LMFDB - Embedded newform 8007.2.a.j.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.69942 q^{2} -1.00000 q^{3} +5.28690 q^{4} +3.29410 q^{5} +2.69942 q^{6} +4.13717 q^{7} -8.87273 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69942 q^{2} -1.00000 q^{3} +5.28690 q^{4} +3.29410 q^{5} +2.69942 q^{6} +4.13717 q^{7} -8.87273 q^{8} +1.00000 q^{9} -8.89217 q^{10} +1.26440 q^{11} -5.28690 q^{12} +5.50466 q^{13} -11.1680 q^{14} -3.29410 q^{15} +13.3775 q^{16} +1.00000 q^{17} -2.69942 q^{18} +3.75022 q^{19} +17.4156 q^{20} -4.13717 q^{21} -3.41316 q^{22} -5.79289 q^{23} +8.87273 q^{24} +5.85108 q^{25} -14.8594 q^{26} -1.00000 q^{27} +21.8728 q^{28} +1.48332 q^{29} +8.89217 q^{30} -5.62716 q^{31} -18.3660 q^{32} -1.26440 q^{33} -2.69942 q^{34} +13.6282 q^{35} +5.28690 q^{36} +9.89414 q^{37} -10.1234 q^{38} -5.50466 q^{39} -29.2276 q^{40} +3.72683 q^{41} +11.1680 q^{42} -3.23636 q^{43} +6.68477 q^{44} +3.29410 q^{45} +15.6375 q^{46} +1.75649 q^{47} -13.3775 q^{48} +10.1162 q^{49} -15.7946 q^{50} -1.00000 q^{51} +29.1025 q^{52} -6.58226 q^{53} +2.69942 q^{54} +4.16507 q^{55} -36.7080 q^{56} -3.75022 q^{57} -4.00411 q^{58} -13.0815 q^{59} -17.4156 q^{60} -1.45833 q^{61} +15.1901 q^{62} +4.13717 q^{63} +22.8228 q^{64} +18.1329 q^{65} +3.41316 q^{66} -15.7266 q^{67} +5.28690 q^{68} +5.79289 q^{69} -36.7884 q^{70} -0.751536 q^{71} -8.87273 q^{72} +8.74535 q^{73} -26.7085 q^{74} -5.85108 q^{75} +19.8270 q^{76} +5.23105 q^{77} +14.8594 q^{78} -8.70356 q^{79} +44.0667 q^{80} +1.00000 q^{81} -10.0603 q^{82} -8.79348 q^{83} -21.8728 q^{84} +3.29410 q^{85} +8.73632 q^{86} -1.48332 q^{87} -11.2187 q^{88} +4.33618 q^{89} -8.89217 q^{90} +22.7737 q^{91} -30.6264 q^{92} +5.62716 q^{93} -4.74151 q^{94} +12.3536 q^{95} +18.3660 q^{96} +12.3848 q^{97} -27.3078 q^{98} +1.26440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69942	−1.90878	−0.954391	−	0.298560i	$-0.903494\pi$
$2$	−2.69942	−1.90878	−0.954391	+	0.298560i	$0.903494\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.28690	2.64345
$5$	3.29410	1.47317	0.736583	−	0.676347i	$-0.236438\pi$
$5$	3.29410	1.47317	0.736583	+	0.676347i	$0.236438\pi$
$6$	2.69942	1.10204
$7$	4.13717	1.56370	0.781851	−	0.623465i	$-0.214276\pi$
$7$	4.13717	1.56370	0.781851	+	0.623465i	$0.214276\pi$
$8$	−8.87273	−3.13698
$9$	1.00000	0.333333
$10$	−8.89217	−2.81195
$11$	1.26440	0.381232	0.190616	−	0.981665i	$-0.438951\pi$
$11$	1.26440	0.381232	0.190616	+	0.981665i	$0.438951\pi$
$12$	−5.28690	−1.52620
$13$	5.50466	1.52672	0.763359	−	0.645975i	$-0.223549\pi$
$13$	5.50466	1.52672	0.763359	+	0.645975i	$0.223549\pi$
$14$	−11.1680	−2.98477
$15$	−3.29410	−0.850532
$16$	13.3775	3.34437
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.69942	−0.636261
$19$	3.75022	0.860359	0.430179	−	0.902743i	$-0.358450\pi$
$19$	3.75022	0.860359	0.430179	+	0.902743i	$0.358450\pi$
$20$	17.4156	3.89424
$21$	−4.13717	−0.902804
$22$	−3.41316	−0.727689
$23$	−5.79289	−1.20790	−0.603951	−	0.797022i	$-0.706408\pi$
$23$	−5.79289	−1.20790	−0.603951	+	0.797022i	$0.706408\pi$
$24$	8.87273	1.81114
$25$	5.85108	1.17022
$26$	−14.8594	−2.91417
$27$	−1.00000	−0.192450
$28$	21.8728	4.13357
$29$	1.48332	0.275445	0.137723	−	0.990471i	$-0.456022\pi$
$29$	1.48332	0.275445	0.137723	+	0.990471i	$0.456022\pi$
$30$	8.89217	1.62348
$31$	−5.62716	−1.01067	−0.505334	−	0.862924i	$-0.668631\pi$
$31$	−5.62716	−1.01067	−0.505334	+	0.862924i	$0.668631\pi$
$32$	−18.3660	−3.24668
$33$	−1.26440	−0.220105
$34$	−2.69942	−0.462948
$35$	13.6282	2.30359
$36$	5.28690	0.881149
$37$	9.89414	1.62659	0.813293	−	0.581854i	$-0.197672\pi$
$37$	9.89414	1.62659	0.813293	+	0.581854i	$0.197672\pi$
$38$	−10.1234	−1.64224
$39$	−5.50466	−0.881451
$40$	−29.2276	−4.62129
$41$	3.72683	0.582033	0.291017	−	0.956718i	$-0.406007\pi$
$41$	3.72683	0.582033	0.291017	+	0.956718i	$0.406007\pi$
$42$	11.1680	1.72326
$43$	−3.23636	−0.493541	−0.246770	−	0.969074i	$-0.579369\pi$
$43$	−3.23636	−0.493541	−0.246770	+	0.969074i	$0.579369\pi$
$44$	6.68477	1.00777
$45$	3.29410	0.491055
$46$	15.6375	2.30562
$47$	1.75649	0.256210	0.128105	−	0.991761i	$-0.459111\pi$
$47$	1.75649	0.256210	0.128105	+	0.991761i	$0.459111\pi$
$48$	−13.3775	−1.93087
$49$	10.1162	1.44517
$50$	−15.7946	−2.23369
$51$	−1.00000	−0.140028
$52$	29.1025	4.03580
$53$	−6.58226	−0.904143	−0.452071	−	0.891982i	$-0.649315\pi$
$53$	−6.58226	−0.904143	−0.452071	+	0.891982i	$0.649315\pi$
$54$	2.69942	0.367345
$55$	4.16507	0.561618
$56$	−36.7080	−4.90531
$57$	−3.75022	−0.496728
$58$	−4.00411	−0.525765
$59$	−13.0815	−1.70307	−0.851536	−	0.524296i	$-0.824328\pi$
$59$	−13.0815	−1.70307	−0.851536	+	0.524296i	$0.824328\pi$
$60$	−17.4156	−2.24834
$61$	−1.45833	−0.186721	−0.0933603	−	0.995632i	$-0.529761\pi$
$61$	−1.45833	−0.186721	−0.0933603	+	0.995632i	$0.529761\pi$
$62$	15.1901	1.92915
$63$	4.13717	0.521234
$64$	22.8228	2.85285
$65$	18.1329	2.24911
$66$	3.41316	0.420132
$67$	−15.7266	−1.92131	−0.960653	−	0.277751i	$-0.910411\pi$
$67$	−15.7266	−1.92131	−0.960653	+	0.277751i	$0.910411\pi$
$68$	5.28690	0.641130
$69$	5.79289	0.697382
$70$	−36.7884	−4.39706
$71$	−0.751536	−0.0891910	−0.0445955	−	0.999005i	$-0.514200\pi$
$71$	−0.751536	−0.0891910	−0.0445955	+	0.999005i	$0.514200\pi$
$72$	−8.87273	−1.04566
$73$	8.74535	1.02357	0.511783	−	0.859115i	$-0.328985\pi$
$73$	8.74535	1.02357	0.511783	+	0.859115i	$0.328985\pi$
$74$	−26.7085	−3.10480
$75$	−5.85108	−0.675625
$76$	19.8270	2.27431
$77$	5.23105	0.596134
