LMFDB - Embedded newform 6015.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50063 q^{2} -1.00000 q^{3} +4.25317 q^{4} +1.00000 q^{5} +2.50063 q^{6} +4.30119 q^{7} -5.63435 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.50063 q^{2} -1.00000 q^{3} +4.25317 q^{4} +1.00000 q^{5} +2.50063 q^{6} +4.30119 q^{7} -5.63435 q^{8} +1.00000 q^{9} -2.50063 q^{10} +2.03167 q^{11} -4.25317 q^{12} -3.82424 q^{13} -10.7557 q^{14} -1.00000 q^{15} +5.58310 q^{16} -5.83716 q^{17} -2.50063 q^{18} -3.96142 q^{19} +4.25317 q^{20} -4.30119 q^{21} -5.08046 q^{22} +7.94350 q^{23} +5.63435 q^{24} +1.00000 q^{25} +9.56303 q^{26} -1.00000 q^{27} +18.2937 q^{28} -7.30513 q^{29} +2.50063 q^{30} -3.05150 q^{31} -2.69260 q^{32} -2.03167 q^{33} +14.5966 q^{34} +4.30119 q^{35} +4.25317 q^{36} +7.99336 q^{37} +9.90607 q^{38} +3.82424 q^{39} -5.63435 q^{40} -7.66922 q^{41} +10.7557 q^{42} +9.24082 q^{43} +8.64103 q^{44} +1.00000 q^{45} -19.8638 q^{46} -8.02261 q^{47} -5.58310 q^{48} +11.5003 q^{49} -2.50063 q^{50} +5.83716 q^{51} -16.2651 q^{52} +8.28924 q^{53} +2.50063 q^{54} +2.03167 q^{55} -24.2344 q^{56} +3.96142 q^{57} +18.2675 q^{58} -10.3622 q^{59} -4.25317 q^{60} +6.76814 q^{61} +7.63068 q^{62} +4.30119 q^{63} -4.43300 q^{64} -3.82424 q^{65} +5.08046 q^{66} -11.0242 q^{67} -24.8264 q^{68} -7.94350 q^{69} -10.7557 q^{70} -4.33240 q^{71} -5.63435 q^{72} -0.442657 q^{73} -19.9885 q^{74} -1.00000 q^{75} -16.8486 q^{76} +8.73861 q^{77} -9.56303 q^{78} -4.50829 q^{79} +5.58310 q^{80} +1.00000 q^{81} +19.1779 q^{82} +0.380750 q^{83} -18.2937 q^{84} -5.83716 q^{85} -23.1079 q^{86} +7.30513 q^{87} -11.4471 q^{88} -7.02525 q^{89} -2.50063 q^{90} -16.4488 q^{91} +33.7851 q^{92} +3.05150 q^{93} +20.0616 q^{94} -3.96142 q^{95} +2.69260 q^{96} +11.6114 q^{97} -28.7580 q^{98} +2.03167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	−2.50063	−1.76821	−0.884107	−	0.467284i	$-0.845233\pi$
$2$	−2.50063	−1.76821	−0.884107	+	0.467284i	$0.845233\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.25317	2.12658
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.50063	1.02088
$7$	4.30119	1.62570	0.812849	−	0.582474i	$-0.197915\pi$
$7$	4.30119	1.62570	0.812849	+	0.582474i	$0.197915\pi$
$8$	−5.63435	−1.99204
$9$	1.00000	0.333333
$10$	−2.50063	−0.790770
$11$	2.03167	0.612571	0.306286	−	0.951940i	$-0.400914\pi$
$11$	2.03167	0.612571	0.306286	+	0.951940i	$0.400914\pi$
$12$	−4.25317	−1.22778
$13$	−3.82424	−1.06065	−0.530327	−	0.847793i	$-0.677931\pi$
$13$	−3.82424	−1.06065	−0.530327	+	0.847793i	$0.677931\pi$
$14$	−10.7557	−2.87458
$15$	−1.00000	−0.258199
$16$	5.58310	1.39578
$17$	−5.83716	−1.41572	−0.707859	−	0.706353i	$-0.750339\pi$
$17$	−5.83716	−1.41572	−0.707859	+	0.706353i	$0.750339\pi$
$18$	−2.50063	−0.589405
$19$	−3.96142	−0.908813	−0.454406	−	0.890794i	$-0.650149\pi$
$19$	−3.96142	−0.908813	−0.454406	+	0.890794i	$0.650149\pi$
$20$	4.25317	0.951037
$21$	−4.30119	−0.938598
$22$	−5.08046	−1.08316
$23$	7.94350	1.65633	0.828167	−	0.560481i	$-0.189384\pi$
$23$	7.94350	1.65633	0.828167	+	0.560481i	$0.189384\pi$
$24$	5.63435	1.15011
$25$	1.00000	0.200000
$26$	9.56303	1.87546
$27$	−1.00000	−0.192450
$28$	18.2937	3.45719
$29$	−7.30513	−1.35653	−0.678264	−	0.734818i	$-0.737268\pi$
$29$	−7.30513	−1.35653	−0.678264	+	0.734818i	$0.737268\pi$
$30$	2.50063	0.456551
$31$	−3.05150	−0.548065	−0.274033	−	0.961720i	$-0.588358\pi$
$31$	−3.05150	−0.548065	−0.274033	+	0.961720i	$0.588358\pi$
$32$	−2.69260	−0.475989
$33$	−2.03167	−0.353668
$34$	14.5966	2.50330
$35$	4.30119	0.727035
$36$	4.25317	0.708861
$37$	7.99336	1.31410	0.657050	−	0.753847i	$-0.271804\pi$
$37$	7.99336	1.31410	0.657050	+	0.753847i	$0.271804\pi$
$38$	9.90607	1.60698
$39$	3.82424	0.612369
$40$	−5.63435	−0.890869
$41$	−7.66922	−1.19773	−0.598865	−	0.800850i	$-0.704381\pi$
$41$	−7.66922	−1.19773	−0.598865	+	0.800850i	$0.704381\pi$
$42$	10.7557	1.65964
$43$	9.24082	1.40921	0.704606	−	0.709599i	$-0.251124\pi$
$43$	9.24082	1.40921	0.704606	+	0.709599i	$0.251124\pi$
$44$	8.64103	1.30268
$45$	1.00000	0.149071
$46$	−19.8638	−2.92876
$47$	−8.02261	−1.17022	−0.585109	−	0.810954i	$-0.698948\pi$
$47$	−8.02261	−1.17022	−0.585109	+	0.810954i	$0.698948\pi$
$48$	−5.58310	−0.805851
$49$	11.5003	1.64290
$50$	−2.50063	−0.353643
$51$	5.83716	0.817366
$52$	−16.2651	−2.25557
$53$	8.28924	1.13861	0.569307	−	0.822125i	$-0.307211\pi$
$53$	8.28924	1.13861	0.569307	+	0.822125i	$0.307211\pi$
$54$	2.50063	0.340293
$55$	2.03167	0.273950
$56$	−24.2344	−3.23846
$57$	3.96142	0.524703
$58$	18.2675	2.39863
$59$	−10.3622	−1.34904	−0.674521	−	0.738256i	$-0.735650\pi$
$59$	−10.3622	−1.34904	−0.674521	+	0.738256i	$0.735650\pi$
$60$	−4.25317	−0.549082
$61$	6.76814	0.866571	0.433286	−	0.901257i	$-0.357354\pi$
$61$	6.76814	0.866571	0.433286	+	0.901257i	$0.357354\pi$
$62$	7.63068	0.969097
$63$	4.30119	0.541900
$64$	−4.43300	−0.554125
$65$	−3.82424	−0.474339
$66$	5.08046	0.625361
$67$	−11.0242	−1.34682	−0.673409	−	0.739270i	$-0.735171\pi$
$67$	−11.0242	−1.34682	−0.673409	+	0.739270i	$0.735171\pi$
$68$	−24.8264	−3.01064
$69$	−7.94350	−0.956285
$70$	−10.7557	−1.28555
$71$	−4.33240	−0.514162	−0.257081	−	0.966390i	$-0.582761\pi$
$71$	−4.33240	−0.514162	−0.257081	+	0.966390i	$0.582761\pi$
$72$	−5.63435	−0.664014
$73$	−0.442657	−0.0518091	−0.0259045	−	0.999664i	$-0.508247\pi$
$73$	−0.442657	−0.0518091	−0.0259045	+	0.999664i	$0.508247\pi$
$74$	−19.9885	−2.32361
$75$	−1.00000	−0.115470
$76$	−16.8486	−1.93267
$77$	8.73861	0.995856
