LMFDB - Embedded newform 8041.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.42660 q^{2} +2.76366 q^{3} +3.88839 q^{4} -0.843592 q^{5} -6.70630 q^{6} -2.86536 q^{7} -4.58236 q^{8} +4.63781 q^{9} +O(q^{10})$	\(q-2.42660 q^{2} +2.76366 q^{3} +3.88839 q^{4} -0.843592 q^{5} -6.70630 q^{6} -2.86536 q^{7} -4.58236 q^{8} +4.63781 q^{9} +2.04706 q^{10} +1.00000 q^{11} +10.7462 q^{12} +6.61280 q^{13} +6.95308 q^{14} -2.33140 q^{15} +3.34279 q^{16} +1.00000 q^{17} -11.2541 q^{18} -0.440775 q^{19} -3.28021 q^{20} -7.91887 q^{21} -2.42660 q^{22} -8.53395 q^{23} -12.6641 q^{24} -4.28835 q^{25} -16.0466 q^{26} +4.52635 q^{27} -11.1416 q^{28} +1.04992 q^{29} +5.65738 q^{30} -4.34917 q^{31} +1.05312 q^{32} +2.76366 q^{33} -2.42660 q^{34} +2.41719 q^{35} +18.0336 q^{36} +7.91675 q^{37} +1.06958 q^{38} +18.2755 q^{39} +3.86565 q^{40} -5.69409 q^{41} +19.2159 q^{42} -1.00000 q^{43} +3.88839 q^{44} -3.91242 q^{45} +20.7085 q^{46} -5.85530 q^{47} +9.23832 q^{48} +1.21028 q^{49} +10.4061 q^{50} +2.76366 q^{51} +25.7131 q^{52} -1.55217 q^{53} -10.9837 q^{54} -0.843592 q^{55} +13.1301 q^{56} -1.21815 q^{57} -2.54773 q^{58} +3.96687 q^{59} -9.06539 q^{60} +4.21255 q^{61} +10.5537 q^{62} -13.2890 q^{63} -9.24107 q^{64} -5.57851 q^{65} -6.70630 q^{66} +10.7958 q^{67} +3.88839 q^{68} -23.5849 q^{69} -5.86556 q^{70} -2.18744 q^{71} -21.2521 q^{72} -7.72875 q^{73} -19.2108 q^{74} -11.8515 q^{75} -1.71390 q^{76} -2.86536 q^{77} -44.3474 q^{78} -8.86007 q^{79} -2.81995 q^{80} -1.40414 q^{81} +13.8173 q^{82} -5.17146 q^{83} -30.7917 q^{84} -0.843592 q^{85} +2.42660 q^{86} +2.90161 q^{87} -4.58236 q^{88} -17.0962 q^{89} +9.49388 q^{90} -18.9480 q^{91} -33.1833 q^{92} -12.0196 q^{93} +14.2085 q^{94} +0.371834 q^{95} +2.91046 q^{96} -9.00032 q^{97} -2.93686 q^{98} +4.63781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42660	−1.71587	−0.857933	−	0.513762i	$-0.828251\pi$
$2$	−2.42660	−1.71587	−0.857933	+	0.513762i	$0.828251\pi$
$3$	2.76366	1.59560	0.797800	−	0.602923i	$-0.205997\pi$
$3$	2.76366	1.59560	0.797800	+	0.602923i	$0.205997\pi$
$4$	3.88839	1.94419
$5$	−0.843592	−0.377266	−0.188633	−	0.982048i	$-0.560406\pi$
$5$	−0.843592	−0.377266	−0.188633	+	0.982048i	$0.560406\pi$
$6$	−6.70630	−2.73783
$7$	−2.86536	−1.08300	−0.541502	−	0.840700i	$-0.682144\pi$
$7$	−2.86536	−1.08300	−0.541502	+	0.840700i	$0.682144\pi$
$8$	−4.58236	−1.62011
$9$	4.63781	1.54594
$10$	2.04706	0.647337
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	10.7462	3.10215
$13$	6.61280	1.83406	0.917030	−	0.398817i	$-0.130579\pi$
$13$	6.61280	1.83406	0.917030	+	0.398817i	$0.130579\pi$
$14$	6.95308	1.85829
$15$	−2.33140	−0.601965
$16$	3.34279	0.835697
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−11.2541	−2.65262
$19$	−0.440775	−0.101121	−0.0505603	−	0.998721i	$-0.516101\pi$
$19$	−0.440775	−0.101121	−0.0505603	+	0.998721i	$0.516101\pi$
$20$	−3.28021	−0.733478
$21$	−7.91887	−1.72804
$22$	−2.42660	−0.517353
$23$	−8.53395	−1.77945	−0.889725	−	0.456496i	$-0.849104\pi$
$23$	−8.53395	−1.77945	−0.889725	+	0.456496i	$0.849104\pi$
$24$	−12.6641	−2.58505
$25$	−4.28835	−0.857670
$26$	−16.0466	−3.14700
$27$	4.52635	0.871097
$28$	−11.1416	−2.10557
$29$	1.04992	0.194964	0.0974822	−	0.995237i	$-0.468921\pi$
$29$	1.04992	0.194964	0.0974822	+	0.995237i	$0.468921\pi$
$30$	5.65738	1.03289
$31$	−4.34917	−0.781134	−0.390567	−	0.920575i	$-0.627721\pi$
$31$	−4.34917	−0.781134	−0.390567	+	0.920575i	$0.627721\pi$
$32$	1.05312	0.186167
$33$	2.76366	0.481091
$34$	−2.42660	−0.416158
$35$	2.41719	0.408580
$36$	18.0336	3.00560
$37$	7.91675	1.30151	0.650753	−	0.759290i	$-0.274453\pi$
$37$	7.91675	1.30151	0.650753	+	0.759290i	$0.274453\pi$
$38$	1.06958	0.173509
$39$	18.2755	2.92643
$40$	3.86565	0.611212
$41$	−5.69409	−0.889267	−0.444633	−	0.895713i	$-0.646666\pi$
$41$	−5.69409	−0.889267	−0.444633	+	0.895713i	$0.646666\pi$
$42$	19.2159	2.96508
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	3.88839	0.586197
$45$	−3.91242	−0.583229
$46$	20.7085	3.05330
$47$	−5.85530	−0.854083	−0.427041	−	0.904232i	$-0.640444\pi$
$47$	−5.85530	−0.854083	−0.427041	+	0.904232i	$0.640444\pi$
$48$	9.23832	1.33344
$49$	1.21028	0.172897
$50$	10.4061	1.47165
$51$	2.76366	0.386990
$52$	25.7131	3.56577
$53$	−1.55217	−0.213207	−0.106603	−	0.994302i	$-0.533998\pi$
$53$	−1.55217	−0.213207	−0.106603	+	0.994302i	$0.533998\pi$
$54$	−10.9837	−1.49469
$55$	−0.843592	−0.113750
$56$	13.1301	1.75458
$57$	−1.21815	−0.161348
$58$	−2.54773	−0.334533
$59$	3.96687	0.516442	0.258221	−	0.966086i	$-0.416864\pi$
$59$	3.96687	0.516442	0.258221	+	0.966086i	$0.416864\pi$
$60$	−9.06539	−1.17034
$61$	4.21255	0.539362	0.269681	−	0.962950i	$-0.413082\pi$
$61$	4.21255	0.539362	0.269681	+	0.962950i	$0.413082\pi$
$62$	10.5537	1.34032
$63$	−13.2890	−1.67426
$64$	−9.24107	−1.15513
$65$	−5.57851	−0.691929
$66$	−6.70630	−0.825488
$67$	10.7958	1.31891	0.659456	−	0.751743i	$-0.270787\pi$
$67$	10.7958	1.31891	0.659456	+	0.751743i	$0.270787\pi$
$68$	3.88839	0.471536
$69$	−23.5849	−2.83929
$70$	−5.86556	−0.701069
$71$	−2.18744	−0.259602	−0.129801	−	0.991540i	$-0.541434\pi$
$71$	−2.18744	−0.259602	−0.129801	+	0.991540i	$0.541434\pi$
$72$	−21.2521	−2.50459
$73$	−7.72875	−0.904582	−0.452291	−	0.891870i	$-0.649393\pi$
$73$	−7.72875	−0.904582	−0.452291	+	0.891870i	$0.649393\pi$
$74$	−19.2108	−2.23321
$75$	−11.8515	−1.36850
$76$	−1.71390	−0.196598
$77$	−2.86536	−0.326538
$78$	−44.3474	−5.02135
$79$	−8.86007	−0.996836	−0.498418	−	0.866937i	$-0.666085\pi$
