LMFDB - Embedded newform 289.4.a.h.1.7

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			1.7
Root			$-0.447590$ 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)

$f(q)$	$=$	$q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +O(q^{10})$	\(q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +5.25584 q^{10} -22.6868 q^{11} +74.2152 q^{12} +67.4022 q^{13} -1.01960 q^{14} -111.732 q^{15} +59.2321 q^{16} +28.4393 q^{18} +42.9965 q^{19} -91.5878 q^{20} +21.6753 q^{21} -10.1544 q^{22} -117.444 q^{23} +67.2892 q^{24} +12.8870 q^{25} +30.1686 q^{26} -347.673 q^{27} +17.7674 q^{28} -226.336 q^{29} -50.0103 q^{30} +0.673139 q^{31} +83.0858 q^{32} +215.869 q^{33} -26.7491 q^{35} -495.581 q^{36} +99.9003 q^{37} +19.2448 q^{38} -641.345 q^{39} -83.0405 q^{40} +154.092 q^{41} +9.70165 q^{42} -321.792 q^{43} +176.949 q^{44} +746.106 q^{45} -52.5667 q^{46} -30.4214 q^{47} -563.604 q^{48} -337.811 q^{49} +5.76808 q^{50} -525.715 q^{52} -361.595 q^{53} -155.615 q^{54} -266.400 q^{55} +16.1093 q^{56} -409.119 q^{57} -101.306 q^{58} +147.417 q^{59} +871.475 q^{60} -321.075 q^{61} +0.301290 q^{62} -144.739 q^{63} -436.668 q^{64} +791.473 q^{65} +96.6208 q^{66} +612.509 q^{67} +1117.50 q^{69} -11.9726 q^{70} -248.823 q^{71} -449.331 q^{72} +701.031 q^{73} +44.7144 q^{74} -122.622 q^{75} -335.358 q^{76} +51.6798 q^{77} -287.059 q^{78} -773.040 q^{79} +695.534 q^{80} +1592.63 q^{81} +68.9702 q^{82} -1005.91 q^{83} -169.060 q^{84} -144.031 q^{86} +2153.63 q^{87} +160.436 q^{88} +1641.08 q^{89} +333.949 q^{90} -153.540 q^{91} +916.023 q^{92} -6.40505 q^{93} -13.6163 q^{94} +504.887 q^{95} -790.577 q^{96} +479.663 q^{97} -151.201 q^{98} -1441.49 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.447590	0.158247	0.0791235	−	0.996865i	$-0.474788\pi$
$2$	0.447590	0.158247	0.0791235	+	0.996865i	$0.474788\pi$
$3$	−9.51519	−1.83120	−0.915599	−	0.402092i	$-0.868283\pi$
$3$	−9.51519	−1.83120	−0.915599	+	0.402092i	$0.868283\pi$
$4$	−7.79966	−0.974958
$5$	11.7425	1.05028	0.525142	−	0.851015i	$-0.324012\pi$
$5$	11.7425	1.05028	0.525142	+	0.851015i	$0.324012\pi$
$6$	−4.25890	−0.289782
$7$	−2.27797	−0.122999	−0.0614994	−	0.998107i	$-0.519588\pi$
$7$	−2.27797	−0.122999	−0.0614994	+	0.998107i	$0.519588\pi$
$8$	−7.07177	−0.312531
$9$	63.5388	2.35329
$10$	5.25584	0.166204
$11$	−22.6868	−0.621848	−0.310924	−	0.950435i	$-0.600638\pi$
$11$	−22.6868	−0.621848	−0.310924	+	0.950435i	$0.600638\pi$
$12$	74.2152	1.78534
$13$	67.4022	1.43800	0.719001	−	0.695009i	$-0.244600\pi$
$13$	67.4022	1.43800	0.719001	+	0.695009i	$0.244600\pi$
$14$	−1.01960	−0.0194642
$15$	−111.732	−1.92328
$16$	59.2321	0.925501
$17$	0	0
$17$	0	0
$18$	28.4393	0.372400
$19$	42.9965	0.519161	0.259581	−	0.965721i	$-0.416416\pi$
$19$	42.9965	0.519161	0.259581	+	0.965721i	$0.416416\pi$
$20$	−91.5878	−1.02398
$21$	21.6753	0.225235
$22$	−10.1544	−0.0984055
$23$	−117.444	−1.06473	−0.532364	−	0.846516i	$-0.678696\pi$
$23$	−117.444	−1.06473	−0.532364	+	0.846516i	$0.678696\pi$
$24$	67.2892	0.572306
$25$	12.8870	0.103096
$26$	30.1686	0.227559
$27$	−347.673	−2.47814
$28$	17.7674	0.119919
$29$	−226.336	−1.44930	−0.724648	−	0.689120i	$-0.757997\pi$
$29$	−226.336	−1.44930	−0.724648	+	0.689120i	$0.757997\pi$
$30$	−50.0103	−0.304353
$31$	0.673139	0.00389998	0.00194999	−	0.999998i	$-0.499379\pi$
$31$	0.673139	0.00389998	0.00194999	+	0.999998i	$0.499379\pi$
$32$	83.0858	0.458989
$33$	215.869	1.13873
$34$	0	0
$35$	−26.7491	−0.129184
$36$	−495.581	−2.29436
$37$	99.9003	0.443878	0.221939	−	0.975060i	$-0.428761\pi$
$37$	99.9003	0.443878	0.221939	+	0.975060i	$0.428761\pi$
$38$	19.2448	0.0821557
$39$	−641.345	−2.63327
$40$	−83.0405	−0.328246
$41$	154.092	0.586956	0.293478	−	0.955966i	$-0.405187\pi$
$41$	154.092	0.586956	0.293478	+	0.955966i	$0.405187\pi$
$42$	9.70165	0.0356428
$43$	−321.792	−1.14123	−0.570615	−	0.821218i	$-0.693295\pi$
$43$	−321.792	−1.14123	−0.570615	+	0.821218i	$0.693295\pi$
$44$	176.949	0.606275
$45$	746.106	2.47162
$46$	−52.5667	−0.168490
$47$	−30.4214	−0.0944132	−0.0472066	−	0.998885i	$-0.515032\pi$
$47$	−30.4214	−0.0944132	−0.0472066	+	0.998885i	$0.515032\pi$
$48$	−563.604	−1.69478
$49$	−337.811	−0.984871
$50$	5.76808	0.0163146
$51$	0	0
$52$	−525.715	−1.40199
$53$	−361.595	−0.937148	−0.468574	−	0.883424i	$-0.655232\pi$
$53$	−361.595	−0.937148	−0.468574	+	0.883424i	$0.655232\pi$
$54$	−155.615	−0.392158
$55$	−266.400	−0.653116
$56$	16.1093	0.0384410
$57$	−409.119	−0.950687
$58$	−101.306	−0.229347
$59$	147.417	0.325289	0.162645	−	0.986685i	$-0.447998\pi$
$59$	147.417	0.325289	0.162645	+	0.986685i	$0.447998\pi$
$60$	871.475	1.87511
$61$	−321.075	−0.673925	−0.336963	−	0.941518i	$-0.609400\pi$
$61$	−321.075	−0.673925	−0.336963	+	0.941518i	$0.609400\pi$
$62$	0.301290	0.000617160 0
$63$	−144.739	−0.289452
$64$	−436.668	−0.852867
$65$	791.473	1.51031
$66$	96.6208	0.180200
$67$	612.509	1.11686	0.558432	−	0.829550i	$-0.311403\pi$
$67$	612.509	1.11686	0.558432	+	0.829550i	$0.311403\pi$
$68$	0	0
$69$	1117.50	1.94973
$70$	−11.9726	−0.0204429
$71$	−248.823	−0.415913	−0.207956	−	0.978138i	$-0.566681\pi$
$71$	−248.823	−0.415913	−0.207956	+	0.978138i	$0.566681\pi$
$72$	−449.331	−0.735475
$73$	701.031	1.12397	0.561983	−	0.827149i	$-0.310039\pi$
$73$	701.031	1.12397	0.561983	+	0.827149i	$0.310039\pi$
$74$	44.7144	0.0702424
$75$	−122.622	−0.188789
$76$	−335.358	−0.506160
$77$	51.6798	0.0764865
$78$	−287.059	−0.416706
