LMFDB - Embedded newform 8030.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
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			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.618034 q^{12} -0.618034 q^{13} +3.23607 q^{14} -0.618034 q^{15} +1.00000 q^{16} -4.00000 q^{17} -2.61803 q^{18} -5.61803 q^{19} -1.00000 q^{20} +2.00000 q^{21} +1.00000 q^{22} +2.00000 q^{23} +0.618034 q^{24} +1.00000 q^{25} -0.618034 q^{26} -3.47214 q^{27} +3.23607 q^{28} -3.23607 q^{29} -0.618034 q^{30} -5.70820 q^{31} +1.00000 q^{32} +0.618034 q^{33} -4.00000 q^{34} -3.23607 q^{35} -2.61803 q^{36} -0.472136 q^{37} -5.61803 q^{38} -0.381966 q^{39} -1.00000 q^{40} -2.00000 q^{41} +2.00000 q^{42} -5.61803 q^{43} +1.00000 q^{44} +2.61803 q^{45} +2.00000 q^{46} +3.32624 q^{47} +0.618034 q^{48} +3.47214 q^{49} +1.00000 q^{50} -2.47214 q^{51} -0.618034 q^{52} +5.52786 q^{53} -3.47214 q^{54} -1.00000 q^{55} +3.23607 q^{56} -3.47214 q^{57} -3.23607 q^{58} -9.56231 q^{59} -0.618034 q^{60} +3.09017 q^{61} -5.70820 q^{62} -8.47214 q^{63} +1.00000 q^{64} +0.618034 q^{65} +0.618034 q^{66} -13.5623 q^{67} -4.00000 q^{68} +1.23607 q^{69} -3.23607 q^{70} -4.85410 q^{71} -2.61803 q^{72} -1.00000 q^{73} -0.472136 q^{74} +0.618034 q^{75} -5.61803 q^{76} +3.23607 q^{77} -0.381966 q^{78} +5.70820 q^{79} -1.00000 q^{80} +5.70820 q^{81} -2.00000 q^{82} -14.6180 q^{83} +2.00000 q^{84} +4.00000 q^{85} -5.61803 q^{86} -2.00000 q^{87} +1.00000 q^{88} +10.7984 q^{89} +2.61803 q^{90} -2.00000 q^{91} +2.00000 q^{92} -3.52786 q^{93} +3.32624 q^{94} +5.61803 q^{95} +0.618034 q^{96} -1.52786 q^{97} +3.47214 q^{98} -2.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + 2 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 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} + 2 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{15} + 2 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} + 4 q^{21} + 2 q^{22} + 4 q^{23} - q^{24} + 2 q^{25} + q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{29} + q^{30} + 2 q^{31} + 2 q^{32} - q^{33} - 8 q^{34} - 2 q^{35} - 3 q^{36} + 8 q^{37} - 9 q^{38} - 3 q^{39} - 2 q^{40} - 4 q^{41} + 4 q^{42} - 9 q^{43} + 2 q^{44} + 3 q^{45} + 4 q^{46} - 9 q^{47} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} + q^{52} + 20 q^{53} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 2 q^{57} - 2 q^{58} + q^{59} + q^{60} - 5 q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - q^{65} - q^{66} - 7 q^{67} - 8 q^{68} - 2 q^{69} - 2 q^{70} - 3 q^{71} - 3 q^{72} - 2 q^{73} + 8 q^{74} - q^{75} - 9 q^{76} + 2 q^{77} - 3 q^{78} - 2 q^{79} - 2 q^{80} - 2 q^{81} - 4 q^{82} - 27 q^{83} + 4 q^{84} + 8 q^{85} - 9 q^{86} - 4 q^{87} + 2 q^{88} - 3 q^{89} + 3 q^{90} - 4 q^{91} + 4 q^{92} - 16 q^{93} - 9 q^{94} + 9 q^{95} - q^{96} - 12 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 + 2 * q^11 - q^12 + q^13 + 2 * q^14 + q^15 + 2 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 + 4 * q^21 + 2 * q^22 + 4 * q^23 - q^24 + 2 * q^25 + q^26 + 2 * q^27 + 2 * q^28 - 2 * q^29 + q^30 + 2 * q^31 + 2 * q^32 - q^33 - 8 * q^34 - 2 * q^35 - 3 * q^36 + 8 * q^37 - 9 * q^38 - 3 * q^39 - 2 * q^40 - 4 * q^41 + 4 * q^42 - 9 * q^43 + 2 * q^44 + 3 * q^45 + 4 * q^46 - 9 * q^47 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 + q^52 + 20 * q^53 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 2 * q^57 - 2 * q^58 + q^59 + q^60 - 5 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 - q^65 - q^66 - 7 * q^67 - 8 * q^68 - 2 * q^69 - 2 * q^70 - 3 * q^71 - 3 * q^72 - 2 * q^73 + 8 * q^74 - q^75 - 9 * q^76 + 2 * q^77 - 3 * q^78 - 2 * q^79 - 2 * q^80 - 2 * q^81 - 4 * q^82 - 27 * q^83 + 4 * q^84 + 8 * q^85 - 9 * q^86 - 4 * q^87 + 2 * q^88 - 3 * q^89 + 3 * q^90 - 4 * q^91 + 4 * q^92 - 16 * q^93 - 9 * q^94 + 9 * q^95 - q^96 - 12 * q^97 - 2 * 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
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.618034	0.252311
$7$	3.23607	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.618034	0.178411
$13$	−0.618034	−0.171412	−0.0857059	−	0.996320i	$-0.527315\pi$
$13$	−0.618034	−0.171412	−0.0857059	+	0.996320i	$0.527315\pi$
$14$	3.23607	0.864876
$15$	−0.618034	−0.159576
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−2.61803	−0.617077
$19$	−5.61803	−1.28887	−0.644433	−	0.764661i	$-0.722906\pi$
$19$	−5.61803	−1.28887	−0.644433	+	0.764661i	$0.722906\pi$
$20$	−1.00000	−0.223607
$21$	2.00000	0.436436
$22$	1.00000	0.213201
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0.618034	0.126156
$25$	1.00000	0.200000
$26$	−0.618034	−0.121206
$27$	−3.47214	−0.668213
$28$	3.23607	0.611559
$29$	−3.23607	−0.600923	−0.300461	−	0.953794i	$-0.597141\pi$
$29$	−3.23607	−0.600923	−0.300461	+	0.953794i	$0.597141\pi$
$30$	−0.618034	−0.112837
$31$	−5.70820	−1.02522	−0.512612	−	0.858620i	$-0.671322\pi$
$31$	−5.70820	−1.02522	−0.512612	+	0.858620i	$0.671322\pi$
$32$	1.00000	0.176777
$33$	0.618034	0.107586
$34$	−4.00000	−0.685994
$35$	−3.23607	−0.546995
$36$	−2.61803	−0.436339
$37$	−0.472136	−0.0776187	−0.0388093	−	0.999247i	$-0.512356\pi$
$37$	−0.472136	−0.0776187	−0.0388093	+	0.999247i	$0.512356\pi$
$38$	−5.61803	−0.911365
$39$	−0.381966	−0.0611635
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	2.00000	0.308607
$43$	−5.61803	−0.856742	−0.428371	−	0.903603i	$-0.640912\pi$
$43$	−5.61803	−0.856742	−0.428371	+	0.903603i	$0.640912\pi$
$44$	1.00000	0.150756
$45$	2.61803	0.390273
$46$	2.00000	0.294884
$47$	3.32624	0.485182	0.242591	−	0.970129i	$-0.422003\pi$
$47$	3.32624	0.485182	0.242591	+	0.970129i	$0.422003\pi$
$48$	0.618034	0.0892055
$49$	3.47214	0.496019
$50$	1.00000	0.141421
$51$	−2.47214	−0.346168
$52$	−0.618034	−0.0857059
$53$	5.52786	0.759311	0.379655	−	0.925128i	$-0.376043\pi$
$53$	5.52786	0.759311	0.379655	+	0.925128i	$0.376043\pi$
$54$	−3.47214	−0.472498
$55$	−1.00000	−0.134840
$56$	3.23607	0.432438
$57$	−3.47214	−0.459896
