0.408760	−	0.912642i	$-0.365961\pi$
$761$	17162.3	0.817520	0.408760	+	0.912642i	$0.365961\pi$
$762$	18040.4	0.857656
$763$	−23294.4	−1.10526
$764$	−19519.1	−0.924317
$765$	0	0
$766$	16847.2	0.794668
$767$	−6368.00	−0.299785
$768$	−1968.39	−0.0924845
$769$	−18387.3	−0.862240	−0.431120	−	0.902295i	$-0.641881\pi$
$769$	−18387.3	−0.862240	−0.431120	+	0.902295i	$0.641881\pi$
$770$	49304.0	2.30752
$771$	−20669.4	−0.965488
$772$	5168.52	0.240957
$773$	4428.78	0.206070	0.103035	−	0.994678i	$-0.467145\pi$
$773$	4428.78	0.206070	0.103035	+	0.994678i	$0.467145\pi$
$774$	−12766.2	−0.592855
$775$	−10738.9	−0.497746
$776$	6982.18	0.322997
$777$	13264.5	0.612435
$778$	29853.4	1.37570
$779$	3632.86	0.167087
$780$	−3499.61	−0.160649
$781$	32173.1	1.47406
$782$	0	0
$783$	−21572.4	−0.984591
$784$	−20479.3	−0.932913
$785$	−4852.97	−0.220650
$786$	12588.3	0.571259
$787$	−17665.8	−0.800151	−0.400075	−	0.916482i	$-0.631016\pi$
$787$	−17665.8	−0.800151	−0.400075	+	0.916482i	$0.631016\pi$
$788$	−10932.8	−0.494243
$789$	−13211.9	−0.596143
$790$	−5488.33	−0.247172
$791$	2171.73	0.0976203
$792$	11880.0	0.533002
$793$	−2085.18	−0.0933756
$794$	22866.4	1.02204
$795$	3027.66	0.135069
$796$	18534.3	0.825290
$797$	12688.4	0.563921	0.281960	−	0.959426i	$-0.409015\pi$
$797$	12688.4	0.563921	0.281960	+	0.959426i	$0.409015\pi$
$798$	41658.3	1.84798
$799$	0	0
$800$	21112.0	0.933029
$801$	−9479.74	−0.418165
$802$	2341.65	0.103100
$803$	−52317.3	−2.29918
$804$	29153.0	1.27879
$805$	−1383.41	−0.0605700
$806$	10118.3	0.442184
$807$	20286.1	0.884886
$808$	19714.1	0.858342
$809$	28633.8	1.24439	0.622194	−	0.782863i	$-0.286242\pi$
$809$	28633.8	1.24439	0.622194	+	0.782863i	$0.286242\pi$
$810$	3737.94	0.162145
$811$	2305.93	0.0998425	0.0499213	−	0.998753i	$-0.484103\pi$
$811$	2305.93	0.0998425	0.0499213	+	0.998753i	$0.484103\pi$
$812$	50455.6	2.18060
$813$	−466.646	−0.0201304
$814$	−41608.3	−1.79161
$815$	−14348.0	−0.616672
$816$	0	0
$817$	18261.6	0.781997
$818$	68465.4	2.92645
$819$	10309.4	0.439852
$820$	2075.60	0.0883938
$821$	−28803.5	−1.22442	−0.612210	−	0.790695i	$-0.709719\pi$
$821$	−28803.5	−1.22442	−0.612210	+	0.790695i	$0.709719\pi$
$822$	12447.3	0.528164
$823$	−14597.0	−0.618248	−0.309124	−	0.951022i	$-0.600036\pi$
$823$	−14597.0	−0.618248	−0.309124	+	0.951022i	$0.600036\pi$
$824$	−11527.3	−0.487347
$825$	−14773.7	−0.623460
$826$	43309.3	1.82436
$827$	−32943.4	−1.38519	−0.692596	−	0.721326i	$-0.743533\pi$
$827$	−32943.4	−1.38519	−0.692596	+	0.721326i	$0.743533\pi$
$828$	−1448.27	−0.0607859
$829$	−35091.9	−1.47020	−0.735098	−	0.677961i	$-0.762864\pi$
$829$	−35091.9	−1.47020	−0.735098	+	0.677961i	$0.762864\pi$
$830$	−615.259	−0.0257300
$831$	−11899.9	−0.496756
