LMFDB - Embedded newform 6041.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26422 q^{2} -1.83534 q^{3} +3.12671 q^{4} +1.84374 q^{5} +4.15563 q^{6} +1.00000 q^{7} -2.55113 q^{8} +0.368489 q^{9} +O(q^{10})$	\(q-2.26422 q^{2} -1.83534 q^{3} +3.12671 q^{4} +1.84374 q^{5} +4.15563 q^{6} +1.00000 q^{7} -2.55113 q^{8} +0.368489 q^{9} -4.17465 q^{10} -4.09366 q^{11} -5.73860 q^{12} -3.93746 q^{13} -2.26422 q^{14} -3.38390 q^{15} -0.477091 q^{16} +6.99137 q^{17} -0.834343 q^{18} -4.65170 q^{19} +5.76486 q^{20} -1.83534 q^{21} +9.26896 q^{22} -0.636658 q^{23} +4.68221 q^{24} -1.60061 q^{25} +8.91530 q^{26} +4.82973 q^{27} +3.12671 q^{28} -9.22256 q^{29} +7.66192 q^{30} -3.51122 q^{31} +6.18250 q^{32} +7.51327 q^{33} -15.8300 q^{34} +1.84374 q^{35} +1.15216 q^{36} -6.93591 q^{37} +10.5325 q^{38} +7.22660 q^{39} -4.70363 q^{40} -10.3404 q^{41} +4.15563 q^{42} -8.46498 q^{43} -12.7997 q^{44} +0.679400 q^{45} +1.44154 q^{46} +4.09615 q^{47} +0.875626 q^{48} +1.00000 q^{49} +3.62415 q^{50} -12.8316 q^{51} -12.3113 q^{52} -13.4441 q^{53} -10.9356 q^{54} -7.54765 q^{55} -2.55113 q^{56} +8.53748 q^{57} +20.8820 q^{58} +3.54000 q^{59} -10.5805 q^{60} +3.99565 q^{61} +7.95018 q^{62} +0.368489 q^{63} -13.0444 q^{64} -7.25967 q^{65} -17.0117 q^{66} -10.1417 q^{67} +21.8600 q^{68} +1.16849 q^{69} -4.17465 q^{70} -5.36963 q^{71} -0.940065 q^{72} +11.3145 q^{73} +15.7045 q^{74} +2.93768 q^{75} -14.5445 q^{76} -4.09366 q^{77} -16.3626 q^{78} +14.1963 q^{79} -0.879632 q^{80} -9.96968 q^{81} +23.4131 q^{82} +17.4633 q^{83} -5.73860 q^{84} +12.8903 q^{85} +19.1666 q^{86} +16.9266 q^{87} +10.4435 q^{88} +6.71228 q^{89} -1.53831 q^{90} -3.93746 q^{91} -1.99065 q^{92} +6.44429 q^{93} -9.27460 q^{94} -8.57655 q^{95} -11.3470 q^{96} +15.8528 q^{97} -2.26422 q^{98} -1.50847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.26422	−1.60105	−0.800524	−	0.599300i	$-0.795446\pi$
$2$	−2.26422	−1.60105	−0.800524	+	0.599300i	$0.795446\pi$
$3$	−1.83534	−1.05964	−0.529818	−	0.848111i	$-0.677740\pi$
$3$	−1.83534	−1.05964	−0.529818	+	0.848111i	$0.677740\pi$
$4$	3.12671	1.56336
$5$	1.84374	0.824547	0.412273	−	0.911060i	$-0.364735\pi$
$5$	1.84374	0.824547	0.412273	+	0.911060i	$0.364735\pi$
$6$	4.15563	1.69653
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.55113	−0.901961
$9$	0.368489	0.122830
$10$	−4.17465	−1.32014
$11$	−4.09366	−1.23428	−0.617142	−	0.786852i	$-0.711710\pi$
$11$	−4.09366	−1.23428	−0.617142	+	0.786852i	$0.711710\pi$
$12$	−5.73860	−1.65659
$13$	−3.93746	−1.09206	−0.546028	−	0.837767i	$-0.683861\pi$
$13$	−3.93746	−1.09206	−0.546028	+	0.837767i	$0.683861\pi$
$14$	−2.26422	−0.605139
$15$	−3.38390	−0.873720
$16$	−0.477091	−0.119273
$17$	6.99137	1.69566	0.847829	−	0.530270i	$-0.177910\pi$
$17$	6.99137	1.69566	0.847829	+	0.530270i	$0.177910\pi$
$18$	−0.834343	−0.196656
$19$	−4.65170	−1.06717	−0.533587	−	0.845745i	$-0.679156\pi$
$19$	−4.65170	−1.06717	−0.533587	+	0.845745i	$0.679156\pi$
$20$	5.76486	1.28906
$21$	−1.83534	−0.400505
$22$	9.26896	1.97615
$23$	−0.636658	−0.132752	−0.0663762	−	0.997795i	$-0.521144\pi$
$23$	−0.636658	−0.132752	−0.0663762	+	0.997795i	$0.521144\pi$
$24$	4.68221	0.955751
$25$	−1.60061	−0.320122
$26$	8.91530	1.74843
$27$	4.82973	0.929482
$28$	3.12671	0.590893
$29$	−9.22256	−1.71259	−0.856293	−	0.516490i	$-0.827238\pi$
$29$	−9.22256	−1.71259	−0.856293	+	0.516490i	$0.827238\pi$
$30$	7.66192	1.39887
$31$	−3.51122	−0.630633	−0.315317	−	0.948987i	$-0.602111\pi$
$31$	−3.51122	−0.630633	−0.315317	+	0.948987i	$0.602111\pi$
$32$	6.18250	1.09292
$33$	7.51327	1.30789
$34$	−15.8300	−2.71483
$35$	1.84374	0.311649
$36$	1.15216	0.192027
$37$	−6.93591	−1.14026	−0.570129	−	0.821556i	$-0.693107\pi$
$37$	−6.93591	−1.14026	−0.570129	+	0.821556i	$0.693107\pi$
$38$	10.5325	1.70860
$39$	7.22660	1.15718
$40$	−4.70363	−0.743709
$41$	−10.3404	−1.61490	−0.807452	−	0.589933i	$-0.799154\pi$
$41$	−10.3404	−1.61490	−0.807452	+	0.589933i	$0.799154\pi$
$42$	4.15563	0.641228
$43$	−8.46498	−1.29090	−0.645449	−	0.763804i	$-0.723330\pi$
$43$	−8.46498	−1.29090	−0.645449	+	0.763804i	$0.723330\pi$
$44$	−12.7997	−1.92963
$45$	0.679400	0.101279
$46$	1.44154	0.212543
$47$	4.09615	0.597485	0.298742	−	0.954334i	$-0.403433\pi$
$47$	4.09615	0.597485	0.298742	+	0.954334i	$0.403433\pi$
$48$	0.875626	0.126386
$49$	1.00000	0.142857
$50$	3.62415	0.512532
$51$	−12.8316	−1.79678
$52$	−12.3113	−1.70727
$53$	−13.4441	−1.84670	−0.923348	−	0.383965i	$-0.874558\pi$
$53$	−13.4441	−1.84670	−0.923348	+	0.383965i	$0.874558\pi$
$54$	−10.9356	−1.48815
$55$	−7.54765	−1.01773
$56$	−2.55113	−0.340909
$57$	8.53748	1.13082
$58$	20.8820	2.74193
$59$	3.54000	0.460869	0.230434	−	0.973088i	$-0.425985\pi$
$59$	3.54000	0.460869	0.230434	+	0.973088i	$0.425985\pi$
$60$	−10.5805	−1.36594
$61$	3.99565	0.511590	0.255795	−	0.966731i	$-0.417663\pi$
$61$	3.99565	0.511590	0.255795	+	0.966731i	$0.417663\pi$
$62$	7.95018	1.00967
$63$	0.368489	0.0464253
$64$	−13.0444	−1.63055
$65$	−7.25967	−0.900451
$66$	−17.0117	−2.09400
$67$	−10.1417	−1.23901	−0.619503	−	0.784994i	$-0.712666\pi$
$67$	−10.1417	−1.23901	−0.619503	+	0.784994i	$0.712666\pi$
$68$	21.8600	2.65092
$69$	1.16849	0.140669
$70$	−4.17465	−0.498966
$71$	−5.36963	−0.637258	−0.318629	−	0.947879i	$-0.603222\pi$
$71$	−5.36963	−0.637258	−0.318629	+	0.947879i	$0.603222\pi$
$72$	−0.940065	−0.110788
$73$	11.3145	1.32426	0.662129	−	0.749390i	$-0.269653\pi$
$73$	11.3145	1.32426	0.662129	+	0.749390i	$0.269653\pi$
$74$	15.7045	1.82561
$75$	2.93768	0.339213