$79$	−8.86007	−0.996836	−0.498418	+	0.866937i	$0.666085\pi$
$80$	−2.81995	−0.315280
$81$	−1.40414	−0.156015
$82$	13.8173	1.52586
$83$	−5.17146	−0.567642	−0.283821	−	0.958877i	$-0.591602\pi$
$83$	−5.17146	−0.567642	−0.283821	+	0.958877i	$0.591602\pi$
$84$	−30.7917	−3.35964
$85$	−0.843592	−0.0915004
$86$	2.42660	0.261667
$87$	2.90161	0.311085
$88$	−4.58236	−0.488482
$89$	−17.0962	−1.81219	−0.906096	−	0.423072i	$-0.860952\pi$
$89$	−17.0962	−1.81219	−0.906096	+	0.423072i	$0.860952\pi$
$90$	9.49388	1.00074
$91$	−18.9480	−1.98629
$92$	−33.1833	−3.45960
$93$	−12.0196	−1.24638
$94$	14.2085	1.46549
$95$	0.371834	0.0381494
$96$	2.91046	0.297048
$97$	−9.00032	−0.913844	−0.456922	−	0.889507i	$-0.651048\pi$
$97$	−9.00032	−0.913844	−0.456922	+	0.889507i	$0.651048\pi$
$98$	−2.93686	−0.296667
$99$	4.63781	0.466118
$100$	−16.6748	−1.66748
$101$	15.7685	1.56902	0.784511	−	0.620114i	$-0.212914\pi$
$101$	15.7685	1.56902	0.784511	+	0.620114i	$0.212914\pi$
$102$	−6.70630	−0.664022
$103$	−5.41968	−0.534016	−0.267008	−	0.963694i	$-0.586035\pi$
$103$	−5.41968	−0.534016	−0.267008	+	0.963694i	$0.586035\pi$
$104$	−30.3023	−2.97138
$105$	6.68030	0.651930
$106$	3.76649	0.365834
$107$	2.86759	0.277220	0.138610	−	0.990347i	$-0.455736\pi$
$107$	2.86759	0.277220	0.138610	+	0.990347i	$0.455736\pi$
$108$	17.6002	1.69358
$109$	9.79410	0.938104	0.469052	−	0.883170i	$-0.344596\pi$
$109$	9.79410	0.938104	0.469052	+	0.883170i	$0.344596\pi$
$110$	2.04706	0.195180
$111$	21.8792	2.07668
$112$	−9.57828	−0.905062
$113$	−8.44913	−0.794828	−0.397414	−	0.917639i	$-0.630092\pi$
$113$	−8.44913	−0.794828	−0.397414	+	0.917639i	$0.630092\pi$
$114$	2.95596	0.276851
$115$	7.19917	0.671326
$116$	4.08248	0.379049
$117$	30.6689	2.83534
$118$	−9.62600	−0.886145
$119$	−2.86536	−0.262667
$120$	10.6833	0.975250
$121$	1.00000	0.0909091
$122$	−10.2222	−0.925473
$123$	−15.7365	−1.41891
$124$	−16.9113	−1.51868
$125$	7.83558	0.700836
$126$	32.2471	2.87280
$127$	−2.29157	−0.203344	−0.101672	−	0.994818i	$-0.532419\pi$
$127$	−2.29157	−0.203344	−0.101672	+	0.994818i	$0.532419\pi$
$128$	20.3182	1.79589
$129$	−2.76366	−0.243327
$130$	13.5368	1.18726
$131$	6.08531	0.531676	0.265838	−	0.964018i	$-0.414351\pi$
$131$	6.08531	0.531676	0.265838	+	0.964018i	$0.414351\pi$
$132$	10.7462	0.935335
$133$	1.26298	0.109514
$134$	−26.1970	−2.26308
$135$	−3.81840	−0.328635
$136$	−4.58236	−0.392934
$137$	−11.2288	−0.959344	−0.479672	−	0.877448i	$-0.659244\pi$
$137$	−11.2288	−0.959344	−0.479672	+	0.877448i	$0.659244\pi$
$138$	57.2312	4.87184
$139$	8.82643	0.748648	0.374324	−	0.927298i	$-0.377875\pi$
$139$	8.82643	0.748648	0.374324	+	0.927298i	$0.377875\pi$
$140$	9.39899	0.794359
$141$	−16.1820	−1.36277
$142$	5.30805	0.445442
$143$	6.61280	0.552990
$144$	15.5032	1.29193
$145$	−0.885701	−0.0735534
$146$	18.7546	1.55214
$147$	3.34479	0.275874
$148$	30.7834	2.53038
$149$	−22.9012	−1.87614	−0.938070	−	0.346447i	$-0.887388\pi$
$149$	−22.9012	−1.87614	−0.938070	+	0.346447i	$0.887388\pi$
$150$	28.7590	2.34816
$151$	−7.78660	−0.633664	−0.316832	−	0.948482i	$-0.602619\pi$
$151$	−7.78660	−0.633664	−0.316832	+	0.948482i	$0.602619\pi$
$152$	2.01979	0.163827
$153$	4.63781	0.374945
$154$	6.95308	0.560295
$155$	3.66893	0.294695
$156$	71.0623	5.68954
$157$	−14.0739	−1.12322	−0.561610	−	0.827402i	$-0.689818\pi$
$157$	−14.0739	−1.12322	−0.561610	+	0.827402i	$0.689818\pi$
$158$	21.4998	1.71044
$159$	−4.28966	−0.340192
$160$	−0.888403	−0.0702344
$161$	24.4528	1.92715
$162$	3.40728	0.267701
$163$	1.64205	0.128615	0.0643075	−	0.997930i	$-0.479516\pi$
$163$	1.64205	0.128615	0.0643075	+	0.997930i	$0.479516\pi$
$164$	−22.1408	−1.72891
$165$	−2.33140	−0.181499
$166$	12.5491	0.973997
$167$	−2.99843	−0.232025	−0.116013	−	0.993248i	$-0.537011\pi$
$167$	−2.99843	−0.232025	−0.116013	+	0.993248i	$0.537011\pi$
$168$	36.2872	2.79961
$169$	30.7291	2.36378
$170$	2.04706	0.157002
$171$	−2.04423	−0.156326
$172$	−3.88839	−0.296487
$173$	−0.609668	−0.0463522	−0.0231761	−	0.999731i	$-0.507378\pi$
$173$	−0.609668	−0.0463522	−0.0231761	+	0.999731i	$0.507378\pi$
$174$	−7.04105	−0.533780
$175$	12.2877	0.928860
$176$	3.34279	0.251972
$177$	10.9631	0.824035
$178$	41.4856	3.10948
$179$	5.33759	0.398950	0.199475	−	0.979903i	$-0.436076\pi$
$179$	5.33759	0.398950	0.199475	+	0.979903i	$0.436076\pi$
$180$	−15.2130	−1.13391
$181$	−6.28882	−0.467444	−0.233722	−	0.972303i	$-0.575091\pi$
$181$	−6.28882	−0.467444	−0.233722	+	0.972303i	$0.575091\pi$
$182$	45.9793	3.40821
$183$	11.6421	0.860606
$184$	39.1056	2.88291
$185$	−6.67851	−0.491013
$186$	29.1668	2.13862
$187$	1.00000	0.0731272
$188$	−22.7677	−1.66050
$189$	−12.9696	−0.943401
$190$	−0.902292	−0.0654592
$191$	−16.3689	−1.18441	−0.592206	−	0.805787i	$-0.701743\pi$
$191$	−16.3689	−1.18441	−0.592206	+	0.805787i	$0.701743\pi$
$192$	−25.5392	−1.84313
$193$	−9.77846	−0.703869	−0.351934	−	0.936025i	$-0.614476\pi$
$193$	−9.77846	−0.703869	−0.351934	+	0.936025i	$0.614476\pi$
$194$	21.8402	1.56803
$195$	−15.4171	−1.10404
$196$	4.70602	0.336145
$197$	−8.44166	−0.601444	−0.300722	−	0.953712i	$-0.597228\pi$
$197$	−8.44166	−0.601444	−0.300722	+	0.953712i	$0.597228\pi$
$198$	−11.2541	−0.799795
$199$	18.0136	1.27695	0.638474	−	0.769643i	$-0.279566\pi$
$199$	18.0136	1.27695	0.638474	+	0.769643i	$0.279566\pi$
$200$	19.6508	1.38952
$201$	29.8358	2.10446
$202$	−38.2638	−2.69223
$203$	−3.00838	−0.211147
$204$	10.7462	0.752383
$205$	4.80349	0.335490
$206$	13.1514	0.916300
$207$	−39.5788	−2.75092
$208$	22.1052	1.53272
