LMFDB - Embedded newform 289.4.a.i.1.4

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			1.4
Root			$2.16473$ 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)

$f(q)$	$=$	$q-2.16473 q^{2} +9.14133 q^{3} -3.31395 q^{4} +16.2298 q^{5} -19.7885 q^{6} +12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} +O(q^{10})$	\(q-2.16473 q^{2} +9.14133 q^{3} -3.31395 q^{4} +16.2298 q^{5} -19.7885 q^{6} +12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} -35.1331 q^{10} -11.1761 q^{11} -30.2939 q^{12} +28.9000 q^{13} -26.4629 q^{14} +148.362 q^{15} -26.5061 q^{16} -122.445 q^{18} -79.5850 q^{19} -53.7848 q^{20} +111.749 q^{21} +24.1932 q^{22} -45.0447 q^{23} +223.886 q^{24} +138.406 q^{25} -62.5606 q^{26} +270.253 q^{27} -40.5117 q^{28} +20.3774 q^{29} -321.163 q^{30} +1.03839 q^{31} -138.555 q^{32} -102.164 q^{33} +198.402 q^{35} -187.450 q^{36} -219.921 q^{37} +172.280 q^{38} +264.184 q^{39} +397.494 q^{40} -310.992 q^{41} -241.906 q^{42} +483.760 q^{43} +37.0371 q^{44} +918.020 q^{45} +97.5095 q^{46} -632.422 q^{47} -242.301 q^{48} -193.560 q^{49} -299.612 q^{50} -95.7732 q^{52} +490.172 q^{53} -585.024 q^{54} -181.386 q^{55} +299.400 q^{56} -727.512 q^{57} -44.1115 q^{58} +147.956 q^{59} -491.665 q^{60} +176.395 q^{61} -2.24783 q^{62} +691.469 q^{63} +511.982 q^{64} +469.041 q^{65} +221.158 q^{66} +809.312 q^{67} -411.768 q^{69} -429.487 q^{70} +714.189 q^{71} +1385.34 q^{72} +780.184 q^{73} +476.070 q^{74} +1265.22 q^{75} +263.741 q^{76} -136.623 q^{77} -571.887 q^{78} -230.265 q^{79} -430.188 q^{80} +943.248 q^{81} +673.213 q^{82} +236.046 q^{83} -370.330 q^{84} -1047.21 q^{86} +186.276 q^{87} -273.721 q^{88} -688.557 q^{89} -1987.26 q^{90} +353.290 q^{91} +149.276 q^{92} +9.49224 q^{93} +1369.02 q^{94} -1291.65 q^{95} -1266.57 q^{96} -1846.11 q^{97} +419.004 q^{98} -632.164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16473	−0.765347	−0.382673	−	0.923884i	$-0.624997\pi$
$2$	−2.16473	−0.765347	−0.382673	+	0.923884i	$0.624997\pi$
$3$	9.14133	1.75925	0.879625	−	0.475668i	$-0.157794\pi$
$3$	9.14133	1.75925	0.879625	+	0.475668i	$0.157794\pi$
$4$	−3.31395	−0.414244
$5$	16.2298	1.45164	0.725819	−	0.687886i	$-0.241461\pi$
$5$	16.2298	1.45164	0.725819	+	0.687886i	$0.241461\pi$
$6$	−19.7885	−1.34644
$7$	12.2246	0.660065	0.330032	−	0.943970i	$-0.392940\pi$
$7$	12.2246	0.660065	0.330032	+	0.943970i	$0.392940\pi$
$8$	24.4916	1.08239
$9$	56.5639	2.09496
$10$	−35.1331	−1.11101
$11$	−11.1761	−0.306338	−0.153169	−	0.988200i	$-0.548948\pi$
$11$	−11.1761	−0.306338	−0.153169	+	0.988200i	$0.548948\pi$
$12$	−30.2939	−0.728759
$13$	28.9000	0.616570	0.308285	−	0.951294i	$-0.400245\pi$
$13$	28.9000	0.616570	0.308285	+	0.951294i	$0.400245\pi$
$14$	−26.4629	−0.505178
$15$	148.362	2.55379
$16$	−26.5061	−0.414158
$17$	0	0
$17$	0	0
$18$	−122.445	−1.60337
$19$	−79.5850	−0.960950	−0.480475	−	0.877009i	$-0.659536\pi$
$19$	−79.5850	−0.960950	−0.480475	+	0.877009i	$0.659536\pi$
$20$	−53.7848	−0.601332
$21$	111.749	1.16122
$22$	24.1932	0.234455
$23$	−45.0447	−0.408368	−0.204184	−	0.978933i	$-0.565454\pi$
$23$	−45.0447	−0.408368	−0.204184	+	0.978933i	$0.565454\pi$
$24$	223.886	1.90419
$25$	138.406	1.10725
$26$	−62.5606	−0.471890
$27$	270.253	1.92631
$28$	−40.5117	−0.273428
$29$	20.3774	0.130482	0.0652411	−	0.997870i	$-0.479218\pi$
$29$	20.3774	0.130482	0.0652411	+	0.997870i	$0.479218\pi$
$30$	−321.163	−1.95454
$31$	1.03839	0.00601613	0.00300806	−	0.999995i	$-0.499043\pi$
$31$	1.03839	0.00601613	0.00300806	+	0.999995i	$0.499043\pi$
$32$	−138.555	−0.765413
$33$	−102.164	−0.538926
$34$	0	0
$35$	198.402	0.958175
$36$	−187.450	−0.867824
$37$	−219.921	−0.977159	−0.488579	−	0.872520i	$-0.662485\pi$
$37$	−219.921	−0.977159	−0.488579	+	0.872520i	$0.662485\pi$
$38$	172.280	0.735460
$39$	264.184	1.08470
$40$	397.494	1.57123
$41$	−310.992	−1.18460	−0.592302	−	0.805716i	$-0.701781\pi$
$41$	−310.992	−1.18460	−0.592302	+	0.805716i	$0.701781\pi$
$42$	−241.906	−0.888735
$43$	483.760	1.71564	0.857822	−	0.513947i	$-0.171817\pi$
$43$	483.760	1.71564	0.857822	+	0.513947i	$0.171817\pi$
$44$	37.0371	0.126899
$45$	918.020	3.04112
$46$	97.5095	0.312543
$47$	−632.422	−1.96273	−0.981364	−	0.192156i	$-0.938452\pi$
$47$	−632.422	−1.96273	−0.981364	+	0.192156i	$0.938452\pi$
$48$	−242.301	−0.728606
$49$	−193.560	−0.564315
$50$	−299.612	−0.847431
$51$	0	0
$52$	−95.7732	−0.255411
$53$	490.172	1.27038	0.635192	−	0.772354i	$-0.280921\pi$
$53$	490.172	1.27038	0.635192	+	0.772354i	$0.280921\pi$
$54$	−585.024	−1.47429
$55$	−181.386	−0.444692
$56$	299.400	0.714446
$57$	−727.512	−1.69055
$58$	−44.1115	−0.0998642
$59$	147.956	0.326478	0.163239	−	0.986587i	$-0.447806\pi$
$59$	147.956	0.326478	0.163239	+	0.986587i	$0.447806\pi$
$60$	−491.665	−1.05789
$61$	176.395	0.370246	0.185123	−	0.982715i	$-0.440732\pi$
$61$	176.395	0.370246	0.185123	+	0.982715i	$0.440732\pi$
$62$	−2.24783	−0.00460442
$63$	691.469	1.38281
$64$	511.982	0.999964
$65$	469.041	0.895037
$66$	221.158	0.412465
$67$	809.312	1.47572	0.737860	−	0.674954i	$-0.235836\pi$
$67$	809.312	1.47572	0.737860	+	0.674954i	$0.235836\pi$
$68$	0	0
$69$	−411.768	−0.718421
$70$	−429.487	−0.733336
$71$	714.189	1.19378	0.596892	−	0.802322i	$-0.296402\pi$
$71$	714.189	1.19378	0.596892	+	0.802322i	$0.296402\pi$
$72$	1385.34	2.26756
$73$	780.184	1.25087	0.625436	−	0.780276i	$-0.284921\pi$
$73$	780.184	1.25087	0.625436	+	0.780276i	$0.284921\pi$
$74$	476.070	0.747865
$75$	1265.22	1.94793