$76$	−14.5445	−1.66837
$77$	−4.09366	−0.466516
$78$	−16.3626	−1.85271
$79$	14.1963	1.59721	0.798606	−	0.601854i	$-0.205571\pi$
$79$	14.1963	1.59721	0.798606	+	0.601854i	$0.205571\pi$
$80$	−0.879632	−0.0983459
$81$	−9.96968	−1.10774
$82$	23.4131	2.58554
$83$	17.4633	1.91685	0.958425	−	0.285345i	$-0.0921081\pi$
$83$	17.4633	1.91685	0.958425	+	0.285345i	$0.0921081\pi$
$84$	−5.73860	−0.626132
$85$	12.8903	1.39815
$86$	19.1666	2.06679
$87$	16.9266	1.81472
$88$	10.4435	1.11328
$89$	6.71228	0.711500	0.355750	−	0.934581i	$-0.384225\pi$
$89$	6.71228	0.711500	0.355750	+	0.934581i	$0.384225\pi$
$90$	−1.53831	−0.162152
$91$	−3.93746	−0.412758
$92$	−1.99065	−0.207539
$93$	6.44429	0.668242
$94$	−9.27460	−0.956602
$95$	−8.57655	−0.879935
$96$	−11.3470	−1.15810
$97$	15.8528	1.60961	0.804806	−	0.593537i	$-0.202269\pi$
$97$	15.8528	1.60961	0.804806	+	0.593537i	$0.202269\pi$
$98$	−2.26422	−0.228721
$99$	−1.50847	−0.151607
$100$	−5.00466	−0.500466
$101$	4.57731	0.455459	0.227730	−	0.973724i	$-0.426870\pi$
$101$	4.57731	0.455459	0.227730	+	0.973724i	$0.426870\pi$
$102$	29.0536	2.87673
$103$	−17.7433	−1.74830	−0.874152	−	0.485653i	$-0.838582\pi$
$103$	−17.7433	−1.74830	−0.874152	+	0.485653i	$0.838582\pi$
$104$	10.0450	0.984992
$105$	−3.38390	−0.330235
$106$	30.4406	2.95665
$107$	−8.27987	−0.800445	−0.400223	−	0.916418i	$-0.631067\pi$
$107$	−8.27987	−0.800445	−0.400223	+	0.916418i	$0.631067\pi$
$108$	15.1012	1.45311
$109$	−3.53671	−0.338755	−0.169378	−	0.985551i	$-0.554176\pi$
$109$	−3.53671	−0.338755	−0.169378	+	0.985551i	$0.554176\pi$
$110$	17.0896	1.62943
$111$	12.7298	1.20826
$112$	−0.477091	−0.0450808
$113$	13.2572	1.24713	0.623567	−	0.781770i	$-0.285683\pi$
$113$	13.2572	1.24713	0.623567	+	0.781770i	$0.285683\pi$
$114$	−19.3308	−1.81049
$115$	−1.17383	−0.109461
$116$	−28.8363	−2.67738
$117$	−1.45091	−0.134137
$118$	−8.01535	−0.737873
$119$	6.99137	0.640898
$120$	8.63278	0.788062
$121$	5.75803	0.523458
$122$	−9.04704	−0.819081
$123$	18.9783	1.71121
$124$	−10.9786	−0.985905
$125$	−12.1698	−1.08850
$126$	−0.834343	−0.0743291
$127$	12.6340	1.12109	0.560544	−	0.828125i	$-0.310592\pi$
$127$	12.6340	1.12109	0.560544	+	0.828125i	$0.310592\pi$
$128$	17.1704	1.51767
$129$	15.5362	1.36788
$130$	16.4375	1.44167
$131$	5.20058	0.454377	0.227188	−	0.973851i	$-0.427047\pi$
$131$	5.20058	0.454377	0.227188	+	0.973851i	$0.427047\pi$
$132$	23.4918	2.04470
$133$	−4.65170	−0.403354
$134$	22.9631	1.98371
$135$	8.90478	0.766401
$136$	−17.8359	−1.52942
$137$	−20.8710	−1.78313	−0.891564	−	0.452895i	$-0.850391\pi$
$137$	−20.8710	−1.78313	−0.891564	+	0.452895i	$0.850391\pi$
$138$	−2.64572	−0.225218
$139$	23.4092	1.98554	0.992771	−	0.120024i	$-0.0382973\pi$
$139$	23.4092	1.98554	0.992771	+	0.120024i	$0.0382973\pi$
$140$	5.76486	0.487219
$141$	−7.51784	−0.633117
$142$	12.1581	1.02028
$143$	16.1186	1.34791
$144$	−0.175803	−0.0146502
$145$	−17.0040	−1.41211
$146$	−25.6185	−2.12020
$147$	−1.83534	−0.151377
$148$	−21.6866	−1.78263
$149$	−6.17957	−0.506250	−0.253125	−	0.967434i	$-0.581458\pi$
$149$	−6.17957	−0.506250	−0.253125	+	0.967434i	$0.581458\pi$
$150$	−6.65156	−0.543097
$151$	5.01492	0.408108	0.204054	−	0.978960i	$-0.434588\pi$
$151$	5.01492	0.408108	0.204054	+	0.978960i	$0.434588\pi$
$152$	11.8671	0.962550
$153$	2.57625	0.208277
$154$	9.26896	0.746914
$155$	−6.47378	−0.519987
$156$	22.5955	1.80909
$157$	−17.9981	−1.43641	−0.718204	−	0.695833i	$-0.755035\pi$
$157$	−17.9981	−1.43641	−0.718204	+	0.695833i	$0.755035\pi$
$158$	−32.1437	−2.55721
$159$	24.6746	1.95683
$160$	11.3989	0.901166
$161$	−0.636658	−0.0501757
$162$	22.5736	1.77355
$163$	23.5559	1.84504	0.922521	−	0.385946i	$-0.126125\pi$
$163$	23.5559	1.84504	0.922521	+	0.385946i	$0.126125\pi$
$164$	−32.3316	−2.52467
$165$	13.8525	1.07842
$166$	−39.5409	−3.06897
$167$	−0.0505672	−0.00391301	−0.00195650	−	0.999998i	$-0.500623\pi$
$167$	−0.0505672	−0.00391301	−0.00195650	+	0.999998i	$0.500623\pi$
$168$	4.68221	0.361240
$169$	2.50362	0.192586
$170$	−29.1865	−2.23850
$171$	−1.71410	−0.131081
$172$	−26.4676	−2.01813
$173$	−18.4878	−1.40560	−0.702800	−	0.711387i	$-0.748067\pi$
$173$	−18.4878	−1.40560	−0.702800	+	0.711387i	$0.748067\pi$
$174$	−38.3256	−2.90545
$175$	−1.60061	−0.120995
$176$	1.95305	0.147216
$177$	−6.49712	−0.488353
$178$	−15.1981	−1.13915
$179$	−13.6924	−1.02341	−0.511707	−	0.859160i	$-0.670987\pi$
$179$	−13.6924	−1.02341	−0.511707	+	0.859160i	$0.670987\pi$
$180$	2.12429	0.158335
$181$	1.42027	0.105568	0.0527839	−	0.998606i	$-0.483191\pi$
$181$	1.42027	0.105568	0.0527839	+	0.998606i	$0.483191\pi$
$182$	8.91530	0.660846
$183$	−7.33339	−0.542100
$184$	1.62420	0.119738
$185$	−12.7880	−0.940195
$186$	−14.5913	−1.06989
$187$	−28.6203	−2.09292
$188$	12.8075	0.934082
$189$	4.82973	0.351311
$190$	19.4192	1.40882
$191$	5.68236	0.411161	0.205580	−	0.978640i	$-0.434092\pi$
$191$	5.68236	0.411161	0.205580	+	0.978640i	$0.434092\pi$
$192$	23.9410	1.72779
$193$	−14.2845	−1.02822	−0.514109	−	0.857725i	$-0.671877\pi$
$193$	−14.2845	−1.02822	−0.514109	+	0.857725i	$0.671877\pi$
$194$	−35.8944	−2.57707
$195$	13.3240	0.954151
$196$	3.12671	0.223337
$197$	21.1914	1.50982	0.754911	−	0.655827i	$-0.227680\pi$
$197$	21.1914	1.50982	0.754911	+	0.655827i	$0.227680\pi$
$198$	3.41551	0.242730
$199$	12.6626	0.897628	0.448814	−	0.893625i	$-0.351846\pi$
$199$	12.6626	0.897628	0.448814	+	0.893625i	$0.351846\pi$
$200$	4.08337	0.288738
$201$	18.6135	1.31290
$202$	−10.3641	−0.729212
$203$	−9.22256	−0.647297
