LMFDB - Embedded newform 211.2.a.a.1.1

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} -0.236068 q^{6} +1.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} -0.236068 q^{6} +1.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} -2.00000 q^{10} -3.00000 q^{11} -0.618034 q^{12} +6.23607 q^{13} -1.00000 q^{14} +1.23607 q^{15} +1.85410 q^{16} +6.61803 q^{17} +1.76393 q^{18} +0.854102 q^{19} -5.23607 q^{20} +0.618034 q^{21} +1.85410 q^{22} +1.76393 q^{23} +0.854102 q^{24} +5.47214 q^{25} -3.85410 q^{26} -2.23607 q^{27} -2.61803 q^{28} -2.23607 q^{29} -0.763932 q^{30} -11.0902 q^{31} -5.61803 q^{32} -1.14590 q^{33} -4.09017 q^{34} +5.23607 q^{35} +4.61803 q^{36} -10.9443 q^{37} -0.527864 q^{38} +2.38197 q^{39} +7.23607 q^{40} -3.00000 q^{41} -0.381966 q^{42} +9.00000 q^{43} +4.85410 q^{44} -9.23607 q^{45} -1.09017 q^{46} +1.61803 q^{47} +0.708204 q^{48} -4.38197 q^{49} -3.38197 q^{50} +2.52786 q^{51} -10.0902 q^{52} +5.38197 q^{53} +1.38197 q^{54} -9.70820 q^{55} +3.61803 q^{56} +0.326238 q^{57} +1.38197 q^{58} -6.70820 q^{59} -2.00000 q^{60} -3.00000 q^{61} +6.85410 q^{62} -4.61803 q^{63} -0.236068 q^{64} +20.1803 q^{65} +0.708204 q^{66} -12.0000 q^{67} -10.7082 q^{68} +0.673762 q^{69} -3.23607 q^{70} +8.18034 q^{71} -6.38197 q^{72} +2.09017 q^{73} +6.76393 q^{74} +2.09017 q^{75} -1.38197 q^{76} -4.85410 q^{77} -1.47214 q^{78} -11.7082 q^{79} +6.00000 q^{80} +7.70820 q^{81} +1.85410 q^{82} -0.472136 q^{83} -1.00000 q^{84} +21.4164 q^{85} -5.56231 q^{86} -0.854102 q^{87} -6.70820 q^{88} +10.8541 q^{89} +5.70820 q^{90} +10.0902 q^{91} -2.85410 q^{92} -4.23607 q^{93} -1.00000 q^{94} +2.76393 q^{95} -2.14590 q^{96} -2.85410 q^{97} +2.70820 q^{98} +8.56231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + q^7 + q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + q^{7} + q^{9} - 4 q^{10} - 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} + 11 q^{17} + 8 q^{18} - 5 q^{19} - 6 q^{20} - q^{21} - 3 q^{22} + 8 q^{23} - 5 q^{24} + 2 q^{25} - q^{26} - 3 q^{28} - 6 q^{30} - 11 q^{31} - 9 q^{32} - 9 q^{33} + 3 q^{34} + 6 q^{35} + 7 q^{36} - 4 q^{37} - 10 q^{38} + 7 q^{39} + 10 q^{40} - 6 q^{41} - 3 q^{42} + 18 q^{43} + 3 q^{44} - 14 q^{45} + 9 q^{46} + q^{47} - 12 q^{48} - 11 q^{49} - 9 q^{50} + 14 q^{51} - 9 q^{52} + 13 q^{53} + 5 q^{54} - 6 q^{55} + 5 q^{56} - 15 q^{57} + 5 q^{58} - 4 q^{60} - 6 q^{61} + 7 q^{62} - 7 q^{63} + 4 q^{64} + 18 q^{65} - 12 q^{66} - 24 q^{67} - 8 q^{68} + 17 q^{69} - 2 q^{70} - 6 q^{71} - 15 q^{72} - 7 q^{73} + 18 q^{74} - 7 q^{75} - 5 q^{76} - 3 q^{77} + 6 q^{78} - 10 q^{79} + 12 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 2 q^{84} + 16 q^{85} + 9 q^{86} + 5 q^{87} + 15 q^{89} - 2 q^{90} + 9 q^{91} + q^{92} - 4 q^{93} - 2 q^{94} + 10 q^{95} - 11 q^{96} + q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + q^7 + q^9 - 4 * q^10 - 6 * q^11 + q^12 + 8 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 + 11 * q^17 + 8 * q^18 - 5 * q^19 - 6 * q^20 - q^21 - 3 * q^22 + 8 * q^23 - 5 * q^24 + 2 * q^25 - q^26 - 3 * q^28 - 6 * q^30 - 11 * q^31 - 9 * q^32 - 9 * q^33 + 3 * q^34 + 6 * q^35 + 7 * q^36 - 4 * q^37 - 10 * q^38 + 7 * q^39 + 10 * q^40 - 6 * q^41 - 3 * q^42 + 18 * q^43 + 3 * q^44 - 14 * q^45 + 9 * q^46 + q^47 - 12 * q^48 - 11 * q^49 - 9 * q^50 + 14 * q^51 - 9 * q^52 + 13 * q^53 + 5 * q^54 - 6 * q^55 + 5 * q^56 - 15 * q^57 + 5 * q^58 - 4 * q^60 - 6 * q^61 + 7 * q^62 - 7 * q^63 + 4 * q^64 + 18 * q^65 - 12 * q^66 - 24 * q^67 - 8 * q^68 + 17 * q^69 - 2 * q^70 - 6 * q^71 - 15 * q^72 - 7 * q^73 + 18 * q^74 - 7 * q^75 - 5 * q^76 - 3 * q^77 + 6 * q^78 - 10 * q^79 + 12 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 2 * q^84 + 16 * q^85 + 9 * q^86 + 5 * q^87 + 15 * q^89 - 2 * q^90 + 9 * q^91 + q^92 - 4 * q^93 - 2 * q^94 + 10 * q^95 - 11 * q^96 + q^97 - 8 * q^98 - 3 * 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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.61803	−0.809017
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	−0.236068	−0.0963743
$7$	1.61803	0.611559	0.305780	−	0.952102i	$-0.401083\pi$
$7$	1.61803	0.611559	0.305780	+	0.952102i	$0.401083\pi$
$8$	2.23607	0.790569
$9$	−2.85410	−0.951367
$10$	−2.00000	−0.632456
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−0.618034	−0.178411
$13$	6.23607	1.72957	0.864787	−	0.502139i	$-0.167453\pi$
$13$	6.23607	1.72957	0.864787	+	0.502139i	$0.167453\pi$
$14$	−1.00000	−0.267261
$15$	1.23607	0.319151
$16$	1.85410	0.463525
$17$	6.61803	1.60511	0.802555	−	0.596579i	$-0.203474\pi$
$17$	6.61803	1.60511	0.802555	+	0.596579i	$0.203474\pi$
$18$	1.76393	0.415763
$19$	0.854102	0.195944	0.0979722	−	0.995189i	$-0.468764\pi$
$19$	0.854102	0.195944	0.0979722	+	0.995189i	$0.468764\pi$
$20$	−5.23607	−1.17082
$21$	0.618034	0.134866
$22$	1.85410	0.395296
$23$	1.76393	0.367805	0.183903	−	0.982944i	$-0.441127\pi$
$23$	1.76393	0.367805	0.183903	+	0.982944i	$0.441127\pi$
$24$	0.854102	0.174343
$25$	5.47214	1.09443
$26$	−3.85410	−0.755852
$27$	−2.23607	−0.430331
$28$	−2.61803	−0.494762
$29$	−2.23607	−0.415227	−0.207614	−	0.978211i	$-0.566570\pi$
$29$	−2.23607	−0.415227	−0.207614	+	0.978211i	$0.566570\pi$
$30$	−0.763932	−0.139474
$31$	−11.0902	−1.99185	−0.995927	−	0.0901670i	$-0.971260\pi$
$31$	−11.0902	−1.99185	−0.995927	+	0.0901670i	$0.971260\pi$
$32$	−5.61803	−0.993137
$33$	−1.14590	−0.199475
$34$	−4.09017	−0.701458
$35$	5.23607	0.885057
$36$	4.61803	0.769672
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	−0.527864	−0.0856309
$39$	2.38197	0.381420
$40$	7.23607	1.14412
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−0.381966	−0.0589386
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	4.85410	0.731783
$45$	−9.23607	−1.37683
$46$	−1.09017	−0.160737
$47$	1.61803	0.236015	0.118007	−	0.993013i	$-0.462349\pi$
$47$	1.61803	0.236015	0.118007	+	0.993013i	$0.462349\pi$
$48$	0.708204	0.102220
$49$	−4.38197	−0.625995
$50$	−3.38197	−0.478282
