LMFDB - Embedded newform 8018.2.a.d.1.4

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			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.56870 q^{3} +1.00000 q^{4} -1.11955 q^{5} -2.56870 q^{6} -1.44974 q^{7} +1.00000 q^{8} +3.59821 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.56870 q^{3} +1.00000 q^{4} -1.11955 q^{5} -2.56870 q^{6} -1.44974 q^{7} +1.00000 q^{8} +3.59821 q^{9} -1.11955 q^{10} -1.59607 q^{11} -2.56870 q^{12} +3.12799 q^{13} -1.44974 q^{14} +2.87579 q^{15} +1.00000 q^{16} -5.27438 q^{17} +3.59821 q^{18} +1.00000 q^{19} -1.11955 q^{20} +3.72395 q^{21} -1.59607 q^{22} -0.783250 q^{23} -2.56870 q^{24} -3.74661 q^{25} +3.12799 q^{26} -1.53663 q^{27} -1.44974 q^{28} +8.48094 q^{29} +2.87579 q^{30} +4.24784 q^{31} +1.00000 q^{32} +4.09983 q^{33} -5.27438 q^{34} +1.62306 q^{35} +3.59821 q^{36} -7.23807 q^{37} +1.00000 q^{38} -8.03487 q^{39} -1.11955 q^{40} -0.308723 q^{41} +3.72395 q^{42} +10.5372 q^{43} -1.59607 q^{44} -4.02838 q^{45} -0.783250 q^{46} +1.70974 q^{47} -2.56870 q^{48} -4.89825 q^{49} -3.74661 q^{50} +13.5483 q^{51} +3.12799 q^{52} +6.97906 q^{53} -1.53663 q^{54} +1.78689 q^{55} -1.44974 q^{56} -2.56870 q^{57} +8.48094 q^{58} -12.0572 q^{59} +2.87579 q^{60} -0.529483 q^{61} +4.24784 q^{62} -5.21648 q^{63} +1.00000 q^{64} -3.50195 q^{65} +4.09983 q^{66} +4.61367 q^{67} -5.27438 q^{68} +2.01193 q^{69} +1.62306 q^{70} -2.79282 q^{71} +3.59821 q^{72} +13.8081 q^{73} -7.23807 q^{74} +9.62390 q^{75} +1.00000 q^{76} +2.31390 q^{77} -8.03487 q^{78} -5.27871 q^{79} -1.11955 q^{80} -6.84751 q^{81} -0.308723 q^{82} +9.23497 q^{83} +3.72395 q^{84} +5.90493 q^{85} +10.5372 q^{86} -21.7850 q^{87} -1.59607 q^{88} -4.76645 q^{89} -4.02838 q^{90} -4.53478 q^{91} -0.783250 q^{92} -10.9114 q^{93} +1.70974 q^{94} -1.11955 q^{95} -2.56870 q^{96} -12.8257 q^{97} -4.89825 q^{98} -5.74301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.56870	−1.48304	−0.741519	−	0.670931i	$-0.765894\pi$
$3$	−2.56870	−1.48304	−0.741519	+	0.670931i	$0.765894\pi$
$4$	1.00000	0.500000
$5$	−1.11955	−0.500678	−0.250339	−	0.968158i	$-0.580542\pi$
$5$	−1.11955	−0.500678	−0.250339	+	0.968158i	$0.580542\pi$
$6$	−2.56870	−1.04867
$7$	−1.44974	−0.547951	−0.273975	−	0.961737i	$-0.588339\pi$
$7$	−1.44974	−0.547951	−0.273975	+	0.961737i	$0.588339\pi$
$8$	1.00000	0.353553
$9$	3.59821	1.19940
$10$	−1.11955	−0.354033
$11$	−1.59607	−0.481234	−0.240617	−	0.970620i	$-0.577350\pi$
$11$	−1.59607	−0.481234	−0.240617	+	0.970620i	$0.577350\pi$
$12$	−2.56870	−0.741519
$13$	3.12799	0.867549	0.433775	−	0.901021i	$-0.357181\pi$
$13$	3.12799	0.867549	0.433775	+	0.901021i	$0.357181\pi$
$14$	−1.44974	−0.387460
$15$	2.87579	0.742525
$16$	1.00000	0.250000
$17$	−5.27438	−1.27922	−0.639612	−	0.768698i	$-0.720905\pi$
$17$	−5.27438	−1.27922	−0.639612	+	0.768698i	$0.720905\pi$
$18$	3.59821	0.848107
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.11955	−0.250339
$21$	3.72395	0.812632
$22$	−1.59607	−0.340284
$23$	−0.783250	−0.163319	−0.0816594	−	0.996660i	$-0.526022\pi$
$23$	−0.783250	−0.163319	−0.0816594	+	0.996660i	$0.526022\pi$
$24$	−2.56870	−0.524333
$25$	−3.74661	−0.749321
$26$	3.12799	0.613450
$27$	−1.53663	−0.295724
$28$	−1.44974	−0.273975
$29$	8.48094	1.57487	0.787435	−	0.616397i	$-0.211408\pi$
$29$	8.48094	1.57487	0.787435	+	0.616397i	$0.211408\pi$
$30$	2.87579	0.525044
$31$	4.24784	0.762934	0.381467	−	0.924382i	$-0.375419\pi$
$31$	4.24784	0.762934	0.381467	+	0.924382i	$0.375419\pi$
$32$	1.00000	0.176777
$33$	4.09983	0.713689
$34$	−5.27438	−0.904548
$35$	1.62306	0.274347
$36$	3.59821	0.599702
$37$	−7.23807	−1.18993	−0.594966	−	0.803751i	$-0.702834\pi$
$37$	−7.23807	−1.18993	−0.594966	+	0.803751i	$0.702834\pi$
$38$	1.00000	0.162221
$39$	−8.03487	−1.28661
$40$	−1.11955	−0.177016
$41$	−0.308723	−0.0482144	−0.0241072	−	0.999709i	$-0.507674\pi$
$41$	−0.308723	−0.0482144	−0.0241072	+	0.999709i	$0.507674\pi$
$42$	3.72395	0.574618
$43$	10.5372	1.60690	0.803452	−	0.595370i	$-0.202995\pi$
$43$	10.5372	1.60690	0.803452	+	0.595370i	$0.202995\pi$
$44$	−1.59607	−0.240617
$45$	−4.02838	−0.600515
$46$	−0.783250	−0.115484
$47$	1.70974	0.249392	0.124696	−	0.992195i	$-0.460204\pi$
$47$	1.70974	0.249392	0.124696	+	0.992195i	$0.460204\pi$
$48$	−2.56870	−0.370760
$49$	−4.89825	−0.699750
$50$	−3.74661	−0.529850
$51$	13.5483	1.89714
$52$	3.12799	0.433775
$53$	6.97906	0.958647	0.479324	−	0.877638i	$-0.340882\pi$
$53$	6.97906	0.958647	0.479324	+	0.877638i	$0.340882\pi$
$54$	−1.53663	−0.209108
$55$	1.78689	0.240944
$56$	−1.44974	−0.193730
$57$	−2.56870	−0.340232
$58$	8.48094	1.11360
$59$	−12.0572	−1.56971	−0.784854	−	0.619681i	$-0.787262\pi$
$59$	−12.0572	−1.56971	−0.784854	+	0.619681i	$0.787262\pi$
$60$	2.87579	0.371262
$61$	−0.529483	−0.0677934	−0.0338967	−	0.999425i	$-0.510792\pi$
$61$	−0.529483	−0.0677934	−0.0338967	+	0.999425i	$0.510792\pi$
$62$	4.24784	0.539476
$63$	−5.21648	−0.657215
$64$	1.00000	0.125000
$65$	−3.50195	−0.434363
$66$	4.09983	0.504655
$67$	4.61367	0.563649	0.281825	−	0.959466i	$-0.409060\pi$
$67$	4.61367	0.563649	0.281825	+	0.959466i	$0.409060\pi$
$68$	−5.27438	−0.639612
$69$	2.01193	0.242208
$70$	1.62306	0.193993
$71$	−2.79282	−0.331447	−0.165723	−	0.986172i	$-0.552996\pi$
$71$	−2.79282	−0.331447	−0.165723	+	0.986172i	$0.552996\pi$
$72$	3.59821	0.424053
$73$	13.8081	1.61612	0.808058	−	0.589103i	$-0.200519\pi$
$73$	13.8081	1.61612	0.808058	+	0.589103i	$0.200519\pi$
$74$	−7.23807	−0.841409
$75$	9.62390	1.11127
$76$	1.00000	0.114708
$77$	2.31390	0.263693
