LMFDB - Embedded newform 8041.2.a.f.1.30

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			1.30
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)

$f(q)$	$=$	$q-0.0750571 q^{2} +0.0713313 q^{3} -1.99437 q^{4} -0.846062 q^{5} -0.00535392 q^{6} +1.77888 q^{7} +0.299806 q^{8} -2.99491 q^{9} +O(q^{10})$	\(q-0.0750571 q^{2} +0.0713313 q^{3} -1.99437 q^{4} -0.846062 q^{5} -0.00535392 q^{6} +1.77888 q^{7} +0.299806 q^{8} -2.99491 q^{9} +0.0635030 q^{10} -1.00000 q^{11} -0.142261 q^{12} +1.06308 q^{13} -0.133518 q^{14} -0.0603507 q^{15} +3.96623 q^{16} +1.00000 q^{17} +0.224790 q^{18} +5.77899 q^{19} +1.68736 q^{20} +0.126890 q^{21} +0.0750571 q^{22} -5.14488 q^{23} +0.0213855 q^{24} -4.28418 q^{25} -0.0797917 q^{26} -0.427625 q^{27} -3.54774 q^{28} +10.3619 q^{29} +0.00452975 q^{30} -7.05081 q^{31} -0.897305 q^{32} -0.0713313 q^{33} -0.0750571 q^{34} -1.50505 q^{35} +5.97295 q^{36} +2.78546 q^{37} -0.433755 q^{38} +0.0758309 q^{39} -0.253654 q^{40} -1.22370 q^{41} -0.00952400 q^{42} -1.00000 q^{43} +1.99437 q^{44} +2.53388 q^{45} +0.386160 q^{46} +10.0650 q^{47} +0.282916 q^{48} -3.83558 q^{49} +0.321558 q^{50} +0.0713313 q^{51} -2.12017 q^{52} -8.56375 q^{53} +0.0320963 q^{54} +0.846062 q^{55} +0.533319 q^{56} +0.412223 q^{57} -0.777738 q^{58} -6.67154 q^{59} +0.120361 q^{60} -12.7490 q^{61} +0.529214 q^{62} -5.32760 q^{63} -7.86511 q^{64} -0.899432 q^{65} +0.00535392 q^{66} +12.9385 q^{67} -1.99437 q^{68} -0.366991 q^{69} +0.112964 q^{70} -5.20962 q^{71} -0.897892 q^{72} +10.3645 q^{73} -0.209068 q^{74} -0.305596 q^{75} -11.5254 q^{76} -1.77888 q^{77} -0.00569165 q^{78} -5.35789 q^{79} -3.35568 q^{80} +8.95423 q^{81} +0.0918474 q^{82} +6.56923 q^{83} -0.253065 q^{84} -0.846062 q^{85} +0.0750571 q^{86} +0.739130 q^{87} -0.299806 q^{88} -5.10131 q^{89} -0.190186 q^{90} +1.89109 q^{91} +10.2608 q^{92} -0.502943 q^{93} -0.755448 q^{94} -4.88939 q^{95} -0.0640060 q^{96} -9.04794 q^{97} +0.287887 q^{98} +2.99491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.0750571	−0.0530734	−0.0265367	−	0.999648i	$-0.508448\pi$
$2$	−0.0750571	−0.0530734	−0.0265367	+	0.999648i	$0.508448\pi$
$3$	0.0713313	0.0411831	0.0205916	−	0.999788i	$-0.493445\pi$
$3$	0.0713313	0.0411831	0.0205916	+	0.999788i	$0.493445\pi$
$4$	−1.99437	−0.997183
$5$	−0.846062	−0.378370	−0.189185	−	0.981941i	$-0.560585\pi$
$5$	−0.846062	−0.378370	−0.189185	+	0.981941i	$0.560585\pi$
$6$	−0.00535392	−0.00218573
$7$	1.77888	0.672354	0.336177	−	0.941799i	$-0.390866\pi$
$7$	1.77888	0.672354	0.336177	+	0.941799i	$0.390866\pi$
$8$	0.299806	0.105997
$9$	−2.99491	−0.998304
$10$	0.0635030	0.0200814
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.142261	−0.0410671
$13$	1.06308	0.294845	0.147423	−	0.989074i	$-0.452902\pi$
$13$	1.06308	0.294845	0.147423	+	0.989074i	$0.452902\pi$
$14$	−0.133518	−0.0356841
$15$	−0.0603507	−0.0155825
$16$	3.96623	0.991558
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.224790	0.0529834
$19$	5.77899	1.32579	0.662896	−	0.748711i	$-0.269327\pi$
$19$	5.77899	1.32579	0.662896	+	0.748711i	$0.269327\pi$
$20$	1.68736	0.377305
$21$	0.126890	0.0276897
$22$	0.0750571	0.0160022
$23$	−5.14488	−1.07278	−0.536390	−	0.843970i	$-0.680213\pi$
$23$	−5.14488	−1.07278	−0.536390	+	0.843970i	$0.680213\pi$
$24$	0.0213855	0.00436530
$25$	−4.28418	−0.856836
$26$	−0.0797917	−0.0156484
$27$	−0.427625	−0.0822964
$28$	−3.54774	−0.670460
$29$	10.3619	1.92416	0.962082	−	0.272761i	$-0.0879368\pi$
$29$	10.3619	1.92416	0.962082	+	0.272761i	$0.0879368\pi$
$30$	0.00452975	0.000827016 0
$31$	−7.05081	−1.26636	−0.633181	−	0.774003i	$-0.718251\pi$
$31$	−7.05081	−1.26636	−0.633181	+	0.774003i	$0.718251\pi$
$32$	−0.897305	−0.158623
$33$	−0.0713313	−0.0124172
$34$	−0.0750571	−0.0128722
$35$	−1.50505	−0.254399
$36$	5.97295	0.995492
$37$	2.78546	0.457926	0.228963	−	0.973435i	$-0.426466\pi$
$37$	2.78546	0.457926	0.228963	+	0.973435i	$0.426466\pi$
$38$	−0.433755	−0.0703643
$39$	0.0758309	0.0121427
$40$	−0.253654	−0.0401063
$41$	−1.22370	−0.191110	−0.0955549	−	0.995424i	$-0.530463\pi$
$41$	−1.22370	−0.191110	−0.0955549	+	0.995424i	$0.530463\pi$
$42$	−0.00952400	−0.00146959
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.99437	0.300662
$45$	2.53388	0.377729
$46$	0.386160	0.0569361
$47$	10.0650	1.46813	0.734064	−	0.679080i	$-0.237621\pi$
$47$	10.0650	1.46813	0.734064	+	0.679080i	$0.237621\pi$
$48$	0.282916	0.0408355
$49$	−3.83558	−0.547940
$50$	0.321558	0.0454752
$51$	0.0713313	0.00998838
$52$	−2.12017	−0.294015
$53$	−8.56375	−1.17632	−0.588160	−	0.808744i	$-0.700148\pi$
$53$	−8.56375	−1.17632	−0.588160	+	0.808744i	$0.700148\pi$
$54$	0.0320963	0.00436775
$55$	0.846062	0.114083
$56$	0.533319	0.0712678
$57$	0.412223	0.0546003
$58$	−0.777738	−0.102122
$59$	−6.67154	−0.868561	−0.434280	−	0.900778i	$-0.642997\pi$
$59$	−6.67154	−0.868561	−0.434280	+	0.900778i	$0.642997\pi$
$60$	0.120361	0.0155386
$61$	−12.7490	−1.63235	−0.816173	−	0.577807i	$-0.803908\pi$
$61$	−12.7490	−1.63235	−0.816173	+	0.577807i	$0.803908\pi$
$62$	0.529214	0.0672102
$63$	−5.32760	−0.671214
$64$	−7.86511	−0.983139
$65$	−0.899432	−0.111561
$66$	0.00535392	0.000659022 0
$67$	12.9385	1.58069	0.790344	−	0.612663i	$-0.209902\pi$
$67$	12.9385	1.58069	0.790344	+	0.612663i	$0.209902\pi$
$68$	−1.99437	−0.241852
$69$	−0.366991	−0.0441805
$70$	0.112964	0.0135018
$71$	−5.20962	−0.618269	−0.309134	−	0.951018i	$-0.600039\pi$
$71$	−5.20962	−0.618269	−0.309134	+	0.951018i	$0.600039\pi$
$72$	−0.897892	−0.105818
$73$	10.3645	1.21308	0.606538	−	0.795055i	$-0.292558\pi$
$73$	10.3645	1.21308	0.606538	+	0.795055i	$0.292558\pi$
$74$	−0.209068	−0.0243037
$75$	−0.305596	−0.0352872
$76$	−11.5254	−1.32206
$77$	−1.77888	−0.202722