$76$	263.741	0.398068
$77$	−136.623	−0.202203
$78$	−571.887	−0.830172
$79$	−230.265	−0.327935	−0.163968	−	0.986466i	$-0.552429\pi$
$79$	−230.265	−0.327935	−0.163968	+	0.986466i	$0.552429\pi$
$80$	−430.188	−0.601207
$81$	943.248	1.29389
$82$	673.213	0.906633
$83$	236.046	0.312161	0.156080	−	0.987744i	$-0.450114\pi$
$83$	236.046	0.312161	0.156080	+	0.987744i	$0.450114\pi$
$84$	−370.330	−0.481028
$85$	0	0
$86$	−1047.21	−1.31306
$87$	186.276	0.229551
$88$	−273.721	−0.331577
$89$	−688.557	−0.820078	−0.410039	−	0.912068i	$-0.634485\pi$
$89$	−688.557	−0.820078	−0.410039	+	0.912068i	$0.634485\pi$
$90$	−1987.26	−2.32751
$91$	353.290	0.406976
$92$	149.276	0.169164
$93$	9.49224	0.0105839
$94$	1369.02	1.50217
$95$	−1291.65	−1.39495
$96$	−1266.57	−1.34655
$97$	−1846.11	−1.93241	−0.966205	−	0.257775i	$-0.917011\pi$
$97$	−1846.11	−1.93241	−0.966205	+	0.257775i	$0.917011\pi$
$98$	419.004	0.431896
$99$	−632.164	−0.641766
$100$	−458.672	−0.458672
$101$	−735.748	−0.724848	−0.362424	−	0.932013i	$-0.618051\pi$
$101$	−735.748	−0.724848	−0.362424	+	0.932013i	$0.618051\pi$
$102$	0	0
$103$	387.334	0.370535	0.185268	−	0.982688i	$-0.440685\pi$
$103$	387.334	0.370535	0.185268	+	0.982688i	$0.440685\pi$
$104$	707.808	0.667368
$105$	1813.66	1.68567
$106$	−1061.09	−0.972284
$107$	793.424	0.716852	0.358426	−	0.933558i	$-0.383314\pi$
$107$	793.424	0.716852	0.358426	+	0.933558i	$0.383314\pi$
$108$	−895.606	−0.797961
$109$	−1709.67	−1.50236	−0.751178	−	0.660100i	$-0.770514\pi$
$109$	−1709.67	−1.50236	−0.751178	+	0.660100i	$0.770514\pi$
$110$	392.651	0.340344
$111$	−2010.37	−1.71907
$112$	−324.025	−0.273371
$113$	42.1279	0.0350713	0.0175357	−	0.999846i	$-0.494418\pi$
$113$	42.1279	0.0350713	0.0175357	+	0.999846i	$0.494418\pi$
$114$	1574.87	1.29386
$115$	−731.066	−0.592802
$116$	−67.5297	−0.0540515
$117$	1634.70	1.29169
$118$	−320.284	−0.249869
$119$	0	0
$120$	3633.63	2.76419
$121$	−1206.09	−0.906157
$122$	−381.846	−0.283367
$123$	−2842.88	−2.08401
$124$	−3.44117	−0.00249215
$125$	217.583	0.155690
$126$	−1496.84	−1.05833
$127$	−1536.78	−1.07376	−0.536878	−	0.843660i	$-0.680397\pi$
$127$	−1536.78	−1.07376	−0.536878	+	0.843660i	$0.680397\pi$
$128$	0.135867	9.38207e−5 0
$129$	4422.21	3.01825
$130$	−1015.35	−0.685013
$131$	−264.718	−0.176554	−0.0882768	−	0.996096i	$-0.528136\pi$
$131$	−264.718	−0.176554	−0.0882768	+	0.996096i	$0.528136\pi$
$132$	338.568	0.223247
$133$	−972.892	−0.634289
$134$	−1751.94	−1.12944
$135$	4386.15	2.79630
$136$	0	0
$137$	686.450	0.428083	0.214042	−	0.976825i	$-0.431337\pi$
$137$	686.450	0.428083	0.214042	+	0.976825i	$0.431337\pi$
$138$	891.366	0.549841
$139$	−43.2364	−0.0263832	−0.0131916	−	0.999913i	$-0.504199\pi$
$139$	−43.2364	−0.0263832	−0.0131916	+	0.999913i	$0.504199\pi$
$140$	−657.496	−0.396918
$141$	−5781.18	−3.45293
$142$	−1546.02	−0.913659
$143$	−322.989	−0.188879
$144$	−1499.29	−0.867643
$145$	330.721	0.189413
$146$	−1688.89	−0.957350
$147$	−1769.39	−0.992770
$148$	728.810	0.404782
$149$	335.407	0.184413	0.0922067	−	0.995740i	$-0.470608\pi$
$149$	335.407	0.184413	0.0922067	+	0.995740i	$0.470608\pi$
$150$	−2738.85	−1.49084
$151$	−2432.29	−1.31084	−0.655421	−	0.755264i	$-0.727509\pi$
$151$	−2432.29	−1.31084	−0.655421	+	0.755264i	$0.727509\pi$
$152$	−1949.17	−1.04012
$153$	0	0
$154$	295.752	0.154756
$155$	16.8528	0.00873324
$156$	−875.494	−0.449331
$157$	2706.98	1.37605	0.688026	−	0.725686i	$-0.258477\pi$
$157$	2706.98	1.37605	0.688026	+	0.725686i	$0.258477\pi$
$158$	498.462	0.250984
$159$	4480.83	2.23492
$160$	−2248.71	−1.11110
$161$	−550.652	−0.269549
$162$	−2041.87	−0.990277
$163$	−190.765	−0.0916678	−0.0458339	−	0.998949i	$-0.514595\pi$
$163$	−190.765	−0.0916678	−0.0458339	+	0.998949i	$0.514595\pi$
$164$	1030.61	0.490715
$165$	−1658.11	−0.782325
$166$	−510.974	−0.238911
$167$	2757.18	1.27759	0.638793	−	0.769379i	$-0.279434\pi$
$167$	2757.18	1.27759	0.638793	+	0.769379i	$0.279434\pi$
$168$	2736.91	1.25689
$169$	−1361.79	−0.619841
$170$	0	0
$171$	−4501.63	−2.01315
$172$	−1603.16	−0.710696
$173$	1453.00	0.638554	0.319277	−	0.947661i	$-0.396560\pi$
$173$	1453.00	0.638554	0.319277	+	0.947661i	$0.396560\pi$
$174$	−403.238	−0.175686
$175$	1691.96	0.730858
$176$	296.235	0.126872
$177$	1352.51	0.574356
$178$	1490.54	0.627644
$179$	−1171.47	−0.489160	−0.244580	−	0.969629i	$-0.578650\pi$
$179$	−1171.47	−0.489160	−0.244580	+	0.969629i	$0.578650\pi$
$180$	−3042.28	−1.25977
$181$	−2737.41	−1.12414	−0.562072	−	0.827089i	$-0.689995\pi$
$181$	−2737.41	−1.12414	−0.562072	+	0.827089i	$0.689995\pi$
$182$	−764.776	−0.311478
$183$	1612.48	0.651355
$184$	−1103.22	−0.442012
$185$	−3569.28	−1.41848
$186$	−20.5481	−0.00810033
$187$	0	0
$188$	2095.82	0.813049
$189$	3303.73	1.27149
$190$	2796.07	1.06762
$191$	−1345.56	−0.509744	−0.254872	−	0.966975i	$-0.582033\pi$
$191$	−1345.56	−0.509744	−0.254872	+	0.966975i	$0.582033\pi$
$192$	4680.19	1.75919
$193$	−3787.61	−1.41263	−0.706317	−	0.707896i	$-0.749645\pi$
$193$	−3787.61	−1.41263	−0.706317	+	0.707896i	$0.749645\pi$
$194$	3996.32	1.47896
$195$	4287.66	1.57459
$196$	641.448	0.233764
$197$	−72.4095	−0.0261876	−0.0130938	−	0.999914i	$-0.504168\pi$
$197$	−72.4095	−0.0261876	−0.0130938	+	0.999914i	$0.504168\pi$
$198$	1368.46	0.491174
$199$	−2703.59	−0.963077	−0.481539	−	0.876425i	$-0.659922\pi$
$199$	−2703.59	−0.963077	−0.481539	+	0.876425i	$0.659922\pi$
$200$	3389.80	1.19847
$201$	7398.19	2.59616
$202$	1592.69	0.554760
$203$	249.105	0.0861267