$79$	−773.040	−1.10093	−0.550467	−	0.834857i	$-0.685550\pi$
$79$	−773.040	−1.10093	−0.550467	+	0.834857i	$0.685550\pi$
$80$	695.534	0.972038
$81$	1592.63	2.18467
$82$	68.9702	0.0928840
$83$	−1005.91	−1.33028	−0.665139	−	0.746720i	$-0.731628\pi$
$83$	−1005.91	−1.33028	−0.665139	+	0.746720i	$0.731628\pi$
$84$	−169.060	−0.219595
$85$	0	0
$86$	−144.031	−0.180596
$87$	2153.63	2.65395
$88$	160.436	0.194347
$89$	1641.08	1.95454	0.977271	−	0.211994i	$-0.0679958\pi$
$89$	1641.08	1.95454	0.977271	+	0.211994i	$0.0679958\pi$
$90$	333.949	0.391126
$91$	−153.540	−0.176872
$92$	916.023	1.03806
$93$	−6.40505	−0.00714164
$94$	−13.6163	−0.0149406
$95$	504.887	0.545267
$96$	−790.577	−0.840499
$97$	479.663	0.502087	0.251043	−	0.967976i	$-0.419226\pi$
$97$	479.663	0.502087	0.251043	+	0.967976i	$0.419226\pi$
$98$	−151.201	−0.155853
$99$	−1441.49	−1.46339
$100$	−100.514	−0.100514
$101$	−814.043	−0.801984	−0.400992	−	0.916082i	$-0.631334\pi$
$101$	−814.043	−0.801984	−0.400992	+	0.916082i	$0.631334\pi$
$102$	0	0
$103$	−543.806	−0.520222	−0.260111	−	0.965579i	$-0.583759\pi$
$103$	−543.806	−0.520222	−0.260111	+	0.965579i	$0.583759\pi$
$104$	−476.653	−0.449420
$105$	254.523	0.236561
$106$	−161.846	−0.148301
$107$	171.706	0.155135	0.0775673	−	0.996987i	$-0.475285\pi$
$107$	171.706	0.155135	0.0775673	+	0.996987i	$0.475285\pi$
$108$	2711.73	2.41608
$109$	−1310.16	−1.15129	−0.575644	−	0.817700i	$-0.695249\pi$
$109$	−1310.16	−1.15129	−0.575644	+	0.817700i	$0.695249\pi$
$110$	−119.238	−0.103354
$111$	−950.570	−0.812830
$112$	−134.929	−0.113836
$113$	−879.939	−0.732546	−0.366273	−	0.930507i	$-0.619366\pi$
$113$	−879.939	−0.732546	−0.366273	+	0.930507i	$0.619366\pi$
$114$	−183.118	−0.150443
$115$	−1379.09	−1.11827
$116$	1765.35	1.41300
$117$	4282.65	3.38403
$118$	65.9824	0.0514760
$119$	0	0
$120$	790.145	0.601084
$121$	−816.310	−0.613306
$122$	−143.710	−0.106647
$123$	−1466.22	−1.07483
$124$	−5.25026	−0.00380232
$125$	−1316.49	−0.942004
$126$	−64.7839	−0.0458048
$127$	−1303.39	−0.910684	−0.455342	−	0.890317i	$-0.650483\pi$
$127$	−1303.39	−0.910684	−0.455342	+	0.890317i	$0.650483\pi$
$128$	−860.135	−0.593952
$129$	3061.91	2.08982
$130$	354.255	0.239002
$131$	−1523.87	−1.01634	−0.508171	−	0.861256i	$-0.669678\pi$
$131$	−1523.87	−1.01634	−0.508171	+	0.861256i	$0.669678\pi$
$132$	−1683.71	−1.11021
$133$	−97.9447	−0.0638562
$134$	274.153	0.176740
$135$	−4082.56	−2.60275
$136$	0	0
$137$	−2617.59	−1.63238	−0.816189	−	0.577785i	$-0.803917\pi$
$137$	−2617.59	−1.63238	−0.816189	+	0.577785i	$0.803917\pi$
$138$	500.182	0.308538
$139$	232.950	0.142148	0.0710741	−	0.997471i	$-0.477357\pi$
$139$	232.950	0.142148	0.0710741	+	0.997471i	$0.477357\pi$
$140$	208.634	0.125949
$141$	289.466	0.172889
$142$	−111.370	−0.0658169
$143$	−1529.14	−0.894218
$144$	3763.53	2.17797
$145$	−2657.76	−1.52217
$146$	313.774	0.177864
$147$	3214.33	1.80349
$148$	−779.189	−0.432763
$149$	429.754	0.236287	0.118144	−	0.992997i	$-0.462306\pi$
$149$	429.754	0.236287	0.118144	+	0.992997i	$0.462306\pi$
$150$	−54.8844	−0.0298753
$151$	−1373.00	−0.739953	−0.369976	−	0.929041i	$-0.620634\pi$
$151$	−1373.00	−0.739953	−0.369976	+	0.929041i	$0.620634\pi$
$152$	−304.061	−0.162254
$153$	0	0
$154$	23.1314	0.0121038
$155$	7.90436	0.00409609
$156$	5002.27	2.56732
$157$	616.059	0.313165	0.156582	−	0.987665i	$-0.449952\pi$
$157$	616.059	0.313165	0.156582	+	0.987665i	$0.449952\pi$
$158$	−346.005	−0.174220
$159$	3440.64	1.71610
$160$	975.638	0.482068
$161$	267.534	0.130960
$162$	712.844	0.345718
$163$	3460.81	1.66301	0.831507	−	0.555515i	$-0.187479\pi$
$163$	3460.81	1.66301	0.831507	+	0.555515i	$0.187479\pi$
$164$	−1201.87	−0.572257
$165$	2534.85	1.19599
$166$	−450.235	−0.210512
$167$	2424.76	1.12355	0.561777	−	0.827288i	$-0.310118\pi$
$167$	2424.76	1.12355	0.561777	+	0.827288i	$0.310118\pi$
$168$	−153.283	−0.0703930
$169$	2346.06	1.06785
$170$	0	0
$171$	2731.94	1.22174
$172$	2509.87	1.11265
$173$	−2853.14	−1.25388	−0.626938	−	0.779069i	$-0.715692\pi$
$173$	−2853.14	−1.25388	−0.626938	+	0.779069i	$0.715692\pi$
$174$	963.943	0.419979
$175$	−29.3562	−0.0126807
$176$	−1343.79	−0.575521
$177$	−1402.70	−0.595669
$178$	734.531	0.309300
$179$	1195.13	0.499040	0.249520	−	0.968370i	$-0.419727\pi$
$179$	1195.13	0.499040	0.249520	+	0.968370i	$0.419727\pi$
$180$	−5819.37	−2.40972
$181$	−2669.80	−1.09638	−0.548190	−	0.836354i	$-0.684683\pi$
$181$	−2669.80	−1.09638	−0.548190	+	0.836354i	$0.684683\pi$
$182$	−68.7231	−0.0279895
$183$	3055.09	1.23409
$184$	830.536	0.332760
$185$	1173.08	0.466198
$186$	−2.86683	−0.00113014
$187$	0	0
$188$	237.277	0.0920489
$189$	791.989	0.304808
$190$	225.982	0.0862868
$191$	−3394.56	−1.28598	−0.642988	−	0.765876i	$-0.722306\pi$
$191$	−3394.56	−1.28598	−0.642988	+	0.765876i	$0.722306\pi$
$192$	4154.98	1.56177
$193$	−3003.88	−1.12033	−0.560165	−	0.828381i	$-0.689262\pi$
$193$	−3003.88	−1.12033	−0.560165	+	0.828381i	$0.689262\pi$
$194$	214.692	0.0794537
$195$	−7531.01	−2.76568
$196$	2634.81	0.960208
$197$	−1636.63	−0.591902	−0.295951	−	0.955203i	$-0.595637\pi$
$197$	−1636.63	−0.591902	−0.295951	+	0.955203i	$0.595637\pi$
$198$	−645.197	−0.231576
$199$	−1600.54	−0.570146	−0.285073	−	0.958506i	$-0.592018\pi$
$199$	−1600.54	−0.570146	−0.285073	+	0.958506i	$0.592018\pi$
$200$	−91.1337	−0.0322206
$201$	−5828.14	−2.04520
$202$	−364.358	−0.126911
$203$	515.587	0.178262
$204$	0	0
$205$	1809.44	0.616470
$206$	−243.402	−0.0823235
$207$	−7462.24	−2.50561
