LMFDB - Embedded newform 8026.2.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.84755 q^{3} +1.00000 q^{4} +2.66905 q^{5} -2.84755 q^{6} +0.0156637 q^{7} +1.00000 q^{8} +5.10852 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.84755 q^{3} +1.00000 q^{4} +2.66905 q^{5} -2.84755 q^{6} +0.0156637 q^{7} +1.00000 q^{8} +5.10852 q^{9} +2.66905 q^{10} -3.79185 q^{11} -2.84755 q^{12} +0.170980 q^{13} +0.0156637 q^{14} -7.60023 q^{15} +1.00000 q^{16} -4.24384 q^{17} +5.10852 q^{18} +1.02606 q^{19} +2.66905 q^{20} -0.0446032 q^{21} -3.79185 q^{22} -3.29430 q^{23} -2.84755 q^{24} +2.12381 q^{25} +0.170980 q^{26} -6.00410 q^{27} +0.0156637 q^{28} +7.44003 q^{29} -7.60023 q^{30} -7.62538 q^{31} +1.00000 q^{32} +10.7975 q^{33} -4.24384 q^{34} +0.0418073 q^{35} +5.10852 q^{36} -0.350539 q^{37} +1.02606 q^{38} -0.486872 q^{39} +2.66905 q^{40} -0.856487 q^{41} -0.0446032 q^{42} +7.76330 q^{43} -3.79185 q^{44} +13.6349 q^{45} -3.29430 q^{46} +1.51479 q^{47} -2.84755 q^{48} -6.99975 q^{49} +2.12381 q^{50} +12.0845 q^{51} +0.170980 q^{52} -5.04395 q^{53} -6.00410 q^{54} -10.1206 q^{55} +0.0156637 q^{56} -2.92175 q^{57} +7.44003 q^{58} +2.90651 q^{59} -7.60023 q^{60} +12.7645 q^{61} -7.62538 q^{62} +0.0800185 q^{63} +1.00000 q^{64} +0.456352 q^{65} +10.7975 q^{66} +5.95761 q^{67} -4.24384 q^{68} +9.38067 q^{69} +0.0418073 q^{70} +5.30812 q^{71} +5.10852 q^{72} +3.53398 q^{73} -0.350539 q^{74} -6.04765 q^{75} +1.02606 q^{76} -0.0593945 q^{77} -0.486872 q^{78} +9.21076 q^{79} +2.66905 q^{80} +1.77140 q^{81} -0.856487 q^{82} +6.61344 q^{83} -0.0446032 q^{84} -11.3270 q^{85} +7.76330 q^{86} -21.1858 q^{87} -3.79185 q^{88} +14.0436 q^{89} +13.6349 q^{90} +0.00267818 q^{91} -3.29430 q^{92} +21.7136 q^{93} +1.51479 q^{94} +2.73860 q^{95} -2.84755 q^{96} +2.54213 q^{97} -6.99975 q^{98} -19.3707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.84755	−1.64403	−0.822016	−	0.569465i	$-0.807150\pi$
$3$	−2.84755	−1.64403	−0.822016	+	0.569465i	$0.807150\pi$
$4$	1.00000	0.500000
$5$	2.66905	1.19363	0.596817	−	0.802377i	$-0.296432\pi$
$5$	2.66905	1.19363	0.596817	+	0.802377i	$0.296432\pi$
$6$	−2.84755	−1.16251
$7$	0.0156637	0.00592034	0.00296017	−	0.999996i	$-0.499058\pi$
$7$	0.0156637	0.00592034	0.00296017	+	0.999996i	$0.499058\pi$
$8$	1.00000	0.353553
$9$	5.10852	1.70284
$10$	2.66905	0.844027
$11$	−3.79185	−1.14328	−0.571642	−	0.820503i	$-0.693693\pi$
$11$	−3.79185	−1.14328	−0.571642	+	0.820503i	$0.693693\pi$
$12$	−2.84755	−0.822016
$13$	0.170980	0.0474212	0.0237106	−	0.999719i	$-0.492452\pi$
$13$	0.170980	0.0474212	0.0237106	+	0.999719i	$0.492452\pi$
$14$	0.0156637	0.00418631
$15$	−7.60023	−1.96237
$16$	1.00000	0.250000
$17$	−4.24384	−1.02928	−0.514642	−	0.857405i	$-0.672075\pi$
$17$	−4.24384	−1.02928	−0.514642	+	0.857405i	$0.672075\pi$
$18$	5.10852	1.20409
$19$	1.02606	0.235394	0.117697	−	0.993050i	$-0.462449\pi$
$19$	1.02606	0.235394	0.117697	+	0.993050i	$0.462449\pi$
$20$	2.66905	0.596817
$21$	−0.0446032	−0.00973322
$22$	−3.79185	−0.808424
$23$	−3.29430	−0.686909	−0.343455	−	0.939169i	$-0.611597\pi$
$23$	−3.29430	−0.686909	−0.343455	+	0.939169i	$0.611597\pi$
$24$	−2.84755	−0.581253
$25$	2.12381	0.424762
$26$	0.170980	0.0335319
$27$	−6.00410	−1.15549
$28$	0.0156637	0.00296017
$29$	7.44003	1.38158	0.690789	−	0.723056i	$-0.257263\pi$
$29$	7.44003	1.38158	0.690789	+	0.723056i	$0.257263\pi$
$30$	−7.60023	−1.38761
$31$	−7.62538	−1.36956	−0.684780	−	0.728750i	$-0.740102\pi$
$31$	−7.62538	−1.36956	−0.684780	+	0.728750i	$0.740102\pi$
$32$	1.00000	0.176777
$33$	10.7975	1.87960
$34$	−4.24384	−0.727813
$35$	0.0418073	0.00706672
$36$	5.10852	0.851420
$37$	−0.350539	−0.0576283	−0.0288142	−	0.999585i	$-0.509173\pi$
$37$	−0.350539	−0.0576283	−0.0288142	+	0.999585i	$0.509173\pi$
$38$	1.02606	0.166449
$39$	−0.486872	−0.0779619
$40$	2.66905	0.422013
$41$	−0.856487	−0.133761	−0.0668804	−	0.997761i	$-0.521305\pi$
$41$	−0.856487	−0.133761	−0.0668804	+	0.997761i	$0.521305\pi$
$42$	−0.0446032	−0.00688243
$43$	7.76330	1.18389	0.591946	−	0.805978i	$-0.298360\pi$
$43$	7.76330	1.18389	0.591946	+	0.805978i	$0.298360\pi$
$44$	−3.79185	−0.571642
$45$	13.6349	2.03257
$46$	−3.29430	−0.485718
$47$	1.51479	0.220954	0.110477	−	0.993879i	$-0.464762\pi$
$47$	1.51479	0.220954	0.110477	+	0.993879i	$0.464762\pi$
$48$	−2.84755	−0.411008
$49$	−6.99975	−0.999965
$50$	2.12381	0.300352
$51$	12.0845	1.69217
$52$	0.170980	0.0237106
$53$	−5.04395	−0.692840	−0.346420	−	0.938080i	$-0.612603\pi$
$53$	−5.04395	−0.692840	−0.346420	+	0.938080i	$0.612603\pi$
$54$	−6.00410	−0.817054
$55$	−10.1206	−1.36466
$56$	0.0156637	0.00209316
$57$	−2.92175	−0.386996
$58$	7.44003	0.976923
$59$	2.90651	0.378395	0.189198	−	0.981939i	$-0.439411\pi$
$59$	2.90651	0.378395	0.189198	+	0.981939i	$0.439411\pi$
$60$	−7.60023	−0.981186
$61$	12.7645	1.63433	0.817166	−	0.576402i	$-0.195544\pi$
$61$	12.7645	1.63433	0.817166	+	0.576402i	$0.195544\pi$
$62$	−7.62538	−0.968425
$63$	0.0800185	0.0100814
$64$	1.00000	0.125000
$65$	0.456352	0.0566036
$66$	10.7975	1.32907
$67$	5.95761	0.727837	0.363919	−	0.931431i	$-0.381439\pi$
$67$	5.95761	0.727837	0.363919	+	0.931431i	$0.381439\pi$
$68$	−4.24384	−0.514642
$69$	9.38067	1.12930
$70$	0.0418073	0.00499692
$71$	5.30812	0.629958	0.314979	−	0.949099i	$-0.398003\pi$
$71$	5.30812	0.629958	0.314979	+	0.949099i	$0.398003\pi$
$72$	5.10852	0.602045
$73$	3.53398	0.413621	0.206810	−	0.978381i	$-0.433692\pi$
$73$	3.53398	0.413621	0.206810	+	0.978381i	$0.433692\pi$
$74$	−0.350539	−0.0407494
$75$	−6.04765	−0.698322
$76$	1.02606	0.117697
$77$	−0.0593945	−0.00676863
