LMFDB - Embedded newform 8041.2.a.f.1.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.51
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.85512 q^{2} -2.98650 q^{3} +1.44147 q^{4} -3.13647 q^{5} -5.54032 q^{6} +3.56809 q^{7} -1.03613 q^{8} +5.91918 q^{9} +O(q^{10})$	\(q+1.85512 q^{2} -2.98650 q^{3} +1.44147 q^{4} -3.13647 q^{5} -5.54032 q^{6} +3.56809 q^{7} -1.03613 q^{8} +5.91918 q^{9} -5.81853 q^{10} -1.00000 q^{11} -4.30496 q^{12} +3.92243 q^{13} +6.61925 q^{14} +9.36707 q^{15} -4.80510 q^{16} +1.00000 q^{17} +10.9808 q^{18} -2.74243 q^{19} -4.52114 q^{20} -10.6561 q^{21} -1.85512 q^{22} +4.40583 q^{23} +3.09441 q^{24} +4.83745 q^{25} +7.27659 q^{26} -8.71814 q^{27} +5.14332 q^{28} +6.77052 q^{29} +17.3771 q^{30} -1.01076 q^{31} -6.84178 q^{32} +2.98650 q^{33} +1.85512 q^{34} -11.1912 q^{35} +8.53235 q^{36} -2.54962 q^{37} -5.08754 q^{38} -11.7143 q^{39} +3.24980 q^{40} -8.54996 q^{41} -19.7684 q^{42} -1.00000 q^{43} -1.44147 q^{44} -18.5653 q^{45} +8.17334 q^{46} +3.28992 q^{47} +14.3504 q^{48} +5.73130 q^{49} +8.97406 q^{50} -2.98650 q^{51} +5.65409 q^{52} +1.03469 q^{53} -16.1732 q^{54} +3.13647 q^{55} -3.69702 q^{56} +8.19027 q^{57} +12.5601 q^{58} -3.45133 q^{59} +13.5024 q^{60} -7.27139 q^{61} -1.87508 q^{62} +21.1202 q^{63} -3.08213 q^{64} -12.3026 q^{65} +5.54032 q^{66} -1.00759 q^{67} +1.44147 q^{68} -13.1580 q^{69} -20.7611 q^{70} -3.94153 q^{71} -6.13305 q^{72} -5.32944 q^{73} -4.72985 q^{74} -14.4470 q^{75} -3.95315 q^{76} -3.56809 q^{77} -21.7315 q^{78} +2.93310 q^{79} +15.0711 q^{80} +8.27918 q^{81} -15.8612 q^{82} +2.66657 q^{83} -15.3605 q^{84} -3.13647 q^{85} -1.85512 q^{86} -20.2202 q^{87} +1.03613 q^{88} +5.04370 q^{89} -34.4410 q^{90} +13.9956 q^{91} +6.35089 q^{92} +3.01864 q^{93} +6.10319 q^{94} +8.60156 q^{95} +20.4330 q^{96} -1.72378 q^{97} +10.6323 q^{98} -5.91918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	1.85512	1.31177	0.655884	−	0.754861i	$-0.272296\pi$
$2$	1.85512	1.31177	0.655884	+	0.754861i	$0.272296\pi$
$3$	−2.98650	−1.72426	−0.862128	−	0.506690i	$-0.830869\pi$
$3$	−2.98650	−1.72426	−0.862128	+	0.506690i	$0.830869\pi$
$4$	1.44147	0.720737
$5$	−3.13647	−1.40267	−0.701336	−	0.712831i	$-0.747413\pi$
$5$	−3.13647	−1.40267	−0.701336	+	0.712831i	$0.747413\pi$
$6$	−5.54032	−2.26183
$7$	3.56809	1.34861	0.674307	−	0.738452i	$-0.264443\pi$
$7$	3.56809	1.34861	0.674307	+	0.738452i	$0.264443\pi$
$8$	−1.03613	−0.366328
$9$	5.91918	1.97306
$10$	−5.81853	−1.83998
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.30496	−1.24274
$13$	3.92243	1.08789	0.543944	−	0.839122i	$-0.316931\pi$
$13$	3.92243	1.08789	0.543944	+	0.839122i	$0.316931\pi$
$14$	6.61925	1.76907
$15$	9.36707	2.41857
$16$	−4.80510	−1.20127
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	10.9808	2.58820
$19$	−2.74243	−0.629157	−0.314579	−	0.949231i	$-0.601863\pi$
$19$	−2.74243	−0.629157	−0.314579	+	0.949231i	$0.601863\pi$
$20$	−4.52114	−1.01096
$21$	−10.6561	−2.32536
$22$	−1.85512	−0.395513
$23$	4.40583	0.918678	0.459339	−	0.888261i	$-0.348086\pi$
$23$	4.40583	0.918678	0.459339	+	0.888261i	$0.348086\pi$
$24$	3.09441	0.631643
$25$	4.83745	0.967490
$26$	7.27659	1.42706
$27$	−8.71814	−1.67781
$28$	5.14332	0.971996
$29$	6.77052	1.25725	0.628627	−	0.777707i	$-0.283617\pi$
$29$	6.77052	1.25725	0.628627	+	0.777707i	$0.283617\pi$
$30$	17.3771	3.17260
$31$	−1.01076	−0.181538	−0.0907691	−	0.995872i	$-0.528933\pi$
$31$	−1.01076	−0.181538	−0.0907691	+	0.995872i	$0.528933\pi$
$32$	−6.84178	−1.20947
$33$	2.98650	0.519883
$34$	1.85512	0.318151
$35$	−11.1912	−1.89166
$36$	8.53235	1.42206
$37$	−2.54962	−0.419154	−0.209577	−	0.977792i	$-0.567209\pi$
$37$	−2.54962	−0.419154	−0.209577	+	0.977792i	$0.567209\pi$
$38$	−5.08754	−0.825309
$39$	−11.7143	−1.87580
$40$	3.24980	0.513838
$41$	−8.54996	−1.33528	−0.667640	−	0.744484i	$-0.732695\pi$
$41$	−8.54996	−1.33528	−0.667640	+	0.744484i	$0.732695\pi$
$42$	−19.7684	−3.05033
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.44147	−0.217311
$45$	−18.5653	−2.76756
$46$	8.17334	1.20509
$47$	3.28992	0.479884	0.239942	−	0.970787i	$-0.422872\pi$
$47$	3.28992	0.479884	0.239942	+	0.970787i	$0.422872\pi$
$48$	14.3504	2.07131
$49$	5.73130	0.818757
$50$	8.97406	1.26912
$51$	−2.98650	−0.418194
$52$	5.65409	0.784081
$53$	1.03469	0.142125	0.0710626	−	0.997472i	$-0.477361\pi$
$53$	1.03469	0.142125	0.0710626	+	0.997472i	$0.477361\pi$
$54$	−16.1732	−2.20089
$55$	3.13647	0.422922
$56$	−3.69702	−0.494035
$57$	8.19027	1.08483
$58$	12.5601	1.64923
$59$	−3.45133	−0.449325	−0.224662	−	0.974437i	$-0.572128\pi$
$59$	−3.45133	−0.449325	−0.224662	+	0.974437i	$0.572128\pi$
$60$	13.5024	1.74315
$61$	−7.27139	−0.931006	−0.465503	−	0.885046i	$-0.654126\pi$
$61$	−7.27139	−0.931006	−0.465503	+	0.885046i	$0.654126\pi$
$62$	−1.87508	−0.238136
$63$	21.1202	2.66090
$64$	−3.08213	−0.385266
$65$	−12.3026	−1.52595
$66$	5.54032	0.681966
$67$	−1.00759	−0.123097	−0.0615485	−	0.998104i	$-0.519604\pi$
$67$	−1.00759	−0.123097	−0.0615485	+	0.998104i	$0.519604\pi$
$68$	1.44147	0.174805
$69$	−13.1580	−1.58404
$70$	−20.7611	−2.48142
$71$	−3.94153	−0.467773	−0.233887	−	0.972264i	$-0.575144\pi$
$71$	−3.94153	−0.467773	−0.233887	+	0.972264i	$0.575144\pi$
$72$	−6.13305	−0.722787
$73$	−5.32944	−0.623764	−0.311882	−	0.950121i	$-0.600959\pi$
$73$	−5.32944	−0.623764	−0.311882	+	0.950121i	$0.600959\pi$
$74$	−4.72985	−0.549834
$75$	−14.4470	−1.66820
$76$	−3.95315	−0.453457
$77$	−3.56809	−0.406622
$78$	−21.7315	−2.46061
