LMFDB - Embedded newform 4026.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.198062 q^{5} +1.00000 q^{6} -5.04892 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.198062 q^{5} +1.00000 q^{6} -5.04892 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.198062 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.64310 q^{13} -5.04892 q^{14} -0.198062 q^{15} +1.00000 q^{16} +3.49396 q^{17} +1.00000 q^{18} +2.02715 q^{19} -0.198062 q^{20} -5.04892 q^{21} +1.00000 q^{22} -2.46681 q^{23} +1.00000 q^{24} -4.96077 q^{25} -1.64310 q^{26} +1.00000 q^{27} -5.04892 q^{28} -4.33513 q^{29} -0.198062 q^{30} -7.43296 q^{31} +1.00000 q^{32} +1.00000 q^{33} +3.49396 q^{34} +1.00000 q^{35} +1.00000 q^{36} -0.643104 q^{37} +2.02715 q^{38} -1.64310 q^{39} -0.198062 q^{40} -9.59179 q^{41} -5.04892 q^{42} +6.89977 q^{43} +1.00000 q^{44} -0.198062 q^{45} -2.46681 q^{46} -3.08815 q^{47} +1.00000 q^{48} +18.4916 q^{49} -4.96077 q^{50} +3.49396 q^{51} -1.64310 q^{52} -12.2295 q^{53} +1.00000 q^{54} -0.198062 q^{55} -5.04892 q^{56} +2.02715 q^{57} -4.33513 q^{58} -10.0489 q^{59} -0.198062 q^{60} +1.00000 q^{61} -7.43296 q^{62} -5.04892 q^{63} +1.00000 q^{64} +0.325437 q^{65} +1.00000 q^{66} +2.26875 q^{67} +3.49396 q^{68} -2.46681 q^{69} +1.00000 q^{70} -11.4330 q^{71} +1.00000 q^{72} -6.33513 q^{73} -0.643104 q^{74} -4.96077 q^{75} +2.02715 q^{76} -5.04892 q^{77} -1.64310 q^{78} +1.34481 q^{79} -0.198062 q^{80} +1.00000 q^{81} -9.59179 q^{82} +14.3545 q^{83} -5.04892 q^{84} -0.692021 q^{85} +6.89977 q^{86} -4.33513 q^{87} +1.00000 q^{88} +18.0954 q^{89} -0.198062 q^{90} +8.29590 q^{91} -2.46681 q^{92} -7.43296 q^{93} -3.08815 q^{94} -0.401501 q^{95} +1.00000 q^{96} -5.65279 q^{97} +18.4916 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 5 q^{10} + 3 q^{11} + 3 q^{12} - 9 q^{13} - 6 q^{14} - 5 q^{15} + 3 q^{16} + q^{17} + 3 q^{18} - 5 q^{20} - 6 q^{21} + 3 q^{22} - 4 q^{23} + 3 q^{24} - 2 q^{25} - 9 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} - 5 q^{30} - 3 q^{31} + 3 q^{32} + 3 q^{33} + q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 9 q^{39} - 5 q^{40} - q^{41} - 6 q^{42} - 2 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} - 13 q^{47} + 3 q^{48} + 5 q^{49} - 2 q^{50} + q^{51} - 9 q^{52} - 16 q^{53} + 3 q^{54} - 5 q^{55} - 6 q^{56} - 12 q^{58} - 21 q^{59} - 5 q^{60} + 3 q^{61} - 3 q^{62} - 6 q^{63} + 3 q^{64} + 22 q^{65} + 3 q^{66} - q^{67} + q^{68} - 4 q^{69} + 3 q^{70} - 15 q^{71} + 3 q^{72} - 18 q^{73} - 6 q^{74} - 2 q^{75} - 6 q^{77} - 9 q^{78} - 19 q^{79} - 5 q^{80} + 3 q^{81} - q^{82} - 2 q^{83} - 6 q^{84} + 3 q^{85} - 2 q^{86} - 12 q^{87} + 3 q^{88} - 5 q^{89} - 5 q^{90} + 11 q^{91} - 4 q^{92} - 3 q^{93} - 13 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} + 5 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 5 * q^10 + 3 * q^11 + 3 * q^12 - 9 * q^13 - 6 * q^14 - 5 * q^15 + 3 * q^16 + q^17 + 3 * q^18 - 5 * q^20 - 6 * q^21 + 3 * q^22 - 4 * q^23 + 3 * q^24 - 2 * q^25 - 9 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 - 5 * q^30 - 3 * q^31 + 3 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 9 * q^39 - 5 * q^40 - q^41 - 6 * q^42 - 2 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 - 13 * q^47 + 3 * q^48 + 5 * q^49 - 2 * q^50 + q^51 - 9 * q^52 - 16 * q^53 + 3 * q^54 - 5 * q^55 - 6 * q^56 - 12 * q^58 - 21 * q^59 - 5 * q^60 + 3 * q^61 - 3 * q^62 - 6 * q^63 + 3 * q^64 + 22 * q^65 + 3 * q^66 - q^67 + q^68 - 4 * q^69 + 3 * q^70 - 15 * q^71 + 3 * q^72 - 18 * q^73 - 6 * q^74 - 2 * q^75 - 6 * q^77 - 9 * q^78 - 19 * q^79 - 5 * q^80 + 3 * q^81 - q^82 - 2 * q^83 - 6 * q^84 + 3 * q^85 - 2 * q^86 - 12 * q^87 + 3 * q^88 - 5 * q^89 - 5 * q^90 + 11 * q^91 - 4 * q^92 - 3 * q^93 - 13 * q^94 - 7 * q^95 + 3 * q^96 + q^97 + 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.198062	−0.0885761	−0.0442881	−	0.999019i	$-0.514102\pi$
$5$	−0.198062	−0.0885761	−0.0442881	+	0.999019i	$0.514102\pi$
$6$	1.00000	0.408248
$7$	−5.04892	−1.90831	−0.954156	−	0.299311i	$-0.903243\pi$
$7$	−5.04892	−1.90831	−0.954156	+	0.299311i	$0.903243\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.198062	−0.0626328
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−1.64310	−0.455715	−0.227858	−	0.973694i	$-0.573172\pi$
$13$	−1.64310	−0.455715	−0.227858	+	0.973694i	$0.573172\pi$
$14$	−5.04892	−1.34938
$15$	−0.198062	−0.0511395
$16$	1.00000	0.250000
$17$	3.49396	0.847410	0.423705	−	0.905800i	$-0.360729\pi$
$17$	3.49396	0.847410	0.423705	+	0.905800i	$0.360729\pi$
$18$	1.00000	0.235702
$19$	2.02715	0.465059	0.232530	−	0.972589i	$-0.425300\pi$
$19$	2.02715	0.465059	0.232530	+	0.972589i	$0.425300\pi$
$20$	−0.198062	−0.0442881
$21$	−5.04892	−1.10176
$22$	1.00000	0.213201
$23$	−2.46681	−0.514366	−0.257183	−	0.966363i	$-0.582794\pi$
$23$	−2.46681	−0.514366	−0.257183	+	0.966363i	$0.582794\pi$
$24$	1.00000	0.204124
$25$	−4.96077	−0.992154
$26$	−1.64310	−0.322239
$27$	1.00000	0.192450
$28$	−5.04892	−0.954156
$29$	−4.33513	−0.805013	−0.402506	−	0.915417i	$-0.631861\pi$
$29$	−4.33513	−0.805013	−0.402506	+	0.915417i	$0.631861\pi$
$30$	−0.198062	−0.0361611
$31$	−7.43296	−1.33500	−0.667500	−	0.744610i	$-0.732635\pi$
$31$	−7.43296	−1.33500	−0.667500	+	0.744610i	$0.732635\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	3.49396	0.599209
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−0.643104	−0.105726	−0.0528628	−	0.998602i	$-0.516835\pi$
$37$	−0.643104	−0.105726	−0.0528628	+	0.998602i	$0.516835\pi$
$38$	2.02715	0.328847
$39$	−1.64310	−0.263107
$40$	−0.198062	−0.0313164
$41$	−9.59179	−1.49799	−0.748993	−	0.662578i	$-0.769462\pi$
$41$	−9.59179	−1.49799	−0.748993	+	0.662578i	$0.769462\pi$
$42$	−5.04892	−0.779065
$43$	6.89977	1.05221	0.526103	−	0.850421i	$-0.323653\pi$
$43$	6.89977	1.05221	0.526103	+	0.850421i	$0.323653\pi$
$44$	1.00000	0.150756
$45$	−0.198062	−0.0295254
$46$	−2.46681	−0.363712
$47$	−3.08815	−0.450452	−0.225226	−	0.974307i	$-0.572312\pi$
$47$	−3.08815	−0.450452	−0.225226	+	0.974307i	$0.572312\pi$