$208$	3992.37	1.33087
$209$	−975.452	−0.322839
$210$	113.922	0.0374350
$211$	4282.36	1.39720	0.698602	−	0.715510i	$-0.253806\pi$
$211$	4282.36	1.39720	0.698602	+	0.715510i	$0.253806\pi$
$212$	2820.32	0.913680
$213$	2367.59	0.761619
$214$	76.8537	0.0245496
$215$	−3778.65	−1.19861
$216$	2458.66	0.774495
$217$	−1.53339	−0.000479693 0
$218$	−586.414	−0.182188
$219$	−6670.44	−2.05820
$220$	2077.83	0.636761
$221$	0	0
$222$	−425.465	−0.128628
$223$	−1396.84	−0.419460	−0.209730	−	0.977759i	$-0.567258\pi$
$223$	−1396.84	−0.419460	−0.209730	+	0.977759i	$0.567258\pi$
$224$	−189.267	−0.0564551
$225$	818.822	0.242614
$226$	−393.852	−0.115923
$227$	1612.43	0.471458	0.235729	−	0.971819i	$-0.424252\pi$
$227$	1612.43	0.471458	0.235729	+	0.971819i	$0.424252\pi$
$228$	3190.99	0.926880
$229$	−2530.45	−0.730204	−0.365102	−	0.930968i	$-0.618966\pi$
$229$	−2530.45	−0.730204	−0.365102	+	0.930968i	$0.618966\pi$
$230$	−617.266	−0.176962
$231$	−491.743	−0.140062
$232$	1600.60	0.452950
$233$	4689.59	1.31856	0.659282	−	0.751896i	$-0.270860\pi$
$233$	4689.59	1.31856	0.659282	+	0.751896i	$0.270860\pi$
$234$	1916.87	0.535512
$235$	−357.225	−0.0991607
$236$	−1149.80	−0.317143
$237$	7355.62	2.01603
$238$	0	0
$239$	−6332.33	−1.71383	−0.856913	−	0.515462i	$-0.827620\pi$
$239$	−6332.33	−1.71383	−0.856913	+	0.515462i	$0.827620\pi$
$240$	−6618.14	−1.78000
$241$	4438.39	1.18631	0.593157	−	0.805087i	$-0.297881\pi$
$241$	4438.39	1.18631	0.593157	+	0.805087i	$0.297881\pi$
$242$	−365.372	−0.0970537
$243$	−5766.97	−1.52243
$244$	2504.28	0.657049
$245$	−3966.75	−1.03439
$246$	−656.265	−0.170089
$247$	2898.06	0.746555
$248$	−4.76029	−0.00121886
$249$	9571.43	2.43600
$250$	−589.248	−0.149069
$251$	2085.26	0.524385	0.262193	−	0.965016i	$-0.415554\pi$
$251$	2085.26	0.524385	0.262193	+	0.965016i	$0.415554\pi$
$252$	1128.92	0.282203
$253$	2664.42	0.662098
$254$	−583.383	−0.144113
$255$	0	0
$256$	3108.36	0.758876
$257$	−537.124	−0.130369	−0.0651846	−	0.997873i	$-0.520764\pi$
$257$	−537.124	−0.130369	−0.0651846	+	0.997873i	$0.520764\pi$
$258$	1370.48	0.330707
$259$	−227.570	−0.0545965
$260$	−6173.22	−1.47249
$261$	−14381.1	−3.41061
$262$	−682.068	−0.160833
$263$	6617.18	1.55146	0.775728	−	0.631068i	$-0.217383\pi$
$263$	6617.18	1.55146	0.775728	+	0.631068i	$0.217383\pi$
$264$	−1526.58	−0.355887
$265$	−4246.03	−0.984271
$266$	−43.8390	−0.0101051
$267$	−15615.2	−3.57915
$268$	−4777.36	−1.08890
$269$	617.429	0.139945	0.0699726	−	0.997549i	$-0.477709\pi$
$269$	617.429	0.139945	0.0699726	+	0.997549i	$0.477709\pi$
$270$	−1827.31	−0.411877
$271$	−5332.00	−1.19519	−0.597594	−	0.801799i	$-0.703877\pi$
$271$	−5332.00	−1.19519	−0.597594	+	0.801799i	$0.703877\pi$
$272$	0	0
$273$	1460.96	0.323889
$274$	−1171.61	−0.258319
$275$	−292.364	−0.0641099
$276$	−8716.12	−1.90090
$277$	2486.63	0.539376	0.269688	−	0.962948i	$-0.413079\pi$
$277$	2486.63	0.539376	0.269688	+	0.962948i	$0.413079\pi$
$278$	104.266	0.0224945
$279$	42.7704	0.00917777
$280$	189.164	0.0403739
$281$	−4951.96	−1.05128	−0.525639	−	0.850708i	$-0.676174\pi$
$281$	−4951.96	−1.05128	−0.525639	+	0.850708i	$0.676174\pi$
$282$	129.562	0.0273592
$283$	8216.86	1.72594	0.862971	−	0.505253i	$-0.168601\pi$
$283$	8216.86	1.72594	0.862971	+	0.505253i	$0.168601\pi$
$284$	1940.73	0.405498
$285$	−4804.10	−0.998491
$286$	−684.428	−0.141507
$287$	−351.018	−0.0721949
$288$	5279.17	1.08013
$289$	0	0
$290$	−1189.59	−0.240879
$291$	−4564.08	−0.919420
$292$	−5467.81	−1.09582
$293$	−737.775	−0.147103	−0.0735516	−	0.997291i	$-0.523433\pi$
$293$	−737.775	−0.147103	−0.0735516	+	0.997291i	$0.523433\pi$
$294$	1438.70	0.285397
$295$	1731.05	0.341646
$296$	−706.472	−0.138726
$297$	7887.59	1.54102
$298$	192.354	0.0373917
$299$	−7915.98	−1.53108
$300$	956.410	0.184061
$301$	733.033	0.140370
$302$	−614.539	−0.117095
$303$	7745.77	1.46859
$304$	2546.77	0.480484
$305$	−3770.23	−0.707813
$306$	0	0
$307$	5994.47	1.11441	0.557203	−	0.830377i	$-0.311875\pi$
$307$	5994.47	1.11441	0.557203	+	0.830377i	$0.311875\pi$
$308$	−403.085	−0.0745712
$309$	5174.42	0.952629
$310$	3.53791	0.000648193 0
$311$	−9460.76	−1.72498	−0.862492	−	0.506070i	$-0.831098\pi$
$311$	−9460.76	−1.72498	−0.862492	+	0.506070i	$0.831098\pi$
$312$	4535.44	0.822977
$313$	4674.92	0.844225	0.422112	−	0.906544i	$-0.361289\pi$
$313$	4674.92	0.844225	0.422112	+	0.906544i	$0.361289\pi$
$314$	275.742	0.0495574
$315$	−1699.61	−0.304006
$316$	6029.45	1.07336
$317$	−692.929	−0.122772	−0.0613861	−	0.998114i	$-0.519552\pi$
$317$	−692.929	−0.122772	−0.0613861	+	0.998114i	$0.519552\pi$
$318$	1540.00	0.271568
$319$	5134.84	0.901241
$320$	−5127.59	−0.895753
$321$	−1633.81	−0.284082
$322$	119.745	0.0207241
$323$	0	0
$324$	−12422.0	−2.12997
$325$	868.611	0.148252
$326$	1549.02	0.263167
$327$	12466.4	2.10824
$328$	−1089.71	−0.183442
$329$	69.2991	0.0116127
$330$	1134.57	0.189261
$331$	−7067.34	−1.17358	−0.586792	−	0.809738i	$-0.699609\pi$
$331$	−7067.34	−1.17358	−0.586792	+	0.809738i	$0.699609\pi$
$332$	7845.76	1.29696
$333$	6347.54	1.04457
$334$	1085.30	0.177799
$335$	7192.40	1.17302
$336$	1283.87	0.208455
$337$	−5897.11	−0.953223	−0.476611	−	0.879114i	$-0.658135\pi$
$337$	−5897.11	−0.953223	−0.476611	+	0.879114i	$0.658135\pi$
$338$	1050.07	0.168984
$339$	8372.78	1.34144
$340$	0	0
$341$	−15.2714	−0.00242519
$342$	1222.79	0.193336
$343$	1550.87	0.244137
$344$	2275.64	0.356669
$345$	13122.3	2.04777
$346$	−1277.04	−0.198422
$347$	−9529.27	−1.47423	−0.737115	−	0.675767i	$-0.763812\pi$
