LMFDB - Embedded newform 4730.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.61803 q^{12} -4.47214 q^{13} -0.381966 q^{14} -1.61803 q^{15} +1.00000 q^{16} +5.09017 q^{17} -0.381966 q^{18} -4.61803 q^{19} +1.00000 q^{20} +0.618034 q^{21} +1.00000 q^{22} -4.00000 q^{23} -1.61803 q^{24} +1.00000 q^{25} -4.47214 q^{26} +5.47214 q^{27} -0.381966 q^{28} +4.47214 q^{29} -1.61803 q^{30} +6.47214 q^{31} +1.00000 q^{32} -1.61803 q^{33} +5.09017 q^{34} -0.381966 q^{35} -0.381966 q^{36} +1.23607 q^{37} -4.61803 q^{38} +7.23607 q^{39} +1.00000 q^{40} -10.0000 q^{41} +0.618034 q^{42} +1.00000 q^{43} +1.00000 q^{44} -0.381966 q^{45} -4.00000 q^{46} -7.61803 q^{47} -1.61803 q^{48} -6.85410 q^{49} +1.00000 q^{50} -8.23607 q^{51} -4.47214 q^{52} -7.09017 q^{53} +5.47214 q^{54} +1.00000 q^{55} -0.381966 q^{56} +7.47214 q^{57} +4.47214 q^{58} +7.61803 q^{59} -1.61803 q^{60} -6.47214 q^{61} +6.47214 q^{62} +0.145898 q^{63} +1.00000 q^{64} -4.47214 q^{65} -1.61803 q^{66} -8.00000 q^{67} +5.09017 q^{68} +6.47214 q^{69} -0.381966 q^{70} -4.09017 q^{71} -0.381966 q^{72} -4.47214 q^{73} +1.23607 q^{74} -1.61803 q^{75} -4.61803 q^{76} -0.381966 q^{77} +7.23607 q^{78} +4.09017 q^{79} +1.00000 q^{80} -7.70820 q^{81} -10.0000 q^{82} -2.56231 q^{83} +0.618034 q^{84} +5.09017 q^{85} +1.00000 q^{86} -7.23607 q^{87} +1.00000 q^{88} -0.472136 q^{89} -0.381966 q^{90} +1.70820 q^{91} -4.00000 q^{92} -10.4721 q^{93} -7.61803 q^{94} -4.61803 q^{95} -1.61803 q^{96} -2.76393 q^{97} -6.85410 q^{98} -0.381966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 3 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 3 * q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 3 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + 2 q^{11} - q^{12} - 3 q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} - 7 q^{19} + 2 q^{20} - q^{21} + 2 q^{22} - 8 q^{23} - q^{24} + 2 q^{25} + 2 q^{27} - 3 q^{28} - q^{30} + 4 q^{31} + 2 q^{32} - q^{33} - q^{34} - 3 q^{35} - 3 q^{36} - 2 q^{37} - 7 q^{38} + 10 q^{39} + 2 q^{40} - 20 q^{41} - q^{42} + 2 q^{43} + 2 q^{44} - 3 q^{45} - 8 q^{46} - 13 q^{47} - q^{48} - 7 q^{49} + 2 q^{50} - 12 q^{51} - 3 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 6 q^{57} + 13 q^{59} - q^{60} - 4 q^{61} + 4 q^{62} + 7 q^{63} + 2 q^{64} - q^{66} - 16 q^{67} - q^{68} + 4 q^{69} - 3 q^{70} + 3 q^{71} - 3 q^{72} - 2 q^{74} - q^{75} - 7 q^{76} - 3 q^{77} + 10 q^{78} - 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} + 15 q^{83} - q^{84} - q^{85} + 2 q^{86} - 10 q^{87} + 2 q^{88} + 8 q^{89} - 3 q^{90} - 10 q^{91} - 8 q^{92} - 12 q^{93} - 13 q^{94} - 7 q^{95} - q^{96} - 10 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 3 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + 2 * q^11 - q^12 - 3 * q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 - 7 * q^19 + 2 * q^20 - q^21 + 2 * q^22 - 8 * q^23 - q^24 + 2 * q^25 + 2 * q^27 - 3 * q^28 - q^30 + 4 * q^31 + 2 * q^32 - q^33 - q^34 - 3 * q^35 - 3 * q^36 - 2 * q^37 - 7 * q^38 + 10 * q^39 + 2 * q^40 - 20 * q^41 - q^42 + 2 * q^43 + 2 * q^44 - 3 * q^45 - 8 * q^46 - 13 * q^47 - q^48 - 7 * q^49 + 2 * q^50 - 12 * q^51 - 3 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 6 * q^57 + 13 * q^59 - q^60 - 4 * q^61 + 4 * q^62 + 7 * q^63 + 2 * q^64 - q^66 - 16 * q^67 - q^68 + 4 * q^69 - 3 * q^70 + 3 * q^71 - 3 * q^72 - 2 * q^74 - q^75 - 7 * q^76 - 3 * q^77 + 10 * q^78 - 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 + 15 * q^83 - q^84 - q^85 + 2 * q^86 - 10 * q^87 + 2 * q^88 + 8 * q^89 - 3 * q^90 - 10 * q^91 - 8 * q^92 - 12 * q^93 - 13 * q^94 - 7 * q^95 - q^96 - 10 * q^97 - 7 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.61803	−0.934172	−0.467086	−	0.884212i	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.61803	−0.660560
$7$	−0.381966	−0.144370	−0.0721848	−	0.997391i	$-0.522997\pi$
$7$	−0.381966	−0.144370	−0.0721848	+	0.997391i	$0.522997\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.61803	−0.467086
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	−0.381966	−0.102085
$15$	−1.61803	−0.417775
$16$	1.00000	0.250000
$17$	5.09017	1.23455	0.617274	−	0.786748i	$-0.288237\pi$
$17$	5.09017	1.23455	0.617274	+	0.786748i	$0.288237\pi$
$18$	−0.381966	−0.0900303
$19$	−4.61803	−1.05945	−0.529725	−	0.848170i	$-0.677705\pi$
$19$	−4.61803	−1.05945	−0.529725	+	0.848170i	$0.677705\pi$
$20$	1.00000	0.223607
$21$	0.618034	0.134866
$22$	1.00000	0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.61803	−0.330280
$25$	1.00000	0.200000
$26$	−4.47214	−0.877058
$27$	5.47214	1.05311
$28$	−0.381966	−0.0721848
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	−1.61803	−0.295411
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	1.00000	0.176777
$33$	−1.61803	−0.281664
$34$	5.09017	0.872957
$35$	−0.381966	−0.0645640
$36$	−0.381966	−0.0636610
$37$	1.23607	0.203208	0.101604	−	0.994825i	$-0.467602\pi$
$37$	1.23607	0.203208	0.101604	+	0.994825i	$0.467602\pi$
$38$	−4.61803	−0.749144
$39$	7.23607	1.15870
$40$	1.00000	0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0.618034	0.0953647
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−0.381966	−0.0569401
$46$	−4.00000	−0.589768
$47$	−7.61803	−1.11120	−0.555602	−	0.831448i	$-0.687512\pi$
$47$	−7.61803	−1.11120	−0.555602	+	0.831448i	$0.687512\pi$
$48$	−1.61803	−0.233543
$49$	−6.85410	−0.979157
$50$	1.00000	0.141421
$51$	−8.23607	−1.15328
$52$	−4.47214	−0.620174
$53$	−7.09017	−0.973910	−0.486955	−	0.873427i	$-0.661892\pi$
$53$	−7.09017	−0.973910	−0.486955	+	0.873427i	$0.661892\pi$
$54$	5.47214	0.744663
$55$	1.00000	0.134840
$56$	−0.381966	−0.0510424
$57$	7.47214	0.989709
$58$	4.47214	0.587220
$59$	7.61803	0.991784	0.495892	−	0.868384i	$-0.334841\pi$
$59$	7.61803	0.991784	0.495892	+	0.868384i	$0.334841\pi$
$60$	−1.61803	−0.208887
$61$	−6.47214	−0.828672	−0.414336	−	0.910124i	$-0.635986\pi$
