LMFDB - Embedded newform 8007.2.a.j.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.11517 q^{2} -1.00000 q^{3} +2.47395 q^{4} +2.21169 q^{5} +2.11517 q^{6} -2.99289 q^{7} -1.00248 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11517 q^{2} -1.00000 q^{3} +2.47395 q^{4} +2.21169 q^{5} +2.11517 q^{6} -2.99289 q^{7} -1.00248 q^{8} +1.00000 q^{9} -4.67809 q^{10} -4.68964 q^{11} -2.47395 q^{12} -6.95442 q^{13} +6.33047 q^{14} -2.21169 q^{15} -2.82747 q^{16} +1.00000 q^{17} -2.11517 q^{18} -3.64474 q^{19} +5.47160 q^{20} +2.99289 q^{21} +9.91940 q^{22} +2.77589 q^{23} +1.00248 q^{24} -0.108448 q^{25} +14.7098 q^{26} -1.00000 q^{27} -7.40425 q^{28} -3.63506 q^{29} +4.67809 q^{30} +4.06933 q^{31} +7.98556 q^{32} +4.68964 q^{33} -2.11517 q^{34} -6.61933 q^{35} +2.47395 q^{36} -8.99989 q^{37} +7.70925 q^{38} +6.95442 q^{39} -2.21718 q^{40} -10.7319 q^{41} -6.33047 q^{42} -5.09670 q^{43} -11.6019 q^{44} +2.21169 q^{45} -5.87148 q^{46} +12.1496 q^{47} +2.82747 q^{48} +1.95738 q^{49} +0.229386 q^{50} -1.00000 q^{51} -17.2049 q^{52} +2.12525 q^{53} +2.11517 q^{54} -10.3720 q^{55} +3.00032 q^{56} +3.64474 q^{57} +7.68878 q^{58} -12.0228 q^{59} -5.47160 q^{60} +2.48960 q^{61} -8.60732 q^{62} -2.99289 q^{63} -11.2359 q^{64} -15.3810 q^{65} -9.91940 q^{66} -5.59912 q^{67} +2.47395 q^{68} -2.77589 q^{69} +14.0010 q^{70} -4.99860 q^{71} -1.00248 q^{72} -16.7937 q^{73} +19.0363 q^{74} +0.108448 q^{75} -9.01690 q^{76} +14.0356 q^{77} -14.7098 q^{78} -7.56114 q^{79} -6.25348 q^{80} +1.00000 q^{81} +22.6999 q^{82} -7.89794 q^{83} +7.40425 q^{84} +2.21169 q^{85} +10.7804 q^{86} +3.63506 q^{87} +4.70129 q^{88} -3.95383 q^{89} -4.67809 q^{90} +20.8138 q^{91} +6.86741 q^{92} -4.06933 q^{93} -25.6986 q^{94} -8.06102 q^{95} -7.98556 q^{96} +6.85456 q^{97} -4.14019 q^{98} -4.68964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.11517	−1.49565	−0.747826	−	0.663895i	$-0.768902\pi$
$2$	−2.11517	−1.49565	−0.747826	+	0.663895i	$0.768902\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.47395	1.23697
$5$	2.21169	0.989096	0.494548	−	0.869150i	$-0.335334\pi$
$5$	2.21169	0.989096	0.494548	+	0.869150i	$0.335334\pi$
$6$	2.11517	0.863515
$7$	−2.99289	−1.13121	−0.565603	−	0.824678i	$-0.691356\pi$
$7$	−2.99289	−1.13121	−0.565603	+	0.824678i	$0.691356\pi$
$8$	−1.00248	−0.354431
$9$	1.00000	0.333333
$10$	−4.67809	−1.47934
$11$	−4.68964	−1.41398	−0.706990	−	0.707223i	$-0.749948\pi$
$11$	−4.68964	−1.41398	−0.706990	+	0.707223i	$0.749948\pi$
$12$	−2.47395	−0.714168
$13$	−6.95442	−1.92881	−0.964405	−	0.264431i	$-0.914816\pi$
$13$	−6.95442	−1.92881	−0.964405	+	0.264431i	$0.914816\pi$
$14$	6.33047	1.69189
$15$	−2.21169	−0.571055
$16$	−2.82747	−0.706869
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.11517	−0.498551
$19$	−3.64474	−0.836160	−0.418080	−	0.908410i	$-0.637297\pi$
$19$	−3.64474	−0.836160	−0.418080	+	0.908410i	$0.637297\pi$
$20$	5.47160	1.22349
$21$	2.99289	0.653102
$22$	9.91940	2.11482
$23$	2.77589	0.578813	0.289407	−	0.957206i	$-0.406542\pi$
$23$	2.77589	0.578813	0.289407	+	0.957206i	$0.406542\pi$
$24$	1.00248	0.204631
$25$	−0.108448	−0.0216896
$26$	14.7098	2.88483
$27$	−1.00000	−0.192450
$28$	−7.40425	−1.39927
$29$	−3.63506	−0.675014	−0.337507	−	0.941323i	$-0.609584\pi$
$29$	−3.63506	−0.675014	−0.337507	+	0.941323i	$0.609584\pi$
$30$	4.67809	0.854099
$31$	4.06933	0.730873	0.365436	−	0.930836i	$-0.380920\pi$
$31$	4.06933	0.730873	0.365436	+	0.930836i	$0.380920\pi$
$32$	7.98556	1.41166
$33$	4.68964	0.816362
$34$	−2.11517	−0.362749
$35$	−6.61933	−1.11887
$36$	2.47395	0.412325
$37$	−8.99989	−1.47957	−0.739787	−	0.672841i	$-0.765074\pi$
$37$	−8.99989	−1.47957	−0.739787	+	0.672841i	$0.765074\pi$
$38$	7.70925	1.25061
$39$	6.95442	1.11360
$40$	−2.21718	−0.350567
$41$	−10.7319	−1.67605	−0.838023	−	0.545635i	$-0.816289\pi$
$41$	−10.7319	−1.67605	−0.838023	+	0.545635i	$0.816289\pi$
$42$	−6.33047	−0.976813
$43$	−5.09670	−0.777240	−0.388620	−	0.921398i	$-0.627048\pi$
$43$	−5.09670	−0.777240	−0.388620	+	0.921398i	$0.627048\pi$
$44$	−11.6019	−1.74906
$45$	2.21169	0.329699
$46$	−5.87148	−0.865703
$47$	12.1496	1.77221	0.886103	−	0.463487i	$-0.153402\pi$
$47$	12.1496	1.77221	0.886103	+	0.463487i	$0.153402\pi$
$48$	2.82747	0.408111
$49$	1.95738	0.279626
$50$	0.229386	0.0324401
$51$	−1.00000	−0.140028
$52$	−17.2049	−2.38589
$53$	2.12525	0.291926	0.145963	−	0.989290i	$-0.453372\pi$
$53$	2.12525	0.291926	0.145963	+	0.989290i	$0.453372\pi$
$54$	2.11517	0.287838
$55$	−10.3720	−1.39856
$56$	3.00032	0.400935
$57$	3.64474	0.482757
$58$	7.68878	1.00959
$59$	−12.0228	−1.56524	−0.782619	−	0.622502i	$-0.786116\pi$
$59$	−12.0228	−1.56524	−0.782619	+	0.622502i	$0.786116\pi$
$60$	−5.47160	−0.706380
$61$	2.48960	0.318761	0.159380	−	0.987217i	$-0.449050\pi$
$61$	2.48960	0.318761	0.159380	+	0.987217i	$0.449050\pi$
$62$	−8.60732	−1.09313
$63$	−2.99289	−0.377068
$64$	−11.2359	−1.40448
$65$	−15.3810	−1.90778
$66$	−9.91940	−1.22099
$67$	−5.59912	−0.684041	−0.342021	−	0.939692i	$-0.611111\pi$
$67$	−5.59912	−0.684041	−0.342021	+	0.939692i	$0.611111\pi$
$68$	2.47395	0.300010
$69$	−2.77589	−0.334178
$70$	14.0010	1.67344
$71$	−4.99860	−0.593224	−0.296612	−	0.954998i	$-0.595857\pi$
$71$	−4.99860	−0.593224	−0.296612	+	0.954998i	$0.595857\pi$
$72$	−1.00248	−0.118144
$73$	−16.7937	−1.96556	−0.982778	−	0.184790i	$-0.940839\pi$
$73$	−16.7937	−1.96556	−0.982778	+	0.184790i	$0.940839\pi$
$74$	19.0363	2.21293
$75$	0.108448	0.0125225
$76$	−9.01690	−1.03431
$77$	14.0356	1.59950
