LMFDB - Embedded newform 2005.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30345 q^{2} -1.22130 q^{3} +3.30589 q^{4} +1.00000 q^{5} +2.81322 q^{6} +3.38528 q^{7} -3.00806 q^{8} -1.50842 q^{9} +O(q^{10})$	\(q-2.30345 q^{2} -1.22130 q^{3} +3.30589 q^{4} +1.00000 q^{5} +2.81322 q^{6} +3.38528 q^{7} -3.00806 q^{8} -1.50842 q^{9} -2.30345 q^{10} +4.10185 q^{11} -4.03750 q^{12} +0.855820 q^{13} -7.79783 q^{14} -1.22130 q^{15} +0.317133 q^{16} +6.68540 q^{17} +3.47456 q^{18} +5.05068 q^{19} +3.30589 q^{20} -4.13446 q^{21} -9.44842 q^{22} +0.648480 q^{23} +3.67375 q^{24} +1.00000 q^{25} -1.97134 q^{26} +5.50615 q^{27} +11.1914 q^{28} +0.367761 q^{29} +2.81322 q^{30} -4.81837 q^{31} +5.28561 q^{32} -5.00961 q^{33} -15.3995 q^{34} +3.38528 q^{35} -4.98666 q^{36} +3.71098 q^{37} -11.6340 q^{38} -1.04522 q^{39} -3.00806 q^{40} +6.73295 q^{41} +9.52352 q^{42} +4.52806 q^{43} +13.5603 q^{44} -1.50842 q^{45} -1.49374 q^{46} +7.65701 q^{47} -0.387316 q^{48} +4.46013 q^{49} -2.30345 q^{50} -8.16491 q^{51} +2.82925 q^{52} +4.90993 q^{53} -12.6831 q^{54} +4.10185 q^{55} -10.1831 q^{56} -6.16841 q^{57} -0.847120 q^{58} -8.44583 q^{59} -4.03750 q^{60} -3.51410 q^{61} +11.0989 q^{62} -5.10641 q^{63} -12.8094 q^{64} +0.855820 q^{65} +11.5394 q^{66} -3.46376 q^{67} +22.1012 q^{68} -0.791992 q^{69} -7.79783 q^{70} -9.91699 q^{71} +4.53740 q^{72} -9.52607 q^{73} -8.54806 q^{74} -1.22130 q^{75} +16.6970 q^{76} +13.8859 q^{77} +2.40761 q^{78} -9.26032 q^{79} +0.317133 q^{80} -2.19943 q^{81} -15.5090 q^{82} -12.6170 q^{83} -13.6681 q^{84} +6.68540 q^{85} -10.4302 q^{86} -0.449148 q^{87} -12.3386 q^{88} +13.4976 q^{89} +3.47456 q^{90} +2.89719 q^{91} +2.14380 q^{92} +5.88470 q^{93} -17.6376 q^{94} +5.05068 q^{95} -6.45534 q^{96} -0.224555 q^{97} -10.2737 q^{98} -6.18730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * 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 $

$2$	−2.30345	−1.62879	−0.814393	−	0.580313i	$-0.802930\pi$
$2$	−2.30345	−1.62879	−0.814393	+	0.580313i	$0.802930\pi$
$3$	−1.22130	−0.705120	−0.352560	−	0.935789i	$-0.614689\pi$
$3$	−1.22130	−0.705120	−0.352560	+	0.935789i	$0.614689\pi$
$4$	3.30589	1.65295
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.81322	1.14849
$7$	3.38528	1.27952	0.639758	−	0.768576i	$-0.279035\pi$
$7$	3.38528	1.27952	0.639758	+	0.768576i	$0.279035\pi$
$8$	−3.00806	−1.06351
$9$	−1.50842	−0.502805
$10$	−2.30345	−0.728415
$11$	4.10185	1.23676	0.618378	−	0.785881i	$-0.287790\pi$
$11$	4.10185	1.23676	0.618378	+	0.785881i	$0.287790\pi$
$12$	−4.03750	−1.16553
$13$	0.855820	0.237362	0.118681	−	0.992932i	$-0.462133\pi$
$13$	0.855820	0.237362	0.118681	+	0.992932i	$0.462133\pi$
$14$	−7.79783	−2.08406
$15$	−1.22130	−0.315339
$16$	0.317133	0.0792833
$17$	6.68540	1.62145	0.810724	−	0.585428i	$-0.199074\pi$
$17$	6.68540	1.62145	0.810724	+	0.585428i	$0.199074\pi$
$18$	3.47456	0.818963
$19$	5.05068	1.15870	0.579352	−	0.815077i	$-0.303306\pi$
$19$	5.05068	1.15870	0.579352	+	0.815077i	$0.303306\pi$
$20$	3.30589	0.739220
$21$	−4.13446	−0.902213
$22$	−9.44842	−2.01441
$23$	0.648480	0.135217	0.0676087	−	0.997712i	$-0.478463\pi$
$23$	0.648480	0.135217	0.0676087	+	0.997712i	$0.478463\pi$
$24$	3.67375	0.749902
$25$	1.00000	0.200000
$26$	−1.97134	−0.386612
$27$	5.50615	1.05966
$28$	11.1914	2.11497
$29$	0.367761	0.0682915	0.0341458	−	0.999417i	$-0.489129\pi$
$29$	0.367761	0.0682915	0.0341458	+	0.999417i	$0.489129\pi$
$30$	2.81322	0.513621
$31$	−4.81837	−0.865405	−0.432702	−	0.901537i	$-0.642440\pi$
$31$	−4.81837	−0.865405	−0.432702	+	0.901537i	$0.642440\pi$
$32$	5.28561	0.934373
$33$	−5.00961	−0.872061
$34$	−15.3995	−2.64099
$35$	3.38528	0.572217
$36$	−4.98666	−0.831110
$37$	3.71098	0.610081	0.305041	−	0.952339i	$-0.401330\pi$
$37$	3.71098	0.610081	0.305041	+	0.952339i	$0.401330\pi$
$38$	−11.6340	−1.88728
$39$	−1.04522	−0.167369
$40$	−3.00806	−0.475616
$41$	6.73295	1.05151	0.525755	−	0.850636i	$-0.323783\pi$
$41$	6.73295	1.05151	0.525755	+	0.850636i	$0.323783\pi$
$42$	9.52352	1.46951
$43$	4.52806	0.690522	0.345261	−	0.938507i	$-0.387790\pi$
$43$	4.52806	0.690522	0.345261	+	0.938507i	$0.387790\pi$
$44$	13.5603	2.04429
$45$	−1.50842	−0.224861
$46$	−1.49374	−0.220240
$47$	7.65701	1.11689	0.558445	−	0.829542i	$-0.311398\pi$
$47$	7.65701	1.11689	0.558445	+	0.829542i	$0.311398\pi$
$48$	−0.387316	−0.0559043
$49$	4.46013	0.637161
$50$	−2.30345	−0.325757
$51$	−8.16491	−1.14332
$52$	2.82925	0.392346
$53$	4.90993	0.674431	0.337216	−	0.941427i	$-0.390515\pi$
$53$	4.90993	0.674431	0.337216	+	0.941427i	$0.390515\pi$
$54$	−12.6831	−1.72596
$55$	4.10185	0.553094
$56$	−10.1831	−1.36078
$57$	−6.16841	−0.817026
$58$	−0.847120	−0.111232
$59$	−8.44583	−1.09955	−0.549777	−	0.835312i	$-0.685287\pi$
$59$	−8.44583	−1.09955	−0.549777	+	0.835312i	$0.685287\pi$
$60$	−4.03750	−0.521239
$61$	−3.51410	−0.449935	−0.224967	−	0.974366i	$-0.572228\pi$
$61$	−3.51410	−0.449935	−0.224967	+	0.974366i	$0.572228\pi$
$62$	11.0989	1.40956
$63$	−5.10641	−0.643347
$64$	−12.8094	−1.60118
$65$	0.855820	0.106151
$66$	11.5394	1.42040
$67$	−3.46376	−0.423165	−0.211583	−	0.977360i	$-0.567862\pi$
$67$	−3.46376	−0.423165	−0.211583	+	0.977360i	$0.567862\pi$
$68$	22.1012	2.68017
$69$	−0.791992	−0.0953446
$70$	−7.79783	−0.932019
$71$	−9.91699	−1.17693	−0.588465	−	0.808523i	$-0.700268\pi$
$71$	−9.91699	−1.17693	−0.588465	+	0.808523i	$0.700268\pi$
$72$	4.53740	0.534738
$73$	−9.52607	−1.11494	−0.557471	−	0.830197i	$-0.688228\pi$
$73$	−9.52607	−1.11494	−0.557471	+	0.830197i	$0.688228\pi$
