LMFDB - Embedded newform 8026.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.70930 q^{3} +1.00000 q^{4} +1.99036 q^{5} +2.70930 q^{6} -3.73074 q^{7} -1.00000 q^{8} +4.34031 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.70930 q^{3} +1.00000 q^{4} +1.99036 q^{5} +2.70930 q^{6} -3.73074 q^{7} -1.00000 q^{8} +4.34031 q^{9} -1.99036 q^{10} -2.09984 q^{11} -2.70930 q^{12} -0.0560417 q^{13} +3.73074 q^{14} -5.39249 q^{15} +1.00000 q^{16} -1.06584 q^{17} -4.34031 q^{18} -7.11716 q^{19} +1.99036 q^{20} +10.1077 q^{21} +2.09984 q^{22} +1.33002 q^{23} +2.70930 q^{24} -1.03846 q^{25} +0.0560417 q^{26} -3.63130 q^{27} -3.73074 q^{28} +5.37910 q^{29} +5.39249 q^{30} -2.16997 q^{31} -1.00000 q^{32} +5.68908 q^{33} +1.06584 q^{34} -7.42551 q^{35} +4.34031 q^{36} +4.02282 q^{37} +7.11716 q^{38} +0.151834 q^{39} -1.99036 q^{40} +11.8257 q^{41} -10.1077 q^{42} -4.36065 q^{43} -2.09984 q^{44} +8.63878 q^{45} -1.33002 q^{46} +10.5641 q^{47} -2.70930 q^{48} +6.91840 q^{49} +1.03846 q^{50} +2.88767 q^{51} -0.0560417 q^{52} +2.41023 q^{53} +3.63130 q^{54} -4.17943 q^{55} +3.73074 q^{56} +19.2825 q^{57} -5.37910 q^{58} -6.27169 q^{59} -5.39249 q^{60} -11.0521 q^{61} +2.16997 q^{62} -16.1925 q^{63} +1.00000 q^{64} -0.111543 q^{65} -5.68908 q^{66} -3.64226 q^{67} -1.06584 q^{68} -3.60344 q^{69} +7.42551 q^{70} +5.93777 q^{71} -4.34031 q^{72} +14.1087 q^{73} -4.02282 q^{74} +2.81350 q^{75} -7.11716 q^{76} +7.83393 q^{77} -0.151834 q^{78} -2.79471 q^{79} +1.99036 q^{80} -3.18265 q^{81} -11.8257 q^{82} +15.1664 q^{83} +10.1077 q^{84} -2.12140 q^{85} +4.36065 q^{86} -14.5736 q^{87} +2.09984 q^{88} -2.69446 q^{89} -8.63878 q^{90} +0.209077 q^{91} +1.33002 q^{92} +5.87910 q^{93} -10.5641 q^{94} -14.1657 q^{95} +2.70930 q^{96} +4.22310 q^{97} -6.91840 q^{98} -9.11393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.70930	−1.56422	−0.782108	−	0.623143i	$-0.785855\pi$
$3$	−2.70930	−1.56422	−0.782108	+	0.623143i	$0.785855\pi$
$4$	1.00000	0.500000
$5$	1.99036	0.890117	0.445058	−	0.895502i	$-0.353183\pi$
$5$	1.99036	0.890117	0.445058	+	0.895502i	$0.353183\pi$
$6$	2.70930	1.10607
$7$	−3.73074	−1.41009	−0.705043	−	0.709165i	$-0.749072\pi$
$7$	−3.73074	−1.41009	−0.705043	+	0.709165i	$0.749072\pi$
$8$	−1.00000	−0.353553
$9$	4.34031	1.44677
$10$	−1.99036	−0.629408
$11$	−2.09984	−0.633124	−0.316562	−	0.948572i	$-0.602529\pi$
$11$	−2.09984	−0.633124	−0.316562	+	0.948572i	$0.602529\pi$
$12$	−2.70930	−0.782108
$13$	−0.0560417	−0.0155432	−0.00777159	−	0.999970i	$-0.502474\pi$
$13$	−0.0560417	−0.0155432	−0.00777159	+	0.999970i	$0.502474\pi$
$14$	3.73074	0.997081
$15$	−5.39249	−1.39233
$16$	1.00000	0.250000
$17$	−1.06584	−0.258504	−0.129252	−	0.991612i	$-0.541258\pi$
$17$	−1.06584	−0.258504	−0.129252	+	0.991612i	$0.541258\pi$
$18$	−4.34031	−1.02302
$19$	−7.11716	−1.63279	−0.816394	−	0.577495i	$-0.804030\pi$