$78$	−0.00569165	−0.000644452 0
$79$	−5.35789	−0.602810	−0.301405	−	0.953496i	$-0.597456\pi$
$79$	−5.35789	−0.602810	−0.301405	+	0.953496i	$0.597456\pi$
$80$	−3.35568	−0.375176
$81$	8.95423	0.994915
$82$	0.0918474	0.0101429
$83$	6.56923	0.721067	0.360533	−	0.932746i	$-0.382595\pi$
$83$	6.56923	0.721067	0.360533	+	0.932746i	$0.382595\pi$
$84$	−0.253065	−0.0276117
$85$	−0.846062	−0.0917683
$86$	0.0750571	0.00809362
$87$	0.739130	0.0792431
$88$	−0.299806	−0.0319594
$89$	−5.10131	−0.540738	−0.270369	−	0.962757i	$-0.587146\pi$
$89$	−5.10131	−0.540738	−0.270369	+	0.962757i	$0.587146\pi$
$90$	−0.190186	−0.0200474
$91$	1.89109	0.198241
$92$	10.2608	1.06976
$93$	−0.502943	−0.0521528
$94$	−0.755448	−0.0779186
$95$	−4.88939	−0.501641
$96$	−0.0640060	−0.00653258
$97$	−9.04794	−0.918679	−0.459340	−	0.888261i	$-0.651914\pi$
$97$	−9.04794	−0.918679	−0.459340	+	0.888261i	$0.651914\pi$
$98$	0.287887	0.0290810
$99$	2.99491	0.301000
$100$	8.54422	0.854422
$101$	−0.985720	−0.0980828	−0.0490414	−	0.998797i	$-0.515617\pi$
$101$	−0.985720	−0.0980828	−0.0490414	+	0.998797i	$0.515617\pi$
$102$	−0.00535392	−0.000530117 0
$103$	9.30041	0.916397	0.458198	−	0.888850i	$-0.348495\pi$
$103$	9.30041	0.916397	0.458198	+	0.888850i	$0.348495\pi$
$104$	0.318717	0.0312528
$105$	−0.107357	−0.0104770
$106$	0.642770	0.0624314
$107$	−9.49847	−0.918252	−0.459126	−	0.888371i	$-0.651837\pi$
$107$	−9.49847	−0.918252	−0.459126	+	0.888371i	$0.651837\pi$
$108$	0.852841	0.0820646
$109$	11.3466	1.08681	0.543403	−	0.839472i	$-0.317136\pi$
$109$	11.3466	1.08681	0.543403	+	0.839472i	$0.317136\pi$
$110$	−0.0635030	−0.00605477
$111$	0.198690	0.0188588
$112$	7.05546	0.666678
$113$	−2.42335	−0.227970	−0.113985	−	0.993482i	$-0.536362\pi$
$113$	−2.42335	−0.227970	−0.113985	+	0.993482i	$0.536362\pi$
$114$	−0.0309403	−0.00289782
$115$	4.35288	0.405909
$116$	−20.6655	−1.91874
$117$	−3.18383	−0.294345
$118$	0.500747	0.0460975
$119$	1.77888	0.163070
$120$	−0.0180935	−0.00165170
$121$	1.00000	0.0909091
$122$	0.956906	0.0866342
$123$	−0.0872881	−0.00787050
$124$	14.0619	1.26280
$125$	7.85499	0.702572
$126$	0.399874	0.0356236
$127$	−22.1446	−1.96501	−0.982507	−	0.186223i	$-0.940375\pi$
$127$	−22.1446	−1.96501	−0.982507	+	0.186223i	$0.940375\pi$
$128$	2.38494	0.210801
$129$	−0.0713313	−0.00628037
$130$	0.0675088	0.00592091
$131$	−2.33469	−0.203983	−0.101991	−	0.994785i	$-0.532521\pi$
$131$	−2.33469	−0.203983	−0.101991	+	0.994785i	$0.532521\pi$
$132$	0.142261	0.0123822
$133$	10.2802	0.891402
$134$	−0.971126	−0.0838925
$135$	0.361797	0.0311385
$136$	0.299806	0.0257081
$137$	4.42453	0.378013	0.189007	−	0.981976i	$-0.439473\pi$
$137$	4.42453	0.378013	0.189007	+	0.981976i	$0.439473\pi$
$138$	0.0275453	0.00234481
$139$	−4.87710	−0.413670	−0.206835	−	0.978376i	$-0.566316\pi$
$139$	−4.87710	−0.413670	−0.206835	+	0.978376i	$0.566316\pi$
$140$	3.00161	0.253682
$141$	0.717948	0.0604621
$142$	0.391019	0.0328136
$143$	−1.06308	−0.0888992
$144$	−11.8785	−0.989876
$145$	−8.76684	−0.728047
$146$	−0.777931	−0.0643821
$147$	−0.273597	−0.0225659
$148$	−5.55522	−0.456636
$149$	14.8778	1.21883	0.609417	−	0.792850i	$-0.291403\pi$
$149$	14.8778	1.21883	0.609417	+	0.792850i	$0.291403\pi$
$150$	0.0229372	0.00187281
$151$	11.5208	0.937547	0.468773	−	0.883319i	$-0.344696\pi$
$151$	11.5208	0.937547	0.468773	+	0.883319i	$0.344696\pi$
$152$	1.73258	0.140530
$153$	−2.99491	−0.242124
$154$	0.133518	0.0107592
$155$	5.96542	0.479154
$156$	−0.151235	−0.0121085
$157$	13.5283	1.07968	0.539839	−	0.841769i	$-0.318485\pi$
$157$	13.5283	1.07968	0.539839	+	0.841769i	$0.318485\pi$
$158$	0.402148	0.0319932
$159$	−0.610863	−0.0484446
$160$	0.759176	0.0600181
$161$	−9.15213	−0.721289
$162$	−0.672079	−0.0528035
$163$	12.7159	0.995984	0.497992	−	0.867182i	$-0.334071\pi$
$163$	12.7159	0.995984	0.497992	+	0.867182i	$0.334071\pi$
$164$	2.44051	0.190572
$165$	0.0603507	0.00469830
$166$	−0.493068	−0.0382695
$167$	16.0699	1.24353	0.621763	−	0.783205i	$-0.286417\pi$
$167$	16.0699	1.24353	0.621763	+	0.783205i	$0.286417\pi$
$168$	0.0380423	0.00293503
$169$	−11.8699	−0.913066
$170$	0.0635030	0.00487046
$171$	−17.3076	−1.32354
$172$	1.99437	0.152069
$173$	−1.83394	−0.139432	−0.0697161	−	0.997567i	$-0.522209\pi$
$173$	−1.83394	−0.139432	−0.0697161	+	0.997567i	$0.522209\pi$
$174$	−0.0554770	−0.00420570
$175$	−7.62105	−0.576097
$176$	−3.96623	−0.298966
$177$	−0.475890	−0.0357701
$178$	0.382890	0.0286988
$179$	2.11848	0.158343	0.0791714	−	0.996861i	$-0.474773\pi$
$179$	2.11848	0.158343	0.0791714	+	0.996861i	$0.474773\pi$
$180$	−5.05349	−0.376665
$181$	6.25333	0.464807	0.232403	−	0.972619i	$-0.425341\pi$
$181$	6.25333	0.464807	0.232403	+	0.972619i	$0.425341\pi$
$182$	−0.141940	−0.0105213
$183$	−0.909405	−0.0672251
$184$	−1.54246	−0.113712
$185$	−2.35667	−0.173266
$186$	0.0377495	0.00276793
$187$	−1.00000	−0.0731272
$188$	−20.0733	−1.46399
$189$	−0.760694	−0.0553324
$190$	0.366983	0.0266238
$191$	16.3111	1.18023	0.590117	−	0.807318i	$-0.299082\pi$
$191$	16.3111	1.18023	0.590117	+	0.807318i	$0.299082\pi$
$192$	−0.561029	−0.0404887
$193$	−4.50115	−0.324000	−0.162000	−	0.986791i	$-0.551794\pi$
$193$	−4.50115	−0.324000	−0.162000	+	0.986791i	$0.551794\pi$
$194$	0.679113	0.0487574
$195$	−0.0641576	−0.00459442
$196$	7.64955	0.546396
$197$	−9.79251	−0.697688	−0.348844	−	0.937181i	$-0.613426\pi$
$197$	−9.79251	−0.697688	−0.348844	+	0.937181i	$0.613426\pi$
$198$	−0.224790	−0.0159751
$199$	−13.9891	−0.991664	−0.495832	−	0.868418i	$-0.665137\pi$
$199$	−13.9891	−0.991664	−0.495832	+	0.868418i	$0.665137\pi$
$200$	−1.28442	−0.0908223
$201$	0.922919	0.0650977
$202$	0.0739854	0.00520559
$203$	18.4327	1.29372
$204$	−0.142261	−0.00996024
$205$	1.03533	0.0723103
