LMFDB - Embedded newform 8031.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62963 q^{2} -1.00000 q^{3} +4.91495 q^{4} +3.86074 q^{5} +2.62963 q^{6} +3.78778 q^{7} -7.66525 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91495 q^{4} +3.86074 q^{5} +2.62963 q^{6} +3.78778 q^{7} -7.66525 q^{8} +1.00000 q^{9} -10.1523 q^{10} +4.64549 q^{11} -4.91495 q^{12} -2.58699 q^{13} -9.96045 q^{14} -3.86074 q^{15} +10.3269 q^{16} +0.576177 q^{17} -2.62963 q^{18} +0.129149 q^{19} +18.9753 q^{20} -3.78778 q^{21} -12.2159 q^{22} +1.63005 q^{23} +7.66525 q^{24} +9.90530 q^{25} +6.80284 q^{26} -1.00000 q^{27} +18.6167 q^{28} +2.60586 q^{29} +10.1523 q^{30} +7.99296 q^{31} -11.8253 q^{32} -4.64549 q^{33} -1.51513 q^{34} +14.6236 q^{35} +4.91495 q^{36} -5.98633 q^{37} -0.339614 q^{38} +2.58699 q^{39} -29.5935 q^{40} -7.39713 q^{41} +9.96045 q^{42} -0.142932 q^{43} +22.8324 q^{44} +3.86074 q^{45} -4.28643 q^{46} +2.08487 q^{47} -10.3269 q^{48} +7.34725 q^{49} -26.0473 q^{50} -0.576177 q^{51} -12.7150 q^{52} -4.23978 q^{53} +2.62963 q^{54} +17.9350 q^{55} -29.0342 q^{56} -0.129149 q^{57} -6.85244 q^{58} -3.60341 q^{59} -18.9753 q^{60} -7.92961 q^{61} -21.0185 q^{62} +3.78778 q^{63} +10.4425 q^{64} -9.98771 q^{65} +12.2159 q^{66} -10.3385 q^{67} +2.83189 q^{68} -1.63005 q^{69} -38.4547 q^{70} +6.04688 q^{71} -7.66525 q^{72} +3.17576 q^{73} +15.7418 q^{74} -9.90530 q^{75} +0.634762 q^{76} +17.5961 q^{77} -6.80284 q^{78} +5.59283 q^{79} +39.8693 q^{80} +1.00000 q^{81} +19.4517 q^{82} +1.90666 q^{83} -18.6167 q^{84} +2.22447 q^{85} +0.375860 q^{86} -2.60586 q^{87} -35.6089 q^{88} +7.21274 q^{89} -10.1523 q^{90} -9.79896 q^{91} +8.01162 q^{92} -7.99296 q^{93} -5.48245 q^{94} +0.498611 q^{95} +11.8253 q^{96} -16.9128 q^{97} -19.3206 q^{98} +4.64549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.62963	−1.85943	−0.929715	−	0.368281i	$-0.879946\pi$
$2$	−2.62963	−1.85943	−0.929715	+	0.368281i	$0.879946\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.91495	2.45748
$5$	3.86074	1.72657	0.863287	−	0.504713i	$-0.168402\pi$
$5$	3.86074	1.72657	0.863287	+	0.504713i	$0.168402\pi$
$6$	2.62963	1.07354
$7$	3.78778	1.43165	0.715823	−	0.698282i	$-0.246052\pi$
$7$	3.78778	1.43165	0.715823	+	0.698282i	$0.246052\pi$
$8$	−7.66525	−2.71007
$9$	1.00000	0.333333
$10$	−10.1523	−3.21044
$11$	4.64549	1.40067	0.700334	−	0.713815i	$-0.253034\pi$
$11$	4.64549	1.40067	0.700334	+	0.713815i	$0.253034\pi$
$12$	−4.91495	−1.41882
$13$	−2.58699	−0.717503	−0.358752	−	0.933433i	$-0.616798\pi$
$13$	−2.58699	−0.717503	−0.358752	+	0.933433i	$0.616798\pi$
$14$	−9.96045	−2.66204
$15$	−3.86074	−0.996838
$16$	10.3269	2.58171
$17$	0.576177	0.139744	0.0698718	−	0.997556i	$-0.477741\pi$
$17$	0.576177	0.139744	0.0698718	+	0.997556i	$0.477741\pi$
$18$	−2.62963	−0.619810
$19$	0.129149	0.0296288	0.0148144	−	0.999890i	$-0.495284\pi$
$19$	0.129149	0.0296288	0.0148144	+	0.999890i	$0.495284\pi$
$20$	18.9753	4.24302
$21$	−3.78778	−0.826561
$22$	−12.2159	−2.60444
$23$	1.63005	0.339889	0.169945	−	0.985454i	$-0.445641\pi$
$23$	1.63005	0.339889	0.169945	+	0.985454i	$0.445641\pi$
$24$	7.66525	1.56466
$25$	9.90530	1.98106
$26$	6.80284	1.33415
$27$	−1.00000	−0.192450
$28$	18.6167	3.51823
$29$	2.60586	0.483896	0.241948	−	0.970289i	$-0.422214\pi$
$29$	2.60586	0.483896	0.241948	+	0.970289i	$0.422214\pi$
$30$	10.1523	1.85355
$31$	7.99296	1.43558	0.717789	−	0.696260i	$-0.245154\pi$
$31$	7.99296	1.43558	0.717789	+	0.696260i	$0.245154\pi$
$32$	−11.8253	−2.09044
$33$	−4.64549	−0.808677
$34$	−1.51513	−0.259843
$35$	14.6236	2.47184
$36$	4.91495	0.819159
$37$	−5.98633	−0.984146	−0.492073	−	0.870554i	$-0.663761\pi$
$37$	−5.98633	−0.984146	−0.492073	+	0.870554i	$0.663761\pi$
$38$	−0.339614	−0.0550927
$39$	2.58699	0.414251
$40$	−29.5935	−4.67915
$41$	−7.39713	−1.15524	−0.577619	−	0.816307i	$-0.696018\pi$
$41$	−7.39713	−1.15524	−0.577619	+	0.816307i	$0.696018\pi$
$42$	9.96045	1.53693
$43$	−0.142932	−0.0217970	−0.0108985	−	0.999941i	$-0.503469\pi$
$43$	−0.142932	−0.0217970	−0.0108985	+	0.999941i	$0.503469\pi$
$44$	22.8324	3.44211
$45$	3.86074	0.575525
$46$	−4.28643	−0.632000
$47$	2.08487	0.304110	0.152055	−	0.988372i	$-0.451411\pi$
$47$	2.08487	0.304110	0.152055	+	0.988372i	$0.451411\pi$
$48$	−10.3269	−1.49055
$49$	7.34725	1.04961
$50$	−26.0473	−3.68364
$51$	−0.576177	−0.0806810
$52$	−12.7150	−1.76325
$53$	−4.23978	−0.582379	−0.291190	−	0.956665i	$-0.594051\pi$
$53$	−4.23978	−0.582379	−0.291190	+	0.956665i	$0.594051\pi$
$54$	2.62963	0.357847
$55$	17.9350	2.41836
$56$	−29.0342	−3.87986
$57$	−0.129149	−0.0171062
$58$	−6.85244	−0.899769
$59$	−3.60341	−0.469125	−0.234562	−	0.972101i	$-0.575366\pi$
$59$	−3.60341	−0.469125	−0.234562	+	0.972101i	$0.575366\pi$
$60$	−18.9753	−2.44971
$61$	−7.92961	−1.01528	−0.507641	−	0.861569i	$-0.669482\pi$
$61$	−7.92961	−1.01528	−0.507641	+	0.861569i	$0.669482\pi$
$62$	−21.0185	−2.66936
$63$	3.78778	0.477215
$64$	10.4425	1.30531
$65$	−9.98771	−1.23882
$66$	12.2159	1.50368
$67$	−10.3385	−1.26305	−0.631525	−	0.775356i	$-0.717570\pi$
$67$	−10.3385	−1.26305	−0.631525	+	0.775356i	$0.717570\pi$
$68$	2.83189	0.343417
$69$	−1.63005	−0.196235
$70$	−38.4547	−4.59622
$71$	6.04688	0.717633	0.358817	−	0.933408i	$-0.383180\pi$
$71$	6.04688	0.717633	0.358817	+	0.933408i	$0.383180\pi$
$72$	−7.66525	−0.903358
$73$	3.17576	0.371695	0.185847	−	0.982579i	$-0.440497\pi$
$73$	3.17576	0.371695	0.185847	+	0.982579i	$0.440497\pi$
$74$	15.7418	1.82995
$75$	−9.90530	−1.14377
$76$	0.634762	0.0728122
