LMFDB - Embedded newform 8041.2.a.f.1.31

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:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
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)

$f(q)$	$=$	$q-0.0639832 q^{2} +2.10088 q^{3} -1.99591 q^{4} -3.38906 q^{5} -0.134421 q^{6} +3.96847 q^{7} +0.255671 q^{8} +1.41371 q^{9} +O(q^{10})$	\(q-0.0639832 q^{2} +2.10088 q^{3} -1.99591 q^{4} -3.38906 q^{5} -0.134421 q^{6} +3.96847 q^{7} +0.255671 q^{8} +1.41371 q^{9} +0.216843 q^{10} -1.00000 q^{11} -4.19317 q^{12} -7.07457 q^{13} -0.253915 q^{14} -7.12002 q^{15} +3.97545 q^{16} +1.00000 q^{17} -0.0904538 q^{18} -2.30259 q^{19} +6.76425 q^{20} +8.33729 q^{21} +0.0639832 q^{22} +0.134437 q^{23} +0.537135 q^{24} +6.48574 q^{25} +0.452654 q^{26} -3.33261 q^{27} -7.92069 q^{28} +5.50727 q^{29} +0.455562 q^{30} +0.217970 q^{31} -0.765704 q^{32} -2.10088 q^{33} -0.0639832 q^{34} -13.4494 q^{35} -2.82164 q^{36} +0.290153 q^{37} +0.147327 q^{38} -14.8628 q^{39} -0.866484 q^{40} -8.30615 q^{41} -0.533446 q^{42} -1.00000 q^{43} +1.99591 q^{44} -4.79116 q^{45} -0.00860173 q^{46} -10.1454 q^{47} +8.35197 q^{48} +8.74873 q^{49} -0.414978 q^{50} +2.10088 q^{51} +14.1202 q^{52} +4.02939 q^{53} +0.213231 q^{54} +3.38906 q^{55} +1.01462 q^{56} -4.83746 q^{57} -0.352373 q^{58} +8.42905 q^{59} +14.2109 q^{60} +8.90189 q^{61} -0.0139464 q^{62} +5.61027 q^{63} -7.90192 q^{64} +23.9761 q^{65} +0.134421 q^{66} +1.21226 q^{67} -1.99591 q^{68} +0.282437 q^{69} +0.860534 q^{70} +10.8719 q^{71} +0.361445 q^{72} -2.49954 q^{73} -0.0185649 q^{74} +13.6258 q^{75} +4.59574 q^{76} -3.96847 q^{77} +0.950972 q^{78} +7.56536 q^{79} -13.4731 q^{80} -11.2426 q^{81} +0.531454 q^{82} +16.3478 q^{83} -16.6404 q^{84} -3.38906 q^{85} +0.0639832 q^{86} +11.5701 q^{87} -0.255671 q^{88} -16.9223 q^{89} +0.306554 q^{90} -28.0752 q^{91} -0.268324 q^{92} +0.457930 q^{93} +0.649133 q^{94} +7.80360 q^{95} -1.60865 q^{96} -1.29781 q^{97} -0.559772 q^{98} -1.41371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−0.0639832	−0.0452429	−0.0226215	−	0.999744i	$-0.507201\pi$
$2$	−0.0639832	−0.0452429	−0.0226215	+	0.999744i	$0.507201\pi$
$3$	2.10088	1.21295	0.606473	−	0.795104i	$-0.292584\pi$
$3$	2.10088	1.21295	0.606473	+	0.795104i	$0.292584\pi$
$4$	−1.99591	−0.997953
$5$	−3.38906	−1.51563	−0.757817	−	0.652467i	$-0.773734\pi$
$5$	−3.38906	−1.51563	−0.757817	+	0.652467i	$0.773734\pi$
$6$	−0.134421	−0.0548772
$7$	3.96847	1.49994	0.749970	−	0.661472i	$-0.230068\pi$
$7$	3.96847	1.49994	0.749970	+	0.661472i	$0.230068\pi$
$8$	0.255671	0.0903933
$9$	1.41371	0.471237
$10$	0.216843	0.0685718
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.19317	−1.21046
$13$	−7.07457	−1.96213	−0.981066	−	0.193672i	$-0.937960\pi$
$13$	−7.07457	−1.96213	−0.981066	+	0.193672i	$0.937960\pi$
$14$	−0.253915	−0.0678617
$15$	−7.12002	−1.83838
$16$	3.97545	0.993863
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0904538	−0.0213202
$19$	−2.30259	−0.528249	−0.264125	−	0.964489i	$-0.585083\pi$
$19$	−2.30259	−0.528249	−0.264125	+	0.964489i	$0.585083\pi$
$20$	6.76425	1.51253
$21$	8.33729	1.81935
$22$	0.0639832	0.0136413
$23$	0.134437	0.0280321	0.0140161	−	0.999902i	$-0.495538\pi$
$23$	0.134437	0.0280321	0.0140161	+	0.999902i	$0.495538\pi$
$24$	0.537135	0.109642
$25$	6.48574	1.29715
$26$	0.452654	0.0887727
$27$	−3.33261	−0.641360
$28$	−7.92069	−1.49687
$29$	5.50727	1.02267	0.511337	−	0.859380i	$-0.329150\pi$
$29$	5.50727	1.02267	0.511337	+	0.859380i	$0.329150\pi$
$30$	0.455562	0.0831738
$31$	0.217970	0.0391486	0.0195743	−	0.999808i	$-0.493769\pi$
$31$	0.217970	0.0391486	0.0195743	+	0.999808i	$0.493769\pi$
$32$	−0.765704	−0.135359
$33$	−2.10088	−0.365717
$34$	−0.0639832	−0.0109730
$35$	−13.4494	−2.27336
$36$	−2.82164	−0.470273
$37$	0.290153	0.0477009	0.0238504	−	0.999716i	$-0.492407\pi$
$37$	0.290153	0.0477009	0.0238504	+	0.999716i	$0.492407\pi$
$38$	0.147327	0.0238996
$39$	−14.8628	−2.37996
$40$	−0.866484	−0.137003
$41$	−8.30615	−1.29720	−0.648601	−	0.761128i	$-0.724646\pi$
$41$	−8.30615	−1.29720	−0.648601	+	0.761128i	$0.724646\pi$
$42$	−0.533446	−0.0823125
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.99591	0.300894
$45$	−4.79116	−0.714224
$46$	−0.00860173	−0.00126826
$47$	−10.1454	−1.47985	−0.739927	−	0.672688i	$-0.765140\pi$
$47$	−10.1454	−1.47985	−0.739927	+	0.672688i	$0.765140\pi$
$48$	8.35197	1.20550
$49$	8.74873	1.24982
$50$	−0.414978	−0.0586868
$51$	2.10088	0.294183
$52$	14.1202	1.95812
$53$	4.02939	0.553479	0.276739	−	0.960945i	$-0.410746\pi$
$53$	4.02939	0.553479	0.276739	+	0.960945i	$0.410746\pi$
$54$	0.213231	0.0290170
$55$	3.38906	0.456981
$56$	1.01462	0.135584
$57$	−4.83746	−0.640738
$58$	−0.352373	−0.0462688
$59$	8.42905	1.09737	0.548684	−	0.836030i	$-0.315129\pi$
$59$	8.42905	1.09737	0.548684	+	0.836030i	$0.315129\pi$
$60$	14.2109	1.83462
$61$	8.90189	1.13977	0.569885	−	0.821724i	$-0.306988\pi$
$61$	8.90189	1.13977	0.569885	+	0.821724i	$0.306988\pi$
$62$	−0.0139464	−0.00177120
$63$	5.61027	0.706828
$64$	−7.90192	−0.987739
$65$	23.9761	2.97388
$66$	0.134421	0.0165461
$67$	1.21226	0.148101	0.0740506	−	0.997254i	$-0.476407\pi$
$67$	1.21226	0.148101	0.0740506	+	0.997254i	$0.476407\pi$
$68$	−1.99591	−0.242039
$69$	0.282437	0.0340015
$70$	0.860534	0.102853
$71$	10.8719	1.29025	0.645127	−	0.764075i	$-0.276804\pi$
$71$	10.8719	1.29025	0.645127	+	0.764075i	$0.276804\pi$
$72$	0.361445	0.0425967
$73$	−2.49954	−0.292549	−0.146274	−	0.989244i	$-0.546728\pi$
$73$	−2.49954	−0.292549	−0.146274	+	0.989244i	$0.546728\pi$
$74$	−0.0185649	−0.00215813
$75$	13.6258	1.57337
$76$	4.59574	0.527168