$206$	−0.698062	−0.0486363
$207$	15.4084	1.07096
$208$	4.21642	0.292356
$209$	−5.77899	−0.399741
$210$	0.00805790	0.000556048 0
$211$	12.5700	0.865356	0.432678	−	0.901548i	$-0.357569\pi$
$211$	12.5700	0.865356	0.432678	+	0.901548i	$0.357569\pi$
$212$	17.0792	1.17301
$213$	−0.371609	−0.0254622
$214$	0.712928	0.0487348
$215$	0.846062	0.0577010
$216$	−0.128204	−0.00872320
$217$	−12.5426	−0.851445
$218$	−0.851643	−0.0576805
$219$	0.739315	0.0499583
$220$	−1.68736	−0.113762
$221$	1.06308	0.0715105
$222$	−0.0149131	−0.00100090
$223$	−11.5850	−0.775786	−0.387893	−	0.921704i	$-0.626797\pi$
$223$	−11.5850	−0.775786	−0.387893	+	0.921704i	$0.626797\pi$
$224$	−1.59620	−0.106651
$225$	12.8307	0.855383
$226$	0.181890	0.0120991
$227$	3.76462	0.249867	0.124933	−	0.992165i	$-0.460128\pi$
$227$	3.76462	0.249867	0.124933	+	0.992165i	$0.460128\pi$
$228$	−0.822124	−0.0544465
$229$	12.9617	0.856532	0.428266	−	0.903653i	$-0.359125\pi$
$229$	12.9617	0.856532	0.428266	+	0.903653i	$0.359125\pi$
$230$	−0.326715	−0.0215430
$231$	−0.126890	−0.00834875
$232$	3.10657	0.203956
$233$	−1.99519	−0.130709	−0.0653547	−	0.997862i	$-0.520818\pi$
$233$	−1.99519	−0.130709	−0.0653547	+	0.997862i	$0.520818\pi$
$234$	0.238969	0.0156219
$235$	−8.51560	−0.555496
$236$	13.3055	0.866114
$237$	−0.382185	−0.0248256
$238$	−0.133518	−0.00865468
$239$	4.60798	0.298065	0.149033	−	0.988832i	$-0.452384\pi$
$239$	4.60798	0.298065	0.149033	+	0.988832i	$0.452384\pi$
$240$	−0.239365	−0.0154509
$241$	−8.77425	−0.565199	−0.282600	−	0.959238i	$-0.591197\pi$
$241$	−8.77425	−0.565199	−0.282600	+	0.959238i	$0.591197\pi$
$242$	−0.0750571	−0.00482486
$243$	1.92159	0.123270
$244$	25.4262	1.62775
$245$	3.24514	0.207324
$246$	0.00655160	0.000417715 0
$247$	6.14353	0.390904
$248$	−2.11387	−0.134231
$249$	0.468592	0.0296958
$250$	−0.589573	−0.0372879
$251$	6.12858	0.386833	0.193416	−	0.981117i	$-0.438043\pi$
$251$	6.12858	0.386833	0.193416	+	0.981117i	$0.438043\pi$
$252$	10.6252	0.669323
$253$	5.14488	0.323456
$254$	1.66211	0.104290
$255$	−0.0603507	−0.00377931
$256$	15.5512	0.971951
$257$	29.5280	1.84191	0.920953	−	0.389673i	$-0.127412\pi$
$257$	29.5280	1.84191	0.920953	+	0.389673i	$0.127412\pi$
$258$	0.00535392	0.000333321 0
$259$	4.95500	0.307889
$260$	1.79380	0.111247
$261$	−31.0331	−1.92090
$262$	0.175235	0.0108261
$263$	−4.90502	−0.302457	−0.151228	−	0.988499i	$-0.548323\pi$
$263$	−4.90502	−0.302457	−0.151228	+	0.988499i	$0.548323\pi$
$264$	−0.0213855	−0.00131619
$265$	7.24546	0.445085
$266$	−0.771599	−0.0473098
$267$	−0.363883	−0.0222693
$268$	−25.8041	−1.57624
$269$	29.2616	1.78411	0.892054	−	0.451928i	$-0.149264\pi$
$269$	29.2616	1.78411	0.892054	+	0.451928i	$0.149264\pi$
$270$	−0.0271555	−0.00165263
$271$	1.89103	0.114872	0.0574359	−	0.998349i	$-0.481708\pi$
$271$	1.89103	0.114872	0.0574359	+	0.998349i	$0.481708\pi$
$272$	3.96623	0.240488
$273$	0.134894	0.00816417
$274$	−0.332093	−0.0200624
$275$	4.28418	0.258346
$276$	0.731914	0.0440560
$277$	8.78656	0.527933	0.263967	−	0.964532i	$-0.414969\pi$
$277$	8.78656	0.527933	0.263967	+	0.964532i	$0.414969\pi$
$278$	0.366061	0.0219549
$279$	21.1166	1.26422
$280$	−0.451221	−0.0269656
$281$	22.9197	1.36728	0.683639	−	0.729821i	$-0.260396\pi$
$281$	22.9197	1.36728	0.683639	+	0.729821i	$0.260396\pi$
$282$	−0.0538871	−0.00320893
$283$	14.0452	0.834903	0.417452	−	0.908699i	$-0.362923\pi$
$283$	14.0452	0.834903	0.417452	+	0.908699i	$0.362923\pi$
$284$	10.3899	0.616527
$285$	−0.348766	−0.0206591
$286$	0.0797917	0.00471818
$287$	−2.17682	−0.128494
$288$	2.68735	0.158354
$289$	1.00000	0.0588235
$290$	0.658014	0.0386399
$291$	−0.645401	−0.0378341
$292$	−20.6707	−1.20966
$293$	11.7723	0.687748	0.343874	−	0.939016i	$-0.388261\pi$
$293$	11.7723	0.687748	0.343874	+	0.939016i	$0.388261\pi$
$294$	0.0205354	0.00119765
$295$	5.64454	0.328638
$296$	0.835096	0.0485390
$297$	0.427625	0.0248133
$298$	−1.11668	−0.0646877
$299$	−5.46941	−0.316304
$300$	0.609470	0.0351878
$301$	−1.77888	−0.102533
$302$	−0.864716	−0.0497588
$303$	−0.0703127	−0.00403936
$304$	22.9208	1.31460
$305$	10.7865	0.617632
$306$	0.224790	0.0128504
$307$	8.42196	0.480667	0.240333	−	0.970690i	$-0.422743\pi$
$307$	8.42196	0.480667	0.240333	+	0.970690i	$0.422743\pi$
$308$	3.54774	0.202151
$309$	0.663410	0.0377401
$310$	−0.447748	−0.0254304
$311$	−8.58441	−0.486777	−0.243389	−	0.969929i	$-0.578259\pi$
$311$	−8.58441	−0.486777	−0.243389	+	0.969929i	$0.578259\pi$
$312$	0.0227345	0.00128709
$313$	11.4565	0.647562	0.323781	−	0.946132i	$-0.395046\pi$
$313$	11.4565	0.647562	0.323781	+	0.946132i	$0.395046\pi$
$314$	−1.01540	−0.0573022
$315$	4.50748	0.253968
$316$	10.6856	0.601112
$317$	6.75347	0.379313	0.189656	−	0.981851i	$-0.439263\pi$
$317$	6.75347	0.379313	0.189656	+	0.981851i	$0.439263\pi$
$318$	0.0458496	0.00257112
$319$	−10.3619	−0.580157
$320$	6.65437	0.371991
$321$	−0.677538	−0.0378165
$322$	0.686933	0.0382813
$323$	5.77899	0.321552
$324$	−17.8580	−0.992112
$325$	−4.55442	−0.252634
$326$	−0.954417	−0.0528603
$327$	0.809367	0.0447581
$328$	−0.366872	−0.0202571
$329$	17.9044	0.987102
$330$	−0.00452975	−0.000249355 0
$331$	−7.76969	−0.427061	−0.213530	−	0.976936i	$-0.568496\pi$
$331$	−7.76969	−0.427061	−0.213530	+	0.976936i	$0.568496\pi$
$332$	−13.1015	−0.719036
$333$	−8.34220	−0.457150
$334$	−1.20616	−0.0659982
$335$	−10.9468	−0.598086
$336$	0.503275	0.0274559
$337$	−15.0677	−0.820788	−0.410394	−	0.911908i	$-0.634609\pi$
$337$	−15.0677	−0.820788	−0.410394	+	0.911908i	$0.634609\pi$
$338$	0.890918	0.0484595
$339$	−0.172861	−0.00938852
$340$	1.68736	0.0915098
$341$	7.05081	0.381823
$342$	1.29906	0.0702450
$343$	−19.2752	−1.04076
$344$	−0.299806	−0.0161644
$345$	0.310497	0.0167166
