LMFDB - Embedded newform 8026.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.39250 q^{3} +1.00000 q^{4} +1.27700 q^{5} -2.39250 q^{6} +3.72505 q^{7} +1.00000 q^{8} +2.72406 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.39250 q^{3} +1.00000 q^{4} +1.27700 q^{5} -2.39250 q^{6} +3.72505 q^{7} +1.00000 q^{8} +2.72406 q^{9} +1.27700 q^{10} +5.70892 q^{11} -2.39250 q^{12} +2.09104 q^{13} +3.72505 q^{14} -3.05522 q^{15} +1.00000 q^{16} -3.61846 q^{17} +2.72406 q^{18} +7.92384 q^{19} +1.27700 q^{20} -8.91220 q^{21} +5.70892 q^{22} +0.657930 q^{23} -2.39250 q^{24} -3.36927 q^{25} +2.09104 q^{26} +0.660186 q^{27} +3.72505 q^{28} +8.28737 q^{29} -3.05522 q^{30} +0.384931 q^{31} +1.00000 q^{32} -13.6586 q^{33} -3.61846 q^{34} +4.75689 q^{35} +2.72406 q^{36} +4.42642 q^{37} +7.92384 q^{38} -5.00282 q^{39} +1.27700 q^{40} -0.620273 q^{41} -8.91220 q^{42} +1.59179 q^{43} +5.70892 q^{44} +3.47862 q^{45} +0.657930 q^{46} +9.63330 q^{47} -2.39250 q^{48} +6.87603 q^{49} -3.36927 q^{50} +8.65717 q^{51} +2.09104 q^{52} -6.79811 q^{53} +0.660186 q^{54} +7.29028 q^{55} +3.72505 q^{56} -18.9578 q^{57} +8.28737 q^{58} -8.52656 q^{59} -3.05522 q^{60} +10.1503 q^{61} +0.384931 q^{62} +10.1473 q^{63} +1.00000 q^{64} +2.67026 q^{65} -13.6586 q^{66} +2.40652 q^{67} -3.61846 q^{68} -1.57410 q^{69} +4.75689 q^{70} -1.48175 q^{71} +2.72406 q^{72} -8.09022 q^{73} +4.42642 q^{74} +8.06099 q^{75} +7.92384 q^{76} +21.2660 q^{77} -5.00282 q^{78} -3.47393 q^{79} +1.27700 q^{80} -9.75168 q^{81} -0.620273 q^{82} -2.31114 q^{83} -8.91220 q^{84} -4.62077 q^{85} +1.59179 q^{86} -19.8275 q^{87} +5.70892 q^{88} +2.26902 q^{89} +3.47862 q^{90} +7.78925 q^{91} +0.657930 q^{92} -0.920947 q^{93} +9.63330 q^{94} +10.1187 q^{95} -2.39250 q^{96} -15.1111 q^{97} +6.87603 q^{98} +15.5514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.39250	−1.38131	−0.690656	−	0.723184i	$-0.742678\pi$
$3$	−2.39250	−1.38131	−0.690656	+	0.723184i	$0.742678\pi$
$4$	1.00000	0.500000
$5$	1.27700	0.571091	0.285546	−	0.958365i	$-0.407825\pi$
$5$	1.27700	0.571091	0.285546	+	0.958365i	$0.407825\pi$
$6$	−2.39250	−0.976734
$7$	3.72505	1.40794	0.703969	−	0.710231i	$-0.251409\pi$
$7$	3.72505	1.40794	0.703969	+	0.710231i	$0.251409\pi$
$8$	1.00000	0.353553
$9$	2.72406	0.908020
$10$	1.27700	0.403822
$11$	5.70892	1.72130	0.860652	−	0.509194i	$-0.170056\pi$
$11$	5.70892	1.72130	0.860652	+	0.509194i	$0.170056\pi$
$12$	−2.39250	−0.690656
$13$	2.09104	0.579951	0.289975	−	0.957034i	$-0.406353\pi$
$13$	2.09104	0.579951	0.289975	+	0.957034i	$0.406353\pi$
$14$	3.72505	0.995563
$15$	−3.05522	−0.788855
$16$	1.00000	0.250000
$17$	−3.61846	−0.877605	−0.438803	−	0.898584i	$-0.644597\pi$
$17$	−3.61846	−0.877605	−0.438803	+	0.898584i	$0.644597\pi$
$18$	2.72406	0.642067
$19$	7.92384	1.81785	0.908927	−	0.416956i	$-0.136903\pi$
$19$	7.92384	1.81785	0.908927	+	0.416956i	$0.136903\pi$
$20$	1.27700	0.285546
$21$	−8.91220	−1.94480
$22$	5.70892	1.21715
$23$	0.657930	0.137188	0.0685940	−	0.997645i	$-0.478149\pi$
$23$	0.657930	0.137188	0.0685940	+	0.997645i	$0.478149\pi$
$24$	−2.39250	−0.488367
$25$	−3.36927	−0.673855
$26$	2.09104	0.410087
$27$	0.660186	0.127053
$28$	3.72505	0.703969
$29$	8.28737	1.53893	0.769463	−	0.638692i	$-0.220524\pi$
$29$	8.28737	1.53893	0.769463	+	0.638692i	$0.220524\pi$
$30$	−3.05522	−0.557804
$31$	0.384931	0.0691356	0.0345678	−	0.999402i	$-0.488995\pi$
$31$	0.384931	0.0691356	0.0345678	+	0.999402i	$0.488995\pi$
$32$	1.00000	0.176777
$33$	−13.6586	−2.37766
$34$	−3.61846	−0.620561
$35$	4.75689	0.804061
$36$	2.72406	0.454010
$37$	4.42642	0.727698	0.363849	−	0.931458i	$-0.381462\pi$
$37$	4.42642	0.727698	0.363849	+	0.931458i	$0.381462\pi$
$38$	7.92384	1.28542
$39$	−5.00282	−0.801093
$40$	1.27700	0.201911
$41$	−0.620273	−0.0968703	−0.0484352	−	0.998826i	$-0.515423\pi$
$41$	−0.620273	−0.0968703	−0.0484352	+	0.998826i	$0.515423\pi$
$42$	−8.91220	−1.37518
$43$	1.59179	0.242746	0.121373	−	0.992607i	$-0.461270\pi$
$43$	1.59179	0.242746	0.121373	+	0.992607i	$0.461270\pi$
$44$	5.70892	0.860652
$45$	3.47862	0.518562
$46$	0.657930	0.0970065
$47$	9.63330	1.40516	0.702581	−	0.711604i	$-0.252031\pi$
$47$	9.63330	1.40516	0.702581	+	0.711604i	$0.252031\pi$
$48$	−2.39250	−0.345328
$49$	6.87603	0.982290
$50$	−3.36927	−0.476487
$51$	8.65717	1.21225
$52$	2.09104	0.289975
$53$	−6.79811	−0.933792	−0.466896	−	0.884312i	$-0.654628\pi$
$53$	−6.79811	−0.933792	−0.466896	+	0.884312i	$0.654628\pi$
$54$	0.660186	0.0898399
$55$	7.29028	0.983021
$56$	3.72505	0.497781
$57$	−18.9578	−2.51102
$58$	8.28737	1.08818
$59$	−8.52656	−1.11006	−0.555032	−	0.831829i	$-0.687294\pi$
$59$	−8.52656	−1.11006	−0.555032	+	0.831829i	$0.687294\pi$
$60$	−3.05522	−0.394427
$61$	10.1503	1.29961	0.649805	−	0.760101i	$-0.274851\pi$
$61$	10.1503	1.29961	0.649805	+	0.760101i	$0.274851\pi$
$62$	0.384931	0.0488863
$63$	10.1473	1.27844
$64$	1.00000	0.125000
$65$	2.67026	0.331205
$66$	−13.6586	−1.68126
$67$	2.40652	0.294003	0.147002	−	0.989136i	$-0.453038\pi$
$67$	2.40652	0.294003	0.147002	+	0.989136i	$0.453038\pi$
$68$	−3.61846	−0.438803
$69$	−1.57410	−0.189499
$70$	4.75689	0.568557
$71$	−1.48175	−0.175851	−0.0879255	−	0.996127i	$-0.528024\pi$
$71$	−1.48175	−0.175851	−0.0879255	+	0.996127i	$0.528024\pi$
$72$	2.72406	0.321034
$73$	−8.09022	−0.946889	−0.473444	−	0.880824i	$-0.656989\pi$
$73$	−8.09022	−0.946889	−0.473444	+	0.880824i	$0.656989\pi$
$74$	4.42642	0.514561
$75$	8.06099	0.930803
$76$	7.92384	0.908927
$77$	21.2660	2.42349
$78$	−5.00282	−0.566458