$204$	−40.1207	−2.80901
$205$	−19.0651	−1.33156
$206$	40.1749	2.79912
$207$	−0.234602	−0.0163059
$208$	1.87853	0.130252
$209$	19.0425	1.31720
$210$	7.66192	0.528723
$211$	−0.894265	−0.0615637	−0.0307819	−	0.999526i	$-0.509800\pi$
$211$	−0.894265	−0.0615637	−0.0307819	+	0.999526i	$0.509800\pi$
$212$	−42.0360	−2.88704
$213$	9.85513	0.675262
$214$	18.7475	1.28155
$215$	−15.6072	−1.06441
$216$	−12.3213	−0.838357
$217$	−3.51122	−0.238357
$218$	8.00790	0.542363
$219$	−20.7659	−1.40323
$220$	−23.5993	−1.59107
$221$	−27.5283	−1.85175
$222$	−28.8231	−1.93448
$223$	15.1715	1.01596	0.507979	−	0.861369i	$-0.330393\pi$
$223$	15.1715	1.01596	0.507979	+	0.861369i	$0.330393\pi$
$224$	6.18250	0.413086
$225$	−0.589809	−0.0393206
$226$	−30.0173	−1.99672
$227$	−13.1612	−0.873540	−0.436770	−	0.899573i	$-0.643878\pi$
$227$	−13.1612	−0.873540	−0.436770	+	0.899573i	$0.643878\pi$
$228$	26.6943	1.76787
$229$	9.33629	0.616959	0.308480	−	0.951231i	$-0.400180\pi$
$229$	9.33629	0.616959	0.308480	+	0.951231i	$0.400180\pi$
$230$	2.65782	0.175252
$231$	7.51327	0.494337
$232$	23.5280	1.54469
$233$	1.15611	0.0757396	0.0378698	−	0.999283i	$-0.487943\pi$
$233$	1.15611	0.0757396	0.0378698	+	0.999283i	$0.487943\pi$
$234$	3.28519	0.214760
$235$	7.55224	0.492654
$236$	11.0686	0.720502
$237$	−26.0552	−1.69246
$238$	−15.8300	−1.02611
$239$	0.350693	0.0226844	0.0113422	−	0.999936i	$-0.496390\pi$
$239$	0.350693	0.0226844	0.0113422	+	0.999936i	$0.496390\pi$
$240$	1.61443	0.104211
$241$	12.8468	0.827532	0.413766	−	0.910383i	$-0.364213\pi$
$241$	12.8468	0.827532	0.413766	+	0.910383i	$0.364213\pi$
$242$	−13.0375	−0.838081
$243$	3.80862	0.244323
$244$	12.4932	0.799798
$245$	1.84374	0.117792
$246$	−42.9711	−2.73973
$247$	18.3159	1.16541
$248$	8.95758	0.568807
$249$	−32.0512	−2.03116
$250$	27.5552	1.74275
$251$	−15.5657	−0.982497	−0.491249	−	0.871019i	$-0.663459\pi$
$251$	−15.5657	−0.982497	−0.491249	+	0.871019i	$0.663459\pi$
$252$	1.15216	0.0725793
$253$	2.60626	0.163854
$254$	−28.6062	−1.79492
$255$	−23.6581	−1.48153
$256$	−12.7889	−0.799308
$257$	−5.03255	−0.313922	−0.156961	−	0.987605i	$-0.550170\pi$
$257$	−5.03255	−0.313922	−0.156961	+	0.987605i	$0.550170\pi$
$258$	−35.1773	−2.19005
$259$	−6.93591	−0.430977
$260$	−22.6989	−1.40773
$261$	−3.39842	−0.210357
$262$	−11.7753	−0.727479
$263$	10.7445	0.662532	0.331266	−	0.943537i	$-0.392524\pi$
$263$	10.7445	0.662532	0.331266	+	0.943537i	$0.392524\pi$
$264$	−19.1673	−1.17967
$265$	−24.7875	−1.52269
$266$	10.5325	0.645789
$267$	−12.3193	−0.753932
$268$	−31.7102	−1.93701
$269$	−2.24346	−0.136786	−0.0683932	−	0.997658i	$-0.521787\pi$
$269$	−2.24346	−0.136786	−0.0683932	+	0.997658i	$0.521787\pi$
$270$	−20.1624	−1.22705
$271$	13.9892	0.849780	0.424890	−	0.905245i	$-0.360313\pi$
$271$	13.9892	0.849780	0.424890	+	0.905245i	$0.360313\pi$
$272$	−3.33552	−0.202246
$273$	7.22660	0.437374
$274$	47.2566	2.85487
$275$	6.55236	0.395122
$276$	3.65352	0.219916
$277$	−13.5539	−0.814376	−0.407188	−	0.913344i	$-0.633491\pi$
$277$	−13.5539	−0.814376	−0.407188	+	0.913344i	$0.633491\pi$
$278$	−53.0037	−3.17895
$279$	−1.29385	−0.0774605
$280$	−4.70363	−0.281096
$281$	2.27941	0.135978	0.0679892	−	0.997686i	$-0.478342\pi$
$281$	2.27941	0.135978	0.0679892	+	0.997686i	$0.478342\pi$
$282$	17.0221	1.01365
$283$	8.42115	0.500585	0.250293	−	0.968170i	$-0.419473\pi$
$283$	8.42115	0.500585	0.250293	+	0.968170i	$0.419473\pi$
$284$	−16.7893	−0.996262
$285$	15.7409	0.932412
$286$	−36.4962	−2.15807
$287$	−10.3404	−0.610377
$288$	2.27819	0.134243
$289$	31.8793	1.87525
$290$	38.5010	2.26085
$291$	−29.0954	−1.70560
$292$	35.3771	2.07029
$293$	2.29106	0.133845	0.0669227	−	0.997758i	$-0.478682\pi$
$293$	2.29106	0.133845	0.0669227	+	0.997758i	$0.478682\pi$
$294$	4.15563	0.242361
$295$	6.52685	0.380008
$296$	17.6944	1.02847
$297$	−19.7713	−1.14724
$298$	13.9919	0.810531
$299$	2.50682	0.144973
$300$	9.18527	0.530312
$301$	−8.46498	−0.487913
$302$	−11.3549	−0.653401
$303$	−8.40094	−0.482621
$304$	2.21928	0.127285
$305$	7.36695	0.421830
$306$	−5.83320	−0.333462
$307$	−14.4987	−0.827483	−0.413742	−	0.910394i	$-0.635778\pi$
$307$	−14.4987	−0.827483	−0.413742	+	0.910394i	$0.635778\pi$
$308$	−12.7997	−0.729330
$309$	32.5651	1.85257
$310$	14.6581	0.832524
$311$	−0.600926	−0.0340754	−0.0170377	−	0.999855i	$-0.505424\pi$
$311$	−0.600926	−0.0340754	−0.0170377	+	0.999855i	$0.505424\pi$
$312$	−18.4360	−1.04373
$313$	−12.3762	−0.699545	−0.349772	−	0.936835i	$-0.613741\pi$
$313$	−12.3762	−0.699545	−0.349772	+	0.936835i	$0.613741\pi$
$314$	40.7518	2.29976
$315$	0.679400	0.0382798
$316$	44.3879	2.49701
$317$	−5.25535	−0.295170	−0.147585	−	0.989049i	$-0.547150\pi$
$317$	−5.25535	−0.295170	−0.147585	+	0.989049i	$0.547150\pi$
$318$	−55.8689	−3.13297
$319$	37.7540	2.11382
$320$	−24.0505	−1.34446
$321$	15.1964	0.848181
$322$	1.44154	0.0803337
$323$	−32.5218	−1.80956
$324$	−31.1723	−1.73180
$325$	6.30235	0.349592
$326$	−53.3359	−2.95400
$327$	6.49107	0.358957
$328$	26.3798	1.45658
$329$	4.09615	0.225828
$330$	−31.3653	−1.72660
$331$	1.45232	0.0798267	0.0399133	−	0.999203i	$-0.487292\pi$
$331$	1.45232	0.0798267	0.0399133	+	0.999203i	$0.487292\pi$
$332$	54.6028	2.99672
$333$	−2.55581	−0.140058
$334$	0.114496	0.00626492
$335$	−18.6987	−1.02162
$336$	0.875626	0.0477693
$337$	−16.7030	−0.909870	−0.454935	−	0.890525i	$-0.650337\pi$
$337$	−16.7030	−0.909870	−0.454935	+	0.890525i	$0.650337\pi$
$338$	−5.66875	−0.308340
$339$	−24.3316	−1.32151
$340$	40.3043	2.18581
$341$	14.3737	0.778381
