LMFDB - Embedded newform 6026.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.43324 q^{3} +1.00000 q^{4} -0.544807 q^{5} +2.43324 q^{6} -1.90449 q^{7} +1.00000 q^{8} +2.92064 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.43324 q^{3} +1.00000 q^{4} -0.544807 q^{5} +2.43324 q^{6} -1.90449 q^{7} +1.00000 q^{8} +2.92064 q^{9} -0.544807 q^{10} -3.84930 q^{11} +2.43324 q^{12} +2.71965 q^{13} -1.90449 q^{14} -1.32564 q^{15} +1.00000 q^{16} -4.26349 q^{17} +2.92064 q^{18} -7.08679 q^{19} -0.544807 q^{20} -4.63408 q^{21} -3.84930 q^{22} -1.00000 q^{23} +2.43324 q^{24} -4.70319 q^{25} +2.71965 q^{26} -0.193096 q^{27} -1.90449 q^{28} +8.83309 q^{29} -1.32564 q^{30} -4.32031 q^{31} +1.00000 q^{32} -9.36626 q^{33} -4.26349 q^{34} +1.03758 q^{35} +2.92064 q^{36} -8.31300 q^{37} -7.08679 q^{38} +6.61756 q^{39} -0.544807 q^{40} -9.86785 q^{41} -4.63408 q^{42} -6.08037 q^{43} -3.84930 q^{44} -1.59119 q^{45} -1.00000 q^{46} +3.53820 q^{47} +2.43324 q^{48} -3.37292 q^{49} -4.70319 q^{50} -10.3741 q^{51} +2.71965 q^{52} +5.56765 q^{53} -0.193096 q^{54} +2.09713 q^{55} -1.90449 q^{56} -17.2438 q^{57} +8.83309 q^{58} -6.23303 q^{59} -1.32564 q^{60} +12.5435 q^{61} -4.32031 q^{62} -5.56233 q^{63} +1.00000 q^{64} -1.48169 q^{65} -9.36626 q^{66} +7.33739 q^{67} -4.26349 q^{68} -2.43324 q^{69} +1.03758 q^{70} -7.91549 q^{71} +2.92064 q^{72} +10.2107 q^{73} -8.31300 q^{74} -11.4440 q^{75} -7.08679 q^{76} +7.33095 q^{77} +6.61756 q^{78} +15.8850 q^{79} -0.544807 q^{80} -9.23178 q^{81} -9.86785 q^{82} +4.21260 q^{83} -4.63408 q^{84} +2.32278 q^{85} -6.08037 q^{86} +21.4930 q^{87} -3.84930 q^{88} +2.53980 q^{89} -1.59119 q^{90} -5.17955 q^{91} -1.00000 q^{92} -10.5123 q^{93} +3.53820 q^{94} +3.86093 q^{95} +2.43324 q^{96} -11.2001 q^{97} -3.37292 q^{98} -11.2424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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
$3$	2.43324	1.40483	0.702415	−	0.711768i	$-0.252105\pi$
$3$	2.43324	1.40483	0.702415	+	0.711768i	$0.252105\pi$
$4$	1.00000	0.500000
$5$	−0.544807	−0.243645	−0.121823	−	0.992552i	$-0.538874\pi$
$5$	−0.544807	−0.243645	−0.121823	+	0.992552i	$0.538874\pi$
$6$	2.43324	0.993365
$7$	−1.90449	−0.719830	−0.359915	−	0.932985i	$-0.617194\pi$
$7$	−1.90449	−0.719830	−0.359915	+	0.932985i	$0.617194\pi$
$8$	1.00000	0.353553
$9$	2.92064	0.973547
$10$	−0.544807	−0.172283
$11$	−3.84930	−1.16061	−0.580304	−	0.814400i	$-0.697066\pi$
$11$	−3.84930	−1.16061	−0.580304	+	0.814400i	$0.697066\pi$
$12$	2.43324	0.702415
$13$	2.71965	0.754296	0.377148	−	0.926153i	$-0.376905\pi$
$13$	2.71965	0.754296	0.377148	+	0.926153i	$0.376905\pi$
$14$	−1.90449	−0.508996
$15$	−1.32564	−0.342280
$16$	1.00000	0.250000
$17$	−4.26349	−1.03405	−0.517025	−	0.855971i	$-0.672960\pi$
$17$	−4.26349	−1.03405	−0.517025	+	0.855971i	$0.672960\pi$
$18$	2.92064	0.688402
$19$	−7.08679	−1.62582	−0.812910	−	0.582389i	$-0.802118\pi$
$19$	−7.08679	−1.62582	−0.812910	+	0.582389i	$0.802118\pi$
$20$	−0.544807	−0.121823
$21$	−4.63408	−1.01124
$22$	−3.84930	−0.820673
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.43324	0.496682
$25$	−4.70319	−0.940637
$26$	2.71965	0.533368
$27$	−0.193096	−0.0371614
$28$	−1.90449	−0.359915
$29$	8.83309	1.64026	0.820132	−	0.572175i	$-0.193900\pi$
$29$	8.83309	1.64026	0.820132	+	0.572175i	$0.193900\pi$
$30$	−1.32564	−0.242029
$31$	−4.32031	−0.775950	−0.387975	−	0.921670i	$-0.626825\pi$
$31$	−4.32031	−0.775950	−0.387975	+	0.921670i	$0.626825\pi$
$32$	1.00000	0.176777
$33$	−9.36626	−1.63046
$34$	−4.26349	−0.731183
$35$	1.03758	0.175383
$36$	2.92064	0.486774
$37$	−8.31300	−1.36665	−0.683324	−	0.730115i	$-0.739466\pi$
$37$	−8.31300	−1.36665	−0.683324	+	0.730115i	$0.739466\pi$
$38$	−7.08679	−1.14963
$39$	6.61756	1.05966
$40$	−0.544807	−0.0861416
$41$	−9.86785	−1.54110	−0.770549	−	0.637380i	$-0.780018\pi$
$41$	−9.86785	−1.54110	−0.770549	+	0.637380i	$0.780018\pi$
$42$	−4.63408	−0.715053
$43$	−6.08037	−0.927247	−0.463624	−	0.886032i	$-0.653451\pi$
$43$	−6.08037	−0.927247	−0.463624	+	0.886032i	$0.653451\pi$
$44$	−3.84930	−0.580304
$45$	−1.59119	−0.237200
$46$	−1.00000	−0.147442
$47$	3.53820	0.516100	0.258050	−	0.966132i	$-0.416920\pi$
$47$	3.53820	0.516100	0.258050	+	0.966132i	$0.416920\pi$
$48$	2.43324	0.351208
$49$	−3.37292	−0.481845
$50$	−4.70319	−0.665131
$51$	−10.3741	−1.45266
$52$	2.71965	0.377148
$53$	5.56765	0.764775	0.382388	−	0.924002i	$-0.375102\pi$
$53$	5.56765	0.764775	0.382388	+	0.924002i	$0.375102\pi$
$54$	−0.193096	−0.0262771
$55$	2.09713	0.282776
$56$	−1.90449	−0.254498
$57$	−17.2438	−2.28400
$58$	8.83309	1.15984
$59$	−6.23303	−0.811471	−0.405736	−	0.913991i	$-0.632985\pi$
$59$	−6.23303	−0.811471	−0.405736	+	0.913991i	$0.632985\pi$
$60$	−1.32564	−0.171140
$61$	12.5435	1.60603	0.803015	−	0.595959i	$-0.203228\pi$
$61$	12.5435	1.60603	0.803015	+	0.595959i	$0.203228\pi$
$62$	−4.32031	−0.548680
$63$	−5.56233	−0.700788
$64$	1.00000	0.125000
$65$	−1.48169	−0.183781
$66$	−9.36626	−1.15291
$67$	7.33739	0.896405	0.448202	−	0.893932i	$-0.352064\pi$
$67$	7.33739	0.896405	0.448202	+	0.893932i	$0.352064\pi$
$68$	−4.26349	−0.517025
$69$	−2.43324	−0.292927
$70$	1.03758	0.124014
$71$	−7.91549	−0.939396	−0.469698	−	0.882827i	$-0.655637\pi$
$71$	−7.91549	−0.939396	−0.469698	+	0.882827i	$0.655637\pi$
$72$	2.92064	0.344201
$73$	10.2107	1.19507	0.597534	−	0.801844i	$-0.296147\pi$
$73$	10.2107	1.19507	0.597534	+	0.801844i	$0.296147\pi$
$74$	−8.31300	−0.966366
$75$	−11.4440	−1.32144
$76$	−7.08679	−0.812910
$77$	7.33095	0.835440
$78$	6.61756	0.749291
