LMFDB - Embedded newform 211.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,2,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("211.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	211.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:	$1.68484348265$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 14x^{7} + 11x^{6} + 66x^{5} - 36x^{4} - 123x^{3} + 38x^{2} + 72x - 8 $ x^9 - x^8 - 14x^7 + 11x^6 + 66x^5 - 36x^4 - 123x^3 + 38x^2 + 72*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.959048$ of defining polynomial
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.959048 q^{2} -3.12841 q^{3} -1.08023 q^{4} +3.31637 q^{5} -3.00030 q^{6} +2.28069 q^{7} -2.95409 q^{8} +6.78696 q^{9} +O(q^{10})$	\(q+0.959048 q^{2} -3.12841 q^{3} -1.08023 q^{4} +3.31637 q^{5} -3.00030 q^{6} +2.28069 q^{7} -2.95409 q^{8} +6.78696 q^{9} +3.18056 q^{10} +3.85098 q^{11} +3.37939 q^{12} +2.87874 q^{13} +2.18729 q^{14} -10.3750 q^{15} -0.672659 q^{16} +1.55207 q^{17} +6.50902 q^{18} -3.65753 q^{19} -3.58243 q^{20} -7.13494 q^{21} +3.69327 q^{22} -7.70506 q^{23} +9.24160 q^{24} +5.99831 q^{25} +2.76086 q^{26} -11.8472 q^{27} -2.46366 q^{28} +4.37909 q^{29} -9.95010 q^{30} +8.26958 q^{31} +5.26306 q^{32} -12.0474 q^{33} +1.48851 q^{34} +7.56362 q^{35} -7.33145 q^{36} +0.631643 q^{37} -3.50775 q^{38} -9.00590 q^{39} -9.79684 q^{40} -10.0558 q^{41} -6.84276 q^{42} -1.77673 q^{43} -4.15993 q^{44} +22.5081 q^{45} -7.38952 q^{46} +3.57315 q^{47} +2.10436 q^{48} -1.79844 q^{49} +5.75267 q^{50} -4.85550 q^{51} -3.10970 q^{52} -6.47005 q^{53} -11.3620 q^{54} +12.7713 q^{55} -6.73736 q^{56} +11.4423 q^{57} +4.19976 q^{58} +9.85690 q^{59} +11.2073 q^{60} -1.41380 q^{61} +7.93093 q^{62} +15.4790 q^{63} +6.39285 q^{64} +9.54698 q^{65} -11.5541 q^{66} -11.0278 q^{67} -1.67658 q^{68} +24.1046 q^{69} +7.25388 q^{70} -13.7060 q^{71} -20.0493 q^{72} -4.83734 q^{73} +0.605776 q^{74} -18.7652 q^{75} +3.95096 q^{76} +8.78290 q^{77} -8.63709 q^{78} +5.87492 q^{79} -2.23079 q^{80} +16.7019 q^{81} -9.64404 q^{82} +10.5728 q^{83} +7.70735 q^{84} +5.14723 q^{85} -1.70397 q^{86} -13.6996 q^{87} -11.3761 q^{88} +0.990375 q^{89} +21.5863 q^{90} +6.56553 q^{91} +8.32320 q^{92} -25.8706 q^{93} +3.42683 q^{94} -12.1297 q^{95} -16.4650 q^{96} -11.2485 q^{97} -1.72479 q^{98} +26.1364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} + 13 q^{11} - 5 q^{12} - 4 q^{13} + 13 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} - 21 q^{18} - 2 q^{19} + 32 q^{20} + 9 q^{21} - 8 q^{22} - 3 q^{23} + 4 q^{24} + 14 q^{25} + 13 q^{26} - 4 q^{27} - 20 q^{28} + 26 q^{29} - 17 q^{30} + 5 q^{31} - 8 q^{32} - 10 q^{33} - 21 q^{34} - 21 q^{35} - 10 q^{36} + 5 q^{37} + 13 q^{38} - 40 q^{39} - 52 q^{40} + 20 q^{41} - 46 q^{42} - 37 q^{43} - 10 q^{44} + 36 q^{45} - 38 q^{46} + 4 q^{47} - 32 q^{48} + 11 q^{49} - 16 q^{50} - 42 q^{51} - 20 q^{52} + 13 q^{53} - 30 q^{54} + 6 q^{55} + 23 q^{56} + 4 q^{57} - 17 q^{58} + 14 q^{59} - 4 q^{60} + 23 q^{61} - 19 q^{62} + q^{63} + 14 q^{64} - 13 q^{65} + 31 q^{66} - 3 q^{67} + 53 q^{68} + 16 q^{69} + 9 q^{70} + 19 q^{71} - 21 q^{72} + 17 q^{73} + 7 q^{74} + 4 q^{75} - 34 q^{76} + 13 q^{77} + 44 q^{78} + 7 q^{79} + 27 q^{80} + 13 q^{81} - 14 q^{82} + 6 q^{83} + 48 q^{84} - 4 q^{85} - 24 q^{86} - 5 q^{87} - 38 q^{88} + 33 q^{89} - 44 q^{90} - 27 q^{91} + 37 q^{92} - 27 q^{93} - 10 q^{94} - 23 q^{95} + 43 q^{96} - 11 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 + 13 * q^11 - 5 * q^12 - 4 * q^13 + 13 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 - 21 * q^18 - 2 * q^19 + 32 * q^20 + 9 * q^21 - 8 * q^22 - 3 * q^23 + 4 * q^24 + 14 * q^25 + 13 * q^26 - 4 * q^27 - 20 * q^28 + 26 * q^29 - 17 * q^30 + 5 * q^31 - 8 * q^32 - 10 * q^33 - 21 * q^34 - 21 * q^35 - 10 * q^36 + 5 * q^37 + 13 * q^38 - 40 * q^39 - 52 * q^40 + 20 * q^41 - 46 * q^42 - 37 * q^43 - 10 * q^44 + 36 * q^45 - 38 * q^46 + 4 * q^47 - 32 * q^48 + 11 * q^49 - 16 * q^50 - 42 * q^51 - 20 * q^52 + 13 * q^53 - 30 * q^54 + 6 * q^55 + 23 * q^56 + 4 * q^57 - 17 * q^58 + 14 * q^59 - 4 * q^60 + 23 * q^61 - 19 * q^62 + q^63 + 14 * q^64 - 13 * q^65 + 31 * q^66 - 3 * q^67 + 53 * q^68 + 16 * q^69 + 9 * q^70 + 19 * q^71 - 21 * q^72 + 17 * q^73 + 7 * q^74 + 4 * q^75 - 34 * q^76 + 13 * q^77 + 44 * q^78 + 7 * q^79 + 27 * q^80 + 13 * q^81 - 14 * q^82 + 6 * q^83 + 48 * q^84 - 4 * q^85 - 24 * q^86 - 5 * q^87 - 38 * q^88 + 33 * q^89 - 44 * q^90 - 27 * q^91 + 37 * q^92 - 27 * q^93 - 10 * q^94 - 23 * q^95 + 43 * q^96 - 11 * q^97 + 26 * q^98 + 2 * 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 $

$2$	0.959048	0.678150	0.339075	−	0.940759i	$-0.389886\pi$
$2$	0.959048	0.678150	0.339075	+	0.940759i	$0.389886\pi$
$3$	−3.12841	−1.80619	−0.903095	−	0.429442i	$-0.858710\pi$
$3$	−3.12841	−1.80619	−0.903095	+	0.429442i	$0.858710\pi$
$4$	−1.08023	−0.540113
$5$	3.31637	1.48313	0.741563	−	0.670883i	$-0.234085\pi$
$5$	3.31637	1.48313	0.741563	+	0.670883i	$0.234085\pi$
$6$	−3.00030	−1.22487
$7$	2.28069	0.862021	0.431010	−	0.902347i	$-0.358157\pi$
$7$	2.28069	0.862021	0.431010	+	0.902347i	$0.358157\pi$
$8$	−2.95409	−1.04443
$9$	6.78696	2.26232
$10$	3.18056	1.00578
$11$	3.85098	1.16111	0.580557	−	0.814220i	$-0.302835\pi$
$11$	3.85098	1.16111	0.580557	+	0.814220i	$0.302835\pi$
$12$	3.37939	0.975546
$13$	2.87874	0.798420	0.399210	−	0.916859i	$-0.369284\pi$
$13$	2.87874	0.798420	0.399210	+	0.916859i	$0.369284\pi$
$14$	2.18729	0.584579
$15$	−10.3750	−2.67881
$16$	−0.672659	−0.168165
$17$	1.55207	0.376431	0.188216	−	0.982128i	$-0.439730\pi$
$17$	1.55207	0.376431	0.188216	+	0.982128i	$0.439730\pi$
$18$	6.50902	1.53419
$19$	−3.65753	−0.839095	−0.419548	−	0.907733i	$-0.637811\pi$
$19$	−3.65753	−0.839095	−0.419548	+	0.907733i	$0.637811\pi$
$20$	−3.58243	−0.801056
$21$	−7.13494	−1.55697
$22$	3.69327	0.787409
$23$	−7.70506	−1.60662	−0.803308	−	0.595564i	$-0.796928\pi$
$23$	−7.70506	−1.60662	−0.803308	+	0.595564i	$0.796928\pi$
$24$	9.24160	1.88643
$25$	5.99831	1.19966
$26$	2.76086	0.541448
$27$	−11.8472	−2.27999
$28$	−2.46366	−0.465589
$29$	4.37909	0.813177	0.406589	−	0.913611i	$-0.366718\pi$