$347$	−9529.27	−1.47423	−0.737115	+	0.675767i	$0.763812\pi$
$348$	−16797.6	−2.58749
$349$	−2516.87	−0.386031	−0.193016	−	0.981196i	$-0.561827\pi$
$349$	−2516.87	−0.386031	−0.193016	+	0.981196i	$0.561827\pi$
$350$	−13.1395	−0.00200668
$351$	−23433.9	−3.56356
$352$	−1884.95	−0.285421
$353$	9296.21	1.40166	0.700832	−	0.713327i	$-0.252812\pi$
$353$	9296.21	1.40166	0.700832	+	0.713327i	$0.252812\pi$
$354$	−627.834	−0.0942628
$355$	−2921.81	−0.436826
$356$	−12799.9	−1.90560
$357$	0	0
$358$	534.928	0.0789716
$359$	10477.8	1.54038	0.770192	−	0.637812i	$-0.220160\pi$
$359$	10477.8	1.54038	0.770192	+	0.637812i	$0.220160\pi$
$360$	−5276.29	−0.772458
$361$	−5010.30	−0.730472
$362$	−1194.98	−0.173499
$363$	7767.34	1.12308
$364$	1197.56	0.172443
$365$	8231.88	1.18048
$366$	1367.43	0.195291
$367$	−2779.47	−0.395332	−0.197666	−	0.980269i	$-0.563336\pi$
$367$	−2779.47	−0.395332	−0.197666	+	0.980269i	$0.563336\pi$
$368$	−6956.44	−0.985406
$369$	9790.84	1.38128
$370$	525.060	0.0737745
$371$	823.702	0.115268
$372$	49.9572	0.00696280
$373$	2548.58	0.353782	0.176891	−	0.984230i	$-0.443396\pi$
$373$	2548.58	0.353782	0.176891	+	0.984230i	$0.443396\pi$
$374$	0	0
$375$	12526.7	1.72500
$376$	215.133	0.0295071
$377$	−15255.6	−2.08409
$378$	354.486	0.0482349
$379$	11378.4	1.54213	0.771067	−	0.636754i	$-0.219723\pi$
$379$	11378.4	1.54213	0.771067	+	0.636754i	$0.219723\pi$
$380$	−3937.95	−0.531612
$381$	12402.0	1.66764
$382$	−1519.37	−0.203502
$383$	−633.266	−0.0844867	−0.0422433	−	0.999107i	$-0.513450\pi$
$383$	−633.266	−0.0844867	−0.0422433	+	0.999107i	$0.513450\pi$
$384$	8184.34	1.08764
$385$	606.852	0.0803326
$386$	−1344.50	−0.177289
$387$	−20446.3	−2.68564
$388$	−3741.21	−0.489513
$389$	12163.4	1.58537	0.792685	−	0.609632i	$-0.208683\pi$
$389$	12163.4	1.58537	0.792685	+	0.609632i	$0.208683\pi$
$390$	−3370.80	−0.437660
$391$	0	0
$392$	2388.92	0.307803
$393$	14499.9	1.86113
$394$	−732.537	−0.0936667
$395$	−9077.45	−1.15629
$396$	11243.1	1.42674
$397$	11911.8	1.50589	0.752944	−	0.658084i	$-0.228633\pi$
$397$	11911.8	1.50589	0.752944	+	0.658084i	$0.228633\pi$
$398$	−716.384	−0.0902239
$399$	931.962	0.116933
$400$	763.322	0.0954153
$401$	−7875.79	−0.980793	−0.490396	−	0.871499i	$-0.663148\pi$
$401$	−7875.79	−0.980793	−0.490396	+	0.871499i	$0.663148\pi$
$402$	−2608.62	−0.323647
$403$	45.3711	0.00560818
$404$	6349.26	0.781900
$405$	18701.5	2.29453
$406$	230.772	0.0282094
$407$	−2266.42	−0.276025
$408$	0	0
$409$	−4351.34	−0.526064	−0.263032	−	0.964787i	$-0.584722\pi$
$409$	−4351.34	−0.526064	−0.263032	+	0.964787i	$0.584722\pi$
$410$	809.885	0.0975545
$411$	24906.9	2.98921
$412$	4241.51	0.507194
$413$	−335.812	−0.0400102
$414$	−3340.02	−0.396505
$415$	−11811.9	−1.39717
$416$	5600.17	0.660026
$417$	−2216.57	−0.260301
$418$	−436.602	−0.0510883
$419$	2066.20	0.240908	0.120454	−	0.992719i	$-0.461565\pi$
$419$	2066.20	0.240908	0.120454	+	0.992719i	$0.461565\pi$
$420$	−1985.19	−0.230637
$421$	10563.5	1.22289	0.611443	−	0.791289i	$-0.290589\pi$
$421$	10563.5	1.22289	0.611443	+	0.791289i	$0.290589\pi$
$422$	1916.74	0.221103
$423$	−1932.94	−0.222181
$424$	2557.11	0.292888
$425$	0	0
$426$	1059.71	0.120524
$427$	731.399	0.0828920
$428$	−1339.25	−0.151250
$429$	14550.1	1.63749
$430$	−1691.29	−0.189677
$431$	4347.98	0.485928	0.242964	−	0.970035i	$-0.421880\pi$
$431$	4347.98	0.485928	0.242964	+	0.970035i	$0.421880\pi$
$432$	−20593.4	−2.29352
$433$	949.003	0.105326	0.0526630	−	0.998612i	$-0.483229\pi$
$433$	949.003	0.105326	0.0526630	+	0.998612i	$0.483229\pi$
$434$	−0.686331	−7.59100e−5 0
$435$	25289.1	2.78740
$436$	10218.8	1.12246
$437$	−5049.67	−0.552765
$438$	−2985.62	−0.325704
$439$	−7256.78	−0.788946	−0.394473	−	0.918908i	$-0.629073\pi$
$439$	−7256.78	−0.788946	−0.394473	+	0.918908i	$0.629073\pi$
$440$	1883.92	0.204119
$441$	−21464.1	−2.31769
$442$	0	0
$443$	−3674.08	−0.394043	−0.197021	−	0.980399i	$-0.563127\pi$
$443$	−3674.08	−0.394043	−0.197021	+	0.980399i	$0.563127\pi$
$444$	7414.12	0.792475
$445$	19270.4	2.05282
$446$	−625.213	−0.0663782
$447$	−4089.19	−0.432689
$448$	994.717	0.104902
$449$	13012.3	1.36769	0.683843	−	0.729630i	$-0.260307\pi$
$449$	13012.3	1.36769	0.683843	+	0.729630i	$0.260307\pi$
$450$	366.497	0.0383929
$451$	−3495.86	−0.364997
$452$	6863.23	0.714201
$453$	13064.3	1.35500
$454$	721.708	0.0746067
$455$	−1802.95	−0.185766
$456$	2893.20	0.297119
$457$	−13.1283	−0.00134380	−0.000671900	−	1.00000i	$-0.500214\pi$
$457$	−13.1283	−0.00134380	−0.000671900		1.00000i	$0.500214\pi$
$458$	−1132.60	−0.115553
$459$	0	0
$460$	10756.4	1.09026
$461$	−14382.6	−1.45307	−0.726537	−	0.687128i	$-0.758871\pi$
$461$	−14382.6	−1.45307	−0.726537	+	0.687128i	$0.758871\pi$
$462$	−220.099	−0.0221644
$463$	−13264.3	−1.33141	−0.665705	−	0.746215i	$-0.731869\pi$
$463$	−13264.3	−1.33141	−0.665705	+	0.746215i	$0.731869\pi$
$464$	−13406.4	−1.34132
$465$	−75.2114	−0.00750075
$466$	2099.01	0.208659
$467$	12992.0	1.28736	0.643681	−	0.765294i	$-0.277406\pi$
$467$	12992.0	1.28736	0.643681	+	0.765294i	$0.277406\pi$
$468$	−33403.3	−3.29929
$469$	−1395.28	−0.137373
$470$	−159.890	−0.0156919
$471$	−5861.92	−0.573467
$472$	−1042.50	−0.101663
$473$	7300.43	0.709671
$474$	3292.30	0.319030
$475$	554.094	0.0535234
$476$	0	0
$477$	−22975.3	−2.20538
$478$	−2834.29	−0.271208
$479$	−8697.74	−0.829665	−0.414833	−	0.909898i	$-0.636160\pi$
$479$	−8697.74	−0.829665	−0.414833	+	0.909898i	$0.636160\pi$