$832$	−14080.2	−0.586711
$833$	0	0
$834$	18416.7	0.764648
$835$	12705.9	0.526594
$836$	−73834.1	−3.05455
$837$	16624.1	0.686517
$838$	32781.5	1.35133
$839$	−19365.1	−0.796848	−0.398424	−	0.917201i	$-0.630443\pi$
$839$	−19365.1	−0.796848	−0.398424	+	0.917201i	$0.630443\pi$
$840$	5478.15	0.225017
$841$	2827.42	0.115930
$842$	−32267.8	−1.32069
$843$	19724.9	0.805887
$844$	−39032.6	−1.59189
$845$	−11794.1	−0.480155
$846$	37293.0	1.51556
$847$	−71634.1	−2.90599
$848$	6531.13	0.264481
$849$	17937.2	0.725094
$850$	0	0
$851$	1167.48	0.0470278
$852$	15531.3	0.624521
$853$	−37350.6	−1.49925	−0.749625	−	0.661863i	$-0.769766\pi$
$853$	−37350.6	−1.49925	−0.749625	+	0.661863i	$0.769766\pi$
$854$	14181.4	0.568242
$855$	−13914.4	−0.556564
$856$	−1259.48	−0.0502899
$857$	14189.2	0.565569	0.282785	−	0.959183i	$-0.408742\pi$
$857$	14189.2	0.565569	0.282785	+	0.959183i	$0.408742\pi$
$858$	13919.9	0.553865
$859$	24014.5	0.953859	0.476930	−	0.878942i	$-0.341750\pi$
$859$	24014.5	0.953859	0.476930	+	0.878942i	$0.341750\pi$
$860$	10433.6	0.413699
$861$	2631.90	0.104175
$862$	−52416.8	−2.07114
$863$	−8498.07	−0.335200	−0.167600	−	0.985855i	$-0.553602\pi$
$863$	−8498.07	−0.335200	−0.167600	+	0.985855i	$0.553602\pi$
$864$	−32682.0	−1.28688
$865$	−11802.7	−0.463933
$866$	−66131.1	−2.59495
$867$	0	0
$868$	−38882.1	−1.52044
$869$	12334.5	0.481497
$870$	12838.6	0.500310
$871$	−18265.2	−0.710554
$872$	8118.78	0.315294
$873$	−12848.2	−0.498106
$874$	3666.57	0.141903
$875$	39247.4	1.51635
$876$	−25255.7	−0.974100
$877$	16013.2	0.616566	0.308283	−	0.951295i	$-0.400246\pi$
$877$	16013.2	0.616566	0.308283	+	0.951295i	$0.400246\pi$
$878$	76476.6	2.93959
$879$	−6535.84	−0.250794
$880$	15291.1	0.585755
$881$	−16824.6	−0.643399	−0.321699	−	0.946842i	$-0.604254\pi$
$881$	−16824.6	−0.643399	−0.321699	+	0.946842i	$0.604254\pi$
$882$	−42349.6	−1.61676
$883$	11327.3	0.431703	0.215851	−	0.976426i	$-0.430747\pi$
$883$	11327.3	0.431703	0.215851	+	0.976426i	$0.430747\pi$
$884$	0	0
$885$	6226.69	0.236506
$886$	1036.24	0.0392926
$887$	−11077.4	−0.419327	−0.209663	−	0.977774i	$-0.567237\pi$
$887$	−11077.4	−0.419327	−0.209663	+	0.977774i	$0.567237\pi$
$888$	−4623.08	−0.174708
$889$	43434.1	1.63862
$890$	13712.0	0.516436
$891$	−8400.68	−0.315862
$892$	−34879.2	−1.30924
$893$	−53346.5	−1.99907
$894$	5190.52	0.194180
$895$	−10335.0	−0.385989
$896$	36914.4	1.37637
$897$	−390.575	−0.0145384
$898$	−62104.5	−2.30785
$899$	−20973.5	−0.778095
$900$	16568.7	0.613657
$901$	0	0
$902$	−8255.78	−0.304753
$903$	13230.0	0.487560
$904$	−756.911	−0.0278479
$905$	4832.70	0.177508
$906$	−19153.1	−0.702339
$907$	1761.65	0.0644924	0.0322462	−	0.999480i	$-0.489734\pi$
$907$	1761.65	0.0644924	0.0322462	+	0.999480i	$0.489734\pi$