$78$	−0.486872	−0.0551274
$79$	9.21076	1.03629	0.518146	−	0.855292i	$-0.326622\pi$
$79$	9.21076	1.03629	0.518146	+	0.855292i	$0.326622\pi$
$80$	2.66905	0.298409
$81$	1.77140	0.196822
$82$	−0.856487	−0.0945832
$83$	6.61344	0.725920	0.362960	−	0.931805i	$-0.381766\pi$
$83$	6.61344	0.725920	0.362960	+	0.931805i	$0.381766\pi$
$84$	−0.0446032	−0.00486661
$85$	−11.3270	−1.22859
$86$	7.76330	0.837138
$87$	−21.1858	−2.27136
$88$	−3.79185	−0.404212
$89$	14.0436	1.48862	0.744309	−	0.667835i	$-0.232779\pi$
$89$	14.0436	1.48862	0.744309	+	0.667835i	$0.232779\pi$
$90$	13.6349	1.43724
$91$	0.00267818	0.000280750 0
$92$	−3.29430	−0.343455
$93$	21.7136	2.25160
$94$	1.51479	0.156238
$95$	2.73860	0.280975
$96$	−2.84755	−0.290626
$97$	2.54213	0.258114	0.129057	−	0.991637i	$-0.458805\pi$
$97$	2.54213	0.258114	0.129057	+	0.991637i	$0.458805\pi$
$98$	−6.99975	−0.707082
$99$	−19.3707	−1.94683
$100$	2.12381	0.212381
$101$	1.71087	0.170238	0.0851189	−	0.996371i	$-0.472873\pi$
$101$	1.71087	0.170238	0.0851189	+	0.996371i	$0.472873\pi$
$102$	12.0845	1.19655
$103$	9.92318	0.977760	0.488880	−	0.872351i	$-0.337406\pi$
$103$	9.92318	0.977760	0.488880	+	0.872351i	$0.337406\pi$
$104$	0.170980	0.0167659
$105$	−0.119048	−0.0116179
$106$	−5.04395	−0.489912
$107$	−14.3850	−1.39065	−0.695327	−	0.718694i	$-0.744740\pi$
$107$	−14.3850	−1.39065	−0.695327	+	0.718694i	$0.744740\pi$
$108$	−6.00410	−0.577745
$109$	3.38304	0.324037	0.162018	−	0.986788i	$-0.448200\pi$
$109$	3.38304	0.324037	0.162018	+	0.986788i	$0.448200\pi$
$110$	−10.1206	−0.964963
$111$	0.998177	0.0947428
$112$	0.0156637	0.00148008
$113$	19.2839	1.81408	0.907040	−	0.421044i	$-0.138336\pi$
$113$	19.2839	1.81408	0.907040	+	0.421044i	$0.138336\pi$
$114$	−2.92175	−0.273647
$115$	−8.79264	−0.819918
$116$	7.44003	0.690789
$117$	0.873452	0.0807507
$118$	2.90651	0.267566
$119$	−0.0664745	−0.00609371
$120$	−7.60023	−0.693803
$121$	3.37810	0.307100
$122$	12.7645	1.15565
$123$	2.43889	0.219907
$124$	−7.62538	−0.684780
$125$	−7.67668	−0.686623
$126$	0.0800185	0.00712861
$127$	−14.4863	−1.28545	−0.642727	−	0.766095i	$-0.722197\pi$
$127$	−14.4863	−1.28545	−0.642727	+	0.766095i	$0.722197\pi$
$128$	1.00000	0.0883883
$129$	−22.1063	−1.94636
$130$	0.456352	0.0400248
$131$	−5.93803	−0.518808	−0.259404	−	0.965769i	$-0.583526\pi$
$131$	−5.93803	−0.518808	−0.259404	+	0.965769i	$0.583526\pi$
$132$	10.7975	0.939798
$133$	0.0160719	0.00139361
$134$	5.95761	0.514659
$135$	−16.0252	−1.37923
$136$	−4.24384	−0.363907
$137$	17.9412	1.53282	0.766410	−	0.642352i	$-0.222041\pi$
$137$	17.9412	1.53282	0.766410	+	0.642352i	$0.222041\pi$
$138$	9.38067	0.798536
$139$	13.6151	1.15482	0.577408	−	0.816456i	$-0.304064\pi$
$139$	13.6151	1.15482	0.577408	+	0.816456i	$0.304064\pi$
$140$	0.0418073	0.00353336
$141$	−4.31343	−0.363256
$142$	5.30812	0.445447
$143$	−0.648328	−0.0542159
$144$	5.10852	0.425710
$145$	19.8578	1.64910
$146$	3.53398	0.292474
$147$	19.9321	1.64397
$148$	−0.350539	−0.0288142
$149$	7.52735	0.616664	0.308332	−	0.951279i	$-0.400229\pi$
$149$	7.52735	0.616664	0.308332	+	0.951279i	$0.400229\pi$
$150$	−6.04765	−0.493788
$151$	21.8744	1.78011	0.890056	−	0.455850i	$-0.150665\pi$
$151$	21.8744	1.78011	0.890056	+	0.455850i	$0.150665\pi$
$152$	1.02606	0.0832245
$153$	−21.6798	−1.75270
$154$	−0.0593945	−0.00478614
$155$	−20.3525	−1.63475
$156$	−0.486872	−0.0389810
$157$	−11.0165	−0.879211	−0.439605	−	0.898191i	$-0.644882\pi$
$157$	−11.0165	−0.879211	−0.439605	+	0.898191i	$0.644882\pi$
$158$	9.21076	0.732769
$159$	14.3629	1.13905
$160$	2.66905	0.211007
$161$	−0.0516011	−0.00406673
$162$	1.77140	0.139174
$163$	−13.8827	−1.08738	−0.543688	−	0.839287i	$-0.682972\pi$
$163$	−13.8827	−1.08738	−0.543688	+	0.839287i	$0.682972\pi$
$164$	−0.856487	−0.0668804
$165$	28.8189	2.24355
$166$	6.61344	0.513303
$167$	−13.9151	−1.07678	−0.538390	−	0.842696i	$-0.680967\pi$
$167$	−13.9151	−1.07678	−0.538390	+	0.842696i	$0.680967\pi$
$168$	−0.0446032	−0.00344121
$169$	−12.9708	−0.997751
$170$	−11.3270	−0.868743
$171$	5.24165	0.400839
$172$	7.76330	0.591946
$173$	23.6917	1.80125	0.900624	−	0.434599i	$-0.143110\pi$
$173$	23.6917	1.80125	0.900624	+	0.434599i	$0.143110\pi$
$174$	−21.1858	−1.60609
$175$	0.0332668	0.00251474
$176$	−3.79185	−0.285821
$177$	−8.27641	−0.622093
$178$	14.0436	1.05261
$179$	−19.3462	−1.44601	−0.723003	−	0.690845i	$-0.757239\pi$
$179$	−19.3462	−1.44601	−0.723003	+	0.690845i	$0.757239\pi$
$180$	13.6349	1.01628
$181$	11.6943	0.869229	0.434615	−	0.900617i	$-0.356885\pi$
$181$	11.6943	0.869229	0.434615	+	0.900617i	$0.356885\pi$
$182$	0.00267818	0.000198520 0
$183$	−36.3476	−2.68689
$184$	−3.29430	−0.242859
$185$	−0.935606	−0.0687871
$186$	21.7136	1.59212
$187$	16.0920	1.17676
$188$	1.51479	0.110477
$189$	−0.0940467	−0.00684089
$190$	2.73860	0.198679
$191$	−21.8333	−1.57980	−0.789900	−	0.613236i	$-0.789868\pi$
$191$	−21.8333	−1.57980	−0.789900	+	0.613236i	$0.789868\pi$
$192$	−2.84755	−0.205504
$193$	−16.9595	−1.22077	−0.610385	−	0.792105i	$-0.708985\pi$
$193$	−16.9595	−1.22077	−0.610385	+	0.792105i	$0.708985\pi$
$194$	2.54213	0.182514
$195$	−1.29948	−0.0930580
$196$	−6.99975	−0.499982
$197$	22.2562	1.58569	0.792843	−	0.609426i	$-0.208600\pi$
$197$	22.2562	1.58569	0.792843	+	0.609426i	$0.208600\pi$
$198$	−19.3707	−1.37662
$199$	−20.8691	−1.47937	−0.739684	−	0.672954i	$-0.765025\pi$
$199$	−20.8691	−1.47937	−0.739684	+	0.672954i	$0.765025\pi$
$200$	2.12381	0.150176
$201$	−16.9646	−1.19659
$202$	1.71087	0.120376
$203$	0.116539	0.00817941
$204$	12.0845	0.846087
$205$	−2.28600	−0.159661
$206$	9.92318	0.691380
$207$	−16.8290	−1.16970