$480$	−9283.37	−0.882763
$481$	6733.50	0.638298
$482$	1986.58	0.187730
$483$	−2545.63	−0.239814
$484$	6366.94	0.597947
$485$	5632.46	0.527333
$486$	−2581.24	−0.240920
$487$	−1219.66	−0.113487	−0.0567435	−	0.998389i	$-0.518072\pi$
$487$	−1219.66	−0.113487	−0.0567435	+	0.998389i	$0.518072\pi$
$488$	2270.57	0.210623
$489$	−32930.2	−3.04531
$490$	−1775.48	−0.163690
$491$	11340.1	1.04231	0.521154	−	0.853463i	$-0.325502\pi$
$491$	11340.1	1.04231	0.521154	+	0.853463i	$0.325502\pi$
$492$	11436.0	1.04792
$493$	0	0
$494$	1297.14	0.118140
$495$	−16926.7	−1.53697
$496$	39.8714	0.00360944
$497$	566.811	0.0511568
$498$	4284.07	0.385490
$499$	7357.73	0.660074	0.330037	−	0.943968i	$-0.392939\pi$
$499$	7357.73	0.660074	0.330037	+	0.943968i	$0.392939\pi$
$500$	10268.2	0.918414
$501$	−23072.1	−2.05745
$502$	933.343	0.0829824
$503$	−4549.92	−0.403321	−0.201661	−	0.979455i	$-0.564634\pi$
$503$	−4549.92	−0.403321	−0.201661	+	0.979455i	$0.564634\pi$
$504$	1023.56	0.0904626
$505$	−9558.93	−0.842310
$506$	1192.57	0.104775
$507$	−22323.2	−1.95544
$508$	10166.0	0.887879
$509$	−13630.1	−1.18692	−0.593461	−	0.804863i	$-0.702239\pi$
$509$	−13630.1	−1.18692	−0.593461	+	0.804863i	$0.702239\pi$
$510$	0	0
$511$	−1596.93	−0.138246
$512$	8272.35	0.714042
$513$	−14948.7	−1.28655
$514$	−240.411	−0.0206305
$515$	−6385.66	−0.546380
$516$	−23881.9	−2.03748
$517$	690.165	0.0587106
$518$	−101.858	−0.00863974
$519$	27148.2	2.29609
$520$	−5597.11	−0.472018
$521$	−14004.2	−1.17761	−0.588805	−	0.808275i	$-0.700402\pi$
$521$	−14004.2	−1.17761	−0.588805	+	0.808275i	$0.700402\pi$
$522$	−6436.84	−0.539718
$523$	−5652.21	−0.472570	−0.236285	−	0.971684i	$-0.575930\pi$
$523$	−5652.21	−0.472570	−0.236285	+	0.971684i	$0.575930\pi$
$524$	11885.7	0.990891
$525$	279.329	0.0232208
$526$	2961.78	0.245513
$527$	0	0
$528$	12786.4	1.05389
$529$	1626.06	0.133645
$530$	−1900.48	−0.155758
$531$	9366.69	0.765499
$532$	763.935	0.0622571
$533$	10386.2	0.844044
$534$	−6989.20	−0.566390
$535$	2016.26	0.162935
$536$	−4331.52	−0.349055
$537$	−11371.9	−0.913842
$538$	276.355	0.0221459
$539$	7663.84	0.612440
$540$	31842.6	2.53757
$541$	−8809.75	−0.700112	−0.350056	−	0.936729i	$-0.613837\pi$
$541$	−8809.75	−0.700112	−0.350056	+	0.936729i	$0.613837\pi$
$542$	−2386.55	−0.189135
$543$	25403.7	2.00769
$544$	0	0
$545$	−15384.6	−1.20918
$546$	653.913	0.0512544
$547$	−2198.83	−0.171874	−0.0859372	−	0.996301i	$-0.527388\pi$
$547$	−2198.83	−0.171874	−0.0859372	+	0.996301i	$0.527388\pi$
$548$	20416.3	1.59150
$549$	−20400.7	−1.58594
$550$	−130.859	−0.0101452
$551$	−9731.65	−0.752418
$552$	−7902.70	−0.609350
$553$	1760.96	0.135414
$554$	1112.99	0.0853546
$555$	−11162.1	−0.853702
$556$	−1816.93	−0.138588
$557$	19799.3	1.50614	0.753072	−	0.657938i	$-0.228571\pi$
$557$	19799.3	1.50614	0.753072	+	0.657938i	$0.228571\pi$
$558$	19.1436	0.00145235
$559$	−21689.5	−1.64109
$560$	−1584.41	−0.119560
$561$	0	0
$562$	−2216.45	−0.166362
$563$	−20671.9	−1.54745	−0.773726	−	0.633521i	$-0.781609\pi$
$563$	−20671.9	−1.54745	−0.773726	+	0.633521i	$0.781609\pi$
$564$	−2257.73	−0.168560
$565$	−10332.7	−0.769381
$566$	3677.78	0.273125
$567$	−3627.96	−0.268712
$568$	1759.62	0.129986
$569$	−10735.1	−0.790928	−0.395464	−	0.918481i	$-0.629416\pi$
$569$	−10735.1	−0.790928	−0.395464	+	0.918481i	$0.629416\pi$
$570$	−2150.26	−0.158008
$571$	−1413.36	−0.103586	−0.0517929	−	0.998658i	$-0.516494\pi$
$571$	−1413.36	−0.103586	−0.0517929	+	0.998658i	$0.516494\pi$
$572$	11926.8	0.871825
$573$	32299.8	2.35488
$574$	−157.112	−0.0114246
$575$	−1513.50	−0.109769
$576$	−27745.3	−2.00704
$577$	13903.6	1.00314	0.501572	−	0.865116i	$-0.332755\pi$
$577$	13903.6	1.00314	0.501572	+	0.865116i	$0.332755\pi$
$578$	0	0
$579$	28582.4	2.05155
$580$	20729.6	1.48405
$581$	2291.43	0.163623
$582$	−2042.84	−0.145495
$583$	8203.42	0.582763
$584$	−4957.53	−0.351274
$585$	50289.2	3.55419
$586$	−330.220	−0.0232786
$587$	7153.64	0.503002	0.251501	−	0.967857i	$-0.419076\pi$
$587$	7153.64	0.503002	0.251501	+	0.967857i	$0.419076\pi$
$588$	−25070.7	−1.75833
$589$	28.9426	0.00202472
$590$	774.800	0.0540644
$591$	15572.8	1.08389
$592$	5917.30	0.410810
$593$	−22686.9	−1.57106	−0.785530	−	0.618824i	$-0.787610\pi$
$593$	−22686.9	−1.57106	−0.785530	+	0.618824i	$0.787610\pi$
$594$	3530.40	0.243862
$595$	0	0
$596$	−3351.94	−0.230370
$597$	15229.4	1.04405
$598$	−3543.11	−0.242289
$599$	9190.22	0.626882	0.313441	−	0.949608i	$-0.398518\pi$
$599$	9190.22	0.626882	0.313441	+	0.949608i	$0.398518\pi$
$600$	867.154	0.0590024
$601$	−12350.7	−0.838260	−0.419130	−	0.907926i	$-0.637665\pi$
$601$	−12350.7	−0.838260	−0.419130	+	0.907926i	$0.637665\pi$
$602$	328.098	0.0222131
$603$	38918.1	2.62830
$604$	10708.9	0.721423
$605$	−9585.54	−0.644145
$606$	3466.93	0.232400
$607$	22662.6	1.51540	0.757698	−	0.652606i	$-0.226324\pi$
$607$	22662.6	1.51540	0.757698	+	0.652606i	$0.226324\pi$
$608$	3572.40	0.238289
$609$	−4905.91	−0.326432
$610$	−1687.52	−0.112009
$611$	−2050.47	−0.135766
$612$	0	0
$613$	5314.94	0.350193	0.175097	−	0.984551i	$-0.443976\pi$
$613$	5314.94	0.350193	0.175097	+	0.984551i	$0.443976\pi$
$614$	2683.06	0.176351
$615$	−17217.1	−1.12888
$616$	−365.468	−0.0239044
$617$	7956.05	0.519122	0.259561	−	0.965727i	$-0.416422\pi$
$617$	7956.05	0.519122	0.259561	+	0.965727i	$0.416422\pi$
$618$	2316.02	0.150751
$619$	−13874.9	−0.900933	−0.450467	−	0.892793i	$-0.648742\pi$
$619$	−13874.9	−0.900933	−0.450467	+	0.892793i	$0.648742\pi$