$78$	−8.03487	−0.909770
$79$	−5.27871	−0.593901	−0.296951	−	0.954893i	$-0.595970\pi$
$79$	−5.27871	−0.593901	−0.296951	+	0.954893i	$0.595970\pi$
$80$	−1.11955	−0.125170
$81$	−6.84751	−0.760834
$82$	−0.308723	−0.0340927
$83$	9.23497	1.01367	0.506835	−	0.862043i	$-0.330815\pi$
$83$	9.23497	1.01367	0.506835	+	0.862043i	$0.330815\pi$
$84$	3.72395	0.406316
$85$	5.90493	0.640480
$86$	10.5372	1.13625
$87$	−21.7850	−2.33559
$88$	−1.59607	−0.170142
$89$	−4.76645	−0.505243	−0.252621	−	0.967565i	$-0.581293\pi$
$89$	−4.76645	−0.505243	−0.252621	+	0.967565i	$0.581293\pi$
$90$	−4.02838	−0.424628
$91$	−4.53478	−0.475374
$92$	−0.783250	−0.0816594
$93$	−10.9114	−1.13146
$94$	1.70974	0.176347
$95$	−1.11955	−0.114863
$96$	−2.56870	−0.262167
$97$	−12.8257	−1.30225	−0.651125	−	0.758970i	$-0.725703\pi$
$97$	−12.8257	−1.30225	−0.651125	+	0.758970i	$0.725703\pi$
$98$	−4.89825	−0.494798
$99$	−5.74301	−0.577195
$100$	−3.74661	−0.374661
$101$	14.1213	1.40512	0.702560	−	0.711625i	$-0.252040\pi$
$101$	14.1213	1.40512	0.702560	+	0.711625i	$0.252040\pi$
$102$	13.5483	1.34148
$103$	10.7149	1.05577	0.527884	−	0.849316i	$-0.322985\pi$
$103$	10.7149	1.05577	0.527884	+	0.849316i	$0.322985\pi$
$104$	3.12799	0.306725
$105$	−4.16915	−0.406867
$106$	6.97906	0.677866
$107$	−10.6703	−1.03154	−0.515770	−	0.856727i	$-0.672494\pi$
$107$	−10.6703	−1.03154	−0.515770	+	0.856727i	$0.672494\pi$
$108$	−1.53663	−0.147862
$109$	−9.54223	−0.913980	−0.456990	−	0.889472i	$-0.651072\pi$
$109$	−9.54223	−0.913980	−0.456990	+	0.889472i	$0.651072\pi$
$110$	1.78689	0.170373
$111$	18.5924	1.76471
$112$	−1.44974	−0.136988
$113$	3.61727	0.340284	0.170142	−	0.985420i	$-0.445577\pi$
$113$	3.61727	0.340284	0.170142	+	0.985420i	$0.445577\pi$
$114$	−2.56870	−0.240581
$115$	0.876887	0.0817702
$116$	8.48094	0.787435
$117$	11.2552	1.04054
$118$	−12.0572	−1.10995
$119$	7.64649	0.700952
$120$	2.87579	0.262522
$121$	−8.45255	−0.768413
$122$	−0.529483	−0.0479372
$123$	0.793016	0.0715038
$124$	4.24784	0.381467
$125$	9.79227	0.875847
$126$	−5.21648	−0.464721
$127$	−8.96922	−0.795890	−0.397945	−	0.917409i	$-0.630277\pi$
$127$	−8.96922	−0.795890	−0.397945	+	0.917409i	$0.630277\pi$
$128$	1.00000	0.0883883
$129$	−27.0668	−2.38310
$130$	−3.50195	−0.307141
$131$	19.2311	1.68023	0.840115	−	0.542408i	$-0.182487\pi$
$131$	19.2311	1.68023	0.840115	+	0.542408i	$0.182487\pi$
$132$	4.09983	0.356845
$133$	−1.44974	−0.125709
$134$	4.61367	0.398560
$135$	1.72033	0.148062
$136$	−5.27438	−0.452274
$137$	8.29430	0.708630	0.354315	−	0.935126i	$-0.384714\pi$
$137$	8.29430	0.708630	0.354315	+	0.935126i	$0.384714\pi$
$138$	2.01193	0.171267
$139$	2.58268	0.219060	0.109530	−	0.993983i	$-0.465065\pi$
$139$	2.58268	0.219060	0.109530	+	0.993983i	$0.465065\pi$
$140$	1.62306	0.137174
$141$	−4.39182	−0.369858
$142$	−2.79282	−0.234368
$143$	−4.99251	−0.417495
$144$	3.59821	0.299851
$145$	−9.49484	−0.788503
$146$	13.8081	1.14277
$147$	12.5821	1.03776
$148$	−7.23807	−0.594966
$149$	−3.79596	−0.310977	−0.155489	−	0.987838i	$-0.549695\pi$
$149$	−3.79596	−0.310977	−0.155489	+	0.987838i	$0.549695\pi$
$150$	9.62390	0.785789
$151$	−4.42526	−0.360122	−0.180061	−	0.983655i	$-0.557630\pi$
$151$	−4.42526	−0.360122	−0.180061	+	0.983655i	$0.557630\pi$
$152$	1.00000	0.0811107
$153$	−18.9783	−1.53431
$154$	2.31390	0.186459
$155$	−4.75567	−0.381984
$156$	−8.03487	−0.643305
$157$	−10.9439	−0.873422	−0.436711	−	0.899602i	$-0.643857\pi$
$157$	−10.9439	−0.873422	−0.436711	+	0.899602i	$0.643857\pi$
$158$	−5.27871	−0.419951
$159$	−17.9271	−1.42171
$160$	−1.11955	−0.0885082
$161$	1.13551	0.0894907
$162$	−6.84751	−0.537991
$163$	−7.68585	−0.602002	−0.301001	−	0.953624i	$-0.597321\pi$
$163$	−7.68585	−0.602002	−0.301001	+	0.953624i	$0.597321\pi$
$164$	−0.308723	−0.0241072
$165$	−4.58997	−0.357329
$166$	9.23497	0.716773
$167$	12.0757	0.934447	0.467223	−	0.884139i	$-0.345254\pi$
$167$	12.0757	0.934447	0.467223	+	0.884139i	$0.345254\pi$
$168$	3.72395	0.287309
$169$	−3.21566	−0.247358
$170$	5.90493	0.452887
$171$	3.59821	0.275162
$172$	10.5372	0.803452
$173$	−12.7449	−0.968976	−0.484488	−	0.874798i	$-0.660994\pi$
$173$	−12.7449	−0.968976	−0.484488	+	0.874798i	$0.660994\pi$
$174$	−21.7850	−1.65151
$175$	5.43161	0.410591
$176$	−1.59607	−0.120309
$177$	30.9712	2.32794
$178$	−4.76645	−0.357260
$179$	20.9073	1.56269	0.781344	−	0.624101i	$-0.214535\pi$
$179$	20.9073	1.56269	0.781344	+	0.624101i	$0.214535\pi$
$180$	−4.02838	−0.300258
$181$	1.33857	0.0994954	0.0497477	−	0.998762i	$-0.484158\pi$
$181$	1.33857	0.0994954	0.0497477	+	0.998762i	$0.484158\pi$
$182$	−4.53478	−0.336140
$183$	1.36008	0.100540
$184$	−0.783250	−0.0577419
$185$	8.10338	0.595773
$186$	−10.9114	−0.800063
$187$	8.41830	0.615607
$188$	1.70974	0.124696
$189$	2.22771	0.162042
$190$	−1.11955	−0.0812207
$191$	−21.7762	−1.57567	−0.787834	−	0.615888i	$-0.788797\pi$
$191$	−21.7762	−1.57567	−0.787834	+	0.615888i	$0.788797\pi$
$192$	−2.56870	−0.185380
$193$	−4.51037	−0.324663	−0.162332	−	0.986736i	$-0.551901\pi$
$193$	−4.51037	−0.324663	−0.162332	+	0.986736i	$0.551901\pi$
$194$	−12.8257	−0.920830
$195$	8.99544	0.644177
$196$	−4.89825	−0.349875
$197$	−6.26163	−0.446122	−0.223061	−	0.974804i	$-0.571605\pi$
$197$	−6.26163	−0.446122	−0.223061	+	0.974804i	$0.571605\pi$
$198$	−5.74301	−0.408138
$199$	−6.13531	−0.434921	−0.217460	−	0.976069i	$-0.569777\pi$
$199$	−6.13531	−0.434921	−0.217460	+	0.976069i	$0.569777\pi$
$200$	−3.74661	−0.264925
$201$	−11.8511	−0.835914
$202$	14.1213	0.993569
$203$	−12.2952	−0.862952
$204$	13.5483	0.948570