$61$	−6.47214	−0.828672	−0.414336	+	0.910124i	$0.635986\pi$
$62$	6.47214	0.821962
$63$	0.145898	0.0183814
$64$	1.00000	0.125000
$65$	−4.47214	−0.554700
$66$	−1.61803	−0.199166
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	5.09017	0.617274
$69$	6.47214	0.779154
$70$	−0.381966	−0.0456537
$71$	−4.09017	−0.485414	−0.242707	−	0.970100i	$-0.578035\pi$
$71$	−4.09017	−0.485414	−0.242707	+	0.970100i	$0.578035\pi$
$72$	−0.381966	−0.0450151
$73$	−4.47214	−0.523424	−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214	−0.523424	−0.261712	+	0.965146i	$0.584287\pi$
$74$	1.23607	0.143690
$75$	−1.61803	−0.186834
$76$	−4.61803	−0.529725
$77$	−0.381966	−0.0435291
$78$	7.23607	0.819323
$79$	4.09017	0.460180	0.230090	−	0.973169i	$-0.426098\pi$
$79$	4.09017	0.460180	0.230090	+	0.973169i	$0.426098\pi$
$80$	1.00000	0.111803
$81$	−7.70820	−0.856467
$82$	−10.0000	−1.10432
$83$	−2.56231	−0.281250	−0.140625	−	0.990063i	$-0.544911\pi$
$83$	−2.56231	−0.281250	−0.140625	+	0.990063i	$0.544911\pi$
$84$	0.618034	0.0674330
$85$	5.09017	0.552106
$86$	1.00000	0.107833
$87$	−7.23607	−0.775788
$88$	1.00000	0.106600
$89$	−0.472136	−0.0500463	−0.0250232	−	0.999687i	$-0.507966\pi$
$89$	−0.472136	−0.0500463	−0.0250232	+	0.999687i	$0.507966\pi$
$90$	−0.381966	−0.0402628
$91$	1.70820	0.179068
$92$	−4.00000	−0.417029
$93$	−10.4721	−1.08591
$94$	−7.61803	−0.785740
$95$	−4.61803	−0.473800
$96$	−1.61803	−0.165140
$97$	−2.76393	−0.280635	−0.140317	−	0.990107i	$-0.544812\pi$
$97$	−2.76393	−0.280635	−0.140317	+	0.990107i	$0.544812\pi$
$98$	−6.85410	−0.692369
$99$	−0.381966	−0.0383890
$100$	1.00000	0.100000
$101$	5.32624	0.529980	0.264990	−	0.964251i	$-0.414631\pi$
$101$	5.32624	0.529980	0.264990	+	0.964251i	$0.414631\pi$
$102$	−8.23607	−0.815492
$103$	9.56231	0.942202	0.471101	−	0.882079i	$-0.343857\pi$
$103$	9.56231	0.942202	0.471101	+	0.882079i	$0.343857\pi$
$104$	−4.47214	−0.438529
$105$	0.618034	0.0603139
$106$	−7.09017	−0.688658
$107$	−8.79837	−0.850571	−0.425285	−	0.905059i	$-0.639826\pi$
$107$	−8.79837	−0.850571	−0.425285	+	0.905059i	$0.639826\pi$
$108$	5.47214	0.526557
$109$	−16.7984	−1.60899	−0.804496	−	0.593958i	$-0.797565\pi$
$109$	−16.7984	−1.60899	−0.804496	+	0.593958i	$0.797565\pi$
$110$	1.00000	0.0953463
$111$	−2.00000	−0.189832
$112$	−0.381966	−0.0360924
$113$	−13.3820	−1.25887	−0.629435	−	0.777053i	$-0.716714\pi$
$113$	−13.3820	−1.25887	−0.629435	+	0.777053i	$0.716714\pi$
$114$	7.47214	0.699830
$115$	−4.00000	−0.373002
$116$	4.47214	0.415227
$117$	1.70820	0.157924
$118$	7.61803	0.701297
$119$	−1.94427	−0.178231
$120$	−1.61803	−0.147706
$121$	1.00000	0.0909091
$122$	−6.47214	−0.585960
$123$	16.1803	1.45893
$124$	6.47214	0.581215
$125$	1.00000	0.0894427
$126$	0.145898	0.0129976
$127$	6.94427	0.616204	0.308102	−	0.951353i	$-0.400306\pi$
$127$	6.94427	0.616204	0.308102	+	0.951353i	$0.400306\pi$
$128$	1.00000	0.0883883
$129$	−1.61803	−0.142460
$130$	−4.47214	−0.392232
$131$	−10.4721	−0.914955	−0.457477	−	0.889221i	$-0.651247\pi$
$131$	−10.4721	−0.914955	−0.457477	+	0.889221i	$0.651247\pi$
$132$	−1.61803	−0.140832
$133$	1.76393	0.152952
$134$	−8.00000	−0.691095
$135$	5.47214	0.470966
$136$	5.09017	0.436478
$137$	6.94427	0.593289	0.296645	−	0.954988i	$-0.404132\pi$
$137$	6.94427	0.593289	0.296645	+	0.954988i	$0.404132\pi$
$138$	6.47214	0.550945
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	−0.381966	−0.0322820
$141$	12.3262	1.03806
$142$	−4.09017	−0.343239
$143$	−4.47214	−0.373979
$144$	−0.381966	−0.0318305
$145$	4.47214	0.371391
$146$	−4.47214	−0.370117
$147$	11.0902	0.914702
$148$	1.23607	0.101604
$149$	10.1803	0.834006	0.417003	−	0.908905i	$-0.363080\pi$
$149$	10.1803	0.834006	0.417003	+	0.908905i	$0.363080\pi$
$150$	−1.61803	−0.132112
$151$	−0.472136	−0.0384219	−0.0192109	−	0.999815i	$-0.506115\pi$
$151$	−0.472136	−0.0384219	−0.0192109	+	0.999815i	$0.506115\pi$
$152$	−4.61803	−0.374572
$153$	−1.94427	−0.157185
$154$	−0.381966	−0.0307797
$155$	6.47214	0.519854
$156$	7.23607	0.579349
$157$	−22.4721	−1.79347	−0.896736	−	0.442566i	$-0.854068\pi$
$157$	−22.4721	−1.79347	−0.896736	+	0.442566i	$0.854068\pi$
$158$	4.09017	0.325396
$159$	11.4721	0.909800
$160$	1.00000	0.0790569
$161$	1.52786	0.120413
$162$	−7.70820	−0.605614
$163$	−9.09017	−0.711997	−0.355999	−	0.934487i	$-0.615859\pi$
$163$	−9.09017	−0.711997	−0.355999	+	0.934487i	$0.615859\pi$
$164$	−10.0000	−0.780869
$165$	−1.61803	−0.125964
$166$	−2.56231	−0.198874
$167$	16.4721	1.27465	0.637326	−	0.770594i	$-0.280040\pi$
$167$	16.4721	1.27465	0.637326	+	0.770594i	$0.280040\pi$
$168$	0.618034	0.0476824
$169$	7.00000	0.538462
$170$	5.09017	0.390398
$171$	1.76393	0.134891
$172$	1.00000	0.0762493
$173$	−21.8885	−1.66416	−0.832078	−	0.554659i	$-0.812849\pi$
$173$	−21.8885	−1.66416	−0.832078	+	0.554659i	$0.812849\pi$
$174$	−7.23607	−0.548565
$175$	−0.381966	−0.0288739
$176$	1.00000	0.0753778
$177$	−12.3262	−0.926497
$178$	−0.472136	−0.0353881
$179$	−10.7639	−0.804534	−0.402267	−	0.915522i	$-0.631778\pi$
$179$	−10.7639	−0.804534	−0.402267	+	0.915522i	$0.631778\pi$
$180$	−0.381966	−0.0284701
$181$	12.9443	0.962140	0.481070	−	0.876682i	$-0.340248\pi$
$181$	12.9443	0.962140	0.481070	+	0.876682i	$0.340248\pi$
$182$	1.70820	0.126620
$183$	10.4721	0.774123
$184$	−4.00000	−0.294884
$185$	1.23607	0.0908775
$186$	−10.4721	−0.767854
$187$	5.09017	0.372230
$188$	−7.61803	−0.555602
$189$	−2.09017	−0.152037
$190$	−4.61803	−0.335027
$191$	−23.2705	−1.68379	−0.841897	−	0.539637i	$-0.818561\pi$
$191$	−23.2705	−1.68379	−0.841897	+	0.539637i	$0.818561\pi$
$192$	−1.61803	−0.116772
$193$	−23.6180	−1.70006	−0.850032	−	0.526732i	$-0.823417\pi$
$193$	−23.6180	−1.70006	−0.850032	+	0.526732i	$0.823417\pi$
$194$	−2.76393	−0.198439
$195$	7.23607	0.518186
$196$	−6.85410	−0.489579
$197$	26.9443	1.91970	0.959850	−	0.280514i	$-0.0905049\pi$
