LMFDB - Embedded newform 8018.2.a.d.1.22

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			1.22
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.01104 q^{3} +1.00000 q^{4} -1.68533 q^{5} +1.01104 q^{6} +2.57733 q^{7} +1.00000 q^{8} -1.97779 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.01104 q^{3} +1.00000 q^{4} -1.68533 q^{5} +1.01104 q^{6} +2.57733 q^{7} +1.00000 q^{8} -1.97779 q^{9} -1.68533 q^{10} +3.74412 q^{11} +1.01104 q^{12} -1.44491 q^{13} +2.57733 q^{14} -1.70394 q^{15} +1.00000 q^{16} -5.57391 q^{17} -1.97779 q^{18} +1.00000 q^{19} -1.68533 q^{20} +2.60579 q^{21} +3.74412 q^{22} -4.47000 q^{23} +1.01104 q^{24} -2.15966 q^{25} -1.44491 q^{26} -5.03276 q^{27} +2.57733 q^{28} +1.04310 q^{29} -1.70394 q^{30} -1.57245 q^{31} +1.00000 q^{32} +3.78546 q^{33} -5.57391 q^{34} -4.34366 q^{35} -1.97779 q^{36} -7.99207 q^{37} +1.00000 q^{38} -1.46086 q^{39} -1.68533 q^{40} -9.16233 q^{41} +2.60579 q^{42} -6.28233 q^{43} +3.74412 q^{44} +3.33324 q^{45} -4.47000 q^{46} +10.0003 q^{47} +1.01104 q^{48} -0.357353 q^{49} -2.15966 q^{50} -5.63546 q^{51} -1.44491 q^{52} -13.6910 q^{53} -5.03276 q^{54} -6.31007 q^{55} +2.57733 q^{56} +1.01104 q^{57} +1.04310 q^{58} -6.06723 q^{59} -1.70394 q^{60} -5.39391 q^{61} -1.57245 q^{62} -5.09744 q^{63} +1.00000 q^{64} +2.43515 q^{65} +3.78546 q^{66} -9.88231 q^{67} -5.57391 q^{68} -4.51936 q^{69} -4.34366 q^{70} +14.4835 q^{71} -1.97779 q^{72} +12.8861 q^{73} -7.99207 q^{74} -2.18351 q^{75} +1.00000 q^{76} +9.64983 q^{77} -1.46086 q^{78} +0.509532 q^{79} -1.68533 q^{80} +0.845055 q^{81} -9.16233 q^{82} +11.4297 q^{83} +2.60579 q^{84} +9.39388 q^{85} -6.28233 q^{86} +1.05461 q^{87} +3.74412 q^{88} +7.25546 q^{89} +3.33324 q^{90} -3.72401 q^{91} -4.47000 q^{92} -1.58981 q^{93} +10.0003 q^{94} -1.68533 q^{95} +1.01104 q^{96} +8.92880 q^{97} -0.357353 q^{98} -7.40509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.01104	0.583725	0.291863	−	0.956460i	$-0.405725\pi$
$3$	1.01104	0.583725	0.291863	+	0.956460i	$0.405725\pi$
$4$	1.00000	0.500000
$5$	−1.68533	−0.753703	−0.376851	−	0.926274i	$-0.622993\pi$
$5$	−1.68533	−0.753703	−0.376851	+	0.926274i	$0.622993\pi$
$6$	1.01104	0.412756
$7$	2.57733	0.974140	0.487070	−	0.873363i	$-0.338066\pi$
$7$	2.57733	0.974140	0.487070	+	0.873363i	$0.338066\pi$
$8$	1.00000	0.353553
$9$	−1.97779	−0.659265
$10$	−1.68533	−0.532948
$11$	3.74412	1.12889	0.564447	−	0.825470i	$-0.309090\pi$
$11$	3.74412	1.12889	0.564447	+	0.825470i	$0.309090\pi$
$12$	1.01104	0.291863
$13$	−1.44491	−0.400746	−0.200373	−	0.979720i	$-0.564215\pi$
$13$	−1.44491	−0.400746	−0.200373	+	0.979720i	$0.564215\pi$
$14$	2.57733	0.688821
$15$	−1.70394	−0.439955
$16$	1.00000	0.250000
$17$	−5.57391	−1.35187	−0.675936	−	0.736960i	$-0.736260\pi$
$17$	−5.57391	−1.35187	−0.675936	+	0.736960i	$0.736260\pi$
$18$	−1.97779	−0.466171
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.68533	−0.376851
$21$	2.60579	0.568630
$22$	3.74412	0.798248
$23$	−4.47000	−0.932060	−0.466030	−	0.884769i	$-0.654316\pi$
$23$	−4.47000	−0.932060	−0.466030	+	0.884769i	$0.654316\pi$
$24$	1.01104	0.206378
$25$	−2.15966	−0.431933
$26$	−1.44491	−0.283370
$27$	−5.03276	−0.968555
$28$	2.57733	0.487070
$29$	1.04310	0.193698	0.0968491	−	0.995299i	$-0.469124\pi$
$29$	1.04310	0.193698	0.0968491	+	0.995299i	$0.469124\pi$
$30$	−1.70394	−0.311095
$31$	−1.57245	−0.282420	−0.141210	−	0.989980i	$-0.545099\pi$
$31$	−1.57245	−0.282420	−0.141210	+	0.989980i	$0.545099\pi$
$32$	1.00000	0.176777
$33$	3.78546	0.658964
$34$	−5.57391	−0.955918
$35$	−4.34366	−0.734212
$36$	−1.97779	−0.329632
$37$	−7.99207	−1.31389	−0.656944	−	0.753939i	$-0.728151\pi$
$37$	−7.99207	−1.31389	−0.656944	+	0.753939i	$0.728151\pi$
$38$	1.00000	0.162221
$39$	−1.46086	−0.233925
$40$	−1.68533	−0.266474
$41$	−9.16233	−1.43092	−0.715458	−	0.698656i	$-0.753782\pi$
$41$	−9.16233	−1.43092	−0.715458	+	0.698656i	$0.753782\pi$
$42$	2.60579	0.402082
$43$	−6.28233	−0.958047	−0.479023	−	0.877802i	$-0.659009\pi$
$43$	−6.28233	−0.958047	−0.479023	+	0.877802i	$0.659009\pi$
$44$	3.74412	0.564447
$45$	3.33324	0.496890
$46$	−4.47000	−0.659066
$47$	10.0003	1.45870	0.729348	−	0.684143i	$-0.239824\pi$
$47$	10.0003	1.45870	0.729348	+	0.684143i	$0.239824\pi$
$48$	1.01104	0.145931
$49$	−0.357353	−0.0510505
$50$	−2.15966	−0.305422
$51$	−5.63546	−0.789122
$52$	−1.44491	−0.200373
$53$	−13.6910	−1.88061	−0.940305	−	0.340333i	$-0.889460\pi$
$53$	−13.6910	−1.88061	−0.940305	+	0.340333i	$0.889460\pi$
$54$	−5.03276	−0.684872
$55$	−6.31007	−0.850850
$56$	2.57733	0.344411
$57$	1.01104	0.133916
$58$	1.04310	0.136965
$59$	−6.06723	−0.789885	−0.394943	−	0.918706i	$-0.629236\pi$
$59$	−6.06723	−0.789885	−0.394943	+	0.918706i	$0.629236\pi$
$60$	−1.70394	−0.219978
$61$	−5.39391	−0.690619	−0.345310	−	0.938489i	$-0.612226\pi$
$61$	−5.39391	−0.690619	−0.345310	+	0.938489i	$0.612226\pi$
$62$	−1.57245	−0.199701
$63$	−5.09744	−0.642217
$64$	1.00000	0.125000
$65$	2.43515	0.302043
$66$	3.78546	0.465958
$67$	−9.88231	−1.20732	−0.603658	−	0.797243i	$-0.706291\pi$
$67$	−9.88231	−1.20732	−0.603658	+	0.797243i	$0.706291\pi$
$68$	−5.57391	−0.675936
$69$	−4.51936	−0.544067
$70$	−4.34366	−0.519166
$71$	14.4835	1.71888	0.859438	−	0.511240i	$-0.170814\pi$
$71$	14.4835	1.71888	0.859438	+	0.511240i	$0.170814\pi$
$72$	−1.97779	−0.233085
$73$	12.8861	1.50821	0.754104	−	0.656755i	$-0.228071\pi$
$73$	12.8861	1.50821	0.754104	+	0.656755i	$0.228071\pi$
$74$	−7.99207	−0.929059
$75$	−2.18351	−0.252130
$76$	1.00000	0.114708
$77$	9.64983	1.09970
$78$	−1.46086	−0.165410