$205$	0.345631	0.0241399
$206$	10.7149	0.746541
$207$	−2.81830	−0.195885
$208$	3.12799	0.216887
$209$	−1.59607	−0.110403
$210$	−4.16915	−0.287699
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.97906	0.479324
$213$	7.17391	0.491548
$214$	−10.6703	−0.729409
$215$	−11.7969	−0.804541
$216$	−1.53663	−0.104554
$217$	−6.15827	−0.418050
$218$	−9.54223	−0.646281
$219$	−35.4688	−2.39676
$220$	1.78689	0.120472
$221$	−16.4982	−1.10979
$222$	18.5924	1.24784
$223$	−13.4467	−0.900459	−0.450229	−	0.892913i	$-0.648658\pi$
$223$	−13.4467	−0.900459	−0.450229	+	0.892913i	$0.648658\pi$
$224$	−1.44974	−0.0968650
$225$	−13.4811	−0.898739
$226$	3.61727	0.240617
$227$	−14.0539	−0.932790	−0.466395	−	0.884577i	$-0.654447\pi$
$227$	−14.0539	−0.932790	−0.466395	+	0.884577i	$0.654447\pi$
$228$	−2.56870	−0.170116
$229$	3.54804	0.234461	0.117230	−	0.993105i	$-0.462598\pi$
$229$	3.54804	0.234461	0.117230	+	0.993105i	$0.462598\pi$
$230$	0.876887	0.0578202
$231$	−5.94370	−0.391067
$232$	8.48094	0.556801
$233$	−26.5635	−1.74024	−0.870118	−	0.492844i	$-0.835957\pi$
$233$	−26.5635	−1.74024	−0.870118	+	0.492844i	$0.835957\pi$
$234$	11.2552	0.735774
$235$	−1.91414	−0.124865
$236$	−12.0572	−0.784854
$237$	13.5594	0.880778
$238$	7.64649	0.495648
$239$	−4.33166	−0.280192	−0.140096	−	0.990138i	$-0.544741\pi$
$239$	−4.33166	−0.280192	−0.140096	+	0.990138i	$0.544741\pi$
$240$	2.87579	0.185631
$241$	17.5154	1.12827	0.564135	−	0.825683i	$-0.309210\pi$
$241$	17.5154	1.12827	0.564135	+	0.825683i	$0.309210\pi$
$242$	−8.45255	−0.543350
$243$	22.1991	1.42407
$244$	−0.529483	−0.0338967
$245$	5.48383	0.350349
$246$	0.793016	0.0505608
$247$	3.12799	0.199029
$248$	4.24784	0.269738
$249$	−23.7218	−1.50331
$250$	9.79227	0.619317
$251$	17.9688	1.13418	0.567091	−	0.823655i	$-0.308069\pi$
$251$	17.9688	1.13418	0.567091	+	0.823655i	$0.308069\pi$
$252$	−5.21648	−0.328607
$253$	1.25012	0.0785947
$254$	−8.96922	−0.562779
$255$	−15.1680	−0.949856
$256$	1.00000	0.0625000
$257$	−13.8193	−0.862023	−0.431011	−	0.902346i	$-0.641843\pi$
$257$	−13.8193	−0.862023	−0.431011	+	0.902346i	$0.641843\pi$
$258$	−27.0668	−1.68511
$259$	10.4933	0.652024
$260$	−3.50195	−0.217181
$261$	30.5162	1.88891
$262$	19.2311	1.18810
$263$	19.3564	1.19357	0.596783	−	0.802402i	$-0.296445\pi$
$263$	19.3564	1.19357	0.596783	+	0.802402i	$0.296445\pi$
$264$	4.09983	0.252327
$265$	−7.81341	−0.479974
$266$	−1.44974	−0.0888894
$267$	12.2436	0.749294
$268$	4.61367	0.281825
$269$	−7.48232	−0.456205	−0.228103	−	0.973637i	$-0.573252\pi$
$269$	−7.48232	−0.456205	−0.228103	+	0.973637i	$0.573252\pi$
$270$	1.72033	0.104696
$271$	22.9387	1.39343	0.696713	−	0.717350i	$-0.254645\pi$
$271$	22.9387	1.39343	0.696713	+	0.717350i	$0.254645\pi$
$272$	−5.27438	−0.319806
$273$	11.6485	0.704999
$274$	8.29430	0.501077
$275$	5.97986	0.360599
$276$	2.01193	0.121104
$277$	−22.6938	−1.36354	−0.681770	−	0.731567i	$-0.738789\pi$
$277$	−22.6938	−1.36354	−0.681770	+	0.731567i	$0.738789\pi$
$278$	2.58268	0.154899
$279$	15.2846	0.915066
$280$	1.62306	0.0969963
$281$	11.2472	0.670951	0.335475	−	0.942049i	$-0.391103\pi$
$281$	11.2472	0.670951	0.335475	+	0.942049i	$0.391103\pi$
$282$	−4.39182	−0.261529
$283$	−33.5810	−1.99618	−0.998091	−	0.0617538i	$-0.980331\pi$
$283$	−33.5810	−1.99618	−0.998091	+	0.0617538i	$0.980331\pi$
$284$	−2.79282	−0.165723
$285$	2.87579	0.170347
$286$	−4.99251	−0.295213
$287$	0.447568	0.0264191
$288$	3.59821	0.212027
$289$	10.8191	0.636415
$290$	−9.49484	−0.557556
$291$	32.9453	1.93129
$292$	13.8081	0.808058
$293$	−16.6218	−0.971057	−0.485528	−	0.874221i	$-0.661373\pi$
$293$	−16.6218	−0.971057	−0.485528	+	0.874221i	$0.661373\pi$
$294$	12.5821	0.733804
$295$	13.4986	0.785918
$296$	−7.23807	−0.420704
$297$	2.45257	0.142312
$298$	−3.79596	−0.219894
$299$	−2.45000	−0.141687
$300$	9.62390	0.555636
$301$	−15.2762	−0.880504
$302$	−4.42526	−0.254645
$303$	−36.2733	−2.08385
$304$	1.00000	0.0573539
$305$	0.592783	0.0339427
$306$	−18.9783	−1.08492
$307$	−23.7172	−1.35361	−0.676806	−	0.736162i	$-0.736636\pi$
$307$	−23.7172	−1.35361	−0.676806	+	0.736162i	$0.736636\pi$
$308$	2.31390	0.131846
$309$	−27.5233	−1.56575
$310$	−4.75567	−0.270104
$311$	−31.4708	−1.78454	−0.892272	−	0.451498i	$-0.850890\pi$
$311$	−31.4708	−1.78454	−0.892272	+	0.451498i	$0.850890\pi$
$312$	−8.03487	−0.454885
$313$	−20.0011	−1.13053	−0.565265	−	0.824910i	$-0.691226\pi$
$313$	−20.0011	−1.13053	−0.565265	+	0.824910i	$0.691226\pi$
$314$	−10.9439	−0.617603
$315$	5.84011	0.329053
$316$	−5.27871	−0.296951
$317$	−20.0539	−1.12634	−0.563169	−	0.826341i	$-0.690418\pi$
$317$	−20.0539	−1.12634	−0.563169	+	0.826341i	$0.690418\pi$
$318$	−17.9271	−1.00530
$319$	−13.5362	−0.757882
$320$	−1.11955	−0.0625848
$321$	27.4089	1.52981
$322$	1.13551	0.0632795
$323$	−5.27438	−0.293474
$324$	−6.84751	−0.380417
$325$	−11.7194	−0.650073
$326$	−7.68585	−0.425680
$327$	24.5111	1.35547
$328$	−0.308723	−0.0170464
$329$	−2.47869	−0.136654
$330$	−4.58997	−0.252669
$331$	6.26128	0.344151	0.172075	−	0.985084i	$-0.444953\pi$
$331$	6.26128	0.344151	0.172075	+	0.985084i	$0.444953\pi$
$332$	9.23497	0.506835
$333$	−26.0441	−1.42721
$334$	12.0757	0.660754
$335$	−5.16523	−0.282207
$336$	3.72395	0.203158
$337$	−14.6756	−0.799431	−0.399715	−	0.916639i	$-0.630891\pi$
$337$	−14.6756	−0.799431	−0.399715	+	0.916639i	$0.630891\pi$
$338$	−3.21566	−0.174909
$339$	−9.29168	−0.504655
$340$	5.90493	0.320240
$341$	−6.77986	−0.367150
$342$	3.59821	0.194569
$343$	17.2494	0.931380
$344$	10.5372	0.568126
$345$	−2.25246	−0.121268
