LMFDB - Embedded newform 8041.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81914 q^{2} -2.58004 q^{3} +1.30927 q^{4} -0.309884 q^{5} +4.69345 q^{6} +2.19724 q^{7} +1.25653 q^{8} +3.65659 q^{9} +O(q^{10})$	\(q-1.81914 q^{2} -2.58004 q^{3} +1.30927 q^{4} -0.309884 q^{5} +4.69345 q^{6} +2.19724 q^{7} +1.25653 q^{8} +3.65659 q^{9} +0.563723 q^{10} +1.00000 q^{11} -3.37797 q^{12} -1.15152 q^{13} -3.99709 q^{14} +0.799513 q^{15} -4.90435 q^{16} -1.00000 q^{17} -6.65184 q^{18} +7.06291 q^{19} -0.405723 q^{20} -5.66896 q^{21} -1.81914 q^{22} +7.05132 q^{23} -3.24189 q^{24} -4.90397 q^{25} +2.09477 q^{26} -1.69401 q^{27} +2.87679 q^{28} -5.56845 q^{29} -1.45443 q^{30} +4.78411 q^{31} +6.40864 q^{32} -2.58004 q^{33} +1.81914 q^{34} -0.680890 q^{35} +4.78747 q^{36} +3.05148 q^{37} -12.8484 q^{38} +2.97095 q^{39} -0.389379 q^{40} +8.46839 q^{41} +10.3126 q^{42} +1.00000 q^{43} +1.30927 q^{44} -1.13312 q^{45} -12.8274 q^{46} -6.45625 q^{47} +12.6534 q^{48} -2.17214 q^{49} +8.92101 q^{50} +2.58004 q^{51} -1.50765 q^{52} -8.12081 q^{53} +3.08165 q^{54} -0.309884 q^{55} +2.76090 q^{56} -18.2226 q^{57} +10.1298 q^{58} +6.52889 q^{59} +1.04678 q^{60} -10.0154 q^{61} -8.70297 q^{62} +8.03439 q^{63} -1.84952 q^{64} +0.356837 q^{65} +4.69345 q^{66} +0.220738 q^{67} -1.30927 q^{68} -18.1927 q^{69} +1.23864 q^{70} -8.42059 q^{71} +4.59461 q^{72} -9.74501 q^{73} -5.55108 q^{74} +12.6524 q^{75} +9.24727 q^{76} +2.19724 q^{77} -5.40458 q^{78} -0.647122 q^{79} +1.51978 q^{80} -6.59914 q^{81} -15.4052 q^{82} +3.78465 q^{83} -7.42221 q^{84} +0.309884 q^{85} -1.81914 q^{86} +14.3668 q^{87} +1.25653 q^{88} -16.2048 q^{89} +2.06130 q^{90} -2.53016 q^{91} +9.23211 q^{92} -12.3432 q^{93} +11.7448 q^{94} -2.18868 q^{95} -16.5345 q^{96} -4.94827 q^{97} +3.95142 q^{98} +3.65659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.81914	−1.28633	−0.643163	−	0.765729i	$-0.722378\pi$
$2$	−1.81914	−1.28633	−0.643163	+	0.765729i	$0.722378\pi$
$3$	−2.58004	−1.48958	−0.744792	−	0.667296i	$-0.767451\pi$
$3$	−2.58004	−1.48958	−0.744792	+	0.667296i	$0.767451\pi$
$4$	1.30927	0.654636
$5$	−0.309884	−0.138585	−0.0692923	−	0.997596i	$-0.522074\pi$
$5$	−0.309884	−0.138585	−0.0692923	+	0.997596i	$0.522074\pi$
$6$	4.69345	1.91609
$7$	2.19724	0.830479	0.415239	−	0.909712i	$-0.363698\pi$
$7$	2.19724	0.830479	0.415239	+	0.909712i	$0.363698\pi$
$8$	1.25653	0.444250
$9$	3.65659	1.21886
$10$	0.563723	0.178265
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.37797	−0.975136
$13$	−1.15152	−0.319373	−0.159687	−	0.987168i	$-0.551048\pi$
$13$	−1.15152	−0.319373	−0.159687	+	0.987168i	$0.551048\pi$
$14$	−3.99709	−1.06827
$15$	0.799513	0.206433
$16$	−4.90435	−1.22609
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.65184	−1.56785
$19$	7.06291	1.62034	0.810171	−	0.586194i	$-0.199374\pi$
$19$	7.06291	1.62034	0.810171	+	0.586194i	$0.199374\pi$
$20$	−0.405723	−0.0907225
$21$	−5.66896	−1.23707
$22$	−1.81914	−0.387842
$23$	7.05132	1.47030	0.735151	−	0.677903i	$-0.237111\pi$
$23$	7.05132	1.47030	0.735151	+	0.677903i	$0.237111\pi$
$24$	−3.24189	−0.661748
$25$	−4.90397	−0.980794
$26$	2.09477	0.410818
$27$	−1.69401	−0.326013
$28$	2.87679	0.543662
$29$	−5.56845	−1.03403	−0.517017	−	0.855975i	$-0.672958\pi$
$29$	−5.56845	−1.03403	−0.517017	+	0.855975i	$0.672958\pi$
$30$	−1.45443	−0.265541
$31$	4.78411	0.859251	0.429626	−	0.903007i	$-0.358646\pi$
$31$	4.78411	0.859251	0.429626	+	0.903007i	$0.358646\pi$
$32$	6.40864	1.13290
$33$	−2.58004	−0.449127
$34$	1.81914	0.311980
$35$	−0.680890	−0.115091
$36$	4.78747	0.797911
$37$	3.05148	0.501661	0.250830	−	0.968031i	$-0.419296\pi$
$37$	3.05148	0.501661	0.250830	+	0.968031i	$0.419296\pi$
$38$	−12.8484	−2.08429
$39$	2.97095	0.475733
$40$	−0.389379	−0.0615662
$41$	8.46839	1.32254	0.661270	−	0.750148i	$-0.270018\pi$
$41$	8.46839	1.32254	0.661270	+	0.750148i	$0.270018\pi$
$42$	10.3126	1.59127
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.30927	0.197380
$45$	−1.13312	−0.168915
$46$	−12.8274	−1.89129
$47$	−6.45625	−0.941740	−0.470870	−	0.882203i	$-0.656060\pi$
$47$	−6.45625	−0.941740	−0.470870	+	0.882203i	$0.656060\pi$
$48$	12.6534	1.82636
$49$	−2.17214	−0.310305
$50$	8.92101	1.26162
$51$	2.58004	0.361277
$52$	−1.50765	−0.209073
$53$	−8.12081	−1.11548	−0.557740	−	0.830016i	$-0.688331\pi$
$53$	−8.12081	−1.11548	−0.557740	+	0.830016i	$0.688331\pi$
$54$	3.08165	0.419359
$55$	−0.309884	−0.0417848
$56$	2.76090	0.368940
$57$	−18.2226	−2.41364
$58$	10.1298	1.33011
$59$	6.52889	0.849989	0.424994	−	0.905196i	$-0.360276\pi$
$59$	6.52889	0.849989	0.424994	+	0.905196i	$0.360276\pi$
$60$	1.04678	0.135139
$61$	−10.0154	−1.28234	−0.641171	−	0.767398i	$-0.721551\pi$
$61$	−10.0154	−1.28234	−0.641171	+	0.767398i	$0.721551\pi$
$62$	−8.70297	−1.10528
$63$	8.03439	1.01224
$64$	−1.84952	−0.231191
$65$	0.356837	0.0442602
$66$	4.69345	0.577724
$67$	0.220738	0.0269674	0.0134837	−	0.999909i	$-0.495708\pi$
$67$	0.220738	0.0269674	0.0134837	+	0.999909i	$0.495708\pi$
$68$	−1.30927	−0.158773
$69$	−18.1927	−2.19014
$70$	1.23864	0.148045
$71$	−8.42059	−0.999340	−0.499670	−	0.866216i	$-0.666545\pi$
$71$	−8.42059	−0.999340	−0.499670	+	0.866216i	$0.666545\pi$
$72$	4.59461	0.541480
$73$	−9.74501	−1.14057	−0.570284	−	0.821448i	$-0.693167\pi$
$73$	−9.74501	−1.14057	−0.570284	+	0.821448i	$0.693167\pi$
$74$	−5.55108	−0.645300
$75$	12.6524	1.46098
$76$	9.24727	1.06073
$77$	2.19724	0.250399
$78$	−5.40458	−0.611948
$79$	−0.647122	−0.0728069	−0.0364034	−	0.999337i	$-0.511590\pi$
