LMFDB - Embedded newform 7942.2.a.bs.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 $ x^12 - 3x^11 - 21x^10 + 59x^9 + 162x^8 - 408x^7 - 581x^6 + 1236x^5 + 972x^4 - 1596x^3 - 621x^2 + 648*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.63824$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.63824 q^{3} +1.00000 q^{4} -1.31219 q^{5} +1.63824 q^{6} +2.28188 q^{7} -1.00000 q^{8} -0.316160 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.63824 q^{3} +1.00000 q^{4} -1.31219 q^{5} +1.63824 q^{6} +2.28188 q^{7} -1.00000 q^{8} -0.316160 q^{9} +1.31219 q^{10} +1.00000 q^{11} -1.63824 q^{12} +3.91243 q^{13} -2.28188 q^{14} +2.14968 q^{15} +1.00000 q^{16} -0.139286 q^{17} +0.316160 q^{18} -1.31219 q^{20} -3.73827 q^{21} -1.00000 q^{22} -6.62346 q^{23} +1.63824 q^{24} -3.27817 q^{25} -3.91243 q^{26} +5.43268 q^{27} +2.28188 q^{28} -2.81365 q^{29} -2.14968 q^{30} +10.8271 q^{31} -1.00000 q^{32} -1.63824 q^{33} +0.139286 q^{34} -2.99425 q^{35} -0.316160 q^{36} +10.6683 q^{37} -6.40951 q^{39} +1.31219 q^{40} -5.77856 q^{41} +3.73827 q^{42} -9.46710 q^{43} +1.00000 q^{44} +0.414861 q^{45} +6.62346 q^{46} -4.13680 q^{47} -1.63824 q^{48} -1.79303 q^{49} +3.27817 q^{50} +0.228184 q^{51} +3.91243 q^{52} -8.62721 q^{53} -5.43268 q^{54} -1.31219 q^{55} -2.28188 q^{56} +2.81365 q^{58} +5.11133 q^{59} +2.14968 q^{60} +0.805400 q^{61} -10.8271 q^{62} -0.721439 q^{63} +1.00000 q^{64} -5.13384 q^{65} +1.63824 q^{66} +2.73417 q^{67} -0.139286 q^{68} +10.8508 q^{69} +2.99425 q^{70} -4.75623 q^{71} +0.316160 q^{72} +14.9213 q^{73} -10.6683 q^{74} +5.37043 q^{75} +2.28188 q^{77} +6.40951 q^{78} -5.82570 q^{79} -1.31219 q^{80} -7.95156 q^{81} +5.77856 q^{82} -16.5221 q^{83} -3.73827 q^{84} +0.182769 q^{85} +9.46710 q^{86} +4.60944 q^{87} -1.00000 q^{88} -4.07919 q^{89} -0.414861 q^{90} +8.92769 q^{91} -6.62346 q^{92} -17.7375 q^{93} +4.13680 q^{94} +1.63824 q^{96} +11.7059 q^{97} +1.79303 q^{98} -0.316160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.63824	−0.945840	−0.472920	−	0.881105i	$-0.656800\pi$
$3$	−1.63824	−0.945840	−0.472920	+	0.881105i	$0.656800\pi$
$4$	1.00000	0.500000
$5$	−1.31219	−0.586828	−0.293414	−	0.955985i	$-0.594791\pi$
$5$	−1.31219	−0.586828	−0.293414	+	0.955985i	$0.594791\pi$
$6$	1.63824	0.668810
$7$	2.28188	0.862469	0.431235	−	0.902240i	$-0.358078\pi$
$7$	2.28188	0.862469	0.431235	+	0.902240i	$0.358078\pi$
$8$	−1.00000	−0.353553
$9$	−0.316160	−0.105387
$10$	1.31219	0.414950
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.63824	−0.472920
$13$	3.91243	1.08511	0.542556	−	0.840020i	$-0.317457\pi$
$13$	3.91243	1.08511	0.542556	+	0.840020i	$0.317457\pi$
$14$	−2.28188	−0.609858
$15$	2.14968	0.555045
$16$	1.00000	0.250000
$17$	−0.139286	−0.0337817	−0.0168909	−	0.999857i	$-0.505377\pi$
$17$	−0.139286	−0.0337817	−0.0168909	+	0.999857i	$0.505377\pi$
$18$	0.316160	0.0745196
$19$	0	0
$19$	0	0
$20$	−1.31219	−0.293414
$21$	−3.73827	−0.815758
$22$	−1.00000	−0.213201
$23$	−6.62346	−1.38109	−0.690544	−	0.723291i	$-0.742629\pi$
$23$	−6.62346	−1.38109	−0.690544	+	0.723291i	$0.742629\pi$
$24$	1.63824	0.334405
$25$	−3.27817	−0.655633
$26$	−3.91243	−0.767290
$27$	5.43268	1.04552
$28$	2.28188	0.431235
$29$	−2.81365	−0.522482	−0.261241	−	0.965274i	$-0.584132\pi$
$29$	−2.81365	−0.522482	−0.261241	+	0.965274i	$0.584132\pi$
$30$	−2.14968	−0.392476
$31$	10.8271	1.94461	0.972304	−	0.233720i	$-0.0750898\pi$
$31$	10.8271	1.94461	0.972304	+	0.233720i	$0.0750898\pi$
$32$	−1.00000	−0.176777
$33$	−1.63824	−0.285182
$34$	0.139286	0.0238873
$35$	−2.99425	−0.506121
$36$	−0.316160	−0.0526933
$37$	10.6683	1.75385	0.876927	−	0.480623i	$-0.159589\pi$
$37$	10.6683	1.75385	0.876927	+	0.480623i	$0.159589\pi$
$38$	0	0
$39$	−6.40951	−1.02634
$40$	1.31219	0.207475
$41$	−5.77856	−0.902460	−0.451230	−	0.892408i	$-0.649015\pi$
$41$	−5.77856	−0.902460	−0.451230	+	0.892408i	$0.649015\pi$
$42$	3.73827	0.576828
$43$	−9.46710	−1.44372	−0.721860	−	0.692039i	$-0.756712\pi$
$43$	−9.46710	−1.44372	−0.721860	+	0.692039i	$0.756712\pi$
$44$	1.00000	0.150756
$45$	0.414861	0.0618438
$46$	6.62346	0.976576
$47$	−4.13680	−0.603415	−0.301707	−	0.953401i	$-0.597557\pi$
$47$	−4.13680	−0.603415	−0.301707	+	0.953401i	$0.597557\pi$
$48$	−1.63824	−0.236460
$49$	−1.79303	−0.256146
$50$	3.27817	0.463603
$51$	0.228184	0.0319521
$52$	3.91243	0.542556
$53$	−8.62721	−1.18504	−0.592519	−	0.805556i	$-0.701867\pi$
$53$	−8.62721	−1.18504	−0.592519	+	0.805556i	$0.701867\pi$
$54$	−5.43268	−0.739294
$55$	−1.31219	−0.176935
$56$	−2.28188	−0.304929
$57$	0	0
$58$	2.81365	0.369450
$59$	5.11133	0.665438	0.332719	−	0.943026i	$-0.392034\pi$
$59$	5.11133	0.665438	0.332719	+	0.943026i	$0.392034\pi$
$60$	2.14968	0.277523
$61$	0.805400	0.103121	0.0515605	−	0.998670i	$-0.483581\pi$
$61$	0.805400	0.103121	0.0515605	+	0.998670i	$0.483581\pi$
$62$	−10.8271	−1.37505
$63$	−0.721439	−0.0908927
$64$	1.00000	0.125000
$65$	−5.13384	−0.636774
$66$	1.63824	0.201654
$67$	2.73417	0.334032	0.167016	−	0.985954i	$-0.446587\pi$
$67$	2.73417	0.334032	0.167016	+	0.985954i	$0.446587\pi$
$68$	−0.139286	−0.0168909
$69$	10.8508	1.30629
$70$	2.99425	0.357882
$71$	−4.75623	−0.564461	−0.282230	−	0.959347i	$-0.591074\pi$
$71$	−4.75623	−0.564461	−0.282230	+	0.959347i	$0.591074\pi$
$72$	0.316160	0.0372598
$73$	14.9213	1.74641	0.873203	−	0.487357i	$-0.162039\pi$
$73$	14.9213	1.74641	0.873203	+	0.487357i	$0.162039\pi$
$74$	−10.6683	−1.24016
$75$	5.37043	0.620124
$76$	0	0
$77$	2.28188	0.260044
$78$	6.40951	0.725734
