LMFDB - Embedded newform 8018.2.a.d.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +3.53697 q^{10} -3.14295 q^{11} +1.37784 q^{12} -3.99759 q^{13} -2.08526 q^{14} +4.87337 q^{15} +1.00000 q^{16} -6.01813 q^{17} -1.10156 q^{18} +1.00000 q^{19} +3.53697 q^{20} -2.87314 q^{21} -3.14295 q^{22} -6.22231 q^{23} +1.37784 q^{24} +7.51017 q^{25} -3.99759 q^{26} -5.65129 q^{27} -2.08526 q^{28} -6.86242 q^{29} +4.87337 q^{30} +6.59507 q^{31} +1.00000 q^{32} -4.33048 q^{33} -6.01813 q^{34} -7.37550 q^{35} -1.10156 q^{36} -3.67195 q^{37} +1.00000 q^{38} -5.50802 q^{39} +3.53697 q^{40} +8.95892 q^{41} -2.87314 q^{42} +0.304255 q^{43} -3.14295 q^{44} -3.89620 q^{45} -6.22231 q^{46} +0.829211 q^{47} +1.37784 q^{48} -2.65170 q^{49} +7.51017 q^{50} -8.29200 q^{51} -3.99759 q^{52} +3.90013 q^{53} -5.65129 q^{54} -11.1165 q^{55} -2.08526 q^{56} +1.37784 q^{57} -6.86242 q^{58} -10.5452 q^{59} +4.87337 q^{60} +2.06867 q^{61} +6.59507 q^{62} +2.29705 q^{63} +1.00000 q^{64} -14.1394 q^{65} -4.33048 q^{66} +4.91181 q^{67} -6.01813 q^{68} -8.57334 q^{69} -7.37550 q^{70} -1.61616 q^{71} -1.10156 q^{72} -2.42349 q^{73} -3.67195 q^{74} +10.3478 q^{75} +1.00000 q^{76} +6.55387 q^{77} -5.50802 q^{78} -2.78453 q^{79} +3.53697 q^{80} -4.48186 q^{81} +8.95892 q^{82} +12.8628 q^{83} -2.87314 q^{84} -21.2859 q^{85} +0.304255 q^{86} -9.45530 q^{87} -3.14295 q^{88} -3.09295 q^{89} -3.89620 q^{90} +8.33600 q^{91} -6.22231 q^{92} +9.08693 q^{93} +0.829211 q^{94} +3.53697 q^{95} +1.37784 q^{96} +2.90999 q^{97} -2.65170 q^{98} +3.46217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	1.37784	0.795495	0.397747	−	0.917495i	$-0.369792\pi$
$3$	1.37784	0.795495	0.397747	+	0.917495i	$0.369792\pi$
$4$	1.00000	0.500000
$5$	3.53697	1.58178	0.790891	−	0.611957i	$-0.209617\pi$
$5$	3.53697	1.58178	0.790891	+	0.611957i	$0.209617\pi$
$6$	1.37784	0.562500
$7$	−2.08526	−0.788153	−0.394076	−	0.919078i	$-0.628935\pi$
$7$	−2.08526	−0.788153	−0.394076	+	0.919078i	$0.628935\pi$
$8$	1.00000	0.353553
$9$	−1.10156	−0.367188
$10$	3.53697	1.11849
$11$	−3.14295	−0.947636	−0.473818	−	0.880623i	$-0.657125\pi$
$11$	−3.14295	−0.947636	−0.473818	+	0.880623i	$0.657125\pi$
$12$	1.37784	0.397747
$13$	−3.99759	−1.10873	−0.554366	−	0.832273i	$-0.687039\pi$
$13$	−3.99759	−1.10873	−0.554366	+	0.832273i	$0.687039\pi$
$14$	−2.08526	−0.557308
$15$	4.87337	1.25830
$16$	1.00000	0.250000
$17$	−6.01813	−1.45961	−0.729805	−	0.683655i	$-0.760389\pi$
$17$	−6.01813	−1.45961	−0.729805	+	0.683655i	$0.760389\pi$
$18$	−1.10156	−0.259641
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.53697	0.790891
$21$	−2.87314	−0.626971
$22$	−3.14295	−0.670080
$23$	−6.22231	−1.29744	−0.648721	−	0.761026i	$-0.724696\pi$
$23$	−6.22231	−1.29744	−0.648721	+	0.761026i	$0.724696\pi$
$24$	1.37784	0.281250
$25$	7.51017	1.50203
$26$	−3.99759	−0.783991
$27$	−5.65129	−1.08759
$28$	−2.08526	−0.394076
$29$	−6.86242	−1.27432	−0.637160	−	0.770732i	$-0.719891\pi$
$29$	−6.86242	−1.27432	−0.637160	+	0.770732i	$0.719891\pi$
$30$	4.87337	0.889752
$31$	6.59507	1.18451	0.592255	−	0.805751i	$-0.298238\pi$
$31$	6.59507	1.18451	0.592255	+	0.805751i	$0.298238\pi$
$32$	1.00000	0.176777
$33$	−4.33048	−0.753840
$34$	−6.01813	−1.03210
$35$	−7.37550	−1.24669
$36$	−1.10156	−0.183594
$37$	−3.67195	−0.603665	−0.301833	−	0.953361i	$-0.597598\pi$
$37$	−3.67195	−0.603665	−0.301833	+	0.953361i	$0.597598\pi$
$38$	1.00000	0.162221
$39$	−5.50802	−0.881990
$40$	3.53697	0.559244
$41$	8.95892	1.39915	0.699574	−	0.714560i	$-0.253373\pi$
$41$	8.95892	1.39915	0.699574	+	0.714560i	$0.253373\pi$
$42$	−2.87314	−0.443336
$43$	0.304255	0.0463985	0.0231993	−	0.999731i	$-0.492615\pi$
$43$	0.304255	0.0463985	0.0231993	+	0.999731i	$0.492615\pi$
$44$	−3.14295	−0.473818
$45$	−3.89620	−0.580812
$46$	−6.22231	−0.917430
$47$	0.829211	0.120953	0.0604764	−	0.998170i	$-0.480738\pi$
$47$	0.829211	0.120953	0.0604764	+	0.998170i	$0.480738\pi$
$48$	1.37784	0.198874
$49$	−2.65170	−0.378815
$50$	7.51017	1.06210
$51$	−8.29200	−1.16111
$52$	−3.99759	−0.554366
$53$	3.90013	0.535724	0.267862	−	0.963457i	$-0.413683\pi$
$53$	3.90013	0.535724	0.267862	+	0.963457i	$0.413683\pi$
$54$	−5.65129	−0.769043
$55$	−11.1165	−1.49895
$56$	−2.08526	−0.278654
$57$	1.37784	0.182499
$58$	−6.86242	−0.901080
$59$	−10.5452	−1.37287	−0.686434	−	0.727192i	$-0.740825\pi$
$59$	−10.5452	−1.37287	−0.686434	+	0.727192i	$0.740825\pi$
$60$	4.87337	0.629150
$61$	2.06867	0.264866	0.132433	−	0.991192i	$-0.457721\pi$
$61$	2.06867	0.264866	0.132433	+	0.991192i	$0.457721\pi$
$62$	6.59507	0.837575
$63$	2.29705	0.289401
$64$	1.00000	0.125000
$65$	−14.1394	−1.75377
$66$	−4.33048	−0.533045
$67$	4.91181	0.600073	0.300037	−	0.953928i	$-0.403001\pi$
$67$	4.91181	0.600073	0.300037	+	0.953928i	$0.403001\pi$
$68$	−6.01813	−0.729805
$69$	−8.57334	−1.03211
$70$	−7.37550	−0.881540
$71$	−1.61616	−0.191803	−0.0959016	−	0.995391i	$-0.530573\pi$
$71$	−1.61616	−0.191803	−0.0959016	+	0.995391i	$0.530573\pi$
$72$	−1.10156	−0.129821
$73$	−2.42349	−0.283648	−0.141824	−	0.989892i	$-0.545297\pi$
$73$	−2.42349	−0.283648	−0.141824	+	0.989892i	$0.545297\pi$
$74$	−3.67195	−0.426856
$75$	10.3478	1.19486
$76$	1.00000	0.114708
$77$	6.55387	0.746883
$78$	−5.50802	−0.623661
$79$	−2.78453	−0.313284	−0.156642	−	0.987655i	$-0.550067\pi$
$79$	−2.78453	−0.313284	−0.156642	+	0.987655i	$0.550067\pi$
$80$	3.53697	0.395446
$81$	−4.48186	−0.497985
$82$	8.95892	0.989347
$83$	12.8628	1.41187	0.705937	−	0.708275i	$-0.250526\pi$
