LMFDB - Embedded newform 231.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(1,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("231.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
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	$\chi$	$=$	231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.618034 q^{10} +1.00000 q^{11} -1.61803 q^{12} +3.47214 q^{13} -0.618034 q^{14} +1.00000 q^{15} +1.85410 q^{16} +5.23607 q^{17} -0.618034 q^{18} -6.70820 q^{19} -1.61803 q^{20} +1.00000 q^{21} -0.618034 q^{22} +5.70820 q^{23} +2.23607 q^{24} -4.00000 q^{25} -2.14590 q^{26} +1.00000 q^{27} -1.61803 q^{28} +5.00000 q^{29} -0.618034 q^{30} -5.23607 q^{31} -5.61803 q^{32} +1.00000 q^{33} -3.23607 q^{34} +1.00000 q^{35} -1.61803 q^{36} -7.00000 q^{37} +4.14590 q^{38} +3.47214 q^{39} +2.23607 q^{40} -2.47214 q^{41} -0.618034 q^{42} +5.70820 q^{43} -1.61803 q^{44} +1.00000 q^{45} -3.52786 q^{46} +0.236068 q^{47} +1.85410 q^{48} +1.00000 q^{49} +2.47214 q^{50} +5.23607 q^{51} -5.61803 q^{52} -12.1803 q^{53} -0.618034 q^{54} +1.00000 q^{55} +2.23607 q^{56} -6.70820 q^{57} -3.09017 q^{58} -11.1803 q^{59} -1.61803 q^{60} +2.00000 q^{61} +3.23607 q^{62} +1.00000 q^{63} -0.236068 q^{64} +3.47214 q^{65} -0.618034 q^{66} -9.76393 q^{67} -8.47214 q^{68} +5.70820 q^{69} -0.618034 q^{70} -2.47214 q^{71} +2.23607 q^{72} +4.52786 q^{73} +4.32624 q^{74} -4.00000 q^{75} +10.8541 q^{76} +1.00000 q^{77} -2.14590 q^{78} -14.4721 q^{79} +1.85410 q^{80} +1.00000 q^{81} +1.52786 q^{82} +6.76393 q^{83} -1.61803 q^{84} +5.23607 q^{85} -3.52786 q^{86} +5.00000 q^{87} +2.23607 q^{88} -4.47214 q^{89} -0.618034 q^{90} +3.47214 q^{91} -9.23607 q^{92} -5.23607 q^{93} -0.145898 q^{94} -6.70820 q^{95} -5.61803 q^{96} +9.70820 q^{97} -0.618034 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{9} + q^{10} + 2 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - 3 q^{16} + 6 q^{17} + q^{18} - q^{20} + 2 q^{21} + q^{22} - 2 q^{23} - 8 q^{25} - 11 q^{26} + 2 q^{27} - q^{28} + 10 q^{29} + q^{30} - 6 q^{31} - 9 q^{32} + 2 q^{33} - 2 q^{34} + 2 q^{35} - q^{36} - 14 q^{37} + 15 q^{38} - 2 q^{39} + 4 q^{41} + q^{42} - 2 q^{43} - q^{44} + 2 q^{45} - 16 q^{46} - 4 q^{47} - 3 q^{48} + 2 q^{49} - 4 q^{50} + 6 q^{51} - 9 q^{52} - 2 q^{53} + q^{54} + 2 q^{55} + 5 q^{58} - q^{60} + 4 q^{61} + 2 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} + q^{66} - 24 q^{67} - 8 q^{68} - 2 q^{69} + q^{70} + 4 q^{71} + 18 q^{73} - 7 q^{74} - 8 q^{75} + 15 q^{76} + 2 q^{77} - 11 q^{78} - 20 q^{79} - 3 q^{80} + 2 q^{81} + 12 q^{82} + 18 q^{83} - q^{84} + 6 q^{85} - 16 q^{86} + 10 q^{87} + q^{90} - 2 q^{91} - 14 q^{92} - 6 q^{93} - 7 q^{94} - 9 q^{96} + 6 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^9 + q^10 + 2 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - 3 * q^16 + 6 * q^17 + q^18 - q^20 + 2 * q^21 + q^22 - 2 * q^23 - 8 * q^25 - 11 * q^26 + 2 * q^27 - q^28 + 10 * q^29 + q^30 - 6 * q^31 - 9 * q^32 + 2 * q^33 - 2 * q^34 + 2 * q^35 - q^36 - 14 * q^37 + 15 * q^38 - 2 * q^39 + 4 * q^41 + q^42 - 2 * q^43 - q^44 + 2 * q^45 - 16 * q^46 - 4 * q^47 - 3 * q^48 + 2 * q^49 - 4 * q^50 + 6 * q^51 - 9 * q^52 - 2 * q^53 + q^54 + 2 * q^55 + 5 * q^58 - q^60 + 4 * q^61 + 2 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 + q^66 - 24 * q^67 - 8 * q^68 - 2 * q^69 + q^70 + 4 * q^71 + 18 * q^73 - 7 * q^74 - 8 * q^75 + 15 * q^76 + 2 * q^77 - 11 * q^78 - 20 * q^79 - 3 * q^80 + 2 * q^81 + 12 * q^82 + 18 * q^83 - q^84 + 6 * q^85 - 16 * q^86 + 10 * q^87 + q^90 - 2 * q^91 - 14 * q^92 - 6 * q^93 - 7 * q^94 - 9 * q^96 + 6 * q^97 + q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61803	−0.809017
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.618034	−0.252311
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	−0.618034	−0.195440
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.61803	−0.467086
$13$	3.47214	0.962997	0.481499	−	0.876447i	$-0.340093\pi$
$13$	3.47214	0.962997	0.481499	+	0.876447i	$0.340093\pi$
$14$	−0.618034	−0.165177
$15$	1.00000	0.258199
$16$	1.85410	0.463525
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	−0.618034	−0.145672
$19$	−6.70820	−1.53897	−0.769484	−	0.638666i	$-0.779486\pi$
$19$	−6.70820	−1.53897	−0.769484	+	0.638666i	$0.779486\pi$
$20$	−1.61803	−0.361803
$21$	1.00000	0.218218
$22$	−0.618034	−0.131765
$23$	5.70820	1.19024	0.595121	−	0.803636i	$-0.297104\pi$
$23$	5.70820	1.19024	0.595121	+	0.803636i	$0.297104\pi$
$24$	2.23607	0.456435
$25$	−4.00000	−0.800000
$26$	−2.14590	−0.420845
$27$	1.00000	0.192450
$28$	−1.61803	−0.305780
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	−0.618034	−0.112837
$31$	−5.23607	−0.940426	−0.470213	−	0.882553i	$-0.655823\pi$
$31$	−5.23607	−0.940426	−0.470213	+	0.882553i	$0.655823\pi$
$32$	−5.61803	−0.993137
$33$	1.00000	0.174078
$34$	−3.23607	−0.554981
$35$	1.00000	0.169031
$36$	−1.61803	−0.269672
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	4.14590	0.672553
$39$	3.47214	0.555987
$40$	2.23607	0.353553
$41$	−2.47214	−0.386083	−0.193041	−	0.981191i	$-0.561835\pi$
$41$	−2.47214	−0.386083	−0.193041	+	0.981191i	$0.561835\pi$
$42$	−0.618034	−0.0953647
$43$	5.70820	0.870493	0.435246	−	0.900311i	$-0.356661\pi$
$43$	5.70820	0.870493	0.435246	+	0.900311i	$0.356661\pi$
$44$	−1.61803	−0.243928
$45$	1.00000	0.149071
$46$	−3.52786	−0.520155
$47$	0.236068	0.0344341	0.0172170	−	0.999852i	$-0.494519\pi$
$47$	0.236068	0.0344341	0.0172170	+	0.999852i	$0.494519\pi$
$48$	1.85410	0.267617
$49$	1.00000	0.142857
$50$	2.47214	0.349613
$51$	5.23607	0.733196
$52$	−5.61803	−0.779081
$53$	−12.1803	−1.67310	−0.836549	−	0.547892i	$-0.815431\pi$
$53$	−12.1803	−1.67310	−0.836549	+	0.547892i	$0.815431\pi$
$54$	−0.618034	−0.0841038
$55$	1.00000	0.134840
$56$	2.23607	0.298807
$57$	−6.70820	−0.888523
$58$	−3.09017	−0.405759
