LMFDB - Embedded newform 2401.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,2,Mod(1,2401)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2401.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:	$19.1720815253$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39799 q^{2} +1.98350 q^{3} -0.0456113 q^{4} -3.04490 q^{5} +2.77292 q^{6} -2.85975 q^{8} +0.934270 q^{9} +O(q^{10})$	\(q+1.39799 q^{2} +1.98350 q^{3} -0.0456113 q^{4} -3.04490 q^{5} +2.77292 q^{6} -2.85975 q^{8} +0.934270 q^{9} -4.25676 q^{10} +5.14272 q^{11} -0.0904700 q^{12} -1.65864 q^{13} -6.03957 q^{15} -3.90670 q^{16} -2.92958 q^{17} +1.30610 q^{18} +0.341540 q^{19} +0.138882 q^{20} +7.18949 q^{22} -3.56937 q^{23} -5.67232 q^{24} +4.27145 q^{25} -2.31876 q^{26} -4.09737 q^{27} -6.00831 q^{29} -8.44328 q^{30} -2.61292 q^{31} +0.257966 q^{32} +10.2006 q^{33} -4.09553 q^{34} -0.0426133 q^{36} -1.61257 q^{37} +0.477471 q^{38} -3.28990 q^{39} +8.70768 q^{40} -3.25689 q^{41} -4.62185 q^{43} -0.234566 q^{44} -2.84476 q^{45} -4.98997 q^{46} -10.2102 q^{47} -7.74893 q^{48} +5.97146 q^{50} -5.81081 q^{51} +0.0756526 q^{52} +2.90418 q^{53} -5.72811 q^{54} -15.6591 q^{55} +0.677444 q^{57} -8.39959 q^{58} -9.31144 q^{59} +0.275473 q^{60} +5.16024 q^{61} -3.65285 q^{62} +8.17403 q^{64} +5.05039 q^{65} +14.2604 q^{66} +11.9841 q^{67} +0.133622 q^{68} -7.07985 q^{69} +1.85724 q^{71} -2.67178 q^{72} -13.1179 q^{73} -2.25437 q^{74} +8.47241 q^{75} -0.0155781 q^{76} -4.59927 q^{78} +13.8387 q^{79} +11.8955 q^{80} -10.9299 q^{81} -4.55311 q^{82} -0.874048 q^{83} +8.92028 q^{85} -6.46133 q^{86} -11.9175 q^{87} -14.7069 q^{88} -0.475767 q^{89} -3.97696 q^{90} +0.162804 q^{92} -5.18273 q^{93} -14.2737 q^{94} -1.03996 q^{95} +0.511675 q^{96} +7.70896 q^{97} +4.80469 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 7 q^{3} + 23 q^{4} - 14 q^{5} - 14 q^{6} - 3 q^{8} + 15 q^{9}+O(q^{10}) $ 24 * q - q^2 - 7 * q^3 + 23 * q^4 - 14 * q^5 - 14 * q^6 - 3 * q^8 + 15 * q^9	$ 24 q - q^{2} - 7 q^{3} + 23 q^{4} - 14 q^{5} - 14 q^{6} - 3 q^{8} + 15 q^{9} - 14 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 15 q^{15} + 17 q^{16} - 28 q^{17} - 2 q^{18} - 21 q^{19} - 42 q^{20} + 4 q^{22} - 8 q^{23} - 21 q^{24} + 4 q^{25} - 28 q^{26} - 28 q^{27} - 8 q^{29} - 11 q^{30} - 35 q^{31} + 18 q^{32} + 7 q^{33} + q^{36} - 8 q^{37} - 14 q^{38} - 14 q^{39} - 7 q^{40} - 35 q^{41} - 8 q^{43} - 20 q^{44} - 42 q^{45} - 6 q^{46} - 70 q^{47} - 42 q^{48} + 20 q^{50} + 24 q^{51} + 21 q^{52} + 24 q^{53} - 14 q^{54} - 56 q^{55} - 20 q^{57} + 19 q^{58} - 84 q^{59} - 56 q^{62} - 9 q^{64} + 14 q^{65} - 11 q^{67} - 77 q^{68} - 42 q^{69} - 8 q^{71} + 40 q^{72} + 7 q^{73} + 43 q^{74} - 49 q^{75} - 7 q^{76} - 15 q^{79} - 70 q^{80} - 36 q^{81} + 56 q^{82} - 56 q^{83} + 36 q^{85} - 86 q^{86} - 70 q^{88} - 70 q^{89} + 56 q^{90} - 68 q^{92} - 11 q^{93} - 84 q^{94} + 54 q^{95} - 56 q^{96} - 8 q^{99}+O(q^{100}) $ 24 * q - q^2 - 7 * q^3 + 23 * q^4 - 14 * q^5 - 14 * q^6 - 3 * q^8 + 15 * q^9 - 14 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 15 * q^15 + 17 * q^16 - 28 * q^17 - 2 * q^18 - 21 * q^19 - 42 * q^20 + 4 * q^22 - 8 * q^23 - 21 * q^24 + 4 * q^25 - 28 * q^26 - 28 * q^27 - 8 * q^29 - 11 * q^30 - 35 * q^31 + 18 * q^32 + 7 * q^33 + q^36 - 8 * q^37 - 14 * q^38 - 14 * q^39 - 7 * q^40 - 35 * q^41 - 8 * q^43 - 20 * q^44 - 42 * q^45 - 6 * q^46 - 70 * q^47 - 42 * q^48 + 20 * q^50 + 24 * q^51 + 21 * q^52 + 24 * q^53 - 14 * q^54 - 56 * q^55 - 20 * q^57 + 19 * q^58 - 84 * q^59 - 56 * q^62 - 9 * q^64 + 14 * q^65 - 11 * q^67 - 77 * q^68 - 42 * q^69 - 8 * q^71 + 40 * q^72 + 7 * q^73 + 43 * q^74 - 49 * q^75 - 7 * q^76 - 15 * q^79 - 70 * q^80 - 36 * q^81 + 56 * q^82 - 56 * q^83 + 36 * q^85 - 86 * q^86 - 70 * q^88 - 70 * q^89 + 56 * q^90 - 68 * q^92 - 11 * q^93 - 84 * q^94 + 54 * q^95 - 56 * q^96 - 8 * 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 $

$2$	1.39799	0.988531	0.494266	−	0.869311i	$-0.335437\pi$
$2$	1.39799	0.988531	0.494266	+	0.869311i	$0.335437\pi$
$3$	1.98350	1.14517	0.572587	−	0.819844i	$-0.305940\pi$
$3$	1.98350	1.14517	0.572587	+	0.819844i	$0.305940\pi$
$4$	−0.0456113	−0.0228057
$5$	−3.04490	−1.36172	−0.680861	−	0.732412i	$-0.738394\pi$
$5$	−3.04490	−1.36172	−0.680861	+	0.732412i	$0.738394\pi$
$6$	2.77292	1.13204
$7$	0	0
$7$	0	0
$8$	−2.85975	−1.01108
$9$	0.934270	0.311423
$10$	−4.25676	−1.34611
$11$	5.14272	1.55059	0.775294	−	0.631600i	$-0.217602\pi$
$11$	5.14272	1.55059	0.775294	+	0.631600i	$0.217602\pi$
$12$	−0.0904700	−0.0261164
$13$	−1.65864	−0.460023	−0.230011	−	0.973188i	$-0.573876\pi$
$13$	−1.65864	−0.460023	−0.230011	+	0.973188i	$0.573876\pi$
$14$	0	0
$15$	−6.03957	−1.55941
$16$	−3.90670	−0.976674
$17$	−2.92958	−0.710527	−0.355263	−	0.934766i	$-0.615609\pi$
$17$	−2.92958	−0.710527	−0.355263	+	0.934766i	$0.615609\pi$
$18$	1.30610	0.307852
$19$	0.341540	0.0783546	0.0391773	−	0.999232i	$-0.487526\pi$
$19$	0.341540	0.0783546	0.0391773	+	0.999232i	$0.487526\pi$
$20$	0.138882	0.0310550
$21$	0	0
$22$	7.18949	1.53281
$23$	−3.56937	−0.744266	−0.372133	−	0.928179i	$-0.621373\pi$
$23$	−3.56937	−0.744266	−0.372133	+	0.928179i	$0.621373\pi$
$24$	−5.67232	−1.15786
$25$	4.27145	0.854289
$26$	−2.31876	−0.454747
$27$	−4.09737	−0.788540
$28$	0	0
$29$	−6.00831	−1.11572	−0.557858	−	0.829936i	$-0.688377\pi$
$29$	−6.00831	−1.11572	−0.557858	+	0.829936i	$0.688377\pi$
$30$	−8.44328	−1.54153
$31$	−2.61292	−0.469294	−0.234647	−	0.972081i	$-0.575393\pi$
$31$	−2.61292	−0.469294	−0.234647	+	0.972081i	$0.575393\pi$
$32$	0.257966	0.0456024
$33$	10.2006	1.77569
$34$	−4.09553	−0.702378
$35$	0	0
$36$	−0.0426133	−0.00710221
$37$	−1.61257	−0.265105	−0.132553	−	0.991176i	$-0.542317\pi$
$37$	−1.61257	−0.265105	−0.132553	+	0.991176i	$0.542317\pi$
$38$	0.477471	0.0774560
$39$	−3.28990	−0.526806
$40$	8.70768	1.37680
$41$	−3.25689	−0.508640	−0.254320	−	0.967120i	$-0.581852\pi$
$41$	−3.25689	−0.508640	−0.254320	+	0.967120i	$0.581852\pi$
