LMFDB - Embedded newform 8043.2.a.t.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.834508 q^{2} -1.00000 q^{3} -1.30360 q^{4} +4.35036 q^{5} +0.834508 q^{6} +1.00000 q^{7} +2.75688 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.834508 q^{2} -1.00000 q^{3} -1.30360 q^{4} +4.35036 q^{5} +0.834508 q^{6} +1.00000 q^{7} +2.75688 q^{8} +1.00000 q^{9} -3.63041 q^{10} -1.94241 q^{11} +1.30360 q^{12} +3.74111 q^{13} -0.834508 q^{14} -4.35036 q^{15} +0.306559 q^{16} -2.70268 q^{17} -0.834508 q^{18} +3.42454 q^{19} -5.67111 q^{20} -1.00000 q^{21} +1.62095 q^{22} -3.21792 q^{23} -2.75688 q^{24} +13.9256 q^{25} -3.12199 q^{26} -1.00000 q^{27} -1.30360 q^{28} +1.78291 q^{29} +3.63041 q^{30} -2.52690 q^{31} -5.76958 q^{32} +1.94241 q^{33} +2.25541 q^{34} +4.35036 q^{35} -1.30360 q^{36} +6.45436 q^{37} -2.85781 q^{38} -3.74111 q^{39} +11.9934 q^{40} -3.78067 q^{41} +0.834508 q^{42} -1.95214 q^{43} +2.53211 q^{44} +4.35036 q^{45} +2.68538 q^{46} -1.00767 q^{47} -0.306559 q^{48} +1.00000 q^{49} -11.6210 q^{50} +2.70268 q^{51} -4.87690 q^{52} -3.13149 q^{53} +0.834508 q^{54} -8.45016 q^{55} +2.75688 q^{56} -3.42454 q^{57} -1.48785 q^{58} -10.8579 q^{59} +5.67111 q^{60} +14.0101 q^{61} +2.10872 q^{62} +1.00000 q^{63} +4.20164 q^{64} +16.2752 q^{65} -1.62095 q^{66} +8.69818 q^{67} +3.52320 q^{68} +3.21792 q^{69} -3.63041 q^{70} -0.279835 q^{71} +2.75688 q^{72} +9.96673 q^{73} -5.38621 q^{74} -13.9256 q^{75} -4.46422 q^{76} -1.94241 q^{77} +3.12199 q^{78} +2.04327 q^{79} +1.33364 q^{80} +1.00000 q^{81} +3.15500 q^{82} -0.411978 q^{83} +1.30360 q^{84} -11.7576 q^{85} +1.62907 q^{86} -1.78291 q^{87} -5.35497 q^{88} -2.78360 q^{89} -3.63041 q^{90} +3.74111 q^{91} +4.19488 q^{92} +2.52690 q^{93} +0.840909 q^{94} +14.8980 q^{95} +5.76958 q^{96} +1.08668 q^{97} -0.834508 q^{98} -1.94241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	−0.834508	−0.590086	−0.295043	−	0.955484i	$-0.595334\pi$
$2$	−0.834508	−0.590086	−0.295043	+	0.955484i	$0.595334\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.30360	−0.651798
$5$	4.35036	1.94554	0.972769	−	0.231775i	$-0.0744534\pi$
$5$	4.35036	1.94554	0.972769	+	0.231775i	$0.0744534\pi$
$6$	0.834508	0.340686
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.75688	0.974703
$9$	1.00000	0.333333
$10$	−3.63041	−1.14804
$11$	−1.94241	−0.585657	−0.292829	−	0.956165i	$-0.594597\pi$
$11$	−1.94241	−0.585657	−0.292829	+	0.956165i	$0.594597\pi$
$12$	1.30360	0.376316
$13$	3.74111	1.03760	0.518799	−	0.854896i	$-0.326379\pi$
$13$	3.74111	1.03760	0.518799	+	0.854896i	$0.326379\pi$
$14$	−0.834508	−0.223032
$15$	−4.35036	−1.12326
$16$	0.306559	0.0766398
$17$	−2.70268	−0.655496	−0.327748	−	0.944765i	$-0.606290\pi$
$17$	−2.70268	−0.655496	−0.327748	+	0.944765i	$0.606290\pi$
$18$	−0.834508	−0.196695
$19$	3.42454	0.785644	0.392822	−	0.919615i	$-0.371499\pi$
$19$	3.42454	0.785644	0.392822	+	0.919615i	$0.371499\pi$
$20$	−5.67111	−1.26810
$21$	−1.00000	−0.218218
$22$	1.62095	0.345588
$23$	−3.21792	−0.670983	−0.335492	−	0.942043i	$-0.608902\pi$
$23$	−3.21792	−0.670983	−0.335492	+	0.942043i	$0.608902\pi$
$24$	−2.75688	−0.562745
$25$	13.9256	2.78512
$26$	−3.12199	−0.612272
$27$	−1.00000	−0.192450
$28$	−1.30360	−0.246357
$29$	1.78291	0.331079	0.165539	−	0.986203i	$-0.447064\pi$
$29$	1.78291	0.331079	0.165539	+	0.986203i	$0.447064\pi$
$30$	3.63041	0.662818
$31$	−2.52690	−0.453845	−0.226922	−	0.973913i	$-0.572866\pi$
$31$	−2.52690	−0.453845	−0.226922	+	0.973913i	$0.572866\pi$
$32$	−5.76958	−1.01993
$33$	1.94241	0.338129
$34$	2.25541	0.386799
$35$	4.35036	0.735345
$36$	−1.30360	−0.217266
$37$	6.45436	1.06109	0.530545	−	0.847657i	$-0.321987\pi$
$37$	6.45436	1.06109	0.530545	+	0.847657i	$0.321987\pi$
$38$	−2.85781	−0.463597
$39$	−3.74111	−0.599058
$40$	11.9934	1.89632
$41$	−3.78067	−0.590442	−0.295221	−	0.955429i	$-0.595393\pi$
$41$	−3.78067	−0.590442	−0.295221	+	0.955429i	$0.595393\pi$
$42$	0.834508	0.128767
$43$	−1.95214	−0.297698	−0.148849	−	0.988860i	$-0.547557\pi$
$43$	−1.95214	−0.297698	−0.148849	+	0.988860i	$0.547557\pi$
$44$	2.53211	0.381730
$45$	4.35036	0.648513
$46$	2.68538	0.395938
$47$	−1.00767	−0.146984	−0.0734919	−	0.997296i	$-0.523414\pi$
$47$	−1.00767	−0.146984	−0.0734919	+	0.997296i	$0.523414\pi$
$48$	−0.306559	−0.0442480
$49$	1.00000	0.142857
$50$	−11.6210	−1.64346
$51$	2.70268	0.378451
$52$	−4.87690	−0.676305
$53$	−3.13149	−0.430143	−0.215072	−	0.976598i	$-0.568999\pi$
$53$	−3.13149	−0.430143	−0.215072	+	0.976598i	$0.568999\pi$
$54$	0.834508	0.113562
$55$	−8.45016	−1.13942
$56$	2.75688	0.368403
$57$	−3.42454	−0.453592
$58$	−1.48785	−0.195365
$59$	−10.8579	−1.41358	−0.706790	−	0.707424i	$-0.749857\pi$
$59$	−10.8579	−1.41358	−0.706790	+	0.707424i	$0.749857\pi$
$60$	5.67111	0.732137
$61$	14.0101	1.79381	0.896907	−	0.442219i	$-0.145809\pi$
$61$	14.0101	1.79381	0.896907	+	0.442219i	$0.145809\pi$
$62$	2.10872	0.267807
$63$	1.00000	0.125988
$64$	4.20164	0.525205
$65$	16.2752	2.01869
$66$	−1.62095	−0.199525
$67$	8.69818	1.06265	0.531326	−	0.847167i	$-0.321694\pi$
$67$	8.69818	1.06265	0.531326	+	0.847167i	$0.321694\pi$
$68$	3.52320	0.427251
$69$	3.21792	0.387392
$70$	−3.63041	−0.433917
$71$	−0.279835	−0.0332103	−0.0166051	−	0.999862i	$-0.505286\pi$
$71$	−0.279835	−0.0332103	−0.0166051	+	0.999862i	$0.505286\pi$
$72$	2.75688	0.324901
$73$	9.96673	1.16652	0.583259	−	0.812286i	$-0.301777\pi$
$73$	9.96673	1.16652	0.583259	+	0.812286i	$0.301777\pi$
$74$	−5.38621	−0.626134
$75$	−13.9256	−1.60799
$76$	−4.46422	−0.512081
$77$	−1.94241	−0.221358