$204$	0	0
$205$	−5047.33	−1.71962
$206$	−838.472	−0.283588
$207$	−2547.90	−0.855514
$208$	−766.025	−0.255357
$209$	889.450	0.294376
$210$	−3926.08	−1.29012
$211$	2338.29	0.762911	0.381456	−	0.924387i	$-0.375423\pi$
$211$	2338.29	0.762911	0.381456	+	0.924387i	$0.375423\pi$
$212$	−1624.41	−0.526249
$213$	6528.64	2.10016
$214$	−1717.55	−0.548640
$215$	7851.33	2.49049
$216$	6618.94	2.08501
$217$	12.6938	0.00397103
$218$	3700.97	1.14982
$219$	7131.91	2.20059
$220$	601.105	0.184211
$221$	0	0
$222$	4351.91	1.31568
$223$	1737.70	0.521815	0.260908	−	0.965364i	$-0.415978\pi$
$223$	1737.70	0.521815	0.260908	+	0.965364i	$0.415978\pi$
$224$	−1693.77	−0.505222
$225$	7828.80	2.31965
$226$	−91.1954	−0.0268417
$227$	4480.83	1.31015	0.655073	−	0.755565i	$-0.272638\pi$
$227$	4480.83	1.31015	0.655073	+	0.755565i	$0.272638\pi$
$228$	2410.94	0.700301
$229$	−3917.73	−1.13053	−0.565264	−	0.824910i	$-0.691226\pi$
$229$	−3917.73	−1.13053	−0.565264	+	0.824910i	$0.691226\pi$
$230$	1582.56	0.453699
$231$	−1248.92	−0.355726
$232$	499.075	0.141232
$233$	4166.02	1.17135	0.585675	−	0.810546i	$-0.300829\pi$
$233$	4166.02	1.17135	0.585675	+	0.810546i	$0.300829\pi$
$234$	−3538.67	−0.988590
$235$	−10264.1	−2.84917
$236$	−490.318	−0.135242
$237$	−2104.93	−0.576920
$238$	0	0
$239$	−1780.06	−0.481768	−0.240884	−	0.970554i	$-0.577437\pi$
$239$	−1780.06	−0.481768	−0.240884	+	0.970554i	$0.577437\pi$
$240$	−3932.49	−1.05767
$241$	2469.12	0.659958	0.329979	−	0.943988i	$-0.392958\pi$
$241$	2469.12	0.659958	0.329979	+	0.943988i	$0.392958\pi$
$242$	2610.87	0.693524
$243$	1325.70	0.349975
$244$	−584.563	−0.153372
$245$	−3141.44	−0.819180
$246$	6154.06	1.59499
$247$	−2300.00	−0.592493
$248$	25.4318	0.00651178
$249$	2157.77	0.549169
$250$	−471.009	−0.119157
$251$	−4824.05	−1.21311	−0.606557	−	0.795040i	$-0.707450\pi$
$251$	−4824.05	−1.21311	−0.606557	+	0.795040i	$0.707450\pi$
$252$	−2291.50	−0.572820
$253$	503.424	0.125099
$254$	3326.71	0.821796
$255$	0	0
$256$	−4096.15	−1.00004
$257$	5558.77	1.34921	0.674604	−	0.738180i	$-0.264314\pi$
$257$	5558.77	1.34921	0.674604	+	0.738180i	$0.264314\pi$
$258$	−9572.88	−2.31000
$259$	−2688.45	−0.644988
$260$	−1554.38	−0.370764
$261$	1152.62	0.273355
$262$	573.043	0.135125
$263$	−3172.23	−0.743757	−0.371878	−	0.928281i	$-0.621286\pi$
$263$	−3172.23	−0.743757	−0.371878	+	0.928281i	$0.621286\pi$
$264$	−2502.17	−0.583326
$265$	7955.40	1.84414
$266$	2106.05	0.485451
$267$	−6294.33	−1.44272
$268$	−2682.02	−0.611309
$269$	2849.92	0.645959	0.322979	−	0.946406i	$-0.395316\pi$
$269$	2849.92	0.645959	0.322979	+	0.946406i	$0.395316\pi$
$270$	−9494.83	−2.14014
$271$	−2565.11	−0.574980	−0.287490	−	0.957784i	$-0.592821\pi$
$271$	−2565.11	−0.574980	−0.287490	+	0.957784i	$0.592821\pi$
$272$	0	0
$273$	3229.54	0.715973
$274$	−1485.98	−0.327632
$275$	−1546.84	−0.339194
$276$	1364.58	0.297602
$277$	6260.95	1.35806	0.679032	−	0.734108i	$-0.262400\pi$
$277$	6260.95	1.35806	0.679032	+	0.734108i	$0.262400\pi$
$278$	93.5951	0.0201923
$279$	58.7352	0.0126035
$280$	4859.20	1.03712
$281$	−1807.59	−0.383744	−0.191872	−	0.981420i	$-0.561456\pi$
$281$	−1807.59	−0.383744	−0.191872	+	0.981420i	$0.561456\pi$
$282$	12514.7	2.64269
$283$	−1264.09	−0.265521	−0.132761	−	0.991148i	$-0.542384\pi$
$283$	−1264.09	−0.265521	−0.132761	+	0.991148i	$0.542384\pi$
$284$	−2366.79	−0.494518
$285$	−11807.4	−2.45407
$286$	699.184	0.144558
$287$	−3801.74	−0.781915
$288$	−7837.18	−1.60351
$289$	0	0
$290$	−715.921	−0.144967
$291$	−16875.9	−3.39959
$292$	−2585.49	−0.518166
$293$	3708.40	0.739410	0.369705	−	0.929149i	$-0.379459\pi$
$293$	3708.40	0.739410	0.369705	+	0.929149i	$0.379459\pi$
$294$	3830.26	0.759813
$295$	2401.29	0.473927
$296$	−5386.24	−1.05766
$297$	−3020.38	−0.590101
$298$	−726.065	−0.141140
$299$	−1301.79	−0.251788
$300$	−4192.88	−0.806919
$301$	5913.76	1.13244
$302$	5265.25	1.00325
$303$	−6725.71	−1.27519
$304$	2109.49	0.397985
$305$	2862.85	0.537463
$306$	0	0
$307$	4689.47	0.871799	0.435899	−	0.899995i	$-0.356430\pi$
$307$	4689.47	0.871799	0.435899	+	0.899995i	$0.356430\pi$
$308$	452.763	0.0837615
$309$	3540.75	0.651864
$310$	−36.4818	−0.00668396
$311$	−2725.79	−0.496995	−0.248497	−	0.968633i	$-0.579937\pi$
$311$	−2725.79	−0.496995	−0.248497	+	0.968633i	$0.579937\pi$
$312$	6470.30	1.17407
$313$	−1406.42	−0.253980	−0.126990	−	0.991904i	$-0.540532\pi$
$313$	−1406.42	−0.253980	−0.126990	+	0.991904i	$0.540532\pi$
$314$	−5859.87	−1.05316
$315$	11222.4	2.00734
$316$	763.089	0.135845
$317$	−836.717	−0.148248	−0.0741241	−	0.997249i	$-0.523616\pi$
$317$	−836.717	−0.148248	−0.0741241	+	0.997249i	$0.523616\pi$
$318$	−9699.77	−1.71049
$319$	−227.740	−0.0399717
$320$	8309.36	1.45159
$321$	7252.95	1.26112
$322$	1192.01	0.206299
$323$	0	0
$324$	−3125.88	−0.535987
$325$	3999.94	0.682698
$326$	412.954	0.0701577
$327$	−15628.7	−2.64302
$328$	−7616.70	−1.28220
$329$	−7731.09	−1.29553
$330$	3589.35	0.598750
$331$	2544.99	0.422614	0.211307	−	0.977420i	$-0.432228\pi$
$331$	2544.99	0.422614	0.211307	+	0.977420i	$0.432228\pi$
$332$	−782.244	−0.129311
$333$	−12439.6	−2.04711
$334$	−5968.54	−0.977796
$335$	13135.0	2.14221
$336$	−2962.02	−0.480927
$337$	−9258.04	−1.49649	−0.748246	−	0.663422i	$-0.769104\pi$
$337$	−9258.04	−1.49649	−0.748246	+	0.663422i	$0.769104\pi$
$338$	2947.91	0.474393
$339$	385.105	0.0616992
$340$	0	0
$341$	−11.6051	−0.00184297
$342$	9744.81	1.54076
$343$	−6559.21	−1.03255
$344$	11848.1	1.85699
$345$	−6682.92	−1.04289
