LMFDB - Embedded newform 5290.2.a.bl.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.75508$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.75508 q^{6} -4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.75508 q^{6} -4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} +1.00000 q^{10} -4.40211 q^{11} +2.75508 q^{12} +2.45989 q^{13} -4.44855 q^{14} +2.75508 q^{15} +1.00000 q^{16} +6.98238 q^{17} +4.59049 q^{18} +3.42347 q^{19} +1.00000 q^{20} -12.2561 q^{21} -4.40211 q^{22} +2.75508 q^{24} +1.00000 q^{25} +2.45989 q^{26} +4.38194 q^{27} -4.44855 q^{28} +5.51384 q^{29} +2.75508 q^{30} -2.05611 q^{31} +1.00000 q^{32} -12.1282 q^{33} +6.98238 q^{34} -4.44855 q^{35} +4.59049 q^{36} +6.73053 q^{37} +3.42347 q^{38} +6.77719 q^{39} +1.00000 q^{40} +3.15936 q^{41} -12.2561 q^{42} +2.76141 q^{43} -4.40211 q^{44} +4.59049 q^{45} +6.18748 q^{47} +2.75508 q^{48} +12.7896 q^{49} +1.00000 q^{50} +19.2371 q^{51} +2.45989 q^{52} +1.99036 q^{53} +4.38194 q^{54} -4.40211 q^{55} -4.44855 q^{56} +9.43196 q^{57} +5.51384 q^{58} +2.00254 q^{59} +2.75508 q^{60} +13.8042 q^{61} -2.05611 q^{62} -20.4210 q^{63} +1.00000 q^{64} +2.45989 q^{65} -12.1282 q^{66} -8.90067 q^{67} +6.98238 q^{68} -4.44855 q^{70} -10.8705 q^{71} +4.59049 q^{72} -8.57546 q^{73} +6.73053 q^{74} +2.75508 q^{75} +3.42347 q^{76} +19.5830 q^{77} +6.77719 q^{78} +11.8628 q^{79} +1.00000 q^{80} -1.69886 q^{81} +3.15936 q^{82} -0.319840 q^{83} -12.2561 q^{84} +6.98238 q^{85} +2.76141 q^{86} +15.1911 q^{87} -4.40211 q^{88} -8.69820 q^{89} +4.59049 q^{90} -10.9429 q^{91} -5.66475 q^{93} +6.18748 q^{94} +3.42347 q^{95} +2.75508 q^{96} -7.30395 q^{97} +12.7896 q^{98} -20.2078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * 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
$3$	2.75508	1.59065	0.795324	−	0.606184i	$-0.207300\pi$
$3$	2.75508	1.59065	0.795324	+	0.606184i	$0.207300\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.75508	1.12476
$7$	−4.44855	−1.68139	−0.840696	−	0.541507i	$-0.817854\pi$
$7$	−4.44855	−1.68139	−0.840696	+	0.541507i	$0.817854\pi$
$8$	1.00000	0.353553
$9$	4.59049	1.53016
$10$	1.00000	0.316228
$11$	−4.40211	−1.32729	−0.663643	−	0.748050i	$-0.730991\pi$
$11$	−4.40211	−1.32729	−0.663643	+	0.748050i	$0.730991\pi$
$12$	2.75508	0.795324
$13$	2.45989	0.682249	0.341125	−	0.940018i	$-0.389192\pi$
$13$	2.45989	0.682249	0.341125	+	0.940018i	$0.389192\pi$
$14$	−4.44855	−1.18892
$15$	2.75508	0.711360
$16$	1.00000	0.250000
$17$	6.98238	1.69348	0.846738	−	0.532010i	$-0.178563\pi$
$17$	6.98238	1.69348	0.846738	+	0.532010i	$0.178563\pi$
$18$	4.59049	1.08199
$19$	3.42347	0.785399	0.392699	−	0.919667i	$-0.371541\pi$
$19$	3.42347	0.785399	0.392699	+	0.919667i	$0.371541\pi$
$20$	1.00000	0.223607
$21$	−12.2561	−2.67451
$22$	−4.40211	−0.938533
$23$	0	0
$23$	0	0
$24$	2.75508	0.562379
$25$	1.00000	0.200000
$26$	2.45989	0.482423
$27$	4.38194	0.843305
$28$	−4.44855	−0.840696
$29$	5.51384	1.02389	0.511947	−	0.859017i	$-0.328924\pi$
$29$	5.51384	1.02389	0.511947	+	0.859017i	$0.328924\pi$
$30$	2.75508	0.503007
$31$	−2.05611	−0.369288	−0.184644	−	0.982805i	$-0.559113\pi$
$31$	−2.05611	−0.369288	−0.184644	+	0.982805i	$0.559113\pi$
$32$	1.00000	0.176777
$33$	−12.1282	−2.11125
$34$	6.98238	1.19747
$35$	−4.44855	−0.751942
$36$	4.59049	0.765082
$37$	6.73053	1.10649	0.553246	−	0.833018i	$-0.313389\pi$
$37$	6.73053	1.10649	0.553246	+	0.833018i	$0.313389\pi$
$38$	3.42347	0.555361
$39$	6.77719	1.08522
$40$	1.00000	0.158114
$41$	3.15936	0.493410	0.246705	−	0.969091i	$-0.420652\pi$
$41$	3.15936	0.493410	0.246705	+	0.969091i	$0.420652\pi$
$42$	−12.2561	−1.89116
$43$	2.76141	0.421111	0.210555	−	0.977582i	$-0.432473\pi$
$43$	2.76141	0.421111	0.210555	+	0.977582i	$0.432473\pi$
$44$	−4.40211	−0.663643
$45$	4.59049	0.684310
$46$	0	0
$47$	6.18748	0.902537	0.451268	−	0.892388i	$-0.350972\pi$
$47$	6.18748	0.902537	0.451268	+	0.892388i	$0.350972\pi$
$48$	2.75508	0.397662
$49$	12.7896	1.82708
$50$	1.00000	0.141421
$51$	19.2371	2.69373
$52$	2.45989	0.341125
$53$	1.99036	0.273397	0.136698	−	0.990613i	$-0.456351\pi$
$53$	1.99036	0.273397	0.136698	+	0.990613i	$0.456351\pi$
$54$	4.38194	0.596307
$55$	−4.40211	−0.593580
$56$	−4.44855	−0.594462
$57$	9.43196	1.24929
$58$	5.51384	0.724003
$59$	2.00254	0.260708	0.130354	−	0.991467i	$-0.458389\pi$
$59$	2.00254	0.260708	0.130354	+	0.991467i	$0.458389\pi$
$60$	2.75508	0.355680
$61$	13.8042	1.76744	0.883721	−	0.468014i	$-0.155030\pi$
$61$	13.8042	1.76744	0.883721	+	0.468014i	$0.155030\pi$
$62$	−2.05611	−0.261126
$63$	−20.4210	−2.57281
$64$	1.00000	0.125000
$65$	2.45989	0.305111
$66$	−12.1282	−1.49288
$67$	−8.90067	−1.08739	−0.543695	−	0.839283i	$-0.682975\pi$
$67$	−8.90067	−1.08739	−0.543695	+	0.839283i	$0.682975\pi$
$68$	6.98238	0.846738
$69$	0	0
$70$	−4.44855	−0.531703
$71$	−10.8705	−1.29010	−0.645048	−	0.764142i	$-0.723162\pi$
$71$	−10.8705	−1.29010	−0.645048	+	0.764142i	$0.723162\pi$
$72$	4.59049	0.540995
$73$	−8.57546	−1.00368	−0.501841	−	0.864960i	$-0.667344\pi$
$73$	−8.57546	−1.00368	−0.501841	+	0.864960i	$0.667344\pi$
$74$	6.73053	0.782408
$75$	2.75508	0.318130
$76$	3.42347	0.392699
$77$	19.5830	2.23169
$78$	6.77719	0.767366
$79$	11.8628	1.33466	0.667332	−	0.744760i	$-0.267436\pi$
$79$	11.8628	1.33466	0.667332	+	0.744760i	$0.267436\pi$
$80$	1.00000	0.111803
$81$	−1.69886	−0.188762
$82$	3.15936	0.348893
$83$	−0.319840	−0.0351069	−0.0175535	−	0.999846i	$-0.505588\pi$
$83$	−0.319840	−0.0351069	−0.0175535	+	0.999846i	$0.505588\pi$
$84$	−12.2561	−1.33725
$85$	6.98238	0.757345
$86$	2.76141	0.297770
$87$	15.1911	1.62866
$88$	−4.40211	−0.469266
$89$	−8.69820	−0.922008	−0.461004	−	0.887398i	$-0.652511\pi$