$78$	−9.56303	−1.08280
$79$	−4.50829	−0.507222	−0.253611	−	0.967306i	$-0.581618\pi$
$79$	−4.50829	−0.507222	−0.253611	+	0.967306i	$0.581618\pi$
$80$	5.58310	0.624210
$81$	1.00000	0.111111
$82$	19.1779	2.11784
$83$	0.380750	0.0417928	0.0208964	−	0.999782i	$-0.493348\pi$
$83$	0.380750	0.0417928	0.0208964	+	0.999782i	$0.493348\pi$
$84$	−18.2937	−1.99601
$85$	−5.83716	−0.633129
$86$	−23.1079	−2.49179
$87$	7.30513	0.783192
$88$	−11.4471	−1.22027
$89$	−7.02525	−0.744675	−0.372338	−	0.928097i	$-0.621444\pi$
$89$	−7.02525	−0.744675	−0.372338	+	0.928097i	$0.621444\pi$
$90$	−2.50063	−0.263590
$91$	−16.4488	−1.72430
$92$	33.7851	3.52234
$93$	3.05150	0.316426
$94$	20.0616	2.06920
$95$	−3.96142	−0.406433
$96$	2.69260	0.274812
$97$	11.6114	1.17896	0.589480	−	0.807783i	$-0.299333\pi$
$97$	11.6114	1.17896	0.589480	+	0.807783i	$0.299333\pi$
$98$	−28.7580	−2.90499
$99$	2.03167	0.204190
$100$	4.25317	0.425317
$101$	−14.4342	−1.43626	−0.718130	−	0.695909i	$-0.755002\pi$
$101$	−14.4342	−1.43626	−0.718130	+	0.695909i	$0.755002\pi$
$102$	−14.5966	−1.44528
$103$	−1.30915	−0.128994	−0.0644971	−	0.997918i	$-0.520544\pi$
$103$	−1.30915	−0.128994	−0.0644971	+	0.997918i	$0.520544\pi$
$104$	21.5471	2.11287
$105$	−4.30119	−0.419754
$106$	−20.7284	−2.01332
$107$	−16.8281	−1.62683	−0.813415	−	0.581684i	$-0.802394\pi$
$107$	−16.8281	−1.62683	−0.813415	+	0.581684i	$0.802394\pi$
$108$	−4.25317	−0.409261
$109$	19.5833	1.87574	0.937868	−	0.346992i	$-0.112797\pi$
$109$	19.5833	1.87574	0.937868	+	0.346992i	$0.112797\pi$
$110$	−5.08046	−0.484403
$111$	−7.99336	−0.758696
$112$	24.0140	2.26911
$113$	−14.5191	−1.36584	−0.682922	−	0.730491i	$-0.739291\pi$
$113$	−14.5191	−1.36584	−0.682922	+	0.730491i	$0.739291\pi$
$114$	−9.90607	−0.927788
$115$	7.94350	0.740735
$116$	−31.0699	−2.88477
$117$	−3.82424	−0.353551
$118$	25.9120	2.38539
$119$	−25.1068	−2.30153
$120$	5.63435	0.514343
$121$	−6.87232	−0.624756
$122$	−16.9246	−1.53228
$123$	7.66922	0.691510
$124$	−12.9785	−1.16551
$125$	1.00000	0.0894427
$126$	−10.7557	−0.958195
$127$	−14.9792	−1.32919	−0.664594	−	0.747205i	$-0.731395\pi$
$127$	−14.9792	−1.32919	−0.664594	+	0.747205i	$0.731395\pi$
$128$	16.4705	1.45580
$129$	−9.24082	−0.813609
$130$	9.56303	0.838733
$131$	−15.2328	−1.33089	−0.665446	−	0.746446i	$-0.731759\pi$
$131$	−15.2328	−1.33089	−0.665446	+	0.746446i	$0.731759\pi$
$132$	−8.64103	−0.752105
$133$	−17.0389	−1.47746
$134$	27.5675	2.38147
$135$	−1.00000	−0.0860663
$136$	32.8886	2.82017
$137$	14.7223	1.25781	0.628905	−	0.777482i	$-0.283504\pi$
$137$	14.7223	1.25781	0.628905	+	0.777482i	$0.283504\pi$
$138$	19.8638	1.69092
$139$	16.3270	1.38484	0.692420	−	0.721495i	$-0.256545\pi$
$139$	16.3270	1.38484	0.692420	+	0.721495i	$0.256545\pi$
$140$	18.2937	1.54610
$141$	8.02261	0.675626
$142$	10.8338	0.909149
$143$	−7.76959	−0.649726
$144$	5.58310	0.465259
$145$	−7.30513	−0.606658
$146$	1.10692	0.0916096
$147$	−11.5003	−0.948527
$148$	33.9971	2.79454
$149$	−0.973240	−0.0797309	−0.0398654	−	0.999205i	$-0.512693\pi$
$149$	−0.973240	−0.0797309	−0.0398654	+	0.999205i	$0.512693\pi$
$150$	2.50063	0.204176
$151$	10.1784	0.828306	0.414153	−	0.910207i	$-0.364078\pi$
$151$	10.1784	0.828306	0.414153	+	0.910207i	$0.364078\pi$
$152$	22.3200	1.81039
$153$	−5.83716	−0.471906
$154$	−21.8520	−1.76089
$155$	−3.05150	−0.245102
$156$	16.2651	1.30225
$157$	−0.494112	−0.0394344	−0.0197172	−	0.999806i	$-0.506277\pi$
$157$	−0.494112	−0.0394344	−0.0197172	+	0.999806i	$0.506277\pi$
$158$	11.2736	0.896878
$159$	−8.28924	−0.657379
$160$	−2.69260	−0.212869
$161$	34.1666	2.69270
$162$	−2.50063	−0.196468
$163$	−13.2756	−1.03983	−0.519913	−	0.854219i	$-0.674036\pi$
$163$	−13.2756	−1.03983	−0.519913	+	0.854219i	$0.674036\pi$
$164$	−32.6185	−2.54707
$165$	−2.03167	−0.158165
$166$	−0.952117	−0.0738986
$167$	19.4152	1.50239	0.751197	−	0.660078i	$-0.229477\pi$
$167$	19.4152	1.50239	0.751197	+	0.660078i	$0.229477\pi$
$168$	24.2344	1.86973
$169$	1.62482	0.124986
$170$	14.5966	1.11951
$171$	−3.96142	−0.302938
$172$	39.3028	2.99681
$173$	−21.2045	−1.61215	−0.806075	−	0.591813i	$-0.798412\pi$
$173$	−21.2045	−1.61215	−0.806075	+	0.591813i	$0.798412\pi$
$174$	−18.2675	−1.38485
$175$	4.30119	0.325140
$176$	11.3430	0.855012
$177$	10.3622	0.778869
$178$	17.5676	1.31675
$179$	16.0660	1.20083	0.600414	−	0.799689i	$-0.295002\pi$
$179$	16.0660	1.20083	0.600414	+	0.799689i	$0.295002\pi$
$180$	4.25317	0.317012
$181$	−12.4092	−0.922368	−0.461184	−	0.887305i	$-0.652575\pi$
$181$	−12.4092	−0.922368	−0.461184	+	0.887305i	$0.652575\pi$
$182$	41.1324	3.04894
$183$	−6.76814	−0.500315
$184$	−44.7565	−3.29949
$185$	7.99336	0.587683
$186$	−7.63068	−0.559508
$187$	−11.8592	−0.867229
$188$	−34.1215	−2.48857
$189$	−4.30119	−0.312866
$190$	9.90607	0.718662
$191$	−21.8853	−1.58356	−0.791781	−	0.610805i	$-0.790846\pi$
$191$	−21.8853	−1.58356	−0.791781	+	0.610805i	$0.790846\pi$
$192$	4.43300	0.319924
$193$	4.99662	0.359664	0.179832	−	0.983697i	$-0.442445\pi$
$193$	4.99662	0.359664	0.179832	+	0.983697i	$0.442445\pi$
$194$	−29.0359	−2.08465
$195$	3.82424	0.273860
$196$	48.9126	3.49376
$197$	8.43385	0.600887	0.300443	−	0.953800i	$-0.402865\pi$
$197$	8.43385	0.600887	0.300443	+	0.953800i	$0.402865\pi$
$198$	−5.08046	−0.361053
$199$	7.28680	0.516548	0.258274	−	0.966072i	$-0.416846\pi$
$199$	7.28680	0.516548	0.258274	+	0.966072i	$0.416846\pi$
$200$	−5.63435	−0.398409
$201$	11.0242	0.777586
$202$	36.0947	2.53962
$203$	−31.4208	−2.20531
$204$	24.8264	1.73820
$205$	−7.66922	−0.535641
