LMFDB - Embedded newform 4026.2.a.bc.1.2

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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.88536$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.88536 q^{5} +1.00000 q^{6} -2.96592 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.88536 q^{5} +1.00000 q^{6} -2.96592 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.88536 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.99514 q^{13} -2.96592 q^{14} -2.88536 q^{15} +1.00000 q^{16} +3.32958 q^{17} +1.00000 q^{18} -5.75894 q^{19} -2.88536 q^{20} -2.96592 q^{21} +1.00000 q^{22} +7.24652 q^{23} +1.00000 q^{24} +3.32531 q^{25} +1.99514 q^{26} +1.00000 q^{27} -2.96592 q^{28} -8.65968 q^{29} -2.88536 q^{30} +6.36115 q^{31} +1.00000 q^{32} +1.00000 q^{33} +3.32958 q^{34} +8.55776 q^{35} +1.00000 q^{36} +0.888652 q^{37} -5.75894 q^{38} +1.99514 q^{39} -2.88536 q^{40} -8.21059 q^{41} -2.96592 q^{42} +8.75258 q^{43} +1.00000 q^{44} -2.88536 q^{45} +7.24652 q^{46} +7.18416 q^{47} +1.00000 q^{48} +1.79670 q^{49} +3.32531 q^{50} +3.32958 q^{51} +1.99514 q^{52} +11.6265 q^{53} +1.00000 q^{54} -2.88536 q^{55} -2.96592 q^{56} -5.75894 q^{57} -8.65968 q^{58} +4.60591 q^{59} -2.88536 q^{60} -1.00000 q^{61} +6.36115 q^{62} -2.96592 q^{63} +1.00000 q^{64} -5.75669 q^{65} +1.00000 q^{66} -0.148761 q^{67} +3.32958 q^{68} +7.24652 q^{69} +8.55776 q^{70} +10.1133 q^{71} +1.00000 q^{72} +13.1127 q^{73} +0.888652 q^{74} +3.32531 q^{75} -5.75894 q^{76} -2.96592 q^{77} +1.99514 q^{78} +0.842774 q^{79} -2.88536 q^{80} +1.00000 q^{81} -8.21059 q^{82} -2.03186 q^{83} -2.96592 q^{84} -9.60705 q^{85} +8.75258 q^{86} -8.65968 q^{87} +1.00000 q^{88} +4.24660 q^{89} -2.88536 q^{90} -5.91742 q^{91} +7.24652 q^{92} +6.36115 q^{93} +7.18416 q^{94} +16.6166 q^{95} +1.00000 q^{96} +15.7876 q^{97} +1.79670 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * 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
$5$	−2.88536	−1.29037	−0.645186	−	0.764025i	$-0.723220\pi$
$5$	−2.88536	−1.29037	−0.645186	+	0.764025i	$0.723220\pi$
$6$	1.00000	0.408248
$7$	−2.96592	−1.12101	−0.560507	−	0.828150i	$-0.689394\pi$
$7$	−2.96592	−1.12101	−0.560507	+	0.828150i	$0.689394\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.88536	−0.912431
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	1.99514	0.553352	0.276676	−	0.960963i	$-0.410767\pi$
$13$	1.99514	0.553352	0.276676	+	0.960963i	$0.410767\pi$
$14$	−2.96592	−0.792676
$15$	−2.88536	−0.744997
$16$	1.00000	0.250000
$17$	3.32958	0.807542	0.403771	−	0.914860i	$-0.367699\pi$
$17$	3.32958	0.807542	0.403771	+	0.914860i	$0.367699\pi$
$18$	1.00000	0.235702
$19$	−5.75894	−1.32119	−0.660595	−	0.750742i	$-0.729696\pi$
$19$	−5.75894	−1.32119	−0.660595	+	0.750742i	$0.729696\pi$
$20$	−2.88536	−0.645186
$21$	−2.96592	−0.647217
$22$	1.00000	0.213201
$23$	7.24652	1.51100	0.755502	−	0.655147i	$-0.227393\pi$
$23$	7.24652	1.51100	0.755502	+	0.655147i	$0.227393\pi$
$24$	1.00000	0.204124
$25$	3.32531	0.665062
$26$	1.99514	0.391279
$27$	1.00000	0.192450
$28$	−2.96592	−0.560507
$29$	−8.65968	−1.60806	−0.804031	−	0.594588i	$-0.797315\pi$
$29$	−8.65968	−1.60806	−0.804031	+	0.594588i	$0.797315\pi$
$30$	−2.88536	−0.526793
$31$	6.36115	1.14250	0.571249	−	0.820777i	$-0.306459\pi$
$31$	6.36115	1.14250	0.571249	+	0.820777i	$0.306459\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	3.32958	0.571018
$35$	8.55776	1.44653
$36$	1.00000	0.166667
$37$	0.888652	0.146094	0.0730468	−	0.997329i	$-0.476728\pi$
$37$	0.888652	0.146094	0.0730468	+	0.997329i	$0.476728\pi$
$38$	−5.75894	−0.934223
$39$	1.99514	0.319478
$40$	−2.88536	−0.456216
$41$	−8.21059	−1.28228	−0.641140	−	0.767424i	$-0.721538\pi$
$41$	−8.21059	−1.28228	−0.641140	+	0.767424i	$0.721538\pi$
$42$	−2.96592	−0.457652
$43$	8.75258	1.33476	0.667378	−	0.744719i	$-0.267417\pi$
$43$	8.75258	1.33476	0.667378	+	0.744719i	$0.267417\pi$
$44$	1.00000	0.150756
$45$	−2.88536	−0.430124
$46$	7.24652	1.06844
$47$	7.18416	1.04792	0.523958	−	0.851744i	$-0.324455\pi$
$47$	7.18416	1.04792	0.523958	+	0.851744i	$0.324455\pi$
$48$	1.00000	0.144338
$49$	1.79670	0.256671
$50$	3.32531	0.470270
$51$	3.32958	0.466235
$52$	1.99514	0.276676
$53$	11.6265	1.59703	0.798514	−	0.601976i	$-0.205620\pi$
$53$	11.6265	1.59703	0.798514	+	0.601976i	$0.205620\pi$
$54$	1.00000	0.136083
$55$	−2.88536	−0.389062
$56$	−2.96592	−0.396338
$57$	−5.75894	−0.762790
$58$	−8.65968	−1.13707
$59$	4.60591	0.599638	0.299819	−	0.953996i	$-0.403074\pi$
$59$	4.60591	0.599638	0.299819	+	0.953996i	$0.403074\pi$
$60$	−2.88536	−0.372499
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	6.36115	0.807867
$63$	−2.96592	−0.373671
$64$	1.00000	0.125000
$65$	−5.75669	−0.714030
$66$	1.00000	0.123091
$67$	−0.148761	−0.0181741	−0.00908703	−	0.999959i	$-0.502893\pi$
$67$	−0.148761	−0.0181741	−0.00908703	+	0.999959i	$0.502893\pi$
$68$	3.32958	0.403771
$69$	7.24652	0.872378
$70$	8.55776	1.02285
$71$	10.1133	1.20022	0.600112	−	0.799916i	$-0.295123\pi$
$71$	10.1133	1.20022	0.600112	+	0.799916i	$0.295123\pi$
$72$	1.00000	0.117851
$73$	13.1127	1.53472	0.767361	−	0.641216i	$-0.221570\pi$
$73$	13.1127	1.53472	0.767361	+	0.641216i	$0.221570\pi$
$74$	0.888652	0.103304
$75$	3.32531	0.383974
$76$	−5.75894	−0.660595
$77$	−2.96592	−0.337998
$78$	1.99514	0.225905
$79$	0.842774	0.0948195	0.0474098	−	0.998876i	$-0.484903\pi$
$79$	0.842774	0.0948195	0.0474098	+	0.998876i	$0.484903\pi$
$80$	−2.88536	−0.322593