$79$	−5.82570	−0.655443	−0.327721	−	0.944774i	$-0.606281\pi$
$79$	−5.82570	−0.655443	−0.327721	+	0.944774i	$0.606281\pi$
$80$	−1.31219	−0.146707
$81$	−7.95156	−0.883507
$82$	5.77856	0.638136
$83$	−16.5221	−1.81354	−0.906771	−	0.421624i	$-0.861460\pi$
$83$	−16.5221	−1.81354	−0.906771	+	0.421624i	$0.861460\pi$
$84$	−3.73827	−0.407879
$85$	0.182769	0.0198241
$86$	9.46710	1.02086
$87$	4.60944	0.494184
$88$	−1.00000	−0.106600
$89$	−4.07919	−0.432393	−0.216197	−	0.976350i	$-0.569365\pi$
$89$	−4.07919	−0.432393	−0.216197	+	0.976350i	$0.569365\pi$
$90$	−0.414861	−0.0437302
$91$	8.92769	0.935876
$92$	−6.62346	−0.690544
$93$	−17.7375	−1.83929
$94$	4.13680	0.426679
$95$	0	0
$96$	1.63824	0.167202
$97$	11.7059	1.18855	0.594277	−	0.804261i	$-0.297438\pi$
$97$	11.7059	1.18855	0.594277	+	0.804261i	$0.297438\pi$
$98$	1.79303	0.181123
$99$	−0.316160	−0.0317753
$100$	−3.27817	−0.327817
$101$	6.73728	0.670384	0.335192	−	0.942150i	$-0.391199\pi$
$101$	6.73728	0.670384	0.335192	+	0.942150i	$0.391199\pi$
$102$	−0.228184	−0.0225936
$103$	3.63613	0.358279	0.179139	−	0.983824i	$-0.442669\pi$
$103$	3.63613	0.358279	0.179139	+	0.983824i	$0.442669\pi$
$104$	−3.91243	−0.383645
$105$	4.90531	0.478710
$106$	8.62721	0.837949
$107$	−7.99909	−0.773302	−0.386651	−	0.922226i	$-0.626368\pi$
$107$	−7.99909	−0.773302	−0.386651	+	0.922226i	$0.626368\pi$
$108$	5.43268	0.522759
$109$	−15.3839	−1.47351	−0.736754	−	0.676161i	$-0.763642\pi$
$109$	−15.3839	−1.47351	−0.736754	+	0.676161i	$0.763642\pi$
$110$	1.31219	0.125112
$111$	−17.4772	−1.65887
$112$	2.28188	0.215617
$113$	−10.6824	−1.00491	−0.502457	−	0.864602i	$-0.667571\pi$
$113$	−10.6824	−1.00491	−0.502457	+	0.864602i	$0.667571\pi$
$114$	0	0
$115$	8.69122	0.810460
$116$	−2.81365	−0.261241
$117$	−1.23695	−0.114356
$118$	−5.11133	−0.470536
$119$	−0.317833	−0.0291357
$120$	−2.14968	−0.196238
$121$	1.00000	0.0909091
$122$	−0.805400	−0.0729175
$123$	9.46669	0.853583
$124$	10.8271	0.972304
$125$	10.8625	0.971572
$126$	0.721439	0.0642709
$127$	3.72502	0.330542	0.165271	−	0.986248i	$-0.447150\pi$
$127$	3.72502	0.330542	0.165271	+	0.986248i	$0.447150\pi$
$128$	−1.00000	−0.0883883
$129$	15.5094	1.36553
$130$	5.13384	0.450267
$131$	18.1177	1.58295	0.791477	−	0.611199i	$-0.209312\pi$
$131$	18.1177	1.58295	0.791477	+	0.611199i	$0.209312\pi$
$132$	−1.63824	−0.142591
$133$	0	0
$134$	−2.73417	−0.236196
$135$	−7.12869	−0.613540
$136$	0.139286	0.0119436
$137$	4.05957	0.346832	0.173416	−	0.984849i	$-0.444519\pi$
$137$	4.05957	0.346832	0.173416	+	0.984849i	$0.444519\pi$
$138$	−10.8508	−0.923685
$139$	1.84455	0.156452	0.0782262	−	0.996936i	$-0.475074\pi$
$139$	1.84455	0.156452	0.0782262	+	0.996936i	$0.475074\pi$
$140$	−2.99425	−0.253061
$141$	6.77709	0.570734
$142$	4.75623	0.399134
$143$	3.91243	0.327174
$144$	−0.316160	−0.0263467
$145$	3.69204	0.306607
$146$	−14.9213	−1.23490
$147$	2.93741	0.242274
$148$	10.6683	0.876927
$149$	19.4539	1.59372	0.796861	−	0.604163i	$-0.206492\pi$
$149$	19.4539	1.59372	0.796861	+	0.604163i	$0.206492\pi$
$150$	−5.37043	−0.438494
$151$	−22.5490	−1.83502	−0.917508	−	0.397718i	$-0.869802\pi$
$151$	−22.5490	−1.83502	−0.917508	+	0.397718i	$0.869802\pi$
$152$	0	0
$153$	0.0440365	0.00356014
$154$	−2.28188	−0.183879
$155$	−14.2072	−1.14115
$156$	−6.40951	−0.513171
$157$	−12.5451	−1.00120	−0.500602	−	0.865677i	$-0.666888\pi$
$157$	−12.5451	−1.00120	−0.500602	+	0.865677i	$0.666888\pi$
$158$	5.82570	0.463468
$159$	14.1335	1.12086
$160$	1.31219	0.103737
$161$	−15.1139	−1.19115
$162$	7.95156	0.624734
$163$	−15.3151	−1.19957	−0.599785	−	0.800161i	$-0.704747\pi$
$163$	−15.3151	−1.19957	−0.599785	+	0.800161i	$0.704747\pi$
$164$	−5.77856	−0.451230
$165$	2.14968	0.167352
$166$	16.5221	1.28237
$167$	20.3013	1.57096	0.785482	−	0.618884i	$-0.212415\pi$
$167$	20.3013	1.57096	0.785482	+	0.618884i	$0.212415\pi$
$168$	3.73827	0.288414
$169$	2.30710	0.177469
$170$	−0.182769	−0.0140177
$171$	0	0
$172$	−9.46710	−0.721860
$173$	11.5036	0.874604	0.437302	−	0.899315i	$-0.355934\pi$
$173$	11.5036	0.874604	0.437302	+	0.899315i	$0.355934\pi$
$174$	−4.60944	−0.349441
$175$	−7.48038	−0.565464
$176$	1.00000	0.0753778
$177$	−8.37360	−0.629398
$178$	4.07919	0.305748
$179$	22.9879	1.71820	0.859100	−	0.511808i	$-0.171024\pi$
$179$	22.9879	1.71820	0.859100	+	0.511808i	$0.171024\pi$
$180$	0.414861	0.0309219
$181$	−6.93665	−0.515597	−0.257799	−	0.966199i	$-0.582997\pi$
$181$	−6.93665	−0.515597	−0.257799	+	0.966199i	$0.582997\pi$
$182$	−8.92769	−0.661764
$183$	−1.31944	−0.0975359
$184$	6.62346	0.488288
$185$	−13.9988	−1.02921
$186$	17.7375	1.30057
$187$	−0.139286	−0.0101856
$188$	−4.13680	−0.301707
$189$	12.3967	0.901728
$190$	0	0
$191$	−23.3238	−1.68765	−0.843827	−	0.536615i	$-0.819703\pi$
$191$	−23.3238	−1.68765	−0.843827	+	0.536615i	$0.819703\pi$
$192$	−1.63824	−0.118230
$193$	−2.17112	−0.156281	−0.0781403	−	0.996942i	$-0.524898\pi$
$193$	−2.17112	−0.156281	−0.0781403	+	0.996942i	$0.524898\pi$
$194$	−11.7059	−0.840434
$195$	8.41047	0.602286
$196$	−1.79303	−0.128073
$197$	2.25131	0.160400	0.0801998	−	0.996779i	$-0.474444\pi$
$197$	2.25131	0.160400	0.0801998	+	0.996779i	$0.474444\pi$
$198$	0.316160	0.0224685
$199$	16.7210	1.18532	0.592662	−	0.805452i	$-0.298077\pi$
$199$	16.7210	1.18532	0.592662	+	0.805452i	$0.298077\pi$
$200$	3.27817	0.231801
$201$	−4.47923	−0.315941
$202$	−6.73728	−0.474033
$203$	−6.42041	−0.450625
$204$	0.228184	0.0159761
$205$	7.58256	0.529589
$206$	−3.63613	−0.253341
$207$	2.09407	0.145548
$208$	3.91243	0.271278