$83$	12.8628	1.41187	0.705937	+	0.708275i	$0.250526\pi$
$84$	−2.87314	−0.313486
$85$	−21.2859	−2.30878
$86$	0.304255	0.0328087
$87$	−9.45530	−1.01371
$88$	−3.14295	−0.335040
$89$	−3.09295	−0.327852	−0.163926	−	0.986473i	$-0.552416\pi$
$89$	−3.09295	−0.327852	−0.163926	+	0.986473i	$0.552416\pi$
$90$	−3.89620	−0.410696
$91$	8.33600	0.873850
$92$	−6.22231	−0.648721
$93$	9.08693	0.942271
$94$	0.829211	0.0855266
$95$	3.53697	0.362886
$96$	1.37784	0.140625
$97$	2.90999	0.295465	0.147732	−	0.989027i	$-0.452803\pi$
$97$	2.90999	0.295465	0.147732	+	0.989027i	$0.452803\pi$
$98$	−2.65170	−0.267863
$99$	3.46217	0.347961
$100$	7.51017	0.751017
$101$	−1.30507	−0.129859	−0.0649296	−	0.997890i	$-0.520682\pi$
$101$	−1.30507	−0.129859	−0.0649296	+	0.997890i	$0.520682\pi$
$102$	−8.29200	−0.821030
$103$	−12.3411	−1.21601	−0.608003	−	0.793935i	$-0.708029\pi$
$103$	−12.3411	−1.21601	−0.608003	+	0.793935i	$0.708029\pi$
$104$	−3.99759	−0.391996
$105$	−10.1622	−0.991732
$106$	3.90013	0.378814
$107$	1.14970	0.111146	0.0555729	−	0.998455i	$-0.482301\pi$
$107$	1.14970	0.111146	0.0555729	+	0.998455i	$0.482301\pi$
$108$	−5.65129	−0.543795
$109$	4.57273	0.437988	0.218994	−	0.975726i	$-0.429722\pi$
$109$	4.57273	0.437988	0.218994	+	0.975726i	$0.429722\pi$
$110$	−11.1165	−1.05992
$111$	−5.05935	−0.480212
$112$	−2.08526	−0.197038
$113$	−1.47352	−0.138617	−0.0693087	−	0.997595i	$-0.522079\pi$
$113$	−1.47352	−0.138617	−0.0693087	+	0.997595i	$0.522079\pi$
$114$	1.37784	0.129046
$115$	−22.0082	−2.05227
$116$	−6.86242	−0.637160
$117$	4.40360	0.407113
$118$	−10.5452	−0.970764
$119$	12.5493	1.15040
$120$	4.87337	0.444876
$121$	−1.12184	−0.101985
$122$	2.06867	0.187288
$123$	12.3439	1.11301
$124$	6.59507	0.592255
$125$	8.87841	0.794109
$126$	2.29705	0.204637
$127$	−12.0006	−1.06488	−0.532442	−	0.846467i	$-0.678725\pi$
$127$	−12.0006	−1.06488	−0.532442	+	0.846467i	$0.678725\pi$
$128$	1.00000	0.0883883
$129$	0.419215	0.0369098
$130$	−14.1394	−1.24010
$131$	−8.37543	−0.731765	−0.365882	−	0.930661i	$-0.619233\pi$
$131$	−8.37543	−0.731765	−0.365882	+	0.930661i	$0.619233\pi$
$132$	−4.33048	−0.376920
$133$	−2.08526	−0.180815
$134$	4.91181	0.424316
$135$	−19.9885	−1.72033
$136$	−6.01813	−0.516050
$137$	−10.7677	−0.919944	−0.459972	−	0.887933i	$-0.652141\pi$
$137$	−10.7677	−0.919944	−0.459972	+	0.887933i	$0.652141\pi$
$138$	−8.57334	−0.729811
$139$	1.42665	0.121007	0.0605035	−	0.998168i	$-0.480729\pi$
$139$	1.42665	0.121007	0.0605035	+	0.998168i	$0.480729\pi$
$140$	−7.37550	−0.623343
$141$	1.14252	0.0962174
$142$	−1.61616	−0.135625
$143$	12.5642	1.05067
$144$	−1.10156	−0.0917971
$145$	−24.2722	−2.01570
$146$	−2.42349	−0.200569
$147$	−3.65362	−0.301345
$148$	−3.67195	−0.301833
$149$	−1.66215	−0.136169	−0.0680843	−	0.997680i	$-0.521689\pi$
$149$	−1.66215	−0.136169	−0.0680843	+	0.997680i	$0.521689\pi$
$150$	10.3478	0.844894
$151$	5.77068	0.469611	0.234806	−	0.972042i	$-0.424555\pi$
$151$	5.77068	0.469611	0.234806	+	0.972042i	$0.424555\pi$
$152$	1.00000	0.0811107
$153$	6.62935	0.535952
$154$	6.55387	0.528126
$155$	23.3266	1.87364
$156$	−5.50802	−0.440995
$157$	−7.85464	−0.626869	−0.313434	−	0.949610i	$-0.601480\pi$
$157$	−7.85464	−0.626869	−0.313434	+	0.949610i	$0.601480\pi$
$158$	−2.78453	−0.221526
$159$	5.37374	0.426166
$160$	3.53697	0.279622
$161$	12.9751	1.02258
$162$	−4.48186	−0.352128
$163$	−4.10851	−0.321803	−0.160902	−	0.986970i	$-0.551440\pi$
$163$	−4.10851	−0.321803	−0.160902	+	0.986970i	$0.551440\pi$
$164$	8.95892	0.699574
$165$	−15.3168	−1.19241
$166$	12.8628	0.998345
$167$	7.06678	0.546844	0.273422	−	0.961894i	$-0.411845\pi$
$167$	7.06678	0.546844	0.273422	+	0.961894i	$0.411845\pi$
$168$	−2.87314	−0.221668
$169$	2.98071	0.229285
$170$	−21.2859	−1.63256
$171$	−1.10156	−0.0842388
$172$	0.304255	0.0231993
$173$	9.71788	0.738837	0.369418	−	0.929263i	$-0.379557\pi$
$173$	9.71788	0.738837	0.369418	+	0.929263i	$0.379557\pi$
$174$	−9.45530	−0.716804
$175$	−15.6606	−1.18383
$176$	−3.14295	−0.236909
$177$	−14.5296	−1.09211
$178$	−3.09295	−0.231826
$179$	−24.7875	−1.85270	−0.926352	−	0.376659i	$-0.877073\pi$
$179$	−24.7875	−1.85270	−0.926352	+	0.376659i	$0.877073\pi$
$180$	−3.89620	−0.290406
$181$	−2.42472	−0.180228	−0.0901142	−	0.995931i	$-0.528723\pi$
$181$	−2.42472	−0.180228	−0.0901142	+	0.995931i	$0.528723\pi$
$182$	8.33600	0.617905
$183$	2.85029	0.210699
$184$	−6.22231	−0.458715
$185$	−12.9876	−0.954867
$186$	9.08693	0.666286
$187$	18.9147	1.38318
$188$	0.829211	0.0604764
$189$	11.7844	0.857188
$190$	3.53697	0.256599
$191$	19.0532	1.37864	0.689322	−	0.724455i	$-0.257909\pi$
$191$	19.0532	1.37864	0.689322	+	0.724455i	$0.257909\pi$
$192$	1.37784	0.0994368
$193$	−6.16409	−0.443701	−0.221850	−	0.975081i	$-0.571210\pi$
$193$	−6.16409	−0.443701	−0.221850	+	0.975081i	$0.571210\pi$
$194$	2.90999	0.208925
$195$	−19.4817	−1.39512
$196$	−2.65170	−0.189407
$197$	3.38890	0.241449	0.120725	−	0.992686i	$-0.461478\pi$
$197$	3.38890	0.241449	0.120725	+	0.992686i	$0.461478\pi$
$198$	3.46217	0.246046
$199$	7.72991	0.547959	0.273979	−	0.961736i	$-0.411660\pi$
$199$	7.72991	0.547959	0.273979	+	0.961736i	$0.411660\pi$
$200$	7.51017	0.531049
$201$	6.76768	0.477355
$202$	−1.30507	−0.0918243
$203$	14.3099	1.00436
$204$	−8.29200	−0.580556
$205$	31.6874	2.21315
$206$	−12.3411	−0.859846
$207$	6.85428	0.476406
$208$	−3.99759	−0.277183
$209$	−3.14295	−0.217403
$210$	−10.1622	−0.701261
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.90013	0.267862
$213$	−2.22681	−0.152578
