LMFDB - Embedded newform 8007.2.a.j.1.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.52
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07058 q^{2} -1.00000 q^{3} +2.28731 q^{4} -0.634479 q^{5} -2.07058 q^{6} +1.13900 q^{7} +0.594905 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.07058 q^{2} -1.00000 q^{3} +2.28731 q^{4} -0.634479 q^{5} -2.07058 q^{6} +1.13900 q^{7} +0.594905 q^{8} +1.00000 q^{9} -1.31374 q^{10} -6.62850 q^{11} -2.28731 q^{12} -4.92251 q^{13} +2.35838 q^{14} +0.634479 q^{15} -3.34283 q^{16} +1.00000 q^{17} +2.07058 q^{18} +7.36572 q^{19} -1.45125 q^{20} -1.13900 q^{21} -13.7248 q^{22} +5.21013 q^{23} -0.594905 q^{24} -4.59744 q^{25} -10.1925 q^{26} -1.00000 q^{27} +2.60524 q^{28} -6.63715 q^{29} +1.31374 q^{30} +9.52449 q^{31} -8.11141 q^{32} +6.62850 q^{33} +2.07058 q^{34} -0.722669 q^{35} +2.28731 q^{36} +2.69371 q^{37} +15.2513 q^{38} +4.92251 q^{39} -0.377455 q^{40} +0.185508 q^{41} -2.35838 q^{42} +6.35022 q^{43} -15.1614 q^{44} -0.634479 q^{45} +10.7880 q^{46} +10.8622 q^{47} +3.34283 q^{48} -5.70269 q^{49} -9.51937 q^{50} -1.00000 q^{51} -11.2593 q^{52} -7.19394 q^{53} -2.07058 q^{54} +4.20564 q^{55} +0.677594 q^{56} -7.36572 q^{57} -13.7428 q^{58} -13.4881 q^{59} +1.45125 q^{60} +11.7625 q^{61} +19.7212 q^{62} +1.13900 q^{63} -10.1097 q^{64} +3.12323 q^{65} +13.7248 q^{66} +9.16192 q^{67} +2.28731 q^{68} -5.21013 q^{69} -1.49635 q^{70} +8.11783 q^{71} +0.594905 q^{72} +11.4970 q^{73} +5.57754 q^{74} +4.59744 q^{75} +16.8477 q^{76} -7.54982 q^{77} +10.1925 q^{78} +1.35281 q^{79} +2.12095 q^{80} +1.00000 q^{81} +0.384110 q^{82} +5.12485 q^{83} -2.60524 q^{84} -0.634479 q^{85} +13.1487 q^{86} +6.63715 q^{87} -3.94333 q^{88} +11.2792 q^{89} -1.31374 q^{90} -5.60672 q^{91} +11.9172 q^{92} -9.52449 q^{93} +22.4911 q^{94} -4.67340 q^{95} +8.11141 q^{96} -8.64411 q^{97} -11.8079 q^{98} -6.62850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.07058	1.46412	0.732062	−	0.681238i	$-0.238558\pi$
$2$	2.07058	1.46412	0.732062	+	0.681238i	$0.238558\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.28731	1.14366
$5$	−0.634479	−0.283748	−0.141874	−	0.989885i	$-0.545313\pi$
$5$	−0.634479	−0.283748	−0.141874	+	0.989885i	$0.545313\pi$
$6$	−2.07058	−0.845312
$7$	1.13900	0.430500	0.215250	−	0.976559i	$-0.430943\pi$
$7$	1.13900	0.430500	0.215250	+	0.976559i	$0.430943\pi$
$8$	0.594905	0.210331
$9$	1.00000	0.333333
$10$	−1.31374	−0.415442
$11$	−6.62850	−1.99857	−0.999283	−	0.0378516i	$-0.987949\pi$
$11$	−6.62850	−1.99857	−0.999283	+	0.0378516i	$0.987949\pi$
$12$	−2.28731	−0.660290
$13$	−4.92251	−1.36526	−0.682629	−	0.730765i	$-0.739164\pi$
$13$	−4.92251	−1.36526	−0.682629	+	0.730765i	$0.739164\pi$
$14$	2.35838	0.630305
$15$	0.634479	0.163822
$16$	−3.34283	−0.835706
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.07058	0.488041
$19$	7.36572	1.68981	0.844906	−	0.534915i	$-0.179656\pi$
$19$	7.36572	1.68981	0.844906	+	0.534915i	$0.179656\pi$
$20$	−1.45125	−0.324510
$21$	−1.13900	−0.248549
$22$	−13.7248	−2.92615
$23$	5.21013	1.08639	0.543193	−	0.839608i	$-0.317215\pi$
$23$	5.21013	1.08639	0.543193	+	0.839608i	$0.317215\pi$
$24$	−0.594905	−0.121435
$25$	−4.59744	−0.919487
$26$	−10.1925	−1.99891
$27$	−1.00000	−0.192450
$28$	2.60524	0.492344
$29$	−6.63715	−1.23249	−0.616244	−	0.787555i	$-0.711346\pi$
$29$	−6.63715	−1.23249	−0.616244	+	0.787555i	$0.711346\pi$
$30$	1.31374	0.239855
$31$	9.52449	1.71065	0.855324	−	0.518093i	$-0.173358\pi$
$31$	9.52449	1.71065	0.855324	+	0.518093i	$0.173358\pi$
$32$	−8.11141	−1.43391
$33$	6.62850	1.15387
$34$	2.07058	0.355102
$35$	−0.722669	−0.122153
$36$	2.28731	0.381219
$37$	2.69371	0.442843	0.221421	−	0.975178i	$-0.428930\pi$
$37$	2.69371	0.442843	0.221421	+	0.975178i	$0.428930\pi$
$38$	15.2513	2.47409
$39$	4.92251	0.788233
$40$	−0.377455	−0.0596809
$41$	0.185508	0.0289715	0.0144857	−	0.999895i	$-0.495389\pi$
$41$	0.185508	0.0289715	0.0144857	+	0.999895i	$0.495389\pi$
$42$	−2.35838	−0.363906
$43$	6.35022	0.968399	0.484200	−	0.874958i	$-0.339111\pi$
$43$	6.35022	0.968399	0.484200	+	0.874958i	$0.339111\pi$
$44$	−15.1614	−2.28567
$45$	−0.634479	−0.0945826
$46$	10.7880	1.59060
$47$	10.8622	1.58442	0.792208	−	0.610251i	$-0.208931\pi$
$47$	10.8622	1.58442	0.792208	+	0.610251i	$0.208931\pi$
$48$	3.34283	0.482495
$49$	−5.70269	−0.814670
$50$	−9.51937	−1.34624
$51$	−1.00000	−0.140028
$52$	−11.2593	−1.56139
$53$	−7.19394	−0.988163	−0.494082	−	0.869416i	$-0.664496\pi$
$53$	−7.19394	−0.988163	−0.494082	+	0.869416i	$0.664496\pi$
$54$	−2.07058	−0.281771
$55$	4.20564	0.567089
$56$	0.677594	0.0905473
$57$	−7.36572	−0.975613
$58$	−13.7428	−1.80451
$59$	−13.4881	−1.75601	−0.878003	−	0.478656i	$-0.841124\pi$
$59$	−13.4881	−1.75601	−0.878003	+	0.478656i	$0.841124\pi$
$60$	1.45125	0.187356
$61$	11.7625	1.50603	0.753014	−	0.658004i	$-0.228599\pi$
$61$	11.7625	1.50603	0.753014	+	0.658004i	$0.228599\pi$
$62$	19.7212	2.50460
$63$	1.13900	0.143500
$64$	−10.1097	−1.26371
$65$	3.12323	0.387389
$66$	13.7248	1.68941
$67$	9.16192	1.11931	0.559653	−	0.828727i	$-0.310934\pi$
$67$	9.16192	1.11931	0.559653	+	0.828727i	$0.310934\pi$
$68$	2.28731	0.277377
$69$	−5.21013	−0.627226
$70$	−1.49635	−0.178848
$71$	8.11783	0.963409	0.481705	−	0.876334i	$-0.340018\pi$
$71$	8.11783	0.963409	0.481705	+	0.876334i	$0.340018\pi$
$72$	0.594905	0.0701102
$73$	11.4970	1.34562	0.672811	−	0.739815i	$-0.265087\pi$
$73$	11.4970	1.34562	0.672811	+	0.739815i	$0.265087\pi$
$74$	5.57754	0.648376
$75$	4.59744	0.530866
$76$	16.8477	1.93256