$79$	15.8850	1.78720	0.893602	−	0.448860i	$-0.148170\pi$
$79$	15.8850	1.78720	0.893602	+	0.448860i	$0.148170\pi$
$80$	−0.544807	−0.0609113
$81$	−9.23178	−1.02575
$82$	−9.86785	−1.08972
$83$	4.21260	0.462393	0.231197	−	0.972907i	$-0.425736\pi$
$83$	4.21260	0.462393	0.231197	+	0.972907i	$0.425736\pi$
$84$	−4.63408	−0.505619
$85$	2.32278	0.251941
$86$	−6.08037	−0.655663
$87$	21.4930	2.30429
$88$	−3.84930	−0.410337
$89$	2.53980	0.269219	0.134609	−	0.990899i	$-0.457022\pi$
$89$	2.53980	0.269219	0.134609	+	0.990899i	$0.457022\pi$
$90$	−1.59119	−0.167726
$91$	−5.17955	−0.542965
$92$	−1.00000	−0.104257
$93$	−10.5123	−1.09008
$94$	3.53820	0.364938
$95$	3.86093	0.396123
$96$	2.43324	0.248341
$97$	−11.2001	−1.13720	−0.568598	−	0.822615i	$-0.692514\pi$
$97$	−11.2001	−1.13720	−0.568598	+	0.822615i	$0.692514\pi$
$98$	−3.37292	−0.340716
$99$	−11.2424	−1.12991
$100$	−4.70319	−0.470319
$101$	0.613701	0.0610655	0.0305328	−	0.999534i	$-0.490280\pi$
$101$	0.613701	0.0610655	0.0305328	+	0.999534i	$0.490280\pi$
$102$	−10.3741	−1.02719
$103$	7.91949	0.780331	0.390165	−	0.920745i	$-0.372418\pi$
$103$	7.91949	0.780331	0.390165	+	0.920745i	$0.372418\pi$
$104$	2.71965	0.266684
$105$	2.52468	0.246383
$106$	5.56765	0.540778
$107$	−3.54230	−0.342448	−0.171224	−	0.985232i	$-0.554772\pi$
$107$	−3.54230	−0.342448	−0.171224	+	0.985232i	$0.554772\pi$
$108$	−0.193096	−0.0185807
$109$	−12.4397	−1.19151	−0.595754	−	0.803167i	$-0.703147\pi$
$109$	−12.4397	−1.19151	−0.595754	+	0.803167i	$0.703147\pi$
$110$	2.09713	0.199953
$111$	−20.2275	−1.91991
$112$	−1.90449	−0.179957
$113$	5.38232	0.506326	0.253163	−	0.967424i	$-0.418529\pi$
$113$	5.38232	0.506326	0.253163	+	0.967424i	$0.418529\pi$
$114$	−17.2438	−1.61503
$115$	0.544807	0.0508035
$116$	8.83309	0.820132
$117$	7.94314	0.734343
$118$	−6.23303	−0.573797
$119$	8.11978	0.744339
$120$	−1.32564	−0.121014
$121$	3.81711	0.347010
$122$	12.5435	1.13563
$123$	−24.0108	−2.16498
$124$	−4.32031	−0.387975
$125$	5.28636	0.472827
$126$	−5.56233	−0.495532
$127$	0.209260	0.0185688	0.00928440	−	0.999957i	$-0.497045\pi$
$127$	0.209260	0.0185688	0.00928440	+	0.999957i	$0.497045\pi$
$128$	1.00000	0.0883883
$129$	−14.7950	−1.30262
$130$	−1.48169	−0.129953
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−9.36626	−0.815228
$133$	13.4967	1.17031
$134$	7.33739	0.633854
$135$	0.105200	0.00905419
$136$	−4.26349	−0.365592
$137$	−18.4186	−1.57361	−0.786803	−	0.617204i	$-0.788265\pi$
$137$	−18.4186	−1.57361	−0.786803	+	0.617204i	$0.788265\pi$
$138$	−2.43324	−0.207131
$139$	16.0301	1.35965	0.679826	−	0.733373i	$-0.262055\pi$
$139$	16.0301	1.35965	0.679826	+	0.733373i	$0.262055\pi$
$140$	1.03758	0.0876915
$141$	8.60929	0.725033
$142$	−7.91549	−0.664253
$143$	−10.4688	−0.875442
$144$	2.92064	0.243387
$145$	−4.81233	−0.399642
$146$	10.2107	0.845041
$147$	−8.20711	−0.676911
$148$	−8.31300	−0.683324
$149$	1.97339	0.161667	0.0808333	−	0.996728i	$-0.474242\pi$
$149$	1.97339	0.161667	0.0808333	+	0.996728i	$0.474242\pi$
$150$	−11.4440	−0.934396
$151$	24.0183	1.95458	0.977291	−	0.211901i	$-0.0679654\pi$
$151$	24.0183	1.95458	0.977291	+	0.211901i	$0.0679654\pi$
$152$	−7.08679	−0.574814
$153$	−12.4521	−1.00670
$154$	7.33095	0.590745
$155$	2.35373	0.189057
$156$	6.61756	0.529829
$157$	3.55649	0.283839	0.141920	−	0.989878i	$-0.454673\pi$
$157$	3.55649	0.283839	0.141920	+	0.989878i	$0.454673\pi$
$158$	15.8850	1.26374
$159$	13.5474	1.07438
$160$	−0.544807	−0.0430708
$161$	1.90449	0.150095
$162$	−9.23178	−0.725317
$163$	1.81503	0.142164	0.0710820	−	0.997470i	$-0.477355\pi$
$163$	1.81503	0.142164	0.0710820	+	0.997470i	$0.477355\pi$
$164$	−9.86785	−0.770549
$165$	5.10280	0.397253
$166$	4.21260	0.326961
$167$	−1.76720	−0.136750	−0.0683750	−	0.997660i	$-0.521781\pi$
$167$	−1.76720	−0.136750	−0.0683750	+	0.997660i	$0.521781\pi$
$168$	−4.63408	−0.357527
$169$	−5.60348	−0.431037
$170$	2.32278	0.178149
$171$	−20.6980	−1.58281
$172$	−6.08037	−0.463624
$173$	−21.3933	−1.62651	−0.813253	−	0.581911i	$-0.802305\pi$
$173$	−21.3933	−1.62651	−0.813253	+	0.581911i	$0.802305\pi$
$174$	21.4930	1.62938
$175$	8.95717	0.677098
$176$	−3.84930	−0.290152
$177$	−15.1664	−1.13998
$178$	2.53980	0.190366
$179$	16.1639	1.20815	0.604075	−	0.796927i	$-0.293543\pi$
$179$	16.1639	1.20815	0.604075	+	0.796927i	$0.293543\pi$
$180$	−1.59119	−0.118600
$181$	−14.0585	−1.04496	−0.522480	−	0.852652i	$-0.674993\pi$
$181$	−14.0585	−1.04496	−0.522480	+	0.852652i	$0.674993\pi$
$182$	−5.17955	−0.383934
$183$	30.5213	2.25620
$184$	−1.00000	−0.0737210
$185$	4.52898	0.332977
$186$	−10.5123	−0.770802
$187$	16.4115	1.20013
$188$	3.53820	0.258050
$189$	0.367750	0.0267499
$190$	3.86093	0.280101
$191$	−22.8847	−1.65588	−0.827939	−	0.560817i	$-0.810487\pi$
$191$	−22.8847	−1.65588	−0.827939	+	0.560817i	$0.810487\pi$
$192$	2.43324	0.175604
$193$	17.9836	1.29449	0.647245	−	0.762282i	$-0.275921\pi$
$193$	17.9836	1.29449	0.647245	+	0.762282i	$0.275921\pi$
$194$	−11.2001	−0.804119
$195$	−3.60529	−0.258181
$196$	−3.37292	−0.240923
$197$	7.50328	0.534586	0.267293	−	0.963615i	$-0.413871\pi$
$197$	7.50328	0.534586	0.267293	+	0.963615i	$0.413871\pi$
$198$	−11.2424	−0.798964
$199$	15.7312	1.11515	0.557576	−	0.830126i	$-0.311732\pi$
$199$	15.7312	1.11515	0.557576	+	0.830126i	$0.311732\pi$
$200$	−4.70319	−0.332565
$201$	17.8536	1.25930
$202$	0.613701	0.0431799
$203$	−16.8225	−1.18071
$204$	−10.3741	−0.726332
$205$	5.37607	0.375481
$206$	7.91949	0.551777
$207$	−2.92064	−0.202999
$208$	2.71965	0.188574
$209$	27.2792	1.88694