$77$	−3.96847	−0.452249
$78$	0.950972	0.107676
$79$	7.56536	0.851170	0.425585	−	0.904918i	$-0.360068\pi$
$79$	7.56536	0.851170	0.425585	+	0.904918i	$0.360068\pi$
$80$	−13.4731	−1.50633
$81$	−11.2426	−1.24917
$82$	0.531454	0.0586893
$83$	16.3478	1.79441	0.897204	−	0.441615i	$-0.145594\pi$
$83$	16.3478	1.79441	0.897204	+	0.441615i	$0.145594\pi$
$84$	−16.6404	−1.81562
$85$	−3.38906	−0.367595
$86$	0.0639832	0.00689948
$87$	11.5701	1.24045
$88$	−0.255671	−0.0272546
$89$	−16.9223	−1.79376	−0.896879	−	0.442277i	$-0.854171\pi$
$89$	−16.9223	−1.79376	−0.896879	+	0.442277i	$0.854171\pi$
$90$	0.306554	0.0323136
$91$	−28.0752	−2.94308
$92$	−0.268324	−0.0279747
$93$	0.457930	0.0474851
$94$	0.649133	0.0669529
$95$	7.80360	0.800633
$96$	−1.60865	−0.164183
$97$	−1.29781	−0.131772	−0.0658862	−	0.997827i	$-0.520987\pi$
$97$	−1.29781	−0.131772	−0.0658862	+	0.997827i	$0.520987\pi$
$98$	−0.559772	−0.0565455
$99$	−1.41371	−0.142083
$100$	−12.9449	−1.29449
$101$	3.53889	0.352133	0.176066	−	0.984378i	$-0.443663\pi$
$101$	3.53889	0.352133	0.176066	+	0.984378i	$0.443663\pi$
$102$	−0.134421	−0.0133097
$103$	−13.1976	−1.30040	−0.650198	−	0.759765i	$-0.725314\pi$
$103$	−13.1976	−1.30040	−0.650198	+	0.759765i	$0.725314\pi$
$104$	−1.80876	−0.177364
$105$	−28.2556	−2.75746
$106$	−0.257813	−0.0250410
$107$	3.64248	0.352132	0.176066	−	0.984378i	$-0.443663\pi$
$107$	3.64248	0.352132	0.176066	+	0.984378i	$0.443663\pi$
$108$	6.65157	0.640047
$109$	10.9970	1.05332	0.526662	−	0.850075i	$-0.323443\pi$
$109$	10.9970	1.05332	0.526662	+	0.850075i	$0.323443\pi$
$110$	−0.216843	−0.0206752
$111$	0.609578	0.0578586
$112$	15.7765	1.49074
$113$	16.9033	1.59013	0.795066	−	0.606522i	$-0.207436\pi$
$113$	16.9033	1.59013	0.795066	+	0.606522i	$0.207436\pi$
$114$	0.309516	0.0289889
$115$	−0.455616	−0.0424865
$116$	−10.9920	−1.02058
$117$	−10.0014	−0.924630
$118$	−0.539317	−0.0496482
$119$	3.96847	0.363789
$120$	−1.82038	−0.166177
$121$	1.00000	0.0909091
$122$	−0.569571	−0.0515666
$123$	−17.4503	−1.57344
$124$	−0.435048	−0.0390684
$125$	−5.03525	−0.450367
$126$	−0.358963	−0.0319790
$127$	−3.71183	−0.329372	−0.164686	−	0.986346i	$-0.552661\pi$
$127$	−3.71183	−0.329372	−0.164686	+	0.986346i	$0.552661\pi$
$128$	2.03700	0.180047
$129$	−2.10088	−0.184972
$130$	−1.53407	−0.134547
$131$	−5.86937	−0.512809	−0.256404	−	0.966570i	$-0.582538\pi$
$131$	−5.86937	−0.512809	−0.256404	+	0.966570i	$0.582538\pi$
$132$	4.19317	0.364968
$133$	−9.13773	−0.792342
$134$	−0.0775643	−0.00670053
$135$	11.2944	0.972068
$136$	0.255671	0.0219236
$137$	2.31704	0.197958	0.0989789	−	0.995090i	$-0.468442\pi$
$137$	2.31704	0.197958	0.0989789	+	0.995090i	$0.468442\pi$
$138$	−0.0180712	−0.00153833
$139$	−3.02296	−0.256404	−0.128202	−	0.991748i	$-0.540921\pi$
$139$	−3.02296	−0.256404	−0.128202	+	0.991748i	$0.540921\pi$
$140$	26.8437	2.26871
$141$	−21.3142	−1.79498
$142$	−0.695617	−0.0583749
$143$	7.07457	0.591605
$144$	5.62015	0.468346
$145$	−18.6645	−1.55000
$146$	0.159928	0.0132358
$147$	18.3801	1.51596
$148$	−0.579118	−0.0476032
$149$	−12.2398	−1.00273	−0.501364	−	0.865237i	$-0.667168\pi$
$149$	−12.2398	−1.00273	−0.501364	+	0.865237i	$0.667168\pi$
$150$	−0.871821	−0.0711839
$151$	4.09351	0.333125	0.166563	−	0.986031i	$-0.446733\pi$
$151$	4.09351	0.333125	0.166563	+	0.986031i	$0.446733\pi$
$152$	−0.588704	−0.0477502
$153$	1.41371	0.114292
$154$	0.253915	0.0204611
$155$	−0.738714	−0.0593349
$156$	29.6648	2.37509
$157$	−21.8316	−1.74235	−0.871175	−	0.490972i	$-0.836642\pi$
$157$	−21.8316	−1.74235	−0.871175	+	0.490972i	$0.836642\pi$
$158$	−0.484056	−0.0385094
$159$	8.46527	0.671340
$160$	2.59502	0.205154
$161$	0.533510	0.0420465
$162$	0.719334	0.0565163
$163$	14.6179	1.14496	0.572480	−	0.819919i	$-0.305982\pi$
$163$	14.6179	1.14496	0.572480	+	0.819919i	$0.305982\pi$
$164$	16.5783	1.29455
$165$	7.12002	0.554293
$166$	−1.04599	−0.0811843
$167$	8.48456	0.656555	0.328278	−	0.944581i	$-0.393532\pi$
$167$	8.48456	0.656555	0.328278	+	0.944581i	$0.393532\pi$
$168$	2.13160	0.164457
$169$	37.0495	2.84996
$170$	0.216843	0.0166311
$171$	−3.25519	−0.248931
$172$	1.99591	0.152186
$173$	−21.8627	−1.66219	−0.831093	−	0.556133i	$-0.812285\pi$
$173$	−21.8627	−1.66219	−0.831093	+	0.556133i	$0.812285\pi$
$174$	−0.740294	−0.0561215
$175$	25.7384	1.94564
$176$	−3.97545	−0.299661
$177$	17.7084	1.33105
$178$	1.08274	0.0811549
$179$	24.1551	1.80544	0.902719	−	0.430231i	$-0.141568\pi$
$179$	24.1551	1.80544	0.902719	+	0.430231i	$0.141568\pi$
$180$	9.56270	0.712762
$181$	−1.64089	−0.121967	−0.0609833	−	0.998139i	$-0.519424\pi$
$181$	−1.64089	−0.121967	−0.0609833	+	0.998139i	$0.519424\pi$
$182$	1.79634	0.133154
$183$	18.7018	1.38248
$184$	0.0343717	0.00253392
$185$	−0.983347	−0.0722971
$186$	−0.0292998	−0.00214837
$187$	−1.00000	−0.0731272
$188$	20.2492	1.47682
$189$	−13.2253	−0.962002
$190$	−0.499299	−0.0362230
$191$	25.5906	1.85167	0.925834	−	0.377930i	$-0.123364\pi$
$191$	25.5906	1.85167	0.925834	+	0.377930i	$0.123364\pi$
$192$	−16.6010	−1.19807
$193$	−5.50385	−0.396176	−0.198088	−	0.980184i	$-0.563473\pi$
$193$	−5.50385	−0.396176	−0.198088	+	0.980184i	$0.563473\pi$
$194$	0.0830379	0.00596177
$195$	50.3711	3.60715
$196$	−17.4616	−1.24726
$197$	−1.69895	−0.121045	−0.0605225	−	0.998167i	$-0.519277\pi$
$197$	−1.69895	−0.121045	−0.0605225	+	0.998167i	$0.519277\pi$
$198$	0.0904538	0.00642827
$199$	−1.40731	−0.0997617	−0.0498808	−	0.998755i	$-0.515884\pi$
$199$	−1.40731	−0.0997617	−0.0498808	+	0.998755i	$0.515884\pi$
$200$	1.65821	0.117253
$201$	2.54682	0.179639
$202$	−0.226429	−0.0159315
$203$	21.8554	1.53395
$204$	−4.19317	−0.293580
$205$	28.1500	1.96608