$78$	3.12199	0.353495
$79$	2.04327	0.229886	0.114943	−	0.993372i	$-0.463331\pi$
$79$	2.04327	0.229886	0.114943	+	0.993372i	$0.463331\pi$
$80$	1.33364	0.149106
$81$	1.00000	0.111111
$82$	3.15500	0.348412
$83$	−0.411978	−0.0452205	−0.0226102	−	0.999744i	$-0.507198\pi$
$83$	−0.411978	−0.0452205	−0.0226102	+	0.999744i	$0.507198\pi$
$84$	1.30360	0.142234
$85$	−11.7576	−1.27529
$86$	1.62907	0.175667
$87$	−1.78291	−0.191148
$88$	−5.35497	−0.570842
$89$	−2.78360	−0.295061	−0.147530	−	0.989058i	$-0.547132\pi$
$89$	−2.78360	−0.295061	−0.147530	+	0.989058i	$0.547132\pi$
$90$	−3.63041	−0.382678
$91$	3.74111	0.392175
$92$	4.19488	0.437346
$93$	2.52690	0.262027
$94$	0.840909	0.0867331
$95$	14.8980	1.52850
$96$	5.76958	0.588855
$97$	1.08668	0.110336	0.0551678	−	0.998477i	$-0.482431\pi$
$97$	1.08668	0.110336	0.0551678	+	0.998477i	$0.482431\pi$
$98$	−0.834508	−0.0842980
$99$	−1.94241	−0.195219
$100$	−18.1534	−1.81534
$101$	9.19042	0.914481	0.457240	−	0.889343i	$-0.348838\pi$
$101$	9.19042	0.914481	0.457240	+	0.889343i	$0.348838\pi$
$102$	−2.25541	−0.223318
$103$	−12.9246	−1.27350	−0.636750	−	0.771071i	$-0.719721\pi$
$103$	−12.9246	−1.27350	−0.636750	+	0.771071i	$0.719721\pi$
$104$	10.3138	1.01135
$105$	−4.35036	−0.424551
$106$	2.61325	0.253822
$107$	18.3463	1.77360	0.886801	−	0.462152i	$-0.152923\pi$
$107$	18.3463	1.77360	0.886801	+	0.462152i	$0.152923\pi$
$108$	1.30360	0.125439
$109$	14.3238	1.37197	0.685987	−	0.727614i	$-0.259371\pi$
$109$	14.3238	1.37197	0.685987	+	0.727614i	$0.259371\pi$
$110$	7.05172	0.672355
$111$	−6.45436	−0.612621
$112$	0.306559	0.0289671
$113$	13.2949	1.25068	0.625341	−	0.780352i	$-0.284960\pi$
$113$	13.2949	1.25068	0.625341	+	0.780352i	$0.284960\pi$
$114$	2.85781	0.267658
$115$	−13.9991	−1.30542
$116$	−2.32420	−0.215797
$117$	3.74111	0.345866
$118$	9.06101	0.834133
$119$	−2.70268	−0.247754
$120$	−11.9934	−1.09484
$121$	−7.22706	−0.657006
$122$	−11.6916	−1.05850
$123$	3.78067	0.340892
$124$	3.29406	0.295815
$125$	38.8296	3.47302
$126$	−0.834508	−0.0743439
$127$	−6.29331	−0.558441	−0.279220	−	0.960227i	$-0.590076\pi$
$127$	−6.29331	−0.558441	−0.279220	+	0.960227i	$0.590076\pi$
$128$	8.03286	0.710011
$129$	1.95214	0.171876
$130$	−13.5818	−1.19120
$131$	11.3761	0.993934	0.496967	−	0.867769i	$-0.334447\pi$
$131$	11.3761	0.993934	0.496967	+	0.867769i	$0.334447\pi$
$132$	−2.53211	−0.220392
$133$	3.42454	0.296945
$134$	−7.25870	−0.627056
$135$	−4.35036	−0.374419
$136$	−7.45095	−0.638914
$137$	−4.20473	−0.359234	−0.179617	−	0.983737i	$-0.557486\pi$
$137$	−4.20473	−0.359234	−0.179617	+	0.983737i	$0.557486\pi$
$138$	−2.68538	−0.228595
$139$	1.27343	0.108011	0.0540056	−	0.998541i	$-0.482801\pi$
$139$	1.27343	0.108011	0.0540056	+	0.998541i	$0.482801\pi$
$140$	−5.67111	−0.479296
$141$	1.00767	0.0848612
$142$	0.233524	0.0195969
$143$	−7.26676	−0.607677
$144$	0.306559	0.0255466
$145$	7.75631	0.644126
$146$	−8.31731	−0.688346
$147$	−1.00000	−0.0824786
$148$	−8.41388	−0.691617
$149$	5.26328	0.431185	0.215592	−	0.976483i	$-0.430832\pi$
$149$	5.26328	0.431185	0.215592	+	0.976483i	$0.430832\pi$
$150$	11.6210	0.948853
$151$	12.4230	1.01097	0.505484	−	0.862836i	$-0.331314\pi$
$151$	12.4230	1.01097	0.505484	+	0.862836i	$0.331314\pi$
$152$	9.44104	0.765769
$153$	−2.70268	−0.218499
$154$	1.62095	0.130620
$155$	−10.9929	−0.882972
$156$	4.87690	0.390465
$157$	−18.2916	−1.45983	−0.729915	−	0.683538i	$-0.760441\pi$
$157$	−18.2916	−1.45983	−0.729915	+	0.683538i	$0.760441\pi$
$158$	−1.70512	−0.135652
$159$	3.13149	0.248343
$160$	−25.0997	−1.98431
$161$	−3.21792	−0.253608
$162$	−0.834508	−0.0655651
$163$	0.836248	0.0655000	0.0327500	−	0.999464i	$-0.489573\pi$
$163$	0.836248	0.0655000	0.0327500	+	0.999464i	$0.489573\pi$
$164$	4.92848	0.384849
$165$	8.45016	0.657844
$166$	0.343799	0.0266840
$167$	12.0968	0.936078	0.468039	−	0.883708i	$-0.344961\pi$
$167$	12.0968	0.936078	0.468039	+	0.883708i	$0.344961\pi$
$168$	−2.75688	−0.212698
$169$	0.995928	0.0766098
$170$	9.81182	0.752532
$171$	3.42454	0.261881
$172$	2.54480	0.194039
$173$	−12.8790	−0.979169	−0.489585	−	0.871956i	$-0.662852\pi$
$173$	−12.8790	−0.979169	−0.489585	+	0.871956i	$0.662852\pi$
$174$	1.48785	0.112794
$175$	13.9256	1.05268
$176$	−0.595462	−0.0448846
$177$	10.8579	0.816130
$178$	2.32293	0.174111
$179$	−7.34079	−0.548676	−0.274338	−	0.961633i	$-0.588459\pi$
$179$	−7.34079	−0.548676	−0.274338	+	0.961633i	$0.588459\pi$
$180$	−5.67111	−0.422700
$181$	−2.59558	−0.192928	−0.0964639	−	0.995336i	$-0.530753\pi$
$181$	−2.59558	−0.192928	−0.0964639	+	0.995336i	$0.530753\pi$
$182$	−3.12199	−0.231417
$183$	−14.0101	−1.03566
$184$	−8.87142	−0.654010
$185$	28.0788	2.06439
$186$	−2.10872	−0.154619
$187$	5.24970	0.383896
$188$	1.31360	0.0958039
$189$	−1.00000	−0.0727393
$190$	−12.4325	−0.901947
$191$	−19.2841	−1.39535	−0.697674	−	0.716415i	$-0.745782\pi$
$191$	−19.2841	−1.39535	−0.697674	+	0.716415i	$0.745782\pi$
$192$	−4.20164	−0.303227
$193$	19.1010	1.37492	0.687460	−	0.726223i	$-0.258726\pi$
$193$	19.1010	1.37492	0.687460	+	0.726223i	$0.258726\pi$
$194$	−0.906842	−0.0651075
$195$	−16.2752	−1.16549
$196$	−1.30360	−0.0931141
$197$	−10.8303	−0.771628	−0.385814	−	0.922577i	$-0.626079\pi$
$197$	−10.8303	−0.771628	−0.385814	+	0.922577i	$0.626079\pi$
$198$	1.62095	0.115196
$199$	1.13271	0.0802958	0.0401479	−	0.999194i	$-0.487217\pi$
$199$	1.13271	0.0802958	0.0401479	+	0.999194i	$0.487217\pi$
$200$	38.3912	2.71467
$201$	−8.69818	−0.613522
$202$	−7.66947	−0.539622
$203$	1.78291	0.125136
$204$	−3.52320	−0.246674
$205$	−16.4473	−1.14873