$77$	17.5961	2.00526
$78$	−6.80284	−0.770270
$79$	5.59283	0.629243	0.314621	−	0.949217i	$-0.398122\pi$
$79$	5.59283	0.629243	0.314621	+	0.949217i	$0.398122\pi$
$80$	39.8693	4.45752
$81$	1.00000	0.111111
$82$	19.4517	2.14808
$83$	1.90666	0.209283	0.104641	−	0.994510i	$-0.466631\pi$
$83$	1.90666	0.209283	0.104641	+	0.994510i	$0.466631\pi$
$84$	−18.6167	−2.03125
$85$	2.22447	0.241278
$86$	0.375860	0.0405300
$87$	−2.60586	−0.279377
$88$	−35.6089	−3.79592
$89$	7.21274	0.764548	0.382274	−	0.924049i	$-0.375141\pi$
$89$	7.21274	0.764548	0.382274	+	0.924049i	$0.375141\pi$
$90$	−10.1523	−1.07015
$91$	−9.79896	−1.02721
$92$	8.01162	0.835269
$93$	−7.99296	−0.828832
$94$	−5.48245	−0.565471
$95$	0.498611	0.0511564
$96$	11.8253	1.20692
$97$	−16.9128	−1.71724	−0.858620	−	0.512613i	$-0.828678\pi$
$97$	−16.9128	−1.71724	−0.858620	+	0.512613i	$0.828678\pi$
$98$	−19.3206	−1.95167
$99$	4.64549	0.466890
$100$	48.6841	4.86841
$101$	3.64850	0.363039	0.181520	−	0.983387i	$-0.441898\pi$
$101$	3.64850	0.363039	0.181520	+	0.983387i	$0.441898\pi$
$102$	1.51513	0.150021
$103$	−8.89782	−0.876728	−0.438364	−	0.898798i	$-0.644442\pi$
$103$	−8.89782	−0.876728	−0.438364	+	0.898798i	$0.644442\pi$
$104$	19.8300	1.94449
$105$	−14.6236	−1.42712
$106$	11.1491	1.08289
$107$	6.48131	0.626572	0.313286	−	0.949659i	$-0.398570\pi$
$107$	6.48131	0.626572	0.313286	+	0.949659i	$0.398570\pi$
$108$	−4.91495	−0.472942
$109$	18.9253	1.81271	0.906356	−	0.422515i	$-0.138852\pi$
$109$	18.9253	1.81271	0.906356	+	0.422515i	$0.138852\pi$
$110$	−47.1625	−4.49677
$111$	5.98633	0.568197
$112$	39.1158	3.69610
$113$	13.6291	1.28212	0.641058	−	0.767492i	$-0.278496\pi$
$113$	13.6291	1.28212	0.641058	+	0.767492i	$0.278496\pi$
$114$	0.339614	0.0318078
$115$	6.29320	0.586844
$116$	12.8077	1.18916
$117$	−2.58699	−0.239168
$118$	9.47564	0.872304
$119$	2.18243	0.200063
$120$	29.5935	2.70151
$121$	10.5806	0.961874
$122$	20.8519	1.88784
$123$	7.39713	0.666977
$124$	39.2850	3.52790
$125$	18.9381	1.69387
$126$	−9.96045	−0.887347
$127$	3.57493	0.317224	0.158612	−	0.987341i	$-0.449298\pi$
$127$	3.57493	0.317224	0.158612	+	0.987341i	$0.449298\pi$
$128$	−3.80927	−0.336695
$129$	0.142932	0.0125845
$130$	26.2640	2.30350
$131$	16.3315	1.42689	0.713444	−	0.700712i	$-0.247134\pi$
$131$	16.3315	1.42689	0.713444	+	0.700712i	$0.247134\pi$
$132$	−22.8324	−1.98730
$133$	0.489188	0.0424180
$134$	27.1864	2.34855
$135$	−3.86074	−0.332279
$136$	−4.41654	−0.378715
$137$	0.973697	0.0831886	0.0415943	−	0.999135i	$-0.486756\pi$
$137$	0.973697	0.0831886	0.0415943	+	0.999135i	$0.486756\pi$
$138$	4.28643	0.364885
$139$	−8.25044	−0.699793	−0.349897	−	0.936788i	$-0.613783\pi$
$139$	−8.25044	−0.699793	−0.349897	+	0.936788i	$0.613783\pi$
$140$	71.8744	6.07449
$141$	−2.08487	−0.175578
$142$	−15.9011	−1.33439
$143$	−12.0179	−1.00498
$144$	10.3269	0.860572
$145$	10.0605	0.835482
$146$	−8.35108	−0.691140
$147$	−7.34725	−0.605991
$148$	−29.4225	−2.41852
$149$	−8.21439	−0.672949	−0.336475	−	0.941693i	$-0.609235\pi$
$149$	−8.21439	−0.672949	−0.336475	+	0.941693i	$0.609235\pi$
$150$	26.0473	2.12675
$151$	−11.0544	−0.899592	−0.449796	−	0.893131i	$-0.648503\pi$
$151$	−11.0544	−0.899592	−0.449796	+	0.893131i	$0.648503\pi$
$152$	−0.989960	−0.0802963
$153$	0.576177	0.0465812
$154$	−46.2712	−3.72864
$155$	30.8587	2.47863
$156$	12.7150	1.01801
$157$	10.0195	0.799645	0.399822	−	0.916593i	$-0.369072\pi$
$157$	10.0195	0.799645	0.399822	+	0.916593i	$0.369072\pi$
$158$	−14.7071	−1.17003
$159$	4.23978	0.336237
$160$	−45.6545	−3.60930
$161$	6.17427	0.486600
$162$	−2.62963	−0.206603
$163$	−20.1649	−1.57944	−0.789718	−	0.613471i	$-0.789773\pi$
$163$	−20.1649	−1.57944	−0.789718	+	0.613471i	$0.789773\pi$
$164$	−36.3565	−2.83897
$165$	−17.9350	−1.39624
$166$	−5.01380	−0.389147
$167$	11.6087	0.898305	0.449153	−	0.893455i	$-0.351726\pi$
$167$	11.6087	0.898305	0.449153	+	0.893455i	$0.351726\pi$
$168$	29.0342	2.24004
$169$	−6.30746	−0.485189
$170$	−5.84953	−0.448639
$171$	0.129149	0.00987628
$172$	−0.702507	−0.0535656
$173$	17.6831	1.34442	0.672210	−	0.740360i	$-0.265345\pi$
$173$	17.6831	1.34442	0.672210	+	0.740360i	$0.265345\pi$
$174$	6.85244	0.519482
$175$	37.5191	2.83618
$176$	47.9734	3.61613
$177$	3.60341	0.270849
$178$	−18.9668	−1.42162
$179$	−6.55739	−0.490123	−0.245061	−	0.969508i	$-0.578808\pi$
$179$	−6.55739	−0.490123	−0.245061	+	0.969508i	$0.578808\pi$
$180$	18.9753	1.41434
$181$	6.15774	0.457701	0.228851	−	0.973462i	$-0.426503\pi$
$181$	6.15774	0.457701	0.228851	+	0.973462i	$0.426503\pi$
$182$	25.7676	1.91002
$183$	7.92961	0.586173
$184$	−12.4947	−0.921125
$185$	−23.1116	−1.69920
$186$	21.0185	1.54115
$187$	2.67663	0.195734
$188$	10.2471	0.747344
$189$	−3.78778	−0.275520
$190$	−1.31116	−0.0951217
$191$	23.5019	1.70054	0.850270	−	0.526346i	$-0.176438\pi$
$191$	23.5019	1.70054	0.850270	+	0.526346i	$0.176438\pi$
$192$	−10.4425	−0.753623
$193$	9.67911	0.696717	0.348359	−	0.937361i	$-0.386739\pi$
$193$	9.67911	0.696717	0.348359	+	0.937361i	$0.386739\pi$
$194$	44.4745	3.19309
$195$	9.98771	0.715235
$196$	36.1114	2.57939
$197$	21.5117	1.53264	0.766322	−	0.642457i	$-0.222085\pi$
$197$	21.5117	1.53264	0.766322	+	0.642457i	$0.222085\pi$
$198$	−12.2159	−0.868148
$199$	15.8183	1.12133	0.560664	−	0.828044i	$-0.310546\pi$
$199$	15.8183	1.12133	0.560664	+	0.828044i	$0.310546\pi$
$200$	−75.9266	−5.36882
$201$	10.3385	0.729222
$202$	−9.59420	−0.675046
$203$	9.87041	0.692767
$204$	−2.83189	−0.198272
$205$	−28.5584	−1.99460
$206$	23.3980	1.63021
