LMFDB - Embedded newform 6010.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.29642 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.29642 q^{6} -4.86493 q^{7} +1.00000 q^{8} +2.27356 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.29642 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.29642 q^{6} -4.86493 q^{7} +1.00000 q^{8} +2.27356 q^{9} -1.00000 q^{10} +5.18828 q^{11} -2.29642 q^{12} +0.351286 q^{13} -4.86493 q^{14} +2.29642 q^{15} +1.00000 q^{16} -3.00662 q^{17} +2.27356 q^{18} +1.17341 q^{19} -1.00000 q^{20} +11.1719 q^{21} +5.18828 q^{22} -7.07517 q^{23} -2.29642 q^{24} +1.00000 q^{25} +0.351286 q^{26} +1.66821 q^{27} -4.86493 q^{28} +1.56276 q^{29} +2.29642 q^{30} +4.54876 q^{31} +1.00000 q^{32} -11.9145 q^{33} -3.00662 q^{34} +4.86493 q^{35} +2.27356 q^{36} +3.19708 q^{37} +1.17341 q^{38} -0.806701 q^{39} -1.00000 q^{40} +2.43460 q^{41} +11.1719 q^{42} +8.67292 q^{43} +5.18828 q^{44} -2.27356 q^{45} -7.07517 q^{46} -1.71095 q^{47} -2.29642 q^{48} +16.6675 q^{49} +1.00000 q^{50} +6.90448 q^{51} +0.351286 q^{52} -11.2342 q^{53} +1.66821 q^{54} -5.18828 q^{55} -4.86493 q^{56} -2.69464 q^{57} +1.56276 q^{58} -2.89191 q^{59} +2.29642 q^{60} -4.11226 q^{61} +4.54876 q^{62} -11.0607 q^{63} +1.00000 q^{64} -0.351286 q^{65} -11.9145 q^{66} +7.34519 q^{67} -3.00662 q^{68} +16.2476 q^{69} +4.86493 q^{70} -0.875606 q^{71} +2.27356 q^{72} +4.65314 q^{73} +3.19708 q^{74} -2.29642 q^{75} +1.17341 q^{76} -25.2406 q^{77} -0.806701 q^{78} +8.99154 q^{79} -1.00000 q^{80} -10.6516 q^{81} +2.43460 q^{82} -10.1143 q^{83} +11.1719 q^{84} +3.00662 q^{85} +8.67292 q^{86} -3.58876 q^{87} +5.18828 q^{88} +12.2406 q^{89} -2.27356 q^{90} -1.70898 q^{91} -7.07517 q^{92} -10.4459 q^{93} -1.71095 q^{94} -1.17341 q^{95} -2.29642 q^{96} +0.409677 q^{97} +16.6675 q^{98} +11.7959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.29642	−1.32584	−0.662921	−	0.748690i	$-0.730683\pi$
$3$	−2.29642	−1.32584	−0.662921	+	0.748690i	$0.730683\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.29642	−0.937511
$7$	−4.86493	−1.83877	−0.919385	−	0.393359i	$-0.871313\pi$
$7$	−4.86493	−1.83877	−0.919385	+	0.393359i	$0.871313\pi$
$8$	1.00000	0.353553
$9$	2.27356	0.757854
$10$	−1.00000	−0.316228
$11$	5.18828	1.56433	0.782163	−	0.623074i	$-0.214117\pi$
$11$	5.18828	1.56433	0.782163	+	0.623074i	$0.214117\pi$
$12$	−2.29642	−0.662921
$13$	0.351286	0.0974291	0.0487145	−	0.998813i	$-0.484488\pi$
$13$	0.351286	0.0974291	0.0487145	+	0.998813i	$0.484488\pi$
$14$	−4.86493	−1.30021
$15$	2.29642	0.592934
$16$	1.00000	0.250000
$17$	−3.00662	−0.729213	−0.364606	−	0.931162i	$-0.618796\pi$
$17$	−3.00662	−0.729213	−0.364606	+	0.931162i	$0.618796\pi$
$18$	2.27356	0.535884
$19$	1.17341	0.269198	0.134599	−	0.990900i	$-0.457025\pi$
$19$	1.17341	0.269198	0.134599	+	0.990900i	$0.457025\pi$
$20$	−1.00000	−0.223607
$21$	11.1719	2.43792
$22$	5.18828	1.10614
$23$	−7.07517	−1.47528	−0.737638	−	0.675197i	$-0.764059\pi$
$23$	−7.07517	−1.47528	−0.737638	+	0.675197i	$0.764059\pi$
$24$	−2.29642	−0.468756
$25$	1.00000	0.200000
$26$	0.351286	0.0688928
$27$	1.66821	0.321047
$28$	−4.86493	−0.919385
$29$	1.56276	0.290197	0.145099	−	0.989417i	$-0.453650\pi$
$29$	1.56276	0.290197	0.145099	+	0.989417i	$0.453650\pi$
$30$	2.29642	0.419268
$31$	4.54876	0.816981	0.408491	−	0.912763i	$-0.366055\pi$
$31$	4.54876	0.816981	0.408491	+	0.912763i	$0.366055\pi$
$32$	1.00000	0.176777
$33$	−11.9145	−2.07405
$34$	−3.00662	−0.515631
$35$	4.86493	0.822323
$36$	2.27356	0.378927
$37$	3.19708	0.525597	0.262798	−	0.964851i	$-0.415355\pi$
$37$	3.19708	0.525597	0.262798	+	0.964851i	$0.415355\pi$
$38$	1.17341	0.190352
$39$	−0.806701	−0.129175
$40$	−1.00000	−0.158114
$41$	2.43460	0.380221	0.190110	−	0.981763i	$-0.439115\pi$
$41$	2.43460	0.380221	0.190110	+	0.981763i	$0.439115\pi$
$42$	11.1719	1.72387
$43$	8.67292	1.32261	0.661304	−	0.750118i	$-0.270003\pi$
$43$	8.67292	1.32261	0.661304	+	0.750118i	$0.270003\pi$
$44$	5.18828	0.782163
$45$	−2.27356	−0.338923
$46$	−7.07517	−1.04318
$47$	−1.71095	−0.249568	−0.124784	−	0.992184i	$-0.539824\pi$
$47$	−1.71095	−0.249568	−0.124784	+	0.992184i	$0.539824\pi$
$48$	−2.29642	−0.331460
$49$	16.6675	2.38108
$50$	1.00000	0.141421
$51$	6.90448	0.966820
$52$	0.351286	0.0487145
$53$	−11.2342	−1.54314	−0.771568	−	0.636147i	$-0.780527\pi$
$53$	−11.2342	−1.54314	−0.771568	+	0.636147i	$0.780527\pi$
$54$	1.66821	0.227014
$55$	−5.18828	−0.699587
$56$	−4.86493	−0.650103
$57$	−2.69464	−0.356914
$58$	1.56276	0.205200
$59$	−2.89191	−0.376495	−0.188247	−	0.982122i	$-0.560281\pi$
$59$	−2.89191	−0.376495	−0.188247	+	0.982122i	$0.560281\pi$
$60$	2.29642	0.296467
$61$	−4.11226	−0.526521	−0.263261	−	0.964725i	$-0.584798\pi$
$61$	−4.11226	−0.526521	−0.263261	+	0.964725i	$0.584798\pi$
$62$	4.54876	0.577693
$63$	−11.0607	−1.39352
$64$	1.00000	0.125000
$65$	−0.351286	−0.0435716
$66$	−11.9145	−1.46657
$67$	7.34519	0.897357	0.448679	−	0.893693i	$-0.351895\pi$
$67$	7.34519	0.897357	0.448679	+	0.893693i	$0.351895\pi$
$68$	−3.00662	−0.364606
$69$	16.2476	1.95598
$70$	4.86493	0.581470
$71$	−0.875606	−0.103915	−0.0519577	−	0.998649i	$-0.516546\pi$
$71$	−0.875606	−0.103915	−0.0519577	+	0.998649i	$0.516546\pi$
$72$	2.27356	0.267942
$73$	4.65314	0.544608	0.272304	−	0.962211i	$-0.412214\pi$
$73$	4.65314	0.544608	0.272304	+	0.962211i	$0.412214\pi$
$74$	3.19708	0.371653
$75$	−2.29642	−0.265168
$76$	1.17341	0.134599
$77$	−25.2406	−2.87643
$78$	−0.806701	−0.0913409
$79$	8.99154	1.01163	0.505814	−	0.862643i	$-0.331192\pi$
