LMFDB - Embedded newform 6022.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.15898 q^{3} +1.00000 q^{4} -0.473594 q^{5} +3.15898 q^{6} -3.23851 q^{7} -1.00000 q^{8} +6.97917 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.15898 q^{3} +1.00000 q^{4} -0.473594 q^{5} +3.15898 q^{6} -3.23851 q^{7} -1.00000 q^{8} +6.97917 q^{9} +0.473594 q^{10} +0.955946 q^{11} -3.15898 q^{12} +2.86168 q^{13} +3.23851 q^{14} +1.49608 q^{15} +1.00000 q^{16} -4.61367 q^{17} -6.97917 q^{18} +4.60609 q^{19} -0.473594 q^{20} +10.2304 q^{21} -0.955946 q^{22} -4.10054 q^{23} +3.15898 q^{24} -4.77571 q^{25} -2.86168 q^{26} -12.5701 q^{27} -3.23851 q^{28} -1.73335 q^{29} -1.49608 q^{30} +10.0802 q^{31} -1.00000 q^{32} -3.01981 q^{33} +4.61367 q^{34} +1.53374 q^{35} +6.97917 q^{36} -10.4246 q^{37} -4.60609 q^{38} -9.03999 q^{39} +0.473594 q^{40} -5.45753 q^{41} -10.2304 q^{42} +8.50782 q^{43} +0.955946 q^{44} -3.30529 q^{45} +4.10054 q^{46} -2.31495 q^{47} -3.15898 q^{48} +3.48797 q^{49} +4.77571 q^{50} +14.5745 q^{51} +2.86168 q^{52} -5.31932 q^{53} +12.5701 q^{54} -0.452730 q^{55} +3.23851 q^{56} -14.5506 q^{57} +1.73335 q^{58} +8.18462 q^{59} +1.49608 q^{60} +1.42522 q^{61} -10.0802 q^{62} -22.6021 q^{63} +1.00000 q^{64} -1.35527 q^{65} +3.01981 q^{66} -8.35319 q^{67} -4.61367 q^{68} +12.9535 q^{69} -1.53374 q^{70} -6.11614 q^{71} -6.97917 q^{72} +13.5163 q^{73} +10.4246 q^{74} +15.0864 q^{75} +4.60609 q^{76} -3.09584 q^{77} +9.03999 q^{78} +14.4245 q^{79} -0.473594 q^{80} +18.7713 q^{81} +5.45753 q^{82} +8.70002 q^{83} +10.2304 q^{84} +2.18501 q^{85} -8.50782 q^{86} +5.47564 q^{87} -0.955946 q^{88} -12.2994 q^{89} +3.30529 q^{90} -9.26758 q^{91} -4.10054 q^{92} -31.8433 q^{93} +2.31495 q^{94} -2.18142 q^{95} +3.15898 q^{96} +18.1556 q^{97} -3.48797 q^{98} +6.67170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.15898	−1.82384	−0.911919	−	0.410369i	$-0.865400\pi$
$3$	−3.15898	−1.82384	−0.911919	+	0.410369i	$0.865400\pi$
$4$	1.00000	0.500000
$5$	−0.473594	−0.211798	−0.105899	−	0.994377i	$-0.533772\pi$
$5$	−0.473594	−0.211798	−0.105899	+	0.994377i	$0.533772\pi$
$6$	3.15898	1.28965
$7$	−3.23851	−1.22404	−0.612021	−	0.790841i	$-0.709643\pi$
$7$	−3.23851	−1.22404	−0.612021	+	0.790841i	$0.709643\pi$
$8$	−1.00000	−0.353553
$9$	6.97917	2.32639
$10$	0.473594	0.149764
$11$	0.955946	0.288228	0.144114	−	0.989561i	$-0.453967\pi$
$11$	0.955946	0.288228	0.144114	+	0.989561i	$0.453967\pi$
$12$	−3.15898	−0.911919
$13$	2.86168	0.793687	0.396843	−	0.917886i	$-0.370106\pi$
$13$	2.86168	0.793687	0.396843	+	0.917886i	$0.370106\pi$
$14$	3.23851	0.865529
$15$	1.49608	0.386285
$16$	1.00000	0.250000
$17$	−4.61367	−1.11898	−0.559489	−	0.828838i	$-0.689003\pi$
$17$	−4.61367	−1.11898	−0.559489	+	0.828838i	$0.689003\pi$
$18$	−6.97917	−1.64501
$19$	4.60609	1.05671	0.528355	−	0.849024i	$-0.322809\pi$
$19$	4.60609	1.05671	0.528355	+	0.849024i	$0.322809\pi$
$20$	−0.473594	−0.105899
$21$	10.2304	2.23246
$22$	−0.955946	−0.203808
$23$	−4.10054	−0.855021	−0.427511	−	0.904010i	$-0.640609\pi$
$23$	−4.10054	−0.855021	−0.427511	+	0.904010i	$0.640609\pi$
$24$	3.15898	0.644824
$25$	−4.77571	−0.955142
$26$	−2.86168	−0.561221
$27$	−12.5701	−2.41912
$28$	−3.23851	−0.612021
$29$	−1.73335	−0.321876	−0.160938	−	0.986965i	$-0.551452\pi$
$29$	−1.73335	−0.321876	−0.160938	+	0.986965i	$0.551452\pi$
$30$	−1.49608	−0.273145
$31$	10.0802	1.81046	0.905232	−	0.424917i	$-0.139697\pi$
$31$	10.0802	1.81046	0.905232	+	0.424917i	$0.139697\pi$
$32$	−1.00000	−0.176777
$33$	−3.01981	−0.525682
$34$	4.61367	0.791237
$35$	1.53374	0.259249
$36$	6.97917	1.16319
$37$	−10.4246	−1.71380	−0.856898	−	0.515486i	$-0.827611\pi$
$37$	−10.4246	−1.71380	−0.856898	+	0.515486i	$0.827611\pi$
$38$	−4.60609	−0.747206
$39$	−9.03999	−1.44756
$40$	0.473594	0.0748818
$41$	−5.45753	−0.852322	−0.426161	−	0.904647i	$-0.640134\pi$
$41$	−5.45753	−0.852322	−0.426161	+	0.904647i	$0.640134\pi$
$42$	−10.2304	−1.57859
$43$	8.50782	1.29743	0.648715	−	0.761031i	$-0.275307\pi$
$43$	8.50782	1.29743	0.648715	+	0.761031i	$0.275307\pi$
$44$	0.955946	0.144114
$45$	−3.30529	−0.492724
$46$	4.10054	0.604591
$47$	−2.31495	−0.337670	−0.168835	−	0.985644i	$-0.554000\pi$
$47$	−2.31495	−0.337670	−0.168835	+	0.985644i	$0.554000\pi$
$48$	−3.15898	−0.455960
$49$	3.48797	0.498281
$50$	4.77571	0.675387
$51$	14.5745	2.04084
$52$	2.86168	0.396843
$53$	−5.31932	−0.730665	−0.365332	−	0.930877i	$-0.619045\pi$
$53$	−5.31932	−0.730665	−0.365332	+	0.930877i	$0.619045\pi$
$54$	12.5701	1.71058
$55$	−0.452730	−0.0610461
$56$	3.23851	0.432764
$57$	−14.5506	−1.92727
$58$	1.73335	0.227601
$59$	8.18462	1.06555	0.532773	−	0.846258i	$-0.321150\pi$
$59$	8.18462	1.06555	0.532773	+	0.846258i	$0.321150\pi$
$60$	1.49608	0.193142
$61$	1.42522	0.182481	0.0912404	−	0.995829i	$-0.470917\pi$
$61$	1.42522	0.182481	0.0912404	+	0.995829i	$0.470917\pi$
$62$	−10.0802	−1.28019
$63$	−22.6021	−2.84760
$64$	1.00000	0.125000
$65$	−1.35527	−0.168101
$66$	3.01981	0.371713
$67$	−8.35319	−1.02050	−0.510252	−	0.860025i	$-0.670448\pi$
$67$	−8.35319	−1.02050	−0.510252	+	0.860025i	$0.670448\pi$
$68$	−4.61367	−0.559489
$69$	12.9535	1.55942
$70$	−1.53374	−0.183317
$71$	−6.11614	−0.725852	−0.362926	−	0.931818i	$-0.618222\pi$
$71$	−6.11614	−0.725852	−0.362926	+	0.931818i	$0.618222\pi$
$72$	−6.97917	−0.822503
$73$	13.5163	1.58196	0.790982	−	0.611840i	$-0.209570\pi$
$73$	13.5163	1.58196	0.790982	+	0.611840i	$0.209570\pi$
$74$	10.4246	1.21184
$75$	15.0864	1.74202
$76$	4.60609	0.528355
$77$	−3.09584	−0.352804
