LMFDB - Embedded newform 8022.2.a.t.1.11

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 30 x^{9} + 36 x^{8} + 260 x^{7} - 346 x^{6} - 842 x^{5} + 1317 x^{4} + 736 x^{3} + \cdots + 68 $ x^11 - x^10 - 30x^9 + 36x^8 + 260x^7 - 346x^6 - 842x^5 + 1317x^4 + 736x^3 - 1771x^2 + 576*x + 68
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$4.03380$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.03380 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.03380 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.03380 q^{10} -0.115980 q^{11} +1.00000 q^{12} -1.61825 q^{13} +1.00000 q^{14} +4.03380 q^{15} +1.00000 q^{16} -1.41749 q^{17} -1.00000 q^{18} -3.95526 q^{19} +4.03380 q^{20} -1.00000 q^{21} +0.115980 q^{22} -1.13106 q^{23} -1.00000 q^{24} +11.2716 q^{25} +1.61825 q^{26} +1.00000 q^{27} -1.00000 q^{28} -9.67716 q^{29} -4.03380 q^{30} -6.11920 q^{31} -1.00000 q^{32} -0.115980 q^{33} +1.41749 q^{34} -4.03380 q^{35} +1.00000 q^{36} -0.241220 q^{37} +3.95526 q^{38} -1.61825 q^{39} -4.03380 q^{40} -11.1280 q^{41} +1.00000 q^{42} -9.89270 q^{43} -0.115980 q^{44} +4.03380 q^{45} +1.13106 q^{46} +2.69958 q^{47} +1.00000 q^{48} +1.00000 q^{49} -11.2716 q^{50} -1.41749 q^{51} -1.61825 q^{52} -0.00329147 q^{53} -1.00000 q^{54} -0.467839 q^{55} +1.00000 q^{56} -3.95526 q^{57} +9.67716 q^{58} +2.90006 q^{59} +4.03380 q^{60} -6.58891 q^{61} +6.11920 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.52769 q^{65} +0.115980 q^{66} -3.30297 q^{67} -1.41749 q^{68} -1.13106 q^{69} +4.03380 q^{70} -3.04330 q^{71} -1.00000 q^{72} -7.62191 q^{73} +0.241220 q^{74} +11.2716 q^{75} -3.95526 q^{76} +0.115980 q^{77} +1.61825 q^{78} +4.74656 q^{79} +4.03380 q^{80} +1.00000 q^{81} +11.1280 q^{82} -1.16521 q^{83} -1.00000 q^{84} -5.71786 q^{85} +9.89270 q^{86} -9.67716 q^{87} +0.115980 q^{88} -18.6378 q^{89} -4.03380 q^{90} +1.61825 q^{91} -1.13106 q^{92} -6.11920 q^{93} -2.69958 q^{94} -15.9548 q^{95} -1.00000 q^{96} -6.44907 q^{97} -1.00000 q^{98} -0.115980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9} - q^{10} + 11 q^{12} - 15 q^{13} + 11 q^{14} + q^{15} + 11 q^{16} - q^{17} - 11 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 5 q^{23} - 11 q^{24} + 6 q^{25} + 15 q^{26} + 11 q^{27} - 11 q^{28} - 12 q^{29} - q^{30} - q^{31} - 11 q^{32} + q^{34} - q^{35} + 11 q^{36} - 12 q^{37} + 3 q^{38} - 15 q^{39} - q^{40} + 8 q^{41} + 11 q^{42} - 14 q^{43} + q^{45} + 5 q^{46} - 3 q^{47} + 11 q^{48} + 11 q^{49} - 6 q^{50} - q^{51} - 15 q^{52} - 14 q^{53} - 11 q^{54} - 27 q^{55} + 11 q^{56} - 3 q^{57} + 12 q^{58} + 33 q^{59} + q^{60} - 46 q^{61} + q^{62} - 11 q^{63} + 11 q^{64} + 12 q^{65} - 8 q^{67} - q^{68} - 5 q^{69} + q^{70} - 16 q^{71} - 11 q^{72} - 26 q^{73} + 12 q^{74} + 6 q^{75} - 3 q^{76} + 15 q^{78} - 24 q^{79} + q^{80} + 11 q^{81} - 8 q^{82} - 4 q^{83} - 11 q^{84} - 32 q^{85} + 14 q^{86} - 12 q^{87} + 5 q^{89} - q^{90} + 15 q^{91} - 5 q^{92} - q^{93} + 3 q^{94} - 19 q^{95} - 11 q^{96} - 36 q^{97} - 11 q^{98}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9 - q^10 + 11 * q^12 - 15 * q^13 + 11 * q^14 + q^15 + 11 * q^16 - q^17 - 11 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 5 * q^23 - 11 * q^24 + 6 * q^25 + 15 * q^26 + 11 * q^27 - 11 * q^28 - 12 * q^29 - q^30 - q^31 - 11 * q^32 + q^34 - q^35 + 11 * q^36 - 12 * q^37 + 3 * q^38 - 15 * q^39 - q^40 + 8 * q^41 + 11 * q^42 - 14 * q^43 + q^45 + 5 * q^46 - 3 * q^47 + 11 * q^48 + 11 * q^49 - 6 * q^50 - q^51 - 15 * q^52 - 14 * q^53 - 11 * q^54 - 27 * q^55 + 11 * q^56 - 3 * q^57 + 12 * q^58 + 33 * q^59 + q^60 - 46 * q^61 + q^62 - 11 * q^63 + 11 * q^64 + 12 * q^65 - 8 * q^67 - q^68 - 5 * q^69 + q^70 - 16 * q^71 - 11 * q^72 - 26 * q^73 + 12 * q^74 + 6 * q^75 - 3 * q^76 + 15 * q^78 - 24 * q^79 + q^80 + 11 * q^81 - 8 * q^82 - 4 * q^83 - 11 * q^84 - 32 * q^85 + 14 * q^86 - 12 * q^87 + 5 * q^89 - q^90 + 15 * q^91 - 5 * q^92 - q^93 + 3 * q^94 - 19 * q^95 - 11 * q^96 - 36 * q^97 - 11 * q^98

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
$5$	4.03380	1.80397	0.901986	−	0.431766i	$-0.142109\pi$
$5$	4.03380	1.80397	0.901986	+	0.431766i	$0.142109\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.03380	−1.27560
$11$	−0.115980	−0.0349692	−0.0174846	−	0.999847i	$-0.505566\pi$
$11$	−0.115980	−0.0349692	−0.0174846	+	0.999847i	$0.505566\pi$
$12$	1.00000	0.288675
$13$	−1.61825	−0.448821	−0.224410	−	0.974495i	$-0.572046\pi$
$13$	−1.61825	−0.448821	−0.224410	+	0.974495i	$0.572046\pi$
$14$	1.00000	0.267261
$15$	4.03380	1.04152
$16$	1.00000	0.250000
$17$	−1.41749	−0.343791	−0.171895	−	0.985115i	$-0.554989\pi$
$17$	−1.41749	−0.343791	−0.171895	+	0.985115i	$0.554989\pi$
$18$	−1.00000	−0.235702
$19$	−3.95526	−0.907400	−0.453700	−	0.891155i	$-0.649896\pi$
$19$	−3.95526	−0.907400	−0.453700	+	0.891155i	$0.649896\pi$
$20$	4.03380	0.901986
$21$	−1.00000	−0.218218
$22$	0.115980	0.0247269
$23$	−1.13106	−0.235842	−0.117921	−	0.993023i	$-0.537623\pi$
$23$	−1.13106	−0.235842	−0.117921	+	0.993023i	$0.537623\pi$
$24$	−1.00000	−0.204124
$25$	11.2716	2.25431
$26$	1.61825	0.317364
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−9.67716	−1.79700	−0.898502	−	0.438970i	$-0.855344\pi$
$29$	−9.67716	−1.79700	−0.898502	+	0.438970i	$0.855344\pi$
$30$	−4.03380	−0.736468
$31$	−6.11920	−1.09904	−0.549520	−	0.835480i	$-0.685189\pi$
$31$	−6.11920	−1.09904	−0.549520	+	0.835480i	$0.685189\pi$
$32$	−1.00000	−0.176777
$33$	−0.115980	−0.0201895
$34$	1.41749	0.243097
$35$	−4.03380	−0.681837
$36$	1.00000	0.166667
$37$	−0.241220	−0.0396563	−0.0198281	−	0.999803i	$-0.506312\pi$
$37$	−0.241220	−0.0396563	−0.0198281	+	0.999803i	$0.506312\pi$
$38$	3.95526	0.641628
$39$	−1.61825	−0.259127
$40$	−4.03380	−0.637800
$41$	−11.1280	−1.73791	−0.868954	−	0.494893i	$-0.835207\pi$
$41$	−11.1280	−1.73791	−0.868954	+	0.494893i	$0.835207\pi$
$42$	1.00000	0.154303
$43$	−9.89270	−1.50862	−0.754311	−	0.656517i	$-0.772029\pi$
$43$	−9.89270	−1.50862	−0.754311	+	0.656517i	$0.772029\pi$
$44$	−0.115980	−0.0174846
$45$	4.03380	0.601324
$46$	1.13106	0.166766