$79$	2.93310	0.329999	0.165000	−	0.986294i	$-0.447238\pi$
$79$	2.93310	0.329999	0.165000	+	0.986294i	$0.447238\pi$
$80$	15.0711	1.68500
$81$	8.27918	0.919909
$82$	−15.8612	−1.75158
$83$	2.66657	0.292695	0.146347	−	0.989233i	$-0.453248\pi$
$83$	2.66657	0.292695	0.146347	+	0.989233i	$0.453248\pi$
$84$	−15.3605	−1.67597
$85$	−3.13647	−0.340198
$86$	−1.85512	−0.200043
$87$	−20.2202	−2.16783
$88$	1.03613	0.110452
$89$	5.04370	0.534631	0.267316	−	0.963609i	$-0.413863\pi$
$89$	5.04370	0.534631	0.267316	+	0.963609i	$0.413863\pi$
$90$	−34.4410	−3.63040
$91$	13.9956	1.46714
$92$	6.35089	0.662126
$93$	3.01864	0.313018
$94$	6.10319	0.629496
$95$	8.60156	0.882501
$96$	20.4330	2.08543
$97$	−1.72378	−0.175023	−0.0875117	−	0.996163i	$-0.527892\pi$
$97$	−1.72378	−0.175023	−0.0875117	+	0.996163i	$0.527892\pi$
$98$	10.6323	1.07402
$99$	−5.91918	−0.594900
$100$	6.97306	0.697306
$101$	16.6322	1.65497	0.827484	−	0.561490i	$-0.189772\pi$
$101$	16.6322	1.65497	0.827484	+	0.561490i	$0.189772\pi$
$102$	−5.54032	−0.548573
$103$	4.18207	0.412072	0.206036	−	0.978544i	$-0.433944\pi$
$103$	4.18207	0.412072	0.206036	+	0.978544i	$0.433944\pi$
$104$	−4.06416	−0.398523
$105$	33.4226	3.26171
$106$	1.91947	0.186435
$107$	−7.24885	−0.700773	−0.350386	−	0.936605i	$-0.613950\pi$
$107$	−7.24885	−0.700773	−0.350386	+	0.936605i	$0.613950\pi$
$108$	−12.5670	−1.20926
$109$	−15.7365	−1.50729	−0.753643	−	0.657284i	$-0.771705\pi$
$109$	−15.7365	−1.50729	−0.753643	+	0.657284i	$0.771705\pi$
$110$	5.81853	0.554775
$111$	7.61443	0.722730
$112$	−17.1451	−1.62006
$113$	14.2184	1.33755	0.668776	−	0.743464i	$-0.266819\pi$
$113$	14.2184	1.33755	0.668776	+	0.743464i	$0.266819\pi$
$114$	15.1940	1.42304
$115$	−13.8187	−1.28860
$116$	9.75954	0.906150
$117$	23.2176	2.14647
$118$	−6.40264	−0.589410
$119$	3.56809	0.327087
$120$	−9.70552	−0.885989
$121$	1.00000	0.0909091
$122$	−13.4893	−1.22126
$123$	25.5345	2.30237
$124$	−1.45699	−0.130841
$125$	0.509835	0.0456010
$126$	39.1805	3.49048
$127$	3.13014	0.277755	0.138877	−	0.990310i	$-0.455651\pi$
$127$	3.13014	0.277755	0.138877	+	0.990310i	$0.455651\pi$
$128$	7.96583	0.704087
$129$	2.98650	0.262947
$130$	−22.8228	−2.00169
$131$	−6.49285	−0.567283	−0.283641	−	0.958930i	$-0.591543\pi$
$131$	−6.49285	−0.567283	−0.283641	+	0.958930i	$0.591543\pi$
$132$	4.30496	0.374699
$133$	−9.78526	−0.848489
$134$	−1.86921	−0.161475
$135$	27.3442	2.35341
$136$	−1.03613	−0.0888476
$137$	3.05810	0.261271	0.130635	−	0.991430i	$-0.458298\pi$
$137$	3.05810	0.261271	0.130635	+	0.991430i	$0.458298\pi$
$138$	−24.4097	−2.07789
$139$	−9.80943	−0.832025	−0.416013	−	0.909359i	$-0.636573\pi$
$139$	−9.80943	−0.832025	−0.416013	+	0.909359i	$0.636573\pi$
$140$	−16.1319	−1.36339
$141$	−9.82534	−0.827443
$142$	−7.31201	−0.613611
$143$	−3.92243	−0.328010
$144$	−28.4423	−2.37019
$145$	−21.2355	−1.76352
$146$	−9.88676	−0.818234
$147$	−17.1165	−1.41175
$148$	−3.67521	−0.302100
$149$	1.67428	0.137162	0.0685812	−	0.997646i	$-0.478153\pi$
$149$	1.67428	0.137162	0.0685812	+	0.997646i	$0.478153\pi$
$150$	−26.8010	−2.18829
$151$	13.4960	1.09829	0.549143	−	0.835728i	$-0.314954\pi$
$151$	13.4960	1.09829	0.549143	+	0.835728i	$0.314954\pi$
$152$	2.84152	0.230478
$153$	5.91918	0.478538
$154$	−6.61925	−0.533394
$155$	3.17022	0.254638
$156$	−16.8859	−1.35196
$157$	0.585710	0.0467447	0.0233724	−	0.999727i	$-0.492560\pi$
$157$	0.585710	0.0467447	0.0233724	+	0.999727i	$0.492560\pi$
$158$	5.44125	0.432883
$159$	−3.09009	−0.245060
$160$	21.4590	1.69649
$161$	15.7204	1.23894
$162$	15.3589	1.20671
$163$	12.0389	0.942962	0.471481	−	0.881876i	$-0.343720\pi$
$163$	12.0389	0.942962	0.471481	+	0.881876i	$0.343720\pi$
$164$	−12.3246	−0.962386
$165$	−9.36707	−0.729225
$166$	4.94682	0.383948
$167$	8.67705	0.671450	0.335725	−	0.941960i	$-0.391019\pi$
$167$	8.67705	0.671450	0.335725	+	0.941960i	$0.391019\pi$
$168$	11.0411	0.851843
$169$	2.38548	0.183498
$170$	−5.81853	−0.446261
$171$	−16.2330	−1.24137
$172$	−1.44147	−0.109911
$173$	−6.50024	−0.494204	−0.247102	−	0.968989i	$-0.579478\pi$
$173$	−6.50024	−0.494204	−0.247102	+	0.968989i	$0.579478\pi$
$174$	−37.5109	−2.84369
$175$	17.2605	1.30477
$176$	4.80510	0.362198
$177$	10.3074	0.774752
$178$	9.35668	0.701313
$179$	18.5858	1.38917	0.694584	−	0.719411i	$-0.255588\pi$
$179$	18.5858	1.38917	0.694584	+	0.719411i	$0.255588\pi$
$180$	−26.7615	−1.99468
$181$	−8.87547	−0.659709	−0.329854	−	0.944032i	$-0.607000\pi$
$181$	−8.87547	−0.659709	−0.329854	+	0.944032i	$0.607000\pi$
$182$	25.9636	1.92455
$183$	21.7160	1.60529
$184$	−4.56502	−0.336538
$185$	7.99680	0.587936
$186$	5.59994	0.410608
$187$	−1.00000	−0.0731272
$188$	4.74233	0.345870
$189$	−31.1072	−2.26271
$190$	15.9569	1.15764
$191$	13.7943	0.998117	0.499058	−	0.866568i	$-0.333679\pi$
$191$	13.7943	0.998117	0.499058	+	0.866568i	$0.333679\pi$
$192$	9.20478	0.664298
$193$	−2.48631	−0.178969	−0.0894843	−	0.995988i	$-0.528522\pi$
$193$	−2.48631	−0.178969	−0.0894843	+	0.995988i	$0.528522\pi$
$194$	−3.19782	−0.229590
$195$	36.7417	2.63113
$196$	8.26152	0.590109
$197$	24.1058	1.71747	0.858735	−	0.512420i	$-0.171251\pi$
$197$	24.1058	1.71747	0.858735	+	0.512420i	$0.171251\pi$
$198$	−10.9808	−0.780372
$199$	1.36799	0.0969742	0.0484871	−	0.998824i	$-0.484560\pi$
$199$	1.36799	0.0969742	0.0484871	+	0.998824i	$0.484560\pi$
$200$	−5.01224	−0.354419
$201$	3.00918	0.212251
$202$	30.8548	2.17093
$203$	24.1579	1.69555
$204$	−4.30496	−0.301408
$205$	26.8167	1.87296
$206$	7.75825	0.540543
$207$	26.0789	1.81261