$78$	9.03999	1.02358
$79$	14.4245	1.62288	0.811442	−	0.584433i	$-0.198683\pi$
$79$	14.4245	1.62288	0.811442	+	0.584433i	$0.198683\pi$
$80$	−0.473594	−0.0529494
$81$	18.7713	2.08569
$82$	5.45753	0.602683
$83$	8.70002	0.954951	0.477475	−	0.878645i	$-0.341552\pi$
$83$	8.70002	0.954951	0.477475	+	0.878645i	$0.341552\pi$
$84$	10.2304	1.11623
$85$	2.18501	0.236997
$86$	−8.50782	−0.917422
$87$	5.47564	0.587050
$88$	−0.955946	−0.101904
$89$	−12.2994	−1.30373	−0.651865	−	0.758335i	$-0.726013\pi$
$89$	−12.2994	−1.30373	−0.651865	+	0.758335i	$0.726013\pi$
$90$	3.30529	0.348408
$91$	−9.26758	−0.971507
$92$	−4.10054	−0.427511
$93$	−31.8433	−3.30200
$94$	2.31495	0.238769
$95$	−2.18142	−0.223809
$96$	3.15898	0.322412
$97$	18.1556	1.84342	0.921709	−	0.387882i	$-0.126793\pi$
$97$	18.1556	1.84342	0.921709	+	0.387882i	$0.126793\pi$
$98$	−3.48797	−0.352338
$99$	6.67170	0.670531
$100$	−4.77571	−0.477571
$101$	−6.90246	−0.686821	−0.343410	−	0.939185i	$-0.611582\pi$
$101$	−6.90246	−0.686821	−0.343410	+	0.939185i	$0.611582\pi$
$102$	−14.5745	−1.44309
$103$	−11.4934	−1.13248	−0.566240	−	0.824240i	$-0.691603\pi$
$103$	−11.4934	−1.13248	−0.566240	+	0.824240i	$0.691603\pi$
$104$	−2.86168	−0.280611
$105$	−4.84506	−0.472829
$106$	5.31932	0.516658
$107$	6.73822	0.651408	0.325704	−	0.945472i	$-0.394399\pi$
$107$	6.73822	0.651408	0.325704	+	0.945472i	$0.394399\pi$
$108$	−12.5701	−1.20956
$109$	13.4619	1.28942	0.644710	−	0.764427i	$-0.276978\pi$
$109$	13.4619	1.28942	0.644710	+	0.764427i	$0.276978\pi$
$110$	0.452730	0.0431661
$111$	32.9312	3.12569
$112$	−3.23851	−0.306011
$113$	17.6138	1.65697	0.828485	−	0.560011i	$-0.189203\pi$
$113$	17.6138	1.65697	0.828485	+	0.560011i	$0.189203\pi$
$114$	14.5506	1.36278
$115$	1.94199	0.181092
$116$	−1.73335	−0.160938
$117$	19.9721	1.84642
$118$	−8.18462	−0.753455
$119$	14.9414	1.36968
$120$	−1.49608	−0.136572
$121$	−10.0862	−0.916924
$122$	−1.42522	−0.129033
$123$	17.2402	1.55450
$124$	10.0802	0.905232
$125$	4.62972	0.414095
$126$	22.6021	2.01356
$127$	−8.62562	−0.765400	−0.382700	−	0.923873i	$-0.625006\pi$
$127$	−8.62562	−0.765400	−0.382700	+	0.923873i	$0.625006\pi$
$128$	−1.00000	−0.0883883
$129$	−26.8760	−2.36630
$130$	1.35527	0.118865
$131$	9.95979	0.870190	0.435095	−	0.900384i	$-0.356715\pi$
$131$	9.95979	0.870190	0.435095	+	0.900384i	$0.356715\pi$
$132$	−3.01981	−0.262841
$133$	−14.9169	−1.29346
$134$	8.35319	0.721606
$135$	5.95313	0.512364
$136$	4.61367	0.395619
$137$	12.0767	1.03178	0.515891	−	0.856654i	$-0.327461\pi$
$137$	12.0767	1.03178	0.515891	+	0.856654i	$0.327461\pi$
$138$	−12.9535	−1.10268
$139$	8.52459	0.723047	0.361523	−	0.932363i	$-0.382257\pi$
$139$	8.52459	0.723047	0.361523	+	0.932363i	$0.382257\pi$
$140$	1.53374	0.129625
$141$	7.31288	0.615855
$142$	6.11614	0.513255
$143$	2.73561	0.228763
$144$	6.97917	0.581597
$145$	0.820906	0.0681726
$146$	−13.5163	−1.11862
$147$	−11.0184	−0.908784
$148$	−10.4246	−0.856898
$149$	−3.44941	−0.282587	−0.141293	−	0.989968i	$-0.545126\pi$
$149$	−3.44941	−0.282587	−0.141293	+	0.989968i	$0.545126\pi$
$150$	−15.0864	−1.23180
$151$	−14.0722	−1.14518	−0.572590	−	0.819842i	$-0.694061\pi$
$151$	−14.0722	−1.14518	−0.572590	+	0.819842i	$0.694061\pi$
$152$	−4.60609	−0.373603
$153$	−32.1995	−2.60318
$154$	3.09584	0.249470
$155$	−4.77394	−0.383452
$156$	−9.03999	−0.723778
$157$	−11.7253	−0.935779	−0.467890	−	0.883787i	$-0.654985\pi$
$157$	−11.7253	−0.935779	−0.467890	+	0.883787i	$0.654985\pi$
$158$	−14.4245	−1.14755
$159$	16.8036	1.33261
$160$	0.473594	0.0374409
$161$	13.2796	1.04658
$162$	−18.7713	−1.47481
$163$	18.9761	1.48632	0.743162	−	0.669112i	$-0.233325\pi$
$163$	18.9761	1.48632	0.743162	+	0.669112i	$0.233325\pi$
$164$	−5.45753	−0.426161
$165$	1.43017	0.111338
$166$	−8.70002	−0.675252
$167$	−23.0666	−1.78495	−0.892475	−	0.451097i	$-0.851033\pi$
$167$	−23.0666	−1.78495	−0.892475	+	0.451097i	$0.851033\pi$
$168$	−10.2304	−0.789293
$169$	−4.81080	−0.370061
$170$	−2.18501	−0.167582
$171$	32.1467	2.45832
$172$	8.50782	0.648715
$173$	17.0498	1.29627	0.648134	−	0.761526i	$-0.275550\pi$
$173$	17.0498	1.29627	0.648134	+	0.761526i	$0.275550\pi$
$174$	−5.47564	−0.415107
$175$	15.4662	1.16913
$176$	0.955946	0.0720571
$177$	−25.8551	−1.94339
$178$	12.2994	0.921876
$179$	20.8735	1.56016	0.780078	−	0.625682i	$-0.215179\pi$
$179$	20.8735	1.56016	0.780078	+	0.625682i	$0.215179\pi$
$180$	−3.30529	−0.246362
$181$	−9.35549	−0.695388	−0.347694	−	0.937608i	$-0.613035\pi$
$181$	−9.35549	−0.695388	−0.347694	+	0.937608i	$0.613035\pi$
$182$	9.26758	0.686959
$183$	−4.50225	−0.332816
$184$	4.10054	0.302296
$185$	4.93703	0.362978
$186$	31.8433	2.33486
$187$	−4.41041	−0.322521
$188$	−2.31495	−0.168835
$189$	40.7085	2.96111
$190$	2.18142	0.158257
$191$	1.45174	0.105044	0.0525221	−	0.998620i	$-0.483274\pi$
$191$	1.45174	0.105044	0.0525221	+	0.998620i	$0.483274\pi$
$192$	−3.15898	−0.227980
$193$	12.2704	0.883244	0.441622	−	0.897201i	$-0.354403\pi$
$193$	12.2704	0.883244	0.441622	+	0.897201i	$0.354403\pi$
$194$	−18.1556	−1.30349
$195$	4.28129	0.306589
$196$	3.48797	0.249140
$197$	−12.9061	−0.919521	−0.459761	−	0.888043i	$-0.652065\pi$
$197$	−12.9061	−0.919521	−0.459761	+	0.888043i	$0.652065\pi$
$198$	−6.67170	−0.474137
$199$	−4.44876	−0.315365	−0.157682	−	0.987490i	$-0.550402\pi$
$199$	−4.44876	−0.315365	−0.157682	+	0.987490i	$0.550402\pi$
$200$	4.77571	0.337694
$201$	26.3876	1.86124
$202$	6.90246	0.485655
$203$	5.61349	0.393990
$204$	14.5745	1.02042
$205$	2.58465	0.180520
$206$	11.4934	0.800785
