LMFDB - Embedded newform 8026.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.32502 q^{3} +1.00000 q^{4} -1.28151 q^{5} -2.32502 q^{6} -2.20923 q^{7} +1.00000 q^{8} +2.40572 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.32502 q^{3} +1.00000 q^{4} -1.28151 q^{5} -2.32502 q^{6} -2.20923 q^{7} +1.00000 q^{8} +2.40572 q^{9} -1.28151 q^{10} +1.89130 q^{11} -2.32502 q^{12} -0.105749 q^{13} -2.20923 q^{14} +2.97953 q^{15} +1.00000 q^{16} -7.82433 q^{17} +2.40572 q^{18} +3.31047 q^{19} -1.28151 q^{20} +5.13651 q^{21} +1.89130 q^{22} +3.37818 q^{23} -2.32502 q^{24} -3.35774 q^{25} -0.105749 q^{26} +1.38171 q^{27} -2.20923 q^{28} +0.00110554 q^{29} +2.97953 q^{30} +4.61086 q^{31} +1.00000 q^{32} -4.39730 q^{33} -7.82433 q^{34} +2.83115 q^{35} +2.40572 q^{36} +4.57224 q^{37} +3.31047 q^{38} +0.245868 q^{39} -1.28151 q^{40} -4.12706 q^{41} +5.13651 q^{42} -10.6873 q^{43} +1.89130 q^{44} -3.08295 q^{45} +3.37818 q^{46} -2.24284 q^{47} -2.32502 q^{48} -2.11929 q^{49} -3.35774 q^{50} +18.1917 q^{51} -0.105749 q^{52} -12.6740 q^{53} +1.38171 q^{54} -2.42371 q^{55} -2.20923 q^{56} -7.69691 q^{57} +0.00110554 q^{58} -0.102501 q^{59} +2.97953 q^{60} -11.8065 q^{61} +4.61086 q^{62} -5.31480 q^{63} +1.00000 q^{64} +0.135518 q^{65} -4.39730 q^{66} -0.850749 q^{67} -7.82433 q^{68} -7.85435 q^{69} +2.83115 q^{70} -1.36761 q^{71} +2.40572 q^{72} +8.53068 q^{73} +4.57224 q^{74} +7.80682 q^{75} +3.31047 q^{76} -4.17831 q^{77} +0.245868 q^{78} -6.48194 q^{79} -1.28151 q^{80} -10.4297 q^{81} -4.12706 q^{82} +12.2280 q^{83} +5.13651 q^{84} +10.0269 q^{85} -10.6873 q^{86} -0.00257041 q^{87} +1.89130 q^{88} -0.818668 q^{89} -3.08295 q^{90} +0.233623 q^{91} +3.37818 q^{92} -10.7203 q^{93} -2.24284 q^{94} -4.24239 q^{95} -2.32502 q^{96} +16.1540 q^{97} -2.11929 q^{98} +4.54993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.32502	−1.34235	−0.671176	−	0.741298i	$-0.734210\pi$
$3$	−2.32502	−1.34235	−0.671176	+	0.741298i	$0.734210\pi$
$4$	1.00000	0.500000
$5$	−1.28151	−0.573107	−0.286554	−	0.958064i	$-0.592510\pi$
$5$	−1.28151	−0.573107	−0.286554	+	0.958064i	$0.592510\pi$
$6$	−2.32502	−0.949186
$7$	−2.20923	−0.835012	−0.417506	−	0.908674i	$-0.637096\pi$
$7$	−2.20923	−0.835012	−0.417506	+	0.908674i	$0.637096\pi$
$8$	1.00000	0.353553
$9$	2.40572	0.801907
$10$	−1.28151	−0.405248
$11$	1.89130	0.570247	0.285123	−	0.958491i	$-0.407965\pi$
$11$	1.89130	0.570247	0.285123	+	0.958491i	$0.407965\pi$
$12$	−2.32502	−0.671176
$13$	−0.105749	−0.0293294	−0.0146647	−	0.999892i	$-0.504668\pi$
$13$	−0.105749	−0.0293294	−0.0146647	+	0.999892i	$0.504668\pi$
$14$	−2.20923	−0.590442
$15$	2.97953	0.769311
$16$	1.00000	0.250000
$17$	−7.82433	−1.89768	−0.948839	−	0.315760i	$-0.897740\pi$
$17$	−7.82433	−1.89768	−0.948839	+	0.315760i	$0.897740\pi$
$18$	2.40572	0.567034
$19$	3.31047	0.759474	0.379737	−	0.925095i	$-0.376015\pi$
$19$	3.31047	0.759474	0.379737	+	0.925095i	$0.376015\pi$
$20$	−1.28151	−0.286554
$21$	5.13651	1.12088
$22$	1.89130	0.403225
$23$	3.37818	0.704400	0.352200	−	0.935925i	$-0.385434\pi$
$23$	3.37818	0.704400	0.352200	+	0.935925i	$0.385434\pi$
$24$	−2.32502	−0.474593
$25$	−3.35774	−0.671548
$26$	−0.105749	−0.0207390
$27$	1.38171	0.265910
$28$	−2.20923	−0.417506
$29$	0.00110554	0.000205294 0	0.000102647	−	1.00000i	$-0.499967\pi$
$29$	0.00110554	0.000205294 0	0.000102647		1.00000i	$0.499967\pi$
$30$	2.97953	0.543985
$31$	4.61086	0.828134	0.414067	−	0.910246i	$-0.364108\pi$
$31$	4.61086	0.828134	0.414067	+	0.910246i	$0.364108\pi$
$32$	1.00000	0.176777
$33$	−4.39730	−0.765472
$34$	−7.82433	−1.34186
$35$	2.83115	0.478551
$36$	2.40572	0.400954
$37$	4.57224	0.751671	0.375836	−	0.926686i	$-0.377356\pi$
$37$	4.57224	0.751671	0.375836	+	0.926686i	$0.377356\pi$
$38$	3.31047	0.537029
$39$	0.245868	0.0393704
$40$	−1.28151	−0.202624
$41$	−4.12706	−0.644539	−0.322269	−	0.946648i	$-0.604446\pi$
$41$	−4.12706	−0.644539	−0.322269	+	0.946648i	$0.604446\pi$
$42$	5.13651	0.792581
$43$	−10.6873	−1.62979	−0.814895	−	0.579608i	$-0.803206\pi$
$43$	−10.6873	−1.62979	−0.814895	+	0.579608i	$0.803206\pi$
$44$	1.89130	0.285123
$45$	−3.08295	−0.459579
$46$	3.37818	0.498086
$47$	−2.24284	−0.327152	−0.163576	−	0.986531i	$-0.552303\pi$
$47$	−2.24284	−0.327152	−0.163576	+	0.986531i	$0.552303\pi$
$48$	−2.32502	−0.335588
$49$	−2.11929	−0.302756
$50$	−3.35774	−0.474856
$51$	18.1917	2.54735
$52$	−0.105749	−0.0146647
$53$	−12.6740	−1.74091	−0.870457	−	0.492245i	$-0.836176\pi$
$53$	−12.6740	−1.74091	−0.870457	+	0.492245i	$0.836176\pi$
$54$	1.38171	0.188027
$55$	−2.42371	−0.326813
$56$	−2.20923	−0.295221
$57$	−7.69691	−1.01948
$58$	0.00110554	0.000145165 0
$59$	−0.102501	−0.0133446	−0.00667228	−	0.999978i	$-0.502124\pi$
$59$	−0.102501	−0.0133446	−0.00667228	+	0.999978i	$0.502124\pi$
$60$	2.97953	0.384656
$61$	−11.8065	−1.51167	−0.755836	−	0.654761i	$-0.772769\pi$
$61$	−11.8065	−1.51167	−0.755836	+	0.654761i	$0.772769\pi$
$62$	4.61086	0.585580
$63$	−5.31480	−0.669602
$64$	1.00000	0.125000
$65$	0.135518	0.0168089
$66$	−4.39730	−0.541270
$67$	−0.850749	−0.103936	−0.0519678	−	0.998649i	$-0.516549\pi$
$67$	−0.850749	−0.103936	−0.0519678	+	0.998649i	$0.516549\pi$
$68$	−7.82433	−0.948839
$69$	−7.85435	−0.945552
$70$	2.83115	0.338387
$71$	−1.36761	−0.162306	−0.0811529	−	0.996702i	$-0.525860\pi$
$71$	−1.36761	−0.162306	−0.0811529	+	0.996702i	$0.525860\pi$
$72$	2.40572	0.283517
$73$	8.53068	0.998440	0.499220	−	0.866475i	$-0.333620\pi$
$73$	8.53068	0.998440	0.499220	+	0.866475i	$0.333620\pi$
$74$	4.57224	0.531512
$75$	7.80682	0.901453
$76$	3.31047	0.379737
$77$	−4.17831	−0.476163
