LMFDB - Embedded newform 8041.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49915 q^{2} -0.148971 q^{3} +0.247445 q^{4} -2.56328 q^{5} +0.223329 q^{6} +2.63900 q^{7} +2.62734 q^{8} -2.97781 q^{9} +O(q^{10})$	\(q-1.49915 q^{2} -0.148971 q^{3} +0.247445 q^{4} -2.56328 q^{5} +0.223329 q^{6} +2.63900 q^{7} +2.62734 q^{8} -2.97781 q^{9} +3.84274 q^{10} +1.00000 q^{11} -0.0368621 q^{12} -3.10475 q^{13} -3.95625 q^{14} +0.381854 q^{15} -4.43366 q^{16} +1.00000 q^{17} +4.46417 q^{18} +0.742462 q^{19} -0.634271 q^{20} -0.393134 q^{21} -1.49915 q^{22} -0.611520 q^{23} -0.391397 q^{24} +1.57040 q^{25} +4.65448 q^{26} +0.890518 q^{27} +0.653008 q^{28} +0.417781 q^{29} -0.572455 q^{30} -2.18140 q^{31} +1.39204 q^{32} -0.148971 q^{33} -1.49915 q^{34} -6.76450 q^{35} -0.736844 q^{36} +6.72485 q^{37} -1.11306 q^{38} +0.462517 q^{39} -6.73461 q^{40} +8.32806 q^{41} +0.589366 q^{42} -1.00000 q^{43} +0.247445 q^{44} +7.63295 q^{45} +0.916759 q^{46} +0.817649 q^{47} +0.660486 q^{48} -0.0356739 q^{49} -2.35427 q^{50} -0.148971 q^{51} -0.768255 q^{52} -7.15729 q^{53} -1.33502 q^{54} -2.56328 q^{55} +6.93355 q^{56} -0.110605 q^{57} -0.626315 q^{58} -5.40324 q^{59} +0.0944878 q^{60} +10.5555 q^{61} +3.27024 q^{62} -7.85844 q^{63} +6.78045 q^{64} +7.95834 q^{65} +0.223329 q^{66} +6.84010 q^{67} +0.247445 q^{68} +0.0910985 q^{69} +10.1410 q^{70} -14.1499 q^{71} -7.82371 q^{72} -1.45025 q^{73} -10.0816 q^{74} -0.233944 q^{75} +0.183718 q^{76} +2.63900 q^{77} -0.693381 q^{78} +1.82869 q^{79} +11.3647 q^{80} +8.80076 q^{81} -12.4850 q^{82} -8.21643 q^{83} -0.0972791 q^{84} -2.56328 q^{85} +1.49915 q^{86} -0.0622371 q^{87} +2.62734 q^{88} -7.06585 q^{89} -11.4429 q^{90} -8.19344 q^{91} -0.151318 q^{92} +0.324965 q^{93} -1.22578 q^{94} -1.90314 q^{95} -0.207373 q^{96} -2.57519 q^{97} +0.0534805 q^{98} -2.97781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−1.49915	−1.06006	−0.530029	−	0.847980i	$-0.677819\pi$
$2$	−1.49915	−1.06006	−0.530029	+	0.847980i	$0.677819\pi$
$3$	−0.148971	−0.0860083	−0.0430041	−	0.999075i	$-0.513693\pi$
$3$	−0.148971	−0.0860083	−0.0430041	+	0.999075i	$0.513693\pi$
$4$	0.247445	0.123723
$5$	−2.56328	−1.14633	−0.573167	−	0.819439i	$-0.694285\pi$
$5$	−2.56328	−1.14633	−0.573167	+	0.819439i	$0.694285\pi$
$6$	0.223329	0.0911738
$7$	2.63900	0.997449	0.498724	−	0.866761i	$-0.333802\pi$
$7$	2.63900	0.997449	0.498724	+	0.866761i	$0.333802\pi$
$8$	2.62734	0.928905
$9$	−2.97781	−0.992603
$10$	3.84274	1.21518
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.0368621	−0.0106412
$13$	−3.10475	−0.861102	−0.430551	−	0.902566i	$-0.641681\pi$
$13$	−3.10475	−0.861102	−0.430551	+	0.902566i	$0.641681\pi$
$14$	−3.95625	−1.05735
$15$	0.381854	0.0985942
$16$	−4.43366	−1.10842
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.46417	1.05222
$19$	0.742462	0.170332	0.0851662	−	0.996367i	$-0.472858\pi$
$19$	0.742462	0.170332	0.0851662	+	0.996367i	$0.472858\pi$
$20$	−0.634271	−0.141827
$21$	−0.393134	−0.0857889
$22$	−1.49915	−0.319619
$23$	−0.611520	−0.127511	−0.0637553	−	0.997966i	$-0.520308\pi$
$23$	−0.611520	−0.127511	−0.0637553	+	0.997966i	$0.520308\pi$
$24$	−0.391397	−0.0798935
$25$	1.57040	0.314081
$26$	4.65448	0.912818
$27$	0.890518	0.171380
$28$	0.653008	0.123407
$29$	0.417781	0.0775800	0.0387900	−	0.999247i	$-0.487650\pi$
$29$	0.417781	0.0775800	0.0387900	+	0.999247i	$0.487650\pi$
$30$	−0.572455	−0.104516
$31$	−2.18140	−0.391791	−0.195895	−	0.980625i	$-0.562761\pi$
$31$	−2.18140	−0.391791	−0.195895	+	0.980625i	$0.562761\pi$
$32$	1.39204	0.246080
$33$	−0.148971	−0.0259325
$34$	−1.49915	−0.257102
$35$	−6.76450	−1.14341
$36$	−0.736844	−0.122807
$37$	6.72485	1.10556	0.552780	−	0.833327i	$-0.313567\pi$
$37$	6.72485	1.10556	0.552780	+	0.833327i	$0.313567\pi$
$38$	−1.11306	−0.180562
$39$	0.462517	0.0740620
$40$	−6.73461	−1.06483
$41$	8.32806	1.30062	0.650312	−	0.759667i	$-0.274638\pi$
$41$	8.32806	1.30062	0.650312	+	0.759667i	$0.274638\pi$
$42$	0.589366	0.0909411
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.247445	0.0373038
$45$	7.63295	1.13785
$46$	0.916759	0.135169
$47$	0.817649	0.119266	0.0596332	−	0.998220i	$-0.481007\pi$
$47$	0.817649	0.119266	0.0596332	+	0.998220i	$0.481007\pi$
$48$	0.660486	0.0953329
$49$	−0.0356739	−0.00509628
$50$	−2.35427	−0.332944
$51$	−0.148971	−0.0208601
$52$	−0.768255	−0.106538
$53$	−7.15729	−0.983129	−0.491565	−	0.870841i	$-0.663575\pi$
$53$	−7.15729	−0.983129	−0.491565	+	0.870841i	$0.663575\pi$
$54$	−1.33502	−0.181673
$55$	−2.56328	−0.345633
$56$	6.93355	0.926535
$57$	−0.110605	−0.0146500
$58$	−0.626315	−0.0822392
$59$	−5.40324	−0.703442	−0.351721	−	0.936105i	$-0.614403\pi$
$59$	−5.40324	−0.703442	−0.351721	+	0.936105i	$0.614403\pi$
$60$	0.0944878	0.0121983
$61$	10.5555	1.35149	0.675747	−	0.737134i	$-0.263821\pi$
$61$	10.5555	1.35149	0.675747	+	0.737134i	$0.263821\pi$
$62$	3.27024	0.415321
$63$	−7.85844	−0.990070
$64$	6.78045	0.847557
$65$	7.95834	0.987111
$66$	0.223329	0.0274899
$67$	6.84010	0.835651	0.417825	−	0.908527i	$-0.362792\pi$
$67$	6.84010	0.835651	0.417825	+	0.908527i	$0.362792\pi$
$68$	0.247445	0.0300071
$69$	0.0910985	0.0109670
$70$	10.1410	1.21208
$71$	−14.1499	−1.67929	−0.839643	−	0.543138i	$-0.817236\pi$
$71$	−14.1499	−1.67929	−0.839643	+	0.543138i	$0.817236\pi$
$72$	−7.82371	−0.922033
$73$	−1.45025	−0.169739	−0.0848696	−	0.996392i	$-0.527047\pi$
$73$	−1.45025	−0.169739	−0.0848696	+	0.996392i	$0.527047\pi$
$74$	−10.0816	−1.17196
$75$	−0.233944	−0.0270135
$76$	0.183718	0.0210740
$77$	2.63900	0.300742
$78$	−0.693381	−0.0785100
$79$	1.82869	0.205744	0.102872	−	0.994695i	$-0.467197\pi$
