LMFDB - Embedded newform 6023.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30551 q^{2} +2.60917 q^{3} +3.31537 q^{4} -2.40173 q^{5} -6.01546 q^{6} +3.07987 q^{7} -3.03260 q^{8} +3.80775 q^{9} +O(q^{10})$	\(q-2.30551 q^{2} +2.60917 q^{3} +3.31537 q^{4} -2.40173 q^{5} -6.01546 q^{6} +3.07987 q^{7} -3.03260 q^{8} +3.80775 q^{9} +5.53721 q^{10} +0.844336 q^{11} +8.65036 q^{12} -3.14234 q^{13} -7.10067 q^{14} -6.26651 q^{15} +0.360950 q^{16} +6.14818 q^{17} -8.77880 q^{18} -1.00000 q^{19} -7.96262 q^{20} +8.03590 q^{21} -1.94662 q^{22} -4.06495 q^{23} -7.91257 q^{24} +0.768298 q^{25} +7.24469 q^{26} +2.10755 q^{27} +10.2109 q^{28} -2.51541 q^{29} +14.4475 q^{30} -10.0867 q^{31} +5.23303 q^{32} +2.20301 q^{33} -14.1747 q^{34} -7.39701 q^{35} +12.6241 q^{36} +10.1752 q^{37} +2.30551 q^{38} -8.19888 q^{39} +7.28349 q^{40} -5.50353 q^{41} -18.5268 q^{42} -12.0050 q^{43} +2.79929 q^{44} -9.14517 q^{45} +9.37178 q^{46} +2.56130 q^{47} +0.941780 q^{48} +2.48561 q^{49} -1.77132 q^{50} +16.0416 q^{51} -10.4180 q^{52} +2.70214 q^{53} -4.85897 q^{54} -2.02787 q^{55} -9.34003 q^{56} -2.60917 q^{57} +5.79929 q^{58} -2.93389 q^{59} -20.7758 q^{60} +0.124901 q^{61} +23.2550 q^{62} +11.7274 q^{63} -12.7867 q^{64} +7.54704 q^{65} -5.07907 q^{66} -10.4066 q^{67} +20.3835 q^{68} -10.6061 q^{69} +17.0539 q^{70} +5.48170 q^{71} -11.5474 q^{72} -7.86690 q^{73} -23.4591 q^{74} +2.00462 q^{75} -3.31537 q^{76} +2.60045 q^{77} +18.9026 q^{78} -10.0905 q^{79} -0.866905 q^{80} -5.92430 q^{81} +12.6884 q^{82} +0.962786 q^{83} +26.6420 q^{84} -14.7662 q^{85} +27.6777 q^{86} -6.56311 q^{87} -2.56054 q^{88} -8.65056 q^{89} +21.0843 q^{90} -9.67800 q^{91} -13.4768 q^{92} -26.3179 q^{93} -5.90509 q^{94} +2.40173 q^{95} +13.6539 q^{96} -0.130985 q^{97} -5.73060 q^{98} +3.21502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.30551	−1.63024	−0.815121	−	0.579291i	$-0.803329\pi$
$2$	−2.30551	−1.63024	−0.815121	+	0.579291i	$0.803329\pi$
$3$	2.60917	1.50640	0.753201	−	0.657790i	$-0.228509\pi$
$3$	2.60917	1.50640	0.753201	+	0.657790i	$0.228509\pi$
$4$	3.31537	1.65769
$5$	−2.40173	−1.07409	−0.537043	−	0.843555i	$-0.680459\pi$
$5$	−2.40173	−1.07409	−0.537043	+	0.843555i	$0.680459\pi$
$6$	−6.01546	−2.45580
$7$	3.07987	1.16408	0.582041	−	0.813159i	$-0.302254\pi$
$7$	3.07987	1.16408	0.582041	+	0.813159i	$0.302254\pi$
$8$	−3.03260	−1.07219
$9$	3.80775	1.26925
$10$	5.53721	1.75102
$11$	0.844336	0.254577	0.127288	−	0.991866i	$-0.459373\pi$
$11$	0.844336	0.254577	0.127288	+	0.991866i	$0.459373\pi$
$12$	8.65036	2.49714
$13$	−3.14234	−0.871528	−0.435764	−	0.900061i	$-0.643522\pi$
$13$	−3.14234	−0.871528	−0.435764	+	0.900061i	$0.643522\pi$
$14$	−7.10067	−1.89773
$15$	−6.26651	−1.61801
$16$	0.360950	0.0902376
$17$	6.14818	1.49115	0.745576	−	0.666421i	$-0.232175\pi$
$17$	6.14818	1.49115	0.745576	+	0.666421i	$0.232175\pi$
$18$	−8.77880	−2.06918
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−7.96262	−1.78050
$21$	8.03590	1.75358
$22$	−1.94662	−0.415022
$23$	−4.06495	−0.847600	−0.423800	−	0.905756i	$-0.639304\pi$
$23$	−4.06495	−0.847600	−0.423800	+	0.905756i	$0.639304\pi$
$24$	−7.91257	−1.61515
$25$	0.768298	0.153660
$26$	7.24469	1.42080
$27$	2.10755	0.405598
$28$	10.2109	1.92968
$29$	−2.51541	−0.467099	−0.233550	−	0.972345i	$-0.575034\pi$
$29$	−2.51541	−0.467099	−0.233550	+	0.972345i	$0.575034\pi$
$30$	14.4475	2.63774
$31$	−10.0867	−1.81162	−0.905812	−	0.423679i	$-0.860738\pi$
$31$	−10.0867	−1.81162	−0.905812	+	0.423679i	$0.860738\pi$
$32$	5.23303	0.925078
$33$	2.20301	0.383495
$34$	−14.1747	−2.43094
$35$	−7.39701	−1.25032
$36$	12.6241	2.10402
$37$	10.1752	1.67280	0.836398	−	0.548123i	$-0.184658\pi$
$37$	10.1752	1.67280	0.836398	+	0.548123i	$0.184658\pi$
$38$	2.30551	0.374003
$39$	−8.19888	−1.31287
$40$	7.28349	1.15162
$41$	−5.50353	−0.859507	−0.429754	−	0.902946i	$-0.641400\pi$
$41$	−5.50353	−0.859507	−0.429754	+	0.902946i	$0.641400\pi$
$42$	−18.5268	−2.85875
$43$	−12.0050	−1.83075	−0.915375	−	0.402603i	$-0.868105\pi$
$43$	−12.0050	−1.83075	−0.915375	+	0.402603i	$0.868105\pi$
$44$	2.79929	0.422009
$45$	−9.14517	−1.36328
$46$	9.37178	1.38179
$47$	2.56130	0.373603	0.186802	−	0.982398i	$-0.440188\pi$
$47$	2.56130	0.373603	0.186802	+	0.982398i	$0.440188\pi$
$48$	0.941780	0.135934
$49$	2.48561	0.355087
$50$	−1.77132	−0.250502
$51$	16.0416	2.24627
$52$	−10.4180	−1.44472
$53$	2.70214	0.371167	0.185584	−	0.982628i	$-0.440582\pi$
$53$	2.70214	0.371167	0.185584	+	0.982628i	$0.440582\pi$
$54$	−4.85897	−0.661222
$55$	−2.02787	−0.273437
$56$	−9.34003	−1.24811
$57$	−2.60917	−0.345592
$58$	5.79929	0.761485
$59$	−2.93389	−0.381960	−0.190980	−	0.981594i	$-0.561167\pi$
$59$	−2.93389	−0.381960	−0.190980	+	0.981594i	$0.561167\pi$
$60$	−20.7758	−2.68215
$61$	0.124901	0.0159920	0.00799598	−	0.999968i	$-0.497455\pi$
$61$	0.124901	0.0159920	0.00799598	+	0.999968i	$0.497455\pi$
$62$	23.2550	2.95338
$63$	11.7274	1.47751
$64$	−12.7867	−1.59834
$65$	7.54704	0.936095
$66$	−5.07907	−0.625190
$67$	−10.4066	−1.27136	−0.635681	−	0.771952i	$-0.719281\pi$
$67$	−10.4066	−1.27136	−0.635681	+	0.771952i	$0.719281\pi$
$68$	20.3835	2.47186
$69$	−10.6061	−1.27683
$70$	17.0539	2.03833
$71$	5.48170	0.650558	0.325279	−	0.945618i	$-0.394542\pi$
$71$	5.48170	0.650558	0.325279	+	0.945618i	$0.394542\pi$
$72$	−11.5474	−1.36087
$73$	−7.86690	−0.920751	−0.460375	−	0.887724i	$-0.652285\pi$
$73$	−7.86690	−0.920751	−0.460375	+	0.887724i	$0.652285\pi$
$74$	−23.4591	−2.72706
$75$	2.00462	0.231473
$76$	−3.31537	−0.380299