$79$	8.99154	1.01163	0.505814	+	0.862643i	$0.331192\pi$
$80$	−1.00000	−0.111803
$81$	−10.6516	−1.18351
$82$	2.43460	0.268857
$83$	−10.1143	−1.11019	−0.555096	−	0.831787i	$-0.687318\pi$
$83$	−10.1143	−1.11019	−0.555096	+	0.831787i	$0.687318\pi$
$84$	11.1719	1.21896
$85$	3.00662	0.326114
$86$	8.67292	0.935225
$87$	−3.58876	−0.384755
$88$	5.18828	0.553072
$89$	12.2406	1.29750	0.648749	−	0.761003i	$-0.275293\pi$
$89$	12.2406	1.29750	0.648749	+	0.761003i	$0.275293\pi$
$90$	−2.27356	−0.239655
$91$	−1.70898	−0.179150
$92$	−7.07517	−0.737638
$93$	−10.4459	−1.08319
$94$	−1.71095	−0.176471
$95$	−1.17341	−0.120389
$96$	−2.29642	−0.234378
$97$	0.409677	0.0415964	0.0207982	−	0.999784i	$-0.493379\pi$
$97$	0.409677	0.0415964	0.0207982	+	0.999784i	$0.493379\pi$
$98$	16.6675	1.68367
$99$	11.7959	1.18553
$100$	1.00000	0.100000
$101$	−18.6442	−1.85516	−0.927581	−	0.373621i	$-0.878116\pi$
$101$	−18.6442	−1.85516	−0.927581	+	0.373621i	$0.878116\pi$
$102$	6.90448	0.683645
$103$	−10.1516	−1.00027	−0.500135	−	0.865947i	$-0.666716\pi$
$103$	−10.1516	−1.00027	−0.500135	+	0.865947i	$0.666716\pi$
$104$	0.351286	0.0344464
$105$	−11.1719	−1.09027
$106$	−11.2342	−1.09116
$107$	13.4821	1.30337	0.651684	−	0.758491i	$-0.274063\pi$
$107$	13.4821	1.30337	0.651684	+	0.758491i	$0.274063\pi$
$108$	1.66821	0.160523
$109$	−13.9899	−1.33999	−0.669997	−	0.742364i	$-0.733705\pi$
$109$	−13.9899	−1.33999	−0.669997	+	0.742364i	$0.733705\pi$
$110$	−5.18828	−0.494683
$111$	−7.34185	−0.696858
$112$	−4.86493	−0.459693
$113$	7.99207	0.751831	0.375915	−	0.926654i	$-0.377328\pi$
$113$	7.99207	0.751831	0.375915	+	0.926654i	$0.377328\pi$
$114$	−2.69464	−0.252376
$115$	7.07517	0.659763
$116$	1.56276	0.145099
$117$	0.798670	0.0738371
$118$	−2.89191	−0.266222
$119$	14.6270	1.34085
$120$	2.29642	0.209634
$121$	15.9182	1.44711
$122$	−4.11226	−0.372307
$123$	−5.59088	−0.504112
$124$	4.54876	0.408491
$125$	−1.00000	−0.0894427
$126$	−11.0607	−0.985367
$127$	6.50166	0.576929	0.288464	−	0.957491i	$-0.406855\pi$
$127$	6.50166	0.576929	0.288464	+	0.957491i	$0.406855\pi$
$128$	1.00000	0.0883883
$129$	−19.9167	−1.75357
$130$	−0.351286	−0.0308098
$131$	−0.675740	−0.0590397	−0.0295198	−	0.999564i	$-0.509398\pi$
$131$	−0.675740	−0.0590397	−0.0295198	+	0.999564i	$0.509398\pi$
$132$	−11.9145	−1.03702
$133$	−5.70855	−0.494994
$134$	7.34519	0.634527
$135$	−1.66821	−0.143576
$136$	−3.00662	−0.257816
$137$	3.27309	0.279639	0.139819	−	0.990177i	$-0.455348\pi$
$137$	3.27309	0.279639	0.139819	+	0.990177i	$0.455348\pi$
$138$	16.2476	1.38309
$139$	12.5350	1.06320	0.531600	−	0.846995i	$-0.321591\pi$
$139$	12.5350	1.06320	0.531600	+	0.846995i	$0.321591\pi$
$140$	4.86493	0.411162
$141$	3.92908	0.330888
$142$	−0.875606	−0.0734792
$143$	1.82257	0.152411
$144$	2.27356	0.189464
$145$	−1.56276	−0.129780
$146$	4.65314	0.385096
$147$	−38.2757	−3.15693
$148$	3.19708	0.262798
$149$	−15.6656	−1.28338	−0.641689	−	0.766965i	$-0.721766\pi$
$149$	−15.6656	−1.28338	−0.641689	+	0.766965i	$0.721766\pi$
$150$	−2.29642	−0.187502
$151$	3.26160	0.265425	0.132713	−	0.991155i	$-0.457631\pi$
$151$	3.26160	0.265425	0.132713	+	0.991155i	$0.457631\pi$
$152$	1.17341	0.0951760
$153$	−6.83574	−0.552637
$154$	−25.2406	−2.03395
$155$	−4.54876	−0.365365
$156$	−0.806701	−0.0645877
$157$	−13.8086	−1.10204	−0.551022	−	0.834490i	$-0.685762\pi$
$157$	−13.8086	−1.10204	−0.551022	+	0.834490i	$0.685762\pi$
$158$	8.99154	0.715328
$159$	25.7985	2.04595
$160$	−1.00000	−0.0790569
$161$	34.4202	2.71269
$162$	−10.6516	−0.836869
$163$	−14.7760	−1.15734	−0.578672	−	0.815560i	$-0.696429\pi$
$163$	−14.7760	−1.15734	−0.578672	+	0.815560i	$0.696429\pi$
$164$	2.43460	0.190110
$165$	11.9145	0.927542
$166$	−10.1143	−0.785024
$167$	−5.86065	−0.453511	−0.226755	−	0.973952i	$-0.572812\pi$
$167$	−5.86065	−0.453511	−0.226755	+	0.973952i	$0.572812\pi$
$168$	11.1719	0.861934
$169$	−12.8766	−0.990508
$170$	3.00662	0.230597
$171$	2.66782	0.204013
$172$	8.67292	0.661304
$173$	−25.4833	−1.93746	−0.968730	−	0.248118i	$-0.920188\pi$
$173$	−25.4833	−1.93746	−0.968730	+	0.248118i	$0.920188\pi$
$174$	−3.58876	−0.272063
$175$	−4.86493	−0.367754
$176$	5.18828	0.391081
$177$	6.64105	0.499172
$178$	12.2406	0.917469
$179$	−5.93790	−0.443820	−0.221910	−	0.975067i	$-0.571229\pi$
$179$	−5.93790	−0.443820	−0.221910	+	0.975067i	$0.571229\pi$
$180$	−2.27356	−0.169461
$181$	−20.0956	−1.49369	−0.746847	−	0.664996i	$-0.768433\pi$
$181$	−20.0956	−1.49369	−0.746847	+	0.664996i	$0.768433\pi$
$182$	−1.70898	−0.126678
$183$	9.44350	0.698083
$184$	−7.07517	−0.521589
$185$	−3.19708	−0.235054
$186$	−10.4459	−0.765929
$187$	−15.5992	−1.14073
$188$	−1.71095	−0.124784
$189$	−8.11571	−0.590331
$190$	−1.17341	−0.0851280
$191$	−12.2944	−0.889593	−0.444797	−	0.895632i	$-0.646724\pi$
$191$	−12.2944	−0.889593	−0.444797	+	0.895632i	$0.646724\pi$
$192$	−2.29642	−0.165730
$193$	1.37934	0.0992869	0.0496435	−	0.998767i	$-0.484192\pi$
$193$	1.37934	0.0992869	0.0496435	+	0.998767i	$0.484192\pi$
$194$	0.409677	0.0294131
$195$	0.806701	0.0577690
$196$	16.6675	1.19054
$197$	4.98090	0.354874	0.177437	−	0.984132i	$-0.443219\pi$
$197$	4.98090	0.354874	0.177437	+	0.984132i	$0.443219\pi$
$198$	11.7959	0.838297
$199$	−21.4843	−1.52298	−0.761491	−	0.648175i	$-0.775532\pi$
$199$	−21.4843	−1.52298	−0.761491	+	0.648175i	$0.775532\pi$
$200$	1.00000	0.0707107
$201$	−16.8677	−1.18975
$202$	−18.6442	−1.31180
$203$	−7.60271	−0.533606
$204$	6.90448	0.483410
$205$	−2.43460	−0.170040
$206$	−10.1516	−0.707298
$207$	−16.0858	−1.11804
