LMFDB - Embedded newform 8026.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.83728 q^{3} +1.00000 q^{4} +3.92961 q^{5} -2.83728 q^{6} +4.49024 q^{7} +1.00000 q^{8} +5.05014 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.83728 q^{3} +1.00000 q^{4} +3.92961 q^{5} -2.83728 q^{6} +4.49024 q^{7} +1.00000 q^{8} +5.05014 q^{9} +3.92961 q^{10} -1.54058 q^{11} -2.83728 q^{12} +5.71071 q^{13} +4.49024 q^{14} -11.1494 q^{15} +1.00000 q^{16} -0.355432 q^{17} +5.05014 q^{18} +2.18624 q^{19} +3.92961 q^{20} -12.7401 q^{21} -1.54058 q^{22} +8.01724 q^{23} -2.83728 q^{24} +10.4418 q^{25} +5.71071 q^{26} -5.81682 q^{27} +4.49024 q^{28} +3.84618 q^{29} -11.1494 q^{30} -7.71805 q^{31} +1.00000 q^{32} +4.37105 q^{33} -0.355432 q^{34} +17.6449 q^{35} +5.05014 q^{36} -7.10244 q^{37} +2.18624 q^{38} -16.2029 q^{39} +3.92961 q^{40} +6.91781 q^{41} -12.7401 q^{42} -5.09687 q^{43} -1.54058 q^{44} +19.8451 q^{45} +8.01724 q^{46} -11.0728 q^{47} -2.83728 q^{48} +13.1623 q^{49} +10.4418 q^{50} +1.00846 q^{51} +5.71071 q^{52} +11.5101 q^{53} -5.81682 q^{54} -6.05387 q^{55} +4.49024 q^{56} -6.20298 q^{57} +3.84618 q^{58} +6.09046 q^{59} -11.1494 q^{60} -8.45252 q^{61} -7.71805 q^{62} +22.6764 q^{63} +1.00000 q^{64} +22.4409 q^{65} +4.37105 q^{66} -0.980042 q^{67} -0.355432 q^{68} -22.7471 q^{69} +17.6449 q^{70} -15.0132 q^{71} +5.05014 q^{72} +12.9574 q^{73} -7.10244 q^{74} -29.6264 q^{75} +2.18624 q^{76} -6.91757 q^{77} -16.2029 q^{78} +11.3784 q^{79} +3.92961 q^{80} +1.35351 q^{81} +6.91781 q^{82} +10.8204 q^{83} -12.7401 q^{84} -1.39671 q^{85} -5.09687 q^{86} -10.9127 q^{87} -1.54058 q^{88} -7.68470 q^{89} +19.8451 q^{90} +25.6425 q^{91} +8.01724 q^{92} +21.8983 q^{93} -11.0728 q^{94} +8.59108 q^{95} -2.83728 q^{96} +14.6917 q^{97} +13.1623 q^{98} -7.78014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−2.83728	−1.63810	−0.819051	−	0.573720i	$-0.805500\pi$
$3$	−2.83728	−1.63810	−0.819051	+	0.573720i	$0.805500\pi$
$4$	1.00000	0.500000
$5$	3.92961	1.75737	0.878687	−	0.477398i	$-0.158420\pi$
$5$	3.92961	1.75737	0.878687	+	0.477398i	$0.158420\pi$
$6$	−2.83728	−1.15831
$7$	4.49024	1.69715	0.848576	−	0.529073i	$-0.177460\pi$
$7$	4.49024	1.69715	0.848576	+	0.529073i	$0.177460\pi$
$8$	1.00000	0.353553
$9$	5.05014	1.68338
$10$	3.92961	1.24265
$11$	−1.54058	−0.464502	−0.232251	−	0.972656i	$-0.574609\pi$
$11$	−1.54058	−0.464502	−0.232251	+	0.972656i	$0.574609\pi$
$12$	−2.83728	−0.819051
$13$	5.71071	1.58387	0.791933	−	0.610608i	$-0.209075\pi$
$13$	5.71071	1.58387	0.791933	+	0.610608i	$0.209075\pi$
$14$	4.49024	1.20007
$15$	−11.1494	−2.87876
$16$	1.00000	0.250000
$17$	−0.355432	−0.0862050	−0.0431025	−	0.999071i	$-0.513724\pi$
$17$	−0.355432	−0.0862050	−0.0431025	+	0.999071i	$0.513724\pi$
$18$	5.05014	1.19033
$19$	2.18624	0.501559	0.250779	−	0.968044i	$-0.419313\pi$
$19$	2.18624	0.501559	0.250779	+	0.968044i	$0.419313\pi$
$20$	3.92961	0.878687
$21$	−12.7401	−2.78011
$22$	−1.54058	−0.328453
$23$	8.01724	1.67171	0.835855	−	0.548951i	$-0.184973\pi$
$23$	8.01724	1.67171	0.835855	+	0.548951i	$0.184973\pi$
$24$	−2.83728	−0.579157
$25$	10.4418	2.08837
$26$	5.71071	1.11996
$27$	−5.81682	−1.11945
$28$	4.49024	0.848576
$29$	3.84618	0.714217	0.357109	−	0.934063i	$-0.383763\pi$
$29$	3.84618	0.714217	0.357109	+	0.934063i	$0.383763\pi$
$30$	−11.1494	−2.03559
$31$	−7.71805	−1.38620	−0.693101	−	0.720840i	$-0.743756\pi$
$31$	−7.71805	−1.38620	−0.693101	+	0.720840i	$0.743756\pi$
$32$	1.00000	0.176777
$33$	4.37105	0.760902
$34$	−0.355432	−0.0609561
$35$	17.6449	2.98253
$36$	5.05014	0.841690
$37$	−7.10244	−1.16763	−0.583817	−	0.811885i	$-0.698441\pi$
$37$	−7.10244	−1.16763	−0.583817	+	0.811885i	$0.698441\pi$
$38$	2.18624	0.354655
$39$	−16.2029	−2.59454
$40$	3.92961	0.621326
$41$	6.91781	1.08038	0.540190	−	0.841543i	$-0.318352\pi$
$41$	6.91781	1.08038	0.540190	+	0.841543i	$0.318352\pi$
$42$	−12.7401	−1.96583
$43$	−5.09687	−0.777266	−0.388633	−	0.921393i	$-0.627053\pi$
$43$	−5.09687	−0.777266	−0.388633	+	0.921393i	$0.627053\pi$
$44$	−1.54058	−0.232251
$45$	19.8451	2.95833
$46$	8.01724	1.18208
$47$	−11.0728	−1.61514	−0.807569	−	0.589773i	$-0.799217\pi$
$47$	−11.0728	−1.61514	−0.807569	+	0.589773i	$0.799217\pi$
$48$	−2.83728	−0.409526
$49$	13.1623	1.88033
$50$	10.4418	1.47670
$51$	1.00846	0.141213
$52$	5.71071	0.791933
$53$	11.5101	1.58103	0.790514	−	0.612444i	$-0.209813\pi$
$53$	11.5101	1.58103	0.790514	+	0.612444i	$0.209813\pi$
$54$	−5.81682	−0.791569
$55$	−6.05387	−0.816304
$56$	4.49024	0.600034
$57$	−6.20298	−0.821604
$58$	3.84618	0.505028
$59$	6.09046	0.792910	0.396455	−	0.918054i	$-0.370240\pi$
$59$	6.09046	0.792910	0.396455	+	0.918054i	$0.370240\pi$
$60$	−11.1494	−1.43938
$61$	−8.45252	−1.08223	−0.541117	−	0.840947i	$-0.681998\pi$
$61$	−8.45252	−1.08223	−0.541117	+	0.840947i	$0.681998\pi$
$62$	−7.71805	−0.980194
$63$	22.6764	2.85695
$64$	1.00000	0.125000
$65$	22.4409	2.78345
$66$	4.37105	0.538039
$67$	−0.980042	−0.119731	−0.0598656	−	0.998206i	$-0.519067\pi$
$67$	−0.980042	−0.119731	−0.0598656	+	0.998206i	$0.519067\pi$
$68$	−0.355432	−0.0431025
$69$	−22.7471	−2.73843
$70$	17.6449	2.10897
$71$	−15.0132	−1.78174	−0.890870	−	0.454259i	$-0.849904\pi$
$71$	−15.0132	−1.78174	−0.890870	+	0.454259i	$0.849904\pi$
$72$	5.05014	0.595165
$73$	12.9574	1.51655	0.758273	−	0.651938i	$-0.226044\pi$
$73$	12.9574	1.51655	0.758273	+	0.651938i	$0.226044\pi$
$74$	−7.10244	−0.825642
$75$	−29.6264	−3.42096
$76$	2.18624	0.250779
$77$	−6.91757	−0.788331
$78$	−16.2029	−1.83461