$620$	−61.6513	−0.00399351
$621$	40832.1	2.63854
$622$	−4234.54	−0.272974
$623$	−3738.33	−0.240406
$624$	−37988.2	−2.43709
$625$	−17069.8	−1.09247
$626$	2092.45	0.133596
$627$	9281.60	0.591183
$628$	−4805.06	−0.305323
$629$	0	0
$630$	−760.727	−0.0481081
$631$	−23668.0	−1.49320	−0.746598	−	0.665276i	$-0.768314\pi$
$631$	−23668.0	−1.49320	−0.746598	+	0.665276i	$0.768314\pi$
$632$	5466.76	0.344076
$633$	−40747.5	−2.55856
$634$	−310.148	−0.0194283
$635$	−15305.1	−0.956477
$636$	−26835.8	−1.67313
$637$	−22769.2	−1.41625
$638$	2298.30	0.142619
$639$	−15809.9	−0.978762
$640$	−10100.2	−0.623818
$641$	−18274.3	−1.12604	−0.563021	−	0.826442i	$-0.690361\pi$
$641$	−18274.3	−1.12604	−0.563021	+	0.826442i	$0.690361\pi$
$642$	−731.277	−0.0449552
$643$	19527.2	1.19763	0.598815	−	0.800887i	$-0.295639\pi$
$643$	19527.2	1.19763	0.598815	+	0.800887i	$0.295639\pi$
$644$	−2086.67	−0.127681
$645$	35954.6	2.19490
$646$	0	0
$647$	−4471.27	−0.271690	−0.135845	−	0.990730i	$-0.543375\pi$
$647$	−4471.27	−0.271690	−0.135845	+	0.990730i	$0.543375\pi$
$648$	−11262.7	−0.682778
$649$	−3344.42	−0.202280
$650$	388.781	0.0234604
$651$	14.5905	0.000878413 0
$652$	−26993.1	−1.62137
$653$	−10869.7	−0.651399	−0.325699	−	0.945473i	$-0.605600\pi$
$653$	−10869.7	−0.651399	−0.325699	+	0.945473i	$0.605600\pi$
$654$	5579.84	0.333622
$655$	−17894.1	−1.06745
$656$	9127.21	0.543228
$657$	44542.6	2.64501
$658$	31.0176	0.00183768
$659$	−3827.54	−0.226252	−0.113126	−	0.993581i	$-0.536086\pi$
$659$	−3827.54	−0.226252	−0.113126	+	0.993581i	$0.536086\pi$
$660$	−19771.0	−1.16604
$661$	15347.3	0.903087	0.451543	−	0.892249i	$-0.350874\pi$
$661$	15347.3	0.903087	0.451543	+	0.892249i	$0.350874\pi$
$662$	−3163.27	−0.185716
$663$	0	0
$664$	7113.57	0.415753
$665$	−1150.12	−0.0670672
$666$	2841.09	0.165301
$667$	26581.8	1.54310
$668$	−18912.3	−1.09542
$669$	13291.2	0.768114
$670$	3219.25	0.185627
$671$	7284.16	0.419079
$672$	1800.91	0.103380
$673$	26133.5	1.49684	0.748418	−	0.663227i	$-0.230814\pi$
$673$	26133.5	1.49684	0.748418	+	0.663227i	$0.230814\pi$
$674$	−2639.49	−0.150845
$675$	−4480.45	−0.255486
$676$	−18298.5	−1.04111
$677$	19539.0	1.10922	0.554612	−	0.832109i	$-0.312867\pi$
$677$	19539.0	1.10922	0.554612	+	0.832109i	$0.312867\pi$
$678$	3747.57	0.212278
$679$	−1092.66	−0.0617561
$680$	0	0
$681$	−15342.6	−0.863332
$682$	−6.83531	−0.000383779 0
$683$	−16057.8	−0.899612	−0.449806	−	0.893126i	$-0.648507\pi$
$683$	−16057.8	−0.899612	−0.449806	+	0.893126i	$0.648507\pi$
$684$	−21308.2	−1.19114
$685$	−30737.1	−1.71446
$686$	694.152	0.0386339
$687$	24077.7	1.33715
$688$	−19060.4	−1.05621
$689$	−24372.3	−1.34762
$690$	5873.40	0.324053
$691$	14698.6	0.809206	0.404603	−	0.914493i	$-0.367410\pi$
$691$	14698.6	0.809206	0.404603	+	0.914493i	$0.367410\pi$
$692$	22253.6	1.22248
$693$	3283.67	0.179995
$694$	−4265.20	−0.233292
$695$	2735.43	0.149296
$696$	−15230.0	−0.829441
$697$	0	0
$698$	−1126.53	−0.0610883
$699$	−44622.3	−2.41455
$700$	228.968	0.0123631
$701$	−7042.75	−0.379459	−0.189730	−	0.981836i	$-0.560761\pi$
$701$	−7042.75	−0.379459	−0.189730	+	0.981836i	$0.560761\pi$
$702$	−10488.8	−0.563923
$703$	4295.36	0.230445
$704$	9906.60	0.530354
$705$	3399.06	0.181583
$706$	4160.89	0.221809
$707$	1854.37	0.0986431
$708$	10940.6	0.580752
$709$	−5951.66	−0.315260	−0.157630	−	0.987498i	$-0.550385\pi$
$709$	−5951.66	−0.315260	−0.157630	+	0.987498i	$0.550385\pi$
$710$	−1307.77	−0.0691265
$711$	−49118.0	−2.59082
$712$	−11605.3	−0.610855
$713$	−79.0561	−0.00415242
$714$	0	0
$715$	−17956.0	−0.939182
$716$	−9321.61	−0.486543
$717$	60253.3	3.13835
$718$	4689.76	0.243761
$719$	34823.3	1.80625	0.903123	−	0.429381i	$-0.141268\pi$
$719$	34823.3	1.80625	0.903123	+	0.429381i	$0.141268\pi$
$720$	44193.4	2.28749
$721$	1238.77	0.0639866
$722$	−2242.56	−0.115595
$723$	−42232.1	−2.17238
$724$	20823.6	1.06892
$725$	−2916.79	−0.149416
$726$	3476.58	0.177725
$727$	−3241.15	−0.165348	−0.0826738	−	0.996577i	$-0.526346\pi$
$727$	−3241.15	−0.165348	−0.0826738	+	0.996577i	$0.526346\pi$
$728$	1085.80	0.0552781
$729$	11872.9	0.603204
$730$	3684.51	0.186808
$731$	0	0
$732$	−23828.7	−1.20319
$733$	18578.8	0.936185	0.468093	−	0.883679i	$-0.344941\pi$
$733$	18578.8	0.936185	0.468093	+	0.883679i	$0.344941\pi$
$734$	−1244.06	−0.0625601
$735$	37744.4	1.89418
$736$	−9757.92	−0.488698
$737$	−13895.9	−0.694519
$738$	4382.28	0.218583
$739$	30393.0	1.51289	0.756444	−	0.654058i	$-0.226935\pi$
$739$	30393.0	1.51289	0.756444	+	0.654058i	$0.226935\pi$
$740$	−9149.64	−0.454524
$741$	−27575.6	−1.36709
$742$	368.681	0.0182408
$743$	−37449.0	−1.84908	−0.924542	−	0.381081i	$-0.875552\pi$
$743$	−37449.0	−1.84908	−0.924542	+	0.381081i	$0.875552\pi$
$744$	45.2950	0.00223198
$745$	5046.40	0.248169
$746$	1140.72	0.0559849
$747$	−63914.3	−3.13052
$748$	0	0
$749$	−391.140	−0.0190814
$750$	5606.80	0.272975
$751$	5541.28	0.269247	0.134623	−	0.990897i	$-0.457018\pi$
$751$	5541.28	0.269247	0.134623	+	0.990897i	$0.457018\pi$
$752$	−1801.92	−0.0873795
$753$	−19841.7	−0.960253
$754$	−6828.23	−0.329801
$755$	−16122.5	−0.777160
$756$	−6177.25	−0.297175
$757$	13531.4	0.649680	0.324840	−	0.945769i	$-0.394690\pi$
$757$	13531.4	0.649680	0.324840	+	0.945769i	$0.394690\pi$
$758$	5092.85	0.244038
$759$	−25352.5	−1.21243
$760$	−3570.45	−0.170413
$761$	−37110.8	−1.76776	−0.883879	−	0.467715i	$-0.845077\pi$
$761$	−37110.8	−1.76776	−0.883879	+	0.467715i	$0.845077\pi$
$762$	5551.00	0.263899