$208$	0.351286	0.0243573
$209$	6.08797	0.421114
$210$	−11.1719	−0.770937
$211$	14.1497	0.974104	0.487052	−	0.873373i	$-0.338072\pi$
$211$	14.1497	0.974104	0.487052	+	0.873373i	$0.338072\pi$
$212$	−11.2342	−0.771568
$213$	2.01076	0.137775
$214$	13.4821	0.921620
$215$	−8.67292	−0.591488
$216$	1.66821	0.113507
$217$	−22.1294	−1.50224
$218$	−13.9899	−0.947519
$219$	−10.6856	−0.722064
$220$	−5.18828	−0.349794
$221$	−1.05618	−0.0710465
$222$	−7.34185	−0.492753
$223$	−18.8333	−1.26117	−0.630584	−	0.776121i	$-0.717185\pi$
$223$	−18.8333	−1.26117	−0.630584	+	0.776121i	$0.717185\pi$
$224$	−4.86493	−0.325052
$225$	2.27356	0.151571
$226$	7.99207	0.531625
$227$	3.88040	0.257551	0.128776	−	0.991674i	$-0.458895\pi$
$227$	3.88040	0.257551	0.128776	+	0.991674i	$0.458895\pi$
$228$	−2.69464	−0.178457
$229$	−7.54441	−0.498549	−0.249274	−	0.968433i	$-0.580192\pi$
$229$	−7.54441	−0.498549	−0.249274	+	0.968433i	$0.580192\pi$
$230$	7.07517	0.466523
$231$	57.9631	3.81369
$232$	1.56276	0.102600
$233$	2.28555	0.149732	0.0748658	−	0.997194i	$-0.476147\pi$
$233$	2.28555	0.149732	0.0748658	+	0.997194i	$0.476147\pi$
$234$	0.798670	0.0522107
$235$	1.71095	0.111610
$236$	−2.89191	−0.188247
$237$	−20.6484	−1.34126
$238$	14.6270	0.948127
$239$	−22.6300	−1.46382	−0.731908	−	0.681404i	$-0.761370\pi$
$239$	−22.6300	−1.46382	−0.731908	+	0.681404i	$0.761370\pi$
$240$	2.29642	0.148234
$241$	−25.4213	−1.63753	−0.818763	−	0.574131i	$-0.805340\pi$
$241$	−25.4213	−1.63753	−0.818763	+	0.574131i	$0.805340\pi$
$242$	15.9182	1.02326
$243$	19.4560	1.24810
$244$	−4.11226	−0.263261
$245$	−16.6675	−1.06485
$246$	−5.59088	−0.356461
$247$	0.412202	0.0262278
$248$	4.54876	0.288846
$249$	23.2268	1.47194
$250$	−1.00000	−0.0632456
$251$	3.04093	0.191942	0.0959710	−	0.995384i	$-0.469404\pi$
$251$	3.04093	0.191942	0.0959710	+	0.995384i	$0.469404\pi$
$252$	−11.0607	−0.696760
$253$	−36.7080	−2.30781
$254$	6.50166	0.407950
$255$	−6.90448	−0.432375
$256$	1.00000	0.0625000
$257$	−5.16161	−0.321972	−0.160986	−	0.986957i	$-0.551467\pi$
$257$	−5.16161	−0.321972	−0.160986	+	0.986957i	$0.551467\pi$
$258$	−19.9167	−1.23996
$259$	−15.5536	−0.966452
$260$	−0.351286	−0.0217858
$261$	3.55303	0.219927
$262$	−0.675740	−0.0417474
$263$	8.74970	0.539530	0.269765	−	0.962926i	$-0.413054\pi$
$263$	8.74970	0.539530	0.269765	+	0.962926i	$0.413054\pi$
$264$	−11.9145	−0.733286
$265$	11.2342	0.690111
$266$	−5.70855	−0.350014
$267$	−28.1095	−1.72028
$268$	7.34519	0.448679
$269$	−11.6149	−0.708171	−0.354086	−	0.935213i	$-0.615208\pi$
$269$	−11.6149	−0.708171	−0.354086	+	0.935213i	$0.615208\pi$
$270$	−1.66821	−0.101524
$271$	24.8207	1.50775	0.753875	−	0.657017i	$-0.228182\pi$
$271$	24.8207	1.50775	0.753875	+	0.657017i	$0.228182\pi$
$272$	−3.00662	−0.182303
$273$	3.92454	0.237524
$274$	3.27309	0.197734
$275$	5.18828	0.312865
$276$	16.2476	0.977990
$277$	2.68405	0.161269	0.0806346	−	0.996744i	$-0.474305\pi$
$277$	2.68405	0.161269	0.0806346	+	0.996744i	$0.474305\pi$
$278$	12.5350	0.751797
$279$	10.3419	0.619153
$280$	4.86493	0.290735
$281$	31.2441	1.86387	0.931934	−	0.362628i	$-0.118121\pi$
$281$	31.2441	1.86387	0.931934	+	0.362628i	$0.118121\pi$
$282$	3.92908	0.233973
$283$	−23.9290	−1.42243	−0.711217	−	0.702973i	$-0.751856\pi$
$283$	−23.9290	−1.42243	−0.711217	+	0.702973i	$0.751856\pi$
$284$	−0.875606	−0.0519577
$285$	2.69464	0.159617
$286$	1.82257	0.107771
$287$	−11.8442	−0.699139
$288$	2.27356	0.133971
$289$	−7.96023	−0.468249
$290$	−1.56276	−0.0917684
$291$	−0.940791	−0.0551502
$292$	4.65314	0.272304
$293$	11.9913	0.700539	0.350270	−	0.936649i	$-0.386090\pi$
$293$	11.9913	0.700539	0.350270	+	0.936649i	$0.386090\pi$
$294$	−38.2757	−2.23228
$295$	2.89191	0.168374
$296$	3.19708	0.185827
$297$	8.65512	0.502221
$298$	−15.6656	−0.907485
$299$	−2.48541	−0.143735
$300$	−2.29642	−0.132584
$301$	−42.1931	−2.43197
$302$	3.26160	0.187684
$303$	42.8149	2.45965
$304$	1.17341	0.0672996
$305$	4.11226	0.235467
$306$	−6.83574	−0.390773
$307$	21.0265	1.20004	0.600022	−	0.799983i	$-0.295158\pi$
$307$	21.0265	1.20004	0.600022	+	0.799983i	$0.295158\pi$
$308$	−25.2406	−1.43822
$309$	23.3125	1.32620
$310$	−4.54876	−0.258352
$311$	2.09035	0.118533	0.0592665	−	0.998242i	$-0.481124\pi$
$311$	2.09035	0.118533	0.0592665	+	0.998242i	$0.481124\pi$
$312$	−0.806701	−0.0456704
$313$	30.7213	1.73647	0.868234	−	0.496154i	$-0.165255\pi$
$313$	30.7213	1.73647	0.868234	+	0.496154i	$0.165255\pi$
$314$	−13.8086	−0.779263
$315$	11.0607	0.623201
$316$	8.99154	0.505814
$317$	24.2135	1.35996	0.679982	−	0.733229i	$-0.261988\pi$
$317$	24.2135	1.35996	0.679982	+	0.733229i	$0.261988\pi$
$318$	25.7985	1.44671
$319$	8.10803	0.453963
$320$	−1.00000	−0.0559017
$321$	−30.9607	−1.72806
$322$	34.4202	1.91816
$323$	−3.52800	−0.196303
$324$	−10.6516	−0.591756
$325$	0.351286	0.0194858
$326$	−14.7760	−0.818366
$327$	32.1269	1.77662
$328$	2.43460	0.134428
$329$	8.32367	0.458899
$330$	11.9145	0.655871
$331$	−13.8290	−0.760112	−0.380056	−	0.924963i	$-0.624095\pi$
$331$	−13.8290	−0.760112	−0.380056	+	0.924963i	$0.624095\pi$
$332$	−10.1143	−0.555096
$333$	7.26877	0.398326
$334$	−5.86065	−0.320681
$335$	−7.34519	−0.401310
$336$	11.1719	0.609479
$337$	−16.9625	−0.924007	−0.462003	−	0.886878i	$-0.652869\pi$
$337$	−16.9625	−0.924007	−0.462003	+	0.886878i	$0.652869\pi$
$338$	−12.8766	−0.700395
$339$	−18.3532	−0.996808
$340$	3.00662	0.163057
$341$	23.6002	1.27802
$342$	2.66782	0.144259
$343$	−47.0318	−2.53948
$344$	8.67292	0.467613
$345$	−16.2476	−0.874741
$346$	−25.4833	−1.36999
