LMFDB - Embedded newform 8022.2.a.ba.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 39 x^{14} + 165 x^{13} + 711 x^{12} - 1949 x^{11} - 7497 x^{10} + 8238 x^{9} + \cdots + 30 $ x^16 - 5x^15 - 39x^14 + 165x^13 + 711x^12 - 1949x^11 - 7497x^10 + 8238x^9 + 42708x^8 + 7872x^7 - 97852x^6 - 109082x^5 - 6830x^4 + 49478x^3 + 28368x^2 + 4947*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.00628856$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00629 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00629 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00629 q^{10} +2.87780 q^{11} +1.00000 q^{12} -0.895144 q^{13} +1.00000 q^{14} +1.00629 q^{15} +1.00000 q^{16} +8.14516 q^{17} +1.00000 q^{18} -1.30576 q^{19} +1.00629 q^{20} +1.00000 q^{21} +2.87780 q^{22} +9.32225 q^{23} +1.00000 q^{24} -3.98738 q^{25} -0.895144 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.66835 q^{29} +1.00629 q^{30} -0.677888 q^{31} +1.00000 q^{32} +2.87780 q^{33} +8.14516 q^{34} +1.00629 q^{35} +1.00000 q^{36} -2.86269 q^{37} -1.30576 q^{38} -0.895144 q^{39} +1.00629 q^{40} -0.449179 q^{41} +1.00000 q^{42} -0.0748457 q^{43} +2.87780 q^{44} +1.00629 q^{45} +9.32225 q^{46} +2.70332 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.98738 q^{50} +8.14516 q^{51} -0.895144 q^{52} +5.65631 q^{53} +1.00000 q^{54} +2.89590 q^{55} +1.00000 q^{56} -1.30576 q^{57} -6.66835 q^{58} -4.68908 q^{59} +1.00629 q^{60} +0.733444 q^{61} -0.677888 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.900773 q^{65} +2.87780 q^{66} +0.0484279 q^{67} +8.14516 q^{68} +9.32225 q^{69} +1.00629 q^{70} +5.60716 q^{71} +1.00000 q^{72} -7.92211 q^{73} -2.86269 q^{74} -3.98738 q^{75} -1.30576 q^{76} +2.87780 q^{77} -0.895144 q^{78} -14.8166 q^{79} +1.00629 q^{80} +1.00000 q^{81} -0.449179 q^{82} -9.59491 q^{83} +1.00000 q^{84} +8.19638 q^{85} -0.0748457 q^{86} -6.66835 q^{87} +2.87780 q^{88} +15.9838 q^{89} +1.00629 q^{90} -0.895144 q^{91} +9.32225 q^{92} -0.677888 q^{93} +2.70332 q^{94} -1.31397 q^{95} +1.00000 q^{96} -4.86164 q^{97} +1.00000 q^{98} +2.87780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00629	0.450026	0.225013	−	0.974356i	$-0.427758\pi$
$5$	1.00629	0.450026	0.225013	+	0.974356i	$0.427758\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00629	0.318216
$11$	2.87780	0.867690	0.433845	−	0.900987i	$-0.357157\pi$
$11$	2.87780	0.867690	0.433845	+	0.900987i	$0.357157\pi$
$12$	1.00000	0.288675
$13$	−0.895144	−0.248268	−0.124134	−	0.992265i	$-0.539615\pi$
$13$	−0.895144	−0.248268	−0.124134	+	0.992265i	$0.539615\pi$
$14$	1.00000	0.267261
$15$	1.00629	0.259823
$16$	1.00000	0.250000
$17$	8.14516	1.97549	0.987746	−	0.156071i	$-0.0498828\pi$
$17$	8.14516	1.97549	0.987746	+	0.156071i	$0.0498828\pi$
$18$	1.00000	0.235702
$19$	−1.30576	−0.299561	−0.149781	−	0.988719i	$-0.547857\pi$
$19$	−1.30576	−0.299561	−0.149781	+	0.988719i	$0.547857\pi$
$20$	1.00629	0.225013
$21$	1.00000	0.218218
$22$	2.87780	0.613550
$23$	9.32225	1.94382	0.971911	−	0.235347i	$-0.0756227\pi$
$23$	9.32225	1.94382	0.971911	+	0.235347i	$0.0756227\pi$
$24$	1.00000	0.204124
$25$	−3.98738	−0.797477
$26$	−0.895144	−0.175552
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.66835	−1.23828	−0.619141	−	0.785280i	$-0.712519\pi$
$29$	−6.66835	−1.23828	−0.619141	+	0.785280i	$0.712519\pi$
$30$	1.00629	0.183722
$31$	−0.677888	−0.121752	−0.0608762	−	0.998145i	$-0.519389\pi$
$31$	−0.677888	−0.121752	−0.0608762	+	0.998145i	$0.519389\pi$
$32$	1.00000	0.176777
$33$	2.87780	0.500961
$34$	8.14516	1.39688
$35$	1.00629	0.170094
$36$	1.00000	0.166667
$37$	−2.86269	−0.470623	−0.235312	−	0.971920i	$-0.575611\pi$
$37$	−2.86269	−0.470623	−0.235312	+	0.971920i	$0.575611\pi$
$38$	−1.30576	−0.211822
$39$	−0.895144	−0.143338
$40$	1.00629	0.159108
$41$	−0.449179	−0.0701500	−0.0350750	−	0.999385i	$-0.511167\pi$
$41$	−0.449179	−0.0701500	−0.0350750	+	0.999385i	$0.511167\pi$
$42$	1.00000	0.154303
$43$	−0.0748457	−0.0114139	−0.00570693	−	0.999984i	$-0.501817\pi$
$43$	−0.0748457	−0.0114139	−0.00570693	+	0.999984i	$0.501817\pi$
$44$	2.87780	0.433845
$45$	1.00629	0.150009
$46$	9.32225	1.37449
$47$	2.70332	0.394320	0.197160	−	0.980371i	$-0.436828\pi$
$47$	2.70332	0.394320	0.197160	+	0.980371i	$0.436828\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−3.98738	−0.563901
$51$	8.14516	1.14055
$52$	−0.895144	−0.124134
$53$	5.65631	0.776954	0.388477	−	0.921459i	$-0.373001\pi$
$53$	5.65631	0.776954	0.388477	+	0.921459i	$0.373001\pi$
$54$	1.00000	0.136083
$55$	2.89590	0.390483
$56$	1.00000	0.133631
$57$	−1.30576	−0.172952
$58$	−6.66835	−0.875598
$59$	−4.68908	−0.610466	−0.305233	−	0.952278i	$-0.598734\pi$
$59$	−4.68908	−0.610466	−0.305233	+	0.952278i	$0.598734\pi$
$60$	1.00629	0.129911
$61$	0.733444	0.0939079	0.0469540	−	0.998897i	$-0.485049\pi$
$61$	0.733444	0.0939079	0.0469540	+	0.998897i	$0.485049\pi$
$62$	−0.677888	−0.0860919
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−0.900773	−0.111727
$66$	2.87780	0.354233
$67$	0.0484279	0.00591641	0.00295821	−	0.999996i	$-0.499058\pi$
$67$	0.0484279	0.00591641	0.00295821	+	0.999996i	$0.499058\pi$
$68$	8.14516	0.987746
$69$	9.32225	1.12227
$70$	1.00629	0.120274
$71$	5.60716	0.665447	0.332724	−	0.943024i	$-0.392032\pi$
$71$	5.60716	0.665447	0.332724	+	0.943024i	$0.392032\pi$
$72$	1.00000	0.117851
$73$	−7.92211	−0.927213	−0.463606	−	0.886041i	$-0.653445\pi$
$73$	−7.92211	−0.927213	−0.463606	+	0.886041i	$0.653445\pi$
$74$	−2.86269	−0.332781
$75$	−3.98738	−0.460423
$76$	−1.30576	−0.149781
$77$	2.87780	0.327956
$78$	−0.895144	−0.101355
