LMFDB - Embedded newform 6010.2.a.j.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.57998 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57998 q^{6} -4.21564 q^{7} +1.00000 q^{8} -0.503648 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.57998 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57998 q^{6} -4.21564 q^{7} +1.00000 q^{8} -0.503648 q^{9} +1.00000 q^{10} -5.96043 q^{11} -1.57998 q^{12} -3.37703 q^{13} -4.21564 q^{14} -1.57998 q^{15} +1.00000 q^{16} +0.836683 q^{17} -0.503648 q^{18} +3.55084 q^{19} +1.00000 q^{20} +6.66065 q^{21} -5.96043 q^{22} +4.00853 q^{23} -1.57998 q^{24} +1.00000 q^{25} -3.37703 q^{26} +5.53571 q^{27} -4.21564 q^{28} -3.76988 q^{29} -1.57998 q^{30} -8.55947 q^{31} +1.00000 q^{32} +9.41739 q^{33} +0.836683 q^{34} -4.21564 q^{35} -0.503648 q^{36} -5.97868 q^{37} +3.55084 q^{38} +5.33565 q^{39} +1.00000 q^{40} +6.38873 q^{41} +6.66065 q^{42} -2.99103 q^{43} -5.96043 q^{44} -0.503648 q^{45} +4.00853 q^{46} -11.9168 q^{47} -1.57998 q^{48} +10.7716 q^{49} +1.00000 q^{50} -1.32195 q^{51} -3.37703 q^{52} -0.622701 q^{53} +5.53571 q^{54} -5.96043 q^{55} -4.21564 q^{56} -5.61027 q^{57} -3.76988 q^{58} -8.49721 q^{59} -1.57998 q^{60} +8.67027 q^{61} -8.55947 q^{62} +2.12320 q^{63} +1.00000 q^{64} -3.37703 q^{65} +9.41739 q^{66} -2.96103 q^{67} +0.836683 q^{68} -6.33341 q^{69} -4.21564 q^{70} -1.88681 q^{71} -0.503648 q^{72} -2.28826 q^{73} -5.97868 q^{74} -1.57998 q^{75} +3.55084 q^{76} +25.1270 q^{77} +5.33565 q^{78} +14.9620 q^{79} +1.00000 q^{80} -7.23540 q^{81} +6.38873 q^{82} -1.87345 q^{83} +6.66065 q^{84} +0.836683 q^{85} -2.99103 q^{86} +5.95636 q^{87} -5.96043 q^{88} +15.9551 q^{89} -0.503648 q^{90} +14.2363 q^{91} +4.00853 q^{92} +13.5238 q^{93} -11.9168 q^{94} +3.55084 q^{95} -1.57998 q^{96} -8.94182 q^{97} +10.7716 q^{98} +3.00196 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.57998	−0.912205	−0.456102	−	0.889927i	$-0.650755\pi$
$3$	−1.57998	−0.912205	−0.456102	+	0.889927i	$0.650755\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.57998	−0.645026
$7$	−4.21564	−1.59336	−0.796681	−	0.604399i	$-0.793413\pi$
$7$	−4.21564	−1.59336	−0.796681	+	0.604399i	$0.793413\pi$
$8$	1.00000	0.353553
$9$	−0.503648	−0.167883
$10$	1.00000	0.316228
$11$	−5.96043	−1.79714	−0.898569	−	0.438833i	$-0.855392\pi$
$11$	−5.96043	−1.79714	−0.898569	+	0.438833i	$0.855392\pi$
$12$	−1.57998	−0.456102
$13$	−3.37703	−0.936619	−0.468309	−	0.883565i	$-0.655137\pi$
$13$	−3.37703	−0.936619	−0.468309	+	0.883565i	$0.655137\pi$
$14$	−4.21564	−1.12668
$15$	−1.57998	−0.407950
$16$	1.00000	0.250000
$17$	0.836683	0.202925	0.101463	−	0.994839i	$-0.467648\pi$
$17$	0.836683	0.202925	0.101463	+	0.994839i	$0.467648\pi$
$18$	−0.503648	−0.118711
$19$	3.55084	0.814619	0.407309	−	0.913290i	$-0.366467\pi$
$19$	3.55084	0.814619	0.407309	+	0.913290i	$0.366467\pi$
$20$	1.00000	0.223607
$21$	6.66065	1.45347
$22$	−5.96043	−1.27077
$23$	4.00853	0.835835	0.417918	−	0.908485i	$-0.362760\pi$
$23$	4.00853	0.835835	0.417918	+	0.908485i	$0.362760\pi$
$24$	−1.57998	−0.322513
$25$	1.00000	0.200000
$26$	−3.37703	−0.662289
$27$	5.53571	1.06535
$28$	−4.21564	−0.796681
$29$	−3.76988	−0.700050	−0.350025	−	0.936740i	$-0.613827\pi$
$29$	−3.76988	−0.700050	−0.350025	+	0.936740i	$0.613827\pi$
$30$	−1.57998	−0.288464
$31$	−8.55947	−1.53733	−0.768663	−	0.639654i	$-0.779078\pi$
$31$	−8.55947	−1.53733	−0.768663	+	0.639654i	$0.779078\pi$
$32$	1.00000	0.176777
$33$	9.41739	1.63936
$34$	0.836683	0.143490
$35$	−4.21564	−0.712574
$36$	−0.503648	−0.0839413
$37$	−5.97868	−0.982889	−0.491445	−	0.870909i	$-0.663531\pi$
$37$	−5.97868	−0.982889	−0.491445	+	0.870909i	$0.663531\pi$
$38$	3.55084	0.576022
$39$	5.33565	0.854388
$40$	1.00000	0.158114
$41$	6.38873	0.997752	0.498876	−	0.866673i	$-0.333746\pi$
$41$	6.38873	0.997752	0.498876	+	0.866673i	$0.333746\pi$
$42$	6.66065	1.02776
$43$	−2.99103	−0.456128	−0.228064	−	0.973646i	$-0.573240\pi$
$43$	−2.99103	−0.456128	−0.228064	+	0.973646i	$0.573240\pi$
$44$	−5.96043	−0.898569
$45$	−0.503648	−0.0750794
$46$	4.00853	0.591025
$47$	−11.9168	−1.73825	−0.869124	−	0.494593i	$-0.835317\pi$
$47$	−11.9168	−1.73825	−0.869124	+	0.494593i	$0.835317\pi$
$48$	−1.57998	−0.228051
$49$	10.7716	1.53881
$50$	1.00000	0.141421
$51$	−1.32195	−0.185110
$52$	−3.37703	−0.468309
$53$	−0.622701	−0.0855345	−0.0427672	−	0.999085i	$-0.513617\pi$
$53$	−0.622701	−0.0855345	−0.0427672	+	0.999085i	$0.513617\pi$
$54$	5.53571	0.753315
$55$	−5.96043	−0.803704
$56$	−4.21564	−0.563339
$57$	−5.61027	−0.743099
$58$	−3.76988	−0.495010
$59$	−8.49721	−1.10624	−0.553121	−	0.833101i	$-0.686563\pi$
$59$	−8.49721	−1.10624	−0.553121	+	0.833101i	$0.686563\pi$
$60$	−1.57998	−0.203975
$61$	8.67027	1.11011	0.555057	−	0.831812i	$-0.312696\pi$
$61$	8.67027	1.11011	0.555057	+	0.831812i	$0.312696\pi$
$62$	−8.55947	−1.08705
$63$	2.12320	0.267498
$64$	1.00000	0.125000
$65$	−3.37703	−0.418869
$66$	9.41739	1.15920
$67$	−2.96103	−0.361748	−0.180874	−	0.983506i	$-0.557893\pi$
$67$	−2.96103	−0.361748	−0.180874	+	0.983506i	$0.557893\pi$
$68$	0.836683	0.101463
$69$	−6.33341	−0.762453
$70$	−4.21564	−0.503866
$71$	−1.88681	−0.223923	−0.111961	−	0.993713i	$-0.535713\pi$
$71$	−1.88681	−0.223923	−0.111961	+	0.993713i	$0.535713\pi$
$72$	−0.503648	−0.0593555
$73$	−2.28826	−0.267821	−0.133910	−	0.990993i	$-0.542753\pi$
$73$	−2.28826	−0.267821	−0.133910	+	0.990993i	$0.542753\pi$
$74$	−5.97868	−0.695008
$75$	−1.57998	−0.182441
$76$	3.55084	0.407309
$77$	25.1270	2.86349
$78$	5.33565	0.604143