$47$	2.69958	0.393774	0.196887	−	0.980426i	$-0.436917\pi$
$47$	2.69958	0.393774	0.196887	+	0.980426i	$0.436917\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−11.2716	−1.59404
$51$	−1.41749	−0.198488
$52$	−1.61825	−0.224410
$53$	−0.00329147	−0.000452118 0	−0.000226059	−	1.00000i	$-0.500072\pi$
$53$	−0.00329147	−0.000452118 0	−0.000226059		1.00000i	$0.500072\pi$
$54$	−1.00000	−0.136083
$55$	−0.467839	−0.0630834
$56$	1.00000	0.133631
$57$	−3.95526	−0.523887
$58$	9.67716	1.27067
$59$	2.90006	0.377555	0.188778	−	0.982020i	$-0.439547\pi$
$59$	2.90006	0.377555	0.188778	+	0.982020i	$0.439547\pi$
$60$	4.03380	0.520762
$61$	−6.58891	−0.843624	−0.421812	−	0.906683i	$-0.638606\pi$
$61$	−6.58891	−0.843624	−0.421812	+	0.906683i	$0.638606\pi$
$62$	6.11920	0.777139
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−6.52769	−0.809660
$66$	0.115980	0.0142761
$67$	−3.30297	−0.403521	−0.201761	−	0.979435i	$-0.564666\pi$
$67$	−3.30297	−0.403521	−0.201761	+	0.979435i	$0.564666\pi$
$68$	−1.41749	−0.171895
$69$	−1.13106	−0.136164
$70$	4.03380	0.482132
$71$	−3.04330	−0.361173	−0.180586	−	0.983559i	$-0.557800\pi$
$71$	−3.04330	−0.361173	−0.180586	+	0.983559i	$0.557800\pi$
$72$	−1.00000	−0.117851
$73$	−7.62191	−0.892078	−0.446039	−	0.895014i	$-0.647166\pi$
$73$	−7.62191	−0.892078	−0.446039	+	0.895014i	$0.647166\pi$
$74$	0.241220	0.0280412
$75$	11.2716	1.30153
$76$	−3.95526	−0.453700
$77$	0.115980	0.0132171
$78$	1.61825	0.183230
$79$	4.74656	0.534030	0.267015	−	0.963692i	$-0.413963\pi$
$79$	4.74656	0.534030	0.267015	+	0.963692i	$0.413963\pi$
$80$	4.03380	0.450993
$81$	1.00000	0.111111
$82$	11.1280	1.22889
$83$	−1.16521	−0.127898	−0.0639492	−	0.997953i	$-0.520370\pi$
$83$	−1.16521	−0.127898	−0.0639492	+	0.997953i	$0.520370\pi$
$84$	−1.00000	−0.109109
$85$	−5.71786	−0.620189
$86$	9.89270	1.06676
$87$	−9.67716	−1.03750
$88$	0.115980	0.0123635
$89$	−18.6378	−1.97560	−0.987799	−	0.155735i	$-0.950225\pi$
$89$	−18.6378	−1.97560	−0.987799	+	0.155735i	$0.950225\pi$
$90$	−4.03380	−0.425200
$91$	1.61825	0.169638
$92$	−1.13106	−0.117921
$93$	−6.11920	−0.634531
$94$	−2.69958	−0.278440
$95$	−15.9548	−1.63692
$96$	−1.00000	−0.102062
$97$	−6.44907	−0.654804	−0.327402	−	0.944885i	$-0.606173\pi$
$97$	−6.44907	−0.654804	−0.327402	+	0.944885i	$0.606173\pi$
$98$	−1.00000	−0.101015
$99$	−0.115980	−0.0116564
$100$	11.2716	1.12716
$101$	11.8491	1.17903	0.589516	−	0.807757i	$-0.299319\pi$
$101$	11.8491	1.17903	0.589516	+	0.807757i	$0.299319\pi$
$102$	1.41749	0.140352
$103$	11.2269	1.10622	0.553111	−	0.833108i	$-0.313441\pi$
$103$	11.2269	1.10622	0.553111	+	0.833108i	$0.313441\pi$
$104$	1.61825	0.158682
$105$	−4.03380	−0.393659
$106$	0.00329147	0.000319696 0
$107$	−3.16453	−0.305926	−0.152963	−	0.988232i	$-0.548882\pi$
$107$	−3.16453	−0.305926	−0.152963	+	0.988232i	$0.548882\pi$
$108$	1.00000	0.0962250
$109$	16.8006	1.60920	0.804602	−	0.593814i	$-0.202379\pi$
$109$	16.8006	1.60920	0.804602	+	0.593814i	$0.202379\pi$
$110$	0.467839	0.0446067
$111$	−0.241220	−0.0228956
$112$	−1.00000	−0.0944911
$113$	−4.82644	−0.454033	−0.227017	−	0.973891i	$-0.572897\pi$
$113$	−4.82644	−0.454033	−0.227017	+	0.973891i	$0.572897\pi$
$114$	3.95526	0.370444
$115$	−4.56248	−0.425453
$116$	−9.67716	−0.898502
$117$	−1.61825	−0.149607
$118$	−2.90006	−0.266972
$119$	1.41749	0.129941
$120$	−4.03380	−0.368234
$121$	−10.9865	−0.998777
$122$	6.58891	0.596532
$123$	−11.1280	−1.00338
$124$	−6.11920	−0.549520
$125$	25.2983	2.26275
$126$	1.00000	0.0890871
$127$	10.0001	0.887366	0.443683	−	0.896184i	$-0.353672\pi$
$127$	10.0001	0.887366	0.443683	+	0.896184i	$0.353672\pi$
$128$	−1.00000	−0.0883883
$129$	−9.89270	−0.871003
$130$	6.52769	0.572516
$131$	8.58719	0.750266	0.375133	−	0.926971i	$-0.377597\pi$
$131$	8.58719	0.750266	0.375133	+	0.926971i	$0.377597\pi$
$132$	−0.115980	−0.0100947
$133$	3.95526	0.342965
$134$	3.30297	0.285333
$135$	4.03380	0.347175
$136$	1.41749	0.121548
$137$	−0.205726	−0.0175764	−0.00878818	−	0.999961i	$-0.502797\pi$
$137$	−0.205726	−0.0175764	−0.00878818	+	0.999961i	$0.502797\pi$
$138$	1.13106	0.0962823
$139$	18.9460	1.60698	0.803489	−	0.595320i	$-0.202975\pi$
$139$	18.9460	1.60698	0.803489	+	0.595320i	$0.202975\pi$
$140$	−4.03380	−0.340919
$141$	2.69958	0.227346
$142$	3.04330	0.255388
$143$	0.187684	0.0156949
$144$	1.00000	0.0833333
$145$	−39.0358	−3.24174
$146$	7.62191	0.630794
$147$	1.00000	0.0824786
$148$	−0.241220	−0.0198281
$149$	−21.1266	−1.73076	−0.865379	−	0.501118i	$-0.832922\pi$
$149$	−21.1266	−1.73076	−0.865379	+	0.501118i	$0.832922\pi$
$150$	−11.2716	−0.920320
$151$	5.75538	0.468366	0.234183	−	0.972193i	$-0.424759\pi$
$151$	5.75538	0.468366	0.234183	+	0.972193i	$0.424759\pi$
$152$	3.95526	0.320814
$153$	−1.41749	−0.114597
$154$	−0.115980	−0.00934590
$155$	−24.6836	−1.98264
$156$	−1.61825	−0.129563
$157$	−5.31805	−0.424426	−0.212213	−	0.977223i	$-0.568067\pi$
$157$	−5.31805	−0.424426	−0.212213	+	0.977223i	$0.568067\pi$
$158$	−4.74656	−0.377616
$159$	−0.00329147	−0.000261031 0
$160$	−4.03380	−0.318900
$161$	1.13106	0.0891401
$162$	−1.00000	−0.0785674
$163$	18.2926	1.43279	0.716394	−	0.697696i	$-0.245791\pi$
$163$	18.2926	1.43279	0.716394	+	0.697696i	$0.245791\pi$
$164$	−11.1280	−0.868954
$165$	−0.467839	−0.0364212
$166$	1.16521	0.0904378
$167$	6.51027	0.503780	0.251890	−	0.967756i	$-0.418948\pi$
$167$	6.51027	0.503780	0.251890	+	0.967756i	$0.418948\pi$
$168$	1.00000	0.0771517
$169$	−10.3813	−0.798560
$170$	5.71786	0.438540
$171$	−3.95526	−0.302467
$172$	−9.89270	−0.754311
$173$	−14.7270	−1.11967	−0.559836	−	0.828604i	$-0.689136\pi$
$173$	−14.7270	−1.11967	−0.559836	+	0.828604i	$0.689136\pi$
$174$	9.67716	0.733624
$175$	−11.2716	−0.852051
$176$	−0.115980	−0.00874229
$177$	2.90006	0.217982
$178$	18.6378	1.39696
$179$	−10.9619	−0.819328	−0.409664	−	0.912237i	$-0.634354\pi$
$179$	−10.9619	−0.819328	−0.409664	+	0.912237i	$0.634354\pi$
$180$	4.03380	0.300662
$181$	−19.7081	−1.46489	−0.732444	−	0.680827i	$-0.761621\pi$
$181$	−19.7081	−1.46489	−0.732444	+	0.680827i	$0.761621\pi$
$182$	−1.61825	−0.119952