$74$	−8.54806	−0.993692
$75$	−1.22130	−0.141024
$76$	16.6970	1.91528
$77$	13.8859	1.58245
$78$	2.40761	0.272608
$79$	−9.26032	−1.04187	−0.520934	−	0.853597i	$-0.674416\pi$
$79$	−9.26032	−1.04187	−0.520934	+	0.853597i	$0.674416\pi$
$80$	0.317133	0.0354566
$81$	−2.19943	−0.244381
$82$	−15.5090	−1.71269
$83$	−12.6170	−1.38489	−0.692446	−	0.721470i	$-0.743467\pi$
$83$	−12.6170	−1.38489	−0.692446	+	0.721470i	$0.743467\pi$
$84$	−13.6681	−1.49131
$85$	6.68540	0.725134
$86$	−10.4302	−1.12471
$87$	−0.449148	−0.0481537
$88$	−12.3386	−1.31530
$89$	13.4976	1.43074	0.715369	−	0.698746i	$-0.246258\pi$
$89$	13.4976	1.43074	0.715369	+	0.698746i	$0.246258\pi$
$90$	3.47456	0.366251
$91$	2.89719	0.303708
$92$	2.14380	0.223507
$93$	5.88470	0.610215
$94$	−17.6376	−1.81918
$95$	5.05068	0.518189
$96$	−6.45534	−0.658846
$97$	−0.224555	−0.0228001	−0.0114000	−	0.999935i	$-0.503629\pi$
$97$	−0.224555	−0.0228001	−0.0114000	+	0.999935i	$0.503629\pi$
$98$	−10.2737	−1.03780
$99$	−6.18730	−0.621847
$100$	3.30589	0.330589
$101$	−15.4022	−1.53258	−0.766290	−	0.642495i	$-0.777899\pi$
$101$	−15.4022	−1.53258	−0.766290	+	0.642495i	$0.777899\pi$
$102$	18.8075	1.86222
$103$	−6.59658	−0.649981	−0.324990	−	0.945717i	$-0.605361\pi$
$103$	−6.59658	−0.649981	−0.324990	+	0.945717i	$0.605361\pi$
$104$	−2.57436	−0.252436
$105$	−4.13446	−0.403482
$106$	−11.3098	−1.09850
$107$	−14.2925	−1.38171	−0.690856	−	0.722992i	$-0.742766\pi$
$107$	−14.2925	−1.38171	−0.690856	+	0.722992i	$0.742766\pi$
$108$	18.2027	1.75156
$109$	−16.7652	−1.60582	−0.802909	−	0.596101i	$-0.796716\pi$
$109$	−16.7652	−1.60582	−0.802909	+	0.596101i	$0.796716\pi$
$110$	−9.44842	−0.900872
$111$	−4.53223	−0.430181
$112$	1.07358	0.101444
$113$	15.3392	1.44299	0.721495	−	0.692420i	$-0.243455\pi$
$113$	15.3392	1.44299	0.721495	+	0.692420i	$0.243455\pi$
$114$	14.2086	1.33076
$115$	0.648480	0.0604711
$116$	1.21578	0.112882
$117$	−1.29093	−0.119347
$118$	19.4546	1.79094
$119$	22.6320	2.07467
$120$	3.67375	0.335366
$121$	5.82521	0.529564
$122$	8.09457	0.732848
$123$	−8.22298	−0.741441
$124$	−15.9290	−1.43047
$125$	1.00000	0.0894427
$126$	11.7624	1.04788
$127$	−1.36153	−0.120816	−0.0604081	−	0.998174i	$-0.519240\pi$
$127$	−1.36153	−0.120816	−0.0604081	+	0.998174i	$0.519240\pi$
$128$	18.9347	1.67360
$129$	−5.53014	−0.486901
$130$	−1.97134	−0.172898
$131$	16.5790	1.44852	0.724258	−	0.689529i	$-0.242183\pi$
$131$	16.5790	1.44852	0.724258	+	0.689529i	$0.242183\pi$
$132$	−16.5612	−1.44147
$133$	17.0980	1.48258
$134$	7.97860	0.689246
$135$	5.50615	0.473894
$136$	−20.1101	−1.72443
$137$	19.6119	1.67556	0.837779	−	0.546009i	$-0.183854\pi$
$137$	19.6119	1.67556	0.837779	+	0.546009i	$0.183854\pi$
$138$	1.82431	0.155296
$139$	16.0231	1.35906	0.679529	−	0.733648i	$-0.262184\pi$
$139$	16.0231	1.35906	0.679529	+	0.733648i	$0.262184\pi$
$140$	11.1914	0.945843
$141$	−9.35154	−0.787542
$142$	22.8433	1.91697
$143$	3.51045	0.293559
$144$	−0.478369	−0.0398641
$145$	0.367761	0.0305409
$146$	21.9428	1.81600
$147$	−5.44717	−0.449275
$148$	12.2681	1.00843
$149$	13.7233	1.12426	0.562128	−	0.827050i	$-0.309983\pi$
$149$	13.7233	1.12426	0.562128	+	0.827050i	$0.309983\pi$
$150$	2.81322	0.229698
$151$	−13.2168	−1.07557	−0.537786	−	0.843082i	$-0.680739\pi$
$151$	−13.2168	−1.07557	−0.537786	+	0.843082i	$0.680739\pi$
$152$	−15.1927	−1.23229
$153$	−10.0844	−0.815273
$154$	−31.9856	−2.57747
$155$	−4.81837	−0.387021
$156$	−3.45537	−0.276651
$157$	−11.1885	−0.892943	−0.446471	−	0.894798i	$-0.647320\pi$
$157$	−11.1885	−0.892943	−0.446471	+	0.894798i	$0.647320\pi$
$158$	21.3307	1.69698
$159$	−5.99652	−0.475555
$160$	5.28561	0.417864
$161$	2.19529	0.173013
$162$	5.06629	0.398045
$163$	18.8779	1.47863	0.739315	−	0.673360i	$-0.235150\pi$
$163$	18.8779	1.47863	0.739315	+	0.673360i	$0.235150\pi$
$164$	22.2584	1.73809
$165$	−5.00961	−0.389998
$166$	29.0626	2.25569
$167$	4.66675	0.361124	0.180562	−	0.983564i	$-0.442208\pi$
$167$	4.66675	0.361124	0.180562	+	0.983564i	$0.442208\pi$
$168$	12.4367	0.959511
$169$	−12.2676	−0.943659
$170$	−15.3995	−1.18109
$171$	−7.61852	−0.582603
$172$	14.9693	1.14140
$173$	−0.997203	−0.0758160	−0.0379080	−	0.999281i	$-0.512069\pi$
$173$	−0.997203	−0.0758160	−0.0379080	+	0.999281i	$0.512069\pi$
$174$	1.03459	0.0784321
$175$	3.38528	0.255903
$176$	1.30083	0.0980540
$177$	10.3149	0.775318
$178$	−31.0910	−2.33037
$179$	8.90707	0.665746	0.332873	−	0.942972i	$-0.391982\pi$
$179$	8.90707	0.665746	0.332873	+	0.942972i	$0.391982\pi$
$180$	−4.98666	−0.371684
$181$	−13.4195	−0.997462	−0.498731	−	0.866757i	$-0.666200\pi$
$181$	−13.4195	−0.997462	−0.498731	+	0.866757i	$0.666200\pi$
$182$	−6.67354	−0.494676
$183$	4.29179	0.317258
$184$	−1.95067	−0.143805
$185$	3.71098	0.272837
$186$	−13.5551	−0.993909
$187$	27.4226	2.00534
$188$	25.3132	1.84616
$189$	18.6399	1.35585
$190$	−11.6340	−0.844019
$191$	−23.0396	−1.66709	−0.833543	−	0.552455i	$-0.813691\pi$
$191$	−23.0396	−1.66709	−0.833543	+	0.552455i	$0.813691\pi$
$192$	15.6442	1.12902
$193$	−18.4082	−1.32505	−0.662525	−	0.749039i	$-0.730515\pi$
$193$	−18.4082	−1.32505	−0.662525	+	0.749039i	$0.730515\pi$
$194$	0.517251	0.0371365
$195$	−1.04522	−0.0748496
$196$	14.7447	1.05319
$197$	−14.9932	−1.06822	−0.534111	−	0.845414i	$-0.679354\pi$
$197$	−14.9932	−1.06822	−0.534111	+	0.845414i	$0.679354\pi$
$198$	14.2522	1.01286
$199$	7.34963	0.521002	0.260501	−	0.965474i	$-0.416112\pi$
$199$	7.34963	0.521002	0.260501	+	0.965474i	$0.416112\pi$
$200$	−3.00806	−0.212702
$201$	4.23030	0.298382
$202$	35.4783	2.49625
