LMFDB - Embedded newform 211.2.a.a.1.2

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			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -1.23607 q^{5} +4.23607 q^{6} -0.618034 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -1.23607 q^{5} +4.23607 q^{6} -0.618034 q^{7} -2.23607 q^{8} +3.85410 q^{9} -2.00000 q^{10} -3.00000 q^{11} +1.61803 q^{12} +1.76393 q^{13} -1.00000 q^{14} -3.23607 q^{15} -4.85410 q^{16} +4.38197 q^{17} +6.23607 q^{18} -5.85410 q^{19} -0.763932 q^{20} -1.61803 q^{21} -4.85410 q^{22} +6.23607 q^{23} -5.85410 q^{24} -3.47214 q^{25} +2.85410 q^{26} +2.23607 q^{27} -0.381966 q^{28} +2.23607 q^{29} -5.23607 q^{30} +0.0901699 q^{31} -3.38197 q^{32} -7.85410 q^{33} +7.09017 q^{34} +0.763932 q^{35} +2.38197 q^{36} +6.94427 q^{37} -9.47214 q^{38} +4.61803 q^{39} +2.76393 q^{40} -3.00000 q^{41} -2.61803 q^{42} +9.00000 q^{43} -1.85410 q^{44} -4.76393 q^{45} +10.0902 q^{46} -0.618034 q^{47} -12.7082 q^{48} -6.61803 q^{49} -5.61803 q^{50} +11.4721 q^{51} +1.09017 q^{52} +7.61803 q^{53} +3.61803 q^{54} +3.70820 q^{55} +1.38197 q^{56} -15.3262 q^{57} +3.61803 q^{58} +6.70820 q^{59} -2.00000 q^{60} -3.00000 q^{61} +0.145898 q^{62} -2.38197 q^{63} +4.23607 q^{64} -2.18034 q^{65} -12.7082 q^{66} -12.0000 q^{67} +2.70820 q^{68} +16.3262 q^{69} +1.23607 q^{70} -14.1803 q^{71} -8.61803 q^{72} -9.09017 q^{73} +11.2361 q^{74} -9.09017 q^{75} -3.61803 q^{76} +1.85410 q^{77} +7.47214 q^{78} +1.70820 q^{79} +6.00000 q^{80} -5.70820 q^{81} -4.85410 q^{82} +8.47214 q^{83} -1.00000 q^{84} -5.41641 q^{85} +14.5623 q^{86} +5.85410 q^{87} +6.70820 q^{88} +4.14590 q^{89} -7.70820 q^{90} -1.09017 q^{91} +3.85410 q^{92} +0.236068 q^{93} -1.00000 q^{94} +7.23607 q^{95} -8.85410 q^{96} +3.85410 q^{97} -10.7082 q^{98} -11.5623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	0.618034	0.309017
$5$	−1.23607	−0.552786	−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607	−0.552786	−0.276393	+	0.961045i	$0.589139\pi$
$6$	4.23607	1.72937
$7$	−0.618034	−0.233595	−0.116797	−	0.993156i	$-0.537263\pi$
$7$	−0.618034	−0.233595	−0.116797	+	0.993156i	$0.537263\pi$
$8$	−2.23607	−0.790569
$9$	3.85410	1.28470
$10$	−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	$0.649385\pi$
$12$	1.61803	0.467086
$13$	1.76393	0.489227	0.244613	−	0.969621i	$-0.421339\pi$
$13$	1.76393	0.489227	0.244613	+	0.969621i	$0.421339\pi$
$14$	−1.00000	−0.267261
$15$	−3.23607	−0.835549
$16$	−4.85410	−1.21353
$17$	4.38197	1.06278	0.531391	−	0.847126i	$-0.321669\pi$
$17$	4.38197	1.06278	0.531391	+	0.847126i	$0.321669\pi$
$18$	6.23607	1.46986
$19$	−5.85410	−1.34302	−0.671512	−	0.740994i	$-0.734355\pi$
$19$	−5.85410	−1.34302	−0.671512	+	0.740994i	$0.734355\pi$
$20$	−0.763932	−0.170820
$21$	−1.61803	−0.353084
$22$	−4.85410	−1.03490
$23$	6.23607	1.30031	0.650155	−	0.759802i	$-0.274704\pi$
$23$	6.23607	1.30031	0.650155	+	0.759802i	$0.274704\pi$
$24$	−5.85410	−1.19496
$25$	−3.47214	−0.694427
$26$	2.85410	0.559735
$27$	2.23607	0.430331
$28$	−0.381966	−0.0721848
$29$	2.23607	0.415227	0.207614	−	0.978211i	$-0.433430\pi$
$29$	2.23607	0.415227	0.207614	+	0.978211i	$0.433430\pi$
$30$	−5.23607	−0.955971
$31$	0.0901699	0.0161950	0.00809750	−	0.999967i	$-0.497422\pi$
$31$	0.0901699	0.0161950	0.00809750	+	0.999967i	$0.497422\pi$
$32$	−3.38197	−0.597853
$33$	−7.85410	−1.36722
$34$	7.09017	1.21595
$35$	0.763932	0.129128
$36$	2.38197	0.396994
$37$	6.94427	1.14163	0.570816	−	0.821078i	$-0.306627\pi$
$37$	6.94427	1.14163	0.570816	+	0.821078i	$0.306627\pi$
$38$	−9.47214	−1.53658
$39$	4.61803	0.739477
$40$	2.76393	0.437016
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−2.61803	−0.403971
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−1.85410	−0.279516
$45$	−4.76393	−0.710165
$46$	10.0902	1.48771
$47$	−0.618034	−0.0901495	−0.0450748	−	0.998984i	$-0.514353\pi$
$47$	−0.618034	−0.0901495	−0.0450748	+	0.998984i	$0.514353\pi$
$48$	−12.7082	−1.83427
$49$	−6.61803	−0.945433
$50$	−5.61803	−0.794510
$51$	11.4721	1.60642
$52$	1.09017	0.151179
$53$	7.61803	1.04642	0.523209	−	0.852205i	$-0.324735\pi$
$53$	7.61803	1.04642	0.523209	+	0.852205i	$0.324735\pi$
$54$	3.61803	0.492352
$55$	3.70820	0.500014
$56$	1.38197	0.184673
$57$	−15.3262	−2.03001
$58$	3.61803	0.475071
$59$	6.70820	0.873334	0.436667	−	0.899623i	$-0.356159\pi$
$59$	6.70820	0.873334	0.436667	+	0.899623i	$0.356159\pi$
$60$	−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	$0.561515\pi$
$62$	0.145898	0.0185291
$63$	−2.38197	−0.300100
$64$	4.23607	0.529508
$65$	−2.18034	−0.270438
$66$	−12.7082	−1.56427
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	2.70820	0.328418
$69$	16.3262	1.96545
$70$	1.23607	0.147738
$71$	−14.1803	−1.68290	−0.841448	−	0.540338i	$-0.818297\pi$
$71$	−14.1803	−1.68290	−0.841448	+	0.540338i	$0.818297\pi$
$72$	−8.61803	−1.01565
$73$	−9.09017	−1.06392	−0.531962	−	0.846768i	$-0.678545\pi$
$73$	−9.09017	−1.06392	−0.531962	+	0.846768i	$0.678545\pi$
$74$	11.2361	1.30617
$75$	−9.09017	−1.04964
$76$	−3.61803	−0.415017
$77$	1.85410	0.211295
$78$	7.47214	0.846053
$79$	1.70820	0.192188	0.0960940	−	0.995372i	$-0.469365\pi$
$79$	1.70820	0.192188	0.0960940	+	0.995372i	$0.469365\pi$
$80$	6.00000	0.670820
$81$	−5.70820	−0.634245
$82$	−4.85410	−0.536046
$83$	8.47214	0.929938	0.464969	−	0.885327i	$-0.346066\pi$
$83$	8.47214	0.929938	0.464969	+	0.885327i	$0.346066\pi$