$79$	−14.8166	−1.66700	−0.833498	−	0.552523i	$-0.813665\pi$
$79$	−14.8166	−1.66700	−0.833498	+	0.552523i	$0.813665\pi$
$80$	1.00629	0.112506
$81$	1.00000	0.111111
$82$	−0.449179	−0.0496036
$83$	−9.59491	−1.05318	−0.526589	−	0.850120i	$-0.676529\pi$
$83$	−9.59491	−1.05318	−0.526589	+	0.850120i	$0.676529\pi$
$84$	1.00000	0.109109
$85$	8.19638	0.889023
$86$	−0.0748457	−0.00807082
$87$	−6.66835	−0.714922
$88$	2.87780	0.306775
$89$	15.9838	1.69428	0.847140	−	0.531370i	$-0.178322\pi$
$89$	15.9838	1.69428	0.847140	+	0.531370i	$0.178322\pi$
$90$	1.00629	0.106072
$91$	−0.895144	−0.0938366
$92$	9.32225	0.971911
$93$	−0.677888	−0.0702938
$94$	2.70332	0.278827
$95$	−1.31397	−0.134810
$96$	1.00000	0.102062
$97$	−4.86164	−0.493625	−0.246812	−	0.969063i	$-0.579383\pi$
$97$	−4.86164	−0.493625	−0.246812	+	0.969063i	$0.579383\pi$
$98$	1.00000	0.101015
$99$	2.87780	0.289230
$100$	−3.98738	−0.398738
$101$	−1.83118	−0.182210	−0.0911049	−	0.995841i	$-0.529040\pi$
$101$	−1.83118	−0.182210	−0.0911049	+	0.995841i	$0.529040\pi$
$102$	8.14516	0.806491
$103$	0.735881	0.0725085	0.0362542	−	0.999343i	$-0.488457\pi$
$103$	0.735881	0.0725085	0.0362542	+	0.999343i	$0.488457\pi$
$104$	−0.895144	−0.0877761
$105$	1.00629	0.0982037
$106$	5.65631	0.549389
$107$	−4.06002	−0.392497	−0.196248	−	0.980554i	$-0.562876\pi$
$107$	−4.06002	−0.392497	−0.196248	+	0.980554i	$0.562876\pi$
$108$	1.00000	0.0962250
$109$	11.2835	1.08077	0.540383	−	0.841419i	$-0.318279\pi$
$109$	11.2835	1.08077	0.540383	+	0.841419i	$0.318279\pi$
$110$	2.89590	0.276113
$111$	−2.86269	−0.271714
$112$	1.00000	0.0944911
$113$	12.5594	1.18149	0.590744	−	0.806859i	$-0.298834\pi$
$113$	12.5594	1.18149	0.590744	+	0.806859i	$0.298834\pi$
$114$	−1.30576	−0.122295
$115$	9.38087	0.874771
$116$	−6.66835	−0.619141
$117$	−0.895144	−0.0827561
$118$	−4.68908	−0.431665
$119$	8.14516	0.746666
$120$	1.00629	0.0918612
$121$	−2.71825	−0.247114
$122$	0.733444	0.0664029
$123$	−0.449179	−0.0405011
$124$	−0.677888	−0.0608762
$125$	−9.04390	−0.808911
$126$	1.00000	0.0890871
$127$	−18.4685	−1.63881	−0.819405	−	0.573215i	$-0.805696\pi$
$127$	−18.4685	−1.63881	−0.819405	+	0.573215i	$0.805696\pi$
$128$	1.00000	0.0883883
$129$	−0.0748457	−0.00658980
$130$	−0.900773	−0.0790030
$131$	12.5673	1.09801	0.549004	−	0.835820i	$-0.315007\pi$
$131$	12.5673	1.09801	0.549004	+	0.835820i	$0.315007\pi$
$132$	2.87780	0.250481
$133$	−1.30576	−0.113223
$134$	0.0484279	0.00418353
$135$	1.00629	0.0866075
$136$	8.14516	0.698442
$137$	−8.10947	−0.692838	−0.346419	−	0.938080i	$-0.612603\pi$
$137$	−8.10947	−0.692838	−0.346419	+	0.938080i	$0.612603\pi$
$138$	9.32225	0.793562
$139$	−17.8122	−1.51081	−0.755404	−	0.655260i	$-0.772559\pi$
$139$	−17.8122	−1.51081	−0.755404	+	0.655260i	$0.772559\pi$
$140$	1.00629	0.0850469
$141$	2.70332	0.227661
$142$	5.60716	0.470542
$143$	−2.57605	−0.215420
$144$	1.00000	0.0833333
$145$	−6.71029	−0.557259
$146$	−7.92211	−0.655638
$147$	1.00000	0.0824786
$148$	−2.86269	−0.235312
$149$	3.64991	0.299013	0.149506	−	0.988761i	$-0.452232\pi$
$149$	3.64991	0.299013	0.149506	+	0.988761i	$0.452232\pi$
$150$	−3.98738	−0.325568
$151$	9.09373	0.740037	0.370019	−	0.929024i	$-0.379351\pi$
$151$	9.09373	0.740037	0.370019	+	0.929024i	$0.379351\pi$
$152$	−1.30576	−0.105911
$153$	8.14516	0.658497
$154$	2.87780	0.231900
$155$	−0.682151	−0.0547917
$156$	−0.895144	−0.0716689
$157$	3.69384	0.294801	0.147400	−	0.989077i	$-0.452909\pi$
$157$	3.69384	0.294801	0.147400	+	0.989077i	$0.452909\pi$
$158$	−14.8166	−1.17874
$159$	5.65631	0.448574
$160$	1.00629	0.0795541
$161$	9.32225	0.734696
$162$	1.00000	0.0785674
$163$	−10.1928	−0.798361	−0.399181	−	0.916872i	$-0.630705\pi$
$163$	−10.1928	−0.798361	−0.399181	+	0.916872i	$0.630705\pi$
$164$	−0.449179	−0.0350750
$165$	2.89590	0.225445
$166$	−9.59491	−0.744709
$167$	2.75016	0.212814	0.106407	−	0.994323i	$-0.466065\pi$
$167$	2.75016	0.212814	0.106407	+	0.994323i	$0.466065\pi$
$168$	1.00000	0.0771517
$169$	−12.1987	−0.938363
$170$	8.19638	0.628634
$171$	−1.30576	−0.0998537
$172$	−0.0748457	−0.00570693
$173$	11.2152	0.852679	0.426339	−	0.904563i	$-0.359803\pi$
$173$	11.2152	0.852679	0.426339	+	0.904563i	$0.359803\pi$
$174$	−6.66835	−0.505527
$175$	−3.98738	−0.301418
$176$	2.87780	0.216923
$177$	−4.68908	−0.352453
$178$	15.9838	1.19804
$179$	−12.8192	−0.958150	−0.479075	−	0.877774i	$-0.659028\pi$
$179$	−12.8192	−0.958150	−0.479075	+	0.877774i	$0.659028\pi$
$180$	1.00629	0.0750043
$181$	−10.8436	−0.806000	−0.403000	−	0.915200i	$-0.632032\pi$
$181$	−10.8436	−0.806000	−0.403000	+	0.915200i	$0.632032\pi$
$182$	−0.895144	−0.0663525
$183$	0.733444	0.0542178
$184$	9.32225	0.687245
$185$	−2.88069	−0.211793
$186$	−0.677888	−0.0497052
$187$	23.4402	1.71411
$188$	2.70332	0.197160
$189$	1.00000	0.0727393
$190$	−1.31397	−0.0953252
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	19.2806	1.38785	0.693923	−	0.720049i	$-0.255881\pi$
$193$	19.2806	1.38785	0.693923	+	0.720049i	$0.255881\pi$
$194$	−4.86164	−0.349045
$195$	−0.900773	−0.0645057
$196$	1.00000	0.0714286
$197$	5.57020	0.396860	0.198430	−	0.980115i	$-0.436416\pi$
$197$	5.57020	0.396860	0.198430	+	0.980115i	$0.436416\pi$
$198$	2.87780	0.204517
$199$	−0.166331	−0.0117909	−0.00589543	−	0.999983i	$-0.501877\pi$
$199$	−0.166331	−0.0117909	−0.00589543	+	0.999983i	$0.501877\pi$
$200$	−3.98738	−0.281951
$201$	0.0484279	0.00341584
$202$	−1.83118	−0.128842
$203$	−6.66835	−0.468027
$204$	8.14516	0.570275
$205$	−0.452004	−0.0315693
$206$	0.735881	0.0512712
$207$	9.32225	0.647941
$208$	−0.895144	−0.0620671