$79$	1.82869	0.205744	0.102872	+	0.994695i	$0.467197\pi$
$80$	11.3647	1.27061
$81$	8.80076	0.977862
$82$	−12.4850	−1.37874
$83$	−8.21643	−0.901870	−0.450935	−	0.892557i	$-0.648909\pi$
$83$	−8.21643	−0.901870	−0.450935	+	0.892557i	$0.648909\pi$
$84$	−0.0972791	−0.0106140
$85$	−2.56328	−0.278027
$86$	1.49915	0.161657
$87$	−0.0622371	−0.00667252
$88$	2.62734	0.280075
$89$	−7.06585	−0.748979	−0.374489	−	0.927231i	$-0.622182\pi$
$89$	−7.06585	−0.748979	−0.374489	+	0.927231i	$0.622182\pi$
$90$	−11.4429	−1.20619
$91$	−8.19344	−0.858905
$92$	−0.151318	−0.0157759
$93$	0.324965	0.0336973
$94$	−1.22578	−0.126429
$95$	−1.90314	−0.195258
$96$	−0.207373	−0.0211649
$97$	−2.57519	−0.261471	−0.130735	−	0.991417i	$-0.541734\pi$
$97$	−2.57519	−0.261471	−0.130735	+	0.991417i	$0.541734\pi$
$98$	0.0534805	0.00540235
$99$	−2.97781	−0.299281
$100$	0.388589	0.0388589
$101$	−2.35634	−0.234465	−0.117232	−	0.993105i	$-0.537402\pi$
$101$	−2.35634	−0.234465	−0.117232	+	0.993105i	$0.537402\pi$
$102$	0.223329	0.0221129
$103$	2.26408	0.223086	0.111543	−	0.993760i	$-0.464421\pi$
$103$	2.26408	0.223086	0.111543	+	0.993760i	$0.464421\pi$
$104$	−8.15723	−0.799882
$105$	1.00771	0.0983426
$106$	10.7298	1.04217
$107$	18.1286	1.75256	0.876279	−	0.481804i	$-0.160018\pi$
$107$	18.1286	1.75256	0.876279	+	0.481804i	$0.160018\pi$
$108$	0.220354	0.0212036
$109$	2.61050	0.250041	0.125020	−	0.992154i	$-0.460100\pi$
$109$	2.61050	0.250041	0.125020	+	0.992154i	$0.460100\pi$
$110$	3.84274	0.366391
$111$	−1.00181	−0.0950873
$112$	−11.7004	−1.10559
$113$	12.3464	1.16146	0.580728	−	0.814098i	$-0.302768\pi$
$113$	12.3464	1.16146	0.580728	+	0.814098i	$0.302768\pi$
$114$	0.165813	0.0155298
$115$	1.56750	0.146170
$116$	0.103378	0.00959839
$117$	9.24535	0.854733
$118$	8.10025	0.745689
$119$	2.63900	0.241917
$120$	1.00326	0.0915846
$121$	1.00000	0.0909091
$122$	−15.8243	−1.43266
$123$	−1.24064	−0.111864
$124$	−0.539777	−0.0484734
$125$	8.79102	0.786292
$126$	11.7810	1.04953
$127$	2.87082	0.254744	0.127372	−	0.991855i	$-0.459346\pi$
$127$	2.87082	0.254744	0.127372	+	0.991855i	$0.459346\pi$
$128$	−12.9490	−1.14454
$129$	0.148971	0.0131161
$130$	−11.9307	−1.04639
$131$	−12.1195	−1.05889	−0.529443	−	0.848345i	$-0.677599\pi$
$131$	−12.1195	−1.05889	−0.529443	+	0.848345i	$0.677599\pi$
$132$	−0.0368621	−0.00320843
$133$	1.95936	0.169898
$134$	−10.2543	−0.885838
$135$	−2.28265	−0.196459
$136$	2.62734	0.225292
$137$	14.8941	1.27249	0.636246	−	0.771486i	$-0.280486\pi$
$137$	14.8941	1.27249	0.636246	+	0.771486i	$0.280486\pi$
$138$	−0.136570	−0.0116256
$139$	−15.6567	−1.32799	−0.663994	−	0.747738i	$-0.731140\pi$
$139$	−15.6567	−1.32799	−0.663994	+	0.747738i	$0.731140\pi$
$140$	−1.67384	−0.141465
$141$	−0.121806	−0.0102579
$142$	21.2128	1.78014
$143$	−3.10475	−0.259632
$144$	13.2026	1.10022
$145$	−1.07089	−0.0889325
$146$	2.17414	0.179933
$147$	0.00531437	0.000438322 0
$148$	1.66403	0.136783
$149$	13.3492	1.09361	0.546805	−	0.837260i	$-0.315844\pi$
$149$	13.3492	1.09361	0.546805	+	0.837260i	$0.315844\pi$
$150$	0.350717	0.0286359
$151$	−2.57988	−0.209948	−0.104974	−	0.994475i	$-0.533476\pi$
$151$	−2.57988	−0.209948	−0.104974	+	0.994475i	$0.533476\pi$
$152$	1.95070	0.158223
$153$	−2.97781	−0.240741
$154$	−3.95625	−0.318804
$155$	5.59154	0.449123
$156$	0.114447	0.00916313
$157$	9.01070	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$157$	9.01070	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$158$	−2.74148	−0.218100
$159$	1.06623	0.0845573
$160$	−3.56818	−0.282089
$161$	−1.61380	−0.127185
$162$	−13.1936	−1.03659
$163$	−6.84029	−0.535773	−0.267886	−	0.963451i	$-0.586325\pi$
$163$	−6.84029	−0.535773	−0.267886	+	0.963451i	$0.586325\pi$
$164$	2.06074	0.160917
$165$	0.381854	0.0297273
$166$	12.3176	0.956034
$167$	−22.6899	−1.75580	−0.877900	−	0.478844i	$-0.841056\pi$
$167$	−22.6899	−1.75580	−0.877900	+	0.478844i	$0.841056\pi$
$168$	−1.03290	−0.0796897
$169$	−3.36053	−0.258503
$170$	3.84274	0.294724
$171$	−2.21091	−0.169072
$172$	−0.247445	−0.0188675
$173$	−3.92065	−0.298082	−0.149041	−	0.988831i	$-0.547619\pi$
$173$	−3.92065	−0.298082	−0.149041	+	0.988831i	$0.547619\pi$
$174$	0.0933027	0.00707326
$175$	4.14430	0.313279
$176$	−4.43366	−0.334200
$177$	0.804924	0.0605018
$178$	10.5928	0.793961
$179$	13.0464	0.975136	0.487568	−	0.873085i	$-0.337884\pi$
$179$	13.0464	0.975136	0.487568	+	0.873085i	$0.337884\pi$
$180$	1.88874	0.140778
$181$	8.07953	0.600547	0.300273	−	0.953853i	$-0.402922\pi$
$181$	8.07953	0.600547	0.300273	+	0.953853i	$0.402922\pi$
$182$	12.2832	0.910489
$183$	−1.57246	−0.116240
$184$	−1.60667	−0.118445
$185$	−17.2377	−1.26734
$186$	−0.487170	−0.0357210
$187$	1.00000	0.0731272
$188$	0.202323	0.0147559
$189$	2.35008	0.170943
$190$	2.85308	0.206984
$191$	25.7131	1.86054	0.930268	−	0.366880i	$-0.119574\pi$
$191$	25.7131	1.86054	0.930268	+	0.366880i	$0.119574\pi$
$192$	−1.01009	−0.0728969
$193$	−26.4953	−1.90718	−0.953588	−	0.301116i	$-0.902641\pi$
$193$	−26.4953	−1.90718	−0.953588	+	0.301116i	$0.902641\pi$
$194$	3.86059	0.277174
$195$	−1.18556	−0.0848997
$196$	−0.00882734	−0.000630524 0
$197$	−20.6196	−1.46908	−0.734542	−	0.678564i	$-0.762603\pi$
$197$	−20.6196	−1.46908	−0.734542	+	0.678564i	$0.762603\pi$
$198$	4.46417	0.317255
$199$	14.6047	1.03530	0.517650	−	0.855593i	$-0.326807\pi$
$199$	14.6047	1.03530	0.517650	+	0.855593i	$0.326807\pi$
$200$	4.12598	0.291751
$201$	−1.01897	−0.0718729
$202$	3.53250	0.248546
$203$	1.10252	0.0773820
$204$	−0.0368621	−0.00258086
$205$	−21.3471	−1.49095
$206$	−3.39418	−0.236484
$207$	1.82099	0.126567
$208$	13.7654	0.954459
$209$	0.742462	0.0513571