$19$	−7.11716	−1.63279	−0.816394	+	0.577495i	$0.804030\pi$
$20$	1.99036	0.445058
$21$	10.1077	2.20568
$22$	2.09984	0.447686
$23$	1.33002	0.277329	0.138665	−	0.990339i	$-0.455719\pi$
$23$	1.33002	0.277329	0.138665	+	0.990339i	$0.455719\pi$
$24$	2.70930	0.553034
$25$	−1.03846	−0.207692
$26$	0.0560417	0.0109907
$27$	−3.63130	−0.698844
$28$	−3.73074	−0.705043
$29$	5.37910	0.998873	0.499436	−	0.866351i	$-0.333540\pi$
$29$	5.37910	0.998873	0.499436	+	0.866351i	$0.333540\pi$
$30$	5.39249	0.984529
$31$	−2.16997	−0.389738	−0.194869	−	0.980829i	$-0.562428\pi$
$31$	−2.16997	−0.389738	−0.194869	+	0.980829i	$0.562428\pi$
$32$	−1.00000	−0.176777
$33$	5.68908	0.990343
$34$	1.06584	0.182790
$35$	−7.42551	−1.25514
$36$	4.34031	0.723385
$37$	4.02282	0.661347	0.330673	−	0.943745i	$-0.392724\pi$
$37$	4.02282	0.661347	0.330673	+	0.943745i	$0.392724\pi$
$38$	7.11716	1.15456
$39$	0.151834	0.0243129
$40$	−1.99036	−0.314704
$41$	11.8257	1.84686	0.923431	−	0.383764i	$-0.125372\pi$
$41$	11.8257	1.84686	0.923431	+	0.383764i	$0.125372\pi$
$42$	−10.1077	−1.55965
$43$	−4.36065	−0.664993	−0.332497	−	0.943104i	$-0.607891\pi$
$43$	−4.36065	−0.664993	−0.332497	+	0.943104i	$0.607891\pi$
$44$	−2.09984	−0.316562
$45$	8.63878	1.28779
$46$	−1.33002	−0.196101
$47$	10.5641	1.54094	0.770470	−	0.637477i	$-0.220022\pi$
$47$	10.5641	1.54094	0.770470	+	0.637477i	$0.220022\pi$
$48$	−2.70930	−0.391054
$49$	6.91840	0.988342
$50$	1.03846	0.146861
$51$	2.88767	0.404355
$52$	−0.0560417	−0.00777159
$53$	2.41023	0.331071	0.165535	−	0.986204i	$-0.447065\pi$
$53$	2.41023	0.331071	0.165535	+	0.986204i	$0.447065\pi$
$54$	3.63130	0.494157
$55$	−4.17943	−0.563554
$56$	3.73074	0.498541
$57$	19.2825	2.55403
$58$	−5.37910	−0.706310
$59$	−6.27169	−0.816504	−0.408252	−	0.912869i	$-0.633862\pi$
$59$	−6.27169	−0.816504	−0.408252	+	0.912869i	$0.633862\pi$
$60$	−5.39249	−0.696167
$61$	−11.0521	−1.41508	−0.707538	−	0.706675i	$-0.750194\pi$
$61$	−11.0521	−1.41508	−0.707538	+	0.706675i	$0.750194\pi$
$62$	2.16997	0.275586
$63$	−16.1925	−2.04007
$64$	1.00000	0.125000
$65$	−0.111543	−0.0138352
$66$	−5.68908	−0.700278
$67$	−3.64226	−0.444973	−0.222487	−	0.974936i	$-0.571417\pi$
$67$	−3.64226	−0.444973	−0.222487	+	0.974936i	$0.571417\pi$
$68$	−1.06584	−0.129252
$69$	−3.60344	−0.433803
$70$	7.42551	0.887519
$71$	5.93777	0.704684	0.352342	−	0.935871i	$-0.385385\pi$
$71$	5.93777	0.704684	0.352342	+	0.935871i	$0.385385\pi$
$72$	−4.34031	−0.511510
$73$	14.1087	1.65130	0.825648	−	0.564186i	$-0.190810\pi$
$73$	14.1087	1.65130	0.825648	+	0.564186i	$0.190810\pi$
$74$	−4.02282	−0.467643
$75$	2.81350	0.324875
$76$	−7.11716	−0.816394
$77$	7.83393	0.892760
$78$	−0.151834	−0.0171918
$79$	−2.79471	−0.314429	−0.157215	−	0.987564i	$-0.550251\pi$
$79$	−2.79471	−0.314429	−0.157215	+	0.987564i	$0.550251\pi$
$80$	1.99036	0.222529
$81$	−3.18265	−0.353628
$82$	−11.8257	−1.30593
$83$	15.1664	1.66473	0.832365	−	0.554228i	$-0.186986\pi$