$208$	−18.8477	−1.30685
$209$	2.74243	0.189698
$210$	62.0030	4.27861
$211$	7.60684	0.523677	0.261838	−	0.965112i	$-0.415671\pi$
$211$	7.60684	0.523677	0.261838	+	0.965112i	$0.415671\pi$
$212$	1.49147	0.102435
$213$	11.7714	0.806562
$214$	−13.4475	−0.919252
$215$	3.13647	0.213906
$216$	9.03314	0.614628
$217$	−3.60649	−0.244825
$218$	−29.1932	−1.97721
$219$	15.9164	1.07553
$220$	4.52114	0.304815
$221$	3.92243	0.263851
$222$	14.1257	0.948055
$223$	24.7321	1.65619	0.828093	−	0.560591i	$-0.189426\pi$
$223$	24.7321	1.65619	0.828093	+	0.560591i	$0.189426\pi$
$224$	−24.4121	−1.63110
$225$	28.6337	1.90892
$226$	26.3768	1.75456
$227$	−15.3605	−1.01951	−0.509756	−	0.860319i	$-0.670264\pi$
$227$	−15.3605	−1.01951	−0.509756	+	0.860319i	$0.670264\pi$
$228$	11.8061	0.781876
$229$	−24.2129	−1.60003	−0.800017	−	0.599977i	$-0.795176\pi$
$229$	−24.2129	−1.60003	−0.800017	+	0.599977i	$0.795176\pi$
$230$	−25.6354	−1.69035
$231$	10.6561	0.701121
$232$	−7.01515	−0.460567
$233$	−8.61319	−0.564269	−0.282134	−	0.959375i	$-0.591042\pi$
$233$	−8.61319	−0.564269	−0.282134	+	0.959375i	$0.591042\pi$
$234$	43.0715	2.81567
$235$	−10.3187	−0.673120
$236$	−4.97501	−0.323845
$237$	−8.75970	−0.569004
$238$	6.61925	0.429062
$239$	18.7296	1.21152	0.605759	−	0.795648i	$-0.292870\pi$
$239$	18.7296	1.21152	0.605759	+	0.795648i	$0.292870\pi$
$240$	−45.0097	−2.90536
$241$	15.1033	0.972891	0.486445	−	0.873711i	$-0.338293\pi$
$241$	15.1033	0.972891	0.486445	+	0.873711i	$0.338293\pi$
$242$	1.85512	0.119252
$243$	1.42865	0.0916479
$244$	−10.4815	−0.671011
$245$	−17.9761	−1.14845
$246$	47.3695	3.02017
$247$	−10.7570	−0.684452
$248$	1.04728	0.0665025
$249$	−7.96372	−0.504681
$250$	0.945806	0.0598180
$251$	−13.4263	−0.847460	−0.423730	−	0.905789i	$-0.639279\pi$
$251$	−13.4263	−0.847460	−0.423730	+	0.905789i	$0.639279\pi$
$252$	30.4442	1.91781
$253$	−4.40583	−0.276992
$254$	5.80678	0.364350
$255$	9.36707	0.586589
$256$	20.9418	1.30887
$257$	28.7738	1.79486	0.897429	−	0.441159i	$-0.145433\pi$
$257$	28.7738	1.79486	0.897429	+	0.441159i	$0.145433\pi$
$258$	5.54032	0.344925
$259$	−9.09727	−0.565277
$260$	−17.7339	−1.09981
$261$	40.0760	2.48064
$262$	−12.0450	−0.744144
$263$	17.2859	1.06589	0.532947	−	0.846149i	$-0.321084\pi$
$263$	17.2859	1.06589	0.532947	+	0.846149i	$0.321084\pi$
$264$	−3.09441	−0.190448
$265$	−3.24526	−0.199355
$266$	−18.1528	−1.11302
$267$	−15.0630	−0.921841
$268$	−1.45242	−0.0887207
$269$	−1.31735	−0.0803203	−0.0401602	−	0.999193i	$-0.512787\pi$
$269$	−1.31735	−0.0803203	−0.0401602	+	0.999193i	$0.512787\pi$
$270$	50.7268	3.08713
$271$	−4.27622	−0.259762	−0.129881	−	0.991530i	$-0.541460\pi$
$271$	−4.27622	−0.259762	−0.129881	+	0.991530i	$0.541460\pi$
$272$	−4.80510	−0.291352
$273$	−41.7979	−2.52972
$274$	5.67314	0.342727
$275$	−4.83745	−0.291709
$276$	−18.9669	−1.14167
$277$	−2.06674	−0.124178	−0.0620892	−	0.998071i	$-0.519776\pi$
$277$	−2.06674	−0.124178	−0.0620892	+	0.998071i	$0.519776\pi$
$278$	−18.1977	−1.09142
$279$	−5.98288	−0.358186
$280$	11.5956	0.692969
$281$	18.7749	1.12002	0.560009	−	0.828486i	$-0.310798\pi$
$281$	18.7749	1.12002	0.560009	+	0.828486i	$0.310798\pi$
$282$	−18.2272	−1.08541
$283$	−5.92185	−0.352018	−0.176009	−	0.984389i	$-0.556319\pi$
$283$	−5.92185	−0.352018	−0.176009	+	0.984389i	$0.556319\pi$
$284$	−5.68162	−0.337142
$285$	−25.6886	−1.52166
$286$	−7.27659	−0.430274
$287$	−30.5071	−1.80078
$288$	−40.4977	−2.38635
$289$	1.00000	0.0588235
$290$	−39.3945	−2.31333
$291$	5.14807	0.301785
$292$	−7.68226	−0.449570
$293$	−10.3836	−0.606619	−0.303309	−	0.952892i	$-0.598092\pi$
$293$	−10.3836	−0.606619	−0.303309	+	0.952892i	$0.598092\pi$
$294$	−31.7532	−1.85189
$295$	10.8250	0.630256
$296$	2.64174	0.153548
$297$	8.71814	0.505878
$298$	3.10599	0.179925
$299$	17.2816	0.999418
$300$	−20.8250	−1.20233
$301$	−3.56809	−0.205662
$302$	25.0367	1.44070
$303$	−49.6721	−2.85359
$304$	13.1777	0.755791
$305$	22.8065	1.30590
$306$	10.9808	0.627731
$307$	24.4298	1.39428	0.697140	−	0.716935i	$-0.254455\pi$
$307$	24.4298	1.39428	0.697140	+	0.716935i	$0.254455\pi$
$308$	−5.14332	−0.293068
$309$	−12.4898	−0.710517
$310$	5.88115	0.334027
$311$	−32.3449	−1.83411	−0.917057	−	0.398756i	$-0.869442\pi$
$311$	−32.3449	−1.83411	−0.917057	+	0.398756i	$0.869442\pi$
$312$	12.1376	0.687157
$313$	33.6606	1.90261	0.951304	−	0.308253i	$-0.0997444\pi$
$313$	33.6606	1.90261	0.951304	+	0.308253i	$0.0997444\pi$
$314$	1.08656	0.0613183
$315$	−66.2429	−3.73237
$316$	4.22799	0.237843
$317$	−9.36980	−0.526261	−0.263130	−	0.964760i	$-0.584755\pi$
$317$	−9.36980	−0.526261	−0.263130	+	0.964760i	$0.584755\pi$
$318$	−5.73249	−0.321462
$319$	−6.77052	−0.379076
$320$	9.66701	0.540402
$321$	21.6487	1.20831
$322$	29.1633	1.62520
$323$	−2.74243	−0.152593
$324$	11.9342	0.663013
$325$	18.9746	1.05252
$326$	22.3337	1.23695
$327$	46.9971	2.59895
$328$	8.85889	0.489150
$329$	11.7387	0.647177
$330$	−17.3771	−0.956575
$331$	15.9540	0.876911	0.438455	−	0.898753i	$-0.355526\pi$
$331$	15.9540	0.876911	0.438455	+	0.898753i	$0.355526\pi$
$332$	3.84380	0.210956
$333$	−15.0917	−0.827017
$334$	16.0970	0.880787
$335$	3.16029	0.172665
$336$	51.2037	2.79339
$337$	1.40233	0.0763899	0.0381949	−	0.999270i	$-0.487839\pi$
$337$	1.40233	0.0763899	0.0381949	+	0.999270i	$0.487839\pi$
$338$	4.42535	0.240707
$339$	−42.4632	−2.30628
$340$	−4.52114	−0.245193
$341$	1.01076	0.0547358
$342$	−30.1141	−1.62838
$343$	−4.52684	−0.244427
$344$	1.03613	0.0558645
$345$	41.2697	2.22189
$346$	−12.0587	−0.648282