$210$	2.52468	0.174219
$211$	−7.84886	−0.540338	−0.270169	−	0.962813i	$-0.587079\pi$
$211$	−7.84886	−0.540338	−0.270169	+	0.962813i	$0.587079\pi$
$212$	5.56765	0.382388
$213$	−19.2603	−1.31969
$214$	−3.54230	−0.242147
$215$	3.31263	0.225919
$216$	−0.193096	−0.0131385
$217$	8.22799	0.558552
$218$	−12.4397	−0.842523
$219$	24.8450	1.67887
$220$	2.09713	0.141388
$221$	−11.5952	−0.779979
$222$	−20.2275	−1.35758
$223$	−10.0839	−0.675268	−0.337634	−	0.941277i	$-0.609627\pi$
$223$	−10.0839	−0.675268	−0.337634	+	0.941277i	$0.609627\pi$
$224$	−1.90449	−0.127249
$225$	−13.7363	−0.915755
$226$	5.38232	0.358026
$227$	−15.6491	−1.03866	−0.519332	−	0.854572i	$-0.673819\pi$
$227$	−15.6491	−1.03866	−0.519332	+	0.854572i	$0.673819\pi$
$228$	−17.2438	−1.14200
$229$	−24.6643	−1.62986	−0.814932	−	0.579557i	$-0.803226\pi$
$229$	−24.6643	−1.62986	−0.814932	+	0.579557i	$0.803226\pi$
$230$	0.544807	0.0359235
$231$	17.8379	1.17365
$232$	8.83309	0.579921
$233$	0.977473	0.0640364	0.0320182	−	0.999487i	$-0.489807\pi$
$233$	0.977473	0.0640364	0.0320182	+	0.999487i	$0.489807\pi$
$234$	7.94314	0.519259
$235$	−1.92764	−0.125745
$236$	−6.23303	−0.405736
$237$	38.6520	2.51072
$238$	8.11978	0.526327
$239$	25.2253	1.63169	0.815845	−	0.578270i	$-0.196272\pi$
$239$	25.2253	1.63169	0.815845	+	0.578270i	$0.196272\pi$
$240$	−1.32564	−0.0855700
$241$	−19.0114	−1.22463	−0.612316	−	0.790613i	$-0.709762\pi$
$241$	−19.0114	−1.22463	−0.612316	+	0.790613i	$0.709762\pi$
$242$	3.81711	0.245373
$243$	−21.8838	−1.40385
$244$	12.5435	0.803015
$245$	1.83759	0.117399
$246$	−24.0108	−1.53087
$247$	−19.2736	−1.22635
$248$	−4.32031	−0.274340
$249$	10.2503	0.649584
$250$	5.28636	0.334339
$251$	15.6669	0.988883	0.494442	−	0.869211i	$-0.335373\pi$
$251$	15.6669	0.988883	0.494442	+	0.869211i	$0.335373\pi$
$252$	−5.56233	−0.350394
$253$	3.84930	0.242003
$254$	0.209260	0.0131301
$255$	5.65188	0.353934
$256$	1.00000	0.0625000
$257$	−3.67019	−0.228940	−0.114470	−	0.993427i	$-0.536517\pi$
$257$	−3.67019	−0.228940	−0.114470	+	0.993427i	$0.536517\pi$
$258$	−14.7950	−0.921095
$259$	15.8320	0.983754
$260$	−1.48169	−0.0918903
$261$	25.7983	1.59687
$262$	1.00000	0.0617802
$263$	−8.43800	−0.520309	−0.260155	−	0.965567i	$-0.583774\pi$
$263$	−8.43800	−0.520309	−0.260155	+	0.965567i	$0.583774\pi$
$264$	−9.36626	−0.576453
$265$	−3.03329	−0.186334
$266$	13.4967	0.827537
$267$	6.17994	0.378206
$268$	7.33739	0.448202
$269$	−20.1901	−1.23101	−0.615506	−	0.788132i	$-0.711048\pi$
$269$	−20.1901	−1.23101	−0.615506	+	0.788132i	$0.711048\pi$
$270$	0.105200	0.00640228
$271$	3.90732	0.237353	0.118676	−	0.992933i	$-0.462135\pi$
$271$	3.90732	0.237353	0.118676	+	0.992933i	$0.462135\pi$
$272$	−4.26349	−0.258512
$273$	−12.6031	−0.762773
$274$	−18.4186	−1.11271
$275$	18.1040	1.09171
$276$	−2.43324	−0.146464
$277$	−15.3088	−0.919817	−0.459908	−	0.887966i	$-0.652118\pi$
$277$	−15.3088	−0.919817	−0.459908	+	0.887966i	$0.652118\pi$
$278$	16.0301	0.961419
$279$	−12.6181	−0.755424
$280$	1.03758	0.0620072
$281$	−30.9643	−1.84717	−0.923587	−	0.383389i	$-0.874757\pi$
$281$	−30.9643	−1.84717	−0.923587	+	0.383389i	$0.874757\pi$
$282$	8.60929	0.512676
$283$	15.2739	0.907940	0.453970	−	0.891017i	$-0.350007\pi$
$283$	15.2739	0.907940	0.453970	+	0.891017i	$0.350007\pi$
$284$	−7.91549	−0.469698
$285$	9.39456	0.556486
$286$	−10.4688	−0.619031
$287$	18.7932	1.10933
$288$	2.92064	0.172100
$289$	1.17738	0.0692575
$290$	−4.81233	−0.282590
$291$	−27.2525	−1.59757
$292$	10.2107	0.597534
$293$	−21.7739	−1.27204	−0.636022	−	0.771671i	$-0.719421\pi$
$293$	−21.7739	−1.27204	−0.636022	+	0.771671i	$0.719421\pi$
$294$	−8.20711	−0.478648
$295$	3.39580	0.197711
$296$	−8.31300	−0.483183
$297$	0.743285	0.0431298
$298$	1.97339	0.114316
$299$	−2.71965	−0.157282
$300$	−11.4440	−0.660718
$301$	11.5800	0.667460
$302$	24.0183	1.38210
$303$	1.49328	0.0857867
$304$	−7.08679	−0.406455
$305$	−6.83378	−0.391301
$306$	−12.4521	−0.711841
$307$	6.96804	0.397687	0.198843	−	0.980031i	$-0.436281\pi$
$307$	6.96804	0.397687	0.198843	+	0.980031i	$0.436281\pi$
$308$	7.33095	0.417720
$309$	19.2700	1.09623
$310$	2.35373	0.133683
$311$	5.61465	0.318378	0.159189	−	0.987248i	$-0.449112\pi$
$311$	5.61465	0.318378	0.159189	+	0.987248i	$0.449112\pi$
$312$	6.61756	0.374646
$313$	−0.857294	−0.0484571	−0.0242286	−	0.999706i	$-0.507713\pi$
$313$	−0.857294	−0.0484571	−0.0242286	+	0.999706i	$0.507713\pi$
$314$	3.55649	0.200705
$315$	3.03040	0.170744
$316$	15.8850	0.893602
$317$	−14.7419	−0.827985	−0.413992	−	0.910280i	$-0.635866\pi$
$317$	−14.7419	−0.827985	−0.413992	+	0.910280i	$0.635866\pi$
$318$	13.5474	0.759701
$319$	−34.0012	−1.90370
$320$	−0.544807	−0.0304556
$321$	−8.61927	−0.481081
$322$	1.90449	0.106133
$323$	30.2145	1.68118
$324$	−9.23178	−0.512876
$325$	−12.7910	−0.709519
$326$	1.81503	0.100525
$327$	−30.2687	−1.67387
$328$	−9.86785	−0.544861
$329$	−6.73848	−0.371504
$330$	5.10280	0.280900
$331$	−24.9409	−1.37087	−0.685437	−	0.728132i	$-0.740389\pi$
$331$	−24.9409	−1.37087	−0.685437	+	0.728132i	$0.740389\pi$
$332$	4.21260	0.231197
$333$	−24.2793	−1.33050
$334$	−1.76720	−0.0966968
$335$	−3.99746	−0.218405
$336$	−4.63408	−0.252810
$337$	−25.1734	−1.37128	−0.685641	−	0.727940i	$-0.740478\pi$
$337$	−25.1734	−1.37128	−0.685641	+	0.727940i	$0.740478\pi$
$338$	−5.60348	−0.304789
$339$	13.0965	0.711302
$340$	2.32278	0.125971
$341$	16.6302	0.900574
$342$	−20.6980	−1.11922
$343$	19.7551	1.06668
$344$	−6.08037	−0.327831
$345$	1.32564	0.0713703
$346$	−21.3933	−1.15011
$347$	23.8893	1.28244	0.641222	−	0.767355i	$-0.278428\pi$