$59$	−11.1803	−1.45556	−0.727778	−	0.685813i	$-0.759447\pi$
$59$	−11.1803	−1.45556	−0.727778	+	0.685813i	$0.759447\pi$
$60$	−1.61803	−0.208887
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	3.23607	0.410981
$63$	1.00000	0.125988
$64$	−0.236068	−0.0295085
$65$	3.47214	0.430665
$66$	−0.618034	−0.0760747
$67$	−9.76393	−1.19285	−0.596427	−	0.802667i	$-0.703414\pi$
$67$	−9.76393	−1.19285	−0.596427	+	0.802667i	$0.703414\pi$
$68$	−8.47214	−1.02740
$69$	5.70820	0.687187
$70$	−0.618034	−0.0738692
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	2.23607	0.263523
$73$	4.52786	0.529946	0.264973	−	0.964256i	$-0.414637\pi$
$73$	4.52786	0.529946	0.264973	+	0.964256i	$0.414637\pi$
$74$	4.32624	0.502915
$75$	−4.00000	−0.461880
$76$	10.8541	1.24505
$77$	1.00000	0.113961
$78$	−2.14590	−0.242975
$79$	−14.4721	−1.62824	−0.814121	−	0.580695i	$-0.802781\pi$
$79$	−14.4721	−1.62824	−0.814121	+	0.580695i	$0.802781\pi$
$80$	1.85410	0.207295
$81$	1.00000	0.111111
$82$	1.52786	0.168724
$83$	6.76393	0.742438	0.371219	−	0.928545i	$-0.378940\pi$
$83$	6.76393	0.742438	0.371219	+	0.928545i	$0.378940\pi$
$84$	−1.61803	−0.176542
$85$	5.23607	0.567931
$86$	−3.52786	−0.380419
$87$	5.00000	0.536056
$88$	2.23607	0.238366
$89$	−4.47214	−0.474045	−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214	−0.474045	−0.237023	+	0.971504i	$0.576172\pi$
$90$	−0.618034	−0.0651465
$91$	3.47214	0.363979
$92$	−9.23607	−0.962927
$93$	−5.23607	−0.542955
$94$	−0.145898	−0.0150482
$95$	−6.70820	−0.688247
$96$	−5.61803	−0.573388
$97$	9.70820	0.985719	0.492859	−	0.870109i	$-0.335952\pi$
$97$	9.70820	0.985719	0.492859	+	0.870109i	$0.335952\pi$
$98$	−0.618034	−0.0624309
$99$	1.00000	0.100504
$100$	6.47214	0.647214
$101$	18.1803	1.80901	0.904506	−	0.426461i	$-0.140240\pi$
$101$	18.1803	1.80901	0.904506	+	0.426461i	$0.140240\pi$
$102$	−3.23607	−0.320418
$103$	17.4164	1.71609	0.858045	−	0.513575i	$-0.171679\pi$
$103$	17.4164	1.71609	0.858045	+	0.513575i	$0.171679\pi$
$104$	7.76393	0.761316
$105$	1.00000	0.0975900
$106$	7.52786	0.731171
$107$	−4.23607	−0.409516	−0.204758	−	0.978813i	$-0.565641\pi$
$107$	−4.23607	−0.409516	−0.204758	+	0.978813i	$0.565641\pi$
$108$	−1.61803	−0.155695
$109$	2.76393	0.264737	0.132368	−	0.991201i	$-0.457742\pi$
$109$	2.76393	0.264737	0.132368	+	0.991201i	$0.457742\pi$
$110$	−0.618034	−0.0589272
$111$	−7.00000	−0.664411
$112$	1.85410	0.175196
$113$	−0.472136	−0.0444148	−0.0222074	−	0.999753i	$-0.507069\pi$
$113$	−0.472136	−0.0444148	−0.0222074	+	0.999753i	$0.507069\pi$
$114$	4.14590	0.388299
$115$	5.70820	0.532293
$116$	−8.09017	−0.751153
$117$	3.47214	0.320999
$118$	6.90983	0.636101
$119$	5.23607	0.479990
$120$	2.23607	0.204124
$121$	1.00000	0.0909091
$122$	−1.23607	−0.111908
$123$	−2.47214	−0.222905
$124$	8.47214	0.760820
$125$	−9.00000	−0.804984
$126$	−0.618034	−0.0550588
$127$	−12.6525	−1.12273	−0.561363	−	0.827570i	$-0.689723\pi$
$127$	−12.6525	−1.12273	−0.561363	+	0.827570i	$0.689723\pi$
$128$	11.3820	1.00603
$129$	5.70820	0.502579
$130$	−2.14590	−0.188208
$131$	0.944272	0.0825014	0.0412507	−	0.999149i	$-0.486866\pi$
$131$	0.944272	0.0825014	0.0412507	+	0.999149i	$0.486866\pi$
$132$	−1.61803	−0.140832
$133$	−6.70820	−0.581675
$134$	6.03444	0.521296
$135$	1.00000	0.0860663
$136$	11.7082	1.00397
$137$	19.7082	1.68379	0.841893	−	0.539645i	$-0.181441\pi$
$137$	19.7082	1.68379	0.841893	+	0.539645i	$0.181441\pi$
$138$	−3.52786	−0.300312
$139$	14.4721	1.22751	0.613755	−	0.789496i	$-0.289658\pi$
$139$	14.4721	1.22751	0.613755	+	0.789496i	$0.289658\pi$
$140$	−1.61803	−0.136749
$141$	0.236068	0.0198805
$142$	1.52786	0.128216
$143$	3.47214	0.290355
$144$	1.85410	0.154508
$145$	5.00000	0.415227
$146$	−2.79837	−0.231595
$147$	1.00000	0.0824786
$148$	11.3262	0.931011
$149$	5.00000	0.409616	0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000	0.409616	0.204808	+	0.978802i	$0.434343\pi$
$150$	2.47214	0.201849
$151$	−14.1803	−1.15398	−0.576990	−	0.816751i	$-0.695773\pi$
$151$	−14.1803	−1.15398	−0.576990	+	0.816751i	$0.695773\pi$
$152$	−15.0000	−1.21666
$153$	5.23607	0.423311
$154$	−0.618034	−0.0498026
$155$	−5.23607	−0.420571
$156$	−5.61803	−0.449803
$157$	−15.4164	−1.23036	−0.615182	−	0.788385i	$-0.710917\pi$
$157$	−15.4164	−1.23036	−0.615182	+	0.788385i	$0.710917\pi$
$158$	8.94427	0.711568
$159$	−12.1803	−0.965964
$160$	−5.61803	−0.444145
$161$	5.70820	0.449869
$162$	−0.618034	−0.0485573
$163$	−22.7082	−1.77864	−0.889322	−	0.457282i	$-0.848823\pi$
$163$	−22.7082	−1.77864	−0.889322	+	0.457282i	$0.848823\pi$
$164$	4.00000	0.312348
$165$	1.00000	0.0778499
$166$	−4.18034	−0.324457
$167$	−22.6525	−1.75290	−0.876451	−	0.481492i	$-0.840095\pi$
$167$	−22.6525	−1.75290	−0.876451	+	0.481492i	$0.840095\pi$
$168$	2.23607	0.172516
$169$	−0.944272	−0.0726363
$170$	−3.23607	−0.248195
$171$	−6.70820	−0.512989
$172$	−9.23607	−0.704244
$173$	−1.52786	−0.116161	−0.0580807	−	0.998312i	$-0.518498\pi$
$173$	−1.52786	−0.116161	−0.0580807	+	0.998312i	$0.518498\pi$
$174$	−3.09017	−0.234265
$175$	−4.00000	−0.302372
$176$	1.85410	0.139758
$177$	−11.1803	−0.840366
$178$	2.76393	0.207165
$179$	8.94427	0.668526	0.334263	−	0.942480i	$-0.391513\pi$
$179$	8.94427	0.668526	0.334263	+	0.942480i	$0.391513\pi$
$180$	−1.61803	−0.120601
$181$	−0.763932	−0.0567826	−0.0283913	−	0.999597i	$-0.509038\pi$
$181$	−0.763932	−0.0567826	−0.0283913	+	0.999597i	$0.509038\pi$
$182$	−2.14590	−0.159065
$183$	2.00000	0.147844
$184$	12.7639	0.940970
$185$	−7.00000	−0.514650
$186$	3.23607	0.237280
$187$	5.23607	0.382899
$188$	−0.381966	−0.0278577
$189$	1.00000	0.0727393
$190$	4.14590	0.300775
$191$	−10.7639	−0.778851	−0.389425	−	0.921058i	$-0.627326\pi$
$191$	−10.7639	−0.778851	−0.389425	+	0.921058i	$0.627326\pi$
$192$	−0.236068	−0.0170367
$193$	14.6525	1.05471	0.527354	−	0.849646i	$-0.323184\pi$
$193$	14.6525	1.05471	0.527354	+	0.849646i	$0.323184\pi$
