LMFDB - Embedded newform 1441.4.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.95472 q^{2} +2.24647 q^{3} +7.63980 q^{4} +7.89434 q^{5} -8.88416 q^{6} +22.8548 q^{7} +1.42449 q^{8} -21.9534 q^{9} +O(q^{10})$	\(q-3.95472 q^{2} +2.24647 q^{3} +7.63980 q^{4} +7.89434 q^{5} -8.88416 q^{6} +22.8548 q^{7} +1.42449 q^{8} -21.9534 q^{9} -31.2199 q^{10} +11.0000 q^{11} +17.1626 q^{12} -67.8596 q^{13} -90.3845 q^{14} +17.7344 q^{15} -66.7519 q^{16} +104.859 q^{17} +86.8194 q^{18} -31.5355 q^{19} +60.3112 q^{20} +51.3427 q^{21} -43.5019 q^{22} +81.2996 q^{23} +3.20007 q^{24} -62.6794 q^{25} +268.366 q^{26} -109.972 q^{27} +174.606 q^{28} +73.1092 q^{29} -70.1346 q^{30} +99.1195 q^{31} +252.589 q^{32} +24.7112 q^{33} -414.689 q^{34} +180.424 q^{35} -167.719 q^{36} -280.517 q^{37} +124.714 q^{38} -152.444 q^{39} +11.2454 q^{40} -435.427 q^{41} -203.046 q^{42} -273.797 q^{43} +84.0378 q^{44} -173.307 q^{45} -321.517 q^{46} -373.903 q^{47} -149.956 q^{48} +179.344 q^{49} +247.879 q^{50} +235.563 q^{51} -518.434 q^{52} +545.235 q^{53} +434.909 q^{54} +86.8378 q^{55} +32.5565 q^{56} -70.8435 q^{57} -289.126 q^{58} -604.366 q^{59} +135.487 q^{60} -787.664 q^{61} -391.990 q^{62} -501.741 q^{63} -464.903 q^{64} -535.707 q^{65} -97.7257 q^{66} -445.757 q^{67} +801.103 q^{68} +182.637 q^{69} -713.526 q^{70} +503.114 q^{71} -31.2723 q^{72} -374.845 q^{73} +1109.37 q^{74} -140.807 q^{75} -240.925 q^{76} +251.403 q^{77} +602.875 q^{78} +1194.04 q^{79} -526.962 q^{80} +345.692 q^{81} +1721.99 q^{82} +228.946 q^{83} +392.248 q^{84} +827.794 q^{85} +1082.79 q^{86} +164.238 q^{87} +15.6694 q^{88} -727.025 q^{89} +685.382 q^{90} -1550.92 q^{91} +621.113 q^{92} +222.669 q^{93} +1478.68 q^{94} -248.952 q^{95} +567.433 q^{96} +240.849 q^{97} -709.255 q^{98} -241.487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) $ 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * 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 $

$2$	−3.95472	−1.39820	−0.699102	−	0.715022i	$-0.746417\pi$
$2$	−3.95472	−1.39820	−0.699102	+	0.715022i	$0.746417\pi$
$3$	2.24647	0.432333	0.216167	−	0.976356i	$-0.430645\pi$
$3$	2.24647	0.432333	0.216167	+	0.976356i	$0.430645\pi$
$4$	7.63980	0.954975
$5$	7.89434	0.706091	0.353046	−	0.935606i	$-0.385146\pi$
$5$	7.89434	0.706091	0.353046	+	0.935606i	$0.385146\pi$
$6$	−8.88416	−0.604490
$7$	22.8548	1.23405	0.617023	−	0.786945i	$-0.288339\pi$
$7$	22.8548	1.23405	0.617023	+	0.786945i	$0.288339\pi$
$8$	1.42449	0.0629541
$9$	−21.9534	−0.813088
$10$	−31.2199	−0.987260
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	17.1626	0.412868
$13$	−67.8596	−1.44776	−0.723879	−	0.689927i	$-0.757643\pi$
$13$	−67.8596	−1.44776	−0.723879	+	0.689927i	$0.757643\pi$
$14$	−90.3845	−1.72545
$15$	17.7344	0.305267
$16$	−66.7519	−1.04300
$17$	104.859	1.49601	0.748003	−	0.663696i	$-0.231013\pi$
$17$	104.859	1.49601	0.748003	+	0.663696i	$0.231013\pi$
$18$	86.8194	1.13686
$19$	−31.5355	−0.380775	−0.190388	−	0.981709i	$-0.560975\pi$
$19$	−31.5355	−0.380775	−0.190388	+	0.981709i	$0.560975\pi$
$20$	60.3112	0.674300
$21$	51.3427	0.533519
$22$	−43.5019	−0.421574
$23$	81.2996	0.737050	0.368525	−	0.929618i	$-0.379863\pi$
$23$	81.2996	0.737050	0.368525	+	0.929618i	$0.379863\pi$
$24$	3.20007	0.0272172
$25$	−62.6794	−0.501435
$26$	268.366	2.02426
$27$	−109.972	−0.783858
$28$	174.606	1.17848
$29$	73.1092	0.468139	0.234070	−	0.972220i	$-0.424796\pi$
$29$	73.1092	0.468139	0.234070	+	0.972220i	$0.424796\pi$
$30$	−70.1346	−0.426825
$31$	99.1195	0.574270	0.287135	−	0.957890i	$-0.407297\pi$
$31$	99.1195	0.574270	0.287135	+	0.957890i	$0.407297\pi$
$32$	252.589	1.39537
$33$	24.7112	0.130353
$34$	−414.689	−2.09172
$35$	180.424	0.871349
$36$	−167.719	−0.776479
$37$	−280.517	−1.24640	−0.623199	−	0.782063i	$-0.714167\pi$
$37$	−280.517	−1.24640	−0.623199	+	0.782063i	$0.714167\pi$
$38$	124.714	0.532402
$39$	−152.444	−0.625914
$40$	11.2454	0.0444513
$41$	−435.427	−1.65859	−0.829295	−	0.558810i	$-0.811258\pi$
$41$	−435.427	−1.65859	−0.829295	+	0.558810i	$0.811258\pi$
$42$	−203.046	−0.745969
$43$	−273.797	−0.971015	−0.485507	−	0.874233i	$-0.661365\pi$
$43$	−273.797	−0.971015	−0.485507	+	0.874233i	$0.661365\pi$
$44$	84.0378	0.287936
$45$	−173.307	−0.574114
$46$	−321.517	−1.03055
$47$	−373.903	−1.16041	−0.580206	−	0.814470i	$-0.697028\pi$
$47$	−373.903	−1.16041	−0.580206	+	0.814470i	$0.697028\pi$
$48$	−149.956	−0.450923
$49$	179.344	0.522869
$50$	247.879	0.701108
$51$	235.563	0.646773
$52$	−518.434	−1.38257
$53$	545.235	1.41309	0.706545	−	0.707668i	$-0.250253\pi$
$53$	545.235	1.41309	0.706545	+	0.707668i	$0.250253\pi$
$54$	434.909	1.09599
$55$	86.8378	0.212895
$56$	32.5565	0.0776882
$57$	−70.8435	−0.164622
$58$	−289.126	−0.654554
$59$	−604.366	−1.33359	−0.666795	−	0.745241i	$-0.732334\pi$
$59$	−604.366	−1.33359	−0.666795	+	0.745241i	$0.732334\pi$
$60$	135.487	0.291522
$61$	−787.664	−1.65328	−0.826640	−	0.562731i	$-0.809751\pi$
$61$	−787.664	−1.65328	−0.826640	+	0.562731i	$0.809751\pi$
$62$	−391.990	−0.802947
$63$	−501.741	−1.00339
$64$	−464.903	−0.908014
$65$	−535.707	−1.02225
$66$	−97.7257	−0.182261
$67$	−445.757	−0.812805	−0.406403	−	0.913694i	$-0.633217\pi$
$67$	−445.757	−0.812805	−0.406403	+	0.913694i	$0.633217\pi$
$68$	801.103	1.42865
$69$	182.637	0.318651
$70$	−713.526	−1.21832
$71$	503.114	0.840967	0.420483	−	0.907300i	$-0.361860\pi$
$71$	503.114	0.840967	0.420483	+	0.907300i	$0.361860\pi$
$72$	−31.2723	−0.0511872
$73$	−374.845	−0.600990	−0.300495	−	0.953783i	$-0.597152\pi$
