LMFDB - Embedded newform 8041.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17121 q^{2} +0.274303 q^{3} +2.71415 q^{4} -0.625848 q^{5} -0.595570 q^{6} -3.36796 q^{7} -1.55058 q^{8} -2.92476 q^{9} +O(q^{10})$	\(q-2.17121 q^{2} +0.274303 q^{3} +2.71415 q^{4} -0.625848 q^{5} -0.595570 q^{6} -3.36796 q^{7} -1.55058 q^{8} -2.92476 q^{9} +1.35885 q^{10} +1.00000 q^{11} +0.744502 q^{12} -5.20112 q^{13} +7.31256 q^{14} -0.171672 q^{15} -2.06168 q^{16} +1.00000 q^{17} +6.35026 q^{18} +1.58120 q^{19} -1.69865 q^{20} -0.923844 q^{21} -2.17121 q^{22} +7.56807 q^{23} -0.425328 q^{24} -4.60831 q^{25} +11.2927 q^{26} -1.62518 q^{27} -9.14117 q^{28} -0.604464 q^{29} +0.372736 q^{30} -3.36767 q^{31} +7.57749 q^{32} +0.274303 q^{33} -2.17121 q^{34} +2.10783 q^{35} -7.93824 q^{36} +0.429268 q^{37} -3.43311 q^{38} -1.42669 q^{39} +0.970424 q^{40} +11.3010 q^{41} +2.00586 q^{42} -1.00000 q^{43} +2.71415 q^{44} +1.83045 q^{45} -16.4319 q^{46} +6.30203 q^{47} -0.565526 q^{48} +4.34318 q^{49} +10.0056 q^{50} +0.274303 q^{51} -14.1166 q^{52} -6.41295 q^{53} +3.52861 q^{54} -0.625848 q^{55} +5.22228 q^{56} +0.433728 q^{57} +1.31242 q^{58} +3.07170 q^{59} -0.465945 q^{60} -7.26157 q^{61} +7.31192 q^{62} +9.85048 q^{63} -12.3290 q^{64} +3.25511 q^{65} -0.595570 q^{66} +4.80309 q^{67} +2.71415 q^{68} +2.07595 q^{69} -4.57655 q^{70} -0.260639 q^{71} +4.53506 q^{72} +8.37502 q^{73} -0.932031 q^{74} -1.26408 q^{75} +4.29161 q^{76} -3.36796 q^{77} +3.09764 q^{78} -1.28282 q^{79} +1.29030 q^{80} +8.32848 q^{81} -24.5369 q^{82} +11.3359 q^{83} -2.50745 q^{84} -0.625848 q^{85} +2.17121 q^{86} -0.165806 q^{87} -1.55058 q^{88} +5.61290 q^{89} -3.97430 q^{90} +17.5172 q^{91} +20.5409 q^{92} -0.923763 q^{93} -13.6830 q^{94} -0.989589 q^{95} +2.07853 q^{96} -2.57185 q^{97} -9.42996 q^{98} -2.92476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.17121	−1.53528	−0.767639	−	0.640883i	$-0.778568\pi$
$2$	−2.17121	−1.53528	−0.767639	+	0.640883i	$0.778568\pi$
$3$	0.274303	0.158369	0.0791846	−	0.996860i	$-0.474768\pi$
$3$	0.274303	0.158369	0.0791846	+	0.996860i	$0.474768\pi$
$4$	2.71415	1.35708
$5$	−0.625848	−0.279888	−0.139944	−	0.990159i	$-0.544692\pi$
$5$	−0.625848	−0.279888	−0.139944	+	0.990159i	$0.544692\pi$
$6$	−0.595570	−0.243141
$7$	−3.36796	−1.27297	−0.636485	−	0.771289i	$-0.719612\pi$
$7$	−3.36796	−1.27297	−0.636485	+	0.771289i	$0.719612\pi$
$8$	−1.55058	−0.548211
$9$	−2.92476	−0.974919
$10$	1.35885	0.429705
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.744502	0.214919
$13$	−5.20112	−1.44253	−0.721266	−	0.692658i	$-0.756440\pi$
$13$	−5.20112	−1.44253	−0.721266	+	0.692658i	$0.756440\pi$
$14$	7.31256	1.95436
$15$	−0.171672	−0.0443256
$16$	−2.06168	−0.515420
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.35026	1.49677
$19$	1.58120	0.362752	0.181376	−	0.983414i	$-0.441945\pi$
$19$	1.58120	0.362752	0.181376	+	0.983414i	$0.441945\pi$
$20$	−1.69865	−0.379829
$21$	−0.923844	−0.201599
$22$	−2.17121	−0.462904
$23$	7.56807	1.57805	0.789026	−	0.614360i	$-0.210586\pi$
$23$	7.56807	1.57805	0.789026	+	0.614360i	$0.210586\pi$
$24$	−0.425328	−0.0868198
$25$	−4.60831	−0.921663
$26$	11.2927	2.21469
$27$	−1.62518	−0.312766
$28$	−9.14117	−1.72752
$29$	−0.604464	−0.112246	−0.0561230	−	0.998424i	$-0.517874\pi$
$29$	−0.604464	−0.112246	−0.0561230	+	0.998424i	$0.517874\pi$
$30$	0.372736	0.0680521
$31$	−3.36767	−0.604851	−0.302426	−	0.953173i	$-0.597796\pi$
$31$	−3.36767	−0.604851	−0.302426	+	0.953173i	$0.597796\pi$
$32$	7.57749	1.33952
$33$	0.274303	0.0477501
$34$	−2.17121	−0.372359
$35$	2.10783	0.356289
$36$	−7.93824	−1.32304
$37$	0.429268	0.0705712	0.0352856	−	0.999377i	$-0.488766\pi$
$37$	0.429268	0.0705712	0.0352856	+	0.999377i	$0.488766\pi$
$38$	−3.43311	−0.556924
$39$	−1.42669	−0.228453
$40$	0.970424	0.153438
$41$	11.3010	1.76493	0.882463	−	0.470382i	$-0.155884\pi$
$41$	11.3010	1.76493	0.882463	+	0.470382i	$0.155884\pi$
$42$	2.00586	0.309511
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.71415	0.409174
$45$	1.83045	0.272868
$46$	−16.4319	−2.42275
$47$	6.30203	0.919245	0.459622	−	0.888114i	$-0.347985\pi$
$47$	6.30203	0.919245	0.459622	+	0.888114i	$0.347985\pi$
$48$	−0.565526	−0.0816267
$49$	4.34318	0.620455
$50$	10.0056	1.41501
$51$	0.274303	0.0384102
$52$	−14.1166	−1.95763
$53$	−6.41295	−0.880886	−0.440443	−	0.897781i	$-0.645179\pi$
$53$	−6.41295	−0.880886	−0.440443	+	0.897781i	$0.645179\pi$
$54$	3.52861	0.480183
$55$	−0.625848	−0.0843893
$56$	5.22228	0.697857
$57$	0.433728	0.0574487
$58$	1.31242	0.172329
$59$	3.07170	0.399901	0.199951	−	0.979806i	$-0.435922\pi$
$59$	3.07170	0.399901	0.199951	+	0.979806i	$0.435922\pi$
$60$	−0.465945	−0.0601532
$61$	−7.26157	−0.929749	−0.464875	−	0.885377i	$-0.653901\pi$
$61$	−7.26157	−0.929749	−0.464875	+	0.885377i	$0.653901\pi$
$62$	7.31192	0.928614
$63$	9.85048	1.24104
$64$	−12.3290	−1.54112
$65$	3.25511	0.403747
$66$	−0.595570	−0.0733097
$67$	4.80309	0.586791	0.293395	−	0.955991i	$-0.405215\pi$
$67$	4.80309	0.586791	0.293395	+	0.955991i	$0.405215\pi$
$68$	2.71415	0.329139
$69$	2.07595	0.249915
$70$	−4.57655	−0.547002
$71$	−0.260639	−0.0309322	−0.0154661	−	0.999880i	$-0.504923\pi$
$71$	−0.260639	−0.0309322	−0.0154661	+	0.999880i	$0.504923\pi$
$72$	4.53506	0.534462
$73$	8.37502	0.980222	0.490111	−	0.871660i	$-0.336956\pi$
$73$	8.37502	0.980222	0.490111	+	0.871660i	$0.336956\pi$
$74$	−0.932031	−0.108346
$75$	−1.26408	−0.145963
$76$	4.29161	0.492282
$77$	−3.36796	−0.383815
$78$	3.09764	0.350738
$79$	−1.28282	−0.144329	−0.0721643	−	0.997393i	$-0.522991\pi$