$197$	26.9443	1.91970	0.959850	+	0.280514i	$0.0905049\pi$
$198$	−0.381966	−0.0271451
$199$	−1.38197	−0.0979650	−0.0489825	−	0.998800i	$-0.515598\pi$
$199$	−1.38197	−0.0979650	−0.0489825	+	0.998800i	$0.515598\pi$
$200$	1.00000	0.0707107
$201$	12.9443	0.913019
$202$	5.32624	0.374753
$203$	−1.70820	−0.119892
$204$	−8.23607	−0.576640
$205$	−10.0000	−0.698430
$206$	9.56231	0.666237
$207$	1.52786	0.106194
$208$	−4.47214	−0.310087
$209$	−4.61803	−0.319436
$210$	0.618034	0.0426484
$211$	0.562306	0.0387107	0.0193554	−	0.999813i	$-0.493839\pi$
$211$	0.562306	0.0387107	0.0193554	+	0.999813i	$0.493839\pi$
$212$	−7.09017	−0.486955
$213$	6.61803	0.453460
$214$	−8.79837	−0.601444
$215$	1.00000	0.0681994
$216$	5.47214	0.372332
$217$	−2.47214	−0.167820
$218$	−16.7984	−1.13773
$219$	7.23607	0.488968
$220$	1.00000	0.0674200
$221$	−22.7639	−1.53127
$222$	−2.00000	−0.134231
$223$	−2.47214	−0.165546	−0.0827732	−	0.996568i	$-0.526378\pi$
$223$	−2.47214	−0.165546	−0.0827732	+	0.996568i	$0.526378\pi$
$224$	−0.381966	−0.0255212
$225$	−0.381966	−0.0254644
$226$	−13.3820	−0.890155
$227$	−9.23607	−0.613019	−0.306510	−	0.951868i	$-0.599161\pi$
$227$	−9.23607	−0.613019	−0.306510	+	0.951868i	$0.599161\pi$
$228$	7.47214	0.494854
$229$	0.763932	0.0504820	0.0252410	−	0.999681i	$-0.491965\pi$
$229$	0.763932	0.0504820	0.0252410	+	0.999681i	$0.491965\pi$
$230$	−4.00000	−0.263752
$231$	0.618034	0.0406637
$232$	4.47214	0.293610
$233$	−23.7082	−1.55318	−0.776588	−	0.630009i	$-0.783051\pi$
$233$	−23.7082	−1.55318	−0.776588	+	0.630009i	$0.783051\pi$
$234$	1.70820	0.111669
$235$	−7.61803	−0.496946
$236$	7.61803	0.495892
$237$	−6.61803	−0.429888
$238$	−1.94427	−0.126028
$239$	−12.7984	−0.827858	−0.413929	−	0.910309i	$-0.635844\pi$
$239$	−12.7984	−0.827858	−0.413929	+	0.910309i	$0.635844\pi$
$240$	−1.61803	−0.104444
$241$	15.9098	1.02484	0.512421	−	0.858734i	$-0.328749\pi$
$241$	15.9098	1.02484	0.512421	+	0.858734i	$0.328749\pi$
$242$	1.00000	0.0642824
$243$	−3.94427	−0.253025
$244$	−6.47214	−0.414336
$245$	−6.85410	−0.437893
$246$	16.1803	1.03162
$247$	20.6525	1.31409
$248$	6.47214	0.410981
$249$	4.14590	0.262736
$250$	1.00000	0.0632456
$251$	5.85410	0.369508	0.184754	−	0.982785i	$-0.440851\pi$
$251$	5.85410	0.369508	0.184754	+	0.982785i	$0.440851\pi$
$252$	0.145898	0.00919071
$253$	−4.00000	−0.251478
$254$	6.94427	0.435722
$255$	−8.23607	−0.515763
$256$	1.00000	0.0625000
$257$	−22.6180	−1.41087	−0.705437	−	0.708773i	$-0.749249\pi$
$257$	−22.6180	−1.41087	−0.705437	+	0.708773i	$0.749249\pi$
$258$	−1.61803	−0.100734
$259$	−0.472136	−0.0293371
$260$	−4.47214	−0.277350
$261$	−1.70820	−0.105735
$262$	−10.4721	−0.646971
$263$	−15.3820	−0.948493	−0.474246	−	0.880392i	$-0.657279\pi$
$263$	−15.3820	−0.948493	−0.474246	+	0.880392i	$0.657279\pi$
$264$	−1.61803	−0.0995831
$265$	−7.09017	−0.435546
$266$	1.76393	0.108154
$267$	0.763932	0.0467519
$268$	−8.00000	−0.488678
$269$	2.47214	0.150729	0.0753644	−	0.997156i	$-0.475988\pi$
$269$	2.47214	0.150729	0.0753644	+	0.997156i	$0.475988\pi$
$270$	5.47214	0.333024
$271$	−0.944272	−0.0573604	−0.0286802	−	0.999589i	$-0.509130\pi$
$271$	−0.944272	−0.0573604	−0.0286802	+	0.999589i	$0.509130\pi$
$272$	5.09017	0.308637
$273$	−2.76393	−0.167281
$274$	6.94427	0.419519
$275$	1.00000	0.0603023
$276$	6.47214	0.389577
$277$	−6.79837	−0.408475	−0.204237	−	0.978921i	$-0.565471\pi$
$277$	−6.79837	−0.408475	−0.204237	+	0.978921i	$0.565471\pi$
$278$	13.4164	0.804663
$279$	−2.47214	−0.148003
$280$	−0.381966	−0.0228268
$281$	−7.52786	−0.449075	−0.224537	−	0.974465i	$-0.572087\pi$
$281$	−7.52786	−0.449075	−0.224537	+	0.974465i	$0.572087\pi$
$282$	12.3262	0.734017
$283$	22.0344	1.30981	0.654906	−	0.755711i	$-0.272708\pi$
$283$	22.0344	1.30981	0.654906	+	0.755711i	$0.272708\pi$
$284$	−4.09017	−0.242707
$285$	7.47214	0.442611
$286$	−4.47214	−0.264443
$287$	3.81966	0.225467
$288$	−0.381966	−0.0225076
$289$	8.90983	0.524108
$290$	4.47214	0.262613
$291$	4.47214	0.262161
$292$	−4.47214	−0.261712
$293$	−17.2361	−1.00694	−0.503471	−	0.864012i	$-0.667944\pi$
$293$	−17.2361	−1.00694	−0.503471	+	0.864012i	$0.667944\pi$
$294$	11.0902	0.646792
$295$	7.61803	0.443539
$296$	1.23607	0.0718450
$297$	5.47214	0.317526
$298$	10.1803	0.589731
$299$	17.8885	1.03452
$300$	−1.61803	−0.0934172
$301$	−0.381966	−0.0220162
$302$	−0.472136	−0.0271684
$303$	−8.61803	−0.495093
$304$	−4.61803	−0.264862
$305$	−6.47214	−0.370593
$306$	−1.94427	−0.111147
$307$	9.61803	0.548930	0.274465	−	0.961597i	$-0.411499\pi$
$307$	9.61803	0.548930	0.274465	+	0.961597i	$0.411499\pi$
$308$	−0.381966	−0.0217645
$309$	−15.4721	−0.880179
$310$	6.47214	0.367593
$311$	−5.23607	−0.296910	−0.148455	−	0.988919i	$-0.547430\pi$
$311$	−5.23607	−0.296910	−0.148455	+	0.988919i	$0.547430\pi$
$312$	7.23607	0.409662
$313$	7.27051	0.410954	0.205477	−	0.978662i	$-0.434126\pi$
$313$	7.27051	0.410954	0.205477	+	0.978662i	$0.434126\pi$
$314$	−22.4721	−1.26818
$315$	0.145898	0.00822042
$316$	4.09017	0.230090
$317$	−20.2705	−1.13851	−0.569253	−	0.822163i	$-0.692767\pi$
$317$	−20.2705	−1.13851	−0.569253	+	0.822163i	$0.692767\pi$
$318$	11.4721	0.643325
$319$	4.47214	0.250392
$320$	1.00000	0.0559017
$321$	14.2361	0.794580
$322$	1.52786	0.0851445
$323$	−23.5066	−1.30794
$324$	−7.70820	−0.428234
$325$	−4.47214	−0.248069
$326$	−9.09017	−0.503458
$327$	27.1803	1.50308
$328$	−10.0000	−0.552158
$329$	2.90983	0.160424
$330$	−1.61803	−0.0890698
$331$	14.9443	0.821411	0.410706	−	0.911768i	$-0.365282\pi$
$331$	14.9443	0.821411	0.410706	+	0.911768i	$0.365282\pi$
$332$	−2.56231	−0.140625
$333$	−0.472136	−0.0258729
$334$	16.4721	0.901315
$335$	−8.00000	−0.437087
$336$	0.618034	0.0337165
$337$	−2.03444	−0.110823	−0.0554116	−	0.998464i	$-0.517647\pi$
$337$	−2.03444	−0.110823	−0.0554116	+	0.998464i	$0.517647\pi$
$338$	7.00000	0.380750
$339$	21.6525	1.17600
$340$	5.09017	0.276053