$78$	0.245868	0.0278391
$79$	−6.48194	−0.729276	−0.364638	−	0.931149i	$-0.618807\pi$
$79$	−6.48194	−0.729276	−0.364638	+	0.931149i	$0.618807\pi$
$80$	−1.28151	−0.143277
$81$	−10.4297	−1.15885
$82$	−4.12706	−0.455758
$83$	12.2280	1.34219	0.671096	−	0.741370i	$-0.265824\pi$
$83$	12.2280	1.34219	0.671096	+	0.741370i	$0.265824\pi$
$84$	5.13651	0.560440
$85$	10.0269	1.08757
$86$	−10.6873	−1.15244
$87$	−0.00257041	−0.000275577 0
$88$	1.89130	0.201613
$89$	−0.818668	−0.0867786	−0.0433893	−	0.999058i	$-0.513816\pi$
$89$	−0.818668	−0.0867786	−0.0433893	+	0.999058i	$0.513816\pi$
$90$	−3.08295	−0.324971
$91$	0.233623	0.0244904
$92$	3.37818	0.352200
$93$	−10.7203	−1.11165
$94$	−2.24284	−0.231331
$95$	−4.24239	−0.435260
$96$	−2.32502	−0.237296
$97$	16.1540	1.64019	0.820097	−	0.572225i	$-0.193919\pi$
$97$	16.1540	1.64019	0.820097	+	0.572225i	$0.193919\pi$
$98$	−2.11929	−0.214081
$99$	4.54993	0.457285
$100$	−3.35774	−0.335774
$101$	19.7579	1.96598	0.982992	−	0.183649i	$-0.0587911\pi$
$101$	19.7579	1.96598	0.982992	+	0.183649i	$0.0587911\pi$
$102$	18.1917	1.80125
$103$	−10.8168	−1.06581	−0.532907	−	0.846174i	$-0.678901\pi$
$103$	−10.8168	−1.06581	−0.532907	+	0.846174i	$0.678901\pi$
$104$	−0.105749	−0.0103695
$105$	−6.58248	−0.642384
$106$	−12.6740	−1.23101
$107$	−15.7864	−1.52613	−0.763067	−	0.646320i	$-0.776307\pi$
$107$	−15.7864	−1.52613	−0.763067	+	0.646320i	$0.776307\pi$
$108$	1.38171	0.132955
$109$	7.99386	0.765673	0.382836	−	0.923816i	$-0.374947\pi$
$109$	7.99386	0.765673	0.382836	+	0.923816i	$0.374947\pi$
$110$	−2.42371	−0.231091
$111$	−10.6305	−1.00901
$112$	−2.20923	−0.208753
$113$	7.49357	0.704936	0.352468	−	0.935824i	$-0.385343\pi$
$113$	7.49357	0.704936	0.352468	+	0.935824i	$0.385343\pi$
$114$	−7.69691	−0.720882
$115$	−4.32917	−0.403697
$116$	0.00110554	0.000102647 0
$117$	−0.254402	−0.0235195
$118$	−0.102501	−0.00943603
$119$	17.2858	1.58458
$120$	2.97953	0.271993
$121$	−7.42300	−0.674818
$122$	−11.8065	−1.06891
$123$	9.59550	0.865197
$124$	4.61086	0.414067
$125$	10.7105	0.957976
$126$	−5.31480	−0.473480
$127$	−8.85975	−0.786176	−0.393088	−	0.919501i	$-0.628593\pi$
$127$	−8.85975	−0.786176	−0.393088	+	0.919501i	$0.628593\pi$
$128$	1.00000	0.0883883
$129$	24.8481	2.18775
$130$	0.135518	0.0118857
$131$	16.6348	1.45339	0.726697	−	0.686958i	$-0.241055\pi$
$131$	16.6348	1.45339	0.726697	+	0.686958i	$0.241055\pi$
$132$	−4.39730	−0.382736
$133$	−7.31360	−0.634169
$134$	−0.850749	−0.0734935
$135$	−1.77067	−0.152395
$136$	−7.82433	−0.670930
$137$	6.42355	0.548801	0.274401	−	0.961615i	$-0.411521\pi$
$137$	6.42355	0.548801	0.274401	+	0.961615i	$0.411521\pi$
$138$	−7.85435	−0.668607
$139$	16.6002	1.40801	0.704007	−	0.710193i	$-0.251392\pi$
$139$	16.6002	1.40801	0.704007	+	0.710193i	$0.251392\pi$
$140$	2.83115	0.239276
$141$	5.21465	0.439153
$142$	−1.36761	−0.114767
$143$	−0.200002	−0.0167250
$144$	2.40572	0.200477
$145$	−0.00141676	−0.000117656 0
$146$	8.53068	0.706004
$147$	4.92739	0.406404
$148$	4.57224	0.375836
$149$	5.93263	0.486020	0.243010	−	0.970024i	$-0.421865\pi$
$149$	5.93263	0.486020	0.243010	+	0.970024i	$0.421865\pi$
$150$	7.80682	0.637424
$151$	2.02334	0.164657	0.0823286	−	0.996605i	$-0.473764\pi$
$151$	2.02334	0.164657	0.0823286	+	0.996605i	$0.473764\pi$
$152$	3.31047	0.268515
$153$	−18.8232	−1.52176
$154$	−4.17831	−0.336698
$155$	−5.90885	−0.474610
$156$	0.245868	0.0196852
$157$	7.31397	0.583718	0.291859	−	0.956461i	$-0.405726\pi$
$157$	7.31397	0.583718	0.291859	+	0.956461i	$0.405726\pi$
$158$	−6.48194	−0.515676
$159$	29.4674	2.33692
$160$	−1.28151	−0.101312
$161$	−7.46320	−0.588182
$162$	−10.4297	−0.819432
$163$	6.68151	0.523336	0.261668	−	0.965158i	$-0.415727\pi$
$163$	6.68151	0.523336	0.261668	+	0.965158i	$0.415727\pi$
$164$	−4.12706	−0.322269
$165$	5.63517	0.438697
$166$	12.2280	0.949073
$167$	−6.68624	−0.517397	−0.258698	−	0.965958i	$-0.583294\pi$
$167$	−6.68624	−0.517397	−0.258698	+	0.965958i	$0.583294\pi$
$168$	5.13651	0.396291
$169$	−12.9888	−0.999140
$170$	10.0269	0.769030
$171$	7.96407	0.609028
$172$	−10.6873	−0.814895
$173$	−15.7371	−1.19647	−0.598234	−	0.801321i	$-0.704131\pi$
$173$	−15.7371	−1.19647	−0.598234	+	0.801321i	$0.704131\pi$
$174$	−0.00257041	−0.000194862 0
$175$	7.41803	0.560750
$176$	1.89130	0.142562
$177$	0.238318	0.0179131
$178$	−0.818668	−0.0613617
$179$	−1.17086	−0.0875138	−0.0437569	−	0.999042i	$-0.513933\pi$
$179$	−1.17086	−0.0875138	−0.0437569	+	0.999042i	$0.513933\pi$
$180$	−3.08295	−0.229789
$181$	−1.91296	−0.142189	−0.0710947	−	0.997470i	$-0.522649\pi$
$181$	−1.91296	−0.142189	−0.0710947	+	0.997470i	$0.522649\pi$
$182$	0.233623	0.0173173
$183$	27.4504	2.02919
$184$	3.37818	0.249043
$185$	−5.85936	−0.430788
$186$	−10.7203	−0.786053
$187$	−14.7981	−1.08215
$188$	−2.24284	−0.163576
$189$	−3.05252	−0.222038
$190$	−4.24239	−0.307775
$191$	9.94861	0.719856	0.359928	−	0.932980i	$-0.382801\pi$
$191$	9.94861	0.719856	0.359928	+	0.932980i	$0.382801\pi$
$192$	−2.32502	−0.167794
$193$	−16.8958	−1.21619	−0.608094	−	0.793865i	$-0.708066\pi$
$193$	−16.8958	−1.21619	−0.608094	+	0.793865i	$0.708066\pi$
$194$	16.1540	1.15979
$195$	−0.315081	−0.0225634
$196$	−2.11929	−0.151378
$197$	20.3177	1.44757	0.723787	−	0.690023i	$-0.242400\pi$
$197$	20.3177	1.44757	0.723787	+	0.690023i	$0.242400\pi$
$198$	4.54993	0.323349
$199$	23.8025	1.68731	0.843656	−	0.536884i	$-0.180399\pi$
$199$	23.8025	1.68731	0.843656	+	0.536884i	$0.180399\pi$
$200$	−3.35774	−0.237428
$201$	1.97801	0.139518
$202$	19.7579	1.39016
$203$	−0.00244240	−0.000171423 0
$204$	18.1917	1.27368
$205$	5.28886	0.369390
