LMFDB - Embedded newform 2013.4.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20148 q^{2} -3.00000 q^{3} -3.15347 q^{4} -19.8720 q^{5} +6.60445 q^{6} -18.3617 q^{7} +24.5542 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.20148 q^{2} -3.00000 q^{3} -3.15347 q^{4} -19.8720 q^{5} +6.60445 q^{6} -18.3617 q^{7} +24.5542 q^{8} +9.00000 q^{9} +43.7479 q^{10} -11.0000 q^{11} +9.46042 q^{12} -69.9841 q^{13} +40.4230 q^{14} +59.6160 q^{15} -28.8278 q^{16} -54.2896 q^{17} -19.8133 q^{18} -142.126 q^{19} +62.6658 q^{20} +55.0851 q^{21} +24.2163 q^{22} -119.298 q^{23} -73.6625 q^{24} +269.897 q^{25} +154.069 q^{26} -27.0000 q^{27} +57.9031 q^{28} -116.253 q^{29} -131.244 q^{30} +253.366 q^{31} -132.969 q^{32} +33.0000 q^{33} +119.518 q^{34} +364.884 q^{35} -28.3812 q^{36} +118.830 q^{37} +312.888 q^{38} +209.952 q^{39} -487.941 q^{40} +329.788 q^{41} -121.269 q^{42} -437.227 q^{43} +34.6882 q^{44} -178.848 q^{45} +262.633 q^{46} -26.3681 q^{47} +86.4835 q^{48} -5.84817 q^{49} -594.173 q^{50} +162.869 q^{51} +220.693 q^{52} -535.605 q^{53} +59.4400 q^{54} +218.592 q^{55} -450.856 q^{56} +426.378 q^{57} +255.930 q^{58} -805.492 q^{59} -187.997 q^{60} +61.0000 q^{61} -557.781 q^{62} -165.255 q^{63} +523.353 q^{64} +1390.73 q^{65} -72.6489 q^{66} +477.025 q^{67} +171.201 q^{68} +357.895 q^{69} -803.285 q^{70} +981.613 q^{71} +220.988 q^{72} +982.490 q^{73} -261.603 q^{74} -809.690 q^{75} +448.190 q^{76} +201.979 q^{77} -462.207 q^{78} +356.956 q^{79} +572.867 q^{80} +81.0000 q^{81} -726.024 q^{82} +519.493 q^{83} -173.709 q^{84} +1078.84 q^{85} +962.549 q^{86} +348.760 q^{87} -270.096 q^{88} +630.379 q^{89} +393.731 q^{90} +1285.03 q^{91} +376.204 q^{92} -760.098 q^{93} +58.0489 q^{94} +2824.33 q^{95} +398.908 q^{96} -1156.88 q^{97} +12.8746 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.20148	−0.778342	−0.389171	−	0.921166i	$-0.627238\pi$
$2$	−2.20148	−0.778342	−0.389171	+	0.921166i	$0.627238\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−3.15347	−0.394184
$5$	−19.8720	−1.77741	−0.888703	−	0.458483i	$-0.848393\pi$
$5$	−19.8720	−1.77741	−0.888703	+	0.458483i	$0.848393\pi$
$6$	6.60445	0.449376
$7$	−18.3617	−0.991438	−0.495719	−	0.868483i	$-0.665095\pi$
$7$	−18.3617	−0.991438	−0.495719	+	0.868483i	$0.665095\pi$
$8$	24.5542	1.08515
$9$	9.00000	0.333333
$10$	43.7479	1.38343
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	9.46042	0.227582
$13$	−69.9841	−1.49309	−0.746543	−	0.665338i	$-0.768288\pi$
$13$	−69.9841	−1.49309	−0.746543	+	0.665338i	$0.768288\pi$
$14$	40.4230	0.771678
$15$	59.6160	1.02619
$16$	−28.8278	−0.450435
$17$	−54.2896	−0.774539	−0.387269	−	0.921967i	$-0.626582\pi$
$17$	−54.2896	−0.774539	−0.387269	+	0.921967i	$0.626582\pi$
$18$	−19.8133	−0.259447
$19$	−142.126	−1.71610	−0.858050	−	0.513566i	$-0.828324\pi$
$19$	−142.126	−1.71610	−0.858050	+	0.513566i	$0.828324\pi$
$20$	62.6658	0.700625
$21$	55.0851	0.572407
$22$	24.2163	0.234679
$23$	−119.298	−1.08154	−0.540770	−	0.841171i	$-0.681867\pi$
$23$	−119.298	−1.08154	−0.540770	+	0.841171i	$0.681867\pi$
$24$	−73.6625	−0.626513
$25$	269.897	2.15917
$26$	154.069	1.16213
$27$	−27.0000	−0.192450
$28$	57.9031	0.390809
$29$	−116.253	−0.744403	−0.372202	−	0.928152i	$-0.621397\pi$
$29$	−116.253	−0.744403	−0.372202	+	0.928152i	$0.621397\pi$
$30$	−131.244	−0.798724
$31$	253.366	1.46793	0.733966	−	0.679187i	$-0.237667\pi$
$31$	253.366	1.46793	0.733966	+	0.679187i	$0.237667\pi$
$32$	−132.969	−0.734559
$33$	33.0000	0.174078
$34$	119.518	0.602856
$35$	364.884	1.76219
$36$	−28.3812	−0.131395
$37$	118.830	0.527989	0.263995	−	0.964524i	$-0.414960\pi$
$37$	118.830	0.527989	0.263995	+	0.964524i	$0.414960\pi$
$38$	312.888	1.33571
$39$	209.952	0.862033
$40$	−487.941	−1.92876
$41$	329.788	1.25620	0.628101	−	0.778132i	$-0.283832\pi$
$41$	329.788	1.25620	0.628101	+	0.778132i	$0.283832\pi$
$42$	−121.269	−0.445528
$43$	−437.227	−1.55062	−0.775309	−	0.631583i	$-0.782406\pi$
$43$	−437.227	−1.55062	−0.775309	+	0.631583i	$0.782406\pi$
$44$	34.6882	0.118851
$45$	−178.848	−0.592469
$46$	262.633	0.841808
$47$	−26.3681	−0.0818337	−0.0409168	−	0.999163i	$-0.513028\pi$
$47$	−26.3681	−0.0818337	−0.0409168	+	0.999163i	$0.513028\pi$
$48$	86.4835	0.260059
$49$	−5.84817	−0.0170500
$50$	−594.173	−1.68058
$51$	162.869	0.447180
$52$	220.693	0.588550
$53$	−535.605	−1.38813	−0.694066	−	0.719911i	$-0.744182\pi$
$53$	−535.605	−1.38813	−0.694066	+	0.719911i	$0.744182\pi$
$54$	59.4400	0.149792
$55$	218.592	0.535908
$56$	−450.856	−1.07586
$57$	426.378	0.990791
$58$	255.930	0.579400
$59$	−805.492	−1.77739	−0.888696	−	0.458498i	$-0.848388\pi$
$59$	−805.492	−1.77739	−0.888696	+	0.458498i	$0.848388\pi$
$60$	−187.997	−0.404506
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−557.781	−1.14255
$63$	−165.255	−0.330479
$64$	523.353	1.02217
$65$	1390.73	2.65382
$66$	−72.6489	−0.135492
$67$	477.025	0.869818	0.434909	−	0.900474i	$-0.356780\pi$
$67$	477.025	0.869818	0.434909	+	0.900474i	$0.356780\pi$
$68$	171.201	0.305311
$69$	357.895	0.624427
$70$	−803.285	−1.37159
$71$	981.613	1.64079	0.820394	−	0.571798i	$-0.193754\pi$
$71$	981.613	1.64079	0.820394	+	0.571798i	$0.193754\pi$
$72$	220.988	0.361717
$73$	982.490	1.57523	0.787615	−	0.616168i	$-0.211316\pi$
$73$	982.490	1.57523	0.787615	+	0.616168i	$0.211316\pi$
$74$	−261.603	−0.410956
$75$	−809.690	−1.24660
$76$	448.190	0.676459
$77$	201.979	0.298930
$78$	−462.207	−0.670957
$79$	356.956	0.508364	0.254182	−	0.967156i	$-0.418194\pi$