$78$	14.8594	1.68250
$79$	−8.70356	−0.979227	−0.489614	−	0.871939i	$-0.662862\pi$
$79$	−8.70356	−0.979227	−0.489614	+	0.871939i	$0.662862\pi$
$80$	44.0667	4.92681
$81$	1.00000	0.111111
$82$	−10.0603	−1.11097
$83$	−8.79348	−0.965210	−0.482605	−	0.875838i	$-0.660309\pi$
$83$	−8.79348	−0.965210	−0.482605	+	0.875838i	$0.660309\pi$
$84$	−21.8728	−2.38652
$85$	3.29410	0.357295
$86$	8.73632	0.942062
$87$	−1.48332	−0.159029
$88$	−11.2187	−1.19592
$89$	4.33618	0.459634	0.229817	−	0.973234i	$-0.426187\pi$
$89$	4.33618	0.459634	0.229817	+	0.973234i	$0.426187\pi$
$90$	−8.89217	−0.937317
$91$	22.7737	2.38733
$92$	−30.6264	−3.19302
$93$	5.62716	0.583510
$94$	−4.74151	−0.489049
$95$	12.3536	1.26745
$96$	18.3660	1.87447
$97$	12.3848	1.25749	0.628744	−	0.777612i	$-0.283569\pi$
$97$	12.3848	1.25749	0.628744	+	0.777612i	$0.283569\pi$
$98$	−27.3078	−2.75851
$99$	1.26440	0.127077
$100$	30.9341	3.09341
$101$	9.24128	0.919542	0.459771	−	0.888038i	$-0.347932\pi$
$101$	9.24128	0.919542	0.459771	+	0.888038i	$0.347932\pi$
$102$	2.69942	0.267283
$103$	−8.06351	−0.794521	−0.397261	−	0.917706i	$-0.630039\pi$
$103$	−8.06351	−0.794521	−0.397261	+	0.917706i	$0.630039\pi$
$104$	−48.8413	−4.78929
$105$	−13.6282	−1.32998
$106$	17.7683	1.72581
$107$	19.4006	1.87553	0.937763	−	0.347277i	$-0.112894\pi$
$107$	19.4006	1.87553	0.937763	+	0.347277i	$0.112894\pi$
$108$	−5.28690	−0.508732
$109$	−8.87914	−0.850467	−0.425234	−	0.905084i	$-0.639808\pi$
$109$	−8.87914	−0.850467	−0.425234	+	0.905084i	$0.639808\pi$
$110$	−11.2433	−1.07201
$111$	−9.89414	−0.939110
$112$	55.3448	5.22960
$113$	12.5063	1.17650	0.588249	−	0.808680i	$-0.299818\pi$
$113$	12.5063	1.17650	0.588249	+	0.808680i	$0.299818\pi$
$114$	10.1234	0.948146
$115$	−19.0824	−1.77944
$116$	7.84215	0.728126
$117$	5.50466	0.508906
$118$	35.3126	3.25079
$119$	4.13717	0.379254
$120$	29.2276	2.66811
$121$	−9.40128	−0.854662
$122$	3.93666	0.356409
$123$	−3.72683	−0.336037
$124$	−29.7502	−2.67165
$125$	2.80355	0.250757
$126$	−11.1680	−0.994922
$127$	2.80959	0.249311	0.124655	−	0.992200i	$-0.460217\pi$
$127$	2.80959	0.249311	0.124655	+	0.992200i	$0.460217\pi$
$128$	−24.8763	−2.19877
$129$	3.23636	0.284946
$130$	−48.9484	−4.29305
$131$	13.3474	1.16617	0.583086	−	0.812410i	$-0.301845\pi$
$131$	13.3474	1.16617	0.583086	+	0.812410i	$0.301845\pi$
$132$	−6.68477	−0.581835
$133$	15.5153	1.34535
$134$	42.4527	3.66735
$135$	−3.29410	−0.283511
$136$	−8.87273	−0.760830
$137$	−12.2063	−1.04285	−0.521426	−	0.853296i	$-0.674600\pi$
$137$	−12.2063	−1.04285	−0.521426	+	0.853296i	$0.674600\pi$
$138$	−15.6375	−1.33115
$139$	14.7339	1.24971	0.624856	−	0.780740i	$-0.285158\pi$
$139$	14.7339	1.24971	0.624856	+	0.780740i	$0.285158\pi$
$140$	72.0511	6.08943
$141$	−1.75649	−0.147923
$142$	2.02872	0.170246
$143$	6.96011	0.582034
$144$	13.3775	1.11479
$145$	4.88620	0.405777
$146$	−23.6074	−1.95376
$147$	−10.1162	−0.834367
$148$	52.3093	4.29980
$149$	3.66511	0.300257	0.150129	−	0.988666i	$-0.452031\pi$
$149$	3.66511	0.300257	0.150129	+	0.988666i	$0.452031\pi$
$150$	15.7946	1.28962
$151$	5.80463	0.472374	0.236187	−	0.971708i	$-0.424102\pi$
$151$	5.80463	0.472374	0.236187	+	0.971708i	$0.424102\pi$
$152$	−33.2747	−2.69893
$153$	1.00000	0.0808452
$154$	−14.1208	−1.13789
$155$	−18.5364	−1.48888
$156$	−29.1025	−2.33007
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	23.4946	1.86913
$159$	6.58226	0.522007
$160$	−60.4995	−4.78290
$161$	−23.9662	−1.88880
$162$	−2.69942	−0.212087
$163$	16.4903	1.29162	0.645812	−	0.763497i	$-0.276519\pi$
$163$	16.4903	1.29162	0.645812	+	0.763497i	$0.276519\pi$
$164$	19.7034	1.53857
$165$	−4.16507	−0.324250
$166$	23.7373	1.84238
$167$	−2.85685	−0.221070	−0.110535	−	0.993872i	$-0.535256\pi$
$167$	−2.85685	−0.221070	−0.110535	+	0.993872i	$0.535256\pi$
$168$	36.7080	2.83208
$169$	17.3013	1.33087
$170$	−8.89217	−0.681998
$171$	3.75022	0.286786
$172$	−17.1103	−1.30465
$173$	24.1347	1.83493	0.917464	−	0.397819i	$-0.130233\pi$
$173$	24.1347	1.83493	0.917464	+	0.397819i	$0.130233\pi$
$174$	4.00411	0.303551
$175$	24.2069	1.82987
$176$	16.9145	1.27498
$177$	13.0815	0.983269
$178$	−11.7052	−0.877341
$179$	−16.6698	−1.24596	−0.622978	−	0.782239i	$-0.714077\pi$
$179$	−16.6698	−1.24596	−0.622978	+	0.782239i	$0.714077\pi$
$180$	17.4156	1.29808
$181$	6.75382	0.502007	0.251004	−	0.967986i	$-0.419239\pi$
$181$	6.75382	0.502007	0.251004	+	0.967986i	$0.419239\pi$
$182$	−61.4759	−4.55690
$183$	1.45833	0.107803
$184$	51.3988	3.78917
$185$	32.5923	2.39623
$186$	−15.1901	−1.11379
$187$	1.26440	0.0924624
$188$	9.28637	0.677278
$189$	−4.13717	−0.300935
$190$	−33.3476	−2.41929
$191$	9.45313	0.684004	0.342002	−	0.939699i	$-0.388895\pi$
$191$	9.45313	0.684004	0.342002	+	0.939699i	$0.388895\pi$
$192$	−22.8228	−1.64709
$193$	12.3474	0.888786	0.444393	−	0.895832i	$-0.353419\pi$
$193$	12.3474	0.888786	0.444393	+	0.895832i	$0.353419\pi$
$194$	−33.4319	−2.40027
$195$	−18.1329	−1.29852
$196$	53.4831	3.82022
$197$	13.4501	0.958279	0.479140	−	0.877739i	$-0.340949\pi$
$197$	13.4501	0.958279	0.479140	+	0.877739i	$0.340949\pi$
$198$	−3.41316	−0.242563
$199$	11.4664	0.812830	0.406415	−	0.913689i	$-0.366779\pi$
$199$	11.4664	0.812830	0.406415	+	0.913689i	$0.366779\pi$
$200$	−51.9151	−3.67095
$201$	15.7266	1.10927
$202$	−24.9461	−1.75520
$203$	6.13674	0.430715
$204$	−5.28690	−0.370157
$205$	12.2765	0.857431
$206$	21.7668	1.51657
$207$	−5.79289	−0.402634
$208$	73.6384	5.10590
$209$	4.74179	0.327997