$29$	4.37909	0.813177	0.406589	+	0.913611i	$0.366718\pi$
$30$	−9.95010	−1.81663
$31$	8.26958	1.48526	0.742630	−	0.669702i	$-0.233578\pi$
$31$	8.26958	1.48526	0.742630	+	0.669702i	$0.233578\pi$
$32$	5.26306	0.930386
$33$	−12.0474	−2.09719
$34$	1.48851	0.255277
$35$	7.56362	1.27849
$36$	−7.33145	−1.22191
$37$	0.631643	0.103841	0.0519207	−	0.998651i	$-0.483466\pi$
$37$	0.631643	0.103841	0.0519207	+	0.998651i	$0.483466\pi$
$38$	−3.50775	−0.569032
$39$	−9.00590	−1.44210
$40$	−9.79684	−1.54902
$41$	−10.0558	−1.57046	−0.785229	−	0.619205i	$-0.787455\pi$
$41$	−10.0558	−1.57046	−0.785229	+	0.619205i	$0.787455\pi$
$42$	−6.84276	−1.05586
$43$	−1.77673	−0.270949	−0.135474	−	0.990781i	$-0.543256\pi$
$43$	−1.77673	−0.270949	−0.135474	+	0.990781i	$0.543256\pi$
$44$	−4.15993	−0.627133
$45$	22.5081	3.35530
$46$	−7.38952	−1.08953
$47$	3.57315	0.521198	0.260599	−	0.965447i	$-0.416080\pi$
$47$	3.57315	0.521198	0.260599	+	0.965447i	$0.416080\pi$
$48$	2.10436	0.303738
$49$	−1.79844	−0.256920
$50$	5.75267	0.813551
$51$	−4.85550	−0.679906
$52$	−3.10970	−0.431237
$53$	−6.47005	−0.888729	−0.444365	−	0.895846i	$-0.646570\pi$
$53$	−6.47005	−0.888729	−0.444365	+	0.895846i	$0.646570\pi$
$54$	−11.3620	−1.54617
$55$	12.7713	1.72208
$56$	−6.73736	−0.900318
$57$	11.4423	1.51556
$58$	4.19976	0.551456
$59$	9.85690	1.28326	0.641630	−	0.767015i	$-0.278259\pi$
$59$	9.85690	1.28326	0.641630	+	0.767015i	$0.278259\pi$
$60$	11.2073	1.44686
$61$	−1.41380	−0.181019	−0.0905093	−	0.995896i	$-0.528849\pi$
$61$	−1.41380	−0.181019	−0.0905093	+	0.995896i	$0.528849\pi$
$62$	7.93093	1.00723
$63$	15.4790	1.95017
$64$	6.39285	0.799106
$65$	9.54698	1.18416
$66$	−11.5541	−1.42221
$67$	−11.0278	−1.34726	−0.673628	−	0.739071i	$-0.735265\pi$
$67$	−11.0278	−1.34726	−0.673628	+	0.739071i	$0.735265\pi$
$68$	−1.67658	−0.203315
$69$	24.1046	2.90185
$70$	7.25388	0.867004
$71$	−13.7060	−1.62660	−0.813299	−	0.581846i	$-0.802331\pi$
$71$	−13.7060	−1.62660	−0.813299	+	0.581846i	$0.802331\pi$
$72$	−20.0493	−2.36283
$73$	−4.83734	−0.566168	−0.283084	−	0.959095i	$-0.591357\pi$
$73$	−4.83734	−0.566168	−0.283084	+	0.959095i	$0.591357\pi$
$74$	0.605776	0.0704200
$75$	−18.7652	−2.16682
$76$	3.95096	0.453206
$77$	8.78290	1.00090
$78$	−8.63709	−0.977958
$79$	5.87492	0.660980	0.330490	−	0.943809i	$-0.392786\pi$
$79$	5.87492	0.660980	0.330490	+	0.943809i	$0.392786\pi$
$80$	−2.23079	−0.249410
$81$	16.7019	1.85577
$82$	−9.64404	−1.06501
$83$	10.5728	1.16051	0.580256	−	0.814434i	$-0.302952\pi$
$83$	10.5728	1.16051	0.580256	+	0.814434i	$0.302952\pi$
$84$	7.70735	0.840941
$85$	5.14723	0.558295
$86$	−1.70397	−0.183744
$87$	−13.6996	−1.46875
$88$	−11.3761	−1.21270
$89$	0.990375	0.104980	0.0524898	−	0.998621i	$-0.483284\pi$
$89$	0.990375	0.104980	0.0524898	+	0.998621i	$0.483284\pi$
$90$	21.5863	2.27540
$91$	6.56553	0.688255
$92$	8.32320	0.867754
$93$	−25.8706	−2.68266
$94$	3.42683	0.353450
$95$	−12.1297	−1.24448
$96$	−16.4650	−1.68045
$97$	−11.2485	−1.14211	−0.571056	−	0.820911i	$-0.693466\pi$
$97$	−11.2485	−1.14211	−0.571056	+	0.820911i	$0.693466\pi$
$98$	−1.72479	−0.174230
$99$	26.1364	2.62681
$100$	−6.47953	−0.647953
$101$	19.6103	1.95129	0.975646	−	0.219349i	$-0.0703933\pi$
$101$	19.6103	1.95129	0.975646	+	0.219349i	$0.0703933\pi$
$102$	−4.65666	−0.461078
$103$	−16.8552	−1.66079	−0.830394	−	0.557177i	$-0.811885\pi$
$103$	−16.8552	−1.66079	−0.830394	+	0.557177i	$0.811885\pi$
$104$	−8.50406	−0.833892
$105$	−23.6621	−2.30919
$106$	−6.20509	−0.602691
$107$	−5.50860	−0.532536	−0.266268	−	0.963899i	$-0.585791\pi$
$107$	−5.50860	−0.532536	−0.266268	+	0.963899i	$0.585791\pi$
$108$	12.7976	1.23145
$109$	−11.5317	−1.10454	−0.552270	−	0.833665i	$-0.686238\pi$
$109$	−11.5317	−1.10454	−0.552270	+	0.833665i	$0.686238\pi$
$110$	12.2483	1.16783
$111$	−1.97604	−0.187557
$112$	−1.53413	−0.144962
$113$	10.8736	1.02290	0.511450	−	0.859313i	$-0.329108\pi$
$113$	10.8736	1.02290	0.511450	+	0.859313i	$0.329108\pi$
$114$	10.9737	1.02778
$115$	−25.5528	−2.38281
$116$	−4.73041	−0.439208
$117$	19.5379	1.80628
$118$	9.45325	0.870242
$119$	3.53978	0.324492
$120$	30.6486	2.79782
$121$	3.83003	0.348185
$122$	−1.35590	−0.122758
$123$	31.4588	2.83654
$124$	−8.93302	−0.802208
$125$	3.31077	0.296124
$126$	14.8451	1.32250
$127$	−11.0300	−0.978755	−0.489378	−	0.872072i	$-0.662776\pi$
$127$	−11.0300	−0.978755	−0.489378	+	0.872072i	$0.662776\pi$
$128$	−4.39507	−0.388473
$129$	5.55834	0.489385
$130$	9.15602	0.803036
$131$	12.3574	1.07967	0.539837	−	0.841769i	$-0.318486\pi$
$131$	12.3574	1.07967	0.539837	+	0.841769i	$0.318486\pi$
$132$	13.0140	1.13272
$133$	−8.34170	−0.723317
$134$	−10.5762	−0.913641
$135$	−39.2896	−3.38151
$136$	−4.58494	−0.393155
$137$	9.55410	0.816262	0.408131	−	0.912923i	$-0.366181\pi$
$137$	9.55410	0.816262	0.408131	+	0.912923i	$0.366181\pi$
$138$	23.1175	1.96789
$139$	−1.67088	−0.141722	−0.0708610	−	0.997486i	$-0.522575\pi$
$139$	−1.67088	−0.141722	−0.0708610	+	0.997486i	$0.522575\pi$
$140$	−8.17042	−0.690526
$141$	−11.1783	−0.941382
$142$	−13.1447	−1.10308
$143$	11.0860	0.927056
$144$	−4.56531	−0.380443
$145$	14.5227	1.20604
$146$	−4.63924	−0.383946
$147$	5.62627	0.464047
$148$	−0.682317	−0.0560861
$149$	−15.7989	−1.29429	−0.647147	−	0.762365i	$-0.724038\pi$
$149$	−15.7989	−1.29429	−0.647147	+	0.762365i	$0.724038\pi$
$150$	−17.9967	−1.46943
$151$	−7.33170	−0.596645	−0.298323	−	0.954465i	$-0.596427\pi$
$151$	−7.33170	−0.596645	−0.298323	+	0.954465i	$0.596427\pi$
$152$	10.8047	0.876374
$153$	10.5338	0.851608
$154$	8.42322	0.678763
$155$	27.4250	2.20283
$156$	9.72841	0.778896
$157$	0.339507	0.0270956	0.0135478	−	0.999908i	$-0.495687\pi$
$157$	0.339507	0.0270956	0.0135478	+	0.999908i	$0.495687\pi$
$158$	5.63433	0.448244
$159$	20.2410	1.60521
$160$	17.4543	1.37988
$161$	−17.5729	−1.38494
$162$	16.0180	1.25849
$163$	−6.81870	−0.534082	−0.267041	−	0.963685i	$-0.586046\pi$
$163$	−6.81870	−0.534082	−0.267041	+	0.963685i	$0.586046\pi$
$164$	10.8626	0.848225
$165$	−39.9538	−3.11040
$166$	10.1398	0.787001
$167$	−22.4475	−1.73704	−0.868518	−	0.495657i	$-0.834927\pi$
$167$	−22.4475	−1.73704	−0.868518	+	0.495657i	$0.834927\pi$
$168$	21.0772	1.62614
$169$	−4.71283	−0.362525