$89$	−8.69820	−0.922008	−0.461004	+	0.887398i	$0.652511\pi$
$90$	4.59049	0.483880
$91$	−10.9429	−1.14713
$92$	0	0
$93$	−5.66475	−0.587408
$94$	6.18748	0.638190
$95$	3.42347	0.351241
$96$	2.75508	0.281190
$97$	−7.30395	−0.741603	−0.370802	−	0.928712i	$-0.620917\pi$
$97$	−7.30395	−0.741603	−0.370802	+	0.928712i	$0.620917\pi$
$98$	12.7896	1.29194
$99$	−20.2078	−2.03097
$100$	1.00000	0.100000
$101$	−9.08953	−0.904442	−0.452221	−	0.891906i	$-0.649368\pi$
$101$	−9.08953	−0.904442	−0.452221	+	0.891906i	$0.649368\pi$
$102$	19.2371	1.90475
$103$	−1.49900	−0.147701	−0.0738504	−	0.997269i	$-0.523529\pi$
$103$	−1.49900	−0.147701	−0.0738504	+	0.997269i	$0.523529\pi$
$104$	2.45989	0.241212
$105$	−12.2561	−1.19608
$106$	1.99036	0.193321
$107$	17.7755	1.71842	0.859211	−	0.511622i	$-0.170955\pi$
$107$	17.7755	1.71842	0.859211	+	0.511622i	$0.170955\pi$
$108$	4.38194	0.421653
$109$	−18.9672	−1.81673	−0.908364	−	0.418181i	$-0.862668\pi$
$109$	−18.9672	−1.81673	−0.908364	+	0.418181i	$0.862668\pi$
$110$	−4.40211	−0.419725
$111$	18.5432	1.76004
$112$	−4.44855	−0.420348
$113$	3.38804	0.318720	0.159360	−	0.987221i	$-0.449057\pi$
$113$	3.38804	0.318720	0.159360	+	0.987221i	$0.449057\pi$
$114$	9.43196	0.883384
$115$	0	0
$116$	5.51384	0.511947
$117$	11.2921	1.04395
$118$	2.00254	0.184349
$119$	−31.0614	−2.84740
$120$	2.75508	0.251504
$121$	8.37857	0.761688
$122$	13.8042	1.24977
$123$	8.70432	0.784842
$124$	−2.05611	−0.184644
$125$	1.00000	0.0894427
$126$	−20.4210	−1.81925
$127$	−5.73551	−0.508945	−0.254472	−	0.967080i	$-0.581902\pi$
$127$	−5.73551	−0.508945	−0.254472	+	0.967080i	$0.581902\pi$
$128$	1.00000	0.0883883
$129$	7.60792	0.669840
$130$	2.45989	0.215746
$131$	−10.6514	−0.930620	−0.465310	−	0.885148i	$-0.654057\pi$
$131$	−10.6514	−0.930620	−0.465310	+	0.885148i	$0.654057\pi$
$132$	−12.1282	−1.05562
$133$	−15.2295	−1.32056
$134$	−8.90067	−0.768901
$135$	4.38194	0.377137
$136$	6.98238	0.598734
$137$	−13.7187	−1.17207	−0.586035	−	0.810285i	$-0.699312\pi$
$137$	−13.7187	−1.17207	−0.586035	+	0.810285i	$0.699312\pi$
$138$	0	0
$139$	−3.55749	−0.301742	−0.150871	−	0.988553i	$-0.548208\pi$
$139$	−3.55749	−0.301742	−0.150871	+	0.988553i	$0.548208\pi$
$140$	−4.44855	−0.375971
$141$	17.0470	1.43562
$142$	−10.8705	−0.912235
$143$	−10.8287	−0.905540
$144$	4.59049	0.382541
$145$	5.51384	0.457899
$146$	−8.57546	−0.709710
$147$	35.2363	2.90624
$148$	6.73053	0.553246
$149$	8.65572	0.709104	0.354552	−	0.935036i	$-0.384633\pi$
$149$	8.65572	0.709104	0.354552	+	0.935036i	$0.384633\pi$
$150$	2.75508	0.224952
$151$	−1.76370	−0.143528	−0.0717640	−	0.997422i	$-0.522863\pi$
$151$	−1.76370	−0.143528	−0.0717640	+	0.997422i	$0.522863\pi$
$152$	3.42347	0.277680
$153$	32.0526	2.59130
$154$	19.5830	1.57804
$155$	−2.05611	−0.165151
$156$	6.77719	0.542610
$157$	12.6015	1.00571	0.502856	−	0.864370i	$-0.332283\pi$
$157$	12.6015	1.00571	0.502856	+	0.864370i	$0.332283\pi$
$158$	11.8628	0.943750
$159$	5.48361	0.434878
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.69886	−0.133475
$163$	2.07678	0.162666	0.0813329	−	0.996687i	$-0.474082\pi$
$163$	2.07678	0.162666	0.0813329	+	0.996687i	$0.474082\pi$
$164$	3.15936	0.246705
$165$	−12.1282	−0.944178
$166$	−0.319840	−0.0248244
$167$	3.48524	0.269696	0.134848	−	0.990866i	$-0.456945\pi$
$167$	3.48524	0.269696	0.134848	+	0.990866i	$0.456945\pi$
$168$	−12.2561	−0.945580
$169$	−6.94896	−0.534536
$170$	6.98238	0.535524
$171$	15.7154	1.20179
$172$	2.76141	0.210555
$173$	23.1699	1.76157	0.880787	−	0.473513i	$-0.157014\pi$
$173$	23.1699	1.76157	0.880787	+	0.473513i	$0.157014\pi$
$174$	15.1911	1.15163
$175$	−4.44855	−0.336278
$176$	−4.40211	−0.331821
$177$	5.51717	0.414696
$178$	−8.69820	−0.651958
$179$	1.26603	0.0946279	0.0473139	−	0.998880i	$-0.484934\pi$
$179$	1.26603	0.0946279	0.0473139	+	0.998880i	$0.484934\pi$
$180$	4.59049	0.342155
$181$	18.3728	1.36564	0.682822	−	0.730585i	$-0.260753\pi$
$181$	18.3728	1.36564	0.682822	+	0.730585i	$0.260753\pi$
$182$	−10.9429	−0.811143
$183$	38.0316	2.81138
$184$	0	0
$185$	6.73053	0.494838
$186$	−5.66475	−0.415360
$187$	−30.7372	−2.24773
$188$	6.18748	0.451268
$189$	−19.4933	−1.41793
$190$	3.42347	0.248365
$191$	−5.84116	−0.422652	−0.211326	−	0.977416i	$-0.567778\pi$
$191$	−5.84116	−0.422652	−0.211326	+	0.977416i	$0.567778\pi$
$192$	2.75508	0.198831
$193$	−0.726448	−0.0522908	−0.0261454	−	0.999658i	$-0.508323\pi$
$193$	−0.726448	−0.0522908	−0.0261454	+	0.999658i	$0.508323\pi$
$194$	−7.30395	−0.524393
$195$	6.77719	0.485325
$196$	12.7896	0.913540
$197$	10.1195	0.720987	0.360493	−	0.932762i	$-0.382608\pi$
$197$	10.1195	0.720987	0.360493	+	0.932762i	$0.382608\pi$
$198$	−20.2078	−1.43611
$199$	−18.5869	−1.31759	−0.658795	−	0.752322i	$-0.728934\pi$
$199$	−18.5869	−1.31759	−0.658795	+	0.752322i	$0.728934\pi$
$200$	1.00000	0.0707107
$201$	−24.5221	−1.72966
$202$	−9.08953	−0.639537
$203$	−24.5286	−1.72157
$204$	19.2371	1.34686
$205$	3.15936	0.220660
$206$	−1.49900	−0.104440
$207$	0	0
$208$	2.45989	0.170562
$209$	−15.0705	−1.04245
$210$	−12.2561	−0.845753
$211$	4.90443	0.337635	0.168817	−	0.985647i	$-0.446005\pi$
$211$	4.90443	0.337635	0.168817	+	0.985647i	$0.446005\pi$
$212$	1.99036	0.136698
$213$	−29.9492	−2.05209
$214$	17.7755	1.21511
$215$	2.76141	0.188327
$216$	4.38194	0.298153
$217$	9.14670	0.620918
$218$	−18.9672	−1.28462
$219$	−23.6261	−1.59651
$220$	−4.40211	−0.296790
$221$	17.1759	1.15537
$222$	18.5432	1.24454
$223$	9.71984	0.650888	0.325444	−	0.945561i	$-0.394486\pi$
$223$	9.71984	0.650888	0.325444	+	0.945561i	$0.394486\pi$
$224$	−4.44855	−0.297231
$225$	4.59049	0.306033
$226$	3.38804	0.225369
$227$	−21.5002	−1.42702	−0.713509	−	0.700646i	$-0.752895\pi$