$346$	0.137651	0.00740014
$347$	22.9720	1.23320	0.616600	−	0.787277i	$-0.288510\pi$
$347$	22.9720	1.23320	0.616600	+	0.787277i	$0.288510\pi$
$348$	−1.47410	−0.0790199
$349$	−12.2095	−0.653560	−0.326780	−	0.945100i	$-0.605964\pi$
$349$	−12.2095	−0.653560	−0.326780	+	0.945100i	$0.605964\pi$
$350$	0.572014	0.0305755
$351$	−0.454599	−0.0242647
$352$	0.897305	0.0478265
$353$	−7.66218	−0.407817	−0.203908	−	0.978990i	$-0.565364\pi$
$353$	−7.66218	−0.407817	−0.203908	+	0.978990i	$0.565364\pi$
$354$	0.0357189	0.00189844
$355$	4.40767	0.233935
$356$	10.1739	0.539215
$357$	0.126890	0.00671573
$358$	−0.159007	−0.00840379
$359$	0.224799	0.0118645	0.00593223	−	0.999982i	$-0.498112\pi$
$359$	0.224799	0.0118645	0.00593223	+	0.999982i	$0.498112\pi$
$360$	0.759672	0.0400382
$361$	14.3968	0.757725
$362$	−0.469357	−0.0246689
$363$	0.0713313	0.00374392
$364$	−3.77153	−0.197682
$365$	−8.76903	−0.458992
$366$	0.0682573	0.00356787
$367$	−11.1932	−0.584281	−0.292140	−	0.956375i	$-0.594367\pi$
$367$	−11.1932	−0.584281	−0.292140	+	0.956375i	$0.594367\pi$
$368$	−20.4058	−1.06372
$369$	3.66487	0.190786
$370$	0.176885	0.00919581
$371$	−15.2339	−0.790904
$372$	1.00305	0.0520059
$373$	5.73606	0.297002	0.148501	−	0.988912i	$-0.452555\pi$
$373$	5.73606	0.297002	0.148501	+	0.988912i	$0.452555\pi$
$374$	0.0750571	0.00388111
$375$	0.560307	0.0289341
$376$	3.01754	0.155618
$377$	11.0156	0.567331
$378$	0.0570955	0.00293668
$379$	16.5778	0.851546	0.425773	−	0.904830i	$-0.360002\pi$
$379$	16.5778	0.851546	0.425773	+	0.904830i	$0.360002\pi$
$380$	9.75123	0.500228
$381$	−1.57960	−0.0809255
$382$	−1.22427	−0.0626390
$383$	17.2371	0.880773	0.440387	−	0.897808i	$-0.354841\pi$
$383$	17.2371	0.880773	0.440387	+	0.897808i	$0.354841\pi$
$384$	0.170121	0.00868146
$385$	1.50505	0.0767042
$386$	0.337843	0.0171958
$387$	2.99491	0.152240
$388$	18.0449	0.916091
$389$	29.0965	1.47525	0.737625	−	0.675211i	$-0.235947\pi$
$389$	29.0965	1.47525	0.737625	+	0.675211i	$0.235947\pi$
$390$	0.00481549	0.000243842 0
$391$	−5.14488	−0.260188
$392$	−1.14993	−0.0580801
$393$	−0.166537	−0.00840066
$394$	0.734998	0.0370287
$395$	4.53311	0.228085
$396$	−5.97295	−0.300152
$397$	−10.1510	−0.509463	−0.254731	−	0.967012i	$-0.581987\pi$
$397$	−10.1510	−0.509463	−0.254731	+	0.967012i	$0.581987\pi$
$398$	1.04999	0.0526310
$399$	0.733296	0.0367107
$400$	−16.9920	−0.849602
$401$	25.9177	1.29427	0.647135	−	0.762375i	$-0.275967\pi$
$401$	25.9177	1.29427	0.647135	+	0.762375i	$0.275967\pi$
$402$	−0.0692717	−0.00345496
$403$	−7.49557	−0.373381
$404$	1.96589	0.0978066
$405$	−7.57584	−0.376446
$406$	−1.38350	−0.0686621
$407$	−2.78546	−0.138070
$408$	0.0213855	0.00105874
$409$	−9.48134	−0.468822	−0.234411	−	0.972138i	$-0.575316\pi$
$409$	−9.48134	−0.468822	−0.234411	+	0.972138i	$0.575316\pi$
$410$	−0.0777086	−0.00383776
$411$	0.315607	0.0155678
$412$	−18.5484	−0.913815
$413$	−11.8679	−0.583981
$414$	−1.15651	−0.0568396
$415$	−5.55798	−0.272830
$416$	−0.953907	−0.0467692
$417$	−0.347890	−0.0170362
$418$	0.433755	0.0212156
$419$	29.6003	1.44607	0.723034	−	0.690812i	$-0.242747\pi$
$419$	29.6003	1.44607	0.723034	+	0.690812i	$0.242747\pi$
$420$	0.214109	0.0104474
$421$	−36.2660	−1.76750	−0.883748	−	0.467963i	$-0.844988\pi$
$421$	−36.2660	−1.76750	−0.883748	+	0.467963i	$0.844988\pi$
$422$	−0.943470	−0.0459274
$423$	−30.1437	−1.46564
$424$	−2.56746	−0.124687
$425$	−4.28418	−0.207813
$426$	0.0278919	0.00135137
$427$	−22.6790	−1.09752
$428$	18.9434	0.915666
$429$	−0.0758309	−0.00366115
$430$	−0.0635030	−0.00306239
$431$	−20.5408	−0.989415	−0.494708	−	0.869059i	$-0.664725\pi$
$431$	−20.5408	−0.989415	−0.494708	+	0.869059i	$0.664725\pi$
$432$	−1.69606	−0.0816017
$433$	−3.80181	−0.182703	−0.0913515	−	0.995819i	$-0.529119\pi$
$433$	−3.80181	−0.182703	−0.0913515	+	0.995819i	$0.529119\pi$
$434$	0.941409	0.0451891
$435$	−0.625350	−0.0299833
$436$	−22.6293	−1.08374
$437$	−29.7322	−1.42228
$438$	−0.0554908	−0.00265146
$439$	19.2915	0.920734	0.460367	−	0.887729i	$-0.347718\pi$
$439$	19.2915	0.920734	0.460367	+	0.887729i	$0.347718\pi$
$440$	0.253654	0.0120925
$441$	11.4872	0.547010
$442$	−0.0797917	−0.00379531
$443$	17.3550	0.824559	0.412279	−	0.911057i	$-0.364733\pi$
$443$	17.3550	0.824559	0.412279	+	0.911057i	$0.364733\pi$
$444$	−0.396261	−0.0188057
$445$	4.31603	0.204599
$446$	0.869534	0.0411736
$447$	1.06125	0.0501955
$448$	−13.9911	−0.661018
$449$	−9.96313	−0.470189	−0.235095	−	0.971972i	$-0.575540\pi$
$449$	−9.96313	−0.470189	−0.235095	+	0.971972i	$0.575540\pi$
$450$	−0.963039	−0.0453981
$451$	1.22370	0.0576218
$452$	4.83306	0.227328
$453$	0.821791	0.0386111
$454$	−0.282562	−0.0132613
$455$	−1.59998	−0.0750084
$456$	0.123587	0.00578748
$457$	−2.47470	−0.115762	−0.0578808	−	0.998323i	$-0.518434\pi$
$457$	−2.47470	−0.115762	−0.0578808	+	0.998323i	$0.518434\pi$
$458$	−0.972866	−0.0454591
$459$	−0.427625	−0.0199598
$460$	−8.68125	−0.404765
$461$	−6.85705	−0.319365	−0.159682	−	0.987168i	$-0.551047\pi$
$461$	−6.85705	−0.319365	−0.159682	+	0.987168i	$0.551047\pi$
$462$	0.00952400	0.000443097 0
$463$	8.48699	0.394424	0.197212	−	0.980361i	$-0.436811\pi$
$463$	8.48699	0.394424	0.197212	+	0.980361i	$0.436811\pi$
$464$	41.0978	1.90792
$465$	0.425521	0.0197331
$466$	0.149753	0.00693719
$467$	9.48264	0.438804	0.219402	−	0.975635i	$-0.429589\pi$
$467$	9.48264	0.438804	0.219402	+	0.975635i	$0.429589\pi$
$468$	6.34972	0.293516
$469$	23.0161	1.06278
$470$	0.639156	0.0294821
$471$	0.964992	0.0444645
$472$	−2.00017	−0.0920651
$473$	1.00000	0.0459800
$474$	0.0286857	0.00131758
$475$	−24.7582	−1.13599
$476$	−3.54774	−0.162611
$477$	25.6477	1.17433
$478$	−0.345862	−0.0158193
$479$	−2.92858	−0.133810	−0.0669051	−	0.997759i	$-0.521312\pi$