$79$	0.509532	0.0573268	0.0286634	−	0.999589i	$-0.490875\pi$
$79$	0.509532	0.0573268	0.0286634	+	0.999589i	$0.490875\pi$
$80$	−1.68533	−0.188426
$81$	0.845055	0.0938949
$82$	−9.16233	−1.01181
$83$	11.4297	1.25457	0.627284	−	0.778791i	$-0.284167\pi$
$83$	11.4297	1.25457	0.627284	+	0.778791i	$0.284167\pi$
$84$	2.60579	0.284315
$85$	9.39388	1.01891
$86$	−6.28233	−0.677441
$87$	1.05461	0.113067
$88$	3.74412	0.399124
$89$	7.25546	0.769078	0.384539	−	0.923109i	$-0.374360\pi$
$89$	7.25546	0.769078	0.384539	+	0.923109i	$0.374360\pi$
$90$	3.33324	0.351354
$91$	−3.72401	−0.390383
$92$	−4.47000	−0.466030
$93$	−1.58981	−0.164856
$94$	10.0003	1.03145
$95$	−1.68533	−0.172911
$96$	1.01104	0.103189
$97$	8.92880	0.906583	0.453291	−	0.891362i	$-0.350250\pi$
$97$	8.92880	0.906583	0.453291	+	0.891362i	$0.350250\pi$
$98$	−0.357353	−0.0360981
$99$	−7.40509	−0.744240
$100$	−2.15966	−0.215966
$101$	−3.26464	−0.324844	−0.162422	−	0.986721i	$-0.551931\pi$
$101$	−3.26464	−0.324844	−0.162422	+	0.986721i	$0.551931\pi$
$102$	−5.63546	−0.557993
$103$	−4.60291	−0.453538	−0.226769	−	0.973949i	$-0.572816\pi$
$103$	−4.60291	−0.453538	−0.226769	+	0.973949i	$0.572816\pi$
$104$	−1.44491	−0.141685
$105$	−4.39162	−0.428578
$106$	−13.6910	−1.32979
$107$	11.3374	1.09603	0.548015	−	0.836468i	$-0.315383\pi$
$107$	11.3374	1.09603	0.548015	+	0.836468i	$0.315383\pi$
$108$	−5.03276	−0.484277
$109$	7.87738	0.754516	0.377258	−	0.926108i	$-0.376867\pi$
$109$	7.87738	0.754516	0.377258	+	0.926108i	$0.376867\pi$
$110$	−6.31007	−0.601642
$111$	−8.08031	−0.766949
$112$	2.57733	0.243535
$113$	−4.88018	−0.459089	−0.229544	−	0.973298i	$-0.573724\pi$
$113$	−4.88018	−0.459089	−0.229544	+	0.973298i	$0.573724\pi$
$114$	1.01104	0.0946927
$115$	7.53343	0.702496
$116$	1.04310	0.0968491
$117$	2.85773	0.264198
$118$	−6.06723	−0.558533
$119$	−14.3658	−1.31691
$120$	−1.70394	−0.155548
$121$	3.01840	0.274400
$122$	−5.39391	−0.488341
$123$	−9.26350	−0.835262
$124$	−1.57245	−0.141210
$125$	12.0664	1.07925
$126$	−5.09744	−0.454116
$127$	1.66016	0.147315	0.0736575	−	0.997284i	$-0.476533\pi$
$127$	1.66016	0.147315	0.0736575	+	0.997284i	$0.476533\pi$
$128$	1.00000	0.0883883
$129$	−6.35170	−0.559236
$130$	2.43515	0.213577
$131$	−18.0867	−1.58024	−0.790119	−	0.612953i	$-0.789982\pi$
$131$	−18.0867	−1.58024	−0.790119	+	0.612953i	$0.789982\pi$
$132$	3.78546	0.329482
$133$	2.57733	0.223483
$134$	−9.88231	−0.853702
$135$	8.48186	0.730002
$136$	−5.57391	−0.477959
$137$	−21.6198	−1.84710	−0.923550	−	0.383477i	$-0.874727\pi$
$137$	−21.6198	−1.84710	−0.923550	+	0.383477i	$0.874727\pi$
$138$	−4.51936	−0.384714
$139$	13.8387	1.17378	0.586890	−	0.809667i	$-0.300352\pi$
$139$	13.8387	1.17378	0.586890	+	0.809667i	$0.300352\pi$
$140$	−4.34366	−0.367106
$141$	10.1107	0.851477
$142$	14.4835	1.21543
$143$	−5.40991	−0.452399
$144$	−1.97779	−0.164816
$145$	−1.75796	−0.145991
$146$	12.8861	1.06646
$147$	−0.361299	−0.0297994
$148$	−7.99207	−0.656944
$149$	−0.207099	−0.0169662	−0.00848312	−	0.999964i	$-0.502700\pi$
$149$	−0.207099	−0.0169662	−0.00848312	+	0.999964i	$0.502700\pi$
$150$	−2.18351	−0.178283
$151$	−15.5150	−1.26259	−0.631297	−	0.775541i	$-0.717477\pi$
$151$	−15.5150	−1.26259	−0.631297	+	0.775541i	$0.717477\pi$
$152$	1.00000	0.0811107
$153$	11.0240	0.891242
$154$	9.64983	0.777606
$155$	2.65009	0.212860
$156$	−1.46086	−0.116963
$157$	−5.68960	−0.454079	−0.227040	−	0.973885i	$-0.572905\pi$
$157$	−5.68960	−0.454079	−0.227040	+	0.973885i	$0.572905\pi$
$158$	0.509532	0.0405362
$159$	−13.8422	−1.09776
$160$	−1.68533	−0.133237
$161$	−11.5207	−0.907958
$162$	0.845055	0.0663938
$163$	1.13101	0.0885875	0.0442937	−	0.999019i	$-0.485896\pi$
$163$	1.13101	0.0885875	0.0442937	+	0.999019i	$0.485896\pi$
$164$	−9.16233	−0.715458
$165$	−6.37975	−0.496662
$166$	11.4297	0.887113
$167$	−16.7676	−1.29751	−0.648757	−	0.760996i	$-0.724711\pi$
$167$	−16.7676	−1.29751	−0.648757	+	0.760996i	$0.724711\pi$
$168$	2.60579	0.201041
$169$	−10.9122	−0.839403
$170$	9.39388	0.720478
$171$	−1.97779	−0.151246
$172$	−6.28233	−0.479023
$173$	−4.47452	−0.340192	−0.170096	−	0.985428i	$-0.554408\pi$
$173$	−4.47452	−0.340192	−0.170096	+	0.985428i	$0.554408\pi$
$174$	1.05461	0.0799501
$175$	−5.56617	−0.420763
$176$	3.74412	0.282223
$177$	−6.13422	−0.461076
$178$	7.25546	0.543820
$179$	11.4421	0.855224	0.427612	−	0.903962i	$-0.359355\pi$
$179$	11.4421	0.855224	0.427612	+	0.903962i	$0.359355\pi$
$180$	3.33324	0.248445
$181$	3.89565	0.289561	0.144781	−	0.989464i	$-0.453752\pi$
$181$	3.89565	0.289561	0.144781	+	0.989464i	$0.453752\pi$
$182$	−3.72401	−0.276042
$183$	−5.45347	−0.403132
$184$	−4.47000	−0.329533
$185$	13.4693	0.990281
$186$	−1.58981	−0.116570
$187$	−20.8694	−1.52612
$188$	10.0003	0.729348
$189$	−12.9711	−0.943508
$190$	−1.68533	−0.122267
$191$	6.12375	0.443099	0.221550	−	0.975149i	$-0.428889\pi$
$191$	6.12375	0.443099	0.221550	+	0.975149i	$0.428889\pi$
$192$	1.01104	0.0729657
$193$	24.8117	1.78599	0.892993	−	0.450071i	$-0.148601\pi$
$193$	24.8117	1.78599	0.892993	+	0.450071i	$0.148601\pi$
$194$	8.92880	0.641051
$195$	2.46204	0.176310
$196$	−0.357353	−0.0255252
$197$	−1.66743	−0.118800	−0.0593998	−	0.998234i	$-0.518919\pi$
$197$	−1.66743	−0.118800	−0.0593998	+	0.998234i	$0.518919\pi$
$198$	−7.40509	−0.526257
$199$	−13.2307	−0.937897	−0.468948	−	0.883226i	$-0.655367\pi$
$199$	−13.2307	−0.937897	−0.468948	+	0.883226i	$0.655367\pi$
$200$	−2.15966	−0.152711
$201$	−9.99143	−0.704741
$202$	−3.26464	−0.229699
$203$	2.68841	0.188689
$204$	−5.63546	−0.394561
$205$	15.4416	1.07848