$214$	1.14970	0.0785920
$215$	1.07614	0.0733924
$216$	−5.65129	−0.384521
$217$	−13.7524	−0.933575
$218$	4.57273	0.309704
$219$	−3.33917	−0.225640
$220$	−11.1165	−0.749477
$221$	24.0580	1.61832
$222$	−5.05935	−0.339562
$223$	−4.53033	−0.303373	−0.151687	−	0.988429i	$-0.548470\pi$
$223$	−4.53033	−0.303373	−0.151687	+	0.988429i	$0.548470\pi$
$224$	−2.08526	−0.139327
$225$	−8.27294	−0.551529
$226$	−1.47352	−0.0980173
$227$	−4.60548	−0.305676	−0.152838	−	0.988251i	$-0.548841\pi$
$227$	−4.60548	−0.305676	−0.152838	+	0.988251i	$0.548841\pi$
$228$	1.37784	0.0912495
$229$	−18.8360	−1.24472	−0.622359	−	0.782732i	$-0.713826\pi$
$229$	−18.8360	−1.24472	−0.622359	+	0.782732i	$0.713826\pi$
$230$	−22.0082	−1.45117
$231$	9.03016	0.594141
$232$	−6.86242	−0.450540
$233$	13.9203	0.911951	0.455976	−	0.889992i	$-0.349290\pi$
$233$	13.9203	0.911951	0.455976	+	0.889992i	$0.349290\pi$
$234$	4.40360	0.287872
$235$	2.93290	0.191321
$236$	−10.5452	−0.686434
$237$	−3.83663	−0.249216
$238$	12.5493	0.813453
$239$	−1.61370	−0.104382	−0.0521909	−	0.998637i	$-0.516620\pi$
$239$	−1.61370	−0.104382	−0.0521909	+	0.998637i	$0.516620\pi$
$240$	4.87337	0.314575
$241$	−5.33913	−0.343924	−0.171962	−	0.985104i	$-0.555011\pi$
$241$	−5.33913	−0.343924	−0.171962	+	0.985104i	$0.555011\pi$
$242$	−1.12184	−0.0721143
$243$	10.7786	0.691447
$244$	2.06867	0.132433
$245$	−9.37900	−0.599203
$246$	12.3439	0.787020
$247$	−3.99759	−0.254360
$248$	6.59507	0.418787
$249$	17.7228	1.12314
$250$	8.87841	0.561520
$251$	−15.5928	−0.984208	−0.492104	−	0.870536i	$-0.663772\pi$
$251$	−15.5928	−0.984208	−0.492104	+	0.870536i	$0.663772\pi$
$252$	2.29705	0.144700
$253$	19.5565	1.22950
$254$	−12.0006	−0.752986
$255$	−29.3286	−1.83663
$256$	1.00000	0.0625000
$257$	16.7444	1.04449	0.522244	−	0.852796i	$-0.325095\pi$
$257$	16.7444	1.04449	0.522244	+	0.852796i	$0.325095\pi$
$258$	0.419215	0.0260992
$259$	7.65696	0.475781
$260$	−14.1394	−0.876886
$261$	7.55940	0.467915
$262$	−8.37543	−0.517436
$263$	16.0204	0.987858	0.493929	−	0.869502i	$-0.335560\pi$
$263$	16.0204	0.987858	0.493929	+	0.869502i	$0.335560\pi$
$264$	−4.33048	−0.266523
$265$	13.7947	0.847399
$266$	−2.08526	−0.127855
$267$	−4.26158	−0.260804
$268$	4.91181	0.300037
$269$	−18.2562	−1.11310	−0.556551	−	0.830813i	$-0.687876\pi$
$269$	−18.2562	−1.11310	−0.556551	+	0.830813i	$0.687876\pi$
$270$	−19.9885	−1.21646
$271$	19.6564	1.19404	0.597022	−	0.802225i	$-0.296351\pi$
$271$	19.6564	1.19404	0.597022	+	0.802225i	$0.296351\pi$
$272$	−6.01813	−0.364902
$273$	11.4856	0.695143
$274$	−10.7677	−0.650499
$275$	−23.6041	−1.42338
$276$	−8.57334	−0.516054
$277$	−20.4390	−1.22806	−0.614030	−	0.789283i	$-0.710452\pi$
$277$	−20.4390	−1.22806	−0.614030	+	0.789283i	$0.710452\pi$
$278$	1.42665	0.0855649
$279$	−7.26490	−0.434938
$280$	−7.37550	−0.440770
$281$	6.65167	0.396805	0.198403	−	0.980121i	$-0.436425\pi$
$281$	6.65167	0.396805	0.198403	+	0.980121i	$0.436425\pi$
$282$	1.14252	0.0680360
$283$	−9.99361	−0.594058	−0.297029	−	0.954868i	$-0.595996\pi$
$283$	−9.99361	−0.594058	−0.297029	+	0.954868i	$0.595996\pi$
$284$	−1.61616	−0.0959016
$285$	4.87337	0.288674
$286$	12.5642	0.742939
$287$	−18.6816	−1.10274
$288$	−1.10156	−0.0649103
$289$	19.2178	1.13046
$290$	−24.2722	−1.42531
$291$	4.00949	0.235041
$292$	−2.42349	−0.141824
$293$	11.8689	0.693387	0.346694	−	0.937978i	$-0.387304\pi$
$293$	11.8689	0.693387	0.346694	+	0.937978i	$0.387304\pi$
$294$	−3.65362	−0.213083
$295$	−37.2981	−2.17158
$296$	−3.67195	−0.213428
$297$	17.7617	1.03064
$298$	−1.66215	−0.0962858
$299$	24.8742	1.43851
$300$	10.3478	0.597430
$301$	−0.634451	−0.0365691
$302$	5.77068	0.332065
$303$	−1.79817	−0.103302
$304$	1.00000	0.0573539
$305$	7.31682	0.418960
$306$	6.62935	0.378975
$307$	0.203433	0.0116105	0.00580526	−	0.999983i	$-0.498152\pi$
$307$	0.203433	0.0116105	0.00580526	+	0.999983i	$0.498152\pi$
$308$	6.55387	0.373441
$309$	−17.0040	−0.967326
$310$	23.3266	1.32486
$311$	6.86918	0.389515	0.194758	−	0.980851i	$-0.437608\pi$
$311$	6.86918	0.389515	0.194758	+	0.980851i	$0.437608\pi$
$312$	−5.50802	−0.311830
$313$	13.2839	0.750852	0.375426	−	0.926852i	$-0.377496\pi$
$313$	13.2839	0.750852	0.375426	+	0.926852i	$0.377496\pi$
$314$	−7.85464	−0.443263
$315$	8.12459	0.457769
$316$	−2.78453	−0.156642
$317$	2.61783	0.147032	0.0735161	−	0.997294i	$-0.476578\pi$
$317$	2.61783	0.147032	0.0735161	+	0.997294i	$0.476578\pi$
$318$	5.37374	0.301345
$319$	21.5683	1.20759
$320$	3.53697	0.197723
$321$	1.58410	0.0884159
$322$	12.9751	0.723075
$323$	−6.01813	−0.334857
$324$	−4.48186	−0.248992
$325$	−30.0226	−1.66535
$326$	−4.10851	−0.227549
$327$	6.30048	0.348417
$328$	8.95892	0.494674
$329$	−1.72912	−0.0953294
$330$	−15.3168	−0.843161
$331$	1.55037	0.0852161	0.0426081	−	0.999092i	$-0.486433\pi$
$331$	1.55037	0.0852161	0.0426081	+	0.999092i	$0.486433\pi$
$332$	12.8628	0.705937
$333$	4.04489	0.221659
$334$	7.06678	0.386677
$335$	17.3729	0.949185
$336$	−2.87314	−0.156743
$337$	−2.68537	−0.146281	−0.0731406	−	0.997322i	$-0.523302\pi$
$337$	−2.68537	−0.146281	−0.0731406	+	0.997322i	$0.523302\pi$
$338$	2.98071	0.162129
$339$	−2.03028	−0.110269
$340$	−21.2859	−1.15439
$341$	−20.7280	−1.12248
$342$	−1.10156	−0.0595658
$343$	20.1263	1.08672
$344$	0.304255	0.0164044
$345$	−30.3237	−1.63257
$346$	9.71788	0.522436
$347$	31.9733	1.71642	0.858209	−	0.513300i	$-0.171577\pi$
$347$	31.9733	1.71642	0.858209	+	0.513300i	$0.171577\pi$
$348$	−9.45530	−0.506857