$206$	0.844423	0.0588338
$207$	0.190056	0.0132098
$208$	−28.1246	−1.95009
$209$	2.30259	0.159273
$210$	1.80788	0.124756
$211$	21.9449	1.51075	0.755373	−	0.655295i	$-0.227456\pi$
$211$	21.9449	1.51075	0.755373	+	0.655295i	$0.227456\pi$
$212$	−8.04228	−0.552346
$213$	22.8406	1.56501
$214$	−0.233058	−0.0159315
$215$	3.38906	0.231132
$216$	−0.852050	−0.0579747
$217$	0.865007	0.0587205
$218$	−0.703624	−0.0476554
$219$	−5.25124	−0.354846
$220$	−6.76425	−0.456046
$221$	−7.07457	−0.475887
$222$	−0.0390027	−0.00261769
$223$	6.40591	0.428971	0.214486	−	0.976727i	$-0.431192\pi$
$223$	6.40591	0.428971	0.214486	+	0.976727i	$0.431192\pi$
$224$	−3.03867	−0.203030
$225$	9.16897	0.611264
$226$	−1.08153	−0.0719423
$227$	3.38788	0.224862	0.112431	−	0.993660i	$-0.464136\pi$
$227$	3.38788	0.224862	0.112431	+	0.993660i	$0.464136\pi$
$228$	9.65513	0.639426
$229$	23.1484	1.52969	0.764846	−	0.644213i	$-0.222815\pi$
$229$	23.1484	1.52969	0.764846	+	0.644213i	$0.222815\pi$
$230$	0.0291518	0.00192221
$231$	−8.33729	−0.548553
$232$	1.40805	0.0924429
$233$	19.0534	1.24823	0.624114	−	0.781333i	$-0.285460\pi$
$233$	19.0534	1.24823	0.624114	+	0.781333i	$0.285460\pi$
$234$	0.639922	0.0418330
$235$	34.3833	2.24292
$236$	−16.8236	−1.09512
$237$	15.8939	1.03242
$238$	−0.253915	−0.0164589
$239$	7.10569	0.459629	0.229814	−	0.973234i	$-0.426188\pi$
$239$	7.10569	0.459629	0.229814	+	0.973234i	$0.426188\pi$
$240$	−28.3053	−1.82710
$241$	3.56100	0.229384	0.114692	−	0.993401i	$-0.463412\pi$
$241$	3.56100	0.229384	0.114692	+	0.993401i	$0.463412\pi$
$242$	−0.0639832	−0.00411300
$243$	−13.6215	−0.873819
$244$	−17.7673	−1.13744
$245$	−29.6500	−1.89427
$246$	1.11652	0.0711869
$247$	16.2898	1.03650
$248$	0.0557286	0.00353877
$249$	34.3449	2.17652
$250$	0.322171	0.0203759
$251$	−21.7233	−1.37117	−0.685583	−	0.727995i	$-0.740453\pi$
$251$	−21.7233	−1.37117	−0.685583	+	0.727995i	$0.740453\pi$
$252$	−11.1976	−0.705381
$253$	−0.134437	−0.00845201
$254$	0.237495	0.0149017
$255$	−7.12002	−0.445873
$256$	15.6735	0.979594
$257$	0.755766	0.0471434	0.0235717	−	0.999722i	$-0.492496\pi$
$257$	0.755766	0.0471434	0.0235717	+	0.999722i	$0.492496\pi$
$258$	0.134421	0.00836870
$259$	1.15146	0.0715484
$260$	−47.8541	−2.96779
$261$	7.78569	0.481922
$262$	0.375541	0.0232010
$263$	11.1975	0.690465	0.345232	−	0.938517i	$-0.387800\pi$
$263$	11.1975	0.690465	0.345232	+	0.938517i	$0.387800\pi$
$264$	−0.537135	−0.0330584
$265$	−13.6558	−0.838871
$266$	0.584661	0.0358479
$267$	−35.5517	−2.17573
$268$	−2.41956	−0.147798
$269$	20.6857	1.26123	0.630614	−	0.776096i	$-0.282803\pi$
$269$	20.6857	1.26123	0.630614	+	0.776096i	$0.282803\pi$
$270$	−0.722652	−0.0439792
$271$	−13.2760	−0.806457	−0.403229	−	0.915099i	$-0.632112\pi$
$271$	−13.2760	−0.806457	−0.403229	+	0.915099i	$0.632112\pi$
$272$	3.97545	0.241047
$273$	−58.9827	−3.56980
$274$	−0.148251	−0.00895619
$275$	−6.48574	−0.391105
$276$	−0.563718	−0.0339319
$277$	−14.4827	−0.870182	−0.435091	−	0.900387i	$-0.643284\pi$
$277$	−14.4827	−0.870182	−0.435091	+	0.900387i	$0.643284\pi$
$278$	0.193418	0.0116005
$279$	0.308147	0.0184483
$280$	−3.43861	−0.205496
$281$	16.8644	1.00605	0.503023	−	0.864273i	$-0.332221\pi$
$281$	16.8644	1.00605	0.503023	+	0.864273i	$0.332221\pi$
$282$	1.36375	0.0812103
$283$	2.14566	0.127546	0.0637730	−	0.997964i	$-0.479687\pi$
$283$	2.14566	0.127546	0.0637730	+	0.997964i	$0.479687\pi$
$284$	−21.6992	−1.28761
$285$	16.3945	0.971124
$286$	−0.452654	−0.0267660
$287$	−32.9627	−1.94573
$288$	−1.08249	−0.0637860
$289$	1.00000	0.0588235
$290$	1.19421	0.0701266
$291$	−2.72654	−0.159833
$292$	4.98884	0.291950
$293$	0.688175	0.0402036	0.0201018	−	0.999798i	$-0.493601\pi$
$293$	0.688175	0.0402036	0.0201018	+	0.999798i	$0.493601\pi$
$294$	−1.17602	−0.0685866
$295$	−28.5666	−1.66321
$296$	0.0741837	0.00431184
$297$	3.33261	0.193377
$298$	0.783144	0.0453663
$299$	−0.951087	−0.0550028
$300$	−27.1958	−1.57015
$301$	−3.96847	−0.228739
$302$	−0.261916	−0.0150716
$303$	7.43479	0.427118
$304$	−9.15382	−0.525008
$305$	−30.1690	−1.72747
$306$	−0.0904538	−0.00517090
$307$	−19.7985	−1.12996	−0.564980	−	0.825105i	$-0.691116\pi$
$307$	−19.7985	−1.12996	−0.564980	+	0.825105i	$0.691116\pi$
$308$	7.92069	0.451323
$309$	−27.7266	−1.57731
$310$	0.0472653	0.00268449
$311$	33.2293	1.88426	0.942130	−	0.335248i	$-0.108820\pi$
$311$	33.2293	1.88426	0.942130	+	0.335248i	$0.108820\pi$
$312$	−3.80000	−0.215132
$313$	32.0875	1.81369	0.906846	−	0.421463i	$-0.138483\pi$
$313$	32.0875	1.81369	0.906846	+	0.421463i	$0.138483\pi$
$314$	1.39685	0.0788291
$315$	−19.0136	−1.07129
$316$	−15.0998	−0.849428
$317$	−18.8871	−1.06080	−0.530401	−	0.847747i	$-0.677959\pi$
$317$	−18.8871	−1.06080	−0.530401	+	0.847747i	$0.677959\pi$
$318$	−0.541635	−0.0303734
$319$	−5.50727	−0.308348
$320$	26.7801	1.49705
$321$	7.65243	0.427117
$322$	−0.0341357	−0.00190231
$323$	−2.30259	−0.128119
$324$	22.4391	1.24662
$325$	−45.8838	−2.54517
$326$	−0.935298	−0.0518013
$327$	23.1035	1.27762
$328$	−2.12364	−0.117258
$329$	−40.2615	−2.21969
$330$	−0.455562	−0.0250779
$331$	−10.8498	−0.596358	−0.298179	−	0.954510i	$-0.596379\pi$
$331$	−10.8498	−0.596358	−0.298179	+	0.954510i	$0.596379\pi$
$332$	−32.6288	−1.79074
$333$	0.410193	0.0224784
$334$	−0.542869	−0.0297045
$335$	−4.10842	−0.224467
$336$	33.1445	1.80818
$337$	−3.40575	−0.185523	−0.0927615	−	0.995688i	$-0.529569\pi$
$337$	−3.40575	−0.185523	−0.0927615	+	0.995688i	$0.529569\pi$
$338$	−2.37055	−0.128941
$339$	35.5120	1.92874
$340$	6.76425	0.366843
$341$	−0.217970	−0.0118037
$342$	0.208278	0.0112624
$343$	6.93978	0.374713
$344$	−0.255671	−0.0137848
$345$	−0.957197	−0.0515338