$42$	0	0
$43$	−4.62185	−0.704826	−0.352413	−	0.935845i	$-0.614639\pi$
$43$	−4.62185	−0.704826	−0.352413	+	0.935845i	$0.614639\pi$
$44$	−0.234566	−0.0353622
$45$	−2.84476	−0.424072
$46$	−4.98997	−0.735730
$47$	−10.2102	−1.48930	−0.744652	−	0.667453i	$-0.767385\pi$
$47$	−10.2102	−1.48930	−0.744652	+	0.667453i	$0.767385\pi$
$48$	−7.74893	−1.11846
$49$	0	0
$50$	5.97146	0.844492
$51$	−5.81081	−0.813677
$52$	0.0756526	0.0104911
$53$	2.90418	0.398920	0.199460	−	0.979906i	$-0.436081\pi$
$53$	2.90418	0.398920	0.199460	+	0.979906i	$0.436081\pi$
$54$	−5.72811	−0.779497
$55$	−15.6591	−2.11147
$56$	0	0
$57$	0.677444	0.0897296
$58$	−8.39959	−1.10292
$59$	−9.31144	−1.21225	−0.606123	−	0.795371i	$-0.707276\pi$
$59$	−9.31144	−1.21225	−0.606123	+	0.795371i	$0.707276\pi$
$60$	0.275473	0.0355634
$61$	5.16024	0.660701	0.330351	−	0.943858i	$-0.392833\pi$
$61$	5.16024	0.660701	0.330351	+	0.943858i	$0.392833\pi$
$62$	−3.65285	−0.463912
$63$	0	0
$64$	8.17403	1.02175
$65$	5.05039	0.626424
$66$	14.2604	1.75533
$67$	11.9841	1.46409	0.732044	−	0.681258i	$-0.238567\pi$
$67$	11.9841	1.46409	0.732044	+	0.681258i	$0.238567\pi$
$68$	0.133622	0.0162040
$69$	−7.07985	−0.852314
$70$	0	0
$71$	1.85724	0.220414	0.110207	−	0.993909i	$-0.464849\pi$
$71$	1.85724	0.220414	0.110207	+	0.993909i	$0.464849\pi$
$72$	−2.67178	−0.314872
$73$	−13.1179	−1.53534	−0.767668	−	0.640848i	$-0.778583\pi$
$73$	−13.1179	−1.53534	−0.767668	+	0.640848i	$0.778583\pi$
$74$	−2.25437	−0.262065
$75$	8.47241	0.978310
$76$	−0.0155781	−0.00178693
$77$	0	0
$78$	−4.59927	−0.520765
$79$	13.8387	1.55698	0.778490	−	0.627657i	$-0.215986\pi$
$79$	13.8387	1.55698	0.778490	+	0.627657i	$0.215986\pi$
$80$	11.8955	1.32996
$81$	−10.9299	−1.21444
$82$	−4.55311	−0.502807
$83$	−0.874048	−0.0959392	−0.0479696	−	0.998849i	$-0.515275\pi$
$83$	−0.874048	−0.0959392	−0.0479696	+	0.998849i	$0.515275\pi$
$84$	0	0
$85$	8.92028	0.967540
$86$	−6.46133	−0.696743
$87$	−11.9175	−1.27769
$88$	−14.7069	−1.56776
$89$	−0.475767	−0.0504312	−0.0252156	−	0.999682i	$-0.508027\pi$
$89$	−0.475767	−0.0504312	−0.0252156	+	0.999682i	$0.508027\pi$
$90$	−3.97696	−0.419209
$91$	0	0
$92$	0.162804	0.0169735
$93$	−5.18273	−0.537424
$94$	−14.2737	−1.47222
$95$	−1.03996	−0.106697
$96$	0.511675	0.0522226
$97$	7.70896	0.782726	0.391363	−	0.920236i	$-0.372004\pi$
$97$	7.70896	0.782726	0.391363	+	0.920236i	$0.372004\pi$
$98$	0	0
$99$	4.80469	0.482889
$100$	−0.194826	−0.0194826
$101$	0.821398	0.0817321	0.0408661	−	0.999165i	$-0.486988\pi$
$101$	0.821398	0.0817321	0.0408661	+	0.999165i	$0.486988\pi$
$102$	−8.12349	−0.804345
$103$	1.28387	0.126503	0.0632515	−	0.997998i	$-0.479853\pi$
$103$	1.28387	0.126503	0.0632515	+	0.997998i	$0.479853\pi$
$104$	4.74329	0.465118
$105$	0	0
$106$	4.06003	0.394345
$107$	8.70124	0.841181	0.420590	−	0.907251i	$-0.361823\pi$
$107$	8.70124	0.841181	0.420590	+	0.907251i	$0.361823\pi$
$108$	0.186887	0.0179832
$109$	−15.1963	−1.45554	−0.727770	−	0.685822i	$-0.759443\pi$
$109$	−15.1963	−1.45554	−0.727770	+	0.685822i	$0.759443\pi$
$110$	−21.8913	−2.08726
$111$	−3.19854	−0.303592
$112$	0	0
$113$	−10.6913	−1.00575	−0.502876	−	0.864358i	$-0.667725\pi$
$113$	−10.6913	−1.00575	−0.502876	+	0.864358i	$0.667725\pi$
$114$	0.947063	0.0887006
$115$	10.8684	1.01348
$116$	0.274047	0.0254446
$117$	−1.54961	−0.143262
$118$	−13.0173	−1.19834
$119$	0	0
$120$	17.2717	1.57668
$121$	15.4476	1.40432
$122$	7.21399	0.653124
$123$	−6.46003	−0.582482
$124$	0.119179	0.0107026
$125$	2.21838	0.198418
$126$	0	0
$127$	−4.87430	−0.432524	−0.216262	−	0.976335i	$-0.569387\pi$
$127$	−4.87430	−0.432524	−0.216262	+	0.976335i	$0.569387\pi$
$128$	10.9113	0.964433
$129$	−9.16745	−0.807149
$130$	7.06042	0.619240
$131$	−4.79572	−0.419004	−0.209502	−	0.977808i	$-0.567184\pi$
$131$	−4.79572	−0.419004	−0.209502	+	0.977808i	$0.567184\pi$
$132$	−0.465262	−0.0404958
$133$	0	0
$134$	16.7537	1.44730
$135$	12.4761	1.07377
$136$	8.37787	0.718396
$137$	17.6848	1.51091	0.755455	−	0.655200i	$-0.227416\pi$
$137$	17.6848	1.51091	0.755455	+	0.655200i	$0.227416\pi$
$138$	−9.89759	−0.842539
$139$	−9.79205	−0.830550	−0.415275	−	0.909696i	$-0.636315\pi$
$139$	−9.79205	−0.830550	−0.415275	+	0.909696i	$0.636315\pi$
$140$	0	0
$141$	−20.2518	−1.70551
$142$	2.59642	0.217886
$143$	−8.52990	−0.713306
$144$	−3.64991	−0.304159
$145$	18.2947	1.51930
$146$	−18.3388	−1.51773
$147$	0	0
$148$	0.0735516	0.00604590
$149$	4.72048	0.386716	0.193358	−	0.981128i	$-0.438062\pi$
$149$	4.72048	0.386716	0.193358	+	0.981128i	$0.438062\pi$
$150$	11.8444	0.967090
$151$	12.2564	0.997414	0.498707	−	0.866771i	$-0.333808\pi$
$151$	12.2564	0.997414	0.498707	+	0.866771i	$0.333808\pi$
$152$	−0.976719	−0.0792224
$153$	−2.73702	−0.221275
$154$	0	0
$155$	7.95609	0.639049
$156$	0.150057	0.0120142
$157$	−18.1707	−1.45018	−0.725091	−	0.688653i	$-0.758203\pi$
$157$	−18.1707	−1.45018	−0.725091	+	0.688653i	$0.758203\pi$
$158$	19.3465	1.53912
$159$	5.76044	0.456832
$160$	−0.785481	−0.0620978
$161$	0	0
$162$	−15.2800	−1.20051
$163$	2.32053	0.181758	0.0908790	−	0.995862i	$-0.471032\pi$
$163$	2.32053	0.181758	0.0908790	+	0.995862i	$0.471032\pi$
$164$	0.148551	0.0115999
$165$	−31.0598	−2.41800
$166$	−1.22191	−0.0948389
$167$	12.1116	0.937223	0.468611	−	0.883404i	$-0.344754\pi$
$167$	12.1116	0.937223	0.468611	+	0.883404i	$0.344754\pi$
$168$	0	0
$169$	−10.2489	−0.788379
$170$	12.4705	0.956444
$171$	0.319090	0.0244014
$172$	0.210809	0.0160740
$173$	2.89919	0.220421	0.110210	−	0.993908i	$-0.464848\pi$
$173$	2.89919	0.220421	0.110210	+	0.993908i	$0.464848\pi$
$174$	−16.6606	−1.26304
$175$	0	0
$176$	−20.0910	−1.51442
$177$	−18.4692	−1.38823
$178$	−0.665119	−0.0498528
$179$	7.71319	0.576511	0.288255	−	0.957554i	$-0.406925\pi$
$179$	7.71319	0.576511	0.288255	+	0.957554i	$0.406925\pi$
$180$	0.129753	0.00967125
$181$	−19.4258	−1.44391	−0.721954	−	0.691941i	$-0.756756\pi$
$181$	−19.4258	−1.44391	−0.721954	+	0.691941i	$0.756756\pi$
$182$	0	0
