LMFDB - Embedded newform 8022.2.a.r.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 $ x^10 - 2x^9 - 19x^8 + 28x^7 + 114x^6 - 110x^5 - 282x^4 + 149x^3 + 285x^2 - 49*x - 79
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.09237$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.09237 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.09237 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.09237 q^{10} -1.01386 q^{11} -1.00000 q^{12} +1.37066 q^{13} +1.00000 q^{14} -2.09237 q^{15} +1.00000 q^{16} +6.65104 q^{17} +1.00000 q^{18} -1.25110 q^{19} +2.09237 q^{20} -1.00000 q^{21} -1.01386 q^{22} +5.57021 q^{23} -1.00000 q^{24} -0.622002 q^{25} +1.37066 q^{26} -1.00000 q^{27} +1.00000 q^{28} +4.22020 q^{29} -2.09237 q^{30} +4.64328 q^{31} +1.00000 q^{32} +1.01386 q^{33} +6.65104 q^{34} +2.09237 q^{35} +1.00000 q^{36} -3.39922 q^{37} -1.25110 q^{38} -1.37066 q^{39} +2.09237 q^{40} -0.205499 q^{41} -1.00000 q^{42} +0.130864 q^{43} -1.01386 q^{44} +2.09237 q^{45} +5.57021 q^{46} -4.38570 q^{47} -1.00000 q^{48} +1.00000 q^{49} -0.622002 q^{50} -6.65104 q^{51} +1.37066 q^{52} -7.54739 q^{53} -1.00000 q^{54} -2.12137 q^{55} +1.00000 q^{56} +1.25110 q^{57} +4.22020 q^{58} -11.5884 q^{59} -2.09237 q^{60} +2.15687 q^{61} +4.64328 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.86792 q^{65} +1.01386 q^{66} +13.2482 q^{67} +6.65104 q^{68} -5.57021 q^{69} +2.09237 q^{70} +8.44044 q^{71} +1.00000 q^{72} +3.50283 q^{73} -3.39922 q^{74} +0.622002 q^{75} -1.25110 q^{76} -1.01386 q^{77} -1.37066 q^{78} +15.2995 q^{79} +2.09237 q^{80} +1.00000 q^{81} -0.205499 q^{82} +4.94352 q^{83} -1.00000 q^{84} +13.9164 q^{85} +0.130864 q^{86} -4.22020 q^{87} -1.01386 q^{88} -10.6692 q^{89} +2.09237 q^{90} +1.37066 q^{91} +5.57021 q^{92} -4.64328 q^{93} -4.38570 q^{94} -2.61775 q^{95} -1.00000 q^{96} -17.7111 q^{97} +1.00000 q^{98} -1.01386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * 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
$5$	2.09237	0.935735	0.467867	−	0.883799i	$-0.345022\pi$
$5$	2.09237	0.935735	0.467867	+	0.883799i	$0.345022\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.09237	0.661664
$11$	−1.01386	−0.305690	−0.152845	−	0.988250i	$-0.548844\pi$
$11$	−1.01386	−0.305690	−0.152845	+	0.988250i	$0.548844\pi$
$12$	−1.00000	−0.288675
$13$	1.37066	0.380152	0.190076	−	0.981769i	$-0.439127\pi$
$13$	1.37066	0.380152	0.190076	+	0.981769i	$0.439127\pi$
$14$	1.00000	0.267261
$15$	−2.09237	−0.540247
$16$	1.00000	0.250000
$17$	6.65104	1.61311	0.806557	−	0.591156i	$-0.201328\pi$
$17$	6.65104	1.61311	0.806557	+	0.591156i	$0.201328\pi$
$18$	1.00000	0.235702
$19$	−1.25110	−0.287021	−0.143511	−	0.989649i	$-0.545839\pi$
$19$	−1.25110	−0.287021	−0.143511	+	0.989649i	$0.545839\pi$
$20$	2.09237	0.467867
$21$	−1.00000	−0.218218
$22$	−1.01386	−0.216156
$23$	5.57021	1.16147	0.580735	−	0.814093i	$-0.302765\pi$
$23$	5.57021	1.16147	0.580735	+	0.814093i	$0.302765\pi$
$24$	−1.00000	−0.204124
$25$	−0.622002	−0.124400
$26$	1.37066	0.268808
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	4.22020	0.783672	0.391836	−	0.920035i	$-0.371840\pi$
$29$	4.22020	0.783672	0.391836	+	0.920035i	$0.371840\pi$
$30$	−2.09237	−0.382012
$31$	4.64328	0.833958	0.416979	−	0.908916i	$-0.363089\pi$
$31$	4.64328	0.833958	0.416979	+	0.908916i	$0.363089\pi$
$32$	1.00000	0.176777
$33$	1.01386	0.176490
$34$	6.65104	1.14064
$35$	2.09237	0.353675
$36$	1.00000	0.166667
$37$	−3.39922	−0.558828	−0.279414	−	0.960171i	$-0.590140\pi$
$37$	−3.39922	−0.558828	−0.279414	+	0.960171i	$0.590140\pi$
$38$	−1.25110	−0.202955
$39$	−1.37066	−0.219481
$40$	2.09237	0.330832
$41$	−0.205499	−0.0320935	−0.0160468	−	0.999871i	$-0.505108\pi$
$41$	−0.205499	−0.0320935	−0.0160468	+	0.999871i	$0.505108\pi$
$42$	−1.00000	−0.154303
$43$	0.130864	0.0199566	0.00997831	−	0.999950i	$-0.496824\pi$
$43$	0.130864	0.0199566	0.00997831	+	0.999950i	$0.496824\pi$
$44$	−1.01386	−0.152845
$45$	2.09237	0.311912
$46$	5.57021	0.821283
$47$	−4.38570	−0.639719	−0.319860	−	0.947465i	$-0.603636\pi$
$47$	−4.38570	−0.639719	−0.319860	+	0.947465i	$0.603636\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−0.622002	−0.0879643
$51$	−6.65104	−0.931332
$52$	1.37066	0.190076
$53$	−7.54739	−1.03671	−0.518357	−	0.855164i	$-0.673456\pi$
$53$	−7.54739	−1.03671	−0.518357	+	0.855164i	$0.673456\pi$
$54$	−1.00000	−0.136083
$55$	−2.12137	−0.286045
$56$	1.00000	0.133631
$57$	1.25110	0.165712
$58$	4.22020	0.554140
$59$	−11.5884	−1.50868	−0.754342	−	0.656482i	$-0.772044\pi$
$59$	−11.5884	−1.50868	−0.754342	+	0.656482i	$0.772044\pi$
$60$	−2.09237	−0.270123
$61$	2.15687	0.276159	0.138080	−	0.990421i	$-0.455907\pi$
$61$	2.15687	0.276159	0.138080	+	0.990421i	$0.455907\pi$
$62$	4.64328	0.589697
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.86792	0.355721
$66$	1.01386	0.124798
$67$	13.2482	1.61852	0.809260	−	0.587451i	$-0.199868\pi$
$67$	13.2482	1.61852	0.809260	+	0.587451i	$0.199868\pi$
$68$	6.65104	0.806557
$69$	−5.57021	−0.670575
$70$	2.09237	0.250086
$71$	8.44044	1.00170	0.500848	−	0.865535i	$-0.333021\pi$
$71$	8.44044	1.00170	0.500848	+	0.865535i	$0.333021\pi$
$72$	1.00000	0.117851
$73$	3.50283	0.409975	0.204988	−	0.978765i	$-0.434285\pi$
$73$	3.50283	0.409975	0.204988	+	0.978765i	$0.434285\pi$
$74$	−3.39922	−0.395151
$75$	0.622002	0.0718226
$76$	−1.25110	−0.143511
$77$	−1.01386	−0.115540
$78$	−1.37066	−0.155196
$79$	15.2995	1.72132	0.860662	−	0.509176i	$-0.170050\pi$
$79$	15.2995	1.72132	0.860662	+	0.509176i	$0.170050\pi$