$349$	−10.4598	−0.559899	−0.279949	−	0.960015i	$-0.590318\pi$
$349$	−10.4598	−0.559899	−0.279949	+	0.960015i	$0.590318\pi$
$350$	−15.6606	−0.837096
$351$	22.5915	1.20585
$352$	−3.14295	−0.167520
$353$	16.4897	0.877659	0.438829	−	0.898570i	$-0.355393\pi$
$353$	16.4897	0.877659	0.438829	+	0.898570i	$0.355393\pi$
$354$	−14.5296	−0.772238
$355$	−5.71632	−0.303391
$356$	−3.09295	−0.163926
$357$	17.2909	0.915134
$358$	−24.7875	−1.31006
$359$	22.9622	1.21190	0.605949	−	0.795504i	$-0.292794\pi$
$359$	22.9622	1.21190	0.605949	+	0.795504i	$0.292794\pi$
$360$	−3.89620	−0.205348
$361$	1.00000	0.0526316
$362$	−2.42472	−0.127441
$363$	−1.54571	−0.0811286
$364$	8.33600	0.436925
$365$	−8.57180	−0.448669
$366$	2.85029	0.148987
$367$	11.1602	0.582558	0.291279	−	0.956638i	$-0.405919\pi$
$367$	11.1602	0.582558	0.291279	+	0.956638i	$0.405919\pi$
$368$	−6.22231	−0.324361
$369$	−9.86883	−0.513751
$370$	−12.9876	−0.675193
$371$	−8.13277	−0.422233
$372$	9.08693	0.471135
$373$	−22.3744	−1.15850	−0.579250	−	0.815150i	$-0.696655\pi$
$373$	−22.3744	−1.15850	−0.579250	+	0.815150i	$0.696655\pi$
$374$	18.9147	0.978056
$375$	12.2330	0.631710
$376$	0.829211	0.0427633
$377$	27.4331	1.41288
$378$	11.7844	0.606123
$379$	−24.4532	−1.25608	−0.628039	−	0.778182i	$-0.716142\pi$
$379$	−24.4532	−1.25608	−0.628039	+	0.778182i	$0.716142\pi$
$380$	3.53697	0.181443
$381$	−16.5349	−0.847109
$382$	19.0532	0.974849
$383$	−25.9429	−1.32562	−0.662811	−	0.748787i	$-0.730637\pi$
$383$	−25.9429	−1.32562	−0.662811	+	0.748787i	$0.730637\pi$
$384$	1.37784	0.0703125
$385$	23.1808	1.18141
$386$	−6.16409	−0.313744
$387$	−0.335157	−0.0170370
$388$	2.90999	0.147732
$389$	24.6340	1.24899	0.624497	−	0.781028i	$-0.285304\pi$
$389$	24.6340	1.24899	0.624497	+	0.781028i	$0.285304\pi$
$390$	−19.4817	−0.986496
$391$	37.4467	1.89376
$392$	−2.65170	−0.133931
$393$	−11.5400	−0.582115
$394$	3.38890	0.170730
$395$	−9.84882	−0.495548
$396$	3.46217	0.173980
$397$	13.3044	0.667728	0.333864	−	0.942621i	$-0.391647\pi$
$397$	13.3044	0.667728	0.333864	+	0.942621i	$0.391647\pi$
$398$	7.72991	0.387465
$399$	−2.87314	−0.143837
$400$	7.51017	0.375509
$401$	16.5602	0.826977	0.413489	−	0.910509i	$-0.364310\pi$
$401$	16.5602	0.826977	0.413489	+	0.910509i	$0.364310\pi$
$402$	6.76768	0.337541
$403$	−26.3644	−1.31330
$404$	−1.30507	−0.0649296
$405$	−15.8522	−0.787703
$406$	14.3099	0.710189
$407$	11.5408	0.572055
$408$	−8.29200	−0.410515
$409$	26.6765	1.31907	0.659534	−	0.751675i	$-0.270754\pi$
$409$	26.6765	1.31907	0.659534	+	0.751675i	$0.270754\pi$
$410$	31.6874	1.56493
$411$	−14.8361	−0.731811
$412$	−12.3411	−0.608003
$413$	21.9894	1.08203
$414$	6.85428	0.336870
$415$	45.4953	2.23328
$416$	−3.99759	−0.195998
$417$	1.96569	0.0962604
$418$	−3.14295	−0.153727
$419$	−27.4551	−1.34127	−0.670635	−	0.741788i	$-0.733978\pi$
$419$	−27.4551	−1.34127	−0.670635	+	0.741788i	$0.733978\pi$
$420$	−10.1622	−0.495866
$421$	11.2610	0.548828	0.274414	−	0.961612i	$-0.411516\pi$
$421$	11.2610	0.548828	0.274414	+	0.961612i	$0.411516\pi$
$422$	−1.00000	−0.0486792
$423$	−0.913430	−0.0444125
$424$	3.90013	0.189407
$425$	−45.1972	−2.19238
$426$	−2.22681	−0.107889
$427$	−4.31370	−0.208755
$428$	1.14970	0.0555729
$429$	17.3115	0.835806
$430$	1.07614	0.0518962
$431$	18.3117	0.882041	0.441021	−	0.897497i	$-0.354617\pi$
$431$	18.3117	0.882041	0.441021	+	0.897497i	$0.354617\pi$
$432$	−5.65129	−0.271898
$433$	−17.6693	−0.849134	−0.424567	−	0.905396i	$-0.639574\pi$
$433$	−17.6693	−0.849134	−0.424567	+	0.905396i	$0.639574\pi$
$434$	−13.7524	−0.660137
$435$	−33.4431	−1.60348
$436$	4.57273	0.218994
$437$	−6.22231	−0.297654
$438$	−3.33917	−0.159552
$439$	13.3069	0.635106	0.317553	−	0.948241i	$-0.397139\pi$
$439$	13.3069	0.635106	0.317553	+	0.948241i	$0.397139\pi$
$440$	−11.1165	−0.529960
$441$	2.92102	0.139096
$442$	24.0580	1.14432
$443$	15.0992	0.717385	0.358693	−	0.933456i	$-0.383223\pi$
$443$	15.0992	0.717385	0.358693	+	0.933456i	$0.383223\pi$
$444$	−5.05935	−0.240106
$445$	−10.9397	−0.518590
$446$	−4.53033	−0.214517
$447$	−2.29017	−0.108321
$448$	−2.08526	−0.0985191
$449$	7.48980	0.353465	0.176733	−	0.984259i	$-0.443447\pi$
$449$	7.48980	0.353465	0.176733	+	0.984259i	$0.443447\pi$
$450$	−8.27294	−0.389990
$451$	−28.1575	−1.32588
$452$	−1.47352	−0.0693087
$453$	7.95106	0.373573
$454$	−4.60548	−0.216146
$455$	29.4842	1.38224
$456$	1.37784	0.0645231
$457$	−13.3573	−0.624827	−0.312413	−	0.949946i	$-0.601137\pi$
$457$	−13.3573	−0.624827	−0.312413	+	0.949946i	$0.601137\pi$
$458$	−18.8360	−0.880149
$459$	34.0102	1.58746
$460$	−22.0082	−1.02614
$461$	−29.7300	−1.38467	−0.692333	−	0.721578i	$-0.743417\pi$
$461$	−29.7300	−1.38467	−0.692333	+	0.721578i	$0.743417\pi$
$462$	9.03016	0.420121
$463$	−15.9808	−0.742691	−0.371345	−	0.928495i	$-0.621103\pi$
$463$	−15.9808	−0.742691	−0.371345	+	0.928495i	$0.621103\pi$
$464$	−6.86242	−0.318580
$465$	32.1402	1.49047
$466$	13.9203	0.644847
$467$	10.1118	0.467920	0.233960	−	0.972246i	$-0.424832\pi$
$467$	10.1118	0.467920	0.233960	+	0.972246i	$0.424832\pi$
$468$	4.40360	0.203557
$469$	−10.2424	−0.472950
$470$	2.93290	0.135284
$471$	−10.8224	−0.498671
$472$	−10.5452	−0.485382
$473$	−0.956261	−0.0439689
$474$	−3.83663	−0.176222
$475$	7.51017	0.344590
$476$	12.5493	0.575198
$477$	−4.29625	−0.196712
$478$	−1.61370	−0.0738091
$479$	−18.6733	−0.853203	−0.426602	−	0.904440i	$-0.640289\pi$
$479$	−18.6733	−0.853203	−0.426602	+	0.904440i	$0.640289\pi$
$480$	4.87337	0.222438
$481$	14.6790	0.669303
$482$	−5.33913	−0.243191