$210$	36.7884	2.53864
$211$	−16.7940	−1.15615	−0.578074	−	0.815985i	$-0.696195\pi$
$211$	−16.7940	−1.15615	−0.578074	+	0.815985i	$0.696195\pi$
$212$	−34.7997	−2.39005
$213$	0.751536	0.0514944
$214$	−52.3704	−3.57997
$215$	−10.6609	−0.727067
$216$	8.87273	0.603713
$217$	−23.2805	−1.58038
$218$	23.9686	1.62336
$219$	−8.74535	−0.590956
$220$	22.0203	1.48461
$221$	5.50466	0.370283
$222$	26.7085	1.79256
$223$	12.6977	0.850299	0.425149	−	0.905123i	$-0.360222\pi$
$223$	12.6977	0.850299	0.425149	+	0.905123i	$0.360222\pi$
$224$	−75.9833	−5.07685
$225$	5.85108	0.390072
$226$	−33.7599	−2.24568
$227$	6.99675	0.464390	0.232195	−	0.972669i	$-0.425409\pi$
$227$	6.99675	0.464390	0.232195	+	0.972669i	$0.425409\pi$
$228$	−19.8270	−1.31308
$229$	23.4790	1.55154	0.775769	−	0.631017i	$-0.217362\pi$
$229$	23.4790	1.55154	0.775769	+	0.631017i	$0.217362\pi$
$230$	51.5114	3.39656
$231$	−5.23105	−0.344178
$232$	−13.1611	−0.864068
$233$	−0.513616	−0.0336481	−0.0168240	−	0.999858i	$-0.505356\pi$
$233$	−0.513616	−0.0336481	−0.0168240	+	0.999858i	$0.505356\pi$
$234$	−14.8594	−0.971390
$235$	5.78604	0.377440
$236$	−69.1607	−4.50198
$237$	8.70356	0.565357
$238$	−11.1680	−0.723912
$239$	1.99661	0.129150	0.0645750	−	0.997913i	$-0.479431\pi$
$239$	1.99661	0.129150	0.0645750	+	0.997913i	$0.479431\pi$
$240$	−44.0667	−2.84449
$241$	8.78995	0.566211	0.283105	−	0.959089i	$-0.408635\pi$
$241$	8.78995	0.566211	0.283105	+	0.959089i	$0.408635\pi$
$242$	25.3781	1.63136
$243$	−1.00000	−0.0641500
$244$	−7.71006	−0.493586
$245$	33.3236	2.12897
$246$	10.0603	0.641421
$247$	20.6437	1.31352
$248$	49.9283	3.17045
$249$	8.79348	0.557264
$250$	−7.56797	−0.478640
$251$	15.1706	0.957559	0.478780	−	0.877935i	$-0.341079\pi$
$251$	15.1706	0.957559	0.478780	+	0.877935i	$0.341079\pi$
$252$	21.8728	1.37786
$253$	−7.32456	−0.460491
$254$	−7.58428	−0.475880
$255$	−3.29410	−0.206284
$256$	21.5061	1.34413
$257$	−6.41622	−0.400233	−0.200116	−	0.979772i	$-0.564132\pi$
$257$	−6.41622	−0.400233	−0.200116	+	0.979772i	$0.564132\pi$
$258$	−8.73632	−0.543900
$259$	40.9337	2.54350
$260$	95.8666	5.94540
$261$	1.48332	0.0918152
$262$	−36.0304	−2.22597
$263$	−13.0807	−0.806588	−0.403294	−	0.915070i	$-0.632135\pi$
$263$	−13.0807	−0.806588	−0.403294	+	0.915070i	$0.632135\pi$
$264$	11.2187	0.690464
$265$	−21.6826	−1.33195
$266$	−41.8823	−2.56797
$267$	−4.33618	−0.265370
$268$	−83.1447	−5.07887
$269$	−23.3216	−1.42194	−0.710971	−	0.703221i	$-0.751744\pi$
$269$	−23.3216	−1.42194	−0.710971	+	0.703221i	$0.751744\pi$
$270$	8.89217	0.541160
$271$	14.2253	0.864125	0.432062	−	0.901844i	$-0.357786\pi$
$271$	14.2253	0.864125	0.432062	+	0.901844i	$0.357786\pi$
$272$	13.3775	0.811128
$273$	−22.7737	−1.37833
$274$	32.9499	1.99058
$275$	7.39813	0.446124
$276$	30.6264	1.84349
$277$	−14.6727	−0.881598	−0.440799	−	0.897606i	$-0.645305\pi$
$277$	−14.6727	−0.881598	−0.440799	+	0.897606i	$0.645305\pi$
$278$	−39.7730	−2.38543
$279$	−5.62716	−0.336889
$280$	−120.920	−7.22633
$281$	−21.5555	−1.28589	−0.642946	−	0.765912i	$-0.722288\pi$
$281$	−21.5555	−1.28589	−0.642946	+	0.765912i	$0.722288\pi$
$282$	4.74151	0.282353
$283$	23.2166	1.38008	0.690042	−	0.723769i	$-0.257592\pi$
$283$	23.2166	1.38008	0.690042	+	0.723769i	$0.257592\pi$
$284$	−3.97329	−0.235772
$285$	−12.3536	−0.731763
$286$	−18.7883	−1.11098
$287$	15.4185	0.910127
$288$	−18.3660	−1.08223
$289$	1.00000	0.0588235
$290$	−13.1899	−0.774539
$291$	−12.3848	−0.726011
$292$	46.2357	2.70574
$293$	−26.1234	−1.52615	−0.763073	−	0.646312i	$-0.776310\pi$
$293$	−26.1234	−1.52615	−0.763073	+	0.646312i	$0.776310\pi$
$294$	27.3078	1.59262
$295$	−43.0919	−2.50891
$296$	−87.7880	−5.10257
$297$	−1.26440	−0.0733682
$298$	−9.89368	−0.573126
$299$	−31.8879	−1.84412
$300$	−30.9341	−1.78598
$301$	−13.3894	−0.771751
$302$	−15.6692	−0.901659
$303$	−9.24128	−0.530898
$304$	50.1684	2.87736
$305$	−4.80390	−0.275070
$306$	−2.69942	−0.154316
$307$	25.8888	1.47755	0.738776	−	0.673951i	$-0.235404\pi$
$307$	25.8888	1.47755	0.738776	+	0.673951i	$0.235404\pi$
$308$	27.6560	1.57585
$309$	8.06351	0.458717
$310$	50.0377	2.84195
$311$	−6.70284	−0.380083	−0.190041	−	0.981776i	$-0.560862\pi$
$311$	−6.70284	−0.380083	−0.190041	+	0.981776i	$0.560862\pi$
$312$	48.8413	2.76510
$313$	10.8671	0.614243	0.307121	−	0.951670i	$-0.400634\pi$
$313$	10.8671	0.614243	0.307121	+	0.951670i	$0.400634\pi$
$314$	2.69942	0.152337
$315$	13.6282	0.767864
$316$	−46.0148	−2.58854
$317$	21.2873	1.19561	0.597806	−	0.801641i	$-0.296039\pi$
$317$	21.2873	1.19561	0.597806	+	0.801641i	$0.296039\pi$
$318$	−17.7683	−0.996397
$319$	1.87552	0.105009
$320$	75.1804	4.20271
$321$	−19.4006	−1.08283
$322$	64.6949	3.60530
$323$	3.75022	0.208668
$324$	5.28690	0.293716
$325$	32.2082	1.78659
$326$	−44.5144	−2.46543
$327$	8.87914	0.491018
$328$	−33.0672	−1.82583
$329$	7.26689	0.400636
$330$	11.2433	0.618923
$331$	6.85976	0.377047	0.188523	−	0.982069i	$-0.439630\pi$
$331$	6.85976	0.377047	0.188523	+	0.982069i	$0.439630\pi$
$332$	−46.4902	−2.55148
$333$	9.89414	0.542196
$334$	7.71185	0.421974
$335$	−51.8049	−2.83040
$336$	−55.3448	−3.01931
$337$	−17.9501	−0.977802	−0.488901	−	0.872339i	$-0.662602\pi$
$337$	−17.9501	−0.977802	−0.488901	+	0.872339i	$0.662602\pi$
$338$	−46.7034	−2.54033
$339$	−12.5063	−0.679251
$340$	17.4156	0.944491
$341$	−7.11501	−0.385299
$342$	−10.1234	−0.547412
$343$	12.8921	0.696108
$344$	28.7154	1.54823
$345$	19.0824	1.02736
$346$	−65.1498	−3.50248
$347$	12.8958	0.692280	0.346140	−	0.938183i	$-0.387492\pi$