$203$	1.24497	0.0873801
$204$	−26.9923	−1.88984
$205$	6.73295	0.470250
$206$	15.1949	1.05868
$207$	−0.978178	−0.0679881
$208$	0.271409	0.0188188
$209$	20.7171	1.43303
$210$	9.52352	0.657186
$211$	18.4996	1.27356	0.636781	−	0.771045i	$-0.280265\pi$
$211$	18.4996	1.27356	0.636781	+	0.771045i	$0.280265\pi$
$212$	16.2317	1.11480
$213$	12.1117	0.829877
$214$	32.9222	2.25051
$215$	4.52806	0.308811
$216$	−16.5628	−1.12696
$217$	−16.3115	−1.10730
$218$	38.6179	2.61554
$219$	11.6342	0.786168
$220$	13.5603	0.914234
$221$	5.72151	0.384870
$222$	10.4398	0.700672
$223$	20.0150	1.34031	0.670153	−	0.742223i	$-0.266228\pi$
$223$	20.0150	1.34031	0.670153	+	0.742223i	$0.266228\pi$
$224$	17.8933	1.19555
$225$	−1.50842	−0.100561
$226$	−35.3331	−2.35032
$227$	22.7238	1.50823	0.754117	−	0.656740i	$-0.228065\pi$
$227$	22.7238	1.50823	0.754117	+	0.656740i	$0.228065\pi$
$228$	−20.3921	−1.35050
$229$	17.7909	1.17565	0.587827	−	0.808987i	$-0.299984\pi$
$229$	17.7909	1.17565	0.587827	+	0.808987i	$0.299984\pi$
$230$	−1.49374	−0.0984945
$231$	−16.9589	−1.11582
$232$	−1.10625	−0.0726286
$233$	−8.15723	−0.534398	−0.267199	−	0.963641i	$-0.586098\pi$
$233$	−8.15723	−0.534398	−0.267199	+	0.963641i	$0.586098\pi$
$234$	2.97360	0.194391
$235$	7.65701	0.499488
$236$	−27.9210	−1.81750
$237$	11.3097	0.734642
$238$	−52.1317	−3.37919
$239$	20.7538	1.34245	0.671225	−	0.741254i	$-0.265768\pi$
$239$	20.7538	1.34245	0.671225	+	0.741254i	$0.265768\pi$
$240$	−0.387316	−0.0250011
$241$	−16.0531	−1.03407	−0.517034	−	0.855965i	$-0.672964\pi$
$241$	−16.0531	−1.03407	−0.517034	+	0.855965i	$0.672964\pi$
$242$	−13.4181	−0.862547
$243$	−13.8323	−0.887340
$244$	−11.6172	−0.743718
$245$	4.46013	0.284947
$246$	18.9412	1.20765
$247$	4.32247	0.275032
$248$	14.4939	0.920366
$249$	15.4092	0.976516
$250$	−2.30345	−0.145683
$251$	−0.398343	−0.0251432	−0.0125716	−	0.999921i	$-0.504002\pi$
$251$	−0.398343	−0.0251432	−0.0125716	+	0.999921i	$0.504002\pi$
$252$	−16.8812	−1.06342
$253$	2.65997	0.167231
$254$	3.13622	0.196784
$255$	−8.16491	−0.511307
$256$	−17.9962	−1.12477
$257$	9.14736	0.570596	0.285298	−	0.958439i	$-0.407907\pi$
$257$	9.14736	0.570596	0.285298	+	0.958439i	$0.407907\pi$
$258$	12.7384	0.793058
$259$	12.5627	0.780609
$260$	2.82925	0.175463
$261$	−0.554737	−0.0343373
$262$	−38.1890	−2.35932
$263$	16.1894	0.998282	0.499141	−	0.866521i	$-0.333649\pi$
$263$	16.1894	0.998282	0.499141	+	0.866521i	$0.333649\pi$
$264$	15.0692	0.927445
$265$	4.90993	0.301615
$266$	−39.3843	−2.41481
$267$	−16.4846	−1.00884
$268$	−11.4508	−0.699469
$269$	−23.4812	−1.43167	−0.715836	−	0.698268i	$-0.753954\pi$
$269$	−23.4812	−1.43167	−0.715836	+	0.698268i	$0.753954\pi$
$270$	−12.6831	−0.771872
$271$	4.91795	0.298744	0.149372	−	0.988781i	$-0.452275\pi$
$271$	4.91795	0.298744	0.149372	+	0.988781i	$0.452275\pi$
$272$	2.12016	0.128554
$273$	−3.53835	−0.214151
$274$	−45.1751	−2.72913
$275$	4.10185	0.247351
$276$	−2.61824	−0.157599
$277$	−13.6169	−0.818161	−0.409080	−	0.912498i	$-0.634150\pi$
$277$	−13.6169	−0.818161	−0.409080	+	0.912498i	$0.634150\pi$
$278$	−36.9084	−2.21362
$279$	7.26811	0.435130
$280$	−10.1831	−0.608558
$281$	−4.04687	−0.241416	−0.120708	−	0.992688i	$-0.538516\pi$
$281$	−4.04687	−0.241416	−0.120708	+	0.992688i	$0.538516\pi$
$282$	21.5408	1.28274
$283$	−11.5889	−0.688889	−0.344444	−	0.938807i	$-0.611933\pi$
$283$	−11.5889	−0.688889	−0.344444	+	0.938807i	$0.611933\pi$
$284$	−32.7845	−1.94540
$285$	−6.16841	−0.365385
$286$	−8.08615	−0.478144
$287$	22.7929	1.34542
$288$	−7.97290	−0.469808
$289$	27.6946	1.62910
$290$	−0.847120	−0.0497446
$291$	0.274250	0.0160768
$292$	−31.4921	−1.84294
$293$	1.19002	0.0695216	0.0347608	−	0.999396i	$-0.488933\pi$
$293$	1.19002	0.0695216	0.0347608	+	0.999396i	$0.488933\pi$
$294$	12.5473	0.731773
$295$	−8.44583	−0.491735
$296$	−11.1628	−0.648827
$297$	22.5854	1.31054
$298$	−31.6110	−1.83117
$299$	0.554983	0.0320955
$300$	−4.03750	−0.233105
$301$	15.3287	0.883534
$302$	30.4444	1.75188
$303$	18.8108	1.08065
$304$	1.60174	0.0918659
$305$	−3.51410	−0.201217
$306$	23.2289	1.32791
$307$	4.96783	0.283529	0.141764	−	0.989900i	$-0.454722\pi$
$307$	4.96783	0.283529	0.141764	+	0.989900i	$0.454722\pi$
$308$	45.9054	2.61570
$309$	8.05644	0.458315
$310$	11.0989	0.630374
$311$	−23.4239	−1.32825	−0.664125	−	0.747622i	$-0.731196\pi$
$311$	−23.4239	−1.32825	−0.664125	+	0.747622i	$0.731196\pi$
$312$	3.14407	0.177998
$313$	5.73841	0.324354	0.162177	−	0.986762i	$-0.448148\pi$
$313$	5.73841	0.324354	0.162177	+	0.986762i	$0.448148\pi$
$314$	25.7723	1.45441
$315$	−5.10641	−0.287714
$316$	−30.6136	−1.72215
$317$	−18.0379	−1.01311	−0.506554	−	0.862208i	$-0.669081\pi$
$317$	−18.0379	−1.01311	−0.506554	+	0.862208i	$0.669081\pi$
$318$	13.8127	0.774578
$319$	1.50850	0.0844599
$320$	−12.8094	−0.716068
$321$	17.4555	0.974273
$322$	−5.05674	−0.281801
$323$	33.7658	1.87878
$324$	−7.27108	−0.403949
$325$	0.855820	0.0474724
$326$	−43.4843	−2.40837
$327$	20.4755	1.13230
$328$	−20.2531	−1.11829
$329$	25.9211	1.42908
$330$	11.5394	0.635223
$331$	28.3494	1.55823	0.779113	−	0.626884i	$-0.215670\pi$
$331$	28.3494	1.55823	0.779113	+	0.626884i	$0.215670\pi$
$332$	−41.7103	−2.28915
$333$	−5.59770	−0.306752
$334$	−10.7496	−0.588194
$335$	−3.46376	−0.189245
$336$	−1.31117	−0.0715304
$337$	19.0704	1.03883	0.519416	−	0.854521i	$-0.326149\pi$
$337$	19.0704	1.03883	0.519416	+	0.854521i	$0.326149\pi$
$338$	28.2578	1.53702
$339$	−18.7338	−1.01748
$340$	22.1012	1.19861
$341$	−19.7643	−1.07029
$342$	17.5489	0.948936