$763$	2984.50	0.141607
$764$	26476.4	1.25377
$765$	0	0
$766$	−283.444	−0.0133698
$767$	9936.24	0.467766
$768$	−29576.6	−1.38965
$769$	−820.351	−0.0384689	−0.0192345	−	0.999815i	$-0.506123\pi$
$769$	−820.351	−0.0384689	−0.0192345	+	0.999815i	$0.506123\pi$
$770$	271.621	0.0127124
$771$	5110.84	0.238732
$772$	23429.2	1.09227
$773$	−25113.2	−1.16851	−0.584255	−	0.811570i	$-0.698613\pi$
$773$	−25113.2	−1.16851	−0.584255	+	0.811570i	$0.698613\pi$
$774$	−9151.55	−0.424994
$775$	8.67473	0.000402072 0
$776$	−3392.07	−0.156918
$777$	2165.37	0.0999771
$778$	5444.21	0.250880
$779$	6625.43	0.304725
$780$	58739.3	2.69642
$781$	5644.99	0.258634
$782$	0	0
$783$	78691.0	3.59155
$784$	−20009.2	−0.911499
$785$	7234.10	0.328912
$786$	6490.00	0.294517
$787$	20784.0	0.941384	0.470692	−	0.882298i	$-0.344004\pi$
$787$	20784.0	0.941384	0.470692	+	0.882298i	$0.344004\pi$
$788$	12765.1	0.577080
$789$	−62963.7	−2.84102
$790$	−4062.97	−0.182980
$791$	2004.47	0.0901023
$792$	10193.9	0.457354
$793$	−21641.2	−0.969105
$794$	5331.62	0.238302
$795$	40401.8	1.80240
$796$	12483.7	0.555868
$797$	4974.23	0.221074	0.110537	−	0.993872i	$-0.464743\pi$
$797$	4974.23	0.221074	0.110537	+	0.993872i	$0.464743\pi$
$798$	417.137	0.0185044
$799$	0	0
$800$	1070.73	0.0473198
$801$	104272.	4.59960
$802$	−3525.12	−0.155207
$803$	−15904.1	−0.698935
$804$	45457.5	1.99398
$805$	3141.52	0.137545
$806$	20.3076	0.000887477 0
$807$	−5874.95	−0.256268
$808$	5756.73	0.250645
$809$	−27460.1	−1.19338	−0.596692	−	0.802471i	$-0.703519\pi$
$809$	−27460.1	−1.19338	−0.596692	+	0.802471i	$0.703519\pi$
$810$	8370.59	0.363102
$811$	−14356.6	−0.621612	−0.310806	−	0.950473i	$-0.600599\pi$
$811$	−14356.6	−0.621612	−0.310806	+	0.950473i	$0.600599\pi$
$812$	−4021.40	−0.173798
$813$	50735.0	2.18863
$814$	−1014.43	−0.0436801
$815$	40638.6	1.74664
$816$	0	0
$817$	−13835.9	−0.592482
$818$	−1947.62	−0.0832480
$819$	−9755.76	−0.416232
$820$	−14113.0	−0.601033
$821$	15953.0	0.678155	0.339077	−	0.940758i	$-0.389885\pi$
$821$	15953.0	0.678155	0.339077	+	0.940758i	$0.389885\pi$
$822$	11148.1	0.473033
$823$	17581.1	0.744641	0.372321	−	0.928104i	$-0.378562\pi$
$823$	17581.1	0.744641	0.372321	+	0.928104i	$0.378562\pi$
$824$	3845.67	0.162585
$825$	2781.90	0.117398
$826$	−150.306	−0.00633149
$827$	−39492.2	−1.66056	−0.830278	−	0.557349i	$-0.811818\pi$
$827$	−39492.2	−1.66056	−0.830278	+	0.557349i	$0.811818\pi$
$828$	58202.9	2.44286
$829$	15789.1	0.661494	0.330747	−	0.943720i	$-0.392699\pi$
$829$	15789.1	0.661494	0.330747	+	0.943720i	$0.392699\pi$
$830$	−5286.90	−0.221098
$831$	−23660.7	−0.987704
$832$	−29432.4	−1.22642
$833$	0	0
$834$	−992.112	−0.0411919
$835$	28472.8	1.18005
$836$	7608.19	0.314755
$837$	−234.032	−0.00966469
$838$	924.812	0.0381230
$839$	−9439.37	−0.388419	−0.194209	−	0.980960i	$-0.562214\pi$
$839$	−9439.37	−0.388419	−0.194209	+	0.980960i	$0.562214\pi$
$840$	−1799.93	−0.0739326
$841$	26839.0	1.10046
$842$	4728.13	0.193518
$843$	47118.8	1.92510
$844$	−33401.0	−1.36222
$845$	27548.7	1.12154
$846$	−865.164	−0.0351595
$847$	1859.53	0.0754359
$848$	−21418.0	−0.867331
$849$	−78185.0	−3.16054
$850$	0	0
$851$	−11732.7	−0.472610
$852$	−18466.4	−0.742546
$853$	−2324.12	−0.0932898	−0.0466449	−	0.998912i	$-0.514853\pi$
$853$	−2324.12	−0.0932898	−0.0466449	+	0.998912i	$0.514853\pi$
$854$	327.367	0.0131174
$855$	32079.9	1.28317
$856$	−1214.26	−0.0484844
$857$	22464.0	0.895399	0.447699	−	0.894184i	$-0.352244\pi$
$857$	22464.0	0.895399	0.447699	+	0.894184i	$0.352244\pi$
$858$	6512.46	0.259128
$859$	−1314.36	−0.0522064	−0.0261032	−	0.999659i	$-0.508310\pi$
$859$	−1314.36	−0.0522064	−0.0261032	+	0.999659i	$0.508310\pi$
$860$	29472.2	1.16860
$861$	3340.00	0.132203
$862$	1946.11	0.0768966
$863$	−15380.5	−0.606674	−0.303337	−	0.952883i	$-0.598101\pi$
$863$	−15380.5	−0.606674	−0.303337	+	0.952883i	$0.598101\pi$
$864$	−28886.7	−1.13744
$865$	−33503.1	−1.31693
$866$	424.764	0.0166675
$867$	0	0
$868$	11.9599	0.000467681 0
$869$	17537.8	0.684614
$870$	11319.1	0.441097
$871$	41284.5	1.60605
$872$	9265.14	0.359813
$873$	30477.2	1.18155
$874$	−2260.18	−0.0874734
$875$	2998.93	0.115865
$876$	52027.2	2.00666
$877$	14688.9	0.565574	0.282787	−	0.959183i	$-0.408741\pi$
$877$	14688.9	0.565574	0.282787	+	0.959183i	$0.408741\pi$
$878$	−3248.06	−0.124848
$879$	7020.06	0.269375
$880$	−15779.4	−0.604460
$881$	−9512.25	−0.363764	−0.181882	−	0.983320i	$-0.558219\pi$
$881$	−9512.25	−0.363764	−0.181882	+	0.983320i	$0.558219\pi$
$882$	−9607.11	−0.366767
$883$	14662.1	0.558798	0.279399	−	0.960175i	$-0.409865\pi$
$883$	14662.1	0.558798	0.279399	+	0.960175i	$0.409865\pi$
$884$	0	0
$885$	−16471.2	−0.625621
$886$	−1644.48	−0.0623561
$887$	27847.1	1.05413	0.527065	−	0.849825i	$-0.323292\pi$
$887$	27847.1	1.05413	0.527065	+	0.849825i	$0.323292\pi$
$888$	6722.21	0.254034
$889$	2969.08	0.112013
$890$	8625.25	0.324853
$891$	−36131.6	−1.35853
$892$	10894.9	0.408956
$893$	−1308.01	−0.0490157
$894$	−1830.28	−0.0684717
$895$	14033.8	0.524134
$896$	1959.36	0.0730554
$897$	75322.0	2.80371
$898$	5824.20	0.216432
$899$	−152.356	−0.00565222
$900$	−6386.54	−0.236538
$901$	0	0
$902$	−1564.71	−0.0577597
$903$	−6974.95	−0.257045
$904$	6222.72	0.228943
$905$	−31350.2	−1.15151
$906$	5847.46	0.214425
$907$	141.986	0.00519799	0.00259899	−	0.999997i	$-0.499173\pi$
$907$	141.986	0.00519799	0.00259899	+	0.999997i	$0.499173\pi$
$908$	−12576.4	−0.459651
$909$	−51723.3	−1.88730
$910$	−806.983	−0.0293969
