LMFDB - Embedded newform 8041.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.44193 q^{2} +2.68271 q^{3} +0.0791741 q^{4} -0.0677310 q^{5} -3.86829 q^{6} +1.81686 q^{7} +2.76970 q^{8} +4.19693 q^{9} +O(q^{10})$	\(q-1.44193 q^{2} +2.68271 q^{3} +0.0791741 q^{4} -0.0677310 q^{5} -3.86829 q^{6} +1.81686 q^{7} +2.76970 q^{8} +4.19693 q^{9} +0.0976637 q^{10} +1.00000 q^{11} +0.212401 q^{12} -6.13491 q^{13} -2.61980 q^{14} -0.181703 q^{15} -4.15208 q^{16} -1.00000 q^{17} -6.05169 q^{18} -3.59000 q^{19} -0.00536255 q^{20} +4.87412 q^{21} -1.44193 q^{22} +5.26780 q^{23} +7.43031 q^{24} -4.99541 q^{25} +8.84614 q^{26} +3.21100 q^{27} +0.143849 q^{28} +6.10004 q^{29} +0.262003 q^{30} -7.71730 q^{31} +0.447617 q^{32} +2.68271 q^{33} +1.44193 q^{34} -0.123058 q^{35} +0.332288 q^{36} +6.73869 q^{37} +5.17655 q^{38} -16.4582 q^{39} -0.187595 q^{40} -8.59264 q^{41} -7.02816 q^{42} +1.00000 q^{43} +0.0791741 q^{44} -0.284262 q^{45} -7.59582 q^{46} +4.32434 q^{47} -11.1388 q^{48} -3.69900 q^{49} +7.20306 q^{50} -2.68271 q^{51} -0.485726 q^{52} -5.19819 q^{53} -4.63005 q^{54} -0.0677310 q^{55} +5.03218 q^{56} -9.63093 q^{57} -8.79585 q^{58} -9.24554 q^{59} -0.0143861 q^{60} -1.51978 q^{61} +11.1278 q^{62} +7.62524 q^{63} +7.65873 q^{64} +0.415524 q^{65} -3.86829 q^{66} -13.7993 q^{67} -0.0791741 q^{68} +14.1320 q^{69} +0.177442 q^{70} +0.0205748 q^{71} +11.6242 q^{72} +5.90546 q^{73} -9.71674 q^{74} -13.4012 q^{75} -0.284235 q^{76} +1.81686 q^{77} +23.7316 q^{78} +8.64303 q^{79} +0.281225 q^{80} -3.97659 q^{81} +12.3900 q^{82} +15.5540 q^{83} +0.385904 q^{84} +0.0677310 q^{85} -1.44193 q^{86} +16.3646 q^{87} +2.76970 q^{88} -2.16176 q^{89} +0.409887 q^{90} -11.1463 q^{91} +0.417073 q^{92} -20.7033 q^{93} -6.23541 q^{94} +0.243155 q^{95} +1.20083 q^{96} -16.5207 q^{97} +5.33372 q^{98} +4.19693 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.44193	−1.01960	−0.509801	−	0.860293i	$-0.670281\pi$
$2$	−1.44193	−1.01960	−0.509801	+	0.860293i	$0.670281\pi$
$3$	2.68271	1.54886	0.774431	−	0.632658i	$-0.218036\pi$
$3$	2.68271	1.54886	0.774431	+	0.632658i	$0.218036\pi$
$4$	0.0791741	0.0395871
$5$	−0.0677310	−0.0302902	−0.0151451	−	0.999885i	$-0.504821\pi$
$5$	−0.0677310	−0.0302902	−0.0151451	+	0.999885i	$0.504821\pi$
$6$	−3.86829	−1.57922
$7$	1.81686	0.686710	0.343355	−	0.939206i	$-0.388437\pi$
$7$	1.81686	0.686710	0.343355	+	0.939206i	$0.388437\pi$
$8$	2.76970	0.979238
$9$	4.19693	1.39898
$10$	0.0976637	0.0308840
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.212401	0.0613149
$13$	−6.13491	−1.70152	−0.850759	−	0.525556i	$-0.823857\pi$
$13$	−6.13491	−1.70152	−0.850759	+	0.525556i	$0.823857\pi$
$14$	−2.61980	−0.700171
$15$	−0.181703	−0.0469154
$16$	−4.15208	−1.03802
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.05169	−1.42640
$19$	−3.59000	−0.823603	−0.411802	−	0.911274i	$-0.635100\pi$
$19$	−3.59000	−0.823603	−0.411802	+	0.911274i	$0.635100\pi$
$20$	−0.00536255	−0.00119910
$21$	4.87412	1.06362
$22$	−1.44193	−0.307421
$23$	5.26780	1.09841	0.549206	−	0.835687i	$-0.314930\pi$
$23$	5.26780	1.09841	0.549206	+	0.835687i	$0.314930\pi$
$24$	7.43031	1.51671
$25$	−4.99541	−0.999083
$26$	8.84614	1.73487
$27$	3.21100	0.617958
$28$	0.143849	0.0271848
$29$	6.10004	1.13275	0.566374	−	0.824148i	$-0.308346\pi$
$29$	6.10004	1.13275	0.566374	+	0.824148i	$0.308346\pi$
$30$	0.262003	0.0478350
$31$	−7.71730	−1.38607	−0.693034	−	0.720905i	$-0.743726\pi$
$31$	−7.71730	−1.38607	−0.693034	+	0.720905i	$0.743726\pi$
$32$	0.447617	0.0791282
$33$	2.68271	0.467000
$34$	1.44193	0.247290
$35$	−0.123058	−0.0208006
$36$	0.332288	0.0553813
$37$	6.73869	1.10783	0.553917	−	0.832572i	$-0.313133\pi$
$37$	6.73869	1.10783	0.553917	+	0.832572i	$0.313133\pi$
$38$	5.17655	0.839747
$39$	−16.4582	−2.63542
$40$	−0.187595	−0.0296614
$41$	−8.59264	−1.34195	−0.670973	−	0.741482i	$-0.734123\pi$
$41$	−8.59264	−1.34195	−0.670973	+	0.741482i	$0.734123\pi$
$42$	−7.02816	−1.08447
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.0791741	0.0119359
$45$	−0.284262	−0.0423753
$46$	−7.59582	−1.11994
$47$	4.32434	0.630769	0.315385	−	0.948964i	$-0.397866\pi$
$47$	4.32434	0.630769	0.315385	+	0.948964i	$0.397866\pi$
$48$	−11.1388	−1.60775
$49$	−3.69900	−0.528429
$50$	7.20306	1.01867
$51$	−2.68271	−0.375654
$52$	−0.485726	−0.0673581
$53$	−5.19819	−0.714027	−0.357013	−	0.934099i	$-0.616205\pi$
$53$	−5.19819	−0.714027	−0.357013	+	0.934099i	$0.616205\pi$
$54$	−4.63005	−0.630071
$55$	−0.0677310	−0.00913285
$56$	5.03218	0.672453
$57$	−9.63093	−1.27565
$58$	−8.79585	−1.15495
$59$	−9.24554	−1.20367	−0.601834	−	0.798622i	$-0.705563\pi$
$59$	−9.24554	−1.20367	−0.601834	+	0.798622i	$0.705563\pi$
$60$	−0.0143861	−0.00185724
$61$	−1.51978	−0.194588	−0.0972940	−	0.995256i	$-0.531019\pi$
$61$	−1.51978	−0.194588	−0.0972940	+	0.995256i	$0.531019\pi$
$62$	11.1278	1.41324
$63$	7.62524	0.960691
$64$	7.65873	0.957341
$65$	0.415524	0.0515394
$66$	−3.86829	−0.476153
$67$	−13.7993	−1.68585	−0.842926	−	0.538029i	$-0.819169\pi$
$67$	−13.7993	−1.68585	−0.842926	+	0.538029i	$0.819169\pi$
$68$	−0.0791741	−0.00960127
$69$	14.1320	1.70129
$70$	0.177442	0.0212083
$71$	0.0205748	0.00244178	0.00122089	−	0.999999i	$-0.499611\pi$
$71$	0.0205748	0.00244178	0.00122089	+	0.999999i	$0.499611\pi$
$72$	11.6242	1.36993
$73$	5.90546	0.691182	0.345591	−	0.938385i	$-0.387678\pi$
$73$	5.90546	0.691182	0.345591	+	0.938385i	$0.387678\pi$
$74$	−9.71674	−1.12955
$75$	−13.4012	−1.54744
$76$	−0.284235	−0.0326040
$77$	1.81686	0.207051
$78$	23.7316	2.68708
$79$	8.64303	0.972417	0.486208	−	0.873843i	$-0.338380\pi$