$347$	−31.9488	−1.71510	−0.857551	−	0.514399i	$-0.828015\pi$
$347$	−31.9488	−1.71510	−0.857551	+	0.514399i	$0.828015\pi$
$348$	−3.58876	−0.192378
$349$	2.86030	0.153108	0.0765540	−	0.997065i	$-0.475608\pi$
$349$	2.86030	0.153108	0.0765540	+	0.997065i	$0.475608\pi$
$350$	−4.86493	−0.260041
$351$	0.586017	0.0312793
$352$	5.18828	0.276536
$353$	−21.9514	−1.16836	−0.584178	−	0.811626i	$-0.698583\pi$
$353$	−21.9514	−1.16836	−0.584178	+	0.811626i	$0.698583\pi$
$354$	6.64105	0.352968
$355$	0.875606	0.0464723
$356$	12.2406	0.648749
$357$	−33.5898	−1.77776
$358$	−5.93790	−0.313828
$359$	0.122382	0.00645908	0.00322954	−	0.999995i	$-0.498972\pi$
$359$	0.122382	0.00645908	0.00322954	+	0.999995i	$0.498972\pi$
$360$	−2.27356	−0.119827
$361$	−17.6231	−0.927532
$362$	−20.0956	−1.05620
$363$	−36.5550	−1.91864
$364$	−1.70898	−0.0895749
$365$	−4.65314	−0.243556
$366$	9.44350	0.493619
$367$	32.0587	1.67345	0.836725	−	0.547623i	$-0.184467\pi$
$367$	32.0587	1.67345	0.836725	+	0.547623i	$0.184467\pi$
$368$	−7.07517	−0.368819
$369$	5.53522	0.288152
$370$	−3.19708	−0.166208
$371$	54.6535	2.83747
$372$	−10.4459	−0.541593
$373$	5.33896	0.276441	0.138221	−	0.990401i	$-0.455862\pi$
$373$	5.33896	0.276441	0.138221	+	0.990401i	$0.455862\pi$
$374$	−15.5992	−0.806615
$375$	2.29642	0.118587
$376$	−1.71095	−0.0882357
$377$	0.548975	0.0282737
$378$	−8.11571	−0.417427
$379$	22.5265	1.15711	0.578555	−	0.815643i	$-0.303617\pi$
$379$	22.5265	1.15711	0.578555	+	0.815643i	$0.303617\pi$
$380$	−1.17341	−0.0601946
$381$	−14.9306	−0.764916
$382$	−12.2944	−0.629037
$383$	−21.5031	−1.09876	−0.549379	−	0.835574i	$-0.685136\pi$
$383$	−21.5031	−1.09876	−0.549379	+	0.835574i	$0.685136\pi$
$384$	−2.29642	−0.117189
$385$	25.2406	1.28638
$386$	1.37934	0.0702064
$387$	19.7184	1.00234
$388$	0.409677	0.0207982
$389$	−29.7813	−1.50997	−0.754986	−	0.655741i	$-0.772357\pi$
$389$	−29.7813	−1.50997	−0.754986	+	0.655741i	$0.772357\pi$
$390$	0.806701	0.0408489
$391$	21.2724	1.07579
$392$	16.6675	0.841837
$393$	1.55179	0.0782773
$394$	4.98090	0.250934
$395$	−8.99154	−0.452413
$396$	11.7959	0.592765
$397$	5.18143	0.260049	0.130024	−	0.991511i	$-0.458494\pi$
$397$	5.18143	0.260049	0.130024	+	0.991511i	$0.458494\pi$
$398$	−21.4843	−1.07691
$399$	13.1092	0.656283
$400$	1.00000	0.0500000
$401$	−6.04014	−0.301630	−0.150815	−	0.988562i	$-0.548190\pi$
$401$	−6.04014	−0.301630	−0.150815	+	0.988562i	$0.548190\pi$
$402$	−16.8677	−0.841282
$403$	1.59791	0.0795977
$404$	−18.6442	−0.927581
$405$	10.6516	0.529282
$406$	−7.60271	−0.377316
$407$	16.5873	0.822204
$408$	6.90448	0.341823
$409$	−18.2325	−0.901540	−0.450770	−	0.892640i	$-0.648850\pi$
$409$	−18.2325	−0.901540	−0.450770	+	0.892640i	$0.648850\pi$
$410$	−2.43460	−0.120236
$411$	−7.51639	−0.370756
$412$	−10.1516	−0.500135
$413$	14.0689	0.692287
$414$	−16.0858	−0.790576
$415$	10.1143	0.496493
$416$	0.351286	0.0172232
$417$	−28.7856	−1.40964
$418$	6.08797	0.297772
$419$	−6.85080	−0.334684	−0.167342	−	0.985899i	$-0.553518\pi$
$419$	−6.85080	−0.334684	−0.167342	+	0.985899i	$0.553518\pi$
$420$	−11.1719	−0.545135
$421$	−9.37321	−0.456822	−0.228411	−	0.973565i	$-0.573353\pi$
$421$	−9.37321	−0.456822	−0.228411	+	0.973565i	$0.573353\pi$
$422$	14.1497	0.688796
$423$	−3.88996	−0.189136
$424$	−11.2342	−0.545581
$425$	−3.00662	−0.145843
$426$	2.01076	0.0974218
$427$	20.0059	0.968151
$428$	13.4821	0.651684
$429$	−4.18539	−0.202072
$430$	−8.67292	−0.418245
$431$	−16.7264	−0.805681	−0.402840	−	0.915270i	$-0.631977\pi$
$431$	−16.7264	−0.805681	−0.402840	+	0.915270i	$0.631977\pi$
$432$	1.66821	0.0802616
$433$	−33.5591	−1.61275	−0.806373	−	0.591407i	$-0.798573\pi$
$433$	−33.5591	−1.61275	−0.806373	+	0.591407i	$0.798573\pi$
$434$	−22.1294	−1.06224
$435$	3.58876	0.172068
$436$	−13.9899	−0.669997
$437$	−8.30207	−0.397142
$438$	−10.6856	−0.510576
$439$	23.9198	1.14163	0.570815	−	0.821078i	$-0.306627\pi$
$439$	23.9198	1.14163	0.570815	+	0.821078i	$0.306627\pi$
$440$	−5.18828	−0.247342
$441$	37.8947	1.80451
$442$	−1.05618	−0.0502375
$443$	13.5186	0.642288	0.321144	−	0.947030i	$-0.395933\pi$
$443$	13.5186	0.642288	0.321144	+	0.947030i	$0.395933\pi$
$444$	−7.34185	−0.348429
$445$	−12.2406	−0.580259
$446$	−18.8333	−0.891781
$447$	35.9749	1.70155
$448$	−4.86493	−0.229846
$449$	−35.9551	−1.69683	−0.848413	−	0.529335i	$-0.822442\pi$
$449$	−35.9551	−1.69683	−0.848413	+	0.529335i	$0.822442\pi$
$450$	2.27356	0.107177
$451$	12.6314	0.594789
$452$	7.99207	0.375915
$453$	−7.49002	−0.351912
$454$	3.88040	0.182116
$455$	1.70898	0.0801182
$456$	−2.69464	−0.126188
$457$	4.68430	0.219122	0.109561	−	0.993980i	$-0.465055\pi$
$457$	4.68430	0.219122	0.109561	+	0.993980i	$0.465055\pi$
$458$	−7.54441	−0.352527
$459$	−5.01567	−0.234111
$460$	7.07517	0.329882
$461$	4.50428	0.209785	0.104893	−	0.994484i	$-0.466550\pi$
$461$	4.50428	0.209785	0.104893	+	0.994484i	$0.466550\pi$
$462$	57.9631	2.69669
$463$	17.6953	0.822371	0.411186	−	0.911552i	$-0.365115\pi$
$463$	17.6953	0.822371	0.411186	+	0.911552i	$0.365115\pi$
$464$	1.56276	0.0725493
$465$	10.4459	0.484416
$466$	2.28555	0.105876
$467$	34.8388	1.61215	0.806073	−	0.591816i	$-0.201589\pi$
$467$	34.8388	1.61215	0.806073	+	0.591816i	$0.201589\pi$
$468$	0.798670	0.0369185
$469$	−35.7338	−1.65003
$470$	1.71095	0.0789204
$471$	31.7104	1.46114
$472$	−2.89191	−0.133111
$473$	44.9975	2.06899
$474$	−20.6484	−0.948412
$475$	1.17341	0.0538397
$476$	14.6270	0.670427
$477$	−25.5416	−1.16947
$478$	−22.6300	−1.03507
$479$	−29.5093	−1.34831	−0.674157	−	0.738588i	$-0.735493\pi$