$80$	2.09237	0.233934
$81$	1.00000	0.111111
$82$	−0.205499	−0.0226936
$83$	4.94352	0.542622	0.271311	−	0.962492i	$-0.412543\pi$
$83$	4.94352	0.542622	0.271311	+	0.962492i	$0.412543\pi$
$84$	−1.00000	−0.109109
$85$	13.9164	1.50945
$86$	0.130864	0.0141115
$87$	−4.22020	−0.452453
$88$	−1.01386	−0.108078
$89$	−10.6692	−1.13093	−0.565466	−	0.824771i	$-0.691304\pi$
$89$	−10.6692	−1.13093	−0.565466	+	0.824771i	$0.691304\pi$
$90$	2.09237	0.220555
$91$	1.37066	0.143684
$92$	5.57021	0.580735
$93$	−4.64328	−0.481486
$94$	−4.38570	−0.452350
$95$	−2.61775	−0.268576
$96$	−1.00000	−0.102062
$97$	−17.7111	−1.79829	−0.899147	−	0.437647i	$-0.855812\pi$
$97$	−17.7111	−1.79829	−0.899147	+	0.437647i	$0.855812\pi$
$98$	1.00000	0.101015
$99$	−1.01386	−0.101897
$100$	−0.622002	−0.0622002
$101$	−4.14216	−0.412160	−0.206080	−	0.978535i	$-0.566071\pi$
$101$	−4.14216	−0.412160	−0.206080	+	0.978535i	$0.566071\pi$
$102$	−6.65104	−0.658551
$103$	12.6608	1.24751	0.623755	−	0.781620i	$-0.285606\pi$
$103$	12.6608	1.24751	0.623755	+	0.781620i	$0.285606\pi$
$104$	1.37066	0.134404
$105$	−2.09237	−0.204194
$106$	−7.54739	−0.733067
$107$	−13.3993	−1.29536	−0.647678	−	0.761914i	$-0.724260\pi$
$107$	−13.3993	−1.29536	−0.647678	+	0.761914i	$0.724260\pi$
$108$	−1.00000	−0.0962250
$109$	−8.81649	−0.844467	−0.422233	−	0.906487i	$-0.638754\pi$
$109$	−8.81649	−0.844467	−0.422233	+	0.906487i	$0.638754\pi$
$110$	−2.12137	−0.202264
$111$	3.39922	0.322640
$112$	1.00000	0.0944911
$113$	−11.3916	−1.07163	−0.535817	−	0.844334i	$-0.679996\pi$
$113$	−11.3916	−1.07163	−0.535817	+	0.844334i	$0.679996\pi$
$114$	1.25110	0.117176
$115$	11.6549	1.08683
$116$	4.22020	0.391836
$117$	1.37066	0.126717
$118$	−11.5884	−1.06680
$119$	6.65104	0.609700
$120$	−2.09237	−0.191006
$121$	−9.97209	−0.906553
$122$	2.15687	0.195274
$123$	0.205499	0.0185292
$124$	4.64328	0.416979
$125$	−11.7633	−1.05214
$126$	1.00000	0.0890871
$127$	5.77668	0.512597	0.256299	−	0.966598i	$-0.417497\pi$
$127$	5.77668	0.512597	0.256299	+	0.966598i	$0.417497\pi$
$128$	1.00000	0.0883883
$129$	−0.130864	−0.0115220
$130$	2.86792	0.251533
$131$	21.4669	1.87557	0.937785	−	0.347217i	$-0.112873\pi$
$131$	21.4669	1.87557	0.937785	+	0.347217i	$0.112873\pi$
$132$	1.01386	0.0882452
$133$	−1.25110	−0.108484
$134$	13.2482	1.14447
$135$	−2.09237	−0.180082
$136$	6.65104	0.570322
$137$	2.68387	0.229299	0.114649	−	0.993406i	$-0.463426\pi$
$137$	2.68387	0.229299	0.114649	+	0.993406i	$0.463426\pi$
$138$	−5.57021	−0.474168
$139$	5.43609	0.461083	0.230541	−	0.973063i	$-0.425950\pi$
$139$	5.43609	0.461083	0.230541	+	0.973063i	$0.425950\pi$
$140$	2.09237	0.176837
$141$	4.38570	0.369342
$142$	8.44044	0.708306
$143$	−1.38966	−0.116209
$144$	1.00000	0.0833333
$145$	8.83021	0.733309
$146$	3.50283	0.289896
$147$	−1.00000	−0.0824786
$148$	−3.39922	−0.279414
$149$	−4.92505	−0.403476	−0.201738	−	0.979440i	$-0.564659\pi$
$149$	−4.92505	−0.403476	−0.201738	+	0.979440i	$0.564659\pi$
$150$	0.622002	0.0507862
$151$	11.0780	0.901517	0.450759	−	0.892646i	$-0.351153\pi$
$151$	11.0780	0.901517	0.450759	+	0.892646i	$0.351153\pi$
$152$	−1.25110	−0.101477
$153$	6.65104	0.537705
$154$	−1.01386	−0.0816992
$155$	9.71545	0.780364
$156$	−1.37066	−0.109740
$157$	2.56736	0.204898	0.102449	−	0.994738i	$-0.467332\pi$
$157$	2.56736	0.204898	0.102449	+	0.994738i	$0.467332\pi$
$158$	15.2995	1.21716
$159$	7.54739	0.598547
$160$	2.09237	0.165416
$161$	5.57021	0.438994
$162$	1.00000	0.0785674
$163$	3.70507	0.290203	0.145102	−	0.989417i	$-0.453649\pi$
$163$	3.70507	0.290203	0.145102	+	0.989417i	$0.453649\pi$
$164$	−0.205499	−0.0160468
$165$	2.12137	0.165148
$166$	4.94352	0.383691
$167$	13.6222	1.05412	0.527059	−	0.849829i	$-0.323295\pi$
$167$	13.6222	1.05412	0.527059	+	0.849829i	$0.323295\pi$
$168$	−1.00000	−0.0771517
$169$	−11.1213	−0.855484
$170$	13.9164	1.06734
$171$	−1.25110	−0.0956738
$172$	0.130864	0.00997831
$173$	13.6219	1.03566	0.517829	−	0.855484i	$-0.326740\pi$
$173$	13.6219	1.03566	0.517829	+	0.855484i	$0.326740\pi$
$174$	−4.22020	−0.319933
$175$	−0.622002	−0.0470189
$176$	−1.01386	−0.0764226
$177$	11.5884	0.871039
$178$	−10.6692	−0.799690
$179$	15.1494	1.13232	0.566158	−	0.824297i	$-0.308429\pi$
$179$	15.1494	1.13232	0.566158	+	0.824297i	$0.308429\pi$
$180$	2.09237	0.155956
$181$	−1.94954	−0.144908	−0.0724540	−	0.997372i	$-0.523083\pi$
$181$	−1.94954	−0.144908	−0.0724540	+	0.997372i	$0.523083\pi$
$182$	1.37066	0.101600
$183$	−2.15687	−0.159441
$184$	5.57021	0.410641
$185$	−7.11241	−0.522915
$186$	−4.64328	−0.340462
$187$	−6.74322	−0.493113
$188$	−4.38570	−0.319860
$189$	−1.00000	−0.0727393
$190$	−2.61775	−0.189912
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	−0.714487	−0.0514299	−0.0257149	−	0.999669i	$-0.508186\pi$
$193$	−0.714487	−0.0514299	−0.0257149	+	0.999669i	$0.508186\pi$
$194$	−17.7111	−1.27159
$195$	−2.86792	−0.205376
$196$	1.00000	0.0714286
$197$	7.13296	0.508203	0.254101	−	0.967178i	$-0.418220\pi$
$197$	7.13296	0.508203	0.254101	+	0.967178i	$0.418220\pi$
$198$	−1.01386	−0.0720519
$199$	5.83078	0.413333	0.206667	−	0.978411i	$-0.433738\pi$
$199$	5.83078	0.413333	0.206667	+	0.978411i	$0.433738\pi$
$200$	−0.622002	−0.0439822
$201$	−13.2482	−0.934453
$202$	−4.14216	−0.291441
$203$	4.22020	0.296200
$204$	−6.65104	−0.465666
$205$	−0.429979	−0.0300310
$206$	12.6608	0.882123
$207$	5.57021	0.387156
$208$	1.37066	0.0950380
$209$	1.26844	0.0877397
$210$	−2.09237	−0.144387
$211$	−4.01806	−0.276615	−0.138307	−	0.990389i	$-0.544166\pi$
$211$	−4.01806	−0.276615	−0.138307	+	0.990389i	$0.544166\pi$