$84$	−1.00000	−0.109109
$85$	−5.41641	−0.587492
$86$	14.5623	1.57029
$87$	5.85410	0.627626
$88$	6.70820	0.715097
$89$	4.14590	0.439464	0.219732	−	0.975560i	$-0.429482\pi$
$89$	4.14590	0.439464	0.219732	+	0.975560i	$0.429482\pi$
$90$	−7.70820	−0.812516
$91$	−1.09017	−0.114281
$92$	3.85410	0.401818
$93$	0.236068	0.0244791
$94$	−1.00000	−0.103142
$95$	7.23607	0.742405
$96$	−8.85410	−0.903668
$97$	3.85410	0.391325	0.195662	−	0.980671i	$-0.437314\pi$
$97$	3.85410	0.391325	0.195662	+	0.980671i	$0.437314\pi$
$98$	−10.7082	−1.08169
$99$	−11.5623	−1.16206
$100$	−2.14590	−0.214590
$101$	5.09017	0.506491	0.253245	−	0.967402i	$-0.418502\pi$
$101$	5.09017	0.506491	0.253245	+	0.967402i	$0.418502\pi$
$102$	18.5623	1.83794
$103$	12.4164	1.22343	0.611713	−	0.791080i	$-0.290481\pi$
$103$	12.4164	1.22343	0.611713	+	0.791080i	$0.290481\pi$
$104$	−3.94427	−0.386768
$105$	2.00000	0.195180
$106$	12.3262	1.19723
$107$	−7.85410	−0.759285	−0.379642	−	0.925133i	$-0.623953\pi$
$107$	−7.85410	−0.759285	−0.379642	+	0.925133i	$0.623953\pi$
$108$	1.38197	0.132980
$109$	1.38197	0.132368	0.0661842	−	0.997807i	$-0.478918\pi$
$109$	1.38197	0.132368	0.0661842	+	0.997807i	$0.478918\pi$
$110$	6.00000	0.572078
$111$	18.1803	1.72560
$112$	3.00000	0.283473
$113$	11.7639	1.10666	0.553329	−	0.832963i	$-0.313357\pi$
$113$	11.7639	1.10666	0.553329	+	0.832963i	$0.313357\pi$
$114$	−24.7984	−2.32258
$115$	−7.70820	−0.718794
$116$	1.38197	0.128312
$117$	6.79837	0.628510
$118$	10.8541	0.999201
$119$	−2.70820	−0.248261
$120$	7.23607	0.660560
$121$	−2.00000	−0.181818
$122$	−4.85410	−0.439470
$123$	−7.85410	−0.708181
$124$	0.0557281	0.00500453
$125$	10.4721	0.936656
$126$	−3.85410	−0.343351
$127$	1.29180	0.114628	0.0573142	−	0.998356i	$-0.481746\pi$
$127$	1.29180	0.114628	0.0573142	+	0.998356i	$0.481746\pi$
$128$	13.6180	1.20368
$129$	23.5623	2.07455
$130$	−3.52786	−0.309414
$131$	−9.18034	−0.802090	−0.401045	−	0.916058i	$-0.631353\pi$
$131$	−9.18034	−0.802090	−0.401045	+	0.916058i	$0.631353\pi$
$132$	−4.85410	−0.422495
$133$	3.61803	0.313723
$134$	−19.4164	−1.67732
$135$	−2.76393	−0.237881
$136$	−9.79837	−0.840204
$137$	2.47214	0.211209	0.105604	−	0.994408i	$-0.466322\pi$
$137$	2.47214	0.211209	0.105604	+	0.994408i	$0.466322\pi$
$138$	26.4164	2.24871
$139$	−20.8541	−1.76882	−0.884411	−	0.466709i	$-0.845440\pi$
$139$	−20.8541	−1.76882	−0.884411	+	0.466709i	$0.845440\pi$
$140$	0.472136	0.0399028
$141$	−1.61803	−0.136263
$142$	−22.9443	−1.92544
$143$	−5.29180	−0.442522
$144$	−18.7082	−1.55902
$145$	−2.76393	−0.229532
$146$	−14.7082	−1.21726
$147$	−17.3262	−1.42904
$148$	4.29180	0.352783
$149$	8.94427	0.732743	0.366372	−	0.930469i	$-0.380600\pi$
$149$	8.94427	0.732743	0.366372	+	0.930469i	$0.380600\pi$
$150$	−14.7082	−1.20092
$151$	−21.0902	−1.71629	−0.858147	−	0.513404i	$-0.828384\pi$
$151$	−21.0902	−1.71629	−0.858147	+	0.513404i	$0.828384\pi$
$152$	13.0902	1.06175
$153$	16.8885	1.36536
$154$	3.00000	0.241747
$155$	−0.111456	−0.00895238
$156$	2.85410	0.228511
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	2.76393	0.219887
$159$	19.9443	1.58168
$160$	4.18034	0.330485
$161$	−3.85410	−0.303746
$162$	−9.23607	−0.725654
$163$	21.5623	1.68889	0.844445	−	0.535642i	$-0.179930\pi$
$163$	21.5623	1.68889	0.844445	+	0.535642i	$0.179930\pi$
$164$	−1.85410	−0.144781
$165$	9.70820	0.755783
$166$	13.7082	1.06396
$167$	20.5623	1.59116	0.795580	−	0.605849i	$-0.207167\pi$
$167$	20.5623	1.59116	0.795580	+	0.605849i	$0.207167\pi$
$168$	3.61803	0.279137
$169$	−9.88854	−0.760657
$170$	−8.76393	−0.672163
$171$	−22.5623	−1.72538
$172$	5.56231	0.424122
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	9.47214	0.718081
$175$	2.14590	0.162215
$176$	14.5623	1.09768
$177$	17.5623	1.32006
$178$	6.70820	0.502801
$179$	9.27051	0.692910	0.346455	−	0.938067i	$-0.387385\pi$
$179$	9.27051	0.692910	0.346455	+	0.938067i	$0.387385\pi$
$180$	−2.94427	−0.219453
$181$	−3.00000	−0.222988	−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000	−0.222988	−0.111494	+	0.993765i	$0.535564\pi$
$182$	−1.76393	−0.130751
$183$	−7.85410	−0.580592
$184$	−13.9443	−1.02799
$185$	−8.58359	−0.631078
$186$	0.381966	0.0280071
$187$	−13.1459	−0.961323
$188$	−0.381966	−0.0278577
$189$	−1.38197	−0.100523
$190$	11.7082	0.849402
$191$	−25.3607	−1.83503	−0.917517	−	0.397696i	$-0.869810\pi$
$191$	−25.3607	−1.83503	−0.917517	+	0.397696i	$0.869810\pi$
$192$	11.0902	0.800364
$193$	−21.9787	−1.58206	−0.791031	−	0.611776i	$-0.790455\pi$
$193$	−21.9787	−1.58206	−0.791031	+	0.611776i	$0.790455\pi$
$194$	6.23607	0.447724
$195$	−5.70820	−0.408773
$196$	−4.09017	−0.292155
$197$	−23.1803	−1.65153	−0.825765	−	0.564014i	$-0.809256\pi$
$197$	−23.1803	−1.65153	−0.825765	+	0.564014i	$0.809256\pi$
$198$	−18.7082	−1.32953
$199$	−24.2705	−1.72049	−0.860245	−	0.509880i	$-0.829690\pi$
$199$	−24.2705	−1.72049	−0.860245	+	0.509880i	$0.829690\pi$
$200$	7.76393	0.548993
$201$	−31.4164	−2.21594
$202$	8.23607	0.579488
$203$	−1.38197	−0.0969950
$204$	7.09017	0.496411
$205$	3.70820	0.258992
$206$	20.0902	1.39975
$207$	24.0344	1.67051
$208$	−8.56231	−0.593689
$209$	17.5623	1.21481
$210$	3.23607	0.223310
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	4.70820	0.323361
$213$	−37.1246	−2.54374
$214$	−12.7082	−0.868715
$215$	−11.1246	−0.758692
$216$	−5.00000	−0.340207
$217$	−0.0557281	−0.00378307