$81$	1.00000	0.111111
$82$	−8.21059	−0.906708
$83$	−2.03186	−0.223025	−0.111513	−	0.993763i	$-0.535570\pi$
$83$	−2.03186	−0.223025	−0.111513	+	0.993763i	$0.535570\pi$
$84$	−2.96592	−0.323609
$85$	−9.60705	−1.04203
$86$	8.75258	0.943815
$87$	−8.65968	−0.928415
$88$	1.00000	0.106600
$89$	4.24660	0.450138	0.225069	−	0.974343i	$-0.427739\pi$
$89$	4.24660	0.450138	0.225069	+	0.974343i	$0.427739\pi$
$90$	−2.88536	−0.304144
$91$	−5.91742	−0.620314
$92$	7.24652	0.755502
$93$	6.36115	0.659621
$94$	7.18416	0.740989
$95$	16.6166	1.70483
$96$	1.00000	0.102062
$97$	15.7876	1.60298	0.801492	−	0.598006i	$-0.204040\pi$
$97$	15.7876	1.60298	0.801492	+	0.598006i	$0.204040\pi$
$98$	1.79670	0.181494
$99$	1.00000	0.100504
$100$	3.32531	0.332531
$101$	−3.16276	−0.314706	−0.157353	−	0.987542i	$-0.550296\pi$
$101$	−3.16276	−0.314706	−0.157353	+	0.987542i	$0.550296\pi$
$102$	3.32958	0.329678
$103$	7.25233	0.714593	0.357296	−	0.933991i	$-0.383699\pi$
$103$	7.25233	0.714593	0.357296	+	0.933991i	$0.383699\pi$
$104$	1.99514	0.195639
$105$	8.55776	0.835152
$106$	11.6265	1.12927
$107$	−15.9751	−1.54437	−0.772186	−	0.635397i	$-0.780836\pi$
$107$	−15.9751	−1.54437	−0.772186	+	0.635397i	$0.780836\pi$
$108$	1.00000	0.0962250
$109$	−7.92043	−0.758640	−0.379320	−	0.925266i	$-0.623842\pi$
$109$	−7.92043	−0.758640	−0.379320	+	0.925266i	$0.623842\pi$
$110$	−2.88536	−0.275108
$111$	0.888652	0.0843472
$112$	−2.96592	−0.280253
$113$	9.60725	0.903775	0.451887	−	0.892075i	$-0.350751\pi$
$113$	9.60725	0.903775	0.451887	+	0.892075i	$0.350751\pi$
$114$	−5.75894	−0.539374
$115$	−20.9088	−1.94976
$116$	−8.65968	−0.804031
$117$	1.99514	0.184451
$118$	4.60591	0.424008
$119$	−9.87528	−0.905265
$120$	−2.88536	−0.263396
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−8.21059	−0.740324
$124$	6.36115	0.571249
$125$	4.83208	0.432194
$126$	−2.96592	−0.264225
$127$	15.7842	1.40062	0.700310	−	0.713839i	$-0.253045\pi$
$127$	15.7842	1.40062	0.700310	+	0.713839i	$0.253045\pi$
$128$	1.00000	0.0883883
$129$	8.75258	0.770622
$130$	−5.75669	−0.504895
$131$	7.43708	0.649781	0.324890	−	0.945752i	$-0.394673\pi$
$131$	7.43708	0.649781	0.324890	+	0.945752i	$0.394673\pi$
$132$	1.00000	0.0870388
$133$	17.0806	1.48107
$134$	−0.148761	−0.0128510
$135$	−2.88536	−0.248332
$136$	3.32958	0.285509
$137$	−18.4993	−1.58050	−0.790251	−	0.612784i	$-0.790050\pi$
$137$	−18.4993	−1.58050	−0.790251	+	0.612784i	$0.790050\pi$
$138$	7.24652	0.616864
$139$	7.48195	0.634611	0.317306	−	0.948323i	$-0.397222\pi$
$139$	7.48195	0.634611	0.317306	+	0.948323i	$0.397222\pi$
$140$	8.55776	0.723263
$141$	7.18416	0.605015
$142$	10.1133	0.848686
$143$	1.99514	0.166842
$144$	1.00000	0.0833333
$145$	24.9863	2.07500
$146$	13.1127	1.08521
$147$	1.79670	0.148189
$148$	0.888652	0.0730468
$149$	24.0818	1.97286	0.986429	−	0.164186i	$-0.0524998\pi$
$149$	24.0818	1.97286	0.986429	+	0.164186i	$0.0524998\pi$
$150$	3.32531	0.271511
$151$	−17.0023	−1.38363	−0.691815	−	0.722075i	$-0.743189\pi$
$151$	−17.0023	−1.38363	−0.691815	+	0.722075i	$0.743189\pi$
$152$	−5.75894	−0.467111
$153$	3.32958	0.269181
$154$	−2.96592	−0.239001
$155$	−18.3542	−1.47425
$156$	1.99514	0.159739
$157$	13.7591	1.09810	0.549049	−	0.835790i	$-0.314990\pi$
$157$	13.7591	1.09810	0.549049	+	0.835790i	$0.314990\pi$
$158$	0.842774	0.0670475
$159$	11.6265	0.922045
$160$	−2.88536	−0.228108
$161$	−21.4926	−1.69385
$162$	1.00000	0.0785674
$163$	−15.4511	−1.21023	−0.605113	−	0.796139i	$-0.706872\pi$
$163$	−15.4511	−1.21023	−0.605113	+	0.796139i	$0.706872\pi$
$164$	−8.21059	−0.641140
$165$	−2.88536	−0.224625
$166$	−2.03186	−0.157703
$167$	11.2006	0.866730	0.433365	−	0.901219i	$-0.357326\pi$
$167$	11.2006	0.866730	0.433365	+	0.901219i	$0.357326\pi$
$168$	−2.96592	−0.228826
$169$	−9.01943	−0.693802
$170$	−9.60705	−0.736827
$171$	−5.75894	−0.440397
$172$	8.75258	0.667378
$173$	−11.0410	−0.839432	−0.419716	−	0.907656i	$-0.637870\pi$
$173$	−11.0410	−0.839432	−0.419716	+	0.907656i	$0.637870\pi$
$174$	−8.65968	−0.656488
$175$	−9.86262	−0.745544
$176$	1.00000	0.0753778
$177$	4.60591	0.346201
$178$	4.24660	0.318296
$179$	−25.0479	−1.87217	−0.936086	−	0.351772i	$-0.885579\pi$
$179$	−25.0479	−1.87217	−0.936086	+	0.351772i	$0.885579\pi$
$180$	−2.88536	−0.215062
$181$	7.72044	0.573856	0.286928	−	0.957952i	$-0.407366\pi$
$181$	7.72044	0.573856	0.286928	+	0.957952i	$0.407366\pi$
$182$	−5.91742	−0.438629
$183$	−1.00000	−0.0739221
$184$	7.24652	0.534220
$185$	−2.56408	−0.188515
$186$	6.36115	0.466423
$187$	3.32958	0.243483
$188$	7.18416	0.523958
$189$	−2.96592	−0.215739
$190$	16.6166	1.20550
$191$	14.3131	1.03566	0.517830	−	0.855484i	$-0.326740\pi$
$191$	14.3131	1.03566	0.517830	+	0.855484i	$0.326740\pi$
$192$	1.00000	0.0721688
$193$	10.8554	0.781390	0.390695	−	0.920520i	$-0.372235\pi$
$193$	10.8554	0.781390	0.390695	+	0.920520i	$0.372235\pi$
$194$	15.7876	1.13348
$195$	−5.75669	−0.412245
$196$	1.79670	0.128335
$197$	−11.8718	−0.845828	−0.422914	−	0.906170i	$-0.638993\pi$
$197$	−11.8718	−0.845828	−0.422914	+	0.906170i	$0.638993\pi$
$198$	1.00000	0.0710669
$199$	8.01638	0.568266	0.284133	−	0.958785i	$-0.408294\pi$
$199$	8.01638	0.568266	0.284133	+	0.958785i	$0.408294\pi$
$200$	3.32531	0.235135
$201$	−0.148761	−0.0104928
$202$	−3.16276	−0.222531
$203$	25.6839	1.80266
$204$	3.32958	0.233117
$205$	23.6905	1.65462
$206$	7.25233	0.505293
$207$	7.24652	0.503668
$208$	1.99514	0.138338
$209$	−5.75894	−0.398354
$210$	8.55776	0.590541
$211$	−9.63240	−0.663122	−0.331561	−	0.943434i	$-0.607575\pi$