$210$	−1.51071	−0.104249
$211$	−6.12932	−0.421960	−0.210980	−	0.977490i	$-0.567665\pi$
$211$	−6.12932	−0.421960	−0.210980	+	0.977490i	$0.567665\pi$
$212$	−1.77104	−0.121635
$213$	2.10792	0.144433
$214$	−27.1775	−1.85781
$215$	2.56328	0.174814
$216$	2.33969	0.159196
$217$	−5.75671	−0.390791
$218$	−3.91353	−0.265058
$219$	0.216045	0.0145990
$220$	−0.634271	−0.0427625
$221$	−3.10475	−0.208848
$222$	1.50186	0.100798
$223$	1.38509	0.0927527	0.0463763	−	0.998924i	$-0.485233\pi$
$223$	1.38509	0.0927527	0.0463763	+	0.998924i	$0.485233\pi$
$224$	3.67358	0.245452
$225$	−4.67636	−0.311757
$226$	−18.5091	−1.23121
$227$	15.9557	1.05902	0.529510	−	0.848304i	$-0.322376\pi$
$227$	15.9557	1.05902	0.529510	+	0.848304i	$0.322376\pi$
$228$	−0.0273687	−0.00181253
$229$	14.1238	0.933324	0.466662	−	0.884436i	$-0.345456\pi$
$229$	14.1238	0.933324	0.466662	+	0.884436i	$0.345456\pi$
$230$	−2.34991	−0.154948
$231$	−0.393134	−0.0258663
$232$	1.09765	0.0720644
$233$	−9.15380	−0.599685	−0.299843	−	0.953989i	$-0.596934\pi$
$233$	−9.15380	−0.599685	−0.299843	+	0.953989i	$0.596934\pi$
$234$	−13.8601	−0.906066
$235$	−2.09586	−0.136719
$236$	−1.33700	−0.0870316
$237$	−0.272421	−0.0176957
$238$	−3.95625	−0.256446
$239$	25.2139	1.63095	0.815475	−	0.578792i	$-0.196476\pi$
$239$	25.2139	1.63095	0.815475	+	0.578792i	$0.196476\pi$
$240$	−1.69301	−0.109283
$241$	20.4505	1.31733	0.658667	−	0.752435i	$-0.271121\pi$
$241$	20.4505	1.31733	0.658667	+	0.752435i	$0.271121\pi$
$242$	−1.49915	−0.0963689
$243$	−3.98261	−0.255485
$244$	2.61191	0.167210
$245$	0.0914423	0.00584203
$246$	1.85990	0.118583
$247$	−2.30516	−0.146674
$248$	−5.73128	−0.363936
$249$	1.22401	0.0775683
$250$	−13.1790	−0.833515
$251$	18.6638	1.17805	0.589023	−	0.808116i	$-0.299513\pi$
$251$	18.6638	1.17805	0.589023	+	0.808116i	$0.299513\pi$
$252$	−1.94453	−0.122494
$253$	−0.611520	−0.0384459
$254$	−4.30379	−0.270044
$255$	0.381854	0.0239126
$256$	5.85153	0.365720
$257$	4.37398	0.272842	0.136421	−	0.990651i	$-0.456440\pi$
$257$	4.37398	0.272842	0.136421	+	0.990651i	$0.456440\pi$
$258$	−0.223329	−0.0139039
$259$	17.7469	1.10274
$260$	1.96925	0.122128
$261$	−1.24407	−0.0770061
$262$	18.1689	1.12248
$263$	11.5265	0.710754	0.355377	−	0.934723i	$-0.384353\pi$
$263$	11.5265	0.710754	0.355377	+	0.934723i	$0.384353\pi$
$264$	−0.391397	−0.0240888
$265$	18.3461	1.12699
$266$	−2.93737	−0.180101
$267$	1.05260	0.0644184
$268$	1.69255	0.103389
$269$	−28.3769	−1.73017	−0.865086	−	0.501624i	$-0.832736\pi$
$269$	−28.3769	−1.73017	−0.865086	+	0.501624i	$0.832736\pi$
$270$	3.42203	0.208258
$271$	23.6621	1.43737	0.718684	−	0.695337i	$-0.244745\pi$
$271$	23.6621	1.43737	0.718684	+	0.695337i	$0.244745\pi$
$272$	−4.43366	−0.268830
$273$	1.22058	0.0738730
$274$	−22.3285	−1.34892
$275$	1.57040	0.0946989
$276$	0.0225419	0.00135686
$277$	16.3641	0.983224	0.491612	−	0.870814i	$-0.336408\pi$
$277$	16.3641	0.983224	0.491612	+	0.870814i	$0.336408\pi$
$278$	23.4718	1.40774
$279$	6.49579	0.388893
$280$	−17.7726	−1.06212
$281$	−14.7510	−0.879968	−0.439984	−	0.898006i	$-0.645016\pi$
$281$	−14.7510	−0.879968	−0.439984	+	0.898006i	$0.645016\pi$
$282$	0.182605	0.0108740
$283$	−2.58342	−0.153568	−0.0767842	−	0.997048i	$-0.524465\pi$
$283$	−2.58342	−0.153568	−0.0767842	+	0.997048i	$0.524465\pi$
$284$	−3.50133	−0.207766
$285$	0.283512	0.0167938
$286$	4.65448	0.275225
$287$	21.9778	1.29731
$288$	−4.14522	−0.244259
$289$	1.00000	0.0588235
$290$	1.60542	0.0942736
$291$	0.383628	0.0224886
$292$	−0.358858	−0.0210006
$293$	−11.4278	−0.667619	−0.333810	−	0.942640i	$-0.608334\pi$
$293$	−11.4278	−0.667619	−0.333810	+	0.942640i	$0.608334\pi$
$294$	−0.00796703	−0.000464647 0
$295$	13.8500	0.806379
$296$	17.6685	1.02696
$297$	0.890518	0.0516731
$298$	−20.0124	−1.15929
$299$	1.89862	0.109800
$300$	−0.0578883	−0.00334218
$301$	−2.63900	−0.152109
$302$	3.86762	0.222557
$303$	0.351026	0.0201659
$304$	−3.29182	−0.188799
$305$	−27.0567	−1.54926
$306$	4.46417	0.255200
$307$	27.0264	1.54248	0.771239	−	0.636546i	$-0.219637\pi$
$307$	27.0264	1.54248	0.771239	+	0.636546i	$0.219637\pi$
$308$	0.653008	0.0372086
$309$	−0.337281	−0.0191872
$310$	−8.38254	−0.476096
$311$	1.10708	0.0627766	0.0313883	−	0.999507i	$-0.490007\pi$
$311$	1.10708	0.0627766	0.0313883	+	0.999507i	$0.490007\pi$
$312$	1.21519	0.0687965
$313$	23.0438	1.30251	0.651255	−	0.758859i	$-0.274243\pi$
$313$	23.0438	1.30251	0.651255	+	0.758859i	$0.274243\pi$
$314$	−13.5084	−0.762322
$315$	20.1434	1.13495
$316$	0.452500	0.0254551
$317$	−34.3729	−1.93057	−0.965287	−	0.261190i	$-0.915885\pi$
$317$	−34.3729	−1.93057	−0.965287	+	0.261190i	$0.915885\pi$
$318$	−1.59843	−0.0896356
$319$	0.417781	0.0233912
$320$	−17.3802	−0.971583
$321$	−2.70063	−0.150735
$322$	2.41933	0.134824
$323$	0.742462	0.0413117
$324$	2.17771	0.120984
$325$	−4.87571	−0.270456
$326$	10.2546	0.567950
$327$	−0.388889	−0.0215056
$328$	21.8806	1.20816
$329$	2.15778	0.118962
$330$	−0.572455	−0.0315126
$331$	−34.0987	−1.87423	−0.937117	−	0.349015i	$-0.886516\pi$
$331$	−34.0987	−1.87423	−0.937117	+	0.349015i	$0.886516\pi$
$332$	−2.03311	−0.111582
$333$	−20.0253	−1.09738
$334$	34.0156	1.86125
$335$	−17.5331	−0.957934
$336$	1.74302	0.0950897
$337$	−33.0739	−1.80165	−0.900824	−	0.434184i	$-0.857037\pi$
$337$	−33.0739	−1.80165	−0.900824	+	0.434184i	$0.857037\pi$
$338$	5.03794	0.274028
$339$	−1.83926	−0.0998948
$340$	−0.634271	−0.0343982
$341$	−2.18140	−0.118129
$342$	3.31448	0.179226
$343$	−18.5672	−1.00253
$344$	−2.62734	−0.141657
$345$	−0.233511	−0.0125718
$346$	5.87764	0.315984
$347$	−26.1113	−1.40173	−0.700865	−	0.713294i	$-0.747202\pi$