$79$	−0.647122	−0.0728069	−0.0364034	+	0.999337i	$0.511590\pi$
$80$	1.51978	0.169917
$81$	−6.59914	−0.733238
$82$	−15.4052	−1.70122
$83$	3.78465	0.415419	0.207710	−	0.978191i	$-0.433399\pi$
$83$	3.78465	0.415419	0.207710	+	0.978191i	$0.433399\pi$
$84$	−7.42221	−0.809830
$85$	0.309884	0.0336117
$86$	−1.81914	−0.196163
$87$	14.3668	1.54028
$88$	1.25653	0.133947
$89$	−16.2048	−1.71771	−0.858853	−	0.512222i	$-0.828822\pi$
$89$	−16.2048	−1.71771	−0.858853	+	0.512222i	$0.828822\pi$
$90$	2.06130	0.217280
$91$	−2.53016	−0.265233
$92$	9.23211	0.962514
$93$	−12.3432	−1.27993
$94$	11.7448	1.21139
$95$	−2.18868	−0.224554
$96$	−16.5345	−1.68755
$97$	−4.94827	−0.502421	−0.251210	−	0.967932i	$-0.580829\pi$
$97$	−4.94827	−0.502421	−0.251210	+	0.967932i	$0.580829\pi$
$98$	3.95142	0.399154
$99$	3.65659	0.367501
$100$	−6.42064	−0.642064
$101$	−1.26342	−0.125715	−0.0628576	−	0.998023i	$-0.520021\pi$
$101$	−1.26342	−0.125715	−0.0628576	+	0.998023i	$0.520021\pi$
$102$	−4.69345	−0.464721
$103$	−14.3964	−1.41852	−0.709258	−	0.704949i	$-0.750970\pi$
$103$	−14.3964	−1.41852	−0.709258	+	0.704949i	$0.750970\pi$
$104$	−1.44691	−0.141882
$105$	1.75672	0.171438
$106$	14.7729	1.43487
$107$	−12.9363	−1.25060	−0.625301	−	0.780384i	$-0.715024\pi$
$107$	−12.9363	−1.25060	−0.625301	+	0.780384i	$0.715024\pi$
$108$	−2.21793	−0.213420
$109$	2.36293	0.226328	0.113164	−	0.993576i	$-0.463901\pi$
$109$	2.36293	0.226328	0.113164	+	0.993576i	$0.463901\pi$
$110$	0.563723	0.0537489
$111$	−7.87294	−0.747266
$112$	−10.7760	−1.01824
$113$	10.4000	0.978352	0.489176	−	0.872185i	$-0.337298\pi$
$113$	10.4000	0.978352	0.489176	+	0.872185i	$0.337298\pi$
$114$	33.1494	3.10472
$115$	−2.18510	−0.203761
$116$	−7.29062	−0.676917
$117$	−4.21062	−0.389272
$118$	−11.8770	−1.09336
$119$	−2.19724	−0.201421
$120$	1.00461	0.0917081
$121$	1.00000	0.0909091
$122$	18.2194	1.64951
$123$	−21.8488	−1.97004
$124$	6.26370	0.562497
$125$	3.06909	0.274507
$126$	−14.6157	−1.30207
$127$	20.7064	1.83740	0.918699	−	0.394958i	$-0.129241\pi$
$127$	20.7064	1.83740	0.918699	+	0.394958i	$0.129241\pi$
$128$	−9.45274	−0.835512
$129$	−2.58004	−0.227159
$130$	−0.649136	−0.0569330
$131$	−7.31949	−0.639506	−0.319753	−	0.947501i	$-0.603600\pi$
$131$	−7.31949	−0.639506	−0.319753	+	0.947501i	$0.603600\pi$
$132$	−3.37797	−0.294015
$133$	15.5189	1.34566
$134$	−0.401553	−0.0346889
$135$	0.524948	0.0451804
$136$	−1.25653	−0.107747
$137$	2.06747	0.176636	0.0883181	−	0.996092i	$-0.471851\pi$
$137$	2.06747	0.176636	0.0883181	+	0.996092i	$0.471851\pi$
$138$	33.0950	2.81724
$139$	−4.04796	−0.343343	−0.171672	−	0.985154i	$-0.554917\pi$
$139$	−4.04796	−0.343343	−0.171672	+	0.985154i	$0.554917\pi$
$140$	−0.891471	−0.0753431
$141$	16.6573	1.40280
$142$	15.3182	1.28548
$143$	−1.15152	−0.0962946
$144$	−17.9332	−1.49443
$145$	1.72557	0.143301
$146$	17.7275	1.46714
$147$	5.60419	0.462226
$148$	3.99523	0.328406
$149$	−22.5253	−1.84534	−0.922671	−	0.385587i	$-0.873999\pi$
$149$	−22.5253	−1.84534	−0.922671	+	0.385587i	$0.873999\pi$
$150$	−23.0165	−1.87929
$151$	−19.1427	−1.55781	−0.778904	−	0.627143i	$-0.784224\pi$
$151$	−19.1427	−1.55781	−0.778904	+	0.627143i	$0.784224\pi$
$152$	8.87475	0.719837
$153$	−3.65659	−0.295617
$154$	−3.99709	−0.322095
$155$	−1.48252	−0.119079
$156$	3.88979	0.311432
$157$	17.4530	1.39290	0.696449	−	0.717606i	$-0.254762\pi$
$157$	17.4530	1.39290	0.696449	+	0.717606i	$0.254762\pi$
$158$	1.17721	0.0936534
$159$	20.9520	1.66160
$160$	−1.98594	−0.157002
$161$	15.4935	1.22105
$162$	12.0048	0.943183
$163$	12.8036	1.00286	0.501428	−	0.865199i	$-0.332808\pi$
$163$	12.8036	1.00286	0.501428	+	0.865199i	$0.332808\pi$
$164$	11.0874	0.865783
$165$	0.799513	0.0622420
$166$	−6.88481	−0.534365
$167$	−5.74237	−0.444358	−0.222179	−	0.975006i	$-0.571317\pi$
$167$	−5.74237	−0.444358	−0.222179	+	0.975006i	$0.571317\pi$
$168$	−7.12321	−0.549568
$169$	−11.6740	−0.898001
$170$	−0.563723	−0.0432356
$171$	25.8261	1.97497
$172$	1.30927	0.0998311
$173$	2.08421	0.158460	0.0792298	−	0.996856i	$-0.474754\pi$
$173$	2.08421	0.158460	0.0792298	+	0.996856i	$0.474754\pi$
$174$	−26.1352	−1.98131
$175$	−10.7752	−0.814529
$176$	−4.90435	−0.369679
$177$	−16.8448	−1.26613
$178$	29.4788	2.20953
$179$	12.4408	0.929867	0.464934	−	0.885346i	$-0.346078\pi$
$179$	12.4408	0.929867	0.464934	+	0.885346i	$0.346078\pi$
$180$	−1.48356	−0.110578
$181$	−11.4110	−0.848176	−0.424088	−	0.905621i	$-0.639405\pi$
$181$	−11.4110	−0.848176	−0.424088	+	0.905621i	$0.639405\pi$
$182$	4.60271	0.341176
$183$	25.8401	1.91016
$184$	8.86020	0.653183
$185$	−0.945607	−0.0695224
$186$	22.4540	1.64640
$187$	−1.00000	−0.0731272
$188$	−8.45299	−0.616498
$189$	−3.72215	−0.270747
$190$	3.98152	0.288850
$191$	−20.9231	−1.51394	−0.756971	−	0.653449i	$-0.773321\pi$
$191$	−20.9231	−1.51394	−0.756971	+	0.653449i	$0.773321\pi$
$192$	4.77184	0.344378
$193$	19.8474	1.42865	0.714324	−	0.699816i	$-0.246735\pi$
$193$	19.8474	1.42865	0.714324	+	0.699816i	$0.246735\pi$
$194$	9.00160	0.646277
$195$	−0.920652	−0.0659293
$196$	−2.84392	−0.203137
$197$	−21.6962	−1.54579	−0.772895	−	0.634534i	$-0.781192\pi$
$197$	−21.6962	−1.54579	−0.772895	+	0.634534i	$0.781192\pi$
$198$	−6.65184	−0.472726
$199$	7.73062	0.548009	0.274005	−	0.961728i	$-0.411652\pi$
$199$	7.73062	0.548009	0.274005	+	0.961728i	$0.411652\pi$
$200$	−6.16199	−0.435718
$201$	−0.569512	−0.0401703
$202$	2.29834	0.161711
$203$	−12.2352	−0.858744
$204$	3.37797	0.236505
$205$	−2.62422	−0.183284
$206$	26.1890	1.82468
$207$	25.7838	1.79210
$208$	5.64744	0.391579
$209$	7.06291	0.488551