$79$	−3.47393	−0.390848	−0.195424	−	0.980719i	$-0.562608\pi$
$79$	−3.47393	−0.390848	−0.195424	+	0.980719i	$0.562608\pi$
$80$	1.27700	0.142773
$81$	−9.75168	−1.08352
$82$	−0.620273	−0.0684977
$83$	−2.31114	−0.253680	−0.126840	−	0.991923i	$-0.540484\pi$
$83$	−2.31114	−0.253680	−0.126840	+	0.991923i	$0.540484\pi$
$84$	−8.91220	−0.972400
$85$	−4.62077	−0.501193
$86$	1.59179	0.171647
$87$	−19.8275	−2.12573
$88$	5.70892	0.608573
$89$	2.26902	0.240516	0.120258	−	0.992743i	$-0.461628\pi$
$89$	2.26902	0.240516	0.120258	+	0.992743i	$0.461628\pi$
$90$	3.47862	0.366679
$91$	7.78925	0.816535
$92$	0.657930	0.0685940
$93$	−0.920947	−0.0954978
$94$	9.63330	0.993599
$95$	10.1187	1.03816
$96$	−2.39250	−0.244184
$97$	−15.1111	−1.53430	−0.767148	−	0.641470i	$-0.778325\pi$
$97$	−15.1111	−1.53430	−0.767148	+	0.641470i	$0.778325\pi$
$98$	6.87603	0.694584
$99$	15.5514	1.56298
$100$	−3.36927	−0.336927
$101$	2.50820	0.249575	0.124787	−	0.992183i	$-0.460175\pi$
$101$	2.50820	0.249575	0.124787	+	0.992183i	$0.460175\pi$
$102$	8.65717	0.857187
$103$	−10.5767	−1.04216	−0.521079	−	0.853508i	$-0.674470\pi$
$103$	−10.5767	−1.04216	−0.521079	+	0.853508i	$0.674470\pi$
$104$	2.09104	0.205044
$105$	−11.3809	−1.11066
$106$	−6.79811	−0.660290
$107$	16.3661	1.58217	0.791087	−	0.611704i	$-0.209516\pi$
$107$	16.3661	1.58217	0.791087	+	0.611704i	$0.209516\pi$
$108$	0.660186	0.0635264
$109$	−17.1222	−1.64001	−0.820004	−	0.572358i	$-0.806029\pi$
$109$	−17.1222	−1.64001	−0.820004	+	0.572358i	$0.806029\pi$
$110$	7.29028	0.695101
$111$	−10.5902	−1.00518
$112$	3.72505	0.351985
$113$	−10.5780	−0.995097	−0.497548	−	0.867436i	$-0.665766\pi$
$113$	−10.5780	−0.995097	−0.497548	+	0.867436i	$0.665766\pi$
$114$	−18.9578	−1.77556
$115$	0.840176	0.0783468
$116$	8.28737	0.769463
$117$	5.69613	0.526607
$118$	−8.52656	−0.784933
$119$	−13.4790	−1.23561
$120$	−3.05522	−0.278902
$121$	21.5918	1.96289
$122$	10.1503	0.918963
$123$	1.48400	0.133808
$124$	0.384931	0.0345678
$125$	−10.6876	−0.955924
$126$	10.1473	0.903991
$127$	−6.67493	−0.592304	−0.296152	−	0.955141i	$-0.595703\pi$
$127$	−6.67493	−0.592304	−0.296152	+	0.955141i	$0.595703\pi$
$128$	1.00000	0.0883883
$129$	−3.80836	−0.335308
$130$	2.67026	0.234197
$131$	8.89195	0.776893	0.388447	−	0.921471i	$-0.373012\pi$
$131$	8.89195	0.776893	0.388447	+	0.921471i	$0.373012\pi$
$132$	−13.6586	−1.18883
$133$	29.5167	2.55943
$134$	2.40652	0.207892
$135$	0.843056	0.0725587
$136$	−3.61846	−0.310280
$137$	−21.1507	−1.80702	−0.903511	−	0.428564i	$-0.859020\pi$
$137$	−21.1507	−1.80702	−0.903511	+	0.428564i	$0.859020\pi$
$138$	−1.57410	−0.133996
$139$	−8.47259	−0.718635	−0.359318	−	0.933215i	$-0.616991\pi$
$139$	−8.47259	−0.718635	−0.359318	+	0.933215i	$0.616991\pi$
$140$	4.75689	0.402031
$141$	−23.0477	−1.94096
$142$	−1.48175	−0.124346
$143$	11.9376	0.998272
$144$	2.72406	0.227005
$145$	10.5830	0.878867
$146$	−8.09022	−0.669551
$147$	−16.4509	−1.35685
$148$	4.42642	0.363849
$149$	−12.1670	−0.996758	−0.498379	−	0.866959i	$-0.666071\pi$
$149$	−12.1670	−0.996758	−0.498379	+	0.866959i	$0.666071\pi$
$150$	8.06099	0.658177
$151$	−16.4280	−1.33689	−0.668447	−	0.743760i	$-0.733040\pi$
$151$	−16.4280	−1.33689	−0.668447	+	0.743760i	$0.733040\pi$
$152$	7.92384	0.642708
$153$	−9.85690	−0.796883
$154$	21.2660	1.71367
$155$	0.491556	0.0394827
$156$	−5.00282	−0.400546
$157$	9.78684	0.781075	0.390537	−	0.920587i	$-0.372289\pi$
$157$	9.78684	0.781075	0.390537	+	0.920587i	$0.372289\pi$
$158$	−3.47393	−0.276371
$159$	16.2645	1.28986
$160$	1.27700	0.100956
$161$	2.45083	0.193152
$162$	−9.75168	−0.766164
$163$	2.86243	0.224203	0.112101	−	0.993697i	$-0.464242\pi$
$163$	2.86243	0.224203	0.112101	+	0.993697i	$0.464242\pi$
$164$	−0.620273	−0.0484352
$165$	−17.4420	−1.35786
$166$	−2.31114	−0.179379
$167$	−15.4030	−1.19192	−0.595960	−	0.803014i	$-0.703228\pi$
$167$	−15.4030	−1.19192	−0.595960	+	0.803014i	$0.703228\pi$
$168$	−8.91220	−0.687591
$169$	−8.62754	−0.663657
$170$	−4.62077	−0.354397
$171$	21.5850	1.65065
$172$	1.59179	0.121373
$173$	5.62302	0.427510	0.213755	−	0.976887i	$-0.431431\pi$
$173$	5.62302	0.427510	0.213755	+	0.976887i	$0.431431\pi$
$174$	−19.8275	−1.50312
$175$	−12.5507	−0.948746
$176$	5.70892	0.430326
$177$	20.3998	1.53334
$178$	2.26902	0.170070
$179$	−7.93544	−0.593123	−0.296561	−	0.955014i	$-0.595840\pi$
$179$	−7.93544	−0.593123	−0.296561	+	0.955014i	$0.595840\pi$
$180$	3.47862	0.259281
$181$	19.5495	1.45311	0.726553	−	0.687111i	$-0.241121\pi$
$181$	19.5495	1.45311	0.726553	+	0.687111i	$0.241121\pi$
$182$	7.78925	0.577378
$183$	−24.2845	−1.79517
$184$	0.657930	0.0485033
$185$	5.65253	0.415582
$186$	−0.920947	−0.0675271
$187$	−20.6575	−1.51062
$188$	9.63330	0.702581
$189$	2.45923	0.178882
$190$	10.1187	0.734090
$191$	5.06025	0.366147	0.183073	−	0.983099i	$-0.441395\pi$
$191$	5.06025	0.366147	0.183073	+	0.983099i	$0.441395\pi$
$192$	−2.39250	−0.172664
$193$	−20.6196	−1.48423	−0.742115	−	0.670273i	$-0.766177\pi$
$193$	−20.6196	−1.48423	−0.742115	+	0.670273i	$0.766177\pi$
$194$	−15.1111	−1.08491
$195$	−6.38860	−0.457497
$196$	6.87603	0.491145
$197$	6.16126	0.438971	0.219486	−	0.975616i	$-0.429562\pi$
$197$	6.16126	0.438971	0.219486	+	0.975616i	$0.429562\pi$
$198$	15.5514	1.10519
$199$	−20.5246	−1.45495	−0.727477	−	0.686132i	$-0.759307\pi$
$199$	−20.5246	−1.45495	−0.727477	+	0.686132i	$0.759307\pi$
$200$	−3.36927	−0.238244
$201$	−5.75760	−0.406110
$202$	2.50820	0.176476
$203$	30.8709	2.16671
$204$	8.65717	0.606123
$205$	−0.792088	−0.0553218
$206$	−10.5767	−0.736917