$79$	14.9620	1.68336	0.841678	−	0.539979i	$-0.181568\pi$
$79$	14.9620	1.68336	0.841678	+	0.539979i	$0.181568\pi$
$80$	1.00000	0.111803
$81$	−7.23540	−0.803933
$82$	6.38873	0.705517
$83$	−1.87345	−0.205638	−0.102819	−	0.994700i	$-0.532786\pi$
$83$	−1.87345	−0.205638	−0.102819	+	0.994700i	$0.532786\pi$
$84$	6.66065	0.726737
$85$	0.836683	0.0907510
$86$	−2.99103	−0.322531
$87$	5.95636	0.638589
$88$	−5.96043	−0.635384
$89$	15.9551	1.69124	0.845620	−	0.533785i	$-0.179231\pi$
$89$	15.9551	1.69124	0.845620	+	0.533785i	$0.179231\pi$
$90$	−0.503648	−0.0530891
$91$	14.2363	1.49237
$92$	4.00853	0.417918
$93$	13.5238	1.40236
$94$	−11.9168	−1.22913
$95$	3.55084	0.364308
$96$	−1.57998	−0.161257
$97$	−8.94182	−0.907904	−0.453952	−	0.891026i	$-0.649986\pi$
$97$	−8.94182	−0.907904	−0.453952	+	0.891026i	$0.649986\pi$
$98$	10.7716	1.08810
$99$	3.00196	0.301708
$100$	1.00000	0.100000
$101$	−2.87441	−0.286014	−0.143007	−	0.989722i	$-0.545677\pi$
$101$	−2.87441	−0.286014	−0.143007	+	0.989722i	$0.545677\pi$
$102$	−1.32195	−0.130892
$103$	16.2237	1.59857	0.799286	−	0.600951i	$-0.205211\pi$
$103$	16.2237	1.59857	0.799286	+	0.600951i	$0.205211\pi$
$104$	−3.37703	−0.331145
$105$	6.66065	0.650013
$106$	−0.622701	−0.0604820
$107$	19.9896	1.93246	0.966232	−	0.257674i	$-0.0829559\pi$
$107$	19.9896	1.93246	0.966232	+	0.257674i	$0.0829559\pi$
$108$	5.53571	0.532674
$109$	0.182924	0.0175210	0.00876049	−	0.999962i	$-0.497211\pi$
$109$	0.182924	0.0175210	0.00876049	+	0.999962i	$0.497211\pi$
$110$	−5.96043	−0.568305
$111$	9.44623	0.896596
$112$	−4.21564	−0.398341
$113$	12.9872	1.22173	0.610864	−	0.791735i	$-0.290822\pi$
$113$	12.9872	1.22173	0.610864	+	0.791735i	$0.290822\pi$
$114$	−5.61027	−0.525450
$115$	4.00853	0.373797
$116$	−3.76988	−0.350025
$117$	1.70083	0.157242
$118$	−8.49721	−0.782231
$119$	−3.52716	−0.323334
$120$	−1.57998	−0.144232
$121$	24.5267	2.22970
$122$	8.67027	0.784969
$123$	−10.0941	−0.910154
$124$	−8.55947	−0.768663
$125$	1.00000	0.0894427
$126$	2.12320	0.189150
$127$	−8.15115	−0.723298	−0.361649	−	0.932314i	$-0.617786\pi$
$127$	−8.15115	−0.723298	−0.361649	+	0.932314i	$0.617786\pi$
$128$	1.00000	0.0883883
$129$	4.72579	0.416082
$130$	−3.37703	−0.296185
$131$	−10.2925	−0.899261	−0.449631	−	0.893215i	$-0.648444\pi$
$131$	−10.2925	−0.899261	−0.449631	+	0.893215i	$0.648444\pi$
$132$	9.41739	0.819679
$133$	−14.9691	−1.29798
$134$	−2.96103	−0.255794
$135$	5.53571	0.476438
$136$	0.836683	0.0717450
$137$	8.47372	0.723958	0.361979	−	0.932186i	$-0.382101\pi$
$137$	8.47372	0.723958	0.361979	+	0.932186i	$0.382101\pi$
$138$	−6.33341	−0.539136
$139$	−2.17118	−0.184157	−0.0920783	−	0.995752i	$-0.529351\pi$
$139$	−2.17118	−0.184157	−0.0920783	+	0.995752i	$0.529351\pi$
$140$	−4.21564	−0.356287
$141$	18.8284	1.58564
$142$	−1.88681	−0.158337
$143$	20.1285	1.68323
$144$	−0.503648	−0.0419706
$145$	−3.76988	−0.313072
$146$	−2.28826	−0.189378
$147$	−17.0190	−1.40371
$148$	−5.97868	−0.491445
$149$	17.1101	1.40171	0.700856	−	0.713302i	$-0.252801\pi$
$149$	17.1101	1.40171	0.700856	+	0.713302i	$0.252801\pi$
$150$	−1.57998	−0.129005
$151$	−7.71991	−0.628238	−0.314119	−	0.949384i	$-0.601709\pi$
$151$	−7.71991	−0.628238	−0.314119	+	0.949384i	$0.601709\pi$
$152$	3.55084	0.288011
$153$	−0.421393	−0.0340676
$154$	25.1270	2.02479
$155$	−8.55947	−0.687513
$156$	5.33565	0.427194
$157$	23.3305	1.86197	0.930987	−	0.365054i	$-0.118949\pi$
$157$	23.3305	1.86197	0.930987	+	0.365054i	$0.118949\pi$
$158$	14.9620	1.19031
$159$	0.983857	0.0780250
$160$	1.00000	0.0790569
$161$	−16.8985	−1.33179
$162$	−7.23540	−0.568466
$163$	−13.5149	−1.05857	−0.529284	−	0.848444i	$-0.677540\pi$
$163$	−13.5149	−1.05857	−0.529284	+	0.848444i	$0.677540\pi$
$164$	6.38873	0.498876
$165$	9.41739	0.733143
$166$	−1.87345	−0.145408
$167$	−6.43900	−0.498265	−0.249132	−	0.968469i	$-0.580145\pi$
$167$	−6.43900	−0.498265	−0.249132	+	0.968469i	$0.580145\pi$
$168$	6.66065	0.513880
$169$	−1.59569	−0.122746
$170$	0.836683	0.0641707
$171$	−1.78837	−0.136760
$172$	−2.99103	−0.228064
$173$	−7.67303	−0.583370	−0.291685	−	0.956514i	$-0.594216\pi$
$173$	−7.67303	−0.583370	−0.291685	+	0.956514i	$0.594216\pi$
$174$	5.95636	0.451551
$175$	−4.21564	−0.318673
$176$	−5.96043	−0.449284
$177$	13.4255	1.00912
$178$	15.9551	1.19589
$179$	−7.74757	−0.579080	−0.289540	−	0.957166i	$-0.593502\pi$
$179$	−7.74757	−0.579080	−0.289540	+	0.957166i	$0.593502\pi$
$180$	−0.503648	−0.0375397
$181$	−1.65695	−0.123160	−0.0615800	−	0.998102i	$-0.519614\pi$
$181$	−1.65695	−0.123160	−0.0615800	+	0.998102i	$0.519614\pi$
$182$	14.2363	1.05527
$183$	−13.6989	−1.01265
$184$	4.00853	0.295512
$185$	−5.97868	−0.439561
$186$	13.5238	0.991615
$187$	−4.98699	−0.364685
$188$	−11.9168	−0.869124
$189$	−23.3366	−1.69749
$190$	3.55084	0.257605
$191$	19.9942	1.44673	0.723363	−	0.690468i	$-0.242595\pi$
$191$	19.9942	1.44673	0.723363	+	0.690468i	$0.242595\pi$
$192$	−1.57998	−0.114026
$193$	19.1356	1.37741	0.688705	−	0.725042i	$-0.258180\pi$
$193$	19.1356	1.37741	0.688705	+	0.725042i	$0.258180\pi$
$194$	−8.94182	−0.641985
$195$	5.33565	0.382094
$196$	10.7716	0.769403
$197$	−4.61434	−0.328758	−0.164379	−	0.986397i	$-0.552562\pi$
$197$	−4.61434	−0.328758	−0.164379	+	0.986397i	$0.552562\pi$
$198$	3.00196	0.213340
$199$	14.1752	1.00485	0.502426	−	0.864620i	$-0.332441\pi$
$199$	14.1752	1.00485	0.502426	+	0.864620i	$0.332441\pi$
$200$	1.00000	0.0707107
$201$	4.67839	0.329988
$202$	−2.87441	−0.202243
$203$	15.8925	1.11543
$204$	−1.32195	−0.0925548
$205$	6.38873	0.446208
$206$	16.2237	1.13036