$210$	−3.19572	−0.220526
$211$	25.6799	1.76787	0.883937	−	0.467606i	$-0.154883\pi$
$211$	25.6799	1.76787	0.883937	+	0.467606i	$0.154883\pi$
$212$	−10.6324	−0.730233
$213$	21.7254	1.48860
$214$	23.5330	1.60868
$215$	−0.309884	−0.0211339
$216$	−2.12858	−0.144831
$217$	10.5118	0.713590
$218$	−4.29851	−0.291132
$219$	25.1425	1.69897
$220$	−0.405723	−0.0273539
$221$	1.15152	0.0774594
$222$	14.3220	0.961229
$223$	1.68734	0.112993	0.0564965	−	0.998403i	$-0.482007\pi$
$223$	1.68734	0.112993	0.0564965	+	0.998403i	$0.482007\pi$
$224$	14.0813	0.940848
$225$	−17.9318	−1.19545
$226$	−18.9191	−1.25848
$227$	−3.37453	−0.223975	−0.111988	−	0.993710i	$-0.535722\pi$
$227$	−3.37453	−0.223975	−0.111988	+	0.993710i	$0.535722\pi$
$228$	−23.8583	−1.58005
$229$	2.96964	0.196239	0.0981196	−	0.995175i	$-0.468717\pi$
$229$	2.96964	0.196239	0.0981196	+	0.995175i	$0.468717\pi$
$230$	3.97500	0.262103
$231$	−5.66896	−0.372990
$232$	−6.99692	−0.459370
$233$	15.7798	1.03377	0.516886	−	0.856055i	$-0.327091\pi$
$233$	15.7798	1.03377	0.516886	+	0.856055i	$0.327091\pi$
$234$	7.65970	0.500731
$235$	2.00069	0.130511
$236$	8.54809	0.556434
$237$	1.66960	0.108452
$238$	3.99709	0.259093
$239$	16.3491	1.05754	0.528768	−	0.848767i	$-0.322654\pi$
$239$	16.3491	1.05754	0.528768	+	0.848767i	$0.322654\pi$
$240$	−3.92109	−0.253105
$241$	−10.0483	−0.647270	−0.323635	−	0.946182i	$-0.604905\pi$
$241$	−10.0483	−0.647270	−0.323635	+	0.946182i	$0.604905\pi$
$242$	−1.81914	−0.116939
$243$	22.1081	1.41823
$244$	−13.1129	−0.839467
$245$	0.673112	0.0430035
$246$	39.7460	2.53411
$247$	−8.13305	−0.517494
$248$	6.01137	0.381723
$249$	−9.76453	−0.618802
$250$	−5.58310	−0.353106
$251$	13.3650	0.843590	0.421795	−	0.906691i	$-0.361400\pi$
$251$	13.3650	0.843590	0.421795	+	0.906691i	$0.361400\pi$
$252$	10.5192	0.662648
$253$	7.05132	0.443313
$254$	−37.6679	−2.36349
$255$	−0.799513	−0.0500674
$256$	20.8949	1.30593
$257$	−14.5126	−0.905268	−0.452634	−	0.891696i	$-0.649516\pi$
$257$	−14.5126	−0.905268	−0.452634	+	0.891696i	$0.649516\pi$
$258$	4.69345	0.292201
$259$	6.70484	0.416619
$260$	0.467197	0.0289743
$261$	−20.3615	−1.26035
$262$	13.3152	0.822614
$263$	10.7646	0.663775	0.331887	−	0.943319i	$-0.392315\pi$
$263$	10.7646	0.663775	0.331887	+	0.943319i	$0.392315\pi$
$264$	−3.24189	−0.199525
$265$	2.51651	0.154588
$266$	−28.2311	−1.73096
$267$	41.8090	2.55867
$268$	0.289006	0.0176539
$269$	−1.97714	−0.120549	−0.0602743	−	0.998182i	$-0.519198\pi$
$269$	−1.97714	−0.120549	−0.0602743	+	0.998182i	$0.519198\pi$
$270$	−0.954955	−0.0581167
$271$	23.6165	1.43460	0.717299	−	0.696765i	$-0.245378\pi$
$271$	23.6165	1.43460	0.717299	+	0.696765i	$0.245378\pi$
$272$	4.90435	0.297370
$273$	6.52790	0.395086
$274$	−3.76103	−0.227212
$275$	−4.90397	−0.295721
$276$	−23.8192	−1.43375
$277$	−0.440317	−0.0264561	−0.0132281	−	0.999913i	$-0.504211\pi$
$277$	−0.440317	−0.0264561	−0.0132281	+	0.999913i	$0.504211\pi$
$278$	7.36380	0.441651
$279$	17.4935	1.04731
$280$	−0.855559	−0.0511294
$281$	−23.9393	−1.42810	−0.714048	−	0.700097i	$-0.753140\pi$
$281$	−23.9393	−1.42810	−0.714048	+	0.700097i	$0.753140\pi$
$282$	−30.3021	−1.80446
$283$	−23.6663	−1.40682	−0.703408	−	0.710786i	$-0.748339\pi$
$283$	−23.6663	−1.40682	−0.703408	+	0.710786i	$0.748339\pi$
$284$	−11.0249	−0.654205
$285$	5.64688	0.334493
$286$	2.09477	0.123866
$287$	18.6071	1.09834
$288$	23.4338	1.38085
$289$	1.00000	0.0588235
$290$	−3.13906	−0.184332
$291$	12.7667	0.748398
$292$	−12.7589	−0.746657
$293$	−12.5915	−0.735604	−0.367802	−	0.929904i	$-0.619890\pi$
$293$	−12.5915	−0.735604	−0.367802	+	0.929904i	$0.619890\pi$
$294$	−10.1948	−0.594574
$295$	−2.02320	−0.117795
$296$	3.83428	0.222863
$297$	−1.69401	−0.0982966
$298$	40.9767	2.37371
$299$	−8.11971	−0.469575
$300$	16.5655	0.956408
$301$	2.19724	0.126647
$302$	34.8232	2.00385
$303$	3.25967	0.187263
$304$	−34.6390	−1.98668
$305$	3.10362	0.177713
$306$	6.65184	0.380261
$307$	−10.5981	−0.604866	−0.302433	−	0.953171i	$-0.597799\pi$
$307$	−10.5981	−0.604866	−0.302433	+	0.953171i	$0.597799\pi$
$308$	2.87679	0.163920
$309$	37.1432	2.11300
$310$	2.69691	0.153174
$311$	11.1184	0.630464	0.315232	−	0.949015i	$-0.397918\pi$
$311$	11.1184	0.630464	0.315232	+	0.949015i	$0.397918\pi$
$312$	3.73309	0.211345
$313$	−21.0730	−1.19112	−0.595559	−	0.803312i	$-0.703069\pi$
$313$	−21.0730	−1.19112	−0.595559	+	0.803312i	$0.703069\pi$
$314$	−31.7494	−1.79172
$315$	−2.48973	−0.140281
$316$	−0.847259	−0.0476620
$317$	2.66256	0.149544	0.0747720	−	0.997201i	$-0.476177\pi$
$317$	2.66256	0.149544	0.0747720	+	0.997201i	$0.476177\pi$
$318$	−38.1146	−2.13736
$319$	−5.56845	−0.311773
$320$	0.573139	0.0320394
$321$	33.3762	1.86288
$322$	−28.1848	−1.57068
$323$	−7.06291	−0.392991
$324$	−8.64008	−0.480004
$325$	5.64700	0.313239
$326$	−23.2916	−1.29000
$327$	−6.09645	−0.337135
$328$	10.6408	0.587539
$329$	−14.1859	−0.782095
$330$	−1.45443	−0.0800635
$331$	17.9004	0.983895	0.491947	−	0.870625i	$-0.336285\pi$
$331$	17.9004	0.983895	0.491947	+	0.870625i	$0.336285\pi$
$332$	4.95514	0.271949
$333$	11.1580	0.611455
$334$	10.4462	0.571589
$335$	−0.0684033	−0.00373727
$336$	27.8026	1.51675
$337$	14.0098	0.763160	0.381580	−	0.924336i	$-0.375380\pi$
$337$	14.0098	0.763160	0.381580	+	0.924336i	$0.375380\pi$
$338$	21.2367	1.15512
$339$	−26.8324	−1.45734
$340$	0.405723	0.0220034
$341$	4.78411	0.259074
$342$	−46.9813	−2.54046
$343$	−20.1534	−1.08818
$344$	1.25653	0.0677475
$345$	5.63763	0.303520
$346$	−3.79147	−0.203831
$347$	22.3568	1.20018	0.600089	−	0.799934i	$-0.295132\pi$