$208$	0.170980	0.0118553
$209$	−3.89066	−0.269123
$210$	−0.119048	−0.00821510
$211$	−12.1868	−0.838976	−0.419488	−	0.907761i	$-0.637790\pi$
$211$	−12.1868	−0.838976	−0.419488	+	0.907761i	$0.637790\pi$
$212$	−5.04395	−0.346420
$213$	−15.1151	−1.03567
$214$	−14.3850	−0.983340
$215$	20.7206	1.41313
$216$	−6.00410	−0.408527
$217$	−0.119442	−0.00810825
$218$	3.38304	0.229128
$219$	−10.0632	−0.680005
$220$	−10.1206	−0.682332
$221$	−0.725611	−0.0488099
$222$	0.998177	0.0669933
$223$	−20.1682	−1.35056	−0.675281	−	0.737560i	$-0.735978\pi$
$223$	−20.1682	−1.35056	−0.675281	+	0.737560i	$0.735978\pi$
$224$	0.0156637	0.00104658
$225$	10.8495	0.723302
$226$	19.2839	1.28275
$227$	8.71852	0.578669	0.289334	−	0.957228i	$-0.406566\pi$
$227$	8.71852	0.578669	0.289334	+	0.957228i	$0.406566\pi$
$228$	−2.92175	−0.193498
$229$	21.0581	1.39156	0.695779	−	0.718256i	$-0.255059\pi$
$229$	21.0581	1.39156	0.695779	+	0.718256i	$0.255059\pi$
$230$	−8.79264	−0.579770
$231$	0.169129	0.0111278
$232$	7.44003	0.488462
$233$	24.9363	1.63363	0.816814	−	0.576901i	$-0.195738\pi$
$233$	24.9363	1.63363	0.816814	+	0.576901i	$0.195738\pi$
$234$	0.873452	0.0570994
$235$	4.04304	0.263739
$236$	2.90651	0.189198
$237$	−26.2281	−1.70370
$238$	−0.0664745	−0.00430890
$239$	7.85045	0.507804	0.253902	−	0.967230i	$-0.418286\pi$
$239$	7.85045	0.507804	0.253902	+	0.967230i	$0.418286\pi$
$240$	−7.60023	−0.490593
$241$	5.88881	0.379331	0.189666	−	0.981849i	$-0.439260\pi$
$241$	5.88881	0.379331	0.189666	+	0.981849i	$0.439260\pi$
$242$	3.37810	0.217152
$243$	12.9682	0.831908
$244$	12.7645	0.817166
$245$	−18.6827	−1.19359
$246$	2.43889	0.155498
$247$	0.175435	0.0111627
$248$	−7.62538	−0.484212
$249$	−18.8321	−1.19343
$250$	−7.67668	−0.485516
$251$	28.2186	1.78115	0.890573	−	0.454841i	$-0.150304\pi$
$251$	28.2186	1.78115	0.890573	+	0.454841i	$0.150304\pi$
$252$	0.0800185	0.00504069
$253$	12.4915	0.785333
$254$	−14.4863	−0.908953
$255$	32.2542	2.01984
$256$	1.00000	0.0625000
$257$	−0.0783916	−0.00488993	−0.00244497	−	0.999997i	$-0.500778\pi$
$257$	−0.0783916	−0.00488993	−0.00244497	+	0.999997i	$0.500778\pi$
$258$	−22.1063	−1.37628
$259$	−0.00549076	−0.000341179 0
$260$	0.456352	0.0283018
$261$	38.0075	2.35261
$262$	−5.93803	−0.366853
$263$	−32.0343	−1.97532	−0.987659	−	0.156622i	$-0.949939\pi$
$263$	−32.0343	−1.97532	−0.987659	+	0.156622i	$0.949939\pi$
$264$	10.7975	0.664537
$265$	−13.4625	−0.826997
$266$	0.0160719	0.000985434 0
$267$	−39.9898	−2.44734
$268$	5.95761	0.363919
$269$	−1.18823	−0.0724480	−0.0362240	−	0.999344i	$-0.511533\pi$
$269$	−1.18823	−0.0724480	−0.0362240	+	0.999344i	$0.511533\pi$
$270$	−16.0252	−0.975264
$271$	26.8082	1.62848	0.814242	−	0.580526i	$-0.197153\pi$
$271$	26.8082	1.62848	0.814242	+	0.580526i	$0.197153\pi$
$272$	−4.24384	−0.257321
$273$	−0.00762624	−0.000461561 0
$274$	17.9412	1.08387
$275$	−8.05316	−0.485624
$276$	9.38067	0.564650
$277$	7.60912	0.457187	0.228594	−	0.973522i	$-0.426587\pi$
$277$	7.60912	0.457187	0.228594	+	0.973522i	$0.426587\pi$
$278$	13.6151	0.816578
$279$	−38.9544	−2.33214
$280$	0.0418073	0.00249846
$281$	29.5649	1.76369	0.881847	−	0.471535i	$-0.156300\pi$
$281$	29.5649	1.76369	0.881847	+	0.471535i	$0.156300\pi$
$282$	−4.31343	−0.256861
$283$	15.9226	0.946503	0.473251	−	0.880927i	$-0.343080\pi$
$283$	15.9226	0.946503	0.473251	+	0.880927i	$0.343080\pi$
$284$	5.30812	0.314979
$285$	−7.79830	−0.461931
$286$	−0.648328	−0.0383365
$287$	−0.0134158	−0.000791909 0
$288$	5.10852	0.301022
$289$	1.01022	0.0594245
$290$	19.8578	1.16609
$291$	−7.23883	−0.424348
$292$	3.53398	0.206810
$293$	15.4143	0.900514	0.450257	−	0.892899i	$-0.351332\pi$
$293$	15.4143	0.900514	0.450257	+	0.892899i	$0.351332\pi$
$294$	19.9321	1.16246
$295$	7.75761	0.451665
$296$	−0.350539	−0.0203747
$297$	22.7666	1.32105
$298$	7.52735	0.436048
$299$	−0.563258	−0.0325741
$300$	−6.04765	−0.349161
$301$	0.121602	0.00700904
$302$	21.8744	1.25873
$303$	−4.87178	−0.279876
$304$	1.02606	0.0588486
$305$	34.0692	1.95079
$306$	−21.6798	−1.23935
$307$	−16.4540	−0.939080	−0.469540	−	0.882911i	$-0.655580\pi$
$307$	−16.4540	−0.939080	−0.469540	+	0.882911i	$0.655580\pi$
$308$	−0.0593945	−0.00338432
$309$	−28.2567	−1.60747
$310$	−20.3525	−1.15594
$311$	−18.4591	−1.04672	−0.523360	−	0.852112i	$-0.675322\pi$
$311$	−18.4591	−1.04672	−0.523360	+	0.852112i	$0.675322\pi$
$312$	−0.486872	−0.0275637
$313$	21.0641	1.19061	0.595305	−	0.803500i	$-0.297031\pi$
$313$	21.0641	1.19061	0.595305	+	0.803500i	$0.297031\pi$
$314$	−11.0165	−0.621696
$315$	0.213573	0.0120335
$316$	9.21076	0.518146
$317$	−3.59155	−0.201721	−0.100861	−	0.994901i	$-0.532160\pi$
$317$	−3.59155	−0.201721	−0.100861	+	0.994901i	$0.532160\pi$
$318$	14.3629	0.805430
$319$	−28.2114	−1.57954
$320$	2.66905	0.149204
$321$	40.9620	2.28628
$322$	−0.0516011	−0.00287561
$323$	−4.35444	−0.242288
$324$	1.77140	0.0984110
$325$	0.363128	0.0201427
$326$	−13.8827	−0.768891
$327$	−9.63337	−0.532726
$328$	−0.856487	−0.0472916
$329$	0.0237272	0.00130812
$330$	28.8189	1.58643
$331$	−13.9272	−0.765508	−0.382754	−	0.923850i	$-0.625024\pi$
$331$	−13.9272	−0.765508	−0.382754	+	0.923850i	$0.625024\pi$
$332$	6.61344	0.362960
$333$	−1.79074	−0.0981318
$334$	−13.9151	−0.761398
$335$	15.9011	0.868772
$336$	−0.0446032	−0.00243330
$337$	−5.09575	−0.277583	−0.138791	−	0.990322i	$-0.544322\pi$
$337$	−5.09575	−0.277583	−0.138791	+	0.990322i	$0.544322\pi$
$338$	−12.9708	−0.705517
$339$	−54.9119	−2.98240
$340$	−11.3270	−0.614294
$341$	28.9143	1.56580
$342$	5.24165	0.283436
$343$	−0.219289	−0.0118405
$344$	7.76330	0.418569
$345$	25.0374	1.34797
$346$	23.6917	1.27368