$207$	−2.01888	−0.140322
$208$	−3.37703	−0.234155
$209$	−21.1645	−1.46398
$210$	6.66065	0.459629
$211$	22.7905	1.56897	0.784483	−	0.620151i	$-0.212928\pi$
$211$	22.7905	1.56897	0.784483	+	0.620151i	$0.212928\pi$
$212$	−0.622701	−0.0427672
$213$	2.98113	0.204263
$214$	19.9896	1.36646
$215$	−2.99103	−0.203987
$216$	5.53571	0.376657
$217$	36.0836	2.44952
$218$	0.182924	0.0123892
$219$	3.61542	0.244307
$220$	−5.96043	−0.401852
$221$	−2.82550	−0.190064
$222$	9.44623	0.633989
$223$	6.59907	0.441907	0.220953	−	0.975284i	$-0.429083\pi$
$223$	6.59907	0.441907	0.220953	+	0.975284i	$0.429083\pi$
$224$	−4.21564	−0.281669
$225$	−0.503648	−0.0335765
$226$	12.9872	0.863893
$227$	−15.8217	−1.05012	−0.525061	−	0.851064i	$-0.675958\pi$
$227$	−15.8217	−1.05012	−0.525061	+	0.851064i	$0.675958\pi$
$228$	−5.61027	−0.371549
$229$	8.35959	0.552417	0.276209	−	0.961098i	$-0.410922\pi$
$229$	8.35959	0.552417	0.276209	+	0.961098i	$0.410922\pi$
$230$	4.00853	0.264314
$231$	−39.7004	−2.61209
$232$	−3.76988	−0.247505
$233$	−15.7420	−1.03129	−0.515646	−	0.856801i	$-0.672448\pi$
$233$	−15.7420	−1.03129	−0.515646	+	0.856801i	$0.672448\pi$
$234$	1.70083	0.111187
$235$	−11.9168	−0.777369
$236$	−8.49721	−0.553121
$237$	−23.6397	−1.53557
$238$	−3.52716	−0.228632
$239$	−4.61778	−0.298700	−0.149350	−	0.988784i	$-0.547718\pi$
$239$	−4.61778	−0.298700	−0.149350	+	0.988784i	$0.547718\pi$
$240$	−1.57998	−0.101988
$241$	−13.9796	−0.900503	−0.450251	−	0.892902i	$-0.648666\pi$
$241$	−13.9796	−0.900503	−0.450251	+	0.892902i	$0.648666\pi$
$242$	24.5267	1.57664
$243$	−5.17532	−0.331997
$244$	8.67027	0.555057
$245$	10.7716	0.688175
$246$	−10.0941	−0.643576
$247$	−11.9913	−0.762987
$248$	−8.55947	−0.543527
$249$	2.96002	0.187584
$250$	1.00000	0.0632456
$251$	18.8106	1.18732	0.593658	−	0.804718i	$-0.297683\pi$
$251$	18.8106	1.18732	0.593658	+	0.804718i	$0.297683\pi$
$252$	2.12320	0.133749
$253$	−23.8925	−1.50211
$254$	−8.15115	−0.511449
$255$	−1.32195	−0.0827835
$256$	1.00000	0.0625000
$257$	12.7435	0.794919	0.397459	−	0.917620i	$-0.369892\pi$
$257$	12.7435	0.794919	0.397459	+	0.917620i	$0.369892\pi$
$258$	4.72579	0.294215
$259$	25.2040	1.56610
$260$	−3.37703	−0.209434
$261$	1.89869	0.117526
$262$	−10.2925	−0.635874
$263$	−18.6133	−1.14775	−0.573873	−	0.818944i	$-0.694560\pi$
$263$	−18.6133	−1.14775	−0.573873	+	0.818944i	$0.694560\pi$
$264$	9.41739	0.579600
$265$	−0.622701	−0.0382522
$266$	−14.9691	−0.917813
$267$	−25.2089	−1.54276
$268$	−2.96103	−0.180874
$269$	−6.81515	−0.415527	−0.207763	−	0.978179i	$-0.566618\pi$
$269$	−6.81515	−0.415527	−0.207763	+	0.978179i	$0.566618\pi$
$270$	5.53571	0.336893
$271$	27.1519	1.64936	0.824679	−	0.565600i	$-0.191355\pi$
$271$	27.1519	1.64936	0.824679	+	0.565600i	$0.191355\pi$
$272$	0.836683	0.0507314
$273$	−22.4932	−1.36135
$274$	8.47372	0.511916
$275$	−5.96043	−0.359428
$276$	−6.33341	−0.381227
$277$	1.06411	0.0639359	0.0319680	−	0.999489i	$-0.489823\pi$
$277$	1.06411	0.0639359	0.0319680	+	0.999489i	$0.489823\pi$
$278$	−2.17118	−0.130218
$279$	4.31096	0.258090
$280$	−4.21564	−0.251933
$281$	2.56904	0.153256	0.0766281	−	0.997060i	$-0.475585\pi$
$281$	2.56904	0.153256	0.0766281	+	0.997060i	$0.475585\pi$
$282$	18.8284	1.12122
$283$	1.55466	0.0924152	0.0462076	−	0.998932i	$-0.485286\pi$
$283$	1.55466	0.0924152	0.0462076	+	0.998932i	$0.485286\pi$
$284$	−1.88681	−0.111961
$285$	−5.61027	−0.332324
$286$	20.1285	1.19022
$287$	−26.9326	−1.58978
$288$	−0.503648	−0.0296777
$289$	−16.3000	−0.958821
$290$	−3.76988	−0.221375
$291$	14.1279	0.828195
$292$	−2.28826	−0.133910
$293$	9.56970	0.559068	0.279534	−	0.960136i	$-0.409820\pi$
$293$	9.56970	0.559068	0.279534	+	0.960136i	$0.409820\pi$
$294$	−17.0190	−0.992570
$295$	−8.49721	−0.494726
$296$	−5.97868	−0.347504
$297$	−32.9952	−1.91458
$298$	17.1101	0.991161
$299$	−13.5369	−0.782859
$300$	−1.57998	−0.0912205
$301$	12.6091	0.726778
$302$	−7.71991	−0.444231
$303$	4.54152	0.260904
$304$	3.55084	0.203655
$305$	8.67027	0.496458
$306$	−0.421393	−0.0240895
$307$	−23.2655	−1.32783	−0.663917	−	0.747806i	$-0.731107\pi$
$307$	−23.2655	−1.32783	−0.663917	+	0.747806i	$0.731107\pi$
$308$	25.1270	1.43175
$309$	−25.6332	−1.45822
$310$	−8.55947	−0.486145
$311$	19.0107	1.07800	0.538998	−	0.842307i	$-0.318803\pi$
$311$	19.0107	1.07800	0.538998	+	0.842307i	$0.318803\pi$
$312$	5.33565	0.302072
$313$	−22.0244	−1.24489	−0.622447	−	0.782662i	$-0.713861\pi$
$313$	−22.0244	−1.24489	−0.622447	+	0.782662i	$0.713861\pi$
$314$	23.3305	1.31661
$315$	2.12320	0.119629
$316$	14.9620	0.841678
$317$	−6.60861	−0.371176	−0.185588	−	0.982628i	$-0.559419\pi$
$317$	−6.60861	−0.371176	−0.185588	+	0.982628i	$0.559419\pi$
$318$	0.983857	0.0551720
$319$	22.4701	1.25809
$320$	1.00000	0.0559017
$321$	−31.5832	−1.76280
$322$	−16.8985	−0.941717
$323$	2.97093	0.165307
$324$	−7.23540	−0.401966
$325$	−3.37703	−0.187324
$326$	−13.5149	−0.748521
$327$	−0.289018	−0.0159827
$328$	6.38873	0.352758
$329$	50.2371	2.76966
$330$	9.41739	0.518410
$331$	−20.4846	−1.12593	−0.562967	−	0.826479i	$-0.690340\pi$
$331$	−20.4846	−1.12593	−0.562967	+	0.826479i	$0.690340\pi$
$332$	−1.87345	−0.102819
$333$	3.01115	0.165010
$334$	−6.43900	−0.352326
$335$	−2.96103	−0.161778
$336$	6.66065	0.363368
$337$	1.39425	0.0759497	0.0379749	−	0.999279i	$-0.487909\pi$
$337$	1.39425	0.0759497	0.0379749	+	0.999279i	$0.487909\pi$
$338$	−1.59569	−0.0867944
$339$	−20.5195	−1.11447
$340$	0.836683	0.0453755
$341$	51.0181	2.76279
$342$	−1.78837	−0.0967041
$343$	−15.8999	−0.858513
$344$	−2.99103	−0.161266