$79$	356.956	0.508364	0.254182	+	0.967156i	$0.418194\pi$
$80$	572.867	0.800606
$81$	81.0000	0.111111
$82$	−726.024	−0.977755
$83$	519.493	0.687009	0.343505	−	0.939151i	$-0.388386\pi$
$83$	519.493	0.687009	0.343505	+	0.939151i	$0.388386\pi$
$84$	−173.709	−0.225634
$85$	1078.84	1.37667
$86$	962.549	1.20691
$87$	348.760	0.429782
$88$	−270.096	−0.327186
$89$	630.379	0.750787	0.375393	−	0.926866i	$-0.377508\pi$
$89$	630.379	0.750787	0.375393	+	0.926866i	$0.377508\pi$
$90$	393.731	0.461143
$91$	1285.03	1.48030
$92$	376.204	0.426326
$93$	−760.098	−0.847510
$94$	58.0489	0.0636946
$95$	2824.33	3.05021
$96$	398.908	0.424098
$97$	−1156.88	−1.21096	−0.605481	−	0.795859i	$-0.707019\pi$
$97$	−1156.88	−1.21096	−0.605481	+	0.795859i	$0.707019\pi$
$98$	12.8746	0.0132708
$99$	−99.0000	−0.100504
$100$	−851.112	−0.851112
$101$	1452.50	1.43098	0.715489	−	0.698624i	$-0.246204\pi$
$101$	1452.50	1.43098	0.715489	+	0.698624i	$0.246204\pi$
$102$	−358.553	−0.348059
$103$	176.395	0.168745	0.0843726	−	0.996434i	$-0.473111\pi$
$103$	176.395	0.168745	0.0843726	+	0.996434i	$0.473111\pi$
$104$	−1718.40	−1.62022
$105$	−1094.65	−1.01740
$106$	1179.13	1.08044
$107$	−1473.01	−1.33085	−0.665425	−	0.746465i	$-0.731750\pi$
$107$	−1473.01	−1.33085	−0.665425	+	0.746465i	$0.731750\pi$
$108$	85.1437	0.0758608
$109$	457.786	0.402275	0.201138	−	0.979563i	$-0.435536\pi$
$109$	457.786	0.402275	0.201138	+	0.979563i	$0.435536\pi$
$110$	−481.227	−0.417120
$111$	−356.491	−0.304835
$112$	529.328	0.446578
$113$	411.477	0.342553	0.171277	−	0.985223i	$-0.445211\pi$
$113$	411.477	0.342553	0.171277	+	0.985223i	$0.445211\pi$
$114$	−938.663	−0.771174
$115$	2370.70	1.92234
$116$	366.602	0.293432
$117$	−629.857	−0.497695
$118$	1773.28	1.38342
$119$	996.849	0.767908
$120$	1463.82	1.11357
$121$	121.000	0.0909091
$122$	−134.290	−0.0996565
$123$	−989.365	−0.725269
$124$	−798.982	−0.578635
$125$	−2879.39	−2.06032
$126$	363.807	0.257226
$127$	−1076.97	−0.752482	−0.376241	−	0.926522i	$-0.622784\pi$
$127$	−1076.97	−0.752482	−0.376241	+	0.926522i	$0.622784\pi$
$128$	−88.3965	−0.0610408
$129$	1311.68	0.895249
$130$	−3061.66	−2.06558
$131$	948.124	0.632351	0.316175	−	0.948701i	$-0.397601\pi$
$131$	948.124	0.632351	0.316175	+	0.948701i	$0.397601\pi$
$132$	−104.065	−0.0686186
$133$	2609.67	1.70141
$134$	−1050.16	−0.677016
$135$	536.544	0.342062
$136$	−1333.04	−0.840492
$137$	2790.34	1.74011	0.870055	−	0.492954i	$-0.164083\pi$
$137$	2790.34	1.74011	0.870055	+	0.492954i	$0.164083\pi$
$138$	−787.900	−0.486018
$139$	−1957.36	−1.19439	−0.597197	−	0.802094i	$-0.703719\pi$
$139$	−1957.36	−1.19439	−0.597197	+	0.802094i	$0.703719\pi$
$140$	−1150.65	−0.694627
$141$	79.1043	0.0472467
$142$	−2161.00	−1.27709
$143$	769.826	0.450182
$144$	−259.451	−0.150145
$145$	2310.19	1.32311
$146$	−2162.94	−1.22607
$147$	17.5445	0.00984385
$148$	−374.728	−0.208125
$149$	1985.00	1.09139	0.545695	−	0.837984i	$-0.316266\pi$
$149$	1985.00	1.09139	0.545695	+	0.837984i	$0.316266\pi$
$150$	1782.52	0.970281
$151$	2231.46	1.20261	0.601303	−	0.799021i	$-0.294649\pi$
$151$	2231.46	1.20261	0.601303	+	0.799021i	$0.294649\pi$
$152$	−3489.78	−1.86223
$153$	−488.606	−0.258180
$154$	−444.653	−0.232670
$155$	−5034.89	−2.60911
$156$	−662.079	−0.339800
$157$	−2636.49	−1.34022	−0.670110	−	0.742262i	$-0.733753\pi$
$157$	−2636.49	−1.34022	−0.670110	+	0.742262i	$0.733753\pi$
$158$	−785.833	−0.395681
$159$	1606.81	0.801438
$160$	2642.37	1.30561
$161$	2190.52	1.07228
$162$	−178.320	−0.0864824
$163$	−1140.10	−0.547852	−0.273926	−	0.961751i	$-0.588322\pi$
$163$	−1140.10	−0.547852	−0.273926	+	0.961751i	$0.588322\pi$
$164$	−1039.98	−0.495175
$165$	−655.776	−0.309407
$166$	−1143.66	−0.534728
$167$	2410.85	1.11711	0.558554	−	0.829468i	$-0.311356\pi$
$167$	2410.85	1.11711	0.558554	+	0.829468i	$0.311356\pi$
$168$	1352.57	0.621149
$169$	2700.78	1.22930
$170$	−2375.06	−1.07152
$171$	−1279.13	−0.572033
$172$	1378.78	0.611229
$173$	2121.20	0.932207	0.466104	−	0.884730i	$-0.345657\pi$
$173$	2121.20	0.932207	0.466104	+	0.884730i	$0.345657\pi$
$174$	−767.789	−0.334517
$175$	−4955.76	−2.14069
$176$	317.106	0.135811
$177$	2416.47	1.02618
$178$	−1387.77	−0.584369
$179$	1351.84	0.564476	0.282238	−	0.959344i	$-0.408923\pi$
$179$	1351.84	0.564476	0.282238	+	0.959344i	$0.408923\pi$
$180$	563.992	0.233542
$181$	−2092.82	−0.859435	−0.429718	−	0.902963i	$-0.641387\pi$
$181$	−2092.82	−0.859435	−0.429718	+	0.902963i	$0.641387\pi$
$182$	−2828.97	−1.15218
$183$	−183.000	−0.0739221
$184$	−2929.27	−1.17363
$185$	−2361.40	−0.938451
$186$	1673.34	0.659653
$187$	597.186	0.233532
$188$	83.1511	0.0322575
$189$	495.766	0.190802
$190$	−6217.71	−2.37410
$191$	−1697.22	−0.642967	−0.321484	−	0.946915i	$-0.604182\pi$
$191$	−1697.22	−0.642967	−0.321484	+	0.946915i	$0.604182\pi$
$192$	−1570.06	−0.590152
$193$	−3333.11	−1.24312	−0.621560	−	0.783366i	$-0.713501\pi$
$193$	−3333.11	−1.24312	−0.621560	+	0.783366i	$0.713501\pi$
$194$	2546.85	0.942543
$195$	−4172.18	−1.53218
$196$	18.4420	0.00672086
$197$	−2811.12	−1.01667	−0.508335	−	0.861160i	$-0.669739\pi$
$197$	−2811.12	−1.01667	−0.508335	+	0.861160i	$0.669739\pi$
$198$	217.947	0.0782263
$199$	−4491.56	−1.59999	−0.799996	−	0.600005i	$-0.795165\pi$
$199$	−4491.56	−1.59999	−0.799996	+	0.600005i	$0.795165\pi$
$200$	6627.09	2.34303
$201$	−1431.07	−0.502190
$202$	−3197.65	−1.11379
$203$	2134.61	0.738030
$204$	−513.602	−0.176271
$205$	−6553.56	−2.23278
$206$	−388.331	−0.131341
$207$	−1073.68	−0.360513
$208$	2017.49	0.672538
$209$	1563.38	0.517424