$211$	−9.63240	−0.663122	−0.331561	+	0.943434i	$0.607575\pi$
$212$	11.6265	0.798514
$213$	10.1133	0.692949
$214$	−15.9751	−1.09204
$215$	−25.2544	−1.72233
$216$	1.00000	0.0680414
$217$	−18.8667	−1.28075
$218$	−7.92043	−0.536439
$219$	13.1127	0.886072
$220$	−2.88536	−0.194531
$221$	6.64297	0.446855
$222$	0.888652	0.0596424
$223$	25.1499	1.68416	0.842080	−	0.539353i	$-0.181331\pi$
$223$	25.1499	1.68416	0.842080	+	0.539353i	$0.181331\pi$
$224$	−2.96592	−0.198169
$225$	3.32531	0.221687
$226$	9.60725	0.639065
$227$	12.8001	0.849574	0.424787	−	0.905293i	$-0.360349\pi$
$227$	12.8001	0.849574	0.424787	+	0.905293i	$0.360349\pi$
$228$	−5.75894	−0.381395
$229$	3.78489	0.250112	0.125056	−	0.992150i	$-0.460089\pi$
$229$	3.78489	0.250112	0.125056	+	0.992150i	$0.460089\pi$
$230$	−20.9088	−1.37869
$231$	−2.96592	−0.195143
$232$	−8.65968	−0.568536
$233$	7.44585	0.487794	0.243897	−	0.969801i	$-0.421574\pi$
$233$	7.44585	0.487794	0.243897	+	0.969801i	$0.421574\pi$
$234$	1.99514	0.130426
$235$	−20.7289	−1.35220
$236$	4.60591	0.299819
$237$	0.842774	0.0547441
$238$	−9.87528	−0.640119
$239$	−18.0695	−1.16882	−0.584411	−	0.811458i	$-0.698674\pi$
$239$	−18.0695	−1.16882	−0.584411	+	0.811458i	$0.698674\pi$
$240$	−2.88536	−0.186249
$241$	24.1062	1.55282	0.776409	−	0.630229i	$-0.217039\pi$
$241$	24.1062	1.55282	0.776409	+	0.630229i	$0.217039\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−5.18412	−0.331201
$246$	−8.21059	−0.523488
$247$	−11.4899	−0.731083
$248$	6.36115	0.403934
$249$	−2.03186	−0.128764
$250$	4.83208	0.305608
$251$	−24.3202	−1.53508	−0.767538	−	0.641004i	$-0.778518\pi$
$251$	−24.3202	−1.53508	−0.767538	+	0.641004i	$0.778518\pi$
$252$	−2.96592	−0.186836
$253$	7.24652	0.455585
$254$	15.7842	0.990387
$255$	−9.60705	−0.601617
$256$	1.00000	0.0625000
$257$	−24.7338	−1.54285	−0.771425	−	0.636320i	$-0.780456\pi$
$257$	−24.7338	−1.54285	−0.771425	+	0.636320i	$0.780456\pi$
$258$	8.75258	0.544912
$259$	−2.63567	−0.163773
$260$	−5.75669	−0.357015
$261$	−8.65968	−0.536020
$262$	7.43708	0.459464
$263$	−14.5208	−0.895389	−0.447694	−	0.894187i	$-0.647755\pi$
$263$	−14.5208	−0.895389	−0.447694	+	0.894187i	$0.647755\pi$
$264$	1.00000	0.0615457
$265$	−33.5468	−2.06076
$266$	17.0806	1.04728
$267$	4.24660	0.259888
$268$	−0.148761	−0.00908703
$269$	20.0593	1.22304	0.611518	−	0.791230i	$-0.290559\pi$
$269$	20.0593	1.22304	0.611518	+	0.791230i	$0.290559\pi$
$270$	−2.88536	−0.175598
$271$	−20.2969	−1.23295	−0.616475	−	0.787375i	$-0.711440\pi$
$271$	−20.2969	−1.23295	−0.616475	+	0.787375i	$0.711440\pi$
$272$	3.32958	0.201886
$273$	−5.91742	−0.358139
$274$	−18.4993	−1.11758
$275$	3.32531	0.200524
$276$	7.24652	0.436189
$277$	8.52674	0.512322	0.256161	−	0.966634i	$-0.417542\pi$
$277$	8.52674	0.512322	0.256161	+	0.966634i	$0.417542\pi$
$278$	7.48195	0.448738
$279$	6.36115	0.380832
$280$	8.55776	0.511424
$281$	−26.5966	−1.58662	−0.793311	−	0.608816i	$-0.791645\pi$
$281$	−26.5966	−1.58662	−0.793311	+	0.608816i	$0.791645\pi$
$282$	7.18416	0.427810
$283$	32.5170	1.93293	0.966467	−	0.256791i	$-0.0826653\pi$
$283$	32.5170	1.93293	0.966467	+	0.256791i	$0.0826653\pi$
$284$	10.1133	0.600112
$285$	16.6166	0.984283
$286$	1.99514	0.117975
$287$	24.3520	1.43745
$288$	1.00000	0.0589256
$289$	−5.91389	−0.347876
$290$	24.9863	1.46725
$291$	15.7876	0.925483
$292$	13.1127	0.767361
$293$	−33.9091	−1.98099	−0.990497	−	0.137536i	$-0.956082\pi$
$293$	−33.9091	−1.98099	−0.990497	+	0.137536i	$0.956082\pi$
$294$	1.79670	0.104785
$295$	−13.2897	−0.773757
$296$	0.888652	0.0516519
$297$	1.00000	0.0580259
$298$	24.0818	1.39502
$299$	14.4578	0.836116
$300$	3.32531	0.191987
$301$	−25.9595	−1.49628
$302$	−17.0023	−0.978374
$303$	−3.16276	−0.181696
$304$	−5.75894	−0.330298
$305$	2.88536	0.165215
$306$	3.32958	0.190339
$307$	6.17590	0.352477	0.176239	−	0.984347i	$-0.443607\pi$
$307$	6.17590	0.352477	0.176239	+	0.984347i	$0.443607\pi$
$308$	−2.96592	−0.168999
$309$	7.25233	0.412570
$310$	−18.3542	−1.04245
$311$	−12.4464	−0.705769	−0.352884	−	0.935667i	$-0.614799\pi$
$311$	−12.4464	−0.705769	−0.352884	+	0.935667i	$0.614799\pi$
$312$	1.99514	0.112952
$313$	21.8357	1.23423	0.617113	−	0.786875i	$-0.288302\pi$
$313$	21.8357	1.23423	0.617113	+	0.786875i	$0.288302\pi$
$314$	13.7591	0.776472
$315$	8.55776	0.482175
$316$	0.842774	0.0474098
$317$	−19.9615	−1.12115	−0.560574	−	0.828104i	$-0.689419\pi$
$317$	−19.9615	−1.12115	−0.560574	+	0.828104i	$0.689419\pi$
$318$	11.6265	0.651984
$319$	−8.65968	−0.484849
$320$	−2.88536	−0.161297
$321$	−15.9751	−0.891643
$322$	−21.4926	−1.19774
$323$	−19.1748	−1.06692
$324$	1.00000	0.0555556
$325$	6.63445	0.368013
$326$	−15.4511	−0.855759
$327$	−7.92043	−0.438001
$328$	−8.21059	−0.453354
$329$	−21.3077	−1.17473
$330$	−2.88536	−0.158834
$331$	−33.3076	−1.83075	−0.915377	−	0.402598i	$-0.868107\pi$
$331$	−33.3076	−1.83075	−0.915377	+	0.402598i	$0.868107\pi$
$332$	−2.03186	−0.111513
$333$	0.888652	0.0486979
$334$	11.2006	0.612871
$335$	0.429230	0.0234513
$336$	−2.96592	−0.161804
$337$	−12.3478	−0.672626	−0.336313	−	0.941750i	$-0.609180\pi$
$337$	−12.3478	−0.672626	−0.336313	+	0.941750i	$0.609180\pi$
$338$	−9.01943	−0.490592
$339$	9.60725	0.521794
$340$	−9.60705	−0.521015
$341$	6.36115	0.344476
$342$	−5.75894	−0.311408
$343$	15.4326	0.833282
$344$	8.75258	0.471907
$345$	−20.9088	−1.12569
$346$	−11.0410	−0.593568
$347$	−9.35061	−0.501967	−0.250983	−	0.967991i	$-0.580754\pi$