$183$	10.2353	0.756618
$184$	10.2075	0.752509
$185$	4.91013	0.361000
$186$	−7.24542	−0.531260
$187$	−15.0660	−1.10173
$188$	0.465699	0.0339646
$189$	0	0
$190$	−1.45385	−0.105474
$191$	1.95540	0.141487	0.0707437	−	0.997495i	$-0.477463\pi$
$191$	1.95540	0.141487	0.0707437	+	0.997495i	$0.477463\pi$
$192$	16.2132	1.17009
$193$	3.54029	0.254836	0.127418	−	0.991849i	$-0.459331\pi$
$193$	3.54029	0.254836	0.127418	+	0.991849i	$0.459331\pi$
$194$	10.7771	0.773750
$195$	10.0174	0.717364
$196$	0	0
$197$	−23.0280	−1.64068	−0.820339	−	0.571877i	$-0.806215\pi$
$197$	−23.0280	−1.64068	−0.820339	+	0.571877i	$0.806215\pi$
$198$	6.71693	0.477351
$199$	16.1938	1.14794	0.573972	−	0.818875i	$-0.305402\pi$
$199$	16.1938	1.14794	0.573972	+	0.818875i	$0.305402\pi$
$200$	−12.2153	−0.863751
$201$	23.7704	1.67663
$202$	1.14831	0.0807948
$203$	0	0
$204$	0.265039	0.0185564
$205$	9.91691	0.692627
$206$	1.79484	0.125052
$207$	−3.33476	−0.231782
$208$	6.47979	0.449293
$209$	1.75644	0.121496
$210$	0	0
$211$	19.7281	1.35814	0.679070	−	0.734074i	$-0.262383\pi$
$211$	19.7281	1.35814	0.679070	+	0.734074i	$0.262383\pi$
$212$	−0.132463	−0.00909763
$213$	3.68384	0.252413
$214$	12.1643	0.831534
$215$	14.0731	0.959778
$216$	11.7175	0.797274
$217$	0	0
$218$	−21.2443	−1.43885
$219$	−26.0194	−1.75823
$220$	0.714232	0.0481535
$221$	4.85910	0.326859
$222$	−4.47154	−0.300110
$223$	−8.36785	−0.560353	−0.280176	−	0.959949i	$-0.590393\pi$
$223$	−8.36785	−0.560353	−0.280176	+	0.959949i	$0.590393\pi$
$224$	0	0
$225$	3.99068	0.266046
$226$	−14.9464	−0.994218
$227$	26.3849	1.75123	0.875613	−	0.483013i	$-0.160458\pi$
$227$	26.3849	1.75123	0.875613	+	0.483013i	$0.160458\pi$
$228$	−0.0308991	−0.00204634
$229$	−3.82510	−0.252770	−0.126385	−	0.991981i	$-0.540337\pi$
$229$	−3.82510	−0.252770	−0.126385	+	0.991981i	$0.540337\pi$
$230$	15.1940	1.00186
$231$	0	0
$232$	17.1823	1.12807
$233$	−0.441332	−0.0289126	−0.0144563	−	0.999896i	$-0.504602\pi$
$233$	−0.441332	−0.0289126	−0.0144563	+	0.999896i	$0.504602\pi$
$234$	−2.16635	−0.141619
$235$	31.0890	2.02802
$236$	0.424707	0.0276461
$237$	27.4491	1.78301
$238$	0	0
$239$	6.32969	0.409434	0.204717	−	0.978821i	$-0.434373\pi$
$239$	6.32969	0.409434	0.204717	+	0.978821i	$0.434373\pi$
$240$	23.5948	1.52304
$241$	13.8127	0.889753	0.444876	−	0.895592i	$-0.353248\pi$
$241$	13.8127	0.889753	0.444876	+	0.895592i	$0.353248\pi$
$242$	21.5956	1.38822
$243$	−9.38742	−0.602204
$244$	−0.235365	−0.0150677
$245$	0	0
$246$	−9.03109	−0.575801
$247$	−0.566490	−0.0360449
$248$	7.47231	0.474492
$249$	−1.73367	−0.109867
$250$	3.10128	0.196142
$251$	12.3818	0.781530	0.390765	−	0.920490i	$-0.372211\pi$
$251$	12.3818	0.781530	0.390765	+	0.920490i	$0.372211\pi$
$252$	0	0
$253$	−18.3563	−1.15405
$254$	−6.81424	−0.427564
$255$	17.6934	1.10800
$256$	−1.09410	−0.0683811
$257$	19.2115	1.19838	0.599191	−	0.800606i	$-0.295489\pi$
$257$	19.2115	1.19838	0.599191	+	0.800606i	$0.295489\pi$
$258$	−12.8160	−0.797892
$259$	0	0
$260$	−0.230355	−0.0142860
$261$	−5.61339	−0.347460
$262$	−6.70438	−0.414198
$263$	−9.18400	−0.566310	−0.283155	−	0.959074i	$-0.591381\pi$
$263$	−9.18400	−0.566310	−0.283155	+	0.959074i	$0.591381\pi$
$264$	−29.1711	−1.79536
$265$	−8.84295	−0.543218
$266$	0	0
$267$	−0.943683	−0.0577525
$268$	−0.546609	−0.0333895
$269$	−17.8626	−1.08910	−0.544552	−	0.838727i	$-0.683300\pi$
$269$	−17.8626	−1.08910	−0.544552	+	0.838727i	$0.683300\pi$
$270$	17.4415	1.06146
$271$	0.0249729	0.00151699	0.000758497	−	1.00000i	$-0.499759\pi$
$271$	0.0249729	0.00151699	0.000758497		1.00000i	$0.499759\pi$
$272$	11.4450	0.693953
$273$	0	0
$274$	24.7232	1.49358
$275$	21.9668	1.32465
$276$	0.322921	0.0194376
$277$	6.00227	0.360641	0.180321	−	0.983608i	$-0.442286\pi$
$277$	6.00227	0.360641	0.180321	+	0.983608i	$0.442286\pi$
$278$	−13.6892	−0.821025
$279$	−2.44117	−0.146149
$280$	0	0
$281$	−23.7231	−1.41520	−0.707600	−	0.706613i	$-0.750222\pi$
$281$	−23.7231	−1.41520	−0.707600	+	0.706613i	$0.750222\pi$
$282$	−28.3120	−1.68595
$283$	20.6256	1.22607	0.613034	−	0.790057i	$-0.289949\pi$
$283$	20.6256	1.22607	0.613034	+	0.790057i	$0.289949\pi$
$284$	−0.0847113	−0.00502669
$285$	−2.06275	−0.122187
$286$	−11.9248	−0.705126
$287$	0	0
$288$	0.241010	0.0142016
$289$	−8.41758	−0.495152
$290$	25.5759	1.50187
$291$	15.2907	0.896358
$292$	0.598326	0.0350144
$293$	−9.60232	−0.560974	−0.280487	−	0.959858i	$-0.590496\pi$
$293$	−9.60232	−0.560974	−0.280487	+	0.959858i	$0.590496\pi$
$294$	0	0
$295$	28.3525	1.65074
$296$	4.61156	0.268042
$297$	−21.0716	−1.22270
$298$	6.59920	0.382281
$299$	5.92029	0.342379
$300$	−0.386438	−0.0223110
$301$	0	0
$302$	17.1344	0.985975
$303$	1.62924	0.0935975
$304$	−1.33429	−0.0765269
$305$	−15.7124	−0.899692
$306$	−3.82633	−0.218737
$307$	1.53045	0.0873473	0.0436736	−	0.999046i	$-0.486094\pi$
$307$	1.53045	0.0873473	0.0436736	+	0.999046i	$0.486094\pi$
$308$	0	0
$309$	2.54655	0.144868
$310$	11.1226	0.631720
$311$	−10.9389	−0.620289	−0.310145	−	0.950689i	$-0.600377\pi$
$311$	−10.9389	−0.620289	−0.310145	+	0.950689i	$0.600377\pi$
$312$	9.40831	0.532641
$313$	26.4486	1.49496	0.747482	−	0.664282i	$-0.231263\pi$
$313$	26.4486	1.49496	0.747482	+	0.664282i	$0.231263\pi$
$314$	−25.4026	−1.43355
$315$	0	0
$316$	−0.631203	−0.0355080
$317$	−17.0048	−0.955087	−0.477543	−	0.878608i	$-0.658473\pi$
$317$	−17.0048	−0.955087	−0.477543	+	0.878608i	$0.658473\pi$
$318$	8.05306	0.451593
$319$	−30.8991	−1.73002
$320$	−24.8891	−1.39135
$321$	17.2589	0.963298
$322$	0	0
$323$	−1.00057	−0.0556730
$324$	0.498529	0.0276961
$325$	−7.08477	−0.392993
$326$	3.24409	0.179673
$327$	−30.1418	−1.66685
$328$	9.31389	0.514274
$329$	0	0
$330$	−43.4214	−2.39027
$331$	13.7224	0.754251	0.377126	−	0.926162i	$-0.376913\pi$
$331$	13.7224	0.754251	0.377126	+	0.926162i	$0.376913\pi$
$332$	0.0398665	0.00218796
$333$	−1.50658	−0.0825600
$334$	16.9319	0.926474
$335$	−36.4903	−1.99368
$336$	0	0
$337$	11.5270	0.627914	0.313957	−	0.949437i	$-0.398345\pi$