$347$	23.8893	1.28244	0.641222	+	0.767355i	$0.278428\pi$
$348$	21.4930	1.15215
$349$	−30.6867	−1.64262	−0.821310	−	0.570481i	$-0.806757\pi$
$349$	−30.6867	−1.64262	−0.821310	+	0.570481i	$0.806757\pi$
$350$	8.95717	0.478781
$351$	−0.525155	−0.0280307
$352$	−3.84930	−0.205168
$353$	17.6704	0.940499	0.470250	−	0.882533i	$-0.344164\pi$
$353$	17.6704	0.940499	0.470250	+	0.882533i	$0.344164\pi$
$354$	−15.1664	−0.806087
$355$	4.31242	0.228879
$356$	2.53980	0.134609
$357$	19.7574	1.04567
$358$	16.1639	0.854291
$359$	−15.5739	−0.821961	−0.410980	−	0.911644i	$-0.634814\pi$
$359$	−15.5739	−0.821961	−0.410980	+	0.911644i	$0.634814\pi$
$360$	−1.59119	−0.0838629
$361$	31.2225	1.64329
$362$	−14.0585	−0.738898
$363$	9.28793	0.487490
$364$	−5.17955	−0.271482
$365$	−5.56284	−0.291172
$366$	30.5213	1.59537
$367$	−18.1630	−0.948101	−0.474051	−	0.880498i	$-0.657209\pi$
$367$	−18.1630	−0.948101	−0.474051	+	0.880498i	$0.657209\pi$
$368$	−1.00000	−0.0521286
$369$	−28.8205	−1.50033
$370$	4.52898	0.235450
$371$	−10.6035	−0.550508
$372$	−10.5123	−0.545039
$373$	−3.77575	−0.195501	−0.0977505	−	0.995211i	$-0.531165\pi$
$373$	−3.77575	−0.195501	−0.0977505	+	0.995211i	$0.531165\pi$
$374$	16.4115	0.848617
$375$	12.8630	0.664241
$376$	3.53820	0.182469
$377$	24.0229	1.23724
$378$	0.367750	0.0189150
$379$	−14.8656	−0.763593	−0.381797	−	0.924246i	$-0.624695\pi$
$379$	−14.8656	−0.763593	−0.381797	+	0.924246i	$0.624695\pi$
$380$	3.86093	0.198062
$381$	0.509179	0.0260860
$382$	−22.8847	−1.17088
$383$	32.3586	1.65345	0.826723	−	0.562610i	$-0.190203\pi$
$383$	32.3586	1.65345	0.826723	+	0.562610i	$0.190203\pi$
$384$	2.43324	0.124171
$385$	−3.99396	−0.203551
$386$	17.9836	0.915342
$387$	−17.7586	−0.902719
$388$	−11.2001	−0.568598
$389$	−0.837309	−0.0424532	−0.0212266	−	0.999775i	$-0.506757\pi$
$389$	−0.837309	−0.0424532	−0.0212266	+	0.999775i	$0.506757\pi$
$390$	−3.60529	−0.182561
$391$	4.26349	0.215614
$392$	−3.37292	−0.170358
$393$	2.43324	0.122741
$394$	7.50328	0.378010
$395$	−8.65427	−0.435444
$396$	−11.2424	−0.564953
$397$	−23.6522	−1.18707	−0.593535	−	0.804809i	$-0.702268\pi$
$397$	−23.6522	−1.18707	−0.593535	+	0.804809i	$0.702268\pi$
$398$	15.7312	0.788531
$399$	32.8407	1.64409
$400$	−4.70319	−0.235159
$401$	14.3015	0.714183	0.357092	−	0.934069i	$-0.383768\pi$
$401$	14.3015	0.714183	0.357092	+	0.934069i	$0.383768\pi$
$402$	17.8536	0.890457
$403$	−11.7497	−0.585296
$404$	0.613701	0.0305328
$405$	5.02954	0.249920
$406$	−16.8225	−0.834888
$407$	31.9992	1.58614
$408$	−10.3741	−0.513594
$409$	22.2861	1.10198	0.550988	−	0.834513i	$-0.314251\pi$
$409$	22.2861	1.10198	0.550988	+	0.834513i	$0.314251\pi$
$410$	5.37607	0.265505
$411$	−44.8168	−2.21065
$412$	7.91949	0.390165
$413$	11.8707	0.584121
$414$	−2.92064	−0.143542
$415$	−2.29506	−0.112660
$416$	2.71965	0.133342
$417$	39.0049	1.91008
$418$	27.2792	1.33427
$419$	29.4035	1.43645	0.718227	−	0.695808i	$-0.244954\pi$
$419$	29.4035	1.43645	0.718227	+	0.695808i	$0.244954\pi$
$420$	2.52468	0.123192
$421$	−9.65538	−0.470574	−0.235287	−	0.971926i	$-0.575603\pi$
$421$	−9.65538	−0.470574	−0.235287	+	0.971926i	$0.575603\pi$
$422$	−7.84886	−0.382076
$423$	10.3338	0.502448
$424$	5.56765	0.270389
$425$	20.0520	0.972665
$426$	−19.2603	−0.933163
$427$	−23.8890	−1.15607
$428$	−3.54230	−0.171224
$429$	−25.4730	−1.22985
$430$	3.31263	0.159749
$431$	−9.39164	−0.452379	−0.226190	−	0.974083i	$-0.572627\pi$
$431$	−9.39164	−0.452379	−0.226190	+	0.974083i	$0.572627\pi$
$432$	−0.193096	−0.00929034
$433$	4.62692	0.222356	0.111178	−	0.993801i	$-0.464538\pi$
$433$	4.62692	0.222356	0.111178	+	0.993801i	$0.464538\pi$
$434$	8.22799	0.394956
$435$	−11.7095	−0.561429
$436$	−12.4397	−0.595754
$437$	7.08679	0.339007
$438$	24.8450	1.18714
$439$	9.93352	0.474101	0.237051	−	0.971497i	$-0.423819\pi$
$439$	9.93352	0.474101	0.237051	+	0.971497i	$0.423819\pi$
$440$	2.09713	0.0999765
$441$	−9.85108	−0.469099
$442$	−11.5952	−0.551529
$443$	2.29811	0.109186	0.0545931	−	0.998509i	$-0.482614\pi$
$443$	2.29811	0.109186	0.0545931	+	0.998509i	$0.482614\pi$
$444$	−20.2275	−0.959954
$445$	−1.38370	−0.0655938
$446$	−10.0839	−0.477487
$447$	4.80173	0.227114
$448$	−1.90449	−0.0899787
$449$	12.7587	0.602122	0.301061	−	0.953605i	$-0.402659\pi$
$449$	12.7587	0.602122	0.301061	+	0.953605i	$0.402659\pi$
$450$	−13.7363	−0.647536
$451$	37.9843	1.78861
$452$	5.38232	0.253163
$453$	58.4422	2.74586
$454$	−15.6491	−0.734447
$455$	2.82186	0.132291
$456$	−17.2438	−0.807516
$457$	15.0752	0.705189	0.352594	−	0.935776i	$-0.385300\pi$
$457$	15.0752	0.705189	0.352594	+	0.935776i	$0.385300\pi$
$458$	−24.6643	−1.15249
$459$	0.823264	0.0384267
$460$	0.544807	0.0254018
$461$	20.3095	0.945907	0.472954	−	0.881087i	$-0.343188\pi$
$461$	20.3095	0.945907	0.472954	+	0.881087i	$0.343188\pi$
$462$	17.8379	0.829896
$463$	−16.3667	−0.760625	−0.380312	−	0.924858i	$-0.624184\pi$
$463$	−16.3667	−0.760625	−0.380312	+	0.924858i	$0.624184\pi$
$464$	8.83309	0.410066
$465$	5.72719	0.265592
$466$	0.977473	0.0452806
$467$	33.9784	1.57233	0.786167	−	0.618013i	$-0.212062\pi$
$467$	33.9784	1.57233	0.786167	+	0.618013i	$0.212062\pi$
$468$	7.94314	0.367172
$469$	−13.9740	−0.645259
$470$	−1.92764	−0.0889154
$471$	8.65379	0.398746
$472$	−6.23303	−0.286898
$473$	23.4052	1.07617
$474$	38.6520	1.77535
$475$	33.3305	1.52931
$476$	8.11978	0.372170
$477$	16.2611	0.744545
$478$	25.2253	1.15378
$479$	11.9333	0.545246	0.272623	−	0.962121i	$-0.412109\pi$
$479$	11.9333	0.545246	0.272623	+	0.962121i	$0.412109\pi$
$480$	−1.32564	−0.0605071