$209$	0	0
$210$	−4.90531	−0.338499
$211$	13.8518	0.953599	0.476799	−	0.879012i	$-0.341797\pi$
$211$	13.8518	0.953599	0.476799	+	0.879012i	$0.341797\pi$
$212$	−8.62721	−0.592519
$213$	7.79186	0.533889
$214$	7.99909	0.546807
$215$	12.4226	0.847215
$216$	−5.43268	−0.369647
$217$	24.7062	1.67716
$218$	15.3839	1.04193
$219$	−24.4447	−1.65182
$220$	−1.31219	−0.0884676
$221$	−0.544945	−0.0366570
$222$	17.4772	1.17300
$223$	0.829172	0.0555255	0.0277627	−	0.999615i	$-0.491162\pi$
$223$	0.829172	0.0555255	0.0277627	+	0.999615i	$0.491162\pi$
$224$	−2.28188	−0.152464
$225$	1.03642	0.0690949
$226$	10.6824	0.710582
$227$	4.88277	0.324081	0.162040	−	0.986784i	$-0.448193\pi$
$227$	4.88277	0.324081	0.162040	+	0.986784i	$0.448193\pi$
$228$	0	0
$229$	−1.05462	−0.0696915	−0.0348458	−	0.999393i	$-0.511094\pi$
$229$	−1.05462	−0.0696915	−0.0348458	+	0.999393i	$0.511094\pi$
$230$	−8.69122	−0.573082
$231$	−3.73827	−0.245960
$232$	2.81365	0.184725
$233$	−5.38163	−0.352563	−0.176281	−	0.984340i	$-0.556407\pi$
$233$	−5.38163	−0.352563	−0.176281	+	0.984340i	$0.556407\pi$
$234$	1.23695	0.0808621
$235$	5.42826	0.354101
$236$	5.11133	0.332719
$237$	9.54392	0.619944
$238$	0.317833	0.0206021
$239$	13.7687	0.890625	0.445312	−	0.895375i	$-0.353093\pi$
$239$	13.7687	0.890625	0.445312	+	0.895375i	$0.353093\pi$
$240$	2.14968	0.138761
$241$	−6.45039	−0.415506	−0.207753	−	0.978181i	$-0.566615\pi$
$241$	−6.45039	−0.415506	−0.207753	+	0.978181i	$0.566615\pi$
$242$	−1.00000	−0.0642824
$243$	−3.27143	−0.209863
$244$	0.805400	0.0515605
$245$	2.35278	0.150314
$246$	−9.46669	−0.603574
$247$	0	0
$248$	−10.8271	−0.687523
$249$	27.0673	1.71532
$250$	−10.8625	−0.687005
$251$	−9.47305	−0.597933	−0.298967	−	0.954264i	$-0.596642\pi$
$251$	−9.47305	−0.597933	−0.298967	+	0.954264i	$0.596642\pi$
$252$	−0.721439	−0.0454464
$253$	−6.62346	−0.416413
$254$	−3.72502	−0.233728
$255$	−0.299420	−0.0187504
$256$	1.00000	0.0625000
$257$	17.7837	1.10932	0.554658	−	0.832079i	$-0.312849\pi$
$257$	17.7837	1.10932	0.554658	+	0.832079i	$0.312849\pi$
$258$	−15.5094	−0.965574
$259$	24.3437	1.51265
$260$	−5.13384	−0.318387
$261$	0.889563	0.0550626
$262$	−18.1177	−1.11932
$263$	−5.90601	−0.364180	−0.182090	−	0.983282i	$-0.558286\pi$
$263$	−5.90601	−0.364180	−0.182090	+	0.983282i	$0.558286\pi$
$264$	1.63824	0.100827
$265$	11.3205	0.695414
$266$	0	0
$267$	6.68270	0.408975
$268$	2.73417	0.167016
$269$	−16.3899	−0.999312	−0.499656	−	0.866224i	$-0.666540\pi$
$269$	−16.3899	−0.999312	−0.499656	+	0.866224i	$0.666540\pi$
$270$	7.12869	0.433838
$271$	−5.43019	−0.329861	−0.164930	−	0.986305i	$-0.552740\pi$
$271$	−5.43019	−0.329861	−0.164930	+	0.986305i	$0.552740\pi$
$272$	−0.139286	−0.00844543
$273$	−14.6257	−0.885189
$274$	−4.05957	−0.245247
$275$	−3.27817	−0.197681
$276$	10.8508	0.653144
$277$	17.1524	1.03059	0.515295	−	0.857013i	$-0.327683\pi$
$277$	17.1524	1.03059	0.515295	+	0.857013i	$0.327683\pi$
$278$	−1.84455	−0.110629
$279$	−3.42310	−0.204936
$280$	2.99425	0.178941
$281$	17.8373	1.06409	0.532043	−	0.846718i	$-0.321425\pi$
$281$	17.8373	1.06409	0.532043	+	0.846718i	$0.321425\pi$
$282$	−6.77709	−0.403570
$283$	−2.09279	−0.124403	−0.0622017	−	0.998064i	$-0.519812\pi$
$283$	−2.09279	−0.124403	−0.0622017	+	0.998064i	$0.519812\pi$
$284$	−4.75623	−0.282230
$285$	0	0
$286$	−3.91243	−0.231347
$287$	−13.1860	−0.778344
$288$	0.316160	0.0186299
$289$	−16.9806	−0.998859
$290$	−3.69204	−0.216804
$291$	−19.1771	−1.12418
$292$	14.9213	0.873203
$293$	2.80549	0.163898	0.0819492	−	0.996637i	$-0.473885\pi$
$293$	2.80549	0.163898	0.0819492	+	0.996637i	$0.473885\pi$
$294$	−2.93741	−0.171313
$295$	−6.70702	−0.390498
$296$	−10.6683	−0.620081
$297$	5.43268	0.315236
$298$	−19.4539	−1.12693
$299$	−25.9138	−1.49863
$300$	5.37043	0.310062
$301$	−21.6028	−1.24516
$302$	22.5490	1.29755
$303$	−11.0373	−0.634076
$304$	0	0
$305$	−1.05684	−0.0605142
$306$	−0.0440365	−0.00251740
$307$	−13.9266	−0.794834	−0.397417	−	0.917638i	$-0.630093\pi$
$307$	−13.9266	−0.794834	−0.397417	+	0.917638i	$0.630093\pi$
$308$	2.28188	0.130022
$309$	−5.95687	−0.338874
$310$	14.2072	0.806915
$311$	12.6677	0.718321	0.359160	−	0.933276i	$-0.383063\pi$
$311$	12.6677	0.718321	0.359160	+	0.933276i	$0.383063\pi$
$312$	6.40951	0.362867
$313$	−24.9880	−1.41241	−0.706203	−	0.708009i	$-0.749594\pi$
$313$	−24.9880	−1.41241	−0.706203	+	0.708009i	$0.749594\pi$
$314$	12.5451	0.707959
$315$	0.946662	0.0533384
$316$	−5.82570	−0.327721
$317$	−0.118044	−0.00662999	−0.00331499	−	0.999995i	$-0.501055\pi$
$317$	−0.118044	−0.00662999	−0.00331499	+	0.999995i	$0.501055\pi$
$318$	−14.1335	−0.792565
$319$	−2.81365	−0.157534
$320$	−1.31219	−0.0733535
$321$	13.1045	0.731420
$322$	15.1139	0.842267
$323$	0	0
$324$	−7.95156	−0.441754
$325$	−12.8256	−0.711436
$326$	15.3151	0.848224
$327$	25.2025	1.39370
$328$	5.77856	0.319068
$329$	−9.43969	−0.520427
$330$	−2.14968	−0.118336
$331$	−23.7123	−1.30335	−0.651673	−	0.758500i	$-0.725933\pi$
$331$	−23.7123	−1.30335	−0.651673	+	0.758500i	$0.725933\pi$
$332$	−16.5221	−0.906771
$333$	−3.37288	−0.184833
$334$	−20.3013	−1.11084
$335$	−3.58774	−0.196019
$336$	−3.73827	−0.203940
$337$	−23.3905	−1.27416	−0.637080	−	0.770798i	$-0.719858\pi$
$337$	−23.3905	−1.27416	−0.637080	+	0.770798i	$0.719858\pi$
$338$	−2.30710	−0.125489
$339$	17.5003	0.950488
$340$	0.182769	0.00991203
$341$	10.8271	0.586321
$342$	0	0
$343$	−20.0646	−1.08339
$344$	9.46710	0.510432
$345$	−14.2383	−0.766566
$346$	−11.5036	−0.618439