$212$	−7.54739	−0.518357
$213$	−8.44044	−0.578330
$214$	−13.3993	−0.915955
$215$	0.273816	0.0186741
$216$	−1.00000	−0.0680414
$217$	4.64328	0.315207
$218$	−8.81649	−0.597128
$219$	−3.50283	−0.236699
$220$	−2.12137	−0.143023
$221$	9.11630	0.613228
$222$	3.39922	0.228141
$223$	9.57094	0.640918	0.320459	−	0.947262i	$-0.396163\pi$
$223$	9.57094	0.640918	0.320459	+	0.947262i	$0.396163\pi$
$224$	1.00000	0.0668153
$225$	−0.622002	−0.0414668
$226$	−11.3916	−0.757760
$227$	−12.7530	−0.846445	−0.423223	−	0.906026i	$-0.639101\pi$
$227$	−12.7530	−0.846445	−0.423223	+	0.906026i	$0.639101\pi$
$228$	1.25110	0.0828559
$229$	−8.87496	−0.586474	−0.293237	−	0.956040i	$-0.594732\pi$
$229$	−8.87496	−0.586474	−0.293237	+	0.956040i	$0.594732\pi$
$230$	11.6549	0.768503
$231$	1.01386	0.0667071
$232$	4.22020	0.277070
$233$	5.11633	0.335182	0.167591	−	0.985857i	$-0.446401\pi$
$233$	5.11633	0.335182	0.167591	+	0.985857i	$0.446401\pi$
$234$	1.37066	0.0896027
$235$	−9.17648	−0.598608
$236$	−11.5884	−0.754342
$237$	−15.2995	−0.993807
$238$	6.65104	0.431123
$239$	−1.56284	−0.101092	−0.0505458	−	0.998722i	$-0.516096\pi$
$239$	−1.56284	−0.101092	−0.0505458	+	0.998722i	$0.516096\pi$
$240$	−2.09237	−0.135062
$241$	1.02297	0.0658954	0.0329477	−	0.999457i	$-0.489511\pi$
$241$	1.02297	0.0658954	0.0329477	+	0.999457i	$0.489511\pi$
$242$	−9.97209	−0.641030
$243$	−1.00000	−0.0641500
$244$	2.15687	0.138080
$245$	2.09237	0.133676
$246$	0.205499	0.0131021
$247$	−1.71483	−0.109112
$248$	4.64328	0.294849
$249$	−4.94352	−0.313283
$250$	−11.7633	−0.743976
$251$	−22.5682	−1.42449	−0.712246	−	0.701930i	$-0.752322\pi$
$251$	−22.5682	−1.42449	−0.712246	+	0.701930i	$0.752322\pi$
$252$	1.00000	0.0629941
$253$	−5.64742	−0.355050
$254$	5.77668	0.362461
$255$	−13.9164	−0.871480
$256$	1.00000	0.0625000
$257$	15.6237	0.974578	0.487289	−	0.873241i	$-0.337986\pi$
$257$	15.6237	0.974578	0.487289	+	0.873241i	$0.337986\pi$
$258$	−0.130864	−0.00814726
$259$	−3.39922	−0.211217
$260$	2.86792	0.177861
$261$	4.22020	0.261224
$262$	21.4669	1.32623
$263$	−4.05617	−0.250114	−0.125057	−	0.992150i	$-0.539911\pi$
$263$	−4.05617	−0.250114	−0.125057	+	0.992150i	$0.539911\pi$
$264$	1.01386	0.0623988
$265$	−15.7919	−0.970089
$266$	−1.25110	−0.0767097
$267$	10.6692	0.652944
$268$	13.2482	0.809260
$269$	32.2718	1.96765	0.983824	−	0.179140i	$-0.0573315\pi$
$269$	32.2718	1.96765	0.983824	+	0.179140i	$0.0573315\pi$
$270$	−2.09237	−0.127337
$271$	−10.8398	−0.658470	−0.329235	−	0.944248i	$-0.606791\pi$
$271$	−10.8398	−0.658470	−0.329235	+	0.944248i	$0.606791\pi$
$272$	6.65104	0.403278
$273$	−1.37066	−0.0829560
$274$	2.68387	0.162139
$275$	0.630623	0.0380280
$276$	−5.57021	−0.335287
$277$	−24.4487	−1.46898	−0.734490	−	0.678619i	$-0.762579\pi$
$277$	−24.4487	−1.46898	−0.734490	+	0.678619i	$0.762579\pi$
$278$	5.43609	0.326035
$279$	4.64328	0.277986
$280$	2.09237	0.125043
$281$	4.87438	0.290781	0.145391	−	0.989374i	$-0.453556\pi$
$281$	4.87438	0.290781	0.145391	+	0.989374i	$0.453556\pi$
$282$	4.38570	0.261164
$283$	15.9856	0.950248	0.475124	−	0.879919i	$-0.342403\pi$
$283$	15.9856	0.950248	0.475124	+	0.879919i	$0.342403\pi$
$284$	8.44044	0.500848
$285$	2.61775	0.155062
$286$	−1.38966	−0.0821720
$287$	−0.205499	−0.0121302
$288$	1.00000	0.0589256
$289$	27.2363	1.60214
$290$	8.83021	0.518528
$291$	17.7111	1.03825
$292$	3.50283	0.204988
$293$	−22.5721	−1.31867	−0.659337	−	0.751848i	$-0.729163\pi$
$293$	−22.5721	−1.31867	−0.659337	+	0.751848i	$0.729163\pi$
$294$	−1.00000	−0.0583212
$295$	−24.2472	−1.41173
$296$	−3.39922	−0.197576
$297$	1.01386	0.0588301
$298$	−4.92505	−0.285300
$299$	7.63485	0.441535
$300$	0.622002	0.0359113
$301$	0.130864	0.00754290
$302$	11.0780	0.637469
$303$	4.14216	0.237961
$304$	−1.25110	−0.0717553
$305$	4.51297	0.258412
$306$	6.65104	0.380215
$307$	−25.5310	−1.45713	−0.728566	−	0.684976i	$-0.759813\pi$
$307$	−25.5310	−1.45713	−0.728566	+	0.684976i	$0.759813\pi$
$308$	−1.01386	−0.0577701
$309$	−12.6608	−0.720250
$310$	9.71545	0.551800
$311$	25.1719	1.42737	0.713683	−	0.700469i	$-0.247026\pi$
$311$	25.1719	1.42737	0.713683	+	0.700469i	$0.247026\pi$
$312$	−1.37066	−0.0775982
$313$	4.47109	0.252721	0.126361	−	0.991984i	$-0.459670\pi$
$313$	4.47109	0.252721	0.126361	+	0.991984i	$0.459670\pi$
$314$	2.56736	0.144885
$315$	2.09237	0.117892
$316$	15.2995	0.860662
$317$	−1.93715	−0.108801	−0.0544005	−	0.998519i	$-0.517325\pi$
$317$	−1.93715	−0.108801	−0.0544005	+	0.998519i	$0.517325\pi$
$318$	7.54739	0.423237
$319$	−4.27869	−0.239561
$320$	2.09237	0.116967
$321$	13.3993	0.747874
$322$	5.57021	0.310416
$323$	−8.32110	−0.462998
$324$	1.00000	0.0555556
$325$	−0.852551	−0.0472910
$326$	3.70507	0.205205
$327$	8.81649	0.487553
$328$	−0.205499	−0.0113468
$329$	−4.38570	−0.241791
$330$	2.12137	0.116777
$331$	−30.6202	−1.68304	−0.841519	−	0.540228i	$-0.818338\pi$
$331$	−30.6202	−1.68304	−0.841519	+	0.540228i	$0.818338\pi$
$332$	4.94352	0.271311
$333$	−3.39922	−0.186276
$334$	13.6222	0.745374
$335$	27.7200	1.51451
$336$	−1.00000	−0.0545545
$337$	7.88240	0.429382	0.214691	−	0.976682i	$-0.431126\pi$
$337$	7.88240	0.429382	0.214691	+	0.976682i	$0.431126\pi$
$338$	−11.1213	−0.604919
$339$	11.3916	0.618708
$340$	13.9164	0.754723
$341$	−4.70764	−0.254933
$342$	−1.25110	−0.0676516
$343$	1.00000	0.0539949
$344$	0.130864	0.00705573
$345$	−11.6549	−0.627480
$346$	13.6219	0.732320
$347$	−9.03193	−0.484860	−0.242430	−	0.970169i	$-0.577944\pi$
$347$	−9.03193	−0.484860	−0.242430	+	0.970169i	$0.577944\pi$
