LMFDB - Embedded newform 289.4.a.i.1.1

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:	$0$
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} + \cdots + 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			1.1
Root			$5.35197$ 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)

$f(q)$	$=$	$q-5.35197 q^{2} +1.66219 q^{3} +20.6436 q^{4} -5.96899 q^{5} -8.89600 q^{6} -27.8210 q^{7} -67.6680 q^{8} -24.2371 q^{9} +O(q^{10})$	\(q-5.35197 q^{2} +1.66219 q^{3} +20.6436 q^{4} -5.96899 q^{5} -8.89600 q^{6} -27.8210 q^{7} -67.6680 q^{8} -24.2371 q^{9} +31.9458 q^{10} +18.6361 q^{11} +34.3136 q^{12} -42.5466 q^{13} +148.897 q^{14} -9.92160 q^{15} +197.008 q^{16} +129.716 q^{18} +31.3435 q^{19} -123.221 q^{20} -46.2438 q^{21} -99.7396 q^{22} +60.3201 q^{23} -112.477 q^{24} -89.3712 q^{25} +227.708 q^{26} -85.1659 q^{27} -574.325 q^{28} +117.647 q^{29} +53.1001 q^{30} -228.520 q^{31} -513.039 q^{32} +30.9767 q^{33} +166.063 q^{35} -500.341 q^{36} +99.4898 q^{37} -167.749 q^{38} -70.7206 q^{39} +403.909 q^{40} +270.844 q^{41} +247.496 q^{42} +108.891 q^{43} +384.715 q^{44} +144.671 q^{45} -322.831 q^{46} -250.032 q^{47} +327.466 q^{48} +431.008 q^{49} +478.312 q^{50} -878.313 q^{52} +294.775 q^{53} +455.805 q^{54} -111.238 q^{55} +1882.59 q^{56} +52.0989 q^{57} -629.643 q^{58} +62.0744 q^{59} -204.817 q^{60} +799.234 q^{61} +1223.03 q^{62} +674.301 q^{63} +1169.70 q^{64} +253.960 q^{65} -165.786 q^{66} -645.320 q^{67} +100.264 q^{69} -888.765 q^{70} +1148.97 q^{71} +1640.08 q^{72} -550.710 q^{73} -532.466 q^{74} -148.552 q^{75} +647.041 q^{76} -518.474 q^{77} +378.494 q^{78} -253.834 q^{79} -1175.94 q^{80} +512.840 q^{81} -1449.55 q^{82} +717.541 q^{83} -954.638 q^{84} -582.784 q^{86} +195.552 q^{87} -1261.06 q^{88} -1590.45 q^{89} -774.275 q^{90} +1183.69 q^{91} +1245.22 q^{92} -379.844 q^{93} +1338.16 q^{94} -187.089 q^{95} -852.769 q^{96} +255.084 q^{97} -2306.74 q^{98} -451.684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.35197	−1.89221	−0.946103	−	0.323865i	$-0.895018\pi$
$2$	−5.35197	−1.89221	−0.946103	+	0.323865i	$0.895018\pi$
$3$	1.66219	0.319889	0.159944	−	0.987126i	$-0.448868\pi$
$3$	1.66219	0.319889	0.159944	+	0.987126i	$0.448868\pi$
$4$	20.6436	2.58045
$5$	−5.96899	−0.533882	−0.266941	−	0.963713i	$-0.586013\pi$
$5$	−5.96899	−0.533882	−0.266941	+	0.963713i	$0.586013\pi$
$6$	−8.89600	−0.605296
$7$	−27.8210	−1.50219	−0.751096	−	0.660193i	$-0.770475\pi$
$7$	−27.8210	−1.50219	−0.751096	+	0.660193i	$0.770475\pi$
$8$	−67.6680	−2.99053
$9$	−24.2371	−0.897671
$10$	31.9458	1.01022
$11$	18.6361	0.510816	0.255408	−	0.966833i	$-0.417790\pi$
$11$	18.6361	0.510816	0.255408	+	0.966833i	$0.417790\pi$
$12$	34.3136	0.825456
$13$	−42.5466	−0.907715	−0.453857	−	0.891074i	$-0.649952\pi$
$13$	−42.5466	−0.907715	−0.453857	+	0.891074i	$0.649952\pi$
$14$	148.897	2.84246
$15$	−9.92160	−0.170783
$16$	197.008	3.07826
$17$	0	0
$17$	0	0
$18$	129.716	1.69858
$19$	31.3435	0.378457	0.189229	−	0.981933i	$-0.439401\pi$
$19$	31.3435	0.378457	0.189229	+	0.981933i	$0.439401\pi$
$20$	−123.221	−1.37765
$21$	−46.2438	−0.480535
$22$	−99.7396	−0.966570
$23$	60.3201	0.546853	0.273426	−	0.961893i	$-0.411843\pi$
$23$	60.3201	0.546853	0.273426	+	0.961893i	$0.411843\pi$
$24$	−112.477	−0.956638
$25$	−89.3712	−0.714970
$26$	227.708	1.71758
$27$	−85.1659	−0.607044
$28$	−574.325	−3.87633
$29$	117.647	0.753327	0.376664	−	0.926350i	$-0.377071\pi$
$29$	117.647	0.753327	0.376664	+	0.926350i	$0.377071\pi$
$30$	53.1001	0.323157
$31$	−228.520	−1.32398	−0.661991	−	0.749512i	$-0.730288\pi$
$31$	−228.520	−1.32398	−0.661991	+	0.749512i	$0.730288\pi$
$32$	−513.039	−2.83417
$33$	30.9767	0.163405
$34$	0	0
$35$	166.063	0.801994
$36$	−500.341	−2.31639
$37$	99.4898	0.442055	0.221027	−	0.975268i	$-0.429059\pi$
$37$	99.4898	0.442055	0.221027	+	0.975268i	$0.429059\pi$
$38$	−167.749	−0.716119
$39$	−70.7206	−0.290368
$40$	403.909	1.59659
$41$	270.844	1.03168	0.515838	−	0.856686i	$-0.327481\pi$
$41$	270.844	1.03168	0.515838	+	0.856686i	$0.327481\pi$
$42$	247.496	0.909271
$43$	108.891	0.386181	0.193091	−	0.981181i	$-0.438149\pi$
$43$	108.891	0.386181	0.193091	+	0.981181i	$0.438149\pi$
$44$	384.715	1.31813
$45$	144.671	0.479251
$46$	−322.831	−1.03476
$47$	−250.032	−0.775975	−0.387988	−	0.921665i	$-0.626830\pi$
$47$	−250.032	−0.775975	−0.387988	+	0.921665i	$0.626830\pi$
$48$	327.466	0.984700
$49$	431.008	1.25658
$50$	478.312	1.35287
$51$	0	0
$52$	−878.313	−2.34231
$53$	294.775	0.763971	0.381985	−	0.924168i	$-0.375240\pi$
$53$	294.775	0.763971	0.381985	+	0.924168i	$0.375240\pi$
$54$	455.805	1.14865
$55$	−111.238	−0.272716
$56$	1882.59	4.49235
$57$	52.0989	0.121064
$58$	−629.643	−1.42545
$59$	62.0744	0.136973	0.0684864	−	0.997652i	$-0.478183\pi$
$59$	62.0744	0.136973	0.0684864	+	0.997652i	$0.478183\pi$
$60$	−204.817	−0.440697
$61$	799.234	1.67757	0.838783	−	0.544466i	$-0.183268\pi$
$61$	799.234	1.67757	0.838783	+	0.544466i	$0.183268\pi$
$62$	1223.03	2.50525
$63$	674.301	1.34847
$64$	1169.70	2.28457
$65$	253.960	0.484613
$66$	−165.786	−0.309195
$67$	−645.320	−1.17669	−0.588346	−	0.808609i	$-0.700221\pi$
$67$	−645.320	−1.17669	−0.588346	+	0.808609i	$0.700221\pi$
$68$	0	0
$69$	100.264	0.174932
$70$	−888.765	−1.51754
$71$	1148.97	1.92053	0.960263	−	0.279096i	$-0.0900348\pi$
$71$	1148.97	1.92053	0.960263	+	0.279096i	$0.0900348\pi$
$72$	1640.08	2.68451
$73$	−550.710	−0.882955	−0.441477	−	0.897272i	$-0.645545\pi$