$73$	−374.845	−0.600990	−0.300495	+	0.953783i	$0.597152\pi$
$74$	1109.37	1.74272
$75$	−140.807	−0.216787
$76$	−240.925	−0.363631
$77$	251.403	0.372079
$78$	602.875	0.875156
$79$	1194.04	1.70051	0.850253	−	0.526374i	$-0.176449\pi$
$79$	1194.04	1.70051	0.850253	+	0.526374i	$0.176449\pi$
$80$	−526.962	−0.736452
$81$	345.692	0.474200
$82$	1721.99	2.31905
$83$	228.946	0.302773	0.151386	−	0.988475i	$-0.451626\pi$
$83$	228.946	0.302773	0.151386	+	0.988475i	$0.451626\pi$
$84$	392.248	0.509497
$85$	827.794	1.05632
$86$	1082.79	1.35768
$87$	164.238	0.202392
$88$	15.6694	0.0189814
$89$	−727.025	−0.865894	−0.432947	−	0.901419i	$-0.642526\pi$
$89$	−727.025	−0.865894	−0.432947	+	0.901419i	$0.642526\pi$
$90$	685.382	0.802729
$91$	−1550.92	−1.78660
$92$	621.113	0.703864
$93$	222.669	0.248276
$94$	1478.68	1.62249
$95$	−248.952	−0.268862
$96$	567.433	0.603265
$97$	240.849	0.252109	0.126054	−	0.992023i	$-0.459769\pi$
$97$	240.849	0.252109	0.126054	+	0.992023i	$0.459769\pi$
$98$	−709.255	−0.731077
$99$	−241.487	−0.245155
$100$	−478.858	−0.478858
$101$	42.7428	0.0421096	0.0210548	−	0.999778i	$-0.493298\pi$
$101$	42.7428	0.0421096	0.0210548	+	0.999778i	$0.493298\pi$
$102$	−931.585	−0.904321
$103$	−898.582	−0.859611	−0.429805	−	0.902922i	$-0.641418\pi$
$103$	−898.582	−0.859611	−0.429805	+	0.902922i	$0.641418\pi$
$104$	−96.6652	−0.0911423
$105$	405.317	0.376713
$106$	−2156.25	−1.97579
$107$	966.274	0.873021	0.436510	−	0.899699i	$-0.356214\pi$
$107$	966.274	0.873021	0.436510	+	0.899699i	$0.356214\pi$
$108$	−840.166	−0.748565
$109$	−1249.35	−1.09786	−0.548928	−	0.835870i	$-0.684964\pi$
$109$	−1249.35	−1.09786	−0.548928	+	0.835870i	$0.684964\pi$
$110$	−343.419	−0.297670
$111$	−630.173	−0.538859
$112$	−1525.60	−1.28711
$113$	−618.520	−0.514916	−0.257458	−	0.966290i	$-0.582885\pi$
$113$	−618.520	−0.514916	−0.257458	+	0.966290i	$0.582885\pi$
$114$	280.166	0.230175
$115$	641.807	0.520425
$116$	558.540	0.447061
$117$	1489.75	1.17716
$118$	2390.10	1.86463
$119$	2396.54	1.84614
$120$	25.2625	0.0192178
$121$	121.000	0.0909091
$122$	3114.99	2.31162
$123$	−978.173	−0.717064
$124$	757.253	0.548414
$125$	−1481.61	−1.06015
$126$	1984.24	1.40294
$127$	1919.78	1.34136	0.670680	−	0.741746i	$-0.266002\pi$
$127$	1919.78	1.34136	0.670680	+	0.741746i	$0.266002\pi$
$128$	−182.150	−0.125781
$129$	−615.076	−0.419802
$130$	2118.57	1.42931
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	188.788	0.124484
$133$	−720.738	−0.469894
$134$	1762.85	1.13647
$135$	−868.159	−0.553476
$136$	149.371	0.0941796
$137$	−2134.40	−1.33105	−0.665526	−	0.746374i	$-0.731793\pi$
$137$	−2134.40	−1.33105	−0.665526	+	0.746374i	$0.731793\pi$
$138$	−722.279	−0.445539
$139$	1552.05	0.947073	0.473537	−	0.880774i	$-0.342977\pi$
$139$	1552.05	0.947073	0.473537	+	0.880774i	$0.342977\pi$
$140$	1378.40	0.832117
$141$	−839.962	−0.501685
$142$	−1989.67	−1.17584
$143$	−746.455	−0.436516
$144$	1465.43	0.848049
$145$	577.149	0.330549
$146$	1482.41	0.840307
$147$	402.891	0.226054
$148$	−2143.09	−1.19028
$149$	1186.00	0.652084	0.326042	−	0.945355i	$-0.394285\pi$
$149$	1186.00	0.652084	0.326042	+	0.945355i	$0.394285\pi$
$150$	556.853	0.303113
$151$	−229.781	−0.123836	−0.0619181	−	0.998081i	$-0.519722\pi$
$151$	−229.781	−0.123836	−0.0619181	+	0.998081i	$0.519722\pi$
$152$	−44.9219	−0.0239714
$153$	−2302.01	−1.21638
$154$	−994.229	−0.520242
$155$	782.483	0.405487
$156$	−1164.65	−0.597732
$157$	882.677	0.448696	0.224348	−	0.974509i	$-0.427975\pi$
$157$	882.677	0.448696	0.224348	+	0.974509i	$0.427975\pi$
$158$	−4722.09	−2.37765
$159$	1224.85	0.610926
$160$	1994.02	0.985259
$161$	1858.09	0.909553
$162$	−1367.11	−0.663028
$163$	−117.233	−0.0563337	−0.0281668	−	0.999603i	$-0.508967\pi$
$163$	−117.233	−0.0563337	−0.0281668	+	0.999603i	$0.508967\pi$
$164$	−3326.57	−1.58391
$165$	195.078	0.0920414
$166$	−905.418	−0.423338
$167$	−1793.43	−0.831019	−0.415509	−	0.909589i	$-0.636397\pi$
$167$	−1793.43	−0.831019	−0.415509	+	0.909589i	$0.636397\pi$
$168$	73.1371	0.0335872
$169$	2407.92	1.09600
$170$	−3273.69	−1.47695
$171$	692.310	0.309604
$172$	−2091.75	−0.927295
$173$	−703.936	−0.309360	−0.154680	−	0.987965i	$-0.549435\pi$
$173$	−703.936	−0.309360	−0.154680	+	0.987965i	$0.549435\pi$
$174$	−649.514	−0.282986
$175$	−1432.53	−0.618794
$176$	−734.270	−0.314476
$177$	−1357.69	−0.576555
$178$	2875.18	1.21070
$179$	−2793.85	−1.16661	−0.583303	−	0.812255i	$-0.698240\pi$
$179$	−2793.85	−1.16661	−0.583303	+	0.812255i	$0.698240\pi$
$180$	−1324.03	−0.548265
$181$	2488.11	1.02177	0.510884	−	0.859650i	$-0.329318\pi$
$181$	2488.11	1.02177	0.510884	+	0.859650i	$0.329318\pi$
$182$	6133.45	2.49803
$183$	−1769.46	−0.714768
$184$	115.810	0.0464003
$185$	−2214.50	−0.880071
$186$	−880.593	−0.347141
$187$	1153.45	0.451063
$188$	−2856.54	−1.10816
$189$	−2513.40	−0.967317
$190$	984.534	0.375924
$191$	2847.99	1.07892	0.539459	−	0.842012i	$-0.318629\pi$
$191$	2847.99	1.07892	0.539459	+	0.842012i	$0.318629\pi$
$192$	−1044.39	−0.392565
$193$	−5289.02	−1.97260	−0.986301	−	0.164955i	$-0.947252\pi$
$193$	−5289.02	−1.97260	−0.986301	+	0.164955i	$0.947252\pi$
$194$	−952.491	−0.352499
$195$	−1203.45	−0.441953
$196$	1370.15	0.499327
$197$	4288.95	1.55114	0.775571	−	0.631260i	$-0.217462\pi$
$197$	4288.95	1.55114	0.775571	+	0.631260i	$0.217462\pi$
$198$	955.014	0.342777
$199$	2749.11	0.979291	0.489646	−	0.871922i	$-0.337126\pi$
$199$	2749.11	0.979291	0.489646	+	0.871922i	$0.337126\pi$
$200$	−89.2860	−0.0315674
$201$	−1001.38	−0.351403
$202$	−169.036	−0.0588778
$203$	1670.90	0.577705