$347$	−26.1113	−1.40173	−0.700865	+	0.713294i	$0.747202\pi$
$348$	−0.0154003	−0.000825541 0
$349$	26.2926	1.40741	0.703706	−	0.710491i	$-0.251527\pi$
$349$	26.2926	1.40741	0.703706	+	0.710491i	$0.251527\pi$
$350$	−6.21291	−0.332094
$351$	−2.76484	−0.147576
$352$	1.39204	0.0741958
$353$	−1.40649	−0.0748600	−0.0374300	−	0.999299i	$-0.511917\pi$
$353$	−1.40649	−0.0748600	−0.0374300	+	0.999299i	$0.511917\pi$
$354$	−1.20670	−0.0641354
$355$	36.2702	1.92502
$356$	−1.74841	−0.0926655
$357$	−0.393134	−0.0208069
$358$	−19.5585	−1.03370
$359$	−12.6314	−0.666657	−0.333329	−	0.942811i	$-0.608172\pi$
$359$	−12.6314	−0.666657	−0.333329	+	0.942811i	$0.608172\pi$
$360$	20.0544	1.05696
$361$	−18.4488	−0.970987
$362$	−12.1124	−0.636614
$363$	−0.148971	−0.00781894
$364$	−2.02743	−0.106266
$365$	3.71740	0.194578
$366$	2.35735	0.123221
$367$	11.1477	0.581904	0.290952	−	0.956738i	$-0.406028\pi$
$367$	11.1477	0.581904	0.290952	+	0.956738i	$0.406028\pi$
$368$	2.71127	0.141335
$369$	−24.7994	−1.29100
$370$	25.8418	1.34345
$371$	−18.8881	−0.980621
$372$	0.0804109	0.00416911
$373$	−0.612603	−0.0317194	−0.0158597	−	0.999874i	$-0.505049\pi$
$373$	−0.612603	−0.0317194	−0.0158597	+	0.999874i	$0.505049\pi$
$374$	−1.49915	−0.0775191
$375$	−1.30960	−0.0676277
$376$	2.14824	0.110787
$377$	−1.29710	−0.0668043
$378$	−3.52312	−0.181210
$379$	2.27952	0.117091	0.0585455	−	0.998285i	$-0.481354\pi$
$379$	2.27952	0.117091	0.0585455	+	0.998285i	$0.481354\pi$
$380$	−0.470922	−0.0241578
$381$	−0.427669	−0.0219101
$382$	−38.5478	−1.97228
$383$	−26.7177	−1.36521	−0.682604	−	0.730788i	$-0.739153\pi$
$383$	−26.7177	−1.36521	−0.682604	+	0.730788i	$0.739153\pi$
$384$	1.92902	0.0984398
$385$	−6.76450	−0.344751
$386$	39.7204	2.02172
$387$	2.97781	0.151370
$388$	−0.637218	−0.0323498
$389$	−16.4201	−0.832530	−0.416265	−	0.909243i	$-0.636661\pi$
$389$	−16.4201	−0.832530	−0.416265	+	0.909243i	$0.636661\pi$
$390$	1.77733	0.0899986
$391$	−0.611520	−0.0309259
$392$	−0.0937276	−0.00473396
$393$	1.80545	0.0910730
$394$	30.9118	1.55731
$395$	−4.68744	−0.235851
$396$	−0.736844	−0.0370278
$397$	−3.53008	−0.177170	−0.0885848	−	0.996069i	$-0.528234\pi$
$397$	−3.53008	−0.177170	−0.0885848	+	0.996069i	$0.528234\pi$
$398$	−21.8946	−1.09748
$399$	−0.291887	−0.0146126
$400$	−6.96264	−0.348132
$401$	12.6292	0.630674	0.315337	−	0.948980i	$-0.397882\pi$
$401$	12.6292	0.630674	0.315337	+	0.948980i	$0.397882\pi$
$402$	1.52759	0.0761894
$403$	6.77270	0.337372
$404$	−0.583065	−0.0290085
$405$	−22.5588	−1.12096
$406$	−1.65285	−0.0820294
$407$	6.72485	0.333339
$408$	−0.391397	−0.0193770
$409$	−22.9106	−1.13286	−0.566429	−	0.824110i	$-0.691675\pi$
$409$	−22.9106	−1.13286	−0.566429	+	0.824110i	$0.691675\pi$
$410$	32.0025	1.58049
$411$	−2.21879	−0.109445
$412$	0.560234	0.0276008
$413$	−14.2591	−0.701647
$414$	−2.72993	−0.134169
$415$	21.0610	1.03384
$416$	−4.32192	−0.211900
$417$	2.33240	0.114218
$418$	−1.11306	−0.0544415
$419$	−24.9702	−1.21988	−0.609938	−	0.792449i	$-0.708806\pi$
$419$	−24.9702	−1.21988	−0.609938	+	0.792449i	$0.708806\pi$
$420$	0.249353	0.0121672
$421$	−31.2869	−1.52483	−0.762416	−	0.647087i	$-0.775987\pi$
$421$	−31.2869	−1.52483	−0.762416	+	0.647087i	$0.775987\pi$
$422$	9.18876	0.447302
$423$	−2.43480	−0.118384
$424$	−18.8046	−0.913233
$425$	1.57040	0.0761758
$426$	−3.16009	−0.153107
$427$	27.8560	1.34805
$428$	4.48583	0.216831
$429$	0.462517	0.0223305
$430$	−3.84274	−0.185313
$431$	−30.5412	−1.47112	−0.735558	−	0.677462i	$-0.763080\pi$
$431$	−30.5412	−1.47112	−0.735558	+	0.677462i	$0.763080\pi$
$432$	−3.94826	−0.189961
$433$	10.9251	0.525028	0.262514	−	0.964928i	$-0.415448\pi$
$433$	10.9251	0.525028	0.262514	+	0.964928i	$0.415448\pi$
$434$	8.63017	0.414261
$435$	0.159531	0.00764893
$436$	0.645956	0.0309357
$437$	−0.454030	−0.0217192
$438$	−0.323884	−0.0154758
$439$	−36.2017	−1.72781	−0.863906	−	0.503653i	$-0.831989\pi$
$439$	−36.2017	−1.72781	−0.863906	+	0.503653i	$0.831989\pi$
$440$	−6.73461	−0.321060
$441$	0.106230	0.00505858
$442$	4.65448	0.221391
$443$	−14.2661	−0.677805	−0.338902	−	0.940822i	$-0.610056\pi$
$443$	−14.2661	−0.677805	−0.338902	+	0.940822i	$0.610056\pi$
$444$	−0.247892	−0.0117644
$445$	18.1118	0.858579
$446$	−2.07646	−0.0983232
$447$	−1.98864	−0.0940595
$448$	17.8936	0.845394
$449$	23.6719	1.11715	0.558574	−	0.829455i	$-0.311349\pi$
$449$	23.6719	1.11715	0.558574	+	0.829455i	$0.311349\pi$
$450$	7.01056	0.330481
$451$	8.32806	0.392153
$452$	3.05507	0.143698
$453$	0.384326	0.0180572
$454$	−23.9200	−1.12262
$455$	21.0021	0.984592
$456$	−0.290597	−0.0136085
$457$	−18.2468	−0.853547	−0.426774	−	0.904359i	$-0.640350\pi$
$457$	−18.2468	−0.853547	−0.426774	+	0.904359i	$0.640350\pi$
$458$	−21.1736	−0.989377
$459$	0.890518	0.0415658
$460$	0.387869	0.0180845
$461$	−1.45341	−0.0676920	−0.0338460	−	0.999427i	$-0.510776\pi$
$461$	−1.45341	−0.0676920	−0.0338460	+	0.999427i	$0.510776\pi$
$462$	0.589366	0.0274198
$463$	−2.65583	−0.123427	−0.0617135	−	0.998094i	$-0.519657\pi$
$463$	−2.65583	−0.123427	−0.0617135	+	0.998094i	$0.519657\pi$
$464$	−1.85230	−0.0859908
$465$	−0.832975	−0.0386283
$466$	13.7229	0.635701
$467$	−0.504970	−0.0233672	−0.0116836	−	0.999932i	$-0.503719\pi$
$467$	−0.504970	−0.0233672	−0.0116836	+	0.999932i	$0.503719\pi$
$468$	2.28772	0.105750
$469$	18.0510	0.833519
$470$	3.14201	0.144930
$471$	−1.34233	−0.0618513
$472$	−14.1961	−0.653430
$473$	−1.00000	−0.0459800
$474$	0.408400	0.0187584
$475$	1.16596	0.0534981
$476$	0.653008	0.0299306
$477$	21.3130	0.975857
$478$	−37.7993	−1.72890
$479$	−12.9874	−0.593411	−0.296705	−	0.954969i	$-0.595888\pi$