$73$	−550.710	−0.882955	−0.441477	+	0.897272i	$0.645545\pi$
$74$	−532.466	−0.836459
$75$	−148.552	−0.228711
$76$	647.041	0.976588
$77$	−518.474	−0.767345
$78$	378.494	0.549436
$79$	−253.834	−0.361501	−0.180750	−	0.983529i	$-0.557853\pi$
$79$	−253.834	−0.361501	−0.180750	+	0.983529i	$0.557853\pi$
$80$	−1175.94	−1.64343
$81$	512.840	0.703484
$82$	−1449.55	−1.95214
$83$	717.541	0.948920	0.474460	−	0.880277i	$-0.342643\pi$
$83$	717.541	0.948920	0.474460	+	0.880277i	$0.342643\pi$
$84$	−954.638	−1.23999
$85$	0	0
$86$	−582.784	−0.730735
$87$	195.552	0.240981
$88$	−1261.06	−1.52761
$89$	−1590.45	−1.89424	−0.947121	−	0.320877i	$-0.896022\pi$
$89$	−1590.45	−1.89424	−0.947121	+	0.320877i	$0.896022\pi$
$90$	−774.275	−0.906841
$91$	1183.69	1.36356
$92$	1245.22	1.41112
$93$	−379.844	−0.423527
$94$	1338.16	1.46831
$95$	−187.089	−0.202052
$96$	−852.769	−0.906619
$97$	255.084	0.267008	0.133504	−	0.991048i	$-0.457377\pi$
$97$	255.084	0.267008	0.133504	+	0.991048i	$0.457377\pi$
$98$	−2306.74	−2.37771
$99$	−451.684	−0.458545
$100$	−1844.94	−1.84494
$101$	1006.58	0.991663	0.495832	−	0.868419i	$-0.334863\pi$
$101$	1006.58	0.991663	0.495832	+	0.868419i	$0.334863\pi$
$102$	0	0
$103$	1631.61	1.56084	0.780422	−	0.625253i	$-0.215004\pi$
$103$	1631.61	1.56084	0.780422	+	0.625253i	$0.215004\pi$
$104$	2879.04	2.71455
$105$	276.029	0.256549
$106$	−1577.63	−1.44559
$107$	−42.5550	−0.0384481	−0.0192241	−	0.999815i	$-0.506120\pi$
$107$	−42.5550	−0.0384481	−0.0192241	+	0.999815i	$0.506120\pi$
$108$	−1758.13	−1.56644
$109$	1862.24	1.63643	0.818214	−	0.574914i	$-0.194964\pi$
$109$	1862.24	1.63643	0.818214	+	0.574914i	$0.194964\pi$
$110$	595.344	0.516035
$111$	165.371	0.141408
$112$	−5480.97	−4.62414
$113$	13.5364	0.0112690	0.00563452	−	0.999984i	$-0.498206\pi$
$113$	13.5364	0.0112690	0.00563452	+	0.999984i	$0.498206\pi$
$114$	−278.832	−0.229079
$115$	−360.050	−0.291955
$116$	2428.65	1.94392
$117$	1031.21	0.814829
$118$	−332.220	−0.259181
$119$	0	0
$120$	671.375	0.510732
$121$	−983.698	−0.739067
$122$	−4277.48	−3.17430
$123$	450.195	0.330022
$124$	−4717.47	−3.41646
$125$	1279.58	0.915592
$126$	−3608.84	−2.55159
$127$	−1239.07	−0.865744	−0.432872	−	0.901455i	$-0.642500\pi$
$127$	−1239.07	−0.865744	−0.432872	+	0.901455i	$0.642500\pi$
$128$	−2155.89	−1.48872
$129$	180.998	0.123535
$130$	−1359.19	−0.916988
$131$	1310.04	0.873733	0.436866	−	0.899526i	$-0.356088\pi$
$131$	1310.04	0.873733	0.436866	+	0.899526i	$0.356088\pi$
$132$	639.470	0.421657
$133$	−872.007	−0.568516
$134$	3453.73	2.22655
$135$	508.354	0.324090
$136$	0	0
$137$	−592.057	−0.369218	−0.184609	−	0.982812i	$-0.559102\pi$
$137$	−592.057	−0.369218	−0.184609	+	0.982812i	$0.559102\pi$
$138$	−536.608	−0.331008
$139$	1723.70	1.05182	0.525908	−	0.850541i	$-0.323725\pi$
$139$	1723.70	1.05182	0.525908	+	0.850541i	$0.323725\pi$
$140$	3428.14	2.06950
$141$	−415.600	−0.248226
$142$	−6149.24	−3.63403
$143$	−792.900	−0.463676
$144$	−4774.92	−2.76326
$145$	−702.233	−0.402188
$146$	2947.38	1.67073
$147$	716.418	0.401967
$148$	2053.82	1.14070
$149$	−230.059	−0.126491	−0.0632456	−	0.997998i	$-0.520145\pi$
$149$	−230.059	−0.126491	−0.0632456	+	0.997998i	$0.520145\pi$
$150$	795.046	0.432768
$151$	−1876.54	−1.01133	−0.505663	−	0.862731i	$-0.668752\pi$
$151$	−1876.54	−1.01133	−0.505663	+	0.862731i	$0.668752\pi$
$152$	−2120.95	−1.13179
$153$	0	0
$154$	2774.85	1.45197
$155$	1364.03	0.706851
$156$	−1459.92	−0.749279
$157$	1076.29	0.547118	0.273559	−	0.961855i	$-0.411799\pi$
$157$	1076.29	0.547118	0.273559	+	0.961855i	$0.411799\pi$
$158$	1358.51	0.684034
$159$	489.973	0.244386
$160$	3062.32	1.51311
$161$	−1678.17	−0.821478
$162$	−2744.70	−1.33114
$163$	−1240.38	−0.596037	−0.298018	−	0.954560i	$-0.596326\pi$
$163$	−1240.38	−0.596037	−0.298018	+	0.954560i	$0.596326\pi$
$164$	5591.18	2.66218
$165$	−184.899	−0.0872388
$166$	−3840.26	−1.79555
$167$	2692.11	1.24743	0.623717	−	0.781650i	$-0.285622\pi$
$167$	2692.11	1.24743	0.623717	+	0.781650i	$0.285622\pi$
$168$	3129.23	1.43705
$169$	−386.790	−0.176054
$170$	0	0
$171$	−759.675	−0.339730
$172$	2247.91	0.996520
$173$	1819.34	0.799548	0.399774	−	0.916614i	$-0.369089\pi$
$173$	1819.34	0.799548	0.399774	+	0.916614i	$0.369089\pi$
$174$	−1046.59	−0.455986
$175$	2486.40	1.07402
$176$	3671.46	1.57242
$177$	103.180	0.0438161
$178$	8512.05	3.58430
$179$	−2087.72	−0.871752	−0.435876	−	0.900007i	$-0.643561\pi$
$179$	−2087.72	−0.871752	−0.435876	+	0.900007i	$0.643561\pi$
$180$	2986.53	1.23668
$181$	−2882.67	−1.18380	−0.591898	−	0.806013i	$-0.701621\pi$
$181$	−2882.67	−1.18380	−0.591898	+	0.806013i	$0.701621\pi$
$182$	−6335.06	−2.58014
$183$	1328.48	0.536635
$184$	−4081.74	−1.63538
$185$	−593.853	−0.236005
$186$	2032.92	0.801401
$187$	0	0
$188$	−5161.54	−2.00236
$189$	2369.40	0.911897
$190$	1001.29	0.382323
$191$	−242.916	−0.0920249	−0.0460124	−	0.998941i	$-0.514651\pi$
$191$	−242.916	−0.0920249	−0.0460124	+	0.998941i	$0.514651\pi$
$192$	1944.27	0.730810
$193$	3202.66	1.19447	0.597234	−	0.802067i	$-0.296266\pi$
$193$	3202.66	1.19447	0.597234	+	0.802067i	$0.296266\pi$
$194$	−1365.20	−0.505235
$195$	422.130	0.155022
$196$	8897.54	3.24254
$197$	−3624.82	−1.31095	−0.655477	−	0.755215i	$-0.727532\pi$
$197$	−3624.82	−1.31095	−0.655477	+	0.755215i	$0.727532\pi$
$198$	2417.40	0.867662
$199$	−65.9115	−0.0234791	−0.0117395	−	0.999931i	$-0.503737\pi$
$199$	−65.9115	−0.0234791	−0.0117395	+	0.999931i	$0.503737\pi$
$200$	6047.57	2.13814
$201$	−1072.65	−0.376411