$206$	10.7857	0.751474
$207$	−3.21792	−0.223661
$208$	1.14687	0.0795213
$209$	−6.65185	−0.460118
$210$	3.63041	0.250522
$211$	−16.5849	−1.14175	−0.570874	−	0.821038i	$-0.693396\pi$
$211$	−16.5849	−1.14175	−0.570874	+	0.821038i	$0.693396\pi$
$212$	4.08220	0.280367
$213$	0.279835	0.0191740
$214$	−15.3101	−1.04658
$215$	−8.49249	−0.579183
$216$	−2.75688	−0.187582
$217$	−2.52690	−0.171537
$218$	−11.9533	−0.809583
$219$	−9.96673	−0.673489
$220$	11.0156	0.742671
$221$	−10.1110	−0.680141
$222$	5.38621	0.361499
$223$	20.7929	1.39239	0.696197	−	0.717851i	$-0.254874\pi$
$223$	20.7929	1.39239	0.696197	+	0.717851i	$0.254874\pi$
$224$	−5.76958	−0.385496
$225$	13.9256	0.928374
$226$	−11.0947	−0.738010
$227$	−21.4450	−1.42336	−0.711679	−	0.702505i	$-0.752065\pi$
$227$	−21.4450	−1.42336	−0.711679	+	0.702505i	$0.752065\pi$
$228$	4.46422	0.295650
$229$	−2.03676	−0.134593	−0.0672964	−	0.997733i	$-0.521437\pi$
$229$	−2.03676	−0.134593	−0.0672964	+	0.997733i	$0.521437\pi$
$230$	11.6824	0.770313
$231$	1.94241	0.127801
$232$	4.91527	0.322703
$233$	1.88898	0.123751	0.0618755	−	0.998084i	$-0.480292\pi$
$233$	1.88898	0.123751	0.0618755	+	0.998084i	$0.480292\pi$
$234$	−3.12199	−0.204091
$235$	−4.38373	−0.285963
$236$	14.1543	0.921369
$237$	−2.04327	−0.132725
$238$	2.25541	0.146196
$239$	−6.43639	−0.416335	−0.208168	−	0.978093i	$-0.566750\pi$
$239$	−6.43639	−0.416335	−0.208168	+	0.978093i	$0.566750\pi$
$240$	−1.33364	−0.0860862
$241$	5.74514	0.370077	0.185038	−	0.982731i	$-0.440759\pi$
$241$	5.74514	0.370077	0.185038	+	0.982731i	$0.440759\pi$
$242$	6.03104	0.387690
$243$	−1.00000	−0.0641500
$244$	−18.2636	−1.16921
$245$	4.35036	0.277934
$246$	−3.15500	−0.201156
$247$	12.8116	0.815182
$248$	−6.96635	−0.442364
$249$	0.411978	0.0261081
$250$	−32.4036	−2.04938
$251$	−17.7413	−1.11982	−0.559911	−	0.828553i	$-0.689165\pi$
$251$	−17.7413	−1.11982	−0.559911	+	0.828553i	$0.689165\pi$
$252$	−1.30360	−0.0821189
$253$	6.25051	0.392966
$254$	5.25181	0.329528
$255$	11.7576	0.736291
$256$	−15.1068	−0.944173
$257$	11.8065	0.736469	0.368234	−	0.929733i	$-0.379962\pi$
$257$	11.8065	0.736469	0.368234	+	0.929733i	$0.379962\pi$
$258$	−1.62907	−0.101422
$259$	6.45436	0.401054
$260$	−21.2163	−1.31578
$261$	1.78291	0.110360
$262$	−9.49344	−0.586506
$263$	8.15420	0.502809	0.251405	−	0.967882i	$-0.419108\pi$
$263$	8.15420	0.502809	0.251405	+	0.967882i	$0.419108\pi$
$264$	5.35497	0.329576
$265$	−13.6231	−0.836861
$266$	−2.85781	−0.175223
$267$	2.78360	0.170353
$268$	−11.3389	−0.692635
$269$	2.75798	0.168157	0.0840786	−	0.996459i	$-0.473205\pi$
$269$	2.75798	0.168157	0.0840786	+	0.996459i	$0.473205\pi$
$270$	3.63041	0.220939
$271$	27.8662	1.69275	0.846377	−	0.532585i	$-0.178779\pi$
$271$	27.8662	1.69275	0.846377	+	0.532585i	$0.178779\pi$
$272$	−0.828531	−0.0502370
$273$	−3.74111	−0.226422
$274$	3.50888	0.211979
$275$	−27.0492	−1.63113
$276$	−4.19488	−0.252502
$277$	−8.35434	−0.501963	−0.250982	−	0.967992i	$-0.580753\pi$
$277$	−8.35434	−0.501963	−0.250982	+	0.967992i	$0.580753\pi$
$278$	−1.06269	−0.0637359
$279$	−2.52690	−0.151282
$280$	11.9934	0.716743
$281$	−14.2681	−0.851162	−0.425581	−	0.904920i	$-0.639930\pi$
$281$	−14.2681	−0.851162	−0.425581	+	0.904920i	$0.639930\pi$
$282$	−0.840909	−0.0500754
$283$	−18.4765	−1.09832	−0.549158	−	0.835718i	$-0.685052\pi$
$283$	−18.4765	−1.09832	−0.549158	+	0.835718i	$0.685052\pi$
$284$	0.364792	0.0216464
$285$	−14.8980	−0.882480
$286$	6.06416	0.358582
$287$	−3.78067	−0.223166
$288$	−5.76958	−0.339976
$289$	−9.69553	−0.570325
$290$	−6.47270	−0.380090
$291$	−1.08668	−0.0637023
$292$	−12.9926	−0.760334
$293$	−19.5460	−1.14189	−0.570943	−	0.820989i	$-0.693422\pi$
$293$	−19.5460	−1.14189	−0.570943	+	0.820989i	$0.693422\pi$
$294$	0.834508	0.0486695
$295$	−47.2358	−2.75017
$296$	17.7939	1.03425
$297$	1.94241	0.112710
$298$	−4.39225	−0.254436
$299$	−12.0386	−0.696211
$300$	18.1534	1.04809
$301$	−1.95214	−0.112519
$302$	−10.3671	−0.596558
$303$	−9.19042	−0.527976
$304$	1.04982	0.0602115
$305$	60.9491	3.48993
$306$	2.25541	0.128933
$307$	−0.513617	−0.0293137	−0.0146568	−	0.999893i	$-0.504666\pi$
$307$	−0.513617	−0.0293137	−0.0146568	+	0.999893i	$0.504666\pi$
$308$	2.53211	0.144281
$309$	12.9246	0.735255
$310$	9.17367	0.521030
$311$	11.0588	0.627089	0.313545	−	0.949573i	$-0.398483\pi$
$311$	11.0588	0.627089	0.313545	+	0.949573i	$0.398483\pi$
$312$	−10.3138	−0.583903
$313$	14.1771	0.801340	0.400670	−	0.916223i	$-0.368777\pi$
$313$	14.1771	0.801340	0.400670	+	0.916223i	$0.368777\pi$
$314$	15.2645	0.861426
$315$	4.35036	0.245115
$316$	−2.66360	−0.149839
$317$	−8.69154	−0.488165	−0.244083	−	0.969754i	$-0.578487\pi$
$317$	−8.69154	−0.488165	−0.244083	+	0.969754i	$0.578487\pi$
$318$	−2.61325	−0.146544
$319$	−3.46314	−0.193899
$320$	18.2786	1.02181
$321$	−18.3463	−1.02399
$322$	2.68538	0.149650
$323$	−9.25543	−0.514986
$324$	−1.30360	−0.0724221
$325$	52.0973	2.88984
$326$	−0.697855	−0.0386506
$327$	−14.3238	−0.792109
$328$	−10.4229	−0.575506
$329$	−1.00767	−0.0555547
$330$	−7.05172	−0.388184
$331$	6.42831	0.353332	0.176666	−	0.984271i	$-0.443469\pi$
$331$	6.42831	0.353332	0.176666	+	0.984271i	$0.443469\pi$
$332$	0.537054	0.0294746
$333$	6.45436	0.353697
$334$	−10.0949	−0.552366
$335$	37.8402	2.06743
$336$	−0.306559	−0.0167242
$337$	−19.4669	−1.06043	−0.530216	−	0.847863i	$-0.677889\pi$
$337$	−19.4669	−1.06043	−0.530216	+	0.847863i	$0.677889\pi$
$338$	−0.831110	−0.0452064
$339$	−13.2949	−0.722082
$340$	15.3272	0.831234
$341$	4.90826	0.265797
$342$	−2.85781	−0.154532