$204$	1799.65	0.617652
$205$	−3437.41	−1.17112
$206$	3553.64	1.20191
$207$	−1784.80	−0.599286
$208$	4529.75	1.51001
$209$	−346.890	−0.114808
$210$	−1602.91	−0.526722
$211$	1283.82	0.418870	0.209435	−	0.977823i	$-0.432838\pi$
$211$	1283.82	0.418870	0.209435	+	0.977823i	$0.432838\pi$
$212$	4165.49	1.34947
$213$	1130.23	0.363578
$214$	−3821.34	−1.22066
$215$	−2161.45	−0.685625
$216$	−156.654	−0.0493471
$217$	2265.36	0.708676
$218$	4940.84	1.53503
$219$	−842.078	−0.259828
$220$	663.423	0.203309
$221$	−7115.70	−2.16585
$222$	2492.16	0.753436
$223$	3020.94	0.907161	0.453580	−	0.891215i	$-0.350147\pi$
$223$	3020.94	0.907161	0.453580	+	0.891215i	$0.350147\pi$
$224$	5772.88	1.72195
$225$	1376.02	0.407711
$226$	2446.07	0.719957
$227$	−6507.75	−1.90280	−0.951398	−	0.307964i	$-0.900352\pi$
$227$	−6507.75	−1.90280	−0.951398	+	0.307964i	$0.900352\pi$
$228$	−541.230	−0.157210
$229$	2126.97	0.613773	0.306887	−	0.951746i	$-0.400713\pi$
$229$	2126.97	0.613773	0.306887	+	0.951746i	$0.400713\pi$
$230$	−2538.17	−0.727660
$231$	564.770	0.160862
$232$	104.143	0.0294713
$233$	−4572.64	−1.28568	−0.642840	−	0.766000i	$-0.722244\pi$
$233$	−4572.64	−1.28568	−0.642840	+	0.766000i	$0.722244\pi$
$234$	−5891.53	−1.64590
$235$	−2951.72	−0.819357
$236$	−4617.24	−1.27354
$237$	2682.37	0.735185
$238$	−9477.64	−2.58128
$239$	−3261.52	−0.882722	−0.441361	−	0.897330i	$-0.645504\pi$
$239$	−3261.52	−0.882722	−0.441361	+	0.897330i	$0.645504\pi$
$240$	−1183.80	−0.318393
$241$	−6138.18	−1.64064	−0.820321	−	0.571903i	$-0.806205\pi$
$241$	−6138.18	−1.64064	−0.820321	+	0.571903i	$0.806205\pi$
$242$	−478.521	−0.127109
$243$	3745.84	0.988871
$244$	−6017.60	−1.57884
$245$	1415.80	0.369193
$246$	3868.40	1.00260
$247$	2139.98	0.551271
$248$	141.195	0.0361527
$249$	514.321	0.130899
$250$	5859.33	1.48231
$251$	5479.19	1.37786	0.688931	−	0.724827i	$-0.258080\pi$
$251$	5479.19	1.37786	0.688931	+	0.724827i	$0.258080\pi$
$252$	−3833.20	−0.958210
$253$	894.296	0.222229
$254$	−7592.19	−1.87550
$255$	1859.61	0.456681
$256$	4439.58	1.08388
$257$	5591.33	1.35711	0.678555	−	0.734549i	$-0.262606\pi$
$257$	5591.33	1.35711	0.678555	+	0.734549i	$0.262606\pi$
$258$	2432.45	0.586969
$259$	−6411.18	−1.53811
$260$	−4092.69	−0.976223
$261$	−1604.99	−0.380638
$262$	518.068	0.122162
$263$	−1662.32	−0.389746	−0.194873	−	0.980829i	$-0.562429\pi$
$263$	−1662.32	−0.389746	−0.194873	+	0.980829i	$0.562429\pi$
$264$	35.2008	0.00820628
$265$	4304.27	0.997771
$266$	2850.32	0.657008
$267$	−1633.24	−0.374355
$268$	−3405.50	−0.776208
$269$	930.758	0.210964	0.105482	−	0.994421i	$-0.466361\pi$
$269$	930.758	0.210964	0.105482	+	0.994421i	$0.466361\pi$
$270$	3433.32	0.773872
$271$	2342.63	0.525109	0.262555	−	0.964917i	$-0.415435\pi$
$271$	2342.63	0.525109	0.262555	+	0.964917i	$0.415435\pi$
$272$	−6999.54	−1.56033
$273$	−3484.10	−0.772407
$274$	8440.96	1.86108
$275$	−689.473	−0.151188
$276$	1395.31	0.304304
$277$	−5601.84	−1.21510	−0.607549	−	0.794282i	$-0.707847\pi$
$277$	−5601.84	−1.21510	−0.607549	+	0.794282i	$0.707847\pi$
$278$	−6137.92	−1.32420
$279$	−2176.01	−0.466932
$280$	257.012	0.0548550
$281$	−6242.59	−1.32527	−0.662637	−	0.748941i	$-0.730563\pi$
$281$	−6242.59	−1.32527	−0.662637	+	0.748941i	$0.730563\pi$
$282$	3321.81	0.701457
$283$	4186.91	0.879456	0.439728	−	0.898131i	$-0.355075\pi$
$283$	4186.91	0.879456	0.439728	+	0.898131i	$0.355075\pi$
$284$	3843.69	0.803102
$285$	−559.263	−0.116238
$286$	2952.02	0.610338
$287$	−9951.61	−2.04678
$288$	−5545.18	−1.13456
$289$	6082.45	1.23803
$290$	−2282.46	−0.462175
$291$	541.061	0.108995
$292$	−2863.74	−0.573931
$293$	−2202.19	−0.439089	−0.219545	−	0.975602i	$-0.570457\pi$
$293$	−2202.19	−0.439089	−0.219545	+	0.975602i	$0.570457\pi$
$294$	−1593.32	−0.316069
$295$	−4771.07	−0.941636
$296$	−399.593	−0.0784659
$297$	−1209.69	−0.236342
$298$	−4690.28	−0.911746
$299$	−5516.96	−1.06707
$300$	−1075.74	−0.207026
$301$	−6257.58	−1.19828
$302$	908.718	0.173148
$303$	96.0204	0.0182054
$304$	2105.05	0.397148
$305$	−6218.09	−1.16737
$306$	9103.81	1.70075
$307$	−5505.71	−1.02354	−0.511771	−	0.859122i	$-0.671010\pi$
$307$	−5505.71	−1.02354	−0.511771	+	0.859122i	$0.671010\pi$
$308$	1920.67	0.355326
$309$	−2018.64	−0.371638
$310$	−3094.50	−0.566954
$311$	4756.80	0.867311	0.433655	−	0.901079i	$-0.357224\pi$
$311$	4756.80	0.867311	0.433655	+	0.901079i	$0.357224\pi$
$312$	−217.155	−0.0394039
$313$	−6992.88	−1.26281	−0.631407	−	0.775451i	$-0.717522\pi$
$313$	−6992.88	−1.26281	−0.631407	+	0.775451i	$0.717522\pi$
$314$	−3490.74	−0.627369
$315$	−3960.92	−0.708483
$316$	9122.22	1.62394
$317$	−3956.53	−0.701012	−0.350506	−	0.936560i	$-0.613990\pi$
$317$	−3956.53	−0.701012	−0.350506	+	0.936560i	$0.613990\pi$
$318$	−4843.95	−0.854200
$319$	804.201	0.141149
$320$	−3670.11	−0.641141
$321$	2170.71	0.377436
$322$	−7348.23	−1.27174
$323$	−3306.78	−0.569642
$324$	2641.02	0.452849
$325$	4253.40	0.725957
$326$	463.623	0.0787660
$327$	−2806.63	−0.474640
$328$	−620.260	−0.104415
$329$	−8545.49	−1.43200
$330$	−771.480	−0.128693
$331$	−3191.55	−0.529980	−0.264990	−	0.964251i	$-0.585369\pi$
$331$	−3191.55	−0.529980	−0.264990	+	0.964251i	$0.585369\pi$
$332$	1749.10	0.289140
$333$	6158.30	1.01343
$334$	7092.53	1.16193
$335$	−3518.96	−0.573915
$336$	−3427.22	−0.556459
$337$	−1335.88	−0.215935	−0.107968	−	0.994154i	$-0.534434\pi$
$337$	−1335.88	−0.215935	−0.107968	+	0.994154i	$0.534434\pi$
$338$	−9522.66	−1.53244
$339$	−1389.49	−0.222615
$340$	6324.18	1.00876
$341$	1090.31	0.173149
$342$	−2737.89	−0.432890
$343$	−3740.33	−0.588802