$347$	12.8849	0.691700	0.345850	−	0.938290i	$-0.387591\pi$
$347$	12.8849	0.691700	0.345850	+	0.938290i	$0.387591\pi$
$348$	−29.1469	−1.56244
$349$	−3.27884	−0.175513	−0.0877563	−	0.996142i	$-0.527970\pi$
$349$	−3.27884	−0.175513	−0.0877563	+	0.996142i	$0.527970\pi$
$350$	32.0203	1.71156
$351$	−34.1963	−1.82526
$352$	6.84178	0.364668
$353$	12.6543	0.673518	0.336759	−	0.941591i	$-0.390669\pi$
$353$	12.6543	0.673518	0.336759	+	0.941591i	$0.390669\pi$
$354$	19.1215	1.01629
$355$	12.3625	0.656133
$356$	7.27037	0.385329
$357$	−10.6561	−0.563981
$358$	34.4789	1.82227
$359$	17.1589	0.905611	0.452805	−	0.891609i	$-0.350423\pi$
$359$	17.1589	0.905611	0.452805	+	0.891609i	$0.350423\pi$
$360$	19.2361	1.01383
$361$	−11.4791	−0.604161
$362$	−16.4651	−0.865385
$363$	−2.98650	−0.156751
$364$	20.1743	1.05742
$365$	16.7156	0.874937
$366$	40.2858	2.10577
$367$	−6.58871	−0.343928	−0.171964	−	0.985103i	$-0.555011\pi$
$367$	−6.58871	−0.343928	−0.171964	+	0.985103i	$0.555011\pi$
$368$	−21.1704	−1.10359
$369$	−50.6088	−2.63459
$370$	14.8350	0.771237
$371$	3.69186	0.191672
$372$	4.35129	0.225604
$373$	16.4703	0.852798	0.426399	−	0.904535i	$-0.359782\pi$
$373$	16.4703	0.852798	0.426399	+	0.904535i	$0.359782\pi$
$374$	−1.85512	−0.0959260
$375$	−1.52262	−0.0786279
$376$	−3.40879	−0.175795
$377$	26.5569	1.36775
$378$	−57.7075	−2.96816
$379$	2.52959	0.129936	0.0649682	−	0.997887i	$-0.479305\pi$
$379$	2.52959	0.129936	0.0649682	+	0.997887i	$0.479305\pi$
$380$	12.3989	0.636052
$381$	−9.34815	−0.478920
$382$	25.5900	1.30930
$383$	7.07618	0.361576	0.180788	−	0.983522i	$-0.442135\pi$
$383$	7.07618	0.361576	0.180788	+	0.983522i	$0.442135\pi$
$384$	−23.7900	−1.21403
$385$	11.1912	0.570358
$386$	−4.61241	−0.234765
$387$	−5.91918	−0.300889
$388$	−2.48479	−0.126146
$389$	−3.70244	−0.187721	−0.0938607	−	0.995585i	$-0.529921\pi$
$389$	−3.70244	−0.187721	−0.0938607	+	0.995585i	$0.529921\pi$
$390$	68.1603	3.45143
$391$	4.40583	0.222812
$392$	−5.93838	−0.299934
$393$	19.3909	0.978141
$394$	44.7192	2.25292
$395$	−9.19958	−0.462881
$396$	−8.53235	−0.428767
$397$	21.2412	1.06607	0.533034	−	0.846094i	$-0.321052\pi$
$397$	21.2412	1.06607	0.533034	+	0.846094i	$0.321052\pi$
$398$	2.53779	0.127208
$399$	29.2237	1.46301
$400$	−23.2444	−1.16222
$401$	−15.1224	−0.755176	−0.377588	−	0.925974i	$-0.623246\pi$
$401$	−15.1224	−0.755176	−0.377588	+	0.925974i	$0.623246\pi$
$402$	5.58239	0.278424
$403$	−3.96464	−0.197493
$404$	23.9749	1.19280
$405$	−25.9674	−1.29033
$406$	44.8158	2.22417
$407$	2.54962	0.126380
$408$	3.09441	0.153196
$409$	−26.6009	−1.31533	−0.657664	−	0.753311i	$-0.728455\pi$
$409$	−26.6009	−1.31533	−0.657664	+	0.753311i	$0.728455\pi$
$410$	49.7483	2.45689
$411$	−9.13301	−0.450498
$412$	6.02835	0.296995
$413$	−12.3147	−0.605966
$414$	48.3795	2.37772
$415$	−8.36363	−0.410555
$416$	−26.8364	−1.31576
$417$	29.2959	1.43463
$418$	5.08754	0.248840
$419$	−22.1950	−1.08430	−0.542149	−	0.840282i	$-0.682389\pi$
$419$	−22.1950	−1.08430	−0.542149	+	0.840282i	$0.682389\pi$
$420$	48.1778	2.35084
$421$	9.97226	0.486018	0.243009	−	0.970024i	$-0.421866\pi$
$421$	9.97226	0.486018	0.243009	+	0.970024i	$0.421866\pi$
$422$	14.1116	0.686943
$423$	19.4736	0.946840
$424$	−1.07207	−0.0520644
$425$	4.83745	0.234651
$426$	21.8373	1.05802
$427$	−25.9450	−1.25557
$428$	−10.4490	−0.505073
$429$	11.7143	0.565574
$430$	5.81853	0.280595
$431$	−13.2868	−0.640000	−0.320000	−	0.947417i	$-0.603683\pi$
$431$	−13.2868	−0.640000	−0.320000	+	0.947417i	$0.603683\pi$
$432$	41.8915	2.01551
$433$	18.9230	0.909381	0.454690	−	0.890650i	$-0.349750\pi$
$433$	18.9230	0.909381	0.454690	+	0.890650i	$0.349750\pi$
$434$	−6.69048	−0.321153
$435$	63.4200	3.04075
$436$	−22.6838	−1.08636
$437$	−12.0827	−0.577993
$438$	29.5268	1.41085
$439$	25.6800	1.22564	0.612819	−	0.790224i	$-0.290036\pi$
$439$	25.6800	1.22564	0.612819	+	0.790224i	$0.290036\pi$
$440$	−3.24980	−0.154928
$441$	33.9246	1.61546
$442$	7.27659	0.346112
$443$	6.67821	0.317291	0.158646	−	0.987336i	$-0.449287\pi$
$443$	6.67821	0.317291	0.158646	+	0.987336i	$0.449287\pi$
$444$	10.9760	0.520898
$445$	−15.8194	−0.749912
$446$	45.8811	2.17253
$447$	−5.00024	−0.236503
$448$	−10.9973	−0.519575
$449$	30.9717	1.46165	0.730823	−	0.682568i	$-0.239137\pi$
$449$	30.9717	1.46165	0.730823	+	0.682568i	$0.239137\pi$
$450$	53.1191	2.50406
$451$	8.54996	0.402602
$452$	20.4954	0.964023
$453$	−40.3057	−1.89373
$454$	−28.4956	−1.33736
$455$	−43.8968	−2.05791
$456$	−8.48620	−0.397403
$457$	−20.9401	−0.979535	−0.489768	−	0.871853i	$-0.662918\pi$
$457$	−20.9401	−0.979535	−0.489768	+	0.871853i	$0.662918\pi$
$458$	−44.9179	−2.09888
$459$	−8.71814	−0.406928
$460$	−19.9194	−0.928746
$461$	37.9587	1.76791	0.883957	−	0.467568i	$-0.154870\pi$
$461$	37.9587	1.76791	0.883957	+	0.467568i	$0.154870\pi$
$462$	19.7684	0.919709
$463$	−11.3698	−0.528400	−0.264200	−	0.964468i	$-0.585108\pi$
$463$	−11.3698	−0.528400	−0.264200	+	0.964468i	$0.585108\pi$
$464$	−32.5330	−1.51031
$465$	−9.46787	−0.439062
$466$	−15.9785	−0.740190
$467$	15.3797	0.711688	0.355844	−	0.934545i	$-0.384194\pi$
$467$	15.3797	0.711688	0.355844	+	0.934545i	$0.384194\pi$
$468$	33.4676	1.54704
$469$	−3.59519	−0.166010
$470$	−19.1425	−0.882977
$471$	−1.74922	−0.0805999
$472$	3.57603	0.164600
$473$	1.00000	0.0459800
$474$	−16.2503	−0.746401
$475$	−13.2664	−0.608703
$476$	5.14332	0.235744
$477$	6.12450	0.280422
$478$	34.7457	1.58923
$479$	25.3046	1.15620	0.578099	−	0.815967i	$-0.303795\pi$