$218$	2.23607	0.151446
$219$	−23.7984	−1.60815
$220$	2.29180	0.154513
$221$	7.72949	0.519942
$222$	29.4164	1.97430
$223$	−27.1803	−1.82013	−0.910065	−	0.414465i	$-0.863969\pi$
$223$	−27.1803	−1.82013	−0.910065	+	0.414465i	$0.863969\pi$
$224$	2.09017	0.139655
$225$	−13.3820	−0.892131
$226$	19.0344	1.26615
$227$	−14.8885	−0.988187	−0.494094	−	0.869409i	$-0.664500\pi$
$227$	−14.8885	−0.988187	−0.494094	+	0.869409i	$0.664500\pi$
$228$	−9.47214	−0.627308
$229$	16.7082	1.10411	0.552055	−	0.833808i	$-0.313844\pi$
$229$	16.7082	1.10411	0.552055	+	0.833808i	$0.313844\pi$
$230$	−12.4721	−0.822388
$231$	4.85410	0.319376
$232$	−5.00000	−0.328266
$233$	−2.38197	−0.156048	−0.0780239	−	0.996951i	$-0.524861\pi$
$233$	−2.38197	−0.156048	−0.0780239	+	0.996951i	$0.524861\pi$
$234$	11.0000	0.719092
$235$	0.763932	0.0498334
$236$	4.14590	0.269875
$237$	4.47214	0.290496
$238$	−4.38197	−0.284041
$239$	20.1246	1.30175	0.650876	−	0.759184i	$-0.274402\pi$
$239$	20.1246	1.30175	0.650876	+	0.759184i	$0.274402\pi$
$240$	15.7082	1.01396
$241$	−1.81966	−0.117215	−0.0586073	−	0.998281i	$-0.518666\pi$
$241$	−1.81966	−0.117215	−0.0586073	+	0.998281i	$0.518666\pi$
$242$	−3.23607	−0.208022
$243$	−21.6525	−1.38901
$244$	−1.85410	−0.118697
$245$	8.18034	0.522623
$246$	−12.7082	−0.810245
$247$	−10.3262	−0.657043
$248$	−0.201626	−0.0128033
$249$	22.1803	1.40562
$250$	16.9443	1.07165
$251$	−27.2705	−1.72130	−0.860650	−	0.509198i	$-0.829942\pi$
$251$	−27.2705	−1.72130	−0.860650	+	0.509198i	$0.829942\pi$
$252$	−1.47214	−0.0927358
$253$	−18.7082	−1.17617
$254$	2.09017	0.131149
$255$	−14.1803	−0.888007
$256$	13.5623	0.847644
$257$	22.5967	1.40955	0.704773	−	0.709433i	$-0.251049\pi$
$257$	22.5967	1.40955	0.704773	+	0.709433i	$0.251049\pi$
$258$	38.1246	2.37353
$259$	−4.29180	−0.266679
$260$	−1.34752	−0.0835699
$261$	8.61803	0.533443
$262$	−14.8541	−0.917689
$263$	−3.76393	−0.232094	−0.116047	−	0.993244i	$-0.537022\pi$
$263$	−3.76393	−0.232094	−0.116047	+	0.993244i	$0.537022\pi$
$264$	17.5623	1.08089
$265$	−9.41641	−0.578445
$266$	5.85410	0.358938
$267$	10.8541	0.664260
$268$	−7.41641	−0.453029
$269$	18.0902	1.10298	0.551489	−	0.834182i	$-0.314060\pi$
$269$	18.0902	1.10298	0.551489	+	0.834182i	$0.314060\pi$
$270$	−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	$0.480652\pi$
$272$	−21.2705	−1.28971
$273$	−2.85410	−0.172738
$274$	4.00000	0.241649
$275$	10.4164	0.628133
$276$	10.0902	0.607357
$277$	−9.56231	−0.574543	−0.287272	−	0.957849i	$-0.592748\pi$
$277$	−9.56231	−0.574543	−0.287272	+	0.957849i	$0.592748\pi$
$278$	−33.7426	−2.02375
$279$	0.347524	0.0208057
$280$	−1.70820	−0.102085
$281$	8.18034	0.487998	0.243999	−	0.969775i	$-0.421541\pi$
$281$	8.18034	0.487998	0.243999	+	0.969775i	$0.421541\pi$
$282$	−2.61803	−0.155902
$283$	29.1246	1.73128	0.865639	−	0.500668i	$-0.166912\pi$
$283$	29.1246	1.73128	0.865639	+	0.500668i	$0.166912\pi$
$284$	−8.76393	−0.520044
$285$	18.9443	1.12216
$286$	−8.56231	−0.506300
$287$	1.85410	0.109444
$288$	−13.0344	−0.768062
$289$	2.20163	0.129507
$290$	−4.47214	−0.262613
$291$	10.0902	0.591496
$292$	−5.61803	−0.328771
$293$	−11.6525	−0.680745	−0.340372	−	0.940291i	$-0.610553\pi$
$293$	−11.6525	−0.680745	−0.340372	+	0.940291i	$0.610553\pi$
$294$	−28.0344	−1.63500
$295$	−8.29180	−0.482767
$296$	−15.5279	−0.902539
$297$	−6.70820	−0.389249
$298$	14.4721	0.838348
$299$	11.0000	0.636146
$300$	−5.61803	−0.324357
$301$	−5.56231	−0.320606
$302$	−34.1246	−1.96365
$303$	13.3262	0.765572
$304$	28.4164	1.62979
$305$	3.70820	0.212331
$306$	27.3262	1.56214
$307$	−1.14590	−0.0653999	−0.0326999	−	0.999465i	$-0.510411\pi$
$307$	−1.14590	−0.0653999	−0.0326999	+	0.999465i	$0.510411\pi$
$308$	1.14590	0.0652936
$309$	32.5066	1.84923
$310$	−0.180340	−0.0102426
$311$	20.0902	1.13921	0.569605	−	0.821919i	$-0.307096\pi$
$311$	20.0902	1.13921	0.569605	+	0.821919i	$0.307096\pi$
$312$	−10.3262	−0.584608
$313$	23.7984	1.34516	0.672582	−	0.740023i	$-0.265185\pi$
$313$	23.7984	1.34516	0.672582	+	0.740023i	$0.265185\pi$
$314$	21.0344	1.18704
$315$	2.94427	0.165891
$316$	1.05573	0.0593893
$317$	−11.7984	−0.662663	−0.331331	−	0.943514i	$-0.607498\pi$
$317$	−11.7984	−0.662663	−0.331331	+	0.943514i	$0.607498\pi$
$318$	32.2705	1.80964
$319$	−6.70820	−0.375587
$320$	−5.23607	−0.292705
$321$	−20.5623	−1.14768
$322$	−6.23607	−0.347522
$323$	−25.6525	−1.42734
$324$	−3.52786	−0.195992
$325$	−6.12461	−0.339732
$326$	34.8885	1.93230
$327$	3.61803	0.200078
$328$	6.70820	0.370399
$329$	0.381966	0.0210585
$330$	15.7082	0.864708
$331$	−24.1803	−1.32907	−0.664536	−	0.747256i	$-0.731371\pi$
$331$	−24.1803	−1.32907	−0.664536	+	0.747256i	$0.731371\pi$
$332$	5.23607	0.287367
$333$	26.7639	1.46665
$334$	33.2705	1.82048
$335$	14.8328	0.810403
$336$	7.85410	0.428476
$337$	14.7082	0.801207	0.400603	−	0.916252i	$-0.368801\pi$
$337$	14.7082	0.801207	0.400603	+	0.916252i	$0.368801\pi$
$338$	−16.0000	−0.870285
$339$	30.7984	1.67274
$340$	−3.34752	−0.181545
$341$	−0.270510	−0.0146489
$342$	−36.5066	−1.97405
$343$	8.41641	0.454443
$344$	−20.1246	−1.08505
$345$	−20.1803	−1.08647
$346$	14.5623	0.782874
$347$	−9.03444	−0.484994	−0.242497	−	0.970152i	$-0.577966\pi$
$347$	−9.03444	−0.484994	−0.242497	+	0.970152i	$0.577966\pi$
$348$	3.61803	0.193947
$349$	19.2705	1.03153	0.515763	−	0.856731i	$-0.327508\pi$
$349$	19.2705	1.03153	0.515763	+	0.856731i	$0.327508\pi$