$479$	−12.9874	−0.593411	−0.296705	+	0.954969i	$0.595888\pi$
$480$	0.531554	0.0242620
$481$	−20.8790	−0.952000
$482$	−30.6583	−1.39645
$483$	0.240409	0.0109390
$484$	0.247445	0.0112475
$485$	6.60093	0.299733
$486$	5.97052	0.270828
$487$	−19.2524	−0.872408	−0.436204	−	0.899848i	$-0.643677\pi$
$487$	−19.2524	−0.872408	−0.436204	+	0.899848i	$0.643677\pi$
$488$	27.7329	1.25541
$489$	1.01900	0.0460809
$490$	−0.137086	−0.00619289
$491$	−42.3780	−1.91249	−0.956247	−	0.292562i	$-0.905492\pi$
$491$	−42.3780	−1.91249	−0.956247	+	0.292562i	$0.905492\pi$
$492$	−0.306990	−0.0138402
$493$	0.417781	0.0188159
$494$	3.45577	0.155483
$495$	7.63295	0.343076
$496$	9.67158	0.434267
$497$	−37.3417	−1.67500
$498$	−1.83497	−0.0822269
$499$	42.6273	1.90826	0.954129	−	0.299395i	$-0.0967848\pi$
$499$	42.6273	1.90826	0.954129	+	0.299395i	$0.0967848\pi$
$500$	2.17529	0.0972821
$501$	3.38014	0.151013
$502$	−27.9797	−1.24880
$503$	−28.8688	−1.28720	−0.643598	−	0.765364i	$-0.722559\pi$
$503$	−28.8688	−1.28720	−0.643598	+	0.765364i	$0.722559\pi$
$504$	−20.6468	−0.919681
$505$	6.03996	0.268775
$506$	0.916759	0.0407549
$507$	0.500621	0.0222334
$508$	0.710371	0.0315176
$509$	3.36943	0.149347	0.0746737	−	0.997208i	$-0.476208\pi$
$509$	3.36943	0.149347	0.0746737	+	0.997208i	$0.476208\pi$
$510$	−0.572455	−0.0253487
$511$	−3.82722	−0.169306
$512$	17.1256	0.756854
$513$	0.661176	0.0291916
$514$	−6.55725	−0.289228
$515$	−5.80346	−0.255731
$516$	0.0368621	0.00162276
$517$	0.817649	0.0359602
$518$	−26.6052	−1.16897
$519$	0.584063	0.0256375
$520$	20.9093	0.916932
$521$	0.380276	0.0166602	0.00833010	−	0.999965i	$-0.497348\pi$
$521$	0.380276	0.0166602	0.00833010	+	0.999965i	$0.497348\pi$
$522$	1.86505	0.0816309
$523$	42.5894	1.86230	0.931152	−	0.364631i	$-0.118805\pi$
$523$	42.5894	1.86230	0.931152	+	0.364631i	$0.118805\pi$
$524$	−2.99891	−0.131008
$525$	−0.617379	−0.0269446
$526$	−17.2799	−0.753440
$527$	−2.18140	−0.0950232
$528$	0.660486	0.0287440
$529$	−22.6260	−0.983741
$530$	−27.5036	−1.19468
$531$	16.0898	0.698238
$532$	0.484833	0.0210202
$533$	−25.8565	−1.11997
$534$	−1.57801	−0.0682872
$535$	−46.4687	−2.00902
$536$	17.9713	0.776240
$537$	−1.94354	−0.0838698
$538$	42.5412	1.83408
$539$	−0.0356739	−0.00153659
$540$	−0.564830	−0.0243064
$541$	−41.1350	−1.76853	−0.884265	−	0.466986i	$-0.845340\pi$
$541$	−41.1350	−1.76853	−0.884265	+	0.466986i	$0.845340\pi$
$542$	−35.4729	−1.52369
$543$	−1.20361	−0.0516520
$544$	1.39204	0.0596830
$545$	−6.69145	−0.286630
$546$	−1.82983	−0.0783096
$547$	28.2055	1.20598	0.602989	−	0.797749i	$-0.293976\pi$
$547$	28.2055	1.20598	0.602989	+	0.797749i	$0.293976\pi$
$548$	3.68548	0.157436
$549$	−31.4323	−1.34150
$550$	−2.35427	−0.100386
$551$	0.310186	0.0132144
$552$	0.239347	0.0101873
$553$	4.82591	0.205219
$554$	−24.5322	−1.04227
$555$	2.56791	0.109002
$556$	−3.87419	−0.164302
$557$	−29.2717	−1.24028	−0.620141	−	0.784491i	$-0.712924\pi$
$557$	−29.2717	−1.24028	−0.620141	+	0.784491i	$0.712924\pi$
$558$	−9.73815	−0.412249
$559$	3.10475	0.131317
$560$	29.9915	1.26737
$561$	−0.148971	−0.00628955
$562$	22.1139	0.932817
$563$	−39.6462	−1.67089	−0.835445	−	0.549575i	$-0.814790\pi$
$563$	−39.6462	−1.67089	−0.835445	+	0.549575i	$0.814790\pi$
$564$	−0.0301402	−0.00126913
$565$	−31.6474	−1.33142
$566$	3.87293	0.162791
$567$	23.2252	0.975368
$568$	−37.1766	−1.55990
$569$	−4.06230	−0.170301	−0.0851503	−	0.996368i	$-0.527137\pi$
$569$	−4.06230	−0.170301	−0.0851503	+	0.996368i	$0.527137\pi$
$570$	−0.425026	−0.0178024
$571$	−20.8308	−0.871741	−0.435870	−	0.900009i	$-0.643559\pi$
$571$	−20.8308	−0.871741	−0.435870	+	0.900009i	$0.643559\pi$
$572$	−0.768255	−0.0321224
$573$	−3.83050	−0.160022
$574$	−32.9479	−1.37522
$575$	−0.960333	−0.0400486
$576$	−20.1909	−0.841287
$577$	14.1102	0.587415	0.293707	−	0.955895i	$-0.405111\pi$
$577$	14.1102	0.587415	0.293707	+	0.955895i	$0.405111\pi$
$578$	−1.49915	−0.0623563
$579$	3.94703	0.164033
$580$	−0.264986	−0.0110030
$581$	−21.6832	−0.899569
$582$	−0.575115	−0.0238393
$583$	−7.15729	−0.296425
$584$	−3.81030	−0.157672
$585$	−23.6984	−0.979809
$586$	17.1320	0.707715
$587$	10.2219	0.421905	0.210952	−	0.977496i	$-0.432344\pi$
$587$	10.2219	0.421905	0.210952	+	0.977496i	$0.432344\pi$
$588$	0.00131502	5.42303e−5 0
$589$	−1.61961	−0.0667347
$590$	−20.7632	−0.854808
$591$	3.07171	0.126353
$592$	−29.8157	−1.22542
$593$	3.64392	0.149638	0.0748188	−	0.997197i	$-0.476162\pi$
$593$	3.64392	0.149638	0.0748188	+	0.997197i	$0.476162\pi$
$594$	−1.33502	−0.0547765
$595$	−6.76450	−0.277317
$596$	3.30320	0.135304
$597$	−2.17567	−0.0890444
$598$	−2.84631	−0.116394
$599$	27.6559	1.12999	0.564995	−	0.825094i	$-0.308878\pi$
$599$	27.6559	1.12999	0.564995	+	0.825094i	$0.308878\pi$
$600$	−0.614651	−0.0250930
$601$	45.9191	1.87308	0.936540	−	0.350561i	$-0.114009\pi$
$601$	45.9191	1.87308	0.936540	+	0.350561i	$0.114009\pi$
$602$	3.95625	0.161245
$603$	−20.3685	−0.829469
$604$	−0.638378	−0.0259752
$605$	−2.56328	−0.104212
$606$	−0.526239	−0.0213770
$607$	−32.2592	−1.30936	−0.654681	−	0.755906i	$-0.727197\pi$
$607$	−32.2592	−1.30936	−0.654681	+	0.755906i	$0.727197\pi$
$608$	1.03353	0.0419153
$609$	−0.164244	−0.00665549
$610$	40.5620	1.64231
$611$	−2.53859	−0.102701
$612$	−0.736844	−0.0297851
$613$	−1.28294	−0.0518176	−0.0259088	−	0.999664i	$-0.508248\pi$
$613$	−1.28294	−0.0518176	−0.0259088	+	0.999664i	$0.508248\pi$
$614$	−40.5166	−1.63512
$615$	3.18010	0.128234
$616$	6.93355	0.279361
$617$	9.42686	0.379511	0.189756	−	0.981831i	$-0.439230\pi$
$617$	9.42686	0.379511	0.189756	+	0.981831i	$0.439230\pi$
$618$	0.505634	0.0203396
$619$	36.8585	1.48147	0.740734	−	0.671798i	$-0.234478\pi$