$77$	2.60045	0.296348
$78$	18.9026	2.14030
$79$	−10.0905	−1.13527	−0.567635	−	0.823280i	$-0.692141\pi$
$79$	−10.0905	−1.13527	−0.567635	+	0.823280i	$0.692141\pi$
$80$	−0.866905	−0.0969229
$81$	−5.92430	−0.658256
$82$	12.6884	1.40120
$83$	0.962786	0.105679	0.0528397	−	0.998603i	$-0.483173\pi$
$83$	0.962786	0.105679	0.0528397	+	0.998603i	$0.483173\pi$
$84$	26.6420	2.90688
$85$	−14.7662	−1.60162
$86$	27.6777	2.98456
$87$	−6.56311	−0.703640
$88$	−2.56054	−0.272954
$89$	−8.65056	−0.916958	−0.458479	−	0.888705i	$-0.651606\pi$
$89$	−8.65056	−0.916958	−0.458479	+	0.888705i	$0.651606\pi$
$90$	21.0843	2.22248
$91$	−9.67800	−1.01453
$92$	−13.4768	−1.40506
$93$	−26.3179	−2.72904
$94$	−5.90509	−0.609064
$95$	2.40173	0.246412
$96$	13.6539	1.39354
$97$	−0.130985	−0.0132995	−0.00664974	−	0.999978i	$-0.502117\pi$
$97$	−0.130985	−0.0132995	−0.00664974	+	0.999978i	$0.502117\pi$
$98$	−5.73060	−0.578878
$99$	3.21502	0.323121
$100$	2.54719	0.254719
$101$	−2.76506	−0.275134	−0.137567	−	0.990492i	$-0.543928\pi$
$101$	−2.76506	−0.275134	−0.137567	+	0.990492i	$0.543928\pi$
$102$	−36.9841	−3.66197
$103$	−11.0342	−1.08724	−0.543618	−	0.839333i	$-0.682946\pi$
$103$	−11.0342	−1.08724	−0.543618	+	0.839333i	$0.682946\pi$
$104$	9.52947	0.934441
$105$	−19.3000	−1.88349
$106$	−6.22981	−0.605092
$107$	13.0360	1.26024	0.630119	−	0.776499i	$-0.283006\pi$
$107$	13.0360	1.26024	0.630119	+	0.776499i	$0.283006\pi$
$108$	6.98730	0.672354
$109$	−11.8198	−1.13213	−0.566067	−	0.824359i	$-0.691536\pi$
$109$	−11.8198	−1.13213	−0.566067	+	0.824359i	$0.691536\pi$
$110$	4.67526	0.445769
$111$	26.5488	2.51990
$112$	1.11168	0.105044
$113$	8.45082	0.794986	0.397493	−	0.917605i	$-0.369880\pi$
$113$	8.45082	0.794986	0.397493	+	0.917605i	$0.369880\pi$
$114$	6.01546	0.563399
$115$	9.76290	0.910395
$116$	−8.33951	−0.774304
$117$	−11.9652	−1.10619
$118$	6.76412	0.622687
$119$	18.9356	1.73582
$120$	19.0038	1.73480
$121$	−10.2871	−0.935191
$122$	−0.287961	−0.0260707
$123$	−14.3596	−1.29476
$124$	−33.4412	−3.00311
$125$	10.1634	0.909042
$126$	−27.0376	−2.40870
$127$	11.7523	1.04285	0.521425	−	0.853297i	$-0.325401\pi$
$127$	11.7523	1.04285	0.521425	+	0.853297i	$0.325401\pi$
$128$	19.0138	1.68060
$129$	−31.3231	−2.75785
$130$	−17.3998	−1.52606
$131$	−9.89520	−0.864547	−0.432274	−	0.901742i	$-0.642289\pi$
$131$	−9.89520	−0.864547	−0.432274	+	0.901742i	$0.642289\pi$
$132$	7.30381	0.635715
$133$	−3.07987	−0.267059
$134$	23.9924	2.07263
$135$	−5.06176	−0.435647
$136$	−18.6450	−1.59879
$137$	14.3140	1.22293	0.611466	−	0.791271i	$-0.290580\pi$
$137$	14.3140	1.22293	0.611466	+	0.791271i	$0.290580\pi$
$138$	24.4525	2.08154
$139$	−4.48599	−0.380497	−0.190248	−	0.981736i	$-0.560929\pi$
$139$	−4.48599	−0.380497	−0.190248	+	0.981736i	$0.560929\pi$
$140$	−24.5239	−2.07264
$141$	6.68285	0.562797
$142$	−12.6381	−1.06057
$143$	−2.65319	−0.221871
$144$	1.37441	0.114534
$145$	6.04132	0.501705
$146$	18.1372	1.50105
$147$	6.48537	0.534904
$148$	33.7346	2.77297
$149$	−6.33757	−0.519194	−0.259597	−	0.965717i	$-0.583590\pi$
$149$	−6.33757	−0.519194	−0.259597	+	0.965717i	$0.583590\pi$
$150$	−4.62166	−0.377357
$151$	19.2425	1.56593	0.782965	−	0.622066i	$-0.213706\pi$
$151$	19.2425	1.56593	0.782965	+	0.622066i	$0.213706\pi$
$152$	3.03260	0.245977
$153$	23.4107	1.89264
$154$	−5.99535	−0.483119
$155$	24.2255	1.94584
$156$	−27.1824	−2.17633
$157$	7.49867	0.598459	0.299229	−	0.954181i	$-0.403270\pi$
$157$	7.49867	0.598459	0.299229	+	0.954181i	$0.403270\pi$
$158$	23.2637	1.85076
$159$	7.05033	0.559128
$160$	−12.5683	−0.993613
$161$	−12.5195	−0.986677
$162$	13.6585	1.07312
$163$	−1.69924	−0.133095	−0.0665474	−	0.997783i	$-0.521198\pi$
$163$	−1.69924	−0.133095	−0.0665474	+	0.997783i	$0.521198\pi$
$164$	−18.2463	−1.42479
$165$	−5.29104	−0.411907
$166$	−2.21971	−0.172283
$167$	−3.52614	−0.272861	−0.136431	−	0.990650i	$-0.543563\pi$
$167$	−3.52614	−0.272861	−0.136431	+	0.990650i	$0.543563\pi$
$168$	−24.3697	−1.88016
$169$	−3.12571	−0.240439
$170$	34.0437	2.61103
$171$	−3.80775	−0.291186
$172$	−39.8011	−3.03481
$173$	9.03444	0.686876	0.343438	−	0.939175i	$-0.388408\pi$
$173$	9.03444	0.686876	0.343438	+	0.939175i	$0.388408\pi$
$174$	15.1313	1.14710
$175$	2.36626	0.178872
$176$	0.304763	0.0229724
$177$	−7.65501	−0.575386
$178$	19.9439	1.49486
$179$	−3.14057	−0.234737	−0.117369	−	0.993088i	$-0.537446\pi$
$179$	−3.14057	−0.234737	−0.117369	+	0.993088i	$0.537446\pi$
$180$	−30.3197	−2.25989
$181$	18.1560	1.34952	0.674762	−	0.738035i	$-0.264246\pi$
$181$	18.1560	1.34952	0.674762	+	0.738035i	$0.264246\pi$
$182$	22.3127	1.65393
$183$	0.325888	0.0240903
$184$	12.3274	0.908786
$185$	−24.4381	−1.79672
$186$	60.6761	4.44899
$187$	5.19113	0.379613
$188$	8.49165	0.619317
$189$	6.49098	0.472149
$190$	−5.53721	−0.401711
$191$	−0.0279119	−0.00201964	−0.00100982	−	0.999999i	$-0.500321\pi$
$191$	−0.0279119	−0.00201964	−0.00100982	+	0.999999i	$0.500321\pi$
$192$	−33.3626	−2.40774
$193$	−15.0972	−1.08672	−0.543362	−	0.839499i	$-0.682849\pi$
$193$	−15.0972	−1.08672	−0.543362	+	0.839499i	$0.682849\pi$
$194$	0.301987	0.0216814
$195$	19.6915	1.41014
$196$	8.24072	0.588623
$197$	−18.9560	−1.35056	−0.675280	−	0.737561i	$-0.735977\pi$
$197$	−18.9560	−1.35056	−0.675280	+	0.737561i	$0.735977\pi$
$198$	−7.41225	−0.526766
$199$	−10.4289	−0.739288	−0.369644	−	0.929173i	$-0.620520\pi$
$199$	−10.4289	−0.739288	−0.369644	+	0.929173i	$0.620520\pi$
$200$	−2.32994	−0.164752
$201$	−27.1524	−1.91518
$202$	6.37488	0.448535
$203$	−7.74713	−0.543742