$207$	−28.6183	−1.98911
$208$	2.86168	0.198422
$209$	4.40317	0.304574
$210$	4.84506	0.334341
$211$	13.2355	0.911167	0.455584	−	0.890193i	$-0.349431\pi$
$211$	13.2355	0.911167	0.455584	+	0.890193i	$0.349431\pi$
$212$	−5.31932	−0.365332
$213$	19.3208	1.32384
$214$	−6.73822	−0.460615
$215$	−4.02925	−0.274793
$216$	12.5701	0.855288
$217$	−32.6450	−2.21609
$218$	−13.4619	−0.911758
$219$	−42.6978	−2.88525
$220$	−0.452730	−0.0305231
$221$	−13.2028	−0.888119
$222$	−32.9312	−2.21019
$223$	11.0283	0.738512	0.369256	−	0.929328i	$-0.379612\pi$
$223$	11.0283	0.738512	0.369256	+	0.929328i	$0.379612\pi$
$224$	3.23851	0.216382
$225$	−33.3305	−2.22203
$226$	−17.6138	−1.17166
$227$	−10.8534	−0.720365	−0.360183	−	0.932882i	$-0.617286\pi$
$227$	−10.8534	−0.720365	−0.360183	+	0.932882i	$0.617286\pi$
$228$	−14.5506	−0.963634
$229$	−21.2904	−1.40691	−0.703456	−	0.710739i	$-0.748361\pi$
$229$	−21.2904	−1.40691	−0.703456	+	0.710739i	$0.748361\pi$
$230$	−1.94199	−0.128051
$231$	9.77971	0.643458
$232$	1.73335	0.113800
$233$	−5.14748	−0.337223	−0.168611	−	0.985683i	$-0.553928\pi$
$233$	−5.14748	−0.337223	−0.168611	+	0.985683i	$0.553928\pi$
$234$	−19.9721	−1.30562
$235$	1.09635	0.0715177
$236$	8.18462	0.532773
$237$	−45.5668	−2.95988
$238$	−14.9414	−0.968508
$239$	18.5965	1.20291	0.601453	−	0.798908i	$-0.294589\pi$
$239$	18.5965	1.20291	0.601453	+	0.798908i	$0.294589\pi$
$240$	1.49608	0.0965712
$241$	−2.62504	−0.169094	−0.0845468	−	0.996420i	$-0.526944\pi$
$241$	−2.62504	−0.169094	−0.0845468	+	0.996420i	$0.526944\pi$
$242$	10.0862	0.648363
$243$	−21.5877	−1.38485
$244$	1.42522	0.0912404
$245$	−1.65188	−0.105535
$246$	−17.2402	−1.09920
$247$	13.1811	0.838696
$248$	−10.0802	−0.640096
$249$	−27.4832	−1.74168
$250$	−4.62972	−0.292809
$251$	10.4421	0.659097	0.329549	−	0.944139i	$-0.393103\pi$
$251$	10.4421	0.659097	0.329549	+	0.944139i	$0.393103\pi$
$252$	−22.6021	−1.42380
$253$	−3.91989	−0.246441
$254$	8.62562	0.541220
$255$	−6.90239	−0.432245
$256$	1.00000	0.0625000
$257$	19.1079	1.19192	0.595960	−	0.803014i	$-0.296772\pi$
$257$	19.1079	1.19192	0.595960	+	0.803014i	$0.296772\pi$
$258$	26.8760	1.67323
$259$	33.7602	2.09776
$260$	−1.35527	−0.0840505
$261$	−12.0974	−0.748808
$262$	−9.95979	−0.615318
$263$	13.4536	0.829587	0.414793	−	0.909916i	$-0.363854\pi$
$263$	13.4536	0.829587	0.414793	+	0.909916i	$0.363854\pi$
$264$	3.01981	0.185857
$265$	2.51920	0.154753
$266$	14.9169	0.914613
$267$	38.8535	2.37779
$268$	−8.35319	−0.510252
$269$	−19.0273	−1.16012	−0.580059	−	0.814575i	$-0.696970\pi$
$269$	−19.0273	−1.16012	−0.580059	+	0.814575i	$0.696970\pi$
$270$	−5.95313	−0.362296
$271$	−9.79922	−0.595260	−0.297630	−	0.954681i	$-0.596196\pi$
$271$	−9.79922	−0.595260	−0.297630	+	0.954681i	$0.596196\pi$
$272$	−4.61367	−0.279745
$273$	29.2761	1.77187
$274$	−12.0767	−0.729580
$275$	−4.56532	−0.275299
$276$	12.9535	0.779710
$277$	6.72827	0.404263	0.202131	−	0.979358i	$-0.435213\pi$
$277$	6.72827	0.404263	0.202131	+	0.979358i	$0.435213\pi$
$278$	−8.52459	−0.511271
$279$	70.3517	4.21184
$280$	−1.53374	−0.0916585
$281$	−18.2994	−1.09165	−0.545825	−	0.837899i	$-0.683784\pi$
$281$	−18.2994	−1.09165	−0.545825	+	0.837899i	$0.683784\pi$
$282$	−7.31288	−0.435475
$283$	19.3099	1.14785	0.573926	−	0.818907i	$-0.305420\pi$
$283$	19.3099	1.14785	0.573926	+	0.818907i	$0.305420\pi$
$284$	−6.11614	−0.362926
$285$	6.89106	0.408191
$286$	−2.73561	−0.161760
$287$	17.6743	1.04328
$288$	−6.97917	−0.411251
$289$	4.28592	0.252113
$290$	−0.820906	−0.0482053
$291$	−57.3531	−3.36210
$292$	13.5163	0.790982
$293$	1.72035	0.100504	0.0502519	−	0.998737i	$-0.483998\pi$
$293$	1.72035	0.100504	0.0502519	+	0.998737i	$0.483998\pi$
$294$	11.0184	0.642607
$295$	−3.87619	−0.225680
$296$	10.4246	0.605918
$297$	−12.0163	−0.697259
$298$	3.44941	0.199819
$299$	−11.7344	−0.678619
$300$	15.0864	0.871012
$301$	−27.5527	−1.58811
$302$	14.0722	0.809765
$303$	21.8047	1.25265
$304$	4.60609	0.264177
$305$	−0.674976	−0.0386490
$306$	32.1995	1.84073
$307$	−9.45337	−0.539533	−0.269766	−	0.962926i	$-0.586946\pi$
$307$	−9.45337	−0.539533	−0.269766	+	0.962926i	$0.586946\pi$
$308$	−3.09584	−0.176402
$309$	36.3075	2.06546
$310$	4.77394	0.271142
$311$	−22.1677	−1.25702	−0.628508	−	0.777803i	$-0.716334\pi$
$311$	−22.1677	−1.25702	−0.628508	+	0.777803i	$0.716334\pi$
$312$	9.03999	0.511789
$313$	11.6238	0.657014	0.328507	−	0.944501i	$-0.393455\pi$
$313$	11.6238	0.657014	0.328507	+	0.944501i	$0.393455\pi$
$314$	11.7253	0.661696
$315$	10.7042	0.603115
$316$	14.4245	0.811442
$317$	13.7024	0.769601	0.384801	−	0.923000i	$-0.374270\pi$
$317$	13.7024	0.769601	0.384801	+	0.923000i	$0.374270\pi$
$318$	−16.8036	−0.942301
$319$	−1.65699	−0.0927738
$320$	−0.473594	−0.0264747
$321$	−21.2859	−1.18806
$322$	−13.2796	−0.740046
$323$	−21.2510	−1.18244
$324$	18.7713	1.04285
$325$	−13.6665	−0.758083
$326$	−18.9761	−1.05099
$327$	−42.5260	−2.35170
$328$	5.45753	0.301341
$329$	7.49699	0.413322
$330$	−1.43017	−0.0787281
$331$	4.25289	0.233760	0.116880	−	0.993146i	$-0.462711\pi$
$331$	4.25289	0.233760	0.116880	+	0.993146i	$0.462711\pi$
$332$	8.70002	0.477475
$333$	−72.7551	−3.98695
$334$	23.0666	1.26215
$335$	3.95602	0.216141
$336$	10.2304	0.558114
$337$	0.455184	0.0247954	0.0123977	−	0.999923i	$-0.496054\pi$
$337$	0.455184	0.0247954	0.0123977	+	0.999923i	$0.496054\pi$
$338$	4.81080	0.261673
$339$	−55.6418	−3.02205
$340$	2.18501	0.118499
$341$	9.63616	0.521827
$342$	−32.1467	−1.73829
$343$	11.3738	0.614126
$344$	−8.50782	−0.458711
$345$	−6.13471	−0.330282