$227$	−21.5002	−1.42702	−0.713509	+	0.700646i	$0.752895\pi$
$228$	9.43196	0.624647
$229$	5.38568	0.355896	0.177948	−	0.984040i	$-0.443054\pi$
$229$	5.38568	0.355896	0.177948	+	0.984040i	$0.443054\pi$
$230$	0	0
$231$	53.9528	3.54983
$232$	5.51384	0.362001
$233$	−29.3533	−1.92300	−0.961498	−	0.274811i	$-0.911385\pi$
$233$	−29.3533	−1.92300	−0.961498	+	0.274811i	$0.911385\pi$
$234$	11.2921	0.738187
$235$	6.18748	0.403627
$236$	2.00254	0.130354
$237$	32.6829	2.12298
$238$	−31.0614	−2.01341
$239$	−8.09013	−0.523307	−0.261653	−	0.965162i	$-0.584268\pi$
$239$	−8.09013	−0.523307	−0.261653	+	0.965162i	$0.584268\pi$
$240$	2.75508	0.177840
$241$	−11.4116	−0.735088	−0.367544	−	0.930006i	$-0.619801\pi$
$241$	−11.4116	−0.735088	−0.367544	+	0.930006i	$0.619801\pi$
$242$	8.37857	0.538595
$243$	−17.8263	−1.14356
$244$	13.8042	0.883721
$245$	12.7896	0.817095
$246$	8.70432	0.554967
$247$	8.42135	0.535838
$248$	−2.05611	−0.130563
$249$	−0.881185	−0.0558428
$250$	1.00000	0.0632456
$251$	−11.7941	−0.744436	−0.372218	−	0.928145i	$-0.621403\pi$
$251$	−11.7941	−0.744436	−0.372218	+	0.928145i	$0.621403\pi$
$252$	−20.4210	−1.28640
$253$	0	0
$254$	−5.73551	−0.359878
$255$	19.2371	1.20467
$256$	1.00000	0.0625000
$257$	2.03939	0.127214	0.0636069	−	0.997975i	$-0.479740\pi$
$257$	2.03939	0.127214	0.0636069	+	0.997975i	$0.479740\pi$
$258$	7.60792	0.473648
$259$	−29.9411	−1.86045
$260$	2.45989	0.152556
$261$	25.3112	1.56673
$262$	−10.6514	−0.658047
$263$	−24.7269	−1.52473	−0.762364	−	0.647149i	$-0.775961\pi$
$263$	−24.7269	−1.52473	−0.762364	+	0.647149i	$0.775961\pi$
$264$	−12.1282	−0.746438
$265$	1.99036	0.122267
$266$	−15.2295	−0.933779
$267$	−23.9643	−1.46659
$268$	−8.90067	−0.543695
$269$	14.4785	0.882770	0.441385	−	0.897318i	$-0.354487\pi$
$269$	14.4785	0.882770	0.441385	+	0.897318i	$0.354487\pi$
$270$	4.38194	0.266676
$271$	19.7153	1.19762	0.598811	−	0.800890i	$-0.295640\pi$
$271$	19.7153	1.19762	0.598811	+	0.800890i	$0.295640\pi$
$272$	6.98238	0.423369
$273$	−30.1487	−1.82468
$274$	−13.7187	−0.828779
$275$	−4.40211	−0.265457
$276$	0	0
$277$	−22.7803	−1.36874	−0.684368	−	0.729136i	$-0.739922\pi$
$277$	−22.7803	−1.36874	−0.684368	+	0.729136i	$0.739922\pi$
$278$	−3.55749	−0.213364
$279$	−9.43855	−0.565071
$280$	−4.44855	−0.265851
$281$	−13.2608	−0.791073	−0.395536	−	0.918450i	$-0.629441\pi$
$281$	−13.2608	−0.791073	−0.395536	+	0.918450i	$0.629441\pi$
$282$	17.0470	1.01514
$283$	−7.87321	−0.468014	−0.234007	−	0.972235i	$-0.575184\pi$
$283$	−7.87321	−0.468014	−0.234007	+	0.972235i	$0.575184\pi$
$284$	−10.8705	−0.645048
$285$	9.43196	0.558701
$286$	−10.8287	−0.640314
$287$	−14.0546	−0.829616
$288$	4.59049	0.270497
$289$	31.7536	1.86786
$290$	5.51384	0.323784
$291$	−20.1230	−1.17963
$292$	−8.57546	−0.501841
$293$	−10.7456	−0.627763	−0.313881	−	0.949462i	$-0.601629\pi$
$293$	−10.7456	−0.627763	−0.313881	+	0.949462i	$0.601629\pi$
$294$	35.2363	2.05502
$295$	2.00254	0.116592
$296$	6.73053	0.391204
$297$	−19.2898	−1.11931
$298$	8.65572	0.501412
$299$	0	0
$300$	2.75508	0.159065
$301$	−12.2843	−0.708053
$302$	−1.76370	−0.101490
$303$	−25.0424	−1.43865
$304$	3.42347	0.196350
$305$	13.8042	0.790424
$306$	32.0526	1.83232
$307$	1.33735	0.0763266	0.0381633	−	0.999272i	$-0.487849\pi$
$307$	1.33735	0.0763266	0.0381633	+	0.999272i	$0.487849\pi$
$308$	19.5830	1.11584
$309$	−4.12987	−0.234940
$310$	−2.05611	−0.116779
$311$	7.12911	0.404255	0.202128	−	0.979359i	$-0.435214\pi$
$311$	7.12911	0.404255	0.202128	+	0.979359i	$0.435214\pi$
$312$	6.77719	0.383683
$313$	13.1855	0.745289	0.372645	−	0.927974i	$-0.378451\pi$
$313$	13.1855	0.745289	0.372645	+	0.927974i	$0.378451\pi$
$314$	12.6015	0.711146
$315$	−20.4210	−1.15059
$316$	11.8628	0.667332
$317$	11.9822	0.672989	0.336494	−	0.941685i	$-0.390759\pi$
$317$	11.9822	0.672989	0.336494	+	0.941685i	$0.390759\pi$
$318$	5.48361	0.307505
$319$	−24.2725	−1.35900
$320$	1.00000	0.0559017
$321$	48.9730	2.73341
$322$	0	0
$323$	23.9040	1.33005
$324$	−1.69886	−0.0943809
$325$	2.45989	0.136450
$326$	2.07678	0.115022
$327$	−52.2562	−2.88978
$328$	3.15936	0.174447
$329$	−27.5253	−1.51752
$330$	−12.1282	−0.667635
$331$	11.5934	0.637229	0.318615	−	0.947884i	$-0.396782\pi$
$331$	11.5934	0.637229	0.318615	+	0.947884i	$0.396782\pi$
$332$	−0.319840	−0.0175535
$333$	30.8964	1.69311
$334$	3.48524	0.190704
$335$	−8.90067	−0.486296
$336$	−12.2561	−0.668626
$337$	−6.87330	−0.374412	−0.187206	−	0.982321i	$-0.559943\pi$
$337$	−6.87330	−0.374412	−0.187206	+	0.982321i	$0.559943\pi$
$338$	−6.94896	−0.377974
$339$	9.33434	0.506972
$340$	6.98238	0.378673
$341$	9.05122	0.490151
$342$	15.7154	0.849793
$343$	−25.7551	−1.39065
$344$	2.76141	0.148885
$345$	0	0
$346$	23.1699	1.24562
$347$	5.76727	0.309603	0.154802	−	0.987946i	$-0.450526\pi$
$347$	5.76727	0.309603	0.154802	+	0.987946i	$0.450526\pi$
$348$	15.1911	0.814328
$349$	−16.4626	−0.881220	−0.440610	−	0.897699i	$-0.645238\pi$
$349$	−16.4626	−0.881220	−0.440610	+	0.897699i	$0.645238\pi$
$350$	−4.44855	−0.237785
$351$	10.7791	0.575344
$352$	−4.40211	−0.234633
$353$	−22.8572	−1.21657	−0.608283	−	0.793720i	$-0.708142\pi$
$353$	−22.8572	−1.21657	−0.608283	+	0.793720i	$0.708142\pi$
$354$	5.51717	0.293234
$355$	−10.8705	−0.576948
$356$	−8.69820	−0.461004
$357$	−85.5769	−4.52921
$358$	1.26603	0.0669120
$359$	−21.1272	−1.11505	−0.557526	−	0.830159i	$-0.688249\pi$
$359$	−21.1272	−1.11505	−0.557526	+	0.830159i	$0.688249\pi$
$360$	4.59049	0.241940
$361$	−7.27983	−0.383149
$362$	18.3728	0.965655
$363$	23.0837	1.21158
$364$	−10.9429	−0.573565
$365$	−8.57546	−0.448860
$366$	38.0316	1.98795
$367$	−12.1222	−0.632773	−0.316386	−	0.948630i	$-0.602470\pi$