$209$	−0.440775	−0.0304890
$210$	−16.2104	−1.11862
$211$	16.7797	1.15516	0.577582	−	0.816332i	$-0.303996\pi$
$211$	16.7797	1.15516	0.577582	+	0.816332i	$0.303996\pi$
$212$	−6.03543	−0.414515
$213$	−6.04535	−0.414221
$214$	−6.95849	−0.475673
$215$	0.843592	0.0575325
$216$	−20.7414	−1.41127
$217$	12.4619	0.845971
$218$	−23.7664	−1.60966
$219$	−21.3596	−1.44335
$220$	−3.28021	−0.221152
$221$	6.61280	0.444825
$222$	−53.0920	−3.56331
$223$	−15.1917	−1.01731	−0.508656	−	0.860970i	$-0.669857\pi$
$223$	−15.1917	−1.01731	−0.508656	+	0.860970i	$0.669857\pi$
$224$	−3.01756	−0.201619
$225$	−19.8886	−1.32590
$226$	20.5027	1.36382
$227$	−10.3541	−0.687226	−0.343613	−	0.939111i	$-0.611651\pi$
$227$	−10.3541	−0.687226	−0.343613	+	0.939111i	$0.611651\pi$
$228$	−4.73664	−0.313692
$229$	4.83851	0.319738	0.159869	−	0.987138i	$-0.448893\pi$
$229$	4.83851	0.319738	0.159869	+	0.987138i	$0.448893\pi$
$230$	−17.4695	−1.15191
$231$	−7.91887	−0.521024
$232$	−4.81110	−0.315864
$233$	20.3107	1.33060	0.665298	−	0.746578i	$-0.268305\pi$
$233$	20.3107	1.33060	0.665298	+	0.746578i	$0.268305\pi$
$234$	−74.4212	−4.86507
$235$	4.93948	0.322216
$236$	15.4247	1.00406
$237$	−24.4862	−1.59055
$238$	6.95308	0.450701
$239$	−23.4682	−1.51803	−0.759016	−	0.651072i	$-0.774319\pi$
$239$	−23.4682	−1.51803	−0.759016	+	0.651072i	$0.774319\pi$
$240$	−7.79338	−0.503060
$241$	−12.9196	−0.832225	−0.416112	−	0.909313i	$-0.636608\pi$
$241$	−12.9196	−0.832225	−0.416112	+	0.909313i	$0.636608\pi$
$242$	−2.42660	−0.155988
$243$	−17.4596	−1.12003
$244$	16.3800	1.04863
$245$	−1.02098	−0.0652280
$246$	38.1862	2.43466
$247$	−2.91475	−0.185461
$248$	19.9295	1.26552
$249$	−14.2922	−0.905729
$250$	−19.0138	−1.20254
$251$	26.9993	1.70418	0.852091	−	0.523393i	$-0.175334\pi$
$251$	26.9993	1.70418	0.852091	+	0.523393i	$0.175334\pi$
$252$	−51.6728	−3.25508
$253$	−8.53395	−0.536525
$254$	5.56073	0.348912
$255$	−2.33140	−0.145998
$256$	−30.8219	−1.92637
$257$	−2.79456	−0.174320	−0.0871599	−	0.996194i	$-0.527779\pi$
$257$	−2.79456	−0.174320	−0.0871599	+	0.996194i	$0.527779\pi$
$258$	6.70630	0.417516
$259$	−22.6843	−1.40953
$260$	−21.6914	−1.34524
$261$	4.86931	0.301403
$262$	−14.7666	−0.912284
$263$	17.9247	1.10529	0.552644	−	0.833418i	$-0.313619\pi$
$263$	17.9247	1.10529	0.552644	+	0.833418i	$0.313619\pi$
$264$	−12.6641	−0.779421
$265$	1.30940	0.0804356
$266$	−3.06474	−0.187911
$267$	−47.2480	−2.89153
$268$	41.9781	2.56422
$269$	−7.07393	−0.431305	−0.215653	−	0.976470i	$-0.569188\pi$
$269$	−7.07393	−0.431305	−0.215653	+	0.976470i	$0.569188\pi$
$270$	9.26572	0.563894
$271$	16.8235	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$271$	16.8235	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$272$	3.34279	0.202686
$273$	−52.3659	−3.16933
$274$	27.2479	1.64611
$275$	−4.28835	−0.258597
$276$	−91.7073	−5.52013
$277$	20.6470	1.24056	0.620280	−	0.784381i	$-0.287019\pi$
$277$	20.6470	1.24056	0.620280	+	0.784381i	$0.287019\pi$
$278$	−21.4182	−1.28458
$279$	−20.1706	−1.20758
$280$	−11.0765	−0.661945
$281$	−10.1783	−0.607188	−0.303594	−	0.952801i	$-0.598187\pi$
$281$	−10.1783	−0.607188	−0.303594	+	0.952801i	$0.598187\pi$
$282$	39.2673	2.33834
$283$	2.08898	0.124177	0.0620884	−	0.998071i	$-0.480224\pi$
$283$	2.08898	0.124177	0.0620884	+	0.998071i	$0.480224\pi$
$284$	−8.50563	−0.504717
$285$	1.02762	0.0608711
$286$	−16.0466	−0.948857
$287$	16.3156	0.963079
$288$	4.88417	0.287802
$289$	1.00000	0.0588235
$290$	2.14924	0.126208
$291$	−24.8738	−1.45813
$292$	−30.0524	−1.75868
$293$	21.2037	1.23873	0.619365	−	0.785103i	$-0.287390\pi$
$293$	21.2037	1.23873	0.619365	+	0.785103i	$0.287390\pi$
$294$	−8.11647	−0.473362
$295$	−3.34642	−0.194836
$296$	−36.2774	−2.10858
$297$	4.52635	0.262646
$298$	55.5720	3.21920
$299$	−56.4333	−3.26362
$300$	−46.0834	−2.66063
$301$	2.86536	0.165156
$302$	18.8950	1.08728
$303$	43.5787	2.50353
$304$	−1.47342	−0.0845062
$305$	−3.55368	−0.203483
$306$	−11.2541	−0.643355
$307$	4.23704	0.241820	0.120910	−	0.992663i	$-0.461419\pi$
$307$	4.23704	0.241820	0.120910	+	0.992663i	$0.461419\pi$
$308$	−11.1416	−0.634853
$309$	−14.9781	−0.852076
$310$	−8.90301	−0.505657
$311$	−7.85093	−0.445185	−0.222593	−	0.974912i	$-0.571452\pi$
$311$	−7.85093	−0.445185	−0.222593	+	0.974912i	$0.571452\pi$
$312$	−83.7451	−4.74113
$313$	8.14340	0.460292	0.230146	−	0.973156i	$-0.426080\pi$
$313$	8.14340	0.460292	0.230146	+	0.973156i	$0.426080\pi$
$314$	34.1517	1.92729
$315$	11.2105	0.631639
$316$	−34.4514	−1.93804
$317$	−27.0702	−1.52041	−0.760207	−	0.649681i	$-0.774902\pi$
$317$	−27.0702	−1.52041	−0.760207	+	0.649681i	$0.774902\pi$
$318$	10.4093	0.583725
$319$	1.04992	0.0587840
$320$	7.79570	0.435793
$321$	7.92504	0.442333
$322$	−59.3372	−3.30673
$323$	−0.440775	−0.0245254
$324$	−5.45983	−0.303324
$325$	−28.3580	−1.57302
$326$	−3.98459	−0.220686
$327$	27.0675	1.49684
$328$	26.0924	1.44071
$329$	16.7775	0.924975
$330$	5.65738	0.311428
$331$	−12.8449	−0.706018	−0.353009	−	0.935620i	$-0.614842\pi$
$331$	−12.8449	−0.706018	−0.353009	+	0.935620i	$0.614842\pi$
$332$	−20.1087	−1.10361
$333$	36.7164	2.01205
$334$	7.27599	0.398124
$335$	−9.10722	−0.497581
$336$	−26.4711	−1.44412
$337$	18.2731	0.995401	0.497701	−	0.867349i	$-0.334178\pi$
$337$	18.2731	0.995401	0.497701	+	0.867349i	$0.334178\pi$
$338$	−74.5673	−4.05593
$339$	−23.3505	−1.26823
$340$	−3.28021	−0.177895
$341$	−4.34917	−0.235521
$342$	4.96053	0.268235
$343$	16.5896	0.895756
$344$	4.58236	0.247064
$345$	19.8961	1.07117
$346$	1.47942	0.0795341