$206$	3.27370	0.228089
$207$	7.94350	0.552112
$208$	−21.3511	−1.48043
$209$	−8.04830	−0.556713
$210$	10.7557	0.742215
$211$	6.41020	0.441297	0.220648	−	0.975353i	$-0.429183\pi$
$211$	6.41020	0.441297	0.220648	+	0.975353i	$0.429183\pi$
$212$	35.2555	2.42136
$213$	4.33240	0.296851
$214$	42.0808	2.87658
$215$	9.24082	0.630219
$216$	5.63435	0.383369
$217$	−13.1251	−0.890989
$218$	−48.9706	−3.31670
$219$	0.442657	0.0299120
$220$	8.64103	0.582578
$221$	22.3227	1.50159
$222$	19.9885	1.34154
$223$	−12.8590	−0.861102	−0.430551	−	0.902566i	$-0.641681\pi$
$223$	−12.8590	−0.861102	−0.430551	+	0.902566i	$0.641681\pi$
$224$	−11.5814	−0.773814
$225$	1.00000	0.0666667
$226$	36.3070	2.41511
$227$	−14.6178	−0.970217	−0.485109	−	0.874454i	$-0.661220\pi$
$227$	−14.6178	−0.970217	−0.485109	+	0.874454i	$0.661220\pi$
$228$	16.8486	1.11583
$229$	−22.6953	−1.49975	−0.749875	−	0.661579i	$-0.769886\pi$
$229$	−22.6953	−1.49975	−0.749875	+	0.661579i	$0.769886\pi$
$230$	−19.8638	−1.30978
$231$	−8.73861	−0.574958
$232$	41.1596	2.70226
$233$	−4.45943	−0.292147	−0.146074	−	0.989274i	$-0.546664\pi$
$233$	−4.45943	−0.292147	−0.146074	+	0.989274i	$0.546664\pi$
$234$	9.56303	0.625155
$235$	−8.02261	−0.523338
$236$	−44.0721	−2.86885
$237$	4.50829	0.292845
$238$	62.7828	4.06960
$239$	−22.9841	−1.48672	−0.743360	−	0.668892i	$-0.766769\pi$
$239$	−22.9841	−1.48672	−0.743360	+	0.668892i	$0.766769\pi$
$240$	−5.58310	−0.360388
$241$	−27.5460	−1.77439	−0.887196	−	0.461393i	$-0.847350\pi$
$241$	−27.5460	−1.77439	−0.887196	+	0.461393i	$0.847350\pi$
$242$	17.1852	1.10470
$243$	−1.00000	−0.0641500
$244$	28.7860	1.84284
$245$	11.5003	0.734726
$246$	−19.1779	−1.22274
$247$	15.1494	0.963936
$248$	17.1932	1.09177
$249$	−0.380750	−0.0241291
$250$	−2.50063	−0.158154
$251$	20.1235	1.27018	0.635091	−	0.772438i	$-0.280963\pi$
$251$	20.1235	1.27018	0.635091	+	0.772438i	$0.280963\pi$
$252$	18.2937	1.15240
$253$	16.1386	1.01462
$254$	37.4575	2.35029
$255$	5.83716	0.365537
$256$	−32.3207	−2.02004
$257$	19.2850	1.20296	0.601482	−	0.798886i	$-0.294577\pi$
$257$	19.2850	1.20296	0.601482	+	0.798886i	$0.294577\pi$
$258$	23.1079	1.43863
$259$	34.3810	2.13633
$260$	−16.2651	−1.00872
$261$	−7.30513	−0.452176
$262$	38.0915	2.35330
$263$	−0.0687599	−0.00423992	−0.00211996	−	0.999998i	$-0.500675\pi$
$263$	−0.0687599	−0.00423992	−0.00211996	+	0.999998i	$0.500675\pi$
$264$	11.4471	0.704522
$265$	8.28924	0.509204
$266$	42.6079	2.61246
$267$	7.02525	0.429938
$268$	−46.8877	−2.86412
$269$	31.1199	1.89741	0.948707	−	0.316158i	$-0.102393\pi$
$269$	31.1199	1.89741	0.948707	+	0.316158i	$0.102393\pi$
$270$	2.50063	0.152184
$271$	−12.7407	−0.773943	−0.386972	−	0.922092i	$-0.626479\pi$
$271$	−12.7407	−0.773943	−0.386972	+	0.922092i	$0.626479\pi$
$272$	−32.5895	−1.97603
$273$	16.4488	0.995527
$274$	−36.8150	−2.22408
$275$	2.03167	0.122514
$276$	−33.7851	−2.03362
$277$	−1.84807	−0.111040	−0.0555200	−	0.998458i	$-0.517682\pi$
$277$	−1.84807	−0.111040	−0.0555200	+	0.998458i	$0.517682\pi$
$278$	−40.8279	−2.44869
$279$	−3.05150	−0.182688
$280$	−24.2344	−1.44828
$281$	−7.70657	−0.459735	−0.229868	−	0.973222i	$-0.573829\pi$
$281$	−7.70657	−0.459735	−0.229868	+	0.973222i	$0.573829\pi$
$282$	−20.0616	−1.19465
$283$	22.7938	1.35495	0.677475	−	0.735545i	$-0.263074\pi$
$283$	22.7938	1.35495	0.677475	+	0.735545i	$0.263074\pi$
$284$	−18.4264	−1.09341
$285$	3.96142	0.234654
$286$	19.4289	1.14886
$287$	−32.9868	−1.94715
$288$	−2.69260	−0.158663
$289$	17.0724	1.00426
$290$	18.2675	1.07270
$291$	−11.6114	−0.680672
$292$	−1.88269	−0.110176
$293$	12.0392	0.703337	0.351668	−	0.936125i	$-0.385615\pi$
$293$	12.0392	0.703337	0.351668	+	0.936125i	$0.385615\pi$
$294$	28.7580	1.67720
$295$	−10.3622	−0.603309
$296$	−45.0373	−2.61774
$297$	−2.03167	−0.117889
$298$	2.43372	0.140981
$299$	−30.3779	−1.75680
$300$	−4.25317	−0.245557
$301$	39.7466	2.29095
$302$	−25.4524	−1.46462
$303$	14.4342	0.829225
$304$	−22.1170	−1.26850
$305$	6.76814	0.387542
$306$	14.5966	0.834432
$307$	−10.0073	−0.571147	−0.285574	−	0.958357i	$-0.592184\pi$
$307$	−10.0073	−0.571147	−0.285574	+	0.958357i	$0.592184\pi$
$308$	37.1668	2.11777
$309$	1.30915	0.0744748
$310$	7.63068	0.433393
$311$	−23.3825	−1.32590	−0.662949	−	0.748665i	$-0.730695\pi$
$311$	−23.3825	−1.32590	−0.662949	+	0.748665i	$0.730695\pi$
$312$	−21.5471	−1.21986
$313$	−4.79042	−0.270770	−0.135385	−	0.990793i	$-0.543227\pi$
$313$	−4.79042	−0.270770	−0.135385	+	0.990793i	$0.543227\pi$
$314$	1.23559	0.0697286
$315$	4.30119	0.242345
$316$	−19.1745	−1.07865
$317$	15.6853	0.880977	0.440488	−	0.897758i	$-0.354805\pi$
$317$	15.6853	0.880977	0.440488	+	0.897758i	$0.354805\pi$
$318$	20.7284	1.16239
$319$	−14.8416	−0.830971
$320$	−4.43300	−0.247812
$321$	16.8281	0.939250
$322$	−85.4380	−4.76127
$323$	23.1235	1.28662
$324$	4.25317	0.236287
$325$	−3.82424	−0.212131
$326$	33.1974	1.83864
$327$	−19.5833	−1.08296
$328$	43.2110	2.38593
$329$	−34.5068	−1.90242
$330$	5.08046	0.279670
$331$	−6.40511	−0.352057	−0.176028	−	0.984385i	$-0.556325\pi$
$331$	−6.40511	−0.352057	−0.176028	+	0.984385i	$0.556325\pi$
$332$	1.61940	0.0888759
$333$	7.99336	0.438033
$334$	−48.5504	−2.65656
$335$	−11.0242	−0.602316
$336$	−24.0140	−1.31007
$337$	−16.4379	−0.895429	−0.447715	−	0.894176i	$-0.647762\pi$
$337$	−16.4379	−0.895429	−0.447715	+	0.894176i	$0.647762\pi$
$338$	−4.06308	−0.221002
$339$	14.5191	0.788570
$340$	−24.8264	−1.34640
$341$	−6.19963	−0.335729
$342$	9.90607	0.535659
$343$	19.3566	1.04516
$344$	−52.0660	−2.80721