$206$	−4.60291	−0.320700
$207$	8.84075	0.614475
$208$	−1.44491	−0.100186
$209$	3.74412	0.258986
$210$	−4.39162	−0.303050
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−13.6910	−0.940305
$213$	14.6434	1.00335
$214$	11.3374	0.775011
$215$	10.5878	0.722082
$216$	−5.03276	−0.342436
$217$	−4.05272	−0.275116
$218$	7.87738	0.533523
$219$	13.0284	0.880379
$220$	−6.31007	−0.425425
$221$	8.05379	0.541757
$222$	−8.08031	−0.542315
$223$	−2.51790	−0.168611	−0.0843054	−	0.996440i	$-0.526867\pi$
$223$	−2.51790	−0.168611	−0.0843054	+	0.996440i	$0.526867\pi$
$224$	2.57733	0.172205
$225$	4.27137	0.284758
$226$	−4.88018	−0.324625
$227$	10.5985	0.703449	0.351724	−	0.936104i	$-0.385595\pi$
$227$	10.5985	0.703449	0.351724	+	0.936104i	$0.385595\pi$
$228$	1.01104	0.0669579
$229$	−8.07516	−0.533622	−0.266811	−	0.963749i	$-0.585970\pi$
$229$	−8.07516	−0.533622	−0.266811	+	0.963749i	$0.585970\pi$
$230$	7.53343	0.496740
$231$	9.75639	0.641923
$232$	1.04310	0.0684827
$233$	24.1277	1.58066	0.790329	−	0.612682i	$-0.209909\pi$
$233$	24.1277	1.58066	0.790329	+	0.612682i	$0.209909\pi$
$234$	2.85773	0.186816
$235$	−16.8538	−1.09942
$236$	−6.06723	−0.394943
$237$	0.515158	0.0334631
$238$	−14.3658	−0.931198
$239$	1.03406	0.0668881	0.0334440	−	0.999441i	$-0.489352\pi$
$239$	1.03406	0.0668881	0.0334440	+	0.999441i	$0.489352\pi$
$240$	−1.70394	−0.109989
$241$	1.59067	0.102464	0.0512320	−	0.998687i	$-0.483685\pi$
$241$	1.59067	0.102464	0.0512320	+	0.998687i	$0.483685\pi$
$242$	3.01840	0.194030
$243$	15.9527	1.02336
$244$	−5.39391	−0.345310
$245$	0.602258	0.0384769
$246$	−9.26350	−0.590619
$247$	−1.44491	−0.0919374
$248$	−1.57245	−0.0998505
$249$	11.5559	0.732323
$250$	12.0664	0.763146
$251$	−19.3498	−1.22135	−0.610675	−	0.791881i	$-0.709102\pi$
$251$	−19.3498	−1.22135	−0.610675	+	0.791881i	$0.709102\pi$
$252$	−5.09744	−0.321108
$253$	−16.7362	−1.05220
$254$	1.66016	0.104167
$255$	9.49760	0.594763
$256$	1.00000	0.0625000
$257$	−12.4504	−0.776635	−0.388318	−	0.921526i	$-0.626944\pi$
$257$	−12.4504	−0.776635	−0.388318	+	0.921526i	$0.626944\pi$
$258$	−6.35170	−0.395440
$259$	−20.5982	−1.27991
$260$	2.43515	0.151022
$261$	−2.06303	−0.127698
$262$	−18.0867	−1.11740
$263$	−18.6737	−1.15147	−0.575735	−	0.817637i	$-0.695284\pi$
$263$	−18.6737	−1.15147	−0.575735	+	0.817637i	$0.695284\pi$
$264$	3.78546	0.232979
$265$	23.0739	1.41742
$266$	2.57733	0.158026
$267$	7.33558	0.448930
$268$	−9.88231	−0.603658
$269$	−9.17178	−0.559214	−0.279607	−	0.960115i	$-0.590204\pi$
$269$	−9.17178	−0.559214	−0.279607	+	0.960115i	$0.590204\pi$
$270$	8.48186	0.516189
$271$	−30.4063	−1.84705	−0.923525	−	0.383539i	$-0.874705\pi$
$271$	−30.4063	−1.84705	−0.923525	+	0.383539i	$0.874705\pi$
$272$	−5.57391	−0.337968
$273$	−3.76513	−0.227876
$274$	−21.6198	−1.30610
$275$	−8.08603	−0.487606
$276$	−4.51936	−0.272034
$277$	−15.4661	−0.929267	−0.464634	−	0.885503i	$-0.653814\pi$
$277$	−15.4661	−0.929267	−0.464634	+	0.885503i	$0.653814\pi$
$278$	13.8387	0.829988
$279$	3.10998	0.186189
$280$	−4.34366	−0.259583
$281$	29.9663	1.78764	0.893819	−	0.448429i	$-0.148016\pi$
$281$	29.9663	1.78764	0.893819	+	0.448429i	$0.148016\pi$
$282$	10.1107	0.602085
$283$	−16.1667	−0.961008	−0.480504	−	0.876993i	$-0.659546\pi$
$283$	−16.1667	−0.961008	−0.480504	+	0.876993i	$0.659546\pi$
$284$	14.4835	0.859438
$285$	−1.70394	−0.100933
$286$	−5.40991	−0.319894
$287$	−23.6144	−1.39391
$288$	−1.97779	−0.116543
$289$	14.0685	0.827557
$290$	−1.75796	−0.103231
$291$	9.02739	0.529195
$292$	12.8861	0.754104
$293$	−18.6016	−1.08671	−0.543357	−	0.839502i	$-0.682847\pi$
$293$	−18.6016	−1.08671	−0.543357	+	0.839502i	$0.682847\pi$
$294$	−0.361299	−0.0210714
$295$	10.2253	0.595339
$296$	−7.99207	−0.464529
$297$	−18.8432	−1.09340
$298$	−0.207099	−0.0119969
$299$	6.45875	0.373519
$300$	−2.18351	−0.126065
$301$	−16.1917	−0.933272
$302$	−15.5150	−0.892788
$303$	−3.30069	−0.189620
$304$	1.00000	0.0573539
$305$	9.09051	0.520521
$306$	11.0240	0.630203
$307$	−32.8798	−1.87655	−0.938275	−	0.345889i	$-0.887577\pi$
$307$	−32.8798	−1.87655	−0.938275	+	0.345889i	$0.887577\pi$
$308$	9.64983	0.549850
$309$	−4.65373	−0.264742
$310$	2.65009	0.150515
$311$	22.2198	1.25997	0.629984	−	0.776608i	$-0.283062\pi$
$311$	22.2198	1.25997	0.629984	+	0.776608i	$0.283062\pi$
$312$	−1.46086	−0.0827051
$313$	−0.633676	−0.0358175	−0.0179087	−	0.999840i	$-0.505701\pi$
$313$	−0.633676	−0.0358175	−0.0179087	+	0.999840i	$0.505701\pi$
$314$	−5.68960	−0.321083
$315$	8.59086	0.484040
$316$	0.509532	0.0286634
$317$	21.6132	1.21392	0.606959	−	0.794733i	$-0.292389\pi$
$317$	21.6132	1.21392	0.606959	+	0.794733i	$0.292389\pi$
$318$	−13.8422	−0.776233
$319$	3.90547	0.218665
$320$	−1.68533	−0.0942128
$321$	11.4626	0.639781
$322$	−11.5207	−0.642023
$323$	−5.57391	−0.310141
$324$	0.845055	0.0469475
$325$	3.12052	0.173095
$326$	1.13101	0.0626408
$327$	7.96436	0.440430
$328$	−9.16233	−0.505905
$329$	25.7741	1.42097
$330$	−6.37975	−0.351193
$331$	21.6767	1.19146	0.595729	−	0.803185i	$-0.296863\pi$
$331$	21.6767	1.19146	0.595729	+	0.803185i	$0.296863\pi$
$332$	11.4297	0.627284
$333$	15.8067	0.866200
$334$	−16.7676	−0.917481
$335$	16.6550	0.909958
$336$	2.60579	0.142158
$337$	−17.6816	−0.963178	−0.481589	−	0.876397i	$-0.659940\pi$
$337$	−17.6816	−0.963178	−0.481589	+	0.876397i	$0.659940\pi$
$338$	−10.9122	−0.593547
$339$	−4.93407	−0.267982
$340$	9.39388	0.509455
$341$	−5.88742	−0.318822
$342$	−1.97779	−0.106947
$343$	−18.9624	−1.02387
$344$	−6.28233	−0.338721
$345$	7.61662	0.410065
$346$	−4.47452	−0.240552