$347$	−20.7178	−1.11219	−0.556095	−	0.831119i	$-0.687701\pi$
$347$	−20.7178	−1.11219	−0.556095	+	0.831119i	$0.687701\pi$
$348$	−21.1858	−1.13568
$349$	27.7284	1.48427	0.742134	−	0.670251i	$-0.233814\pi$
$349$	27.7284	1.48427	0.742134	+	0.670251i	$0.233814\pi$
$350$	0.0332668	0.00177819
$351$	−1.02658	−0.0547947
$352$	−3.79185	−0.202106
$353$	−28.9504	−1.54088	−0.770438	−	0.637515i	$-0.779962\pi$
$353$	−28.9504	−1.54088	−0.770438	+	0.637515i	$0.779962\pi$
$354$	−8.27641	−0.439886
$355$	14.1676	0.751939
$356$	14.0436	0.744309
$357$	0.189289	0.0100182
$358$	−19.3462	−1.02248
$359$	20.3491	1.07398	0.536991	−	0.843588i	$-0.319561\pi$
$359$	20.3491	1.07398	0.536991	+	0.843588i	$0.319561\pi$
$360$	13.6349	0.718621
$361$	−17.9472	−0.944589
$362$	11.6943	0.614638
$363$	−9.61929	−0.504882
$364$	0.00267818	0.000140375 0
$365$	9.43235	0.493712
$366$	−36.3476	−1.89992
$367$	−3.80246	−0.198487	−0.0992433	−	0.995063i	$-0.531642\pi$
$367$	−3.80246	−0.198487	−0.0992433	+	0.995063i	$0.531642\pi$
$368$	−3.29430	−0.171727
$369$	−4.37538	−0.227773
$370$	−0.935606	−0.0486398
$371$	−0.0790071	−0.00410184
$372$	21.7136	1.12580
$373$	30.9978	1.60501	0.802504	−	0.596647i	$-0.203501\pi$
$373$	30.9978	1.60501	0.802504	+	0.596647i	$0.203501\pi$
$374$	16.0920	0.832098
$375$	21.8597	1.12883
$376$	1.51479	0.0781192
$377$	1.27209	0.0655161
$378$	−0.0940467	−0.00483724
$379$	31.8280	1.63490	0.817448	−	0.576002i	$-0.195388\pi$
$379$	31.8280	1.63490	0.817448	+	0.576002i	$0.195388\pi$
$380$	2.73860	0.140487
$381$	41.2505	2.11333
$382$	−21.8333	−1.11709
$383$	26.0281	1.32997	0.664987	−	0.746855i	$-0.268437\pi$
$383$	26.0281	1.32997	0.664987	+	0.746855i	$0.268437\pi$
$384$	−2.84755	−0.145313
$385$	−0.158527	−0.00807927
$386$	−16.9595	−0.863215
$387$	39.6589	2.01598
$388$	2.54213	0.129057
$389$	−7.84925	−0.397973	−0.198986	−	0.980002i	$-0.563765\pi$
$389$	−7.84925	−0.397973	−0.198986	+	0.980002i	$0.563765\pi$
$390$	−1.29948	−0.0658020
$391$	13.9805	0.707024
$392$	−6.99975	−0.353541
$393$	16.9088	0.852937
$394$	22.2562	1.12125
$395$	24.5840	1.23695
$396$	−19.3707	−0.973415
$397$	−26.3640	−1.32317	−0.661586	−	0.749870i	$-0.730116\pi$
$397$	−26.3640	−1.32317	−0.661586	+	0.749870i	$0.730116\pi$
$398$	−20.8691	−1.04607
$399$	−0.0457656	−0.00229115
$400$	2.12381	0.106191
$401$	−8.53458	−0.426197	−0.213098	−	0.977031i	$-0.568355\pi$
$401$	−8.53458	−0.426197	−0.213098	+	0.977031i	$0.568355\pi$
$402$	−16.9646	−0.846115
$403$	−1.30378	−0.0649461
$404$	1.71087	0.0851189
$405$	4.72794	0.234933
$406$	0.116539	0.00578372
$407$	1.32919	0.0658856
$408$	12.0845	0.598274
$409$	12.8855	0.637147	0.318574	−	0.947898i	$-0.396796\pi$
$409$	12.8855	0.637147	0.318574	+	0.947898i	$0.396796\pi$
$410$	−2.28600	−0.112898
$411$	−51.0884	−2.52000
$412$	9.92318	0.488880
$413$	0.0455268	0.00224023
$414$	−16.8290	−0.827100
$415$	17.6516	0.866482
$416$	0.170980	0.00838296
$417$	−38.7695	−1.89855
$418$	−3.89066	−0.190299
$419$	−11.5626	−0.564868	−0.282434	−	0.959287i	$-0.591142\pi$
$419$	−11.5626	−0.564868	−0.282434	+	0.959287i	$0.591142\pi$
$420$	−0.119048	−0.00580895
$421$	−13.8054	−0.672833	−0.336416	−	0.941713i	$-0.609215\pi$
$421$	−13.8054	−0.672833	−0.336416	+	0.941713i	$0.609215\pi$
$422$	−12.1868	−0.593246
$423$	7.73832	0.376250
$424$	−5.04395	−0.244956
$425$	−9.01312	−0.437201
$426$	−15.1151	−0.732330
$427$	0.199940	0.00967580
$428$	−14.3850	−0.695327
$429$	1.84614	0.0891327
$430$	20.7206	0.999236
$431$	27.9166	1.34470	0.672348	−	0.740235i	$-0.265286\pi$
$431$	27.9166	1.34470	0.672348	+	0.740235i	$0.265286\pi$
$432$	−6.00410	−0.288872
$433$	8.63242	0.414847	0.207424	−	0.978251i	$-0.433492\pi$
$433$	8.63242	0.414847	0.207424	+	0.978251i	$0.433492\pi$
$434$	−0.119442	−0.00573340
$435$	−56.5459	−2.71117
$436$	3.38304	0.162018
$437$	−3.38015	−0.161695
$438$	−10.0632	−0.480836
$439$	26.3936	1.25970	0.629849	−	0.776718i	$-0.283117\pi$
$439$	26.3936	1.25970	0.629849	+	0.776718i	$0.283117\pi$
$440$	−10.1206	−0.482481
$441$	−35.7584	−1.70278
$442$	−0.725611	−0.0345138
$443$	21.1540	1.00506	0.502528	−	0.864561i	$-0.332403\pi$
$443$	21.1540	1.00506	0.502528	+	0.864561i	$0.332403\pi$
$444$	0.998177	0.0473714
$445$	37.4830	1.77687
$446$	−20.1682	−0.954992
$447$	−21.4345	−1.01382
$448$	0.0156637	0.000740042 0
$449$	26.1213	1.23274	0.616371	−	0.787456i	$-0.288602\pi$
$449$	26.1213	1.23274	0.616371	+	0.787456i	$0.288602\pi$
$450$	10.8495	0.511451
$451$	3.24767	0.152927
$452$	19.2839	0.907040
$453$	−62.2883	−2.92656
$454$	8.71852	0.409181
$455$	0.00714819	0.000335112 0
$456$	−2.92175	−0.136824
$457$	2.23359	0.104483	0.0522414	−	0.998634i	$-0.483363\pi$
$457$	2.23359	0.104483	0.0522414	+	0.998634i	$0.483363\pi$
$458$	21.0581	0.983980
$459$	25.4805	1.18933
$460$	−8.79264	−0.409959
$461$	32.3683	1.50754	0.753771	−	0.657137i	$-0.228233\pi$
$461$	32.3683	1.50754	0.753771	+	0.657137i	$0.228233\pi$
$462$	0.169129	0.00786857
$463$	20.3548	0.945968	0.472984	−	0.881071i	$-0.343177\pi$
$463$	20.3548	0.945968	0.472984	+	0.881071i	$0.343177\pi$
$464$	7.44003	0.345395
$465$	57.9547	2.68758
$466$	24.9363	1.15515
$467$	−2.07529	−0.0960327	−0.0480164	−	0.998847i	$-0.515290\pi$
$467$	−2.07529	−0.0960327	−0.0480164	+	0.998847i	$0.515290\pi$
$468$	0.873452	0.0403753
$469$	0.0933184	0.00430904
$470$	4.04304	0.186491
$471$	31.3699	1.44545
$472$	2.90651	0.133783
$473$	−29.4372	−1.35353
$474$	−26.2281	−1.20470
$475$	2.17916	0.0999866
$476$	−0.0664745	−0.00304685
$477$	−25.7671	−1.17979
$478$	7.85045	0.359071
$479$	15.2167	0.695268	0.347634	−	0.937630i	$-0.386985\pi$
$479$	15.2167	0.695268	0.347634	+	0.937630i	$0.386985\pi$