$206$	−10.8168	−0.753645
$207$	8.12697	0.564864
$208$	−0.105749	−0.00733235
$209$	6.26107	0.433088
$210$	−6.58248	−0.454234
$211$	0.937998	0.0645745	0.0322872	−	0.999479i	$-0.489721\pi$
$211$	0.937998	0.0645745	0.0322872	+	0.999479i	$0.489721\pi$
$212$	−12.6740	−0.870457
$213$	3.17973	0.217871
$214$	−15.7864	−1.07914
$215$	13.6958	0.934045
$216$	1.38171	0.0940134
$217$	−10.1865	−0.691502
$218$	7.99386	0.541412
$219$	−19.8340	−1.34026
$220$	−2.42371	−0.163406
$221$	0.827412	0.0556578
$222$	−10.6305	−0.713476
$223$	−11.8497	−0.793515	−0.396758	−	0.917923i	$-0.629865\pi$
$223$	−11.8497	−0.793515	−0.396758	+	0.917923i	$0.629865\pi$
$224$	−2.20923	−0.147611
$225$	−8.07779	−0.538519
$226$	7.49357	0.498465
$227$	−18.9488	−1.25767	−0.628837	−	0.777537i	$-0.716469\pi$
$227$	−18.9488	−1.25767	−0.628837	+	0.777537i	$0.716469\pi$
$228$	−7.69691	−0.509740
$229$	13.0838	0.864603	0.432302	−	0.901729i	$-0.357702\pi$
$229$	13.0838	0.864603	0.432302	+	0.901729i	$0.357702\pi$
$230$	−4.32917	−0.285457
$231$	9.71466	0.639178
$232$	0.00110554	7.25824e−5 0
$233$	−7.23408	−0.473920	−0.236960	−	0.971519i	$-0.576151\pi$
$233$	−7.23408	−0.473920	−0.236960	+	0.971519i	$0.576151\pi$
$234$	−0.254402	−0.0166308
$235$	2.87421	0.187493
$236$	−0.102501	−0.00667228
$237$	15.0707	0.978944
$238$	17.2858	1.12047
$239$	−15.2448	−0.986107	−0.493053	−	0.869999i	$-0.664119\pi$
$239$	−15.2448	−0.986107	−0.493053	+	0.869999i	$0.664119\pi$
$240$	2.97953	0.192328
$241$	14.8005	0.953387	0.476693	−	0.879070i	$-0.341835\pi$
$241$	14.8005	0.953387	0.476693	+	0.879070i	$0.341835\pi$
$242$	−7.42300	−0.477169
$243$	20.1041	1.28968
$244$	−11.8065	−0.755836
$245$	2.71588	0.173511
$246$	9.59550	0.611787
$247$	−0.350078	−0.0222749
$248$	4.61086	0.292790
$249$	−28.4302	−1.80169
$250$	10.7105	0.677392
$251$	6.39131	0.403416	0.201708	−	0.979446i	$-0.435351\pi$
$251$	6.39131	0.403416	0.201708	+	0.979446i	$0.435351\pi$
$252$	−5.31480	−0.334801
$253$	6.38914	0.401682
$254$	−8.85975	−0.555910
$255$	−23.3128	−1.45991
$256$	1.00000	0.0625000
$257$	20.3482	1.26929	0.634643	−	0.772806i	$-0.281147\pi$
$257$	20.3482	1.26929	0.634643	+	0.772806i	$0.281147\pi$
$258$	24.8481	1.54697
$259$	−10.1011	−0.627654
$260$	0.135518	0.00840445
$261$	0.00265963	0.000164627 0
$262$	16.6348	1.02770
$263$	19.9997	1.23323	0.616617	−	0.787263i	$-0.288503\pi$
$263$	19.9997	1.23323	0.616617	+	0.787263i	$0.288503\pi$
$264$	−4.39730	−0.270635
$265$	16.2419	0.997730
$266$	−7.31360	−0.448426
$267$	1.90342	0.116487
$268$	−0.850749	−0.0519678
$269$	22.9930	1.40191	0.700955	−	0.713205i	$-0.252757\pi$
$269$	22.9930	1.40191	0.700955	+	0.713205i	$0.252757\pi$
$270$	−1.77067	−0.107760
$271$	−11.1366	−0.676503	−0.338252	−	0.941056i	$-0.609836\pi$
$271$	−11.1366	−0.676503	−0.338252	+	0.941056i	$0.609836\pi$
$272$	−7.82433	−0.474419
$273$	−0.543179	−0.0328747
$274$	6.42355	0.388061
$275$	−6.35048	−0.382948
$276$	−7.85435	−0.472776
$277$	−15.3145	−0.920159	−0.460079	−	0.887878i	$-0.652179\pi$
$277$	−15.3145	−0.920159	−0.460079	+	0.887878i	$0.652179\pi$
$278$	16.6002	0.995617
$279$	11.0924	0.664087
$280$	2.83115	0.169193
$281$	−13.5182	−0.806427	−0.403214	−	0.915106i	$-0.632107\pi$
$281$	−13.5182	−0.806427	−0.403214	+	0.915106i	$0.632107\pi$
$282$	5.21465	0.310528
$283$	6.83915	0.406545	0.203273	−	0.979122i	$-0.434842\pi$
$283$	6.83915	0.406545	0.203273	+	0.979122i	$0.434842\pi$
$284$	−1.36761	−0.0811529
$285$	9.86364	0.584272
$286$	−0.200002	−0.0118264
$287$	9.11764	0.538197
$288$	2.40572	0.141759
$289$	44.2201	2.60118
$290$	−0.00141676	−8.31951e−5 0
$291$	−37.5585	−2.20172
$292$	8.53068	0.499220
$293$	28.0638	1.63951	0.819753	−	0.572718i	$-0.194111\pi$
$293$	28.0638	1.63951	0.819753	+	0.572718i	$0.194111\pi$
$294$	4.92739	0.287371
$295$	0.131356	0.00764786
$296$	4.57224	0.265756
$297$	2.61322	0.151634
$298$	5.93263	0.343668
$299$	−0.357239	−0.0206596
$300$	7.80682	0.450727
$301$	23.6106	1.36089
$302$	2.02334	0.116430
$303$	−45.9375	−2.63904
$304$	3.31047	0.189868
$305$	15.1301	0.866350
$306$	−18.8232	−1.07605
$307$	−13.8903	−0.792763	−0.396381	−	0.918086i	$-0.629734\pi$
$307$	−13.8903	−0.792763	−0.396381	+	0.918086i	$0.629734\pi$
$308$	−4.17831	−0.238081
$309$	25.1494	1.43070
$310$	−5.90885	−0.335600
$311$	−20.5660	−1.16619	−0.583095	−	0.812404i	$-0.698158\pi$
$311$	−20.5660	−1.16619	−0.583095	+	0.812404i	$0.698158\pi$
$312$	0.245868	0.0139195
$313$	10.0673	0.569039	0.284520	−	0.958670i	$-0.408166\pi$
$313$	10.0673	0.569039	0.284520	+	0.958670i	$0.408166\pi$
$314$	7.31397	0.412751
$315$	6.81095	0.383754
$316$	−6.48194	−0.364638
$317$	11.3074	0.635085	0.317543	−	0.948244i	$-0.397142\pi$
$317$	11.3074	0.635085	0.317543	+	0.948244i	$0.397142\pi$
$318$	29.4674	1.65245
$319$	0.00209091	0.000117068 0
$320$	−1.28151	−0.0716384
$321$	36.7038	2.04861
$322$	−7.46320	−0.415908
$323$	−25.9022	−1.44124
$324$	−10.4297	−0.579426
$325$	0.355077	0.0196961
$326$	6.68151	0.370054
$327$	−18.5859	−1.02780
$328$	−4.12706	−0.227879
$329$	4.95496	0.273176
$330$	5.63517	0.310206
$331$	18.8633	1.03682	0.518411	−	0.855132i	$-0.326524\pi$
$331$	18.8633	1.03682	0.518411	+	0.855132i	$0.326524\pi$
$332$	12.2280	0.671096
$333$	10.9995	0.602771
$334$	−6.68624	−0.365855
$335$	1.09024	0.0595662
$336$	5.13651	0.280220
$337$	−1.35953	−0.0740583	−0.0370292	−	0.999314i	$-0.511789\pi$
$337$	−1.35953	−0.0740583	−0.0370292	+	0.999314i	$0.511789\pi$
$338$	−12.9888	−0.706499
$339$	−17.4227	−0.946271
$340$	10.0269	0.543787
$341$	8.72049	0.472241
$342$	7.96407	0.430648
$343$	20.1466	1.08782
$344$	−10.6873	−0.576218
$345$	10.0654	0.541903
$346$	−15.7371	−0.846031