$207$	1.63005	0.113296
$208$	−26.7155	−1.85239
$209$	0.599961	0.0415002
$210$	38.4547	2.65363
$211$	25.6446	1.76545	0.882724	−	0.469892i	$-0.155707\pi$
$211$	25.6446	1.76545	0.882724	+	0.469892i	$0.155707\pi$
$212$	−20.8383	−1.43118
$213$	−6.04688	−0.414326
$214$	−17.0434	−1.16507
$215$	−0.551825	−0.0376342
$216$	7.66525	0.521554
$217$	30.2756	2.05524
$218$	−49.7665	−3.37061
$219$	−3.17576	−0.214598
$220$	88.1499	5.94306
$221$	−1.49057	−0.100266
$222$	−15.7418	−1.05652
$223$	0.0115337	0.000772356 0	0.000386178	−	1.00000i	$-0.499877\pi$
$223$	0.0115337	0.000772356 0	0.000386178		1.00000i	$0.499877\pi$
$224$	−44.7917	−2.99277
$225$	9.90530	0.660353
$226$	−35.8394	−2.38400
$227$	−10.8274	−0.718641	−0.359320	−	0.933214i	$-0.616991\pi$
$227$	−10.8274	−0.718641	−0.359320	+	0.933214i	$0.616991\pi$
$228$	−0.634762	−0.0420381
$229$	−23.7966	−1.57252	−0.786262	−	0.617894i	$-0.787986\pi$
$229$	−23.7966	−1.57252	−0.786262	+	0.617894i	$0.787986\pi$
$230$	−16.5488	−1.09119
$231$	−17.5961	−1.15774
$232$	−19.9745	−1.31139
$233$	−12.1012	−0.792776	−0.396388	−	0.918083i	$-0.629736\pi$
$233$	−12.1012	−0.792776	−0.396388	+	0.918083i	$0.629736\pi$
$234$	6.80284	0.444716
$235$	8.04915	0.525069
$236$	−17.7106	−1.15286
$237$	−5.59283	−0.363293
$238$	−5.73899	−0.372003
$239$	8.04534	0.520410	0.260205	−	0.965553i	$-0.416210\pi$
$239$	8.04534	0.520410	0.260205	+	0.965553i	$0.416210\pi$
$240$	−39.8693	−2.57355
$241$	−4.05638	−0.261294	−0.130647	−	0.991429i	$-0.541705\pi$
$241$	−4.05638	−0.261294	−0.130647	+	0.991429i	$0.541705\pi$
$242$	−27.8231	−1.78854
$243$	−1.00000	−0.0641500
$244$	−38.9736	−2.49503
$245$	28.3658	1.81223
$246$	−19.4517	−1.24020
$247$	−0.334108	−0.0212588
$248$	−61.2681	−3.89053
$249$	−1.90666	−0.120829
$250$	−49.8002	−3.14964
$251$	5.73837	0.362202	0.181101	−	0.983464i	$-0.442034\pi$
$251$	5.73837	0.362202	0.181101	+	0.983464i	$0.442034\pi$
$252$	18.6167	1.17274
$253$	7.57239	0.476072
$254$	−9.40075	−0.589856
$255$	−2.22447	−0.139302
$256$	−10.8680	−0.679252
$257$	4.64666	0.289851	0.144925	−	0.989443i	$-0.453706\pi$
$257$	4.64666	0.289851	0.144925	+	0.989443i	$0.453706\pi$
$258$	−0.375860	−0.0234000
$259$	−22.6749	−1.40895
$260$	−49.0891	−3.04438
$261$	2.60586	0.161299
$262$	−42.9457	−2.65320
$263$	23.8114	1.46827	0.734136	−	0.679003i	$-0.237588\pi$
$263$	23.8114	1.46827	0.734136	+	0.679003i	$0.237588\pi$
$264$	35.6089	2.19157
$265$	−16.3687	−1.00552
$266$	−1.28638	−0.0788732
$267$	−7.21274	−0.441412
$268$	−50.8133	−3.10391
$269$	3.22155	0.196422	0.0982108	−	0.995166i	$-0.468688\pi$
$269$	3.22155	0.196422	0.0982108	+	0.995166i	$0.468688\pi$
$270$	10.1523	0.617850
$271$	17.6849	1.07428	0.537140	−	0.843493i	$-0.319505\pi$
$271$	17.6849	1.07428	0.537140	+	0.843493i	$0.319505\pi$
$272$	5.95010	0.360778
$273$	9.79896	0.593060
$274$	−2.56046	−0.154683
$275$	46.0150	2.77481
$276$	−8.01162	−0.482243
$277$	−14.0507	−0.844222	−0.422111	−	0.906544i	$-0.638711\pi$
$277$	−14.0507	−0.844222	−0.422111	+	0.906544i	$0.638711\pi$
$278$	21.6956	1.30122
$279$	7.99296	0.478526
$280$	−112.094	−6.69888
$281$	−9.72806	−0.580328	−0.290164	−	0.956977i	$-0.593710\pi$
$281$	−9.72806	−0.580328	−0.290164	+	0.956977i	$0.593710\pi$
$282$	5.48245	0.326475
$283$	7.28186	0.432862	0.216431	−	0.976298i	$-0.430558\pi$
$283$	7.28186	0.432862	0.216431	+	0.976298i	$0.430558\pi$
$284$	29.7201	1.76357
$285$	−0.498611	−0.0295352
$286$	31.6025	1.86870
$287$	−28.0187	−1.65389
$288$	−11.8253	−0.696814
$289$	−16.6680	−0.980472
$290$	−26.4555	−1.55352
$291$	16.9128	0.991449
$292$	15.6087	0.913431
$293$	21.4690	1.25423	0.627115	−	0.778927i	$-0.284236\pi$
$293$	21.4690	1.25423	0.627115	+	0.778927i	$0.284236\pi$
$294$	19.3206	1.12680
$295$	−13.9118	−0.809979
$296$	45.8867	2.66711
$297$	−4.64549	−0.269559
$298$	21.6008	1.25130
$299$	−4.21693	−0.243872
$300$	−48.6841	−2.81078
$301$	−0.541396	−0.0312056
$302$	29.0689	1.67273
$303$	−3.64850	−0.209601
$304$	1.33370	0.0764932
$305$	−30.6141	−1.75296
$306$	−1.51513	−0.0866144
$307$	−22.5390	−1.28637	−0.643183	−	0.765712i	$-0.722387\pi$
$307$	−22.5390	−1.28637	−0.643183	+	0.765712i	$0.722387\pi$
$308$	86.4840	4.92788
$309$	8.89782	0.506179
$310$	−81.1471	−4.60884
$311$	13.7757	0.781151	0.390575	−	0.920571i	$-0.372276\pi$
$311$	13.7757	0.781151	0.390575	+	0.920571i	$0.372276\pi$
$312$	−19.8300	−1.12265
$313$	5.24248	0.296322	0.148161	−	0.988963i	$-0.452665\pi$
$313$	5.24248	0.296322	0.148161	+	0.988963i	$0.452665\pi$
$314$	−26.3476	−1.48688
$315$	14.6236	0.823947
$316$	27.4885	1.54635
$317$	−3.34199	−0.187705	−0.0938525	−	0.995586i	$-0.529918\pi$
$317$	−3.34199	−0.187705	−0.0938525	+	0.995586i	$0.529918\pi$
$318$	−11.1491	−0.625208
$319$	12.1055	0.677777
$320$	40.3158	2.25372
$321$	−6.48131	−0.361752
$322$	−16.2360	−0.904799
$323$	0.0744128	0.00414044
$324$	4.91495	0.273053
$325$	−25.6250	−1.42142
$326$	53.0262	2.93685
$327$	−18.9253	−1.04657
$328$	56.7008	3.13078
$329$	7.89704	0.435378
$330$	47.1625	2.59621
$331$	−10.6605	−0.585952	−0.292976	−	0.956120i	$-0.594646\pi$
$331$	−10.6605	−0.585952	−0.292976	+	0.956120i	$0.594646\pi$
$332$	9.37113	0.514308
$333$	−5.98633	−0.328049
$334$	−30.5265	−1.67034
$335$	−39.9143	−2.18075
$336$	−39.1158	−2.13394
$337$	11.8350	0.644692	0.322346	−	0.946622i	$-0.395529\pi$
$337$	11.8350	0.644692	0.322346	+	0.946622i	$0.395529\pi$
$338$	16.5863	0.902175
$339$	−13.6291	−0.740230
$340$	10.9332	0.592934
$341$	37.1313	2.01077
$342$	−0.339614	−0.0183642
$343$	1.31532	0.0710204
$344$	1.09561	0.0590715