$202$	−5387.16	−1.87643
$203$	−3273.06	−1.13164
$204$	0	0
$205$	−1616.66	−0.550793
$206$	−8732.31	−2.95344
$207$	−1461.99	−0.490894
$208$	−8382.03	−2.79418
$209$	584.119	0.193322
$210$	−1477.30	−0.485444
$211$	3523.72	1.14968	0.574841	−	0.818265i	$-0.305064\pi$
$211$	3523.72	1.14968	0.574841	+	0.818265i	$0.305064\pi$
$212$	6085.21	1.97139
$213$	1909.80	0.614355
$214$	227.753	0.0727518
$215$	−649.972	−0.206175
$216$	5763.01	1.81538
$217$	6357.66	1.98888
$218$	−9966.68	−3.09646
$219$	−915.385	−0.282447
$220$	−2296.36	−0.703729
$221$	0	0
$222$	−885.061	−0.267574
$223$	−935.115	−0.280807	−0.140404	−	0.990094i	$-0.544840\pi$
$223$	−935.115	−0.280807	−0.140404	+	0.990094i	$0.544840\pi$
$224$	14273.3	4.25747
$225$	2166.10	0.641808
$226$	−72.4466	−0.0213233
$227$	−4987.57	−1.45831	−0.729155	−	0.684349i	$-0.760087\pi$
$227$	−4987.57	−1.45831	−0.729155	+	0.684349i	$0.760087\pi$
$228$	1075.51	0.312400
$229$	−181.488	−0.0523714	−0.0261857	−	0.999657i	$-0.508336\pi$
$229$	−181.488	−0.0523714	−0.0261857	+	0.999657i	$0.508336\pi$
$230$	1926.98	0.552439
$231$	−861.803	−0.245465
$232$	−7960.94	−2.25285
$233$	−2290.78	−0.644095	−0.322048	−	0.946723i	$-0.604371\pi$
$233$	−2290.78	−0.644095	−0.322048	+	0.946723i	$0.604371\pi$
$234$	−5518.98	−1.54183
$235$	1492.43	0.414280
$236$	1281.44	0.353451
$237$	−421.921	−0.115640
$238$	0	0
$239$	809.874	0.219190	0.109595	−	0.993976i	$-0.465045\pi$
$239$	809.874	0.219190	0.109595	+	0.993976i	$0.465045\pi$
$240$	−1954.64	−0.525714
$241$	−5634.28	−1.50596	−0.752979	−	0.658044i	$-0.771384\pi$
$241$	−5634.28	−1.50596	−0.752979	+	0.658044i	$0.771384\pi$
$242$	5264.72	1.39847
$243$	3151.92	0.832081
$244$	16499.1	4.32887
$245$	−2572.68	−0.670867
$246$	−2409.43	−0.624469
$247$	−1333.56	−0.343531
$248$	15463.5	3.95941
$249$	1192.69	0.303549
$250$	−6848.27	−1.73249
$251$	3676.86	0.924627	0.462314	−	0.886717i	$-0.347019\pi$
$251$	3676.86	0.924627	0.462314	+	0.886717i	$0.347019\pi$
$252$	13920.0	3.47967
$253$	1124.13	0.279341
$254$	6631.45	1.63817
$255$	0	0
$256$	2180.66	0.532389
$257$	−180.020	−0.0436938	−0.0218469	−	0.999761i	$-0.506955\pi$
$257$	−180.020	−0.0436938	−0.0218469	+	0.999761i	$0.506955\pi$
$258$	−968.698	−0.233754
$259$	−2767.91	−0.664051
$260$	5242.64	1.25052
$261$	−2851.42	−0.676240
$262$	−7011.31	−1.65328
$263$	−2035.20	−0.477171	−0.238586	−	0.971121i	$-0.576684\pi$
$263$	−2035.20	−0.477171	−0.238586	+	0.971121i	$0.576684\pi$
$264$	−2096.13	−0.488666
$265$	−1759.51	−0.407871
$266$	4666.95	1.07575
$267$	−2643.64	−0.605947
$268$	−13321.7	−3.03639
$269$	2036.45	0.461578	0.230789	−	0.973004i	$-0.425869\pi$
$269$	2036.45	0.461578	0.230789	+	0.973004i	$0.425869\pi$
$270$	−2720.70	−0.613245
$271$	5126.86	1.14920	0.574602	−	0.818433i	$-0.305157\pi$
$271$	5126.86	1.14920	0.574602	+	0.818433i	$0.305157\pi$
$272$	0	0
$273$	1967.52	0.436189
$274$	3168.67	0.698637
$275$	−1665.53	−0.365218
$276$	2069.80	0.451403
$277$	4012.79	0.870415	0.435208	−	0.900330i	$-0.356675\pi$
$277$	4012.79	0.870415	0.435208	+	0.900330i	$0.356675\pi$
$278$	−9225.20	−1.99025
$279$	5538.67	1.18850
$280$	−11237.2	−2.39839
$281$	−6603.25	−1.40184	−0.700920	−	0.713240i	$-0.747227\pi$
$281$	−6603.25	−1.40184	−0.700920	+	0.713240i	$0.747227\pi$
$282$	2224.28	0.469695
$283$	108.788	0.0228508	0.0114254	−	0.999935i	$-0.496363\pi$
$283$	108.788	0.0228508	0.0114254	+	0.999935i	$0.496363\pi$
$284$	23718.8	4.95582
$285$	−310.977	−0.0646341
$286$	4243.58	0.877370
$287$	−7535.15	−1.54978
$288$	12434.6	2.54415
$289$	0	0
$290$	3758.33	0.761023
$291$	423.998	0.0854131
$292$	−11368.6	−2.27842
$293$	9133.49	1.82111	0.910553	−	0.413393i	$-0.135656\pi$
$293$	9133.49	1.82111	0.910553	+	0.413393i	$0.135656\pi$
$294$	−3834.25	−0.760605
$295$	−370.521	−0.0731274
$296$	−6732.27	−1.32198
$297$	−1587.16	−0.310088
$298$	1231.27	0.239348
$299$	−2566.41	−0.496387
$300$	−3066.65	−0.590176
$301$	−3029.47	−0.580119
$302$	10043.2	1.91364
$303$	1673.12	0.317222
$304$	6174.93	1.16499
$305$	−4770.62	−0.895622
$306$	0	0
$307$	−4469.59	−0.830921	−0.415461	−	0.909611i	$-0.636380\pi$
$307$	−4469.59	−0.830921	−0.415461	+	0.909611i	$0.636380\pi$
$308$	−10703.1	−1.98009
$309$	2712.04	0.499297
$310$	−7300.27	−1.33751
$311$	−9396.83	−1.71333	−0.856664	−	0.515874i	$-0.827467\pi$
$311$	−9396.83	−1.71333	−0.856664	+	0.515874i	$0.827467\pi$
$312$	4785.52	0.868355
$313$	−10276.8	−1.85583	−0.927917	−	0.372786i	$-0.878403\pi$
$313$	−10276.8	−1.85583	−0.927917	+	0.372786i	$0.878403\pi$
$314$	−5760.29	−1.03526
$315$	−4024.89	−0.719927
$316$	−5240.04	−0.932833
$317$	−7547.44	−1.33724	−0.668622	−	0.743602i	$-0.733116\pi$
$317$	−7547.44	−1.33724	−0.668622	+	0.743602i	$0.733116\pi$
$318$	−2622.32	−0.462429
$319$	2192.48	0.384812
$320$	−6981.93	−1.21969
$321$	−70.7346	−0.0122991
$322$	8981.49	1.55441
$323$	0	0
$324$	10586.9	1.81530
$325$	3802.44	0.648989
$326$	6638.47	1.12782
$327$	3095.41	0.523475
$328$	−18327.5	−3.08526
$329$	6956.13	1.16566
$330$	989.576	0.165074
$331$	6285.90	1.04382	0.521910	−	0.853000i	$-0.325220\pi$
$331$	6285.90	1.04382	0.521910	+	0.853000i	$0.325220\pi$
$332$	14812.6	2.44864
$333$	−2411.35	−0.396820
$334$	−14408.1	−2.36040
$335$	3851.91	0.628215
$336$	−9110.43	−1.47921
$337$	464.322	0.0750541	0.0375271	−	0.999296i	$-0.488052\pi$
$337$	464.322	0.0750541	0.0375271	+	0.999296i	$0.488052\pi$
$338$	2070.09	0.333130
$339$	22.5002	0.00360484
$340$	0	0
$341$	−4258.71	−0.676312
$342$	4065.76	0.642839
$343$	−2448.47	−0.385437