$51$	2.52786	0.353972
$52$	−10.0902	−1.39925
$53$	5.38197	0.739270	0.369635	−	0.929177i	$-0.379483\pi$
$53$	5.38197	0.739270	0.369635	+	0.929177i	$0.379483\pi$
$54$	1.38197	0.188062
$55$	−9.70820	−1.30905
$56$	3.61803	0.483480
$57$	0.326238	0.0432113
$58$	1.38197	0.181461
$59$	−6.70820	−0.873334	−0.436667	−	0.899623i	$-0.643841\pi$
$59$	−6.70820	−0.873334	−0.436667	+	0.899623i	$0.643841\pi$
$60$	−2.00000	−0.258199
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	6.85410	0.870472
$63$	−4.61803	−0.581818
$64$	−0.236068	−0.0295085
$65$	20.1803	2.50306
$66$	0.708204	0.0871739
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−10.7082	−1.29856
$69$	0.673762	0.0811114
$70$	−3.23607	−0.386784
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	−6.38197	−0.752122
$73$	2.09017	0.244636	0.122318	−	0.992491i	$-0.460967\pi$
$73$	2.09017	0.244636	0.122318	+	0.992491i	$0.460967\pi$
$74$	6.76393	0.786291
$75$	2.09017	0.241352
$76$	−1.38197	−0.158522
$77$	−4.85410	−0.553176
$78$	−1.47214	−0.166687
$79$	−11.7082	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$79$	−11.7082	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$80$	6.00000	0.670820
$81$	7.70820	0.856467
$82$	1.85410	0.204751
$83$	−0.472136	−0.0518237	−0.0259118	−	0.999664i	$-0.508249\pi$
$83$	−0.472136	−0.0518237	−0.0259118	+	0.999664i	$0.508249\pi$
$84$	−1.00000	−0.109109
$85$	21.4164	2.32294
$86$	−5.56231	−0.599799
$87$	−0.854102	−0.0915693
$88$	−6.70820	−0.715097
$89$	10.8541	1.15053	0.575266	−	0.817966i	$-0.304898\pi$
$89$	10.8541	1.15053	0.575266	+	0.817966i	$0.304898\pi$
$90$	5.70820	0.601698
$91$	10.0902	1.05774
$92$	−2.85410	−0.297561
$93$	−4.23607	−0.439260
$94$	−1.00000	−0.103142
$95$	2.76393	0.283573
$96$	−2.14590	−0.219015
$97$	−2.85410	−0.289790	−0.144895	−	0.989447i	$-0.546284\pi$
$97$	−2.85410	−0.289790	−0.144895	+	0.989447i	$0.546284\pi$
$98$	2.70820	0.273570
$99$	8.56231	0.860544
$100$	−8.85410	−0.885410
$101$	−6.09017	−0.605995	−0.302997	−	0.952991i	$-0.597987\pi$
$101$	−6.09017	−0.605995	−0.302997	+	0.952991i	$0.597987\pi$
$102$	−1.56231	−0.154691
$103$	−14.4164	−1.42049	−0.710245	−	0.703954i	$-0.751416\pi$
$103$	−14.4164	−1.42049	−0.710245	+	0.703954i	$0.751416\pi$
$104$	13.9443	1.36735
$105$	2.00000	0.195180
$106$	−3.32624	−0.323073
$107$	−1.14590	−0.110778	−0.0553891	−	0.998465i	$-0.517640\pi$
$107$	−1.14590	−0.110778	−0.0553891	+	0.998465i	$0.517640\pi$
$108$	3.61803	0.348145
$109$	3.61803	0.346545	0.173272	−	0.984874i	$-0.444566\pi$
$109$	3.61803	0.346545	0.173272	+	0.984874i	$0.444566\pi$
$110$	6.00000	0.572078
$111$	−4.18034	−0.396780
$112$	3.00000	0.283473
$113$	16.2361	1.52736	0.763680	−	0.645594i	$-0.223390\pi$
$113$	16.2361	1.52736	0.763680	+	0.645594i	$0.223390\pi$
$114$	−0.201626	−0.0188840
$115$	5.70820	0.532293
$116$	3.61803	0.335926
$117$	−17.7984	−1.64546
$118$	4.14590	0.381661
$119$	10.7082	0.981619
$120$	2.76393	0.252311
$121$	−2.00000	−0.181818
$122$	1.85410	0.167863
$123$	−1.14590	−0.103322
$124$	17.9443	1.61144
$125$	1.52786	0.136656
$126$	2.85410	0.254264
$127$	14.7082	1.30514	0.652571	−	0.757728i	$-0.273690\pi$
$127$	14.7082	1.30514	0.652571	+	0.757728i	$0.273690\pi$
$128$	11.3820	1.00603
$129$	3.43769	0.302672
$130$	−12.4721	−1.09388
$131$	13.1803	1.15157	0.575786	−	0.817601i	$-0.304696\pi$
$131$	13.1803	1.15157	0.575786	+	0.817601i	$0.304696\pi$
$132$	1.85410	0.161379
$133$	1.38197	0.119832
$134$	7.41641	0.640680
$135$	−7.23607	−0.622782
$136$	14.7984	1.26895
$137$	−6.47214	−0.552952	−0.276476	−	0.961021i	$-0.589167\pi$
$137$	−6.47214	−0.552952	−0.276476	+	0.961021i	$0.589167\pi$
$138$	−0.416408	−0.0354470
$139$	−14.1459	−1.19984	−0.599920	−	0.800060i	$-0.704801\pi$
$139$	−14.1459	−1.19984	−0.599920	+	0.800060i	$0.704801\pi$
$140$	−8.47214	−0.716026
$141$	0.618034	0.0520479
$142$	−5.05573	−0.424267
$143$	−18.7082	−1.56446
$144$	−5.29180	−0.440983
$145$	−7.23607	−0.600923
$146$	−1.29180	−0.106910
$147$	−1.67376	−0.138050
$148$	17.7082	1.45561
$149$	−8.94427	−0.732743	−0.366372	−	0.930469i	$-0.619400\pi$
$149$	−8.94427	−0.732743	−0.366372	+	0.930469i	$0.619400\pi$
$150$	−1.29180	−0.105475
$151$	−9.90983	−0.806451	−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983	−0.806451	−0.403225	+	0.915101i	$0.632111\pi$
$152$	1.90983	0.154908
$153$	−18.8885	−1.52705
$154$	3.00000	0.241747
$155$	−35.8885	−2.88264
$156$	−3.85410	−0.308575
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	7.23607	0.575671
$159$	2.05573	0.163030
$160$	−18.1803	−1.43728
$161$	2.85410	0.224935
$162$	−4.76393	−0.374290
$163$	1.43769	0.112609	0.0563044	−	0.998414i	$-0.482068\pi$
$163$	1.43769	0.112609	0.0563044	+	0.998414i	$0.482068\pi$
$164$	4.85410	0.379042
$165$	−3.70820	−0.288683
$166$	0.291796	0.0226478
$167$	0.437694	0.0338698	0.0169349	−	0.999857i	$-0.494609\pi$
$167$	0.437694	0.0338698	0.0169349	+	0.999857i	$0.494609\pi$
$168$	1.38197	0.106621
$169$	25.8885	1.99143
$170$	−13.2361	−1.01516
$171$	−2.43769	−0.186415
$172$	−14.5623	−1.11037
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0.527864	0.0400173
$175$	8.85410	0.669307
$176$	−5.56231	−0.419275
$177$	−2.56231	−0.192595
$178$	−6.70820	−0.502801
$179$	−24.2705	−1.81406	−0.907032	−	0.421063i	$-0.861657\pi$
$179$	−24.2705	−1.81406	−0.907032	+	0.421063i	$0.861657\pi$
$180$	14.9443	1.11388
$181$	−3.00000	−0.222988	−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000	−0.222988	−0.111494	+	0.993765i	$0.535564\pi$
$182$	−6.23607	−0.462248
$183$	−1.14590	−0.0847072
$184$	3.94427	0.290776
$185$	−35.4164	−2.60387
$186$	2.61803	0.191964
$187$	−19.8541	−1.45188
$188$	−2.61803	−0.190940
$189$	−3.61803	−0.263173
$190$	−1.70820	−0.123926
$191$	19.3607	1.40089	0.700445	−	0.713707i	$-0.252985\pi$
$191$	19.3607	1.40089	0.700445	+	0.713707i	$0.252985\pi$
$192$	−0.0901699	−0.00650746
$193$	24.9787	1.79801	0.899004	−	0.437941i	$-0.144292\pi$
$193$	24.9787	1.79801	0.899004	+	0.437941i	$0.144292\pi$
$194$	1.76393	0.126643