$194$	−6.00000	−0.430775
$195$	3.47214	0.248645
$196$	−1.61803	−0.115574
$197$	−16.4721	−1.17359	−0.586796	−	0.809735i	$-0.699611\pi$
$197$	−16.4721	−1.17359	−0.586796	+	0.809735i	$0.699611\pi$
$198$	−0.618034	−0.0439218
$199$	−3.81966	−0.270769	−0.135384	−	0.990793i	$-0.543227\pi$
$199$	−3.81966	−0.270769	−0.135384	+	0.990793i	$0.543227\pi$
$200$	−8.94427	−0.632456
$201$	−9.76393	−0.688695
$202$	−11.2361	−0.790567
$203$	5.00000	0.350931
$204$	−8.47214	−0.593168
$205$	−2.47214	−0.172661
$206$	−10.7639	−0.749959
$207$	5.70820	0.396748
$208$	6.43769	0.446374
$209$	−6.70820	−0.464016
$210$	−0.618034	−0.0426484
$211$	5.41641	0.372881	0.186440	−	0.982466i	$-0.440305\pi$
$211$	5.41641	0.372881	0.186440	+	0.982466i	$0.440305\pi$
$212$	19.7082	1.35357
$213$	−2.47214	−0.169388
$214$	2.61803	0.178965
$215$	5.70820	0.389296
$216$	2.23607	0.152145
$217$	−5.23607	−0.355447
$218$	−1.70820	−0.115694
$219$	4.52786	0.305965
$220$	−1.61803	−0.109088
$221$	18.1803	1.22294
$222$	4.32624	0.290358
$223$	−6.00000	−0.401790	−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000	−0.401790	−0.200895	+	0.979613i	$0.564385\pi$
$224$	−5.61803	−0.375371
$225$	−4.00000	−0.266667
$226$	0.291796	0.0194100
$227$	−2.00000	−0.132745	−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000	−0.132745	−0.0663723	+	0.997795i	$0.521143\pi$
$228$	10.8541	0.718830
$229$	7.23607	0.478173	0.239086	−	0.970998i	$-0.423152\pi$
$229$	7.23607	0.478173	0.239086	+	0.970998i	$0.423152\pi$
$230$	−3.52786	−0.232620
$231$	1.00000	0.0657952
$232$	11.1803	0.734025
$233$	−14.9443	−0.979032	−0.489516	−	0.871994i	$-0.662826\pi$
$233$	−14.9443	−0.979032	−0.489516	+	0.871994i	$0.662826\pi$
$234$	−2.14590	−0.140282
$235$	0.236068	0.0153994
$236$	18.0902	1.17757
$237$	−14.4721	−0.940066
$238$	−3.23607	−0.209763
$239$	10.1246	0.654907	0.327453	−	0.944867i	$-0.393810\pi$
$239$	10.1246	0.654907	0.327453	+	0.944867i	$0.393810\pi$
$240$	1.85410	0.119682
$241$	25.9443	1.67122	0.835609	−	0.549325i	$-0.185115\pi$
$241$	25.9443	1.67122	0.835609	+	0.549325i	$0.185115\pi$
$242$	−0.618034	−0.0397287
$243$	1.00000	0.0641500
$244$	−3.23607	−0.207168
$245$	1.00000	0.0638877
$246$	1.52786	0.0974131
$247$	−23.2918	−1.48202
$248$	−11.7082	−0.743472
$249$	6.76393	0.428647
$250$	5.56231	0.351791
$251$	12.1246	0.765299	0.382649	−	0.923894i	$-0.375012\pi$
$251$	12.1246	0.765299	0.382649	+	0.923894i	$0.375012\pi$
$252$	−1.61803	−0.101927
$253$	5.70820	0.358872
$254$	7.81966	0.490649
$255$	5.23607	0.327895
$256$	−6.56231	−0.410144
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	−3.52786	−0.219635
$259$	−7.00000	−0.434959
$260$	−5.61803	−0.348416
$261$	5.00000	0.309492
$262$	−0.583592	−0.0360544
$263$	−26.1246	−1.61091	−0.805456	−	0.592655i	$-0.798080\pi$
$263$	−26.1246	−1.61091	−0.805456	+	0.592655i	$0.798080\pi$
$264$	2.23607	0.137620
$265$	−12.1803	−0.748232
$266$	4.14590	0.254201
$267$	−4.47214	−0.273690
$268$	15.7984	0.965039
$269$	1.05573	0.0643689	0.0321844	−	0.999482i	$-0.489754\pi$
$269$	1.05573	0.0643689	0.0321844	+	0.999482i	$0.489754\pi$
$270$	−0.618034	−0.0376124
$271$	5.29180	0.321454	0.160727	−	0.986999i	$-0.448616\pi$
$271$	5.29180	0.321454	0.160727	+	0.986999i	$0.448616\pi$
$272$	9.70820	0.588646
$273$	3.47214	0.210143
$274$	−12.1803	−0.735841
$275$	−4.00000	−0.241209
$276$	−9.23607	−0.555946
$277$	−6.47214	−0.388873	−0.194436	−	0.980915i	$-0.562288\pi$
$277$	−6.47214	−0.388873	−0.194436	+	0.980915i	$0.562288\pi$
$278$	−8.94427	−0.536442
$279$	−5.23607	−0.313475
$280$	2.23607	0.133631
$281$	11.4721	0.684370	0.342185	−	0.939633i	$-0.388833\pi$
$281$	11.4721	0.684370	0.342185	+	0.939633i	$0.388833\pi$
$282$	−0.145898	−0.00868810
$283$	−13.7639	−0.818181	−0.409090	−	0.912494i	$-0.634154\pi$
$283$	−13.7639	−0.818181	−0.409090	+	0.912494i	$0.634154\pi$
$284$	4.00000	0.237356
$285$	−6.70820	−0.397360
$286$	−2.14590	−0.126890
$287$	−2.47214	−0.145926
$288$	−5.61803	−0.331046
$289$	10.4164	0.612730
$290$	−3.09017	−0.181461
$291$	9.70820	0.569105
$292$	−7.32624	−0.428736
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	−0.618034	−0.0360445
$295$	−11.1803	−0.650945
$296$	−15.6525	−0.909782
$297$	1.00000	0.0580259
$298$	−3.09017	−0.179009
$299$	19.8197	1.14620
$300$	6.47214	0.373669
$301$	5.70820	0.329015
$302$	8.76393	0.504308
$303$	18.1803	1.04443
$304$	−12.4377	−0.713351
$305$	2.00000	0.114520
$306$	−3.23607	−0.184994
$307$	−20.9443	−1.19535	−0.597676	−	0.801737i	$-0.703909\pi$
$307$	−20.9443	−1.19535	−0.597676	+	0.801737i	$0.703909\pi$
$308$	−1.61803	−0.0921960
$309$	17.4164	0.990785
$310$	3.23607	0.183796
$311$	9.88854	0.560728	0.280364	−	0.959894i	$-0.409545\pi$
$311$	9.88854	0.560728	0.280364	+	0.959894i	$0.409545\pi$
$312$	7.76393	0.439546
$313$	24.6525	1.39344	0.696720	−	0.717343i	$-0.254642\pi$
$313$	24.6525	1.39344	0.696720	+	0.717343i	$0.254642\pi$
$314$	9.52786	0.537688
$315$	1.00000	0.0563436
$316$	23.4164	1.31728
$317$	24.1803	1.35810	0.679052	−	0.734091i	$-0.262391\pi$
$317$	24.1803	1.35810	0.679052	+	0.734091i	$0.262391\pi$
$318$	7.52786	0.422142
$319$	5.00000	0.279946
$320$	−0.236068	−0.0131966
$321$	−4.23607	−0.236434
$322$	−3.52786	−0.196600
$323$	−35.1246	−1.95439
$324$	−1.61803	−0.0898908
$325$	−13.8885	−0.770398
$326$	14.0344	0.777296
$327$	2.76393	0.152846
$328$	−5.52786	−0.305225
$329$	0.236068	0.0130148
$330$	−0.618034	−0.0340217
$331$	−11.4164	−0.627503	−0.313751	−	0.949505i	$-0.601586\pi$
$331$	−11.4164	−0.627503	−0.313751	+	0.949505i	$0.601586\pi$
$332$	−10.9443	−0.600645
$333$	−7.00000	−0.383598
$334$	14.0000	0.766046
$335$	−9.76393	−0.533461
$336$	1.85410	0.101150
$337$	−8.18034	−0.445612	−0.222806	−	0.974863i	$-0.571522\pi$
$337$	−8.18034	−0.445612	−0.222806	+	0.974863i	$0.571522\pi$
$338$	0.583592	0.0317432
$339$	−0.472136	−0.0256429
$340$	−8.47214	−0.459466
$341$	−5.23607	−0.283549