$344$	−390.020	−0.0611293
$345$	1441.80	0.224997
$346$	2783.87	0.432548
$347$	1673.91	0.258964	0.129482	−	0.991582i	$-0.458669\pi$
$347$	1673.91	0.258964	0.129482	+	0.991582i	$0.458669\pi$
$348$	1254.74	0.193279
$349$	−10054.5	−1.54214	−0.771070	−	0.636750i	$-0.780278\pi$
$349$	−10054.5	−1.54214	−0.771070	+	0.636750i	$0.780278\pi$
$350$	5665.24	0.865200
$351$	7462.67	1.13484
$352$	2778.48	0.420720
$353$	−11954.4	−1.80246	−0.901228	−	0.433345i	$-0.857333\pi$
$353$	−11954.4	−1.80246	−0.901228	+	0.433345i	$0.857333\pi$
$354$	5369.28	0.806142
$355$	3971.75	0.593800
$356$	−5554.33	−0.826907
$357$	5383.76	0.798147
$358$	11048.9	1.63115
$359$	−6472.07	−0.951484	−0.475742	−	0.879585i	$-0.657820\pi$
$359$	−6472.07	−0.951484	−0.475742	+	0.879585i	$0.657820\pi$
$360$	−246.874	−0.0361429
$361$	−5864.51	−0.855010
$362$	−9839.79	−1.42864
$363$	271.823	0.0393030
$364$	−11848.7	−1.70616
$365$	−2959.15	−0.424354
$366$	6997.73	0.999392
$367$	−3023.46	−0.430037	−0.215018	−	0.976610i	$-0.568981\pi$
$367$	−3023.46	−0.430037	−0.215018	+	0.976610i	$0.568981\pi$
$368$	−5426.90	−0.768741
$369$	9559.09	1.34858
$370$	8757.72	1.23052
$371$	12461.3	1.74382
$372$	1701.15	0.237098
$373$	−6063.56	−0.841714	−0.420857	−	0.907127i	$-0.638271\pi$
$373$	−6063.56	−0.841714	−0.420857	+	0.907127i	$0.638271\pi$
$374$	−4561.57	−0.630678
$375$	−3328.38	−0.458338
$376$	−532.620	−0.0730527
$377$	−4961.16	−0.677753
$378$	9939.79	1.35251
$379$	9909.72	1.34308	0.671541	−	0.740967i	$-0.265633\pi$
$379$	9909.72	1.34308	0.671541	+	0.740967i	$0.265633\pi$
$380$	−1901.94	−0.256757
$381$	4312.72	0.579915
$382$	−11263.0	−1.50855
$383$	6231.51	0.831371	0.415685	−	0.909508i	$-0.363542\pi$
$383$	6231.51	0.831371	0.415685	+	0.909508i	$0.363542\pi$
$384$	−409.194	−0.0543791
$385$	1984.66	0.262722
$386$	20916.6	2.75810
$387$	6010.76	0.789520
$388$	1840.04	0.240758
$389$	7017.98	0.914719	0.457360	−	0.889282i	$-0.348795\pi$
$389$	7017.98	0.914719	0.457360	+	0.889282i	$0.348795\pi$
$390$	4759.30	0.617940
$391$	8525.01	1.10263
$392$	255.473	0.0329167
$393$	−294.288	−0.0377731
$394$	−16961.6	−2.16881
$395$	9426.16	1.20071
$396$	−1844.91	−0.234117
$397$	−357.972	−0.0452546	−0.0226273	−	0.999744i	$-0.507203\pi$
$397$	−357.972	−0.0452546	−0.0226273	+	0.999744i	$0.507203\pi$
$398$	−10871.9	−1.36925
$399$	−1619.12	−0.203151
$400$	4183.96	0.522995
$401$	5448.19	0.678478	0.339239	−	0.940700i	$-0.389830\pi$
$401$	5448.19	0.678478	0.339239	+	0.940700i	$0.389830\pi$
$402$	3960.18	0.491333
$403$	−6726.21	−0.831405
$404$	326.546	0.0402136
$405$	2729.01	0.334828
$406$	−6607.94	−0.807750
$407$	−3085.69	−0.375803
$408$	335.557	0.0407170
$409$	−15572.9	−1.88272	−0.941360	−	0.337405i	$-0.890451\pi$
$409$	−15572.9	−1.88272	−0.941360	+	0.337405i	$0.890451\pi$
$410$	13594.0	1.63746
$411$	−4794.87	−0.575458
$412$	−6864.99	−0.820907
$413$	−13812.7	−1.64571
$414$	7058.39	0.837925
$415$	1807.38	0.213785
$416$	−17140.6	−2.02016
$417$	3486.63	0.409451
$418$	1371.85	0.160525
$419$	6790.66	0.791755	0.395878	−	0.918303i	$-0.370440\pi$
$419$	6790.66	0.791755	0.395878	+	0.918303i	$0.370440\pi$
$420$	3096.54	0.359752
$421$	−3237.08	−0.374740	−0.187370	−	0.982289i	$-0.559996\pi$
$421$	−3237.08	−0.374740	−0.187370	+	0.982289i	$0.559996\pi$
$422$	−5077.14	−0.585666
$423$	8208.43	0.943517
$424$	776.681	0.0889599
$425$	−6572.51	−0.750149
$426$	−4469.74	−0.508356
$427$	−18001.9	−2.04022
$428$	7382.14	0.833713
$429$	−1676.89	−0.188720
$430$	8547.91	0.958644
$431$	−11733.4	−1.31132	−0.655660	−	0.755056i	$-0.727610\pi$
$431$	−11733.4	−1.31132	−0.655660	+	0.755056i	$0.727610\pi$
$432$	7340.85	0.817562
$433$	−4936.48	−0.547880	−0.273940	−	0.961747i	$-0.588327\pi$
$433$	−4936.48	−0.547880	−0.273940	+	0.961747i	$0.588327\pi$
$434$	−8958.86	−0.990874
$435$	1296.55	0.142907
$436$	−9544.81	−1.04843
$437$	−2563.82	−0.280650
$438$	3330.18	0.363293
$439$	11619.9	1.26330	0.631648	−	0.775255i	$-0.282379\pi$
$439$	11619.9	1.26330	0.631648	+	0.775255i	$0.282379\pi$
$440$	123.699	0.0134026
$441$	−3937.21	−0.425138
$442$	28140.6	3.02831
$443$	648.831	0.0695867	0.0347933	−	0.999395i	$-0.488923\pi$
$443$	648.831	0.0695867	0.0347933	+	0.999395i	$0.488923\pi$
$444$	−4814.40	−0.514597
$445$	−5739.39	−0.611400
$446$	−11947.0	−1.26840
$447$	2664.30	0.281918
$448$	−10625.3	−1.12053
$449$	77.4459	0.00814008	0.00407004	−	0.999992i	$-0.498704\pi$
$449$	77.4459	0.00814008	0.00407004	+	0.999992i	$0.498704\pi$
$450$	−5441.79	−0.570063
$451$	−4789.69	−0.500084
$452$	−4725.37	−0.491732
$453$	−516.195	−0.0535386
$454$	25736.3	2.66050
$455$	−12243.5	−1.26150
$456$	−100.916	−0.0103636
$457$	7030.17	0.719600	0.359800	−	0.933029i	$-0.382845\pi$
$457$	7030.17	0.719600	0.359800	+	0.933029i	$0.382845\pi$
$458$	−8411.56	−0.858180
$459$	−11531.6	−1.17266
$460$	4903.28	0.496992
$461$	11073.6	1.11876	0.559379	−	0.828912i	$-0.311040\pi$
$461$	11073.6	1.11876	0.559379	+	0.828912i	$0.311040\pi$
$462$	−2233.51	−0.224918
$463$	−8430.09	−0.846176	−0.423088	−	0.906089i	$-0.639054\pi$
$463$	−8430.09	−0.846176	−0.423088	+	0.906089i	$0.639054\pi$
$464$	−4880.17	−0.488268
$465$	1757.82	0.175306
$466$	18083.5	1.79764
$467$	−2858.02	−0.283197	−0.141599	−	0.989924i	$-0.545224\pi$
$467$	−2858.02	−0.283197	−0.141599	+	0.989924i	$0.545224\pi$
$468$	11381.4	1.12415
$469$	−10187.7	−1.00304
$470$	11673.2	1.14563
$471$	1982.91	0.193986
$472$	−860.913	−0.0839549
$473$	−3011.77	−0.292772
$474$	−10608.0	−1.02794
$475$	1976.62	0.190934
$476$	18309.1	1.76302
$477$	−11969.8	−1.14897
$478$	12898.4	1.23423