$342$	3.88112	0.209867
$343$	1.00000	0.0539949
$344$	21.5953	1.16434
$345$	2.15439	0.115988
$346$	41.8605	2.25043
$347$	−33.5259	−1.79977	−0.899883	−	0.436132i	$-0.856348\pi$
$347$	−33.5259	−1.79977	−0.899883	+	0.436132i	$0.856348\pi$
$348$	52.9246	2.83705
$349$	−1.70421	−0.0912242	−0.0456121	−	0.998959i	$-0.514524\pi$
$349$	−1.70421	−0.0912242	−0.0456121	+	0.998959i	$0.514524\pi$
$350$	3.62415	0.193719
$351$	−19.0169	−1.01505
$352$	−25.3091	−1.34898
$353$	21.0054	1.11800	0.559001	−	0.829167i	$-0.311185\pi$
$353$	21.0054	1.11800	0.559001	+	0.829167i	$0.311185\pi$
$354$	14.7109	0.781877
$355$	−9.90022	−0.525449
$356$	20.9874	1.11233
$357$	−12.8316	−0.679119
$358$	31.0026	1.63854
$359$	−10.7416	−0.566919	−0.283460	−	0.958984i	$-0.591482\pi$
$359$	−10.7416	−0.566919	−0.283460	+	0.958984i	$0.591482\pi$
$360$	−1.73324	−0.0913497
$361$	2.63836	0.138861
$362$	−3.21581	−0.169019
$363$	−10.5680	−0.554675
$364$	−12.3113	−0.645288
$365$	20.8610	1.09191
$366$	16.6044	0.867928
$367$	−36.0310	−1.88080	−0.940401	−	0.340068i	$-0.889550\pi$
$367$	−36.0310	−1.88080	−0.940401	+	0.340068i	$0.889550\pi$
$368$	0.303744	0.0158337
$369$	−3.81034	−0.198358
$370$	28.9550	1.50530
$371$	−13.4441	−0.697985
$372$	20.1495	1.04470
$373$	15.2208	0.788102	0.394051	−	0.919089i	$-0.371073\pi$
$373$	15.2208	0.788102	0.394051	+	0.919089i	$0.371073\pi$
$374$	64.8028	3.35087
$375$	22.3358	1.15342
$376$	−10.4498	−0.538908
$377$	36.3135	1.87024
$378$	−10.9356	−0.562466
$379$	35.9547	1.84687	0.923434	−	0.383758i	$-0.125370\pi$
$379$	35.9547	1.84687	0.923434	+	0.383758i	$0.125370\pi$
$380$	−26.8164	−1.37565
$381$	−23.1878	−1.18795
$382$	−12.8661	−0.658288
$383$	2.03383	0.103924	0.0519620	−	0.998649i	$-0.483453\pi$
$383$	2.03383	0.103924	0.0519620	+	0.998649i	$0.483453\pi$
$384$	−31.5137	−1.60818
$385$	−7.54765	−0.384664
$386$	32.3432	1.64623
$387$	−3.11926	−0.158561
$388$	49.5673	2.51640
$389$	7.72004	0.391422	0.195711	−	0.980662i	$-0.437299\pi$
$389$	7.72004	0.391422	0.195711	+	0.980662i	$0.437299\pi$
$390$	−30.1685	−1.52764
$391$	−4.45111	−0.225103
$392$	−2.55113	−0.128852
$393$	−9.54485	−0.481474
$394$	−47.9820	−2.41730
$395$	26.1744	1.31698
$396$	−4.71655	−0.237016
$397$	8.69939	0.436610	0.218305	−	0.975881i	$-0.429947\pi$
$397$	8.69939	0.436610	0.218305	+	0.975881i	$0.429947\pi$
$398$	−28.6710	−1.43715
$399$	8.53748	0.427409
$400$	0.763637	0.0381819
$401$	−24.9235	−1.24462	−0.622311	−	0.782770i	$-0.713806\pi$
$401$	−24.9235	−1.24462	−0.622311	+	0.782770i	$0.713806\pi$
$402$	−42.1452	−2.10201
$403$	13.8253	0.688687
$404$	14.3119	0.712045
$405$	−18.3815	−0.913386
$406$	20.8820	1.03635
$407$	28.3933	1.40740
$408$	32.7351	1.62063
$409$	22.9581	1.13521	0.567603	−	0.823302i	$-0.307871\pi$
$409$	22.9581	1.13521	0.567603	+	0.823302i	$0.307871\pi$
$410$	43.1677	2.13190
$411$	38.3054	1.88947
$412$	−55.4783	−2.73322
$413$	3.54000	0.174192
$414$	0.531191	0.0261066
$415$	32.1979	1.58053
$416$	−24.3434	−1.19353
$417$	−42.9639	−2.10395
$418$	−43.1165	−2.10890
$419$	37.0080	1.80796	0.903979	−	0.427577i	$-0.140633\pi$
$419$	37.0080	1.80796	0.903979	+	0.427577i	$0.140633\pi$
$420$	−10.5805	−0.516275
$421$	21.0392	1.02539	0.512695	−	0.858571i	$-0.328647\pi$
$421$	21.0392	1.02539	0.512695	+	0.858571i	$0.328647\pi$
$422$	2.02482	0.0985665
$423$	1.50939	0.0733889
$424$	34.2978	1.66565
$425$	−11.1905	−0.542818
$426$	−22.3142	−1.08113
$427$	3.99565	0.193363
$428$	−25.8888	−1.25138
$429$	−29.5832	−1.42829
$430$	35.3383	1.70416
$431$	12.1906	0.587200	0.293600	−	0.955928i	$-0.405147\pi$
$431$	12.1906	0.587200	0.293600	+	0.955928i	$0.405147\pi$
$432$	−2.30422	−0.110862
$433$	−1.29556	−0.0622606	−0.0311303	−	0.999515i	$-0.509911\pi$
$433$	−1.29556	−0.0622606	−0.0311303	+	0.999515i	$0.509911\pi$
$434$	7.95018	0.381621
$435$	31.2083	1.49632
$436$	−11.0583	−0.529595
$437$	2.96155	0.141670
$438$	47.0188	2.24664
$439$	6.15175	0.293607	0.146803	−	0.989166i	$-0.453102\pi$
$439$	6.15175	0.293607	0.146803	+	0.989166i	$0.453102\pi$
$440$	19.2551	0.917949
$441$	0.368489	0.0175471
$442$	62.3302	2.96475
$443$	5.27310	0.250532	0.125266	−	0.992123i	$-0.460021\pi$
$443$	5.27310	0.250532	0.125266	+	0.992123i	$0.460021\pi$
$444$	39.8024	1.88894
$445$	12.3757	0.586665
$446$	−34.3517	−1.62660
$447$	11.3416	0.536441
$448$	−13.0444	−0.616290
$449$	−17.7339	−0.836917	−0.418458	−	0.908236i	$-0.637429\pi$
$449$	−17.7339	−0.836917	−0.418458	+	0.908236i	$0.637429\pi$
$450$	1.33546	0.0629541
$451$	42.3302	1.99325
$452$	41.4515	1.94971
$453$	−9.20410	−0.432446
$454$	29.7999	1.39858
$455$	−7.25967	−0.340339
$456$	−21.7802	−1.01995
$457$	25.7157	1.20293	0.601465	−	0.798899i	$-0.294584\pi$
$457$	25.7157	1.20293	0.601465	+	0.798899i	$0.294584\pi$
$458$	−21.1395	−0.987782
$459$	33.7664	1.57608
$460$	−3.67024	−0.171126
$461$	−28.9624	−1.34891	−0.674456	−	0.738315i	$-0.735622\pi$
$461$	−28.9624	−1.34891	−0.674456	+	0.738315i	$0.735622\pi$
$462$	−17.0117	−0.791458
$463$	39.9602	1.85711	0.928555	−	0.371195i	$-0.121052\pi$
$463$	39.9602	1.85711	0.928555	+	0.371195i	$0.121052\pi$
$464$	4.40000	0.204265
$465$	11.8816	0.550997
$466$	−2.61770	−0.121263
$467$	22.5022	1.04128	0.520638	−	0.853777i	$-0.325694\pi$
$467$	22.5022	1.04128	0.520638	+	0.853777i	$0.325694\pi$
$468$	−4.53659	−0.209704
$469$	−10.1417	−0.468300
$470$	−17.1000	−0.788763
$471$	33.0328	1.52207
$472$	−9.03100	−0.415686
$473$	34.6527	1.59333
$474$	58.9947	2.70972
$475$	7.44558	0.341626
$476$	21.8600	1.00195
$477$	−4.95402	−0.226829
$478$	−0.794048	−0.0363189