$48$	1.00000	0.144338
$49$	18.4916	2.64165
$50$	−4.96077	−0.701559
$51$	3.49396	0.489252
$52$	−1.64310	−0.227858
$53$	−12.2295	−1.67985	−0.839927	−	0.542699i	$-0.817402\pi$
$53$	−12.2295	−1.67985	−0.839927	+	0.542699i	$0.817402\pi$
$54$	1.00000	0.136083
$55$	−0.198062	−0.0267067
$56$	−5.04892	−0.674690
$57$	2.02715	0.268502
$58$	−4.33513	−0.569230
$59$	−10.0489	−1.30826	−0.654129	−	0.756383i	$-0.726965\pi$
$59$	−10.0489	−1.30826	−0.654129	+	0.756383i	$0.726965\pi$
$60$	−0.198062	−0.0255697
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−7.43296	−0.943987
$63$	−5.04892	−0.636104
$64$	1.00000	0.125000
$65$	0.325437	0.0403655
$66$	1.00000	0.123091
$67$	2.26875	0.277172	0.138586	−	0.990350i	$-0.455744\pi$
$67$	2.26875	0.277172	0.138586	+	0.990350i	$0.455744\pi$
$68$	3.49396	0.423705
$69$	−2.46681	−0.296969
$70$	1.00000	0.119523
$71$	−11.4330	−1.35684	−0.678421	−	0.734673i	$-0.737336\pi$
$71$	−11.4330	−1.35684	−0.678421	+	0.734673i	$0.737336\pi$
$72$	1.00000	0.117851
$73$	−6.33513	−0.741470	−0.370735	−	0.928739i	$-0.620894\pi$
$73$	−6.33513	−0.741470	−0.370735	+	0.928739i	$0.620894\pi$
$74$	−0.643104	−0.0747593
$75$	−4.96077	−0.572821
$76$	2.02715	0.232530
$77$	−5.04892	−0.575378
$78$	−1.64310	−0.186045
$79$	1.34481	0.151303	0.0756517	−	0.997134i	$-0.475896\pi$
$79$	1.34481	0.151303	0.0756517	+	0.997134i	$0.475896\pi$
$80$	−0.198062	−0.0221440
$81$	1.00000	0.111111
$82$	−9.59179	−1.05924
$83$	14.3545	1.57561	0.787806	−	0.615924i	$-0.211217\pi$
$83$	14.3545	1.57561	0.787806	+	0.615924i	$0.211217\pi$
$84$	−5.04892	−0.550882
$85$	−0.692021	−0.0750603
$86$	6.89977	0.744022
$87$	−4.33513	−0.464774
$88$	1.00000	0.106600
$89$	18.0954	1.91811	0.959056	−	0.283215i	$-0.0914009\pi$
$89$	18.0954	1.91811	0.959056	+	0.283215i	$0.0914009\pi$
$90$	−0.198062	−0.0208776
$91$	8.29590	0.869646
$92$	−2.46681	−0.257183
$93$	−7.43296	−0.770762
$94$	−3.08815	−0.318518
$95$	−0.401501	−0.0411932
$96$	1.00000	0.102062
$97$	−5.65279	−0.573954	−0.286977	−	0.957937i	$-0.592650\pi$
$97$	−5.65279	−0.573954	−0.286977	+	0.957937i	$0.592650\pi$
$98$	18.4916	1.86793
$99$	1.00000	0.100504
$100$	−4.96077	−0.496077
$101$	−13.4601	−1.33933	−0.669665	−	0.742663i	$-0.733562\pi$
$101$	−13.4601	−1.33933	−0.669665	+	0.742663i	$0.733562\pi$
$102$	3.49396	0.345954
$103$	9.00969	0.887751	0.443876	−	0.896088i	$-0.353603\pi$
$103$	9.00969	0.887751	0.443876	+	0.896088i	$0.353603\pi$
$104$	−1.64310	−0.161120
$105$	1.00000	0.0975900
$106$	−12.2295	−1.18784
$107$	7.64310	0.738887	0.369443	−	0.929253i	$-0.379548\pi$
$107$	7.64310	0.738887	0.369443	+	0.929253i	$0.379548\pi$
$108$	1.00000	0.0962250
$109$	−7.78448	−0.745618	−0.372809	−	0.927908i	$-0.621605\pi$
$109$	−7.78448	−0.745618	−0.372809	+	0.927908i	$0.621605\pi$
$110$	−0.198062	−0.0188845
$111$	−0.643104	−0.0610407
$112$	−5.04892	−0.477078
$113$	−3.47219	−0.326636	−0.163318	−	0.986573i	$-0.552220\pi$
$113$	−3.47219	−0.326636	−0.163318	+	0.986573i	$0.552220\pi$
$114$	2.02715	0.189860
$115$	0.488582	0.0455605
$116$	−4.33513	−0.402506
$117$	−1.64310	−0.151905
$118$	−10.0489	−0.925078
$119$	−17.6407	−1.61712
$120$	−0.198062	−0.0180805
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−9.59179	−0.864863
$124$	−7.43296	−0.667500
$125$	1.97285	0.176457
$126$	−5.04892	−0.449793
$127$	−18.0858	−1.60485	−0.802426	−	0.596752i	$-0.796458\pi$
$127$	−18.0858	−1.60485	−0.802426	+	0.596752i	$0.796458\pi$
$128$	1.00000	0.0883883
$129$	6.89977	0.607491
$130$	0.325437	0.0285427
$131$	−17.0954	−1.49364	−0.746818	−	0.665029i	$-0.768419\pi$
$131$	−17.0954	−1.49364	−0.746818	+	0.665029i	$0.768419\pi$
$132$	1.00000	0.0870388
$133$	−10.2349	−0.887478
$134$	2.26875	0.195990
$135$	−0.198062	−0.0170465
$136$	3.49396	0.299605
$137$	−8.03146	−0.686174	−0.343087	−	0.939304i	$-0.611473\pi$
$137$	−8.03146	−0.686174	−0.343087	+	0.939304i	$0.611473\pi$
$138$	−2.46681	−0.209989
$139$	−15.1250	−1.28288	−0.641442	−	0.767171i	$-0.721664\pi$
$139$	−15.1250	−1.28288	−0.641442	+	0.767171i	$0.721664\pi$
$140$	1.00000	0.0845154
$141$	−3.08815	−0.260069
$142$	−11.4330	−0.959433
$143$	−1.64310	−0.137403
$144$	1.00000	0.0833333
$145$	0.858625	0.0713049
$146$	−6.33513	−0.524299
$147$	18.4916	1.52516
$148$	−0.643104	−0.0528628
$149$	8.65817	0.709305	0.354652	−	0.934998i	$-0.384599\pi$
$149$	8.65817	0.709305	0.354652	+	0.934998i	$0.384599\pi$
$150$	−4.96077	−0.405045
$151$	19.6233	1.59692	0.798459	−	0.602049i	$-0.205649\pi$
$151$	19.6233	1.59692	0.798459	+	0.602049i	$0.205649\pi$
$152$	2.02715	0.164423
$153$	3.49396	0.282470
$154$	−5.04892	−0.406853
$155$	1.47219	0.118249
$156$	−1.64310	−0.131554
$157$	−23.7385	−1.89454	−0.947271	−	0.320433i	$-0.896172\pi$
$157$	−23.7385	−1.89454	−0.947271	+	0.320433i	$0.896172\pi$
$158$	1.34481	0.106988
$159$	−12.2295	−0.969864
$160$	−0.198062	−0.0156582
$161$	12.4547	0.981570
$162$	1.00000	0.0785674
$163$	21.4209	1.67781	0.838906	−	0.544276i	$-0.183195\pi$
$163$	21.4209	1.67781	0.838906	+	0.544276i	$0.183195\pi$
$164$	−9.59179	−0.748993
$165$	−0.198062	−0.0154191
$166$	14.3545	1.11413
$167$	−10.8455	−0.839248	−0.419624	−	0.907698i	$-0.637838\pi$
$167$	−10.8455	−0.839248	−0.419624	+	0.907698i	$0.637838\pi$
$168$	−5.04892	−0.389532
$169$	−10.3002	−0.792324
$170$	−0.692021	−0.0530756
$171$	2.02715	0.155020
$172$	6.89977	0.526103
$173$	18.6528	1.41815	0.709073	−	0.705135i	$-0.249114\pi$
$173$	18.6528	1.41815	0.709073	+	0.705135i	$0.249114\pi$
$174$	−4.33513	−0.328645
$175$	25.0465	1.89334
$176$	1.00000	0.0753778
$177$	−10.0489	−0.755323
$178$	18.0954	1.35631
$179$	−14.7899	−1.10545	−0.552723	−	0.833365i	$-0.686411\pi$
$179$	−14.7899	−1.10545	−0.552723	+	0.833365i	$0.686411\pi$
$180$	−0.198062	−0.0147627
$181$	−17.4940	−1.30032	−0.650158	−	0.759799i	$-0.725297\pi$
$181$	−17.4940	−1.30032	−0.650158	+	0.759799i	$0.725297\pi$
$182$	8.29590	0.614933
$183$	1.00000	0.0739221
$184$	−2.46681	−0.181856
$185$	0.127375	0.00936477
$186$	−7.43296	−0.545011
$187$	3.49396	0.255504
$188$	−3.08815	−0.225226
$189$	−5.04892	−0.367255