$58$	−3.23607	−0.424917
$59$	−9.56231	−1.24491	−0.622453	−	0.782657i	$-0.713864\pi$
$59$	−9.56231	−1.24491	−0.622453	+	0.782657i	$0.713864\pi$
$60$	−0.618034	−0.0797878
$61$	3.09017	0.395656	0.197828	−	0.980237i	$-0.436611\pi$
$61$	3.09017	0.395656	0.197828	+	0.980237i	$0.436611\pi$
$62$	−5.70820	−0.724943
$63$	−8.47214	−1.06739
$64$	1.00000	0.125000
$65$	0.618034	0.0766577
$66$	0.618034	0.0760747
$67$	−13.5623	−1.65690	−0.828450	−	0.560063i	$-0.810777\pi$
$67$	−13.5623	−1.65690	−0.828450	+	0.560063i	$0.810777\pi$
$68$	−4.00000	−0.485071
$69$	1.23607	0.148805
$70$	−3.23607	−0.386784
$71$	−4.85410	−0.576076	−0.288038	−	0.957619i	$-0.593003\pi$
$71$	−4.85410	−0.576076	−0.288038	+	0.957619i	$0.593003\pi$
$72$	−2.61803	−0.308538
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−0.472136	−0.0548847
$75$	0.618034	0.0713644
$76$	−5.61803	−0.644433
$77$	3.23607	0.368784
$78$	−0.381966	−0.0432491
$79$	5.70820	0.642223	0.321112	−	0.947041i	$-0.395944\pi$
$79$	5.70820	0.642223	0.321112	+	0.947041i	$0.395944\pi$
$80$	−1.00000	−0.111803
$81$	5.70820	0.634245
$82$	−2.00000	−0.220863
$83$	−14.6180	−1.60454	−0.802269	−	0.596963i	$-0.796374\pi$
$83$	−14.6180	−1.60454	−0.802269	+	0.596963i	$0.796374\pi$
$84$	2.00000	0.218218
$85$	4.00000	0.433861
$86$	−5.61803	−0.605808
$87$	−2.00000	−0.214423
$88$	1.00000	0.106600
$89$	10.7984	1.14463	0.572313	−	0.820035i	$-0.306046\pi$
$89$	10.7984	1.14463	0.572313	+	0.820035i	$0.306046\pi$
$90$	2.61803	0.275965
$91$	−2.00000	−0.209657
$92$	2.00000	0.208514
$93$	−3.52786	−0.365822
$94$	3.32624	0.343075
$95$	5.61803	0.576398
$96$	0.618034	0.0630778
$97$	−1.52786	−0.155131	−0.0775655	−	0.996987i	$-0.524715\pi$
$97$	−1.52786	−0.155131	−0.0775655	+	0.996987i	$0.524715\pi$
$98$	3.47214	0.350739
$99$	−2.61803	−0.263122
$100$	1.00000	0.100000
$101$	−8.94427	−0.889988	−0.444994	−	0.895533i	$-0.646794\pi$
$101$	−8.94427	−0.889988	−0.444994	+	0.895533i	$0.646794\pi$
$102$	−2.47214	−0.244778
$103$	−5.52786	−0.544677	−0.272338	−	0.962202i	$-0.587797\pi$
$103$	−5.52786	−0.544677	−0.272338	+	0.962202i	$0.587797\pi$
$104$	−0.618034	−0.0606032
$105$	−2.00000	−0.195180
$106$	5.52786	0.536914
$107$	5.61803	0.543116	0.271558	−	0.962422i	$-0.412461\pi$
$107$	5.61803	0.543116	0.271558	+	0.962422i	$0.412461\pi$
$108$	−3.47214	−0.334106
$109$	−6.94427	−0.665141	−0.332570	−	0.943078i	$-0.607916\pi$
$109$	−6.94427	−0.665141	−0.332570	+	0.943078i	$0.607916\pi$
$110$	−1.00000	−0.0953463
$111$	−0.291796	−0.0276961
$112$	3.23607	0.305780
$113$	−3.14590	−0.295941	−0.147971	−	0.988992i	$-0.547274\pi$
$113$	−3.14590	−0.295941	−0.147971	+	0.988992i	$0.547274\pi$
$114$	−3.47214	−0.325195
$115$	−2.00000	−0.186501
$116$	−3.23607	−0.300461
$117$	1.61803	0.149587
$118$	−9.56231	−0.880282
$119$	−12.9443	−1.18660
$120$	−0.618034	−0.0564185
$121$	1.00000	0.0909091
$122$	3.09017	0.279771
$123$	−1.23607	−0.111452
$124$	−5.70820	−0.512612
$125$	−1.00000	−0.0894427
$126$	−8.47214	−0.754758
$127$	15.3820	1.36493	0.682464	−	0.730919i	$-0.260908\pi$
$127$	15.3820	1.36493	0.682464	+	0.730919i	$0.260908\pi$
$128$	1.00000	0.0883883
$129$	−3.47214	−0.305705
$130$	0.618034	0.0542052
$131$	12.9443	1.13095	0.565473	−	0.824767i	$-0.308694\pi$
$131$	12.9443	1.13095	0.565473	+	0.824767i	$0.308694\pi$
$132$	0.618034	0.0537930
$133$	−18.1803	−1.57644
$134$	−13.5623	−1.17160
$135$	3.47214	0.298834
$136$	−4.00000	−0.342997
$137$	−17.7082	−1.51291	−0.756457	−	0.654043i	$-0.773071\pi$
$137$	−17.7082	−1.51291	−0.756457	+	0.654043i	$0.773071\pi$
$138$	1.23607	0.105221
$139$	−2.29180	−0.194388	−0.0971938	−	0.995265i	$-0.530987\pi$
$139$	−2.29180	−0.194388	−0.0971938	+	0.995265i	$0.530987\pi$
$140$	−3.23607	−0.273498
$141$	2.05573	0.173124
$142$	−4.85410	−0.407347
$143$	−0.618034	−0.0516826
$144$	−2.61803	−0.218169
$145$	3.23607	0.268741
$146$	−1.00000	−0.0827606
$147$	2.14590	0.176991
$148$	−0.472136	−0.0388093
$149$	−1.61803	−0.132555	−0.0662773	−	0.997801i	$-0.521112\pi$
$149$	−1.61803	−0.132555	−0.0662773	+	0.997801i	$0.521112\pi$
$150$	0.618034	0.0504623
$151$	21.5623	1.75472	0.877358	−	0.479837i	$-0.159304\pi$
$151$	21.5623	1.75472	0.877358	+	0.479837i	$0.159304\pi$
$152$	−5.61803	−0.455683
$153$	10.4721	0.846622
$154$	3.23607	0.260770
$155$	5.70820	0.458494
$156$	−0.381966	−0.0305818
$157$	−3.23607	−0.258266	−0.129133	−	0.991627i	$-0.541219\pi$
$157$	−3.23607	−0.258266	−0.129133	+	0.991627i	$0.541219\pi$
$158$	5.70820	0.454120
$159$	3.41641	0.270939
$160$	−1.00000	−0.0790569
$161$	6.47214	0.510076
$162$	5.70820	0.448479
$163$	−11.2361	−0.880077	−0.440038	−	0.897979i	$-0.645035\pi$
$163$	−11.2361	−0.880077	−0.440038	+	0.897979i	$0.645035\pi$
$164$	−2.00000	−0.156174
$165$	−0.618034	−0.0481139
$166$	−14.6180	−1.13458
$167$	7.52786	0.582524	0.291262	−	0.956643i	$-0.405925\pi$
$167$	7.52786	0.582524	0.291262	+	0.956643i	$0.405925\pi$
$168$	2.00000	0.154303
$169$	−12.6180	−0.970618
$170$	4.00000	0.306786
$171$	14.7082	1.12476
$172$	−5.61803	−0.428371
$173$	−23.8885	−1.81621	−0.908106	−	0.418740i	$-0.862472\pi$
$173$	−23.8885	−1.81621	−0.908106	+	0.418740i	$0.862472\pi$
$174$	−2.00000	−0.151620
$175$	3.23607	0.244624
$176$	1.00000	0.0753778
$177$	−5.90983	−0.444210
$178$	10.7984	0.809372
$179$	17.3262	1.29502	0.647512	−	0.762055i	$-0.275810\pi$
$179$	17.3262	1.29502	0.647512	+	0.762055i	$0.275810\pi$
$180$	2.61803	0.195137
$181$	1.70820	0.126970	0.0634849	−	0.997983i	$-0.479779\pi$
$181$	1.70820	0.126970	0.0634849	+	0.997983i	$0.479779\pi$
$182$	−2.00000	−0.148250
$183$	1.90983	0.141179
$184$	2.00000	0.147442
$185$	0.472136	0.0347121
$186$	−3.52786	−0.258676
$187$	−4.00000	−0.292509
$188$	3.32624	0.242591
$189$	−11.2361	−0.817304
$190$	5.61803	0.407575
$191$	13.8885	1.00494	0.502470	−	0.864595i	$-0.332425\pi$
$191$	13.8885	1.00494	0.502470	+	0.864595i	$0.332425\pi$
$192$	0.618034	0.0446028
$193$	2.18034	0.156944	0.0784721	−	0.996916i	$-0.474996\pi$
$193$	2.18034	0.156944	0.0784721	+	0.996916i	$0.474996\pi$