$347$	12.8958	0.692280	0.346140	+	0.938183i	$0.387492\pi$
$348$	−7.84215	−0.420384
$349$	−24.5721	−1.31531	−0.657657	−	0.753317i	$-0.728453\pi$
$349$	−24.5721	−1.31531	−0.657657	+	0.753317i	$0.728453\pi$
$350$	−65.3447	−3.49282
$351$	−5.50466	−0.293817
$352$	−23.2221	−1.23774
$353$	16.8630	0.897525	0.448762	−	0.893651i	$-0.351865\pi$
$353$	16.8630	0.897525	0.448762	+	0.893651i	$0.351865\pi$
$354$	−35.3126	−1.87685
$355$	−2.47563	−0.131393
$356$	22.9249	1.21502
$357$	−4.13717	−0.218962
$358$	44.9988	2.37826
$359$	−32.0361	−1.69080	−0.845400	−	0.534133i	$-0.820638\pi$
$359$	−32.0361	−1.69080	−0.845400	+	0.534133i	$0.820638\pi$
$360$	−29.2276	−1.54043
$361$	−4.93587	−0.259783
$362$	−18.2314	−0.958222
$363$	9.40128	0.493439
$364$	120.402	6.31079
$365$	28.8080	1.50788
$366$	−3.93666	−0.205773
$367$	−6.99587	−0.365181	−0.182591	−	0.983189i	$-0.558448\pi$
$367$	−6.99587	−0.365181	−0.182591	+	0.983189i	$0.558448\pi$
$368$	−77.4942	−4.03967
$369$	3.72683	0.194011
$370$	−87.9804	−4.57388
$371$	−27.2319	−1.41381
$372$	29.7502	1.54248
$373$	−13.1290	−0.679796	−0.339898	−	0.940462i	$-0.610393\pi$
$373$	−13.1290	−0.679796	−0.339898	+	0.940462i	$0.610393\pi$
$374$	−3.41316	−0.176491
$375$	−2.80355	−0.144775
$376$	−15.5848	−0.803727
$377$	8.16516	0.420527
$378$	11.1680	0.574419
$379$	−14.3639	−0.737822	−0.368911	−	0.929465i	$-0.620269\pi$
$379$	−14.3639	−0.737822	−0.368911	+	0.929465i	$0.620269\pi$
$380$	65.3121	3.35044
$381$	−2.80959	−0.143940
$382$	−25.5180	−1.30562
$383$	−15.1396	−0.773598	−0.386799	−	0.922164i	$-0.626419\pi$
$383$	−15.1396	−0.773598	−0.386799	+	0.922164i	$0.626419\pi$
$384$	24.8763	1.26946
$385$	17.2316	0.878204
$386$	−33.3309	−1.69650
$387$	−3.23636	−0.164514
$388$	65.4772	3.32410
$389$	−10.9027	−0.552790	−0.276395	−	0.961044i	$-0.589140\pi$
$389$	−10.9027	−0.552790	−0.276395	+	0.961044i	$0.589140\pi$
$390$	48.9484	2.47860
$391$	−5.79289	−0.292959
$392$	−89.7580	−4.53346
$393$	−13.3474	−0.673290
$394$	−36.3075	−1.82915
$395$	−28.6704	−1.44256
$396$	6.68477	0.335923
$397$	−33.6495	−1.68882	−0.844409	−	0.535699i	$-0.820048\pi$
$397$	−33.6495	−1.68882	−0.844409	+	0.535699i	$0.820048\pi$
$398$	−30.9526	−1.55151
$399$	−15.5153	−0.776736
$400$	78.2727	3.91363
$401$	15.4442	0.771244	0.385622	−	0.922657i	$-0.373987\pi$
$401$	15.4442	0.771244	0.385622	+	0.922657i	$0.373987\pi$
$402$	−42.4527	−2.11735
$403$	−30.9756	−1.54300
$404$	48.8577	2.43076
$405$	3.29410	0.163685
$406$	−16.5657	−0.822141
$407$	12.5102	0.620107
$408$	8.87273	0.439265
$409$	−34.8077	−1.72113	−0.860565	−	0.509340i	$-0.829890\pi$
$409$	−34.8077	−1.72113	−0.860565	+	0.509340i	$0.829890\pi$
$410$	−33.1396	−1.63665
$411$	12.2063	0.602091
$412$	−42.6309	−2.10028
$413$	−54.1205	−2.66310
$414$	15.6375	0.768540
$415$	−28.9666	−1.42191
$416$	−101.099	−4.95677
$417$	−14.7339	−0.721521
$418$	−12.8001	−0.626074
$419$	−23.5329	−1.14966	−0.574829	−	0.818273i	$-0.694932\pi$
$419$	−23.5329	−1.14966	−0.574829	+	0.818273i	$0.694932\pi$
$420$	−72.0511	−3.51573
$421$	0.165111	0.00804701	0.00402350	−	0.999992i	$-0.498719\pi$
$421$	0.165111	0.00804701	0.00402350	+	0.999992i	$0.498719\pi$
$422$	45.3342	2.20683
$423$	1.75649	0.0854034
$424$	58.4026	2.83628
$425$	5.85108	0.283819
$426$	−2.02872	−0.0982916
$427$	−6.03337	−0.291975
$428$	102.569	4.95785
$429$	−6.96011	−0.336037
$430$	28.7783	1.38781
$431$	16.3564	0.787859	0.393929	−	0.919141i	$-0.371115\pi$
$431$	16.3564	0.787859	0.393929	+	0.919141i	$0.371115\pi$
$432$	−13.3775	−0.643624
$433$	−21.1189	−1.01491	−0.507454	−	0.861679i	$-0.669413\pi$
$433$	−21.1189	−1.01491	−0.507454	+	0.861679i	$0.669413\pi$
$434$	62.8440	3.01661
$435$	−4.88620	−0.234275
$436$	−46.9431	−2.24817
$437$	−21.7246	−1.03923
$438$	23.6074	1.12801
$439$	−7.14242	−0.340889	−0.170445	−	0.985367i	$-0.554520\pi$
$439$	−7.14242	−0.340889	−0.170445	+	0.985367i	$0.554520\pi$
$440$	−36.9555	−1.76179
$441$	10.1162	0.481722
$442$	−14.8594	−0.706790
$443$	22.1067	1.05032	0.525159	−	0.851004i	$-0.324006\pi$
$443$	22.1067	1.05032	0.525159	+	0.851004i	$0.324006\pi$
$444$	−52.3093	−2.48249
$445$	14.2838	0.677117
$446$	−34.2764	−1.62303
$447$	−3.66511	−0.173354
$448$	94.4216	4.46100
$449$	8.84021	0.417195	0.208598	−	0.978002i	$-0.433110\pi$
$449$	8.84021	0.417195	0.208598	+	0.978002i	$0.433110\pi$
$450$	−15.7946	−0.744563
$451$	4.71222	0.221890
$452$	66.1197	3.11001
$453$	−5.80463	−0.272725
$454$	−18.8872	−0.886420
$455$	75.0188	3.51693
$456$	33.2747	1.55823
$457$	7.66476	0.358542	0.179271	−	0.983800i	$-0.442626\pi$
$457$	7.66476	0.358542	0.179271	+	0.983800i	$0.442626\pi$
$458$	−63.3799	−2.96155
$459$	−1.00000	−0.0466760
$460$	−100.886	−4.70385
$461$	35.1633	1.63772	0.818860	−	0.573994i	$-0.194607\pi$
$461$	35.1633	1.63772	0.818860	+	0.573994i	$0.194607\pi$
$462$	14.1208	0.656961
$463$	19.5807	0.909992	0.454996	−	0.890493i	$-0.349641\pi$
$463$	19.5807	0.909992	0.454996	+	0.890493i	$0.349641\pi$
$464$	19.8431	0.921191
$465$	18.5364	0.859606
$466$	1.38647	0.0642268
$467$	13.9284	0.644532	0.322266	−	0.946649i	$-0.395556\pi$
$467$	13.9284	0.644532	0.322266	+	0.946649i	$0.395556\pi$
$468$	29.1025	1.34527
$469$	−65.0635	−3.00435
$470$	−15.6190	−0.720450
$471$	1.00000	0.0460776
$472$	116.069	5.34251
$473$	−4.09207	−0.188154
$474$	−23.4946	−1.07914
$475$	21.9428	1.00681
$476$	21.8728	1.00254
$477$	−6.58226	−0.301381
$478$	−5.38970	−0.246519
$479$	24.4521	1.11725	0.558623	−	0.829422i	$-0.311330\pi$