$210$	2409.86	0.791885
$211$	3016.31	0.984131	0.492065	−	0.870558i	$-0.336242\pi$
$211$	3016.31	0.984131	0.492065	+	0.870558i	$0.336242\pi$
$212$	1689.02	0.547180
$213$	−2944.84	−0.947310
$214$	3242.80	1.03586
$215$	8688.58	2.75608
$216$	−662.963	−0.208838
$217$	−4652.23	−1.45536
$218$	−1007.81	−0.313108
$219$	−2947.47	−0.909459
$220$	−689.324	−0.211246
$221$	3799.41	1.15645
$222$	784.809	0.237266
$223$	−3845.68	−1.15482	−0.577412	−	0.816453i	$-0.695937\pi$
$223$	−3845.68	−1.15482	−0.577412	+	0.816453i	$0.695937\pi$
$224$	2441.54	0.728270
$225$	2429.07	0.719725
$226$	−905.861	−0.266624
$227$	2056.83	0.601395	0.300697	−	0.953720i	$-0.402781\pi$
$227$	2056.83	0.601395	0.300697	+	0.953720i	$0.402781\pi$
$228$	−1344.57	−0.390554
$229$	−5691.47	−1.64237	−0.821185	−	0.570662i	$-0.806687\pi$
$229$	−5691.47	−1.64237	−0.821185	+	0.570662i	$0.806687\pi$
$230$	−5219.05	−1.49623
$231$	−605.936	−0.172587
$232$	−2854.51	−0.807791
$233$	4203.70	1.18195	0.590973	−	0.806691i	$-0.298744\pi$
$233$	4203.70	1.18195	0.590973	+	0.806691i	$0.298744\pi$
$234$	1386.62	0.387377
$235$	523.987	0.145452
$236$	2540.10	0.700619
$237$	−1070.87	−0.293504
$238$	−2194.55	−0.597695
$239$	−4259.47	−1.15281	−0.576407	−	0.817163i	$-0.695546\pi$
$239$	−4259.47	−1.15281	−0.576407	+	0.817163i	$0.695546\pi$
$240$	−1718.60	−0.462230
$241$	−3366.74	−0.899878	−0.449939	−	0.893059i	$-0.648554\pi$
$241$	−3366.74	−0.899878	−0.449939	+	0.893059i	$0.648554\pi$
$242$	−266.379	−0.0707583
$243$	−243.000	−0.0641500
$244$	−192.362	−0.0504701
$245$	116.215	0.0303049
$246$	2178.07	0.564507
$247$	9946.56	2.56228
$248$	6221.19	1.59293
$249$	−1558.48	−0.396645
$250$	6338.93	1.60364
$251$	−2371.25	−0.596302	−0.298151	−	0.954519i	$-0.596370\pi$
$251$	−2371.25	−0.596302	−0.298151	+	0.954519i	$0.596370\pi$
$252$	521.128	0.130270
$253$	1312.28	0.326097
$254$	2370.92	0.585688
$255$	−3236.53	−0.794821
$256$	−3992.22	−0.974663
$257$	−2321.06	−0.563360	−0.281680	−	0.959508i	$-0.590892\pi$
$257$	−2321.06	−0.563360	−0.281680	+	0.959508i	$0.590892\pi$
$258$	−2887.65	−0.696810
$259$	−2181.93	−0.523469
$260$	−4385.61	−1.04609
$261$	−1046.28	−0.248134
$262$	−2087.28	−0.492185
$263$	380.489	0.0892090	0.0446045	−	0.999005i	$-0.485797\pi$
$263$	380.489	0.0892090	0.0446045	+	0.999005i	$0.485797\pi$
$264$	810.288	0.188901
$265$	10643.5	2.46727
$266$	−5745.15	−1.32428
$267$	−1891.14	−0.433467
$268$	−1504.28	−0.342869
$269$	1455.74	0.329956	0.164978	−	0.986297i	$-0.447245\pi$
$269$	1455.74	0.329956	0.164978	+	0.986297i	$0.447245\pi$
$270$	−1181.19	−0.266241
$271$	843.062	0.188976	0.0944878	−	0.995526i	$-0.469879\pi$
$271$	843.062	0.188976	0.0944878	+	0.995526i	$0.469879\pi$
$272$	1565.05	0.348879
$273$	−3855.08	−0.854653
$274$	−6142.89	−1.35440
$275$	−2968.86	−0.651015
$276$	−1128.61	−0.246139
$277$	1641.22	0.355998	0.177999	−	0.984031i	$-0.443038\pi$
$277$	1641.22	0.355998	0.177999	+	0.984031i	$0.443038\pi$
$278$	4309.09	0.929647
$279$	2280.29	0.489310
$280$	8959.42	1.91224
$281$	1458.64	0.309662	0.154831	−	0.987941i	$-0.450517\pi$
$281$	1458.64	0.309662	0.154831	+	0.987941i	$0.450517\pi$
$282$	−174.147	−0.0367741
$283$	−3163.00	−0.664385	−0.332193	−	0.943212i	$-0.607788\pi$
$283$	−3163.00	−0.664385	−0.332193	+	0.943212i	$0.607788\pi$
$284$	−3095.49	−0.646773
$285$	−8472.98	−1.76104
$286$	−1694.76	−0.350396
$287$	−6055.47	−1.24545
$288$	−1196.73	−0.244853
$289$	−1965.64	−0.400090
$290$	−5085.84	−1.02983
$291$	3470.64	0.699150
$292$	−3098.25	−0.620930
$293$	−3792.87	−0.756253	−0.378126	−	0.925754i	$-0.623431\pi$
$293$	−3792.87	−0.756253	−0.378126	+	0.925754i	$0.623431\pi$
$294$	−38.6239	−0.00766188
$295$	16006.7	3.15915
$296$	2917.78	0.572948
$297$	297.000	0.0580259
$298$	−4369.94	−0.849475
$299$	8348.99	1.61483
$300$	2553.34	0.491390
$301$	8028.23	1.53734
$302$	−4912.52	−0.936038
$303$	−4357.49	−0.826176
$304$	4097.18	0.772991
$305$	−1212.19	−0.227574
$306$	1075.66	0.200952
$307$	−3554.96	−0.660886	−0.330443	−	0.943826i	$-0.607198\pi$
$307$	−3554.96	−0.660886	−0.330443	+	0.943826i	$0.607198\pi$
$308$	−636.934	−0.117833
$309$	−529.186	−0.0974251
$310$	11084.2	2.03078
$311$	−2730.78	−0.497905	−0.248952	−	0.968516i	$-0.580086\pi$
$311$	−2730.78	−0.497905	−0.248952	+	0.968516i	$0.580086\pi$
$312$	5155.21	0.935437
$313$	3732.91	0.674110	0.337055	−	0.941485i	$-0.390569\pi$
$313$	3732.91	0.674110	0.337055	+	0.941485i	$0.390569\pi$
$314$	5804.18	1.04315
$315$	3283.95	0.587396
$316$	−1125.65	−0.200389
$317$	3334.75	0.590846	0.295423	−	0.955367i	$-0.404539\pi$
$317$	3334.75	0.590846	0.295423	+	0.955367i	$0.404539\pi$
$318$	−3537.38	−0.623793
$319$	1278.79	0.224446
$320$	−10400.1	−1.81682
$321$	4419.02	0.768366
$322$	−4822.39	−0.834600
$323$	7715.95	1.32919
$324$	−255.431	−0.0437982
$325$	−18888.5	−3.22383
$326$	2509.92	0.426416
$327$	−1373.36	−0.232254
$328$	8097.68	1.36317
$329$	484.163	0.0811330
$330$	1443.68	0.240824
$331$	−1123.86	−0.186626	−0.0933129	−	0.995637i	$-0.529746\pi$
$331$	−1123.86	−0.186626	−0.0933129	+	0.995637i	$0.529746\pi$
$332$	−1638.21	−0.270808
$333$	1069.47	0.175996
$334$	−5307.44	−0.869492
$335$	−9479.44	−1.54602
$336$	−1587.98	−0.257832
$337$	−3379.64	−0.546293	−0.273146	−	0.961972i	$-0.588064\pi$
$337$	−3379.64	−0.546293	−0.273146	+	0.961972i	$0.588064\pi$
$338$	−5945.72	−0.956819
$339$	−1234.43	−0.197773
$340$	−3402.10	−0.542661
$341$	−2787.03	−0.442598
$342$	2815.99	0.445238
$343$	6405.44	1.00834
$344$	−10735.8	−1.68265
$345$	−7112.09	−1.10986
$346$	−4669.79	−0.725576