$347$	22.3568	1.20018	0.600089	+	0.799934i	$0.295132\pi$
$348$	18.8101	1.00832
$349$	1.92500	0.103043	0.0515214	−	0.998672i	$-0.483593\pi$
$349$	1.92500	0.103043	0.0515214	+	0.998672i	$0.483593\pi$
$350$	19.6016	1.04775
$351$	1.95068	0.104120
$352$	6.40864	0.341582
$353$	11.9600	0.636568	0.318284	−	0.947995i	$-0.396893\pi$
$353$	11.9600	0.636568	0.318284	+	0.947995i	$0.396893\pi$
$354$	30.6430	1.62866
$355$	2.60941	0.138493
$356$	−21.2165	−1.12447
$357$	5.66896	0.300033
$358$	−22.6315	−1.19611
$359$	−28.6711	−1.51320	−0.756602	−	0.653876i	$-0.773142\pi$
$359$	−28.6711	−1.51320	−0.756602	+	0.653876i	$0.773142\pi$
$360$	−1.42380	−0.0750407
$361$	30.8846	1.62551
$362$	20.7583	1.09103
$363$	−2.58004	−0.135417
$364$	−3.31267	−0.173631
$365$	3.01983	0.158065
$366$	−47.0068	−2.45708
$367$	−10.8826	−0.568066	−0.284033	−	0.958815i	$-0.591673\pi$
$367$	−10.8826	−0.568066	−0.284033	+	0.958815i	$0.591673\pi$
$368$	−34.5822	−1.80272
$369$	30.9654	1.61199
$370$	1.72019	0.0894286
$371$	−17.8434	−0.926382
$372$	−16.1606	−0.837887
$373$	−22.0617	−1.14231	−0.571156	−	0.820842i	$-0.693505\pi$
$373$	−22.0617	−1.14231	−0.571156	+	0.820842i	$0.693505\pi$
$374$	1.81914	0.0940655
$375$	−7.91835	−0.408902
$376$	−8.11246	−0.418368
$377$	6.41216	0.330243
$378$	6.77112	0.348269
$379$	26.8791	1.38069	0.690343	−	0.723482i	$-0.257460\pi$
$379$	26.8791	1.38069	0.690343	+	0.723482i	$0.257460\pi$
$380$	−2.86559	−0.147001
$381$	−53.4233	−2.73696
$382$	38.0620	1.94742
$383$	23.1962	1.18527	0.592634	−	0.805472i	$-0.298088\pi$
$383$	23.1962	1.18527	0.592634	+	0.805472i	$0.298088\pi$
$384$	24.3884	1.24457
$385$	−0.680890	−0.0347014
$386$	−36.1052	−1.83771
$387$	3.65659	0.185875
$388$	−6.47864	−0.328903
$389$	−18.8278	−0.954608	−0.477304	−	0.878738i	$-0.658386\pi$
$389$	−18.8278	−0.954608	−0.477304	+	0.878738i	$0.658386\pi$
$390$	1.67480	0.0848066
$391$	−7.05132	−0.356601
$392$	−2.72936	−0.137853
$393$	18.8845	0.952599
$394$	39.4684	1.98839
$395$	0.200533	0.0100899
$396$	4.78747	0.240579
$397$	−13.1898	−0.661979	−0.330989	−	0.943634i	$-0.607382\pi$
$397$	−13.1898	−0.661979	−0.330989	+	0.943634i	$0.607382\pi$
$398$	−14.0631	−0.704919
$399$	−40.0393	−2.00447
$400$	24.0508	1.20254
$401$	−0.392752	−0.0196131	−0.00980656	−	0.999952i	$-0.503122\pi$
$401$	−0.392752	−0.0196131	−0.00980656	+	0.999952i	$0.503122\pi$
$402$	1.03602	0.0516721
$403$	−5.50898	−0.274422
$404$	−1.65416	−0.0822977
$405$	2.04497	0.101615
$406$	22.2576	1.10462
$407$	3.05148	0.151256
$408$	3.24189	0.160498
$409$	−15.5698	−0.769880	−0.384940	−	0.922942i	$-0.625778\pi$
$409$	−15.5698	−0.769880	−0.384940	+	0.922942i	$0.625778\pi$
$410$	4.77383	0.235763
$411$	−5.33416	−0.263115
$412$	−18.8488	−0.928613
$413$	14.3455	0.705897
$414$	−46.9043	−2.30522
$415$	−1.17280	−0.0575707
$416$	−7.37966	−0.361817
$417$	10.4439	0.511439
$418$	−12.8484	−0.628437
$419$	31.4633	1.53708	0.768542	−	0.639799i	$-0.220982\pi$
$419$	31.4633	1.53708	0.768542	+	0.639799i	$0.220982\pi$
$420$	2.30003	0.112230
$421$	25.4469	1.24021	0.620103	−	0.784520i	$-0.287091\pi$
$421$	25.4469	1.24021	0.620103	+	0.784520i	$0.287091\pi$
$422$	−46.7153	−2.27406
$423$	−23.6078	−1.14785
$424$	−10.2040	−0.495552
$425$	4.90397	0.237878
$426$	−39.5216	−1.91483
$427$	−22.0062	−1.06496
$428$	−16.9372	−0.818690
$429$	2.97095	0.143439
$430$	0.563723	0.0271852
$431$	−18.6120	−0.896508	−0.448254	−	0.893906i	$-0.647954\pi$
$431$	−18.6120	−0.896508	−0.448254	+	0.893906i	$0.647954\pi$
$432$	8.30804	0.399721
$433$	11.8804	0.570934	0.285467	−	0.958389i	$-0.407851\pi$
$433$	11.8804	0.570934	0.285467	+	0.958389i	$0.407851\pi$
$434$	−19.1225	−0.917910
$435$	−4.45204	−0.213459
$436$	3.09372	0.148163
$437$	49.8028	2.38239
$438$	−45.7377	−2.18543
$439$	−6.86067	−0.327442	−0.163721	−	0.986507i	$-0.552350\pi$
$439$	−6.86067	−0.327442	−0.163721	+	0.986507i	$0.552350\pi$
$440$	−0.389379	−0.0185629
$441$	−7.94261	−0.378219
$442$	−2.09477	−0.0996380
$443$	−27.2426	−1.29434	−0.647168	−	0.762348i	$-0.724047\pi$
$443$	−27.2426	−1.29434	−0.647168	+	0.762348i	$0.724047\pi$
$444$	−10.3078	−0.489188
$445$	5.02162	0.238047
$446$	−3.06952	−0.145346
$447$	58.1160	2.74879
$448$	−4.06385	−0.191999
$449$	−13.2869	−0.627049	−0.313524	−	0.949580i	$-0.601510\pi$
$449$	−13.2869	−0.627049	−0.313524	+	0.949580i	$0.601510\pi$
$450$	32.6205	1.53774
$451$	8.46839	0.398761
$452$	13.6165	0.640465
$453$	49.3888	2.32049
$454$	6.13874	0.288105
$455$	0.784056	0.0367571
$456$	−22.8972	−1.07226
$457$	0.235046	0.0109950	0.00549749	−	0.999985i	$-0.498250\pi$
$457$	0.235046	0.0109950	0.00549749	+	0.999985i	$0.498250\pi$
$458$	−5.40219	−0.252428
$459$	1.69401	0.0790698
$460$	−2.86089	−0.133390
$461$	22.2093	1.03439	0.517196	−	0.855867i	$-0.326976\pi$
$461$	22.2093	1.03439	0.517196	+	0.855867i	$0.326976\pi$
$462$	10.3126	0.479787
$463$	−24.2188	−1.12554	−0.562772	−	0.826612i	$-0.690265\pi$
$463$	−24.2188	−1.12554	−0.562772	+	0.826612i	$0.690265\pi$
$464$	27.3096	1.26782
$465$	3.82496	0.177378
$466$	−28.7057	−1.32977
$467$	0.578902	0.0267884	0.0133942	−	0.999910i	$-0.495736\pi$
$467$	0.578902	0.0267884	0.0133942	+	0.999910i	$0.495736\pi$
$468$	−5.51285	−0.254831
$469$	0.485014	0.0223959
$470$	−3.63954	−0.167879
$471$	−45.0293	−2.07484
$472$	8.20374	0.377608
$473$	1.00000	0.0459800
$474$	−3.03723	−0.139505
$475$	−34.6363	−1.58922
$476$	−2.87679	−0.131857
$477$	−29.6944	−1.35962
$478$	−29.7413	−1.36034
$479$	−14.7416	−0.673562	−0.336781	−	0.941583i	$-0.609338\pi$
$479$	−14.7416	−0.673562	−0.336781	+	0.941583i	$0.609338\pi$