$343$	1.00000	0.0539949
$344$	−5.38180	−0.290167
$345$	13.9991	0.753687
$346$	10.7476	0.577794
$347$	30.7511	1.65080	0.825402	−	0.564546i	$-0.190949\pi$
$347$	30.7511	1.65080	0.825402	+	0.564546i	$0.190949\pi$
$348$	2.32420	0.124590
$349$	11.0641	0.592250	0.296125	−	0.955149i	$-0.404305\pi$
$349$	11.0641	0.592250	0.296125	+	0.955149i	$0.404305\pi$
$350$	−11.6210	−0.621170
$351$	−3.74111	−0.199686
$352$	11.2069	0.597328
$353$	17.2843	0.919950	0.459975	−	0.887932i	$-0.347858\pi$
$353$	17.2843	0.919950	0.459975	+	0.887932i	$0.347858\pi$
$354$	−9.06101	−0.481587
$355$	−1.21738	−0.0646119
$356$	3.62869	0.192320
$357$	2.70268	0.143041
$358$	6.12594	0.323766
$359$	5.44838	0.287554	0.143777	−	0.989610i	$-0.454075\pi$
$359$	5.44838	0.287554	0.143777	+	0.989610i	$0.454075\pi$
$360$	11.9934	0.632108
$361$	−7.27252	−0.382764
$362$	2.16603	0.113844
$363$	7.22706	0.379322
$364$	−4.87690	−0.255619
$365$	43.3588	2.26951
$366$	11.6916	0.611128
$367$	11.7565	0.613683	0.306842	−	0.951761i	$-0.400728\pi$
$367$	11.7565	0.613683	0.306842	+	0.951761i	$0.400728\pi$
$368$	−0.986483	−0.0514240
$369$	−3.78067	−0.196814
$370$	−23.4319	−1.21817
$371$	−3.13149	−0.162579
$372$	−3.29406	−0.170789
$373$	11.9246	0.617434	0.308717	−	0.951154i	$-0.400100\pi$
$373$	11.9246	0.617434	0.308717	+	0.951154i	$0.400100\pi$
$374$	−4.38091	−0.226532
$375$	−38.8296	−2.00515
$376$	−2.77802	−0.143266
$377$	6.67008	0.343527
$378$	0.834508	0.0429224
$379$	28.7777	1.47821	0.739107	−	0.673588i	$-0.235248\pi$
$379$	28.7777	1.47821	0.739107	+	0.673588i	$0.235248\pi$
$380$	−19.4210	−0.996274
$381$	6.29331	0.322416
$382$	16.0927	0.823375
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−8.03286	−0.409925
$385$	−8.45016	−0.430660
$386$	−15.9399	−0.811321
$387$	−1.95214	−0.0992327
$388$	−1.41659	−0.0719166
$389$	4.43495	0.224861	0.112430	−	0.993660i	$-0.464136\pi$
$389$	4.43495	0.224861	0.112430	+	0.993660i	$0.464136\pi$
$390$	13.5818	0.687739
$391$	8.69701	0.439827
$392$	2.75688	0.139243
$393$	−11.3761	−0.573848
$394$	9.03799	0.455327
$395$	8.88895	0.447252
$396$	2.53211	0.127243
$397$	−8.83366	−0.443349	−0.221674	−	0.975121i	$-0.571152\pi$
$397$	−8.83366	−0.443349	−0.221674	+	0.975121i	$0.571152\pi$
$398$	−0.945257	−0.0473814
$399$	−3.42454	−0.171441
$400$	4.26902	0.213451
$401$	18.9708	0.947356	0.473678	−	0.880698i	$-0.342926\pi$
$401$	18.9708	0.947356	0.473678	+	0.880698i	$0.342926\pi$
$402$	7.25870	0.362031
$403$	−9.45342	−0.470908
$404$	−11.9806	−0.596057
$405$	4.35036	0.216171
$406$	−1.48785	−0.0738410
$407$	−12.5370	−0.621435
$408$	7.45095	0.368877
$409$	−3.00064	−0.148372	−0.0741860	−	0.997244i	$-0.523636\pi$
$409$	−3.00064	−0.148372	−0.0741860	+	0.997244i	$0.523636\pi$
$410$	13.7254	0.677848
$411$	4.20473	0.207404
$412$	16.8485	0.830065
$413$	−10.8579	−0.534283
$414$	2.68538	0.131979
$415$	−1.79225	−0.0879782
$416$	−21.5847	−1.05827
$417$	−1.27343	−0.0623603
$418$	5.55102	0.271509
$419$	11.8419	0.578516	0.289258	−	0.957251i	$-0.406592\pi$
$419$	11.8419	0.578516	0.289258	+	0.957251i	$0.406592\pi$
$420$	5.67111	0.276722
$421$	7.87463	0.383786	0.191893	−	0.981416i	$-0.438537\pi$
$421$	7.87463	0.383786	0.191893	+	0.981416i	$0.438537\pi$
$422$	13.8402	0.673730
$423$	−1.00767	−0.0489946
$424$	−8.63314	−0.419262
$425$	−37.6364	−1.82564
$426$	−0.233524	−0.0113143
$427$	14.0101	0.677998
$428$	−23.9161	−1.15603
$429$	7.26676	0.350842
$430$	7.08705	0.341768
$431$	−6.95581	−0.335049	−0.167525	−	0.985868i	$-0.553577\pi$
$431$	−6.95581	−0.335049	−0.167525	+	0.985868i	$0.553577\pi$
$432$	−0.306559	−0.0147493
$433$	−26.5433	−1.27559	−0.637796	−	0.770205i	$-0.720154\pi$
$433$	−26.5433	−1.27559	−0.637796	+	0.770205i	$0.720154\pi$
$434$	2.10872	0.101222
$435$	−7.75631	−0.371886
$436$	−18.6725	−0.894250
$437$	−11.0199	−0.527154
$438$	8.31731	0.397417
$439$	30.0467	1.43405	0.717026	−	0.697046i	$-0.245503\pi$
$439$	30.0467	1.43405	0.717026	+	0.697046i	$0.245503\pi$
$440$	−23.2960	−1.11060
$441$	1.00000	0.0476190
$442$	8.43773	0.401342
$443$	17.0973	0.812318	0.406159	−	0.913802i	$-0.366868\pi$
$443$	17.0973	0.812318	0.406159	+	0.913802i	$0.366868\pi$
$444$	8.41388	0.399305
$445$	−12.1096	−0.574052
$446$	−17.3518	−0.821632
$447$	−5.26328	−0.248945
$448$	4.20164	0.198509
$449$	−9.28356	−0.438118	−0.219059	−	0.975712i	$-0.570299\pi$
$449$	−9.28356	−0.438118	−0.219059	+	0.975712i	$0.570299\pi$
$450$	−11.6210	−0.547820
$451$	7.34360	0.345797
$452$	−17.3312	−0.815193
$453$	−12.4230	−0.583682
$454$	17.8961	0.839904
$455$	16.2752	0.762992
$456$	−9.44104	−0.442117
$457$	−6.04699	−0.282866	−0.141433	−	0.989948i	$-0.545171\pi$
$457$	−6.04699	−0.282866	−0.141433	+	0.989948i	$0.545171\pi$
$458$	1.69969	0.0794213
$459$	2.70268	0.126150
$460$	18.2492	0.850873
$461$	18.7515	0.873345	0.436673	−	0.899620i	$-0.356157\pi$
$461$	18.7515	0.873345	0.436673	+	0.899620i	$0.356157\pi$
$462$	−1.62095	−0.0754135
$463$	0.567584	0.0263779	0.0131889	−	0.999913i	$-0.495802\pi$
$463$	0.567584	0.0263779	0.0131889	+	0.999913i	$0.495802\pi$
$464$	0.546568	0.0253738
$465$	10.9929	0.509784
$466$	−1.57637	−0.0730238
$467$	−28.2902	−1.30911	−0.654557	−	0.756012i	$-0.727145\pi$
$467$	−28.2902	−1.30911	−0.654557	+	0.756012i	$0.727145\pi$
$468$	−4.87690	−0.225435
$469$	8.69818	0.401645
$470$	3.65825	0.168743
$471$	18.2916	0.842834
$472$	−29.9339	−1.37782
$473$	3.79184	0.174349
$474$	1.70512	0.0783189
$475$	47.6888	2.18811
$476$	3.52320	0.161486
$477$	−3.13149	−0.143381
$478$	5.37121	0.245674
$479$	38.3683	1.75309	0.876546	−	0.481318i	$-0.159842\pi$