$77$	−7.54982	−0.860382
$78$	10.1925	1.15407
$79$	1.35281	0.152203	0.0761017	−	0.997100i	$-0.475753\pi$
$79$	1.35281	0.152203	0.0761017	+	0.997100i	$0.475753\pi$
$80$	2.12095	0.237130
$81$	1.00000	0.111111
$82$	0.384110	0.0424178
$83$	5.12485	0.562525	0.281262	−	0.959631i	$-0.409247\pi$
$83$	5.12485	0.562525	0.281262	+	0.959631i	$0.409247\pi$
$84$	−2.60524	−0.284255
$85$	−0.634479	−0.0688190
$86$	13.1487	1.41786
$87$	6.63715	0.711577
$88$	−3.94333	−0.420360
$89$	11.2792	1.19559	0.597794	−	0.801650i	$-0.296044\pi$
$89$	11.2792	1.19559	0.597794	+	0.801650i	$0.296044\pi$
$90$	−1.31374	−0.138481
$91$	−5.60672	−0.587743
$92$	11.9172	1.24245
$93$	−9.52449	−0.987644
$94$	22.4911	2.31978
$95$	−4.67340	−0.479480
$96$	8.11141	0.827867
$97$	−8.64411	−0.877676	−0.438838	−	0.898566i	$-0.644610\pi$
$97$	−8.64411	−0.877676	−0.438838	+	0.898566i	$0.644610\pi$
$98$	−11.8079	−1.19278
$99$	−6.62850	−0.666189
$100$	−10.5158	−1.05158
$101$	4.36623	0.434456	0.217228	−	0.976121i	$-0.430298\pi$
$101$	4.36623	0.434456	0.217228	+	0.976121i	$0.430298\pi$
$102$	−2.07058	−0.205018
$103$	16.5442	1.63015	0.815074	−	0.579357i	$-0.196696\pi$
$103$	16.5442	1.63015	0.815074	+	0.579357i	$0.196696\pi$
$104$	−2.92843	−0.287156
$105$	0.722669	0.0705253
$106$	−14.8956	−1.44679
$107$	0.0116714	0.00112832	0.000564159	−	1.00000i	$-0.499820\pi$
$107$	0.0116714	0.00112832	0.000564159		1.00000i	$0.499820\pi$
$108$	−2.28731	−0.220097
$109$	−15.7440	−1.50800	−0.754000	−	0.656875i	$-0.771878\pi$
$109$	−15.7440	−1.50800	−0.754000	+	0.656875i	$0.771878\pi$
$110$	8.70813	0.830288
$111$	−2.69371	−0.255675
$112$	−3.80746	−0.359771
$113$	2.93701	0.276291	0.138145	−	0.990412i	$-0.455886\pi$
$113$	2.93701	0.276291	0.138145	+	0.990412i	$0.455886\pi$
$114$	−15.2513	−1.42842
$115$	−3.30572	−0.308260
$116$	−15.1812	−1.40954
$117$	−4.92251	−0.455086
$118$	−27.9283	−2.57101
$119$	1.13900	0.104412
$120$	0.377455	0.0344568
$121$	32.9370	2.99427
$122$	24.3551	2.20501
$123$	−0.185508	−0.0167267
$124$	21.7855	1.95639
$125$	6.08938	0.544650
$126$	2.35838	0.210102
$127$	10.5650	0.937493	0.468746	−	0.883333i	$-0.344706\pi$
$127$	10.5650	0.937493	0.468746	+	0.883333i	$0.344706\pi$
$128$	−4.71013	−0.416321
$129$	−6.35022	−0.559105
$130$	6.46691	0.567185
$131$	−13.7703	−1.20312	−0.601558	−	0.798829i	$-0.705453\pi$
$131$	−13.7703	−1.20312	−0.601558	+	0.798829i	$0.705453\pi$
$132$	15.1614	1.31963
$133$	8.38952	0.727463
$134$	18.9705	1.63880
$135$	0.634479	0.0546073
$136$	0.594905	0.0510127
$137$	1.53784	0.131387	0.0656933	−	0.997840i	$-0.479074\pi$
$137$	1.53784	0.131387	0.0656933	+	0.997840i	$0.479074\pi$
$138$	−10.7880	−0.918336
$139$	14.9495	1.26800	0.634001	−	0.773332i	$-0.281411\pi$
$139$	14.9495	1.26800	0.634001	+	0.773332i	$0.281411\pi$
$140$	−1.65297	−0.139701
$141$	−10.8622	−0.914763
$142$	16.8086	1.41055
$143$	32.6288	2.72856
$144$	−3.34283	−0.278569
$145$	4.21113	0.349716
$146$	23.8055	1.97016
$147$	5.70269	0.470350
$148$	6.16135	0.506460
$149$	14.2527	1.16762	0.583812	−	0.811889i	$-0.301561\pi$
$149$	14.2527	1.16762	0.583812	+	0.811889i	$0.301561\pi$
$150$	9.51937	0.777253
$151$	−3.42034	−0.278344	−0.139172	−	0.990268i	$-0.544444\pi$
$151$	−3.42034	−0.278344	−0.139172	+	0.990268i	$0.544444\pi$
$152$	4.38190	0.355419
$153$	1.00000	0.0808452
$154$	−15.6325	−1.25971
$155$	−6.04309	−0.485393
$156$	11.2593	0.901467
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	2.80111	0.222845
$159$	7.19394	0.570516
$160$	5.14652	0.406868
$161$	5.93431	0.467689
$162$	2.07058	0.162680
$163$	−18.6771	−1.46290	−0.731452	−	0.681893i	$-0.761157\pi$
$163$	−18.6771	−1.46290	−0.731452	+	0.681893i	$0.761157\pi$
$164$	0.424315	0.0331334
$165$	−4.20564	−0.327409
$166$	10.6114	0.823606
$167$	−2.80564	−0.217107	−0.108553	−	0.994091i	$-0.534622\pi$
$167$	−2.80564	−0.217107	−0.108553	+	0.994091i	$0.534622\pi$
$168$	−0.677594	−0.0522775
$169$	11.2311	0.863931
$170$	−1.31374	−0.100759
$171$	7.36572	0.563270
$172$	14.5249	1.10752
$173$	0.442574	0.0336483	0.0168241	−	0.999858i	$-0.494644\pi$
$173$	0.442574	0.0336483	0.0168241	+	0.999858i	$0.494644\pi$
$174$	13.7428	1.04184
$175$	−5.23646	−0.395839
$176$	22.1579	1.67021
$177$	13.4881	1.01383
$178$	23.3544	1.75049
$179$	2.13653	0.159692	0.0798459	−	0.996807i	$-0.474557\pi$
$179$	2.13653	0.159692	0.0798459	+	0.996807i	$0.474557\pi$
$180$	−1.45125	−0.108170
$181$	−25.9374	−1.92791	−0.963954	−	0.266068i	$-0.914275\pi$
$181$	−25.9374	−1.92791	−0.963954	+	0.266068i	$0.914275\pi$
$182$	−11.6092	−0.860529
$183$	−11.7625	−0.869506
$184$	3.09953	0.228501
$185$	−1.70910	−0.125656
$186$	−19.7212	−1.44603
$187$	−6.62850	−0.484724
$188$	24.8453	1.81203
$189$	−1.13900	−0.0828497
$190$	−9.67665	−0.702018
$191$	2.75632	0.199440	0.0997202	−	0.995016i	$-0.468205\pi$
$191$	2.75632	0.199440	0.0997202	+	0.995016i	$0.468205\pi$
$192$	10.1097	0.729604
$193$	−9.10626	−0.655483	−0.327742	−	0.944767i	$-0.606288\pi$
$193$	−9.10626	−0.655483	−0.327742	+	0.944767i	$0.606288\pi$
$194$	−17.8983	−1.28503
$195$	−3.12323	−0.223659
$196$	−13.0438	−0.931703
$197$	−25.3969	−1.80945	−0.904727	−	0.425993i	$-0.859925\pi$
$197$	−25.3969	−1.80945	−0.904727	+	0.425993i	$0.859925\pi$
$198$	−13.7248	−0.975383
$199$	11.0930	0.786362	0.393181	−	0.919461i	$-0.371375\pi$
$199$	11.0930	0.786362	0.393181	+	0.919461i	$0.371375\pi$
$200$	−2.73504	−0.193396
$201$	−9.16192	−0.646232
$202$	9.04065	0.636098
$203$	−7.55968	−0.530586
$204$	−2.28731	−0.160144
$205$	−0.117701	−0.00822060
$206$	34.2561	2.38674
$207$	5.21013	0.362129
$208$	16.4551	1.14096