$207$	1.79224	0.124569
$208$	2.09104	0.144988
$209$	45.2366	3.12908
$210$	−11.3809	−0.785354
$211$	−2.32561	−0.160102	−0.0800509	−	0.996791i	$-0.525508\pi$
$211$	−2.32561	−0.160102	−0.0800509	+	0.996791i	$0.525508\pi$
$212$	−6.79811	−0.466896
$213$	3.54508	0.242905
$214$	16.3661	1.11877
$215$	2.03272	0.138630
$216$	0.660186	0.0449199
$217$	1.43389	0.0973387
$218$	−17.1222	−1.15966
$219$	19.3559	1.30795
$220$	7.29028	0.491511
$221$	−7.56635	−0.508968
$222$	−10.5902	−0.710768
$223$	4.23177	0.283380	0.141690	−	0.989911i	$-0.454746\pi$
$223$	4.23177	0.283380	0.141690	+	0.989911i	$0.454746\pi$
$224$	3.72505	0.248891
$225$	−9.17811	−0.611874
$226$	−10.5780	−0.703640
$227$	−5.60126	−0.371768	−0.185884	−	0.982572i	$-0.559515\pi$
$227$	−5.60126	−0.371768	−0.185884	+	0.982572i	$0.559515\pi$
$228$	−18.9578	−1.25551
$229$	−17.9761	−1.18790	−0.593948	−	0.804504i	$-0.702431\pi$
$229$	−17.9761	−1.18790	−0.593948	+	0.804504i	$0.702431\pi$
$230$	0.840176	0.0553996
$231$	−50.8790	−3.34759
$232$	8.28737	0.544092
$233$	−18.3706	−1.20350	−0.601750	−	0.798684i	$-0.705530\pi$
$233$	−18.3706	−1.20350	−0.601750	+	0.798684i	$0.705530\pi$
$234$	5.69613	0.372368
$235$	12.3017	0.802475
$236$	−8.52656	−0.555032
$237$	8.31138	0.539882
$238$	−13.4790	−0.873711
$239$	8.96537	0.579922	0.289961	−	0.957039i	$-0.406358\pi$
$239$	8.96537	0.579922	0.289961	+	0.957039i	$0.406358\pi$
$240$	−3.05522	−0.197214
$241$	9.57416	0.616726	0.308363	−	0.951269i	$-0.400219\pi$
$241$	9.57416	0.616726	0.308363	+	0.951269i	$0.400219\pi$
$242$	21.5918	1.38797
$243$	21.3503	1.36962
$244$	10.1503	0.649805
$245$	8.78068	0.560977
$246$	1.48400	0.0946166
$247$	16.5691	1.05427
$248$	0.384931	0.0244431
$249$	5.52940	0.350411
$250$	−10.6876	−0.675940
$251$	1.64720	0.103970	0.0519851	−	0.998648i	$-0.483445\pi$
$251$	1.64720	0.103970	0.0519851	+	0.998648i	$0.483445\pi$
$252$	10.1473	0.639218
$253$	3.75607	0.236142
$254$	−6.67493	−0.418822
$255$	11.0552	0.692303
$256$	1.00000	0.0625000
$257$	19.2633	1.20161	0.600805	−	0.799395i	$-0.294847\pi$
$257$	19.2633	1.20161	0.600805	+	0.799395i	$0.294847\pi$
$258$	−3.80836	−0.237098
$259$	16.4886	1.02455
$260$	2.67026	0.165602
$261$	22.5753	1.39738
$262$	8.89195	0.549347
$263$	−14.9341	−0.920877	−0.460438	−	0.887692i	$-0.652308\pi$
$263$	−14.9341	−0.920877	−0.460438	+	0.887692i	$0.652308\pi$
$264$	−13.6586	−0.840628
$265$	−8.68117	−0.533280
$266$	29.5167	1.80979
$267$	−5.42864	−0.332227
$268$	2.40652	0.147002
$269$	17.9977	1.09734	0.548669	−	0.836039i	$-0.315135\pi$
$269$	17.9977	1.09734	0.548669	+	0.836039i	$0.315135\pi$
$270$	0.843056	0.0513068
$271$	5.18649	0.315057	0.157528	−	0.987514i	$-0.449647\pi$
$271$	5.18649	0.315057	0.157528	+	0.987514i	$0.449647\pi$
$272$	−3.61846	−0.219401
$273$	−18.6358	−1.12789
$274$	−21.1507	−1.27776
$275$	−19.2349	−1.15991
$276$	−1.57410	−0.0947496
$277$	14.5674	0.875271	0.437636	−	0.899152i	$-0.355816\pi$
$277$	14.5674	0.875271	0.437636	+	0.899152i	$0.355816\pi$
$278$	−8.47259	−0.508152
$279$	1.04857	0.0627765
$280$	4.75689	0.284279
$281$	0.0182862	0.00109086	0.000545431	−	1.00000i	$-0.499826\pi$
$281$	0.0182862	0.00109086	0.000545431		1.00000i	$0.499826\pi$
$282$	−23.0477	−1.37247
$283$	17.0100	1.01114	0.505569	−	0.862786i	$-0.331283\pi$
$283$	17.0100	1.01114	0.505569	+	0.862786i	$0.331283\pi$
$284$	−1.48175	−0.0879255
$285$	−24.2091	−1.43402
$286$	11.9376	0.705885
$287$	−2.31055	−0.136387
$288$	2.72406	0.160517
$289$	−3.90676	−0.229809
$290$	10.5830	0.621453
$291$	36.1532	2.11934
$292$	−8.09022	−0.473444
$293$	−22.2830	−1.30178	−0.650892	−	0.759170i	$-0.725605\pi$
$293$	−22.2830	−1.30178	−0.650892	+	0.759170i	$0.725605\pi$
$294$	−16.4509	−0.959436
$295$	−10.8884	−0.633947
$296$	4.42642	0.257280
$297$	3.76895	0.218696
$298$	−12.1670	−0.704815
$299$	1.37576	0.0795623
$300$	8.06099	0.465402
$301$	5.92951	0.341771
$302$	−16.4280	−0.945326
$303$	−6.00086	−0.344741
$304$	7.92384	0.454463
$305$	12.9619	0.742196
$306$	−9.85690	−0.563481
$307$	−22.0570	−1.25886	−0.629429	−	0.777058i	$-0.716711\pi$
$307$	−22.0570	−1.25886	−0.629429	+	0.777058i	$0.716711\pi$
$308$	21.2660	1.21174
$309$	25.3049	1.43954
$310$	0.491556	0.0279185
$311$	25.3530	1.43764	0.718819	−	0.695197i	$-0.244683\pi$
$311$	25.3530	1.43764	0.718819	+	0.695197i	$0.244683\pi$
$312$	−5.00282	−0.283229
$313$	19.1017	1.07969	0.539846	−	0.841764i	$-0.318482\pi$
$313$	19.1017	1.07969	0.539846	+	0.841764i	$0.318482\pi$
$314$	9.78684	0.552303
$315$	12.9581	0.730104
$316$	−3.47393	−0.195424
$317$	9.43398	0.529865	0.264932	−	0.964267i	$-0.414650\pi$
$317$	9.43398	0.529865	0.264932	+	0.964267i	$0.414650\pi$
$318$	16.2645	0.912066
$319$	47.3119	2.64896
$320$	1.27700	0.0713864
$321$	−39.1560	−2.18547
$322$	2.45083	0.136579
$323$	−28.6721	−1.59536
$324$	−9.75168	−0.541760
$325$	−7.04530	−0.390803
$326$	2.86243	0.158535
$327$	40.9648	2.26536
$328$	−0.620273	−0.0342488
$329$	35.8846	1.97838
$330$	−17.4420	−0.960151
$331$	−9.74999	−0.535908	−0.267954	−	0.963432i	$-0.586348\pi$
$331$	−9.74999	−0.535908	−0.267954	+	0.963432i	$0.586348\pi$
$332$	−2.31114	−0.126840
$333$	12.0578	0.660765
$334$	−15.4030	−0.842815
$335$	3.07312	0.167903
$336$	−8.91220	−0.486200
$337$	−13.3092	−0.724999	−0.362500	−	0.931984i	$-0.618077\pi$
$337$	−13.3092	−0.724999	−0.362500	+	0.931984i	$0.618077\pi$
$338$	−8.62754	−0.469276
$339$	25.3079	1.37454
$340$	−4.62077	−0.250596
$341$	2.19754	0.119003
$342$	21.5850	1.16718
$343$	−0.461796	−0.0249346
$344$	1.59179	0.0858237
$345$	−2.01012	−0.108221
$346$	5.62302	0.302295