$479$	38.3683	1.75309	0.876546	+	0.481318i	$0.159842\pi$
$480$	25.0997	1.14564
$481$	24.1465	1.10098
$482$	−4.79436	−0.218377
$483$	3.21792	0.146421
$484$	9.42118	0.428235
$485$	4.72744	0.214662
$486$	0.834508	0.0378540
$487$	−24.8608	−1.12655	−0.563276	−	0.826269i	$-0.690459\pi$
$487$	−24.8608	−1.12655	−0.563276	+	0.826269i	$0.690459\pi$
$488$	38.6242	1.74844
$489$	−0.836248	−0.0378164
$490$	−3.63041	−0.164005
$491$	−19.6386	−0.886279	−0.443140	−	0.896453i	$-0.646135\pi$
$491$	−19.6386	−0.886279	−0.443140	+	0.896453i	$0.646135\pi$
$492$	−4.92848	−0.222193
$493$	−4.81864	−0.217021
$494$	−10.6914	−0.481028
$495$	−8.45016	−0.379806
$496$	−0.774644	−0.0347825
$497$	−0.279835	−0.0125523
$498$	−0.343799	−0.0154060
$499$	−6.26280	−0.280362	−0.140181	−	0.990126i	$-0.544768\pi$
$499$	−6.26280	−0.280362	−0.140181	+	0.990126i	$0.544768\pi$
$500$	−50.6181	−2.26371
$501$	−12.0968	−0.540445
$502$	14.8053	0.660791
$503$	−30.9928	−1.38190	−0.690950	−	0.722902i	$-0.742808\pi$
$503$	−30.9928	−1.38190	−0.690950	+	0.722902i	$0.742808\pi$
$504$	2.75688	0.122801
$505$	39.9816	1.77916
$506$	−5.21610	−0.231884
$507$	−0.995928	−0.0442307
$508$	8.20393	0.363991
$509$	−8.20451	−0.363658	−0.181829	−	0.983330i	$-0.558202\pi$
$509$	−8.20451	−0.363658	−0.181829	+	0.983330i	$0.558202\pi$
$510$	−9.81182	−0.434475
$511$	9.96673	0.440902
$512$	−3.45901	−0.152868
$513$	−3.42454	−0.151197
$514$	−9.85261	−0.434580
$515$	−56.2266	−2.47764
$516$	−2.54480	−0.112029
$517$	1.95730	0.0860822
$518$	−5.38621	−0.236657
$519$	12.8790	0.565324
$520$	44.8687	1.96762
$521$	−24.3423	−1.06645	−0.533227	−	0.845972i	$-0.679021\pi$
$521$	−24.3423	−1.06645	−0.533227	+	0.845972i	$0.679021\pi$
$522$	−1.48785	−0.0651216
$523$	13.6936	0.598780	0.299390	−	0.954131i	$-0.403217\pi$
$523$	13.6936	0.598780	0.299390	+	0.954131i	$0.403217\pi$
$524$	−14.8298	−0.647845
$525$	−13.9256	−0.607763
$526$	−6.80474	−0.296701
$527$	6.82940	0.297493
$528$	0.595462	0.0259142
$529$	−12.6450	−0.549781
$530$	11.3686	0.493820
$531$	−10.8579	−0.471193
$532$	−4.46422	−0.193549
$533$	−14.1439	−0.612642
$534$	−2.32293	−0.100523
$535$	79.8128	3.45061
$536$	23.9798	1.03577
$537$	7.34079	0.316778
$538$	−2.30156	−0.0992272
$539$	−1.94241	−0.0836653
$540$	5.67111	0.244046
$541$	31.0530	1.33507	0.667537	−	0.744577i	$-0.267349\pi$
$541$	31.0530	1.33507	0.667537	+	0.744577i	$0.267349\pi$
$542$	−23.2546	−0.998870
$543$	2.59558	0.111387
$544$	15.5933	0.668558
$545$	62.3138	2.66923
$546$	3.12199	0.133609
$547$	−31.5283	−1.34805	−0.674026	−	0.738708i	$-0.735436\pi$
$547$	−31.5283	−1.34805	−0.674026	+	0.738708i	$0.735436\pi$
$548$	5.48127	0.234148
$549$	14.0101	0.597938
$550$	22.5727	0.962505
$551$	6.10566	0.260110
$552$	8.87142	0.377593
$553$	2.04327	0.0868887
$554$	6.97176	0.296202
$555$	−28.0788	−1.19188
$556$	−1.66004	−0.0704016
$557$	29.3517	1.24367	0.621835	−	0.783148i	$-0.286387\pi$
$557$	29.3517	1.24367	0.621835	+	0.783148i	$0.286387\pi$
$558$	2.10872	0.0892691
$559$	−7.30316	−0.308891
$560$	1.33364	0.0563566
$561$	−5.24970	−0.221642
$562$	11.9068	0.502259
$563$	33.8368	1.42605	0.713025	−	0.701139i	$-0.247325\pi$
$563$	33.8368	1.42605	0.713025	+	0.701139i	$0.247325\pi$
$564$	−1.31360	−0.0553124
$565$	57.8377	2.43325
$566$	15.4188	0.648101
$567$	1.00000	0.0419961
$568$	−0.771470	−0.0323702
$569$	−3.18426	−0.133491	−0.0667456	−	0.997770i	$-0.521262\pi$
$569$	−3.18426	−0.133491	−0.0667456	+	0.997770i	$0.521262\pi$
$570$	12.4325	0.520739
$571$	6.30587	0.263893	0.131946	−	0.991257i	$-0.457877\pi$
$571$	6.30587	0.263893	0.131946	+	0.991257i	$0.457877\pi$
$572$	9.47292	0.396083
$573$	19.2841	0.805604
$574$	3.15500	0.131687
$575$	−44.8115	−1.86877
$576$	4.20164	0.175068
$577$	−32.3197	−1.34549	−0.672743	−	0.739876i	$-0.734884\pi$
$577$	−32.3197	−1.34549	−0.672743	+	0.739876i	$0.734884\pi$
$578$	8.09099	0.336541
$579$	−19.1010	−0.793810
$580$	−10.1111	−0.419841
$581$	−0.411978	−0.0170917
$582$	0.906842	0.0375898
$583$	6.08262	0.251917
$584$	27.4771	1.13701
$585$	16.2752	0.672896
$586$	16.3112	0.673811
$587$	10.1443	0.418699	0.209349	−	0.977841i	$-0.432865\pi$
$587$	10.1443	0.418699	0.209349	+	0.977841i	$0.432865\pi$
$588$	1.30360	0.0537594
$589$	−8.65347	−0.356560
$590$	39.4186	1.62284
$591$	10.8303	0.445500
$592$	1.97864	0.0813217
$593$	43.7211	1.79541	0.897706	−	0.440595i	$-0.145233\pi$
$593$	43.7211	1.79541	0.897706	+	0.440595i	$0.145233\pi$
$594$	−1.62095	−0.0665085
$595$	−11.7576	−0.482015
$596$	−6.86120	−0.281046
$597$	−1.13271	−0.0463588
$598$	10.0463	0.410824
$599$	13.3764	0.546543	0.273272	−	0.961937i	$-0.411894\pi$
$599$	13.3764	0.546543	0.273272	+	0.961937i	$0.411894\pi$
$600$	−38.3912	−1.56731
$601$	31.1232	1.26954	0.634771	−	0.772700i	$-0.281094\pi$
$601$	31.1232	1.26954	0.634771	+	0.772700i	$0.281094\pi$
$602$	1.62907	0.0663961
$603$	8.69818	0.354217
$604$	−16.1946	−0.658947
$605$	−31.4403	−1.27823
$606$	7.66947	0.311551
$607$	34.5673	1.40304	0.701521	−	0.712649i	$-0.252505\pi$
$607$	34.5673	1.40304	0.701521	+	0.712649i	$0.252505\pi$
$608$	−19.7582	−0.801299
$609$	−1.78291	−0.0722473
$610$	−50.8625	−2.05936
$611$	−3.76981	−0.152510
$612$	3.52320	0.142417
$613$	−31.6330	−1.27765	−0.638823	−	0.769354i	$-0.720578\pi$
$613$	−31.6330	−1.27765	−0.638823	+	0.769354i	$0.720578\pi$
$614$	0.428617	0.0172976
$615$	16.4473	0.663218
$616$	−5.35497	−0.215758
$617$	−14.5502	−0.585770	−0.292885	−	0.956148i	$-0.594615\pi$
$617$	−14.5502	−0.585770	−0.292885	+	0.956148i	$0.594615\pi$
$618$	−10.7857	−0.433864
$619$	7.33812	0.294944	0.147472	−	0.989066i	$-0.452886\pi$