$209$	−48.8236	−3.37720
$210$	1.49635	0.103258
$211$	19.2312	1.32393	0.661965	−	0.749535i	$-0.269723\pi$
$211$	19.2312	1.32393	0.661965	+	0.749535i	$0.269723\pi$
$212$	−16.4548	−1.13012
$213$	−8.11783	−0.556225
$214$	0.0241666	0.00165200
$215$	−4.02908	−0.274781
$216$	−0.594905	−0.0404782
$217$	10.8483	0.736434
$218$	−32.5992	−2.20790
$219$	−11.4970	−0.776895
$220$	9.61962	0.648555
$221$	−4.92251	−0.331124
$222$	−5.57754	−0.374340
$223$	−13.9069	−0.931272	−0.465636	−	0.884976i	$-0.654174\pi$
$223$	−13.9069	−0.931272	−0.465636	+	0.884976i	$0.654174\pi$
$224$	−9.23885	−0.617297
$225$	−4.59744	−0.306496
$226$	6.08133	0.404524
$227$	−3.08337	−0.204650	−0.102325	−	0.994751i	$-0.532628\pi$
$227$	−3.08337	−0.204650	−0.102325	+	0.994751i	$0.532628\pi$
$228$	−16.8477	−1.11577
$229$	4.28916	0.283436	0.141718	−	0.989907i	$-0.454737\pi$
$229$	4.28916	0.283436	0.141718	+	0.989907i	$0.454737\pi$
$230$	−6.84477	−0.451330
$231$	7.54982	0.496742
$232$	−3.94847	−0.259230
$233$	−27.0245	−1.77044	−0.885218	−	0.465176i	$-0.845991\pi$
$233$	−27.0245	−1.77044	−0.885218	+	0.465176i	$0.845991\pi$
$234$	−10.1925	−0.666302
$235$	−6.89185	−0.449575
$236$	−30.8516	−2.00827
$237$	−1.35281	−0.0878747
$238$	2.35838	0.152871
$239$	29.4671	1.90607	0.953034	−	0.302862i	$-0.0979420\pi$
$239$	29.4671	1.90607	0.953034	+	0.302862i	$0.0979420\pi$
$240$	−2.12095	−0.136907
$241$	22.7285	1.46407	0.732037	−	0.681265i	$-0.238570\pi$
$241$	22.7285	1.46407	0.732037	+	0.681265i	$0.238570\pi$
$242$	68.1987	4.38398
$243$	−1.00000	−0.0641500
$244$	26.9044	1.72238
$245$	3.61824	0.231161
$246$	−0.384110	−0.0244899
$247$	−36.2578	−2.30703
$248$	5.66617	0.359802
$249$	−5.12485	−0.324774
$250$	12.6086	0.797435
$251$	15.4490	0.975133	0.487566	−	0.873086i	$-0.337885\pi$
$251$	15.4490	0.975133	0.487566	+	0.873086i	$0.337885\pi$
$252$	2.60524	0.164115
$253$	−34.5353	−2.17122
$254$	21.8757	1.37260
$255$	0.634479	0.0397326
$256$	10.4667	0.654166
$257$	11.4620	0.714979	0.357490	−	0.933917i	$-0.383633\pi$
$257$	11.4620	0.714979	0.357490	+	0.933917i	$0.383633\pi$
$258$	−13.1487	−0.818599
$259$	3.06812	0.190644
$260$	7.14381	0.443040
$261$	−6.63715	−0.410829
$262$	−28.5125	−1.76151
$263$	6.26399	0.386254	0.193127	−	0.981174i	$-0.438137\pi$
$263$	6.26399	0.386254	0.193127	+	0.981174i	$0.438137\pi$
$264$	3.94333	0.242695
$265$	4.56440	0.280389
$266$	17.3712	1.06510
$267$	−11.2792	−0.690273
$268$	20.9562	1.28010
$269$	−8.76872	−0.534638	−0.267319	−	0.963608i	$-0.586138\pi$
$269$	−8.76872	−0.534638	−0.267319	+	0.963608i	$0.586138\pi$
$270$	1.31374	0.0799518
$271$	−3.62960	−0.220483	−0.110241	−	0.993905i	$-0.535162\pi$
$271$	−3.62960	−0.220483	−0.110241	+	0.993905i	$0.535162\pi$
$272$	−3.34283	−0.202689
$273$	5.60672	0.339334
$274$	3.18423	0.192366
$275$	30.4741	1.83766
$276$	−11.9172	−0.717331
$277$	2.45386	0.147438	0.0737192	−	0.997279i	$-0.476513\pi$
$277$	2.45386	0.147438	0.0737192	+	0.997279i	$0.476513\pi$
$278$	30.9542	1.85651
$279$	9.52449	0.570216
$280$	−0.429919	−0.0256926
$281$	−22.3574	−1.33373	−0.666866	−	0.745178i	$-0.732364\pi$
$281$	−22.3574	−1.33373	−0.666866	+	0.745178i	$0.732364\pi$
$282$	−22.4911	−1.33933
$283$	−13.8890	−0.825613	−0.412807	−	0.910819i	$-0.635451\pi$
$283$	−13.8890	−0.825613	−0.412807	+	0.910819i	$0.635451\pi$
$284$	18.5680	1.10181
$285$	4.67340	0.276828
$286$	67.5607	3.99495
$287$	0.211293	0.0124722
$288$	−8.11141	−0.477969
$289$	1.00000	0.0588235
$290$	8.71950	0.512027
$291$	8.64411	0.506727
$292$	26.2972	1.53893
$293$	11.8968	0.695017	0.347509	−	0.937677i	$-0.387028\pi$
$293$	11.8968	0.695017	0.347509	+	0.937677i	$0.387028\pi$
$294$	11.8079	0.688650
$295$	8.55794	0.498263
$296$	1.60250	0.0931434
$297$	6.62850	0.384624
$298$	29.5113	1.70954
$299$	−25.6469	−1.48320
$300$	10.5158	0.607129
$301$	7.23287	0.416895
$302$	−7.08210	−0.407529
$303$	−4.36623	−0.250833
$304$	−24.6223	−1.41219
$305$	−7.46304	−0.427332
$306$	2.07058	0.118367
$307$	17.9862	1.02652	0.513262	−	0.858232i	$-0.328437\pi$
$307$	17.9862	1.02652	0.513262	+	0.858232i	$0.328437\pi$
$308$	−17.2688	−0.983982
$309$	−16.5442	−0.941166
$310$	−12.5127	−0.710675
$311$	19.0869	1.08232	0.541159	−	0.840920i	$-0.317986\pi$
$311$	19.0869	1.08232	0.541159	+	0.840920i	$0.317986\pi$
$312$	2.92843	0.165790
$313$	22.9307	1.29612	0.648059	−	0.761591i	$-0.275581\pi$
$313$	22.9307	1.29612	0.648059	+	0.761591i	$0.275581\pi$
$314$	−2.07058	−0.116850
$315$	−0.722669	−0.0407178
$316$	3.09431	0.174068
$317$	25.3288	1.42261	0.711303	−	0.702886i	$-0.248105\pi$
$317$	25.3288	1.42261	0.711303	+	0.702886i	$0.248105\pi$
$318$	14.8956	0.835306
$319$	43.9943	2.46321
$320$	6.41439	0.358575
$321$	−0.0116714	−0.000651435 0
$322$	12.2875	0.684755
$323$	7.36572	0.409839
$324$	2.28731	0.127073
$325$	22.6309	1.25534
$326$	−38.6725	−2.14187
$327$	15.7440	0.870644
$328$	0.110360	0.00609359
$329$	12.3720	0.682091
$330$	−8.70813	−0.479367
$331$	11.1884	0.614968	0.307484	−	0.951553i	$-0.400513\pi$
$331$	11.1884	0.614968	0.307484	+	0.951553i	$0.400513\pi$
$332$	11.7221	0.643335
$333$	2.69371	0.147614
$334$	−5.80930	−0.317871
$335$	−5.81305	−0.317601
$336$	3.80746	0.207714
$337$	−17.7611	−0.967506	−0.483753	−	0.875204i	$-0.660727\pi$
$337$	−17.7611	−0.967506	−0.483753	+	0.875204i	$0.660727\pi$
$338$	23.2549	1.26490
$339$	−2.93701	−0.159517
$340$	−1.45125	−0.0787052
$341$	−63.1330	−3.41885
$342$	15.2513	0.824697
$343$	−14.4683	−0.781215
$344$	3.77778	0.203684
$345$	3.30572	0.177974
$346$	0.916386	0.0492652
$347$	−6.70800	−0.360105	−0.180052	−	0.983657i	$-0.557627\pi$