$344$	−7368.47	−1.15489
$345$	−598.472	−0.0933932
$346$	−9737.05	−1.51291
$347$	7445.29	1.15183	0.575914	−	0.817510i	$-0.304646\pi$
$347$	7445.29	1.15183	0.575914	+	0.817510i	$0.304646\pi$
$348$	4036.89	0.621839
$349$	6395.90	0.980987	0.490494	−	0.871445i	$-0.336816\pi$
$349$	6395.90	0.980987	0.490494	+	0.871445i	$0.336816\pi$
$350$	−13307.1	−2.03227
$351$	3623.52	0.551023
$352$	−9561.02	−1.44774
$353$	−8031.82	−1.21102	−0.605511	−	0.795837i	$-0.707031\pi$
$353$	−8031.82	−1.21102	−0.605511	+	0.795837i	$0.707031\pi$
$354$	−552.214	−0.0829091
$355$	−6858.17	−1.02534
$356$	−32832.6	−4.88799
$357$	0	0
$358$	11173.4	1.64953
$359$	−2730.88	−0.401477	−0.200738	−	0.979645i	$-0.564334\pi$
$359$	−2730.88	−0.401477	−0.200738	+	0.979645i	$0.564334\pi$
$360$	−9789.60	−1.43321
$361$	−5876.59	−0.856770
$362$	15428.0	2.23999
$363$	−1635.09	−0.236419
$364$	24435.5	3.51860
$365$	3287.18	0.471394
$366$	−7109.99	−1.01542
$367$	2802.02	0.398541	0.199270	−	0.979945i	$-0.436143\pi$
$367$	2802.02	0.398541	0.199270	+	0.979945i	$0.436143\pi$
$368$	11883.6	1.68335
$369$	−6564.48	−0.926106
$370$	3178.28	0.446570
$371$	−8200.93	−1.14763
$372$	−7841.35	−1.09289
$373$	8987.58	1.24761	0.623806	−	0.781579i	$-0.285585\pi$
$373$	8987.58	1.24761	0.623806	+	0.781579i	$0.285585\pi$
$374$	0	0
$375$	2126.91	0.292888
$376$	16919.1	2.32058
$377$	−5005.47	−0.683807
$378$	−12681.0	−1.72550
$379$	7786.77	1.05536	0.527678	−	0.849445i	$-0.323063\pi$
$379$	7786.77	1.05536	0.527678	+	0.849445i	$0.323063\pi$
$380$	−3862.18	−0.521383
$381$	−2059.57	−0.276942
$382$	1300.08	0.174130
$383$	7557.45	1.00827	0.504135	−	0.863625i	$-0.331811\pi$
$383$	7557.45	1.00827	0.504135	+	0.863625i	$0.331811\pi$
$384$	−3583.51	−0.476225
$385$	3094.76	0.409672
$386$	−17140.5	−2.26018
$387$	−2639.22	−0.346664
$388$	5265.84	0.689001
$389$	10883.8	1.41859	0.709296	−	0.704911i	$-0.249013\pi$
$389$	10883.8	1.41859	0.709296	+	0.704911i	$0.249013\pi$
$390$	−2259.23	−0.293334
$391$	0	0
$392$	−29165.4	−3.75785
$393$	2177.54	0.279497
$394$	19399.9	2.48060
$395$	1515.13	0.192999
$396$	−9324.37	−1.18325
$397$	2103.72	0.265952	0.132976	−	0.991119i	$-0.457547\pi$
$397$	2103.72	0.265952	0.132976	+	0.991119i	$0.457547\pi$
$398$	352.756	0.0444273
$399$	−1449.44	−0.181862
$400$	−17606.9	−2.20086
$401$	10029.6	1.24901	0.624505	−	0.781021i	$-0.285301\pi$
$401$	10029.6	1.24901	0.624505	+	0.781021i	$0.285301\pi$
$402$	5740.77	0.712247
$403$	9722.75	1.20180
$404$	20779.3	2.55893
$405$	−3061.13	−0.375578
$406$	17517.3	2.14130
$407$	1854.10	0.225809
$408$	0	0
$409$	−515.825	−0.0623616	−0.0311808	−	0.999514i	$-0.509927\pi$
$409$	−515.825	−0.0623616	−0.0311808	+	0.999514i	$0.509927\pi$
$410$	8652.33	1.04222
$411$	−984.113	−0.118109
$412$	33682.2	4.02767
$413$	−1726.97	−0.205760
$414$	7824.50	0.928873
$415$	−4282.99	−0.506611
$416$	21828.1	2.57262
$417$	2865.12	0.336465
$418$	−3126.18	−0.365805
$419$	9370.98	1.09261	0.546304	−	0.837587i	$-0.316034\pi$
$419$	9370.98	1.09261	0.546304	+	0.837587i	$0.316034\pi$
$420$	5698.22	0.662011
$421$	−283.696	−0.0328421	−0.0164210	−	0.999865i	$-0.505227\pi$
$421$	−283.696	−0.0328421	−0.0164210	+	0.999865i	$0.505227\pi$
$422$	−18858.8	−2.17544
$423$	6060.04	0.696571
$424$	−19946.8	−2.28468
$425$	0	0
$426$	−10221.2	−1.16249
$427$	−22235.5	−2.52003
$428$	−878.487	−0.0992133
$429$	−1317.95	−0.148325
$430$	3478.63	0.390126
$431$	−8243.79	−0.921321	−0.460661	−	0.887576i	$-0.652387\pi$
$431$	−8243.79	−0.921321	−0.460661	+	0.887576i	$0.652387\pi$
$432$	−16778.4	−1.86864
$433$	−1340.39	−0.148765	−0.0743824	−	0.997230i	$-0.523699\pi$
$433$	−1340.39	−0.148765	−0.0743824	+	0.997230i	$0.523699\pi$
$434$	−34026.0	−3.76336
$435$	−1167.25	−0.128656
$436$	38443.4	4.22272
$437$	1890.64	0.206960
$438$	4899.11	0.534449
$439$	4717.90	0.512923	0.256461	−	0.966554i	$-0.417443\pi$
$439$	4717.90	0.512923	0.256461	+	0.966554i	$0.417443\pi$
$440$	7527.27	0.815565
$441$	−10446.4	−1.12800
$442$	0	0
$443$	14002.0	1.50171	0.750855	−	0.660467i	$-0.229642\pi$
$443$	14002.0	1.50171	0.750855	+	0.660467i	$0.229642\pi$
$444$	3413.85	0.364897
$445$	9493.38	1.01130
$446$	5004.71	0.531345
$447$	−382.403	−0.0404632
$448$	−32542.3	−3.43187
$449$	−4574.27	−0.480787	−0.240393	−	0.970676i	$-0.577276\pi$
$449$	−4574.27	−0.480787	−0.240393	+	0.970676i	$0.577276\pi$
$450$	−11592.9	−1.21443
$451$	5047.46	0.526997
$452$	279.440	0.0290791
$453$	−3119.16	−0.323512
$454$	26693.3	2.75942
$455$	−7065.42	−0.727982
$456$	−3525.43	−0.362046
$457$	−1535.79	−0.157202	−0.0786009	−	0.996906i	$-0.525045\pi$
$457$	−1535.79	−0.157202	−0.0786009	+	0.996906i	$0.525045\pi$
$458$	971.318	0.0990976
$459$	0	0
$460$	−7432.72	−0.753374
$461$	14514.7	1.46642	0.733209	−	0.680003i	$-0.238022\pi$
$461$	14514.7	1.46642	0.733209	+	0.680003i	$0.238022\pi$
$462$	4612.34	0.464471
$463$	145.386	0.0145932	0.00729659	−	0.999973i	$-0.497677\pi$
$463$	145.386	0.0145932	0.00729659	+	0.999973i	$0.497677\pi$
$464$	23177.4	2.31894
$465$	2267.29	0.226114
$466$	12260.2	1.21876
$467$	6038.32	0.598330	0.299165	−	0.954201i	$-0.403292\pi$
$467$	6038.32	0.598330	0.299165	+	0.954201i	$0.403292\pi$
$468$	21287.8	2.10262
$469$	17953.4	1.76762
$470$	−7987.46	−0.783903
$471$	1789.01	0.175017
$472$	−4200.45	−0.409622
$473$	2029.31	0.197268
$474$	2258.11	0.218815
$475$	−2801.20	−0.270585
$476$	0	0
$477$	−7144.50	−0.685795
$478$	−4334.42	−0.414753
$479$	9142.21	0.872063	0.436031	−	0.899931i	$-0.356384\pi$