$345$	−7.94350	−0.427664
$346$	53.0247	2.85063
$347$	−26.7212	−1.43447	−0.717234	−	0.696832i	$-0.754592\pi$
$347$	−26.7212	−1.43447	−0.717234	+	0.696832i	$0.754592\pi$
$348$	31.0699	1.66552
$349$	−30.0666	−1.60943	−0.804714	−	0.593662i	$-0.797681\pi$
$349$	−30.0666	−1.60943	−0.804714	+	0.593662i	$0.797681\pi$
$350$	−10.7557	−0.574917
$351$	3.82424	0.204123
$352$	−5.47047	−0.291577
$353$	35.9859	1.91533	0.957667	−	0.287877i	$-0.0929495\pi$
$353$	35.9859	1.91533	0.957667	+	0.287877i	$0.0929495\pi$
$354$	−25.9120	−1.37721
$355$	−4.33240	−0.229940
$356$	−29.8796	−1.58361
$357$	25.1068	1.32879
$358$	−40.1751	−2.12332
$359$	13.4858	0.711752	0.355876	−	0.934533i	$-0.384183\pi$
$359$	13.4858	0.711752	0.355876	+	0.934533i	$0.384183\pi$
$360$	−5.63435	−0.296956
$361$	−3.30713	−0.174059
$362$	31.0308	1.63095
$363$	6.87232	0.360703
$364$	−69.9595	−3.66688
$365$	−0.442657	−0.0231697
$366$	16.9246	0.884665
$367$	−26.2420	−1.36982	−0.684911	−	0.728626i	$-0.740159\pi$
$367$	−26.2420	−1.36982	−0.684911	+	0.728626i	$0.740159\pi$
$368$	44.3494	2.31187
$369$	−7.66922	−0.399243
$370$	−19.9885	−1.03915
$371$	35.6536	1.85104
$372$	12.9785	0.672906
$373$	13.7142	0.710092	0.355046	−	0.934849i	$-0.384465\pi$
$373$	13.7142	0.710092	0.355046	+	0.934849i	$0.384465\pi$
$374$	29.6555	1.53345
$375$	−1.00000	−0.0516398
$376$	45.2022	2.33113
$377$	27.9366	1.43881
$378$	10.7557	0.553214
$379$	9.00245	0.462425	0.231212	−	0.972903i	$-0.425731\pi$
$379$	9.00245	0.462425	0.231212	+	0.972903i	$0.425731\pi$
$380$	−16.8486	−0.864315
$381$	14.9792	0.767407
$382$	54.7270	2.80008
$383$	24.3845	1.24599	0.622994	−	0.782227i	$-0.285916\pi$
$383$	24.3845	1.24599	0.622994	+	0.782227i	$0.285916\pi$
$384$	−16.4705	−0.840507
$385$	8.73861	0.445361
$386$	−12.4947	−0.635964
$387$	9.24082	0.469737
$388$	49.3852	2.50716
$389$	19.0654	0.966654	0.483327	−	0.875440i	$-0.339428\pi$
$389$	19.0654	0.966654	0.483327	+	0.875440i	$0.339428\pi$
$390$	−9.56303	−0.484243
$391$	−46.3675	−2.34490
$392$	−64.7965	−3.27272
$393$	15.2328	0.768391
$394$	−21.0900	−1.06250
$395$	−4.50829	−0.226837
$396$	8.64103	0.434228
$397$	16.5281	0.829521	0.414761	−	0.909931i	$-0.363865\pi$
$397$	16.5281	0.829521	0.414761	+	0.909931i	$0.363865\pi$
$398$	−18.2216	−0.913368
$399$	17.0389	0.853010
$400$	5.58310	0.279155
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−27.5675	−1.37494
$403$	11.6697	0.581307
$404$	−61.3912	−3.05433
$405$	1.00000	0.0496904
$406$	78.5719	3.89946
$407$	16.2399	0.804980
$408$	−32.8886	−1.62823
$409$	−7.78684	−0.385035	−0.192517	−	0.981294i	$-0.561665\pi$
$409$	−7.78684	−0.385035	−0.192517	+	0.981294i	$0.561665\pi$
$410$	19.1779	0.947129
$411$	−14.7223	−0.726196
$412$	−5.56802	−0.274317
$413$	−44.5698	−2.19313
$414$	−19.8638	−0.976252
$415$	0.380750	0.0186903
$416$	10.2971	0.504859
$417$	−16.3270	−0.799538
$418$	20.1259	0.984388
$419$	8.82026	0.430898	0.215449	−	0.976515i	$-0.430879\pi$
$419$	8.82026	0.430898	0.215449	+	0.976515i	$0.430879\pi$
$420$	−18.2937	−0.892641
$421$	−30.1505	−1.46945	−0.734724	−	0.678366i	$-0.762688\pi$
$421$	−30.1505	−1.46945	−0.734724	+	0.678366i	$0.762688\pi$
$422$	−16.0296	−0.780307
$423$	−8.02261	−0.390073
$424$	−46.7045	−2.26817
$425$	−5.83716	−0.283144
$426$	−10.8338	−0.524897
$427$	29.1111	1.40878
$428$	−71.5725	−3.45959
$429$	7.76959	0.375119
$430$	−23.1079	−1.11436
$431$	−19.0815	−0.919122	−0.459561	−	0.888146i	$-0.651993\pi$
$431$	−19.0815	−0.919122	−0.459561	+	0.888146i	$0.651993\pi$
$432$	−5.58310	−0.268617
$433$	−12.9892	−0.624219	−0.312109	−	0.950046i	$-0.601036\pi$
$433$	−12.9892	−0.624219	−0.312109	+	0.950046i	$0.601036\pi$
$434$	32.8210	1.57546
$435$	7.30513	0.350254
$436$	83.2909	3.98891
$437$	−31.4676	−1.50530
$438$	−1.10692	−0.0528908
$439$	23.2752	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$439$	23.2752	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$440$	−11.4471	−0.545721
$441$	11.5003	0.547632
$442$	−55.8209	−2.65513
$443$	−23.8819	−1.13466	−0.567331	−	0.823490i	$-0.692024\pi$
$443$	−23.8819	−1.13466	−0.567331	+	0.823490i	$0.692024\pi$
$444$	−33.9971	−1.61343
$445$	−7.02525	−0.333029
$446$	32.1556	1.52261
$447$	0.973240	0.0460327
$448$	−19.0672	−0.900841
$449$	−12.6271	−0.595908	−0.297954	−	0.954580i	$-0.596304\pi$
$449$	−12.6271	−0.595908	−0.297954	+	0.954580i	$0.596304\pi$
$450$	−2.50063	−0.117881
$451$	−15.5813	−0.733695
$452$	−61.7523	−2.90458
$453$	−10.1784	−0.478223
$454$	36.5538	1.71555
$455$	−16.4488	−0.771132
$456$	−22.3200	−1.04523
$457$	−35.3176	−1.65209	−0.826045	−	0.563605i	$-0.809414\pi$
$457$	−35.3176	−1.65209	−0.826045	+	0.563605i	$0.809414\pi$
$458$	56.7527	2.65188
$459$	5.83716	0.272455
$460$	33.7851	1.57524
$461$	27.7628	1.29304	0.646520	−	0.762897i	$-0.276224\pi$
$461$	27.7628	1.29304	0.646520	+	0.762897i	$0.276224\pi$
$462$	21.8520	1.01665
$463$	14.5409	0.675774	0.337887	−	0.941187i	$-0.390288\pi$
$463$	14.5409	0.675774	0.337887	+	0.941187i	$0.390288\pi$
$464$	−40.7853	−1.89341
$465$	3.05150	0.141510
$466$	11.1514	0.516579
$467$	−11.2746	−0.521726	−0.260863	−	0.965376i	$-0.584007\pi$
$467$	−11.2746	−0.521726	−0.260863	+	0.965376i	$0.584007\pi$
$468$	−16.2651	−0.751856
$469$	−47.4172	−2.18952
$470$	20.0616	0.925373
$471$	0.494112	0.0227675
$472$	58.3841	2.68735
$473$	18.7743	0.863243
$474$	−11.2736	−0.517813
$475$	−3.96142	−0.181763
$476$	−106.783	−4.89440
$477$	8.28924	0.379538
$478$	57.4749	2.62884
$479$	4.18281	0.191118	0.0955588	−	0.995424i	$-0.469536\pi$