$347$	−9.35061	−0.501967	−0.250983	+	0.967991i	$0.580754\pi$
$348$	−8.65968	−0.464207
$349$	−17.6910	−0.946977	−0.473489	−	0.880800i	$-0.657006\pi$
$349$	−17.6910	−0.946977	−0.473489	+	0.880800i	$0.657006\pi$
$350$	−9.86262	−0.527179
$351$	1.99514	0.106493
$352$	1.00000	0.0533002
$353$	0.997385	0.0530855	0.0265427	−	0.999648i	$-0.491550\pi$
$353$	0.997385	0.0530855	0.0265427	+	0.999648i	$0.491550\pi$
$354$	4.60591	0.244801
$355$	−29.1804	−1.54874
$356$	4.24660	0.225069
$357$	−9.87528	−0.522655
$358$	−25.0479	−1.32383
$359$	13.6560	0.720738	0.360369	−	0.932810i	$-0.382651\pi$
$359$	13.6560	0.720738	0.360369	+	0.932810i	$0.382651\pi$
$360$	−2.88536	−0.152072
$361$	14.1653	0.745545
$362$	7.72044	0.405778
$363$	1.00000	0.0524864
$364$	−5.91742	−0.310157
$365$	−37.8348	−1.98036
$366$	−1.00000	−0.0522708
$367$	−25.9368	−1.35389	−0.676946	−	0.736033i	$-0.736697\pi$
$367$	−25.9368	−1.35389	−0.676946	+	0.736033i	$0.736697\pi$
$368$	7.24652	0.377751
$369$	−8.21059	−0.427426
$370$	−2.56408	−0.133300
$371$	−34.4834	−1.79029
$372$	6.36115	0.329811
$373$	11.3492	0.587638	0.293819	−	0.955861i	$-0.405074\pi$
$373$	11.3492	0.587638	0.293819	+	0.955861i	$0.405074\pi$
$374$	3.32958	0.172169
$375$	4.83208	0.249528
$376$	7.18416	0.370495
$377$	−17.2772	−0.889823
$378$	−2.96592	−0.152551
$379$	−15.4499	−0.793607	−0.396803	−	0.917904i	$-0.629881\pi$
$379$	−15.4499	−0.793607	−0.396803	+	0.917904i	$0.629881\pi$
$380$	16.6166	0.852414
$381$	15.7842	0.808648
$382$	14.3131	0.732322
$383$	10.7110	0.547306	0.273653	−	0.961828i	$-0.411768\pi$
$383$	10.7110	0.547306	0.273653	+	0.961828i	$0.411768\pi$
$384$	1.00000	0.0510310
$385$	8.55776	0.436144
$386$	10.8554	0.552526
$387$	8.75258	0.444919
$388$	15.7876	0.801492
$389$	11.1350	0.564568	0.282284	−	0.959331i	$-0.408908\pi$
$389$	11.1350	0.564568	0.282284	+	0.959331i	$0.408908\pi$
$390$	−5.75669	−0.291501
$391$	24.1279	1.22020
$392$	1.79670	0.0907469
$393$	7.43708	0.375151
$394$	−11.8718	−0.598091
$395$	−2.43171	−0.122353
$396$	1.00000	0.0502519
$397$	6.36784	0.319593	0.159796	−	0.987150i	$-0.448916\pi$
$397$	6.36784	0.319593	0.159796	+	0.987150i	$0.448916\pi$
$398$	8.01638	0.401825
$399$	17.0806	0.855097
$400$	3.32531	0.166266
$401$	11.5521	0.576884	0.288442	−	0.957497i	$-0.406863\pi$
$401$	11.5521	0.576884	0.288442	+	0.957497i	$0.406863\pi$
$402$	−0.148761	−0.00741953
$403$	12.6914	0.632203
$404$	−3.16276	−0.157353
$405$	−2.88536	−0.143375
$406$	25.6839	1.27467
$407$	0.888652	0.0440489
$408$	3.32958	0.164839
$409$	−25.0051	−1.23642	−0.618211	−	0.786012i	$-0.712142\pi$
$409$	−25.0051	−1.23642	−0.618211	+	0.786012i	$0.712142\pi$
$410$	23.6905	1.16999
$411$	−18.4993	−0.912503
$412$	7.25233	0.357296
$413$	−13.6608	−0.672202
$414$	7.24652	0.356147
$415$	5.86265	0.287786
$416$	1.99514	0.0978197
$417$	7.48195	0.366393
$418$	−5.75894	−0.281679
$419$	−38.6289	−1.88715	−0.943574	−	0.331163i	$-0.892559\pi$
$419$	−38.6289	−1.88715	−0.943574	+	0.331163i	$0.892559\pi$
$420$	8.55776	0.417576
$421$	−30.2729	−1.47541	−0.737705	−	0.675124i	$-0.764090\pi$
$421$	−30.2729	−1.47541	−0.737705	+	0.675124i	$0.764090\pi$
$422$	−9.63240	−0.468898
$423$	7.18416	0.349306
$424$	11.6265	0.564635
$425$	11.0719	0.537066
$426$	10.1133	0.489989
$427$	2.96592	0.143531
$428$	−15.9751	−0.772186
$429$	1.99514	0.0963261
$430$	−25.2544	−1.21787
$431$	15.8946	0.765615	0.382808	−	0.923828i	$-0.374957\pi$
$431$	15.8946	0.765615	0.382808	+	0.923828i	$0.374957\pi$
$432$	1.00000	0.0481125
$433$	15.3948	0.739826	0.369913	−	0.929066i	$-0.379388\pi$
$433$	15.3948	0.739826	0.369913	+	0.929066i	$0.379388\pi$
$434$	−18.8667	−0.905630
$435$	24.9863	1.19800
$436$	−7.92043	−0.379320
$437$	−41.7322	−1.99632
$438$	13.1127	0.626547
$439$	27.8185	1.32770	0.663852	−	0.747864i	$-0.268920\pi$
$439$	27.8185	1.32770	0.663852	+	0.747864i	$0.268920\pi$
$440$	−2.88536	−0.137554
$441$	1.79670	0.0855570
$442$	6.64297	0.315974
$443$	25.2358	1.19899	0.599493	−	0.800380i	$-0.295369\pi$
$443$	25.2358	1.19899	0.599493	+	0.800380i	$0.295369\pi$
$444$	0.888652	0.0421736
$445$	−12.2530	−0.580846
$446$	25.1499	1.19088
$447$	24.0818	1.13903
$448$	−2.96592	−0.140127
$449$	−39.0786	−1.84423	−0.922117	−	0.386912i	$-0.873542\pi$
$449$	−39.0786	−1.84423	−0.922117	+	0.386912i	$0.873542\pi$
$450$	3.32531	0.156757
$451$	−8.21059	−0.386622
$452$	9.60725	0.451887
$453$	−17.0023	−0.798839
$454$	12.8001	0.600740
$455$	17.0739	0.800437
$456$	−5.75894	−0.269687
$457$	34.4683	1.61236	0.806181	−	0.591669i	$-0.201531\pi$
$457$	34.4683	1.61236	0.806181	+	0.591669i	$0.201531\pi$
$458$	3.78489	0.176856
$459$	3.32958	0.155412
$460$	−20.9088	−0.974879
$461$	31.0021	1.44391	0.721956	−	0.691939i	$-0.243244\pi$
$461$	31.0021	1.44391	0.721956	+	0.691939i	$0.243244\pi$
$462$	−2.96592	−0.137987
$463$	−18.5190	−0.860649	−0.430325	−	0.902674i	$-0.641601\pi$
$463$	−18.5190	−0.860649	−0.430325	+	0.902674i	$0.641601\pi$
$464$	−8.65968	−0.402015
$465$	−18.3542	−0.851157
$466$	7.44585	0.344922
$467$	2.19750	0.101688	0.0508440	−	0.998707i	$-0.483809\pi$
$467$	2.19750	0.101688	0.0508440	+	0.998707i	$0.483809\pi$
$468$	1.99514	0.0922253
$469$	0.441214	0.0203734
$470$	−20.7289	−0.956152
$471$	13.7591	0.633987
$472$	4.60591	0.212004
$473$	8.75258	0.402444
$474$	0.842774	0.0387099
$475$	−19.1503	−0.878674
$476$	−9.87528	−0.452633
$477$	11.6265	0.532343
$478$	−18.0695	−0.826481
$479$	−25.6028	−1.16982	−0.584912	−	0.811097i	$-0.698871\pi$
$479$	−25.6028	−1.16982	−0.584912	+	0.811097i	$0.698871\pi$