$908$	−20665.6	−0.755299
$909$	−36276.8	−1.32368
$910$	−14912.1	−0.543220
$911$	−44996.2	−1.63643	−0.818217	−	0.574909i	$-0.805037\pi$
$911$	−44996.2	−1.63643	−0.818217	+	0.574909i	$0.805037\pi$
$912$	12919.9	0.469102
$913$	1382.74	0.0501227
$914$	−7781.63	−0.281612
$915$	2038.90	0.0736657
$916$	54073.8	1.95049
$917$	30307.6	1.09144
$918$	0	0
$919$	34461.8	1.23699	0.618493	−	0.785790i	$-0.287743\pi$
$919$	34461.8	1.23699	0.618493	+	0.785790i	$0.287743\pi$
$920$	482.160	0.0172786
$921$	−6556.21	−0.234565
$922$	−57613.1	−2.05790
$923$	−9730.78	−0.347012
$924$	−53490.8	−1.90446
$925$	−13356.4	−0.474763
$926$	−71163.9	−2.52548
$927$	21212.0	0.751557
$928$	41232.7	1.45854
$929$	−37878.7	−1.33774	−0.668870	−	0.743379i	$-0.733222\pi$
$929$	−37878.7	−1.33774	−0.668870	+	0.743379i	$0.733222\pi$
$930$	−9893.71	−0.348847
$931$	60579.8	2.13257
$932$	59261.5	2.08281
$933$	16461.6	0.577630
$934$	−16914.6	−0.592573
$935$	0	0
$936$	−3593.12	−0.125475
$937$	−599.505	−0.0209018	−0.0104509	−	0.999945i	$-0.503327\pi$
$937$	−599.505	−0.0209018	−0.0104509	+	0.999945i	$0.503327\pi$
$938$	124223.	4.32412
$939$	7980.22	0.277342
$940$	−30479.0	−1.05757
$941$	10118.0	0.350519	0.175260	−	0.984522i	$-0.443924\pi$
$941$	10118.0	0.350519	0.175260	+	0.984522i	$0.443924\pi$
$942$	9318.32	0.322301
$943$	231.647	0.00799945
$944$	13431.9	0.463106
$945$	−24500.3	−0.843380
$946$	−41500.0	−1.42630
$947$	39320.2	1.34924	0.674622	−	0.738163i	$-0.264307\pi$
$947$	39320.2	1.34924	0.674622	+	0.738163i	$0.264307\pi$
$948$	5954.39	0.203997
$949$	15823.4	0.541254
$950$	−41947.0	−1.43257
$951$	14652.3	0.499616
$952$	0	0
$953$	−41203.8	−1.40055	−0.700274	−	0.713874i	$-0.746939\pi$
$953$	−41203.8	−1.40055	−0.700274	+	0.713874i	$0.746939\pi$
$954$	13505.9	0.458353
$955$	−11957.9	−0.405182
$956$	14736.0	0.498531
$957$	−28853.7	−0.974615
$958$	47872.3	1.61449
$959$	29968.3	1.00910
$960$	13767.7	0.462867
$961$	−13628.3	−0.457465
$962$	12584.5	0.421766
$963$	2317.63	0.0775540
$964$	−64592.6	−2.15808
$965$	3166.37	0.105626
$966$	2656.33	0.0884740
$967$	9403.83	0.312727	0.156363	−	0.987700i	$-0.450023\pi$
$967$	9403.83	0.312727	0.156363	+	0.987700i	$0.450023\pi$
$968$	24966.6	0.828984
$969$	0	0
$970$	18584.4	0.615164
$971$	−44819.8	−1.48129	−0.740646	−	0.671895i	$-0.765481\pi$
$971$	−44819.8	−1.48129	−0.740646	+	0.671895i	$0.765481\pi$
$972$	−40744.6	−1.34453
$973$	44340.1	1.46092
$974$	42817.1	1.40857
$975$	4468.33	0.146770
$976$	4398.23	0.144246
$977$	13700.4	0.448632	0.224316	−	0.974516i	$-0.427985\pi$
$977$	13700.4	0.448632	0.224316	+	0.974516i	$0.427985\pi$
$978$	27549.9	0.900766
$979$	−30816.6	−1.00603
$980$	34611.6	1.12819
$981$	−14939.7	−0.486227
$982$	−84226.0	−2.73703