$479$	−11229.0	−1.07112	−0.535560	−	0.844497i	$-0.679899\pi$
$479$	−11229.0	−1.07112	−0.535560	+	0.844497i	$0.679899\pi$
$480$	4479.51	0.425960
$481$	19035.8	1.80448
$482$	24274.8	2.29395
$483$	4174.14	0.393230
$484$	924.416	0.0868159
$485$	1901.35	0.178012
$486$	−14813.7	−1.38264
$487$	12499.0	1.16300	0.581502	−	0.813545i	$-0.302465\pi$
$487$	12499.0	1.16300	0.581502	+	0.813545i	$0.302465\pi$
$488$	−1122.02	−0.104081
$489$	−263.360	−0.0243549
$490$	−5599.10	−0.516208
$491$	18954.0	1.74212	0.871061	−	0.491174i	$-0.163432\pi$
$491$	18954.0	1.74212	0.871061	+	0.491174i	$0.163432\pi$
$492$	−7473.05	−0.684778
$493$	7666.17	0.700339
$494$	−8463.04	−0.770789
$495$	−1906.38	−0.173102
$496$	−6616.41	−0.598963
$497$	11498.6	1.03779
$498$	−2034.00	−0.183023
$499$	3496.69	0.313694	0.156847	−	0.987623i	$-0.449867\pi$
$499$	3496.69	0.313694	0.156847	+	0.987623i	$0.449867\pi$
$500$	−11319.2	−1.01242
$501$	−4028.90	−0.359277
$502$	−21668.7	−1.92653
$503$	11935.2	1.05798	0.528990	−	0.848628i	$-0.322571\pi$
$503$	11935.2	1.05798	0.528990	+	0.848628i	$0.322571\pi$
$504$	−714.724	−0.0631674
$505$	337.426	0.0297332
$506$	−3536.69	−0.310721
$507$	5409.33	0.473839
$508$	14666.7	1.28097
$509$	−3035.33	−0.264319	−0.132160	−	0.991228i	$-0.542191\pi$
$509$	−3035.33	−0.264319	−0.132160	+	0.991228i	$0.542191\pi$
$510$	−7354.25	−0.638533
$511$	−8567.02	−0.741649
$512$	−16100.1	−1.38971
$513$	3468.03	0.298474
$514$	−22112.1	−1.89752
$515$	−7093.71	−0.606964
$516$	−4699.06	−0.400900
$517$	−4112.93	−0.349877
$518$	25354.4	2.15060
$519$	−1581.37	−0.133747
$520$	−763.108	−0.0643548
$521$	−3453.27	−0.290385	−0.145193	−	0.989403i	$-0.546380\pi$
$521$	−3453.27	−0.290385	−0.145193	+	0.989403i	$0.546380\pi$
$522$	6347.30	0.532210
$523$	5906.70	0.493847	0.246923	−	0.969035i	$-0.420580\pi$
$523$	5906.70	0.493847	0.246923	+	0.969035i	$0.420580\pi$
$524$	−1000.81	−0.0834366
$525$	−3218.13	−0.267525
$526$	6574.01	0.544944
$527$	10393.6	0.859111
$528$	−1649.52	−0.135958
$529$	−5557.37	−0.456758
$530$	−17022.2	−1.39509
$531$	13267.9	1.08433
$532$	−5506.30	−0.448737
$533$	29547.9	2.40124
$534$	6459.01	0.523424
$535$	7628.10	0.616433
$536$	−634.976	−0.0511694
$537$	−6276.30	−0.504362
$538$	−3680.88	−0.294971
$539$	1972.78	0.157651
$540$	−6632.56	−0.528555
$541$	−10799.8	−0.858261	−0.429130	−	0.903243i	$-0.641180\pi$
$541$	−10799.8	−0.858261	−0.429130	+	0.903243i	$0.641180\pi$
$542$	−9264.44	−0.734210
$543$	5589.47	0.441744
$544$	26486.3	2.08748
$545$	−9862.82	−0.775187
$546$	13778.6	1.07998
$547$	6363.44	0.497406	0.248703	−	0.968580i	$-0.419996\pi$
$547$	6363.44	0.497406	0.248703	+	0.968580i	$0.419996\pi$
$548$	−16306.4	−1.27112
$549$	17291.9	1.34426
$550$	2726.67	0.211392
$551$	−2305.53	−0.178256
$552$	260.165	0.0200604
$553$	27289.6	2.09850
$554$	22153.7	1.69895
$555$	−4974.80	−0.380484
$556$	11857.4	0.904431
$557$	−3106.09	−0.236282	−0.118141	−	0.992997i	$-0.537694\pi$
$557$	−3106.09	−0.236282	−0.118141	+	0.992997i	$0.537694\pi$
$558$	8605.49	0.652867
$559$	18579.7	1.40579
$560$	−12043.6	−0.908815
$561$	2591.19	0.195009
$562$	24687.7	1.85300
$563$	4646.28	0.347811	0.173905	−	0.984762i	$-0.444361\pi$
$563$	4646.28	0.347811	0.173905	+	0.984762i	$0.444361\pi$
$564$	−6417.14	−0.479096
$565$	−4882.81	−0.363577
$566$	−16558.1	−1.22966
$567$	7900.73	0.585184
$568$	716.680	0.0529423
$569$	−1700.52	−0.125289	−0.0626445	−	0.998036i	$-0.519953\pi$
$569$	−1700.52	−0.125289	−0.0626445	+	0.998036i	$0.519953\pi$
$570$	2211.73	0.162525
$571$	−20910.3	−1.53252	−0.766258	−	0.642533i	$-0.777884\pi$
$571$	−20910.3	−1.53252	−0.766258	+	0.642533i	$0.777884\pi$
$572$	−5702.77	−0.416862
$573$	6397.93	0.466452
$574$	39355.8	2.86181
$575$	−5095.81	−0.369582
$576$	10206.2	0.738295
$577$	15617.5	1.12680	0.563400	−	0.826184i	$-0.309493\pi$
$577$	15617.5	1.12680	0.563400	+	0.826184i	$0.309493\pi$
$578$	−24054.4	−1.73102
$579$	−11881.6	−0.852822
$580$	4409.30	0.315666
$581$	5232.53	0.373635
$582$	−2139.74	−0.152397
$583$	5997.59	0.426063
$584$	−533.962	−0.0378348
$585$	11760.6	0.831179
$586$	8709.04	0.613937
$587$	−11118.9	−0.781814	−0.390907	−	0.920430i	$-0.627839\pi$
$587$	−11118.9	−0.781814	−0.390907	+	0.920430i	$0.627839\pi$
$588$	3078.01	0.215876
$589$	−3125.78	−0.218668
$590$	18868.3	1.31660
$591$	9635.00	0.670611
$592$	18725.0	1.29999
$593$	−27574.4	−1.90952	−0.954761	−	0.297373i	$-0.903889\pi$
$593$	−27574.4	−1.90952	−0.954761	+	0.297373i	$0.903889\pi$
$594$	4784.00	0.330455
$595$	18919.1	1.30354
$596$	9060.77	0.622724
$597$	6175.78	0.423380
$598$	21818.0	1.49198
$599$	21588.5	1.47259	0.736296	−	0.676659i	$-0.236573\pi$
$599$	21588.5	1.47259	0.736296	+	0.676659i	$0.236573\pi$
$600$	−200.578	−0.0136476
$601$	−1973.18	−0.133923	−0.0669614	−	0.997756i	$-0.521330\pi$
$601$	−1973.18	−0.133923	−0.0669614	+	0.997756i	$0.521330\pi$
$602$	24747.0	1.67544
$603$	9785.88	0.660882
$604$	−1755.48	−0.118261
$605$	955.215	0.0641901
$606$	−379.734	−0.0254548
$607$	−12889.7	−0.861907	−0.430953	−	0.902374i	$-0.641823\pi$
$607$	−12889.7	−0.861907	−0.430953	+	0.902374i	$0.641823\pi$
$608$	−7965.51	−0.531323
$609$	3753.63	0.249761
$610$	24590.8	1.63222
$611$	25372.9	1.68000
$612$	−17586.9	−1.16162
$613$	−55.2247	−0.00363867	−0.00181933	−	0.999998i	$-0.500579\pi$
$613$	−55.2247	−0.00363867	−0.00181933	+	0.999998i	$0.500579\pi$
$614$	21773.5	1.43112
$615$	−7722.03	−0.506313
$616$	358.121	0.0234239
$617$	10661.2	0.695628	0.347814	−	0.937564i	$-0.386924\pi$
$617$	10661.2	0.695628	0.347814	+	0.937564i	$0.386924\pi$
$618$	7983.14	0.519626