$347$	9.84021	0.528250	0.264125	−	0.964488i	$-0.414917\pi$
$347$	9.84021	0.528250	0.264125	+	0.964488i	$0.414917\pi$
$348$	−0.00257041	−0.000137788 0
$349$	−26.1353	−1.39899	−0.699494	−	0.714638i	$-0.746591\pi$
$349$	−26.1353	−1.39899	−0.699494	+	0.714638i	$0.746591\pi$
$350$	7.41803	0.396510
$351$	−0.146114	−0.00779898
$352$	1.89130	0.100806
$353$	19.1479	1.01914	0.509569	−	0.860430i	$-0.329805\pi$
$353$	19.1479	1.01914	0.509569	+	0.860430i	$0.329805\pi$
$354$	0.238318	0.0126665
$355$	1.75260	0.0930186
$356$	−0.818668	−0.0433893
$357$	−40.1898	−2.12707
$358$	−1.17086	−0.0618816
$359$	−10.6771	−0.563513	−0.281757	−	0.959486i	$-0.590917\pi$
$359$	−10.6771	−0.563513	−0.281757	+	0.959486i	$0.590917\pi$
$360$	−3.08295	−0.162486
$361$	−8.04079	−0.423200
$362$	−1.91296	−0.100543
$363$	17.2586	0.905843
$364$	0.233623	0.0122452
$365$	−10.9321	−0.572213
$366$	27.4504	1.43486
$367$	−33.5960	−1.75370	−0.876848	−	0.480768i	$-0.840358\pi$
$367$	−33.5960	−1.75370	−0.876848	+	0.480768i	$0.840358\pi$
$368$	3.37818	0.176100
$369$	−9.92856	−0.516860
$370$	−5.85936	−0.304613
$371$	27.9999	1.45368
$372$	−10.7203	−0.555824
$373$	36.1669	1.87265	0.936324	−	0.351136i	$-0.114205\pi$
$373$	36.1669	1.87265	0.936324	+	0.351136i	$0.114205\pi$
$374$	−14.7981	−0.765192
$375$	−24.9021	−1.28594
$376$	−2.24284	−0.115666
$377$	−0.000116910 0	−6.02116e−6 0
$378$	−3.05252	−0.157005
$379$	−13.7001	−0.703726	−0.351863	−	0.936051i	$-0.614452\pi$
$379$	−13.7001	−0.703726	−0.351863	+	0.936051i	$0.614452\pi$
$380$	−4.24239	−0.217630
$381$	20.5991	1.05532
$382$	9.94861	0.509015
$383$	12.0694	0.616720	0.308360	−	0.951270i	$-0.400220\pi$
$383$	12.0694	0.616720	0.308360	+	0.951270i	$0.400220\pi$
$384$	−2.32502	−0.118648
$385$	5.35454	0.272892
$386$	−16.8958	−0.859975
$387$	−25.7106	−1.30694
$388$	16.1540	0.820097
$389$	−11.8532	−0.600982	−0.300491	−	0.953785i	$-0.597151\pi$
$389$	−11.8532	−0.600982	−0.300491	+	0.953785i	$0.597151\pi$
$390$	−0.315081	−0.0159548
$391$	−26.4320	−1.33672
$392$	−2.11929	−0.107040
$393$	−38.6764	−1.95096
$394$	20.3177	1.02359
$395$	8.30665	0.417953
$396$	4.54993	0.228643
$397$	7.44679	0.373744	0.186872	−	0.982384i	$-0.440165\pi$
$397$	7.44679	0.373744	0.186872	+	0.982384i	$0.440165\pi$
$398$	23.8025	1.19311
$399$	17.0043	0.851278
$400$	−3.35774	−0.167887
$401$	6.04663	0.301954	0.150977	−	0.988537i	$-0.451758\pi$
$401$	6.04663	0.301954	0.150977	+	0.988537i	$0.451758\pi$
$402$	1.97801	0.0986542
$403$	−0.487592	−0.0242887
$404$	19.7579	0.982992
$405$	13.3657	0.664147
$406$	−0.00244240	−0.000121214 0
$407$	8.64745	0.428638
$408$	18.1917	0.900624
$409$	36.9896	1.82902	0.914510	−	0.404564i	$-0.132577\pi$
$409$	36.9896	1.82902	0.914510	+	0.404564i	$0.132577\pi$
$410$	5.28886	0.261198
$411$	−14.9349	−0.736684
$412$	−10.8168	−0.532907
$413$	0.226450	0.0111429
$414$	8.12697	0.399419
$415$	−15.6702	−0.769220
$416$	−0.105749	−0.00518476
$417$	−38.5959	−1.89005
$418$	6.26107	0.306239
$419$	20.4931	1.00116	0.500578	−	0.865692i	$-0.333121\pi$
$419$	20.4931	1.00116	0.500578	+	0.865692i	$0.333121\pi$
$420$	−6.58248	−0.321192
$421$	29.7034	1.44765	0.723827	−	0.689982i	$-0.242382\pi$
$421$	29.7034	1.44765	0.723827	+	0.689982i	$0.242382\pi$
$422$	0.937998	0.0456611
$423$	−5.39565	−0.262345
$424$	−12.6740	−0.615506
$425$	26.2721	1.27438
$426$	3.17973	0.154058
$427$	26.0834	1.26226
$428$	−15.7864	−0.763067
$429$	0.465009	0.0224508
$430$	13.6958	0.660470
$431$	19.9792	0.962366	0.481183	−	0.876620i	$-0.340207\pi$
$431$	19.9792	0.962366	0.481183	+	0.876620i	$0.340207\pi$
$432$	1.38171	0.0664775
$433$	−9.51611	−0.457315	−0.228657	−	0.973507i	$-0.573434\pi$
$433$	−9.51611	−0.457315	−0.228657	+	0.973507i	$0.573434\pi$
$434$	−10.1865	−0.488966
$435$	0.00329400	0.000157935 0
$436$	7.99386	0.382836
$437$	11.1834	0.534973
$438$	−19.8340	−0.947705
$439$	32.2061	1.53711	0.768556	−	0.639783i	$-0.220976\pi$
$439$	32.2061	1.53711	0.768556	+	0.639783i	$0.220976\pi$
$440$	−2.42371	−0.115546
$441$	−5.09842	−0.242782
$442$	0.827412	0.0393560
$443$	30.2391	1.43670	0.718352	−	0.695680i	$-0.244897\pi$
$443$	30.2391	1.43670	0.718352	+	0.695680i	$0.244897\pi$
$444$	−10.6305	−0.504504
$445$	1.04913	0.0497335
$446$	−11.8497	−0.561100
$447$	−13.7935	−0.652409
$448$	−2.20923	−0.104376
$449$	11.5252	0.543905	0.271953	−	0.962311i	$-0.412331\pi$
$449$	11.5252	0.543905	0.271953	+	0.962311i	$0.412331\pi$
$450$	−8.07779	−0.380791
$451$	−7.80549	−0.367546
$452$	7.49357	0.352468
$453$	−4.70431	−0.221028
$454$	−18.9488	−0.889310
$455$	−0.299390	−0.0140356
$456$	−7.69691	−0.360441
$457$	39.3875	1.84247	0.921236	−	0.389005i	$-0.127181\pi$
$457$	39.3875	1.84247	0.921236	+	0.389005i	$0.127181\pi$
$458$	13.0838	0.611367
$459$	−10.8109	−0.504612
$460$	−4.32917	−0.201848
$461$	−16.4352	−0.765464	−0.382732	−	0.923859i	$-0.625017\pi$
$461$	−16.4352	−0.765464	−0.382732	+	0.923859i	$0.625017\pi$
$462$	9.71466	0.451967
$463$	28.8567	1.34108	0.670541	−	0.741872i	$-0.266062\pi$
$463$	28.8567	1.34108	0.670541	+	0.741872i	$0.266062\pi$
$464$	0.00110554	5.13235e−5 0
$465$	13.7382	0.637093
$466$	−7.23408	−0.335112
$467$	28.6805	1.32717	0.663587	−	0.748099i	$-0.269033\pi$
$467$	28.6805	1.32717	0.663587	+	0.748099i	$0.269033\pi$
$468$	−0.254402	−0.0117597
$469$	1.87950	0.0867874
$470$	2.87421	0.132578
$471$	−17.0051	−0.783555
$472$	−0.102501	−0.00471801
$473$	−20.2127	−0.929383
$474$	15.0707	0.692218
$475$	−11.1157	−0.510023
$476$	17.2858	0.792292
$477$	−30.4902	−1.39605
$478$	−15.2448	−0.697283
$479$	30.4671	1.39208	0.696040	−	0.718003i	$-0.254944\pi$
$479$	30.4671	1.39208	0.696040	+	0.718003i	$0.254944\pi$