$342$	4.14590	0.224184
$343$	1.00000	0.0539949
$344$	12.7639	0.688185
$345$	5.70820	0.307319
$346$	0.944272	0.0507644
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	−8.09017	−0.433679
$349$	1.58359	0.0847677	0.0423839	−	0.999101i	$-0.486505\pi$
$349$	1.58359	0.0847677	0.0423839	+	0.999101i	$0.486505\pi$
$350$	2.47214	0.132141
$351$	3.47214	0.185329
$352$	−5.61803	−0.299442
$353$	24.5279	1.30549	0.652743	−	0.757579i	$-0.273618\pi$
$353$	24.5279	1.30549	0.652743	+	0.757579i	$0.273618\pi$
$354$	6.90983	0.367253
$355$	−2.47214	−0.131207
$356$	7.23607	0.383511
$357$	5.23607	0.277122
$358$	−5.52786	−0.292157
$359$	23.4164	1.23587	0.617935	−	0.786229i	$-0.287969\pi$
$359$	23.4164	1.23587	0.617935	+	0.786229i	$0.287969\pi$
$360$	2.23607	0.117851
$361$	26.0000	1.36842
$362$	0.472136	0.0248149
$363$	1.00000	0.0524864
$364$	−5.61803	−0.294465
$365$	4.52786	0.236999
$366$	−1.23607	−0.0646103
$367$	−19.8885	−1.03817	−0.519087	−	0.854722i	$-0.673728\pi$
$367$	−19.8885	−1.03817	−0.519087	+	0.854722i	$0.673728\pi$
$368$	10.5836	0.551708
$369$	−2.47214	−0.128694
$370$	4.32624	0.224910
$371$	−12.1803	−0.632372
$372$	8.47214	0.439260
$373$	4.65248	0.240896	0.120448	−	0.992720i	$-0.461567\pi$
$373$	4.65248	0.240896	0.120448	+	0.992720i	$0.461567\pi$
$374$	−3.23607	−0.167333
$375$	−9.00000	−0.464758
$376$	0.527864	0.0272225
$377$	17.3607	0.894120
$378$	−0.618034	−0.0317882
$379$	−31.1803	−1.60163	−0.800813	−	0.598914i	$-0.795599\pi$
$379$	−31.1803	−1.60163	−0.800813	+	0.598914i	$0.795599\pi$
$380$	10.8541	0.556804
$381$	−12.6525	−0.648206
$382$	6.65248	0.340370
$383$	32.9443	1.68337	0.841687	−	0.539966i	$-0.181563\pi$
$383$	32.9443	1.68337	0.841687	+	0.539966i	$0.181563\pi$
$384$	11.3820	0.580834
$385$	1.00000	0.0509647
$386$	−9.05573	−0.460924
$387$	5.70820	0.290164
$388$	−15.7082	−0.797463
$389$	11.0557	0.560548	0.280274	−	0.959920i	$-0.409575\pi$
$389$	11.0557	0.560548	0.280274	+	0.959920i	$0.409575\pi$
$390$	−2.14590	−0.108662
$391$	29.8885	1.51153
$392$	2.23607	0.112938
$393$	0.944272	0.0476322
$394$	10.1803	0.512878
$395$	−14.4721	−0.728172
$396$	−1.61803	−0.0813093
$397$	23.1246	1.16059	0.580295	−	0.814406i	$-0.302937\pi$
$397$	23.1246	1.16059	0.580295	+	0.814406i	$0.302937\pi$
$398$	2.36068	0.118330
$399$	−6.70820	−0.335830
$400$	−7.41641	−0.370820
$401$	−29.7082	−1.48356	−0.741778	−	0.670645i	$-0.766017\pi$
$401$	−29.7082	−1.48356	−0.741778	+	0.670645i	$0.766017\pi$
$402$	6.03444	0.300971
$403$	−18.1803	−0.905627
$404$	−29.4164	−1.46352
$405$	1.00000	0.0496904
$406$	−3.09017	−0.153363
$407$	−7.00000	−0.346977
$408$	11.7082	0.579642
$409$	21.0557	1.04114	0.520569	−	0.853819i	$-0.325720\pi$
$409$	21.0557	1.04114	0.520569	+	0.853819i	$0.325720\pi$
$410$	1.52786	0.0754558
$411$	19.7082	0.972134
$412$	−28.1803	−1.38835
$413$	−11.1803	−0.550149
$414$	−3.52786	−0.173385
$415$	6.76393	0.332028
$416$	−19.5066	−0.956389
$417$	14.4721	0.708704
$418$	4.14590	0.202783
$419$	−1.18034	−0.0576634	−0.0288317	−	0.999584i	$-0.509179\pi$
$419$	−1.18034	−0.0576634	−0.0288317	+	0.999584i	$0.509179\pi$
$420$	−1.61803	−0.0789520
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	−3.34752	−0.162955
$423$	0.236068	0.0114780
$424$	−27.2361	−1.32270
$425$	−20.9443	−1.01595
$426$	1.52786	0.0740253
$427$	2.00000	0.0967868
$428$	6.85410	0.331306
$429$	3.47214	0.167636
$430$	−3.52786	−0.170129
$431$	8.70820	0.419459	0.209730	−	0.977759i	$-0.432742\pi$
$431$	8.70820	0.419459	0.209730	+	0.977759i	$0.432742\pi$
$432$	1.85410	0.0892055
$433$	−10.4721	−0.503259	−0.251629	−	0.967824i	$-0.580966\pi$
$433$	−10.4721	−0.503259	−0.251629	+	0.967824i	$0.580966\pi$
$434$	3.23607	0.155336
$435$	5.00000	0.239732
$436$	−4.47214	−0.214176
$437$	−38.2918	−1.83175
$438$	−2.79837	−0.133711
$439$	11.1803	0.533609	0.266804	−	0.963751i	$-0.414032\pi$
$439$	11.1803	0.533609	0.266804	+	0.963751i	$0.414032\pi$
$440$	2.23607	0.106600
$441$	1.00000	0.0476190
$442$	−11.2361	−0.534445
$443$	18.4721	0.877638	0.438819	−	0.898576i	$-0.355397\pi$
$443$	18.4721	0.877638	0.438819	+	0.898576i	$0.355397\pi$
$444$	11.3262	0.537519
$445$	−4.47214	−0.212000
$446$	3.70820	0.175589
$447$	5.00000	0.236492
$448$	−0.236068	−0.0111532
$449$	20.0000	0.943858	0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000	0.943858	0.471929	+	0.881636i	$0.343558\pi$
$450$	2.47214	0.116538
$451$	−2.47214	−0.116408
$452$	0.763932	0.0359323
$453$	−14.1803	−0.666250
$454$	1.23607	0.0580115
$455$	3.47214	0.162776
$456$	−15.0000	−0.702439
$457$	15.2361	0.712713	0.356357	−	0.934350i	$-0.384019\pi$
$457$	15.2361	0.712713	0.356357	+	0.934350i	$0.384019\pi$
$458$	−4.47214	−0.208969
$459$	5.23607	0.244399
$460$	−9.23607	−0.430634
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	−0.618034	−0.0287535
$463$	−4.81966	−0.223989	−0.111994	−	0.993709i	$-0.535724\pi$
$463$	−4.81966	−0.223989	−0.111994	+	0.993709i	$0.535724\pi$
$464$	9.27051	0.430373
$465$	−5.23607	−0.242817
$466$	9.23607	0.427853
$467$	29.1803	1.35031	0.675153	−	0.737678i	$-0.264078\pi$
$467$	29.1803	1.35031	0.675153	+	0.737678i	$0.264078\pi$
$468$	−5.61803	−0.259694
$469$	−9.76393	−0.450856
$470$	−0.145898	−0.00672977
$471$	−15.4164	−0.710351
$472$	−25.0000	−1.15072
$473$	5.70820	0.262463
$474$	8.94427	0.410824
$475$	26.8328	1.23117
$476$	−8.47214	−0.388320
$477$	−12.1803	−0.557699
$478$	−6.25735	−0.286205
$479$	11.7082	0.534961	0.267481	−	0.963563i	$-0.413809\pi$
$479$	11.7082	0.534961	0.267481	+	0.963563i	$0.413809\pi$
$480$	−5.61803	−0.256427
$481$	−24.3050	−1.10821
$482$	−16.0344	−0.730349
$483$	5.70820	0.259732
$484$	−1.61803	−0.0735470
$485$	9.70820	0.440827
$486$	−0.618034	−0.0280346
$487$	16.9443	0.767818	0.383909	−	0.923371i	$-0.374578\pi$
$487$	16.9443	0.767818	0.383909	+	0.923371i	$0.374578\pi$
$488$	4.47214	0.202444
$489$	−22.7082	−1.02690
$490$	−0.618034	−0.0279199