$170$	4.93644	0.378608
$171$	−24.8235	−1.89830
$172$	1.91927	0.146343
$173$	−1.02885	−0.0782222	−0.0391111	−	0.999235i	$-0.512453\pi$
$173$	−1.02885	−0.0782222	−0.0391111	+	0.999235i	$0.512453\pi$
$174$	−13.1386	−0.996034
$175$	13.6803	1.03413
$176$	−2.59040	−0.195259
$177$	−30.8364	−2.31781
$178$	0.949818	0.0711918
$179$	6.99999	0.523204	0.261602	−	0.965176i	$-0.415749\pi$
$179$	6.99999	0.523204	0.261602	+	0.965176i	$0.415749\pi$
$180$	−24.3138	−1.81224
$181$	14.0785	1.04645	0.523224	−	0.852195i	$-0.324729\pi$
$181$	14.0785	1.04645	0.523224	+	0.852195i	$0.324729\pi$
$182$	6.29666	0.466740
$183$	4.42295	0.326954
$184$	22.7614	1.67799
$185$	2.09476	0.154010
$186$	−24.8112	−1.81925
$187$	5.97697	0.437079
$188$	−3.85981	−0.281506
$189$	−27.0197	−1.96540
$190$	−11.6330	−0.843946
$191$	−1.92370	−0.139194	−0.0695971	−	0.997575i	$-0.522171\pi$
$191$	−1.92370	−0.139194	−0.0695971	+	0.997575i	$0.522171\pi$
$192$	−19.9995	−1.44334
$193$	−5.65745	−0.407232	−0.203616	−	0.979051i	$-0.565269\pi$
$193$	−5.65745	−0.407232	−0.203616	+	0.979051i	$0.565269\pi$
$194$	−10.7879	−0.774523
$195$	−29.8669	−2.13881
$196$	1.94272	0.138766
$197$	−8.57186	−0.610720	−0.305360	−	0.952237i	$-0.598777\pi$
$197$	−8.57186	−0.610720	−0.305360	+	0.952237i	$0.598777\pi$
$198$	25.0661	1.78137
$199$	14.0205	0.993888	0.496944	−	0.867783i	$-0.334455\pi$
$199$	14.0205	0.993888	0.496944	+	0.867783i	$0.334455\pi$
$200$	−17.7195	−1.25296
$201$	34.4994	2.43340
$202$	18.8072	1.32327
$203$	9.98736	0.700976
$204$	5.24504	0.367226
$205$	−33.3489	−2.32919
$206$	−16.1649	−1.12626
$207$	−52.2939	−3.63468
$208$	−1.93641	−0.134266
$209$	−14.0851	−0.974285
$210$	−22.6931	−1.56597
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	6.98911	0.480014
$213$	42.8779	2.93794
$214$	−5.28301	−0.361139
$215$	−5.89229	−0.401851
$216$	34.9975	2.38128
$217$	18.8604	1.28033
$218$	−11.0595	−0.749043
$219$	15.1332	1.02261
$220$	−13.7959	−0.930117
$221$	4.46800	0.300550
$222$	−1.89512	−0.127192
$223$	−11.3947	−0.763048	−0.381524	−	0.924359i	$-0.624601\pi$
$223$	−11.3947	−0.763048	−0.381524	+	0.924359i	$0.624601\pi$
$224$	12.0034	0.802012
$225$	40.7103	2.71402
$226$	10.4283	0.693680
$227$	20.0190	1.32871	0.664355	−	0.747417i	$-0.268706\pi$
$227$	20.0190	1.32871	0.664355	+	0.747417i	$0.268706\pi$
$228$	−12.3602	−0.818576
$229$	6.88503	0.454976	0.227488	−	0.973781i	$-0.426949\pi$
$229$	6.88503	0.454976	0.227488	+	0.973781i	$0.426949\pi$
$230$	−24.5064	−1.61590
$231$	−27.4765	−1.80782
$232$	−12.9362	−0.849304
$233$	−14.0117	−0.917934	−0.458967	−	0.888453i	$-0.651780\pi$
$233$	−14.0117	−0.917934	−0.458967	+	0.888453i	$0.651780\pi$
$234$	18.7378	1.22493
$235$	11.8499	0.773002
$236$	−10.6477	−0.693105
$237$	−18.3792	−1.19386
$238$	3.39482	0.220054
$239$	11.4089	0.737981	0.368990	−	0.929433i	$-0.379704\pi$
$239$	11.4089	0.737981	0.368990	+	0.929433i	$0.379704\pi$
$240$	6.97882	0.450481
$241$	7.30164	0.470340	0.235170	−	0.971954i	$-0.424435\pi$
$241$	7.30164	0.470340	0.235170	+	0.971954i	$0.424435\pi$
$242$	3.67319	0.236121
$243$	−16.7090	−1.07188
$244$	1.52722	0.0977705
$245$	−5.96430	−0.381045
$246$	30.1705	1.92360
$247$	−10.5291	−0.669951
$248$	−24.4290	−1.55125
$249$	−33.0760	−2.09610
$250$	3.17519	0.200817
$251$	26.3299	1.66193	0.830964	−	0.556326i	$-0.187790\pi$
$251$	26.3299	1.66193	0.830964	+	0.556326i	$0.187790\pi$
$252$	−16.7208	−1.05331
$253$	−29.6720	−1.86546
$254$	−10.5783	−0.663742
$255$	−16.1026	−1.00839
$256$	−17.0008	−1.06255
$257$	14.3137	0.892864	0.446432	−	0.894818i	$-0.352694\pi$
$257$	14.3137	0.892864	0.446432	+	0.894818i	$0.352694\pi$
$258$	5.33072	0.331876
$259$	1.44058	0.0895135
$260$	−10.3129	−0.639579
$261$	29.7207	1.83967
$262$	11.8514	0.732181
$263$	18.4930	1.14033	0.570165	−	0.821530i	$-0.306879\pi$
$263$	18.4930	1.14033	0.570165	+	0.821530i	$0.306879\pi$
$264$	35.5892	2.19036
$265$	−21.4571	−1.31810
$266$	−8.00010	−0.490517
$267$	−3.09830	−0.189613
$268$	11.9125	0.727671
$269$	1.12246	0.0684375	0.0342187	−	0.999414i	$-0.489106\pi$
$269$	1.12246	0.0684375	0.0342187	+	0.999414i	$0.489106\pi$
$270$	−37.6806	−2.29317
$271$	9.42972	0.572815	0.286407	−	0.958108i	$-0.407539\pi$
$271$	9.42972	0.572815	0.286407	+	0.958108i	$0.407539\pi$
$272$	−1.04401	−0.0633025
$273$	−20.5397	−1.24312
$274$	9.16284	0.553547
$275$	23.0994	1.39294
$276$	−26.0384	−1.56733
$277$	9.35995	0.562385	0.281193	−	0.959651i	$-0.409270\pi$
$277$	9.35995	0.562385	0.281193	+	0.959651i	$0.409270\pi$
$278$	−1.60245	−0.0961087
$279$	56.1253	3.36013
$280$	−22.3436	−1.33528
$281$	−16.6079	−0.990745	−0.495373	−	0.868681i	$-0.664968\pi$
$281$	−16.6079	−0.990745	−0.495373	+	0.868681i	$0.664968\pi$
$282$	−10.7205	−0.638398
$283$	17.6072	1.04664	0.523321	−	0.852136i	$-0.324693\pi$
$283$	17.6072	1.04664	0.523321	+	0.852136i	$0.324693\pi$
$284$	14.8055	0.878547
$285$	37.9468	2.24777
$286$	10.6320	0.628683
$287$	−22.9343	−1.35377
$288$	35.7202	2.10483
$289$	−14.5911	−0.858299
$290$	13.9280	0.817878
$291$	35.1899	2.06287
$292$	5.22542	0.305794
$293$	0.650053	0.0379765	0.0189882	−	0.999820i	$-0.493955\pi$
$293$	0.650053	0.0379765	0.0189882	+	0.999820i	$0.493955\pi$
$294$	5.39586	0.314693
$295$	32.6891	1.90324
$296$	−1.86593	−0.108455
$297$	−45.6232	−2.64732
$298$	−15.1519	−0.877725
$299$	−22.1809	−1.28275
$300$	20.2706	1.17033
$301$	−4.05217	−0.233563
$302$	−7.03146	−0.404615
$303$	−61.3489	−3.52440
$304$	2.46027	0.141106
$305$	−4.68869	−0.268473
$306$	10.1024	0.577518
$307$	14.3236	0.817493	0.408747	−	0.912648i	$-0.365966\pi$
$307$	14.3236	0.817493	0.408747	+	0.912648i	$0.365966\pi$
$308$	−9.48751	−0.540601
$309$	52.7299	2.99970
$310$	26.3019	1.49385
$311$	17.0107	0.964588	0.482294	−	0.876010i	$-0.339804\pi$
$311$	17.0107	0.964588	0.482294	+	0.876010i	$0.339804\pi$
$312$	26.6042	1.50617
$313$	1.65949	0.0937998	0.0468999	−	0.998900i	$-0.485066\pi$
$313$	1.65949	0.0937998	0.0468999	+	0.998900i	$0.485066\pi$
$314$	0.325604	0.0183749
$315$	51.3340	2.89234
$316$	−6.34624	−0.357004
$317$	3.98562	0.223855	0.111927	−	0.993716i	$-0.464298\pi$
$317$	3.98562	0.223855	0.111927	+	0.993716i	$0.464298\pi$
$318$	19.4121	1.08857
$319$	16.8638	0.944191