$79$	−1.28282	−0.144329	−0.0721643	+	0.997393i	$0.522991\pi$
$80$	1.29030	0.144260
$81$	8.32848	0.925387
$82$	−24.5369	−2.70965
$83$	11.3359	1.24427	0.622136	−	0.782909i	$-0.286265\pi$
$83$	11.3359	1.24427	0.622136	+	0.782909i	$0.286265\pi$
$84$	−2.50745	−0.273586
$85$	−0.625848	−0.0678827
$86$	2.17121	0.234128
$87$	−0.165806	−0.0177763
$88$	−1.55058	−0.165292
$89$	5.61290	0.594966	0.297483	−	0.954727i	$-0.403853\pi$
$89$	5.61290	0.594966	0.297483	+	0.954727i	$0.403853\pi$
$90$	−3.97430	−0.418928
$91$	17.5172	1.83630
$92$	20.5409	2.14154
$93$	−0.923763	−0.0957898
$94$	−13.6830	−1.41130
$95$	−0.989589	−0.101530
$96$	2.07853	0.212139
$97$	−2.57185	−0.261132	−0.130566	−	0.991440i	$-0.541679\pi$
$97$	−2.57185	−0.261132	−0.130566	+	0.991440i	$0.541679\pi$
$98$	−9.42996	−0.952570
$99$	−2.92476	−0.293949
$100$	−12.5077	−1.25077
$101$	8.40859	0.836686	0.418343	−	0.908289i	$-0.362611\pi$
$101$	8.40859	0.836686	0.418343	+	0.908289i	$0.362611\pi$
$102$	−0.595570	−0.0589703
$103$	−10.4968	−1.03428	−0.517138	−	0.855902i	$-0.673003\pi$
$103$	−10.4968	−1.03428	−0.517138	+	0.855902i	$0.673003\pi$
$104$	8.06474	0.790813
$105$	0.578186	0.0564252
$106$	13.9239	1.35240
$107$	6.15244	0.594779	0.297390	−	0.954756i	$-0.403884\pi$
$107$	6.15244	0.594779	0.297390	+	0.954756i	$0.403884\pi$
$108$	−4.41099	−0.424448
$109$	−5.36601	−0.513970	−0.256985	−	0.966415i	$-0.582729\pi$
$109$	−5.36601	−0.513970	−0.256985	+	0.966415i	$0.582729\pi$
$110$	1.35885	0.129561
$111$	0.117750	0.0111763
$112$	6.94367	0.656115
$113$	−7.70993	−0.725290	−0.362645	−	0.931927i	$-0.618126\pi$
$113$	−7.70993	−0.725290	−0.362645	+	0.931927i	$0.618126\pi$
$114$	−0.941715	−0.0881997
$115$	−4.73646	−0.441677
$116$	−1.64061	−0.152326
$117$	15.2120	1.40635
$118$	−6.66930	−0.613959
$119$	−3.36796	−0.308741
$120$	0.266191	0.0242998
$121$	1.00000	0.0909091
$122$	15.7664	1.42742
$123$	3.09991	0.279510
$124$	−9.14037	−0.820829
$125$	6.01334	0.537850
$126$	−21.3875	−1.90535
$127$	17.7194	1.57234	0.786169	−	0.618011i	$-0.212061\pi$
$127$	17.7194	1.57234	0.786169	+	0.618011i	$0.212061\pi$
$128$	11.6138	1.02652
$129$	−0.274303	−0.0241511
$130$	−7.06753	−0.619864
$131$	4.12900	0.360752	0.180376	−	0.983598i	$-0.442269\pi$
$131$	4.12900	0.360752	0.180376	+	0.983598i	$0.442269\pi$
$132$	0.744502	0.0648005
$133$	−5.32542	−0.461772
$134$	−10.4285	−0.900886
$135$	1.01712	0.0875394
$136$	−1.55058	−0.132961
$137$	−6.01039	−0.513502	−0.256751	−	0.966478i	$-0.582652\pi$
$137$	−6.01039	−0.513502	−0.256751	+	0.966478i	$0.582652\pi$
$138$	−4.50732	−0.383689
$139$	10.8188	0.917636	0.458818	−	0.888530i	$-0.348273\pi$
$139$	10.8188	0.917636	0.458818	+	0.888530i	$0.348273\pi$
$140$	5.72098	0.483511
$141$	1.72867	0.145580
$142$	0.565903	0.0474895
$143$	−5.20112	−0.434940
$144$	6.02991	0.502493
$145$	0.378302	0.0314163
$146$	−18.1839	−1.50491
$147$	1.19135	0.0982609
$148$	1.16510	0.0957706
$149$	−8.00249	−0.655590	−0.327795	−	0.944749i	$-0.606305\pi$
$149$	−8.00249	−0.655590	−0.327795	+	0.944749i	$0.606305\pi$
$150$	2.74458	0.224094
$151$	17.7866	1.44746	0.723728	−	0.690086i	$-0.242427\pi$
$151$	17.7866	1.44746	0.723728	+	0.690086i	$0.242427\pi$
$152$	−2.45177	−0.198865
$153$	−2.92476	−0.236453
$154$	7.31256	0.589263
$155$	2.10765	0.169290
$156$	−3.87225	−0.310028
$157$	−0.249395	−0.0199039	−0.00995195	−	0.999950i	$-0.503168\pi$
$157$	−0.249395	−0.0199039	−0.00995195	+	0.999950i	$0.503168\pi$
$158$	2.78527	0.221584
$159$	−1.75909	−0.139505
$160$	−4.74236	−0.374916
$161$	−25.4890	−2.00881
$162$	−18.0829	−1.42073
$163$	11.7024	0.916603	0.458302	−	0.888797i	$-0.348458\pi$
$163$	11.7024	0.916603	0.458302	+	0.888797i	$0.348458\pi$
$164$	30.6727	2.39514
$165$	−0.171672	−0.0133647
$166$	−24.6125	−1.91030
$167$	−13.2113	−1.02232	−0.511161	−	0.859485i	$-0.670784\pi$
$167$	−13.2113	−1.02232	−0.511161	+	0.859485i	$0.670784\pi$
$168$	1.43249	0.110519
$169$	14.0517	1.08090
$170$	1.35885	0.104219
$171$	−4.62462	−0.353654
$172$	−2.71415	−0.206952
$173$	−7.39466	−0.562206	−0.281103	−	0.959678i	$-0.590700\pi$
$173$	−7.39466	−0.562206	−0.281103	+	0.959678i	$0.590700\pi$
$174$	0.360001	0.0272916
$175$	15.5206	1.17325
$176$	−2.06168	−0.155405
$177$	0.842578	0.0633320
$178$	−12.1868	−0.913437
$179$	3.41749	0.255435	0.127718	−	0.991811i	$-0.459235\pi$
$179$	3.41749	0.255435	0.127718	+	0.991811i	$0.459235\pi$
$180$	4.96813	0.370302
$181$	−24.1792	−1.79723	−0.898614	−	0.438741i	$-0.855425\pi$
$181$	−24.1792	−1.79723	−0.898614	+	0.438741i	$0.855425\pi$
$182$	−38.0335	−2.81923
$183$	−1.99188	−0.147244
$184$	−11.7349	−0.865106
$185$	−0.268657	−0.0197520
$186$	2.00568	0.147064
$187$	1.00000	0.0731272
$188$	17.1047	1.24749
$189$	5.47355	0.398142
$190$	2.14861	0.155876
$191$	−24.9583	−1.80592	−0.902958	−	0.429728i	$-0.858609\pi$
$191$	−24.9583	−1.80592	−0.902958	+	0.429728i	$0.858609\pi$
$192$	−3.38188	−0.244066
$193$	15.0101	1.08045	0.540224	−	0.841521i	$-0.318339\pi$
$193$	15.0101	1.08045	0.540224	+	0.841521i	$0.318339\pi$
$194$	5.58403	0.400910
$195$	0.892889	0.0639411
$196$	11.7881	0.842004
$197$	−8.00582	−0.570391	−0.285196	−	0.958469i	$-0.592059\pi$
$197$	−8.00582	−0.570391	−0.285196	+	0.958469i	$0.592059\pi$
$198$	6.35026	0.451294
$199$	6.19132	0.438891	0.219445	−	0.975625i	$-0.429575\pi$
$199$	6.19132	0.438891	0.219445	+	0.975625i	$0.429575\pi$
$200$	7.14554	0.505266
$201$	1.31750	0.0929296
$202$	−18.2568	−1.28455
$203$	2.03581	0.142886
$204$	0.744502	0.0521255
$205$	−7.07273	−0.493981
$206$	22.7907	1.58790
$207$	−22.1348	−1.53847
$208$	10.7231	0.743510
$209$	1.58120	0.109374