$481$	−22.6085	−1.03086
$482$	−19.0114	−0.865946
$483$	4.63408	0.210858
$484$	3.81711	0.173505
$485$	6.10188	0.277072
$486$	−21.8838	−0.992670
$487$	28.6387	1.29774	0.648872	−	0.760898i	$-0.275241\pi$
$487$	28.6387	1.29774	0.648872	+	0.760898i	$0.275241\pi$
$488$	12.5435	0.567817
$489$	4.41639	0.199716
$490$	1.83759	0.0830138
$491$	−9.49334	−0.428428	−0.214214	−	0.976787i	$-0.568719\pi$
$491$	−9.49334	−0.428428	−0.214214	+	0.976787i	$0.568719\pi$
$492$	−24.0108	−1.08249
$493$	−37.6598	−1.69611
$494$	−19.2736	−0.867160
$495$	6.12495	0.275296
$496$	−4.32031	−0.193988
$497$	15.0750	0.676205
$498$	10.2503	0.459325
$499$	1.48014	0.0662603	0.0331302	−	0.999451i	$-0.489452\pi$
$499$	1.48014	0.0662603	0.0331302	+	0.999451i	$0.489452\pi$
$500$	5.28636	0.236413
$501$	−4.30001	−0.192110
$502$	15.6669	0.699246
$503$	24.7541	1.10373	0.551865	−	0.833934i	$-0.313917\pi$
$503$	24.7541	1.10373	0.551865	+	0.833934i	$0.313917\pi$
$504$	−5.56233	−0.247766
$505$	−0.334349	−0.0148783
$506$	3.84930	0.171122
$507$	−13.6346	−0.605534
$508$	0.209260	0.00928440
$509$	0.549670	0.0243637	0.0121818	−	0.999926i	$-0.496122\pi$
$509$	0.549670	0.0243637	0.0121818	+	0.999926i	$0.496122\pi$
$510$	5.65188	0.250269
$511$	−19.4461	−0.860245
$512$	1.00000	0.0441942
$513$	1.36843	0.0604177
$514$	−3.67019	−0.161885
$515$	−4.31460	−0.190124
$516$	−14.7950	−0.651312
$517$	−13.6196	−0.598990
$518$	15.8320	0.695619
$519$	−52.0551	−2.28496
$520$	−1.48169	−0.0649763
$521$	35.1299	1.53907	0.769535	−	0.638605i	$-0.220488\pi$
$521$	35.1299	1.53907	0.769535	+	0.638605i	$0.220488\pi$
$522$	25.7983	1.12916
$523$	−24.5280	−1.07253	−0.536267	−	0.844048i	$-0.680166\pi$
$523$	−24.5280	−1.07253	−0.536267	+	0.844048i	$0.680166\pi$
$524$	1.00000	0.0436852
$525$	21.7949	0.951208
$526$	−8.43800	−0.367914
$527$	18.4196	0.802371
$528$	−9.36626	−0.407614
$529$	1.00000	0.0434783
$530$	−3.03329	−0.131758
$531$	−18.2044	−0.790006
$532$	13.4967	0.585157
$533$	−26.8371	−1.16245
$534$	6.17994	0.267432
$535$	1.92987	0.0834357
$536$	7.33739	0.316927
$537$	39.3307	1.69725
$538$	−20.1901	−0.870457
$539$	12.9834	0.559233
$540$	0.105200	0.00452709
$541$	−2.38867	−0.102697	−0.0513484	−	0.998681i	$-0.516352\pi$
$541$	−2.38867	−0.102697	−0.0513484	+	0.998681i	$0.516352\pi$
$542$	3.90732	0.167834
$543$	−34.2077	−1.46799
$544$	−4.26349	−0.182796
$545$	6.77724	0.290305
$546$	−12.6031	−0.539362
$547$	−0.0853579	−0.00364964	−0.00182482	−	0.999998i	$-0.500581\pi$
$547$	−0.0853579	−0.00364964	−0.00182482	+	0.999998i	$0.500581\pi$
$548$	−18.4186	−0.786803
$549$	36.6350	1.56355
$550$	18.1040	0.771956
$551$	−62.5982	−2.66677
$552$	−2.43324	−0.103565
$553$	−30.2529	−1.28648
$554$	−15.3088	−0.650409
$555$	11.0201	0.467776
$556$	16.0301	0.679826
$557$	−16.8111	−0.712311	−0.356156	−	0.934427i	$-0.615913\pi$
$557$	−16.8111	−0.712311	−0.356156	+	0.934427i	$0.615913\pi$
$558$	−12.6181	−0.534166
$559$	−16.5365	−0.699419
$560$	1.03758	0.0438457
$561$	39.9330	1.68597
$562$	−30.9643	−1.30615
$563$	−0.143355	−0.00604171	−0.00302086	−	0.999995i	$-0.500962\pi$
$563$	−0.143355	−0.00604171	−0.00302086	+	0.999995i	$0.500962\pi$
$564$	8.60929	0.362517
$565$	−2.93232	−0.123364
$566$	15.2739	0.642010
$567$	17.5818	0.738367
$568$	−7.91549	−0.332127
$569$	8.30129	0.348008	0.174004	−	0.984745i	$-0.444329\pi$
$569$	8.30129	0.348008	0.174004	+	0.984745i	$0.444329\pi$
$570$	9.39456	0.393495
$571$	−21.5966	−0.903790	−0.451895	−	0.892071i	$-0.649252\pi$
$571$	−21.5966	−0.903790	−0.451895	+	0.892071i	$0.649252\pi$
$572$	−10.4688	−0.437721
$573$	−55.6839	−2.32623
$574$	18.7932	0.784414
$575$	4.70319	0.196136
$576$	2.92064	0.121693
$577$	9.56123	0.398039	0.199020	−	0.979995i	$-0.436224\pi$
$577$	9.56123	0.398039	0.199020	+	0.979995i	$0.436224\pi$
$578$	1.17738	0.0489725
$579$	43.7584	1.81854
$580$	−4.81233	−0.199821
$581$	−8.02286	−0.332844
$582$	−27.2525	−1.12965
$583$	−21.4315	−0.887604
$584$	10.2107	0.422520
$585$	−4.32748	−0.178919
$586$	−21.7739	−0.899471
$587$	33.0100	1.36247	0.681234	−	0.732065i	$-0.261443\pi$
$587$	33.0100	1.36247	0.681234	+	0.732065i	$0.261443\pi$
$588$	−8.20711	−0.338455
$589$	30.6171	1.26156
$590$	3.39580	0.139803
$591$	18.2573	0.751003
$592$	−8.31300	−0.341662
$593$	−38.9670	−1.60018	−0.800092	−	0.599877i	$-0.795216\pi$
$593$	−38.9670	−1.60018	−0.800092	+	0.599877i	$0.795216\pi$
$594$	0.743285	0.0304973
$595$	−4.42371	−0.181355
$596$	1.97339	0.0808333
$597$	38.2776	1.56660
$598$	−2.71965	−0.111215
$599$	40.2127	1.64305	0.821523	−	0.570175i	$-0.193125\pi$
$599$	40.2127	1.64305	0.821523	+	0.570175i	$0.193125\pi$
$600$	−11.4440	−0.467198
$601$	21.1266	0.861773	0.430887	−	0.902406i	$-0.358201\pi$
$601$	21.1266	0.861773	0.430887	+	0.902406i	$0.358201\pi$
$602$	11.5800	0.471965
$603$	21.4299	0.872693
$604$	24.0183	0.977291
$605$	−2.07959	−0.0845472
$606$	1.49328	0.0606604
$607$	−25.9335	−1.05261	−0.526304	−	0.850297i	$-0.676422\pi$
$607$	−25.9335	−1.05261	−0.526304	+	0.850297i	$0.676422\pi$
$608$	−7.08679	−0.287407
$609$	−40.9332	−1.65870
$610$	−6.83378	−0.276692
$611$	9.62269	0.389292
$612$	−12.4521	−0.503348
$613$	−7.28172	−0.294106	−0.147053	−	0.989129i	$-0.546979\pi$
$613$	−7.28172	−0.294106	−0.147053	+	0.989129i	$0.546979\pi$
$614$	6.96804	0.281207
$615$	13.0813	0.527487
$616$	7.33095	0.295373
$617$	−47.8465	−1.92623	−0.963113	−	0.269097i	$-0.913275\pi$
$617$	−47.8465	−1.92623	−0.963113	+	0.269097i	$0.913275\pi$
$618$	19.2700	0.775153
$619$	1.90473	0.0765574	0.0382787	−	0.999267i	$-0.487813\pi$
$619$	1.90473	0.0765574	0.0382787	+	0.999267i	$0.487813\pi$