$983$	34126.9	1.10730	0.553652	−	0.832748i	$-0.313234\pi$
$983$	34126.9	1.10730	0.553652	+	0.832748i	$0.313234\pi$
$984$	−917.297	−0.0297178
$985$	−6697.69	−0.216656
$986$	0	0
$987$	−38648.1	−1.24638
$988$	22331.2	0.719080
$989$	1164.44	0.0374389
$990$	31620.9	1.01513
$991$	38645.7	1.23877	0.619386	−	0.785087i	$-0.287382\pi$
$991$	38645.7	1.23877	0.619386	+	0.785087i	$0.287382\pi$
$992$	−31774.8	−1.01699
$993$	−1309.78	−0.0418577
$994$	66179.7	2.11176
$995$	11354.6	0.361773
$996$	667.505	0.0212356
$997$	13993.3	0.444505	0.222252	−	0.974989i	$-0.428659\pi$
$997$	13993.3	0.444505	0.222252	+	0.974989i	$0.428659\pi$
$998$	24720.7	0.784088
$999$	20676.1	0.654817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.10	✓	12
17.4	even	4		289.4.b.f.288.6		24
17.13	even	4		289.4.b.f.288.5		24
17.16	even	2		289.4.a.i.1.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.10	✓	12	1.1	even	1	trivial
289.4.a.i.1.10	yes	12	17.16	even	2
289.4.b.f.288.5		24	17.13	even	4
289.4.b.f.288.6		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)

\(f(q)\)	\(=\)	\(q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +O(q^{10})\)	\(q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +27.3023 q^{10} -61.3595 q^{11} -29.6207 q^{12} +18.5582 q^{13} -126.216 q^{14} -18.1464 q^{15} -39.1446 q^{16} -80.9480 q^{18} +115.793 q^{19} +66.1574 q^{20} +83.8892 q^{21} -263.144 q^{22} +7.38352 q^{23} -29.2379 q^{24} -84.4703 q^{25} +79.5883 q^{26} +130.762 q^{27} -305.840 q^{28} -164.974 q^{29} -77.8221 q^{30} +127.132 q^{31} -249.934 q^{32} +174.898 q^{33} -187.365 q^{35} -196.149 q^{36} +158.120 q^{37} +496.588 q^{38} -52.8982 q^{39} +65.3022 q^{40} +31.3736 q^{41} +359.764 q^{42} +157.708 q^{43} -637.637 q^{44} -120.166 q^{45} +31.6647 q^{46} -460.704 q^{47} +111.577 q^{48} +523.171 q^{49} -362.257 q^{50} +192.854 q^{52} -166.846 q^{53} +560.783 q^{54} -390.632 q^{55} -301.886 q^{56} -330.056 q^{57} -707.502 q^{58} -343.136 q^{59} -188.574 q^{60} -112.359 q^{61} +545.216 q^{62} +555.515 q^{63} -758.704 q^{64} +118.147 q^{65} +750.063 q^{66} -984.209 q^{67} -21.0459 q^{69} -803.528 q^{70} -524.337 q^{71} -193.613 q^{72} +852.636 q^{73} +678.106 q^{74} +240.773 q^{75} +1203.30 q^{76} +1805.86 q^{77} -226.858 q^{78} -201.021 q^{79} -249.206 q^{80} +136.909 q^{81} +134.548 q^{82} -22.5351 q^{83} +871.761 q^{84} +676.342 q^{86} +470.240 q^{87} -629.395 q^{88} +502.230 q^{89} -515.338 q^{90} -546.184 q^{91} +76.7282 q^{92} -362.377 q^{93} -1975.76 q^{94} +737.175 q^{95} +712.410 q^{96} +680.691 q^{97} +2243.65 q^{98} +1158.18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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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