$183$	−6.58891	−0.487067
$184$	1.13106	0.0833829
$185$	−0.973033	−0.0715388
$186$	6.11920	0.448681
$187$	0.164399	0.0120221
$188$	2.69958	0.196887
$189$	−1.00000	−0.0727393
$190$	15.9548	1.15748
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	1.00000	0.0721688
$193$	−3.19979	−0.230326	−0.115163	−	0.993347i	$-0.536739\pi$
$193$	−3.19979	−0.230326	−0.115163	+	0.993347i	$0.536739\pi$
$194$	6.44907	0.463016
$195$	−6.52769	−0.467458
$196$	1.00000	0.0714286
$197$	3.39955	0.242208	0.121104	−	0.992640i	$-0.461357\pi$
$197$	3.39955	0.242208	0.121104	+	0.992640i	$0.461357\pi$
$198$	0.115980	0.00824231
$199$	7.54342	0.534739	0.267369	−	0.963594i	$-0.413846\pi$
$199$	7.54342	0.534739	0.267369	+	0.963594i	$0.413846\pi$
$200$	−11.2716	−0.797020
$201$	−3.30297	−0.232973
$202$	−11.8491	−0.833701
$203$	9.67716	0.679204
$204$	−1.41749	−0.0992439
$205$	−44.8883	−3.13514
$206$	−11.2269	−0.782216
$207$	−1.13106	−0.0786142
$208$	−1.61825	−0.112205
$209$	0.458730	0.0317310
$210$	4.03380	0.278359
$211$	−23.2744	−1.60227	−0.801137	−	0.598480i	$-0.795771\pi$
$211$	−23.2744	−1.60227	−0.801137	+	0.598480i	$0.795771\pi$
$212$	−0.00329147	−0.000226059 0
$213$	−3.04330	−0.208523
$214$	3.16453	0.216323
$215$	−39.9052	−2.72151
$216$	−1.00000	−0.0680414
$217$	6.11920	0.415398
$218$	−16.8006	−1.13788
$219$	−7.62191	−0.515041
$220$	−0.467839	−0.0315417
$221$	2.29384	0.154301
$222$	0.241220	0.0161896
$223$	8.13147	0.544524	0.272262	−	0.962223i	$-0.412228\pi$
$223$	8.13147	0.544524	0.272262	+	0.962223i	$0.412228\pi$
$224$	1.00000	0.0668153
$225$	11.2716	0.751438
$226$	4.82644	0.321050
$227$	−10.6339	−0.705795	−0.352897	−	0.935662i	$-0.614803\pi$
$227$	−10.6339	−0.705795	−0.352897	+	0.935662i	$0.614803\pi$
$228$	−3.95526	−0.261944
$229$	11.8309	0.781810	0.390905	−	0.920431i	$-0.372162\pi$
$229$	11.8309	0.781810	0.390905	+	0.920431i	$0.372162\pi$
$230$	4.56248	0.300841
$231$	0.115980	0.00763090
$232$	9.67716	0.635337
$233$	12.2030	0.799443	0.399722	−	0.916637i	$-0.369107\pi$
$233$	12.2030	0.799443	0.399722	+	0.916637i	$0.369107\pi$
$234$	1.61825	0.105788
$235$	10.8896	0.710357
$236$	2.90006	0.188778
$237$	4.74656	0.308322
$238$	−1.41749	−0.0918820
$239$	−5.23760	−0.338792	−0.169396	−	0.985548i	$-0.554182\pi$
$239$	−5.23760	−0.338792	−0.169396	+	0.985548i	$0.554182\pi$
$240$	4.03380	0.260381
$241$	22.5229	1.45083	0.725415	−	0.688312i	$-0.241648\pi$
$241$	22.5229	1.45083	0.725415	+	0.688312i	$0.241648\pi$
$242$	10.9865	0.706242
$243$	1.00000	0.0641500
$244$	−6.58891	−0.421812
$245$	4.03380	0.257710
$246$	11.1280	0.709498
$247$	6.40059	0.407260
$248$	6.11920	0.388569
$249$	−1.16521	−0.0738421
$250$	−25.2983	−1.60000
$251$	29.4588	1.85942	0.929711	−	0.368291i	$-0.120057\pi$
$251$	29.4588	1.85942	0.929711	+	0.368291i	$0.120057\pi$
$252$	−1.00000	−0.0629941
$253$	0.131180	0.00824721
$254$	−10.0001	−0.627462
$255$	−5.71786	−0.358066
$256$	1.00000	0.0625000
$257$	6.65319	0.415014	0.207507	−	0.978233i	$-0.433465\pi$
$257$	6.65319	0.415014	0.207507	+	0.978233i	$0.433465\pi$
$258$	9.89270	0.615892
$259$	0.241220	0.0149887
$260$	−6.52769	−0.404830
$261$	−9.67716	−0.599001
$262$	−8.58719	−0.530518
$263$	−13.8662	−0.855025	−0.427512	−	0.904009i	$-0.640610\pi$
$263$	−13.8662	−0.855025	−0.427512	+	0.904009i	$0.640610\pi$
$264$	0.115980	0.00713805
$265$	−0.0132771	−0.000815608 0
$266$	−3.95526	−0.242513
$267$	−18.6378	−1.14061
$268$	−3.30297	−0.201761
$269$	18.4540	1.12516	0.562579	−	0.826743i	$-0.309809\pi$
$269$	18.4540	1.12516	0.562579	+	0.826743i	$0.309809\pi$
$270$	−4.03380	−0.245489
$271$	0.0927594	0.00563473	0.00281736	−	0.999996i	$-0.499103\pi$
$271$	0.0927594	0.00563473	0.00281736	+	0.999996i	$0.499103\pi$
$272$	−1.41749	−0.0859477
$273$	1.61825	0.0979408
$274$	0.205726	0.0124284
$275$	−1.30727	−0.0788315
$276$	−1.13106	−0.0680819
$277$	−3.84532	−0.231043	−0.115521	−	0.993305i	$-0.536854\pi$
$277$	−3.84532	−0.231043	−0.115521	+	0.993305i	$0.536854\pi$
$278$	−18.9460	−1.13630
$279$	−6.11920	−0.366347
$280$	4.03380	0.241066
$281$	30.8386	1.83968	0.919838	−	0.392298i	$-0.128320\pi$
$281$	30.8386	1.83968	0.919838	+	0.392298i	$0.128320\pi$
$282$	−2.69958	−0.160758
$283$	17.4764	1.03886	0.519432	−	0.854512i	$-0.326143\pi$
$283$	17.4764	1.03886	0.519432	+	0.854512i	$0.326143\pi$
$284$	−3.04330	−0.180586
$285$	−15.9548	−0.945078
$286$	−0.187684	−0.0110980
$287$	11.1280	0.656867
$288$	−1.00000	−0.0589256
$289$	−14.9907	−0.881808
$290$	39.0358	2.29226
$291$	−6.44907	−0.378051
$292$	−7.62191	−0.446039
$293$	−1.88509	−0.110128	−0.0550642	−	0.998483i	$-0.517536\pi$
$293$	−1.88509	−0.110128	−0.0550642	+	0.998483i	$0.517536\pi$
$294$	−1.00000	−0.0583212
$295$	11.6983	0.681099
$296$	0.241220	0.0140206
$297$	−0.115980	−0.00672982
$298$	21.1266	1.22383
$299$	1.83034	0.105851
$300$	11.2716	0.650764
$301$	9.89270	0.570205
$302$	−5.75538	−0.331185
$303$	11.8491	0.680714
$304$	−3.95526	−0.226850
$305$	−26.5784	−1.52187
$306$	1.41749	0.0810323
$307$	13.8775	0.792033	0.396016	−	0.918243i	$-0.370392\pi$
$307$	13.8775	0.792033	0.396016	+	0.918243i	$0.370392\pi$
$308$	0.115980	0.00660855
$309$	11.2269	0.638677
$310$	24.6836	1.40194
$311$	7.28937	0.413342	0.206671	−	0.978410i	$-0.433737\pi$
$311$	7.28937	0.413342	0.206671	+	0.978410i	$0.433737\pi$
$312$	1.61825	0.0916152
$313$	−26.5911	−1.50302	−0.751508	−	0.659724i	$-0.770673\pi$
$313$	−26.5911	−1.50302	−0.751508	+	0.659724i	$0.770673\pi$
$314$	5.31805	0.300115
$315$	−4.03380	−0.227279
$316$	4.74656	0.267015
$317$	21.5657	1.21125	0.605626	−	0.795750i	$-0.292923\pi$
$317$	21.5657	1.21125	0.605626	+	0.795750i	$0.292923\pi$
$318$	0.00329147	0.000184576 0
$319$	1.12235	0.0628397
$320$	4.03380	0.225496
$321$	−3.16453	−0.176627
$322$	−1.13106	−0.0630315
$323$	5.60653	0.311956
$324$	1.00000	0.0555556
$325$	−18.2402	−1.01178
$326$	−18.2926	−1.01313
$327$	16.8006	0.929075
$328$	11.1280	0.614443
$329$	−2.69958	−0.148833
$330$	0.467839	0.0257537
$331$	−22.6212	−1.24337	−0.621687	−	0.783265i	$-0.713553\pi$
$331$	−22.6212	−1.24337	−0.621687	+	0.783265i	$0.713553\pi$