$348$	−4.22020	−0.226227
$349$	0.785811	0.0420635	0.0210317	−	0.999779i	$-0.493305\pi$
$349$	0.785811	0.0420635	0.0210317	+	0.999779i	$0.493305\pi$
$350$	−0.622002	−0.0332474
$351$	−1.37066	−0.0731603
$352$	−1.01386	−0.0540389
$353$	16.0710	0.855373	0.427686	−	0.903927i	$-0.359329\pi$
$353$	16.0710	0.855373	0.427686	+	0.903927i	$0.359329\pi$
$354$	11.5884	0.615918
$355$	17.6605	0.937322
$356$	−10.6692	−0.565466
$357$	−6.65104	−0.352010
$358$	15.1494	0.800669
$359$	−26.3068	−1.38842	−0.694211	−	0.719771i	$-0.744247\pi$
$359$	−26.3068	−1.38842	−0.694211	+	0.719771i	$0.744247\pi$
$360$	2.09237	0.110277
$361$	−17.4348	−0.917619
$362$	−1.94954	−0.102465
$363$	9.97209	0.523399
$364$	1.37066	0.0718420
$365$	7.32920	0.383628
$366$	−2.15687	−0.112742
$367$	17.3431	0.905302	0.452651	−	0.891688i	$-0.350478\pi$
$367$	17.3431	0.905302	0.452651	+	0.891688i	$0.350478\pi$
$368$	5.57021	0.290367
$369$	−0.205499	−0.0106978
$370$	−7.11241	−0.369757
$371$	−7.54739	−0.391841
$372$	−4.64328	−0.240743
$373$	−3.03504	−0.157148	−0.0785741	−	0.996908i	$-0.525037\pi$
$373$	−3.03504	−0.157148	−0.0785741	+	0.996908i	$0.525037\pi$
$374$	−6.74322	−0.348684
$375$	11.7633	0.607454
$376$	−4.38570	−0.226175
$377$	5.78445	0.297914
$378$	−1.00000	−0.0514344
$379$	−16.9309	−0.869683	−0.434842	−	0.900507i	$-0.643196\pi$
$379$	−16.9309	−0.869683	−0.434842	+	0.900507i	$0.643196\pi$
$380$	−2.61775	−0.134288
$381$	−5.77668	−0.295948
$382$	1.00000	0.0511645
$383$	−11.3195	−0.578400	−0.289200	−	0.957269i	$-0.593389\pi$
$383$	−11.3195	−0.578400	−0.289200	+	0.957269i	$0.593389\pi$
$384$	−1.00000	−0.0510310
$385$	−2.12137	−0.108115
$386$	−0.714487	−0.0363664
$387$	0.130864	0.00665221
$388$	−17.7111	−0.899147
$389$	23.6008	1.19661	0.598304	−	0.801269i	$-0.295841\pi$
$389$	23.6008	1.19661	0.598304	+	0.801269i	$0.295841\pi$
$390$	−2.86792	−0.145223
$391$	37.0477	1.87358
$392$	1.00000	0.0505076
$393$	−21.4669	−1.08286
$394$	7.13296	0.359353
$395$	32.0121	1.61070
$396$	−1.01386	−0.0509484
$397$	−25.4949	−1.27955	−0.639777	−	0.768560i	$-0.720973\pi$
$397$	−25.4949	−1.27955	−0.639777	+	0.768560i	$0.720973\pi$
$398$	5.83078	0.292271
$399$	1.25110	0.0626332
$400$	−0.622002	−0.0311001
$401$	−12.7602	−0.637212	−0.318606	−	0.947887i	$-0.603215\pi$
$401$	−12.7602	−0.637212	−0.318606	+	0.947887i	$0.603215\pi$
$402$	−13.2482	−0.660758
$403$	6.36435	0.317031
$404$	−4.14216	−0.206080
$405$	2.09237	0.103971
$406$	4.22020	0.209445
$407$	3.44633	0.170828
$408$	−6.65104	−0.329275
$409$	−20.1163	−0.994687	−0.497344	−	0.867554i	$-0.665691\pi$
$409$	−20.1163	−0.994687	−0.497344	+	0.867554i	$0.665691\pi$
$410$	−0.429979	−0.0212351
$411$	−2.68387	−0.132386
$412$	12.6608	0.623755
$413$	−11.5884	−0.570229
$414$	5.57021	0.273761
$415$	10.3437	0.507750
$416$	1.37066	0.0672020
$417$	−5.43609	−0.266206
$418$	1.26844	0.0620413
$419$	12.4309	0.607291	0.303645	−	0.952785i	$-0.401796\pi$
$419$	12.4309	0.607291	0.303645	+	0.952785i	$0.401796\pi$
$420$	−2.09237	−0.102097
$421$	25.5848	1.24692	0.623462	−	0.781853i	$-0.285725\pi$
$421$	25.5848	1.24692	0.623462	+	0.781853i	$0.285725\pi$
$422$	−4.01806	−0.195596
$423$	−4.38570	−0.213240
$424$	−7.54739	−0.366534
$425$	−4.13696	−0.200672
$426$	−8.44044	−0.408941
$427$	2.15687	0.104378
$428$	−13.3993	−0.647678
$429$	1.38966	0.0670932
$430$	0.273816	0.0132046
$431$	−15.9096	−0.766337	−0.383169	−	0.923678i	$-0.625167\pi$
$431$	−15.9096	−0.766337	−0.383169	+	0.923678i	$0.625167\pi$
$432$	−1.00000	−0.0481125
$433$	33.5644	1.61300	0.806502	−	0.591231i	$-0.201358\pi$
$433$	33.5644	1.61300	0.806502	+	0.591231i	$0.201358\pi$
$434$	4.64328	0.222885
$435$	−8.83021	−0.423376
$436$	−8.81649	−0.422233
$437$	−6.96888	−0.333367
$438$	−3.50283	−0.167372
$439$	29.2009	1.39368	0.696841	−	0.717225i	$-0.254588\pi$
$439$	29.2009	1.39368	0.696841	+	0.717225i	$0.254588\pi$
$440$	−2.12137	−0.101132
$441$	1.00000	0.0476190
$442$	9.11630	0.433618
$443$	−36.7869	−1.74780	−0.873899	−	0.486108i	$-0.838416\pi$
$443$	−36.7869	−1.74780	−0.873899	+	0.486108i	$0.838416\pi$
$444$	3.39922	0.161320
$445$	−22.3239	−1.05825
$446$	9.57094	0.453197
$447$	4.92505	0.232947
$448$	1.00000	0.0472456
$449$	−8.20244	−0.387097	−0.193549	−	0.981091i	$-0.562000\pi$
$449$	−8.20244	−0.387097	−0.193549	+	0.981091i	$0.562000\pi$
$450$	−0.622002	−0.0293214
$451$	0.208347	0.00981068
$452$	−11.3916	−0.535817
$453$	−11.0780	−0.520491
$454$	−12.7530	−0.598527
$455$	2.86792	0.134450
$456$	1.25110	0.0585880
$457$	15.0490	0.703965	0.351982	−	0.936007i	$-0.385508\pi$
$457$	15.0490	0.703965	0.351982	+	0.936007i	$0.385508\pi$
$458$	−8.87496	−0.414700
$459$	−6.65104	−0.310444
$460$	11.6549	0.543414
$461$	28.6558	1.33463	0.667316	−	0.744775i	$-0.267443\pi$
$461$	28.6558	1.33463	0.667316	+	0.744775i	$0.267443\pi$
$462$	1.01386	0.0471691
$463$	−23.2119	−1.07875	−0.539375	−	0.842066i	$-0.681340\pi$
$463$	−23.2119	−1.07875	−0.539375	+	0.842066i	$0.681340\pi$
$464$	4.22020	0.195918
$465$	−9.71545	−0.450543
$466$	5.11633	0.237010
$467$	23.0247	1.06546	0.532729	−	0.846286i	$-0.321167\pi$
$467$	23.0247	1.06546	0.532729	+	0.846286i	$0.321167\pi$
$468$	1.37066	0.0633587
$469$	13.2482	0.611743
$470$	−9.17648	−0.423280
$471$	−2.56736	−0.118298
$472$	−11.5884	−0.533400
$473$	−0.132678	−0.00610055
$474$	−15.2995	−0.702728
$475$	0.778185	0.0357056
$476$	6.65104	0.304850
$477$	−7.54739	−0.345571
$478$	−1.56284	−0.0714825
$479$	31.1263	1.42220	0.711098	−	0.703093i	$-0.248198\pi$
$479$	31.1263	1.42220	0.711098	+	0.703093i	$0.248198\pi$
$480$	−2.09237	−0.0955030