$320$	21.2010	1.18517
$321$	17.2332	0.961861
$322$	−16.8532	−0.939193
$323$	−5.67673	−0.315862
$324$	−18.0419	−1.00233
$325$	17.2676	0.957834
$326$	−6.53946	−0.362187
$327$	36.0760	1.99501
$328$	29.7058	1.64023
$329$	8.14927	0.449284
$330$	−38.3176	−2.10932
$331$	15.5407	0.854193	0.427096	−	0.904206i	$-0.359537\pi$
$331$	15.5407	0.854193	0.427096	+	0.904206i	$0.359537\pi$
$332$	−11.4210	−0.626808
$333$	4.28693	0.234923
$334$	−21.5282	−1.17797
$335$	−36.5722	−1.99815
$336$	4.79939	0.261828
$337$	1.60152	0.0872402	0.0436201	−	0.999048i	$-0.486111\pi$
$337$	1.60152	0.0872402	0.0436201	+	0.999048i	$0.486111\pi$
$338$	−4.51983	−0.245846
$339$	−34.0171	−1.84755
$340$	−5.56017	−0.301542
$341$	31.8460	1.72456
$342$	−23.8070	−1.28733
$343$	−20.0665	−1.08349
$344$	5.24861	0.282986
$345$	79.9397	4.30381
$346$	−0.986719	−0.0530463
$347$	8.31586	0.446419	0.223209	−	0.974771i	$-0.428347\pi$
$347$	8.31586	0.446419	0.223209	+	0.974771i	$0.428347\pi$
$348$	14.7987	0.793292
$349$	−34.9504	−1.87085	−0.935427	−	0.353520i	$-0.884985\pi$
$349$	−34.9504	−1.87085	−0.935427	+	0.353520i	$0.884985\pi$
$350$	13.1201	0.701297
$351$	−34.1050	−1.82039
$352$	20.2679	1.08028
$353$	−9.41839	−0.501290	−0.250645	−	0.968079i	$-0.580643\pi$
$353$	−9.41839	−0.501290	−0.250645	+	0.968079i	$0.580643\pi$
$354$	−29.5736	−1.57182
$355$	−45.4540	−2.41245
$356$	−1.06983	−0.0567008
$357$	−11.0739	−0.586093
$358$	6.71333	0.354811
$359$	9.41410	0.496857	0.248429	−	0.968650i	$-0.420086\pi$
$359$	9.41410	0.496857	0.248429	+	0.968650i	$0.420086\pi$
$360$	−66.4908	−3.50437
$361$	−5.62246	−0.295919
$362$	13.5020	0.709649
$363$	−11.9819	−0.628887
$364$	−7.09226	−0.371735
$365$	−16.0424	−0.839698
$366$	4.24182	0.221724
$367$	−35.1856	−1.83667	−0.918337	−	0.395800i	$-0.870467\pi$
$367$	−35.1856	−1.83667	−0.918337	+	0.395800i	$0.870467\pi$
$368$	5.18288	0.270176
$369$	−68.2486	−3.55288
$370$	2.00898	0.104442
$371$	−14.7562	−0.766103
$372$	27.9461	1.44894
$373$	−9.29284	−0.481165	−0.240583	−	0.970629i	$-0.577338\pi$
$373$	−9.29284	−0.481165	−0.240583	+	0.970629i	$0.577338\pi$
$374$	5.73221	0.296405
$375$	−10.3574	−0.534856
$376$	−10.5554	−0.544353
$377$	12.6063	0.649257
$378$	−25.9132	−1.33283
$379$	−4.81960	−0.247566	−0.123783	−	0.992309i	$-0.539503\pi$
$379$	−4.81960	−0.247566	−0.123783	+	0.992309i	$0.539503\pi$
$380$	13.1028	0.672162
$381$	34.5064	1.76782
$382$	−1.84492	−0.0943945
$383$	−30.4897	−1.55795	−0.778975	−	0.627055i	$-0.784260\pi$
$383$	−30.4897	−1.55795	−0.778975	+	0.627055i	$0.784260\pi$
$384$	13.7496	0.701655
$385$	29.1273	1.48447
$386$	−5.42577	−0.276165
$387$	−12.0586	−0.612973
$388$	12.1509	0.616869
$389$	−3.77603	−0.191452	−0.0957261	−	0.995408i	$-0.530517\pi$
$389$	−3.77603	−0.191452	−0.0957261	+	0.995408i	$0.530517\pi$
$390$	−28.6438	−1.45043
$391$	−11.9588	−0.604780
$392$	5.31275	0.268335
$393$	−38.6591	−1.95010
$394$	−8.22083	−0.414160
$395$	19.4834	0.980317
$396$	−28.2333	−1.41877
$397$	9.36839	0.470186	0.235093	−	0.971973i	$-0.424461\pi$
$397$	9.36839	0.470186	0.235093	+	0.971973i	$0.424461\pi$
$398$	13.4464	0.674005
$399$	26.0963	1.30645
$400$	−4.03482	−0.201741
$401$	−1.82619	−0.0911953	−0.0455977	−	0.998960i	$-0.514519\pi$
$401$	−1.82619	−0.0911953	−0.0455977	+	0.998960i	$0.514519\pi$
$402$	33.0866	1.65021
$403$	23.8060	1.18586
$404$	−21.1835	−1.05392
$405$	55.3898	2.75234
$406$	9.57837	0.475366
$407$	2.43244	0.120572
$408$	14.3436	0.710112
$409$	4.49084	0.222058	0.111029	−	0.993817i	$-0.464585\pi$
$409$	4.49084	0.222058	0.111029	+	0.993817i	$0.464585\pi$
$410$	−31.9832	−1.57954
$411$	−29.8891	−1.47432
$412$	18.2074	0.897013
$413$	22.4806	1.10620
$414$	−50.1524	−2.46485
$415$	35.0632	1.72119
$416$	15.1510	0.742839
$417$	5.22719	0.255977
$418$	−13.5083	−0.660711
$419$	−8.44103	−0.412372	−0.206186	−	0.978513i	$-0.566105\pi$
$419$	−8.44103	−0.412372	−0.206186	+	0.978513i	$0.566105\pi$
$420$	25.5604	1.24722
$421$	−8.54239	−0.416331	−0.208165	−	0.978094i	$-0.566749\pi$
$421$	−8.54239	−0.416331	−0.208165	+	0.978094i	$0.566749\pi$
$422$	0.959048	0.0466857
$423$	24.2508	1.17912
$424$	19.1131	0.928213
$425$	9.30977	0.451590
$426$	41.1220	1.99237
$427$	−3.22444	−0.156042
$428$	5.95053	0.287630
$429$	−34.6815	−1.67444
$430$	−5.65099	−0.272515
$431$	30.1402	1.45180	0.725900	−	0.687800i	$-0.241423\pi$
$431$	30.1402	1.45180	0.725900	+	0.687800i	$0.241423\pi$
$432$	7.96911	0.383414
$433$	5.31907	0.255618	0.127809	−	0.991799i	$-0.459205\pi$
$433$	5.31907	0.255618	0.127809	+	0.991799i	$0.459205\pi$
$434$	18.0880	0.868252
$435$	−45.4330	−2.17834
$436$	12.4569	0.596577
$437$	28.1815	1.34810
$438$	14.5135	0.693480
$439$	−1.78459	−0.0851739	−0.0425870	−	0.999093i	$-0.513560\pi$
$439$	−1.78459	−0.0851739	−0.0425870	+	0.999093i	$0.513560\pi$
$440$	−37.7274	−1.79858
$441$	−12.2060	−0.581236
$442$	4.28503	0.203818
$443$	−5.80077	−0.275603	−0.137802	−	0.990460i	$-0.544004\pi$
$443$	−5.80077	−0.275603	−0.137802	+	0.990460i	$0.544004\pi$
$444$	2.13457	0.101302
$445$	3.28445	0.155698
$446$	−10.9281	−0.517461
$447$	49.4254	2.33774
$448$	14.5801	0.688846
$449$	9.39737	0.443489	0.221745	−	0.975105i	$-0.428825\pi$
$449$	9.39737	0.443489	0.221745	+	0.975105i	$0.428825\pi$
$450$	39.0431	1.84051
$451$	−38.7248	−1.82348
$452$	−11.7459	−0.552482
$453$	22.9366	1.07765
$454$	19.1992	0.901064
$455$	21.7737	1.02077
$456$	−33.8014	−1.58290
$457$	−12.1077	−0.566373	−0.283187	−	0.959065i	$-0.591392\pi$
$457$	−12.1077	−0.566373	−0.283187	+	0.959065i	$0.591392\pi$
$458$	6.60308	0.308541
$459$	−18.3876	−0.858259
$460$	27.6028	1.28699
$461$	−38.4166	−1.78924	−0.894620	−	0.446827i	$-0.852554\pi$
$461$	−38.4166	−1.78924	−0.894620	+	0.446827i	$0.852554\pi$
$462$	−26.3513	−1.22597
$463$	31.9387	1.48432	0.742159	−	0.670224i	$-0.233802\pi$
$463$	31.9387	1.48432	0.742159	+	0.670224i	$0.233802\pi$
$464$	−2.94564	−0.136748
$465$	−85.7966	−3.97872
$466$	−13.4379	−0.622497
$467$	−5.80135	−0.268455	−0.134227	−	0.990951i	$-0.542855\pi$
$467$	−5.80135	−0.268455	−0.134227	+	0.990951i	$0.542855\pi$
$468$	−21.1054	−0.975596
$469$	−25.1509	−1.16136
$470$	11.3646	0.524211
$471$	−1.06212	−0.0489398
$472$	−29.1181	−1.34027