$347$	2.08092	0.111710	0.0558549	−	0.998439i	$-0.482212\pi$
$347$	2.08092	0.111710	0.0558549	+	0.998439i	$0.482212\pi$
$348$	−19.8275	−1.06287
$349$	−30.4313	−1.62895	−0.814474	−	0.580200i	$-0.802974\pi$
$349$	−30.4313	−1.62895	−0.814474	+	0.580200i	$0.802974\pi$
$350$	−12.5507	−0.670865
$351$	1.38048	0.0736844
$352$	5.70892	0.304286
$353$	13.6586	0.726976	0.363488	−	0.931599i	$-0.381586\pi$
$353$	13.6586	0.726976	0.363488	+	0.931599i	$0.381586\pi$
$354$	20.3998	1.08424
$355$	−1.89219	−0.100427
$356$	2.26902	0.120258
$357$	32.2484	1.70677
$358$	−7.93544	−0.419401
$359$	4.39473	0.231945	0.115973	−	0.993252i	$-0.463002\pi$
$359$	4.39473	0.231945	0.115973	+	0.993252i	$0.463002\pi$
$360$	3.47862	0.183339
$361$	43.7872	2.30459
$362$	19.5495	1.02750
$363$	−51.6583	−2.71136
$364$	7.78925	0.408268
$365$	−10.3312	−0.540760
$366$	−24.2845	−1.26937
$367$	−23.7517	−1.23983	−0.619914	−	0.784669i	$-0.712833\pi$
$367$	−23.7517	−1.23983	−0.619914	+	0.784669i	$0.712833\pi$
$368$	0.657930	0.0342970
$369$	−1.68966	−0.0879602
$370$	5.65253	0.293861
$371$	−25.3233	−1.31472
$372$	−0.920947	−0.0477489
$373$	−18.5517	−0.960568	−0.480284	−	0.877113i	$-0.659466\pi$
$373$	−18.5517	−0.960568	−0.480284	+	0.877113i	$0.659466\pi$
$374$	−20.6575	−1.06817
$375$	25.5700	1.32043
$376$	9.63330	0.496799
$377$	17.3292	0.892501
$378$	2.45923	0.126489
$379$	23.5187	1.20807	0.604037	−	0.796956i	$-0.293558\pi$
$379$	23.5187	1.20807	0.604037	+	0.796956i	$0.293558\pi$
$380$	10.1187	0.519080
$381$	15.9698	0.818156
$382$	5.06025	0.258905
$383$	−23.6221	−1.20703	−0.603515	−	0.797351i	$-0.706234\pi$
$383$	−23.6221	−1.20703	−0.603515	+	0.797351i	$0.706234\pi$
$384$	−2.39250	−0.122092
$385$	27.1567	1.38403
$386$	−20.6196	−1.04951
$387$	4.33614	0.220418
$388$	−15.1111	−0.767148
$389$	−11.6802	−0.592208	−0.296104	−	0.955156i	$-0.595687\pi$
$389$	−11.6802	−0.592208	−0.296104	+	0.955156i	$0.595687\pi$
$390$	−6.38860	−0.323499
$391$	−2.38069	−0.120397
$392$	6.87603	0.347292
$393$	−21.2740	−1.07313
$394$	6.16126	0.310400
$395$	−4.43621	−0.223210
$396$	15.5514	0.781489
$397$	15.7564	0.790791	0.395395	−	0.918511i	$-0.370608\pi$
$397$	15.7564	0.790791	0.395395	+	0.918511i	$0.370608\pi$
$398$	−20.5246	−1.02881
$399$	−70.6188	−3.53536
$400$	−3.36927	−0.168464
$401$	−7.26663	−0.362878	−0.181439	−	0.983402i	$-0.558075\pi$
$401$	−7.26663	−0.362878	−0.181439	+	0.983402i	$0.558075\pi$
$402$	−5.75760	−0.287163
$403$	0.804907	0.0400953
$404$	2.50820	0.124787
$405$	−12.4529	−0.618788
$406$	30.8709	1.53210
$407$	25.2701	1.25259
$408$	8.65717	0.428594
$409$	27.3993	1.35481	0.677403	−	0.735612i	$-0.263105\pi$
$409$	27.3993	1.35481	0.677403	+	0.735612i	$0.263105\pi$
$410$	−0.792088	−0.0391184
$411$	50.6030	2.49606
$412$	−10.5767	−0.521079
$413$	−31.7619	−1.56290
$414$	1.79224	0.0880839
$415$	−2.95132	−0.144875
$416$	2.09104	0.102522
$417$	20.2707	0.992659
$418$	45.2366	2.21259
$419$	6.53541	0.319276	0.159638	−	0.987176i	$-0.448967\pi$
$419$	6.53541	0.319276	0.159638	+	0.987176i	$0.448967\pi$
$420$	−11.3809	−0.555329
$421$	29.6671	1.44589	0.722944	−	0.690906i	$-0.242788\pi$
$421$	29.6671	1.44589	0.722944	+	0.690906i	$0.242788\pi$
$422$	−2.32561	−0.113209
$423$	26.2417	1.27591
$424$	−6.79811	−0.330145
$425$	12.1916	0.591378
$426$	3.54508	0.171760
$427$	37.8103	1.82977
$428$	16.3661	0.791087
$429$	−28.5607	−1.37892
$430$	2.03272	0.0980263
$431$	8.52420	0.410596	0.205298	−	0.978699i	$-0.434184\pi$
$431$	8.52420	0.410596	0.205298	+	0.978699i	$0.434184\pi$
$432$	0.660186	0.0317632
$433$	4.29661	0.206482	0.103241	−	0.994656i	$-0.467079\pi$
$433$	4.29661	0.206482	0.103241	+	0.994656i	$0.467079\pi$
$434$	1.43389	0.0688288
$435$	−25.3197	−1.21399
$436$	−17.1222	−0.820004
$437$	5.21333	0.249388
$438$	19.3559	0.924859
$439$	−1.49737	−0.0714658	−0.0357329	−	0.999361i	$-0.511377\pi$
$439$	−1.49737	−0.0714658	−0.0357329	+	0.999361i	$0.511377\pi$
$440$	7.29028	0.347551
$441$	18.7307	0.891939
$442$	−7.56635	−0.359895
$443$	21.0002	0.997750	0.498875	−	0.866674i	$-0.333747\pi$
$443$	21.0002	0.997750	0.498875	+	0.866674i	$0.333747\pi$
$444$	−10.5902	−0.502589
$445$	2.89754	0.137357
$446$	4.23177	0.200380
$447$	29.1095	1.37683
$448$	3.72505	0.175992
$449$	36.5879	1.72669	0.863346	−	0.504613i	$-0.168365\pi$
$449$	36.5879	1.72669	0.863346	+	0.504613i	$0.168365\pi$
$450$	−9.17811	−0.432660
$451$	−3.54109	−0.166743
$452$	−10.5780	−0.497548
$453$	39.3040	1.84667
$454$	−5.60126	−0.262880
$455$	9.94686	0.466316
$456$	−18.9578	−0.887780
$457$	−10.7943	−0.504935	−0.252468	−	0.967605i	$-0.581242\pi$
$457$	−10.7943	−0.504935	−0.252468	+	0.967605i	$0.581242\pi$
$458$	−17.9761	−0.839969
$459$	−2.38885	−0.111502
$460$	0.840176	0.0391734
$461$	33.6511	1.56729	0.783643	−	0.621211i	$-0.213359\pi$
$461$	33.6511	1.56729	0.783643	+	0.621211i	$0.213359\pi$
$462$	−50.8790	−2.36711
$463$	1.48531	0.0690281	0.0345140	−	0.999404i	$-0.489012\pi$
$463$	1.48531	0.0690281	0.0345140	+	0.999404i	$0.489012\pi$
$464$	8.28737	0.384731
$465$	−1.17605	−0.0545380
$466$	−18.3706	−0.851004
$467$	16.9757	0.785544	0.392772	−	0.919636i	$-0.371516\pi$
$467$	16.9757	0.785544	0.392772	+	0.919636i	$0.371516\pi$
$468$	5.69613	0.263304
$469$	8.96441	0.413938
$470$	12.3017	0.567436
$471$	−23.4150	−1.07891
$472$	−8.52656	−0.392467
$473$	9.08741	0.417840
$474$	8.31138	0.381755
$475$	−26.6976	−1.22497
$476$	−13.4790	−0.617807
$477$	−18.5185	−0.847902
$478$	8.96537	0.410066
$479$	3.03191	0.138532	0.0692658	−	0.997598i	$-0.477934\pi$
$479$	3.03191	0.138532	0.0692658	+	0.997598i	$0.477934\pi$
