LMFDB - Embedded newform 289.4.a.h.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:	$1$
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			1.1
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	$-0.551132\pi$
$3$	−1.66219	−0.319889	−0.159944	+	0.987126i	$0.551132\pi$
$4$	20.6436	2.58045
$5$	5.96899	0.533882	0.266941	−	0.963713i	$-0.413987\pi$
$5$	5.96899	0.533882	0.266941	+	0.963713i	$0.413987\pi$
$6$	8.89600	0.605296
$7$	27.8210	1.50219	0.751096	−	0.660193i	$-0.229525\pi$
$7$	27.8210	1.50219	0.751096	+	0.660193i	$0.229525\pi$
$8$	−67.6680	−2.99053
$9$	−24.2371	−0.897671
$10$	−31.9458	−1.01022
$11$	−18.6361	−0.510816	−0.255408	−	0.966833i	$-0.582210\pi$
$11$	−18.6361	−0.510816	−0.255408	+	0.966833i	$0.582210\pi$
$12$	−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	$-0.588157\pi$
$23$	−60.3201	−0.546853	−0.273426	+	0.961893i	$0.588157\pi$
$24$	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	$-0.622929\pi$
$29$	−117.647	−0.753327	−0.376664	+	0.926350i	$0.622929\pi$
$30$	53.1001	0.323157
$31$	228.520	1.32398	0.661991	−	0.749512i	$-0.269712\pi$
$31$	228.520	1.32398	0.661991	+	0.749512i	$0.269712\pi$
$32$	−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	$-0.570941\pi$
$37$	−99.4898	−0.442055	−0.221027	+	0.975268i	$0.570941\pi$
$38$	−167.749	−0.716119
$39$	70.7206	0.290368
$40$	−403.909	−1.59659
$41$	−270.844	−1.03168	−0.515838	−	0.856686i	$-0.672519\pi$
$41$	−270.844	−1.03168	−0.515838	+	0.856686i	$0.672519\pi$
$42$	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	$-0.816732\pi$
$61$	−799.234	−1.67757	−0.838783	+	0.544466i	$0.816732\pi$
$62$	−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	$-0.909965\pi$
$71$	−1148.97	−1.92053	−0.960263	+	0.279096i	$0.909965\pi$
$72$	1640.08	2.68451
$73$	550.710	0.882955	0.441477	−	0.897272i	$-0.354455\pi$
$73$	550.710	0.882955	0.441477	+	0.897272i	$0.354455\pi$
$74$	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	$-0.442147\pi$
$79$	253.834	0.361501	0.180750	+	0.983529i	$0.442147\pi$
$80$	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	$-0.542623\pi$
$97$	−255.084	−0.267008	−0.133504	+	0.991048i	$0.542623\pi$
$98$	−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	$-0.493880\pi$
$107$	42.5550	0.0384481	0.0192241	+	0.999815i	$0.493880\pi$
$108$	1758.13	1.56644
$109$	−1862.24	−1.63643	−0.818214	−	0.574914i	$-0.805036\pi$
$109$	−1862.24	−1.63643	−0.818214	+	0.574914i	$0.805036\pi$
$110$	595.344	0.516035
$111$	165.371	0.141408
$112$	5480.97	4.62414
$113$	−13.5364	−0.0112690	−0.00563452	−	0.999984i	$-0.501794\pi$
$113$	−13.5364	−0.0112690	−0.00563452	+	0.999984i	$0.501794\pi$
$114$	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	$-0.643912\pi$
$131$	−1310.04	−0.873733	−0.436866	+	0.899526i	$0.643912\pi$
$132$	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	$-0.676275\pi$
$139$	−1723.70	−1.05182	−0.525908	+	0.850541i	$0.676275\pi$
$140$	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	$-0.403674\pi$
$163$	1240.38	0.596037	0.298018	+	0.954560i	$0.403674\pi$
$164$	−5591.18	−2.66218
$165$	184.899	0.0872388
$166$	−3840.26	−1.79555
$167$	−2692.11	−1.24743	−0.623717	−	0.781650i	$-0.714378\pi$
$167$	−2692.11	−1.24743	−0.623717	+	0.781650i	$0.714378\pi$
$168$	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	$-0.630911\pi$