$480$	−2.88536	−0.131698
$481$	1.77298	0.0808411
$482$	24.1062	1.09801
$483$	−21.4926	−0.977947
$484$	1.00000	0.0454545
$485$	−45.5528	−2.06845
$486$	1.00000	0.0453609
$487$	2.27931	0.103285	0.0516427	−	0.998666i	$-0.483554\pi$
$487$	2.27931	0.103285	0.0516427	+	0.998666i	$0.483554\pi$
$488$	−1.00000	−0.0452679
$489$	−15.4511	−0.698725
$490$	−5.18412	−0.234195
$491$	−22.6588	−1.02258	−0.511289	−	0.859409i	$-0.670832\pi$
$491$	−22.6588	−1.02258	−0.511289	+	0.859409i	$0.670832\pi$
$492$	−8.21059	−0.370162
$493$	−28.8331	−1.29858
$494$	−11.4899	−0.516954
$495$	−2.88536	−0.129687
$496$	6.36115	0.285624
$497$	−29.9951	−1.34547
$498$	−2.03186	−0.0910498
$499$	44.3558	1.98564	0.992820	−	0.119619i	$-0.0381674\pi$
$499$	44.3558	1.98564	0.992820	+	0.119619i	$0.0381674\pi$
$500$	4.83208	0.216097
$501$	11.2006	0.500407
$502$	−24.3202	−1.08546
$503$	−31.2750	−1.39448	−0.697242	−	0.716836i	$-0.745589\pi$
$503$	−31.2750	−1.39448	−0.697242	+	0.716836i	$0.745589\pi$
$504$	−2.96592	−0.132113
$505$	9.12569	0.406088
$506$	7.24652	0.322147
$507$	−9.01943	−0.400567
$508$	15.7842	0.700310
$509$	−24.4621	−1.08426	−0.542131	−	0.840294i	$-0.682382\pi$
$509$	−24.4621	−1.08426	−0.542131	+	0.840294i	$0.682382\pi$
$510$	−9.60705	−0.425407
$511$	−38.8911	−1.72044
$512$	1.00000	0.0441942
$513$	−5.75894	−0.254263
$514$	−24.7338	−1.09096
$515$	−20.9256	−0.922091
$516$	8.75258	0.385311
$517$	7.18416	0.315959
$518$	−2.63567	−0.115805
$519$	−11.0410	−0.484646
$520$	−5.75669	−0.252448
$521$	30.7879	1.34884	0.674421	−	0.738347i	$-0.264393\pi$
$521$	30.7879	1.34884	0.674421	+	0.738347i	$0.264393\pi$
$522$	−8.65968	−0.379024
$523$	34.0818	1.49029	0.745146	−	0.666901i	$-0.232380\pi$
$523$	34.0818	1.49029	0.745146	+	0.666901i	$0.232380\pi$
$524$	7.43708	0.324890
$525$	−9.86262	−0.430440
$526$	−14.5208	−0.633136
$527$	21.1800	0.922614
$528$	1.00000	0.0435194
$529$	29.5120	1.28313
$530$	−33.5468	−1.45718
$531$	4.60591	0.199879
$532$	17.0806	0.740536
$533$	−16.3813	−0.709551
$534$	4.24660	0.183768
$535$	46.0939	1.99281
$536$	−0.148761	−0.00642550
$537$	−25.0479	−1.08090
$538$	20.0593	0.864817
$539$	1.79670	0.0773892
$540$	−2.88536	−0.124166
$541$	4.51198	0.193985	0.0969925	−	0.995285i	$-0.469078\pi$
$541$	4.51198	0.193985	0.0969925	+	0.995285i	$0.469078\pi$
$542$	−20.2969	−0.871827
$543$	7.72044	0.331316
$544$	3.32958	0.142755
$545$	22.8533	0.978928
$546$	−5.91742	−0.253242
$547$	19.6521	0.840262	0.420131	−	0.907463i	$-0.361984\pi$
$547$	19.6521	0.840262	0.420131	+	0.907463i	$0.361984\pi$
$548$	−18.4993	−0.790251
$549$	−1.00000	−0.0426790
$550$	3.32531	0.141792
$551$	49.8705	2.12456
$552$	7.24652	0.308432
$553$	−2.49960	−0.106294
$554$	8.52674	0.362267
$555$	−2.56408	−0.108839
$556$	7.48195	0.317306
$557$	2.05303	0.0869896	0.0434948	−	0.999054i	$-0.486151\pi$
$557$	2.05303	0.0869896	0.0434948	+	0.999054i	$0.486151\pi$
$558$	6.36115	0.269289
$559$	17.4626	0.738589
$560$	8.55776	0.361631
$561$	3.32958	0.140575
$562$	−26.5966	−1.12191
$563$	15.8242	0.666912	0.333456	−	0.942766i	$-0.391785\pi$
$563$	15.8242	0.666912	0.333456	+	0.942766i	$0.391785\pi$
$564$	7.18416	0.302508
$565$	−27.7204	−1.16621
$566$	32.5170	1.36679
$567$	−2.96592	−0.124557
$568$	10.1133	0.424343
$569$	−1.69727	−0.0711532	−0.0355766	−	0.999367i	$-0.511327\pi$
$569$	−1.69727	−0.0711532	−0.0355766	+	0.999367i	$0.511327\pi$
$570$	16.6166	0.695993
$571$	−23.2580	−0.973319	−0.486659	−	0.873592i	$-0.661785\pi$
$571$	−23.2580	−0.973319	−0.486659	+	0.873592i	$0.661785\pi$
$572$	1.99514	0.0834209
$573$	14.3131	0.597938
$574$	24.3520	1.01643
$575$	24.0969	1.00491
$576$	1.00000	0.0416667
$577$	−24.3451	−1.01350	−0.506750	−	0.862093i	$-0.669153\pi$
$577$	−24.3451	−1.01350	−0.506750	+	0.862093i	$0.669153\pi$
$578$	−5.91389	−0.245985
$579$	10.8554	0.451136
$580$	24.9863	1.03750
$581$	6.02634	0.250015
$582$	15.7876	0.654415
$583$	11.6265	0.481522
$584$	13.1127	0.542606
$585$	−5.75669	−0.238010
$586$	−33.9091	−1.40077
$587$	21.2752	0.878122	0.439061	−	0.898457i	$-0.355311\pi$
$587$	21.2752	0.878122	0.439061	+	0.898457i	$0.355311\pi$
$588$	1.79670	0.0740945
$589$	−36.6335	−1.50946
$590$	−13.2897	−0.547129
$591$	−11.8718	−0.488339
$592$	0.888652	0.0365234
$593$	−8.19254	−0.336427	−0.168214	−	0.985751i	$-0.553800\pi$
$593$	−8.19254	−0.336427	−0.168214	+	0.985751i	$0.553800\pi$
$594$	1.00000	0.0410305
$595$	28.4938	1.16813
$596$	24.0818	0.986429
$597$	8.01638	0.328088
$598$	14.4578	0.591223
$599$	27.5630	1.12619	0.563096	−	0.826391i	$-0.309610\pi$
$599$	27.5630	1.12619	0.563096	+	0.826391i	$0.309610\pi$
$600$	3.32531	0.135755
$601$	7.77377	0.317099	0.158549	−	0.987351i	$-0.449318\pi$
$601$	7.77377	0.317099	0.158549	+	0.987351i	$0.449318\pi$
$602$	−25.9595	−1.05803
$603$	−0.148761	−0.00605802
$604$	−17.0023	−0.691815
$605$	−2.88536	−0.117307
$606$	−3.16276	−0.128478
$607$	15.7812	0.640540	0.320270	−	0.947326i	$-0.396226\pi$
$607$	15.7812	0.640540	0.320270	+	0.947326i	$0.396226\pi$
$608$	−5.75894	−0.233556
$609$	25.6839	1.04077
$610$	2.88536	0.116825
$611$	14.3334	0.579866
$612$	3.32958	0.134590
$613$	18.3830	0.742483	0.371241	−	0.928536i	$-0.378932\pi$
$613$	18.3830	0.742483	0.371241	+	0.928536i	$0.378932\pi$
$614$	6.17590	0.249239
$615$	23.6905	0.955294
$616$	−2.96592	−0.119500
$617$	30.3423	1.22153	0.610767	−	0.791810i	$-0.290861\pi$
$617$	30.3423	1.22153	0.610767	+	0.791810i	$0.290861\pi$
$618$	7.25233	0.291731
$619$	−24.7389	−0.994342	−0.497171	−	0.867653i	$-0.665628\pi$