$78$	−14.7098	−1.66556
$79$	−7.56114	−0.850695	−0.425347	−	0.905030i	$-0.639848\pi$
$79$	−7.56114	−0.850695	−0.425347	+	0.905030i	$0.639848\pi$
$80$	−6.25348	−0.699161
$81$	1.00000	0.111111
$82$	22.6999	2.50678
$83$	−7.89794	−0.866912	−0.433456	−	0.901175i	$-0.642706\pi$
$83$	−7.89794	−0.866912	−0.433456	+	0.901175i	$0.642706\pi$
$84$	7.40425	0.807870
$85$	2.21169	0.239891
$86$	10.7804	1.16248
$87$	3.63506	0.389720
$88$	4.70129	0.501159
$89$	−3.95383	−0.419105	−0.209552	−	0.977797i	$-0.567201\pi$
$89$	−3.95383	−0.419105	−0.209552	+	0.977797i	$0.567201\pi$
$90$	−4.67809	−0.493114
$91$	20.8138	2.18188
$92$	6.86741	0.715977
$93$	−4.06933	−0.421969
$94$	−25.6986	−2.65060
$95$	−8.06102	−0.827043
$96$	−7.98556	−0.815023
$97$	6.85456	0.695975	0.347988	−	0.937499i	$-0.386865\pi$
$97$	6.85456	0.695975	0.347988	+	0.937499i	$0.386865\pi$
$98$	−4.14019	−0.418223
$99$	−4.68964	−0.471327
$100$	−0.268295	−0.0268295
$101$	10.2019	1.01512	0.507562	−	0.861615i	$-0.330547\pi$
$101$	10.2019	1.01512	0.507562	+	0.861615i	$0.330547\pi$
$102$	2.11517	0.209433
$103$	−8.15582	−0.803617	−0.401808	−	0.915724i	$-0.631618\pi$
$103$	−8.15582	−0.803617	−0.401808	+	0.915724i	$0.631618\pi$
$104$	6.97169	0.683630
$105$	6.61933	0.645980
$106$	−4.49527	−0.436619
$107$	−15.2536	−1.47462	−0.737310	−	0.675555i	$-0.763904\pi$
$107$	−15.2536	−1.47462	−0.737310	+	0.675555i	$0.763904\pi$
$108$	−2.47395	−0.238056
$109$	9.54476	0.914222	0.457111	−	0.889410i	$-0.348884\pi$
$109$	9.54476	0.914222	0.457111	+	0.889410i	$0.348884\pi$
$110$	21.9386	2.09176
$111$	8.99989	0.854232
$112$	8.46231	0.799614
$113$	16.2493	1.52860	0.764300	−	0.644860i	$-0.223084\pi$
$113$	16.2493	1.52860	0.764300	+	0.644860i	$0.223084\pi$
$114$	−7.70925	−0.722037
$115$	6.13940	0.572502
$116$	−8.99296	−0.834975
$117$	−6.95442	−0.642936
$118$	25.4303	2.34105
$119$	−2.99289	−0.274358
$120$	2.21718	0.202400
$121$	10.9928	0.999341
$122$	−5.26593	−0.476755
$123$	10.7319	0.967666
$124$	10.0673	0.904071
$125$	−11.2983	−1.01055
$126$	6.33047	0.563963
$127$	−9.93243	−0.881361	−0.440680	−	0.897664i	$-0.645263\pi$
$127$	−9.93243	−0.881361	−0.440680	+	0.897664i	$0.645263\pi$
$128$	7.79468	0.688959
$129$	5.09670	0.448740
$130$	32.5334	2.85337
$131$	−21.7380	−1.89926	−0.949629	−	0.313376i	$-0.898540\pi$
$131$	−21.7380	−1.89926	−0.949629	+	0.313376i	$0.898540\pi$
$132$	11.6019	1.00982
$133$	10.9083	0.945869
$134$	11.8431	1.02309
$135$	−2.21169	−0.190352
$136$	−1.00248	−0.0859622
$137$	1.01464	0.0866867	0.0433433	−	0.999060i	$-0.486199\pi$
$137$	1.01464	0.0866867	0.0433433	+	0.999060i	$0.486199\pi$
$138$	5.87148	0.499814
$139$	9.47463	0.803628	0.401814	−	0.915721i	$-0.368380\pi$
$139$	9.47463	0.803628	0.401814	+	0.915721i	$0.368380\pi$
$140$	−16.3759	−1.38401
$141$	−12.1496	−1.02318
$142$	10.5729	0.887257
$143$	32.6137	2.72730
$144$	−2.82747	−0.235623
$145$	−8.03962	−0.667654
$146$	35.5216	2.93979
$147$	−1.95738	−0.161442
$148$	−22.2653	−1.83019
$149$	−9.83733	−0.805905	−0.402953	−	0.915221i	$-0.632016\pi$
$149$	−9.83733	−0.805905	−0.402953	+	0.915221i	$0.632016\pi$
$150$	−0.229386	−0.0187293
$151$	12.2730	0.998762	0.499381	−	0.866382i	$-0.333561\pi$
$151$	12.2730	0.998762	0.499381	+	0.866382i	$0.333561\pi$
$152$	3.65379	0.296362
$153$	1.00000	0.0808452
$154$	−29.6876	−2.39230
$155$	9.00007	0.722903
$156$	17.2049	1.37749
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	15.9931	1.27234
$159$	−2.12525	−0.168543
$160$	17.6615	1.39627
$161$	−8.30793	−0.654757
$162$	−2.11517	−0.166184
$163$	−9.37235	−0.734099	−0.367050	−	0.930201i	$-0.619632\pi$
$163$	−9.37235	−0.734099	−0.367050	+	0.930201i	$0.619632\pi$
$164$	−26.5503	−2.07323
$165$	10.3720	0.807460
$166$	16.7055	1.29660
$167$	−24.8082	−1.91972	−0.959859	−	0.280484i	$-0.909505\pi$
$167$	−24.8082	−1.91972	−0.959859	+	0.280484i	$0.909505\pi$
$168$	−3.00032	−0.231480
$169$	35.3640	2.72030
$170$	−4.67809	−0.358793
$171$	−3.64474	−0.278720
$172$	−12.6090	−0.961426
$173$	11.7404	0.892603	0.446301	−	0.894883i	$-0.352741\pi$
$173$	11.7404	0.892603	0.446301	+	0.894883i	$0.352741\pi$
$174$	−7.68878	−0.582885
$175$	0.324573	0.0245354
$176$	13.2598	0.999498
$177$	12.0228	0.903690
$178$	8.36302	0.626835
$179$	8.94912	0.668888	0.334444	−	0.942416i	$-0.391451\pi$
$179$	8.94912	0.668888	0.334444	+	0.942416i	$0.391451\pi$
$180$	5.47160	0.407829
$181$	13.0507	0.970052	0.485026	−	0.874500i	$-0.338810\pi$
$181$	13.0507	0.970052	0.485026	+	0.874500i	$0.338810\pi$
$182$	−44.0247	−3.26333
$183$	−2.48960	−0.184037
$184$	−2.78278	−0.205150
$185$	−19.9049	−1.46344
$186$	8.60732	0.631119
$187$	−4.68964	−0.342941
$188$	30.0576	2.19217
$189$	2.99289	0.217701
$190$	17.0504	1.23697
$191$	19.3245	1.39827	0.699135	−	0.714990i	$-0.253569\pi$
$191$	19.3245	1.39827	0.699135	+	0.714990i	$0.253569\pi$
$192$	11.2359	0.810879
$193$	7.91560	0.569777	0.284889	−	0.958561i	$-0.408043\pi$
$193$	7.91560	0.569777	0.284889	+	0.958561i	$0.408043\pi$
$194$	−14.4986	−1.04094
$195$	15.3810	1.10146
$196$	4.84246	0.345890
$197$	17.5967	1.25371	0.626855	−	0.779136i	$-0.284342\pi$
$197$	17.5967	1.25371	0.626855	+	0.779136i	$0.284342\pi$
$198$	9.91940	0.704941
$199$	−19.0361	−1.34943	−0.674715	−	0.738078i	$-0.735734\pi$
$199$	−19.0361	−1.34943	−0.674715	+	0.738078i	$0.735734\pi$
$200$	0.108717	0.00768749
$201$	5.59912	0.394931
$202$	−21.5787	−1.51827
$203$	10.8793	0.763580
$204$	−2.47395	−0.173211
$205$	−23.7357	−1.65777
$206$	17.2510	1.20193
$207$	2.77589	0.192938
$208$	19.6634	1.36341
$209$	17.0925	1.18231