$346$	−12.7449	−0.685170
$347$	−31.6736	−1.70033	−0.850163	−	0.526520i	$-0.823497\pi$
$347$	−31.6736	−1.70033	−0.850163	+	0.526520i	$0.823497\pi$
$348$	−21.7850	−1.16780
$349$	−4.24754	−0.227366	−0.113683	−	0.993517i	$-0.536265\pi$
$349$	−4.24754	−0.227366	−0.113683	+	0.993517i	$0.536265\pi$
$350$	5.43161	0.290332
$351$	−4.80655	−0.256555
$352$	−1.59607	−0.0850710
$353$	24.0277	1.27886	0.639432	−	0.768848i	$-0.279169\pi$
$353$	24.0277	1.27886	0.639432	+	0.768848i	$0.279169\pi$
$354$	30.9712	1.64610
$355$	3.12670	0.165948
$356$	−4.76645	−0.252621
$357$	−19.6415	−1.03954
$358$	20.9073	1.10499
$359$	23.1048	1.21943	0.609713	−	0.792622i	$-0.291285\pi$
$359$	23.1048	1.21943	0.609713	+	0.792622i	$0.291285\pi$
$360$	−4.02838	−0.212314
$361$	1.00000	0.0526316
$362$	1.33857	0.0703539
$363$	21.7120	1.13959
$364$	−4.53478	−0.237687
$365$	−15.4589	−0.809154
$366$	1.36008	0.0710927
$367$	9.79259	0.511169	0.255584	−	0.966787i	$-0.417732\pi$
$367$	9.79259	0.511169	0.255584	+	0.966787i	$0.417732\pi$
$368$	−0.783250	−0.0408297
$369$	−1.11085	−0.0578285
$370$	8.10338	0.421275
$371$	−10.1178	−0.525292
$372$	−10.9114	−0.565730
$373$	−14.7854	−0.765561	−0.382781	−	0.923839i	$-0.625033\pi$
$373$	−14.7854	−0.765561	−0.382781	+	0.923839i	$0.625033\pi$
$374$	8.41830	0.435300
$375$	−25.1534	−1.29891
$376$	1.70974	0.0881733
$377$	26.5283	1.36628
$378$	2.22771	0.114581
$379$	−32.9460	−1.69232	−0.846160	−	0.532929i	$-0.821091\pi$
$379$	−32.9460	−1.69232	−0.846160	+	0.532929i	$0.821091\pi$
$380$	−1.11955	−0.0574317
$381$	23.0392	1.18034
$382$	−21.7762	−1.11416
$383$	−2.22797	−0.113844	−0.0569220	−	0.998379i	$-0.518129\pi$
$383$	−2.22797	−0.113844	−0.0569220	+	0.998379i	$0.518129\pi$
$384$	−2.56870	−0.131083
$385$	−2.59052	−0.132025
$386$	−4.51037	−0.229572
$387$	37.9150	1.92733
$388$	−12.8257	−0.651125
$389$	−15.9564	−0.809022	−0.404511	−	0.914533i	$-0.632558\pi$
$389$	−15.9564	−0.809022	−0.404511	+	0.914533i	$0.632558\pi$
$390$	8.99544	0.455502
$391$	4.13115	0.208921
$392$	−4.89825	−0.247399
$393$	−49.3989	−2.49185
$394$	−6.26163	−0.315456
$395$	5.90978	0.297353
$396$	−5.74301	−0.288597
$397$	−16.5148	−0.828855	−0.414427	−	0.910082i	$-0.636018\pi$
$397$	−16.5148	−0.828855	−0.414427	+	0.910082i	$0.636018\pi$
$398$	−6.13531	−0.307535
$399$	3.72395	0.186431
$400$	−3.74661	−0.187330
$401$	−1.36916	−0.0683726	−0.0341863	−	0.999415i	$-0.510884\pi$
$401$	−1.36916	−0.0683726	−0.0341863	+	0.999415i	$0.510884\pi$
$402$	−11.8511	−0.591080
$403$	13.2872	0.661883
$404$	14.1213	0.702560
$405$	7.66613	0.380933
$406$	−12.2952	−0.610199
$407$	11.5525	0.572636
$408$	13.5483	0.670740
$409$	−33.9138	−1.67693	−0.838464	−	0.544958i	$-0.816546\pi$
$409$	−33.9138	−1.67693	−0.838464	+	0.544958i	$0.816546\pi$
$410$	0.345631	0.0170695
$411$	−21.3056	−1.05093
$412$	10.7149	0.527884
$413$	17.4798	0.860123
$414$	−2.81830	−0.138512
$415$	−10.3390	−0.507522
$416$	3.12799	0.153362
$417$	−6.63413	−0.324875
$418$	−1.59607	−0.0780665
$419$	−4.70812	−0.230007	−0.115003	−	0.993365i	$-0.536688\pi$
$419$	−4.70812	−0.230007	−0.115003	+	0.993365i	$0.536688\pi$
$420$	−4.16915	−0.203434
$421$	−5.43867	−0.265065	−0.132532	−	0.991179i	$-0.542311\pi$
$421$	−5.43867	−0.265065	−0.132532	+	0.991179i	$0.542311\pi$
$422$	−1.00000	−0.0486792
$423$	6.15202	0.299121
$424$	6.97906	0.338933
$425$	19.7610	0.958550
$426$	7.17391	0.347577
$427$	0.767614	0.0371474
$428$	−10.6703	−0.515770
$429$	12.8243	0.619161
$430$	−11.7969	−0.568897
$431$	24.7539	1.19235	0.596177	−	0.802853i	$-0.296686\pi$
$431$	24.7539	1.19235	0.596177	+	0.802853i	$0.296686\pi$
$432$	−1.53663	−0.0739309
$433$	−17.4451	−0.838360	−0.419180	−	0.907903i	$-0.637682\pi$
$433$	−17.4451	−0.838360	−0.419180	+	0.907903i	$0.637682\pi$
$434$	−6.15827	−0.295606
$435$	24.3894	1.16938
$436$	−9.54223	−0.456990
$437$	−0.783250	−0.0374679
$438$	−35.4688	−1.69477
$439$	27.0520	1.29112	0.645561	−	0.763708i	$-0.276623\pi$
$439$	27.0520	1.29112	0.645561	+	0.763708i	$0.276623\pi$
$440$	1.78689	0.0851864
$441$	−17.6249	−0.839283
$442$	−16.4982	−0.784740
$443$	−11.9016	−0.565460	−0.282730	−	0.959199i	$-0.591240\pi$
$443$	−11.9016	−0.565460	−0.282730	+	0.959199i	$0.591240\pi$
$444$	18.5924	0.882357
$445$	5.33628	0.252964
$446$	−13.4467	−0.636721
$447$	9.75068	0.461191
$448$	−1.44974	−0.0684939
$449$	−10.4434	−0.492855	−0.246427	−	0.969161i	$-0.579257\pi$
$449$	−10.4434	−0.492855	−0.246427	+	0.969161i	$0.579257\pi$
$450$	−13.4811	−0.635505
$451$	0.492745	0.0232024
$452$	3.61727	0.170142
$453$	11.3672	0.534075
$454$	−14.0539	−0.659582
$455$	5.07692	0.238010
$456$	−2.56870	−0.120290
$457$	−6.79423	−0.317821	−0.158910	−	0.987293i	$-0.550798\pi$
$457$	−6.79423	−0.317821	−0.158910	+	0.987293i	$0.550798\pi$
$458$	3.54804	0.165789
$459$	8.10474	0.378297
$460$	0.876887	0.0408851
$461$	−16.7365	−0.779498	−0.389749	−	0.920921i	$-0.627438\pi$
$461$	−16.7365	−0.779498	−0.389749	+	0.920921i	$0.627438\pi$
$462$	−5.94370	−0.276526
$463$	1.46440	0.0680564	0.0340282	−	0.999421i	$-0.489166\pi$
$463$	1.46440	0.0680564	0.0340282	+	0.999421i	$0.489166\pi$
$464$	8.48094	0.393718
$465$	12.2159	0.566497
$466$	−26.5635	−1.23053
$467$	−10.8327	−0.501278	−0.250639	−	0.968081i	$-0.580641\pi$
$467$	−10.8327	−0.501278	−0.250639	+	0.968081i	$0.580641\pi$
$468$	11.2552	0.520271
$469$	−6.68863	−0.308852
$470$	−1.91414	−0.0882929
$471$	28.1117	1.29532
$472$	−12.0572	−0.554975
$473$	−16.8181	−0.773297
$474$	13.5594	0.622804
$475$	−3.74661	−0.171906
$476$	7.64649	0.350476
$477$	25.1121	1.14981
$478$	−4.33166	−0.198125