$347$	−6.57036	−0.352716	−0.176358	−	0.984326i	$-0.556432\pi$
$347$	−6.57036	−0.352716	−0.176358	+	0.984326i	$0.556432\pi$
$348$	11.2826	0.604810
$349$	−23.7648	−1.27210	−0.636050	−	0.771648i	$-0.719433\pi$
$349$	−23.7648	−1.27210	−0.636050	+	0.771648i	$0.719433\pi$
$350$	−29.8172	−1.59380
$351$	29.9319	1.59765
$352$	1.05312	0.0561315
$353$	29.6115	1.57606	0.788031	−	0.615636i	$-0.211101\pi$
$353$	29.6115	1.57606	0.788031	+	0.615636i	$0.211101\pi$
$354$	−26.6030	−1.41393
$355$	1.84531	0.0979389
$356$	−66.4766	−3.52325
$357$	−7.91887	−0.419111
$358$	−12.9522	−0.684544
$359$	−26.9261	−1.42110	−0.710552	−	0.703645i	$-0.751555\pi$
$359$	−26.9261	−1.42110	−0.710552	+	0.703645i	$0.751555\pi$
$360$	17.9281	0.944896
$361$	−18.8057	−0.989775
$362$	15.2605	0.802072
$363$	2.76366	0.145054
$364$	−73.6773	−3.86174
$365$	6.51992	0.341268
$366$	−28.2506	−1.47668
$367$	1.71600	0.0895744	0.0447872	−	0.998997i	$-0.485739\pi$
$367$	1.71600	0.0895744	0.0447872	+	0.998997i	$0.485739\pi$
$368$	−28.5272	−1.48708
$369$	−26.4081	−1.37475
$370$	16.2061	0.842513
$371$	4.44752	0.230904
$372$	−46.7370	−2.42320
$373$	−1.82874	−0.0946887	−0.0473444	−	0.998879i	$-0.515076\pi$
$373$	−1.82874	−0.0946887	−0.0473444	+	0.998879i	$0.515076\pi$
$374$	−2.42660	−0.125477
$375$	21.6549	1.11825
$376$	26.8311	1.38371
$377$	6.94288	0.357577
$378$	31.4721	1.61875
$379$	29.4747	1.51401	0.757007	−	0.653406i	$-0.226661\pi$
$379$	29.4747	1.51401	0.757007	+	0.653406i	$0.226661\pi$
$380$	1.44583	0.0741698
$381$	−6.33313	−0.324456
$382$	39.7208	2.03229
$383$	−35.5713	−1.81761	−0.908803	−	0.417225i	$-0.863003\pi$
$383$	−35.5713	−1.81761	−0.908803	+	0.417225i	$0.863003\pi$
$384$	56.1524	2.86552
$385$	2.41719	0.123192
$386$	23.7284	1.20774
$387$	−4.63781	−0.235753
$388$	−34.9967	−1.77669
$389$	6.05986	0.307247	0.153624	−	0.988129i	$-0.450906\pi$
$389$	6.05986	0.307247	0.153624	+	0.988129i	$0.450906\pi$
$390$	37.4111	1.89439
$391$	−8.53395	−0.431580
$392$	−5.54592	−0.280111
$393$	16.8177	0.848342
$394$	20.4845	1.03200
$395$	7.47428	0.376072
$396$	18.0336	0.906223
$397$	0.989797	0.0496765	0.0248382	−	0.999691i	$-0.492093\pi$
$397$	0.989797	0.0496765	0.0248382	+	0.999691i	$0.492093\pi$
$398$	−43.7117	−2.19107
$399$	3.49044	0.174740
$400$	−14.3350	−0.716752
$401$	24.0590	1.20145	0.600724	−	0.799457i	$-0.294879\pi$
$401$	24.0590	1.20145	0.600724	+	0.799457i	$0.294879\pi$
$402$	−72.3996	−3.61096
$403$	−28.7602	−1.43265
$404$	61.3140	3.05048
$405$	1.18452	0.0588592
$406$	7.30015	0.362300
$407$	7.91675	0.392419
$408$	−12.6641	−0.626966
$409$	−20.7628	−1.02665	−0.513326	−	0.858194i	$-0.671587\pi$
$409$	−20.7628	−1.02665	−0.513326	+	0.858194i	$0.671587\pi$
$410$	−11.6561	−0.575656
$411$	−31.0327	−1.53073
$412$	−21.0738	−1.03823
$413$	−11.3665	−0.559309
$414$	96.0420	4.72021
$415$	4.36261	0.214152
$416$	6.96407	0.341442
$417$	24.3932	1.19454
$418$	1.06958	0.0523150
$419$	−25.6207	−1.25166	−0.625828	−	0.779961i	$-0.715239\pi$
$419$	−25.6207	−1.25166	−0.625828	+	0.779961i	$0.715239\pi$
$420$	25.9756	1.26748
$421$	−18.2001	−0.887019	−0.443510	−	0.896270i	$-0.646267\pi$
$421$	−18.2001	−0.887019	−0.443510	+	0.896270i	$0.646267\pi$
$422$	−40.7177	−1.98211
$423$	−27.1558	−1.32036
$424$	7.11260	0.345418
$425$	−4.28835	−0.208016
$426$	14.6697	0.710747
$427$	−12.0705	−0.584131
$428$	11.1503	0.538970
$429$	18.2755	0.882351
$430$	−2.04706	−0.0987180
$431$	−2.66324	−0.128284	−0.0641418	−	0.997941i	$-0.520431\pi$
$431$	−2.66324	−0.128284	−0.0641418	+	0.997941i	$0.520431\pi$
$432$	15.1306	0.727973
$433$	−0.896392	−0.0430778	−0.0215389	−	0.999768i	$-0.506857\pi$
$433$	−0.896392	−0.0430778	−0.0215389	+	0.999768i	$0.506857\pi$
$434$	−30.2401	−1.45157
$435$	−2.44777	−0.117362
$436$	38.0832	1.82386
$437$	3.76155	0.179939
$438$	51.8313	2.47660
$439$	−7.74705	−0.369747	−0.184873	−	0.982762i	$-0.559187\pi$
$439$	−7.74705	−0.369747	−0.184873	+	0.982762i	$0.559187\pi$
$440$	3.86565	0.184287
$441$	5.61303	0.267287
$442$	−16.0466	−0.763260
$443$	−21.0787	−1.00148	−0.500740	−	0.865598i	$-0.666939\pi$
$443$	−21.0787	−1.00148	−0.500740	+	0.865598i	$0.666939\pi$
$444$	85.0748	4.03747
$445$	14.4222	0.683678
$446$	36.8642	1.74557
$447$	−63.2911	−2.99357
$448$	26.4790	1.25101
$449$	−2.87113	−0.135497	−0.0677485	−	0.997702i	$-0.521582\pi$
$449$	−2.87113	−0.135497	−0.0677485	+	0.997702i	$0.521582\pi$
$450$	48.2616	2.27507
$451$	−5.69409	−0.268124
$452$	−32.8535	−1.54530
$453$	−21.5195	−1.01107
$454$	25.1253	1.17919
$455$	15.9844	0.749361
$456$	5.58201	0.261402
$457$	18.4775	0.864340	0.432170	−	0.901792i	$-0.357748\pi$
$457$	18.4775	0.864340	0.432170	+	0.901792i	$0.357748\pi$
$458$	−11.7411	−0.548627
$459$	4.52635	0.211272
$460$	27.9932	1.30519
$461$	−6.60573	−0.307660	−0.153830	−	0.988097i	$-0.549161\pi$
$461$	−6.60573	−0.307660	−0.153830	+	0.988097i	$0.549161\pi$
$462$	19.2159	0.894006
$463$	−3.68166	−0.171101	−0.0855506	−	0.996334i	$-0.527265\pi$
$463$	−3.68166	−0.171101	−0.0855506	+	0.996334i	$0.527265\pi$
$464$	3.50964	0.162931
$465$	10.1397	0.470215
$466$	−49.2858	−2.28312
$467$	−27.6420	−1.27912	−0.639559	−	0.768742i	$-0.720883\pi$
$467$	−27.6420	−1.27912	−0.639559	+	0.768742i	$0.720883\pi$
$468$	119.253	5.51246
$469$	−30.9337	−1.42839
$470$	−11.9861	−0.552880
$471$	−38.8955	−1.79221
$472$	−18.1776	−0.836693
$473$	−1.00000	−0.0459800
$474$	59.4183	2.72917
$475$	1.89020	0.0867282
$476$	−11.1416	−0.510676
$477$	−7.19866	−0.329604
$478$	56.9479	2.60474
$479$	−14.8728	−0.679558	−0.339779	−	0.940505i	$-0.610352\pi$