$483$	17.8776	0.813459
$484$	−1.12184	−0.0509925
$485$	10.2926	0.467361
$486$	10.7786	0.488927
$487$	7.80494	0.353676	0.176838	−	0.984240i	$-0.443413\pi$
$487$	7.80494	0.353676	0.176838	+	0.984240i	$0.443413\pi$
$488$	2.06867	0.0936442
$489$	−5.66085	−0.255993
$490$	−9.37900	−0.423700
$491$	30.4261	1.37311	0.686556	−	0.727077i	$-0.259122\pi$
$491$	30.4261	1.37311	0.686556	+	0.727077i	$0.259122\pi$
$492$	12.3439	0.556507
$493$	41.2989	1.86001
$494$	−3.99759	−0.179860
$495$	12.2456	0.550398
$496$	6.59507	0.296127
$497$	3.37011	0.151170
$498$	17.7228	0.794178
$499$	−27.5678	−1.23411	−0.617053	−	0.786922i	$-0.711673\pi$
$499$	−27.5678	−1.23411	−0.617053	+	0.786922i	$0.711673\pi$
$500$	8.87841	0.397055
$501$	9.73687	0.435011
$502$	−15.5928	−0.695940
$503$	−21.2454	−0.947283	−0.473642	−	0.880718i	$-0.657061\pi$
$503$	−21.2454	−0.947283	−0.473642	+	0.880718i	$0.657061\pi$
$504$	2.29705	0.102319
$505$	−4.61599	−0.205409
$506$	19.5565	0.869390
$507$	4.10693	0.182395
$508$	−12.0006	−0.532442
$509$	−8.63307	−0.382654	−0.191327	−	0.981526i	$-0.561279\pi$
$509$	−8.63307	−0.382654	−0.191327	+	0.981526i	$0.561279\pi$
$510$	−29.3286	−1.29869
$511$	5.05359	0.223558
$512$	1.00000	0.0441942
$513$	−5.65129	−0.249510
$514$	16.7444	0.738564
$515$	−43.6502	−1.92346
$516$	0.419215	0.0184549
$517$	−2.60617	−0.114619
$518$	7.65696	0.336428
$519$	13.3897	0.587741
$520$	−14.1394	−0.620052
$521$	39.7373	1.74092	0.870461	−	0.492237i	$-0.163821\pi$
$521$	39.7373	1.74092	0.870461	+	0.492237i	$0.163821\pi$
$522$	7.55940	0.330866
$523$	−12.5368	−0.548196	−0.274098	−	0.961702i	$-0.588379\pi$
$523$	−12.5368	−0.548196	−0.274098	+	0.961702i	$0.588379\pi$
$524$	−8.37543	−0.365882
$525$	−21.5778	−0.941733
$526$	16.0204	0.698521
$527$	−39.6900	−1.72892
$528$	−4.33048	−0.188460
$529$	15.7172	0.683357
$530$	13.7947	0.599201
$531$	11.6162	0.504101
$532$	−2.08526	−0.0904073
$533$	−35.8141	−1.55128
$534$	−4.26158	−0.184417
$535$	4.06646	0.175809
$536$	4.91181	0.212158
$537$	−34.1531	−1.47382
$538$	−18.2562	−0.787082
$539$	8.33419	0.358979
$540$	−19.9885	−0.860166
$541$	29.9048	1.28571	0.642855	−	0.765988i	$-0.277750\pi$
$541$	29.9048	1.28571	0.642855	+	0.765988i	$0.277750\pi$
$542$	19.6564	0.844317
$543$	−3.34087	−0.143371
$544$	−6.01813	−0.258025
$545$	16.1736	0.692802
$546$	11.4856	0.491540
$547$	17.3234	0.740696	0.370348	−	0.928893i	$-0.379238\pi$
$547$	17.3234	0.740696	0.370348	+	0.928893i	$0.379238\pi$
$548$	−10.7677	−0.459972
$549$	−2.27877	−0.0972556
$550$	−23.6041	−1.00648
$551$	−6.86242	−0.292349
$552$	−8.57334	−0.364905
$553$	5.80647	0.246916
$554$	−20.4390	−0.868369
$555$	−17.8948	−0.759592
$556$	1.42665	0.0605035
$557$	−29.8705	−1.26565	−0.632827	−	0.774293i	$-0.718106\pi$
$557$	−29.8705	−1.26565	−0.632827	+	0.774293i	$0.718106\pi$
$558$	−7.26490	−0.307548
$559$	−1.21629	−0.0514435
$560$	−7.37550	−0.311672
$561$	26.0614	1.10031
$562$	6.65167	0.280584
$563$	21.5489	0.908178	0.454089	−	0.890956i	$-0.349965\pi$
$563$	21.5489	0.908178	0.454089	+	0.890956i	$0.349965\pi$
$564$	1.14252	0.0481087
$565$	−5.21181	−0.219263
$566$	−9.99361	−0.420063
$567$	9.34583	0.392488
$568$	−1.61616	−0.0678126
$569$	−27.9037	−1.16979	−0.584893	−	0.811111i	$-0.698863\pi$
$569$	−27.9037	−1.16979	−0.584893	+	0.811111i	$0.698863\pi$
$570$	4.87337	0.204123
$571$	32.8503	1.37474	0.687371	−	0.726307i	$-0.258765\pi$
$571$	32.8503	1.37474	0.687371	+	0.726307i	$0.258765\pi$
$572$	12.5642	0.525337
$573$	26.2523	1.09670
$574$	−18.6816	−0.779757
$575$	−46.7307	−1.94880
$576$	−1.10156	−0.0458985
$577$	−5.47732	−0.228024	−0.114012	−	0.993479i	$-0.536370\pi$
$577$	−5.47732	−0.228024	−0.114012	+	0.993479i	$0.536370\pi$
$578$	19.2178	0.799356
$579$	−8.49311	−0.352962
$580$	−24.2722	−1.00785
$581$	−26.8222	−1.11277
$582$	4.00949	0.166199
$583$	−12.2579	−0.507672
$584$	−2.42349	−0.100285
$585$	15.5754	0.643964
$586$	11.8689	0.490299
$587$	−11.0692	−0.456873	−0.228437	−	0.973559i	$-0.573361\pi$
$587$	−11.0692	−0.456873	−0.228437	+	0.973559i	$0.573361\pi$
$588$	−3.65362	−0.150673
$589$	6.59507	0.271745
$590$	−37.2981	−1.53554
$591$	4.66935	0.192071
$592$	−3.67195	−0.150916
$593$	−14.4974	−0.595337	−0.297669	−	0.954669i	$-0.596209\pi$
$593$	−14.4974	−0.595337	−0.297669	+	0.954669i	$0.596209\pi$
$594$	17.7617	0.728773
$595$	44.3867	1.81968
$596$	−1.66215	−0.0680843
$597$	10.6506	0.435898
$598$	24.8742	1.01718
$599$	17.2497	0.704802	0.352401	−	0.935849i	$-0.385365\pi$
$599$	17.2497	0.704802	0.352401	+	0.935849i	$0.385365\pi$
$600$	10.3478	0.422447
$601$	−27.1951	−1.10931	−0.554655	−	0.832081i	$-0.687150\pi$
$601$	−27.1951	−1.10931	−0.554655	+	0.832081i	$0.687150\pi$
$602$	−0.634451	−0.0258583
$603$	−5.41068	−0.220340
$604$	5.77068	0.234806
$605$	−3.96790	−0.161318
$606$	−1.79817	−0.0730458
$607$	29.3930	1.19303	0.596513	−	0.802604i	$-0.296553\pi$
$607$	29.3930	1.19303	0.596513	+	0.802604i	$0.296553\pi$
$608$	1.00000	0.0405554
$609$	19.7167	0.798962
$610$	7.31682	0.296250
$611$	−3.31484	−0.134104
$612$	6.62935	0.267976
$613$	−26.7405	−1.08004	−0.540020	−	0.841652i	$-0.681583\pi$
$613$	−26.7405	−1.08004	−0.540020	+	0.841652i	$0.681583\pi$
$614$	0.203433	0.00820988
$615$	43.6601	1.76055
$616$	6.55387	0.264063
$617$	−2.53854	−0.102198	−0.0510989	−	0.998694i	$-0.516272\pi$
$617$	−2.53854	−0.102198	−0.0510989	+	0.998694i	$0.516272\pi$
$618$	−17.0040	−0.684003
$619$	4.50555	0.181093	0.0905467	−	0.995892i	$-0.471139\pi$
$619$	4.50555	0.181093	0.0905467	+	0.995892i	$0.471139\pi$