$83$	15.1664	1.66473	0.832365	+	0.554228i	$0.186986\pi$
$84$	10.1077	1.10284
$85$	−2.12140	−0.230098
$86$	4.36065	0.470221
$87$	−14.5736	−1.56245
$88$	2.09984	0.223843
$89$	−2.69446	−0.285612	−0.142806	−	0.989751i	$-0.545613\pi$
$89$	−2.69446	−0.285612	−0.142806	+	0.989751i	$0.545613\pi$
$90$	−8.63878	−0.910608
$91$	0.209077	0.0219172
$92$	1.33002	0.138665
$93$	5.87910	0.609634
$94$	−10.5641	−1.08961
$95$	−14.1657	−1.45337
$96$	2.70930	0.276517
$97$	4.22310	0.428791	0.214395	−	0.976747i	$-0.431222\pi$
$97$	4.22310	0.428791	0.214395	+	0.976747i	$0.431222\pi$
$98$	−6.91840	−0.698864
$99$	−9.11393	−0.915985
$100$	−1.03846	−0.103846
$101$	−7.06071	−0.702567	−0.351283	−	0.936269i	$-0.614255\pi$
$101$	−7.06071	−0.702567	−0.351283	+	0.936269i	$0.614255\pi$
$102$	−2.88767	−0.285922
$103$	14.2881	1.40784	0.703922	−	0.710277i	$-0.251430\pi$
$103$	14.2881	1.40784	0.703922	+	0.710277i	$0.251430\pi$
$104$	0.0560417	0.00549534
$105$	20.1179	1.96331
$106$	−2.41023	−0.234102
$107$	−4.09624	−0.395998	−0.197999	−	0.980202i	$-0.563444\pi$
$107$	−4.09624	−0.395998	−0.197999	+	0.980202i	$0.563444\pi$
$108$	−3.63130	−0.349422
$109$	−8.47072	−0.811347	−0.405674	−	0.914018i	$-0.632963\pi$
$109$	−8.47072	−0.811347	−0.405674	+	0.914018i	$0.632963\pi$
$110$	4.17943	0.398493
$111$	−10.8990	−1.03449
$112$	−3.73074	−0.352521
$113$	0.587298	0.0552484	0.0276242	−	0.999618i	$-0.491206\pi$
$113$	0.587298	0.0552484	0.0276242	+	0.999618i	$0.491206\pi$
$114$	−19.2825	−1.80597
$115$	2.64723	0.246855
$116$	5.37910	0.499436
$117$	−0.243238	−0.0224874
$118$	6.27169	0.577355
$119$	3.97636	0.364512
$120$	5.39249	0.492264
$121$	−6.59069	−0.599154
$122$	11.0521	1.00061
$123$	−32.0394	−2.88889
$124$	−2.16997	−0.194869
$125$	−12.0187	−1.07499
$126$	16.1925	1.44255
$127$	−11.6263	−1.03166	−0.515832	−	0.856690i	$-0.672517\pi$
$127$	−11.6263	−1.03166	−0.515832	+	0.856690i	$0.672517\pi$
$128$	−1.00000	−0.0883883
$129$	11.8143	1.04019
$130$	0.111543	0.00978299
$131$	16.0122	1.39899	0.699494	−	0.714638i	$-0.253409\pi$
$131$	16.0122	1.39899	0.699494	+	0.714638i	$0.253409\pi$
$132$	5.68908	0.495171
$133$	26.5523	2.30237
$134$	3.64226	0.314644
$135$	−7.22760	−0.622052
$136$	1.06584	0.0913948
$137$	5.45669	0.466197	0.233098	−	0.972453i	$-0.425114\pi$
$137$	5.45669	0.466197	0.233098	+	0.972453i	$0.425114\pi$
$138$	3.60344	0.306745
$139$	−5.45191	−0.462425	−0.231212	−	0.972903i	$-0.574269\pi$
$139$	−5.45191	−0.462425	−0.231212	+	0.972903i	$0.574269\pi$
$140$	−7.42551	−0.627571
$141$	−28.6214	−2.41036
$142$	−5.93777	−0.498287
$143$	0.117678	0.00984076
$144$	4.34031	0.361692
$145$	10.7063	0.889114
$146$	−14.1087	−1.16764
$147$	−18.7440	−1.54598
$148$	4.02282	0.330673
$149$	17.2939	1.41677	0.708385	−	0.705826i	$-0.249424\pi$
$149$	17.2939	1.41677	0.708385	+	0.705826i	$0.249424\pi$
$150$	−2.81350	−0.229722
$151$	−3.62836	−0.295272	−0.147636	−	0.989042i	$-0.547166\pi$