$479$	24.4521	1.11725	0.558623	+	0.829422i	$0.311330\pi$
$480$	60.4995	2.76141
$481$	54.4639	2.48334
$482$	−23.7278	−1.08077
$483$	23.9662	1.09050
$484$	−49.7036	−2.25925
$485$	40.7968	1.85249
$486$	2.69942	0.122448
$487$	−23.0199	−1.04313	−0.521566	−	0.853211i	$-0.674652\pi$
$487$	−23.0199	−1.04313	−0.521566	+	0.853211i	$0.674652\pi$
$488$	12.9394	0.585739
$489$	−16.4903	−0.745719
$490$	−89.9547	−4.06374
$491$	41.0352	1.85189	0.925947	−	0.377654i	$-0.123269\pi$
$491$	41.0352	1.85189	0.925947	+	0.377654i	$0.123269\pi$
$492$	−19.7034	−0.888296
$493$	1.48332	0.0668053
$494$	−55.7260	−2.50723
$495$	4.16507	0.187206
$496$	−75.2772	−3.38005
$497$	−3.10923	−0.139468
$498$	−23.7373	−1.06370
$499$	−39.1034	−1.75051	−0.875254	−	0.483663i	$-0.839306\pi$
$499$	−39.1034	−1.75051	−0.875254	+	0.483663i	$0.839306\pi$
$500$	14.8221	0.662863
$501$	2.85685	0.127635
$502$	−40.9519	−1.82777
$503$	0.772059	0.0344244	0.0172122	−	0.999852i	$-0.494521\pi$
$503$	0.772059	0.0344244	0.0172122	+	0.999852i	$0.494521\pi$
$504$	−36.7080	−1.63510
$505$	30.4417	1.35464
$506$	19.7721	0.878977
$507$	−17.3013	−0.768376
$508$	14.8540	0.659040
$509$	−36.1631	−1.60290	−0.801450	−	0.598061i	$-0.795938\pi$
$509$	−36.1631	−1.60290	−0.801450	+	0.598061i	$0.795938\pi$
$510$	8.89217	0.393752
$511$	36.1810	1.60055
$512$	−8.30164	−0.366884
$513$	−3.75022	−0.165576
$514$	17.3201	0.763957
$515$	−26.5620	−1.17046
$516$	17.1103	0.753240
$517$	2.22091	0.0976756
$518$	−110.498	−4.85498
$519$	−24.1347	−1.05940
$520$	−160.888	−7.05541
$521$	15.7118	0.688346	0.344173	−	0.938906i	$-0.388159\pi$
$521$	15.7118	0.688346	0.344173	+	0.938906i	$0.388159\pi$
$522$	−4.00411	−0.175255
$523$	35.2225	1.54017	0.770087	−	0.637939i	$-0.220213\pi$
$523$	35.2225	1.54017	0.770087	+	0.637939i	$0.220213\pi$
$524$	70.5666	3.08271
$525$	−24.2069	−1.05648
$526$	35.3103	1.53960
$527$	−5.62716	−0.245123
$528$	−16.9145	−0.736111
$529$	10.5576	0.459026
$530$	58.5306	2.54240
$531$	−13.0815	−0.567691
$532$	82.0277	3.55635
$533$	20.5149	0.888600
$534$	11.7052	0.506533
$535$	63.9074	2.76296
$536$	139.538	6.02710
$537$	16.6698	0.719353
$538$	62.9549	2.71418
$539$	12.7909	0.550944
$540$	−17.4156	−0.749446
$541$	−18.0113	−0.774367	−0.387183	−	0.922003i	$-0.626552\pi$
$541$	−18.0113	−0.774367	−0.387183	+	0.922003i	$0.626552\pi$
$542$	−38.4001	−1.64943
$543$	−6.75382	−0.289834
$544$	−18.3660	−0.787437
$545$	−29.2488	−1.25288
$546$	61.4759	2.63092
$547$	19.9297	0.852133	0.426066	−	0.904692i	$-0.359899\pi$
$547$	19.9297	0.852133	0.426066	+	0.904692i	$0.359899\pi$
$548$	−64.5333	−2.75673
$549$	−1.45833	−0.0622402
$550$	−19.9707	−0.851554
$551$	5.56277	0.236982
$552$	−51.3988	−2.18768
$553$	−36.0081	−1.53122
$554$	39.6079	1.68278
$555$	−32.5923	−1.38346
$556$	77.8965	3.30355
$557$	−12.8291	−0.543586	−0.271793	−	0.962356i	$-0.587617\pi$
$557$	−12.8291	−0.543586	−0.271793	+	0.962356i	$0.587617\pi$
$558$	15.1901	0.643048
$559$	−17.8151	−0.753497
$560$	182.311	7.70406
$561$	−1.26440	−0.0533832
$562$	58.1874	2.45449
$563$	−26.8621	−1.13210	−0.566052	−	0.824370i	$-0.691530\pi$
$563$	−26.8621	−1.13210	−0.566052	+	0.824370i	$0.691530\pi$
$564$	−9.28637	−0.391027
$565$	41.1971	1.73318
$566$	−62.6715	−2.63428
$567$	4.13717	0.173745
$568$	6.66818	0.279790
$569$	−11.9965	−0.502920	−0.251460	−	0.967868i	$-0.580911\pi$
$569$	−11.9965	−0.502920	−0.251460	+	0.967868i	$0.580911\pi$
$570$	33.3476	1.39678
$571$	9.73093	0.407227	0.203613	−	0.979051i	$-0.434731\pi$
$571$	9.73093	0.407227	0.203613	+	0.979051i	$0.434731\pi$
$572$	36.7974	1.53858
$573$	−9.45313	−0.394910
$574$	−41.6212	−1.73723
$575$	−33.8947	−1.41351
$576$	22.8228	0.950948
$577$	44.0985	1.83584	0.917922	−	0.396760i	$-0.129865\pi$
$577$	44.0985	1.83584	0.917922	+	0.396760i	$0.129865\pi$
$578$	−2.69942	−0.112281
$579$	−12.3474	−0.513141
$580$	25.8328	1.07265
$581$	−36.3801	−1.50930
$582$	33.4319	1.38580
$583$	−8.32264	−0.344688
$584$	−77.5951	−3.21091
$585$	18.1329	0.749702
$586$	70.5182	2.91308
$587$	−6.53569	−0.269757	−0.134878	−	0.990862i	$-0.543064\pi$
$587$	−6.53569	−0.269757	−0.134878	+	0.990862i	$0.543064\pi$
$588$	−53.4831	−2.20561
$589$	−21.1031	−0.869537
$590$	116.323	4.78895
$591$	−13.4501	−0.553263
$592$	132.359	5.43990
$593$	31.7624	1.30432	0.652162	−	0.758080i	$-0.273862\pi$
$593$	31.7624	1.30432	0.652162	+	0.758080i	$0.273862\pi$
$594$	3.41316	0.140044
$595$	13.6282	0.558703
$596$	19.3770	0.793714
$597$	−11.4664	−0.469287
$598$	86.0790	3.52003
$599$	−15.8996	−0.649640	−0.324820	−	0.945776i	$-0.605304\pi$
$599$	−15.8996	−0.649640	−0.324820	+	0.945776i	$0.605304\pi$
$600$	51.9151	2.11942
$601$	21.8923	0.893006	0.446503	−	0.894782i	$-0.352669\pi$
$601$	21.8923	0.893006	0.446503	+	0.894782i	$0.352669\pi$
$602$	36.1436	1.47310
$603$	−15.7266	−0.640435
$604$	30.6885	1.24870
$605$	−30.9687	−1.25906
$606$	24.9461	1.01337
$607$	−39.9993	−1.62352	−0.811761	−	0.583990i	$-0.801491\pi$
$607$	−39.9993	−1.62352	−0.811761	+	0.583990i	$0.801491\pi$
$608$	−68.8766	−2.79331
$609$	−6.13674	−0.248673
$610$	12.9678	0.525049
$611$	9.66886	0.391160
$612$	5.28690	0.213710
$613$	10.2120	0.412458	0.206229	−	0.978504i	$-0.433881\pi$
$613$	10.2120	0.412458	0.206229	+	0.978504i	$0.433881\pi$
$614$	−69.8849	−2.82032
$615$	−12.2765	−0.495038
$616$	−46.4137	−1.87006
$617$	23.5999	0.950096	0.475048	−	0.879960i	$-0.342431\pi$
$617$	23.5999	0.950096	0.475048	+	0.879960i	$0.342431\pi$
$618$	−21.7668	−0.875591
$619$	13.6338	0.547988	0.273994	−	0.961731i	$-0.411655\pi$