$479$	−2.92858	−0.133810	−0.0669051	+	0.997759i	$0.521312\pi$
$480$	0.0541530	0.00247174
$481$	2.96116	0.135017
$482$	0.658570	0.0299971
$483$	−0.652833	−0.0297049
$484$	−1.99437	−0.0906530
$485$	7.65512	0.347601
$486$	−0.144229	−0.00654237
$487$	17.9221	0.812128	0.406064	−	0.913845i	$-0.366901\pi$
$487$	17.9221	0.812128	0.406064	+	0.913845i	$0.366901\pi$
$488$	−3.82223	−0.173024
$489$	0.907040	0.0410177
$490$	−0.243571	−0.0110034
$491$	−7.94117	−0.358380	−0.179190	−	0.983815i	$-0.557348\pi$
$491$	−7.94117	−0.358380	−0.179190	+	0.983815i	$0.557348\pi$
$492$	0.174084	0.00784833
$493$	10.3619	0.466678
$494$	−0.461116	−0.0207466
$495$	−2.53388	−0.113890
$496$	−27.9651	−1.25567
$497$	−9.26731	−0.415696
$498$	−0.0351711	−0.00157606
$499$	14.8983	0.666941	0.333471	−	0.942760i	$-0.391780\pi$
$499$	14.8983	0.666941	0.333471	+	0.942760i	$0.391780\pi$
$500$	−15.6657	−0.700593
$501$	1.14629	0.0512123
$502$	−0.459994	−0.0205305
$503$	−19.6098	−0.874360	−0.437180	−	0.899374i	$-0.644023\pi$
$503$	−19.6098	−0.874360	−0.437180	+	0.899374i	$0.644023\pi$
$504$	−1.59724	−0.0711469
$505$	0.833981	0.0371117
$506$	−0.386160	−0.0171669
$507$	−0.846693	−0.0376029
$508$	44.1644	1.95948
$509$	17.5267	0.776857	0.388429	−	0.921479i	$-0.373018\pi$
$509$	17.5267	0.776857	0.388429	+	0.921479i	$0.373018\pi$
$510$	0.00452975	0.000200581 0
$511$	18.4373	0.815616
$512$	−5.93712	−0.262386
$513$	−2.47124	−0.109108
$514$	−2.21629	−0.0977563
$515$	−7.86873	−0.346737
$516$	0.142261	0.00626268
$517$	−10.0650	−0.442657
$518$	−0.371908	−0.0163407
$519$	−0.130818	−0.00574225
$520$	−0.269655	−0.0118251
$521$	−43.2026	−1.89274	−0.946370	−	0.323084i	$-0.895281\pi$
$521$	−43.2026	−1.89274	−0.946370	+	0.323084i	$0.895281\pi$
$522$	2.32926	0.101949
$523$	6.58633	0.288000	0.144000	−	0.989578i	$-0.454003\pi$
$523$	6.58633	0.288000	0.144000	+	0.989578i	$0.454003\pi$
$524$	4.65623	0.203408
$525$	−0.543619	−0.0237255
$526$	0.368157	0.0160524
$527$	−7.05081	−0.307138
$528$	−0.282916	−0.0123124
$529$	3.46975	0.150859
$530$	−0.543824	−0.0236222
$531$	19.9807	0.867088
$532$	−20.5024	−0.888891
$533$	−1.30089	−0.0563478
$534$	0.0273120	0.00118191
$535$	8.03630	0.347440
$536$	3.87903	0.167549
$537$	0.151114	0.00652105
$538$	−2.19629	−0.0946887
$539$	3.83558	0.165210
$540$	−0.721556	−0.0310508
$541$	18.5563	0.797799	0.398900	−	0.916995i	$-0.369392\pi$
$541$	18.5563	0.797799	0.398900	+	0.916995i	$0.369392\pi$
$542$	−0.141935	−0.00609664
$543$	0.446058	0.0191422
$544$	−0.897305	−0.0384717
$545$	−9.59992	−0.411215
$546$	−0.0101248	−0.000433300 0
$547$	21.8517	0.934312	0.467156	−	0.884175i	$-0.345279\pi$
$547$	21.8517	0.934312	0.467156	+	0.884175i	$0.345279\pi$
$548$	−8.82413	−0.376948
$549$	38.1822	1.62958
$550$	−0.321558	−0.0137113
$551$	59.8816	2.55104
$552$	−0.110026	−0.00468301
$553$	−9.53105	−0.405302
$554$	−0.659494	−0.0280192
$555$	−0.168104	−0.00713563
$556$	9.72672	0.412505
$557$	18.9913	0.804688	0.402344	−	0.915489i	$-0.368196\pi$
$557$	18.9913	0.804688	0.402344	+	0.915489i	$0.368196\pi$
$558$	−1.58495	−0.0670962
$559$	−1.06308	−0.0449635
$560$	−5.96936	−0.252251
$561$	−0.0713313	−0.00301161
$562$	−1.72029	−0.0725661
$563$	32.7986	1.38230	0.691148	−	0.722714i	$-0.257105\pi$
$563$	32.7986	1.38230	0.691148	+	0.722714i	$0.257105\pi$
$564$	−1.43185	−0.0602918
$565$	2.05031	0.0862571
$566$	−1.05420	−0.0443112
$567$	15.9285	0.668935
$568$	−1.56188	−0.0655348
$569$	−7.82006	−0.327834	−0.163917	−	0.986474i	$-0.552413\pi$
$569$	−7.82006	−0.327834	−0.163917	+	0.986474i	$0.552413\pi$
$570$	0.0261774	0.00109645
$571$	11.2162	0.469384	0.234692	−	0.972070i	$-0.424592\pi$
$571$	11.2162	0.469384	0.234692	+	0.972070i	$0.424592\pi$
$572$	2.12017	0.0886488
$573$	1.16350	0.0486057
$574$	0.163386	0.00681959
$575$	22.0416	0.919197
$576$	23.5553	0.981471
$577$	26.3844	1.09840	0.549198	−	0.835692i	$-0.314933\pi$
$577$	26.3844	1.09840	0.549198	+	0.835692i	$0.314933\pi$
$578$	−0.0750571	−0.00312197
$579$	−0.321072	−0.0133433
$580$	17.4843	0.725996
$581$	11.6859	0.484812
$582$	0.0484420	0.00200798
$583$	8.56375	0.354674
$584$	3.10734	0.128583
$585$	2.69372	0.111372
$586$	−0.883598	−0.0365011
$587$	−28.9670	−1.19560	−0.597798	−	0.801646i	$-0.703958\pi$
$587$	−28.9670	−1.19560	−0.597798	+	0.801646i	$0.703958\pi$
$588$	0.545652	0.0225023
$589$	−40.7466	−1.67893
$590$	−0.423663	−0.0174419
$591$	−0.698513	−0.0287330
$592$	11.0478	0.454060
$593$	−1.21568	−0.0499221	−0.0249610	−	0.999688i	$-0.507946\pi$
$593$	−1.21568	−0.0499221	−0.0249610	+	0.999688i	$0.507946\pi$
$594$	−0.0320963	−0.00131693
$595$	−1.50505	−0.0617008
$596$	−29.6717	−1.21540
$597$	−0.997864	−0.0408398
$598$	0.410519	0.0167874
$599$	−30.2326	−1.23527	−0.617636	−	0.786464i	$-0.711909\pi$
$599$	−30.2326	−1.23527	−0.617636	+	0.786464i	$0.711909\pi$
$600$	−0.0916194	−0.00374035
$601$	−39.2523	−1.60114	−0.800568	−	0.599242i	$-0.795469\pi$
$601$	−39.2523	−1.60114	−0.800568	+	0.599242i	$0.795469\pi$
$602$	0.133518	0.00544178
$603$	−38.7496	−1.57801
$604$	−22.9766	−0.934906
$605$	−0.846062	−0.0343973
$606$	0.00527747	0.000214383 0
$607$	45.5376	1.84832	0.924158	−	0.382011i	$-0.124768\pi$
$607$	45.5376	1.84832	0.924158	+	0.382011i	$0.124768\pi$
$608$	−5.18552	−0.210301
$609$	1.31483	0.0532794
$610$	−0.809602	−0.0327798
$611$	10.6999	0.432871
$612$	5.97295	0.241442
$613$	43.5562	1.75922	0.879610	−	0.475696i	$-0.157804\pi$
$613$	43.5562	1.75922	0.879610	+	0.475696i	$0.157804\pi$
$614$	−0.632128	−0.0255106
$615$	0.0738512	0.00297797
$616$	−0.533319	−0.0214880
$617$	28.8075	1.15975	0.579874	−	0.814706i	$-0.303102\pi$
$617$	28.8075	1.15975	0.579874	+	0.814706i	$0.303102\pi$
$618$	−0.0497937	−0.00200300
$619$	−12.0907	−0.485965	−0.242982	−	0.970031i	$-0.578126\pi$