$343$	−8.59819	−0.464258
$344$	−13.6207	−0.734377
$345$	−0.791992	−0.0426394
$346$	2.29701	0.123488
$347$	−9.11968	−0.489570	−0.244785	−	0.969577i	$-0.578717\pi$
$347$	−9.11968	−0.489570	−0.244785	+	0.969577i	$0.578717\pi$
$348$	−1.48483	−0.0795955
$349$	−13.2978	−0.711812	−0.355906	−	0.934522i	$-0.615828\pi$
$349$	−13.2978	−0.711812	−0.355906	+	0.934522i	$0.615828\pi$
$350$	−7.79783	−0.416812
$351$	4.71227	0.251523
$352$	21.6808	1.15559
$353$	−3.10729	−0.165385	−0.0826923	−	0.996575i	$-0.526352\pi$
$353$	−3.10729	−0.165385	−0.0826923	+	0.996575i	$0.526352\pi$
$354$	−23.7599	−1.26283
$355$	−9.91699	−0.526339
$356$	44.6215	2.36493
$357$	−27.6405	−1.46289
$358$	−20.5170	−1.08436
$359$	17.9286	0.946238	0.473119	−	0.880999i	$-0.343128\pi$
$359$	17.9286	0.946238	0.473119	+	0.880999i	$0.343128\pi$
$360$	4.53740	0.239142
$361$	6.50934	0.342597
$362$	30.9111	1.62465
$363$	−7.11435	−0.373406
$364$	9.57780	0.502013
$365$	−9.52607	−0.498617
$366$	−9.88593	−0.516746
$367$	21.0886	1.10082	0.550408	−	0.834896i	$-0.314472\pi$
$367$	21.0886	1.10082	0.550408	+	0.834896i	$0.314472\pi$
$368$	0.205655	0.0107205
$369$	−10.1561	−0.528705
$370$	−8.54806	−0.444393
$371$	16.6215	0.862945
$372$	19.4542	1.00865
$373$	−33.2198	−1.72005	−0.860027	−	0.510248i	$-0.829553\pi$
$373$	−33.2198	−1.72005	−0.860027	+	0.510248i	$0.829553\pi$
$374$	−63.1665	−3.26626
$375$	−1.22130	−0.0630679
$376$	−23.0327	−1.18782
$377$	0.314737	0.0162098
$378$	−42.9360	−2.20839
$379$	−35.2420	−1.81026	−0.905129	−	0.425136i	$-0.860226\pi$
$379$	−35.2420	−1.81026	−0.905129	+	0.425136i	$0.860226\pi$
$380$	16.6970	0.856537
$381$	1.66284	0.0851900
$382$	53.0706	2.71533
$383$	−6.74820	−0.344817	−0.172408	−	0.985026i	$-0.555155\pi$
$383$	−6.74820	−0.344817	−0.172408	+	0.985026i	$0.555155\pi$
$384$	−23.1250	−1.18009
$385$	13.8859	0.707692
$386$	42.4024	2.15823
$387$	−6.83020	−0.347198
$388$	−0.742354	−0.0376873
$389$	−4.65255	−0.235894	−0.117947	−	0.993020i	$-0.537631\pi$
$389$	−4.65255	−0.235894	−0.117947	+	0.993020i	$0.537631\pi$
$390$	2.40761	0.121914
$391$	4.33535	0.219248
$392$	−13.4163	−0.677626
$393$	−20.2480	−1.02138
$394$	34.5362	1.73991
$395$	−9.26032	−0.465937
$396$	−20.4545	−1.02788
$397$	23.3318	1.17099	0.585495	−	0.810676i	$-0.300900\pi$
$397$	23.3318	1.17099	0.585495	+	0.810676i	$0.300900\pi$
$398$	−16.9295	−0.848601
$399$	−20.8818	−1.04540
$400$	0.317133	0.0158567
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−9.74430	−0.486001
$403$	−4.12366	−0.205414
$404$	−50.9181	−2.53327
$405$	−2.19943	−0.109291
$406$	−2.86774	−0.142323
$407$	15.2219	0.754521
$408$	24.5605	1.21593
$409$	0.217949	0.0107769	0.00538845	−	0.999985i	$-0.498285\pi$
$409$	0.217949	0.0107769	0.00538845	+	0.999985i	$0.498285\pi$
$410$	−15.5090	−0.765936
$411$	−23.9521	−1.18147
$412$	−21.8076	−1.07438
$413$	−28.5915	−1.40690
$414$	2.25319	0.110738
$415$	−12.6170	−0.619343
$416$	4.52354	0.221785
$417$	−19.5690	−0.958300
$418$	−47.7209	−2.33411
$419$	12.7411	0.622444	0.311222	−	0.950337i	$-0.399262\pi$
$419$	12.7411	0.622444	0.311222	+	0.950337i	$0.399262\pi$
$420$	−13.6681	−0.666933
$421$	−4.11633	−0.200618	−0.100309	−	0.994956i	$-0.531983\pi$
$421$	−4.11633	−0.200618	−0.100309	+	0.994956i	$0.531983\pi$
$422$	−42.6129	−2.07436
$423$	−11.5500	−0.561578
$424$	−14.7694	−0.717263
$425$	6.68540	0.324290
$426$	−27.8986	−1.35169
$427$	−11.8962	−0.575699
$428$	−47.2496	−2.28390
$429$	−4.28733	−0.206994
$430$	−10.4302	−0.502987
$431$	9.76917	0.470564	0.235282	−	0.971927i	$-0.424399\pi$
$431$	9.76917	0.470564	0.235282	+	0.971927i	$0.424399\pi$
$432$	1.74618	0.0840132
$433$	30.3244	1.45730	0.728649	−	0.684887i	$-0.240149\pi$
$433$	30.3244	1.45730	0.728649	+	0.684887i	$0.240149\pi$
$434$	37.5728	1.80355
$435$	−0.449148	−0.0215350
$436$	−55.4240	−2.65433
$437$	3.27526	0.156677
$438$	−26.7989	−1.28050
$439$	−17.7056	−0.845044	−0.422522	−	0.906353i	$-0.638855\pi$
$439$	−17.7056	−0.845044	−0.422522	+	0.906353i	$0.638855\pi$
$440$	−12.3386	−0.588220
$441$	−6.72773	−0.320368
$442$	−13.1792	−0.626871
$443$	−31.5404	−1.49853	−0.749265	−	0.662270i	$-0.769593\pi$
$443$	−31.5404	−1.49853	−0.749265	+	0.662270i	$0.769593\pi$
$444$	−14.9831	−0.711065
$445$	13.4976	0.639846
$446$	−46.1037	−2.18307
$447$	−16.7603	−0.792736
$448$	−43.3635	−2.04873
$449$	9.05204	0.427192	0.213596	−	0.976922i	$-0.431482\pi$
$449$	9.05204	0.427192	0.213596	+	0.976922i	$0.431482\pi$
$450$	3.47456	0.163793
$451$	27.6176	1.30046
$452$	50.7097	2.38518
$453$	16.1418	0.758407
$454$	−52.3432	−2.45659
$455$	2.89719	0.135822
$456$	18.5549	0.868915
$457$	−28.4502	−1.33085	−0.665423	−	0.746466i	$-0.731749\pi$
$457$	−28.4502	−1.33085	−0.665423	+	0.746466i	$0.731749\pi$
$458$	−40.9804	−1.91489
$459$	36.8108	1.71818
$460$	2.14380	0.0999554
$461$	6.86595	0.319779	0.159890	−	0.987135i	$-0.448886\pi$
$461$	6.86595	0.319779	0.159890	+	0.987135i	$0.448886\pi$
$462$	39.0641	1.81743
$463$	−3.38179	−0.157165	−0.0785826	−	0.996908i	$-0.525039\pi$
$463$	−3.38179	−0.157165	−0.0785826	+	0.996908i	$0.525039\pi$
$464$	0.116629	0.00541438
$465$	5.88470	0.272896
$466$	18.7898	0.870420
$467$	29.3513	1.35822	0.679109	−	0.734038i	$-0.262367\pi$
$467$	29.3513	1.35822	0.679109	+	0.734038i	$0.262367\pi$
$468$	−4.26769	−0.197274
$469$	−11.7258	−0.541447
$470$	−17.6376	−0.813560
$471$	13.6646	0.629632
$472$	25.4055	1.16938
$473$	18.5734	0.854007
$474$	−26.0513	−1.19657
$475$	5.05068	0.231741
$476$	74.8188	3.42932
$477$	−7.40622	−0.339108
$478$	−47.8053	−2.18656