$350$	3.47214	0.185593
$351$	3.94427	0.210530
$352$	10.1459	0.540778
$353$	14.1246	0.751777	0.375889	−	0.926665i	$-0.377338\pi$
$353$	14.1246	0.751777	0.375889	+	0.926665i	$0.377338\pi$
$354$	28.4164	1.51032
$355$	17.5279	0.930282
$356$	2.56231	0.135802
$357$	−7.09017	−0.375252
$358$	15.0000	0.792775
$359$	−22.3607	−1.18015	−0.590076	−	0.807348i	$-0.700902\pi$
$359$	−22.3607	−1.18015	−0.590076	+	0.807348i	$0.700902\pi$
$360$	10.6525	0.561435
$361$	15.2705	0.803711
$362$	−4.85410	−0.255126
$363$	−5.23607	−0.274822
$364$	−0.673762	−0.0353147
$365$	11.2361	0.588123
$366$	−12.7082	−0.664268
$367$	−17.5279	−0.914947	−0.457474	−	0.889223i	$-0.651246\pi$
$367$	−17.5279	−0.914947	−0.457474	+	0.889223i	$0.651246\pi$
$368$	−30.2705	−1.57796
$369$	−11.5623	−0.601910
$370$	−13.8885	−0.722031
$371$	−4.70820	−0.244438
$372$	0.145898	0.00756446
$373$	−11.6525	−0.603342	−0.301671	−	0.953412i	$-0.597544\pi$
$373$	−11.6525	−0.603342	−0.301671	+	0.953412i	$0.597544\pi$
$374$	−21.2705	−1.09987
$375$	27.4164	1.41578
$376$	1.38197	0.0712695
$377$	3.94427	0.203140
$378$	−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
$381$	3.38197	0.173263
$382$	−41.0344	−2.09950
$383$	24.6525	1.25968	0.629841	−	0.776724i	$-0.283120\pi$
$383$	24.6525	1.25968	0.629841	+	0.776724i	$0.283120\pi$
$384$	35.6525	1.81938
$385$	−2.29180	−0.116801
$386$	−35.5623	−1.81007
$387$	34.6869	1.76324
$388$	2.38197	0.120926
$389$	−21.1803	−1.07389	−0.536943	−	0.843619i	$-0.680421\pi$
$389$	−21.1803	−1.07389	−0.536943	+	0.843619i	$0.680421\pi$
$390$	−9.23607	−0.467686
$391$	27.3262	1.38195
$392$	14.7984	0.747431
$393$	−24.0344	−1.21238
$394$	−37.5066	−1.88955
$395$	−2.11146	−0.106239
$396$	−7.14590	−0.359095
$397$	34.8328	1.74821	0.874104	−	0.485738i	$-0.161449\pi$
$397$	34.8328	1.74821	0.874104	+	0.485738i	$0.161449\pi$
$398$	−39.2705	−1.96845
$399$	9.47214	0.474200
$400$	16.8541	0.842705
$401$	28.1803	1.40726	0.703630	−	0.710567i	$-0.251561\pi$
$401$	28.1803	1.40726	0.703630	+	0.710567i	$0.251561\pi$
$402$	−50.8328	−2.53531
$403$	0.159054	0.00792303
$404$	3.14590	0.156514
$405$	7.05573	0.350602
$406$	−2.23607	−0.110974
$407$	−20.8328	−1.03264
$408$	−25.6525	−1.26999
$409$	−32.0344	−1.58400	−0.792001	−	0.610520i	$-0.790960\pi$
$409$	−32.0344	−1.58400	−0.792001	+	0.610520i	$0.790960\pi$
$410$	6.00000	0.296319
$411$	6.47214	0.319247
$412$	7.67376	0.378059
$413$	−4.14590	−0.204006
$414$	38.8885	1.91127
$415$	−10.4721	−0.514057
$416$	−5.96556	−0.292486
$417$	−54.5967	−2.67361
$418$	28.4164	1.38989
$419$	19.4721	0.951276	0.475638	−	0.879641i	$-0.342217\pi$
$419$	19.4721	0.951276	0.475638	+	0.879641i	$0.342217\pi$
$420$	1.23607	0.0603139
$421$	14.3607	0.699897	0.349948	−	0.936769i	$-0.386199\pi$
$421$	14.3607	0.699897	0.349948	+	0.936769i	$0.386199\pi$
$422$	1.61803	0.0787647
$423$	−2.38197	−0.115815
$424$	−17.0344	−0.827266
$425$	−15.2148	−0.738025
$426$	−60.0689	−2.91035
$427$	1.85410	0.0897263
$428$	−4.85410	−0.234632
$429$	−13.8541	−0.668882
$430$	−18.0000	−0.868037
$431$	−16.0902	−0.775036	−0.387518	−	0.921862i	$-0.626668\pi$
$431$	−16.0902	−0.775036	−0.387518	+	0.921862i	$0.626668\pi$
$432$	−10.8541	−0.522218
$433$	−7.70820	−0.370433	−0.185216	−	0.982698i	$-0.559299\pi$
$433$	−7.70820	−0.370433	−0.185216	+	0.982698i	$0.559299\pi$
$434$	−0.0901699	−0.00432830
$435$	−7.23607	−0.346943
$436$	0.854102	0.0409041
$437$	−36.5066	−1.74635
$438$	−38.5066	−1.83992
$439$	−3.94427	−0.188250	−0.0941249	−	0.995560i	$-0.530005\pi$
$439$	−3.94427	−0.188250	−0.0941249	+	0.995560i	$0.530005\pi$
$440$	−8.29180	−0.395296
$441$	−25.5066	−1.21460
$442$	12.5066	0.594877
$443$	4.20163	0.199625	0.0998126	−	0.995006i	$-0.468176\pi$
$443$	4.20163	0.199625	0.0998126	+	0.995006i	$0.468176\pi$
$444$	11.2361	0.533240
$445$	−5.12461	−0.242930
$446$	−43.9787	−2.08245
$447$	23.4164	1.10756
$448$	−2.61803	−0.123690
$449$	32.2361	1.52131	0.760657	−	0.649154i	$-0.224877\pi$
$449$	32.2361	1.52131	0.760657	+	0.649154i	$0.224877\pi$
$450$	−21.6525	−1.02071
$451$	9.00000	0.423793
$452$	7.27051	0.341976
$453$	−55.2148	−2.59422
$454$	−24.0902	−1.13061
$455$	1.34752	0.0631729
$456$	34.2705	1.60486
$457$	−29.5623	−1.38287	−0.691433	−	0.722440i	$-0.743020\pi$
$457$	−29.5623	−1.38287	−0.691433	+	0.722440i	$0.743020\pi$
$458$	27.0344	1.26324
$459$	9.79837	0.457349
$460$	−4.76393	−0.222119
$461$	35.0902	1.63431	0.817156	−	0.576416i	$-0.195549\pi$
$461$	35.0902	1.63431	0.817156	+	0.576416i	$0.195549\pi$
$462$	7.85410	0.365406
$463$	21.5623	1.00209	0.501043	−	0.865423i	$-0.332950\pi$
$463$	21.5623	1.00209	0.501043	+	0.865423i	$0.332950\pi$
$464$	−10.8541	−0.503889
$465$	−0.291796	−0.0135317
$466$	−3.85410	−0.178538
$467$	−32.7771	−1.51674	−0.758371	−	0.651823i	$-0.774005\pi$
$467$	−32.7771	−1.51674	−0.758371	+	0.651823i	$0.774005\pi$
$468$	4.20163	0.194220
$469$	7.41641	0.342458
$470$	1.23607	0.0570156
$471$	34.0344	1.56822
$472$	−15.0000	−0.690431
$473$	−27.0000	−1.24146
$474$	7.23607	0.332364
$475$	20.3262	0.932632
$476$	−1.67376	−0.0767168
$477$	29.3607	1.34433
$478$	32.5623	1.48937
$479$	−23.2918	−1.06423	−0.532115	−	0.846672i	$-0.678602\pi$
$479$	−23.2918	−1.06423	−0.532115	+	0.846672i	$0.678602\pi$
$480$	10.9443	0.499535
$481$	12.2492	0.558517
$482$	−2.94427	−0.134108
$483$	−10.0902	−0.459119
$484$	−1.23607	−0.0561849
$485$	−4.76393	−0.216319