$204$	53.1839	3.72362
$205$	13.2180	0.923184
$206$	25.4395	1.77246
$207$	−15.4783	−1.07582
$208$	−1.13423	−0.0786446
$209$	−0.844336	−0.0584039
$210$	44.4964	3.07054
$211$	20.7296	1.42709	0.713543	−	0.700612i	$-0.247089\pi$
$211$	20.7296	1.42709	0.713543	+	0.700612i	$0.247089\pi$
$212$	8.95860	0.615279
$213$	14.3027	0.980002
$214$	−30.0546	−2.05449
$215$	28.8328	1.96638
$216$	−6.39136	−0.434877
$217$	−31.0657	−2.10888
$218$	27.2507	1.84565
$219$	−20.5260	−1.38702
$220$	−6.72313	−0.453273
$221$	−19.3196	−1.29958
$222$	−61.2086	−4.10805
$223$	28.3112	1.89586	0.947929	−	0.318483i	$-0.103173\pi$
$223$	28.3112	1.89586	0.947929	+	0.318483i	$0.103173\pi$
$224$	16.1171	1.07687
$225$	2.92548	0.195032
$226$	−19.4834	−1.29602
$227$	−5.69973	−0.378305	−0.189152	−	0.981948i	$-0.560574\pi$
$227$	−5.69973	−0.378305	−0.189152	+	0.981948i	$0.560574\pi$
$228$	−8.65036	−0.572884
$229$	−15.3214	−1.01247	−0.506233	−	0.862396i	$-0.668963\pi$
$229$	−15.3214	−1.01247	−0.506233	+	0.862396i	$0.668963\pi$
$230$	−22.5085	−1.48416
$231$	6.78500	0.446420
$232$	7.62823	0.500818
$233$	−22.5553	−1.47765	−0.738824	−	0.673898i	$-0.764619\pi$
$233$	−22.5553	−1.47765	−0.738824	+	0.673898i	$0.764619\pi$
$234$	27.5860	1.80335
$235$	−6.15154	−0.401282
$236$	−9.72695	−0.633170
$237$	−26.3278	−1.71017
$238$	−43.6562	−2.82981
$239$	−6.95185	−0.449678	−0.224839	−	0.974396i	$-0.572186\pi$
$239$	−6.95185	−0.449678	−0.224839	+	0.974396i	$0.572186\pi$
$240$	−2.26190	−0.146005
$241$	−9.55654	−0.615591	−0.307795	−	0.951453i	$-0.599591\pi$
$241$	−9.55654	−0.615591	−0.307795	+	0.951453i	$0.599591\pi$
$242$	23.7170	1.52459
$243$	−21.7801	−1.39720
$244$	0.414094	0.0265097
$245$	−5.96976	−0.381394
$246$	33.1063	2.11078
$247$	3.14234	0.199942
$248$	30.5890	1.94240
$249$	2.51207	0.159196
$250$	−23.4318	−1.48196
$251$	3.59023	0.226613	0.113307	−	0.993560i	$-0.463856\pi$
$251$	3.59023	0.226613	0.113307	+	0.993560i	$0.463856\pi$
$252$	38.8806	2.44925
$253$	−3.43218	−0.215779
$254$	−27.0951	−1.70010
$255$	−38.5276	−2.41269
$256$	−18.2631	−1.14144
$257$	1.34236	0.0837341	0.0418670	−	0.999123i	$-0.486669\pi$
$257$	1.34236	0.0837341	0.0418670	+	0.999123i	$0.486669\pi$
$258$	72.2157	4.49595
$259$	31.3384	1.94727
$260$	25.0213	1.55175
$261$	−9.57803	−0.592865
$262$	22.8135	1.40942
$263$	−16.8192	−1.03711	−0.518557	−	0.855043i	$-0.673531\pi$
$263$	−16.8192	−1.03711	−0.518557	+	0.855043i	$0.673531\pi$
$264$	−6.68086	−0.411179
$265$	−6.48980	−0.398666
$266$	7.10067	0.435370
$267$	−22.5707	−1.38131
$268$	−34.5016	−2.10752
$269$	−13.6212	−0.830500	−0.415250	−	0.909707i	$-0.636306\pi$
$269$	−13.6212	−0.830500	−0.415250	+	0.909707i	$0.636306\pi$
$270$	11.6699	0.710209
$271$	−9.98790	−0.606722	−0.303361	−	0.952876i	$-0.598109\pi$
$271$	−9.98790	−0.606722	−0.303361	+	0.952876i	$0.598109\pi$
$272$	2.21919	0.134558
$273$	−25.2515	−1.52829
$274$	−33.0012	−1.99367
$275$	0.648701	0.0391182
$276$	−35.1633	−2.11658
$277$	22.5904	1.35732	0.678662	−	0.734451i	$-0.262560\pi$
$277$	22.5904	1.35732	0.678662	+	0.734451i	$0.262560\pi$
$278$	10.3425	0.620301
$279$	−38.4076	−2.29940
$280$	22.4322	1.34058
$281$	12.5607	0.749307	0.374653	−	0.927165i	$-0.377762\pi$
$281$	12.5607	0.749307	0.374653	+	0.927165i	$0.377762\pi$
$282$	−15.4074	−0.917495
$283$	12.1383	0.721545	0.360773	−	0.932654i	$-0.382513\pi$
$283$	12.1383	0.721545	0.360773	+	0.932654i	$0.382513\pi$
$284$	18.1739	1.07842
$285$	6.26651	0.371196
$286$	6.11695	0.361703
$287$	−16.9502	−1.00054
$288$	19.9261	1.17415
$289$	20.8001	1.22353
$290$	−13.9283	−0.817899
$291$	−0.341761	−0.0200344
$292$	−26.0817	−1.52632
$293$	21.5483	1.25887	0.629433	−	0.777055i	$-0.283287\pi$
$293$	21.5483	1.25887	0.629433	+	0.777055i	$0.283287\pi$
$294$	−14.9521	−0.872023
$295$	7.04641	0.410258
$296$	−30.8574	−1.79355
$297$	1.77948	0.103256
$298$	14.6113	0.846411
$299$	12.7734	0.738707
$300$	6.64605	0.383710
$301$	−36.9739	−2.13114
$302$	−44.3637	−2.55284
$303$	−7.21451	−0.414462
$304$	−0.360950	−0.0207019
$305$	−0.299979	−0.0171767
$306$	−53.9736	−3.08546
$307$	10.9893	0.627193	0.313596	−	0.949556i	$-0.398466\pi$
$307$	10.9893	0.627193	0.313596	+	0.949556i	$0.398466\pi$
$308$	8.62145	0.491253
$309$	−28.7902	−1.63781
$310$	−55.8521	−3.17219
$311$	−6.84222	−0.387987	−0.193993	−	0.981003i	$-0.562144\pi$
$311$	−6.84222	−0.387987	−0.193993	+	0.981003i	$0.562144\pi$
$312$	24.8640	1.40764
$313$	−20.5589	−1.16206	−0.581030	−	0.813882i	$-0.697350\pi$
$313$	−20.5589	−1.16206	−0.581030	+	0.813882i	$0.697350\pi$
$314$	−17.2883	−0.975632
$315$	−28.1660	−1.58697
$316$	−33.4538	−1.88192
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−16.2546	−0.911513
$319$	−2.12385	−0.118913
$320$	30.7102	1.71675
$321$	34.0131	1.89843
$322$	28.8639	1.60852
$323$	−6.14818	−0.342094
$324$	−19.6413	−1.09118
$325$	−2.41425	−0.133919
$326$	3.91762	0.216977
$327$	−30.8399	−1.70545
$328$	16.6900	0.921553
$329$	7.88846	0.434905
$330$	12.1985	0.671507
$331$	3.15236	0.173270	0.0866348	−	0.996240i	$-0.472389\pi$
$331$	3.15236	0.173270	0.0866348	+	0.996240i	$0.472389\pi$
$332$	3.19199	0.175183
$333$	38.7447	2.12319
$334$	8.12955	0.444829
$335$	24.9937	1.36555
$336$	2.90056	0.158239
$337$	−4.12736	−0.224832	−0.112416	−	0.993661i	$-0.535859\pi$
$337$	−4.12736	−0.224832	−0.112416	+	0.993661i	$0.535859\pi$
$338$	7.20635	0.391974
$339$	22.0496	1.19757
$340$	−48.9556	−2.65499
$341$	−8.51656	−0.461198
$342$	8.77880	0.474703
$343$	−13.9037	−0.750731
$344$	36.4065	1.96291
$345$	25.4730	1.37142
$346$	−20.8290	−1.11977