$194$	−1.52786	−0.109694
$195$	0.381966	0.0273532
$196$	3.47214	0.248010
$197$	16.0902	1.14638	0.573189	−	0.819423i	$-0.305706\pi$
$197$	16.0902	1.14638	0.573189	+	0.819423i	$0.305706\pi$
$198$	−2.61803	−0.186056
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	1.00000	0.0707107
$201$	−8.38197	−0.591218
$202$	−8.94427	−0.629317
$203$	−10.4721	−0.735000
$204$	−2.47214	−0.173084
$205$	2.00000	0.139686
$206$	−5.52786	−0.385145
$207$	−5.23607	−0.363932
$208$	−0.618034	−0.0428529
$209$	−5.61803	−0.388608
$210$	−2.00000	−0.138013
$211$	4.85410	0.334170	0.167085	−	0.985942i	$-0.446565\pi$
$211$	4.85410	0.334170	0.167085	+	0.985942i	$0.446565\pi$
$212$	5.52786	0.379655
$213$	−3.00000	−0.205557
$214$	5.61803	0.384041
$215$	5.61803	0.383147
$216$	−3.47214	−0.236249
$217$	−18.4721	−1.25397
$218$	−6.94427	−0.470325
$219$	−0.618034	−0.0417629
$220$	−1.00000	−0.0674200
$221$	2.47214	0.166294
$222$	−0.291796	−0.0195841
$223$	22.1803	1.48531	0.742653	−	0.669677i	$-0.233567\pi$
$223$	22.1803	1.48531	0.742653	+	0.669677i	$0.233567\pi$
$224$	3.23607	0.216219
$225$	−2.61803	−0.174536
$226$	−3.14590	−0.209262
$227$	−17.2361	−1.14400	−0.571999	−	0.820254i	$-0.693832\pi$
$227$	−17.2361	−1.14400	−0.571999	+	0.820254i	$0.693832\pi$
$228$	−3.47214	−0.229948
$229$	−9.14590	−0.604378	−0.302189	−	0.953248i	$-0.597717\pi$
$229$	−9.14590	−0.604378	−0.302189	+	0.953248i	$0.597717\pi$
$230$	−2.00000	−0.131876
$231$	2.00000	0.131590
$232$	−3.23607	−0.212458
$233$	16.0000	1.04819	0.524097	−	0.851658i	$-0.324403\pi$
$233$	16.0000	1.04819	0.524097	+	0.851658i	$0.324403\pi$
$234$	1.61803	0.105774
$235$	−3.32624	−0.216980
$236$	−9.56231	−0.622453
$237$	3.52786	0.229159
$238$	−12.9443	−0.839053
$239$	−14.1459	−0.915022	−0.457511	−	0.889204i	$-0.651259\pi$
$239$	−14.1459	−0.915022	−0.457511	+	0.889204i	$0.651259\pi$
$240$	−0.618034	−0.0398939
$241$	−9.41641	−0.606564	−0.303282	−	0.952901i	$-0.598082\pi$
$241$	−9.41641	−0.606564	−0.303282	+	0.952901i	$0.598082\pi$
$242$	1.00000	0.0642824
$243$	13.9443	0.894525
$244$	3.09017	0.197828
$245$	−3.47214	−0.221827
$246$	−1.23607	−0.0788088
$247$	3.47214	0.220927
$248$	−5.70820	−0.362471
$249$	−9.03444	−0.572534
$250$	−1.00000	−0.0632456
$251$	−10.4721	−0.660995	−0.330498	−	0.943807i	$-0.607217\pi$
$251$	−10.4721	−0.660995	−0.330498	+	0.943807i	$0.607217\pi$
$252$	−8.47214	−0.533694
$253$	2.00000	0.125739
$254$	15.3820	0.965150
$255$	2.47214	0.154811
$256$	1.00000	0.0625000
$257$	−20.7639	−1.29522	−0.647609	−	0.761973i	$-0.724231\pi$
$257$	−20.7639	−1.29522	−0.647609	+	0.761973i	$0.724231\pi$
$258$	−3.47214	−0.216166
$259$	−1.52786	−0.0949369
$260$	0.618034	0.0383288
$261$	8.47214	0.524412
$262$	12.9443	0.799700
$263$	10.0000	0.616626	0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000	0.616626	0.308313	+	0.951285i	$0.400236\pi$
$264$	0.618034	0.0380374
$265$	−5.52786	−0.339574
$266$	−18.1803	−1.11471
$267$	6.67376	0.408428
$268$	−13.5623	−0.828450
$269$	−29.1246	−1.77576	−0.887879	−	0.460076i	$-0.847822\pi$
$269$	−29.1246	−1.77576	−0.887879	+	0.460076i	$0.847822\pi$
$270$	3.47214	0.211307
$271$	4.32624	0.262800	0.131400	−	0.991329i	$-0.458053\pi$
$271$	4.32624	0.262800	0.131400	+	0.991329i	$0.458053\pi$
$272$	−4.00000	−0.242536
$273$	−1.23607	−0.0748102
$274$	−17.7082	−1.06979
$275$	1.00000	0.0603023
$276$	1.23607	0.0744025
$277$	−5.61803	−0.337555	−0.168777	−	0.985654i	$-0.553982\pi$
$277$	−5.61803	−0.337555	−0.168777	+	0.985654i	$0.553982\pi$
$278$	−2.29180	−0.137453
$279$	14.9443	0.894690
$280$	−3.23607	−0.193392
$281$	−26.9787	−1.60942	−0.804708	−	0.593671i	$-0.797678\pi$
$281$	−26.9787	−1.60942	−0.804708	+	0.593671i	$0.797678\pi$
$282$	2.05573	0.122417
$283$	−12.1803	−0.724046	−0.362023	−	0.932169i	$-0.617914\pi$
$283$	−12.1803	−0.724046	−0.362023	+	0.932169i	$0.617914\pi$
$284$	−4.85410	−0.288038
$285$	3.47214	0.205672
$286$	−0.618034	−0.0365451
$287$	−6.47214	−0.382038
$288$	−2.61803	−0.154269
$289$	−1.00000	−0.0588235
$290$	3.23607	0.190028
$291$	−0.944272	−0.0553542
$292$	−1.00000	−0.0585206
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	2.14590	0.125151
$295$	9.56231	0.556739
$296$	−0.472136	−0.0274423
$297$	−3.47214	−0.201474
$298$	−1.61803	−0.0937302
$299$	−1.23607	−0.0714837
$300$	0.618034	0.0356822
$301$	−18.1803	−1.04790
$302$	21.5623	1.24077
$303$	−5.52786	−0.317567
$304$	−5.61803	−0.322216
$305$	−3.09017	−0.176943
$306$	10.4721	0.598652
$307$	29.9787	1.71098	0.855488	−	0.517823i	$-0.173257\pi$
$307$	29.9787	1.71098	0.855488	+	0.517823i	$0.173257\pi$
$308$	3.23607	0.184392
$309$	−3.41641	−0.194353
$310$	5.70820	0.324204
$311$	29.7426	1.68655	0.843275	−	0.537482i	$-0.180624\pi$
$311$	29.7426	1.68655	0.843275	+	0.537482i	$0.180624\pi$
$312$	−0.381966	−0.0216246
$313$	14.3820	0.812917	0.406458	−	0.913669i	$-0.366764\pi$
$313$	14.3820	0.812917	0.406458	+	0.913669i	$0.366764\pi$
$314$	−3.23607	−0.182622
$315$	8.47214	0.477351
$316$	5.70820	0.321112
$317$	29.6869	1.66738	0.833692	−	0.552230i	$-0.186223\pi$
$317$	29.6869	1.66738	0.833692	+	0.552230i	$0.186223\pi$
$318$	3.41641	0.191583
$319$	−3.23607	−0.181185
$320$	−1.00000	−0.0559017
$321$	3.47214	0.193796
$322$	6.47214	0.360678
$323$	22.4721	1.25038
$324$	5.70820	0.317122
$325$	−0.618034	−0.0342824
$326$	−11.2361	−0.622308
$327$	−4.29180	−0.237337
$328$	−2.00000	−0.110432
$329$	10.7639	0.593435
$330$	−0.618034	−0.0340217
$331$	−6.43769	−0.353848	−0.176924	−	0.984225i	$-0.556615\pi$
$331$	−6.43769	−0.353848	−0.176924	+	0.984225i	$0.556615\pi$
$332$	−14.6180	−0.802269
$333$	1.23607	0.0677361
$334$	7.52786	0.411906
$335$	13.5623	0.740988
$336$	2.00000	0.109109
$337$	−28.6525	−1.56080	−0.780400	−	0.625281i	$-0.784984\pi$
$337$	−28.6525	−1.56080	−0.780400	+	0.625281i	$0.784984\pi$
$338$	−12.6180	−0.686331
$339$	−1.94427	−0.105598
$340$	4.00000	0.216930
$341$	−5.70820	−0.309117
$342$	14.7082	0.795329
$343$	−11.4164	−0.616428
$344$	−5.61803	−0.302904