$620$	23.3266	0.936818
$621$	35.1641	1.41109
$622$	6.86918	0.275429
$623$	6.44959	0.258398
$624$	−5.50802	−0.220497
$625$	−6.14817	−0.245927
$626$	13.2839	0.530933
$627$	−4.33048	−0.172943
$628$	−7.85464	−0.313434
$629$	22.0983	0.881116
$630$	8.12459	0.323691
$631$	14.0791	0.560478	0.280239	−	0.959930i	$-0.409586\pi$
$631$	14.0791	0.560478	0.280239	+	0.959930i	$0.409586\pi$
$632$	−2.78453	−0.110763
$633$	−1.37784	−0.0547641
$634$	2.61783	0.103967
$635$	−42.4459	−1.68441
$636$	5.37374	0.213083
$637$	10.6004	0.420004
$638$	21.5683	0.853896
$639$	1.78031	0.0704278
$640$	3.53697	0.139811
$641$	−24.3660	−0.962399	−0.481199	−	0.876611i	$-0.659799\pi$
$641$	−24.3660	−0.962399	−0.481199	+	0.876611i	$0.659799\pi$
$642$	1.58410	0.0625195
$643$	45.0314	1.77586	0.887932	−	0.459975i	$-0.152142\pi$
$643$	45.0314	1.77586	0.887932	+	0.459975i	$0.152142\pi$
$644$	12.9751	0.511292
$645$	1.48275	0.0583832
$646$	−6.01813	−0.236780
$647$	−7.60264	−0.298891	−0.149445	−	0.988770i	$-0.547749\pi$
$647$	−7.60264	−0.298891	−0.149445	+	0.988770i	$0.547749\pi$
$648$	−4.48186	−0.176064
$649$	33.1431	1.30098
$650$	−30.0226	−1.17758
$651$	−18.9486	−0.742654
$652$	−4.10851	−0.160902
$653$	−21.0806	−0.824948	−0.412474	−	0.910969i	$-0.635335\pi$
$653$	−21.0806	−0.824948	−0.412474	+	0.910969i	$0.635335\pi$
$654$	6.30048	0.246368
$655$	−29.6237	−1.15749
$656$	8.95892	0.349787
$657$	2.66963	0.104152
$658$	−1.72912	−0.0674081
$659$	28.7679	1.12064	0.560320	−	0.828276i	$-0.310678\pi$
$659$	28.7679	1.12064	0.560320	+	0.828276i	$0.310678\pi$
$660$	−15.3168	−0.596205
$661$	−29.5633	−1.14988	−0.574940	−	0.818196i	$-0.694975\pi$
$661$	−29.5633	−1.14988	−0.574940	+	0.818196i	$0.694975\pi$
$662$	1.55037	0.0602569
$663$	33.1480	1.28736
$664$	12.8628	0.499173
$665$	−7.37550	−0.286009
$666$	4.04489	0.156736
$667$	42.7001	1.65336
$668$	7.06678	0.273422
$669$	−6.24206	−0.241332
$670$	17.3729	0.671175
$671$	−6.50173	−0.250997
$672$	−2.87314	−0.110834
$673$	−19.2315	−0.741318	−0.370659	−	0.928769i	$-0.620868\pi$
$673$	−19.2315	−0.741318	−0.370659	+	0.928769i	$0.620868\pi$
$674$	−2.68537	−0.103436
$675$	−42.4422	−1.63360
$676$	2.98071	0.114643
$677$	13.8011	0.530421	0.265210	−	0.964191i	$-0.414559\pi$
$677$	13.8011	0.530421	0.265210	+	0.964191i	$0.414559\pi$
$678$	−2.03028	−0.0779723
$679$	−6.06808	−0.232871
$680$	−21.2859	−0.816279
$681$	−6.34560	−0.243164
$682$	−20.7280	−0.793716
$683$	−19.4834	−0.745511	−0.372756	−	0.927930i	$-0.621587\pi$
$683$	−19.4834	−0.745511	−0.372756	+	0.927930i	$0.621587\pi$
$684$	−1.10156	−0.0421194
$685$	−38.0850	−1.45515
$686$	20.1263	0.768425
$687$	−25.9529	−0.990167
$688$	0.304255	0.0115996
$689$	−15.5911	−0.593974
$690$	−30.3237	−1.15440
$691$	37.7494	1.43605	0.718027	−	0.696015i	$-0.245045\pi$
$691$	37.7494	1.43605	0.718027	+	0.696015i	$0.245045\pi$
$692$	9.71788	0.369418
$693$	−7.21951	−0.274246
$694$	31.9733	1.21369
$695$	5.04603	0.191407
$696$	−9.45530	−0.358402
$697$	−53.9159	−2.04221
$698$	−10.4598	−0.395908
$699$	19.1799	0.725452
$700$	−15.6606	−0.591917
$701$	−28.1212	−1.06212	−0.531061	−	0.847334i	$-0.678206\pi$
$701$	−28.1212	−1.06212	−0.531061	+	0.847334i	$0.678206\pi$
$702$	22.5915	0.852662
$703$	−3.67195	−0.138490
$704$	−3.14295	−0.118455
$705$	4.04105	0.152195
$706$	16.4897	0.620598
$707$	2.72140	0.102349
$708$	−14.5296	−0.546054
$709$	−8.69213	−0.326440	−0.163220	−	0.986590i	$-0.552188\pi$
$709$	−8.69213	−0.326440	−0.163220	+	0.986590i	$0.552188\pi$
$710$	−5.71632	−0.214530
$711$	3.06734	0.115034
$712$	−3.09295	−0.115913
$713$	−41.0366	−1.53683
$714$	17.2909	0.647097
$715$	44.4394	1.66194
$716$	−24.7875	−0.926352
$717$	−2.22342	−0.0830352
$718$	22.9622	0.856941
$719$	18.3861	0.685686	0.342843	−	0.939393i	$-0.388610\pi$
$719$	18.3861	0.685686	0.342843	+	0.939393i	$0.388610\pi$
$720$	−3.89620	−0.145203
$721$	25.7344	0.958399
$722$	1.00000	0.0372161
$723$	−7.35646	−0.273590
$724$	−2.42472	−0.0901142
$725$	−51.5380	−1.91407
$726$	−1.54571	−0.0573666
$727$	17.5555	0.651097	0.325548	−	0.945525i	$-0.394451\pi$
$727$	17.5555	0.651097	0.325548	+	0.945525i	$0.394451\pi$
$728$	8.33600	0.308953
$729$	28.2967	1.04803
$730$	−8.57180	−0.317257
$731$	−1.83105	−0.0677237
$732$	2.85029	0.105350
$733$	−46.1061	−1.70297	−0.851483	−	0.524382i	$-0.824296\pi$
$733$	−46.1061	−1.70297	−0.851483	+	0.524382i	$0.824296\pi$
$734$	11.1602	0.411931
$735$	−12.9227	−0.476662
$736$	−6.22231	−0.229358
$737$	−15.4376	−0.568651
$738$	−9.86883	−0.363277
$739$	22.4589	0.826162	0.413081	−	0.910694i	$-0.364453\pi$
$739$	22.4589	0.826162	0.413081	+	0.910694i	$0.364453\pi$
$740$	−12.9876	−0.477433
$741$	−5.50802	−0.202342
$742$	−8.13277	−0.298564
$743$	−49.4864	−1.81548	−0.907741	−	0.419531i	$-0.862194\pi$
$743$	−49.4864	−1.81548	−0.907741	+	0.419531i	$0.862194\pi$
$744$	9.08693	0.333143
$745$	−5.87898	−0.215389
$746$	−22.3744	−0.819183
$747$	−14.1692	−0.518423
$748$	18.9147	0.691590
$749$	−2.39742	−0.0875999
$750$	12.2330	0.446686
$751$	−20.0847	−0.732900	−0.366450	−	0.930438i	$-0.619427\pi$
$751$	−20.0847	−0.732900	−0.366450	+	0.930438i	$0.619427\pi$
$752$	0.829211	0.0302382
$753$	−21.4843	−0.782932
$754$	27.4331	0.999056
$755$	20.4107	0.742823
$756$	11.7844	0.428594
$757$	−26.3031	−0.956003	−0.478002	−	0.878359i	$-0.658639\pi$
$757$	−26.3031	−0.956003	−0.478002	+	0.878359i	$0.658639\pi$
$758$	−24.4532	−0.888181
$759$	26.9456	0.978064
$760$	3.53697	0.128299
$761$	−28.8315	−1.04514	−0.522570	−	0.852597i	$-0.675027\pi$