$347$	−2.36299	−0.126852	−0.0634260	−	0.997987i	$-0.520203\pi$
$347$	−2.36299	−0.126852	−0.0634260	+	0.997987i	$0.520203\pi$
$348$	4.60944	0.247092
$349$	−10.7950	−0.577844	−0.288922	−	0.957353i	$-0.593297\pi$
$349$	−10.7950	−0.577844	−0.288922	+	0.957353i	$0.593297\pi$
$350$	7.48038	0.399843
$351$	21.2550	1.13451
$352$	−1.00000	−0.0533002
$353$	−16.5787	−0.882396	−0.441198	−	0.897410i	$-0.645446\pi$
$353$	−16.5787	−0.882396	−0.441198	+	0.897410i	$0.645446\pi$
$354$	8.37360	0.445052
$355$	6.24106	0.331241
$356$	−4.07919	−0.216197
$357$	0.520688	0.0275577
$358$	−22.9879	−1.21495
$359$	−21.1854	−1.11812	−0.559061	−	0.829126i	$-0.688838\pi$
$359$	−21.1854	−1.11812	−0.559061	+	0.829126i	$0.688838\pi$
$360$	−0.414861	−0.0218651
$361$	0	0
$362$	6.93665	0.364582
$363$	−1.63824	−0.0859855
$364$	8.92769	0.467938
$365$	−19.5795	−1.02484
$366$	1.31944	0.0689683
$367$	25.4016	1.32595	0.662977	−	0.748640i	$-0.269293\pi$
$367$	25.4016	1.32595	0.662977	+	0.748640i	$0.269293\pi$
$368$	−6.62346	−0.345272
$369$	1.82695	0.0951072
$370$	13.9988	0.727762
$371$	−19.6863	−1.02206
$372$	−17.7375	−0.919644
$373$	−7.92963	−0.410581	−0.205290	−	0.978701i	$-0.565814\pi$
$373$	−7.92963	−0.410581	−0.205290	+	0.978701i	$0.565814\pi$
$374$	0.139286	0.00720229
$375$	−17.7954	−0.918951
$376$	4.13680	0.213339
$377$	−11.0082	−0.566952
$378$	−12.3967	−0.637618
$379$	−18.7755	−0.964434	−0.482217	−	0.876052i	$-0.660168\pi$
$379$	−18.7755	−0.964434	−0.482217	+	0.876052i	$0.660168\pi$
$380$	0	0
$381$	−6.10248	−0.312640
$382$	23.3238	1.19335
$383$	23.3654	1.19392	0.596958	−	0.802273i	$-0.296376\pi$
$383$	23.3654	1.19392	0.596958	+	0.802273i	$0.296376\pi$
$384$	1.63824	0.0836012
$385$	−2.99425	−0.152601
$386$	2.17112	0.110507
$387$	2.99312	0.152149
$388$	11.7059	0.594277
$389$	−8.52843	−0.432408	−0.216204	−	0.976348i	$-0.569368\pi$
$389$	−8.52843	−0.432408	−0.216204	+	0.976348i	$0.569368\pi$
$390$	−8.41047	−0.425881
$391$	0.922553	0.0466555
$392$	1.79303	0.0905614
$393$	−29.6813	−1.49722
$394$	−2.25131	−0.113420
$395$	7.64441	0.384632
$396$	−0.316160	−0.0158876
$397$	10.4778	0.525868	0.262934	−	0.964814i	$-0.415310\pi$
$397$	10.4778	0.525868	0.262934	+	0.964814i	$0.415310\pi$
$398$	−16.7210	−0.838150
$399$	0	0
$400$	−3.27817	−0.163908
$401$	−0.403820	−0.0201658	−0.0100829	−	0.999949i	$-0.503210\pi$
$401$	−0.403820	−0.0201658	−0.0100829	+	0.999949i	$0.503210\pi$
$402$	4.47923	0.223404
$403$	42.3603	2.11012
$404$	6.73728	0.335192
$405$	10.4339	0.518467
$406$	6.42041	0.318640
$407$	10.6683	0.528807
$408$	−0.228184	−0.0112968
$409$	3.62192	0.179093	0.0895463	−	0.995983i	$-0.471458\pi$
$409$	3.62192	0.179093	0.0895463	+	0.995983i	$0.471458\pi$
$410$	−7.58256	−0.374476
$411$	−6.65056	−0.328048
$412$	3.63613	0.179139
$413$	11.6634	0.573920
$414$	−2.09407	−0.102918
$415$	21.6801	1.06424
$416$	−3.91243	−0.191823
$417$	−3.02182	−0.147979
$418$	0	0
$419$	−24.0514	−1.17499	−0.587494	−	0.809229i	$-0.699885\pi$
$419$	−24.0514	−1.17499	−0.587494	+	0.809229i	$0.699885\pi$
$420$	4.90531	0.239355
$421$	−16.7744	−0.817532	−0.408766	−	0.912639i	$-0.634041\pi$
$421$	−16.7744	−0.817532	−0.408766	+	0.912639i	$0.634041\pi$
$422$	−13.8518	−0.674296
$423$	1.30789	0.0635918
$424$	8.62721	0.418974
$425$	0.456601	0.0221484
$426$	−7.79186	−0.377517
$427$	1.83783	0.0889387
$428$	−7.99909	−0.386651
$429$	−6.40951	−0.309454
$430$	−12.4226	−0.599071
$431$	−5.45055	−0.262544	−0.131272	−	0.991346i	$-0.541906\pi$
$431$	−5.45055	−0.262544	−0.131272	+	0.991346i	$0.541906\pi$
$432$	5.43268	0.261380
$433$	13.1201	0.630510	0.315255	−	0.949007i	$-0.397910\pi$
$433$	13.1201	0.630510	0.315255	+	0.949007i	$0.397910\pi$
$434$	−24.7062	−1.18593
$435$	−6.04845	−0.290001
$436$	−15.3839	−0.736754
$437$	0	0
$438$	24.4447	1.16801
$439$	24.3157	1.16053	0.580263	−	0.814429i	$-0.302950\pi$
$439$	24.3157	1.16053	0.580263	+	0.814429i	$0.302950\pi$
$440$	1.31219	0.0625561
$441$	0.566883	0.0269944
$442$	0.544945	0.0259204
$443$	−32.4992	−1.54408	−0.772042	−	0.635571i	$-0.780765\pi$
$443$	−32.4992	−1.54408	−0.772042	+	0.635571i	$0.780765\pi$
$444$	−17.4772	−0.829433
$445$	5.35266	0.253740
$446$	−0.829172	−0.0392624
$447$	−31.8701	−1.50741
$448$	2.28188	0.107809
$449$	−22.6003	−1.06657	−0.533287	−	0.845935i	$-0.679043\pi$
$449$	−22.6003	−1.06657	−0.533287	+	0.845935i	$0.679043\pi$
$450$	−1.03642	−0.0488575
$451$	−5.77856	−0.272102
$452$	−10.6824	−0.502457
$453$	36.9408	1.73563
$454$	−4.88277	−0.229160
$455$	−11.7148	−0.549198
$456$	0	0
$457$	−37.6043	−1.75906	−0.879528	−	0.475848i	$-0.842141\pi$
$457$	−37.6043	−1.75906	−0.879528	+	0.475848i	$0.842141\pi$
$458$	1.05462	0.0492793
$459$	−0.756694	−0.0353194
$460$	8.69122	0.405230
$461$	18.7652	0.873984	0.436992	−	0.899465i	$-0.356044\pi$
$461$	18.7652	0.873984	0.436992	+	0.899465i	$0.356044\pi$
$462$	3.73827	0.173920
$463$	0.559907	0.0260211	0.0130105	−	0.999915i	$-0.495858\pi$
$463$	0.559907	0.0260211	0.0130105	+	0.999915i	$0.495858\pi$
$464$	−2.81365	−0.130620
$465$	23.2749	1.07935
$466$	5.38163	0.249299
$467$	−25.2550	−1.16866	−0.584331	−	0.811515i	$-0.698643\pi$
$467$	−25.2550	−1.16866	−0.584331	+	0.811515i	$0.698643\pi$
$468$	−1.23695	−0.0571782
$469$	6.23904	0.288092
$470$	−5.42826	−0.250387
$471$	20.5519	0.946980
$472$	−5.11133	−0.235268
$473$	−9.46710	−0.435298
$474$	−9.54392	−0.438367
$475$	0	0
$476$	−0.317833	−0.0145679
$477$	2.72758	0.124887
$478$	−13.7687	−0.629767
$479$	4.70962	0.215188	0.107594	−	0.994195i	$-0.465685\pi$
$479$	4.70962	0.215188	0.107594	+	0.994195i	$0.465685\pi$