$479$	23.8898	1.09155	0.545776	−	0.837931i	$-0.316235\pi$
$479$	23.8898	1.09155	0.545776	+	0.837931i	$0.316235\pi$
$480$	−6.45534	−0.294645
$481$	3.17593	0.144810
$482$	36.9774	1.68428
$483$	−2.68111	−0.121995
$484$	19.2575	0.875341
$485$	−0.224555	−0.0101965
$486$	31.8620	1.44529
$487$	−17.4151	−0.789155	−0.394577	−	0.918863i	$-0.629109\pi$
$487$	−17.4151	−0.789155	−0.394577	+	0.918863i	$0.629109\pi$
$488$	10.5706	0.478510
$489$	−23.0556	−1.04261
$490$	−10.2737	−0.464118
$491$	36.1073	1.62950	0.814749	−	0.579814i	$-0.196875\pi$
$491$	36.1073	1.62950	0.814749	+	0.579814i	$0.196875\pi$
$492$	−27.1843	−1.22556
$493$	2.45863	0.110731
$494$	−9.95661	−0.447969
$495$	−6.18730	−0.278099
$496$	−1.52806	−0.0686121
$497$	−33.5718	−1.50590
$498$	−35.4942	−1.59054
$499$	38.8702	1.74007	0.870035	−	0.492990i	$-0.164096\pi$
$499$	38.8702	1.74007	0.870035	+	0.492990i	$0.164096\pi$
$500$	3.30589	0.147844
$501$	−5.69952	−0.254636
$502$	0.917563	0.0409528
$503$	−40.8829	−1.82288	−0.911439	−	0.411436i	$-0.865027\pi$
$503$	−40.8829	−1.82288	−0.911439	+	0.411436i	$0.865027\pi$
$504$	15.3604	0.684206
$505$	−15.4022	−0.685391
$506$	−6.12712	−0.272384
$507$	14.9824	0.665393
$508$	−4.50107	−0.199703
$509$	−20.8627	−0.924723	−0.462362	−	0.886691i	$-0.652998\pi$
$509$	−20.8627	−0.924723	−0.462362	+	0.886691i	$0.652998\pi$
$510$	18.8075	0.832809
$511$	−32.2484	−1.42659
$512$	3.58415	0.158399
$513$	27.8098	1.22783
$514$	−21.0705	−0.929380
$515$	−6.59658	−0.290680
$516$	−18.2820	−0.804821
$517$	31.4079	1.38132
$518$	−28.9376	−1.27144
$519$	1.21789	0.0534594
$520$	−2.57436	−0.112893
$521$	21.2252	0.929894	0.464947	−	0.885338i	$-0.346073\pi$
$521$	21.2252	0.929894	0.464947	+	0.885338i	$0.346073\pi$
$522$	1.27781	0.0559282
$523$	0.852698	0.0372859	0.0186429	−	0.999826i	$-0.494065\pi$
$523$	0.852698	0.0372859	0.0186429	+	0.999826i	$0.494065\pi$
$524$	54.8084	2.39432
$525$	−4.13446	−0.180443
$526$	−37.2915	−1.62599
$527$	−32.2128	−1.40321
$528$	−1.58871	−0.0691399
$529$	−22.5795	−0.981716
$530$	−11.3098	−0.491266
$531$	12.7398	0.552862
$532$	56.5240	2.45063
$533$	5.76220	0.249588
$534$	37.9716	1.64319
$535$	−14.2925	−0.617921
$536$	10.4192	0.450040
$537$	−10.8782	−0.469431
$538$	54.0877	2.33189
$539$	18.2948	0.788012
$540$	18.2027	0.783320
$541$	−16.1134	−0.692769	−0.346385	−	0.938093i	$-0.612591\pi$
$541$	−16.1134	−0.692769	−0.346385	+	0.938093i	$0.612591\pi$
$542$	−11.3283	−0.486590
$543$	16.3893	0.703331
$544$	35.3365	1.51504
$545$	−16.7652	−0.718144
$546$	8.15043	0.348806
$547$	19.0821	0.815892	0.407946	−	0.913006i	$-0.366245\pi$
$547$	19.0821	0.815892	0.407946	+	0.913006i	$0.366245\pi$
$548$	64.8348	2.76961
$549$	5.30073	0.226230
$550$	−9.44842	−0.402882
$551$	1.85744	0.0791297
$552$	2.38236	0.101400
$553$	−31.3488	−1.33309
$554$	31.3659	1.33261
$555$	−4.53223	−0.192383
$556$	52.9705	2.24645
$557$	20.7054	0.877315	0.438657	−	0.898654i	$-0.355454\pi$
$557$	20.7054	0.877315	0.438657	+	0.898654i	$0.355454\pi$
$558$	−16.7417	−0.708734
$559$	3.87521	0.163904
$560$	1.07358	0.0453672
$561$	−33.4913	−1.41400
$562$	9.32177	0.393215
$563$	−18.7509	−0.790254	−0.395127	−	0.918626i	$-0.629300\pi$
$563$	−18.7509	−0.790254	−0.395127	+	0.918626i	$0.629300\pi$
$564$	−30.9152	−1.30176
$565$	15.3392	0.645325
$566$	26.6945	1.12205
$567$	−7.44569	−0.312690
$568$	29.8309	1.25168
$569$	−11.8144	−0.495287	−0.247644	−	0.968851i	$-0.579656\pi$
$569$	−11.8144	−0.495287	−0.247644	+	0.968851i	$0.579656\pi$
$570$	14.2086	0.595135
$571$	−8.50620	−0.355973	−0.177987	−	0.984033i	$-0.556958\pi$
$571$	−8.50620	−0.355973	−0.177987	+	0.984033i	$0.556958\pi$
$572$	11.6052	0.485236
$573$	28.1383	1.17550
$574$	−52.5024	−2.19141
$575$	0.648480	0.0270435
$576$	19.3219	0.805081
$577$	−16.5145	−0.687507	−0.343754	−	0.939060i	$-0.611698\pi$
$577$	−16.5145	−0.687507	−0.343754	+	0.939060i	$0.611698\pi$
$578$	−63.7933	−2.65345
$579$	22.4820	0.934320
$580$	1.21578	0.0504824
$581$	−42.7120	−1.77199
$582$	−0.631721	−0.0261857
$583$	20.1398	0.834106
$584$	28.6549	1.18575
$585$	−1.29093	−0.0533735
$586$	−2.74115	−0.113236
$587$	8.45740	0.349074	0.174537	−	0.984651i	$-0.444157\pi$
$587$	8.45740	0.349074	0.174537	+	0.984651i	$0.444157\pi$
$588$	−18.0078	−0.742627
$589$	−24.3360	−1.00275
$590$	19.4546	0.800932
$591$	18.3113	0.753225
$592$	1.17687	0.0483692
$593$	30.5774	1.25566	0.627832	−	0.778349i	$-0.283943\pi$
$593$	30.5774	1.25566	0.627832	+	0.778349i	$0.283943\pi$
$594$	−52.0244	−2.13459
$595$	22.6320	0.927820
$596$	45.3678	1.85834
$597$	−8.97614	−0.367369
$598$	−1.27838	−0.0522767
$599$	−34.2986	−1.40140	−0.700701	−	0.713455i	$-0.747129\pi$
$599$	−34.2986	−1.40140	−0.700701	+	0.713455i	$0.747129\pi$
$600$	3.67375	0.149980
$601$	−16.0641	−0.655268	−0.327634	−	0.944805i	$-0.606251\pi$
$601$	−16.0641	−0.655268	−0.327634	+	0.944805i	$0.606251\pi$
$602$	−35.3090	−1.43909
$603$	5.22479	0.212770
$604$	−43.6934	−1.77786
$605$	5.82521	0.236828
$606$	−43.3298	−1.76015
$607$	−22.1887	−0.900613	−0.450306	−	0.892874i	$-0.648685\pi$
$607$	−22.1887	−0.900613	−0.450306	+	0.892874i	$0.648685\pi$
$608$	26.6959	1.08266
$609$	−1.52049	−0.0616135
$610$	8.09457	0.327740
$611$	6.55303	0.265107
$612$	−33.3378	−1.34760
$613$	34.9442	1.41138	0.705692	−	0.708519i	$-0.250636\pi$
$613$	34.9442	1.41138	0.705692	+	0.708519i	$0.250636\pi$
$614$	−11.4431	−0.461808
$615$	−8.22298	−0.331583
$616$	−41.7697	−1.68295
$617$	−15.5635	−0.626563	−0.313281	−	0.949660i	$-0.601428\pi$
$617$	−15.5635	−0.626563	−0.313281	+	0.949660i	$0.601428\pi$
$618$	−18.5576	−0.746497