$209$	−3.75771	−0.259926
$210$	1.00629	0.0694405
$211$	−0.755402	−0.0520040	−0.0260020	−	0.999662i	$-0.508278\pi$
$211$	−0.755402	−0.0520040	−0.0260020	+	0.999662i	$0.508278\pi$
$212$	5.65631	0.388477
$213$	5.60716	0.384196
$214$	−4.06002	−0.277537
$215$	−0.0753164	−0.00513654
$216$	1.00000	0.0680414
$217$	−0.677888	−0.0460181
$218$	11.2835	0.764217
$219$	−7.92211	−0.535326
$220$	2.89590	0.195242
$221$	−7.29109	−0.490452
$222$	−2.86269	−0.192131
$223$	2.34324	0.156915	0.0784576	−	0.996917i	$-0.475000\pi$
$223$	2.34324	0.156915	0.0784576	+	0.996917i	$0.475000\pi$
$224$	1.00000	0.0668153
$225$	−3.98738	−0.265826
$226$	12.5594	0.835438
$227$	8.63146	0.572890	0.286445	−	0.958097i	$-0.407526\pi$
$227$	8.63146	0.572890	0.286445	+	0.958097i	$0.407526\pi$
$228$	−1.30576	−0.0864758
$229$	24.3646	1.61006	0.805029	−	0.593236i	$-0.202150\pi$
$229$	24.3646	1.61006	0.805029	+	0.593236i	$0.202150\pi$
$230$	9.38087	0.618556
$231$	2.87780	0.189346
$232$	−6.66835	−0.437799
$233$	28.2984	1.85389	0.926944	−	0.375200i	$-0.122426\pi$
$233$	28.2984	1.85389	0.926944	+	0.375200i	$0.122426\pi$
$234$	−0.895144	−0.0585174
$235$	2.72032	0.177454
$236$	−4.68908	−0.305233
$237$	−14.8166	−0.962440
$238$	8.14516	0.527972
$239$	12.0954	0.782386	0.391193	−	0.920309i	$-0.372062\pi$
$239$	12.0954	0.782386	0.391193	+	0.920309i	$0.372062\pi$
$240$	1.00629	0.0649556
$241$	8.39579	0.540821	0.270410	−	0.962745i	$-0.412841\pi$
$241$	8.39579	0.540821	0.270410	+	0.962745i	$0.412841\pi$
$242$	−2.71825	−0.174736
$243$	1.00000	0.0641500
$244$	0.733444	0.0469540
$245$	1.00629	0.0642894
$246$	−0.449179	−0.0286386
$247$	1.16884	0.0743715
$248$	−0.677888	−0.0430460
$249$	−9.59491	−0.608053
$250$	−9.04390	−0.571987
$251$	5.68724	0.358976	0.179488	−	0.983760i	$-0.442556\pi$
$251$	5.68724	0.358976	0.179488	+	0.983760i	$0.442556\pi$
$252$	1.00000	0.0629941
$253$	26.8276	1.68664
$254$	−18.4685	−1.15881
$255$	8.19638	0.513277
$256$	1.00000	0.0625000
$257$	4.50667	0.281119	0.140559	−	0.990072i	$-0.455110\pi$
$257$	4.50667	0.281119	0.140559	+	0.990072i	$0.455110\pi$
$258$	−0.0748457	−0.00465969
$259$	−2.86269	−0.177879
$260$	−0.900773	−0.0558636
$261$	−6.66835	−0.412761
$262$	12.5673	0.776409
$263$	−11.9469	−0.736679	−0.368340	−	0.929691i	$-0.620074\pi$
$263$	−11.9469	−0.736679	−0.368340	+	0.929691i	$0.620074\pi$
$264$	2.87780	0.177117
$265$	5.69188	0.349649
$266$	−1.30576	−0.0800611
$267$	15.9838	0.978193
$268$	0.0484279	0.00295821
$269$	−19.9590	−1.21692	−0.608460	−	0.793584i	$-0.708212\pi$
$269$	−19.9590	−1.21692	−0.608460	+	0.793584i	$0.708212\pi$
$270$	1.00629	0.0612408
$271$	11.2408	0.682828	0.341414	−	0.939913i	$-0.389094\pi$
$271$	11.2408	0.682828	0.341414	+	0.939913i	$0.389094\pi$
$272$	8.14516	0.493873
$273$	−0.895144	−0.0541766
$274$	−8.10947	−0.489911
$275$	−11.4749	−0.691963
$276$	9.32225	0.561133
$277$	−20.9964	−1.26155	−0.630775	−	0.775965i	$-0.717263\pi$
$277$	−20.9964	−1.26155	−0.630775	+	0.775965i	$0.717263\pi$
$278$	−17.8122	−1.06830
$279$	−0.677888	−0.0405841
$280$	1.00629	0.0601372
$281$	−9.71324	−0.579444	−0.289722	−	0.957111i	$-0.593563\pi$
$281$	−9.71324	−0.579444	−0.289722	+	0.957111i	$0.593563\pi$
$282$	2.70332	0.160981
$283$	22.9609	1.36488	0.682441	−	0.730941i	$-0.260919\pi$
$283$	22.9609	1.36488	0.682441	+	0.730941i	$0.260919\pi$
$284$	5.60716	0.332724
$285$	−1.31397	−0.0778327
$286$	−2.57605	−0.152325
$287$	−0.449179	−0.0265142
$288$	1.00000	0.0589256
$289$	49.3437	2.90257
$290$	−6.71029	−0.394042
$291$	−4.86164	−0.284994
$292$	−7.92211	−0.463606
$293$	0.504153	0.0294529	0.0147265	−	0.999892i	$-0.495312\pi$
$293$	0.504153	0.0294529	0.0147265	+	0.999892i	$0.495312\pi$
$294$	1.00000	0.0583212
$295$	−4.71856	−0.274725
$296$	−2.86269	−0.166390
$297$	2.87780	0.166987
$298$	3.64991	0.211434
$299$	−8.34475	−0.482589
$300$	−3.98738	−0.230212
$301$	−0.0748457	−0.00431404
$302$	9.09373	0.523285
$303$	−1.83118	−0.105199
$304$	−1.30576	−0.0748903
$305$	0.738057	0.0422610
$306$	8.14516	0.465628
$307$	9.22411	0.526448	0.263224	−	0.964735i	$-0.415214\pi$
$307$	9.22411	0.526448	0.263224	+	0.964735i	$0.415214\pi$
$308$	2.87780	0.163978
$309$	0.735881	0.0418628
$310$	−0.682151	−0.0387436
$311$	2.28627	0.129642	0.0648212	−	0.997897i	$-0.479352\pi$
$311$	2.28627	0.129642	0.0648212	+	0.997897i	$0.479352\pi$
$312$	−0.895144	−0.0506775
$313$	−20.9662	−1.18508	−0.592539	−	0.805542i	$-0.701874\pi$
$313$	−20.9662	−1.18508	−0.592539	+	0.805542i	$0.701874\pi$
$314$	3.69384	0.208456
$315$	1.00629	0.0566979
$316$	−14.8166	−0.833498
$317$	−19.4985	−1.09515	−0.547573	−	0.836758i	$-0.684448\pi$
$317$	−19.4985	−1.09515	−0.547573	+	0.836758i	$0.684448\pi$
$318$	5.65631	0.317190
$319$	−19.1902	−1.07445
$320$	1.00629	0.0562532
$321$	−4.06002	−0.226608
$322$	9.32225	0.519508
$323$	−10.6356	−0.591780
$324$	1.00000	0.0555556
$325$	3.56928	0.197988
$326$	−10.1928	−0.564527
$327$	11.2835	0.623980
$328$	−0.449179	−0.0248018
$329$	2.70332	0.149039
$330$	2.89590	0.159414
$331$	21.1483	1.16242	0.581208	−	0.813755i	$-0.302580\pi$
$331$	21.1483	1.16242	0.581208	+	0.813755i	$0.302580\pi$
$332$	−9.59491	−0.526589
$333$	−2.86269	−0.156874
$334$	2.75016	0.150482
$335$	0.0487324	0.00266254
$336$	1.00000	0.0545545
$337$	−18.5338	−1.00960	−0.504800	−	0.863236i	$-0.668434\pi$
$337$	−18.5338	−1.00960	−0.504800	+	0.863236i	$0.668434\pi$
$338$	−12.1987	−0.663523
$339$	12.5594	0.682132
$340$	8.19638	0.444511
$341$	−1.95083	−0.105643
$342$	−1.30576	−0.0706072
$343$	1.00000	0.0539949
$344$	−0.0748457	−0.00403541
$345$	9.38087	0.505049
$346$	11.2152	0.602935