$210$	−1.25536	−0.0866283
$211$	−13.6856	−0.942157	−0.471078	−	0.882091i	$-0.656135\pi$
$211$	−13.6856	−0.942157	−0.471078	+	0.882091i	$0.656135\pi$
$212$	−17.4057	−1.19543
$213$	−0.0714943	−0.00489871
$214$	−13.3582	−0.913151
$215$	0.625848	0.0426825
$216$	2.51997	0.171462
$217$	11.3422	0.769958
$218$	11.6507	0.789087
$219$	2.29730	0.155237
$220$	−1.69865	−0.114523
$221$	−5.20112	−0.349865
$222$	−0.255659	−0.0171587
$223$	−4.89072	−0.327507	−0.163753	−	0.986501i	$-0.552360\pi$
$223$	−4.89072	−0.327507	−0.163753	+	0.986501i	$0.552360\pi$
$224$	−25.5207	−1.70517
$225$	13.4782	0.898547
$226$	16.7399	1.11352
$227$	6.40185	0.424905	0.212453	−	0.977171i	$-0.431855\pi$
$227$	6.40185	0.424905	0.212453	+	0.977171i	$0.431855\pi$
$228$	1.17720	0.0779623
$229$	−23.1100	−1.52715	−0.763575	−	0.645719i	$-0.776558\pi$
$229$	−23.1100	−1.52715	−0.763575	+	0.645719i	$0.776558\pi$
$230$	10.2839	0.678097
$231$	−0.923844	−0.0607845
$232$	0.937266	0.0615346
$233$	−2.78085	−0.182180	−0.0910898	−	0.995843i	$-0.529035\pi$
$233$	−2.78085	−0.182180	−0.0910898	+	0.995843i	$0.529035\pi$
$234$	−33.0285	−2.15914
$235$	−3.94411	−0.257285
$236$	8.33706	0.542696
$237$	−0.351882	−0.0228572
$238$	7.31256	0.474003
$239$	−19.1618	−1.23948	−0.619738	−	0.784809i	$-0.712761\pi$
$239$	−19.1618	−1.23948	−0.619738	+	0.784809i	$0.712761\pi$
$240$	0.353933	0.0228463
$241$	−15.6606	−1.00879	−0.504393	−	0.863474i	$-0.668284\pi$
$241$	−15.6606	−1.00879	−0.504393	+	0.863474i	$0.668284\pi$
$242$	−2.17121	−0.139571
$243$	7.16008	0.459319
$244$	−19.7090	−1.26174
$245$	−2.71817	−0.173658
$246$	−6.73057	−0.429125
$247$	−8.22401	−0.523281
$248$	5.22182	0.331586
$249$	3.10947	0.197055
$250$	−13.0562	−0.825748
$251$	27.0193	1.70545	0.852723	−	0.522364i	$-0.174950\pi$
$251$	27.0193	1.70545	0.852723	+	0.522364i	$0.174950\pi$
$252$	26.7357	1.68419
$253$	7.56807	0.475801
$254$	−38.4724	−2.41398
$255$	−0.171672	−0.0107505
$256$	−0.558044	−0.0348778
$257$	16.2711	1.01496	0.507481	−	0.861663i	$-0.330577\pi$
$257$	16.2711	1.01496	0.507481	+	0.861663i	$0.330577\pi$
$258$	0.595570	0.0370786
$259$	−1.44576	−0.0898351
$260$	8.83487	0.547915
$261$	1.76791	0.109431
$262$	−8.96492	−0.553855
$263$	−4.97877	−0.307004	−0.153502	−	0.988148i	$-0.549055\pi$
$263$	−4.97877	−0.307004	−0.153502	+	0.988148i	$0.549055\pi$
$264$	−0.425328	−0.0261771
$265$	4.01353	0.246549
$266$	11.5626	0.708949
$267$	1.53964	0.0942243
$268$	13.0363	0.796320
$269$	6.91803	0.421800	0.210900	−	0.977508i	$-0.432361\pi$
$269$	6.91803	0.421800	0.210900	+	0.977508i	$0.432361\pi$
$270$	−2.20837	−0.134397
$271$	−7.85753	−0.477311	−0.238656	−	0.971104i	$-0.576707\pi$
$271$	−7.85753	−0.477311	−0.238656	+	0.971104i	$0.576707\pi$
$272$	−2.06168	−0.125008
$273$	4.80503	0.290814
$274$	13.0498	0.788368
$275$	−4.60831	−0.277892
$276$	5.63444	0.339154
$277$	16.6317	0.999300	0.499650	−	0.866227i	$-0.333462\pi$
$277$	16.6317	0.999300	0.499650	+	0.866227i	$0.333462\pi$
$278$	−23.4898	−1.40883
$279$	9.84961	0.589681
$280$	−3.26835	−0.195322
$281$	−6.48074	−0.386608	−0.193304	−	0.981139i	$-0.561920\pi$
$281$	−6.48074	−0.386608	−0.193304	+	0.981139i	$0.561920\pi$
$282$	−3.75330	−0.223506
$283$	1.84914	0.109920	0.0549599	−	0.998489i	$-0.482497\pi$
$283$	1.84914	0.109920	0.0549599	+	0.998489i	$0.482497\pi$
$284$	−0.707415	−0.0419774
$285$	−0.271448	−0.0160792
$286$	11.2927	0.667753
$287$	−38.0615	−2.24670
$288$	−22.1623	−1.30593
$289$	1.00000	0.0588235
$290$	−0.821373	−0.0482327
$291$	−0.705468	−0.0413553
$292$	22.7311	1.33024
$293$	25.9711	1.51725	0.758625	−	0.651527i	$-0.225871\pi$
$293$	25.9711	1.51725	0.758625	+	0.651527i	$0.225871\pi$
$294$	−2.58667	−0.150858
$295$	−1.92242	−0.111927
$296$	−0.665613	−0.0386880
$297$	−1.62518	−0.0943026
$298$	17.3751	1.00651
$299$	−39.3625	−2.27639
$300$	−3.43090	−0.198083
$301$	3.36796	0.194126
$302$	−38.6185	−2.22225
$303$	2.30651	0.132505
$304$	−3.25992	−0.186970
$305$	4.54464	0.260225
$306$	6.35026	0.363020
$307$	−31.9626	−1.82420	−0.912100	−	0.409968i	$-0.865540\pi$
$307$	−31.9626	−1.82420	−0.912100	+	0.409968i	$0.865540\pi$
$308$	−9.14117	−0.520866
$309$	−2.87930	−0.163797
$310$	−4.57615	−0.259908
$311$	−15.0151	−0.851429	−0.425714	−	0.904858i	$-0.639977\pi$
$311$	−15.0151	−0.851429	−0.425714	+	0.904858i	$0.639977\pi$
$312$	2.21219	0.125240
$313$	−5.22088	−0.295102	−0.147551	−	0.989054i	$-0.547139\pi$
$313$	−5.22088	−0.295102	−0.147551	+	0.989054i	$0.547139\pi$
$314$	0.541489	0.0305580
$315$	−6.16490	−0.347353
$316$	−3.48177	−0.195865
$317$	−28.7792	−1.61640	−0.808202	−	0.588906i	$-0.799559\pi$
$317$	−28.7792	−1.61640	−0.808202	+	0.588906i	$0.799559\pi$
$318$	3.81936	0.214179
$319$	−0.604464	−0.0338435
$320$	7.71606	0.431341
$321$	1.68764	0.0941947
$322$	55.3420	3.08409
$323$	1.58120	0.0879802
$324$	22.6048	1.25582
$325$	23.9684	1.32953
$326$	−25.4084	−1.40724
$327$	−1.47192	−0.0813971
$328$	−17.5231	−0.967552
$329$	−21.2250	−1.17017
$330$	0.372736	0.0205185
$331$	18.8439	1.03575	0.517877	−	0.855455i	$-0.326722\pi$
$331$	18.8439	1.03575	0.517877	+	0.855455i	$0.326722\pi$
$332$	30.7673	1.68857
$333$	−1.25551	−0.0688013
$334$	28.6845	1.56955
$335$	−3.00600	−0.164235
$336$	1.90467	0.103908
$337$	3.22295	0.175565	0.0877825	−	0.996140i	$-0.472022\pi$
$337$	3.22295	0.175565	0.0877825	+	0.996140i	$0.472022\pi$
$338$	−30.5092	−1.65948
$339$	−2.11486	−0.114864
$340$	−1.69865	−0.0921220
$341$	−3.36767	−0.182369
$342$	10.0410	0.542956
$343$	8.94806	0.483150
$344$	1.55058	0.0836014
$345$	−1.29923	−0.0699481
$346$	16.0554	0.863141