$345$	−6.33341	−0.340979
$346$	−7.67303	−0.412505
$347$	2.58751	0.138905	0.0694524	−	0.997585i	$-0.477875\pi$
$347$	2.58751	0.138905	0.0694524	+	0.997585i	$0.477875\pi$
$348$	5.95636	0.319294
$349$	7.47922	0.400354	0.200177	−	0.979760i	$-0.435848\pi$
$349$	7.47922	0.400354	0.200177	+	0.979760i	$0.435848\pi$
$350$	−4.21564	−0.225336
$351$	−18.6942	−0.997825
$352$	−5.96043	−0.317692
$353$	−23.4210	−1.24658	−0.623288	−	0.781992i	$-0.714204\pi$
$353$	−23.4210	−1.24658	−0.623288	+	0.781992i	$0.714204\pi$
$354$	13.4255	0.713555
$355$	−1.88681	−0.100141
$356$	15.9551	0.845620
$357$	5.57285	0.294947
$358$	−7.74757	−0.409472
$359$	−21.3872	−1.12877	−0.564386	−	0.825511i	$-0.690887\pi$
$359$	−21.3872	−1.12877	−0.564386	+	0.825511i	$0.690887\pi$
$360$	−0.503648	−0.0265446
$361$	−6.39154	−0.336397
$362$	−1.65695	−0.0870873
$363$	−38.7519	−2.03395
$364$	14.2363	0.746187
$365$	−2.28826	−0.119773
$366$	−13.6989	−0.716053
$367$	2.30627	0.120386	0.0601931	−	0.998187i	$-0.480828\pi$
$367$	2.30627	0.120386	0.0601931	+	0.998187i	$0.480828\pi$
$368$	4.00853	0.208959
$369$	−3.21767	−0.167505
$370$	−5.97868	−0.310817
$371$	2.62508	0.136287
$372$	13.5238	0.701178
$373$	2.80590	0.145284	0.0726421	−	0.997358i	$-0.476857\pi$
$373$	2.80590	0.145284	0.0726421	+	0.997358i	$0.476857\pi$
$374$	−4.98699	−0.257871
$375$	−1.57998	−0.0815901
$376$	−11.9168	−0.614564
$377$	12.7310	0.655680
$378$	−23.3366	−1.20030
$379$	5.72622	0.294136	0.147068	−	0.989126i	$-0.453016\pi$
$379$	5.72622	0.294136	0.147068	+	0.989126i	$0.453016\pi$
$380$	3.55084	0.182154
$381$	12.8787	0.659796
$382$	19.9942	1.02299
$383$	11.9011	0.608116	0.304058	−	0.952654i	$-0.401658\pi$
$383$	11.9011	0.608116	0.304058	+	0.952654i	$0.401658\pi$
$384$	−1.57998	−0.0806283
$385$	25.1270	1.28059
$386$	19.1356	0.973976
$387$	1.50643	0.0765760
$388$	−8.94182	−0.453952
$389$	19.5707	0.992275	0.496137	−	0.868244i	$-0.334751\pi$
$389$	19.5707	0.992275	0.496137	+	0.868244i	$0.334751\pi$
$390$	5.33565	0.270181
$391$	3.35387	0.169612
$392$	10.7716	0.544050
$393$	16.2620	0.820310
$394$	−4.61434	−0.232467
$395$	14.9620	0.752820
$396$	3.00196	0.150854
$397$	29.1997	1.46549	0.732745	−	0.680504i	$-0.238239\pi$
$397$	29.1997	1.46549	0.732745	+	0.680504i	$0.238239\pi$
$398$	14.1752	0.710537
$399$	23.6509	1.18403
$400$	1.00000	0.0500000
$401$	0.0843911	0.00421429	0.00210715	−	0.999998i	$-0.499329\pi$
$401$	0.0843911	0.00421429	0.00210715	+	0.999998i	$0.499329\pi$
$402$	4.67839	0.233337
$403$	28.9055	1.43989
$404$	−2.87441	−0.143007
$405$	−7.23540	−0.359530
$406$	15.8925	0.788731
$407$	35.6355	1.76639
$408$	−1.32195	−0.0654461
$409$	−21.7504	−1.07549	−0.537745	−	0.843107i	$-0.680724\pi$
$409$	−21.7504	−1.07549	−0.537745	+	0.843107i	$0.680724\pi$
$410$	6.38873	0.315517
$411$	−13.3883	−0.660398
$412$	16.2237	0.799286
$413$	35.8212	1.76264
$414$	−2.01888	−0.0992228
$415$	−1.87345	−0.0919641
$416$	−3.37703	−0.165572
$417$	3.43042	0.167989
$418$	−21.1645	−1.03519
$419$	−30.0178	−1.46647	−0.733234	−	0.679976i	$-0.761990\pi$
$419$	−30.0178	−1.46647	−0.733234	+	0.679976i	$0.761990\pi$
$420$	6.66065	0.325006
$421$	34.3583	1.67452	0.837261	−	0.546803i	$-0.184155\pi$
$421$	34.3583	1.67452	0.837261	+	0.546803i	$0.184155\pi$
$422$	22.7905	1.10943
$423$	6.00189	0.291822
$424$	−0.622701	−0.0302410
$425$	0.836683	0.0405851
$426$	2.98113	0.144436
$427$	−36.5508	−1.76882
$428$	19.9896	0.966232
$429$	−31.8028	−1.53545
$430$	−2.99103	−0.144240
$431$	−23.1137	−1.11335	−0.556673	−	0.830731i	$-0.687923\pi$
$431$	−23.1137	−1.11335	−0.556673	+	0.830731i	$0.687923\pi$
$432$	5.53571	0.266337
$433$	−24.9827	−1.20059	−0.600295	−	0.799779i	$-0.704950\pi$
$433$	−24.9827	−1.20059	−0.600295	+	0.799779i	$0.704950\pi$
$434$	36.0836	1.73207
$435$	5.95636	0.285586
$436$	0.182924	0.00876049
$437$	14.2336	0.680887
$438$	3.61542	0.172751
$439$	34.7895	1.66041	0.830205	−	0.557458i	$-0.188223\pi$
$439$	34.7895	1.66041	0.830205	+	0.557458i	$0.188223\pi$
$440$	−5.96043	−0.284152
$441$	−5.42511	−0.258339
$442$	−2.82550	−0.134395
$443$	−22.0727	−1.04871	−0.524353	−	0.851501i	$-0.675693\pi$
$443$	−22.0727	−1.04871	−0.524353	+	0.851501i	$0.675693\pi$
$444$	9.44623	0.448298
$445$	15.9551	0.756346
$446$	6.59907	0.312475
$447$	−27.0337	−1.27865
$448$	−4.21564	−0.199170
$449$	14.4904	0.683845	0.341923	−	0.939728i	$-0.388922\pi$
$449$	14.4904	0.683845	0.341923	+	0.939728i	$0.388922\pi$
$450$	−0.503648	−0.0237422
$451$	−38.0796	−1.79310
$452$	12.9872	0.610864
$453$	12.1973	0.573081
$454$	−15.8217	−0.742549
$455$	14.2363	0.667410
$456$	−5.61027	−0.262725
$457$	23.3215	1.09093	0.545467	−	0.838132i	$-0.316352\pi$
$457$	23.3215	1.09093	0.545467	+	0.838132i	$0.316352\pi$
$458$	8.35959	0.390618
$459$	4.63164	0.216186
$460$	4.00853	0.186898
$461$	1.72028	0.0801217	0.0400608	−	0.999197i	$-0.487245\pi$
$461$	1.72028	0.0801217	0.0400608	+	0.999197i	$0.487245\pi$
$462$	−39.7004	−1.84703
$463$	12.4704	0.579549	0.289774	−	0.957095i	$-0.406420\pi$
$463$	12.4704	0.579549	0.289774	+	0.957095i	$0.406420\pi$
$464$	−3.76988	−0.175013
$465$	13.5238	0.627152
$466$	−15.7420	−0.729234
$467$	−11.8789	−0.549690	−0.274845	−	0.961489i	$-0.588627\pi$
$467$	−11.8789	−0.549690	−0.274845	+	0.961489i	$0.588627\pi$
$468$	1.70083	0.0786210
$469$	12.4827	0.576395
$470$	−11.9168	−0.549683
$471$	−36.8618	−1.69850
$472$	−8.49721	−0.391116
$473$	17.8279	0.819725
$474$	−23.6397	−1.08581
$475$	3.55084	0.162924
$476$	−3.52716	−0.161667
$477$	0.313622	0.0143598
$478$	−4.61778	−0.211213
$479$	−25.0543	−1.14476	−0.572379	−	0.819989i	$-0.693980\pi$