$761$	−28.8315	−1.04514	−0.522570	+	0.852597i	$0.675027\pi$
$762$	−16.5349	−0.598997
$763$	−9.53532	−0.345202
$764$	19.0532	0.689322
$765$	23.4478	0.847759
$766$	−25.9429	−0.937356
$767$	42.1553	1.52214
$768$	1.37784	0.0497184
$769$	17.7757	0.641007	0.320503	−	0.947247i	$-0.396148\pi$
$769$	17.7757	0.641007	0.320503	+	0.947247i	$0.396148\pi$
$770$	23.1808	0.835380
$771$	23.0711	0.830884
$772$	−6.16409	−0.221850
$773$	−1.54444	−0.0555497	−0.0277749	−	0.999614i	$-0.508842\pi$
$773$	−1.54444	−0.0555497	−0.0277749	+	0.999614i	$0.508842\pi$
$774$	−0.335157	−0.0120470
$775$	49.5301	1.77917
$776$	2.90999	0.104463
$777$	10.5500	0.378481
$778$	24.6340	0.883171
$779$	8.95892	0.320987
$780$	−19.4817	−0.697558
$781$	5.07952	0.181760
$782$	37.4467	1.33909
$783$	38.7815	1.38594
$784$	−2.65170	−0.0947037
$785$	−27.7817	−0.991570
$786$	−11.5400	−0.411617
$787$	−14.7378	−0.525345	−0.262673	−	0.964885i	$-0.584604\pi$
$787$	−14.7378	−0.525345	−0.262673	+	0.964885i	$0.584604\pi$
$788$	3.38890	0.120725
$789$	22.0734	0.785835
$790$	−9.84882	−0.350405
$791$	3.07267	0.109252
$792$	3.46217	0.123023
$793$	−8.26968	−0.293665
$794$	13.3044	0.472155
$795$	19.0068	0.674101
$796$	7.72991	0.273979
$797$	−14.7054	−0.520892	−0.260446	−	0.965488i	$-0.583870\pi$
$797$	−14.7054	−0.520892	−0.260446	+	0.965488i	$0.583870\pi$
$798$	−2.87314	−0.101708
$799$	−4.99030	−0.176544
$800$	7.51017	0.265525
$801$	3.40708	0.120383
$802$	16.5602	0.584761
$803$	7.61691	0.268795
$804$	6.76768	0.238678
$805$	45.8927	1.61750
$806$	−26.3644	−0.928645
$807$	−25.1541	−0.885467
$808$	−1.30507	−0.0459122
$809$	21.3092	0.749191	0.374596	−	0.927188i	$-0.377782\pi$
$809$	21.3092	0.749191	0.374596	+	0.927188i	$0.377782\pi$
$810$	−15.8522	−0.556990
$811$	55.7967	1.95929	0.979644	−	0.200745i	$-0.0643363\pi$
$811$	55.7967	1.95929	0.979644	+	0.200745i	$0.0643363\pi$
$812$	14.3099	0.502179
$813$	27.0834	0.949856
$814$	11.5408	0.404504
$815$	−14.5317	−0.509022
$816$	−8.29200	−0.290278
$817$	0.304255	0.0106446
$818$	26.6765	0.932721
$819$	−9.18264	−0.320867
$820$	31.6874	1.10657
$821$	−36.2826	−1.26627	−0.633136	−	0.774041i	$-0.718232\pi$
$821$	−36.2826	−1.26627	−0.633136	+	0.774041i	$0.718232\pi$
$822$	−14.8361	−0.517468
$823$	40.4131	1.40871	0.704356	−	0.709847i	$-0.251236\pi$
$823$	40.4131	1.40871	0.704356	+	0.709847i	$0.251236\pi$
$824$	−12.3411	−0.429923
$825$	−32.5227	−1.13229
$826$	21.9894	0.765110
$827$	−14.6019	−0.507759	−0.253879	−	0.967236i	$-0.581707\pi$
$827$	−14.6019	−0.507759	−0.253879	+	0.967236i	$0.581707\pi$
$828$	6.85428	0.238203
$829$	−47.6614	−1.65535	−0.827674	−	0.561209i	$-0.810336\pi$
$829$	−47.6614	−1.65535	−0.827674	+	0.561209i	$0.810336\pi$
$830$	45.4953	1.57916
$831$	−28.1616	−0.976915
$832$	−3.99759	−0.138591
$833$	15.9583	0.552922
$834$	1.96569	0.0680664
$835$	24.9950	0.864987
$836$	−3.14295	−0.108701
$837$	−37.2706	−1.28826
$838$	−27.4551	−0.948421
$839$	30.1178	1.03978	0.519890	−	0.854233i	$-0.325973\pi$
$839$	30.1178	1.03978	0.519890	+	0.854233i	$0.325973\pi$
$840$	−10.1622	−0.350630
$841$	18.0928	0.623891
$842$	11.2610	0.388080
$843$	9.16491	0.315656
$844$	−1.00000	−0.0344214
$845$	10.5427	0.362679
$846$	−0.913430	−0.0314044
$847$	2.33932	0.0803798
$848$	3.90013	0.133931
$849$	−13.7696	−0.472570
$850$	−45.1972	−1.55025
$851$	22.8480	0.783221
$852$	−2.22681	−0.0762892
$853$	−33.0738	−1.13243	−0.566213	−	0.824259i	$-0.691592\pi$
$853$	−33.0738	−1.13243	−0.566213	+	0.824259i	$0.691592\pi$
$854$	−4.31370	−0.147612
$855$	−3.89620	−0.133247
$856$	1.14970	0.0392960
$857$	−42.3024	−1.44502	−0.722512	−	0.691358i	$-0.757013\pi$
$857$	−42.3024	−1.44502	−0.722512	+	0.691358i	$0.757013\pi$
$858$	17.3115	0.591004
$859$	−21.3341	−0.727909	−0.363955	−	0.931417i	$-0.618574\pi$
$859$	−21.3341	−0.727909	−0.363955	+	0.931417i	$0.618574\pi$
$860$	1.07614	0.0366962
$861$	−25.7403	−0.877226
$862$	18.3117	0.623697
$863$	−32.4571	−1.10485	−0.552427	−	0.833561i	$-0.686298\pi$
$863$	−32.4571	−1.10485	−0.552427	+	0.833561i	$0.686298\pi$
$864$	−5.65129	−0.192261
$865$	34.3719	1.16868
$866$	−17.6693	−0.600429
$867$	26.4790	0.899276
$868$	−13.7524	−0.466787
$869$	8.75166	0.296880
$870$	−33.4431	−1.13383
$871$	−19.6354	−0.665320
$872$	4.57273	0.154852
$873$	−3.20554	−0.108491
$874$	−6.22231	−0.210473
$875$	−18.5138	−0.625880
$876$	−3.33917	−0.112820
$877$	0.468896	0.0158335	0.00791675	−	0.999969i	$-0.497480\pi$
$877$	0.468896	0.0158335	0.00791675	+	0.999969i	$0.497480\pi$
$878$	13.3069	0.449087
$879$	16.3534	0.551586
$880$	−11.1165	−0.374739
$881$	−36.5735	−1.23219	−0.616096	−	0.787671i	$-0.711287\pi$
$881$	−36.5735	−1.23219	−0.616096	+	0.787671i	$0.711287\pi$
$882$	2.92102	0.0983560
$883$	−34.1591	−1.14954	−0.574772	−	0.818313i	$-0.694909\pi$
$883$	−34.1591	−1.14954	−0.574772	+	0.818313i	$0.694909\pi$
$884$	24.0580	0.809158
$885$	−51.3907	−1.72748
$886$	15.0992	0.507268
$887$	−48.8571	−1.64046	−0.820230	−	0.572034i	$-0.806155\pi$
$887$	−48.8571	−1.64046	−0.820230	+	0.572034i	$0.806155\pi$
$888$	−5.05935	−0.169781
$889$	25.0244	0.839291
$890$	−10.9397	−0.366699
$891$	14.0863	0.471908
$892$	−4.53033	−0.151687
$893$	0.829211	0.0277485
$894$	−2.29017	−0.0765948
$895$	−87.6727	−2.93057
$896$	−2.08526	−0.0696635
$897$	34.2727	1.14433
$898$	7.48980	0.249938
$899$	−45.2581	−1.50944
$900$	−8.27294	−0.275765
$901$	−23.4715	−0.781948
$902$	−28.1575	−0.937541
$903$	−0.874170	−0.0290906
$904$	−1.47352	−0.0490087
$905$	−8.57618	−0.285082
$906$	7.95106	0.264156