$346$	1.39884	0.0752022
$347$	−10.0590	−0.539998	−0.269999	−	0.962861i	$-0.587023\pi$
$347$	−10.0590	−0.539998	−0.269999	+	0.962861i	$0.587023\pi$
$348$	−23.0929	−1.23791
$349$	36.4463	1.95093	0.975463	−	0.220162i	$-0.0706587\pi$
$349$	36.4463	1.95093	0.975463	+	0.220162i	$0.0706587\pi$
$350$	−1.64683	−0.0880266
$351$	23.5768	1.25843
$352$	0.765704	0.0408122
$353$	−5.23208	−0.278475	−0.139238	−	0.990259i	$-0.544465\pi$
$353$	−5.23208	−0.278475	−0.139238	+	0.990259i	$0.544465\pi$
$354$	−1.13304	−0.0602206
$355$	−36.8455	−1.95555
$356$	33.7753	1.79009
$357$	8.33729	0.441256
$358$	−1.54552	−0.0816833
$359$	23.4733	1.23888	0.619438	−	0.785046i	$-0.287361\pi$
$359$	23.4733	1.23888	0.619438	+	0.785046i	$0.287361\pi$
$360$	−1.22496	−0.0645610
$361$	−13.6981	−0.720953
$362$	0.104990	0.00551813
$363$	2.10088	0.110268
$364$	56.0355	2.93706
$365$	8.47108	0.443397
$366$	−1.19660	−0.0625474
$367$	2.17722	0.113650	0.0568249	−	0.998384i	$-0.481902\pi$
$367$	2.17722	0.113650	0.0568249	+	0.998384i	$0.481902\pi$
$368$	0.534450	0.0278601
$369$	−11.7425	−0.611290
$370$	0.0629176	0.00327093
$371$	15.9905	0.830185
$372$	−0.913985	−0.0473879
$373$	−2.01006	−0.104077	−0.0520384	−	0.998645i	$-0.516572\pi$
$373$	−2.01006	−0.104077	−0.0520384	+	0.998645i	$0.516572\pi$
$374$	0.0639832	0.00330849
$375$	−10.5785	−0.546270
$376$	−2.59387	−0.133769
$377$	−38.9615	−2.00662
$378$	0.846199	0.0435238
$379$	26.0507	1.33814	0.669068	−	0.743201i	$-0.266694\pi$
$379$	26.0507	1.33814	0.669068	+	0.743201i	$0.266694\pi$
$380$	−15.5753	−0.798994
$381$	−7.79812	−0.399510
$382$	−1.63737	−0.0837749
$383$	18.9917	0.970430	0.485215	−	0.874395i	$-0.338741\pi$
$383$	18.9917	0.970430	0.485215	+	0.874395i	$0.338741\pi$
$384$	4.27949	0.218387
$385$	13.4494	0.685444
$386$	0.352154	0.0179242
$387$	−1.41371	−0.0718630
$388$	2.59030	0.131503
$389$	−25.2573	−1.28060	−0.640299	−	0.768126i	$-0.721190\pi$
$389$	−25.2573	−1.28060	−0.640299	+	0.768126i	$0.721190\pi$
$390$	−3.22290	−0.163198
$391$	0.134437	0.00679879
$392$	2.23679	0.112975
$393$	−12.3309	−0.622009
$394$	0.108704	0.00547643
$395$	−25.6395	−1.29006
$396$	2.82164	0.141793
$397$	−17.3501	−0.870775	−0.435388	−	0.900243i	$-0.643389\pi$
$397$	−17.3501	−0.870775	−0.435388	+	0.900243i	$0.643389\pi$
$398$	0.0900443	0.00451351
$399$	−19.1973	−0.961068
$400$	25.7837	1.28919
$401$	10.4222	0.520460	0.260230	−	0.965547i	$-0.416202\pi$
$401$	10.4222	0.520460	0.260230	+	0.965547i	$0.416202\pi$
$402$	−0.162954	−0.00812738
$403$	−1.54204	−0.0768147
$404$	−7.06329	−0.351412
$405$	38.1017	1.89329
$406$	−1.39838	−0.0694004
$407$	−0.290153	−0.0143824
$408$	0.537135	0.0265921
$409$	16.8047	0.830938	0.415469	−	0.909607i	$-0.363618\pi$
$409$	16.8047	0.830938	0.415469	+	0.909607i	$0.363618\pi$
$410$	−1.80113	−0.0889514
$411$	4.86782	0.240112
$412$	26.3411	1.29773
$413$	33.4504	1.64599
$414$	−0.0121604	−0.000597650 0
$415$	−55.4038	−2.71967
$416$	5.41702	0.265591
$417$	−6.35088	−0.311004
$418$	−0.147327	−0.00720599
$419$	10.0317	0.490079	0.245039	−	0.969513i	$-0.421199\pi$
$419$	10.0317	0.490079	0.245039	+	0.969513i	$0.421199\pi$
$420$	56.3955	2.75182
$421$	−8.13602	−0.396525	−0.198263	−	0.980149i	$-0.563530\pi$
$421$	−8.13602	−0.396525	−0.198263	+	0.980149i	$0.563530\pi$
$422$	−1.40410	−0.0683506
$423$	−14.3426	−0.697362
$424$	1.03020	0.0500308
$425$	6.48574	0.314604
$426$	−1.46141	−0.0708056
$427$	35.3269	1.70959
$428$	−7.27005	−0.351411
$429$	14.8628	0.717585
$430$	−0.216843	−0.0104571
$431$	27.8976	1.34378	0.671890	−	0.740651i	$-0.265483\pi$
$431$	27.8976	1.34378	0.671890	+	0.740651i	$0.265483\pi$
$432$	−13.2486	−0.637425
$433$	14.2149	0.683122	0.341561	−	0.939860i	$-0.389044\pi$
$433$	14.2149	0.683122	0.341561	+	0.939860i	$0.389044\pi$
$434$	−0.0553459	−0.00265669
$435$	−39.2119	−1.88007
$436$	−21.9490	−1.05117
$437$	−0.309554	−0.0148080
$438$	0.335991	0.0160543
$439$	−3.77318	−0.180084	−0.0900420	−	0.995938i	$-0.528700\pi$
$439$	−3.77318	−0.180084	−0.0900420	+	0.995938i	$0.528700\pi$
$440$	0.866484	0.0413080
$441$	12.3682	0.588961
$442$	0.452654	0.0215305
$443$	−14.0427	−0.667187	−0.333594	−	0.942717i	$-0.608261\pi$
$443$	−14.0427	−0.667187	−0.333594	+	0.942717i	$0.608261\pi$
$444$	−1.21666	−0.0577401
$445$	57.3506	2.71868
$446$	−0.409870	−0.0194079
$447$	−25.7145	−1.21625
$448$	−31.3585	−1.48155
$449$	27.9145	1.31737	0.658683	−	0.752421i	$-0.271114\pi$
$449$	27.9145	1.31737	0.658683	+	0.752421i	$0.271114\pi$
$450$	−0.586660	−0.0276554
$451$	8.30615	0.391121
$452$	−33.7375	−1.58688
$453$	8.59999	0.404063
$454$	−0.216767	−0.0101734
$455$	95.1486	4.46063
$456$	−1.23680	−0.0579184
$457$	−4.70021	−0.219866	−0.109933	−	0.993939i	$-0.535064\pi$
$457$	−4.70021	−0.219866	−0.109933	+	0.993939i	$0.535064\pi$
$458$	−1.48111	−0.0692078
$459$	−3.33261	−0.155553
$460$	0.909368	0.0423995
$461$	21.3117	0.992583	0.496291	−	0.868156i	$-0.334695\pi$
$461$	21.3117	0.992583	0.496291	+	0.868156i	$0.334695\pi$
$462$	0.533446	0.0248182
$463$	15.2276	0.707685	0.353842	−	0.935305i	$-0.384875\pi$
$463$	15.2276	0.707685	0.353842	+	0.935305i	$0.384875\pi$
$464$	21.8939	1.01640
$465$	−1.55195	−0.0719700
$466$	−1.21910	−0.0564735
$467$	−35.0101	−1.62007	−0.810037	−	0.586379i	$-0.800553\pi$
$467$	−35.0101	−1.62007	−0.810037	+	0.586379i	$0.800553\pi$
$468$	19.9619	0.922738
$469$	4.81082	0.222143
$470$	−2.19995	−0.101476
$471$	−45.8656	−2.11338
$472$	2.15506	0.0991947
$473$	1.00000	0.0459800
$474$	−1.01695	−0.0467099
$475$	−14.9340	−0.685217
$476$	−7.92069	−0.363044
$477$	5.69639	0.260820
$478$	−0.454645	−0.0207950
$479$	7.86547	0.359383	0.179691	−	0.983723i	$-0.442490\pi$