$332$	−1.16521	−0.0639492
$333$	−0.241220	−0.0132188
$334$	−6.51027	−0.356226
$335$	−13.3235	−0.727941
$336$	−1.00000	−0.0545545
$337$	−17.2949	−0.942112	−0.471056	−	0.882103i	$-0.656127\pi$
$337$	−17.2949	−0.942112	−0.471056	+	0.882103i	$0.656127\pi$
$338$	10.3813	0.564667
$339$	−4.82644	−0.262136
$340$	−5.71786	−0.310094
$341$	0.709702	0.0384325
$342$	3.95526	0.213876
$343$	−1.00000	−0.0539949
$344$	9.89270	0.533378
$345$	−4.56248	−0.245635
$346$	14.7270	0.791727
$347$	−2.46200	−0.132167	−0.0660834	−	0.997814i	$-0.521050\pi$
$347$	−2.46200	−0.132167	−0.0660834	+	0.997814i	$0.521050\pi$
$348$	−9.67716	−0.518750
$349$	−30.4141	−1.62803	−0.814016	−	0.580843i	$-0.802723\pi$
$349$	−30.4141	−1.62803	−0.814016	+	0.580843i	$0.802723\pi$
$350$	11.2716	0.602491
$351$	−1.61825	−0.0863756
$352$	0.115980	0.00618173
$353$	25.4647	1.35535	0.677675	−	0.735362i	$-0.262988\pi$
$353$	25.4647	1.35535	0.677675	+	0.735362i	$0.262988\pi$
$354$	−2.90006	−0.154136
$355$	−12.2761	−0.651545
$356$	−18.6378	−0.987799
$357$	1.41749	0.0750213
$358$	10.9619	0.579352
$359$	28.2081	1.48877	0.744383	−	0.667753i	$-0.232744\pi$
$359$	28.2081	1.48877	0.744383	+	0.667753i	$0.232744\pi$
$360$	−4.03380	−0.212600
$361$	−3.35589	−0.176626
$362$	19.7081	1.03583
$363$	−10.9865	−0.576644
$364$	1.61825	0.0848192
$365$	−30.7453	−1.60928
$366$	6.58891	0.344408
$367$	1.08473	0.0566226	0.0283113	−	0.999599i	$-0.490987\pi$
$367$	1.08473	0.0566226	0.0283113	+	0.999599i	$0.490987\pi$
$368$	−1.13106	−0.0589606
$369$	−11.1280	−0.579303
$370$	0.973033	0.0505856
$371$	0.00329147	0.000170885 0
$372$	−6.11920	−0.317266
$373$	0.845067	0.0437559	0.0218780	−	0.999761i	$-0.493035\pi$
$373$	0.845067	0.0437559	0.0218780	+	0.999761i	$0.493035\pi$
$374$	−0.164399	−0.00850089
$375$	25.2983	1.30640
$376$	−2.69958	−0.139220
$377$	15.6600	0.806533
$378$	1.00000	0.0514344
$379$	11.7007	0.601027	0.300513	−	0.953778i	$-0.402842\pi$
$379$	11.7007	0.601027	0.300513	+	0.953778i	$0.402842\pi$
$380$	−15.9548	−0.818462
$381$	10.0001	0.512321
$382$	−1.00000	−0.0511645
$383$	18.7475	0.957954	0.478977	−	0.877827i	$-0.341008\pi$
$383$	18.7475	0.957954	0.478977	+	0.877827i	$0.341008\pi$
$384$	−1.00000	−0.0510310
$385$	0.467839	0.0238433
$386$	3.19979	0.162865
$387$	−9.89270	−0.502874
$388$	−6.44907	−0.327402
$389$	27.9075	1.41497	0.707484	−	0.706729i	$-0.249830\pi$
$389$	27.9075	1.41497	0.707484	+	0.706729i	$0.249830\pi$
$390$	6.52769	0.330542
$391$	1.60326	0.0810805
$392$	−1.00000	−0.0505076
$393$	8.58719	0.433166
$394$	−3.39955	−0.171267
$395$	19.1467	0.963374
$396$	−0.115980	−0.00582819
$397$	−25.7429	−1.29200	−0.645999	−	0.763339i	$-0.723559\pi$
$397$	−25.7429	−1.29200	−0.645999	+	0.763339i	$0.723559\pi$
$398$	−7.54342	−0.378117
$399$	3.95526	0.198011
$400$	11.2716	0.563578
$401$	36.7874	1.83708	0.918538	−	0.395334i	$-0.129371\pi$
$401$	36.7874	1.83708	0.918538	+	0.395334i	$0.129371\pi$
$402$	3.30297	0.164737
$403$	9.90237	0.493272
$404$	11.8491	0.589516
$405$	4.03380	0.200441
$406$	−9.67716	−0.480269
$407$	0.0279766	0.00138675
$408$	1.41749	0.0701760
$409$	22.9295	1.13379	0.566896	−	0.823789i	$-0.308144\pi$
$409$	22.9295	1.13379	0.566896	+	0.823789i	$0.308144\pi$
$410$	44.8883	2.21688
$411$	−0.205726	−0.0101477
$412$	11.2269	0.553111
$413$	−2.90006	−0.142703
$414$	1.13106	0.0555886
$415$	−4.70022	−0.230725
$416$	1.61825	0.0793411
$417$	18.9460	0.927789
$418$	−0.458730	−0.0224372
$419$	28.7209	1.40311	0.701554	−	0.712616i	$-0.252490\pi$
$419$	28.7209	1.40311	0.701554	+	0.712616i	$0.252490\pi$
$420$	−4.03380	−0.196829
$421$	−37.4734	−1.82634	−0.913170	−	0.407578i	$-0.866373\pi$
$421$	−37.4734	−1.82634	−0.913170	+	0.407578i	$0.866373\pi$
$422$	23.2744	1.13298
$423$	2.69958	0.131258
$424$	0.00329147	0.000159848 0
$425$	−15.9773	−0.775012
$426$	3.04330	0.147448
$427$	6.58891	0.318860
$428$	−3.16453	−0.152963
$429$	0.187684	0.00906145
$430$	39.9052	1.92440
$431$	−24.3966	−1.17514	−0.587572	−	0.809172i	$-0.699916\pi$
$431$	−24.3966	−1.17514	−0.587572	+	0.809172i	$0.699916\pi$
$432$	1.00000	0.0481125
$433$	−17.4392	−0.838073	−0.419036	−	0.907969i	$-0.637632\pi$
$433$	−17.4392	−0.838073	−0.419036	+	0.907969i	$0.637632\pi$
$434$	−6.11920	−0.293731
$435$	−39.0358	−1.87162
$436$	16.8006	0.804602
$437$	4.47364	0.214003
$438$	7.62191	0.364189
$439$	−25.0566	−1.19589	−0.597944	−	0.801538i	$-0.704015\pi$
$439$	−25.0566	−1.19589	−0.597944	+	0.801538i	$0.704015\pi$
$440$	0.467839	0.0223033
$441$	1.00000	0.0476190
$442$	−2.29384	−0.109107
$443$	3.73155	0.177291	0.0886457	−	0.996063i	$-0.471746\pi$
$443$	3.73155	0.177291	0.0886457	+	0.996063i	$0.471746\pi$
$444$	−0.241220	−0.0114478
$445$	−75.1810	−3.56392
$446$	−8.13147	−0.385036
$447$	−21.1266	−0.999253
$448$	−1.00000	−0.0472456
$449$	−2.74530	−0.129559	−0.0647793	−	0.997900i	$-0.520634\pi$
$449$	−2.74530	−0.129559	−0.0647793	+	0.997900i	$0.520634\pi$
$450$	−11.2716	−0.531347
$451$	1.29063	0.0607732
$452$	−4.82644	−0.227017
$453$	5.75538	0.270411
$454$	10.6339	0.499072
$455$	6.52769	0.306023
$456$	3.95526	0.185222
$457$	31.3008	1.46419	0.732095	−	0.681202i	$-0.238543\pi$
$457$	31.3008	1.46419	0.732095	+	0.681202i	$0.238543\pi$
$458$	−11.8309	−0.552823
$459$	−1.41749	−0.0661626
$460$	−4.56248	−0.212727
$461$	−6.84452	−0.318781	−0.159390	−	0.987216i	$-0.550953\pi$
$461$	−6.84452	−0.318781	−0.159390	+	0.987216i	$0.550953\pi$
$462$	−0.115980	−0.00539586
$463$	14.5897	0.678040	0.339020	−	0.940779i	$-0.389905\pi$
$463$	14.5897	0.678040	0.339020	+	0.940779i	$0.389905\pi$
$464$	−9.67716	−0.449251
$465$	−24.6836	−1.14468
$466$	−12.2030	−0.565292
$467$	40.8584	1.89070	0.945351	−	0.326056i	$-0.105720\pi$
$467$	40.8584	1.89070	0.945351	+	0.326056i	$0.105720\pi$
$468$	−1.61825	−0.0748035
$469$	3.30297	0.152517
$470$	−10.8896	−0.502298
$471$	−5.31805	−0.245043
$472$	−2.90006	−0.133486
$473$	1.14735	0.0527552
$474$	−4.74656	−0.218017
$475$	−44.5820	−2.04556
$476$	1.41749	0.0649704
$477$	−0.00329147	−0.000150706 0
$478$	5.23760	0.239562
$479$	14.0511	0.642011	0.321005	−	0.947077i	$-0.395979\pi$