$347$	20.6562	1.10888	0.554441	−	0.832223i	$-0.312932\pi$
$347$	20.6562	1.10888	0.554441	+	0.832223i	$0.312932\pi$
$348$	1.05461	0.0565333
$349$	−12.4860	−0.668362	−0.334181	−	0.942509i	$-0.608460\pi$
$349$	−12.4860	−0.668362	−0.334181	+	0.942509i	$0.608460\pi$
$350$	−5.56617	−0.297524
$351$	7.27188	0.388144
$352$	3.74412	0.199562
$353$	−10.3879	−0.552895	−0.276447	−	0.961029i	$-0.589157\pi$
$353$	−10.3879	−0.552895	−0.276447	+	0.961029i	$0.589157\pi$
$354$	−6.13422	−0.326030
$355$	−24.4095	−1.29552
$356$	7.25546	0.384539
$357$	−14.5244	−0.768715
$358$	11.4421	0.604735
$359$	13.9369	0.735563	0.367782	−	0.929912i	$-0.380117\pi$
$359$	13.9369	0.735563	0.367782	+	0.929912i	$0.380117\pi$
$360$	3.33324	0.175677
$361$	1.00000	0.0526316
$362$	3.89565	0.204751
$363$	3.05173	0.160174
$364$	−3.72401	−0.195191
$365$	−21.7174	−1.13674
$366$	−5.45347	−0.285057
$367$	1.57396	0.0821602	0.0410801	−	0.999156i	$-0.486920\pi$
$367$	1.57396	0.0821602	0.0410801	+	0.999156i	$0.486920\pi$
$368$	−4.47000	−0.233015
$369$	18.1212	0.943352
$370$	13.4693	0.700234
$371$	−35.2864	−1.83198
$372$	−1.58981	−0.0824278
$373$	31.2405	1.61757	0.808785	−	0.588104i	$-0.200125\pi$
$373$	31.2405	1.61757	0.808785	+	0.588104i	$0.200125\pi$
$374$	−20.8694	−1.07913
$375$	12.1996	0.629986
$376$	10.0003	0.515727
$377$	−1.50718	−0.0776237
$378$	−12.9711	−0.667161
$379$	1.62362	0.0833996	0.0416998	−	0.999130i	$-0.486723\pi$
$379$	1.62362	0.0833996	0.0416998	+	0.999130i	$0.486723\pi$
$380$	−1.68533	−0.0864556
$381$	1.67849	0.0859915
$382$	6.12375	0.313318
$383$	17.3625	0.887184	0.443592	−	0.896229i	$-0.353704\pi$
$383$	17.3625	0.887184	0.443592	+	0.896229i	$0.353704\pi$
$384$	1.01104	0.0515945
$385$	−16.2632	−0.828847
$386$	24.8117	1.26288
$387$	12.4252	0.631607
$388$	8.92880	0.453291
$389$	−1.73177	−0.0878044	−0.0439022	−	0.999036i	$-0.513979\pi$
$389$	−1.73177	−0.0878044	−0.0439022	+	0.999036i	$0.513979\pi$
$390$	2.46204	0.124670
$391$	24.9154	1.26003
$392$	−0.357353	−0.0180491
$393$	−18.2864	−0.922425
$394$	−1.66743	−0.0840040
$395$	−0.858729	−0.0432073
$396$	−7.40509	−0.372120
$397$	27.9981	1.40519	0.702593	−	0.711592i	$-0.252025\pi$
$397$	27.9981	1.40519	0.702593	+	0.711592i	$0.252025\pi$
$398$	−13.2307	−0.663193
$399$	2.60579	0.130453
$400$	−2.15966	−0.107983
$401$	−2.12186	−0.105961	−0.0529803	−	0.998596i	$-0.516872\pi$
$401$	−2.12186	−0.105961	−0.0529803	+	0.998596i	$0.516872\pi$
$402$	−9.99143	−0.498327
$403$	2.27204	0.113178
$404$	−3.26464	−0.162422
$405$	−1.42420	−0.0707689
$406$	2.68841	0.133423
$407$	−29.9232	−1.48324
$408$	−5.63546	−0.278997
$409$	5.34213	0.264151	0.132076	−	0.991240i	$-0.457836\pi$
$409$	5.34213	0.264151	0.132076	+	0.991240i	$0.457836\pi$
$410$	15.4416	0.762604
$411$	−21.8585	−1.07820
$412$	−4.60291	−0.226769
$413$	−15.6373	−0.769459
$414$	8.84075	0.434499
$415$	−19.2627	−0.945571
$416$	−1.44491	−0.0708425
$417$	13.9915	0.685165
$418$	3.74412	0.183131
$419$	25.6150	1.25137	0.625686	−	0.780075i	$-0.284819\pi$
$419$	25.6150	1.25137	0.625686	+	0.780075i	$0.284819\pi$
$420$	−4.39162	−0.214289
$421$	15.5235	0.756570	0.378285	−	0.925689i	$-0.376514\pi$
$421$	15.5235	0.756570	0.378285	+	0.925689i	$0.376514\pi$
$422$	−1.00000	−0.0486792
$423$	−19.7786	−0.961666
$424$	−13.6910	−0.664896
$425$	12.0378	0.583917
$426$	14.6434	0.709477
$427$	−13.9019	−0.672760
$428$	11.3374	0.548015
$429$	−5.46964	−0.264077
$430$	10.5878	0.510589
$431$	−5.18770	−0.249883	−0.124941	−	0.992164i	$-0.539874\pi$
$431$	−5.18770	−0.249883	−0.124941	+	0.992164i	$0.539874\pi$
$432$	−5.03276	−0.242139
$433$	6.17574	0.296787	0.148394	−	0.988928i	$-0.452590\pi$
$433$	6.17574	0.296787	0.148394	+	0.988928i	$0.452590\pi$
$434$	−4.05272	−0.194537
$435$	−1.77737	−0.0852185
$436$	7.87738	0.377258
$437$	−4.47000	−0.213829
$438$	13.0284	0.622522
$439$	5.60800	0.267655	0.133828	−	0.991005i	$-0.457273\pi$
$439$	5.60800	0.267655	0.133828	+	0.991005i	$0.457273\pi$
$440$	−6.31007	−0.300821
$441$	0.706771	0.0336558
$442$	8.05379	0.383080
$443$	−34.0124	−1.61598	−0.807988	−	0.589198i	$-0.799444\pi$
$443$	−34.0124	−1.61598	−0.807988	+	0.589198i	$0.799444\pi$
$444$	−8.08031	−0.383475
$445$	−12.2279	−0.579656
$446$	−2.51790	−0.119226
$447$	−0.209386	−0.00990362
$448$	2.57733	0.121768
$449$	−23.5141	−1.10970	−0.554848	−	0.831951i	$-0.687224\pi$
$449$	−23.5141	−1.10970	−0.554848	+	0.831951i	$0.687224\pi$
$450$	4.27137	0.201354
$451$	−34.3048	−1.61535
$452$	−4.88018	−0.229544
$453$	−15.6863	−0.737008
$454$	10.5985	0.497413
$455$	6.27619	0.294232
$456$	1.01104	0.0473464
$457$	−14.4030	−0.673744	−0.336872	−	0.941550i	$-0.609369\pi$
$457$	−14.4030	−0.673744	−0.336872	+	0.941550i	$0.609369\pi$
$458$	−8.07516	−0.377327
$459$	28.0521	1.30936
$460$	7.53343	0.351248
$461$	13.9062	0.647678	0.323839	−	0.946112i	$-0.395026\pi$
$461$	13.9062	0.647678	0.323839	+	0.946112i	$0.395026\pi$
$462$	9.75639	0.453908
$463$	−16.2496	−0.755185	−0.377592	−	0.925972i	$-0.623248\pi$
$463$	−16.2496	−0.755185	−0.377592	+	0.925972i	$0.623248\pi$
$464$	1.04310	0.0484245
$465$	2.67935	0.124252
$466$	24.1277	1.11769
$467$	20.4585	0.946708	0.473354	−	0.880872i	$-0.343043\pi$
$467$	20.4585	0.946708	0.473354	+	0.880872i	$0.343043\pi$
$468$	2.85773	0.132099
$469$	−25.4700	−1.17610
$470$	−16.8538	−0.777409
$471$	−5.75242	−0.265058
$472$	−6.06723	−0.279267
$473$	−23.5218	−1.08153
$474$	0.515158	0.0236620
$475$	−2.15966	−0.0990921
$476$	−14.3658	−0.658456
$477$	27.0781	1.23982
$478$	1.03406	0.0472970
$479$	−26.4103	−1.20672	−0.603359	−	0.797470i	$-0.706171\pi$
$479$	−26.4103	−1.20672	−0.603359	+	0.797470i	$0.706171\pi$