$480$	5.12379	0.233868
$481$	−3.51383	−0.160217
$482$	18.2793	0.832600
$483$	−39.9737	−1.81886
$484$	1.30927	0.0595124
$485$	1.53339	0.0696278
$486$	−40.2177	−1.82431
$487$	28.9754	1.31300	0.656500	−	0.754326i	$-0.272036\pi$
$487$	28.9754	1.31300	0.656500	+	0.754326i	$0.272036\pi$
$488$	−12.5847	−0.569681
$489$	−33.0338	−1.49384
$490$	−1.22448	−0.0553166
$491$	−21.2332	−0.958239	−0.479120	−	0.877750i	$-0.659044\pi$
$491$	−21.2332	−0.958239	−0.479120	+	0.877750i	$0.659044\pi$
$492$	−28.6060	−1.28966
$493$	5.56845	0.250790
$494$	14.7952	0.665666
$495$	−1.13312	−0.0509299
$496$	−23.4629	−1.05352
$497$	−18.5021	−0.829931
$498$	17.7631	0.795982
$499$	−9.13575	−0.408972	−0.204486	−	0.978869i	$-0.565552\pi$
$499$	−9.13575	−0.408972	−0.204486	+	0.978869i	$0.565552\pi$
$500$	4.01827	0.179703
$501$	14.8155	0.661908
$502$	−24.3128	−1.08513
$503$	−19.3213	−0.861494	−0.430747	−	0.902473i	$-0.641750\pi$
$503$	−19.3213	−0.861494	−0.430747	+	0.902473i	$0.641750\pi$
$504$	10.0955	0.449687
$505$	0.391515	0.0174222
$506$	−12.8274	−0.570245
$507$	30.1194	1.33765
$508$	27.1104	1.20283
$509$	−32.9010	−1.45831	−0.729156	−	0.684347i	$-0.760087\pi$
$509$	−32.9010	−1.45831	−0.729156	+	0.684347i	$0.760087\pi$
$510$	1.45443	0.0644031
$511$	−21.4121	−0.947217
$512$	−19.1053	−0.844343
$513$	−11.9647	−0.528253
$514$	26.4004	1.16447
$515$	4.46121	0.196584
$516$	−3.37797	−0.148707
$517$	−6.45625	−0.283945
$518$	−12.1971	−0.535908
$519$	−5.37734	−0.236039
$520$	0.448376	0.0196626
$521$	3.89339	0.170573	0.0852863	−	0.996356i	$-0.472819\pi$
$521$	3.89339	0.170573	0.0852863	+	0.996356i	$0.472819\pi$
$522$	37.0404	1.62122
$523$	−22.0813	−0.965548	−0.482774	−	0.875745i	$-0.660371\pi$
$523$	−22.0813	−0.965548	−0.482774	+	0.875745i	$0.660371\pi$
$524$	−9.58320	−0.418644
$525$	27.8004	1.21331
$526$	−19.5823	−0.853831
$527$	−4.78411	−0.208399
$528$	12.6534	0.550669
$529$	26.7212	1.16179
$530$	−4.57789	−0.198851
$531$	23.8734	1.03602
$532$	20.3185	0.880918
$533$	−9.75149	−0.422384
$534$	−76.0564	−3.29128
$535$	4.00877	0.173314
$536$	0.277364	0.0119803
$537$	−32.0977	−1.38512
$538$	3.59670	0.155065
$539$	−2.17214	−0.0935606
$540$	0.687301	0.0295767
$541$	11.3058	0.486073	0.243036	−	0.970017i	$-0.421857\pi$
$541$	11.3058	0.486073	0.243036	+	0.970017i	$0.421857\pi$
$542$	−42.9617	−1.84536
$543$	29.4409	1.26343
$544$	−6.40864	−0.274768
$545$	−0.732236	−0.0313656
$546$	−11.8752	−0.508210
$547$	3.12396	0.133571	0.0667855	−	0.997767i	$-0.478726\pi$
$547$	3.12396	0.133571	0.0667855	+	0.997767i	$0.478726\pi$
$548$	2.70689	0.115633
$549$	−36.6222	−1.56300
$550$	8.92101	0.380393
$551$	−39.3294	−1.67549
$552$	−22.8596	−0.972971
$553$	−1.42188	−0.0604646
$554$	0.800999	0.0340312
$555$	2.43970	0.103560
$556$	−5.29988	−0.224765
$557$	23.5934	0.999684	0.499842	−	0.866117i	$-0.333391\pi$
$557$	23.5934	0.999684	0.499842	+	0.866117i	$0.333391\pi$
$558$	−31.8231	−1.34718
$559$	−1.15152	−0.0487039
$560$	3.33932	0.141112
$561$	2.58004	0.108929
$562$	43.5489	1.83700
$563$	−44.1143	−1.85919	−0.929597	−	0.368577i	$-0.879845\pi$
$563$	−44.1143	−1.85919	−0.929597	+	0.368577i	$0.879845\pi$
$564$	21.8090	0.918325
$565$	−3.22280	−0.135584
$566$	43.0524	1.80963
$567$	−14.4999	−0.608938
$568$	−10.5807	−0.443957
$569$	−34.9418	−1.46484	−0.732418	−	0.680855i	$-0.761608\pi$
$569$	−34.9418	−1.46484	−0.732418	+	0.680855i	$0.761608\pi$
$570$	−10.2725	−0.430267
$571$	−36.0562	−1.50890	−0.754452	−	0.656355i	$-0.772097\pi$
$571$	−36.0562	−1.50890	−0.754452	+	0.656355i	$0.772097\pi$
$572$	−1.50765	−0.0630380
$573$	53.9823	2.25514
$574$	−33.8489	−1.41283
$575$	−34.5795	−1.44206
$576$	−6.76294	−0.281789
$577$	20.8119	0.866412	0.433206	−	0.901295i	$-0.357382\pi$
$577$	20.8119	0.866412	0.433206	+	0.901295i	$0.357382\pi$
$578$	−1.81914	−0.0756663
$579$	−51.2070	−2.12809
$580$	2.25925	0.0938102
$581$	8.31578	0.344997
$582$	−23.2245	−0.962685
$583$	−8.12081	−0.336330
$584$	−12.2449	−0.506697
$585$	1.30480	0.0539470
$586$	22.9057	0.946228
$587$	−22.4810	−0.927889	−0.463945	−	0.885864i	$-0.653566\pi$
$587$	−22.4810	−0.927889	−0.463945	+	0.885864i	$0.653566\pi$
$588$	7.33742	0.302590
$589$	33.7897	1.39228
$590$	3.68049	0.151523
$591$	55.9770	2.30259
$592$	−14.9655	−0.615080
$593$	3.62206	0.148740	0.0743701	−	0.997231i	$-0.476305\pi$
$593$	3.62206	0.148740	0.0743701	+	0.997231i	$0.476305\pi$
$594$	3.08165	0.126442
$595$	0.680890	0.0279138
$596$	−29.4917	−1.20803
$597$	−19.9453	−0.816306
$598$	14.7709	0.604027
$599$	−19.8201	−0.809827	−0.404913	−	0.914355i	$-0.632698\pi$
$599$	−19.8201	−0.809827	−0.404913	+	0.914355i	$0.632698\pi$
$600$	15.8981	0.649039
$601$	−16.7579	−0.683568	−0.341784	−	0.939779i	$-0.611031\pi$
$601$	−16.7579	−0.683568	−0.341784	+	0.939779i	$0.611031\pi$
$602$	−3.99709	−0.162909
$603$	0.807147	0.0328696
$604$	−25.0630	−1.01980
$605$	−0.309884	−0.0125986
$606$	−5.92981	−0.240882
$607$	−12.1182	−0.491861	−0.245930	−	0.969287i	$-0.579093\pi$
$607$	−12.1182	−0.491861	−0.245930	+	0.969287i	$0.579093\pi$
$608$	45.2636	1.83568
$609$	31.5673	1.27917
$610$	−5.64592	−0.228597
$611$	7.43447	0.300767
$612$	−4.78747	−0.193522
$613$	−5.54652	−0.224022	−0.112011	−	0.993707i	$-0.535729\pi$
$613$	−5.54652	−0.224022	−0.112011	+	0.993707i	$0.535729\pi$
$614$	19.2795	0.778055
$615$	6.77059	0.273016
$616$	2.76090	0.111240
$617$	−23.0873	−0.929462	−0.464731	−	0.885452i	$-0.653849\pi$
$617$	−23.0873	−0.929462	−0.464731	+	0.885452i	$0.653849\pi$
$618$	−67.5686	−2.71801
$619$	3.92856	0.157902	0.0789511	−	0.996878i	$-0.474843\pi$