$479$	−14.8728	−0.679558	−0.339779	+	0.940505i	$0.610352\pi$
$480$	−2.45524	−0.112066
$481$	52.3519	2.38704
$482$	31.3507	1.42799
$483$	67.5792	3.07496
$484$	3.88839	0.176745
$485$	7.59260	0.344762
$486$	42.3675	1.92183
$487$	−6.32436	−0.286584	−0.143292	−	0.989680i	$-0.545769\pi$
$487$	−6.32436	−0.286584	−0.143292	+	0.989680i	$0.545769\pi$
$488$	−19.3035	−0.873826
$489$	4.53806	0.205218
$490$	2.47751	0.111922
$491$	34.8855	1.57436	0.787180	−	0.616724i	$-0.211541\pi$
$491$	34.8855	1.57436	0.787180	+	0.616724i	$0.211541\pi$
$492$	−61.1897	−2.75864
$493$	1.04992	0.0472858
$494$	7.07294	0.318227
$495$	−3.91242	−0.175850
$496$	−14.5383	−0.652791
$497$	6.26781	0.281150
$498$	34.6814	1.55411
$499$	−31.3721	−1.40441	−0.702205	−	0.711975i	$-0.747801\pi$
$499$	−31.3721	−1.40441	−0.702205	+	0.711975i	$0.747801\pi$
$500$	30.4678	1.36256
$501$	−8.28664	−0.370220
$502$	−65.5166	−2.92415
$503$	−32.0264	−1.42799	−0.713993	−	0.700153i	$-0.753115\pi$
$503$	−32.0264	−1.42799	−0.713993	+	0.700153i	$0.753115\pi$
$504$	60.8950	2.71248
$505$	−13.3022	−0.591939
$506$	20.7085	0.920604
$507$	84.9248	3.77164
$508$	−8.91053	−0.395341
$509$	−9.22077	−0.408703	−0.204352	−	0.978898i	$-0.565509\pi$
$509$	−9.22077	−0.408703	−0.204352	+	0.978898i	$0.565509\pi$
$510$	5.65738	0.250513
$511$	22.1456	0.979666
$512$	34.1561	1.50950
$513$	−1.99510	−0.0880859
$514$	6.78128	0.299109
$515$	4.57199	0.201466
$516$	−10.7462	−0.473074
$517$	−5.85530	−0.257516
$518$	55.0458	2.41857
$519$	−1.68491	−0.0739595
$520$	25.5627	1.12100
$521$	11.6136	0.508799	0.254400	−	0.967099i	$-0.418122\pi$
$521$	11.6136	0.508799	0.254400	+	0.967099i	$0.418122\pi$
$522$	−11.8159	−0.517167
$523$	16.5966	0.725717	0.362859	−	0.931844i	$-0.381801\pi$
$523$	16.5966	0.725717	0.362859	+	0.931844i	$0.381801\pi$
$524$	23.6620	1.03368
$525$	33.9589	1.48209
$526$	−43.4962	−1.89652
$527$	−4.34917	−0.189453
$528$	9.23832	0.402046
$529$	49.8282	2.16645
$530$	−3.17738	−0.138017
$531$	18.3976	0.798387
$532$	4.91094	0.212916
$533$	−37.6539	−1.63097
$534$	114.652	4.96148
$535$	−2.41908	−0.104586
$536$	−49.4701	−2.13678
$537$	14.7513	0.636564
$538$	17.1656	0.740062
$539$	1.21028	0.0521303
$540$	−14.8474	−0.638931
$541$	3.66343	0.157503	0.0787515	−	0.996894i	$-0.474907\pi$
$541$	3.66343	0.157503	0.0787515	+	0.996894i	$0.474907\pi$
$542$	−40.8238	−1.75353
$543$	−17.3802	−0.745854
$544$	1.05312	0.0451521
$545$	−8.26222	−0.353915
$546$	127.071	5.43814
$547$	11.5522	0.493935	0.246967	−	0.969024i	$-0.420566\pi$
$547$	11.5522	0.493935	0.246967	+	0.969024i	$0.420566\pi$
$548$	−43.6621	−1.86515
$549$	19.5370	0.833820
$550$	10.4061	0.443718
$551$	−0.462776	−0.0197149
$552$	108.075	4.59996
$553$	25.3873	1.07958
$554$	−50.1021	−2.12863
$555$	−18.4571	−0.783461
$556$	34.3206	1.45552
$557$	−21.5556	−0.913342	−0.456671	−	0.889636i	$-0.650958\pi$
$557$	−21.5556	−0.913342	−0.456671	+	0.889636i	$0.650958\pi$
$558$	48.9461	2.07205
$559$	−6.61280	−0.279692
$560$	8.08016	0.341449
$561$	2.76366	0.116682
$562$	24.6987	1.04185
$563$	−35.9828	−1.51649	−0.758246	−	0.651968i	$-0.773944\pi$
$563$	−35.9828	−1.51649	−0.758246	+	0.651968i	$0.773944\pi$
$564$	−62.9221	−2.64950
$565$	7.12762	0.299861
$566$	−5.06911	−0.213071
$567$	4.02335	0.168965
$568$	10.0237	0.420584
$569$	8.58312	0.359823	0.179912	−	0.983683i	$-0.442419\pi$
$569$	8.58312	0.359823	0.179912	+	0.983683i	$0.442419\pi$
$570$	−2.49363	−0.104447
$571$	23.1429	0.968500	0.484250	−	0.874930i	$-0.339093\pi$
$571$	23.1429	0.968500	0.484250	+	0.874930i	$0.339093\pi$
$572$	25.7131	1.07512
$573$	−45.2380	−1.88985
$574$	−39.5914	−1.65251
$575$	36.5966	1.52618
$576$	−42.8584	−1.78577
$577$	−9.55464	−0.397765	−0.198882	−	0.980023i	$-0.563731\pi$
$577$	−9.55464	−0.397765	−0.198882	+	0.980023i	$0.563731\pi$
$578$	−2.42660	−0.100933
$579$	−27.0243	−1.12309
$580$	−3.44395	−0.143002
$581$	14.8181	0.614758
$582$	60.3588	2.50195
$583$	−1.55217	−0.0642842
$584$	35.4160	1.46552
$585$	−25.8721	−1.06968
$586$	−51.4528	−2.12550
$587$	11.5857	0.478195	0.239097	−	0.970996i	$-0.423148\pi$
$587$	11.5857	0.478195	0.239097	+	0.970996i	$0.423148\pi$
$588$	13.0058	0.536352
$589$	1.91700	0.0789888
$590$	8.12042	0.334312
$591$	−23.3299	−0.959663
$592$	26.4640	1.08766
$593$	−8.40540	−0.345169	−0.172584	−	0.984995i	$-0.555212\pi$
$593$	−8.40540	−0.345169	−0.172584	+	0.984995i	$0.555212\pi$
$594$	−10.9837	−0.450665
$595$	2.41719	0.0990953
$596$	−89.0487	−3.64758
$597$	49.7834	2.03750
$598$	136.941	5.59994
$599$	−2.44501	−0.0999003	−0.0499501	−	0.998752i	$-0.515906\pi$
$599$	−2.44501	−0.0999003	−0.0499501	+	0.998752i	$0.515906\pi$
$600$	54.3081	2.21712
$601$	−6.82012	−0.278198	−0.139099	−	0.990278i	$-0.544421\pi$
$601$	−6.82012	−0.278198	−0.139099	+	0.990278i	$0.544421\pi$
$602$	−6.95308	−0.283386
$603$	50.0687	2.03896
$604$	−30.2773	−1.23197
$605$	−0.843592	−0.0342969
$606$	−105.748	−4.29572
$607$	13.0880	0.531225	0.265613	−	0.964080i	$-0.414426\pi$
$607$	13.0880	0.531225	0.265613	+	0.964080i	$0.414426\pi$
$608$	−0.464188	−0.0188253
$609$	−8.31415	−0.336906
$610$	8.62336	0.349149
$611$	−38.7199	−1.56644
$612$	18.0336	0.728966
$613$	41.5835	1.67954	0.839770	−	0.542942i	$-0.182690\pi$
$613$	41.5835	1.67954	0.839770	+	0.542942i	$0.182690\pi$
$614$	−10.2816	−0.414931
$615$	13.2752	0.535308
$616$	13.1301	0.529027
$617$	40.1026	1.61447	0.807234	−	0.590232i	$-0.200964\pi$
$617$	40.1026	1.61447	0.807234	+	0.590232i	$0.200964\pi$
$618$	36.3459	1.46205
$619$	41.2423	1.65767	0.828835	−	0.559494i	$-0.189004\pi$