$480$	−1.70394	−0.0777738
$481$	11.5478	0.526535
$482$	1.59067	0.0724530
$483$	−11.6479	−0.529998
$484$	3.01840	0.137200
$485$	−15.0480	−0.683294
$486$	15.9527	0.723627
$487$	−16.0578	−0.727647	−0.363823	−	0.931468i	$-0.618529\pi$
$487$	−16.0578	−0.727647	−0.363823	+	0.931468i	$0.618529\pi$
$488$	−5.39391	−0.244171
$489$	1.14350	0.0517107
$490$	0.602258	0.0272072
$491$	−39.3758	−1.77700	−0.888502	−	0.458872i	$-0.848254\pi$
$491$	−39.3758	−1.77700	−0.888502	+	0.458872i	$0.848254\pi$
$492$	−9.26350	−0.417631
$493$	−5.81413	−0.261855
$494$	−1.44491	−0.0650095
$495$	12.4800	0.560935
$496$	−1.57245	−0.0706049
$497$	37.3288	1.67443
$498$	11.5559	0.517831
$499$	−18.2886	−0.818712	−0.409356	−	0.912375i	$-0.634247\pi$
$499$	−18.2886	−0.818712	−0.409356	+	0.912375i	$0.634247\pi$
$500$	12.0664	0.539626
$501$	−16.9527	−0.757391
$502$	−19.3498	−0.863625
$503$	35.8327	1.59770	0.798851	−	0.601529i	$-0.205442\pi$
$503$	35.8327	1.59770	0.798851	+	0.601529i	$0.205442\pi$
$504$	−5.09744	−0.227058
$505$	5.50200	0.244836
$506$	−16.7362	−0.744015
$507$	−11.0327	−0.489981
$508$	1.66016	0.0736575
$509$	−16.6152	−0.736454	−0.368227	−	0.929736i	$-0.620035\pi$
$509$	−16.6152	−0.736454	−0.368227	+	0.929736i	$0.620035\pi$
$510$	9.49760	0.420561
$511$	33.2119	1.46921
$512$	1.00000	0.0441942
$513$	−5.03276	−0.222202
$514$	−12.4504	−0.549164
$515$	7.75742	0.341833
$516$	−6.35170	−0.279618
$517$	37.4423	1.64671
$518$	−20.5982	−0.905034
$519$	−4.52393	−0.198578
$520$	2.43515	0.106788
$521$	39.9992	1.75240	0.876199	−	0.481949i	$-0.160071\pi$
$521$	39.9992	1.75240	0.876199	+	0.481949i	$0.160071\pi$
$522$	−2.06303	−0.0902964
$523$	−24.3489	−1.06470	−0.532350	−	0.846524i	$-0.678691\pi$
$523$	−24.3489	−1.06470	−0.532350	+	0.846524i	$0.678691\pi$
$524$	−18.0867	−0.790119
$525$	−5.62763	−0.245610
$526$	−18.6737	−0.814212
$527$	8.76468	0.381795
$528$	3.78546	0.164741
$529$	−3.01906	−0.131264
$530$	23.0739	1.00227
$531$	11.9997	0.520744
$532$	2.57733	0.111742
$533$	13.2387	0.573433
$534$	7.33558	0.317442
$535$	−19.1073	−0.826081
$536$	−9.88231	−0.426851
$537$	11.5685	0.499216
$538$	−9.17178	−0.395424
$539$	−1.33797	−0.0576305
$540$	8.48186	0.365001
$541$	6.00983	0.258383	0.129191	−	0.991620i	$-0.458762\pi$
$541$	6.00983	0.258383	0.129191	+	0.991620i	$0.458762\pi$
$542$	−30.4063	−1.30606
$543$	3.93867	0.169024
$544$	−5.57391	−0.238979
$545$	−13.2760	−0.568681
$546$	−3.76513	−0.161133
$547$	−13.3809	−0.572125	−0.286063	−	0.958211i	$-0.592347\pi$
$547$	−13.3809	−0.572125	−0.286063	+	0.958211i	$0.592347\pi$
$548$	−21.6198	−0.923550
$549$	10.6680	0.455301
$550$	−8.08603	−0.344789
$551$	1.04310	0.0444374
$552$	−4.51936	−0.192357
$553$	1.31323	0.0558443
$554$	−15.4661	−0.657091
$555$	13.6180	0.578052
$556$	13.8387	0.586890
$557$	18.9792	0.804175	0.402087	−	0.915601i	$-0.368285\pi$
$557$	18.9792	0.804175	0.402087	+	0.915601i	$0.368285\pi$
$558$	3.10998	0.131656
$559$	9.07740	0.383933
$560$	−4.34366	−0.183553
$561$	−21.0998	−0.890834
$562$	29.9663	1.26405
$563$	7.10793	0.299564	0.149782	−	0.988719i	$-0.452143\pi$
$563$	7.10793	0.299564	0.149782	+	0.988719i	$0.452143\pi$
$564$	10.1107	0.425739
$565$	8.22471	0.346016
$566$	−16.1667	−0.679535
$567$	2.17799	0.0914669
$568$	14.4835	0.607715
$569$	31.2765	1.31118	0.655591	−	0.755117i	$-0.272420\pi$
$569$	31.2765	1.31118	0.655591	+	0.755117i	$0.272420\pi$
$570$	−1.70394	−0.0713702
$571$	−1.93350	−0.0809146	−0.0404573	−	0.999181i	$-0.512881\pi$
$571$	−1.93350	−0.0809146	−0.0404573	+	0.999181i	$0.512881\pi$
$572$	−5.40991	−0.226200
$573$	6.19137	0.258648
$574$	−23.6144	−0.985645
$575$	9.65370	0.402587
$576$	−1.97779	−0.0824081
$577$	−45.9571	−1.91322	−0.956610	−	0.291372i	$-0.905888\pi$
$577$	−45.9571	−1.91322	−0.956610	+	0.291372i	$0.905888\pi$
$578$	14.0685	0.585171
$579$	25.0857	1.04252
$580$	−1.75796	−0.0729954
$581$	29.4580	1.22213
$582$	9.02739	0.374198
$583$	−51.2609	−2.12301
$584$	12.8861	0.533232
$585$	−4.81622	−0.199126
$586$	−18.6016	−0.768423
$587$	−18.5439	−0.765389	−0.382694	−	0.923875i	$-0.625004\pi$
$587$	−18.5439	−0.765389	−0.382694	+	0.923875i	$0.625004\pi$
$588$	−0.361299	−0.0148997
$589$	−1.57245	−0.0647915
$590$	10.2253	0.420968
$591$	−1.68584	−0.0693463
$592$	−7.99207	−0.328472
$593$	4.14516	0.170221	0.0851106	−	0.996372i	$-0.472876\pi$
$593$	4.14516	0.170221	0.0851106	+	0.996372i	$0.472876\pi$
$594$	−18.8432	−0.773147
$595$	24.2112	0.992561
$596$	−0.207099	−0.00848312
$597$	−13.3768	−0.547474
$598$	6.45875	0.264118
$599$	−0.180105	−0.00735888	−0.00367944	−	0.999993i	$-0.501171\pi$
$599$	−0.180105	−0.00735888	−0.00367944	+	0.999993i	$0.501171\pi$
$600$	−2.18351	−0.0891414
$601$	27.7291	1.13109	0.565547	−	0.824716i	$-0.308665\pi$
$601$	27.7291	1.13109	0.565547	+	0.824716i	$0.308665\pi$
$602$	−16.1917	−0.659923
$603$	19.5452	0.795941
$604$	−15.5150	−0.631297
$605$	−5.08700	−0.206816
$606$	−3.30069	−0.134081
$607$	−21.7901	−0.884434	−0.442217	−	0.896908i	$-0.645808\pi$
$607$	−21.7901	−0.884434	−0.442217	+	0.896908i	$0.645808\pi$
$608$	1.00000	0.0405554
$609$	2.71809	0.110143
$610$	9.09051	0.368064
$611$	−14.4495	−0.584566
$612$	11.0240	0.445621
$613$	38.1825	1.54218	0.771088	−	0.636729i	$-0.219713\pi$
$613$	38.1825	1.54218	0.771088	+	0.636729i	$0.219713\pi$
$614$	−32.8798	−1.32692
$615$	15.6121	0.629539
$616$	9.64983	0.388803
$617$	−7.58764	−0.305467	−0.152733	−	0.988267i	$-0.548808\pi$
$617$	−7.58764	−0.305467	−0.152733	+	0.988267i	$0.548808\pi$
$618$	−4.65373	−0.187201
$619$	24.1956	0.972504	0.486252	−	0.873819i	$-0.338364\pi$