$346$	−3145.36	−0.488716
$347$	11972.3	1.85217	0.926087	−	0.377310i	$-0.123151\pi$
$347$	11972.3	1.85217	0.926087	+	0.377310i	$0.123151\pi$
$348$	−617.311	−0.0950901
$349$	1887.57	0.289511	0.144755	−	0.989467i	$-0.453760\pi$
$349$	1887.57	0.289511	0.144755	+	0.989467i	$0.453760\pi$
$350$	−3662.63	−0.559360
$351$	7810.31	1.18770
$352$	1548.50	0.234475
$353$	7441.02	1.12194	0.560971	−	0.827836i	$-0.310428\pi$
$353$	7441.02	1.12194	0.560971	+	0.827836i	$0.310428\pi$
$354$	−2927.82	−0.439581
$355$	11591.1	1.73294
$356$	2281.85	0.339712
$357$	0	0
$358$	2535.91	0.374377
$359$	11518.8	1.69342	0.846711	−	0.532052i	$-0.178579\pi$
$359$	11518.8	1.69342	0.846711	+	0.532052i	$0.178579\pi$
$360$	22483.8	3.29167
$361$	−525.233	−0.0765757
$362$	5925.74	0.860359
$363$	−11025.3	−1.59416
$364$	−1170.79	−0.168588
$365$	12662.2	1.81581
$366$	−3490.58	−0.498513
$367$	−702.580	−0.0999302	−0.0499651	−	0.998751i	$-0.515911\pi$
$367$	−702.580	−0.0999302	−0.0499651	+	0.998751i	$0.515911\pi$
$368$	1193.96	0.169129
$369$	−17590.9	−2.48170
$370$	7726.52	1.08563
$371$	5992.15	0.838536
$372$	−31.4569	−0.00438431
$373$	8797.32	1.22120	0.610600	−	0.791939i	$-0.290928\pi$
$373$	8797.32	1.22120	0.610600	+	0.791939i	$0.290928\pi$
$374$	0	0
$375$	1989.00	0.273897
$376$	−15489.0	−2.12443
$377$	588.906	0.0804515
$378$	−7151.67	−0.973128
$379$	−3113.75	−0.422012	−0.211006	−	0.977485i	$-0.567674\pi$
$379$	−3113.75	−0.422012	−0.211006	+	0.977485i	$0.567674\pi$
$380$	4280.46	0.577850
$381$	−14048.2	−1.88901
$382$	2912.77	0.390131
$383$	−9735.60	−1.29887	−0.649434	−	0.760418i	$-0.724994\pi$
$383$	−9735.60	−1.29887	−0.649434	+	0.760418i	$0.724994\pi$
$384$	1.24200	0.000165054 0
$385$	−2217.37	−0.293526
$386$	8199.15	1.08115
$387$	27363.3	3.59420
$388$	6117.91	0.800490
$389$	−1772.22	−0.230990	−0.115495	−	0.993308i	$-0.536845\pi$
$389$	−1772.22	−0.230990	−0.115495	+	0.993308i	$0.536845\pi$
$390$	−9281.61	−1.20511
$391$	0	0
$392$	−4740.60	−0.610807
$393$	−2419.88	−0.310602
$394$	156.747	0.0200426
$395$	−3737.16	−0.476043
$396$	2094.96	0.265848
$397$	1201.80	0.151931	0.0759653	−	0.997110i	$-0.475796\pi$
$397$	1201.80	0.151931	0.0759653	+	0.997110i	$0.475796\pi$
$398$	5852.54	0.737088
$399$	−8893.53	−1.11587
$400$	−3668.61	−0.458576
$401$	−13633.2	−1.69778	−0.848892	−	0.528566i	$-0.822730\pi$
$401$	−13633.2	−1.69778	−0.848892	+	0.528566i	$0.822730\pi$
$402$	−16015.1	−1.98696
$403$	30.0094	0.00370937
$404$	2438.23	0.300264
$405$	15308.7	1.87826
$406$	−539.244	−0.0659168
$407$	2457.87	0.299341
$408$	0	0
$409$	7345.95	0.888103	0.444051	−	0.896001i	$-0.353541\pi$
$409$	7345.95	0.888103	0.444051	+	0.896001i	$0.353541\pi$
$410$	10926.1	1.31610
$411$	6275.07	0.753105
$412$	−1283.61	−0.153492
$413$	1808.69	0.215496
$414$	5515.51	0.654765
$415$	3830.97	0.453145
$416$	−4004.23	−0.471931
$417$	−395.238	−0.0464146
$418$	−1925.42	−0.225300
$419$	−3293.55	−0.384011	−0.192005	−	0.981394i	$-0.561499\pi$
$419$	−3293.55	−0.384011	−0.192005	+	0.981394i	$0.561499\pi$
$420$	−6010.39	−0.698278
$421$	−9775.57	−1.13167	−0.565834	−	0.824519i	$-0.691446\pi$
$421$	−9775.57	−1.13167	−0.565834	+	0.824519i	$0.691446\pi$
$422$	−5061.75	−0.583892
$423$	−35772.2	−4.11184
$424$	12005.1	1.37505
$425$	0	0
$426$	−14132.7	−1.60735
$427$	2156.35	0.244386
$428$	−2629.37	−0.296952
$429$	−2952.55	−0.332286
$430$	−16996.0	−1.90609
$431$	7842.98	0.876527	0.438263	−	0.898847i	$-0.355594\pi$
$431$	7842.98	0.876527	0.438263	+	0.898847i	$0.355594\pi$
$432$	−7163.35	−0.797794
$433$	−5178.49	−0.574740	−0.287370	−	0.957820i	$-0.592781\pi$
$433$	−5178.49	−0.574740	−0.287370	+	0.957820i	$0.592781\pi$
$434$	−27.4787	−0.00303922
$435$	3023.23	0.333225
$436$	5665.77	0.622342
$437$	3584.88	0.392421
$438$	−15438.7	−1.68422
$439$	5661.88	0.615550	0.307775	−	0.951459i	$-0.400416\pi$
$439$	5661.88	0.615550	0.307775	+	0.951459i	$0.400416\pi$
$440$	−4442.44	−0.481329
$441$	−10948.5	−1.18222
$442$	0	0
$443$	−3020.29	−0.323924	−0.161962	−	0.986797i	$-0.551782\pi$
$443$	−3020.29	−0.323924	−0.161962	+	0.986797i	$0.551782\pi$
$444$	6662.29	0.712113
$445$	−11175.1	−1.19046
$446$	−3761.64	−0.399370
$447$	3066.06	0.324429
$448$	6258.76	0.660041
$449$	−13308.6	−1.39883	−0.699413	−	0.714718i	$-0.746555\pi$
$449$	−13308.6	−1.39883	−0.699413	+	0.714718i	$0.746555\pi$
$450$	−16947.2	−1.77533
$451$	3475.68	0.362890
$452$	−139.610	−0.0145281
$453$	−22234.4	−2.30610
$454$	−9699.78	−1.00272
$455$	5733.82	0.590782
$456$	−17818.0	−1.82983
$457$	7260.23	0.743150	0.371575	−	0.928403i	$-0.378818\pi$
$457$	7260.23	0.743150	0.371575	+	0.928403i	$0.378818\pi$
$458$	8480.83	0.865247
$459$	0	0
$460$	2422.72	0.245565
$461$	−2580.20	−0.260677	−0.130338	−	0.991470i	$-0.541606\pi$
$461$	−2580.20	−0.260677	−0.130338	+	0.991470i	$0.541606\pi$
$462$	2703.56	0.272254
$463$	14392.8	1.44469	0.722345	−	0.691533i	$-0.243064\pi$
$463$	14392.8	1.44469	0.722345	+	0.691533i	$0.243064\pi$
$464$	−540.125	−0.0540402
$465$	154.057	0.0153639
$466$	−9018.29	−0.896490
$467$	−11696.0	−1.15894	−0.579471	−	0.814993i	$-0.696741\pi$
$467$	−11696.0	−1.15894	−0.579471	+	0.814993i	$0.696741\pi$
$468$	−5417.30	−0.535075
$469$	9893.50	0.974071
$470$	22218.9	2.18060
$471$	24745.4	2.42082
$472$	3623.68	0.353375
$473$	−5406.55	−0.525568
$474$	4556.61	0.441544
$475$	−11015.1	−1.06401
$476$	0	0
$477$	27726.0	2.66140
$478$	3853.35	0.368720
$479$	13997.5	1.33520	0.667599	−	0.744521i	$-0.267322\pi$
$479$	13997.5	1.33520	0.667599	+	0.744521i	$0.267322\pi$