$79$	11.3784	1.28017	0.640083	−	0.768306i	$-0.278900\pi$
$79$	11.3784	1.28017	0.640083	+	0.768306i	$0.278900\pi$
$80$	3.92961	0.439344
$81$	1.35351	0.150390
$82$	6.91781	0.763945
$83$	10.8204	1.18770	0.593849	−	0.804576i	$-0.297608\pi$
$83$	10.8204	1.18770	0.593849	+	0.804576i	$0.297608\pi$
$84$	−12.7401	−1.39005
$85$	−1.39671	−0.151494
$86$	−5.09687	−0.549610
$87$	−10.9127	−1.16996
$88$	−1.54058	−0.164226
$89$	−7.68470	−0.814576	−0.407288	−	0.913300i	$-0.633526\pi$
$89$	−7.68470	−0.814576	−0.407288	+	0.913300i	$0.633526\pi$
$90$	19.8451	2.09186
$91$	25.6425	2.68806
$92$	8.01724	0.835855
$93$	21.8983	2.27074
$94$	−11.0728	−1.14208
$95$	8.59108	0.881426
$96$	−2.83728	−0.289578
$97$	14.6917	1.49171	0.745856	−	0.666108i	$-0.232041\pi$
$97$	14.6917	1.49171	0.745856	+	0.666108i	$0.232041\pi$
$98$	13.1623	1.32959
$99$	−7.78014	−0.781934
$100$	10.4418	1.04418
$101$	−6.88583	−0.685166	−0.342583	−	0.939488i	$-0.611302\pi$
$101$	−6.88583	−0.685166	−0.342583	+	0.939488i	$0.611302\pi$
$102$	1.00846	0.0998524
$103$	−8.17259	−0.805269	−0.402634	−	0.915361i	$-0.631905\pi$
$103$	−8.17259	−0.805269	−0.402634	+	0.915361i	$0.631905\pi$
$104$	5.71071	0.559981
$105$	−50.0635	−4.88569
$106$	11.5101	1.11796
$107$	−5.12297	−0.495257	−0.247628	−	0.968855i	$-0.579651\pi$
$107$	−5.12297	−0.495257	−0.247628	+	0.968855i	$0.579651\pi$
$108$	−5.81682	−0.559724
$109$	−13.7197	−1.31411	−0.657056	−	0.753842i	$-0.728198\pi$
$109$	−13.7197	−1.31411	−0.657056	+	0.753842i	$0.728198\pi$
$110$	−6.05387	−0.577214
$111$	20.1516	1.91270
$112$	4.49024	0.424288
$113$	−9.71490	−0.913901	−0.456951	−	0.889492i	$-0.651058\pi$
$113$	−9.71490	−0.913901	−0.456951	+	0.889492i	$0.651058\pi$
$114$	−6.20298	−0.580962
$115$	31.5046	2.93782
$116$	3.84618	0.357109
$117$	28.8399	2.66625
$118$	6.09046	0.560672
$119$	−1.59598	−0.146303
$120$	−11.1494	−1.01780
$121$	−8.62662	−0.784238
$122$	−8.45252	−0.765255
$123$	−19.6278	−1.76977
$124$	−7.71805	−0.693101
$125$	21.3843	1.91267
$126$	22.6764	2.02017
$127$	8.65328	0.767854	0.383927	−	0.923363i	$-0.374571\pi$
$127$	8.65328	0.767854	0.383927	+	0.923363i	$0.374571\pi$
$128$	1.00000	0.0883883
$129$	14.4612	1.27324
$130$	22.4409	1.96819
$131$	−14.8189	−1.29473	−0.647365	−	0.762180i	$-0.724129\pi$
$131$	−14.8189	−1.29473	−0.647365	+	0.762180i	$0.724129\pi$
$132$	4.37105	0.380451
$133$	9.81676	0.851221
$134$	−0.980042	−0.0846628
$135$	−22.8578	−1.96729
$136$	−0.355432	−0.0304781
$137$	−22.2305	−1.89928	−0.949638	−	0.313348i	$-0.898549\pi$
$137$	−22.2305	−1.89928	−0.949638	+	0.313348i	$0.898549\pi$
$138$	−22.7471	−1.93636
$139$	−13.0847	−1.10983	−0.554917	−	0.831906i	$-0.687250\pi$
$139$	−13.0847	−1.10983	−0.554917	+	0.831906i	$0.687250\pi$
$140$	17.6449	1.49127
$141$	31.4167	2.64576
$142$	−15.0132	−1.25988
$143$	−8.79780	−0.735709
$144$	5.05014	0.420845
$145$	15.1140	1.25515
$146$	12.9574	1.07236
$147$	−37.3450	−3.08017
$148$	−7.10244	−0.583817
$149$	−5.12850	−0.420143	−0.210072	−	0.977686i	$-0.567370\pi$
$149$	−5.12850	−0.420143	−0.210072	+	0.977686i	$0.567370\pi$
$150$	−29.6264	−2.41898
$151$	−19.6911	−1.60244	−0.801221	−	0.598369i	$-0.795816\pi$
$151$	−19.6911	−1.60244	−0.801221	+	0.598369i	$0.795816\pi$
$152$	2.18624	0.177328
$153$	−1.79498	−0.145116
$154$	−6.91757	−0.557434
$155$	−30.3289	−2.43608
$156$	−16.2029	−1.29727
$157$	−20.7136	−1.65313	−0.826564	−	0.562843i	$-0.809707\pi$
$157$	−20.7136	−1.65313	−0.826564	+	0.562843i	$0.809707\pi$
$158$	11.3784	0.905213
$159$	−32.6572	−2.58989
$160$	3.92961	0.310663
$161$	35.9993	2.83714
$162$	1.35351	0.106342
$163$	6.00535	0.470375	0.235188	−	0.971950i	$-0.424430\pi$
$163$	6.00535	0.470375	0.235188	+	0.971950i	$0.424430\pi$
$164$	6.91781	0.540190
$165$	17.1765	1.33719
$166$	10.8204	0.839830
$167$	−17.7857	−1.37630	−0.688149	−	0.725569i	$-0.741577\pi$
$167$	−17.7857	−1.37630	−0.688149	+	0.725569i	$0.741577\pi$
$168$	−12.7401	−0.982917
$169$	19.6122	1.50863
$170$	−1.39671	−0.107123
$171$	11.0408	0.844314
$172$	−5.09687	−0.388633
$173$	6.34882	0.482692	0.241346	−	0.970439i	$-0.422411\pi$
$173$	6.34882	0.482692	0.241346	+	0.970439i	$0.422411\pi$
$174$	−10.9127	−0.827287
$175$	46.8864	3.54428
$176$	−1.54058	−0.116126
$177$	−17.2803	−1.29887
$178$	−7.68470	−0.575992
$179$	−8.69929	−0.650215	−0.325108	−	0.945677i	$-0.605401\pi$
$179$	−8.69929	−0.650215	−0.325108	+	0.945677i	$0.605401\pi$
$180$	19.8451	1.47917
$181$	−17.6335	−1.31069	−0.655345	−	0.755330i	$-0.727477\pi$
$181$	−17.6335	−1.31069	−0.655345	+	0.755330i	$0.727477\pi$
$182$	25.6425	1.90075
$183$	23.9821	1.77281
$184$	8.01724	0.591038
$185$	−27.9098	−2.05197
$186$	21.8983	1.60566
$187$	0.547571	0.0400424
$188$	−11.0728	−0.807569
$189$	−26.1189	−1.89987
$190$	8.59108	0.623263
$191$	−5.76062	−0.416824	−0.208412	−	0.978041i	$-0.566829\pi$
$191$	−5.76062	−0.416824	−0.208412	+	0.978041i	$0.566829\pi$
$192$	−2.83728	−0.204763
$193$	−14.0886	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$193$	−14.0886	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$194$	14.6917	1.05480
$195$	−63.6709	−4.55957
$196$	13.1623	0.940163
$197$	−2.60340	−0.185485	−0.0927423	−	0.995690i	$-0.529563\pi$
$197$	−2.60340	−0.185485	−0.0927423	+	0.995690i	$0.529563\pi$
$198$	−7.78014	−0.552911
$199$	3.66621	0.259891	0.129945	−	0.991521i	$-0.458520\pi$
$199$	3.66621	0.259891	0.129945	+	0.991521i	$0.458520\pi$
$200$	10.4418	0.738349
$201$	2.78065	0.196132
$202$	−6.88583	−0.484486
$203$	17.2703	1.21213
$204$	1.00846	0.0706063
$205$	27.1843	1.89863