$195$	7.70820	0.551996
$196$	7.09017	0.506441
$197$	−0.819660	−0.0583984	−0.0291992	−	0.999574i	$-0.509296\pi$
$197$	−0.819660	−0.0583984	−0.0291992	+	0.999574i	$0.509296\pi$
$198$	−5.29180	−0.376072
$199$	9.27051	0.657169	0.328585	−	0.944475i	$-0.393428\pi$
$199$	9.27051	0.657169	0.328585	+	0.944475i	$0.393428\pi$
$200$	12.2361	0.865221
$201$	−4.58359	−0.323302
$202$	3.76393	0.264829
$203$	−3.61803	−0.253936
$204$	−4.09017	−0.286369
$205$	−9.70820	−0.678050
$206$	8.90983	0.620777
$207$	−5.03444	−0.349918
$208$	11.5623	0.801702
$209$	−2.56231	−0.177238
$210$	−1.23607	−0.0852968
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−8.70820	−0.598082
$213$	3.12461	0.214095
$214$	0.708204	0.0484118
$215$	29.1246	1.98628
$216$	−5.00000	−0.340207
$217$	−17.9443	−1.21814
$218$	−2.23607	−0.151446
$219$	0.798374	0.0539491
$220$	15.7082	1.05905
$221$	41.2705	2.77615
$222$	2.58359	0.173399
$223$	−4.81966	−0.322748	−0.161374	−	0.986893i	$-0.551593\pi$
$223$	−4.81966	−0.322748	−0.161374	+	0.986893i	$0.551593\pi$
$224$	−9.09017	−0.607363
$225$	−15.6180	−1.04120
$226$	−10.0344	−0.667481
$227$	20.8885	1.38642	0.693211	−	0.720735i	$-0.256196\pi$
$227$	20.8885	1.38642	0.693211	+	0.720735i	$0.256196\pi$
$228$	−0.527864	−0.0349587
$229$	3.29180	0.217528	0.108764	−	0.994068i	$-0.465311\pi$
$229$	3.29180	0.217528	0.108764	+	0.994068i	$0.465311\pi$
$230$	−3.52786	−0.232620
$231$	−1.85410	−0.121991
$232$	−5.00000	−0.328266
$233$	−4.61803	−0.302537	−0.151269	−	0.988493i	$-0.548336\pi$
$233$	−4.61803	−0.302537	−0.151269	+	0.988493i	$0.548336\pi$
$234$	11.0000	0.719092
$235$	5.23607	0.341563
$236$	10.8541	0.706542
$237$	−4.47214	−0.290496
$238$	−6.61803	−0.428983
$239$	−20.1246	−1.30175	−0.650876	−	0.759184i	$-0.725598\pi$
$239$	−20.1246	−1.30175	−0.650876	+	0.759184i	$0.725598\pi$
$240$	2.29180	0.147935
$241$	−24.1803	−1.55759	−0.778796	−	0.627277i	$-0.784169\pi$
$241$	−24.1803	−1.55759	−0.778796	+	0.627277i	$0.784169\pi$
$242$	1.23607	0.0794575
$243$	9.65248	0.619207
$244$	4.85410	0.310752
$245$	−14.1803	−0.905949
$246$	0.708204	0.0451534
$247$	5.32624	0.338900
$248$	−24.7984	−1.57470
$249$	−0.180340	−0.0114286
$250$	−0.944272	−0.0597210
$251$	6.27051	0.395791	0.197896	−	0.980223i	$-0.436589\pi$
$251$	6.27051	0.395791	0.197896	+	0.980223i	$0.436589\pi$
$252$	7.47214	0.470700
$253$	−5.29180	−0.332692
$254$	−9.09017	−0.570368
$255$	8.18034	0.512273
$256$	−6.56231	−0.410144
$257$	−26.5967	−1.65906	−0.829530	−	0.558462i	$-0.811391\pi$
$257$	−26.5967	−1.65906	−0.829530	+	0.558462i	$0.811391\pi$
$258$	−2.12461	−0.132273
$259$	−17.7082	−1.10033
$260$	−32.6525	−2.02502
$261$	6.38197	0.395034
$262$	−8.14590	−0.503255
$263$	−8.23607	−0.507858	−0.253929	−	0.967223i	$-0.581723\pi$
$263$	−8.23607	−0.507858	−0.253929	+	0.967223i	$0.581723\pi$
$264$	−2.56231	−0.157699
$265$	17.4164	1.06988
$266$	−0.854102	−0.0523684
$267$	4.14590	0.253725
$268$	19.4164	1.18605
$269$	6.90983	0.421300	0.210650	−	0.977562i	$-0.432442\pi$
$269$	6.90983	0.421300	0.210650	+	0.977562i	$0.432442\pi$
$270$	4.47214	0.272166
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	12.2705	0.744009
$273$	3.85410	0.233261
$274$	4.00000	0.241649
$275$	−16.4164	−0.989947
$276$	−1.09017	−0.0656205
$277$	10.5623	0.634627	0.317314	−	0.948321i	$-0.397219\pi$
$277$	10.5623	0.634627	0.317314	+	0.948321i	$0.397219\pi$
$278$	8.74265	0.524349
$279$	31.6525	1.89498
$280$	11.7082	0.699699
$281$	−14.1803	−0.845928	−0.422964	−	0.906146i	$-0.639010\pi$
$281$	−14.1803	−0.845928	−0.422964	+	0.906146i	$0.639010\pi$
$282$	−0.381966	−0.0227457
$283$	−11.1246	−0.661290	−0.330645	−	0.943755i	$-0.607266\pi$
$283$	−11.1246	−0.661290	−0.330645	+	0.943755i	$0.607266\pi$
$284$	−13.2361	−0.785416
$285$	1.05573	0.0625359
$286$	11.5623	0.683693
$287$	−4.85410	−0.286529
$288$	16.0344	0.944839
$289$	26.7984	1.57637
$290$	4.47214	0.262613
$291$	−1.09017	−0.0639069
$292$	−3.38197	−0.197915
$293$	19.6525	1.14811	0.574055	−	0.818817i	$-0.305370\pi$
$293$	19.6525	1.14811	0.574055	+	0.818817i	$0.305370\pi$
$294$	1.03444	0.0603299
$295$	−21.7082	−1.26390
$296$	−24.4721	−1.42241
$297$	6.70820	0.389249
$298$	5.52786	0.320221
$299$	11.0000	0.636146
$300$	−3.38197	−0.195258
$301$	14.5623	0.839357
$302$	6.12461	0.352432
$303$	−2.32624	−0.133639
$304$	1.58359	0.0908252
$305$	−9.70820	−0.555890
$306$	11.6738	0.667345
$307$	−7.85410	−0.448257	−0.224129	−	0.974560i	$-0.571954\pi$
$307$	−7.85410	−0.448257	−0.224129	+	0.974560i	$0.571954\pi$
$308$	7.85410	0.447529
$309$	−5.50658	−0.313258
$310$	22.1803	1.25976
$311$	8.90983	0.505230	0.252615	−	0.967567i	$-0.418709\pi$
$311$	8.90983	0.505230	0.252615	+	0.967567i	$0.418709\pi$
$312$	5.32624	0.301539
$313$	−0.798374	−0.0451268	−0.0225634	−	0.999745i	$-0.507183\pi$
$313$	−0.798374	−0.0451268	−0.0225634	+	0.999745i	$0.507183\pi$
$314$	−8.03444	−0.453410
$315$	−14.9443	−0.842014
$316$	18.9443	1.06570
$317$	12.7984	0.718828	0.359414	−	0.933178i	$-0.382977\pi$
$317$	12.7984	0.718828	0.359414	+	0.933178i	$0.382977\pi$
$318$	−1.27051	−0.0712467
$319$	6.70820	0.375587
$320$	−0.763932	−0.0427051
$321$	−0.437694	−0.0244297
$322$	−1.76393	−0.0983001
$323$	5.65248	0.314512
$324$	−12.4721	−0.692896
$325$	34.1246	1.89289
$326$	−0.888544	−0.0492119
$327$	1.38197	0.0764229
$328$	−6.70820	−0.370399
$329$	2.61803	0.144337
$330$	2.29180	0.126159
$331$	−1.81966	−0.100018	−0.0500088	−	0.998749i	$-0.515925\pi$
$331$	−1.81966	−0.100018	−0.0500088	+	0.998749i	$0.515925\pi$
$332$	0.763932	0.0419262
$333$	31.2361	1.71173
$334$	−0.270510	−0.0148016
$335$	−38.8328	−2.12166
$336$	1.14590	0.0625139
$337$	1.29180	0.0703686	0.0351843	−	0.999381i	$-0.488798\pi$
$337$	1.29180	0.0703686	0.0351843	+	0.999381i	$0.488798\pi$
$338$	−16.0000	−0.870285
$339$	6.20163	0.336826
$340$	−34.6525	−1.87929
$341$	33.2705	1.80170
$342$	1.50658	0.0814664
$343$	−18.4164	−0.994393
$344$	20.1246	1.08505
$345$	2.18034	0.117386
$346$	−5.56231	−0.299031