$619$	−24.7389	−0.994342	−0.497171	+	0.867653i	$0.665628\pi$
$620$	−18.3542	−0.737124
$621$	7.24652	0.290793
$622$	−12.4464	−0.499054
$623$	−12.5951	−0.504611
$624$	1.99514	0.0798694
$625$	−30.5689	−1.22275
$626$	21.8357	0.872729
$627$	−5.75894	−0.229990
$628$	13.7591	0.549049
$629$	2.95884	0.117977
$630$	8.55776	0.340949
$631$	3.17154	0.126257	0.0631286	−	0.998005i	$-0.479892\pi$
$631$	3.17154	0.126257	0.0631286	+	0.998005i	$0.479892\pi$
$632$	0.842774	0.0335238
$633$	−9.63240	−0.382854
$634$	−19.9615	−0.792771
$635$	−45.5431	−1.80732
$636$	11.6265	0.461022
$637$	3.58466	0.142029
$638$	−8.65968	−0.342840
$639$	10.1133	0.400074
$640$	−2.88536	−0.114054
$641$	14.1212	0.557752	0.278876	−	0.960327i	$-0.410038\pi$
$641$	14.1212	0.557752	0.278876	+	0.960327i	$0.410038\pi$
$642$	−15.9751	−0.630487
$643$	−37.6992	−1.48671	−0.743355	−	0.668897i	$-0.766767\pi$
$643$	−37.6992	−1.48671	−0.743355	+	0.668897i	$0.766767\pi$
$644$	−21.4926	−0.846927
$645$	−25.2544	−0.994389
$646$	−19.1748	−0.754424
$647$	6.23224	0.245015	0.122507	−	0.992468i	$-0.460907\pi$
$647$	6.23224	0.245015	0.122507	+	0.992468i	$0.460907\pi$
$648$	1.00000	0.0392837
$649$	4.60591	0.180798
$650$	6.63445	0.260225
$651$	−18.8667	−0.739444
$652$	−15.4511	−0.605113
$653$	50.1533	1.96265	0.981326	−	0.192352i	$-0.0616117\pi$
$653$	50.1533	1.96265	0.981326	+	0.192352i	$0.0616117\pi$
$654$	−7.92043	−0.309713
$655$	−21.4587	−0.838459
$656$	−8.21059	−0.320570
$657$	13.1127	0.511574
$658$	−21.3077	−0.830659
$659$	−11.1019	−0.432469	−0.216234	−	0.976342i	$-0.569377\pi$
$659$	−11.1019	−0.432469	−0.216234	+	0.976342i	$0.569377\pi$
$660$	−2.88536	−0.112313
$661$	42.8342	1.66606	0.833028	−	0.553231i	$-0.186605\pi$
$661$	42.8342	1.66606	0.833028	+	0.553231i	$0.186605\pi$
$662$	−33.3076	−1.29454
$663$	6.64297	0.257992
$664$	−2.03186	−0.0788514
$665$	−49.2836	−1.91114
$666$	0.888652	0.0344346
$667$	−62.7525	−2.42979
$668$	11.2006	0.433365
$669$	25.1499	0.972350
$670$	0.429230	0.0165826
$671$	−1.00000	−0.0386046
$672$	−2.96592	−0.114413
$673$	−5.14234	−0.198223	−0.0991113	−	0.995076i	$-0.531600\pi$
$673$	−5.14234	−0.198223	−0.0991113	+	0.995076i	$0.531600\pi$
$674$	−12.3478	−0.475619
$675$	3.32531	0.127991
$676$	−9.01943	−0.346901
$677$	16.7004	0.641850	0.320925	−	0.947105i	$-0.396006\pi$
$677$	16.7004	0.641850	0.320925	+	0.947105i	$0.396006\pi$
$678$	9.60725	0.368964
$679$	−46.8247	−1.79697
$680$	−9.60705	−0.368413
$681$	12.8001	0.490502
$682$	6.36115	0.243581
$683$	−35.9382	−1.37514	−0.687568	−	0.726120i	$-0.741322\pi$
$683$	−35.9382	−1.37514	−0.687568	+	0.726120i	$0.741322\pi$
$684$	−5.75894	−0.220198
$685$	53.3771	2.03944
$686$	15.4326	0.589219
$687$	3.78489	0.144403
$688$	8.75258	0.333689
$689$	23.1966	0.883718
$690$	−20.9088	−0.795985
$691$	−20.4301	−0.777196	−0.388598	−	0.921407i	$-0.627041\pi$
$691$	−20.4301	−0.777196	−0.388598	+	0.921407i	$0.627041\pi$
$692$	−11.0410	−0.419716
$693$	−2.96592	−0.112666
$694$	−9.35061	−0.354944
$695$	−21.5881	−0.818885
$696$	−8.65968	−0.328244
$697$	−27.3378	−1.03549
$698$	−17.6910	−0.669614
$699$	7.44585	0.281628
$700$	−9.86262	−0.372772
$701$	1.91477	0.0723200	0.0361600	−	0.999346i	$-0.488487\pi$
$701$	1.91477	0.0723200	0.0361600	+	0.999346i	$0.488487\pi$
$702$	1.99514	0.0753016
$703$	−5.11769	−0.193017
$704$	1.00000	0.0376889
$705$	−20.7289	−0.780695
$706$	0.997385	0.0375371
$707$	9.38049	0.352790
$708$	4.60591	0.173101
$709$	44.0106	1.65285	0.826427	−	0.563044i	$-0.190370\pi$
$709$	44.0106	1.65285	0.826427	+	0.563044i	$0.190370\pi$
$710$	−29.1804	−1.09512
$711$	0.842774	0.0316065
$712$	4.24660	0.159148
$713$	46.0962	1.72632
$714$	−9.87528	−0.369573
$715$	−5.75669	−0.215288
$716$	−25.0479	−0.936086
$717$	−18.0695	−0.674819
$718$	13.6560	0.509639
$719$	−1.88569	−0.0703244	−0.0351622	−	0.999382i	$-0.511195\pi$
$719$	−1.88569	−0.0703244	−0.0351622	+	0.999382i	$0.511195\pi$
$720$	−2.88536	−0.107531
$721$	−21.5098	−0.801068
$722$	14.1653	0.527180
$723$	24.1062	0.896520
$724$	7.72044	0.286928
$725$	−28.7961	−1.06946
$726$	1.00000	0.0371135
$727$	23.8893	0.886007	0.443003	−	0.896520i	$-0.353913\pi$
$727$	23.8893	0.886007	0.443003	+	0.896520i	$0.353913\pi$
$728$	−5.91742	−0.219314
$729$	1.00000	0.0370370
$730$	−37.8348	−1.40033
$731$	29.1424	1.07787
$732$	−1.00000	−0.0369611
$733$	8.97824	0.331619	0.165809	−	0.986158i	$-0.446976\pi$
$733$	8.97824	0.331619	0.165809	+	0.986158i	$0.446976\pi$
$734$	−25.9368	−0.957346
$735$	−5.18412	−0.191219
$736$	7.24652	0.267110
$737$	−0.148761	−0.00547968
$738$	−8.21059	−0.302236
$739$	−26.9515	−0.991426	−0.495713	−	0.868487i	$-0.665093\pi$
$739$	−26.9515	−0.991426	−0.495713	+	0.868487i	$0.665093\pi$
$740$	−2.56408	−0.0942576
$741$	−11.4899	−0.422091
$742$	−34.4834	−1.26593
$743$	31.0780	1.14014	0.570070	−	0.821596i	$-0.306916\pi$
$743$	31.0780	1.14014	0.570070	+	0.821596i	$0.306916\pi$
$744$	6.36115	0.233211
$745$	−69.4847	−2.54572
$746$	11.3492	0.415523
$747$	−2.03186	−0.0743418
$748$	3.32958	0.121742
$749$	47.3809	1.73126
$750$	4.83208	0.176443
$751$	24.2425	0.884621	0.442311	−	0.896862i	$-0.354159\pi$
$751$	24.2425	0.884621	0.442311	+	0.896862i	$0.354159\pi$
$752$	7.18416	0.261979
$753$	−24.3202	−0.886276
$754$	−17.2772	−0.629200
$755$	49.0579	1.78540
$756$	−2.96592	−0.107870
$757$	19.8834	0.722675	0.361337	−	0.932435i	$-0.382320\pi$
$757$	19.8834	0.722675	0.361337	+	0.932435i	$0.382320\pi$
$758$	−15.4499	−0.561165
$759$	7.24652	0.263032
$760$	16.6166	0.602748