$190$	−0.401501	−0.0291280
$191$	0.850855	0.0615657	0.0307829	−	0.999526i	$-0.490200\pi$
$191$	0.850855	0.0615657	0.0307829	+	0.999526i	$0.490200\pi$
$192$	1.00000	0.0721688
$193$	−13.4330	−0.966926	−0.483463	−	0.875365i	$-0.660621\pi$
$193$	−13.4330	−0.966926	−0.483463	+	0.875365i	$0.660621\pi$
$194$	−5.65279	−0.405847
$195$	0.325437	0.0233050
$196$	18.4916	1.32083
$197$	−9.06829	−0.646089	−0.323045	−	0.946384i	$-0.604706\pi$
$197$	−9.06829	−0.646089	−0.323045	+	0.946384i	$0.604706\pi$
$198$	1.00000	0.0710669
$199$	10.2935	0.729687	0.364844	−	0.931069i	$-0.381122\pi$
$199$	10.2935	0.729687	0.364844	+	0.931069i	$0.381122\pi$
$200$	−4.96077	−0.350780
$201$	2.26875	0.160025
$202$	−13.4601	−0.947050
$203$	21.8877	1.53621
$204$	3.49396	0.244626
$205$	1.89977	0.132686
$206$	9.00969	0.627735
$207$	−2.46681	−0.171455
$208$	−1.64310	−0.113929
$209$	2.02715	0.140221
$210$	1.00000	0.0690066
$211$	2.89008	0.198962	0.0994808	−	0.995039i	$-0.468282\pi$
$211$	2.89008	0.198962	0.0994808	+	0.995039i	$0.468282\pi$
$212$	−12.2295	−0.839927
$213$	−11.4330	−0.783374
$214$	7.64310	0.522472
$215$	−1.36658	−0.0932003
$216$	1.00000	0.0680414
$217$	37.5284	2.54759
$218$	−7.78448	−0.527231
$219$	−6.33513	−0.428088
$220$	−0.198062	−0.0133534
$221$	−5.74094	−0.386177
$222$	−0.643104	−0.0431623
$223$	0.0639828	0.00428461	0.00214230	−	0.999998i	$-0.499318\pi$
$223$	0.0639828	0.00428461	0.00214230	+	0.999998i	$0.499318\pi$
$224$	−5.04892	−0.337345
$225$	−4.96077	−0.330718
$226$	−3.47219	−0.230967
$227$	5.34721	0.354907	0.177453	−	0.984129i	$-0.443214\pi$
$227$	5.34721	0.354907	0.177453	+	0.984129i	$0.443214\pi$
$228$	2.02715	0.134251
$229$	23.3870	1.54546	0.772729	−	0.634736i	$-0.218891\pi$
$229$	23.3870	1.54546	0.772729	+	0.634736i	$0.218891\pi$
$230$	0.488582	0.0322162
$231$	−5.04892	−0.332194
$232$	−4.33513	−0.284615
$233$	15.6039	1.02224	0.511122	−	0.859508i	$-0.329230\pi$
$233$	15.6039	1.02224	0.511122	+	0.859508i	$0.329230\pi$
$234$	−1.64310	−0.107413
$235$	0.611645	0.0398993
$236$	−10.0489	−0.654129
$237$	1.34481	0.0873551
$238$	−17.6407	−1.14348
$239$	23.6256	1.52822	0.764108	−	0.645088i	$-0.223179\pi$
$239$	23.6256	1.52822	0.764108	+	0.645088i	$0.223179\pi$
$240$	−0.198062	−0.0127849
$241$	12.2664	0.790146	0.395073	−	0.918650i	$-0.370719\pi$
$241$	12.2664	0.790146	0.395073	+	0.918650i	$0.370719\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−3.66248	−0.233987
$246$	−9.59179	−0.611550
$247$	−3.33081	−0.211935
$248$	−7.43296	−0.471993
$249$	14.3545	0.909680
$250$	1.97285	0.124774
$251$	17.3230	1.09342	0.546710	−	0.837322i	$-0.315880\pi$
$251$	17.3230	1.09342	0.546710	+	0.837322i	$0.315880\pi$
$252$	−5.04892	−0.318052
$253$	−2.46681	−0.155087
$254$	−18.0858	−1.13480
$255$	−0.692021	−0.0433361
$256$	1.00000	0.0625000
$257$	−12.2795	−0.765974	−0.382987	−	0.923754i	$-0.625105\pi$
$257$	−12.2795	−0.765974	−0.382987	+	0.923754i	$0.625105\pi$
$258$	6.89977	0.429561
$259$	3.24698	0.201757
$260$	0.325437	0.0201827
$261$	−4.33513	−0.268338
$262$	−17.0954	−1.05616
$263$	24.3980	1.50445	0.752224	−	0.658908i	$-0.228981\pi$
$263$	24.3980	1.50445	0.752224	+	0.658908i	$0.228981\pi$
$264$	1.00000	0.0615457
$265$	2.42221	0.148795
$266$	−10.2349	−0.627542
$267$	18.0954	1.10742
$268$	2.26875	0.138586
$269$	25.0194	1.52546	0.762729	−	0.646718i	$-0.223859\pi$
$269$	25.0194	1.52546	0.762729	+	0.646718i	$0.223859\pi$
$270$	−0.198062	−0.0120537
$271$	−6.01639	−0.365470	−0.182735	−	0.983162i	$-0.558495\pi$
$271$	−6.01639	−0.365470	−0.182735	+	0.983162i	$0.558495\pi$
$272$	3.49396	0.211852
$273$	8.29590	0.502091
$274$	−8.03146	−0.485198
$275$	−4.96077	−0.299146
$276$	−2.46681	−0.148485
$277$	−14.1914	−0.852676	−0.426338	−	0.904564i	$-0.640197\pi$
$277$	−14.1914	−0.852676	−0.426338	+	0.904564i	$0.640197\pi$
$278$	−15.1250	−0.907136
$279$	−7.43296	−0.445000
$280$	1.00000	0.0597614
$281$	13.5972	0.811139	0.405570	−	0.914064i	$-0.367073\pi$
$281$	13.5972	0.811139	0.405570	+	0.914064i	$0.367073\pi$
$282$	−3.08815	−0.183896
$283$	−13.8092	−0.820874	−0.410437	−	0.911889i	$-0.634624\pi$
$283$	−13.8092	−0.820874	−0.410437	+	0.911889i	$0.634624\pi$
$284$	−11.4330	−0.678421
$285$	−0.401501	−0.0237829
$286$	−1.64310	−0.0971588
$287$	48.4282	2.85862
$288$	1.00000	0.0589256
$289$	−4.79225	−0.281897
$290$	0.858625	0.0504202
$291$	−5.65279	−0.331373
$292$	−6.33513	−0.370735
$293$	−20.1511	−1.17724	−0.588619	−	0.808411i	$-0.700328\pi$
$293$	−20.1511	−1.17724	−0.588619	+	0.808411i	$0.700328\pi$
$294$	18.4916	1.07845
$295$	1.99031	0.115880
$296$	−0.643104	−0.0373797
$297$	1.00000	0.0580259
$298$	8.65817	0.501554
$299$	4.05323	0.234404
$300$	−4.96077	−0.286410
$301$	−34.8364	−2.00794
$302$	19.6233	1.12919
$303$	−13.4601	−0.773263
$304$	2.02715	0.116265
$305$	−0.198062	−0.0113410
$306$	3.49396	0.199736
$307$	21.4198	1.22249	0.611247	−	0.791440i	$-0.290668\pi$
$307$	21.4198	1.22249	0.611247	+	0.791440i	$0.290668\pi$
$308$	−5.04892	−0.287689
$309$	9.00969	0.512543
$310$	1.47219	0.0836147
$311$	13.2107	0.749112	0.374556	−	0.927204i	$-0.377795\pi$
$311$	13.2107	0.749112	0.374556	+	0.927204i	$0.377795\pi$
$312$	−1.64310	−0.0930225
$313$	−18.0465	−1.02005	−0.510025	−	0.860160i	$-0.670364\pi$
$313$	−18.0465	−1.02005	−0.510025	+	0.860160i	$0.670364\pi$
$314$	−23.7385	−1.33964
$315$	1.00000	0.0563436
$316$	1.34481	0.0756517
$317$	14.2731	0.801655	0.400828	−	0.916154i	$-0.368723\pi$
$317$	14.2731	0.801655	0.400828	+	0.916154i	$0.368723\pi$
$318$	−12.2295	−0.685797
$319$	−4.33513	−0.242720
$320$	−0.198062	−0.0110720
$321$	7.64310	0.426596
$322$	12.4547	0.694075
$323$	7.08277	0.394096
$324$	1.00000	0.0555556
$325$	8.15106	0.452140
$326$	21.4209	1.18639
$327$	−7.78448	−0.430483
$328$	−9.59179	−0.529618
$329$	15.5918	0.859603
$330$	−0.198062	−0.0109030
$331$	−2.31229	−0.127095	−0.0635475	−	0.997979i	$-0.520241\pi$
$331$	−2.31229	−0.127095	−0.0635475	+	0.997979i	$0.520241\pi$
$332$	14.3545	0.787806
$333$	−0.643104	−0.0352419
$334$	−10.8455	−0.593438
$335$	−0.449354	−0.0245508
$336$	−5.04892	−0.275441