$619$	3.92856	0.157902	0.0789511	+	0.996878i	$0.474843\pi$
$620$	−1.94102	−0.0779534
$621$	−11.9450	−0.479338
$622$	−20.2258	−0.810983
$623$	−35.6058	−1.42652
$624$	−14.5706	−0.583291
$625$	23.5688	0.942752
$626$	38.3348	1.53217
$627$	−18.2226	−0.727739
$628$	22.8507	0.911842
$629$	−3.05148	−0.121671
$630$	4.52918	0.180447
$631$	−29.9224	−1.19119	−0.595595	−	0.803285i	$-0.703084\pi$
$631$	−29.9224	−1.19119	−0.595595	+	0.803285i	$0.703084\pi$
$632$	−0.813128	−0.0323445
$633$	−66.2550	−2.63340
$634$	−4.84356	−0.192362
$635$	−6.41660	−0.254635
$636$	27.4319	1.08774
$637$	2.50125	0.0991032
$638$	10.1298	0.401042
$639$	−30.7906	−1.21806
$640$	2.92926	0.115789
$641$	7.91602	0.312664	0.156332	−	0.987705i	$-0.450033\pi$
$641$	7.91602	0.312664	0.156332	+	0.987705i	$0.450033\pi$
$642$	−60.7160	−2.39627
$643$	33.3893	1.31674	0.658372	−	0.752693i	$-0.271245\pi$
$643$	33.3893	1.31674	0.658372	+	0.752693i	$0.271245\pi$
$644$	20.2852	0.799347
$645$	0.799513	0.0314808
$646$	12.8484	0.505514
$647$	45.2258	1.77801	0.889006	−	0.457896i	$-0.151397\pi$
$647$	45.2258	1.77801	0.889006	+	0.457896i	$0.151397\pi$
$648$	−8.29202	−0.325741
$649$	6.52889	0.256281
$650$	−10.2727	−0.402928
$651$	−27.1209	−1.06295
$652$	16.7634	0.656506
$653$	41.5869	1.62742	0.813710	−	0.581270i	$-0.197444\pi$
$653$	41.5869	1.62742	0.813710	+	0.581270i	$0.197444\pi$
$654$	11.0903	0.433665
$655$	2.26819	0.0886257
$656$	−41.5320	−1.62155
$657$	−35.6335	−1.39019
$658$	25.8062	1.00603
$659$	14.5441	0.566559	0.283280	−	0.959037i	$-0.408578\pi$
$659$	14.5441	0.566559	0.283280	+	0.959037i	$0.408578\pi$
$660$	1.04678	0.0407459
$661$	7.00903	0.272620	0.136310	−	0.990666i	$-0.456476\pi$
$661$	7.00903	0.272620	0.136310	+	0.990666i	$0.456476\pi$
$662$	−32.5633	−1.26561
$663$	−2.97095	−0.115382
$664$	4.75553	0.184550
$665$	−4.80906	−0.186488
$666$	−20.2980	−0.786531
$667$	−39.2649	−1.52034
$668$	−7.51832	−0.290893
$669$	−4.35341	−0.168312
$670$	0.124435	0.00480735
$671$	−10.0154	−0.386640
$672$	−36.3303	−1.40147
$673$	30.6146	1.18010	0.590052	−	0.807365i	$-0.299107\pi$
$673$	30.6146	1.18010	0.590052	+	0.807365i	$0.299107\pi$
$674$	−25.4857	−0.981673
$675$	8.30739	0.319752
$676$	−15.2845	−0.587864
$677$	−27.0109	−1.03811	−0.519056	−	0.854740i	$-0.673717\pi$
$677$	−27.0109	−1.03811	−0.519056	+	0.854740i	$0.673717\pi$
$678$	48.8120	1.87461
$679$	−10.8725	−0.417250
$680$	0.389379	0.0149320
$681$	8.70640	0.333630
$682$	−8.70297	−0.333254
$683$	−25.6333	−0.980832	−0.490416	−	0.871488i	$-0.663155\pi$
$683$	−25.6333	−0.980832	−0.490416	+	0.871488i	$0.663155\pi$
$684$	33.8134	1.29289
$685$	−0.640678	−0.0244790
$686$	36.6618	1.39976
$687$	−7.66177	−0.292315
$688$	−4.90435	−0.186977
$689$	9.35125	0.356254
$690$	−10.2556	−0.390425
$691$	36.1227	1.37417	0.687086	−	0.726576i	$-0.258889\pi$
$691$	36.1227	1.37417	0.687086	+	0.726576i	$0.258889\pi$
$692$	2.72880	0.103733
$693$	8.03439	0.305201
$694$	−40.6702	−1.54382
$695$	1.25440	0.0475820
$696$	18.0523	0.684271
$697$	−8.46839	−0.320763
$698$	−3.50184	−0.132547
$699$	−40.7125	−1.53989
$700$	−14.1077	−0.533220
$701$	−43.6549	−1.64882	−0.824411	−	0.565992i	$-0.808493\pi$
$701$	−43.6549	−1.64882	−0.824411	+	0.565992i	$0.808493\pi$
$702$	−3.54857	−0.133932
$703$	21.5523	0.812862
$704$	−1.84952	−0.0697066
$705$	−5.16185	−0.194407
$706$	−21.7570	−0.818835
$707$	−2.77604	−0.104404
$708$	−22.0544	−0.828855
$709$	−24.9206	−0.935912	−0.467956	−	0.883752i	$-0.655009\pi$
$709$	−24.9206	−0.935912	−0.467956	+	0.883752i	$0.655009\pi$
$710$	−4.74688	−0.178147
$711$	−2.36626	−0.0887415
$712$	−20.3618	−0.763091
$713$	33.7343	1.26336
$714$	−10.3126	−0.385941
$715$	0.356837	0.0133449
$716$	16.2884	0.608725
$717$	−42.1813	−1.57529
$718$	52.1568	1.94647
$719$	−35.3816	−1.31951	−0.659755	−	0.751481i	$-0.729340\pi$
$719$	−35.3816	−1.31951	−0.659755	+	0.751481i	$0.729340\pi$
$720$	5.55721	0.207105
$721$	−31.6323	−1.17805
$722$	−56.1835	−2.09093
$723$	25.9250	0.964163
$724$	−14.9402	−0.555247
$725$	27.3075	1.01418
$726$	4.69345	0.174190
$727$	5.80904	0.215445	0.107723	−	0.994181i	$-0.465644\pi$
$727$	5.80904	0.215445	0.107723	+	0.994181i	$0.465644\pi$
$728$	−3.17922	−0.117830
$729$	−37.2422	−1.37934
$730$	−5.49349	−0.203323
$731$	−1.00000	−0.0369863
$732$	33.8318	1.25046
$733$	42.7645	1.57954	0.789771	−	0.613402i	$-0.210199\pi$
$733$	42.7645	1.57954	0.789771	+	0.613402i	$0.210199\pi$
$734$	19.7969	0.730718
$735$	−1.73665	−0.0640574
$736$	45.1894	1.66570
$737$	0.220738	0.00813099
$738$	−56.3304	−2.07355
$739$	38.9973	1.43454	0.717270	−	0.696796i	$-0.245392\pi$
$739$	38.9973	1.43454	0.717270	+	0.696796i	$0.245392\pi$
$740$	−1.23806	−0.0455119
$741$	20.9836	0.770850
$742$	32.4596	1.19163
$743$	20.6670	0.758200	0.379100	−	0.925356i	$-0.376234\pi$
$743$	20.6670	0.758200	0.379100	+	0.925356i	$0.376234\pi$
$744$	−15.5096	−0.568608
$745$	6.98023	0.255736
$746$	40.1333	1.46939
$747$	13.8389	0.506339
$748$	−1.30927	−0.0478718
$749$	−28.4242	−1.03860
$750$	14.4046	0.525982
$751$	−35.3895	−1.29138	−0.645690	−	0.763599i	$-0.723430\pi$
$751$	−35.3895	−1.29138	−0.645690	+	0.763599i	$0.723430\pi$
$752$	31.6637	1.15466
$753$	−34.4821	−1.25660
$754$	−11.6646	−0.424800
$755$	5.93201	0.215888
$756$	−4.87332	−0.177241
$757$	−16.7523	−0.608871	−0.304436	−	0.952533i	$-0.598468\pi$
$757$	−16.7523	−0.608871	−0.304436	+	0.952533i	$0.598468\pi$
$758$	−48.8969	−1.77601
$759$	−18.1927	−0.660352
$760$	−2.75015	−0.0997583
$761$	47.7997	1.73274	0.866370	−	0.499404i	$-0.166447\pi$
$761$	47.7997	1.73274	0.866370	+	0.499404i	$0.166447\pi$