$761$	0.821022	0.0297620	0.0148810	−	0.999889i	$-0.495263\pi$
$761$	0.821022	0.0297620	0.0148810	+	0.999889i	$0.495263\pi$
$762$	15.7842	0.571800
$763$	23.4914	0.850445
$764$	14.3131	0.517830
$765$	−9.60705	−0.347343
$766$	10.7110	0.387004
$767$	9.18942	0.331811
$768$	1.00000	0.0360844
$769$	13.9751	0.503953	0.251977	−	0.967733i	$-0.418919\pi$
$769$	13.9751	0.503953	0.251977	+	0.967733i	$0.418919\pi$
$770$	8.55776	0.308400
$771$	−24.7338	−0.890765
$772$	10.8554	0.390695
$773$	−35.8935	−1.29100	−0.645500	−	0.763760i	$-0.723351\pi$
$773$	−35.8935	−1.29100	−0.645500	+	0.763760i	$0.723351\pi$
$774$	8.75258	0.314605
$775$	21.1528	0.759832
$776$	15.7876	0.566740
$777$	−2.63567	−0.0945543
$778$	11.1350	0.399210
$779$	47.2843	1.69414
$780$	−5.75669	−0.206123
$781$	10.1133	0.361881
$782$	24.1279	0.862811
$783$	−8.65968	−0.309472
$784$	1.79670	0.0641677
$785$	−39.7000	−1.41696
$786$	7.43708	0.265272
$787$	−29.9454	−1.06744	−0.533718	−	0.845662i	$-0.679206\pi$
$787$	−29.9454	−1.06744	−0.533718	+	0.845662i	$0.679206\pi$
$788$	−11.8718	−0.422914
$789$	−14.5208	−0.516953
$790$	−2.43171	−0.0865163
$791$	−28.4944	−1.01314
$792$	1.00000	0.0355335
$793$	−1.99514	−0.0708494
$794$	6.36784	0.225986
$795$	−33.5468	−1.18978
$796$	8.01638	0.284133
$797$	−35.1881	−1.24643	−0.623214	−	0.782051i	$-0.714173\pi$
$797$	−35.1881	−1.24643	−0.623214	+	0.782051i	$0.714173\pi$
$798$	17.0806	0.604645
$799$	23.9202	0.846237
$800$	3.32531	0.117568
$801$	4.24660	0.150046
$802$	11.5521	0.407918
$803$	13.1127	0.462736
$804$	−0.148761	−0.00524640
$805$	62.0139	2.18570
$806$	12.6914	0.447035
$807$	20.0593	0.706120
$808$	−3.16276	−0.111265
$809$	19.4803	0.684889	0.342445	−	0.939538i	$-0.388745\pi$
$809$	19.4803	0.684889	0.342445	+	0.939538i	$0.388745\pi$
$810$	−2.88536	−0.101381
$811$	9.44906	0.331802	0.165901	−	0.986142i	$-0.446947\pi$
$811$	9.44906	0.331802	0.165901	+	0.986142i	$0.446947\pi$
$812$	25.6839	0.901329
$813$	−20.2969	−0.711844
$814$	0.888652	0.0311473
$815$	44.5821	1.56164
$816$	3.32958	0.116559
$817$	−50.4055	−1.76347
$818$	−25.0051	−0.874282
$819$	−5.91742	−0.206771
$820$	23.6905	0.827309
$821$	41.1035	1.43452	0.717261	−	0.696805i	$-0.245396\pi$
$821$	41.1035	1.43452	0.717261	+	0.696805i	$0.245396\pi$
$822$	−18.4993	−0.645237
$823$	3.00428	0.104723	0.0523613	−	0.998628i	$-0.483325\pi$
$823$	3.00428	0.104723	0.0523613	+	0.998628i	$0.483325\pi$
$824$	7.25233	0.252647
$825$	3.32531	0.115773
$826$	−13.6608	−0.475319
$827$	−38.8510	−1.35098	−0.675491	−	0.737368i	$-0.736068\pi$
$827$	−38.8510	−1.35098	−0.675491	+	0.737368i	$0.736068\pi$
$828$	7.24652	0.251834
$829$	−5.07419	−0.176234	−0.0881170	−	0.996110i	$-0.528085\pi$
$829$	−5.07419	−0.176234	−0.0881170	+	0.996110i	$0.528085\pi$
$830$	5.86265	0.203495
$831$	8.52674	0.295789
$832$	1.99514	0.0691689
$833$	5.98225	0.207273
$834$	7.48195	0.259079
$835$	−32.3178	−1.11840
$836$	−5.75894	−0.199177
$837$	6.36115	0.219874
$838$	−38.6289	−1.33441
$839$	−15.5199	−0.535806	−0.267903	−	0.963446i	$-0.586331\pi$
$839$	−15.5199	−0.535806	−0.267903	+	0.963446i	$0.586331\pi$
$840$	8.55776	0.295271
$841$	45.9900	1.58586
$842$	−30.2729	−1.04327
$843$	−26.5966	−0.916037
$844$	−9.63240	−0.331561
$845$	26.0243	0.895263
$846$	7.18416	0.246996
$847$	−2.96592	−0.101910
$848$	11.6265	0.399257
$849$	32.5170	1.11598
$850$	11.0719	0.379763
$851$	6.43963	0.220748
$852$	10.1133	0.346475
$853$	47.1609	1.61476	0.807379	−	0.590033i	$-0.200885\pi$
$853$	47.1609	1.61476	0.807379	+	0.590033i	$0.200885\pi$
$854$	2.96592	0.101492
$855$	16.6166	0.568276
$856$	−15.9751	−0.546018
$857$	24.2134	0.827115	0.413557	−	0.910478i	$-0.364286\pi$
$857$	24.2134	0.827115	0.413557	+	0.910478i	$0.364286\pi$
$858$	1.99514	0.0681129
$859$	−30.9536	−1.05612	−0.528061	−	0.849206i	$-0.677081\pi$
$859$	−30.9536	−1.05612	−0.528061	+	0.849206i	$0.677081\pi$
$860$	−25.2544	−0.861166
$861$	24.3520	0.829913
$862$	15.8946	0.541372
$863$	−38.2083	−1.30063	−0.650313	−	0.759666i	$-0.725362\pi$
$863$	−38.2083	−1.30063	−0.650313	+	0.759666i	$0.725362\pi$
$864$	1.00000	0.0340207
$865$	31.8573	1.08318
$866$	15.3948	0.523136
$867$	−5.91389	−0.200846
$868$	−18.8667	−0.640377
$869$	0.842774	0.0285892
$870$	24.9863	0.847115
$871$	−0.296799	−0.0100566
$872$	−7.92043	−0.268220
$873$	15.7876	0.534328
$874$	−41.7322	−1.41161
$875$	−14.3316	−0.484496
$876$	13.1127	0.443036
$877$	42.3533	1.43017	0.715085	−	0.699037i	$-0.246388\pi$
$877$	42.3533	1.43017	0.715085	+	0.699037i	$0.246388\pi$
$878$	27.8185	0.938829
$879$	−33.9091	−1.14373
$880$	−2.88536	−0.0972655
$881$	6.97035	0.234837	0.117419	−	0.993083i	$-0.462538\pi$
$881$	6.97035	0.234837	0.117419	+	0.993083i	$0.462538\pi$
$882$	1.79670	0.0604979
$883$	45.1815	1.52048	0.760239	−	0.649643i	$-0.225082\pi$
$883$	45.1815	1.52048	0.760239	+	0.649643i	$0.225082\pi$
$884$	6.64297	0.223427
$885$	−13.2897	−0.446729
$886$	25.2358	0.847812
$887$	−14.6704	−0.492585	−0.246292	−	0.969196i	$-0.579212\pi$
$887$	−14.6704	−0.492585	−0.246292	+	0.969196i	$0.579212\pi$
$888$	0.888652	0.0298212
$889$	−46.8147	−1.57011
$890$	−12.2530	−0.410720
$891$	1.00000	0.0335013
$892$	25.1499	0.842080
$893$	−41.3731	−1.38450
$894$	24.0818	0.805416
$895$	72.2724	2.41580
$896$	−2.96592	−0.0990845
$897$	14.4578	0.482732
$898$	−39.0786	−1.30407
$899$	−55.0855	−1.83721
$900$	3.32531	0.110844
$901$	38.7115	1.28967
$902$	−8.21059	−0.273383
$903$	−25.9595	−0.863877
$904$	9.60725	0.319533
$905$	−22.2763	−0.740488
$906$	−17.0023	−0.564864