$481$	−4.65917	−0.212440
$482$	1.02297	0.0465951
$483$	−5.57021	−0.253453
$484$	−9.97209	−0.453277
$485$	−37.0582	−1.68273
$486$	−1.00000	−0.0453609
$487$	35.1907	1.59464	0.797320	−	0.603556i	$-0.206250\pi$
$487$	35.1907	1.59464	0.797320	+	0.603556i	$0.206250\pi$
$488$	2.15687	0.0976371
$489$	−3.70507	−0.167549
$490$	2.09237	0.0945235
$491$	−5.15757	−0.232758	−0.116379	−	0.993205i	$-0.537129\pi$
$491$	−5.15757	−0.232758	−0.116379	+	0.993205i	$0.537129\pi$
$492$	0.205499	0.00926461
$493$	28.0687	1.26415
$494$	−1.71483	−0.0771537
$495$	−2.12137	−0.0953484
$496$	4.64328	0.208490
$497$	8.44044	0.378606
$498$	−4.94352	−0.221524
$499$	30.5944	1.36959	0.684796	−	0.728735i	$-0.259891\pi$
$499$	30.5944	1.36959	0.684796	+	0.728735i	$0.259891\pi$
$500$	−11.7633	−0.526070
$501$	−13.6222	−0.608595
$502$	−22.5682	−1.00727
$503$	−2.84866	−0.127015	−0.0635077	−	0.997981i	$-0.520229\pi$
$503$	−2.84866	−0.127015	−0.0635077	+	0.997981i	$0.520229\pi$
$504$	1.00000	0.0445435
$505$	−8.66691	−0.385672
$506$	−5.64742	−0.251058
$507$	11.1213	0.493914
$508$	5.77668	0.256299
$509$	17.7544	0.786952	0.393476	−	0.919335i	$-0.371272\pi$
$509$	17.7544	0.786952	0.393476	+	0.919335i	$0.371272\pi$
$510$	−13.9164	−0.616229
$511$	3.50283	0.154956
$512$	1.00000	0.0441942
$513$	1.25110	0.0552373
$514$	15.6237	0.689131
$515$	26.4911	1.16734
$516$	−0.130864	−0.00576098
$517$	4.44648	0.195556
$518$	−3.39922	−0.149353
$519$	−13.6219	−0.597937
$520$	2.86792	0.125767
$521$	36.0232	1.57821	0.789103	−	0.614261i	$-0.210546\pi$
$521$	36.0232	1.57821	0.789103	+	0.614261i	$0.210546\pi$
$522$	4.22020	0.184713
$523$	12.2086	0.533843	0.266922	−	0.963718i	$-0.413994\pi$
$523$	12.2086	0.533843	0.266922	+	0.963718i	$0.413994\pi$
$524$	21.4669	0.937785
$525$	0.622002	0.0271464
$526$	−4.05617	−0.176858
$527$	30.8827	1.34527
$528$	1.01386	0.0441226
$529$	8.02726	0.349011
$530$	−15.7919	−0.685957
$531$	−11.5884	−0.502895
$532$	−1.25110	−0.0542419
$533$	−0.281669	−0.0122004
$534$	10.6692	0.461701
$535$	−28.0362	−1.21211
$536$	13.2482	0.572233
$537$	−15.1494	−0.653743
$538$	32.2718	1.39134
$539$	−1.01386	−0.0436701
$540$	−2.09237	−0.0900411
$541$	−19.9836	−0.859164	−0.429582	−	0.903028i	$-0.641339\pi$
$541$	−19.9836	−0.859164	−0.429582	+	0.903028i	$0.641339\pi$
$542$	−10.8398	−0.465609
$543$	1.94954	0.0836627
$544$	6.65104	0.285161
$545$	−18.4473	−0.790197
$546$	−1.37066	−0.0586587
$547$	−23.6507	−1.01123	−0.505616	−	0.862759i	$-0.668735\pi$
$547$	−23.6507	−1.01123	−0.505616	+	0.862759i	$0.668735\pi$
$548$	2.68387	0.114649
$549$	2.15687	0.0920531
$550$	0.630623	0.0268899
$551$	−5.27988	−0.224931
$552$	−5.57021	−0.237084
$553$	15.2995	0.650600
$554$	−24.4487	−1.03873
$555$	7.11241	0.301905
$556$	5.43609	0.230541
$557$	−32.2226	−1.36531	−0.682657	−	0.730739i	$-0.739176\pi$
$557$	−32.2226	−1.36531	−0.682657	+	0.730739i	$0.739176\pi$
$558$	4.64328	0.196566
$559$	0.179370	0.00758655
$560$	2.09237	0.0884186
$561$	6.74322	0.284699
$562$	4.87438	0.205613
$563$	13.8310	0.582908	0.291454	−	0.956585i	$-0.405861\pi$
$563$	13.8310	0.582908	0.291454	+	0.956585i	$0.405861\pi$
$564$	4.38570	0.184671
$565$	−23.8355	−1.00277
$566$	15.9856	0.671926
$567$	1.00000	0.0419961
$568$	8.44044	0.354153
$569$	32.4219	1.35920	0.679599	−	0.733584i	$-0.262154\pi$
$569$	32.4219	1.35920	0.679599	+	0.733584i	$0.262154\pi$
$570$	2.61775	0.109646
$571$	−31.6534	−1.32465	−0.662326	−	0.749216i	$-0.730431\pi$
$571$	−31.6534	−1.32465	−0.662326	+	0.749216i	$0.730431\pi$
$572$	−1.38966	−0.0581044
$573$	−1.00000	−0.0417756
$574$	−0.205499	−0.00857736
$575$	−3.46468	−0.144487
$576$	1.00000	0.0416667
$577$	4.75337	0.197886	0.0989428	−	0.995093i	$-0.468454\pi$
$577$	4.75337	0.197886	0.0989428	+	0.995093i	$0.468454\pi$
$578$	27.2363	1.13288
$579$	0.714487	0.0296931
$580$	8.83021	0.366654
$581$	4.94352	0.205092
$582$	17.7111	0.734150
$583$	7.65200	0.316913
$584$	3.50283	0.144948
$585$	2.86792	0.118574
$586$	−22.5721	−0.932443
$587$	−6.94931	−0.286829	−0.143414	−	0.989663i	$-0.545808\pi$
$587$	−6.94931	−0.286829	−0.143414	+	0.989663i	$0.545808\pi$
$588$	−1.00000	−0.0412393
$589$	−5.80920	−0.239364
$590$	−24.2472	−0.998243
$591$	−7.13296	−0.293411
$592$	−3.39922	−0.139707
$593$	−20.4554	−0.840003	−0.420002	−	0.907523i	$-0.637970\pi$
$593$	−20.4554	−0.840003	−0.420002	+	0.907523i	$0.637970\pi$
$594$	1.01386	0.0415992
$595$	13.9164	0.570517
$596$	−4.92505	−0.201738
$597$	−5.83078	−0.238638
$598$	7.63485	0.312212
$599$	−3.29749	−0.134732	−0.0673660	−	0.997728i	$-0.521460\pi$
$599$	−3.29749	−0.134732	−0.0673660	+	0.997728i	$0.521460\pi$
$600$	0.622002	0.0253931
$601$	−3.78489	−0.154389	−0.0771945	−	0.997016i	$-0.524596\pi$
$601$	−3.78489	−0.154389	−0.0771945	+	0.997016i	$0.524596\pi$
$602$	0.130864	0.00533363
$603$	13.2482	0.539507
$604$	11.0780	0.450759
$605$	−20.8653	−0.848294
$606$	4.14216	0.168264
$607$	12.8879	0.523103	0.261552	−	0.965189i	$-0.415766\pi$
$607$	12.8879	0.523103	0.261552	+	0.965189i	$0.415766\pi$
$608$	−1.25110	−0.0507387
$609$	−4.22020	−0.171011
$610$	4.51297	0.182725
$611$	−6.01129	−0.243191
$612$	6.65104	0.268852
$613$	−14.3803	−0.580813	−0.290407	−	0.956903i	$-0.593791\pi$
$613$	−14.3803	−0.580813	−0.290407	+	0.956903i	$0.593791\pi$
$614$	−25.5310	−1.03035
$615$	0.429979	0.0173384
$616$	−1.01386	−0.0408496
$617$	−8.65563	−0.348462	−0.174231	−	0.984705i	$-0.555744\pi$
$617$	−8.65563	−0.348462	−0.174231	+	0.984705i	$0.555744\pi$
$618$	−12.6608	−0.509294
$619$	42.7458	1.71810	0.859050	−	0.511892i	$-0.171055\pi$