$479$	−25.0543	−1.14476	−0.572379	+	0.819989i	$0.693980\pi$
$480$	−1.57998	−0.0721161
$481$	20.1902	0.920592
$482$	−13.9796	−0.636752
$483$	26.6994	1.21486
$484$	24.5267	1.11485
$485$	−8.94182	−0.406027
$486$	−5.17532	−0.234757
$487$	−26.7307	−1.21128	−0.605641	−	0.795738i	$-0.707083\pi$
$487$	−26.7307	−1.21128	−0.605641	+	0.795738i	$0.707083\pi$
$488$	8.67027	0.392485
$489$	21.3533	0.965632
$490$	10.7716	0.486613
$491$	26.9451	1.21602	0.608009	−	0.793930i	$-0.291969\pi$
$491$	26.9451	1.21602	0.608009	+	0.793930i	$0.291969\pi$
$492$	−10.0941	−0.455077
$493$	−3.15420	−0.142058
$494$	−11.9913	−0.539513
$495$	3.00196	0.134928
$496$	−8.55947	−0.384331
$497$	7.95410	0.356790
$498$	2.96002	0.132642
$499$	6.54015	0.292777	0.146389	−	0.989227i	$-0.453235\pi$
$499$	6.54015	0.292777	0.146389	+	0.989227i	$0.453235\pi$
$500$	1.00000	0.0447214
$501$	10.1735	0.454519
$502$	18.8106	0.839559
$503$	−11.6437	−0.519168	−0.259584	−	0.965721i	$-0.583585\pi$
$503$	−11.6437	−0.519168	−0.259584	+	0.965721i	$0.583585\pi$
$504$	2.12320	0.0945748
$505$	−2.87441	−0.127910
$506$	−23.8925	−1.06215
$507$	2.52117	0.111969
$508$	−8.15115	−0.361649
$509$	−3.58361	−0.158841	−0.0794204	−	0.996841i	$-0.525307\pi$
$509$	−3.58361	−0.158841	−0.0794204	+	0.996841i	$0.525307\pi$
$510$	−1.32195	−0.0585368
$511$	9.64649	0.426736
$512$	1.00000	0.0441942
$513$	19.6564	0.867852
$514$	12.7435	0.562093
$515$	16.2237	0.714903
$516$	4.72579	0.208041
$517$	71.0295	3.12387
$518$	25.2040	1.10740
$519$	12.1233	0.532152
$520$	−3.37703	−0.148092
$521$	40.3888	1.76946	0.884732	−	0.466100i	$-0.154341\pi$
$521$	40.3888	1.76946	0.884732	+	0.466100i	$0.154341\pi$
$522$	1.89869	0.0831036
$523$	−21.9156	−0.958301	−0.479151	−	0.877733i	$-0.659055\pi$
$523$	−21.9156	−0.958301	−0.479151	+	0.877733i	$0.659055\pi$
$524$	−10.2925	−0.449631
$525$	6.66065	0.290695
$526$	−18.6133	−0.811579
$527$	−7.16156	−0.311962
$528$	9.41739	0.409839
$529$	−6.93172	−0.301379
$530$	−0.622701	−0.0270484
$531$	4.27960	0.185719
$532$	−14.9691	−0.648992
$533$	−21.5749	−0.934513
$534$	−25.2089	−1.09089
$535$	19.9896	0.864224
$536$	−2.96103	−0.127897
$537$	12.2410	0.528240
$538$	−6.81515	−0.293822
$539$	−64.2036	−2.76545
$540$	5.53571	0.238219
$541$	0.848828	0.0364940	0.0182470	−	0.999834i	$-0.494191\pi$
$541$	0.848828	0.0364940	0.0182470	+	0.999834i	$0.494191\pi$
$542$	27.1519	1.16627
$543$	2.61795	0.112347
$544$	0.836683	0.0358725
$545$	0.182924	0.00783562
$546$	−22.4932	−0.962620
$547$	−12.7584	−0.545508	−0.272754	−	0.962084i	$-0.587935\pi$
$547$	−12.7584	−0.545508	−0.272754	+	0.962084i	$0.587935\pi$
$548$	8.47372	0.361979
$549$	−4.36676	−0.186369
$550$	−5.96043	−0.254154
$551$	−13.3863	−0.570274
$552$	−6.33341	−0.269568
$553$	−63.0744	−2.68220
$554$	1.06411	0.0452095
$555$	9.44623	0.400970
$556$	−2.17118	−0.0920783
$557$	2.18300	0.0924965	0.0462483	−	0.998930i	$-0.485273\pi$
$557$	2.18300	0.0924965	0.0462483	+	0.998930i	$0.485273\pi$
$558$	4.31096	0.182497
$559$	10.1008	0.427218
$560$	−4.21564	−0.178143
$561$	7.87937	0.332667
$562$	2.56904	0.108368
$563$	−22.8094	−0.961304	−0.480652	−	0.876912i	$-0.659600\pi$
$563$	−22.8094	−0.961304	−0.480652	+	0.876912i	$0.659600\pi$
$564$	18.8284	0.792819
$565$	12.9872	0.546374
$566$	1.55466	0.0653474
$567$	30.5018	1.28096
$568$	−1.88681	−0.0791686
$569$	20.7573	0.870191	0.435096	−	0.900384i	$-0.356715\pi$
$569$	20.7573	0.870191	0.435096	+	0.900384i	$0.356715\pi$
$570$	−5.61027	−0.234988
$571$	−5.74340	−0.240354	−0.120177	−	0.992752i	$-0.538346\pi$
$571$	−5.74340	−0.240354	−0.120177	+	0.992752i	$0.538346\pi$
$572$	20.1285	0.841616
$573$	−31.5905	−1.31971
$574$	−26.9326	−1.12414
$575$	4.00853	0.167167
$576$	−0.503648	−0.0209853
$577$	29.2490	1.21765	0.608826	−	0.793304i	$-0.291641\pi$
$577$	29.2490	1.21765	0.608826	+	0.793304i	$0.291641\pi$
$578$	−16.3000	−0.677989
$579$	−30.2339	−1.25648
$580$	−3.76988	−0.156536
$581$	7.89780	0.327656
$582$	14.1279	0.585622
$583$	3.71156	0.153717
$584$	−2.28826	−0.0946890
$585$	1.70083	0.0703207
$586$	9.56970	0.395321
$587$	−18.5160	−0.764237	−0.382118	−	0.924113i	$-0.624805\pi$
$587$	−18.5160	−0.764237	−0.382118	+	0.924113i	$0.624805\pi$
$588$	−17.0190	−0.701853
$589$	−30.3933	−1.25233
$590$	−8.49721	−0.349824
$591$	7.29059	0.299895
$592$	−5.97868	−0.245722
$593$	24.3726	1.00086	0.500431	−	0.865776i	$-0.333175\pi$
$593$	24.3726	1.00086	0.500431	+	0.865776i	$0.333175\pi$
$594$	−32.9952	−1.35381
$595$	−3.52716	−0.144599
$596$	17.1101	0.700856
$597$	−22.3966	−0.916630
$598$	−13.5369	−0.553565
$599$	27.8655	1.13855	0.569277	−	0.822146i	$-0.307223\pi$
$599$	27.8655	1.13855	0.569277	+	0.822146i	$0.307223\pi$
$600$	−1.57998	−0.0645026
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	12.6091	0.513910
$603$	1.49132	0.0607311
$604$	−7.71991	−0.314119
$605$	24.5267	0.997154
$606$	4.54152	0.184487
$607$	−11.7430	−0.476635	−0.238318	−	0.971187i	$-0.576596\pi$
$607$	−11.7430	−0.476635	−0.238318	+	0.971187i	$0.576596\pi$
$608$	3.55084	0.144006
$609$	−25.1099	−1.01750
$610$	8.67027	0.351049
$611$	40.2435	1.62808
$612$	−0.421393	−0.0170338
$613$	4.50493	0.181952	0.0909762	−	0.995853i	$-0.471001\pi$
$613$	4.50493	0.181952	0.0909762	+	0.995853i	$0.471001\pi$
$614$	−23.2655	−0.938921
$615$	−10.0941	−0.407033
$616$	25.1270	1.01240
$617$	−16.1639	−0.650735	−0.325367	−	0.945588i	$-0.605488\pi$
$617$	−16.1639	−0.650735	−0.325367	+	0.945588i	$0.605488\pi$
$618$	−25.6332	−1.03112
$619$	−18.0399	−0.725083	−0.362542	−	0.931968i	$-0.618091\pi$