$79$	8.64303	0.972417	0.486208	+	0.873843i	$0.338380\pi$
$80$	0.281225	0.0314419
$81$	−3.97659	−0.441844
$82$	12.3900	1.36825
$83$	15.5540	1.70728	0.853639	−	0.520866i	$-0.174391\pi$
$83$	15.5540	1.70728	0.853639	+	0.520866i	$0.174391\pi$
$84$	0.385904	0.0421056
$85$	0.0677310	0.00734646
$86$	−1.44193	−0.155488
$87$	16.3646	1.75447
$88$	2.76970	0.295251
$89$	−2.16176	−0.229146	−0.114573	−	0.993415i	$-0.536550\pi$
$89$	−2.16176	−0.229146	−0.114573	+	0.993415i	$0.536550\pi$
$90$	0.409887	0.0432059
$91$	−11.1463	−1.16845
$92$	0.417073	0.0434829
$93$	−20.7033	−2.14683
$94$	−6.23541	−0.643133
$95$	0.243155	0.0249471
$96$	1.20083	0.122559
$97$	−16.5207	−1.67742	−0.838711	−	0.544578i	$-0.816690\pi$
$97$	−16.5207	−1.67742	−0.838711	+	0.544578i	$0.816690\pi$
$98$	5.33372	0.538787
$99$	4.19693	0.421807
$100$	−0.395507	−0.0395507
$101$	17.2150	1.71295	0.856477	−	0.516185i	$-0.172648\pi$
$101$	17.2150	1.71295	0.856477	+	0.516185i	$0.172648\pi$
$102$	3.86829	0.383018
$103$	−7.70970	−0.759659	−0.379830	−	0.925056i	$-0.624017\pi$
$103$	−7.70970	−0.759659	−0.379830	+	0.925056i	$0.624017\pi$
$104$	−16.9919	−1.66619
$105$	−0.330129	−0.0322173
$106$	7.49545	0.728023
$107$	−14.7051	−1.42159	−0.710797	−	0.703398i	$-0.751665\pi$
$107$	−14.7051	−1.42159	−0.710797	+	0.703398i	$0.751665\pi$
$108$	0.254228	0.0244631
$109$	−18.5516	−1.77693	−0.888463	−	0.458949i	$-0.848226\pi$
$109$	−18.5516	−1.77693	−0.888463	+	0.458949i	$0.848226\pi$
$110$	0.0976637	0.00931187
$111$	18.0779	1.71588
$112$	−7.54377	−0.712819
$113$	−1.41878	−0.133468	−0.0667339	−	0.997771i	$-0.521258\pi$
$113$	−1.41878	−0.133468	−0.0667339	+	0.997771i	$0.521258\pi$
$114$	13.8872	1.30065
$115$	−0.356793	−0.0332712
$116$	0.482965	0.0448422
$117$	−25.7478	−2.38038
$118$	13.3315	1.22726
$119$	−1.81686	−0.166552
$120$	−0.503263	−0.0459414
$121$	1.00000	0.0909091
$122$	2.19142	0.198402
$123$	−23.0516	−2.07849
$124$	−0.611010	−0.0548703
$125$	0.677000	0.0605527
$126$	−10.9951	−0.979521
$127$	5.28291	0.468783	0.234391	−	0.972142i	$-0.424690\pi$
$127$	5.28291	0.468783	0.234391	+	0.972142i	$0.424690\pi$
$128$	−11.9386	−1.05523
$129$	2.68271	0.236199
$130$	−0.599158	−0.0525496
$131$	17.3876	1.51916	0.759582	−	0.650412i	$-0.225404\pi$
$131$	17.3876	1.51916	0.759582	+	0.650412i	$0.225404\pi$
$132$	0.212401	0.0184871
$133$	−6.52255	−0.565577
$134$	19.8977	1.71890
$135$	−0.217485	−0.0187181
$136$	−2.76970	−0.237500
$137$	2.63953	0.225510	0.112755	−	0.993623i	$-0.464032\pi$
$137$	2.63953	0.225510	0.112755	+	0.993623i	$0.464032\pi$
$138$	−20.3774	−1.73464
$139$	−14.5299	−1.23241	−0.616206	−	0.787585i	$-0.711331\pi$
$139$	−14.5299	−1.23241	−0.616206	+	0.787585i	$0.711331\pi$
$140$	−0.00974302	−0.000823435 0
$141$	11.6009	0.976975
$142$	−0.0296675	−0.00248964
$143$	−6.13491	−0.513027
$144$	−17.4260	−1.45216
$145$	−0.413162	−0.0343112
$146$	−8.51529	−0.704730
$147$	−9.92335	−0.818464
$148$	0.533530	0.0438559
$149$	−15.3633	−1.25861	−0.629303	−	0.777160i	$-0.716660\pi$
$149$	−15.3633	−1.25861	−0.629303	+	0.777160i	$0.716660\pi$
$150$	19.3237	1.57777
$151$	−6.13355	−0.499141	−0.249571	−	0.968357i	$-0.580289\pi$
$151$	−6.13355	−0.499141	−0.249571	+	0.968357i	$0.580289\pi$
$152$	−9.94325	−0.806504
$153$	−4.19693	−0.339301
$154$	−2.61980	−0.211109
$155$	0.522701	0.0419843
$156$	−1.30306	−0.104328
$157$	−17.6672	−1.41000	−0.704999	−	0.709208i	$-0.749053\pi$
$157$	−17.6672	−1.41000	−0.704999	+	0.709208i	$0.749053\pi$
$158$	−12.4627	−0.991478
$159$	−13.9452	−1.10593
$160$	−0.0303175	−0.00239681
$161$	9.57087	0.754290
$162$	5.73398	0.450504
$163$	−15.1818	−1.18913	−0.594566	−	0.804047i	$-0.702676\pi$
$163$	−15.1818	−1.18913	−0.594566	+	0.804047i	$0.702676\pi$
$164$	−0.680315	−0.0531237
$165$	−0.181703	−0.0141455
$166$	−22.4279	−1.74074
$167$	−11.1887	−0.865811	−0.432906	−	0.901439i	$-0.642512\pi$
$167$	−11.1887	−0.865811	−0.432906	+	0.901439i	$0.642512\pi$
$168$	13.4999	1.04154
$169$	24.6371	1.89516
$170$	−0.0976637	−0.00749046
$171$	−15.0670	−1.15220
$172$	0.0791741	0.00603697
$173$	5.24989	0.399142	0.199571	−	0.979883i	$-0.436045\pi$
$173$	5.24989	0.399142	0.199571	+	0.979883i	$0.436045\pi$
$174$	−23.5967	−1.78886
$175$	−9.07599	−0.686080
$176$	−4.15208	−0.312975
$177$	−24.8031	−1.86431
$178$	3.11711	0.233637
$179$	1.01587	0.0759297	0.0379649	−	0.999279i	$-0.487913\pi$
$179$	1.01587	0.0759297	0.0379649	+	0.999279i	$0.487913\pi$
$180$	−0.0225062	−0.00167751
$181$	7.35848	0.546952	0.273476	−	0.961879i	$-0.411827\pi$
$181$	7.35848	0.546952	0.273476	+	0.961879i	$0.411827\pi$
$182$	16.0722	1.19135
$183$	−4.07713	−0.301390
$184$	14.5902	1.07561
$185$	−0.456418	−0.0335565
$186$	29.8527	2.18891
$187$	−1.00000	−0.0731272
$188$	0.342375	0.0249703
$189$	5.83396	0.424358
$190$	−0.350613	−0.0254361
$191$	−4.42703	−0.320328	−0.160164	−	0.987090i	$-0.551202\pi$
$191$	−4.42703	−0.320328	−0.160164	+	0.987090i	$0.551202\pi$
$192$	20.5461	1.48279
$193$	−15.5594	−1.11999	−0.559995	−	0.828496i	$-0.689197\pi$
$193$	−15.5594	−1.11999	−0.559995	+	0.828496i	$0.689197\pi$
$194$	23.8217	1.71030
$195$	1.11473	0.0798275
$196$	−0.292865	−0.0209190
$197$	3.26452	0.232587	0.116294	−	0.993215i	$-0.462899\pi$
$197$	3.26452	0.232587	0.116294	+	0.993215i	$0.462899\pi$
$198$	−6.05169	−0.430075
$199$	−7.88046	−0.558631	−0.279315	−	0.960199i	$-0.590107\pi$
$199$	−7.88046	−0.558631	−0.279315	+	0.960199i	$0.590107\pi$
$200$	−13.8358	−0.978340
$201$	−37.0195	−2.61115
$202$	−24.8229	−1.74653
$203$	11.0829	0.777870
$204$	−0.212401	−0.0148711
$205$	0.581989	0.0406478
$206$	11.1169	0.774550
$207$	22.1086	1.53665
$208$	25.4726	1.76621