$480$	−7.60023	−0.346902
$481$	−0.0599351	−0.00273280
$482$	5.88881	0.268228
$483$	0.146936	0.00668584
$484$	3.37810	0.153550
$485$	6.78506	0.308094
$486$	12.9682	0.588248
$487$	−12.2902	−0.556921	−0.278461	−	0.960448i	$-0.589824\pi$
$487$	−12.2902	−0.556921	−0.278461	+	0.960448i	$0.589824\pi$
$488$	12.7645	0.577824
$489$	39.5316	1.78768
$490$	−18.6827	−0.843997
$491$	31.4890	1.42108	0.710540	−	0.703657i	$-0.248451\pi$
$491$	31.4890	1.42108	0.710540	+	0.703657i	$0.248451\pi$
$492$	2.43889	0.109953
$493$	−31.5743	−1.42204
$494$	0.175435	0.00789321
$495$	−51.7013	−2.32380
$496$	−7.62538	−0.342390
$497$	0.0831450	0.00372956
$498$	−18.8321	−0.843886
$499$	−31.8659	−1.42651	−0.713257	−	0.700903i	$-0.752781\pi$
$499$	−31.8659	−1.42651	−0.713257	+	0.700903i	$0.752781\pi$
$500$	−7.67668	−0.343312
$501$	39.6238	1.77026
$502$	28.2186	1.25946
$503$	17.6818	0.788393	0.394197	−	0.919026i	$-0.371023\pi$
$503$	17.6818	0.788393	0.394197	+	0.919026i	$0.371023\pi$
$504$	0.0800185	0.00356431
$505$	4.56639	0.203202
$506$	12.4915	0.555314
$507$	36.9349	1.64033
$508$	−14.4863	−0.642727
$509$	−36.7034	−1.62685	−0.813424	−	0.581671i	$-0.802399\pi$
$509$	−36.7034	−1.62685	−0.813424	+	0.581671i	$0.802399\pi$
$510$	32.2542	1.42824
$511$	0.0553553	0.00244877
$512$	1.00000	0.0441942
$513$	−6.16057	−0.271996
$514$	−0.0783916	−0.00345771
$515$	26.4854	1.16709
$516$	−22.1063	−0.973178
$517$	−5.74384	−0.252614
$518$	−0.00549076	−0.000241250 0
$519$	−67.4633	−2.96131
$520$	0.456352	0.0200124
$521$	14.8399	0.650150	0.325075	−	0.945688i	$-0.394611\pi$
$521$	14.8399	0.650150	0.325075	+	0.945688i	$0.394611\pi$
$522$	38.0075	1.66354
$523$	−0.119125	−0.00520896	−0.00260448	−	0.999997i	$-0.500829\pi$
$523$	−0.119125	−0.00520896	−0.00260448	+	0.999997i	$0.500829\pi$
$524$	−5.93803	−0.259404
$525$	−0.0947288	−0.00413430
$526$	−32.0343	−1.39676
$527$	32.3609	1.40966
$528$	10.7975	0.469899
$529$	−12.1476	−0.528156
$530$	−13.4625	−0.584775
$531$	14.8479	0.644346
$532$	0.0160719	0.000696807 0
$533$	−0.146442	−0.00634310
$534$	−39.9898	−1.73053
$535$	−38.3943	−1.65993
$536$	5.95761	0.257329
$537$	55.0893	2.37728
$538$	−1.18823	−0.0512284
$539$	26.5420	1.14324
$540$	−16.0252	−0.689616
$541$	−21.1218	−0.908096	−0.454048	−	0.890977i	$-0.650021\pi$
$541$	−21.1218	−0.908096	−0.454048	+	0.890977i	$0.650021\pi$
$542$	26.8082	1.15151
$543$	−33.3000	−1.42904
$544$	−4.24384	−0.181953
$545$	9.02950	0.386781
$546$	−0.00762624	−0.000326373 0
$547$	30.4608	1.30241	0.651205	−	0.758902i	$-0.274264\pi$
$547$	30.4608	1.30241	0.651205	+	0.758902i	$0.274264\pi$
$548$	17.9412	0.766410
$549$	65.2079	2.78300
$550$	−8.05316	−0.343388
$551$	7.63392	0.325216
$552$	9.38067	0.399268
$553$	0.144275	0.00613520
$554$	7.60912	0.323280
$555$	2.66418	0.113088
$556$	13.6151	0.577408
$557$	30.5739	1.29546	0.647729	−	0.761871i	$-0.275719\pi$
$557$	30.5739	1.29546	0.647729	+	0.761871i	$0.275719\pi$
$558$	−38.9544	−1.64907
$559$	1.32737	0.0561416
$560$	0.0418073	0.00176668
$561$	−45.8227	−1.93464
$562$	29.5649	1.24712
$563$	−41.1625	−1.73479	−0.867396	−	0.497619i	$-0.834208\pi$
$563$	−41.1625	−1.73479	−0.867396	+	0.497619i	$0.834208\pi$
$564$	−4.31343	−0.181628
$565$	51.4697	2.16535
$566$	15.9226	0.669279
$567$	0.0277467	0.00116525
$568$	5.30812	0.222724
$569$	11.5334	0.483504	0.241752	−	0.970338i	$-0.422278\pi$
$569$	11.5334	0.483504	0.241752	+	0.970338i	$0.422278\pi$
$570$	−7.79830	−0.326635
$571$	3.35966	0.140597	0.0702987	−	0.997526i	$-0.477605\pi$
$571$	3.35966	0.140597	0.0702987	+	0.997526i	$0.477605\pi$
$572$	−0.648328	−0.0271080
$573$	62.1712	2.59724
$574$	−0.0134158	−0.000559964 0
$575$	−6.99647	−0.291773
$576$	5.10852	0.212855
$577$	−0.204780	−0.00852509	−0.00426254	−	0.999991i	$-0.501357\pi$
$577$	−0.204780	−0.00852509	−0.00426254	+	0.999991i	$0.501357\pi$
$578$	1.01022	0.0420195
$579$	48.2929	2.00699
$580$	19.8578	0.824549
$581$	0.103591	0.00429769
$582$	−7.23883	−0.300059
$583$	19.1259	0.792113
$584$	3.53398	0.146237
$585$	2.33128	0.0963868
$586$	15.4143	0.636759
$587$	23.2581	0.959964	0.479982	−	0.877278i	$-0.340643\pi$
$587$	23.2581	0.959964	0.479982	+	0.877278i	$0.340643\pi$
$588$	19.9321	0.821987
$589$	−7.82410	−0.322387
$590$	7.75761	0.319376
$591$	−63.3754	−2.60692
$592$	−0.350539	−0.0144071
$593$	−28.2832	−1.16145	−0.580725	−	0.814100i	$-0.697231\pi$
$593$	−28.2832	−1.16145	−0.580725	+	0.814100i	$0.697231\pi$
$594$	22.7666	0.934126
$595$	−0.177423	−0.00727365
$596$	7.52735	0.308332
$597$	59.4256	2.43213
$598$	−0.563258	−0.0230333
$599$	30.8655	1.26113	0.630565	−	0.776136i	$-0.282823\pi$
$599$	30.8655	1.26113	0.630565	+	0.776136i	$0.282823\pi$
$600$	−6.04765	−0.246894
$601$	−2.83208	−0.115523	−0.0577615	−	0.998330i	$-0.518396\pi$
$601$	−2.83208	−0.115523	−0.0577615	+	0.998330i	$0.518396\pi$
$602$	0.121602	0.00495614
$603$	30.4345	1.23939
$604$	21.8744	0.890056
$605$	9.01630	0.366565
$606$	−4.87178	−0.197903
$607$	23.1497	0.939616	0.469808	−	0.882769i	$-0.344323\pi$
$607$	23.1497	0.939616	0.469808	+	0.882769i	$0.344323\pi$
$608$	1.02606	0.0416122
$609$	−0.331849	−0.0134472
$610$	34.0692	1.37942
$611$	0.258998	0.0104779
$612$	−21.6798	−0.876352
$613$	6.11791	0.247100	0.123550	−	0.992338i	$-0.460572\pi$
$613$	6.11791	0.247100	0.123550	+	0.992338i	$0.460572\pi$
$614$	−16.4540	−0.664030
$615$	6.50950	0.262488
$616$	−0.0593945	−0.00239307
$617$	−22.1188	−0.890471	−0.445236	−	0.895413i	$-0.646880\pi$
$617$	−22.1188	−0.890471	−0.445236	+	0.895413i	$0.646880\pi$
$618$	−28.2567	−1.13665
$619$	−24.1610	−0.971112	−0.485556	−	0.874206i	$-0.661383\pi$