$486$	−35.0344	−1.58919
$487$	−4.56231	−0.206738	−0.103369	−	0.994643i	$-0.532962\pi$
$487$	−4.56231	−0.206738	−0.103369	+	0.994643i	$0.532962\pi$
$488$	6.70820	0.303666
$489$	56.4508	2.55280
$490$	13.2361	0.597945
$491$	3.18034	0.143527	0.0717634	−	0.997422i	$-0.477137\pi$
$491$	3.18034	0.143527	0.0717634	+	0.997422i	$0.477137\pi$
$492$	−4.85410	−0.218840
$493$	9.79837	0.441297
$494$	−16.7082	−0.751738
$495$	14.2918	0.642368
$496$	−0.437694	−0.0196530
$497$	8.76393	0.393116
$498$	35.8885	1.60820
$499$	−16.5066	−0.738936	−0.369468	−	0.929243i	$-0.620460\pi$
$499$	−16.5066	−0.738936	−0.369468	+	0.929243i	$0.620460\pi$
$500$	6.47214	0.289443
$501$	53.8328	2.40507
$502$	−44.1246	−1.96938
$503$	15.3820	0.685848	0.342924	−	0.939363i	$-0.388583\pi$
$503$	15.3820	0.685848	0.342924	+	0.939363i	$0.388583\pi$
$504$	5.32624	0.237249
$505$	−6.29180	−0.279981
$506$	−30.2705	−1.34569
$507$	−25.8885	−1.14975
$508$	0.798374	0.0354221
$509$	32.8885	1.45776	0.728880	−	0.684642i	$-0.240041\pi$
$509$	32.8885	1.45776	0.728880	+	0.684642i	$0.240041\pi$
$510$	−22.9443	−1.01599
$511$	5.61803	0.248527
$512$	−5.29180	−0.233867
$513$	−13.0902	−0.577945
$514$	36.5623	1.61269
$515$	−15.3475	−0.676293
$516$	14.5623	0.641070
$517$	1.85410	0.0815433
$518$	−6.94427	−0.305114
$519$	23.5623	1.03427
$520$	4.87539	0.213800
$521$	−12.2705	−0.537581	−0.268790	−	0.963199i	$-0.586624\pi$
$521$	−12.2705	−0.537581	−0.268790	+	0.963199i	$0.586624\pi$
$522$	13.9443	0.610324
$523$	20.9098	0.914323	0.457162	−	0.889384i	$-0.348866\pi$
$523$	20.9098	0.914323	0.457162	+	0.889384i	$0.348866\pi$
$524$	−5.67376	−0.247859
$525$	5.61803	0.245191
$526$	−6.09017	−0.265544
$527$	0.395122	0.0172118
$528$	38.1246	1.65916
$529$	15.8885	0.690806
$530$	−15.2361	−0.661813
$531$	25.8541	1.12197
$532$	2.23607	0.0969458
$533$	−5.29180	−0.229213
$534$	17.5623	0.759995
$535$	9.70820	0.419722
$536$	26.8328	1.15900
$537$	24.2705	1.04735
$538$	29.2705	1.26194
$539$	19.8541	0.855177
$540$	−1.70820	−0.0735094
$541$	−17.2705	−0.742517	−0.371259	−	0.928530i	$-0.621074\pi$
$541$	−17.2705	−0.742517	−0.371259	+	0.928530i	$0.621074\pi$
$542$	3.23607	0.139001
$543$	−7.85410	−0.337052
$544$	−14.8197	−0.635388
$545$	−1.70820	−0.0731714
$546$	−4.61803	−0.197634
$547$	34.7082	1.48402	0.742008	−	0.670391i	$-0.233874\pi$
$547$	34.7082	1.48402	0.742008	+	0.670391i	$0.233874\pi$
$548$	1.52786	0.0652671
$549$	−11.5623	−0.493467
$550$	16.8541	0.718661
$551$	−13.0902	−0.557660
$552$	−36.5066	−1.55382
$553$	−1.05573	−0.0448941
$554$	−15.4721	−0.657348
$555$	−22.4721	−0.953889
$556$	−12.8885	−0.546596
$557$	7.34752	0.311325	0.155662	−	0.987810i	$-0.450249\pi$
$557$	7.34752	0.311325	0.155662	+	0.987810i	$0.450249\pi$
$558$	0.562306	0.0238043
$559$	15.8754	0.671457
$560$	−3.70820	−0.156700
$561$	−34.4164	−1.45306
$562$	13.2361	0.558330
$563$	−1.52786	−0.0643918	−0.0321959	−	0.999482i	$-0.510250\pi$
$563$	−1.52786	−0.0643918	−0.0321959	+	0.999482i	$0.510250\pi$
$564$	−1.00000	−0.0421076
$565$	−14.5410	−0.611745
$566$	47.1246	1.98080
$567$	3.52786	0.148156
$568$	31.7082	1.33045
$569$	−32.2361	−1.35141	−0.675703	−	0.737174i	$-0.736160\pi$
$569$	−32.2361	−1.35141	−0.675703	+	0.737174i	$0.736160\pi$
$570$	30.6525	1.28389
$571$	29.3607	1.22871	0.614353	−	0.789031i	$-0.289417\pi$
$571$	29.3607	1.22871	0.614353	+	0.789031i	$0.289417\pi$
$572$	−3.27051	−0.136747
$573$	−66.3951	−2.77370
$574$	3.00000	0.125218
$575$	−21.6525	−0.902971
$576$	16.3262	0.680260
$577$	7.14590	0.297488	0.148744	−	0.988876i	$-0.452477\pi$
$577$	7.14590	0.297488	0.148744	+	0.988876i	$0.452477\pi$
$578$	3.56231	0.148172
$579$	−57.5410	−2.39132
$580$	−1.70820	−0.0709293
$581$	−5.23607	−0.217229
$582$	16.3262	0.676744
$583$	−22.8541	−0.946520
$584$	20.3262	0.841106
$585$	−8.40325	−0.347432
$586$	−18.8541	−0.778856
$587$	44.5066	1.83698	0.918492	−	0.395441i	$-0.129408\pi$
$587$	44.5066	1.83698	0.918492	+	0.395441i	$0.129408\pi$
$588$	−10.7082	−0.441599
$589$	−0.527864	−0.0217503
$590$	−13.4164	−0.552345
$591$	−60.6869	−2.49633
$592$	−33.7082	−1.38540
$593$	−7.90983	−0.324818	−0.162409	−	0.986724i	$-0.551926\pi$
$593$	−7.90983	−0.324818	−0.162409	+	0.986724i	$0.551926\pi$
$594$	−10.8541	−0.445349
$595$	3.34752	0.137235
$596$	5.52786	0.226430
$597$	−63.5410	−2.60056
$598$	17.7984	0.727830
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	20.3262	0.829815
$601$	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
$603$	−46.2492	−1.88341
$604$	−13.0344	−0.530364
$605$	2.47214	0.100507
$606$	21.5623	0.875909
$607$	16.8197	0.682689	0.341344	−	0.939938i	$-0.389118\pi$
$607$	16.8197	0.682689	0.341344	+	0.939938i	$0.389118\pi$
$608$	19.7984	0.802930
$609$	−3.61803	−0.146610
$610$	6.00000	0.242933
$611$	−1.09017	−0.0441036
$612$	10.4377	0.421919
$613$	−3.23607	−0.130704	−0.0653518	−	0.997862i	$-0.520817\pi$
$613$	−3.23607	−0.130704	−0.0653518	+	0.997862i	$0.520817\pi$
$614$	−1.85410	−0.0748255
$615$	9.70820	0.391473
$616$	−4.14590	−0.167043
$617$	12.4721	0.502109	0.251055	−	0.967973i	$-0.419223\pi$
$617$	12.4721	0.502109	0.251055	+	0.967973i	$0.419223\pi$
$618$	52.5967	2.11575
$619$	30.0000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$620$	−0.0688837	−0.00276644
$621$	13.9443	0.559564
$622$	32.5066	1.30340
$623$	−2.56231	−0.102657
$624$	−22.4164	−0.897375
$625$	4.41641	0.176656
$626$	38.5066	1.53903