$479$	−20.9816	−0.958672	−0.479336	−	0.877631i	$-0.659123\pi$
$479$	−20.9816	−0.958672	−0.479336	+	0.877631i	$0.659123\pi$
$480$	2.87579	0.131261
$481$	−22.6406	−1.03232
$482$	17.5154	0.797807
$483$	−2.91678	−0.132718
$484$	−8.45255	−0.384207
$485$	14.3590	0.652008
$486$	22.1991	1.00697
$487$	−19.9002	−0.901764	−0.450882	−	0.892584i	$-0.648890\pi$
$487$	−19.9002	−0.901764	−0.450882	+	0.892584i	$0.648890\pi$
$488$	−0.529483	−0.0239686
$489$	19.7426	0.892792
$490$	5.48383	0.247734
$491$	41.2744	1.86269	0.931345	−	0.364139i	$-0.118637\pi$
$491$	41.2744	1.86269	0.931345	+	0.364139i	$0.118637\pi$
$492$	0.793016	0.0357519
$493$	−44.7317	−2.01461
$494$	3.12799	0.140735
$495$	6.42959	0.288989
$496$	4.24784	0.190733
$497$	4.04887	0.181617
$498$	−23.7218	−1.06300
$499$	−21.2431	−0.950972	−0.475486	−	0.879723i	$-0.657728\pi$
$499$	−21.2431	−0.950972	−0.475486	+	0.879723i	$0.657728\pi$
$500$	9.79227	0.437923
$501$	−31.0189	−1.38582
$502$	17.9688	0.801988
$503$	24.6494	1.09906	0.549531	−	0.835473i	$-0.314806\pi$
$503$	24.6494	1.09906	0.549531	+	0.835473i	$0.314806\pi$
$504$	−5.21648	−0.232360
$505$	−15.8095	−0.703512
$506$	1.25012	0.0555748
$507$	8.26006	0.366842
$508$	−8.96922	−0.397945
$509$	−32.1847	−1.42656	−0.713281	−	0.700878i	$-0.752792\pi$
$509$	−32.1847	−1.42656	−0.713281	+	0.700878i	$0.752792\pi$
$510$	−15.1680	−0.671650
$511$	−20.0182	−0.885552
$512$	1.00000	0.0441942
$513$	−1.53663	−0.0678437
$514$	−13.8193	−0.609542
$515$	−11.9958	−0.528600
$516$	−27.0668	−1.19155
$517$	−2.72888	−0.120016
$518$	10.4933	0.461051
$519$	32.7378	1.43703
$520$	−3.50195	−0.153570
$521$	30.9918	1.35777	0.678887	−	0.734243i	$-0.262463\pi$
$521$	30.9918	1.35777	0.678887	+	0.734243i	$0.262463\pi$
$522$	30.5162	1.33566
$523$	19.9724	0.873332	0.436666	−	0.899624i	$-0.356159\pi$
$523$	19.9724	0.873332	0.436666	+	0.899624i	$0.356159\pi$
$524$	19.2311	0.840115
$525$	−13.9522	−0.608923
$526$	19.3564	0.843979
$527$	−22.4047	−0.975963
$528$	4.09983	0.178422
$529$	−22.3865	−0.973327
$530$	−7.81341	−0.339393
$531$	−43.3842	−1.88271
$532$	−1.44974	−0.0628543
$533$	−0.965683	−0.0418284
$534$	12.2436	0.529831
$535$	11.9460	0.516470
$536$	4.61367	0.199280
$537$	−53.7046	−2.31753
$538$	−7.48232	−0.322586
$539$	7.81797	0.336744
$540$	1.72033	0.0740312
$541$	−19.8748	−0.854483	−0.427242	−	0.904137i	$-0.640515\pi$
$541$	−19.8748	−0.854483	−0.427242	+	0.904137i	$0.640515\pi$
$542$	22.9387	0.985300
$543$	−3.43839	−0.147556
$544$	−5.27438	−0.226137
$545$	10.6830	0.457610
$546$	11.6485	0.498509
$547$	−3.92524	−0.167831	−0.0839156	−	0.996473i	$-0.526743\pi$
$547$	−3.92524	−0.167831	−0.0839156	+	0.996473i	$0.526743\pi$
$548$	8.29430	0.354315
$549$	−1.90519	−0.0813116
$550$	5.97986	0.254982
$551$	8.48094	0.361300
$552$	2.01193	0.0856335
$553$	7.65277	0.325429
$554$	−22.6938	−0.964168
$555$	−20.8151	−0.883554
$556$	2.58268	0.109530
$557$	16.5212	0.700027	0.350014	−	0.936745i	$-0.386177\pi$
$557$	16.5212	0.700027	0.350014	+	0.936745i	$0.386177\pi$
$558$	15.2846	0.647049
$559$	32.9602	1.39407
$560$	1.62306	0.0685868
$561$	−21.6241	−0.912969
$562$	11.2472	0.474434
$563$	−25.7588	−1.08560	−0.542801	−	0.839861i	$-0.682636\pi$
$563$	−25.7588	−1.08560	−0.542801	+	0.839861i	$0.682636\pi$
$564$	−4.39182	−0.184929
$565$	−4.04972	−0.170373
$566$	−33.5810	−1.41151
$567$	9.92712	0.416900
$568$	−2.79282	−0.117184
$569$	27.8785	1.16873	0.584364	−	0.811492i	$-0.301344\pi$
$569$	27.8785	1.16873	0.584364	+	0.811492i	$0.301344\pi$
$570$	2.87579	0.120453
$571$	−9.63791	−0.403334	−0.201667	−	0.979454i	$-0.564636\pi$
$571$	−9.63791	−0.403334	−0.201667	+	0.979454i	$0.564636\pi$
$572$	−4.99251	−0.208747
$573$	55.9364	2.33678
$574$	0.447568	0.0186811
$575$	2.93453	0.122378
$576$	3.59821	0.149925
$577$	−10.3302	−0.430052	−0.215026	−	0.976608i	$-0.568984\pi$
$577$	−10.3302	−0.430052	−0.215026	+	0.976608i	$0.568984\pi$
$578$	10.8191	0.450013
$579$	11.5858	0.481488
$580$	−9.49484	−0.394252
$581$	−13.3883	−0.555441
$582$	32.9453	1.36563
$583$	−11.1391	−0.461334
$584$	13.8081	0.571383
$585$	−12.6007	−0.520977
$586$	−16.6218	−0.686641
$587$	42.4384	1.75162	0.875810	−	0.482655i	$-0.160328\pi$
$587$	42.4384	1.75162	0.875810	+	0.482655i	$0.160328\pi$
$588$	12.5821	0.518878
$589$	4.24784	0.175029
$590$	13.4986	0.555728
$591$	16.0842	0.661617
$592$	−7.23807	−0.297483
$593$	−13.3131	−0.546702	−0.273351	−	0.961914i	$-0.588132\pi$
$593$	−13.3131	−0.546702	−0.273351	+	0.961914i	$0.588132\pi$
$594$	2.45257	0.100630
$595$	−8.56062	−0.350951
$596$	−3.79596	−0.155489
$597$	15.7598	0.645004
$598$	−2.45000	−0.100188
$599$	7.22746	0.295306	0.147653	−	0.989039i	$-0.452828\pi$
$599$	7.22746	0.295306	0.147653	+	0.989039i	$0.452828\pi$
$600$	9.62390	0.392894
$601$	11.0629	0.451264	0.225632	−	0.974213i	$-0.427555\pi$
$601$	11.0629	0.451264	0.225632	+	0.974213i	$0.427555\pi$
$602$	−15.2762	−0.622610
$603$	16.6010	0.676043
$604$	−4.42526	−0.180061
$605$	9.46305	0.384728
$606$	−36.2733	−1.47350
$607$	−18.4308	−0.748083	−0.374041	−	0.927412i	$-0.622028\pi$
$607$	−18.4308	−0.748083	−0.374041	+	0.927412i	$0.622028\pi$
$608$	1.00000	0.0405554
$609$	31.5826	1.27979
$610$	0.592783	0.0240011
$611$	5.34807	0.216360
$612$	−18.9783	−0.767153
$613$	−6.26812	−0.253167	−0.126583	−	0.991956i	$-0.540401\pi$
$613$	−6.26812	−0.253167	−0.126583	+	0.991956i	$0.540401\pi$
$614$	−23.7172	−0.957148
$615$	−0.887821	−0.0358004
$616$	2.31390	0.0932295
$617$	−7.67738	−0.309080	−0.154540	−	0.987987i	$-0.549390\pi$
$617$	−7.67738	−0.309080	−0.154540	+	0.987987i	$0.549390\pi$