$480$	2.97953	0.135996
$481$	−0.483508	−0.0220461
$482$	14.8005	0.674146
$483$	17.3521	0.789547
$484$	−7.42300	−0.337409
$485$	−20.7015	−0.940007
$486$	20.1041	0.911939
$487$	−29.5877	−1.34075	−0.670374	−	0.742024i	$-0.733866\pi$
$487$	−29.5877	−1.34075	−0.670374	+	0.742024i	$0.733866\pi$
$488$	−11.8065	−0.534456
$489$	−15.5346	−0.702501
$490$	2.71588	0.122691
$491$	−15.1373	−0.683136	−0.341568	−	0.939857i	$-0.610958\pi$
$491$	−15.1373	−0.683136	−0.341568	+	0.939857i	$0.610958\pi$
$492$	9.59550	0.432599
$493$	−0.00865013	−0.000389582 0
$494$	−0.350078	−0.0157507
$495$	−5.83077	−0.262073
$496$	4.61086	0.207034
$497$	3.02137	0.135527
$498$	−28.4302	−1.27399
$499$	3.95261	0.176943	0.0884716	−	0.996079i	$-0.471802\pi$
$499$	3.95261	0.176943	0.0884716	+	0.996079i	$0.471802\pi$
$500$	10.7105	0.478988
$501$	15.5456	0.694528
$502$	6.39131	0.285258
$503$	0.332286	0.0148159	0.00740796	−	0.999973i	$-0.497642\pi$
$503$	0.332286	0.0148159	0.00740796	+	0.999973i	$0.497642\pi$
$504$	−5.31480	−0.236740
$505$	−25.3199	−1.12672
$506$	6.38914	0.284032
$507$	30.1993	1.34120
$508$	−8.85975	−0.393088
$509$	7.99536	0.354388	0.177194	−	0.984176i	$-0.443298\pi$
$509$	7.99536	0.354388	0.177194	+	0.984176i	$0.443298\pi$
$510$	−23.3128	−1.03231
$511$	−18.8463	−0.833709
$512$	1.00000	0.0441942
$513$	4.57411	0.201952
$514$	20.3482	0.897521
$515$	13.8619	0.610826
$516$	24.8481	1.09388
$517$	−4.24187	−0.186557
$518$	−10.1011	−0.443819
$519$	36.5890	1.60608
$520$	0.135518	0.00594284
$521$	26.3692	1.15525	0.577627	−	0.816301i	$-0.303979\pi$
$521$	26.3692	1.15525	0.577627	+	0.816301i	$0.303979\pi$
$522$	0.00265963	0.000116409 0
$523$	−33.3890	−1.46000	−0.729999	−	0.683449i	$-0.760479\pi$
$523$	−33.3890	−1.46000	−0.729999	+	0.683449i	$0.760479\pi$
$524$	16.6348	0.726697
$525$	−17.2471	−0.752724
$526$	19.9997	0.872029
$527$	−36.0769	−1.57153
$528$	−4.39730	−0.191368
$529$	−11.5879	−0.503820
$530$	16.2419	0.705502
$531$	−0.246590	−0.0107011
$532$	−7.31360	−0.317085
$533$	0.436431	0.0189039
$534$	1.90342	0.0823690
$535$	20.2304	0.874638
$536$	−0.850749	−0.0367468
$537$	2.72226	0.117474
$538$	22.9930	0.991300
$539$	−4.00820	−0.172645
$540$	−1.77067	−0.0761975
$541$	43.1106	1.85347	0.926735	−	0.375716i	$-0.122603\pi$
$541$	43.1106	1.85347	0.926735	+	0.375716i	$0.122603\pi$
$542$	−11.1366	−0.478360
$543$	4.44768	0.190868
$544$	−7.82433	−0.335465
$545$	−10.2442	−0.438813
$546$	−0.543179	−0.0232459
$547$	−15.1376	−0.647237	−0.323619	−	0.946188i	$-0.604899\pi$
$547$	−15.1376	−0.647237	−0.323619	+	0.946188i	$0.604899\pi$
$548$	6.42355	0.274401
$549$	−28.4032	−1.21222
$550$	−6.35048	−0.270785
$551$	0.00365987	0.000155916 0
$552$	−7.85435	−0.334303
$553$	14.3201	0.608954
$554$	−15.3145	−0.650651
$555$	13.6231	0.578269
$556$	16.6002	0.704007
$557$	−41.2102	−1.74613	−0.873067	−	0.487600i	$-0.837872\pi$
$557$	−41.2102	−1.74613	−0.873067	+	0.487600i	$0.837872\pi$
$558$	11.0924	0.469580
$559$	1.13016	0.0478008
$560$	2.83115	0.119638
$561$	34.4059	1.45262
$562$	−13.5182	−0.570230
$563$	44.7823	1.88735	0.943675	−	0.330874i	$-0.107343\pi$
$563$	44.7823	1.88735	0.943675	+	0.330874i	$0.107343\pi$
$564$	5.21465	0.219576
$565$	−9.60306	−0.404004
$566$	6.83915	0.287471
$567$	23.0416	0.967655
$568$	−1.36761	−0.0573837
$569$	34.7005	1.45472	0.727360	−	0.686256i	$-0.240747\pi$
$569$	34.7005	1.45472	0.727360	+	0.686256i	$0.240747\pi$
$570$	9.86364	0.413143
$571$	−16.0634	−0.672232	−0.336116	−	0.941821i	$-0.609113\pi$
$571$	−16.0634	−0.672232	−0.336116	+	0.941821i	$0.609113\pi$
$572$	−0.200002	−0.00836250
$573$	−23.1307	−0.966300
$574$	9.11764	0.380563
$575$	−11.3431	−0.473038
$576$	2.40572	0.100238
$577$	20.8004	0.865933	0.432966	−	0.901410i	$-0.357467\pi$
$577$	20.8004	0.865933	0.432966	+	0.901410i	$0.357467\pi$
$578$	44.2201	1.83931
$579$	39.2831	1.63255
$580$	−0.00141676	−5.88278e−5 0
$581$	−27.0144	−1.12075
$582$	−37.5585	−1.55685
$583$	−23.9704	−0.992750
$584$	8.53068	0.353002
$585$	0.326018	0.0134792
$586$	28.0638	1.15931
$587$	16.3854	0.676299	0.338150	−	0.941092i	$-0.390199\pi$
$587$	16.3854	0.676299	0.338150	+	0.941092i	$0.390199\pi$
$588$	4.92739	0.203202
$589$	15.2641	0.628946
$590$	0.131356	0.00540786
$591$	−47.2390	−1.94315
$592$	4.57224	0.187918
$593$	−4.97537	−0.204314	−0.102157	−	0.994768i	$-0.532574\pi$
$593$	−4.97537	−0.204314	−0.102157	+	0.994768i	$0.532574\pi$
$594$	2.61322	0.107222
$595$	−22.1518	−0.908136
$596$	5.93263	0.243010
$597$	−55.3412	−2.26497
$598$	−0.357239	−0.0146086
$599$	−1.78967	−0.0731237	−0.0365619	−	0.999331i	$-0.511641\pi$
$599$	−1.78967	−0.0731237	−0.0365619	+	0.999331i	$0.511641\pi$
$600$	7.80682	0.318712
$601$	23.5649	0.961234	0.480617	−	0.876931i	$-0.340413\pi$
$601$	23.5649	0.961234	0.480617	+	0.876931i	$0.340413\pi$
$602$	23.6106	0.962297
$603$	−2.04667	−0.0833467
$604$	2.02334	0.0823286
$605$	9.51263	0.386743
$606$	−45.9375	−1.86608
$607$	−25.1488	−1.02076	−0.510378	−	0.859950i	$-0.670495\pi$
$607$	−25.1488	−1.02076	−0.510378	+	0.859950i	$0.670495\pi$
$608$	3.31047	0.134257
$609$	0.00567863	0.000230110 0
$610$	15.1301	0.612602
$611$	0.237177	0.00959517
$612$	−18.8232	−0.760881
$613$	−7.98829	−0.322644	−0.161322	−	0.986902i	$-0.551576\pi$
$613$	−7.98829	−0.322644	−0.161322	+	0.986902i	$0.551576\pi$
$614$	−13.8903	−0.560568
$615$	−12.2967	−0.495851
$616$	−4.17831	−0.168349
$617$	−33.2361	−1.33803	−0.669017	−	0.743247i	$-0.733285\pi$
$617$	−33.2361	−1.33803	−0.669017	+	0.743247i	$0.733285\pi$
$618$	25.1494	1.01166
$619$	8.93652	0.359189	0.179595	−	0.983741i	$-0.442521\pi$