$479$	25.3046	1.15620	0.578099	+	0.815967i	$0.303795\pi$
$480$	−64.0874	−2.92518
$481$	−10.0007	−0.455993
$482$	28.0185	1.27621
$483$	−46.9490	−2.13625
$484$	1.44147	0.0655216
$485$	5.40659	0.245501
$486$	2.65032	0.120221
$487$	18.1348	0.821766	0.410883	−	0.911688i	$-0.365221\pi$
$487$	18.1348	0.821766	0.410883	+	0.911688i	$0.365221\pi$
$488$	7.53412	0.341053
$489$	−35.9543	−1.62591
$490$	−33.3478	−1.50650
$491$	12.1993	0.550546	0.275273	−	0.961366i	$-0.411232\pi$
$491$	12.1993	0.550546	0.275273	+	0.961366i	$0.411232\pi$
$492$	36.8073	1.65940
$493$	6.77052	0.304929
$494$	−19.9555	−0.897843
$495$	18.5653	0.834450
$496$	4.85681	0.218077
$497$	−14.0637	−0.630845
$498$	−14.7737	−0.662024
$499$	−17.7598	−0.795037	−0.397518	−	0.917594i	$-0.630128\pi$
$499$	−17.7598	−0.795037	−0.397518	+	0.917594i	$0.630128\pi$
$500$	0.734914	0.0328664
$501$	−25.9140	−1.15775
$502$	−24.9074	−1.11167
$503$	23.4399	1.04513	0.522566	−	0.852599i	$-0.324975\pi$
$503$	23.4399	1.04513	0.522566	+	0.852599i	$0.324975\pi$
$504$	−21.8833	−0.974761
$505$	−52.1665	−2.32138
$506$	−8.17334	−0.363349
$507$	−7.12423	−0.316398
$508$	4.51201	0.200188
$509$	−26.3570	−1.16826	−0.584128	−	0.811662i	$-0.698563\pi$
$509$	−26.3570	−1.16826	−0.584128	+	0.811662i	$0.698563\pi$
$510$	17.3771	0.769469
$511$	−19.0160	−0.841216
$512$	22.9180	1.01284
$513$	23.9089	1.05560
$514$	53.3788	2.35444
$515$	−13.1169	−0.578001
$516$	4.30496	0.189516
$517$	−3.28992	−0.144690
$518$	−16.8765	−0.741513
$519$	19.4130	0.852135
$520$	12.7471	0.558998
$521$	−39.7869	−1.74309	−0.871547	−	0.490312i	$-0.836883\pi$
$521$	−39.7869	−1.74309	−0.871547	+	0.490312i	$0.836883\pi$
$522$	74.3458	3.25403
$523$	−0.218874	−0.00957070	−0.00478535	−	0.999989i	$-0.501523\pi$
$523$	−0.218874	−0.00957070	−0.00478535	+	0.999989i	$0.501523\pi$
$524$	−9.35928	−0.408862
$525$	−51.5484	−2.24976
$526$	32.0674	1.39821
$527$	−1.01076	−0.0440295
$528$	−14.3504	−0.624522
$529$	−3.58870	−0.156030
$530$	−6.02036	−0.261508
$531$	−20.4291	−0.886546
$532$	−14.1052	−0.611538
$533$	−33.5367	−1.45263
$534$	−27.9437	−1.20924
$535$	22.7358	0.982955
$536$	1.04400	0.0450939
$537$	−55.5065	−2.39528
$538$	−2.44385	−0.105362
$539$	−5.73130	−0.246865
$540$	39.4160	1.69619
$541$	29.9518	1.28773	0.643864	−	0.765140i	$-0.277330\pi$
$541$	29.9518	1.28773	0.643864	+	0.765140i	$0.277330\pi$
$542$	−7.93291	−0.340748
$543$	26.5066	1.13751
$544$	−6.84178	−0.293339
$545$	49.3571	2.11423
$546$	−77.5402	−3.31841
$547$	−8.08581	−0.345724	−0.172862	−	0.984946i	$-0.555301\pi$
$547$	−8.08581	−0.345724	−0.172862	+	0.984946i	$0.555301\pi$
$548$	4.40817	0.188308
$549$	−43.0407	−1.83693
$550$	−8.97406	−0.382655
$551$	−18.5677	−0.791010
$552$	13.6334	0.580277
$553$	10.4656	0.445041
$554$	−3.83405	−0.162893
$555$	−23.8824	−1.01375
$556$	−14.1401	−0.599672
$557$	23.7987	1.00838	0.504191	−	0.863592i	$-0.331791\pi$
$557$	23.7987	1.00838	0.504191	+	0.863592i	$0.331791\pi$
$558$	−11.0990	−0.469857
$559$	−3.92243	−0.165901
$560$	53.7750	2.27241
$561$	2.98650	0.126090
$562$	34.8298	1.46921
$563$	13.0834	0.551400	0.275700	−	0.961244i	$-0.411090\pi$
$563$	13.0834	0.551400	0.275700	+	0.961244i	$0.411090\pi$
$564$	−14.1630	−0.596369
$565$	−44.5955	−1.87615
$566$	−10.9858	−0.461766
$567$	29.5409	1.24060
$568$	4.08394	0.171358
$569$	−46.7272	−1.95891	−0.979453	−	0.201674i	$-0.935362\pi$
$569$	−46.7272	−1.95891	−0.979453	+	0.201674i	$0.935362\pi$
$570$	−47.6554	−1.99606
$571$	6.18664	0.258903	0.129451	−	0.991586i	$-0.458678\pi$
$571$	6.18664	0.258903	0.129451	+	0.991586i	$0.458678\pi$
$572$	−5.65409	−0.236409
$573$	−41.1965	−1.72101
$574$	−56.5943	−2.36220
$575$	21.3130	0.888812
$576$	−18.2437	−0.760154
$577$	6.22443	0.259126	0.129563	−	0.991571i	$-0.458643\pi$
$577$	6.22443	0.259126	0.129563	+	0.991571i	$0.458643\pi$
$578$	1.85512	0.0771629
$579$	7.42537	0.308588
$580$	−30.6105	−1.27103
$581$	9.51459	0.394732
$582$	9.55030	0.395873
$583$	−1.03469	−0.0428523
$584$	5.52201	0.228502
$585$	−72.8213	−3.01079
$586$	−19.2629	−0.795744
$587$	11.1705	0.461055	0.230527	−	0.973066i	$-0.425955\pi$
$587$	11.1705	0.461055	0.230527	+	0.973066i	$0.425955\pi$
$588$	−24.6730	−1.01750
$589$	2.77194	0.114216
$590$	20.0817	0.826750
$591$	−71.9921	−2.96136
$592$	12.2512	0.503520
$593$	28.7915	1.18233	0.591164	−	0.806552i	$-0.298669\pi$
$593$	28.7915	1.18233	0.591164	+	0.806552i	$0.298669\pi$
$594$	16.1732	0.663595
$595$	−11.1912	−0.458795
$596$	2.41343	0.0988581
$597$	−4.08550	−0.167208
$598$	32.0594	1.31101
$599$	−31.6893	−1.29479	−0.647395	−	0.762155i	$-0.724142\pi$
$599$	−31.6893	−1.29479	−0.647395	+	0.762155i	$0.724142\pi$
$600$	14.9690	0.611109
$601$	11.5034	0.469234	0.234617	−	0.972088i	$-0.424616\pi$
$601$	11.5034	0.469234	0.234617	+	0.972088i	$0.424616\pi$
$602$	−6.61925	−0.269780
$603$	−5.96413	−0.242878
$604$	19.4541	0.791576
$605$	−3.13647	−0.127516
$606$	−92.1478	−3.74325
$607$	16.1214	0.654347	0.327174	−	0.944964i	$-0.393904\pi$
$607$	16.1214	0.654347	0.327174	+	0.944964i	$0.393904\pi$
$608$	18.7631	0.760945
$609$	−72.1475	−2.92356
$610$	42.3088	1.71303
$611$	12.9045	0.522059
$612$	8.53235	0.344900
$613$	−33.1926	−1.34064	−0.670319	−	0.742073i	$-0.733843\pi$
$613$	−33.1926	−1.34064	−0.670319	+	0.742073i	$0.733843\pi$
$614$	45.3202	1.82897
$615$	−80.0881	−3.22946
$616$	3.69702	0.148957
$617$	1.47719	0.0594695	0.0297347	−	0.999558i	$-0.490534\pi$
$617$	1.47719	0.0594695	0.0297347	+	0.999558i	$0.490534\pi$
$618$	−23.1700	−0.932034
$619$	5.20253	0.209107	0.104554	−	0.994519i	$-0.466659\pi$