$347$	−6.70800	−0.360105	−0.180052	+	0.983657i	$0.557627\pi$
$348$	15.1812	0.813800
$349$	17.0236	0.911255	0.455627	−	0.890171i	$-0.349415\pi$
$349$	17.0236	0.911255	0.455627	+	0.890171i	$0.349415\pi$
$350$	−10.8425	−0.579557
$351$	4.92251	0.262744
$352$	53.7664	2.86576
$353$	−31.0226	−1.65117	−0.825583	−	0.564281i	$-0.809154\pi$
$353$	−31.0226	−1.65117	−0.825583	+	0.564281i	$0.809154\pi$
$354$	27.9283	1.48437
$355$	−5.15060	−0.273365
$356$	25.7990	1.36734
$357$	−1.13900	−0.0602820
$358$	4.42386	0.233808
$359$	−0.362907	−0.0191535	−0.00957676	−	0.999954i	$-0.503048\pi$
$359$	−0.362907	−0.0191535	−0.00957676	+	0.999954i	$0.503048\pi$
$360$	−0.377455	−0.0198936
$361$	35.2538	1.85546
$362$	−53.7054	−2.82270
$363$	−32.9370	−1.72874
$364$	−12.8243	−0.672177
$365$	−7.29461	−0.381817
$366$	−24.3551	−1.27306
$367$	2.29191	0.119637	0.0598184	−	0.998209i	$-0.480948\pi$
$367$	2.29191	0.119637	0.0598184	+	0.998209i	$0.480948\pi$
$368$	−17.4166	−0.907901
$369$	0.185508	0.00965716
$370$	−3.53884	−0.183975
$371$	−8.19386	−0.425404
$372$	−21.7855	−1.12952
$373$	−3.97280	−0.205704	−0.102852	−	0.994697i	$-0.532797\pi$
$373$	−3.97280	−0.205704	−0.102852	+	0.994697i	$0.532797\pi$
$374$	−13.7248	−0.709695
$375$	−6.08938	−0.314454
$376$	6.46198	0.333251
$377$	32.6714	1.68266
$378$	−2.35838	−0.121302
$379$	−19.1618	−0.984273	−0.492137	−	0.870518i	$-0.663784\pi$
$379$	−19.1618	−0.984273	−0.492137	+	0.870518i	$0.663784\pi$
$380$	−10.6895	−0.548361
$381$	−10.5650	−0.541262
$382$	5.70719	0.292005
$383$	11.2741	0.576082	0.288041	−	0.957618i	$-0.406996\pi$
$383$	11.2741	0.576082	0.288041	+	0.957618i	$0.406996\pi$
$384$	4.71013	0.240363
$385$	4.79021	0.244132
$386$	−18.8553	−0.959708
$387$	6.35022	0.322800
$388$	−19.7718	−1.00376
$389$	−7.21147	−0.365636	−0.182818	−	0.983147i	$-0.558522\pi$
$389$	−7.21147	−0.365636	−0.182818	+	0.983147i	$0.558522\pi$
$390$	−6.46691	−0.327465
$391$	5.21013	0.263488
$392$	−3.39256	−0.171350
$393$	13.7703	0.694620
$394$	−52.5864	−2.64926
$395$	−0.858332	−0.0431874
$396$	−15.1614	−0.761891
$397$	18.2371	0.915294	0.457647	−	0.889134i	$-0.348692\pi$
$397$	18.2371	0.915294	0.457647	+	0.889134i	$0.348692\pi$
$398$	22.9690	1.15133
$399$	−8.38952	−0.420001
$400$	15.3684	0.768421
$401$	−23.4063	−1.16886	−0.584428	−	0.811445i	$-0.698681\pi$
$401$	−23.4063	−1.16886	−0.584428	+	0.811445i	$0.698681\pi$
$402$	−18.9705	−0.946163
$403$	−46.8844	−2.33548
$404$	9.98694	0.496869
$405$	−0.634479	−0.0315275
$406$	−15.6529	−0.776843
$407$	−17.8552	−0.885050
$408$	−0.594905	−0.0294522
$409$	29.8796	1.47745	0.738725	−	0.674007i	$-0.235428\pi$
$409$	29.8796	1.47745	0.738725	+	0.674007i	$0.235428\pi$
$410$	−0.243710	−0.0120360
$411$	−1.53784	−0.0758561
$412$	37.8417	1.86433
$413$	−15.3629	−0.755960
$414$	10.7880	0.530201
$415$	−3.25161	−0.159615
$416$	39.9285	1.95766
$417$	−14.9495	−0.732082
$418$	−101.093	−4.94464
$419$	−11.4491	−0.559325	−0.279662	−	0.960098i	$-0.590223\pi$
$419$	−11.4491	−0.559325	−0.279662	+	0.960098i	$0.590223\pi$
$420$	1.65297	0.0806567
$421$	14.4594	0.704709	0.352355	−	0.935867i	$-0.385381\pi$
$421$	14.4594	0.704709	0.352355	+	0.935867i	$0.385381\pi$
$422$	39.8198	1.93840
$423$	10.8622	0.528139
$424$	−4.27971	−0.207841
$425$	−4.59744	−0.223008
$426$	−16.8086	−0.814381
$427$	13.3974	0.648345
$428$	0.0266962	0.00129041
$429$	−32.6288	−1.57534
$430$	−8.34255	−0.402313
$431$	26.9911	1.30011	0.650057	−	0.759886i	$-0.274745\pi$
$431$	26.9911	1.30011	0.650057	+	0.759886i	$0.274745\pi$
$432$	3.34283	0.160832
$433$	−5.11726	−0.245920	−0.122960	−	0.992412i	$-0.539239\pi$
$433$	−5.11726	−0.245920	−0.122960	+	0.992412i	$0.539239\pi$
$434$	22.4624	1.07823
$435$	−4.21113	−0.201908
$436$	−36.0114	−1.72463
$437$	38.3763	1.83579
$438$	−23.8055	−1.13747
$439$	−4.36606	−0.208381	−0.104190	−	0.994557i	$-0.533225\pi$
$439$	−4.36606	−0.208381	−0.104190	+	0.994557i	$0.533225\pi$
$440$	2.50196	0.119276
$441$	−5.70269	−0.271557
$442$	−10.1925	−0.484806
$443$	−18.5026	−0.879085	−0.439542	−	0.898222i	$-0.644859\pi$
$443$	−18.5026	−0.879085	−0.439542	+	0.898222i	$0.644859\pi$
$444$	−6.16135	−0.292405
$445$	−7.15639	−0.339246
$446$	−28.7953	−1.36350
$447$	−14.2527	−0.674128
$448$	−11.5149	−0.544027
$449$	12.1078	0.571405	0.285702	−	0.958318i	$-0.407773\pi$
$449$	12.1078	0.571405	0.285702	+	0.958318i	$0.407773\pi$
$450$	−9.51937	−0.448747
$451$	−1.22964	−0.0579015
$452$	6.71787	0.315982
$453$	3.42034	0.160702
$454$	−6.38437	−0.299633
$455$	3.55735	0.166771
$456$	−4.38190	−0.205201
$457$	26.1011	1.22096	0.610479	−	0.792032i	$-0.290977\pi$
$457$	26.1011	1.22096	0.610479	+	0.792032i	$0.290977\pi$
$458$	8.88107	0.414985
$459$	−1.00000	−0.0466760
$460$	−7.56121	−0.352543
$461$	13.6625	0.636327	0.318164	−	0.948036i	$-0.396934\pi$
$461$	13.6625	0.636327	0.318164	+	0.948036i	$0.396934\pi$
$462$	15.6325	0.727291
$463$	10.0074	0.465083	0.232542	−	0.972586i	$-0.425296\pi$
$463$	10.0074	0.465083	0.232542	+	0.972586i	$0.425296\pi$
$464$	22.1868	1.03000
$465$	6.04309	0.280242
$466$	−55.9565	−2.59214
$467$	17.6222	0.815457	0.407728	−	0.913103i	$-0.366321\pi$
$467$	17.6222	0.815457	0.407728	+	0.913103i	$0.366321\pi$
$468$	−11.2593	−0.520462
$469$	10.4354	0.481861
$470$	−14.2701	−0.658232
$471$	1.00000	0.0460776
$472$	−8.02416	−0.369342
$473$	−42.0924	−1.93541
$474$	−2.80111	−0.128659
$475$	−33.8634	−1.55376
$476$	2.60524	0.119411
$477$	−7.19394	−0.329388
$478$	61.0141	2.79072
$479$	−26.8508	−1.22684	−0.613422	−	0.789755i	$-0.710207\pi$