$151$	−3.62836	−0.295272	−0.147636	+	0.989042i	$0.547166\pi$
$152$	7.11716	0.577278
$153$	−4.62606	−0.373995
$154$	−7.83393	−0.631276
$155$	−4.31903	−0.346912
$156$	0.151834	0.0121564
$157$	20.8857	1.66686	0.833432	−	0.552622i	$-0.186373\pi$
$157$	20.8857	1.66686	0.833432	+	0.552622i	$0.186373\pi$
$158$	2.79471	0.222335
$159$	−6.53004	−0.517866
$160$	−1.99036	−0.157352
$161$	−4.96197	−0.391058
$162$	3.18265	0.250052
$163$	−8.99841	−0.704810	−0.352405	−	0.935848i	$-0.614636\pi$
$163$	−8.99841	−0.704810	−0.352405	+	0.935848i	$0.614636\pi$
$164$	11.8257	0.923431
$165$	11.3233	0.881520
$166$	−15.1664	−1.17714
$167$	25.2738	1.95575	0.977873	−	0.209200i	$-0.0670858\pi$
$167$	25.2738	1.95575	0.977873	+	0.209200i	$0.0670858\pi$
$168$	−10.1077	−0.779825
$169$	−12.9969	−0.999758
$170$	2.12140	0.162704
$171$	−30.8907	−2.36227
$172$	−4.36065	−0.332497
$173$	−4.80537	−0.365346	−0.182673	−	0.983174i	$-0.558475\pi$
$173$	−4.80537	−0.365346	−0.182673	+	0.983174i	$0.558475\pi$
$174$	14.5736	1.10482
$175$	3.87422	0.292864
$176$	−2.09984	−0.158281
$177$	16.9919	1.27719
$178$	2.69446	0.201958
$179$	−12.0582	−0.901270	−0.450635	−	0.892708i	$-0.648802\pi$
$179$	−12.0582	−0.901270	−0.450635	+	0.892708i	$0.648802\pi$
$180$	8.63878	0.643897
$181$	−14.4761	−1.07600	−0.538000	−	0.842945i	$-0.680820\pi$
$181$	−14.4761	−1.07600	−0.538000	+	0.842945i	$0.680820\pi$
$182$	−0.209077	−0.0154978
$183$	29.9434	2.21348
$184$	−1.33002	−0.0980507
$185$	8.00686	0.588676
$186$	−5.87910	−0.431077
$187$	2.23808	0.163665
$188$	10.5641	0.770470
$189$	13.5474	0.985430
$190$	14.1657	1.02769
$191$	−14.7950	−1.07053	−0.535264	−	0.844685i	$-0.679788\pi$
$191$	−14.7950	−1.07053	−0.535264	+	0.844685i	$0.679788\pi$
$192$	−2.70930	−0.195527
$193$	−9.31915	−0.670807	−0.335403	−	0.942075i	$-0.608873\pi$
$193$	−9.31915	−0.670807	−0.335403	+	0.942075i	$0.608873\pi$
$194$	−4.22310	−0.303201
$195$	0.302204	0.0216413
$196$	6.91840	0.494171
$197$	3.12080	0.222348	0.111174	−	0.993801i	$-0.464539\pi$
$197$	3.12080	0.222348	0.111174	+	0.993801i	$0.464539\pi$
$198$	9.11393	0.647699
$199$	8.57627	0.607956	0.303978	−	0.952679i	$-0.401685\pi$
$199$	8.57627	0.607956	0.303978	+	0.952679i	$0.401685\pi$
$200$	1.03846	0.0734303
$201$	9.86799	0.696034
$202$	7.06071	0.496790
$203$	−20.0680	−1.40850
$204$	2.88767	0.202178
$205$	23.5374	1.64392
$206$	−14.2881	−0.995496
$207$	5.77272	0.401232
$208$	−0.0560417	−0.00388579
$209$	14.9449	1.03376
$210$	−20.1179	−1.38827
$211$	0.343650	0.0236579	0.0118289	−	0.999930i	$-0.496235\pi$
$211$	0.343650	0.0236579	0.0118289	+	0.999930i	$0.496235\pi$
$212$	2.41023	0.165535
$213$	−16.0872	−1.10228
$214$	4.09624	0.280013
$215$	−8.67927	−0.591922
$216$	3.63130	0.247079
$217$	8.09559	0.549564
$218$	8.47072	0.573709
$219$	−38.2246	−2.58298
$220$	−4.17943	−0.281777
$221$	0.0597314	0.00401797
$222$	10.8990	0.731494