$210$	−14.0010	−0.966161
$211$	−17.4733	−1.20291	−0.601457	−	0.798905i	$-0.705413\pi$
$211$	−17.4733	−1.20291	−0.601457	+	0.798905i	$0.705413\pi$
$212$	5.25776	0.361105
$213$	4.99860	0.342498
$214$	32.2639	2.20552
$215$	−11.2723	−0.768765
$216$	1.00248	0.0682103
$217$	−12.1790	−0.826767
$218$	−20.1888	−1.36736
$219$	16.7937	1.13481
$220$	−25.6598	−1.72999
$221$	−6.95442	−0.467805
$222$	−19.0363	−1.27763
$223$	25.5231	1.70915	0.854576	−	0.519326i	$-0.173817\pi$
$223$	25.5231	1.70915	0.854576	+	0.519326i	$0.173817\pi$
$224$	−23.8999	−1.59688
$225$	−0.108448	−0.00722988
$226$	−34.3699	−2.28625
$227$	−12.0584	−0.800343	−0.400172	−	0.916440i	$-0.631049\pi$
$227$	−12.0584	−0.800343	−0.400172	+	0.916440i	$0.631049\pi$
$228$	9.01690	0.597159
$229$	−13.1585	−0.869536	−0.434768	−	0.900542i	$-0.643170\pi$
$229$	−13.1585	−0.869536	−0.434768	+	0.900542i	$0.643170\pi$
$230$	−12.9859	−0.856263
$231$	−14.0356	−0.923473
$232$	3.64409	0.239246
$233$	−3.11835	−0.204290	−0.102145	−	0.994770i	$-0.532571\pi$
$233$	−3.11835	−0.204290	−0.102145	+	0.994770i	$0.532571\pi$
$234$	14.7098	0.961609
$235$	26.8712	1.75288
$236$	−29.7438	−1.93616
$237$	7.56114	0.491149
$238$	6.33047	0.410343
$239$	0.545179	0.0352647	0.0176324	−	0.999845i	$-0.494387\pi$
$239$	0.545179	0.0352647	0.0176324	+	0.999845i	$0.494387\pi$
$240$	6.25348	0.403661
$241$	−23.4255	−1.50897	−0.754484	−	0.656319i	$-0.772113\pi$
$241$	−23.4255	−1.50897	−0.754484	+	0.656319i	$0.772113\pi$
$242$	−23.2516	−1.49467
$243$	−1.00000	−0.0641500
$244$	6.15915	0.394299
$245$	4.32911	0.276576
$246$	−22.6999	−1.44729
$247$	25.3470	1.61279
$248$	−4.07943	−0.259044
$249$	7.89794	0.500512
$250$	23.8978	1.51143
$251$	16.2359	1.02480	0.512402	−	0.858746i	$-0.328756\pi$
$251$	16.2359	1.02480	0.512402	+	0.858746i	$0.328756\pi$
$252$	−7.40425	−0.466424
$253$	−13.0179	−0.818431
$254$	21.0088	1.31821
$255$	−2.21169	−0.138501
$256$	5.98467	0.374042
$257$	−31.4934	−1.96450	−0.982251	−	0.187570i	$-0.939939\pi$
$257$	−31.4934	−1.96450	−0.982251	+	0.187570i	$0.939939\pi$
$258$	−10.7804	−0.671158
$259$	26.9357	1.67370
$260$	−38.0518	−2.35987
$261$	−3.63506	−0.225005
$262$	45.9796	2.84063
$263$	−12.5384	−0.773151	−0.386576	−	0.922258i	$-0.626342\pi$
$263$	−12.5384	−0.773151	−0.386576	+	0.922258i	$0.626342\pi$
$264$	−4.70129	−0.289344
$265$	4.70039	0.288742
$266$	−23.0729	−1.41469
$267$	3.95383	0.241970
$268$	−13.8519	−0.846142
$269$	−27.3995	−1.67058	−0.835290	−	0.549810i	$-0.814700\pi$
$269$	−27.3995	−1.67058	−0.835290	+	0.549810i	$0.814700\pi$
$270$	4.67809	0.284700
$271$	−24.1438	−1.46663	−0.733317	−	0.679887i	$-0.762029\pi$
$271$	−24.1438	−1.46663	−0.733317	+	0.679887i	$0.762029\pi$
$272$	−2.82747	−0.171441
$273$	−20.8138	−1.25971
$274$	−2.14614	−0.129653
$275$	0.508583	0.0306687
$276$	−6.86741	−0.413370
$277$	17.7425	1.06604	0.533021	−	0.846102i	$-0.321057\pi$
$277$	17.7425	1.06604	0.533021	+	0.846102i	$0.321057\pi$
$278$	−20.0405	−1.20195
$279$	4.06933	0.243624
$280$	6.63576	0.396563
$281$	−15.2451	−0.909446	−0.454723	−	0.890633i	$-0.650262\pi$
$281$	−15.2451	−0.909446	−0.454723	+	0.890633i	$0.650262\pi$
$282$	25.6986	1.53033
$283$	−0.603246	−0.0358593	−0.0179296	−	0.999839i	$-0.505707\pi$
$283$	−0.603246	−0.0358593	−0.0179296	+	0.999839i	$0.505707\pi$
$284$	−12.3663	−0.733803
$285$	8.06102	0.477493
$286$	−68.9837	−4.07909
$287$	32.1195	1.89595
$288$	7.98556	0.470554
$289$	1.00000	0.0588235
$290$	17.0052	0.998578
$291$	−6.85456	−0.401821
$292$	−41.5468	−2.43134
$293$	12.3145	0.719419	0.359710	−	0.933064i	$-0.382876\pi$
$293$	12.3145	0.719419	0.359710	+	0.933064i	$0.382876\pi$
$294$	4.14019	0.241461
$295$	−26.5907	−1.54817
$296$	9.02224	0.524407
$297$	4.68964	0.272121
$298$	20.8076	1.20535
$299$	−19.3047	−1.11642
$300$	0.268295	0.0154900
$301$	15.2539	0.879218
$302$	−25.9595	−1.49380
$303$	−10.2019	−0.586083
$304$	10.3054	0.591056
$305$	5.50621	0.315285
$306$	−2.11517	−0.120916
$307$	6.64694	0.379361	0.189680	−	0.981846i	$-0.439255\pi$
$307$	6.64694	0.379361	0.189680	+	0.981846i	$0.439255\pi$
$308$	34.7233	1.97854
$309$	8.15582	0.463968
$310$	−19.0367	−1.08121
$311$	10.3816	0.588685	0.294343	−	0.955700i	$-0.404899\pi$
$311$	10.3816	0.588685	0.294343	+	0.955700i	$0.404899\pi$
$312$	−6.97169	−0.394694
$313$	13.3531	0.754763	0.377382	−	0.926058i	$-0.376825\pi$
$313$	13.3531	0.754763	0.377382	+	0.926058i	$0.376825\pi$
$314$	2.11517	0.119366
$315$	−6.61933	−0.372957
$316$	−18.7059	−1.05229
$317$	9.25260	0.519678	0.259839	−	0.965652i	$-0.416331\pi$
$317$	9.25260	0.519678	0.259839	+	0.965652i	$0.416331\pi$
$318$	4.49527	0.252082
$319$	17.0471	0.954457
$320$	−24.8502	−1.38917
$321$	15.2536	0.851372
$322$	17.5727	0.979288
$323$	−3.64474	−0.202799
$324$	2.47395	0.137442
$325$	0.754194	0.0418352
$326$	19.8241	1.09796
$327$	−9.54476	−0.527826
$328$	10.7586	0.594043
$329$	−36.3625	−2.00473
$330$	−21.9386	−1.20768
$331$	−24.4559	−1.34422	−0.672109	−	0.740452i	$-0.734611\pi$
$331$	−24.4559	−1.34422	−0.672109	+	0.740452i	$0.734611\pi$
$332$	−19.5391	−1.07235
$333$	−8.99989	−0.493191
$334$	52.4736	2.87123
$335$	−12.3835	−0.676582
$336$	−8.46231	−0.461657
$337$	18.2007	0.991456	0.495728	−	0.868478i	$-0.334901\pi$
$337$	18.2007	0.991456	0.495728	+	0.868478i	$0.334901\pi$
$338$	−74.8008	−4.06863
$339$	−16.2493	−0.882538
$340$	5.47160	0.296739
$341$	−19.0837	−1.03344
$342$	7.70925	0.416868
$343$	15.0920	0.814891
$344$	5.10936	0.275478
$345$	−6.13940	−0.330534
$346$	−24.8329	−1.33502