$347$	4.42454	0.237522	0.118761	−	0.992923i	$-0.462108\pi$
$347$	4.42454	0.237522	0.118761	+	0.992923i	$0.462108\pi$
$348$	−0.450024	−0.0241238
$349$	8.34838	0.446878	0.223439	−	0.974718i	$-0.428272\pi$
$349$	8.34838	0.446878	0.223439	+	0.974718i	$0.428272\pi$
$350$	−33.6986	−1.80126
$351$	8.45277	0.451176
$352$	7.57749	0.403882
$353$	−21.8732	−1.16419	−0.582097	−	0.813119i	$-0.697768\pi$
$353$	−21.8732	−1.16419	−0.582097	+	0.813119i	$0.697768\pi$
$354$	−1.82941	−0.0972322
$355$	0.163121	0.00865754
$356$	15.2343	0.807414
$357$	−0.923844	−0.0488950
$358$	−7.42008	−0.392164
$359$	32.5760	1.71930	0.859649	−	0.510886i	$-0.170682\pi$
$359$	32.5760	1.71930	0.859649	+	0.510886i	$0.170682\pi$
$360$	−2.83826	−0.149589
$361$	−16.4998	−0.868411
$362$	52.4982	2.75924
$363$	0.274303	0.0143972
$364$	47.5444	2.49200
$365$	−5.24149	−0.274352
$366$	4.32478	0.226060
$367$	−16.6405	−0.868626	−0.434313	−	0.900762i	$-0.643009\pi$
$367$	−16.6405	−0.868626	−0.434313	+	0.900762i	$0.643009\pi$
$368$	−15.6029	−0.813360
$369$	−33.0528	−1.72066
$370$	0.583310	0.0303248
$371$	21.5986	1.12134
$372$	−2.50723	−0.129994
$373$	−28.4054	−1.47077	−0.735387	−	0.677647i	$-0.763000\pi$
$373$	−28.4054	−1.47077	−0.735387	+	0.677647i	$0.763000\pi$
$374$	−2.17121	−0.112271
$375$	1.64948	0.0851788
$376$	−9.77177	−0.503940
$377$	3.14389	0.161919
$378$	−11.8842	−0.611259
$379$	−4.70596	−0.241729	−0.120865	−	0.992669i	$-0.538567\pi$
$379$	−4.70596	−0.241729	−0.120865	+	0.992669i	$0.538567\pi$
$380$	−2.68590	−0.137784
$381$	4.86048	0.249010
$382$	54.1896	2.77258
$383$	24.5762	1.25579	0.627893	−	0.778299i	$-0.283917\pi$
$383$	24.5762	1.25579	0.627893	+	0.778299i	$0.283917\pi$
$384$	3.18570	0.162570
$385$	2.10783	0.107425
$386$	−32.5900	−1.65879
$387$	2.92476	0.148674
$388$	−6.98040	−0.354376
$389$	−5.02363	−0.254708	−0.127354	−	0.991857i	$-0.540648\pi$
$389$	−5.02363	−0.254708	−0.127354	+	0.991857i	$0.540648\pi$
$390$	−1.93865	−0.0981673
$391$	7.56807	0.382734
$392$	−6.73443	−0.340140
$393$	1.13260	0.0571321
$394$	17.3823	0.875708
$395$	0.802850	0.0403958
$396$	−7.93824	−0.398912
$397$	16.3438	0.820273	0.410137	−	0.912024i	$-0.365481\pi$
$397$	16.3438	0.820273	0.410137	+	0.912024i	$0.365481\pi$
$398$	−13.4426	−0.673819
$399$	−1.46078	−0.0731305
$400$	9.50087	0.475044
$401$	−10.0231	−0.500529	−0.250265	−	0.968177i	$-0.580518\pi$
$401$	−10.0231	−0.500529	−0.250265	+	0.968177i	$0.580518\pi$
$402$	−2.86058	−0.142673
$403$	17.5157	0.872517
$404$	22.8222	1.13545
$405$	−5.21236	−0.259004
$406$	−4.42017	−0.219370
$407$	0.429268	0.0212780
$408$	−0.425328	−0.0210569
$409$	−3.74875	−0.185364	−0.0926818	−	0.995696i	$-0.529544\pi$
$409$	−3.74875	−0.185364	−0.0926818	+	0.995696i	$0.529544\pi$
$410$	15.3564	0.758398
$411$	−1.64867	−0.0813229
$412$	−28.4898	−1.40359
$413$	−10.3454	−0.509063
$414$	48.0593	2.36198
$415$	−7.09453	−0.348257
$416$	−39.4115	−1.93231
$417$	2.96763	0.145325
$418$	−3.43311	−0.167919
$419$	7.29351	0.356311	0.178156	−	0.984002i	$-0.442987\pi$
$419$	7.29351	0.356311	0.178156	+	0.984002i	$0.442987\pi$
$420$	1.56928	0.0765733
$421$	−30.6150	−1.49208	−0.746042	−	0.665898i	$-0.768048\pi$
$421$	−30.6150	−1.49208	−0.746042	+	0.665898i	$0.768048\pi$
$422$	29.7143	1.44647
$423$	−18.4319	−0.896189
$424$	9.94376	0.482912
$425$	−4.60831	−0.223536
$426$	0.155229	0.00752087
$427$	24.4567	1.18354
$428$	16.6987	0.807161
$429$	−1.42669	−0.0688811
$430$	−1.35885	−0.0655294
$431$	39.3896	1.89733	0.948665	−	0.316283i	$-0.102435\pi$
$431$	39.3896	1.89733	0.948665	+	0.316283i	$0.102435\pi$
$432$	3.35061	0.161206
$433$	−19.1160	−0.918658	−0.459329	−	0.888266i	$-0.651910\pi$
$433$	−19.1160	−0.918658	−0.459329	+	0.888266i	$0.651910\pi$
$434$	−24.6263	−1.18210
$435$	0.103770	0.00497537
$436$	−14.5642	−0.697497
$437$	11.9666	0.572441
$438$	−4.98792	−0.238332
$439$	−23.6185	−1.12725	−0.563625	−	0.826031i	$-0.690594\pi$
$439$	−23.6185	−1.12725	−0.563625	+	0.826031i	$0.690594\pi$
$440$	0.970424	0.0462632
$441$	−12.7028	−0.604893
$442$	11.2927	0.537141
$443$	12.9590	0.615703	0.307851	−	0.951434i	$-0.400390\pi$
$443$	12.9590	0.615703	0.307851	+	0.951434i	$0.400390\pi$
$444$	0.319591	0.0151671
$445$	−3.51282	−0.166524
$446$	10.6188	0.502814
$447$	−2.19511	−0.103825
$448$	41.5235	1.96180
$449$	−5.31548	−0.250853	−0.125427	−	0.992103i	$-0.540030\pi$
$449$	−5.31548	−0.250853	−0.125427	+	0.992103i	$0.540030\pi$
$450$	−29.2640	−1.37952
$451$	11.3010	0.532145
$452$	−20.9259	−0.984273
$453$	4.87893	0.229232
$454$	−13.8997	−0.652348
$455$	−10.9631	−0.513958
$456$	−0.672528	−0.0314940
$457$	5.29564	0.247720	0.123860	−	0.992300i	$-0.460473\pi$
$457$	5.29564	0.247720	0.123860	+	0.992300i	$0.460473\pi$
$458$	50.1766	2.34460
$459$	−1.62518	−0.0758570
$460$	−12.8555	−0.599390
$461$	−32.5598	−1.51646	−0.758230	−	0.651987i	$-0.773936\pi$
$461$	−32.5598	−1.51646	−0.758230	+	0.651987i	$0.773936\pi$
$462$	2.00586	0.0933211
$463$	21.2525	0.987686	0.493843	−	0.869551i	$-0.335592\pi$
$463$	21.2525	0.987686	0.493843	+	0.869551i	$0.335592\pi$
$464$	1.24621	0.0578539
$465$	0.578135	0.0268104
$466$	6.03781	0.279696
$467$	2.58354	0.119552	0.0597759	−	0.998212i	$-0.480961\pi$
$467$	2.58354	0.119552	0.0597759	+	0.998212i	$0.480961\pi$
$468$	41.2878	1.90853
$469$	−16.1766	−0.746967
$470$	8.56349	0.395004
$471$	−0.0684100	−0.00315216
$472$	−4.76290	−0.219230
$473$	−1.00000	−0.0459800
$474$	0.764010	0.0350921
$475$	−7.28666	−0.334335
$476$	−9.14117	−0.418985
$477$	18.7563	0.858793
$478$	41.6044	1.90294
$479$	23.5091	1.07416	0.537079	−	0.843532i	$-0.319528\pi$