$341$	6.47214	0.350486
$342$	1.76393	0.0953825
$343$	5.29180	0.285730
$344$	1.00000	0.0539164
$345$	6.47214	0.348448
$346$	−21.8885	−1.17674
$347$	−11.7082	−0.628529	−0.314265	−	0.949335i	$-0.601758\pi$
$347$	−11.7082	−0.628529	−0.314265	+	0.949335i	$0.601758\pi$
$348$	−7.23607	−0.387894
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	−0.381966	−0.0204169
$351$	−24.4721	−1.30623
$352$	1.00000	0.0533002
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	−12.3262	−0.655132
$355$	−4.09017	−0.217084
$356$	−0.472136	−0.0250232
$357$	3.14590	0.166499
$358$	−10.7639	−0.568891
$359$	−1.88854	−0.0996735	−0.0498368	−	0.998757i	$-0.515870\pi$
$359$	−1.88854	−0.0996735	−0.0498368	+	0.998757i	$0.515870\pi$
$360$	−0.381966	−0.0201314
$361$	2.32624	0.122434
$362$	12.9443	0.680336
$363$	−1.61803	−0.0849248
$364$	1.70820	0.0895342
$365$	−4.47214	−0.234082
$366$	10.4721	0.547387
$367$	−29.9230	−1.56197	−0.780984	−	0.624552i	$-0.785282\pi$
$367$	−29.9230	−1.56197	−0.780984	+	0.624552i	$0.785282\pi$
$368$	−4.00000	−0.208514
$369$	3.81966	0.198844
$370$	1.23607	0.0642601
$371$	2.70820	0.140603
$372$	−10.4721	−0.542955
$373$	16.8541	0.872672	0.436336	−	0.899784i	$-0.356276\pi$
$373$	16.8541	0.872672	0.436336	+	0.899784i	$0.356276\pi$
$374$	5.09017	0.263206
$375$	−1.61803	−0.0835549
$376$	−7.61803	−0.392870
$377$	−20.0000	−1.03005
$378$	−2.09017	−0.107507
$379$	17.1459	0.880726	0.440363	−	0.897820i	$-0.354850\pi$
$379$	17.1459	0.880726	0.440363	+	0.897820i	$0.354850\pi$
$380$	−4.61803	−0.236900
$381$	−11.2361	−0.575641
$382$	−23.2705	−1.19062
$383$	−9.41641	−0.481156	−0.240578	−	0.970630i	$-0.577337\pi$
$383$	−9.41641	−0.481156	−0.240578	+	0.970630i	$0.577337\pi$
$384$	−1.61803	−0.0825700
$385$	−0.381966	−0.0194668
$386$	−23.6180	−1.20213
$387$	−0.381966	−0.0194164
$388$	−2.76393	−0.140317
$389$	7.61803	0.386250	0.193125	−	0.981174i	$-0.438138\pi$
$389$	7.61803	0.386250	0.193125	+	0.981174i	$0.438138\pi$
$390$	7.23607	0.366413
$391$	−20.3607	−1.02968
$392$	−6.85410	−0.346184
$393$	16.9443	0.854725
$394$	26.9443	1.35743
$395$	4.09017	0.205799
$396$	−0.381966	−0.0191945
$397$	14.7426	0.739912	0.369956	−	0.929049i	$-0.379373\pi$
$397$	14.7426	0.739912	0.369956	+	0.929049i	$0.379373\pi$
$398$	−1.38197	−0.0692717
$399$	−2.85410	−0.142884
$400$	1.00000	0.0500000
$401$	12.9098	0.644686	0.322343	−	0.946623i	$-0.395530\pi$
$401$	12.9098	0.644686	0.322343	+	0.946623i	$0.395530\pi$
$402$	12.9443	0.645602
$403$	−28.9443	−1.44182
$404$	5.32624	0.264990
$405$	−7.70820	−0.383024
$406$	−1.70820	−0.0847767
$407$	1.23607	0.0612696
$408$	−8.23607	−0.407746
$409$	−25.5623	−1.26397	−0.631987	−	0.774979i	$-0.717761\pi$
$409$	−25.5623	−1.26397	−0.631987	+	0.774979i	$0.717761\pi$
$410$	−10.0000	−0.493865
$411$	−11.2361	−0.554234
$412$	9.56231	0.471101
$413$	−2.90983	−0.143183
$414$	1.52786	0.0750904
$415$	−2.56231	−0.125779
$416$	−4.47214	−0.219265
$417$	−21.7082	−1.06306
$418$	−4.61803	−0.225875
$419$	5.05573	0.246988	0.123494	−	0.992345i	$-0.460590\pi$
$419$	5.05573	0.246988	0.123494	+	0.992345i	$0.460590\pi$
$420$	0.618034	0.0301570
$421$	−7.20163	−0.350986	−0.175493	−	0.984481i	$-0.556152\pi$
$421$	−7.20163	−0.350986	−0.175493	+	0.984481i	$0.556152\pi$
$422$	0.562306	0.0273726
$423$	2.90983	0.141481
$424$	−7.09017	−0.344329
$425$	5.09017	0.246910
$426$	6.61803	0.320645
$427$	2.47214	0.119635
$428$	−8.79837	−0.425285
$429$	7.23607	0.349361
$430$	1.00000	0.0482243
$431$	32.2705	1.55442	0.777208	−	0.629244i	$-0.216635\pi$
$431$	32.2705	1.55442	0.777208	+	0.629244i	$0.216635\pi$
$432$	5.47214	0.263278
$433$	−5.41641	−0.260296	−0.130148	−	0.991495i	$-0.541545\pi$
$433$	−5.41641	−0.260296	−0.130148	+	0.991495i	$0.541545\pi$
$434$	−2.47214	−0.118666
$435$	−7.23607	−0.346943
$436$	−16.7984	−0.804496
$437$	18.4721	0.883642
$438$	7.23607	0.345753
$439$	−2.90983	−0.138879	−0.0694393	−	0.997586i	$-0.522121\pi$
$439$	−2.90983	−0.138879	−0.0694393	+	0.997586i	$0.522121\pi$
$440$	1.00000	0.0476731
$441$	2.61803	0.124668
$442$	−22.7639	−1.08277
$443$	−33.5967	−1.59623	−0.798115	−	0.602505i	$-0.794169\pi$
$443$	−33.5967	−1.59623	−0.798115	+	0.602505i	$0.794169\pi$
$444$	−2.00000	−0.0949158
$445$	−0.472136	−0.0223814
$446$	−2.47214	−0.117059
$447$	−16.4721	−0.779105
$448$	−0.381966	−0.0180462
$449$	17.5279	0.827191	0.413596	−	0.910461i	$-0.364273\pi$
$449$	17.5279	0.827191	0.413596	+	0.910461i	$0.364273\pi$
$450$	−0.381966	−0.0180061
$451$	−10.0000	−0.470882
$452$	−13.3820	−0.629435
$453$	0.763932	0.0358927
$454$	−9.23607	−0.433470
$455$	1.70820	0.0800818
$456$	7.47214	0.349915
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	0.763932	0.0356962
$459$	27.8541	1.30012
$460$	−4.00000	−0.186501
$461$	28.1459	1.31089	0.655443	−	0.755245i	$-0.272482\pi$
$461$	28.1459	1.31089	0.655443	+	0.755245i	$0.272482\pi$
$462$	0.618034	0.0287535
$463$	39.1246	1.81827	0.909137	−	0.416496i	$-0.136742\pi$
$463$	39.1246	1.81827	0.909137	+	0.416496i	$0.136742\pi$
$464$	4.47214	0.207614
$465$	−10.4721	−0.485634
$466$	−23.7082	−1.09826
$467$	12.5066	0.578735	0.289368	−	0.957218i	$-0.406555\pi$
$467$	12.5066	0.578735	0.289368	+	0.957218i	$0.406555\pi$
$468$	1.70820	0.0789618
$469$	3.05573	0.141100
$470$	−7.61803	−0.351394
$471$	36.3607	1.67541
$472$	7.61803	0.350648
$473$	1.00000	0.0459800
$474$	−6.61803	−0.303976
$475$	−4.61803	−0.211890
$476$	−1.94427	−0.0891156
$477$	2.70820	0.124000
$478$	−12.7984	−0.585384
$479$	−4.00000	−0.182765	−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000	−0.182765	−0.0913823	+	0.995816i	$0.529129\pi$
$480$	−1.61803	−0.0738528
$481$	−5.52786	−0.252049
$482$	15.9098	0.724673
$483$	−2.47214	−0.112486
$484$	1.00000	0.0454545
$485$	−2.76393	−0.125504
$486$	−3.94427	−0.178916
$487$	−7.61803	−0.345206	−0.172603	−	0.984991i	$-0.555218\pi$
$487$	−7.61803	−0.345206	−0.172603	+	0.984991i	$0.555218\pi$