$345$	−1.23607	−0.0665477
$346$	−23.8885	−1.28426
$347$	−20.7639	−1.11467	−0.557333	−	0.830289i	$-0.688175\pi$
$347$	−20.7639	−1.11467	−0.557333	+	0.830289i	$0.688175\pi$
$348$	−2.00000	−0.107211
$349$	−4.67376	−0.250181	−0.125090	−	0.992145i	$-0.539922\pi$
$349$	−4.67376	−0.250181	−0.125090	+	0.992145i	$0.539922\pi$
$350$	3.23607	0.172975
$351$	2.14590	0.114540
$352$	1.00000	0.0533002
$353$	23.4164	1.24633	0.623165	−	0.782091i	$-0.285847\pi$
$353$	23.4164	1.24633	0.623165	+	0.782091i	$0.285847\pi$
$354$	−5.90983	−0.314104
$355$	4.85410	0.257629
$356$	10.7984	0.572313
$357$	−8.00000	−0.423405
$358$	17.3262	0.915720
$359$	−0.944272	−0.0498368	−0.0249184	−	0.999689i	$-0.507933\pi$
$359$	−0.944272	−0.0498368	−0.0249184	+	0.999689i	$0.507933\pi$
$360$	2.61803	0.137983
$361$	12.5623	0.661174
$362$	1.70820	0.0897812
$363$	0.618034	0.0324384
$364$	−2.00000	−0.104828
$365$	1.00000	0.0523424
$366$	1.90983	0.0998284
$367$	−14.9443	−0.780085	−0.390042	−	0.920797i	$-0.627540\pi$
$367$	−14.9443	−0.780085	−0.390042	+	0.920797i	$0.627540\pi$
$368$	2.00000	0.104257
$369$	5.23607	0.272579
$370$	0.472136	0.0245452
$371$	17.8885	0.928727
$372$	−3.52786	−0.182911
$373$	−11.5279	−0.596890	−0.298445	−	0.954427i	$-0.596468\pi$
$373$	−11.5279	−0.596890	−0.298445	+	0.954427i	$0.596468\pi$
$374$	−4.00000	−0.206835
$375$	−0.618034	−0.0319151
$376$	3.32624	0.171538
$377$	2.00000	0.103005
$378$	−11.2361	−0.577921
$379$	−22.6738	−1.16467	−0.582336	−	0.812948i	$-0.697861\pi$
$379$	−22.6738	−1.16467	−0.582336	+	0.812948i	$0.697861\pi$
$380$	5.61803	0.288199
$381$	9.50658	0.487037
$382$	13.8885	0.710600
$383$	−11.8885	−0.607476	−0.303738	−	0.952756i	$-0.598235\pi$
$383$	−11.8885	−0.607476	−0.303738	+	0.952756i	$0.598235\pi$
$384$	0.618034	0.0315389
$385$	−3.23607	−0.164925
$386$	2.18034	0.110976
$387$	14.7082	0.747660
$388$	−1.52786	−0.0775655
$389$	28.8328	1.46188	0.730941	−	0.682441i	$-0.239081\pi$
$389$	28.8328	1.46188	0.730941	+	0.682441i	$0.239081\pi$
$390$	0.381966	0.0193416
$391$	−8.00000	−0.404577
$392$	3.47214	0.175369
$393$	8.00000	0.403547
$394$	16.0902	0.810611
$395$	−5.70820	−0.287211
$396$	−2.61803	−0.131561
$397$	32.5623	1.63426	0.817128	−	0.576457i	$-0.195565\pi$
$397$	32.5623	1.63426	0.817128	+	0.576457i	$0.195565\pi$
$398$	2.00000	0.100251
$399$	−11.2361	−0.562507
$400$	1.00000	0.0500000
$401$	0.326238	0.0162915	0.00814577	−	0.999967i	$-0.497407\pi$
$401$	0.326238	0.0162915	0.00814577	+	0.999967i	$0.497407\pi$
$402$	−8.38197	−0.418054
$403$	3.52786	0.175735
$404$	−8.94427	−0.444994
$405$	−5.70820	−0.283643
$406$	−10.4721	−0.519723
$407$	−0.472136	−0.0234029
$408$	−2.47214	−0.122389
$409$	−25.1459	−1.24338	−0.621692	−	0.783262i	$-0.713555\pi$
$409$	−25.1459	−1.24338	−0.621692	+	0.783262i	$0.713555\pi$
$410$	2.00000	0.0987730
$411$	−10.9443	−0.539841
$412$	−5.52786	−0.272338
$413$	−30.9443	−1.52267
$414$	−5.23607	−0.257339
$415$	14.6180	0.717571
$416$	−0.618034	−0.0303016
$417$	−1.41641	−0.0693618
$418$	−5.61803	−0.274787
$419$	−11.0557	−0.540108	−0.270054	−	0.962845i	$-0.587042\pi$
$419$	−11.0557	−0.540108	−0.270054	+	0.962845i	$0.587042\pi$
$420$	−2.00000	−0.0975900
$421$	21.0902	1.02787	0.513936	−	0.857829i	$-0.328187\pi$
$421$	21.0902	1.02787	0.513936	+	0.857829i	$0.328187\pi$
$422$	4.85410	0.236294
$423$	−8.70820	−0.423407
$424$	5.52786	0.268457
$425$	−4.00000	−0.194029
$426$	−3.00000	−0.145350
$427$	10.0000	0.483934
$428$	5.61803	0.271558
$429$	−0.381966	−0.0184415
$430$	5.61803	0.270926
$431$	19.4508	0.936914	0.468457	−	0.883486i	$-0.344810\pi$
$431$	19.4508	0.936914	0.468457	+	0.883486i	$0.344810\pi$
$432$	−3.47214	−0.167053
$433$	−41.0344	−1.97199	−0.985995	−	0.166777i	$-0.946664\pi$
$433$	−41.0344	−1.97199	−0.985995	+	0.166777i	$0.946664\pi$
$434$	−18.4721	−0.886691
$435$	2.00000	0.0958927
$436$	−6.94427	−0.332570
$437$	−11.2361	−0.537494
$438$	−0.618034	−0.0295308
$439$	9.70820	0.463347	0.231674	−	0.972794i	$-0.425580\pi$
$439$	9.70820	0.463347	0.231674	+	0.972794i	$0.425580\pi$
$440$	−1.00000	−0.0476731
$441$	−9.09017	−0.432865
$442$	2.47214	0.117588
$443$	−31.4164	−1.49264	−0.746319	−	0.665588i	$-0.768181\pi$
$443$	−31.4164	−1.49264	−0.746319	+	0.665588i	$0.768181\pi$
$444$	−0.291796	−0.0138480
$445$	−10.7984	−0.511892
$446$	22.1803	1.05027
$447$	−1.00000	−0.0472984
$448$	3.23607	0.152890
$449$	16.4721	0.777368	0.388684	−	0.921371i	$-0.372930\pi$
$449$	16.4721	0.777368	0.388684	+	0.921371i	$0.372930\pi$
$450$	−2.61803	−0.123415
$451$	−2.00000	−0.0941763
$452$	−3.14590	−0.147971
$453$	13.3262	0.626121
$454$	−17.2361	−0.808929
$455$	2.00000	0.0937614
$456$	−3.47214	−0.162598
$457$	−5.14590	−0.240715	−0.120357	−	0.992731i	$-0.538404\pi$
$457$	−5.14590	−0.240715	−0.120357	+	0.992731i	$0.538404\pi$
$458$	−9.14590	−0.427360
$459$	13.8885	0.648262
$460$	−2.00000	−0.0932505
$461$	16.6738	0.776575	0.388287	−	0.921538i	$-0.373067\pi$
$461$	16.6738	0.776575	0.388287	+	0.921538i	$0.373067\pi$
$462$	2.00000	0.0930484
$463$	−3.81966	−0.177515	−0.0887573	−	0.996053i	$-0.528290\pi$
$463$	−3.81966	−0.177515	−0.0887573	+	0.996053i	$0.528290\pi$
$464$	−3.23607	−0.150231
$465$	3.52786	0.163601
$466$	16.0000	0.741186
$467$	−39.4164	−1.82397	−0.911987	−	0.410219i	$-0.865452\pi$
$467$	−39.4164	−1.82397	−0.911987	+	0.410219i	$0.865452\pi$
$468$	1.61803	0.0747936
$469$	−43.8885	−2.02658
$470$	−3.32624	−0.153428
$471$	−2.00000	−0.0921551
$472$	−9.56231	−0.440141
$473$	−5.61803	−0.258317
$474$	3.52786	0.162040
$475$	−5.61803	−0.257773
$476$	−12.9443	−0.593300
$477$	−14.4721	−0.662634
$478$	−14.1459	−0.647018
$479$	−23.1246	−1.05659	−0.528295	−	0.849061i	$-0.677169\pi$
$479$	−23.1246	−1.05659	−0.528295	+	0.849061i	$0.677169\pi$
$480$	−0.618034	−0.0282093
$481$	0.291796	0.0133048
$482$	−9.41641	−0.428906
$483$	4.00000	0.182006
$484$	1.00000	0.0454545
$485$	1.52786	0.0693767
$486$	13.9443	0.632525
$487$	−29.8885	−1.35438	−0.677190	−	0.735809i	$-0.736802\pi$