$619$	19.8850	0.799245	0.399623	−	0.916680i	$-0.369141\pi$
$619$	19.8850	0.799245	0.399623	+	0.916680i	$0.369141\pi$
$620$	−15.9290	−0.639724
$621$	3.57063	0.143284
$622$	53.9559	2.16344
$623$	45.6930	1.83065
$624$	−0.331473	−0.0132695
$625$	1.00000	0.0400000
$626$	−13.2181	−0.528303
$627$	−25.3019	−1.01046
$628$	−36.9881	−1.47599
$629$	24.8094	0.989216
$630$	11.7624	0.468624
$631$	10.6701	0.424771	0.212385	−	0.977186i	$-0.431877\pi$
$631$	10.6701	0.424771	0.212385	+	0.977186i	$0.431877\pi$
$632$	27.8556	1.10803
$633$	−22.5936	−0.898015
$634$	41.5494	1.65014
$635$	−1.36153	−0.0540307
$636$	−19.8238	−0.786067
$637$	3.81707	0.151238
$638$	−3.47476	−0.137567
$639$	14.9589	0.591767
$640$	18.9347	0.748458
$641$	−34.9016	−1.37853	−0.689266	−	0.724509i	$-0.742067\pi$
$641$	−34.9016	−1.37853	−0.689266	+	0.724509i	$0.742067\pi$
$642$	−40.2080	−1.58688
$643$	7.58135	0.298979	0.149490	−	0.988763i	$-0.452237\pi$
$643$	7.58135	0.298979	0.149490	+	0.988763i	$0.452237\pi$
$644$	7.25738	0.285981
$645$	−5.53014	−0.217749
$646$	−77.7779	−3.06013
$647$	33.0501	1.29933	0.649666	−	0.760220i	$-0.274909\pi$
$647$	33.0501	1.29933	0.649666	+	0.760220i	$0.274909\pi$
$648$	6.61602	0.259902
$649$	−34.6436	−1.35988
$650$	−1.97134	−0.0773224
$651$	19.9213	0.780779
$652$	62.4082	2.44409
$653$	−20.6579	−0.808406	−0.404203	−	0.914669i	$-0.632451\pi$
$653$	−20.6579	−0.808406	−0.404203	+	0.914669i	$0.632451\pi$
$654$	−47.1642	−1.84427
$655$	16.5790	0.647796
$656$	2.13524	0.0833672
$657$	14.3693	0.560599
$658$	−59.7081	−2.32766
$659$	5.81824	0.226646	0.113323	−	0.993558i	$-0.463850\pi$
$659$	5.81824	0.226646	0.113323	+	0.993558i	$0.463850\pi$
$660$	−16.5612	−0.644645
$661$	27.6975	1.07731	0.538654	−	0.842527i	$-0.318933\pi$
$661$	27.6975	1.07731	0.538654	+	0.842527i	$0.318933\pi$
$662$	−65.3016	−2.53802
$663$	−6.98770	−0.271380
$664$	37.9526	1.47285
$665$	17.0980	0.663030
$666$	12.8940	0.499634
$667$	0.238486	0.00923421
$668$	15.4278	0.596918
$669$	−24.4445	−0.945077
$670$	7.97860	0.308240
$671$	−14.4143	−0.556459
$672$	−21.8531	−0.843003
$673$	−48.9533	−1.88701	−0.943505	−	0.331359i	$-0.892493\pi$
$673$	−48.9533	−1.88701	−0.943505	+	0.331359i	$0.892493\pi$
$674$	−43.9278	−1.69204
$675$	5.50615	0.211932
$676$	−40.5553	−1.55982
$677$	20.9540	0.805328	0.402664	−	0.915348i	$-0.368084\pi$
$677$	20.9540	0.805328	0.402664	+	0.915348i	$0.368084\pi$
$678$	43.1524	1.65726
$679$	−0.760181	−0.0291731
$680$	−20.1101	−0.771186
$681$	−27.7527	−1.06349
$682$	45.5260	1.74328
$683$	−43.8730	−1.67875	−0.839376	−	0.543551i	$-0.817079\pi$
$683$	−43.8730	−1.67875	−0.839376	+	0.543551i	$0.817079\pi$
$684$	−25.1860	−0.963011
$685$	19.6119	0.749333
$686$	19.8055	0.756178
$687$	−21.7280	−0.828977
$688$	1.43600	0.0547469
$689$	4.20202	0.160084
$690$	1.82431	0.0694505
$691$	−42.1690	−1.60419	−0.802093	−	0.597199i	$-0.796280\pi$
$691$	−42.1690	−1.60419	−0.802093	+	0.597199i	$0.796280\pi$
$692$	−3.29665	−0.125320
$693$	−20.9458	−0.795664
$694$	21.0067	0.797405
$695$	16.0231	0.607790
$696$	1.35106	0.0512119
$697$	45.0125	1.70497
$698$	30.6307	1.15939
$699$	9.96246	0.376815
$700$	11.1914	0.422994
$701$	21.4905	0.811684	0.405842	−	0.913943i	$-0.366978\pi$
$701$	21.4905	0.811684	0.405842	+	0.913943i	$0.366978\pi$
$702$	−10.8545	−0.409677
$703$	18.7430	0.706904
$704$	−52.5424	−1.98027
$705$	−9.35154	−0.352199
$706$	7.15750	0.269376
$707$	−52.1409	−1.96096
$708$	34.1000	1.28156
$709$	30.5275	1.14649	0.573243	−	0.819386i	$-0.305685\pi$
$709$	30.5275	1.14649	0.573243	+	0.819386i	$0.305685\pi$
$710$	22.8433	0.857294
$711$	13.9684	0.523856
$712$	−40.6014	−1.52160
$713$	−3.12462	−0.117018
$714$	63.6686	2.38274
$715$	3.51045	0.131283
$716$	29.4458	1.10044
$717$	−25.3467	−0.946589
$718$	−41.2978	−1.54122
$719$	−25.5496	−0.952838	−0.476419	−	0.879218i	$-0.658066\pi$
$719$	−25.5496	−0.952838	−0.476419	+	0.879218i	$0.658066\pi$
$720$	−0.478369	−0.0178278
$721$	−22.3313	−0.831661
$722$	−14.9940	−0.558017
$723$	19.6057	0.729142
$724$	−44.3633	−1.64875
$725$	0.367761	0.0136583
$726$	16.3876	0.608199
$727$	−4.29315	−0.159224	−0.0796120	−	0.996826i	$-0.525368\pi$
$727$	−4.29315	−0.159224	−0.0796120	+	0.996826i	$0.525368\pi$
$728$	−8.71492	−0.322996
$729$	23.4917	0.870063
$730$	21.9428	0.812141
$731$	30.2719	1.11965
$732$	14.1882	0.524410
$733$	−15.2940	−0.564895	−0.282448	−	0.959283i	$-0.591146\pi$
$733$	−15.2940	−0.564895	−0.282448	+	0.959283i	$0.591146\pi$
$734$	−48.5766	−1.79300
$735$	−5.44717	−0.200922
$736$	3.42762	0.126344
$737$	−14.2078	−0.523352
$738$	23.3941	0.861148
$739$	29.0989	1.07042	0.535211	−	0.844718i	$-0.320232\pi$
$739$	29.0989	1.07042	0.535211	+	0.844718i	$0.320232\pi$
$740$	12.2681	0.450984
$741$	−5.27905	−0.193931
$742$	−38.2868	−1.40555
$743$	1.24936	0.0458347	0.0229173	−	0.999737i	$-0.492705\pi$
$743$	1.24936	0.0458347	0.0229173	+	0.999737i	$0.492705\pi$
$744$	−17.7015	−0.648968
$745$	13.7233	0.502783
$746$	76.5201	2.80160
$747$	19.0316	0.696331
$748$	90.6560	3.31471
$749$	−48.3843	−1.76792
$750$	2.81322	0.102724
$751$	−2.26402	−0.0826152	−0.0413076	−	0.999146i	$-0.513152\pi$
$751$	−2.26402	−0.0826152	−0.0413076	+	0.999146i	$0.513152\pi$
$752$	2.42829	0.0885507
$753$	0.486497	0.0177290
$754$	−0.724983	−0.0264023
$755$	−13.2168	−0.481010
$756$	61.6213	2.24115
$757$	−20.3426	−0.739363	−0.369682	−	0.929158i	$-0.620533\pi$
$757$	−20.3426	−0.739363	−0.369682	+	0.929158i	$0.620533\pi$
$758$	81.1782	2.94852
$759$	−3.24863	−0.117918
$760$	−15.1927	−0.551098
$761$	19.5200	0.707598	0.353799	−	0.935322i	$-0.384890\pi$