$347$	−10.0358	−0.538752	−0.269376	−	0.963035i	$-0.586817\pi$
$347$	−10.0358	−0.538752	−0.269376	+	0.963035i	$0.586817\pi$
$348$	−21.7592	−1.16641
$349$	−22.2393	−1.19044	−0.595221	−	0.803562i	$-0.702935\pi$
$349$	−22.2393	−1.19044	−0.595221	+	0.803562i	$0.702935\pi$
$350$	−5.45543	−0.291605
$351$	−6.62263	−0.353490
$352$	4.41844	0.235504
$353$	0.128942	0.00686288	0.00343144	−	0.999994i	$-0.498908\pi$
$353$	0.128942	0.00686288	0.00343144	+	0.999994i	$0.498908\pi$
$354$	17.6487	0.938018
$355$	−13.1655	−0.698755
$356$	−28.6798	−1.52003
$357$	49.4061	2.61485
$358$	7.24061	0.382678
$359$	−3.53690	−0.186671	−0.0933353	−	0.995635i	$-0.529753\pi$
$359$	−3.53690	−0.186671	−0.0933353	+	0.995635i	$0.529753\pi$
$360$	27.7337	1.46169
$361$	1.00000	0.0526316
$362$	−41.8588	−2.20005
$363$	−26.8407	−1.40877
$364$	−32.0862	−1.68177
$365$	18.8941	0.988965
$366$	−0.751338	−0.0392730
$367$	25.0769	1.30900	0.654502	−	0.756061i	$-0.272879\pi$
$367$	25.0769	1.30900	0.654502	+	0.756061i	$0.272879\pi$
$368$	−1.46724	−0.0764854
$369$	−20.9561	−1.09093
$370$	56.3423	2.92909
$371$	8.32224	0.432069
$372$	−87.2536	−4.52389
$373$	17.4144	0.901686	0.450843	−	0.892603i	$-0.351124\pi$
$373$	17.4144	0.901686	0.450843	+	0.892603i	$0.351124\pi$
$374$	−11.9682	−0.618860
$375$	26.5180	1.36938
$376$	−7.76740	−0.400573
$377$	7.90426	0.407090
$378$	−14.9650	−0.769717
$379$	−12.0486	−0.618893	−0.309447	−	0.950917i	$-0.600144\pi$
$379$	−12.0486	−0.618893	−0.309447	+	0.950917i	$0.600144\pi$
$380$	7.96262	0.408474
$381$	30.6638	1.57095
$382$	0.0643512	0.00329250
$383$	20.7513	1.06034	0.530172	−	0.847890i	$-0.322128\pi$
$383$	20.7513	1.06034	0.530172	+	0.847890i	$0.322128\pi$
$384$	49.6102	2.53166
$385$	−6.24557	−0.318303
$386$	34.8068	1.77162
$387$	−45.7121	−2.32368
$388$	−0.434263	−0.0220464
$389$	−5.52185	−0.279969	−0.139984	−	0.990154i	$-0.544705\pi$
$389$	−5.52185	−0.279969	−0.139984	+	0.990154i	$0.544705\pi$
$390$	−45.3989	−2.29886
$391$	−24.9920	−1.26390
$392$	−7.53787	−0.380720
$393$	−25.8182	−1.30236
$394$	43.7033	2.20174
$395$	24.2346	1.21938
$396$	10.6590	0.535634
$397$	−6.99177	−0.350907	−0.175453	−	0.984488i	$-0.556139\pi$
$397$	−6.99177	−0.350907	−0.175453	+	0.984488i	$0.556139\pi$
$398$	24.0440	1.20522
$399$	−8.03590	−0.402298
$400$	0.277317	0.0138659
$401$	15.8587	0.791943	0.395972	−	0.918263i	$-0.370408\pi$
$401$	15.8587	0.791943	0.395972	+	0.918263i	$0.370408\pi$
$402$	62.6002	3.12221
$403$	31.6958	1.57888
$404$	−9.16721	−0.456086
$405$	14.2286	0.707023
$406$	17.8611	0.886431
$407$	8.59130	0.425855
$408$	−48.6478	−2.40843
$409$	−28.1892	−1.39386	−0.696932	−	0.717137i	$-0.745452\pi$
$409$	−28.1892	−1.39386	−0.696932	+	0.717137i	$0.745452\pi$
$410$	−30.4742	−1.50501
$411$	37.3477	1.84223
$412$	−36.5826	−1.80230
$413$	−9.03601	−0.444633
$414$	35.6854	1.75384
$415$	−2.31235	−0.113509
$416$	−16.4440	−0.806232
$417$	−11.7047	−0.573181
$418$	1.94662	0.0952125
$419$	−11.8947	−0.581096	−0.290548	−	0.956860i	$-0.593838\pi$
$419$	−11.8947	−0.581096	−0.290548	+	0.956860i	$0.593838\pi$
$420$	−63.9868	−3.12224
$421$	−11.0341	−0.537769	−0.268884	−	0.963172i	$-0.586655\pi$
$421$	−11.0341	−0.537769	−0.268884	+	0.963172i	$0.586655\pi$
$422$	−47.7923	−2.32649
$423$	9.75277	0.474196
$424$	−8.19452	−0.397961
$425$	4.72363	0.229130
$426$	−32.9749	−1.59764
$427$	0.384680	0.0186160
$428$	43.2192	2.08908
$429$	−6.92261	−0.334227
$430$	−66.4743	−3.20568
$431$	19.0607	0.918120	0.459060	−	0.888405i	$-0.348186\pi$
$431$	19.0607	0.918120	0.459060	+	0.888405i	$0.348186\pi$
$432$	0.760720	0.0366002
$433$	−1.40924	−0.0677239	−0.0338620	−	0.999427i	$-0.510781\pi$
$433$	−1.40924	−0.0677239	−0.0338620	+	0.999427i	$0.510781\pi$
$434$	71.6223	3.43798
$435$	15.7628	0.755769
$436$	−39.1871	−1.87672
$437$	4.06495	0.194453
$438$	47.3230	2.26118
$439$	7.83372	0.373883	0.186942	−	0.982371i	$-0.440143\pi$
$439$	7.83372	0.373883	0.186942	+	0.982371i	$0.440143\pi$
$440$	6.14971	0.293176
$441$	9.46458	0.450694
$442$	44.5416	2.11863
$443$	−16.0685	−0.763437	−0.381719	−	0.924279i	$-0.624668\pi$
$443$	−16.0685	−0.763437	−0.381719	+	0.924279i	$0.624668\pi$
$444$	88.0193	4.17721
$445$	20.7763	0.984891
$446$	−65.2717	−3.09070
$447$	−16.5358	−0.782115
$448$	−39.3814	−1.86060
$449$	34.1153	1.61000	0.805001	−	0.593273i	$-0.202165\pi$
$449$	34.1153	1.61000	0.805001	+	0.593273i	$0.202165\pi$
$450$	−6.74473	−0.317950
$451$	−4.64683	−0.218811
$452$	28.0176	1.31784
$453$	50.2068	2.35892
$454$	13.1408	0.616728
$455$	23.2439	1.08969
$456$	7.91257	0.370540
$457$	6.11868	0.286220	0.143110	−	0.989707i	$-0.454290\pi$
$457$	6.11868	0.286220	0.143110	+	0.989707i	$0.454290\pi$
$458$	35.3236	1.65057
$459$	12.9576	0.604808
$460$	32.3677	1.50915
$461$	37.6355	1.75286	0.876429	−	0.481531i	$-0.159919\pi$
$461$	37.6355	1.75286	0.876429	+	0.481531i	$0.159919\pi$
$462$	−15.6429	−0.727772
$463$	30.7212	1.42774	0.713868	−	0.700280i	$-0.246941\pi$
$463$	30.7212	1.42774	0.713868	+	0.700280i	$0.246941\pi$
$464$	−0.907937	−0.0421499
$465$	63.2084	2.93122
$466$	52.0015	2.40892
$467$	39.0635	1.80764	0.903821	−	0.427911i	$-0.140750\pi$
$467$	39.0635	1.80764	0.903821	+	0.427911i	$0.140750\pi$
$468$	−39.6692	−1.83371
$469$	−32.0508	−1.47997
$470$	14.1824	0.654186
$471$	19.5653	0.901520
$472$	8.89733	0.409533
$473$	−10.1363	−0.466066
$474$	60.6989	2.78800
$475$	−0.768298	−0.0352519
$476$	62.7785	2.87745
$477$	10.2891	0.471104
$478$	16.0276	0.733084
$479$	12.3208	0.562949	0.281475	−	0.959569i	$-0.409176\pi$
$479$	12.3208	0.562949	0.281475	+	0.959569i	$0.409176\pi$