$173$	−1819.34	−0.799548	−0.399774	+	0.916614i	$0.630911\pi$
$174$	−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	$-0.298379\pi$
$181$	2882.67	1.18380	0.591898	+	0.806013i	$0.298379\pi$
$182$	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	$-0.703734\pi$
$193$	−3202.66	−1.19447	−0.597234	+	0.802067i	$0.703734\pi$
$194$	1365.20	0.505235
$195$	422.130	0.155022
$196$	8897.54	3.24254
$197$	3624.82	1.31095	0.655477	−	0.755215i	$-0.272468\pi$
$197$	3624.82	1.31095	0.655477	+	0.755215i	$0.272468\pi$
$198$	−2417.40	−0.867662
$199$	65.9115	0.0234791	0.0117395	−	0.999931i	$-0.496263\pi$
$199$	65.9115	0.0234791	0.0117395	+	0.999931i	$0.496263\pi$
$200$	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	$-0.694936\pi$
$211$	−3523.72	−1.14968	−0.574841	+	0.818265i	$0.694936\pi$
$212$	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	$-0.239913\pi$
$227$	4987.57	1.45831	0.729155	+	0.684349i	$0.239913\pi$
$228$	−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	$-0.395629\pi$
$233$	2290.78	0.644095	0.322048	+	0.946723i	$0.395629\pi$
$234$	−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	$-0.228616\pi$
$241$	5634.28	1.50596	0.752979	+	0.658044i	$0.228616\pi$
$242$	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	$-0.574131\pi$
$269$	−2036.45	−0.461578	−0.230789	+	0.973004i	$0.574131\pi$
$270$	−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	$-0.643325\pi$
$277$	−4012.79	−0.870415	−0.435208	+	0.900330i	$0.643325\pi$
$278$	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	$-0.503637\pi$
$283$	−108.788	−0.0228508	−0.0114254	+	0.999935i	$0.503637\pi$
$284$	−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	$-0.172533\pi$
$311$	9396.83	1.71333	0.856664	+	0.515874i	$0.172533\pi$
$312$	−4785.52	−0.868355
$313$	10276.8	1.85583	0.927917	−	0.372786i	$-0.121597\pi$
$313$	10276.8	1.85583	0.927917	+	0.372786i	$0.121597\pi$
$314$	−5760.29	−1.03526
$315$	−4024.89	−0.719927
$316$	5240.04	0.932833
$317$	7547.44	1.33724	0.668622	−	0.743602i	$-0.266884\pi$
$317$	7547.44	1.33724	0.668622	+	0.743602i	$0.266884\pi$
$318$	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	$-0.511948\pi$
$337$	−464.322	−0.0750541	−0.0375271	+	0.999296i	$0.511948\pi$
$338$	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	$-0.695354\pi$
$347$	−7445.29	−1.15183	−0.575914	+	0.817510i	$0.695354\pi$
$348$	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	$-0.563857\pi$
$367$	−2802.02	−0.398541	−0.199270	+	0.979945i	$0.563857\pi$
$368$	−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	$-0.676937\pi$
$379$	−7786.77	−1.05536	−0.527678	+	0.849445i	$0.676937\pi$
$380$	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	$-0.542453\pi$
$397$	−2103.72	−0.265952	−0.132976	+	0.991119i	$0.542453\pi$
$398$	−352.756	−0.0444273
$399$	−1449.44	−0.181862
$400$	−17606.9	−2.20086
$401$	−10029.6	−1.24901	−0.624505	−	0.781021i	$-0.714699\pi$
$401$	−10029.6	−1.24901	−0.624505	+	0.781021i	$0.714699\pi$
$402$	−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	$-0.683966\pi$
$419$	−9370.98	−1.09261	−0.546304	+	0.837587i	$0.683966\pi$
$420$	−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	$-0.347613\pi$
$431$	8243.79	0.921321	0.460661	+	0.887576i	$0.347613\pi$
$432$	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	$-0.582557\pi$