$346$	−17.0498	−0.916600
$347$	19.9121	1.06894	0.534468	−	0.845188i	$-0.320512\pi$
$347$	19.9121	1.06894	0.534468	+	0.845188i	$0.320512\pi$
$348$	5.47564	0.293525
$349$	−13.7241	−0.734633	−0.367317	−	0.930096i	$-0.619723\pi$
$349$	−13.7241	−0.734633	−0.367317	+	0.930096i	$0.619723\pi$
$350$	−15.4662	−0.826703
$351$	−35.9716	−1.92002
$352$	−0.955946	−0.0509521
$353$	−34.9483	−1.86011	−0.930056	−	0.367418i	$-0.880242\pi$
$353$	−34.9483	−1.86011	−0.930056	+	0.367418i	$0.880242\pi$
$354$	25.8551	1.37418
$355$	2.89657	0.153734
$356$	−12.2994	−0.651865
$357$	−47.1997	−2.49807
$358$	−20.8735	−1.10320
$359$	4.27038	0.225382	0.112691	−	0.993630i	$-0.464053\pi$
$359$	4.27038	0.225382	0.112691	+	0.993630i	$0.464053\pi$
$360$	3.30529	0.174204
$361$	2.21606	0.116635
$362$	9.35549	0.491713
$363$	31.8620	1.67232
$364$	−9.26758	−0.485753
$365$	−6.40124	−0.335056
$366$	4.50225	0.235336
$367$	4.21026	0.219774	0.109887	−	0.993944i	$-0.464951\pi$
$367$	4.21026	0.219774	0.109887	+	0.993944i	$0.464951\pi$
$368$	−4.10054	−0.213755
$369$	−38.0890	−1.98283
$370$	−4.93703	−0.256664
$371$	17.2267	0.894365
$372$	−31.8433	−1.65100
$373$	−30.5979	−1.58430	−0.792148	−	0.610329i	$-0.791037\pi$
$373$	−30.5979	−1.58430	−0.792148	+	0.610329i	$0.791037\pi$
$374$	4.41041	0.228057
$375$	−14.6252	−0.755242
$376$	2.31495	0.119384
$377$	−4.96030	−0.255469
$378$	−40.7085	−2.09382
$379$	11.4511	0.588203	0.294101	−	0.955774i	$-0.404980\pi$
$379$	11.4511	0.588203	0.294101	+	0.955774i	$0.404980\pi$
$380$	−2.18142	−0.111904
$381$	27.2482	1.39597
$382$	−1.45174	−0.0742775
$383$	−20.1608	−1.03017	−0.515083	−	0.857140i	$-0.672239\pi$
$383$	−20.1608	−1.03017	−0.515083	+	0.857140i	$0.672239\pi$
$384$	3.15898	0.161206
$385$	1.46617	0.0747231
$386$	−12.2704	−0.624548
$387$	59.3775	3.01833
$388$	18.1556	0.921709
$389$	14.1311	0.716474	0.358237	−	0.933631i	$-0.383378\pi$
$389$	14.1311	0.716474	0.358237	+	0.933631i	$0.383378\pi$
$390$	−4.28129	−0.216791
$391$	18.9185	0.956750
$392$	−3.48797	−0.176169
$393$	−31.4628	−1.58709
$394$	12.9061	0.650200
$395$	−6.83136	−0.343723
$396$	6.67170	0.335266
$397$	−37.6053	−1.88736	−0.943678	−	0.330866i	$-0.892659\pi$
$397$	−37.6053	−1.88736	−0.943678	+	0.330866i	$0.892659\pi$
$398$	4.44876	0.222996
$399$	47.1222	2.35906
$400$	−4.77571	−0.238785
$401$	−25.5607	−1.27644	−0.638220	−	0.769854i	$-0.720329\pi$
$401$	−25.5607	−1.27644	−0.638220	+	0.769854i	$0.720329\pi$
$402$	−26.3876	−1.31609
$403$	28.8464	1.43694
$404$	−6.90246	−0.343410
$405$	−8.88995	−0.441745
$406$	−5.61349	−0.278593
$407$	−9.96536	−0.493965
$408$	−14.5745	−0.721545
$409$	34.8176	1.72162	0.860810	−	0.508927i	$-0.169958\pi$
$409$	34.8176	1.72162	0.860810	+	0.508927i	$0.169958\pi$
$410$	−2.58465	−0.127647
$411$	−38.1501	−1.88180
$412$	−11.4934	−0.566240
$413$	−26.5060	−1.30428
$414$	28.6183	1.40651
$415$	−4.12028	−0.202256
$416$	−2.86168	−0.140305
$417$	−26.9290	−1.31872
$418$	−4.40317	−0.215366
$419$	−20.4836	−1.00069	−0.500344	−	0.865826i	$-0.666793\pi$
$419$	−20.4836	−1.00069	−0.500344	+	0.865826i	$0.666793\pi$
$420$	−4.84506	−0.236415
$421$	11.6820	0.569347	0.284674	−	0.958625i	$-0.408115\pi$
$421$	11.6820	0.569347	0.284674	+	0.958625i	$0.408115\pi$
$422$	−13.2355	−0.644293
$423$	−16.1564	−0.785551
$424$	5.31932	0.258329
$425$	22.0335	1.06878
$426$	−19.3208	−0.936094
$427$	−4.61560	−0.223364
$428$	6.73822	0.325704
$429$	−8.64174	−0.417227
$430$	4.02925	0.194308
$431$	−16.5039	−0.794964	−0.397482	−	0.917610i	$-0.630116\pi$
$431$	−16.5039	−0.794964	−0.397482	+	0.917610i	$0.630116\pi$
$432$	−12.5701	−0.604780
$433$	3.24676	0.156029	0.0780147	−	0.996952i	$-0.475142\pi$
$433$	3.24676	0.156029	0.0780147	+	0.996952i	$0.475142\pi$
$434$	32.6450	1.56701
$435$	−2.59323	−0.124336
$436$	13.4619	0.644710
$437$	−18.8874	−0.903509
$438$	42.6978	2.04018
$439$	−22.9646	−1.09604	−0.548021	−	0.836464i	$-0.684619\pi$
$439$	−22.9646	−1.09604	−0.548021	+	0.836464i	$0.684619\pi$
$440$	0.452730	0.0215831
$441$	24.3431	1.15919
$442$	13.2028	0.627995
$443$	−32.0189	−1.52126	−0.760632	−	0.649183i	$-0.775111\pi$
$443$	−32.0189	−1.52126	−0.760632	+	0.649183i	$0.775111\pi$
$444$	32.9312	1.56284
$445$	5.82491	0.276127
$446$	−11.0283	−0.522207
$447$	10.8966	0.515393
$448$	−3.23851	−0.153005
$449$	−29.2922	−1.38238	−0.691192	−	0.722672i	$-0.742914\pi$
$449$	−29.2922	−1.38238	−0.691192	+	0.722672i	$0.742914\pi$
$450$	33.3305	1.57121
$451$	−5.21710	−0.245664
$452$	17.6138	0.828485
$453$	44.4539	2.08863
$454$	10.8534	0.509375
$455$	4.38907	0.205763
$456$	14.5506	0.681392
$457$	−15.2789	−0.714718	−0.357359	−	0.933967i	$-0.616323\pi$
$457$	−15.2789	−0.714718	−0.357359	+	0.933967i	$0.616323\pi$
$458$	21.2904	0.994837
$459$	57.9943	2.70694
$460$	1.94199	0.0905458
$461$	7.67718	0.357562	0.178781	−	0.983889i	$-0.442785\pi$
$461$	7.67718	0.357562	0.178781	+	0.983889i	$0.442785\pi$
$462$	−9.77971	−0.454993
$463$	25.3981	1.18035	0.590174	−	0.807276i	$-0.299059\pi$
$463$	25.3981	1.18035	0.590174	+	0.807276i	$0.299059\pi$
$464$	−1.73335	−0.0804690
$465$	15.0808	0.699355
$466$	5.14748	0.238453
$467$	−38.5042	−1.78176	−0.890880	−	0.454239i	$-0.849911\pi$
$467$	−38.5042	−1.78176	−0.890880	+	0.454239i	$0.849911\pi$
$468$	19.9721	0.923212
$469$	27.0519	1.24914
$470$	−1.09635	−0.0505706
$471$	37.0399	1.70671
$472$	−8.18462	−0.376728
$473$	8.13301	0.373956
$474$	45.5668	2.09295
$475$	−21.9973	−1.00931
$476$	14.9414	0.684839
$477$	−37.1244	−1.69981
$478$	−18.5965	−0.850583
$479$	18.3388	0.837923	0.418962	−	0.908004i	$-0.362394\pi$