$911$	32439.3	1.17976	0.589881	−	0.807490i	$-0.299175\pi$
$911$	32439.3	1.17976	0.589881	+	0.807490i	$0.299175\pi$
$912$	−24233.0	−0.879862
$913$	22820.9	0.827230
$914$	−5.87610	−0.000212652 0
$915$	35874.5	1.29615
$916$	19736.6	0.711918
$917$	3471.32	0.125009
$918$	0	0
$919$	11802.3	0.423638	0.211819	−	0.977309i	$-0.432061\pi$
$919$	11802.3	0.423638	0.211819	+	0.977309i	$0.432061\pi$
$920$	9752.59	0.349493
$921$	−57038.5	−2.04070
$922$	−6437.53	−0.229944
$923$	−16771.2	−0.598083
$924$	3835.43	0.136555
$925$	1287.41	0.0457620
$926$	−5936.95	−0.210691
$927$	−34552.8	−1.22423
$928$	−18805.3	−0.665210
$929$	30089.9	1.06267	0.531334	−	0.847163i	$-0.321691\pi$
$929$	30089.9	1.06267	0.531334	+	0.847163i	$0.321691\pi$
$930$	−33.6639	−0.00118697
$931$	−14524.7	−0.511307
$932$	−36577.2	−1.28554
$933$	90020.9	3.15879
$934$	5815.09	0.203721
$935$	0	0
$936$	−30285.9	−1.05761
$937$	−34961.5	−1.21894	−0.609468	−	0.792810i	$-0.708617\pi$
$937$	−34961.5	−1.21894	−0.609468	+	0.792810i	$0.708617\pi$
$938$	−624.512	−0.0217389
$939$	−44482.8	−1.54594
$940$	2786.23	0.0966775
$941$	−8933.80	−0.309494	−0.154747	−	0.987954i	$-0.549456\pi$
$941$	−8933.80	−0.309494	−0.154747	+	0.987954i	$0.549456\pi$
$942$	−2623.74	−0.0907494
$943$	−18097.2	−0.624948
$944$	8731.81	0.301055
$945$	9299.95	0.320135
$946$	3267.60	0.112303
$947$	−17816.2	−0.611350	−0.305675	−	0.952136i	$-0.598882\pi$
$947$	−17816.2	−0.611350	−0.305675	+	0.952136i	$0.598882\pi$
$948$	−57371.4	−1.96554
$949$	47251.1	1.61626
$950$	248.007	0.00846991
$951$	6593.35	0.224820
$952$	0	0
$953$	36249.3	1.23214	0.616070	−	0.787691i	$-0.288724\pi$
$953$	36249.3	1.23214	0.616070	+	0.787691i	$0.288724\pi$
$954$	−10283.5	−0.348994
$955$	−39860.7	−1.35064
$956$	49390.0	1.67091
$957$	−48858.9	−1.65035
$958$	−3893.02	−0.131292
$959$	5962.79	0.200781
$960$	48789.9	1.64030
$961$	−29790.5	−0.999985
$962$	3013.85	0.101009
$963$	10910.0	0.365076
$964$	−34617.9	−1.15661
$965$	−35273.1	−1.17666
$966$	−1139.40	−0.0379499
$967$	10020.3	0.333227	0.166613	−	0.986022i	$-0.446717\pi$
$967$	10020.3	0.333227	0.166613	+	0.986022i	$0.446717\pi$
$968$	5772.75	0.191677
$969$	0	0
$970$	2521.03	0.0834489
$971$	24562.5	0.811789	0.405894	−	0.913920i	$-0.366960\pi$
$971$	24562.5	0.811789	0.405894	+	0.913920i	$0.366960\pi$
$972$	44980.4	1.48431
$973$	−530.654	−0.0174841
$974$	−545.908	−0.0179590
$975$	−8264.99	−0.271479
$976$	−19017.9	−0.623718
$977$	−17102.8	−0.560048	−0.280024	−	0.959993i	$-0.590342\pi$
$977$	−17102.8	−0.560048	−0.280024	+	0.959993i	$0.590342\pi$
$978$	−14739.2	−0.481911
$979$	−37230.9	−1.21543
$980$	30939.3	1.00849
$981$	−83245.8	−2.70931
$982$	5075.73	0.164942
$983$	−51204.2	−1.66140	−0.830702	−	0.556718i	$-0.812061\pi$
$983$	−51204.2	−1.66140	−0.830702	+	0.556718i	$0.812061\pi$
$984$	10368.8	0.335919
$985$	−19218.1	−0.621665
$986$	0	0
$987$	−659.394	−0.0212652
$988$	−22603.9	−0.727859
$989$	37792.5	1.21510
$990$	−7576.24	−0.243221
$991$	−19176.3	−0.614686	−0.307343	−	0.951599i	$-0.599440\pi$
$991$	−19176.3	−0.614686	−0.307343	+	0.951599i	$0.599440\pi$
$992$	55.9283	0.00179005
$993$	67247.0	2.14906
$994$	253.699	0.00809541
$995$	−18794.4	−0.598815
$996$	−74653.9	−2.37500
$997$	−18251.7	−0.579775	−0.289888	−	0.957061i	$-0.593618\pi$
$997$	−18251.7	−0.579775	−0.289888	+	0.957061i	$0.593618\pi$
$998$	3293.24	0.104455
$999$	−34732.6	−1.09999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.7	✓	12
17.4	even	4		289.4.b.f.288.11		24
17.13	even	4		289.4.b.f.288.12		24
17.16	even	2		289.4.a.i.1.7	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.7	✓	12	1.1	even	1	trivial
289.4.a.i.1.7	yes	12	17.16	even	2
289.4.b.f.288.11		24	17.4	even	4
289.4.b.f.288.12		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)

\(f(q)\)	\(=\)	\(q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +O(q^{10})\)	\(q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +5.25584 q^{10} -22.6868 q^{11} +74.2152 q^{12} +67.4022 q^{13} -1.01960 q^{14} -111.732 q^{15} +59.2321 q^{16} +28.4393 q^{18} +42.9965 q^{19} -91.5878 q^{20} +21.6753 q^{21} -10.1544 q^{22} -117.444 q^{23} +67.2892 q^{24} +12.8870 q^{25} +30.1686 q^{26} -347.673 q^{27} +17.7674 q^{28} -226.336 q^{29} -50.0103 q^{30} +0.673139 q^{31} +83.0858 q^{32} +215.869 q^{33} -26.7491 q^{35} -495.581 q^{36} +99.9003 q^{37} +19.2448 q^{38} -641.345 q^{39} -83.0405 q^{40} +154.092 q^{41} +9.70165 q^{42} -321.792 q^{43} +176.949 q^{44} +746.106 q^{45} -52.5667 q^{46} -30.4214 q^{47} -563.604 q^{48} -337.811 q^{49} +5.76808 q^{50} -525.715 q^{52} -361.595 q^{53} -155.615 q^{54} -266.400 q^{55} +16.1093 q^{56} -409.119 q^{57} -101.306 q^{58} +147.417 q^{59} +871.475 q^{60} -321.075 q^{61} +0.301290 q^{62} -144.739 q^{63} -436.668 q^{64} +791.473 q^{65} +96.6208 q^{66} +612.509 q^{67} +1117.50 q^{69} -11.9726 q^{70} -248.823 q^{71} -449.331 q^{72} +701.031 q^{73} +44.7144 q^{74} -122.622 q^{75} -335.358 q^{76} +51.6798 q^{77} -287.059 q^{78} -773.040 q^{79} +695.534 q^{80} +1592.63 q^{81} +68.9702 q^{82} -1005.91 q^{83} -169.060 q^{84} -144.031 q^{86} +2153.63 q^{87} +160.436 q^{88} +1641.08 q^{89} +333.949 q^{90} -153.540 q^{91} +916.023 q^{92} -6.40505 q^{93} -13.6163 q^{94} +504.887 q^{95} -790.577 q^{96} +479.663 q^{97} -151.201 q^{98} -1441.49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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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