$367$	−12.1222	−0.632773	−0.316386	+	0.948630i	$0.602470\pi$
$368$	0	0
$369$	14.5030	0.754998
$370$	6.73053	0.349904
$371$	−8.85420	−0.459687
$372$	−5.66475	−0.293704
$373$	18.1236	0.938402	0.469201	−	0.883091i	$-0.344542\pi$
$373$	18.1236	0.938402	0.469201	+	0.883091i	$0.344542\pi$
$374$	−30.7372	−1.58938
$375$	2.75508	0.142272
$376$	6.18748	0.319095
$377$	13.5634	0.698551
$378$	−19.4933	−1.00263
$379$	−18.0644	−0.927906	−0.463953	−	0.885860i	$-0.653569\pi$
$379$	−18.0644	−0.927906	−0.463953	+	0.885860i	$0.653569\pi$
$380$	3.42347	0.175620
$381$	−15.8018	−0.809552
$382$	−5.84116	−0.298860
$383$	−20.5709	−1.05112	−0.525561	−	0.850756i	$-0.676145\pi$
$383$	−20.5709	−1.05112	−0.525561	+	0.850756i	$0.676145\pi$
$384$	2.75508	0.140595
$385$	19.5830	0.998041
$386$	−0.726448	−0.0369752
$387$	12.6762	0.644369
$388$	−7.30395	−0.370802
$389$	4.21880	0.213902	0.106951	−	0.994264i	$-0.465891\pi$
$389$	4.21880	0.213902	0.106951	+	0.994264i	$0.465891\pi$
$390$	6.77719	0.343177
$391$	0	0
$392$	12.7896	0.645970
$393$	−29.3456	−1.48029
$394$	10.1195	0.509815
$395$	11.8628	0.596880
$396$	−20.2078	−1.01548
$397$	22.9773	1.15320	0.576598	−	0.817028i	$-0.304380\pi$
$397$	22.9773	1.15320	0.576598	+	0.817028i	$0.304380\pi$
$398$	−18.5869	−0.931677
$399$	−41.9585	−2.10055
$400$	1.00000	0.0500000
$401$	30.9372	1.54493	0.772465	−	0.635057i	$-0.219023\pi$
$401$	30.9372	1.54493	0.772465	+	0.635057i	$0.219023\pi$
$402$	−24.5221	−1.22305
$403$	−5.05779	−0.251947
$404$	−9.08953	−0.452221
$405$	−1.69886	−0.0844169
$406$	−24.5286	−1.21733
$407$	−29.6285	−1.46863
$408$	19.2371	0.952376
$409$	0.576257	0.0284941	0.0142470	−	0.999899i	$-0.495465\pi$
$409$	0.576257	0.0284941	0.0142470	+	0.999899i	$0.495465\pi$
$410$	3.15936	0.156030
$411$	−37.7963	−1.86435
$412$	−1.49900	−0.0738504
$413$	−8.90839	−0.438353
$414$	0	0
$415$	−0.319840	−0.0157003
$416$	2.45989	0.120606
$417$	−9.80118	−0.479966
$418$	−15.0705	−0.737122
$419$	−7.93865	−0.387828	−0.193914	−	0.981018i	$-0.562118\pi$
$419$	−7.93865	−0.387828	−0.193914	+	0.981018i	$0.562118\pi$
$420$	−12.2561	−0.598038
$421$	−3.08985	−0.150590	−0.0752951	−	0.997161i	$-0.523990\pi$
$421$	−3.08985	−0.150590	−0.0752951	+	0.997161i	$0.523990\pi$
$422$	4.90443	0.238744
$423$	28.4036	1.38103
$424$	1.99036	0.0966603
$425$	6.98238	0.338695
$426$	−29.9492	−1.45105
$427$	−61.4085	−2.97176
$428$	17.7755	0.859211
$429$	−29.8339	−1.44040
$430$	2.76141	0.133167
$431$	−3.77328	−0.181752	−0.0908762	−	0.995862i	$-0.528967\pi$
$431$	−3.77328	−0.181752	−0.0908762	+	0.995862i	$0.528967\pi$
$432$	4.38194	0.210826
$433$	−8.51858	−0.409377	−0.204689	−	0.978827i	$-0.565618\pi$
$433$	−8.51858	−0.409377	−0.204689	+	0.978827i	$0.565618\pi$
$434$	9.14670	0.439055
$435$	15.1911	0.728357
$436$	−18.9672	−0.908364
$437$	0	0
$438$	−23.6261	−1.12890
$439$	−31.7255	−1.51417	−0.757087	−	0.653314i	$-0.773378\pi$
$439$	−31.7255	−1.51417	−0.757087	+	0.653314i	$0.773378\pi$
$440$	−4.40211	−0.209862
$441$	58.7104	2.79573
$442$	17.1759	0.816972
$443$	3.57155	0.169690	0.0848448	−	0.996394i	$-0.472961\pi$
$443$	3.57155	0.169690	0.0848448	+	0.996394i	$0.472961\pi$
$444$	18.5432	0.880020
$445$	−8.69820	−0.412334
$446$	9.71984	0.460248
$447$	23.8472	1.12794
$448$	−4.44855	−0.210174
$449$	31.6916	1.49562	0.747810	−	0.663913i	$-0.231106\pi$
$449$	31.6916	1.49562	0.747810	+	0.663913i	$0.231106\pi$
$450$	4.59049	0.216398
$451$	−13.9079	−0.654896
$452$	3.38804	0.159360
$453$	−4.85915	−0.228303
$454$	−21.5002	−1.00905
$455$	−10.9429	−0.513012
$456$	9.43196	0.441692
$457$	35.5083	1.66101	0.830503	−	0.557014i	$-0.188053\pi$
$457$	35.5083	1.66101	0.830503	+	0.557014i	$0.188053\pi$
$458$	5.38568	0.251656
$459$	30.5964	1.42812
$460$	0	0
$461$	−35.4649	−1.65177	−0.825883	−	0.563842i	$-0.809323\pi$
$461$	−35.4649	−1.65177	−0.825883	+	0.563842i	$0.809323\pi$
$462$	53.9528	2.51011
$463$	3.37272	0.156744	0.0783719	−	0.996924i	$-0.475028\pi$
$463$	3.37272	0.156744	0.0783719	+	0.996924i	$0.475028\pi$
$464$	5.51384	0.255974
$465$	−5.66475	−0.262697
$466$	−29.3533	−1.35976
$467$	−17.6398	−0.816273	−0.408136	−	0.912921i	$-0.633821\pi$
$467$	−17.6398	−0.816273	−0.408136	+	0.912921i	$0.633821\pi$
$468$	11.2921	0.521977
$469$	39.5951	1.82833
$470$	6.18748	0.285407
$471$	34.7183	1.59973
$472$	2.00254	0.0921744
$473$	−12.1560	−0.558935
$474$	32.6829	1.50118
$475$	3.42347	0.157080
$476$	−31.0614	−1.42370
$477$	9.13673	0.418342
$478$	−8.09013	−0.370034
$479$	31.4181	1.43553	0.717766	−	0.696285i	$-0.245165\pi$
$479$	31.4181	1.43553	0.717766	+	0.696285i	$0.245165\pi$
$480$	2.75508	0.125752
$481$	16.5563	0.754904
$482$	−11.4116	−0.519786
$483$	0	0
$484$	8.37857	0.380844
$485$	−7.30395	−0.331655
$486$	−17.8263	−0.808618
$487$	−2.67284	−0.121118	−0.0605590	−	0.998165i	$-0.519288\pi$
$487$	−2.67284	−0.121118	−0.0605590	+	0.998165i	$0.519288\pi$
$488$	13.8042	0.624885
$489$	5.72170	0.258744
$490$	12.7896	0.577774
$491$	6.39355	0.288537	0.144268	−	0.989539i	$-0.453917\pi$
$491$	6.39355	0.288537	0.144268	+	0.989539i	$0.453917\pi$
$492$	8.70432	0.392421
$493$	38.4997	1.73394
$494$	8.42135	0.378895
$495$	−20.2078	−0.908275
$496$	−2.05611	−0.0923220
$497$	48.3581	2.16916
$498$	−0.881185	−0.0394868
$499$	−2.98791	−0.133757	−0.0668785	−	0.997761i	$-0.521304\pi$
$499$	−2.98791	−0.133757	−0.0668785	+	0.997761i	$0.521304\pi$
$500$	1.00000	0.0447214
$501$	9.60214	0.428992
$502$	−11.7941	−0.526396
$503$	32.6689	1.45663	0.728316	−	0.685241i	$-0.240303\pi$
$503$	32.6689	1.45663	0.728316	+	0.685241i	$0.240303\pi$
$504$	−20.4210	−0.909624
$505$	−9.08953	−0.404479
$506$	0	0
$507$	−19.1450	−0.850259
$508$	−5.73551	−0.254472
$509$	6.90839	0.306209	0.153105	−	0.988210i	$-0.451073\pi$