$223$	−10.0333	−0.671877	−0.335939	−	0.941884i	$-0.609053\pi$
$223$	−10.0333	−0.671877	−0.335939	+	0.941884i	$0.609053\pi$
$224$	3.73074	0.249270
$225$	−4.50724	−0.300483
$226$	−0.587298	−0.0390665
$227$	−26.0999	−1.73231	−0.866155	−	0.499775i	$-0.833416\pi$
$227$	−26.0999	−1.73231	−0.866155	+	0.499775i	$0.833416\pi$
$228$	19.2825	1.27702
$229$	10.6621	0.704569	0.352285	−	0.935893i	$-0.385405\pi$
$229$	10.6621	0.704569	0.352285	+	0.935893i	$0.385405\pi$
$230$	−2.64723	−0.174553
$231$	−21.2245	−1.39647
$232$	−5.37910	−0.353155
$233$	−15.5280	−1.01728	−0.508638	−	0.860981i	$-0.669851\pi$
$233$	−15.5280	−1.01728	−0.508638	+	0.860981i	$0.669851\pi$
$234$	0.243238	0.0159010
$235$	21.0265	1.37162
$236$	−6.27169	−0.408252
$237$	7.57171	0.491835
$238$	−3.97636	−0.257749
$239$	25.5379	1.65191	0.825955	−	0.563737i	$-0.190637\pi$
$239$	25.5379	1.65191	0.825955	+	0.563737i	$0.190637\pi$
$240$	−5.39249	−0.348084
$241$	−2.48598	−0.160136	−0.0800679	−	0.996789i	$-0.525514\pi$
$241$	−2.48598	−0.160136	−0.0800679	+	0.996789i	$0.525514\pi$
$242$	6.59069	0.423666
$243$	19.5166	1.25199
$244$	−11.0521	−0.707538
$245$	13.7701	0.879740
$246$	32.0394	2.04275
$247$	0.398858	0.0253787
$248$	2.16997	0.137793
$249$	−41.0904	−2.60400
$250$	12.0187	0.760131
$251$	16.1002	1.01623	0.508117	−	0.861288i	$-0.330342\pi$
$251$	16.1002	1.01623	0.508117	+	0.861288i	$0.330342\pi$
$252$	−16.1925	−1.02003
$253$	−2.79283	−0.175584
$254$	11.6263	0.729497
$255$	5.74752	0.359923
$256$	1.00000	0.0625000
$257$	29.1843	1.82046	0.910232	−	0.414099i	$-0.135903\pi$
$257$	29.1843	1.82046	0.910232	+	0.414099i	$0.135903\pi$
$258$	−11.8143	−0.735527
$259$	−15.0081	−0.932556
$260$	−0.111543	−0.00691762
$261$	23.3469	1.44514
$262$	−16.0122	−0.989234
$263$	13.3144	0.821003	0.410502	−	0.911860i	$-0.365354\pi$
$263$	13.3144	0.821003	0.410502	+	0.911860i	$0.365354\pi$
$264$	−5.68908	−0.350139
$265$	4.79723	0.294691
$266$	−26.5523	−1.62802
$267$	7.30010	0.446759
$268$	−3.64226	−0.222487
$269$	−22.7223	−1.38541	−0.692703	−	0.721223i	$-0.743580\pi$
$269$	−22.7223	−1.38541	−0.692703	+	0.721223i	$0.743580\pi$
$270$	7.22760	0.439857
$271$	−1.17923	−0.0716329	−0.0358164	−	0.999358i	$-0.511403\pi$
$271$	−1.17923	−0.0716329	−0.0358164	+	0.999358i	$0.511403\pi$
$272$	−1.06584	−0.0646259
$273$	−0.566452	−0.0342832
$274$	−5.45669	−0.329651
$275$	2.18060	0.131495
$276$	−3.60344	−0.216901
$277$	21.5260	1.29337	0.646687	−	0.762755i	$-0.276154\pi$
$277$	21.5260	1.29337	0.646687	+	0.762755i	$0.276154\pi$
$278$	5.45191	0.326984
$279$	−9.41834	−0.563861
$280$	7.42551	0.443759
$281$	27.0524	1.61381	0.806906	−	0.590680i	$-0.201140\pi$
$281$	27.0524	1.61381	0.806906	+	0.590680i	$0.201140\pi$
$282$	28.6214	1.70438
$283$	4.66465	0.277284	0.138642	−	0.990343i	$-0.455726\pi$
$283$	4.66465	0.277284	0.138642	+	0.990343i	$0.455726\pi$
$284$	5.93777	0.352342
$285$	38.3792	2.27339
$286$	−0.117678	−0.00695847