$473$	−6.84215	−0.314602
$474$	−17.6265	−0.809613
$475$	−21.9390	−1.00663
$476$	−3.82377	−0.175262
$477$	−43.9119	−2.01059
$478$	10.9417	0.500461
$479$	1.40931	0.0643931	0.0321965	−	0.999482i	$-0.489750\pi$
$479$	1.40931	0.0643931	0.0321965	+	0.999482i	$0.489750\pi$
$480$	−54.6041	−2.49232
$481$	1.81834	0.0829091
$482$	7.00263	0.318961
$483$	54.9751	2.50146
$484$	−4.13730	−0.188059
$485$	−37.3042	−1.69390
$486$	−16.0248	−0.726898
$487$	3.52451	0.159711	0.0798553	−	0.996806i	$-0.474554\pi$
$487$	3.52451	0.159711	0.0798553	+	0.996806i	$0.474554\pi$
$488$	4.17649	0.189061
$489$	21.3317	0.964652
$490$	−5.72005	−0.258406
$491$	−3.55024	−0.160220	−0.0801101	−	0.996786i	$-0.525527\pi$
$491$	−3.55024	−0.160220	−0.0801101	+	0.996786i	$0.525527\pi$
$492$	−33.9826	−1.53205
$493$	6.79664	0.306105
$494$	−10.0979	−0.454327
$495$	86.6781	3.89589
$496$	−5.56261	−0.249769
$497$	−31.2591	−1.40216
$498$	−31.7215	−1.42147
$499$	−21.4330	−0.959474	−0.479737	−	0.877412i	$-0.659268\pi$
$499$	−21.4330	−0.959474	−0.479737	+	0.877412i	$0.659268\pi$
$500$	−3.57638	−0.159941
$501$	70.2249	3.13742
$502$	25.2516	1.12704
$503$	14.1894	0.632673	0.316337	−	0.948647i	$-0.397547\pi$
$503$	14.1894	0.632673	0.316337	+	0.948647i	$0.397547\pi$
$504$	−45.7262	−2.03681
$505$	65.0349	2.89401
$506$	−28.4569	−1.26506
$507$	14.7437	0.654789
$508$	11.9149	0.528638
$509$	8.67588	0.384551	0.192276	−	0.981341i	$-0.438413\pi$
$509$	8.67588	0.384551	0.192276	+	0.981341i	$0.438413\pi$
$510$	−15.4432	−0.683837
$511$	−11.0325	−0.488048
$512$	−7.51443	−0.332094
$513$	43.3314	1.91313
$514$	13.7275	0.605496
$515$	−55.8979	−2.46316
$516$	−6.00427	−0.264323
$517$	13.7601	0.605170
$518$	1.38159	0.0607035
$519$	3.21867	0.141284
$520$	−28.2026	−1.23677
$521$	−30.2011	−1.32313	−0.661567	−	0.749886i	$-0.730108\pi$
$521$	−30.2011	−1.32313	−0.661567	+	0.749886i	$0.730108\pi$
$522$	28.5036	1.24757
$523$	−8.56017	−0.374310	−0.187155	−	0.982330i	$-0.559927\pi$
$523$	−8.56017	−0.374310	−0.187155	+	0.982330i	$0.559927\pi$
$524$	−13.3488	−0.583146
$525$	−42.7976	−1.86784
$526$	17.7357	0.773315
$527$	12.8349	0.559098
$528$	8.10383	0.352674
$529$	36.3679	1.58121
$530$	−20.5784	−0.893867
$531$	66.8984	2.90314
$532$	9.01093	0.390673
$533$	−28.9482	−1.25389
$534$	−2.97142	−0.128586
$535$	−18.2686	−0.789818
$536$	32.5770	1.40711
$537$	−21.8989	−0.945005
$538$	1.07649	0.0464108
$539$	−6.92576	−0.298314
$540$	42.4416	1.82640
$541$	33.1240	1.42411	0.712056	−	0.702122i	$-0.247764\pi$
$541$	33.1240	1.42411	0.712056	+	0.702122i	$0.247764\pi$
$542$	9.04356	0.388454
$543$	−44.0434	−1.89008
$544$	8.16861	0.350226
$545$	−38.2435	−1.63817
$546$	−19.6985	−0.843020
$547$	−12.8910	−0.551178	−0.275589	−	0.961276i	$-0.588873\pi$
$547$	−12.8910	−0.551178	−0.275589	+	0.961276i	$0.588873\pi$
$548$	−10.3206	−0.440873
$549$	−9.59541	−0.409522
$550$	22.1534	0.944625
$551$	−16.0167	−0.682333
$552$	−71.2070	−3.03077
$553$	13.3989	0.569779
$554$	8.97665	0.381381
$555$	−6.55328	−0.278171
$556$	1.80493	0.0765459
$557$	−17.9273	−0.759602	−0.379801	−	0.925068i	$-0.624008\pi$
$557$	−17.9273	−0.759602	−0.379801	+	0.925068i	$0.624008\pi$
$558$	53.8269	2.27867
$559$	−5.11475	−0.216331
$560$	−5.08774	−0.214996
$561$	−18.6984	−0.789448
$562$	−15.9278	−0.671873
$563$	−7.19160	−0.303090	−0.151545	−	0.988450i	$-0.548425\pi$
$563$	−7.19160	−0.303090	−0.151545	+	0.988450i	$0.548425\pi$
$564$	12.0751	0.508453
$565$	36.0608	1.51709
$566$	16.8862	0.709779
$567$	38.0920	1.59971
$568$	40.4886	1.69886
$569$	32.6873	1.37032	0.685162	−	0.728391i	$-0.259731\pi$
$569$	32.6873	1.37032	0.685162	+	0.728391i	$0.259731\pi$
$570$	36.3928	1.52433
$571$	39.5764	1.65622	0.828110	−	0.560565i	$-0.189416\pi$
$571$	39.5764	1.65622	0.828110	+	0.560565i	$0.189416\pi$
$572$	−11.9754	−0.500715
$573$	6.01813	0.251411
$574$	−21.9951	−0.918057
$575$	−46.2173	−1.92740
$576$	43.3880	1.80783
$577$	−21.0813	−0.877625	−0.438813	−	0.898579i	$-0.644601\pi$
$577$	−21.0813	−0.877625	−0.438813	+	0.898579i	$0.644601\pi$
$578$	−13.9936	−0.582056
$579$	17.6988	0.735539
$580$	−15.6878	−0.651400
$581$	24.1132	1.00039
$582$	33.7488	1.39893
$583$	−24.9160	−1.03192
$584$	14.2899	0.591321
$585$	64.7950	2.67894
$586$	0.623432	0.0257537
$587$	−27.3146	−1.12740	−0.563698	−	0.825981i	$-0.690622\pi$
$587$	−27.3146	−1.12740	−0.563698	+	0.825981i	$0.690622\pi$
$588$	−6.07764	−0.250638
$589$	−30.2462	−1.24627
$590$	31.3505	1.29068
$591$	26.8163	1.10308
$592$	−0.424881	−0.0174625
$593$	41.4573	1.70245	0.851224	−	0.524802i	$-0.175861\pi$
$593$	41.4573	1.70245	0.851224	+	0.524802i	$0.175861\pi$
$594$	−43.7548	−1.79528
$595$	11.7392	0.481262
$596$	17.0664	0.699065
$597$	−43.8620	−1.79515
$598$	−21.2725	−0.869899
$599$	−33.4416	−1.36638	−0.683192	−	0.730238i	$-0.739409\pi$
$599$	−33.4416	−1.36638	−0.683192	+	0.730238i	$0.739409\pi$
$600$	55.4340	2.26308
$601$	−26.9109	−1.09772	−0.548858	−	0.835915i	$-0.684937\pi$
$601$	−26.9109	−1.09772	−0.548858	+	0.835915i	$0.684937\pi$
$602$	−3.88623	−0.158391
$603$	−74.8450	−3.04792
$604$	7.91989	0.322256
$605$	12.7018	0.516402
$606$	−58.8366	−2.39007
$607$	11.4260	0.463768	0.231884	−	0.972743i	$-0.425511\pi$
$607$	11.4260	0.463768	0.231884	+	0.972743i	$0.425511\pi$
$608$	−19.2498	−0.780683
$609$	−31.2446	−1.26609
$610$	−4.49668	−0.182065
$611$	10.2862	0.416135
$612$	−11.3789	−0.459964
$613$	−21.0686	−0.850954	−0.425477	−	0.904969i	$-0.639894\pi$
$613$	−21.0686	−0.850954	−0.425477	+	0.904969i	$0.639894\pi$
$614$	13.7371	0.554383
$615$	104.329	4.20695
$616$	−25.9454	−1.04537
$617$	42.4557	1.70920	0.854602	−	0.519284i	$-0.173801\pi$
$617$	42.4557	1.70920	0.854602	+	0.519284i	$0.173801\pi$
$618$	50.5705	2.03424
$619$	5.71766	0.229812	0.114906	−	0.993376i	$-0.463343\pi$
$619$	5.71766	0.229812	0.114906	+	0.993376i	$0.463343\pi$
$620$	−29.6252	−1.18978
$621$	91.2831	3.66306
$622$	16.3141	0.654135
$623$	2.25874	0.0904945
$624$	6.05790	0.242510
$625$	−19.0118	−0.760473
$626$	1.59153	0.0636103
$627$	44.0639	1.75974
$628$	−0.366745	−0.0146347
$629$	0.980351	0.0390892
$630$	49.2318	1.96144
$631$	−19.6872	−0.783734	−0.391867	−	0.920022i	$-0.628171\pi$
$631$	−19.6872	−0.783734	−0.391867	+	0.920022i	$0.628171\pi$