$337$	−22.7439	−1.23894	−0.619470	−	0.785020i	$-0.712653\pi$
$337$	−22.7439	−1.23894	−0.619470	+	0.785020i	$0.712653\pi$
$338$	−10.3002	−0.560257
$339$	−3.47219	−0.188583
$340$	−0.692021	−0.0375301
$341$	−7.43296	−0.402517
$342$	2.02715	0.109616
$343$	−58.0200	−3.13278
$344$	6.89977	0.372011
$345$	0.488582	0.0263044
$346$	18.6528	1.00278
$347$	17.7584	0.953321	0.476660	−	0.879088i	$-0.341847\pi$
$347$	17.7584	0.953321	0.476660	+	0.879088i	$0.341847\pi$
$348$	−4.33513	−0.232387
$349$	36.0737	1.93098	0.965490	−	0.260441i	$-0.0838681\pi$
$349$	36.0737	1.93098	0.965490	+	0.260441i	$0.0838681\pi$
$350$	25.0465	1.33879
$351$	−1.64310	−0.0877024
$352$	1.00000	0.0533002
$353$	−19.8582	−1.05694	−0.528471	−	0.848951i	$-0.677235\pi$
$353$	−19.8582	−1.05694	−0.528471	+	0.848951i	$0.677235\pi$
$354$	−10.0489	−0.534094
$355$	2.26444	0.120184
$356$	18.0954	0.959056
$357$	−17.6407	−0.933645
$358$	−14.7899	−0.781668
$359$	11.3177	0.597324	0.298662	−	0.954359i	$-0.403460\pi$
$359$	11.3177	0.597324	0.298662	+	0.954359i	$0.403460\pi$
$360$	−0.198062	−0.0104388
$361$	−14.8907	−0.783720
$362$	−17.4940	−0.919462
$363$	1.00000	0.0524864
$364$	8.29590	0.434823
$365$	1.25475	0.0656766
$366$	1.00000	0.0522708
$367$	30.2814	1.58068	0.790339	−	0.612670i	$-0.209905\pi$
$367$	30.2814	1.58068	0.790339	+	0.612670i	$0.209905\pi$
$368$	−2.46681	−0.128591
$369$	−9.59179	−0.499329
$370$	0.127375	0.00662189
$371$	61.7458	3.20568
$372$	−7.43296	−0.385381
$373$	−8.39075	−0.434456	−0.217228	−	0.976121i	$-0.569702\pi$
$373$	−8.39075	−0.434456	−0.217228	+	0.976121i	$0.569702\pi$
$374$	3.49396	0.180668
$375$	1.97285	0.101878
$376$	−3.08815	−0.159259
$377$	7.12306	0.366856
$378$	−5.04892	−0.259688
$379$	7.39612	0.379913	0.189957	−	0.981792i	$-0.439165\pi$
$379$	7.39612	0.379913	0.189957	+	0.981792i	$0.439165\pi$
$380$	−0.401501	−0.0205966
$381$	−18.0858	−0.926561
$382$	0.850855	0.0435335
$383$	6.42758	0.328434	0.164217	−	0.986424i	$-0.447490\pi$
$383$	6.42758	0.328434	0.164217	+	0.986424i	$0.447490\pi$
$384$	1.00000	0.0510310
$385$	1.00000	0.0509647
$386$	−13.4330	−0.683720
$387$	6.89977	0.350735
$388$	−5.65279	−0.286977
$389$	−14.8485	−0.752847	−0.376423	−	0.926448i	$-0.622846\pi$
$389$	−14.8485	−0.752847	−0.376423	+	0.926448i	$0.622846\pi$
$390$	0.325437	0.0164791
$391$	−8.61894	−0.435879
$392$	18.4916	0.933965
$393$	−17.0954	−0.862351
$394$	−9.06829	−0.456854
$395$	−0.266357	−0.0134019
$396$	1.00000	0.0502519
$397$	10.0683	0.505313	0.252657	−	0.967556i	$-0.418696\pi$
$397$	10.0683	0.505313	0.252657	+	0.967556i	$0.418696\pi$
$398$	10.2935	0.515967
$399$	−10.2349	−0.512386
$400$	−4.96077	−0.248039
$401$	14.8901	0.743575	0.371788	−	0.928318i	$-0.378745\pi$
$401$	14.8901	0.743575	0.371788	+	0.928318i	$0.378745\pi$
$402$	2.26875	0.113155
$403$	12.2131	0.608379
$404$	−13.4601	−0.669665
$405$	−0.198062	−0.00984179
$406$	21.8877	1.08627
$407$	−0.643104	−0.0318775
$408$	3.49396	0.172977
$409$	38.3075	1.89418	0.947092	−	0.320962i	$-0.104006\pi$
$409$	38.3075	1.89418	0.947092	+	0.320962i	$0.104006\pi$
$410$	1.89977	0.0938231
$411$	−8.03146	−0.396163
$412$	9.00969	0.443876
$413$	50.7362	2.49656
$414$	−2.46681	−0.121237
$415$	−2.84309	−0.139562
$416$	−1.64310	−0.0805598
$417$	−15.1250	−0.740674
$418$	2.02715	0.0991510
$419$	−35.9259	−1.75509	−0.877546	−	0.479492i	$-0.840821\pi$
$419$	−35.9259	−1.75509	−0.877546	+	0.479492i	$0.840821\pi$
$420$	1.00000	0.0487950
$421$	−25.1564	−1.22605	−0.613025	−	0.790064i	$-0.710047\pi$
$421$	−25.1564	−1.22605	−0.613025	+	0.790064i	$0.710047\pi$
$422$	2.89008	0.140687
$423$	−3.08815	−0.150151
$424$	−12.2295	−0.593918
$425$	−17.3327	−0.840761
$426$	−11.4330	−0.553929
$427$	−5.04892	−0.244334
$428$	7.64310	0.369443
$429$	−1.64310	−0.0793298
$430$	−1.36658	−0.0659026
$431$	20.0508	0.965815	0.482907	−	0.875671i	$-0.339581\pi$
$431$	20.0508	0.965815	0.482907	+	0.875671i	$0.339581\pi$
$432$	1.00000	0.0481125
$433$	−10.0207	−0.481564	−0.240782	−	0.970579i	$-0.577404\pi$
$433$	−10.0207	−0.481564	−0.240782	+	0.970579i	$0.577404\pi$
$434$	37.5284	1.80142
$435$	0.858625	0.0411679
$436$	−7.78448	−0.372809
$437$	−5.00059	−0.239211
$438$	−6.33513	−0.302704
$439$	22.3521	1.06681	0.533404	−	0.845861i	$-0.320913\pi$
$439$	22.3521	1.06681	0.533404	+	0.845861i	$0.320913\pi$
$440$	−0.198062	−0.00944225
$441$	18.4916	0.880551
$442$	−5.74094	−0.273069
$443$	26.2204	1.24577	0.622885	−	0.782313i	$-0.285960\pi$
$443$	26.2204	1.24577	0.622885	+	0.782313i	$0.285960\pi$
$444$	−0.643104	−0.0305204
$445$	−3.58402	−0.169899
$446$	0.0639828	0.00302967
$447$	8.65817	0.409517
$448$	−5.04892	−0.238539
$449$	−36.8297	−1.73810	−0.869050	−	0.494724i	$-0.835269\pi$
$449$	−36.8297	−1.73810	−0.869050	+	0.494724i	$0.835269\pi$
$450$	−4.96077	−0.233853
$451$	−9.59179	−0.451660
$452$	−3.47219	−0.163318
$453$	19.6233	0.921981
$454$	5.34721	0.250957
$455$	−1.64310	−0.0770299
$456$	2.02715	0.0949299
$457$	38.0006	1.77759	0.888796	−	0.458302i	$-0.151542\pi$
$457$	38.0006	1.77759	0.888796	+	0.458302i	$0.151542\pi$
$458$	23.3870	1.09280
$459$	3.49396	0.163084
$460$	0.488582	0.0227803
$461$	26.9202	1.25380	0.626900	−	0.779100i	$-0.284324\pi$
$461$	26.9202	1.25380	0.626900	+	0.779100i	$0.284324\pi$
$462$	−5.04892	−0.234897
$463$	12.0586	0.560411	0.280205	−	0.959940i	$-0.409597\pi$
$463$	12.0586	0.560411	0.280205	+	0.959940i	$0.409597\pi$
$464$	−4.33513	−0.201253
$465$	1.47219	0.0682711
$466$	15.6039	0.722836
$467$	−34.5599	−1.59924	−0.799620	−	0.600507i	$-0.794966\pi$
$467$	−34.5599	−1.59924	−0.799620	+	0.600507i	$0.794966\pi$
$468$	−1.64310	−0.0759525
$469$	−11.4547	−0.528930
$470$	0.611645	0.0282131
$471$	−23.7385	−1.09381
$472$	−10.0489	−0.462539
$473$	6.89977	0.317252
$474$	1.34481	0.0617694
$475$	−10.0562	−0.461411
$476$	−17.6407	−0.808561
$477$	−12.2295	−0.559951
$478$	23.6256	1.08061
$479$	−17.1545	−0.783810	−0.391905	−	0.920006i	$-0.628184\pi$
$479$	−17.1545	−0.783810	−0.391905	+	0.920006i	$0.628184\pi$
$480$	−0.198062	−0.00904026
$481$	1.05669	0.0481808
$482$	12.2664	0.558717