$347$	−4574.65	−0.707724	−0.353862	−	0.935298i	$-0.615132\pi$
$347$	−4574.65	−0.707724	−0.353862	+	0.935298i	$0.615132\pi$
$348$	−1099.80	−0.169413
$349$	2116.56	0.324632	0.162316	−	0.986739i	$-0.448104\pi$
$349$	2116.56	0.324632	0.162316	+	0.986739i	$0.448104\pi$
$350$	10910.0	1.66619
$351$	1889.57	0.287344
$352$	1462.66	0.221478
$353$	−6791.57	−1.02402	−0.512010	−	0.858980i	$-0.671099\pi$
$353$	−6791.57	−1.02402	−0.512010	+	0.858980i	$0.671099\pi$
$354$	−5319.83	−0.798717
$355$	−19506.6	−2.91635
$356$	−1987.88	−0.295948
$357$	−2990.55	−0.443352
$358$	−2976.05	−0.439355
$359$	6866.47	1.00947	0.504733	−	0.863275i	$-0.331591\pi$
$359$	6866.47	1.00947	0.504733	+	0.863275i	$0.331591\pi$
$360$	−4391.47	−0.642919
$361$	13340.8	1.94500
$362$	4607.30	0.668934
$363$	−363.000	−0.0524864
$364$	−4052.30	−0.583511
$365$	−19524.0	−2.79982
$366$	402.871	0.0575367
$367$	13773.2	1.95900	0.979501	−	0.201438i	$-0.0645614\pi$
$367$	13773.2	1.95900	0.979501	+	0.201438i	$0.0645614\pi$
$368$	3439.11	0.487163
$369$	2968.10	0.418734
$370$	5198.58	0.730436
$371$	9834.62	1.37625
$372$	2396.95	0.334075
$373$	−6296.68	−0.874074	−0.437037	−	0.899444i	$-0.643972\pi$
$373$	−6296.68	−0.874074	−0.437037	+	0.899444i	$0.643972\pi$
$374$	−1314.69	−0.181768
$375$	8638.17	1.18953
$376$	−647.447	−0.0888019
$377$	8135.89	1.11146
$378$	−1091.42	−0.148509
$379$	1626.72	0.220473	0.110236	−	0.993905i	$-0.464839\pi$
$379$	1626.72	0.220473	0.110236	+	0.993905i	$0.464839\pi$
$380$	−8906.43	−1.20234
$381$	3230.90	0.434446
$382$	3736.41	0.500448
$383$	6283.76	0.838342	0.419171	−	0.907907i	$-0.362321\pi$
$383$	6283.76	0.838342	0.419171	+	0.907907i	$0.362321\pi$
$384$	265.189	0.0352419
$385$	−4013.72	−0.531320
$386$	7337.78	0.967573
$387$	−3935.05	−0.516872
$388$	3648.19	0.477342
$389$	2064.35	0.269066	0.134533	−	0.990909i	$-0.457047\pi$
$389$	2064.35	0.269066	0.134533	+	0.990909i	$0.457047\pi$
$390$	9184.98	1.19256
$391$	6476.66	0.837695
$392$	−143.597	−0.0185019
$393$	−2844.37	−0.365088
$394$	6188.63	0.791316
$395$	−7093.44	−0.903569
$396$	312.194	0.0396170
$397$	9447.44	1.19434	0.597170	−	0.802114i	$-0.296292\pi$
$397$	9447.44	1.19434	0.597170	+	0.802114i	$0.296292\pi$
$398$	9888.10	1.24534
$399$	−7829.01	−0.982308
$400$	−7780.54	−0.972567
$401$	12297.3	1.53142	0.765708	−	0.643188i	$-0.222389\pi$
$401$	12297.3	1.53142	0.765708	+	0.643188i	$0.222389\pi$
$402$	3150.48	0.390875
$403$	−17731.6	−2.19175
$404$	−4580.41	−0.564069
$405$	−1609.63	−0.197490
$406$	−4699.30	−0.574440
$407$	−1307.13	−0.159195
$408$	3999.11	0.485258
$409$	10999.7	1.32983	0.664913	−	0.746921i	$-0.268469\pi$
$409$	10999.7	1.32983	0.664913	+	0.746921i	$0.268469\pi$
$410$	14427.5	1.73787
$411$	−8371.03	−1.00465
$412$	−556.258	−0.0665166
$413$	14790.2	1.76217
$414$	2363.70	0.280603
$415$	−10323.4	−1.22110
$416$	9305.75	1.09676
$417$	5872.07	0.689584
$418$	−3441.76	−0.402732
$419$	−1929.91	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$419$	−1929.91	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$420$	3451.95	0.401043
$421$	4813.28	0.557209	0.278604	−	0.960406i	$-0.410128\pi$
$421$	4813.28	0.557209	0.278604	+	0.960406i	$0.410128\pi$
$422$	−6640.36	−0.765990
$423$	−237.313	−0.0272779
$424$	−13151.3	−1.50633
$425$	−14652.6	−1.67236
$426$	6483.01	0.737331
$427$	−1120.06	−0.126941
$428$	4645.08	0.524600
$429$	−2309.48	−0.259913
$430$	−19127.8	−2.14517
$431$	−7443.86	−0.831922	−0.415961	−	0.909383i	$-0.636555\pi$
$431$	−7443.86	−0.831922	−0.415961	+	0.909383i	$0.636555\pi$
$432$	778.352	0.0866862
$433$	−4170.51	−0.462869	−0.231434	−	0.972851i	$-0.574342\pi$
$433$	−4170.51	−0.462869	−0.231434	+	0.972851i	$0.574342\pi$
$434$	10241.8	1.13277
$435$	−6930.56	−0.763896
$436$	−1443.62	−0.158570
$437$	16955.4	1.85603
$438$	6488.81	0.707870
$439$	11338.4	1.23270	0.616349	−	0.787473i	$-0.288611\pi$
$439$	11338.4	1.23270	0.616349	+	0.787473i	$0.288611\pi$
$440$	5367.35	0.581542
$441$	−52.6335	−0.00568335
$442$	−8364.34	−0.900115
$443$	−6300.09	−0.675680	−0.337840	−	0.941204i	$-0.609696\pi$
$443$	−6300.09	−0.675680	−0.337840	+	0.941204i	$0.609696\pi$
$444$	1124.19	0.120161
$445$	−12526.9	−1.33445
$446$	8466.20	0.898848
$447$	−5954.99	−0.630115
$448$	−9609.64	−1.01342
$449$	−4838.26	−0.508534	−0.254267	−	0.967134i	$-0.581834\pi$
$449$	−4838.26	−0.508534	−0.254267	+	0.967134i	$0.581834\pi$
$450$	−5347.56	−0.560192
$451$	−3627.67	−0.378759
$452$	−1297.58	−0.135029
$453$	−6694.37	−0.694325
$454$	−4528.08	−0.468091
$455$	−25536.1	−2.63110
$456$	10469.4	1.07516
$457$	−13143.3	−1.34533	−0.672666	−	0.739946i	$-0.734851\pi$
$457$	−13143.3	−1.34533	−0.672666	+	0.739946i	$0.734851\pi$
$458$	12529.7	1.27833
$459$	1465.82	0.149060
$460$	−7475.93	−0.757754
$461$	10609.0	1.07182	0.535912	−	0.844274i	$-0.319968\pi$
$461$	10609.0	1.07182	0.535912	+	0.844274i	$0.319968\pi$
$462$	1333.96	0.134332
$463$	−4147.53	−0.416312	−0.208156	−	0.978096i	$-0.566746\pi$
$463$	−4147.53	−0.416312	−0.208156	+	0.978096i	$0.566746\pi$
$464$	3351.33	0.335305
$465$	15104.7	1.50637
$466$	−9254.37	−0.919958
$467$	−10126.7	−1.00344	−0.501720	−	0.865030i	$-0.667299\pi$
$467$	−10126.7	−1.00344	−0.501720	+	0.865030i	$0.667299\pi$
$468$	1986.24	0.196183
$469$	−8758.98	−0.862371
$470$	−1153.55	−0.113211
$471$	7909.46	0.773776
$472$	−19778.2	−1.92874
$473$	4809.50	0.467529
$474$	2357.50	0.228446
$475$	−38359.3	−3.70536
$476$	−3143.54	−0.302697
$477$	−4820.44	−0.462711
$478$	9377.16	0.897283
$479$	2962.68	0.282606	0.141303	−	0.989966i	$-0.454871\pi$