$479$	18.3388	0.837923	0.418962	+	0.908004i	$0.362394\pi$
$480$	−1.49608	−0.0682862
$481$	−29.8319	−1.36022
$482$	2.62504	0.119567
$483$	−41.9502	−1.90880
$484$	−10.0862	−0.458462
$485$	−8.59837	−0.390432
$486$	21.5877	0.979239
$487$	40.0658	1.81555	0.907777	−	0.419453i	$-0.137778\pi$
$487$	40.0658	1.81555	0.907777	+	0.419453i	$0.137778\pi$
$488$	−1.42522	−0.0645167
$489$	−59.9452	−2.71081
$490$	1.65188	0.0746243
$491$	−40.3449	−1.82074	−0.910370	−	0.413795i	$-0.864203\pi$
$491$	−40.3449	−1.82074	−0.910370	+	0.413795i	$0.864203\pi$
$492$	17.2402	0.777249
$493$	7.99712	0.360172
$494$	−13.1811	−0.593048
$495$	−3.15968	−0.142017
$496$	10.0802	0.452616
$497$	19.8072	0.888474
$498$	27.4832	1.23155
$499$	−32.8441	−1.47030	−0.735152	−	0.677902i	$-0.762889\pi$
$499$	−32.8441	−1.47030	−0.735152	+	0.677902i	$0.762889\pi$
$500$	4.62972	0.207047
$501$	72.8671	3.25546
$502$	−10.4421	−0.466052
$503$	20.3230	0.906157	0.453078	−	0.891471i	$-0.350326\pi$
$503$	20.3230	0.906157	0.453078	+	0.891471i	$0.350326\pi$
$504$	22.6021	1.00678
$505$	3.26896	0.145467
$506$	3.91989	0.174260
$507$	15.1972	0.674932
$508$	−8.62562	−0.382700
$509$	34.5114	1.52969	0.764846	−	0.644213i	$-0.222815\pi$
$509$	34.5114	1.52969	0.764846	+	0.644213i	$0.222815\pi$
$510$	6.90239	0.305643
$511$	−43.7727	−1.93639
$512$	−1.00000	−0.0441942
$513$	−57.8991	−2.55631
$514$	−19.1079	−0.842815
$515$	5.44322	0.239857
$516$	−26.8760	−1.18315
$517$	−2.21296	−0.0973260
$518$	−33.7602	−1.48334
$519$	−53.8599	−2.36419
$520$	1.35527	0.0594327
$521$	8.03846	0.352171	0.176086	−	0.984375i	$-0.443656\pi$
$521$	8.03846	0.352171	0.176086	+	0.984375i	$0.443656\pi$
$522$	12.0974	0.529487
$523$	−35.2804	−1.54270	−0.771352	−	0.636409i	$-0.780419\pi$
$523$	−35.2804	−1.54270	−0.771352	+	0.636409i	$0.780419\pi$
$524$	9.95979	0.435095
$525$	−48.8574	−2.13231
$526$	−13.4536	−0.586606
$527$	−46.5069	−2.02587
$528$	−3.01981	−0.131421
$529$	−6.18559	−0.268939
$530$	−2.51920	−0.109427
$531$	57.1218	2.47888
$532$	−14.9169	−0.646729
$533$	−15.6177	−0.676477
$534$	−38.8535	−1.68135
$535$	−3.19118	−0.137967
$536$	8.35319	0.360803
$537$	−65.9389	−2.84547
$538$	19.0273	0.820327
$539$	3.33431	0.143619
$540$	5.95313	0.256182
$541$	6.06965	0.260955	0.130477	−	0.991451i	$-0.458349\pi$
$541$	6.06965	0.260955	0.130477	+	0.991451i	$0.458349\pi$
$542$	9.79922	0.420912
$543$	29.5538	1.26828
$544$	4.61367	0.197809
$545$	−6.37550	−0.273096
$546$	−29.2761	−1.25290
$547$	−8.44751	−0.361189	−0.180595	−	0.983558i	$-0.557802\pi$
$547$	−8.44751	−0.361189	−0.180595	+	0.983558i	$0.557802\pi$
$548$	12.0767	0.515891
$549$	9.94685	0.424521
$550$	4.56532	0.194666
$551$	−7.98399	−0.340129
$552$	−12.9535	−0.551339
$553$	−46.7140	−1.98648
$554$	−6.72827	−0.285857
$555$	−15.5960	−0.662013
$556$	8.52459	0.361523
$557$	−14.4754	−0.613344	−0.306672	−	0.951815i	$-0.599215\pi$
$557$	−14.4754	−0.613344	−0.306672	+	0.951815i	$0.599215\pi$
$558$	−70.3517	−2.97822
$559$	24.3466	1.02975
$560$	1.53374	0.0648124
$561$	13.9324	0.588227
$562$	18.2994	0.771913
$563$	14.7234	0.620515	0.310258	−	0.950652i	$-0.399585\pi$
$563$	14.7234	0.620515	0.310258	+	0.950652i	$0.399585\pi$
$564$	7.31288	0.307928
$565$	−8.34181	−0.350943
$566$	−19.3099	−0.811654
$567$	−60.7909	−2.55298
$568$	6.11614	0.256627
$569$	−6.40066	−0.268330	−0.134165	−	0.990959i	$-0.542835\pi$
$569$	−6.40066	−0.268330	−0.134165	+	0.990959i	$0.542835\pi$
$570$	−6.89106	−0.288635
$571$	−10.6599	−0.446103	−0.223051	−	0.974807i	$-0.571602\pi$
$571$	−10.6599	−0.446103	−0.223051	+	0.974807i	$0.571602\pi$
$572$	2.73561	0.114382
$573$	−4.58602	−0.191584
$574$	−17.6743	−0.737710
$575$	19.5830	0.816666
$576$	6.97917	0.290799
$577$	34.3086	1.42829	0.714144	−	0.699999i	$-0.246816\pi$
$577$	34.3086	1.42829	0.714144	+	0.699999i	$0.246816\pi$
$578$	−4.28592	−0.178271
$579$	−38.7620	−1.61089
$580$	0.820906	0.0340863
$581$	−28.1751	−1.16890
$582$	57.3531	2.37736
$583$	−5.08498	−0.210598
$584$	−13.5163	−0.559309
$585$	−9.45868	−0.391068
$586$	−1.72035	−0.0710670
$587$	−10.4037	−0.429408	−0.214704	−	0.976679i	$-0.568879\pi$
$587$	−10.4037	−0.429408	−0.214704	+	0.976679i	$0.568879\pi$
$588$	−11.0184	−0.454392
$589$	46.4305	1.91313
$590$	3.87619	0.159580
$591$	40.7701	1.67706
$592$	−10.4246	−0.428449
$593$	22.2742	0.914692	0.457346	−	0.889289i	$-0.348800\pi$
$593$	22.2742	0.914692	0.457346	+	0.889289i	$0.348800\pi$
$594$	12.0163	0.493036
$595$	−7.07617	−0.290095
$596$	−3.44941	−0.141293
$597$	14.0536	0.575174
$598$	11.7344	0.479856
$599$	−43.4390	−1.77487	−0.887435	−	0.460933i	$-0.847515\pi$
$599$	−43.4390	−1.77487	−0.887435	+	0.460933i	$0.847515\pi$
$600$	−15.0864	−0.615899
$601$	−28.6110	−1.16707	−0.583533	−	0.812089i	$-0.698330\pi$
$601$	−28.6110	−1.16707	−0.583533	+	0.812089i	$0.698330\pi$
$602$	27.5527	1.12296
$603$	−58.2983	−2.37409
$604$	−14.0722	−0.572590
$605$	4.77675	0.194202
$606$	−21.8047	−0.885757
$607$	−23.8011	−0.966058	−0.483029	−	0.875604i	$-0.660463\pi$
$607$	−23.8011	−0.966058	−0.483029	+	0.875604i	$0.660463\pi$
$608$	−4.60609	−0.186802
$609$	−17.7329	−0.718574
$610$	0.674976	0.0273290
$611$	−6.62463	−0.268004
$612$	−32.1995	−1.30159
$613$	29.4432	1.18920	0.594599	−	0.804022i	$-0.297311\pi$
$613$	29.4432	1.18920	0.594599	+	0.804022i	$0.297311\pi$
$614$	9.45337	0.381507
$615$	−8.16487	−0.329239
$616$	3.09584	0.124735
$617$	−14.9606	−0.602289	−0.301145	−	0.953578i	$-0.597369\pi$
$617$	−14.9606	−0.602289	−0.301145	+	0.953578i	$0.597369\pi$
$618$	−36.3075	−1.46050