$479$	23.5091	1.07416	0.537079	+	0.843532i	$0.319528\pi$
$480$	−1.30084	−0.0593752
$481$	−2.23268	−0.101801
$482$	34.0024	1.54877
$483$	−6.99172	−0.318134
$484$	2.71415	0.123371
$485$	1.60959	0.0730876
$486$	−15.5460	−0.705182
$487$	11.1054	0.503235	0.251618	−	0.967827i	$-0.419037\pi$
$487$	11.1054	0.503235	0.251618	+	0.967827i	$0.419037\pi$
$488$	11.2596	0.509699
$489$	3.21001	0.145162
$490$	5.90172	0.266613
$491$	−7.32663	−0.330646	−0.165323	−	0.986239i	$-0.552867\pi$
$491$	−7.32663	−0.330646	−0.165323	+	0.986239i	$0.552867\pi$
$492$	8.41364	0.379316
$493$	−0.604464	−0.0272237
$494$	17.8560	0.803382
$495$	1.83045	0.0822727
$496$	6.94306	0.311752
$497$	0.877824	0.0393758
$498$	−6.75131	−0.302533
$499$	13.1980	0.590825	0.295413	−	0.955370i	$-0.404543\pi$
$499$	13.1980	0.590825	0.295413	+	0.955370i	$0.404543\pi$
$500$	16.3211	0.729903
$501$	−3.62391	−0.161904
$502$	−58.6647	−2.61833
$503$	10.2310	0.456178	0.228089	−	0.973640i	$-0.426752\pi$
$503$	10.2310	0.456178	0.228089	+	0.973640i	$0.426752\pi$
$504$	−15.2739	−0.680354
$505$	−5.26250	−0.234178
$506$	−16.4319	−0.730486
$507$	3.85443	0.171181
$508$	48.0930	2.13378
$509$	10.6856	0.473633	0.236816	−	0.971554i	$-0.423896\pi$
$509$	10.6856	0.473633	0.236816	+	0.971554i	$0.423896\pi$
$510$	0.372736	0.0165050
$511$	−28.2068	−1.24779
$512$	−22.0159	−0.972977
$513$	−2.56973	−0.113457
$514$	−35.3279	−1.55825
$515$	6.56937	0.289481
$516$	−0.744502	−0.0327749
$517$	6.30203	0.277163
$518$	3.13905	0.137922
$519$	−2.02838	−0.0890360
$520$	−5.04730	−0.221339
$521$	−17.9453	−0.786196	−0.393098	−	0.919497i	$-0.628597\pi$
$521$	−17.9453	−0.786196	−0.393098	+	0.919497i	$0.628597\pi$
$522$	−3.83850	−0.168007
$523$	−11.1316	−0.486749	−0.243374	−	0.969932i	$-0.578254\pi$
$523$	−11.1316	−0.486749	−0.243374	+	0.969932i	$0.578254\pi$
$524$	11.2067	0.489568
$525$	4.25737	0.185807
$526$	10.8099	0.471336
$527$	−3.36767	−0.146698
$528$	−0.565526	−0.0246114
$529$	34.2757	1.49025
$530$	−8.71421	−0.378521
$531$	−8.98398	−0.389871
$532$	−14.4540	−0.626660
$533$	−58.7781	−2.54596
$534$	−3.34288	−0.144660
$535$	−3.85049	−0.166471
$536$	−7.44755	−0.321685
$537$	0.937429	0.0404530
$538$	−15.0205	−0.647580
$539$	4.34318	0.187074
$540$	2.76061	0.118798
$541$	−20.6835	−0.889254	−0.444627	−	0.895716i	$-0.646664\pi$
$541$	−20.6835	−0.889254	−0.444627	+	0.895716i	$0.646664\pi$
$542$	17.0604	0.732805
$543$	−6.63244	−0.284625
$544$	7.57749	0.324882
$545$	3.35830	0.143854
$546$	−10.4327	−0.446480
$547$	9.35704	0.400078	0.200039	−	0.979788i	$-0.435893\pi$
$547$	9.35704	0.400078	0.200039	+	0.979788i	$0.435893\pi$
$548$	−16.3131	−0.696862
$549$	21.2383	0.906430
$550$	10.0056	0.426641
$551$	−0.955777	−0.0407175
$552$	−3.21892	−0.137006
$553$	4.32049	0.183726
$554$	−36.1108	−1.53420
$555$	−0.0736934	−0.00312811
$556$	29.3638	1.24530
$557$	−11.4233	−0.484019	−0.242009	−	0.970274i	$-0.577807\pi$
$557$	−11.4233	−0.484019	−0.242009	+	0.970274i	$0.577807\pi$
$558$	−21.3856	−0.905324
$559$	5.20112	0.219984
$560$	−4.34568	−0.183638
$561$	0.274303	0.0115811
$562$	14.0710	0.593551
$563$	37.4121	1.57673	0.788366	−	0.615207i	$-0.210928\pi$
$563$	37.4121	1.57673	0.788366	+	0.615207i	$0.210928\pi$
$564$	4.69187	0.197563
$565$	4.82524	0.203000
$566$	−4.01487	−0.168757
$567$	−28.0500	−1.17799
$568$	0.404141	0.0169574
$569$	14.9417	0.626390	0.313195	−	0.949689i	$-0.398601\pi$
$569$	14.9417	0.626390	0.313195	+	0.949689i	$0.398601\pi$
$570$	0.589370	0.0246860
$571$	−2.68391	−0.112318	−0.0561592	−	0.998422i	$-0.517885\pi$
$571$	−2.68391	−0.112318	−0.0561592	+	0.998422i	$0.517885\pi$
$572$	−14.1166	−0.590247
$573$	−6.84614	−0.286002
$574$	82.6395	3.44931
$575$	−34.8761	−1.45443
$576$	36.0592	1.50247
$577$	−14.4336	−0.600877	−0.300439	−	0.953801i	$-0.597133\pi$
$577$	−14.4336	−0.600877	−0.300439	+	0.953801i	$0.597133\pi$
$578$	−2.17121	−0.0903104
$579$	4.11731	0.171110
$580$	1.02677	0.0426343
$581$	−38.1788	−1.58392
$582$	1.53172	0.0634918
$583$	−6.41295	−0.265597
$584$	−12.9861	−0.537369
$585$	−9.52041	−0.393621
$586$	−56.3888	−2.32940
$587$	1.22596	0.0506007	0.0253003	−	0.999680i	$-0.491946\pi$
$587$	1.22596	0.0506007	0.0253003	+	0.999680i	$0.491946\pi$
$588$	3.23351	0.133348
$589$	−5.32495	−0.219411
$590$	4.17397	0.171840
$591$	−2.19602	−0.0903324
$592$	−0.885014	−0.0363738
$593$	−9.75990	−0.400791	−0.200396	−	0.979715i	$-0.564223\pi$
$593$	−9.75990	−0.400791	−0.200396	+	0.979715i	$0.564223\pi$
$594$	3.52861	0.144781
$595$	2.10783	0.0864127
$596$	−21.7200	−0.889685
$597$	1.69830	0.0695068
$598$	85.4642	3.49489
$599$	1.06649	0.0435755	0.0217877	−	0.999763i	$-0.493064\pi$
$599$	1.06649	0.0435755	0.0217877	+	0.999763i	$0.493064\pi$
$600$	1.96005	0.0800186
$601$	12.7502	0.520090	0.260045	−	0.965597i	$-0.416263\pi$
$601$	12.7502	0.520090	0.260045	+	0.965597i	$0.416263\pi$
$602$	−7.31256	−0.298038
$603$	−14.0479	−0.572073
$604$	48.2756	1.96431
$605$	−0.625848	−0.0254443
$606$	−5.00791	−0.203432
$607$	1.65117	0.0670189	0.0335094	−	0.999438i	$-0.489332\pi$
$607$	1.65117	0.0670189	0.0335094	+	0.999438i	$0.489332\pi$
$608$	11.9815	0.485915
$609$	0.558430	0.0226287
$610$	−9.86737	−0.399518
$611$	−32.7776	−1.32604
$612$	−7.93824	−0.320884
$613$	40.6819	1.64313	0.821563	−	0.570118i	$-0.193103\pi$
$613$	40.6819	1.64313	0.821563	+	0.570118i	$0.193103\pi$
$614$	69.3974	2.80065
$615$	−1.94007	−0.0782314
$616$	5.22228	0.210412
$617$	−6.84645	−0.275628	−0.137814	−	0.990458i	$-0.544008\pi$
$617$	−6.84645	−0.275628	−0.137814	+	0.990458i	$0.544008\pi$
$618$	6.25156	0.251475
$619$	−28.2813	−1.13672	−0.568360	−	0.822780i	$-0.692422\pi$