$619$	7.33812	0.294944	0.147472	+	0.989066i	$0.452886\pi$
$620$	14.3303	0.575520
$621$	3.21792	0.129131
$622$	−9.22869	−0.370037
$623$	−2.78360	−0.111522
$624$	−1.14687	−0.0459116
$625$	99.2944	3.97178
$626$	−11.8309	−0.472859
$627$	6.65185	0.265649
$628$	23.8449	0.951515
$629$	−17.4441	−0.695540
$630$	−3.63041	−0.144639
$631$	0.451826	0.0179869	0.00899346	−	0.999960i	$-0.497137\pi$
$631$	0.451826	0.0179869	0.00899346	+	0.999960i	$0.497137\pi$
$632$	5.63304	0.224070
$633$	16.5849	0.659189
$634$	7.25316	0.288060
$635$	−27.3781	−1.08647
$636$	−4.08220	−0.161870
$637$	3.74111	0.148228
$638$	2.89002	0.114417
$639$	−0.279835	−0.0110701
$640$	34.9458	1.38135
$641$	49.2441	1.94502	0.972512	−	0.232853i	$-0.0748062\pi$
$641$	49.2441	1.94502	0.972512	+	0.232853i	$0.0748062\pi$
$642$	15.3101	0.604242
$643$	−5.03511	−0.198565	−0.0992827	−	0.995059i	$-0.531655\pi$
$643$	−5.03511	−0.198565	−0.0992827	+	0.995059i	$0.531655\pi$
$644$	4.19488	0.165301
$645$	8.49249	0.334391
$646$	7.72373	0.303886
$647$	−28.5426	−1.12213	−0.561063	−	0.827773i	$-0.689607\pi$
$647$	−28.5426	−1.12213	−0.561063	+	0.827773i	$0.689607\pi$
$648$	2.75688	0.108300
$649$	21.0905	0.827873
$650$	−43.4756	−1.70525
$651$	2.52690	0.0990370
$652$	−1.09013	−0.0426928
$653$	34.7396	1.35947	0.679733	−	0.733460i	$-0.262096\pi$
$653$	34.7396	1.35947	0.679733	+	0.733460i	$0.262096\pi$
$654$	11.9533	0.467413
$655$	49.4901	1.93374
$656$	−1.15900	−0.0452513
$657$	9.96673	0.388839
$658$	0.840909	0.0327820
$659$	−1.27141	−0.0495271	−0.0247636	−	0.999693i	$-0.507883\pi$
$659$	−1.27141	−0.0495271	−0.0247636	+	0.999693i	$0.507883\pi$
$660$	−11.0156	−0.428782
$661$	38.0353	1.47940	0.739702	−	0.672935i	$-0.234967\pi$
$661$	38.0353	1.47940	0.739702	+	0.672935i	$0.234967\pi$
$662$	−5.36447	−0.208496
$663$	10.1110	0.392680
$664$	−1.13577	−0.0440766
$665$	14.8980	0.577719
$666$	−5.38621	−0.208711
$667$	−5.73728	−0.222148
$668$	−15.7693	−0.610134
$669$	−20.7929	−0.803899
$670$	−31.5779	−1.21996
$671$	−27.2134	−1.05056
$672$	5.76958	0.222566
$673$	43.8105	1.68877	0.844385	−	0.535737i	$-0.179966\pi$
$673$	43.8105	1.68877	0.844385	+	0.535737i	$0.179966\pi$
$674$	16.2453	0.625746
$675$	−13.9256	−0.535997
$676$	−1.29829	−0.0499342
$677$	26.1621	1.00549	0.502745	−	0.864435i	$-0.332324\pi$
$677$	26.1621	1.00549	0.502745	+	0.864435i	$0.332324\pi$
$678$	11.0947	0.426090
$679$	1.08668	0.0417029
$680$	−32.4143	−1.24303
$681$	21.4450	0.821776
$682$	−4.09598	−0.156843
$683$	−39.1700	−1.49880	−0.749398	−	0.662119i	$-0.769657\pi$
$683$	−39.1700	−1.49880	−0.749398	+	0.662119i	$0.769657\pi$
$684$	−4.46422	−0.170694
$685$	−18.2921	−0.698904
$686$	−0.834508	−0.0318617
$687$	2.03676	0.0777072
$688$	−0.598445	−0.0228155
$689$	−11.7153	−0.446316
$690$	−11.6824	−0.444740
$691$	42.5813	1.61987	0.809935	−	0.586520i	$-0.199502\pi$
$691$	42.5813	1.61987	0.809935	+	0.586520i	$0.199502\pi$
$692$	16.7890	0.638221
$693$	−1.94241	−0.0737859
$694$	−25.6620	−0.974116
$695$	5.53989	0.210140
$696$	−4.91527	−0.186313
$697$	10.2179	0.387032
$698$	−9.23311	−0.349479
$699$	−1.88898	−0.0714477
$700$	−18.1534	−0.686133
$701$	−46.6112	−1.76048	−0.880240	−	0.474529i	$-0.842619\pi$
$701$	−46.6112	−1.76048	−0.880240	+	0.474529i	$0.842619\pi$
$702$	3.12199	0.117832
$703$	22.1032	0.833639
$704$	−8.16129	−0.307590
$705$	4.38373	0.165101
$706$	−14.4239	−0.542850
$707$	9.19042	0.345641
$708$	−14.1543	−0.531952
$709$	−25.6131	−0.961921	−0.480961	−	0.876742i	$-0.659712\pi$
$709$	−25.6131	−0.961921	−0.480961	+	0.876742i	$0.659712\pi$
$710$	1.01591	0.0381266
$711$	2.04327	0.0766286
$712$	−7.67403	−0.287596
$713$	8.13137	0.304522
$714$	−2.25541	−0.0844065
$715$	−31.6130	−1.18226
$716$	9.56943	0.357626
$717$	6.43639	0.240371
$718$	−4.54671	−0.169682
$719$	22.4583	0.837555	0.418777	−	0.908089i	$-0.362459\pi$
$719$	22.4583	0.837555	0.418777	+	0.908089i	$0.362459\pi$
$720$	1.33364	0.0497019
$721$	−12.9246	−0.481337
$722$	6.06897	0.225864
$723$	−5.74514	−0.213664
$724$	3.38359	0.125750
$725$	24.8281	0.922094
$726$	−6.03104	−0.223833
$727$	12.4462	0.461604	0.230802	−	0.973001i	$-0.425865\pi$
$727$	12.4462	0.461604	0.230802	+	0.973001i	$0.425865\pi$
$728$	10.3138	0.382254
$729$	1.00000	0.0370370
$730$	−36.1833	−1.33920
$731$	5.27600	0.195140
$732$	18.2636	0.675041
$733$	−16.7490	−0.618638	−0.309319	−	0.950958i	$-0.600101\pi$
$733$	−16.7490	−0.618638	−0.309319	+	0.950958i	$0.600101\pi$
$734$	−9.81088	−0.362126
$735$	−4.35036	−0.160465
$736$	18.5661	0.684354
$737$	−16.8954	−0.622350
$738$	3.15500	0.116137
$739$	−31.8730	−1.17247	−0.586234	−	0.810142i	$-0.699390\pi$
$739$	−31.8730	−1.17247	−0.586234	+	0.810142i	$0.699390\pi$
$740$	−36.6034	−1.34557
$741$	−12.8116	−0.470646
$742$	2.61325	0.0959355
$743$	−9.46830	−0.347358	−0.173679	−	0.984802i	$-0.555566\pi$
$743$	−9.46830	−0.347358	−0.173679	+	0.984802i	$0.555566\pi$
$744$	6.96635	0.255399
$745$	22.8972	0.838887
$746$	−9.95119	−0.364339
$747$	−0.411978	−0.0150735
$748$	−6.84349	−0.250223
$749$	18.3463	0.670358
$750$	32.4036	1.18321
$751$	9.69594	0.353810	0.176905	−	0.984228i	$-0.443391\pi$
$751$	9.69594	0.353810	0.176905	+	0.984228i	$0.443391\pi$
$752$	−0.308911	−0.0112648
$753$	17.7413	0.646529
$754$	−5.56623	−0.202710
$755$	54.0444	1.96688
$756$	1.30360	0.0474114
$757$	−16.5091	−0.600032	−0.300016	−	0.953934i	$-0.596992\pi$
$757$	−16.5091	−0.600032	−0.300016	+	0.953934i	$0.596992\pi$
$758$	−24.0152	−0.872273
$759$	−6.25051	−0.226879
$760$	41.0719	1.48983
$761$	−17.2371	−0.624844	−0.312422	−	0.949943i	$-0.601140\pi$