$487$	−29.8885	−1.35438	−0.677190	+	0.735809i	$0.736802\pi$
$488$	3.09017	0.139885
$489$	−6.94427	−0.314031
$490$	−3.47214	−0.156855
$491$	−7.52786	−0.339728	−0.169864	−	0.985468i	$-0.554333\pi$
$491$	−7.52786	−0.339728	−0.169864	+	0.985468i	$0.554333\pi$
$492$	−1.23607	−0.0557262
$493$	12.9443	0.582981
$494$	3.47214	0.156219
$495$	2.61803	0.117672
$496$	−5.70820	−0.256306
$497$	−15.7082	−0.704609
$498$	−9.03444	−0.404843
$499$	26.9443	1.20619	0.603096	−	0.797669i	$-0.293934\pi$
$499$	26.9443	1.20619	0.603096	+	0.797669i	$0.293934\pi$
$500$	−1.00000	−0.0447214
$501$	4.65248	0.207857
$502$	−10.4721	−0.467394
$503$	1.90983	0.0851551	0.0425776	−	0.999093i	$-0.486443\pi$
$503$	1.90983	0.0851551	0.0425776	+	0.999093i	$0.486443\pi$
$504$	−8.47214	−0.377379
$505$	8.94427	0.398015
$506$	2.00000	0.0889108
$507$	−7.79837	−0.346338
$508$	15.3820	0.682464
$509$	38.3607	1.70031	0.850154	−	0.526535i	$-0.176509\pi$
$509$	38.3607	1.70031	0.850154	+	0.526535i	$0.176509\pi$
$510$	2.47214	0.109468
$511$	−3.23607	−0.143155
$512$	1.00000	0.0441942
$513$	19.5066	0.861236
$514$	−20.7639	−0.915858
$515$	5.52786	0.243587
$516$	−3.47214	−0.152852
$517$	3.32624	0.146288
$518$	−1.52786	−0.0671305
$519$	−14.7639	−0.648065
$520$	0.618034	0.0271026
$521$	26.6525	1.16767	0.583833	−	0.811874i	$-0.301552\pi$
$521$	26.6525	1.16767	0.583833	+	0.811874i	$0.301552\pi$
$522$	8.47214	0.370815
$523$	−8.83282	−0.386232	−0.193116	−	0.981176i	$-0.561859\pi$
$523$	−8.83282	−0.386232	−0.193116	+	0.981176i	$0.561859\pi$
$524$	12.9443	0.565473
$525$	2.00000	0.0872872
$526$	10.0000	0.436021
$527$	22.8328	0.994613
$528$	0.618034	0.0268965
$529$	−19.0000	−0.826087
$530$	−5.52786	−0.240115
$531$	25.0344	1.08640
$532$	−18.1803	−0.788218
$533$	1.23607	0.0535400
$534$	6.67376	0.288802
$535$	−5.61803	−0.242889
$536$	−13.5623	−0.585802
$537$	10.7082	0.462093
$538$	−29.1246	−1.25565
$539$	3.47214	0.149555
$540$	3.47214	0.149417
$541$	−13.1246	−0.564271	−0.282136	−	0.959375i	$-0.591043\pi$
$541$	−13.1246	−0.564271	−0.282136	+	0.959375i	$0.591043\pi$
$542$	4.32624	0.185828
$543$	1.05573	0.0453056
$544$	−4.00000	−0.171499
$545$	6.94427	0.297460
$546$	−1.23607	−0.0528988
$547$	−42.5410	−1.81892	−0.909461	−	0.415789i	$-0.863506\pi$
$547$	−42.5410	−1.81892	−0.909461	+	0.415789i	$0.863506\pi$
$548$	−17.7082	−0.756457
$549$	−8.09017	−0.345280
$550$	1.00000	0.0426401
$551$	18.1803	0.774509
$552$	1.23607	0.0526105
$553$	18.4721	0.785515
$554$	−5.61803	−0.238687
$555$	0.291796	0.0123861
$556$	−2.29180	−0.0971938
$557$	34.6525	1.46827	0.734136	−	0.679002i	$-0.237587\pi$
$557$	34.6525	1.46827	0.734136	+	0.679002i	$0.237587\pi$
$558$	14.9443	0.632641
$559$	3.47214	0.146856
$560$	−3.23607	−0.136749
$561$	−2.47214	−0.104374
$562$	−26.9787	−1.13803
$563$	−30.4721	−1.28425	−0.642124	−	0.766601i	$-0.721946\pi$
$563$	−30.4721	−1.28425	−0.642124	+	0.766601i	$0.721946\pi$
$564$	2.05573	0.0865618
$565$	3.14590	0.132349
$566$	−12.1803	−0.511978
$567$	18.4721	0.775757
$568$	−4.85410	−0.203674
$569$	13.4164	0.562445	0.281223	−	0.959643i	$-0.409260\pi$
$569$	13.4164	0.562445	0.281223	+	0.959643i	$0.409260\pi$
$570$	3.47214	0.145432
$571$	27.4164	1.14734	0.573670	−	0.819086i	$-0.305519\pi$
$571$	27.4164	1.14734	0.573670	+	0.819086i	$0.305519\pi$
$572$	−0.618034	−0.0258413
$573$	8.58359	0.358585
$574$	−6.47214	−0.270142
$575$	2.00000	0.0834058
$576$	−2.61803	−0.109085
$577$	−21.8541	−0.909798	−0.454899	−	0.890543i	$-0.650325\pi$
$577$	−21.8541	−0.909798	−0.454899	+	0.890543i	$0.650325\pi$
$578$	−1.00000	−0.0415945
$579$	1.34752	0.0560012
$580$	3.23607	0.134370
$581$	−47.3050	−1.96254
$582$	−0.944272	−0.0391413
$583$	5.52786	0.228941
$584$	−1.00000	−0.0413803
$585$	−1.61803	−0.0668975
$586$	12.0000	0.495715
$587$	−15.4164	−0.636303	−0.318152	−	0.948040i	$-0.603062\pi$
$587$	−15.4164	−0.636303	−0.318152	+	0.948040i	$0.603062\pi$
$588$	2.14590	0.0884953
$589$	32.0689	1.32138
$590$	9.56231	0.393674
$591$	9.94427	0.409053
$592$	−0.472136	−0.0194047
$593$	−44.1591	−1.81339	−0.906697	−	0.421782i	$-0.861405\pi$
$593$	−44.1591	−1.81339	−0.906697	+	0.421782i	$0.861405\pi$
$594$	−3.47214	−0.142463
$595$	12.9443	0.530663
$596$	−1.61803	−0.0662773
$597$	1.23607	0.0505889
$598$	−1.23607	−0.0505466
$599$	−12.2918	−0.502229	−0.251115	−	0.967957i	$-0.580797\pi$
$599$	−12.2918	−0.502229	−0.251115	+	0.967957i	$0.580797\pi$
$600$	0.618034	0.0252311
$601$	−8.50658	−0.346991	−0.173495	−	0.984835i	$-0.555506\pi$
$601$	−8.50658	−0.346991	−0.173495	+	0.984835i	$0.555506\pi$
$602$	−18.1803	−0.740975
$603$	35.5066	1.44594
$604$	21.5623	0.877358
$605$	−1.00000	−0.0406558
$606$	−5.52786	−0.224554
$607$	15.0344	0.610229	0.305115	−	0.952316i	$-0.401305\pi$
$607$	15.0344	0.610229	0.305115	+	0.952316i	$0.401305\pi$
$608$	−5.61803	−0.227841
$609$	−6.47214	−0.262264
$610$	−3.09017	−0.125117
$611$	−2.05573	−0.0831659
$612$	10.4721	0.423311
$613$	2.43769	0.0984575	0.0492288	−	0.998788i	$-0.484324\pi$
$613$	2.43769	0.0984575	0.0492288	+	0.998788i	$0.484324\pi$
$614$	29.9787	1.20984
$615$	1.23607	0.0498431
$616$	3.23607	0.130385
$617$	−0.0344419	−0.00138658	−0.000693288	−	1.00000i	$-0.500221\pi$
$617$	−0.0344419	−0.00138658	−0.000693288		1.00000i	$0.500221\pi$
$618$	−3.41641	−0.137428
$619$	−13.3475	−0.536482	−0.268241	−	0.963352i	$-0.586442\pi$
$619$	−13.3475	−0.536482	−0.268241	+	0.963352i	$0.586442\pi$
$620$	5.70820	0.229247
$621$	−6.94427	−0.278664
$622$	29.7426	1.19257
$623$	34.9443	1.40001
$624$	−0.381966	−0.0152909
$625$	1.00000	0.0400000
$626$	14.3820	0.574819
$627$	−3.47214	−0.138664
$628$	−3.23607	−0.129133
$629$	1.88854	0.0753012
$630$	8.47214	0.337538
$631$	26.4721	1.05384	0.526920	−	0.849915i	$-0.323347\pi$
$631$	26.4721	1.05384	0.526920	+	0.849915i	$0.323347\pi$
$632$	5.70820	0.227060
$633$	3.00000	0.119239
$634$	29.6869	1.17902
$635$	−15.3820	−0.610415
$636$	3.41641	0.135469
$637$	−2.14590	−0.0850236
$638$	−3.23607	−0.128117
$639$	12.7082	0.502729