$479$	2962.68	0.282606	0.141303	+	0.989966i	$0.454871\pi$
$480$	−7927.11	−0.753795
$481$	−8316.25	−0.788333
$482$	7411.82	0.700413
$483$	−6571.56	−0.619081
$484$	−381.570	−0.0358349
$485$	22989.5	2.15237
$486$	534.960	0.0499307
$487$	6950.28	0.646709	0.323354	−	0.946278i	$-0.395189\pi$
$487$	6950.28	0.646709	0.323354	+	0.946278i	$0.395189\pi$
$488$	1497.81	0.138939
$489$	3420.31	0.316302
$490$	−255.845	−0.0235875
$491$	20596.7	1.89311	0.946554	−	0.322545i	$-0.104538\pi$
$491$	20596.7	1.89311	0.946554	+	0.322545i	$0.104538\pi$
$492$	3119.94	0.285889
$493$	6311.35	0.576569
$494$	−21897.2	−1.99433
$495$	1967.33	0.178636
$496$	−7303.99	−0.661207
$497$	−18024.1	−1.62674
$498$	3430.97	0.308725
$499$	−6368.22	−0.571304	−0.285652	−	0.958333i	$-0.592210\pi$
$499$	−6368.22	−0.571304	−0.285652	+	0.958333i	$0.592210\pi$
$500$	9080.07	0.812146
$501$	−7232.55	−0.644963
$502$	5220.26	0.464127
$503$	−17458.6	−1.54760	−0.773798	−	0.633433i	$-0.781645\pi$
$503$	−17458.6	−1.54760	−0.773798	+	0.633433i	$0.781645\pi$
$504$	−4057.71	−0.358620
$505$	−28864.0	−2.54343
$506$	−2888.96	−0.253815
$507$	−8102.34	−0.709739
$508$	3396.18	0.296616
$509$	−15619.1	−1.36012	−0.680062	−	0.733154i	$-0.738047\pi$
$509$	−15619.1	−1.36012	−0.680062	+	0.733154i	$0.738047\pi$
$510$	7125.17	0.618642
$511$	−18040.2	−1.56174
$512$	9495.97	0.819661
$513$	3837.40	0.330264
$514$	5109.77	0.438487
$515$	−3505.33	−0.299929
$516$	−4136.35	−0.352893
$517$	290.049	0.0246738
$518$	4803.48	0.407438
$519$	−6363.60	−0.538210
$520$	34148.1	2.87980
$521$	−17965.5	−1.51071	−0.755357	−	0.655313i	$-0.772537\pi$
$521$	−17965.5	−1.51071	−0.755357	+	0.655313i	$0.772537\pi$
$522$	2303.37	0.193133
$523$	−661.791	−0.0553310	−0.0276655	−	0.999617i	$-0.508807\pi$
$523$	−661.791	−0.0553310	−0.0276655	+	0.999617i	$0.508807\pi$
$524$	−2989.88	−0.249263
$525$	14867.3	1.23593
$526$	−837.641	−0.0694351
$527$	−13755.1	−1.13697
$528$	−951.319	−0.0784107
$529$	2065.08	0.169728
$530$	−23431.6	−1.92038
$531$	−7249.42	−0.592464
$532$	−8229.53	−0.670668
$533$	−23080.0	−1.87562
$534$	4163.31	0.337385
$535$	29271.6	2.36546
$536$	11712.9	0.943885
$537$	−4055.52	−0.325900
$538$	−3204.79	−0.256819
$539$	64.3298	0.00514078
$540$	−1691.98	−0.134835
$541$	−9554.10	−0.759266	−0.379633	−	0.925137i	$-0.623950\pi$
$541$	−9554.10	−0.759266	−0.379633	+	0.925137i	$0.623950\pi$
$542$	−1855.99	−0.147088
$543$	6278.45	0.496195
$544$	7218.86	0.568945
$545$	−9097.14	−0.715006
$546$	8486.90	0.665212
$547$	8141.36	0.636379	0.318190	−	0.948027i	$-0.396925\pi$
$547$	8141.36	0.636379	0.318190	+	0.948027i	$0.396925\pi$
$548$	−8799.27	−0.685924
$549$	549.000	0.0426790
$550$	6535.90	0.506712
$551$	16522.6	1.27747
$552$	8787.82	0.677598
$553$	−6554.32	−0.504011
$554$	−3613.12	−0.277088
$555$	7084.20	0.541815
$556$	6172.47	0.470811
$557$	11979.5	0.911288	0.455644	−	0.890162i	$-0.349409\pi$
$557$	11979.5	0.911288	0.455644	+	0.890162i	$0.349409\pi$
$558$	−5020.03	−0.380851
$559$	30599.0	2.31520
$560$	−10518.8	−0.793751
$561$	−1791.56	−0.134830
$562$	−3211.17	−0.241023
$563$	−2796.64	−0.209351	−0.104675	−	0.994506i	$-0.533380\pi$
$563$	−2796.64	−0.209351	−0.104675	+	0.994506i	$0.533380\pi$
$564$	−249.453	−0.0186239
$565$	−8176.88	−0.608857
$566$	6963.30	0.517119
$567$	−1487.30	−0.110160
$568$	24102.7	1.78050
$569$	1326.14	0.0977057	0.0488528	−	0.998806i	$-0.484443\pi$
$569$	1326.14	0.0977057	0.0488528	+	0.998806i	$0.484443\pi$
$570$	18653.1	1.37069
$571$	21809.3	1.59841	0.799203	−	0.601062i	$-0.205255\pi$
$571$	21809.3	1.59841	0.799203	+	0.601062i	$0.205255\pi$
$572$	−2427.62	−0.177455
$573$	5091.67	0.371217
$574$	13331.0	0.969384
$575$	−32198.2	−2.33523
$576$	4710.17	0.340724
$577$	−16368.3	−1.18097	−0.590487	−	0.807047i	$-0.701064\pi$
$577$	−16368.3	−1.18097	−0.590487	+	0.807047i	$0.701064\pi$
$578$	4327.32	0.311406
$579$	9999.32	0.717716
$580$	−7285.11	−0.521548
$581$	−9538.78	−0.681128
$582$	−7640.56	−0.544177
$583$	5891.65	0.418538
$584$	24124.2	1.70936
$585$	12516.5	0.884607
$586$	8349.95	0.588623
$587$	7098.89	0.499153	0.249576	−	0.968355i	$-0.419709\pi$
$587$	7098.89	0.499153	0.249576	+	0.968355i	$0.419709\pi$
$588$	−55.3261	−0.00388029
$589$	−36009.8	−2.51912
$590$	−35238.6	−2.45890
$591$	8433.35	0.586974
$592$	−3425.62	−0.237825
$593$	22768.5	1.57671	0.788355	−	0.615221i	$-0.210933\pi$
$593$	22768.5	1.57671	0.788355	+	0.615221i	$0.210933\pi$
$594$	−653.840	−0.0451640
$595$	−19809.4	−1.36488
$596$	−6259.63	−0.430209
$597$	13474.7	0.923756
$598$	−18380.2	−1.25689
$599$	5240.01	0.357431	0.178715	−	0.983901i	$-0.442806\pi$
$599$	5240.01	0.357431	0.178715	+	0.983901i	$0.442806\pi$
$600$	−19881.3	−1.35275
$601$	−697.277	−0.0473253	−0.0236626	−	0.999720i	$-0.507533\pi$
$601$	−697.277	−0.0473253	−0.0236626	+	0.999720i	$0.507533\pi$
$602$	−17674.0	−1.19658
$603$	4293.22	0.289939
$604$	−7036.84	−0.474048
$605$	−2404.51	−0.161582
$606$	9592.94	0.643047
$607$	29368.7	1.96382	0.981911	−	0.189343i	$-0.0606358\pi$
$607$	29368.7	1.96382	0.981911	+	0.189343i	$0.0606358\pi$
$608$	18898.4	1.26058
$609$	−6403.82	−0.426102
$610$	2668.62	0.177130
$611$	1845.35	0.122185
$612$	1540.81	0.101770
$613$	−28109.9	−1.85212	−0.926058	−	0.377381i	$-0.876825\pi$
$613$	−28109.9	−1.85212	−0.926058	+	0.377381i	$0.876825\pi$
$614$	7826.18	0.514395
$615$	19660.7	1.28910
$616$	4959.42	0.324384
$617$	19398.0	1.26570	0.632849	−	0.774275i	$-0.281886\pi$
$617$	19398.0	1.26570	0.632849	+	0.774275i	$0.281886\pi$
$618$	1164.99	0.0758300