$479$	−6.24138	−0.285176	−0.142588	−	0.989782i	$-0.545542\pi$
$479$	−6.24138	−0.285176	−0.142588	+	0.989782i	$0.545542\pi$
$480$	−20.9210	−0.954908
$481$	27.3099	1.24522
$482$	−29.0879	−1.32492
$483$	1.16849	0.0531680
$484$	18.0037	0.818351
$485$	29.2286	1.32720
$486$	−8.62357	−0.391173
$487$	−31.0674	−1.40780	−0.703900	−	0.710299i	$-0.748560\pi$
$487$	−31.0674	−1.40780	−0.703900	+	0.710299i	$0.748560\pi$
$488$	−10.1934	−0.461435
$489$	−43.2332	−1.95507
$490$	−4.17465	−0.188591
$491$	−31.7564	−1.43315	−0.716574	−	0.697511i	$-0.754291\pi$
$491$	−31.7564	−1.43315	−0.716574	+	0.697511i	$0.754291\pi$
$492$	59.3396	2.67524
$493$	−64.4784	−2.90396
$494$	−41.4714	−1.86588
$495$	−2.78123	−0.125007
$496$	1.67517	0.0752173
$497$	−5.36963	−0.240861
$498$	72.5712	3.25199
$499$	−18.0042	−0.805977	−0.402988	−	0.915205i	$-0.632029\pi$
$499$	−18.0042	−0.805977	−0.402988	+	0.915205i	$0.632029\pi$
$500$	−38.0516	−1.70172
$501$	0.0928082	0.00414637
$502$	35.2442	1.57303
$503$	7.97197	0.355452	0.177726	−	0.984080i	$-0.443126\pi$
$503$	7.97197	0.355452	0.177726	+	0.984080i	$0.443126\pi$
$504$	−0.940065	−0.0418738
$505$	8.43938	0.375547
$506$	−5.90116	−0.262338
$507$	−4.59500	−0.204071
$508$	39.5029	1.75266
$509$	26.9104	1.19278	0.596391	−	0.802694i	$-0.296601\pi$
$509$	26.9104	1.19278	0.596391	+	0.802694i	$0.296601\pi$
$510$	53.5673	2.37200
$511$	11.3145	0.500523
$512$	−5.38386	−0.237935
$513$	−22.4665	−0.991919
$514$	11.3948	0.502604
$515$	−32.7142	−1.44156
$516$	48.5771	2.13849
$517$	−16.7682	−0.737466
$518$	15.7045	0.690015
$519$	33.9315	1.48943
$520$	18.5204	0.812172
$521$	−22.2290	−0.973869	−0.486934	−	0.873439i	$-0.661885\pi$
$521$	−22.2290	−0.973869	−0.486934	+	0.873439i	$0.661885\pi$
$522$	7.69478	0.336791
$523$	8.13677	0.355796	0.177898	−	0.984049i	$-0.443070\pi$
$523$	8.13677	0.355796	0.177898	+	0.984049i	$0.443070\pi$
$524$	16.2607	0.710353
$525$	2.93768	0.128211
$526$	−24.3279	−1.06075
$527$	−24.5482	−1.06934
$528$	−3.58451	−0.155996
$529$	−22.5947	−0.982377
$530$	56.1246	2.43790
$531$	1.30445	0.0566084
$532$	−14.5445	−0.630586
$533$	40.7151	1.76357
$534$	27.8938	1.20708
$535$	−15.2660	−0.660005
$536$	25.8728	1.11754
$537$	25.1302	1.08445
$538$	5.07970	0.219002
$539$	−4.09366	−0.176326
$540$	27.8427	1.19816
$541$	−14.1295	−0.607476	−0.303738	−	0.952756i	$-0.598235\pi$
$541$	−14.1295	−0.607476	−0.303738	+	0.952756i	$0.598235\pi$
$542$	−31.6746	−1.36054
$543$	−2.60668	−0.111864
$544$	43.2242	1.85322
$545$	−6.52078	−0.279319
$546$	−16.3626	−0.700257
$547$	27.6916	1.18401	0.592005	−	0.805935i	$-0.298337\pi$
$547$	27.6916	1.18401	0.592005	+	0.805935i	$0.298337\pi$
$548$	−65.2575	−2.78766
$549$	1.47235	0.0628385
$550$	−14.8360	−0.632610
$551$	42.9006	1.82763
$552$	−2.98096	−0.126878
$553$	14.1963	0.603689
$554$	30.6891	1.30386
$555$	23.4705	0.996265
$556$	73.1938	3.10411
$557$	2.82031	0.119500	0.0597502	−	0.998213i	$-0.480970\pi$
$557$	2.82031	0.119500	0.0597502	+	0.998213i	$0.480970\pi$
$558$	2.92956	0.124018
$559$	33.3306	1.40973
$560$	−0.879632	−0.0371713
$561$	52.5281	2.21774
$562$	−5.16110	−0.217708
$563$	5.66128	0.238595	0.119297	−	0.992859i	$-0.461936\pi$
$563$	5.66128	0.238595	0.119297	+	0.992859i	$0.461936\pi$
$564$	−23.5061	−0.989787
$565$	24.4429	1.02832
$566$	−19.0674	−0.801461
$567$	−9.96968	−0.418687
$568$	13.6986	0.574782
$569$	−28.7445	−1.20503	−0.602516	−	0.798107i	$-0.705835\pi$
$569$	−28.7445	−1.20503	−0.602516	+	0.798107i	$0.705835\pi$
$570$	−35.6410	−1.49284
$571$	−20.8234	−0.871432	−0.435716	−	0.900084i	$-0.643505\pi$
$571$	−20.8234	−0.871432	−0.435716	+	0.900084i	$0.643505\pi$
$572$	50.3983	2.10726
$573$	−10.4291	−0.435681
$574$	23.4131	0.977243
$575$	1.01904	0.0424970
$576$	−4.80672	−0.200280
$577$	−13.9613	−0.581217	−0.290609	−	0.956842i	$-0.593858\pi$
$577$	−13.9613	−0.581217	−0.290609	+	0.956842i	$0.593858\pi$
$578$	−72.1819	−3.00237
$579$	26.2169	1.08954
$580$	−53.1667	−2.20763
$581$	17.4633	0.724501
$582$	65.8786	2.73076
$583$	55.0357	2.27935
$584$	−28.8647	−1.19443
$585$	−2.67511	−0.110602
$586$	−5.18748	−0.214293
$587$	11.2413	0.463980	0.231990	−	0.972718i	$-0.425476\pi$
$587$	11.2413	0.463980	0.231990	+	0.972718i	$0.425476\pi$
$588$	−5.73860	−0.236656
$589$	16.3331	0.672995
$590$	−14.7782	−0.608411
$591$	−38.8935	−1.59986
$592$	3.30906	0.136001
$593$	−23.1764	−0.951741	−0.475871	−	0.879515i	$-0.657867\pi$
$593$	−23.1764	−0.951741	−0.475871	+	0.879515i	$0.657867\pi$
$594$	44.7666	1.83679
$595$	12.8903	0.528451
$596$	−19.3217	−0.791450
$597$	−23.2402	−0.951160
$598$	−5.67600	−0.232109
$599$	40.4613	1.65320	0.826601	−	0.562788i	$-0.190271\pi$
$599$	40.4613	1.65320	0.826601	+	0.562788i	$0.190271\pi$
$600$	−7.49440	−0.305957
$601$	3.84778	0.156954	0.0784772	−	0.996916i	$-0.474994\pi$
$601$	3.84778	0.156954	0.0784772	+	0.996916i	$0.474994\pi$
$602$	19.1666	0.781173
$603$	−3.73711	−0.152187
$604$	15.6802	0.638018
$605$	10.6163	0.431615
$606$	19.0216	0.772700
$607$	1.50603	0.0611279	0.0305640	−	0.999533i	$-0.490270\pi$
$607$	1.50603	0.0611279	0.0305640	+	0.999533i	$0.490270\pi$
$608$	−28.7592	−1.16634
$609$	16.9266	0.685900
$610$	−16.6804	−0.675371
$611$	−16.1284	−0.652487
$612$	8.05518	0.325612
$613$	−37.2836	−1.50587	−0.752935	−	0.658095i	$-0.771363\pi$
$613$	−37.2836	−1.50587	−0.752935	+	0.658095i	$0.771363\pi$
$614$	32.8283	1.32484
$615$	34.9910	1.41097
$616$	10.4435	0.420779
$617$	−15.3056	−0.616182	−0.308091	−	0.951357i	$-0.599690\pi$
$617$	−15.3056	−0.616182	−0.308091	+	0.951357i	$0.599690\pi$