$347$	−20.0161	−1.07452	−0.537259	−	0.843417i	$-0.680540\pi$
$347$	−20.0161	−1.07452	−0.537259	+	0.843417i	$0.680540\pi$
$348$	−6.66835	−0.357461
$349$	7.23549	0.387307	0.193653	−	0.981070i	$-0.437966\pi$
$349$	7.23549	0.387307	0.193653	+	0.981070i	$0.437966\pi$
$350$	−3.98738	−0.213135
$351$	−0.895144	−0.0477792
$352$	2.87780	0.153387
$353$	−15.7627	−0.838966	−0.419483	−	0.907763i	$-0.637789\pi$
$353$	−15.7627	−0.838966	−0.419483	+	0.907763i	$0.637789\pi$
$354$	−4.68908	−0.249222
$355$	5.64242	0.299468
$356$	15.9838	0.847140
$357$	8.14516	0.431088
$358$	−12.8192	−0.677514
$359$	9.69437	0.511649	0.255825	−	0.966723i	$-0.417653\pi$
$359$	9.69437	0.511649	0.255825	+	0.966723i	$0.417653\pi$
$360$	1.00629	0.0530361
$361$	−17.2950	−0.910263
$362$	−10.8436	−0.569928
$363$	−2.71825	−0.142671
$364$	−0.895144	−0.0469183
$365$	−7.97193	−0.417270
$366$	0.733444	0.0383378
$367$	−17.2969	−0.902891	−0.451445	−	0.892299i	$-0.649091\pi$
$367$	−17.2969	−0.902891	−0.451445	+	0.892299i	$0.649091\pi$
$368$	9.32225	0.485956
$369$	−0.449179	−0.0233833
$370$	−2.88069	−0.149760
$371$	5.65631	0.293661
$372$	−0.677888	−0.0351469
$373$	1.76417	0.0913451	0.0456726	−	0.998956i	$-0.485457\pi$
$373$	1.76417	0.0913451	0.0456726	+	0.998956i	$0.485457\pi$
$374$	23.4402	1.21206
$375$	−9.04390	−0.467025
$376$	2.70332	0.139413
$377$	5.96913	0.307426
$378$	1.00000	0.0514344
$379$	19.6001	1.00679	0.503395	−	0.864056i	$-0.332084\pi$
$379$	19.6001	1.00679	0.503395	+	0.864056i	$0.332084\pi$
$380$	−1.31397	−0.0674051
$381$	−18.4685	−0.946168
$382$	−1.00000	−0.0511645
$383$	21.8003	1.11394	0.556971	−	0.830532i	$-0.311964\pi$
$383$	21.8003	1.11394	0.556971	+	0.830532i	$0.311964\pi$
$384$	1.00000	0.0510310
$385$	2.89590	0.147589
$386$	19.2806	0.981356
$387$	−0.0748457	−0.00380462
$388$	−4.86164	−0.246812
$389$	−32.2414	−1.63471	−0.817353	−	0.576137i	$-0.804559\pi$
$389$	−32.2414	−1.63471	−0.817353	+	0.576137i	$0.804559\pi$
$390$	−0.900773	−0.0456124
$391$	75.9312	3.84001
$392$	1.00000	0.0505076
$393$	12.5673	0.633935
$394$	5.57020	0.280622
$395$	−14.9098	−0.750191
$396$	2.87780	0.144615
$397$	−29.2564	−1.46834	−0.734168	−	0.678968i	$-0.762428\pi$
$397$	−29.2564	−1.46834	−0.734168	+	0.678968i	$0.762428\pi$
$398$	−0.166331	−0.00833740
$399$	−1.30576	−0.0653696
$400$	−3.98738	−0.199369
$401$	−8.77312	−0.438109	−0.219054	−	0.975713i	$-0.570297\pi$
$401$	−8.77312	−0.438109	−0.219054	+	0.975713i	$0.570297\pi$
$402$	0.0484279	0.00241536
$403$	0.606808	0.0302272
$404$	−1.83118	−0.0911049
$405$	1.00629	0.0500029
$406$	−6.66835	−0.330945
$407$	−8.23826	−0.408355
$408$	8.14516	0.403246
$409$	22.2968	1.10250	0.551252	−	0.834339i	$-0.314150\pi$
$409$	22.2968	1.10250	0.551252	+	0.834339i	$0.314150\pi$
$410$	−0.452004	−0.0223229
$411$	−8.10947	−0.400010
$412$	0.735881	0.0362542
$413$	−4.68908	−0.230734
$414$	9.32225	0.458163
$415$	−9.65525	−0.473957
$416$	−0.895144	−0.0438880
$417$	−17.8122	−0.872265
$418$	−3.75771	−0.183796
$419$	−29.8518	−1.45835	−0.729177	−	0.684325i	$-0.760097\pi$
$419$	−29.8518	−1.45835	−0.729177	+	0.684325i	$0.760097\pi$
$420$	1.00629	0.0491019
$421$	−18.0829	−0.881304	−0.440652	−	0.897678i	$-0.645253\pi$
$421$	−18.0829	−0.881304	−0.440652	+	0.897678i	$0.645253\pi$
$422$	−0.755402	−0.0367724
$423$	2.70332	0.131440
$424$	5.65631	0.274695
$425$	−32.4779	−1.57541
$426$	5.60716	0.271668
$427$	0.733444	0.0354939
$428$	−4.06002	−0.196248
$429$	−2.57605	−0.124373
$430$	−0.0753164	−0.00363208
$431$	14.3067	0.689131	0.344565	−	0.938762i	$-0.388026\pi$
$431$	14.3067	0.689131	0.344565	+	0.938762i	$0.388026\pi$
$432$	1.00000	0.0481125
$433$	−17.0525	−0.819490	−0.409745	−	0.912200i	$-0.634382\pi$
$433$	−17.0525	−0.819490	−0.409745	+	0.912200i	$0.634382\pi$
$434$	−0.677888	−0.0325397
$435$	−6.71029	−0.321734
$436$	11.2835	0.540383
$437$	−12.1726	−0.582294
$438$	−7.92211	−0.378533
$439$	−8.66189	−0.413409	−0.206705	−	0.978403i	$-0.566274\pi$
$439$	−8.66189	−0.413409	−0.206705	+	0.978403i	$0.566274\pi$
$440$	2.89590	0.138057
$441$	1.00000	0.0476190
$442$	−7.29109	−0.346802
$443$	−10.6224	−0.504686	−0.252343	−	0.967638i	$-0.581201\pi$
$443$	−10.6224	−0.504686	−0.252343	+	0.967638i	$0.581201\pi$
$444$	−2.86269	−0.135857
$445$	16.0843	0.762470
$446$	2.34324	0.110956
$447$	3.64991	0.172635
$448$	1.00000	0.0472456
$449$	12.0008	0.566351	0.283176	−	0.959068i	$-0.408612\pi$
$449$	12.0008	0.566351	0.283176	+	0.959068i	$0.408612\pi$
$450$	−3.98738	−0.187967
$451$	−1.29265	−0.0608685
$452$	12.5594	0.590744
$453$	9.09373	0.427261
$454$	8.63146	0.405094
$455$	−0.900773	−0.0422289
$456$	−1.30576	−0.0611477
$457$	−13.1713	−0.616128	−0.308064	−	0.951366i	$-0.599681\pi$
$457$	−13.1713	−0.616128	−0.308064	+	0.951366i	$0.599681\pi$
$458$	24.3646	1.13848
$459$	8.14516	0.380184
$460$	9.38087	0.437385
$461$	3.47126	0.161673	0.0808364	−	0.996727i	$-0.474241\pi$
$461$	3.47126	0.161673	0.0808364	+	0.996727i	$0.474241\pi$
$462$	2.87780	0.133887
$463$	−34.2024	−1.58952	−0.794759	−	0.606925i	$-0.792403\pi$
$463$	−34.2024	−1.58952	−0.794759	+	0.606925i	$0.792403\pi$
$464$	−6.66835	−0.309571
$465$	−0.682151	−0.0316340
$466$	28.2984	1.31090
$467$	13.7055	0.634215	0.317108	−	0.948390i	$-0.397288\pi$
$467$	13.7055	0.634215	0.317108	+	0.948390i	$0.397288\pi$
$468$	−0.895144	−0.0413780
$469$	0.0484279	0.00223619
$470$	2.72032	0.125479
$471$	3.69384	0.170203
$472$	−4.68908	−0.215832
$473$	−0.215391	−0.00990370
$474$	−14.8166	−0.680548
$475$	5.20655	0.238893
$476$	8.14516	0.373333
$477$	5.65631	0.258985
$478$	12.0954	0.553231
$479$	18.8534	0.861433	0.430716	−	0.902487i	$-0.358261\pi$