$480$	−3.05522	−0.139451
$481$	9.25583	0.422029
$482$	9.57416	0.436091
$483$	−5.86360	−0.266803
$484$	21.5918	0.981443
$485$	−19.2968	−0.876223
$486$	21.3503	0.968471
$487$	−32.7655	−1.48475	−0.742374	−	0.669986i	$-0.766300\pi$
$487$	−32.7655	−1.48475	−0.742374	+	0.669986i	$0.766300\pi$
$488$	10.1503	0.459481
$489$	−6.84837	−0.309694
$490$	8.78068	0.396671
$491$	−18.7709	−0.847119	−0.423559	−	0.905868i	$-0.639219\pi$
$491$	−18.7709	−0.847119	−0.423559	+	0.905868i	$0.639219\pi$
$492$	1.48400	0.0669040
$493$	−29.9875	−1.35057
$494$	16.5691	0.745479
$495$	19.8592	0.892603
$496$	0.384931	0.0172839
$497$	−5.51959	−0.247587
$498$	5.52940	0.247778
$499$	1.31359	0.0588046	0.0294023	−	0.999568i	$-0.490640\pi$
$499$	1.31359	0.0588046	0.0294023	+	0.999568i	$0.490640\pi$
$500$	−10.6876	−0.477962
$501$	36.8517	1.64641
$502$	1.64720	0.0735180
$503$	−6.95995	−0.310329	−0.155164	−	0.987889i	$-0.549591\pi$
$503$	−6.95995	−0.310329	−0.155164	+	0.987889i	$0.549591\pi$
$504$	10.1473	0.451995
$505$	3.20296	0.142530
$506$	3.75607	0.166978
$507$	20.6414	0.916717
$508$	−6.67493	−0.296152
$509$	−26.9033	−1.19247	−0.596234	−	0.802810i	$-0.703337\pi$
$509$	−26.9033	−1.19247	−0.596234	+	0.802810i	$0.703337\pi$
$510$	11.0552	0.489532
$511$	−30.1365	−1.33316
$512$	1.00000	0.0441942
$513$	5.23120	0.230963
$514$	19.2633	0.849667
$515$	−13.5065	−0.595167
$516$	−3.80836	−0.167654
$517$	54.9957	2.41871
$518$	16.4886	0.724469
$519$	−13.4531	−0.590524
$520$	2.67026	0.117099
$521$	−8.43800	−0.369676	−0.184838	−	0.982769i	$-0.559176\pi$
$521$	−8.43800	−0.369676	−0.184838	+	0.982769i	$0.559176\pi$
$522$	22.5753	0.988093
$523$	12.3508	0.540063	0.270032	−	0.962851i	$-0.412966\pi$
$523$	12.3508	0.540063	0.270032	+	0.962851i	$0.412966\pi$
$524$	8.89195	0.388447
$525$	30.0276	1.31051
$526$	−14.9341	−0.651158
$527$	−1.39286	−0.0606738
$528$	−13.6586	−0.594414
$529$	−22.5671	−0.981179
$530$	−8.68117	−0.377086
$531$	−23.2269	−1.00796
$532$	29.5167	1.27971
$533$	−1.29702	−0.0561800
$534$	−5.42864	−0.234920
$535$	20.8995	0.903565
$536$	2.40652	0.103946
$537$	18.9856	0.819287
$538$	17.9977	0.775936
$539$	39.2547	1.69082
$540$	0.843056	0.0362794
$541$	37.0156	1.59143	0.795713	−	0.605674i	$-0.207097\pi$
$541$	37.0156	1.59143	0.795713	+	0.605674i	$0.207097\pi$
$542$	5.18649	0.222779
$543$	−46.7723	−2.00719
$544$	−3.61846	−0.155140
$545$	−21.8650	−0.936594
$546$	−18.6358	−0.797538
$547$	−21.6608	−0.926151	−0.463076	−	0.886319i	$-0.653254\pi$
$547$	−21.6608	−0.926151	−0.463076	+	0.886319i	$0.653254\pi$
$548$	−21.1507	−0.903511
$549$	27.6500	1.18007
$550$	−19.2349	−0.820179
$551$	65.6678	2.79754
$552$	−1.57410	−0.0669981
$553$	−12.9406	−0.550290
$554$	14.5674	0.618910
$555$	−13.5237	−0.574048
$556$	−8.47259	−0.359318
$557$	22.4267	0.950250	0.475125	−	0.879918i	$-0.342403\pi$
$557$	22.4267	0.950250	0.475125	+	0.879918i	$0.342403\pi$
$558$	1.04857	0.0443897
$559$	3.32851	0.140781
$560$	4.75689	0.201015
$561$	49.4231	2.08664
$562$	0.0182862	0.000771356 0
$563$	−22.6831	−0.955980	−0.477990	−	0.878365i	$-0.658634\pi$
$563$	−22.6831	−0.955980	−0.477990	+	0.878365i	$0.658634\pi$
$564$	−23.0477	−0.970482
$565$	−13.5081	−0.568291
$566$	17.0100	0.714982
$567$	−36.3255	−1.52553
$568$	−1.48175	−0.0621728
$569$	33.4083	1.40055	0.700275	−	0.713873i	$-0.253061\pi$
$569$	33.4083	1.40055	0.700275	+	0.713873i	$0.253061\pi$
$570$	−24.2091	−1.01401
$571$	5.78608	0.242140	0.121070	−	0.992644i	$-0.461367\pi$
$571$	5.78608	0.242140	0.121070	+	0.992644i	$0.461367\pi$
$572$	11.9376	0.499136
$573$	−12.1067	−0.505763
$574$	−2.31055	−0.0964405
$575$	−2.21675	−0.0924448
$576$	2.72406	0.113503
$577$	5.34747	0.222618	0.111309	−	0.993786i	$-0.464496\pi$
$577$	5.34747	0.222618	0.111309	+	0.993786i	$0.464496\pi$
$578$	−3.90676	−0.162500
$579$	49.3323	2.05018
$580$	10.5830	0.439433
$581$	−8.60911	−0.357166
$582$	36.1532	1.49860
$583$	−38.8098	−1.60734
$584$	−8.09022	−0.334776
$585$	7.27395	0.300741
$586$	−22.2830	−0.920501
$587$	14.3606	0.592726	0.296363	−	0.955075i	$-0.404226\pi$
$587$	14.3606	0.592726	0.296363	+	0.955075i	$0.404226\pi$
$588$	−16.4509	−0.678424
$589$	3.05013	0.125678
$590$	−10.8884	−0.448268
$591$	−14.7408	−0.606356
$592$	4.42642	0.181925
$593$	38.5904	1.58472	0.792358	−	0.610056i	$-0.208853\pi$
$593$	38.5904	1.58472	0.792358	+	0.610056i	$0.208853\pi$
$594$	3.76895	0.154642
$595$	−17.2126	−0.705648
$596$	−12.1670	−0.498379
$597$	49.1052	2.00974
$598$	1.37576	0.0562590
$599$	0.427755	0.0174776	0.00873880	−	0.999962i	$-0.497218\pi$
$599$	0.427755	0.0174776	0.00873880	+	0.999962i	$0.497218\pi$
$600$	8.06099	0.329089
$601$	34.6955	1.41526	0.707630	−	0.706583i	$-0.249764\pi$
$601$	34.6955	1.41526	0.707630	+	0.706583i	$0.249764\pi$
$602$	5.92951	0.241669
$603$	6.55550	0.266961
$604$	−16.4280	−0.668447
$605$	27.5726	1.12099
$606$	−6.00086	−0.243768
$607$	6.04932	0.245534	0.122767	−	0.992435i	$-0.460823\pi$
$607$	6.04932	0.245534	0.122767	+	0.992435i	$0.460823\pi$
$608$	7.92384	0.321354
$609$	−73.8586	−2.99290
$610$	12.9619	0.524812
$611$	20.1436	0.814925
$612$	−9.85690	−0.398442
$613$	−28.2688	−1.14177	−0.570883	−	0.821031i	$-0.693399\pi$
$613$	−28.2688	−1.14177	−0.570883	+	0.821031i	$0.693399\pi$
$614$	−22.0570	−0.890147
$615$	1.89507	0.0764166
$616$	21.2660	0.856833
$617$	−14.9187	−0.600603	−0.300302	−	0.953844i	$-0.597087\pi$
$617$	−14.9187	−0.600603	−0.300302	+	0.953844i	$0.597087\pi$
$618$	25.3049	1.01791
$619$	−32.9734	−1.32531	−0.662656	−	0.748924i	$-0.730571\pi$