$479$	−26.8508	−1.22684	−0.613422	+	0.789755i	$0.710207\pi$
$480$	−5.14652	−0.234905
$481$	−13.2598	−0.604595
$482$	47.0613	2.14358
$483$	−5.93431	−0.270021
$484$	75.3371	3.42442
$485$	5.48451	0.249039
$486$	−2.07058	−0.0939235
$487$	−24.8895	−1.12785	−0.563925	−	0.825826i	$-0.690709\pi$
$487$	−24.8895	−1.12785	−0.563925	+	0.825826i	$0.690709\pi$
$488$	6.99755	0.316764
$489$	18.6771	0.844608
$490$	7.49186	0.338448
$491$	−29.2609	−1.32053	−0.660264	−	0.751034i	$-0.729556\pi$
$491$	−29.2609	−1.32053	−0.660264	+	0.751034i	$0.729556\pi$
$492$	−0.424315	−0.0191296
$493$	−6.63715	−0.298922
$494$	−75.0748	−3.37778
$495$	4.20564	0.189030
$496$	−31.8387	−1.42960
$497$	9.24617	0.414747
$498$	−10.6114	−0.475509
$499$	7.11064	0.318316	0.159158	−	0.987253i	$-0.449122\pi$
$499$	7.11064	0.318316	0.159158	+	0.987253i	$0.449122\pi$
$500$	13.9283	0.622893
$501$	2.80564	0.125347
$502$	31.9884	1.42771
$503$	−19.2566	−0.858610	−0.429305	−	0.903160i	$-0.641241\pi$
$503$	−19.2566	−0.858610	−0.429305	+	0.903160i	$0.641241\pi$
$504$	0.677594	0.0301824
$505$	−2.77028	−0.123276
$506$	−71.5082	−3.17893
$507$	−11.2311	−0.498791
$508$	24.1655	1.07217
$509$	30.0220	1.33070	0.665350	−	0.746532i	$-0.268282\pi$
$509$	30.0220	1.33070	0.665350	+	0.746532i	$0.268282\pi$
$510$	1.31374	0.0581735
$511$	13.0950	0.579290
$512$	31.0923	1.37410
$513$	−7.36572	−0.325204
$514$	23.7330	1.04682
$515$	−10.4969	−0.462551
$516$	−14.5249	−0.639425
$517$	−72.0001	−3.16656
$518$	6.35279	0.279126
$519$	−0.442574	−0.0194268
$520$	1.85803	0.0814798
$521$	6.77911	0.296998	0.148499	−	0.988913i	$-0.452556\pi$
$521$	6.77911	0.296998	0.148499	+	0.988913i	$0.452556\pi$
$522$	−13.7428	−0.601505
$523$	−6.76418	−0.295777	−0.147889	−	0.989004i	$-0.547248\pi$
$523$	−6.76418	−0.295777	−0.147889	+	0.989004i	$0.547248\pi$
$524$	−31.4970	−1.37595
$525$	5.23646	0.228538
$526$	12.9701	0.565524
$527$	9.52449	0.414893
$528$	−22.1579	−0.964299
$529$	4.14544	0.180237
$530$	9.45098	0.410524
$531$	−13.4881	−0.585335
$532$	19.1894	0.831968
$533$	−0.913165	−0.0395536
$534$	−23.3544	−1.01064
$535$	−0.00740527	−0.000320158 0
$536$	5.45047	0.235425
$537$	−2.13653	−0.0921981
$538$	−18.1564	−0.782777
$539$	37.8003	1.62817
$540$	1.45125	0.0624520
$541$	35.6578	1.53305	0.766525	−	0.642215i	$-0.221984\pi$
$541$	35.6578	1.53305	0.766525	+	0.642215i	$0.221984\pi$
$542$	−7.51539	−0.322814
$543$	25.9374	1.11308
$544$	−8.11141	−0.347774
$545$	9.98923	0.427892
$546$	11.6092	0.496827
$547$	−13.9106	−0.594774	−0.297387	−	0.954757i	$-0.596115\pi$
$547$	−13.9106	−0.594774	−0.297387	+	0.954757i	$0.596115\pi$
$548$	3.51752	0.150261
$549$	11.7625	0.502009
$550$	63.0991	2.69056
$551$	−48.8874	−2.08267
$552$	−3.09953	−0.131925
$553$	1.54085	0.0655235
$554$	5.08093	0.215868
$555$	1.70910	0.0725473
$556$	34.1942	1.45016
$557$	14.7448	0.624755	0.312378	−	0.949958i	$-0.398875\pi$
$557$	14.7448	0.624755	0.312378	+	0.949958i	$0.398875\pi$
$558$	19.7212	0.834867
$559$	−31.2590	−1.32212
$560$	2.41576	0.102084
$561$	6.62850	0.279855
$562$	−46.2929	−1.95275
$563$	6.74379	0.284217	0.142108	−	0.989851i	$-0.454612\pi$
$563$	6.74379	0.284217	0.142108	+	0.989851i	$0.454612\pi$
$564$	−24.8453	−1.04617
$565$	−1.86347	−0.0783969
$566$	−28.7582	−1.20880
$567$	1.13900	0.0478333
$568$	4.82934	0.202635
$569$	−26.0565	−1.09235	−0.546173	−	0.837673i	$-0.683916\pi$
$569$	−26.0565	−1.09235	−0.546173	+	0.837673i	$0.683916\pi$
$570$	9.67665	0.405310
$571$	30.1037	1.25980	0.629900	−	0.776676i	$-0.283096\pi$
$571$	30.1037	1.25980	0.629900	+	0.776676i	$0.283096\pi$
$572$	74.6324	3.12054
$573$	−2.75632	−0.115147
$574$	0.437499	0.0182609
$575$	−23.9532	−0.998919
$576$	−10.1097	−0.421237
$577$	−27.4499	−1.14276	−0.571378	−	0.820687i	$-0.693591\pi$
$577$	−27.4499	−1.14276	−0.571378	+	0.820687i	$0.693591\pi$
$578$	2.07058	0.0861249
$579$	9.10626	0.378443
$580$	9.63218	0.399955
$581$	5.83717	0.242167
$582$	17.8983	0.741910
$583$	47.6850	1.97491
$584$	6.83962	0.283026
$585$	3.12323	0.129130
$586$	24.6333	1.01759
$587$	8.89284	0.367047	0.183523	−	0.983015i	$-0.441250\pi$
$587$	8.89284	0.367047	0.183523	+	0.983015i	$0.441250\pi$
$588$	13.0438	0.537919
$589$	70.1547	2.89067
$590$	17.7199	0.729518
$591$	25.3969	1.04469
$592$	−9.00459	−0.370086
$593$	43.0272	1.76692	0.883458	−	0.468510i	$-0.155209\pi$
$593$	43.0272	1.76692	0.883458	+	0.468510i	$0.155209\pi$
$594$	13.7248	0.563137
$595$	−0.722669	−0.0296265
$596$	32.6003	1.33536
$597$	−11.0930	−0.454006
$598$	−53.1041	−2.17159
$599$	38.7617	1.58376	0.791879	−	0.610678i	$-0.209103\pi$
$599$	38.7617	1.58376	0.791879	+	0.610678i	$0.209103\pi$
$600$	2.73504	0.111657
$601$	−40.7300	−1.66141	−0.830705	−	0.556712i	$-0.812063\pi$
$601$	−40.7300	−1.66141	−0.830705	+	0.556712i	$0.812063\pi$
$602$	14.9762	0.610386
$603$	9.16192	0.373102
$604$	−7.82340	−0.318329
$605$	−20.8978	−0.849617
$606$	−9.04065	−0.367251
$607$	−25.0671	−1.01744	−0.508720	−	0.860932i	$-0.669881\pi$
$607$	−25.0671	−1.01744	−0.508720	+	0.860932i	$0.669881\pi$
$608$	−59.7463	−2.42303
$609$	7.55968	0.306334
$610$	−15.4528	−0.625667
$611$	−53.4693	−2.16314
$612$	2.28731	0.0924591
$613$	−17.6876	−0.714397	−0.357199	−	0.934028i	$-0.616268\pi$
$613$	−17.6876	−0.714397	−0.357199	+	0.934028i	$0.616268\pi$
$614$	37.2418	1.50296
$615$	0.117701	0.00474616
$616$	−4.49143	−0.180965
$617$	9.43991	0.380037	0.190018	−	0.981781i	$-0.439145\pi$
$617$	9.43991	0.380037	0.190018	+	0.981781i	$0.439145\pi$
$618$	−34.2561	−1.37798
$619$	−4.39582	−0.176683	−0.0883415	−	0.996090i	$-0.528157\pi$
$619$	−4.39582	−0.176683	−0.0883415	+	0.996090i	$0.528157\pi$