$480$	−20556.2	−1.95471
$481$	−6355.73	−0.602487
$482$	−5344.97	−0.505097
$483$	−5033.69	−0.474205
$484$	3996.94	0.375370
$485$	−29961.9	−2.80516
$486$	−2869.78	−0.267852
$487$	2888.42	0.268761	0.134381	−	0.990930i	$-0.457095\pi$
$487$	2888.42	0.268761	0.134381	+	0.990930i	$0.457095\pi$
$488$	4320.19	0.400750
$489$	−1743.84	−0.161267
$490$	6800.36	0.626957
$491$	−9420.11	−0.865832	−0.432916	−	0.901434i	$-0.642515\pi$
$491$	−9420.11	−0.865832	−0.432916	+	0.901434i	$0.642515\pi$
$492$	9421.17	0.863291
$493$	0	0
$494$	4978.88	0.453463
$495$	−10259.9	−0.931612
$496$	−27.5236	−0.00249162
$497$	8730.65	0.787975
$498$	−4670.98	−0.420305
$499$	713.936	0.0640484	0.0320242	−	0.999487i	$-0.489805\pi$
$499$	713.936	0.0640484	0.0320242	+	0.999487i	$0.489805\pi$
$500$	−721.061	−0.0644937
$501$	25204.3	2.24759
$502$	10442.8	0.928453
$503$	17604.4	1.56052	0.780260	−	0.625456i	$-0.215087\pi$
$503$	17604.4	1.56052	0.780260	+	0.625456i	$0.215087\pi$
$504$	16935.2	1.49673
$505$	−11941.0	−1.05222
$506$	−1089.78	−0.0957440
$507$	−12448.6	−1.09046
$508$	5092.81	0.444797
$509$	12291.2	1.07033	0.535165	−	0.844748i	$-0.320249\pi$
$509$	12291.2	1.07033	0.535165	+	0.844748i	$0.320249\pi$
$510$	0	0
$511$	9537.41	0.825656
$512$	8865.96	0.765280
$513$	−21508.1	−1.85108
$514$	−12033.2	−1.03261
$515$	6286.35	0.537883
$516$	−14655.0	−1.25029
$517$	7068.02	0.601259
$518$	5819.75	0.493639
$519$	13282.4	1.12338
$520$	11487.6	0.968776
$521$	8736.73	0.734670	0.367335	−	0.930089i	$-0.380270\pi$
$521$	8736.73	0.734670	0.367335	+	0.930089i	$0.380270\pi$
$522$	−2495.12	−0.209211
$523$	−2513.00	−0.210107	−0.105053	−	0.994467i	$-0.533501\pi$
$523$	−2513.00	−0.210107	−0.105053	+	0.994467i	$0.533501\pi$
$524$	877.264	0.0731363
$525$	15466.8	1.28576
$526$	6867.01	0.569232
$527$	0	0
$528$	2707.98	0.223200
$529$	−10138.0	−0.833236
$530$	−17221.3	−1.41140
$531$	8368.95	0.683957
$532$	3224.12	0.262751
$533$	−8987.66	−0.730392
$534$	13625.5	1.10418
$535$	12877.1	1.04061
$536$	19821.4	1.59730
$537$	−10708.8	−0.860554
$538$	−6169.31	−0.494383
$539$	2163.25	0.172871
$540$	−14535.5	−1.15835
$541$	9702.15	0.771031	0.385516	−	0.922701i	$-0.374024\pi$
$541$	9702.15	0.771031	0.385516	+	0.922701i	$0.374024\pi$
$542$	5552.77	0.440059
$543$	−25023.5	−1.97765
$544$	0	0
$545$	−27747.6	−2.18088
$546$	−6991.07	−0.547968
$547$	16198.6	1.26618	0.633092	−	0.774077i	$-0.281785\pi$
$547$	16198.6	1.26618	0.633092	+	0.774077i	$0.281785\pi$
$548$	−2274.86	−0.177331
$549$	9977.56	0.775650
$550$	3348.50	0.259601
$551$	−1621.73	−0.125387
$552$	−10084.9	−0.777610
$553$	−2814.90	−0.216459
$554$	−13553.2	−1.03939
$555$	−32628.0	−2.49546
$556$	143.283	0.0109291
$557$	−9873.27	−0.751066	−0.375533	−	0.926809i	$-0.622540\pi$
$557$	−9873.27	−0.751066	−0.375533	+	0.926809i	$0.622540\pi$
$558$	−127.146	−0.00964608
$559$	13980.7	1.05782
$560$	−5258.87	−0.396835
$561$	0	0
$562$	3912.95	0.293697
$563$	3283.56	0.245801	0.122900	−	0.992419i	$-0.460780\pi$
$563$	3283.56	0.245801	0.122900	+	0.992419i	$0.460780\pi$
$564$	19158.6	1.43036
$565$	683.727	0.0509108
$566$	2736.42	0.203216
$567$	11530.8	0.854053
$568$	17491.7	1.29214
$569$	−15065.3	−1.10996	−0.554982	−	0.831862i	$-0.687275\pi$
$569$	−15065.3	−1.10996	−0.554982	+	0.831862i	$0.687275\pi$
$570$	25559.8	1.87821
$571$	−2567.87	−0.188200	−0.0941000	−	0.995563i	$-0.529997\pi$
$571$	−2567.87	−0.188200	−0.0941000	+	0.995563i	$0.529997\pi$
$572$	1070.37	0.0782421
$573$	−12300.2	−0.896767
$574$	8229.73	0.598436
$575$	−6234.47	−0.452166
$576$	28959.7	2.09488
$577$	−23042.3	−1.66250	−0.831249	−	0.555900i	$-0.812374\pi$
$577$	−23042.3	−1.66250	−0.831249	+	0.555900i	$0.812374\pi$
$578$	0	0
$579$	−34623.8	−2.48517
$580$	−1095.99	−0.0784632
$581$	2885.56	0.206046
$582$	36531.7	2.60187
$583$	−5478.22	−0.389167
$584$	19108.0	1.35393
$585$	26530.8	1.87506
$586$	−8027.68	−0.565905
$587$	−4094.68	−0.287914	−0.143957	−	0.989584i	$-0.545983\pi$
$587$	−4094.68	−0.287914	−0.143957	+	0.989584i	$0.545983\pi$
$588$	5863.69	0.411249
$589$	−82.6401	−0.00578120
$590$	−5198.14	−0.362719
$591$	−661.919	−0.0460706
$592$	5829.26	0.404698
$593$	−25698.4	−1.77961	−0.889803	−	0.456344i	$-0.849159\pi$
$593$	−25698.4	−1.77961	−0.889803	+	0.456344i	$0.849159\pi$
$594$	6538.30	0.451632
$595$	0	0
$596$	−1111.52	−0.0763922
$597$	−24714.4	−1.69429
$598$	2818.02	0.192705
$599$	1085.55	0.0740472	0.0370236	−	0.999314i	$-0.488212\pi$
$599$	1085.55	0.0740472	0.0370236	+	0.999314i	$0.488212\pi$
$600$	30987.3	2.10842
$601$	−11163.9	−0.757713	−0.378857	−	0.925455i	$-0.623683\pi$
$601$	−11163.9	−0.757713	−0.378857	+	0.925455i	$0.623683\pi$
$602$	−12801.7	−0.866706
$603$	45777.8	3.09157
$604$	8060.50	0.543008
$605$	−19574.7	−1.31541
$606$	14559.3	0.975961
$607$	−167.486	−0.0111994	−0.00559971	−	0.999984i	$-0.501782\pi$
$607$	−167.486	−0.0111994	−0.00559971	+	0.999984i	$0.501782\pi$
$608$	11026.9	0.735524
$609$	2277.15	0.151518
$610$	−6197.29	−0.411346
$611$	−18277.0	−1.21016
$612$	0	0
$613$	−6533.58	−0.430487	−0.215244	−	0.976560i	$-0.569055\pi$
$613$	−6533.58	−0.430487	−0.215244	+	0.976560i	$0.569055\pi$
$614$	−10151.4	−0.667228
$615$	−46139.3	−3.02523
$616$	−3346.12	−0.218862
$617$	9073.82	0.592056	0.296028	−	0.955179i	$-0.404338\pi$
$617$	9073.82	0.592056	0.296028	+	0.955179i	$0.404338\pi$
$618$	−7664.75	−0.498902
$619$	26617.2	1.72833	0.864163	−	0.503212i	$-0.167849\pi$
$619$	26617.2	1.72833	0.864163	+	0.503212i	$0.167849\pi$
$620$	−55.8495	−0.00361769