$206$	−8.17259	−0.569411
$207$	40.4882	2.81412
$208$	5.71071	0.395966
$209$	−3.36808	−0.232975
$210$	−50.0635	−3.45471
$211$	1.09523	0.0753985	0.0376992	−	0.999289i	$-0.487997\pi$
$211$	1.09523	0.0753985	0.0376992	+	0.999289i	$0.487997\pi$
$212$	11.5101	0.790514
$213$	42.5966	2.91867
$214$	−5.12297	−0.350199
$215$	−20.0287	−1.36595
$216$	−5.81682	−0.395785
$217$	−34.6559	−2.35260
$218$	−13.7197	−0.929217
$219$	−36.7636	−2.48426
$220$	−6.05387	−0.408152
$221$	−2.02977	−0.136537
$222$	20.1516	1.35249
$223$	3.37335	0.225896	0.112948	−	0.993601i	$-0.463971\pi$
$223$	3.37335	0.225896	0.112948	+	0.993601i	$0.463971\pi$
$224$	4.49024	0.300017
$225$	52.7327	3.51552
$226$	−9.71490	−0.646226
$227$	−28.4721	−1.88976	−0.944879	−	0.327419i	$-0.893821\pi$
$227$	−28.4721	−1.88976	−0.944879	+	0.327419i	$0.893821\pi$
$228$	−6.20298	−0.410802
$229$	24.0938	1.59216	0.796081	−	0.605189i	$-0.206903\pi$
$229$	24.0938	1.59216	0.796081	+	0.605189i	$0.206903\pi$
$230$	31.5046	2.07735
$231$	19.6271	1.29137
$232$	3.84618	0.252514
$233$	22.6628	1.48469	0.742346	−	0.670017i	$-0.233713\pi$
$233$	22.6628	1.48469	0.742346	+	0.670017i	$0.233713\pi$
$234$	28.8399	1.88532
$235$	−43.5119	−2.83840
$236$	6.09046	0.396455
$237$	−32.2836	−2.09704
$238$	−1.59598	−0.103452
$239$	1.44421	0.0934182	0.0467091	−	0.998909i	$-0.485127\pi$
$239$	1.44421	0.0934182	0.0467091	+	0.998909i	$0.485127\pi$
$240$	−11.1494	−0.719690
$241$	3.72108	0.239696	0.119848	−	0.992792i	$-0.461759\pi$
$241$	3.72108	0.239696	0.119848	+	0.992792i	$0.461759\pi$
$242$	−8.62662	−0.554540
$243$	13.6102	0.873094
$244$	−8.45252	−0.541117
$245$	51.7226	3.30444
$246$	−19.6278	−1.25142
$247$	12.4850	0.794401
$248$	−7.71805	−0.490097
$249$	−30.7006	−1.94557
$250$	21.3843	1.35246
$251$	−13.0899	−0.826229	−0.413114	−	0.910679i	$-0.635559\pi$
$251$	−13.0899	−0.826229	−0.413114	+	0.910679i	$0.635559\pi$
$252$	22.6764	1.42848
$253$	−12.3512	−0.776512
$254$	8.65328	0.542955
$255$	3.96285	0.248163
$256$	1.00000	0.0625000
$257$	−0.638109	−0.0398041	−0.0199021	−	0.999802i	$-0.506335\pi$
$257$	−0.638109	−0.0398041	−0.0199021	+	0.999802i	$0.506335\pi$
$258$	14.4612	0.900318
$259$	−31.8917	−1.98165
$260$	22.4409	1.39172
$261$	19.4237	1.20230
$262$	−14.8189	−0.915513
$263$	12.3881	0.763885	0.381942	−	0.924186i	$-0.375255\pi$
$263$	12.3881	0.763885	0.381942	+	0.924186i	$0.375255\pi$
$264$	4.37105	0.269020
$265$	45.2300	2.77846
$266$	9.81676	0.601904
$267$	21.8036	1.33436
$268$	−0.980042	−0.0598656
$269$	−18.6856	−1.13928	−0.569640	−	0.821894i	$-0.692917\pi$
$269$	−18.6856	−1.13928	−0.569640	+	0.821894i	$0.692917\pi$
$270$	−22.8578	−1.39108
$271$	0.170295	0.0103447	0.00517235	−	0.999987i	$-0.498354\pi$
$271$	0.170295	0.0103447	0.00517235	+	0.999987i	$0.498354\pi$
$272$	−0.355432	−0.0215512
$273$	−72.7548	−4.40332
$274$	−22.2305	−1.34299
$275$	−16.0865	−0.970051
$276$	−22.7471	−1.36922
$277$	5.05897	0.303964	0.151982	−	0.988383i	$-0.451434\pi$
$277$	5.05897	0.303964	0.151982	+	0.988383i	$0.451434\pi$
$278$	−13.0847	−0.784771
$279$	−38.9773	−2.33351
$280$	17.6449	1.05448
$281$	4.47171	0.266760	0.133380	−	0.991065i	$-0.457417\pi$
$281$	4.47171	0.266760	0.133380	+	0.991065i	$0.457417\pi$
$282$	31.4167	1.87084
$283$	−13.3147	−0.791478	−0.395739	−	0.918363i	$-0.629511\pi$
$283$	−13.3147	−0.791478	−0.395739	+	0.918363i	$0.629511\pi$
$284$	−15.0132	−0.890870
$285$	−24.3753	−1.44387
$286$	−8.79780	−0.520225
$287$	31.0627	1.83357
$288$	5.05014	0.297582
$289$	−16.8737	−0.992569
$290$	15.1140	0.887523
$291$	−41.6843	−2.44358
$292$	12.9574	0.758273
$293$	0.410300	0.0239700	0.0119850	−	0.999928i	$-0.496185\pi$
$293$	0.410300	0.0239700	0.0119850	+	0.999928i	$0.496185\pi$
$294$	−37.3450	−2.17801
$295$	23.9331	1.39344
$296$	−7.10244	−0.412821
$297$	8.96128	0.519986
$298$	−5.12850	−0.297086
$299$	45.7841	2.64776
$300$	−29.6264	−1.71048
$301$	−22.8862	−1.31914
$302$	−19.6911	−1.13310
$303$	19.5370	1.12237
$304$	2.18624	0.125390
$305$	−33.2151	−1.90189
$306$	−1.79498	−0.102612
$307$	2.13235	0.121699	0.0608497	−	0.998147i	$-0.480619\pi$
$307$	2.13235	0.121699	0.0608497	+	0.998147i	$0.480619\pi$
$308$	−6.91757	−0.394165
$309$	23.1879	1.31911
$310$	−30.3289	−1.72257
$311$	5.00463	0.283786	0.141893	−	0.989882i	$-0.454681\pi$
$311$	5.00463	0.283786	0.141893	+	0.989882i	$0.454681\pi$
$312$	−16.2029	−0.917307
$313$	−5.55939	−0.314235	−0.157118	−	0.987580i	$-0.550220\pi$
$313$	−5.55939	−0.314235	−0.157118	+	0.987580i	$0.550220\pi$
$314$	−20.7136	−1.16894
$315$	89.1093	5.02074
$316$	11.3784	0.640083
$317$	31.2898	1.75741	0.878705	−	0.477365i	$-0.158408\pi$
$317$	31.2898	1.75741	0.878705	+	0.477365i	$0.158408\pi$
$318$	−32.6572	−1.83133
$319$	−5.92534	−0.331755
$320$	3.92961	0.219672
$321$	14.5353	0.811281
$322$	35.9993	2.00616
$323$	−0.777061	−0.0432368
$324$	1.35351	0.0751951
$325$	59.6303	3.30769
$326$	6.00535	0.332605
$327$	38.9267	2.15265
$328$	6.91781	0.381972
$329$	−49.7197	−2.74114
$330$	17.1765	0.945536
$331$	5.04434	0.277262	0.138631	−	0.990344i	$-0.455730\pi$
$331$	5.04434	0.277262	0.138631	+	0.990344i	$0.455730\pi$
$332$	10.8204	0.593849
$333$	−35.8683	−1.96557
$334$	−17.7857	−0.973190
$335$	−3.85118	−0.210413
$336$	−12.7401	−0.695027
$337$	−18.3985	−1.00223	−0.501116	−	0.865380i	$-0.667077\pi$
$337$	−18.3985	−1.00223	−0.501116	+	0.865380i	$0.667077\pi$
$338$	19.6122	1.06676
$339$	27.5639	1.49706
$340$	−1.39671	−0.0757472
$341$	11.8903	0.643894
$342$	11.0408	0.597020
$343$	27.6701	1.49405
$344$	−5.09687	−0.274805