$619$	27692.4	1.79815	0.899074	−	0.437797i	$-0.144241\pi$
$619$	27692.4	1.79815	0.899074	+	0.437797i	$0.144241\pi$
$620$	15877.4	1.02847
$621$	3221.05	0.208142
$622$	6011.77	0.387540
$623$	−11574.8	−0.744359
$624$	−6052.47	−0.388290
$625$	23482.1	1.50286
$626$	−8217.93	−0.524688
$627$	−4690.15	−0.298735
$628$	8314.08	0.528293
$629$	−6451.26	−0.408948
$630$	−7229.57	−0.457195
$631$	−18249.2	−1.15133	−0.575666	−	0.817685i	$-0.695257\pi$
$631$	−18249.2	−1.15133	−0.575666	+	0.817685i	$0.695257\pi$
$632$	8764.77	0.551652
$633$	−9048.94	−0.568188
$634$	−7341.40	−0.459880
$635$	21401.5	1.33747
$636$	−5067.05	−0.315914
$637$	409.279	0.0254572
$638$	−2815.23	−0.174696
$639$	8834.52	0.546930
$640$	1756.62	0.108494
$641$	5565.03	0.342910	0.171455	−	0.985192i	$-0.445153\pi$
$641$	5565.03	0.342910	0.171455	+	0.985192i	$0.445153\pi$
$642$	−9728.40	−0.598052
$643$	−26054.8	−1.59798	−0.798989	−	0.601346i	$-0.794631\pi$
$643$	−26054.8	−1.59798	−0.798989	+	0.601346i	$0.794631\pi$
$644$	−6907.74	−0.422676
$645$	−26065.8	−1.59122
$646$	−16986.5	−1.03456
$647$	25292.0	1.53683	0.768417	−	0.639949i	$-0.221045\pi$
$647$	25292.0	1.53683	0.768417	+	0.639949i	$0.221045\pi$
$648$	1988.89	0.120572
$649$	8860.41	0.535904
$650$	41582.7	2.50924
$651$	13956.7	0.840254
$652$	3595.29	0.215954
$653$	19554.3	1.17185	0.585926	−	0.810365i	$-0.300731\pi$
$653$	19554.3	1.17185	0.585926	+	0.810365i	$0.300731\pi$
$654$	3023.43	0.180773
$655$	−18841.1	−1.12394
$656$	−9507.09	−0.565837
$657$	8842.41	0.525076
$658$	−1065.88	−0.0631492
$659$	−2175.80	−0.128615	−0.0643074	−	0.997930i	$-0.520484\pi$
$659$	−2175.80	−0.128615	−0.0643074	+	0.997930i	$0.520484\pi$
$660$	2067.97	0.121963
$661$	−20595.0	−1.21188	−0.605941	−	0.795509i	$-0.707203\pi$
$661$	−20595.0	−1.21188	−0.605941	+	0.795509i	$0.707203\pi$
$662$	2474.17	0.145259
$663$	−11398.2	−0.667678
$664$	12755.7	0.745509
$665$	−51859.4	−3.02409
$666$	−2354.43	−0.136985
$667$	13868.8	0.805102
$668$	−7602.55	−0.440346
$669$	11537.0	0.666738
$670$	20868.8	1.20333
$671$	−671.000	−0.0386046
$672$	−7324.63	−0.420467
$673$	27480.0	1.57396	0.786981	−	0.616978i	$-0.211643\pi$
$673$	27480.0	1.57396	0.786981	+	0.616978i	$0.211643\pi$
$674$	7440.22	0.425203
$675$	−7287.21	−0.415533
$676$	−8516.84	−0.484572
$677$	13007.6	0.738436	0.369218	−	0.929343i	$-0.379626\pi$
$677$	13007.6	0.738436	0.369218	+	0.929343i	$0.379626\pi$
$678$	2717.58	0.153935
$679$	21242.3	1.20059
$680$	26490.1	1.49390
$681$	−6170.49	−0.347216
$682$	6135.59	0.344492
$683$	3367.08	0.188635	0.0943175	−	0.995542i	$-0.469933\pi$
$683$	3367.08	0.188635	0.0943175	+	0.995542i	$0.469933\pi$
$684$	4033.71	0.225486
$685$	−55449.7	−3.09288
$686$	−14101.5	−0.784835
$687$	17074.4	0.948223
$688$	12604.3	0.698452
$689$	37483.9	2.07260
$690$	15657.1	0.863851
$691$	−25350.4	−1.39562	−0.697810	−	0.716283i	$-0.745842\pi$
$691$	−25350.4	−1.39562	−0.697810	+	0.716283i	$0.745842\pi$
$692$	−6689.15	−0.367461
$693$	1817.81	0.0996433
$694$	10071.0	0.550851
$695$	38896.6	2.12292
$696$	8563.52	0.466378
$697$	−17904.1	−0.972978
$698$	−4659.57	−0.252675
$699$	−12611.1	−0.682397
$700$	15627.9	0.843825
$701$	−13993.9	−0.753986	−0.376993	−	0.926216i	$-0.623042\pi$
$701$	−13993.9	−0.753986	−0.376993	+	0.926216i	$0.623042\pi$
$702$	−4159.86	−0.223652
$703$	−16888.9	−0.906082
$704$	−5756.88	−0.308197
$705$	−1571.96	−0.0839766
$706$	14951.5	0.797037
$707$	−26670.3	−1.41873
$708$	−7620.29	−0.404503
$709$	7921.56	0.419606	0.209803	−	0.977744i	$-0.432718\pi$
$709$	7921.56	0.419606	0.209803	+	0.977744i	$0.432718\pi$
$710$	42943.5	2.26992
$711$	3212.61	0.169455
$712$	15478.4	0.814718
$713$	−30226.1	−1.58763
$714$	6583.64	0.345079
$715$	−15298.0	−0.800157
$716$	−4262.99	−0.222507
$717$	12778.4	0.665577
$718$	−15116.4	−0.785710
$719$	2363.10	0.122571	0.0612857	−	0.998120i	$-0.480480\pi$
$719$	2363.10	0.122571	0.0612857	+	0.998120i	$0.480480\pi$
$720$	5155.80	0.266869
$721$	−3238.92	−0.167300
$722$	−29369.4	−1.51387
$723$	10100.2	0.519545
$724$	6599.64	0.338776
$725$	−31376.4	−1.60730
$726$	799.138	0.0408524
$727$	−21783.5	−1.11129	−0.555644	−	0.831421i	$-0.687528\pi$
$727$	−21783.5	−1.11129	−0.555644	+	0.831421i	$0.687528\pi$
$728$	31552.8	1.60635
$729$	729.000	0.0370370
$730$	42981.9	2.17922
$731$	23736.9	1.20101
$732$	577.085	0.0291389
$733$	1128.92	0.0568865	0.0284432	−	0.999595i	$-0.490945\pi$
$733$	1128.92	0.0568865	0.0284432	+	0.999595i	$0.490945\pi$
$734$	−30321.4	−1.52477
$735$	−348.644	−0.0174965
$736$	15863.0	0.794455
$737$	−5247.27	−0.262260
$738$	−6534.21	−0.325918
$739$	25428.6	1.26577	0.632886	−	0.774245i	$-0.281870\pi$
$739$	25428.6	1.26577	0.632886	+	0.774245i	$0.281870\pi$
$740$	7446.61	0.369923
$741$	−29839.7	−1.47934
$742$	−21650.7	−1.07119
$743$	30696.7	1.51569	0.757843	−	0.652437i	$-0.226253\pi$
$743$	30696.7	1.51569	0.757843	+	0.652437i	$0.226253\pi$
$744$	−18663.6	−0.919677
$745$	−39445.9	−1.93985
$746$	13862.0	0.680328
$747$	4675.44	0.229003
$748$	−1883.21	−0.0920547
$749$	27046.9	1.31946
$750$	−19016.8	−0.925859
$751$	−27468.1	−1.33466	−0.667328	−	0.744764i	$-0.732562\pi$
$751$	−27468.1	−1.33466	−0.667328	+	0.744764i	$0.732562\pi$
$752$	760.135	0.0368607
$753$	7113.75	0.344275
$754$	−17911.0	−0.865094
$755$	−44343.5	−2.13752
$756$	−1563.38	−0.0752113
$757$	24192.2	1.16153	0.580766	−	0.814071i	$-0.302753\pi$
$757$	24192.2	1.16153	0.580766	+	0.814071i	$0.302753\pi$
$758$	−3581.21	−0.171603
$759$	−3936.84	−0.188272
$760$	69349.0	3.30994