$483$	12.4547	0.566710
$484$	1.00000	0.0454545
$485$	1.11960	0.0508386
$486$	1.00000	0.0453609
$487$	39.5623	1.79274	0.896368	−	0.443310i	$-0.146196\pi$
$487$	39.5623	1.79274	0.896368	+	0.443310i	$0.146196\pi$
$488$	1.00000	0.0452679
$489$	21.4209	0.968686
$490$	−3.66248	−0.165454
$491$	−7.37435	−0.332800	−0.166400	−	0.986058i	$-0.553214\pi$
$491$	−7.37435	−0.332800	−0.166400	+	0.986058i	$0.553214\pi$
$492$	−9.59179	−0.432431
$493$	−15.1468	−0.682175
$494$	−3.33081	−0.149860
$495$	−0.198062	−0.00890224
$496$	−7.43296	−0.333750
$497$	57.7241	2.58928
$498$	14.3545	0.643241
$499$	−25.1202	−1.12453	−0.562267	−	0.826956i	$-0.690071\pi$
$499$	−25.1202	−1.12453	−0.562267	+	0.826956i	$0.690071\pi$
$500$	1.97285	0.0882287
$501$	−10.8455	−0.484540
$502$	17.3230	0.773165
$503$	−12.2204	−0.544882	−0.272441	−	0.962173i	$-0.587831\pi$
$503$	−12.2204	−0.544882	−0.272441	+	0.962173i	$0.587831\pi$
$504$	−5.04892	−0.224897
$505$	2.66594	0.118633
$506$	−2.46681	−0.109663
$507$	−10.3002	−0.457448
$508$	−18.0858	−0.802426
$509$	−30.3749	−1.34635	−0.673173	−	0.739485i	$-0.735069\pi$
$509$	−30.3749	−1.34635	−0.673173	+	0.739485i	$0.735069\pi$
$510$	−0.692021	−0.0306432
$511$	31.9855	1.41496
$512$	1.00000	0.0441942
$513$	2.02715	0.0895007
$514$	−12.2795	−0.541626
$515$	−1.78448	−0.0786336
$516$	6.89977	0.303746
$517$	−3.08815	−0.135817
$518$	3.24698	0.142664
$519$	18.6528	0.818767
$520$	0.325437	0.0142714
$521$	30.5066	1.33652	0.668260	−	0.743928i	$-0.267039\pi$
$521$	30.5066	1.33652	0.668260	+	0.743928i	$0.267039\pi$
$522$	−4.33513	−0.189743
$523$	−37.2476	−1.62872	−0.814361	−	0.580358i	$-0.802913\pi$
$523$	−37.2476	−1.62872	−0.814361	+	0.580358i	$0.802913\pi$
$524$	−17.0954	−0.746818
$525$	25.0465	1.09312
$526$	24.3980	1.06381
$527$	−25.9705	−1.13129
$528$	1.00000	0.0435194
$529$	−16.9148	−0.735428
$530$	2.42221	0.105214
$531$	−10.0489	−0.436086
$532$	−10.2349	−0.443739
$533$	15.7603	0.682655
$534$	18.0954	0.783066
$535$	−1.51381	−0.0654477
$536$	2.26875	0.0979951
$537$	−14.7899	−0.638229
$538$	25.0194	1.07866
$539$	18.4916	0.796488
$540$	−0.198062	−0.00852324
$541$	−3.82477	−0.164440	−0.0822199	−	0.996614i	$-0.526201\pi$
$541$	−3.82477	−0.164440	−0.0822199	+	0.996614i	$0.526201\pi$
$542$	−6.01639	−0.258426
$543$	−17.4940	−0.750738
$544$	3.49396	0.149802
$545$	1.54181	0.0660440
$546$	8.29590	0.355032
$547$	11.2905	0.482748	0.241374	−	0.970432i	$-0.422402\pi$
$547$	11.2905	0.482748	0.241374	+	0.970432i	$0.422402\pi$
$548$	−8.03146	−0.343087
$549$	1.00000	0.0426790
$550$	−4.96077	−0.211528
$551$	−8.78794	−0.374379
$552$	−2.46681	−0.104994
$553$	−6.78986	−0.288734
$554$	−14.1914	−0.602933
$555$	0.127375	0.00540675
$556$	−15.1250	−0.641442
$557$	44.5730	1.88862	0.944309	−	0.329059i	$-0.106731\pi$
$557$	44.5730	1.88862	0.944309	+	0.329059i	$0.106731\pi$
$558$	−7.43296	−0.314662
$559$	−11.3370	−0.479506
$560$	1.00000	0.0422577
$561$	3.49396	0.147515
$562$	13.5972	0.573562
$563$	23.3913	0.985827	0.492914	−	0.870078i	$-0.335932\pi$
$563$	23.3913	0.985827	0.492914	+	0.870078i	$0.335932\pi$
$564$	−3.08815	−0.130034
$565$	0.687710	0.0289322
$566$	−13.8092	−0.580445
$567$	−5.04892	−0.212035
$568$	−11.4330	−0.479716
$569$	7.57912	0.317733	0.158867	−	0.987300i	$-0.449216\pi$
$569$	7.57912	0.317733	0.158867	+	0.987300i	$0.449216\pi$
$570$	−0.401501	−0.0168170
$571$	−39.9057	−1.67000	−0.835002	−	0.550247i	$-0.814533\pi$
$571$	−39.9057	−1.67000	−0.835002	+	0.550247i	$0.814533\pi$
$572$	−1.64310	−0.0687016
$573$	0.850855	0.0355450
$574$	48.4282	2.02135
$575$	12.2373	0.510330
$576$	1.00000	0.0416667
$577$	−15.0151	−0.625085	−0.312543	−	0.949904i	$-0.601181\pi$
$577$	−15.0151	−0.625085	−0.312543	+	0.949904i	$0.601181\pi$
$578$	−4.79225	−0.199331
$579$	−13.4330	−0.558255
$580$	0.858625	0.0356525
$581$	−72.4747	−3.00676
$582$	−5.65279	−0.234316
$583$	−12.2295	−0.506495
$584$	−6.33513	−0.262149
$585$	0.325437	0.0134552
$586$	−20.1511	−0.832433
$587$	−12.3338	−0.509070	−0.254535	−	0.967064i	$-0.581922\pi$
$587$	−12.3338	−0.509070	−0.254535	+	0.967064i	$0.581922\pi$
$588$	18.4916	0.762579
$589$	−15.0677	−0.620854
$590$	1.99031	0.0819398
$591$	−9.06829	−0.373020
$592$	−0.643104	−0.0264314
$593$	12.1424	0.498630	0.249315	−	0.968422i	$-0.419795\pi$
$593$	12.1424	0.498630	0.249315	+	0.968422i	$0.419795\pi$
$594$	1.00000	0.0410305
$595$	3.49396	0.143238
$596$	8.65817	0.354652
$597$	10.2935	0.421285
$598$	4.05323	0.165749
$599$	−38.9353	−1.59085	−0.795426	−	0.606050i	$-0.792753\pi$
$599$	−38.9353	−1.59085	−0.795426	+	0.606050i	$0.792753\pi$
$600$	−4.96077	−0.202523
$601$	24.6969	1.00741	0.503704	−	0.863876i	$-0.331970\pi$
$601$	24.6969	1.00741	0.503704	+	0.863876i	$0.331970\pi$
$602$	−34.8364	−1.41982
$603$	2.26875	0.0923906
$604$	19.6233	0.798459
$605$	−0.198062	−0.00805238
$606$	−13.4601	−0.546779
$607$	21.2946	0.864320	0.432160	−	0.901797i	$-0.357752\pi$
$607$	21.2946	0.864320	0.432160	+	0.901797i	$0.357752\pi$
$608$	2.02715	0.0822117
$609$	21.8877	0.886934
$610$	−0.198062	−0.00801931
$611$	5.07415	0.205278
$612$	3.49396	0.141235
$613$	−35.8896	−1.44957	−0.724784	−	0.688976i	$-0.758060\pi$
$613$	−35.8896	−1.44957	−0.724784	+	0.688976i	$0.758060\pi$
$614$	21.4198	0.864433
$615$	1.89977	0.0766062
$616$	−5.04892	−0.203427
$617$	−30.6829	−1.23525	−0.617624	−	0.786474i	$-0.711905\pi$
$617$	−30.6829	−1.23525	−0.617624	+	0.786474i	$0.711905\pi$
$618$	9.00969	0.362423
$619$	−22.5351	−0.905762	−0.452881	−	0.891571i	$-0.649604\pi$
$619$	−22.5351	−0.905762	−0.452881	+	0.891571i	$0.649604\pi$
$620$	1.47219	0.0591245
$621$	−2.46681	−0.0989898
$622$	13.2107	0.529702
$623$	−91.3624	−3.66036
$624$	−1.64310	−0.0657768
$625$	24.4131	0.976524
$626$	−18.0465	−0.721284
$627$	2.02715	0.0809565
$628$	−23.7385	−0.947271
$629$	−2.24698	−0.0895929
$630$	1.00000	0.0398410
$631$	−19.1347	−0.761739	−0.380870	−	0.924629i	$-0.624375\pi$
$631$	−19.1347	−0.761739	−0.380870	+	0.924629i	$0.624375\pi$
$632$	1.34481	0.0534938
$633$	2.89008	0.114871
$634$	14.2731	0.566856
$635$	3.58211	0.142152