$619$	−18.0399	−0.725083	−0.362542	+	0.931968i	$0.618091\pi$
$620$	−8.55947	−0.343756
$621$	22.1900	0.890456
$622$	19.0107	0.762258
$623$	−67.2611	−2.69476
$624$	5.33565	0.213597
$625$	1.00000	0.0400000
$626$	−22.0244	−0.880273
$627$	33.4396	1.33545
$628$	23.3305	0.930987
$629$	−5.00226	−0.199453
$630$	2.12320	0.0845903
$631$	19.6642	0.782821	0.391411	−	0.920216i	$-0.371987\pi$
$631$	19.6642	0.782821	0.391411	+	0.920216i	$0.371987\pi$
$632$	14.9620	0.595156
$633$	−36.0087	−1.43122
$634$	−6.60861	−0.262461
$635$	−8.15115	−0.323469
$636$	0.983857	0.0390125
$637$	−36.3761	−1.44127
$638$	22.4701	0.889601
$639$	0.950286	0.0375927
$640$	1.00000	0.0395285
$641$	8.26348	0.326388	0.163194	−	0.986594i	$-0.447820\pi$
$641$	8.26348	0.326388	0.163194	+	0.986594i	$0.447820\pi$
$642$	−31.5832	−1.24649
$643$	−46.1204	−1.81881	−0.909406	−	0.415911i	$-0.863463\pi$
$643$	−46.1204	−1.81881	−0.909406	+	0.415911i	$0.863463\pi$
$644$	−16.8985	−0.665895
$645$	4.72579	0.186078
$646$	2.97093	0.116890
$647$	−11.8533	−0.466003	−0.233001	−	0.972476i	$-0.574855\pi$
$647$	−11.8533	−0.466003	−0.233001	+	0.972476i	$0.574855\pi$
$648$	−7.23540	−0.284233
$649$	50.6470	1.98807
$650$	−3.37703	−0.132458
$651$	−57.0116	−2.23446
$652$	−13.5149	−0.529284
$653$	−12.7001	−0.496993	−0.248496	−	0.968633i	$-0.579936\pi$
$653$	−12.7001	−0.496993	−0.248496	+	0.968633i	$0.579936\pi$
$654$	−0.289018	−0.0113015
$655$	−10.2925	−0.402162
$656$	6.38873	0.249438
$657$	1.15248	0.0449624
$658$	50.2371	1.95845
$659$	28.8883	1.12533	0.562665	−	0.826685i	$-0.309776\pi$
$659$	28.8883	1.12533	0.562665	+	0.826685i	$0.309776\pi$
$660$	9.41739	0.366571
$661$	−27.7567	−1.07961	−0.539806	−	0.841790i	$-0.681502\pi$
$661$	−27.7567	−1.07961	−0.539806	+	0.841790i	$0.681502\pi$
$662$	−20.4846	−0.796156
$663$	4.46425	0.173377
$664$	−1.87345	−0.0727040
$665$	−14.9691	−0.580476
$666$	3.01115	0.116680
$667$	−15.1117	−0.585127
$668$	−6.43900	−0.249132
$669$	−10.4264	−0.403109
$670$	−2.96103	−0.114395
$671$	−51.6786	−1.99503
$672$	6.66065	0.256940
$673$	−40.5475	−1.56299	−0.781496	−	0.623910i	$-0.785543\pi$
$673$	−40.5475	−1.56299	−0.781496	+	0.623910i	$0.785543\pi$
$674$	1.39425	0.0537046
$675$	5.53571	0.213070
$676$	−1.59569	−0.0613729
$677$	−6.04964	−0.232507	−0.116253	−	0.993220i	$-0.537088\pi$
$677$	−6.04964	−0.232507	−0.116253	+	0.993220i	$0.537088\pi$
$678$	−20.5195	−0.788047
$679$	37.6955	1.44662
$680$	0.836683	0.0320853
$681$	24.9980	0.957927
$682$	51.0181	1.95358
$683$	−30.2003	−1.15558	−0.577791	−	0.816185i	$-0.696085\pi$
$683$	−30.2003	−1.15558	−0.577791	+	0.816185i	$0.696085\pi$
$684$	−1.78837	−0.0683801
$685$	8.47372	0.323764
$686$	−15.8999	−0.607060
$687$	−13.2080	−0.503918
$688$	−2.99103	−0.114032
$689$	2.10288	0.0801132
$690$	−6.33341	−0.241109
$691$	3.23334	0.123002	0.0615009	−	0.998107i	$-0.480411\pi$
$691$	3.23334	0.123002	0.0615009	+	0.998107i	$0.480411\pi$
$692$	−7.67303	−0.291685
$693$	−12.6552	−0.480730
$694$	2.58751	0.0982206
$695$	−2.17118	−0.0823574
$696$	5.95636	0.225775
$697$	5.34534	0.202469
$698$	7.47922	0.283093
$699$	24.8721	0.940750
$700$	−4.21564	−0.159336
$701$	12.3796	0.467572	0.233786	−	0.972288i	$-0.424888\pi$
$701$	12.3796	0.467572	0.233786	+	0.972288i	$0.424888\pi$
$702$	−18.6942	−0.705569
$703$	−21.2293	−0.800680
$704$	−5.96043	−0.224642
$705$	18.8284	0.709119
$706$	−23.4210	−0.881462
$707$	12.1175	0.455725
$708$	13.4255	0.504560
$709$	38.6998	1.45340	0.726702	−	0.686953i	$-0.241052\pi$
$709$	38.6998	1.45340	0.726702	+	0.686953i	$0.241052\pi$
$710$	−1.88681	−0.0708106
$711$	−7.53558	−0.282606
$712$	15.9551	0.597944
$713$	−34.3108	−1.28495
$714$	5.57285	0.208559
$715$	20.1285	0.752764
$716$	−7.74757	−0.289540
$717$	7.29603	0.272475
$718$	−21.3872	−0.798163
$719$	44.6345	1.66459	0.832294	−	0.554335i	$-0.187027\pi$
$719$	44.6345	1.66459	0.832294	+	0.554335i	$0.187027\pi$
$720$	−0.503648	−0.0187698
$721$	−68.3934	−2.54710
$722$	−6.39154	−0.237868
$723$	22.0875	0.821443
$724$	−1.65695	−0.0615800
$725$	−3.76988	−0.140010
$726$	−38.7519	−1.43822
$727$	27.4477	1.01798	0.508990	−	0.860773i	$-0.330019\pi$
$727$	27.4477	1.01798	0.508990	+	0.860773i	$0.330019\pi$
$728$	14.2363	0.527634
$729$	29.8831	1.10678
$730$	−2.28826	−0.0846924
$731$	−2.50255	−0.0925601
$732$	−13.6989	−0.506326
$733$	−10.4513	−0.386028	−0.193014	−	0.981196i	$-0.561826\pi$
$733$	−10.4513	−0.386028	−0.193014	+	0.981196i	$0.561826\pi$
$734$	2.30627	0.0851259
$735$	−17.0190	−0.627756
$736$	4.00853	0.147756
$737$	17.6490	0.650110
$738$	−3.21767	−0.118444
$739$	16.1407	0.593745	0.296872	−	0.954917i	$-0.404056\pi$
$739$	16.1407	0.593745	0.296872	+	0.954917i	$0.404056\pi$
$740$	−5.97868	−0.219781
$741$	18.9460	0.696000
$742$	2.62508	0.0963698
$743$	−9.23207	−0.338692	−0.169346	−	0.985557i	$-0.554166\pi$
$743$	−9.23207	−0.338692	−0.169346	+	0.985557i	$0.554166\pi$
$744$	13.5238	0.495808
$745$	17.1101	0.626865
$746$	2.80590	0.102731
$747$	0.943559	0.0345230
$748$	−4.98699	−0.182342
$749$	−84.2688	−3.07912
$750$	−1.57998	−0.0576929
$751$	−22.4261	−0.818342	−0.409171	−	0.912458i	$-0.634182\pi$
$751$	−22.4261	−0.818342	−0.409171	+	0.912458i	$0.634182\pi$
$752$	−11.9168	−0.434562
$753$	−29.7205	−1.08307
$754$	12.7310	0.463636
$755$	−7.71991	−0.280956
$756$	−23.3366	−0.848743
$757$	−5.70327	−0.207289	−0.103644	−	0.994614i	$-0.533050\pi$
$757$	−5.70327	−0.207289	−0.103644	+	0.994614i	$0.533050\pi$
$758$	5.72622	0.207986
$759$	37.7499	1.37023
$760$	3.55084	0.128802
$761$	−20.9642	−0.759951	−0.379976	−	0.924997i	$-0.624068\pi$
$761$	−20.9642	−0.759951	−0.379976	+	0.924997i	$0.624068\pi$