$287$	−44.1185	−2.60424
$288$	−4.34031	−0.255755
$289$	−15.8640	−0.933176
$290$	−10.7063	−0.628698
$291$	−11.4416	−0.670721
$292$	14.1087	0.825648
$293$	−22.2070	−1.29735	−0.648675	−	0.761066i	$-0.724676\pi$
$293$	−22.2070	−1.29735	−0.648675	+	0.761066i	$0.724676\pi$
$294$	18.7440	1.09317
$295$	−12.4829	−0.726784
$296$	−4.02282	−0.233821
$297$	7.62513	0.442455
$298$	−17.2939	−1.00181
$299$	−0.0745368	−0.00431058
$300$	2.81350	0.162438
$301$	16.2684	0.937698
$302$	3.62836	0.208789
$303$	19.1296	1.09897
$304$	−7.11716	−0.408197
$305$	−21.9977	−1.25958
$306$	4.62606	0.264454
$307$	18.0904	1.03247	0.516236	−	0.856446i	$-0.327333\pi$
$307$	18.0904	1.03247	0.516236	+	0.856446i	$0.327333\pi$
$308$	7.83393	0.446380
$309$	−38.7107	−2.20217
$310$	4.31903	0.245304
$311$	−7.92331	−0.449290	−0.224645	−	0.974441i	$-0.572122\pi$
$311$	−7.92331	−0.449290	−0.224645	+	0.974441i	$0.572122\pi$
$312$	−0.151834	−0.00859590
$313$	−31.2483	−1.76626	−0.883129	−	0.469129i	$-0.844568\pi$
$313$	−31.2483	−1.76626	−0.883129	+	0.469129i	$0.844568\pi$
$314$	−20.8857	−1.17865
$315$	−32.2290	−1.81590
$316$	−2.79471	−0.157215
$317$	−6.46094	−0.362882	−0.181441	−	0.983402i	$-0.558076\pi$
$317$	−6.46094	−0.362882	−0.181441	+	0.983402i	$0.558076\pi$
$318$	6.53004	0.366186
$319$	−11.2952	−0.632411
$320$	1.99036	0.111265
$321$	11.0979	0.619426
$322$	4.96197	0.276520
$323$	7.58574	0.422082
$324$	−3.18265	−0.176814
$325$	0.0581971	0.00322820
$326$	8.99841	0.498376
$327$	22.9497	1.26912
$328$	−11.8257	−0.652965
$329$	−39.4120	−2.17286
$330$	−11.3233	−0.623329
$331$	−8.62997	−0.474346	−0.237173	−	0.971467i	$-0.576221\pi$
$331$	−8.62997	−0.474346	−0.237173	+	0.971467i	$0.576221\pi$
$332$	15.1664	0.832365
$333$	17.4603	0.956816
$334$	−25.2738	−1.38292
$335$	−7.24942	−0.396078
$336$	10.1077	0.551419
$337$	19.5269	1.06370	0.531849	−	0.846839i	$-0.321497\pi$
$337$	19.5269	1.06370	0.531849	+	0.846839i	$0.321497\pi$
$338$	12.9969	0.706936
$339$	−1.59117	−0.0864203
$340$	−2.12140	−0.115049
$341$	4.55658	0.246753
$342$	30.8907	1.67038
$343$	0.304442	0.0164383
$344$	4.36065	0.235111
$345$	−7.17214	−0.386135
$346$	4.80537	0.258338
$347$	30.5519	1.64011	0.820055	−	0.572284i	$-0.193943\pi$
$347$	30.5519	1.64011	0.820055	+	0.572284i	$0.193943\pi$
$348$	−14.5736	−0.781226
$349$	−1.57622	−0.0843729	−0.0421865	−	0.999110i	$-0.513432\pi$
$349$	−1.57622	−0.0843729	−0.0421865	+	0.999110i	$0.513432\pi$
$350$	−3.87422	−0.207086
$351$	0.203504	0.0108622
$352$	2.09984	0.111922
$353$	12.1035	0.644206	0.322103	−	0.946705i	$-0.395610\pi$
$353$	12.1035	0.644206	0.322103	+	0.946705i	$0.395610\pi$
$354$	−16.9919	−0.903108
$355$	11.8183	0.627251
$356$	−2.69446	−0.142806
$357$	−10.7732	−0.570176
$358$	12.0582	0.637294
$359$	22.1772	1.17047	0.585233	−	0.810865i	$-0.301003\pi$
$359$	22.1772	1.17047	0.585233	+	0.810865i	$0.301003\pi$
$360$	−8.63878	−0.455304
$361$	31.6540	1.66600