$479$	9142.21	0.872063	0.436031	+	0.899931i	$0.356384\pi$
$480$	5090.17	0.484028
$481$	−4232.95	−0.401260
$482$	30154.5	2.84958
$483$	−2789.43	−0.262782
$484$	−20307.0	−1.90712
$485$	−1522.59	−0.142551
$486$	−16869.0	−1.57447
$487$	4376.57	0.407231	0.203615	−	0.979051i	$-0.434731\pi$
$487$	4376.57	0.407231	0.203615	+	0.979051i	$0.434731\pi$
$488$	−54082.6	−5.01681
$489$	−2061.75	−0.190666
$490$	13768.9	1.26942
$491$	9490.30	0.872284	0.436142	−	0.899878i	$-0.356345\pi$
$491$	9490.30	0.872284	0.436142	+	0.899878i	$0.356345\pi$
$492$	9293.62	0.851603
$493$	0	0
$494$	7137.16	0.650032
$495$	2696.10	0.244809
$496$	−45020.4	−4.07556
$497$	−31965.4	−2.88500
$498$	−6383.24	−0.574377
$499$	−2331.32	−0.209147	−0.104573	−	0.994517i	$-0.533348\pi$
$499$	−2331.32	−0.209147	−0.104573	+	0.994517i	$0.533348\pi$
$500$	26415.1	2.36264
$501$	4474.80	0.399041
$502$	−19678.4	−1.74959
$503$	4372.95	0.387635	0.193817	−	0.981038i	$-0.437913\pi$
$503$	4372.95	0.387635	0.193817	+	0.981038i	$0.437913\pi$
$504$	−45628.6	−4.03266
$505$	−6008.23	−0.529431
$506$	−6016.30	−0.528572
$507$	−642.919	−0.0563176
$508$	−25578.8	−2.23401
$509$	4983.33	0.433954	0.216977	−	0.976177i	$-0.430380\pi$
$509$	4983.33	0.433954	0.216977	+	0.976177i	$0.430380\pi$
$510$	0	0
$511$	15321.3	1.32637
$512$	5576.30	0.481328
$513$	−2669.40	−0.229740
$514$	963.460	0.0826778
$515$	−9739.03	−0.833307
$516$	3736.46	0.318776
$517$	−4659.60	−0.396381
$518$	14813.7	1.25652
$519$	3024.09	0.255767
$520$	−17185.0	−1.44925
$521$	−6480.02	−0.544903	−0.272452	−	0.962169i	$-0.587834\pi$
$521$	−6480.02	−0.544903	−0.272452	+	0.962169i	$0.587834\pi$
$522$	15260.7	1.27959
$523$	−15597.0	−1.30403	−0.652017	−	0.758204i	$-0.726077\pi$
$523$	−15597.0	−1.30403	−0.652017	+	0.758204i	$0.726077\pi$
$524$	27044.0	2.25462
$525$	4132.87	0.343568
$526$	10892.4	0.902907
$527$	0	0
$528$	6102.67	0.503001
$529$	−8528.48	−0.700952
$530$	9416.83	0.771775
$531$	−1504.50	−0.122957
$532$	−18001.3	−1.46702
$533$	−11523.5	−0.936468
$534$	14148.7	1.14658
$535$	254.010	0.0205268
$536$	43667.5	3.51894
$537$	−3470.19	−0.278864
$538$	−10899.0	−0.873402
$539$	8032.29	0.641883
$540$	10494.2	0.836297
$541$	−10629.6	−0.844739	−0.422370	−	0.906424i	$-0.638802\pi$
$541$	−10629.6	−0.844739	−0.422370	+	0.906424i	$0.638802\pi$
$542$	−27438.8	−2.17453
$543$	−4791.55	−0.378683
$544$	0	0
$545$	−11115.7	−0.873660
$546$	−10530.1	−0.825359
$547$	12199.5	0.953588	0.476794	−	0.879015i	$-0.341799\pi$
$547$	12199.5	0.953588	0.476794	+	0.879015i	$0.341799\pi$
$548$	−12222.2	−0.952747
$549$	−19371.1	−1.50590
$550$	8913.85	0.691068
$551$	3687.46	0.285102
$552$	−6784.64	−0.523140
$553$	7061.91	0.543044
$554$	−21476.3	−1.64701
$555$	−987.098	−0.0754954
$556$	35583.4	2.71416
$557$	−17588.3	−1.33796	−0.668978	−	0.743282i	$-0.733268\pi$
$557$	−17588.3	−1.33796	−0.668978	+	0.743282i	$0.733268\pi$
$558$	−29642.8	−2.24889
$559$	−4632.96	−0.350542
$560$	32715.8	2.46874
$561$	0	0
$562$	35340.4	2.65257
$563$	−4001.08	−0.299513	−0.149756	−	0.988723i	$-0.547849\pi$
$563$	−4001.08	−0.299513	−0.149756	+	0.988723i	$0.547849\pi$
$564$	−8579.48	−0.640534
$565$	−80.7988	−0.00601634
$566$	−582.229	−0.0432384
$567$	−14267.7	−1.05677
$568$	−77748.3	−5.74339
$569$	−8055.37	−0.593495	−0.296747	−	0.954956i	$-0.595902\pi$
$569$	−8055.37	−0.593495	−0.296747	+	0.954956i	$0.595902\pi$
$570$	1664.34	0.122301
$571$	12525.5	0.917998	0.458999	−	0.888437i	$-0.348208\pi$
$571$	12525.5	0.917998	0.458999	+	0.888437i	$0.348208\pi$
$572$	−16368.3	−1.19649
$573$	−403.772	−0.0294378
$574$	40327.9	2.93250
$575$	−5390.88	−0.390983
$576$	−28350.2	−2.05080
$577$	7783.77	0.561599	0.280799	−	0.959766i	$-0.409400\pi$
$577$	7783.77	0.561599	0.280799	+	0.959766i	$0.409400\pi$
$578$	0	0
$579$	5323.43	0.382097
$580$	−14496.6	−1.03782
$581$	−19962.7	−1.42546
$582$	−2269.22	−0.161619
$583$	5493.44	0.390249
$584$	37265.4	2.64050
$585$	−6155.25	−0.435023
$586$	−48882.1	−3.44591
$587$	17282.7	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$587$	17282.7	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$588$	14789.4	1.03725
$589$	−7162.62	−0.501070
$590$	1983.02	0.138372
$591$	−6025.15	−0.419360
$592$	19600.3	1.36076
$593$	22285.6	1.54327	0.771636	−	0.636065i	$-0.219439\pi$
$593$	22285.6	1.54327	0.771636	+	0.636065i	$0.219439\pi$
$594$	8494.41	0.586751
$595$	0	0
$596$	−4749.25	−0.326404
$597$	−109.557	−0.00751070
$598$	13735.4	0.939266
$599$	14494.3	0.988681	0.494340	−	0.869268i	$-0.335410\pi$
$599$	14494.3	0.988681	0.494340	+	0.869268i	$0.335410\pi$
$600$	10052.2	0.683967
$601$	13389.8	0.908790	0.454395	−	0.890800i	$-0.349856\pi$
$601$	13389.8	0.908790	0.454395	+	0.890800i	$0.349856\pi$
$602$	16213.6	1.09770
$603$	15640.7	1.05628
$604$	−38738.4	−2.60967
$605$	5871.68	0.394575
$606$	−8954.49	−0.600250
$607$	5081.09	0.339761	0.169881	−	0.985465i	$-0.445662\pi$
$607$	5081.09	0.339761	0.169881	+	0.985465i	$0.445662\pi$
$608$	−16080.4	−1.07261
$609$	−5440.45	−0.362000
$610$	25532.2	1.69470
$611$	10638.0	0.704365
$612$	0	0
$613$	−29310.1	−1.93120	−0.965598	−	0.260040i	$-0.916264\pi$
$613$	−29310.1	−1.93120	−0.965598	+	0.260040i	$0.916264\pi$
$614$	23921.1	1.57227
$615$	−2687.20	−0.176193
$616$	35084.1	2.29477
$617$	−9815.75	−0.640466	−0.320233	−	0.947339i	$-0.603761\pi$
$617$	−9815.75	−0.640466	−0.320233	+	0.947339i	$0.603761\pi$
$618$	−14514.8	−0.944773
$619$	10696.9	0.694579	0.347290	−	0.937758i	$-0.387102\pi$
$619$	10696.9	0.694579	0.347290	+	0.937758i	$0.387102\pi$