$337$	11.5270	0.627914	0.313957	+	0.949437i	$0.398345\pi$
$338$	−14.3279	−0.779337
$339$	−21.2062	−1.15176
$340$	−0.406866	−0.0220654
$341$	−13.4375	−0.727682
$342$	0.446086	0.0241216
$343$	0	0
$344$	13.2174	0.712633
$345$	21.5575	1.16062
$346$	4.05305	0.217893
$347$	8.63885	0.463758	0.231879	−	0.972745i	$-0.425513\pi$
$347$	8.63885	0.463758	0.231879	+	0.972745i	$0.425513\pi$
$348$	0.543572	0.0291385
$349$	−35.1669	−1.88244	−0.941219	−	0.337796i	$-0.890319\pi$
$349$	−35.1669	−1.88244	−0.941219	+	0.337796i	$0.890319\pi$
$350$	0	0
$351$	6.79605	0.362747
$352$	1.32665	0.0707105
$353$	20.7184	1.10273	0.551365	−	0.834264i	$-0.314107\pi$
$353$	20.7184	1.10273	0.551365	+	0.834264i	$0.314107\pi$
$354$	−25.8199	−1.37231
$355$	−5.65513	−0.300143
$356$	0.0217003	0.00115012
$357$	0	0
$358$	10.7830	0.569899
$359$	−29.4021	−1.55179	−0.775893	−	0.630865i	$-0.782700\pi$
$359$	−29.4021	−1.55179	−0.775893	+	0.630865i	$0.782700\pi$
$360$	8.13532	0.428769
$361$	−18.8834	−0.993861
$362$	−27.1571	−1.42735
$363$	30.6402	1.60819
$364$	0	0
$365$	39.9428	2.09070
$366$	14.3089	0.747940
$367$	33.1678	1.73135	0.865674	−	0.500609i	$-0.166890\pi$
$367$	33.1678	1.73135	0.865674	+	0.500609i	$0.166890\pi$
$368$	13.9445	0.726905
$369$	−3.04281	−0.158402
$370$	6.86434	0.356860
$371$	0	0
$372$	0.236391	0.0122563
$373$	−9.49491	−0.491628	−0.245814	−	0.969317i	$-0.579055\pi$
$373$	−9.49491	−0.491628	−0.245814	+	0.969317i	$0.579055\pi$
$374$	−21.0622	−1.08910
$375$	4.40015	0.227223
$376$	29.1985	1.50580
$377$	9.96561	0.513255
$378$	0	0
$379$	−13.2179	−0.678957	−0.339478	−	0.940614i	$-0.610251\pi$
$379$	−13.2179	−0.678957	−0.339478	+	0.940614i	$0.610251\pi$
$380$	0.0474338	0.00243330
$381$	−9.66817	−0.495315
$382$	2.73363	0.139865
$383$	2.92160	0.149287	0.0746435	−	0.997210i	$-0.476218\pi$
$383$	2.92160	0.149287	0.0746435	+	0.997210i	$0.476218\pi$
$384$	21.6426	1.10444
$385$	0	0
$386$	4.94931	0.251913
$387$	−4.31806	−0.219499
$388$	−0.351616	−0.0178506
$389$	−13.1493	−0.666695	−0.333347	−	0.942804i	$-0.608178\pi$
$389$	−13.1493	−0.666695	−0.333347	+	0.942804i	$0.608178\pi$
$390$	14.0043	0.709137
$391$	10.4568	0.528821
$392$	0	0
$393$	−9.51230	−0.479832
$394$	−32.1930	−1.62186
$395$	−42.1377	−2.12018
$396$	−0.219148	−0.0110126
$397$	−10.0482	−0.504306	−0.252153	−	0.967687i	$-0.581139\pi$
$397$	−10.0482	−0.504306	−0.252153	+	0.967687i	$0.581139\pi$
$398$	22.6388	1.13478
$399$	0	0
$400$	−16.6872	−0.834362
$401$	−16.6640	−0.832159	−0.416079	−	0.909328i	$-0.636596\pi$
$401$	−16.6640	−0.832159	−0.416079	+	0.909328i	$0.636596\pi$
$402$	33.2309	1.65741
$403$	4.33388	0.215886
$404$	−0.0374650	−0.00186395
$405$	33.2807	1.65373
$406$	0	0
$407$	−8.29301	−0.411069
$408$	16.6175	0.822689
$409$	−9.70222	−0.479744	−0.239872	−	0.970805i	$-0.577105\pi$
$409$	−9.70222	−0.479744	−0.239872	+	0.970805i	$0.577105\pi$
$410$	13.8638	0.684684
$411$	35.0777	1.73026
$412$	−0.0585588	−0.00288499
$413$	0	0
$414$	−4.66197	−0.229124
$415$	2.66139	0.130643
$416$	−0.427872	−0.0209781
$417$	−19.4225	−0.951125
$418$	2.45550	0.120102
$419$	20.6627	1.00944	0.504719	−	0.863284i	$-0.331596\pi$
$419$	20.6627	1.00944	0.504719	+	0.863284i	$0.331596\pi$
$420$	0	0
$421$	5.28020	0.257341	0.128671	−	0.991687i	$-0.458929\pi$
$421$	5.28020	0.257341	0.128671	+	0.991687i	$0.458929\pi$
$422$	27.5798	1.34256
$423$	−9.53904	−0.463804
$424$	−8.30524	−0.403338
$425$	−12.5135	−0.606995
$426$	5.14999	0.249518
$427$	0	0
$428$	−0.396875	−0.0191837
$429$	−16.9191	−0.816860
$430$	19.6741	0.948771
$431$	−21.8948	−1.05464	−0.527318	−	0.849668i	$-0.676802\pi$
$431$	−21.8948	−1.05464	−0.527318	+	0.849668i	$0.676802\pi$
$432$	16.0072	0.770147
$433$	33.3136	1.60095	0.800474	−	0.599368i	$-0.204581\pi$
$433$	33.3136	1.60095	0.800474	+	0.599368i	$0.204581\pi$
$434$	0	0
$435$	36.2876	1.73986
$436$	0.693122	0.0331945
$437$	−1.21908	−0.0583167
$438$	−36.3750	−1.73806
$439$	−18.6494	−0.890089	−0.445045	−	0.895508i	$-0.646812\pi$
$439$	−18.6494	−0.890089	−0.445045	+	0.895508i	$0.646812\pi$
$440$	44.7811	2.13486
$441$	0	0
$442$	6.79300	0.323110
$443$	−38.1167	−1.81098	−0.905489	−	0.424370i	$-0.860496\pi$
$443$	−38.1167	−1.81098	−0.905489	+	0.424370i	$0.860496\pi$
$444$	0.145889	0.00692361
$445$	1.44866	0.0686733
$446$	−11.6982	−0.553926
$447$	9.36306	0.442858
$448$	0	0
$449$	−14.3401	−0.676753	−0.338376	−	0.941011i	$-0.609878\pi$
$449$	−14.3401	−0.676753	−0.338376	+	0.941011i	$0.609878\pi$
$450$	5.57895	0.262994
$451$	−16.7493	−0.788692
$452$	0.487644	0.0229368
$453$	24.3106	1.14221
$454$	36.8859	1.73114
$455$	0	0
$456$	−1.93732	−0.0907234
$457$	17.6261	0.824514	0.412257	−	0.911068i	$-0.364741\pi$
$457$	17.6261	0.824514	0.412257	+	0.911068i	$0.364741\pi$
$458$	−5.34747	−0.249871
$459$	12.0036	0.560279
$460$	−0.495722	−0.0231132
$461$	1.55267	0.0723153	0.0361576	−	0.999346i	$-0.488488\pi$
$461$	1.55267	0.0723153	0.0361576	+	0.999346i	$0.488488\pi$
$462$	0	0
$463$	−14.1041	−0.655475	−0.327737	−	0.944769i	$-0.606286\pi$
$463$	−14.1041	−0.655475	−0.327737	+	0.944769i	$0.606286\pi$
$464$	23.4727	1.08969
$465$	15.7809	0.731822
$466$	−0.616980	−0.0285811
$467$	−12.3839	−0.573058	−0.286529	−	0.958072i	$-0.592501\pi$
$467$	−12.3839	−0.573058	−0.286529	+	0.958072i	$0.592501\pi$
$468$	0.0706799	0.00326718
$469$	0	0
$470$	43.4622	2.00476
$471$	−36.0417	−1.66071
$472$	26.6284	1.22567
$473$	−23.7689	−1.09290
$474$	38.3738	1.76256
$475$	1.45887	0.0669375
$476$	0	0
$477$	2.71329	0.124233
$478$	8.84887	0.404738
$479$	−37.0464	−1.69269	−0.846347	−	0.532632i	$-0.821203\pi$
$479$	−37.0464	−1.69269	−0.846347	+	0.532632i	$0.821203\pi$
$480$	−1.55800	−0.0711127
$481$	2.67467	0.121955
$482$	19.3100	0.879548
$483$	0	0
$484$	−0.704584	−0.0320265
$485$	−23.4731	−1.06586
$486$	−13.1236	−0.595297
$487$	29.4209	1.33319	0.666595	−	0.745420i	$-0.267751\pi$
$487$	29.4209	1.33319	0.666595	+	0.745420i	$0.267751\pi$
$488$	−14.7570	−0.668019
$489$	4.60277	0.208144
$490$	0	0