$479$	14.0511	0.642011	0.321005	+	0.947077i	$0.395979\pi$
$480$	−4.03380	−0.184117
$481$	0.390353	0.0177986
$482$	−22.5229	−1.02589
$483$	1.13106	0.0514650
$484$	−10.9865	−0.499389
$485$	−26.0143	−1.18125
$486$	−1.00000	−0.0453609
$487$	26.8121	1.21497	0.607485	−	0.794331i	$-0.292178\pi$
$487$	26.8121	1.21497	0.607485	+	0.794331i	$0.292178\pi$
$488$	6.58891	0.298266
$489$	18.2926	0.827221
$490$	−4.03380	−0.182229
$491$	0.246313	0.0111159	0.00555797	−	0.999985i	$-0.498231\pi$
$491$	0.246313	0.0111159	0.00555797	+	0.999985i	$0.498231\pi$
$492$	−11.1280	−0.501691
$493$	13.7172	0.617793
$494$	−6.40059	−0.287976
$495$	−0.467839	−0.0210278
$496$	−6.11920	−0.274760
$497$	3.04330	0.136510
$498$	1.16521	0.0522143
$499$	12.6866	0.567929	0.283964	−	0.958835i	$-0.408350\pi$
$499$	12.6866	0.567929	0.283964	+	0.958835i	$0.408350\pi$
$500$	25.2983	1.13137
$501$	6.51027	0.290857
$502$	−29.4588	−1.31481
$503$	−18.9832	−0.846418	−0.423209	−	0.906032i	$-0.639096\pi$
$503$	−18.9832	−0.846418	−0.423209	+	0.906032i	$0.639096\pi$
$504$	1.00000	0.0445435
$505$	47.7970	2.12694
$506$	−0.131180	−0.00583166
$507$	−10.3813	−0.461049
$508$	10.0001	0.443683
$509$	13.6392	0.604547	0.302273	−	0.953221i	$-0.402254\pi$
$509$	13.6392	0.604547	0.302273	+	0.953221i	$0.402254\pi$
$510$	5.71786	0.253191
$511$	7.62191	0.337174
$512$	−1.00000	−0.0441942
$513$	−3.95526	−0.174629
$514$	−6.65319	−0.293460
$515$	45.2872	1.99559
$516$	−9.89270	−0.435502
$517$	−0.313096	−0.0137699
$518$	−0.241220	−0.0105986
$519$	−14.7270	−0.646442
$520$	6.52769	0.286258
$521$	9.20592	0.403318	0.201659	−	0.979456i	$-0.435367\pi$
$521$	9.20592	0.403318	0.201659	+	0.979456i	$0.435367\pi$
$522$	9.67716	0.423558
$523$	−13.5105	−0.590774	−0.295387	−	0.955378i	$-0.595449\pi$
$523$	−13.5105	−0.590774	−0.295387	+	0.955378i	$0.595449\pi$
$524$	8.58719	0.375133
$525$	−11.2716	−0.491932
$526$	13.8662	0.604594
$527$	8.67388	0.377840
$528$	−0.115980	−0.00504736
$529$	−21.7207	−0.944378
$530$	0.0132771	0.000576722 0
$531$	2.90006	0.125852
$532$	3.95526	0.171482
$533$	18.0079	0.780009
$534$	18.6378	0.806534
$535$	−12.7651	−0.551882
$536$	3.30297	0.142666
$537$	−10.9619	−0.473039
$538$	−18.4540	−0.795607
$539$	−0.115980	−0.00499559
$540$	4.03380	0.173587
$541$	5.66519	0.243565	0.121783	−	0.992557i	$-0.461139\pi$
$541$	5.66519	0.243565	0.121783	+	0.992557i	$0.461139\pi$
$542$	−0.0927594	−0.00398436
$543$	−19.7081	−0.845754
$544$	1.41749	0.0607742
$545$	67.7703	2.90296
$546$	−1.61825	−0.0692546
$547$	−12.7784	−0.546367	−0.273183	−	0.961962i	$-0.588077\pi$
$547$	−12.7784	−0.546367	−0.273183	+	0.961962i	$0.588077\pi$
$548$	−0.205726	−0.00878818
$549$	−6.58891	−0.281208
$550$	1.30727	0.0557423
$551$	38.2757	1.63060
$552$	1.13106	0.0481411
$553$	−4.74656	−0.201844
$554$	3.84532	0.163372
$555$	−0.973033	−0.0413030
$556$	18.9460	0.803489
$557$	−22.9963	−0.974384	−0.487192	−	0.873295i	$-0.661979\pi$
$557$	−22.9963	−0.974384	−0.487192	+	0.873295i	$0.661979\pi$
$558$	6.11920	0.259046
$559$	16.0088	0.677101
$560$	−4.03380	−0.170459
$561$	0.164399	0.00694095
$562$	−30.8386	−1.30085
$563$	−27.5084	−1.15934	−0.579670	−	0.814852i	$-0.696818\pi$
$563$	−27.5084	−1.15934	−0.579670	+	0.814852i	$0.696818\pi$
$564$	2.69958	0.113673
$565$	−19.4689	−0.819063
$566$	−17.4764	−0.734588
$567$	−1.00000	−0.0419961
$568$	3.04330	0.127694
$569$	19.1787	0.804012	0.402006	−	0.915637i	$-0.368313\pi$
$569$	19.1787	0.804012	0.402006	+	0.915637i	$0.368313\pi$
$570$	15.9548	0.668271
$571$	−3.18141	−0.133138	−0.0665690	−	0.997782i	$-0.521205\pi$
$571$	−3.18141	−0.133138	−0.0665690	+	0.997782i	$0.521205\pi$
$572$	0.187684	0.00784744
$573$	1.00000	0.0417756
$574$	−11.1280	−0.464475
$575$	−12.7488	−0.531663
$576$	1.00000	0.0416667
$577$	−14.5494	−0.605698	−0.302849	−	0.953039i	$-0.597938\pi$
$577$	−14.5494	−0.605698	−0.302849	+	0.953039i	$0.597938\pi$
$578$	14.9907	0.623532
$579$	−3.19979	−0.132979
$580$	−39.0358	−1.62087
$581$	1.16521	0.0483410
$582$	6.44907	0.267322
$583$	0.000381743 0	1.58102e−5 0
$584$	7.62191	0.315397
$585$	−6.52769	−0.269887
$586$	1.88509	0.0778725
$587$	−20.8596	−0.860966	−0.430483	−	0.902599i	$-0.641657\pi$
$587$	−20.8596	−0.860966	−0.430483	+	0.902599i	$0.641657\pi$
$588$	1.00000	0.0412393
$589$	24.2030	0.997269
$590$	−11.6983	−0.481610
$591$	3.39955	0.139839
$592$	−0.241220	−0.00991407
$593$	−28.9850	−1.19027	−0.595136	−	0.803625i	$-0.702902\pi$
$593$	−28.9850	−1.19027	−0.595136	+	0.803625i	$0.702902\pi$
$594$	0.115980	0.00475870
$595$	5.71786	0.234409
$596$	−21.1266	−0.865379
$597$	7.54342	0.308731
$598$	−1.83034	−0.0748480
$599$	−1.68737	−0.0689440	−0.0344720	−	0.999406i	$-0.510975\pi$
$599$	−1.68737	−0.0689440	−0.0344720	+	0.999406i	$0.510975\pi$
$600$	−11.2716	−0.460160
$601$	9.85564	0.402020	0.201010	−	0.979589i	$-0.435578\pi$
$601$	9.85564	0.402020	0.201010	+	0.979589i	$0.435578\pi$
$602$	−9.89270	−0.403196
$603$	−3.30297	−0.134507
$604$	5.75538	0.234183
$605$	−44.3176	−1.80177
$606$	−11.8491	−0.481338
$607$	−23.8553	−0.968258	−0.484129	−	0.874997i	$-0.660863\pi$
$607$	−23.8553	−0.968258	−0.484129	+	0.874997i	$0.660863\pi$
$608$	3.95526	0.160407
$609$	9.67716	0.392138
$610$	26.5784	1.07613
$611$	−4.36858	−0.176734
$612$	−1.41749	−0.0572985
$613$	26.3287	1.06341	0.531703	−	0.846931i	$-0.321552\pi$
$613$	26.3287	1.06341	0.531703	+	0.846931i	$0.321552\pi$
$614$	−13.8775	−0.560052
$615$	−44.8883	−1.81007
$616$	−0.115980	−0.00467295
$617$	13.6879	0.551054	0.275527	−	0.961293i	$-0.411148\pi$
$617$	13.6879	0.551054	0.275527	+	0.961293i	$0.411148\pi$
$618$	−11.2269	−0.451613
$619$	−27.6936	−1.11310	−0.556551	−	0.830814i	$-0.687876\pi$
$619$	−27.6936	−1.11310	−0.556551	+	0.830814i	$0.687876\pi$
$620$	−24.6836	−0.991319
$621$	−1.13106	−0.0453879
$622$	−7.28937	−0.292277
$623$	18.6378	0.746706
$624$	−1.61825	−0.0647817
$625$	45.6904	1.82762
$626$	26.5911	1.06279
$627$	0.458730	0.0183199
$628$	−5.31805	−0.212213
$629$	0.341926	0.0136335
$630$	4.03380	0.160711
$631$	−1.57463	−0.0626852	−0.0313426	−	0.999509i	$-0.509978\pi$
$631$	−1.57463	−0.0626852	−0.0313426	+	0.999509i	$0.509978\pi$