$480$	−32.7928	−1.49678
$481$	−31.9740	−1.45789
$482$	22.0327	1.00356
$483$	−32.6655	−1.48633
$484$	−34.1056	−1.55025
$485$	0.314590	0.0142848
$486$	50.2143	2.27777
$487$	−6.30218	−0.285579	−0.142790	−	0.989753i	$-0.545607\pi$
$487$	−6.30218	−0.285579	−0.142790	+	0.989753i	$0.545607\pi$
$488$	−0.378776	−0.0171464
$489$	−4.43360	−0.200494
$490$	13.7633	0.621764
$491$	21.0356	0.949323	0.474662	−	0.880168i	$-0.342570\pi$
$491$	21.0356	0.949323	0.474662	+	0.880168i	$0.342570\pi$
$492$	−47.6075	−2.14631
$493$	−15.4652	−0.696516
$494$	−7.24469	−0.325954
$495$	−7.72160	−0.347060
$496$	−3.64080	−0.163477
$497$	16.8829	0.757303
$498$	−5.79160	−0.259528
$499$	−28.4324	−1.27281	−0.636405	−	0.771355i	$-0.719579\pi$
$499$	−28.4324	−1.27281	−0.636405	+	0.771355i	$0.719579\pi$
$500$	33.6955	1.50691
$501$	−9.20029	−0.411039
$502$	−8.27731	−0.369434
$503$	−11.6335	−0.518710	−0.259355	−	0.965782i	$-0.583510\pi$
$503$	−11.6335	−0.518710	−0.259355	+	0.965782i	$0.583510\pi$
$504$	−35.5645	−1.58417
$505$	6.64093	0.295517
$506$	7.91293	0.351773
$507$	−8.15549	−0.362198
$508$	38.9633	1.72872
$509$	9.05113	0.401184	0.200592	−	0.979675i	$-0.435713\pi$
$509$	9.05113	0.401184	0.200592	+	0.979675i	$0.435713\pi$
$510$	88.8257	3.93327
$511$	−24.2290	−1.07183
$512$	4.07810	0.180228
$513$	−2.10755	−0.0930505
$514$	−3.09482	−0.136507
$515$	26.5012	1.16778
$516$	−103.848	−4.57164
$517$	2.16259	0.0951108
$518$	−72.2509	−3.17452
$519$	23.5724	1.03471
$520$	−22.8872	−1.00367
$521$	−34.5083	−1.51184	−0.755918	−	0.654666i	$-0.772809\pi$
$521$	−34.5083	−1.51184	−0.755918	+	0.654666i	$0.772809\pi$
$522$	22.0822	0.966514
$523$	−34.7348	−1.51885	−0.759424	−	0.650597i	$-0.774519\pi$
$523$	−34.7348	−1.51885	−0.759424	+	0.650597i	$0.774519\pi$
$524$	−32.8063	−1.43315
$525$	6.17396	0.269454
$526$	38.7768	1.69075
$527$	−62.0148	−2.70141
$528$	0.795178	0.0346057
$529$	−6.47619	−0.281573
$530$	14.9623	0.649921
$531$	−11.1715	−0.484803
$532$	−10.2109	−0.442700
$533$	17.2940	0.749085
$534$	52.0371	2.25186
$535$	−31.3089	−1.35360
$536$	31.5589	1.36314
$537$	−8.19426	−0.353609
$538$	31.4038	1.35391
$539$	2.09869	0.0903970
$540$	−16.7816	−0.722165
$541$	−11.2467	−0.483535	−0.241768	−	0.970334i	$-0.577727\pi$
$541$	−11.2467	−0.483535	−0.241768	+	0.970334i	$0.577727\pi$
$542$	23.0272	0.989103
$543$	47.3720	2.03293
$544$	32.1736	1.37943
$545$	28.3880	1.21601
$546$	58.2176	2.49148
$547$	−22.0700	−0.943644	−0.471822	−	0.881694i	$-0.656403\pi$
$547$	−22.0700	−0.943644	−0.471822	+	0.881694i	$0.656403\pi$
$548$	47.4564	2.02724
$549$	0.475592	0.0202978
$550$	−1.49559	−0.0637720
$551$	2.51541	0.107160
$552$	32.1642	1.36900
$553$	−31.0774	−1.32155
$554$	−52.0823	−2.21276
$555$	−63.7631	−2.70659
$556$	−14.8727	−0.630744
$557$	24.0806	1.02033	0.510164	−	0.860077i	$-0.329585\pi$
$557$	24.0806	1.02033	0.510164	+	0.860077i	$0.329585\pi$
$558$	88.5491	3.74858
$559$	37.7239	1.59555
$560$	−2.66996	−0.112826
$561$	13.5445	0.571850
$562$	−28.9587	−1.22155
$563$	−41.0811	−1.73136	−0.865682	−	0.500595i	$-0.833115\pi$
$563$	−41.0811	−1.73136	−0.865682	+	0.500595i	$0.833115\pi$
$564$	22.1561	0.932941
$565$	−20.2966	−0.853883
$566$	−27.9849	−1.17629
$567$	−18.2461	−0.766264
$568$	−16.6238	−0.697520
$569$	−21.0383	−0.881971	−0.440985	−	0.897514i	$-0.645371\pi$
$569$	−21.0383	−0.881971	−0.440985	+	0.897514i	$0.645371\pi$
$570$	−14.4475	−0.605139
$571$	−29.5547	−1.23682	−0.618412	−	0.785854i	$-0.712224\pi$
$571$	−29.5547	−1.23682	−0.618412	+	0.785854i	$0.712224\pi$
$572$	−8.79631	−0.367792
$573$	−0.0728269	−0.00304239
$574$	39.0788	1.63112
$575$	−3.12309	−0.130242
$576$	−48.6885	−2.02869
$577$	11.3295	0.471655	0.235828	−	0.971795i	$-0.424220\pi$
$577$	11.3295	0.471655	0.235828	+	0.971795i	$0.424220\pi$
$578$	−47.9547	−1.99465
$579$	−39.3912	−1.63704
$580$	20.0292	0.831669
$581$	2.96526	0.123020
$582$	0.787933	0.0326609
$583$	2.28151	0.0944906
$584$	23.8572	0.987217
$585$	28.7372	1.18814
$586$	−49.6798	−2.05225
$587$	−27.9458	−1.15345	−0.576724	−	0.816939i	$-0.695669\pi$
$587$	−27.9458	−1.15345	−0.576724	+	0.816939i	$0.695669\pi$
$588$	21.5014	0.886704
$589$	10.0867	0.415615
$590$	−16.2456	−0.668819
$591$	−49.4594	−2.03449
$592$	3.67275	0.150949
$593$	−7.47525	−0.306972	−0.153486	−	0.988151i	$-0.549050\pi$
$593$	−7.47525	−0.306972	−0.153486	+	0.988151i	$0.549050\pi$
$594$	−4.10260	−0.168332
$595$	−45.4781	−1.86442
$596$	−21.0114	−0.860660
$597$	−27.2108	−1.11367
$598$	−29.4493	−1.20427
$599$	−42.8856	−1.75226	−0.876128	−	0.482078i	$-0.839882\pi$
$599$	−42.8856	−1.75226	−0.876128	+	0.482078i	$0.839882\pi$
$600$	−6.07921	−0.248183
$601$	38.3259	1.56335	0.781673	−	0.623689i	$-0.214367\pi$
$601$	38.3259	1.56335	0.781673	+	0.623689i	$0.214367\pi$
$602$	85.2438	3.47428
$603$	−39.6255	−1.61368
$604$	63.7959	2.59582
$605$	24.7068	1.00447
$606$	16.6331	0.675674
$607$	1.81492	0.0736655	0.0368328	−	0.999321i	$-0.488273\pi$
$607$	1.81492	0.0736655	0.0368328	+	0.999321i	$0.488273\pi$
$608$	−5.23303	−0.212228
$609$	−20.2135	−0.819094
$610$	0.691604	0.0280022
$611$	−8.04846	−0.325606
$612$	77.6152	3.13741
$613$	20.7243	0.837045	0.418522	−	0.908206i	$-0.362548\pi$
$613$	20.7243	0.837045	0.418522	+	0.908206i	$0.362548\pi$
$614$	−25.3359	−1.02248
$615$	34.4879	1.39069
$616$	−7.88612	−0.317741
$617$	−27.7305	−1.11639	−0.558195	−	0.829710i	$-0.688506\pi$
$617$	−27.7305	−1.11639	−0.558195	+	0.829710i	$0.688506\pi$
$618$	66.3760	2.67003
$619$	20.7828	0.835332	0.417666	−	0.908601i	$-0.362848\pi$