$632$	−17.3550	−0.690346
$633$	−3.12841	−0.124343
$634$	3.82241	0.151807
$635$	−36.5796	−1.45162
$636$	−21.8648	−0.866996
$637$	−5.17726	−0.205130
$638$	16.1732	0.640303
$639$	−93.0218	−3.67988
$640$	−14.5757	−0.576154
$641$	26.6527	1.05272	0.526359	−	0.850263i	$-0.323557\pi$
$641$	26.6527	1.05272	0.526359	+	0.850263i	$0.323557\pi$
$642$	16.5274	0.652286
$643$	47.6274	1.87824	0.939121	−	0.343588i	$-0.111642\pi$
$643$	47.6274	1.87824	0.939121	+	0.343588i	$0.111642\pi$
$644$	18.9827	0.748022
$645$	18.4335	0.725819
$646$	−5.44426	−0.214202
$647$	25.5564	1.00473	0.502363	−	0.864657i	$-0.332464\pi$
$647$	25.5564	1.00473	0.502363	+	0.864657i	$0.332464\pi$
$648$	−49.3389	−1.93822
$649$	37.9587	1.49001
$650$	16.5605	0.649555
$651$	−59.0030	−2.31251
$652$	7.36574	0.288464
$653$	21.2048	0.829807	0.414903	−	0.909866i	$-0.363815\pi$
$653$	21.2048	0.829807	0.414903	+	0.909866i	$0.363815\pi$
$654$	34.5986	1.35291
$655$	40.9818	1.60129
$656$	6.76416	0.264096
$657$	−32.8308	−1.28085
$658$	7.81554	0.304681
$659$	−11.7791	−0.458848	−0.229424	−	0.973327i	$-0.573684\pi$
$659$	−11.7791	−0.458848	−0.229424	+	0.973327i	$0.573684\pi$
$660$	43.1591	1.67997
$661$	12.5573	0.488422	0.244211	−	0.969722i	$-0.421471\pi$
$661$	12.5573	0.488422	0.244211	+	0.969722i	$0.421471\pi$
$662$	14.9043	0.579270
$663$	−13.9777	−0.542851
$664$	−31.2329	−1.21207
$665$	−27.6642	−1.07277
$666$	4.11138	0.159313
$667$	−33.7412	−1.30646
$668$	24.2483	0.938196
$669$	35.6474	1.37821
$670$	−35.0745	−1.35504
$671$	−5.44452	−0.210183
$672$	−37.5516	−1.44859
$673$	12.9356	0.498629	0.249314	−	0.968423i	$-0.419795\pi$
$673$	12.9356	0.498629	0.249314	+	0.968423i	$0.419795\pi$
$674$	1.53593	0.0591619
$675$	−71.0630	−2.73522
$676$	5.09092	0.195805
$677$	5.43857	0.209021	0.104511	−	0.994524i	$-0.466672\pi$
$677$	5.43857	0.209021	0.104511	+	0.994524i	$0.466672\pi$
$678$	−32.6240	−1.25292
$679$	−25.6544	−0.984524
$680$	−15.2053	−0.583098
$681$	−62.6278	−2.39990
$682$	30.5418	1.16951
$683$	40.9347	1.56632	0.783162	−	0.621817i	$-0.213605\pi$
$683$	40.9347	1.56632	0.783162	+	0.621817i	$0.213605\pi$
$684$	26.8150	1.02530
$685$	31.6849	1.21062
$686$	−19.2448	−0.734769
$687$	−21.5392	−0.821772
$688$	1.19513	0.0455641
$689$	−18.6256	−0.709579
$690$	76.6661	2.91863
$691$	−24.5238	−0.932930	−0.466465	−	0.884540i	$-0.654473\pi$
$691$	−24.5238	−0.932930	−0.466465	+	0.884540i	$0.654473\pi$
$692$	1.11139	0.0422488
$693$	59.6091	2.26436
$694$	7.97531	0.302739
$695$	−5.54125	−0.210192
$696$	40.4698	1.53400
$697$	−15.6073	−0.591170
$698$	−33.5192	−1.26872
$699$	43.8342	1.65796
$700$	−14.7778	−0.558549
$701$	−5.67940	−0.214508	−0.107254	−	0.994232i	$-0.534206\pi$
$701$	−5.67940	−0.214508	−0.107254	+	0.994232i	$0.534206\pi$
$702$	−32.7083	−1.23450
$703$	−2.31025	−0.0871329
$704$	24.6187	0.927853
$705$	−37.0714	−1.39619
$706$	−9.03270	−0.339950
$707$	44.7249	1.68205
$708$	33.3103	1.25188
$709$	6.90012	0.259140	0.129570	−	0.991570i	$-0.458640\pi$
$709$	6.90012	0.259140	0.129570	+	0.991570i	$0.458640\pi$
$710$	−43.5926	−1.63600
$711$	39.8728	1.49535
$712$	−2.92565	−0.109643
$713$	−63.7176	−2.38624
$714$	−10.6204	−0.397459
$715$	36.7652	1.37494
$716$	−7.56157	−0.282589
$717$	−35.6918	−1.33293
$718$	9.02858	0.336944
$719$	18.0237	0.672170	0.336085	−	0.941832i	$-0.390897\pi$
$719$	18.0237	0.672170	0.336085	+	0.941832i	$0.390897\pi$
$720$	−15.1403	−0.564244
$721$	−38.4414	−1.43163
$722$	−5.39221	−0.200677
$723$	−22.8425	−0.849523
$724$	−15.2080	−0.565201
$725$	26.2672	0.975538
$726$	−11.4912	−0.426480
$727$	−29.2365	−1.08432	−0.542161	−	0.840275i	$-0.682394\pi$
$727$	−29.2365	−1.08432	−0.542161	+	0.840275i	$0.682394\pi$
$728$	−19.3951	−0.718832
$729$	2.16688	0.0802548
$730$	−15.3854	−0.569441
$731$	−2.75760	−0.101994
$732$	−4.77779	−0.176592
$733$	−9.39422	−0.346983	−0.173492	−	0.984835i	$-0.555505\pi$
$733$	−9.39422	−0.346983	−0.173492	+	0.984835i	$0.555505\pi$
$734$	−33.7447	−1.24554
$735$	18.6588	0.688240
$736$	−40.5522	−1.49477
$737$	−42.4677	−1.56432
$738$	−65.4537	−2.40938
$739$	−11.2371	−0.413364	−0.206682	−	0.978408i	$-0.566267\pi$
$739$	−11.2371	−0.413364	−0.206682	+	0.978408i	$0.566267\pi$
$740$	−2.26282	−0.0831828
$741$	32.9394	1.21006
$742$	−14.1519	−0.519532
$743$	−9.94446	−0.364827	−0.182413	−	0.983222i	$-0.558391\pi$
$743$	−9.94446	−0.364827	−0.182413	+	0.983222i	$0.558391\pi$
$744$	76.4241	2.80184
$745$	−52.3949	−1.91960
$746$	−8.91228	−0.326302
$747$	71.7569	2.62545
$748$	−6.45648	−0.236072
$749$	−12.5634	−0.459057
$750$	−9.93330	−0.362713
$751$	−34.6899	−1.26585	−0.632927	−	0.774211i	$-0.718147\pi$
$751$	−34.6899	−1.26585	−0.632927	+	0.774211i	$0.718147\pi$
$752$	−2.40352	−0.0876472
$753$	−82.3707	−3.00176
$754$	12.0900	0.440293
$755$	−24.3146	−0.884900
$756$	29.1874	1.06154
$757$	29.9340	1.08797	0.543985	−	0.839095i	$-0.316915\pi$
$757$	29.9340	1.08797	0.543985	+	0.839095i	$0.316915\pi$
$758$	−4.62223	−0.167887
$759$	92.8262	3.36938
$760$	35.8323	1.29977
$761$	19.6377	0.711865	0.355932	−	0.934512i	$-0.384163\pi$
$761$	19.6377	0.711865	0.355932	+	0.934512i	$0.384163\pi$
$762$	33.0933	1.19884
$763$	−26.3003	−0.952136
$764$	2.07803	0.0751806
$765$	34.9340	1.26304
$766$	−29.2411	−1.05652
$767$	28.3755	1.02458
$768$	53.1854	1.91916
$769$	−24.7975	−0.894221	−0.447110	−	0.894479i	$-0.647547\pi$
$769$	−24.7975	−0.894221	−0.447110	+	0.894479i	$0.647547\pi$
$770$	27.9345	1.00669
$771$	−44.7792	−1.61268
$772$	6.11133	0.219952
$773$	7.17356	0.258015	0.129008	−	0.991644i	$-0.458821\pi$
$773$	7.17356	0.258015	0.129008	+	0.991644i	$0.458821\pi$
$774$	−11.5648	−0.415687
$775$	49.6035	1.78181
$776$	33.2290	1.19285
$777$	−4.50674	−0.161678
$778$	−3.62139	−0.129833
$779$	36.7796	1.31776
$780$	32.2630	1.15520
$781$	−52.7814	−1.88867
$782$	−11.4690	−0.410131
$783$	−51.8798	−1.85403
$784$	1.20974	0.0432050
$785$	1.12593	0.0401862
$786$	−37.0760	−1.32246
$787$	42.0483	1.49886	0.749431	−	0.662083i	$-0.230327\pi$
$787$	42.0483	1.49886	0.749431	+	0.662083i	$0.230327\pi$
$788$	9.25955	0.329858
$789$	−57.8539	−2.05965
$790$	18.6855	0.664802
$791$	24.7993	0.881762
$792$	−77.2093	−2.74351
$793$	−4.06997	−0.144529