$618$	−73.7348	−2.96605
$619$	−42.4160	−1.70484	−0.852421	−	0.522856i	$-0.824867\pi$
$619$	−42.4160	−1.70484	−0.852421	+	0.522856i	$0.824867\pi$
$620$	−20.2417	−0.812924
$621$	−3.07489	−0.123391
$622$	1.36063	0.0545563
$623$	6.71228	0.268922
$624$	−3.44774	−0.138020
$625$	−14.4350	−0.577399
$626$	28.0225	1.12000
$627$	−34.9495	−1.39575
$628$	−56.2750	−2.24562
$629$	−48.4916	−1.93349
$630$	−1.53831	−0.0612879
$631$	1.95402	0.0777884	0.0388942	−	0.999243i	$-0.487616\pi$
$631$	1.95402	0.0777884	0.0388942	+	0.999243i	$0.487616\pi$
$632$	−36.2167	−1.44062
$633$	1.64128	0.0652352
$634$	11.8993	0.472581
$635$	23.2939	0.924389
$636$	77.1505	3.05922
$637$	−3.93746	−0.156008
$638$	−85.4836	−3.38433
$639$	−1.97865	−0.0782743
$640$	31.6579	1.25139
$641$	5.98473	0.236383	0.118191	−	0.992991i	$-0.462290\pi$
$641$	5.98473	0.236383	0.118191	+	0.992991i	$0.462290\pi$
$642$	−34.4081	−1.35798
$643$	−3.02394	−0.119253	−0.0596263	−	0.998221i	$-0.518991\pi$
$643$	−3.02394	−0.119253	−0.0596263	+	0.998221i	$0.518991\pi$
$644$	−1.99065	−0.0784425
$645$	28.6447	1.12788
$646$	73.6367	2.89720
$647$	5.88434	0.231337	0.115669	−	0.993288i	$-0.463099\pi$
$647$	5.88434	0.231337	0.115669	+	0.993288i	$0.463099\pi$
$648$	25.4340	0.999141
$649$	−14.4915	−0.568843
$650$	−14.2699	−0.559713
$651$	6.44429	0.252572
$652$	73.6526	2.88446
$653$	−29.2544	−1.14481	−0.572407	−	0.819970i	$-0.693990\pi$
$653$	−29.2544	−1.14481	−0.572407	+	0.819970i	$0.693990\pi$
$654$	−14.6973	−0.574708
$655$	9.58853	0.374655
$656$	4.93333	0.192614
$657$	4.16926	0.162658
$658$	−9.27460	−0.361562
$659$	−23.3660	−0.910209	−0.455105	−	0.890438i	$-0.650398\pi$
$659$	−23.3660	−0.910209	−0.455105	+	0.890438i	$0.650398\pi$
$660$	43.3129	1.68595
$661$	16.0112	0.622762	0.311381	−	0.950285i	$-0.399208\pi$
$661$	16.0112	0.622762	0.311381	+	0.950285i	$0.399208\pi$
$662$	−3.28838	−0.127806
$663$	50.5239	1.96218
$664$	−44.5513	−1.72892
$665$	−8.57655	−0.332584
$666$	5.78693	0.224239
$667$	5.87162	0.227350
$668$	−0.158109	−0.00611743
$669$	−27.8449	−1.07655
$670$	42.3380	1.63566
$671$	−16.3568	−0.631448
$672$	−11.3470	−0.437721
$673$	−0.630073	−0.0242875	−0.0121438	−	0.999926i	$-0.503866\pi$
$673$	−0.630073	−0.0242875	−0.0121438	+	0.999926i	$0.503866\pi$
$674$	37.8193	1.45675
$675$	−7.73052	−0.297548
$676$	7.82809	0.301081
$677$	13.6729	0.525491	0.262745	−	0.964865i	$-0.415372\pi$
$677$	13.6729	0.525491	0.262745	+	0.964865i	$0.415372\pi$
$678$	55.0921	2.11580
$679$	15.8528	0.608376
$680$	−32.8848	−1.26108
$681$	24.1553	0.925635
$682$	−32.5453	−1.24623
$683$	18.5849	0.711133	0.355566	−	0.934651i	$-0.384288\pi$
$683$	18.5849	0.711133	0.355566	+	0.934651i	$0.384288\pi$
$684$	−5.35951	−0.204926
$685$	−38.4807	−1.47027
$686$	−2.26422	−0.0864485
$687$	−17.1353	−0.653753
$688$	4.03856	0.153969
$689$	52.9358	2.01669
$690$	−4.87802	−0.185703
$691$	31.1894	1.18650	0.593251	−	0.805018i	$-0.297844\pi$
$691$	31.1894	1.18650	0.593251	+	0.805018i	$0.297844\pi$
$692$	−57.8060	−2.19745
$693$	−1.50847	−0.0573020
$694$	75.9102	2.88151
$695$	43.1605	1.63717
$696$	−43.1819	−1.63681
$697$	−72.2939	−2.73833
$698$	3.85871	0.146054
$699$	−2.12187	−0.0802564
$700$	−5.00466	−0.189158
$701$	36.8567	1.39206	0.696029	−	0.718014i	$-0.254949\pi$
$701$	36.8567	1.39206	0.696029	+	0.718014i	$0.254949\pi$
$702$	43.0585	1.62514
$703$	32.2638	1.21685
$704$	53.3993	2.01256
$705$	−13.8610	−0.522034
$706$	−47.5609	−1.78998
$707$	4.57731	0.172147
$708$	−20.3146	−0.763470
$709$	26.2784	0.986906	0.493453	−	0.869772i	$-0.335734\pi$
$709$	26.2784	0.986906	0.493453	+	0.869772i	$0.335734\pi$
$710$	22.4163	0.841270
$711$	5.23120	0.196185
$712$	−17.1239	−0.641746
$713$	2.23544	0.0837181
$714$	29.0536	1.08730
$715$	29.7186	1.11141
$716$	−42.8121	−1.59996
$717$	−0.643643	−0.0240373
$718$	24.3214	0.907665
$719$	17.2952	0.645004	0.322502	−	0.946569i	$-0.395476\pi$
$719$	17.2952	0.645004	0.322502	+	0.946569i	$0.395476\pi$
$720$	−0.324135	−0.0120798
$721$	−17.7433	−0.660797
$722$	−5.97383	−0.222323
$723$	−23.5782	−0.876883
$724$	4.44078	0.165040
$725$	14.7617	0.548238
$726$	23.9283	0.888061
$727$	−6.61551	−0.245356	−0.122678	−	0.992447i	$-0.539148\pi$
$727$	−6.61551	−0.245356	−0.122678	+	0.992447i	$0.539148\pi$
$728$	10.0450	0.372292
$729$	22.9189	0.848849
$730$	−47.2339	−1.74821
$731$	−59.1818	−2.18892
$732$	−22.9294	−0.847495
$733$	8.65614	0.319722	0.159861	−	0.987140i	$-0.448895\pi$
$733$	8.65614	0.319722	0.159861	+	0.987140i	$0.448895\pi$
$734$	81.5822	3.01126
$735$	−3.38390	−0.124817
$736$	−3.93614	−0.145088
$737$	41.5167	1.52929
$738$	8.62747	0.317581
$739$	−29.0683	−1.06929	−0.534647	−	0.845076i	$-0.679555\pi$
$739$	−29.0683	−1.06929	−0.534647	+	0.845076i	$0.679555\pi$
$740$	−39.9845	−1.46986
$741$	−33.6160	−1.23492
$742$	30.4406	1.11751
$743$	−22.8121	−0.836894	−0.418447	−	0.908241i	$-0.637426\pi$
$743$	−22.8121	−0.836894	−0.418447	+	0.908241i	$0.637426\pi$
$744$	−16.4402	−0.602728
$745$	−11.3935	−0.417427
$746$	−34.4633	−1.26179
$747$	6.43505	0.235446
$748$	−89.4874	−3.27199
$749$	−8.27987	−0.302540
$750$	−50.5733	−1.84668
$751$	28.6368	1.04497	0.522485	−	0.852648i	$-0.325005\pi$
$751$	28.6368	1.04497	0.522485	+	0.852648i	$0.325005\pi$
$752$	−1.95423	−0.0712636
$753$	28.5684	1.04109
$754$	−82.2219	−2.99435
$755$	9.24622	0.336504
$756$	15.1012	0.549224
$757$	−10.8520	−0.394423	−0.197211	−	0.980361i	$-0.563188\pi$
$757$	−10.8520	−0.394423	−0.197211	+	0.980361i	$0.563188\pi$
$758$	−81.4095	−2.95692
$759$	−4.78338	−0.173626