$619$	8.93652	0.359189	0.179595	+	0.983741i	$0.442521\pi$
$620$	−5.90885	−0.237305
$621$	4.66767	0.187307
$622$	−20.5660	−0.824620
$623$	1.80863	0.0724611
$624$	0.245868	0.00984259
$625$	3.06312	0.122525
$626$	10.0673	0.402371
$627$	−14.5571	−0.581356
$628$	7.31397	0.291859
$629$	−35.7747	−1.42643
$630$	6.81095	0.271355
$631$	35.4558	1.41147	0.705737	−	0.708474i	$-0.250616\pi$
$631$	35.4558	1.41147	0.705737	+	0.708474i	$0.250616\pi$
$632$	−6.48194	−0.257838
$633$	−2.18087	−0.0866816
$634$	11.3074	0.449073
$635$	11.3538	0.450563
$636$	29.4674	1.16846
$637$	0.224112	0.00887964
$638$	0.00209091	8.27798e−5 0
$639$	−3.29009	−0.130154
$640$	−1.28151	−0.0506560
$641$	33.2353	1.31271	0.656357	−	0.754451i	$-0.272097\pi$
$641$	33.2353	1.31271	0.656357	+	0.754451i	$0.272097\pi$
$642$	36.7038	1.44858
$643$	−35.6575	−1.40619	−0.703096	−	0.711095i	$-0.748200\pi$
$643$	−35.6575	−1.40619	−0.703096	+	0.711095i	$0.748200\pi$
$644$	−7.46320	−0.294091
$645$	−31.8430	−1.25382
$646$	−25.9022	−1.01911
$647$	39.8163	1.56534	0.782670	−	0.622437i	$-0.213857\pi$
$647$	39.8163	1.56534	0.782670	+	0.622437i	$0.213857\pi$
$648$	−10.4297	−0.409716
$649$	−0.193861	−0.00760969
$650$	0.355077	0.0139272
$651$	23.6837	0.928239
$652$	6.68151	0.261668
$653$	−20.8709	−0.816742	−0.408371	−	0.912816i	$-0.633903\pi$
$653$	−20.8709	−0.816742	−0.408371	+	0.912816i	$0.633903\pi$
$654$	−18.5859	−0.726766
$655$	−21.3177	−0.832950
$656$	−4.12706	−0.161135
$657$	20.5224	0.800657
$658$	4.95496	0.193164
$659$	−34.7852	−1.35504	−0.677519	−	0.735505i	$-0.736945\pi$
$659$	−34.7852	−1.35504	−0.677519	+	0.735505i	$0.736945\pi$
$660$	5.63517	0.219349
$661$	23.7217	0.922667	0.461333	−	0.887227i	$-0.347371\pi$
$661$	23.7217	0.922667	0.461333	+	0.887227i	$0.347371\pi$
$662$	18.8633	0.733144
$663$	−1.92375	−0.0747123
$664$	12.2280	0.474537
$665$	9.37243	0.363447
$666$	10.9995	0.426223
$667$	0.00373473	0.000144609 0
$668$	−6.68624	−0.258698
$669$	27.5508	1.06518
$670$	1.09024	0.0421197
$671$	−22.3296	−0.862026
$672$	5.13651	0.198145
$673$	−31.5819	−1.21739	−0.608696	−	0.793404i	$-0.708307\pi$
$673$	−31.5819	−1.21739	−0.608696	+	0.793404i	$0.708307\pi$
$674$	−1.35953	−0.0523672
$675$	−4.63942	−0.178571
$676$	−12.9888	−0.499570
$677$	−1.67006	−0.0641854	−0.0320927	−	0.999485i	$-0.510217\pi$
$677$	−1.67006	−0.0641854	−0.0320927	+	0.999485i	$0.510217\pi$
$678$	−17.4227	−0.669115
$679$	−35.6880	−1.36958
$680$	10.0269	0.384515
$681$	44.0563	1.68824
$682$	8.72049	0.333925
$683$	−50.0787	−1.91621	−0.958105	−	0.286418i	$-0.907535\pi$
$683$	−50.0787	−1.91621	−0.958105	+	0.286418i	$0.907535\pi$
$684$	7.96407	0.304514
$685$	−8.23183	−0.314522
$686$	20.1466	0.769202
$687$	−30.4202	−1.16060
$688$	−10.6873	−0.407448
$689$	1.34026	0.0510600
$690$	10.0654	0.383183
$691$	−28.5232	−1.08507	−0.542537	−	0.840032i	$-0.682536\pi$
$691$	−28.5232	−1.08507	−0.542537	+	0.840032i	$0.682536\pi$
$692$	−15.7371	−0.598234
$693$	−10.0519	−0.381838
$694$	9.84021	0.373529
$695$	−21.2733	−0.806944
$696$	−0.00257041	−9.74311e−5 0
$697$	32.2915	1.22313
$698$	−26.1353	−0.989235
$699$	16.8194	0.636168
$700$	7.41803	0.280375
$701$	0.685494	0.0258908	0.0129454	−	0.999916i	$-0.495879\pi$
$701$	0.685494	0.0258908	0.0129454	+	0.999916i	$0.495879\pi$
$702$	−0.146114	−0.00551471
$703$	15.1363	0.570875
$704$	1.89130	0.0712809
$705$	−6.68261	−0.251682
$706$	19.1479	0.720640
$707$	−43.6498	−1.64162
$708$	0.238318	0.00895654
$709$	3.42209	0.128519	0.0642596	−	0.997933i	$-0.479531\pi$
$709$	3.42209	0.128519	0.0642596	+	0.997933i	$0.479531\pi$
$710$	1.75260	0.0657741
$711$	−15.5938	−0.584811
$712$	−0.818668	−0.0306809
$713$	15.5763	0.583338
$714$	−40.1898	−1.50406
$715$	0.256304	0.00958522
$716$	−1.17086	−0.0437569
$717$	35.4446	1.32370
$718$	−10.6771	−0.398464
$719$	−16.9057	−0.630475	−0.315237	−	0.949013i	$-0.602084\pi$
$719$	−16.9057	−0.630475	−0.315237	+	0.949013i	$0.602084\pi$
$720$	−3.08295	−0.114895
$721$	23.8969	0.889968
$722$	−8.04079	−0.299247
$723$	−34.4116	−1.27978
$724$	−1.91296	−0.0710947
$725$	−0.00371213	−0.000137865 0
$726$	17.2586	0.640528
$727$	6.42289	0.238212	0.119106	−	0.992882i	$-0.461997\pi$
$727$	6.42289	0.238212	0.119106	+	0.992882i	$0.461997\pi$
$728$	0.233623	0.00865866
$729$	−15.4534	−0.572347
$730$	−10.9321	−0.404616
$731$	83.6205	3.09282
$732$	27.4504	1.01460
$733$	0.883580	0.0326358	0.0163179	−	0.999867i	$-0.494806\pi$
$733$	0.883580	0.0326358	0.0163179	+	0.999867i	$0.494806\pi$
$734$	−33.5960	−1.24005
$735$	−6.31449	−0.232913
$736$	3.37818	0.124522
$737$	−1.60902	−0.0592689
$738$	−9.92856	−0.365475
$739$	43.6061	1.60408	0.802038	−	0.597273i	$-0.203749\pi$
$739$	43.6061	1.60408	0.802038	+	0.597273i	$0.203749\pi$
$740$	−5.85936	−0.215394
$741$	0.813938	0.0299008
$742$	27.9999	1.02791
$743$	−22.1705	−0.813358	−0.406679	−	0.913571i	$-0.633313\pi$
$743$	−22.1705	−0.813358	−0.406679	+	0.913571i	$0.633313\pi$
$744$	−10.7203	−0.393027
$745$	−7.60270	−0.278541
$746$	36.1669	1.32416
$747$	29.4171	1.07631
$748$	−14.7981	−0.541073
$749$	34.8759	1.27434
$750$	−24.9021	−0.909298
$751$	−19.6411	−0.716716	−0.358358	−	0.933584i	$-0.616663\pi$
$751$	−19.6411	−0.716716	−0.358358	+	0.933584i	$0.616663\pi$
$752$	−2.24284	−0.0817879
$753$	−14.8599	−0.541525
$754$	−0.000116910 0	−4.25760e−6 0
$755$	−2.59293	−0.0943662
$756$	−3.05252	−0.111019
$757$	7.93600	0.288439	0.144219	−	0.989546i	$-0.453933\pi$
$757$	7.93600	0.288439	0.144219	+	0.989546i	$0.453933\pi$
$758$	−13.7001	−0.497610
$759$	−14.8549	−0.539198
$760$	−4.24239	−0.153888
$761$	−6.34978	−0.230179	−0.115090	−	0.993355i	$-0.536716\pi$
$761$	−6.34978	−0.230179	−0.115090	+	0.993355i	$0.536716\pi$