$619$	36.8585	1.48147	0.740734	+	0.671798i	$0.234478\pi$
$620$	1.38360	0.0555666
$621$	−0.544570	−0.0218528
$622$	−1.65967	−0.0665468
$623$	−18.6468	−0.747068
$624$	−2.05064	−0.0820914
$625$	−30.3859	−1.21543
$626$	−34.5460	−1.38074
$627$	−0.110605	−0.00441714
$628$	2.22965	0.0889729
$629$	6.72485	0.268137
$630$	−30.1979	−1.20311
$631$	36.1757	1.44013	0.720065	−	0.693906i	$-0.244112\pi$
$631$	36.1757	1.44013	0.720065	+	0.693906i	$0.244112\pi$
$632$	4.80459	0.191116
$633$	0.913089	0.0362920
$634$	51.5301	2.04652
$635$	−7.35872	−0.292022
$636$	0.263833	0.0104616
$637$	0.110759	0.00438842
$638$	−0.626315	−0.0247961
$639$	42.1357	1.66686
$640$	33.1919	1.31202
$641$	−31.9265	−1.26102	−0.630511	−	0.776180i	$-0.717155\pi$
$641$	−31.9265	−1.26102	−0.630511	+	0.776180i	$0.717155\pi$
$642$	4.04865	0.159787
$643$	−12.8955	−0.508548	−0.254274	−	0.967132i	$-0.581837\pi$
$643$	−12.8955	−0.508548	−0.254274	+	0.967132i	$0.581837\pi$
$644$	−0.399327	−0.0157357
$645$	−0.381854	−0.0150355
$646$	−1.11306	−0.0437928
$647$	−41.5333	−1.63284	−0.816420	−	0.577458i	$-0.804045\pi$
$647$	−41.5333	−1.63284	−0.816420	+	0.577458i	$0.804045\pi$
$648$	23.1226	0.908341
$649$	−5.40324	−0.212096
$650$	7.30941	0.286699
$651$	0.857582	0.0336113
$652$	−1.69260	−0.0662872
$653$	18.0332	0.705692	0.352846	−	0.935681i	$-0.385214\pi$
$653$	18.0332	0.705692	0.352846	+	0.935681i	$0.385214\pi$
$654$	0.583002	0.0227972
$655$	31.0657	1.21384
$656$	−36.9238	−1.44163
$657$	4.31857	0.168484
$658$	−3.23483	−0.126107
$659$	−13.2953	−0.517910	−0.258955	−	0.965889i	$-0.583378\pi$
$659$	−13.2953	−0.517910	−0.258955	+	0.965889i	$0.583378\pi$
$660$	0.0944878	0.00367793
$661$	6.72516	0.261578	0.130789	−	0.991410i	$-0.458249\pi$
$661$	6.72516	0.261578	0.130789	+	0.991410i	$0.458249\pi$
$662$	51.1190	1.98680
$663$	0.462517	0.0179627
$664$	−21.5873	−0.837751
$665$	−5.02238	−0.194760
$666$	30.0209	1.16329
$667$	−0.255481	−0.00989227
$668$	−5.61451	−0.217232
$669$	−0.206338	−0.00797750
$670$	26.2847	1.01547
$671$	10.5555	0.407491
$672$	−0.547257	−0.0211109
$673$	41.3126	1.59248	0.796241	−	0.604979i	$-0.206819\pi$
$673$	41.3126	1.59248	0.796241	+	0.604979i	$0.206819\pi$
$674$	49.5826	1.90985
$675$	1.39847	0.0538273
$676$	−0.831547	−0.0319826
$677$	−40.8591	−1.57034	−0.785171	−	0.619279i	$-0.787425\pi$
$677$	−40.8591	−1.57034	−0.785171	+	0.619279i	$0.787425\pi$
$678$	2.75732	0.105894
$679$	−6.79592	−0.260804
$680$	−6.73461	−0.258260
$681$	−2.37694	−0.0910845
$682$	3.27024	0.125224
$683$	−20.4600	−0.782882	−0.391441	−	0.920203i	$-0.628023\pi$
$683$	−20.4600	−0.782882	−0.391441	+	0.920203i	$0.628023\pi$
$684$	−0.547078	−0.0209181
$685$	−38.1779	−1.45870
$686$	27.8349	1.06274
$687$	−2.10403	−0.0802736
$688$	4.43366	0.169032
$689$	22.2216	0.846575
$690$	0.350068	0.0133268
$691$	13.8366	0.526369	0.263185	−	0.964745i	$-0.415227\pi$
$691$	13.8366	0.526369	0.263185	+	0.964745i	$0.415227\pi$
$692$	−0.970147	−0.0368794
$693$	−7.85844	−0.298517
$694$	39.1447	1.48591
$695$	40.1326	1.52232
$696$	−0.163518	−0.00619813
$697$	8.32806	0.315448
$698$	−39.4166	−1.49194
$699$	1.36365	0.0515779
$700$	1.02549	0.0387597
$701$	−24.6411	−0.930682	−0.465341	−	0.885132i	$-0.654068\pi$
$701$	−24.6411	−0.930682	−0.465341	+	0.885132i	$0.654068\pi$
$702$	4.14490	0.156439
$703$	4.99295	0.188313
$704$	6.78045	0.255548
$705$	0.312222	0.0117590
$706$	2.10854	0.0793560
$707$	−6.21838	−0.233866
$708$	0.199175	0.00748544
$709$	31.3852	1.17870	0.589349	−	0.807879i	$-0.299384\pi$
$709$	31.3852	1.17870	0.589349	+	0.807879i	$0.299384\pi$
$710$	−54.3744	−2.04064
$711$	−5.44549	−0.204222
$712$	−18.5644	−0.695730
$713$	1.33397	0.0499575
$714$	0.589366	0.0220565
$715$	7.95834	0.297625
$716$	3.22828	0.120646
$717$	−3.75613	−0.140275
$718$	18.9363	0.706695
$719$	−41.6436	−1.55305	−0.776523	−	0.630089i	$-0.783018\pi$
$719$	−41.6436	−1.55305	−0.776523	+	0.630089i	$0.783018\pi$
$720$	−33.8419	−1.26121
$721$	5.97490	0.222517
$722$	27.6574	1.02930
$723$	−3.04653	−0.113302
$724$	1.99924	0.0743011
$725$	0.656084	0.0243664
$726$	0.223329	0.00828852
$727$	−12.7097	−0.471378	−0.235689	−	0.971829i	$-0.575735\pi$
$727$	−12.7097	−0.471378	−0.235689	+	0.971829i	$0.575735\pi$
$728$	−21.5269	−0.797841
$729$	−25.8090	−0.955889
$730$	−5.57294	−0.206264
$731$	−1.00000	−0.0369863
$732$	−0.389098	−0.0143815
$733$	−29.9887	−1.10766	−0.553829	−	0.832630i	$-0.686834\pi$
$733$	−29.9887	−1.10766	−0.553829	+	0.832630i	$0.686834\pi$
$734$	−16.7120	−0.616852
$735$	−0.0136222	−0.000502463 0
$736$	−0.851257	−0.0313778
$737$	6.84010	0.251958
$738$	37.1779	1.36854
$739$	8.74863	0.321823	0.160912	−	0.986969i	$-0.448557\pi$
$739$	8.74863	0.321823	0.160912	+	0.986969i	$0.448557\pi$
$740$	−4.26538	−0.156798
$741$	0.343401	0.0126151
$742$	28.3160	1.03951
$743$	30.0170	1.10122	0.550609	−	0.834764i	$-0.314396\pi$
$743$	30.0170	1.10122	0.550609	+	0.834764i	$0.314396\pi$
$744$	0.853792	0.0313015
$745$	−34.2178	−1.25364
$746$	0.918383	0.0336244
$747$	24.4669	0.895199
$748$	0.247445	0.00904749
$749$	47.8414	1.74809
$750$	1.96329	0.0716892
$751$	17.9244	0.654072	0.327036	−	0.945012i	$-0.393950\pi$
$751$	17.9244	0.654072	0.327036	+	0.945012i	$0.393950\pi$
$752$	−3.62518	−0.132197
$753$	−2.78035	−0.101322
$754$	1.94455	0.0708164
$755$	6.61295	0.240670
$756$	0.581515	0.0211495
$757$	−20.3069	−0.738066	−0.369033	−	0.929416i	$-0.620311\pi$
$757$	−20.3069	−0.738066	−0.369033	+	0.929416i	$0.620311\pi$
$758$	−3.41734	−0.124123
$759$	0.0910985	0.00330667
$760$	−5.00019	−0.181376
$761$	−18.1478	−0.657857	−0.328929	−	0.944355i	$-0.606688\pi$
$761$	−18.1478	−0.657857	−0.328929	+	0.944355i	$0.606688\pi$