$479$	18.8534	0.861433	0.430716	+	0.902487i	$0.358261\pi$
$480$	1.00629	0.0459306
$481$	2.56252	0.116841
$482$	8.39579	0.382418
$483$	9.32225	0.424177
$484$	−2.71825	−0.123557
$485$	−4.89221	−0.222144
$486$	1.00000	0.0453609
$487$	8.45906	0.383317	0.191658	−	0.981462i	$-0.438613\pi$
$487$	8.45906	0.383317	0.191658	+	0.981462i	$0.438613\pi$
$488$	0.733444	0.0332015
$489$	−10.1928	−0.460934
$490$	1.00629	0.0454595
$491$	−2.68334	−0.121097	−0.0605487	−	0.998165i	$-0.519285\pi$
$491$	−2.68334	−0.121097	−0.0605487	+	0.998165i	$0.519285\pi$
$492$	−0.449179	−0.0202506
$493$	−54.3148	−2.44622
$494$	1.16884	0.0525886
$495$	2.89590	0.130161
$496$	−0.677888	−0.0304381
$497$	5.60716	0.251515
$498$	−9.59491	−0.429958
$499$	−35.1785	−1.57481	−0.787404	−	0.616438i	$-0.788575\pi$
$499$	−35.1785	−1.57481	−0.787404	+	0.616438i	$0.788575\pi$
$500$	−9.04390	−0.404456
$501$	2.75016	0.122868
$502$	5.68724	0.253834
$503$	−26.9447	−1.20141	−0.600703	−	0.799472i	$-0.705113\pi$
$503$	−26.9447	−1.20141	−0.600703	+	0.799472i	$0.705113\pi$
$504$	1.00000	0.0445435
$505$	−1.84270	−0.0819991
$506$	26.8276	1.19263
$507$	−12.1987	−0.541764
$508$	−18.4685	−0.819405
$509$	−0.773165	−0.0342699	−0.0171350	−	0.999853i	$-0.505454\pi$
$509$	−0.773165	−0.0342699	−0.0171350	+	0.999853i	$0.505454\pi$
$510$	8.19638	0.362942
$511$	−7.92211	−0.350453
$512$	1.00000	0.0441942
$513$	−1.30576	−0.0576506
$514$	4.50667	0.198781
$515$	0.740508	0.0326307
$516$	−0.0748457	−0.00329490
$517$	7.77963	0.342148
$518$	−2.86269	−0.125779
$519$	11.2152	0.492294
$520$	−0.900773	−0.0395015
$521$	13.9209	0.609884	0.304942	−	0.952371i	$-0.401363\pi$
$521$	13.9209	0.609884	0.304942	+	0.952371i	$0.401363\pi$
$522$	−6.66835	−0.291866
$523$	−7.81110	−0.341555	−0.170778	−	0.985310i	$-0.554628\pi$
$523$	−7.81110	−0.341555	−0.170778	+	0.985310i	$0.554628\pi$
$524$	12.5673	0.549004
$525$	−3.98738	−0.174024
$526$	−11.9469	−0.520911
$527$	−5.52151	−0.240521
$528$	2.87780	0.125240
$529$	63.9043	2.77845
$530$	5.69188	0.247239
$531$	−4.68908	−0.203489
$532$	−1.30576	−0.0566117
$533$	0.402080	0.0174160
$534$	15.9838	0.691687
$535$	−4.08555	−0.176634
$536$	0.0484279	0.00209177
$537$	−12.8192	−0.553188
$538$	−19.9590	−0.860493
$539$	2.87780	0.123956
$540$	1.00629	0.0433038
$541$	4.94412	0.212564	0.106282	−	0.994336i	$-0.466105\pi$
$541$	4.94412	0.212564	0.106282	+	0.994336i	$0.466105\pi$
$542$	11.2408	0.482832
$543$	−10.8436	−0.465344
$544$	8.14516	0.349221
$545$	11.3545	0.486373
$546$	−0.895144	−0.0383086
$547$	14.3615	0.614052	0.307026	−	0.951701i	$-0.400666\pi$
$547$	14.3615	0.614052	0.307026	+	0.951701i	$0.400666\pi$
$548$	−8.10947	−0.346419
$549$	0.733444	0.0313026
$550$	−11.4749	−0.489291
$551$	8.70725	0.370941
$552$	9.32225	0.396781
$553$	−14.8166	−0.630065
$554$	−20.9964	−0.892051
$555$	−2.88069	−0.122279
$556$	−17.8122	−0.755404
$557$	−35.7663	−1.51547	−0.757734	−	0.652564i	$-0.773693\pi$
$557$	−35.7663	−1.51547	−0.757734	+	0.652564i	$0.773693\pi$
$558$	−0.677888	−0.0286973
$559$	0.0669977	0.00283370
$560$	1.00629	0.0425235
$561$	23.4402	0.989645
$562$	−9.71324	−0.409728
$563$	27.7235	1.16841	0.584204	−	0.811607i	$-0.301407\pi$
$563$	27.7235	1.16841	0.584204	+	0.811607i	$0.301407\pi$
$564$	2.70332	0.113830
$565$	12.6384	0.531700
$566$	22.9609	0.965117
$567$	1.00000	0.0419961
$568$	5.60716	0.235271
$569$	31.3909	1.31597	0.657987	−	0.753030i	$-0.271408\pi$
$569$	31.3909	1.31597	0.657987	+	0.753030i	$0.271408\pi$
$570$	−1.31397	−0.0550361
$571$	14.0799	0.589226	0.294613	−	0.955617i	$-0.404809\pi$
$571$	14.0799	0.589226	0.294613	+	0.955617i	$0.404809\pi$
$572$	−2.57605	−0.107710
$573$	−1.00000	−0.0417756
$574$	−0.449179	−0.0187484
$575$	−37.1714	−1.55015
$576$	1.00000	0.0416667
$577$	5.08009	0.211487	0.105743	−	0.994393i	$-0.466278\pi$
$577$	5.08009	0.211487	0.105743	+	0.994393i	$0.466278\pi$
$578$	49.3437	2.05243
$579$	19.2806	0.801274
$580$	−6.71029	−0.278630
$581$	−9.59491	−0.398064
$582$	−4.86164	−0.201522
$583$	16.2777	0.674155
$584$	−7.92211	−0.327819
$585$	−0.900773	−0.0372424
$586$	0.504153	0.0208264
$587$	8.09615	0.334164	0.167082	−	0.985943i	$-0.446566\pi$
$587$	8.09615	0.334164	0.167082	+	0.985943i	$0.446566\pi$
$588$	1.00000	0.0412393
$589$	0.885157	0.0364723
$590$	−4.71856	−0.194260
$591$	5.57020	0.229127
$592$	−2.86269	−0.117656
$593$	18.1016	0.743344	0.371672	−	0.928364i	$-0.378785\pi$
$593$	18.1016	0.743344	0.371672	+	0.928364i	$0.378785\pi$
$594$	2.87780	0.118078
$595$	8.19638	0.336019
$596$	3.64991	0.149506
$597$	−0.166331	−0.00680746
$598$	−8.34475	−0.341242
$599$	18.6646	0.762614	0.381307	−	0.924448i	$-0.375474\pi$
$599$	18.6646	0.762614	0.381307	+	0.924448i	$0.375474\pi$
$600$	−3.98738	−0.162784
$601$	−15.1549	−0.618183	−0.309091	−	0.951032i	$-0.600025\pi$
$601$	−15.1549	−0.618183	−0.309091	+	0.951032i	$0.600025\pi$
$602$	−0.0748457	−0.00305048
$603$	0.0484279	0.00197214
$604$	9.09373	0.370019
$605$	−2.73535	−0.111208
$606$	−1.83118	−0.0743868
$607$	10.6618	0.432749	0.216375	−	0.976310i	$-0.430577\pi$
$607$	10.6618	0.432749	0.216375	+	0.976310i	$0.430577\pi$
$608$	−1.30576	−0.0529554
$609$	−6.66835	−0.270215
$610$	0.738057	0.0298830
$611$	−2.41986	−0.0978972
$612$	8.14516	0.329249
$613$	−16.0553	−0.648467	−0.324233	−	0.945977i	$-0.605106\pi$
$613$	−16.0553	−0.648467	−0.324233	+	0.945977i	$0.605106\pi$
$614$	9.22411	0.372255
$615$	−0.452004	−0.0182266
$616$	2.87780	0.115950
$617$	−13.3701	−0.538259	−0.269129	−	0.963104i	$-0.586736\pi$
$617$	−13.3701	−0.538259	−0.269129	+	0.963104i	$0.586736\pi$
$618$	0.735881	0.0296015