$347$	20.0344	1.07551	0.537753	−	0.843103i	$-0.319273\pi$
$347$	20.0344	1.07551	0.537753	+	0.843103i	$0.319273\pi$
$348$	1.38197	0.0740812
$349$	−14.2705	−0.763883	−0.381941	−	0.924187i	$-0.624744\pi$
$349$	−14.2705	−0.763883	−0.381941	+	0.924187i	$0.624744\pi$
$350$	−5.47214	−0.292498
$351$	−13.9443	−0.744290
$352$	16.8541	0.898327
$353$	−26.1246	−1.39047	−0.695236	−	0.718781i	$-0.744700\pi$
$353$	−26.1246	−1.39047	−0.695236	+	0.718781i	$0.744700\pi$
$354$	1.58359	0.0841670
$355$	26.4721	1.40500
$356$	−17.5623	−0.930800
$357$	4.09017	0.216475
$358$	15.0000	0.792775
$359$	22.3607	1.18015	0.590076	−	0.807348i	$-0.299098\pi$
$359$	22.3607	1.18015	0.590076	+	0.807348i	$0.299098\pi$
$360$	−20.6525	−1.08848
$361$	−18.2705	−0.961606
$362$	1.85410	0.0974494
$363$	−0.763932	−0.0400960
$364$	−16.3262	−0.855727
$365$	6.76393	0.354040
$366$	0.708204	0.0370184
$367$	−26.4721	−1.38183	−0.690917	−	0.722934i	$-0.742793\pi$
$367$	−26.4721	−1.38183	−0.690917	+	0.722934i	$0.742793\pi$
$368$	3.27051	0.170487
$369$	8.56231	0.445736
$370$	21.8885	1.13793
$371$	8.70820	0.452107
$372$	6.85410	0.355369
$373$	19.6525	1.01757	0.508783	−	0.860895i	$-0.330095\pi$
$373$	19.6525	1.01757	0.508783	+	0.860895i	$0.330095\pi$
$374$	12.2705	0.634493
$375$	0.583592	0.0301366
$376$	3.61803	0.186586
$377$	−13.9443	−0.718167
$378$	2.23607	0.115011
$379$	15.0000	0.770498	0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000	0.770498	0.385249	+	0.922813i	$0.374116\pi$
$380$	−4.47214	−0.229416
$381$	5.61803	0.287821
$382$	−11.9656	−0.612211
$383$	−6.65248	−0.339926	−0.169963	−	0.985450i	$-0.554365\pi$
$383$	−6.65248	−0.339926	−0.169963	+	0.985450i	$0.554365\pi$
$384$	4.34752	0.221859
$385$	−15.7082	−0.800564
$386$	−15.4377	−0.785758
$387$	−25.6869	−1.30574
$388$	4.61803	0.234445
$389$	1.18034	0.0598456	0.0299228	−	0.999552i	$-0.490474\pi$
$389$	1.18034	0.0598456	0.0299228	+	0.999552i	$0.490474\pi$
$390$	−4.76393	−0.241231
$391$	11.6738	0.590368
$392$	−9.79837	−0.494893
$393$	5.03444	0.253954
$394$	0.506578	0.0255210
$395$	−37.8885	−1.90638
$396$	−13.8541	−0.696195
$397$	−18.8328	−0.945192	−0.472596	−	0.881279i	$-0.656683\pi$
$397$	−18.8328	−0.945192	−0.472596	+	0.881279i	$0.656683\pi$
$398$	−5.72949	−0.287193
$399$	0.527864	0.0264263
$400$	10.1459	0.507295
$401$	5.81966	0.290620	0.145310	−	0.989386i	$-0.453582\pi$
$401$	5.81966	0.290620	0.145310	+	0.989386i	$0.453582\pi$
$402$	2.83282	0.141288
$403$	−69.1591	−3.44506
$404$	9.85410	0.490260
$405$	24.9443	1.23949
$406$	2.23607	0.110974
$407$	32.8328	1.62746
$408$	5.65248	0.279839
$409$	−2.96556	−0.146637	−0.0733187	−	0.997309i	$-0.523359\pi$
$409$	−2.96556	−0.146637	−0.0733187	+	0.997309i	$0.523359\pi$
$410$	6.00000	0.296319
$411$	−2.47214	−0.121941
$412$	23.3262	1.14920
$413$	−10.8541	−0.534095
$414$	3.11146	0.152920
$415$	−1.52786	−0.0749999
$416$	−35.0344	−1.71770
$417$	−5.40325	−0.264598
$418$	1.58359	0.0774560
$419$	10.5279	0.514320	0.257160	−	0.966369i	$-0.417213\pi$
$419$	10.5279	0.514320	0.257160	+	0.966369i	$0.417213\pi$
$420$	−3.23607	−0.157904
$421$	−30.3607	−1.47969	−0.739844	−	0.672778i	$-0.765101\pi$
$421$	−30.3607	−1.47969	−0.739844	+	0.672778i	$0.765101\pi$
$422$	−0.618034	−0.0300854
$423$	−4.61803	−0.224536
$424$	12.0344	0.584444
$425$	36.2148	1.75667
$426$	−1.93112	−0.0935629
$427$	−4.85410	−0.234906
$428$	1.85410	0.0896214
$429$	−7.14590	−0.345007
$430$	−18.0000	−0.868037
$431$	−4.90983	−0.236498	−0.118249	−	0.992984i	$-0.537728\pi$
$431$	−4.90983	−0.236498	−0.118249	+	0.992984i	$0.537728\pi$
$432$	−4.14590	−0.199470
$433$	5.70820	0.274319	0.137159	−	0.990549i	$-0.456203\pi$
$433$	5.70820	0.274319	0.137159	+	0.990549i	$0.456203\pi$
$434$	11.0902	0.532345
$435$	−2.76393	−0.132520
$436$	−5.85410	−0.280361
$437$	1.50658	0.0720694
$438$	−0.493422	−0.0235766
$439$	13.9443	0.665524	0.332762	−	0.943011i	$-0.392019\pi$
$439$	13.9443	0.665524	0.332762	+	0.943011i	$0.392019\pi$
$440$	−21.7082	−1.03490
$441$	12.5066	0.595551
$442$	−25.5066	−1.21322
$443$	28.7984	1.36825	0.684126	−	0.729364i	$-0.260184\pi$
$443$	28.7984	1.36825	0.684126	+	0.729364i	$0.260184\pi$
$444$	6.76393	0.321002
$445$	35.1246	1.66507
$446$	2.97871	0.141046
$447$	−3.41641	−0.161591
$448$	−0.381966	−0.0180462
$449$	27.7639	1.31026	0.655130	−	0.755516i	$-0.272614\pi$
$449$	27.7639	1.31026	0.655130	+	0.755516i	$0.272614\pi$
$450$	9.65248	0.455022
$451$	9.00000	0.423793
$452$	−26.2705	−1.23566
$453$	−3.78522	−0.177845
$454$	−12.9098	−0.605888
$455$	32.6525	1.53077
$456$	0.729490	0.0341615
$457$	−9.43769	−0.441477	−0.220738	−	0.975333i	$-0.570847\pi$
$457$	−9.43769	−0.441477	−0.220738	+	0.975333i	$0.570847\pi$
$458$	−2.03444	−0.0950632
$459$	−14.7984	−0.690729
$460$	−9.23607	−0.430634
$461$	23.9098	1.11359	0.556796	−	0.830649i	$-0.312031\pi$
$461$	23.9098	1.11359	0.556796	+	0.830649i	$0.312031\pi$
$462$	1.14590	0.0533120
$463$	1.43769	0.0668153	0.0334077	−	0.999442i	$-0.489364\pi$
$463$	1.43769	0.0668153	0.0334077	+	0.999442i	$0.489364\pi$
$464$	−4.14590	−0.192468
$465$	−13.7082	−0.635703
$466$	2.85410	0.132214
$467$	38.7771	1.79439	0.897195	−	0.441635i	$-0.145601\pi$
$467$	38.7771	1.79439	0.897195	+	0.441635i	$0.145601\pi$
$468$	28.7984	1.33121
$469$	−19.4164	−0.896566
$470$	−3.23607	−0.149269
$471$	4.96556	0.228801
$472$	−15.0000	−0.690431
$473$	−27.0000	−1.24146
$474$	2.76393	0.126952
$475$	4.67376	0.214447
$476$	−17.3262	−0.794147
$477$	−15.3607	−0.703317
$478$	12.4377	0.568887
$479$	−36.7082	−1.67724	−0.838620	−	0.544716i	$-0.816637\pi$
$479$	−36.7082	−1.67724	−0.838620	+	0.544716i	$0.816637\pi$
$480$	−6.94427	−0.316961
$481$	−68.2492	−3.11190
$482$	14.9443	0.680693
$483$	1.09017	0.0496045
$484$	3.23607	0.147094
$485$	−9.23607	−0.419388
$486$	−5.96556	−0.270603
$487$	15.5623	0.705195	0.352598	−	0.935775i	$-0.385298\pi$
$487$	15.5623	0.705195	0.352598	+	0.935775i	$0.385298\pi$
$488$	−6.70820	−0.303666
$489$	0.549150	0.0248334
$490$	8.76393	0.395914