$345$	−6.29320	−0.338814
$346$	−46.5000	−2.49985
$347$	−10.3938	−0.557970	−0.278985	−	0.960295i	$-0.589998\pi$
$347$	−10.3938	−0.557970	−0.278985	+	0.960295i	$0.589998\pi$
$348$	−12.8077	−0.686563
$349$	11.3781	0.609054	0.304527	−	0.952504i	$-0.401502\pi$
$349$	11.3781	0.609054	0.304527	+	0.952504i	$0.401502\pi$
$350$	−98.6613	−5.27367
$351$	2.58699	0.138084
$352$	−54.9345	−2.92802
$353$	−34.4232	−1.83216	−0.916080	−	0.400996i	$-0.868664\pi$
$353$	−34.4232	−1.83216	−0.916080	+	0.400996i	$0.868664\pi$
$354$	−9.47564	−0.503625
$355$	23.3454	1.23905
$356$	35.4503	1.87886
$357$	−2.18243	−0.115507
$358$	17.2435	0.911348
$359$	37.2895	1.96807	0.984034	−	0.177983i	$-0.0569572\pi$
$359$	37.2895	1.96807	0.984034	+	0.177983i	$0.0569572\pi$
$360$	−29.5935	−1.55972
$361$	−18.9833	−0.999122
$362$	−16.1926	−0.851063
$363$	−10.5806	−0.555338
$364$	−48.1614	−2.52434
$365$	12.2608	0.641759
$366$	−20.8519	−1.08995
$367$	23.6383	1.23391	0.616954	−	0.786999i	$-0.288366\pi$
$367$	23.6383	1.23391	0.616954	+	0.786999i	$0.288366\pi$
$368$	16.8333	0.877497
$369$	−7.39713	−0.385079
$370$	60.7751	3.15955
$371$	−16.0594	−0.833760
$372$	−39.2850	−2.03683
$373$	−34.6712	−1.79521	−0.897604	−	0.440802i	$-0.854694\pi$
$373$	−34.6712	−1.79521	−0.897604	+	0.440802i	$0.854694\pi$
$374$	−7.03854	−0.363954
$375$	−18.9381	−0.977959
$376$	−15.9811	−0.824161
$377$	−6.74134	−0.347197
$378$	9.96045	0.512310
$379$	−13.2368	−0.679930	−0.339965	−	0.940438i	$-0.610415\pi$
$379$	−13.2368	−0.679930	−0.339965	+	0.940438i	$0.610415\pi$
$380$	2.45065	0.125716
$381$	−3.57493	−0.183149
$382$	−61.8014	−3.16203
$383$	25.3445	1.29504	0.647522	−	0.762046i	$-0.275805\pi$
$383$	25.3445	1.29504	0.647522	+	0.762046i	$0.275805\pi$
$384$	3.80927	0.194391
$385$	67.9339	3.46223
$386$	−25.4525	−1.29550
$387$	−0.142932	−0.00726567
$388$	−83.1259	−4.22008
$389$	−8.67039	−0.439606	−0.219803	−	0.975544i	$-0.570542\pi$
$389$	−8.67039	−0.439606	−0.219803	+	0.975544i	$0.570542\pi$
$390$	−26.2640	−1.32993
$391$	0.939198	0.0474973
$392$	−56.3185	−2.84451
$393$	−16.3315	−0.823814
$394$	−56.5678	−2.84984
$395$	21.5925	1.08643
$396$	22.8324	1.14737
$397$	−4.04569	−0.203047	−0.101524	−	0.994833i	$-0.532372\pi$
$397$	−4.04569	−0.203047	−0.101524	+	0.994833i	$0.532372\pi$
$398$	−41.5962	−2.08503
$399$	−0.489188	−0.0244900
$400$	102.291	5.11453
$401$	−32.4689	−1.62142	−0.810711	−	0.585447i	$-0.800919\pi$
$401$	−32.4689	−1.62142	−0.810711	+	0.585447i	$0.800919\pi$
$402$	−27.1864	−1.35594
$403$	−20.6778	−1.03003
$404$	17.9322	0.892160
$405$	3.86074	0.191842
$406$	−25.9555	−1.28815
$407$	−27.8094	−1.37846
$408$	4.41654	0.218651
$409$	30.7755	1.52175	0.760876	−	0.648898i	$-0.224770\pi$
$409$	30.7755	1.52175	0.760876	+	0.648898i	$0.224770\pi$
$410$	75.0980	3.70882
$411$	−0.973697	−0.0480289
$412$	−43.7324	−2.15454
$413$	−13.6489	−0.671620
$414$	−4.28643	−0.210667
$415$	7.36111	0.361342
$416$	30.5920	1.49990
$417$	8.25044	0.404026
$418$	−1.57768	−0.0771667
$419$	2.90879	0.142104	0.0710518	−	0.997473i	$-0.477364\pi$
$419$	2.90879	0.142104	0.0710518	+	0.997473i	$0.477364\pi$
$420$	−71.8744	−3.50711
$421$	30.5871	1.49072	0.745361	−	0.666661i	$-0.232277\pi$
$421$	30.5871	1.49072	0.745361	+	0.666661i	$0.232277\pi$
$422$	−67.4358	−3.28272
$423$	2.08487	0.101370
$424$	32.4990	1.57829
$425$	5.70721	0.276840
$426$	15.9011	0.770409
$427$	−30.0356	−1.45352
$428$	31.8553	1.53979
$429$	12.0179	0.580228
$430$	1.45110	0.0699780
$431$	−32.5854	−1.56958	−0.784791	−	0.619760i	$-0.787230\pi$
$431$	−32.5854	−1.56958	−0.784791	+	0.619760i	$0.787230\pi$
$432$	−10.3269	−0.496851
$433$	20.8329	1.00117	0.500583	−	0.865689i	$-0.333119\pi$
$433$	20.8329	1.00117	0.500583	+	0.865689i	$0.333119\pi$
$434$	−79.6135	−3.82157
$435$	−10.0605	−0.482366
$436$	93.0168	4.45470
$437$	0.210520	0.0100705
$438$	8.35108	0.399030
$439$	40.5447	1.93509	0.967546	−	0.252696i	$-0.0813174\pi$
$439$	40.5447	1.93509	0.967546	+	0.252696i	$0.0813174\pi$
$440$	−137.477	−6.55394
$441$	7.34725	0.349869
$442$	3.91964	0.186438
$443$	−15.8394	−0.752554	−0.376277	−	0.926507i	$-0.622796\pi$
$443$	−15.8394	−0.752554	−0.376277	+	0.926507i	$0.622796\pi$
$444$	29.4225	1.39633
$445$	27.8465	1.32005
$446$	−0.0303294	−0.00143614
$447$	8.21439	0.388527
$448$	39.5539	1.86874
$449$	14.0962	0.665239	0.332620	−	0.943061i	$-0.392068\pi$
$449$	14.0962	0.665239	0.332620	+	0.943061i	$0.392068\pi$
$450$	−26.0473	−1.22788
$451$	−34.3633	−1.61810
$452$	66.9863	3.15077
$453$	11.0544	0.519380
$454$	28.4721	1.33626
$455$	−37.8312	−1.77355
$456$	0.989960	0.0463591
$457$	5.51603	0.258029	0.129015	−	0.991643i	$-0.458819\pi$
$457$	5.51603	0.258029	0.129015	+	0.991643i	$0.458819\pi$
$458$	62.5762	2.92400
$459$	−0.576177	−0.0268937
$460$	30.9308	1.44215
$461$	−21.2489	−0.989661	−0.494831	−	0.868989i	$-0.664770\pi$
$461$	−21.2489	−0.989661	−0.494831	+	0.868989i	$0.664770\pi$
$462$	46.2712	2.15273
$463$	13.4349	0.624375	0.312187	−	0.950021i	$-0.398938\pi$
$463$	13.4349	0.624375	0.312187	+	0.950021i	$0.398938\pi$
$464$	26.9103	1.24928
$465$	−30.8587	−1.43104
$466$	31.8217	1.47411
$467$	13.8457	0.640702	0.320351	−	0.947299i	$-0.396199\pi$
$467$	13.8457	0.640702	0.320351	+	0.947299i	$0.396199\pi$
$468$	−12.7150	−0.587749
$469$	−39.1599	−1.80824
$470$	−21.1663	−0.976328
$471$	−10.0195	−0.461675
$472$	27.6211	1.27136
$473$	−0.663992	−0.0305304
$474$	14.7071	0.675519
$475$	1.27926	0.0586965
$476$	10.7265	0.491651
$477$	−4.23978	−0.194126
$478$	−21.1563	−0.967665