$762$	0.641139	0.0232260
$763$	6.88912	0.249403
$764$	6.36259	0.230190
$765$	7.63295	0.275970
$766$	40.0537	1.44720
$767$	16.7757	0.605735
$768$	−0.871706	−0.0314550
$769$	23.7896	0.857876	0.428938	−	0.903334i	$-0.358888\pi$
$769$	23.7896	0.857876	0.428938	+	0.903334i	$0.358888\pi$
$770$	10.1410	0.365456
$771$	−0.651596	−0.0234666
$772$	−6.55614	−0.235961
$773$	−49.4635	−1.77908	−0.889539	−	0.456859i	$-0.848974\pi$
$773$	−49.4635	−1.77908	−0.889539	+	0.456859i	$0.848974\pi$
$774$	−4.46417	−0.160461
$775$	−3.42568	−0.123054
$776$	−6.76589	−0.242881
$777$	−2.64377	−0.0948447
$778$	24.6161	0.882530
$779$	6.18327	0.221538
$780$	−0.293361	−0.0105040
$781$	−14.1499	−0.506324
$782$	0.916759	0.0327832
$783$	0.372042	0.0132957
$784$	0.158166	0.00564879
$785$	−23.0970	−0.824366
$786$	−2.70664	−0.0965426
$787$	−5.49476	−0.195867	−0.0979335	−	0.995193i	$-0.531223\pi$
$787$	−5.49476	−0.195867	−0.0979335	+	0.995193i	$0.531223\pi$
$788$	−5.10221	−0.181759
$789$	−1.71711	−0.0611307
$790$	7.02717	0.250016
$791$	32.5823	1.15849
$792$	−7.82371	−0.278003
$793$	−32.7722	−1.16377
$794$	5.29211	0.187810
$795$	−2.73304	−0.0969308
$796$	3.61386	0.128090
$797$	−53.0456	−1.87897	−0.939485	−	0.342590i	$-0.888696\pi$
$797$	−53.0456	−1.87897	−0.939485	+	0.342590i	$0.888696\pi$
$798$	0.437582	0.0154902
$799$	0.817649	0.0289263
$800$	2.18606	0.0772888
$801$	21.0407	0.743438
$802$	−18.9331	−0.668551
$803$	−1.45025	−0.0511783
$804$	−0.252140	−0.00889230
$805$	4.13662	0.145797
$806$	−10.1533	−0.357634
$807$	4.22733	0.148809
$808$	−6.19090	−0.217795
$809$	−47.7817	−1.67991	−0.839957	−	0.542653i	$-0.817420\pi$
$809$	−47.7817	−1.67991	−0.839957	+	0.542653i	$0.817420\pi$
$810$	33.8190	1.18828
$811$	−9.51607	−0.334154	−0.167077	−	0.985944i	$-0.553433\pi$
$811$	−9.51607	−0.334154	−0.167077	+	0.985944i	$0.553433\pi$
$812$	0.272814	0.00957390
$813$	−3.52495	−0.123626
$814$	−10.0816	−0.353358
$815$	17.5336	0.614174
$816$	0.660486	0.0231216
$817$	−0.742462	−0.0259754
$818$	34.3464	1.20090
$819$	24.3985	0.852552
$820$	−5.28225	−0.184464
$821$	27.5386	0.961103	0.480551	−	0.876967i	$-0.340437\pi$
$821$	27.5386	0.961103	0.480551	+	0.876967i	$0.340437\pi$
$822$	3.32630	0.116018
$823$	−46.2775	−1.61313	−0.806565	−	0.591145i	$-0.798676\pi$
$823$	−46.2775	−1.61313	−0.806565	+	0.591145i	$0.798676\pi$
$824$	5.94850	0.207226
$825$	−0.233944	−0.00814489
$826$	21.3766	0.743786
$827$	33.4844	1.16437	0.582183	−	0.813058i	$-0.302199\pi$
$827$	33.4844	1.16437	0.582183	+	0.813058i	$0.302199\pi$
$828$	0.450595	0.0156592
$829$	24.8190	0.862001	0.431001	−	0.902352i	$-0.358161\pi$
$829$	24.8190	0.862001	0.431001	+	0.902352i	$0.358161\pi$
$830$	−31.5736	−1.09593
$831$	−2.43777	−0.0845655
$832$	−21.0516	−0.729833
$833$	−0.0356739	−0.00123603
$834$	−3.49661	−0.121078
$835$	58.1607	2.01273
$836$	0.183718	0.00635404
$837$	−1.94258	−0.0671453
$838$	37.4341	1.29314
$839$	−5.44379	−0.187940	−0.0939702	−	0.995575i	$-0.529956\pi$
$839$	−5.44379	−0.187940	−0.0939702	+	0.995575i	$0.529956\pi$
$840$	2.64760	0.0913509
$841$	−28.8255	−0.993981
$842$	46.9038	1.61641
$843$	2.19746	0.0756845
$844$	−1.51667	−0.0522059
$845$	8.61399	0.296330
$846$	3.65013	0.125494
$847$	2.63900	0.0906771
$848$	31.7330	1.08972
$849$	0.384854	0.0132082
$850$	−2.35427	−0.0807507
$851$	−4.11238	−0.140971
$852$	0.521595	0.0178696
$853$	25.5466	0.874698	0.437349	−	0.899292i	$-0.355918\pi$
$853$	25.5466	0.874698	0.437349	+	0.899292i	$0.355918\pi$
$854$	−41.7602	−1.42901
$855$	5.66718	0.193813
$856$	47.6300	1.62796
$857$	−27.0559	−0.924212	−0.462106	−	0.886825i	$-0.652906\pi$
$857$	−27.0559	−0.924212	−0.462106	+	0.886825i	$0.652906\pi$
$858$	−0.693381	−0.0236716
$859$	3.86746	0.131956	0.0659779	−	0.997821i	$-0.478983\pi$
$859$	3.86746	0.131956	0.0659779	+	0.997821i	$0.478983\pi$
$860$	0.634271	0.0216285
$861$	−3.27404	−0.111579
$862$	45.7857	1.55947
$863$	7.23822	0.246392	0.123196	−	0.992382i	$-0.460686\pi$
$863$	7.23822	0.246392	0.123196	+	0.992382i	$0.460686\pi$
$864$	1.23963	0.0421732
$865$	10.0497	0.341701
$866$	−16.3784	−0.556560
$867$	−0.148971	−0.00505931
$868$	−1.42447	−0.0483497
$869$	1.82869	0.0620341
$870$	−0.239161	−0.00810831
$871$	−21.2368	−0.719581
$872$	6.85868	0.232264
$873$	7.66841	0.259537
$874$	0.680658	0.0230236
$875$	23.1995	0.784286
$876$	0.0534593	0.00180622
$877$	33.5322	1.13230	0.566151	−	0.824302i	$-0.308432\pi$
$877$	33.5322	1.13230	0.566151	+	0.824302i	$0.308432\pi$
$878$	54.2717	1.83158
$879$	1.70241	0.0574208
$880$	11.3647	0.383104
$881$	−25.3903	−0.855422	−0.427711	−	0.903916i	$-0.640680\pi$
$881$	−25.3903	−0.855422	−0.427711	+	0.903916i	$0.640680\pi$
$882$	−0.159255	−0.00536239
$883$	−55.8547	−1.87966	−0.939831	−	0.341640i	$-0.889018\pi$
$883$	−55.8547	−1.87966	−0.939831	+	0.341640i	$0.889018\pi$
$884$	−0.768255	−0.0258392
$885$	−2.06325	−0.0693553
$886$	21.3871	0.718512
$887$	27.5730	0.925812	0.462906	−	0.886407i	$-0.346807\pi$
$887$	27.5730	0.925812	0.462906	+	0.886407i	$0.346807\pi$
$888$	−2.63209	−0.0883270
$889$	7.57611	0.254094
$890$	−27.1522	−0.910144
$891$	8.80076	0.294837
$892$	0.342734	0.0114756
$893$	0.607073	0.0203149
$894$	2.98127	0.0997085
$895$	−33.4417	−1.11783
$896$	−34.1724	−1.14162
$897$	−0.282838	−0.00944369
$898$	−35.4877	−1.18424
$899$	−0.911347	−0.0303951
$900$	−1.15714	−0.0385714
$901$	−7.15729	−0.238444
$902$	−12.4850	−0.415705
$903$	0.393134	0.0130827
$904$	32.4383	1.07888
$905$	−20.7101	−0.688427
$906$	−0.576162	−0.0191417
$907$	20.9374	0.695214	0.347607	−	0.937640i	$-0.386994\pi$
$907$	20.9374	0.695214	0.347607	+	0.937640i	$0.386994\pi$