$794$	8.98474	0.318857
$795$	67.1265	2.38073
$796$	−15.1453	−0.536812
$797$	40.9818	1.45165	0.725825	−	0.687879i	$-0.241458\pi$
$797$	40.9818	1.45165	0.725825	+	0.687879i	$0.241458\pi$
$798$	25.0276	0.885967
$799$	5.54577	0.196195
$800$	31.5695	1.11615
$801$	6.72163	0.237497
$802$	−1.75140	−0.0618441
$803$	−18.6285	−0.657385
$804$	−37.2671	−1.31431
$805$	−58.2781	−2.05403
$806$	22.8311	0.804192
$807$	−3.51151	−0.123611
$808$	−57.9304	−2.03798
$809$	−36.2122	−1.27315	−0.636577	−	0.771213i	$-0.719650\pi$
$809$	−36.2122	−1.27315	−0.636577	+	0.771213i	$0.719650\pi$
$810$	53.1215	1.86650
$811$	−9.95457	−0.349552	−0.174776	−	0.984608i	$-0.555920\pi$
$811$	−9.95457	−0.349552	−0.174776	+	0.984608i	$0.555920\pi$
$812$	−10.7886	−0.378606
$813$	−29.5000	−1.03461
$814$	2.33283	0.0817657
$815$	−22.6133	−0.792110
$816$	3.26610	0.114336
$817$	6.49844	0.227352
$818$	4.30693	0.150588
$819$	44.5600	1.55705
$820$	36.0243	1.25802
$821$	26.1762	0.913556	0.456778	−	0.889581i	$-0.349003\pi$
$821$	26.1762	0.913556	0.456778	+	0.889581i	$0.349003\pi$
$822$	−28.6651	−0.999811
$823$	38.0951	1.32791	0.663955	−	0.747772i	$-0.268877\pi$
$823$	38.0951	1.32791	0.663955	+	0.747772i	$0.268877\pi$
$824$	49.7916	1.73457
$825$	−72.2643	−2.51592
$826$	21.5599	0.750167
$827$	−21.7664	−0.756892	−0.378446	−	0.925623i	$-0.623541\pi$
$827$	−21.7664	−0.756892	−0.378446	+	0.925623i	$0.623541\pi$
$828$	56.4892	1.96314
$829$	4.32144	0.150090	0.0750448	−	0.997180i	$-0.476090\pi$
$829$	4.32144	0.150090	0.0750448	+	0.997180i	$0.476090\pi$
$830$	33.6273	1.16722
$831$	−29.2818	−1.01577
$832$	18.4034	0.638022
$833$	−2.79130	−0.0967129
$834$	5.01313	0.173591
$835$	−74.4441	−2.57624
$836$	15.2151	0.526224
$837$	−97.9711	−3.38638
$838$	−8.09536	−0.279650
$839$	−23.0578	−0.796043	−0.398021	−	0.917376i	$-0.630303\pi$
$839$	−23.0578	−0.796043	−0.398021	+	0.917376i	$0.630303\pi$
$840$	69.8999	2.41178
$841$	−9.82354	−0.338743
$842$	−8.19257	−0.282335
$843$	51.9564	1.78947
$844$	−1.08023	−0.0371829
$845$	−15.6295	−0.537671
$846$	23.2577	0.799618
$847$	8.73512	0.300142
$848$	4.35214	0.149453
$849$	−55.0827	−1.89043
$850$	8.92852	0.306246
$851$	−4.86684	−0.166833
$852$	−46.3178	−1.58682
$853$	19.0333	0.651687	0.325843	−	0.945424i	$-0.394352\pi$
$853$	19.0333	0.651687	0.325843	+	0.945424i	$0.394352\pi$
$854$	−3.09240	−0.105820
$855$	−82.3240	−2.81542
$856$	16.2729	0.556195
$857$	44.7500	1.52863	0.764315	−	0.644843i	$-0.223077\pi$
$857$	44.7500	1.52863	0.764315	+	0.644843i	$0.223077\pi$
$858$	−33.2613	−1.13552
$859$	−26.6956	−0.910843	−0.455422	−	0.890276i	$-0.650511\pi$
$859$	−26.6956	−0.910843	−0.455422	+	0.890276i	$0.650511\pi$
$860$	6.36501	0.217045
$861$	71.7478	2.44516
$862$	28.9059	0.984538
$863$	7.86784	0.267824	0.133912	−	0.990993i	$-0.457246\pi$
$863$	7.86784	0.267824	0.133912	+	0.990993i	$0.457246\pi$
$864$	−62.3523	−2.12127
$865$	−3.41205	−0.116013
$866$	5.10125	0.173347
$867$	45.6469	1.55025
$868$	−20.3735	−0.691520
$869$	22.6242	0.767473
$870$	−43.5724	−1.47724
$871$	−31.7461	−1.07568
$872$	34.0657	1.15361
$873$	−76.3431	−2.58382
$874$	27.0274	0.914216
$875$	7.55085	0.255265
$876$	−16.3473	−0.552323
$877$	0.751297	0.0253695	0.0126848	−	0.999920i	$-0.495962\pi$
$877$	0.751297	0.0253695	0.0126848	+	0.999920i	$0.495962\pi$
$878$	−1.71151	−0.0577607
$879$	−2.03363	−0.0685927
$880$	−8.59071	−0.289593
$881$	−8.60755	−0.289996	−0.144998	−	0.989432i	$-0.546318\pi$
$881$	−8.60755	−0.289996	−0.144998	+	0.989432i	$0.546318\pi$
$882$	−11.7061	−0.394165
$883$	34.0722	1.14662	0.573310	−	0.819338i	$-0.305659\pi$
$883$	34.0722	1.14662	0.573310	+	0.819338i	$0.305659\pi$
$884$	−4.82645	−0.162331
$885$	−102.265	−3.43760
$886$	−5.56322	−0.186900
$887$	28.5927	0.960048	0.480024	−	0.877255i	$-0.340628\pi$
$887$	28.5927	0.960048	0.480024	+	0.877255i	$0.340628\pi$
$888$	5.83739	0.195890
$889$	−25.1561	−0.843707
$890$	3.14995	0.105586
$891$	64.3188	2.15476
$892$	12.3089	0.412132
$893$	−13.0689	−0.437335
$894$	47.4013	1.58534
$895$	23.2146	0.775977
$896$	−10.0238	−0.334872
$897$	69.3909	2.31690
$898$	9.01254	0.300752
$899$	36.2133	1.20778
$900$	−43.9763	−1.46588
$901$	−10.0419	−0.334545
$902$	−37.1390	−1.23659
$903$	12.6769	0.421860
$904$	−32.1215	−1.06835
$905$	46.6896	1.55202
$906$	21.9973	0.730811
$907$	−18.9340	−0.628694	−0.314347	−	0.949308i	$-0.601786\pi$
$907$	−18.9340	−0.628694	−0.314347	+	0.949308i	$0.601786\pi$
$908$	−21.6251	−0.717654
$909$	133.094	4.41445
$910$	20.8821	0.692234
$911$	22.9725	0.761112	0.380556	−	0.924758i	$-0.375733\pi$
$911$	22.9725	0.761112	0.380556	+	0.924758i	$0.375733\pi$
$912$	−7.69675	−0.254865
$913$	40.7155	1.34749
$914$	−11.6119	−0.384086
$915$	14.6681	0.484914
$916$	−7.43739	−0.245738
$917$	28.1835	0.930702
$918$	−17.6346	−0.582028
$919$	18.0769	0.596302	0.298151	−	0.954519i	$-0.403630\pi$
$919$	18.0769	0.596302	0.298151	+	0.954519i	$0.403630\pi$
$920$	75.4852	2.48867
$921$	−44.8102	−1.47655
$922$	−36.8434	−1.21337
$923$	−39.4560	−1.29871
$924$	29.6808	0.976428
$925$	3.78879	0.124575
$926$	30.6308	1.00659
$927$	−114.395	−3.75723
$928$	23.0474	0.756569
$929$	60.1567	1.97368	0.986838	−	0.161711i	$-0.0517012\pi$
$929$	60.1567	1.97368	0.986838	+	0.161711i	$0.0517012\pi$
$930$	−82.2831	−2.69817
$931$	6.57786	0.215581
$932$	15.1358	0.495788
$933$	−53.2164	−1.74223
$934$	−5.56378	−0.182052
$935$	19.8219	0.648244
$936$	−57.7167	−1.88653
$937$	−13.1289	−0.428901	−0.214451	−	0.976735i	$-0.568796\pi$
$937$	−13.1289	−0.428901	−0.214451	+	0.976735i	$0.568796\pi$
$938$	−24.1210	−0.787578
$939$	−5.19156	−0.169420
$940$	−12.8006	−0.417509
$941$	46.6633	1.52118	0.760589	−	0.649233i	$-0.224910\pi$
$941$	46.6633	1.52118	0.760589	+	0.649233i	$0.224910\pi$
$942$	−1.01862	−0.0331885
$943$	77.4808	2.52312
$944$	−6.63034	−0.215799
$945$	−89.6074	−2.91493
$946$	−6.56195	−0.213347
$947$	−35.7522	−1.16179	−0.580895	−	0.813979i	$-0.697297\pi$
$947$	−35.7522	−1.16179	−0.580895	+	0.813979i	$0.697297\pi$
$948$	19.8537	0.644817
$949$	−13.9255	−0.452040
$950$	−21.0406	−0.682646
$951$	−12.4687	−0.404324
$952$	−10.4568	−0.338908
$953$	13.7760	0.446249	0.223124	−	0.974790i	$-0.428374\pi$