$619$	−30.6584	−1.23226	−0.616132	−	0.787643i	$-0.711301\pi$
$619$	−30.6584	−1.23226	−0.616132	+	0.787643i	$0.711301\pi$
$620$	−4.77394	−0.191726
$621$	51.5442	2.06840
$622$	22.1677	0.888845
$623$	39.8316	1.59582
$624$	−9.03999	−0.361889
$625$	21.6859	0.867437
$626$	−11.6238	−0.464579
$627$	−13.9095	−0.555493
$628$	−11.7253	−0.467890
$629$	48.0957	1.91770
$630$	−10.7042	−0.426467
$631$	−23.0193	−0.916383	−0.458191	−	0.888854i	$-0.651503\pi$
$631$	−23.0193	−0.916383	−0.458191	+	0.888854i	$0.651503\pi$
$632$	−14.4245	−0.573776
$633$	−41.8106	−1.66182
$634$	−13.7024	−0.544190
$635$	4.08504	0.162110
$636$	16.8036	0.666307
$637$	9.98144	0.395479
$638$	1.65699	0.0656010
$639$	−42.6855	−1.68861
$640$	0.473594	0.0187204
$641$	27.8904	1.10161	0.550803	−	0.834635i	$-0.314322\pi$
$641$	27.8904	1.10161	0.550803	+	0.834635i	$0.314322\pi$
$642$	21.2859	0.840088
$643$	−8.17193	−0.322269	−0.161135	−	0.986932i	$-0.551515\pi$
$643$	−8.17193	−0.322269	−0.161135	+	0.986932i	$0.551515\pi$
$644$	13.2796	0.523291
$645$	12.7283	0.501178
$646$	21.2510	0.836108
$647$	21.9341	0.862319	0.431159	−	0.902276i	$-0.358105\pi$
$647$	21.9341	0.862319	0.431159	+	0.902276i	$0.358105\pi$
$648$	−18.7713	−0.737404
$649$	7.82405	0.307121
$650$	13.6665	0.536046
$651$	103.125	4.04178
$652$	18.9761	0.743162
$653$	−5.46970	−0.214046	−0.107023	−	0.994257i	$-0.534132\pi$
$653$	−5.46970	−0.214046	−0.107023	+	0.994257i	$0.534132\pi$
$654$	42.5260	1.66290
$655$	−4.71690	−0.184304
$656$	−5.45753	−0.213081
$657$	94.3325	3.68026
$658$	−7.49699	−0.292263
$659$	−12.5895	−0.490419	−0.245209	−	0.969470i	$-0.578857\pi$
$659$	−12.5895	−0.490419	−0.245209	+	0.969470i	$0.578857\pi$
$660$	1.43017	0.0556691
$661$	−9.40362	−0.365758	−0.182879	−	0.983135i	$-0.558542\pi$
$661$	−9.40362	−0.365758	−0.182879	+	0.983135i	$0.558542\pi$
$662$	−4.25289	−0.165293
$663$	41.7075	1.61979
$664$	−8.70002	−0.337626
$665$	7.06455	0.273951
$666$	72.7551	2.81920
$667$	7.10769	0.275211
$668$	−23.0666	−0.892475
$669$	−34.8383	−1.34693
$670$	−3.95602	−0.152834
$671$	1.36243	0.0525962
$672$	−10.2304	−0.394646
$673$	−2.71933	−0.104822	−0.0524112	−	0.998626i	$-0.516691\pi$
$673$	−2.71933	−0.104822	−0.0524112	+	0.998626i	$0.516691\pi$
$674$	−0.455184	−0.0175330
$675$	60.0312	2.31060
$676$	−4.81080	−0.185031
$677$	−11.4664	−0.440691	−0.220346	−	0.975422i	$-0.570719\pi$
$677$	−11.4664	−0.440691	−0.220346	+	0.975422i	$0.570719\pi$
$678$	55.6418	2.13691
$679$	−58.7970	−2.25642
$680$	−2.18501	−0.0837911
$681$	34.2857	1.31383
$682$	−9.63616	−0.368988
$683$	0.222892	0.00852872	0.00426436	−	0.999991i	$-0.498643\pi$
$683$	0.222892	0.00852872	0.00426436	+	0.999991i	$0.498643\pi$
$684$	32.1467	1.22916
$685$	−5.71945	−0.218529
$686$	−11.3738	−0.434252
$687$	67.2561	2.56598
$688$	8.50782	0.324358
$689$	−15.2222	−0.579919
$690$	6.13471	0.233544
$691$	3.62899	0.138053	0.0690267	−	0.997615i	$-0.478011\pi$
$691$	3.62899	0.138053	0.0690267	+	0.997615i	$0.478011\pi$
$692$	17.0498	0.648134
$693$	−21.6064	−0.820759
$694$	−19.9121	−0.755853
$695$	−4.03720	−0.153140
$696$	−5.47564	−0.207553
$697$	25.1792	0.953731
$698$	13.7241	0.519464
$699$	16.2608	0.615040
$700$	15.4662	0.584567
$701$	−2.08329	−0.0786847	−0.0393424	−	0.999226i	$-0.512526\pi$
$701$	−2.08329	−0.0786847	−0.0393424	+	0.999226i	$0.512526\pi$
$702$	35.9716	1.35766
$703$	−48.0167	−1.81098
$704$	0.955946	0.0360286
$705$	−3.46333	−0.130437
$706$	34.9483	1.31530
$707$	22.3537	0.840698
$708$	−25.8551	−0.971693
$709$	−27.9804	−1.05083	−0.525413	−	0.850847i	$-0.676089\pi$
$709$	−27.9804	−1.05083	−0.525413	+	0.850847i	$0.676089\pi$
$710$	−2.89657	−0.108706
$711$	100.671	3.77546
$712$	12.2994	0.460938
$713$	−41.3344	−1.54799
$714$	47.1997	1.76640
$715$	−1.29557	−0.0484515
$716$	20.8735	0.780078
$717$	−58.7459	−2.19391
$718$	−4.27038	−0.159369
$719$	−26.6127	−0.992487	−0.496243	−	0.868183i	$-0.665288\pi$
$719$	−26.6127	−0.992487	−0.496243	+	0.868183i	$0.665288\pi$
$720$	−3.30529	−0.123181
$721$	37.2216	1.38620
$722$	−2.21606	−0.0824733
$723$	8.29245	0.308399
$724$	−9.35549	−0.347694
$725$	8.27800	0.307437
$726$	−31.8620	−1.18251
$727$	21.7851	0.807964	0.403982	−	0.914767i	$-0.367626\pi$
$727$	21.7851	0.807964	0.403982	+	0.914767i	$0.367626\pi$
$728$	9.26758	0.343479
$729$	11.8814	0.440053
$730$	6.40124	0.236921
$731$	−39.2522	−1.45180
$732$	−4.50225	−0.166408
$733$	−14.5883	−0.538830	−0.269415	−	0.963024i	$-0.586830\pi$
$733$	−14.5883	−0.538830	−0.269415	+	0.963024i	$0.586830\pi$
$734$	−4.21026	−0.155403
$735$	5.21826	0.192478
$736$	4.10054	0.151148
$737$	−7.98519	−0.294138
$738$	38.0890	1.40207
$739$	−0.938698	−0.0345306	−0.0172653	−	0.999851i	$-0.505496\pi$
$739$	−0.938698	−0.0345306	−0.0172653	+	0.999851i	$0.505496\pi$
$740$	4.93703	0.181489
$741$	−41.6390	−1.52965
$742$	−17.2267	−0.632412
$743$	−40.4292	−1.48320	−0.741602	−	0.670840i	$-0.765934\pi$
$743$	−40.4292	−1.48320	−0.741602	+	0.670840i	$0.765934\pi$
$744$	31.8433	1.16743
$745$	1.63362	0.0598513
$746$	30.5979	1.12027
$747$	60.7189	2.22159
$748$	−4.41041	−0.161261
$749$	−21.8218	−0.797351
$750$	14.6252	0.534037
$751$	30.9446	1.12919	0.564593	−	0.825370i	$-0.309033\pi$
$751$	30.9446	1.12919	0.564593	+	0.825370i	$0.309033\pi$
$752$	−2.31495	−0.0844174
$753$	−32.9863	−1.20209
$754$	4.96030	0.180644
$755$	6.66452	0.242547
$756$	40.7085	1.48055
$757$	27.6058	1.00335	0.501675	−	0.865056i	$-0.332717\pi$
$757$	27.6058	1.00335	0.501675	+	0.865056i	$0.332717\pi$
$758$	−11.4511	−0.415922
$759$	12.3829	0.449469
$760$	2.18142	0.0791283