$619$	42.7458	1.71810	0.859050	+	0.511892i	$0.171055\pi$
$620$	9.71545	0.390182
$621$	−5.57021	−0.223525
$622$	25.1719	1.00930
$623$	−10.6692	−0.427452
$624$	−1.37066	−0.0548702
$625$	−21.5031	−0.860124
$626$	4.47109	0.178701
$627$	−1.26844	−0.0506565
$628$	2.56736	0.102449
$629$	−22.6083	−0.901454
$630$	2.09237	0.0833619
$631$	25.6940	1.02286	0.511431	−	0.859324i	$-0.329116\pi$
$631$	25.6940	1.02286	0.511431	+	0.859324i	$0.329116\pi$
$632$	15.2995	0.608580
$633$	4.01806	0.159704
$634$	−1.93715	−0.0769340
$635$	12.0869	0.479655
$636$	7.54739	0.299274
$637$	1.37066	0.0543074
$638$	−4.27869	−0.169395
$639$	8.44044	0.333899
$640$	2.09237	0.0827081
$641$	17.7078	0.699415	0.349708	−	0.936859i	$-0.386281\pi$
$641$	17.7078	0.699415	0.349708	+	0.936859i	$0.386281\pi$
$642$	13.3993	0.528827
$643$	3.38925	0.133659	0.0668294	−	0.997764i	$-0.478712\pi$
$643$	3.38925	0.133659	0.0668294	+	0.997764i	$0.478712\pi$
$644$	5.57021	0.219497
$645$	−0.273816	−0.0107815
$646$	−8.32110	−0.327389
$647$	−5.39032	−0.211915	−0.105958	−	0.994371i	$-0.533791\pi$
$647$	−5.39032	−0.211915	−0.105958	+	0.994371i	$0.533791\pi$
$648$	1.00000	0.0392837
$649$	11.7490	0.461190
$650$	−0.852551	−0.0334398
$651$	−4.64328	−0.181985
$652$	3.70507	0.145102
$653$	27.7379	1.08547	0.542733	−	0.839905i	$-0.317389\pi$
$653$	27.7379	1.08547	0.542733	+	0.839905i	$0.317389\pi$
$654$	8.81649	0.344752
$655$	44.9166	1.75504
$656$	−0.205499	−0.00802338
$657$	3.50283	0.136658
$658$	−4.38570	−0.170972
$659$	15.9850	0.622689	0.311344	−	0.950297i	$-0.399221\pi$
$659$	15.9850	0.622689	0.311344	+	0.950297i	$0.399221\pi$
$660$	2.12137	0.0825741
$661$	2.25191	0.0875892	0.0437946	−	0.999041i	$-0.486055\pi$
$661$	2.25191	0.0875892	0.0437946	+	0.999041i	$0.486055\pi$
$662$	−30.6202	−1.19009
$663$	−9.11630	−0.354048
$664$	4.94352	0.191846
$665$	−2.61775	−0.101512
$666$	−3.39922	−0.131717
$667$	23.5074	0.910211
$668$	13.6222	0.527059
$669$	−9.57094	−0.370034
$670$	27.7200	1.07092
$671$	−2.18677	−0.0844193
$672$	−1.00000	−0.0385758
$673$	−32.2630	−1.24365	−0.621823	−	0.783158i	$-0.713608\pi$
$673$	−32.2630	−1.24365	−0.621823	+	0.783158i	$0.713608\pi$
$674$	7.88240	0.303619
$675$	0.622002	0.0239409
$676$	−11.1213	−0.427742
$677$	−28.9510	−1.11268	−0.556339	−	0.830955i	$-0.687795\pi$
$677$	−28.9510	−1.11268	−0.556339	+	0.830955i	$0.687795\pi$
$678$	11.3916	0.437493
$679$	−17.7111	−0.679691
$680$	13.9164	0.533670
$681$	12.7530	0.488695
$682$	−4.70764	−0.180265
$683$	8.05179	0.308093	0.154047	−	0.988064i	$-0.450769\pi$
$683$	8.05179	0.308093	0.154047	+	0.988064i	$0.450769\pi$
$684$	−1.25110	−0.0478369
$685$	5.61564	0.214563
$686$	1.00000	0.0381802
$687$	8.87496	0.338601
$688$	0.130864	0.00498916
$689$	−10.3449	−0.394109
$690$	−11.6549	−0.443695
$691$	−48.9621	−1.86261	−0.931303	−	0.364245i	$-0.881327\pi$
$691$	−48.9621	−1.86261	−0.931303	+	0.364245i	$0.881327\pi$
$692$	13.6219	0.517829
$693$	−1.01386	−0.0385134
$694$	−9.03193	−0.342847
$695$	11.3743	0.431451
$696$	−4.22020	−0.159966
$697$	−1.36678	−0.0517705
$698$	0.785811	0.0297434
$699$	−5.11633	−0.193518
$700$	−0.622002	−0.0235095
$701$	−18.5323	−0.699954	−0.349977	−	0.936758i	$-0.613811\pi$
$701$	−18.5323	−0.699954	−0.349977	+	0.936758i	$0.613811\pi$
$702$	−1.37066	−0.0517321
$703$	4.25275	0.160396
$704$	−1.01386	−0.0382113
$705$	9.17648	0.345606
$706$	16.0710	0.604840
$707$	−4.14216	−0.155782
$708$	11.5884	0.435520
$709$	−3.68481	−0.138386	−0.0691930	−	0.997603i	$-0.522042\pi$
$709$	−3.68481	−0.138386	−0.0691930	+	0.997603i	$0.522042\pi$
$710$	17.6605	0.662787
$711$	15.2995	0.573775
$712$	−10.6692	−0.399845
$713$	25.8641	0.968617
$714$	−6.65104	−0.248909
$715$	−2.90767	−0.108741
$716$	15.1494	0.566158
$717$	1.56284	0.0583653
$718$	−26.3068	−0.981763
$719$	−18.9799	−0.707830	−0.353915	−	0.935278i	$-0.615150\pi$
$719$	−18.9799	−0.707830	−0.353915	+	0.935278i	$0.615150\pi$
$720$	2.09237	0.0779779
$721$	12.6608	0.471514
$722$	−17.4348	−0.648854
$723$	−1.02297	−0.0380447
$724$	−1.94954	−0.0724540
$725$	−2.62497	−0.0974890
$726$	9.97209	0.370099
$727$	7.83142	0.290451	0.145226	−	0.989399i	$-0.453609\pi$
$727$	7.83142	0.290451	0.145226	+	0.989399i	$0.453609\pi$
$728$	1.37066	0.0507999
$729$	1.00000	0.0370370
$730$	7.32920	0.271266
$731$	0.870384	0.0321923
$732$	−2.15687	−0.0797204
$733$	−31.5857	−1.16664	−0.583322	−	0.812241i	$-0.698248\pi$
$733$	−31.5857	−1.16664	−0.583322	+	0.812241i	$0.698248\pi$
$734$	17.3431	0.640145
$735$	−2.09237	−0.0771781
$736$	5.57021	0.205321
$737$	−13.4318	−0.494766
$738$	−0.205499	−0.00756452
$739$	−17.6192	−0.648134	−0.324067	−	0.946034i	$-0.605050\pi$
$739$	−17.6192	−0.648134	−0.324067	+	0.946034i	$0.605050\pi$
$740$	−7.11241	−0.261458
$741$	1.71483	0.0629957
$742$	−7.54739	−0.277073
$743$	8.75847	0.321317	0.160659	−	0.987010i	$-0.448638\pi$
$743$	8.75847	0.321317	0.160659	+	0.987010i	$0.448638\pi$
$744$	−4.64328	−0.170231
$745$	−10.3050	−0.377546
$746$	−3.03504	−0.111121
$747$	4.94352	0.180874
$748$	−6.74322	−0.246557
$749$	−13.3993	−0.489599
$750$	11.7633	0.429535
$751$	−7.56512	−0.276055	−0.138028	−	0.990428i	$-0.544076\pi$
$751$	−7.56512	−0.276055	−0.138028	+	0.990428i	$0.544076\pi$
$752$	−4.38570	−0.159930
$753$	22.5682	0.822431
$754$	5.78445	0.210657
$755$	23.1793	0.843581
$756$	−1.00000	−0.0363696
$757$	36.6144	1.33077	0.665386	−	0.746499i	$-0.268267\pi$
$757$	36.6144	1.33077	0.665386	+	0.746499i	$0.268267\pi$
$758$	−16.9309	−0.614959
$759$	5.64742	0.204988
$760$	−2.61775	−0.0949559
$761$	−39.5878	−1.43506	−0.717529	−	0.696528i	$-0.754727\pi$