$908$	3.94817	0.131025
$909$	7.01672	0.232730
$910$	−31.4852	−1.04372
$911$	−25.7702	−0.853804	−0.426902	−	0.904298i	$-0.640395\pi$
$911$	−25.7702	−0.853804	−0.426902	+	0.904298i	$0.640395\pi$
$912$	0.490385	0.0162383
$913$	−8.21643	−0.271924
$914$	27.3546	0.904809
$915$	4.03066	0.133249
$916$	3.49485	0.115473
$917$	−31.9834	−1.05618
$918$	−1.33502	−0.0440622
$919$	−18.2717	−0.602727	−0.301363	−	0.953509i	$-0.597442\pi$
$919$	−18.2717	−0.602727	−0.301363	+	0.953509i	$0.597442\pi$
$920$	4.11834	0.135778
$921$	−4.02614	−0.132666
$922$	2.17887	0.0717574
$923$	43.9320	1.44604
$924$	−0.0972791	−0.00320025
$925$	10.5607	0.347235
$926$	3.98149	0.130840
$927$	−6.74198	−0.221436
$928$	0.581566	0.0190908
$929$	20.9894	0.688639	0.344320	−	0.938852i	$-0.388110\pi$
$929$	20.9894	0.688639	0.344320	+	0.938852i	$0.388110\pi$
$930$	1.24875	0.0409482
$931$	−0.0264865	−0.000868061 0
$932$	−2.26506	−0.0741946
$933$	−0.164922	−0.00539930
$934$	0.757024	0.0247706
$935$	−2.56328	−0.0838282
$936$	24.2907	0.793965
$937$	2.31259	0.0755490	0.0377745	−	0.999286i	$-0.487973\pi$
$937$	2.31259	0.0755490	0.0377745	+	0.999286i	$0.487973\pi$
$938$	−27.0611	−0.883578
$939$	−3.43285	−0.112027
$940$	−0.518611	−0.0169152
$941$	−23.6595	−0.771277	−0.385638	−	0.922650i	$-0.626019\pi$
$941$	−23.6595	−0.771277	−0.385638	+	0.922650i	$0.626019\pi$
$942$	2.01235	0.0655660
$943$	−5.09277	−0.165844
$944$	23.9561	0.779705
$945$	−6.02391	−0.195958
$946$	1.49915	0.0487415
$947$	16.0210	0.520612	0.260306	−	0.965526i	$-0.416177\pi$
$947$	16.0210	0.520612	0.260306	+	0.965526i	$0.416177\pi$
$948$	−0.0674093	−0.00218935
$949$	4.50267	0.146163
$950$	−1.74795	−0.0567111
$951$	5.12056	0.166045
$952$	6.93355	0.224718
$953$	−46.7350	−1.51390	−0.756948	−	0.653476i	$-0.773310\pi$
$953$	−46.7350	−1.51390	−0.756948	+	0.653476i	$0.773310\pi$
$954$	−31.9514	−1.03446
$955$	−65.9099	−2.13280
$956$	6.23905	0.201785
$957$	−0.0622371	−0.00201184
$958$	19.4701	0.629050
$959$	39.3057	1.26925
$960$	2.58914	0.0835642
$961$	−26.2415	−0.846500
$962$	31.3007	1.00917
$963$	−53.9835	−1.73959
$964$	5.06038	0.162984
$965$	67.9149	2.18626
$966$	−0.360409	−0.0115960
$967$	−6.25528	−0.201156	−0.100578	−	0.994929i	$-0.532069\pi$
$967$	−6.25528	−0.201156	−0.100578	+	0.994929i	$0.532069\pi$
$968$	2.62734	0.0844459
$969$	−0.110605	−0.00355315
$970$	−9.89577	−0.317734
$971$	3.71117	0.119097	0.0595485	−	0.998225i	$-0.481034\pi$
$971$	3.71117	0.119097	0.0595485	+	0.998225i	$0.481034\pi$
$972$	−0.985478	−0.0316092
$973$	−41.3182	−1.32460
$974$	28.8622	0.924803
$975$	0.726338	0.0232614
$976$	−46.7995	−1.49802
$977$	−21.2321	−0.679277	−0.339638	−	0.940556i	$-0.610305\pi$
$977$	−21.2321	−0.679277	−0.339638	+	0.940556i	$0.610305\pi$
$978$	−1.52764	−0.0488484
$979$	−7.06585	−0.225826
$980$	0.0226269	0.000722791 0
$981$	−7.77358	−0.248191
$982$	63.5309	2.02735
$983$	−29.9117	−0.954036	−0.477018	−	0.878894i	$-0.658282\pi$
$983$	−29.9117	−0.954036	−0.477018	+	0.878894i	$0.658282\pi$
$984$	−3.25958	−0.103911
$985$	52.8537	1.68406
$986$	−0.626315	−0.0199459
$987$	−0.321445	−0.0102317
$988$	−0.570400	−0.0181468
$989$	0.611520	0.0194452
$990$	−11.4429	−0.363680
$991$	−49.2349	−1.56400	−0.781999	−	0.623279i	$-0.785800\pi$
$991$	−49.2349	−1.56400	−0.781999	+	0.623279i	$0.785800\pi$
$992$	−3.03659	−0.0964117
$993$	5.07971	0.161200
$994$	55.9807	1.77560
$995$	−37.4359	−1.18680
$996$	0.302875	0.00959695
$997$	−33.0403	−1.04640	−0.523198	−	0.852211i	$-0.675261\pi$
$997$	−33.0403	−1.04640	−0.523198	+	0.852211i	$0.675261\pi$
$998$	−63.9046	−2.02286
$999$	5.98861	0.189471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.17	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.17	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.49915 q^{2} -0.148971 q^{3} +0.247445 q^{4} -2.56328 q^{5} +0.223329 q^{6} +2.63900 q^{7} +2.62734 q^{8} -2.97781 q^{9} +O(q^{10})\)	\(q-1.49915 q^{2} -0.148971 q^{3} +0.247445 q^{4} -2.56328 q^{5} +0.223329 q^{6} +2.63900 q^{7} +2.62734 q^{8} -2.97781 q^{9} +3.84274 q^{10} +1.00000 q^{11} -0.0368621 q^{12} -3.10475 q^{13} -3.95625 q^{14} +0.381854 q^{15} -4.43366 q^{16} +1.00000 q^{17} +4.46417 q^{18} +0.742462 q^{19} -0.634271 q^{20} -0.393134 q^{21} -1.49915 q^{22} -0.611520 q^{23} -0.391397 q^{24} +1.57040 q^{25} +4.65448 q^{26} +0.890518 q^{27} +0.653008 q^{28} +0.417781 q^{29} -0.572455 q^{30} -2.18140 q^{31} +1.39204 q^{32} -0.148971 q^{33} -1.49915 q^{34} -6.76450 q^{35} -0.736844 q^{36} +6.72485 q^{37} -1.11306 q^{38} +0.462517 q^{39} -6.73461 q^{40} +8.32806 q^{41} +0.589366 q^{42} -1.00000 q^{43} +0.247445 q^{44} +7.63295 q^{45} +0.916759 q^{46} +0.817649 q^{47} +0.660486 q^{48} -0.0356739 q^{49} -2.35427 q^{50} -0.148971 q^{51} -0.768255 q^{52} -7.15729 q^{53} -1.33502 q^{54} -2.56328 q^{55} +6.93355 q^{56} -0.110605 q^{57} -0.626315 q^{58} -5.40324 q^{59} +0.0944878 q^{60} +10.5555 q^{61} +3.27024 q^{62} -7.85844 q^{63} +6.78045 q^{64} +7.95834 q^{65} +0.223329 q^{66} +6.84010 q^{67} +0.247445 q^{68} +0.0910985 q^{69} +10.1410 q^{70} -14.1499 q^{71} -7.82371 q^{72} -1.45025 q^{73} -10.0816 q^{74} -0.233944 q^{75} +0.183718 q^{76} +2.63900 q^{77} -0.693381 q^{78} +1.82869 q^{79} +11.3647 q^{80} +8.80076 q^{81} -12.4850 q^{82} -8.21643 q^{83} -0.0972791 q^{84} -2.56328 q^{85} +1.49915 q^{86} -0.0622371 q^{87} +2.62734 q^{88} -7.06585 q^{89} -11.4429 q^{90} -8.19344 q^{91} -0.151318 q^{92} +0.324965 q^{93} -1.22578 q^{94} -1.90314 q^{95} -0.207373 q^{96} -2.57519 q^{97} +0.0534805 q^{98} -2.97781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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