$479$	7.86547	0.359383	0.179691	+	0.983723i	$0.442490\pi$
$480$	5.45183	0.248841
$481$	−2.05271	−0.0935954
$482$	−0.227844	−0.0103780
$483$	1.12084	0.0510001
$484$	−1.99591	−0.0907230
$485$	4.39835	0.199719
$486$	0.871546	0.0395341
$487$	8.34469	0.378134	0.189067	−	0.981964i	$-0.439454\pi$
$487$	8.34469	0.378134	0.189067	+	0.981964i	$0.439454\pi$
$488$	2.27595	0.103028
$489$	30.7104	1.38877
$490$	1.89710	0.0857023
$491$	−15.3267	−0.691685	−0.345843	−	0.938293i	$-0.612407\pi$
$491$	−15.3267	−0.691685	−0.345843	+	0.938293i	$0.612407\pi$
$492$	34.8291	1.57022
$493$	5.50727	0.248035
$494$	−1.04227	−0.0468941
$495$	4.79116	0.215347
$496$	0.866530	0.0389083
$497$	43.1447	1.93530
$498$	−2.19750	−0.0984722
$499$	28.9250	1.29486	0.647429	−	0.762125i	$-0.275844\pi$
$499$	28.9250	1.29486	0.647429	+	0.762125i	$0.275844\pi$
$500$	10.0499	0.449445
$501$	17.8251	0.796366
$502$	1.38993	0.0620356
$503$	−10.2378	−0.456483	−0.228241	−	0.973605i	$-0.573298\pi$
$503$	−10.2378	−0.456483	−0.228241	+	0.973605i	$0.573298\pi$
$504$	1.43438	0.0638925
$505$	−11.9935	−0.533704
$506$	0.00860173	0.000382394 0
$507$	77.8368	3.45685
$508$	7.40846	0.328697
$509$	22.0179	0.975924	0.487962	−	0.872865i	$-0.337740\pi$
$509$	22.0179	0.975924	0.487962	+	0.872865i	$0.337740\pi$
$510$	0.455562	0.0201726
$511$	−9.91933	−0.438805
$512$	−5.07684	−0.224367
$513$	7.67361	0.338798
$514$	−0.0483563	−0.00213291
$515$	44.7274	1.97092
$516$	4.19317	0.184594
$517$	10.1454	0.446193
$518$	−0.0736743	−0.00323706
$519$	−45.9309	−2.01614
$520$	6.13000	0.268818
$521$	9.32920	0.408720	0.204360	−	0.978896i	$-0.434489\pi$
$521$	9.32920	0.408720	0.204360	+	0.978896i	$0.434489\pi$
$522$	−0.498153	−0.0218036
$523$	−31.6332	−1.38322	−0.691611	−	0.722270i	$-0.743099\pi$
$523$	−31.6332	−1.38322	−0.691611	+	0.722270i	$0.743099\pi$
$524$	11.7147	0.511759
$525$	54.0734	2.35996
$526$	−0.716449	−0.0312386
$527$	0.217970	0.00949492
$528$	−8.35197	−0.363473
$529$	−22.9819	−0.999214
$530$	0.873744	0.0379530
$531$	11.9162	0.517121
$532$	18.2381	0.790720
$533$	58.7624	2.54528
$534$	2.27471	0.0984365
$535$	−12.3446	−0.533703
$536$	0.309940	0.0133874
$537$	50.7471	2.18990
$538$	−1.32354	−0.0570617
$539$	−8.74873	−0.376834
$540$	−22.5426	−0.970078
$541$	−28.2673	−1.21530	−0.607652	−	0.794203i	$-0.707889\pi$
$541$	−28.2673	−1.21530	−0.607652	+	0.794203i	$0.707889\pi$
$542$	0.849438	0.0364865
$543$	−3.44732	−0.147939
$544$	−0.765704	−0.0328293
$545$	−37.2696	−1.59645
$546$	3.77390	0.161508
$547$	17.4121	0.744490	0.372245	−	0.928135i	$-0.378588\pi$
$547$	17.4121	0.744490	0.372245	+	0.928135i	$0.378588\pi$
$548$	−4.62459	−0.197553
$549$	12.5847	0.537102
$550$	0.414978	0.0176947
$551$	−12.6810	−0.540227
$552$	0.0722110	0.00307350
$553$	30.0229	1.27670
$554$	0.926650	0.0393696
$555$	−2.06590	−0.0876924
$556$	6.03354	0.255879
$557$	−0.864872	−0.0366458	−0.0183229	−	0.999832i	$-0.505833\pi$
$557$	−0.864872	−0.0366458	−0.0183229	+	0.999832i	$0.505833\pi$
$558$	−0.0197162	−0.000834654 0
$559$	7.07457	0.299222
$560$	−53.4674	−2.25941
$561$	−2.10088	−0.0886994
$562$	−1.07904	−0.0455165
$563$	−3.34014	−0.140770	−0.0703852	−	0.997520i	$-0.522423\pi$
$563$	−3.34014	−0.140770	−0.0703852	+	0.997520i	$0.522423\pi$
$564$	42.5412	1.79131
$565$	−57.2865	−2.41006
$566$	−0.137286	−0.00577056
$567$	−44.6157	−1.87368
$568$	2.77962	0.116630
$569$	−26.7333	−1.12072	−0.560360	−	0.828249i	$-0.689337\pi$
$569$	−26.7333	−1.12072	−0.560360	+	0.828249i	$0.689337\pi$
$570$	−1.04897	−0.0439365
$571$	−2.58046	−0.107989	−0.0539944	−	0.998541i	$-0.517195\pi$
$571$	−2.58046	−0.107989	−0.0539944	+	0.998541i	$0.517195\pi$
$572$	−14.1202	−0.590394
$573$	53.7628	2.24597
$574$	2.10906	0.0880303
$575$	0.871925	0.0363618
$576$	−11.1710	−0.465460
$577$	13.5716	0.564994	0.282497	−	0.959268i	$-0.408837\pi$
$577$	13.5716	0.564994	0.282497	+	0.959268i	$0.408837\pi$
$578$	−0.0639832	−0.00266135
$579$	−11.5629	−0.480540
$580$	37.2525	1.54683
$581$	64.8759	2.69150
$582$	0.174453	0.00723131
$583$	−4.02939	−0.166880
$584$	−0.639059	−0.0264444
$585$	33.8954	1.40140
$586$	−0.0440316	−0.00181893
$587$	−9.50308	−0.392234	−0.196117	−	0.980580i	$-0.562833\pi$
$587$	−9.50308	−0.392234	−0.196117	+	0.980580i	$0.562833\pi$
$588$	−36.6849	−1.51286
$589$	−0.501895	−0.0206802
$590$	1.82778	0.0752485
$591$	−3.56929	−0.146821
$592$	1.15349	0.0474081
$593$	−21.5719	−0.885853	−0.442927	−	0.896558i	$-0.646060\pi$
$593$	−21.5719	−0.885853	−0.442927	+	0.896558i	$0.646060\pi$
$594$	−0.213231	−0.00874896
$595$	−13.4494	−0.551371
$596$	24.4296	1.00067
$597$	−2.95660	−0.121006
$598$	0.0608535	0.00248849
$599$	−2.19841	−0.0898248	−0.0449124	−	0.998991i	$-0.514301\pi$
$599$	−2.19841	−0.0898248	−0.0449124	+	0.998991i	$0.514301\pi$
$600$	3.48371	0.142222
$601$	−12.3704	−0.504599	−0.252300	−	0.967649i	$-0.581187\pi$
$601$	−12.3704	−0.504599	−0.252300	+	0.967649i	$0.581187\pi$
$602$	0.253915	0.0103488
$603$	1.71379	0.0697908
$604$	−8.17027	−0.332443
$605$	−3.38906	−0.137785
$606$	−0.475702	−0.0193241
$607$	−21.4705	−0.871462	−0.435731	−	0.900077i	$-0.643510\pi$
$607$	−21.4705	−0.871462	−0.435731	+	0.900077i	$0.643510\pi$
$608$	1.76310	0.0715031
$609$	45.9157	1.86060
$610$	1.93031	0.0781560
$611$	71.7741	2.90367
$612$	−2.82164	−0.114058
$613$	−5.00594	−0.202188	−0.101094	−	0.994877i	$-0.532234\pi$
$613$	−5.00594	−0.202188	−0.101094	+	0.994877i	$0.532234\pi$
$614$	1.26677	0.0511227
$615$	59.1400	2.38475
$616$	−1.01462	−0.0408803
$617$	47.5516	1.91435	0.957177	−	0.289504i	$-0.0934904\pi$
$617$	47.5516	1.91435	0.957177	+	0.289504i	$0.0934904\pi$
$618$	1.77403	0.0713622
$619$	25.5571	1.02723	0.513613	−	0.858022i	$-0.328307\pi$