$761$	−39.5878	−1.43506	−0.717529	+	0.696528i	$0.754727\pi$
$762$	−5.77668	−0.209267
$763$	−8.81649	−0.319178
$764$	1.00000	0.0361787
$765$	13.9164	0.503149
$766$	−11.3195	−0.408990
$767$	−15.8838	−0.573529
$768$	−1.00000	−0.0360844
$769$	−7.67645	−0.276820	−0.138410	−	0.990375i	$-0.544199\pi$
$769$	−7.67645	−0.276820	−0.138410	+	0.990375i	$0.544199\pi$
$770$	−2.12137	−0.0764488
$771$	−15.6237	−0.562673
$772$	−0.714487	−0.0257149
$773$	35.2158	1.26662	0.633312	−	0.773896i	$-0.281695\pi$
$773$	35.2158	1.26662	0.633312	+	0.773896i	$0.281695\pi$
$774$	0.130864	0.00470382
$775$	−2.88813	−0.103745
$776$	−17.7111	−0.635793
$777$	3.39922	0.121946
$778$	23.6008	0.846130
$779$	0.257099	0.00921153
$780$	−2.86792	−0.102688
$781$	−8.55743	−0.306209
$782$	37.0477	1.32482
$783$	−4.22020	−0.150818
$784$	1.00000	0.0357143
$785$	5.37187	0.191730
$786$	−21.4669	−0.765698
$787$	−40.3297	−1.43760	−0.718799	−	0.695218i	$-0.755308\pi$
$787$	−40.3297	−1.43760	−0.718799	+	0.695218i	$0.755308\pi$
$788$	7.13296	0.254101
$789$	4.05617	0.144404
$790$	32.0121	1.13894
$791$	−11.3916	−0.405040
$792$	−1.01386	−0.0360260
$793$	2.95634	0.104983
$794$	−25.4949	−0.904782
$795$	15.7919	0.560081
$796$	5.83078	0.206667
$797$	32.5574	1.15324	0.576621	−	0.817012i	$-0.304371\pi$
$797$	32.5574	1.15324	0.576621	+	0.817012i	$0.304371\pi$
$798$	1.25110	0.0442884
$799$	−29.1694	−1.03194
$800$	−0.622002	−0.0219911
$801$	−10.6692	−0.376978
$802$	−12.7602	−0.450577
$803$	−3.55138	−0.125325
$804$	−13.2482	−0.467226
$805$	11.6549	0.410782
$806$	6.36435	0.224175
$807$	−32.2718	−1.13602
$808$	−4.14216	−0.145721
$809$	−14.1827	−0.498637	−0.249319	−	0.968421i	$-0.580207\pi$
$809$	−14.1827	−0.498637	−0.249319	+	0.968421i	$0.580207\pi$
$810$	2.09237	0.0735183
$811$	29.3370	1.03016	0.515081	−	0.857142i	$-0.327762\pi$
$811$	29.3370	1.03016	0.515081	+	0.857142i	$0.327762\pi$
$812$	4.22020	0.148100
$813$	10.8398	0.380168
$814$	3.44633	0.120794
$815$	7.75236	0.271553
$816$	−6.65104	−0.232833
$817$	−0.163724	−0.00572798
$818$	−20.1163	−0.703350
$819$	1.37066	0.0478946
$820$	−0.429979	−0.0150155
$821$	53.6346	1.87186	0.935931	−	0.352183i	$-0.114561\pi$
$821$	53.6346	1.87186	0.935931	+	0.352183i	$0.114561\pi$
$822$	−2.68387	−0.0936108
$823$	−11.4748	−0.399986	−0.199993	−	0.979797i	$-0.564092\pi$
$823$	−11.4748	−0.399986	−0.199993	+	0.979797i	$0.564092\pi$
$824$	12.6608	0.441061
$825$	−0.630623	−0.0219555
$826$	−11.5884	−0.403213
$827$	31.6260	1.09974	0.549872	−	0.835249i	$-0.314676\pi$
$827$	31.6260	1.09974	0.549872	+	0.835249i	$0.314676\pi$
$828$	5.57021	0.193578
$829$	26.1378	0.907804	0.453902	−	0.891052i	$-0.350032\pi$
$829$	26.1378	0.907804	0.453902	+	0.891052i	$0.350032\pi$
$830$	10.3437	0.359033
$831$	24.4487	0.848116
$832$	1.37066	0.0475190
$833$	6.65104	0.230445
$834$	−5.43609	−0.188236
$835$	28.5026	0.986374
$836$	1.26844	0.0438698
$837$	−4.64328	−0.160495
$838$	12.4309	0.429420
$839$	32.7644	1.13115	0.565577	−	0.824695i	$-0.308653\pi$
$839$	32.7644	1.13115	0.565577	+	0.824695i	$0.308653\pi$
$840$	−2.09237	−0.0721935
$841$	−11.1899	−0.385859
$842$	25.5848	0.881709
$843$	−4.87438	−0.167882
$844$	−4.01806	−0.138307
$845$	−23.2698	−0.800507
$846$	−4.38570	−0.150783
$847$	−9.97209	−0.342645
$848$	−7.54739	−0.259178
$849$	−15.9856	−0.548626
$850$	−4.13696	−0.141896
$851$	−18.9344	−0.649062
$852$	−8.44044	−0.289165
$853$	−36.1040	−1.23618	−0.618089	−	0.786108i	$-0.712093\pi$
$853$	−36.1040	−1.23618	−0.618089	+	0.786108i	$0.712093\pi$
$854$	2.15687	0.0738067
$855$	−2.61775	−0.0895253
$856$	−13.3993	−0.457978
$857$	−40.5582	−1.38544	−0.692722	−	0.721205i	$-0.743589\pi$
$857$	−40.5582	−1.38544	−0.692722	+	0.721205i	$0.743589\pi$
$858$	1.38966	0.0474420
$859$	−8.27642	−0.282388	−0.141194	−	0.989982i	$-0.545094\pi$
$859$	−8.27642	−0.282388	−0.141194	+	0.989982i	$0.545094\pi$
$860$	0.273816	0.00933706
$861$	0.205499	0.00700338
$862$	−15.9096	−0.541882
$863$	34.8794	1.18731	0.593655	−	0.804720i	$-0.297684\pi$
$863$	34.8794	1.18731	0.593655	+	0.804720i	$0.297684\pi$
$864$	−1.00000	−0.0340207
$865$	28.5021	0.969101
$866$	33.5644	1.14057
$867$	−27.2363	−0.924994
$868$	4.64328	0.157603
$869$	−15.5115	−0.526192
$870$	−8.83021	−0.299372
$871$	18.1587	0.615284
$872$	−8.81649	−0.298564
$873$	−17.7111	−0.599431
$874$	−6.96888	−0.235726
$875$	−11.7633	−0.397672
$876$	−3.50283	−0.118350
$877$	−6.82145	−0.230344	−0.115172	−	0.993346i	$-0.536742\pi$
$877$	−6.82145	−0.230344	−0.115172	+	0.993346i	$0.536742\pi$
$878$	29.2009	0.985482
$879$	22.5721	0.761337
$880$	−2.12137	−0.0715113
$881$	−2.43880	−0.0821652	−0.0410826	−	0.999156i	$-0.513081\pi$
$881$	−2.43880	−0.0821652	−0.0410826	+	0.999156i	$0.513081\pi$
$882$	1.00000	0.0336718
$883$	−23.7792	−0.800235	−0.400118	−	0.916464i	$-0.631031\pi$
$883$	−23.7792	−0.800235	−0.400118	+	0.916464i	$0.631031\pi$
$884$	9.11630	0.306614
$885$	24.2472	0.815062
$886$	−36.7869	−1.23588
$887$	−34.8452	−1.16999	−0.584994	−	0.811037i	$-0.698903\pi$
$887$	−34.8452	−1.16999	−0.584994	+	0.811037i	$0.698903\pi$
$888$	3.39922	0.114070
$889$	5.77668	0.193744
$890$	−22.3239	−0.748298
$891$	−1.01386	−0.0339656
$892$	9.57094	0.320459
$893$	5.48693	0.183613
$894$	4.92505	0.164718
$895$	31.6980	1.05955
$896$	1.00000	0.0334077
$897$	−7.63485	−0.254920
$898$	−8.20244	−0.273719
$899$	19.5956	0.653549
$900$	−0.622002	−0.0207334
$901$	−50.1980	−1.67234
$902$	0.208347	0.00693720
$903$	−0.130864	−0.00435489
$904$	−11.3916	−0.378880
$905$	−4.07915	−0.135596
$906$	−11.0780	−0.368043