$619$	41.2423	1.65767	0.828835	+	0.559494i	$0.189004\pi$
$620$	14.2662	0.572945
$621$	−38.6277	−1.55007
$622$	19.0511	0.763878
$623$	48.9867	1.96261
$624$	61.0912	2.44561
$625$	14.8317	0.593269
$626$	−19.7608	−0.789799
$627$	−1.21815	−0.0486483
$628$	−54.7248	−2.18376
$629$	7.91675	0.315661
$630$	−27.2034	−1.08381
$631$	−37.2046	−1.48109	−0.740547	−	0.672005i	$-0.765433\pi$
$631$	−37.2046	−1.48109	−0.740547	+	0.672005i	$0.765433\pi$
$632$	40.6001	1.61498
$633$	46.3735	1.84318
$634$	65.6885	2.60882
$635$	1.93315	0.0767149
$636$	−16.6799	−0.661400
$637$	8.00331	0.317103
$638$	−2.54773	−0.100865
$639$	−10.1450	−0.401328
$640$	−17.1402	−0.677527
$641$	7.17484	0.283389	0.141695	−	0.989910i	$-0.454745\pi$
$641$	7.17484	0.283389	0.141695	+	0.989910i	$0.454745\pi$
$642$	−19.2309	−0.758983
$643$	−9.26345	−0.365315	−0.182657	−	0.983177i	$-0.558470\pi$
$643$	−9.26345	−0.365315	−0.182657	+	0.983177i	$0.558470\pi$
$644$	95.0820	3.74676
$645$	2.33140	0.0917988
$646$	1.06958	0.0420822
$647$	−10.8143	−0.425156	−0.212578	−	0.977144i	$-0.568186\pi$
$647$	−10.8143	−0.425156	−0.212578	+	0.977144i	$0.568186\pi$
$648$	6.43426	0.252762
$649$	3.96687	0.155713
$650$	68.8136	2.69909
$651$	34.4405	1.34983
$652$	6.38491	0.250052
$653$	0.232258	0.00908897	0.00454448	−	0.999990i	$-0.498553\pi$
$653$	0.232258	0.00908897	0.00454448	+	0.999990i	$0.498553\pi$
$654$	−65.6821	−2.56837
$655$	−5.13352	−0.200583
$656$	−19.0341	−0.743157
$657$	−35.8445	−1.39843
$658$	−40.7123	−1.58713
$659$	−46.5836	−1.81464	−0.907320	−	0.420442i	$-0.861875\pi$
$659$	−46.5836	−1.81464	−0.907320	+	0.420442i	$0.861875\pi$
$660$	−9.06539	−0.352870
$661$	−23.4521	−0.912180	−0.456090	−	0.889934i	$-0.650751\pi$
$661$	−23.4521	−0.912180	−0.456090	+	0.889934i	$0.650751\pi$
$662$	31.1694	1.21143
$663$	18.2755	0.709763
$664$	23.6975	0.919642
$665$	−1.06544	−0.0413159
$666$	−89.0960	−3.45240
$667$	−8.95993	−0.346930
$668$	−11.6591	−0.451102
$669$	−41.9847	−1.62322
$670$	22.0996	0.853782
$671$	4.21255	0.162624
$672$	−8.33952	−0.321704
$673$	−18.9666	−0.731110	−0.365555	−	0.930790i	$-0.619121\pi$
$673$	−18.9666	−0.731110	−0.365555	+	0.930790i	$0.619121\pi$
$674$	−44.3416	−1.70797
$675$	−19.4106	−0.747114
$676$	119.487	4.59565
$677$	−48.2960	−1.85617	−0.928083	−	0.372374i	$-0.878544\pi$
$677$	−48.2960	−1.85617	−0.928083	+	0.372374i	$0.878544\pi$
$678$	56.6624	2.17611
$679$	25.7891	0.989696
$680$	3.86565	0.148241
$681$	−28.6152	−1.09654
$682$	10.5537	0.404122
$683$	−32.7875	−1.25458	−0.627290	−	0.778786i	$-0.715836\pi$
$683$	−32.7875	−1.25458	−0.627290	+	0.778786i	$0.715836\pi$
$684$	−7.94876	−0.303928
$685$	9.47256	0.361928
$686$	−40.2564	−1.53700
$687$	13.3720	0.510173
$688$	−3.34279	−0.127443
$689$	−10.2642	−0.391034
$690$	−48.2798	−1.83798
$691$	−11.7385	−0.446554	−0.223277	−	0.974755i	$-0.571675\pi$
$691$	−11.7385	−0.446554	−0.223277	+	0.974755i	$0.571675\pi$
$692$	−2.37063	−0.0901176
$693$	−13.2890	−0.504807
$694$	15.9436	0.605212
$695$	−7.44590	−0.282439
$696$	−13.2962	−0.503992
$697$	−5.69409	−0.215679
$698$	57.6676	2.18275
$699$	56.1317	2.12310
$700$	47.7792	1.80588
$701$	−35.8278	−1.35320	−0.676598	−	0.736353i	$-0.736546\pi$
$701$	−35.8278	−1.35320	−0.676598	+	0.736353i	$0.736546\pi$
$702$	−72.6327	−2.74134
$703$	−3.48950	−0.131609
$704$	−9.24107	−0.348286
$705$	13.6510	0.514128
$706$	−71.8553	−2.70431
$707$	−45.1824	−1.69926
$708$	42.6287	1.60208
$709$	−28.0129	−1.05205	−0.526024	−	0.850470i	$-0.676318\pi$
$709$	−28.0129	−1.05205	−0.526024	+	0.850470i	$0.676318\pi$
$710$	−4.47783	−0.168050
$711$	−41.0913	−1.54105
$712$	78.3409	2.93595
$713$	37.1156	1.38999
$714$	19.2159	0.719138
$715$	−5.57851	−0.208624
$716$	20.7546	0.775636
$717$	−64.8581	−2.42217
$718$	65.3388	2.43842
$719$	−9.85795	−0.367640	−0.183820	−	0.982960i	$-0.558846\pi$
$719$	−9.85795	−0.367640	−0.183820	+	0.982960i	$0.558846\pi$
$720$	−13.0784	−0.487403
$721$	15.5293	0.578342
$722$	45.6340	1.69832
$723$	−35.7054	−1.32790
$724$	−24.4534	−0.908803
$725$	−4.50241	−0.167215
$726$	−6.70630	−0.248894
$727$	7.20139	0.267085	0.133542	−	0.991043i	$-0.457365\pi$
$727$	7.20139	0.267085	0.133542	+	0.991043i	$0.457365\pi$
$728$	86.8268	3.21802
$729$	−44.0400	−1.63111
$730$	−15.8212	−0.585570
$731$	−1.00000	−0.0369863
$732$	45.2689	1.67319
$733$	16.0407	0.592477	0.296238	−	0.955114i	$-0.404268\pi$
$733$	16.0407	0.592477	0.296238	+	0.955114i	$0.404268\pi$
$734$	−4.16404	−0.153698
$735$	−2.82164	−0.104078
$736$	−8.98726	−0.331275
$737$	10.7958	0.397667
$738$	64.0819	2.35889
$739$	−38.3798	−1.41182	−0.705911	−	0.708300i	$-0.749462\pi$
$739$	−38.3798	−1.41182	−0.705911	+	0.708300i	$0.749462\pi$
$740$	−25.9686	−0.954626
$741$	−8.05539	−0.295922
$742$	−10.7923	−0.396200
$743$	−44.9342	−1.64848	−0.824238	−	0.566244i	$-0.808396\pi$
$743$	−44.9342	−1.64848	−0.824238	+	0.566244i	$0.808396\pi$
$744$	55.0783	2.01927
$745$	19.3193	0.707803
$746$	4.43763	0.162473
$747$	−23.9843	−0.877539
$748$	3.88839	0.142174
$749$	−8.21667	−0.300231
$750$	−52.5477	−1.91877
$751$	0.830267	0.0302969	0.0151484	−	0.999885i	$-0.495178\pi$
$751$	0.830267	0.0302969	0.0151484	+	0.999885i	$0.495178\pi$
$752$	−19.5730	−0.713754
$753$	74.6170	2.71919
$754$	−16.8476	−0.613554
$755$	6.56871	0.239060
$756$	−50.4309	−1.83416
$757$	1.06847	0.0388341	0.0194171	−	0.999811i	$-0.493819\pi$
$757$	1.06847	0.0388341	0.0194171	+	0.999811i	$0.493819\pi$
$758$	−71.5234	−2.59785
$759$	−23.5849	−0.856078
$760$	−1.70388	−0.0618062
$761$	−24.7848	−0.898447	−0.449223	−	0.893419i	$-0.648299\pi$