$636$	−12.2295	−0.484932
$637$	−30.3836	−1.20384
$638$	−4.33513	−0.171629
$639$	−11.4330	−0.452281
$640$	−0.198062	−0.00782910
$641$	6.48321	0.256071	0.128036	−	0.991770i	$-0.459133\pi$
$641$	6.48321	0.256071	0.128036	+	0.991770i	$0.459133\pi$
$642$	7.64310	0.301649
$643$	−21.9734	−0.866548	−0.433274	−	0.901262i	$-0.642642\pi$
$643$	−21.9734	−0.866548	−0.433274	+	0.901262i	$0.642642\pi$
$644$	12.4547	0.490785
$645$	−1.36658	−0.0538092
$646$	7.08277	0.278668
$647$	4.97823	0.195714	0.0978572	−	0.995200i	$-0.468801\pi$
$647$	4.97823	0.195714	0.0978572	+	0.995200i	$0.468801\pi$
$648$	1.00000	0.0392837
$649$	−10.0489	−0.394455
$650$	8.15106	0.319711
$651$	37.5284	1.47085
$652$	21.4209	0.838906
$653$	−29.2935	−1.14634	−0.573172	−	0.819435i	$-0.694287\pi$
$653$	−29.2935	−1.14634	−0.573172	+	0.819435i	$0.694287\pi$
$654$	−7.78448	−0.304397
$655$	3.38596	0.132300
$656$	−9.59179	−0.374497
$657$	−6.33513	−0.247157
$658$	15.5918	0.607831
$659$	36.6848	1.42904	0.714519	−	0.699616i	$-0.246645\pi$
$659$	36.6848	1.42904	0.714519	+	0.699616i	$0.246645\pi$
$660$	−0.198062	−0.00770956
$661$	−30.0271	−1.16792	−0.583960	−	0.811782i	$-0.698498\pi$
$661$	−30.0271	−1.16792	−0.583960	+	0.811782i	$0.698498\pi$
$662$	−2.31229	−0.0898697
$663$	−5.74094	−0.222960
$664$	14.3545	0.557063
$665$	2.02715	0.0786094
$666$	−0.643104	−0.0249198
$667$	10.6939	0.414071
$668$	−10.8455	−0.419624
$669$	0.0639828	0.00247372
$670$	−0.449354	−0.0173600
$671$	1.00000	0.0386046
$672$	−5.04892	−0.194766
$673$	−16.2368	−0.625883	−0.312942	−	0.949772i	$-0.601314\pi$
$673$	−16.2368	−0.625883	−0.312942	+	0.949772i	$0.601314\pi$
$674$	−22.7439	−0.876063
$675$	−4.96077	−0.190940
$676$	−10.3002	−0.396162
$677$	−19.7041	−0.757290	−0.378645	−	0.925542i	$-0.623610\pi$
$677$	−19.7041	−0.757290	−0.378645	+	0.925542i	$0.623610\pi$
$678$	−3.47219	−0.133349
$679$	28.5405	1.09528
$680$	−0.692021	−0.0265378
$681$	5.34721	0.204905
$682$	−7.43296	−0.284623
$683$	−15.5690	−0.595730	−0.297865	−	0.954608i	$-0.596274\pi$
$683$	−15.5690	−0.595730	−0.297865	+	0.954608i	$0.596274\pi$
$684$	2.02715	0.0775099
$685$	1.59073	0.0607786
$686$	−58.0200	−2.21521
$687$	23.3870	0.892271
$688$	6.89977	0.263051
$689$	20.0944	0.765535
$690$	0.488582	0.0186000
$691$	42.8015	1.62824	0.814122	−	0.580694i	$-0.197219\pi$
$691$	42.8015	1.62824	0.814122	+	0.580694i	$0.197219\pi$
$692$	18.6528	0.709073
$693$	−5.04892	−0.191793
$694$	17.7584	0.674100
$695$	2.99569	0.113633
$696$	−4.33513	−0.164323
$697$	−33.5133	−1.26941
$698$	36.0737	1.36541
$699$	15.6039	0.590193
$700$	25.0465	0.946670
$701$	52.2228	1.97243	0.986214	−	0.165473i	$-0.0529152\pi$
$701$	52.2228	1.97243	0.986214	+	0.165473i	$0.0529152\pi$
$702$	−1.64310	−0.0620150
$703$	−1.30367	−0.0491687
$704$	1.00000	0.0376889
$705$	0.611645	0.0230359
$706$	−19.8582	−0.747371
$707$	67.9590	2.55586
$708$	−10.0489	−0.377661
$709$	28.6655	1.07655	0.538277	−	0.842768i	$-0.319075\pi$
$709$	28.6655	1.07655	0.538277	+	0.842768i	$0.319075\pi$
$710$	2.26444	0.0849828
$711$	1.34481	0.0504345
$712$	18.0954	0.678155
$713$	18.3357	0.686678
$714$	−17.6407	−0.660187
$715$	0.325437	0.0121707
$716$	−14.7899	−0.552723
$717$	23.6256	0.882316
$718$	11.3177	0.422372
$719$	−16.1457	−0.602133	−0.301066	−	0.953603i	$-0.597343\pi$
$719$	−16.1457	−0.602133	−0.301066	+	0.953603i	$0.597343\pi$
$720$	−0.198062	−0.00738134
$721$	−45.4892	−1.69411
$722$	−14.8907	−0.554174
$723$	12.2664	0.456191
$724$	−17.4940	−0.650158
$725$	21.5056	0.798697
$726$	1.00000	0.0371135
$727$	17.6528	0.654706	0.327353	−	0.944902i	$-0.393843\pi$
$727$	17.6528	0.654706	0.327353	+	0.944902i	$0.393843\pi$
$728$	8.29590	0.307466
$729$	1.00000	0.0370370
$730$	1.25475	0.0464404
$731$	24.1075	0.891649
$732$	1.00000	0.0369611
$733$	6.89067	0.254513	0.127256	−	0.991870i	$-0.459383\pi$
$733$	6.89067	0.254513	0.127256	+	0.991870i	$0.459383\pi$
$734$	30.2814	1.11771
$735$	−3.66248	−0.135093
$736$	−2.46681	−0.0909279
$737$	2.26875	0.0835705
$738$	−9.59179	−0.353079
$739$	−26.2107	−0.964177	−0.482089	−	0.876122i	$-0.660122\pi$
$739$	−26.2107	−0.964177	−0.482089	+	0.876122i	$0.660122\pi$
$740$	0.127375	0.00468239
$741$	−3.33081	−0.122361
$742$	61.7458	2.26676
$743$	42.9724	1.57650	0.788252	−	0.615353i	$-0.210986\pi$
$743$	42.9724	1.57650	0.788252	+	0.615353i	$0.210986\pi$
$744$	−7.43296	−0.272506
$745$	−1.71486	−0.0628275
$746$	−8.39075	−0.307207
$747$	14.3545	0.525204
$748$	3.49396	0.127752
$749$	−38.5894	−1.41003
$750$	1.97285	0.0720384
$751$	−25.8756	−0.944214	−0.472107	−	0.881541i	$-0.656506\pi$
$751$	−25.8756	−0.944214	−0.472107	+	0.881541i	$0.656506\pi$
$752$	−3.08815	−0.112613
$753$	17.3230	0.631287
$754$	7.12306	0.259407
$755$	−3.88663	−0.141449
$756$	−5.04892	−0.183627
$757$	23.0731	0.838605	0.419303	−	0.907846i	$-0.362275\pi$
$757$	23.0731	0.838605	0.419303	+	0.907846i	$0.362275\pi$
$758$	7.39612	0.268639
$759$	−2.46681	−0.0895396
$760$	−0.401501	−0.0145640
$761$	−35.2314	−1.27714	−0.638569	−	0.769564i	$-0.720473\pi$
$761$	−35.2314	−1.27714	−0.638569	+	0.769564i	$0.720473\pi$
$762$	−18.0858	−0.655178
$763$	39.3032	1.42287
$764$	0.850855	0.0307829
$765$	−0.692021	−0.0250201
$766$	6.42758	0.232238
$767$	16.5114	0.596193
$768$	1.00000	0.0360844
$769$	−29.9922	−1.08155	−0.540774	−	0.841168i	$-0.681868\pi$
$769$	−29.9922	−1.08155	−0.540774	+	0.841168i	$0.681868\pi$
$770$	1.00000	0.0360375
$771$	−12.2795	−0.442236
$772$	−13.4330	−0.483463
$773$	−1.58402	−0.0569734	−0.0284867	−	0.999594i	$-0.509069\pi$
$773$	−1.58402	−0.0569734	−0.0284867	+	0.999594i	$0.509069\pi$
$774$	6.89977	0.248007
$775$	36.8732	1.32453
$776$	−5.65279	−0.202923
$777$	3.24698	0.116485
$778$	−14.8485	−0.532343
$779$	−19.4440	−0.696653
$780$	0.325437	0.0116525
$781$	−11.4330	−0.409103
$782$	−8.61894	−0.308213
$783$	−4.33513	−0.154925
$784$	18.4916	0.660413
$785$	4.70171	0.167811
$786$	−17.0954	−0.609774
$787$	11.4252	0.407264	0.203632	−	0.979047i	$-0.434725\pi$
$787$	11.4252	0.407264	0.203632	+	0.979047i	$0.434725\pi$
$788$	−9.06829	−0.323045
$789$	24.3980	0.868593