$619$	−24.1610	−0.971112	−0.485556	+	0.874206i	$0.661383\pi$
$620$	−20.3525	−0.817376
$621$	19.7793	0.793716
$622$	−18.4591	−0.740143
$623$	0.219975	0.00881312
$624$	−0.486872	−0.0194905
$625$	−31.1085	−1.24434
$626$	21.0641	0.841889
$627$	11.0788	0.442446
$628$	−11.0165	−0.439605
$629$	1.48763	0.0593159
$630$	0.213573	0.00850896
$631$	25.5023	1.01523	0.507616	−	0.861583i	$-0.330527\pi$
$631$	25.5023	1.01523	0.507616	+	0.861583i	$0.330527\pi$
$632$	9.21076	0.366384
$633$	34.7026	1.37930
$634$	−3.59155	−0.142639
$635$	−38.6647	−1.53436
$636$	14.3629	0.569525
$637$	−1.19682	−0.0474195
$638$	−28.2114	−1.11690
$639$	27.1166	1.07272
$640$	2.66905	0.105503
$641$	17.3188	0.684052	0.342026	−	0.939691i	$-0.388887\pi$
$641$	17.3188	0.684052	0.342026	+	0.939691i	$0.388887\pi$
$642$	40.9620	1.61664
$643$	−9.07456	−0.357866	−0.178933	−	0.983861i	$-0.557265\pi$
$643$	−9.07456	−0.357866	−0.178933	+	0.983861i	$0.557265\pi$
$644$	−0.0516011	−0.00203337
$645$	−59.0029	−2.32324
$646$	−4.35444	−0.171323
$647$	49.8554	1.96002	0.980009	−	0.198955i	$-0.0637549\pi$
$647$	49.8554	1.96002	0.980009	+	0.198955i	$0.0637549\pi$
$648$	1.77140	0.0695871
$649$	−11.0210	−0.432613
$650$	0.363128	0.0142431
$651$	0.340117	0.0133302
$652$	−13.8827	−0.543688
$653$	−2.81691	−0.110234	−0.0551171	−	0.998480i	$-0.517553\pi$
$653$	−2.81691	−0.110234	−0.0551171	+	0.998480i	$0.517553\pi$
$654$	−9.63337	−0.376694
$655$	−15.8489	−0.619267
$656$	−0.856487	−0.0334402
$657$	18.0534	0.704329
$658$	0.0237272	0.000924984 0
$659$	20.1302	0.784162	0.392081	−	0.919931i	$-0.371755\pi$
$659$	20.1302	0.784162	0.392081	+	0.919931i	$0.371755\pi$
$660$	28.8189	1.12177
$661$	1.05292	0.0409537	0.0204769	−	0.999790i	$-0.493482\pi$
$661$	1.05292	0.0409537	0.0204769	+	0.999790i	$0.493482\pi$
$662$	−13.9272	−0.541296
$663$	2.06621	0.0802449
$664$	6.61344	0.256651
$665$	0.0428968	0.00166347
$666$	−1.79074	−0.0693896
$667$	−24.5097	−0.949019
$668$	−13.9151	−0.538390
$669$	57.4299	2.22037
$670$	15.9011	0.614314
$671$	−48.4012	−1.86851
$672$	−0.0446032	−0.00172061
$673$	−26.1841	−1.00932	−0.504661	−	0.863317i	$-0.668383\pi$
$673$	−26.1841	−1.00932	−0.504661	+	0.863317i	$0.668383\pi$
$674$	−5.09575	−0.196281
$675$	−12.7516	−0.490808
$676$	−12.9708	−0.498876
$677$	−35.4101	−1.36092	−0.680461	−	0.732784i	$-0.738221\pi$
$677$	−35.4101	−1.36092	−0.680461	+	0.732784i	$0.738221\pi$
$678$	−54.9119	−2.10888
$679$	0.0398192	0.00152812
$680$	−11.3270	−0.434371
$681$	−24.8264	−0.951350
$682$	28.9143	1.10718
$683$	4.71856	0.180551	0.0902753	−	0.995917i	$-0.471225\pi$
$683$	4.71856	0.180551	0.0902753	+	0.995917i	$0.471225\pi$
$684$	5.24165	0.200419
$685$	47.8859	1.82962
$686$	−0.219289	−0.00837247
$687$	−59.9639	−2.28777
$688$	7.76330	0.295973
$689$	−0.862412	−0.0328553
$690$	25.0374	0.953159
$691$	26.4670	1.00685	0.503427	−	0.864038i	$-0.332072\pi$
$691$	26.4670	1.00685	0.503427	+	0.864038i	$0.332072\pi$
$692$	23.6917	0.900624
$693$	−0.303418	−0.0115259
$694$	−20.7178	−0.786437
$695$	36.3393	1.37843
$696$	−21.1858	−0.803046
$697$	3.63480	0.137678
$698$	27.7284	1.04954
$699$	−71.0071	−2.68574
$700$	0.0332668	0.00125737
$701$	−12.0577	−0.455413	−0.227707	−	0.973730i	$-0.573123\pi$
$701$	−12.0577	−0.455413	−0.227707	+	0.973730i	$0.573123\pi$
$702$	−1.02658	−0.0387457
$703$	−0.359675	−0.0135654
$704$	−3.79185	−0.142911
$705$	−11.5127	−0.433595
$706$	−28.9504	−1.08956
$707$	0.0267986	0.00100787
$708$	−8.27641	−0.311047
$709$	−39.2532	−1.47419	−0.737093	−	0.675791i	$-0.763802\pi$
$709$	−39.2532	−1.47419	−0.737093	+	0.675791i	$0.763802\pi$
$710$	14.1676	0.531701
$711$	47.0533	1.76464
$712$	14.0436	0.526306
$713$	25.1203	0.940763
$714$	0.189289	0.00708397
$715$	−1.73042	−0.0647140
$716$	−19.3462	−0.723003
$717$	−22.3545	−0.834845
$718$	20.3491	0.759420
$719$	−15.6747	−0.584569	−0.292284	−	0.956331i	$-0.594415\pi$
$719$	−15.6747	−0.584569	−0.292284	+	0.956331i	$0.594415\pi$
$720$	13.6349	0.508142
$721$	0.155434	0.00578867
$722$	−17.9472	−0.667926
$723$	−16.7687	−0.623633
$724$	11.6943	0.434615
$725$	15.8012	0.586842
$726$	−9.61929	−0.357005
$727$	−22.8361	−0.846942	−0.423471	−	0.905910i	$-0.639188\pi$
$727$	−22.8361	−0.846942	−0.423471	+	0.905910i	$0.639188\pi$
$728$	0.00267818	9.92599e−5 0
$729$	−42.2416	−1.56450
$730$	9.43235	0.349107
$731$	−32.9462	−1.21856
$732$	−36.3476	−1.34345
$733$	−31.2081	−1.15270	−0.576348	−	0.817204i	$-0.695523\pi$
$733$	−31.2081	−1.15270	−0.576348	+	0.817204i	$0.695523\pi$
$734$	−3.80246	−0.140351
$735$	53.1998	1.96230
$736$	−3.29430	−0.121430
$737$	−22.5903	−0.832125
$738$	−4.37538	−0.161060
$739$	1.44790	0.0532618	0.0266309	−	0.999645i	$-0.491522\pi$
$739$	1.44790	0.0532618	0.0266309	+	0.999645i	$0.491522\pi$
$740$	−0.935606	−0.0343936
$741$	−0.499560	−0.0183518
$742$	−0.0790071	−0.00290044
$743$	11.1181	0.407883	0.203942	−	0.978983i	$-0.434625\pi$
$743$	11.1181	0.407883	0.203942	+	0.978983i	$0.434625\pi$
$744$	21.7136	0.796060
$745$	20.0908	0.736072
$746$	30.9978	1.13491
$747$	33.7849	1.23612
$748$	16.0920	0.588382
$749$	−0.225323	−0.00823314
$750$	21.8597	0.798204
$751$	−21.3645	−0.779603	−0.389802	−	0.920899i	$-0.627456\pi$
$751$	−21.3645	−0.779603	−0.389802	+	0.920899i	$0.627456\pi$
$752$	1.51479	0.0552386
$753$	−80.3539	−2.92826
$754$	1.27209	0.0463269
$755$	58.3838	2.12480
$756$	−0.0940467	−0.00342044
$757$	26.0456	0.946642	0.473321	−	0.880890i	$-0.343055\pi$
$757$	26.0456	0.946642	0.473321	+	0.880890i	$0.343055\pi$
$758$	31.8280	1.15605
$759$	−35.5701	−1.29111
$760$	2.73860	0.0993396
$761$	−6.28916	−0.227982	−0.113991	−	0.993482i	$-0.536363\pi$