$480$	−2.14968	−0.0981191
$481$	41.7389	1.90313
$482$	6.45039	0.293807
$483$	24.7603	1.12663
$484$	1.00000	0.0454545
$485$	−15.3603	−0.697476
$486$	3.27143	0.148395
$487$	19.3717	0.877816	0.438908	−	0.898532i	$-0.355365\pi$
$487$	19.3717	0.877816	0.438908	+	0.898532i	$0.355365\pi$
$488$	−0.805400	−0.0364588
$489$	25.0898	1.13460
$490$	−2.35278	−0.106288
$491$	−20.5144	−0.925804	−0.462902	−	0.886410i	$-0.653192\pi$
$491$	−20.5144	−0.925804	−0.462902	+	0.886410i	$0.653192\pi$
$492$	9.46669	0.426791
$493$	0.391901	0.0176503
$494$	0	0
$495$	0.414861	0.0186466
$496$	10.8271	0.486152
$497$	−10.8531	−0.486830
$498$	−27.0673	−1.21291
$499$	21.9133	0.980972	0.490486	−	0.871449i	$-0.336819\pi$
$499$	21.9133	0.980972	0.490486	+	0.871449i	$0.336819\pi$
$500$	10.8625	0.485786
$501$	−33.2585	−1.48588
$502$	9.47305	0.422803
$503$	8.39697	0.374402	0.187201	−	0.982322i	$-0.440058\pi$
$503$	8.39697	0.374402	0.187201	+	0.982322i	$0.440058\pi$
$504$	0.721439	0.0321354
$505$	−8.84057	−0.393400
$506$	6.62346	0.294449
$507$	−3.77958	−0.167857
$508$	3.72502	0.165271
$509$	29.9096	1.32572	0.662860	−	0.748744i	$-0.269343\pi$
$509$	29.9096	1.32572	0.662860	+	0.748744i	$0.269343\pi$
$510$	0.299420	0.0132585
$511$	34.0486	1.50622
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−17.7837	−0.784405
$515$	−4.77128	−0.210248
$516$	15.5094	0.682764
$517$	−4.13680	−0.181936
$518$	−24.3437	−1.06960
$519$	−18.8457	−0.827236
$520$	5.13384	0.225134
$521$	−28.3510	−1.24208	−0.621040	−	0.783779i	$-0.713290\pi$
$521$	−28.3510	−1.24208	−0.621040	+	0.783779i	$0.713290\pi$
$522$	−0.889563	−0.0389351
$523$	−31.7395	−1.38787	−0.693935	−	0.720038i	$-0.744125\pi$
$523$	−31.7395	−1.38787	−0.693935	+	0.720038i	$0.744125\pi$
$524$	18.1177	0.791477
$525$	12.2547	0.534838
$526$	5.90601	0.257514
$527$	−1.50806	−0.0656922
$528$	−1.63824	−0.0712954
$529$	20.8702	0.907402
$530$	−11.3205	−0.491732
$531$	−1.61600	−0.0701283
$532$	0	0
$533$	−22.6082	−0.979271
$534$	−6.68270	−0.289189
$535$	10.4963	0.453795
$536$	−2.73417	−0.118098
$537$	−37.6598	−1.62514
$538$	16.3899	0.706620
$539$	−1.79303	−0.0772311
$540$	−7.12869	−0.306770
$541$	6.41564	0.275830	0.137915	−	0.990444i	$-0.455960\pi$
$541$	6.41564	0.275830	0.137915	+	0.990444i	$0.455960\pi$
$542$	5.43019	0.233247
$543$	11.3639	0.487672
$544$	0.139286	0.00597182
$545$	20.1865	0.864695
$546$	14.6257	0.625923
$547$	−8.62333	−0.368707	−0.184354	−	0.982860i	$-0.559019\pi$
$547$	−8.62333	−0.368707	−0.184354	+	0.982860i	$0.559019\pi$
$548$	4.05957	0.173416
$549$	−0.254635	−0.0108676
$550$	3.27817	0.139781
$551$	0	0
$552$	−10.8508	−0.461842
$553$	−13.2936	−0.565299
$554$	−17.1524	−0.728736
$555$	22.9334	0.973469
$556$	1.84455	0.0782262
$557$	−27.1560	−1.15064	−0.575319	−	0.817929i	$-0.695122\pi$
$557$	−27.1560	−1.15064	−0.575319	+	0.817929i	$0.695122\pi$
$558$	3.42310	0.144911
$559$	−37.0394	−1.56660
$560$	−2.99425	−0.126530
$561$	0.228184	0.00963392
$562$	−17.8373	−0.752422
$563$	33.5078	1.41219	0.706093	−	0.708119i	$-0.250456\pi$
$563$	33.5078	1.41219	0.706093	+	0.708119i	$0.250456\pi$
$564$	6.77709	0.285367
$565$	14.0173	0.589712
$566$	2.09279	0.0879665
$567$	−18.1445	−0.761998
$568$	4.75623	0.199567
$569$	17.8067	0.746495	0.373248	−	0.927732i	$-0.378244\pi$
$569$	17.8067	0.746495	0.373248	+	0.927732i	$0.378244\pi$
$570$	0	0
$571$	32.7815	1.37186	0.685931	−	0.727667i	$-0.259395\pi$
$571$	32.7815	1.37186	0.685931	+	0.727667i	$0.259395\pi$
$572$	3.91243	0.163587
$573$	38.2101	1.59625
$574$	13.1860	0.550372
$575$	21.7128	0.905486
$576$	−0.316160	−0.0131733
$577$	−17.9193	−0.745989	−0.372995	−	0.927834i	$-0.621669\pi$
$577$	−17.9193	−0.745989	−0.372995	+	0.927834i	$0.621669\pi$
$578$	16.9806	0.706300
$579$	3.55682	0.147816
$580$	3.69204	0.153303
$581$	−37.7015	−1.56412
$582$	19.1771	0.794916
$583$	−8.62721	−0.357303
$584$	−14.9213	−0.617448
$585$	1.62311	0.0671075
$586$	−2.80549	−0.115894
$587$	−24.5063	−1.01148	−0.505741	−	0.862685i	$-0.668781\pi$
$587$	−24.5063	−1.01148	−0.505741	+	0.862685i	$0.668781\pi$
$588$	2.93741	0.121137
$589$	0	0
$590$	6.70702	0.276123
$591$	−3.68820	−0.151712
$592$	10.6683	0.438464
$593$	19.8958	0.817022	0.408511	−	0.912753i	$-0.366048\pi$
$593$	19.8958	0.817022	0.408511	+	0.912753i	$0.366048\pi$
$594$	−5.43268	−0.222905
$595$	0.417056	0.0170976
$596$	19.4539	0.796861
$597$	−27.3931	−1.12113
$598$	25.9138	1.05969
$599$	−19.7708	−0.807815	−0.403907	−	0.914800i	$-0.632348\pi$
$599$	−19.7708	−0.807815	−0.403907	+	0.914800i	$0.632348\pi$
$600$	−5.37043	−0.219247
$601$	−9.60260	−0.391698	−0.195849	−	0.980634i	$-0.562746\pi$
$601$	−9.60260	−0.391698	−0.195849	+	0.980634i	$0.562746\pi$
$602$	21.6028	0.880464
$603$	−0.864434	−0.0352025
$604$	−22.5490	−0.917508
$605$	−1.31219	−0.0533480
$606$	11.0373	0.448360
$607$	−43.2433	−1.75519	−0.877595	−	0.479403i	$-0.840853\pi$
$607$	−43.2433	−1.75519	−0.877595	+	0.479403i	$0.840853\pi$
$608$	0	0
$609$	10.5182	0.426219
$610$	1.05684	0.0427900
$611$	−16.1849	−0.654773
$612$	0.0440365	0.00178007
$613$	−36.8939	−1.49013	−0.745066	−	0.666991i	$-0.767582\pi$
$613$	−36.8939	−1.49013	−0.745066	+	0.666991i	$0.767582\pi$
$614$	13.9266	0.562033
$615$	−12.4221	−0.500906
$616$	−2.28188	−0.0919396
$617$	−21.6159	−0.870222	−0.435111	−	0.900377i	$-0.643291\pi$
$617$	−21.6159	−0.870222	−0.435111	+	0.900377i	$0.643291\pi$
$618$	5.95687	0.239620
$619$	16.9771	0.682369	0.341185	−	0.939996i	$-0.389172\pi$
$619$	16.9771	0.682369	0.341185	+	0.939996i	$0.389172\pi$
$620$	−14.2072	−0.570575