$479$	−29.5093	−1.34831	−0.674157	+	0.738588i	$0.735493\pi$
$480$	2.29642	0.104817
$481$	1.12309	0.0512084
$482$	−25.4213	−1.15791
$483$	−79.0434	−3.59660
$484$	15.9182	0.723556
$485$	−0.409677	−0.0186025
$486$	19.4560	0.882541
$487$	11.6116	0.526172	0.263086	−	0.964772i	$-0.415260\pi$
$487$	11.6116	0.526172	0.263086	+	0.964772i	$0.415260\pi$
$488$	−4.11226	−0.186153
$489$	33.9319	1.53445
$490$	−16.6675	−0.752962
$491$	−7.61142	−0.343499	−0.171749	−	0.985141i	$-0.554942\pi$
$491$	−7.61142	−0.343499	−0.171749	+	0.985141i	$0.554942\pi$
$492$	−5.59088	−0.252056
$493$	−4.69863	−0.211616
$494$	0.412202	0.0185458
$495$	−11.7959	−0.530185
$496$	4.54876	0.204245
$497$	4.25976	0.191076
$498$	23.2268	1.04082
$499$	−8.62675	−0.386186	−0.193093	−	0.981180i	$-0.561852\pi$
$499$	−8.62675	−0.386186	−0.193093	+	0.981180i	$0.561852\pi$
$500$	−1.00000	−0.0447214
$501$	13.4585	0.601283
$502$	3.04093	0.135724
$503$	18.2301	0.812839	0.406419	−	0.913687i	$-0.366777\pi$
$503$	18.2301	0.812839	0.406419	+	0.913687i	$0.366777\pi$
$504$	−11.0607	−0.492684
$505$	18.6442	0.829654
$506$	−36.7080	−1.63187
$507$	29.5701	1.31326
$508$	6.50166	0.288464
$509$	15.8964	0.704596	0.352298	−	0.935888i	$-0.385400\pi$
$509$	15.8964	0.704596	0.352298	+	0.935888i	$0.385400\pi$
$510$	−6.90448	−0.305735
$511$	−22.6372	−1.00141
$512$	1.00000	0.0441942
$513$	1.95749	0.0864252
$514$	−5.16161	−0.227669
$515$	10.1516	0.447335
$516$	−19.9167	−0.876784
$517$	−8.87691	−0.390406
$518$	−15.5536	−0.683385
$519$	58.5205	2.56876
$520$	−0.351286	−0.0154049
$521$	20.8790	0.914724	0.457362	−	0.889281i	$-0.348794\pi$
$521$	20.8790	0.914724	0.457362	+	0.889281i	$0.348794\pi$
$522$	3.55303	0.155512
$523$	−13.8763	−0.606768	−0.303384	−	0.952868i	$-0.598116\pi$
$523$	−13.8763	−0.606768	−0.303384	+	0.952868i	$0.598116\pi$
$524$	−0.675740	−0.0295198
$525$	11.1719	0.487583
$526$	8.74970	0.381505
$527$	−13.6764	−0.595753
$528$	−11.9145	−0.518512
$529$	27.0581	1.17644
$530$	11.2342	0.487982
$531$	−6.57494	−0.285328
$532$	−5.70855	−0.247497
$533$	0.855240	0.0370446
$534$	−28.1095	−1.21642
$535$	−13.4821	−0.582884
$536$	7.34519	0.317264
$537$	13.6359	0.588434
$538$	−11.6149	−0.500753
$539$	86.4758	3.72478
$540$	−1.66821	−0.0717882
$541$	4.14835	0.178352	0.0891758	−	0.996016i	$-0.471577\pi$
$541$	4.14835	0.178352	0.0891758	+	0.996016i	$0.471577\pi$
$542$	24.8207	1.06614
$543$	46.1480	1.98040
$544$	−3.00662	−0.128908
$545$	13.9899	0.599264
$546$	3.92454	0.167955
$547$	−2.44039	−0.104343	−0.0521717	−	0.998638i	$-0.516614\pi$
$547$	−2.44039	−0.104343	−0.0521717	+	0.998638i	$0.516614\pi$
$548$	3.27309	0.139819
$549$	−9.34949	−0.399026
$550$	5.18828	0.221229
$551$	1.83376	0.0781206
$552$	16.2476	0.691544
$553$	−43.7432	−1.86015
$554$	2.68405	0.114035
$555$	7.34185	0.311644
$556$	12.5350	0.531600
$557$	7.49168	0.317433	0.158716	−	0.987324i	$-0.449264\pi$
$557$	7.49168	0.317433	0.158716	+	0.987324i	$0.449264\pi$
$558$	10.3419	0.437807
$559$	3.04667	0.128860
$560$	4.86493	0.205581
$561$	35.8224	1.51242
$562$	31.2441	1.31795
$563$	0.682515	0.0287646	0.0143823	−	0.999897i	$-0.495422\pi$
$563$	0.682515	0.0287646	0.0143823	+	0.999897i	$0.495422\pi$
$564$	3.92908	0.165444
$565$	−7.99207	−0.336229
$566$	−23.9290	−1.00581
$567$	51.8193	2.17620
$568$	−0.875606	−0.0367396
$569$	16.2916	0.682981	0.341490	−	0.939885i	$-0.389068\pi$
$569$	16.2916	0.682981	0.341490	+	0.939885i	$0.389068\pi$
$570$	2.69464	0.112866
$571$	17.7048	0.740923	0.370461	−	0.928848i	$-0.379200\pi$
$571$	17.7048	0.740923	0.370461	+	0.928848i	$0.379200\pi$
$572$	1.82257	0.0762054
$573$	28.2332	1.17946
$574$	−11.8442	−0.494366
$575$	−7.07517	−0.295055
$576$	2.27356	0.0947318
$577$	−8.19944	−0.341347	−0.170674	−	0.985328i	$-0.554594\pi$
$577$	−8.19944	−0.341347	−0.170674	+	0.985328i	$0.554594\pi$
$578$	−7.96023	−0.331102
$579$	−3.16754	−0.131639
$580$	−1.56276	−0.0648901
$581$	49.2055	2.04139
$582$	−0.940791	−0.0389971
$583$	−58.2861	−2.41396
$584$	4.65314	0.192548
$585$	−0.798670	−0.0330209
$586$	11.9913	0.495356
$587$	−14.2987	−0.590169	−0.295085	−	0.955471i	$-0.595348\pi$
$587$	−14.2987	−0.590169	−0.295085	+	0.955471i	$0.595348\pi$
$588$	−38.2757	−1.57846
$589$	5.33755	0.219930
$590$	2.89191	0.119058
$591$	−11.4383	−0.470507
$592$	3.19708	0.131399
$593$	−15.3948	−0.632188	−0.316094	−	0.948728i	$-0.602371\pi$
$593$	−15.3948	−0.632188	−0.316094	+	0.948728i	$0.602371\pi$
$594$	8.65512	0.355124
$595$	−14.6270	−0.599648
$596$	−15.6656	−0.641689
$597$	49.3371	2.01923
$598$	−2.48541	−0.101636
$599$	24.9884	1.02100	0.510499	−	0.859878i	$-0.329461\pi$
$599$	24.9884	1.02100	0.510499	+	0.859878i	$0.329461\pi$
$600$	−2.29642	−0.0937511
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−42.1931	−1.71966
$603$	16.6997	0.680066
$604$	3.26160	0.132713
$605$	−15.9182	−0.647169
$606$	42.8149	1.73924
$607$	−1.25935	−0.0511154	−0.0255577	−	0.999673i	$-0.508136\pi$
$607$	−1.25935	−0.0511154	−0.0255577	+	0.999673i	$0.508136\pi$
$608$	1.17341	0.0475880
$609$	17.4591	0.707477
$610$	4.11226	0.166501
$611$	−0.601034	−0.0243152
$612$	−6.83574	−0.276319
$613$	4.19468	0.169421	0.0847107	−	0.996406i	$-0.473003\pi$
$613$	4.19468	0.169421	0.0847107	+	0.996406i	$0.473003\pi$
$614$	21.0265	0.848560
$615$	5.59088	0.225446
$616$	−25.2406	−1.01697
$617$	−42.4175	−1.70766	−0.853832	−	0.520549i	$-0.825727\pi$
$617$	−42.4175	−1.70766	−0.853832	+	0.520549i	$0.825727\pi$
$618$	23.3125	0.937765
$619$	24.1574	0.970968	0.485484	−	0.874246i	$-0.338643\pi$