$790$	−0.266357	−0.00947656
$791$	17.5308	0.623323
$792$	1.00000	0.0355335
$793$	−1.64310	−0.0583483
$794$	10.0683	0.357310
$795$	2.42221	0.0859068
$796$	10.2935	0.364844
$797$	50.0732	1.77368	0.886842	−	0.462073i	$-0.152894\pi$
$797$	50.0732	1.77368	0.886842	+	0.462073i	$0.152894\pi$
$798$	−10.2349	−0.362311
$799$	−10.7899	−0.381718
$800$	−4.96077	−0.175390
$801$	18.0954	0.639371
$802$	14.8901	0.525787
$803$	−6.33513	−0.223562
$804$	2.26875	0.0800126
$805$	−2.46681	−0.0869437
$806$	12.2131	0.430189
$807$	25.0194	0.880724
$808$	−13.4601	−0.473525
$809$	−8.72455	−0.306739	−0.153369	−	0.988169i	$-0.549012\pi$
$809$	−8.72455	−0.306739	−0.153369	+	0.988169i	$0.549012\pi$
$810$	−0.198062	−0.00695920
$811$	−17.8412	−0.626488	−0.313244	−	0.949673i	$-0.601416\pi$
$811$	−17.8412	−0.626488	−0.313244	+	0.949673i	$0.601416\pi$
$812$	21.8877	0.768107
$813$	−6.01639	−0.211004
$814$	−0.643104	−0.0225408
$815$	−4.24267	−0.148614
$816$	3.49396	0.122313
$817$	13.9869	0.489338
$818$	38.3075	1.33939
$819$	8.29590	0.289882
$820$	1.89977	0.0663429
$821$	−15.3612	−0.536110	−0.268055	−	0.963404i	$-0.586381\pi$
$821$	−15.3612	−0.536110	−0.268055	+	0.963404i	$0.586381\pi$
$822$	−8.03146	−0.280129
$823$	−4.49157	−0.156566	−0.0782831	−	0.996931i	$-0.524944\pi$
$823$	−4.49157	−0.156566	−0.0782831	+	0.996931i	$0.524944\pi$
$824$	9.00969	0.313867
$825$	−4.96077	−0.172712
$826$	50.7362	1.76534
$827$	4.72289	0.164231	0.0821155	−	0.996623i	$-0.473832\pi$
$827$	4.72289	0.164231	0.0821155	+	0.996623i	$0.473832\pi$
$828$	−2.46681	−0.0857276
$829$	−33.1696	−1.15203	−0.576014	−	0.817440i	$-0.695393\pi$
$829$	−33.1696	−1.15203	−0.576014	+	0.817440i	$0.695393\pi$
$830$	−2.84309	−0.0986849
$831$	−14.1914	−0.492293
$832$	−1.64310	−0.0569644
$833$	64.6088	2.23856
$834$	−15.1250	−0.523735
$835$	2.14808	0.0743374
$836$	2.02715	0.0701103
$837$	−7.43296	−0.256921
$838$	−35.9259	−1.24104
$839$	−32.4698	−1.12098	−0.560491	−	0.828161i	$-0.689388\pi$
$839$	−32.4698	−1.12098	−0.560491	+	0.828161i	$0.689388\pi$
$840$	1.00000	0.0345033
$841$	−10.2067	−0.351955
$842$	−25.1564	−0.866948
$843$	13.5972	0.468311
$844$	2.89008	0.0994808
$845$	2.04008	0.0701810
$846$	−3.08815	−0.106173
$847$	−5.04892	−0.173483
$848$	−12.2295	−0.419963
$849$	−13.8092	−0.473932
$850$	−17.3327	−0.594508
$851$	1.58642	0.0543817
$852$	−11.4330	−0.391687
$853$	−27.7047	−0.948591	−0.474295	−	0.880366i	$-0.657297\pi$
$853$	−27.7047	−0.948591	−0.474295	+	0.880366i	$0.657297\pi$
$854$	−5.04892	−0.172770
$855$	−0.401501	−0.0137311
$856$	7.64310	0.261236
$857$	−7.58211	−0.259000	−0.129500	−	0.991579i	$-0.541337\pi$
$857$	−7.58211	−0.259000	−0.129500	+	0.991579i	$0.541337\pi$
$858$	−1.64310	−0.0560947
$859$	−13.4474	−0.458821	−0.229410	−	0.973330i	$-0.573680\pi$
$859$	−13.4474	−0.458821	−0.229410	+	0.973330i	$0.573680\pi$
$860$	−1.36658	−0.0466001
$861$	48.4282	1.65043
$862$	20.0508	0.682934
$863$	−24.0954	−0.820218	−0.410109	−	0.912036i	$-0.634509\pi$
$863$	−24.0954	−0.820218	−0.410109	+	0.912036i	$0.634509\pi$
$864$	1.00000	0.0340207
$865$	−3.69441	−0.125614
$866$	−10.0207	−0.340517
$867$	−4.79225	−0.162753
$868$	37.5284	1.27380
$869$	1.34481	0.0456197
$870$	0.858625	0.0291101
$871$	−3.72779	−0.126311
$872$	−7.78448	−0.263616
$873$	−5.65279	−0.191318
$874$	−5.00059	−0.169148
$875$	−9.96077	−0.336736
$876$	−6.33513	−0.214044
$877$	56.3997	1.90448	0.952241	−	0.305347i	$-0.0987723\pi$
$877$	56.3997	1.90448	0.952241	+	0.305347i	$0.0987723\pi$
$878$	22.3521	0.754347
$879$	−20.1511	−0.679679
$880$	−0.198062	−0.00667668
$881$	−30.2174	−1.01805	−0.509026	−	0.860751i	$-0.669994\pi$
$881$	−30.2174	−1.01805	−0.509026	+	0.860751i	$0.669994\pi$
$882$	18.4916	0.622643
$883$	11.1263	0.374430	0.187215	−	0.982319i	$-0.440054\pi$
$883$	11.1263	0.374430	0.187215	+	0.982319i	$0.440054\pi$
$884$	−5.74094	−0.193089
$885$	1.99031	0.0669036
$886$	26.2204	0.880892
$887$	19.9715	0.670578	0.335289	−	0.942115i	$-0.391166\pi$
$887$	19.9715	0.670578	0.335289	+	0.942115i	$0.391166\pi$
$888$	−0.643104	−0.0215812
$889$	91.3135	3.06256
$890$	−3.58402	−0.120137
$891$	1.00000	0.0335013
$892$	0.0639828	0.00214230
$893$	−6.26013	−0.209487
$894$	8.65817	0.289573
$895$	2.92931	0.0979161
$896$	−5.04892	−0.168672
$897$	4.05323	0.135333
$898$	−36.8297	−1.22902
$899$	32.2228	1.07469
$900$	−4.96077	−0.165359
$901$	−42.7294	−1.42352
$902$	−9.59179	−0.319372
$903$	−34.8364	−1.15928
$904$	−3.47219	−0.115483
$905$	3.46489	0.115177
$906$	19.6233	0.651939
$907$	−49.7120	−1.65066	−0.825330	−	0.564651i	$-0.809011\pi$
$907$	−49.7120	−1.65066	−0.825330	+	0.564651i	$0.809011\pi$
$908$	5.34721	0.177453
$909$	−13.4601	−0.446444
$910$	−1.64310	−0.0544684
$911$	−40.8562	−1.35363	−0.676814	−	0.736154i	$-0.736640\pi$
$911$	−40.8562	−1.35363	−0.676814	+	0.736154i	$0.736640\pi$
$912$	2.02715	0.0671255
$913$	14.3545	0.475065
$914$	38.0006	1.25695
$915$	−0.198062	−0.00654774
$916$	23.3870	0.772729
$917$	86.3135	2.85032
$918$	3.49396	0.115318
$919$	−35.2640	−1.16325	−0.581625	−	0.813457i	$-0.697583\pi$
$919$	−35.2640	−1.16325	−0.581625	+	0.813457i	$0.697583\pi$
$920$	0.488582	0.0161081
$921$	21.4198	0.705807
$922$	26.9202	0.886570
$923$	18.7855	0.618334
$924$	−5.04892	−0.166097
$925$	3.19029	0.104896
$926$	12.0586	0.396270
$927$	9.00969	0.295917
$928$	−4.33513	−0.142307
$929$	−45.2103	−1.48330	−0.741650	−	0.670787i	$-0.765957\pi$
$929$	−45.2103	−1.48330	−0.741650	+	0.670787i	$0.765957\pi$
$930$	1.47219	0.0482750
$931$	37.4851	1.22853
$932$	15.6039	0.511122
$933$	13.2107	0.432500
$934$	−34.5599	−1.13083
$935$	−0.692021	−0.0226315
$936$	−1.64310	−0.0537065
$937$	14.3784	0.469722	0.234861	−	0.972029i	$-0.424537\pi$
$937$	14.3784	0.469722	0.234861	+	0.972029i	$0.424537\pi$
$938$	−11.4547	−0.374010
$939$	−18.0465	−0.588926
$940$	0.611645	0.0199497
$941$	−33.7332	−1.09967	−0.549835	−	0.835273i	$-0.685309\pi$
$941$	−33.7332	−1.09967	−0.549835	+	0.835273i	$0.685309\pi$
$942$	−23.7385	−0.773444
$943$	23.6612	0.770513
$944$	−10.0489	−0.327064
$945$	1.00000	0.0325300