$620$	2.35373	0.0945283
$621$	0.193096	0.00774868
$622$	5.61465	0.225127
$623$	−4.83703	−0.193792
$624$	6.61756	0.264914
$625$	20.6359	0.825435
$626$	−0.857294	−0.0342644
$627$	66.3767	2.65083
$628$	3.55649	0.141920
$629$	35.4424	1.41318
$630$	3.03040	0.120734
$631$	−17.4315	−0.693938	−0.346969	−	0.937877i	$-0.612789\pi$
$631$	−17.4315	−0.693938	−0.346969	+	0.937877i	$0.612789\pi$
$632$	15.8850	0.631872
$633$	−19.0981	−0.759082
$634$	−14.7419	−0.585474
$635$	−0.114006	−0.00452420
$636$	13.5474	0.537190
$637$	−9.17317	−0.363454
$638$	−34.0012	−1.34612
$639$	−23.1183	−0.914547
$640$	−0.544807	−0.0215354
$641$	−24.8772	−0.982589	−0.491294	−	0.870994i	$-0.663476\pi$
$641$	−24.8772	−0.982589	−0.491294	+	0.870994i	$0.663476\pi$
$642$	−8.61927	−0.340175
$643$	10.1365	0.399744	0.199872	−	0.979822i	$-0.435947\pi$
$643$	10.1365	0.399744	0.199872	+	0.979822i	$0.435947\pi$
$644$	1.90449	0.0750474
$645$	8.06041	0.317378
$646$	30.2145	1.18877
$647$	−29.8350	−1.17294	−0.586468	−	0.809972i	$-0.699482\pi$
$647$	−29.8350	−1.17294	−0.586468	+	0.809972i	$0.699482\pi$
$648$	−9.23178	−0.362658
$649$	23.9928	0.941799
$650$	−12.7910	−0.501706
$651$	20.0206	0.784671
$652$	1.81503	0.0710820
$653$	−10.3014	−0.403124	−0.201562	−	0.979476i	$-0.564602\pi$
$653$	−10.3014	−0.403124	−0.201562	+	0.979476i	$0.564602\pi$
$654$	−30.2687	−1.18360
$655$	−0.544807	−0.0212874
$656$	−9.86785	−0.385275
$657$	29.8217	1.16346
$658$	−6.73848	−0.262693
$659$	−28.1854	−1.09795	−0.548973	−	0.835840i	$-0.684981\pi$
$659$	−28.1854	−1.09795	−0.548973	+	0.835840i	$0.684981\pi$
$660$	5.10280	0.198626
$661$	49.3497	1.91948	0.959741	−	0.280887i	$-0.0906285\pi$
$661$	49.3497	1.91948	0.959741	+	0.280887i	$0.0906285\pi$
$662$	−24.9409	−0.969355
$663$	−28.2139	−1.09574
$664$	4.21260	0.163481
$665$	−7.35311	−0.285141
$666$	−24.2793	−0.940804
$667$	−8.83309	−0.342019
$668$	−1.76720	−0.0683750
$669$	−24.5365	−0.948637
$670$	−3.99746	−0.154435
$671$	−48.2836	−1.86397
$672$	−4.63408	−0.178763
$673$	−43.1980	−1.66516	−0.832580	−	0.553905i	$-0.813137\pi$
$673$	−43.1980	−1.66516	−0.832580	+	0.553905i	$0.813137\pi$
$674$	−25.1734	−0.969642
$675$	0.908167	0.0349554
$676$	−5.60348	−0.215519
$677$	45.5339	1.75001	0.875005	−	0.484114i	$-0.160858\pi$
$677$	45.5339	1.75001	0.875005	+	0.484114i	$0.160858\pi$
$678$	13.0965	0.502966
$679$	21.3304	0.818587
$680$	2.32278	0.0890746
$681$	−38.0779	−1.45915
$682$	16.6302	0.636802
$683$	12.5328	0.479556	0.239778	−	0.970828i	$-0.422925\pi$
$683$	12.5328	0.479556	0.239778	+	0.970828i	$0.422925\pi$
$684$	−20.6980	−0.791407
$685$	10.0346	0.383402
$686$	19.7551	0.754254
$687$	−60.0141	−2.28968
$688$	−6.08037	−0.231812
$689$	15.1421	0.576867
$690$	1.32564	0.0504664
$691$	−7.17521	−0.272958	−0.136479	−	0.990643i	$-0.543579\pi$
$691$	−7.17521	−0.272958	−0.136479	+	0.990643i	$0.543579\pi$
$692$	−21.3933	−0.813253
$693$	21.4111	0.813340
$694$	23.8893	0.906825
$695$	−8.73329	−0.331273
$696$	21.4930	0.814690
$697$	42.0715	1.59357
$698$	−30.6867	−1.16151
$699$	2.37842	0.0899603
$700$	8.95717	0.338549
$701$	−0.895581	−0.0338256	−0.0169128	−	0.999857i	$-0.505384\pi$
$701$	−0.895581	−0.0338256	−0.0169128	+	0.999857i	$0.505384\pi$
$702$	−0.525155	−0.0198207
$703$	58.9124	2.22192
$704$	−3.84930	−0.145076
$705$	−4.69040	−0.176651
$706$	17.6704	0.665033
$707$	−1.16879	−0.0439568
$708$	−15.1664	−0.569990
$709$	37.2763	1.39994	0.699970	−	0.714172i	$-0.253197\pi$
$709$	37.2763	1.39994	0.699970	+	0.714172i	$0.253197\pi$
$710$	4.31242	0.161842
$711$	46.3944	1.73993
$712$	2.53980	0.0951832
$713$	4.32031	0.161797
$714$	19.7574	0.739400
$715$	5.70346	0.213297
$716$	16.1639	0.604075
$717$	61.3792	2.29225
$718$	−15.5739	−0.581214
$719$	−35.7960	−1.33497	−0.667484	−	0.744624i	$-0.732629\pi$
$719$	−35.7960	−1.33497	−0.667484	+	0.744624i	$0.732629\pi$
$720$	−1.59119	−0.0593000
$721$	−15.0826	−0.561705
$722$	31.2225	1.16198
$723$	−46.2593	−1.72040
$724$	−14.0585	−0.522480
$725$	−41.5437	−1.54289
$726$	9.28793	0.344707
$727$	−13.3709	−0.495899	−0.247950	−	0.968773i	$-0.579757\pi$
$727$	−13.3709	−0.495899	−0.247950	+	0.968773i	$0.579757\pi$
$728$	−5.17955	−0.191967
$729$	−25.5532	−0.946414
$730$	−5.56284	−0.205890
$731$	25.9236	0.958819
$732$	30.5213	1.12810
$733$	22.0956	0.816119	0.408060	−	0.912955i	$-0.366206\pi$
$733$	22.0956	0.816119	0.408060	+	0.912955i	$0.366206\pi$
$734$	−18.1630	−0.670409
$735$	4.47129	0.164926
$736$	−1.00000	−0.0368605
$737$	−28.2438	−1.04037
$738$	−28.8205	−1.06090
$739$	−43.9535	−1.61686	−0.808428	−	0.588595i	$-0.799681\pi$
$739$	−43.9535	−1.61686	−0.808428	+	0.588595i	$0.799681\pi$
$740$	4.52898	0.166489
$741$	−46.8972	−1.72281
$742$	−10.6035	−0.389268
$743$	6.95216	0.255050	0.127525	−	0.991835i	$-0.459297\pi$
$743$	6.95216	0.255050	0.127525	+	0.991835i	$0.459297\pi$
$744$	−10.5123	−0.385401
$745$	−1.07512	−0.0393893
$746$	−3.77575	−0.138240
$747$	12.3035	0.450162
$748$	16.4115	0.600063
$749$	6.74628	0.246504
$750$	12.8630	0.469689
$751$	−27.2535	−0.994495	−0.497248	−	0.867609i	$-0.665656\pi$
$751$	−27.2535	−0.994495	−0.497248	+	0.867609i	$0.665656\pi$
$752$	3.53820	0.129025
$753$	38.1212	1.38921
$754$	24.0229	0.874864
$755$	−13.0853	−0.476224
$756$	0.367750	0.0133749
$757$	−13.0193	−0.473193	−0.236597	−	0.971608i	$-0.576032\pi$
$757$	−13.0193	−0.473193	−0.236597	+	0.971608i	$0.576032\pi$
$758$	−14.8656	−0.539942
$759$	9.36626	0.339974
$760$	3.86093	0.140051
$761$	−32.7825	−1.18836	−0.594182	−	0.804331i	$-0.702524\pi$
$761$	−32.7825	−1.18836	−0.594182	+	0.804331i	$0.702524\pi$