$619$	25.5571	1.02723	0.513613	+	0.858022i	$0.328307\pi$
$620$	1.47440	0.0592135
$621$	−0.448027	−0.0179787
$622$	−2.12612	−0.0852495
$623$	−67.1555	−2.69053
$624$	−59.0866	−2.36536
$625$	−15.3639	−0.614556
$626$	−2.05306	−0.0820567
$627$	4.83746	0.193190
$628$	43.5738	1.73878
$629$	0.290153	0.0115692
$630$	1.21655	0.0484684
$631$	31.1258	1.23910	0.619550	−	0.784958i	$-0.287315\pi$
$631$	31.1258	1.23910	0.619550	+	0.784958i	$0.287315\pi$
$632$	1.93424	0.0769400
$633$	46.1036	1.83245
$634$	1.20845	0.0479938
$635$	12.5796	0.499207
$636$	−16.8959	−0.669965
$637$	−61.8935	−2.45231
$638$	0.352373	0.0139506
$639$	15.3697	0.608016
$640$	−6.90351	−0.272885
$641$	7.29183	0.288010	0.144005	−	0.989577i	$-0.454002\pi$
$641$	7.29183	0.288010	0.144005	+	0.989577i	$0.454002\pi$
$642$	−0.489627	−0.0193240
$643$	−44.1716	−1.74196	−0.870979	−	0.491321i	$-0.836514\pi$
$643$	−44.1716	−1.74196	−0.870979	+	0.491321i	$0.836514\pi$
$644$	−1.06484	−0.0419604
$645$	7.12002	0.280351
$646$	0.147327	0.00579649
$647$	−49.1737	−1.93322	−0.966608	−	0.256259i	$-0.917510\pi$
$647$	−49.1737	−1.93322	−0.966608	+	0.256259i	$0.917510\pi$
$648$	−2.87439	−0.112917
$649$	−8.42905	−0.330869
$650$	2.93579	0.115151
$651$	1.81728	0.0712248
$652$	−29.1759	−1.14262
$653$	−26.9621	−1.05511	−0.527555	−	0.849521i	$-0.676891\pi$
$653$	−26.9621	−1.05511	−0.527555	+	0.849521i	$0.676891\pi$
$654$	−1.47823	−0.0578035
$655$	19.8916	0.777231
$656$	−33.0207	−1.28924
$657$	−3.53363	−0.137860
$658$	2.57606	0.100425
$659$	44.6157	1.73798	0.868990	−	0.494829i	$-0.164769\pi$
$659$	44.6157	1.73798	0.868990	+	0.494829i	$0.164769\pi$
$660$	−14.2109	−0.553158
$661$	−35.5063	−1.38103	−0.690517	−	0.723317i	$-0.742617\pi$
$661$	−35.5063	−1.38103	−0.690517	+	0.723317i	$0.742617\pi$
$662$	0.694204	0.0269810
$663$	−14.8628	−0.577225
$664$	4.17967	0.162203
$665$	30.9683	1.20090
$666$	−0.0262455	−0.00101699
$667$	0.740383	0.0286677
$668$	−16.9344	−0.655211
$669$	13.4581	0.520319
$670$	0.262870	0.0101556
$671$	−8.90189	−0.343654
$672$	−6.38389	−0.246264
$673$	12.4568	0.480175	0.240088	−	0.970751i	$-0.422824\pi$
$673$	12.4568	0.480175	0.240088	+	0.970751i	$0.422824\pi$
$674$	0.217911	0.00839360
$675$	−21.6144	−0.831939
$676$	−73.9474	−2.84413
$677$	17.5173	0.673243	0.336621	−	0.941640i	$-0.390716\pi$
$677$	17.5173	0.673243	0.336621	+	0.941640i	$0.390716\pi$
$678$	−2.27217	−0.0872621
$679$	−5.15031	−0.197651
$680$	−0.866484	−0.0332281
$681$	7.11754	0.272745
$682$	0.0139464	0.000534036 0
$683$	−17.2626	−0.660534	−0.330267	−	0.943888i	$-0.607139\pi$
$683$	−17.2626	−0.660534	−0.330267	+	0.943888i	$0.607139\pi$
$684$	6.49706	0.248421
$685$	−7.85258	−0.300031
$686$	−0.444029	−0.0169531
$687$	48.6322	1.85543
$688$	−3.97545	−0.151563
$689$	−28.5062	−1.08600
$690$	0.0612445	0.00233154
$691$	1.45134	0.0552114	0.0276057	−	0.999619i	$-0.491212\pi$
$691$	1.45134	0.0552114	0.0276057	+	0.999619i	$0.491212\pi$
$692$	43.6358	1.65878
$693$	−5.61027	−0.213117
$694$	0.643610	0.0244311
$695$	10.2450	0.388614
$696$	2.95814	0.112128
$697$	−8.30615	−0.314618
$698$	−2.33195	−0.0882657
$699$	40.0289	1.51403
$700$	−51.3715	−1.94166
$701$	−43.0052	−1.62428	−0.812142	−	0.583459i	$-0.801699\pi$
$701$	−43.0052	−1.62428	−0.812142	+	0.583459i	$0.801699\pi$
$702$	−1.50852	−0.0569353
$703$	−0.668102	−0.0251980
$704$	7.90192	0.297815
$705$	72.2352	2.72054
$706$	0.334765	0.0125990
$707$	14.0440	0.528178
$708$	−35.3444	−1.32832
$709$	27.3861	1.02851	0.514253	−	0.857639i	$-0.328069\pi$
$709$	27.3861	1.02851	0.514253	+	0.857639i	$0.328069\pi$
$710$	2.35749	0.0884750
$711$	10.6952	0.401103
$712$	−4.32653	−0.162144
$713$	0.0293033	0.00109742
$714$	−0.533446	−0.0199637
$715$	−23.9761	−0.896657
$716$	−48.2113	−1.80174
$717$	14.9282	0.557505
$718$	−1.50190	−0.0560504
$719$	34.0743	1.27076	0.635379	−	0.772200i	$-0.280844\pi$
$719$	34.0743	1.27076	0.635379	+	0.772200i	$0.280844\pi$
$720$	−19.0470	−0.709841
$721$	−52.3742	−1.95052
$722$	0.876448	0.0326180
$723$	7.48125	0.278231
$724$	3.27507	0.121717
$725$	35.7187	1.32656
$726$	−0.134421	−0.00498884
$727$	2.95011	0.109413	0.0547067	−	0.998502i	$-0.482578\pi$
$727$	2.95011	0.109413	0.0547067	+	0.998502i	$0.482578\pi$
$728$	−7.17801	−0.266035
$729$	5.11051	0.189278
$730$	−0.542007	−0.0200606
$731$	−1.00000	−0.0369863
$732$	−37.3271	−1.37965
$733$	29.1928	1.07826	0.539130	−	0.842222i	$-0.318753\pi$
$733$	29.1928	1.07826	0.539130	+	0.842222i	$0.318753\pi$
$734$	−0.139305	−0.00514186
$735$	−62.2912	−2.29764
$736$	−0.102939	−0.00379439
$737$	−1.21226	−0.0446542
$738$	0.751323	0.0276566
$739$	−45.8816	−1.68778	−0.843891	−	0.536514i	$-0.819741\pi$
$739$	−45.8816	−1.68778	−0.843891	+	0.536514i	$0.819741\pi$
$740$	1.96267	0.0721491
$741$	34.2230	1.25721
$742$	−1.02312	−0.0375600
$743$	12.0572	0.442337	0.221168	−	0.975236i	$-0.429013\pi$
$743$	12.0572	0.442337	0.221168	+	0.975236i	$0.429013\pi$
$744$	0.117079	0.00429233
$745$	41.4816	1.51977
$746$	0.128610	0.00470874
$747$	23.1111	0.845593
$748$	1.99591	0.0729776
$749$	14.4551	0.528177
$750$	0.676845	0.0247149
$751$	−3.26191	−0.119029	−0.0595145	−	0.998227i	$-0.518955\pi$
$751$	−3.26191	−0.119029	−0.0595145	+	0.998227i	$0.518955\pi$
$752$	−40.3324	−1.47077
$753$	−45.6382	−1.66315
$754$	2.49288	0.0907855
$755$	−13.8732	−0.504896
$756$	26.3965	0.960032
$757$	1.18837	0.0431922	0.0215961	−	0.999767i	$-0.493125\pi$
$757$	1.18837	0.0431922	0.0215961	+	0.999767i	$0.493125\pi$
$758$	−1.66681	−0.0605412
$759$	−0.282437	−0.0102518
$760$	1.99515	0.0723718
$761$	3.33902	0.121039	0.0605197	−	0.998167i	$-0.480724\pi$
$761$	3.33902	0.121039	0.0605197	+	0.998167i	$0.480724\pi$