$761$	−24.7848	−0.898447	−0.449223	+	0.893419i	$0.648299\pi$
$762$	15.3680	0.556723
$763$	−28.0636	−1.01597
$764$	−63.6486	−2.30273
$765$	−3.91242	−0.141454
$766$	86.3172	3.11877
$767$	26.2321	0.947186
$768$	−85.1812	−3.07371
$769$	9.28360	0.334775	0.167388	−	0.985891i	$-0.446467\pi$
$769$	9.28360	0.334775	0.167388	+	0.985891i	$0.446467\pi$
$770$	−5.86556	−0.211380
$771$	−7.72321	−0.278145
$772$	−38.0224	−1.36846
$773$	37.3356	1.34287	0.671434	−	0.741065i	$-0.265679\pi$
$773$	37.3356	1.34287	0.671434	+	0.741065i	$0.265679\pi$
$774$	11.2541	0.404521
$775$	18.6508	0.669956
$776$	41.2427	1.48053
$777$	−62.6917	−2.24905
$778$	−14.7049	−0.527195
$779$	2.50981	0.0899232
$780$	−59.9476	−2.14647
$781$	−2.18744	−0.0782729
$782$	20.7085	0.740534
$783$	4.75229	0.169833
$784$	4.04569	0.144489
$785$	11.8726	0.423753
$786$	−40.8099	−1.45564
$787$	−17.5126	−0.624258	−0.312129	−	0.950040i	$-0.601042\pi$
$787$	−17.5126	−0.624258	−0.312129	+	0.950040i	$0.601042\pi$
$788$	−32.8245	−1.16932
$789$	49.5379	1.76360
$790$	−18.1371	−0.645289
$791$	24.2098	0.860801
$792$	−21.2521	−0.755162
$793$	27.8568	0.989223
$794$	−2.40184	−0.0852382
$795$	3.61873	0.128343
$796$	70.0437	2.48263
$797$	43.1834	1.52963	0.764817	−	0.644248i	$-0.222829\pi$
$797$	43.1834	1.52963	0.764817	+	0.644248i	$0.222829\pi$
$798$	−8.46990	−0.299831
$799$	−5.85530	−0.207145
$800$	−4.51615	−0.159670
$801$	−79.2889	−2.80154
$802$	−58.3815	−2.06152
$803$	−7.72875	−0.272742
$804$	116.013	4.09147
$805$	−20.6282	−0.727048
$806$	69.7895	2.45823
$807$	−19.5499	−0.688190
$808$	−72.2569	−2.54199
$809$	36.4679	1.28214	0.641071	−	0.767481i	$-0.278490\pi$
$809$	36.4679	1.28214	0.641071	+	0.767481i	$0.278490\pi$
$810$	−2.87435	−0.100994
$811$	4.35978	0.153092	0.0765462	−	0.997066i	$-0.475611\pi$
$811$	4.35978	0.153092	0.0765462	+	0.997066i	$0.475611\pi$
$812$	−11.6978	−0.410511
$813$	46.4943	1.63063
$814$	−19.2108	−0.673338
$815$	−1.38522	−0.0485220
$816$	9.23832	0.323406
$817$	0.440775	0.0154207
$818$	50.3829	1.76160
$819$	−87.8774	−3.07069
$820$	18.6778	0.652258
$821$	−4.32902	−0.151084	−0.0755420	−	0.997143i	$-0.524069\pi$
$821$	−4.32902	−0.151084	−0.0755420	+	0.997143i	$0.524069\pi$
$822$	75.3039	2.62653
$823$	−43.3216	−1.51010	−0.755048	−	0.655669i	$-0.772387\pi$
$823$	−43.3216	−1.51010	−0.755048	+	0.655669i	$0.772387\pi$
$824$	24.8349	0.865165
$825$	−11.8515	−0.412618
$826$	27.5819	0.959699
$827$	28.6656	0.996802	0.498401	−	0.866947i	$-0.333921\pi$
$827$	28.6656	0.996802	0.498401	+	0.866947i	$0.333921\pi$
$828$	−153.898	−5.34832
$829$	23.8150	0.827131	0.413565	−	0.910474i	$-0.364283\pi$
$829$	23.8150	0.827131	0.413565	+	0.910474i	$0.364283\pi$
$830$	−10.5863	−0.367456
$831$	57.0613	1.97944
$832$	−61.1094	−2.11859
$833$	1.21028	0.0419336
$834$	−59.1926	−2.04967
$835$	2.52945	0.0875353
$836$	−1.71390	−0.0592766
$837$	−19.6859	−0.680444
$838$	62.1713	2.14767
$839$	−53.2718	−1.83915	−0.919573	−	0.392918i	$-0.871465\pi$
$839$	−53.2718	−1.83915	−0.919573	+	0.392918i	$0.871465\pi$
$840$	−30.6116	−1.05620
$841$	−27.8977	−0.961989
$842$	44.1644	1.52201
$843$	−28.1294	−0.968829
$844$	65.2461	2.24586
$845$	−25.9229	−0.891773
$846$	65.8962	2.26556
$847$	−2.86536	−0.0984549
$848$	−5.18857	−0.178176
$849$	5.77322	0.198136
$850$	10.4061	0.356927
$851$	−67.5611	−2.31596
$852$	−23.5067	−0.805325
$853$	6.30693	0.215945	0.107973	−	0.994154i	$-0.465564\pi$
$853$	6.30693	0.215945	0.107973	+	0.994154i	$0.465564\pi$
$854$	29.2902	1.00229
$855$	1.72450	0.0589765
$856$	−13.1403	−0.449127
$857$	46.4544	1.58685	0.793426	−	0.608667i	$-0.208295\pi$
$857$	46.4544	1.58685	0.793426	+	0.608667i	$0.208295\pi$
$858$	−44.3474	−1.51400
$859$	7.91115	0.269925	0.134963	−	0.990851i	$-0.456909\pi$
$859$	7.91115	0.269925	0.134963	+	0.990851i	$0.456909\pi$
$860$	3.28021	0.111854
$861$	45.0907	1.53669
$862$	6.46262	0.220118
$863$	−5.88870	−0.200454	−0.100227	−	0.994965i	$-0.531957\pi$
$863$	−5.88870	−0.200454	−0.100227	+	0.994965i	$0.531957\pi$
$864$	4.76679	0.162170
$865$	0.514311	0.0174871
$866$	2.17518	0.0739158
$867$	2.76366	0.0938588
$868$	48.4568	1.64473
$869$	−8.86007	−0.300557
$870$	5.93977	0.201377
$871$	71.3902	2.41897
$872$	−44.8801	−1.51983
$873$	−41.7418	−1.41275
$874$	−9.12777	−0.308751
$875$	−22.4517	−0.759007
$876$	−83.0546	−2.80615
$877$	40.9296	1.38210	0.691048	−	0.722809i	$-0.257149\pi$
$877$	40.9296	1.38210	0.691048	+	0.722809i	$0.257149\pi$
$878$	18.7990	0.634436
$879$	58.5997	1.97652
$880$	−2.81995	−0.0950604
$881$	29.0313	0.978088	0.489044	−	0.872259i	$-0.337346\pi$
$881$	29.0313	0.978088	0.489044	+	0.872259i	$0.337346\pi$
$882$	−13.6206	−0.458629
$883$	10.9351	0.367995	0.183998	−	0.982927i	$-0.441096\pi$
$883$	10.9351	0.367995	0.183998	+	0.982927i	$0.441096\pi$
$884$	25.7131	0.864826
$885$	−9.24836	−0.310880
$886$	51.1496	1.71840
$887$	−54.6043	−1.83343	−0.916716	−	0.399539i	$-0.869170\pi$
$887$	−54.6043	−1.83343	−0.916716	+	0.399539i	$0.869170\pi$
$888$	−100.258	−3.36445
$889$	6.56618	0.220223
$890$	−34.9969	−1.17310
$891$	−1.40414	−0.0470403
$892$	−59.0712	−1.97785
$893$	2.58087	0.0863654
$894$	153.582	5.13656
$895$	−4.50274	−0.150510
$896$	−58.2188	−1.94495
$897$	−155.962	−5.20743
$898$	6.96708	0.232495
$899$	−4.56626	−0.152293
$900$	−77.3345	−2.57782
$901$	−1.55217	−0.0517102
$902$	13.8173	0.460065
$903$	7.91887	0.263524
$904$	38.7170	1.28771
$905$	5.30520	0.176351
$906$	52.2192	1.73487
$907$	51.7482	1.71827	0.859135	−	0.511749i	$-0.171002\pi$
$907$	51.7482	1.71827	0.859135	+	0.511749i	$0.171002\pi$