$761$	−6.28916	−0.227982	−0.113991	+	0.993482i	$0.536363\pi$
$762$	41.2505	1.49435
$763$	0.0529911	0.00191841
$764$	−21.8333	−0.789900
$765$	−57.8643	−2.09209
$766$	26.0281	0.940434
$767$	0.496953	0.0179439
$768$	−2.84755	−0.102752
$769$	−36.6635	−1.32212	−0.661061	−	0.750333i	$-0.729893\pi$
$769$	−36.6635	−1.32212	−0.661061	+	0.750333i	$0.729893\pi$
$770$	−0.158527	−0.00571290
$771$	0.223224	0.00803921
$772$	−16.9595	−0.610385
$773$	−46.1121	−1.65854	−0.829268	−	0.558851i	$-0.811242\pi$
$773$	−46.1121	−1.65854	−0.829268	+	0.558851i	$0.811242\pi$
$774$	39.6589	1.42551
$775$	−16.1949	−0.581737
$776$	2.54213	0.0912571
$777$	0.0156352	0.000560909 0
$778$	−7.84925	−0.281409
$779$	−0.878807	−0.0314865
$780$	−1.29948	−0.0465290
$781$	−20.1276	−0.720221
$782$	13.9805	0.499942
$783$	−44.6707	−1.59640
$784$	−6.99975	−0.249991
$785$	−29.4035	−1.04946
$786$	16.9088	0.603117
$787$	8.87892	0.316499	0.158250	−	0.987399i	$-0.449415\pi$
$787$	8.87892	0.316499	0.158250	+	0.987399i	$0.449415\pi$
$788$	22.2562	0.792843
$789$	91.2190	3.24748
$790$	24.5840	0.874658
$791$	0.302059	0.0107400
$792$	−19.3707	−0.688308
$793$	2.18248	0.0775020
$794$	−26.3640	−0.935623
$795$	38.3352	1.35961
$796$	−20.8691	−0.739684
$797$	−15.2274	−0.539383	−0.269691	−	0.962947i	$-0.586922\pi$
$797$	−15.2274	−0.539383	−0.269691	+	0.962947i	$0.586922\pi$
$798$	−0.0457656	−0.00162008
$799$	−6.42852	−0.227425
$800$	2.12381	0.0750880
$801$	71.7420	2.53488
$802$	−8.53458	−0.301367
$803$	−13.4003	−0.472886
$804$	−16.9646	−0.598294
$805$	−0.137726	−0.00485419
$806$	−1.30378	−0.0459239
$807$	3.38355	0.119107
$808$	1.71087	0.0601882
$809$	−7.62744	−0.268166	−0.134083	−	0.990970i	$-0.542809\pi$
$809$	−7.62744	−0.268166	−0.134083	+	0.990970i	$0.542809\pi$
$810$	4.72794	0.166123
$811$	26.9204	0.945304	0.472652	−	0.881249i	$-0.343297\pi$
$811$	26.9204	0.945304	0.472652	+	0.881249i	$0.343297\pi$
$812$	0.116539	0.00408970
$813$	−76.3376	−2.67728
$814$	1.32919	0.0465881
$815$	−37.0535	−1.29793
$816$	12.0845	0.423044
$817$	7.96561	0.278681
$818$	12.8855	0.450531
$819$	0.0136815	0.000478071 0
$820$	−2.28600	−0.0798307
$821$	9.93219	0.346636	0.173318	−	0.984866i	$-0.444551\pi$
$821$	9.93219	0.346636	0.173318	+	0.984866i	$0.444551\pi$
$822$	−51.0884	−1.78191
$823$	−14.1660	−0.493797	−0.246899	−	0.969041i	$-0.579411\pi$
$823$	−14.1660	−0.493797	−0.246899	+	0.969041i	$0.579411\pi$
$824$	9.92318	0.345690
$825$	22.9318	0.798381
$826$	0.0455268	0.00158408
$827$	30.8581	1.07304	0.536520	−	0.843888i	$-0.319739\pi$
$827$	30.8581	1.07304	0.536520	+	0.843888i	$0.319739\pi$
$828$	−16.8290	−0.584848
$829$	8.60548	0.298881	0.149440	−	0.988771i	$-0.452253\pi$
$829$	8.60548	0.298881	0.149440	+	0.988771i	$0.452253\pi$
$830$	17.6516	0.612695
$831$	−21.6673	−0.751630
$832$	0.170980	0.00592765
$833$	29.7059	1.02925
$834$	−38.7695	−1.34248
$835$	−37.1399	−1.28528
$836$	−3.89066	−0.134561
$837$	45.7836	1.58251
$838$	−11.5626	−0.399422
$839$	−7.10080	−0.245147	−0.122573	−	0.992459i	$-0.539115\pi$
$839$	−7.10080	−0.245147	−0.122573	+	0.992459i	$0.539115\pi$
$840$	−0.119048	−0.00410755
$841$	26.3540	0.908758
$842$	−13.8054	−0.475765
$843$	−84.1874	−2.89957
$844$	−12.1868	−0.419488
$845$	−34.6196	−1.19095
$846$	7.73832	0.266049
$847$	0.0529136	0.00181813
$848$	−5.04395	−0.173210
$849$	−45.3405	−1.55608
$850$	−9.01312	−0.309148
$851$	1.15478	0.0395854
$852$	−15.1151	−0.517835
$853$	−39.1959	−1.34204	−0.671021	−	0.741438i	$-0.734144\pi$
$853$	−39.1959	−1.34204	−0.671021	+	0.741438i	$0.734144\pi$
$854$	0.199940	0.00684182
$855$	13.9902	0.478455
$856$	−14.3850	−0.491670
$857$	28.1956	0.963145	0.481572	−	0.876406i	$-0.340066\pi$
$857$	28.1956	0.963145	0.481572	+	0.876406i	$0.340066\pi$
$858$	1.84614	0.0630263
$859$	−10.9843	−0.374780	−0.187390	−	0.982286i	$-0.560003\pi$
$859$	−10.9843	−0.374780	−0.187390	+	0.982286i	$0.560003\pi$
$860$	20.7206	0.706567
$861$	0.0382021	0.00130192
$862$	27.9166	0.950844
$863$	−4.42287	−0.150556	−0.0752781	−	0.997163i	$-0.523984\pi$
$863$	−4.42287	−0.150556	−0.0752781	+	0.997163i	$0.523984\pi$
$864$	−6.00410	−0.204264
$865$	63.2343	2.15003
$866$	8.63242	0.293341
$867$	−2.87664	−0.0976958
$868$	−0.119442	−0.00405413
$869$	−34.9258	−1.18478
$870$	−56.5459	−1.91709
$871$	1.01863	0.0345149
$872$	3.38304	0.114564
$873$	12.9865	0.439527
$874$	−3.38015	−0.114335
$875$	−0.120246	−0.00406504
$876$	−10.0632	−0.340003
$877$	−33.3639	−1.12662	−0.563309	−	0.826246i	$-0.690472\pi$
$877$	−33.3639	−1.12662	−0.563309	+	0.826246i	$0.690472\pi$
$878$	26.3936	0.890741
$879$	−43.8930	−1.48047
$880$	−10.1206	−0.341166
$881$	0.855443	0.0288206	0.0144103	−	0.999896i	$-0.495413\pi$
$881$	0.855443	0.0288206	0.0144103	+	0.999896i	$0.495413\pi$
$882$	−35.7584	−1.20405
$883$	36.0009	1.21153	0.605764	−	0.795645i	$-0.292868\pi$
$883$	36.0009	1.21153	0.605764	+	0.795645i	$0.292868\pi$
$884$	−0.725611	−0.0244049
$885$	−22.0901	−0.742552
$886$	21.1540	0.710681
$887$	−47.8350	−1.60614	−0.803071	−	0.595883i	$-0.796802\pi$
$887$	−47.8350	−1.60614	−0.803071	+	0.595883i	$0.796802\pi$
$888$	0.998177	0.0334966
$889$	−0.226910	−0.00761032
$890$	37.4830	1.25643
$891$	−6.71687	−0.225023
$892$	−20.1682	−0.675281
$893$	1.55426	0.0520114
$894$	−21.4345	−0.716876
$895$	−51.6360	−1.72600
$896$	0.0156637	0.000523289 0
$897$	1.60390	0.0535528
$898$	26.1213	0.871680
$899$	−56.7331	−1.89215
$900$	10.8495	0.361651
$901$	21.4057	0.713128
$902$	3.24767	0.108135
$903$	−0.346268	−0.0115231
$904$	19.2839	0.641374
$905$	31.2126	1.03754
$906$	−62.2883	−2.06939
$907$	47.8441	1.58864	0.794319	−	0.607502i	$-0.207828\pi$
$907$	47.8441	1.58864	0.794319	+	0.607502i	$0.207828\pi$