$627$	45.9787	1.83621
$628$	8.03444	0.320609
$629$	30.4296	1.21331
$630$	4.76393	0.189800
$631$	12.0000	0.477712	0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000	0.477712	0.238856	+	0.971055i	$0.423228\pi$
$632$	−3.81966	−0.151938
$633$	2.61803	0.104058
$634$	−19.0902	−0.758168
$635$	−1.59675	−0.0633650
$636$	12.3262	0.488767
$637$	−11.6738	−0.462531
$638$	−10.8541	−0.429718
$639$	−54.6525	−2.16202
$640$	−16.8328	−0.665375
$641$	−6.81966	−0.269360	−0.134680	−	0.990889i	$-0.543001\pi$
$641$	−6.81966	−0.269360	−0.134680	+	0.990889i	$0.543001\pi$
$642$	−33.2705	−1.31308
$643$	7.61803	0.300426	0.150213	−	0.988654i	$-0.452004\pi$
$643$	7.61803	0.300426	0.150213	+	0.988654i	$0.452004\pi$
$644$	−2.38197	−0.0938626
$645$	−29.1246	−1.14678
$646$	−41.5066	−1.63305
$647$	−19.3607	−0.761147	−0.380573	−	0.924751i	$-0.624273\pi$
$647$	−19.3607	−0.761147	−0.380573	+	0.924751i	$0.624273\pi$
$648$	12.7639	0.501415
$649$	−20.1246	−0.789960
$650$	−9.90983	−0.388696
$651$	−0.145898	−0.00571819
$652$	13.3262	0.521896
$653$	51.0344	1.99713	0.998566	−	0.0535342i	$-0.0170486\pi$
$653$	51.0344	1.99713	0.998566	+	0.0535342i	$0.0170486\pi$
$654$	5.85410	0.228914
$655$	11.3475	0.443384
$656$	14.5623	0.568563
$657$	−35.0344	−1.36682
$658$	0.618034	0.0240935
$659$	7.36068	0.286731	0.143366	−	0.989670i	$-0.454207\pi$
$659$	7.36068	0.286731	0.143366	+	0.989670i	$0.454207\pi$
$660$	6.00000	0.233550
$661$	20.0902	0.781417	0.390709	−	0.920514i	$-0.372230\pi$
$661$	20.0902	0.781417	0.390709	+	0.920514i	$0.372230\pi$
$662$	−39.1246	−1.52062
$663$	20.2361	0.785904
$664$	−18.9443	−0.735180
$665$	−4.47214	−0.173422
$666$	43.3050	1.67803
$667$	13.9443	0.539924
$668$	12.7082	0.491695
$669$	−71.1591	−2.75117
$670$	24.0000	0.927201
$671$	9.00000	0.347441
$672$	5.47214	0.211092
$673$	18.2705	0.704276	0.352138	−	0.935948i	$-0.385455\pi$
$673$	18.2705	0.704276	0.352138	+	0.935948i	$0.385455\pi$
$674$	23.7984	0.916679
$675$	−7.76393	−0.298834
$676$	−6.11146	−0.235056
$677$	−18.7082	−0.719015	−0.359507	−	0.933142i	$-0.617055\pi$
$677$	−18.7082	−0.719015	−0.359507	+	0.933142i	$0.617055\pi$
$678$	49.8328	1.91382
$679$	−2.38197	−0.0914115
$680$	12.1115	0.464453
$681$	−38.9787	−1.49367
$682$	−0.437694	−0.0167602
$683$	−43.3607	−1.65915	−0.829575	−	0.558395i	$-0.811417\pi$
$683$	−43.3607	−1.65915	−0.829575	+	0.558395i	$0.811417\pi$
$684$	−13.9443	−0.533173
$685$	−3.05573	−0.116753
$686$	13.6180	0.519939
$687$	43.7426	1.66889
$688$	−43.6869	−1.66555
$689$	13.4377	0.511935
$690$	−32.6525	−1.24306
$691$	−20.3607	−0.774557	−0.387278	−	0.921963i	$-0.626585\pi$
$691$	−20.3607	−0.774557	−0.387278	+	0.921963i	$0.626585\pi$
$692$	5.56231	0.211447
$693$	7.14590	0.271450
$694$	−14.6180	−0.554893
$695$	25.7771	0.977781
$696$	−13.0902	−0.496182
$697$	−13.1459	−0.497936
$698$	31.1803	1.18019
$699$	−6.23607	−0.235870
$700$	1.32624	0.0501271
$701$	5.09017	0.192253	0.0961265	−	0.995369i	$-0.469355\pi$
$701$	5.09017	0.192253	0.0961265	+	0.995369i	$0.469355\pi$
$702$	6.38197	0.240872
$703$	−40.6525	−1.53324
$704$	−12.7082	−0.478958
$705$	2.00000	0.0753244
$706$	22.8541	0.860125
$707$	−3.14590	−0.118314
$708$	10.8541	0.407922
$709$	0.854102	0.0320765	0.0160382	−	0.999871i	$-0.494895\pi$
$709$	0.854102	0.0320765	0.0160382	+	0.999871i	$0.494895\pi$
$710$	28.3607	1.06436
$711$	6.58359	0.246904
$712$	−9.27051	−0.347427
$713$	0.562306	0.0210585
$714$	−11.4721	−0.429334
$715$	6.54102	0.244620
$716$	5.72949	0.214121
$717$	52.6869	1.96763
$718$	−36.1803	−1.35024
$719$	−4.14590	−0.154616	−0.0773080	−	0.997007i	$-0.524632\pi$
$719$	−4.14590	−0.154616	−0.0773080	+	0.997007i	$0.524632\pi$
$720$	23.1246	0.861803
$721$	−7.67376	−0.285786
$722$	24.7082	0.919544
$723$	−4.76393	−0.177173
$724$	−1.85410	−0.0689072
$725$	−7.76393	−0.288345
$726$	−8.47214	−0.314430
$727$	3.72949	0.138319	0.0691596	−	0.997606i	$-0.477968\pi$
$727$	3.72949	0.138319	0.0691596	+	0.997606i	$0.477968\pi$
$728$	2.43769	0.0903470
$729$	−39.5623	−1.46527
$730$	18.1803	0.672885
$731$	39.4377	1.45866
$732$	−4.85410	−0.179413
$733$	−26.1246	−0.964935	−0.482467	−	0.875914i	$-0.660259\pi$
$733$	−26.1246	−0.964935	−0.482467	+	0.875914i	$0.660259\pi$
$734$	−28.3607	−1.04681
$735$	21.4164	0.789956
$736$	−21.0902	−0.777394
$737$	36.0000	1.32608
$738$	−18.7082	−0.688659
$739$	29.1459	1.07215	0.536075	−	0.844171i	$-0.319907\pi$
$739$	29.1459	1.07215	0.536075	+	0.844171i	$0.319907\pi$
$740$	−5.30495	−0.195014
$741$	−27.0344	−0.993135
$742$	−7.61803	−0.279667
$743$	−22.1803	−0.813718	−0.406859	−	0.913491i	$-0.633376\pi$
$743$	−22.1803	−0.813718	−0.406859	+	0.913491i	$0.633376\pi$
$744$	−0.527864	−0.0193524
$745$	−11.0557	−0.405051
$746$	−18.8541	−0.690298
$747$	32.6525	1.19469
$748$	−8.12461	−0.297065
$749$	4.85410	0.177365
$750$	44.3607	1.61982
$751$	48.6312	1.77458	0.887289	−	0.461215i	$-0.152586\pi$
$751$	48.6312	1.77458	0.887289	+	0.461215i	$0.152586\pi$
$752$	3.00000	0.109399
$753$	−71.3951	−2.60178
$754$	6.38197	0.232417
$755$	26.0689	0.948744
$756$	−0.854102	−0.0310634
$757$	−15.9443	−0.579504	−0.289752	−	0.957102i	$-0.593573\pi$
$757$	−15.9443	−0.579504	−0.289752	+	0.957102i	$0.593573\pi$
$758$	24.2705	0.881545
$759$	−48.9787	−1.77781
$760$	−16.1803	−0.586923
$761$	23.1803	0.840287	0.420143	−	0.907458i	$-0.361980\pi$
$761$	23.1803	0.840287	0.420143	+	0.907458i	$0.361980\pi$
$762$	5.47214	0.198235