$640$	−1.00000	−0.0395285
$641$	4.11146	0.162393	0.0811964	−	0.996698i	$-0.474126\pi$
$641$	4.11146	0.162393	0.0811964	+	0.996698i	$0.474126\pi$
$642$	3.47214	0.137034
$643$	27.7771	1.09542	0.547711	−	0.836668i	$-0.315499\pi$
$643$	27.7771	1.09542	0.547711	+	0.836668i	$0.315499\pi$
$644$	6.47214	0.255038
$645$	3.47214	0.136715
$646$	22.4721	0.884154
$647$	34.5623	1.35878	0.679392	−	0.733775i	$-0.262244\pi$
$647$	34.5623	1.35878	0.679392	+	0.733775i	$0.262244\pi$
$648$	5.70820	0.224239
$649$	−9.56231	−0.375353
$650$	−0.618034	−0.0242413
$651$	−11.4164	−0.447444
$652$	−11.2361	−0.440038
$653$	39.5623	1.54819	0.774096	−	0.633068i	$-0.218205\pi$
$653$	39.5623	1.54819	0.774096	+	0.633068i	$0.218205\pi$
$654$	−4.29180	−0.167823
$655$	−12.9443	−0.505775
$656$	−2.00000	−0.0780869
$657$	2.61803	0.102139
$658$	10.7639	0.419622
$659$	20.2705	0.789627	0.394813	−	0.918761i	$-0.370809\pi$
$659$	20.2705	0.789627	0.394813	+	0.918761i	$0.370809\pi$
$660$	−0.618034	−0.0240569
$661$	10.1115	0.393290	0.196645	−	0.980475i	$-0.436995\pi$
$661$	10.1115	0.393290	0.196645	+	0.980475i	$0.436995\pi$
$662$	−6.43769	−0.250208
$663$	1.52786	0.0593373
$664$	−14.6180	−0.567290
$665$	18.1803	0.705003
$666$	1.23607	0.0478967
$667$	−6.47214	−0.250602
$668$	7.52786	0.291262
$669$	13.7082	0.529990
$670$	13.5623	0.523958
$671$	3.09017	0.119295
$672$	2.00000	0.0771517
$673$	23.5623	0.908260	0.454130	−	0.890935i	$-0.349950\pi$
$673$	23.5623	0.908260	0.454130	+	0.890935i	$0.349950\pi$
$674$	−28.6525	−1.10365
$675$	−3.47214	−0.133643
$676$	−12.6180	−0.485309
$677$	−36.2705	−1.39399	−0.696994	−	0.717077i	$-0.745480\pi$
$677$	−36.2705	−1.39399	−0.696994	+	0.717077i	$0.745480\pi$
$678$	−1.94427	−0.0746693
$679$	−4.94427	−0.189744
$680$	4.00000	0.153393
$681$	−10.6525	−0.408204
$682$	−5.70820	−0.218578
$683$	−4.29180	−0.164221	−0.0821105	−	0.996623i	$-0.526166\pi$
$683$	−4.29180	−0.164221	−0.0821105	+	0.996623i	$0.526166\pi$
$684$	14.7082	0.562382
$685$	17.7082	0.676596
$686$	−11.4164	−0.435880
$687$	−5.65248	−0.215655
$688$	−5.61803	−0.214186
$689$	−3.41641	−0.130155
$690$	−1.23607	−0.0470563
$691$	14.4377	0.549236	0.274618	−	0.961553i	$-0.411449\pi$
$691$	14.4377	0.549236	0.274618	+	0.961553i	$0.411449\pi$
$692$	−23.8885	−0.908106
$693$	−8.47214	−0.321830
$694$	−20.7639	−0.788188
$695$	2.29180	0.0869328
$696$	−2.00000	−0.0758098
$697$	8.00000	0.303022
$698$	−4.67376	−0.176905
$699$	9.88854	0.374019
$700$	3.23607	0.122312
$701$	0.583592	0.0220420	0.0110210	−	0.999939i	$-0.496492\pi$
$701$	0.583592	0.0220420	0.0110210	+	0.999939i	$0.496492\pi$
$702$	2.14590	0.0809917
$703$	2.65248	0.100040
$704$	1.00000	0.0376889
$705$	−2.05573	−0.0774232
$706$	23.4164	0.881288
$707$	−28.9443	−1.08856
$708$	−5.90983	−0.222105
$709$	−42.9787	−1.61410	−0.807050	−	0.590483i	$-0.798937\pi$
$709$	−42.9787	−1.61410	−0.807050	+	0.590483i	$0.798937\pi$
$710$	4.85410	0.182171
$711$	−14.9443	−0.560454
$712$	10.7984	0.404686
$713$	−11.4164	−0.427548
$714$	−8.00000	−0.299392
$715$	0.618034	0.0231132
$716$	17.3262	0.647512
$717$	−8.74265	−0.326500
$718$	−0.944272	−0.0352399
$719$	18.3607	0.684738	0.342369	−	0.939566i	$-0.388771\pi$
$719$	18.3607	0.684738	0.342369	+	0.939566i	$0.388771\pi$
$720$	2.61803	0.0975684
$721$	−17.8885	−0.666204
$722$	12.5623	0.467521
$723$	−5.81966	−0.216435
$724$	1.70820	0.0634849
$725$	−3.23607	−0.120185
$726$	0.618034	0.0229374
$727$	−5.81966	−0.215839	−0.107920	−	0.994160i	$-0.534419\pi$
$727$	−5.81966	−0.215839	−0.107920	+	0.994160i	$0.534419\pi$
$728$	−2.00000	−0.0741249
$729$	−8.50658	−0.315058
$730$	1.00000	0.0370117
$731$	22.4721	0.831162
$732$	1.90983	0.0705894
$733$	−0.180340	−0.00666101	−0.00333050	−	0.999994i	$-0.501060\pi$
$733$	−0.180340	−0.00666101	−0.00333050	+	0.999994i	$0.501060\pi$
$734$	−14.9443	−0.551603
$735$	−2.14590	−0.0791526
$736$	2.00000	0.0737210
$737$	−13.5623	−0.499574
$738$	5.23607	0.192742
$739$	−12.5836	−0.462895	−0.231447	−	0.972847i	$-0.574346\pi$
$739$	−12.5836	−0.462895	−0.231447	+	0.972847i	$0.574346\pi$
$740$	0.472136	0.0173561
$741$	2.14590	0.0788315
$742$	17.8885	0.656709
$743$	48.0689	1.76348	0.881738	−	0.471739i	$-0.156374\pi$
$743$	48.0689	1.76348	0.881738	+	0.471739i	$0.156374\pi$
$744$	−3.52786	−0.129338
$745$	1.61803	0.0592802
$746$	−11.5279	−0.422065
$747$	38.2705	1.40024
$748$	−4.00000	−0.146254
$749$	18.1803	0.664295
$750$	−0.618034	−0.0225674
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	3.32624	0.121295
$753$	−6.47214	−0.235858
$754$	2.00000	0.0728357
$755$	−21.5623	−0.784733
$756$	−11.2361	−0.408652
$757$	−10.4508	−0.379843	−0.189921	−	0.981799i	$-0.560823\pi$
$757$	−10.4508	−0.379843	−0.189921	+	0.981799i	$0.560823\pi$
$758$	−22.6738	−0.823548
$759$	1.23607	0.0448664
$760$	5.61803	0.203788
$761$	19.0344	0.689998	0.344999	−	0.938603i	$-0.387879\pi$
$761$	19.0344	0.689998	0.344999	+	0.938603i	$0.387879\pi$
$762$	9.50658	0.344387
$763$	−22.4721	−0.813546
$764$	13.8885	0.502470
$765$	−10.4721	−0.378621
$766$	−11.8885	−0.429551
$767$	5.90983	0.213392
$768$	0.618034	0.0223014
$769$	−1.14590	−0.0413221	−0.0206611	−	0.999787i	$-0.506577\pi$
$769$	−1.14590	−0.0413221	−0.0206611	+	0.999787i	$0.506577\pi$
$770$	−3.23607	−0.116620
$771$	−12.8328	−0.462163
$772$	2.18034	0.0784721
$773$	19.4164	0.698360	0.349180	−	0.937056i	$-0.386460\pi$
$773$	19.4164	0.698360	0.349180	+	0.937056i	$0.386460\pi$
$774$	14.7082	0.528675
$775$	−5.70820	−0.205045
$776$	−1.52786	−0.0548471
$777$	−0.944272	−0.0338756
$778$	28.8328	1.03371
$779$	11.2361	0.402574
$780$	0.381966	0.0136766
$781$	−4.85410	−0.173693
$782$	−8.00000	−0.286079
$783$	11.2361	0.401544
$784$	3.47214	0.124005
$785$	3.23607	0.115500
$786$	8.00000	0.285351
$787$	42.3607	1.51000	0.754998	−	0.655728i	$-0.227638\pi$
$787$	42.3607	1.51000	0.754998	+	0.655728i	$0.227638\pi$
$788$	16.0902	0.573189
$789$	6.18034	0.220026
$790$	−5.70820	−0.203089
$791$	−10.1803	−0.361971
$792$	−2.61803	−0.0930278