$620$	28158.5	1.82399
$621$	−5137.22	−0.331964
$622$	50291.5	3.24197
$623$	44247.9	2.84552
$624$	−13932.5	−0.893827
$625$	3533.62	0.226151
$626$	55000.8	3.51162
$627$	970.917	0.0618416
$628$	22218.5	1.41181
$629$	0	0
$630$	21541.1	1.36225
$631$	−6104.87	−0.385152	−0.192576	−	0.981282i	$-0.561684\pi$
$631$	−6104.87	−0.385152	−0.192576	+	0.981282i	$0.561684\pi$
$632$	17176.4	1.08108
$633$	5857.10	0.367771
$634$	40393.7	2.53034
$635$	7395.98	0.462205
$636$	10114.8	0.630625
$637$	−18337.9	−1.14062
$638$	−11734.1	−0.728144
$639$	−27847.7	−1.72400
$640$	12868.5	0.794800
$641$	−3753.93	−0.231312	−0.115656	−	0.993289i	$-0.536897\pi$
$641$	−3753.93	−0.231312	−0.115656	+	0.993289i	$0.536897\pi$
$642$	378.569	0.0232725
$643$	22480.9	1.37879	0.689394	−	0.724386i	$-0.257877\pi$
$643$	22480.9	1.37879	0.689394	+	0.724386i	$0.257877\pi$
$644$	−34643.3	−2.11978
$645$	−1080.38	−0.0659532
$646$	0	0
$647$	20385.1	1.23867	0.619337	−	0.785126i	$-0.287402\pi$
$647$	20385.1	1.23867	0.619337	+	0.785126i	$0.287402\pi$
$648$	−34702.9	−2.10379
$649$	1156.82	0.0699680
$650$	−20350.5	−1.22802
$651$	10567.7	0.636220
$652$	−25605.9	−1.53804
$653$	7944.24	0.476083	0.238041	−	0.971255i	$-0.423495\pi$
$653$	7944.24	0.476083	0.238041	+	0.971255i	$0.423495\pi$
$654$	−16566.5	−0.990524
$655$	−7819.63	−0.466470
$656$	53358.5	3.17576
$657$	13347.6	0.792603
$658$	−37229.0	−2.20568
$659$	−672.385	−0.0397457	−0.0198728	−	0.999803i	$-0.506326\pi$
$659$	−672.385	−0.0397457	−0.0198728	+	0.999803i	$0.506326\pi$
$660$	−3816.98	−0.225115
$661$	−7967.64	−0.468843	−0.234421	−	0.972135i	$-0.575320\pi$
$661$	−7967.64	−0.468843	−0.234421	+	0.972135i	$0.575320\pi$
$662$	−33642.0	−1.97512
$663$	0	0
$664$	−48554.5	−2.83777
$665$	5205.00	0.303520
$666$	12905.4	0.750865
$667$	7096.48	0.411959
$668$	55574.7	3.21894
$669$	−1554.34	−0.0898271
$670$	−20615.3	−1.18871
$671$	14894.6	0.856928
$672$	23724.9	1.36192
$673$	20798.2	1.19125	0.595626	−	0.803262i	$-0.296904\pi$
$673$	20798.2	1.19125	0.595626	+	0.803262i	$0.296904\pi$
$674$	−2485.04	−0.142018
$675$	7611.38	0.434018
$676$	−7984.72	−0.454297
$677$	−19180.9	−1.08890	−0.544449	−	0.838794i	$-0.683261\pi$
$677$	−19180.9	−1.08890	−0.544449	+	0.838794i	$0.683261\pi$
$678$	−120.420	−0.00682110
$679$	−7096.68	−0.401098
$680$	0	0
$681$	−8290.29	−0.466497
$682$	22792.5	1.27972
$683$	−7081.83	−0.396748	−0.198374	−	0.980126i	$-0.563566\pi$
$683$	−7081.83	−0.396748	−0.198374	+	0.980126i	$0.563566\pi$
$684$	−15682.4	−0.876655
$685$	3533.98	0.197119
$686$	13104.1	0.729326
$687$	−301.668	−0.0167530
$688$	21452.5	1.18876
$689$	−12541.7	−0.693468
$690$	3203.00	0.176719
$691$	−27665.8	−1.52309	−0.761547	−	0.648110i	$-0.775560\pi$
$691$	−27665.8	−1.52309	−0.761547	+	0.648110i	$0.775560\pi$
$692$	37557.7	2.06319
$693$	12566.3	0.688823
$694$	−39847.0	−2.17950
$695$	−10288.8	−0.561546
$696$	−13232.6	−0.720662
$697$	0	0
$698$	−34230.7	−1.85623
$699$	−3807.72	−0.206039
$700$	51328.1	2.77146
$701$	−7813.26	−0.420974	−0.210487	−	0.977597i	$-0.567505\pi$
$701$	−7813.26	−0.420974	−0.210487	+	0.977597i	$0.567505\pi$
$702$	−19393.0	−1.04265
$703$	3118.36	0.167299
$704$	21798.6	1.16700
$705$	2480.71	0.132523
$706$	42986.0	2.29150
$707$	−28003.9	−1.48967
$708$	2129.99	0.113065
$709$	−21810.2	−1.15529	−0.577645	−	0.816288i	$-0.696028\pi$
$709$	−21810.2	−1.15529	−0.577645	+	0.816288i	$0.696028\pi$
$710$	36704.7	1.94015
$711$	6152.20	0.324509
$712$	107623.	5.66479
$713$	−13784.4	−0.724023
$714$	0	0
$715$	4732.81	0.247548
$716$	−43098.0	−2.24951
$717$	1346.17	0.0701164
$718$	14615.6	0.759677
$719$	−2333.31	−0.121026	−0.0605131	−	0.998167i	$-0.519274\pi$
$719$	−2333.31	−0.121026	−0.0605131	+	0.998167i	$0.519274\pi$
$720$	28501.4	1.47526
$721$	−45392.9	−2.34469
$722$	31451.3	1.62119
$723$	−9365.26	−0.481740
$724$	−59508.6	−3.05472
$725$	−10514.3	−0.538606
$726$	8750.97	0.447354
$727$	545.182	0.0278125	0.0139063	−	0.999903i	$-0.495573\pi$
$727$	545.182	0.0278125	0.0139063	+	0.999903i	$0.495573\pi$
$728$	−80097.8	−4.07778
$729$	−8607.59	−0.437311
$730$	−17592.9	−0.891975
$731$	0	0
$732$	27424.6	1.38476
$733$	−2753.41	−0.138744	−0.0693721	−	0.997591i	$-0.522100\pi$
$733$	−2753.41	−0.138744	−0.0693721	+	0.997591i	$0.522100\pi$
$734$	−14996.4	−0.754122
$735$	−4276.29	−0.214603
$736$	−30946.6	−1.54987
$737$	−12026.2	−0.601074
$738$	35132.9	1.75238
$739$	25776.3	1.28308	0.641540	−	0.767089i	$-0.278296\pi$
$739$	25776.3	1.28308	0.641540	+	0.767089i	$0.278296\pi$
$740$	−12259.2	−0.608999
$741$	−2216.63	−0.109892
$742$	43891.1	2.17156
$743$	−17597.0	−0.868872	−0.434436	−	0.900703i	$-0.643052\pi$
$743$	−17597.0	−0.868872	−0.434436	+	0.900703i	$0.643052\pi$
$744$	25703.3	1.26657
$745$	1373.22	0.0675314
$746$	−48101.3	−2.36074
$747$	−17391.1	−0.851818
$748$	0	0
$749$	1183.92	0.0577565
$750$	−11383.1	−0.554204
$751$	1515.51	0.0736373	0.0368186	−	0.999322i	$-0.488278\pi$
$751$	1515.51	0.0736373	0.0368186	+	0.999322i	$0.488278\pi$
$752$	−49258.3	−2.38865
$753$	6111.65	0.295778
$754$	26789.1	1.29390
$755$	11201.0	0.539929
$756$	48912.9	2.35310
$757$	19464.1	0.934523	0.467261	−	0.884119i	$-0.345241\pi$
$757$	19464.1	0.934523	0.467261	+	0.884119i	$0.345241\pi$
$758$	−41674.6	−1.99695
$759$	1868.52	0.0893583
$760$	12659.9	0.604242
$761$	11937.8	0.568652	0.284326	−	0.958728i	$-0.408230\pi$
$761$	11937.8	0.568652	0.284326	+	0.958728i	$0.408230\pi$
$762$	11022.7	0.524031
$763$	−51809.5	−2.45823
$764$	−5014.65	−0.237465