$763$	−0.854102	−0.0309206
$764$	−15.6738	−0.567057
$765$	−20.8754	−0.754751
$766$	39.8885	1.44123
$767$	11.8328	0.427258
$768$	35.5066	1.28123
$769$	6.70820	0.241904	0.120952	−	0.992658i	$-0.461405\pi$
$769$	6.70820	0.241904	0.120952	+	0.992658i	$0.461405\pi$
$770$	−3.70820	−0.133634
$771$	59.1591	2.13056
$772$	−13.5836	−0.488884
$773$	24.9787	0.898422	0.449211	−	0.893426i	$-0.351705\pi$
$773$	24.9787	0.898422	0.449211	+	0.893426i	$0.351705\pi$
$774$	56.1246	2.01736
$775$	−0.313082	−0.0112462
$776$	−8.61803	−0.309369
$777$	−11.2361	−0.403092
$778$	−34.2705	−1.22866
$779$	17.5623	0.629235
$780$	−3.52786	−0.126318
$781$	42.5410	1.52224
$782$	44.2148	1.58112
$783$	5.00000	0.178685
$784$	32.1246	1.14731
$785$	−16.0689	−0.573523
$786$	−38.8885	−1.38711
$787$	−27.1246	−0.966888	−0.483444	−	0.875375i	$-0.660614\pi$
$787$	−27.1246	−0.966888	−0.483444	+	0.875375i	$0.660614\pi$
$788$	−14.3262	−0.510351
$789$	−9.85410	−0.350815
$790$	−3.41641	−0.121550
$791$	−7.27051	−0.258510
$792$	25.8541	0.918686
$793$	−5.29180	−0.187917
$794$	56.3607	2.00017
$795$	−24.6525	−0.874333
$796$	−15.0000	−0.531661
$797$	14.8328	0.525405	0.262703	−	0.964877i	$-0.415386\pi$
$797$	14.8328	0.525405	0.262703	+	0.964877i	$0.415386\pi$
$798$	15.3262	0.542543
$799$	−2.70820	−0.0958094
$800$	11.7426	0.415165
$801$	15.9787	0.564580
$802$	45.5967	1.61008
$803$	27.2705	0.962355
$804$	−19.4164	−0.684764
$805$	4.76393	0.167907
$806$	0.257354	0.00906492
$807$	47.3607	1.66717
$808$	−11.3820	−0.400416
$809$	−52.6869	−1.85237	−0.926187	−	0.377065i	$-0.876933\pi$
$809$	−52.6869	−1.85237	−0.926187	+	0.377065i	$0.876933\pi$
$810$	11.4164	0.401132
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	−0.854102	−0.0299731
$813$	5.23607	0.183637
$814$	−33.7082	−1.18147
$815$	−26.6525	−0.933596
$816$	−55.6869	−1.94943
$817$	−52.6869	−1.84328
$818$	−51.8328	−1.81229
$819$	−4.20163	−0.146817
$820$	2.29180	0.0800330
$821$	−31.0902	−1.08505	−0.542527	−	0.840038i	$-0.682532\pi$
$821$	−31.0902	−1.08505	−0.542527	+	0.840038i	$0.682532\pi$
$822$	10.4721	0.365258
$823$	−0.798374	−0.0278296	−0.0139148	−	0.999903i	$-0.504429\pi$
$823$	−0.798374	−0.0278296	−0.0139148	+	0.999903i	$0.504429\pi$
$824$	−27.7639	−0.967202
$825$	27.2705	0.949437
$826$	−6.70820	−0.233408
$827$	−27.9787	−0.972915	−0.486458	−	0.873704i	$-0.661711\pi$
$827$	−27.9787	−0.972915	−0.486458	+	0.873704i	$0.661711\pi$
$828$	14.8541	0.516216
$829$	−47.3607	−1.64490	−0.822452	−	0.568834i	$-0.807395\pi$
$829$	−47.3607	−1.64490	−0.822452	+	0.568834i	$0.807395\pi$
$830$	−16.9443	−0.588144
$831$	−25.0344	−0.868435
$832$	7.47214	0.259050
$833$	−29.0000	−1.00479
$834$	−88.3394	−3.05894
$835$	−25.4164	−0.879571
$836$	10.8541	0.375397
$837$	0.201626	0.00696922
$838$	31.5066	1.08838
$839$	4.79837	0.165658	0.0828291	−	0.996564i	$-0.473604\pi$
$839$	4.79837	0.165658	0.0828291	+	0.996564i	$0.473604\pi$
$840$	−4.47214	−0.154303
$841$	−24.0000	−0.827586
$842$	23.2361	0.800768
$843$	21.4164	0.737620
$844$	0.618034	0.0212736
$845$	12.2229	0.420481
$846$	−3.85410	−0.132507
$847$	1.23607	0.0424718
$848$	−36.9787	−1.26985
$849$	76.2492	2.61687
$850$	−24.6180	−0.844392
$851$	43.3050	1.48447
$852$	−22.9443	−0.786058
$853$	51.6869	1.76973	0.884863	−	0.465851i	$-0.154252\pi$
$853$	51.6869	1.76973	0.884863	+	0.465851i	$0.154252\pi$
$854$	3.00000	0.102658
$855$	27.8885	0.953768
$856$	17.5623	0.600267
$857$	−29.1591	−0.996054	−0.498027	−	0.867161i	$-0.665942\pi$
$857$	−29.1591	−0.996054	−0.498027	+	0.867161i	$0.665942\pi$
$858$	−22.4164	−0.765284
$859$	−44.2705	−1.51049	−0.755245	−	0.655442i	$-0.772482\pi$
$859$	−44.2705	−1.51049	−0.755245	+	0.655442i	$0.772482\pi$
$860$	−6.87539	−0.234449
$861$	4.85410	0.165427
$862$	−26.0344	−0.886737
$863$	−19.4164	−0.660942	−0.330471	−	0.943816i	$-0.607208\pi$
$863$	−19.4164	−0.660942	−0.330471	+	0.943816i	$0.607208\pi$
$864$	−7.56231	−0.257275
$865$	−11.1246	−0.378248
$866$	−12.4721	−0.423820
$867$	5.76393	0.195753
$868$	−0.0344419	−0.00116903
$869$	−5.12461	−0.173841
$870$	−11.7082	−0.396945
$871$	−21.1672	−0.717223
$872$	−3.09017	−0.104646
$873$	14.8541	0.502735
$874$	−59.0689	−1.99803
$875$	−6.47214	−0.218798
$876$	−14.7082	−0.496944
$877$	52.2705	1.76505	0.882525	−	0.470266i	$-0.155842\pi$
$877$	52.2705	1.76505	0.882525	+	0.470266i	$0.155842\pi$
$878$	−6.38197	−0.215381
$879$	−30.5066	−1.02896
$880$	−18.0000	−0.606780
$881$	27.4508	0.924843	0.462421	−	0.886660i	$-0.346981\pi$
$881$	27.4508	0.924843	0.462421	+	0.886660i	$0.346981\pi$
$882$	−41.2705	−1.38965
$883$	−3.43769	−0.115688	−0.0578438	−	0.998326i	$-0.518423\pi$
$883$	−3.43769	−0.115688	−0.0578438	+	0.998326i	$0.518423\pi$
$884$	4.77709	0.160671
$885$	−21.7082	−0.729713
$886$	6.79837	0.228396
$887$	−43.6312	−1.46499	−0.732496	−	0.680771i	$-0.761645\pi$
$887$	−43.6312	−1.46499	−0.732496	+	0.680771i	$0.761645\pi$
$888$	−40.6525	−1.36421
$889$	−0.798374	−0.0267766
$890$	−8.29180	−0.277942
$891$	17.1246	0.573696
$892$	−16.7984	−0.562451
$893$	3.61803	0.121073
$894$	37.8885	1.26718
$895$	−11.4590	−0.383031
$896$	−8.41641	−0.281172
$897$	28.7984	0.961550
$898$	52.1591	1.74057
$899$	0.201626	0.00672461
$900$	−8.27051	−0.275684
$901$	33.3820	1.11211
$902$	14.5623	0.484872
$903$	−14.5623	−0.484603
$904$	−26.3050	−0.874890
$905$	3.70820	0.123265
$906$	−89.3394	−2.96810
$907$	0.639320	0.0212283	0.0106141	−	0.999944i	$-0.496621\pi$