$491$	−18.1246	−0.817952	−0.408976	−	0.912545i	$-0.634114\pi$
$491$	−18.1246	−0.817952	−0.408976	+	0.912545i	$0.634114\pi$
$492$	4.00000	0.180334
$493$	26.1803	1.17910
$494$	14.3951	0.647667
$495$	1.00000	0.0449467
$496$	−9.70820	−0.435911
$497$	−2.47214	−0.110890
$498$	−4.18034	−0.187326
$499$	−2.23607	−0.100100	−0.0500501	−	0.998747i	$-0.515938\pi$
$499$	−2.23607	−0.100100	−0.0500501	+	0.998747i	$0.515938\pi$
$500$	14.5623	0.651246
$501$	−22.6525	−1.01204
$502$	−7.49342	−0.334448
$503$	2.29180	0.102186	0.0510931	−	0.998694i	$-0.483729\pi$
$503$	2.29180	0.102186	0.0510931	+	0.998694i	$0.483729\pi$
$504$	2.23607	0.0996024
$505$	18.1803	0.809015
$506$	−3.52786	−0.156833
$507$	−0.944272	−0.0419366
$508$	20.4721	0.908304
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	−3.23607	−0.143295
$511$	4.52786	0.200301
$512$	−18.7082	−0.826794
$513$	−6.70820	−0.296174
$514$	4.32624	0.190822
$515$	17.4164	0.767459
$516$	−9.23607	−0.406595
$517$	0.236068	0.0103823
$518$	4.32624	0.190084
$519$	−1.52786	−0.0670658
$520$	7.76393	0.340471
$521$	38.3050	1.67817	0.839085	−	0.544000i	$-0.183091\pi$
$521$	38.3050	1.67817	0.839085	+	0.544000i	$0.183091\pi$
$522$	−3.09017	−0.135253
$523$	−21.6525	−0.946797	−0.473398	−	0.880848i	$-0.656973\pi$
$523$	−21.6525	−0.946797	−0.473398	+	0.880848i	$0.656973\pi$
$524$	−1.52786	−0.0667451
$525$	−4.00000	−0.174574
$526$	16.1459	0.703995
$527$	−27.4164	−1.19428
$528$	1.85410	0.0806894
$529$	9.58359	0.416678
$530$	7.52786	0.326990
$531$	−11.1803	−0.485185
$532$	10.8541	0.470585
$533$	−8.58359	−0.371797
$534$	2.76393	0.119607
$535$	−4.23607	−0.183141
$536$	−21.8328	−0.943034
$537$	8.94427	0.385974
$538$	−0.652476	−0.0281302
$539$	1.00000	0.0430730
$540$	−1.61803	−0.0696291
$541$	−36.9443	−1.58836	−0.794179	−	0.607684i	$-0.792099\pi$
$541$	−36.9443	−1.58836	−0.794179	+	0.607684i	$0.792099\pi$
$542$	−3.27051	−0.140480
$543$	−0.763932	−0.0327835
$544$	−29.4164	−1.26122
$545$	2.76393	0.118394
$546$	−2.14590	−0.0918360
$547$	14.8328	0.634205	0.317103	−	0.948391i	$-0.397290\pi$
$547$	14.8328	0.634205	0.317103	+	0.948391i	$0.397290\pi$
$548$	−31.8885	−1.36221
$549$	2.00000	0.0853579
$550$	2.47214	0.105412
$551$	−33.5410	−1.42890
$552$	12.7639	0.543269
$553$	−14.4721	−0.615418
$554$	4.00000	0.169944
$555$	−7.00000	−0.297133
$556$	−23.4164	−0.993077
$557$	−12.5279	−0.530823	−0.265411	−	0.964135i	$-0.585508\pi$
$557$	−12.5279	−0.530823	−0.265411	+	0.964135i	$0.585508\pi$
$558$	3.23607	0.136994
$559$	19.8197	0.838282
$560$	1.85410	0.0783501
$561$	5.23607	0.221067
$562$	−7.09017	−0.299081
$563$	34.6525	1.46043	0.730214	−	0.683219i	$-0.239420\pi$
$563$	34.6525	1.46043	0.730214	+	0.683219i	$0.239420\pi$
$564$	−0.381966	−0.0160837
$565$	−0.472136	−0.0198629
$566$	8.50658	0.357558
$567$	1.00000	0.0419961
$568$	−5.52786	−0.231944
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	4.14590	0.173653
$571$	17.5279	0.733518	0.366759	−	0.930316i	$-0.380467\pi$
$571$	17.5279	0.733518	0.366759	+	0.930316i	$0.380467\pi$
$572$	−5.61803	−0.234902
$573$	−10.7639	−0.449670
$574$	1.52786	0.0637718
$575$	−22.8328	−0.952194
$576$	−0.236068	−0.00983617
$577$	7.34752	0.305881	0.152941	−	0.988235i	$-0.451126\pi$
$577$	7.34752	0.305881	0.152941	+	0.988235i	$0.451126\pi$
$578$	−6.43769	−0.267773
$579$	14.6525	0.608936
$580$	−8.09017	−0.335926
$581$	6.76393	0.280615
$582$	−6.00000	−0.248708
$583$	−12.1803	−0.504458
$584$	10.1246	0.418959
$585$	3.47214	0.143555
$586$	9.88854	0.408492
$587$	46.0132	1.89917	0.949583	−	0.313515i	$-0.101507\pi$
$587$	46.0132	1.89917	0.949583	+	0.313515i	$0.101507\pi$
$588$	−1.61803	−0.0667266
$589$	35.1246	1.44728
$590$	6.90983	0.284473
$591$	−16.4721	−0.677573
$592$	−12.9787	−0.533422
$593$	−22.8328	−0.937631	−0.468816	−	0.883296i	$-0.655319\pi$
$593$	−22.8328	−0.937631	−0.468816	+	0.883296i	$0.655319\pi$
$594$	−0.618034	−0.0253582
$595$	5.23607	0.214658
$596$	−8.09017	−0.331386
$597$	−3.81966	−0.156328
$598$	−12.2492	−0.500908
$599$	−25.5279	−1.04304	−0.521520	−	0.853239i	$-0.674635\pi$
$599$	−25.5279	−1.04304	−0.521520	+	0.853239i	$0.674635\pi$
$600$	−8.94427	−0.365148
$601$	27.0000	1.10135	0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000	1.10135	0.550676	+	0.834719i	$0.314370\pi$
$602$	−3.52786	−0.143785
$603$	−9.76393	−0.397618
$604$	22.9443	0.933589
$605$	1.00000	0.0406558
$606$	−11.2361	−0.456434
$607$	6.81966	0.276801	0.138401	−	0.990376i	$-0.455804\pi$
$607$	6.81966	0.276801	0.138401	+	0.990376i	$0.455804\pi$
$608$	37.6869	1.52841
$609$	5.00000	0.202610
$610$	−1.23607	−0.0500469
$611$	0.819660	0.0331599
$612$	−8.47214	−0.342466
$613$	13.5967	0.549167	0.274584	−	0.961563i	$-0.411460\pi$
$613$	13.5967	0.549167	0.274584	+	0.961563i	$0.411460\pi$
$614$	12.9443	0.522388
$615$	−2.47214	−0.0996861
$616$	2.23607	0.0900937
$617$	32.4721	1.30728	0.653639	−	0.756806i	$-0.273241\pi$
$617$	32.4721	1.30728	0.653639	+	0.756806i	$0.273241\pi$
$618$	−10.7639	−0.432989
$619$	−44.0689	−1.77128	−0.885639	−	0.464374i	$-0.846279\pi$
$619$	−44.0689	−1.77128	−0.885639	+	0.464374i	$0.846279\pi$
$620$	8.47214	0.340249
$621$	5.70820	0.229062
$622$	−6.11146	−0.245047
$623$	−4.47214	−0.179172
$624$	6.43769	0.257714
$625$	11.0000	0.440000
$626$	−15.2361	−0.608956
$627$	−6.70820	−0.267900
$628$	24.9443	0.995385
$629$	−36.6525	−1.46143
$630$	−0.618034	−0.0246231
$631$	44.3607	1.76597	0.882985	−	0.469400i	$-0.155530\pi$
$631$	44.3607	1.76597	0.882985	+	0.469400i	$0.155530\pi$
$632$	−32.3607	−1.28724
$633$	5.41641	0.215283
$634$	−14.9443	−0.593513
$635$	−12.6525	−0.502098
$636$	19.7082	0.781481
$637$	3.47214	0.137571
$638$	−3.09017	−0.122341
$639$	−2.47214	−0.0977962
$640$	11.3820	0.449912
$641$	−46.5410	−1.83826	−0.919130	−	0.393955i	$-0.871107\pi$
$641$	−46.5410	−1.83826	−0.919130	+	0.393955i	$0.871107\pi$
$642$	2.61803	0.103326