$908$	8.71852	0.289334
$909$	8.74001	0.289888
$910$	0.00714819	0.000236960 0
$911$	24.1043	0.798611	0.399305	−	0.916818i	$-0.369251\pi$
$911$	24.1043	0.798611	0.399305	+	0.916818i	$0.369251\pi$
$912$	−2.92175	−0.0967489
$913$	−25.0772	−0.829933
$914$	2.23359	0.0738805
$915$	−97.0135	−3.20717
$916$	21.0581	0.695779
$917$	−0.0930118	−0.00307152
$918$	25.4805	0.840981
$919$	29.4588	0.971757	0.485878	−	0.874026i	$-0.338500\pi$
$919$	29.4588	0.971757	0.485878	+	0.874026i	$0.338500\pi$
$920$	−8.79264	−0.289885
$921$	46.8536	1.54388
$922$	32.3683	1.06599
$923$	0.907580	0.0298734
$924$	0.169129	0.00556392
$925$	−0.744479	−0.0244783
$926$	20.3548	0.668901
$927$	50.6927	1.66497
$928$	7.44003	0.244231
$929$	−21.2417	−0.696918	−0.348459	−	0.937324i	$-0.613295\pi$
$929$	−21.2417	−0.696918	−0.348459	+	0.937324i	$0.613295\pi$
$930$	57.9547	1.90041
$931$	−7.18217	−0.235386
$932$	24.9363	0.816814
$933$	52.5632	1.72084
$934$	−2.07529	−0.0679054
$935$	42.9503	1.40463
$936$	0.873452	0.0285497
$937$	−29.0250	−0.948204	−0.474102	−	0.880470i	$-0.657227\pi$
$937$	−29.0250	−0.948204	−0.474102	+	0.880470i	$0.657227\pi$
$938$	0.0933184	0.00304695
$939$	−59.9808	−1.95740
$940$	4.04304	0.131869
$941$	−15.5610	−0.507274	−0.253637	−	0.967299i	$-0.581627\pi$
$941$	−15.5610	−0.507274	−0.253637	+	0.967299i	$0.581627\pi$
$942$	31.3699	1.02209
$943$	2.82153	0.0918815
$944$	2.90651	0.0945988
$945$	−0.251015	−0.00816552
$946$	−29.4372	−0.957087
$947$	9.35205	0.303901	0.151950	−	0.988388i	$-0.451445\pi$
$947$	9.35205	0.303901	0.151950	+	0.988388i	$0.451445\pi$
$948$	−26.2281	−0.851848
$949$	0.604238	0.0196144
$950$	2.17916	0.0707012
$951$	10.2271	0.331636
$952$	−0.0664745	−0.00215445
$953$	−31.1283	−1.00835	−0.504173	−	0.863603i	$-0.668203\pi$
$953$	−31.1283	−1.00835	−0.504173	+	0.863603i	$0.668203\pi$
$954$	−25.7671	−0.834241
$955$	−58.2740	−1.88570
$956$	7.85045	0.253902
$957$	80.3334	2.59681
$958$	15.2167	0.491629
$959$	0.281026	0.00907481
$960$	−7.60023	−0.245296
$961$	27.1465	0.875692
$962$	−0.0599351	−0.00193238
$963$	−73.4862	−2.36806
$964$	5.88881	0.189666
$965$	−45.2657	−1.45715
$966$	0.146936	0.00472760
$967$	1.70063	0.0546886	0.0273443	−	0.999626i	$-0.491295\pi$
$967$	1.70063	0.0546886	0.0273443	+	0.999626i	$0.491295\pi$
$968$	3.37810	0.108576
$969$	12.3995	0.398328
$970$	6.78506	0.217855
$971$	−49.5461	−1.59001	−0.795005	−	0.606603i	$-0.792532\pi$
$971$	−49.5461	−1.59001	−0.795005	+	0.606603i	$0.792532\pi$
$972$	12.9682	0.415954
$973$	0.213263	0.00683690
$974$	−12.2902	−0.393803
$975$	−1.03402	−0.0331153
$976$	12.7645	0.408583
$977$	−23.5699	−0.754066	−0.377033	−	0.926200i	$-0.623056\pi$
$977$	−23.5699	−0.754066	−0.377033	+	0.926200i	$0.623056\pi$
$978$	39.5316	1.26408
$979$	−53.2512	−1.70191
$980$	−18.6827	−0.596796
$981$	17.2823	0.551782
$982$	31.4890	1.00486
$983$	−9.22823	−0.294335	−0.147167	−	0.989112i	$-0.547016\pi$
$983$	−9.22823	−0.294335	−0.147167	+	0.989112i	$0.547016\pi$
$984$	2.43889	0.0777488
$985$	59.4027	1.89273
$986$	−31.5743	−1.00553
$987$	−0.0675644	−0.00215060
$988$	0.175435	0.00558134
$989$	−25.5746	−0.813226
$990$	−51.7013	−1.64318
$991$	14.1547	0.449640	0.224820	−	0.974400i	$-0.427821\pi$
$991$	14.1547	0.449640	0.224820	+	0.974400i	$0.427821\pi$
$992$	−7.62538	−0.242106
$993$	39.6583	1.25852
$994$	0.0831450	0.00263720
$995$	−55.7005	−1.76583
$996$	−18.8321	−0.596717
$997$	−40.9887	−1.29813	−0.649063	−	0.760735i	$-0.724839\pi$
$997$	−40.9887	−1.29813	−0.649063	+	0.760735i	$0.724839\pi$
$998$	−31.8659	−1.00870
$999$	2.10467	0.0665889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.9	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.84755 q^{3} +1.00000 q^{4} +2.66905 q^{5} -2.84755 q^{6} +0.0156637 q^{7} +1.00000 q^{8} +5.10852 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.84755 q^{3} +1.00000 q^{4} +2.66905 q^{5} -2.84755 q^{6} +0.0156637 q^{7} +1.00000 q^{8} +5.10852 q^{9} +2.66905 q^{10} -3.79185 q^{11} -2.84755 q^{12} +0.170980 q^{13} +0.0156637 q^{14} -7.60023 q^{15} +1.00000 q^{16} -4.24384 q^{17} +5.10852 q^{18} +1.02606 q^{19} +2.66905 q^{20} -0.0446032 q^{21} -3.79185 q^{22} -3.29430 q^{23} -2.84755 q^{24} +2.12381 q^{25} +0.170980 q^{26} -6.00410 q^{27} +0.0156637 q^{28} +7.44003 q^{29} -7.60023 q^{30} -7.62538 q^{31} +1.00000 q^{32} +10.7975 q^{33} -4.24384 q^{34} +0.0418073 q^{35} +5.10852 q^{36} -0.350539 q^{37} +1.02606 q^{38} -0.486872 q^{39} +2.66905 q^{40} -0.856487 q^{41} -0.0446032 q^{42} +7.76330 q^{43} -3.79185 q^{44} +13.6349 q^{45} -3.29430 q^{46} +1.51479 q^{47} -2.84755 q^{48} -6.99975 q^{49} +2.12381 q^{50} +12.0845 q^{51} +0.170980 q^{52} -5.04395 q^{53} -6.00410 q^{54} -10.1206 q^{55} +0.0156637 q^{56} -2.92175 q^{57} +7.44003 q^{58} +2.90651 q^{59} -7.60023 q^{60} +12.7645 q^{61} -7.62538 q^{62} +0.0800185 q^{63} +1.00000 q^{64} +0.456352 q^{65} +10.7975 q^{66} +5.95761 q^{67} -4.24384 q^{68} +9.38067 q^{69} +0.0418073 q^{70} +5.30812 q^{71} +5.10852 q^{72} +3.53398 q^{73} -0.350539 q^{74} -6.04765 q^{75} +1.02606 q^{76} -0.0593945 q^{77} -0.486872 q^{78} +9.21076 q^{79} +2.66905 q^{80} +1.77140 q^{81} -0.856487 q^{82} +6.61344 q^{83} -0.0446032 q^{84} -11.3270 q^{85} +7.76330 q^{86} -21.1858 q^{87} -3.79185 q^{88} +14.0436 q^{89} +13.6349 q^{90} +0.00267818 q^{91} -3.29430 q^{92} +21.7136 q^{93} +1.51479 q^{94} +2.73860 q^{95} -2.84755 q^{96} +2.54213 q^{97} -6.99975 q^{98} -19.3707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 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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