$491$	−19.1247	−0.863086	−0.431543	−	0.902092i	$-0.642031\pi$
$491$	−19.1247	−0.863086	−0.431543	+	0.902092i	$0.642031\pi$
$492$	0.294651	0.0132839
$493$	17.6018	0.792746
$494$	−0.791950	−0.0356315
$495$	−14.6298	−0.657561
$496$	10.2079	0.458348
$497$	0	0
$498$	−2.42367	−0.108607
$499$	−30.9896	−1.38728	−0.693642	−	0.720319i	$-0.743995\pi$
$499$	−30.9896	−1.38728	−0.693642	+	0.720319i	$0.743995\pi$
$500$	−0.101183	−0.00452505
$501$	24.0233	1.07328
$502$	17.3096	0.772567
$503$	−32.9556	−1.46942	−0.734710	−	0.678382i	$-0.762682\pi$
$503$	−32.9556	−1.46942	−0.734710	+	0.678382i	$0.762682\pi$
$504$	0	0
$505$	−2.50108	−0.111296
$506$	−25.6620	−1.14081
$507$	−20.3287	−0.902831
$508$	0.222323	0.00986399
$509$	−16.3901	−0.726479	−0.363240	−	0.931696i	$-0.618329\pi$
$509$	−16.3901	−0.726479	−0.363240	+	0.931696i	$0.618329\pi$
$510$	24.7352	1.09529
$511$	0	0
$512$	−23.3522	−1.03203
$513$	−1.39942	−0.0617857
$514$	26.8576	1.18464
$515$	−3.90925	−0.172262
$516$	0.418139	0.0184076
$517$	−52.5080	−2.30930
$518$	0	0
$519$	5.75053	0.252420
$520$	−14.4429	−0.633362
$521$	−35.4467	−1.55295	−0.776474	−	0.630149i	$-0.782994\pi$
$521$	−35.4467	−1.55295	−0.776474	+	0.630149i	$0.782994\pi$
$522$	−7.84748	−0.343475
$523$	30.7539	1.34477	0.672386	−	0.740201i	$-0.265270\pi$
$523$	30.7539	1.34477	0.672386	+	0.740201i	$0.265270\pi$
$524$	0.218739	0.00955565
$525$	0	0
$526$	−12.8392	−0.559815
$527$	7.65475	0.333446
$528$	−39.8506	−1.73427
$529$	−10.2596	−0.446068
$530$	−12.3624	−0.536988
$531$	−8.69940	−0.377522
$532$	0	0
$533$	5.40199	0.233986
$534$	−1.31926	−0.0570901
$535$	−26.4945	−1.14546
$536$	−34.2715	−1.48030
$537$	15.2991	0.660205
$538$	−24.9718	−1.07661
$539$	0	0
$540$	−0.569052	−0.0244881
$541$	−10.7777	−0.463368	−0.231684	−	0.972791i	$-0.574424\pi$
$541$	−10.7777	−0.463368	−0.231684	+	0.972791i	$0.574424\pi$
$542$	0.0349120	0.00149960
$543$	−38.5310	−1.65353
$544$	−0.755731	−0.0324017
$545$	46.2712	1.98204
$546$	0	0
$547$	−16.9008	−0.722627	−0.361313	−	0.932444i	$-0.617672\pi$
$547$	−16.9008	−0.722627	−0.361313	+	0.932444i	$0.617672\pi$
$548$	−0.806625	−0.0344573
$549$	4.82106	0.205758
$550$	30.7095	1.30946
$551$	−2.05208	−0.0874215
$552$	20.2466	0.861754
$553$	0	0
$554$	8.39114	0.356505
$555$	9.73924	0.413408
$556$	0.446628	0.0189412
$557$	−18.2133	−0.771722	−0.385861	−	0.922557i	$-0.626096\pi$
$557$	−18.2133	−0.771722	−0.385861	+	0.922557i	$0.626096\pi$
$558$	−3.41275	−0.144473
$559$	7.66598	0.324236
$560$	0	0
$561$	−29.8834	−1.26168
$562$	−33.1647	−1.39897
$563$	11.3721	0.479275	0.239638	−	0.970862i	$-0.422971\pi$
$563$	11.3721	0.479275	0.239638	+	0.970862i	$0.422971\pi$
$564$	0.923713	0.0388953
$565$	32.5540	1.36956
$566$	28.8345	1.21201
$567$	0	0
$568$	−5.31126	−0.222855
$569$	13.3327	0.558934	0.279467	−	0.960155i	$-0.409842\pi$
$569$	13.3327	0.558934	0.279467	+	0.960155i	$0.409842\pi$
$570$	−2.88372	−0.120786
$571$	32.9079	1.37715	0.688577	−	0.725164i	$-0.258236\pi$
$571$	32.9079	1.37715	0.688577	+	0.725164i	$0.258236\pi$
$572$	0.389060	0.0162674
$573$	3.87853	0.162028
$574$	0	0
$575$	−15.2464	−0.635818
$576$	7.63675	0.318198
$577$	9.72522	0.404866	0.202433	−	0.979296i	$-0.435115\pi$
$577$	9.72522	0.404866	0.202433	+	0.979296i	$0.435115\pi$
$578$	−11.7677	−0.489473
$579$	7.02217	0.291831
$580$	−0.834447	−0.0346485
$581$	0	0
$582$	21.3763	0.886078
$583$	14.9354	0.618560
$584$	37.5140	1.55234
$585$	4.71843	0.195083
$586$	−13.4240	−0.554540
$587$	9.81759	0.405216	0.202608	−	0.979260i	$-0.435058\pi$
$587$	9.81759	0.405216	0.202608	+	0.979260i	$0.435058\pi$
$588$	0	0
$589$	−0.892416	−0.0367714
$590$	39.6366	1.63181
$591$	−45.6761	−1.87886
$592$	6.29983	0.258922
$593$	−33.7566	−1.38622	−0.693109	−	0.720832i	$-0.743760\pi$
$593$	−33.7566	−1.38622	−0.693109	+	0.720832i	$0.743760\pi$
$594$	−29.4580	−1.20868
$595$	0	0
$596$	−0.215307	−0.00881932
$597$	32.1203	1.31460
$598$	8.27654	0.338453
$599$	−8.17547	−0.334040	−0.167020	−	0.985953i	$-0.553415\pi$
$599$	−8.17547	−0.334040	−0.167020	+	0.985953i	$0.553415\pi$
$600$	−24.2290	−0.989145
$601$	−26.5229	−1.08189	−0.540946	−	0.841058i	$-0.681933\pi$
$601$	−26.5229	−1.08189	−0.540946	+	0.841058i	$0.681933\pi$
$602$	0	0
$603$	11.1964	0.455951
$604$	−0.559032	−0.0227467
$605$	−47.0364	−1.91230
$606$	2.27767	0.0925240
$607$	−31.8261	−1.29178	−0.645890	−	0.763431i	$-0.723513\pi$
$607$	−31.8261	−1.29178	−0.645890	+	0.763431i	$0.723513\pi$
$608$	0.0881056	0.00357315
$609$	0	0
$610$	−21.9659	−0.889373
$611$	16.9349	0.685114
$612$	0.124839	0.00504631
$613$	38.7777	1.56622	0.783109	−	0.621885i	$-0.213633\pi$
$613$	38.7777	1.56622	0.783109	+	0.621885i	$0.213633\pi$
$614$	2.13956	0.0863455
$615$	19.6702	0.793178
$616$	0	0
$617$	5.64000	0.227058	0.113529	−	0.993535i	$-0.463785\pi$
$617$	5.64000	0.227058	0.113529	+	0.993535i	$0.463785\pi$
$618$	3.56006	0.143207
$619$	−23.2697	−0.935287	−0.467644	−	0.883917i	$-0.654897\pi$
$619$	−23.2697	−0.935287	−0.467644	+	0.883917i	$0.654897\pi$
$620$	−0.362888	−0.0145739
$621$	14.6251	0.586884
$622$	−15.2925	−0.613175
$623$	0	0
$624$	12.8527	0.514518
$625$	−28.1120	−1.12448
$626$	36.9750	1.47782
$627$	3.48390	0.139134
$628$	0.828791	0.0330724
$629$	4.72416	0.188364
$630$	0	0
$631$	−8.60576	−0.342590	−0.171295	−	0.985220i	$-0.554795\pi$
$631$	−8.60576	−0.342590	−0.171295	+	0.985220i	$0.554795\pi$
$632$	−39.5754	−1.57423
$633$	39.1307	1.55531
$634$	−23.7727	−0.944133
$635$	14.8418	0.588978
$636$	−0.262741	−0.0104184
$637$	0	0
$638$	−43.1967	−1.71017
$639$	1.73517	0.0686421
$640$	−33.2239	−1.31329
$641$	1.51895	0.0599950	0.0299975	−	0.999550i	$-0.490450\pi$
$641$	1.51895	0.0599950	0.0299975	+	0.999550i	$0.490450\pi$
$642$	24.1279	0.952251
$643$	27.8302	1.09751	0.548757	−	0.835982i	$-0.315101\pi$
$643$	27.8302	1.09751	0.548757	+	0.835982i	$0.315101\pi$
$644$	0	0
$645$	27.9140	1.09911
$646$	−1.39879	−0.0550345
$647$	3.22818	0.126913	0.0634564	−	0.997985i	$-0.479788\pi$