$762$	12.8787	0.466546
$763$	−0.771144	−0.0279173
$764$	19.9942	0.723363
$765$	−0.421393	−0.0152355
$766$	11.9011	0.430003
$767$	28.6953	1.03613
$768$	−1.57998	−0.0570128
$769$	37.4581	1.35077	0.675387	−	0.737463i	$-0.263977\pi$
$769$	37.4581	1.35077	0.675387	+	0.737463i	$0.263977\pi$
$770$	25.1270	0.905516
$771$	−20.1346	−0.725129
$772$	19.1356	0.688705
$773$	−20.9727	−0.754336	−0.377168	−	0.926145i	$-0.623102\pi$
$773$	−20.9727	−0.754336	−0.377168	+	0.926145i	$0.623102\pi$
$774$	1.50643	0.0541474
$775$	−8.55947	−0.307465
$776$	−8.94182	−0.320993
$777$	−39.8219	−1.42860
$778$	19.5707	0.701644
$779$	22.6853	0.812787
$780$	5.33565	0.191047
$781$	11.2462	0.402420
$782$	3.35387	0.119934
$783$	−20.8690	−0.745797
$784$	10.7716	0.384701
$785$	23.3305	0.832700
$786$	16.2620	0.580047
$787$	25.5433	0.910521	0.455260	−	0.890358i	$-0.349546\pi$
$787$	25.5433	0.910521	0.455260	+	0.890358i	$0.349546\pi$
$788$	−4.61434	−0.164379
$789$	29.4088	1.04698
$790$	14.9620	0.532324
$791$	−54.7492	−1.94666
$792$	3.00196	0.106670
$793$	−29.2797	−1.03975
$794$	29.1997	1.03626
$795$	0.983857	0.0348938
$796$	14.1752	0.502426
$797$	54.8784	1.94389	0.971947	−	0.235201i	$-0.0755748\pi$
$797$	54.8784	1.94389	0.971947	+	0.235201i	$0.0755748\pi$
$798$	23.6509	0.837233
$799$	−9.97061	−0.352735
$800$	1.00000	0.0353553
$801$	−8.03577	−0.283930
$802$	0.0843911	0.00297995
$803$	13.6390	0.481311
$804$	4.67839	0.164994
$805$	−16.8985	−0.595594
$806$	28.9055	1.01815
$807$	10.7678	0.379046
$808$	−2.87441	−0.101121
$809$	13.0612	0.459207	0.229604	−	0.973284i	$-0.426257\pi$
$809$	13.0612	0.459207	0.229604	+	0.973284i	$0.426257\pi$
$810$	−7.23540	−0.254226
$811$	−2.51088	−0.0881690	−0.0440845	−	0.999028i	$-0.514037\pi$
$811$	−2.51088	−0.0881690	−0.0440845	+	0.999028i	$0.514037\pi$
$812$	15.8925	0.557717
$813$	−42.8996	−1.50455
$814$	35.6355	1.24902
$815$	−13.5149	−0.473406
$816$	−1.32195	−0.0462774
$817$	−10.6207	−0.371571
$818$	−21.7504	−0.760487
$819$	−7.17010	−0.250543
$820$	6.38873	0.223104
$821$	−25.0753	−0.875133	−0.437566	−	0.899186i	$-0.644159\pi$
$821$	−25.0753	−0.875133	−0.437566	+	0.899186i	$0.644159\pi$
$822$	−13.3883	−0.466972
$823$	−26.5478	−0.925398	−0.462699	−	0.886516i	$-0.653119\pi$
$823$	−26.5478	−0.925398	−0.462699	+	0.886516i	$0.653119\pi$
$824$	16.2237	0.565180
$825$	9.41739	0.327871
$826$	35.8212	1.24638
$827$	9.85678	0.342754	0.171377	−	0.985206i	$-0.445178\pi$
$827$	9.85678	0.342754	0.171377	+	0.985206i	$0.445178\pi$
$828$	−2.01888	−0.0701611
$829$	−47.3572	−1.64478	−0.822392	−	0.568922i	$-0.807361\pi$
$829$	−47.3572	−1.64478	−0.822392	+	0.568922i	$0.807361\pi$
$830$	−1.87345	−0.0650284
$831$	−1.68127	−0.0583227
$832$	−3.37703	−0.117077
$833$	9.01245	0.312263
$834$	3.43042	0.118786
$835$	−6.43900	−0.222831
$836$	−21.1645	−0.731991
$837$	−47.3827	−1.63779
$838$	−30.0178	−1.03695
$839$	57.5968	1.98846	0.994231	−	0.107262i	$-0.0342083\pi$
$839$	57.5968	1.98846	0.994231	+	0.107262i	$0.0342083\pi$
$840$	6.66065	0.229814
$841$	−14.7880	−0.509930
$842$	34.3583	1.18407
$843$	−4.05905	−0.139801
$844$	22.7905	0.784483
$845$	−1.59569	−0.0548936
$846$	6.00189	0.206349
$847$	−103.396	−3.55273
$848$	−0.622701	−0.0213836
$849$	−2.45635	−0.0843015
$850$	0.836683	0.0286980
$851$	−23.9657	−0.821534
$852$	2.98113	0.102132
$853$	2.75582	0.0943575	0.0471788	−	0.998886i	$-0.484977\pi$
$853$	2.75582	0.0943575	0.0471788	+	0.998886i	$0.484977\pi$
$854$	−36.5508	−1.25074
$855$	−1.78837	−0.0611610
$856$	19.9896	0.683229
$857$	8.77783	0.299845	0.149922	−	0.988698i	$-0.452098\pi$
$857$	8.77783	0.299845	0.149922	+	0.988698i	$0.452098\pi$
$858$	−31.8028	−1.08573
$859$	16.4239	0.560375	0.280187	−	0.959945i	$-0.409603\pi$
$859$	16.4239	0.560375	0.280187	+	0.959945i	$0.409603\pi$
$860$	−2.99103	−0.101993
$861$	42.5531	1.45021
$862$	−23.1137	−0.787255
$863$	−12.0666	−0.410750	−0.205375	−	0.978683i	$-0.565841\pi$
$863$	−12.0666	−0.410750	−0.205375	+	0.978683i	$0.565841\pi$
$864$	5.53571	0.188329
$865$	−7.67303	−0.260891
$866$	−24.9827	−0.848945
$867$	25.7537	0.874641
$868$	36.0836	1.22476
$869$	−89.1800	−3.02522
$870$	5.95636	0.201940
$871$	9.99948	0.338820
$872$	0.182924	0.00619461
$873$	4.50353	0.152421
$874$	14.2336	0.481460
$875$	−4.21564	−0.142515
$876$	3.61542	0.122154
$877$	12.8113	0.432607	0.216303	−	0.976326i	$-0.430600\pi$
$877$	12.8113	0.432607	0.216303	+	0.976326i	$0.430600\pi$
$878$	34.7895	1.17409
$879$	−15.1200	−0.509984
$880$	−5.96043	−0.200926
$881$	21.6202	0.728403	0.364201	−	0.931320i	$-0.381342\pi$
$881$	21.6202	0.728403	0.364201	+	0.931320i	$0.381342\pi$
$882$	−5.42511	−0.182673
$883$	8.20717	0.276193	0.138097	−	0.990419i	$-0.455902\pi$
$883$	8.20717	0.276193	0.138097	+	0.990419i	$0.455902\pi$
$884$	−2.82550	−0.0950319
$885$	13.4255	0.451292
$886$	−22.0727	−0.741547
$887$	−46.5274	−1.56224	−0.781119	−	0.624382i	$-0.785351\pi$
$887$	−46.5274	−1.56224	−0.781119	+	0.624382i	$0.785351\pi$
$888$	9.44623	0.316995
$889$	34.3623	1.15248
$890$	15.9551	0.534817
$891$	43.1261	1.44478
$892$	6.59907	0.220953
$893$	−42.3148	−1.41601
$894$	−27.0337	−0.904141
$895$	−7.74757	−0.258973
$896$	−4.21564	−0.140835
$897$	21.3881	0.714128
$898$	14.4904	0.483552
$899$	32.2682	1.07620
$900$	−0.503648	−0.0167883
$901$	−0.521003	−0.0173571
$902$	−38.0796	−1.26791
$903$	−19.9222	−0.662970
$904$	12.9872	0.431946
$905$	−1.65695	−0.0550788
$906$	12.1973	0.405230
$907$	27.6266	0.917328	0.458664	−	0.888610i	$-0.348328\pi$
$907$	27.6266	0.917328	0.458664	+	0.888610i	$0.348328\pi$