$209$	−3.59000	−0.248326
$210$	0.476024	0.0328488
$211$	−10.8803	−0.749031	−0.374515	−	0.927221i	$-0.622191\pi$
$211$	−10.8803	−0.749031	−0.374515	+	0.927221i	$0.622191\pi$
$212$	−0.411562	−0.0282662
$213$	0.0551962	0.00378198
$214$	21.2038	1.44946
$215$	−0.0677310	−0.00461922
$216$	8.89353	0.605128
$217$	−14.0213	−0.951827
$218$	26.7502	1.81176
$219$	15.8426	1.07055
$220$	−0.00536255	−0.000361543 0
$221$	6.13491	0.412679
$222$	−26.0672	−1.74952
$223$	6.76656	0.453123	0.226561	−	0.973997i	$-0.427252\pi$
$223$	6.76656	0.453123	0.226561	+	0.973997i	$0.427252\pi$
$224$	0.813259	0.0543381
$225$	−20.9654	−1.39769
$226$	2.04579	0.136084
$227$	21.8056	1.44729	0.723645	−	0.690172i	$-0.242465\pi$
$227$	21.8056	1.44729	0.723645	+	0.690172i	$0.242465\pi$
$228$	−0.762521	−0.0504992
$229$	11.9213	0.787779	0.393890	−	0.919158i	$-0.371129\pi$
$229$	11.9213	0.787779	0.393890	+	0.919158i	$0.371129\pi$
$230$	0.514473	0.0339233
$231$	4.87412	0.320693
$232$	16.8953	1.10923
$233$	−25.1923	−1.65041	−0.825203	−	0.564837i	$-0.808939\pi$
$233$	−25.1923	−1.65041	−0.825203	+	0.564837i	$0.808939\pi$
$234$	37.1266	2.42704
$235$	−0.292892	−0.0191062
$236$	−0.732008	−0.0476496
$237$	23.1867	1.50614
$238$	2.61980	0.169816
$239$	1.95023	0.126150	0.0630749	−	0.998009i	$-0.479909\pi$
$239$	1.95023	0.126150	0.0630749	+	0.998009i	$0.479909\pi$
$240$	0.754444	0.0486991
$241$	18.8724	1.21568	0.607840	−	0.794060i	$-0.292036\pi$
$241$	18.8724	1.21568	0.607840	+	0.794060i	$0.292036\pi$
$242$	−1.44193	−0.0926910
$243$	−20.3010	−1.30231
$244$	−0.120327	−0.00770316
$245$	0.250537	0.0160062
$246$	33.2388	2.11923
$247$	22.0244	1.40138
$248$	−21.3746	−1.35729
$249$	41.7269	2.64434
$250$	−0.976189	−0.0617396
$251$	19.0271	1.20098	0.600490	−	0.799632i	$-0.294972\pi$
$251$	19.0271	1.20098	0.600490	+	0.799632i	$0.294972\pi$
$252$	0.603722	0.0380309
$253$	5.26780	0.331184
$254$	−7.61761	−0.477972
$255$	0.181703	0.0113787
$256$	1.89724	0.118578
$257$	16.3217	1.01812	0.509061	−	0.860731i	$-0.329993\pi$
$257$	16.3217	1.01812	0.509061	+	0.860731i	$0.329993\pi$
$258$	−3.86829	−0.240829
$259$	12.2433	0.760761
$260$	0.0328987	0.00204029
$261$	25.6014	1.58469
$262$	−25.0718	−1.54894
$263$	−10.5140	−0.648324	−0.324162	−	0.946002i	$-0.605082\pi$
$263$	−10.5140	−0.648324	−0.324162	+	0.946002i	$0.605082\pi$
$264$	7.43031	0.457304
$265$	0.352079	0.0216280
$266$	9.40509	0.576663
$267$	−5.79936	−0.354915
$268$	−1.09255	−0.0667380
$269$	23.7671	1.44911	0.724554	−	0.689218i	$-0.242046\pi$
$269$	23.7671	1.44911	0.724554	+	0.689218i	$0.242046\pi$
$270$	0.313598	0.0190850
$271$	−17.5800	−1.06791	−0.533953	−	0.845514i	$-0.679294\pi$
$271$	−17.5800	−1.06791	−0.533953	+	0.845514i	$0.679294\pi$
$272$	4.15208	0.251757
$273$	−29.9023	−1.80977
$274$	−3.80602	−0.229930
$275$	−4.99541	−0.301235
$276$	1.11889	0.0673490
$277$	17.3665	1.04345	0.521727	−	0.853112i	$-0.325288\pi$
$277$	17.3665	1.04345	0.521727	+	0.853112i	$0.325288\pi$
$278$	20.9512	1.25657
$279$	−32.3889	−1.93907
$280$	−0.340835	−0.0203688
$281$	27.0096	1.61126	0.805628	−	0.592422i	$-0.201828\pi$
$281$	27.0096	1.61126	0.805628	+	0.592422i	$0.201828\pi$
$282$	−16.7278	−0.996125
$283$	7.76914	0.461827	0.230914	−	0.972974i	$-0.425828\pi$
$283$	7.76914	0.461827	0.230914	+	0.972974i	$0.425828\pi$
$284$	0.00162899	9.66628e−5 0
$285$	0.652313	0.0386397
$286$	8.84614	0.523083
$287$	−15.6117	−0.921527
$288$	1.87861	0.110698
$289$	1.00000	0.0588235
$290$	0.595752	0.0349838
$291$	−44.3202	−2.59809
$292$	0.467560	0.0273619
$293$	−7.19167	−0.420142	−0.210071	−	0.977686i	$-0.567370\pi$
$293$	−7.19167	−0.420142	−0.210071	+	0.977686i	$0.567370\pi$
$294$	14.3088	0.834507
$295$	0.626210	0.0364594
$296$	18.6642	1.08483
$297$	3.21100	0.186321
$298$	22.1528	1.28328
$299$	−32.3175	−1.86897
$300$	−1.06103	−0.0612587
$301$	1.81686	0.104722
$302$	8.84418	0.508925
$303$	46.1828	2.65313
$304$	14.9060	0.854916
$305$	0.102936	0.00589412
$306$	6.05169	0.345952
$307$	11.0231	0.629121	0.314561	−	0.949237i	$-0.398143\pi$
$307$	11.0231	0.629121	0.314561	+	0.949237i	$0.398143\pi$
$308$	0.143849	0.00819654
$309$	−20.6829	−1.17661
$310$	−0.753700	−0.0428073
$311$	−17.5128	−0.993058	−0.496529	−	0.868020i	$-0.665392\pi$
$311$	−17.5128	−0.993058	−0.496529	+	0.868020i	$0.665392\pi$
$312$	−45.5843	−2.58070
$313$	6.06282	0.342691	0.171346	−	0.985211i	$-0.445189\pi$
$313$	6.06282	0.342691	0.171346	+	0.985211i	$0.445189\pi$
$314$	25.4750	1.43764
$315$	−0.516466	−0.0290995
$316$	0.684304	0.0384951
$317$	−9.65409	−0.542228	−0.271114	−	0.962547i	$-0.587392\pi$
$317$	−9.65409	−0.542228	−0.271114	+	0.962547i	$0.587392\pi$
$318$	20.1081	1.12761
$319$	6.10004	0.341537
$320$	−0.518733	−0.0289981
$321$	−39.4494	−2.20185
$322$	−13.8006	−0.769076
$323$	3.59000	0.199753
$324$	−0.314843	−0.0174913
$325$	30.6464	1.69996
$326$	21.8912	1.21244
$327$	−49.7687	−2.75221
$328$	−23.7991	−1.31408
$329$	7.85673	0.433156
$330$	0.262003	0.0144228
$331$	−34.5298	−1.89793	−0.948965	−	0.315381i	$-0.897868\pi$
$331$	−34.5298	−1.89793	−0.948965	+	0.315381i	$0.897868\pi$
$332$	1.23148	0.0675861
$333$	28.2818	1.54983
$334$	16.1334	0.882782
$335$	0.934641	0.0510649
$336$	−20.2377	−1.10406
$337$	−7.95364	−0.433262	−0.216631	−	0.976254i	$-0.569507\pi$
$337$	−7.95364	−0.433262	−0.216631	+	0.976254i	$0.569507\pi$
$338$	−35.5251	−1.93231
$339$	−3.80618	−0.206723
$340$	0.00536255	0.000290825 0
$341$	−7.71730	−0.417915
$342$	21.7256	1.17479
$343$	−19.4386	−1.04959
$344$	2.76970	0.149332
$345$	−0.957173	−0.0515324
$346$	−7.56999	−0.406965
$347$	27.0318	1.45114	0.725572	−	0.688146i	$-0.241575\pi$