$362$	14.4761	0.760846
$363$	17.8562	0.937205
$364$	0.209077	0.0109586
$365$	28.0814	1.46985
$366$	−29.9434	−1.56517
$367$	−14.3109	−0.747024	−0.373512	−	0.927625i	$-0.621847\pi$
$367$	−14.3109	−0.747024	−0.373512	+	0.927625i	$0.621847\pi$
$368$	1.33002	0.0693323
$369$	51.3271	2.67198
$370$	−8.00686	−0.416257
$371$	−8.99194	−0.466838
$372$	5.87910	0.304817
$373$	13.6950	0.709101	0.354550	−	0.935037i	$-0.384634\pi$
$373$	13.6950	0.709101	0.354550	+	0.935037i	$0.384634\pi$
$374$	−2.23808	−0.115729
$375$	32.5623	1.68151
$376$	−10.5641	−0.544804
$377$	−0.301454	−0.0155257
$378$	−13.5474	−0.696804
$379$	19.8792	1.02113	0.510563	−	0.859841i	$-0.329437\pi$
$379$	19.8792	1.02113	0.510563	+	0.859841i	$0.329437\pi$
$380$	−14.1657	−0.726686
$381$	31.4991	1.61375
$382$	14.7950	0.756977
$383$	35.6083	1.81950	0.909750	−	0.415157i	$-0.136273\pi$
$383$	35.6083	1.81950	0.909750	+	0.415157i	$0.136273\pi$
$384$	2.70930	0.138258
$385$	15.5924	0.794660
$386$	9.31915	0.474332
$387$	−18.9266	−0.962092
$388$	4.22310	0.214395
$389$	−12.6316	−0.640447	−0.320224	−	0.947342i	$-0.603758\pi$
$389$	−12.6316	−0.640447	−0.320224	+	0.947342i	$0.603758\pi$
$390$	−0.302204	−0.0153027
$391$	−1.41759	−0.0716906
$392$	−6.91840	−0.349432
$393$	−43.3817	−2.18832
$394$	−3.12080	−0.157224
$395$	−5.56248	−0.279879
$396$	−9.11393	−0.457992
$397$	−26.0023	−1.30502	−0.652508	−	0.757782i	$-0.726283\pi$
$397$	−26.0023	−1.30502	−0.652508	+	0.757782i	$0.726283\pi$
$398$	−8.57627	−0.429890
$399$	−71.9380	−3.60141
$400$	−1.03846	−0.0519231
$401$	−18.3997	−0.918835	−0.459418	−	0.888220i	$-0.651942\pi$
$401$	−18.3997	−0.918835	−0.459418	+	0.888220i	$0.651942\pi$
$402$	−9.86799	−0.492171
$403$	0.121609	0.00605777
$404$	−7.06071	−0.351283
$405$	−6.33462	−0.314770
$406$	20.0680	0.995958
$407$	−8.44725	−0.418715
$408$	−2.88767	−0.142961
$409$	−11.5467	−0.570948	−0.285474	−	0.958386i	$-0.592151\pi$
$409$	−11.5467	−0.570948	−0.285474	+	0.958386i	$0.592151\pi$
$410$	−23.5374	−1.16243
$411$	−14.7838	−0.729232
$412$	14.2881	0.703922
$413$	23.3980	1.15134
$414$	−5.77272	−0.283714
$415$	30.1866	1.48180
$416$	0.0560417	0.00274767
$417$	14.7709	0.723332
$418$	−14.9449	−0.730977
$419$	8.44652	0.412640	0.206320	−	0.978485i	$-0.433851\pi$
$419$	8.44652	0.412640	0.206320	+	0.978485i	$0.433851\pi$
$420$	20.1179	0.981655
$421$	−7.29503	−0.355538	−0.177769	−	0.984072i	$-0.556888\pi$
$421$	−7.29503	−0.355538	−0.177769	+	0.984072i	$0.556888\pi$
$422$	−0.343650	−0.0167286
$423$	45.8516	2.22938
$424$	−2.41023	−0.117051
$425$	1.10683	0.0536892
$426$	16.0872	0.779428
$427$	41.2325	1.99538
$428$	−4.09624	−0.197999
$429$	−0.318826	−0.0153931
$430$	8.67927	0.418552
$431$	−22.5907	−1.08816	−0.544078	−	0.839035i	$-0.683120\pi$
$431$	−22.5907	−1.08816	−0.544078	+	0.839035i	$0.683120\pi$
$432$	−3.63130	−0.174711
$433$	−15.5705	−0.748270	−0.374135	−	0.927374i	$-0.622060\pi$