$620$	−13.8224	−0.555123
$621$	−5.21013	−0.209075
$622$	39.5210	1.58465
$623$	12.8469	0.514700
$624$	−16.4551	−0.658731
$625$	19.1236	0.764944
$626$	47.4798	1.89767
$627$	48.8236	1.94983
$628$	−2.28731	−0.0912737
$629$	2.69371	0.107405
$630$	−1.49635	−0.0596158
$631$	−10.8491	−0.431895	−0.215948	−	0.976405i	$-0.569284\pi$
$631$	−10.8491	−0.431895	−0.215948	+	0.976405i	$0.569284\pi$
$632$	0.804796	0.0320131
$633$	−19.2312	−0.764371
$634$	52.4453	2.08287
$635$	−6.70328	−0.266011
$636$	16.4548	0.652475
$637$	28.0716	1.11224
$638$	91.0939	3.60644
$639$	8.11783	0.321136
$640$	2.98848	0.118130
$641$	36.9212	1.45830	0.729150	−	0.684354i	$-0.239916\pi$
$641$	36.9212	1.45830	0.729150	+	0.684354i	$0.239916\pi$
$642$	−0.0241666	−0.000953780 0
$643$	−41.8607	−1.65083	−0.825413	−	0.564530i	$-0.809057\pi$
$643$	−41.8607	−1.65083	−0.825413	+	0.564530i	$0.809057\pi$
$644$	13.5736	0.534876
$645$	4.02908	0.158645
$646$	15.2513	0.600055
$647$	34.0685	1.33937	0.669685	−	0.742645i	$-0.266429\pi$
$647$	34.0685	1.33937	0.669685	+	0.742645i	$0.266429\pi$
$648$	0.594905	0.0233701
$649$	89.4060	3.50949
$650$	46.8592	1.83797
$651$	−10.8483	−0.425180
$652$	−42.7204	−1.67306
$653$	−2.50539	−0.0980433	−0.0490217	−	0.998798i	$-0.515610\pi$
$653$	−2.50539	−0.0980433	−0.0490217	+	0.998798i	$0.515610\pi$
$654$	32.5992	1.27473
$655$	8.73697	0.341382
$656$	−0.620121	−0.0242117
$657$	11.4970	0.448540
$658$	25.6173	0.998665
$659$	−1.47502	−0.0574588	−0.0287294	−	0.999587i	$-0.509146\pi$
$659$	−1.47502	−0.0574588	−0.0287294	+	0.999587i	$0.509146\pi$
$660$	−9.61962	−0.374443
$661$	−28.3524	−1.10278	−0.551391	−	0.834247i	$-0.685903\pi$
$661$	−28.3524	−1.10278	−0.551391	+	0.834247i	$0.685903\pi$
$662$	23.1664	0.900389
$663$	4.92251	0.191174
$664$	3.04880	0.118316
$665$	−5.32297	−0.206416
$666$	5.57754	0.216125
$667$	−34.5804	−1.33896
$668$	−6.41737	−0.248295
$669$	13.9069	0.537670
$670$	−12.0364	−0.465007
$671$	−77.9674	−3.00990
$672$	9.23885	0.356396
$673$	12.1470	0.468234	0.234117	−	0.972208i	$-0.424780\pi$
$673$	12.1470	0.468234	0.234117	+	0.972208i	$0.424780\pi$
$674$	−36.7757	−1.41655
$675$	4.59744	0.176955
$676$	25.6891	0.988041
$677$	11.0240	0.423686	0.211843	−	0.977304i	$-0.432053\pi$
$677$	11.0240	0.423686	0.211843	+	0.977304i	$0.432053\pi$
$678$	−6.08133	−0.233552
$679$	−9.84560	−0.377839
$680$	−0.377455	−0.0144747
$681$	3.08337	0.118155
$682$	−130.722	−5.00561
$683$	−27.8642	−1.06619	−0.533097	−	0.846054i	$-0.678972\pi$
$683$	−27.8642	−1.06619	−0.533097	+	0.846054i	$0.678972\pi$
$684$	16.8477	0.644188
$685$	−0.975728	−0.0372807
$686$	−29.9578	−1.14379
$687$	−4.28916	−0.163642
$688$	−21.2277	−0.809297
$689$	35.4122	1.34910
$690$	6.84477	0.260576
$691$	9.59934	0.365176	0.182588	−	0.983190i	$-0.441553\pi$
$691$	9.59934	0.365176	0.182588	+	0.983190i	$0.441553\pi$
$692$	1.01231	0.0384821
$693$	−7.54982	−0.286794
$694$	−13.8895	−0.527237
$695$	−9.48517	−0.359793
$696$	3.94847	0.149667
$697$	0.185508	0.00702662
$698$	35.2489	1.33419
$699$	27.0245	1.02216
$700$	−11.9774	−0.452704
$701$	−33.6340	−1.27034	−0.635169	−	0.772373i	$-0.719070\pi$
$701$	−33.6340	−1.27034	−0.635169	+	0.772373i	$0.719070\pi$
$702$	10.1925	0.384690
$703$	19.8411	0.748320
$704$	67.0120	2.52561
$705$	6.89185	0.259562
$706$	−64.2348	−2.41751
$707$	4.97312	0.187033
$708$	30.8516	1.15947
$709$	3.82689	0.143722	0.0718610	−	0.997415i	$-0.477106\pi$
$709$	3.82689	0.143722	0.0718610	+	0.997415i	$0.477106\pi$
$710$	−10.6647	−0.400240
$711$	1.35281	0.0507345
$712$	6.71003	0.251469
$713$	49.6238	1.85843
$714$	−2.35838	−0.0882603
$715$	−20.7023	−0.774223
$716$	4.88691	0.182633
$717$	−29.4671	−1.10047
$718$	−0.751430	−0.0280431
$719$	48.5477	1.81052	0.905261	−	0.424855i	$-0.139675\pi$
$719$	48.5477	1.81052	0.905261	+	0.424855i	$0.139675\pi$
$720$	2.12095	0.0790433
$721$	18.8438	0.701778
$722$	72.9959	2.71663
$723$	−22.7285	−0.845284
$724$	−59.3268	−2.20486
$725$	30.5139	1.13326
$726$	−68.1987	−2.53109
$727$	−18.5701	−0.688726	−0.344363	−	0.938837i	$-0.611905\pi$
$727$	−18.5701	−0.688726	−0.344363	+	0.938837i	$0.611905\pi$
$728$	−3.33546	−0.123621
$729$	1.00000	0.0370370
$730$	−15.1041	−0.559027
$731$	6.35022	0.234871
$732$	−26.9044	−0.994416
$733$	31.9533	1.18022	0.590111	−	0.807322i	$-0.299084\pi$
$733$	31.9533	1.18022	0.590111	+	0.807322i	$0.299084\pi$
$734$	4.74559	0.175163
$735$	−3.61824	−0.133461
$736$	−42.2615	−1.55778
$737$	−60.7298	−2.23701
$738$	0.384110	0.0141393
$739$	45.3009	1.66642	0.833210	−	0.552956i	$-0.186500\pi$
$739$	45.3009	1.66642	0.833210	+	0.552956i	$0.186500\pi$
$740$	−3.90925	−0.143707
$741$	36.2578	1.33196
$742$	−16.9661	−0.622844
$743$	−14.1578	−0.519398	−0.259699	−	0.965690i	$-0.583623\pi$
$743$	−14.1578	−0.519398	−0.259699	+	0.965690i	$0.583623\pi$
$744$	−5.66617	−0.207732
$745$	−9.04302	−0.331311
$746$	−8.22601	−0.301176
$747$	5.12485	0.187508
$748$	−15.1614	−0.554357
$749$	0.0132937	0.000485740 0
$750$	−12.6086	−0.460399
$751$	14.5774	0.531937	0.265969	−	0.963982i	$-0.414308\pi$
$751$	14.5774	0.531937	0.265969	+	0.963982i	$0.414308\pi$
$752$	−36.3105	−1.32411
$753$	−15.4490	−0.562993
$754$	67.6489	2.46363
$755$	2.17014	0.0789794
$756$	−2.60524	−0.0947516
$757$	−19.3436	−0.703056	−0.351528	−	0.936177i	$-0.614338\pi$
$757$	−19.3436	−0.703056	−0.351528	+	0.936177i	$0.614338\pi$
$758$	−39.6760	−1.44110
$759$	34.5353	1.25355
$760$	−2.78023	−0.100849
$761$	−44.4389	−1.61091	−0.805455	−	0.592657i	$-0.798079\pi$
$761$	−44.4389	−1.61091	−0.805455	+	0.592657i	$0.798079\pi$