$619$	24.1956	0.972504	0.486252	+	0.873819i	$0.338364\pi$
$620$	2.65009	0.106430
$621$	22.4965	0.902752
$622$	22.2198	0.890932
$623$	18.6998	0.749190
$624$	−1.46086	−0.0584813
$625$	−9.53754	−0.381502
$626$	−0.633676	−0.0253268
$627$	3.78546	0.151177
$628$	−5.68960	−0.227040
$629$	44.5471	1.77621
$630$	8.59086	0.342268
$631$	−14.6141	−0.581778	−0.290889	−	0.956757i	$-0.593951\pi$
$631$	−14.6141	−0.581778	−0.290889	+	0.956757i	$0.593951\pi$
$632$	0.509532	0.0202681
$633$	−1.01104	−0.0401853
$634$	21.6132	0.858370
$635$	−2.79791	−0.111032
$636$	−13.8422	−0.548880
$637$	0.516343	0.0204583
$638$	3.90547	0.154619
$639$	−28.6454	−1.13319
$640$	−1.68533	−0.0666185
$641$	−10.9177	−0.431224	−0.215612	−	0.976479i	$-0.569175\pi$
$641$	−10.9177	−0.431224	−0.215612	+	0.976479i	$0.569175\pi$
$642$	11.4626	0.452393
$643$	31.2271	1.23147	0.615737	−	0.787951i	$-0.288858\pi$
$643$	31.2271	1.23147	0.615737	+	0.787951i	$0.288858\pi$
$644$	−11.5207	−0.453979
$645$	10.7047	0.421498
$646$	−5.57391	−0.219303
$647$	12.1831	0.478969	0.239484	−	0.970900i	$-0.423022\pi$
$647$	12.1831	0.478969	0.239484	+	0.970900i	$0.423022\pi$
$648$	0.845055	0.0331969
$649$	−22.7164	−0.891696
$650$	3.12052	0.122397
$651$	−4.09747	−0.160592
$652$	1.13101	0.0442937
$653$	12.5853	0.492501	0.246251	−	0.969206i	$-0.420801\pi$
$653$	12.5853	0.492501	0.246251	+	0.969206i	$0.420801\pi$
$654$	7.96436	0.311431
$655$	30.4820	1.19103
$656$	−9.16233	−0.357729
$657$	−25.4861	−0.994309
$658$	25.7741	1.00478
$659$	−49.9120	−1.94429	−0.972147	−	0.234371i	$-0.924697\pi$
$659$	−49.9120	−1.94429	−0.972147	+	0.234371i	$0.924697\pi$
$660$	−6.37975	−0.248331
$661$	21.2963	0.828330	0.414165	−	0.910202i	$-0.364074\pi$
$661$	21.2963	0.828330	0.414165	+	0.910202i	$0.364074\pi$
$662$	21.6767	0.842488
$663$	8.14272	0.316237
$664$	11.4297	0.443557
$665$	−4.34366	−0.168440
$666$	15.8067	0.612496
$667$	−4.66265	−0.180538
$668$	−16.7676	−0.648757
$669$	−2.54570	−0.0984224
$670$	16.6550	0.643437
$671$	−20.1954	−0.779635
$672$	2.60579	0.100521
$673$	3.85953	0.148774	0.0743870	−	0.997229i	$-0.476300\pi$
$673$	3.85953	0.148774	0.0743870	+	0.997229i	$0.476300\pi$
$674$	−17.6816	−0.681070
$675$	10.8691	0.418350
$676$	−10.9122	−0.419701
$677$	−6.85542	−0.263475	−0.131738	−	0.991285i	$-0.542056\pi$
$677$	−6.85542	−0.263475	−0.131738	+	0.991285i	$0.542056\pi$
$678$	−4.93407	−0.189492
$679$	23.0125	0.883139
$680$	9.39388	0.360239
$681$	10.7156	0.410621
$682$	−5.88742	−0.225441
$683$	4.06976	0.155725	0.0778624	−	0.996964i	$-0.475191\pi$
$683$	4.06976	0.155725	0.0778624	+	0.996964i	$0.475191\pi$
$684$	−1.97779	−0.0756229
$685$	36.4364	1.39216
$686$	−18.9624	−0.723986
$687$	−8.16432	−0.311488
$688$	−6.28233	−0.239512
$689$	19.7823	0.753646
$690$	7.61662	0.289960
$691$	39.3245	1.49597	0.747986	−	0.663714i	$-0.231021\pi$
$691$	39.3245	1.49597	0.747986	+	0.663714i	$0.231021\pi$
$692$	−4.47452	−0.170096
$693$	−19.0854	−0.724994
$694$	20.6562	0.784099
$695$	−23.3227	−0.884681
$696$	1.05461	0.0399751
$697$	51.0700	1.93441
$698$	−12.4860	−0.472603
$699$	24.3941	0.922670
$700$	−5.56617	−0.210381
$701$	36.1835	1.36663	0.683317	−	0.730122i	$-0.260537\pi$
$701$	36.1835	1.36663	0.683317	+	0.730122i	$0.260537\pi$
$702$	7.27188	0.274459
$703$	−7.99207	−0.301427
$704$	3.74412	0.141112
$705$	−17.0399	−0.641761
$706$	−10.3879	−0.390956
$707$	−8.41407	−0.316444
$708$	−6.13422	−0.230538
$709$	−35.4217	−1.33029	−0.665145	−	0.746714i	$-0.731630\pi$
$709$	−35.4217	−1.33029	−0.665145	+	0.746714i	$0.731630\pi$
$710$	−24.4095	−0.916072
$711$	−1.00775	−0.0377935
$712$	7.25546	0.271910
$713$	7.02884	0.263232
$714$	−14.5244	−0.543564
$715$	9.11748	0.340974
$716$	11.4421	0.427612
$717$	1.04548	0.0390443
$718$	13.9369	0.520122
$719$	23.4183	0.873354	0.436677	−	0.899618i	$-0.356155\pi$
$719$	23.4183	0.873354	0.436677	+	0.899618i	$0.356155\pi$
$720$	3.33324	0.124222
$721$	−11.8632	−0.441810
$722$	1.00000	0.0372161
$723$	1.60823	0.0598108
$724$	3.89565	0.144781
$725$	−2.25274	−0.0836646
$726$	3.05173	0.113260
$727$	26.6586	0.988711	0.494356	−	0.869260i	$-0.335404\pi$
$727$	26.6586	0.988711	0.494356	+	0.869260i	$0.335404\pi$
$728$	−3.72401	−0.138021
$729$	13.5936	0.503468
$730$	−21.7174	−0.803797
$731$	35.0172	1.29516
$732$	−5.45347	−0.201566
$733$	0.770683	0.0284658	0.0142329	−	0.999899i	$-0.495469\pi$
$733$	0.770683	0.0284658	0.0142329	+	0.999899i	$0.495469\pi$
$734$	1.57396	0.0580960
$735$	0.608908	0.0224599
$736$	−4.47000	−0.164767
$737$	−37.0005	−1.36293
$738$	18.1212	0.667051
$739$	−0.516291	−0.0189921	−0.00949604	−	0.999955i	$-0.503023\pi$
$739$	−0.516291	−0.0189921	−0.00949604	+	0.999955i	$0.503023\pi$
$740$	13.4693	0.495140
$741$	−1.46086	−0.0536662
$742$	−35.2864	−1.29540
$743$	25.1931	0.924247	0.462124	−	0.886816i	$-0.347088\pi$
$743$	25.1931	0.924247	0.462124	+	0.886816i	$0.347088\pi$
$744$	−1.58981	−0.0582852
$745$	0.349031	0.0127875
$746$	31.2405	1.14379
$747$	−22.6055	−0.827092
$748$	−20.8694	−0.763060
$749$	29.2203	1.06769
$750$	12.1996	0.445467
$751$	−43.2515	−1.57827	−0.789134	−	0.614221i	$-0.789471\pi$
$751$	−43.2515	−1.57827	−0.789134	+	0.614221i	$0.789471\pi$
$752$	10.0003	0.364674
$753$	−19.5635	−0.712933
$754$	−1.50718	−0.0548883
$755$	26.1479	0.951620
$756$	−12.9711	−0.471754
$757$	−17.4231	−0.633254	−0.316627	−	0.948550i	$-0.602550\pi$
$757$	−17.4231	−0.633254	−0.316627	+	0.948550i	$0.602550\pi$
$758$	1.62362	0.0589724
$759$	−16.9210	−0.614194
$760$	−1.68533	−0.0611333
$761$	−4.35960	−0.158035	−0.0790177	−	0.996873i	$-0.525178\pi$