$761$	−12931.5	−0.615986	−0.307993	−	0.951389i	$-0.599657\pi$
$761$	−12931.5	−0.615986	−0.307993	+	0.951389i	$0.599657\pi$
$762$	−7112.76	−0.338147
$763$	−8405.73	−0.398831
$764$	5352.15	0.253447
$765$	9709.59	0.458890
$766$	−13833.6	−0.652517
$767$	56371.6	2.65380
$768$	11976.7	0.562722
$769$	−18780.1	−0.880659	−0.440329	−	0.897836i	$-0.645138\pi$
$769$	−18780.1	−0.880659	−0.440329	+	0.897836i	$0.645138\pi$
$770$	8836.14	0.413549
$771$	6963.17	0.325256
$772$	10510.9	0.490018
$773$	32879.2	1.52986	0.764930	−	0.644113i	$-0.222773\pi$
$773$	32879.2	1.52986	0.764930	+	0.644113i	$0.222773\pi$
$774$	8662.94	0.402303
$775$	68382.6	3.16952
$776$	−28406.2	−1.31408
$777$	6545.78	0.302225
$778$	−4544.63	−0.209425
$779$	−46871.5	−2.15577
$780$	13156.8	0.603962
$781$	−10797.7	−0.494716
$782$	−14258.2	−0.652013
$783$	3138.84	0.143261
$784$	168.590	0.00767994
$785$	52392.3	2.38211
$786$	6261.83	0.284163
$787$	23569.0	1.06753	0.533764	−	0.845634i	$-0.320777\pi$
$787$	23569.0	1.06753	0.533764	+	0.845634i	$0.320777\pi$
$788$	8864.78	0.400755
$789$	−1141.47	−0.0515049
$790$	15616.1	0.703285
$791$	−7555.42	−0.339621
$792$	−2430.86	−0.109062
$793$	−4269.03	−0.191170
$794$	−20798.4	−0.929605
$795$	−31930.6	−1.42448
$796$	14164.0	0.630691
$797$	11667.9	0.518569	0.259285	−	0.965801i	$-0.416513\pi$
$797$	11667.9	0.518569	0.259285	+	0.965801i	$0.416513\pi$
$798$	17235.4	0.764571
$799$	1431.51	0.0633834
$800$	−35888.0	−1.58604
$801$	5673.41	0.250262
$802$	−27072.3	−1.19197
$803$	−10807.4	−0.474950
$804$	4512.85	0.197955
$805$	−43530.0	−1.90588
$806$	39035.8	1.70593
$807$	−4367.23	−0.190500
$808$	35664.9	1.55283
$809$	−12681.2	−0.551111	−0.275556	−	0.961285i	$-0.588862\pi$
$809$	−12681.2	−0.551111	−0.275556	+	0.961285i	$0.588862\pi$
$810$	3543.58	0.153714
$811$	−5578.12	−0.241522	−0.120761	−	0.992682i	$-0.538533\pi$
$811$	−5578.12	−0.241522	−0.120761	+	0.992682i	$0.538533\pi$
$812$	−6731.43	−0.290920
$813$	−2529.19	−0.109105
$814$	2877.63	0.123908
$815$	22656.2	0.973755
$816$	−4695.15	−0.201426
$817$	62141.3	2.66101
$818$	−24215.6	−1.03506
$819$	11565.2	0.493434
$820$	20666.5	0.880127
$821$	38839.8	1.65106	0.825528	−	0.564361i	$-0.190877\pi$
$821$	38839.8	1.65106	0.825528	+	0.564361i	$0.190877\pi$
$822$	18428.7	0.781964
$823$	−25515.1	−1.08068	−0.540340	−	0.841447i	$-0.681704\pi$
$823$	−25515.1	−1.08068	−0.540340	+	0.841447i	$0.681704\pi$
$824$	4331.24	0.183114
$825$	8906.59	0.375864
$826$	−32560.4	−1.37157
$827$	9775.59	0.411041	0.205520	−	0.978653i	$-0.434111\pi$
$827$	9775.59	0.411041	0.205520	+	0.978653i	$0.434111\pi$
$828$	3385.83	0.142109
$829$	15011.5	0.628914	0.314457	−	0.949272i	$-0.398178\pi$
$829$	15011.5	0.628914	0.314457	+	0.949272i	$0.398178\pi$
$830$	22726.7	0.950429
$831$	−4923.66	−0.205535
$832$	−36626.4	−1.52619
$833$	317.495	0.0132059
$834$	−12927.3	−0.536732
$835$	−47908.4	−1.98556
$836$	−4930.09	−0.203960
$837$	−6840.88	−0.282503
$838$	4248.67	0.175141
$839$	16248.6	0.668610	0.334305	−	0.942465i	$-0.391499\pi$
$839$	16248.6	0.668610	0.334305	+	0.942465i	$0.391499\pi$
$840$	−26878.3	−1.10403
$841$	−10874.2	−0.445864
$842$	−10596.4	−0.433699
$843$	−4375.91	−0.178783
$844$	−9511.86	−0.387929
$845$	−53669.9	−2.18497
$846$	522.440	0.0212315
$847$	−2221.77	−0.0901308
$848$	15440.3	0.625263
$849$	9489.01	0.383583
$850$	32257.4	1.30167
$851$	−14176.3	−0.571041
$852$	9286.47	0.373414
$853$	25726.0	1.03264	0.516319	−	0.856396i	$-0.327302\pi$
$853$	25726.0	1.03264	0.516319	+	0.856396i	$0.327302\pi$
$854$	2465.80	0.0988032
$855$	25418.9	1.01674
$856$	−36168.5	−1.44417
$857$	19261.4	0.767744	0.383872	−	0.923386i	$-0.374590\pi$
$857$	19261.4	0.767744	0.383872	+	0.923386i	$0.374590\pi$
$858$	5084.27	0.202301
$859$	38576.9	1.53228	0.766139	−	0.642675i	$-0.222175\pi$
$859$	38576.9	1.53228	0.766139	+	0.642675i	$0.222175\pi$
$860$	−27399.2	−1.08640
$861$	18166.4	0.719059
$862$	16387.5	0.647519
$863$	−23463.5	−0.925501	−0.462750	−	0.886489i	$-0.653137\pi$
$863$	−23463.5	−0.925501	−0.462750	+	0.886489i	$0.653137\pi$
$864$	3590.18	0.141366
$865$	−42152.5	−1.65691
$866$	9181.31	0.360270
$867$	5896.92	0.230992
$868$	14670.7	0.573681
$869$	−3926.52	−0.153277
$870$	15257.5	0.594573
$871$	−33384.2	−1.29871
$872$	11240.6	0.436530
$873$	−10411.9	−0.403654
$874$	−37327.0	−1.44463
$875$	52870.5	2.04268
$876$	9294.76	0.358494
$877$	−43434.5	−1.67238	−0.836190	−	0.548439i	$-0.815222\pi$
$877$	−43434.5	−1.67238	−0.836190	+	0.548439i	$0.815222\pi$
$878$	−24961.4	−0.959461
$879$	11378.6	0.436623
$880$	−6301.54	−0.241392
$881$	−44641.5	−1.70716	−0.853582	−	0.520959i	$-0.825574\pi$
$881$	−44641.5	−1.70716	−0.853582	+	0.520959i	$0.825574\pi$
$882$	115.872	0.00442359
$883$	−10065.9	−0.383628	−0.191814	−	0.981431i	$-0.561437\pi$
$883$	−10065.9	−0.383628	−0.191814	+	0.981431i	$0.561437\pi$
$884$	−11981.3	−0.455855
$885$	−48020.2	−1.82393
$886$	13869.5	0.525910
$887$	1054.86	0.0399311	0.0199655	−	0.999801i	$-0.493644\pi$
$887$	1054.86	0.0399311	0.0199655	+	0.999801i	$0.493644\pi$
$888$	−8753.35	−0.330792
$889$	19774.9	0.746039
$890$	27577.7	1.03866
$891$	−891.000	−0.0335013
$892$	12127.2	0.455213
$893$	3747.59	0.140435
$894$	13109.8	0.490445
$895$	−26863.8	−1.00330
$896$	1623.11	0.0605182
$897$	−25047.0	−0.932323
$898$	10651.3	0.395813
$899$	−29454.6	−1.09273
$900$	−7660.01	−0.283704
$901$	29077.8	1.07516
$902$	7986.26	0.294804
$903$	−24084.7	−0.887584
$904$	10103.5	0.371722
$905$	41588.5	1.52757
$906$	14737.5	0.540422
$907$	44115.0	1.61501	0.807506	−	0.589860i	$-0.200817\pi$