$908$	−15.8217	−0.525061
$909$	1.44769	0.0480168
$910$	14.2363	0.471930
$911$	27.8149	0.921549	0.460775	−	0.887517i	$-0.347572\pi$
$911$	27.8149	0.921549	0.460775	+	0.887517i	$0.347572\pi$
$912$	−5.61027	−0.185775
$913$	11.1666	0.369560
$914$	23.3215	0.771407
$915$	−13.6989	−0.452872
$916$	8.35959	0.276209
$917$	43.3896	1.43285
$918$	4.63164	0.152867
$919$	34.6381	1.14260	0.571302	−	0.820740i	$-0.306439\pi$
$919$	34.6381	1.14260	0.571302	+	0.820740i	$0.306439\pi$
$920$	4.00853	0.132157
$921$	36.7592	1.21126
$922$	1.72028	0.0566546
$923$	6.37179	0.209730
$924$	−39.7004	−1.30605
$925$	−5.97868	−0.196578
$926$	12.4704	0.409803
$927$	−8.17104	−0.268372
$928$	−3.76988	−0.123753
$929$	−47.4767	−1.55766	−0.778830	−	0.627235i	$-0.784187\pi$
$929$	−47.4767	−1.55766	−0.778830	+	0.627235i	$0.784187\pi$
$930$	13.5238	0.443464
$931$	38.2484	1.25354
$932$	−15.7420	−0.515646
$933$	−30.0366	−0.983353
$934$	−11.8789	−0.388689
$935$	−4.98699	−0.163092
$936$	1.70083	0.0555934
$937$	44.7026	1.46037	0.730184	−	0.683250i	$-0.239434\pi$
$937$	44.7026	1.46037	0.730184	+	0.683250i	$0.239434\pi$
$938$	12.4827	0.407573
$939$	34.7983	1.13560
$940$	−11.9168	−0.388684
$941$	−43.0001	−1.40176	−0.700882	−	0.713277i	$-0.747210\pi$
$941$	−43.0001	−1.40176	−0.700882	+	0.713277i	$0.747210\pi$
$942$	−36.8618	−1.20102
$943$	25.6094	0.833956
$944$	−8.49721	−0.276560
$945$	−23.3366	−0.759139
$946$	17.8279	0.579633
$947$	−24.8703	−0.808177	−0.404088	−	0.914720i	$-0.632411\pi$
$947$	−24.8703	−0.808177	−0.404088	+	0.914720i	$0.632411\pi$
$948$	−23.6397	−0.767783
$949$	7.72752	0.250846
$950$	3.55084	0.115204
$951$	10.4415	0.338589
$952$	−3.52716	−0.114316
$953$	−38.1893	−1.23707	−0.618536	−	0.785757i	$-0.712274\pi$
$953$	−38.1893	−1.23707	−0.618536	+	0.785757i	$0.712274\pi$
$954$	0.313622	0.0101539
$955$	19.9942	0.646996
$956$	−4.61778	−0.149350
$957$	−35.5025	−1.14763
$958$	−25.0543	−0.809467
$959$	−35.7222	−1.15353
$960$	−1.57998	−0.0509938
$961$	42.2645	1.36337
$962$	20.1902	0.650957
$963$	−10.0677	−0.324427
$964$	−13.9796	−0.450251
$965$	19.1356	0.615996
$966$	26.6994	0.859039
$967$	−13.4272	−0.431789	−0.215894	−	0.976417i	$-0.569267\pi$
$967$	−13.4272	−0.431789	−0.215894	+	0.976417i	$0.569267\pi$
$968$	24.5267	0.788319
$969$	−4.69402	−0.150794
$970$	−8.94182	−0.287105
$971$	−13.2886	−0.426452	−0.213226	−	0.977003i	$-0.568397\pi$
$971$	−13.2886	−0.426452	−0.213226	+	0.977003i	$0.568397\pi$
$972$	−5.17532	−0.165998
$973$	9.15290	0.293428
$974$	−26.7307	−0.856506
$975$	5.33565	0.170878
$976$	8.67027	0.277529
$977$	50.8513	1.62688	0.813439	−	0.581651i	$-0.197593\pi$
$977$	50.8513	1.62688	0.813439	+	0.581651i	$0.197593\pi$
$978$	21.3533	0.682805
$979$	−95.0995	−3.03939
$980$	10.7716	0.344087
$981$	−0.0921295	−0.00294147
$982$	26.9451	0.859854
$983$	45.5517	1.45287	0.726437	−	0.687233i	$-0.241175\pi$
$983$	45.5517	1.45287	0.726437	+	0.687233i	$0.241175\pi$
$984$	−10.0941	−0.321788
$985$	−4.61434	−0.147025
$986$	−3.15420	−0.100450
$987$	−79.3739	−2.52650
$988$	−11.9913	−0.381493
$989$	−11.9896	−0.381248
$990$	3.00196	0.0954085
$991$	37.5118	1.19160	0.595801	−	0.803132i	$-0.296835\pi$
$991$	37.5118	1.19160	0.595801	+	0.803132i	$0.296835\pi$
$992$	−8.55947	−0.271763
$993$	32.3653	1.02708
$994$	7.95410	0.252289
$995$	14.1752	0.449383
$996$	2.96002	0.0937919
$997$	5.50512	0.174349	0.0871745	−	0.996193i	$-0.472216\pi$
$997$	5.50512	0.174349	0.0871745	+	0.996193i	$0.472216\pi$
$998$	6.54015	0.207025
$999$	−33.0963	−1.04712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.8	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.8	✓	33	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.57998 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57998 q^{6} -4.21564 q^{7} +1.00000 q^{8} -0.503648 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.57998 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57998 q^{6} -4.21564 q^{7} +1.00000 q^{8} -0.503648 q^{9} +1.00000 q^{10} -5.96043 q^{11} -1.57998 q^{12} -3.37703 q^{13} -4.21564 q^{14} -1.57998 q^{15} +1.00000 q^{16} +0.836683 q^{17} -0.503648 q^{18} +3.55084 q^{19} +1.00000 q^{20} +6.66065 q^{21} -5.96043 q^{22} +4.00853 q^{23} -1.57998 q^{24} +1.00000 q^{25} -3.37703 q^{26} +5.53571 q^{27} -4.21564 q^{28} -3.76988 q^{29} -1.57998 q^{30} -8.55947 q^{31} +1.00000 q^{32} +9.41739 q^{33} +0.836683 q^{34} -4.21564 q^{35} -0.503648 q^{36} -5.97868 q^{37} +3.55084 q^{38} +5.33565 q^{39} +1.00000 q^{40} +6.38873 q^{41} +6.66065 q^{42} -2.99103 q^{43} -5.96043 q^{44} -0.503648 q^{45} +4.00853 q^{46} -11.9168 q^{47} -1.57998 q^{48} +10.7716 q^{49} +1.00000 q^{50} -1.32195 q^{51} -3.37703 q^{52} -0.622701 q^{53} +5.53571 q^{54} -5.96043 q^{55} -4.21564 q^{56} -5.61027 q^{57} -3.76988 q^{58} -8.49721 q^{59} -1.57998 q^{60} +8.67027 q^{61} -8.55947 q^{62} +2.12320 q^{63} +1.00000 q^{64} -3.37703 q^{65} +9.41739 q^{66} -2.96103 q^{67} +0.836683 q^{68} -6.33341 q^{69} -4.21564 q^{70} -1.88681 q^{71} -0.503648 q^{72} -2.28826 q^{73} -5.97868 q^{74} -1.57998 q^{75} +3.55084 q^{76} +25.1270 q^{77} +5.33565 q^{78} +14.9620 q^{79} +1.00000 q^{80} -7.23540 q^{81} +6.38873 q^{82} -1.87345 q^{83} +6.66065 q^{84} +0.836683 q^{85} -2.99103 q^{86} +5.95636 q^{87} -5.96043 q^{88} +15.9551 q^{89} -0.503648 q^{90} +14.2363 q^{91} +4.00853 q^{92} +13.5238 q^{93} -11.9168 q^{94} +3.55084 q^{95} -1.57998 q^{96} -8.94182 q^{97} +10.7716 q^{98} +3.00196 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

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