$619$	24.1574	0.970968	0.485484	+	0.874246i	$0.338643\pi$
$620$	−4.54876	−0.182683
$621$	−11.8029	−0.473632
$622$	2.09035	0.0838155
$623$	−59.5495	−2.38580
$624$	−0.806701	−0.0322939
$625$	1.00000	0.0400000
$626$	30.7213	1.22787
$627$	−13.9806	−0.558330
$628$	−13.8086	−0.551022
$629$	−9.61241	−0.383272
$630$	11.0607	0.440670
$631$	5.80965	0.231278	0.115639	−	0.993291i	$-0.463108\pi$
$631$	5.80965	0.231278	0.115639	+	0.993291i	$0.463108\pi$
$632$	8.99154	0.357664
$633$	−32.4937	−1.29151
$634$	24.2135	0.961640
$635$	−6.50166	−0.258010
$636$	25.7985	1.02298
$637$	5.85506	0.231986
$638$	8.10803	0.321000
$639$	−1.99075	−0.0787527
$640$	−1.00000	−0.0395285
$641$	−2.33321	−0.0921562	−0.0460781	−	0.998938i	$-0.514672\pi$
$641$	−2.33321	−0.0921562	−0.0460781	+	0.998938i	$0.514672\pi$
$642$	−30.9607	−1.22192
$643$	−42.9456	−1.69361	−0.846805	−	0.531904i	$-0.821477\pi$
$643$	−42.9456	−1.69361	−0.846805	+	0.531904i	$0.821477\pi$
$644$	34.4202	1.35635
$645$	19.9167	0.784219
$646$	−3.52800	−0.138807
$647$	20.0208	0.787098	0.393549	−	0.919304i	$-0.371247\pi$
$647$	20.0208	0.787098	0.393549	+	0.919304i	$0.371247\pi$
$648$	−10.6516	−0.418434
$649$	−15.0040	−0.588960
$650$	0.351286	0.0137786
$651$	50.8184	1.99173
$652$	−14.7760	−0.578672
$653$	20.2248	0.791457	0.395729	−	0.918367i	$-0.370492\pi$
$653$	20.2248	0.791457	0.395729	+	0.918367i	$0.370492\pi$
$654$	32.1269	1.25626
$655$	0.675740	0.0264034
$656$	2.43460	0.0950552
$657$	10.5792	0.412734
$658$	8.32367	0.324490
$659$	−23.8392	−0.928645	−0.464322	−	0.885666i	$-0.653702\pi$
$659$	−23.8392	−0.928645	−0.464322	+	0.885666i	$0.653702\pi$
$660$	11.9145	0.463771
$661$	32.4230	1.26111	0.630554	−	0.776145i	$-0.282828\pi$
$661$	32.4230	1.26111	0.630554	+	0.776145i	$0.282828\pi$
$662$	−13.8290	−0.537481
$663$	2.42544	0.0941964
$664$	−10.1143	−0.392512
$665$	5.70855	0.221368
$666$	7.26877	0.281659
$667$	−11.0568	−0.428121
$668$	−5.86065	−0.226755
$669$	43.2491	1.67211
$670$	−7.34519	−0.283769
$671$	−21.3356	−0.823650
$672$	11.1719	0.430967
$673$	−15.5696	−0.600166	−0.300083	−	0.953913i	$-0.597014\pi$
$673$	−15.5696	−0.600166	−0.300083	+	0.953913i	$0.597014\pi$
$674$	−16.9625	−0.653372
$675$	1.66821	0.0642093
$676$	−12.8766	−0.495254
$677$	48.5093	1.86436	0.932182	−	0.361990i	$-0.117903\pi$
$677$	48.5093	1.86436	0.932182	+	0.361990i	$0.117903\pi$
$678$	−18.3532	−0.704850
$679$	−1.99305	−0.0764861
$680$	3.00662	0.115299
$681$	−8.91104	−0.341472
$682$	23.6002	0.903699
$683$	16.7952	0.642652	0.321326	−	0.946969i	$-0.395872\pi$
$683$	16.7952	0.642652	0.321326	+	0.946969i	$0.395872\pi$
$684$	2.66782	0.102007
$685$	−3.27309	−0.125058
$686$	−47.0318	−1.79568
$687$	17.3252	0.660996
$688$	8.67292	0.330652
$689$	−3.94641	−0.150346
$690$	−16.2476	−0.618535
$691$	−44.8007	−1.70430	−0.852149	−	0.523299i	$-0.824701\pi$
$691$	−44.8007	−1.70430	−0.852149	+	0.523299i	$0.824701\pi$
$692$	−25.4833	−0.968730
$693$	−57.3861	−2.17992
$694$	−31.9488	−1.21276
$695$	−12.5350	−0.475478
$696$	−3.58876	−0.136032
$697$	−7.31992	−0.277262
$698$	2.86030	0.108264
$699$	−5.24860	−0.198520
$700$	−4.86493	−0.183877
$701$	−23.7995	−0.898894	−0.449447	−	0.893307i	$-0.648379\pi$
$701$	−23.7995	−0.898894	−0.449447	+	0.893307i	$0.648379\pi$
$702$	0.586017	0.0221178
$703$	3.75148	0.141490
$704$	5.18828	0.195541
$705$	−3.92908	−0.147978
$706$	−21.9514	−0.826152
$707$	90.7025	3.41122
$708$	6.64105	0.249586
$709$	−1.48129	−0.0556310	−0.0278155	−	0.999613i	$-0.508855\pi$
$709$	−1.48129	−0.0556310	−0.0278155	+	0.999613i	$0.508855\pi$
$710$	0.875606	0.0328609
$711$	20.4428	0.766666
$712$	12.2406	0.458735
$713$	−32.1832	−1.20527
$714$	−33.5898	−1.25707
$715$	−1.82257	−0.0681602
$716$	−5.93790	−0.221910
$717$	51.9682	1.94079
$718$	0.122382	0.00456726
$719$	−34.9193	−1.30227	−0.651136	−	0.758961i	$-0.725707\pi$
$719$	−34.9193	−1.30227	−0.651136	+	0.758961i	$0.725707\pi$
$720$	−2.27356	−0.0847307
$721$	49.3870	1.83927
$722$	−17.6231	−0.655864
$723$	58.3780	2.17110
$724$	−20.0956	−0.746847
$725$	1.56276	0.0580394
$726$	−36.5550	−1.35668
$727$	−34.9673	−1.29687	−0.648433	−	0.761271i	$-0.724575\pi$
$727$	−34.9673	−1.29687	−0.648433	+	0.761271i	$0.724575\pi$
$728$	−1.70898	−0.0633390
$729$	−12.7244	−0.471272
$730$	−4.65314	−0.172220
$731$	−26.0762	−0.964463
$732$	9.44350	0.349042
$733$	−48.3906	−1.78735	−0.893675	−	0.448716i	$-0.851882\pi$
$733$	−48.3906	−1.78735	−0.893675	+	0.448716i	$0.851882\pi$
$734$	32.0587	1.18331
$735$	38.2757	1.41182
$736$	−7.07517	−0.260794
$737$	38.1089	1.40376
$738$	5.53522	0.203754
$739$	−32.0572	−1.17924	−0.589622	−	0.807679i	$-0.700723\pi$
$739$	−32.0572	−1.17924	−0.589622	+	0.807679i	$0.700723\pi$
$740$	−3.19708	−0.117527
$741$	−0.946589	−0.0347738
$742$	54.6535	2.00639
$743$	36.4275	1.33639	0.668197	−	0.743984i	$-0.267066\pi$
$743$	36.4275	1.33639	0.668197	+	0.743984i	$0.267066\pi$
$744$	−10.4459	−0.382964
$745$	15.6656	0.573944
$746$	5.33896	0.195473
$747$	−22.9956	−0.841363
$748$	−15.5992	−0.570363
$749$	−65.5896	−2.39659
$750$	2.29642	0.0838535
$751$	26.5827	0.970016	0.485008	−	0.874510i	$-0.338817\pi$
$751$	26.5827	0.970016	0.485008	+	0.874510i	$0.338817\pi$
$752$	−1.71095	−0.0623921
$753$	−6.98327	−0.254485
$754$	0.548975	0.0199925
$755$	−3.26160	−0.118702
$756$	−8.11571	−0.295165
$757$	−10.4235	−0.378848	−0.189424	−	0.981895i	$-0.560662\pi$
$757$	−10.4235	−0.378848	−0.189424	+	0.981895i	$0.560662\pi$
$758$	22.5265	0.818200
$759$	84.2971	3.05979
$760$	−1.17341	−0.0425640
$761$	12.8738	0.466676	0.233338	−	0.972396i	$-0.425035\pi$