$643$	−47.9574	−1.89126	−0.945628	−	0.325250i	$-0.894552\pi$
$643$	−47.9574	−1.89126	−0.945628	+	0.325250i	$0.894552\pi$
$644$	−9.23607	−0.363952
$645$	5.70820	0.224760
$646$	21.7082	0.854098
$647$	12.3475	0.485431	0.242716	−	0.970097i	$-0.421962\pi$
$647$	12.3475	0.485431	0.242716	+	0.970097i	$0.421962\pi$
$648$	2.23607	0.0878410
$649$	−11.1803	−0.438867
$650$	8.58359	0.336676
$651$	−5.23607	−0.205218
$652$	36.7426	1.43895
$653$	−44.9443	−1.75881	−0.879403	−	0.476079i	$-0.842058\pi$
$653$	−44.9443	−1.75881	−0.879403	+	0.476079i	$0.842058\pi$
$654$	−1.70820	−0.0667961
$655$	0.944272	0.0368958
$656$	−4.58359	−0.178959
$657$	4.52786	0.176649
$658$	−0.145898	−0.00568770
$659$	23.5410	0.917028	0.458514	−	0.888687i	$-0.348382\pi$
$659$	23.5410	0.917028	0.458514	+	0.888687i	$0.348382\pi$
$660$	−1.61803	−0.0629819
$661$	40.5410	1.57686	0.788431	−	0.615123i	$-0.210894\pi$
$661$	40.5410	1.57686	0.788431	+	0.615123i	$0.210894\pi$
$662$	7.05573	0.274229
$663$	18.1803	0.706066
$664$	15.1246	0.586949
$665$	−6.70820	−0.260133
$666$	4.32624	0.167638
$667$	28.5410	1.10511
$668$	36.6525	1.41813
$669$	−6.00000	−0.231973
$670$	6.03444	0.233131
$671$	2.00000	0.0772091
$672$	−5.61803	−0.216720
$673$	3.59675	0.138644	0.0693222	−	0.997594i	$-0.477916\pi$
$673$	3.59675	0.138644	0.0693222	+	0.997594i	$0.477916\pi$
$674$	5.05573	0.194739
$675$	−4.00000	−0.153960
$676$	1.52786	0.0587640
$677$	19.3050	0.741950	0.370975	−	0.928643i	$-0.379024\pi$
$677$	19.3050	0.741950	0.370975	+	0.928643i	$0.379024\pi$
$678$	0.291796	0.0112064
$679$	9.70820	0.372567
$680$	11.7082	0.448989
$681$	−2.00000	−0.0766402
$682$	3.23607	0.123915
$683$	37.0132	1.41627	0.708135	−	0.706078i	$-0.249537\pi$
$683$	37.0132	1.41627	0.708135	+	0.706078i	$0.249537\pi$
$684$	10.8541	0.415017
$685$	19.7082	0.753012
$686$	−0.618034	−0.0235966
$687$	7.23607	0.276073
$688$	10.5836	0.403496
$689$	−42.2918	−1.61119
$690$	−3.52786	−0.134303
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	2.47214	0.0939765
$693$	1.00000	0.0379869
$694$	−17.3050	−0.656887
$695$	14.4721	0.548959
$696$	11.1803	0.423790
$697$	−12.9443	−0.490299
$698$	−0.978714	−0.0370449
$699$	−14.9443	−0.565244
$700$	6.47214	0.244624
$701$	4.11146	0.155288	0.0776438	−	0.996981i	$-0.475260\pi$
$701$	4.11146	0.155288	0.0776438	+	0.996981i	$0.475260\pi$
$702$	−2.14590	−0.0809917
$703$	46.9574	1.77103
$704$	−0.236068	−0.00889715
$705$	0.236068	0.00889083
$706$	−15.1591	−0.570519
$707$	18.1803	0.683742
$708$	18.0902	0.679870
$709$	−49.7214	−1.86732	−0.933662	−	0.358154i	$-0.883406\pi$
$709$	−49.7214	−1.86732	−0.933662	+	0.358154i	$0.883406\pi$
$710$	1.52786	0.0573397
$711$	−14.4721	−0.542748
$712$	−10.0000	−0.374766
$713$	−29.8885	−1.11933
$714$	−3.23607	−0.121107
$715$	3.47214	0.129851
$716$	−14.4721	−0.540849
$717$	10.1246	0.378111
$718$	−14.4721	−0.540095
$719$	7.76393	0.289546	0.144773	−	0.989465i	$-0.453755\pi$
$719$	7.76393	0.289546	0.144773	+	0.989465i	$0.453755\pi$
$720$	1.85410	0.0690983
$721$	17.4164	0.648621
$722$	−16.0689	−0.598022
$723$	25.9443	0.964878
$724$	1.23607	0.0459381
$725$	−20.0000	−0.742781
$726$	−0.618034	−0.0229374
$727$	24.1803	0.896799	0.448400	−	0.893833i	$-0.351994\pi$
$727$	24.1803	0.896799	0.448400	+	0.893833i	$0.351994\pi$
$728$	7.76393	0.287750
$729$	1.00000	0.0370370
$730$	−2.79837	−0.103572
$731$	29.8885	1.10547
$732$	−3.23607	−0.119609
$733$	−8.11146	−0.299603	−0.149802	−	0.988716i	$-0.547864\pi$
$733$	−8.11146	−0.299603	−0.149802	+	0.988716i	$0.547864\pi$
$734$	12.2918	0.453698
$735$	1.00000	0.0368856
$736$	−32.0689	−1.18207
$737$	−9.76393	−0.359659
$738$	1.52786	0.0562415
$739$	34.0689	1.25324	0.626622	−	0.779323i	$-0.284437\pi$
$739$	34.0689	1.25324	0.626622	+	0.779323i	$0.284437\pi$
$740$	11.3262	0.416361
$741$	−23.2918	−0.855646
$742$	7.52786	0.276357
$743$	2.81966	0.103443	0.0517216	−	0.998662i	$-0.483529\pi$
$743$	2.81966	0.103443	0.0517216	+	0.998662i	$0.483529\pi$
$744$	−11.7082	−0.429244
$745$	5.00000	0.183186
$746$	−2.87539	−0.105275
$747$	6.76393	0.247479
$748$	−8.47214	−0.309772
$749$	−4.23607	−0.154783
$750$	5.56231	0.203107
$751$	39.7639	1.45101	0.725503	−	0.688219i	$-0.241607\pi$
$751$	39.7639	1.45101	0.725503	+	0.688219i	$0.241607\pi$
$752$	0.437694	0.0159611
$753$	12.1246	0.441845
$754$	−10.7295	−0.390745
$755$	−14.1803	−0.516075
$756$	−1.61803	−0.0588473
$757$	−51.7214	−1.87984	−0.939922	−	0.341388i	$-0.889103\pi$
$757$	−51.7214	−1.87984	−0.939922	+	0.341388i	$0.889103\pi$
$758$	19.2705	0.699936
$759$	5.70820	0.207195
$760$	−15.0000	−0.544107
$761$	27.7771	1.00692	0.503459	−	0.864019i	$-0.332060\pi$
$761$	27.7771	1.00692	0.503459	+	0.864019i	$0.332060\pi$
$762$	7.81966	0.283276
$763$	2.76393	0.100061
$764$	17.4164	0.630104
$765$	5.23607	0.189310
$766$	−20.3607	−0.735661
$767$	−38.8197	−1.40170
$768$	−6.56231	−0.236797
$769$	13.9443	0.502843	0.251422	−	0.967878i	$-0.419102\pi$
$769$	13.9443	0.502843	0.251422	+	0.967878i	$0.419102\pi$
$770$	−0.618034	−0.0222724
$771$	−7.00000	−0.252099
$772$	−23.7082	−0.853277
$773$	−5.47214	−0.196819	−0.0984095	−	0.995146i	$-0.531376\pi$
$773$	−5.47214	−0.196819	−0.0984095	+	0.995146i	$0.531376\pi$
$774$	−3.52786	−0.126806
$775$	20.9443	0.752340
$776$	21.7082	0.779279
$777$	−7.00000	−0.251124
$778$	−6.83282	−0.244968
$779$	16.5836	0.594169
$780$	−5.61803	−0.201158
$781$	−2.47214	−0.0884600
$782$	−18.4721	−0.660562
$783$	5.00000	0.178685
$784$	1.85410	0.0662179
$785$	−15.4164	−0.550235
$786$	−0.583592	−0.0208160
$787$	3.65248	0.130197	0.0650984	−	0.997879i	$-0.479264\pi$
$787$	3.65248	0.130197	0.0650984	+	0.997879i	$0.479264\pi$
$788$	26.6525	0.949455
$789$	−26.1246	−0.930061
$790$	8.94427	0.318223
$791$	−0.472136	−0.0167872
$792$	2.23607	0.0794552
$793$	6.94427	0.246598
$794$	−14.2918	−0.507197
$795$	−12.1803	−0.431992
$796$	6.18034	0.219056