$760$	21.8799	0.793668
$761$	−21.0205	−0.761993	−0.380997	−	0.924576i	$-0.624419\pi$
$761$	−21.0205	−0.761993	−0.380997	+	0.924576i	$0.624419\pi$
$762$	52.5023	1.90196
$763$	−3.53671	−0.128037
$764$	17.7671	0.642791
$765$	4.74994	0.171734
$766$	−4.60506	−0.166388
$767$	−13.9386	−0.503294
$768$	23.4721	0.846976
$769$	15.9036	0.573497	0.286748	−	0.958006i	$-0.407426\pi$
$769$	15.9036	0.573497	0.286748	+	0.958006i	$0.407426\pi$
$770$	17.0896	0.615866
$771$	9.23647	0.332643
$772$	−44.6634	−1.60747
$773$	23.4483	0.843376	0.421688	−	0.906741i	$-0.361438\pi$
$773$	23.4483	0.843376	0.421688	+	0.906741i	$0.361438\pi$
$774$	7.06269	0.253863
$775$	5.62010	0.201880
$776$	−40.4427	−1.45181
$777$	12.7298	0.456679
$778$	−17.4799	−0.626685
$779$	48.1007	1.72338
$780$	41.6603	1.49168
$781$	21.9814	0.786558
$782$	10.0783	0.360400
$783$	−44.5425	−1.59182
$784$	−0.477091	−0.0170390
$785$	−33.1839	−1.18439
$786$	21.6117	0.770864
$787$	41.8206	1.49074	0.745372	−	0.666649i	$-0.232272\pi$
$787$	41.8206	1.49074	0.745372	+	0.666649i	$0.232272\pi$
$788$	66.2593	2.36039
$789$	−19.7198	−0.702043
$790$	−59.2647	−2.10854
$791$	13.2572	0.471372
$792$	3.84830	0.136744
$793$	−15.7327	−0.558685
$794$	−19.6974	−0.699034
$795$	45.4937	1.61349
$796$	39.5923	1.40331
$797$	22.9401	0.812579	0.406289	−	0.913744i	$-0.366822\pi$
$797$	22.9401	0.812579	0.406289	+	0.913744i	$0.366822\pi$
$798$	−19.3308	−0.684302
$799$	28.6377	1.01313
$800$	−9.89579	−0.349869
$801$	2.47340	0.0873934
$802$	56.4325	1.99270
$803$	−46.3176	−1.63451
$804$	58.1991	2.05253
$805$	−1.17383	−0.0413722
$806$	−31.3036	−1.10262
$807$	4.11753	0.144944
$808$	−11.6773	−0.410807
$809$	36.1740	1.27181	0.635905	−	0.771768i	$-0.280627\pi$
$809$	36.1740	1.27181	0.635905	+	0.771768i	$0.280627\pi$
$810$	41.6199	1.46237
$811$	33.5614	1.17850	0.589250	−	0.807951i	$-0.299423\pi$
$811$	33.5614	1.17850	0.589250	+	0.807951i	$0.299423\pi$
$812$	−28.8363	−1.01196
$813$	−25.6749	−0.900458
$814$	−64.2887	−2.25332
$815$	43.4311	1.52132
$816$	6.12183	0.214307
$817$	39.3766	1.37761
$818$	−51.9823	−1.81752
$819$	−1.45091	−0.0506990
$820$	−59.6111	−2.08171
$821$	−48.2017	−1.68225	−0.841125	−	0.540840i	$-0.818106\pi$
$821$	−48.2017	−1.68225	−0.841125	+	0.540840i	$0.818106\pi$
$822$	−86.7321	−3.02513
$823$	35.9918	1.25460	0.627298	−	0.778780i	$-0.284161\pi$
$823$	35.9918	1.25460	0.627298	+	0.778780i	$0.284161\pi$
$824$	45.2656	1.57690
$825$	−12.0258	−0.418686
$826$	−8.01535	−0.278890
$827$	21.8807	0.760868	0.380434	−	0.924808i	$-0.375775\pi$
$827$	21.8807	0.760868	0.380434	+	0.924808i	$0.375775\pi$
$828$	−0.733532	−0.0254920
$829$	10.3642	0.359964	0.179982	−	0.983670i	$-0.442396\pi$
$829$	10.3642	0.359964	0.179982	+	0.983670i	$0.442396\pi$
$830$	−72.9033	−2.53051
$831$	24.8761	0.862943
$832$	51.3618	1.78065
$833$	6.99137	0.242237
$834$	97.2800	3.36853
$835$	−0.0932329	−0.00322646
$836$	59.5404	2.05925
$837$	−16.9582	−0.586162
$838$	−83.7944	−2.89463
$839$	−39.8212	−1.37478	−0.687391	−	0.726288i	$-0.741244\pi$
$839$	−39.8212	−1.37478	−0.687391	+	0.726288i	$0.741244\pi$
$840$	8.63278	0.297859
$841$	56.0557	1.93295
$842$	−47.6376	−1.64170
$843$	−4.18351	−0.144088
$844$	−2.79611	−0.0962461
$845$	4.61603	0.158796
$846$	−3.41759	−0.117499
$847$	5.75803	0.197848
$848$	6.41408	0.220260
$849$	−15.4557	−0.530438
$850$	25.3378	0.869078
$851$	4.41580	0.151372
$852$	30.8142	1.05568
$853$	−1.49025	−0.0510253	−0.0255126	−	0.999674i	$-0.508122\pi$
$853$	−1.49025	−0.0510253	−0.0255126	+	0.999674i	$0.508122\pi$
$854$	−9.04704	−0.309583
$855$	−3.16037	−0.108082
$856$	21.1230	0.721971
$857$	7.09138	0.242237	0.121119	−	0.992638i	$-0.461352\pi$
$857$	7.09138	0.242237	0.121119	+	0.992638i	$0.461352\pi$
$858$	66.9831	2.28676
$859$	−10.8869	−0.371457	−0.185728	−	0.982601i	$-0.559464\pi$
$859$	−10.8869	−0.371457	−0.185728	+	0.982601i	$0.559464\pi$
$860$	−48.7994	−1.66405
$861$	18.9783	0.646777
$862$	−27.6022	−0.940135
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	29.8598	1.01585
$865$	−34.0867	−1.15898
$866$	2.93344	0.0996822
$867$	−58.5095	−1.98709
$868$	−10.9786	−0.372637
$869$	−58.1149	−1.97141
$870$	−70.6625	−2.39568
$871$	39.9326	1.35306
$872$	9.02260	0.305544
$873$	5.84160	0.197708
$874$	−6.70560	−0.226820
$875$	−12.1698	−0.411415
$876$	−64.9292	−2.19375
$877$	−25.5673	−0.863347	−0.431674	−	0.902030i	$-0.642077\pi$
$877$	−25.5673	−0.863347	−0.431674	+	0.902030i	$0.642077\pi$
$878$	−13.9289	−0.470079
$879$	−4.20489	−0.141827
$880$	3.60091	0.121387
$881$	22.3644	0.753476	0.376738	−	0.926320i	$-0.377046\pi$
$881$	22.3644	0.753476	0.376738	+	0.926320i	$0.377046\pi$
$882$	−0.834343	−0.0280938
$883$	29.8754	1.00539	0.502694	−	0.864464i	$-0.332342\pi$
$883$	29.8754	1.00539	0.502694	+	0.864464i	$0.332342\pi$
$884$	−86.0730	−2.89495
$885$	−11.9790	−0.402670
$886$	−11.9395	−0.401115
$887$	−17.2558	−0.579394	−0.289697	−	0.957118i	$-0.593555\pi$
$887$	−17.2558	−0.579394	−0.289697	+	0.957118i	$0.593555\pi$
$888$	−32.4754	−1.08980
$889$	12.6340	0.423731
$890$	−28.0214	−0.939280
$891$	40.8125	1.36727
$892$	47.4369	1.58831
$893$	−19.0541	−0.637620
$894$	−25.6800	−0.858868
$895$	−25.2452	−0.843853
$896$	17.1704	0.573624
$897$	−4.60087	−0.153619
$898$	40.1536	1.33994
$899$	32.3824	1.08001
$900$	−1.84416	−0.0614721
$901$	−93.9931	−3.13136
$902$	−95.8451	−3.19129
$903$	15.5362	0.517011
$904$	−33.8209	−1.12487
$905$	2.61861	0.0870456
$906$	20.8401	0.692368
$907$	−14.2245	−0.472318	−0.236159	−	0.971714i	$-0.575889\pi$