$345$	−89.3873	−4.81245
$346$	6.34882	0.341315
$347$	22.5414	1.21008	0.605042	−	0.796194i	$-0.293156\pi$
$347$	22.5414	1.21008	0.605042	+	0.796194i	$0.293156\pi$
$348$	−10.9127	−0.584980
$349$	−11.3626	−0.608226	−0.304113	−	0.952636i	$-0.598360\pi$
$349$	−11.3626	−0.608226	−0.304113	+	0.952636i	$0.598360\pi$
$350$	46.8864	2.50618
$351$	−33.2182	−1.77306
$352$	−1.54058	−0.0821131
$353$	16.7399	0.890974	0.445487	−	0.895289i	$-0.353031\pi$
$353$	16.7399	0.890974	0.445487	+	0.895289i	$0.353031\pi$
$354$	−17.2803	−0.918438
$355$	−58.9960	−3.13118
$356$	−7.68470	−0.407288
$357$	4.52823	0.239659
$358$	−8.69929	−0.459772
$359$	0.592096	0.0312496	0.0156248	−	0.999878i	$-0.495026\pi$
$359$	0.592096	0.0312496	0.0156248	+	0.999878i	$0.495026\pi$
$360$	19.8451	1.04593
$361$	−14.2203	−0.748439
$362$	−17.6335	−0.926797
$363$	24.4761	1.28466
$364$	25.6425	1.34403
$365$	50.9174	2.66514
$366$	23.9821	1.25357
$367$	17.3529	0.905813	0.452906	−	0.891558i	$-0.350387\pi$
$367$	17.3529	0.905813	0.452906	+	0.891558i	$0.350387\pi$
$368$	8.01724	0.417927
$369$	34.9359	1.81869
$370$	−27.9098	−1.45096
$371$	51.6830	2.68325
$372$	21.8983	1.13537
$373$	−2.01245	−0.104201	−0.0521005	−	0.998642i	$-0.516592\pi$
$373$	−2.01245	−0.104201	−0.0521005	+	0.998642i	$0.516592\pi$
$374$	0.547571	0.0283142
$375$	−60.6731	−3.13315
$376$	−11.0728	−0.571038
$377$	21.9644	1.13122
$378$	−26.1189	−1.34341
$379$	5.44016	0.279442	0.139721	−	0.990191i	$-0.455379\pi$
$379$	5.44016	0.279442	0.139721	+	0.990191i	$0.455379\pi$
$380$	8.59108	0.440713
$381$	−24.5518	−1.25782
$382$	−5.76062	−0.294739
$383$	−29.0431	−1.48403	−0.742017	−	0.670381i	$-0.766131\pi$
$383$	−29.0431	−1.48403	−0.742017	+	0.670381i	$0.766131\pi$
$384$	−2.83728	−0.144789
$385$	−27.1834	−1.38539
$386$	−14.0886	−0.717089
$387$	−25.7399	−1.30843
$388$	14.6917	0.745856
$389$	−35.7858	−1.81441	−0.907206	−	0.420687i	$-0.861789\pi$
$389$	−35.7858	−1.81441	−0.907206	+	0.420687i	$0.861789\pi$
$390$	−63.6709	−3.22410
$391$	−2.84958	−0.144110
$392$	13.1623	0.664795
$393$	42.0452	2.12090
$394$	−2.60340	−0.131157
$395$	44.7125	2.24973
$396$	−7.78014	−0.390967
$397$	20.4592	1.02682	0.513408	−	0.858145i	$-0.328383\pi$
$397$	20.4592	1.02682	0.513408	+	0.858145i	$0.328383\pi$
$398$	3.66621	0.183770
$399$	−27.8529	−1.39439
$400$	10.4418	0.522092
$401$	13.7467	0.686475	0.343238	−	0.939249i	$-0.388476\pi$
$401$	13.7467	0.686475	0.343238	+	0.939249i	$0.388476\pi$
$402$	2.78065	0.138686
$403$	−44.0756	−2.19556
$404$	−6.88583	−0.342583
$405$	5.31877	0.264292
$406$	17.2703	0.857109
$407$	10.9419	0.542368
$408$	1.00846	0.0499262
$409$	7.63292	0.377424	0.188712	−	0.982033i	$-0.439569\pi$
$409$	7.63292	0.377424	0.188712	+	0.982033i	$0.439569\pi$
$410$	27.1843	1.34254
$411$	63.0740	3.11121
$412$	−8.17259	−0.402634
$413$	27.3476	1.34569
$414$	40.4882	1.98989
$415$	42.5201	2.08723
$416$	5.71071	0.279991
$417$	37.1250	1.81802
$418$	−3.36808	−0.164738
$419$	21.7930	1.06466	0.532328	−	0.846538i	$-0.321317\pi$
$419$	21.7930	1.06466	0.532328	+	0.846538i	$0.321317\pi$
$420$	−50.0635	−2.44285
$421$	−22.8959	−1.11588	−0.557939	−	0.829882i	$-0.688408\pi$
$421$	−22.8959	−1.11588	−0.557939	+	0.829882i	$0.688408\pi$
$422$	1.09523	0.0533148
$423$	−55.9194	−2.71889
$424$	11.5101	0.558978
$425$	−3.71136	−0.180028
$426$	42.5966	2.06381
$427$	−37.9539	−1.83672
$428$	−5.12297	−0.247628
$429$	24.9618	1.20517
$430$	−20.0287	−0.965871
$431$	−28.8537	−1.38983	−0.694917	−	0.719090i	$-0.744559\pi$
$431$	−28.8537	−1.38983	−0.694917	+	0.719090i	$0.744559\pi$
$432$	−5.81682	−0.279862
$433$	−1.40907	−0.0677157	−0.0338578	−	0.999427i	$-0.510779\pi$
$433$	−1.40907	−0.0677157	−0.0338578	+	0.999427i	$0.510779\pi$
$434$	−34.6559	−1.66354
$435$	−42.8825	−2.05606
$436$	−13.7197	−0.657056
$437$	17.5276	0.838460
$438$	−36.7636	−1.75663
$439$	22.4397	1.07099	0.535495	−	0.844538i	$-0.320125\pi$
$439$	22.4397	1.07099	0.535495	+	0.844538i	$0.320125\pi$
$440$	−6.05387	−0.288607
$441$	66.4714	3.16530
$442$	−2.02977	−0.0965463
$443$	13.5422	0.643407	0.321704	−	0.946840i	$-0.395745\pi$
$443$	13.5422	0.643407	0.321704	+	0.946840i	$0.395745\pi$
$444$	20.1516	0.956352
$445$	−30.1979	−1.43152
$446$	3.37335	0.159733
$447$	14.5510	0.688238
$448$	4.49024	0.212144
$449$	0.981901	0.0463388	0.0231694	−	0.999732i	$-0.492624\pi$
$449$	0.981901	0.0463388	0.0231694	+	0.999732i	$0.492624\pi$
$450$	52.7327	2.48585
$451$	−10.6574	−0.501839
$452$	−9.71490	−0.456951
$453$	55.8692	2.62496
$454$	−28.4721	−1.33626
$455$	100.765	4.72393
$456$	−6.20298	−0.290481
$457$	26.8374	1.25540	0.627700	−	0.778455i	$-0.283996\pi$
$457$	26.8374	1.25540	0.627700	+	0.778455i	$0.283996\pi$
$458$	24.0938	1.12583
$459$	2.06749	0.0965020
$460$	31.5046	1.46891
$461$	36.4524	1.69776	0.848878	−	0.528588i	$-0.177278\pi$
$461$	36.4524	1.69776	0.848878	+	0.528588i	$0.177278\pi$
$462$	19.6271	0.913134
$463$	29.1332	1.35393	0.676966	−	0.736014i	$-0.263294\pi$
$463$	29.1332	1.35393	0.676966	+	0.736014i	$0.263294\pi$
$464$	3.84618	0.178554
$465$	86.0516	3.99055
$466$	22.6628	1.04984
$467$	25.1540	1.16399	0.581994	−	0.813193i	$-0.302273\pi$
$467$	25.1540	1.16399	0.581994	+	0.813193i	$0.302273\pi$
$468$	28.8399	1.33312
$469$	−4.40063	−0.203202
$470$	−43.5119	−2.00705
$471$	58.7703	2.70799
$472$	6.09046	0.280336
$473$	7.85214	0.361042
$474$	−32.2836	−1.48283
$475$	22.8284	1.04744
$476$	−1.59598	−0.0731515
$477$	58.1274	2.66147
$478$	1.44421	0.0660567
$479$	−30.9019	−1.41194	−0.705972	−	0.708240i	$-0.749489\pi$