$762$	−21.8757	−0.792474
$763$	−17.9323	−0.649193
$764$	6.30457	0.228091
$765$	−0.634479	−0.0229397
$766$	23.3440	0.843455
$767$	66.3955	2.39740
$768$	−10.4667	−0.377683
$769$	24.4818	0.882837	0.441418	−	0.897301i	$-0.354475\pi$
$769$	24.4818	0.882837	0.441418	+	0.897301i	$0.354475\pi$
$770$	9.91852	0.357439
$771$	−11.4620	−0.412793
$772$	−20.8289	−0.749648
$773$	48.7342	1.75285	0.876424	−	0.481540i	$-0.159923\pi$
$773$	48.7342	1.75285	0.876424	+	0.481540i	$0.159923\pi$
$774$	13.1487	0.472618
$775$	−43.7882	−1.57292
$776$	−5.14243	−0.184602
$777$	−3.06812	−0.110068
$778$	−14.9319	−0.535336
$779$	1.36640	0.0489564
$780$	−7.14381	−0.255789
$781$	−53.8090	−1.92544
$782$	10.7880	0.385778
$783$	6.63715	0.237192
$784$	19.0631	0.680825
$785$	0.634479	0.0226455
$786$	28.5125	1.01701
$787$	48.9062	1.74332	0.871659	−	0.490113i	$-0.163045\pi$
$787$	48.9062	1.74332	0.871659	+	0.490113i	$0.163045\pi$
$788$	−58.0906	−2.06939
$789$	−6.26399	−0.223004
$790$	−1.77725	−0.0632317
$791$	3.34524	0.118943
$792$	−3.94333	−0.140120
$793$	−57.9008	−2.05612
$794$	37.7614	1.34010
$795$	−4.56440	−0.161883
$796$	25.3732	0.899328
$797$	−14.1322	−0.500589	−0.250295	−	0.968170i	$-0.580527\pi$
$797$	−14.1322	−0.500589	−0.250295	+	0.968170i	$0.580527\pi$
$798$	−17.3712	−0.614933
$799$	10.8622	0.384277
$800$	37.2917	1.31846
$801$	11.2792	0.398529
$802$	−48.4648	−1.71135
$803$	−76.2078	−2.68931
$804$	−20.9562	−0.739068
$805$	−3.76520	−0.132706
$806$	−97.0780	−3.41943
$807$	8.76872	0.308674
$808$	2.59749	0.0913795
$809$	−20.5640	−0.722991	−0.361495	−	0.932374i	$-0.617734\pi$
$809$	−20.5640	−0.722991	−0.361495	+	0.932374i	$0.617734\pi$
$810$	−1.31374	−0.0461602
$811$	−49.8840	−1.75166	−0.875832	−	0.482616i	$-0.839687\pi$
$811$	−49.8840	−1.75166	−0.875832	+	0.482616i	$0.839687\pi$
$812$	−17.2914	−0.606808
$813$	3.62960	0.127296
$814$	−36.9707	−1.29582
$815$	11.8502	0.415096
$816$	3.34283	0.117022
$817$	46.7739	1.63641
$818$	61.8681	2.16317
$819$	−5.60672	−0.195914
$820$	−0.269219	−0.00940154
$821$	18.3742	0.641265	0.320633	−	0.947204i	$-0.396105\pi$
$821$	18.3742	0.641265	0.320633	+	0.947204i	$0.396105\pi$
$822$	−3.18423	−0.111063
$823$	40.1658	1.40009	0.700047	−	0.714097i	$-0.253163\pi$
$823$	40.1658	1.40009	0.700047	+	0.714097i	$0.253163\pi$
$824$	9.84222	0.342870
$825$	−30.4741	−1.06097
$826$	−31.8102	−1.10682
$827$	48.1791	1.67535	0.837676	−	0.546167i	$-0.183914\pi$
$827$	48.1791	1.67535	0.837676	+	0.546167i	$0.183914\pi$
$828$	11.9172	0.414151
$829$	3.06724	0.106530	0.0532649	−	0.998580i	$-0.483037\pi$
$829$	3.06724	0.106530	0.0532649	+	0.998580i	$0.483037\pi$
$830$	−6.73273	−0.233696
$831$	−2.45386	−0.0851236
$832$	49.7650	1.72529
$833$	−5.70269	−0.197587
$834$	−30.9542	−1.07186
$835$	1.78012	0.0616035
$836$	−111.675	−3.86236
$837$	−9.52449	−0.329215
$838$	−23.7063	−0.818920
$839$	−30.8912	−1.06648	−0.533242	−	0.845963i	$-0.679027\pi$
$839$	−30.8912	−1.06648	−0.533242	+	0.845963i	$0.679027\pi$
$840$	0.429919	0.0148336
$841$	15.0517	0.519026
$842$	29.9394	1.03178
$843$	22.3574	0.770030
$844$	43.9878	1.51412
$845$	−7.12591	−0.245139
$846$	22.4911	0.773260
$847$	37.5150	1.28903
$848$	24.0481	0.825814
$849$	13.8890	0.476668
$850$	−9.51937	−0.326512
$851$	14.0346	0.481098
$852$	−18.5680	−0.636130
$853$	16.2712	0.557115	0.278557	−	0.960420i	$-0.410144\pi$
$853$	16.2712	0.557115	0.278557	+	0.960420i	$0.410144\pi$
$854$	27.7404	0.949257
$855$	−4.67340	−0.159827
$856$	0.00694338	0.000237320 0
$857$	−9.69885	−0.331306	−0.165653	−	0.986184i	$-0.552973\pi$
$857$	−9.69885	−0.331306	−0.165653	+	0.986184i	$0.552973\pi$
$858$	−67.5607	−2.30648
$859$	39.2635	1.33965	0.669827	−	0.742517i	$-0.266368\pi$
$859$	39.2635	1.33965	0.669827	+	0.742517i	$0.266368\pi$
$860$	−9.21577	−0.314255
$861$	−0.211293	−0.00720084
$862$	55.8872	1.90353
$863$	6.67220	0.227124	0.113562	−	0.993531i	$-0.463774\pi$
$863$	6.67220	0.227124	0.113562	+	0.993531i	$0.463774\pi$
$864$	8.11141	0.275956
$865$	−0.280804	−0.00954763
$866$	−10.5957	−0.360057
$867$	−1.00000	−0.0339618
$868$	24.8136	0.842227
$869$	−8.96712	−0.304189
$870$	−8.71950	−0.295619
$871$	−45.0997	−1.52814
$872$	−9.36617	−0.317179
$873$	−8.64411	−0.292559
$874$	79.4614	2.68782
$875$	6.93577	0.234472
$876$	−26.2972	−0.888501
$877$	41.7049	1.40827	0.704137	−	0.710064i	$-0.251334\pi$
$877$	41.7049	1.40827	0.704137	+	0.710064i	$0.251334\pi$
$878$	−9.04029	−0.305095
$879$	−11.8968	−0.401268
$880$	−14.0587	−0.473920
$881$	−29.5092	−0.994190	−0.497095	−	0.867696i	$-0.665600\pi$
$881$	−29.5092	−0.994190	−0.497095	+	0.867696i	$0.665600\pi$
$882$	−11.8079	−0.397592
$883$	−41.8655	−1.40889	−0.704443	−	0.709761i	$-0.748803\pi$
$883$	−41.8655	−1.40889	−0.704443	+	0.709761i	$0.748803\pi$
$884$	−11.2593	−0.378692
$885$	−8.55794	−0.287672
$886$	−38.3112	−1.28709
$887$	−33.3794	−1.12077	−0.560385	−	0.828232i	$-0.689347\pi$
$887$	−33.3794	−1.12077	−0.560385	+	0.828232i	$0.689347\pi$
$888$	−1.60250	−0.0537764
$889$	12.0335	0.403590
$890$	−14.8179	−0.496697
$891$	−6.62850	−0.222063
$892$	−31.8093	−1.06506
$893$	80.0080	2.67736
$894$	−29.5113	−0.987006
$895$	−1.35558	−0.0453122
$896$	−5.36482	−0.179226
$897$	25.6469	0.856326
$898$	25.0703	0.836607
$899$	−63.2155	−2.10835
$900$	−10.5158	−0.350526
$901$	−7.19394	−0.239665
$902$	−2.54607	−0.0847749
$903$	−7.23287	−0.240695
$904$	1.74724	0.0581125
$905$	16.4567	0.547040
$906$	7.08210	0.235287
$907$	8.37066	0.277943	0.138972	−	0.990296i	$-0.455620\pi$
$907$	8.37066	0.277943	0.138972	+	0.990296i	$0.455620\pi$