$907$	4.43750	0.147345	0.0736725	−	0.997282i	$-0.476528\pi$
$907$	4.43750	0.147345	0.0736725	+	0.997282i	$0.476528\pi$
$908$	12.8001	0.424787
$909$	−3.16276	−0.104902
$910$	17.0739	0.565994
$911$	−34.3335	−1.13752	−0.568759	−	0.822504i	$-0.692576\pi$
$911$	−34.3335	−1.13752	−0.568759	+	0.822504i	$0.692576\pi$
$912$	−5.75894	−0.190697
$913$	−2.03186	−0.0672447
$914$	34.4683	1.14011
$915$	2.88536	0.0953871
$916$	3.78489	0.125056
$917$	−22.0578	−0.728413
$918$	3.32958	0.109893
$919$	−35.7346	−1.17878	−0.589388	−	0.807850i	$-0.700631\pi$
$919$	−35.7346	−1.17878	−0.589388	+	0.807850i	$0.700631\pi$
$920$	−20.9088	−0.689343
$921$	6.17590	0.203503
$922$	31.0021	1.02100
$923$	20.1773	0.664145
$924$	−2.96592	−0.0975717
$925$	2.95505	0.0971613
$926$	−18.5190	−0.608571
$927$	7.25233	0.238198
$928$	−8.65968	−0.284268
$929$	22.1124	0.725486	0.362743	−	0.931889i	$-0.381840\pi$
$929$	22.1124	0.725486	0.362743	+	0.931889i	$0.381840\pi$
$930$	−18.3542	−0.601859
$931$	−10.3471	−0.339111
$932$	7.44585	0.243897
$933$	−12.4464	−0.407476
$934$	2.19750	0.0719043
$935$	−9.60705	−0.314184
$936$	1.99514	0.0652131
$937$	16.3301	0.533481	0.266741	−	0.963768i	$-0.414053\pi$
$937$	16.3301	0.533481	0.266741	+	0.963768i	$0.414053\pi$
$938$	0.441214	0.0144061
$939$	21.8357	0.712580
$940$	−20.7289	−0.676102
$941$	−12.0909	−0.394151	−0.197075	−	0.980388i	$-0.563144\pi$
$941$	−12.0909	−0.394151	−0.197075	+	0.980388i	$0.563144\pi$
$942$	13.7591	0.448296
$943$	−59.4982	−1.93753
$944$	4.60591	0.149909
$945$	8.55776	0.278384
$946$	8.75258	0.284571
$947$	45.4711	1.47761	0.738806	−	0.673918i	$-0.235390\pi$
$947$	45.4711	1.47761	0.738806	+	0.673918i	$0.235390\pi$
$948$	0.842774	0.0273720
$949$	26.1616	0.849240
$950$	−19.1503	−0.621317
$951$	−19.9615	−0.647295
$952$	−9.87528	−0.320060
$953$	−21.3656	−0.692100	−0.346050	−	0.938216i	$-0.612477\pi$
$953$	−21.3656	−0.692100	−0.346050	+	0.938216i	$0.612477\pi$
$954$	11.6265	0.376423
$955$	−41.2985	−1.33639
$956$	−18.0695	−0.584411
$957$	−8.65968	−0.279928
$958$	−25.6028	−0.827190
$959$	54.8675	1.77176
$960$	−2.88536	−0.0931246
$961$	9.46429	0.305300
$962$	1.77298	0.0571633
$963$	−15.9751	−0.514790
$964$	24.1062	0.776409
$965$	−31.3218	−1.00828
$966$	−21.4926	−0.691513
$967$	−39.2761	−1.26303	−0.631517	−	0.775362i	$-0.717568\pi$
$967$	−39.2761	−1.26303	−0.631517	+	0.775362i	$0.717568\pi$
$968$	1.00000	0.0321412
$969$	−19.1748	−0.615985
$970$	−45.5528	−1.46261
$971$	41.0843	1.31846	0.659229	−	0.751942i	$-0.270883\pi$
$971$	41.0843	1.31846	0.659229	+	0.751942i	$0.270883\pi$
$972$	1.00000	0.0320750
$973$	−22.1909	−0.711408
$974$	2.27931	0.0730338
$975$	6.63445	0.212473
$976$	−1.00000	−0.0320092
$977$	35.6970	1.14205	0.571023	−	0.820934i	$-0.306547\pi$
$977$	35.6970	1.14205	0.571023	+	0.820934i	$0.306547\pi$
$978$	−15.4511	−0.494073
$979$	4.24660	0.135722
$980$	−5.18412	−0.165601
$981$	−7.92043	−0.252880
$982$	−22.6588	−0.723072
$983$	−41.0849	−1.31041	−0.655203	−	0.755453i	$-0.727417\pi$
$983$	−41.0849	−1.31041	−0.655203	+	0.755453i	$0.727417\pi$
$984$	−8.21059	−0.261744
$985$	34.2543	1.09143
$986$	−28.8331	−0.918233
$987$	−21.3077	−0.678230
$988$	−11.4899	−0.365541
$989$	63.4257	2.01682
$990$	−2.88536	−0.0917028
$991$	25.4687	0.809039	0.404519	−	0.914529i	$-0.367439\pi$
$991$	25.4687	0.809039	0.404519	+	0.914529i	$0.367439\pi$
$992$	6.36115	0.201967
$993$	−33.3076	−1.05699
$994$	−29.9951	−0.951388
$995$	−23.1301	−0.733275
$996$	−2.03186	−0.0643819
$997$	28.4319	0.900448	0.450224	−	0.892916i	$-0.351344\pi$
$997$	28.4319	0.900448	0.450224	+	0.892916i	$0.351344\pi$
$998$	44.3558	1.40406
$999$	0.888652	0.0281157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.2	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.88536 q^{5} +1.00000 q^{6} -2.96592 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.88536 q^{5} +1.00000 q^{6} -2.96592 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.88536 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.99514 q^{13} -2.96592 q^{14} -2.88536 q^{15} +1.00000 q^{16} +3.32958 q^{17} +1.00000 q^{18} -5.75894 q^{19} -2.88536 q^{20} -2.96592 q^{21} +1.00000 q^{22} +7.24652 q^{23} +1.00000 q^{24} +3.32531 q^{25} +1.99514 q^{26} +1.00000 q^{27} -2.96592 q^{28} -8.65968 q^{29} -2.88536 q^{30} +6.36115 q^{31} +1.00000 q^{32} +1.00000 q^{33} +3.32958 q^{34} +8.55776 q^{35} +1.00000 q^{36} +0.888652 q^{37} -5.75894 q^{38} +1.99514 q^{39} -2.88536 q^{40} -8.21059 q^{41} -2.96592 q^{42} +8.75258 q^{43} +1.00000 q^{44} -2.88536 q^{45} +7.24652 q^{46} +7.18416 q^{47} +1.00000 q^{48} +1.79670 q^{49} +3.32531 q^{50} +3.32958 q^{51} +1.99514 q^{52} +11.6265 q^{53} +1.00000 q^{54} -2.88536 q^{55} -2.96592 q^{56} -5.75894 q^{57} -8.65968 q^{58} +4.60591 q^{59} -2.88536 q^{60} -1.00000 q^{61} +6.36115 q^{62} -2.96592 q^{63} +1.00000 q^{64} -5.75669 q^{65} +1.00000 q^{66} -0.148761 q^{67} +3.32958 q^{68} +7.24652 q^{69} +8.55776 q^{70} +10.1133 q^{71} +1.00000 q^{72} +13.1127 q^{73} +0.888652 q^{74} +3.32531 q^{75} -5.75894 q^{76} -2.96592 q^{77} +1.99514 q^{78} +0.842774 q^{79} -2.88536 q^{80} +1.00000 q^{81} -8.21059 q^{82} -2.03186 q^{83} -2.96592 q^{84} -9.60705 q^{85} +8.75258 q^{86} -8.65968 q^{87} +1.00000 q^{88} +4.24660 q^{89} -2.88536 q^{90} -5.91742 q^{91} +7.24652 q^{92} +6.36115 q^{93} +7.18416 q^{94} +16.6166 q^{95} +1.00000 q^{96} +15.7876 q^{97} +1.79670 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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