$491$	−19.1803	−0.865597	−0.432798	−	0.901491i	$-0.642474\pi$
$491$	−19.1803	−0.865597	−0.432798	+	0.901491i	$0.642474\pi$
$492$	1.85410	0.0835894
$493$	−14.7984	−0.666485
$494$	−3.29180	−0.148105
$495$	27.7082	1.24539
$496$	−20.5623	−0.923275
$497$	13.2361	0.593719
$498$	0.111456	0.00499447
$499$	21.5066	0.962767	0.481383	−	0.876510i	$-0.340135\pi$
$499$	21.5066	0.962767	0.481383	+	0.876510i	$0.340135\pi$
$500$	−2.47214	−0.110557
$501$	0.167184	0.00746924
$502$	−3.87539	−0.172967
$503$	17.6180	0.785549	0.392775	−	0.919635i	$-0.371515\pi$
$503$	17.6180	0.785549	0.392775	+	0.919635i	$0.371515\pi$
$504$	−10.3262	−0.459967
$505$	−19.7082	−0.877004
$506$	3.27051	0.145392
$507$	9.88854	0.439166
$508$	−23.7984	−1.05588
$509$	−2.88854	−0.128032	−0.0640162	−	0.997949i	$-0.520391\pi$
$509$	−2.88854	−0.128032	−0.0640162	+	0.997949i	$0.520391\pi$
$510$	−5.05573	−0.223871
$511$	3.38197	0.149609
$512$	−18.7082	−0.826794
$513$	−1.90983	−0.0843211
$514$	16.4377	0.725036
$515$	−46.6525	−2.05575
$516$	−5.56231	−0.244867
$517$	−4.85410	−0.213483
$518$	10.9443	0.480864
$519$	3.43769	0.150898
$520$	45.1246	1.97885
$521$	21.2705	0.931878	0.465939	−	0.884817i	$-0.345717\pi$
$521$	21.2705	0.931878	0.465939	+	0.884817i	$0.345717\pi$
$522$	−3.94427	−0.172636
$523$	32.0902	1.40321	0.701603	−	0.712568i	$-0.252468\pi$
$523$	32.0902	1.40321	0.701603	+	0.712568i	$0.252468\pi$
$524$	−21.3262	−0.931641
$525$	3.38197	0.147601
$526$	5.09017	0.221942
$527$	−73.3951	−3.19714
$528$	−2.12461	−0.0924619
$529$	−19.8885	−0.864719
$530$	−10.7639	−0.467555
$531$	19.1459	0.830861
$532$	−2.23607	−0.0969458
$533$	−18.7082	−0.810342
$534$	−2.56231	−0.110882
$535$	−3.70820	−0.160320
$536$	−26.8328	−1.15900
$537$	−9.27051	−0.400052
$538$	−4.27051	−0.184115
$539$	13.1459	0.566234
$540$	11.7082	0.503841
$541$	16.2705	0.699524	0.349762	−	0.936839i	$-0.386262\pi$
$541$	16.2705	0.699524	0.349762	+	0.936839i	$0.386262\pi$
$542$	−1.23607	−0.0530937
$543$	−1.14590	−0.0491752
$544$	−37.1803	−1.59409
$545$	11.7082	0.501524
$546$	−2.38197	−0.101939
$547$	21.2918	0.910371	0.455186	−	0.890397i	$-0.349573\pi$
$547$	21.2918	0.910371	0.455186	+	0.890397i	$0.349573\pi$
$548$	10.4721	0.447347
$549$	8.56231	0.365430
$550$	10.1459	0.432623
$551$	−1.90983	−0.0813615
$552$	1.50658	0.0641242
$553$	−18.9443	−0.805592
$554$	−6.52786	−0.277342
$555$	−13.5279	−0.574226
$556$	22.8885	0.970690
$557$	38.6525	1.63776	0.818879	−	0.573966i	$-0.194596\pi$
$557$	38.6525	1.63776	0.818879	+	0.573966i	$0.194596\pi$
$558$	−19.5623	−0.828138
$559$	56.1246	2.37382
$560$	9.70820	0.410246
$561$	−7.58359	−0.320180
$562$	8.76393	0.369684
$563$	−10.4721	−0.441348	−0.220674	−	0.975348i	$-0.570826\pi$
$563$	−10.4721	−0.441348	−0.220674	+	0.975348i	$0.570826\pi$
$564$	−1.00000	−0.0421076
$565$	52.5410	2.21042
$566$	6.87539	0.288994
$567$	12.4721	0.523780
$568$	18.2918	0.767507
$569$	−27.7639	−1.16392	−0.581962	−	0.813216i	$-0.697715\pi$
$569$	−27.7639	−1.16392	−0.581962	+	0.813216i	$0.697715\pi$
$570$	−0.652476	−0.0273292
$571$	−15.3607	−0.642824	−0.321412	−	0.946939i	$-0.604158\pi$
$571$	−15.3607	−0.642824	−0.321412	+	0.946939i	$0.604158\pi$
$572$	30.2705	1.26567
$573$	7.39512	0.308936
$574$	3.00000	0.125218
$575$	9.65248	0.402536
$576$	0.673762	0.0280734
$577$	13.8541	0.576754	0.288377	−	0.957517i	$-0.406884\pi$
$577$	13.8541	0.576754	0.288377	+	0.957517i	$0.406884\pi$
$578$	−16.5623	−0.688901
$579$	9.54102	0.396511
$580$	11.7082	0.486157
$581$	−0.763932	−0.0316932
$582$	0.673762	0.0279283
$583$	−16.1459	−0.668695
$584$	4.67376	0.193402
$585$	−57.5967	−2.38133
$586$	−12.1459	−0.501742
$587$	6.49342	0.268012	0.134006	−	0.990981i	$-0.457216\pi$
$587$	6.49342	0.268012	0.134006	+	0.990981i	$0.457216\pi$
$588$	2.70820	0.111684
$589$	−9.47214	−0.390293
$590$	13.4164	0.552345
$591$	−0.313082	−0.0128785
$592$	−20.2918	−0.833988
$593$	−19.0902	−0.783939	−0.391970	−	0.919978i	$-0.628206\pi$
$593$	−19.0902	−0.783939	−0.391970	+	0.919978i	$0.628206\pi$
$594$	−4.14590	−0.170108
$595$	34.6525	1.42061
$596$	14.4721	0.592802
$597$	3.54102	0.144924
$598$	−6.79837	−0.278006
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	4.67376	0.190806
$601$	27.0000	1.10135	0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000	1.10135	0.550676	+	0.834719i	$0.314370\pi$
$602$	−9.00000	−0.366813
$603$	34.2492	1.39474
$604$	16.0344	0.652432
$605$	−6.47214	−0.263130
$606$	1.43769	0.0584023
$607$	39.1803	1.59028	0.795140	−	0.606425i	$-0.207397\pi$
$607$	39.1803	1.59028	0.795140	+	0.606425i	$0.207397\pi$
$608$	−4.79837	−0.194600
$609$	−1.38197	−0.0560001
$610$	6.00000	0.242933
$611$	10.0902	0.408205
$612$	30.5623	1.23541
$613$	1.23607	0.0499243	0.0249622	−	0.999688i	$-0.492053\pi$
$613$	1.23607	0.0499243	0.0249622	+	0.999688i	$0.492053\pi$
$614$	4.85410	0.195896
$615$	−3.70820	−0.149529
$616$	−10.8541	−0.437324
$617$	3.52786	0.142026	0.0710132	−	0.997475i	$-0.477377\pi$
$617$	3.52786	0.142026	0.0710132	+	0.997475i	$0.477377\pi$
$618$	3.40325	0.136899
$619$	30.0000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$620$	58.0689	2.33210
$621$	−3.94427	−0.158278
$622$	−5.50658	−0.220794
$623$	17.5623	0.703619
$624$	4.41641	0.176798
$625$	−22.4164	−0.896656
$626$	0.493422	0.0197211
$627$	−0.978714	−0.0390861
$628$	−21.0344	−0.839366
$629$	−72.4296	−2.88796
$630$	9.23607	0.367974
$631$	12.0000	0.477712	0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000	0.477712	0.238856	+	0.971055i	$0.423228\pi$
$632$	−26.1803	−1.04140
$633$	0.381966	0.0151818
$634$	−7.90983	−0.314139
$635$	47.5967	1.88882
$636$	−3.32624	−0.131894
$637$	−27.3262	−1.08270
$638$	−4.14590	−0.164138
$639$	−23.3475	−0.923614
$640$	36.8328	1.45594
$641$	−29.1803	−1.15255	−0.576277	−	0.817254i	$-0.695495\pi$
$641$	−29.1803	−1.15255	−0.576277	+	0.817254i	$0.695495\pi$
$642$	0.270510	0.0106762
$643$	5.38197	0.212244	0.106122	−	0.994353i	$-0.466157\pi$
$643$	5.38197	0.212244	0.106122	+	0.994353i	$0.466157\pi$
$644$	−4.61803	−0.181976