$765$	0	0
$766$	−40447.2	−1.90786
$767$	−2641.05	−0.124332
$768$	3624.68	0.170305
$769$	26884.3	1.26069	0.630345	−	0.776315i	$-0.282913\pi$
$769$	26884.3	1.26069	0.630345	+	0.776315i	$0.282913\pi$
$770$	−16563.1	−0.775184
$771$	−299.227	−0.0139772
$772$	66114.3	3.08226
$773$	−12551.4	−0.584013	−0.292006	−	0.956416i	$-0.594323\pi$
$773$	−12551.4	−0.584013	−0.292006	+	0.956416i	$0.594323\pi$
$774$	14125.0	0.655959
$775$	20423.1	0.946607
$776$	−17261.0	−0.798497
$777$	−4600.79	−0.212423
$778$	−58249.9	−2.68427
$779$	8489.19	0.390445
$780$	8714.27	0.400027
$781$	21412.2	0.981036
$782$	0	0
$783$	−10019.5	−0.457303
$784$	84912.2	3.86808
$785$	−6424.38	−0.292097
$786$	−11654.1	−0.528867
$787$	17781.7	0.805400	0.402700	−	0.915332i	$-0.368072\pi$
$787$	17781.7	0.805400	0.402700	+	0.915332i	$0.368072\pi$
$788$	−74829.3	−3.38285
$789$	−3382.90	−0.152642
$790$	−8108.94	−0.365194
$791$	−376.597	−0.0169283
$792$	30564.6	1.37129
$793$	−34004.7	−1.52275
$794$	−11259.1	−0.503235
$795$	−2924.64	−0.130473
$796$	−1360.65	−0.0605865
$797$	36529.5	1.62352	0.811758	−	0.583995i	$-0.198511\pi$
$797$	36529.5	1.62352	0.811758	+	0.583995i	$0.198511\pi$
$798$	7757.37	0.344120
$799$	0	0
$800$	45850.9	2.02634
$801$	38548.0	1.70041
$802$	−53677.9	−2.36338
$803$	−10263.1	−0.451028
$804$	−22143.2	−0.971308
$805$	10017.0	0.438573
$806$	−52035.9	−2.27405
$807$	3384.97	0.147654
$808$	−68112.9	−2.96560
$809$	−19732.6	−0.857555	−0.428777	−	0.903410i	$-0.641055\pi$
$809$	−19732.6	−0.857555	−0.428777	+	0.903410i	$0.641055\pi$
$810$	16383.1	0.710671
$811$	−14943.7	−0.647035	−0.323517	−	0.946222i	$-0.604865\pi$
$811$	−14943.7	−0.647035	−0.323517	+	0.946222i	$0.604865\pi$
$812$	−67567.6	−2.92014
$813$	8521.82	0.367618
$814$	−9923.07	−0.427277
$815$	7403.80	0.318213
$816$	0	0
$817$	3413.04	0.146153
$818$	2760.68	0.118001
$819$	−28689.2	−1.22403
$820$	−33373.7	−1.42129
$821$	31002.2	1.31789	0.658943	−	0.752193i	$-0.271004\pi$
$821$	31002.2	1.31789	0.658943	+	0.752193i	$0.271004\pi$
$822$	5266.94	0.223486
$823$	27393.7	1.16025	0.580124	−	0.814528i	$-0.303004\pi$
$823$	27393.7	1.16025	0.580124	+	0.814528i	$0.303004\pi$
$824$	−110408.	−4.66775
$825$	−2768.42	−0.116829
$826$	9242.70	0.389340
$827$	674.496	0.0283610	0.0141805	−	0.999899i	$-0.495486\pi$
$827$	674.496	0.0283610	0.0141805	+	0.999899i	$0.495486\pi$
$828$	−30180.6	−1.26673
$829$	42790.2	1.79272	0.896359	−	0.443328i	$-0.146202\pi$
$829$	42790.2	1.79272	0.896359	+	0.443328i	$0.146202\pi$
$830$	22922.4	0.958613
$831$	6670.02	0.278436
$832$	−49766.8	−2.07374
$833$	0	0
$834$	−15334.1	−0.636661
$835$	−16069.2	−0.665983
$836$	12058.3	0.498857
$837$	19462.1	0.803715
$838$	−50153.2	−2.06744
$839$	−25582.3	−1.05268	−0.526340	−	0.850274i	$-0.676436\pi$
$839$	−25582.3	−1.05268	−0.526340	+	0.850274i	$0.676436\pi$
$840$	−18678.3	−0.767218
$841$	−10548.2	−0.432498
$842$	1518.33	0.0621440
$843$	−10975.9	−0.448433
$844$	72742.2	2.96669
$845$	2308.74	0.0939919
$846$	−32433.2	−1.31806
$847$	27367.4	1.11022
$848$	58073.2	2.35170
$849$	180.826	0.00730971
$850$	0	0
$851$	6001.24	0.241739
$852$	39425.2	1.58531
$853$	−26776.3	−1.07480	−0.537400	−	0.843328i	$-0.680593\pi$
$853$	−26776.3	−1.07480	−0.537400	+	0.843328i	$0.680593\pi$
$854$	119004.	4.76841
$855$	4534.49	0.181376
$856$	2879.61	0.114980
$857$	2239.80	0.0892767	0.0446383	−	0.999003i	$-0.485786\pi$
$857$	2239.80	0.0892767	0.0446383	+	0.999003i	$0.485786\pi$
$858$	7053.64	0.280661
$859$	−13841.5	−0.549784	−0.274892	−	0.961475i	$-0.588642\pi$
$859$	−13841.5	−0.549784	−0.274892	+	0.961475i	$0.588642\pi$
$860$	−13417.7	−0.532024
$861$	−12524.9	−0.495756
$862$	44120.5	1.74333
$863$	41377.2	1.63209	0.816046	−	0.577987i	$-0.196161\pi$
$863$	41377.2	1.63209	0.816046	+	0.577987i	$0.196161\pi$
$864$	43693.4	1.72046
$865$	−10859.6	−0.426864
$866$	7173.74	0.281494
$867$	0	0
$868$	131245.	5.13219
$869$	−4730.46	−0.184660
$870$	6247.07	0.243443
$871$	27456.2	1.06810
$872$	−126014.	−4.89379
$873$	−6182.49	−0.239686
$874$	−10118.7	−0.391612
$875$	−35599.2	−1.37540
$876$	−18896.8	−0.728840
$877$	−12605.0	−0.485337	−0.242668	−	0.970109i	$-0.578023\pi$
$877$	−12605.0	−0.485337	−0.242668	+	0.970109i	$0.578023\pi$
$878$	−25250.1	−0.970556
$879$	15181.6	0.582552
$880$	−21914.9	−0.839489
$881$	−20007.8	−0.765132	−0.382566	−	0.923928i	$-0.624960\pi$
$881$	−20007.8	−0.765132	−0.382566	+	0.923928i	$0.624960\pi$
$882$	55908.8	2.13441
$883$	43309.8	1.65061	0.825307	−	0.564685i	$-0.191002\pi$
$883$	43309.8	1.65061	0.825307	+	0.564685i	$0.191002\pi$
$884$	0	0
$885$	−615.877	−0.0233926
$886$	−74938.5	−2.84154
$887$	39472.3	1.49420	0.747098	−	0.664714i	$-0.231447\pi$
$887$	39472.3	1.49420	0.747098	+	0.664714i	$0.231447\pi$
$888$	−11190.3	−0.422886
$889$	34472.1	1.30051
$890$	−50808.3	−1.91359
$891$	9557.31	0.359351
$892$	−19304.1	−0.724607
$893$	−7836.86	−0.293673
$894$	2046.61	0.0765647
$895$	12461.6	0.465413
$896$	59979.1	2.23634
$897$	−4265.87	−0.158789
$898$	24481.4	0.909748
$899$	−26884.7	−0.997392
$900$	44716.1	1.65615
$901$	0	0
$902$	−27013.9	−0.997187
$903$	−5035.56	−0.185574
$904$	−915.984	−0.0337004
$905$	17206.6	0.632008
$906$	16693.7	0.612152
$907$	−8879.42	−0.325068	−0.162534	−	0.986703i	$-0.551967\pi$
$907$	−8879.42	−0.325068	−0.162534	+	0.986703i	$0.551967\pi$
$908$	−102961.	−3.76309
$909$	−24396.5	−0.890187
$910$	37813.9	1.37749
$911$	9321.10	0.338992	0.169496	−	0.985531i	$-0.445786\pi$
$911$	9321.10	0.338992	0.169496	+	0.985531i	$0.445786\pi$