$347$	27.0318	1.45114	0.725572	+	0.688146i	$0.241575\pi$
$348$	1.29565	0.0694544
$349$	−5.58064	−0.298725	−0.149362	−	0.988783i	$-0.547722\pi$
$349$	−5.58064	−0.298725	−0.149362	+	0.988783i	$0.547722\pi$
$350$	13.0870	0.699528
$351$	−19.6992	−1.05147
$352$	0.447617	0.0238580
$353$	−10.3724	−0.552069	−0.276035	−	0.961148i	$-0.589020\pi$
$353$	−10.3724	−0.552069	−0.276035	+	0.961148i	$0.589020\pi$
$354$	35.7644	1.90086
$355$	−0.00139355	−7.39621e−5 0
$356$	−0.171155	−0.00907120
$357$	−4.87412	−0.257966
$358$	−1.46482	−0.0774180
$359$	−13.7553	−0.725976	−0.362988	−	0.931794i	$-0.618243\pi$
$359$	−13.7553	−0.725976	−0.362988	+	0.931794i	$0.618243\pi$
$360$	−0.787322	−0.0414955
$361$	−6.11188	−0.321678
$362$	−10.6104	−0.557673
$363$	2.68271	0.140806
$364$	−0.882499	−0.0462555
$365$	−0.399983	−0.0209361
$366$	5.87895	0.307298
$367$	11.3327	0.591561	0.295780	−	0.955256i	$-0.404420\pi$
$367$	11.3327	0.591561	0.295780	+	0.955256i	$0.404420\pi$
$368$	−21.8723	−1.14017
$369$	−36.0627	−1.87735
$370$	0.658125	0.0342143
$371$	−9.44441	−0.490329
$372$	−1.63916	−0.0849866
$373$	−0.639608	−0.0331176	−0.0165588	−	0.999863i	$-0.505271\pi$
$373$	−0.639608	−0.0331176	−0.0165588	+	0.999863i	$0.505271\pi$
$374$	1.44193	0.0745606
$375$	1.81619	0.0937878
$376$	11.9771	0.617673
$377$	−37.4232	−1.92739
$378$	−8.41218	−0.432676
$379$	34.9521	1.79537	0.897686	−	0.440637i	$-0.145247\pi$
$379$	34.9521	1.79537	0.897686	+	0.440637i	$0.145247\pi$
$380$	0.0192516	0.000987584 0
$381$	14.1725	0.726080
$382$	6.38348	0.326607
$383$	28.4091	1.45164	0.725819	−	0.687886i	$-0.241461\pi$
$383$	28.4091	1.45164	0.725819	+	0.687886i	$0.241461\pi$
$384$	−32.0278	−1.63441
$385$	−0.123058	−0.00627162
$386$	22.4356	1.14194
$387$	4.19693	0.213342
$388$	−1.30801	−0.0664042
$389$	−11.3736	−0.576667	−0.288333	−	0.957530i	$-0.593101\pi$
$389$	−11.3736	−0.576667	−0.288333	+	0.957530i	$0.593101\pi$
$390$	−1.60737	−0.0813922
$391$	−5.26780	−0.266404
$392$	−10.2451	−0.517458
$393$	46.6459	2.35297
$394$	−4.70722	−0.237146
$395$	−0.585401	−0.0294547
$396$	0.332288	0.0166981
$397$	−31.8351	−1.59776	−0.798880	−	0.601491i	$-0.794574\pi$
$397$	−31.8351	−1.59776	−0.798880	+	0.601491i	$0.794574\pi$
$398$	11.3631	0.569581
$399$	−17.4981	−0.876001
$400$	20.7414	1.03707
$401$	−13.8671	−0.692489	−0.346244	−	0.938144i	$-0.612543\pi$
$401$	−13.8671	−0.692489	−0.346244	+	0.938144i	$0.612543\pi$
$402$	53.3797	2.66234
$403$	47.3449	2.35842
$404$	1.36298	0.0678108
$405$	0.269339	0.0133835
$406$	−15.9809	−0.793117
$407$	6.73869	0.334024
$408$	−7.43031	−0.367855
$409$	−26.5224	−1.31145	−0.655725	−	0.755000i	$-0.727637\pi$
$409$	−26.5224	−1.31145	−0.655725	+	0.755000i	$0.727637\pi$
$410$	−0.839189	−0.0414446
$411$	7.08108	0.349284
$412$	−0.610409	−0.0300727
$413$	−16.7979	−0.826570
$414$	−31.8791	−1.56677
$415$	−1.05349	−0.0517138
$416$	−2.74609	−0.134638
$417$	−38.9796	−1.90884
$418$	5.17655	0.253193
$419$	−21.1903	−1.03521	−0.517606	−	0.855619i	$-0.673177\pi$
$419$	−21.1903	−1.03521	−0.517606	+	0.855619i	$0.673177\pi$
$420$	−0.0261377	−0.00127539
$421$	−12.2595	−0.597492	−0.298746	−	0.954333i	$-0.596568\pi$
$421$	−12.2595	−0.597492	−0.298746	+	0.954333i	$0.596568\pi$
$422$	15.6887	0.763713
$423$	18.1489	0.882431
$424$	−14.3975	−0.699202
$425$	4.99541	0.242313
$426$	−0.0795892	−0.00385611
$427$	−2.76123	−0.133626
$428$	−1.16426	−0.0562767
$429$	−16.4582	−0.794608
$430$	0.0976637	0.00470976
$431$	−18.8291	−0.906965	−0.453482	−	0.891265i	$-0.649818\pi$
$431$	−18.8291	−0.906965	−0.453482	+	0.891265i	$0.649818\pi$
$432$	−13.3323	−0.641452
$433$	19.4370	0.934082	0.467041	−	0.884236i	$-0.345320\pi$
$433$	19.4370	0.934082	0.467041	+	0.884236i	$0.345320\pi$
$434$	20.2178	0.970484
$435$	−1.10839	−0.0531434
$436$	−1.46881	−0.0703432
$437$	−18.9114	−0.904655
$438$	−22.8440	−1.09153
$439$	25.0963	1.19778	0.598891	−	0.800831i	$-0.295608\pi$
$439$	25.0963	1.19778	0.598891	+	0.800831i	$0.295608\pi$
$440$	−0.187595	−0.00894324
$441$	−15.5244	−0.739259
$442$	−8.84614	−0.420768
$443$	−30.7156	−1.45934	−0.729671	−	0.683798i	$-0.760327\pi$
$443$	−30.7156	−1.45934	−0.729671	+	0.683798i	$0.760327\pi$
$444$	1.43130	0.0679267
$445$	0.146418	0.00694088
$446$	−9.75694	−0.462004
$447$	−41.2151	−1.94941
$448$	13.9149	0.657416
$449$	−9.18451	−0.433444	−0.216722	−	0.976233i	$-0.569536\pi$
$449$	−9.18451	−0.433444	−0.216722	+	0.976233i	$0.569536\pi$
$450$	30.2307	1.42509
$451$	−8.59264	−0.404612
$452$	−0.112331	−0.00528360
$453$	−16.4545	−0.773101
$454$	−31.4423	−1.47566
$455$	0.754951	0.0353926
$456$	−26.6748	−1.24916
$457$	10.9588	0.512630	0.256315	−	0.966593i	$-0.417492\pi$
$457$	10.9588	0.512630	0.256315	+	0.966593i	$0.417492\pi$
$458$	−17.1897	−0.803221
$459$	−3.21100	−0.149877
$460$	−0.0282488	−0.00131711
$461$	2.17769	0.101425	0.0507126	−	0.998713i	$-0.483851\pi$
$461$	2.17769	0.101425	0.0507126	+	0.998713i	$0.483851\pi$
$462$	−7.02816	−0.326979
$463$	29.4396	1.36817	0.684087	−	0.729401i	$-0.260201\pi$
$463$	29.4396	1.36817	0.684087	+	0.729401i	$0.260201\pi$
$464$	−25.3278	−1.17582
$465$	1.40225	0.0650279
$466$	36.3257	1.68276
$467$	−23.8414	−1.10325	−0.551624	−	0.834093i	$-0.685992\pi$
$467$	−23.8414	−1.10325	−0.551624	+	0.834093i	$0.685992\pi$
$468$	−2.03856	−0.0942323
$469$	−25.0715	−1.15769
$470$	0.422331	0.0194807
$471$	−47.3960	−2.18389
$472$	−25.6074	−1.17868
$473$	1.00000	0.0459800
$474$	−33.4337	−1.53566
$475$	17.9335	0.822848
$476$	−0.143849	−0.00659329
$477$	−21.8164	−0.998906
$478$	−2.81210	−0.128622
$479$	17.2415	0.787783	0.393891	−	0.919157i	$-0.371129\pi$