$632$	−4.74656	−0.188808
$633$	−23.2744	−0.925074
$634$	−21.5657	−0.856484
$635$	40.3385	1.60078
$636$	−0.00329147	−0.000130515 0
$637$	−1.61825	−0.0641173
$638$	−1.12235	−0.0444344
$639$	−3.04330	−0.120391
$640$	−4.03380	−0.159450
$641$	14.4947	0.572508	0.286254	−	0.958154i	$-0.407590\pi$
$641$	14.4947	0.572508	0.286254	+	0.958154i	$0.407590\pi$
$642$	3.16453	0.124894
$643$	−12.2851	−0.484475	−0.242238	−	0.970217i	$-0.577881\pi$
$643$	−12.2851	−0.484475	−0.242238	+	0.970217i	$0.577881\pi$
$644$	1.13106	0.0445700
$645$	−39.9052	−1.57127
$646$	−5.60653	−0.220586
$647$	−27.1102	−1.06581	−0.532906	−	0.846174i	$-0.678900\pi$
$647$	−27.1102	−1.06581	−0.532906	+	0.846174i	$0.678900\pi$
$648$	−1.00000	−0.0392837
$649$	−0.336348	−0.0132028
$650$	18.2402	0.715439
$651$	6.11920	0.239830
$652$	18.2926	0.716394
$653$	36.2047	1.41680	0.708399	−	0.705812i	$-0.249418\pi$
$653$	36.2047	1.41680	0.708399	+	0.705812i	$0.249418\pi$
$654$	−16.8006	−0.656955
$655$	34.6390	1.35346
$656$	−11.1280	−0.434477
$657$	−7.62191	−0.297359
$658$	2.69958	0.105241
$659$	−15.0813	−0.587485	−0.293743	−	0.955885i	$-0.594901\pi$
$659$	−15.0813	−0.587485	−0.293743	+	0.955885i	$0.594901\pi$
$660$	−0.467839	−0.0182106
$661$	−8.09797	−0.314975	−0.157487	−	0.987521i	$-0.550339\pi$
$661$	−8.09797	−0.314975	−0.157487	+	0.987521i	$0.550339\pi$
$662$	22.6212	0.879199
$663$	2.29384	0.0890854
$664$	1.16521	0.0452189
$665$	15.9548	0.618699
$666$	0.241220	0.00934708
$667$	10.9455	0.423810
$668$	6.51027	0.251890
$669$	8.13147	0.314381
$670$	13.3235	0.514732
$671$	0.764180	0.0295008
$672$	1.00000	0.0385758
$673$	−14.7821	−0.569807	−0.284903	−	0.958556i	$-0.591962\pi$
$673$	−14.7821	−0.569807	−0.284903	+	0.958556i	$0.591962\pi$
$674$	17.2949	0.666174
$675$	11.2716	0.433843
$676$	−10.3813	−0.399280
$677$	28.4785	1.09452	0.547258	−	0.836964i	$-0.315672\pi$
$677$	28.4785	1.09452	0.547258	+	0.836964i	$0.315672\pi$
$678$	4.82644	0.185358
$679$	6.44907	0.247492
$680$	5.71786	0.219270
$681$	−10.6339	−0.407491
$682$	−0.709702	−0.0271759
$683$	−17.2051	−0.658336	−0.329168	−	0.944271i	$-0.606768\pi$
$683$	−17.2051	−0.658336	−0.329168	+	0.944271i	$0.606768\pi$
$684$	−3.95526	−0.151233
$685$	−0.829858	−0.0317072
$686$	1.00000	0.0381802
$687$	11.8309	0.451378
$688$	−9.89270	−0.377155
$689$	0.00532641	0.000202920 0
$690$	4.56248	0.173691
$691$	−22.9221	−0.871998	−0.435999	−	0.899947i	$-0.643605\pi$
$691$	−22.9221	−0.871998	−0.435999	+	0.899947i	$0.643605\pi$
$692$	−14.7270	−0.559836
$693$	0.115980	0.00440570
$694$	2.46200	0.0934561
$695$	76.4244	2.89894
$696$	9.67716	0.366812
$697$	15.7738	0.597477
$698$	30.4141	1.15119
$699$	12.2030	0.461559
$700$	−11.2716	−0.426025
$701$	23.7808	0.898189	0.449094	−	0.893484i	$-0.351747\pi$
$701$	23.7808	0.898189	0.449094	+	0.893484i	$0.351747\pi$
$702$	1.61825	0.0610768
$703$	0.954088	0.0359841
$704$	−0.115980	−0.00437114
$705$	10.8896	0.410125
$706$	−25.4647	−0.958377
$707$	−11.8491	−0.445632
$708$	2.90006	0.108991
$709$	−32.1612	−1.20784	−0.603919	−	0.797045i	$-0.706395\pi$
$709$	−32.1612	−1.20784	−0.603919	+	0.797045i	$0.706395\pi$
$710$	12.2761	0.460712
$711$	4.74656	0.178010
$712$	18.6378	0.698479
$713$	6.92118	0.259200
$714$	−1.41749	−0.0530481
$715$	0.757079	0.0283131
$716$	−10.9619	−0.409664
$717$	−5.23760	−0.195602
$718$	−28.2081	−1.05272
$719$	−35.2862	−1.31595	−0.657977	−	0.753038i	$-0.728588\pi$
$719$	−35.2862	−1.31595	−0.657977	+	0.753038i	$0.728588\pi$
$720$	4.03380	0.150331
$721$	−11.2269	−0.418112
$722$	3.35589	0.124893
$723$	22.5229	0.837637
$724$	−19.7081	−0.732444
$725$	−109.077	−4.05101
$726$	10.9865	0.407749
$727$	−5.40374	−0.200414	−0.100207	−	0.994967i	$-0.531950\pi$
$727$	−5.40374	−0.200414	−0.100207	+	0.994967i	$0.531950\pi$
$728$	−1.61825	−0.0599762
$729$	1.00000	0.0370370
$730$	30.7453	1.13793
$731$	14.0228	0.518650
$732$	−6.58891	−0.243533
$733$	−11.3002	−0.417383	−0.208691	−	0.977982i	$-0.566920\pi$
$733$	−11.3002	−0.417383	−0.208691	+	0.977982i	$0.566920\pi$
$734$	−1.08473	−0.0400382
$735$	4.03380	0.148789
$736$	1.13106	0.0416915
$737$	0.383077	0.0141108
$738$	11.1280	0.409629
$739$	−1.15819	−0.0426046	−0.0213023	−	0.999773i	$-0.506781\pi$
$739$	−1.15819	−0.0426046	−0.0213023	+	0.999773i	$0.506781\pi$
$740$	−0.973033	−0.0357694
$741$	6.40059	0.235132
$742$	−0.00329147	−0.000120834 0
$743$	−31.7478	−1.16472	−0.582358	−	0.812933i	$-0.697870\pi$
$743$	−31.7478	−1.16472	−0.582358	+	0.812933i	$0.697870\pi$
$744$	6.11920	0.224341
$745$	−85.2205	−3.12224
$746$	−0.845067	−0.0309401
$747$	−1.16521	−0.0426328
$748$	0.164399	0.00601104
$749$	3.16453	0.115629
$750$	−25.2983	−0.923762
$751$	−8.46686	−0.308960	−0.154480	−	0.987996i	$-0.549370\pi$
$751$	−8.46686	−0.308960	−0.154480	+	0.987996i	$0.549370\pi$
$752$	2.69958	0.0984435
$753$	29.4588	1.07354
$754$	−15.6600	−0.570305
$755$	23.2161	0.844919
$756$	−1.00000	−0.0363696
$757$	−18.9420	−0.688457	−0.344229	−	0.938886i	$-0.611859\pi$
$757$	−18.9420	−0.688457	−0.344229	+	0.938886i	$0.611859\pi$
$758$	−11.7007	−0.424990
$759$	0.131180	0.00476153
$760$	15.9548	0.578740
$761$	−5.94523	−0.215515	−0.107757	−	0.994177i	$-0.534367\pi$
$761$	−5.94523	−0.215515	−0.107757	+	0.994177i	$0.534367\pi$
$762$	−10.0001	−0.362266
$763$	−16.8006	−0.608222
$764$	1.00000	0.0361787
$765$	−5.71786	−0.206730
$766$	−18.7475	−0.677376
$767$	−4.69301	−0.169455
$768$	1.00000	0.0360844
$769$	5.73097	0.206664	0.103332	−	0.994647i	$-0.467050\pi$
$769$	5.73097	0.206664	0.103332	+	0.994647i	$0.467050\pi$
$770$	−0.467839	−0.0168597
$771$	6.65319	0.239609
$772$	−3.19979	−0.115163
$773$	−29.6065	−1.06487	−0.532435	−	0.846471i	$-0.678723\pi$
$773$	−29.6065	−1.06487	−0.532435	+	0.846471i	$0.678723\pi$
$774$	9.89270	0.355586
$775$	−68.9730	−2.47758
$776$	6.44907	0.231508
$777$	0.241220	0.00865371
$778$	−27.9075	−1.00053
$779$	44.0143	1.57698
$780$	−6.52769	−0.233729
$781$	0.352960	0.0126299
$782$	−1.60326	−0.0573326
$783$	−9.67716	−0.345834
$784$	1.00000	0.0357143
$785$	−21.4520	−0.765653
$786$	−8.58719	−0.306295