$621$	−35.9831	−1.44395
$622$	−12.6677	−0.507930
$623$	−9.30822	−0.372926
$624$	−6.40951	−0.256586
$625$	2.13720	0.0854878
$626$	24.9880	0.998722
$627$	0	0
$628$	−12.5451	−0.500602
$629$	−1.48594	−0.0592482
$630$	−0.946662	−0.0377159
$631$	−3.21360	−0.127931	−0.0639657	−	0.997952i	$-0.520375\pi$
$631$	−3.21360	−0.127931	−0.0639657	+	0.997952i	$0.520375\pi$
$632$	5.82570	0.231734
$633$	−22.6926	−0.901952
$634$	0.118044	0.00468811
$635$	−4.88792	−0.193971
$636$	14.1335	0.560428
$637$	−7.01508	−0.277948
$638$	2.81365	0.111394
$639$	1.50373	0.0594866
$640$	1.31219	0.0518687
$641$	−34.3929	−1.35844	−0.679218	−	0.733936i	$-0.737681\pi$
$641$	−34.3929	−1.35844	−0.679218	+	0.733936i	$0.737681\pi$
$642$	−13.1045	−0.517192
$643$	−13.4131	−0.528961	−0.264481	−	0.964391i	$-0.585201\pi$
$643$	−13.4131	−0.528961	−0.264481	+	0.964391i	$0.585201\pi$
$644$	−15.1139	−0.595573
$645$	−20.3513	−0.801330
$646$	0	0
$647$	3.55611	0.139805	0.0699026	−	0.997554i	$-0.477731\pi$
$647$	3.55611	0.139805	0.0699026	+	0.997554i	$0.477731\pi$
$648$	7.95156	0.312367
$649$	5.11133	0.200637
$650$	12.8256	0.503061
$651$	−40.4747	−1.58633
$652$	−15.3151	−0.599785
$653$	−1.94832	−0.0762436	−0.0381218	−	0.999273i	$-0.512137\pi$
$653$	−1.94832	−0.0762436	−0.0381218	+	0.999273i	$0.512137\pi$
$654$	−25.2025	−0.985497
$655$	−23.7739	−0.928922
$656$	−5.77856	−0.225615
$657$	−4.71751	−0.184048
$658$	9.43969	0.367997
$659$	−3.98209	−0.155120	−0.0775601	−	0.996988i	$-0.524713\pi$
$659$	−3.98209	−0.155120	−0.0775601	+	0.996988i	$0.524713\pi$
$660$	2.14968	0.0836762
$661$	−35.0102	−1.36174	−0.680870	−	0.732404i	$-0.738398\pi$
$661$	−35.0102	−1.36174	−0.680870	+	0.732404i	$0.738398\pi$
$662$	23.7123	0.921605
$663$	0.892752	0.0346716
$664$	16.5221	0.641184
$665$	0	0
$666$	3.37288	0.130697
$667$	18.6361	0.721593
$668$	20.3013	0.785482
$669$	−1.35839	−0.0525182
$670$	3.58774	0.138606
$671$	0.805400	0.0310921
$672$	3.73827	0.144207
$673$	−13.6380	−0.525706	−0.262853	−	0.964836i	$-0.584663\pi$
$673$	−13.6380	−0.525706	−0.262853	+	0.964836i	$0.584663\pi$
$674$	23.3905	0.900967
$675$	−17.8092	−0.685477
$676$	2.30710	0.0887344
$677$	−14.0911	−0.541565	−0.270782	−	0.962641i	$-0.587282\pi$
$677$	−14.0911	−0.541565	−0.270782	+	0.962641i	$0.587282\pi$
$678$	−17.5003	−0.672097
$679$	26.7114	1.02509
$680$	−0.182769	−0.00700886
$681$	−7.99916	−0.306528
$682$	−10.8271	−0.414592
$683$	38.6886	1.48038	0.740190	−	0.672398i	$-0.234736\pi$
$683$	38.6886	1.48038	0.740190	+	0.672398i	$0.234736\pi$
$684$	0	0
$685$	−5.32691	−0.203531
$686$	20.0646	0.766071
$687$	1.72773	0.0659170
$688$	−9.46710	−0.360930
$689$	−33.7533	−1.28590
$690$	14.2383	0.542044
$691$	−9.87072	−0.375500	−0.187750	−	0.982217i	$-0.560119\pi$
$691$	−9.87072	−0.375500	−0.187750	+	0.982217i	$0.560119\pi$
$692$	11.5036	0.437302
$693$	−0.721439	−0.0274052
$694$	2.36299	0.0896980
$695$	−2.42039	−0.0918107
$696$	−4.60944	−0.174721
$697$	0.804871	0.0304867
$698$	10.7950	0.408597
$699$	8.81643	0.333468
$700$	−7.48038	−0.282732
$701$	27.6822	1.04554	0.522771	−	0.852473i	$-0.324898\pi$
$701$	27.6822	1.04554	0.522771	+	0.852473i	$0.324898\pi$
$702$	−21.2550	−0.802217
$703$	0	0
$704$	1.00000	0.0376889
$705$	−8.89281	−0.334922
$706$	16.5787	0.623948
$707$	15.3737	0.578186
$708$	−8.37360	−0.314699
$709$	29.0842	1.09228	0.546139	−	0.837694i	$-0.316097\pi$
$709$	29.0842	1.09228	0.546139	+	0.837694i	$0.316097\pi$
$710$	−6.24106	−0.234223
$711$	1.84185	0.0690749
$712$	4.07919	0.152874
$713$	−71.7130	−2.68567
$714$	−0.520688	−0.0194862
$715$	−5.13384	−0.191995
$716$	22.9879	0.859100
$717$	−22.5565	−0.842389
$718$	21.1854	0.790632
$719$	9.54597	0.356004	0.178002	−	0.984030i	$-0.443037\pi$
$719$	9.54597	0.356004	0.178002	+	0.984030i	$0.443037\pi$
$720$	0.414861	0.0154609
$721$	8.29721	0.309004
$722$	0	0
$723$	10.5673	0.393002
$724$	−6.93665	−0.257799
$725$	9.22361	0.342556
$726$	1.63824	0.0608009
$727$	−6.20737	−0.230219	−0.115109	−	0.993353i	$-0.536722\pi$
$727$	−6.20737	−0.230219	−0.115109	+	0.993353i	$0.536722\pi$
$728$	−8.92769	−0.330882
$729$	29.2141	1.08200
$730$	19.5795	0.724671
$731$	1.31863	0.0487713
$732$	−1.31944	−0.0487680
$733$	−18.0295	−0.665933	−0.332967	−	0.942939i	$-0.608050\pi$
$733$	−18.0295	−0.665933	−0.332967	+	0.942939i	$0.608050\pi$
$734$	−25.4016	−0.937591
$735$	−3.85443	−0.142173
$736$	6.62346	0.244144
$737$	2.73417	0.100714
$738$	−1.82695	−0.0672510
$739$	−41.5570	−1.52870	−0.764350	−	0.644802i	$-0.776940\pi$
$739$	−41.5570	−1.52870	−0.764350	+	0.644802i	$0.776940\pi$
$740$	−13.9988	−0.514605
$741$	0	0
$742$	19.6863	0.722705
$743$	−7.27218	−0.266790	−0.133395	−	0.991063i	$-0.542588\pi$
$743$	−7.27218	−0.266790	−0.133395	+	0.991063i	$0.542588\pi$
$744$	17.7375	0.650287
$745$	−25.5271	−0.935240
$746$	7.92963	0.290324
$747$	5.22364	0.191123
$748$	−0.139286	−0.00509279
$749$	−18.2530	−0.666949
$750$	17.7954	0.649797
$751$	52.1647	1.90352	0.951758	−	0.306849i	$-0.0992746\pi$
$751$	52.1647	1.90352	0.951758	+	0.306849i	$0.0992746\pi$
$752$	−4.13680	−0.150854
$753$	15.5192	0.565549
$754$	11.0082	0.400895
$755$	29.5886	1.07684
$756$	12.3967	0.450864
$757$	−14.4099	−0.523737	−0.261868	−	0.965104i	$-0.584339\pi$
$757$	−14.4099	−0.523737	−0.261868	+	0.965104i	$0.584339\pi$
$758$	18.7755	0.681958
$759$	10.8508	0.393861
$760$	0	0
$761$	−14.1626	−0.513394	−0.256697	−	0.966492i	$-0.582634\pi$
$761$	−14.1626	−0.513394	−0.256697	+	0.966492i	$0.582634\pi$
$762$	6.10248	0.221070
$763$	−35.1042	−1.27086
$764$	−23.3238	−0.843827