$479$	−19.0846	−0.871997	−0.435998	−	0.899947i	$-0.643605\pi$
$479$	−19.0846	−0.871997	−0.435998	+	0.899947i	$0.643605\pi$
$480$	45.6545	2.08383
$481$	15.4866	0.706128
$482$	10.6668	0.485858
$483$	−6.17427	−0.280939
$484$	52.0032	2.36378
$485$	−65.2961	−2.96494
$486$	2.62963	0.119282
$487$	−33.0028	−1.49550	−0.747750	−	0.663980i	$-0.768866\pi$
$487$	−33.0028	−1.49550	−0.747750	+	0.663980i	$0.768866\pi$
$488$	60.7824	2.75149
$489$	20.1649	0.911887
$490$	−74.5916	−3.36971
$491$	−20.0215	−0.903559	−0.451779	−	0.892130i	$-0.649211\pi$
$491$	−20.0215	−0.903559	−0.451779	+	0.892130i	$0.649211\pi$
$492$	36.3565	1.63908
$493$	1.50144	0.0676213
$494$	0.878580	0.0395292
$495$	17.9350	0.806120
$496$	82.5422	3.70625
$497$	22.9042	1.02740
$498$	5.01380	0.224674
$499$	−16.8208	−0.753000	−0.376500	−	0.926417i	$-0.622873\pi$
$499$	−16.8208	−0.753000	−0.376500	+	0.926417i	$0.622873\pi$
$500$	93.0798	4.16266
$501$	−11.6087	−0.518637
$502$	−15.0898	−0.673490
$503$	−17.7990	−0.793618	−0.396809	−	0.917901i	$-0.629882\pi$
$503$	−17.7990	−0.793618	−0.396809	+	0.917901i	$0.629882\pi$
$504$	−29.0342	−1.29329
$505$	14.0859	0.626814
$506$	−19.9126	−0.885222
$507$	6.30746	0.280124
$508$	17.5706	0.779571
$509$	−24.3396	−1.07884	−0.539418	−	0.842038i	$-0.681356\pi$
$509$	−24.3396	−1.07884	−0.539418	+	0.842038i	$0.681356\pi$
$510$	5.84953	0.259022
$511$	12.0291	0.532135
$512$	36.1974	1.59972
$513$	−0.129149	−0.00570207
$514$	−12.2190	−0.538957
$515$	−34.3522	−1.51374
$516$	0.702507	0.0309261
$517$	9.68527	0.425958
$518$	59.6265	2.61984
$519$	−17.6831	−0.776201
$520$	76.5583	3.35730
$521$	−29.4573	−1.29055	−0.645273	−	0.763952i	$-0.723257\pi$
$521$	−29.4573	−1.29055	−0.645273	+	0.763952i	$0.723257\pi$
$522$	−6.85244	−0.299923
$523$	−13.4348	−0.587465	−0.293732	−	0.955888i	$-0.594897\pi$
$523$	−13.4348	−0.587465	−0.293732	+	0.955888i	$0.594897\pi$
$524$	80.2685	3.50654
$525$	−37.5191	−1.63747
$526$	−62.6151	−2.73015
$527$	4.60537	0.200613
$528$	−47.9734	−2.08777
$529$	−20.3429	−0.884475
$530$	43.0436	1.86970
$531$	−3.60341	−0.156375
$532$	2.40434	0.104241
$533$	19.1363	0.828887
$534$	18.9668	0.820775
$535$	25.0226	1.08182
$536$	79.2472	3.42296
$537$	6.55739	0.282972
$538$	−8.47149	−0.365232
$539$	34.1316	1.47015
$540$	−18.9753	−0.816569
$541$	−9.66835	−0.415675	−0.207837	−	0.978163i	$-0.566642\pi$
$541$	−9.66835	−0.415675	−0.207837	+	0.978163i	$0.566642\pi$
$542$	−46.5047	−1.99755
$543$	−6.15774	−0.264254
$544$	−6.81348	−0.292126
$545$	73.0655	3.12978
$546$	−25.7676	−1.10275
$547$	−20.9466	−0.895610	−0.447805	−	0.894131i	$-0.647794\pi$
$547$	−20.9466	−0.895610	−0.447805	+	0.894131i	$0.647794\pi$
$548$	4.78568	0.204434
$549$	−7.92961	−0.338427
$550$	−121.002	−5.15956
$551$	0.336544	0.0143373
$552$	12.4947	0.531812
$553$	21.1844	0.900852
$554$	36.9480	1.56977
$555$	23.1116	0.981035
$556$	−40.5505	−1.71973
$557$	6.45175	0.273369	0.136685	−	0.990615i	$-0.456355\pi$
$557$	6.45175	0.273369	0.136685	+	0.990615i	$0.456355\pi$
$558$	−21.0185	−0.889786
$559$	0.369766	0.0156394
$560$	151.016	6.38159
$561$	−2.67663	−0.113007
$562$	25.5812	1.07908
$563$	−22.2290	−0.936842	−0.468421	−	0.883505i	$-0.655177\pi$
$563$	−22.2290	−0.936842	−0.468421	+	0.883505i	$0.655177\pi$
$564$	−10.2471	−0.431479
$565$	52.6183	2.21367
$566$	−19.1486	−0.804875
$567$	3.78778	0.159072
$568$	−46.3509	−1.94484
$569$	24.6832	1.03477	0.517386	−	0.855752i	$-0.326905\pi$
$569$	24.6832	1.03477	0.517386	+	0.855752i	$0.326905\pi$
$570$	1.31116	0.0549185
$571$	10.4061	0.435481	0.217740	−	0.976007i	$-0.430131\pi$
$571$	10.4061	0.435481	0.217740	+	0.976007i	$0.430131\pi$
$572$	−59.0673	−2.46973
$573$	−23.5019	−0.981808
$574$	73.6787	3.07529
$575$	16.1461	0.673341
$576$	10.4425	0.435104
$577$	−36.5264	−1.52061	−0.760306	−	0.649565i	$-0.774951\pi$
$577$	−36.5264	−1.52061	−0.760306	+	0.649565i	$0.774951\pi$
$578$	43.8307	1.82312
$579$	−9.67911	−0.402250
$580$	49.4471	2.05318
$581$	7.22199	0.299619
$582$	−44.4745	−1.84353
$583$	−19.6959	−0.815720
$584$	−24.3430	−1.00732
$585$	−9.98771	−0.412941
$586$	−56.4554	−2.33215
$587$	−32.2761	−1.33218	−0.666089	−	0.745872i	$-0.732033\pi$
$587$	−32.2761	−1.33218	−0.666089	+	0.745872i	$0.732033\pi$
$588$	−36.1114	−1.48921
$589$	1.03228	0.0425345
$590$	36.5830	1.50610
$591$	−21.5117	−0.884872
$592$	−61.8200	−2.54079
$593$	35.2156	1.44613	0.723065	−	0.690780i	$-0.242732\pi$
$593$	35.2156	1.44613	0.723065	+	0.690780i	$0.242732\pi$
$594$	12.2159	0.501226
$595$	8.42580	0.345424
$596$	−40.3734	−1.65376
$597$	−15.8183	−0.647399
$598$	11.0890	0.453462
$599$	−13.8158	−0.564499	−0.282250	−	0.959341i	$-0.591081\pi$
$599$	−13.8158	−0.564499	−0.282250	+	0.959341i	$0.591081\pi$
$600$	75.9266	3.09969
$601$	25.0090	1.02014	0.510069	−	0.860134i	$-0.329620\pi$
$601$	25.0090	1.02014	0.510069	+	0.860134i	$0.329620\pi$
$602$	1.42367	0.0580245
$603$	−10.3385	−0.421016
$604$	−54.3317	−2.21073
$605$	40.8490	1.66075
$606$	9.59420	0.389738
$607$	−13.5046	−0.548136	−0.274068	−	0.961710i	$-0.588369\pi$
$607$	−13.5046	−0.548136	−0.274068	+	0.961710i	$0.588369\pi$
$608$	−1.52723	−0.0619373
$609$	−9.87041	−0.399969
$610$	80.5038	3.25951
$611$	−5.39356	−0.218200
$612$	2.83189	0.114472
$613$	23.6948	0.957022	0.478511	−	0.878082i	$-0.341177\pi$
$613$	23.6948	0.957022	0.478511	+	0.878082i	$0.341177\pi$
$614$	59.2691	2.39191
$615$	28.5584	1.15158
$616$	−134.878	−5.43441
$617$	−1.04216	−0.0419557	−0.0209779	−	0.999780i	$-0.506678\pi$
$617$	−1.04216	−0.0419557	−0.0209779	+	0.999780i	$0.506678\pi$
$618$	−23.3980	−0.941204