$761$	−17.2371	−0.624844	−0.312422	+	0.949943i	$0.601140\pi$
$762$	−5.25181	−0.190253
$763$	14.3238	0.518557
$764$	25.1387	0.909486
$765$	−11.7576	−0.425098
$766$	0.834508	0.0301520
$767$	−40.6207	−1.46673
$768$	15.1068	0.545118
$769$	36.8013	1.32709	0.663544	−	0.748137i	$-0.269052\pi$
$769$	36.8013	1.32709	0.663544	+	0.748137i	$0.269052\pi$
$770$	7.05172	0.254126
$771$	−11.8065	−0.425201
$772$	−24.9000	−0.896170
$773$	−7.55123	−0.271599	−0.135800	−	0.990736i	$-0.543360\pi$
$773$	−7.55123	−0.271599	−0.135800	+	0.990736i	$0.543360\pi$
$774$	1.62907	0.0585558
$775$	−35.1886	−1.26401
$776$	2.99584	0.107544
$777$	−6.45436	−0.231549
$778$	−3.70100	−0.132687
$779$	−12.9471	−0.463877
$780$	21.2163	0.759664
$781$	0.543553	0.0194498
$782$	−7.25772	−0.259536
$783$	−1.78291	−0.0637161
$784$	0.306559	0.0109485
$785$	−79.5751	−2.84016
$786$	9.49344	0.338620
$787$	47.0522	1.67723	0.838614	−	0.544726i	$-0.183366\pi$
$787$	47.0522	1.67723	0.838614	+	0.544726i	$0.183366\pi$
$788$	14.1184	0.502946
$789$	−8.15420	−0.290297
$790$	−7.41790	−0.263917
$791$	13.2949	0.472713
$792$	−5.35497	−0.190281
$793$	52.4135	1.86126
$794$	7.37176	0.261614
$795$	13.6231	0.483162
$796$	−1.47660	−0.0523367
$797$	−18.0117	−0.638008	−0.319004	−	0.947753i	$-0.603348\pi$
$797$	−18.0117	−0.638008	−0.319004	+	0.947753i	$0.603348\pi$
$798$	2.85781	0.101165
$799$	2.72341	0.0963473
$800$	−80.3449	−2.84062
$801$	−2.78360	−0.0983535
$802$	−15.8313	−0.559022
$803$	−19.3594	−0.683179
$804$	11.3389	0.399893
$805$	−13.9991	−0.493404
$806$	7.88895	0.277876
$807$	−2.75798	−0.0970856
$808$	25.3368	0.891347
$809$	16.1433	0.567567	0.283784	−	0.958888i	$-0.408410\pi$
$809$	16.1433	0.567567	0.283784	+	0.958888i	$0.408410\pi$
$810$	−3.63041	−0.127559
$811$	−10.1648	−0.356934	−0.178467	−	0.983946i	$-0.557114\pi$
$811$	−10.1648	−0.356934	−0.178467	+	0.983946i	$0.557114\pi$
$812$	−2.32420	−0.0815634
$813$	−27.8662	−0.977312
$814$	10.4622	0.366700
$815$	3.63798	0.127433
$816$	0.828531	0.0290044
$817$	−6.68517	−0.233885
$818$	2.50406	0.0875523
$819$	3.74111	0.130725
$820$	21.4406	0.748739
$821$	−47.9201	−1.67242	−0.836211	−	0.548408i	$-0.815234\pi$
$821$	−47.9201	−1.67242	−0.836211	+	0.548408i	$0.815234\pi$
$822$	−3.50888	−0.122386
$823$	33.7727	1.17724	0.588621	−	0.808409i	$-0.299671\pi$
$823$	33.7727	1.17724	0.588621	+	0.808409i	$0.299671\pi$
$824$	−35.6315	−1.24128
$825$	27.0492	0.941731
$826$	9.06101	0.315273
$827$	49.5147	1.72180	0.860898	−	0.508777i	$-0.169902\pi$
$827$	49.5147	1.72180	0.860898	+	0.508777i	$0.169902\pi$
$828$	4.19488	0.145782
$829$	−31.6023	−1.09759	−0.548796	−	0.835956i	$-0.684914\pi$
$829$	−31.6023	−1.09759	−0.548796	+	0.835956i	$0.684914\pi$
$830$	1.49565	0.0519147
$831$	8.35434	0.289809
$832$	15.7188	0.544952
$833$	−2.70268	−0.0936423
$834$	1.06269	0.0367980
$835$	52.6254	1.82118
$836$	8.67133	0.299904
$837$	2.52690	0.0873425
$838$	−9.88217	−0.341374
$839$	−2.43715	−0.0841398	−0.0420699	−	0.999115i	$-0.513395\pi$
$839$	−2.43715	−0.0841398	−0.0420699	+	0.999115i	$0.513395\pi$
$840$	−11.9934	−0.413812
$841$	−25.8212	−0.890387
$842$	−6.57144	−0.226467
$843$	14.2681	0.491419
$844$	21.6200	0.744190
$845$	4.33264	0.149047
$846$	0.840909	0.0289110
$847$	−7.22706	−0.248325
$848$	−0.959987	−0.0329661
$849$	18.4765	0.634113
$850$	31.4079	1.07728
$851$	−20.7696	−0.711974
$852$	−0.364792	−0.0124976
$853$	38.2042	1.30809	0.654044	−	0.756456i	$-0.273071\pi$
$853$	38.2042	1.30809	0.654044	+	0.756456i	$0.273071\pi$
$854$	−11.6916	−0.400077
$855$	14.8980	0.509500
$856$	50.5784	1.72873
$857$	−33.2476	−1.13572	−0.567858	−	0.823126i	$-0.692228\pi$
$857$	−33.2476	−1.13572	−0.567858	+	0.823126i	$0.692228\pi$
$858$	−6.06416	−0.207027
$859$	−29.2224	−0.997055	−0.498528	−	0.866874i	$-0.666126\pi$
$859$	−29.2224	−0.997055	−0.498528	+	0.866874i	$0.666126\pi$
$860$	11.0708	0.377511
$861$	3.78067	0.128845
$862$	5.80467	0.197708
$863$	−32.4552	−1.10479	−0.552395	−	0.833583i	$-0.686286\pi$
$863$	−32.4552	−1.10479	−0.552395	+	0.833583i	$0.686286\pi$
$864$	5.76958	0.196285
$865$	−56.0281	−1.90501
$866$	22.1506	0.752709
$867$	9.69553	0.329277
$868$	3.29406	0.111808
$869$	−3.96886	−0.134634
$870$	6.47270	0.219445
$871$	32.5409	1.10261
$872$	39.4890	1.33727
$873$	1.08668	0.0367785
$874$	9.19620	0.311066
$875$	38.8296	1.31268
$876$	12.9926	0.438979
$877$	29.4534	0.994570	0.497285	−	0.867587i	$-0.334330\pi$
$877$	29.4534	0.994570	0.497285	+	0.867587i	$0.334330\pi$
$878$	−25.0742	−0.846214
$879$	19.5460	0.659269
$880$	−2.59047	−0.0873248
$881$	18.2832	0.615975	0.307988	−	0.951390i	$-0.400345\pi$
$881$	18.2832	0.615975	0.307988	+	0.951390i	$0.400345\pi$
$882$	−0.834508	−0.0280993
$883$	3.98504	0.134107	0.0670536	−	0.997749i	$-0.478640\pi$
$883$	3.98504	0.134107	0.0670536	+	0.997749i	$0.478640\pi$
$884$	13.1807	0.443315
$885$	47.2358	1.58781
$886$	−14.2678	−0.479337
$887$	2.47396	0.0830676	0.0415338	−	0.999137i	$-0.486776\pi$
$887$	2.47396	0.0830676	0.0415338	+	0.999137i	$0.486776\pi$
$888$	−17.7939	−0.597123
$889$	−6.29331	−0.211071
$890$	10.1056	0.338740
$891$	−1.94241	−0.0650730
$892$	−27.1055	−0.907560
$893$	−3.45081	−0.115477
$894$	4.39225	0.146899
$895$	−31.9350	−1.06747
$896$	8.03286	0.268359
$897$	12.0386	0.401958
$898$	7.74720	0.258527
$899$	−4.50524	−0.150258
$900$	−18.1534	−0.605113
$901$	8.46341	0.281957
$902$	−6.12829	−0.204050
$903$	1.95214	0.0649630
$904$	36.6525	1.21904
$905$	−11.2917	−0.375348
$906$	10.3671	0.344423
$907$	3.73482	0.124013	0.0620063	−	0.998076i	$-0.480250\pi$
$907$	3.73482	0.124013	0.0620063	+	0.998076i	$0.480250\pi$