$619$	11.9497	0.480300	0.240150	−	0.970736i	$-0.422803\pi$
$619$	11.9497	0.480300	0.240150	+	0.970736i	$0.422803\pi$
$620$	−0.682151	−0.0273959
$621$	9.32225	0.374089
$622$	2.28627	0.0916710
$623$	15.9838	0.640378
$624$	−0.895144	−0.0358344
$625$	10.8361	0.433446
$626$	−20.9662	−0.837977
$627$	−3.75771	−0.150068
$628$	3.69384	0.147400
$629$	−23.3171	−0.929712
$630$	1.00629	0.0400915
$631$	20.5855	0.819495	0.409748	−	0.912199i	$-0.365617\pi$
$631$	20.5855	0.819495	0.409748	+	0.912199i	$0.365617\pi$
$632$	−14.8166	−0.589372
$633$	−0.755402	−0.0300245
$634$	−19.4985	−0.774385
$635$	−18.5846	−0.737507
$636$	5.65631	0.224287
$637$	−0.895144	−0.0354669
$638$	−19.1902	−0.759747
$639$	5.60716	0.221816
$640$	1.00629	0.0397770
$641$	−16.3682	−0.646506	−0.323253	−	0.946313i	$-0.604776\pi$
$641$	−16.3682	−0.646506	−0.323253	+	0.946313i	$0.604776\pi$
$642$	−4.06002	−0.160236
$643$	38.0233	1.49949	0.749746	−	0.661726i	$-0.230176\pi$
$643$	38.0233	1.49949	0.749746	+	0.661726i	$0.230176\pi$
$644$	9.32225	0.367348
$645$	−0.0753164	−0.00296558
$646$	−10.6356	−0.418452
$647$	−20.2557	−0.796334	−0.398167	−	0.917313i	$-0.630354\pi$
$647$	−20.2557	−0.796334	−0.398167	+	0.917313i	$0.630354\pi$
$648$	1.00000	0.0392837
$649$	−13.4942	−0.529695
$650$	3.56928	0.139999
$651$	−0.677888	−0.0265685
$652$	−10.1928	−0.399181
$653$	29.5676	1.15707	0.578535	−	0.815657i	$-0.303625\pi$
$653$	29.5676	1.15707	0.578535	+	0.815657i	$0.303625\pi$
$654$	11.2835	0.441221
$655$	12.6463	0.494132
$656$	−0.449179	−0.0175375
$657$	−7.92211	−0.309071
$658$	2.70332	0.105387
$659$	−16.0412	−0.624875	−0.312437	−	0.949938i	$-0.601145\pi$
$659$	−16.0412	−0.624875	−0.312437	+	0.949938i	$0.601145\pi$
$660$	2.89590	0.112723
$661$	1.55409	0.0604470	0.0302235	−	0.999543i	$-0.490378\pi$
$661$	1.55409	0.0604470	0.0302235	+	0.999543i	$0.490378\pi$
$662$	21.1483	0.821952
$663$	−7.29109	−0.283163
$664$	−9.59491	−0.372355
$665$	−1.31397	−0.0509535
$666$	−2.86269	−0.110927
$667$	−62.1640	−2.40700
$668$	2.75016	0.106407
$669$	2.34324	0.0905950
$670$	0.0487324	0.00188270
$671$	2.11071	0.0814830
$672$	1.00000	0.0385758
$673$	43.9478	1.69406	0.847032	−	0.531543i	$-0.178387\pi$
$673$	43.9478	1.69406	0.847032	+	0.531543i	$0.178387\pi$
$674$	−18.5338	−0.713895
$675$	−3.98738	−0.153474
$676$	−12.1987	−0.469181
$677$	−3.75616	−0.144361	−0.0721805	−	0.997392i	$-0.522996\pi$
$677$	−3.75616	−0.144361	−0.0721805	+	0.997392i	$0.522996\pi$
$678$	12.5594	0.482340
$679$	−4.86164	−0.186573
$680$	8.19638	0.314317
$681$	8.63146	0.330758
$682$	−1.95083	−0.0747011
$683$	−18.6397	−0.713228	−0.356614	−	0.934252i	$-0.616069\pi$
$683$	−18.6397	−0.713228	−0.356614	+	0.934252i	$0.616069\pi$
$684$	−1.30576	−0.0499268
$685$	−8.16046	−0.311795
$686$	1.00000	0.0381802
$687$	24.3646	0.929567
$688$	−0.0748457	−0.00285347
$689$	−5.06321	−0.192893
$690$	9.38087	0.357124
$691$	4.45423	0.169447	0.0847235	−	0.996405i	$-0.472999\pi$
$691$	4.45423	0.169447	0.0847235	+	0.996405i	$0.472999\pi$
$692$	11.2152	0.426339
$693$	2.87780	0.109319
$694$	−20.0161	−0.759799
$695$	−17.9242	−0.679903
$696$	−6.66835	−0.252763
$697$	−3.65864	−0.138581
$698$	7.23549	0.273867
$699$	28.2984	1.07034
$700$	−3.98738	−0.150709
$701$	9.95087	0.375839	0.187920	−	0.982184i	$-0.439826\pi$
$701$	9.95087	0.375839	0.187920	+	0.982184i	$0.439826\pi$
$702$	−0.895144	−0.0337850
$703$	3.73798	0.140980
$704$	2.87780	0.108461
$705$	2.72032	0.102453
$706$	−15.7627	−0.593239
$707$	−1.83118	−0.0688688
$708$	−4.68908	−0.176226
$709$	8.24846	0.309777	0.154889	−	0.987932i	$-0.450498\pi$
$709$	8.24846	0.309777	0.154889	+	0.987932i	$0.450498\pi$
$710$	5.64242	0.211756
$711$	−14.8166	−0.555665
$712$	15.9838	0.599018
$713$	−6.31944	−0.236665
$714$	8.14516	0.304825
$715$	−2.59225	−0.0969445
$716$	−12.8192	−0.479075
$717$	12.0954	0.451711
$718$	9.69437	0.361791
$719$	−28.7142	−1.07086	−0.535429	−	0.844580i	$-0.679850\pi$
$719$	−28.7142	−1.07086	−0.535429	+	0.844580i	$0.679850\pi$
$720$	1.00629	0.0375022
$721$	0.735881	0.0274056
$722$	−17.2950	−0.643653
$723$	8.39579	0.312243
$724$	−10.8436	−0.403000
$725$	26.5893	0.987501
$726$	−2.71825	−0.100884
$727$	−29.7996	−1.10521	−0.552603	−	0.833445i	$-0.686365\pi$
$727$	−29.7996	−1.10521	−0.552603	+	0.833445i	$0.686365\pi$
$728$	−0.895144	−0.0331762
$729$	1.00000	0.0370370
$730$	−7.97193	−0.295054
$731$	−0.609631	−0.0225480
$732$	0.733444	0.0271089
$733$	−43.4066	−1.60326	−0.801630	−	0.597820i	$-0.796034\pi$
$733$	−43.4066	−1.60326	−0.801630	+	0.597820i	$0.796034\pi$
$734$	−17.2969	−0.638440
$735$	1.00629	0.0371175
$736$	9.32225	0.343623
$737$	0.139366	0.00513361
$738$	−0.449179	−0.0165345
$739$	−45.1240	−1.65991	−0.829957	−	0.557828i	$-0.811635\pi$
$739$	−45.1240	−1.65991	−0.829957	+	0.557828i	$0.811635\pi$
$740$	−2.88069	−0.105896
$741$	1.16884	0.0429384
$742$	5.65631	0.207650
$743$	6.82427	0.250358	0.125179	−	0.992134i	$-0.460049\pi$
$743$	6.82427	0.250358	0.125179	+	0.992134i	$0.460049\pi$
$744$	−0.677888	−0.0248526
$745$	3.67287	0.134563
$746$	1.76417	0.0645908
$747$	−9.59491	−0.351059
$748$	23.4402	0.857057
$749$	−4.06002	−0.148350
$750$	−9.04390	−0.330237
$751$	−34.8657	−1.27227	−0.636134	−	0.771578i	$-0.719468\pi$
$751$	−34.8657	−1.27227	−0.636134	+	0.771578i	$0.719468\pi$
$752$	2.70332	0.0985801
$753$	5.68724	0.207255
$754$	5.96913	0.217383
$755$	9.15092	0.333036
$756$	1.00000	0.0363696
$757$	−28.3455	−1.03023	−0.515117	−	0.857120i	$-0.672252\pi$
$757$	−28.3455	−1.03023	−0.515117	+	0.857120i	$0.672252\pi$
$758$	19.6001	0.711909
$759$	26.8276	0.973780
$760$	−1.31397	−0.0476626