$618$	−27.5233	−1.10715
$619$	20.6025	0.828086	0.414043	−	0.910257i	$-0.364116\pi$
$619$	20.6025	0.828086	0.414043	+	0.910257i	$0.364116\pi$
$620$	−4.75567	−0.190992
$621$	1.20356	0.0482973
$622$	−31.4708	−1.26186
$623$	6.91012	0.276848
$624$	−8.03487	−0.321652
$625$	7.77010	0.310804
$626$	−20.0011	−0.799405
$627$	4.09983	0.163732
$628$	−10.9439	−0.436711
$629$	38.1763	1.52219
$630$	5.84011	0.232676
$631$	−20.8444	−0.829803	−0.414901	−	0.909866i	$-0.636184\pi$
$631$	−20.8444	−0.829803	−0.414901	+	0.909866i	$0.636184\pi$
$632$	−5.27871	−0.209976
$633$	2.56870	0.102097
$634$	−20.0539	−0.796442
$635$	10.0415	0.398485
$636$	−17.9271	−0.710856
$637$	−15.3217	−0.607067
$638$	−13.5362	−0.535904
$639$	−10.0492	−0.397538
$640$	−1.11955	−0.0442541
$641$	13.9591	0.551350	0.275675	−	0.961251i	$-0.411099\pi$
$641$	13.9591	0.551350	0.275675	+	0.961251i	$0.411099\pi$
$642$	27.4089	1.08174
$643$	15.3604	0.605756	0.302878	−	0.953029i	$-0.402052\pi$
$643$	15.3604	0.605756	0.302878	+	0.953029i	$0.402052\pi$
$644$	1.13551	0.0447454
$645$	30.3027	1.19317
$646$	−5.27438	−0.207518
$647$	−27.6543	−1.08720	−0.543602	−	0.839343i	$-0.682940\pi$
$647$	−27.6543	−1.08720	−0.543602	+	0.839343i	$0.682940\pi$
$648$	−6.84751	−0.268996
$649$	19.2441	0.755397
$650$	−11.7194	−0.459671
$651$	15.8187	0.619985
$652$	−7.68585	−0.301001
$653$	1.42887	0.0559159	0.0279580	−	0.999609i	$-0.491100\pi$
$653$	1.42887	0.0559159	0.0279580	+	0.999609i	$0.491100\pi$
$654$	24.5111	0.958460
$655$	−21.5302	−0.841255
$656$	−0.308723	−0.0120536
$657$	49.6845	1.93838
$658$	−2.47869	−0.0966293
$659$	−11.5309	−0.449180	−0.224590	−	0.974453i	$-0.572104\pi$
$659$	−11.5309	−0.449180	−0.224590	+	0.974453i	$0.572104\pi$
$660$	−4.58997	−0.178664
$661$	19.5495	0.760386	0.380193	−	0.924907i	$-0.375858\pi$
$661$	19.5495	0.760386	0.380193	+	0.924907i	$0.375858\pi$
$662$	6.26128	0.243351
$663$	42.3789	1.64586
$664$	9.23497	0.358386
$665$	1.62306	0.0629395
$666$	−26.0441	−1.00919
$667$	−6.64269	−0.257206
$668$	12.0757	0.467223
$669$	34.5406	1.33542
$670$	−5.16523	−0.199550
$671$	0.845094	0.0326245
$672$	3.72395	0.143654
$673$	27.2522	1.05050	0.525248	−	0.850949i	$-0.323972\pi$
$673$	27.2522	1.05050	0.525248	+	0.850949i	$0.323972\pi$
$674$	−14.6756	−0.565283
$675$	5.75713	0.221592
$676$	−3.21566	−0.123679
$677$	−22.8576	−0.878489	−0.439245	−	0.898367i	$-0.644754\pi$
$677$	−22.8576	−0.878489	−0.439245	+	0.898367i	$0.644754\pi$
$678$	−9.29168	−0.356845
$679$	18.5939	0.713569
$680$	5.90493	0.226444
$681$	36.1002	1.38336
$682$	−6.77986	−0.259614
$683$	1.86134	0.0712221	0.0356111	−	0.999366i	$-0.488662\pi$
$683$	1.86134	0.0712221	0.0356111	+	0.999366i	$0.488662\pi$
$684$	3.59821	0.137581
$685$	−9.28589	−0.354796
$686$	17.2494	0.658585
$687$	−9.11384	−0.347715
$688$	10.5372	0.401726
$689$	21.8304	0.831674
$690$	−2.25246	−0.0857497
$691$	40.4717	1.53962	0.769808	−	0.638276i	$-0.220352\pi$
$691$	40.4717	1.53962	0.769808	+	0.638276i	$0.220352\pi$
$692$	−12.7449	−0.484488
$693$	8.32589	0.316274
$694$	−31.6736	−1.20231
$695$	−2.89144	−0.109679
$696$	−21.7850	−0.825757
$697$	1.62832	0.0616770
$698$	−4.24754	−0.160772
$699$	68.2337	2.58084
$700$	5.43161	0.205296
$701$	−6.54368	−0.247151	−0.123576	−	0.992335i	$-0.539436\pi$
$701$	−6.54368	−0.247151	−0.123576	+	0.992335i	$0.539436\pi$
$702$	−4.80655	−0.181412
$703$	−7.23807	−0.272989
$704$	−1.59607	−0.0601543
$705$	4.91686	0.185180
$706$	24.0277	0.904294
$707$	−20.4722	−0.769936
$708$	30.9712	1.16397
$709$	−37.5896	−1.41171	−0.705854	−	0.708358i	$-0.749436\pi$
$709$	−37.5896	−1.41171	−0.705854	+	0.708358i	$0.749436\pi$
$710$	3.12670	0.117343
$711$	−18.9939	−0.712327
$712$	−4.76645	−0.178630
$713$	−3.32712	−0.124601
$714$	−19.6415	−0.735065
$715$	5.58936	0.209030
$716$	20.9073	0.781344
$717$	11.1267	0.415535
$718$	23.1048	0.862264
$719$	41.8677	1.56140	0.780702	−	0.624904i	$-0.214862\pi$
$719$	41.8677	1.56140	0.780702	+	0.624904i	$0.214862\pi$
$720$	−4.02838	−0.150129
$721$	−15.5338	−0.578509
$722$	1.00000	0.0372161
$723$	−44.9919	−1.67327
$724$	1.33857	0.0497477
$725$	−31.7747	−1.18008
$726$	21.7120	0.805810
$727$	−31.8289	−1.18047	−0.590234	−	0.807232i	$-0.700965\pi$
$727$	−31.8289	−1.18047	−0.590234	+	0.807232i	$0.700965\pi$
$728$	−4.53478	−0.168070
$729$	−36.4802	−1.35112
$730$	−15.4589	−0.572158
$731$	−55.5770	−2.05559
$732$	1.36008	0.0502701
$733$	0.782883	0.0289164	0.0144582	−	0.999895i	$-0.495398\pi$
$733$	0.782883	0.0289164	0.0144582	+	0.999895i	$0.495398\pi$
$734$	9.79259	0.361451
$735$	−14.0863	−0.519582
$736$	−0.783250	−0.0288710
$737$	−7.36376	−0.271247
$738$	−1.11085	−0.0408910
$739$	−12.9409	−0.476038	−0.238019	−	0.971260i	$-0.576498\pi$
$739$	−12.9409	−0.476038	−0.238019	+	0.971260i	$0.576498\pi$
$740$	8.10338	0.297886
$741$	−8.03487	−0.295168
$742$	−10.1178	−0.371437
$743$	−21.3676	−0.783901	−0.391950	−	0.919986i	$-0.628199\pi$
$743$	−21.3676	−0.783901	−0.391950	+	0.919986i	$0.628199\pi$
$744$	−10.9114	−0.400032
$745$	4.24977	0.155699
$746$	−14.7854	−0.541333
$747$	33.2294	1.21580
$748$	8.41830	0.307803
$749$	15.4692	0.565233
$750$	−25.1534	−0.918472
$751$	17.7401	0.647345	0.323673	−	0.946169i	$-0.395082\pi$
$751$	17.7401	0.647345	0.323673	+	0.946169i	$0.395082\pi$
$752$	1.70974	0.0623479
$753$	−46.1565	−1.68204
$754$	26.5283	0.966104
$755$	4.95430	0.180305
$756$	2.22771	0.0810210
$757$	7.83074	0.284613	0.142307	−	0.989823i	$-0.454548\pi$
$757$	7.83074	0.284613	0.142307	+	0.989823i	$0.454548\pi$
$758$	−32.9460	−1.19665
$759$	−3.21119	−0.116559