$619$	20.7828	0.835332	0.417666	+	0.908601i	$0.362848\pi$
$620$	80.3166	3.22559
$621$	−8.56707	−0.343785
$622$	15.7748	0.632512
$623$	−26.6426	−1.06741
$624$	−2.95939	−0.118470
$625$	−28.2512	−1.13005
$626$	47.3988	1.89444
$627$	−2.20301	−0.0879799
$628$	24.8609	0.992057
$629$	62.5590	2.49439
$630$	64.9369	2.58715
$631$	2.78791	0.110985	0.0554924	−	0.998459i	$-0.482327\pi$
$631$	2.78791	0.110985	0.0554924	+	0.998459i	$0.482327\pi$
$632$	30.6005	1.21722
$633$	54.0870	2.14977
$634$	2.30551	0.0915635
$635$	−28.2259	−1.12011
$636$	23.3745	0.926858
$637$	−7.81063	−0.309468
$638$	4.89655	0.193856
$639$	20.8729	0.825720
$640$	−45.6660	−1.80511
$641$	−38.9042	−1.53662	−0.768312	−	0.640076i	$-0.778903\pi$
$641$	−38.9042	−1.53662	−0.768312	+	0.640076i	$0.778903\pi$
$642$	−78.4175	−3.09489
$643$	7.95320	0.313644	0.156822	−	0.987627i	$-0.449875\pi$
$643$	7.95320	0.313644	0.156822	+	0.987627i	$0.449875\pi$
$644$	−41.5069	−1.63560
$645$	75.2296	2.96216
$646$	14.1747	0.557695
$647$	17.4271	0.685131	0.342565	−	0.939494i	$-0.388704\pi$
$647$	17.4271	0.685131	0.342565	+	0.939494i	$0.388704\pi$
$648$	17.9661	0.705773
$649$	−2.47719	−0.0972382
$650$	5.56608	0.218320
$651$	−81.0557	−3.17682
$652$	−5.63362	−0.220630
$653$	−30.7322	−1.20264	−0.601322	−	0.799007i	$-0.705359\pi$
$653$	−30.7322	−1.20264	−0.601322	+	0.799007i	$0.705359\pi$
$654$	71.1016	2.78029
$655$	23.7656	0.928598
$656$	−1.98650	−0.0775599
$657$	−29.9552	−1.16866
$658$	−18.1869	−0.709000
$659$	−1.32947	−0.0517887	−0.0258944	−	0.999665i	$-0.508243\pi$
$659$	−1.32947	−0.0517887	−0.0258944	+	0.999665i	$0.508243\pi$
$660$	−17.5418	−0.682812
$661$	−33.5193	−1.30375	−0.651874	−	0.758327i	$-0.726017\pi$
$661$	−33.5193	−1.30375	−0.651874	+	0.758327i	$0.726017\pi$
$662$	−7.26780	−0.282471
$663$	−50.4082	−1.95769
$664$	−2.91975	−0.113308
$665$	7.39701	0.286844
$666$	−89.3262	−3.46132
$667$	10.2250	0.395914
$668$	−11.6905	−0.452318
$669$	73.8686	2.85592
$670$	−57.6232	−2.22618
$671$	0.105459	0.00407118
$672$	42.0521	1.62220
$673$	−27.7690	−1.07042	−0.535208	−	0.844720i	$-0.679767\pi$
$673$	−27.7690	−1.07042	−0.535208	+	0.844720i	$0.679767\pi$
$674$	9.51566	0.366530
$675$	1.61922	0.0623239
$676$	−10.3629	−0.398573
$677$	41.8151	1.60708	0.803542	−	0.595249i	$-0.202946\pi$
$677$	41.8151	1.60708	0.803542	+	0.595249i	$0.202946\pi$
$678$	−50.8355	−1.95233
$679$	−0.403416	−0.0154817
$680$	44.7802	1.71724
$681$	−14.8715	−0.569879
$682$	19.6350	0.751863
$683$	23.4050	0.895568	0.447784	−	0.894142i	$-0.352213\pi$
$683$	23.4050	0.895568	0.447784	+	0.894142i	$0.352213\pi$
$684$	−12.6241	−0.482695
$685$	−34.3784	−1.31353
$686$	32.0552	1.22387
$687$	−39.9761	−1.52518
$688$	−4.33322	−0.165202
$689$	−8.49104	−0.323483
$690$	−58.7283	−2.23575
$691$	2.60738	0.0991892	0.0495946	−	0.998769i	$-0.484207\pi$
$691$	2.60738	0.0991892	0.0495946	+	0.998769i	$0.484207\pi$
$692$	29.9525	1.13862
$693$	9.90184	0.376140
$694$	23.1377	0.878295
$695$	10.7741	0.408686
$696$	19.9033	0.754434
$697$	−33.8367	−1.28166
$698$	51.2729	1.94071
$699$	−58.8506	−2.22593
$700$	7.84503	0.296514
$701$	−47.5963	−1.79769	−0.898844	−	0.438269i	$-0.855592\pi$
$701$	−47.5963	−1.79769	−0.898844	+	0.438269i	$0.855592\pi$
$702$	15.2685	0.576273
$703$	−10.1752	−0.383766
$704$	−10.7963	−0.406900
$705$	−16.0504	−0.604492
$706$	−0.297276	−0.0111881
$707$	−8.51604	−0.320278
$708$	−25.3792	−0.953809
$709$	10.1603	0.381576	0.190788	−	0.981631i	$-0.438896\pi$
$709$	10.1603	0.381576	0.190788	+	0.981631i	$0.438896\pi$
$710$	30.3533	1.13914
$711$	−38.4221	−1.44094
$712$	26.2337	0.983150
$713$	41.0019	1.53553
$714$	−113.906	−4.26283
$715$	6.37224	0.238308
$716$	−10.4122	−0.389120
$717$	−18.1385	−0.677396
$718$	8.15437	0.304318
$719$	20.7575	0.774125	0.387063	−	0.922053i	$-0.373490\pi$
$719$	20.7575	0.774125	0.387063	+	0.922053i	$0.373490\pi$
$720$	−3.30095	−0.123019
$721$	−33.9840	−1.26563
$722$	−2.30551	−0.0858022
$723$	−24.9346	−0.927328
$724$	60.1939	2.23709
$725$	−1.93258	−0.0717742
$726$	61.8816	2.29664
$727$	14.3863	0.533559	0.266779	−	0.963758i	$-0.414040\pi$
$727$	14.3863	0.533559	0.266779	+	0.963758i	$0.414040\pi$
$728$	29.3495	1.08777
$729$	−39.0551	−1.44648
$730$	−43.5606	−1.61225
$731$	−73.8090	−2.72992
$732$	1.08044	0.0399342
$733$	14.7498	0.544798	0.272399	−	0.962184i	$-0.412183\pi$
$733$	14.7498	0.544798	0.272399	+	0.962184i	$0.412183\pi$
$734$	−57.8150	−2.13399
$735$	−15.5761	−0.574533
$736$	−21.2720	−0.784097
$737$	−8.78663	−0.323660
$738$	48.3144	1.77848
$739$	−30.7085	−1.12963	−0.564815	−	0.825217i	$-0.691053\pi$
$739$	−30.7085	−1.12963	−0.564815	+	0.825217i	$0.691053\pi$
$740$	−81.0214	−2.97841
$741$	8.19888	0.301194
$742$	−19.1870	−0.704377
$743$	−0.0550381	−0.00201915	−0.00100958	−	0.999999i	$-0.500321\pi$
$743$	−0.0550381	−0.00201915	−0.00100958	+	0.999999i	$0.500321\pi$
$744$	79.8117	2.92604
$745$	15.2211	0.557658
$746$	−40.1492	−1.46996
$747$	3.66605	0.134134
$748$	17.2105	0.629279
$749$	40.1492	1.46702
$750$	−61.1375	−2.23243
$751$	−41.1707	−1.50234	−0.751170	−	0.660109i	$-0.770510\pi$
$751$	−41.1707	−1.50234	−0.751170	+	0.660109i	$0.770510\pi$
$752$	0.924501	0.0337131
$753$	9.36750	0.341371
$754$	−18.2233	−0.663655
$755$	−46.2152	−1.68194
$756$	21.5200	0.782675
$757$	−8.00867	−0.291080	−0.145540	−	0.989352i	$-0.546492\pi$
$757$	−8.00867	−0.291080	−0.145540	+	0.989352i	$0.546492\pi$
$758$	27.7781	1.00894
$759$	−8.95513	−0.325051
$760$	−7.28349	−0.264200
$761$	15.5504	0.563702	0.281851	−	0.959458i	$-0.409052\pi$