$765$	−0.0577841	−0.00208919
$766$	−23.3654	−0.844226
$767$	19.9977	0.722075
$768$	−1.63824	−0.0591150
$769$	−24.3424	−0.877810	−0.438905	−	0.898533i	$-0.644634\pi$
$769$	−24.3424	−0.877810	−0.438905	+	0.898533i	$0.644634\pi$
$770$	2.99425	0.107905
$771$	−29.1340	−1.04924
$772$	−2.17112	−0.0781403
$773$	0.591112	0.0212608	0.0106304	−	0.999943i	$-0.496616\pi$
$773$	0.591112	0.0212608	0.0106304	+	0.999943i	$0.496616\pi$
$774$	−2.99312	−0.107585
$775$	−35.4931	−1.27495
$776$	−11.7059	−0.420217
$777$	−39.8810	−1.43072
$778$	8.52843	0.305759
$779$	0	0
$780$	8.41047	0.301143
$781$	−4.75623	−0.170191
$782$	−0.922553	−0.0329904
$783$	−15.2857	−0.546265
$784$	−1.79303	−0.0640366
$785$	16.4615	0.587535
$786$	29.6813	1.05870
$787$	−35.7690	−1.27503	−0.637513	−	0.770439i	$-0.720037\pi$
$787$	−35.7690	−1.27503	−0.637513	+	0.770439i	$0.720037\pi$
$788$	2.25131	0.0801998
$789$	9.67547	0.344456
$790$	−7.64441	−0.271976
$791$	−24.3759	−0.866708
$792$	0.316160	0.0112343
$793$	3.15107	0.111898
$794$	−10.4778	−0.371845
$795$	−18.5458	−0.657750
$796$	16.7210	0.592662
$797$	−24.1675	−0.856055	−0.428028	−	0.903766i	$-0.640791\pi$
$797$	−24.1675	−0.856055	−0.428028	+	0.903766i	$0.640791\pi$
$798$	0	0
$799$	0.576197	0.0203844
$800$	3.27817	0.115901
$801$	1.28968	0.0455685
$802$	0.403820	0.0142594
$803$	14.9213	0.526561
$804$	−4.47923	−0.157970
$805$	19.8323	0.698997
$806$	−42.3603	−1.49208
$807$	26.8507	0.945190
$808$	−6.73728	−0.237017
$809$	−41.3049	−1.45220	−0.726102	−	0.687587i	$-0.758670\pi$
$809$	−41.3049	−1.45220	−0.726102	+	0.687587i	$0.758670\pi$
$810$	−10.4339	−0.366611
$811$	−12.2972	−0.431813	−0.215907	−	0.976414i	$-0.569271\pi$
$811$	−12.2972	−0.431813	−0.215907	+	0.976414i	$0.569271\pi$
$812$	−6.42041	−0.225312
$813$	8.89597	0.311995
$814$	−10.6683	−0.373923
$815$	20.0963	0.703941
$816$	0.228184	0.00798803
$817$	0	0
$818$	−3.62192	−0.126638
$819$	−2.82258	−0.0986288
$820$	7.58256	0.264794
$821$	−44.8649	−1.56580	−0.782898	−	0.622150i	$-0.786259\pi$
$821$	−44.8649	−1.56580	−0.782898	+	0.622150i	$0.786259\pi$
$822$	6.65056	0.231965
$823$	−14.5455	−0.507025	−0.253513	−	0.967332i	$-0.581586\pi$
$823$	−14.5455	−0.507025	−0.253513	+	0.967332i	$0.581586\pi$
$824$	−3.63613	−0.126671
$825$	5.37043	0.186974
$826$	−11.6634	−0.405823
$827$	1.20715	0.0419767	0.0209884	−	0.999780i	$-0.493319\pi$
$827$	1.20715	0.0419767	0.0209884	+	0.999780i	$0.493319\pi$
$828$	2.09407	0.0727741
$829$	−41.5720	−1.44386	−0.721928	−	0.691969i	$-0.756744\pi$
$829$	−41.5720	−1.44386	−0.721928	+	0.691969i	$0.756744\pi$
$830$	−21.6801	−0.752529
$831$	−28.0998	−0.974772
$832$	3.91243	0.135639
$833$	0.249743	0.00865307
$834$	3.02182	0.104637
$835$	−26.6391	−0.921885
$836$	0	0
$837$	58.8202	2.03312
$838$	24.0514	0.830841
$839$	−47.4069	−1.63667	−0.818334	−	0.574742i	$-0.805102\pi$
$839$	−47.4069	−1.63667	−0.818334	+	0.574742i	$0.805102\pi$
$840$	−4.90531	−0.169249
$841$	−21.0834	−0.727013
$842$	16.7744	0.578082
$843$	−29.2219	−1.00645
$844$	13.8518	0.476799
$845$	−3.02734	−0.104144
$846$	−1.30789	−0.0449662
$847$	2.28188	0.0784063
$848$	−8.62721	−0.296260
$849$	3.42850	0.117666
$850$	−0.456601	−0.0156613
$851$	−70.6610	−2.42223
$852$	7.79186	0.266945
$853$	−43.5865	−1.49237	−0.746187	−	0.665737i	$-0.768117\pi$
$853$	−43.5865	−1.49237	−0.746187	+	0.665737i	$0.768117\pi$
$854$	−1.83783	−0.0628891
$855$	0	0
$856$	7.99909	0.273403
$857$	−25.6918	−0.877615	−0.438807	−	0.898581i	$-0.644599\pi$
$857$	−25.6918	−0.877615	−0.438807	+	0.898581i	$0.644599\pi$
$858$	6.40951	0.218817
$859$	35.1751	1.20016	0.600080	−	0.799940i	$-0.295135\pi$
$859$	35.1751	1.20016	0.600080	+	0.799940i	$0.295135\pi$
$860$	12.4226	0.423607
$861$	21.6019	0.736189
$862$	5.45055	0.185647
$863$	1.90744	0.0649299	0.0324649	−	0.999473i	$-0.489664\pi$
$863$	1.90744	0.0649299	0.0324649	+	0.999473i	$0.489664\pi$
$864$	−5.43268	−0.184823
$865$	−15.0949	−0.513242
$866$	−13.1201	−0.445838
$867$	27.8183	0.944761
$868$	24.7062	0.838582
$869$	−5.82570	−0.197623
$870$	6.04845	0.205062
$871$	10.6972	0.362462
$872$	15.3839	0.520964
$873$	−3.70093	−0.125258
$874$	0	0
$875$	24.7869	0.837951
$876$	−24.4447	−0.825910
$877$	7.06750	0.238653	0.119326	−	0.992855i	$-0.461927\pi$
$877$	7.06750	0.238653	0.119326	+	0.992855i	$0.461927\pi$
$878$	−24.3157	−0.820616
$879$	−4.59607	−0.155022
$880$	−1.31219	−0.0442338
$881$	−22.7271	−0.765696	−0.382848	−	0.923811i	$-0.625057\pi$
$881$	−22.7271	−0.765696	−0.382848	+	0.923811i	$0.625057\pi$
$882$	−0.566883	−0.0190879
$883$	−39.7614	−1.33808	−0.669038	−	0.743228i	$-0.733294\pi$
$883$	−39.7614	−1.33808	−0.669038	+	0.743228i	$0.733294\pi$
$884$	−0.544945	−0.0183285
$885$	10.9877	0.369348
$886$	32.4992	1.09183
$887$	−50.3791	−1.69157	−0.845783	−	0.533528i	$-0.820866\pi$
$887$	−50.3791	−1.69157	−0.845783	+	0.533528i	$0.820866\pi$
$888$	17.4772	0.586498
$889$	8.50004	0.285082
$890$	−5.35266	−0.179422
$891$	−7.95156	−0.266387
$892$	0.829172	0.0277627
$893$	0	0
$894$	31.8701	1.06590
$895$	−30.1645	−1.00829
$896$	−2.28188	−0.0762322
$897$	42.4531	1.41747
$898$	22.6003	0.754181
$899$	−30.4637	−1.01602
$900$	1.03642	0.0345475
$901$	1.20165	0.0400326
$902$	5.77856	0.192405
$903$	35.3906	1.17773
$904$	10.6824	0.355291
$905$	9.10218	0.302567
$906$	−36.9408	−1.22728
$907$	24.1316	0.801275	0.400638	−	0.916237i	$-0.368789\pi$
$907$	24.1316	0.801275	0.400638	+	0.916237i	$0.368789\pi$
$908$	4.88277	0.162040
$909$	−2.13006	−0.0706495
$910$	11.7148	0.388342
$911$	50.3929	1.66959	0.834795	−	0.550561i	$-0.185586\pi$