$760$	−1.11955	−0.0406104
$761$	24.5923	0.891469	0.445735	−	0.895165i	$-0.352943\pi$
$761$	24.5923	0.891469	0.445735	+	0.895165i	$0.352943\pi$
$762$	23.0392	0.834623
$763$	13.8338	0.500816
$764$	−21.7762	−0.787834
$765$	21.2472	0.768194
$766$	−2.22797	−0.0804999
$767$	−37.7147	−1.36180
$768$	−2.56870	−0.0926899
$769$	47.8044	1.72387	0.861936	−	0.507017i	$-0.169252\pi$
$769$	47.8044	1.72387	0.861936	+	0.507017i	$0.169252\pi$
$770$	−2.59052	−0.0933560
$771$	35.4976	1.27841
$772$	−4.51037	−0.162332
$773$	−27.1576	−0.976789	−0.488395	−	0.872623i	$-0.662417\pi$
$773$	−27.1576	−0.976789	−0.488395	+	0.872623i	$0.662417\pi$
$774$	37.9150	1.36283
$775$	−15.9150	−0.571683
$776$	−12.8257	−0.460415
$777$	−26.9542	−0.966977
$778$	−15.9564	−0.572065
$779$	−0.308723	−0.0110611
$780$	8.99544	0.322088
$781$	4.45755	0.159504
$782$	4.13115	0.147730
$783$	−13.0320	−0.465727
$784$	−4.89825	−0.174937
$785$	12.2523	0.437303
$786$	−49.3989	−1.76200
$787$	−31.5415	−1.12433	−0.562167	−	0.827024i	$-0.690032\pi$
$787$	−31.5415	−1.12433	−0.562167	+	0.827024i	$0.690032\pi$
$788$	−6.26163	−0.223061
$789$	−49.7208	−1.77011
$790$	5.90978	0.210261
$791$	−5.24411	−0.186459
$792$	−5.74301	−0.204069
$793$	−1.65622	−0.0588141
$794$	−16.5148	−0.586089
$795$	20.0703	0.711820
$796$	−6.13531	−0.217460
$797$	23.5790	0.835210	0.417605	−	0.908629i	$-0.362870\pi$
$797$	23.5790	0.835210	0.417605	+	0.908629i	$0.362870\pi$
$798$	3.72395	0.131826
$799$	−9.01783	−0.319028
$800$	−3.74661	−0.132463
$801$	−17.1507	−0.605990
$802$	−1.36916	−0.0483467
$803$	−22.0387	−0.777731
$804$	−11.8511	−0.417957
$805$	−1.27126	−0.0448060
$806$	13.2872	0.468022
$807$	19.2198	0.676570
$808$	14.1213	0.496785
$809$	−15.7494	−0.553721	−0.276861	−	0.960910i	$-0.589294\pi$
$809$	−15.7494	−0.553721	−0.276861	+	0.960910i	$0.589294\pi$
$810$	7.66613	0.269360
$811$	1.28089	0.0449780	0.0224890	−	0.999747i	$-0.492841\pi$
$811$	1.28089	0.0449780	0.0224890	+	0.999747i	$0.492841\pi$
$812$	−12.2952	−0.431476
$813$	−58.9225	−2.06650
$814$	11.5525	0.404915
$815$	8.60469	0.301409
$816$	13.5483	0.474285
$817$	10.5372	0.368649
$818$	−33.9138	−1.18577
$819$	−16.3171	−0.570166
$820$	0.345631	0.0120699
$821$	5.21179	0.181893	0.0909464	−	0.995856i	$-0.471011\pi$
$821$	5.21179	0.181893	0.0909464	+	0.995856i	$0.471011\pi$
$822$	−21.3056	−0.743117
$823$	5.52758	0.192679	0.0963396	−	0.995349i	$-0.469287\pi$
$823$	5.52758	0.192679	0.0963396	+	0.995349i	$0.469287\pi$
$824$	10.7149	0.373271
$825$	−15.3605	−0.534783
$826$	17.4798	0.608199
$827$	7.72995	0.268797	0.134398	−	0.990927i	$-0.457090\pi$
$827$	7.72995	0.268797	0.134398	+	0.990927i	$0.457090\pi$
$828$	−2.81830	−0.0979426
$829$	−24.6254	−0.855277	−0.427638	−	0.903950i	$-0.640654\pi$
$829$	−24.6254	−0.855277	−0.427638	+	0.903950i	$0.640654\pi$
$830$	−10.3390	−0.358872
$831$	58.2936	2.02218
$832$	3.12799	0.108444
$833$	25.8352	0.895137
$834$	−6.63413	−0.229721
$835$	−13.5194	−0.467857
$836$	−1.59607	−0.0552014
$837$	−6.52733	−0.225618
$838$	−4.70812	−0.162639
$839$	41.7298	1.44067	0.720337	−	0.693624i	$-0.243987\pi$
$839$	41.7298	1.44067	0.720337	+	0.693624i	$0.243987\pi$
$840$	−4.16915	−0.143849
$841$	42.9263	1.48022
$842$	−5.43867	−0.187429
$843$	−28.8906	−0.995046
$844$	−1.00000	−0.0344214
$845$	3.60009	0.123847
$846$	6.15202	0.211511
$847$	12.2540	0.421053
$848$	6.97906	0.239662
$849$	86.2594	2.96042
$850$	19.7610	0.677797
$851$	5.66922	0.194338
$852$	7.17391	0.245774
$853$	−38.6648	−1.32386	−0.661929	−	0.749566i	$-0.730262\pi$
$853$	−38.6648	−1.32386	−0.661929	+	0.749566i	$0.730262\pi$
$854$	0.767614	0.0262672
$855$	−4.02838	−0.137768
$856$	−10.6703	−0.364705
$857$	10.7384	0.366815	0.183408	−	0.983037i	$-0.441287\pi$
$857$	10.7384	0.366815	0.183408	+	0.983037i	$0.441287\pi$
$858$	12.8243	0.437813
$859$	43.6837	1.49047	0.745235	−	0.666802i	$-0.232337\pi$
$859$	43.6837	1.49047	0.745235	+	0.666802i	$0.232337\pi$
$860$	−11.7969	−0.402271
$861$	−1.14967	−0.0391806
$862$	24.7539	0.843121
$863$	−31.2451	−1.06360	−0.531798	−	0.846871i	$-0.678483\pi$
$863$	−31.2451	−1.06360	−0.531798	+	0.846871i	$0.678483\pi$
$864$	−1.53663	−0.0522771
$865$	14.2685	0.485145
$866$	−17.4451	−0.592810
$867$	−27.7909	−0.943828
$868$	−6.15827	−0.209025
$869$	8.42521	0.285806
$870$	24.3894	0.826877
$871$	14.4315	0.488993
$872$	−9.54223	−0.323141
$873$	−46.1495	−1.56192
$874$	−0.783250	−0.0264938
$875$	−14.1963	−0.479921
$876$	−35.4688	−1.19838
$877$	21.0182	0.709733	0.354866	−	0.934917i	$-0.384526\pi$
$877$	21.0182	0.709733	0.354866	+	0.934917i	$0.384526\pi$
$878$	27.0520	0.912962
$879$	42.6964	1.44011
$880$	1.78689	0.0602359
$881$	50.9134	1.71532	0.857658	−	0.514220i	$-0.171919\pi$
$881$	50.9134	1.71532	0.857658	+	0.514220i	$0.171919\pi$
$882$	−17.6249	−0.593462
$883$	48.8130	1.64269	0.821344	−	0.570434i	$-0.193225\pi$
$883$	48.8130	1.64269	0.821344	+	0.570434i	$0.193225\pi$
$884$	−16.4982	−0.554895
$885$	−34.6738	−1.16555
$886$	−11.9016	−0.399841
$887$	−3.52130	−0.118234	−0.0591168	−	0.998251i	$-0.518828\pi$
$887$	−3.52130	−0.118234	−0.0591168	+	0.998251i	$0.518828\pi$
$888$	18.5924	0.623921
$889$	13.0031	0.436109
$890$	5.33628	0.178872
$891$	10.9291	0.366140
$892$	−13.4467	−0.450229
$893$	1.70974	0.0572144
$894$	9.75068	0.326111
$895$	−23.4068	−0.782403
$896$	−1.44974	−0.0484325
$897$	6.29331	0.210128
$898$	−10.4434	−0.348501
$899$	36.0256	1.20152
$900$	−13.4811	−0.449370
$901$	−36.8102	−1.22633
$902$	0.492745	0.0164066
$903$	39.2399	1.30582
$904$	3.61727	0.120309
$905$	−1.49860	−0.0498152
$906$	11.3672	0.377648