$907$	44115.0	1.61501	0.807506	+	0.589860i	$0.200817\pi$
$908$	−6486.16	−0.237060
$909$	13072.5	0.476993
$910$	56217.2	2.04789
$911$	1626.88	0.0591669	0.0295834	−	0.999562i	$-0.490582\pi$
$911$	1626.88	0.0591669	0.0295834	+	0.999562i	$0.490582\pi$
$912$	−12291.5	−0.446287
$913$	−5714.43	−0.207141
$914$	28934.7	1.04713
$915$	3636.58	0.131390
$916$	17947.9	0.647396
$917$	−17409.2	−0.626937
$918$	−3226.98	−0.116020
$919$	26999.6	0.969136	0.484568	−	0.874754i	$-0.338977\pi$
$919$	26999.6	0.969136	0.484568	+	0.874754i	$0.338977\pi$
$920$	58210.5	2.08603
$921$	10664.9	0.381563
$922$	−23355.5	−0.834245
$923$	−68697.3	−2.44984
$924$	1910.80	0.0680311
$925$	32071.9	1.14002
$926$	9130.73	0.324033
$927$	1587.56	0.0562484
$928$	15458.1	0.546809
$929$	−3767.83	−0.133066	−0.0665331	−	0.997784i	$-0.521194\pi$
$929$	−3767.83	−0.133066	−0.0665331	+	0.997784i	$0.521194\pi$
$930$	−33252.7	−1.17247
$931$	831.176	0.0292596
$932$	−13256.2	−0.465904
$933$	8192.35	0.287466
$934$	22293.7	0.781019
$935$	−11867.3	−0.415082
$936$	−15465.6	−0.540075
$937$	18864.3	0.657704	0.328852	−	0.944382i	$-0.393338\pi$
$937$	18864.3	0.657704	0.328852	+	0.944382i	$0.393338\pi$
$938$	19282.7	0.671220
$939$	−11198.7	−0.389198
$940$	−1652.38	−0.0573347
$941$	33213.9	1.15063	0.575315	−	0.817932i	$-0.304879\pi$
$941$	33213.9	1.15063	0.575315	+	0.817932i	$0.304879\pi$
$942$	−17412.5	−0.602262
$943$	−39343.2	−1.35863
$944$	23220.6	0.800599
$945$	−9851.86	−0.339133
$946$	−10588.0	−0.363897
$947$	35648.4	1.22325	0.611624	−	0.791149i	$-0.290517\pi$
$947$	35648.4	1.22325	0.611624	+	0.791149i	$0.290517\pi$
$948$	3376.96	0.115695
$949$	−68758.7	−2.35195
$950$	84447.3	2.88404
$951$	−10004.3	−0.341125
$952$	24476.8	0.833296
$953$	−24224.1	−0.823395	−0.411697	−	0.911321i	$-0.635064\pi$
$953$	−24224.1	−0.823395	−0.411697	+	0.911321i	$0.635064\pi$
$954$	10612.1	0.360147
$955$	33727.2	1.14281
$956$	13432.1	0.454421
$957$	−3836.36	−0.129584
$958$	−6522.29	−0.219964
$959$	−51235.4	−1.72521
$960$	31200.2	1.04894
$961$	34403.3	1.15482
$962$	18308.1	0.613592
$963$	−13257.1	−0.443617
$964$	10616.9	0.354718
$965$	66235.5	2.20953
$966$	14467.2	0.481857
$967$	−34009.8	−1.13100	−0.565502	−	0.824747i	$-0.691318\pi$
$967$	−34009.8	−1.13100	−0.565502	+	0.824747i	$0.691318\pi$
$968$	2971.06	0.0986502
$969$	−23147.9	−0.767406
$970$	−50611.1	−1.67528
$971$	−28573.3	−0.944347	−0.472174	−	0.881506i	$-0.656530\pi$
$971$	−28573.3	−0.944347	−0.472174	+	0.881506i	$0.656530\pi$
$972$	766.294	0.0252869
$973$	35940.4	1.18417
$974$	−15300.9	−0.503361
$975$	56665.5	1.86128
$976$	−1758.50	−0.0576723
$977$	5402.41	0.176907	0.0884536	−	0.996080i	$-0.471807\pi$
$977$	5402.41	0.176907	0.0884536	+	0.996080i	$0.471807\pi$
$978$	−7529.76	−0.246191
$979$	−6934.17	−0.226371
$980$	−366.480	−0.0119457
$981$	4120.08	0.134092
$982$	−45343.3	−1.47349
$983$	−32360.7	−1.04999	−0.524997	−	0.851104i	$-0.675934\pi$
$983$	−32360.7	−1.04999	−0.524997	+	0.851104i	$0.675934\pi$
$984$	−24293.1	−0.787027
$985$	55862.5	1.80703
$986$	−13894.3	−0.448768
$987$	−1452.49	−0.0468422
$988$	−31366.2	−1.01001
$989$	52160.5	1.67705
$990$	−4331.04	−0.139040
$991$	26509.1	0.849736	0.424868	−	0.905255i	$-0.360321\pi$
$991$	26509.1	0.849736	0.424868	+	0.905255i	$0.360321\pi$
$992$	−33689.9	−1.07828
$993$	3371.59	0.107748
$994$	39679.7	1.26616
$995$	89256.4	2.84384
$996$	4914.62	0.156351
$997$	−9591.90	−0.304693	−0.152346	−	0.988327i	$-0.548683\pi$
$997$	−9591.90	−0.304693	−0.152346	+	0.988327i	$0.548683\pi$
$998$	14019.5	0.444670
$999$	−3208.42	−0.101612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.b.1.11	✓	36	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20148 q^{2} -3.00000 q^{3} -3.15347 q^{4} -19.8720 q^{5} +6.60445 q^{6} -18.3617 q^{7} +24.5542 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.20148 q^{2} -3.00000 q^{3} -3.15347 q^{4} -19.8720 q^{5} +6.60445 q^{6} -18.3617 q^{7} +24.5542 q^{8} +9.00000 q^{9} +43.7479 q^{10} -11.0000 q^{11} +9.46042 q^{12} -69.9841 q^{13} +40.4230 q^{14} +59.6160 q^{15} -28.8278 q^{16} -54.2896 q^{17} -19.8133 q^{18} -142.126 q^{19} +62.6658 q^{20} +55.0851 q^{21} +24.2163 q^{22} -119.298 q^{23} -73.6625 q^{24} +269.897 q^{25} +154.069 q^{26} -27.0000 q^{27} +57.9031 q^{28} -116.253 q^{29} -131.244 q^{30} +253.366 q^{31} -132.969 q^{32} +33.0000 q^{33} +119.518 q^{34} +364.884 q^{35} -28.3812 q^{36} +118.830 q^{37} +312.888 q^{38} +209.952 q^{39} -487.941 q^{40} +329.788 q^{41} -121.269 q^{42} -437.227 q^{43} +34.6882 q^{44} -178.848 q^{45} +262.633 q^{46} -26.3681 q^{47} +86.4835 q^{48} -5.84817 q^{49} -594.173 q^{50} +162.869 q^{51} +220.693 q^{52} -535.605 q^{53} +59.4400 q^{54} +218.592 q^{55} -450.856 q^{56} +426.378 q^{57} +255.930 q^{58} -805.492 q^{59} -187.997 q^{60} +61.0000 q^{61} -557.781 q^{62} -165.255 q^{63} +523.353 q^{64} +1390.73 q^{65} -72.6489 q^{66} +477.025 q^{67} +171.201 q^{68} +357.895 q^{69} -803.285 q^{70} +981.613 q^{71} +220.988 q^{72} +982.490 q^{73} -261.603 q^{74} -809.690 q^{75} +448.190 q^{76} +201.979 q^{77} -462.207 q^{78} +356.956 q^{79} +572.867 q^{80} +81.0000 q^{81} -726.024 q^{82} +519.493 q^{83} -173.709 q^{84} +1078.84 q^{85} +962.549 q^{86} +348.760 q^{87} -270.096 q^{88} +630.379 q^{89} +393.731 q^{90} +1285.03 q^{91} +376.204 q^{92} -760.098 q^{93} +58.0489 q^{94} +2824.33 q^{95} +398.908 q^{96} -1156.88 q^{97} +12.8746 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

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