$908$	27.9557	0.927743
$909$	9.19042	0.304827
$910$	−13.5818	−0.450231
$911$	27.0100	0.894882	0.447441	−	0.894313i	$-0.352335\pi$
$911$	27.0100	0.894882	0.447441	+	0.894313i	$0.352335\pi$
$912$	−1.04982	−0.0347631
$913$	0.800229	0.0264837
$914$	5.04626	0.166915
$915$	−60.9491	−2.01491
$916$	2.65511	0.0877274
$917$	11.3761	0.375672
$918$	−2.25541	−0.0744395
$919$	25.6932	0.847539	0.423770	−	0.905770i	$-0.360707\pi$
$919$	25.6932	0.847539	0.423770	+	0.905770i	$0.360707\pi$
$920$	−38.5938	−1.27240
$921$	0.513617	0.0169242
$922$	−15.6483	−0.515349
$923$	−1.04689	−0.0344589
$924$	−2.53211	−0.0833004
$925$	89.8808	2.95526
$926$	−0.473653	−0.0155652
$927$	−12.9246	−0.424500
$928$	−10.2867	−0.337676
$929$	−10.2634	−0.336733	−0.168366	−	0.985724i	$-0.553849\pi$
$929$	−10.2634	−0.336733	−0.168366	+	0.985724i	$0.553849\pi$
$930$	−9.17367	−0.300817
$931$	3.42454	0.112235
$932$	−2.46247	−0.0806607
$933$	−11.0588	−0.362050
$934$	23.6084	0.772490
$935$	22.8381	0.746884
$936$	10.3138	0.337117
$937$	45.2032	1.47672	0.738361	−	0.674405i	$-0.235600\pi$
$937$	45.2032	1.47672	0.738361	+	0.674405i	$0.235600\pi$
$938$	−7.25870	−0.237005
$939$	−14.1771	−0.462654
$940$	5.71461	0.186390
$941$	−18.9157	−0.616634	−0.308317	−	0.951284i	$-0.599766\pi$
$941$	−18.9157	−0.616634	−0.308317	+	0.951284i	$0.599766\pi$
$942$	−15.2645	−0.497344
$943$	12.1659	0.396177
$944$	−3.32859	−0.108336
$945$	−4.35036	−0.141517
$946$	−3.16432	−0.102881
$947$	28.5425	0.927505	0.463753	−	0.885965i	$-0.346503\pi$
$947$	28.5425	0.927505	0.463753	+	0.885965i	$0.346503\pi$
$948$	2.66360	0.0865097
$949$	37.2867	1.21038
$950$	−39.7967	−1.29117
$951$	8.69154	0.281842
$952$	−7.45095	−0.241487
$953$	32.1286	1.04075	0.520374	−	0.853939i	$-0.325793\pi$
$953$	32.1286	1.04075	0.520374	+	0.853939i	$0.325793\pi$
$954$	2.61325	0.0846072
$955$	−83.8927	−2.71470
$956$	8.39045	0.271367
$957$	3.46314	0.111947
$958$	−32.0186	−1.03448
$959$	−4.20473	−0.135778
$960$	−18.2786	−0.589940
$961$	−24.6148	−0.794025
$962$	−20.1504	−0.649676
$963$	18.3463	0.591200
$964$	−7.48934	−0.241216
$965$	83.0961	2.67496
$966$	−2.68538	−0.0864007
$967$	8.51191	0.273724	0.136862	−	0.990590i	$-0.456298\pi$
$967$	8.51191	0.273724	0.136862	+	0.990590i	$0.456298\pi$
$968$	−19.9241	−0.640386
$969$	9.25543	0.297327
$970$	−3.94509	−0.126669
$971$	−40.2623	−1.29208	−0.646039	−	0.763304i	$-0.723576\pi$
$971$	−40.2623	−1.29208	−0.646039	+	0.763304i	$0.723576\pi$
$972$	1.30360	0.0418129
$973$	1.27343	0.0408244
$974$	20.7466	0.664763
$975$	−52.0973	−1.66845
$976$	4.29493	0.137477
$977$	6.61565	0.211653	0.105827	−	0.994385i	$-0.466251\pi$
$977$	6.61565	0.211653	0.105827	+	0.994385i	$0.466251\pi$
$978$	0.697855	0.0223150
$979$	5.40687	0.172804
$980$	−5.67111	−0.181157
$981$	14.3238	0.457325
$982$	16.3886	0.522981
$983$	36.8514	1.17538	0.587689	−	0.809087i	$-0.300038\pi$
$983$	36.8514	1.17538	0.587689	+	0.809087i	$0.300038\pi$
$984$	10.4229	0.332268
$985$	−47.1158	−1.50123
$986$	4.02119	0.128061
$987$	1.00767	0.0320745
$988$	−16.7012	−0.531335
$989$	6.28183	0.199750
$990$	7.05172	0.224118
$991$	1.07498	0.0341477	0.0170739	−	0.999854i	$-0.494565\pi$
$991$	1.07498	0.0341477	0.0170739	+	0.999854i	$0.494565\pi$
$992$	14.5792	0.462889
$993$	−6.42831	−0.203996
$994$	0.233524	0.00740694
$995$	4.92770	0.156219
$996$	−0.537054	−0.0170172
$997$	50.6797	1.60504	0.802520	−	0.596625i	$-0.203492\pi$
$997$	50.6797	1.60504	0.802520	+	0.596625i	$0.203492\pi$
$998$	5.22636	0.165437
$999$	−6.45436	−0.204207

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.21	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.21	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.834508 q^{2} -1.00000 q^{3} -1.30360 q^{4} +4.35036 q^{5} +0.834508 q^{6} +1.00000 q^{7} +2.75688 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.834508 q^{2} -1.00000 q^{3} -1.30360 q^{4} +4.35036 q^{5} +0.834508 q^{6} +1.00000 q^{7} +2.75688 q^{8} +1.00000 q^{9} -3.63041 q^{10} -1.94241 q^{11} +1.30360 q^{12} +3.74111 q^{13} -0.834508 q^{14} -4.35036 q^{15} +0.306559 q^{16} -2.70268 q^{17} -0.834508 q^{18} +3.42454 q^{19} -5.67111 q^{20} -1.00000 q^{21} +1.62095 q^{22} -3.21792 q^{23} -2.75688 q^{24} +13.9256 q^{25} -3.12199 q^{26} -1.00000 q^{27} -1.30360 q^{28} +1.78291 q^{29} +3.63041 q^{30} -2.52690 q^{31} -5.76958 q^{32} +1.94241 q^{33} +2.25541 q^{34} +4.35036 q^{35} -1.30360 q^{36} +6.45436 q^{37} -2.85781 q^{38} -3.74111 q^{39} +11.9934 q^{40} -3.78067 q^{41} +0.834508 q^{42} -1.95214 q^{43} +2.53211 q^{44} +4.35036 q^{45} +2.68538 q^{46} -1.00767 q^{47} -0.306559 q^{48} +1.00000 q^{49} -11.6210 q^{50} +2.70268 q^{51} -4.87690 q^{52} -3.13149 q^{53} +0.834508 q^{54} -8.45016 q^{55} +2.75688 q^{56} -3.42454 q^{57} -1.48785 q^{58} -10.8579 q^{59} +5.67111 q^{60} +14.0101 q^{61} +2.10872 q^{62} +1.00000 q^{63} +4.20164 q^{64} +16.2752 q^{65} -1.62095 q^{66} +8.69818 q^{67} +3.52320 q^{68} +3.21792 q^{69} -3.63041 q^{70} -0.279835 q^{71} +2.75688 q^{72} +9.96673 q^{73} -5.38621 q^{74} -13.9256 q^{75} -4.46422 q^{76} -1.94241 q^{77} +3.12199 q^{78} +2.04327 q^{79} +1.33364 q^{80} +1.00000 q^{81} +3.15500 q^{82} -0.411978 q^{83} +1.30360 q^{84} -11.7576 q^{85} +1.62907 q^{86} -1.78291 q^{87} -5.35497 q^{88} -2.78360 q^{89} -3.63041 q^{90} +3.74111 q^{91} +4.19488 q^{92} +2.52690 q^{93} +0.840909 q^{94} +14.8980 q^{95} +5.76958 q^{96} +1.08668 q^{97} -0.834508 q^{98} -1.94241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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