$509$	6.90839	0.306209	0.153105	+	0.988210i	$0.451073\pi$
$510$	19.2371	0.851831
$511$	38.1483	1.68758
$512$	1.00000	0.0441942
$513$	15.0015	0.662331
$514$	2.03939	0.0899538
$515$	−1.49900	−0.0660538
$516$	7.60792	0.334920
$517$	−27.2380	−1.19792
$518$	−29.9411	−1.31554
$519$	63.8350	2.80205
$520$	2.45989	0.107873
$521$	25.5985	1.12149	0.560746	−	0.827988i	$-0.310515\pi$
$521$	25.5985	1.12149	0.560746	+	0.827988i	$0.310515\pi$
$522$	25.3112	1.10784
$523$	38.7838	1.69590	0.847948	−	0.530080i	$-0.177838\pi$
$523$	38.7838	1.69590	0.847948	+	0.530080i	$0.177838\pi$
$524$	−10.6514	−0.465310
$525$	−12.2561	−0.534901
$526$	−24.7269	−1.07815
$527$	−14.3565	−0.625380
$528$	−12.1282	−0.527811
$529$	0	0
$530$	1.99036	0.0864556
$531$	9.19264	0.398927
$532$	−15.2295	−0.660282
$533$	7.77168	0.336629
$534$	−23.9643	−1.03704
$535$	17.7755	0.768501
$536$	−8.90067	−0.384451
$537$	3.48803	0.150520
$538$	14.4785	0.624213
$539$	−56.3011	−2.42506
$540$	4.38194	0.188569
$541$	−12.2853	−0.528186	−0.264093	−	0.964497i	$-0.585073\pi$
$541$	−12.2853	−0.528186	−0.264093	+	0.964497i	$0.585073\pi$
$542$	19.7153	0.846847
$543$	50.6188	2.17226
$544$	6.98238	0.299367
$545$	−18.9672	−0.812465
$546$	−30.1487	−1.29024
$547$	−40.4153	−1.72803	−0.864016	−	0.503465i	$-0.832058\pi$
$547$	−40.4153	−1.72803	−0.864016	+	0.503465i	$0.832058\pi$
$548$	−13.7187	−0.586035
$549$	63.3679	2.70448
$550$	−4.40211	−0.187707
$551$	18.8765	0.804165
$552$	0	0
$553$	−52.7720	−2.24409
$554$	−22.7803	−0.967843
$555$	18.5432	0.787114
$556$	−3.55749	−0.150871
$557$	−20.7658	−0.879874	−0.439937	−	0.898029i	$-0.644999\pi$
$557$	−20.7658	−0.879874	−0.439937	+	0.898029i	$0.644999\pi$
$558$	−9.43855	−0.399566
$559$	6.79275	0.287303
$560$	−4.44855	−0.187985
$561$	−84.6836	−3.57534
$562$	−13.2608	−0.559373
$563$	9.46288	0.398813	0.199406	−	0.979917i	$-0.436099\pi$
$563$	9.46288	0.398813	0.199406	+	0.979917i	$0.436099\pi$
$564$	17.0470	0.717809
$565$	3.38804	0.142536
$566$	−7.87321	−0.330936
$567$	7.55744	0.317383
$568$	−10.8705	−0.456118
$569$	−21.9043	−0.918276	−0.459138	−	0.888365i	$-0.651842\pi$
$569$	−21.9043	−0.918276	−0.459138	+	0.888365i	$0.651842\pi$
$570$	9.43196	0.395061
$571$	−15.5220	−0.649575	−0.324788	−	0.945787i	$-0.605293\pi$
$571$	−15.5220	−0.649575	−0.324788	+	0.945787i	$0.605293\pi$
$572$	−10.8287	−0.452770
$573$	−16.0929	−0.672291
$574$	−14.0546	−0.586627
$575$	0	0
$576$	4.59049	0.191271
$577$	−42.9640	−1.78862	−0.894308	−	0.447452i	$-0.852331\pi$
$577$	−42.9640	−1.78862	−0.894308	+	0.447452i	$0.852331\pi$
$578$	31.7536	1.32078
$579$	−2.00142	−0.0831764
$580$	5.51384	0.228950
$581$	1.42282	0.0590286
$582$	−20.1230	−0.834125
$583$	−8.76178	−0.362876
$584$	−8.57546	−0.354855
$585$	11.2921	0.466870
$586$	−10.7456	−0.443895
$587$	35.7584	1.47591	0.737954	−	0.674852i	$-0.235792\pi$
$587$	35.7584	1.47591	0.737954	+	0.674852i	$0.235792\pi$
$588$	35.2363	1.45312
$589$	−7.03903	−0.290038
$590$	2.00254	0.0824433
$591$	27.8802	1.14684
$592$	6.73053	0.276623
$593$	−35.7883	−1.46965	−0.734824	−	0.678258i	$-0.762735\pi$
$593$	−35.7883	−1.46965	−0.734824	+	0.678258i	$0.762735\pi$
$594$	−19.2898	−0.791469
$595$	−31.0614	−1.27339
$596$	8.65572	0.354552
$597$	−51.2085	−2.09582
$598$	0	0
$599$	43.5055	1.77759	0.888794	−	0.458307i	$-0.151544\pi$
$599$	43.5055	1.77759	0.888794	+	0.458307i	$0.151544\pi$
$600$	2.75508	0.112476
$601$	−34.9867	−1.42714	−0.713569	−	0.700585i	$-0.752923\pi$
$601$	−34.9867	−1.42714	−0.713569	+	0.700585i	$0.752923\pi$
$602$	−12.2843	−0.500669
$603$	−40.8585	−1.66389
$604$	−1.76370	−0.0717640
$605$	8.37857	0.340637
$606$	−25.0424	−1.01728
$607$	18.5267	0.751974	0.375987	−	0.926625i	$-0.377304\pi$
$607$	18.5267	0.751974	0.375987	+	0.926625i	$0.377304\pi$
$608$	3.42347	0.138840
$609$	−67.5783	−2.73841
$610$	13.8042	0.558914
$611$	15.2205	0.615755
$612$	32.0526	1.29565
$613$	−16.0330	−0.647568	−0.323784	−	0.946131i	$-0.604955\pi$
$613$	−16.0330	−0.647568	−0.323784	+	0.946131i	$0.604955\pi$
$614$	1.33735	0.0539711
$615$	8.70432	0.350992
$616$	19.5830	0.789021
$617$	−11.4406	−0.460581	−0.230291	−	0.973122i	$-0.573968\pi$
$617$	−11.4406	−0.460581	−0.230291	+	0.973122i	$0.573968\pi$
$618$	−4.12987	−0.166128
$619$	9.90379	0.398067	0.199033	−	0.979993i	$-0.436220\pi$
$619$	9.90379	0.398067	0.199033	+	0.979993i	$0.436220\pi$
$620$	−2.05611	−0.0825753
$621$	0	0
$622$	7.12911	0.285851
$623$	38.6944	1.55026
$624$	6.77719	0.271305
$625$	1.00000	0.0400000
$626$	13.1855	0.526999
$627$	−41.5205	−1.65817
$628$	12.6015	0.502856
$629$	46.9951	1.87382
$630$	−20.4210	−0.813593
$631$	23.1560	0.921828	0.460914	−	0.887445i	$-0.347522\pi$
$631$	23.1560	0.921828	0.460914	+	0.887445i	$0.347522\pi$
$632$	11.8628	0.471875
$633$	13.5121	0.537058
$634$	11.9822	0.475875
$635$	−5.73551	−0.227607
$636$	5.48361	0.217439
$637$	31.4609	1.24652
$638$	−24.2725	−0.960958
$639$	−49.9011	−1.97406
$640$	1.00000	0.0395285
$641$	−10.8851	−0.429938	−0.214969	−	0.976621i	$-0.568965\pi$
$641$	−10.8851	−0.429938	−0.214969	+	0.976621i	$0.568965\pi$
$642$	48.9730	1.93281
$643$	38.3078	1.51071	0.755356	−	0.655315i	$-0.227464\pi$
$643$	38.3078	1.51071	0.755356	+	0.655315i	$0.227464\pi$
$644$	0	0
$645$	7.60792	0.299561
$646$	23.9040	0.940490
$647$	−31.6382	−1.24382	−0.621912	−	0.783087i	$-0.713644\pi$
$647$	−31.6382	−1.24382	−0.621912	+	0.783087i	$0.713644\pi$
$648$	−1.69886	−0.0667374
$649$	−8.81540	−0.346035
$650$	2.45989	0.0964846
$651$	25.1999	0.987663
$652$	2.07678	0.0813329
$653$	−21.8844	−0.856404	−0.428202	−	0.903683i	$-0.640853\pi$
$653$	−21.8844	−0.856404	−0.428202	+	0.903683i	$0.640853\pi$
$654$	−52.2562	−2.04338
$655$	−10.6514	−0.416186