$619$	−7376.09	−0.478950	−0.239475	−	0.970903i	$-0.576975\pi$
$619$	−7376.09	−0.478950	−0.239475	+	0.970903i	$0.576975\pi$
$620$	5978.01	0.387230
$621$	−8940.70	−0.577743
$622$	−18811.8	−1.21268
$623$	−16616.1	−1.06855
$624$	10176.0	0.652827
$625$	−3861.38	−0.247128
$626$	27654.9	1.76567
$627$	−779.278	−0.0496354
$628$	6743.47	0.428493
$629$	−29414.8	−1.86462
$630$	15664.3	0.990605
$631$	−16427.0	−1.03637	−0.518184	−	0.855269i	$-0.673392\pi$
$631$	−16427.0	−1.03637	−0.518184	+	0.855269i	$0.673392\pi$
$632$	1700.90	0.107054
$633$	2884.06	0.181092
$634$	15647.0	0.980159
$635$	15155.4	0.947123
$636$	9357.64	0.583419
$637$	−12170.2	−0.756988
$638$	−3180.39	−0.197356
$639$	−11045.0	−0.683780
$640$	−1437.95	−0.0888126
$641$	−3742.87	−0.230631	−0.115316	−	0.993329i	$-0.536788\pi$
$641$	−3742.87	−0.230631	−0.115316	+	0.993329i	$0.536788\pi$
$642$	−8584.53	−0.527733
$643$	10368.3	0.635905	0.317953	−	0.948107i	$-0.397005\pi$
$643$	10368.3	0.635905	0.317953	+	0.948107i	$0.397005\pi$
$644$	14195.4	0.868600
$645$	−4855.62	−0.296419
$646$	13077.4	0.796476
$647$	−11623.9	−0.706313	−0.353156	−	0.935564i	$-0.614892\pi$
$647$	−11623.9	−0.706313	−0.353156	+	0.935564i	$0.614892\pi$
$648$	492.434	0.0298528
$649$	−6648.03	−0.402092
$650$	−16821.0	−1.01504
$651$	5089.06	0.306384
$652$	−895.636	−0.0537973
$653$	−16436.2	−0.984987	−0.492493	−	0.870316i	$-0.663914\pi$
$653$	−16436.2	−0.984987	−0.492493	+	0.870316i	$0.663914\pi$
$654$	11099.4	0.663643
$655$	−1034.16	−0.0616915
$656$	29065.5	1.72991
$657$	8229.11	0.488658
$658$	33795.0	2.00223
$659$	12296.3	0.726853	0.363426	−	0.931623i	$-0.381607\pi$
$659$	12296.3	0.726853	0.363426	+	0.931623i	$0.381607\pi$
$660$	1490.36	0.0878973
$661$	24662.5	1.45123	0.725614	−	0.688102i	$-0.241556\pi$
$661$	24662.5	1.45123	0.725614	+	0.688102i	$0.241556\pi$
$662$	12621.7	0.741020
$663$	−15985.2	−0.936371
$664$	326.131	0.0190608
$665$	−5689.76	−0.331788
$666$	−24354.3	−1.41698
$667$	5943.75	0.345042
$668$	−13701.5	−0.793602
$669$	6786.44	0.392196
$670$	13916.5	0.802450
$671$	−8664.31	−0.498483
$672$	12968.6	0.744456
$673$	−16872.8	−0.966416	−0.483208	−	0.875506i	$-0.660528\pi$
$673$	−16872.8	−0.966416	−0.483208	+	0.875506i	$0.660528\pi$
$674$	5283.05	0.301922
$675$	6892.99	0.393054
$676$	18396.0	1.04666
$677$	16003.7	0.908528	0.454264	−	0.890867i	$-0.349902\pi$
$677$	16003.7	0.908528	0.454264	+	0.890867i	$0.349902\pi$
$678$	5495.03	0.311261
$679$	5504.57	0.311114
$680$	1179.18	0.0664994
$681$	−14619.5	−0.822642
$682$	−4311.89	−0.242098
$683$	6150.71	0.344583	0.172292	−	0.985046i	$-0.444883\pi$
$683$	6150.71	0.344583	0.172292	+	0.985046i	$0.444883\pi$
$684$	5289.11	0.295664
$685$	−16849.7	−0.939845
$686$	14792.0	0.823265
$687$	4778.17	0.265355
$688$	18276.4	1.01277
$689$	−36999.4	−2.04581
$690$	−5701.91	−0.314592
$691$	19155.3	1.05456	0.527282	−	0.849690i	$-0.323211\pi$
$691$	19155.3	1.05456	0.527282	+	0.849690i	$0.323211\pi$
$692$	−5377.93	−0.295431
$693$	−5519.15	−0.302533
$694$	−6619.86	−0.362084
$695$	12252.4	0.668720
$696$	233.955	0.0127414
$697$	−45658.5	−2.48126
$698$	39762.9	2.15623
$699$	−10272.3	−0.555842
$700$	−10944.2	−0.590932
$701$	−32407.4	−1.74609	−0.873047	−	0.487637i	$-0.837859\pi$
$701$	−32407.4	−1.74609	−0.873047	+	0.487637i	$0.837859\pi$
$702$	−29512.8	−1.58673
$703$	8846.24	0.474598
$704$	−5113.94	−0.273777
$705$	−6630.94	−0.354235
$706$	47276.2	2.52020
$707$	976.880	0.0519651
$708$	−10372.5	−0.550596
$709$	−11725.4	−0.621093	−0.310546	−	0.950558i	$-0.600512\pi$
$709$	−11725.4	−0.621093	−0.310546	+	0.950558i	$0.600512\pi$
$710$	−15707.2	−0.830253
$711$	−26213.2	−1.38266
$712$	−1035.64	−0.0545115
$713$	8058.38	0.423266
$714$	−21291.2	−1.11597
$715$	−5892.77	−0.308220
$716$	−21344.5	−1.11408
$717$	−7326.92	−0.381630
$718$	25595.2	1.33037
$719$	19466.9	1.00973	0.504864	−	0.863199i	$-0.331543\pi$
$719$	19466.9	1.00973	0.504864	+	0.863199i	$0.331543\pi$
$720$	11568.6	0.598800
$721$	−20537.0	−1.06080
$722$	23192.5	1.19548
$723$	−13789.2	−0.709305
$724$	19008.7	0.975763
$725$	−4582.44	−0.234741
$726$	−1074.98	−0.0549537
$727$	−6912.57	−0.352645	−0.176323	−	0.984332i	$-0.556420\pi$
$727$	−6912.57	−0.352645	−0.176323	+	0.984332i	$0.556420\pi$
$728$	−2209.27	−0.112474
$729$	−918.766	−0.0466782
$730$	11702.6	0.593334
$731$	−28710.1	−1.45264
$732$	−13518.4	−0.682586
$733$	25891.9	1.30469	0.652346	−	0.757921i	$-0.273785\pi$
$733$	25891.9	1.30469	0.652346	+	0.757921i	$0.273785\pi$
$734$	11956.9	0.601279
$735$	3180.56	0.159615
$736$	20535.4	1.02846
$737$	−4903.33	−0.245070
$738$	−37803.5	−1.88559
$739$	−18319.2	−0.911884	−0.455942	−	0.890010i	$-0.650697\pi$
$739$	−18319.2	−0.911884	−0.455942	+	0.890010i	$0.650697\pi$
$740$	−16918.3	−0.840446
$741$	4807.41	0.238333
$742$	−49280.8	−2.43821
$743$	2366.91	0.116869	0.0584343	−	0.998291i	$-0.481389\pi$
$743$	2366.91	0.116869	0.0584343	+	0.998291i	$0.481389\pi$
$744$	317.189	0.0156300
$745$	9362.65	0.460431
$746$	23979.7	1.17689
$747$	−5026.14	−0.246181
$748$	8812.14	0.430753
$749$	22084.0	1.07735
$750$	13162.8	0.640851
$751$	−36424.0	−1.76981	−0.884907	−	0.465767i	$-0.845778\pi$
$751$	−36424.0	−1.76981	−0.884907	+	0.465767i	$0.845778\pi$
$752$	24958.7	1.21031
$753$	12308.8	0.595696
$754$	19620.0	0.947636
$755$	−1813.97	−0.0874397
$756$	−19201.9	−0.923764
$757$	34914.9	1.67636	0.838180	−	0.545393i	$-0.183620\pi$
$757$	34914.9	1.67636	0.838180	+	0.545393i	$0.183620\pi$
$758$	−39190.2	−1.87790
$759$	2009.01	0.0960769
$760$	−354.629	−0.0169260
$761$	−11855.5	−0.564735	−0.282367	−	0.959306i	$-0.591120\pi$