$619$	−1.07569	−0.0432355	−0.0216177	−	0.999766i	$-0.506882\pi$
$619$	−1.07569	−0.0432355	−0.0216177	+	0.999766i	$0.506882\pi$
$620$	151.669	6.09118
$621$	−1.63005	−0.0654117
$622$	−36.2251	−1.45249
$623$	27.3202	1.09456
$624$	26.7155	1.06948
$625$	23.5885	0.943540
$626$	−13.7858	−0.550990
$627$	−0.599961	−0.0239601
$628$	49.2455	1.96511
$629$	−3.44919	−0.137528
$630$	−38.4547	−1.53207
$631$	9.26239	0.368730	0.184365	−	0.982858i	$-0.440977\pi$
$631$	9.26239	0.368730	0.184365	+	0.982858i	$0.440977\pi$
$632$	−42.8704	−1.70529
$633$	−25.6446	−1.01928
$634$	8.78821	0.349024
$635$	13.8019	0.547711
$636$	20.8383	0.826294
$637$	−19.0073	−0.753097
$638$	−31.8330	−1.26028
$639$	6.04688	0.239211
$640$	−14.7066	−0.581329
$641$	4.38776	0.173306	0.0866530	−	0.996239i	$-0.472383\pi$
$641$	4.38776	0.173306	0.0866530	+	0.996239i	$0.472383\pi$
$642$	17.0434	0.672651
$643$	−38.0028	−1.49869	−0.749343	−	0.662182i	$-0.769630\pi$
$643$	−38.0028	−1.49869	−0.749343	+	0.662182i	$0.769630\pi$
$644$	30.3462	1.19581
$645$	0.551825	0.0217281
$646$	−0.195678	−0.00769885
$647$	−28.6177	−1.12508	−0.562539	−	0.826771i	$-0.690175\pi$
$647$	−28.6177	−1.12508	−0.562539	+	0.826771i	$0.690175\pi$
$648$	−7.66525	−0.301119
$649$	−16.7396	−0.657088
$650$	67.3842	2.64302
$651$	−30.2756	−1.18659
$652$	−99.1094	−3.88143
$653$	27.2474	1.06627	0.533137	−	0.846029i	$-0.321013\pi$
$653$	27.2474	1.06627	0.533137	+	0.846029i	$0.321013\pi$
$654$	49.7665	1.94602
$655$	63.0516	2.46363
$656$	−76.3891	−2.98249
$657$	3.17576	0.123898
$658$	−20.7663	−0.809554
$659$	24.9922	0.973558	0.486779	−	0.873525i	$-0.338172\pi$
$659$	24.9922	0.973558	0.486779	+	0.873525i	$0.338172\pi$
$660$	−88.1499	−3.43123
$661$	29.2137	1.13628	0.568141	−	0.822931i	$-0.307663\pi$
$661$	29.2137	1.13628	0.568141	+	0.822931i	$0.307663\pi$
$662$	28.0331	1.08954
$663$	1.49057	0.0578889
$664$	−14.6150	−0.567172
$665$	1.88863	0.0732378
$666$	15.7418	0.609983
$667$	4.24768	0.164471
$668$	57.0560	2.20756
$669$	−0.0115337	−0.000445920 0
$670$	104.960	4.05495
$671$	−36.8369	−1.42207
$672$	44.7917	1.72788
$673$	46.2479	1.78273	0.891364	−	0.453289i	$-0.149749\pi$
$673$	46.2479	1.78273	0.891364	+	0.453289i	$0.149749\pi$
$674$	−31.1216	−1.19876
$675$	−9.90530	−0.381255
$676$	−31.0009	−1.19234
$677$	−29.5930	−1.13735	−0.568676	−	0.822562i	$-0.692544\pi$
$677$	−29.5930	−1.13735	−0.568676	+	0.822562i	$0.692544\pi$
$678$	35.8394	1.37641
$679$	−64.0621	−2.45848
$680$	−17.0511	−0.653881
$681$	10.8274	0.414907
$682$	−97.6415	−3.73889
$683$	−5.40396	−0.206777	−0.103388	−	0.994641i	$-0.532968\pi$
$683$	−5.40396	−0.206777	−0.103388	+	0.994641i	$0.532968\pi$
$684$	0.634762	0.0242707
$685$	3.75919	0.143631
$686$	−3.45879	−0.132057
$687$	23.7966	0.907897
$688$	−1.47604	−0.0562736
$689$	10.9683	0.417859
$690$	16.5488	0.630001
$691$	22.1122	0.841187	0.420594	−	0.907249i	$-0.361822\pi$
$691$	22.1122	0.841187	0.420594	+	0.907249i	$0.361822\pi$
$692$	86.9116	3.30388
$693$	17.5961	0.668420
$694$	27.3319	1.03751
$695$	−31.8528	−1.20825
$696$	19.9745	0.757133
$697$	−4.26206	−0.161437
$698$	−29.9201	−1.13249
$699$	12.1012	0.457709
$700$	184.404	6.96983
$701$	−11.2559	−0.425130	−0.212565	−	0.977147i	$-0.568182\pi$
$701$	−11.2559	−0.425130	−0.212565	+	0.977147i	$0.568182\pi$
$702$	−6.80284	−0.256757
$703$	−0.773129	−0.0291591
$704$	48.5106	1.82831
$705$	−8.04915	−0.303149
$706$	90.5202	3.40677
$707$	13.8197	0.519743
$708$	17.7106	0.665606
$709$	7.32842	0.275225	0.137612	−	0.990486i	$-0.456057\pi$
$709$	7.32842	0.275225	0.137612	+	0.990486i	$0.456057\pi$
$710$	−61.3899	−2.30392
$711$	5.59283	0.209748
$712$	−55.2874	−2.07198
$713$	13.0289	0.487937
$714$	5.73899	0.214776
$715$	−46.3978	−1.73518
$716$	−32.2293	−1.20446
$717$	−8.04534	−0.300459
$718$	−98.0577	−3.65948
$719$	−6.68232	−0.249209	−0.124604	−	0.992207i	$-0.539766\pi$
$719$	−6.68232	−0.249209	−0.124604	+	0.992207i	$0.539766\pi$
$720$	39.8693	1.48584
$721$	−33.7030	−1.25516
$722$	49.9191	1.85780
$723$	4.05638	0.150858
$724$	30.2650	1.12479
$725$	25.8118	0.958626
$726$	27.8231	1.03261
$727$	−36.5598	−1.35593	−0.677964	−	0.735095i	$-0.737137\pi$
$727$	−36.5598	−1.35593	−0.677964	+	0.735095i	$0.737137\pi$
$728$	75.1115	2.78382
$729$	1.00000	0.0370370
$730$	−32.2413	−1.19330
$731$	−0.0823545	−0.00304599
$732$	38.9736	1.44051
$733$	−48.5358	−1.79271	−0.896356	−	0.443335i	$-0.853795\pi$
$733$	−48.5358	−1.79271	−0.896356	+	0.443335i	$0.853795\pi$
$734$	−62.1600	−2.29437
$735$	−28.3658	−1.04629
$736$	−19.2759	−0.710518
$737$	−48.0274	−1.76911
$738$	19.4517	0.716027
$739$	−46.8917	−1.72494	−0.862470	−	0.506108i	$-0.831084\pi$
$739$	−46.8917	−1.72494	−0.862470	+	0.506108i	$0.831084\pi$
$740$	−113.593	−4.17575
$741$	0.334108	0.0122738
$742$	42.2302	1.55032
$743$	21.7509	0.797963	0.398982	−	0.916959i	$-0.369364\pi$
$743$	21.7509	0.797963	0.398982	+	0.916959i	$0.369364\pi$
$744$	61.2681	2.24620
$745$	−31.7136	−1.16190
$746$	91.1725	3.33806
$747$	1.90666	0.0697609
$748$	13.1555	0.481013
$749$	24.5498	0.897029
$750$	49.8002	1.81844
$751$	12.2920	0.448540	0.224270	−	0.974527i	$-0.428000\pi$
$751$	12.2920	0.448540	0.224270	+	0.974527i	$0.428000\pi$
$752$	21.5302	0.785126
$753$	−5.73837	−0.209118
$754$	17.7272	0.645588
$755$	−42.6780	−1.55321
$756$	−18.6167	−0.677085
$757$	23.2431	0.844786	0.422393	−	0.906413i	$-0.361190\pi$
$757$	23.2431	0.844786	0.422393	+	0.906413i	$0.361190\pi$
$758$	34.8080	1.26428
$759$	−7.57239	−0.274860
$760$	−3.82198	−0.138638