$761$	19.5200	0.707598	0.353799	+	0.935322i	$0.384890\pi$
$762$	−3.83028	−0.138756
$763$	−56.7550	−2.05467
$764$	−76.1663	−2.75560
$765$	−10.0844	−0.364601
$766$	15.5442	0.561633
$767$	−7.22812	−0.260992
$768$	21.9789	0.793095
$769$	11.6945	0.421715	0.210858	−	0.977517i	$-0.432374\pi$
$769$	11.6945	0.421715	0.210858	+	0.977517i	$0.432374\pi$
$770$	−31.9856	−1.15268
$771$	−11.1717	−0.402339
$772$	−60.8555	−2.19024
$773$	13.1881	0.474343	0.237171	−	0.971468i	$-0.423780\pi$
$773$	13.1881	0.474343	0.237171	+	0.971468i	$0.423780\pi$
$774$	15.7330	0.565512
$775$	−4.81837	−0.173081
$776$	0.675474	0.0242481
$777$	−15.3429	−0.550423
$778$	10.7169	0.384220
$779$	34.0060	1.21839
$780$	−3.45537	−0.123722
$781$	−40.6780	−1.45557
$782$	−9.98628	−0.357109
$783$	2.02495	0.0723657
$784$	1.41445	0.0505162
$785$	−11.1885	−0.399336
$786$	46.6403	1.66361
$787$	29.6596	1.05725	0.528626	−	0.848855i	$-0.322708\pi$
$787$	29.6596	1.05725	0.528626	+	0.848855i	$0.322708\pi$
$788$	−49.5660	−1.76571
$789$	−19.7722	−0.703909
$790$	21.3307	0.758912
$791$	51.9275	1.84633
$792$	18.6118	0.661340
$793$	−3.00744	−0.106797
$794$	−53.7437	−1.90729
$795$	−5.99652	−0.212675
$796$	24.2971	0.861188
$797$	46.1054	1.63314	0.816569	−	0.577248i	$-0.195873\pi$
$797$	46.1054	1.63314	0.816569	+	0.577248i	$0.195873\pi$
$798$	48.1002	1.70273
$799$	51.1902	1.81098
$800$	5.28561	0.186875
$801$	−20.3599	−0.719383
$802$	2.30345	0.0813377
$803$	−39.0745	−1.37891
$804$	13.9849	0.493210
$805$	2.19529	0.0773737
$806$	9.49865	0.334576
$807$	28.6776	1.00950
$808$	46.3308	1.62991
$809$	−35.1661	−1.23638	−0.618188	−	0.786030i	$-0.712133\pi$
$809$	−35.1661	−1.23638	−0.618188	+	0.786030i	$0.712133\pi$
$810$	5.06629	0.178011
$811$	7.14801	0.251001	0.125500	−	0.992094i	$-0.459946\pi$
$811$	7.14801	0.251001	0.125500	+	0.992094i	$0.459946\pi$
$812$	4.11575	0.144434
$813$	−6.00631	−0.210651
$814$	−35.0629	−1.22895
$815$	18.8779	0.661263
$816$	−2.58936	−0.0906459
$817$	22.8698	0.800112
$818$	−0.502036	−0.0175533
$819$	−4.37017	−0.152706
$820$	22.2584	0.777297
$821$	40.7228	1.42124	0.710618	−	0.703578i	$-0.248416\pi$
$821$	40.7228	1.42124	0.710618	+	0.703578i	$0.248416\pi$
$822$	55.1725	1.92436
$823$	4.08456	0.142379	0.0711894	−	0.997463i	$-0.477321\pi$
$823$	4.08456	0.142379	0.0711894	+	0.997463i	$0.477321\pi$
$824$	19.8429	0.691260
$825$	−5.00961	−0.174412
$826$	65.8592	2.29153
$827$	12.9544	0.450470	0.225235	−	0.974304i	$-0.427685\pi$
$827$	12.9544	0.450470	0.225235	+	0.974304i	$0.427685\pi$
$828$	−3.23375	−0.112381
$829$	12.9043	0.448185	0.224093	−	0.974568i	$-0.428058\pi$
$829$	12.9043	0.448185	0.224093	+	0.974568i	$0.428058\pi$
$830$	29.0626	1.00878
$831$	16.6304	0.576902
$832$	−10.9626	−0.380059
$833$	29.8177	1.03312
$834$	45.0763	1.56087
$835$	4.66675	0.161500
$836$	68.4886	2.36873
$837$	−26.5307	−0.917034
$838$	−29.3486	−1.01383
$839$	21.9989	0.759485	0.379742	−	0.925092i	$-0.376013\pi$
$839$	21.9989	0.759485	0.379742	+	0.925092i	$0.376013\pi$
$840$	12.4367	0.429106
$841$	−28.8648	−0.995336
$842$	9.48178	0.326764
$843$	4.94246	0.170227
$844$	61.1575	2.10513
$845$	−12.2676	−0.422017
$846$	26.6048	0.914691
$847$	19.7200	0.677586
$848$	1.55710	0.0534711
$849$	14.1536	0.485749
$850$	−15.3995	−0.528199
$851$	2.40650	0.0824936
$852$	40.0398	1.37174
$853$	−3.22886	−0.110554	−0.0552770	−	0.998471i	$-0.517604\pi$
$853$	−3.22886	−0.110554	−0.0552770	+	0.998471i	$0.517604\pi$
$854$	27.4024	0.937690
$855$	−7.61852	−0.260548
$856$	42.9928	1.46946
$857$	25.0997	0.857391	0.428695	−	0.903449i	$-0.358973\pi$
$857$	25.0997	0.857391	0.428695	+	0.903449i	$0.358973\pi$
$858$	9.87565	0.337149
$859$	0.740236	0.0252565	0.0126283	−	0.999920i	$-0.495980\pi$
$859$	0.740236	0.0252565	0.0126283	+	0.999920i	$0.495980\pi$
$860$	14.9693	0.510448
$861$	−27.8371	−0.948686
$862$	−22.5028	−0.766449
$863$	−53.8947	−1.83460	−0.917298	−	0.398200i	$-0.869635\pi$
$863$	−53.8947	−1.83460	−0.917298	+	0.398200i	$0.869635\pi$
$864$	29.1034	0.990117
$865$	−0.997203	−0.0339059
$866$	−69.8508	−2.37363
$867$	−33.8236	−1.14871
$868$	−53.9242	−1.83031
$869$	−37.9845	−1.28853
$870$	1.03459	0.0350759
$871$	−2.96435	−0.100443
$872$	50.4308	1.70780
$873$	0.338722	0.0114640
$874$	−7.54441	−0.255194
$875$	3.38528	0.114443
$876$	38.4615	1.29949
$877$	12.0915	0.408302	0.204151	−	0.978939i	$-0.434557\pi$
$877$	12.0915	0.408302	0.204151	+	0.978939i	$0.434557\pi$
$878$	40.7841	1.37640
$879$	−1.45337	−0.0490211
$880$	1.30083	0.0438511
$881$	−7.28079	−0.245296	−0.122648	−	0.992450i	$-0.539139\pi$
$881$	−7.28079	−0.245296	−0.122648	+	0.992450i	$0.539139\pi$
$882$	15.4970	0.521811
$883$	2.33060	0.0784310	0.0392155	−	0.999231i	$-0.487514\pi$
$883$	2.33060	0.0784310	0.0392155	+	0.999231i	$0.487514\pi$
$884$	18.9147	0.636169
$885$	10.3149	0.346733
$886$	72.6518	2.44079
$887$	−49.1637	−1.65076	−0.825378	−	0.564580i	$-0.809038\pi$
$887$	−49.1637	−1.65076	−0.825378	+	0.564580i	$0.809038\pi$
$888$	13.6332	0.457501
$889$	−4.60916	−0.154586
$890$	−31.0910	−1.04217
$891$	−9.02175	−0.302240
$892$	66.1675	2.21545
$893$	38.6731	1.29415
$894$	38.6066	1.29120
$895$	8.90707	0.297731
$896$	64.0992	2.14140
$897$	−0.677803	−0.0226312
$898$	−20.8509	−0.695805
$899$	−1.77201	−0.0590998
$900$	−4.98666	−0.166222
$901$	32.8249	1.09356
$902$	−63.6158	−2.11817
$903$	−18.7211	−0.622998
$904$	−46.1412	−1.53463
$905$	−13.4195	−0.446079
$906$	−37.1818	−1.23528
$907$	−7.68141	−0.255057	−0.127529	−	0.991835i	$-0.540704\pi$
$907$	−7.68141	−0.255057	−0.127529	+	0.991835i	$0.540704\pi$