$479$	17.2415	0.787783	0.393891	+	0.919157i	$0.371129\pi$
$480$	−0.0813331	−0.00371233
$481$	−41.3413	−1.88500
$482$	−27.2128	−1.23951
$483$	25.6759	1.16829
$484$	0.0791741	0.00359882
$485$	1.11896	0.0508095
$486$	29.2728	1.32784
$487$	27.8500	1.26200	0.631001	−	0.775782i	$-0.282644\pi$
$487$	27.8500	1.26200	0.631001	+	0.775782i	$0.282644\pi$
$488$	−4.20934	−0.190548
$489$	−40.7284	−1.84180
$490$	−0.361258	−0.0163200
$491$	−6.93556	−0.312997	−0.156499	−	0.987678i	$-0.550021\pi$
$491$	−6.93556	−0.312997	−0.156499	+	0.987678i	$0.550021\pi$
$492$	−1.82509	−0.0822812
$493$	−6.10004	−0.274732
$494$	−31.7577	−1.42884
$495$	−0.284262	−0.0127766
$496$	32.0428	1.43877
$497$	0.0373816	0.00167679
$498$	−60.1675	−2.69617
$499$	31.6285	1.41589	0.707943	−	0.706269i	$-0.249623\pi$
$499$	31.6285	1.41589	0.707943	+	0.706269i	$0.249623\pi$
$500$	0.0536009	0.00239710
$501$	−30.0161	−1.34102
$502$	−27.4358	−1.22452
$503$	13.6034	0.606545	0.303273	−	0.952904i	$-0.401921\pi$
$503$	13.6034	0.606545	0.303273	+	0.952904i	$0.401921\pi$
$504$	21.1197	0.940745
$505$	−1.16599	−0.0518858
$506$	−7.59582	−0.337675
$507$	66.0943	2.93535
$508$	0.418270	0.0185577
$509$	−6.69655	−0.296819	−0.148410	−	0.988926i	$-0.547415\pi$
$509$	−6.69655	−0.296819	−0.148410	+	0.988926i	$0.547415\pi$
$510$	−0.262003	−0.0116017
$511$	10.7294	0.474642
$512$	21.1415	0.934332
$513$	−11.5275	−0.508952
$514$	−23.5349	−1.03808
$515$	0.522186	0.0230103
$516$	0.212401	0.00935044
$517$	4.32434	0.190184
$518$	−17.6540	−0.775673
$519$	14.0839	0.618215
$520$	1.15088	0.0504694
$521$	30.6701	1.34368	0.671840	−	0.740696i	$-0.265504\pi$
$521$	30.6701	1.34368	0.671840	+	0.740696i	$0.265504\pi$
$522$	−36.9155	−1.61575
$523$	27.0957	1.18481	0.592406	−	0.805639i	$-0.298178\pi$
$523$	27.0957	1.18481	0.592406	+	0.805639i	$0.298178\pi$
$524$	1.37665	0.0601392
$525$	−24.3482	−1.06264
$526$	15.1606	0.661032
$527$	7.71730	0.336171
$528$	−11.1388	−0.484755
$529$	4.74969	0.206508
$530$	−0.507675	−0.0220520
$531$	−38.8029	−1.68390
$532$	−0.516417	−0.0223895
$533$	52.7151	2.28334
$534$	8.36229	0.361872
$535$	0.995990	0.0430604
$536$	−38.2200	−1.65085
$537$	2.72528	0.117605
$538$	−34.2707	−1.47751
$539$	−3.69900	−0.159327
$540$	−0.0172191	−0.000740994 0
$541$	−12.8140	−0.550919	−0.275459	−	0.961313i	$-0.588830\pi$
$541$	−12.8140	−0.550919	−0.275459	+	0.961313i	$0.588830\pi$
$542$	25.3491	1.08884
$543$	19.7407	0.847153
$544$	−0.447617	−0.0191914
$545$	1.25652	0.0538235
$546$	43.1171	1.84524
$547$	−23.1262	−0.988803	−0.494402	−	0.869234i	$-0.664613\pi$
$547$	−23.1262	−0.988803	−0.494402	+	0.869234i	$0.664613\pi$
$548$	0.208982	0.00892728
$549$	−6.37840	−0.272224
$550$	7.20306	0.307139
$551$	−21.8992	−0.932935
$552$	39.1414	1.66597
$553$	15.7032	0.667769
$554$	−25.0414	−1.06391
$555$	−1.22444	−0.0519745
$556$	−1.15039	−0.0487876
$557$	−18.3097	−0.775809	−0.387904	−	0.921700i	$-0.626801\pi$
$557$	−18.3097	−0.775809	−0.387904	+	0.921700i	$0.626801\pi$
$558$	46.7027	1.97708
$559$	−6.13491	−0.259479
$560$	0.510947	0.0215915
$561$	−2.68271	−0.113264
$562$	−38.9460	−1.64284
$563$	−22.3262	−0.940938	−0.470469	−	0.882417i	$-0.655915\pi$
$563$	−22.3262	−0.940938	−0.470469	+	0.882417i	$0.655915\pi$
$564$	0.918494	0.0386756
$565$	0.0960956	0.00404277
$566$	−11.2026	−0.470880
$567$	−7.22493	−0.303418
$568$	0.0569861	0.00239108
$569$	7.21625	0.302521	0.151261	−	0.988494i	$-0.451667\pi$
$569$	7.21625	0.302521	0.151261	+	0.988494i	$0.451667\pi$
$570$	−0.940592	−0.0393971
$571$	26.9899	1.12949	0.564746	−	0.825264i	$-0.308974\pi$
$571$	26.9899	1.12949	0.564746	+	0.825264i	$0.308974\pi$
$572$	−0.485726	−0.0203092
$573$	−11.8764	−0.496145
$574$	22.5110	0.939591
$575$	−26.3148	−1.09740
$576$	32.1431	1.33930
$577$	−41.1263	−1.71211	−0.856054	−	0.516886i	$-0.827091\pi$
$577$	−41.1263	−1.71211	−0.856054	+	0.516886i	$0.827091\pi$
$578$	−1.44193	−0.0599766
$579$	−41.7413	−1.73471
$580$	−0.0327117	−0.00135828
$581$	28.2596	1.17240
$582$	63.9068	2.64902
$583$	−5.19819	−0.215287
$584$	16.3564	0.676832
$585$	1.74392	0.0721023
$586$	10.3699	0.428377
$587$	−34.0280	−1.40448	−0.702242	−	0.711938i	$-0.747818\pi$
$587$	−34.0280	−1.40448	−0.702242	+	0.711938i	$0.747818\pi$
$588$	−0.785672	−0.0324006
$589$	27.7051	1.14157
$590$	−0.902954	−0.0371740
$591$	8.75776	0.360246
$592$	−27.9796	−1.14995
$593$	34.7098	1.42536	0.712680	−	0.701490i	$-0.247481\pi$
$593$	34.7098	1.42536	0.712680	+	0.701490i	$0.247481\pi$
$594$	−4.63005	−0.189973
$595$	0.123058	0.00504489
$596$	−1.21637	−0.0498245
$597$	−21.1410	−0.865242
$598$	46.5997	1.90560
$599$	−17.2161	−0.703430	−0.351715	−	0.936107i	$-0.614401\pi$
$599$	−17.2161	−0.703430	−0.351715	+	0.936107i	$0.614401\pi$
$600$	−37.1175	−1.51531
$601$	32.9291	1.34321	0.671604	−	0.740910i	$-0.265606\pi$
$601$	32.9291	1.34321	0.671604	+	0.740910i	$0.265606\pi$
$602$	−2.61980	−0.106775
$603$	−57.9146	−2.35847
$604$	−0.485618	−0.0197595
$605$	−0.0677310	−0.00275366
$606$	−66.5925	−2.70514
$607$	21.4711	0.871486	0.435743	−	0.900071i	$-0.356486\pi$
$607$	21.4711	0.871486	0.435743	+	0.900071i	$0.356486\pi$
$608$	−1.60695	−0.0651702
$609$	29.7323	1.20481
$610$	−0.148427	−0.00600965
$611$	−26.5294	−1.07327
$612$	−0.332288	−0.0134319
$613$	40.7061	1.64410	0.822051	−	0.569414i	$-0.192830\pi$
$613$	40.7061	1.64410	0.822051	+	0.569414i	$0.192830\pi$
$614$	−15.8946	−0.641453
$615$	1.56131	0.0629579
$616$	5.03218	0.202752
$617$	−10.9688	−0.441589	−0.220794	−	0.975320i	$-0.570865\pi$
$617$	−10.9688	−0.441589	−0.220794	+	0.975320i	$0.570865\pi$
$618$	29.8233	1.19967
$619$	−11.2911	−0.453829	−0.226915	−	0.973915i	$-0.572864\pi$