$762$	20.5991	0.746227
$763$	−17.6603	−0.639346
$764$	9.94861	0.359928
$765$	24.1220	0.872133
$766$	12.0694	0.436087
$767$	0.0108394	0.000391388 0
$768$	−2.32502	−0.0838970
$769$	21.0693	0.759777	0.379888	−	0.925032i	$-0.375962\pi$
$769$	21.0693	0.759777	0.379888	+	0.925032i	$0.375962\pi$
$770$	5.35454	0.192964
$771$	−47.3100	−1.70383
$772$	−16.8958	−0.608094
$773$	−48.2526	−1.73553	−0.867763	−	0.496979i	$-0.834443\pi$
$773$	−48.2526	−1.73553	−0.867763	+	0.496979i	$0.834443\pi$
$774$	−25.7106	−0.924147
$775$	−15.4821	−0.556132
$776$	16.1540	0.579896
$777$	23.4854	0.842533
$778$	−11.8532	−0.424958
$779$	−13.6625	−0.489510
$780$	−0.315081	−0.0112817
$781$	−2.58656	−0.0925543
$782$	−26.4320	−0.945207
$783$	0.00152754	5.45898e−5 0
$784$	−2.11929	−0.0756889
$785$	−9.37290	−0.334533
$786$	−38.6764	−1.37954
$787$	−0.377085	−0.0134416	−0.00672081	−	0.999977i	$-0.502139\pi$
$787$	−0.377085	−0.0134416	−0.00672081	+	0.999977i	$0.502139\pi$
$788$	20.3177	0.723787
$789$	−46.4997	−1.65543
$790$	8.30665	0.295538
$791$	−16.5550	−0.588630
$792$	4.54993	0.161675
$793$	1.24852	0.0443364
$794$	7.44679	0.264277
$795$	−37.7627	−1.33930
$796$	23.8025	0.843656
$797$	−27.3845	−0.970008	−0.485004	−	0.874512i	$-0.661182\pi$
$797$	−27.3845	−0.970008	−0.485004	+	0.874512i	$0.661182\pi$
$798$	17.0043	0.601945
$799$	17.5487	0.620829
$800$	−3.35774	−0.118714
$801$	−1.96949	−0.0695884
$802$	6.04663	0.213514
$803$	16.1340	0.569358
$804$	1.97801	0.0697590
$805$	9.56414	0.337092
$806$	−0.487592	−0.0171747
$807$	−53.4593	−1.88186
$808$	19.7579	0.695080
$809$	16.8161	0.591224	0.295612	−	0.955308i	$-0.404477\pi$
$809$	16.8161	0.591224	0.295612	+	0.955308i	$0.404477\pi$
$810$	13.3657	0.469623
$811$	−40.2388	−1.41298	−0.706489	−	0.707724i	$-0.749722\pi$
$811$	−40.2388	−1.41298	−0.706489	+	0.707724i	$0.749722\pi$
$812$	−0.00244240	−8.57115e−5 0
$813$	25.8929	0.908105
$814$	8.64745	0.303093
$815$	−8.56240	−0.299928
$816$	18.1917	0.636838
$817$	−35.3798	−1.23778
$818$	36.9896	1.29331
$819$	0.562033	0.0196390
$820$	5.28886	0.184695
$821$	−22.4213	−0.782508	−0.391254	−	0.920283i	$-0.627959\pi$
$821$	−22.4213	−0.782508	−0.391254	+	0.920283i	$0.627959\pi$
$822$	−14.9349	−0.520914
$823$	−28.4778	−0.992675	−0.496338	−	0.868130i	$-0.665322\pi$
$823$	−28.4778	−0.992675	−0.496338	+	0.868130i	$0.665322\pi$
$824$	−10.8168	−0.376822
$825$	14.7650	0.514051
$826$	0.226450	0.00787919
$827$	19.4598	0.676683	0.338342	−	0.941023i	$-0.390134\pi$
$827$	19.4598	0.676683	0.338342	+	0.941023i	$0.390134\pi$
$828$	8.12697	0.282432
$829$	−36.3513	−1.26253	−0.631266	−	0.775567i	$-0.717464\pi$
$829$	−36.3513	−1.26253	−0.631266	+	0.775567i	$0.717464\pi$
$830$	−15.6702	−0.543921
$831$	35.6065	1.23518
$832$	−0.105749	−0.00366618
$833$	16.5820	0.574533
$834$	−38.5959	−1.33647
$835$	8.56846	0.296524
$836$	6.26107	0.216544
$837$	6.37086	0.220209
$838$	20.4931	0.707924
$839$	−43.7942	−1.51194	−0.755971	−	0.654605i	$-0.772835\pi$
$839$	−43.7942	−1.51194	−0.755971	+	0.654605i	$0.772835\pi$
$840$	−6.58248	−0.227117
$841$	−29.0000	−1.00000
$842$	29.7034	1.02365
$843$	31.4301	1.08251
$844$	0.937998	0.0322872
$845$	16.6453	0.572614
$846$	−5.39565	−0.185506
$847$	16.3991	0.563481
$848$	−12.6740	−0.435228
$849$	−15.9012	−0.545727
$850$	26.2721	0.901124
$851$	15.4459	0.529477
$852$	3.17973	0.108936
$853$	−26.5744	−0.909890	−0.454945	−	0.890520i	$-0.650341\pi$
$853$	−26.5744	−0.909890	−0.454945	+	0.890520i	$0.650341\pi$
$854$	26.0834	0.892555
$855$	−10.2060	−0.349038
$856$	−15.7864	−0.539570
$857$	−16.9451	−0.578833	−0.289417	−	0.957203i	$-0.593461\pi$
$857$	−16.9451	−0.578833	−0.289417	+	0.957203i	$0.593461\pi$
$858$	0.465009	0.0158751
$859$	33.6925	1.14957	0.574787	−	0.818303i	$-0.305085\pi$
$859$	33.6925	1.14957	0.574787	+	0.818303i	$0.305085\pi$
$860$	13.6958	0.467022
$861$	−21.1987	−0.722450
$862$	19.9792	0.680495
$863$	0.392059	0.0133458	0.00667292	−	0.999978i	$-0.497876\pi$
$863$	0.392059	0.0133458	0.00667292	+	0.999978i	$0.497876\pi$
$864$	1.38171	0.0470067
$865$	20.1672	0.685705
$866$	−9.51611	−0.323370
$867$	−102.813	−3.49170
$868$	−10.1865	−0.345751
$869$	−12.2593	−0.415867
$870$	0.00329400	0.000111677 0
$871$	0.0899656	0.00304837
$872$	7.99386	0.270706
$873$	38.8621	1.31528
$874$	11.1834	0.378283
$875$	−23.6620	−0.799921
$876$	−19.8340	−0.670129
$877$	−25.8199	−0.871876	−0.435938	−	0.899977i	$-0.643583\pi$
$877$	−25.8199	−0.871876	−0.435938	+	0.899977i	$0.643583\pi$
$878$	32.2061	1.08690
$879$	−65.2489	−2.20079
$880$	−2.42371	−0.0817032
$881$	5.90141	0.198824	0.0994118	−	0.995046i	$-0.468304\pi$
$881$	5.90141	0.198824	0.0994118	+	0.995046i	$0.468304\pi$
$882$	−5.09842	−0.171673
$883$	−8.84875	−0.297784	−0.148892	−	0.988853i	$-0.547571\pi$
$883$	−8.84875	−0.297784	−0.148892	+	0.988853i	$0.547571\pi$
$884$	0.827412	0.0278289
$885$	−0.305406	−0.0102661
$886$	30.2391	1.01590
$887$	44.1826	1.48351	0.741753	−	0.670673i	$-0.233995\pi$
$887$	44.1826	1.48351	0.741753	+	0.670673i	$0.233995\pi$
$888$	−10.6305	−0.356738
$889$	19.5732	0.656466
$890$	1.04913	0.0351669
$891$	−19.7256	−0.660832
$892$	−11.8497	−0.396758
$893$	−7.42485	−0.248463
$894$	−13.7935	−0.461323
$895$	1.50046	0.0501548
$896$	−2.20923	−0.0738053
$897$	0.830587	0.0277325
$898$	11.5252	0.384599
$899$	0.00509750	0.000170011 0
$900$	−8.07779	−0.269260
$901$	99.1658	3.30369
$902$	−7.80549	−0.259894
$903$	−54.8952	−1.82680
$904$	7.49357	0.249232
$905$	2.45147	0.0814897
$906$	−4.70431	−0.156290
$907$	25.5648	0.848865	0.424432	−	0.905460i	$-0.360474\pi$
$907$	25.5648	0.848865	0.424432	+	0.905460i	$0.360474\pi$