$761$	15.5504	0.563702	0.281851	+	0.959458i	$0.409052\pi$
$762$	−70.6956	−2.56103
$763$	−36.4035	−1.31790
$764$	−0.0925385	−0.00334792
$765$	−56.2261	−2.03286
$766$	−47.8424	−1.72861
$767$	9.21928	0.332889
$768$	−47.6514	−1.71947
$769$	51.1094	1.84305	0.921527	−	0.388315i	$-0.126943\pi$
$769$	51.1094	1.84305	0.921527	+	0.388315i	$0.126943\pi$
$770$	14.3992	0.518911
$771$	3.50244	0.126137
$772$	−50.0530	−1.80145
$773$	16.1831	0.582066	0.291033	−	0.956713i	$-0.406001\pi$
$773$	16.1831	0.582066	0.291033	+	0.956713i	$0.406001\pi$
$774$	105.390	3.78815
$775$	−7.74959	−0.278373
$776$	0.397225	0.0142595
$777$	81.7670	2.93337
$778$	12.7307	0.456416
$779$	5.50353	0.197185
$780$	65.2846	2.33756
$781$	4.62840	0.165617
$782$	57.6193	2.06046
$783$	−5.30134	−0.189454
$784$	0.897182	0.0320422
$785$	−18.0098	−0.642796
$786$	59.5241	2.12316
$787$	−2.87606	−0.102521	−0.0512603	−	0.998685i	$-0.516324\pi$
$787$	−2.87606	−0.102521	−0.0512603	+	0.998685i	$0.516324\pi$
$788$	−62.8463	−2.23881
$789$	−43.8840	−1.56231
$790$	−55.8732	−1.98788
$791$	26.0274	0.925429
$792$	−9.74988	−0.346447
$793$	−0.392482	−0.0139374
$794$	16.1196	0.572063
$795$	−16.9330	−0.600551
$796$	−34.5758	−1.22551
$797$	−4.77768	−0.169234	−0.0846171	−	0.996414i	$-0.526967\pi$
$797$	−4.77768	−0.169234	−0.0846171	+	0.996414i	$0.526967\pi$
$798$	18.5268	0.655843
$799$	15.7473	0.557099
$800$	4.02053	0.142147
$801$	−32.9392	−1.16385
$802$	−36.5623	−1.29106
$803$	−6.64230	−0.234402
$804$	−90.0204	−3.17477
$805$	30.0685	1.05977
$806$	−73.0750	−2.57396
$807$	−35.5400	−1.25107
$808$	8.38534	0.294995
$809$	−50.7959	−1.78589	−0.892945	−	0.450166i	$-0.851365\pi$
$809$	−50.7959	−1.78589	−0.892945	+	0.450166i	$0.851365\pi$
$810$	−32.8041	−1.15262
$811$	35.1819	1.23540	0.617702	−	0.786412i	$-0.288064\pi$
$811$	35.1819	1.23540	0.617702	+	0.786412i	$0.288064\pi$
$812$	−25.6846	−0.901354
$813$	−26.0601	−0.913967
$814$	−19.8073	−0.694246
$815$	4.08112	0.142955
$816$	5.79023	0.202698
$817$	12.0050	0.420003
$818$	64.9904	2.27234
$819$	−36.8514	−1.28769
$820$	43.8226	1.53035
$821$	3.76859	0.131525	0.0657623	−	0.997835i	$-0.479052\pi$
$821$	3.76859	0.131525	0.0657623	+	0.997835i	$0.479052\pi$
$822$	−86.1055	−3.00327
$823$	43.8325	1.52791	0.763953	−	0.645272i	$-0.223256\pi$
$823$	43.8325	1.52791	0.763953	+	0.645272i	$0.223256\pi$
$824$	33.4625	1.16572
$825$	1.69257	0.0589277
$826$	20.8326	0.724859
$827$	16.7129	0.581166	0.290583	−	0.956850i	$-0.406151\pi$
$827$	16.7129	0.581166	0.290583	+	0.956850i	$0.406151\pi$
$828$	−51.3163	−1.78337
$829$	4.78930	0.166339	0.0831697	−	0.996535i	$-0.473496\pi$
$829$	4.78930	0.166339	0.0831697	+	0.996535i	$0.473496\pi$
$830$	5.33114	0.185047
$831$	58.9420	2.04468
$832$	40.1802	1.39300
$833$	15.2820	0.529489
$834$	26.9853	0.934423
$835$	8.46883	0.293076
$836$	−2.79929	−0.0968154
$837$	−21.2582	−0.734791
$838$	27.4234	0.947327
$839$	−12.5972	−0.434905	−0.217452	−	0.976071i	$-0.569775\pi$
$839$	−12.5972	−0.434905	−0.217452	+	0.976071i	$0.569775\pi$
$840$	58.5294	2.01946
$841$	−22.6727	−0.781818
$842$	25.4392	0.876692
$843$	32.7729	1.12876
$844$	68.7264	2.36566
$845$	7.50710	0.258252
$846$	−22.4851	−0.773054
$847$	−31.6829	−1.08864
$848$	0.975338	0.0334933
$849$	31.6708	1.08694
$850$	−10.8904	−0.373537
$851$	−41.3617	−1.41786
$852$	47.4187	1.62454
$853$	−3.93449	−0.134714	−0.0673572	−	0.997729i	$-0.521457\pi$
$853$	−3.93449	−0.134714	−0.0673572	+	0.997729i	$0.521457\pi$
$854$	−0.886882	−0.0303485
$855$	9.14517	0.312758
$856$	−39.5330	−1.35121
$857$	−38.7534	−1.32379	−0.661896	−	0.749596i	$-0.730248\pi$
$857$	−38.7534	−1.32379	−0.661896	+	0.749596i	$0.730248\pi$
$858$	15.9601	0.544870
$859$	25.4345	0.867813	0.433906	−	0.900958i	$-0.357135\pi$
$859$	25.4345	0.867813	0.433906	+	0.900958i	$0.357135\pi$
$860$	95.5915	3.25964
$861$	−44.2258	−1.50721
$862$	−43.9445	−1.49676
$863$	41.1827	1.40187	0.700937	−	0.713223i	$-0.252765\pi$
$863$	41.1827	1.40187	0.700937	+	0.713223i	$0.252765\pi$
$864$	11.0289	0.375210
$865$	−21.6983	−0.737763
$866$	3.24902	0.110406
$867$	54.2708	1.84313
$868$	−102.995	−3.49586
$869$	−8.51977	−0.289013
$870$	−36.3413	−1.23209
$871$	32.7009	1.10803
$872$	35.8448	1.21386
$873$	−0.498757	−0.0168804
$874$	−9.37178	−0.317005
$875$	31.3020	1.05820
$876$	−68.0515	−2.29925
$877$	−21.4016	−0.722679	−0.361340	−	0.932434i	$-0.617681\pi$
$877$	−21.4016	−0.722679	−0.361340	+	0.932434i	$0.617681\pi$
$878$	−18.0607	−0.609520
$879$	56.2231	1.89636
$880$	−0.731959	−0.0246743
$881$	36.8108	1.24019	0.620093	−	0.784528i	$-0.287095\pi$
$881$	36.8108	1.24019	0.620093	+	0.784528i	$0.287095\pi$
$882$	−21.8207	−0.734740
$883$	−24.8980	−0.837884	−0.418942	−	0.908013i	$-0.637599\pi$
$883$	−24.8980	−0.837884	−0.418942	+	0.908013i	$0.637599\pi$
$884$	−64.0518	−2.15430
$885$	18.3853	0.618014
$886$	37.0461	1.24459
$887$	27.1751	0.912450	0.456225	−	0.889865i	$-0.349201\pi$
$887$	27.1751	0.912450	0.456225	+	0.889865i	$0.349201\pi$
$888$	−80.5121	−2.70181
$889$	36.1956	1.21396
$890$	−47.8999	−1.60561
$891$	−5.00210	−0.167577
$892$	93.8621	3.14274
$893$	−2.56130	−0.0857105
$894$	38.1234	1.27504
$895$	7.54279	0.252128
$896$	58.5601	1.95635
$897$	33.3280	1.11279
$898$	−78.6532	−2.62469
$899$	25.3721	0.846209
$900$	9.69907	0.323302
$901$	16.6132	0.553467
$902$	10.7133	0.356714
$903$	−96.4711	−3.21036
$904$	−25.6280	−0.852374
$905$	−43.6057	−1.44950
$906$	−115.752	−3.84561
$907$	−38.3004	−1.27174	−0.635872	−	0.771795i	$-0.719359\pi$
$907$	−38.3004	−1.27174	−0.635872	+	0.771795i	$0.719359\pi$