$621$	−12173.5	−0.786641
$622$	5900.60	0.380374
$623$	−8417.32	−0.541304
$624$	−7002.49	−0.449237
$625$	−13769.5	−0.881246
$626$	3044.52	0.194383
$627$	8130.76	0.517881
$628$	−8970.79	−0.570022
$629$	0	0
$630$	−24293.5	−1.53631
$631$	5977.98	0.377147	0.188573	−	0.982059i	$-0.439614\pi$
$631$	5977.98	0.377147	0.188573	+	0.982059i	$0.439614\pi$
$632$	−5639.58	−0.354953
$633$	21375.0	1.34215
$634$	1811.26	0.113461
$635$	−24941.6	−1.55870
$636$	−14849.2	−0.925803
$637$	−5593.88	−0.347940
$638$	492.995	0.0305922
$639$	40397.3	2.50093
$640$	2.20509	0.000136194 0
$641$	−7927.25	−0.488467	−0.244234	−	0.969716i	$-0.578536\pi$
$641$	−7927.25	−0.488467	−0.244234	+	0.969716i	$0.578536\pi$
$642$	−15700.7	−0.965195
$643$	−9197.33	−0.564086	−0.282043	−	0.959402i	$-0.591012\pi$
$643$	−9197.33	−0.564086	−0.282043	+	0.959402i	$0.591012\pi$
$644$	1824.83	0.111659
$645$	71771.5	4.38140
$646$	0	0
$647$	19035.8	1.15669	0.578343	−	0.815794i	$-0.303700\pi$
$647$	19035.8	1.15669	0.578343	+	0.815794i	$0.303700\pi$
$648$	23101.7	1.40049
$649$	−1653.57	−0.100013
$650$	−8658.79	−0.522501
$651$	116.039	0.00698604
$652$	632.186	0.0379729
$653$	19349.6	1.15958	0.579792	−	0.814764i	$-0.303134\pi$
$653$	19349.6	1.15958	0.579792	+	0.814764i	$0.303134\pi$
$654$	33831.8	2.02283
$655$	−4296.32	−0.256292
$656$	8243.17	0.490613
$657$	44130.2	2.62052
$658$	16735.7	0.991528
$659$	16666.8	0.985201	0.492600	−	0.870256i	$-0.336046\pi$
$659$	16666.8	0.985201	0.492600	+	0.870256i	$0.336046\pi$
$660$	5494.90	0.324074
$661$	−6024.30	−0.354490	−0.177245	−	0.984167i	$-0.556719\pi$
$661$	−6024.30	−0.354490	−0.177245	+	0.984167i	$0.556719\pi$
$662$	−5509.21	−0.323446
$663$	0	0
$664$	5781.14	0.337879
$665$	−15789.8	−0.920758
$666$	26928.4	1.56675
$667$	−917.893	−0.0532848
$668$	−9137.16	−0.529232
$669$	15884.9	0.918003
$670$	−28433.7	−1.63953
$671$	−1971.40	−0.113421
$672$	−15483.3	−0.888812
$673$	−27296.1	−1.56343	−0.781714	−	0.623637i	$-0.785654\pi$
$673$	−27296.1	−1.56343	−0.781714	+	0.623637i	$0.785654\pi$
$674$	20041.1	1.14534
$675$	37404.8	2.13290
$676$	4512.91	0.256766
$677$	13081.5	0.742632	0.371316	−	0.928507i	$-0.378907\pi$
$677$	13081.5	0.742632	0.371316	+	0.928507i	$0.378907\pi$
$678$	−833.647	−0.0472213
$679$	−22567.9	−1.27552
$680$	0	0
$681$	40960.8	2.30487
$682$	25.1220	0.00141051
$683$	−15698.0	−0.879452	−0.439726	−	0.898132i	$-0.644925\pi$
$683$	−15698.0	−0.879452	−0.439726	+	0.898132i	$0.644925\pi$
$684$	14918.2	0.833936
$685$	11140.9	0.621422
$686$	14198.9	0.790258
$687$	−35813.3	−1.98888
$688$	−12822.6	−0.710547
$689$	14166.0	0.783281
$690$	14466.7	0.798170
$691$	13621.7	0.749919	0.374959	−	0.927041i	$-0.377657\pi$
$691$	13621.7	0.749919	0.374959	+	0.927041i	$0.377657\pi$
$692$	−4815.19	−0.264517
$693$	−7727.93	−0.423607
$694$	−25916.7	−1.41756
$695$	−701.718	−0.0382988
$696$	4562.21	0.248463
$697$	0	0
$698$	−4086.08	−0.221576
$699$	38082.9	2.06070
$700$	−5607.07	−0.302753
$701$	5733.01	0.308892	0.154446	−	0.988001i	$-0.450641\pi$
$701$	5733.01	0.308892	0.154446	+	0.988001i	$0.450641\pi$
$702$	−16907.2	−0.909004
$703$	17502.4	0.939000
$704$	−5721.96	−0.306327
$705$	−93827.4	−5.01240
$706$	−16107.8	−0.858674
$707$	−8994.20	−0.478447
$708$	−4482.16	−0.237924
$709$	25474.5	1.34939	0.674694	−	0.738097i	$-0.264275\pi$
$709$	25474.5	1.34939	0.674694	+	0.738097i	$0.264275\pi$
$710$	−25091.7	−1.32630
$711$	−13024.7	−0.687011
$712$	−16863.9	−0.887642
$713$	−46.7739	−0.00245679
$714$	0	0
$715$	−5242.05	−0.274184
$716$	3882.19	0.202632
$717$	−16272.1	−0.847551
$718$	−24935.1	−1.29606
$719$	15508.0	0.804380	0.402190	−	0.915556i	$-0.368249\pi$
$719$	15508.0	0.804380	0.402190	+	0.915556i	$0.368249\pi$
$720$	−24333.1	−1.25950
$721$	4734.99	0.244577
$722$	1136.99	0.0586070
$723$	22571.0	1.16103
$724$	9071.64	0.465670
$725$	2820.36	0.144477
$726$	23866.8	1.22008
$727$	−32127.0	−1.63896	−0.819481	−	0.573106i	$-0.805738\pi$
$727$	−32127.0	−1.63896	−0.819481	+	0.573106i	$0.805738\pi$
$728$	8652.65	0.440506
$729$	−13349.0	−0.678200
$730$	−27410.3	−1.38973
$731$	0	0
$732$	−5343.68	−0.269820
$733$	1723.27	0.0868353	0.0434177	−	0.999057i	$-0.486175\pi$
$733$	1723.27	0.0868353	0.0434177	+	0.999057i	$0.486175\pi$
$734$	1520.89	0.0764812
$735$	−28716.9	−1.44114
$736$	6241.15	0.312570
$737$	−9044.96	−0.452070
$738$	38079.5	1.89936
$739$	22411.5	1.11559	0.557796	−	0.829978i	$-0.311647\pi$
$739$	22411.5	1.11559	0.557796	+	0.829978i	$0.311647\pi$
$740$	11828.4	0.587597
$741$	−21025.1	−1.04234
$742$	−12971.4	−0.641771
$743$	−23971.3	−1.18361	−0.591804	−	0.806082i	$-0.701584\pi$
$743$	−23971.3	−1.18361	−0.591804	+	0.806082i	$0.701584\pi$
$744$	232.481	0.0114558
$745$	5443.59	0.267701
$746$	−19043.8	−0.934642
$747$	13351.7	0.653964
$748$	0	0
$749$	9699.26	0.473169
$750$	−4305.64	−0.209627
$751$	26268.1	1.27635	0.638175	−	0.769892i	$-0.279690\pi$
$751$	26268.1	1.27635	0.638175	+	0.769892i	$0.279690\pi$
$752$	16763.0	0.812879
$753$	−44098.3	−2.13417
$754$	−1274.82	−0.0615733
$755$	−39475.6	−1.90287
$756$	−10948.4	−0.526706
$757$	−345.842	−0.0166048	−0.00830239	−	0.999966i	$-0.502643\pi$
$757$	−345.842	−0.0166048	−0.00830239	+	0.999966i	$0.502643\pi$
$758$	6740.42	0.322986
$759$	4601.97	0.220080
$760$	−31634.6	−1.50988
$761$	28929.2	1.37803	0.689015	−	0.724747i	$-0.258043\pi$
$761$	28929.2	1.37803	0.689015	+	0.724747i	$0.258043\pi$
$762$	30410.5	1.44574
$763$	−20900.0	−0.991652
$764$	4459.11	0.211159
$765$	0	0
$766$	21074.9	0.994084