$762$	97.1845	3.52062
$763$	5.19193	0.187961
$764$	−27.3940	−0.991081
$765$	1.13312	0.0409680
$766$	−42.1971	−1.52464
$767$	−7.51812	−0.271464
$768$	−53.9096	−1.94530
$769$	30.1859	1.08853	0.544266	−	0.838912i	$-0.316808\pi$
$769$	30.1859	1.08853	0.544266	+	0.838912i	$0.316808\pi$
$770$	1.23864	0.0446373
$771$	37.4429	1.34847
$772$	25.9857	0.935244
$773$	4.00349	0.143996	0.0719979	−	0.997405i	$-0.477063\pi$
$773$	4.00349	0.143996	0.0719979	+	0.997405i	$0.477063\pi$
$774$	−6.65184	−0.239096
$775$	−23.4611	−0.842749
$776$	−6.21765	−0.223201
$777$	−17.2987	−0.620589
$778$	34.2504	1.22794
$779$	59.8115	2.14297
$780$	−1.20538	−0.0431597
$781$	−8.42059	−0.301312
$782$	12.8274	0.458705
$783$	9.43302	0.337109
$784$	10.6529	0.380462
$785$	−5.40840	−0.193034
$786$	−34.3536	−1.22535
$787$	−39.0476	−1.39190	−0.695949	−	0.718091i	$-0.745016\pi$
$787$	−39.0476	−1.39190	−0.695949	+	0.718091i	$0.745016\pi$
$788$	−28.4063	−1.01193
$789$	−27.7731	−0.988748
$790$	−0.364798	−0.0129789
$791$	22.8513	0.812500
$792$	4.59461	0.163262
$793$	11.5329	0.409545
$794$	23.9942	0.851521
$795$	−6.49269	−0.230272
$796$	10.1215	0.358747
$797$	−6.61123	−0.234182	−0.117091	−	0.993121i	$-0.537357\pi$
$797$	−6.61123	−0.234182	−0.117091	+	0.993121i	$0.537357\pi$
$798$	72.8371	2.57841
$799$	6.45625	0.228406
$800$	−31.4278	−1.11114
$801$	−59.2542	−2.09365
$802$	0.714472	0.0252289
$803$	−9.74501	−0.343894
$804$	−0.745646	−0.0262969
$805$	−4.80118	−0.169219
$806$	10.0216	0.352996
$807$	5.10110	0.179567
$808$	−1.58753	−0.0558490
$809$	−54.5466	−1.91775	−0.958877	−	0.283820i	$-0.908398\pi$
$809$	−54.5466	−1.91775	−0.958877	+	0.283820i	$0.908398\pi$
$810$	−3.72009	−0.130711
$811$	−0.537046	−0.0188582	−0.00942912	−	0.999956i	$-0.503001\pi$
$811$	−0.537046	−0.0188582	−0.00942912	+	0.999956i	$0.503001\pi$
$812$	−16.0192	−0.562165
$813$	−60.9313	−2.13696
$814$	−5.55108	−0.194565
$815$	−3.96764	−0.138980
$816$	−12.6534	−0.442958
$817$	7.06291	0.247100
$818$	28.3237	0.990317
$819$	−9.25173	−0.323282
$820$	−3.43582	−0.119984
$821$	3.05513	0.106625	0.0533123	−	0.998578i	$-0.483022\pi$
$821$	3.05513	0.106625	0.0533123	+	0.998578i	$0.483022\pi$
$822$	9.70358	0.338451
$823$	−23.1245	−0.806071	−0.403035	−	0.915184i	$-0.632045\pi$
$823$	−23.1245	−0.806071	−0.403035	+	0.915184i	$0.632045\pi$
$824$	−18.0895	−0.630176
$825$	12.6524	0.440501
$826$	−26.0965	−0.908015
$827$	27.8644	0.968942	0.484471	−	0.874807i	$-0.339012\pi$
$827$	27.8644	0.968942	0.484471	+	0.874807i	$0.339012\pi$
$828$	33.7580	1.17317
$829$	−7.16435	−0.248828	−0.124414	−	0.992230i	$-0.539705\pi$
$829$	−7.16435	−0.248828	−0.124414	+	0.992230i	$0.539705\pi$
$830$	2.13350	0.0740547
$831$	1.13603	0.0394086
$832$	2.12976	0.0738361
$833$	2.17214	0.0752601
$834$	−18.9989	−0.657877
$835$	1.77947	0.0615811
$836$	9.24727	0.319824
$837$	−8.10434	−0.280127
$838$	−57.2363	−1.97719
$839$	11.5562	0.398965	0.199482	−	0.979901i	$-0.436074\pi$
$839$	11.5562	0.398965	0.199482	+	0.979901i	$0.436074\pi$
$840$	2.20737	0.0761616
$841$	2.00760	0.0692276
$842$	−46.2915	−1.59531
$843$	61.7641	2.12727
$844$	33.6219	1.15732
$845$	3.61759	0.124449
$846$	42.9459	1.47651
$847$	2.19724	0.0754980
$848$	39.8273	1.36768
$849$	61.0600	2.09557
$850$	−8.92101	−0.305988
$851$	21.5170	0.737594
$852$	28.4445	0.974493
$853$	43.4723	1.48846	0.744232	−	0.667921i	$-0.232816\pi$
$853$	43.4723	1.48846	0.744232	+	0.667921i	$0.232816\pi$
$854$	40.0325	1.36988
$855$	−8.00311	−0.273701
$856$	−16.2549	−0.555580
$857$	−15.1271	−0.516732	−0.258366	−	0.966047i	$-0.583184\pi$
$857$	−15.1271	−0.516732	−0.258366	+	0.966047i	$0.583184\pi$
$858$	−5.40458	−0.184509
$859$	46.6582	1.59196	0.795978	−	0.605326i	$-0.206957\pi$
$859$	46.6582	1.59196	0.795978	+	0.605326i	$0.206957\pi$
$860$	−0.405723	−0.0138350
$861$	−48.0070	−1.63607
$862$	33.8578	1.15320
$863$	−30.6550	−1.04351	−0.521754	−	0.853096i	$-0.674722\pi$
$863$	−30.6550	−1.04351	−0.521754	+	0.853096i	$0.674722\pi$
$864$	−10.8563	−0.369340
$865$	−0.645864	−0.0219600
$866$	−21.6121	−0.734408
$867$	−2.58004	−0.0876226
$868$	13.7629	0.467142
$869$	−0.647122	−0.0219521
$870$	8.09890	0.274578
$871$	−0.254183	−0.00861267
$872$	2.96910	0.100546
$873$	−18.0938	−0.612382
$874$	−90.5984	−3.06454
$875$	6.74352	0.227973
$876$	32.9184	1.11221
$877$	36.1948	1.22221	0.611105	−	0.791550i	$-0.290725\pi$
$877$	36.1948	1.22221	0.611105	+	0.791550i	$0.290725\pi$
$878$	12.4805	0.421198
$879$	32.4866	1.09574
$880$	1.51978	0.0512318
$881$	−30.6032	−1.03105	−0.515524	−	0.856875i	$-0.672403\pi$
$881$	−30.6032	−1.03105	−0.515524	+	0.856875i	$0.672403\pi$
$882$	14.4487	0.486514
$883$	32.5655	1.09592	0.547959	−	0.836505i	$-0.315405\pi$
$883$	32.5655	1.09592	0.547959	+	0.836505i	$0.315405\pi$
$884$	1.50765	0.0507077
$885$	5.21993	0.175466
$886$	49.5581	1.66494
$887$	−26.4979	−0.889711	−0.444856	−	0.895602i	$-0.646745\pi$
$887$	−26.4979	−0.889711	−0.444856	+	0.895602i	$0.646745\pi$
$888$	−9.89258	−0.331973
$889$	45.4970	1.52592
$890$	−9.13503	−0.306207
$891$	−6.59914	−0.221080
$892$	2.20919	0.0739693
$893$	−45.5999	−1.52594
$894$	−105.721	−3.53585
$895$	−3.85520	−0.128865
$896$	−20.7699	−0.693875
$897$	20.9492	0.699472
$898$	24.1708	0.806589
$899$	−26.6401	−0.888496
$900$	−23.4776	−0.782587
$901$	8.12081	0.270543
$902$	−15.4052	−0.512937
$903$	−5.66896	−0.188651
$904$	13.0679	0.434633
$905$	3.53610	0.117544
$906$	−89.8451	−2.98490
$907$	45.0243	1.49501	0.747504	−	0.664257i	$-0.231252\pi$
$907$	45.0243	1.49501	0.747504	+	0.664257i	$0.231252\pi$