$761$	−4.35960	−0.158035	−0.0790177	+	0.996873i	$0.525178\pi$
$762$	1.67849	0.0608052
$763$	20.3026	0.735005
$764$	6.12375	0.221550
$765$	−18.5792	−0.671731
$766$	17.3625	0.627334
$767$	8.76659	0.316543
$768$	1.01104	0.0364828
$769$	13.5028	0.486923	0.243461	−	0.969911i	$-0.421717\pi$
$769$	13.5028	0.486923	0.243461	+	0.969911i	$0.421717\pi$
$770$	−16.2632	−0.586083
$771$	−12.5879	−0.453342
$772$	24.8117	0.892993
$773$	−46.6843	−1.67912	−0.839559	−	0.543268i	$-0.817187\pi$
$773$	−46.6843	−1.67912	−0.839559	+	0.543268i	$0.817187\pi$
$774$	12.4252	0.446613
$775$	3.39595	0.121986
$776$	8.92880	0.320525
$777$	−20.8257	−0.747116
$778$	−1.73177	−0.0620871
$779$	−9.16233	−0.328275
$780$	2.46204	0.0881551
$781$	54.2279	1.94043
$782$	24.9154	0.890973
$783$	−5.24965	−0.187607
$784$	−0.357353	−0.0127626
$785$	9.58885	0.342241
$786$	−18.2864	−0.652253
$787$	−51.1253	−1.82242	−0.911210	−	0.411941i	$-0.864851\pi$
$787$	−51.1253	−1.82242	−0.911210	+	0.411941i	$0.864851\pi$
$788$	−1.66743	−0.0593998
$789$	−18.8799	−0.672142
$790$	−0.858729	−0.0305522
$791$	−12.5778	−0.447217
$792$	−7.40509	−0.263128
$793$	7.79371	0.276763
$794$	27.9981	0.993617
$795$	23.3287	0.827384
$796$	−13.2307	−0.468948
$797$	−7.98537	−0.282856	−0.141428	−	0.989949i	$-0.545169\pi$
$797$	−7.98537	−0.282856	−0.141428	+	0.989949i	$0.545169\pi$
$798$	2.60579	0.0922440
$799$	−55.7408	−1.97197
$800$	−2.15966	−0.0763556
$801$	−14.3498	−0.507026
$802$	−2.12186	−0.0749255
$803$	48.2472	1.70261
$804$	−9.99143	−0.352371
$805$	19.4162	0.684330
$806$	2.27204	0.0800293
$807$	−9.27306	−0.326427
$808$	−3.26464	−0.114850
$809$	27.4850	0.966322	0.483161	−	0.875532i	$-0.339489\pi$
$809$	27.4850	0.966322	0.483161	+	0.875532i	$0.339489\pi$
$810$	−1.42420	−0.0500411
$811$	7.87048	0.276370	0.138185	−	0.990406i	$-0.455873\pi$
$811$	7.87048	0.276370	0.138185	+	0.990406i	$0.455873\pi$
$812$	2.68841	0.0943446
$813$	−30.7420	−1.07817
$814$	−29.9232	−1.04881
$815$	−1.90612	−0.0667686
$816$	−5.63546	−0.197280
$817$	−6.28233	−0.219791
$818$	5.34213	0.186783
$819$	7.36533	0.257365
$820$	15.4416	0.539242
$821$	51.3089	1.79069	0.895347	−	0.445370i	$-0.146928\pi$
$821$	51.3089	1.79069	0.895347	+	0.445370i	$0.146928\pi$
$822$	−21.8585	−0.762402
$823$	−52.5129	−1.83048	−0.915242	−	0.402905i	$-0.868001\pi$
$823$	−52.5129	−1.83048	−0.915242	+	0.402905i	$0.868001\pi$
$824$	−4.60291	−0.160350
$825$	−8.17531	−0.284628
$826$	−15.6373	−0.544090
$827$	−49.2204	−1.71156	−0.855781	−	0.517339i	$-0.826923\pi$
$827$	−49.2204	−1.71156	−0.855781	+	0.517339i	$0.826923\pi$
$828$	8.84075	0.307237
$829$	−11.8128	−0.410277	−0.205138	−	0.978733i	$-0.565764\pi$
$829$	−11.8128	−0.410277	−0.205138	+	0.978733i	$0.565764\pi$
$830$	−19.2627	−0.668620
$831$	−15.6369	−0.542437
$832$	−1.44491	−0.0500932
$833$	1.99185	0.0690137
$834$	13.9915	0.484485
$835$	28.2589	0.977939
$836$	3.74412	0.129493
$837$	7.91374	0.273539
$838$	25.6150	0.884854
$839$	52.9688	1.82869	0.914344	−	0.404939i	$-0.132707\pi$
$839$	52.9688	1.82869	0.914344	+	0.404939i	$0.132707\pi$
$840$	−4.39162	−0.151525
$841$	−27.9119	−0.962481
$842$	15.5235	0.534976
$843$	30.2971	1.04349
$844$	−1.00000	−0.0344214
$845$	18.3907	0.632660
$846$	−19.7786	−0.680001
$847$	7.77943	0.267304
$848$	−13.6910	−0.470152
$849$	−16.3452	−0.560965
$850$	12.0378	0.412892
$851$	35.7246	1.22462
$852$	14.6434	0.501676
$853$	32.6522	1.11799	0.558995	−	0.829171i	$-0.311187\pi$
$853$	32.6522	1.11799	0.558995	+	0.829171i	$0.311187\pi$
$854$	−13.9019	−0.475713
$855$	3.33324	0.113994
$856$	11.3374	0.387505
$857$	−6.63050	−0.226493	−0.113247	−	0.993567i	$-0.536125\pi$
$857$	−6.63050	−0.226493	−0.113247	+	0.993567i	$0.536125\pi$
$858$	−5.46964	−0.186730
$859$	35.9505	1.22661	0.613307	−	0.789844i	$-0.289839\pi$
$859$	35.9505	1.22661	0.613307	+	0.789844i	$0.289839\pi$
$860$	10.5878	0.361041
$861$	−23.8751	−0.813662
$862$	−5.18770	−0.176694
$863$	−0.132464	−0.00450914	−0.00225457	−	0.999997i	$-0.500718\pi$
$863$	−0.132464	−0.00450914	−0.00225457	+	0.999997i	$0.500718\pi$
$864$	−5.03276	−0.171218
$865$	7.54105	0.256403
$866$	6.17574	0.209860
$867$	14.2238	0.483066
$868$	−4.05272	−0.137558
$869$	1.90775	0.0647158
$870$	−1.77737	−0.0602586
$871$	14.2790	0.483827
$872$	7.87738	0.266762
$873$	−17.6593	−0.597678
$874$	−4.47000	−0.151200
$875$	31.0991	1.05134
$876$	13.0284	0.440190
$877$	−24.1327	−0.814903	−0.407452	−	0.913227i	$-0.633582\pi$
$877$	−24.1327	−0.814903	−0.407452	+	0.913227i	$0.633582\pi$
$878$	5.60800	0.189261
$879$	−18.8069	−0.634343
$880$	−6.31007	−0.212712
$881$	16.6925	0.562385	0.281192	−	0.959651i	$-0.409270\pi$
$881$	16.6925	0.562385	0.281192	+	0.959651i	$0.409270\pi$
$882$	0.706771	0.0237982
$883$	−29.9575	−1.00815	−0.504075	−	0.863660i	$-0.668166\pi$
$883$	−29.9575	−1.00815	−0.504075	+	0.863660i	$0.668166\pi$
$884$	8.05379	0.270878
$885$	10.3382	0.347514
$886$	−34.0124	−1.14267
$887$	−13.3155	−0.447091	−0.223546	−	0.974693i	$-0.571763\pi$
$887$	−13.3155	−0.447091	−0.223546	+	0.974693i	$0.571763\pi$
$888$	−8.08031	−0.271158
$889$	4.27878	0.143506
$890$	−12.2279	−0.409879
$891$	3.16398	0.105997
$892$	−2.51790	−0.0843054
$893$	10.0003	0.334648
$894$	−0.209386	−0.00700291
$895$	−19.2837	−0.644584
$896$	2.57733	0.0861027
$897$	6.53007	0.218033
$898$	−23.5141	−0.784674
$899$	−1.64021	−0.0547042
$900$	4.27137	0.142379
$901$	76.3127	2.54234
$902$	−34.3048	−1.14223
$903$	−16.3705	−0.544775
$904$	−4.88018	−0.162312
$905$	−6.56546	−0.218243
$906$	−15.6863	−0.521143
$907$	12.0656	0.400633	0.200316	−	0.979731i	$-0.435803\pi$
$907$	12.0656	0.400633	0.200316	+	0.979731i	$0.435803\pi$