$761$	−7.54017	−0.273331	−0.136665	−	0.990617i	$-0.543639\pi$
$761$	−7.54017	−0.273331	−0.136665	+	0.990617i	$0.543639\pi$
$762$	−18.4685	−0.669042
$763$	11.2835	0.408491
$764$	−1.00000	−0.0361787
$765$	8.19638	0.296341
$766$	21.8003	0.787675
$767$	4.19740	0.151559
$768$	1.00000	0.0360844
$769$	31.3037	1.12884	0.564420	−	0.825487i	$-0.309100\pi$
$769$	31.3037	1.12884	0.564420	+	0.825487i	$0.309100\pi$
$770$	2.89590	0.104361
$771$	4.50667	0.162304
$772$	19.2806	0.693923
$773$	−8.82618	−0.317456	−0.158728	−	0.987322i	$-0.550739\pi$
$773$	−8.82618	−0.317456	−0.158728	+	0.987322i	$0.550739\pi$
$774$	−0.0748457	−0.00269027
$775$	2.70300	0.0970947
$776$	−4.86164	−0.174523
$777$	−2.86269	−0.102698
$778$	−32.2414	−1.15591
$779$	0.586519	0.0210142
$780$	−0.900773	−0.0322528
$781$	16.1363	0.577402
$782$	75.9312	2.71529
$783$	−6.66835	−0.238307
$784$	1.00000	0.0357143
$785$	3.71707	0.132668
$786$	12.5673	0.448260
$787$	6.71432	0.239340	0.119670	−	0.992814i	$-0.461816\pi$
$787$	6.71432	0.239340	0.119670	+	0.992814i	$0.461816\pi$
$788$	5.57020	0.198430
$789$	−11.9469	−0.425322
$790$	−14.9098	−0.530465
$791$	12.5594	0.446560
$792$	2.87780	0.102258
$793$	−0.656538	−0.0233144
$794$	−29.2564	−1.03827
$795$	5.69188	0.201870
$796$	−0.166331	−0.00589543
$797$	0.0453206	0.00160534	0.000802668	−	1.00000i	$-0.499745\pi$
$797$	0.0453206	0.00160534	0.000802668		1.00000i	$0.499745\pi$
$798$	−1.30576	−0.0462233
$799$	22.0190	0.778977
$800$	−3.98738	−0.140975
$801$	15.9838	0.564760
$802$	−8.77312	−0.309790
$803$	−22.7983	−0.804533
$804$	0.0484279	0.00170792
$805$	9.38087	0.330632
$806$	0.606808	0.0213739
$807$	−19.9590	−0.702589
$808$	−1.83118	−0.0644209
$809$	−1.98007	−0.0696155	−0.0348078	−	0.999394i	$-0.511082\pi$
$809$	−1.98007	−0.0696155	−0.0348078	+	0.999394i	$0.511082\pi$
$810$	1.00629	0.0353574
$811$	3.87963	0.136232	0.0681161	−	0.997677i	$-0.478301\pi$
$811$	3.87963	0.136232	0.0681161	+	0.997677i	$0.478301\pi$
$812$	−6.66835	−0.234013
$813$	11.2408	0.394231
$814$	−8.23826	−0.288751
$815$	−10.2569	−0.359283
$816$	8.14516	0.285138
$817$	0.0977303	0.00341915
$818$	22.2968	0.779588
$819$	−0.895144	−0.0312789
$820$	−0.452004	−0.0157847
$821$	−47.8715	−1.67073	−0.835363	−	0.549698i	$-0.814743\pi$
$821$	−47.8715	−1.67073	−0.835363	+	0.549698i	$0.814743\pi$
$822$	−8.10947	−0.282850
$823$	−11.8101	−0.411675	−0.205838	−	0.978586i	$-0.565992\pi$
$823$	−11.8101	−0.411675	−0.205838	+	0.978586i	$0.565992\pi$
$824$	0.735881	0.0256356
$825$	−11.4749	−0.399505
$826$	−4.68908	−0.163154
$827$	−27.1150	−0.942882	−0.471441	−	0.881898i	$-0.656266\pi$
$827$	−27.1150	−0.942882	−0.471441	+	0.881898i	$0.656266\pi$
$828$	9.32225	0.323970
$829$	35.2208	1.22327	0.611635	−	0.791140i	$-0.290512\pi$
$829$	35.2208	1.22327	0.611635	+	0.791140i	$0.290512\pi$
$830$	−9.65525	−0.335138
$831$	−20.9964	−0.728357
$832$	−0.895144	−0.0310335
$833$	8.14516	0.282213
$834$	−17.8122	−0.616785
$835$	2.76746	0.0957717
$836$	−3.75771	−0.129963
$837$	−0.677888	−0.0234313
$838$	−29.8518	−1.03121
$839$	14.7367	0.508766	0.254383	−	0.967104i	$-0.418128\pi$
$839$	14.7367	0.508766	0.254383	+	0.967104i	$0.418128\pi$
$840$	1.00629	0.0347203
$841$	15.4669	0.533342
$842$	−18.0829	−0.623176
$843$	−9.71324	−0.334542
$844$	−0.755402	−0.0260020
$845$	−12.2754	−0.422288
$846$	2.70332	0.0929422
$847$	−2.71825	−0.0934003
$848$	5.65631	0.194238
$849$	22.9609	0.788015
$850$	−32.4779	−1.11398
$851$	−26.6867	−0.914808
$852$	5.60716	0.192098
$853$	−42.3718	−1.45078	−0.725391	−	0.688337i	$-0.758341\pi$
$853$	−42.3718	−1.45078	−0.725391	+	0.688337i	$0.758341\pi$
$854$	0.733444	0.0250980
$855$	−1.31397	−0.0449368
$856$	−4.06002	−0.138768
$857$	29.1453	0.995584	0.497792	−	0.867296i	$-0.334144\pi$
$857$	29.1453	0.995584	0.497792	+	0.867296i	$0.334144\pi$
$858$	−2.57605	−0.0879448
$859$	−35.4696	−1.21021	−0.605103	−	0.796147i	$-0.706868\pi$
$859$	−35.4696	−1.21021	−0.605103	+	0.796147i	$0.706868\pi$
$860$	−0.0753164	−0.00256827
$861$	−0.449179	−0.0153080
$862$	14.3067	0.487289
$863$	9.31463	0.317074	0.158537	−	0.987353i	$-0.449322\pi$
$863$	9.31463	0.317074	0.158537	+	0.987353i	$0.449322\pi$
$864$	1.00000	0.0340207
$865$	11.2858	0.383727
$866$	−17.0525	−0.579467
$867$	49.3437	1.67580
$868$	−0.677888	−0.0230090
$869$	−42.6392	−1.44644
$870$	−6.71029	−0.227500
$871$	−0.0433499	−0.00146886
$872$	11.2835	0.382108
$873$	−4.86164	−0.164542
$874$	−12.1726	−0.411744
$875$	−9.04390	−0.305740
$876$	−7.92211	−0.267663
$877$	15.7740	0.532650	0.266325	−	0.963883i	$-0.414191\pi$
$877$	15.7740	0.532650	0.266325	+	0.963883i	$0.414191\pi$
$878$	−8.66189	−0.292325
$879$	0.504153	0.0170047
$880$	2.89590	0.0976208
$881$	40.0201	1.34831	0.674155	−	0.738590i	$-0.264508\pi$
$881$	40.0201	1.34831	0.674155	+	0.738590i	$0.264508\pi$
$882$	1.00000	0.0336718
$883$	−5.40124	−0.181766	−0.0908830	−	0.995862i	$-0.528969\pi$
$883$	−5.40124	−0.181766	−0.0908830	+	0.995862i	$0.528969\pi$
$884$	−7.29109	−0.245226
$885$	−4.71856	−0.158613
$886$	−10.6224	−0.356867
$887$	20.6645	0.693846	0.346923	−	0.937894i	$-0.387227\pi$
$887$	20.6645	0.693846	0.346923	+	0.937894i	$0.387227\pi$
$888$	−2.86269	−0.0960656
$889$	−18.4685	−0.619412
$890$	16.0843	0.539148
$891$	2.87780	0.0964100
$892$	2.34324	0.0784576
$893$	−3.52988	−0.118123
$894$	3.64991	0.122071
$895$	−12.8998	−0.431192
$896$	1.00000	0.0334077
$897$	−8.34475	−0.278623
$898$	12.0008	0.400471
$899$	4.52040	0.150764
$900$	−3.98738	−0.132913
$901$	46.0715	1.53487
$902$	−1.29265	−0.0430405
$903$	−0.0748457	−0.00249071
$904$	12.5594	0.417719
$905$	−10.9118	−0.362721