$439$	−4717.90	−0.512923	−0.256461	+	0.966554i	$0.582557\pi$
$440$	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	$-0.422724\pi$
$449$	4574.27	0.480787	0.240393	+	0.970676i	$0.422724\pi$
$450$	−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	$-0.643616\pi$
$479$	−9142.21	−0.872063	−0.436031	+	0.899931i	$0.643616\pi$
$480$	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	$-0.565269\pi$
$487$	−4376.57	−0.407231	−0.203615	+	0.979051i	$0.565269\pi$
$488$	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	$-0.466652\pi$
$499$	2331.32	0.209147	0.104573	+	0.994517i	$0.466652\pi$
$500$	−26415.1	−2.36264
$501$	4474.80	0.399041
$502$	−19678.4	−1.74959
$503$	−4372.95	−0.387635	−0.193817	−	0.981038i	$-0.562087\pi$
$503$	−4372.95	−0.387635	−0.193817	+	0.981038i	$0.562087\pi$
$504$	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	$-0.412166\pi$
$521$	6480.02	0.544903	0.272452	+	0.962169i	$0.412166\pi$
$522$	−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	$-0.361198\pi$
$541$	10629.6	0.844739	0.422370	+	0.906424i	$0.361198\pi$
$542$	−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	$-0.658201\pi$
$547$	−12199.5	−0.953588	−0.476794	+	0.879015i	$0.658201\pi$
$548$	−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	$-0.651792\pi$
$571$	−12525.5	−0.917998	−0.458999	+	0.888437i	$0.651792\pi$
$572$	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	$-0.650144\pi$
$601$	−13389.8	−0.908790	−0.454395	+	0.890800i	$0.650144\pi$
$602$	−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	$-0.554338\pi$
$607$	−5081.09	−0.339761	−0.169881	+	0.985465i	$0.554338\pi$
$608$	−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	$-0.396239\pi$
$617$	9815.75	0.640466	0.320233	+	0.947339i	$0.396239\pi$
$618$	14514.8	0.944773
$619$	−10696.9	−0.694579	−0.347290	−	0.937758i	$-0.612898\pi$
$619$	−10696.9	−0.694579	−0.347290	+	0.937758i	$0.612898\pi$
$620$	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	$-0.463103\pi$
$641$	3753.93	0.231312	0.115656	+	0.993289i	$0.463103\pi$
$642$	378.569	0.0232725
$643$	−22480.9	−1.37879	−0.689394	−	0.724386i	$-0.742123\pi$
$643$	−22480.9	−1.37879	−0.689394	+	0.724386i	$0.742123\pi$
$644$	−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	$-0.576505\pi$
$653$	−7944.24	−0.476083	−0.238041	+	0.971255i	$0.576505\pi$
$654$	−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	$-0.703096\pi$
$673$	−20798.2	−1.19125	−0.595626	+	0.803262i	$0.703096\pi$
$674$	2485.04	0.142018
$675$	−7611.38	−0.434018
$676$	−7984.72	−0.454297
$677$	19180.9	1.08890	0.544449	−	0.838794i	$-0.316739\pi$
$677$	19180.9	1.08890	0.544449	+	0.838794i	$0.316739\pi$
$678$	−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	$-0.436434\pi$
$683$	7081.83	0.396748	0.198374	+	0.980126i	$0.436434\pi$
$684$	−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	$-0.224440\pi$
$691$	27665.8	1.52309	0.761547	+	0.648110i	$0.224440\pi$
$692$	−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	$-0.303972\pi$
$709$	21810.2	1.15529	0.577645	+	0.816288i	$0.303972\pi$
$710$	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	$-0.480726\pi$
$719$	2333.31	0.121026	0.0605131	+	0.998167i	$0.480726\pi$
$720$	−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	$-0.356948\pi$
$743$	17597.0	0.868872	0.434436	+	0.900703i	$0.356948\pi$