$619$	5.20253	0.209107	0.104554	+	0.994519i	$0.466659\pi$
$620$	4.56980	0.183527
$621$	−38.4106	−1.54136
$622$	−60.0038	−2.40593
$623$	17.9964	0.721011
$624$	56.2886	2.25335
$625$	−25.7863	−1.03145
$626$	62.4445	2.49578
$627$	−8.19027	−0.327088
$628$	0.844286	0.0336907
$629$	−2.54962	−0.101660
$630$	−122.889	−4.89600
$631$	19.6116	0.780727	0.390363	−	0.920661i	$-0.372349\pi$
$631$	19.6116	0.780727	0.390363	+	0.920661i	$0.372349\pi$
$632$	−3.03908	−0.120888
$633$	−22.7178	−0.902953
$634$	−17.3821	−0.690332
$635$	−9.81758	−0.389599
$636$	−4.45429	−0.176624
$637$	22.4806	0.890715
$638$	−12.5601	−0.497261
$639$	−23.3306	−0.922946
$640$	−24.9846	−0.987603
$641$	49.0675	1.93805	0.969024	−	0.246966i	$-0.0794337\pi$
$641$	49.0675	1.93805	0.969024	+	0.246966i	$0.0794337\pi$
$642$	40.1609	1.58503
$643$	−26.1888	−1.03279	−0.516393	−	0.856352i	$-0.672726\pi$
$643$	−26.1888	−1.03279	−0.516393	+	0.856352i	$0.672726\pi$
$644$	22.6606	0.892951
$645$	−9.36707	−0.368828
$646$	−5.08754	−0.200167
$647$	31.8597	1.25253	0.626267	−	0.779609i	$-0.284582\pi$
$647$	31.8597	1.25253	0.626267	+	0.779609i	$0.284582\pi$
$648$	−8.57832	−0.336988
$649$	3.45133	0.135477
$650$	35.2001	1.38066
$651$	10.7708	0.422141
$652$	17.3538	0.679628
$653$	−22.4307	−0.877782	−0.438891	−	0.898540i	$-0.644629\pi$
$653$	−22.4307	−0.877782	−0.438891	+	0.898540i	$0.644629\pi$
$654$	87.1854	3.40922
$655$	20.3646	0.795712
$656$	41.0834	1.60404
$657$	−31.5459	−1.23072
$658$	21.7768	0.848947
$659$	−31.4363	−1.22458	−0.612291	−	0.790632i	$-0.709752\pi$
$659$	−31.4363	−1.22458	−0.612291	+	0.790632i	$0.709752\pi$
$660$	−13.5024	−0.525580
$661$	−18.8228	−0.732122	−0.366061	−	0.930591i	$-0.619294\pi$
$661$	−18.8228	−0.732122	−0.366061	+	0.930591i	$0.619294\pi$
$662$	29.5966	1.15030
$663$	−11.7143	−0.454947
$664$	−2.76292	−0.107222
$665$	30.6912	1.19015
$666$	−27.9968	−1.08486
$667$	29.8297	1.15501
$668$	12.5077	0.483939
$669$	−73.8625	−2.85569
$670$	5.86271	0.226496
$671$	7.27139	0.280709
$672$	72.9068	2.81244
$673$	45.8730	1.76827	0.884137	−	0.467228i	$-0.154747\pi$
$673$	45.8730	1.76827	0.884137	+	0.467228i	$0.154747\pi$
$674$	2.60150	0.100206
$675$	−42.1736	−1.62326
$676$	3.43860	0.132254
$677$	30.3084	1.16484	0.582422	−	0.812886i	$-0.302105\pi$
$677$	30.3084	1.16484	0.582422	+	0.812886i	$0.302105\pi$
$678$	−78.7743	−3.02531
$679$	−6.15062	−0.236039
$680$	3.24980	0.124624
$681$	45.8741	1.75790
$682$	1.87508	0.0718007
$683$	39.5059	1.51165	0.755825	−	0.654774i	$-0.227236\pi$
$683$	39.5059	1.51165	0.755825	+	0.654774i	$0.227236\pi$
$684$	−23.3994	−0.894699
$685$	−9.59163	−0.366477
$686$	−8.39784	−0.320631
$687$	72.3119	2.75887
$688$	4.80510	0.183193
$689$	4.05849	0.154616
$690$	76.5603	2.91460
$691$	−38.4571	−1.46298	−0.731489	−	0.681853i	$-0.761174\pi$
$691$	−38.4571	−1.46298	−0.731489	+	0.681853i	$0.761174\pi$
$692$	−9.36993	−0.356191
$693$	−21.1202	−0.802290
$694$	23.9031	0.907350
$695$	30.7670	1.16706
$696$	20.9508	0.794136
$697$	−8.54996	−0.323853
$698$	−6.08265	−0.230232
$699$	25.7233	0.972944
$700$	24.8805	0.940396
$701$	19.0103	0.718008	0.359004	−	0.933336i	$-0.383116\pi$
$701$	19.0103	0.718008	0.359004	+	0.933336i	$0.383116\pi$
$702$	−63.4383	−2.39433
$703$	6.99215	0.263714
$704$	3.08213	0.116162
$705$	30.8169	1.16063
$706$	23.4752	0.883500
$707$	59.3453	2.23191
$708$	14.8579	0.558392
$709$	24.9819	0.938214	0.469107	−	0.883141i	$-0.344576\pi$
$709$	24.9819	0.938214	0.469107	+	0.883141i	$0.344576\pi$
$710$	22.9339	0.860695
$711$	17.3615	0.651109
$712$	−5.22594	−0.195850
$713$	−4.45324	−0.166775
$714$	−19.7684	−0.739813
$715$	12.3026	0.460091
$716$	26.7910	1.00123
$717$	−55.9360	−2.08897
$718$	31.8318	1.18795
$719$	−32.7484	−1.22131	−0.610654	−	0.791897i	$-0.709094\pi$
$719$	−32.7484	−1.22131	−0.610654	+	0.791897i	$0.709094\pi$
$720$	89.2083	3.32460
$721$	14.9220	0.555725
$722$	−21.2951	−0.792520
$723$	−45.1061	−1.67751
$724$	−12.7938	−0.475477
$725$	32.7521	1.21638
$726$	−5.54032	−0.205621
$727$	−50.1524	−1.86005	−0.930025	−	0.367496i	$-0.880215\pi$
$727$	−50.1524	−1.86005	−0.930025	+	0.367496i	$0.880215\pi$
$728$	−14.5013	−0.537454
$729$	−29.1042	−1.07793
$730$	31.0095	1.14771
$731$	−1.00000	−0.0369863
$732$	31.3031	1.15699
$733$	−21.5585	−0.796283	−0.398142	−	0.917324i	$-0.630345\pi$
$733$	−21.5585	−0.796283	−0.398142	+	0.917324i	$0.630345\pi$
$734$	−12.2229	−0.451154
$735$	53.6855	1.98022
$736$	−30.1437	−1.11111
$737$	1.00759	0.0371152
$738$	−93.8855	−3.45597
$739$	30.4231	1.11913	0.559565	−	0.828786i	$-0.310968\pi$
$739$	30.4231	1.11913	0.559565	+	0.828786i	$0.310968\pi$
$740$	11.5272	0.423748
$741$	32.1258	1.18017
$742$	6.84885	0.251429
$743$	−36.5283	−1.34009	−0.670046	−	0.742320i	$-0.733726\pi$
$743$	−36.5283	−1.34009	−0.670046	+	0.742320i	$0.733726\pi$
$744$	−3.12771	−0.114667
$745$	−5.25133	−0.192394
$746$	30.5543	1.11867
$747$	15.7839	0.577504
$748$	−1.44147	−0.0527055
$749$	−25.8646	−0.945071
$750$	−2.82465	−0.103142
$751$	−45.6991	−1.66759	−0.833793	−	0.552078i	$-0.813835\pi$
$751$	−45.6991	−1.66759	−0.833793	+	0.552078i	$0.813835\pi$
$752$	−15.8084	−0.576472
$753$	40.0976	1.46124
$754$	49.2663	1.79417
$755$	−42.3297	−1.54054
$756$	−44.8402	−1.63082
$757$	1.24192	0.0451385	0.0225693	−	0.999745i	$-0.492815\pi$
$757$	1.24192	0.0451385	0.0225693	+	0.999745i	$0.492815\pi$
$758$	4.69270	0.170447
$759$	13.1580	0.477605
$760$	−8.91235	−0.323285
$761$	−6.66542	−0.241621	−0.120811	−	0.992676i	$-0.538549\pi$
$761$	−6.66542	−0.241621	−0.120811	+	0.992676i	$0.538549\pi$