$908$	−7.05263	−0.234050
$909$	4.36623	0.144819
$910$	7.36578	0.244173
$911$	−17.8701	−0.592062	−0.296031	−	0.955178i	$-0.595663\pi$
$911$	−17.8701	−0.592062	−0.296031	+	0.955178i	$0.595663\pi$
$912$	24.6223	0.815326
$913$	−33.9700	−1.12424
$914$	54.0445	1.78763
$915$	7.46304	0.246720
$916$	9.81066	0.324153
$917$	−15.6843	−0.517941
$918$	−2.07058	−0.0683394
$919$	−42.4932	−1.40172	−0.700861	−	0.713298i	$-0.747201\pi$
$919$	−42.4932	−1.40172	−0.700861	+	0.713298i	$0.747201\pi$
$920$	−1.96659	−0.0648365
$921$	−17.9862	−0.592664
$922$	28.2894	0.931662
$923$	−39.9601	−1.31530
$924$	17.2688	0.568102
$925$	−12.3841	−0.407188
$926$	20.7212	0.680939
$927$	16.5442	0.543382
$928$	53.8366	1.76727
$929$	−46.7987	−1.53542	−0.767708	−	0.640800i	$-0.778603\pi$
$929$	−46.7987	−1.53542	−0.767708	+	0.640800i	$0.778603\pi$
$930$	12.5127	0.410308
$931$	−42.0044	−1.37664
$932$	−61.8136	−2.02477
$933$	−19.0869	−0.624877
$934$	36.4882	1.19393
$935$	4.20564	0.137539
$936$	−2.92843	−0.0957186
$937$	8.72002	0.284871	0.142435	−	0.989804i	$-0.454507\pi$
$937$	8.72002	0.284871	0.142435	+	0.989804i	$0.454507\pi$
$938$	21.6073	0.705504
$939$	−22.9307	−0.748314
$940$	−15.7638	−0.514159
$941$	23.3953	0.762665	0.381333	−	0.924438i	$-0.375465\pi$
$941$	23.3953	0.762665	0.381333	+	0.924438i	$0.375465\pi$
$942$	2.07058	0.0674632
$943$	0.966521	0.0314742
$944$	45.0885	1.46750
$945$	0.722669	0.0235084
$946$	−87.1558	−2.83368
$947$	18.5285	0.602094	0.301047	−	0.953609i	$-0.402664\pi$
$947$	18.5285	0.602094	0.301047	+	0.953609i	$0.402664\pi$
$948$	−3.09431	−0.100498
$949$	−56.5941	−1.83712
$950$	−70.1170	−2.27490
$951$	−25.3288	−0.821342
$952$	0.677594	0.0219609
$953$	20.9188	0.677627	0.338813	−	0.940854i	$-0.389974\pi$
$953$	20.9188	0.677627	0.338813	+	0.940854i	$0.389974\pi$
$954$	−14.8956	−0.482264
$955$	−1.74883	−0.0565907
$956$	67.4005	2.17989
$957$	−43.9943	−1.42213
$958$	−55.5968	−1.79625
$959$	1.75159	0.0565619
$960$	−6.41439	−0.207024
$961$	59.7159	1.92632
$962$	−27.4555	−0.885201
$963$	0.0116714	0.000376106 0
$964$	51.9873	1.67440
$965$	5.77774	0.185992
$966$	−12.2875	−0.395343
$967$	5.24261	0.168591	0.0842955	−	0.996441i	$-0.473136\pi$
$967$	5.24261	0.168591	0.0842955	+	0.996441i	$0.473136\pi$
$968$	19.5944	0.629787
$969$	−7.36572	−0.236621
$970$	11.3561	0.364623
$971$	13.7938	0.442663	0.221332	−	0.975199i	$-0.428960\pi$
$971$	13.7938	0.442663	0.221332	+	0.975199i	$0.428960\pi$
$972$	−2.28731	−0.0733656
$973$	17.0274	0.545875
$974$	−51.5357	−1.65131
$975$	−22.6309	−0.724770
$976$	−39.3198	−1.25860
$977$	−0.322911	−0.0103308	−0.00516542	−	0.999987i	$-0.501644\pi$
$977$	−0.322911	−0.0103308	−0.00516542	+	0.999987i	$0.501644\pi$
$978$	38.6725	1.23661
$979$	−74.7638	−2.38946
$980$	8.27605	0.264369
$981$	−15.7440	−0.502666
$982$	−60.5872	−1.93342
$983$	−24.3312	−0.776044	−0.388022	−	0.921650i	$-0.626841\pi$
$983$	−24.3312	−0.776044	−0.388022	+	0.921650i	$0.626841\pi$
$984$	−0.110360	−0.00351814
$985$	16.1138	0.513428
$986$	−13.7428	−0.437659
$987$	−12.3720	−0.393805
$988$	−82.9330	−2.63845
$989$	33.0855	1.05206
$990$	8.70813	0.276763
$991$	−12.0733	−0.383521	−0.191760	−	0.981442i	$-0.561420\pi$
$991$	−12.0733	−0.383521	−0.191760	+	0.981442i	$0.561420\pi$
$992$	−77.2570	−2.45291
$993$	−11.1884	−0.355052
$994$	19.1450	0.607241
$995$	−7.03828	−0.223128
$996$	−11.7221	−0.371430
$997$	41.3194	1.30860	0.654299	−	0.756236i	$-0.272964\pi$
$997$	41.3194	1.30860	0.654299	+	0.756236i	$0.272964\pi$
$998$	14.7232	0.466054
$999$	−2.69371	−0.0852251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.52	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.52	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07058 q^{2} -1.00000 q^{3} +2.28731 q^{4} -0.634479 q^{5} -2.07058 q^{6} +1.13900 q^{7} +0.594905 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.07058 q^{2} -1.00000 q^{3} +2.28731 q^{4} -0.634479 q^{5} -2.07058 q^{6} +1.13900 q^{7} +0.594905 q^{8} +1.00000 q^{9} -1.31374 q^{10} -6.62850 q^{11} -2.28731 q^{12} -4.92251 q^{13} +2.35838 q^{14} +0.634479 q^{15} -3.34283 q^{16} +1.00000 q^{17} +2.07058 q^{18} +7.36572 q^{19} -1.45125 q^{20} -1.13900 q^{21} -13.7248 q^{22} +5.21013 q^{23} -0.594905 q^{24} -4.59744 q^{25} -10.1925 q^{26} -1.00000 q^{27} +2.60524 q^{28} -6.63715 q^{29} +1.31374 q^{30} +9.52449 q^{31} -8.11141 q^{32} +6.62850 q^{33} +2.07058 q^{34} -0.722669 q^{35} +2.28731 q^{36} +2.69371 q^{37} +15.2513 q^{38} +4.92251 q^{39} -0.377455 q^{40} +0.185508 q^{41} -2.35838 q^{42} +6.35022 q^{43} -15.1614 q^{44} -0.634479 q^{45} +10.7880 q^{46} +10.8622 q^{47} +3.34283 q^{48} -5.70269 q^{49} -9.51937 q^{50} -1.00000 q^{51} -11.2593 q^{52} -7.19394 q^{53} -2.07058 q^{54} +4.20564 q^{55} +0.677594 q^{56} -7.36572 q^{57} -13.7428 q^{58} -13.4881 q^{59} +1.45125 q^{60} +11.7625 q^{61} +19.7212 q^{62} +1.13900 q^{63} -10.1097 q^{64} +3.12323 q^{65} +13.7248 q^{66} +9.16192 q^{67} +2.28731 q^{68} -5.21013 q^{69} -1.49635 q^{70} +8.11783 q^{71} +0.594905 q^{72} +11.4970 q^{73} +5.57754 q^{74} +4.59744 q^{75} +16.8477 q^{76} -7.54982 q^{77} +10.1925 q^{78} +1.35281 q^{79} +2.12095 q^{80} +1.00000 q^{81} +0.384110 q^{82} +5.12485 q^{83} -2.60524 q^{84} -0.634479 q^{85} +13.1487 q^{86} +6.63715 q^{87} -3.94333 q^{88} +11.2792 q^{89} -1.31374 q^{90} -5.60672 q^{91} +11.9172 q^{92} -9.52449 q^{93} +22.4911 q^{94} -4.67340 q^{95} +8.11141 q^{96} -8.64411 q^{97} -11.8079 q^{98} -6.62850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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