$911$	50.3929	1.66959	0.834795	+	0.550561i	$0.185586\pi$
$912$	0	0
$913$	−16.5221	−0.546803
$914$	37.6043	1.24384
$915$	1.73135	0.0572368
$916$	−1.05462	−0.0348458
$917$	41.3425	1.36525
$918$	0.756694	0.0249746
$919$	14.4377	0.476256	0.238128	−	0.971234i	$-0.423466\pi$
$919$	14.4377	0.476256	0.238128	+	0.971234i	$0.423466\pi$
$920$	−8.69122	−0.286541
$921$	22.8152	0.751786
$922$	−18.7652	−0.618000
$923$	−18.6084	−0.612503
$924$	−3.73827	−0.122980
$925$	−34.9724	−1.14989
$926$	−0.559907	−0.0183997
$927$	−1.14960	−0.0377578
$928$	2.81365	0.0923626
$929$	31.5108	1.03384	0.516918	−	0.856035i	$-0.327079\pi$
$929$	31.5108	1.03384	0.516918	+	0.856035i	$0.327079\pi$
$930$	−23.2749	−0.763213
$931$	0	0
$932$	−5.38163	−0.176281
$933$	−20.7528	−0.679417
$934$	25.2550	0.826369
$935$	0.182769	0.00597718
$936$	1.23695	0.0404311
$937$	15.7832	0.515614	0.257807	−	0.966196i	$-0.417000\pi$
$937$	15.7832	0.515614	0.257807	+	0.966196i	$0.417000\pi$
$938$	−6.23904	−0.203712
$939$	40.9365	1.33591
$940$	5.42826	0.177050
$941$	30.4916	0.993997	0.496999	−	0.867751i	$-0.334435\pi$
$941$	30.4916	0.993997	0.496999	+	0.867751i	$0.334435\pi$
$942$	−20.5519	−0.669616
$943$	38.2741	1.24638
$944$	5.11133	0.166360
$945$	−16.2668	−0.529159
$946$	9.46710	0.307802
$947$	−47.5267	−1.54441	−0.772206	−	0.635373i	$-0.780846\pi$
$947$	−47.5267	−1.54441	−0.772206	+	0.635373i	$0.780846\pi$
$948$	9.54392	0.309972
$949$	58.3785	1.89505
$950$	0	0
$951$	0.193384	0.00627091
$952$	0.317833	0.0103010
$953$	−52.4328	−1.69847	−0.849233	−	0.528019i	$-0.822935\pi$
$953$	−52.4328	−1.69847	−0.849233	+	0.528019i	$0.822935\pi$
$954$	−2.72758	−0.0883086
$955$	30.6052	0.990362
$956$	13.7687	0.445312
$957$	4.60944	0.149002
$958$	−4.70962	−0.152161
$959$	9.26344	0.299132
$960$	2.14968	0.0693807
$961$	86.2265	2.78150
$962$	−41.7389	−1.34572
$963$	2.52899	0.0814956
$964$	−6.45039	−0.207753
$965$	2.84892	0.0917098
$966$	−24.7603	−0.796650
$967$	10.5582	0.339529	0.169764	−	0.985485i	$-0.445699\pi$
$967$	10.5582	0.339529	0.169764	+	0.985485i	$0.445699\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	15.3603	0.493190
$971$	56.0001	1.79713	0.898565	−	0.438841i	$-0.144611\pi$
$971$	56.0001	1.79713	0.898565	+	0.438841i	$0.144611\pi$
$972$	−3.27143	−0.104931
$973$	4.20904	0.134935
$974$	−19.3717	−0.620710
$975$	21.0114	0.672904
$976$	0.805400	0.0257802
$977$	−2.91192	−0.0931605	−0.0465802	−	0.998915i	$-0.514832\pi$
$977$	−2.91192	−0.0931605	−0.0465802	+	0.998915i	$0.514832\pi$
$978$	−25.0898	−0.802285
$979$	−4.07919	−0.130371
$980$	2.35278	0.0751569
$981$	4.86376	0.155288
$982$	20.5144	0.654642
$983$	36.4167	1.16151	0.580757	−	0.814077i	$-0.302757\pi$
$983$	36.4167	1.16151	0.580757	+	0.814077i	$0.302757\pi$
$984$	−9.46669	−0.301787
$985$	−2.95415	−0.0941269
$986$	−0.391901	−0.0124807
$987$	15.4645	0.492240
$988$	0	0
$989$	62.7050	1.99390
$990$	−0.414861	−0.0131851
$991$	−56.4587	−1.79347	−0.896736	−	0.442567i	$-0.854068\pi$
$991$	−56.4587	−1.79347	−0.896736	+	0.442567i	$0.854068\pi$
$992$	−10.8271	−0.343761
$993$	38.8465	1.23276
$994$	10.8531	0.344241
$995$	−21.9411	−0.695581
$996$	27.0673	0.857660
$997$	−32.2796	−1.02231	−0.511153	−	0.859490i	$-0.670781\pi$
$997$	−32.2796	−1.02231	−0.511153	+	0.859490i	$0.670781\pi$
$998$	−21.9133	−0.693652
$999$	57.9573	1.83369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bs.1.4		12
19.2	odd	18		418.2.j.b.23.3	✓	24
19.10	odd	18		418.2.j.b.309.3	yes	24
19.18	odd	2		7942.2.a.bw.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.b.23.3	✓	24	19.2	odd	18
418.2.j.b.309.3	yes	24	19.10	odd	18
7942.2.a.bs.1.4		12	1.1	even	1	trivial
7942.2.a.bw.1.9		12	19.18	odd	2

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.63824 q^{3} +1.00000 q^{4} -1.31219 q^{5} +1.63824 q^{6} +2.28188 q^{7} -1.00000 q^{8} -0.316160 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.63824 q^{3} +1.00000 q^{4} -1.31219 q^{5} +1.63824 q^{6} +2.28188 q^{7} -1.00000 q^{8} -0.316160 q^{9} +1.31219 q^{10} +1.00000 q^{11} -1.63824 q^{12} +3.91243 q^{13} -2.28188 q^{14} +2.14968 q^{15} +1.00000 q^{16} -0.139286 q^{17} +0.316160 q^{18} -1.31219 q^{20} -3.73827 q^{21} -1.00000 q^{22} -6.62346 q^{23} +1.63824 q^{24} -3.27817 q^{25} -3.91243 q^{26} +5.43268 q^{27} +2.28188 q^{28} -2.81365 q^{29} -2.14968 q^{30} +10.8271 q^{31} -1.00000 q^{32} -1.63824 q^{33} +0.139286 q^{34} -2.99425 q^{35} -0.316160 q^{36} +10.6683 q^{37} -6.40951 q^{39} +1.31219 q^{40} -5.77856 q^{41} +3.73827 q^{42} -9.46710 q^{43} +1.00000 q^{44} +0.414861 q^{45} +6.62346 q^{46} -4.13680 q^{47} -1.63824 q^{48} -1.79303 q^{49} +3.27817 q^{50} +0.228184 q^{51} +3.91243 q^{52} -8.62721 q^{53} -5.43268 q^{54} -1.31219 q^{55} -2.28188 q^{56} +2.81365 q^{58} +5.11133 q^{59} +2.14968 q^{60} +0.805400 q^{61} -10.8271 q^{62} -0.721439 q^{63} +1.00000 q^{64} -5.13384 q^{65} +1.63824 q^{66} +2.73417 q^{67} -0.139286 q^{68} +10.8508 q^{69} +2.99425 q^{70} -4.75623 q^{71} +0.316160 q^{72} +14.9213 q^{73} -10.6683 q^{74} +5.37043 q^{75} +2.28188 q^{77} +6.40951 q^{78} -5.82570 q^{79} -1.31219 q^{80} -7.95156 q^{81} +5.77856 q^{82} -16.5221 q^{83} -3.73827 q^{84} +0.182769 q^{85} +9.46710 q^{86} +4.60944 q^{87} -1.00000 q^{88} -4.07919 q^{89} -0.414861 q^{90} +8.92769 q^{91} -6.62346 q^{92} -17.7375 q^{93} +4.13680 q^{94} +1.63824 q^{96} +11.7059 q^{97} +1.79303 q^{98} -0.316160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

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