$619$	−11.2911	−0.453829	−0.226915	+	0.973915i	$0.572864\pi$
$620$	0.0413844	0.00166204
$621$	16.9149	0.678772
$622$	25.2522	1.01252
$623$	−3.92762	−0.157357
$624$	68.3357	2.73562
$625$	24.9312	0.997248
$626$	−8.74219	−0.349408
$627$	−9.63093	−0.384622
$628$	−1.39879	−0.0558177
$629$	−6.73869	−0.268689
$630$	0.744710	0.0296699
$631$	−39.1955	−1.56035	−0.780175	−	0.625562i	$-0.784870\pi$
$631$	−39.1955	−1.56035	−0.780175	+	0.625562i	$0.784870\pi$
$632$	23.9386	0.952228
$633$	−29.1887	−1.16015
$634$	13.9206	0.552856
$635$	−0.357817	−0.0141995
$636$	−1.10410	−0.0437805
$637$	22.6931	0.899132
$638$	−8.79585	−0.348231
$639$	0.0863509	0.00341599
$640$	0.808615	0.0319633
$641$	−14.4255	−0.569774	−0.284887	−	0.958561i	$-0.591956\pi$
$641$	−14.4255	−0.569774	−0.284887	+	0.958561i	$0.591956\pi$
$642$	56.8835	2.24501
$643$	43.6737	1.72232	0.861161	−	0.508332i	$-0.169738\pi$
$643$	43.6737	1.72232	0.861161	+	0.508332i	$0.169738\pi$
$644$	0.757765	0.0298601
$645$	−0.181703	−0.00715453
$646$	−5.17655	−0.203669
$647$	21.6892	0.852691	0.426345	−	0.904560i	$-0.359801\pi$
$647$	21.6892	0.852691	0.426345	+	0.904560i	$0.359801\pi$
$648$	−11.0140	−0.432670
$649$	−9.24554	−0.362919
$650$	−44.1901	−1.73328
$651$	−37.6150	−1.47425
$652$	−1.20201	−0.0470742
$653$	−18.4751	−0.722985	−0.361492	−	0.932375i	$-0.617733\pi$
$653$	−18.4751	−0.722985	−0.361492	+	0.932375i	$0.617733\pi$
$654$	71.7631	2.80616
$655$	−1.17768	−0.0460158
$656$	35.6773	1.39297
$657$	24.7848	0.966947
$658$	−11.3289	−0.441646
$659$	8.95429	0.348810	0.174405	−	0.984674i	$-0.444200\pi$
$659$	8.95429	0.348810	0.174405	+	0.984674i	$0.444200\pi$
$660$	−0.0143861	−0.000559980 0
$661$	−33.7782	−1.31382	−0.656911	−	0.753968i	$-0.728137\pi$
$661$	−33.7782	−1.31382	−0.656911	+	0.753968i	$0.728137\pi$
$662$	49.7897	1.93513
$663$	16.4582	0.639183
$664$	43.0801	1.67183
$665$	0.441779	0.0171315
$666$	−40.7805	−1.58021
$667$	32.1338	1.24422
$668$	−0.885859	−0.0342749
$669$	18.1527	0.701825
$670$	−1.34769	−0.0520658
$671$	−1.51978	−0.0586705
$672$	2.18174	0.0841623
$673$	−30.2707	−1.16685	−0.583424	−	0.812168i	$-0.698287\pi$
$673$	−30.2707	−1.16685	−0.583424	+	0.812168i	$0.698287\pi$
$674$	11.4686	0.441755
$675$	−16.0403	−0.617391
$676$	1.95062	0.0750240
$677$	−29.5575	−1.13599	−0.567994	−	0.823032i	$-0.692280\pi$
$677$	−29.5575	−1.13599	−0.567994	+	0.823032i	$0.692280\pi$
$678$	5.48826	0.210775
$679$	−30.0158	−1.15190
$680$	0.187595	0.00719394
$681$	58.4981	2.24165
$682$	11.1278	0.426107
$683$	−25.6342	−0.980867	−0.490433	−	0.871479i	$-0.663161\pi$
$683$	−25.6342	−0.980867	−0.490433	+	0.871479i	$0.663161\pi$
$684$	−1.19291	−0.0456122
$685$	−0.178778	−0.00683075
$686$	28.0292	1.07016
$687$	31.9813	1.22016
$688$	−4.15208	−0.158297
$689$	31.8905	1.21493
$690$	1.38018	0.0525426
$691$	24.4939	0.931793	0.465897	−	0.884839i	$-0.345732\pi$
$691$	24.4939	0.931793	0.465897	+	0.884839i	$0.345732\pi$
$692$	0.415655	0.0158008
$693$	7.62524	0.289659
$694$	−38.9781	−1.47959
$695$	0.984127	0.0373301
$696$	45.3252	1.71805
$697$	8.59264	0.325469
$698$	8.04691	0.304580
$699$	−67.5837	−2.55625
$700$	−0.718583	−0.0271599
$701$	−12.6563	−0.478021	−0.239010	−	0.971017i	$-0.576823\pi$
$701$	−12.6563	−0.478021	−0.239010	+	0.971017i	$0.576823\pi$
$702$	28.4050	1.07208
$703$	−24.1919	−0.912415
$704$	7.65873	0.288649
$705$	−0.785743	−0.0295928
$706$	14.9564	0.562891
$707$	31.2773	1.17630
$708$	−1.96376	−0.0738027
$709$	1.43384	0.0538489	0.0269245	−	0.999637i	$-0.491429\pi$
$709$	1.43384	0.0538489	0.0269245	+	0.999637i	$0.491429\pi$
$710$	0.00200941	7.54118e−5 0
$711$	36.2742	1.36039
$712$	−5.98742	−0.224388
$713$	−40.6532	−1.52247
$714$	7.02816	0.263022
$715$	0.415524	0.0155397
$716$	0.0804306	0.00300583
$717$	5.23189	0.195389
$718$	19.8342	0.740207
$719$	30.7377	1.14632	0.573161	−	0.819443i	$-0.305717\pi$
$719$	30.7377	1.14632	0.573161	+	0.819443i	$0.305717\pi$
$720$	1.18028	0.0439864
$721$	−14.0075	−0.521666
$722$	8.81293	0.327983
$723$	50.6292	1.88292
$724$	0.582601	0.0216522
$725$	−30.4722	−1.13171
$726$	−3.86829	−0.143566
$727$	−49.5222	−1.83668	−0.918338	−	0.395797i	$-0.870469\pi$
$727$	−49.5222	−1.83668	−0.918338	+	0.395797i	$0.870469\pi$
$728$	−30.8720	−1.14419
$729$	−42.5320	−1.57526
$730$	0.576749	0.0213464
$731$	−1.00000	−0.0369863
$732$	−0.322803	−0.0119311
$733$	−30.2963	−1.11902	−0.559510	−	0.828824i	$-0.689011\pi$
$733$	−30.2963	−1.11902	−0.559510	+	0.828824i	$0.689011\pi$
$734$	−16.3410	−0.603156
$735$	0.672119	0.0247915
$736$	2.35795	0.0869153
$737$	−13.7993	−0.508304
$738$	52.0000	1.91415
$739$	38.8816	1.43028	0.715141	−	0.698980i	$-0.246362\pi$
$739$	38.8816	1.43028	0.715141	+	0.698980i	$0.246362\pi$
$740$	−0.0361365	−0.00132840
$741$	59.0849	2.17054
$742$	13.6182	0.499941
$743$	−45.6162	−1.67349	−0.836747	−	0.547589i	$-0.815546\pi$
$743$	−45.6162	−1.67349	−0.836747	+	0.547589i	$0.815546\pi$
$744$	−57.3419	−2.10226
$745$	1.04057	0.0381235
$746$	0.922273	0.0337668
$747$	65.2791	2.38844
$748$	−0.0791741	−0.00289489
$749$	−26.7171	−0.976223
$750$	−2.61883	−0.0956262
$751$	42.5672	1.55330	0.776649	−	0.629933i	$-0.216918\pi$
$751$	42.5672	1.55330	0.776649	+	0.629933i	$0.216918\pi$
$752$	−17.9550	−0.654751
$753$	51.0442	1.86015
$754$	53.9618	1.96517
$755$	0.415432	0.0151191
$756$	0.461898	0.0167991
$757$	−21.6746	−0.787775	−0.393888	−	0.919159i	$-0.628870\pi$
$757$	−21.6746	−0.787775	−0.393888	+	0.919159i	$0.628870\pi$
$758$	−50.3987	−1.83056
$759$	14.1320	0.512958
$760$	0.673466	0.0244292
$761$	−11.5122	−0.417317	−0.208659	−	0.977989i	$-0.566910\pi$