$619$	−12.0907	−0.485965	−0.242982	+	0.970031i	$0.578126\pi$
$620$	−11.8972	−0.477805
$621$	2.20008	0.0882860
$622$	0.644321	0.0258349
$623$	−9.07464	−0.363568
$624$	0.300763	0.0120401
$625$	14.7751	0.591003
$626$	−0.859896	−0.0343683
$627$	−0.412223	−0.0164626
$628$	−26.9804	−1.07664
$629$	2.78546	0.111063
$630$	−0.338318	−0.0134789
$631$	7.10972	0.283034	0.141517	−	0.989936i	$-0.454802\pi$
$631$	7.10972	0.283034	0.141517	+	0.989936i	$0.454802\pi$
$632$	−1.60633	−0.0638962
$633$	0.896636	0.0356381
$634$	−0.506896	−0.0201314
$635$	18.7357	0.743504
$636$	1.21828	0.0483081
$637$	−4.07753	−0.161557
$638$	0.777738	0.0307909
$639$	15.6024	0.617220
$640$	−2.01781	−0.0797610
$641$	−11.7604	−0.464506	−0.232253	−	0.972655i	$-0.574610\pi$
$641$	−11.7604	−0.464506	−0.232253	+	0.972655i	$0.574610\pi$
$642$	0.0508541	0.00200705
$643$	−8.02066	−0.316304	−0.158152	−	0.987415i	$-0.550554\pi$
$643$	−8.02066	−0.316304	−0.158152	+	0.987415i	$0.550554\pi$
$644$	18.2527	0.719257
$645$	0.0603507	0.00237631
$646$	−0.433755	−0.0170659
$647$	−27.8584	−1.09523	−0.547613	−	0.836732i	$-0.684463\pi$
$647$	−27.8584	−1.09523	−0.547613	+	0.836732i	$0.684463\pi$
$648$	2.68453	0.105458
$649$	6.67154	0.261881
$650$	0.341842	0.0134082
$651$	−0.894677	−0.0350652
$652$	−25.3601	−0.993179
$653$	48.0019	1.87846	0.939230	−	0.343289i	$-0.111541\pi$
$653$	48.0019	1.87846	0.939230	+	0.343289i	$0.111541\pi$
$654$	−0.0607488	−0.00237546
$655$	1.97529	0.0771811
$656$	−4.85348	−0.189496
$657$	−31.0408	−1.21102
$658$	−1.34385	−0.0523889
$659$	46.4456	1.80926	0.904631	−	0.426195i	$-0.140146\pi$
$659$	46.4456	1.80926	0.904631	+	0.426195i	$0.140146\pi$
$660$	−0.120361	−0.00468506
$661$	39.1306	1.52200	0.761002	−	0.648750i	$-0.224708\pi$
$661$	39.1306	1.52200	0.761002	+	0.648750i	$0.224708\pi$
$662$	0.583170	0.0226656
$663$	0.0758309	0.00294503
$664$	1.96949	0.0764311
$665$	−8.69765	−0.337280
$666$	0.626142	0.0242625
$667$	−53.3109	−2.06421
$668$	−32.0493	−1.24002
$669$	−0.826370	−0.0319493
$670$	0.821633	0.0317425
$671$	12.7490	0.492171
$672$	−0.113859	−0.00439221
$673$	2.83675	0.109349	0.0546743	−	0.998504i	$-0.482588\pi$
$673$	2.83675	0.109349	0.0546743	+	0.998504i	$0.482588\pi$
$674$	1.13094	0.0435620
$675$	1.83202	0.0705145
$676$	23.6729	0.910494
$677$	43.9376	1.68866	0.844330	−	0.535823i	$-0.179998\pi$
$677$	43.9376	1.68866	0.844330	+	0.535823i	$0.179998\pi$
$678$	0.0129745	0.000498281 0
$679$	−16.0952	−0.617678
$680$	−0.253654	−0.00972720
$681$	0.268535	0.0102903
$682$	−0.529214	−0.0202646
$683$	20.7602	0.794366	0.397183	−	0.917739i	$-0.369988\pi$
$683$	20.7602	0.794366	0.397183	+	0.917739i	$0.369988\pi$
$684$	34.5176	1.31982
$685$	−3.74343	−0.143029
$686$	1.44674	0.0552369
$687$	0.924573	0.0352747
$688$	−3.96623	−0.151211
$689$	−9.10395	−0.346833
$690$	−0.0233050	−0.000887207 0
$691$	1.32847	0.0505374	0.0252687	−	0.999681i	$-0.491956\pi$
$691$	1.32847	0.0505374	0.0252687	+	0.999681i	$0.491956\pi$
$692$	3.65756	0.139039
$693$	5.32760	0.202379
$694$	−1.72421	−0.0654501
$695$	4.12633	0.156521
$696$	0.221596	0.00839956
$697$	−1.22370	−0.0463509
$698$	0.916411	0.0346867
$699$	−0.142320	−0.00538302
$700$	15.1992	0.574475
$701$	−27.6684	−1.04502	−0.522510	−	0.852633i	$-0.675004\pi$
$701$	−27.6684	−1.04502	−0.522510	+	0.852633i	$0.675004\pi$
$702$	0.0341209	0.00128781
$703$	16.0971	0.607115
$704$	7.86511	0.296428
$705$	−0.607428	−0.0228771
$706$	0.575101	0.0216442
$707$	−1.75348	−0.0659464
$708$	0.949098	0.0356693
$709$	−11.5620	−0.434219	−0.217110	−	0.976147i	$-0.569663\pi$
$709$	−11.5620	−0.434219	−0.217110	+	0.976147i	$0.569663\pi$
$710$	−0.330827	−0.0124157
$711$	16.0464	0.601787
$712$	−1.52940	−0.0573168
$713$	36.2755	1.35853
$714$	−0.00952400	−0.000356427 0
$715$	0.899432	0.0336368
$716$	−4.22503	−0.157897
$717$	0.328693	0.0122753
$718$	−0.0168728	−0.000629687 0
$719$	16.1067	0.600679	0.300339	−	0.953832i	$-0.402900\pi$
$719$	16.1067	0.600679	0.300339	+	0.953832i	$0.402900\pi$
$720$	10.0500	0.374540
$721$	16.5443	0.616143
$722$	−1.08058	−0.0402150
$723$	−0.625879	−0.0232767
$724$	−12.4714	−0.463497
$725$	−44.3924	−1.64869
$726$	−0.00535392	−0.000198703 0
$727$	0.719090	0.0266696	0.0133348	−	0.999911i	$-0.495755\pi$
$727$	0.719090	0.0266696	0.0133348	+	0.999911i	$0.495755\pi$
$728$	0.566961	0.0210130
$729$	−26.7256	−0.989838
$730$	0.658178	0.0243603
$731$	−1.00000	−0.0369863
$732$	1.81369	0.0670358
$733$	29.7726	1.09968	0.549838	−	0.835271i	$-0.314689\pi$
$733$	29.7726	1.09968	0.549838	+	0.835271i	$0.314689\pi$
$734$	0.840130	0.0310098
$735$	0.231480	0.00853826
$736$	4.61652	0.170167
$737$	−12.9385	−0.476595
$738$	−0.275075	−0.0101256
$739$	14.6037	0.537206	0.268603	−	0.963251i	$-0.413438\pi$
$739$	14.6037	0.537206	0.268603	+	0.963251i	$0.413438\pi$
$740$	4.70006	0.172778
$741$	0.438226	0.0160986
$742$	1.14341	0.0419760
$743$	−21.0250	−0.771331	−0.385666	−	0.922639i	$-0.626028\pi$
$743$	−21.0250	−0.771331	−0.385666	+	0.922639i	$0.626028\pi$
$744$	−0.150785	−0.00552806
$745$	−12.5875	−0.461171
$746$	−0.430533	−0.0157629
$747$	−19.6743	−0.719844
$748$	1.99437	0.0729213
$749$	−16.8967	−0.617391
$750$	−0.0420550	−0.00153563
$751$	1.58820	0.0579543	0.0289771	−	0.999580i	$-0.490775\pi$
$751$	1.58820	0.0579543	0.0289771	+	0.999580i	$0.490775\pi$
$752$	39.9200	1.45573
$753$	0.437160	0.0159310
$754$	−0.826797	−0.0301102
$755$	−9.74728	−0.354740
$756$	1.51710	0.0551765
$757$	−35.0100	−1.27246	−0.636231	−	0.771499i	$-0.719507\pi$
$757$	−35.0100	−1.27246	−0.636231	+	0.771499i	$0.719507\pi$
$758$	−1.24428	−0.0451944
$759$	0.366991	0.0133209
$760$	−1.46587	−0.0531726
$761$	16.8649	0.611351	0.305676	−	0.952136i	$-0.401118\pi$