$787$	21.1406	0.753581	0.376791	−	0.926298i	$-0.377028\pi$
$787$	21.1406	0.753581	0.376791	+	0.926298i	$0.377028\pi$
$788$	3.39955	0.121104
$789$	−13.8662	−0.493649
$790$	−19.1467	−0.681208
$791$	4.82644	0.171608
$792$	0.115980	0.00412115
$793$	10.6625	0.378636
$794$	25.7429	0.913580
$795$	−0.0132771	−0.000470892 0
$796$	7.54342	0.267369
$797$	−39.2910	−1.39176	−0.695879	−	0.718159i	$-0.744985\pi$
$797$	−39.2910	−1.39176	−0.695879	+	0.718159i	$0.744985\pi$
$798$	−3.95526	−0.140015
$799$	−3.82661	−0.135376
$800$	−11.2716	−0.398510
$801$	−18.6378	−0.658533
$802$	−36.7874	−1.29901
$803$	0.883986	0.0311952
$804$	−3.30297	−0.116487
$805$	4.56248	0.160806
$806$	−9.90237	−0.348796
$807$	18.4540	0.649611
$808$	−11.8491	−0.416851
$809$	−21.8857	−0.769461	−0.384730	−	0.923029i	$-0.625706\pi$
$809$	−21.8857	−0.769461	−0.384730	+	0.923029i	$0.625706\pi$
$810$	−4.03380	−0.141733
$811$	−1.90595	−0.0669271	−0.0334635	−	0.999440i	$-0.510654\pi$
$811$	−1.90595	−0.0669271	−0.0334635	+	0.999440i	$0.510654\pi$
$812$	9.67716	0.339602
$813$	0.0927594	0.00325321
$814$	−0.0279766	−0.000980578 0
$815$	73.7888	2.58471
$816$	−1.41749	−0.0496219
$817$	39.1282	1.36892
$818$	−22.9295	−0.801712
$819$	1.61825	0.0565461
$820$	−44.8883	−1.56757
$821$	−37.6494	−1.31397	−0.656986	−	0.753903i	$-0.728169\pi$
$821$	−37.6494	−1.31397	−0.656986	+	0.753903i	$0.728169\pi$
$822$	0.205726	0.00717552
$823$	56.2449	1.96057	0.980287	−	0.197581i	$-0.0633084\pi$
$823$	56.2449	1.96057	0.980287	+	0.197581i	$0.0633084\pi$
$824$	−11.2269	−0.391108
$825$	−1.30727	−0.0455134
$826$	2.90006	0.100906
$827$	−7.26146	−0.252506	−0.126253	−	0.991998i	$-0.540295\pi$
$827$	−7.26146	−0.252506	−0.126253	+	0.991998i	$0.540295\pi$
$828$	−1.13106	−0.0393071
$829$	−7.99796	−0.277781	−0.138890	−	0.990308i	$-0.544354\pi$
$829$	−7.99796	−0.277781	−0.138890	+	0.990308i	$0.544354\pi$
$830$	4.70022	0.163147
$831$	−3.84532	−0.133393
$832$	−1.61825	−0.0561026
$833$	−1.41749	−0.0491130
$834$	−18.9460	−0.656046
$835$	26.2611	0.908804
$836$	0.458730	0.0158655
$837$	−6.11920	−0.211510
$838$	−28.7209	−0.992147
$839$	40.8137	1.40905	0.704523	−	0.709681i	$-0.251161\pi$
$839$	40.8137	1.40905	0.704523	+	0.709681i	$0.251161\pi$
$840$	4.03380	0.139179
$841$	64.6475	2.22922
$842$	37.4734	1.29142
$843$	30.8386	1.06214
$844$	−23.2744	−0.801137
$845$	−41.8760	−1.44058
$846$	−2.69958	−0.0928134
$847$	10.9865	0.377502
$848$	−0.00329147	−0.000113030 0
$849$	17.4764	0.599789
$850$	15.9773	0.548017
$851$	0.272834	0.00935264
$852$	−3.04330	−0.104262
$853$	−12.9291	−0.442683	−0.221341	−	0.975196i	$-0.571043\pi$
$853$	−12.9291	−0.442683	−0.221341	+	0.975196i	$0.571043\pi$
$854$	−6.58891	−0.225468
$855$	−15.9548	−0.545641
$856$	3.16453	0.108161
$857$	−40.7173	−1.39088	−0.695438	−	0.718586i	$-0.744790\pi$
$857$	−40.7173	−1.39088	−0.695438	+	0.718586i	$0.744790\pi$
$858$	−0.187684	−0.00640741
$859$	−26.0914	−0.890228	−0.445114	−	0.895474i	$-0.646837\pi$
$859$	−26.0914	−0.890228	−0.445114	+	0.895474i	$0.646837\pi$
$860$	−39.9052	−1.36076
$861$	11.1280	0.379243
$862$	24.3966	0.830953
$863$	25.5136	0.868494	0.434247	−	0.900794i	$-0.357014\pi$
$863$	25.5136	0.868494	0.434247	+	0.900794i	$0.357014\pi$
$864$	−1.00000	−0.0340207
$865$	−59.4057	−2.01985
$866$	17.4392	0.592607
$867$	−14.9907	−0.509112
$868$	6.11920	0.207699
$869$	−0.550504	−0.0186746
$870$	39.0358	1.32344
$871$	5.34501	0.181109
$872$	−16.8006	−0.568940
$873$	−6.44907	−0.218268
$874$	−4.47364	−0.151323
$875$	−25.2983	−0.855238
$876$	−7.62191	−0.257521
$877$	−8.40621	−0.283857	−0.141929	−	0.989877i	$-0.545330\pi$
$877$	−8.40621	−0.283857	−0.141929	+	0.989877i	$0.545330\pi$
$878$	25.0566	0.845620
$879$	−1.88509	−0.0635826
$880$	−0.467839	−0.0157708
$881$	−28.2867	−0.953004	−0.476502	−	0.879173i	$-0.658096\pi$
$881$	−28.2867	−0.953004	−0.476502	+	0.879173i	$0.658096\pi$
$882$	−1.00000	−0.0336718
$883$	−38.0173	−1.27938	−0.639691	−	0.768632i	$-0.720938\pi$
$883$	−38.0173	−1.27938	−0.639691	+	0.768632i	$0.720938\pi$
$884$	2.29384	0.0771503
$885$	11.6983	0.393233
$886$	−3.73155	−0.125364
$887$	−26.2826	−0.882485	−0.441242	−	0.897388i	$-0.645462\pi$
$887$	−26.2826	−0.882485	−0.441242	+	0.897388i	$0.645462\pi$
$888$	0.241220	0.00809481
$889$	−10.0001	−0.335393
$890$	75.1810	2.52007
$891$	−0.115980	−0.00388546
$892$	8.13147	0.272262
$893$	−10.6775	−0.357310
$894$	21.1266	0.706579
$895$	−44.2180	−1.47804
$896$	1.00000	0.0334077
$897$	1.83034	0.0611131
$898$	2.74530	0.0916118
$899$	59.2165	1.97498
$900$	11.2716	0.375719
$901$	0.00466561	0.000155434 0
$902$	−1.29063	−0.0429731
$903$	9.89270	0.329208
$904$	4.82644	0.160525
$905$	−79.4984	−2.64262
$906$	−5.75538	−0.191210
$907$	−21.4903	−0.713573	−0.356787	−	0.934186i	$-0.616128\pi$
$907$	−21.4903	−0.713573	−0.356787	+	0.934186i	$0.616128\pi$
$908$	−10.6339	−0.352897
$909$	11.8491	0.393010
$910$	−6.52769	−0.216391
$911$	−37.8479	−1.25396	−0.626978	−	0.779037i	$-0.715709\pi$
$911$	−37.8479	−1.25396	−0.626978	+	0.779037i	$0.715709\pi$
$912$	−3.95526	−0.130972
$913$	0.135140	0.00447250
$914$	−31.3008	−1.03534
$915$	−26.5784	−0.878654
$916$	11.8309	0.390905
$917$	−8.58719	−0.283574
$918$	1.41749	0.0467840
$919$	44.7964	1.47770	0.738848	−	0.673872i	$-0.235370\pi$
$919$	44.7964	1.47770	0.738848	+	0.673872i	$0.235370\pi$
$920$	4.56248	0.150420
$921$	13.8775	0.457280
$922$	6.84452	0.225412
$923$	4.92480	0.162102
$924$	0.115980	0.00381545
$925$	−2.71893	−0.0893977
$926$	−14.5897	−0.479447
$927$	11.2269	0.368740
$928$	9.67716	0.317668
$929$	15.4886	0.508163	0.254082	−	0.967183i	$-0.418227\pi$
$929$	15.4886	0.508163	0.254082	+	0.967183i	$0.418227\pi$
$930$	24.6836	0.809409
$931$	−3.95526	−0.129629
$932$	12.2030	0.399722
$933$	7.28937	0.238643
$934$	−40.8584	−1.33693
$935$	0.663155	0.0216875
$936$	1.61825	0.0528941
$937$	−11.7412	−0.383567	−0.191783	−	0.981437i	$-0.561427\pi$
$937$	−11.7412	−0.383567	−0.191783	+	0.981437i	$0.561427\pi$
$938$	−3.30297	−0.107846
$939$	−26.5911	−0.867767
$940$	10.8896	0.355179
$941$	18.1478	0.591600	0.295800	−	0.955250i	$-0.404414\pi$