$479$	−30.9019	−1.41194	−0.705972	+	0.708240i	$0.749489\pi$
$480$	−11.1494	−0.508898
$481$	−40.5600	−1.84937
$482$	3.72108	0.169491
$483$	−102.140	−4.64753
$484$	−8.62662	−0.392119
$485$	57.7325	2.62150
$486$	13.6102	0.617370
$487$	19.4180	0.879916	0.439958	−	0.898018i	$-0.354993\pi$
$487$	19.4180	0.879916	0.439958	+	0.898018i	$0.354993\pi$
$488$	−8.45252	−0.382628
$489$	−17.0388	−0.770523
$490$	51.7226	2.33659
$491$	17.8999	0.807813	0.403907	−	0.914800i	$-0.367652\pi$
$491$	17.8999	0.807813	0.403907	+	0.914800i	$0.367652\pi$
$492$	−19.6278	−0.884887
$493$	−1.36705	−0.0615691
$494$	12.4850	0.561727
$495$	−30.5729	−1.37415
$496$	−7.71805	−0.346551
$497$	−67.4129	−3.02388
$498$	−30.7006	−1.37573
$499$	−3.91758	−0.175375	−0.0876875	−	0.996148i	$-0.527948\pi$
$499$	−3.91758	−0.175375	−0.0876875	+	0.996148i	$0.527948\pi$
$500$	21.3843	0.956334
$501$	50.4630	2.25452
$502$	−13.0899	−0.584232
$503$	0.632735	0.0282123	0.0141061	−	0.999901i	$-0.495510\pi$
$503$	0.632735	0.0282123	0.0141061	+	0.999901i	$0.495510\pi$
$504$	22.6764	1.01009
$505$	−27.0586	−1.20409
$506$	−12.3512	−0.549077
$507$	−55.6453	−2.47129
$508$	8.65328	0.383927
$509$	−13.4974	−0.598262	−0.299131	−	0.954212i	$-0.596697\pi$
$509$	−13.4974	−0.598262	−0.299131	+	0.954212i	$0.596697\pi$
$510$	3.96285	0.175478
$511$	58.1817	2.57381
$512$	1.00000	0.0441942
$513$	−12.7170	−0.561469
$514$	−0.638109	−0.0281458
$515$	−32.1151	−1.41516
$516$	14.4612	0.636621
$517$	17.0586	0.750235
$518$	−31.8917	−1.40124
$519$	−18.0134	−0.790699
$520$	22.4409	0.984097
$521$	7.77183	0.340490	0.170245	−	0.985402i	$-0.445544\pi$
$521$	7.77183	0.340490	0.170245	+	0.985402i	$0.445544\pi$
$522$	19.4237	0.850154
$523$	−32.4690	−1.41977	−0.709886	−	0.704317i	$-0.751254\pi$
$523$	−32.4690	−1.41977	−0.709886	+	0.704317i	$0.751254\pi$
$524$	−14.8189	−0.647365
$525$	−133.030	−5.80589
$526$	12.3881	0.540148
$527$	2.74324	0.119498
$528$	4.37105	0.190226
$529$	41.2761	1.79461
$530$	45.2300	1.96467
$531$	30.7577	1.33477
$532$	9.81676	0.425611
$533$	39.5056	1.71118
$534$	21.8036	0.943535
$535$	−20.1313	−0.870352
$536$	−0.980042	−0.0423314
$537$	24.6823	1.06512
$538$	−18.6856	−0.805592
$539$	−20.2775	−0.873415
$540$	−22.8578	−0.983645
$541$	7.49572	0.322266	0.161133	−	0.986933i	$-0.448485\pi$
$541$	7.49572	0.322266	0.161133	+	0.986933i	$0.448485\pi$
$542$	0.170295	0.00731481
$543$	50.0312	2.14704
$544$	−0.355432	−0.0152390
$545$	−53.9132	−2.30939
$546$	−72.7548	−3.11362
$547$	−33.1921	−1.41919	−0.709595	−	0.704609i	$-0.751122\pi$
$547$	−33.1921	−1.41919	−0.709595	+	0.704609i	$0.751122\pi$
$548$	−22.2305	−0.949638
$549$	−42.6864	−1.82181
$550$	−16.0865	−0.685929
$551$	8.40868	0.358222
$552$	−22.7471	−0.968182
$553$	51.0916	2.17263
$554$	5.05897	0.214935
$555$	79.1879	3.36134
$556$	−13.0847	−0.554917
$557$	15.6653	0.663762	0.331881	−	0.943321i	$-0.392317\pi$
$557$	15.6653	0.663762	0.331881	+	0.943321i	$0.392317\pi$
$558$	−38.9773	−1.65004
$559$	−29.1068	−1.23109
$560$	17.6449	0.745633
$561$	−1.55361	−0.0655935
$562$	4.47171	0.188628
$563$	25.6200	1.07975	0.539877	−	0.841744i	$-0.318471\pi$
$563$	25.6200	1.07975	0.539877	+	0.841744i	$0.318471\pi$
$564$	31.4167	1.32288
$565$	−38.1758	−1.60607
$566$	−13.3147	−0.559659
$567$	6.07759	0.255235
$568$	−15.0132	−0.629940
$569$	7.31577	0.306693	0.153347	−	0.988172i	$-0.450995\pi$
$569$	7.31577	0.306693	0.153347	+	0.988172i	$0.450995\pi$
$570$	−24.3753	−1.02097
$571$	−37.7534	−1.57993	−0.789966	−	0.613151i	$-0.789902\pi$
$571$	−37.7534	−1.57993	−0.789966	+	0.613151i	$0.789902\pi$
$572$	−8.79780	−0.367855
$573$	16.3445	0.682800
$574$	31.0627	1.29653
$575$	83.7146	3.49114
$576$	5.05014	0.210423
$577$	−23.4548	−0.976434	−0.488217	−	0.872722i	$-0.662353\pi$
$577$	−23.4548	−0.976434	−0.488217	+	0.872722i	$0.662353\pi$
$578$	−16.8737	−0.701852
$579$	39.9731	1.66123
$580$	15.1140	0.627574
$581$	48.5864	2.01570
$582$	−41.6843	−1.72787
$583$	−17.7322	−0.734391
$584$	12.9574	0.536180
$585$	113.330	4.68560
$586$	0.410300	0.0169493
$587$	−32.8836	−1.35725	−0.678626	−	0.734484i	$-0.737424\pi$
$587$	−32.8836	−1.35725	−0.678626	+	0.734484i	$0.737424\pi$
$588$	−37.3450	−1.54008
$589$	−16.8735	−0.695262
$590$	23.9331	0.985311
$591$	7.38657	0.303843
$592$	−7.10244	−0.291908
$593$	21.9697	0.902186	0.451093	−	0.892477i	$-0.351034\pi$
$593$	21.9697	0.902186	0.451093	+	0.892477i	$0.351034\pi$
$594$	8.96128	0.367686
$595$	−6.27156	−0.257109
$596$	−5.12850	−0.210072
$597$	−10.4020	−0.425728
$598$	45.7841	1.87225
$599$	22.8732	0.934573	0.467287	−	0.884106i	$-0.345232\pi$
$599$	22.8732	0.934573	0.467287	+	0.884106i	$0.345232\pi$
$600$	−29.6264	−1.20949
$601$	27.2513	1.11160	0.555802	−	0.831315i	$-0.312411\pi$
$601$	27.2513	1.11160	0.555802	+	0.831315i	$0.312411\pi$
$602$	−22.8862	−0.932772
$603$	−4.94935	−0.201553
$604$	−19.6911	−0.801221
$605$	−33.8992	−1.37820
$606$	19.5370	0.793637
$607$	−27.0274	−1.09701	−0.548504	−	0.836148i	$-0.684802\pi$
$607$	−27.0274	−1.09701	−0.548504	+	0.836148i	$0.684802\pi$
$608$	2.18624	0.0886639
$609$	−49.0005	−1.98560
$610$	−33.2151	−1.34484
$611$	−63.2337	−2.55816
$612$	−1.79498	−0.0725579
$613$	24.8003	1.00168	0.500838	−	0.865541i	$-0.333025\pi$
$613$	24.8003	1.00168	0.500838	+	0.865541i	$0.333025\pi$
$614$	2.13235	0.0860545
$615$	−77.1294	−3.11016
$616$	−6.91757	−0.278717
$617$	15.4277	0.621094	0.310547	−	0.950558i	$-0.399488\pi$
$617$	15.4277	0.621094	0.310547	+	0.950558i	$0.399488\pi$
$618$	23.1879	0.932754