$946$	6.89977	0.224331
$947$	23.9038	0.776770	0.388385	−	0.921497i	$-0.373033\pi$
$947$	23.9038	0.776770	0.388385	+	0.921497i	$0.373033\pi$
$948$	1.34481	0.0436775
$949$	10.4093	0.337899
$950$	−10.0562	−0.326267
$951$	14.2731	0.462836
$952$	−17.6407	−0.571739
$953$	51.6829	1.67417	0.837087	−	0.547070i	$-0.184257\pi$
$953$	51.6829	1.67417	0.837087	+	0.547070i	$0.184257\pi$
$954$	−12.2295	−0.395945
$955$	−0.168522	−0.00545325
$956$	23.6256	0.764108
$957$	−4.33513	−0.140135
$958$	−17.1545	−0.554237
$959$	40.5502	1.30943
$960$	−0.198062	−0.00639243
$961$	24.2489	0.782223
$962$	1.05669	0.0340690
$963$	7.64310	0.246296
$964$	12.2664	0.395073
$965$	2.66056	0.0856465
$966$	12.4547	0.400724
$967$	43.6515	1.40374	0.701868	−	0.712307i	$-0.252350\pi$
$967$	43.6515	1.40374	0.701868	+	0.712307i	$0.252350\pi$
$968$	1.00000	0.0321412
$969$	7.08277	0.227531
$970$	1.11960	0.0359483
$971$	16.3907	0.526004	0.263002	−	0.964795i	$-0.415287\pi$
$971$	16.3907	0.526004	0.263002	+	0.964795i	$0.415287\pi$
$972$	1.00000	0.0320750
$973$	76.3648	2.44814
$974$	39.5623	1.26766
$975$	8.15106	0.261043
$976$	1.00000	0.0320092
$977$	26.0713	0.834094	0.417047	−	0.908885i	$-0.363065\pi$
$977$	26.0713	0.834094	0.417047	+	0.908885i	$0.363065\pi$
$978$	21.4209	0.684964
$979$	18.0954	0.578333
$980$	−3.66248	−0.116994
$981$	−7.78448	−0.248539
$982$	−7.37435	−0.235325
$983$	16.7918	0.535574	0.267787	−	0.963478i	$-0.413708\pi$
$983$	16.7918	0.535574	0.267787	+	0.963478i	$0.413708\pi$
$984$	−9.59179	−0.305775
$985$	1.79609	0.0572281
$986$	−15.1468	−0.482371
$987$	15.5918	0.496292
$988$	−3.33081	−0.105967
$989$	−17.0204	−0.541219
$990$	−0.198062	−0.00629483
$991$	39.0874	1.24165	0.620826	−	0.783948i	$-0.286797\pi$
$991$	39.0874	1.24165	0.620826	+	0.783948i	$0.286797\pi$
$992$	−7.43296	−0.235997
$993$	−2.31229	−0.0733783
$994$	57.7241	1.83090
$995$	−2.03875	−0.0646329
$996$	14.3545	0.454840
$997$	−20.2145	−0.640198	−0.320099	−	0.947384i	$-0.603716\pi$
$997$	−20.2145	−0.640198	−0.320099	+	0.947384i	$0.603716\pi$
$998$	−25.1202	−0.795166
$999$	−0.643104	−0.0203469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.p.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.p.1.3	✓	3	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.198062 q^{5} +1.00000 q^{6} -5.04892 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.198062 q^{5} +1.00000 q^{6} -5.04892 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.198062 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.64310 q^{13} -5.04892 q^{14} -0.198062 q^{15} +1.00000 q^{16} +3.49396 q^{17} +1.00000 q^{18} +2.02715 q^{19} -0.198062 q^{20} -5.04892 q^{21} +1.00000 q^{22} -2.46681 q^{23} +1.00000 q^{24} -4.96077 q^{25} -1.64310 q^{26} +1.00000 q^{27} -5.04892 q^{28} -4.33513 q^{29} -0.198062 q^{30} -7.43296 q^{31} +1.00000 q^{32} +1.00000 q^{33} +3.49396 q^{34} +1.00000 q^{35} +1.00000 q^{36} -0.643104 q^{37} +2.02715 q^{38} -1.64310 q^{39} -0.198062 q^{40} -9.59179 q^{41} -5.04892 q^{42} +6.89977 q^{43} +1.00000 q^{44} -0.198062 q^{45} -2.46681 q^{46} -3.08815 q^{47} +1.00000 q^{48} +18.4916 q^{49} -4.96077 q^{50} +3.49396 q^{51} -1.64310 q^{52} -12.2295 q^{53} +1.00000 q^{54} -0.198062 q^{55} -5.04892 q^{56} +2.02715 q^{57} -4.33513 q^{58} -10.0489 q^{59} -0.198062 q^{60} +1.00000 q^{61} -7.43296 q^{62} -5.04892 q^{63} +1.00000 q^{64} +0.325437 q^{65} +1.00000 q^{66} +2.26875 q^{67} +3.49396 q^{68} -2.46681 q^{69} +1.00000 q^{70} -11.4330 q^{71} +1.00000 q^{72} -6.33513 q^{73} -0.643104 q^{74} -4.96077 q^{75} +2.02715 q^{76} -5.04892 q^{77} -1.64310 q^{78} +1.34481 q^{79} -0.198062 q^{80} +1.00000 q^{81} -9.59179 q^{82} +14.3545 q^{83} -5.04892 q^{84} -0.692021 q^{85} +6.89977 q^{86} -4.33513 q^{87} +1.00000 q^{88} +18.0954 q^{89} -0.198062 q^{90} +8.29590 q^{91} -2.46681 q^{92} -7.43296 q^{93} -3.08815 q^{94} -0.401501 q^{95} +1.00000 q^{96} -5.65279 q^{97} +18.4916 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 5 q^{10} + 3 q^{11} + 3 q^{12} - 9 q^{13} - 6 q^{14} - 5 q^{15} + 3 q^{16} + q^{17} + 3 q^{18} - 5 q^{20} - 6 q^{21} + 3 q^{22} - 4 q^{23} + 3 q^{24} - 2 q^{25} - 9 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} - 5 q^{30} - 3 q^{31} + 3 q^{32} + 3 q^{33} + q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 9 q^{39} - 5 q^{40} - q^{41} - 6 q^{42} - 2 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} - 13 q^{47} + 3 q^{48} + 5 q^{49} - 2 q^{50} + q^{51} - 9 q^{52} - 16 q^{53} + 3 q^{54} - 5 q^{55} - 6 q^{56} - 12 q^{58} - 21 q^{59} - 5 q^{60} + 3 q^{61} - 3 q^{62} - 6 q^{63} + 3 q^{64} + 22 q^{65} + 3 q^{66} - q^{67} + q^{68} - 4 q^{69} + 3 q^{70} - 15 q^{71} + 3 q^{72} - 18 q^{73} - 6 q^{74} - 2 q^{75} - 6 q^{77} - 9 q^{78} - 19 q^{79} - 5 q^{80} + 3 q^{81} - q^{82} - 2 q^{83} - 6 q^{84} + 3 q^{85} - 2 q^{86} - 12 q^{87} + 3 q^{88} - 5 q^{89} - 5 q^{90} + 11 q^{91} - 4 q^{92} - 3 q^{93} - 13 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} + 5 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 5 * q^10 + 3 * q^11 + 3 * q^12 - 9 * q^13 - 6 * q^14 - 5 * q^15 + 3 * q^16 + q^17 + 3 * q^18 - 5 * q^20 - 6 * q^21 + 3 * q^22 - 4 * q^23 + 3 * q^24 - 2 * q^25 - 9 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 - 5 * q^30 - 3 * q^31 + 3 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 9 * q^39 - 5 * q^40 - q^41 - 6 * q^42 - 2 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 - 13 * q^47 + 3 * q^48 + 5 * q^49 - 2 * q^50 + q^51 - 9 * q^52 - 16 * q^53 + 3 * q^54 - 5 * q^55 - 6 * q^56 - 12 * q^58 - 21 * q^59 - 5 * q^60 + 3 * q^61 - 3 * q^62 - 6 * q^63 + 3 * q^64 + 22 * q^65 + 3 * q^66 - q^67 + q^68 - 4 * q^69 + 3 * q^70 - 15 * q^71 + 3 * q^72 - 18 * q^73 - 6 * q^74 - 2 * q^75 - 6 * q^77 - 9 * q^78 - 19 * q^79 - 5 * q^80 + 3 * q^81 - q^82 - 2 * q^83 - 6 * q^84 + 3 * q^85 - 2 * q^86 - 12 * q^87 + 3 * q^88 - 5 * q^89 - 5 * q^90 + 11 * q^91 - 4 * q^92 - 3 * q^93 - 13 * q^94 - 7 * q^95 + 3 * q^96 + q^97 + 5 * q^98 + 3 * q^99

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