$647$	3.22818	0.126913	0.0634564	+	0.997985i	$0.479788\pi$
$648$	31.2570	1.22789
$649$	−47.8861	−1.87970
$650$	−9.90448	−0.388486
$651$	0	0
$652$	−0.105842	−0.00414511
$653$	−35.2528	−1.37955	−0.689774	−	0.724025i	$-0.742290\pi$
$653$	−35.2528	−1.37955	−0.689774	+	0.724025i	$0.742290\pi$
$654$	−42.1381	−1.64773
$655$	14.6025	0.570567
$656$	12.7237	0.496776
$657$	−12.2557	−0.478139
$658$	0	0
$659$	17.3774	0.676929	0.338465	−	0.940979i	$-0.390092\pi$
$659$	17.3774	0.676929	0.338465	+	0.940979i	$0.390092\pi$
$660$	1.41668	0.0551441
$661$	−48.2778	−1.87779	−0.938895	−	0.344203i	$-0.888149\pi$
$661$	−48.2778	−1.87779	−0.938895	+	0.344203i	$0.888149\pi$
$662$	19.1838	0.745601
$663$	9.63803	0.374310
$664$	2.49956	0.0970018
$665$	0	0
$666$	−2.10619	−0.0816131
$667$	21.4459	0.830389
$668$	−0.552426	−0.0213740
$669$	−16.5976	−0.641702
$670$	−51.0133	−1.97082
$671$	26.5377	1.02448
$672$	0	0
$673$	−36.7705	−1.41740	−0.708700	−	0.705510i	$-0.750718\pi$
$673$	−36.7705	−1.41740	−0.708700	+	0.705510i	$0.750718\pi$
$674$	16.1146	0.620712
$675$	−17.5017	−0.673641
$676$	0.467467	0.0179795
$677$	−40.3961	−1.55255	−0.776273	−	0.630397i	$-0.782892\pi$
$677$	−40.3961	−1.55255	−0.776273	+	0.630397i	$0.782892\pi$
$678$	−29.6461	−1.13855
$679$	0	0
$680$	−25.5098	−0.978256
$681$	52.3344	2.00546
$682$	−18.7856	−0.719337
$683$	36.4250	1.39377	0.696883	−	0.717185i	$-0.254570\pi$
$683$	36.4250	1.39377	0.696883	+	0.717185i	$0.254570\pi$
$684$	−0.0145541	−0.000556491 0
$685$	−53.8484	−2.05744
$686$	0	0
$687$	−7.58708	−0.289465
$688$	18.0562	0.688386
$689$	−4.81698	−0.183512
$690$	30.1372	1.14730
$691$	−3.02833	−0.115203	−0.0576016	−	0.998340i	$-0.518345\pi$
$691$	−3.02833	−0.115203	−0.0576016	+	0.998340i	$0.518345\pi$
$692$	−0.132236	−0.00502685
$693$	0	0
$694$	12.0771	0.458439
$695$	29.8158	1.13098
$696$	34.0811	1.29184
$697$	9.54130	0.361402
$698$	−49.1631	−1.86085
$699$	−0.875382	−0.0331100
$700$	0	0
$701$	16.2373	0.613276	0.306638	−	0.951826i	$-0.400796\pi$
$701$	16.2373	0.613276	0.306638	+	0.951826i	$0.400796\pi$
$702$	9.50085	0.358586
$703$	−0.550758	−0.0207722
$704$	42.0367	1.58432
$705$	61.6649	2.32244
$706$	28.9642	1.09008
$707$	0	0
$708$	0.842406	0.0316596
$709$	17.5093	0.657576	0.328788	−	0.944404i	$-0.393360\pi$
$709$	17.5093	0.657576	0.328788	+	0.944404i	$0.393360\pi$
$710$	−7.90584	−0.296701
$711$	12.9291	0.484880
$712$	1.36058	0.0509897
$713$	9.32649	0.349280
$714$	0	0
$715$	25.9727	0.971325
$716$	−0.351809	−0.0131477
$717$	12.5549	0.468873
$718$	−41.1040	−1.53399
$719$	−1.22472	−0.0456745	−0.0228372	−	0.999739i	$-0.507270\pi$
$719$	−1.22472	−0.0456745	−0.0228372	+	0.999739i	$0.507270\pi$
$720$	11.1136	0.414180
$721$	0	0
$722$	−26.3988	−0.982462
$723$	27.3974	1.01892
$724$	0.886036	0.0329293
$725$	−25.6642	−0.953144
$726$	42.8349	1.58975
$727$	25.9365	0.961933	0.480966	−	0.876739i	$-0.340286\pi$
$727$	25.9365	0.961933	0.480966	+	0.876739i	$0.340286\pi$
$728$	0	0
$729$	14.1699	0.524811
$730$	55.8398	2.06673
$731$	13.5401	0.500798
$732$	−0.466847	−0.0172552
$733$	−22.5392	−0.832505	−0.416253	−	0.909249i	$-0.636657\pi$
$733$	−22.5392	−0.832505	−0.416253	+	0.909249i	$0.636657\pi$
$734$	46.3685	1.71149
$735$	0	0
$736$	−0.920777	−0.0339403
$737$	61.6307	2.27020
$738$	−4.25383	−0.156586
$739$	12.6407	0.464997	0.232498	−	0.972597i	$-0.425310\pi$
$739$	12.6407	0.464997	0.232498	+	0.972597i	$0.425310\pi$
$740$	−0.223958	−0.00823284
$741$	−1.12363	−0.0412777
$742$	0	0
$743$	16.4544	0.603652	0.301826	−	0.953363i	$-0.402404\pi$
$743$	16.4544	0.603652	0.301826	+	0.953363i	$0.402404\pi$
$744$	14.8213	0.543376
$745$	−14.3734	−0.526601
$746$	−13.2738	−0.485990
$747$	−0.816597	−0.0298777
$748$	0.687180	0.0251258
$749$	0	0
$750$	6.15139	0.224617
$751$	46.3973	1.69306	0.846530	−	0.532340i	$-0.178687\pi$
$751$	46.3973	1.69306	0.846530	+	0.532340i	$0.178687\pi$
$752$	39.8880	1.45457
$753$	24.5592	0.894988
$754$	13.9319	0.507369
$755$	−37.3196	−1.35820
$756$	0	0
$757$	−50.8127	−1.84682	−0.923409	−	0.383818i	$-0.874609\pi$
$757$	−50.8127	−1.84682	−0.923409	+	0.383818i	$0.874609\pi$
$758$	−18.4785	−0.671170
$759$	−36.4097	−1.32159
$760$	2.97402	0.107879
$761$	43.0317	1.55990	0.779949	−	0.625843i	$-0.215245\pi$
$761$	43.0317	1.55990	0.779949	+	0.625843i	$0.215245\pi$
$762$	−13.5160	−0.489635
$763$	0	0
$764$	−0.0891882	−0.00322671
$765$	8.33395	0.301315
$766$	4.08438	0.147575
$767$	15.4443	0.557661
$768$	−2.17014	−0.0783083
$769$	16.8484	0.607569	0.303785	−	0.952741i	$-0.401750\pi$
$769$	16.8484	0.607569	0.303785	+	0.952741i	$0.401750\pi$
$770$	0	0
$771$	38.1061	1.37236
$772$	−0.161477	−0.00581170
$773$	8.87904	0.319357	0.159679	−	0.987169i	$-0.448954\pi$
$773$	8.87904	0.319357	0.159679	+	0.987169i	$0.448954\pi$
$774$	−6.03662	−0.216982
$775$	−11.1609	−0.400913
$776$	−22.0457	−0.791395
$777$	0	0
$778$	−18.3826	−0.659049
$779$	−1.11236	−0.0398543
$780$	−0.456909	−0.0163600
$781$	9.55128	0.341772
$782$	14.6185	0.522756
$783$	24.6183	0.879787
$784$	0	0
$785$	55.3282	1.97475
$786$	−13.2981	−0.474329
$787$	35.3194	1.25900	0.629500	−	0.777000i	$-0.283260\pi$
$787$	35.3194	1.25900	0.629500	+	0.777000i	$0.283260\pi$
$788$	1.05034	0.0374167
$789$	−18.2165	−0.648523
$790$	−58.9082	−2.09586
$791$	0	0
$792$	−13.7402	−0.488238
$793$	−8.55896	−0.303938
$794$	−14.0474	−0.498522
$795$	−17.5400	−0.622079
$796$	−0.738618	−0.0261796
$797$	48.4090	1.71473	0.857367	−	0.514705i	$-0.172099\pi$
$797$	48.4090	1.71473	0.857367	+	0.514705i	$0.172099\pi$
$798$	0	0
$799$	29.9114	1.05819
$800$	1.10189	0.0389576
$801$	−0.444494	−0.0157054
$802$	−23.2961	−0.822615
$803$	−67.4618	−2.38067
$804$	−1.08420	−0.0382367
$805$	0	0
$806$	6.05875	0.213410
$807$	−35.4305	−1.24721
$808$	−2.34899	−0.0826373
$809$	−32.0740	−1.12766	−0.563832	−	0.825890i	$-0.690673\pi$
$809$	−32.0740	−1.12766	−0.563832	+	0.825890i	$0.690673\pi$
$810$	46.5262	1.63476
$811$	24.1209	0.847000	0.423500	−	0.905896i	$-0.360801\pi$
$811$	24.1209	0.847000	0.423500	+	0.905896i	$0.360801\pi$