$619$	−32.9734	−1.32531	−0.662656	+	0.748924i	$0.730571\pi$
$620$	0.491556	0.0197414
$621$	0.434356	0.0174301
$622$	25.3530	1.01656
$623$	8.45223	0.338632
$624$	−5.00282	−0.200273
$625$	3.19838	0.127935
$626$	19.1017	0.763457
$627$	−108.228	−4.32223
$628$	9.78684	0.390537
$629$	−16.0168	−0.638632
$630$	12.9581	0.516261
$631$	0.432113	0.0172022	0.00860108	−	0.999963i	$-0.497262\pi$
$631$	0.432113	0.0172022	0.00860108	+	0.999963i	$0.497262\pi$
$632$	−3.47393	−0.138186
$633$	5.56403	0.221150
$634$	9.43398	0.374671
$635$	−8.52387	−0.338260
$636$	16.2645	0.644928
$637$	14.3781	0.569680
$638$	47.3119	1.87310
$639$	−4.03637	−0.159676
$640$	1.27700	0.0504778
$641$	6.88156	0.271805	0.135903	−	0.990722i	$-0.456607\pi$
$641$	6.88156	0.271805	0.135903	+	0.990722i	$0.456607\pi$
$642$	−39.1560	−1.54536
$643$	−20.8519	−0.822318	−0.411159	−	0.911564i	$-0.634876\pi$
$643$	−20.8519	−0.822318	−0.411159	+	0.911564i	$0.634876\pi$
$644$	2.45083	0.0965761
$645$	−4.86328	−0.191491
$646$	−28.6721	−1.12809
$647$	−46.4209	−1.82500	−0.912498	−	0.409082i	$-0.865849\pi$
$647$	−46.4209	−1.82500	−0.912498	+	0.409082i	$0.865849\pi$
$648$	−9.75168	−0.383082
$649$	−48.6774	−1.91076
$650$	−7.04530	−0.276339
$651$	−3.43058	−0.134455
$652$	2.86243	0.112101
$653$	−29.8425	−1.16783	−0.583913	−	0.811816i	$-0.698479\pi$
$653$	−29.8425	−1.16783	−0.583913	+	0.811816i	$0.698479\pi$
$654$	40.9648	1.60185
$655$	11.3550	0.443677
$656$	−0.620273	−0.0242176
$657$	−22.0382	−0.859794
$658$	35.8846	1.39893
$659$	−36.2363	−1.41157	−0.705784	−	0.708427i	$-0.749405\pi$
$659$	−36.2363	−1.41157	−0.705784	+	0.708427i	$0.749405\pi$
$660$	−17.4420	−0.678929
$661$	−35.5809	−1.38394	−0.691968	−	0.721928i	$-0.743256\pi$
$661$	−35.5809	−1.38394	−0.691968	+	0.721928i	$0.743256\pi$
$662$	−9.74999	−0.378944
$663$	18.1025	0.703043
$664$	−2.31114	−0.0896895
$665$	37.6928	1.46167
$666$	12.0578	0.467231
$667$	5.45251	0.211122
$668$	−15.4030	−0.595960
$669$	−10.1245	−0.391436
$670$	3.07312	0.118725
$671$	57.9471	2.23702
$672$	−8.91220	−0.343795
$673$	7.45739	0.287461	0.143731	−	0.989617i	$-0.454090\pi$
$673$	7.45739	0.287461	0.143731	+	0.989617i	$0.454090\pi$
$674$	−13.3092	−0.512652
$675$	−2.22435	−0.0856151
$676$	−8.62754	−0.331828
$677$	−11.1966	−0.430321	−0.215160	−	0.976579i	$-0.569027\pi$
$677$	−11.1966	−0.430321	−0.215160	+	0.976579i	$0.569027\pi$
$678$	25.3079	0.971945
$679$	−56.2895	−2.16019
$680$	−4.62077	−0.177198
$681$	13.4010	0.513528
$682$	2.19754	0.0841481
$683$	3.80792	0.145706	0.0728530	−	0.997343i	$-0.476790\pi$
$683$	3.80792	0.145706	0.0728530	+	0.997343i	$0.476790\pi$
$684$	21.5850	0.825324
$685$	−27.0094	−1.03197
$686$	−0.461796	−0.0176314
$687$	43.0079	1.64085
$688$	1.59179	0.0606865
$689$	−14.2151	−0.541553
$690$	−2.01012	−0.0765240
$691$	44.0358	1.67520	0.837600	−	0.546284i	$-0.183958\pi$
$691$	44.0358	1.67520	0.837600	+	0.546284i	$0.183958\pi$
$692$	5.62302	0.213755
$693$	57.9300	2.20058
$694$	2.08092	0.0789908
$695$	−10.8195	−0.410406
$696$	−19.8275	−0.751561
$697$	2.24443	0.0850139
$698$	−30.4313	−1.15184
$699$	43.9518	1.66241
$700$	−12.5507	−0.474373
$701$	18.8788	0.713041	0.356521	−	0.934287i	$-0.383963\pi$
$701$	18.8788	0.713041	0.356521	+	0.934287i	$0.383963\pi$
$702$	1.38048	0.0521027
$703$	35.0742	1.32285
$704$	5.70892	0.215163
$705$	−29.4319	−1.10847
$706$	13.6586	0.514049
$707$	9.34317	0.351386
$708$	20.3998	0.766671
$709$	−24.1516	−0.907032	−0.453516	−	0.891248i	$-0.649831\pi$
$709$	−24.1516	−0.907032	−0.453516	+	0.891248i	$0.649831\pi$
$710$	−1.89219	−0.0710126
$711$	−9.46320	−0.354898
$712$	2.26902	0.0850352
$713$	0.253258	0.00948457
$714$	32.2484	1.20687
$715$	15.2443	0.570104
$716$	−7.93544	−0.296561
$717$	−21.4497	−0.801052
$718$	4.39473	0.164010
$719$	21.1140	0.787421	0.393711	−	0.919234i	$-0.371191\pi$
$719$	21.1140	0.787421	0.393711	+	0.919234i	$0.371191\pi$
$720$	3.47862	0.129641
$721$	−39.3990	−1.46729
$722$	43.7872	1.62959
$723$	−22.9062	−0.851890
$724$	19.5495	0.726553
$725$	−27.9224	−1.03701
$726$	−51.6583	−1.91722
$727$	24.2416	0.899070	0.449535	−	0.893263i	$-0.351590\pi$
$727$	24.2416	0.899070	0.449535	+	0.893263i	$0.351590\pi$
$728$	7.78925	0.288689
$729$	−21.8257	−0.808358
$730$	−10.3312	−0.382375
$731$	−5.75983	−0.213035
$732$	−24.2845	−0.897583
$733$	13.2137	0.488060	0.244030	−	0.969768i	$-0.421530\pi$
$733$	13.2137	0.488060	0.244030	+	0.969768i	$0.421530\pi$
$734$	−23.7517	−0.876691
$735$	−21.0078	−0.774884
$736$	0.657930	0.0242516
$737$	13.7386	0.506069
$738$	−1.68966	−0.0621973
$739$	−6.91317	−0.254305	−0.127152	−	0.991883i	$-0.540584\pi$
$739$	−6.91317	−0.254305	−0.127152	+	0.991883i	$0.540584\pi$
$740$	5.65253	0.207791
$741$	−39.6416	−1.45627
$742$	−25.3233	−0.929648
$743$	−36.0162	−1.32131	−0.660654	−	0.750691i	$-0.729721\pi$
$743$	−36.0162	−1.32131	−0.660654	+	0.750691i	$0.729721\pi$
$744$	−0.920947	−0.0337636
$745$	−15.5372	−0.569240
$746$	−18.5517	−0.679224
$747$	−6.29568	−0.230347
$748$	−20.6575	−0.755312
$749$	60.9647	2.22760
$750$	25.5700	0.933684
$751$	21.0416	0.767818	0.383909	−	0.923371i	$-0.374578\pi$
$751$	21.0416	0.767818	0.383909	+	0.923371i	$0.374578\pi$
$752$	9.63330	0.351290
$753$	−3.94092	−0.143615
$754$	17.3292	0.631094
$755$	−20.9786	−0.763488
$756$	2.45923	0.0894412
$757$	21.8946	0.795773	0.397887	−	0.917435i	$-0.369744\pi$
$757$	21.8946	0.795773	0.397887	+	0.917435i	$0.369744\pi$
$758$	23.5187	0.854237
$759$	−8.98640	−0.326186
$760$	10.1187	0.367045
$761$	−28.7209	−1.04113	−0.520565	−	0.853822i	$-0.674279\pi$