$761$	−16.7130	−0.605845	−0.302923	−	0.953015i	$-0.597962\pi$
$761$	−16.7130	−0.605845	−0.302923	+	0.953015i	$0.597962\pi$
$762$	9.40075	0.340553
$763$	71.6847	2.59516
$764$	115.511	4.17904
$765$	2.22447	0.0804259
$766$	−66.6467	−2.40804
$767$	9.32201	0.336598
$768$	10.8680	0.392166
$769$	44.9865	1.62226	0.811128	−	0.584869i	$-0.198854\pi$
$769$	44.9865	1.62226	0.811128	+	0.584869i	$0.198854\pi$
$770$	−178.641	−6.43778
$771$	−4.64666	−0.167345
$772$	47.5724	1.71217
$773$	4.81845	0.173307	0.0866537	−	0.996238i	$-0.472383\pi$
$773$	4.81845	0.173307	0.0866537	+	0.996238i	$0.472383\pi$
$774$	0.375860	0.0135100
$775$	79.1727	2.84397
$776$	129.641	4.65385
$777$	22.6749	0.813457
$778$	22.7999	0.817417
$779$	−0.955332	−0.0342283
$780$	49.0891	1.75767
$781$	28.0908	1.00517
$782$	−2.46974	−0.0883179
$783$	−2.60586	−0.0931257
$784$	75.8740	2.70979
$785$	38.6828	1.38065
$786$	42.9457	1.53182
$787$	−34.8029	−1.24059	−0.620295	−	0.784369i	$-0.712987\pi$
$787$	−34.8029	−1.24059	−0.620295	+	0.784369i	$0.712987\pi$
$788$	105.729	3.76644
$789$	−23.8114	−0.847707
$790$	−56.7802	−2.02015
$791$	51.6239	1.83554
$792$	−35.6089	−1.26531
$793$	20.5138	0.728468
$794$	10.6387	0.377552
$795$	16.3687	0.580538
$796$	77.7460	2.75564
$797$	37.1888	1.31730	0.658648	−	0.752451i	$-0.271129\pi$
$797$	37.1888	1.31730	0.658648	+	0.752451i	$0.271129\pi$
$798$	1.28638	0.0455375
$799$	1.20126	0.0424974
$800$	−117.133	−4.14129
$801$	7.21274	0.254849
$802$	85.3813	3.01492
$803$	14.7530	0.520621
$804$	50.8133	1.79205
$805$	23.8372	0.840152
$806$	54.3748	1.91527
$807$	−3.22155	−0.113404
$808$	−27.9666	−0.983863
$809$	49.3153	1.73383	0.866916	−	0.498454i	$-0.166099\pi$
$809$	49.3153	1.73383	0.866916	+	0.498454i	$0.166099\pi$
$810$	−10.1523	−0.356716
$811$	41.9990	1.47479	0.737393	−	0.675464i	$-0.236057\pi$
$811$	41.9990	1.47479	0.737393	+	0.675464i	$0.236057\pi$
$812$	48.5126	1.70246
$813$	−17.6849	−0.620236
$814$	73.1286	2.56315
$815$	−77.8513	−2.72701
$816$	−5.95010	−0.208295
$817$	−0.0184596	−0.000645820 0
$818$	−80.9282	−2.82959
$819$	−9.79896	−0.342403
$820$	−140.363	−4.90169
$821$	11.7064	0.408557	0.204279	−	0.978913i	$-0.434515\pi$
$821$	11.7064	0.408557	0.204279	+	0.978913i	$0.434515\pi$
$822$	2.56046	0.0893064
$823$	28.3093	0.986801	0.493401	−	0.869802i	$-0.335754\pi$
$823$	28.3093	0.986801	0.493401	+	0.869802i	$0.335754\pi$
$824$	68.2040	2.37600
$825$	−46.0150	−1.60204
$826$	35.8916	1.24883
$827$	−33.5081	−1.16519	−0.582595	−	0.812763i	$-0.697963\pi$
$827$	−33.5081	−1.16519	−0.582595	+	0.812763i	$0.697963\pi$
$828$	8.01162	0.278423
$829$	41.8572	1.45376	0.726880	−	0.686765i	$-0.240970\pi$
$829$	41.8572	1.45376	0.726880	+	0.686765i	$0.240970\pi$
$830$	−19.3570	−0.671891
$831$	14.0507	0.487412
$832$	−27.0147	−0.936566
$833$	4.23332	0.146676
$834$	−21.6956	−0.751257
$835$	44.8180	1.55099
$836$	2.94878	0.101986
$837$	−7.99296	−0.276277
$838$	−7.64903	−0.264231
$839$	−48.1781	−1.66329	−0.831646	−	0.555306i	$-0.812601\pi$
$839$	−48.1781	−1.66329	−0.831646	+	0.555306i	$0.812601\pi$
$840$	112.094	3.86760
$841$	−22.2095	−0.765845
$842$	−80.4327	−2.77189
$843$	9.72806	0.335052
$844$	126.042	4.33855
$845$	−24.3514	−0.837715
$846$	−5.48245	−0.188490
$847$	40.0770	1.37706
$848$	−43.7837	−1.50354
$849$	−7.28186	−0.249913
$850$	−15.0079	−0.514765
$851$	−9.75802	−0.334501
$852$	−29.7201	−1.01820
$853$	6.51997	0.223240	0.111620	−	0.993751i	$-0.464396\pi$
$853$	6.51997	0.223240	0.111620	+	0.993751i	$0.464396\pi$
$854$	78.9824	2.70272
$855$	0.498611	0.0170521
$856$	−49.6809	−1.69806
$857$	5.47781	0.187119	0.0935593	−	0.995614i	$-0.470176\pi$
$857$	5.47781	0.187119	0.0935593	+	0.995614i	$0.470176\pi$
$858$	−31.6025	−1.07889
$859$	9.31925	0.317969	0.158984	−	0.987281i	$-0.449178\pi$
$859$	9.31925	0.317969	0.158984	+	0.987281i	$0.449178\pi$
$860$	−2.71219	−0.0924850
$861$	28.0187	0.954874
$862$	85.6875	2.91853
$863$	20.4304	0.695458	0.347729	−	0.937595i	$-0.386953\pi$
$863$	20.4304	0.695458	0.347729	+	0.937595i	$0.386953\pi$
$864$	11.8253	0.402306
$865$	68.2698	2.32124
$866$	−54.7828	−1.86160
$867$	16.6680	0.566076
$868$	148.803	5.05070
$869$	25.9815	0.881361
$870$	26.4555	0.896925
$871$	26.7457	0.906242
$872$	−145.067	−4.91259
$873$	−16.9128	−0.572413
$874$	−0.553588	−0.0187254
$875$	71.7332	2.42503
$876$	−15.6087	−0.527370
$877$	−6.98390	−0.235830	−0.117915	−	0.993024i	$-0.537621\pi$
$877$	−6.98390	−0.235830	−0.117915	+	0.993024i	$0.537621\pi$
$878$	−106.617	−3.59817
$879$	−21.4690	−0.724130
$880$	185.213	6.24352
$881$	18.4148	0.620409	0.310205	−	0.950670i	$-0.399602\pi$
$881$	18.4148	0.620409	0.310205	+	0.950670i	$0.399602\pi$
$882$	−19.3206	−0.650557
$883$	−50.2857	−1.69225	−0.846124	−	0.532986i	$-0.821070\pi$
$883$	−50.2857	−1.69225	−0.846124	+	0.532986i	$0.821070\pi$
$884$	−7.32607	−0.246403
$885$	13.9118	0.467641
$886$	41.6518	1.39932
$887$	−21.0630	−0.707227	−0.353613	−	0.935392i	$-0.615047\pi$
$887$	−21.0630	−0.707227	−0.353613	+	0.935392i	$0.615047\pi$
$888$	−45.8867	−1.53986
$889$	13.5410	0.454152
$890$	−73.2260	−2.45454
$891$	4.64549	0.155630
$892$	0.0566877	0.00189805
$893$	0.269260	0.00901043
$894$	−21.6008	−0.722439
$895$	−25.3164	−0.846233
$896$	−14.4287	−0.482028
$897$	4.21693	0.140799
$898$	−37.0677	−1.23696
$899$	20.8285	0.694670
$900$	48.6841	1.62280
$901$	−2.44287	−0.0813837
$902$	90.3628	3.00875
$903$	0.541396	0.0180165
$904$	−104.470	−3.47463
$905$	23.7734	0.790256
$906$	−29.0689	−0.965750
$907$	−53.2585	−1.76842	−0.884210	−	0.467089i	$-0.845303\pi$