$953$	13.7760	0.446249	0.223124	+	0.974790i	$0.428374\pi$
$954$	−42.1137	−1.36348
$955$	−6.37971	−0.206442
$956$	−12.3242	−0.398593
$957$	−52.7569	−1.70539
$958$	1.35160	0.0436681
$959$	21.7900	0.703634
$960$	−66.3256	−2.14065
$961$	37.3859	1.20600
$962$	1.74387	0.0562248
$963$	−37.3866	−1.20477
$964$	−7.88742	−0.254037
$965$	−18.7622	−0.603977
$966$	52.7238	1.69636
$967$	55.7095	1.79150	0.895748	−	0.444561i	$-0.146640\pi$
$967$	55.7095	1.79150	0.895748	+	0.444561i	$0.146640\pi$
$968$	−11.3142	−0.363654
$969$	17.7591	0.570506
$970$	−35.7765	−1.14871
$971$	−46.2719	−1.48493	−0.742467	−	0.669882i	$-0.766345\pi$
$971$	−46.2719	−1.48493	−0.742467	+	0.669882i	$0.766345\pi$
$972$	18.0495	0.578938
$973$	−3.81076	−0.122167
$974$	3.38017	0.108308
$975$	−54.0202	−1.73003
$976$	0.951007	0.0304410
$977$	44.9118	1.43686	0.718428	−	0.695602i	$-0.244862\pi$
$977$	44.9118	1.43686	0.718428	+	0.695602i	$0.244862\pi$
$978$	20.4581	0.654179
$979$	3.81391	0.121893
$980$	6.44279	0.205808
$981$	−78.2654	−2.49882
$982$	−3.40486	−0.108653
$983$	−42.3546	−1.35090	−0.675451	−	0.737405i	$-0.736051\pi$
$983$	−42.3546	−1.35090	−0.675451	+	0.737405i	$0.736051\pi$
$984$	−92.9320	−2.96256
$985$	−28.4275	−0.905775
$986$	6.51831	0.207585
$987$	−25.4943	−0.811491
$988$	11.3738	0.361849
$989$	13.6898	0.435310
$990$	83.1285	2.64200
$991$	46.8869	1.48941	0.744705	−	0.667393i	$-0.232590\pi$
$991$	46.8869	1.48941	0.744705	+	0.667393i	$0.232590\pi$
$992$	43.5233	1.38187
$993$	−48.6176	−1.54283
$994$	−29.9790	−0.950875
$995$	46.4972	1.47406
$996$	35.7295	1.13213
$997$	1.86161	0.0589579	0.0294789	−	0.999565i	$-0.490615\pi$
$997$	1.86161	0.0589579	0.0294789	+	0.999565i	$0.490615\pi$
$998$	−20.5553	−0.650667
$999$	−7.48318	−0.236757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.d.1.6	✓	9
3.2	odd	2		1899.2.a.j.1.4		9
4.3	odd	2		3376.2.a.s.1.9		9
5.4	even	2		5275.2.a.o.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.d.1.6	✓	9	1.1	even	1	trivial
1899.2.a.j.1.4		9	3.2	odd	2
3376.2.a.s.1.9		9	4.3	odd	2
5275.2.a.o.1.4		9	5.4	even	2

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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q+0.959048 q^{2} -3.12841 q^{3} -1.08023 q^{4} +3.31637 q^{5} -3.00030 q^{6} +2.28069 q^{7} -2.95409 q^{8} +6.78696 q^{9} +O(q^{10})\)	\(q+0.959048 q^{2} -3.12841 q^{3} -1.08023 q^{4} +3.31637 q^{5} -3.00030 q^{6} +2.28069 q^{7} -2.95409 q^{8} +6.78696 q^{9} +3.18056 q^{10} +3.85098 q^{11} +3.37939 q^{12} +2.87874 q^{13} +2.18729 q^{14} -10.3750 q^{15} -0.672659 q^{16} +1.55207 q^{17} +6.50902 q^{18} -3.65753 q^{19} -3.58243 q^{20} -7.13494 q^{21} +3.69327 q^{22} -7.70506 q^{23} +9.24160 q^{24} +5.99831 q^{25} +2.76086 q^{26} -11.8472 q^{27} -2.46366 q^{28} +4.37909 q^{29} -9.95010 q^{30} +8.26958 q^{31} +5.26306 q^{32} -12.0474 q^{33} +1.48851 q^{34} +7.56362 q^{35} -7.33145 q^{36} +0.631643 q^{37} -3.50775 q^{38} -9.00590 q^{39} -9.79684 q^{40} -10.0558 q^{41} -6.84276 q^{42} -1.77673 q^{43} -4.15993 q^{44} +22.5081 q^{45} -7.38952 q^{46} +3.57315 q^{47} +2.10436 q^{48} -1.79844 q^{49} +5.75267 q^{50} -4.85550 q^{51} -3.10970 q^{52} -6.47005 q^{53} -11.3620 q^{54} +12.7713 q^{55} -6.73736 q^{56} +11.4423 q^{57} +4.19976 q^{58} +9.85690 q^{59} +11.2073 q^{60} -1.41380 q^{61} +7.93093 q^{62} +15.4790 q^{63} +6.39285 q^{64} +9.54698 q^{65} -11.5541 q^{66} -11.0278 q^{67} -1.67658 q^{68} +24.1046 q^{69} +7.25388 q^{70} -13.7060 q^{71} -20.0493 q^{72} -4.83734 q^{73} +0.605776 q^{74} -18.7652 q^{75} +3.95096 q^{76} +8.78290 q^{77} -8.63709 q^{78} +5.87492 q^{79} -2.23079 q^{80} +16.7019 q^{81} -9.64404 q^{82} +10.5728 q^{83} +7.70735 q^{84} +5.14723 q^{85} -1.70397 q^{86} -13.6996 q^{87} -11.3761 q^{88} +0.990375 q^{89} +21.5863 q^{90} +6.56553 q^{91} +8.32320 q^{92} -25.8706 q^{93} +3.42683 q^{94} -12.1297 q^{95} -16.4650 q^{96} -11.2485 q^{97} -1.72479 q^{98} +26.1364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} + 13 q^{11} - 5 q^{12} - 4 q^{13} + 13 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} - 21 q^{18} - 2 q^{19} + 32 q^{20} + 9 q^{21} - 8 q^{22} - 3 q^{23} + 4 q^{24} + 14 q^{25} + 13 q^{26} - 4 q^{27} - 20 q^{28} + 26 q^{29} - 17 q^{30} + 5 q^{31} - 8 q^{32} - 10 q^{33} - 21 q^{34} - 21 q^{35} - 10 q^{36} + 5 q^{37} + 13 q^{38} - 40 q^{39} - 52 q^{40} + 20 q^{41} - 46 q^{42} - 37 q^{43} - 10 q^{44} + 36 q^{45} - 38 q^{46} + 4 q^{47} - 32 q^{48} + 11 q^{49} - 16 q^{50} - 42 q^{51} - 20 q^{52} + 13 q^{53} - 30 q^{54} + 6 q^{55} + 23 q^{56} + 4 q^{57} - 17 q^{58} + 14 q^{59} - 4 q^{60} + 23 q^{61} - 19 q^{62} + q^{63} + 14 q^{64} - 13 q^{65} + 31 q^{66} - 3 q^{67} + 53 q^{68} + 16 q^{69} + 9 q^{70} + 19 q^{71} - 21 q^{72} + 17 q^{73} + 7 q^{74} + 4 q^{75} - 34 q^{76} + 13 q^{77} + 44 q^{78} + 7 q^{79} + 27 q^{80} + 13 q^{81} - 14 q^{82} + 6 q^{83} + 48 q^{84} - 4 q^{85} - 24 q^{86} - 5 q^{87} - 38 q^{88} + 33 q^{89} - 44 q^{90} - 27 q^{91} + 37 q^{92} - 27 q^{93} - 10 q^{94} - 23 q^{95} + 43 q^{96} - 11 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 + 13 * q^11 - 5 * q^12 - 4 * q^13 + 13 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 - 21 * q^18 - 2 * q^19 + 32 * q^20 + 9 * q^21 - 8 * q^22 - 3 * q^23 + 4 * q^24 + 14 * q^25 + 13 * q^26 - 4 * q^27 - 20 * q^28 + 26 * q^29 - 17 * q^30 + 5 * q^31 - 8 * q^32 - 10 * q^33 - 21 * q^34 - 21 * q^35 - 10 * q^36 + 5 * q^37 + 13 * q^38 - 40 * q^39 - 52 * q^40 + 20 * q^41 - 46 * q^42 - 37 * q^43 - 10 * q^44 + 36 * q^45 - 38 * q^46 + 4 * q^47 - 32 * q^48 + 11 * q^49 - 16 * q^50 - 42 * q^51 - 20 * q^52 + 13 * q^53 - 30 * q^54 + 6 * q^55 + 23 * q^56 + 4 * q^57 - 17 * q^58 + 14 * q^59 - 4 * q^60 + 23 * q^61 - 19 * q^62 + q^63 + 14 * q^64 - 13 * q^65 + 31 * q^66 - 3 * q^67 + 53 * q^68 + 16 * q^69 + 9 * q^70 + 19 * q^71 - 21 * q^72 + 17 * q^73 + 7 * q^74 + 4 * q^75 - 34 * q^76 + 13 * q^77 + 44 * q^78 + 7 * q^79 + 27 * q^80 + 13 * q^81 - 14 * q^82 + 6 * q^83 + 48 * q^84 - 4 * q^85 - 24 * q^86 - 5 * q^87 - 38 * q^88 + 33 * q^89 - 44 * q^90 - 27 * q^91 + 37 * q^92 - 27 * q^93 - 10 * q^94 - 23 * q^95 + 43 * q^96 - 11 * q^97 + 26 * q^98 + 2 * q^99

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