$907$	−14.2245	−0.472318	−0.236159	+	0.971714i	$0.575889\pi$
$908$	−41.1513	−1.36565
$909$	1.68669	0.0559439
$910$	16.4375	0.544899
$911$	−9.83375	−0.325807	−0.162903	−	0.986642i	$-0.552086\pi$
$911$	−9.83375	−0.325807	−0.162903	+	0.986642i	$0.552086\pi$
$912$	−4.07315	−0.134876
$913$	−71.4889	−2.36594
$914$	−58.2262	−1.92595
$915$	−13.5209	−0.446987
$916$	29.1919	0.964527
$917$	5.20058	0.171738
$918$	−76.4548	−2.52338
$919$	3.54559	0.116958	0.0584791	−	0.998289i	$-0.481375\pi$
$919$	3.54559	0.116958	0.0584791	+	0.998289i	$0.481375\pi$
$920$	2.99460	0.0987292
$921$	26.6101	0.876832
$922$	65.5774	2.15968
$923$	21.1427	0.695922
$924$	23.4918	0.772825
$925$	11.1017	0.365022
$926$	−90.4790	−2.97332
$927$	−6.53823	−0.214744
$928$	−57.0185	−1.87173
$929$	1.81336	0.0594946	0.0297473	−	0.999557i	$-0.490530\pi$
$929$	1.81336	0.0594946	0.0297473	+	0.999557i	$0.490530\pi$
$930$	−26.9027	−0.882173
$931$	−4.65170	−0.152453
$932$	3.61484	0.118408
$933$	1.10291	0.0361075
$934$	−50.9500	−1.66713
$935$	−52.7685	−1.72571
$936$	3.70147	0.120986
$937$	31.6072	1.03256	0.516281	−	0.856419i	$-0.327316\pi$
$937$	31.6072	1.03256	0.516281	+	0.856419i	$0.327316\pi$
$938$	22.9631	0.749772
$939$	22.7146	0.741263
$940$	23.6137	0.770194
$941$	39.7611	1.29617	0.648087	−	0.761566i	$-0.275569\pi$
$941$	39.7611	1.29617	0.648087	+	0.761566i	$0.275569\pi$
$942$	−74.7936	−2.43691
$943$	6.58332	0.214382
$944$	−1.68890	−0.0549690
$945$	8.90478	0.289672
$946$	−78.4616	−2.55101
$947$	7.37886	0.239781	0.119890	−	0.992787i	$-0.461746\pi$
$947$	7.37886	0.239781	0.119890	+	0.992787i	$0.461746\pi$
$948$	−81.4670	−2.64593
$949$	−44.5503	−1.44616
$950$	−16.8585	−0.546961
$951$	9.64537	0.312773
$952$	−17.8359	−0.578065
$953$	53.2555	1.72512	0.862558	−	0.505959i	$-0.168861\pi$
$953$	53.2555	1.72512	0.862558	+	0.505959i	$0.168861\pi$
$954$	11.2170	0.363165
$955$	10.4768	0.339021
$956$	1.09652	0.0354639
$957$	−69.2916	−2.23988
$958$	14.1319	0.456580
$959$	−20.8710	−0.673959
$960$	44.1410	1.42464
$961$	−18.6714	−0.602302
$962$	−61.8358	−1.99366
$963$	−3.05104	−0.0983185
$964$	40.1681	1.29373
$965$	−26.3369	−0.847813
$966$	−2.64572	−0.0851245
$967$	37.7789	1.21489	0.607443	−	0.794363i	$-0.292195\pi$
$967$	37.7789	1.21489	0.607443	+	0.794363i	$0.292195\pi$
$968$	−14.6895	−0.472138
$969$	59.6887	1.91748
$970$	−66.1801	−2.12491
$971$	49.4932	1.58831	0.794156	−	0.607714i	$-0.207913\pi$
$971$	49.4932	1.58831	0.794156	+	0.607714i	$0.207913\pi$
$972$	11.9085	0.381964
$973$	23.4092	0.750464
$974$	70.3437	2.25396
$975$	−11.5670	−0.370440
$976$	−1.90629	−0.0610187
$977$	24.7603	0.792154	0.396077	−	0.918217i	$-0.370371\pi$
$977$	24.7603	0.792154	0.396077	+	0.918217i	$0.370371\pi$
$978$	97.8898	3.13017
$979$	−27.4778	−0.878194
$980$	5.76486	0.184152
$981$	−1.30324	−0.0416092
$982$	71.9037	2.29454
$983$	−7.25055	−0.231257	−0.115628	−	0.993293i	$-0.536888\pi$
$983$	−7.25055	−0.231257	−0.115628	+	0.993293i	$0.536888\pi$
$984$	−48.4161	−1.54345
$985$	39.0714	1.24492
$986$	145.994	4.64938
$987$	−7.51784	−0.239296
$988$	57.2686	1.82196
$989$	5.38930	0.171370
$990$	6.29733	0.200142
$991$	23.9449	0.760635	0.380318	−	0.924856i	$-0.375815\pi$
$991$	23.9449	0.760635	0.380318	+	0.924856i	$0.375815\pi$
$992$	−21.7081	−0.689233
$993$	−2.66551	−0.0845873
$994$	12.1581	0.385630
$995$	23.3466	0.740137
$996$	−100.215	−3.17543
$997$	26.5566	0.841056	0.420528	−	0.907280i	$-0.361845\pi$
$997$	26.5566	0.841056	0.420528	+	0.907280i	$0.361845\pi$
$998$	40.7655	1.29041
$999$	−33.4986	−1.05985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.17	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.17	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26422 q^{2} -1.83534 q^{3} +3.12671 q^{4} +1.84374 q^{5} +4.15563 q^{6} +1.00000 q^{7} -2.55113 q^{8} +0.368489 q^{9} +O(q^{10})\)	\(q-2.26422 q^{2} -1.83534 q^{3} +3.12671 q^{4} +1.84374 q^{5} +4.15563 q^{6} +1.00000 q^{7} -2.55113 q^{8} +0.368489 q^{9} -4.17465 q^{10} -4.09366 q^{11} -5.73860 q^{12} -3.93746 q^{13} -2.26422 q^{14} -3.38390 q^{15} -0.477091 q^{16} +6.99137 q^{17} -0.834343 q^{18} -4.65170 q^{19} +5.76486 q^{20} -1.83534 q^{21} +9.26896 q^{22} -0.636658 q^{23} +4.68221 q^{24} -1.60061 q^{25} +8.91530 q^{26} +4.82973 q^{27} +3.12671 q^{28} -9.22256 q^{29} +7.66192 q^{30} -3.51122 q^{31} +6.18250 q^{32} +7.51327 q^{33} -15.8300 q^{34} +1.84374 q^{35} +1.15216 q^{36} -6.93591 q^{37} +10.5325 q^{38} +7.22660 q^{39} -4.70363 q^{40} -10.3404 q^{41} +4.15563 q^{42} -8.46498 q^{43} -12.7997 q^{44} +0.679400 q^{45} +1.44154 q^{46} +4.09615 q^{47} +0.875626 q^{48} +1.00000 q^{49} +3.62415 q^{50} -12.8316 q^{51} -12.3113 q^{52} -13.4441 q^{53} -10.9356 q^{54} -7.54765 q^{55} -2.55113 q^{56} +8.53748 q^{57} +20.8820 q^{58} +3.54000 q^{59} -10.5805 q^{60} +3.99565 q^{61} +7.95018 q^{62} +0.368489 q^{63} -13.0444 q^{64} -7.25967 q^{65} -17.0117 q^{66} -10.1417 q^{67} +21.8600 q^{68} +1.16849 q^{69} -4.17465 q^{70} -5.36963 q^{71} -0.940065 q^{72} +11.3145 q^{73} +15.7045 q^{74} +2.93768 q^{75} -14.5445 q^{76} -4.09366 q^{77} -16.3626 q^{78} +14.1963 q^{79} -0.879632 q^{80} -9.96968 q^{81} +23.4131 q^{82} +17.4633 q^{83} -5.73860 q^{84} +12.8903 q^{85} +19.1666 q^{86} +16.9266 q^{87} +10.4435 q^{88} +6.71228 q^{89} -1.53831 q^{90} -3.93746 q^{91} -1.99065 q^{92} +6.44429 q^{93} -9.27460 q^{94} -8.57655 q^{95} -11.3470 q^{96} +15.8528 q^{97} -2.26422 q^{98} -1.50847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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