$619$	−28.2813	−1.13672	−0.568360	+	0.822780i	$0.692422\pi$
$620$	5.72048	0.229740
$621$	−12.2995	−0.493562
$622$	32.6010	1.30718
$623$	−18.9040	−0.757374
$624$	2.94137	0.117749
$625$	19.2781	0.771125
$626$	11.3356	0.453063
$627$	0.433728	0.0173214
$628$	−0.676897	−0.0270111
$629$	0.429268	0.0171160
$630$	13.3853	0.533283
$631$	−27.9950	−1.11446	−0.557231	−	0.830357i	$-0.688136\pi$
$631$	−27.9950	−1.11446	−0.557231	+	0.830357i	$0.688136\pi$
$632$	1.98911	0.0791225
$633$	−3.75401	−0.149209
$634$	62.4858	2.48163
$635$	−11.0896	−0.440078
$636$	−4.77445	−0.189319
$637$	−22.5894	−0.895026
$638$	1.31242	0.0519591
$639$	0.762307	0.0301564
$640$	−7.26846	−0.287311
$641$	−40.8502	−1.61349	−0.806744	−	0.590902i	$-0.798772\pi$
$641$	−40.8502	−1.61349	−0.806744	+	0.590902i	$0.798772\pi$
$642$	−3.66421	−0.144615
$643$	−8.58507	−0.338562	−0.169281	−	0.985568i	$-0.554145\pi$
$643$	−8.58507	−0.338562	−0.169281	+	0.985568i	$0.554145\pi$
$644$	−69.1810	−2.72611
$645$	0.171672	0.00675959
$646$	−3.43311	−0.135074
$647$	−27.5062	−1.08138	−0.540690	−	0.841222i	$-0.681837\pi$
$647$	−27.5062	−1.08138	−0.540690	+	0.841222i	$0.681837\pi$
$648$	−12.9139	−0.507307
$649$	3.07170	0.120575
$650$	−52.0405	−2.04120
$651$	3.11120	0.121938
$652$	31.7621	1.24390
$653$	44.1990	1.72964	0.864820	−	0.502082i	$-0.167432\pi$
$653$	44.1990	1.72964	0.864820	+	0.502082i	$0.167432\pi$
$654$	3.19584	0.124967
$655$	−2.58412	−0.100970
$656$	−23.2991	−0.909678
$657$	−24.4949	−0.955637
$658$	46.0839	1.79654
$659$	3.10099	0.120797	0.0603987	−	0.998174i	$-0.480763\pi$
$659$	3.10099	0.120797	0.0603987	+	0.998174i	$0.480763\pi$
$660$	−0.465945	−0.0181369
$661$	−15.9019	−0.618514	−0.309257	−	0.950979i	$-0.600080\pi$
$661$	−15.9019	−0.618514	−0.309257	+	0.950979i	$0.600080\pi$
$662$	−40.9141	−1.59017
$663$	−1.42669	−0.0554079
$664$	−17.5771	−0.682124
$665$	3.33290	0.129244
$666$	2.72597	0.105629
$667$	−4.57462	−0.177130
$668$	−35.8575	−1.38737
$669$	−1.34154	−0.0518670
$670$	6.52666	0.252147
$671$	−7.26157	−0.280330
$672$	−7.00042	−0.270047
$673$	−24.6144	−0.948816	−0.474408	−	0.880305i	$-0.657338\pi$
$673$	−24.6144	−0.948816	−0.474408	+	0.880305i	$0.657338\pi$
$674$	−6.99769	−0.269541
$675$	7.48935	0.288265
$676$	38.1384	1.46686
$677$	22.6827	0.871769	0.435884	−	0.900003i	$-0.356436\pi$
$677$	22.6827	0.871769	0.435884	+	0.900003i	$0.356436\pi$
$678$	4.59181	0.176347
$679$	8.66191	0.332413
$680$	0.970424	0.0372141
$681$	1.75605	0.0672919
$682$	7.31192	0.279988
$683$	23.7689	0.909492	0.454746	−	0.890621i	$-0.349730\pi$
$683$	23.7689	0.909492	0.454746	+	0.890621i	$0.349730\pi$
$684$	−12.5519	−0.479935
$685$	3.76159	0.143723
$686$	−19.4281	−0.741769
$687$	−6.33915	−0.241854
$688$	2.06168	0.0786008
$689$	33.3545	1.27071
$690$	2.82090	0.107390
$691$	−23.5790	−0.896987	−0.448493	−	0.893786i	$-0.648039\pi$
$691$	−23.5790	−0.896987	−0.448493	+	0.893786i	$0.648039\pi$
$692$	−20.0702	−0.762956
$693$	9.85048	0.374189
$694$	−9.60661	−0.364662
$695$	−6.77090	−0.256835
$696$	0.257095	0.00974518
$697$	11.3010	0.428057
$698$	−18.1261	−0.686082
$699$	−0.762797	−0.0288517
$700$	42.1254	1.59219
$701$	0.747009	0.0282141	0.0141071	−	0.999900i	$-0.495509\pi$
$701$	0.747009	0.0282141	0.0141071	+	0.999900i	$0.495509\pi$
$702$	−18.3527	−0.692680
$703$	0.678758	0.0255998
$704$	−12.3290	−0.464665
$705$	−1.08188	−0.0407461
$706$	47.4914	1.78736
$707$	−28.3198	−1.06508
$708$	2.28689	0.0859464
$709$	25.4866	0.957168	0.478584	−	0.878042i	$-0.341150\pi$
$709$	25.4866	0.957168	0.478584	+	0.878042i	$0.341150\pi$
$710$	−0.354169	−0.0132917
$711$	3.75194	0.140709
$712$	−8.70322	−0.326167
$713$	−25.4868	−0.954487
$714$	2.00586	0.0750674
$715$	3.25511	0.121734
$716$	9.27558	0.346645
$717$	−5.25616	−0.196295
$718$	−70.7294	−2.63960
$719$	−46.8929	−1.74881	−0.874405	−	0.485196i	$-0.838748\pi$
$719$	−46.8929	−1.74881	−0.874405	+	0.485196i	$0.838748\pi$
$720$	−3.77381	−0.140642
$721$	35.3527	1.31660
$722$	35.8246	1.33325
$723$	−4.29575	−0.159761
$724$	−65.6261	−2.43897
$725$	2.78556	0.103453
$726$	−0.595570	−0.0221037
$727$	11.1622	0.413984	0.206992	−	0.978343i	$-0.433633\pi$
$727$	11.1622	0.413984	0.206992	+	0.978343i	$0.433633\pi$
$728$	−27.1617	−1.00668
$729$	−23.0214	−0.852645
$730$	11.3804	0.421206
$731$	−1.00000	−0.0369863
$732$	−5.40625	−0.199821
$733$	10.3014	0.380489	0.190245	−	0.981737i	$-0.439072\pi$
$733$	10.3014	0.380489	0.190245	+	0.981737i	$0.439072\pi$
$734$	36.1300	1.33358
$735$	−0.745604	−0.0275020
$736$	57.3470	2.11384
$737$	4.80309	0.176924
$738$	71.7646	2.64169
$739$	29.5454	1.08684	0.543422	−	0.839460i	$-0.317128\pi$
$739$	29.5454	1.08684	0.543422	+	0.839460i	$0.317128\pi$
$740$	−0.729175	−0.0268050
$741$	−2.25587	−0.0828716
$742$	−46.8950	−1.72157
$743$	21.1921	0.777461	0.388730	−	0.921352i	$-0.372914\pi$
$743$	21.1921	0.777461	0.388730	+	0.921352i	$0.372914\pi$
$744$	1.43236	0.0525130
$745$	5.00834	0.183491
$746$	61.6740	2.25805
$747$	−33.1547	−1.21307
$748$	2.71415	0.0992393
$749$	−20.7212	−0.757137
$750$	−3.58137	−0.130773
$751$	−19.2916	−0.703959	−0.351980	−	0.936008i	$-0.614491\pi$
$751$	−19.2916	−0.703959	−0.351980	+	0.936008i	$0.614491\pi$
$752$	−12.9928	−0.473797
$753$	7.41150	0.270090
$754$	−6.82605	−0.248590
$755$	−11.1317	−0.405125
$756$	14.8561	0.540310
$757$	5.85695	0.212875	0.106437	−	0.994319i	$-0.466056\pi$
$757$	5.85695	0.212875	0.106437	+	0.994319i	$0.466056\pi$
$758$	10.2176	0.371121
$759$	2.07595	0.0753522
$760$	1.53443	0.0556597
$761$	−21.8434	−0.791822	−0.395911	−	0.918289i	$-0.629571\pi$