$479$	4.18281	0.191118	0.0955588	+	0.995424i	$0.469536\pi$
$480$	2.69260	0.122900
$481$	−30.5685	−1.39380
$482$	68.8824	3.13751
$483$	−34.1666	−1.55463
$484$	−29.2291	−1.32860
$485$	11.6114	0.527247
$486$	2.50063	0.113431
$487$	−1.74756	−0.0791896	−0.0395948	−	0.999216i	$-0.512607\pi$
$487$	−1.74756	−0.0791896	−0.0395948	+	0.999216i	$0.512607\pi$
$488$	−38.1340	−1.72625
$489$	13.2756	0.600344
$490$	−28.7580	−1.29915
$491$	7.17861	0.323966	0.161983	−	0.986794i	$-0.448211\pi$
$491$	7.17861	0.323966	0.161983	+	0.986794i	$0.448211\pi$
$492$	32.6185	1.47055
$493$	42.6412	1.92046
$494$	−37.8832	−1.70445
$495$	2.03167	0.0913167
$496$	−17.0368	−0.764976
$497$	−18.6345	−0.835872
$498$	0.952117	0.0426654
$499$	40.5619	1.81580	0.907901	−	0.419186i	$-0.137684\pi$
$499$	40.5619	1.81580	0.907901	+	0.419186i	$0.137684\pi$
$500$	4.25317	0.190207
$501$	−19.4152	−0.867408
$502$	−50.3214	−2.24595
$503$	25.9496	1.15703	0.578517	−	0.815670i	$-0.303632\pi$
$503$	25.9496	1.15703	0.578517	+	0.815670i	$0.303632\pi$
$504$	−24.2344	−1.07949
$505$	−14.4342	−0.642315
$506$	−40.3567	−1.79407
$507$	−1.62482	−0.0721607
$508$	−63.7090	−2.82663
$509$	3.67678	0.162970	0.0814851	−	0.996675i	$-0.474034\pi$
$509$	3.67678	0.162970	0.0814851	+	0.996675i	$0.474034\pi$
$510$	−14.5966	−0.646348
$511$	−1.90395	−0.0842260
$512$	47.8812	2.11607
$513$	3.96142	0.174901
$514$	−48.2247	−2.12710
$515$	−1.30915	−0.0576879
$516$	−39.3028	−1.73021
$517$	−16.2993	−0.716842
$518$	−85.9742	−3.77749
$519$	21.2045	0.930775
$520$	21.5471	0.944903
$521$	36.6437	1.60539	0.802695	−	0.596390i	$-0.203399\pi$
$521$	36.6437	1.60539	0.802695	+	0.596390i	$0.203399\pi$
$522$	18.2675	0.799545
$523$	30.2733	1.32376	0.661879	−	0.749611i	$-0.269759\pi$
$523$	30.2733	1.32376	0.661879	+	0.749611i	$0.269759\pi$
$524$	−64.7875	−2.83025
$525$	−4.30119	−0.187720
$526$	0.171943	0.00749709
$527$	17.8121	0.775906
$528$	−11.3430	−0.493642
$529$	40.0992	1.74344
$530$	−20.7284	−0.900382
$531$	−10.3622	−0.449680
$532$	−72.4691	−3.14193
$533$	29.3289	1.27038
$534$	−17.5676	−0.760224
$535$	−16.8281	−0.727540
$536$	62.1141	2.68292
$537$	−16.0660	−0.693298
$538$	−77.8194	−3.35503
$539$	23.3648	1.00639
$540$	−4.25317	−0.183027
$541$	−19.8456	−0.853228	−0.426614	−	0.904434i	$-0.640294\pi$
$541$	−19.8456	−0.853228	−0.426614	+	0.904434i	$0.640294\pi$
$542$	31.8598	1.36850
$543$	12.4092	0.532529
$544$	15.7171	0.673866
$545$	19.5833	0.838855
$546$	−41.1324	−1.76031
$547$	−14.9340	−0.638530	−0.319265	−	0.947665i	$-0.603436\pi$
$547$	−14.9340	−0.638530	−0.319265	+	0.947665i	$0.603436\pi$
$548$	62.6163	2.67484
$549$	6.76814	0.288857
$550$	−5.08046	−0.216632
$551$	28.9387	1.23283
$552$	44.7565	1.90496
$553$	−19.3910	−0.824591
$554$	4.62136	0.196343
$555$	−7.99336	−0.339299
$556$	69.4416	2.94498
$557$	−37.3682	−1.58334	−0.791671	−	0.610947i	$-0.790789\pi$
$557$	−37.3682	−1.58334	−0.791671	+	0.610947i	$0.790789\pi$
$558$	7.63068	0.323032
$559$	−35.3391	−1.49469
$560$	24.0140	1.01478
$561$	11.8592	0.500695
$562$	19.2713	0.812911
$563$	−16.9470	−0.714233	−0.357116	−	0.934060i	$-0.616240\pi$
$563$	−16.9470	−0.714233	−0.357116	+	0.934060i	$0.616240\pi$
$564$	34.1215	1.43678
$565$	−14.5191	−0.610824
$566$	−56.9989	−2.39584
$567$	4.30119	0.180633
$568$	24.4103	1.02423
$569$	15.2623	0.639829	0.319915	−	0.947446i	$-0.396346\pi$
$569$	15.2623	0.639829	0.319915	+	0.947446i	$0.396346\pi$
$570$	−9.90607	−0.414920
$571$	7.11474	0.297743	0.148871	−	0.988857i	$-0.452436\pi$
$571$	7.11474	0.297743	0.148871	+	0.988857i	$0.452436\pi$
$572$	−33.0454	−1.38170
$573$	21.8853	0.914270
$574$	82.4879	3.44298
$575$	7.94350	0.331267
$576$	−4.43300	−0.184708
$577$	−12.7607	−0.531237	−0.265618	−	0.964078i	$-0.585576\pi$
$577$	−12.7607	−0.531237	−0.265618	+	0.964078i	$0.585576\pi$
$578$	−42.6918	−1.77575
$579$	−4.99662	−0.207652
$580$	−31.0699	−1.29011
$581$	1.63768	0.0679425
$582$	29.0359	1.20358
$583$	16.8410	0.697483
$584$	2.49408	0.103206
$585$	−3.82424	−0.158113
$586$	−30.1056	−1.24365
$587$	21.0879	0.870391	0.435196	−	0.900336i	$-0.356679\pi$
$587$	21.0879	0.870391	0.435196	+	0.900336i	$0.356679\pi$
$588$	−48.9126	−2.01712
$589$	12.0883	0.498089
$590$	25.9120	1.06678
$591$	−8.43385	−0.346922
$592$	44.6277	1.83419
$593$	17.5778	0.721835	0.360917	−	0.932598i	$-0.382464\pi$
$593$	17.5778	0.721835	0.360917	+	0.932598i	$0.382464\pi$
$594$	5.08046	0.208454
$595$	−25.1068	−1.02928
$596$	−4.13935	−0.169554
$597$	−7.28680	−0.298229
$598$	75.9639	3.10640
$599$	11.6226	0.474886	0.237443	−	0.971401i	$-0.423691\pi$
$599$	11.6226	0.474886	0.237443	+	0.971401i	$0.423691\pi$
$600$	5.63435	0.230021
$601$	−17.2750	−0.704661	−0.352330	−	0.935876i	$-0.614611\pi$
$601$	−17.2750	−0.704661	−0.352330	+	0.935876i	$0.614611\pi$
$602$	−99.3916	−4.05090
$603$	−11.0242	−0.448940
$604$	43.2904	1.76146
$605$	−6.87232	−0.279400
$606$	−36.0947	−1.46625
$607$	−19.7946	−0.803437	−0.401719	−	0.915763i	$-0.631587\pi$
$607$	−19.7946	−0.803437	−0.401719	+	0.915763i	$0.631587\pi$
$608$	10.6665	0.432585
$609$	31.4208	1.27323
$610$	−16.9246	−0.685258
$611$	30.6804	1.24120
$612$	−24.8264	−1.00355
$613$	−27.3734	−1.10560	−0.552802	−	0.833313i	$-0.686441\pi$
$613$	−27.3734	−1.10560	−0.552802	+	0.833313i	$0.686441\pi$
$614$	25.0246	1.00991
$615$	7.66922	0.309253
$616$	−49.2363	−1.98379
$617$	24.8624	1.00092	0.500461	−	0.865759i	$-0.333164\pi$
$617$	24.8624	1.00092	0.500461	+	0.865759i	$0.333164\pi$
$618$	−3.27370	−0.131687
$619$	−19.7439	−0.793573	−0.396786	−	0.917911i	$-0.629875\pi$