$908$	−18.9488	−0.628837
$909$	47.5320	1.57654
$910$	−0.299390	−0.00992469
$911$	−31.7188	−1.05089	−0.525446	−	0.850827i	$-0.676101\pi$
$911$	−31.7188	−1.05089	−0.525446	+	0.850827i	$0.676101\pi$
$912$	−7.69691	−0.254870
$913$	23.1267	0.765381
$914$	39.3875	1.30282
$915$	−35.1779	−1.16295
$916$	13.0838	0.432302
$917$	−36.7503	−1.21360
$918$	−10.8109	−0.356814
$919$	6.80694	0.224540	0.112270	−	0.993678i	$-0.464188\pi$
$919$	6.80694	0.224540	0.112270	+	0.993678i	$0.464188\pi$
$920$	−4.32917	−0.142728
$921$	32.2953	1.06417
$922$	−16.4352	−0.541265
$923$	0.144623	0.00476033
$924$	9.71466	0.319589
$925$	−15.3524	−0.504783
$926$	28.8567	0.948288
$927$	−26.0223	−0.854685
$928$	0.00110554	3.62912e−5 0
$929$	−52.3855	−1.71871	−0.859356	−	0.511377i	$-0.829135\pi$
$929$	−52.3855	−1.71871	−0.859356	+	0.511377i	$0.829135\pi$
$930$	13.7382	0.450493
$931$	−7.01584	−0.229935
$932$	−7.23408	−0.236960
$933$	47.8163	1.56544
$934$	28.6805	0.938454
$935$	18.9639	0.620185
$936$	−0.254402	−0.00831539
$937$	5.61747	0.183515	0.0917574	−	0.995781i	$-0.470752\pi$
$937$	5.61747	0.183515	0.0917574	+	0.995781i	$0.470752\pi$
$938$	1.87950	0.0613680
$939$	−23.4068	−0.763851
$940$	2.87421	0.0937465
$941$	−11.0878	−0.361451	−0.180725	−	0.983534i	$-0.557845\pi$
$941$	−11.0878	−0.361451	−0.180725	+	0.983534i	$0.557845\pi$
$942$	−17.0051	−0.554057
$943$	−13.9420	−0.454013
$944$	−0.102501	−0.00333614
$945$	3.91182	0.127252
$946$	−20.2127	−0.657173
$947$	−9.26231	−0.300985	−0.150492	−	0.988611i	$-0.548086\pi$
$947$	−9.26231	−0.300985	−0.150492	+	0.988611i	$0.548086\pi$
$948$	15.0707	0.489472
$949$	−0.902108	−0.0292837
$950$	−11.1157	−0.360641
$951$	−26.2899	−0.852508
$952$	17.2858	0.560235
$953$	−49.0227	−1.58800	−0.794001	−	0.607916i	$-0.792006\pi$
$953$	−49.0227	−1.58800	−0.794001	+	0.607916i	$0.792006\pi$
$954$	−30.4902	−0.987157
$955$	−12.7492	−0.412555
$956$	−15.2448	−0.493053
$957$	−0.00486140	−0.000157147 0
$958$	30.4671	0.984349
$959$	−14.1911	−0.458255
$960$	2.97953	0.0961639
$961$	−9.73999	−0.314193
$962$	−0.483508	−0.0155889
$963$	−37.9778	−1.22382
$964$	14.8005	0.476693
$965$	21.6521	0.697006
$966$	17.3521	0.558294
$967$	−30.8542	−0.992204	−0.496102	−	0.868264i	$-0.665236\pi$
$967$	−30.8542	−0.992204	−0.496102	+	0.868264i	$0.665236\pi$
$968$	−7.42300	−0.238584
$969$	60.2231	1.93465
$970$	−20.7015	−0.664685
$971$	33.1290	1.06316	0.531580	−	0.847008i	$-0.321599\pi$
$971$	33.1290	1.06316	0.531580	+	0.847008i	$0.321599\pi$
$972$	20.1041	0.644838
$973$	−36.6738	−1.17571
$974$	−29.5877	−0.948051
$975$	−0.825560	−0.0264391
$976$	−11.8065	−0.377918
$977$	−21.6264	−0.691889	−0.345945	−	0.938255i	$-0.612442\pi$
$977$	−21.6264	−0.691889	−0.345945	+	0.938255i	$0.612442\pi$
$978$	−15.5346	−0.496743
$979$	−1.54834	−0.0494852
$980$	2.71588	0.0867557
$981$	19.2310	0.613999
$982$	−15.1373	−0.483050
$983$	−48.5733	−1.54925	−0.774624	−	0.632422i	$-0.782061\pi$
$983$	−48.5733	−1.54925	−0.774624	+	0.632422i	$0.782061\pi$
$984$	9.59550	0.305893
$985$	−26.0372	−0.829616
$986$	−0.00865013	−0.000275476 0
$987$	−11.5204	−0.366698
$988$	−0.350078	−0.0111375
$989$	−36.1035	−1.14802
$990$	−5.83077	−0.185314
$991$	−45.0558	−1.43124	−0.715622	−	0.698488i	$-0.753857\pi$
$991$	−45.0558	−1.43124	−0.715622	+	0.698488i	$0.753857\pi$
$992$	4.61086	0.146395
$993$	−43.8576	−1.39178
$994$	3.02137	0.0958322
$995$	−30.5030	−0.967011
$996$	−28.4302	−0.900847
$997$	10.2423	0.324377	0.162188	−	0.986760i	$-0.448145\pi$
$997$	10.2423	0.324377	0.162188	+	0.986760i	$0.448145\pi$
$998$	3.95261	0.125118
$999$	6.31750	0.199877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.18	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.32502 q^{3} +1.00000 q^{4} -1.28151 q^{5} -2.32502 q^{6} -2.20923 q^{7} +1.00000 q^{8} +2.40572 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.32502 q^{3} +1.00000 q^{4} -1.28151 q^{5} -2.32502 q^{6} -2.20923 q^{7} +1.00000 q^{8} +2.40572 q^{9} -1.28151 q^{10} +1.89130 q^{11} -2.32502 q^{12} -0.105749 q^{13} -2.20923 q^{14} +2.97953 q^{15} +1.00000 q^{16} -7.82433 q^{17} +2.40572 q^{18} +3.31047 q^{19} -1.28151 q^{20} +5.13651 q^{21} +1.89130 q^{22} +3.37818 q^{23} -2.32502 q^{24} -3.35774 q^{25} -0.105749 q^{26} +1.38171 q^{27} -2.20923 q^{28} +0.00110554 q^{29} +2.97953 q^{30} +4.61086 q^{31} +1.00000 q^{32} -4.39730 q^{33} -7.82433 q^{34} +2.83115 q^{35} +2.40572 q^{36} +4.57224 q^{37} +3.31047 q^{38} +0.245868 q^{39} -1.28151 q^{40} -4.12706 q^{41} +5.13651 q^{42} -10.6873 q^{43} +1.89130 q^{44} -3.08295 q^{45} +3.37818 q^{46} -2.24284 q^{47} -2.32502 q^{48} -2.11929 q^{49} -3.35774 q^{50} +18.1917 q^{51} -0.105749 q^{52} -12.6740 q^{53} +1.38171 q^{54} -2.42371 q^{55} -2.20923 q^{56} -7.69691 q^{57} +0.00110554 q^{58} -0.102501 q^{59} +2.97953 q^{60} -11.8065 q^{61} +4.61086 q^{62} -5.31480 q^{63} +1.00000 q^{64} +0.135518 q^{65} -4.39730 q^{66} -0.850749 q^{67} -7.82433 q^{68} -7.85435 q^{69} +2.83115 q^{70} -1.36761 q^{71} +2.40572 q^{72} +8.53068 q^{73} +4.57224 q^{74} +7.80682 q^{75} +3.31047 q^{76} -4.17831 q^{77} +0.245868 q^{78} -6.48194 q^{79} -1.28151 q^{80} -10.4297 q^{81} -4.12706 q^{82} +12.2280 q^{83} +5.13651 q^{84} +10.0269 q^{85} -10.6873 q^{86} -0.00257041 q^{87} +1.89130 q^{88} -0.818668 q^{89} -3.08295 q^{90} +0.233623 q^{91} +3.37818 q^{92} -10.7203 q^{93} -2.24284 q^{94} -4.24239 q^{95} -2.32502 q^{96} +16.1540 q^{97} -2.11929 q^{98} +4.54993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 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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