$912$	10263.9	0.372667
$913$	13372.1	0.484724
$914$	8219.50	0.297458
$915$	−7929.68	−0.286500
$916$	−3746.56	−0.135142
$917$	−36446.7	−1.31251
$918$	0	0
$919$	−8783.98	−0.315296	−0.157648	−	0.987495i	$-0.550391\pi$
$919$	−8783.98	−0.315296	−0.157648	+	0.987495i	$0.550391\pi$
$920$	24363.9	0.873101
$921$	−7429.31	−0.265803
$922$	−77682.5	−2.77477
$923$	−48884.6	−1.74329
$924$	−17790.7	−0.633410
$925$	−8891.52	−0.316056
$926$	−778.100	−0.0276133
$927$	−39545.4	−1.40112
$928$	−60357.5	−2.13506
$929$	−24381.1	−0.861054	−0.430527	−	0.902578i	$-0.641672\pi$
$929$	−24381.1	−0.861054	−0.430527	+	0.902578i	$0.641672\pi$
$930$	−12134.4	−0.427854
$931$	13509.3	0.475563
$932$	−47289.9	−1.66205
$933$	−15619.3	−0.548075
$934$	−32316.9	−1.13216
$935$	0	0
$936$	−69779.7	−2.43677
$937$	23120.9	0.806113	0.403056	−	0.915175i	$-0.367948\pi$
$937$	23120.9	0.806113	0.403056	+	0.915175i	$0.367948\pi$
$938$	−96086.3	−3.34470
$939$	−17081.9	−0.593661
$940$	30809.2	1.06903
$941$	46768.5	1.62020	0.810101	−	0.586291i	$-0.199412\pi$
$941$	46768.5	1.62020	0.810101	+	0.586291i	$0.199412\pi$
$942$	−9574.70	−0.331168
$943$	16337.3	0.564175
$944$	12229.2	0.421638
$945$	−14142.9	−0.486846
$946$	−10860.8	−0.373271
$947$	38093.5	1.30715	0.653576	−	0.756861i	$-0.273268\pi$
$947$	38093.5	1.30715	0.653576	+	0.756861i	$0.273268\pi$
$948$	−8709.95	−0.298403
$949$	23430.8	0.801471
$950$	14992.0	0.512003
$951$	−12545.3	−0.427770
$952$	0	0
$953$	−31247.7	−1.06213	−0.531066	−	0.847330i	$-0.678208\pi$
$953$	−31247.7	−1.06213	−0.531066	+	0.847330i	$0.678208\pi$
$954$	38237.1	1.29767
$955$	1449.96	0.0491305
$956$	16718.7	0.565608
$957$	3644.31	0.123097
$958$	−48928.8	−1.65012
$959$	16471.6	0.554637
$960$	−11605.3	−0.390166
$961$	22430.5	0.752928
$962$	22654.6	0.759266
$963$	1031.41	0.0345138
$964$	−116312.	−3.88604
$965$	−19116.6	−0.637705
$966$	14929.0	0.497238
$967$	−48567.3	−1.61512	−0.807558	−	0.589788i	$-0.799211\pi$
$967$	−48567.3	−1.61512	−0.807558	+	0.589788i	$0.799211\pi$
$968$	66564.8	2.21020
$969$	0	0
$970$	8148.86	0.269736
$971$	16286.5	0.538267	0.269133	−	0.963103i	$-0.413263\pi$
$971$	16286.5	0.538267	0.269133	+	0.963103i	$0.413263\pi$
$972$	65066.9	2.14714
$973$	−47955.1	−1.58003
$974$	−23423.3	−0.770565
$975$	6320.38	0.207604
$976$	157456.	5.16398
$977$	12003.7	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$977$	12003.7	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$978$	11034.4	0.360779
$979$	−29639.7	−0.967610
$980$	−53109.3	−1.73114
$981$	−45135.4	−1.46897
$982$	−50791.8	−1.65054
$983$	10008.2	0.324731	0.162365	−	0.986731i	$-0.448088\pi$
$983$	10008.2	0.324731	0.162365	+	0.986731i	$0.448088\pi$
$984$	−30463.8	−0.986940
$985$	21636.5	0.699895
$986$	0	0
$987$	11562.4	0.372883
$988$	−27529.4	−0.886464
$989$	6568.35	0.211184
$990$	−14429.4	−0.463229
$991$	13384.7	0.429040	0.214520	−	0.976720i	$-0.431181\pi$
$991$	13384.7	0.429040	0.214520	+	0.976720i	$0.431181\pi$
$992$	117240.	3.75239
$993$	10448.4	0.333907
$994$	171078.	5.45902
$995$	393.425	0.0125351
$996$	24621.4	0.783292
$997$	21615.7	0.686635	0.343317	−	0.939219i	$-0.388449\pi$
$997$	21615.7	0.686635	0.343317	+	0.939219i	$0.388449\pi$
$998$	12477.1	0.395748
$999$	−8473.14	−0.268347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.i.1.1	yes	12
17.4	even	4		289.4.b.f.288.24		24
17.13	even	4		289.4.b.f.288.23		24
17.16	even	2		289.4.a.h.1.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.1	✓	12	17.16	even	2
289.4.a.i.1.1	yes	12	1.1	even	1	trivial
289.4.b.f.288.23		24	17.13	even	4
289.4.b.f.288.24		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)

\(f(q)\)	\(=\)	\(q-5.35197 q^{2} +1.66219 q^{3} +20.6436 q^{4} -5.96899 q^{5} -8.89600 q^{6} -27.8210 q^{7} -67.6680 q^{8} -24.2371 q^{9} +O(q^{10})\)	\(q-5.35197 q^{2} +1.66219 q^{3} +20.6436 q^{4} -5.96899 q^{5} -8.89600 q^{6} -27.8210 q^{7} -67.6680 q^{8} -24.2371 q^{9} +31.9458 q^{10} +18.6361 q^{11} +34.3136 q^{12} -42.5466 q^{13} +148.897 q^{14} -9.92160 q^{15} +197.008 q^{16} +129.716 q^{18} +31.3435 q^{19} -123.221 q^{20} -46.2438 q^{21} -99.7396 q^{22} +60.3201 q^{23} -112.477 q^{24} -89.3712 q^{25} +227.708 q^{26} -85.1659 q^{27} -574.325 q^{28} +117.647 q^{29} +53.1001 q^{30} -228.520 q^{31} -513.039 q^{32} +30.9767 q^{33} +166.063 q^{35} -500.341 q^{36} +99.4898 q^{37} -167.749 q^{38} -70.7206 q^{39} +403.909 q^{40} +270.844 q^{41} +247.496 q^{42} +108.891 q^{43} +384.715 q^{44} +144.671 q^{45} -322.831 q^{46} -250.032 q^{47} +327.466 q^{48} +431.008 q^{49} +478.312 q^{50} -878.313 q^{52} +294.775 q^{53} +455.805 q^{54} -111.238 q^{55} +1882.59 q^{56} +52.0989 q^{57} -629.643 q^{58} +62.0744 q^{59} -204.817 q^{60} +799.234 q^{61} +1223.03 q^{62} +674.301 q^{63} +1169.70 q^{64} +253.960 q^{65} -165.786 q^{66} -645.320 q^{67} +100.264 q^{69} -888.765 q^{70} +1148.97 q^{71} +1640.08 q^{72} -550.710 q^{73} -532.466 q^{74} -148.552 q^{75} +647.041 q^{76} -518.474 q^{77} +378.494 q^{78} -253.834 q^{79} -1175.94 q^{80} +512.840 q^{81} -1449.55 q^{82} +717.541 q^{83} -954.638 q^{84} -582.784 q^{86} +195.552 q^{87} -1261.06 q^{88} -1590.45 q^{89} -774.275 q^{90} +1183.69 q^{91} +1245.22 q^{92} -379.844 q^{93} +1338.16 q^{94} -187.089 q^{95} -852.769 q^{96} +255.084 q^{97} -2306.74 q^{98} -451.684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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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