$761$	15.6376	0.566864	0.283432	−	0.958992i	$-0.408527\pi$
$761$	15.6376	0.566864	0.283432	+	0.958992i	$0.408527\pi$
$762$	−27.2482	−0.987098
$763$	−43.5967	−1.57831
$764$	1.45174	0.0525221
$765$	15.2495	0.551347
$766$	20.1608	0.728438
$767$	23.4218	0.845711
$768$	−3.15898	−0.113990
$769$	−45.8660	−1.65397	−0.826985	−	0.562224i	$-0.809946\pi$
$769$	−45.8660	−1.65397	−0.826985	+	0.562224i	$0.809946\pi$
$770$	−1.46617	−0.0528372
$771$	−60.3616	−2.17387
$772$	12.2704	0.441622
$773$	35.4680	1.27570	0.637848	−	0.770162i	$-0.279825\pi$
$773$	35.4680	1.27570	0.637848	+	0.770162i	$0.279825\pi$
$774$	−59.3775	−2.13428
$775$	−48.1403	−1.72925
$776$	−18.1556	−0.651747
$777$	−106.648	−3.82598
$778$	−14.1311	−0.506623
$779$	−25.1379	−0.900657
$780$	4.28129	0.153295
$781$	−5.84669	−0.209211
$782$	−18.9185	−0.676525
$783$	21.7885	0.778656
$784$	3.48797	0.124570
$785$	5.55302	0.198196
$786$	31.4628	1.12224
$787$	−22.8089	−0.813051	−0.406526	−	0.913639i	$-0.633260\pi$
$787$	−22.8089	−0.813051	−0.406526	+	0.913639i	$0.633260\pi$
$788$	−12.9061	−0.459761
$789$	−42.4998	−1.51303
$790$	6.83136	0.243049
$791$	−57.0426	−2.02820
$792$	−6.67170	−0.237069
$793$	4.07852	0.144833
$794$	37.6053	1.33456
$795$	−7.95810	−0.282245
$796$	−4.44876	−0.157682
$797$	−26.8060	−0.949519	−0.474759	−	0.880116i	$-0.657465\pi$
$797$	−26.8060	−0.949519	−0.474759	+	0.880116i	$0.657465\pi$
$798$	−47.1222	−1.66811
$799$	10.6804	0.377845
$800$	4.77571	0.168847
$801$	−85.8393	−3.03298
$802$	25.5607	0.902580
$803$	12.9208	0.455967
$804$	26.3876	0.930618
$805$	−6.28916	−0.221664
$806$	−28.8464	−1.01607
$807$	60.1070	2.11587
$808$	6.90246	0.242828
$809$	−16.9365	−0.595456	−0.297728	−	0.954651i	$-0.596229\pi$
$809$	−16.9365	−0.595456	−0.297728	+	0.954651i	$0.596229\pi$
$810$	8.88995	0.312361
$811$	−31.2247	−1.09645	−0.548224	−	0.836331i	$-0.684696\pi$
$811$	−31.2247	−1.09645	−0.548224	+	0.836331i	$0.684696\pi$
$812$	5.61349	0.196995
$813$	30.9556	1.08566
$814$	9.96536	0.349286
$815$	−8.98697	−0.314800
$816$	14.5745	0.510209
$817$	39.1878	1.37101
$818$	−34.8176	−1.21737
$819$	−64.6800	−2.26010
$820$	2.58465	0.0902600
$821$	9.63748	0.336350	0.168175	−	0.985757i	$-0.446213\pi$
$821$	9.63748	0.336350	0.168175	+	0.985757i	$0.446213\pi$
$822$	38.1501	1.33064
$823$	47.3335	1.64994	0.824971	−	0.565175i	$-0.191191\pi$
$823$	47.3335	1.64994	0.824971	+	0.565175i	$0.191191\pi$
$824$	11.4934	0.400392
$825$	14.4218	0.502101
$826$	26.5060	0.922262
$827$	54.6465	1.90025	0.950123	−	0.311877i	$-0.100958\pi$
$827$	54.6465	1.90025	0.950123	+	0.311877i	$0.100958\pi$
$828$	−28.6183	−0.994556
$829$	−45.2883	−1.57293	−0.786463	−	0.617637i	$-0.788090\pi$
$829$	−45.2883	−1.57293	−0.786463	+	0.617637i	$0.788090\pi$
$830$	4.12028	0.143017
$831$	−21.2545	−0.737310
$832$	2.86168	0.0992109
$833$	−16.0923	−0.557566
$834$	26.9290	0.932476
$835$	10.9242	0.378048
$836$	4.40317	0.152287
$837$	−126.710	−4.37973
$838$	20.4836	0.707594
$839$	−27.6203	−0.953558	−0.476779	−	0.879023i	$-0.658196\pi$
$839$	−27.6203	−0.953558	−0.476779	+	0.879023i	$0.658196\pi$
$840$	4.84506	0.167170
$841$	−25.9955	−0.896396
$842$	−11.6820	−0.402589
$843$	57.8075	1.99099
$844$	13.2355	0.455584
$845$	2.27836	0.0783781
$846$	16.1564	0.555468
$847$	32.6642	1.12235
$848$	−5.31932	−0.182666
$849$	−60.9995	−2.09350
$850$	−22.0335	−0.755744
$851$	42.7465	1.46533
$852$	19.3208	0.661918
$853$	44.2405	1.51477	0.757383	−	0.652971i	$-0.226477\pi$
$853$	44.2405	1.51477	0.757383	+	0.652971i	$0.226477\pi$
$854$	4.61560	0.157942
$855$	−15.2245	−0.520666
$856$	−6.73822	−0.230308
$857$	−15.6940	−0.536096	−0.268048	−	0.963406i	$-0.586379\pi$
$857$	−15.6940	−0.536096	−0.268048	+	0.963406i	$0.586379\pi$
$858$	8.64174	0.295024
$859$	−1.94243	−0.0662748	−0.0331374	−	0.999451i	$-0.510550\pi$
$859$	−1.94243	−0.0662748	−0.0331374	+	0.999451i	$0.510550\pi$
$860$	−4.02925	−0.137396
$861$	−55.8327	−1.90277
$862$	16.5039	0.562125
$863$	−32.5877	−1.10930	−0.554650	−	0.832084i	$-0.687148\pi$
$863$	−32.5877	−1.10930	−0.554650	+	0.832084i	$0.687148\pi$
$864$	12.5701	0.427644
$865$	−8.07466	−0.274547
$866$	−3.24676	−0.110329
$867$	−13.5391	−0.459813
$868$	−32.6450	−1.10804
$869$	13.7890	0.467761
$870$	2.59323	0.0879187
$871$	−23.9041	−0.809961
$872$	−13.4619	−0.455879
$873$	126.711	4.28851
$874$	18.8874	0.638877
$875$	−14.9934	−0.506869
$876$	−42.6978	−1.44262
$877$	−13.0162	−0.439525	−0.219763	−	0.975553i	$-0.570528\pi$
$877$	−13.0162	−0.439525	−0.219763	+	0.975553i	$0.570528\pi$
$878$	22.9646	0.775019
$879$	−5.43455	−0.183303
$880$	−0.452730	−0.0152615
$881$	46.9784	1.58274	0.791371	−	0.611336i	$-0.209368\pi$
$881$	46.9784	1.58274	0.791371	+	0.611336i	$0.209368\pi$
$882$	−24.3431	−0.819675
$883$	−1.44007	−0.0484621	−0.0242311	−	0.999706i	$-0.507714\pi$
$883$	−1.44007	−0.0484621	−0.0242311	+	0.999706i	$0.507714\pi$
$884$	−13.2028	−0.444059
$885$	12.2448	0.411605
$886$	32.0189	1.07570
$887$	−38.1036	−1.27939	−0.639696	−	0.768628i	$-0.720940\pi$
$887$	−38.1036	−1.27939	−0.639696	+	0.768628i	$0.720940\pi$
$888$	−32.9312	−1.10510
$889$	27.9342	0.936883
$890$	−5.82491	−0.195251
$891$	17.9443	0.601157
$892$	11.0283	0.369256
$893$	−10.6629	−0.356819
$894$	−10.8966	−0.364438
$895$	−9.88555	−0.330437
$896$	3.23851	0.108191
$897$	37.0688	1.23769
$898$	29.2922	0.977492
$899$	−17.4726	−0.582745
$900$	−33.3305	−1.11102
$901$	24.5416	0.817598
$902$	5.21710	0.173710
$903$	87.0384	2.89646
$904$	−17.6138	−0.585828
$905$	4.43070	0.147282
$906$	−44.4539	−1.47688
$907$	−50.6752	−1.68264	−0.841321	−	0.540536i	$-0.818221\pi$