$761$	−28.7209	−1.04113	−0.520565	+	0.853822i	$0.674279\pi$
$762$	15.9698	0.578524
$763$	−63.7810	−2.30903
$764$	5.06025	0.183073
$765$	−12.5872	−0.455093
$766$	−23.6221	−0.853500
$767$	−17.8294	−0.643782
$768$	−2.39250	−0.0863319
$769$	−19.2592	−0.694505	−0.347253	−	0.937772i	$-0.612885\pi$
$769$	−19.2592	−0.694505	−0.347253	+	0.937772i	$0.612885\pi$
$770$	27.1567	0.978659
$771$	−46.0874	−1.65980
$772$	−20.6196	−0.742115
$773$	46.9897	1.69010	0.845051	−	0.534686i	$-0.179570\pi$
$773$	46.9897	1.69010	0.845051	+	0.534686i	$0.179570\pi$
$774$	4.33614	0.155859
$775$	−1.29694	−0.0465874
$776$	−15.1111	−0.542455
$777$	−39.4491	−1.41523
$778$	−11.6802	−0.418754
$779$	−4.91494	−0.176096
$780$	−6.38860	−0.228748
$781$	−8.45918	−0.302693
$782$	−2.38069	−0.0851334
$783$	5.47120	0.195525
$784$	6.87603	0.245572
$785$	12.4978	0.446065
$786$	−21.2740	−0.758818
$787$	−9.38623	−0.334583	−0.167291	−	0.985907i	$-0.553502\pi$
$787$	−9.38623	−0.334583	−0.167291	+	0.985907i	$0.553502\pi$
$788$	6.16126	0.219486
$789$	35.7299	1.27202
$790$	−4.43621	−0.157833
$791$	−39.4037	−1.40103
$792$	15.5514	0.552596
$793$	21.2247	0.753710
$794$	15.7564	0.559174
$795$	20.7697	0.736626
$796$	−20.5246	−0.727477
$797$	16.1279	0.571278	0.285639	−	0.958337i	$-0.407794\pi$
$797$	16.1279	0.571278	0.285639	+	0.958337i	$0.407794\pi$
$798$	−70.6188	−2.49988
$799$	−34.8577	−1.23318
$800$	−3.36927	−0.119122
$801$	6.18096	0.218393
$802$	−7.26663	−0.256594
$803$	−46.1864	−1.62988
$804$	−5.75760	−0.203055
$805$	3.12970	0.110307
$806$	0.804907	0.0283516
$807$	−43.0595	−1.51577
$808$	2.50820	0.0882381
$809$	4.25675	0.149659	0.0748297	−	0.997196i	$-0.476159\pi$
$809$	4.25675	0.149659	0.0748297	+	0.997196i	$0.476159\pi$
$810$	−12.4529	−0.437550
$811$	−5.59211	−0.196366	−0.0981828	−	0.995168i	$-0.531303\pi$
$811$	−5.59211	−0.196366	−0.0981828	+	0.995168i	$0.531303\pi$
$812$	30.8709	1.08336
$813$	−12.4087	−0.435191
$814$	25.2701	0.885715
$815$	3.65532	0.128040
$816$	8.65717	0.303061
$817$	12.6131	0.441277
$818$	27.3993	0.957993
$819$	21.2184	0.741430
$820$	−0.792088	−0.0276609
$821$	37.8931	1.32248	0.661239	−	0.750176i	$-0.270031\pi$
$821$	37.8931	1.32248	0.661239	+	0.750176i	$0.270031\pi$
$822$	50.6030	1.76498
$823$	−15.3567	−0.535302	−0.267651	−	0.963516i	$-0.586247\pi$
$823$	−15.3567	−0.535302	−0.267651	+	0.963516i	$0.586247\pi$
$824$	−10.5767	−0.368459
$825$	46.0195	1.60219
$826$	−31.7619	−1.10514
$827$	18.9343	0.658411	0.329206	−	0.944258i	$-0.393219\pi$
$827$	18.9343	0.658411	0.329206	+	0.944258i	$0.393219\pi$
$828$	1.79224	0.0622847
$829$	12.2030	0.423829	0.211914	−	0.977288i	$-0.432030\pi$
$829$	12.2030	0.423829	0.211914	+	0.977288i	$0.432030\pi$
$830$	−2.95132	−0.102442
$831$	−34.8526	−1.20902
$832$	2.09104	0.0724939
$833$	−24.8806	−0.862063
$834$	20.2707	0.701916
$835$	−19.6696	−0.680695
$836$	45.2366	1.56454
$837$	0.254126	0.00878387
$838$	6.53541	0.225762
$839$	36.3343	1.25440	0.627199	−	0.778859i	$-0.284201\pi$
$839$	36.3343	1.25440	0.627199	+	0.778859i	$0.284201\pi$
$840$	−11.3809	−0.392677
$841$	39.6804	1.36829
$842$	29.6671	1.02240
$843$	−0.0437497	−0.00150682
$844$	−2.32561	−0.0800509
$845$	−11.0174	−0.379009
$846$	26.2417	0.902208
$847$	80.4304	2.76362
$848$	−6.79811	−0.233448
$849$	−40.6964	−1.39670
$850$	12.1916	0.418168
$851$	2.91227	0.0998315
$852$	3.54508	0.121453
$853$	41.1142	1.40772	0.703862	−	0.710337i	$-0.251457\pi$
$853$	41.1142	1.40772	0.703862	+	0.710337i	$0.251457\pi$
$854$	37.8103	1.29384
$855$	27.5640	0.942670
$856$	16.3661	0.559383
$857$	11.9937	0.409696	0.204848	−	0.978794i	$-0.434330\pi$
$857$	11.9937	0.409696	0.204848	+	0.978794i	$0.434330\pi$
$858$	−28.5607	−0.975046
$859$	−33.7761	−1.15242	−0.576212	−	0.817300i	$-0.695470\pi$
$859$	−33.7761	−1.15242	−0.576212	+	0.817300i	$0.695470\pi$
$860$	2.03272	0.0693150
$861$	5.52799	0.188393
$862$	8.52420	0.290335
$863$	−4.56010	−0.155228	−0.0776138	−	0.996984i	$-0.524730\pi$
$863$	−4.56010	−0.155228	−0.0776138	+	0.996984i	$0.524730\pi$
$864$	0.660186	0.0224600
$865$	7.18059	0.244147
$866$	4.29661	0.146005
$867$	9.34692	0.317438
$868$	1.43389	0.0486693
$869$	−19.8324	−0.672768
$870$	−25.3197	−0.858419
$871$	5.03213	0.170507
$872$	−17.1222	−0.579830
$873$	−41.1634	−1.39317
$874$	5.21333	0.176344
$875$	−39.8117	−1.34588
$876$	19.3559	0.653974
$877$	−37.1933	−1.25593	−0.627964	−	0.778242i	$-0.716111\pi$
$877$	−37.1933	−1.25593	−0.627964	+	0.778242i	$0.716111\pi$
$878$	−1.49737	−0.0505339
$879$	53.3120	1.79817
$880$	7.29028	0.245755
$881$	9.43038	0.317718	0.158859	−	0.987301i	$-0.449219\pi$
$881$	9.43038	0.317718	0.158859	+	0.987301i	$0.449219\pi$
$882$	18.7307	0.630696
$883$	−39.1804	−1.31853	−0.659263	−	0.751913i	$-0.729132\pi$
$883$	−39.1804	−1.31853	−0.659263	+	0.751913i	$0.729132\pi$
$884$	−7.56635	−0.254484
$885$	26.0505	0.875678
$886$	21.0002	0.705516
$887$	18.0403	0.605733	0.302867	−	0.953033i	$-0.402056\pi$
$887$	18.0403	0.605733	0.302867	+	0.953033i	$0.402056\pi$
$888$	−10.5902	−0.355384
$889$	−24.8645	−0.833927
$890$	2.89754	0.0971257
$891$	−55.6715	−1.86507
$892$	4.23177	0.141690
$893$	76.3327	2.55438
$894$	29.1095	0.973568
$895$	−10.1335	−0.338727
$896$	3.72505	0.124445
$897$	−3.29151	−0.109900
$898$	36.5879	1.22095
$899$	3.19006	0.106395
$900$	−9.17811	−0.305937
$901$	24.5987	0.819500
$902$	−3.54109	−0.117905
$903$	−14.1864	−0.472093
$904$	−10.5780	−0.351820
$905$	24.9647	0.829856
$906$	39.3040	1.30579
$907$	−17.0336	−0.565590	−0.282795	−	0.959180i	$-0.591262\pi$
$907$	−17.0336	−0.565590	−0.282795	+	0.959180i	$0.591262\pi$