$793$	−1.90983	−0.0678201
$794$	32.5623	1.15559
$795$	−3.41641	−0.121168
$796$	2.00000	0.0708881
$797$	6.03444	0.213751	0.106875	−	0.994272i	$-0.465915\pi$
$797$	6.03444	0.213751	0.106875	+	0.994272i	$0.465915\pi$
$798$	−11.2361	−0.397752
$799$	−13.3050	−0.470695
$800$	1.00000	0.0353553
$801$	−28.2705	−0.998889
$802$	0.326238	0.0115199
$803$	−1.00000	−0.0352892
$804$	−8.38197	−0.295609
$805$	−6.47214	−0.228113
$806$	3.52786	0.124264
$807$	−18.0000	−0.633630
$808$	−8.94427	−0.314658
$809$	23.5967	0.829617	0.414809	−	0.909909i	$-0.363848\pi$
$809$	23.5967	0.829617	0.414809	+	0.909909i	$0.363848\pi$
$810$	−5.70820	−0.200566
$811$	−11.4164	−0.400884	−0.200442	−	0.979706i	$-0.564238\pi$
$811$	−11.4164	−0.400884	−0.200442	+	0.979706i	$0.564238\pi$
$812$	−10.4721	−0.367500
$813$	2.67376	0.0937729
$814$	−0.472136	−0.0165484
$815$	11.2361	0.393582
$816$	−2.47214	−0.0865421
$817$	31.5623	1.10423
$818$	−25.1459	−0.879206
$819$	5.23607	0.182963
$820$	2.00000	0.0698430
$821$	−14.7426	−0.514522	−0.257261	−	0.966342i	$-0.582820\pi$
$821$	−14.7426	−0.514522	−0.257261	+	0.966342i	$0.582820\pi$
$822$	−10.9443	−0.381725
$823$	−35.6869	−1.24397	−0.621984	−	0.783030i	$-0.713673\pi$
$823$	−35.6869	−1.24397	−0.621984	+	0.783030i	$0.713673\pi$
$824$	−5.52786	−0.192572
$825$	0.618034	0.0215172
$826$	−30.9443	−1.07669
$827$	35.3050	1.22767	0.613837	−	0.789433i	$-0.289625\pi$
$827$	35.3050	1.22767	0.613837	+	0.789433i	$0.289625\pi$
$828$	−5.23607	−0.181966
$829$	−29.7771	−1.03420	−0.517101	−	0.855925i	$-0.672989\pi$
$829$	−29.7771	−1.03420	−0.517101	+	0.855925i	$0.672989\pi$
$830$	14.6180	0.507399
$831$	−3.47214	−0.120447
$832$	−0.618034	−0.0214265
$833$	−13.8885	−0.481210
$834$	−1.41641	−0.0490462
$835$	−7.52786	−0.260512
$836$	−5.61803	−0.194304
$837$	19.8197	0.685068
$838$	−11.0557	−0.381914
$839$	−22.3262	−0.770787	−0.385394	−	0.922752i	$-0.625934\pi$
$839$	−22.3262	−0.770787	−0.385394	+	0.922752i	$0.625934\pi$
$840$	−2.00000	−0.0690066
$841$	−18.5279	−0.638892
$842$	21.0902	0.726815
$843$	−16.6738	−0.574275
$844$	4.85410	0.167085
$845$	12.6180	0.434074
$846$	−8.70820	−0.299394
$847$	3.23607	0.111193
$848$	5.52786	0.189828
$849$	−7.52786	−0.258356
$850$	−4.00000	−0.137199
$851$	−0.944272	−0.0323692
$852$	−3.00000	−0.102778
$853$	−31.1246	−1.06569	−0.532843	−	0.846214i	$-0.678876\pi$
$853$	−31.1246	−1.06569	−0.532843	+	0.846214i	$0.678876\pi$
$854$	10.0000	0.342193
$855$	−14.7082	−0.503010
$856$	5.61803	0.192020
$857$	29.3262	1.00177	0.500883	−	0.865515i	$-0.333009\pi$
$857$	29.3262	1.00177	0.500883	+	0.865515i	$0.333009\pi$
$858$	−0.381966	−0.0130401
$859$	18.4508	0.629535	0.314767	−	0.949169i	$-0.398073\pi$
$859$	18.4508	0.629535	0.314767	+	0.949169i	$0.398073\pi$
$860$	5.61803	0.191573
$861$	−4.00000	−0.136320
$862$	19.4508	0.662499
$863$	42.3262	1.44080	0.720401	−	0.693558i	$-0.243958\pi$
$863$	42.3262	1.44080	0.720401	+	0.693558i	$0.243958\pi$
$864$	−3.47214	−0.118124
$865$	23.8885	0.812235
$866$	−41.0344	−1.39441
$867$	−0.618034	−0.0209895
$868$	−18.4721	−0.626985
$869$	5.70820	0.193638
$870$	2.00000	0.0678064
$871$	8.38197	0.284012
$872$	−6.94427	−0.235163
$873$	4.00000	0.135379
$874$	−11.2361	−0.380066
$875$	−3.23607	−0.109399
$876$	−0.618034	−0.0208814
$877$	−22.6525	−0.764920	−0.382460	−	0.923972i	$-0.624923\pi$
$877$	−22.6525	−0.764920	−0.382460	+	0.923972i	$0.624923\pi$
$878$	9.70820	0.327636
$879$	7.41641	0.250149
$880$	−1.00000	−0.0337100
$881$	24.0689	0.810901	0.405451	−	0.914117i	$-0.367115\pi$
$881$	24.0689	0.810901	0.405451	+	0.914117i	$0.367115\pi$
$882$	−9.09017	−0.306082
$883$	−11.8885	−0.400081	−0.200041	−	0.979788i	$-0.564107\pi$
$883$	−11.8885	−0.400081	−0.200041	+	0.979788i	$0.564107\pi$
$884$	2.47214	0.0831469
$885$	5.90983	0.198657
$886$	−31.4164	−1.05545
$887$	−7.30495	−0.245276	−0.122638	−	0.992451i	$-0.539135\pi$
$887$	−7.30495	−0.245276	−0.122638	+	0.992451i	$0.539135\pi$
$888$	−0.291796	−0.00979203
$889$	49.7771	1.66947
$890$	−10.7984	−0.361962
$891$	5.70820	0.191232
$892$	22.1803	0.742653
$893$	−18.6869	−0.625334
$894$	−1.00000	−0.0334450
$895$	−17.3262	−0.579152
$896$	3.23607	0.108109
$897$	−0.763932	−0.0255069
$898$	16.4721	0.549682
$899$	18.4721	0.616080
$900$	−2.61803	−0.0872678
$901$	−22.1115	−0.736639
$902$	−2.00000	−0.0665927
$903$	−11.2361	−0.373913
$904$	−3.14590	−0.104631
$905$	−1.70820	−0.0567826
$906$	13.3262	0.442735
$907$	10.9443	0.363399	0.181699	−	0.983354i	$-0.441840\pi$
$907$	10.9443	0.363399	0.181699	+	0.983354i	$0.441840\pi$
$908$	−17.2361	−0.571999
$909$	23.4164	0.776673
$910$	2.00000	0.0662994
$911$	−28.2705	−0.936644	−0.468322	−	0.883558i	$-0.655141\pi$
$911$	−28.2705	−0.936644	−0.468322	+	0.883558i	$0.655141\pi$
$912$	−3.47214	−0.114974
$913$	−14.6180	−0.483786
$914$	−5.14590	−0.170211
$915$	−1.90983	−0.0631370
$916$	−9.14590	−0.302189
$917$	41.8885	1.38328
$918$	13.8885	0.458390
$919$	−20.9230	−0.690186	−0.345093	−	0.938569i	$-0.612153\pi$
$919$	−20.9230	−0.690186	−0.345093	+	0.938569i	$0.612153\pi$
$920$	−2.00000	−0.0659380
$921$	18.5279	0.610514
$922$	16.6738	0.549121
$923$	3.00000	0.0987462
$924$	2.00000	0.0657952
$925$	−0.472136	−0.0155237
$926$	−3.81966	−0.125522
$927$	14.4721	0.475327
$928$	−3.23607	−0.106229
$929$	−9.59675	−0.314859	−0.157430	−	0.987530i	$-0.550321\pi$
$929$	−9.59675	−0.314859	−0.157430	+	0.987530i	$0.550321\pi$
$930$	3.52786	0.115683
$931$	−19.5066	−0.639302
$932$	16.0000	0.524097
$933$	18.3820	0.601799
$934$	−39.4164	−1.28974
$935$	4.00000	0.130814
$936$	1.61803	0.0528871
$937$	−11.4377	−0.373653	−0.186827	−	0.982393i	$-0.559820\pi$
$937$	−11.4377	−0.373653	−0.186827	+	0.982393i	$0.559820\pi$
$938$	−43.8885	−1.43301
$939$	8.88854	0.290067
$940$	−3.32624	−0.108490
$941$	32.9787	1.07508	0.537538	−	0.843240i	$-0.319355\pi$
$941$	32.9787	1.07508	0.537538	+	0.843240i	$0.319355\pi$
$942$	−2.00000	−0.0651635
$943$	−4.00000	−0.130258
$944$	−9.56231	−0.311227
$945$	11.2361	0.365509
$946$	−5.61803	−0.182658