$907$	48.9809	1.62639	0.813193	−	0.581994i	$-0.197727\pi$
$907$	48.9809	1.62639	0.813193	+	0.581994i	$0.197727\pi$
$908$	−14.0539	−0.466395
$909$	50.8113	1.68531
$910$	5.07692	0.168298
$911$	−22.5447	−0.746939	−0.373470	−	0.927642i	$-0.621832\pi$
$911$	−22.5447	−0.746939	−0.373470	+	0.927642i	$0.621832\pi$
$912$	−2.56870	−0.0850581
$913$	−14.7397	−0.487813
$914$	−6.79423	−0.224733
$915$	−1.52268	−0.0503383
$916$	3.54804	0.117230
$917$	−27.8802	−0.920684
$918$	8.10474	0.267496
$919$	−40.3174	−1.32995	−0.664975	−	0.746866i	$-0.731558\pi$
$919$	−40.3174	−1.32995	−0.664975	+	0.746866i	$0.731558\pi$
$920$	0.876887	0.0289101
$921$	60.9223	2.00746
$922$	−16.7365	−0.551188
$923$	−8.73592	−0.287546
$924$	−5.94370	−0.195533
$925$	27.1182	0.891641
$926$	1.46440	0.0481231
$927$	38.5544	1.26629
$928$	8.48094	0.278400
$929$	−19.3473	−0.634764	−0.317382	−	0.948298i	$-0.602804\pi$
$929$	−19.3473	−0.634764	−0.317382	+	0.948298i	$0.602804\pi$
$930$	12.2159	0.400574
$931$	−4.89825	−0.160534
$932$	−26.5635	−0.870118
$933$	80.8390	2.64655
$934$	−10.8327	−0.354457
$935$	−9.42471	−0.308221
$936$	11.2552	0.367887
$937$	19.3382	0.631752	0.315876	−	0.948800i	$-0.397702\pi$
$937$	19.3382	0.631752	0.315876	+	0.948800i	$0.397702\pi$
$938$	−6.68863	−0.218391
$939$	51.3768	1.67662
$940$	−1.91414	−0.0624325
$941$	22.1728	0.722811	0.361406	−	0.932409i	$-0.382297\pi$
$941$	22.1728	0.722811	0.361406	+	0.932409i	$0.382297\pi$
$942$	28.1117	0.915929
$943$	0.241807	0.00787432
$944$	−12.0572	−0.392427
$945$	−2.49403	−0.0811309
$946$	−16.8181	−0.546804
$947$	49.7447	1.61648	0.808242	−	0.588850i	$-0.200419\pi$
$947$	49.7447	1.61648	0.808242	+	0.588850i	$0.200419\pi$
$948$	13.5594	0.440389
$949$	43.1916	1.40206
$950$	−3.74661	−0.121556
$951$	51.5124	1.67040
$952$	7.64649	0.247824
$953$	−43.1522	−1.39784	−0.698918	−	0.715202i	$-0.746335\pi$
$953$	−43.1522	−1.39784	−0.698918	+	0.715202i	$0.746335\pi$
$954$	25.1121	0.813035
$955$	24.3795	0.788902
$956$	−4.33166	−0.140096
$957$	34.7704	1.12397
$958$	−20.9816	−0.677884
$959$	−12.0246	−0.388295
$960$	2.87579	0.0928156
$961$	−12.9559	−0.417932
$962$	−22.6406	−0.729963
$963$	−38.3941	−1.23723
$964$	17.5154	0.564135
$965$	5.04958	0.162552
$966$	−2.91678	−0.0938459
$967$	−10.6831	−0.343546	−0.171773	−	0.985137i	$-0.554950\pi$
$967$	−10.6831	−0.343546	−0.171773	+	0.985137i	$0.554950\pi$
$968$	−8.45255	−0.271675
$969$	13.5483	0.435234
$970$	14.3590	0.461039
$971$	−12.6516	−0.406010	−0.203005	−	0.979178i	$-0.565071\pi$
$971$	−12.6516	−0.406010	−0.203005	+	0.979178i	$0.565071\pi$
$972$	22.1991	0.712035
$973$	−3.74422	−0.120034
$974$	−19.9002	−0.637643
$975$	30.1035	0.964084
$976$	−0.529483	−0.0169483
$977$	−17.7318	−0.567291	−0.283646	−	0.958929i	$-0.591544\pi$
$977$	−17.7318	−0.567291	−0.283646	+	0.958929i	$0.591544\pi$
$978$	19.7426	0.631299
$979$	7.60761	0.243140
$980$	5.48383	0.175175
$981$	−34.3350	−1.09623
$982$	41.2744	1.31712
$983$	25.9136	0.826516	0.413258	−	0.910614i	$-0.364391\pi$
$983$	25.9136	0.826516	0.413258	+	0.910614i	$0.364391\pi$
$984$	0.793016	0.0252804
$985$	7.01020	0.223364
$986$	−44.7317	−1.42455
$987$	6.36700	0.202664
$988$	3.12799	0.0995147
$989$	−8.25324	−0.262438
$990$	6.42959	0.204346
$991$	−23.8788	−0.758535	−0.379267	−	0.925287i	$-0.623824\pi$
$991$	−23.8788	−0.758535	−0.379267	+	0.925287i	$0.623824\pi$
$992$	4.24784	0.134869
$993$	−16.0833	−0.510389
$994$	4.04887	0.128422
$995$	6.86879	0.217755
$996$	−23.7218	−0.751656
$997$	−36.2352	−1.14758	−0.573790	−	0.819003i	$-0.694527\pi$
$997$	−36.2352	−1.14758	−0.573790	+	0.819003i	$0.694527\pi$
$998$	−21.2431	−0.672439
$999$	11.1222	0.351891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.56870 q^{3} +1.00000 q^{4} -1.11955 q^{5} -2.56870 q^{6} -1.44974 q^{7} +1.00000 q^{8} +3.59821 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.56870 q^{3} +1.00000 q^{4} -1.11955 q^{5} -2.56870 q^{6} -1.44974 q^{7} +1.00000 q^{8} +3.59821 q^{9} -1.11955 q^{10} -1.59607 q^{11} -2.56870 q^{12} +3.12799 q^{13} -1.44974 q^{14} +2.87579 q^{15} +1.00000 q^{16} -5.27438 q^{17} +3.59821 q^{18} +1.00000 q^{19} -1.11955 q^{20} +3.72395 q^{21} -1.59607 q^{22} -0.783250 q^{23} -2.56870 q^{24} -3.74661 q^{25} +3.12799 q^{26} -1.53663 q^{27} -1.44974 q^{28} +8.48094 q^{29} +2.87579 q^{30} +4.24784 q^{31} +1.00000 q^{32} +4.09983 q^{33} -5.27438 q^{34} +1.62306 q^{35} +3.59821 q^{36} -7.23807 q^{37} +1.00000 q^{38} -8.03487 q^{39} -1.11955 q^{40} -0.308723 q^{41} +3.72395 q^{42} +10.5372 q^{43} -1.59607 q^{44} -4.02838 q^{45} -0.783250 q^{46} +1.70974 q^{47} -2.56870 q^{48} -4.89825 q^{49} -3.74661 q^{50} +13.5483 q^{51} +3.12799 q^{52} +6.97906 q^{53} -1.53663 q^{54} +1.78689 q^{55} -1.44974 q^{56} -2.56870 q^{57} +8.48094 q^{58} -12.0572 q^{59} +2.87579 q^{60} -0.529483 q^{61} +4.24784 q^{62} -5.21648 q^{63} +1.00000 q^{64} -3.50195 q^{65} +4.09983 q^{66} +4.61367 q^{67} -5.27438 q^{68} +2.01193 q^{69} +1.62306 q^{70} -2.79282 q^{71} +3.59821 q^{72} +13.8081 q^{73} -7.23807 q^{74} +9.62390 q^{75} +1.00000 q^{76} +2.31390 q^{77} -8.03487 q^{78} -5.27871 q^{79} -1.11955 q^{80} -6.84751 q^{81} -0.308723 q^{82} +9.23497 q^{83} +3.72395 q^{84} +5.90493 q^{85} +10.5372 q^{86} -21.7850 q^{87} -1.59607 q^{88} -4.76645 q^{89} -4.02838 q^{90} -4.53478 q^{91} -0.783250 q^{92} -10.9114 q^{93} +1.70974 q^{94} -1.11955 q^{95} -2.56870 q^{96} -12.8257 q^{97} -4.89825 q^{98} -5.74301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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