$645$	11.1246	0.438031
$646$	−3.49342	−0.137447
$647$	25.3607	0.997031	0.498516	−	0.866881i	$-0.333879\pi$
$647$	25.3607	0.997031	0.498516	+	0.866881i	$0.333879\pi$
$648$	17.2361	0.677097
$649$	20.1246	0.789960
$650$	−21.0902	−0.827225
$651$	−6.85410	−0.268633
$652$	−2.32624	−0.0911025
$653$	21.9656	0.859579	0.429789	−	0.902929i	$-0.358588\pi$
$653$	21.9656	0.859579	0.429789	+	0.902929i	$0.358588\pi$
$654$	−0.854102	−0.0333980
$655$	42.6525	1.66657
$656$	−5.56231	−0.217172
$657$	−5.96556	−0.232739
$658$	−1.61803	−0.0630775
$659$	−37.3607	−1.45537	−0.727683	−	0.685914i	$-0.759403\pi$
$659$	−37.3607	−1.45537	−0.727683	+	0.685914i	$0.759403\pi$
$660$	6.00000	0.233550
$661$	8.90983	0.346552	0.173276	−	0.984873i	$-0.444565\pi$
$661$	8.90983	0.346552	0.173276	+	0.984873i	$0.444565\pi$
$662$	1.12461	0.0437093
$663$	15.7639	0.612220
$664$	−1.05573	−0.0409702
$665$	4.47214	0.173422
$666$	−19.3050	−0.748052
$667$	−3.94427	−0.152723
$668$	−0.708204	−0.0274012
$669$	−1.84095	−0.0711751
$670$	24.0000	0.927201
$671$	9.00000	0.347441
$672$	−3.47214	−0.133941
$673$	−15.2705	−0.588635	−0.294317	−	0.955708i	$-0.595092\pi$
$673$	−15.2705	−0.588635	−0.294317	+	0.955708i	$0.595092\pi$
$674$	−0.798374	−0.0307522
$675$	−12.2361	−0.470966
$676$	−41.8885	−1.61110
$677$	−5.29180	−0.203380	−0.101690	−	0.994816i	$-0.532425\pi$
$677$	−5.29180	−0.203380	−0.101690	+	0.994816i	$0.532425\pi$
$678$	−3.83282	−0.147198
$679$	−4.61803	−0.177224
$680$	47.8885	1.83644
$681$	7.97871	0.305745
$682$	−20.5623	−0.787371
$683$	1.36068	0.0520650	0.0260325	−	0.999661i	$-0.491713\pi$
$683$	1.36068	0.0520650	0.0260325	+	0.999661i	$0.491713\pi$
$684$	3.94427	0.150813
$685$	−20.9443	−0.800239
$686$	11.3820	0.434565
$687$	1.25735	0.0479711
$688$	16.6869	0.636183
$689$	33.5623	1.27862
$690$	−1.34752	−0.0512994
$691$	24.3607	0.926724	0.463362	−	0.886169i	$-0.346643\pi$
$691$	24.3607	0.926724	0.463362	+	0.886169i	$0.346643\pi$
$692$	−14.5623	−0.553576
$693$	13.8541	0.526274
$694$	−12.3820	−0.470013
$695$	−45.7771	−1.73642
$696$	−1.90983	−0.0723919
$697$	−19.8541	−0.752028
$698$	8.81966	0.333829
$699$	−1.76393	−0.0667180
$700$	−14.3262	−0.541481
$701$	−6.09017	−0.230023	−0.115011	−	0.993364i	$-0.536690\pi$
$701$	−6.09017	−0.230023	−0.115011	+	0.993364i	$0.536690\pi$
$702$	8.61803	0.325267
$703$	−9.34752	−0.352549
$704$	0.708204	0.0266914
$705$	2.00000	0.0753244
$706$	16.1459	0.607659
$707$	−9.85410	−0.370602
$708$	4.14590	0.155812
$709$	−5.85410	−0.219855	−0.109928	−	0.993940i	$-0.535062\pi$
$709$	−5.85410	−0.219855	−0.109928	+	0.993940i	$0.535062\pi$
$710$	−16.3607	−0.614005
$711$	33.4164	1.25321
$712$	24.2705	0.909576
$713$	−19.5623	−0.732614
$714$	−2.52786	−0.0946029
$715$	−60.5410	−2.26411
$716$	39.2705	1.46761
$717$	−7.68692	−0.287073
$718$	−13.8197	−0.515745
$719$	−10.8541	−0.404790	−0.202395	−	0.979304i	$-0.564872\pi$
$719$	−10.8541	−0.404790	−0.202395	+	0.979304i	$0.564872\pi$
$720$	−17.1246	−0.638197
$721$	−23.3262	−0.868714
$722$	11.2918	0.420237
$723$	−9.23607	−0.343493
$724$	4.85410	0.180401
$725$	−12.2361	−0.454436
$726$	0.472136	0.0175226
$727$	37.2705	1.38229	0.691143	−	0.722718i	$-0.257107\pi$
$727$	37.2705	1.38229	0.691143	+	0.722718i	$0.257107\pi$
$728$	22.5623	0.836215
$729$	−19.4377	−0.719915
$730$	−4.18034	−0.154721
$731$	59.5623	2.20299
$732$	1.85410	0.0685296
$733$	14.1246	0.521704	0.260852	−	0.965379i	$-0.415996\pi$
$733$	14.1246	0.521704	0.260852	+	0.965379i	$0.415996\pi$
$734$	16.3607	0.603884
$735$	−5.41641	−0.199787
$736$	−9.90983	−0.365281
$737$	36.0000	1.32608
$738$	−5.29180	−0.194794
$739$	35.8541	1.31891	0.659457	−	0.751742i	$-0.270786\pi$
$739$	35.8541	1.31891	0.659457	+	0.751742i	$0.270786\pi$
$740$	57.3050	2.10657
$741$	2.03444	0.0747371
$742$	−5.38197	−0.197578
$743$	0.180340	0.00661603	0.00330801	−	0.999995i	$-0.498947\pi$
$743$	0.180340	0.00661603	0.00330801	+	0.999995i	$0.498947\pi$
$744$	−9.47214	−0.347265
$745$	−28.9443	−1.06044
$746$	−12.1459	−0.444693
$747$	1.34752	0.0493033
$748$	32.1246	1.17459
$749$	−1.85410	−0.0677474
$750$	−0.360680	−0.0131702
$751$	−29.6312	−1.08126	−0.540629	−	0.841261i	$-0.681814\pi$
$751$	−29.6312	−1.08126	−0.540629	+	0.841261i	$0.681814\pi$
$752$	3.00000	0.109399
$753$	2.39512	0.0872831
$754$	8.61803	0.313850
$755$	−32.0689	−1.16711
$756$	5.85410	0.212912
$757$	1.94427	0.0706658	0.0353329	−	0.999376i	$-0.488751\pi$
$757$	1.94427	0.0706658	0.0353329	+	0.999376i	$0.488751\pi$
$758$	−9.27051	−0.336720
$759$	−2.02129	−0.0733680
$760$	6.18034	0.224184
$761$	0.819660	0.0297127	0.0148563	−	0.999890i	$-0.495271\pi$
$761$	0.819660	0.0297127	0.0148563	+	0.999890i	$0.495271\pi$
$762$	−3.47214	−0.125782
$763$	5.85410	0.211933
$764$	−31.3262	−1.13334
$765$	−61.1246	−2.20997
$766$	4.11146	0.148553
$767$	−41.8328	−1.51050
$768$	−2.50658	−0.0904483
$769$	−6.70820	−0.241904	−0.120952	−	0.992658i	$-0.538595\pi$
$769$	−6.70820	−0.241904	−0.120952	+	0.992658i	$0.538595\pi$
$770$	9.70820	0.349859
$771$	−10.1591	−0.365869
$772$	−40.4164	−1.45462
$773$	−21.9787	−0.790519	−0.395260	−	0.918569i	$-0.629345\pi$
$773$	−21.9787	−0.790519	−0.395260	+	0.918569i	$0.629345\pi$
$774$	15.8754	0.570629
$775$	−60.6869	−2.17994
$776$	−6.38197	−0.229099
$777$	−6.76393	−0.242655
$778$	−0.729490	−0.0261535
$779$	−2.56231	−0.0918041
$780$	−12.4721	−0.446574
$781$	−24.5410	−0.878147
$782$	−7.21478	−0.258000
$783$	5.00000	0.178685
$784$	−8.12461	−0.290165
$785$	42.0689	1.50150
$786$	−3.11146	−0.110982
$787$	13.1246	0.467842	0.233921	−	0.972256i	$-0.424844\pi$
$787$	13.1246	0.467842	0.233921	+	0.972256i	$0.424844\pi$
$788$	1.32624	0.0472453
$789$	−3.14590	−0.111997
$790$	23.4164	0.833118
$791$	26.2705	0.934072
$792$	19.1459	0.680320
$793$	−18.7082	−0.664348
$794$	11.6393	0.413064
$795$	6.65248	0.235939
$796$	−15.0000	−0.531661
$797$	−38.8328	−1.37553	−0.687764	−	0.725934i	$-0.741408\pi$
$797$	−38.8328	−1.37553	−0.687764	+	0.725934i	$0.741408\pi$
$798$	−0.326238	−0.0115487