$619$	−19.7439	−0.793573	−0.396786	+	0.917911i	$0.629875\pi$
$620$	−12.9785	−0.521230
$621$	−7.94350	−0.318762
$622$	58.4710	2.34447
$623$	−30.2170	−1.21062
$624$	21.3511	0.854729
$625$	1.00000	0.0400000
$626$	11.9791	0.478780
$627$	8.04830	0.321418
$628$	−2.10154	−0.0838606
$629$	−46.6585	−1.86040
$630$	−10.7557	−0.428518
$631$	4.09771	0.163127	0.0815636	−	0.996668i	$-0.474009\pi$
$631$	4.09771	0.163127	0.0815636	+	0.996668i	$0.474009\pi$
$632$	25.4013	1.01041
$633$	−6.41020	−0.254783
$634$	−39.2233	−1.55776
$635$	−14.9792	−0.594431
$636$	−35.2555	−1.39797
$637$	−43.9798	−1.74254
$638$	37.1134	1.46933
$639$	−4.33240	−0.171387
$640$	16.4705	0.651054
$641$	−35.8749	−1.41697	−0.708487	−	0.705724i	$-0.750622\pi$
$641$	−35.8749	−1.41697	−0.708487	+	0.705724i	$0.750622\pi$
$642$	−42.0808	−1.66080
$643$	−25.3055	−0.997950	−0.498975	−	0.866616i	$-0.666290\pi$
$643$	−25.3055	−0.997950	−0.498975	+	0.866616i	$0.666290\pi$
$644$	145.316	5.72626
$645$	−9.24082	−0.363857
$646$	−57.8233	−2.27503
$647$	−33.6828	−1.32421	−0.662104	−	0.749412i	$-0.730336\pi$
$647$	−33.6828	−1.32421	−0.662104	+	0.749412i	$0.730336\pi$
$648$	−5.63435	−0.221338
$649$	−21.0525	−0.826384
$650$	9.56303	0.375093
$651$	13.1251	0.514413
$652$	−56.4634	−2.21128
$653$	−33.3159	−1.30375	−0.651875	−	0.758326i	$-0.726017\pi$
$653$	−33.3159	−1.30375	−0.651875	+	0.758326i	$0.726017\pi$
$654$	48.9706	1.91490
$655$	−15.2328	−0.595193
$656$	−42.8180	−1.67176
$657$	−0.442657	−0.0172697
$658$	86.2889	3.36389
$659$	−45.4321	−1.76978	−0.884892	−	0.465797i	$-0.845768\pi$
$659$	−45.4321	−1.76978	−0.884892	+	0.465797i	$0.845768\pi$
$660$	−8.64103	−0.336352
$661$	−29.7376	−1.15666	−0.578329	−	0.815803i	$-0.696295\pi$
$661$	−29.7376	−1.15666	−0.578329	+	0.815803i	$0.696295\pi$
$662$	16.0168	0.622512
$663$	−22.3227	−0.866942
$664$	−2.14528	−0.0832530
$665$	−17.0389	−0.660738
$666$	−19.9885	−0.774537
$667$	−58.0283	−2.24687
$668$	82.5762	3.19497
$669$	12.8590	0.497157
$670$	27.5675	1.06502
$671$	13.7506	0.530837
$672$	11.5814	0.446762
$673$	42.5991	1.64207	0.821037	−	0.570875i	$-0.193396\pi$
$673$	42.5991	1.64207	0.821037	+	0.570875i	$0.193396\pi$
$674$	41.1052	1.58331
$675$	−1.00000	−0.0384900
$676$	6.91063	0.265793
$677$	−20.3766	−0.783138	−0.391569	−	0.920149i	$-0.628068\pi$
$677$	−20.3766	−0.783138	−0.391569	+	0.920149i	$0.628068\pi$
$678$	−36.3070	−1.39436
$679$	49.9429	1.91663
$680$	32.8886	1.26122
$681$	14.6178	0.560155
$682$	15.5030	0.593641
$683$	−15.4813	−0.592374	−0.296187	−	0.955130i	$-0.595715\pi$
$683$	−15.4813	−0.592374	−0.296187	+	0.955130i	$0.595715\pi$
$684$	−16.8486	−0.644222
$685$	14.7223	0.562509
$686$	−48.4037	−1.84806
$687$	22.6953	0.865881
$688$	51.5924	1.96694
$689$	−31.7001	−1.20768
$690$	19.8638	0.756202
$691$	20.7916	0.790951	0.395476	−	0.918477i	$-0.370580\pi$
$691$	20.7916	0.790951	0.395476	+	0.918477i	$0.370580\pi$
$692$	−90.1864	−3.42837
$693$	8.73861	0.331952
$694$	66.8199	2.53645
$695$	16.3270	0.619319
$696$	−41.1596	−1.56015
$697$	44.7664	1.69565
$698$	75.1856	2.84582
$699$	4.45943	0.168671
$700$	18.2937	0.691437
$701$	−39.5163	−1.49251	−0.746255	−	0.665660i	$-0.768150\pi$
$701$	−39.5163	−1.49251	−0.746255	+	0.665660i	$0.768150\pi$
$702$	−9.56303	−0.360933
$703$	−31.6651	−1.19427
$704$	−9.00640	−0.339441
$705$	8.02261	0.302149
$706$	−89.9875	−3.38672
$707$	−62.0845	−2.33493
$708$	44.0721	1.65633
$709$	9.88160	0.371111	0.185556	−	0.982634i	$-0.440591\pi$
$709$	9.88160	0.371111	0.185556	+	0.982634i	$0.440591\pi$
$710$	10.8338	0.406584
$711$	−4.50829	−0.169074
$712$	39.5827	1.48342
$713$	−24.2396	−0.907779
$714$	−62.7828	−2.34959
$715$	−7.76959	−0.290566
$716$	68.3313	2.55366
$717$	22.9841	0.858358
$718$	−33.7230	−1.25853
$719$	−13.5305	−0.504604	−0.252302	−	0.967649i	$-0.581188\pi$
$719$	−13.5305	−0.504604	−0.252302	+	0.967649i	$0.581188\pi$
$720$	5.58310	0.208070
$721$	−5.63090	−0.209706
$722$	8.26991	0.307774
$723$	27.5460	1.02445
$724$	−52.7784	−1.96149
$725$	−7.30513	−0.271306
$726$	−17.1852	−0.637801
$727$	26.6914	0.989928	0.494964	−	0.868913i	$-0.335181\pi$
$727$	26.6914	0.989928	0.494964	+	0.868913i	$0.335181\pi$
$728$	92.6783	3.43489
$729$	1.00000	0.0370370
$730$	1.10692	0.0409691
$731$	−53.9401	−1.99505
$732$	−28.7860	−1.06396
$733$	−31.8632	−1.17690	−0.588448	−	0.808535i	$-0.700261\pi$
$733$	−31.8632	−1.17690	−0.588448	+	0.808535i	$0.700261\pi$
$734$	65.6217	2.42214
$735$	−11.5003	−0.424194
$736$	−21.3887	−0.788397
$737$	−22.3975	−0.825023
$738$	19.1779	0.705948
$739$	11.6539	0.428696	0.214348	−	0.976757i	$-0.431237\pi$
$739$	11.6539	0.428696	0.214348	+	0.976757i	$0.431237\pi$
$740$	33.9971	1.24976
$741$	−15.1494	−0.556528
$742$	−89.1567	−3.27304
$743$	8.91625	0.327106	0.163553	−	0.986535i	$-0.447705\pi$
$743$	8.91625	0.327106	0.163553	+	0.986535i	$0.447705\pi$
$744$	−17.1932	−0.630333
$745$	−0.973240	−0.0356567
$746$	−34.2941	−1.25560
$747$	0.380750	0.0139309
$748$	−50.4391	−1.84423
$749$	−72.3807	−2.64473
$750$	2.50063	0.0913102
$751$	−24.3681	−0.889206	−0.444603	−	0.895728i	$-0.646655\pi$
$751$	−24.3681	−0.889206	−0.444603	+	0.895728i	$0.646655\pi$
$752$	−44.7911	−1.63336
$753$	−20.1235	−0.733340
$754$	−69.8591	−2.54412
$755$	10.1784	0.370430
$756$	−18.2937	−0.665336
$757$	33.3535	1.21225	0.606126	−	0.795369i	$-0.292723\pi$
$757$	33.3535	1.21225	0.606126	+	0.795369i	$0.292723\pi$
$758$	−22.5118	−0.817666
$759$	−16.1386	−0.585793
$760$	22.3200	0.809633
$761$	−34.8218	−1.26229	−0.631144	−	0.775666i	$-0.717414\pi$