$744$	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	$-0.511722\pi$
$751$	−1515.51	−0.0736373	−0.0368186	+	0.999322i	$0.511722\pi$
$752$	−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	$-0.631928\pi$
$787$	−17781.7	−0.805400	−0.402700	+	0.915332i	$0.631928\pi$
$788$	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	$-0.358945\pi$
$809$	19732.6	0.857555	0.428777	+	0.903410i	$0.358945\pi$
$810$	−16383.1	−0.710671
$811$	14943.7	0.647035	0.323517	−	0.946222i	$-0.395135\pi$
$811$	14943.7	0.647035	0.323517	+	0.946222i	$0.395135\pi$
$812$	−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	$-0.728996\pi$
$821$	−31002.2	−1.31789	−0.658943	+	0.752193i	$0.728996\pi$
$822$	−5266.94	−0.223486
$823$	−27393.7	−1.16025	−0.580124	−	0.814528i	$-0.696996\pi$
$823$	−27393.7	−1.16025	−0.580124	+	0.814528i	$0.696996\pi$
$824$	−110408.	−4.66775
$825$	−2768.42	−0.116829
$826$	−9242.70	−0.389340
$827$	−674.496	−0.0283610	−0.0141805	−	0.999899i	$-0.504514\pi$
$827$	−674.496	−0.0283610	−0.0141805	+	0.999899i	$0.504514\pi$
$828$	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	$-0.323564\pi$
$839$	25582.3	1.05268	0.526340	+	0.850274i	$0.323564\pi$
$840$	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	$-0.319407\pi$
$853$	26776.3	1.07480	0.537400	+	0.843328i	$0.319407\pi$
$854$	119004.	4.76841
$855$	−4534.49	−0.181376
$856$	−2879.61	−0.114980
$857$	−2239.80	−0.0892767	−0.0446383	−	0.999003i	$-0.514214\pi$
$857$	−2239.80	−0.0892767	−0.0446383	+	0.999003i	$0.514214\pi$
$858$	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	$-0.421977\pi$
$877$	12605.0	0.485337	0.242668	+	0.970109i	$0.421977\pi$
$878$	25250.1	0.970556
$879$	−15181.6	−0.582552
$880$	−21914.9	−0.839489
$881$	20007.8	0.765132	0.382566	−	0.923928i	$-0.375040\pi$
$881$	20007.8	0.765132	0.382566	+	0.923928i	$0.375040\pi$
$882$	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	$-0.768553\pi$
$887$	−39472.3	−1.49420	−0.747098	+	0.664714i	$0.768553\pi$
$888$	−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	$-0.448033\pi$
$907$	8879.42	0.325068	0.162534	+	0.986703i	$0.448033\pi$
$908$	102961.	3.76309
$909$	−24396.5	−0.890187
$910$	37813.9	1.37749
$911$	−9321.10	−0.338992	−0.169496	−	0.985531i	$-0.554214\pi$
$911$	−9321.10	−0.338992	−0.169496	+	0.985531i	$0.554214\pi$
$912$	−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	$-0.358328\pi$
$929$	24381.1	0.861054	0.430527	+	0.902578i	$0.358328\pi$
$930$	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	$-0.800588\pi$
$941$	−46768.5	−1.62020	−0.810101	+	0.586291i	$0.800588\pi$
$942$	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	$-0.726732\pi$
$947$	−38093.5	−1.30715	−0.653576	+	0.756861i	$0.726732\pi$
$948$	−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	$-0.551912\pi$
$983$	−10008.2	−0.324731	−0.162365	+	0.986731i	$0.551912\pi$
$984$	−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	$-0.568819\pi$
$991$	−13384.7	−0.429040	−0.214520	+	0.976720i	$0.568819\pi$
$992$	−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	$-0.611551\pi$
$997$	−21615.7	−0.686635	−0.343317	+	0.939219i	$0.611551\pi$
$998$	−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.h.1.1	✓	12
17.4	even	4		289.4.b.f.288.23		24
17.13	even	4		289.4.b.f.288.24		24
17.16	even	2		289.4.a.i.1.1	yes	12

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