$488$	−6.47214	−0.292980
$489$	14.7082	0.665128
$490$	−6.85410	−0.309637
$491$	43.2148	1.95026	0.975128	−	0.221643i	$-0.0711419\pi$
$491$	43.2148	1.95026	0.975128	+	0.221643i	$0.0711419\pi$
$492$	16.1803	0.729466
$493$	22.7639	1.02524
$494$	20.6525	0.929199
$495$	−0.381966	−0.0171681
$496$	6.47214	0.290607
$497$	1.56231	0.0700790
$498$	4.14590	0.185782
$499$	36.8328	1.64886	0.824432	−	0.565962i	$-0.191495\pi$
$499$	36.8328	1.64886	0.824432	+	0.565962i	$0.191495\pi$
$500$	1.00000	0.0447214
$501$	−26.6525	−1.19074
$502$	5.85410	0.261281
$503$	−5.85410	−0.261022	−0.130511	−	0.991447i	$-0.541662\pi$
$503$	−5.85410	−0.261022	−0.130511	+	0.991447i	$0.541662\pi$
$504$	0.145898	0.00649881
$505$	5.32624	0.237014
$506$	−4.00000	−0.177822
$507$	−11.3262	−0.503016
$508$	6.94427	0.308102
$509$	8.29180	0.367527	0.183764	−	0.982970i	$-0.441172\pi$
$509$	8.29180	0.367527	0.183764	+	0.982970i	$0.441172\pi$
$510$	−8.23607	−0.364699
$511$	1.70820	0.0755665
$512$	1.00000	0.0441942
$513$	−25.2705	−1.11572
$514$	−22.6180	−0.997639
$515$	9.56231	0.421366
$516$	−1.61803	−0.0712300
$517$	−7.61803	−0.335041
$518$	−0.472136	−0.0207445
$519$	35.4164	1.55461
$520$	−4.47214	−0.196116
$521$	−7.23607	−0.317018	−0.158509	−	0.987358i	$-0.550669\pi$
$521$	−7.23607	−0.317018	−0.158509	+	0.987358i	$0.550669\pi$
$522$	−1.70820	−0.0747661
$523$	29.7771	1.30206	0.651031	−	0.759052i	$-0.274337\pi$
$523$	29.7771	1.30206	0.651031	+	0.759052i	$0.274337\pi$
$524$	−10.4721	−0.457477
$525$	0.618034	0.0269732
$526$	−15.3820	−0.670686
$527$	32.9443	1.43508
$528$	−1.61803	−0.0704159
$529$	−7.00000	−0.304348
$530$	−7.09017	−0.307977
$531$	−2.90983	−0.126276
$532$	1.76393	0.0764762
$533$	44.7214	1.93710
$534$	0.763932	0.0330586
$535$	−8.79837	−0.380387
$536$	−8.00000	−0.345547
$537$	17.4164	0.751573
$538$	2.47214	0.106581
$539$	−6.85410	−0.295227
$540$	5.47214	0.235483
$541$	−15.0344	−0.646381	−0.323191	−	0.946334i	$-0.604755\pi$
$541$	−15.0344	−0.646381	−0.323191	+	0.946334i	$0.604755\pi$
$542$	−0.944272	−0.0405600
$543$	−20.9443	−0.898805
$544$	5.09017	0.218239
$545$	−16.7984	−0.719563
$546$	−2.76393	−0.118285
$547$	−14.5623	−0.622639	−0.311320	−	0.950305i	$-0.600771\pi$
$547$	−14.5623	−0.622639	−0.311320	+	0.950305i	$0.600771\pi$
$548$	6.94427	0.296645
$549$	2.47214	0.105508
$550$	1.00000	0.0426401
$551$	−20.6525	−0.879825
$552$	6.47214	0.275472
$553$	−1.56231	−0.0664360
$554$	−6.79837	−0.288835
$555$	−2.00000	−0.0848953
$556$	13.4164	0.568982
$557$	11.1246	0.471365	0.235682	−	0.971830i	$-0.424267\pi$
$557$	11.1246	0.471365	0.235682	+	0.971830i	$0.424267\pi$
$558$	−2.47214	−0.104654
$559$	−4.47214	−0.189151
$560$	−0.381966	−0.0161410
$561$	−8.23607	−0.347727
$562$	−7.52786	−0.317544
$563$	16.3607	0.689520	0.344760	−	0.938691i	$-0.387960\pi$
$563$	16.3607	0.689520	0.344760	+	0.938691i	$0.387960\pi$
$564$	12.3262	0.519028
$565$	−13.3820	−0.562984
$566$	22.0344	0.926177
$567$	2.94427	0.123648
$568$	−4.09017	−0.171620
$569$	45.1246	1.89172	0.945861	−	0.324572i	$-0.105220\pi$
$569$	45.1246	1.89172	0.945861	+	0.324572i	$0.105220\pi$
$570$	7.47214	0.312973
$571$	−44.1033	−1.84567	−0.922833	−	0.385199i	$-0.874133\pi$
$571$	−44.1033	−1.84567	−0.922833	+	0.385199i	$0.874133\pi$
$572$	−4.47214	−0.186989
$573$	37.6525	1.57295
$574$	3.81966	0.159430
$575$	−4.00000	−0.166812
$576$	−0.381966	−0.0159153
$577$	23.9787	0.998247	0.499123	−	0.866531i	$-0.333655\pi$
$577$	23.9787	0.998247	0.499123	+	0.866531i	$0.333655\pi$
$578$	8.90983	0.370600
$579$	38.2148	1.58815
$580$	4.47214	0.185695
$581$	0.978714	0.0406039
$582$	4.47214	0.185376
$583$	−7.09017	−0.293645
$584$	−4.47214	−0.185058
$585$	1.70820	0.0706255
$586$	−17.2361	−0.712015
$587$	17.6180	0.727174	0.363587	−	0.931560i	$-0.381552\pi$
$587$	17.6180	0.727174	0.363587	+	0.931560i	$0.381552\pi$
$588$	11.0902	0.457351
$589$	−29.8885	−1.23154
$590$	7.61803	0.313629
$591$	−43.5967	−1.79333
$592$	1.23607	0.0508021
$593$	29.7771	1.22280	0.611399	−	0.791322i	$-0.290607\pi$
$593$	29.7771	1.22280	0.611399	+	0.791322i	$0.290607\pi$
$594$	5.47214	0.224524
$595$	−1.94427	−0.0797074
$596$	10.1803	0.417003
$597$	2.23607	0.0915162
$598$	17.8885	0.731517
$599$	−5.41641	−0.221308	−0.110654	−	0.993859i	$-0.535295\pi$
$599$	−5.41641	−0.221308	−0.110654	+	0.993859i	$0.535295\pi$
$600$	−1.61803	−0.0660560
$601$	−9.79837	−0.399684	−0.199842	−	0.979828i	$-0.564043\pi$
$601$	−9.79837	−0.399684	−0.199842	+	0.979828i	$0.564043\pi$
$602$	−0.381966	−0.0155678
$603$	3.05573	0.124439
$604$	−0.472136	−0.0192109
$605$	1.00000	0.0406558
$606$	−8.61803	−0.350084
$607$	11.6738	0.473823	0.236912	−	0.971531i	$-0.423865\pi$
$607$	11.6738	0.473823	0.236912	+	0.971531i	$0.423865\pi$
$608$	−4.61803	−0.187286
$609$	2.76393	0.112000
$610$	−6.47214	−0.262049
$611$	34.0689	1.37828
$612$	−1.94427	−0.0785925
$613$	−16.5836	−0.669805	−0.334902	−	0.942253i	$-0.608703\pi$
$613$	−16.5836	−0.669805	−0.334902	+	0.942253i	$0.608703\pi$
$614$	9.61803	0.388152
$615$	16.1803	0.652454
$616$	−0.381966	−0.0153898
$617$	−43.8885	−1.76689	−0.883443	−	0.468538i	$-0.844781\pi$
$617$	−43.8885	−1.76689	−0.883443	+	0.468538i	$0.844781\pi$
$618$	−15.4721	−0.622381
$619$	−24.0344	−0.966026	−0.483013	−	0.875613i	$-0.660458\pi$
$619$	−24.0344	−0.966026	−0.483013	+	0.875613i	$0.660458\pi$
$620$	6.47214	0.259927
$621$	−21.8885	−0.878357
$622$	−5.23607	−0.209947
$623$	0.180340	0.00722517
$624$	7.23607	0.289675
$625$	1.00000	0.0400000
$626$	7.27051	0.290588
$627$	7.47214	0.298408
$628$	−22.4721	−0.896736
$629$	6.29180	0.250870
$630$	0.145898	0.00581272
$631$	−5.61803	−0.223650	−0.111825	−	0.993728i	$-0.535670\pi$
$631$	−5.61803	−0.223650	−0.111825	+	0.993728i	$0.535670\pi$
$632$	4.09017	0.162698
$633$	−0.909830	−0.0361625
$634$	−20.2705	−0.805045
$635$	6.94427	0.275575
$636$	11.4721	0.454900
$637$	30.6525	1.21450
$638$	4.47214	0.177054
$639$	1.56231	0.0618039