$908$	10.5985	0.351724
$909$	6.45679	0.214158
$910$	6.27619	0.208054
$911$	0.177498	0.00588076	0.00294038	−	0.999996i	$-0.499064\pi$
$911$	0.177498	0.00588076	0.00294038	+	0.999996i	$0.499064\pi$
$912$	1.01104	0.0334789
$913$	42.7940	1.41627
$914$	−14.4030	−0.476409
$915$	9.19089	0.303841
$916$	−8.07516	−0.266811
$917$	−46.6153	−1.53937
$918$	28.0521	0.925859
$919$	−14.4948	−0.478140	−0.239070	−	0.971002i	$-0.576843\pi$
$919$	−14.4948	−0.478140	−0.239070	+	0.971002i	$0.576843\pi$
$920$	7.53343	0.248370
$921$	−33.2429	−1.09539
$922$	13.9062	0.457977
$923$	−20.9274	−0.688832
$924$	9.75639	0.320962
$925$	17.2602	0.567511
$926$	−16.2496	−0.533996
$927$	9.10360	0.299002
$928$	1.04310	0.0342413
$929$	−32.3632	−1.06180	−0.530901	−	0.847434i	$-0.678146\pi$
$929$	−32.3632	−1.06180	−0.530901	+	0.847434i	$0.678146\pi$
$930$	2.67935	0.0878595
$931$	−0.357353	−0.0117118
$932$	24.1277	0.790329
$933$	22.4651	0.735475
$934$	20.4585	0.669424
$935$	35.1718	1.15024
$936$	2.85773	0.0934079
$937$	−28.2187	−0.921866	−0.460933	−	0.887435i	$-0.652485\pi$
$937$	−28.2187	−0.921866	−0.460933	+	0.887435i	$0.652485\pi$
$938$	−25.4700	−0.831625
$939$	−0.640673	−0.0209076
$940$	−16.8538	−0.549711
$941$	12.9846	0.423287	0.211643	−	0.977347i	$-0.432118\pi$
$941$	12.9846	0.423287	0.211643	+	0.977347i	$0.432118\pi$
$942$	−5.75242	−0.187424
$943$	40.9557	1.33370
$944$	−6.06723	−0.197471
$945$	21.8606	0.711125
$946$	−23.5218	−0.764759
$947$	20.6004	0.669423	0.334712	−	0.942321i	$-0.391361\pi$
$947$	20.6004	0.669423	0.334712	+	0.942321i	$0.391361\pi$
$948$	0.515158	0.0167315
$949$	−18.6193	−0.604408
$950$	−2.15966	−0.0700687
$951$	21.8519	0.708595
$952$	−14.3658	−0.465599
$953$	−36.6239	−1.18636	−0.593182	−	0.805068i	$-0.702129\pi$
$953$	−36.6239	−1.18636	−0.593182	+	0.805068i	$0.702129\pi$
$954$	27.0781	0.876685
$955$	−10.3205	−0.333965
$956$	1.03406	0.0334440
$957$	3.94860	0.127640
$958$	−26.4103	−0.853279
$959$	−55.7213	−1.79934
$960$	−1.70394	−0.0549944
$961$	−28.5274	−0.920239
$962$	11.5478	0.372316
$963$	−22.4231	−0.722575
$964$	1.59067	0.0512320
$965$	−41.8159	−1.34610
$966$	−11.6479	−0.374765
$967$	−37.4466	−1.20420	−0.602101	−	0.798420i	$-0.705670\pi$
$967$	−37.4466	−1.20420	−0.602101	+	0.798420i	$0.705670\pi$
$968$	3.01840	0.0970151
$969$	−5.63546	−0.181037
$970$	−15.0480	−0.483162
$971$	−39.1062	−1.25498	−0.627488	−	0.778626i	$-0.715917\pi$
$971$	−39.1062	−1.25498	−0.627488	+	0.778626i	$0.715917\pi$
$972$	15.9527	0.511682
$973$	35.6668	1.14343
$974$	−16.0578	−0.514524
$975$	3.15497	0.101040
$976$	−5.39391	−0.172655
$977$	−0.509503	−0.0163005	−0.00815023	−	0.999967i	$-0.502594\pi$
$977$	−0.509503	−0.0163005	−0.00815023	+	0.999967i	$0.502594\pi$
$978$	1.14350	0.0365650
$979$	27.1653	0.868207
$980$	0.602258	0.0192384
$981$	−15.5798	−0.497426
$982$	−39.3758	−1.25653
$983$	23.9076	0.762535	0.381267	−	0.924465i	$-0.375488\pi$
$983$	23.9076	0.762535	0.381267	+	0.924465i	$0.375488\pi$
$984$	−9.26350	−0.295310
$985$	2.81017	0.0895396
$986$	−5.81413	−0.185160
$987$	26.0587	0.829458
$988$	−1.44491	−0.0459687
$989$	28.0821	0.892958
$990$	12.4800	0.396641
$991$	23.1786	0.736293	0.368146	−	0.929768i	$-0.379992\pi$
$991$	23.1786	0.736293	0.368146	+	0.929768i	$0.379992\pi$
$992$	−1.57245	−0.0499252
$993$	21.9160	0.695484
$994$	37.3288	1.18400
$995$	22.2980	0.706895
$996$	11.5559	0.366161
$997$	3.53304	0.111893	0.0559463	−	0.998434i	$-0.482182\pi$
$997$	3.53304	0.111893	0.0559463	+	0.998434i	$0.482182\pi$
$998$	−18.2886	−0.578917
$999$	40.2221	1.27257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.22	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.22	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.01104 q^{3} +1.00000 q^{4} -1.68533 q^{5} +1.01104 q^{6} +2.57733 q^{7} +1.00000 q^{8} -1.97779 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.01104 q^{3} +1.00000 q^{4} -1.68533 q^{5} +1.01104 q^{6} +2.57733 q^{7} +1.00000 q^{8} -1.97779 q^{9} -1.68533 q^{10} +3.74412 q^{11} +1.01104 q^{12} -1.44491 q^{13} +2.57733 q^{14} -1.70394 q^{15} +1.00000 q^{16} -5.57391 q^{17} -1.97779 q^{18} +1.00000 q^{19} -1.68533 q^{20} +2.60579 q^{21} +3.74412 q^{22} -4.47000 q^{23} +1.01104 q^{24} -2.15966 q^{25} -1.44491 q^{26} -5.03276 q^{27} +2.57733 q^{28} +1.04310 q^{29} -1.70394 q^{30} -1.57245 q^{31} +1.00000 q^{32} +3.78546 q^{33} -5.57391 q^{34} -4.34366 q^{35} -1.97779 q^{36} -7.99207 q^{37} +1.00000 q^{38} -1.46086 q^{39} -1.68533 q^{40} -9.16233 q^{41} +2.60579 q^{42} -6.28233 q^{43} +3.74412 q^{44} +3.33324 q^{45} -4.47000 q^{46} +10.0003 q^{47} +1.01104 q^{48} -0.357353 q^{49} -2.15966 q^{50} -5.63546 q^{51} -1.44491 q^{52} -13.6910 q^{53} -5.03276 q^{54} -6.31007 q^{55} +2.57733 q^{56} +1.01104 q^{57} +1.04310 q^{58} -6.06723 q^{59} -1.70394 q^{60} -5.39391 q^{61} -1.57245 q^{62} -5.09744 q^{63} +1.00000 q^{64} +2.43515 q^{65} +3.78546 q^{66} -9.88231 q^{67} -5.57391 q^{68} -4.51936 q^{69} -4.34366 q^{70} +14.4835 q^{71} -1.97779 q^{72} +12.8861 q^{73} -7.99207 q^{74} -2.18351 q^{75} +1.00000 q^{76} +9.64983 q^{77} -1.46086 q^{78} +0.509532 q^{79} -1.68533 q^{80} +0.845055 q^{81} -9.16233 q^{82} +11.4297 q^{83} +2.60579 q^{84} +9.39388 q^{85} -6.28233 q^{86} +1.05461 q^{87} +3.74412 q^{88} +7.25546 q^{89} +3.33324 q^{90} -3.72401 q^{91} -4.47000 q^{92} -1.58981 q^{93} +10.0003 q^{94} -1.68533 q^{95} +1.01104 q^{96} +8.92880 q^{97} -0.357353 q^{98} -7.40509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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