$762$	0.509179	0.0184456
$763$	23.6913	0.857682
$764$	−22.8847	−0.827939
$765$	6.78401	0.245277
$766$	32.3586	1.16916
$767$	−16.9517	−0.612090
$768$	2.43324	0.0878019
$769$	30.8303	1.11177	0.555884	−	0.831260i	$-0.312380\pi$
$769$	30.8303	1.11177	0.555884	+	0.831260i	$0.312380\pi$
$770$	−3.99396	−0.143932
$771$	−8.93043	−0.321622
$772$	17.9836	0.647245
$773$	−34.4560	−1.23930	−0.619648	−	0.784880i	$-0.712725\pi$
$773$	−34.4560	−1.23930	−0.619648	+	0.784880i	$0.712725\pi$
$774$	−17.7586	−0.638319
$775$	20.3192	0.729888
$776$	−11.2001	−0.402060
$777$	38.5231	1.38201
$778$	−0.837309	−0.0300190
$779$	69.9313	2.50555
$780$	−3.60529	−0.129090
$781$	30.4691	1.09027
$782$	4.26349	0.152462
$783$	−1.70564	−0.0609544
$784$	−3.37292	−0.120461
$785$	−1.93760	−0.0691560
$786$	2.43324	0.0867907
$787$	−41.8407	−1.49146	−0.745731	−	0.666248i	$-0.767899\pi$
$787$	−41.8407	−1.49146	−0.745731	+	0.666248i	$0.767899\pi$
$788$	7.50328	0.267293
$789$	−20.5316	−0.730946
$790$	−8.65427	−0.307905
$791$	−10.2506	−0.364468
$792$	−11.2424	−0.399482
$793$	34.1139	1.21142
$794$	−23.6522	−0.839385
$795$	−7.38072	−0.261767
$796$	15.7312	0.557576
$797$	34.6511	1.22740	0.613702	−	0.789538i	$-0.289680\pi$
$797$	34.6511	1.22740	0.613702	+	0.789538i	$0.289680\pi$
$798$	32.8407	1.16255
$799$	−15.0851	−0.533673
$800$	−4.70319	−0.166283
$801$	7.41786	0.262097
$802$	14.3015	0.505004
$803$	−39.3039	−1.38700
$804$	17.8536	0.629648
$805$	−1.03758	−0.0365699
$806$	−11.7497	−0.413867
$807$	−49.1273	−1.72936
$808$	0.613701	0.0215899
$809$	11.3181	0.397922	0.198961	−	0.980007i	$-0.436243\pi$
$809$	11.3181	0.397922	0.198961	+	0.980007i	$0.436243\pi$
$810$	5.02954	0.176720
$811$	−5.60571	−0.196843	−0.0984216	−	0.995145i	$-0.531379\pi$
$811$	−5.60571	−0.196843	−0.0984216	+	0.995145i	$0.531379\pi$
$812$	−16.8225	−0.590355
$813$	9.50743	0.333440
$814$	31.9992	1.12157
$815$	−0.988840	−0.0346376
$816$	−10.3741	−0.363166
$817$	43.0903	1.50754
$818$	22.2861	0.779215
$819$	−15.1276	−0.528602
$820$	5.37607	0.187741
$821$	−1.54229	−0.0538262	−0.0269131	−	0.999638i	$-0.508568\pi$
$821$	−1.54229	−0.0538262	−0.0269131	+	0.999638i	$0.508568\pi$
$822$	−44.8168	−1.56317
$823$	1.42905	0.0498134	0.0249067	−	0.999690i	$-0.492071\pi$
$823$	1.42905	0.0498134	0.0249067	+	0.999690i	$0.492071\pi$
$824$	7.91949	0.275889
$825$	44.0512	1.53367
$826$	11.8707	0.413036
$827$	14.0878	0.489882	0.244941	−	0.969538i	$-0.421231\pi$
$827$	14.0878	0.489882	0.244941	+	0.969538i	$0.421231\pi$
$828$	−2.92064	−0.101499
$829$	7.22263	0.250852	0.125426	−	0.992103i	$-0.459970\pi$
$829$	7.22263	0.250852	0.125426	+	0.992103i	$0.459970\pi$
$830$	−2.29506	−0.0796626
$831$	−37.2499	−1.29219
$832$	2.71965	0.0942870
$833$	14.3804	0.498252
$834$	39.0049	1.35063
$835$	0.962782	0.0333184
$836$	27.2792	0.943470
$837$	0.834235	0.0288354
$838$	29.4035	1.01573
$839$	37.8232	1.30580	0.652901	−	0.757443i	$-0.273552\pi$
$839$	37.8232	1.30580	0.652901	+	0.757443i	$0.273552\pi$
$840$	2.52468	0.0871096
$841$	49.0235	1.69047
$842$	−9.65538	−0.332746
$843$	−75.3434	−2.59497
$844$	−7.84886	−0.270169
$845$	3.05282	0.105020
$846$	10.3338	0.355284
$847$	−7.26964	−0.249788
$848$	5.56765	0.191194
$849$	37.1650	1.27550
$850$	20.0520	0.687778
$851$	8.31300	0.284966
$852$	−19.2603	−0.659846
$853$	−18.5076	−0.633690	−0.316845	−	0.948477i	$-0.602623\pi$
$853$	−18.5076	−0.633690	−0.316845	+	0.948477i	$0.602623\pi$
$854$	−23.8890	−0.817463
$855$	11.2764	0.385645
$856$	−3.54230	−0.121073
$857$	0.898156	0.0306804	0.0153402	−	0.999882i	$-0.495117\pi$
$857$	0.898156	0.0306804	0.0153402	+	0.999882i	$0.495117\pi$
$858$	−25.4730	−0.869633
$859$	−46.2836	−1.57918	−0.789589	−	0.613637i	$-0.789706\pi$
$859$	−46.2836	−1.57918	−0.789589	+	0.613637i	$0.789706\pi$
$860$	3.31263	0.112960
$861$	45.7284	1.55842
$862$	−9.39164	−0.319880
$863$	51.9697	1.76907	0.884535	−	0.466474i	$-0.154476\pi$
$863$	51.9697	1.76907	0.884535	+	0.466474i	$0.154476\pi$
$864$	−0.193096	−0.00656926
$865$	11.6552	0.396290
$866$	4.62692	0.157229
$867$	2.86484	0.0972950
$868$	8.22799	0.279276
$869$	−61.1462	−2.07424
$870$	−11.7095	−0.396991
$871$	19.9552	0.676155
$872$	−12.4397	−0.421261
$873$	−32.7114	−1.10711
$874$	7.08679	0.239714
$875$	−10.0678	−0.340355
$876$	24.8450	0.839434
$877$	−46.5593	−1.57220	−0.786099	−	0.618101i	$-0.787902\pi$
$877$	−46.5593	−1.57220	−0.786099	+	0.618101i	$0.787902\pi$
$878$	9.93352	0.335240
$879$	−52.9810	−1.78701
$880$	2.09713	0.0706941
$881$	31.6715	1.06704	0.533520	−	0.845787i	$-0.320869\pi$
$881$	31.6715	1.06704	0.533520	+	0.845787i	$0.320869\pi$
$882$	−9.85108	−0.331703
$883$	−28.1924	−0.948748	−0.474374	−	0.880323i	$-0.657326\pi$
$883$	−28.1924	−0.948748	−0.474374	+	0.880323i	$0.657326\pi$
$884$	−11.5952	−0.389990
$885$	8.26278	0.277750
$886$	2.29811	0.0772064
$887$	−2.82394	−0.0948187	−0.0474093	−	0.998876i	$-0.515097\pi$
$887$	−2.82394	−0.0948187	−0.0474093	+	0.998876i	$0.515097\pi$
$888$	−20.2275	−0.678790
$889$	−0.398533	−0.0133664
$890$	−1.38370	−0.0463818
$891$	35.5359	1.19050
$892$	−10.0839	−0.337634
$893$	−25.0745	−0.839086
$894$	4.80173	0.160594
$895$	−8.80623	−0.294360
$896$	−1.90449	−0.0636246
$897$	−6.61756	−0.220954
$898$	12.7587	0.425764
$899$	−38.1617	−1.27276
$900$	−13.7363	−0.457877
$901$	−23.7376	−0.790815
$902$	37.9843	1.26474
$903$	28.1769	0.937668
$904$	5.38232	0.179013
$905$	7.65917	0.254599
$906$	58.4422	1.94161
$907$	24.1902	0.803221	0.401611	−	0.915810i	$-0.368450\pi$
$907$	24.1902	0.803221	0.401611	+	0.915810i	$0.368450\pi$