$347$	8.80901	0.472892	0.236446	−	0.971645i	$-0.424017\pi$
$347$	8.80901	0.472892	0.236446	+	0.971645i	$0.424017\pi$
$348$	8.99296	0.482073
$349$	4.21599	0.225677	0.112838	−	0.993613i	$-0.464006\pi$
$349$	4.21599	0.225677	0.112838	+	0.993613i	$0.464006\pi$
$350$	−0.686528	−0.0366965
$351$	6.95442	0.371199
$352$	−37.4494	−1.99606
$353$	−5.00317	−0.266292	−0.133146	−	0.991096i	$-0.542508\pi$
$353$	−5.00317	−0.266292	−0.133146	+	0.991096i	$0.542508\pi$
$354$	−25.4303	−1.35161
$355$	−11.0553	−0.586755
$356$	−9.78156	−0.518422
$357$	2.99289	0.158400
$358$	−18.9289	−1.00042
$359$	−10.5320	−0.555858	−0.277929	−	0.960602i	$-0.589648\pi$
$359$	−10.5320	−0.555858	−0.277929	+	0.960602i	$0.589648\pi$
$360$	−2.21718	−0.116856
$361$	−5.71588	−0.300836
$362$	−27.6045	−1.45086
$363$	−10.9928	−0.576970
$364$	51.4923	2.69893
$365$	−37.1424	−1.94412
$366$	5.26593	0.275255
$367$	4.38556	0.228924	0.114462	−	0.993428i	$-0.463486\pi$
$367$	4.38556	0.228924	0.114462	+	0.993428i	$0.463486\pi$
$368$	−7.84876	−0.409145
$369$	−10.7319	−0.558682
$370$	42.1023	2.18880
$371$	−6.36064	−0.330228
$372$	−10.0673	−0.521965
$373$	10.4074	0.538875	0.269438	−	0.963018i	$-0.413162\pi$
$373$	10.4074	0.538875	0.269438	+	0.963018i	$0.413162\pi$
$374$	9.91940	0.512920
$375$	11.2983	0.583441
$376$	−12.1798	−0.628126
$377$	25.2798	1.30197
$378$	−6.33047	−0.325604
$379$	−16.0605	−0.824972	−0.412486	−	0.910964i	$-0.635339\pi$
$379$	−16.0605	−0.824972	−0.412486	+	0.910964i	$0.635339\pi$
$380$	−19.9425	−1.02303
$381$	9.93243	0.508854
$382$	−40.8746	−2.09132
$383$	−25.8834	−1.32258	−0.661290	−	0.750130i	$-0.729991\pi$
$383$	−25.8834	−1.32258	−0.661290	+	0.750130i	$0.729991\pi$
$384$	−7.79468	−0.397771
$385$	31.0423	1.58206
$386$	−16.7428	−0.852188
$387$	−5.09670	−0.259080
$388$	16.9578	0.860904
$389$	17.8472	0.904889	0.452444	−	0.891793i	$-0.350552\pi$
$389$	17.8472	0.904889	0.452444	+	0.891793i	$0.350552\pi$
$390$	−32.5334	−1.64739
$391$	2.77589	0.140383
$392$	−1.96224	−0.0991081
$393$	21.7380	1.09654
$394$	−37.2200	−1.87511
$395$	−16.7229	−0.841419
$396$	−11.6019	−0.583019
$397$	16.6494	0.835609	0.417805	−	0.908537i	$-0.362800\pi$
$397$	16.6494	0.835609	0.417805	+	0.908537i	$0.362800\pi$
$398$	40.2645	2.01828
$399$	−10.9083	−0.546098
$400$	0.306634	0.0153317
$401$	−4.02629	−0.201063	−0.100532	−	0.994934i	$-0.532054\pi$
$401$	−4.02629	−0.201063	−0.100532	+	0.994934i	$0.532054\pi$
$402$	−11.8431	−0.590680
$403$	−28.2998	−1.40971
$404$	25.2389	1.25568
$405$	2.21169	0.109900
$406$	−23.0117	−1.14205
$407$	42.2063	2.09209
$408$	1.00248	0.0496303
$409$	−12.2830	−0.607356	−0.303678	−	0.952775i	$-0.598215\pi$
$409$	−12.2830	−0.607356	−0.303678	+	0.952775i	$0.598215\pi$
$410$	50.2050	2.47945
$411$	−1.01464	−0.0500486
$412$	−20.1771	−0.994053
$413$	35.9829	1.77060
$414$	−5.87148	−0.288568
$415$	−17.4678	−0.857459
$416$	−55.5349	−2.72282
$417$	−9.47463	−0.463975
$418$	−36.1536	−1.76833
$419$	4.96217	0.242418	0.121209	−	0.992627i	$-0.461323\pi$
$419$	4.96217	0.242418	0.121209	+	0.992627i	$0.461323\pi$
$420$	16.3759	0.799061
$421$	5.39691	0.263029	0.131515	−	0.991314i	$-0.458016\pi$
$421$	5.39691	0.263029	0.131515	+	0.991314i	$0.458016\pi$
$422$	36.9591	1.79914
$423$	12.1496	0.590736
$424$	−2.13053	−0.103468
$425$	−0.108448	−0.00526051
$426$	−10.5729	−0.512258
$427$	−7.45110	−0.360584
$428$	−37.7366	−1.82407
$429$	−32.6137	−1.57461
$430$	23.8428	1.14980
$431$	−15.1582	−0.730145	−0.365072	−	0.930979i	$-0.618956\pi$
$431$	−15.1582	−0.730145	−0.365072	+	0.930979i	$0.618956\pi$
$432$	2.82747	0.136037
$433$	7.10789	0.341583	0.170792	−	0.985307i	$-0.445368\pi$
$433$	7.10789	0.341583	0.170792	+	0.985307i	$0.445368\pi$
$434$	25.7607	1.23656
$435$	8.03962	0.385470
$436$	23.6132	1.13087
$437$	−10.1174	−0.483981
$438$	−35.5216	−1.69729
$439$	13.1216	0.626260	0.313130	−	0.949710i	$-0.398622\pi$
$439$	13.1216	0.626260	0.313130	+	0.949710i	$0.398622\pi$
$440$	10.3978	0.495694
$441$	1.95738	0.0932085
$442$	14.7098	0.699673
$443$	−25.8189	−1.22669	−0.613346	−	0.789814i	$-0.710177\pi$
$443$	−25.8189	−1.22669	−0.613346	+	0.789814i	$0.710177\pi$
$444$	22.2653	1.05666
$445$	−8.74462	−0.414535
$446$	−53.9857	−2.55630
$447$	9.83733	0.465290
$448$	33.6277	1.58876
$449$	−12.1983	−0.575675	−0.287837	−	0.957679i	$-0.592936\pi$
$449$	−12.1983	−0.575675	−0.287837	+	0.957679i	$0.592936\pi$
$450$	0.229386	0.0108134
$451$	50.3289	2.36990
$452$	40.1998	1.89084
$453$	−12.2730	−0.576636
$454$	25.5055	1.19703
$455$	46.0336	2.15809
$456$	−3.65379	−0.171104
$457$	33.8724	1.58449	0.792243	−	0.610206i	$-0.208913\pi$
$457$	33.8724	1.58449	0.792243	+	0.610206i	$0.208913\pi$
$458$	27.8324	1.30052
$459$	−1.00000	−0.0466760
$460$	15.1886	0.708170
$461$	29.5625	1.37686	0.688430	−	0.725302i	$-0.258300\pi$
$461$	29.5625	1.37686	0.688430	+	0.725302i	$0.258300\pi$
$462$	29.6876	1.38119
$463$	27.5942	1.28241	0.641207	−	0.767368i	$-0.278434\pi$
$463$	27.5942	1.28241	0.641207	+	0.767368i	$0.278434\pi$
$464$	10.2780	0.477146
$465$	−9.00007	−0.417368
$466$	6.59584	0.305546
$467$	−2.87292	−0.132943	−0.0664714	−	0.997788i	$-0.521174\pi$
$467$	−2.87292	−0.132943	−0.0664714	+	0.997788i	$0.521174\pi$
$468$	−17.2049	−0.795296
$469$	16.7575	0.773791
$470$	−56.8371	−2.62170
$471$	1.00000	0.0460776
$472$	12.0527	0.554769
$473$	23.9017	1.09900
$474$	−15.9931	−0.734588
$475$	0.395265	0.0181360
$476$	−7.40425	−0.339373
$477$	2.12525	0.0973086
$478$	−1.15315	−0.0527437
$479$	−18.6693	−0.853021	−0.426510	−	0.904483i	$-0.640257\pi$