$799$	10.7082	0.378829
$800$	−30.7426	−1.08692
$801$	−30.9787	−1.09458
$802$	−3.59675	−0.127006
$803$	−6.27051	−0.221281
$804$	7.41641	0.261557
$805$	9.23607	0.325529
$806$	42.7426	1.50555
$807$	2.63932	0.0929085
$808$	−13.6180	−0.479081
$809$	7.68692	0.270258	0.135129	−	0.990828i	$-0.456855\pi$
$809$	7.68692	0.270258	0.135129	+	0.990828i	$0.456855\pi$
$810$	−15.4164	−0.541677
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	5.85410	0.205439
$813$	0.763932	0.0267923
$814$	−20.2918	−0.711227
$815$	4.65248	0.162969
$816$	4.68692	0.164075
$817$	7.68692	0.268931
$818$	1.83282	0.0640829
$819$	−28.7984	−1.00630
$820$	15.7082	0.548554
$821$	−19.9098	−0.694858	−0.347429	−	0.937706i	$-0.612945\pi$
$821$	−19.9098	−0.694858	−0.347429	+	0.937706i	$0.612945\pi$
$822$	1.52786	0.0532904
$823$	23.7984	0.829559	0.414780	−	0.909922i	$-0.363859\pi$
$823$	23.7984	0.829559	0.414780	+	0.909922i	$0.363859\pi$
$824$	−32.2361	−1.12300
$825$	−6.27051	−0.218311
$826$	6.70820	0.233408
$827$	18.9787	0.659955	0.329977	−	0.943989i	$-0.392959\pi$
$827$	18.9787	0.659955	0.329977	+	0.943989i	$0.392959\pi$
$828$	8.14590	0.283090
$829$	−2.63932	−0.0916674	−0.0458337	−	0.998949i	$-0.514594\pi$
$829$	−2.63932	−0.0916674	−0.0458337	+	0.998949i	$0.514594\pi$
$830$	0.944272	0.0327762
$831$	4.03444	0.139953
$832$	−1.47214	−0.0510371
$833$	−29.0000	−1.00479
$834$	3.33939	0.115634
$835$	1.41641	0.0490168
$836$	4.14590	0.143389
$837$	24.7984	0.857157
$838$	−6.50658	−0.224766
$839$	−19.7984	−0.683516	−0.341758	−	0.939788i	$-0.611022\pi$
$839$	−19.7984	−0.683516	−0.341758	+	0.939788i	$0.611022\pi$
$840$	4.47214	0.154303
$841$	−24.0000	−0.827586
$842$	18.7639	0.646648
$843$	−5.41641	−0.186551
$844$	−1.61803	−0.0556950
$845$	83.7771	2.88202
$846$	2.85410	0.0981260
$847$	−3.23607	−0.111193
$848$	9.97871	0.342670
$849$	−4.24922	−0.145833
$850$	−22.3820	−0.767695
$851$	−19.3050	−0.661765
$852$	−5.05573	−0.173206
$853$	−8.68692	−0.297434	−0.148717	−	0.988880i	$-0.547514\pi$
$853$	−8.68692	−0.297434	−0.148717	+	0.988880i	$0.547514\pi$
$854$	3.00000	0.102658
$855$	−7.88854	−0.269783
$856$	−2.56231	−0.0875778
$857$	40.1591	1.37181	0.685904	−	0.727692i	$-0.259407\pi$
$857$	40.1591	1.37181	0.685904	+	0.727692i	$0.259407\pi$
$858$	4.41641	0.150774
$859$	−10.7295	−0.366085	−0.183043	−	0.983105i	$-0.558595\pi$
$859$	−10.7295	−0.366085	−0.183043	+	0.983105i	$0.558595\pi$
$860$	−47.1246	−1.60694
$861$	−1.85410	−0.0631876
$862$	3.03444	0.103353
$863$	7.41641	0.252457	0.126229	−	0.992001i	$-0.459713\pi$
$863$	7.41641	0.252457	0.126229	+	0.992001i	$0.459713\pi$
$864$	12.5623	0.427378
$865$	29.1246	0.990267
$866$	−3.52786	−0.119882
$867$	10.2361	0.347635
$868$	29.0344	0.985493
$869$	35.1246	1.19152
$870$	1.70820	0.0579135
$871$	−74.8328	−2.53561
$872$	8.09017	0.273968
$873$	8.14590	0.275697
$874$	−0.931116	−0.0314955
$875$	2.47214	0.0835734
$876$	−1.29180	−0.0436457
$877$	18.7295	0.632450	0.316225	−	0.948684i	$-0.397585\pi$
$877$	18.7295	0.632450	0.316225	+	0.948684i	$0.397585\pi$
$878$	−8.61803	−0.290845
$879$	7.50658	0.253191
$880$	−18.0000	−0.606780
$881$	−28.4508	−0.958533	−0.479267	−	0.877669i	$-0.659097\pi$
$881$	−28.4508	−0.958533	−0.479267	+	0.877669i	$0.659097\pi$
$882$	−7.72949	−0.260265
$883$	−23.5623	−0.792935	−0.396467	−	0.918049i	$-0.629764\pi$
$883$	−23.5623	−0.792935	−0.396467	+	0.918049i	$0.629764\pi$
$884$	−66.7771	−2.24596
$885$	−8.29180	−0.278726
$886$	−17.7984	−0.597948
$887$	34.6312	1.16280	0.581401	−	0.813617i	$-0.302505\pi$
$887$	34.6312	1.16280	0.581401	+	0.813617i	$0.302505\pi$
$888$	−9.34752	−0.313682
$889$	23.7984	0.798172
$890$	−21.7082	−0.727661
$891$	−23.1246	−0.774704
$892$	7.79837	0.261109
$893$	1.38197	0.0462457
$894$	2.11146	0.0706177
$895$	−78.5410	−2.62534
$896$	18.4164	0.615249
$897$	4.20163	0.140288
$898$	−17.1591	−0.572605
$899$	24.7984	0.827072
$900$	25.2705	0.842350
$901$	35.6180	1.18661
$902$	−5.56231	−0.185205
$903$	5.56231	0.185102
$904$	36.3050	1.20748
$905$	−9.70820	−0.322712
$906$	2.33939	0.0777211
$907$	45.3607	1.50618	0.753088	−	0.657919i	$-0.228563\pi$
$907$	45.3607	1.50618	0.753088	+	0.657919i	$0.228563\pi$
$908$	−33.7984	−1.12164
$909$	17.3820	0.576523
$910$	−20.1803	−0.668972
$911$	−44.6312	−1.47870	−0.739349	−	0.673323i	$-0.764866\pi$
$911$	−44.6312	−1.47870	−0.739349	+	0.673323i	$0.764866\pi$
$912$	0.604878	0.0200295
$913$	1.41641	0.0468763
$914$	5.83282	0.192932
$915$	−3.70820	−0.122589
$916$	−5.32624	−0.175984
$917$	21.3262	0.704254
$918$	9.14590	0.301860
$919$	1.83282	0.0604590	0.0302295	−	0.999543i	$-0.490376\pi$
$919$	1.83282	0.0604590	0.0302295	+	0.999543i	$0.490376\pi$
$920$	12.7639	0.420814
$921$	−3.00000	−0.0988534
$922$	−14.7771	−0.486657
$923$	51.0132	1.67912
$924$	3.00000	0.0986928
$925$	−59.8885	−1.96912
$926$	−0.888544	−0.0291994
$927$	41.1459	1.35141
$928$	12.5623	0.412378
$929$	−44.3951	−1.45656	−0.728278	−	0.685281i	$-0.759679\pi$
$929$	−44.3951	−1.45656	−0.728278	+	0.685281i	$0.759679\pi$
$930$	8.47214	0.277812
$931$	−3.74265	−0.122660
$932$	7.47214	0.244758
$933$	3.40325	0.111417
$934$	−23.9656	−0.784177
$935$	−64.2492	−2.10117
$936$	−39.7984	−1.30085
$937$	−22.1246	−0.722780	−0.361390	−	0.932415i	$-0.617698\pi$
$937$	−22.1246	−0.722780	−0.361390	+	0.932415i	$0.617698\pi$
$938$	12.0000	0.391814
$939$	−0.304952	−0.00995172
$940$	−8.47214	−0.276331
$941$	35.0902	1.14391	0.571953	−	0.820286i	$-0.306186\pi$
$941$	35.0902	1.14391	0.571953	+	0.820286i	$0.306186\pi$
$942$	−3.06888	−0.0999896
$943$	−5.29180	−0.172325
$944$	−12.4377	−0.404812
$945$	−11.7082	−0.380868
$946$	16.6869	0.542538
$947$	7.47214	0.242812	0.121406	−	0.992603i	$-0.461260\pi$
$947$	7.47214	0.242812	0.121406	+	0.992603i	$0.461260\pi$
$948$	7.23607	0.235017
$949$	13.0344	0.423116
$950$	−2.88854	−0.0937167
$951$	4.88854	0.158522
$952$	23.9443	0.776038
$953$	24.6525	0.798572	0.399286	−	0.916826i	$-0.369258\pi$
$953$	24.6525	0.798572	0.399286	+	0.916826i	$0.369258\pi$