$767$	4275.92	0.201297
$768$	−37444.2	−1.75931
$769$	−29320.3	−1.37492	−0.687462	−	0.726221i	$-0.741275\pi$
$769$	−29320.3	−1.37492	−0.687462	+	0.726221i	$0.741275\pi$
$770$	4799.99	0.224649
$771$	50814.6	2.37359
$772$	12552.0	0.585175
$773$	25830.3	1.20188	0.600938	−	0.799296i	$-0.294794\pi$
$773$	25830.3	1.20188	0.600938	+	0.799296i	$0.294794\pi$
$774$	−59234.2	−2.75081
$775$	143.720	0.00666137
$776$	−45214.2	−2.09162
$777$	−24576.0	−1.13469
$778$	3836.37	0.176787
$779$	24750.3	1.13834
$780$	−14209.1	−0.652266
$781$	−7981.85	−0.365702
$782$	0	0
$783$	5507.05	0.251349
$784$	5130.51	0.233715
$785$	43933.7	1.99753
$786$	5238.37	0.237718
$787$	13639.9	0.617801	0.308900	−	0.951094i	$-0.400039\pi$
$787$	13639.9	0.617801	0.308900	+	0.951094i	$0.400039\pi$
$788$	239.962	0.0108481
$789$	−28998.4	−1.30845
$790$	8089.94	0.364338
$791$	514.995	0.0231493
$792$	−15482.7	−0.694640
$793$	5097.80	0.228283
$794$	−2601.56	−0.116280
$795$	72722.9	3.24430
$796$	8959.57	0.398949
$797$	35932.1	1.59697	0.798483	−	0.602017i	$-0.205636\pi$
$797$	35932.1	1.59697	0.798483	+	0.602017i	$0.205636\pi$
$798$	19252.1	0.854030
$799$	0	0
$800$	−19176.8	−0.847505
$801$	−38947.5	−1.71803
$802$	29512.3	1.29939
$803$	−8719.42	−0.383190
$804$	−24517.3	−1.07544
$805$	−8936.97	−0.391288
$806$	−64.9622	−0.00283895
$807$	26052.1	1.13640
$808$	−18019.7	−0.784566
$809$	19296.4	0.838598	0.419299	−	0.907848i	$-0.362276\pi$
$809$	19296.4	0.838598	0.419299	+	0.907848i	$0.362276\pi$
$810$	−33139.2	−1.43752
$811$	−5464.45	−0.236600	−0.118300	−	0.992978i	$-0.537744\pi$
$811$	−5464.45	−0.236600	−0.118300	+	0.992978i	$0.537744\pi$
$812$	−825.522	−0.0356775
$813$	−23448.6	−1.01153
$814$	−5320.61	−0.229100
$815$	−3096.08	−0.133068
$816$	0	0
$817$	−38500.0	−1.64865
$818$	−15902.0	−0.679707
$819$	19983.4	0.852598
$820$	16726.6	0.712341
$821$	16693.5	0.709631	0.354816	−	0.934936i	$-0.384544\pi$
$821$	16693.5	0.709631	0.354816	+	0.934936i	$0.384544\pi$
$822$	−13583.8	−0.576387
$823$	−5833.41	−0.247072	−0.123536	−	0.992340i	$-0.539423\pi$
$823$	−5833.41	−0.247072	−0.123536	+	0.992340i	$0.539423\pi$
$824$	9486.44	0.401063
$825$	−14140.2	−0.596726
$826$	−3915.33	−0.164930
$827$	−11048.3	−0.464556	−0.232278	−	0.972649i	$-0.574618\pi$
$827$	−11048.3	−0.464556	−0.232278	+	0.972649i	$0.574618\pi$
$828$	8443.63	0.354392
$829$	−26287.1	−1.10131	−0.550657	−	0.834732i	$-0.685623\pi$
$829$	−26287.1	−1.10131	−0.550657	+	0.834732i	$0.685623\pi$
$830$	−8293.01	−0.346813
$831$	57233.4	2.38917
$832$	14796.3	0.616548
$833$	0	0
$834$	855.583	0.0355233
$835$	44748.4	1.85459
$836$	−2947.60	−0.121943
$837$	280.628	0.0115889
$838$	7129.64	0.293901
$839$	−8311.95	−0.342027	−0.171013	−	0.985269i	$-0.554704\pi$
$839$	−8311.95	−0.342027	−0.171013	+	0.985269i	$0.554704\pi$
$840$	44419.5	1.82455
$841$	−23973.8	−0.982974
$842$	21161.5	0.866119
$843$	−16523.8	−0.675101
$844$	−7748.97	−0.316032
$845$	−22101.6	−0.899785
$846$	77437.2	3.14698
$847$	−14744.0	−0.598122
$848$	−12992.5	−0.526139
$849$	−11555.5	−0.467118
$850$	0	0
$851$	9906.29	0.399040
$852$	−21635.6	−0.869981
$853$	−3875.16	−0.155549	−0.0777743	−	0.996971i	$-0.524781\pi$
$853$	−3875.16	−0.155549	−0.0777743	+	0.996971i	$0.524781\pi$
$854$	−4667.91	−0.187040
$855$	−73060.6	−2.92236
$856$	19432.2	0.775912
$857$	31317.9	1.24831	0.624154	−	0.781301i	$-0.285444\pi$
$857$	31317.9	1.24831	0.624154	+	0.781301i	$0.285444\pi$
$858$	6391.47	0.254314
$859$	35801.6	1.42204	0.711021	−	0.703171i	$-0.248233\pi$
$859$	35801.6	1.42204	0.711021	+	0.703171i	$0.248233\pi$
$860$	−26018.9	−1.03167
$861$	−34753.0	−1.37558
$862$	−16977.9	−0.670847
$863$	−5935.67	−0.234128	−0.117064	−	0.993124i	$-0.537348\pi$
$863$	−5935.67	−0.234128	−0.117064	+	0.993124i	$0.537348\pi$
$864$	−37444.8	−1.47442
$865$	23582.0	0.926950
$866$	11210.0	0.439875
$867$	0	0
$868$	−42.0668	−0.00164498
$869$	2573.47	0.100459
$870$	−6544.46	−0.255032
$871$	23389.1	0.909885
$872$	−41872.6	−1.62613
$873$	−104423.	−4.04832
$874$	−7760.29	−0.300338
$875$	2659.86	0.102765
$876$	−23634.8	−0.911583
$877$	−43699.3	−1.68258	−0.841290	−	0.540585i	$-0.818203\pi$
$877$	−43699.3	−1.68258	−0.841290	+	0.540585i	$0.818203\pi$
$878$	−12256.4	−0.471110
$879$	33899.7	1.30081
$880$	4807.83	0.184173
$881$	−30329.5	−1.15985	−0.579924	−	0.814671i	$-0.696918\pi$
$881$	−30329.5	−1.15985	−0.579924	+	0.814671i	$0.696918\pi$
$882$	23700.5	0.904805
$883$	35558.7	1.35521	0.677603	−	0.735428i	$-0.263019\pi$
$883$	35558.7	1.35521	0.677603	+	0.735428i	$0.263019\pi$
$884$	0	0
$885$	21951.0	0.833757
$886$	6538.11	0.247914
$887$	23689.6	0.896752	0.448376	−	0.893845i	$-0.352003\pi$
$887$	23689.6	0.896752	0.448376	+	0.893845i	$0.352003\pi$
$888$	−49237.3	−1.86069
$889$	−18786.5	−0.708749
$890$	24191.1	0.911111
$891$	−10541.8	−0.396369
$892$	−5758.65	−0.216159
$893$	50331.3	1.88608
$894$	−6637.19	−0.248301
$895$	−19012.7	−0.710083
$896$	1.66091	6.19277e−5 0
$897$	−11900.1	−0.442957
$898$	28809.6	1.07059
$899$	21.1596	0.000784998 0
$900$	−25944.3	−0.960900
$901$	0	0
$902$	−7523.90	−0.277737
$903$	54059.6	1.99224
$904$	1031.78	0.0379608
$905$	−44427.6	−1.63185
$906$	48131.4	1.76496
$907$	12176.0	0.445752	0.222876	−	0.974847i	$-0.428456\pi$
$907$	12176.0	0.445752	0.222876	+	0.974847i	$0.428456\pi$
$908$	−14849.3	−0.542721
$909$	−41616.8	−1.51853
$910$	−12412.2	−0.452153
$911$	34830.5	1.26673	0.633363	−	0.773855i	$-0.281674\pi$
$911$	34830.5	1.26673	0.633363	+	0.773855i	$0.281674\pi$