$797$	−2.52786	−0.0895415	−0.0447708	−	0.998997i	$-0.514256\pi$
$797$	−2.52786	−0.0895415	−0.0447708	+	0.998997i	$0.514256\pi$
$798$	4.14590	0.146763
$799$	1.23607	0.0437289
$800$	22.4721	0.794510
$801$	−4.47214	−0.158015
$802$	18.3607	0.648338
$803$	4.52786	0.159785
$804$	15.7984	0.557166
$805$	5.70820	0.201188
$806$	11.2361	0.395774
$807$	1.05573	0.0371634
$808$	40.6525	1.43015
$809$	−56.3050	−1.97958	−0.989788	−	0.142545i	$-0.954471\pi$
$809$	−56.3050	−1.97958	−0.989788	+	0.142545i	$0.954471\pi$
$810$	−0.618034	−0.0217155
$811$	15.2918	0.536968	0.268484	−	0.963284i	$-0.413477\pi$
$811$	15.2918	0.536968	0.268484	+	0.963284i	$0.413477\pi$
$812$	−8.09017	−0.283909
$813$	5.29180	0.185591
$814$	4.32624	0.151635
$815$	−22.7082	−0.795434
$816$	9.70820	0.339855
$817$	−38.2918	−1.33966
$818$	−13.0132	−0.454994
$819$	3.47214	0.121326
$820$	4.00000	0.139686
$821$	−7.47214	−0.260779	−0.130390	−	0.991463i	$-0.541623\pi$
$821$	−7.47214	−0.260779	−0.130390	+	0.991463i	$0.541623\pi$
$822$	−12.1803	−0.424838
$823$	−17.1803	−0.598869	−0.299435	−	0.954117i	$-0.596798\pi$
$823$	−17.1803	−0.598869	−0.299435	+	0.954117i	$0.596798\pi$
$824$	38.9443	1.35669
$825$	−4.00000	−0.139262
$826$	6.90983	0.240424
$827$	12.3475	0.429365	0.214683	−	0.976684i	$-0.431128\pi$
$827$	12.3475	0.429365	0.214683	+	0.976684i	$0.431128\pi$
$828$	−9.23607	−0.320976
$829$	35.7771	1.24259	0.621295	−	0.783577i	$-0.286607\pi$
$829$	35.7771	1.24259	0.621295	+	0.783577i	$0.286607\pi$
$830$	−4.18034	−0.145102
$831$	−6.47214	−0.224516
$832$	−0.819660	−0.0284166
$833$	5.23607	0.181419
$834$	−8.94427	−0.309715
$835$	−22.6525	−0.783921
$836$	10.8541	0.375397
$837$	−5.23607	−0.180985
$838$	0.729490	0.0251998
$839$	−23.5410	−0.812726	−0.406363	−	0.913712i	$-0.633203\pi$
$839$	−23.5410	−0.812726	−0.406363	+	0.913712i	$0.633203\pi$
$840$	2.23607	0.0771517
$841$	−4.00000	−0.137931
$842$	8.03444	0.276885
$843$	11.4721	0.395121
$844$	−8.76393	−0.301667
$845$	−0.944272	−0.0324839
$846$	−0.145898	−0.00501608
$847$	1.00000	0.0343604
$848$	−22.5836	−0.775524
$849$	−13.7639	−0.472377
$850$	12.9443	0.443985
$851$	−39.9574	−1.36972
$852$	4.00000	0.137038
$853$	−29.4164	−1.00720	−0.503599	−	0.863937i	$-0.667991\pi$
$853$	−29.4164	−1.00720	−0.503599	+	0.863937i	$0.667991\pi$
$854$	−1.23607	−0.0422974
$855$	−6.70820	−0.229416
$856$	−9.47214	−0.323751
$857$	0.111456	0.00380727	0.00190364	−	0.999998i	$-0.499394\pi$
$857$	0.111456	0.00380727	0.00190364	+	0.999998i	$0.499394\pi$
$858$	−2.14590	−0.0732598
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	−9.23607	−0.314947
$861$	−2.47214	−0.0842502
$862$	−5.38197	−0.183310
$863$	−43.2361	−1.47177	−0.735886	−	0.677105i	$-0.763234\pi$
$863$	−43.2361	−1.47177	−0.735886	+	0.677105i	$0.763234\pi$
$864$	−5.61803	−0.191129
$865$	−1.52786	−0.0519489
$866$	6.47214	0.219932
$867$	10.4164	0.353760
$868$	8.47214	0.287563
$869$	−14.4721	−0.490934
$870$	−3.09017	−0.104767
$871$	−33.9017	−1.14872
$872$	6.18034	0.209293
$873$	9.70820	0.328573
$874$	23.6656	0.800502
$875$	−9.00000	−0.304256
$876$	−7.32624	−0.247531
$877$	4.58359	0.154777	0.0773885	−	0.997001i	$-0.475342\pi$
$877$	4.58359	0.154777	0.0773885	+	0.997001i	$0.475342\pi$
$878$	−6.90983	−0.233195
$879$	−16.0000	−0.539667
$880$	1.85410	0.0625018
$881$	54.8885	1.84924	0.924621	−	0.380888i	$-0.124382\pi$
$881$	54.8885	1.84924	0.924621	+	0.380888i	$0.124382\pi$
$882$	−0.618034	−0.0208103
$883$	−14.8197	−0.498721	−0.249361	−	0.968411i	$-0.580220\pi$
$883$	−14.8197	−0.498721	−0.249361	+	0.968411i	$0.580220\pi$
$884$	−29.4164	−0.989381
$885$	−11.1803	−0.375823
$886$	−11.4164	−0.383542
$887$	10.7639	0.361417	0.180709	−	0.983537i	$-0.442161\pi$
$887$	10.7639	0.361417	0.180709	+	0.983537i	$0.442161\pi$
$888$	−15.6525	−0.525263
$889$	−12.6525	−0.424350
$890$	2.76393	0.0926472
$891$	1.00000	0.0335013
$892$	9.70820	0.325055
$893$	−1.58359	−0.0529929
$894$	−3.09017	−0.103351
$895$	8.94427	0.298974
$896$	11.3820	0.380245
$897$	19.8197	0.661759
$898$	−12.3607	−0.412481
$899$	−26.1803	−0.873163
$900$	6.47214	0.215738
$901$	−63.7771	−2.12472
$902$	1.52786	0.0508723
$903$	5.70820	0.189957
$904$	−1.05573	−0.0351130
$905$	−0.763932	−0.0253940
$906$	8.76393	0.291162
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	3.23607	0.107393
$909$	18.1803	0.603004
$910$	−2.14590	−0.0711358
$911$	−14.5836	−0.483176	−0.241588	−	0.970379i	$-0.577668\pi$
$911$	−14.5836	−0.483176	−0.241588	+	0.970379i	$0.577668\pi$
$912$	−12.4377	−0.411853
$913$	6.76393	0.223853
$914$	−9.41641	−0.311467
$915$	2.00000	0.0661180
$916$	−11.7082	−0.386850
$917$	0.944272	0.0311826
$918$	−3.23607	−0.106806
$919$	39.5967	1.30618	0.653088	−	0.757282i	$-0.273473\pi$
$919$	39.5967	1.30618	0.653088	+	0.757282i	$0.273473\pi$
$920$	12.7639	0.420814
$921$	−20.9443	−0.690137
$922$	17.3050	0.569908
$923$	−8.58359	−0.282532
$924$	−1.61803	−0.0532294
$925$	28.0000	0.920634
$926$	2.97871	0.0978866
$927$	17.4164	0.572030
$928$	−28.0902	−0.922105
$929$	12.8885	0.422859	0.211430	−	0.977393i	$-0.432188\pi$
$929$	12.8885	0.422859	0.211430	+	0.977393i	$0.432188\pi$
$930$	3.23607	0.106115
$931$	−6.70820	−0.219853
$932$	24.1803	0.792053
$933$	9.88854	0.323736
$934$	−18.0344	−0.590105
$935$	5.23607	0.171238
$936$	7.76393	0.253772
$937$	−39.8885	−1.30310	−0.651551	−	0.758605i	$-0.725881\pi$
$937$	−39.8885	−1.30310	−0.651551	+	0.758605i	$0.725881\pi$
$938$	6.03444	0.197032
$939$	24.6525	0.804503
$940$	−0.381966	−0.0124584
$941$	−60.3607	−1.96770	−0.983851	−	0.178990i	$-0.942717\pi$
$941$	−60.3607	−1.96770	−0.983851	+	0.178990i	$0.942717\pi$
$942$	9.52786	0.310435
$943$	−14.1115	−0.459532
$944$	−20.7295	−0.674687
$945$	1.00000	0.0325300
$946$	−3.52786	−0.114701
$947$	−5.41641	−0.176010	−0.0880048	−	0.996120i	$-0.528049\pi$
$947$	−5.41641	−0.176010	−0.0880048	+	0.996120i	$0.528049\pi$
$948$	23.4164	0.760530
$949$	15.7214	0.510337