$762$	−17.3420	−0.628233
$763$	−56.1494	−2.03274
$764$	19.8841	0.719380
$765$	−18.5653	−0.671231
$766$	13.1272	0.474304
$767$	−13.5376	−0.488815
$768$	−62.5428	−2.25682
$769$	−5.76595	−0.207926	−0.103963	−	0.994581i	$-0.533152\pi$
$769$	−5.76595	−0.207926	−0.103963	+	0.994581i	$0.533152\pi$
$770$	20.7611	0.748177
$771$	−85.9328	−3.09480
$772$	−3.58395	−0.128989
$773$	25.7286	0.925392	0.462696	−	0.886517i	$-0.346882\pi$
$773$	25.7286	0.925392	0.462696	+	0.886517i	$0.346882\pi$
$774$	−10.9808	−0.394697
$775$	−4.88951	−0.175636
$776$	1.78606	0.0641160
$777$	27.1690	0.974683
$778$	−6.86848	−0.246247
$779$	23.4477	0.840101
$780$	52.9622	1.89635
$781$	3.94153	0.141039
$782$	8.17334	0.292278
$783$	−59.0264	−2.10943
$784$	−27.5395	−0.983552
$785$	−1.83706	−0.0655676
$786$	35.9725	1.28309
$787$	−45.7975	−1.63250	−0.816251	−	0.577697i	$-0.803952\pi$
$787$	−45.7975	−1.63250	−0.816251	+	0.577697i	$0.803952\pi$
$788$	34.7479	1.23784
$789$	−51.6243	−1.83788
$790$	−17.0663	−0.607193
$791$	50.7325	1.80384
$792$	6.13305	0.217929
$793$	−28.5215	−1.01283
$794$	39.4051	1.39843
$795$	9.69198	0.343739
$796$	1.97192	0.0698930
$797$	−15.1243	−0.535731	−0.267866	−	0.963456i	$-0.586318\pi$
$797$	−15.1243	−0.535731	−0.267866	+	0.963456i	$0.586318\pi$
$798$	54.2135	1.91914
$799$	3.28992	0.116389
$800$	−33.0968	−1.17015
$801$	29.8546	1.05486
$802$	−28.0539	−0.990617
$803$	5.32944	0.188072
$804$	4.33765	0.152977
$805$	−49.3066	−1.73783
$806$	−7.35489	−0.259065
$807$	3.93427	0.138493
$808$	−17.2332	−0.606261
$809$	32.9329	1.15786	0.578930	−	0.815377i	$-0.303470\pi$
$809$	32.9329	1.15786	0.578930	+	0.815377i	$0.303470\pi$
$810$	−48.1727	−1.69262
$811$	48.9175	1.71773	0.858863	−	0.512206i	$-0.171171\pi$
$811$	48.9175	1.71773	0.858863	+	0.512206i	$0.171171\pi$
$812$	34.8229	1.22205
$813$	12.7709	0.447896
$814$	4.72985	0.165781
$815$	−37.7597	−1.32267
$816$	14.3504	0.502366
$817$	2.74243	0.0959456
$818$	−49.3479	−1.72541
$819$	82.8426	2.89475
$820$	38.6556	1.34991
$821$	18.5172	0.646256	0.323128	−	0.946355i	$-0.395266\pi$
$821$	18.5172	0.646256	0.323128	+	0.946355i	$0.395266\pi$
$822$	−16.9428	−0.590949
$823$	47.8651	1.66847	0.834237	−	0.551407i	$-0.185909\pi$
$823$	47.8651	1.66847	0.834237	+	0.551407i	$0.185909\pi$
$824$	−4.33318	−0.150953
$825$	14.4470	0.502981
$826$	−22.8452	−0.794887
$827$	44.5495	1.54914	0.774569	−	0.632490i	$-0.217967\pi$
$827$	44.5495	1.54914	0.774569	+	0.632490i	$0.217967\pi$
$828$	37.5921	1.30641
$829$	−7.56528	−0.262753	−0.131376	−	0.991333i	$-0.541940\pi$
$829$	−7.56528	−0.262753	−0.131376	+	0.991333i	$0.541940\pi$
$830$	−15.5156	−0.538553
$831$	6.17232	0.214115
$832$	−12.0894	−0.419126
$833$	5.73130	0.198578
$834$	54.3474	1.88190
$835$	−27.2153	−0.941825
$836$	3.95315	0.136722
$837$	8.81196	0.304586
$838$	−41.1745	−1.42235
$839$	23.2915	0.804111	0.402055	−	0.915615i	$-0.368296\pi$
$839$	23.2915	0.804111	0.402055	+	0.915615i	$0.368296\pi$
$840$	−34.6302	−1.19486
$841$	16.8400	0.580688
$842$	18.4997	0.637543
$843$	−56.0714	−1.93120
$844$	10.9651	0.377433
$845$	−7.48198	−0.257388
$846$	36.1259	1.24203
$847$	3.56809	0.122601
$848$	−4.97177	−0.170731
$849$	17.6856	0.606969
$850$	8.97406	0.307808
$851$	−11.2332	−0.385068
$852$	16.9681	0.581319
$853$	−40.6508	−1.39186	−0.695929	−	0.718110i	$-0.745007\pi$
$853$	−40.6508	−1.39186	−0.695929	+	0.718110i	$0.745007\pi$
$854$	−48.1311	−1.64701
$855$	50.9142	1.74123
$856$	7.51076	0.256713
$857$	−49.4404	−1.68885	−0.844426	−	0.535672i	$-0.820058\pi$
$857$	−49.4404	−1.68885	−0.844426	+	0.535672i	$0.820058\pi$
$858$	21.7315	0.741902
$859$	41.6331	1.42050	0.710252	−	0.703947i	$-0.248581\pi$
$859$	41.6331	1.42050	0.710252	+	0.703947i	$0.248581\pi$
$860$	4.52114	0.154170
$861$	91.1094	3.10500
$862$	−24.6485	−0.839533
$863$	−21.1743	−0.720782	−0.360391	−	0.932801i	$-0.617357\pi$
$863$	−21.1743	−0.720782	−0.360391	+	0.932801i	$0.617357\pi$
$864$	59.6476	2.02925
$865$	20.3878	0.693207
$866$	35.1044	1.19290
$867$	−2.98650	−0.101427
$868$	−5.19867	−0.176454
$869$	−2.93310	−0.0994985
$870$	117.652	3.98877
$871$	−3.95222	−0.133916
$872$	16.3051	0.552161
$873$	−10.2034	−0.345332
$874$	−22.4148	−0.758193
$875$	1.81914	0.0614982
$876$	22.9431	0.775174
$877$	12.6486	0.427113	0.213556	−	0.976931i	$-0.431495\pi$
$877$	12.6486	0.427113	0.213556	+	0.976931i	$0.431495\pi$
$878$	47.6394	1.60775
$879$	31.0107	1.04597
$880$	−15.0711	−0.508045
$881$	−0.457428	−0.0154111	−0.00770557	−	0.999970i	$-0.502453\pi$
$881$	−0.457428	−0.0154111	−0.00770557	+	0.999970i	$0.502453\pi$
$882$	62.9343	2.11911
$883$	−42.2583	−1.42210	−0.711052	−	0.703139i	$-0.751781\pi$
$883$	−42.2583	−1.42210	−0.711052	+	0.703139i	$0.751781\pi$
$884$	5.65409	0.190168
$885$	−32.3289	−1.08672
$886$	12.3889	0.416213
$887$	−19.5007	−0.654769	−0.327384	−	0.944891i	$-0.606167\pi$
$887$	−19.5007	−0.654769	−0.327384	+	0.944891i	$0.606167\pi$
$888$	−7.88956	−0.264756
$889$	11.1686	0.374584
$890$	−29.3469	−0.983712
$891$	−8.27918	−0.277363
$892$	35.6507	1.19367
$893$	−9.02237	−0.301922
$894$	−9.27605	−0.310237
$895$	−58.2938	−1.94855
$896$	28.4228	0.949541
$897$	−51.6114	−1.72325
$898$	57.4563	1.91734
$899$	−6.84338	−0.228240
$900$	41.2748	1.37583
$901$	1.03469	0.0344704
$902$	15.8612	0.528121
$903$	10.6561	0.354613
$904$	−14.7321	−0.489982
$905$	27.8377	0.925355
$906$	−74.7720	−2.48413
$907$	4.88949	0.162353	0.0811764	−	0.996700i	$-0.474132\pi$
$907$	4.88949	0.162353	0.0811764	+	0.996700i	$0.474132\pi$