$908$	75.1225	2.49303
$909$	23.2330	0.770589
$910$	−6.67354	−0.221226
$911$	−23.2901	−0.771636	−0.385818	−	0.922575i	$-0.626081\pi$
$911$	−23.2901	−0.771636	−0.385818	+	0.922575i	$0.626081\pi$
$912$	−1.95621	−0.0647765
$913$	−51.7530	−1.71277
$914$	65.5338	2.16766
$915$	4.29179	0.141882
$916$	58.8146	1.94329
$917$	56.1246	1.85340
$918$	−84.7920	−2.79855
$919$	17.5932	0.580348	0.290174	−	0.956974i	$-0.406287\pi$
$919$	17.5932	0.580348	0.290174	+	0.956974i	$0.406287\pi$
$920$	−1.95067	−0.0643115
$921$	−6.06723	−0.199922
$922$	−15.8154	−0.520852
$923$	−8.48716	−0.279358
$924$	−56.0644	−1.84438
$925$	3.71098	0.122016
$926$	7.78980	0.255989
$927$	9.95039	0.326814
$928$	1.94384	0.0638098
$929$	−51.2865	−1.68265	−0.841327	−	0.540526i	$-0.818225\pi$
$929$	−51.2865	−1.68265	−0.841327	+	0.540526i	$0.818225\pi$
$930$	−13.5551	−0.444490
$931$	22.5267	0.738281
$932$	−26.9669	−0.883330
$933$	28.6078	0.936576
$934$	−67.6094	−2.21225
$935$	27.4226	0.896813
$936$	3.88320	0.126926
$937$	4.32819	0.141396	0.0706979	−	0.997498i	$-0.477477\pi$
$937$	4.32819	0.141396	0.0706979	+	0.997498i	$0.477477\pi$
$938$	27.0098	0.881901
$939$	−7.00834	−0.228709
$940$	25.3132	0.825627
$941$	8.37105	0.272888	0.136444	−	0.990648i	$-0.456433\pi$
$941$	8.37105	0.272888	0.136444	+	0.990648i	$0.456433\pi$
$942$	−31.4758	−1.02554
$943$	4.36619	0.142183
$944$	−2.67845	−0.0871762
$945$	18.6399	0.606355
$946$	−42.7830	−1.39100
$947$	−19.8502	−0.645046	−0.322523	−	0.946562i	$-0.604531\pi$
$947$	−19.8502	−0.645046	−0.322523	+	0.946562i	$0.604531\pi$
$948$	37.3885	1.21432
$949$	−8.15260	−0.264645
$950$	−11.6340	−0.377457
$951$	22.0297	0.714363
$952$	−68.0783	−2.20643
$953$	−4.47210	−0.144866	−0.0724328	−	0.997373i	$-0.523076\pi$
$953$	−4.47210	−0.144866	−0.0724328	+	0.997373i	$0.523076\pi$
$954$	17.0599	0.552334
$955$	−23.0396	−0.745543
$956$	68.6097	2.21900
$957$	−1.84234	−0.0595544
$958$	−55.0290	−1.77790
$959$	66.3918	2.14390
$960$	15.6442	0.504914
$961$	−7.78331	−0.251074
$962$	−7.31561	−0.235865
$963$	21.5591	0.694732
$964$	−53.0697	−1.70926
$965$	−18.4082	−0.592581
$966$	6.17582	0.198704
$967$	20.9698	0.674343	0.337171	−	0.941443i	$-0.390530\pi$
$967$	20.9698	0.674343	0.337171	+	0.941443i	$0.390530\pi$
$968$	−17.5226	−0.563196
$969$	−41.2383	−1.32477
$970$	0.517251	0.0166079
$971$	−28.9848	−0.930165	−0.465083	−	0.885267i	$-0.653975\pi$
$971$	−28.9848	−0.930165	−0.465083	+	0.885267i	$0.653975\pi$
$972$	−45.7280	−1.46673
$973$	54.2426	1.73894
$974$	40.1149	1.28536
$975$	−1.04522	−0.0334737
$976$	−1.11444	−0.0356723
$977$	0.833207	0.0266567	0.0133283	−	0.999911i	$-0.495757\pi$
$977$	0.833207	0.0266567	0.0133283	+	0.999911i	$0.495757\pi$
$978$	53.1075	1.69819
$979$	55.3650	1.76947
$980$	14.7447	0.471002
$981$	25.2890	0.807414
$982$	−83.1713	−2.65410
$983$	−19.9843	−0.637399	−0.318700	−	0.947856i	$-0.603246\pi$
$983$	−19.9843	−0.637399	−0.318700	+	0.947856i	$0.603246\pi$
$984$	24.7352	0.788529
$985$	−14.9932	−0.477724
$986$	−5.66334	−0.180357
$987$	−31.6576	−1.00767
$988$	14.2896	0.454614
$989$	2.93636	0.0933707
$990$	14.2522	0.452963
$991$	6.07163	0.192872	0.0964359	−	0.995339i	$-0.469256\pi$
$991$	6.07163	0.192872	0.0964359	+	0.995339i	$0.469256\pi$
$992$	−25.4680	−0.808611
$993$	−34.6233	−1.09874
$994$	77.3310	2.45279
$995$	7.34963	0.232999
$996$	50.9410	1.61413
$997$	−50.8669	−1.61097	−0.805485	−	0.592616i	$-0.798095\pi$
$997$	−50.8669	−1.61097	−0.805485	+	0.592616i	$0.798095\pi$
$998$	−89.5357	−2.83420
$999$	20.4332	0.646478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.3	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.3	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30345 q^{2} -1.22130 q^{3} +3.30589 q^{4} +1.00000 q^{5} +2.81322 q^{6} +3.38528 q^{7} -3.00806 q^{8} -1.50842 q^{9} +O(q^{10})\)	\(q-2.30345 q^{2} -1.22130 q^{3} +3.30589 q^{4} +1.00000 q^{5} +2.81322 q^{6} +3.38528 q^{7} -3.00806 q^{8} -1.50842 q^{9} -2.30345 q^{10} +4.10185 q^{11} -4.03750 q^{12} +0.855820 q^{13} -7.79783 q^{14} -1.22130 q^{15} +0.317133 q^{16} +6.68540 q^{17} +3.47456 q^{18} +5.05068 q^{19} +3.30589 q^{20} -4.13446 q^{21} -9.44842 q^{22} +0.648480 q^{23} +3.67375 q^{24} +1.00000 q^{25} -1.97134 q^{26} +5.50615 q^{27} +11.1914 q^{28} +0.367761 q^{29} +2.81322 q^{30} -4.81837 q^{31} +5.28561 q^{32} -5.00961 q^{33} -15.3995 q^{34} +3.38528 q^{35} -4.98666 q^{36} +3.71098 q^{37} -11.6340 q^{38} -1.04522 q^{39} -3.00806 q^{40} +6.73295 q^{41} +9.52352 q^{42} +4.52806 q^{43} +13.5603 q^{44} -1.50842 q^{45} -1.49374 q^{46} +7.65701 q^{47} -0.387316 q^{48} +4.46013 q^{49} -2.30345 q^{50} -8.16491 q^{51} +2.82925 q^{52} +4.90993 q^{53} -12.6831 q^{54} +4.10185 q^{55} -10.1831 q^{56} -6.16841 q^{57} -0.847120 q^{58} -8.44583 q^{59} -4.03750 q^{60} -3.51410 q^{61} +11.0989 q^{62} -5.10641 q^{63} -12.8094 q^{64} +0.855820 q^{65} +11.5394 q^{66} -3.46376 q^{67} +22.1012 q^{68} -0.791992 q^{69} -7.79783 q^{70} -9.91699 q^{71} +4.53740 q^{72} -9.52607 q^{73} -8.54806 q^{74} -1.22130 q^{75} +16.6970 q^{76} +13.8859 q^{77} +2.40761 q^{78} -9.26032 q^{79} +0.317133 q^{80} -2.19943 q^{81} -15.5090 q^{82} -12.6170 q^{83} -13.6681 q^{84} +6.68540 q^{85} -10.4302 q^{86} -0.449148 q^{87} -12.3386 q^{88} +13.4976 q^{89} +3.47456 q^{90} +2.89719 q^{91} +2.14380 q^{92} +5.88470 q^{93} -17.6376 q^{94} +5.05068 q^{95} -6.45534 q^{96} -0.224555 q^{97} -10.2737 q^{98} -6.18730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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