$908$	−5.60126	−0.185884
$909$	6.83248	0.226619
$910$	9.94686	0.329735
$911$	−39.6628	−1.31409	−0.657044	−	0.753852i	$-0.728193\pi$
$911$	−39.6628	−1.31409	−0.657044	+	0.753852i	$0.728193\pi$
$912$	−18.9578	−0.627755
$913$	−13.1941	−0.436661
$914$	−10.7943	−0.357043
$915$	−31.0113	−1.02520
$916$	−17.9761	−0.593948
$917$	33.1230	1.09382
$918$	−2.38885	−0.0788439
$919$	17.3224	0.571414	0.285707	−	0.958317i	$-0.407772\pi$
$919$	17.3224	0.571414	0.285707	+	0.958317i	$0.407772\pi$
$920$	0.840176	0.0276998
$921$	52.7713	1.73887
$922$	33.6511	1.10824
$923$	−3.09840	−0.101985
$924$	−50.8790	−1.67380
$925$	−14.9138	−0.490363
$926$	1.48531	0.0488102
$927$	−28.8117	−0.946301
$928$	8.28737	0.272046
$929$	−48.9154	−1.60486	−0.802431	−	0.596745i	$-0.796460\pi$
$929$	−48.9154	−1.60486	−0.802431	+	0.596745i	$0.796460\pi$
$930$	−1.17605	−0.0385642
$931$	54.4846	1.78566
$932$	−18.3706	−0.601750
$933$	−60.6571	−1.98583
$934$	16.9757	0.555463
$935$	−26.3796	−0.862705
$936$	5.69613	0.186184
$937$	−42.8775	−1.40075	−0.700374	−	0.713776i	$-0.746983\pi$
$937$	−42.8775	−1.40075	−0.700374	+	0.713776i	$0.746983\pi$
$938$	8.96441	0.292698
$939$	−45.7008	−1.49139
$940$	12.3017	0.401238
$941$	−10.5642	−0.344385	−0.172192	−	0.985063i	$-0.555085\pi$
$941$	−10.5642	−0.344385	−0.172192	+	0.985063i	$0.555085\pi$
$942$	−23.4150	−0.762903
$943$	−0.408096	−0.0132894
$944$	−8.52656	−0.277516
$945$	3.14043	0.102158
$946$	9.08741	0.295457
$947$	−8.17742	−0.265730	−0.132865	−	0.991134i	$-0.542418\pi$
$947$	−8.17742	−0.265730	−0.132865	+	0.991134i	$0.542418\pi$
$948$	8.31138	0.269941
$949$	−16.9170	−0.549149
$950$	−26.6976	−0.866184
$951$	−22.5708	−0.731908
$952$	−13.4790	−0.436855
$953$	−37.1200	−1.20243	−0.601217	−	0.799086i	$-0.705317\pi$
$953$	−37.1200	−1.20243	−0.601217	+	0.799086i	$0.705317\pi$
$954$	−18.5185	−0.599557
$955$	6.46193	0.209103
$956$	8.96537	0.289961
$957$	−113.194	−3.65903
$958$	3.03191	0.0979566
$959$	−78.7874	−2.54418
$960$	−3.05522	−0.0986068
$961$	−30.8518	−0.995220
$962$	9.25583	0.298420
$963$	44.5823	1.43665
$964$	9.57416	0.308363
$965$	−26.3312	−0.847630
$966$	−5.86360	−0.188658
$967$	50.4070	1.62098	0.810490	−	0.585752i	$-0.199201\pi$
$967$	50.4070	1.62098	0.810490	+	0.585752i	$0.199201\pi$
$968$	21.5918	0.693985
$969$	68.5980	2.20368
$970$	−19.2968	−0.619583
$971$	−15.5488	−0.498984	−0.249492	−	0.968377i	$-0.580264\pi$
$971$	−15.5488	−0.498984	−0.249492	+	0.968377i	$0.580264\pi$
$972$	21.3503	0.684812
$973$	−31.5608	−1.01179
$974$	−32.7655	−1.04988
$975$	16.8559	0.539820
$976$	10.1503	0.324902
$977$	6.85145	0.219197	0.109599	−	0.993976i	$-0.465043\pi$
$977$	6.85145	0.219197	0.109599	+	0.993976i	$0.465043\pi$
$978$	−6.84837	−0.218987
$979$	12.9537	0.414001
$980$	8.78068	0.280489
$981$	−46.6418	−1.48916
$982$	−18.7709	−0.599003
$983$	19.0532	0.607704	0.303852	−	0.952719i	$-0.401727\pi$
$983$	19.0532	0.607704	0.303852	+	0.952719i	$0.401727\pi$
$984$	1.48400	0.0473083
$985$	7.86792	0.250693
$986$	−29.9875	−0.954996
$987$	−85.8538	−2.73276
$988$	16.5691	0.527133
$989$	1.04729	0.0333018
$990$	19.8592	0.631166
$991$	−22.0558	−0.700624	−0.350312	−	0.936633i	$-0.613924\pi$
$991$	−22.0558	−0.700624	−0.350312	+	0.936633i	$0.613924\pi$
$992$	0.384931	0.0122216
$993$	23.3269	0.740256
$994$	−5.51959	−0.175071
$995$	−26.2099	−0.830911
$996$	5.52940	0.175206
$997$	22.0136	0.697179	0.348589	−	0.937276i	$-0.386661\pi$
$997$	22.0136	0.697179	0.348589	+	0.937276i	$0.386661\pi$
$998$	1.31359	0.0415811
$999$	2.92226	0.0924561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.16	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.16	✓	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.39250 q^{3} +1.00000 q^{4} +1.27700 q^{5} -2.39250 q^{6} +3.72505 q^{7} +1.00000 q^{8} +2.72406 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.39250 q^{3} +1.00000 q^{4} +1.27700 q^{5} -2.39250 q^{6} +3.72505 q^{7} +1.00000 q^{8} +2.72406 q^{9} +1.27700 q^{10} +5.70892 q^{11} -2.39250 q^{12} +2.09104 q^{13} +3.72505 q^{14} -3.05522 q^{15} +1.00000 q^{16} -3.61846 q^{17} +2.72406 q^{18} +7.92384 q^{19} +1.27700 q^{20} -8.91220 q^{21} +5.70892 q^{22} +0.657930 q^{23} -2.39250 q^{24} -3.36927 q^{25} +2.09104 q^{26} +0.660186 q^{27} +3.72505 q^{28} +8.28737 q^{29} -3.05522 q^{30} +0.384931 q^{31} +1.00000 q^{32} -13.6586 q^{33} -3.61846 q^{34} +4.75689 q^{35} +2.72406 q^{36} +4.42642 q^{37} +7.92384 q^{38} -5.00282 q^{39} +1.27700 q^{40} -0.620273 q^{41} -8.91220 q^{42} +1.59179 q^{43} +5.70892 q^{44} +3.47862 q^{45} +0.657930 q^{46} +9.63330 q^{47} -2.39250 q^{48} +6.87603 q^{49} -3.36927 q^{50} +8.65717 q^{51} +2.09104 q^{52} -6.79811 q^{53} +0.660186 q^{54} +7.29028 q^{55} +3.72505 q^{56} -18.9578 q^{57} +8.28737 q^{58} -8.52656 q^{59} -3.05522 q^{60} +10.1503 q^{61} +0.384931 q^{62} +10.1473 q^{63} +1.00000 q^{64} +2.67026 q^{65} -13.6586 q^{66} +2.40652 q^{67} -3.61846 q^{68} -1.57410 q^{69} +4.75689 q^{70} -1.48175 q^{71} +2.72406 q^{72} -8.09022 q^{73} +4.42642 q^{74} +8.06099 q^{75} +7.92384 q^{76} +21.2660 q^{77} -5.00282 q^{78} -3.47393 q^{79} +1.27700 q^{80} -9.75168 q^{81} -0.620273 q^{82} -2.31114 q^{83} -8.91220 q^{84} -4.62077 q^{85} +1.59179 q^{86} -19.8275 q^{87} +5.70892 q^{88} +2.26902 q^{89} +3.47862 q^{90} +7.78925 q^{91} +0.657930 q^{92} -0.920947 q^{93} +9.63330 q^{94} +10.1187 q^{95} -2.39250 q^{96} -15.1111 q^{97} +6.87603 q^{98} +15.5514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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