$908$	−22.1418	−0.734800
$909$	98.4492	3.26535
$910$	−81.4339	−2.69951
$911$	11.2237	0.371859	0.185930	−	0.982563i	$-0.440470\pi$
$911$	11.2237	0.371859	0.185930	+	0.982563i	$0.440470\pi$
$912$	−39.3551	−1.30318
$913$	−2.66657	−0.0882507
$914$	−38.8464	−1.28492
$915$	−68.1116	−2.25170
$916$	−34.9023	−1.15320
$917$	−23.1671	−0.765045
$918$	−16.1732	−0.533795
$919$	−45.0940	−1.48751	−0.743756	−	0.668451i	$-0.766958\pi$
$919$	−45.0940	−1.48751	−0.743756	+	0.668451i	$0.766958\pi$
$920$	14.3180	0.472052
$921$	−72.9595	−2.40410
$922$	70.4180	2.31909
$923$	−15.4604	−0.508885
$924$	15.3605	0.505324
$925$	−12.3336	−0.405528
$926$	−21.0924	−0.693139
$927$	24.7544	0.813042
$928$	−46.3224	−1.52061
$929$	−13.8521	−0.454471	−0.227236	−	0.973840i	$-0.572969\pi$
$929$	−13.8521	−0.454471	−0.227236	+	0.973840i	$0.572969\pi$
$930$	−17.5641	−0.575948
$931$	−15.7177	−0.515127
$932$	−12.4157	−0.406690
$933$	96.5982	3.16248
$934$	28.5312	0.933570
$935$	3.13647	0.102574
$936$	−24.0565	−0.786311
$937$	4.80236	0.156886	0.0784432	−	0.996919i	$-0.475005\pi$
$937$	4.80236	0.156886	0.0784432	+	0.996919i	$0.475005\pi$
$938$	−6.66951	−0.217767
$939$	−100.527	−3.28059
$940$	−14.8742	−0.485143
$941$	−33.9312	−1.10612	−0.553062	−	0.833140i	$-0.686541\pi$
$941$	−33.9312	−1.10612	−0.553062	+	0.833140i	$0.686541\pi$
$942$	−3.24502	−0.105728
$943$	−37.6697	−1.22669
$944$	16.5840	0.539763
$945$	97.5667	3.17384
$946$	1.85512	0.0603152
$947$	−1.21595	−0.0395130	−0.0197565	−	0.999805i	$-0.506289\pi$
$947$	−1.21595	−0.0395130	−0.0197565	+	0.999805i	$0.506289\pi$
$948$	−12.6269	−0.410102
$949$	−20.9044	−0.678585
$950$	−24.6107	−0.798478
$951$	27.9829	0.907408
$952$	−3.69702	−0.119821
$953$	33.9294	1.09908	0.549541	−	0.835467i	$-0.314803\pi$
$953$	33.9294	1.09908	0.549541	+	0.835467i	$0.314803\pi$
$954$	11.3617	0.367848
$955$	−43.2653	−1.40003
$956$	26.9983	0.873186
$957$	20.2202	0.653625
$958$	46.9431	1.51666
$959$	10.9116	0.352353
$960$	−28.8705	−0.931792
$961$	−29.9784	−0.967044
$962$	−18.5525	−0.598157
$963$	−42.9073	−1.38267
$964$	21.7711	0.701199
$965$	7.79824	0.251034
$966$	−87.0961	−2.80227
$967$	21.4407	0.689487	0.344743	−	0.938697i	$-0.387966\pi$
$967$	21.4407	0.689487	0.344743	+	0.938697i	$0.387966\pi$
$968$	−1.03613	−0.0333025
$969$	8.19027	0.263110
$970$	10.0299	0.322040
$971$	18.6973	0.600025	0.300013	−	0.953935i	$-0.403009\pi$
$971$	18.6973	0.600025	0.300013	+	0.953935i	$0.403009\pi$
$972$	2.05936	0.0660541
$973$	−35.0010	−1.12208
$974$	33.6422	1.07797
$975$	−56.6676	−1.81481
$976$	34.9397	1.11839
$977$	−6.01435	−0.192416	−0.0962080	−	0.995361i	$-0.530671\pi$
$977$	−6.01435	−0.192416	−0.0962080	+	0.995361i	$0.530671\pi$
$978$	−66.6995	−2.13282
$979$	−5.04370	−0.161197
$980$	−25.9120	−0.827729
$981$	−93.1473	−2.97397
$982$	22.6312	0.722189
$983$	27.8742	0.889050	0.444525	−	0.895766i	$-0.353373\pi$
$983$	27.8742	0.889050	0.444525	+	0.895766i	$0.353373\pi$
$984$	−26.4571	−0.843421
$985$	−75.6072	−2.40905
$986$	12.5601	0.399996
$987$	−35.0577	−1.11590
$988$	−15.5060	−0.493310
$989$	−4.40583	−0.140097
$990$	34.4410	1.09461
$991$	29.4508	0.935535	0.467768	−	0.883851i	$-0.345058\pi$
$991$	29.4508	0.935535	0.467768	+	0.883851i	$0.345058\pi$
$992$	6.91541	0.219564
$993$	−47.6466	−1.51202
$994$	−26.0900	−0.827523
$995$	−4.29066	−0.136023
$996$	−11.4795	−0.363742
$997$	36.1144	1.14375	0.571877	−	0.820340i	$-0.306216\pi$
$997$	36.1144	1.14375	0.571877	+	0.820340i	$0.306216\pi$
$998$	−32.9465	−1.04290
$999$	22.2279	0.703260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.51	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.51	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q+1.85512 q^{2} -2.98650 q^{3} +1.44147 q^{4} -3.13647 q^{5} -5.54032 q^{6} +3.56809 q^{7} -1.03613 q^{8} +5.91918 q^{9} +O(q^{10})\)	\(q+1.85512 q^{2} -2.98650 q^{3} +1.44147 q^{4} -3.13647 q^{5} -5.54032 q^{6} +3.56809 q^{7} -1.03613 q^{8} +5.91918 q^{9} -5.81853 q^{10} -1.00000 q^{11} -4.30496 q^{12} +3.92243 q^{13} +6.61925 q^{14} +9.36707 q^{15} -4.80510 q^{16} +1.00000 q^{17} +10.9808 q^{18} -2.74243 q^{19} -4.52114 q^{20} -10.6561 q^{21} -1.85512 q^{22} +4.40583 q^{23} +3.09441 q^{24} +4.83745 q^{25} +7.27659 q^{26} -8.71814 q^{27} +5.14332 q^{28} +6.77052 q^{29} +17.3771 q^{30} -1.01076 q^{31} -6.84178 q^{32} +2.98650 q^{33} +1.85512 q^{34} -11.1912 q^{35} +8.53235 q^{36} -2.54962 q^{37} -5.08754 q^{38} -11.7143 q^{39} +3.24980 q^{40} -8.54996 q^{41} -19.7684 q^{42} -1.00000 q^{43} -1.44147 q^{44} -18.5653 q^{45} +8.17334 q^{46} +3.28992 q^{47} +14.3504 q^{48} +5.73130 q^{49} +8.97406 q^{50} -2.98650 q^{51} +5.65409 q^{52} +1.03469 q^{53} -16.1732 q^{54} +3.13647 q^{55} -3.69702 q^{56} +8.19027 q^{57} +12.5601 q^{58} -3.45133 q^{59} +13.5024 q^{60} -7.27139 q^{61} -1.87508 q^{62} +21.1202 q^{63} -3.08213 q^{64} -12.3026 q^{65} +5.54032 q^{66} -1.00759 q^{67} +1.44147 q^{68} -13.1580 q^{69} -20.7611 q^{70} -3.94153 q^{71} -6.13305 q^{72} -5.32944 q^{73} -4.72985 q^{74} -14.4470 q^{75} -3.95315 q^{76} -3.56809 q^{77} -21.7315 q^{78} +2.93310 q^{79} +15.0711 q^{80} +8.27918 q^{81} -15.8612 q^{82} +2.66657 q^{83} -15.3605 q^{84} -3.13647 q^{85} -1.85512 q^{86} -20.2202 q^{87} +1.03613 q^{88} +5.04370 q^{89} -34.4410 q^{90} +13.9956 q^{91} +6.35089 q^{92} +3.01864 q^{93} +6.10319 q^{94} +8.60156 q^{95} +20.4330 q^{96} -1.72378 q^{97} +10.6323 q^{98} -5.91918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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