$907$	0.639320	0.0212283	0.0106141	+	0.999944i	$0.496621\pi$
$908$	−9.20163	−0.305367
$909$	19.6180	0.650689
$910$	2.18034	0.0722776
$911$	33.6312	1.11425	0.557126	−	0.830428i	$-0.311904\pi$
$911$	33.6312	1.11425	0.557126	+	0.830428i	$0.311904\pi$
$912$	74.3951	2.46347
$913$	−25.4164	−0.841160
$914$	−47.8328	−1.58217
$915$	9.70820	0.320943
$916$	10.3262	0.341189
$917$	5.67376	0.187364
$918$	15.8541	0.523263
$919$	−51.8328	−1.70981	−0.854903	−	0.518787i	$-0.826384\pi$
$919$	−51.8328	−1.70981	−0.854903	+	0.518787i	$0.826384\pi$
$920$	17.2361	0.568256
$921$	−3.00000	−0.0988534
$922$	56.7771	1.86985
$923$	−25.0132	−0.823318
$924$	3.00000	0.0986928
$925$	−24.1115	−0.792780
$926$	34.8885	1.14651
$927$	47.8541	1.57173
$928$	−7.56231	−0.248245
$929$	29.3951	0.964423	0.482211	−	0.876055i	$-0.339834\pi$
$929$	29.3951	0.964423	0.482211	+	0.876055i	$0.339834\pi$
$930$	−0.472136	−0.0154819
$931$	38.7426	1.26974
$932$	−1.47214	−0.0482214
$933$	52.5967	1.72194
$934$	−53.0344	−1.73534
$935$	16.2492	0.531406
$936$	−15.2016	−0.496881
$937$	18.1246	0.592105	0.296053	−	0.955172i	$-0.404330\pi$
$937$	18.1246	0.592105	0.296053	+	0.955172i	$0.404330\pi$
$938$	12.0000	0.391814
$939$	62.3050	2.03325
$940$	0.472136	0.0153994
$941$	23.9098	0.779438	0.389719	−	0.920934i	$-0.372572\pi$
$941$	23.9098	0.779438	0.389719	+	0.920934i	$0.372572\pi$
$942$	55.0689	1.79424
$943$	−18.7082	−0.609223
$944$	−32.5623	−1.05981
$945$	1.70820	0.0555679
$946$	−43.6869	−1.42038
$947$	−1.47214	−0.0478380	−0.0239190	−	0.999714i	$-0.507614\pi$
$947$	−1.47214	−0.0478380	−0.0239190	+	0.999714i	$0.507614\pi$
$948$	2.76393	0.0897683
$949$	−16.0344	−0.520500
$950$	32.8885	1.06705
$951$	−30.8885	−1.00163
$952$	6.05573	0.196267
$953$	−6.65248	−0.215495	−0.107747	−	0.994178i	$-0.534364\pi$
$953$	−6.65248	−0.215495	−0.107747	+	0.994178i	$0.534364\pi$
$954$	47.5066	1.53808
$955$	31.3475	1.01438
$956$	12.4377	0.402264
$957$	−17.5623	−0.567709
$958$	−37.6869	−1.21761
$959$	−1.52786	−0.0493373
$960$	−13.7082	−0.442430
$961$	−30.9919	−0.999738
$962$	19.8197	0.639011
$963$	−30.2705	−0.975454
$964$	−1.12461	−0.0362213
$965$	27.1672	0.874543
$966$	−16.3262	−0.525288
$967$	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
$969$	−67.1591	−2.15746
$970$	−7.70820	−0.247496
$971$	−5.63932	−0.180974	−0.0904872	−	0.995898i	$-0.528842\pi$
$971$	−5.63932	−0.180974	−0.0904872	+	0.995898i	$0.528842\pi$
$972$	−13.3820	−0.429227
$973$	12.8885	0.413188
$974$	−7.38197	−0.236533
$975$	−16.0344	−0.513513
$976$	14.5623	0.466128
$977$	17.3951	0.556519	0.278260	−	0.960506i	$-0.410242\pi$
$977$	17.3951	0.556519	0.278260	+	0.960506i	$0.410242\pi$
$978$	91.3394	2.92071
$979$	−12.4377	−0.397510
$980$	5.05573	0.161499
$981$	5.32624	0.170054
$982$	5.14590	0.164212
$983$	−41.7771	−1.33248	−0.666241	−	0.745736i	$-0.732098\pi$
$983$	−41.7771	−1.33248	−0.666241	+	0.745736i	$0.732098\pi$
$984$	17.5623	0.559866
$985$	28.6525	0.912944
$986$	15.8541	0.504897
$987$	1.00000	0.0318304
$988$	−6.38197	−0.203037
$989$	56.1246	1.78466
$990$	23.1246	0.734948
$991$	−48.4508	−1.53909	−0.769546	−	0.638591i	$-0.779517\pi$
$991$	−48.4508	−1.53909	−0.769546	+	0.638591i	$0.779517\pi$
$992$	−0.304952	−0.00968223
$993$	−63.3050	−2.00892
$994$	14.1803	0.449773
$995$	30.0000	0.951064
$996$	13.7082	0.434361
$997$	−35.0902	−1.11132	−0.555658	−	0.831411i	$-0.687534\pi$
$997$	−35.0902	−1.11132	−0.555658	+	0.831411i	$0.687534\pi$
$998$	−26.7082	−0.845433
$999$	15.5279	0.491280

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -1.23607 q^{5} +4.23607 q^{6} -0.618034 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} -1.23607 q^{5} +4.23607 q^{6} -0.618034 q^{7} -2.23607 q^{8} +3.85410 q^{9} -2.00000 q^{10} -3.00000 q^{11} +1.61803 q^{12} +1.76393 q^{13} -1.00000 q^{14} -3.23607 q^{15} -4.85410 q^{16} +4.38197 q^{17} +6.23607 q^{18} -5.85410 q^{19} -0.763932 q^{20} -1.61803 q^{21} -4.85410 q^{22} +6.23607 q^{23} -5.85410 q^{24} -3.47214 q^{25} +2.85410 q^{26} +2.23607 q^{27} -0.381966 q^{28} +2.23607 q^{29} -5.23607 q^{30} +0.0901699 q^{31} -3.38197 q^{32} -7.85410 q^{33} +7.09017 q^{34} +0.763932 q^{35} +2.38197 q^{36} +6.94427 q^{37} -9.47214 q^{38} +4.61803 q^{39} +2.76393 q^{40} -3.00000 q^{41} -2.61803 q^{42} +9.00000 q^{43} -1.85410 q^{44} -4.76393 q^{45} +10.0902 q^{46} -0.618034 q^{47} -12.7082 q^{48} -6.61803 q^{49} -5.61803 q^{50} +11.4721 q^{51} +1.09017 q^{52} +7.61803 q^{53} +3.61803 q^{54} +3.70820 q^{55} +1.38197 q^{56} -15.3262 q^{57} +3.61803 q^{58} +6.70820 q^{59} -2.00000 q^{60} -3.00000 q^{61} +0.145898 q^{62} -2.38197 q^{63} +4.23607 q^{64} -2.18034 q^{65} -12.7082 q^{66} -12.0000 q^{67} +2.70820 q^{68} +16.3262 q^{69} +1.23607 q^{70} -14.1803 q^{71} -8.61803 q^{72} -9.09017 q^{73} +11.2361 q^{74} -9.09017 q^{75} -3.61803 q^{76} +1.85410 q^{77} +7.47214 q^{78} +1.70820 q^{79} +6.00000 q^{80} -5.70820 q^{81} -4.85410 q^{82} +8.47214 q^{83} -1.00000 q^{84} -5.41641 q^{85} +14.5623 q^{86} +5.85410 q^{87} +6.70820 q^{88} +4.14590 q^{89} -7.70820 q^{90} -1.09017 q^{91} +3.85410 q^{92} +0.236068 q^{93} -1.00000 q^{94} +7.23607 q^{95} -8.85410 q^{96} +3.85410 q^{97} -10.7082 q^{98} -11.5623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 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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