$640$	1.00000	0.0395285
$641$	−22.0000	−0.868948	−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000	−0.868948	−0.434474	+	0.900684i	$0.643066\pi$
$642$	14.2361	0.561853
$643$	4.36068	0.171968	0.0859842	−	0.996296i	$-0.472597\pi$
$643$	4.36068	0.171968	0.0859842	+	0.996296i	$0.472597\pi$
$644$	1.52786	0.0602063
$645$	−1.61803	−0.0637100
$646$	−23.5066	−0.924854
$647$	−18.7639	−0.737686	−0.368843	−	0.929492i	$-0.620246\pi$
$647$	−18.7639	−0.737686	−0.368843	+	0.929492i	$0.620246\pi$
$648$	−7.70820	−0.302807
$649$	7.61803	0.299034
$650$	−4.47214	−0.175412
$651$	4.00000	0.156772
$652$	−9.09017	−0.355999
$653$	−6.47214	−0.253274	−0.126637	−	0.991949i	$-0.540418\pi$
$653$	−6.47214	−0.253274	−0.126637	+	0.991949i	$0.540418\pi$
$654$	27.1803	1.06284
$655$	−10.4721	−0.409180
$656$	−10.0000	−0.390434
$657$	1.70820	0.0666434
$658$	2.90983	0.113437
$659$	28.6525	1.11614	0.558071	−	0.829793i	$-0.311542\pi$
$659$	28.6525	1.11614	0.558071	+	0.829793i	$0.311542\pi$
$660$	−1.61803	−0.0629819
$661$	−13.7082	−0.533187	−0.266594	−	0.963809i	$-0.585898\pi$
$661$	−13.7082	−0.533187	−0.266594	+	0.963809i	$0.585898\pi$
$662$	14.9443	0.580826
$663$	36.8328	1.43047
$664$	−2.56231	−0.0994368
$665$	1.76393	0.0684023
$666$	−0.472136	−0.0182949
$667$	−17.8885	−0.692647
$668$	16.4721	0.637326
$669$	4.00000	0.154649
$670$	−8.00000	−0.309067
$671$	−6.47214	−0.249854
$672$	0.618034	0.0238412
$673$	39.2361	1.51244	0.756220	−	0.654318i	$-0.227044\pi$
$673$	39.2361	1.51244	0.756220	+	0.654318i	$0.227044\pi$
$674$	−2.03444	−0.0783638
$675$	5.47214	0.210623
$676$	7.00000	0.269231
$677$	−39.3262	−1.51143	−0.755715	−	0.654901i	$-0.772710\pi$
$677$	−39.3262	−1.51143	−0.755715	+	0.654901i	$0.772710\pi$
$678$	21.6525	0.831558
$679$	1.05573	0.0405151
$680$	5.09017	0.195199
$681$	14.9443	0.572666
$682$	6.47214	0.247831
$683$	28.6525	1.09636	0.548178	−	0.836362i	$-0.315322\pi$
$683$	28.6525	1.09636	0.548178	+	0.836362i	$0.315322\pi$
$684$	1.76393	0.0674456
$685$	6.94427	0.265327
$686$	5.29180	0.202042
$687$	−1.23607	−0.0471589
$688$	1.00000	0.0381246
$689$	31.7082	1.20799
$690$	6.47214	0.246390
$691$	47.2361	1.79694	0.898472	−	0.439030i	$-0.144678\pi$
$691$	47.2361	1.79694	0.898472	+	0.439030i	$0.144678\pi$
$692$	−21.8885	−0.832078
$693$	0.145898	0.00554221
$694$	−11.7082	−0.444437
$695$	13.4164	0.508913
$696$	−7.23607	−0.274282
$697$	−50.9017	−1.92804
$698$	6.00000	0.227103
$699$	38.3607	1.45093
$700$	−0.381966	−0.0144370
$701$	11.2705	0.425681	0.212841	−	0.977087i	$-0.431728\pi$
$701$	11.2705	0.425681	0.212841	+	0.977087i	$0.431728\pi$
$702$	−24.4721	−0.923641
$703$	−5.70820	−0.215289
$704$	1.00000	0.0376889
$705$	12.3262	0.464233
$706$	6.00000	0.225813
$707$	−2.03444	−0.0765131
$708$	−12.3262	−0.463248
$709$	−12.0000	−0.450669	−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000	−0.450669	−0.225335	+	0.974281i	$0.572348\pi$
$710$	−4.09017	−0.153501
$711$	−1.56231	−0.0585910
$712$	−0.472136	−0.0176940
$713$	−25.8885	−0.969534
$714$	3.14590	0.117732
$715$	−4.47214	−0.167248
$716$	−10.7639	−0.402267
$717$	20.7082	0.773362
$718$	−1.88854	−0.0704798
$719$	33.7771	1.25967	0.629836	−	0.776728i	$-0.283122\pi$
$719$	33.7771	1.25967	0.629836	+	0.776728i	$0.283122\pi$
$720$	−0.381966	−0.0142350
$721$	−3.65248	−0.136025
$722$	2.32624	0.0865736
$723$	−25.7426	−0.957379
$724$	12.9443	0.481070
$725$	4.47214	0.166091
$726$	−1.61803	−0.0600509
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	1.70820	0.0633102
$729$	29.5066	1.09284
$730$	−4.47214	−0.165521
$731$	5.09017	0.188267
$732$	10.4721	0.387061
$733$	−20.6180	−0.761544	−0.380772	−	0.924669i	$-0.624342\pi$
$733$	−20.6180	−0.761544	−0.380772	+	0.924669i	$0.624342\pi$
$734$	−29.9230	−1.10448
$735$	11.0902	0.409067
$736$	−4.00000	−0.147442
$737$	−8.00000	−0.294684
$738$	3.81966	0.140604
$739$	7.03444	0.258766	0.129383	−	0.991595i	$-0.458700\pi$
$739$	7.03444	0.258766	0.129383	+	0.991595i	$0.458700\pi$
$740$	1.23607	0.0454388
$741$	−33.4164	−1.22758
$742$	2.70820	0.0994213
$743$	−7.21478	−0.264685	−0.132342	−	0.991204i	$-0.542250\pi$
$743$	−7.21478	−0.264685	−0.132342	+	0.991204i	$0.542250\pi$
$744$	−10.4721	−0.383927
$745$	10.1803	0.372979
$746$	16.8541	0.617073
$747$	0.978714	0.0358093
$748$	5.09017	0.186115
$749$	3.36068	0.122797
$750$	−1.61803	−0.0590822
$751$	−19.3262	−0.705224	−0.352612	−	0.935770i	$-0.614707\pi$
$751$	−19.3262	−0.705224	−0.352612	+	0.935770i	$0.614707\pi$
$752$	−7.61803	−0.277801
$753$	−9.47214	−0.345184
$754$	−20.0000	−0.728357
$755$	−0.472136	−0.0171828
$756$	−2.09017	−0.0760187
$757$	−37.5967	−1.36648	−0.683239	−	0.730195i	$-0.739429\pi$
$757$	−37.5967	−1.36648	−0.683239	+	0.730195i	$0.739429\pi$
$758$	17.1459	0.622767
$759$	6.47214	0.234924
$760$	−4.61803	−0.167514
$761$	−42.3607	−1.53557	−0.767787	−	0.640706i	$-0.778642\pi$
$761$	−42.3607	−1.53557	−0.767787	+	0.640706i	$0.778642\pi$
$762$	−11.2361	−0.407040
$763$	6.41641	0.232290
$764$	−23.2705	−0.841897
$765$	−1.94427	−0.0702953
$766$	−9.41641	−0.340229
$767$	−34.0689	−1.23016
$768$	−1.61803	−0.0583858
$769$	47.5967	1.71638	0.858191	−	0.513330i	$-0.171588\pi$
$769$	47.5967	1.71638	0.858191	+	0.513330i	$0.171588\pi$
$770$	−0.381966	−0.0137651
$771$	36.5967	1.31800
$772$	−23.6180	−0.850032
$773$	−16.6525	−0.598948	−0.299474	−	0.954104i	$-0.596811\pi$
$773$	−16.6525	−0.598948	−0.299474	+	0.954104i	$0.596811\pi$
$774$	−0.381966	−0.0137295
$775$	6.47214	0.232486
$776$	−2.76393	−0.0992194
$777$	0.763932	0.0274059
$778$	7.61803	0.273120
$779$	46.1803	1.65458
$780$	7.23607	0.259093
$781$	−4.09017	−0.146358
$782$	−20.3607	−0.728096
$783$	24.4721	0.874563
$784$	−6.85410	−0.244789
$785$	−22.4721	−0.802065
$786$	16.9443	0.604382
$787$	−26.6869	−0.951286	−0.475643	−	0.879638i	$-0.657785\pi$
$787$	−26.6869	−0.951286	−0.475643	+	0.879638i	$0.657785\pi$
$788$	26.9443	0.959850