$812$	0	0
$813$	0.0495337	0.00173722
$814$	−11.5936	−0.406355
$815$	−7.06579	−0.247504
$816$	22.7011	0.794697
$817$	−1.57855	−0.0552264
$818$	−13.5636	−0.474242
$819$	0	0
$820$	−0.452323	−0.0157958
$821$	−49.9112	−1.74191	−0.870957	−	0.491360i	$-0.836500\pi$
$821$	−49.9112	−1.74191	−0.870957	+	0.491360i	$0.836500\pi$
$822$	49.0384	1.71041
$823$	11.7380	0.409160	0.204580	−	0.978850i	$-0.434417\pi$
$823$	11.7380	0.409160	0.204580	+	0.978850i	$0.434417\pi$
$824$	−3.67154	−0.127904
$825$	43.5712	1.51696
$826$	0	0
$827$	−3.88857	−0.135219	−0.0676094	−	0.997712i	$-0.521537\pi$
$827$	−3.88857	−0.135219	−0.0676094	+	0.997712i	$0.521537\pi$
$828$	0.152103	0.00528594
$829$	−9.78308	−0.339780	−0.169890	−	0.985463i	$-0.554341\pi$
$829$	−9.78308	−0.339780	−0.169890	+	0.985463i	$0.554341\pi$
$830$	3.72061	0.129144
$831$	11.9055	0.412997
$832$	−13.5577	−0.470030
$833$	0	0
$834$	−27.1526	−0.940217
$835$	−36.8786	−1.27624
$836$	−0.0801137	−0.00277079
$837$	10.7061	0.370057
$838$	28.8863	0.997861
$839$	−5.56620	−0.192166	−0.0960832	−	0.995373i	$-0.530631\pi$
$839$	−5.56620	−0.192166	−0.0960832	+	0.995373i	$0.530631\pi$
$840$	0	0
$841$	7.09983	0.244822
$842$	7.38169	0.254390
$843$	−47.0547	−1.62065
$844$	−0.899826	−0.0309733
$845$	31.2070	1.07355
$846$	−13.3355	−0.458485
$847$	0	0
$848$	−11.3457	−0.389615
$849$	40.9110	1.40406
$850$	−17.4938	−0.600034
$851$	5.75588	0.197309
$852$	−0.168025	−0.00575644
$853$	46.4542	1.59056	0.795281	−	0.606240i	$-0.207323\pi$
$853$	46.4542	1.59056	0.795281	+	0.606240i	$0.207323\pi$
$854$	0	0
$855$	−0.971600	−0.0332280
$856$	−24.8834	−0.850497
$857$	27.4114	0.936357	0.468178	−	0.883634i	$-0.344910\pi$
$857$	27.4114	0.936357	0.468178	+	0.883634i	$0.344910\pi$
$858$	−23.6527	−0.807491
$859$	−9.57050	−0.326541	−0.163271	−	0.986581i	$-0.552204\pi$
$859$	−9.57050	−0.326541	−0.163271	+	0.986581i	$0.552204\pi$
$860$	−0.641893	−0.0218884
$861$	0	0
$862$	−30.6088	−1.04254
$863$	2.10530	0.0716652	0.0358326	−	0.999358i	$-0.488592\pi$
$863$	2.10530	0.0716652	0.0358326	+	0.999358i	$0.488592\pi$
$864$	−1.05698	−0.0359593
$865$	−8.82774	−0.300152
$866$	46.5722	1.58259
$867$	−16.6963	−0.567035
$868$	0	0
$869$	71.1688	2.41424
$870$	50.7299	1.71990
$871$	−19.8772	−0.673514
$872$	43.4576	1.47166
$873$	7.20225	0.243759
$874$	−1.70427	−0.0576478
$875$	0	0
$876$	1.18678	0.0400975
$877$	−12.5653	−0.424301	−0.212151	−	0.977237i	$-0.568047\pi$
$877$	−12.5653	−0.424301	−0.212151	+	0.977237i	$0.568047\pi$
$878$	−26.0718	−0.879881
$879$	−19.0462	−0.642412
$880$	61.1753	2.06222
$881$	−7.94150	−0.267556	−0.133778	−	0.991011i	$-0.542711\pi$
$881$	−7.94150	−0.267556	−0.133778	+	0.991011i	$0.542711\pi$
$882$	0	0
$883$	−3.75050	−0.126215	−0.0631073	−	0.998007i	$-0.520101\pi$
$883$	−3.75050	−0.126215	−0.0631073	+	0.998007i	$0.520101\pi$
$884$	−0.221630	−0.00745423
$885$	56.2371	1.89039
$886$	−53.2869	−1.79021
$887$	18.1410	0.609114	0.304557	−	0.952494i	$-0.401492\pi$
$887$	18.1410	0.609114	0.304557	+	0.952494i	$0.401492\pi$
$888$	9.14703	0.306954
$889$	0	0
$890$	2.02522	0.0678857
$891$	−56.2097	−1.88309
$892$	0.381669	0.0127792
$893$	−3.48717	−0.116694
$894$	13.0895	0.437779
$895$	−23.4859	−0.785048
$896$	0	0
$897$	11.7429	0.392084
$898$	−20.0474	−0.668992
$899$	15.6992	0.523599
$900$	−0.182020	−0.00606734
$901$	−8.50802	−0.283443
$902$	−23.4154	−0.779646
$903$	0	0
$904$	30.5745	1.01689
$905$	59.1497	1.96620
$906$	33.9861	1.12911
$907$	18.1293	0.601974	0.300987	−	0.953628i	$-0.402684\pi$
$907$	18.1293	0.601974	0.300987	+	0.953628i	$0.402684\pi$
$908$	−1.20345	−0.0399379
$909$	0.767407	0.0254533
$910$	0	0
$911$	10.1307	0.335645	0.167823	−	0.985817i	$-0.446326\pi$
$911$	10.1307	0.335645	0.167823	+	0.985817i	$0.446326\pi$
$912$	−2.64657	−0.0876366
$913$	−4.49498	−0.148762
$914$	24.6412	0.815058
$915$	−31.1656	−1.03030
$916$	0.174468	0.00576458
$917$	0	0
$918$	16.7809	0.553853
$919$	21.2900	0.702292	0.351146	−	0.936321i	$-0.385792\pi$
$919$	21.2900	0.702292	0.351146	+	0.936321i	$0.385792\pi$
$920$	−31.0810	−1.02471
$921$	3.03564	0.100028
$922$	2.17063	0.0714859
$923$	−3.08049	−0.101396
$924$	0	0
$925$	−6.88802	−0.226477
$926$	−19.7175	−0.647958
$927$	1.19948	0.0393960
$928$	−1.54994	−0.0508793
$929$	−46.4231	−1.52309	−0.761546	−	0.648111i	$-0.775559\pi$
$929$	−46.4231	−1.52309	−0.761546	+	0.648111i	$0.775559\pi$
$930$	22.0616	0.723429
$931$	0	0
$932$	0.0201297	0.000659372 0
$933$	−21.6973	−0.710339
$934$	−17.3126	−0.566486
$935$	45.8745	1.50026
$936$	4.43151	0.144849
$937$	−12.5444	−0.409806	−0.204903	−	0.978782i	$-0.565688\pi$
$937$	−12.5444	−0.409806	−0.204903	+	0.978782i	$0.565688\pi$
$938$	0	0
$939$	52.4608	1.71199
$940$	−1.41801	−0.0462503
$941$	25.6360	0.835711	0.417855	−	0.908514i	$-0.362782\pi$
$941$	25.6360	0.835711	0.417855	+	0.908514i	$0.362782\pi$
$942$	−50.3860	−1.64167
$943$	11.6250	0.378564
$944$	36.3770	1.18397
$945$	0	0
$946$	−33.2288	−1.08036
$947$	−38.4122	−1.24823	−0.624114	−	0.781333i	$-0.714540\pi$
$947$	−38.4122	−1.24823	−0.624114	+	0.781333i	$0.714540\pi$
$948$	−1.25199	−0.0406628
$949$	21.7579	0.706290
$950$	2.03949	0.0661698
$951$	−33.7291	−1.09374
$952$	0	0
$953$	28.7580	0.931564	0.465782	−	0.884899i	$-0.345773\pi$
$953$	28.7580	0.931564	0.465782	+	0.884899i	$0.345773\pi$
$954$	3.79316	0.122808
$955$	−5.95399	−0.192667
$956$	−0.288706	−0.00933740
$957$	−61.2883	−1.98117
$958$	−51.7907	−1.67328
$959$	0	0
$960$	−49.3676	−1.59333
$961$	−24.1726	−0.779763
$962$	3.73918	0.120556
$963$	8.12931	0.261963
$964$	−0.630014	−0.0202914
$965$	−10.7799	−0.347016
$966$	0	0
$967$	32.1158	1.03277	0.516387	−	0.856355i	$-0.327276\pi$
$967$	32.1158	1.03277	0.516387	+	0.856355i	$0.327276\pi$
$968$	−44.1762	−1.41988
$969$	−1.98462	−0.0637553
$970$	−32.8152	−1.05363
$971$	−51.8573	−1.66418	−0.832091	−	0.554640i	$-0.812856\pi$
$971$	−51.8573	−1.66418	−0.832091	+	0.554640i	$0.812856\pi$
$972$	0.428173	0.0137336
$973$	0	0
$974$	41.1303	1.31790