$619$	1.77042	0.0711594	0.0355797	−	0.999367i	$-0.488672\pi$
$619$	1.77042	0.0711594	0.0355797	+	0.999367i	$0.488672\pi$
$620$	−30.3289	−1.21804
$621$	−46.6348	−1.87139
$622$	5.00463	0.200667
$623$	−34.5062	−1.38246
$624$	−16.2029	−0.648634
$625$	31.8227	1.27291
$626$	−5.55939	−0.222198
$627$	9.55618	0.381637
$628$	−20.7136	−0.826564
$629$	2.52443	0.100656
$630$	89.1093	3.55020
$631$	29.8723	1.18920	0.594598	−	0.804023i	$-0.297311\pi$
$631$	29.8723	1.18920	0.594598	+	0.804023i	$0.297311\pi$
$632$	11.3784	0.452607
$633$	−3.10746	−0.123510
$634$	31.2898	1.24268
$635$	34.0040	1.34941
$636$	−32.6572	−1.29494
$637$	75.1659	2.97818
$638$	−5.92534	−0.234586
$639$	−75.8188	−2.99935
$640$	3.92961	0.155331
$641$	36.8735	1.45641	0.728207	−	0.685357i	$-0.240354\pi$
$641$	36.8735	1.45641	0.728207	+	0.685357i	$0.240354\pi$
$642$	14.5353	0.573663
$643$	37.6712	1.48561	0.742803	−	0.669510i	$-0.233496\pi$
$643$	37.6712	1.48561	0.742803	+	0.669510i	$0.233496\pi$
$644$	35.9993	1.41857
$645$	56.8271	2.23756
$646$	−0.777061	−0.0305731
$647$	24.4117	0.959723	0.479861	−	0.877344i	$-0.340687\pi$
$647$	24.4117	0.959723	0.479861	+	0.877344i	$0.340687\pi$
$648$	1.35351	0.0531709
$649$	−9.38283	−0.368308
$650$	59.6303	2.33889
$651$	98.3285	3.85380
$652$	6.00535	0.235188
$653$	−37.7143	−1.47587	−0.737937	−	0.674870i	$-0.764200\pi$
$653$	−37.7143	−1.47587	−0.737937	+	0.674870i	$0.764200\pi$
$654$	38.9267	1.52215
$655$	−58.2324	−2.27533
$656$	6.91781	0.270095
$657$	65.4365	2.55292
$658$	−49.7197	−1.93828
$659$	27.6489	1.07705	0.538523	−	0.842611i	$-0.318982\pi$
$659$	27.6489	1.07705	0.538523	+	0.842611i	$0.318982\pi$
$660$	17.1765	0.668595
$661$	−11.4944	−0.447081	−0.223540	−	0.974695i	$-0.571761\pi$
$661$	−11.4944	−0.447081	−0.223540	+	0.974695i	$0.571761\pi$
$662$	5.04434	0.196054
$663$	5.75902	0.223662
$664$	10.8204	0.419915
$665$	38.5760	1.49591
$666$	−35.8683	−1.38987
$667$	30.8357	1.19396
$668$	−17.7857	−0.688149
$669$	−9.57112	−0.370041
$670$	−3.85118	−0.148784
$671$	13.0218	0.502700
$672$	−12.7401	−0.491459
$673$	42.7561	1.64813	0.824064	−	0.566497i	$-0.191702\pi$
$673$	42.7561	1.64813	0.824064	+	0.566497i	$0.191702\pi$
$674$	−18.3985	−0.708685
$675$	−60.7383	−2.33782
$676$	19.6122	0.754316
$677$	4.47723	0.172074	0.0860369	−	0.996292i	$-0.472580\pi$
$677$	4.47723	0.172074	0.0860369	+	0.996292i	$0.472580\pi$
$678$	27.5639	1.05858
$679$	65.9691	2.53166
$680$	−1.39671	−0.0535614
$681$	80.7832	3.09562
$682$	11.8903	0.455302
$683$	−23.8033	−0.910806	−0.455403	−	0.890285i	$-0.650505\pi$
$683$	−23.8033	−0.910806	−0.455403	+	0.890285i	$0.650505\pi$
$684$	11.0408	0.422157
$685$	−87.3570	−3.33774
$686$	27.6701	1.05645
$687$	−68.3608	−2.60813
$688$	−5.09687	−0.194317
$689$	65.7306	2.50414
$690$	−89.3873	−3.40292
$691$	−40.7356	−1.54966	−0.774828	−	0.632172i	$-0.782164\pi$
$691$	−40.7356	−1.54966	−0.774828	+	0.632172i	$0.782164\pi$
$692$	6.34882	0.241346
$693$	−34.9347	−1.32706
$694$	22.5414	0.855658
$695$	−51.4179	−1.95039
$696$	−10.9127	−0.413644
$697$	−2.45881	−0.0931342
$698$	−11.3626	−0.430081
$699$	−64.3007	−2.43208
$700$	46.8864	1.77214
$701$	5.76572	0.217768	0.108884	−	0.994054i	$-0.465272\pi$
$701$	5.76572	0.217768	0.108884	+	0.994054i	$0.465272\pi$
$702$	−33.2182	−1.25374
$703$	−15.5277	−0.585637
$704$	−1.54058	−0.0580628
$705$	123.455	4.64960
$706$	16.7399	0.630013
$707$	−30.9191	−1.16283
$708$	−17.2803	−0.649434
$709$	44.3558	1.66582	0.832908	−	0.553412i	$-0.186674\pi$
$709$	44.3558	1.66582	0.832908	+	0.553412i	$0.186674\pi$
$710$	−58.9960	−2.21408
$711$	57.4623	2.15501
$712$	−7.68470	−0.287996
$713$	−61.8774	−2.31733
$714$	4.52823	0.169465
$715$	−34.5719	−1.29292
$716$	−8.69929	−0.325108
$717$	−4.09763	−0.153029
$718$	0.592096	0.0220968
$719$	31.7224	1.18305	0.591523	−	0.806288i	$-0.298527\pi$
$719$	31.7224	1.18305	0.591523	+	0.806288i	$0.298527\pi$
$720$	19.8451	0.739583
$721$	−36.6969	−1.36666
$722$	−14.2203	−0.529226
$723$	−10.5577	−0.392646
$724$	−17.6335	−0.655345
$725$	40.1611	1.49155
$726$	24.4761	0.908393
$727$	−26.5981	−0.986470	−0.493235	−	0.869896i	$-0.664186\pi$
$727$	−26.5981	−0.986470	−0.493235	+	0.869896i	$0.664186\pi$
$728$	25.6425	0.950373
$729$	−42.6764	−1.58061
$730$	50.9174	1.88454
$731$	1.81159	0.0670042
$732$	23.9821	0.886405
$733$	−14.2663	−0.526938	−0.263469	−	0.964668i	$-0.584867\pi$
$733$	−14.2663	−0.526938	−0.263469	+	0.964668i	$0.584867\pi$
$734$	17.3529	0.640506
$735$	−146.751	−5.41301
$736$	8.01724	0.295519
$737$	1.50983	0.0556154
$738$	34.9359	1.28601
$739$	−41.2610	−1.51781	−0.758904	−	0.651202i	$-0.774265\pi$
$739$	−41.2610	−1.51781	−0.758904	+	0.651202i	$0.774265\pi$
$740$	−27.9098	−1.02598
$741$	−35.4234	−1.30131
$742$	51.6830	1.89734
$743$	18.2962	0.671224	0.335612	−	0.942000i	$-0.391057\pi$
$743$	18.2962	0.671224	0.335612	+	0.942000i	$0.391057\pi$
$744$	21.8983	0.802829
$745$	−20.1530	−0.738349
$746$	−2.01245	−0.0736812
$747$	54.6448	1.99935
$748$	0.547571	0.0200212
$749$	−23.0034	−0.840526
$750$	−60.6731	−2.21547
$751$	−7.35825	−0.268506	−0.134253	−	0.990947i	$-0.542864\pi$
$751$	−7.35825	−0.268506	−0.134253	+	0.990947i	$0.542864\pi$
$752$	−11.0728	−0.403785
$753$	37.1397	1.35345
$754$	21.9644	0.799896
$755$	−77.3785	−2.81609
$756$	−26.1189	−0.949937
$757$	−24.6570	−0.896173	−0.448086	−	0.893990i	$-0.647894\pi$
$757$	−24.6570	−0.896173	−0.448086	+	0.893990i	$0.647894\pi$
$758$	5.44016	0.197595
$759$	35.0437	1.27201
$760$	8.59108	0.311631
$761$	29.6454	1.07465	0.537323	−	0.843377i	$-0.319436\pi$