$761$	−21.8434	−0.791822	−0.395911	+	0.918289i	$0.629571\pi$
$762$	−10.5531	−0.382299
$763$	18.0725	0.654269
$764$	−67.7406	−2.45077
$765$	1.83045	0.0661802
$766$	−53.3601	−1.92798
$767$	−15.9763	−0.576870
$768$	−0.153074	−0.00552357
$769$	−22.3509	−0.805993	−0.402997	−	0.915201i	$-0.632031\pi$
$769$	−22.3509	−0.805993	−0.402997	+	0.915201i	$0.632031\pi$
$770$	−4.57655	−0.164927
$771$	4.46321	0.160739
$772$	40.7396	1.46625
$773$	2.63808	0.0948851	0.0474425	−	0.998874i	$-0.484893\pi$
$773$	2.63808	0.0948851	0.0474425	+	0.998874i	$0.484893\pi$
$774$	−6.35026	−0.228255
$775$	15.5193	0.557469
$776$	3.98785	0.143156
$777$	−0.396577	−0.0142271
$778$	10.9074	0.391047
$779$	17.8692	0.640230
$780$	2.42344	0.0867729
$781$	−0.260639	−0.00932641
$782$	−16.4319	−0.587603
$783$	0.982363	0.0351068
$784$	−8.95425	−0.319795
$785$	0.156083	0.00557086
$786$	−2.45911	−0.0877135
$787$	−23.5140	−0.838182	−0.419091	−	0.907944i	$-0.637651\pi$
$787$	−23.5140	−0.838182	−0.419091	+	0.907944i	$0.637651\pi$
$788$	−21.7290	−0.774064
$789$	−1.36569	−0.0486200
$790$	−1.74316	−0.0620187
$791$	25.9668	0.923272
$792$	4.53506	0.161146
$793$	37.7683	1.34119
$794$	−35.4859	−1.25935
$795$	1.10092	0.0390458
$796$	16.8042	0.595608
$797$	13.9854	0.495389	0.247694	−	0.968838i	$-0.420327\pi$
$797$	13.9854	0.495389	0.247694	+	0.968838i	$0.420327\pi$
$798$	3.17166	0.112276
$799$	6.30203	0.222950
$800$	−34.9195	−1.23459
$801$	−16.4164	−0.580044
$802$	21.7622	0.768451
$803$	8.37502	0.295548
$804$	3.57591	0.126113
$805$	15.9522	0.562242
$806$	−38.0302	−1.33956
$807$	1.89764	0.0668001
$808$	−13.0382	−0.458681
$809$	−13.5802	−0.477456	−0.238728	−	0.971087i	$-0.576730\pi$
$809$	−13.5802	−0.477456	−0.238728	+	0.971087i	$0.576730\pi$
$810$	11.3171	0.397643
$811$	−24.9459	−0.875970	−0.437985	−	0.898982i	$-0.644308\pi$
$811$	−24.9459	−0.875970	−0.437985	+	0.898982i	$0.644308\pi$
$812$	5.52550	0.193907
$813$	−2.15535	−0.0755914
$814$	−0.932031	−0.0326677
$815$	−7.32393	−0.256546
$816$	−0.565526	−0.0197974
$817$	−1.58120	−0.0553191
$818$	8.13932	0.284585
$819$	−51.2336	−1.79025
$820$	−19.1965	−0.670370
$821$	39.5627	1.38075	0.690374	−	0.723453i	$-0.257446\pi$
$821$	39.5627	1.38075	0.690374	+	0.723453i	$0.257446\pi$
$822$	3.57961	0.124853
$823$	14.3249	0.499333	0.249666	−	0.968332i	$-0.419679\pi$
$823$	14.3249	0.499333	0.249666	+	0.968332i	$0.419679\pi$
$824$	16.2760	0.567002
$825$	−1.26408	−0.0440095
$826$	22.4620	0.781552
$827$	−11.2384	−0.390798	−0.195399	−	0.980724i	$-0.562600\pi$
$827$	−11.2384	−0.390798	−0.195399	+	0.980724i	$0.562600\pi$
$828$	−60.0772	−2.08783
$829$	7.52084	0.261210	0.130605	−	0.991435i	$-0.458308\pi$
$829$	7.52084	0.261210	0.130605	+	0.991435i	$0.458308\pi$
$830$	15.4037	0.534670
$831$	4.56212	0.158258
$832$	64.1245	2.22312
$833$	4.34318	0.150482
$834$	−6.44334	−0.223115
$835$	8.26827	0.286135
$836$	4.29161	0.148429
$837$	5.47307	0.189177
$838$	−15.8357	−0.547037
$839$	−36.7227	−1.26781	−0.633904	−	0.773412i	$-0.718548\pi$
$839$	−36.7227	−1.26781	−0.633904	+	0.773412i	$0.718548\pi$
$840$	−0.896521	−0.0309329
$841$	−28.6346	−0.987401
$842$	66.4716	2.29076
$843$	−1.77769	−0.0612269
$844$	−37.1449	−1.27858
$845$	−8.79422	−0.302530
$846$	40.0195	1.37590
$847$	−3.36796	−0.115725
$848$	13.2214	0.454026
$849$	0.507225	0.0174079
$850$	10.0056	0.343190
$851$	3.24873	0.111365
$852$	−0.194046	−0.00664792
$853$	6.04936	0.207126	0.103563	−	0.994623i	$-0.466976\pi$
$853$	6.04936	0.207126	0.103563	+	0.994623i	$0.466976\pi$
$854$	−53.1007	−1.81707
$855$	2.89431	0.0989833
$856$	−9.53983	−0.326065
$857$	−29.9290	−1.02235	−0.511177	−	0.859476i	$-0.670790\pi$
$857$	−29.9290	−1.02235	−0.511177	+	0.859476i	$0.670790\pi$
$858$	3.09764	0.105752
$859$	−9.21307	−0.314346	−0.157173	−	0.987571i	$-0.550238\pi$
$859$	−9.21307	−0.314346	−0.157173	+	0.987571i	$0.550238\pi$
$860$	1.69865	0.0579234
$861$	−10.4404	−0.355808
$862$	−85.5231	−2.91293
$863$	−32.9024	−1.12001	−0.560005	−	0.828489i	$-0.689201\pi$
$863$	−32.9024	−1.12001	−0.560005	+	0.828489i	$0.689201\pi$
$864$	−12.3148	−0.418958
$865$	4.62793	0.157354
$866$	41.5049	1.41040
$867$	0.274303	0.00931584
$868$	30.7844	1.04489
$869$	−1.28282	−0.0435167
$870$	−0.225306	−0.00763857
$871$	−24.9815	−0.846464
$872$	8.32040	0.281764
$873$	7.52204	0.254583
$874$	−25.9821	−0.878856
$875$	−20.2527	−0.684667
$876$	6.23522	0.210668
$877$	−0.572287	−0.0193248	−0.00966238	−	0.999953i	$-0.503076\pi$
$877$	−0.572287	−0.0193248	−0.00966238	+	0.999953i	$0.503076\pi$
$878$	51.2808	1.73064
$879$	7.12398	0.240286
$880$	1.29030	0.0434959
$881$	−27.1909	−0.916085	−0.458043	−	0.888930i	$-0.651449\pi$
$881$	−27.1909	−0.916085	−0.458043	+	0.888930i	$0.651449\pi$
$882$	27.5804	0.928679
$883$	11.6270	0.391278	0.195639	−	0.980676i	$-0.437322\pi$
$883$	11.6270	0.391278	0.195639	+	0.980676i	$0.437322\pi$
$884$	−14.1166	−0.474794
$885$	−0.527325	−0.0177259
$886$	−28.1368	−0.945275
$887$	−49.2836	−1.65478	−0.827390	−	0.561628i	$-0.810175\pi$
$887$	−49.2836	−1.65478	−0.827390	+	0.561628i	$0.810175\pi$
$888$	−0.182580	−0.00612698
$889$	−59.6782	−2.00154
$890$	7.62707	0.255660
$891$	8.32848	0.279015
$892$	−13.2742	−0.444452
$893$	9.96475	0.333458
$894$	4.76605	0.159400
$895$	−2.13883	−0.0714931
$896$	−39.1148	−1.30673
$897$	−10.7973	−0.360510
$898$	11.5410	0.385129
$899$	2.03563	0.0678922
$900$	36.5819	1.21940
$901$	−6.41295	−0.213646
$902$	−24.5369	−0.816990
$903$	0.923844	0.0307436
$904$	11.9548	0.397612
$905$	15.1325	0.503022
$906$	−10.5932	−0.351935
$907$	−15.9313	−0.528992	−0.264496	−	0.964387i	$-0.585206\pi$