$479$	−18.6693	−0.853021	−0.426510	+	0.904483i	$0.640257\pi$
$480$	−17.6615	−0.806135
$481$	62.5890	2.85381
$482$	49.5489	2.25689
$483$	8.30793	0.378024
$484$	27.1955	1.23616
$485$	15.1601	0.688386
$486$	2.11517	0.0959461
$487$	19.4921	0.883273	0.441636	−	0.897194i	$-0.354398\pi$
$487$	19.4921	0.883273	0.441636	+	0.897194i	$0.354398\pi$
$488$	−2.49578	−0.112979
$489$	9.37235	0.423832
$490$	−9.15680	−0.413662
$491$	−29.2036	−1.31794	−0.658970	−	0.752169i	$-0.729008\pi$
$491$	−29.2036	−1.31794	−0.658970	+	0.752169i	$0.729008\pi$
$492$	26.5503	1.19698
$493$	−3.63506	−0.163715
$494$	−53.6133	−2.41218
$495$	−10.3720	−0.466187
$496$	−11.5059	−0.516631
$497$	14.9602	0.671058
$498$	−16.7055	−0.748591
$499$	−39.9318	−1.78759	−0.893797	−	0.448473i	$-0.851968\pi$
$499$	−39.9318	−1.78759	−0.893797	+	0.448473i	$0.851968\pi$
$500$	−27.9514	−1.25002
$501$	24.8082	1.10835
$502$	−34.3418	−1.53275
$503$	24.3591	1.08612	0.543060	−	0.839694i	$-0.317266\pi$
$503$	24.3591	1.08612	0.543060	+	0.839694i	$0.317266\pi$
$504$	3.00032	0.133645
$505$	22.5633	1.00406
$506$	27.5352	1.22409
$507$	−35.3640	−1.57057
$508$	−24.5723	−1.09022
$509$	−11.9945	−0.531645	−0.265823	−	0.964022i	$-0.585644\pi$
$509$	−11.9945	−0.531645	−0.265823	+	0.964022i	$0.585644\pi$
$510$	4.67809	0.207149
$511$	50.2617	2.22345
$512$	−28.2480	−1.24839
$513$	3.64474	0.160919
$514$	66.6139	2.93821
$515$	−18.0381	−0.794854
$516$	12.6090	0.555079
$517$	−56.9775	−2.50587
$518$	−56.9736	−2.50327
$519$	−11.7404	−0.515344
$520$	15.4192	0.676176
$521$	−16.2521	−0.712016	−0.356008	−	0.934483i	$-0.615862\pi$
$521$	−16.2521	−0.712016	−0.356008	+	0.934483i	$0.615862\pi$
$522$	7.68878	0.336529
$523$	10.7979	0.472157	0.236079	−	0.971734i	$-0.424138\pi$
$523$	10.7979	0.472157	0.236079	+	0.971734i	$0.424138\pi$
$524$	−53.7787	−2.34933
$525$	−0.324573	−0.0141655
$526$	26.5209	1.15637
$527$	4.06933	0.177263
$528$	−13.2598	−0.577061
$529$	−15.2944	−0.664975
$530$	−9.94212	−0.431858
$531$	−12.0228	−0.521746
$532$	26.9866	1.17002
$533$	74.6344	3.23277
$534$	−8.36302	−0.361903
$535$	−33.7361	−1.45854
$536$	5.61302	0.242446
$537$	−8.94912	−0.386183
$538$	57.9547	2.49861
$539$	−9.17941	−0.395385
$540$	−5.47160	−0.235460
$541$	7.82090	0.336247	0.168123	−	0.985766i	$-0.446229\pi$
$541$	7.82090	0.336247	0.168123	+	0.985766i	$0.446229\pi$
$542$	51.0683	2.19357
$543$	−13.0507	−0.560060
$544$	7.98556	0.342378
$545$	21.1100	0.904253
$546$	44.0247	1.88409
$547$	−19.1823	−0.820175	−0.410087	−	0.912046i	$-0.634502\pi$
$547$	−19.1823	−0.820175	−0.410087	+	0.912046i	$0.634502\pi$
$548$	2.51017	0.107229
$549$	2.48960	0.106254
$550$	−1.07574	−0.0458697
$551$	13.2489	0.564420
$552$	2.78278	0.118443
$553$	22.6296	0.962311
$554$	−37.5284	−1.59443
$555$	19.9049	0.844917
$556$	23.4398	0.994067
$557$	−13.3471	−0.565535	−0.282768	−	0.959188i	$-0.591252\pi$
$557$	−13.3471	−0.565535	−0.282768	+	0.959188i	$0.591252\pi$
$558$	−8.60732	−0.364377
$559$	35.4446	1.49915
$560$	18.7160	0.790894
$561$	4.68964	0.197997
$562$	32.2460	1.36021
$563$	−0.865035	−0.0364569	−0.0182284	−	0.999834i	$-0.505803\pi$
$563$	−0.865035	−0.0364569	−0.0182284	+	0.999834i	$0.505803\pi$
$564$	−30.0576	−1.26565
$565$	35.9382	1.51193
$566$	1.27597	0.0536330
$567$	−2.99289	−0.125689
$568$	5.01101	0.210257
$569$	12.0048	0.503267	0.251634	−	0.967823i	$-0.419032\pi$
$569$	12.0048	0.503267	0.251634	+	0.967823i	$0.419032\pi$
$570$	−17.0504	−0.714164
$571$	−25.6057	−1.07156	−0.535782	−	0.844356i	$-0.679983\pi$
$571$	−25.6057	−1.07156	−0.535782	+	0.844356i	$0.679983\pi$
$572$	80.6848	3.37360
$573$	−19.3245	−0.807291
$574$	−67.9382	−2.83568
$575$	−0.301040	−0.0125542
$576$	−11.2359	−0.468161
$577$	11.8436	0.493056	0.246528	−	0.969136i	$-0.420710\pi$
$577$	11.8436	0.493056	0.246528	+	0.969136i	$0.420710\pi$
$578$	−2.11517	−0.0879795
$579$	−7.91560	−0.328961
$580$	−19.8896	−0.825871
$581$	23.6377	0.980655
$582$	14.4986	0.600985
$583$	−9.96667	−0.412777
$584$	16.8354	0.696655
$585$	−15.3810	−0.635926
$586$	−26.0472	−1.07600
$587$	14.5040	0.598643	0.299322	−	0.954152i	$-0.403240\pi$
$587$	14.5040	0.598643	0.299322	+	0.954152i	$0.403240\pi$
$588$	−4.84246	−0.199700
$589$	−14.8316	−0.611127
$590$	56.2438	2.31552
$591$	−17.5967	−0.723830
$592$	25.4470	1.04586
$593$	1.28751	0.0528717	0.0264359	−	0.999651i	$-0.491584\pi$
$593$	1.28751	0.0528717	0.0264359	+	0.999651i	$0.491584\pi$
$594$	−9.91940	−0.406998
$595$	−6.61933	−0.271366
$596$	−24.3370	−0.996884
$597$	19.0361	0.779094
$598$	40.8328	1.66978
$599$	42.3012	1.72838	0.864190	−	0.503166i	$-0.167832\pi$
$599$	42.3012	1.72838	0.864190	+	0.503166i	$0.167832\pi$
$600$	−0.108717	−0.00443837
$601$	9.10385	0.371354	0.185677	−	0.982611i	$-0.440552\pi$
$601$	9.10385	0.371354	0.185677	+	0.982611i	$0.440552\pi$
$602$	−32.2645	−1.31500
$603$	−5.59912	−0.228014
$604$	30.3628	1.23544
$605$	24.3125	0.988444
$606$	21.5787	0.876575
$607$	19.1639	0.777839	0.388920	−	0.921272i	$-0.372848\pi$
$607$	19.1639	0.777839	0.388920	+	0.921272i	$0.372848\pi$
$608$	−29.1053	−1.18037
$609$	−10.8793	−0.440853
$610$	−11.6466	−0.471557
$611$	−84.4937	−3.41825
$612$	2.47395	0.100003
$613$	−1.50860	−0.0609319	−0.0304660	−	0.999536i	$-0.509699\pi$
$613$	−1.50860	−0.0609319	−0.0304660	+	0.999536i	$0.509699\pi$
$614$	−14.0594	−0.567392
$615$	23.7357	0.957114
$616$	−14.0704	−0.566914
$617$	7.44653	0.299786	0.149893	−	0.988702i	$-0.452107\pi$
$617$	7.44653	0.299786	0.149893	+	0.988702i	$0.452107\pi$
$618$	−17.2510	−0.693935
$619$	−34.9998	−1.40676	−0.703380	−	0.710814i	$-0.748327\pi$