$761$	−11.5122	−0.417317	−0.208659	+	0.977989i	$0.566910\pi$
$762$	−20.4358	−0.740312
$763$	−33.7058	−1.22023
$764$	−0.350506	−0.0126809
$765$	0.284262	0.0102775
$766$	−40.9641	−1.48009
$767$	56.7206	2.04806
$768$	5.08974	0.183660
$769$	30.3976	1.09617	0.548083	−	0.836424i	$-0.315358\pi$
$769$	30.3976	1.09617	0.548083	+	0.836424i	$0.315358\pi$
$770$	0.177442	0.00639455
$771$	43.7864	1.57693
$772$	−1.23190	−0.0443371
$773$	−37.3231	−1.34242	−0.671210	−	0.741267i	$-0.734225\pi$
$773$	−37.3231	−1.34242	−0.671210	+	0.741267i	$0.734225\pi$
$774$	−6.05169	−0.217524
$775$	38.5511	1.38480
$776$	−45.7574	−1.64260
$777$	32.8452	1.17831
$778$	16.4001	0.587970
$779$	30.8476	1.10523
$780$	0.0882577	0.00316013
$781$	0.0205748	0.000736224 0
$782$	7.59582	0.271626
$783$	19.5872	0.699991
$784$	15.3586	0.548520
$785$	1.19662	0.0427092
$786$	−67.2603	−2.39910
$787$	−34.4357	−1.22750	−0.613751	−	0.789500i	$-0.710340\pi$
$787$	−34.4357	−1.22750	−0.613751	+	0.789500i	$0.710340\pi$
$788$	0.258465	0.00920745
$789$	−28.2061	−1.00416
$790$	0.844110	0.0300321
$791$	−2.57774	−0.0916537
$792$	11.6242	0.413050
$793$	9.32372	0.331095
$794$	45.9042	1.62908
$795$	0.944526	0.0334989
$796$	−0.623928	−0.0221145
$797$	−23.4889	−0.832020	−0.416010	−	0.909360i	$-0.636572\pi$
$797$	−23.4889	−0.832020	−0.416010	+	0.909360i	$0.636572\pi$
$798$	25.2311	0.893171
$799$	−4.32434	−0.152984
$800$	−2.23603	−0.0790556
$801$	−9.07273	−0.320569
$802$	19.9954	0.706063
$803$	5.90546	0.208399
$804$	−2.93099	−0.103368
$805$	−0.648245	−0.0228476
$806$	−68.2683	−2.40465
$807$	63.7603	2.24447
$808$	47.6804	1.67739
$809$	7.43690	0.261467	0.130734	−	0.991418i	$-0.458267\pi$
$809$	7.43690	0.261467	0.130734	+	0.991418i	$0.458267\pi$
$810$	−0.388369	−0.0136459
$811$	−0.524276	−0.0184098	−0.00920491	−	0.999958i	$-0.502930\pi$
$811$	−0.524276	−0.0184098	−0.00920491	+	0.999958i	$0.502930\pi$
$812$	0.877482	0.0307936
$813$	−47.1619	−1.65404
$814$	−9.71674	−0.340572
$815$	1.02828	0.0360191
$816$	11.1388	0.389937
$817$	−3.59000	−0.125598
$818$	38.2436	1.33716
$819$	−46.7802	−1.63463
$820$	0.0460784	0.00160913
$821$	12.1724	0.424819	0.212410	−	0.977181i	$-0.431869\pi$
$821$	12.1724	0.424819	0.212410	+	0.977181i	$0.431869\pi$
$822$	−10.2105	−0.356130
$823$	−1.81993	−0.0634387	−0.0317193	−	0.999497i	$-0.510098\pi$
$823$	−1.81993	−0.0634387	−0.0317193	+	0.999497i	$0.510098\pi$
$824$	−21.3536	−0.743888
$825$	−13.4012	−0.466571
$826$	24.2215	0.842772
$827$	8.07191	0.280688	0.140344	−	0.990103i	$-0.455179\pi$
$827$	8.07191	0.280688	0.140344	+	0.990103i	$0.455179\pi$
$828$	1.75043	0.0608315
$829$	−19.5157	−0.677808	−0.338904	−	0.940821i	$-0.610056\pi$
$829$	−19.5157	−0.677808	−0.338904	+	0.940821i	$0.610056\pi$
$830$	1.51906	0.0527275
$831$	46.5894	1.61617
$832$	−46.9856	−1.62893
$833$	3.69900	0.128163
$834$	56.2060	1.94625
$835$	0.757825	0.0262256
$836$	−0.284235	−0.00983048
$837$	−24.7803	−0.856531
$838$	30.5550	1.05550
$839$	16.6801	0.575861	0.287931	−	0.957651i	$-0.407033\pi$
$839$	16.6801	0.575861	0.287931	+	0.957651i	$0.407033\pi$
$840$	−0.914360	−0.0315484
$841$	8.21046	0.283119
$842$	17.6774	0.609204
$843$	72.4588	2.49561
$844$	−0.861438	−0.0296519
$845$	−1.66870	−0.0574050
$846$	−26.1695	−0.899727
$847$	1.81686	0.0624282
$848$	21.5833	0.741174
$849$	20.8423	0.715307
$850$	−7.20306	−0.247063
$851$	35.4980	1.21686
$852$	0.00437011	0.000149717 0
$853$	36.7780	1.25925	0.629627	−	0.776898i	$-0.283208\pi$
$853$	36.7780	1.25925	0.629627	+	0.776898i	$0.283208\pi$
$854$	3.98152	0.136245
$855$	1.02050	0.0349004
$856$	−40.7287	−1.39208
$857$	−36.0612	−1.23183	−0.615913	−	0.787814i	$-0.711213\pi$
$857$	−36.0612	−1.23183	−0.615913	+	0.787814i	$0.711213\pi$
$858$	23.7316	0.810184
$859$	−31.4225	−1.07212	−0.536062	−	0.844179i	$-0.680089\pi$
$859$	−31.4225	−1.07212	−0.536062	+	0.844179i	$0.680089\pi$
$860$	−0.00536255	−0.000182861 0
$861$	−41.8815	−1.42732
$862$	27.1503	0.924742
$863$	5.27722	0.179639	0.0898193	−	0.995958i	$-0.471371\pi$
$863$	5.27722	0.179639	0.0898193	+	0.995958i	$0.471371\pi$
$864$	1.43730	0.0488979
$865$	−0.355580	−0.0120901
$866$	−28.0269	−0.952391
$867$	2.68271	0.0911096
$868$	−1.11012	−0.0376800
$869$	8.64303	0.293195
$870$	1.59823	0.0541851
$871$	84.6575	2.86851
$872$	−51.3826	−1.74003
$873$	−69.3361	−2.34667
$874$	27.2690	0.922388
$875$	1.23002	0.0415822
$876$	1.25433	0.0423798
$877$	5.22327	0.176377	0.0881886	−	0.996104i	$-0.471892\pi$
$877$	5.22327	0.176377	0.0881886	+	0.996104i	$0.471892\pi$
$878$	−36.1872	−1.22126
$879$	−19.2932	−0.650742
$880$	0.281225	0.00948008
$881$	10.4182	0.350998	0.175499	−	0.984480i	$-0.443846\pi$
$881$	10.4182	0.350998	0.175499	+	0.984480i	$0.443846\pi$
$882$	22.3852	0.753750
$883$	3.87444	0.130385	0.0651927	−	0.997873i	$-0.479234\pi$
$883$	3.87444	0.130385	0.0651927	+	0.997873i	$0.479234\pi$
$884$	0.485726	0.0163367
$885$	1.67994	0.0564705
$886$	44.2899	1.48795
$887$	−23.6773	−0.795006	−0.397503	−	0.917601i	$-0.630123\pi$
$887$	−23.6773	−0.795006	−0.397503	+	0.917601i	$0.630123\pi$
$888$	50.0705	1.68026
$889$	9.59834	0.321918
$890$	−0.211125	−0.00707693
$891$	−3.97659	−0.133221
$892$	0.535737	0.0179378
$893$	−15.5244	−0.519504
$894$	59.4295	1.98762
$895$	−0.0688059	−0.00229993
$896$	−21.6908	−0.724640
$897$	−86.6984	−2.89477
$898$	13.2435	0.441940
$899$	−47.0758	−1.57007
$900$	−1.65992	−0.0553305
$901$	5.19819	0.173177
$902$	12.3900	0.412543
$903$	4.87412	0.162200
$904$	−3.92961	−0.130697
$905$	−0.498398	−0.0165673
$906$	23.7263	0.788255
$907$	21.4546	0.712389	0.356194	−	0.934412i	$-0.384074\pi$
$907$	21.4546	0.712389	0.356194	+	0.934412i	$0.384074\pi$