$619$	13.6338	0.547988	0.273994	+	0.961731i	$0.411655\pi$
$620$	−98.0001	−3.93578
$621$	5.79289	0.232461
$622$	18.0938	0.725495
$623$	17.9395	0.718731
$624$	−73.6384	−2.94789
$625$	−20.0202	−0.800810
$626$	−29.3348	−1.17246
$627$	−4.74179	−0.189369
$628$	−5.28690	−0.210970
$629$	9.89414	0.394505
$630$	−36.7884	−1.46569
$631$	−45.5123	−1.81182	−0.905909	−	0.423472i	$-0.860811\pi$
$631$	−45.5123	−1.81182	−0.905909	+	0.423472i	$0.860811\pi$
$632$	77.2243	3.07182
$633$	16.7940	0.667502
$634$	−57.4634	−2.28216
$635$	9.25507	0.367276
$636$	34.7997	1.37990
$637$	55.6860	2.20636
$638$	−5.06281	−0.200439
$639$	−0.751536	−0.0297303
$640$	−81.9449	−3.23916
$641$	−33.4518	−1.32127	−0.660633	−	0.750709i	$-0.729712\pi$
$641$	−33.4518	−1.32127	−0.660633	+	0.750709i	$0.729712\pi$
$642$	52.3704	2.06690
$643$	7.51082	0.296198	0.148099	−	0.988973i	$-0.452685\pi$
$643$	7.51082	0.296198	0.148099	+	0.988973i	$0.452685\pi$
$644$	−126.707	−4.99294
$645$	10.6609	0.419773
$646$	−10.1234	−0.398301
$647$	−16.9500	−0.666374	−0.333187	−	0.942861i	$-0.608124\pi$
$647$	−16.9500	−0.666374	−0.333187	+	0.942861i	$0.608124\pi$
$648$	−8.87273	−0.348554
$649$	−16.5404	−0.649266
$650$	−86.9436	−3.41021
$651$	23.2805	0.912436
$652$	87.1827	3.41434
$653$	−32.0471	−1.25410	−0.627049	−	0.778980i	$-0.715738\pi$
$653$	−32.0471	−1.25410	−0.627049	+	0.778980i	$0.715738\pi$
$654$	−23.9686	−0.937245
$655$	43.9678	1.71796
$656$	49.8556	1.94653
$657$	8.74535	0.341188
$658$	−19.6164	−0.764728
$659$	12.3092	0.479497	0.239749	−	0.970835i	$-0.422935\pi$
$659$	12.3092	0.479497	0.239749	+	0.970835i	$0.422935\pi$
$660$	−22.0203	−0.857139
$661$	−17.5377	−0.682138	−0.341069	−	0.940038i	$-0.610789\pi$
$661$	−17.5377	−0.682138	−0.341069	+	0.940038i	$0.610789\pi$
$662$	−18.5174	−0.719700
$663$	−5.50466	−0.213783
$664$	78.0222	3.02785
$665$	51.1089	1.98192
$666$	−26.7085	−1.03493
$667$	−8.59271	−0.332711
$668$	−15.1039	−0.584386
$669$	−12.6977	−0.490920
$670$	139.843	5.40262
$671$	−1.84392	−0.0711839
$672$	75.9833	2.93112
$673$	−10.9126	−0.420648	−0.210324	−	0.977632i	$-0.567452\pi$
$673$	−10.9126	−0.420648	−0.210324	+	0.977632i	$0.567452\pi$
$674$	48.4548	1.86641
$675$	−5.85108	−0.225208
$676$	91.4699	3.51807
$677$	16.7562	0.643994	0.321997	−	0.946741i	$-0.395646\pi$
$677$	16.7562	0.643994	0.321997	+	0.946741i	$0.395646\pi$
$678$	33.7599	1.29654
$679$	51.2381	1.96634
$680$	−29.2276	−1.12083
$681$	−6.99675	−0.268116
$682$	19.2064	0.735452
$683$	43.1298	1.65031	0.825157	−	0.564903i	$-0.191086\pi$
$683$	43.1298	1.65031	0.825157	+	0.564903i	$0.191086\pi$
$684$	19.8270	0.758105
$685$	−40.2087	−1.53629
$686$	−34.8013	−1.32872
$687$	−23.4790	−0.895781
$688$	−43.2944	−1.65058
$689$	−36.2331	−1.38037
$690$	−51.5114	−1.96101
$691$	28.0457	1.06691	0.533455	−	0.845829i	$-0.320893\pi$
$691$	28.0457	1.06691	0.533455	+	0.845829i	$0.320893\pi$
$692$	127.598	4.85054
$693$	5.23105	0.198711
$694$	−34.8111	−1.32141
$695$	48.5348	1.84103
$696$	13.1611	0.498870
$697$	3.72683	0.141164
$698$	66.3306	2.51065
$699$	0.513616	0.0194267
$700$	127.979	4.83717
$701$	−47.0710	−1.77785	−0.888924	−	0.458056i	$-0.848546\pi$
$701$	−47.0710	−1.77785	−0.888924	+	0.458056i	$0.848546\pi$
$702$	14.8594	0.560832
$703$	37.1052	1.39945
$704$	28.8572	1.08760
$705$	−5.78604	−0.217915
$706$	−45.5203	−1.71318
$707$	38.2327	1.43789
$708$	69.1607	2.59922
$709$	47.8561	1.79727	0.898637	−	0.438693i	$-0.144558\pi$
$709$	47.8561	1.79727	0.898637	+	0.438693i	$0.144558\pi$
$710$	6.68279	0.250801
$711$	−8.70356	−0.326409
$712$	−38.4737	−1.44186
$713$	32.5975	1.22079
$714$	11.1680	0.417951
$715$	22.9273	0.857432
$716$	−88.1313	−3.29362
$717$	−1.99661	−0.0745648
$718$	86.4790	3.22737
$719$	−36.5954	−1.36478	−0.682389	−	0.730989i	$-0.739059\pi$
$719$	−36.5954	−1.36478	−0.682389	+	0.730989i	$0.739059\pi$
$720$	44.0667	1.64227
$721$	−33.3601	−1.24240
$722$	13.3240	0.495868
$723$	−8.78995	−0.326902
$724$	35.7067	1.32703
$725$	8.67902	0.322331
$726$	−25.3781	−0.941868
$727$	−47.6172	−1.76602	−0.883011	−	0.469352i	$-0.844488\pi$
$727$	−47.6172	−1.76602	−0.883011	+	0.469352i	$0.844488\pi$
$728$	−202.065	−7.48902
$729$	1.00000	0.0370370
$730$	−77.7651	−2.87822
$731$	−3.23636	−0.119701
$732$	7.71006	0.284972
$733$	24.2235	0.894714	0.447357	−	0.894355i	$-0.352365\pi$
$733$	24.2235	0.894714	0.447357	+	0.894355i	$0.352365\pi$
$734$	18.8848	0.697051
$735$	−33.3236	−1.22916
$736$	106.392	3.92168
$737$	−19.8847	−0.732464
$738$	−10.0603	−0.370325
$739$	−22.0238	−0.810160	−0.405080	−	0.914281i	$-0.632756\pi$
$739$	−22.0238	−0.810160	−0.405080	+	0.914281i	$0.632756\pi$
$740$	172.312	6.33431
$741$	−20.6437	−0.758364
$742$	73.5105	2.69866
$743$	−35.8856	−1.31652	−0.658258	−	0.752792i	$-0.728707\pi$
$743$	−35.8856	−1.31652	−0.658258	+	0.752792i	$0.728707\pi$
$744$	−49.9283	−1.83046
$745$	12.0732	0.442329
$746$	35.4409	1.29758
$747$	−8.79348	−0.321737
$748$	6.68477	0.244420
$749$	80.2635	2.93276
$750$	7.56797	0.276343
$751$	−5.11360	−0.186598	−0.0932989	−	0.995638i	$-0.529741\pi$
$751$	−5.11360	−0.186598	−0.0932989	+	0.995638i	$0.529741\pi$
$752$	23.4974	0.856861
$753$	−15.1706	−0.552847
$754$	−22.0412	−0.802695
$755$	19.1210	0.695885
$756$	−21.8728	−0.795505
$757$	38.7193	1.40728	0.703638	−	0.710558i	$-0.251557\pi$
$757$	38.7193	1.40728	0.703638	+	0.710558i	$0.251557\pi$
$758$	38.7742	1.40834
$759$	7.32456	0.265865
$760$	−109.610	−3.97597
$761$	15.8585	0.574870	0.287435	−	0.957800i	$-0.407198\pi$