$761$	−34.8218	−1.26229	−0.631144	+	0.775666i	$0.717414\pi$
$762$	−37.4575	−1.35694
$763$	84.2314	3.04938
$764$	−93.0817	−3.36758
$765$	−5.83716	−0.211043
$766$	−60.9766	−2.20318
$767$	39.6275	1.43087
$768$	32.3207	1.16627
$769$	22.6190	0.815662	0.407831	−	0.913057i	$-0.366285\pi$
$769$	22.6190	0.815662	0.407831	+	0.913057i	$0.366285\pi$
$770$	−21.8520	−0.787493
$771$	−19.2850	−0.694532
$772$	21.2515	0.764857
$773$	−22.9177	−0.824294	−0.412147	−	0.911117i	$-0.635221\pi$
$773$	−22.9177	−0.824294	−0.412147	+	0.911117i	$0.635221\pi$
$774$	−23.1079	−0.830596
$775$	−3.05150	−0.109613
$776$	−65.4227	−2.34854
$777$	−34.3810	−1.23341
$778$	−47.6756	−1.70925
$779$	30.3810	1.08851
$780$	16.2651	0.582385
$781$	−8.80201	−0.314961
$782$	115.948	4.14629
$783$	7.30513	0.261064
$784$	64.2072	2.29311
$785$	−0.494112	−0.0176356
$786$	−38.0915	−1.35868
$787$	−24.1066	−0.859309	−0.429654	−	0.902993i	$-0.641365\pi$
$787$	−24.1066	−0.859309	−0.429654	+	0.902993i	$0.641365\pi$
$788$	35.8706	1.27784
$789$	0.0687599	0.00244792
$790$	11.2736	0.401096
$791$	−62.4496	−2.22045
$792$	−11.4471	−0.406756
$793$	−25.8830	−0.919132
$794$	−41.3307	−1.46677
$795$	−8.28924	−0.293989
$796$	30.9920	1.09848
$797$	−11.5244	−0.408214	−0.204107	−	0.978949i	$-0.565429\pi$
$797$	−11.5244	−0.408214	−0.204107	+	0.978949i	$0.565429\pi$
$798$	−42.6079	−1.50830
$799$	46.8293	1.65670
$800$	−2.69260	−0.0951977
$801$	−7.02525	−0.248225
$802$	−2.50063	−0.0883004
$803$	−0.899333	−0.0317368
$804$	46.8877	1.65360
$805$	34.1666	1.20421
$806$	−29.1815	−1.02788
$807$	−31.1199	−1.09547
$808$	81.3275	2.86109
$809$	−18.4359	−0.648171	−0.324085	−	0.946028i	$-0.605057\pi$
$809$	−18.4359	−0.648171	−0.324085	+	0.946028i	$0.605057\pi$
$810$	−2.50063	−0.0878633
$811$	−9.28949	−0.326198	−0.163099	−	0.986610i	$-0.552149\pi$
$811$	−9.28949	−0.326198	−0.163099	+	0.986610i	$0.552149\pi$
$812$	−133.638	−4.68977
$813$	12.7407	0.446836
$814$	−40.6099	−1.42338
$815$	−13.2756	−0.465024
$816$	32.5895	1.14086
$817$	−36.6068	−1.28071
$818$	19.4720	0.680824
$819$	−16.4488	−0.574768
$820$	−32.6185	−1.13909
$821$	53.4584	1.86571	0.932856	−	0.360249i	$-0.117308\pi$
$821$	53.4584	1.86571	0.932856	+	0.360249i	$0.117308\pi$
$822$	36.8150	1.28407
$823$	27.3865	0.954632	0.477316	−	0.878732i	$-0.341610\pi$
$823$	27.3865	0.954632	0.477316	+	0.878732i	$0.341610\pi$
$824$	7.37619	0.256962
$825$	−2.03167	−0.0707336
$826$	111.453	3.87793
$827$	−9.51015	−0.330700	−0.165350	−	0.986235i	$-0.552875\pi$
$827$	−9.51015	−0.330700	−0.165350	+	0.986235i	$0.552875\pi$
$828$	33.7851	1.17411
$829$	16.8397	0.584866	0.292433	−	0.956286i	$-0.405535\pi$
$829$	16.8397	0.584866	0.292433	+	0.956286i	$0.405535\pi$
$830$	−0.952117	−0.0330485
$831$	1.84807	0.0641090
$832$	16.9529	0.587735
$833$	−67.1289	−2.32588
$834$	40.8279	1.41375
$835$	19.4152	0.671891
$836$	−34.2308	−1.18390
$837$	3.05150	0.105475
$838$	−22.0562	−0.761920
$839$	−41.6430	−1.43768	−0.718838	−	0.695178i	$-0.755326\pi$
$839$	−41.6430	−1.43768	−0.718838	+	0.695178i	$0.755326\pi$
$840$	24.2344	0.836167
$841$	24.3649	0.840170
$842$	75.3955	2.59830
$843$	7.70657	0.265428
$844$	27.2637	0.938454
$845$	1.62482	0.0558955
$846$	20.0616	0.689733
$847$	−29.5592	−1.01567
$848$	46.2797	1.58925
$849$	−22.7938	−0.782281
$850$	14.5966	0.500659
$851$	63.4952	2.17659
$852$	18.4264	0.631280
$853$	−10.5660	−0.361774	−0.180887	−	0.983504i	$-0.557897\pi$
$853$	−10.5660	−0.361774	−0.180887	+	0.983504i	$0.557897\pi$
$854$	−72.7961	−2.49103
$855$	−3.96142	−0.135478
$856$	94.8151	3.24071
$857$	−3.03445	−0.103655	−0.0518274	−	0.998656i	$-0.516505\pi$
$857$	−3.03445	−0.103655	−0.0518274	+	0.998656i	$0.516505\pi$
$858$	−19.4289	−0.663292
$859$	57.1232	1.94902	0.974509	−	0.224346i	$-0.0720247\pi$
$859$	57.1232	1.94902	0.974509	+	0.224346i	$0.0720247\pi$
$860$	39.3028	1.34021
$861$	32.9868	1.12419
$862$	47.7158	1.62521
$863$	9.44671	0.321570	0.160785	−	0.986989i	$-0.448597\pi$
$863$	9.44671	0.321570	0.160785	+	0.986989i	$0.448597\pi$
$864$	2.69260	0.0916041
$865$	−21.2045	−0.720975
$866$	32.4811	1.10375
$867$	−17.0724	−0.579810
$868$	−55.8232	−1.89476
$869$	−9.15935	−0.310710
$870$	−18.2675	−0.619325
$871$	42.1591	1.42851
$872$	−110.339	−3.73655
$873$	11.6114	0.392986
$874$	78.6889	2.66169
$875$	4.30119	0.145407
$876$	1.88269	0.0636104
$877$	12.5514	0.423830	0.211915	−	0.977288i	$-0.432030\pi$
$877$	12.5514	0.423830	0.211915	+	0.977288i	$0.432030\pi$
$878$	−58.2027	−1.96425
$879$	−12.0392	−0.406072
$880$	11.3430	0.382373
$881$	−20.1271	−0.678100	−0.339050	−	0.940768i	$-0.610106\pi$
$881$	−20.1271	−0.678100	−0.339050	+	0.940768i	$0.610106\pi$
$882$	−28.7580	−0.968331
$883$	56.0438	1.88602	0.943012	−	0.332759i	$-0.107980\pi$
$883$	56.0438	1.88602	0.943012	+	0.332759i	$0.107980\pi$
$884$	94.9422	3.19325
$885$	10.3622	0.348321
$886$	59.7198	2.00632
$887$	33.9517	1.13999	0.569994	−	0.821649i	$-0.306946\pi$
$887$	33.9517	1.13999	0.569994	+	0.821649i	$0.306946\pi$
$888$	45.0373	1.51135
$889$	−64.4284	−2.16086
$890$	17.5676	0.588867
$891$	2.03167	0.0680635
$892$	−54.6915	−1.83121
$893$	31.7810	1.06351
$894$	−2.43372	−0.0813956
$895$	16.0660	0.537027
$896$	70.8429	2.36669
$897$	30.3779	1.01429
$898$	31.5757	1.05369
$899$	22.2916	0.743466
$900$	4.25317	0.141772
$901$	−48.3856	−1.61196
$902$	38.9632	1.29733
$903$	−39.7466	−1.32268
$904$	81.8058	2.72082
$905$	−12.4092	−0.412496
$906$	25.4524	0.845600
$907$	−3.70915	−0.123160	−0.0615801	−	0.998102i	$-0.519614\pi$
$907$	−3.70915	−0.123160	−0.0615801	+	0.998102i	$0.519614\pi$