$908$	1.72644	0.0572940
$909$	72.2500	2.39638
$910$	−1.08859	−0.0360864
$911$	−22.8467	−0.756944	−0.378472	−	0.925613i	$-0.623550\pi$
$911$	−22.8467	−0.756944	−0.378472	+	0.925613i	$0.623550\pi$
$912$	39.9884	1.32415
$913$	15.5540	0.514763
$914$	−15.8018	−0.522678
$915$	0.276148	0.00912917
$916$	0.943856	0.0311859
$917$	31.5909	1.04322
$918$	4.63005	0.152815
$919$	−30.4159	−1.00333	−0.501665	−	0.865062i	$-0.667279\pi$
$919$	−30.4159	−1.00333	−0.501665	+	0.865062i	$0.667279\pi$
$920$	−0.988212	−0.0325804
$921$	29.5717	0.974422
$922$	−3.14008	−0.103413
$923$	−0.126225	−0.00415473
$924$	0.385904	0.0126953
$925$	−33.6625	−1.10682
$926$	−42.4500	−1.39499
$927$	−32.3570	−1.06274
$928$	2.73048	0.0896323
$929$	−26.1508	−0.857979	−0.428989	−	0.903309i	$-0.641130\pi$
$929$	−26.1508	−0.857979	−0.428989	+	0.903309i	$0.641130\pi$
$930$	−2.02196	−0.0663026
$931$	13.2794	0.435216
$932$	−1.99458	−0.0653347
$933$	−46.9816	−1.53811
$934$	34.3777	1.12487
$935$	0.0677310	0.00221504
$936$	−71.3137	−2.33096
$937$	−12.2081	−0.398821	−0.199410	−	0.979916i	$-0.563903\pi$
$937$	−12.2081	−0.398821	−0.199410	+	0.979916i	$0.563903\pi$
$938$	36.1514	1.18038
$939$	16.2648	0.530781
$940$	−0.0231894	−0.000756356 0
$941$	34.2749	1.11733	0.558665	−	0.829394i	$-0.311314\pi$
$941$	34.2749	1.11733	0.558665	+	0.829394i	$0.311314\pi$
$942$	68.3419	2.22670
$943$	−45.2643	−1.47401
$944$	38.3882	1.24943
$945$	−0.395140	−0.0128539
$946$	−1.44193	−0.0468813
$947$	−52.8383	−1.71701	−0.858507	−	0.512802i	$-0.828607\pi$
$947$	−52.8383	−1.71701	−0.858507	+	0.512802i	$0.828607\pi$
$948$	1.83579	0.0596237
$949$	−36.2295	−1.17606
$950$	−25.8590	−0.838976
$951$	−25.8991	−0.839836
$952$	−5.03218	−0.163094
$953$	29.2455	0.947354	0.473677	−	0.880699i	$-0.342926\pi$
$953$	29.2455	0.947354	0.473677	+	0.880699i	$0.342926\pi$
$954$	31.4579	1.01849
$955$	0.299847	0.00970283
$956$	0.154408	0.00499390
$957$	16.3646	0.528993
$958$	−24.8611	−0.803224
$959$	4.79566	0.154860
$960$	−1.39161	−0.0449140
$961$	28.5567	0.921183
$962$	59.6114	1.92195
$963$	−61.7161	−1.98877
$964$	1.49421	0.0481252
$965$	1.05385	0.0339248
$966$	−37.0229	−1.19119
$967$	23.4440	0.753909	0.376955	−	0.926232i	$-0.376971\pi$
$967$	23.4440	0.753909	0.376955	+	0.926232i	$0.376971\pi$
$968$	2.76970	0.0890217
$969$	9.63093	0.309390
$970$	−1.61347	−0.0518054
$971$	0.932839	0.0299362	0.0149681	−	0.999888i	$-0.495235\pi$
$971$	0.932839	0.0299362	0.0149681	+	0.999888i	$0.495235\pi$
$972$	−1.60732	−0.0515547
$973$	−26.3989	−0.846310
$974$	−40.1578	−1.28674
$975$	82.2154	2.63300
$976$	6.31025	0.201986
$977$	−36.9271	−1.18140	−0.590701	−	0.806890i	$-0.701149\pi$
$977$	−36.9271	−1.18140	−0.590701	+	0.806890i	$0.701149\pi$
$978$	58.7277	1.87790
$979$	−2.16176	−0.0690900
$980$	0.0198361	0.000633640 0
$981$	−77.8599	−2.48587
$982$	10.0006	0.319132
$983$	45.2768	1.44411	0.722054	−	0.691837i	$-0.243198\pi$
$983$	45.2768	1.44411	0.722054	+	0.691837i	$0.243198\pi$
$984$	−63.8460	−2.03534
$985$	−0.221109	−0.00704513
$986$	8.79585	0.280117
$987$	21.0773	0.670899
$988$	1.74376	0.0554764
$989$	5.26780	0.167506
$990$	0.409887	0.0130271
$991$	28.8094	0.915161	0.457580	−	0.889168i	$-0.348716\pi$
$991$	28.8094	0.915161	0.457580	+	0.889168i	$0.348716\pi$
$992$	−3.45439	−0.109677
$993$	−92.6334	−2.93963
$994$	−0.0539018	−0.00170966
$995$	0.533751	0.0169211
$996$	3.30369	0.104682
$997$	5.54900	0.175739	0.0878693	−	0.996132i	$-0.471994\pi$
$997$	5.54900	0.175739	0.0878693	+	0.996132i	$0.471994\pi$
$998$	−45.6062	−1.44364
$999$	21.6379	0.684594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.18	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.44193 q^{2} +2.68271 q^{3} +0.0791741 q^{4} -0.0677310 q^{5} -3.86829 q^{6} +1.81686 q^{7} +2.76970 q^{8} +4.19693 q^{9} +O(q^{10})\)	\(q-1.44193 q^{2} +2.68271 q^{3} +0.0791741 q^{4} -0.0677310 q^{5} -3.86829 q^{6} +1.81686 q^{7} +2.76970 q^{8} +4.19693 q^{9} +0.0976637 q^{10} +1.00000 q^{11} +0.212401 q^{12} -6.13491 q^{13} -2.61980 q^{14} -0.181703 q^{15} -4.15208 q^{16} -1.00000 q^{17} -6.05169 q^{18} -3.59000 q^{19} -0.00536255 q^{20} +4.87412 q^{21} -1.44193 q^{22} +5.26780 q^{23} +7.43031 q^{24} -4.99541 q^{25} +8.84614 q^{26} +3.21100 q^{27} +0.143849 q^{28} +6.10004 q^{29} +0.262003 q^{30} -7.71730 q^{31} +0.447617 q^{32} +2.68271 q^{33} +1.44193 q^{34} -0.123058 q^{35} +0.332288 q^{36} +6.73869 q^{37} +5.17655 q^{38} -16.4582 q^{39} -0.187595 q^{40} -8.59264 q^{41} -7.02816 q^{42} +1.00000 q^{43} +0.0791741 q^{44} -0.284262 q^{45} -7.59582 q^{46} +4.32434 q^{47} -11.1388 q^{48} -3.69900 q^{49} +7.20306 q^{50} -2.68271 q^{51} -0.485726 q^{52} -5.19819 q^{53} -4.63005 q^{54} -0.0677310 q^{55} +5.03218 q^{56} -9.63093 q^{57} -8.79585 q^{58} -9.24554 q^{59} -0.0143861 q^{60} -1.51978 q^{61} +11.1278 q^{62} +7.62524 q^{63} +7.65873 q^{64} +0.415524 q^{65} -3.86829 q^{66} -13.7993 q^{67} -0.0791741 q^{68} +14.1320 q^{69} +0.177442 q^{70} +0.0205748 q^{71} +11.6242 q^{72} +5.90546 q^{73} -9.71674 q^{74} -13.4012 q^{75} -0.284235 q^{76} +1.81686 q^{77} +23.7316 q^{78} +8.64303 q^{79} +0.281225 q^{80} -3.97659 q^{81} +12.3900 q^{82} +15.5540 q^{83} +0.385904 q^{84} +0.0677310 q^{85} -1.44193 q^{86} +16.3646 q^{87} +2.76970 q^{88} -2.16176 q^{89} +0.409887 q^{90} -11.1463 q^{91} +0.417073 q^{92} -20.7033 q^{93} -6.23541 q^{94} +0.243155 q^{95} +1.20083 q^{96} -16.5207 q^{97} +5.33372 q^{98} +4.19693 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 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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