$761$	15.8585	0.574870	0.287435	+	0.957800i	$0.407198\pi$
$762$	7.58428	0.274749
$763$	−36.7345	−1.32988
$764$	49.9777	1.80813
$765$	3.29410	0.119098
$766$	40.8682	1.47663
$767$	−72.0094	−2.60011
$768$	−21.5061	−0.776036
$769$	14.1488	0.510221	0.255110	−	0.966912i	$-0.417888\pi$
$769$	14.1488	0.510221	0.255110	+	0.966912i	$0.417888\pi$
$770$	−46.5154	−1.67630
$771$	6.41622	0.231074
$772$	65.2795	2.34946
$773$	−51.4829	−1.85171	−0.925855	−	0.377879i	$-0.876654\pi$
$773$	−51.4829	−1.85171	−0.925855	+	0.377879i	$0.876654\pi$
$774$	8.73632	0.314021
$775$	−32.9250	−1.18270
$776$	−109.887	−3.94472
$777$	−40.9337	−1.46849
$778$	29.4311	1.05515
$779$	13.9764	0.500757
$780$	−95.8666	−3.43258
$781$	−0.950246	−0.0340025
$782$	15.6375	0.559195
$783$	−1.48332	−0.0530095
$784$	135.329	4.83317
$785$	−3.29410	−0.117571
$786$	36.0304	1.28516
$787$	22.7733	0.811782	0.405891	−	0.913922i	$-0.366961\pi$
$787$	22.7733	0.811782	0.405891	+	0.913922i	$0.366961\pi$
$788$	71.1092	2.53316
$789$	13.0807	0.465684
$790$	77.3936	2.75354
$791$	51.7408	1.83969
$792$	−11.2187	−0.398640
$793$	−8.02763	−0.285069
$794$	90.8342	3.22358
$795$	21.6826	0.769003
$796$	60.6215	2.14867
$797$	−25.9350	−0.918667	−0.459333	−	0.888264i	$-0.651912\pi$
$797$	−25.9350	−0.918667	−0.459333	+	0.888264i	$0.651912\pi$
$798$	41.8823	1.48262
$799$	1.75649	0.0621401
$800$	−107.461	−3.79932
$801$	4.33618	0.153211
$802$	−41.6903	−1.47214
$803$	11.0577	0.390216
$804$	83.1447	2.93229
$805$	−78.9469	−2.78251
$806$	83.6163	2.94526
$807$	23.3216	0.820958
$808$	−81.9954	−2.88459
$809$	−35.4632	−1.24682	−0.623410	−	0.781895i	$-0.714253\pi$
$809$	−35.4632	−1.24682	−0.623410	+	0.781895i	$0.714253\pi$
$810$	−8.89217	−0.312439
$811$	−16.2439	−0.570399	−0.285200	−	0.958468i	$-0.592060\pi$
$811$	−16.2439	−0.570399	−0.285200	+	0.958468i	$0.592060\pi$
$812$	32.4443	1.13857
$813$	−14.2253	−0.498903
$814$	−33.7703	−1.18365
$815$	54.3208	1.90277
$816$	−13.3775	−0.468305
$817$	−12.1371	−0.424622
$818$	93.9608	3.28526
$819$	22.7737	0.795777
$820$	64.9048	2.26657
$821$	−15.2862	−0.533491	−0.266745	−	0.963767i	$-0.585948\pi$
$821$	−15.2862	−0.533491	−0.266745	+	0.963767i	$0.585948\pi$
$822$	−32.9499	−1.14926
$823$	54.5763	1.90241	0.951204	−	0.308562i	$-0.0998477\pi$
$823$	54.5763	1.90241	0.951204	+	0.308562i	$0.0998477\pi$
$824$	71.5453	2.49240
$825$	−7.39813	−0.257570
$826$	146.094	5.08327
$827$	−29.6884	−1.03237	−0.516184	−	0.856478i	$-0.672648\pi$
$827$	−29.6884	−1.03237	−0.516184	+	0.856478i	$0.672648\pi$
$828$	−30.6264	−1.06434
$829$	−20.6662	−0.717767	−0.358884	−	0.933382i	$-0.616842\pi$
$829$	−20.6662	−0.717767	−0.358884	+	0.933382i	$0.616842\pi$
$830$	78.1931	2.71412
$831$	14.6727	0.508991
$832$	125.631	4.35549
$833$	10.1162	0.350504
$834$	39.7730	1.37723
$835$	−9.41074	−0.325672
$836$	25.0694	0.867042
$837$	5.62716	0.194503
$838$	63.5254	2.19445
$839$	−4.74449	−0.163798	−0.0818990	−	0.996641i	$-0.526098\pi$
$839$	−4.74449	−0.163798	−0.0818990	+	0.996641i	$0.526098\pi$
$840$	120.920	4.17212
$841$	−26.7998	−0.924130
$842$	−0.445704	−0.0153600
$843$	21.5555	0.742410
$844$	−88.7881	−3.05621
$845$	56.9920	1.96059
$846$	−4.74151	−0.163016
$847$	−38.8947	−1.33644
$848$	−88.0540	−3.02379
$849$	−23.2166	−0.796792
$850$	−15.7946	−0.541749
$851$	−57.3157	−1.96476
$852$	3.97329	0.136123
$853$	51.6619	1.76887	0.884434	−	0.466664i	$-0.154544\pi$
$853$	51.6619	1.76887	0.884434	+	0.466664i	$0.154544\pi$
$854$	16.2866	0.557317
$855$	12.3536	0.422484
$856$	−172.136	−5.88349
$857$	3.30949	0.113050	0.0565250	−	0.998401i	$-0.481998\pi$
$857$	3.30949	0.113050	0.0565250	+	0.998401i	$0.481998\pi$
$858$	18.7883	0.641422
$859$	9.46105	0.322807	0.161403	−	0.986889i	$-0.448398\pi$
$859$	9.46105	0.322807	0.161403	+	0.986889i	$0.448398\pi$
$860$	−56.3631	−1.92196
$861$	−15.4185	−0.525462
$862$	−44.1528	−1.50385
$863$	−32.3737	−1.10201	−0.551007	−	0.834501i	$-0.685756\pi$
$863$	−32.3737	−1.10201	−0.551007	+	0.834501i	$0.685756\pi$
$864$	18.3660	0.624825
$865$	79.5021	2.70315
$866$	57.0088	1.93724
$867$	−1.00000	−0.0339618
$868$	−123.082	−4.17766
$869$	−11.0048	−0.373313
$870$	13.1899	0.447180
$871$	−86.5694	−2.93329
$872$	78.7822	2.66790
$873$	12.3848	0.419163
$874$	58.6439	1.98366
$875$	11.5988	0.392109
$876$	−46.2357	−1.56216
$877$	28.0649	0.947683	0.473842	−	0.880610i	$-0.342867\pi$
$877$	28.0649	0.947683	0.473842	+	0.880610i	$0.342867\pi$
$878$	19.2804	0.650683
$879$	26.1234	0.881121
$880$	55.7181	1.87826
$881$	11.9638	0.403072	0.201536	−	0.979481i	$-0.435407\pi$
$881$	11.9638	0.403072	0.201536	+	0.979481i	$0.435407\pi$
$882$	−27.3078	−0.919502
$883$	37.9825	1.27821	0.639107	−	0.769118i	$-0.279304\pi$
$883$	37.9825	1.27821	0.639107	+	0.769118i	$0.279304\pi$
$884$	29.1025	0.978825
$885$	43.0919	1.44852
$886$	−59.6753	−2.00483
$887$	47.2865	1.58772	0.793862	−	0.608098i	$-0.208067\pi$
$887$	47.2865	1.58772	0.793862	+	0.608098i	$0.208067\pi$
$888$	87.7880	2.94597
$889$	11.6238	0.389848
$890$	−38.5580	−1.29247
$891$	1.26440	0.0423591
$892$	67.1312	2.24772
$893$	6.58721	0.220433
$894$	9.89368	0.330894
$895$	−54.9118	−1.83550
$896$	−102.917	−3.43823
$897$	31.8879	1.06471
$898$	−23.8635	−0.796335
$899$	−8.34688	−0.278384
$900$	30.9341	1.03114
$901$	−6.58226	−0.219287
$902$	−12.7203	−0.423539
$903$	13.3894	0.445571
$904$	−110.965	−3.69065
$905$	22.2477	0.739540
$906$	15.6692	0.520573
$907$	−31.8598	−1.05789	−0.528943	−	0.848657i	$-0.677412\pi$