$906$	9.09373	0.302119
$907$	−1.74049	−0.0577921	−0.0288961	−	0.999582i	$-0.509199\pi$
$907$	−1.74049	−0.0577921	−0.0288961	+	0.999582i	$0.509199\pi$
$908$	8.63146	0.286445
$909$	−1.83118	−0.0607366
$910$	−0.900773	−0.0298603
$911$	4.11880	0.136462	0.0682309	−	0.997670i	$-0.478265\pi$
$911$	4.11880	0.136462	0.0682309	+	0.997670i	$0.478265\pi$
$912$	−1.30576	−0.0432379
$913$	−27.6122	−0.913832
$914$	−13.1713	−0.435668
$915$	0.738057	0.0243994
$916$	24.3646	0.805029
$917$	12.5673	0.415008
$918$	8.14516	0.268830
$919$	58.7873	1.93921	0.969606	−	0.244670i	$-0.0786796\pi$
$919$	58.7873	1.93921	0.969606	+	0.244670i	$0.0786796\pi$
$920$	9.38087	0.309278
$921$	9.22411	0.303945
$922$	3.47126	0.114320
$923$	−5.01921	−0.165209
$924$	2.87780	0.0946728
$925$	11.4146	0.375311
$926$	−34.2024	−1.12396
$927$	0.735881	0.0241695
$928$	−6.66835	−0.218899
$929$	−10.4392	−0.342500	−0.171250	−	0.985228i	$-0.554781\pi$
$929$	−10.4392	−0.342500	−0.171250	+	0.985228i	$0.554781\pi$
$930$	−0.682151	−0.0223686
$931$	−1.30576	−0.0427944
$932$	28.2984	0.926944
$933$	2.28627	0.0748491
$934$	13.7055	0.448458
$935$	23.5876	0.771396
$936$	−0.895144	−0.0292587
$937$	−45.3793	−1.48248	−0.741238	−	0.671242i	$-0.765761\pi$
$937$	−45.3793	−1.48248	−0.741238	+	0.671242i	$0.765761\pi$
$938$	0.0484279	0.00158123
$939$	−20.9662	−0.684205
$940$	2.72032	0.0887272
$941$	14.6631	0.478005	0.239002	−	0.971019i	$-0.423180\pi$
$941$	14.6631	0.478005	0.239002	+	0.971019i	$0.423180\pi$
$942$	3.69384	0.120352
$943$	−4.18736	−0.136359
$944$	−4.68908	−0.152616
$945$	1.00629	0.0327346
$946$	−0.215391	−0.00700297
$947$	−42.3692	−1.37681	−0.688407	−	0.725325i	$-0.741690\pi$
$947$	−42.3692	−1.37681	−0.688407	+	0.725325i	$0.741690\pi$
$948$	−14.8166	−0.481220
$949$	7.09143	0.230197
$950$	5.20655	0.168923
$951$	−19.4985	−0.632283
$952$	8.14516	0.263986
$953$	−14.4991	−0.469671	−0.234836	−	0.972035i	$-0.575455\pi$
$953$	−14.4991	−0.469671	−0.234836	+	0.972035i	$0.575455\pi$
$954$	5.65631	0.183130
$955$	−1.00629	−0.0325627
$956$	12.0954	0.391193
$957$	−19.1902	−0.620331
$958$	18.8534	0.609125
$959$	−8.10947	−0.261868
$960$	1.00629	0.0324778
$961$	−30.5405	−0.985176
$962$	2.56252	0.0826189
$963$	−4.06002	−0.130832
$964$	8.39579	0.270410
$965$	19.4018	0.624567
$966$	9.32225	0.299938
$967$	10.6638	0.342925	0.171462	−	0.985191i	$-0.445151\pi$
$967$	10.6638	0.342925	0.171462	+	0.985191i	$0.445151\pi$
$968$	−2.71825	−0.0873679
$969$	−10.6356	−0.341665
$970$	−4.89221	−0.157080
$971$	−3.90461	−0.125305	−0.0626525	−	0.998035i	$-0.519956\pi$
$971$	−3.90461	−0.125305	−0.0626525	+	0.998035i	$0.519956\pi$
$972$	1.00000	0.0320750
$973$	−17.8122	−0.571032
$974$	8.45906	0.271046
$975$	3.56928	0.114308
$976$	0.733444	0.0234770
$977$	−51.6751	−1.65323	−0.826616	−	0.562767i	$-0.809737\pi$
$977$	−51.6751	−1.65323	−0.826616	+	0.562767i	$0.809737\pi$
$978$	−10.1928	−0.325930
$979$	45.9982	1.47011
$980$	1.00629	0.0321447
$981$	11.2835	0.360255
$982$	−2.68334	−0.0856289
$983$	34.4147	1.09766	0.548829	−	0.835935i	$-0.315074\pi$
$983$	34.4147	1.09766	0.548829	+	0.835935i	$0.315074\pi$
$984$	−0.449179	−0.0143193
$985$	5.60523	0.178597
$986$	−54.3148	−1.72974
$987$	2.70332	0.0860477
$988$	1.16884	0.0371858
$989$	−0.697730	−0.0221865
$990$	2.89590	0.0920377
$991$	−25.5418	−0.811361	−0.405680	−	0.914015i	$-0.632965\pi$
$991$	−25.5418	−0.811361	−0.405680	+	0.914015i	$0.632965\pi$
$992$	−0.677888	−0.0215230
$993$	21.1483	0.671121
$994$	5.60716	0.177848
$995$	−0.167377	−0.00530620
$996$	−9.59491	−0.304026
$997$	−18.6531	−0.590748	−0.295374	−	0.955382i	$-0.595444\pi$
$997$	−18.6531	−0.590748	−0.295374	+	0.955382i	$0.595444\pi$
$998$	−35.1785	−1.11356
$999$	−2.86269	−0.0905715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.7	✓	16	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00629 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00629 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00629 q^{10} +2.87780 q^{11} +1.00000 q^{12} -0.895144 q^{13} +1.00000 q^{14} +1.00629 q^{15} +1.00000 q^{16} +8.14516 q^{17} +1.00000 q^{18} -1.30576 q^{19} +1.00629 q^{20} +1.00000 q^{21} +2.87780 q^{22} +9.32225 q^{23} +1.00000 q^{24} -3.98738 q^{25} -0.895144 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.66835 q^{29} +1.00629 q^{30} -0.677888 q^{31} +1.00000 q^{32} +2.87780 q^{33} +8.14516 q^{34} +1.00629 q^{35} +1.00000 q^{36} -2.86269 q^{37} -1.30576 q^{38} -0.895144 q^{39} +1.00629 q^{40} -0.449179 q^{41} +1.00000 q^{42} -0.0748457 q^{43} +2.87780 q^{44} +1.00629 q^{45} +9.32225 q^{46} +2.70332 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.98738 q^{50} +8.14516 q^{51} -0.895144 q^{52} +5.65631 q^{53} +1.00000 q^{54} +2.89590 q^{55} +1.00000 q^{56} -1.30576 q^{57} -6.66835 q^{58} -4.68908 q^{59} +1.00629 q^{60} +0.733444 q^{61} -0.677888 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.900773 q^{65} +2.87780 q^{66} +0.0484279 q^{67} +8.14516 q^{68} +9.32225 q^{69} +1.00629 q^{70} +5.60716 q^{71} +1.00000 q^{72} -7.92211 q^{73} -2.86269 q^{74} -3.98738 q^{75} -1.30576 q^{76} +2.87780 q^{77} -0.895144 q^{78} -14.8166 q^{79} +1.00629 q^{80} +1.00000 q^{81} -0.449179 q^{82} -9.59491 q^{83} +1.00000 q^{84} +8.19638 q^{85} -0.0748457 q^{86} -6.66835 q^{87} +2.87780 q^{88} +15.9838 q^{89} +1.00629 q^{90} -0.895144 q^{91} +9.32225 q^{92} -0.677888 q^{93} +2.70332 q^{94} -1.31397 q^{95} +1.00000 q^{96} -4.86164 q^{97} +1.00000 q^{98} +2.87780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * q^99

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