$789$	24.8885	0.886056
$790$	4.09017	0.145522
$791$	5.11146	0.181742
$792$	−0.381966	−0.0135726
$793$	28.9443	1.02784
$794$	14.7426	0.523197
$795$	11.4721	0.406875
$796$	−1.38197	−0.0489825
$797$	39.5066	1.39939	0.699697	−	0.714439i	$-0.253318\pi$
$797$	39.5066	1.39939	0.699697	+	0.714439i	$0.253318\pi$
$798$	−2.85410	−0.101034
$799$	−38.7771	−1.37183
$800$	1.00000	0.0353553
$801$	0.180340	0.00637200
$802$	12.9098	0.455862
$803$	−4.47214	−0.157818
$804$	12.9443	0.456509
$805$	1.52786	0.0538501
$806$	−28.9443	−1.01952
$807$	−4.00000	−0.140807
$808$	5.32624	0.187376
$809$	−16.6525	−0.585470	−0.292735	−	0.956194i	$-0.594565\pi$
$809$	−16.6525	−0.585470	−0.292735	+	0.956194i	$0.594565\pi$
$810$	−7.70820	−0.270839
$811$	38.4508	1.35019	0.675096	−	0.737730i	$-0.264102\pi$
$811$	38.4508	1.35019	0.675096	+	0.737730i	$0.264102\pi$
$812$	−1.70820	−0.0599462
$813$	1.52786	0.0535845
$814$	1.23607	0.0433242
$815$	−9.09017	−0.318415
$816$	−8.23607	−0.288320
$817$	−4.61803	−0.161565
$818$	−25.5623	−0.893765
$819$	−0.652476	−0.0227994
$820$	−10.0000	−0.349215
$821$	7.79837	0.272165	0.136083	−	0.990697i	$-0.456549\pi$
$821$	7.79837	0.272165	0.136083	+	0.990697i	$0.456549\pi$
$822$	−11.2361	−0.391903
$823$	4.58359	0.159774	0.0798870	−	0.996804i	$-0.474544\pi$
$823$	4.58359	0.159774	0.0798870	+	0.996804i	$0.474544\pi$
$824$	9.56231	0.333119
$825$	−1.61803	−0.0563327
$826$	−2.90983	−0.101246
$827$	10.1115	0.351610	0.175805	−	0.984425i	$-0.443747\pi$
$827$	10.1115	0.351610	0.175805	+	0.984425i	$0.443747\pi$
$828$	1.52786	0.0530969
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	−2.56231	−0.0889389
$831$	11.0000	0.381586
$832$	−4.47214	−0.155043
$833$	−34.8885	−1.20882
$834$	−21.7082	−0.751694
$835$	16.4721	0.570042
$836$	−4.61803	−0.159718
$837$	35.4164	1.22417
$838$	5.05573	0.174647
$839$	8.94427	0.308791	0.154395	−	0.988009i	$-0.450657\pi$
$839$	8.94427	0.308791	0.154395	+	0.988009i	$0.450657\pi$
$840$	0.618034	0.0213242
$841$	−9.00000	−0.310345
$842$	−7.20163	−0.248184
$843$	12.1803	0.419513
$844$	0.562306	0.0193554
$845$	7.00000	0.240807
$846$	2.90983	0.100042
$847$	−0.381966	−0.0131245
$848$	−7.09017	−0.243477
$849$	−35.6525	−1.22359
$850$	5.09017	0.174591
$851$	−4.94427	−0.169487
$852$	6.61803	0.226730
$853$	−39.1246	−1.33960	−0.669801	−	0.742541i	$-0.733620\pi$
$853$	−39.1246	−1.33960	−0.669801	+	0.742541i	$0.733620\pi$
$854$	2.47214	0.0845948
$855$	1.76393	0.0603252
$856$	−8.79837	−0.300722
$857$	−15.9787	−0.545822	−0.272911	−	0.962039i	$-0.587987\pi$
$857$	−15.9787	−0.545822	−0.272911	+	0.962039i	$0.587987\pi$
$858$	7.23607	0.247035
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	1.00000	0.0340997
$861$	−6.18034	−0.210625
$862$	32.2705	1.09914
$863$	−24.4721	−0.833041	−0.416521	−	0.909126i	$-0.636751\pi$
$863$	−24.4721	−0.833041	−0.416521	+	0.909126i	$0.636751\pi$
$864$	5.47214	0.186166
$865$	−21.8885	−0.744233
$866$	−5.41641	−0.184057
$867$	−14.4164	−0.489607
$868$	−2.47214	−0.0839098
$869$	4.09017	0.138750
$870$	−7.23607	−0.245326
$871$	35.7771	1.21226
$872$	−16.7984	−0.568865
$873$	1.05573	0.0357310
$874$	18.4721	0.624829
$875$	−0.381966	−0.0129128
$876$	7.23607	0.244484
$877$	−40.4721	−1.36665	−0.683323	−	0.730116i	$-0.739466\pi$
$877$	−40.4721	−1.36665	−0.683323	+	0.730116i	$0.739466\pi$
$878$	−2.90983	−0.0982020
$879$	27.8885	0.940657
$880$	1.00000	0.0337100
$881$	30.5623	1.02967	0.514835	−	0.857289i	$-0.327853\pi$
$881$	30.5623	1.02967	0.514835	+	0.857289i	$0.327853\pi$
$882$	2.61803	0.0881538
$883$	−36.0689	−1.21381	−0.606907	−	0.794773i	$-0.707590\pi$
$883$	−36.0689	−1.21381	−0.606907	+	0.794773i	$0.707590\pi$
$884$	−22.7639	−0.765634
$885$	−12.3262	−0.414342
$886$	−33.5967	−1.12870
$887$	29.5623	0.992605	0.496303	−	0.868150i	$-0.334691\pi$
$887$	29.5623	0.992605	0.496303	+	0.868150i	$0.334691\pi$
$888$	−2.00000	−0.0671156
$889$	−2.65248	−0.0889612
$890$	−0.472136	−0.0158260
$891$	−7.70820	−0.258235
$892$	−2.47214	−0.0827732
$893$	35.1803	1.17727
$894$	−16.4721	−0.550911
$895$	−10.7639	−0.359799
$896$	−0.381966	−0.0127606
$897$	−28.9443	−0.966421
$898$	17.5279	0.584912
$899$	28.9443	0.965346
$900$	−0.381966	−0.0127322
$901$	−36.0902	−1.20234
$902$	−10.0000	−0.332964
$903$	0.618034	0.0205669
$904$	−13.3820	−0.445078
$905$	12.9443	0.430282
$906$	0.763932	0.0253799
$907$	41.4853	1.37750	0.688748	−	0.725001i	$-0.258161\pi$
$907$	41.4853	1.37750	0.688748	+	0.725001i	$0.258161\pi$
$908$	−9.23607	−0.306510
$909$	−2.03444	−0.0674782
$910$	1.70820	0.0566264
$911$	22.6180	0.749369	0.374684	−	0.927152i	$-0.377751\pi$
$911$	22.6180	0.749369	0.374684	+	0.927152i	$0.377751\pi$
$912$	7.47214	0.247427
$913$	−2.56231	−0.0847999
$914$	2.00000	0.0661541
$915$	10.4721	0.346198
$916$	0.763932	0.0252410
$917$	4.00000	0.132092
$918$	27.8541	0.919322
$919$	25.7984	0.851010	0.425505	−	0.904956i	$-0.360097\pi$
$919$	25.7984	0.851010	0.425505	+	0.904956i	$0.360097\pi$
$920$	−4.00000	−0.131876
$921$	−15.5623	−0.512795
$922$	28.1459	0.926936
$923$	18.2918	0.602082
$924$	0.618034	0.0203318
$925$	1.23607	0.0406417
$926$	39.1246	1.28571
$927$	−3.65248	−0.119963
$928$	4.47214	0.146805
$929$	23.0557	0.756434	0.378217	−	0.925717i	$-0.376537\pi$
$929$	23.0557	0.756434	0.378217	+	0.925717i	$0.376537\pi$
$930$	−10.4721	−0.343395
$931$	31.6525	1.03737
$932$	−23.7082	−0.776588
$933$	8.47214	0.277365
$934$	12.5066	0.409228
$935$	5.09017	0.166466
$936$	1.70820	0.0558344
$937$	−16.9443	−0.553545	−0.276773	−	0.960935i	$-0.589265\pi$
$937$	−16.9443	−0.553545	−0.276773	+	0.960935i	$0.589265\pi$
$938$	3.05573	0.0997731
$939$	−11.7639	−0.383901
$940$	−7.61803	−0.248473
$941$	44.7984	1.46039	0.730193	−	0.683241i	$-0.239430\pi$
$941$	44.7984	1.46039	0.730193	+	0.683241i	$0.239430\pi$
$942$	36.3607	1.18469
$943$	40.0000	1.30258
$944$	7.61803	0.247946
$945$	−2.09017	−0.0679932
$946$	1.00000	0.0325128