$947$	−39.7426	−1.29146	−0.645731	−	0.763565i	$-0.723447\pi$
$947$	−39.7426	−1.29146	−0.645731	+	0.763565i	$0.723447\pi$
$948$	3.52786	0.114580
$949$	0.618034	0.0200622
$950$	−5.61803	−0.182273
$951$	18.3475	0.594959
$952$	−12.9443	−0.419526
$953$	24.7295	0.801067	0.400533	−	0.916282i	$-0.368825\pi$
$953$	24.7295	0.801067	0.400533	+	0.916282i	$0.368825\pi$
$954$	−14.4721	−0.468553
$955$	−13.8885	−0.449423
$956$	−14.1459	−0.457511
$957$	−2.00000	−0.0646508
$958$	−23.1246	−0.747122
$959$	−57.3050	−1.85047
$960$	−0.618034	−0.0199470
$961$	1.58359	0.0510836
$962$	0.291796	0.00940788
$963$	−14.7082	−0.473965
$964$	−9.41641	−0.303282
$965$	−2.18034	−0.0701876
$966$	4.00000	0.128698
$967$	10.2148	0.328485	0.164243	−	0.986420i	$-0.447482\pi$
$967$	10.2148	0.328485	0.164243	+	0.986420i	$0.447482\pi$
$968$	1.00000	0.0321412
$969$	13.8885	0.446164
$970$	1.52786	0.0490568
$971$	14.2705	0.457962	0.228981	−	0.973431i	$-0.426461\pi$
$971$	14.2705	0.457962	0.228981	+	0.973431i	$0.426461\pi$
$972$	13.9443	0.447263
$973$	−7.41641	−0.237759
$974$	−29.8885	−0.957691
$975$	−0.381966	−0.0122327
$976$	3.09017	0.0989139
$977$	57.3394	1.83445	0.917225	−	0.398370i	$-0.130424\pi$
$977$	57.3394	1.83445	0.917225	+	0.398370i	$0.130424\pi$
$978$	−6.94427	−0.222053
$979$	10.7984	0.345118
$980$	−3.47214	−0.110913
$981$	18.1803	0.580454
$982$	−7.52786	−0.240224
$983$	−17.2148	−0.549066	−0.274533	−	0.961578i	$-0.588523\pi$
$983$	−17.2148	−0.549066	−0.274533	+	0.961578i	$0.588523\pi$
$984$	−1.23607	−0.0394044
$985$	−16.0902	−0.512675
$986$	12.9443	0.412230
$987$	6.65248	0.211751
$988$	3.47214	0.110463
$989$	−11.2361	−0.357286
$990$	2.61803	0.0832066
$991$	32.4721	1.03151	0.515756	−	0.856736i	$-0.327511\pi$
$991$	32.4721	1.03151	0.515756	+	0.856736i	$0.327511\pi$
$992$	−5.70820	−0.181236
$993$	−3.97871	−0.126261
$994$	−15.7082	−0.498234
$995$	−2.00000	−0.0634043
$996$	−9.03444	−0.286267
$997$	17.5967	0.557295	0.278647	−	0.960394i	$-0.410114\pi$
$997$	17.5967	0.557295	0.278647	+	0.960394i	$0.410114\pi$
$998$	26.9443	0.852906
$999$	1.63932	0.0518658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.o.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.o.1.2	✓	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.618034 q^{6} +3.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.618034 q^{12} -0.618034 q^{13} +3.23607 q^{14} -0.618034 q^{15} +1.00000 q^{16} -4.00000 q^{17} -2.61803 q^{18} -5.61803 q^{19} -1.00000 q^{20} +2.00000 q^{21} +1.00000 q^{22} +2.00000 q^{23} +0.618034 q^{24} +1.00000 q^{25} -0.618034 q^{26} -3.47214 q^{27} +3.23607 q^{28} -3.23607 q^{29} -0.618034 q^{30} -5.70820 q^{31} +1.00000 q^{32} +0.618034 q^{33} -4.00000 q^{34} -3.23607 q^{35} -2.61803 q^{36} -0.472136 q^{37} -5.61803 q^{38} -0.381966 q^{39} -1.00000 q^{40} -2.00000 q^{41} +2.00000 q^{42} -5.61803 q^{43} +1.00000 q^{44} +2.61803 q^{45} +2.00000 q^{46} +3.32624 q^{47} +0.618034 q^{48} +3.47214 q^{49} +1.00000 q^{50} -2.47214 q^{51} -0.618034 q^{52} +5.52786 q^{53} -3.47214 q^{54} -1.00000 q^{55} +3.23607 q^{56} -3.47214 q^{57} -3.23607 q^{58} -9.56231 q^{59} -0.618034 q^{60} +3.09017 q^{61} -5.70820 q^{62} -8.47214 q^{63} +1.00000 q^{64} +0.618034 q^{65} +0.618034 q^{66} -13.5623 q^{67} -4.00000 q^{68} +1.23607 q^{69} -3.23607 q^{70} -4.85410 q^{71} -2.61803 q^{72} -1.00000 q^{73} -0.472136 q^{74} +0.618034 q^{75} -5.61803 q^{76} +3.23607 q^{77} -0.381966 q^{78} +5.70820 q^{79} -1.00000 q^{80} +5.70820 q^{81} -2.00000 q^{82} -14.6180 q^{83} +2.00000 q^{84} +4.00000 q^{85} -5.61803 q^{86} -2.00000 q^{87} +1.00000 q^{88} +10.7984 q^{89} +2.61803 q^{90} -2.00000 q^{91} +2.00000 q^{92} -3.52786 q^{93} +3.32624 q^{94} +5.61803 q^{95} +0.618034 q^{96} -1.52786 q^{97} +3.47214 q^{98} -2.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} + 2 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{15} + 2 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} + 4 q^{21} + 2 q^{22} + 4 q^{23} - q^{24} + 2 q^{25} + q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{29} + q^{30} + 2 q^{31} + 2 q^{32} - q^{33} - 8 q^{34} - 2 q^{35} - 3 q^{36} + 8 q^{37} - 9 q^{38} - 3 q^{39} - 2 q^{40} - 4 q^{41} + 4 q^{42} - 9 q^{43} + 2 q^{44} + 3 q^{45} + 4 q^{46} - 9 q^{47} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} + q^{52} + 20 q^{53} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 2 q^{57} - 2 q^{58} + q^{59} + q^{60} - 5 q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - q^{65} - q^{66} - 7 q^{67} - 8 q^{68} - 2 q^{69} - 2 q^{70} - 3 q^{71} - 3 q^{72} - 2 q^{73} + 8 q^{74} - q^{75} - 9 q^{76} + 2 q^{77} - 3 q^{78} - 2 q^{79} - 2 q^{80} - 2 q^{81} - 4 q^{82} - 27 q^{83} + 4 q^{84} + 8 q^{85} - 9 q^{86} - 4 q^{87} + 2 q^{88} - 3 q^{89} + 3 q^{90} - 4 q^{91} + 4 q^{92} - 16 q^{93} - 9 q^{94} + 9 q^{95} - q^{96} - 12 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 + 2 * q^11 - q^12 + q^13 + 2 * q^14 + q^15 + 2 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 + 4 * q^21 + 2 * q^22 + 4 * q^23 - q^24 + 2 * q^25 + q^26 + 2 * q^27 + 2 * q^28 - 2 * q^29 + q^30 + 2 * q^31 + 2 * q^32 - q^33 - 8 * q^34 - 2 * q^35 - 3 * q^36 + 8 * q^37 - 9 * q^38 - 3 * q^39 - 2 * q^40 - 4 * q^41 + 4 * q^42 - 9 * q^43 + 2 * q^44 + 3 * q^45 + 4 * q^46 - 9 * q^47 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 + q^52 + 20 * q^53 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 2 * q^57 - 2 * q^58 + q^59 + q^60 - 5 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 - q^65 - q^66 - 7 * q^67 - 8 * q^68 - 2 * q^69 - 2 * q^70 - 3 * q^71 - 3 * q^72 - 2 * q^73 + 8 * q^74 - q^75 - 9 * q^76 + 2 * q^77 - 3 * q^78 - 2 * q^79 - 2 * q^80 - 2 * q^81 - 4 * q^82 - 27 * q^83 + 4 * q^84 + 8 * q^85 - 9 * q^86 - 4 * q^87 + 2 * q^88 - 3 * q^89 + 3 * q^90 - 4 * q^91 + 4 * q^92 - 16 * q^93 - 9 * q^94 + 9 * q^95 - q^96 - 12 * q^97 - 2 * q^98 - 3 * q^99

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