$908$	−40.2608	−1.33610
$909$	73.1313	2.42561
$910$	−38.7878	−1.28580
$911$	−46.7485	−1.54885	−0.774424	−	0.632667i	$-0.781960\pi$
$911$	−46.7485	−1.54885	−0.774424	+	0.632667i	$0.781960\pi$
$912$	−4.07202	−0.134838
$913$	−5.17146	−0.171150
$914$	−44.8375	−1.48309
$915$	−9.82115	−0.324677
$916$	18.8140	0.621632
$917$	−17.4366	−0.575807
$918$	−10.9837	−0.362515
$919$	−44.9269	−1.48200	−0.741001	−	0.671504i	$-0.765649\pi$
$919$	−44.9269	−1.48200	−0.741001	+	0.671504i	$0.765649\pi$
$920$	−32.9892	−1.08762
$921$	11.7097	0.385849
$922$	16.0295	0.527903
$923$	−14.4651	−0.476126
$924$	−30.7917	−1.01297
$925$	−33.9498	−1.11626
$926$	8.93391	0.293587
$927$	−25.1354	−0.825556
$928$	1.10569	0.0362959
$929$	−54.8221	−1.79866	−0.899328	−	0.437275i	$-0.855944\pi$
$929$	−54.8221	−1.79866	−0.899328	+	0.437275i	$0.855944\pi$
$930$	−24.6049	−0.806826
$931$	−0.533459	−0.0174834
$932$	78.9757	2.58694
$933$	−21.6973	−0.710337
$934$	67.0760	2.19479
$935$	−0.843592	−0.0275884
$936$	−140.536	−4.59357
$937$	−5.84415	−0.190920	−0.0954600	−	0.995433i	$-0.530432\pi$
$937$	−5.84415	−0.190920	−0.0954600	+	0.995433i	$0.530432\pi$
$938$	75.0638	2.45092
$939$	22.5056	0.734442
$940$	19.2066	0.626451
$941$	42.4314	1.38323	0.691613	−	0.722269i	$-0.256901\pi$
$941$	42.4314	1.38323	0.691613	+	0.722269i	$0.256901\pi$
$942$	94.3838	3.07519
$943$	48.5930	1.58241
$944$	13.2604	0.431589
$945$	10.9411	0.355913
$946$	2.42660	0.0788956
$947$	−47.6988	−1.55000	−0.775001	−	0.631959i	$-0.782251\pi$
$947$	−47.6988	−1.55000	−0.775001	+	0.631959i	$0.782251\pi$
$948$	−95.2119	−3.09234
$949$	−51.1087	−1.65906
$950$	−4.58675	−0.148814
$951$	−74.8128	−2.42597
$952$	13.1301	0.425549
$953$	9.49255	0.307494	0.153747	−	0.988110i	$-0.450866\pi$
$953$	9.49255	0.307494	0.153747	+	0.988110i	$0.450866\pi$
$954$	17.4683	0.565556
$955$	13.8087	0.446838
$956$	−91.2535	−2.95135
$957$	2.90161	0.0937957
$958$	36.0904	1.16603
$959$	32.1746	1.03897
$960$	21.5446	0.695350
$961$	−12.0847	−0.389830
$962$	−127.037	−4.09584
$963$	13.2993	0.428565
$964$	−50.2364	−1.61801
$965$	8.24903	0.265546
$966$	−163.988	−5.27622
$967$	10.4382	0.335670	0.167835	−	0.985815i	$-0.446322\pi$
$967$	10.4382	0.335670	0.167835	+	0.985815i	$0.446322\pi$
$968$	−4.58236	−0.147283
$969$	−1.21815	−0.0391326
$970$	−18.4242	−0.591565
$971$	20.9199	0.671352	0.335676	−	0.941978i	$-0.391035\pi$
$971$	20.9199	0.671352	0.335676	+	0.941978i	$0.391035\pi$
$972$	−67.8898	−2.17757
$973$	−25.2909	−0.810788
$974$	15.3467	0.491740
$975$	−78.3719	−2.50991
$976$	14.0817	0.450743
$977$	33.2805	1.06474	0.532369	−	0.846512i	$-0.321302\pi$
$977$	33.2805	1.06474	0.532369	+	0.846512i	$0.321302\pi$
$978$	−11.0120	−0.352126
$979$	−17.0962	−0.546396
$980$	−3.96996	−0.126816
$981$	45.4232	1.45025
$982$	−84.6531	−2.70139
$983$	47.8834	1.52724	0.763621	−	0.645665i	$-0.223420\pi$
$983$	47.8834	1.52724	0.763621	+	0.645665i	$0.223420\pi$
$984$	72.1104	2.29880
$985$	7.12132	0.226904
$986$	−2.54773	−0.0811361
$987$	46.3673	1.47589
$988$	−11.3337	−0.360573
$989$	8.53395	0.271364
$990$	9.49388	0.301735
$991$	−25.6280	−0.814102	−0.407051	−	0.913405i	$-0.633443\pi$
$991$	−25.6280	−0.814102	−0.407051	+	0.913405i	$0.633443\pi$
$992$	−4.58020	−0.145421
$993$	−35.4989	−1.12652
$994$	−15.2095	−0.482415
$995$	−15.1961	−0.481749
$996$	−55.5735	−1.76091
$997$	−27.8202	−0.881073	−0.440537	−	0.897735i	$-0.645212\pi$
$997$	−27.8202	−0.881073	−0.440537	+	0.897735i	$0.645212\pi$
$998$	76.1276	2.40978
$999$	35.8340	1.13374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.6	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.42660 q^{2} +2.76366 q^{3} +3.88839 q^{4} -0.843592 q^{5} -6.70630 q^{6} -2.86536 q^{7} -4.58236 q^{8} +4.63781 q^{9} +O(q^{10})\)	\(q-2.42660 q^{2} +2.76366 q^{3} +3.88839 q^{4} -0.843592 q^{5} -6.70630 q^{6} -2.86536 q^{7} -4.58236 q^{8} +4.63781 q^{9} +2.04706 q^{10} +1.00000 q^{11} +10.7462 q^{12} +6.61280 q^{13} +6.95308 q^{14} -2.33140 q^{15} +3.34279 q^{16} +1.00000 q^{17} -11.2541 q^{18} -0.440775 q^{19} -3.28021 q^{20} -7.91887 q^{21} -2.42660 q^{22} -8.53395 q^{23} -12.6641 q^{24} -4.28835 q^{25} -16.0466 q^{26} +4.52635 q^{27} -11.1416 q^{28} +1.04992 q^{29} +5.65738 q^{30} -4.34917 q^{31} +1.05312 q^{32} +2.76366 q^{33} -2.42660 q^{34} +2.41719 q^{35} +18.0336 q^{36} +7.91675 q^{37} +1.06958 q^{38} +18.2755 q^{39} +3.86565 q^{40} -5.69409 q^{41} +19.2159 q^{42} -1.00000 q^{43} +3.88839 q^{44} -3.91242 q^{45} +20.7085 q^{46} -5.85530 q^{47} +9.23832 q^{48} +1.21028 q^{49} +10.4061 q^{50} +2.76366 q^{51} +25.7131 q^{52} -1.55217 q^{53} -10.9837 q^{54} -0.843592 q^{55} +13.1301 q^{56} -1.21815 q^{57} -2.54773 q^{58} +3.96687 q^{59} -9.06539 q^{60} +4.21255 q^{61} +10.5537 q^{62} -13.2890 q^{63} -9.24107 q^{64} -5.57851 q^{65} -6.70630 q^{66} +10.7958 q^{67} +3.88839 q^{68} -23.5849 q^{69} -5.86556 q^{70} -2.18744 q^{71} -21.2521 q^{72} -7.72875 q^{73} -19.2108 q^{74} -11.8515 q^{75} -1.71390 q^{76} -2.86536 q^{77} -44.3474 q^{78} -8.86007 q^{79} -2.81995 q^{80} -1.40414 q^{81} +13.8173 q^{82} -5.17146 q^{83} -30.7917 q^{84} -0.843592 q^{85} +2.42660 q^{86} +2.90161 q^{87} -4.58236 q^{88} -17.0962 q^{89} +9.49388 q^{90} -18.9480 q^{91} -33.1833 q^{92} -12.0196 q^{93} +14.2085 q^{94} +0.371834 q^{95} +2.91046 q^{96} -9.00032 q^{97} -2.93686 q^{98} +4.63781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 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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