$907$	30.6310	1.01709	0.508543	−	0.861036i	$-0.330184\pi$
$907$	30.6310	1.01709	0.508543	+	0.861036i	$0.330184\pi$
$908$	−12.7530	−0.423223
$909$	−4.14216	−0.137387
$910$	2.86792	0.0950706
$911$	−4.06153	−0.134564	−0.0672822	−	0.997734i	$-0.521433\pi$
$911$	−4.06153	−0.134564	−0.0672822	+	0.997734i	$0.521433\pi$
$912$	1.25110	0.0414280
$913$	−5.01204	−0.165874
$914$	15.0490	0.497778
$915$	−4.51297	−0.149194
$916$	−8.87496	−0.293237
$917$	21.4669	0.708899
$918$	−6.65104	−0.219517
$919$	−49.6704	−1.63848	−0.819238	−	0.573454i	$-0.805603\pi$
$919$	−49.6704	−1.63848	−0.819238	+	0.573454i	$0.805603\pi$
$920$	11.6549	0.384251
$921$	25.5310	0.841275
$922$	28.6558	0.943727
$923$	11.5690	0.380797
$924$	1.01386	0.0333536
$925$	2.11432	0.0695184
$926$	−23.2119	−0.762792
$927$	12.6608	0.415837
$928$	4.22020	0.138535
$929$	9.35347	0.306878	0.153439	−	0.988158i	$-0.450965\pi$
$929$	9.35347	0.306878	0.153439	+	0.988158i	$0.450965\pi$
$930$	−9.71545	−0.318582
$931$	−1.25110	−0.0410031
$932$	5.11633	0.167591
$933$	−25.1719	−0.824090
$934$	23.0247	0.753392
$935$	−14.1093	−0.461423
$936$	1.37066	0.0448013
$937$	−35.2193	−1.15057	−0.575283	−	0.817954i	$-0.695108\pi$
$937$	−35.2193	−1.15057	−0.575283	+	0.817954i	$0.695108\pi$
$938$	13.2482	0.432568
$939$	−4.47109	−0.145909
$940$	−9.17648	−0.299304
$941$	38.9751	1.27055	0.635276	−	0.772285i	$-0.280886\pi$
$941$	38.9751	1.27055	0.635276	+	0.772285i	$0.280886\pi$
$942$	−2.56736	−0.0836492
$943$	−1.14467	−0.0372757
$944$	−11.5884	−0.377171
$945$	−2.09237	−0.0680647
$946$	−0.132678	−0.00431374
$947$	−44.5093	−1.44636	−0.723179	−	0.690661i	$-0.757320\pi$
$947$	−44.5093	−1.44636	−0.723179	+	0.690661i	$0.757320\pi$
$948$	−15.2995	−0.496904
$949$	4.80118	0.155853
$950$	0.778185	0.0252476
$951$	1.93715	0.0628163
$952$	6.65104	0.215561
$953$	4.66685	0.151174	0.0755871	−	0.997139i	$-0.475917\pi$
$953$	4.66685	0.151174	0.0755871	+	0.997139i	$0.475917\pi$
$954$	−7.54739	−0.244356
$955$	2.09237	0.0677074
$956$	−1.56284	−0.0505458
$957$	4.27869	0.138311
$958$	31.1263	1.00564
$959$	2.68387	0.0866667
$960$	−2.09237	−0.0675308
$961$	−9.43993	−0.304514
$962$	−4.65917	−0.150218
$963$	−13.3993	−0.431785
$964$	1.02297	0.0329477
$965$	−1.49497	−0.0481247
$966$	−5.57021	−0.179219
$967$	−6.80403	−0.218803	−0.109401	−	0.993998i	$-0.534893\pi$
$967$	−6.80403	−0.218803	−0.109401	+	0.993998i	$0.534893\pi$
$968$	−9.97209	−0.320515
$969$	8.32110	0.267312
$970$	−37.0582	−1.18987
$971$	−48.5344	−1.55754	−0.778772	−	0.627307i	$-0.784157\pi$
$971$	−48.5344	−1.55754	−0.778772	+	0.627307i	$0.784157\pi$
$972$	−1.00000	−0.0320750
$973$	5.43609	0.174273
$974$	35.1907	1.12758
$975$	0.852551	0.0273035
$976$	2.15687	0.0690399
$977$	14.5723	0.466210	0.233105	−	0.972452i	$-0.425111\pi$
$977$	14.5723	0.466210	0.233105	+	0.972452i	$0.425111\pi$
$978$	−3.70507	−0.118475
$979$	10.8171	0.345715
$980$	2.09237	0.0668382
$981$	−8.81649	−0.281489
$982$	−5.15757	−0.164585
$983$	−0.834948	−0.0266307	−0.0133153	−	0.999911i	$-0.504239\pi$
$983$	−0.834948	−0.0266307	−0.0133153	+	0.999911i	$0.504239\pi$
$984$	0.205499	0.00655107
$985$	14.9248	0.475543
$986$	28.0687	0.893890
$987$	4.38570	0.139598
$988$	−1.71483	−0.0545559
$989$	0.728942	0.0231790
$990$	−2.12137	−0.0674215
$991$	−54.0721	−1.71766	−0.858829	−	0.512263i	$-0.828807\pi$
$991$	−54.0721	−1.71766	−0.858829	+	0.512263i	$0.828807\pi$
$992$	4.64328	0.147424
$993$	30.6202	0.971702
$994$	8.44044	0.267715
$995$	12.2001	0.386770
$996$	−4.94352	−0.156641
$997$	20.6603	0.654320	0.327160	−	0.944969i	$-0.393908\pi$
$997$	20.6603	0.654320	0.327160	+	0.944969i	$0.393908\pi$
$998$	30.5944	0.968448
$999$	3.39922	0.107547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.r.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.r.1.7	✓	10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.09237 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.09237 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.09237 q^{10} -1.01386 q^{11} -1.00000 q^{12} +1.37066 q^{13} +1.00000 q^{14} -2.09237 q^{15} +1.00000 q^{16} +6.65104 q^{17} +1.00000 q^{18} -1.25110 q^{19} +2.09237 q^{20} -1.00000 q^{21} -1.01386 q^{22} +5.57021 q^{23} -1.00000 q^{24} -0.622002 q^{25} +1.37066 q^{26} -1.00000 q^{27} +1.00000 q^{28} +4.22020 q^{29} -2.09237 q^{30} +4.64328 q^{31} +1.00000 q^{32} +1.01386 q^{33} +6.65104 q^{34} +2.09237 q^{35} +1.00000 q^{36} -3.39922 q^{37} -1.25110 q^{38} -1.37066 q^{39} +2.09237 q^{40} -0.205499 q^{41} -1.00000 q^{42} +0.130864 q^{43} -1.01386 q^{44} +2.09237 q^{45} +5.57021 q^{46} -4.38570 q^{47} -1.00000 q^{48} +1.00000 q^{49} -0.622002 q^{50} -6.65104 q^{51} +1.37066 q^{52} -7.54739 q^{53} -1.00000 q^{54} -2.12137 q^{55} +1.00000 q^{56} +1.25110 q^{57} +4.22020 q^{58} -11.5884 q^{59} -2.09237 q^{60} +2.15687 q^{61} +4.64328 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.86792 q^{65} +1.01386 q^{66} +13.2482 q^{67} +6.65104 q^{68} -5.57021 q^{69} +2.09237 q^{70} +8.44044 q^{71} +1.00000 q^{72} +3.50283 q^{73} -3.39922 q^{74} +0.622002 q^{75} -1.25110 q^{76} -1.01386 q^{77} -1.37066 q^{78} +15.2995 q^{79} +2.09237 q^{80} +1.00000 q^{81} -0.205499 q^{82} +4.94352 q^{83} -1.00000 q^{84} +13.9164 q^{85} +0.130864 q^{86} -4.22020 q^{87} -1.01386 q^{88} -10.6692 q^{89} +2.09237 q^{90} +1.37066 q^{91} +5.57021 q^{92} -4.64328 q^{93} -4.38570 q^{94} -2.61775 q^{95} -1.00000 q^{96} -17.7111 q^{97} +1.00000 q^{98} -1.01386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

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