$761$	29.6454	1.07465	0.537323	+	0.843377i	$0.319436\pi$
$762$	−24.5518	−0.889416
$763$	−61.6049	−2.23025
$764$	−5.76062	−0.208412
$765$	−7.05358	−0.255023
$766$	−29.0431	−1.04937
$767$	34.7808	1.25586
$768$	−2.83728	−0.102381
$769$	29.0166	1.04637	0.523183	−	0.852220i	$-0.324744\pi$
$769$	29.0166	1.04637	0.523183	+	0.852220i	$0.324744\pi$
$770$	−27.1834	−0.979620
$771$	1.81049	0.0652033
$772$	−14.0886	−0.507058
$773$	−28.7691	−1.03475	−0.517376	−	0.855758i	$-0.673091\pi$
$773$	−28.7691	−1.03475	−0.517376	+	0.855758i	$0.673091\pi$
$774$	−25.7399	−0.925203
$775$	−80.5906	−2.89490
$776$	14.6917	0.527400
$777$	90.4855	3.24615
$778$	−35.7858	−1.28298
$779$	15.1240	0.541874
$780$	−63.6709	−2.27979
$781$	23.1290	0.827622
$782$	−2.84958	−0.101901
$783$	−22.3725	−0.799529
$784$	13.1623	0.470081
$785$	−81.3965	−2.90516
$786$	42.0452	1.49970
$787$	−30.3314	−1.08120	−0.540599	−	0.841280i	$-0.681803\pi$
$787$	−30.3314	−1.08120	−0.540599	+	0.841280i	$0.681803\pi$
$788$	−2.60340	−0.0927423
$789$	−35.1486	−1.25132
$790$	44.7125	1.59080
$791$	−43.6223	−1.55103
$792$	−7.78014	−0.276455
$793$	−48.2699	−1.71411
$794$	20.4592	0.726069
$795$	−128.330	−4.55140
$796$	3.66621	0.129945
$797$	8.59117	0.304315	0.152157	−	0.988356i	$-0.451378\pi$
$797$	8.59117	0.304315	0.152157	+	0.988356i	$0.451378\pi$
$798$	−27.8529	−0.985981
$799$	3.93564	0.139233
$800$	10.4418	0.369175
$801$	−38.8088	−1.37124
$802$	13.7467	0.485411
$803$	−19.9618	−0.704438
$804$	2.78065	0.0980660
$805$	141.463	4.98593
$806$	−44.0756	−1.55250
$807$	53.0162	1.86626
$808$	−6.88583	−0.242243
$809$	−14.8768	−0.523039	−0.261519	−	0.965198i	$-0.584224\pi$
$809$	−14.8768	−0.523039	−0.261519	+	0.965198i	$0.584224\pi$
$810$	5.31877	0.186883
$811$	21.9638	0.771252	0.385626	−	0.922655i	$-0.373986\pi$
$811$	21.9638	0.771252	0.385626	+	0.922655i	$0.373986\pi$
$812$	17.2703	0.606067
$813$	−0.483175	−0.0169457
$814$	10.9419	0.383512
$815$	23.5987	0.826625
$816$	1.00846	0.0353031
$817$	−11.1430	−0.389844
$818$	7.63292	0.266879
$819$	129.498	4.52503
$820$	27.1843	0.949317
$821$	−8.38072	−0.292489	−0.146245	−	0.989248i	$-0.546719\pi$
$821$	−8.38072	−0.292489	−0.146245	+	0.989248i	$0.546719\pi$
$822$	63.0740	2.19996
$823$	−41.3392	−1.44100	−0.720498	−	0.693457i	$-0.756087\pi$
$823$	−41.3392	−1.44100	−0.720498	+	0.693457i	$0.756087\pi$
$824$	−8.17259	−0.284706
$825$	45.6418	1.58904
$826$	27.3476	0.951546
$827$	7.72790	0.268725	0.134363	−	0.990932i	$-0.457101\pi$
$827$	7.72790	0.268725	0.134363	+	0.990932i	$0.457101\pi$
$828$	40.4882	1.40706
$829$	−0.900738	−0.0312839	−0.0156420	−	0.999878i	$-0.504979\pi$
$829$	−0.900738	−0.0312839	−0.0156420	+	0.999878i	$0.504979\pi$
$830$	42.5201	1.47590
$831$	−14.3537	−0.497924
$832$	5.71071	0.197983
$833$	−4.67830	−0.162093
$834$	37.1250	1.28554
$835$	−69.8908	−2.41867
$836$	−3.36808	−0.116487
$837$	44.8945	1.55178
$838$	21.7930	0.752826
$839$	−9.49778	−0.327900	−0.163950	−	0.986469i	$-0.552424\pi$
$839$	−9.49778	−0.327900	−0.163950	+	0.986469i	$0.552424\pi$
$840$	−50.0635	−1.72735
$841$	−14.2069	−0.489894
$842$	−22.8959	−0.789045
$843$	−12.6875	−0.436980
$844$	1.09523	0.0376992
$845$	77.0683	2.65123
$846$	−55.9194	−1.92255
$847$	−38.7356	−1.33097
$848$	11.5101	0.395257
$849$	37.7775	1.29652
$850$	−3.71136	−0.127299
$851$	−56.9419	−1.95194
$852$	42.5966	1.45934
$853$	31.4173	1.07571	0.537854	−	0.843038i	$-0.319235\pi$
$853$	31.4173	1.07571	0.537854	+	0.843038i	$0.319235\pi$
$854$	−37.9539	−1.29875
$855$	43.3862	1.48378
$856$	−5.12297	−0.175100
$857$	−33.7586	−1.15317	−0.576586	−	0.817036i	$-0.695615\pi$
$857$	−33.7586	−1.15317	−0.576586	+	0.817036i	$0.695615\pi$
$858$	24.9618	0.852182
$859$	7.04655	0.240425	0.120213	−	0.992748i	$-0.461642\pi$
$859$	7.04655	0.240425	0.120213	+	0.992748i	$0.461642\pi$
$860$	−20.0287	−0.682974
$861$	−88.1334	−3.00358
$862$	−28.8537	−0.982761
$863$	18.8290	0.640947	0.320474	−	0.947257i	$-0.396158\pi$
$863$	18.8290	0.640947	0.320474	+	0.947257i	$0.396158\pi$
$864$	−5.81682	−0.197892
$865$	24.9484	0.848270
$866$	−1.40907	−0.0478822
$867$	47.8753	1.62593
$868$	−34.6559	−1.17630
$869$	−17.5293	−0.594639
$870$	−42.8825	−1.45385
$871$	−5.59674	−0.189638
$872$	−13.7197	−0.464609
$873$	74.1949	2.51112
$874$	17.5276	0.592881
$875$	96.0206	3.24609
$876$	−36.7636	−1.24213
$877$	16.8382	0.568586	0.284293	−	0.958737i	$-0.408241\pi$
$877$	16.8382	0.568586	0.284293	+	0.958737i	$0.408241\pi$
$878$	22.4397	0.757304
$879$	−1.16413	−0.0392653
$880$	−6.05387	−0.204076
$881$	16.3202	0.549843	0.274922	−	0.961467i	$-0.411348\pi$
$881$	16.3202	0.549843	0.274922	+	0.961467i	$0.411348\pi$
$882$	66.4714	2.23821
$883$	29.7743	1.00198	0.500992	−	0.865452i	$-0.332969\pi$
$883$	29.7743	1.00198	0.500992	+	0.865452i	$0.332969\pi$
$884$	−2.02977	−0.0682686
$885$	−67.9049	−2.28260
$886$	13.5422	0.454957
$887$	28.7379	0.964925	0.482462	−	0.875917i	$-0.339742\pi$
$887$	28.7379	0.964925	0.482462	+	0.875917i	$0.339742\pi$
$888$	20.1516	0.676243
$889$	38.8553	1.30317
$890$	−30.1979	−1.01223
$891$	−2.08519	−0.0698565
$892$	3.37335	0.112948
$893$	−24.2079	−0.810086
$894$	14.5510	0.486658
$895$	−34.1848	−1.14267
$896$	4.49024	0.150008
$897$	−129.902	−4.33731
$898$	0.981901	0.0327665
$899$	−29.6850	−0.990050
$900$	52.7327	1.75776
$901$	−4.09105	−0.136292
$902$	−10.6574	−0.354854
$903$	64.9345	2.16088
$904$	−9.71490	−0.323113
$905$	−69.2929	−2.30337
$906$	55.8692	1.85613
$907$	−6.55721	−0.217729	−0.108864	−	0.994057i	$-0.534721\pi$
$907$	−6.55721	−0.217729	−0.108864	+	0.994057i	$0.534721\pi$