$656$	3.15936	0.123352
$657$	−39.3656	−1.53580
$658$	−27.5253	−1.07305
$659$	−14.4063	−0.561191	−0.280595	−	0.959826i	$-0.590532\pi$
$659$	−14.4063	−0.561191	−0.280595	+	0.959826i	$0.590532\pi$
$660$	−12.1282	−0.472089
$661$	2.90302	0.112914	0.0564571	−	0.998405i	$-0.482020\pi$
$661$	2.90302	0.112914	0.0564571	+	0.998405i	$0.482020\pi$
$662$	11.5934	0.450589
$663$	47.3209	1.83779
$664$	−0.319840	−0.0124122
$665$	−15.2295	−0.590574
$666$	30.8964	1.19721
$667$	0	0
$668$	3.48524	0.134848
$669$	26.7790	1.03533
$670$	−8.90067	−0.343863
$671$	−60.7674	−2.34590
$672$	−12.2561	−0.472790
$673$	13.9422	0.537433	0.268717	−	0.963219i	$-0.413400\pi$
$673$	13.9422	0.537433	0.268717	+	0.963219i	$0.413400\pi$
$674$	−6.87330	−0.264749
$675$	4.38194	0.168661
$676$	−6.94896	−0.267268
$677$	14.1958	0.545591	0.272795	−	0.962072i	$-0.412052\pi$
$677$	14.1958	0.545591	0.272795	+	0.962072i	$0.412052\pi$
$678$	9.33434	0.358483
$679$	32.4919	1.24693
$680$	6.98238	0.267762
$681$	−59.2349	−2.26988
$682$	9.05122	0.346589
$683$	−0.587432	−0.0224775	−0.0112387	−	0.999937i	$-0.503577\pi$
$683$	−0.587432	−0.0224775	−0.0112387	+	0.999937i	$0.503577\pi$
$684$	15.7154	0.600894
$685$	−13.7187	−0.524166
$686$	−25.7551	−0.983336
$687$	14.8380	0.566105
$688$	2.76141	0.105278
$689$	4.89605	0.186525
$690$	0	0
$691$	−37.3834	−1.42213	−0.711066	−	0.703126i	$-0.751787\pi$
$691$	−37.3834	−1.42213	−0.711066	+	0.703126i	$0.751787\pi$
$692$	23.1699	0.880787
$693$	89.8955	3.41485
$694$	5.76727	0.218923
$695$	−3.55749	−0.134943
$696$	15.1911	0.575817
$697$	22.0599	0.835578
$698$	−16.4626	−0.623117
$699$	−80.8707	−3.05881
$700$	−4.44855	−0.168139
$701$	−18.6885	−0.705857	−0.352928	−	0.935650i	$-0.614814\pi$
$701$	−18.6885	−0.705857	−0.352928	+	0.935650i	$0.614814\pi$
$702$	10.7791	0.406830
$703$	23.0418	0.869037
$704$	−4.40211	−0.165911
$705$	17.0470	0.642028
$706$	−22.8572	−0.860243
$707$	40.4352	1.52072
$708$	5.51717	0.207348
$709$	−41.3053	−1.55125	−0.775627	−	0.631192i	$-0.782566\pi$
$709$	−41.3053	−1.55125	−0.775627	+	0.631192i	$0.782566\pi$
$710$	−10.8705	−0.407964
$711$	54.4559	2.04226
$712$	−8.69820	−0.325979
$713$	0	0
$714$	−85.5769	−3.20264
$715$	−10.8287	−0.404970
$716$	1.26603	0.0473139
$717$	−22.2890	−0.832397
$718$	−21.1272	−0.788461
$719$	36.3270	1.35477	0.677383	−	0.735630i	$-0.263114\pi$
$719$	36.3270	1.35477	0.677383	+	0.735630i	$0.263114\pi$
$720$	4.59049	0.171078
$721$	6.66837	0.248343
$722$	−7.27983	−0.270927
$723$	−31.4400	−1.16927
$724$	18.3728	0.682822
$725$	5.51384	0.204779
$726$	23.0837	0.856715
$727$	5.17645	0.191984	0.0959920	−	0.995382i	$-0.469398\pi$
$727$	5.17645	0.191984	0.0959920	+	0.995382i	$0.469398\pi$
$728$	−10.9429	−0.405571
$729$	−44.0165	−1.63024
$730$	−8.57546	−0.317392
$731$	19.2812	0.713141
$732$	38.0316	1.40569
$733$	3.74165	0.138201	0.0691006	−	0.997610i	$-0.477987\pi$
$733$	3.74165	0.138201	0.0691006	+	0.997610i	$0.477987\pi$
$734$	−12.1222	−0.447438
$735$	35.2363	1.29971
$736$	0	0
$737$	39.1817	1.44328
$738$	14.5030	0.533864
$739$	−15.7153	−0.578097	−0.289049	−	0.957314i	$-0.593339\pi$
$739$	−15.7153	−0.578097	−0.289049	+	0.957314i	$0.593339\pi$
$740$	6.73053	0.247419
$741$	23.2015	0.852330
$742$	−8.85420	−0.325048
$743$	−48.5703	−1.78187	−0.890936	−	0.454130i	$-0.849950\pi$
$743$	−48.5703	−1.78187	−0.890936	+	0.454130i	$0.849950\pi$
$744$	−5.66475	−0.207680
$745$	8.65572	0.317121
$746$	18.1236	0.663551
$747$	−1.46822	−0.0537194
$748$	−30.7372	−1.12386
$749$	−79.0751	−2.88934
$750$	2.75508	0.100601
$751$	36.1176	1.31795	0.658975	−	0.752165i	$-0.270990\pi$
$751$	36.1176	1.31795	0.658975	+	0.752165i	$0.270990\pi$
$752$	6.18748	0.225634
$753$	−32.4937	−1.18414
$754$	13.5634	0.493950
$755$	−1.76370	−0.0641877
$756$	−19.4933	−0.708963
$757$	−16.6016	−0.603397	−0.301698	−	0.953403i	$-0.597554\pi$
$757$	−16.6016	−0.603397	−0.301698	+	0.953403i	$0.597554\pi$
$758$	−18.0644	−0.656129
$759$	0	0
$760$	3.42347	0.124182
$761$	−10.6287	−0.385291	−0.192645	−	0.981268i	$-0.561707\pi$
$761$	−10.6287	−0.385291	−0.192645	+	0.981268i	$0.561707\pi$
$762$	−15.8018	−0.572440
$763$	84.3764	3.05463
$764$	−5.84116	−0.211326
$765$	32.0526	1.15886
$766$	−20.5709	−0.743256
$767$	4.92602	0.177868
$768$	2.75508	0.0994156
$769$	42.5639	1.53489	0.767446	−	0.641113i	$-0.221527\pi$
$769$	42.5639	1.53489	0.767446	+	0.641113i	$0.221527\pi$
$770$	19.5830	0.705722
$771$	5.61870	0.202353
$772$	−0.726448	−0.0261454
$773$	23.6457	0.850475	0.425238	−	0.905082i	$-0.360190\pi$
$773$	23.6457	0.850475	0.425238	+	0.905082i	$0.360190\pi$
$774$	12.6762	0.455638
$775$	−2.05611	−0.0738576
$776$	−7.30395	−0.262196
$777$	−82.4902	−2.95932
$778$	4.21880	0.151251
$779$	10.8160	0.387523
$780$	6.77719	0.242662
$781$	47.8533	1.71233
$782$	0	0
$783$	24.1613	0.863455
$784$	12.7896	0.456770
$785$	12.6015	0.449768
$786$	−29.3456	−1.04672
$787$	47.0801	1.67822	0.839112	−	0.543959i	$-0.183075\pi$
$787$	47.0801	1.67822	0.839112	+	0.543959i	$0.183075\pi$
$788$	10.1195	0.360493
$789$	−68.1248	−2.42531
$790$	11.8628	0.422058
$791$	−15.0719	−0.535893
$792$	−20.2078	−0.718055
$793$	33.9567	1.20584
$794$	22.9773	0.815433
$795$	5.48361	0.194483
$796$	−18.5869	−0.658795
$797$	15.0160	0.531894	0.265947	−	0.963988i	$-0.414315\pi$
$797$	15.0160	0.531894	0.265947	+	0.963988i	$0.414315\pi$
$798$	−41.9585	−1.48531
$799$	43.2033	1.52842
$800$	1.00000	0.0353553
$801$	−39.9290	−1.41082
$802$	30.9372	1.09243
$803$	37.7501	1.33217
$804$	−24.5221	−0.864828
$805$	0	0
$806$	−5.05779	−0.178153
$807$	39.8895	1.40418
$808$	−9.08953	−0.319769
$809$	−47.7657	−1.67935	−0.839675	−	0.543088i	$-0.817255\pi$
$809$	−47.7657	−1.67935	−0.839675	+	0.543088i	$0.817255\pi$