$907$	−15.9313	−0.528992	−0.264496	+	0.964387i	$0.585206\pi$
$908$	17.3756	0.576629
$909$	−24.5931	−0.815702
$910$	23.8032	0.789068
$911$	−51.0527	−1.69145	−0.845725	−	0.533619i	$-0.820832\pi$
$911$	−51.0527	−1.69145	−0.845725	+	0.533619i	$0.820832\pi$
$912$	−0.894209	−0.0296102
$913$	11.3359	0.375162
$914$	−11.4980	−0.380319
$915$	1.24661	0.0412117
$916$	−62.7240	−2.07246
$917$	−13.9063	−0.459227
$918$	3.52861	0.116462
$919$	−14.8719	−0.490579	−0.245289	−	0.969450i	$-0.578883\pi$
$919$	−14.8719	−0.490579	−0.245289	+	0.969450i	$0.578883\pi$
$920$	7.34424	0.242132
$921$	−8.76744	−0.288897
$922$	70.6941	2.32819
$923$	1.35562	0.0446207
$924$	−2.50745	−0.0824892
$925$	−1.97820	−0.0650429
$926$	−46.1436	−1.51637
$927$	30.7005	1.00834
$928$	−4.58032	−0.150356
$929$	−54.1348	−1.77611	−0.888053	−	0.459742i	$-0.847942\pi$
$929$	−54.1348	−1.77611	−0.888053	+	0.459742i	$0.847942\pi$
$930$	−1.25525	−0.0411614
$931$	6.86743	0.225071
$932$	−7.54766	−0.247232
$933$	−4.11870	−0.134840
$934$	−5.60940	−0.183545
$935$	−0.625848	−0.0204674
$936$	−23.5874	−0.770978
$937$	19.8746	0.649275	0.324638	−	0.945839i	$-0.394758\pi$
$937$	19.8746	0.649275	0.324638	+	0.945839i	$0.394758\pi$
$938$	35.1229	1.14680
$939$	−1.43211	−0.0467350
$940$	−10.7049	−0.349156
$941$	2.79502	0.0911152	0.0455576	−	0.998962i	$-0.485494\pi$
$941$	2.79502	0.0911152	0.0455576	+	0.998962i	$0.485494\pi$
$942$	0.148532	0.00483945
$943$	85.5271	2.78515
$944$	−6.33286	−0.206117
$945$	−3.42561	−0.111435
$946$	2.17121	0.0705921
$947$	−8.92734	−0.290100	−0.145050	−	0.989424i	$-0.546334\pi$
$947$	−8.92734	−0.290100	−0.145050	+	0.989424i	$0.546334\pi$
$948$	−0.955062	−0.0310190
$949$	−43.5595	−1.41400
$950$	15.8209	0.513297
$951$	−7.89425	−0.255989
$952$	5.22228	0.169255
$953$	18.7671	0.607926	0.303963	−	0.952684i	$-0.401690\pi$
$953$	18.7671	0.607926	0.303963	+	0.952684i	$0.401690\pi$
$954$	−40.7239	−1.31848
$955$	15.6201	0.505454
$956$	−52.0081	−1.68206
$957$	−0.165806	−0.00535976
$958$	−51.0432	−1.64913
$959$	20.2428	0.653673
$960$	2.11654	0.0683111
$961$	−19.6588	−0.634155
$962$	4.84761	0.156293
$963$	−17.9944	−0.579862
$964$	−42.5052	−1.36900
$965$	−9.39402	−0.302404
$966$	15.1805	0.488424
$967$	10.5986	0.340827	0.170413	−	0.985373i	$-0.445490\pi$
$967$	10.5986	0.340827	0.170413	+	0.985373i	$0.445490\pi$
$968$	−1.55058	−0.0498374
$969$	0.433728	0.0139334
$970$	−3.49475	−0.112210
$971$	19.0626	0.611747	0.305873	−	0.952072i	$-0.401052\pi$
$971$	19.0626	0.611747	0.305873	+	0.952072i	$0.401052\pi$
$972$	19.4335	0.623331
$973$	−36.4372	−1.16812
$974$	−24.1122	−0.772606
$975$	6.57462	0.210556
$976$	14.9710	0.479211
$977$	23.0302	0.736801	0.368400	−	0.929667i	$-0.379906\pi$
$977$	23.0302	0.736801	0.368400	+	0.929667i	$0.379906\pi$
$978$	−6.96961	−0.222864
$979$	5.61290	0.179389
$980$	−7.37753	−0.235667
$981$	15.6943	0.501080
$982$	15.9076	0.507633
$983$	−23.8634	−0.761124	−0.380562	−	0.924755i	$-0.624269\pi$
$983$	−23.8634	−0.761124	−0.380562	+	0.924755i	$0.624269\pi$
$984$	−4.80665	−0.153230
$985$	5.01042	0.159645
$986$	1.31242	0.0417959
$987$	−5.82209	−0.185319
$988$	−22.3212	−0.710132
$989$	−7.56807	−0.240651
$990$	−3.97430	−0.126311
$991$	−51.7865	−1.64505	−0.822526	−	0.568728i	$-0.807436\pi$
$991$	−51.7865	−1.64505	−0.822526	+	0.568728i	$0.807436\pi$
$992$	−25.5185	−0.810213
$993$	5.16895	0.164032
$994$	−1.90594	−0.0604527
$995$	−3.87482	−0.122840
$996$	8.43957	0.267418
$997$	−51.0742	−1.61754	−0.808768	−	0.588128i	$-0.799865\pi$
$997$	−51.0742	−1.61754	−0.808768	+	0.588128i	$0.799865\pi$
$998$	−28.6557	−0.907081
$999$	−0.697639	−0.0220723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.9	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17121 q^{2} +0.274303 q^{3} +2.71415 q^{4} -0.625848 q^{5} -0.595570 q^{6} -3.36796 q^{7} -1.55058 q^{8} -2.92476 q^{9} +O(q^{10})\)	\(q-2.17121 q^{2} +0.274303 q^{3} +2.71415 q^{4} -0.625848 q^{5} -0.595570 q^{6} -3.36796 q^{7} -1.55058 q^{8} -2.92476 q^{9} +1.35885 q^{10} +1.00000 q^{11} +0.744502 q^{12} -5.20112 q^{13} +7.31256 q^{14} -0.171672 q^{15} -2.06168 q^{16} +1.00000 q^{17} +6.35026 q^{18} +1.58120 q^{19} -1.69865 q^{20} -0.923844 q^{21} -2.17121 q^{22} +7.56807 q^{23} -0.425328 q^{24} -4.60831 q^{25} +11.2927 q^{26} -1.62518 q^{27} -9.14117 q^{28} -0.604464 q^{29} +0.372736 q^{30} -3.36767 q^{31} +7.57749 q^{32} +0.274303 q^{33} -2.17121 q^{34} +2.10783 q^{35} -7.93824 q^{36} +0.429268 q^{37} -3.43311 q^{38} -1.42669 q^{39} +0.970424 q^{40} +11.3010 q^{41} +2.00586 q^{42} -1.00000 q^{43} +2.71415 q^{44} +1.83045 q^{45} -16.4319 q^{46} +6.30203 q^{47} -0.565526 q^{48} +4.34318 q^{49} +10.0056 q^{50} +0.274303 q^{51} -14.1166 q^{52} -6.41295 q^{53} +3.52861 q^{54} -0.625848 q^{55} +5.22228 q^{56} +0.433728 q^{57} +1.31242 q^{58} +3.07170 q^{59} -0.465945 q^{60} -7.26157 q^{61} +7.31192 q^{62} +9.85048 q^{63} -12.3290 q^{64} +3.25511 q^{65} -0.595570 q^{66} +4.80309 q^{67} +2.71415 q^{68} +2.07595 q^{69} -4.57655 q^{70} -0.260639 q^{71} +4.53506 q^{72} +8.37502 q^{73} -0.932031 q^{74} -1.26408 q^{75} +4.29161 q^{76} -3.36796 q^{77} +3.09764 q^{78} -1.28282 q^{79} +1.29030 q^{80} +8.32848 q^{81} -24.5369 q^{82} +11.3359 q^{83} -2.50745 q^{84} -0.625848 q^{85} +2.17121 q^{86} -0.165806 q^{87} -1.55058 q^{88} +5.61290 q^{89} -3.97430 q^{90} +17.5172 q^{91} +20.5409 q^{92} -0.923763 q^{93} -13.6830 q^{94} -0.989589 q^{95} +2.07853 q^{96} -2.57185 q^{97} -9.42996 q^{98} -2.92476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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