$761$	−11855.5	−0.564735	−0.282367	+	0.959306i	$0.591120\pi$
$762$	−17055.6	−0.810840
$763$	−28553.8	−1.35480
$764$	21758.1	1.03034
$765$	−18172.9	−0.858878
$766$	−24643.9	−1.16243
$767$	41012.0	1.93072
$768$	9973.37	0.468598
$769$	−25966.6	−1.21766	−0.608828	−	0.793302i	$-0.708360\pi$
$769$	−25966.6	−1.21766	−0.608828	+	0.793302i	$0.708360\pi$
$770$	−7848.79	−0.367339
$771$	12560.7	0.586724
$772$	−40407.1	−1.88379
$773$	30279.0	1.40887	0.704437	−	0.709766i	$-0.251199\pi$
$773$	30279.0	1.40887	0.704437	+	0.709766i	$0.251199\pi$
$774$	−23770.9	−1.10391
$775$	−6212.74	−0.287959
$776$	343.087	0.0158713
$777$	−14402.5	−0.664977
$778$	−27754.1	−1.27896
$779$	13731.4	0.631551
$780$	−9194.11	−0.422054
$781$	5534.25	0.253561
$782$	−33714.0	−1.54170
$783$	−8039.98	−0.366955
$784$	−11971.5	−0.545351
$785$	6968.15	0.316820
$786$	1163.82	0.0528146
$787$	36131.1	1.63651	0.818255	−	0.574855i	$-0.194941\pi$
$787$	36131.1	1.63651	0.818255	+	0.574855i	$0.194941\pi$
$788$	32766.7	1.48130
$789$	−3734.35	−0.168500
$790$	−37277.8	−1.67884
$791$	−14136.2	−0.635429
$792$	−343.996	−0.0154335
$793$	53450.6	2.39355
$794$	1415.68	0.0632752
$795$	9669.42	0.431370
$796$	21002.6	0.935199
$797$	−25082.3	−1.11475	−0.557377	−	0.830259i	$-0.688192\pi$
$797$	−25082.3	−1.11475	−0.557377	+	0.830259i	$0.688192\pi$
$798$	6403.15	0.284047
$799$	−39207.2	−1.73598
$800$	−15832.1	−0.699687
$801$	15960.7	0.704048
$802$	−21546.1	−0.948651
$803$	−4123.29	−0.181205
$804$	−7650.35	−0.335581
$805$	14668.4	0.642228
$806$	26600.3	1.16247
$807$	2090.92	0.0912067
$808$	60.8866	0.00265097
$809$	−8401.49	−0.365118	−0.182559	−	0.983195i	$-0.558438\pi$
$809$	−8401.49	−0.365118	−0.182559	+	0.983195i	$0.558438\pi$
$810$	−10792.5	−0.468159
$811$	18778.5	0.813073	0.406536	−	0.913635i	$-0.366736\pi$
$811$	18778.5	0.813073	0.406536	+	0.913635i	$0.366736\pi$
$812$	12765.3	0.551694
$813$	5262.65	0.227022
$814$	12203.0	0.525450
$815$	−925.477	−0.0397767
$816$	−15724.3	−0.674583
$817$	8634.31	0.369739
$818$	61586.6	2.63243
$819$	34047.9	1.45266
$820$	−26261.1	−1.11839
$821$	10476.8	0.445362	0.222681	−	0.974891i	$-0.428519\pi$
$821$	10476.8	0.445362	0.222681	+	0.974891i	$0.428519\pi$
$822$	18962.4	0.804608
$823$	−27704.8	−1.17343	−0.586713	−	0.809795i	$-0.699578\pi$
$823$	−27704.8	−1.17343	−0.586713	+	0.809795i	$0.699578\pi$
$824$	−1280.02	−0.0541160
$825$	−1548.88	−0.0653637
$826$	54625.3	2.30104
$827$	−42263.3	−1.77707	−0.888537	−	0.458805i	$-0.848277\pi$
$827$	−42263.3	−1.77707	−0.888537	+	0.458805i	$0.848277\pi$
$828$	−13635.5	−0.572303
$829$	36308.1	1.52115	0.760575	−	0.649250i	$-0.224917\pi$
$829$	36308.1	1.52115	0.760575	+	0.649250i	$0.224917\pi$
$830$	−7147.68	−0.298915
$831$	−12584.4	−0.525327
$832$	31548.1	1.31459
$833$	18805.9	0.782214
$834$	−13788.7	−0.572496
$835$	−14158.0	−0.586775
$836$	−2650.17	−0.109639
$837$	−10900.4	−0.450147
$838$	−26855.1	−1.10704
$839$	−34662.1	−1.42630	−0.713151	−	0.701010i	$-0.752733\pi$
$839$	−34662.1	−1.42630	−0.713151	+	0.701010i	$0.752733\pi$
$840$	577.369	0.0237156
$841$	−19044.0	−0.780846
$842$	12801.7	0.523963
$843$	−14023.8	−0.572960
$844$	9808.11	0.400011
$845$	19009.0	0.773880
$846$	−32462.0	−1.31923
$847$	2765.44	0.112186
$848$	−36395.5	−1.47385
$849$	9405.77	0.380218
$850$	25992.4	1.04886
$851$	−22805.9	−0.918657
$852$	8634.73	0.347208
$853$	6640.42	0.266546	0.133273	−	0.991079i	$-0.457451\pi$
$853$	6640.42	0.266546	0.133273	+	0.991079i	$0.457451\pi$
$854$	71192.6	2.85265
$855$	5465.33	0.218609
$856$	1376.45	0.0549602
$857$	22738.6	0.906342	0.453171	−	0.891424i	$-0.350293\pi$
$857$	22738.6	0.906342	0.453171	+	0.891424i	$0.350293\pi$
$858$	6631.63	0.263869
$859$	−36991.5	−1.46930	−0.734652	−	0.678444i	$-0.762655\pi$
$859$	−36991.5	−1.46930	−0.734652	+	0.678444i	$0.762655\pi$
$860$	−16513.0	−0.654755
$861$	−22356.0	−0.884890
$862$	46402.4	1.83349
$863$	−15128.5	−0.596732	−0.298366	−	0.954452i	$-0.596442\pi$
$863$	−15128.5	−0.596732	−0.298366	+	0.954452i	$0.596442\pi$
$864$	−27777.8	−1.09377
$865$	−5557.11	−0.218436
$866$	19522.4	0.766048
$867$	13664.0	0.535242
$868$	17306.9	0.676768
$869$	13134.4	0.512722
$870$	−5127.48	−0.199814
$871$	30248.9	1.17675
$872$	−1779.69	−0.0691145
$873$	−5287.46	−0.204987
$874$	10139.2	0.392407
$875$	−33861.9	−1.30827
$876$	−6433.31	−0.248129
$877$	27225.5	1.04828	0.524138	−	0.851633i	$-0.324387\pi$
$877$	27225.5	1.04828	0.524138	+	0.851633i	$0.324387\pi$
$878$	−45953.4	−1.76635
$879$	−4947.15	−0.189833
$880$	−5796.58	−0.222049
$881$	−31529.5	−1.20574	−0.602869	−	0.797840i	$-0.705976\pi$
$881$	−31529.5	−1.20574	−0.602869	+	0.797840i	$0.705976\pi$
$882$	15570.5	0.594430
$883$	22741.6	0.866721	0.433360	−	0.901221i	$-0.357328\pi$
$883$	22741.6	0.866721	0.433360	+	0.901221i	$0.357328\pi$
$884$	−54362.5	−2.06834
$885$	−10718.1	−0.407101
$886$	−2565.94	−0.0972964
$887$	−2506.69	−0.0948889	−0.0474444	−	0.998874i	$-0.515108\pi$
$887$	−2506.69	−0.0948889	−0.0474444	+	0.998874i	$0.515108\pi$
$888$	−897.675	−0.0339234
$889$	43876.2	1.65530
$890$	22697.7	0.854862
$891$	3802.61	0.142977
$892$	23079.3	0.866316
$893$	11791.2	0.441856
$894$	−10536.6	−0.394178
$895$	−22055.6	−0.823730
$896$	−4163.00	−0.155219
$897$	−12393.7	−0.461330
$898$	−306.277	−0.0113815
$899$	7246.54	0.268838
$900$	10512.5	0.389353
$901$	57172.9	2.11399
$902$	18941.9	0.699220
$903$	−14057.5	−0.518055
$904$	−881.075	−0.0324160
$905$	19642.0	0.721462
$906$	2041.41	0.0748578
$907$	−3918.81	−0.143464	−0.0717321	−	0.997424i	$-0.522853\pi$