$908$	−4.41818	−0.146622
$909$	−4.61981	−0.153229
$910$	−1.42631	−0.0472817
$911$	−12.9460	−0.428921	−0.214460	−	0.976733i	$-0.568799\pi$
$911$	−12.9460	−0.428921	−0.214460	+	0.976733i	$0.568799\pi$
$912$	89.3698	2.95933
$913$	3.78465	0.125254
$914$	−0.427581	−0.0141431
$915$	−8.00745	−0.264718
$916$	3.88807	0.128465
$917$	−16.0827	−0.531096
$918$	−3.08165	−0.101710
$919$	4.57273	0.150840	0.0754202	−	0.997152i	$-0.475970\pi$
$919$	4.57273	0.150840	0.0754202	+	0.997152i	$0.475970\pi$
$920$	−2.74564	−0.0905210
$921$	27.3435	0.900999
$922$	−40.4019	−1.33057
$923$	9.69645	0.319162
$924$	−7.42221	−0.244173
$925$	−14.9644	−0.492026
$926$	44.0575	1.44782
$927$	−52.6416	−1.72898
$928$	−35.6862	−1.17146
$929$	−8.75389	−0.287206	−0.143603	−	0.989635i	$-0.545869\pi$
$929$	−8.75389	−0.287206	−0.143603	+	0.989635i	$0.545869\pi$
$930$	−6.95813	−0.228166
$931$	−15.3416	−0.502801
$932$	20.6601	0.676744
$933$	−28.6858	−0.939129
$934$	−1.05310	−0.0344586
$935$	0.309884	0.0101343
$936$	−5.29076	−0.172934
$937$	21.8245	0.712976	0.356488	−	0.934300i	$-0.383974\pi$
$937$	21.8245	0.712976	0.356488	+	0.934300i	$0.383974\pi$
$938$	−0.882309	−0.0288084
$939$	54.3692	1.77427
$940$	2.61945	0.0854370
$941$	−22.7396	−0.741291	−0.370646	−	0.928774i	$-0.620864\pi$
$941$	−22.7396	−0.741291	−0.370646	+	0.928774i	$0.620864\pi$
$942$	81.9146	2.66892
$943$	59.7134	1.94454
$944$	−32.0199	−1.04216
$945$	1.15344	0.0375213
$946$	−1.81914	−0.0591454
$947$	−2.67403	−0.0868944	−0.0434472	−	0.999056i	$-0.513834\pi$
$947$	−2.67403	−0.0868944	−0.0434472	+	0.999056i	$0.513834\pi$
$948$	2.18596	0.0709966
$949$	11.2215	0.364266
$950$	63.0083	2.04426
$951$	−6.86949	−0.222758
$952$	−2.76090	−0.0894812
$953$	29.6142	0.959297	0.479648	−	0.877461i	$-0.340764\pi$
$953$	29.6142	0.959297	0.479648	+	0.877461i	$0.340764\pi$
$954$	54.0184	1.74891
$955$	6.48374	0.209809
$956$	21.4054	0.692301
$957$	14.3668	0.464412
$958$	26.8171	0.866421
$959$	4.54274	0.146693
$960$	−1.47872	−0.0477254
$961$	−8.11230	−0.261687
$962$	6.39216	0.206091
$963$	−47.3028	−1.52431
$964$	−13.1560	−0.423726
$965$	−6.15040	−0.197988
$966$	72.7177	2.33965
$967$	−36.5168	−1.17430	−0.587150	−	0.809478i	$-0.699750\pi$
$967$	−36.5168	−1.17430	−0.587150	+	0.809478i	$0.699750\pi$
$968$	1.25653	0.0403864
$969$	18.2226	0.585393
$970$	−2.78946	−0.0895640
$971$	−34.3183	−1.10133	−0.550664	−	0.834727i	$-0.685625\pi$
$971$	−34.3183	−1.10133	−0.550664	+	0.834727i	$0.685625\pi$
$972$	28.9455	0.928427
$973$	−8.89433	−0.285139
$974$	−52.7103	−1.68895
$975$	−14.5695	−0.466596
$976$	49.1191	1.57226
$977$	−5.34626	−0.171042	−0.0855209	−	0.996336i	$-0.527255\pi$
$977$	−5.34626	−0.171042	−0.0855209	+	0.996336i	$0.527255\pi$
$978$	60.0931	1.92156
$979$	−16.2048	−0.517908
$980$	0.881287	0.0281517
$981$	8.64027	0.275863
$982$	38.6261	1.23261
$983$	5.35795	0.170892	0.0854460	−	0.996343i	$-0.472768\pi$
$983$	5.35795	0.170892	0.0854460	+	0.996343i	$0.472768\pi$
$984$	−27.4536	−0.875189
$985$	6.72331	0.214223
$986$	−10.1298	−0.322598
$987$	36.6002	1.16500
$988$	−10.6484	−0.338770
$989$	7.05132	0.224219
$990$	2.06130	0.0655125
$991$	−19.3325	−0.614118	−0.307059	−	0.951690i	$-0.599345\pi$
$991$	−19.3325	−0.614118	−0.307059	+	0.951690i	$0.599345\pi$
$992$	30.6596	0.973445
$993$	−46.1837	−1.46559
$994$	33.6578	1.06756
$995$	−2.39560	−0.0759456
$996$	−12.7844	−0.405091
$997$	−14.1636	−0.448567	−0.224284	−	0.974524i	$-0.572004\pi$
$997$	−14.1636	−0.448567	−0.224284	+	0.974524i	$0.572004\pi$
$998$	16.6192	0.526072
$999$	−5.16926	−0.163548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.14	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.14	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81914 q^{2} -2.58004 q^{3} +1.30927 q^{4} -0.309884 q^{5} +4.69345 q^{6} +2.19724 q^{7} +1.25653 q^{8} +3.65659 q^{9} +O(q^{10})\)	\(q-1.81914 q^{2} -2.58004 q^{3} +1.30927 q^{4} -0.309884 q^{5} +4.69345 q^{6} +2.19724 q^{7} +1.25653 q^{8} +3.65659 q^{9} +0.563723 q^{10} +1.00000 q^{11} -3.37797 q^{12} -1.15152 q^{13} -3.99709 q^{14} +0.799513 q^{15} -4.90435 q^{16} -1.00000 q^{17} -6.65184 q^{18} +7.06291 q^{19} -0.405723 q^{20} -5.66896 q^{21} -1.81914 q^{22} +7.05132 q^{23} -3.24189 q^{24} -4.90397 q^{25} +2.09477 q^{26} -1.69401 q^{27} +2.87679 q^{28} -5.56845 q^{29} -1.45443 q^{30} +4.78411 q^{31} +6.40864 q^{32} -2.58004 q^{33} +1.81914 q^{34} -0.680890 q^{35} +4.78747 q^{36} +3.05148 q^{37} -12.8484 q^{38} +2.97095 q^{39} -0.389379 q^{40} +8.46839 q^{41} +10.3126 q^{42} +1.00000 q^{43} +1.30927 q^{44} -1.13312 q^{45} -12.8274 q^{46} -6.45625 q^{47} +12.6534 q^{48} -2.17214 q^{49} +8.92101 q^{50} +2.58004 q^{51} -1.50765 q^{52} -8.12081 q^{53} +3.08165 q^{54} -0.309884 q^{55} +2.76090 q^{56} -18.2226 q^{57} +10.1298 q^{58} +6.52889 q^{59} +1.04678 q^{60} -10.0154 q^{61} -8.70297 q^{62} +8.03439 q^{63} -1.84952 q^{64} +0.356837 q^{65} +4.69345 q^{66} +0.220738 q^{67} -1.30927 q^{68} -18.1927 q^{69} +1.23864 q^{70} -8.42059 q^{71} +4.59461 q^{72} -9.74501 q^{73} -5.55108 q^{74} +12.6524 q^{75} +9.24727 q^{76} +2.19724 q^{77} -5.40458 q^{78} -0.647122 q^{79} +1.51978 q^{80} -6.59914 q^{81} -15.4052 q^{82} +3.78465 q^{83} -7.42221 q^{84} +0.309884 q^{85} -1.81914 q^{86} +14.3668 q^{87} +1.25653 q^{88} -16.2048 q^{89} +2.06130 q^{90} -2.53016 q^{91} +9.23211 q^{92} -12.3432 q^{93} +11.7448 q^{94} -2.18868 q^{95} -16.5345 q^{96} -4.94827 q^{97} +3.95142 q^{98} +3.65659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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