$619$	−34.9998	−1.40676	−0.703380	+	0.710814i	$0.748327\pi$
$620$	22.2657	0.894213
$621$	−2.77589	−0.111393
$622$	−21.9588	−0.880468
$623$	11.8334	0.474093
$624$	−19.6634	−0.787168
$625$	−24.4460	−0.977840
$626$	−28.2441	−1.12886
$627$	−17.0925	−0.682610
$628$	−2.47395	−0.0987213
$629$	−8.99989	−0.358849
$630$	14.0010	0.557814
$631$	−4.55011	−0.181137	−0.0905686	−	0.995890i	$-0.528868\pi$
$631$	−4.55011	−0.181137	−0.0905686	+	0.995890i	$0.528868\pi$
$632$	7.57992	0.301513
$633$	17.4733	0.694502
$634$	−19.5708	−0.777257
$635$	−21.9674	−0.871750
$636$	−5.25776	−0.208484
$637$	−13.6124	−0.539344
$638$	−36.0576	−1.42754
$639$	−4.99860	−0.197741
$640$	17.2394	0.681446
$641$	15.7780	0.623193	0.311596	−	0.950215i	$-0.399136\pi$
$641$	15.7780	0.623193	0.311596	+	0.950215i	$0.399136\pi$
$642$	−32.2639	−1.27336
$643$	13.7775	0.543331	0.271665	−	0.962392i	$-0.412426\pi$
$643$	13.7775	0.543331	0.271665	+	0.962392i	$0.412426\pi$
$644$	−20.5534	−0.809917
$645$	11.2723	0.443846
$646$	7.70925	0.303316
$647$	17.9724	0.706568	0.353284	−	0.935516i	$-0.385065\pi$
$647$	17.9724	0.706568	0.353284	+	0.935516i	$0.385065\pi$
$648$	−1.00248	−0.0393813
$649$	56.3827	2.21322
$650$	−1.59525	−0.0625708
$651$	12.1790	0.477334
$652$	−23.1867	−0.908062
$653$	22.5831	0.883745	0.441873	−	0.897078i	$-0.354314\pi$
$653$	22.5831	0.883745	0.441873	+	0.897078i	$0.354314\pi$
$654$	20.1888	0.789444
$655$	−48.0776	−1.87855
$656$	30.3443	1.18474
$657$	−16.7937	−0.655185
$658$	76.9129	2.99838
$659$	−47.4653	−1.84899	−0.924493	−	0.381200i	$-0.875511\pi$
$659$	−47.4653	−1.84899	−0.924493	+	0.381200i	$0.875511\pi$
$660$	25.6598	0.998808
$661$	−34.7572	−1.35190	−0.675950	−	0.736948i	$-0.736266\pi$
$661$	−34.7572	−1.35190	−0.675950	+	0.736948i	$0.736266\pi$
$662$	51.7284	2.01048
$663$	6.95442	0.270087
$664$	7.91755	0.307261
$665$	24.1257	0.935555
$666$	19.0363	0.737642
$667$	−10.0905	−0.390707
$668$	−61.3743	−2.37464
$669$	−25.5231	−0.986779
$670$	26.1932	1.01193
$671$	−11.6753	−0.450722
$672$	23.8999	0.921958
$673$	3.53855	0.136401	0.0682005	−	0.997672i	$-0.478274\pi$
$673$	3.53855	0.136401	0.0682005	+	0.997672i	$0.478274\pi$
$674$	−38.4976	−1.48287
$675$	0.108448	0.00417417
$676$	87.4886	3.36495
$677$	37.6929	1.44866	0.724328	−	0.689456i	$-0.242150\pi$
$677$	37.6929	1.44866	0.724328	+	0.689456i	$0.242150\pi$
$678$	34.3699	1.31997
$679$	−20.5149	−0.787291
$680$	−2.21718	−0.0850249
$681$	12.0584	0.462078
$682$	40.3653	1.54567
$683$	12.0601	0.461465	0.230733	−	0.973017i	$-0.425888\pi$
$683$	12.0601	0.461465	0.230733	+	0.973017i	$0.425888\pi$
$684$	−9.01690	−0.344770
$685$	2.24407	0.0857414
$686$	−31.9222	−1.21879
$687$	13.1585	0.502027
$688$	14.4108	0.549406
$689$	−14.7799	−0.563069
$690$	12.9859	0.494364
$691$	5.84913	0.222511	0.111256	−	0.993792i	$-0.464513\pi$
$691$	5.84913	0.222511	0.111256	+	0.993792i	$0.464513\pi$
$692$	29.0450	1.10413
$693$	14.0356	0.533167
$694$	−18.6326	−0.707282
$695$	20.9549	0.794865
$696$	−3.64409	−0.138129
$697$	−10.7319	−0.406501
$698$	−8.91754	−0.337534
$699$	3.11835	0.117947
$700$	0.802978	0.0303497
$701$	−38.6454	−1.45962	−0.729808	−	0.683652i	$-0.760390\pi$
$701$	−38.6454	−1.45962	−0.729808	+	0.683652i	$0.760390\pi$
$702$	−14.7098	−0.555185
$703$	32.8023	1.23716
$704$	52.6922	1.98591
$705$	−26.8712	−1.01203
$706$	10.5826	0.398280
$707$	−30.5331	−1.14831
$708$	29.7438	1.11784
$709$	43.4457	1.63164	0.815819	−	0.578308i	$-0.196287\pi$
$709$	43.4457	1.63164	0.815819	+	0.578308i	$0.196287\pi$
$710$	23.3839	0.877582
$711$	−7.56114	−0.283565
$712$	3.96364	0.148544
$713$	11.2960	0.423039
$714$	−6.33047	−0.236912
$715$	72.1313	2.69756
$716$	22.1397	0.827398
$717$	−0.545179	−0.0203601
$718$	22.2770	0.831370
$719$	−20.9423	−0.781015	−0.390507	−	0.920600i	$-0.627700\pi$
$719$	−20.9423	−0.781015	−0.390507	+	0.920600i	$0.627700\pi$
$720$	−6.25348	−0.233054
$721$	24.4095	0.909056
$722$	12.0901	0.449945
$723$	23.4255	0.871203
$724$	32.2868	1.19993
$725$	0.394216	0.0146408
$726$	23.2516	0.862946
$727$	−21.1461	−0.784264	−0.392132	−	0.919909i	$-0.628262\pi$
$727$	−21.1461	−0.784264	−0.392132	+	0.919909i	$0.628262\pi$
$728$	−20.8655	−0.773326
$729$	1.00000	0.0370370
$730$	78.5626	2.90773
$731$	−5.09670	−0.188508
$732$	−6.15915	−0.227649
$733$	23.2197	0.857638	0.428819	−	0.903390i	$-0.358930\pi$
$733$	23.2197	0.857638	0.428819	+	0.903390i	$0.358930\pi$
$734$	−9.27621	−0.342391
$735$	−4.32911	−0.159681
$736$	22.1670	0.817088
$737$	26.2579	0.967221
$738$	22.6999	0.835594
$739$	1.84687	0.0679381	0.0339690	−	0.999423i	$-0.489185\pi$
$739$	1.84687	0.0679381	0.0339690	+	0.999423i	$0.489185\pi$
$740$	−49.2438	−1.81024
$741$	−25.3470	−0.931147
$742$	13.4538	0.493906
$743$	−2.62844	−0.0964282	−0.0482141	−	0.998837i	$-0.515353\pi$
$743$	−2.62844	−0.0964282	−0.0482141	+	0.998837i	$0.515353\pi$
$744$	4.07943	0.149559
$745$	−21.7571	−0.797118
$746$	−22.0135	−0.805970
$747$	−7.89794	−0.288971
$748$	−11.6019	−0.424209
$749$	45.6523	1.66810
$750$	−23.8978	−0.872624
$751$	−0.923927	−0.0337146	−0.0168573	−	0.999858i	$-0.505366\pi$
$751$	−0.923927	−0.0337146	−0.0168573	+	0.999858i	$0.505366\pi$
$752$	−34.3528	−1.25272
$753$	−16.2359	−0.591670
$754$	−53.4710	−1.94730
$755$	27.1440	0.987871
$756$	7.40425	0.269290
$757$	18.1811	0.660804	0.330402	−	0.943840i	$-0.392816\pi$
$757$	18.1811	0.660804	0.330402	+	0.943840i	$0.392816\pi$
$758$	33.9707	1.23387
$759$	13.0179	0.472521
$760$	8.08103	0.293130
$761$	13.2886	0.481710	0.240855	−	0.970561i	$-0.422572\pi$