$954$	9.49342	0.307361
$955$	62.6525	2.02739
$956$	32.5623	1.05314
$957$	2.56231	0.0828276
$958$	22.6869	0.732981
$959$	−10.4721	−0.338163
$960$	−0.291796	−0.00941768
$961$	91.9919	2.96748
$962$	42.1803	1.35995
$963$	3.27051	0.105391
$964$	39.1246	1.26012
$965$	80.8328	2.60210
$966$	−0.673762	−0.0216779
$967$	33.0000	1.06121	0.530604	−	0.847620i	$-0.321965\pi$
$967$	33.0000	1.06121	0.530604	+	0.847620i	$0.321965\pi$
$968$	−4.47214	−0.143740
$969$	2.15905	0.0693588
$970$	5.70820	0.183279
$971$	−50.3607	−1.61615	−0.808076	−	0.589079i	$-0.799491\pi$
$971$	−50.3607	−1.61615	−0.808076	+	0.589079i	$0.799491\pi$
$972$	−15.6180	−0.500949
$973$	−22.8885	−0.733773
$974$	−9.61803	−0.308182
$975$	13.0344	0.417436
$976$	−5.56231	−0.178045
$977$	−56.3951	−1.80424	−0.902120	−	0.431485i	$-0.857990\pi$
$977$	−56.3951	−1.80424	−0.902120	+	0.431485i	$0.857990\pi$
$978$	−0.339394	−0.0108526
$979$	−32.5623	−1.04070
$980$	22.9443	0.732928
$981$	−10.3262	−0.329691
$982$	11.8541	0.378280
$983$	29.7771	0.949742	0.474871	−	0.880056i	$-0.342495\pi$
$983$	29.7771	0.949742	0.474871	+	0.880056i	$0.342495\pi$
$984$	−2.56231	−0.0816833
$985$	−2.65248	−0.0845149
$986$	9.14590	0.291265
$987$	1.00000	0.0318304
$988$	−8.61803	−0.274176
$989$	15.8754	0.504808
$990$	−17.1246	−0.544256
$991$	7.45085	0.236684	0.118342	−	0.992973i	$-0.462242\pi$
$991$	7.45085	0.236684	0.118342	+	0.992973i	$0.462242\pi$
$992$	62.3050	1.97818
$993$	−0.695048	−0.0220567
$994$	−8.18034	−0.259465
$995$	30.0000	0.951064
$996$	0.291796	0.00924591
$997$	−23.9098	−0.757232	−0.378616	−	0.925554i	$-0.623600\pi$
$997$	−23.9098	−0.757232	−0.378616	+	0.925554i	$0.623600\pi$
$998$	−13.2918	−0.420744
$999$	24.4721	0.774264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.a.1.1	✓	2
3.2	odd	2		1899.2.a.d.1.2		2
4.3	odd	2		3376.2.a.f.1.2		2
5.4	even	2		5275.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.a.1.1	✓	2	1.1	even	1	trivial
1899.2.a.d.1.2		2	3.2	odd	2
3376.2.a.f.1.2		2	4.3	odd	2
5275.2.a.d.1.2		2	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)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} -0.236068 q^{6} +1.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} -0.236068 q^{6} +1.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} -2.00000 q^{10} -3.00000 q^{11} -0.618034 q^{12} +6.23607 q^{13} -1.00000 q^{14} +1.23607 q^{15} +1.85410 q^{16} +6.61803 q^{17} +1.76393 q^{18} +0.854102 q^{19} -5.23607 q^{20} +0.618034 q^{21} +1.85410 q^{22} +1.76393 q^{23} +0.854102 q^{24} +5.47214 q^{25} -3.85410 q^{26} -2.23607 q^{27} -2.61803 q^{28} -2.23607 q^{29} -0.763932 q^{30} -11.0902 q^{31} -5.61803 q^{32} -1.14590 q^{33} -4.09017 q^{34} +5.23607 q^{35} +4.61803 q^{36} -10.9443 q^{37} -0.527864 q^{38} +2.38197 q^{39} +7.23607 q^{40} -3.00000 q^{41} -0.381966 q^{42} +9.00000 q^{43} +4.85410 q^{44} -9.23607 q^{45} -1.09017 q^{46} +1.61803 q^{47} +0.708204 q^{48} -4.38197 q^{49} -3.38197 q^{50} +2.52786 q^{51} -10.0902 q^{52} +5.38197 q^{53} +1.38197 q^{54} -9.70820 q^{55} +3.61803 q^{56} +0.326238 q^{57} +1.38197 q^{58} -6.70820 q^{59} -2.00000 q^{60} -3.00000 q^{61} +6.85410 q^{62} -4.61803 q^{63} -0.236068 q^{64} +20.1803 q^{65} +0.708204 q^{66} -12.0000 q^{67} -10.7082 q^{68} +0.673762 q^{69} -3.23607 q^{70} +8.18034 q^{71} -6.38197 q^{72} +2.09017 q^{73} +6.76393 q^{74} +2.09017 q^{75} -1.38197 q^{76} -4.85410 q^{77} -1.47214 q^{78} -11.7082 q^{79} +6.00000 q^{80} +7.70820 q^{81} +1.85410 q^{82} -0.472136 q^{83} -1.00000 q^{84} +21.4164 q^{85} -5.56231 q^{86} -0.854102 q^{87} -6.70820 q^{88} +10.8541 q^{89} +5.70820 q^{90} +10.0902 q^{91} -2.85410 q^{92} -4.23607 q^{93} -1.00000 q^{94} +2.76393 q^{95} -2.14590 q^{96} -2.85410 q^{97} +2.70820 q^{98} +8.56231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + q^7 + q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + q^{7} + q^{9} - 4 q^{10} - 6 q^{11} + q^{12} + 8 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} + 11 q^{17} + 8 q^{18} - 5 q^{19} - 6 q^{20} - q^{21} - 3 q^{22} + 8 q^{23} - 5 q^{24} + 2 q^{25} - q^{26} - 3 q^{28} - 6 q^{30} - 11 q^{31} - 9 q^{32} - 9 q^{33} + 3 q^{34} + 6 q^{35} + 7 q^{36} - 4 q^{37} - 10 q^{38} + 7 q^{39} + 10 q^{40} - 6 q^{41} - 3 q^{42} + 18 q^{43} + 3 q^{44} - 14 q^{45} + 9 q^{46} + q^{47} - 12 q^{48} - 11 q^{49} - 9 q^{50} + 14 q^{51} - 9 q^{52} + 13 q^{53} + 5 q^{54} - 6 q^{55} + 5 q^{56} - 15 q^{57} + 5 q^{58} - 4 q^{60} - 6 q^{61} + 7 q^{62} - 7 q^{63} + 4 q^{64} + 18 q^{65} - 12 q^{66} - 24 q^{67} - 8 q^{68} + 17 q^{69} - 2 q^{70} - 6 q^{71} - 15 q^{72} - 7 q^{73} + 18 q^{74} - 7 q^{75} - 5 q^{76} - 3 q^{77} + 6 q^{78} - 10 q^{79} + 12 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 2 q^{84} + 16 q^{85} + 9 q^{86} + 5 q^{87} + 15 q^{89} - 2 q^{90} + 9 q^{91} + q^{92} - 4 q^{93} - 2 q^{94} + 10 q^{95} - 11 q^{96} + q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + q^7 + q^9 - 4 * q^10 - 6 * q^11 + q^12 + 8 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 + 11 * q^17 + 8 * q^18 - 5 * q^19 - 6 * q^20 - q^21 - 3 * q^22 + 8 * q^23 - 5 * q^24 + 2 * q^25 - q^26 - 3 * q^28 - 6 * q^30 - 11 * q^31 - 9 * q^32 - 9 * q^33 + 3 * q^34 + 6 * q^35 + 7 * q^36 - 4 * q^37 - 10 * q^38 + 7 * q^39 + 10 * q^40 - 6 * q^41 - 3 * q^42 + 18 * q^43 + 3 * q^44 - 14 * q^45 + 9 * q^46 + q^47 - 12 * q^48 - 11 * q^49 - 9 * q^50 + 14 * q^51 - 9 * q^52 + 13 * q^53 + 5 * q^54 - 6 * q^55 + 5 * q^56 - 15 * q^57 + 5 * q^58 - 4 * q^60 - 6 * q^61 + 7 * q^62 - 7 * q^63 + 4 * q^64 + 18 * q^65 - 12 * q^66 - 24 * q^67 - 8 * q^68 + 17 * q^69 - 2 * q^70 - 6 * q^71 - 15 * q^72 - 7 * q^73 + 18 * q^74 - 7 * q^75 - 5 * q^76 - 3 * q^77 + 6 * q^78 - 10 * q^79 + 12 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 2 * q^84 + 16 * q^85 + 9 * q^86 + 5 * q^87 + 15 * q^89 - 2 * q^90 + 9 * q^91 + q^92 - 4 * q^93 - 2 * q^94 + 10 * q^95 - 11 * q^96 + q^97 - 8 * q^98 - 3 * q^99

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