$907$	−31.8598	−1.05789	−0.528943	+	0.848657i	$0.677412\pi$
$908$	36.9911	1.22759
$909$	9.24128	0.306514
$910$	−202.508	−6.71306
$911$	47.7384	1.58164	0.790822	−	0.612046i	$-0.209653\pi$
$911$	47.7384	1.58164	0.790822	+	0.612046i	$0.209653\pi$
$912$	−50.1684	−1.66124
$913$	−11.1185	−0.367969
$914$	−20.6904	−0.684379
$915$	4.80390	0.158812
$916$	124.131	4.10141
$917$	55.2206	1.82355
$918$	2.69942	0.0890943
$919$	−52.6185	−1.73573	−0.867863	−	0.496804i	$-0.834507\pi$
$919$	−52.6185	−1.73573	−0.867863	+	0.496804i	$0.834507\pi$
$920$	169.313	5.58207
$921$	−25.8888	−0.853065
$922$	−94.9208	−3.12605
$923$	−4.13695	−0.136169
$924$	−27.6560	−0.909817
$925$	57.8914	1.90346
$926$	−52.8566	−1.73698
$927$	−8.06351	−0.264840
$928$	−27.2427	−0.894285
$929$	−4.06466	−0.133357	−0.0666786	−	0.997775i	$-0.521240\pi$
$929$	−4.06466	−0.133357	−0.0666786	+	0.997775i	$0.521240\pi$
$930$	−50.0377	−1.64080
$931$	37.9378	1.24336
$932$	−2.71543	−0.0889469
$933$	6.70284	0.219441
$934$	−37.5988	−1.23027
$935$	4.16507	0.136212
$936$	−48.8413	−1.59643
$937$	−31.1634	−1.01807	−0.509033	−	0.860747i	$-0.669997\pi$
$937$	−31.1634	−1.01807	−0.509033	+	0.860747i	$0.669997\pi$
$938$	175.634	5.73465
$939$	−10.8671	−0.354633
$940$	30.5902	0.997743
$941$	23.8033	0.775965	0.387983	−	0.921667i	$-0.373172\pi$
$941$	23.8033	0.775965	0.387983	+	0.921667i	$0.373172\pi$
$942$	−2.69942	−0.0879520
$943$	−21.5891	−0.703039
$944$	−174.998	−5.69570
$945$	−13.6282	−0.443327
$946$	11.0462	0.359144
$947$	23.4461	0.761895	0.380948	−	0.924597i	$-0.375598\pi$
$947$	23.4461	0.761895	0.380948	+	0.924597i	$0.375598\pi$
$948$	46.0148	1.49449
$949$	48.1401	1.56269
$950$	−59.2330	−1.92177
$951$	−21.2873	−0.690287
$952$	−36.7080	−1.18971
$953$	10.6565	0.345197	0.172599	−	0.984992i	$-0.444784\pi$
$953$	10.6565	0.345197	0.172599	+	0.984992i	$0.444784\pi$
$954$	17.7683	0.575270
$955$	31.1395	1.00765
$956$	10.5559	0.341401
$957$	−1.87552	−0.0606268
$958$	−66.0066	−2.13258
$959$	−50.4994	−1.63071
$960$	−75.1804	−2.42644
$961$	0.664961	0.0214504
$962$	−147.021	−4.74015
$963$	19.4006	0.625175
$964$	46.4716	1.49675
$965$	40.6736	1.30933
$966$	−64.6949	−2.08152
$967$	5.48941	0.176528	0.0882638	−	0.996097i	$-0.471868\pi$
$967$	5.48941	0.176528	0.0882638	+	0.996097i	$0.471868\pi$
$968$	83.4150	2.68106
$969$	−3.75022	−0.120474
$970$	−110.128	−3.53599
$971$	−42.0415	−1.34918	−0.674588	−	0.738195i	$-0.735679\pi$
$971$	−42.0415	−1.34918	−0.674588	+	0.738195i	$0.735679\pi$
$972$	−5.28690	−0.169577
$973$	60.9566	1.95418
$974$	62.1405	1.99111
$975$	−32.2082	−1.03149
$976$	−19.5088	−0.624462
$977$	50.2521	1.60771	0.803854	−	0.594827i	$-0.202779\pi$
$977$	50.2521	1.60771	0.803854	+	0.594827i	$0.202779\pi$
$978$	44.5144	1.42341
$979$	5.48268	0.175227
$980$	176.179	5.62782
$981$	−8.87914	−0.283489
$982$	−110.772	−3.53486
$983$	23.2261	0.740797	0.370398	−	0.928873i	$-0.379221\pi$
$983$	23.2261	0.740797	0.370398	+	0.928873i	$0.379221\pi$
$984$	33.0672	1.05414
$985$	44.3059	1.41170
$986$	−4.00411	−0.127517
$987$	−7.26689	−0.231308
$988$	109.141	3.47223
$989$	18.7479	0.596149
$990$	−11.2433	−0.357336
$991$	−35.1600	−1.11689	−0.558447	−	0.829540i	$-0.688603\pi$
$991$	−35.1600	−1.11689	−0.558447	+	0.829540i	$0.688603\pi$
$992$	103.349	3.28132
$993$	−6.85976	−0.217688
$994$	8.39314	0.266214
$995$	37.7714	1.19743
$996$	46.4902	1.47310
$997$	−46.4104	−1.46983	−0.734917	−	0.678157i	$-0.762779\pi$
$997$	−46.4104	−1.46983	−0.734917	+	0.678157i	$0.762779\pi$
$998$	105.557	3.34134
$999$	−9.89414	−0.313037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.2	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.69942 q^{2} -1.00000 q^{3} +5.28690 q^{4} +3.29410 q^{5} +2.69942 q^{6} +4.13717 q^{7} -8.87273 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69942 q^{2} -1.00000 q^{3} +5.28690 q^{4} +3.29410 q^{5} +2.69942 q^{6} +4.13717 q^{7} -8.87273 q^{8} +1.00000 q^{9} -8.89217 q^{10} +1.26440 q^{11} -5.28690 q^{12} +5.50466 q^{13} -11.1680 q^{14} -3.29410 q^{15} +13.3775 q^{16} +1.00000 q^{17} -2.69942 q^{18} +3.75022 q^{19} +17.4156 q^{20} -4.13717 q^{21} -3.41316 q^{22} -5.79289 q^{23} +8.87273 q^{24} +5.85108 q^{25} -14.8594 q^{26} -1.00000 q^{27} +21.8728 q^{28} +1.48332 q^{29} +8.89217 q^{30} -5.62716 q^{31} -18.3660 q^{32} -1.26440 q^{33} -2.69942 q^{34} +13.6282 q^{35} +5.28690 q^{36} +9.89414 q^{37} -10.1234 q^{38} -5.50466 q^{39} -29.2276 q^{40} +3.72683 q^{41} +11.1680 q^{42} -3.23636 q^{43} +6.68477 q^{44} +3.29410 q^{45} +15.6375 q^{46} +1.75649 q^{47} -13.3775 q^{48} +10.1162 q^{49} -15.7946 q^{50} -1.00000 q^{51} +29.1025 q^{52} -6.58226 q^{53} +2.69942 q^{54} +4.16507 q^{55} -36.7080 q^{56} -3.75022 q^{57} -4.00411 q^{58} -13.0815 q^{59} -17.4156 q^{60} -1.45833 q^{61} +15.1901 q^{62} +4.13717 q^{63} +22.8228 q^{64} +18.1329 q^{65} +3.41316 q^{66} -15.7266 q^{67} +5.28690 q^{68} +5.79289 q^{69} -36.7884 q^{70} -0.751536 q^{71} -8.87273 q^{72} +8.74535 q^{73} -26.7085 q^{74} -5.85108 q^{75} +19.8270 q^{76} +5.23105 q^{77} +14.8594 q^{78} -8.70356 q^{79} +44.0667 q^{80} +1.00000 q^{81} -10.0603 q^{82} -8.79348 q^{83} -21.8728 q^{84} +3.29410 q^{85} +8.73632 q^{86} -1.48332 q^{87} -11.2187 q^{88} +4.33618 q^{89} -8.89217 q^{90} +22.7737 q^{91} -30.6264 q^{92} +5.62716 q^{93} -4.74151 q^{94} +12.3536 q^{95} +18.3660 q^{96} +12.3848 q^{97} -27.3078 q^{98} +1.26440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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