$761$	13.2886	0.481710	0.240855	+	0.970561i	$0.422572\pi$
$762$	−21.0088	−0.761068
$763$	−28.5664	−1.03417
$764$	47.8077	1.72962
$765$	2.21169	0.0799637
$766$	54.7478	1.97812
$767$	83.6117	3.01904
$768$	−5.98467	−0.215953
$769$	15.6726	0.565168	0.282584	−	0.959243i	$-0.408808\pi$
$769$	15.6726	0.565168	0.282584	+	0.959243i	$0.408808\pi$
$770$	−65.6597	−2.36621
$771$	31.4934	1.13421
$772$	19.5828	0.704800
$773$	−20.3744	−0.732818	−0.366409	−	0.930454i	$-0.619413\pi$
$773$	−20.3744	−0.732818	−0.366409	+	0.930454i	$0.619413\pi$
$774$	10.7804	0.387493
$775$	−0.441311	−0.0158524
$776$	−6.87158	−0.246675
$777$	−26.9357	−0.966312
$778$	−37.7499	−1.35340
$779$	39.1151	1.40144
$780$	38.0518	1.36247
$781$	23.4416	0.838807
$782$	−5.87148	−0.209964
$783$	3.63506	0.129907
$784$	−5.53444	−0.197659
$785$	−2.21169	−0.0789384
$786$	−45.9796	−1.64004
$787$	−6.38489	−0.227597	−0.113798	−	0.993504i	$-0.536302\pi$
$787$	−6.38489	−0.227597	−0.113798	+	0.993504i	$0.536302\pi$
$788$	43.5332	1.55081
$789$	12.5384	0.446379
$790$	35.3717	1.25847
$791$	−48.6322	−1.72916
$792$	4.70129	0.167053
$793$	−17.3137	−0.614829
$794$	−35.2163	−1.24978
$795$	−4.70039	−0.166706
$796$	−47.0942	−1.66921
$797$	−11.4414	−0.405276	−0.202638	−	0.979254i	$-0.564951\pi$
$797$	−11.4414	−0.405276	−0.202638	+	0.979254i	$0.564951\pi$
$798$	23.0729	0.816772
$799$	12.1496	0.429823
$800$	−0.866019	−0.0306184
$801$	−3.95383	−0.139702
$802$	8.51629	0.300721
$803$	78.7565	2.77926
$804$	13.8519	0.488520
$805$	−18.3745	−0.647617
$806$	59.8589	2.10844
$807$	27.3995	0.964510
$808$	−10.2272	−0.359792
$809$	3.89624	0.136985	0.0684923	−	0.997652i	$-0.478181\pi$
$809$	3.89624	0.136985	0.0684923	+	0.997652i	$0.478181\pi$
$810$	−4.67809	−0.164371
$811$	−19.7153	−0.692298	−0.346149	−	0.938179i	$-0.612511\pi$
$811$	−19.7153	−0.692298	−0.346149	+	0.938179i	$0.612511\pi$
$812$	26.9149	0.944529
$813$	24.1438	0.846761
$814$	−89.2735	−3.12904
$815$	−20.7287	−0.726094
$816$	2.82747	0.0989814
$817$	18.5762	0.649897
$818$	25.9807	0.908393
$819$	20.8138	0.727293
$820$	−58.7208	−2.05062
$821$	2.43074	0.0848334	0.0424167	−	0.999100i	$-0.486494\pi$
$821$	2.43074	0.0848334	0.0424167	+	0.999100i	$0.486494\pi$
$822$	2.14614	0.0748552
$823$	−42.4943	−1.48126	−0.740630	−	0.671913i	$-0.765473\pi$
$823$	−42.4943	−1.48126	−0.740630	+	0.671913i	$0.765473\pi$
$824$	8.17607	0.284827
$825$	−0.508583	−0.0177066
$826$	−76.1101	−2.64821
$827$	−18.0549	−0.627831	−0.313915	−	0.949451i	$-0.601641\pi$
$827$	−18.0549	−0.627831	−0.313915	+	0.949451i	$0.601641\pi$
$828$	6.86741	0.238659
$829$	−22.3010	−0.774546	−0.387273	−	0.921965i	$-0.626583\pi$
$829$	−22.3010	−0.774546	−0.387273	+	0.921965i	$0.626583\pi$
$830$	36.9473	1.28246
$831$	−17.7425	−0.615479
$832$	78.1390	2.70898
$833$	1.95738	0.0678192
$834$	20.0405	0.693945
$835$	−54.8680	−1.89878
$836$	42.2860	1.46249
$837$	−4.06933	−0.140656
$838$	−10.4958	−0.362573
$839$	−46.1079	−1.59182	−0.795910	−	0.605415i	$-0.793007\pi$
$839$	−46.1079	−1.59182	−0.795910	+	0.605415i	$0.793007\pi$
$840$	−6.63576	−0.228956
$841$	−15.7863	−0.544356
$842$	−11.4154	−0.393400
$843$	15.2451	0.525069
$844$	−43.2281	−1.48797
$845$	78.2139	2.69064
$846$	−25.6986	−0.883535
$847$	−32.9001	−1.13046
$848$	−6.00909	−0.206353
$849$	0.603246	0.0207034
$850$	0.229386	0.00786789
$851$	−24.9827	−0.856397
$852$	12.3663	0.423661
$853$	−35.6243	−1.21975	−0.609876	−	0.792497i	$-0.708781\pi$
$853$	−35.6243	−1.21975	−0.609876	+	0.792497i	$0.708781\pi$
$854$	15.7603	0.539308
$855$	−8.06102	−0.275681
$856$	15.2915	0.522651
$857$	13.0494	0.445758	0.222879	−	0.974846i	$-0.428454\pi$
$857$	13.0494	0.445758	0.222879	+	0.974846i	$0.428454\pi$
$858$	68.9837	2.35506
$859$	0.382639	0.0130555	0.00652773	−	0.999979i	$-0.497922\pi$
$859$	0.382639	0.0130555	0.00652773	+	0.999979i	$0.497922\pi$
$860$	−27.8871	−0.950942
$861$	−32.1195	−1.09463
$862$	32.0622	1.09204
$863$	38.0383	1.29484	0.647419	−	0.762134i	$-0.275848\pi$
$863$	38.0383	1.29484	0.647419	+	0.762134i	$0.275848\pi$
$864$	−7.98556	−0.271674
$865$	25.9660	0.882870
$866$	−15.0344	−0.510890
$867$	−1.00000	−0.0339618
$868$	−30.1303	−1.02269
$869$	35.4591	1.20287
$870$	−17.0052	−0.576529
$871$	38.9386	1.31938
$872$	−9.56846	−0.324029
$873$	6.85456	0.231992
$874$	21.4000	0.723867
$875$	33.8145	1.14314
$876$	41.5468	1.40374
$877$	−7.75974	−0.262028	−0.131014	−	0.991381i	$-0.541823\pi$
$877$	−7.75974	−0.262028	−0.131014	+	0.991381i	$0.541823\pi$
$878$	−27.7544	−0.936667
$879$	−12.3145	−0.415357
$880$	29.3266	0.988600
$881$	−29.7293	−1.00161	−0.500803	−	0.865561i	$-0.666962\pi$
$881$	−29.7293	−1.00161	−0.500803	+	0.865561i	$0.666962\pi$
$882$	−4.14019	−0.139408
$883$	−46.3870	−1.56105	−0.780523	−	0.625127i	$-0.785047\pi$
$883$	−46.3870	−1.56105	−0.780523	+	0.625127i	$0.785047\pi$
$884$	−17.2049	−0.578663
$885$	26.5907	0.893836
$886$	54.6114	1.83471
$887$	32.1160	1.07835	0.539175	−	0.842194i	$-0.318736\pi$
$887$	32.1160	1.07835	0.539175	+	0.842194i	$0.318736\pi$
$888$	−9.02224	−0.302767
$889$	29.7267	0.997000
$890$	18.4964	0.620000
$891$	−4.68964	−0.157109
$892$	63.1428	2.11418
$893$	−44.2823	−1.48185
$894$	−20.8076	−0.695911
$895$	19.7926	0.661595
$896$	−23.3286	−0.779354
$897$	19.3047	0.644565
$898$	25.8016	0.861009
$899$	−14.7923	−0.493349
$900$	−0.268295	−0.00894318
$901$	2.12525	0.0708024
$902$	−106.454	−3.54454
$903$	−15.2539	−0.507617
$904$	−16.2896	−0.541784
$905$	28.8641	0.959474
$906$	25.9595	0.862446
$907$	46.8974	1.55720	0.778601	−	0.627520i	$-0.215930\pi$