$810$	−1.69886	−0.0596917
$811$	55.8820	1.96228	0.981142	−	0.193289i	$-0.0619154\pi$
$811$	55.8820	1.96228	0.981142	+	0.193289i	$0.0619154\pi$
$812$	−24.5286	−0.860784
$813$	54.3174	1.90500
$814$	−29.6285	−1.03848
$815$	2.07678	0.0727464
$816$	19.2371	0.673431
$817$	9.45361	0.330740
$818$	0.576257	0.0201484
$819$	−50.2334	−1.75530
$820$	3.15936	0.110330
$821$	−7.19232	−0.251014	−0.125507	−	0.992093i	$-0.540056\pi$
$821$	−7.19232	−0.251014	−0.125507	+	0.992093i	$0.540056\pi$
$822$	−37.7963	−1.31830
$823$	12.3438	0.430278	0.215139	−	0.976583i	$-0.430980\pi$
$823$	12.3438	0.430278	0.215139	+	0.976583i	$0.430980\pi$
$824$	−1.49900	−0.0522201
$825$	−12.1282	−0.422249
$826$	−8.90839	−0.309963
$827$	−48.0835	−1.67203	−0.836013	−	0.548710i	$-0.815119\pi$
$827$	−48.0835	−1.67203	−0.836013	+	0.548710i	$0.815119\pi$
$828$	0	0
$829$	36.8346	1.27932	0.639658	−	0.768659i	$-0.279076\pi$
$829$	36.8346	1.27932	0.639658	+	0.768659i	$0.279076\pi$
$830$	−0.319840	−0.0111018
$831$	−62.7617	−2.17718
$832$	2.45989	0.0852812
$833$	89.3016	3.09412
$834$	−9.80118	−0.339387
$835$	3.48524	0.120612
$836$	−15.0705	−0.521224
$837$	−9.00975	−0.311422
$838$	−7.93865	−0.274236
$839$	15.9647	0.551164	0.275582	−	0.961278i	$-0.411130\pi$
$839$	15.9647	0.551164	0.275582	+	0.961278i	$0.411130\pi$
$840$	−12.2561	−0.422876
$841$	1.40242	0.0483595
$842$	−3.08985	−0.106483
$843$	−36.5346	−1.25832
$844$	4.90443	0.168817
$845$	−6.94896	−0.239052
$846$	28.4036	0.976535
$847$	−37.2724	−1.28070
$848$	1.99036	0.0683492
$849$	−21.6914	−0.744446
$850$	6.98238	0.239494
$851$	0	0
$852$	−29.9492	−1.02604
$853$	28.0441	0.960213	0.480107	−	0.877210i	$-0.340598\pi$
$853$	28.0441	0.960213	0.480107	+	0.877210i	$0.340598\pi$
$854$	−61.4085	−2.10135
$855$	15.7154	0.537456
$856$	17.7755	0.607554
$857$	−4.37547	−0.149463	−0.0747316	−	0.997204i	$-0.523810\pi$
$857$	−4.37547	−0.149463	−0.0747316	+	0.997204i	$0.523810\pi$
$858$	−29.8339	−1.01851
$859$	−6.77691	−0.231225	−0.115613	−	0.993294i	$-0.536883\pi$
$859$	−6.77691	−0.231225	−0.115613	+	0.993294i	$0.536883\pi$
$860$	2.76141	0.0941633
$861$	−38.7216	−1.31963
$862$	−3.77328	−0.128518
$863$	25.2591	0.859830	0.429915	−	0.902869i	$-0.358544\pi$
$863$	25.2591	0.859830	0.429915	+	0.902869i	$0.358544\pi$
$864$	4.38194	0.149077
$865$	23.1699	0.787800
$866$	−8.51858	−0.289473
$867$	87.4840	2.97111
$868$	9.14670	0.310459
$869$	−52.2211	−1.77148
$870$	15.1911	0.515026
$871$	−21.8946	−0.741872
$872$	−18.9672	−0.642310
$873$	−33.5287	−1.13478
$874$	0	0
$875$	−4.44855	−0.150388
$876$	−23.6261	−0.798253
$877$	56.1429	1.89581	0.947906	−	0.318550i	$-0.103196\pi$
$877$	56.1429	1.89581	0.947906	+	0.318550i	$0.103196\pi$
$878$	−31.7255	−1.07068
$879$	−29.6050	−0.998550
$880$	−4.40211	−0.148395
$881$	16.0725	0.541497	0.270749	−	0.962650i	$-0.412729\pi$
$881$	16.0725	0.541497	0.270749	+	0.962650i	$0.412729\pi$
$882$	58.7104	1.97688
$883$	−51.9366	−1.74781	−0.873903	−	0.486100i	$-0.838419\pi$
$883$	−51.9366	−1.74781	−0.873903	+	0.486100i	$0.838419\pi$
$884$	17.1759	0.577687
$885$	5.51717	0.185458
$886$	3.57155	0.119989
$887$	9.49221	0.318717	0.159359	−	0.987221i	$-0.449057\pi$
$887$	9.49221	0.318717	0.159359	+	0.987221i	$0.449057\pi$
$888$	18.5432	0.622268
$889$	25.5147	0.855736
$890$	−8.69820	−0.291564
$891$	7.47855	0.250541
$892$	9.71984	0.325444
$893$	21.1827	0.708851
$894$	23.8472	0.797571
$895$	1.26603	0.0423189
$896$	−4.44855	−0.148615
$897$	0	0
$898$	31.6916	1.05756
$899$	−11.3371	−0.378112
$900$	4.59049	0.153016
$901$	13.8974	0.462991
$902$	−13.9079	−0.463081
$903$	−33.8442	−1.12626
$904$	3.38804	0.112685
$905$	18.3728	0.610734
$906$	−4.85915	−0.161434
$907$	−22.6681	−0.752680	−0.376340	−	0.926482i	$-0.622818\pi$
$907$	−22.6681	−0.752680	−0.376340	+	0.926482i	$0.622818\pi$
$908$	−21.5002	−0.713509
$909$	−41.7254	−1.38394
$910$	−10.9429	−0.362754
$911$	−18.0437	−0.597815	−0.298908	−	0.954282i	$-0.596622\pi$
$911$	−18.0437	−0.597815	−0.298908	+	0.954282i	$0.596622\pi$
$912$	9.43196	0.312323
$913$	1.40797	0.0465970
$914$	35.5083	1.17451
$915$	38.0316	1.25729
$916$	5.38568	0.177948
$917$	47.3834	1.56474
$918$	30.5964	1.00983
$919$	3.42259	0.112901	0.0564505	−	0.998405i	$-0.482022\pi$
$919$	3.42259	0.112901	0.0564505	+	0.998405i	$0.482022\pi$
$920$	0	0
$921$	3.68451	0.121409
$922$	−35.4649	−1.16797
$923$	−26.7403	−0.880167
$924$	53.9528	1.77492
$925$	6.73053	0.221298
$926$	3.37272	0.110835
$927$	−6.88115	−0.226007
$928$	5.51384	0.181001
$929$	5.28457	0.173381	0.0866906	−	0.996235i	$-0.472371\pi$
$929$	5.28457	0.173381	0.0866906	+	0.996235i	$0.472371\pi$
$930$	−5.66475	−0.185755
$931$	43.7847	1.43499
$932$	−29.3533	−0.961498
$933$	19.6413	0.643028
$934$	−17.6398	−0.577192
$935$	−30.7372	−1.00521
$936$	11.2921	0.369093
$937$	9.57867	0.312921	0.156461	−	0.987684i	$-0.449992\pi$
$937$	9.57867	0.312921	0.156461	+	0.987684i	$0.449992\pi$
$938$	39.5951	1.29282
$939$	36.3272	1.18549
$940$	6.18748	0.201813
$941$	18.7350	0.610744	0.305372	−	0.952233i	$-0.401219\pi$
$941$	18.7350	0.610744	0.305372	+	0.952233i	$0.401219\pi$
$942$	34.7183	1.13118
$943$	0	0
$944$	2.00254	0.0651771
$945$	−19.4933	−0.634116
$946$	−12.1560	−0.395226
$947$	48.5733	1.57842	0.789211	−	0.614122i	$-0.210490\pi$
$947$	48.5733	1.57842	0.789211	+	0.614122i	$0.210490\pi$
$948$	32.6829	1.06149
$949$	−21.0947	−0.684761
$950$	3.42347	0.111072
$951$	33.0120	1.07049
$952$	−31.0614	−1.00671
$953$	−3.40802	−0.110397	−0.0551983	−	0.998475i	$-0.517579\pi$
$953$	−3.40802	−0.110397	−0.0551983	+	0.998475i	$0.517579\pi$
$954$	9.13673	0.295812
$955$	−5.84116	−0.189016
$956$	−8.09013	−0.261653
$957$	−66.8729	−2.16169
$958$	31.4181	1.01507
$959$	61.0284	1.97071