$947$	−7.63932	−0.248245	−0.124122	−	0.992267i	$-0.539612\pi$
$947$	−7.63932	−0.248245	−0.124122	+	0.992267i	$0.539612\pi$
$948$	−6.61803	−0.214944
$949$	20.0000	0.649227
$950$	−4.61803	−0.149829
$951$	32.7984	1.06356
$952$	−1.94427	−0.0630142
$953$	34.6525	1.12250	0.561252	−	0.827645i	$-0.310320\pi$
$953$	34.6525	1.12250	0.561252	+	0.827645i	$0.310320\pi$
$954$	2.70820	0.0876813
$955$	−23.2705	−0.753016
$956$	−12.7984	−0.413929
$957$	−7.23607	−0.233909
$958$	−4.00000	−0.129234
$959$	−2.65248	−0.0856529
$960$	−1.61803	−0.0522218
$961$	10.8885	0.351243
$962$	−5.52786	−0.178225
$963$	3.36068	0.108296
$964$	15.9098	0.512421
$965$	−23.6180	−0.760291
$966$	−2.47214	−0.0795397
$967$	−1.34752	−0.0433335	−0.0216667	−	0.999765i	$-0.506897\pi$
$967$	−1.34752	−0.0433335	−0.0216667	+	0.999765i	$0.506897\pi$
$968$	1.00000	0.0321412
$969$	38.0344	1.22184
$970$	−2.76393	−0.0887445
$971$	18.7984	0.603269	0.301634	−	0.953424i	$-0.402468\pi$
$971$	18.7984	0.603269	0.301634	+	0.953424i	$0.402468\pi$
$972$	−3.94427	−0.126513
$973$	−5.12461	−0.164288
$974$	−7.61803	−0.244098
$975$	7.23607	0.231740
$976$	−6.47214	−0.207168
$977$	−13.5279	−0.432795	−0.216397	−	0.976305i	$-0.569431\pi$
$977$	−13.5279	−0.432795	−0.216397	+	0.976305i	$0.569431\pi$
$978$	14.7082	0.470317
$979$	−0.472136	−0.0150895
$980$	−6.85410	−0.218946
$981$	6.41641	0.204860
$982$	43.2148	1.37904
$983$	6.47214	0.206429	0.103215	−	0.994659i	$-0.467087\pi$
$983$	6.47214	0.206429	0.103215	+	0.994659i	$0.467087\pi$
$984$	16.1803	0.515810
$985$	26.9443	0.858516
$986$	22.7639	0.724951
$987$	−4.70820	−0.149864
$988$	20.6525	0.657043
$989$	−4.00000	−0.127193
$990$	−0.381966	−0.0121397
$991$	18.4721	0.586787	0.293393	−	0.955992i	$-0.405215\pi$
$991$	18.4721	0.586787	0.293393	+	0.955992i	$0.405215\pi$
$992$	6.47214	0.205491
$993$	−24.1803	−0.767340
$994$	1.56231	0.0495533
$995$	−1.38197	−0.0438113
$996$	4.14590	0.131368
$997$	48.8115	1.54588	0.772938	−	0.634481i	$-0.218786\pi$
$997$	48.8115	1.54588	0.772938	+	0.634481i	$0.218786\pi$
$998$	36.8328	1.16592
$999$	6.76393	0.214001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.q.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.q.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.61803 q^{12} -4.47214 q^{13} -0.381966 q^{14} -1.61803 q^{15} +1.00000 q^{16} +5.09017 q^{17} -0.381966 q^{18} -4.61803 q^{19} +1.00000 q^{20} +0.618034 q^{21} +1.00000 q^{22} -4.00000 q^{23} -1.61803 q^{24} +1.00000 q^{25} -4.47214 q^{26} +5.47214 q^{27} -0.381966 q^{28} +4.47214 q^{29} -1.61803 q^{30} +6.47214 q^{31} +1.00000 q^{32} -1.61803 q^{33} +5.09017 q^{34} -0.381966 q^{35} -0.381966 q^{36} +1.23607 q^{37} -4.61803 q^{38} +7.23607 q^{39} +1.00000 q^{40} -10.0000 q^{41} +0.618034 q^{42} +1.00000 q^{43} +1.00000 q^{44} -0.381966 q^{45} -4.00000 q^{46} -7.61803 q^{47} -1.61803 q^{48} -6.85410 q^{49} +1.00000 q^{50} -8.23607 q^{51} -4.47214 q^{52} -7.09017 q^{53} +5.47214 q^{54} +1.00000 q^{55} -0.381966 q^{56} +7.47214 q^{57} +4.47214 q^{58} +7.61803 q^{59} -1.61803 q^{60} -6.47214 q^{61} +6.47214 q^{62} +0.145898 q^{63} +1.00000 q^{64} -4.47214 q^{65} -1.61803 q^{66} -8.00000 q^{67} +5.09017 q^{68} +6.47214 q^{69} -0.381966 q^{70} -4.09017 q^{71} -0.381966 q^{72} -4.47214 q^{73} +1.23607 q^{74} -1.61803 q^{75} -4.61803 q^{76} -0.381966 q^{77} +7.23607 q^{78} +4.09017 q^{79} +1.00000 q^{80} -7.70820 q^{81} -10.0000 q^{82} -2.56231 q^{83} +0.618034 q^{84} +5.09017 q^{85} +1.00000 q^{86} -7.23607 q^{87} +1.00000 q^{88} -0.472136 q^{89} -0.381966 q^{90} +1.70820 q^{91} -4.00000 q^{92} -10.4721 q^{93} -7.61803 q^{94} -4.61803 q^{95} -1.61803 q^{96} -2.76393 q^{97} -6.85410 q^{98} -0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 3 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 3 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 3 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + 2 q^{11} - q^{12} - 3 q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} - 7 q^{19} + 2 q^{20} - q^{21} + 2 q^{22} - 8 q^{23} - q^{24} + 2 q^{25} + 2 q^{27} - 3 q^{28} - q^{30} + 4 q^{31} + 2 q^{32} - q^{33} - q^{34} - 3 q^{35} - 3 q^{36} - 2 q^{37} - 7 q^{38} + 10 q^{39} + 2 q^{40} - 20 q^{41} - q^{42} + 2 q^{43} + 2 q^{44} - 3 q^{45} - 8 q^{46} - 13 q^{47} - q^{48} - 7 q^{49} + 2 q^{50} - 12 q^{51} - 3 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 6 q^{57} + 13 q^{59} - q^{60} - 4 q^{61} + 4 q^{62} + 7 q^{63} + 2 q^{64} - q^{66} - 16 q^{67} - q^{68} + 4 q^{69} - 3 q^{70} + 3 q^{71} - 3 q^{72} - 2 q^{74} - q^{75} - 7 q^{76} - 3 q^{77} + 10 q^{78} - 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} + 15 q^{83} - q^{84} - q^{85} + 2 q^{86} - 10 q^{87} + 2 q^{88} + 8 q^{89} - 3 q^{90} - 10 q^{91} - 8 q^{92} - 12 q^{93} - 13 q^{94} - 7 q^{95} - q^{96} - 10 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 3 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + 2 * q^11 - q^12 - 3 * q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 - 7 * q^19 + 2 * q^20 - q^21 + 2 * q^22 - 8 * q^23 - q^24 + 2 * q^25 + 2 * q^27 - 3 * q^28 - q^30 + 4 * q^31 + 2 * q^32 - q^33 - q^34 - 3 * q^35 - 3 * q^36 - 2 * q^37 - 7 * q^38 + 10 * q^39 + 2 * q^40 - 20 * q^41 - q^42 + 2 * q^43 + 2 * q^44 - 3 * q^45 - 8 * q^46 - 13 * q^47 - q^48 - 7 * q^49 + 2 * q^50 - 12 * q^51 - 3 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 6 * q^57 + 13 * q^59 - q^60 - 4 * q^61 + 4 * q^62 + 7 * q^63 + 2 * q^64 - q^66 - 16 * q^67 - q^68 + 4 * q^69 - 3 * q^70 + 3 * q^71 - 3 * q^72 - 2 * q^74 - q^75 - 7 * q^76 - 3 * q^77 + 10 * q^78 - 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 + 15 * q^83 - q^84 - q^85 + 2 * q^86 - 10 * q^87 + 2 * q^88 + 8 * q^89 - 3 * q^90 - 10 * q^91 - 8 * q^92 - 12 * q^93 - 13 * q^94 - 7 * q^95 - q^96 - 10 * q^97 - 7 * q^98 - 3 * q^99

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