$907$	46.8974	1.55720	0.778601	+	0.627520i	$0.215930\pi$
$908$	−29.8318	−0.990004
$909$	10.2019	0.338375
$910$	−97.3689	−3.22775
$911$	40.6151	1.34564	0.672820	−	0.739806i	$-0.265083\pi$
$911$	40.6151	1.34564	0.672820	+	0.739806i	$0.265083\pi$
$912$	−10.3054	−0.341246
$913$	37.0385	1.22580
$914$	−71.6460	−2.36984
$915$	−5.50621	−0.182030
$916$	−32.5534	−1.07559
$917$	65.0594	2.14845
$918$	2.11517	0.0698111
$919$	52.3789	1.72782	0.863910	−	0.503647i	$-0.168009\pi$
$919$	52.3789	1.72782	0.863910	+	0.503647i	$0.168009\pi$
$920$	−6.15464	−0.202913
$921$	−6.64694	−0.219024
$922$	−62.5296	−2.05930
$923$	34.7623	1.14422
$924$	−34.7233	−1.14231
$925$	0.976022	0.0320914
$926$	−58.3665	−1.91804
$927$	−8.15582	−0.267872
$928$	−29.0280	−0.952891
$929$	25.3934	0.833131	0.416566	−	0.909106i	$-0.363234\pi$
$929$	25.3934	0.833131	0.416566	+	0.909106i	$0.363234\pi$
$930$	19.0367	0.624238
$931$	−7.13414	−0.233812
$932$	−7.71463	−0.252701
$933$	−10.3816	−0.339878
$934$	6.07671	0.198836
$935$	−10.3720	−0.339201
$936$	6.97169	0.227877
$937$	34.9127	1.14055	0.570274	−	0.821454i	$-0.306837\pi$
$937$	34.9127	1.14055	0.570274	+	0.821454i	$0.306837\pi$
$938$	−35.4451	−1.15732
$939$	−13.3531	−0.435763
$940$	66.4779	2.16827
$941$	25.4958	0.831138	0.415569	−	0.909562i	$-0.363582\pi$
$941$	25.4958	0.831138	0.415569	+	0.909562i	$0.363582\pi$
$942$	−2.11517	−0.0689160
$943$	−29.7907	−0.970118
$944$	33.9942	1.10642
$945$	6.61933	0.215327
$946$	−50.5562	−1.64372
$947$	−5.90348	−0.191837	−0.0959187	−	0.995389i	$-0.530579\pi$
$947$	−5.90348	−0.191837	−0.0959187	+	0.995389i	$0.530579\pi$
$948$	18.7059	0.607539
$949$	116.791	3.79118
$950$	−0.836054	−0.0271252
$951$	−9.25260	−0.300036
$952$	3.00032	0.0972409
$953$	12.0090	0.389010	0.194505	−	0.980902i	$-0.437690\pi$
$953$	12.0090	0.389010	0.194505	+	0.980902i	$0.437690\pi$
$954$	−4.49527	−0.145540
$955$	42.7396	1.38302
$956$	1.34875	0.0436215
$957$	−17.0471	−0.551056
$958$	39.4887	1.27582
$959$	−3.03671	−0.0980604
$960$	24.8502	0.802037
$961$	−14.4406	−0.465825
$962$	−132.387	−4.26831
$963$	−15.2536	−0.491540
$964$	−57.9534	−1.86655
$965$	17.5068	0.563564
$966$	−17.5727	−0.565392
$967$	38.3175	1.23221	0.616104	−	0.787665i	$-0.288710\pi$
$967$	38.3175	1.23221	0.616104	+	0.787665i	$0.288710\pi$
$968$	−11.0201	−0.354198
$969$	3.64474	0.117086
$970$	−32.0663	−1.02959
$971$	2.10520	0.0675590	0.0337795	−	0.999429i	$-0.489246\pi$
$971$	2.10520	0.0675590	0.0337795	+	0.999429i	$0.489246\pi$
$972$	−2.47395	−0.0793520
$973$	−28.3565	−0.909068
$974$	−41.2292	−1.32107
$975$	−0.754194	−0.0241535
$976$	−7.03928	−0.225322
$977$	2.62543	0.0839948	0.0419974	−	0.999118i	$-0.486628\pi$
$977$	2.62543	0.0839948	0.0419974	+	0.999118i	$0.486628\pi$
$978$	−19.8241	−0.633906
$979$	18.5420	0.592606
$980$	10.7100	0.342118
$981$	9.54476	0.304741
$982$	61.7706	1.97118
$983$	−32.0679	−1.02281	−0.511404	−	0.859340i	$-0.670874\pi$
$983$	−32.0679	−1.02281	−0.511404	+	0.859340i	$0.670874\pi$
$984$	−10.7586	−0.342971
$985$	38.9183	1.24004
$986$	7.68878	0.244861
$987$	36.3625	1.15743
$988$	62.7073	1.99498
$989$	−14.1479	−0.449877
$990$	21.9386	0.697254
$991$	−25.0986	−0.797283	−0.398642	−	0.917107i	$-0.630518\pi$
$991$	−25.0986	−0.797283	−0.398642	+	0.917107i	$0.630518\pi$
$992$	32.4958	1.03174
$993$	24.4559	0.776084
$994$	−31.6435	−1.00367
$995$	−42.1018	−1.33472
$996$	19.5391	0.619120
$997$	36.6615	1.16108	0.580540	−	0.814231i	$-0.302841\pi$
$997$	36.6615	1.16108	0.580540	+	0.814231i	$0.302841\pi$
$998$	84.4626	2.67362
$999$	8.99989	0.284744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.11	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.11517 q^{2} -1.00000 q^{3} +2.47395 q^{4} +2.21169 q^{5} +2.11517 q^{6} -2.99289 q^{7} -1.00248 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11517 q^{2} -1.00000 q^{3} +2.47395 q^{4} +2.21169 q^{5} +2.11517 q^{6} -2.99289 q^{7} -1.00248 q^{8} +1.00000 q^{9} -4.67809 q^{10} -4.68964 q^{11} -2.47395 q^{12} -6.95442 q^{13} +6.33047 q^{14} -2.21169 q^{15} -2.82747 q^{16} +1.00000 q^{17} -2.11517 q^{18} -3.64474 q^{19} +5.47160 q^{20} +2.99289 q^{21} +9.91940 q^{22} +2.77589 q^{23} +1.00248 q^{24} -0.108448 q^{25} +14.7098 q^{26} -1.00000 q^{27} -7.40425 q^{28} -3.63506 q^{29} +4.67809 q^{30} +4.06933 q^{31} +7.98556 q^{32} +4.68964 q^{33} -2.11517 q^{34} -6.61933 q^{35} +2.47395 q^{36} -8.99989 q^{37} +7.70925 q^{38} +6.95442 q^{39} -2.21718 q^{40} -10.7319 q^{41} -6.33047 q^{42} -5.09670 q^{43} -11.6019 q^{44} +2.21169 q^{45} -5.87148 q^{46} +12.1496 q^{47} +2.82747 q^{48} +1.95738 q^{49} +0.229386 q^{50} -1.00000 q^{51} -17.2049 q^{52} +2.12525 q^{53} +2.11517 q^{54} -10.3720 q^{55} +3.00032 q^{56} +3.64474 q^{57} +7.68878 q^{58} -12.0228 q^{59} -5.47160 q^{60} +2.48960 q^{61} -8.60732 q^{62} -2.99289 q^{63} -11.2359 q^{64} -15.3810 q^{65} -9.91940 q^{66} -5.59912 q^{67} +2.47395 q^{68} -2.77589 q^{69} +14.0010 q^{70} -4.99860 q^{71} -1.00248 q^{72} -16.7937 q^{73} +19.0363 q^{74} +0.108448 q^{75} -9.01690 q^{76} +14.0356 q^{77} -14.7098 q^{78} -7.56114 q^{79} -6.25348 q^{80} +1.00000 q^{81} +22.6999 q^{82} -7.89794 q^{83} +7.40425 q^{84} +2.21169 q^{85} +10.7804 q^{86} +3.63506 q^{87} +4.70129 q^{88} -3.95383 q^{89} -4.67809 q^{90} +20.8138 q^{91} +6.86741 q^{92} -4.06933 q^{93} -25.6986 q^{94} -8.06102 q^{95} -7.98556 q^{96} +6.85456 q^{97} -4.14019 q^{98} -4.68964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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