$908$	−28.4721	−0.944879
$909$	−34.7744	−1.15340
$910$	100.765	3.34032
$911$	−35.3265	−1.17042	−0.585210	−	0.810882i	$-0.698988\pi$
$911$	−35.3265	−1.17042	−0.585210	+	0.810882i	$0.698988\pi$
$912$	−6.20298	−0.205401
$913$	−16.6698	−0.551688
$914$	26.8374	0.887702
$915$	94.2405	3.11549
$916$	24.0938	0.796081
$917$	−66.5403	−2.19736
$918$	2.06749	0.0682372
$919$	49.4151	1.63006	0.815028	−	0.579422i	$-0.196722\pi$
$919$	49.4151	1.63006	0.815028	+	0.579422i	$0.196722\pi$
$920$	31.5046	1.03868
$921$	−6.05006	−0.199356
$922$	36.4524	1.20050
$923$	−85.7360	−2.82204
$924$	19.6271	0.645683
$925$	−74.1625	−2.43845
$926$	29.1332	0.957375
$927$	−41.2727	−1.35557
$928$	3.84618	0.126257
$929$	−50.2657	−1.64917	−0.824583	−	0.565742i	$-0.808590\pi$
$929$	−50.2657	−1.64917	−0.824583	+	0.565742i	$0.808590\pi$
$930$	86.0516	2.82174
$931$	28.7759	0.943093
$932$	22.6628	0.742346
$933$	−14.1995	−0.464871
$934$	25.1540	0.823063
$935$	2.15174	0.0703695
$936$	28.8399	0.942662
$937$	10.7023	0.349629	0.174814	−	0.984601i	$-0.444067\pi$
$937$	10.7023	0.349629	0.174814	+	0.984601i	$0.444067\pi$
$938$	−4.40063	−0.143686
$939$	15.7735	0.514750
$940$	−43.5119	−1.41920
$941$	−26.6775	−0.869663	−0.434832	−	0.900512i	$-0.643192\pi$
$941$	−26.6775	−0.869663	−0.434832	+	0.900512i	$0.643192\pi$
$942$	58.7703	1.91484
$943$	55.4617	1.80608
$944$	6.09046	0.198227
$945$	−102.637	−3.33879
$946$	7.85214	0.255295
$947$	8.70665	0.282928	0.141464	−	0.989943i	$-0.454819\pi$
$947$	8.70665	0.282928	0.141464	+	0.989943i	$0.454819\pi$
$948$	−32.2836	−1.04852
$949$	73.9958	2.40200
$950$	22.8284	0.740650
$951$	−88.7778	−2.87882
$952$	−1.59598	−0.0517259
$953$	−14.9784	−0.485198	−0.242599	−	0.970127i	$-0.578000\pi$
$953$	−14.9784	−0.485198	−0.242599	+	0.970127i	$0.578000\pi$
$954$	58.1274	1.88195
$955$	−22.6370	−0.732515
$956$	1.44421	0.0467091
$957$	16.8118	0.543449
$958$	−30.9019	−0.998395
$959$	−99.8202	−3.22336
$960$	−11.1494	−0.359845
$961$	28.5683	0.921559
$962$	−40.5600	−1.30771
$963$	−25.8718	−0.833706
$964$	3.72108	0.119848
$965$	−55.3625	−1.78218
$966$	−102.140	−3.28630
$967$	−2.30425	−0.0740996	−0.0370498	−	0.999313i	$-0.511796\pi$
$967$	−2.30425	−0.0740996	−0.0370498	+	0.999313i	$0.511796\pi$
$968$	−8.62662	−0.277270
$969$	2.20474	0.0708264
$970$	57.7325	1.85368
$971$	24.3110	0.780176	0.390088	−	0.920777i	$-0.372445\pi$
$971$	24.3110	0.780176	0.390088	+	0.920777i	$0.372445\pi$
$972$	13.6102	0.436547
$973$	−58.7537	−1.88356
$974$	19.4180	0.622194
$975$	−169.188	−5.41834
$976$	−8.45252	−0.270559
$977$	10.3273	0.330399	0.165200	−	0.986260i	$-0.447173\pi$
$977$	10.3273	0.330399	0.165200	+	0.986260i	$0.447173\pi$
$978$	−17.0388	−0.544842
$979$	11.8389	0.378372
$980$	51.7226	1.65222
$981$	−69.2866	−2.21215
$982$	17.8999	0.571210
$983$	−32.1310	−1.02482	−0.512410	−	0.858741i	$-0.671247\pi$
$983$	−32.1310	−1.02482	−0.512410	+	0.858741i	$0.671247\pi$
$984$	−19.6278	−0.625710
$985$	−10.2303	−0.325966
$986$	−1.36705	−0.0435359
$987$	141.069	4.49026
$988$	12.4850	0.397201
$989$	−40.8628	−1.29936
$990$	−30.5729	−0.971672
$991$	−48.5024	−1.54073	−0.770365	−	0.637604i	$-0.779926\pi$
$991$	−48.5024	−1.54073	−0.770365	+	0.637604i	$0.779926\pi$
$992$	−7.71805	−0.245048
$993$	−14.3122	−0.454184
$994$	−67.4129	−2.13821
$995$	14.4068	0.456725
$996$	−30.7006	−0.972786
$997$	31.9161	1.01079	0.505396	−	0.862888i	$-0.331346\pi$
$997$	31.9161	1.01079	0.505396	+	0.862888i	$0.331346\pi$
$998$	−3.91758	−0.124009
$999$	41.3136	1.30710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.10	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.10	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.83728 q^{3} +1.00000 q^{4} +3.92961 q^{5} -2.83728 q^{6} +4.49024 q^{7} +1.00000 q^{8} +5.05014 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.83728 q^{3} +1.00000 q^{4} +3.92961 q^{5} -2.83728 q^{6} +4.49024 q^{7} +1.00000 q^{8} +5.05014 q^{9} +3.92961 q^{10} -1.54058 q^{11} -2.83728 q^{12} +5.71071 q^{13} +4.49024 q^{14} -11.1494 q^{15} +1.00000 q^{16} -0.355432 q^{17} +5.05014 q^{18} +2.18624 q^{19} +3.92961 q^{20} -12.7401 q^{21} -1.54058 q^{22} +8.01724 q^{23} -2.83728 q^{24} +10.4418 q^{25} +5.71071 q^{26} -5.81682 q^{27} +4.49024 q^{28} +3.84618 q^{29} -11.1494 q^{30} -7.71805 q^{31} +1.00000 q^{32} +4.37105 q^{33} -0.355432 q^{34} +17.6449 q^{35} +5.05014 q^{36} -7.10244 q^{37} +2.18624 q^{38} -16.2029 q^{39} +3.92961 q^{40} +6.91781 q^{41} -12.7401 q^{42} -5.09687 q^{43} -1.54058 q^{44} +19.8451 q^{45} +8.01724 q^{46} -11.0728 q^{47} -2.83728 q^{48} +13.1623 q^{49} +10.4418 q^{50} +1.00846 q^{51} +5.71071 q^{52} +11.5101 q^{53} -5.81682 q^{54} -6.05387 q^{55} +4.49024 q^{56} -6.20298 q^{57} +3.84618 q^{58} +6.09046 q^{59} -11.1494 q^{60} -8.45252 q^{61} -7.71805 q^{62} +22.6764 q^{63} +1.00000 q^{64} +22.4409 q^{65} +4.37105 q^{66} -0.980042 q^{67} -0.355432 q^{68} -22.7471 q^{69} +17.6449 q^{70} -15.0132 q^{71} +5.05014 q^{72} +12.9574 q^{73} -7.10244 q^{74} -29.6264 q^{75} +2.18624 q^{76} -6.91757 q^{77} -16.2029 q^{78} +11.3784 q^{79} +3.92961 q^{80} +1.35351 q^{81} +6.91781 q^{82} +10.8204 q^{83} -12.7401 q^{84} -1.39671 q^{85} -5.09687 q^{86} -10.9127 q^{87} -1.54058 q^{88} -7.68470 q^{89} +19.8451 q^{90} +25.6425 q^{91} +8.01724 q^{92} +21.8983 q^{93} -11.0728 q^{94} +8.59108 q^{95} -2.83728 q^{96} +14.6917 q^{97} +13.1623 q^{98} -7.78014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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