$908$	−62.1720	−2.06325
$909$	−14.4342	−0.478753
$910$	41.1324	1.36353
$911$	18.6021	0.616317	0.308158	−	0.951335i	$-0.400287\pi$
$911$	18.6021	0.616317	0.308158	+	0.951335i	$0.400287\pi$
$912$	22.1170	0.732368
$913$	0.773559	0.0256011
$914$	88.3165	2.92125
$915$	−6.76814	−0.223748
$916$	−96.5271	−3.18934
$917$	−65.5191	−2.16363
$918$	−14.5966	−0.481759
$919$	−28.6985	−0.946675	−0.473338	−	0.880881i	$-0.656951\pi$
$919$	−28.6985	−0.946675	−0.473338	+	0.880881i	$0.656951\pi$
$920$	−44.7565	−1.47558
$921$	10.0073	0.329752
$922$	−69.4245	−2.28637
$923$	16.5682	0.545348
$924$	−37.1668	−1.22270
$925$	7.99336	0.262820
$926$	−36.3615	−1.19491
$927$	−1.30915	−0.0429980
$928$	19.6698	0.645692
$929$	19.5093	0.640080	0.320040	−	0.947404i	$-0.396304\pi$
$929$	19.5093	0.640080	0.320040	+	0.947404i	$0.396304\pi$
$930$	−7.63068	−0.250220
$931$	−45.5575	−1.49309
$932$	−18.9667	−0.621276
$933$	23.3825	0.765507
$934$	28.1936	0.922524
$935$	−11.8592	−0.387836
$936$	21.5471	0.704289
$937$	−44.1020	−1.44075	−0.720375	−	0.693585i	$-0.756030\pi$
$937$	−44.1020	−1.44075	−0.720375	+	0.693585i	$0.756030\pi$
$938$	118.573	3.87154
$939$	4.79042	0.156329
$940$	−34.1215	−1.11292
$941$	−33.0616	−1.07778	−0.538889	−	0.842377i	$-0.681156\pi$
$941$	−33.0616	−1.07778	−0.538889	+	0.842377i	$0.681156\pi$
$942$	−1.23559	−0.0402578
$943$	−60.9204	−1.98384
$944$	−57.8531	−1.88296
$945$	−4.30119	−0.139918
$946$	−46.9476	−1.52640
$947$	53.5600	1.74047	0.870233	−	0.492641i	$-0.163968\pi$
$947$	53.5600	1.74047	0.870233	+	0.492641i	$0.163968\pi$
$948$	19.1745	0.622759
$949$	1.69283	0.0549515
$950$	9.90607	0.321395
$951$	−15.6853	−0.508632
$952$	141.460	4.58475
$953$	31.3849	1.01666	0.508329	−	0.861163i	$-0.330263\pi$
$953$	31.3849	1.01666	0.508329	+	0.861163i	$0.330263\pi$
$954$	−20.7284	−0.671105
$955$	−21.8853	−0.708190
$956$	−97.7554	−3.16164
$957$	14.8416	0.479761
$958$	−10.4597	−0.337937
$959$	63.3234	2.04482
$960$	4.43300	0.143075
$961$	−21.6884	−0.699625
$962$	76.4407	2.46455
$963$	−16.8281	−0.542276
$964$	−117.158	−3.77339
$965$	4.99662	0.160847
$966$	85.4380	2.74892
$967$	25.7342	0.827557	0.413779	−	0.910377i	$-0.364209\pi$
$967$	25.7342	0.827557	0.413779	+	0.910377i	$0.364209\pi$
$968$	38.7210	1.24454
$969$	−23.1235	−0.742832
$970$	−29.0359	−0.932285
$971$	0.750028	0.0240695	0.0120348	−	0.999928i	$-0.496169\pi$
$971$	0.750028	0.0240695	0.0120348	+	0.999928i	$0.496169\pi$
$972$	−4.25317	−0.136420
$973$	70.2257	2.25133
$974$	4.37001	0.140024
$975$	3.82424	0.122474
$976$	37.7872	1.20954
$977$	−33.5222	−1.07247	−0.536235	−	0.844068i	$-0.680154\pi$
$977$	−33.5222	−1.07247	−0.536235	+	0.844068i	$0.680154\pi$
$978$	−33.1974	−1.06154
$979$	−14.2730	−0.456167
$980$	48.9126	1.56246
$981$	19.5833	0.625245
$982$	−17.9511	−0.572842
$983$	−2.91297	−0.0929092	−0.0464546	−	0.998920i	$-0.514792\pi$
$983$	−2.91297	−0.0929092	−0.0464546	+	0.998920i	$0.514792\pi$
$984$	−43.2110	−1.37752
$985$	8.43385	0.268725
$986$	−106.630	−3.39579
$987$	34.5068	1.09836
$988$	64.4331	2.04989
$989$	73.4045	2.33413
$990$	−5.08046	−0.161468
$991$	13.0828	0.415590	0.207795	−	0.978172i	$-0.433371\pi$
$991$	13.0828	0.415590	0.207795	+	0.978172i	$0.433371\pi$
$992$	8.21646	0.260873
$993$	6.40511	0.203260
$994$	46.5981	1.47800
$995$	7.28680	0.231007
$996$	−1.61940	−0.0513125
$997$	0.273929	0.00867543	0.00433771	−	0.999991i	$-0.498619\pi$
$997$	0.273929	0.00867543	0.00433771	+	0.999991i	$0.498619\pi$
$998$	−101.431	−3.21073
$999$	−7.99336	−0.252899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.2	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.2	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50063 q^{2} -1.00000 q^{3} +4.25317 q^{4} +1.00000 q^{5} +2.50063 q^{6} +4.30119 q^{7} -5.63435 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.50063 q^{2} -1.00000 q^{3} +4.25317 q^{4} +1.00000 q^{5} +2.50063 q^{6} +4.30119 q^{7} -5.63435 q^{8} +1.00000 q^{9} -2.50063 q^{10} +2.03167 q^{11} -4.25317 q^{12} -3.82424 q^{13} -10.7557 q^{14} -1.00000 q^{15} +5.58310 q^{16} -5.83716 q^{17} -2.50063 q^{18} -3.96142 q^{19} +4.25317 q^{20} -4.30119 q^{21} -5.08046 q^{22} +7.94350 q^{23} +5.63435 q^{24} +1.00000 q^{25} +9.56303 q^{26} -1.00000 q^{27} +18.2937 q^{28} -7.30513 q^{29} +2.50063 q^{30} -3.05150 q^{31} -2.69260 q^{32} -2.03167 q^{33} +14.5966 q^{34} +4.30119 q^{35} +4.25317 q^{36} +7.99336 q^{37} +9.90607 q^{38} +3.82424 q^{39} -5.63435 q^{40} -7.66922 q^{41} +10.7557 q^{42} +9.24082 q^{43} +8.64103 q^{44} +1.00000 q^{45} -19.8638 q^{46} -8.02261 q^{47} -5.58310 q^{48} +11.5003 q^{49} -2.50063 q^{50} +5.83716 q^{51} -16.2651 q^{52} +8.28924 q^{53} +2.50063 q^{54} +2.03167 q^{55} -24.2344 q^{56} +3.96142 q^{57} +18.2675 q^{58} -10.3622 q^{59} -4.25317 q^{60} +6.76814 q^{61} +7.63068 q^{62} +4.30119 q^{63} -4.43300 q^{64} -3.82424 q^{65} +5.08046 q^{66} -11.0242 q^{67} -24.8264 q^{68} -7.94350 q^{69} -10.7557 q^{70} -4.33240 q^{71} -5.63435 q^{72} -0.442657 q^{73} -19.9885 q^{74} -1.00000 q^{75} -16.8486 q^{76} +8.73861 q^{77} -9.56303 q^{78} -4.50829 q^{79} +5.58310 q^{80} +1.00000 q^{81} +19.1779 q^{82} +0.380750 q^{83} -18.2937 q^{84} -5.83716 q^{85} -23.1079 q^{86} +7.30513 q^{87} -11.4471 q^{88} -7.02525 q^{89} -2.50063 q^{90} -16.4488 q^{91} +33.7851 q^{92} +3.05150 q^{93} +20.0616 q^{94} -3.96142 q^{95} +2.69260 q^{96} +11.6114 q^{97} -28.7580 q^{98} +2.03167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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