$908$	−18.8967	−0.627110
$909$	−10.5287	−0.349214
$910$	−53.5891	−1.77646
$911$	−26.4863	−0.877530	−0.438765	−	0.898602i	$-0.644584\pi$
$911$	−26.4863	−0.877530	−0.438765	+	0.898602i	$0.644584\pi$
$912$	−0.941780	−0.0311854
$913$	0.812915	0.0269036
$914$	−14.1067	−0.466608
$915$	−0.782694	−0.0258751
$916$	−50.7962	−1.67835
$917$	−30.4759	−1.00640
$918$	−29.8738	−0.985982
$919$	−15.4876	−0.510889	−0.255445	−	0.966824i	$-0.582222\pi$
$919$	−15.4876	−0.510889	−0.255445	+	0.966824i	$0.582222\pi$
$920$	−29.6070	−0.976114
$921$	28.6729	0.944805
$922$	−86.7689	−2.85758
$923$	−17.2254	−0.566979
$924$	22.4948	0.740024
$925$	7.81759	0.257041
$926$	−70.8281	−2.32756
$927$	−42.0156	−1.37997
$928$	−13.1632	−0.432103
$929$	−26.7547	−0.877792	−0.438896	−	0.898538i	$-0.644630\pi$
$929$	−26.7547	−0.877792	−0.438896	+	0.898538i	$0.644630\pi$
$930$	−145.727	−4.77859
$931$	−2.48561	−0.0814626
$932$	−74.7793	−2.44948
$933$	−17.8525	−0.584464
$934$	−90.0612	−2.94689
$935$	−12.4677	−0.407736
$936$	36.2858	1.18604
$937$	29.5719	0.966072	0.483036	−	0.875600i	$-0.339534\pi$
$937$	29.5719	0.966072	0.483036	+	0.875600i	$0.339534\pi$
$938$	73.8935	2.41271
$939$	−53.6417	−1.75053
$940$	−20.3946	−0.665200
$941$	−34.5602	−1.12663	−0.563315	−	0.826243i	$-0.690474\pi$
$941$	−34.5602	−1.12663	−0.563315	+	0.826243i	$0.690474\pi$
$942$	−45.1079	−1.46970
$943$	22.3716	0.728519
$944$	−1.05899	−0.0344672
$945$	−15.5896	−0.507128
$946$	23.3693	0.759801
$947$	37.7324	1.22614	0.613069	−	0.790029i	$-0.289935\pi$
$947$	37.7324	1.22614	0.613069	+	0.790029i	$0.289935\pi$
$948$	−87.2864	−2.83493
$949$	24.7205	0.802460
$950$	1.77132	0.0574691
$951$	−2.60917	−0.0846080
$952$	−57.4241	−1.86113
$953$	−52.6080	−1.70414	−0.852070	−	0.523427i	$-0.824653\pi$
$953$	−52.6080	−1.70414	−0.852070	+	0.523427i	$0.824653\pi$
$954$	−23.7215	−0.768013
$955$	0.0670369	0.00216926
$956$	−23.0480	−0.745425
$957$	−5.54147	−0.179130
$958$	−28.4056	−0.917743
$959$	44.0854	1.42359
$960$	80.1280	2.58612
$961$	70.7415	2.28198
$962$	73.7163	2.37671
$963$	49.6378	1.59956
$964$	−31.6835	−1.02046
$965$	36.2595	1.16723
$966$	75.3106	2.42308
$967$	−37.8037	−1.21569	−0.607843	−	0.794057i	$-0.707965\pi$
$967$	−37.8037	−1.21569	−0.607843	+	0.794057i	$0.707965\pi$
$968$	31.1967	1.00270
$969$	−16.0416	−0.515331
$970$	−0.725289	−0.0232876
$971$	−27.9189	−0.895961	−0.447981	−	0.894043i	$-0.647857\pi$
$971$	−27.9189	−0.895961	−0.447981	+	0.894043i	$0.647857\pi$
$972$	−72.2092	−2.31611
$973$	−13.8163	−0.442929
$974$	14.5297	0.465563
$975$	−6.29918	−0.201735
$976$	0.0450831	0.00144308
$977$	27.2956	0.873263	0.436631	−	0.899640i	$-0.356171\pi$
$977$	27.2956	0.873263	0.436631	+	0.899640i	$0.356171\pi$
$978$	10.2217	0.326854
$979$	−7.30398	−0.233436
$980$	−19.7920	−0.632232
$981$	−45.0069	−1.43696
$982$	−48.4978	−1.54763
$983$	−52.4363	−1.67246	−0.836229	−	0.548380i	$-0.815245\pi$
$983$	−52.4363	−1.67246	−0.836229	+	0.548380i	$0.815245\pi$
$984$	43.5471	1.38823
$985$	45.5272	1.45062
$986$	35.6551	1.13549
$987$	20.5823	0.655142
$988$	10.4180	0.331441
$989$	48.7998	1.55174
$990$	17.8022	0.565792
$991$	−52.4246	−1.66532	−0.832661	−	0.553784i	$-0.813183\pi$
$991$	−52.4246	−1.66532	−0.832661	+	0.553784i	$0.813183\pi$
$992$	−52.7840	−1.67589
$993$	8.22504	0.261014
$994$	−38.9238	−1.23459
$995$	25.0475	0.794058
$996$	8.32844	0.263897
$997$	−61.6117	−1.95126	−0.975631	−	0.219416i	$-0.929585\pi$
$997$	−61.6117	−1.95126	−0.975631	+	0.219416i	$0.929585\pi$
$998$	65.5512	2.07499
$999$	21.4447	0.678482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.12	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.12	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30551 q^{2} +2.60917 q^{3} +3.31537 q^{4} -2.40173 q^{5} -6.01546 q^{6} +3.07987 q^{7} -3.03260 q^{8} +3.80775 q^{9} +O(q^{10})\)	\(q-2.30551 q^{2} +2.60917 q^{3} +3.31537 q^{4} -2.40173 q^{5} -6.01546 q^{6} +3.07987 q^{7} -3.03260 q^{8} +3.80775 q^{9} +5.53721 q^{10} +0.844336 q^{11} +8.65036 q^{12} -3.14234 q^{13} -7.10067 q^{14} -6.26651 q^{15} +0.360950 q^{16} +6.14818 q^{17} -8.77880 q^{18} -1.00000 q^{19} -7.96262 q^{20} +8.03590 q^{21} -1.94662 q^{22} -4.06495 q^{23} -7.91257 q^{24} +0.768298 q^{25} +7.24469 q^{26} +2.10755 q^{27} +10.2109 q^{28} -2.51541 q^{29} +14.4475 q^{30} -10.0867 q^{31} +5.23303 q^{32} +2.20301 q^{33} -14.1747 q^{34} -7.39701 q^{35} +12.6241 q^{36} +10.1752 q^{37} +2.30551 q^{38} -8.19888 q^{39} +7.28349 q^{40} -5.50353 q^{41} -18.5268 q^{42} -12.0050 q^{43} +2.79929 q^{44} -9.14517 q^{45} +9.37178 q^{46} +2.56130 q^{47} +0.941780 q^{48} +2.48561 q^{49} -1.77132 q^{50} +16.0416 q^{51} -10.4180 q^{52} +2.70214 q^{53} -4.85897 q^{54} -2.02787 q^{55} -9.34003 q^{56} -2.60917 q^{57} +5.79929 q^{58} -2.93389 q^{59} -20.7758 q^{60} +0.124901 q^{61} +23.2550 q^{62} +11.7274 q^{63} -12.7867 q^{64} +7.54704 q^{65} -5.07907 q^{66} -10.4066 q^{67} +20.3835 q^{68} -10.6061 q^{69} +17.0539 q^{70} +5.48170 q^{71} -11.5474 q^{72} -7.86690 q^{73} -23.4591 q^{74} +2.00462 q^{75} -3.31537 q^{76} +2.60045 q^{77} +18.9026 q^{78} -10.0905 q^{79} -0.866905 q^{80} -5.92430 q^{81} +12.6884 q^{82} +0.962786 q^{83} +26.6420 q^{84} -14.7662 q^{85} +27.6777 q^{86} -6.56311 q^{87} -2.56054 q^{88} -8.65056 q^{89} +21.0843 q^{90} -9.67800 q^{91} -13.4768 q^{92} -26.3179 q^{93} -5.90509 q^{94} +2.40173 q^{95} +13.6539 q^{96} -0.130985 q^{97} -5.73060 q^{98} +3.21502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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