$907$	−3918.81	−0.143464	−0.0717321	+	0.997424i	$0.522853\pi$
$908$	−49717.9	−1.81712
$909$	−938.348	−0.0342388
$910$	48419.6	1.76384
$911$	−11321.4	−0.411741	−0.205870	−	0.978579i	$-0.566003\pi$
$911$	−11321.4	−0.411741	−0.205870	+	0.978579i	$0.566003\pi$
$912$	4728.93	0.171700
$913$	2518.41	0.0912894
$914$	−27802.3	−1.00615
$915$	−13968.8	−0.504692
$916$	16249.6	0.586138
$917$	−2993.98	−0.107819
$918$	45604.2	1.63961
$919$	44357.1	1.59217	0.796086	−	0.605183i	$-0.206900\pi$
$919$	44357.1	1.59217	0.796086	+	0.605183i	$0.206900\pi$
$920$	914.247	0.0327629
$921$	−12368.4	−0.442511
$922$	−43792.8	−1.56425
$923$	−34141.1	−1.21752
$924$	4314.73	0.153619
$925$	17582.6	0.624988
$926$	33338.6	1.18313
$927$	19726.9	0.698939
$928$	18466.6	0.653227
$929$	−12919.5	−0.456270	−0.228135	−	0.973630i	$-0.573263\pi$
$929$	−12919.5	−0.456270	−0.228135	+	0.973630i	$0.573263\pi$
$930$	−6951.70	−0.245113
$931$	−5655.70	−0.199096
$932$	−34934.0	−1.22779
$933$	10686.0	0.374967
$934$	11302.6	0.395968
$935$	9105.74	0.318491
$936$	2122.13	0.0741067
$937$	43184.8	1.50564	0.752821	−	0.658225i	$-0.228692\pi$
$937$	43184.8	1.50564	0.752821	+	0.658225i	$0.228692\pi$
$938$	40289.6	1.40245
$939$	−15709.3	−0.545957
$940$	−22550.5	−0.782465
$941$	4250.95	0.147266	0.0736328	−	0.997285i	$-0.476541\pi$
$941$	4250.95	0.147266	0.0736328	+	0.997285i	$0.476541\pi$
$942$	−7841.84	−0.271232
$943$	−35400.0	−1.22246
$944$	40342.6	1.39093
$945$	−19841.6	−0.683014
$946$	11910.7	0.409355
$947$	32123.8	1.10231	0.551153	−	0.834404i	$-0.314188\pi$
$947$	32123.8	1.10231	0.551153	+	0.834404i	$0.314188\pi$
$948$	20492.8	0.702084
$949$	25436.8	0.870089
$950$	−7816.99	−0.266965
$951$	−8888.23	−0.303071
$952$	3413.84	0.116222
$953$	14939.5	0.507805	0.253903	−	0.967230i	$-0.418286\pi$
$953$	14939.5	0.507805	0.253903	+	0.967230i	$0.418286\pi$
$954$	47337.0	1.60649
$955$	22483.0	0.761815
$956$	−24917.4	−0.842977
$957$	1806.61	0.0610235
$958$	44407.5	1.49764
$959$	−48781.4	−1.64258
$960$	−8244.78	−0.277187
$961$	−19966.3	−0.670214
$962$	−75281.1	−2.52304
$963$	−21213.0	−0.709843
$964$	−46894.5	−1.56677
$965$	−41753.4	−1.39284
$966$	−16507.6	−0.549816
$967$	−4040.27	−0.134360	−0.0671801	−	0.997741i	$-0.521400\pi$
$967$	−4040.27	−0.134360	−0.0671801	+	0.997741i	$0.521400\pi$
$968$	172.363	0.00572310
$969$	−7428.59	−0.246275
$970$	−7519.29	−0.248897
$971$	−19326.4	−0.638738	−0.319369	−	0.947630i	$-0.603471\pi$
$971$	−19326.4	−0.638738	−0.319369	+	0.947630i	$0.603471\pi$
$972$	28617.4	0.944347
$973$	35471.9	1.16873
$974$	−49430.0	−1.62612
$975$	9555.12	0.313855
$976$	52578.1	1.72437
$977$	−42320.6	−1.38583	−0.692915	−	0.721020i	$-0.743674\pi$
$977$	−42320.6	−1.38583	−0.692915	+	0.721020i	$0.743674\pi$
$978$	1041.52	0.0340532
$979$	−7997.28	−0.261077
$980$	10816.5	0.352570
$981$	27427.5	0.892653
$982$	−74957.8	−2.43584
$983$	30896.5	1.00249	0.501243	−	0.865306i	$-0.332876\pi$
$983$	30896.5	1.00249	0.501243	+	0.865306i	$0.332876\pi$
$984$	−1393.40	−0.0451421
$985$	33858.5	1.09525
$986$	−30317.5	−0.979216
$987$	−19197.2	−0.619102
$988$	16349.1	0.526450
$989$	−22259.6	−0.715686
$990$	7539.20	0.242032
$991$	−55495.7	−1.77889	−0.889445	−	0.457043i	$-0.848909\pi$
$991$	−55495.7	−1.77889	−0.889445	+	0.457043i	$0.848909\pi$
$992$	25036.5	0.801319
$993$	−7169.72	−0.229128
$994$	−45473.7	−1.45104
$995$	21702.4	0.691469
$996$	3929.31	0.125005
$997$	9471.28	0.300861	0.150431	−	0.988621i	$-0.451934\pi$
$997$	9471.28	0.300861	0.150431	+	0.988621i	$0.451934\pi$
$998$	−13828.4	−0.438609
$999$	30849.1	0.977000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.17	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.17	✓	79	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-3.95472 q^{2} +2.24647 q^{3} +7.63980 q^{4} +7.89434 q^{5} -8.88416 q^{6} +22.8548 q^{7} +1.42449 q^{8} -21.9534 q^{9} +O(q^{10})\)	\(q-3.95472 q^{2} +2.24647 q^{3} +7.63980 q^{4} +7.89434 q^{5} -8.88416 q^{6} +22.8548 q^{7} +1.42449 q^{8} -21.9534 q^{9} -31.2199 q^{10} +11.0000 q^{11} +17.1626 q^{12} -67.8596 q^{13} -90.3845 q^{14} +17.7344 q^{15} -66.7519 q^{16} +104.859 q^{17} +86.8194 q^{18} -31.5355 q^{19} +60.3112 q^{20} +51.3427 q^{21} -43.5019 q^{22} +81.2996 q^{23} +3.20007 q^{24} -62.6794 q^{25} +268.366 q^{26} -109.972 q^{27} +174.606 q^{28} +73.1092 q^{29} -70.1346 q^{30} +99.1195 q^{31} +252.589 q^{32} +24.7112 q^{33} -414.689 q^{34} +180.424 q^{35} -167.719 q^{36} -280.517 q^{37} +124.714 q^{38} -152.444 q^{39} +11.2454 q^{40} -435.427 q^{41} -203.046 q^{42} -273.797 q^{43} +84.0378 q^{44} -173.307 q^{45} -321.517 q^{46} -373.903 q^{47} -149.956 q^{48} +179.344 q^{49} +247.879 q^{50} +235.563 q^{51} -518.434 q^{52} +545.235 q^{53} +434.909 q^{54} +86.8378 q^{55} +32.5565 q^{56} -70.8435 q^{57} -289.126 q^{58} -604.366 q^{59} +135.487 q^{60} -787.664 q^{61} -391.990 q^{62} -501.741 q^{63} -464.903 q^{64} -535.707 q^{65} -97.7257 q^{66} -445.757 q^{67} +801.103 q^{68} +182.637 q^{69} -713.526 q^{70} +503.114 q^{71} -31.2723 q^{72} -374.845 q^{73} +1109.37 q^{74} -140.807 q^{75} -240.925 q^{76} +251.403 q^{77} +602.875 q^{78} +1194.04 q^{79} -526.962 q^{80} +345.692 q^{81} +1721.99 q^{82} +228.946 q^{83} +392.248 q^{84} +827.794 q^{85} +1082.79 q^{86} +164.238 q^{87} +15.6694 q^{88} -727.025 q^{89} +685.382 q^{90} -1550.92 q^{91} +621.113 q^{92} +222.669 q^{93} +1478.68 q^{94} -248.952 q^{95} +567.433 q^{96} +240.849 q^{97} -709.255 q^{98} -241.487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

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