$762$	0.498949	0.0180750
$763$	43.6413	1.57992
$764$	−51.0764	−1.84788
$765$	−4.79116	−0.173225
$766$	−1.21515	−0.0439051
$767$	−59.6319	−2.15318
$768$	32.9282	1.18819
$769$	−25.7016	−0.926822	−0.463411	−	0.886143i	$-0.653375\pi$
$769$	−25.7016	−0.926822	−0.463411	+	0.886143i	$0.653375\pi$
$770$	−0.860534	−0.0310115
$771$	1.58778	0.0571824
$772$	10.9852	0.395365
$773$	27.9248	1.00439	0.502193	−	0.864756i	$-0.332527\pi$
$773$	27.9248	1.00439	0.502193	+	0.864756i	$0.332527\pi$
$774$	0.0904538	0.00325130
$775$	1.41370	0.0507815
$776$	−0.331812	−0.0119113
$777$	2.41909	0.0867844
$778$	1.61605	0.0579380
$779$	19.1256	0.685246
$780$	−100.536	−3.59977
$781$	−10.8719	−0.389026
$782$	−0.00860173	−0.000307597 0
$783$	−18.3536	−0.655902
$784$	34.7802	1.24215
$785$	73.9886	2.64077
$786$	0.788967	0.0281415
$787$	−12.6651	−0.451461	−0.225731	−	0.974190i	$-0.572477\pi$
$787$	−12.6651	−0.451461	−0.225731	+	0.974190i	$0.572477\pi$
$788$	3.39094	0.120797
$789$	23.5245	0.837496
$790$	1.64050	0.0583662
$791$	67.0804	2.38510
$792$	−0.361445	−0.0128434
$793$	−62.9770	−2.23638
$794$	1.11011	0.0393964
$795$	−28.6893	−1.01751
$796$	2.80886	0.0995575
$797$	23.8448	0.844626	0.422313	−	0.906450i	$-0.361218\pi$
$797$	23.8448	0.844626	0.422313	+	0.906450i	$0.361218\pi$
$798$	1.22831	0.0434815
$799$	−10.1454	−0.358917
$800$	−4.96615	−0.175580
$801$	−23.9232	−0.845286
$802$	−0.666846	−0.0235472
$803$	2.49954	0.0882067
$804$	−5.08321	−0.179271
$805$	−1.80810	−0.0637271
$806$	0.0986649	0.00347532
$807$	43.4582	1.52980
$808$	0.904791	0.0318304
$809$	25.9788	0.913365	0.456683	−	0.889630i	$-0.349038\pi$
$809$	25.9788	0.913365	0.456683	+	0.889630i	$0.349038\pi$
$810$	−2.43787	−0.0856580
$811$	−13.6041	−0.477705	−0.238852	−	0.971056i	$-0.576771\pi$
$811$	−13.6041	−0.477705	−0.238852	+	0.971056i	$0.576771\pi$
$812$	−43.6213	−1.53081
$813$	−27.8913	−0.978189
$814$	0.0185649	0.000650700 0
$815$	−49.5408	−1.73534
$816$	8.35197	0.292377
$817$	2.30259	0.0805573
$818$	−1.07522	−0.0375941
$819$	−39.6903	−1.38689
$820$	−56.1848	−1.96206
$821$	55.0828	1.92240	0.961201	−	0.275849i	$-0.0889590\pi$
$821$	55.0828	1.92240	0.961201	+	0.275849i	$0.0889590\pi$
$822$	−0.311459	−0.0108634
$823$	−30.0616	−1.04788	−0.523941	−	0.851754i	$-0.675539\pi$
$823$	−30.0616	−1.04788	−0.523941	+	0.851754i	$0.675539\pi$
$824$	−3.37424	−0.117547
$825$	−13.6258	−0.474389
$826$	−2.14026	−0.0744693
$827$	−4.07088	−0.141558	−0.0707792	−	0.997492i	$-0.522549\pi$
$827$	−4.07088	−0.141558	−0.0707792	+	0.997492i	$0.522549\pi$
$828$	−0.379334	−0.0131828
$829$	−37.3803	−1.29827	−0.649136	−	0.760673i	$-0.724869\pi$
$829$	−37.3803	−1.29827	−0.649136	+	0.760673i	$0.724869\pi$
$830$	3.54491	0.123046
$831$	−30.4265	−1.05548
$832$	55.9026	1.93808
$833$	8.74873	0.303126
$834$	0.406350	0.0140707
$835$	−28.7547	−0.995097
$836$	−4.59574	−0.158947
$837$	−0.726408	−0.0251083
$838$	−0.641858	−0.0221726
$839$	10.4295	0.360066	0.180033	−	0.983661i	$-0.442380\pi$
$839$	10.4295	0.360066	0.180033	+	0.983661i	$0.442380\pi$
$840$	−7.22413	−0.249256
$841$	1.33000	0.0458620
$842$	0.520568	0.0179400
$843$	35.4302	1.22028
$844$	−43.7999	−1.50765
$845$	−125.563	−4.31950
$846$	0.917687	0.0315507
$847$	3.96847	0.136358
$848$	16.0186	0.550082
$849$	4.50778	0.154706
$850$	−0.414978	−0.0142336
$851$	0.0390074	0.00133716
$852$	−45.5876	−1.56181
$853$	−1.49181	−0.0510786	−0.0255393	−	0.999674i	$-0.508130\pi$
$853$	−1.49181	−0.0510786	−0.0255393	+	0.999674i	$0.508130\pi$
$854$	−2.26032	−0.0773467
$855$	11.0321	0.377288
$856$	0.931276	0.0318304
$857$	5.03828	0.172104	0.0860522	−	0.996291i	$-0.472575\pi$
$857$	5.03828	0.172104	0.0860522	+	0.996291i	$0.472575\pi$
$858$	−0.950972	−0.0324657
$859$	−45.2460	−1.54378	−0.771888	−	0.635759i	$-0.780687\pi$
$859$	−45.2460	−1.54378	−0.771888	+	0.635759i	$0.780687\pi$
$860$	−6.76425	−0.230659
$861$	−69.2507	−2.36006
$862$	−1.78498	−0.0607965
$863$	49.9418	1.70004	0.850019	−	0.526752i	$-0.176590\pi$
$863$	49.9418	1.70004	0.850019	+	0.526752i	$0.176590\pi$
$864$	2.55179	0.0868136
$865$	74.0939	2.51927
$866$	−0.909512	−0.0309065
$867$	2.10088	0.0713498
$868$	−1.72647	−0.0586003
$869$	−7.56536	−0.256637
$870$	2.50890	0.0850597
$871$	−8.57622	−0.290594
$872$	2.81162	0.0952133
$873$	−1.83473	−0.0620961
$874$	0.0198062	0.000669955 0
$875$	−19.9822	−0.675523
$876$	10.4810	0.354119
$877$	−8.27245	−0.279341	−0.139670	−	0.990198i	$-0.544604\pi$
$877$	−8.27245	−0.279341	−0.139670	+	0.990198i	$0.544604\pi$
$878$	0.241420	0.00814753
$879$	1.44578	0.0487648
$880$	13.4731	0.454177
$881$	56.1132	1.89050	0.945252	−	0.326343i	$-0.105816\pi$
$881$	56.1132	1.89050	0.945252	+	0.326343i	$0.105816\pi$
$882$	−0.791356	−0.0266463
$883$	2.62485	0.0883333	0.0441667	−	0.999024i	$-0.485937\pi$
$883$	2.62485	0.0883333	0.0441667	+	0.999024i	$0.485937\pi$
$884$	14.1202	0.474913
$885$	−60.0150	−2.01738
$886$	0.898495	0.0301855
$887$	12.8555	0.431645	0.215823	−	0.976433i	$-0.430757\pi$
$887$	12.8555	0.431645	0.215823	+	0.976433i	$0.430757\pi$
$888$	0.155851	0.00523003
$889$	−14.7303	−0.494037
$890$	−3.66948	−0.123001
$891$	11.2426	0.376640
$892$	−12.7856	−0.428093
$893$	23.3606	0.781731
$894$	1.64530	0.0550269
$895$	−81.8631	−2.73638
$896$	8.08376	0.270059
$897$	−1.99812	−0.0667154
$898$	−1.78606	−0.0596015
$899$	1.20042	0.0400362
$900$	−18.3004	−0.610013
$901$	4.02939	0.134238
$902$	−0.531454	−0.0176955
$903$	−8.33729	−0.277448
$904$	4.32169	0.143737
$905$	5.56109	0.184857
$906$	−0.550255	−0.0182810
$907$	−54.3833	−1.80577	−0.902885	−	0.429883i	$-0.858555\pi$
$907$	−54.3833	−1.80577	−0.902885	+	0.429883i	$0.858555\pi$