$761$	16.8649	0.611351	0.305676	+	0.952136i	$0.401118\pi$
$762$	0.118560	0.00429499
$763$	20.1842	0.730719
$764$	−32.5304	−1.17691
$765$	2.53388	0.0916127
$766$	−1.29377	−0.0467457
$767$	−7.09238	−0.256091
$768$	1.10929	0.0400280
$769$	10.4765	0.377793	0.188896	−	0.981997i	$-0.439509\pi$
$769$	10.4765	0.377793	0.188896	+	0.981997i	$0.439509\pi$
$770$	−0.112964	−0.00407095
$771$	2.10627	0.0758555
$772$	8.97693	0.323087
$773$	37.0972	1.33429	0.667147	−	0.744926i	$-0.267515\pi$
$773$	37.0972	1.33429	0.667147	+	0.744926i	$0.267515\pi$
$774$	−0.224790	−0.00807989
$775$	30.2069	1.08507
$776$	−2.71262	−0.0973775
$777$	0.353447	0.0126798
$778$	−2.18390	−0.0782965
$779$	−7.07175	−0.253372
$780$	0.127954	0.00458148
$781$	5.20962	0.186415
$782$	0.386160	0.0138090
$783$	−4.43102	−0.158352
$784$	−15.2128	−0.543314
$785$	−11.4458	−0.408518
$786$	0.0124998	0.000445852 0
$787$	−7.62544	−0.271818	−0.135909	−	0.990721i	$-0.543395\pi$
$787$	−7.62544	−0.271818	−0.135909	+	0.990721i	$0.543395\pi$
$788$	19.5299	0.695722
$789$	−0.349882	−0.0124561
$790$	−0.340242	−0.0121053
$791$	−4.31086	−0.153277
$792$	0.897892	0.0319052
$793$	−13.5532	−0.481290
$794$	0.761903	0.0270389
$795$	0.516828	0.0183300
$796$	27.8995	0.988871
$797$	19.9798	0.707720	0.353860	−	0.935298i	$-0.384869\pi$
$797$	19.9798	0.707720	0.353860	+	0.935298i	$0.384869\pi$
$798$	−0.0550391	−0.00194836
$799$	10.0650	0.356073
$800$	3.84422	0.135914
$801$	15.2780	0.539821
$802$	−1.94531	−0.0686913
$803$	−10.3645	−0.365756
$804$	−1.84064	−0.0649143
$805$	7.74327	0.272914
$806$	0.562596	0.0198166
$807$	2.08726	0.0734752
$808$	−0.295525	−0.0103965
$809$	0.288574	0.0101457	0.00507287	−	0.999987i	$-0.498385\pi$
$809$	0.288574	0.0101457	0.00507287	+	0.999987i	$0.498385\pi$
$810$	0.568621	0.0199793
$811$	9.84864	0.345832	0.172916	−	0.984937i	$-0.444681\pi$
$811$	9.84864	0.345832	0.172916	+	0.984937i	$0.444681\pi$
$812$	−36.7615	−1.29008
$813$	0.134890	0.00473078
$814$	0.209068	0.00732784
$815$	−10.7584	−0.376851
$816$	0.282916	0.00990405
$817$	−5.77899	−0.202181
$818$	0.711642	0.0248820
$819$	−5.66366	−0.197904
$820$	−2.06482	−0.0721066
$821$	−55.1362	−1.92427	−0.962134	−	0.272578i	$-0.912124\pi$
$821$	−55.1362	−1.92427	−0.962134	+	0.272578i	$0.912124\pi$
$822$	−0.0236886	−0.000826234 0
$823$	−9.89998	−0.345092	−0.172546	−	0.985001i	$-0.555199\pi$
$823$	−9.89998	−0.345092	−0.172546	+	0.985001i	$0.555199\pi$
$824$	2.78832	0.0971356
$825$	0.305596	0.0106395
$826$	0.890770	0.0309938
$827$	−45.3590	−1.57729	−0.788643	−	0.614852i	$-0.789216\pi$
$827$	−45.3590	−1.57729	−0.788643	+	0.614852i	$0.789216\pi$
$828$	−30.7301	−1.06794
$829$	54.8074	1.90354	0.951770	−	0.306813i	$-0.0992627\pi$
$829$	54.8074	1.90354	0.951770	+	0.306813i	$0.0992627\pi$
$830$	0.417166	0.0144800
$831$	0.626757	0.0217419
$832$	−8.36124	−0.289874
$833$	−3.83558	−0.132895
$834$	0.0261116	0.000904171 0
$835$	−13.5961	−0.470514
$836$	11.5254	0.398615
$837$	3.01510	0.104217
$838$	−2.22171	−0.0767478
$839$	−24.4956	−0.845682	−0.422841	−	0.906204i	$-0.638967\pi$
$839$	−24.4956	−0.845682	−0.422841	+	0.906204i	$0.638967\pi$
$840$	−0.0321862	−0.00111053
$841$	78.3698	2.70241
$842$	2.72202	0.0938071
$843$	1.63489	0.0563088
$844$	−25.0692	−0.862919
$845$	10.0426	0.345477
$846$	2.26250	0.0777864
$847$	1.77888	0.0611231
$848$	−33.9658	−1.16639
$849$	1.00187	0.0343839
$850$	0.321558	0.0110294
$851$	−14.3308	−0.491254
$852$	0.741125	0.0253905
$853$	−25.9274	−0.887738	−0.443869	−	0.896092i	$-0.646395\pi$
$853$	−25.9274	−0.887738	−0.443869	+	0.896092i	$0.646395\pi$
$854$	1.70222	0.0582489
$855$	14.6433	0.500790
$856$	−2.84770	−0.0973323
$857$	5.11969	0.174885	0.0874427	−	0.996170i	$-0.472131\pi$
$857$	5.11969	0.174885	0.0874427	+	0.996170i	$0.472131\pi$
$858$	0.00569165	0.000194310 0
$859$	12.2794	0.418968	0.209484	−	0.977812i	$-0.432822\pi$
$859$	12.2794	0.418968	0.209484	+	0.977812i	$0.432822\pi$
$860$	−1.68736	−0.0575384
$861$	−0.155275	−0.00529177
$862$	1.54173	0.0525117
$863$	14.6136	0.497453	0.248727	−	0.968574i	$-0.419988\pi$
$863$	14.6136	0.497453	0.248727	+	0.968574i	$0.419988\pi$
$864$	0.383710	0.0130541
$865$	1.55163	0.0527570
$866$	0.285353	0.00969668
$867$	0.0713313	0.00242254
$868$	25.0145	0.849046
$869$	5.35789	0.181754
$870$	0.0469370	0.00159131
$871$	13.7547	0.466059
$872$	3.40177	0.115199
$873$	27.0978	0.917121
$874$	2.23161	0.0754855
$875$	13.9731	0.472377
$876$	−1.47446	−0.0498175
$877$	15.1130	0.510329	0.255165	−	0.966898i	$-0.417870\pi$
$877$	15.1130	0.510329	0.255165	+	0.966898i	$0.417870\pi$
$878$	−1.44797	−0.0488665
$879$	0.839736	0.0283236
$880$	3.35568	0.113120
$881$	55.6651	1.87541	0.937703	−	0.347439i	$-0.112948\pi$
$881$	55.6651	1.87541	0.937703	+	0.347439i	$0.112948\pi$
$882$	−0.862198	−0.0290317
$883$	−24.6833	−0.830660	−0.415330	−	0.909671i	$-0.636334\pi$
$883$	−24.6833	−0.830660	−0.415330	+	0.909671i	$0.636334\pi$
$884$	−2.12017	−0.0713091
$885$	0.402632	0.0135343
$886$	−1.30261	−0.0437622
$887$	26.5447	0.891283	0.445641	−	0.895212i	$-0.352976\pi$
$887$	26.5447	0.891283	0.445641	+	0.895212i	$0.352976\pi$
$888$	0.0595685	0.00199899
$889$	−39.3926	−1.32119
$890$	−0.323949	−0.0108588
$891$	−8.95423	−0.299978
$892$	23.1046	0.773601
$893$	58.1654	1.94643
$894$	−0.0796545	−0.00266404
$895$	−1.79237	−0.0599123
$896$	4.24253	0.141733
$897$	−0.390140	−0.0130264
$898$	0.747804	0.0249545
$899$	−73.0601	−2.43669
$900$	−25.5892	−0.852973
$901$	−8.56375	−0.285300
$902$	−0.0918474	−0.00305819
$903$	−0.126890	−0.00422263
$904$	−0.726536	−0.0241642
$905$	−5.29071	−0.175869
$906$	−0.0616813	−0.00204922
$907$	−45.6287	−1.51507	−0.757537	−	0.652792i	$-0.773598\pi$
$907$	−45.6287	−1.51507	−0.757537	+	0.652792i	$0.773598\pi$
$908$	−7.50803	−0.249163