$761$	12.8738	0.466676	0.233338	+	0.972396i	$0.425035\pi$
$762$	−14.9306	−0.540877
$763$	68.0601	2.46394
$764$	−12.2944	−0.444797
$765$	6.83574	0.247147
$766$	−21.5031	−0.776939
$767$	−1.01589	−0.0366815
$768$	−2.29642	−0.0828651
$769$	−20.2577	−0.730510	−0.365255	−	0.930908i	$-0.619018\pi$
$769$	−20.2577	−0.730510	−0.365255	+	0.930908i	$0.619018\pi$
$770$	25.2406	0.909608
$771$	11.8532	0.426884
$772$	1.37934	0.0496435
$773$	−8.94259	−0.321643	−0.160821	−	0.986984i	$-0.551414\pi$
$773$	−8.94259	−0.321643	−0.160821	+	0.986984i	$0.551414\pi$
$774$	19.7184	0.708764
$775$	4.54876	0.163396
$776$	0.409677	0.0147065
$777$	35.7176	1.28136
$778$	−29.7813	−1.06771
$779$	2.85678	0.102355
$780$	0.806701	0.0288845
$781$	−4.54289	−0.162557
$782$	21.2724	0.760698
$783$	2.60701	0.0931668
$784$	16.6675	0.595269
$785$	13.8086	0.492849
$786$	1.55179	0.0553504
$787$	16.1320	0.575042	0.287521	−	0.957774i	$-0.407169\pi$
$787$	16.1320	0.575042	0.287521	+	0.957774i	$0.407169\pi$
$788$	4.98090	0.177437
$789$	−20.0930	−0.715330
$790$	−8.99154	−0.319905
$791$	−38.8808	−1.38244
$792$	11.7959	0.419148
$793$	−1.44458	−0.0512985
$794$	5.18143	0.183882
$795$	−25.7985	−0.914977
$796$	−21.4843	−0.761491
$797$	19.5796	0.693544	0.346772	−	0.937949i	$-0.387278\pi$
$797$	19.5796	0.693544	0.346772	+	0.937949i	$0.387278\pi$
$798$	13.1092	0.464062
$799$	5.14419	0.181988
$800$	1.00000	0.0353553
$801$	27.8297	0.983314
$802$	−6.04014	−0.213285
$803$	24.1418	0.851944
$804$	−16.8677	−0.594877
$805$	−34.4202	−1.21315
$806$	1.59791	0.0562841
$807$	26.6727	0.938923
$808$	−18.6442	−0.655899
$809$	−12.2254	−0.429824	−0.214912	−	0.976633i	$-0.568946\pi$
$809$	−12.2254	−0.429824	−0.214912	+	0.976633i	$0.568946\pi$
$810$	10.6516	0.374259
$811$	−13.6415	−0.479019	−0.239510	−	0.970894i	$-0.576987\pi$
$811$	−13.6415	−0.479019	−0.239510	+	0.970894i	$0.576987\pi$
$812$	−7.60271	−0.266803
$813$	−56.9989	−1.99904
$814$	16.5873	0.581386
$815$	14.7760	0.517580
$816$	6.90448	0.241705
$817$	10.1769	0.356044
$818$	−18.2325	−0.637485
$819$	−3.88547	−0.135769
$820$	−2.43460	−0.0850199
$821$	33.7301	1.17719	0.588595	−	0.808428i	$-0.299681\pi$
$821$	33.7301	1.17719	0.588595	+	0.808428i	$0.299681\pi$
$822$	−7.51639	−0.262164
$823$	47.4573	1.65426	0.827128	−	0.562013i	$-0.189973\pi$
$823$	47.4573	1.65426	0.827128	+	0.562013i	$0.189973\pi$
$824$	−10.1516	−0.353649
$825$	−11.9145	−0.414809
$826$	14.0689	0.489521
$827$	17.2125	0.598538	0.299269	−	0.954169i	$-0.403257\pi$
$827$	17.2125	0.598538	0.299269	+	0.954169i	$0.403257\pi$
$828$	−16.0858	−0.559022
$829$	−1.09597	−0.0380647	−0.0190324	−	0.999819i	$-0.506059\pi$
$829$	−1.09597	−0.0380647	−0.0190324	+	0.999819i	$0.506059\pi$
$830$	10.1143	0.351073
$831$	−6.16372	−0.213817
$832$	0.351286	0.0121786
$833$	−50.1129	−1.73631
$834$	−28.7856	−0.996763
$835$	5.86065	0.202816
$836$	6.08797	0.210557
$837$	7.58827	0.262289
$838$	−6.85080	−0.236657
$839$	−29.3072	−1.01180	−0.505898	−	0.862593i	$-0.668839\pi$
$839$	−29.3072	−1.01180	−0.505898	+	0.862593i	$0.668839\pi$
$840$	−11.1719	−0.385468
$841$	−26.5578	−0.915786
$842$	−9.37321	−0.323022
$843$	−71.7497	−2.47119
$844$	14.1497	0.487052
$845$	12.8766	0.442968
$846$	−3.88996	−0.133740
$847$	−77.4411	−2.66091
$848$	−11.2342	−0.385784
$849$	54.9512	1.88592
$850$	−3.00662	−0.103126
$851$	−22.6199	−0.775400
$852$	2.01076	0.0688876
$853$	−7.07174	−0.242132	−0.121066	−	0.992644i	$-0.538631\pi$
$853$	−7.07174	−0.242132	−0.121066	+	0.992644i	$0.538631\pi$
$854$	20.0059	0.684586
$855$	−2.66782	−0.0912375
$856$	13.4821	0.460810
$857$	−45.9048	−1.56808	−0.784039	−	0.620711i	$-0.786844\pi$
$857$	−45.9048	−1.56808	−0.784039	+	0.620711i	$0.786844\pi$
$858$	−4.18539	−0.142887
$859$	25.9505	0.885418	0.442709	−	0.896665i	$-0.354017\pi$
$859$	25.9505	0.885418	0.442709	+	0.896665i	$0.354017\pi$
$860$	−8.67292	−0.295744
$861$	27.1992	0.926947
$862$	−16.7264	−0.569702
$863$	−7.03813	−0.239581	−0.119790	−	0.992799i	$-0.538222\pi$
$863$	−7.03813	−0.239581	−0.119790	+	0.992799i	$0.538222\pi$
$864$	1.66821	0.0567536
$865$	25.4833	0.866458
$866$	−33.5591	−1.14038
$867$	18.2801	0.620823
$868$	−22.1294	−0.751120
$869$	46.6506	1.58251
$870$	3.58876	0.121670
$871$	2.58026	0.0874287
$872$	−13.9899	−0.473759
$873$	0.931426	0.0315240
$874$	−8.30207	−0.280822
$875$	4.86493	0.164465
$876$	−10.6856	−0.361032
$877$	36.5763	1.23509	0.617547	−	0.786534i	$-0.288126\pi$
$877$	36.5763	1.23509	0.617547	+	0.786534i	$0.288126\pi$
$878$	23.9198	0.807255
$879$	−27.5371	−0.928804
$880$	−5.18828	−0.174897
$881$	−53.5108	−1.80282	−0.901412	−	0.432963i	$-0.857468\pi$
$881$	−53.5108	−1.80282	−0.901412	+	0.432963i	$0.857468\pi$
$882$	37.8947	1.27598
$883$	−8.54930	−0.287707	−0.143853	−	0.989599i	$-0.545949\pi$
$883$	−8.54930	−0.287707	−0.143853	+	0.989599i	$0.545949\pi$
$884$	−1.05618	−0.0355233
$885$	−6.64105	−0.223237
$886$	13.5186	0.454167
$887$	−18.2668	−0.613340	−0.306670	−	0.951816i	$-0.599215\pi$
$887$	−18.2668	−0.613340	−0.306670	+	0.951816i	$0.599215\pi$
$888$	−7.34185	−0.246376
$889$	−31.6301	−1.06084
$890$	−12.2406	−0.410305
$891$	−55.2635	−1.85140
$892$	−18.8333	−0.630584
$893$	−2.00765	−0.0671834
$894$	35.9749	1.20318
$895$	5.93790	0.198482
$896$	−4.86493	−0.162526
$897$	5.70755	0.190569
$898$	−35.9551	−1.19984
$899$	7.10862	0.237086
$900$	2.27356	0.0757854
$901$	33.7770	1.12527
$902$	12.6314	0.420579
$903$	96.8933	3.22441
$904$	7.99207	0.265812
$905$	20.0956	0.668000
$906$	−7.49002	−0.248839
$907$	43.0685	1.43006	0.715032	−	0.699091i	$-0.246412\pi$