$908$	−6.76189	−0.224401
$909$	5.00297	0.165938
$910$	−6.08791	−0.201812
$911$	34.4674	1.14196	0.570978	−	0.820965i	$-0.306564\pi$
$911$	34.4674	1.14196	0.570978	+	0.820965i	$0.306564\pi$
$912$	−19.2311	−0.636806
$913$	−16.3478	−0.541035
$914$	0.300734	0.00994740
$915$	−63.3817	−2.09533
$916$	−46.2021	−1.52656
$917$	−23.2924	−0.769182
$918$	0.213231	0.00703766
$919$	−19.5494	−0.644876	−0.322438	−	0.946591i	$-0.604502\pi$
$919$	−19.5494	−0.644876	−0.322438	+	0.946591i	$0.604502\pi$
$920$	−0.116488	−0.00384049
$921$	−41.5943	−1.37058
$922$	−1.36359	−0.0449074
$923$	−76.9139	−2.53165
$924$	16.6404	0.547430
$925$	1.88186	0.0618751
$926$	−0.974308	−0.0320177
$927$	−18.6576	−0.612795
$928$	−4.21694	−0.138428
$929$	−33.0366	−1.08390	−0.541948	−	0.840412i	$-0.682313\pi$
$929$	−33.0366	−1.08390	−0.541948	+	0.840412i	$0.682313\pi$
$930$	0.0992988	0.00325614
$931$	−20.1447	−0.660216
$932$	−38.0287	−1.24567
$933$	69.8109	2.28551
$934$	2.24006	0.0732969
$935$	3.38906	0.110834
$936$	−2.55707	−0.0835804
$937$	−26.4604	−0.864422	−0.432211	−	0.901772i	$-0.642267\pi$
$937$	−26.4604	−0.864422	−0.432211	+	0.901772i	$0.642267\pi$
$938$	−0.307811	−0.0100504
$939$	67.4121	2.19991
$940$	−68.6257	−2.23833
$941$	43.7134	1.42501	0.712507	−	0.701665i	$-0.247560\pi$
$941$	43.7134	1.42501	0.712507	+	0.701665i	$0.247560\pi$
$942$	2.93463	0.0956154
$943$	−1.11666	−0.0363633
$944$	33.5093	1.09063
$945$	44.8215	1.45804
$946$	−0.0639832	−0.00208027
$947$	53.7527	1.74673	0.873364	−	0.487068i	$-0.161933\pi$
$947$	53.7527	1.74673	0.873364	+	0.487068i	$0.161933\pi$
$948$	−31.7228	−1.03031
$949$	17.6831	0.574019
$950$	0.955523	0.0310012
$951$	−39.6795	−1.28670
$952$	1.01462	0.0328841
$953$	−34.6202	−1.12146	−0.560729	−	0.828000i	$-0.689479\pi$
$953$	−34.6202	−1.12146	−0.560729	+	0.828000i	$0.689479\pi$
$954$	−0.364473	−0.0118003
$955$	−86.7280	−2.80645
$956$	−14.1823	−0.458688
$957$	−11.5701	−0.374009
$958$	−0.503258	−0.0162595
$959$	9.19508	0.296925
$960$	56.2618	1.81584
$961$	−30.9525	−0.998467
$962$	0.131339	0.00423453
$963$	5.14942	0.165938
$964$	−7.10742	−0.228915
$965$	18.6529	0.600457
$966$	−0.0717151	−0.00230740
$967$	−23.5719	−0.758022	−0.379011	−	0.925392i	$-0.623736\pi$
$967$	−23.5719	−0.758022	−0.379011	+	0.925392i	$0.623736\pi$
$968$	0.255671	0.00821757
$969$	−4.83746	−0.155402
$970$	−0.281420	−0.00903587
$971$	−38.0119	−1.21986	−0.609930	−	0.792456i	$-0.708802\pi$
$971$	−38.0119	−1.21986	−0.609930	+	0.792456i	$0.708802\pi$
$972$	27.1872	0.872030
$973$	−11.9965	−0.384590
$974$	−0.533920	−0.0171079
$975$	−96.3965	−3.08716
$976$	35.3890	1.13278
$977$	28.7770	0.920657	0.460329	−	0.887749i	$-0.347732\pi$
$977$	28.7770	0.920657	0.460329	+	0.887749i	$0.347732\pi$
$978$	−1.96495	−0.0628322
$979$	16.9223	0.540838
$980$	59.1786	1.89039
$981$	15.5466	0.496365
$982$	0.980652	0.0312939
$983$	−11.0005	−0.350861	−0.175430	−	0.984492i	$-0.556132\pi$
$983$	−11.0005	−0.350861	−0.175430	+	0.984492i	$0.556132\pi$
$984$	−4.46152	−0.142228
$985$	5.75784	0.183460
$986$	−0.352373	−0.0112218
$987$	−84.5848	−2.69236
$988$	−32.5129	−1.03437
$989$	−0.134437	−0.00427486
$990$	−0.306554	−0.00974291
$991$	7.16597	0.227635	0.113817	−	0.993502i	$-0.463692\pi$
$991$	7.16597	0.227635	0.113817	+	0.993502i	$0.463692\pi$
$992$	−0.166900	−0.00529910
$993$	−22.7941	−0.723350
$994$	−2.76053	−0.0875588
$995$	4.76947	0.151202
$996$	−68.5492	−2.17207
$997$	46.7461	1.48047	0.740233	−	0.672351i	$-0.234715\pi$
$997$	46.7461	1.48047	0.740233	+	0.672351i	$0.234715\pi$
$998$	−1.85071	−0.0585832
$999$	−0.966966	−0.0305934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.31	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.31	✓	66	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)

\(f(q)\)	\(=\)	\(q-0.0639832 q^{2} +2.10088 q^{3} -1.99591 q^{4} -3.38906 q^{5} -0.134421 q^{6} +3.96847 q^{7} +0.255671 q^{8} +1.41371 q^{9} +O(q^{10})\)	\(q-0.0639832 q^{2} +2.10088 q^{3} -1.99591 q^{4} -3.38906 q^{5} -0.134421 q^{6} +3.96847 q^{7} +0.255671 q^{8} +1.41371 q^{9} +0.216843 q^{10} -1.00000 q^{11} -4.19317 q^{12} -7.07457 q^{13} -0.253915 q^{14} -7.12002 q^{15} +3.97545 q^{16} +1.00000 q^{17} -0.0904538 q^{18} -2.30259 q^{19} +6.76425 q^{20} +8.33729 q^{21} +0.0639832 q^{22} +0.134437 q^{23} +0.537135 q^{24} +6.48574 q^{25} +0.452654 q^{26} -3.33261 q^{27} -7.92069 q^{28} +5.50727 q^{29} +0.455562 q^{30} +0.217970 q^{31} -0.765704 q^{32} -2.10088 q^{33} -0.0639832 q^{34} -13.4494 q^{35} -2.82164 q^{36} +0.290153 q^{37} +0.147327 q^{38} -14.8628 q^{39} -0.866484 q^{40} -8.30615 q^{41} -0.533446 q^{42} -1.00000 q^{43} +1.99591 q^{44} -4.79116 q^{45} -0.00860173 q^{46} -10.1454 q^{47} +8.35197 q^{48} +8.74873 q^{49} -0.414978 q^{50} +2.10088 q^{51} +14.1202 q^{52} +4.02939 q^{53} +0.213231 q^{54} +3.38906 q^{55} +1.01462 q^{56} -4.83746 q^{57} -0.352373 q^{58} +8.42905 q^{59} +14.2109 q^{60} +8.90189 q^{61} -0.0139464 q^{62} +5.61027 q^{63} -7.90192 q^{64} +23.9761 q^{65} +0.134421 q^{66} +1.21226 q^{67} -1.99591 q^{68} +0.282437 q^{69} +0.860534 q^{70} +10.8719 q^{71} +0.361445 q^{72} -2.49954 q^{73} -0.0185649 q^{74} +13.6258 q^{75} +4.59574 q^{76} -3.96847 q^{77} +0.950972 q^{78} +7.56536 q^{79} -13.4731 q^{80} -11.2426 q^{81} +0.531454 q^{82} +16.3478 q^{83} -16.6404 q^{84} -3.38906 q^{85} +0.0639832 q^{86} +11.5701 q^{87} -0.255671 q^{88} -16.9223 q^{89} +0.306554 q^{90} -28.0752 q^{91} -0.268324 q^{92} +0.457930 q^{93} +0.649133 q^{94} +7.80360 q^{95} -1.60865 q^{96} -1.29781 q^{97} -0.559772 q^{98} -1.41371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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