$909$	2.95215	0.0979165
$910$	0.120090	0.00398095
$911$	−30.6372	−1.01506	−0.507528	−	0.861635i	$-0.669441\pi$
$911$	−30.6372	−1.01506	−0.507528	+	0.861635i	$0.669441\pi$
$912$	1.63497	0.0541393
$913$	−6.56923	−0.217410
$914$	0.185744	0.00614387
$915$	0.769413	0.0254360
$916$	−25.8503	−0.854119
$917$	−4.15314	−0.137149
$918$	0.0320963	0.00105934
$919$	−15.5862	−0.514141	−0.257070	−	0.966393i	$-0.582757\pi$
$919$	−15.5862	−0.514141	−0.257070	+	0.966393i	$0.582757\pi$
$920$	1.30502	0.0430252
$921$	0.600749	0.0197954
$922$	0.514670	0.0169498
$923$	−5.53825	−0.182294
$924$	0.253065	0.00832523
$925$	−11.9334	−0.392368
$926$	−0.637009	−0.0209334
$927$	−27.8539	−0.914842
$928$	−9.29782	−0.305216
$929$	−51.2923	−1.68284	−0.841422	−	0.540378i	$-0.818281\pi$
$929$	−51.2923	−1.68284	−0.841422	+	0.540378i	$0.818281\pi$
$930$	−0.0319384	−0.00104730
$931$	−22.1658	−0.726454
$932$	3.97914	0.130341
$933$	−0.612337	−0.0200470
$934$	−0.711740	−0.0232888
$935$	0.846062	0.0276692
$936$	−0.954531	−0.0311998
$937$	19.2388	0.628503	0.314251	−	0.949340i	$-0.398246\pi$
$937$	19.2388	0.628503	0.314251	+	0.949340i	$0.398246\pi$
$938$	−1.72752	−0.0564055
$939$	0.817210	0.0266687
$940$	16.9832	0.553932
$941$	20.9441	0.682757	0.341378	−	0.939926i	$-0.389106\pi$
$941$	20.9441	0.682757	0.341378	+	0.939926i	$0.389106\pi$
$942$	−0.0724296	−0.00235988
$943$	6.29578	0.205019
$944$	−26.4609	−0.861228
$945$	0.643595	0.0209361
$946$	−0.0750571	−0.00244032
$947$	3.85239	0.125186	0.0625929	−	0.998039i	$-0.480063\pi$
$947$	3.85239	0.125186	0.0625929	+	0.998039i	$0.480063\pi$
$948$	0.762217	0.0247557
$949$	11.0183	0.357670
$950$	1.85828	0.0602907
$951$	0.481734	0.0156213
$952$	0.533319	0.0172850
$953$	47.3184	1.53279	0.766397	−	0.642367i	$-0.222048\pi$
$953$	47.3184	1.53279	0.766397	+	0.642367i	$0.222048\pi$
$954$	−1.92504	−0.0623255
$955$	−13.8002	−0.446565
$956$	−9.19000	−0.297226
$957$	−0.739130	−0.0238927
$958$	0.219811	0.00710177
$959$	7.87072	0.254159
$960$	0.474665	0.0153197
$961$	18.7139	0.603675
$962$	−0.222256	−0.00716584
$963$	28.4471	0.916695
$964$	17.4991	0.563607
$965$	3.80825	0.122592
$966$	0.0489998	0.00157654
$967$	−54.2198	−1.74359	−0.871796	−	0.489869i	$-0.837045\pi$
$967$	−54.2198	−1.74359	−0.871796	+	0.489869i	$0.837045\pi$
$968$	0.299806	0.00963612
$969$	0.412223	0.0132425
$970$	−0.574571	−0.0184484
$971$	−24.3121	−0.780213	−0.390107	−	0.920770i	$-0.627562\pi$
$971$	−24.3121	−0.780213	−0.390107	+	0.920770i	$0.627562\pi$
$972$	−3.83236	−0.122923
$973$	−8.67578	−0.278133
$974$	−1.34518	−0.0431024
$975$	−0.324873	−0.0104043
$976$	−50.5656	−1.61857
$977$	−42.4990	−1.35966	−0.679831	−	0.733368i	$-0.737947\pi$
$977$	−42.4990	−1.35966	−0.679831	+	0.733368i	$0.737947\pi$
$978$	−0.0680798	−0.00217695
$979$	5.10131	0.163039
$980$	−6.47199	−0.206740
$981$	−33.9820	−1.08496
$982$	0.596041	0.0190204
$983$	−48.1594	−1.53605	−0.768023	−	0.640423i	$-0.778759\pi$
$983$	−48.1594	−1.53605	−0.768023	+	0.640423i	$0.778759\pi$
$984$	−0.0261695	−0.000834252 0
$985$	8.28507	0.263984
$986$	−0.777738	−0.0247682
$987$	1.27714	0.0406520
$988$	−12.2525	−0.389802
$989$	5.14488	0.163598
$990$	0.190186	0.00604450
$991$	40.1743	1.27618	0.638089	−	0.769963i	$-0.279725\pi$
$991$	40.1743	1.27618	0.638089	+	0.769963i	$0.279725\pi$
$992$	6.32673	0.200874
$993$	−0.554222	−0.0175877
$994$	0.695578	0.0220624
$995$	11.8357	0.375216
$996$	−0.934543	−0.0296121
$997$	−58.8583	−1.86406	−0.932031	−	0.362379i	$-0.881965\pi$
$997$	−58.8583	−1.86406	−0.932031	+	0.362379i	$0.881965\pi$
$998$	−1.11823	−0.0353969
$999$	−1.19113	−0.0376857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.30	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.30	✓	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)

\(f(q)\)	\(=\)	\(q-0.0750571 q^{2} +0.0713313 q^{3} -1.99437 q^{4} -0.846062 q^{5} -0.00535392 q^{6} +1.77888 q^{7} +0.299806 q^{8} -2.99491 q^{9} +O(q^{10})\)	\(q-0.0750571 q^{2} +0.0713313 q^{3} -1.99437 q^{4} -0.846062 q^{5} -0.00535392 q^{6} +1.77888 q^{7} +0.299806 q^{8} -2.99491 q^{9} +0.0635030 q^{10} -1.00000 q^{11} -0.142261 q^{12} +1.06308 q^{13} -0.133518 q^{14} -0.0603507 q^{15} +3.96623 q^{16} +1.00000 q^{17} +0.224790 q^{18} +5.77899 q^{19} +1.68736 q^{20} +0.126890 q^{21} +0.0750571 q^{22} -5.14488 q^{23} +0.0213855 q^{24} -4.28418 q^{25} -0.0797917 q^{26} -0.427625 q^{27} -3.54774 q^{28} +10.3619 q^{29} +0.00452975 q^{30} -7.05081 q^{31} -0.897305 q^{32} -0.0713313 q^{33} -0.0750571 q^{34} -1.50505 q^{35} +5.97295 q^{36} +2.78546 q^{37} -0.433755 q^{38} +0.0758309 q^{39} -0.253654 q^{40} -1.22370 q^{41} -0.00952400 q^{42} -1.00000 q^{43} +1.99437 q^{44} +2.53388 q^{45} +0.386160 q^{46} +10.0650 q^{47} +0.282916 q^{48} -3.83558 q^{49} +0.321558 q^{50} +0.0713313 q^{51} -2.12017 q^{52} -8.56375 q^{53} +0.0320963 q^{54} +0.846062 q^{55} +0.533319 q^{56} +0.412223 q^{57} -0.777738 q^{58} -6.67154 q^{59} +0.120361 q^{60} -12.7490 q^{61} +0.529214 q^{62} -5.32760 q^{63} -7.86511 q^{64} -0.899432 q^{65} +0.00535392 q^{66} +12.9385 q^{67} -1.99437 q^{68} -0.366991 q^{69} +0.112964 q^{70} -5.20962 q^{71} -0.897892 q^{72} +10.3645 q^{73} -0.209068 q^{74} -0.305596 q^{75} -11.5254 q^{76} -1.77888 q^{77} -0.00569165 q^{78} -5.35789 q^{79} -3.35568 q^{80} +8.95423 q^{81} +0.0918474 q^{82} +6.56923 q^{83} -0.253065 q^{84} -0.846062 q^{85} +0.0750571 q^{86} +0.739130 q^{87} -0.299806 q^{88} -5.10131 q^{89} -0.190186 q^{90} +1.89109 q^{91} +10.2608 q^{92} -0.502943 q^{93} -0.755448 q^{94} -4.88939 q^{95} -0.0640060 q^{96} -9.04794 q^{97} +0.287887 q^{98} +2.99491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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