$907$	43.0685	1.43006	0.715032	+	0.699091i	$0.246412\pi$
$908$	3.88040	0.128776
$909$	−42.3887	−1.40594
$910$	1.70898	0.0566521
$911$	16.0248	0.530925	0.265463	−	0.964121i	$-0.414475\pi$
$911$	16.0248	0.530925	0.265463	+	0.964121i	$0.414475\pi$
$912$	−2.69464	−0.0892286
$913$	−52.4759	−1.73670
$914$	4.68430	0.154943
$915$	−9.44350	−0.312192
$916$	−7.54441	−0.249274
$917$	3.28743	0.108560
$918$	−5.01567	−0.165542
$919$	6.27665	0.207047	0.103524	−	0.994627i	$-0.466988\pi$
$919$	6.27665	0.207047	0.103524	+	0.994627i	$0.466988\pi$
$920$	7.07517	0.233261
$921$	−48.2857	−1.59107
$922$	4.50428	0.148341
$923$	−0.307588	−0.0101244
$924$	57.9631	1.90685
$925$	3.19708	0.105119
$926$	17.6953	0.581504
$927$	−23.0804	−0.758060
$928$	1.56276	0.0513001
$929$	−36.8738	−1.20979	−0.604895	−	0.796305i	$-0.706785\pi$
$929$	−36.8738	−1.20979	−0.604895	+	0.796305i	$0.706785\pi$
$930$	10.4459	0.342534
$931$	19.5578	0.640982
$932$	2.28555	0.0748658
$933$	−4.80034	−0.157156
$934$	34.8388	1.13996
$935$	15.5992	0.510148
$936$	0.798670	0.0261053
$937$	0.605775	0.0197898	0.00989490	−	0.999951i	$-0.496850\pi$
$937$	0.605775	0.0197898	0.00989490	+	0.999951i	$0.496850\pi$
$938$	−35.7338	−1.16675
$939$	−70.5490	−2.30228
$940$	1.71095	0.0558052
$941$	14.8707	0.484770	0.242385	−	0.970180i	$-0.422070\pi$
$941$	14.8707	0.484770	0.242385	+	0.970180i	$0.422070\pi$
$942$	31.7104	1.03318
$943$	−17.2252	−0.560930
$944$	−2.89191	−0.0941237
$945$	8.11571	0.264004
$946$	44.9975	1.46300
$947$	14.6651	0.476553	0.238276	−	0.971197i	$-0.423418\pi$
$947$	14.6651	0.476553	0.238276	+	0.971197i	$0.423418\pi$
$948$	−20.6484	−0.670628
$949$	1.63458	0.0530607
$950$	1.17341	0.0380704
$951$	−55.6044	−1.80310
$952$	14.6270	0.474064
$953$	26.7964	0.868021	0.434011	−	0.900908i	$-0.357098\pi$
$953$	26.7964	0.868021	0.434011	+	0.900908i	$0.357098\pi$
$954$	−25.5416	−0.826941
$955$	12.2944	0.397838
$956$	−22.6300	−0.731908
$957$	−18.6195	−0.601882
$958$	−29.5093	−0.953402
$959$	−15.9233	−0.514191
$960$	2.29642	0.0741168
$961$	−10.3088	−0.332542
$962$	1.12309	0.0362098
$963$	30.6525	0.987763
$964$	−25.4213	−0.818763
$965$	−1.37934	−0.0444025
$966$	−79.0434	−2.54318
$967$	−23.0703	−0.741890	−0.370945	−	0.928655i	$-0.620966\pi$
$967$	−23.0703	−0.741890	−0.370945	+	0.928655i	$0.620966\pi$
$968$	15.9182	0.511632
$969$	8.10177	0.260266
$970$	−0.409677	−0.0131539
$971$	−61.1943	−1.96382	−0.981909	−	0.189353i	$-0.939361\pi$
$971$	−61.1943	−1.96382	−0.981909	+	0.189353i	$0.939361\pi$
$972$	19.4560	0.624050
$973$	−60.9817	−1.95498
$974$	11.6116	0.372060
$975$	−0.806701	−0.0258351
$976$	−4.11226	−0.131630
$977$	−53.6732	−1.71716	−0.858579	−	0.512681i	$-0.828652\pi$
$977$	−53.6732	−1.71716	−0.858579	+	0.512681i	$0.828652\pi$
$978$	33.9319	1.08502
$979$	63.5075	2.02971
$980$	−16.6675	−0.532425
$981$	−31.8070	−1.01552
$982$	−7.61142	−0.242890
$983$	59.2849	1.89089	0.945447	−	0.325777i	$-0.105626\pi$
$983$	59.2849	1.89089	0.945447	+	0.325777i	$0.105626\pi$
$984$	−5.59088	−0.178231
$985$	−4.98090	−0.158705
$986$	−4.69863	−0.149635
$987$	−19.1147	−0.608427
$988$	0.412202	0.0131139
$989$	−61.3624	−1.95121
$990$	−11.7959	−0.374898
$991$	6.77290	0.215148	0.107574	−	0.994197i	$-0.465692\pi$
$991$	6.77290	0.215148	0.107574	+	0.994197i	$0.465692\pi$
$992$	4.54876	0.144423
$993$	31.7573	1.00779
$994$	4.25976	0.135111
$995$	21.4843	0.681098
$996$	23.2268	0.735968
$997$	−31.5030	−0.997709	−0.498855	−	0.866686i	$-0.666246\pi$
$997$	−31.5030	−0.997709	−0.498855	+	0.866686i	$0.666246\pi$
$998$	−8.62675	−0.273075
$999$	5.33339	0.168741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.4	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.29642 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.29642 q^{6} -4.86493 q^{7} +1.00000 q^{8} +2.27356 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.29642 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.29642 q^{6} -4.86493 q^{7} +1.00000 q^{8} +2.27356 q^{9} -1.00000 q^{10} +5.18828 q^{11} -2.29642 q^{12} +0.351286 q^{13} -4.86493 q^{14} +2.29642 q^{15} +1.00000 q^{16} -3.00662 q^{17} +2.27356 q^{18} +1.17341 q^{19} -1.00000 q^{20} +11.1719 q^{21} +5.18828 q^{22} -7.07517 q^{23} -2.29642 q^{24} +1.00000 q^{25} +0.351286 q^{26} +1.66821 q^{27} -4.86493 q^{28} +1.56276 q^{29} +2.29642 q^{30} +4.54876 q^{31} +1.00000 q^{32} -11.9145 q^{33} -3.00662 q^{34} +4.86493 q^{35} +2.27356 q^{36} +3.19708 q^{37} +1.17341 q^{38} -0.806701 q^{39} -1.00000 q^{40} +2.43460 q^{41} +11.1719 q^{42} +8.67292 q^{43} +5.18828 q^{44} -2.27356 q^{45} -7.07517 q^{46} -1.71095 q^{47} -2.29642 q^{48} +16.6675 q^{49} +1.00000 q^{50} +6.90448 q^{51} +0.351286 q^{52} -11.2342 q^{53} +1.66821 q^{54} -5.18828 q^{55} -4.86493 q^{56} -2.69464 q^{57} +1.56276 q^{58} -2.89191 q^{59} +2.29642 q^{60} -4.11226 q^{61} +4.54876 q^{62} -11.0607 q^{63} +1.00000 q^{64} -0.351286 q^{65} -11.9145 q^{66} +7.34519 q^{67} -3.00662 q^{68} +16.2476 q^{69} +4.86493 q^{70} -0.875606 q^{71} +2.27356 q^{72} +4.65314 q^{73} +3.19708 q^{74} -2.29642 q^{75} +1.17341 q^{76} -25.2406 q^{77} -0.806701 q^{78} +8.99154 q^{79} -1.00000 q^{80} -10.6516 q^{81} +2.43460 q^{82} -10.1143 q^{83} +11.1719 q^{84} +3.00662 q^{85} +8.67292 q^{86} -3.58876 q^{87} +5.18828 q^{88} +12.2406 q^{89} -2.27356 q^{90} -1.70898 q^{91} -7.07517 q^{92} -10.4459 q^{93} -1.71095 q^{94} -1.17341 q^{95} -2.29642 q^{96} +0.409677 q^{97} +16.6675 q^{98} +11.7959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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