$960$	2.75508	0.0889200
$961$	−26.7724	−0.863626
$962$	16.5563	0.533798
$963$	81.5982	2.62947
$964$	−11.4116	−0.367544
$965$	−0.726448	−0.0233852
$966$	0	0
$967$	−13.2945	−0.427524	−0.213762	−	0.976886i	$-0.568572\pi$
$967$	−13.2945	−0.427524	−0.213762	+	0.976886i	$0.568572\pi$
$968$	8.37857	0.269297
$969$	65.8575	2.11565
$970$	−7.30395	−0.234516
$971$	9.61364	0.308516	0.154258	−	0.988031i	$-0.450701\pi$
$971$	9.61364	0.308516	0.154258	+	0.988031i	$0.450701\pi$
$972$	−17.8263	−0.571779
$973$	15.8256	0.507347
$974$	−2.67284	−0.0856434
$975$	6.77719	0.217044
$976$	13.8042	0.441861
$977$	49.8942	1.59626	0.798129	−	0.602487i	$-0.205823\pi$
$977$	49.8942	1.59626	0.798129	+	0.602487i	$0.205823\pi$
$978$	5.72170	0.182960
$979$	38.2904	1.22377
$980$	12.7896	0.408548
$981$	−87.0688	−2.77989
$982$	6.39355	0.204026
$983$	28.8271	0.919443	0.459721	−	0.888063i	$-0.347949\pi$
$983$	28.8271	0.919443	0.459721	+	0.888063i	$0.347949\pi$
$984$	8.70432	0.277484
$985$	10.1195	0.322435
$986$	38.4997	1.22608
$987$	−75.8345	−2.41384
$988$	8.42135	0.267919
$989$	0	0
$990$	−20.2078	−0.642248
$991$	−6.23589	−0.198090	−0.0990448	−	0.995083i	$-0.531579\pi$
$991$	−6.23589	−0.198090	−0.0990448	+	0.995083i	$0.531579\pi$
$992$	−2.05611	−0.0652815
$993$	31.9407	1.01361
$994$	48.3581	1.53383
$995$	−18.5869	−0.589244
$996$	−0.881185	−0.0279214
$997$	−43.3422	−1.37266	−0.686330	−	0.727290i	$-0.740779\pi$
$997$	−43.3422	−1.37266	−0.686330	+	0.727290i	$0.740779\pi$
$998$	−2.98791	−0.0945805
$999$	29.4928	0.933110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bl.1.12		15
23.15	odd	22		230.2.g.d.41.1	✓	30
23.20	odd	22		230.2.g.d.101.1	yes	30
23.22	odd	2		5290.2.a.bk.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.41.1	✓	30	23.15	odd	22
230.2.g.d.101.1	yes	30	23.20	odd	22
5290.2.a.bk.1.12		15	23.22	odd	2
5290.2.a.bl.1.12		15	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.75508 q^{6} -4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.75508 q^{6} -4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} +1.00000 q^{10} -4.40211 q^{11} +2.75508 q^{12} +2.45989 q^{13} -4.44855 q^{14} +2.75508 q^{15} +1.00000 q^{16} +6.98238 q^{17} +4.59049 q^{18} +3.42347 q^{19} +1.00000 q^{20} -12.2561 q^{21} -4.40211 q^{22} +2.75508 q^{24} +1.00000 q^{25} +2.45989 q^{26} +4.38194 q^{27} -4.44855 q^{28} +5.51384 q^{29} +2.75508 q^{30} -2.05611 q^{31} +1.00000 q^{32} -12.1282 q^{33} +6.98238 q^{34} -4.44855 q^{35} +4.59049 q^{36} +6.73053 q^{37} +3.42347 q^{38} +6.77719 q^{39} +1.00000 q^{40} +3.15936 q^{41} -12.2561 q^{42} +2.76141 q^{43} -4.40211 q^{44} +4.59049 q^{45} +6.18748 q^{47} +2.75508 q^{48} +12.7896 q^{49} +1.00000 q^{50} +19.2371 q^{51} +2.45989 q^{52} +1.99036 q^{53} +4.38194 q^{54} -4.40211 q^{55} -4.44855 q^{56} +9.43196 q^{57} +5.51384 q^{58} +2.00254 q^{59} +2.75508 q^{60} +13.8042 q^{61} -2.05611 q^{62} -20.4210 q^{63} +1.00000 q^{64} +2.45989 q^{65} -12.1282 q^{66} -8.90067 q^{67} +6.98238 q^{68} -4.44855 q^{70} -10.8705 q^{71} +4.59049 q^{72} -8.57546 q^{73} +6.73053 q^{74} +2.75508 q^{75} +3.42347 q^{76} +19.5830 q^{77} +6.77719 q^{78} +11.8628 q^{79} +1.00000 q^{80} -1.69886 q^{81} +3.15936 q^{82} -0.319840 q^{83} -12.2561 q^{84} +6.98238 q^{85} +2.76141 q^{86} +15.1911 q^{87} -4.40211 q^{88} -8.69820 q^{89} +4.59049 q^{90} -10.9429 q^{91} -5.66475 q^{93} +6.18748 q^{94} +3.42347 q^{95} +2.75508 q^{96} -7.30395 q^{97} +12.7896 q^{98} -20.2078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} + 15 q^{5} + 5 q^{6} - 4 q^{7} + 15 q^{8} + 28 q^{9} + 15 q^{10} + 7 q^{11} + 5 q^{12} + 17 q^{13} - 4 q^{14} + 5 q^{15} + 15 q^{16} + 2 q^{17} + 28 q^{18} + 18 q^{19} + 15 q^{20} + 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} - 4 q^{28} + 35 q^{29} + 5 q^{30} + 19 q^{31} + 15 q^{32} - 21 q^{33} + 2 q^{34} - 4 q^{35} + 28 q^{36} - 12 q^{37} + 18 q^{38} + 26 q^{39} + 15 q^{40} + 27 q^{41} + 12 q^{43} + 7 q^{44} + 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} - 27 q^{51} + 17 q^{52} - 20 q^{53} + 29 q^{54} + 7 q^{55} - 4 q^{56} - 11 q^{57} + 35 q^{58} + 15 q^{59} + 5 q^{60} + 28 q^{61} + 19 q^{62} - 51 q^{63} + 15 q^{64} + 17 q^{65} - 21 q^{66} + 4 q^{67} + 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} - 12 q^{74} + 5 q^{75} + 18 q^{76} + 45 q^{77} + 26 q^{78} - 2 q^{79} + 15 q^{80} + 79 q^{81} + 27 q^{82} - 29 q^{83} + 2 q^{85} + 12 q^{86} - 7 q^{87} + 7 q^{88} + 20 q^{89} + 28 q^{90} + 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} - 22 q^{97} + 29 q^{98} + 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 + 15 * q^5 + 5 * q^6 - 4 * q^7 + 15 * q^8 + 28 * q^9 + 15 * q^10 + 7 * q^11 + 5 * q^12 + 17 * q^13 - 4 * q^14 + 5 * q^15 + 15 * q^16 + 2 * q^17 + 28 * q^18 + 18 * q^19 + 15 * q^20 + 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 - 4 * q^28 + 35 * q^29 + 5 * q^30 + 19 * q^31 + 15 * q^32 - 21 * q^33 + 2 * q^34 - 4 * q^35 + 28 * q^36 - 12 * q^37 + 18 * q^38 + 26 * q^39 + 15 * q^40 + 27 * q^41 + 12 * q^43 + 7 * q^44 + 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 - 27 * q^51 + 17 * q^52 - 20 * q^53 + 29 * q^54 + 7 * q^55 - 4 * q^56 - 11 * q^57 + 35 * q^58 + 15 * q^59 + 5 * q^60 + 28 * q^61 + 19 * q^62 - 51 * q^63 + 15 * q^64 + 17 * q^65 - 21 * q^66 + 4 * q^67 + 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 - 12 * q^74 + 5 * q^75 + 18 * q^76 + 45 * q^77 + 26 * q^78 - 2 * q^79 + 15 * q^80 + 79 * q^81 + 27 * q^82 - 29 * q^83 + 2 * q^85 + 12 * q^86 - 7 * q^87 + 7 * q^88 + 20 * q^89 + 28 * q^90 + 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 - 22 * q^97 + 29 * q^98 + 23 * q^99

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