$907$	−0.521839	−0.0173274	−0.00866370	−	0.999962i	$-0.502758\pi$
$907$	−0.521839	−0.0173274	−0.00866370	+	0.999962i	$0.502758\pi$
$908$	−4.60548	−0.152838
$909$	1.43762	0.0476828
$910$	29.4842	0.977391
$911$	−12.0419	−0.398967	−0.199484	−	0.979901i	$-0.563926\pi$
$911$	−12.0419	−0.398967	−0.199484	+	0.979901i	$0.563926\pi$
$912$	1.37784	0.0456247
$913$	−40.4271	−1.33794
$914$	−13.3573	−0.441819
$915$	10.0814	0.333280
$916$	−18.8360	−0.622359
$917$	17.4649	0.576743
$918$	34.0102	1.12250
$919$	45.3593	1.49626	0.748132	−	0.663550i	$-0.230951\pi$
$919$	45.3593	1.49626	0.748132	+	0.663550i	$0.230951\pi$
$920$	−22.0082	−0.725587
$921$	0.280297	0.00923611
$922$	−29.7300	−0.979106
$923$	6.46075	0.212658
$924$	9.03016	0.297071
$925$	−27.5770	−0.906726
$926$	−15.9808	−0.525162
$927$	13.5945	0.446503
$928$	−6.86242	−0.225270
$929$	−21.1047	−0.692421	−0.346211	−	0.938157i	$-0.612532\pi$
$929$	−21.1047	−0.692421	−0.346211	+	0.938157i	$0.612532\pi$
$930$	32.1402	1.05392
$931$	−2.65170	−0.0869061
$932$	13.9203	0.455976
$933$	9.46461	0.309857
$934$	10.1118	0.330869
$935$	66.9008	2.18789
$936$	4.40360	0.143936
$937$	21.8671	0.714368	0.357184	−	0.934034i	$-0.383737\pi$
$937$	21.8671	0.714368	0.357184	+	0.934034i	$0.383737\pi$
$938$	−10.2424	−0.334426
$939$	18.3031	0.597299
$940$	2.93290	0.0956606
$941$	9.59255	0.312708	0.156354	−	0.987701i	$-0.450026\pi$
$941$	9.59255	0.312708	0.156354	+	0.987701i	$0.450026\pi$
$942$	−10.8224	−0.352614
$943$	−55.7452	−1.81531
$944$	−10.5452	−0.343217
$945$	41.6811	1.35588
$946$	−0.956261	−0.0310907
$947$	−34.1196	−1.10874	−0.554368	−	0.832271i	$-0.687040\pi$
$947$	−34.1196	−1.10874	−0.554368	+	0.832271i	$0.687040\pi$
$948$	−3.83663	−0.124608
$949$	9.68810	0.314489
$950$	7.51017	0.243662
$951$	3.60695	0.116963
$952$	12.5493	0.406726
$953$	−41.1267	−1.33223	−0.666113	−	0.745851i	$-0.732043\pi$
$953$	−41.1267	−1.33223	−0.666113	+	0.745851i	$0.732043\pi$
$954$	−4.29625	−0.139096
$955$	67.3908	2.18071
$956$	−1.61370	−0.0521909
$957$	29.7176	0.960633
$958$	−18.6733	−0.603306
$959$	22.4534	0.725057
$960$	4.87337	0.157287
$961$	12.4949	0.403062
$962$	14.6790	0.473268
$963$	−1.26647	−0.0408115
$964$	−5.33913	−0.171962
$965$	−21.8022	−0.701838
$966$	17.8776	0.575203
$967$	−48.9448	−1.57396	−0.786980	−	0.616979i	$-0.788357\pi$
$967$	−48.9448	−1.57396	−0.786980	+	0.616979i	$0.788357\pi$
$968$	−1.12184	−0.0360572
$969$	−8.29200	−0.266377
$970$	10.2926	0.330474
$971$	−51.4521	−1.65118	−0.825589	−	0.564272i	$-0.809157\pi$
$971$	−51.4521	−1.65118	−0.825589	+	0.564272i	$0.809157\pi$
$972$	10.7786	0.345723
$973$	−2.97494	−0.0953720
$974$	7.80494	0.250087
$975$	−41.3662	−1.32478
$976$	2.06867	0.0662165
$977$	−16.1395	−0.516349	−0.258175	−	0.966098i	$-0.583121\pi$
$977$	−16.1395	−0.516349	−0.258175	+	0.966098i	$0.583121\pi$
$978$	−5.66085	−0.181014
$979$	9.72100	0.310684
$980$	−9.37900	−0.299601
$981$	−5.03716	−0.160824
$982$	30.4261	0.970937
$983$	−17.2121	−0.548981	−0.274490	−	0.961590i	$-0.588509\pi$
$983$	−17.2121	−0.548981	−0.274490	+	0.961590i	$0.588509\pi$
$984$	12.3439	0.393510
$985$	11.9864	0.381920
$986$	41.2989	1.31523
$987$	−2.38244	−0.0758340
$988$	−3.99759	−0.127180
$989$	−1.89317	−0.0601994
$990$	12.2456	0.389190
$991$	−6.25321	−0.198640	−0.0993198	−	0.995056i	$-0.531667\pi$
$991$	−6.25321	−0.198640	−0.0993198	+	0.995056i	$0.531667\pi$
$992$	6.59507	0.209394
$993$	2.13616	0.0677890
$994$	3.37011	0.106893
$995$	27.3405	0.866751
$996$	17.7228	0.561569
$997$	−10.4092	−0.329663	−0.164832	−	0.986322i	$-0.552708\pi$
$997$	−10.4092	−0.329663	−0.164832	+	0.986322i	$0.552708\pi$
$998$	−27.5678	−0.872644
$999$	20.7513	0.656541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.23	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.23	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.37784 q^{3} +1.00000 q^{4} +3.53697 q^{5} +1.37784 q^{6} -2.08526 q^{7} +1.00000 q^{8} -1.10156 q^{9} +3.53697 q^{10} -3.14295 q^{11} +1.37784 q^{12} -3.99759 q^{13} -2.08526 q^{14} +4.87337 q^{15} +1.00000 q^{16} -6.01813 q^{17} -1.10156 q^{18} +1.00000 q^{19} +3.53697 q^{20} -2.87314 q^{21} -3.14295 q^{22} -6.22231 q^{23} +1.37784 q^{24} +7.51017 q^{25} -3.99759 q^{26} -5.65129 q^{27} -2.08526 q^{28} -6.86242 q^{29} +4.87337 q^{30} +6.59507 q^{31} +1.00000 q^{32} -4.33048 q^{33} -6.01813 q^{34} -7.37550 q^{35} -1.10156 q^{36} -3.67195 q^{37} +1.00000 q^{38} -5.50802 q^{39} +3.53697 q^{40} +8.95892 q^{41} -2.87314 q^{42} +0.304255 q^{43} -3.14295 q^{44} -3.89620 q^{45} -6.22231 q^{46} +0.829211 q^{47} +1.37784 q^{48} -2.65170 q^{49} +7.51017 q^{50} -8.29200 q^{51} -3.99759 q^{52} +3.90013 q^{53} -5.65129 q^{54} -11.1165 q^{55} -2.08526 q^{56} +1.37784 q^{57} -6.86242 q^{58} -10.5452 q^{59} +4.87337 q^{60} +2.06867 q^{61} +6.59507 q^{62} +2.29705 q^{63} +1.00000 q^{64} -14.1394 q^{65} -4.33048 q^{66} +4.91181 q^{67} -6.01813 q^{68} -8.57334 q^{69} -7.37550 q^{70} -1.61616 q^{71} -1.10156 q^{72} -2.42349 q^{73} -3.67195 q^{74} +10.3478 q^{75} +1.00000 q^{76} +6.55387 q^{77} -5.50802 q^{78} -2.78453 q^{79} +3.53697 q^{80} -4.48186 q^{81} +8.95892 q^{82} +12.8628 q^{83} -2.87314 q^{84} -21.2859 q^{85} +0.304255 q^{86} -9.45530 q^{87} -3.14295 q^{88} -3.09295 q^{89} -3.89620 q^{90} +8.33600 q^{91} -6.22231 q^{92} +9.08693 q^{93} +0.829211 q^{94} +3.53697 q^{95} +1.37784 q^{96} +2.90999 q^{97} -2.65170 q^{98} +3.46217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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