$941$	18.1478	0.591600	0.295800	+	0.955250i	$0.404414\pi$
$942$	5.31805	0.173271
$943$	12.5865	0.409872
$944$	2.90006	0.0943889
$945$	−4.03380	−0.131220
$946$	−1.14735	−0.0373036
$947$	−23.0773	−0.749911	−0.374955	−	0.927043i	$-0.622342\pi$
$947$	−23.0773	−0.749911	−0.374955	+	0.927043i	$0.622342\pi$
$948$	4.74656	0.154161
$949$	12.3341	0.400383
$950$	44.5820	1.44643
$951$	21.5657	0.699317
$952$	−1.41749	−0.0459410
$953$	−31.7340	−1.02796	−0.513982	−	0.857801i	$-0.671830\pi$
$953$	−31.7340	−1.02796	−0.513982	+	0.857801i	$0.671830\pi$
$954$	0.00329147	0.000106565 0
$955$	4.03380	0.130531
$956$	−5.23760	−0.169396
$957$	1.12235	0.0362805
$958$	−14.0511	−0.453970
$959$	0.205726	0.00664324
$960$	4.03380	0.130190
$961$	6.44459	0.207890
$962$	−0.390353	−0.0125855
$963$	−3.16453	−0.101975
$964$	22.5229	0.725415
$965$	−12.9073	−0.415501
$966$	−1.13106	−0.0363913
$967$	20.8470	0.670396	0.335198	−	0.942148i	$-0.391197\pi$
$967$	20.8470	0.670396	0.335198	+	0.942148i	$0.391197\pi$
$968$	10.9865	0.353121
$969$	5.60653	0.180108
$970$	26.0143	0.835268
$971$	−20.7520	−0.665963	−0.332982	−	0.942933i	$-0.608055\pi$
$971$	−20.7520	−0.665963	−0.332982	+	0.942933i	$0.608055\pi$
$972$	1.00000	0.0320750
$973$	−18.9460	−0.607380
$974$	−26.8121	−0.859114
$975$	−18.2402	−0.584153
$976$	−6.58891	−0.210906
$977$	−42.2018	−1.35016	−0.675078	−	0.737747i	$-0.735890\pi$
$977$	−42.2018	−1.35016	−0.675078	+	0.737747i	$0.735890\pi$
$978$	−18.2926	−0.584933
$979$	2.16160	0.0690850
$980$	4.03380	0.128855
$981$	16.8006	0.536402
$982$	−0.246313	−0.00786015
$983$	−52.3583	−1.66997	−0.834985	−	0.550273i	$-0.814524\pi$
$983$	−52.3583	−1.66997	−0.834985	+	0.550273i	$0.814524\pi$
$984$	11.1280	0.354749
$985$	13.7131	0.436937
$986$	−13.7172	−0.436846
$987$	−2.69958	−0.0859285
$988$	6.40059	0.203630
$989$	11.1892	0.355797
$990$	0.467839	0.0148689
$991$	24.7706	0.786863	0.393431	−	0.919354i	$-0.371288\pi$
$991$	24.7706	0.786863	0.393431	+	0.919354i	$0.371288\pi$
$992$	6.11920	0.194285
$993$	−22.6212	−0.717863
$994$	−3.04330	−0.0965275
$995$	30.4287	0.964653
$996$	−1.16521	−0.0369211
$997$	−26.5131	−0.839678	−0.419839	−	0.907599i	$-0.637913\pi$
$997$	−26.5131	−0.839678	−0.419839	+	0.907599i	$0.637913\pi$
$998$	−12.6866	−0.401586
$999$	−0.241220	−0.00763186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.t.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.t.1.11	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.03380 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.03380 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.03380 q^{10} -0.115980 q^{11} +1.00000 q^{12} -1.61825 q^{13} +1.00000 q^{14} +4.03380 q^{15} +1.00000 q^{16} -1.41749 q^{17} -1.00000 q^{18} -3.95526 q^{19} +4.03380 q^{20} -1.00000 q^{21} +0.115980 q^{22} -1.13106 q^{23} -1.00000 q^{24} +11.2716 q^{25} +1.61825 q^{26} +1.00000 q^{27} -1.00000 q^{28} -9.67716 q^{29} -4.03380 q^{30} -6.11920 q^{31} -1.00000 q^{32} -0.115980 q^{33} +1.41749 q^{34} -4.03380 q^{35} +1.00000 q^{36} -0.241220 q^{37} +3.95526 q^{38} -1.61825 q^{39} -4.03380 q^{40} -11.1280 q^{41} +1.00000 q^{42} -9.89270 q^{43} -0.115980 q^{44} +4.03380 q^{45} +1.13106 q^{46} +2.69958 q^{47} +1.00000 q^{48} +1.00000 q^{49} -11.2716 q^{50} -1.41749 q^{51} -1.61825 q^{52} -0.00329147 q^{53} -1.00000 q^{54} -0.467839 q^{55} +1.00000 q^{56} -3.95526 q^{57} +9.67716 q^{58} +2.90006 q^{59} +4.03380 q^{60} -6.58891 q^{61} +6.11920 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.52769 q^{65} +0.115980 q^{66} -3.30297 q^{67} -1.41749 q^{68} -1.13106 q^{69} +4.03380 q^{70} -3.04330 q^{71} -1.00000 q^{72} -7.62191 q^{73} +0.241220 q^{74} +11.2716 q^{75} -3.95526 q^{76} +0.115980 q^{77} +1.61825 q^{78} +4.74656 q^{79} +4.03380 q^{80} +1.00000 q^{81} +11.1280 q^{82} -1.16521 q^{83} -1.00000 q^{84} -5.71786 q^{85} +9.89270 q^{86} -9.67716 q^{87} +0.115980 q^{88} -18.6378 q^{89} -4.03380 q^{90} +1.61825 q^{91} -1.13106 q^{92} -6.11920 q^{93} -2.69958 q^{94} -15.9548 q^{95} -1.00000 q^{96} -6.44907 q^{97} -1.00000 q^{98} -0.115980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9} - q^{10} + 11 q^{12} - 15 q^{13} + 11 q^{14} + q^{15} + 11 q^{16} - q^{17} - 11 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 5 q^{23} - 11 q^{24} + 6 q^{25} + 15 q^{26} + 11 q^{27} - 11 q^{28} - 12 q^{29} - q^{30} - q^{31} - 11 q^{32} + q^{34} - q^{35} + 11 q^{36} - 12 q^{37} + 3 q^{38} - 15 q^{39} - q^{40} + 8 q^{41} + 11 q^{42} - 14 q^{43} + q^{45} + 5 q^{46} - 3 q^{47} + 11 q^{48} + 11 q^{49} - 6 q^{50} - q^{51} - 15 q^{52} - 14 q^{53} - 11 q^{54} - 27 q^{55} + 11 q^{56} - 3 q^{57} + 12 q^{58} + 33 q^{59} + q^{60} - 46 q^{61} + q^{62} - 11 q^{63} + 11 q^{64} + 12 q^{65} - 8 q^{67} - q^{68} - 5 q^{69} + q^{70} - 16 q^{71} - 11 q^{72} - 26 q^{73} + 12 q^{74} + 6 q^{75} - 3 q^{76} + 15 q^{78} - 24 q^{79} + q^{80} + 11 q^{81} - 8 q^{82} - 4 q^{83} - 11 q^{84} - 32 q^{85} + 14 q^{86} - 12 q^{87} + 5 q^{89} - q^{90} + 15 q^{91} - 5 q^{92} - q^{93} + 3 q^{94} - 19 q^{95} - 11 q^{96} - 36 q^{97} - 11 q^{98}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9 - q^10 + 11 * q^12 - 15 * q^13 + 11 * q^14 + q^15 + 11 * q^16 - q^17 - 11 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 5 * q^23 - 11 * q^24 + 6 * q^25 + 15 * q^26 + 11 * q^27 - 11 * q^28 - 12 * q^29 - q^30 - q^31 - 11 * q^32 + q^34 - q^35 + 11 * q^36 - 12 * q^37 + 3 * q^38 - 15 * q^39 - q^40 + 8 * q^41 + 11 * q^42 - 14 * q^43 + q^45 + 5 * q^46 - 3 * q^47 + 11 * q^48 + 11 * q^49 - 6 * q^50 - q^51 - 15 * q^52 - 14 * q^53 - 11 * q^54 - 27 * q^55 + 11 * q^56 - 3 * q^57 + 12 * q^58 + 33 * q^59 + q^60 - 46 * q^61 + q^62 - 11 * q^63 + 11 * q^64 + 12 * q^65 - 8 * q^67 - q^68 - 5 * q^69 + q^70 - 16 * q^71 - 11 * q^72 - 26 * q^73 + 12 * q^74 + 6 * q^75 - 3 * q^76 + 15 * q^78 - 24 * q^79 + q^80 + 11 * q^81 - 8 * q^82 - 4 * q^83 - 11 * q^84 - 32 * q^85 + 14 * q^86 - 12 * q^87 + 5 * q^89 - q^90 + 15 * q^91 - 5 * q^92 - q^93 + 3 * q^94 - 19 * q^95 - 11 * q^96 - 36 * q^97 - 11 * q^98

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