$907$	−50.6752	−1.68264	−0.841321	+	0.540536i	$0.818221\pi$
$908$	−10.8534	−0.360183
$909$	−48.1734	−1.59781
$910$	−4.38907	−0.145496
$911$	57.2335	1.89623	0.948115	−	0.317928i	$-0.102987\pi$
$911$	57.2335	1.89623	0.948115	+	0.317928i	$0.102987\pi$
$912$	−14.5506	−0.481817
$913$	8.31674	0.275244
$914$	15.2789	0.505382
$915$	2.13224	0.0704896
$916$	−21.2904	−0.703456
$917$	−32.2549	−1.06515
$918$	−57.9943	−1.91410
$919$	30.7057	1.01289	0.506443	−	0.862273i	$-0.330960\pi$
$919$	30.7057	1.01289	0.506443	+	0.862273i	$0.330960\pi$
$920$	−1.94199	−0.0640255
$921$	29.8630	0.984020
$922$	−7.67718	−0.252835
$923$	−17.5024	−0.576099
$924$	9.77971	0.321729
$925$	49.7849	1.63692
$926$	−25.3981	−0.834632
$927$	−80.2145	−2.63459
$928$	1.73335	0.0569002
$929$	−26.1751	−0.858778	−0.429389	−	0.903120i	$-0.641271\pi$
$929$	−26.1751	−0.858778	−0.429389	+	0.903120i	$0.641271\pi$
$930$	−15.0808	−0.494519
$931$	16.0659	0.526538
$932$	−5.14748	−0.168611
$933$	70.0274	2.29260
$934$	38.5042	1.25989
$935$	2.08875	0.0683093
$936$	−19.9721	−0.652809
$937$	51.8869	1.69507	0.847536	−	0.530738i	$-0.178085\pi$
$937$	51.8869	1.69507	0.847536	+	0.530738i	$0.178085\pi$
$938$	−27.0519	−0.883276
$939$	−36.7193	−1.19829
$940$	1.09635	0.0357588
$941$	−25.2756	−0.823961	−0.411981	−	0.911193i	$-0.635163\pi$
$941$	−25.2756	−0.823961	−0.411981	+	0.911193i	$0.635163\pi$
$942$	−37.0399	−1.20683
$943$	22.3788	0.728754
$944$	8.18462	0.266387
$945$	−19.2793	−0.627155
$946$	−8.13301	−0.264427
$947$	−20.1415	−0.654510	−0.327255	−	0.944936i	$-0.606124\pi$
$947$	−20.1415	−0.654510	−0.327255	+	0.944936i	$0.606124\pi$
$948$	−45.5668	−1.47994
$949$	38.6793	1.25558
$950$	21.9973	0.713688
$951$	−43.2855	−1.40363
$952$	−14.9414	−0.484254
$953$	6.94727	0.225044	0.112522	−	0.993649i	$-0.464107\pi$
$953$	6.94727	0.225044	0.112522	+	0.993649i	$0.464107\pi$
$954$	37.1244	1.20195
$955$	−0.687535	−0.0222481
$956$	18.5965	0.601453
$957$	5.23441	0.169204
$958$	−18.3388	−0.592501
$959$	−39.1106	−1.26295
$960$	1.49608	0.0482856
$961$	70.6112	2.27778
$962$	29.8319	0.961819
$963$	47.0271	1.51543
$964$	−2.62504	−0.0845468
$965$	−5.81120	−0.187069
$966$	41.9502	1.34972
$967$	56.0652	1.80294	0.901468	−	0.432847i	$-0.142491\pi$
$967$	56.0652	1.80294	0.901468	+	0.432847i	$0.142491\pi$
$968$	10.0862	0.324182
$969$	67.1314	2.15657
$970$	8.59837	0.276077
$971$	−2.79292	−0.0896292	−0.0448146	−	0.998995i	$-0.514270\pi$
$971$	−2.79292	−0.0896292	−0.0448146	+	0.998995i	$0.514270\pi$
$972$	−21.5877	−0.692426
$973$	−27.6070	−0.885040
$974$	−40.0658	−1.28379
$975$	43.1724	1.38262
$976$	1.42522	0.0456202
$977$	−41.0432	−1.31309	−0.656543	−	0.754288i	$-0.727982\pi$
$977$	−41.0432	−1.31309	−0.656543	+	0.754288i	$0.727982\pi$
$978$	59.9452	1.91684
$979$	−11.7575	−0.375772
$980$	−1.65188	−0.0527674
$981$	93.9531	2.99969
$982$	40.3449	1.28746
$983$	−49.2967	−1.57232	−0.786161	−	0.618022i	$-0.787934\pi$
$983$	−49.2967	−1.57232	−0.786161	+	0.618022i	$0.787934\pi$
$984$	−17.2402	−0.549598
$985$	6.11225	0.194752
$986$	−7.99712	−0.254680
$987$	−23.6828	−0.753833
$988$	13.1811	0.419348
$989$	−34.8866	−1.10933
$990$	3.15968	0.100421
$991$	37.9583	1.20578	0.602892	−	0.797823i	$-0.294015\pi$
$991$	37.9583	1.20578	0.602892	+	0.797823i	$0.294015\pi$
$992$	−10.0802	−0.320048
$993$	−13.4348	−0.426340
$994$	−19.8072	−0.628246
$995$	2.10691	0.0667935
$996$	−27.4832	−0.870838
$997$	−47.3353	−1.49912	−0.749562	−	0.661934i	$-0.769736\pi$
$997$	−47.3353	−1.49912	−0.749562	+	0.661934i	$0.769736\pi$
$998$	32.8441	1.03966
$999$	131.039	4.14588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.3	✓	64	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.15898 q^{3} +1.00000 q^{4} -0.473594 q^{5} +3.15898 q^{6} -3.23851 q^{7} -1.00000 q^{8} +6.97917 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.15898 q^{3} +1.00000 q^{4} -0.473594 q^{5} +3.15898 q^{6} -3.23851 q^{7} -1.00000 q^{8} +6.97917 q^{9} +0.473594 q^{10} +0.955946 q^{11} -3.15898 q^{12} +2.86168 q^{13} +3.23851 q^{14} +1.49608 q^{15} +1.00000 q^{16} -4.61367 q^{17} -6.97917 q^{18} +4.60609 q^{19} -0.473594 q^{20} +10.2304 q^{21} -0.955946 q^{22} -4.10054 q^{23} +3.15898 q^{24} -4.77571 q^{25} -2.86168 q^{26} -12.5701 q^{27} -3.23851 q^{28} -1.73335 q^{29} -1.49608 q^{30} +10.0802 q^{31} -1.00000 q^{32} -3.01981 q^{33} +4.61367 q^{34} +1.53374 q^{35} +6.97917 q^{36} -10.4246 q^{37} -4.60609 q^{38} -9.03999 q^{39} +0.473594 q^{40} -5.45753 q^{41} -10.2304 q^{42} +8.50782 q^{43} +0.955946 q^{44} -3.30529 q^{45} +4.10054 q^{46} -2.31495 q^{47} -3.15898 q^{48} +3.48797 q^{49} +4.77571 q^{50} +14.5745 q^{51} +2.86168 q^{52} -5.31932 q^{53} +12.5701 q^{54} -0.452730 q^{55} +3.23851 q^{56} -14.5506 q^{57} +1.73335 q^{58} +8.18462 q^{59} +1.49608 q^{60} +1.42522 q^{61} -10.0802 q^{62} -22.6021 q^{63} +1.00000 q^{64} -1.35527 q^{65} +3.01981 q^{66} -8.35319 q^{67} -4.61367 q^{68} +12.9535 q^{69} -1.53374 q^{70} -6.11614 q^{71} -6.97917 q^{72} +13.5163 q^{73} +10.4246 q^{74} +15.0864 q^{75} +4.60609 q^{76} -3.09584 q^{77} +9.03999 q^{78} +14.4245 q^{79} -0.473594 q^{80} +18.7713 q^{81} +5.45753 q^{82} +8.70002 q^{83} +10.2304 q^{84} +2.18501 q^{85} -8.50782 q^{86} +5.47564 q^{87} -0.955946 q^{88} -12.2994 q^{89} +3.30529 q^{90} -9.26758 q^{91} -4.10054 q^{92} -31.8433 q^{93} +2.31495 q^{94} -2.18142 q^{95} +3.15898 q^{96} +18.1556 q^{97} -3.48797 q^{98} +6.67170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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