$950$	−16.5836	−0.538043
$951$	24.1803	0.784101
$952$	11.7082	0.379465
$953$	44.7771	1.45047	0.725236	−	0.688500i	$-0.241731\pi$
$953$	44.7771	1.45047	0.725236	+	0.688500i	$0.241731\pi$
$954$	7.52786	0.243724
$955$	−10.7639	−0.348313
$956$	−16.3820	−0.529831
$957$	5.00000	0.161627
$958$	−7.23607	−0.233787
$959$	19.7082	0.636411
$960$	−0.236068	−0.00761906
$961$	−3.58359	−0.115600
$962$	15.0213	0.484306
$963$	−4.23607	−0.136505
$964$	−41.9787	−1.35204
$965$	14.6525	0.471680
$966$	−3.52786	−0.113507
$967$	−61.1935	−1.96785	−0.983925	−	0.178582i	$-0.942849\pi$
$967$	−61.1935	−1.96785	−0.983925	+	0.178582i	$0.942849\pi$
$968$	2.23607	0.0718699
$969$	−35.1246	−1.12837
$970$	−6.00000	−0.192648
$971$	32.1246	1.03093	0.515464	−	0.856911i	$-0.327620\pi$
$971$	32.1246	1.03093	0.515464	+	0.856911i	$0.327620\pi$
$972$	−1.61803	−0.0518985
$973$	14.4721	0.463955
$974$	−10.4721	−0.335549
$975$	−13.8885	−0.444789
$976$	3.70820	0.118697
$977$	4.18034	0.133741	0.0668705	−	0.997762i	$-0.478699\pi$
$977$	4.18034	0.133741	0.0668705	+	0.997762i	$0.478699\pi$
$978$	14.0344	0.448772
$979$	−4.47214	−0.142930
$980$	−1.61803	−0.0516862
$981$	2.76393	0.0882456
$982$	11.2016	0.357458
$983$	27.4164	0.874448	0.437224	−	0.899353i	$-0.355962\pi$
$983$	27.4164	0.874448	0.437224	+	0.899353i	$0.355962\pi$
$984$	−5.52786	−0.176222
$985$	−16.4721	−0.524846
$986$	−16.1803	−0.515287
$987$	0.236068	0.00751413
$988$	37.6869	1.19898
$989$	32.5836	1.03610
$990$	−0.618034	−0.0196424
$991$	−29.1803	−0.926944	−0.463472	−	0.886112i	$-0.653397\pi$
$991$	−29.1803	−0.926944	−0.463472	+	0.886112i	$0.653397\pi$
$992$	29.4164	0.933972
$993$	−11.4164	−0.362289
$994$	1.52786	0.0484609
$995$	−3.81966	−0.121091
$996$	−10.9443	−0.346783
$997$	26.9443	0.853334	0.426667	−	0.904409i	$-0.359688\pi$
$997$	26.9443	0.853334	0.426667	+	0.904409i	$0.359688\pi$
$998$	1.38197	0.0437454
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.a.c.1.1	✓	2
3.2	odd	2		693.2.a.f.1.2		2
4.3	odd	2		3696.2.a.be.1.2		2
5.4	even	2		5775.2.a.be.1.2		2
7.6	odd	2		1617.2.a.p.1.1		2
11.10	odd	2		2541.2.a.t.1.2		2
21.20	even	2		4851.2.a.w.1.2		2
33.32	even	2		7623.2.a.bm.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.a.c.1.1	✓	2	1.1	even	1	trivial
693.2.a.f.1.2		2	3.2	odd	2
1617.2.a.p.1.1		2	7.6	odd	2
2541.2.a.t.1.2		2	11.10	odd	2
3696.2.a.be.1.2		2	4.3	odd	2
4851.2.a.w.1.2		2	21.20	even	2
5775.2.a.be.1.2		2	5.4	even	2
7623.2.a.bm.1.1		2	33.32	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.618034 q^{10} +1.00000 q^{11} -1.61803 q^{12} +3.47214 q^{13} -0.618034 q^{14} +1.00000 q^{15} +1.85410 q^{16} +5.23607 q^{17} -0.618034 q^{18} -6.70820 q^{19} -1.61803 q^{20} +1.00000 q^{21} -0.618034 q^{22} +5.70820 q^{23} +2.23607 q^{24} -4.00000 q^{25} -2.14590 q^{26} +1.00000 q^{27} -1.61803 q^{28} +5.00000 q^{29} -0.618034 q^{30} -5.23607 q^{31} -5.61803 q^{32} +1.00000 q^{33} -3.23607 q^{34} +1.00000 q^{35} -1.61803 q^{36} -7.00000 q^{37} +4.14590 q^{38} +3.47214 q^{39} +2.23607 q^{40} -2.47214 q^{41} -0.618034 q^{42} +5.70820 q^{43} -1.61803 q^{44} +1.00000 q^{45} -3.52786 q^{46} +0.236068 q^{47} +1.85410 q^{48} +1.00000 q^{49} +2.47214 q^{50} +5.23607 q^{51} -5.61803 q^{52} -12.1803 q^{53} -0.618034 q^{54} +1.00000 q^{55} +2.23607 q^{56} -6.70820 q^{57} -3.09017 q^{58} -11.1803 q^{59} -1.61803 q^{60} +2.00000 q^{61} +3.23607 q^{62} +1.00000 q^{63} -0.236068 q^{64} +3.47214 q^{65} -0.618034 q^{66} -9.76393 q^{67} -8.47214 q^{68} +5.70820 q^{69} -0.618034 q^{70} -2.47214 q^{71} +2.23607 q^{72} +4.52786 q^{73} +4.32624 q^{74} -4.00000 q^{75} +10.8541 q^{76} +1.00000 q^{77} -2.14590 q^{78} -14.4721 q^{79} +1.85410 q^{80} +1.00000 q^{81} +1.52786 q^{82} +6.76393 q^{83} -1.61803 q^{84} +5.23607 q^{85} -3.52786 q^{86} +5.00000 q^{87} +2.23607 q^{88} -4.47214 q^{89} -0.618034 q^{90} +3.47214 q^{91} -9.23607 q^{92} -5.23607 q^{93} -0.145898 q^{94} -6.70820 q^{95} -5.61803 q^{96} +9.70820 q^{97} -0.618034 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{9} + q^{10} + 2 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - 3 q^{16} + 6 q^{17} + q^{18} - q^{20} + 2 q^{21} + q^{22} - 2 q^{23} - 8 q^{25} - 11 q^{26} + 2 q^{27} - q^{28} + 10 q^{29} + q^{30} - 6 q^{31} - 9 q^{32} + 2 q^{33} - 2 q^{34} + 2 q^{35} - q^{36} - 14 q^{37} + 15 q^{38} - 2 q^{39} + 4 q^{41} + q^{42} - 2 q^{43} - q^{44} + 2 q^{45} - 16 q^{46} - 4 q^{47} - 3 q^{48} + 2 q^{49} - 4 q^{50} + 6 q^{51} - 9 q^{52} - 2 q^{53} + q^{54} + 2 q^{55} + 5 q^{58} - q^{60} + 4 q^{61} + 2 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} + q^{66} - 24 q^{67} - 8 q^{68} - 2 q^{69} + q^{70} + 4 q^{71} + 18 q^{73} - 7 q^{74} - 8 q^{75} + 15 q^{76} + 2 q^{77} - 11 q^{78} - 20 q^{79} - 3 q^{80} + 2 q^{81} + 12 q^{82} + 18 q^{83} - q^{84} + 6 q^{85} - 16 q^{86} + 10 q^{87} + q^{90} - 2 q^{91} - 14 q^{92} - 6 q^{93} - 7 q^{94} - 9 q^{96} + 6 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^9 + q^10 + 2 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - 3 * q^16 + 6 * q^17 + q^18 - q^20 + 2 * q^21 + q^22 - 2 * q^23 - 8 * q^25 - 11 * q^26 + 2 * q^27 - q^28 + 10 * q^29 + q^30 - 6 * q^31 - 9 * q^32 + 2 * q^33 - 2 * q^34 + 2 * q^35 - q^36 - 14 * q^37 + 15 * q^38 - 2 * q^39 + 4 * q^41 + q^42 - 2 * q^43 - q^44 + 2 * q^45 - 16 * q^46 - 4 * q^47 - 3 * q^48 + 2 * q^49 - 4 * q^50 + 6 * q^51 - 9 * q^52 - 2 * q^53 + q^54 + 2 * q^55 + 5 * q^58 - q^60 + 4 * q^61 + 2 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 + q^66 - 24 * q^67 - 8 * q^68 - 2 * q^69 + q^70 + 4 * q^71 + 18 * q^73 - 7 * q^74 - 8 * q^75 + 15 * q^76 + 2 * q^77 - 11 * q^78 - 20 * q^79 - 3 * q^80 + 2 * q^81 + 12 * q^82 + 18 * q^83 - q^84 + 6 * q^85 - 16 * q^86 + 10 * q^87 + q^90 - 2 * q^91 - 14 * q^92 - 6 * q^93 - 7 * q^94 - 9 * q^96 + 6 * q^97 + q^98 + 2 * q^99

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