$975$	−14.0526	−0.450045
$976$	−20.1595	−0.645290
$977$	4.99968	0.159954	0.0799770	−	0.996797i	$-0.474515\pi$
$977$	4.99968	0.159954	0.0799770	+	0.996797i	$0.474515\pi$
$978$	6.43465	0.205757
$979$	−2.44673	−0.0781980
$980$	0	0
$981$	−14.1974	−0.453289
$982$	−26.7362	−0.853188
$983$	−31.7099	−1.01139	−0.505695	−	0.862713i	$-0.668764\pi$
$983$	−31.7099	−1.01139	−0.505695	+	0.862713i	$0.668764\pi$
$984$	18.4741	0.588933
$985$	70.1181	2.23415
$986$	24.6072	0.783654
$987$	0	0
$988$	0.0258384	0.000822028 0
$989$	16.4971	0.524578
$990$	−20.4524	−0.650020
$991$	13.5094	0.429140	0.214570	−	0.976709i	$-0.431165\pi$
$991$	13.5094	0.429140	0.214570	+	0.976709i	$0.431165\pi$
$992$	−0.674044	−0.0214009
$993$	27.2184	0.863749
$994$	0	0
$995$	−49.3084	−1.56318
$996$	0.0790751	0.00250559
$997$	33.5402	1.06223	0.531114	−	0.847300i	$-0.321773\pi$
$997$	33.5402	1.06223	0.531114	+	0.847300i	$0.321773\pi$
$998$	−43.3233	−1.37137
$999$	6.60731	0.209046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.2.a.h.1.19		24
7.6	odd	2		2401.2.a.i.1.19		24
49.3	odd	42		343.2.g.g.177.2		48
49.5	odd	42		343.2.g.h.67.3		48
49.6	odd	14		343.2.e.c.246.2		48
49.8	even	7		343.2.e.d.99.2		48
49.10	odd	42		343.2.g.h.128.3		48
49.16	even	21		49.2.g.a.11.2	yes	48
49.33	odd	42		343.2.g.g.312.2		48
49.39	even	21		343.2.g.i.128.3		48
49.41	odd	14		343.2.e.c.99.2		48
49.43	even	7		343.2.e.d.246.2		48
49.44	even	21		343.2.g.i.67.3		48
49.46	even	21		49.2.g.a.9.2	✓	48
147.65	odd	42		441.2.bb.d.109.3		48
147.95	odd	42		441.2.bb.d.352.3		48
196.95	odd	42		784.2.bg.c.401.3		48
196.163	odd	42		784.2.bg.c.305.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.2	✓	48	49.46	even	21
49.2.g.a.11.2	yes	48	49.16	even	21
343.2.e.c.99.2		48	49.41	odd	14
343.2.e.c.246.2		48	49.6	odd	14
343.2.e.d.99.2		48	49.8	even	7
343.2.e.d.246.2		48	49.43	even	7
343.2.g.g.177.2		48	49.3	odd	42
343.2.g.g.312.2		48	49.33	odd	42
343.2.g.h.67.3		48	49.5	odd	42
343.2.g.h.128.3		48	49.10	odd	42
343.2.g.i.67.3		48	49.44	even	21
343.2.g.i.128.3		48	49.39	even	21
441.2.bb.d.109.3		48	147.65	odd	42
441.2.bb.d.352.3		48	147.95	odd	42
784.2.bg.c.305.3		48	196.163	odd	42
784.2.bg.c.401.3		48	196.95	odd	42
2401.2.a.h.1.19		24	1.1	even	1	trivial
2401.2.a.i.1.19		24	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q+1.39799 q^{2} +1.98350 q^{3} -0.0456113 q^{4} -3.04490 q^{5} +2.77292 q^{6} -2.85975 q^{8} +0.934270 q^{9} +O(q^{10})\)	\(q+1.39799 q^{2} +1.98350 q^{3} -0.0456113 q^{4} -3.04490 q^{5} +2.77292 q^{6} -2.85975 q^{8} +0.934270 q^{9} -4.25676 q^{10} +5.14272 q^{11} -0.0904700 q^{12} -1.65864 q^{13} -6.03957 q^{15} -3.90670 q^{16} -2.92958 q^{17} +1.30610 q^{18} +0.341540 q^{19} +0.138882 q^{20} +7.18949 q^{22} -3.56937 q^{23} -5.67232 q^{24} +4.27145 q^{25} -2.31876 q^{26} -4.09737 q^{27} -6.00831 q^{29} -8.44328 q^{30} -2.61292 q^{31} +0.257966 q^{32} +10.2006 q^{33} -4.09553 q^{34} -0.0426133 q^{36} -1.61257 q^{37} +0.477471 q^{38} -3.28990 q^{39} +8.70768 q^{40} -3.25689 q^{41} -4.62185 q^{43} -0.234566 q^{44} -2.84476 q^{45} -4.98997 q^{46} -10.2102 q^{47} -7.74893 q^{48} +5.97146 q^{50} -5.81081 q^{51} +0.0756526 q^{52} +2.90418 q^{53} -5.72811 q^{54} -15.6591 q^{55} +0.677444 q^{57} -8.39959 q^{58} -9.31144 q^{59} +0.275473 q^{60} +5.16024 q^{61} -3.65285 q^{62} +8.17403 q^{64} +5.05039 q^{65} +14.2604 q^{66} +11.9841 q^{67} +0.133622 q^{68} -7.07985 q^{69} +1.85724 q^{71} -2.67178 q^{72} -13.1179 q^{73} -2.25437 q^{74} +8.47241 q^{75} -0.0155781 q^{76} -4.59927 q^{78} +13.8387 q^{79} +11.8955 q^{80} -10.9299 q^{81} -4.55311 q^{82} -0.874048 q^{83} +8.92028 q^{85} -6.46133 q^{86} -11.9175 q^{87} -14.7069 q^{88} -0.475767 q^{89} -3.97696 q^{90} +0.162804 q^{92} -5.18273 q^{93} -14.2737 q^{94} -1.03996 q^{95} +0.511675 q^{96} +7.70896 q^{97} +4.80469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 7 q^{3} + 23 q^{4} - 14 q^{5} - 14 q^{6} - 3 q^{8} + 15 q^{9}+O(q^{10}) \) 24 * q - q^2 - 7 * q^3 + 23 * q^4 - 14 * q^5 - 14 * q^6 - 3 * q^8 + 15 * q^9	\( 24 q - q^{2} - 7 q^{3} + 23 q^{4} - 14 q^{5} - 14 q^{6} - 3 q^{8} + 15 q^{9} - 14 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 15 q^{15} + 17 q^{16} - 28 q^{17} - 2 q^{18} - 21 q^{19} - 42 q^{20} + 4 q^{22} - 8 q^{23} - 21 q^{24} + 4 q^{25} - 28 q^{26} - 28 q^{27} - 8 q^{29} - 11 q^{30} - 35 q^{31} + 18 q^{32} + 7 q^{33} + q^{36} - 8 q^{37} - 14 q^{38} - 14 q^{39} - 7 q^{40} - 35 q^{41} - 8 q^{43} - 20 q^{44} - 42 q^{45} - 6 q^{46} - 70 q^{47} - 42 q^{48} + 20 q^{50} + 24 q^{51} + 21 q^{52} + 24 q^{53} - 14 q^{54} - 56 q^{55} - 20 q^{57} + 19 q^{58} - 84 q^{59} - 56 q^{62} - 9 q^{64} + 14 q^{65} - 11 q^{67} - 77 q^{68} - 42 q^{69} - 8 q^{71} + 40 q^{72} + 7 q^{73} + 43 q^{74} - 49 q^{75} - 7 q^{76} - 15 q^{79} - 70 q^{80} - 36 q^{81} + 56 q^{82} - 56 q^{83} + 36 q^{85} - 86 q^{86} - 70 q^{88} - 70 q^{89} + 56 q^{90} - 68 q^{92} - 11 q^{93} - 84 q^{94} + 54 q^{95} - 56 q^{96} - 8 q^{99}+O(q^{100}) \) 24 * q - q^2 - 7 * q^3 + 23 * q^4 - 14 * q^5 - 14 * q^6 - 3 * q^8 + 15 * q^9 - 14 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 15 * q^15 + 17 * q^16 - 28 * q^17 - 2 * q^18 - 21 * q^19 - 42 * q^20 + 4 * q^22 - 8 * q^23 - 21 * q^24 + 4 * q^25 - 28 * q^26 - 28 * q^27 - 8 * q^29 - 11 * q^30 - 35 * q^31 + 18 * q^32 + 7 * q^33 + q^36 - 8 * q^37 - 14 * q^38 - 14 * q^39 - 7 * q^40 - 35 * q^41 - 8 * q^43 - 20 * q^44 - 42 * q^45 - 6 * q^46 - 70 * q^47 - 42 * q^48 + 20 * q^50 + 24 * q^51 + 21 * q^52 + 24 * q^53 - 14 * q^54 - 56 * q^55 - 20 * q^57 + 19 * q^58 - 84 * q^59 - 56 * q^62 - 9 * q^64 + 14 * q^65 - 11 * q^67 - 77 * q^68 - 42 * q^69 - 8 * q^71 + 40 * q^72 + 7 * q^73 + 43 * q^74 - 49 * q^75 - 7 * q^76 - 15 * q^79 - 70 * q^80 - 36 * q^81 + 56 * q^82 - 56 * q^83 + 36 * q^85 - 86 * q^86 - 70 * q^88 - 70 * q^89 + 56 * q^90 - 68 * q^92 - 11 * q^93 - 84 * q^94 + 54 * q^95 - 56 * q^96 - 8 * q^99

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