$908$	−15.6491	−0.519332
$909$	1.79240	0.0594502
$910$	2.82186	0.0935437
$911$	−1.68068	−0.0556836	−0.0278418	−	0.999612i	$-0.508863\pi$
$911$	−1.68068	−0.0556836	−0.0278418	+	0.999612i	$0.508863\pi$
$912$	−17.2438	−0.571000
$913$	−16.2156	−0.536657
$914$	15.0752	0.498644
$915$	−16.6282	−0.549712
$916$	−24.6643	−0.814932
$917$	−1.90449	−0.0628918
$918$	0.823264	0.0271718
$919$	−10.8326	−0.357335	−0.178668	−	0.983909i	$-0.557179\pi$
$919$	−10.8326	−0.357335	−0.178668	+	0.983909i	$0.557179\pi$
$920$	0.544807	0.0179618
$921$	16.9549	0.558683
$922$	20.3095	0.668857
$923$	−21.5274	−0.708583
$924$	17.8379	0.586825
$925$	39.0976	1.28552
$926$	−16.3667	−0.537843
$927$	23.1300	0.759689
$928$	8.83309	0.289960
$929$	18.6793	0.612846	0.306423	−	0.951895i	$-0.400868\pi$
$929$	18.6793	0.612846	0.306423	+	0.951895i	$0.400868\pi$
$930$	5.72719	0.187802
$931$	23.9031	0.783394
$932$	0.977473	0.0320182
$933$	13.6618	0.447267
$934$	33.9784	1.11181
$935$	−8.94108	−0.292405
$936$	7.94314	0.259630
$937$	−15.2883	−0.499447	−0.249724	−	0.968317i	$-0.580340\pi$
$937$	−15.2883	−0.499447	−0.249724	+	0.968317i	$0.580340\pi$
$938$	−13.9740	−0.456267
$939$	−2.08600	−0.0680740
$940$	−1.92764	−0.0628727
$941$	26.0888	0.850471	0.425236	−	0.905083i	$-0.360191\pi$
$941$	26.0888	0.850471	0.425236	+	0.905083i	$0.360191\pi$
$942$	8.65379	0.281956
$943$	9.86785	0.321341
$944$	−6.23303	−0.202868
$945$	−0.200353	−0.00651747
$946$	23.4052	0.760967
$947$	25.3644	0.824233	0.412117	−	0.911131i	$-0.364790\pi$
$947$	25.3644	0.824233	0.412117	+	0.911131i	$0.364790\pi$
$948$	38.6520	1.25536
$949$	27.7695	0.901435
$950$	33.3305	1.08138
$951$	−35.8704	−1.16318
$952$	8.11978	0.263164
$953$	−47.4807	−1.53805	−0.769025	−	0.639218i	$-0.779258\pi$
$953$	−47.4807	−1.53805	−0.769025	+	0.639218i	$0.779258\pi$
$954$	16.2611	0.526473
$955$	12.4677	0.403447
$956$	25.2253	0.815845
$957$	−82.7330	−2.67438
$958$	11.9333	0.385547
$959$	35.0780	1.13273
$960$	−1.32564	−0.0427850
$961$	−12.3349	−0.397901
$962$	−22.6085	−0.728927
$963$	−10.3458	−0.333389
$964$	−19.0114	−0.612316
$965$	−9.79760	−0.315396
$966$	4.63408	0.149099
$967$	−27.0434	−0.869657	−0.434828	−	0.900513i	$-0.643191\pi$
$967$	−27.0434	−0.869657	−0.434828	+	0.900513i	$0.643191\pi$
$968$	3.81711	0.122686
$969$	73.5190	2.36177
$970$	6.10188	0.195920
$971$	−5.52052	−0.177162	−0.0885810	−	0.996069i	$-0.528233\pi$
$971$	−5.52052	−0.177162	−0.0885810	+	0.996069i	$0.528233\pi$
$972$	−21.8838	−0.701924
$973$	−30.5291	−0.978718
$974$	28.6387	0.917643
$975$	−31.1236	−0.996754
$976$	12.5435	0.401507
$977$	−25.2576	−0.808063	−0.404032	−	0.914745i	$-0.632391\pi$
$977$	−25.2576	−0.808063	−0.404032	+	0.914745i	$0.632391\pi$
$978$	4.41639	0.141221
$979$	−9.77647	−0.312457
$980$	1.83759	0.0586996
$981$	−36.3319	−1.15999
$982$	−9.49334	−0.302945
$983$	0.222300	0.00709026	0.00354513	−	0.999994i	$-0.498872\pi$
$983$	0.222300	0.00709026	0.00354513	+	0.999994i	$0.498872\pi$
$984$	−24.0108	−0.765437
$985$	−4.08784	−0.130249
$986$	−37.6598	−1.19933
$987$	−16.3963	−0.521900
$988$	−19.2736	−0.613175
$989$	6.08037	0.193344
$990$	6.12495	0.194664
$991$	−17.3035	−0.549664	−0.274832	−	0.961492i	$-0.588622\pi$
$991$	−17.3035	−0.549664	−0.274832	+	0.961492i	$0.588622\pi$
$992$	−4.32031	−0.137170
$993$	−60.6871	−1.92585
$994$	15.0750	0.478149
$995$	−8.57044	−0.271701
$996$	10.2503	0.324792
$997$	16.6367	0.526890	0.263445	−	0.964674i	$-0.415141\pi$
$997$	16.6367	0.526890	0.263445	+	0.964674i	$0.415141\pi$
$998$	1.48014	0.0468531
$999$	1.60521	0.0507865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.19	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.19	✓	21	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.43324 q^{3} +1.00000 q^{4} -0.544807 q^{5} +2.43324 q^{6} -1.90449 q^{7} +1.00000 q^{8} +2.92064 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.43324 q^{3} +1.00000 q^{4} -0.544807 q^{5} +2.43324 q^{6} -1.90449 q^{7} +1.00000 q^{8} +2.92064 q^{9} -0.544807 q^{10} -3.84930 q^{11} +2.43324 q^{12} +2.71965 q^{13} -1.90449 q^{14} -1.32564 q^{15} +1.00000 q^{16} -4.26349 q^{17} +2.92064 q^{18} -7.08679 q^{19} -0.544807 q^{20} -4.63408 q^{21} -3.84930 q^{22} -1.00000 q^{23} +2.43324 q^{24} -4.70319 q^{25} +2.71965 q^{26} -0.193096 q^{27} -1.90449 q^{28} +8.83309 q^{29} -1.32564 q^{30} -4.32031 q^{31} +1.00000 q^{32} -9.36626 q^{33} -4.26349 q^{34} +1.03758 q^{35} +2.92064 q^{36} -8.31300 q^{37} -7.08679 q^{38} +6.61756 q^{39} -0.544807 q^{40} -9.86785 q^{41} -4.63408 q^{42} -6.08037 q^{43} -3.84930 q^{44} -1.59119 q^{45} -1.00000 q^{46} +3.53820 q^{47} +2.43324 q^{48} -3.37292 q^{49} -4.70319 q^{50} -10.3741 q^{51} +2.71965 q^{52} +5.56765 q^{53} -0.193096 q^{54} +2.09713 q^{55} -1.90449 q^{56} -17.2438 q^{57} +8.83309 q^{58} -6.23303 q^{59} -1.32564 q^{60} +12.5435 q^{61} -4.32031 q^{62} -5.56233 q^{63} +1.00000 q^{64} -1.48169 q^{65} -9.36626 q^{66} +7.33739 q^{67} -4.26349 q^{68} -2.43324 q^{69} +1.03758 q^{70} -7.91549 q^{71} +2.92064 q^{72} +10.2107 q^{73} -8.31300 q^{74} -11.4440 q^{75} -7.08679 q^{76} +7.33095 q^{77} +6.61756 q^{78} +15.8850 q^{79} -0.544807 q^{80} -9.23178 q^{81} -9.86785 q^{82} +4.21260 q^{83} -4.63408 q^{84} +2.32278 q^{85} -6.08037 q^{86} +21.4930 q^{87} -3.84930 q^{88} +2.53980 q^{89} -1.59119 q^{90} -5.17955 q^{91} -1.00000 q^{92} -10.5123 q^{93} +3.53820 q^{94} +3.86093 q^{95} +2.43324 q^{96} -11.2001 q^{97} -3.37292 q^{98} -11.2424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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