$907$	−53.2585	−1.76842	−0.884210	+	0.467089i	$0.845303\pi$
$908$	−53.2162	−1.76604
$909$	3.64850	0.121013
$910$	99.4821	3.29780
$911$	−30.6703	−1.01615	−0.508077	−	0.861312i	$-0.669643\pi$
$911$	−30.6703	−1.01615	−0.508077	+	0.861312i	$0.669643\pi$
$912$	−1.33370	−0.0441634
$913$	8.85736	0.293136
$914$	−14.5051	−0.479787
$915$	30.6141	1.01207
$916$	−116.959	−3.86444
$917$	61.8600	2.04280
$918$	1.51513	0.0500069
$919$	−24.5746	−0.810642	−0.405321	−	0.914174i	$-0.632840\pi$
$919$	−24.5746	−0.810642	−0.405321	+	0.914174i	$0.632840\pi$
$920$	−48.2389	−1.59039
$921$	22.5390	0.742684
$922$	55.8768	1.84020
$923$	−15.6433	−0.514904
$924$	−86.4840	−2.84511
$925$	−59.2964	−1.94965
$926$	−35.3289	−1.16098
$927$	−8.89782	−0.292243
$928$	−30.8151	−1.01156
$929$	−3.31213	−0.108667	−0.0543337	−	0.998523i	$-0.517303\pi$
$929$	−3.31213	−0.108667	−0.0543337	+	0.998523i	$0.517303\pi$
$930$	81.1471	2.66092
$931$	0.948891	0.0310986
$932$	−59.4768	−1.94823
$933$	−13.7757	−0.450998
$934$	−36.4091	−1.19134
$935$	10.3338	0.337950
$936$	19.8300	0.648162
$937$	−32.9296	−1.07576	−0.537882	−	0.843020i	$-0.680775\pi$
$937$	−32.9296	−1.07576	−0.537882	+	0.843020i	$0.680775\pi$
$938$	102.976	3.36229
$939$	−5.24248	−0.171082
$940$	39.5612	1.29034
$941$	−10.1927	−0.332273	−0.166137	−	0.986103i	$-0.553129\pi$
$941$	−10.1927	−0.332273	−0.166137	+	0.986103i	$0.553129\pi$
$942$	26.3476	0.858452
$943$	−12.0577	−0.392652
$944$	−37.2119	−1.21115
$945$	−14.6236	−0.475706
$946$	1.74605	0.0567691
$947$	21.8576	0.710276	0.355138	−	0.934814i	$-0.384434\pi$
$947$	21.8576	0.710276	0.355138	+	0.934814i	$0.384434\pi$
$948$	−27.4885	−0.892785
$949$	−8.21568	−0.266692
$950$	−3.36398	−0.109142
$951$	3.34199	0.108372
$952$	−16.7289	−0.542186
$953$	17.4662	0.565787	0.282893	−	0.959151i	$-0.408706\pi$
$953$	17.4662	0.565787	0.282893	+	0.959151i	$0.408706\pi$
$954$	11.1491	0.360964
$955$	90.7348	2.93611
$956$	39.5425	1.27890
$957$	−12.1055	−0.391315
$958$	50.1854	1.62142
$959$	3.68815	0.119096
$960$	−40.3158	−1.30119
$961$	32.8875	1.06089
$962$	−40.7240	−1.31300
$963$	6.48131	0.208857
$964$	−19.9369	−0.642124
$965$	37.3685	1.20293
$966$	16.2360	0.522386
$967$	−26.6239	−0.856166	−0.428083	−	0.903739i	$-0.640811\pi$
$967$	−26.6239	−0.856166	−0.428083	+	0.903739i	$0.640811\pi$
$968$	−81.1030	−2.60675
$969$	−0.0744128	−0.00239048
$970$	171.705	5.51310
$971$	19.4030	0.622673	0.311336	−	0.950300i	$-0.399223\pi$
$971$	19.4030	0.622673	0.311336	+	0.950300i	$0.399223\pi$
$972$	−4.91495	−0.157647
$973$	−31.2508	−1.00186
$974$	86.7852	2.78078
$975$	25.6250	0.820656
$976$	−81.8879	−2.62117
$977$	−24.5701	−0.786068	−0.393034	−	0.919524i	$-0.628574\pi$
$977$	−24.5701	−0.786068	−0.393034	+	0.919524i	$0.628574\pi$
$978$	−53.0262	−1.69559
$979$	33.5067	1.07088
$980$	139.417	4.45350
$981$	18.9253	0.604237
$982$	52.6492	1.68010
$983$	22.2552	0.709832	0.354916	−	0.934898i	$-0.384510\pi$
$983$	22.2552	0.709832	0.354916	+	0.934898i	$0.384510\pi$
$984$	−56.7008	−1.80756
$985$	83.0510	2.64622
$986$	−3.94822	−0.125737
$987$	−7.89704	−0.251365
$988$	−1.64213	−0.0522430
$989$	−0.232987	−0.00740856
$990$	−47.1625	−1.49892
$991$	−1.69419	−0.0538178	−0.0269089	−	0.999638i	$-0.508566\pi$
$991$	−1.69419	−0.0538178	−0.0269089	+	0.999638i	$0.508566\pi$
$992$	−94.5194	−3.00099
$993$	10.6605	0.338300
$994$	−60.2297	−1.91037
$995$	61.0702	1.93606
$996$	−9.37113	−0.296936
$997$	−11.2538	−0.356410	−0.178205	−	0.983993i	$-0.557029\pi$
$997$	−11.2538	−0.356410	−0.178205	+	0.983993i	$0.557029\pi$
$998$	44.2324	1.40015
$999$	5.98633	0.189399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.5	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.5	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91495 q^{4} +3.86074 q^{5} +2.62963 q^{6} +3.78778 q^{7} -7.66525 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91495 q^{4} +3.86074 q^{5} +2.62963 q^{6} +3.78778 q^{7} -7.66525 q^{8} +1.00000 q^{9} -10.1523 q^{10} +4.64549 q^{11} -4.91495 q^{12} -2.58699 q^{13} -9.96045 q^{14} -3.86074 q^{15} +10.3269 q^{16} +0.576177 q^{17} -2.62963 q^{18} +0.129149 q^{19} +18.9753 q^{20} -3.78778 q^{21} -12.2159 q^{22} +1.63005 q^{23} +7.66525 q^{24} +9.90530 q^{25} +6.80284 q^{26} -1.00000 q^{27} +18.6167 q^{28} +2.60586 q^{29} +10.1523 q^{30} +7.99296 q^{31} -11.8253 q^{32} -4.64549 q^{33} -1.51513 q^{34} +14.6236 q^{35} +4.91495 q^{36} -5.98633 q^{37} -0.339614 q^{38} +2.58699 q^{39} -29.5935 q^{40} -7.39713 q^{41} +9.96045 q^{42} -0.142932 q^{43} +22.8324 q^{44} +3.86074 q^{45} -4.28643 q^{46} +2.08487 q^{47} -10.3269 q^{48} +7.34725 q^{49} -26.0473 q^{50} -0.576177 q^{51} -12.7150 q^{52} -4.23978 q^{53} +2.62963 q^{54} +17.9350 q^{55} -29.0342 q^{56} -0.129149 q^{57} -6.85244 q^{58} -3.60341 q^{59} -18.9753 q^{60} -7.92961 q^{61} -21.0185 q^{62} +3.78778 q^{63} +10.4425 q^{64} -9.98771 q^{65} +12.2159 q^{66} -10.3385 q^{67} +2.83189 q^{68} -1.63005 q^{69} -38.4547 q^{70} +6.04688 q^{71} -7.66525 q^{72} +3.17576 q^{73} +15.7418 q^{74} -9.90530 q^{75} +0.634762 q^{76} +17.5961 q^{77} -6.80284 q^{78} +5.59283 q^{79} +39.8693 q^{80} +1.00000 q^{81} +19.4517 q^{82} +1.90666 q^{83} -18.6167 q^{84} +2.22447 q^{85} +0.375860 q^{86} -2.60586 q^{87} -35.6089 q^{88} +7.21274 q^{89} -10.1523 q^{90} -9.79896 q^{91} +8.01162 q^{92} -7.99296 q^{93} -5.48245 q^{94} +0.498611 q^{95} +11.8253 q^{96} -16.9128 q^{97} -19.3206 q^{98} +4.64549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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