$912$	19283.5	0.700154
$913$	−2638.07	−0.0956269
$914$	−15716.4	−0.568767
$915$	26170.2	0.945531
$916$	12983.2	0.468315
$917$	−3236.07	−0.116537
$918$	0	0
$919$	−15886.7	−0.570244	−0.285122	−	0.958491i	$-0.592034\pi$
$919$	−15886.7	−0.570244	−0.285122	+	0.958491i	$0.592034\pi$
$920$	−17905.0	−0.641642
$921$	42868.0	1.53371
$922$	5585.44	0.199508
$923$	20640.1	0.736052
$924$	4138.85	0.147357
$925$	−30438.5	−1.08196
$926$	−31156.6	−1.10569
$927$	21909.1	0.776256
$928$	−2823.38	−0.0998728
$929$	−14115.7	−0.498514	−0.249257	−	0.968437i	$-0.580186\pi$
$929$	−14115.7	−0.498514	−0.249257	+	0.968437i	$0.580186\pi$
$930$	−333.492	−0.0117587
$931$	15404.5	0.542278
$932$	−13806.0	−0.485225
$933$	−24917.4	−0.874338
$934$	25318.6	0.886993
$935$	0	0
$936$	40036.4	1.39811
$937$	−39312.3	−1.37063	−0.685314	−	0.728248i	$-0.740335\pi$
$937$	−39312.3	−1.37063	−0.685314	+	0.728248i	$0.740335\pi$
$938$	−21416.7	−0.745502
$939$	−12856.6	−0.446814
$940$	34014.7	1.18025
$941$	30478.0	1.05585	0.527924	−	0.849291i	$-0.322970\pi$
$941$	30478.0	1.05585	0.527924	+	0.849291i	$0.322970\pi$
$942$	−53567.0	−1.85277
$943$	14008.5	0.483754
$944$	−3921.73	−0.135213
$945$	53618.8	1.84574
$946$	11703.7	0.402242
$947$	45331.1	1.55551	0.777753	−	0.628570i	$-0.216360\pi$
$947$	45331.1	1.55551	0.777753	+	0.628570i	$0.216360\pi$
$948$	6975.65	0.238986
$949$	22547.3	0.771250
$950$	23844.6	0.814339
$951$	−7648.70	−0.260806
$952$	0	0
$953$	33782.9	1.14830	0.574152	−	0.818748i	$-0.305332\pi$
$953$	33782.9	1.14830	0.574152	+	0.818748i	$0.305332\pi$
$954$	−60019.3	−2.03690
$955$	−21838.1	−0.739964
$956$	5899.04	0.199570
$957$	−2081.84	−0.0703202
$958$	−30300.7	−1.02189
$959$	8391.56	0.282563
$960$	75958.6	2.55370
$961$	−29789.9	−0.999964
$962$	13758.4	0.461111
$963$	44879.1	1.50178
$964$	−8182.55	−0.273384
$965$	−61472.2	−2.05063
$966$	10896.6	0.362931
$967$	−45742.7	−1.52119	−0.760593	−	0.649229i	$-0.775092\pi$
$967$	−45742.7	−1.52119	−0.760593	+	0.649229i	$0.775092\pi$
$968$	−29539.2	−0.980813
$969$	0	0
$970$	64859.5	2.14692
$971$	7001.98	0.231415	0.115708	−	0.993283i	$-0.463086\pi$
$971$	7001.98	0.231415	0.115708	+	0.993283i	$0.463086\pi$
$972$	−4393.31	−0.144975
$973$	−528.547	−0.0174146
$974$	−6252.64	−0.205696
$975$	36564.8	1.20104
$976$	−4675.53	−0.153340
$977$	36142.8	1.18353	0.591767	−	0.806109i	$-0.298431\pi$
$977$	36142.8	1.18353	0.591767	+	0.806109i	$0.298431\pi$
$978$	3774.95	0.123425
$979$	7695.39	0.251221
$980$	10410.6	0.339341
$981$	−96705.6	−3.14737
$982$	20392.0	0.662662
$983$	−21919.3	−0.711207	−0.355603	−	0.934637i	$-0.615725\pi$
$983$	−21919.3	−0.711207	−0.355603	+	0.934637i	$0.615725\pi$
$984$	−69626.7	−2.25571
$985$	−1175.19	−0.0380150
$986$	0	0
$987$	−70672.4	−2.27916
$988$	7622.11	0.245437
$989$	−21790.8	−0.700614
$990$	22209.9	0.713006
$991$	19931.0	0.638880	0.319440	−	0.947607i	$-0.396505\pi$
$991$	19931.0	0.638880	0.319440	+	0.947607i	$0.396505\pi$
$992$	−143.873	−0.00460482
$993$	23264.6	0.743483
$994$	−18899.5	−0.603074
$995$	−43878.7	−1.39804
$996$	−7150.75	−0.227490
$997$	18298.2	0.581253	0.290626	−	0.956837i	$-0.406136\pi$
$997$	18298.2	0.581253	0.290626	+	0.956837i	$0.406136\pi$
$998$	−1545.48	−0.0490193
$999$	−59434.5	−1.88231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.i.1.4	yes	12
17.4	even	4		289.4.b.f.288.17		24
17.13	even	4		289.4.b.f.288.18		24
17.16	even	2		289.4.a.h.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.4	✓	12	17.16	even	2
289.4.a.i.1.4	yes	12	1.1	even	1	trivial
289.4.b.f.288.17		24	17.4	even	4
289.4.b.f.288.18		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)

\(f(q)\)	\(=\)	\(q-2.16473 q^{2} +9.14133 q^{3} -3.31395 q^{4} +16.2298 q^{5} -19.7885 q^{6} +12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} +O(q^{10})\)	\(q-2.16473 q^{2} +9.14133 q^{3} -3.31395 q^{4} +16.2298 q^{5} -19.7885 q^{6} +12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} -35.1331 q^{10} -11.1761 q^{11} -30.2939 q^{12} +28.9000 q^{13} -26.4629 q^{14} +148.362 q^{15} -26.5061 q^{16} -122.445 q^{18} -79.5850 q^{19} -53.7848 q^{20} +111.749 q^{21} +24.1932 q^{22} -45.0447 q^{23} +223.886 q^{24} +138.406 q^{25} -62.5606 q^{26} +270.253 q^{27} -40.5117 q^{28} +20.3774 q^{29} -321.163 q^{30} +1.03839 q^{31} -138.555 q^{32} -102.164 q^{33} +198.402 q^{35} -187.450 q^{36} -219.921 q^{37} +172.280 q^{38} +264.184 q^{39} +397.494 q^{40} -310.992 q^{41} -241.906 q^{42} +483.760 q^{43} +37.0371 q^{44} +918.020 q^{45} +97.5095 q^{46} -632.422 q^{47} -242.301 q^{48} -193.560 q^{49} -299.612 q^{50} -95.7732 q^{52} +490.172 q^{53} -585.024 q^{54} -181.386 q^{55} +299.400 q^{56} -727.512 q^{57} -44.1115 q^{58} +147.956 q^{59} -491.665 q^{60} +176.395 q^{61} -2.24783 q^{62} +691.469 q^{63} +511.982 q^{64} +469.041 q^{65} +221.158 q^{66} +809.312 q^{67} -411.768 q^{69} -429.487 q^{70} +714.189 q^{71} +1385.34 q^{72} +780.184 q^{73} +476.070 q^{74} +1265.22 q^{75} +263.741 q^{76} -136.623 q^{77} -571.887 q^{78} -230.265 q^{79} -430.188 q^{80} +943.248 q^{81} +673.213 q^{82} +236.046 q^{83} -370.330 q^{84} -1047.21 q^{86} +186.276 q^{87} -273.721 q^{88} -688.557 q^{89} -1987.26 q^{90} +353.290 q^{91} +149.276 q^{92} +9.49224 q^{93} +1369.02 q^{94} -1291.65 q^{95} -1266.57 q^{96} -1846.11 q^{97} +419.004 q^{98} -632.164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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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