$433$	−15.5705	−0.748270	−0.374135	+	0.927374i	$0.622060\pi$
$434$	−8.09559	−0.388601
$435$	−29.0067	−1.39076
$436$	−8.47072	−0.405674
$437$	−9.46600	−0.452820
$438$	38.2246	1.82644
$439$	−28.9085	−1.37973	−0.689863	−	0.723940i	$-0.742329\pi$
$439$	−28.9085	−1.37973	−0.689863	+	0.723940i	$0.742329\pi$
$440$	4.17943	0.199247
$441$	30.0280	1.42990
$442$	−0.0597314	−0.00284113
$443$	−35.2291	−1.67378	−0.836892	−	0.547369i	$-0.815630\pi$
$443$	−35.2291	−1.67378	−0.836892	+	0.547369i	$0.815630\pi$
$444$	−10.8990	−0.517244
$445$	−5.36295	−0.254228
$446$	10.0333	0.475089
$447$	−46.8543	−2.21613
$448$	−3.73074	−0.176261
$449$	−17.0986	−0.806933	−0.403467	−	0.914994i	$-0.632195\pi$
$449$	−17.0986	−0.806933	−0.403467	+	0.914994i	$0.632195\pi$
$450$	4.50724	0.212473
$451$	−24.8320	−1.16929
$452$	0.587298	0.0276242
$453$	9.83032	0.461869
$454$	26.0999	1.22493
$455$	0.416138	0.0195089
$456$	−19.2825	−0.902987
$457$	−8.18456	−0.382857	−0.191429	−	0.981507i	$-0.561312\pi$
$457$	−8.18456	−0.382857	−0.191429	+	0.981507i	$0.561312\pi$
$458$	−10.6621	−0.498206
$459$	3.87037	0.180654
$460$	2.64723	0.123428
$461$	−35.9486	−1.67429	−0.837147	−	0.546978i	$-0.815778\pi$
$461$	−35.9486	−1.67429	−0.837147	+	0.546978i	$0.815778\pi$
$462$	21.2245	0.987452
$463$	−30.7560	−1.42935	−0.714676	−	0.699455i	$-0.753426\pi$
$463$	−30.7560	−1.42935	−0.714676	+	0.699455i	$0.753426\pi$
$464$	5.37910	0.249718
$465$	11.7015	0.542646
$466$	15.5280	0.719322
$467$	−3.33174	−0.154174	−0.0770872	−	0.997024i	$-0.524562\pi$
$467$	−3.33174	−0.154174	−0.0770872	+	0.997024i	$0.524562\pi$
$468$	−0.243238	−0.0112437
$469$	13.5883	0.627451
$470$	−21.0265	−0.969879
$471$	−56.5858	−2.60733
$472$	6.27169	0.288678
$473$	9.15665	0.421023
$474$	−7.57171	−0.347780
$475$	7.39090	0.339118
$476$	3.97636	0.182256
$477$	10.4611	0.478983
$478$	−25.5379	−1.16808
$479$	−23.7113	−1.08340	−0.541699	−	0.840573i	$-0.682219\pi$
$479$	−23.7113	−1.08340	−0.541699	+	0.840573i	$0.682219\pi$
$480$	5.39249	0.246132
$481$	−0.225445	−0.0102794
$482$	2.48598	0.113233
$483$	13.4435	0.611699
$484$	−6.59069	−0.299577
$485$	8.40550	0.381674
$486$	−19.5166	−0.885293
$487$	3.27314	0.148320	0.0741601	−	0.997246i	$-0.476372\pi$
$487$	3.27314	0.148320	0.0741601	+	0.997246i	$0.476372\pi$
$488$	11.0521	0.500305
$489$	24.3794	1.10247
$490$	−13.7701	−0.622070
$491$	8.04876	0.363235	0.181618	−	0.983369i	$-0.441867\pi$
$491$	8.04876	0.363235	0.181618	+	0.983369i	$0.441867\pi$
$492$	−32.0394	−1.44445
$493$	−5.73324	−0.258212
$494$	−0.398858	−0.0179455
$495$	−18.1400	−0.815333
$496$	−2.16997	−0.0974345
$497$	−22.1523	−0.993665
$498$	41.0904	1.84130
$499$	34.7193	1.55425	0.777125	−	0.629346i	$-0.216677\pi$
$499$	34.7193	1.55425	0.777125	+	0.629346i	$0.216677\pi$
$500$	−12.0187	−0.537494
$501$	−68.4743	−3.05921
$502$	−16.1002	−0.718586
$503$	−32.0309	−1.42819	−0.714093	−	0.700051i	$-0.753160\pi$
$503$	−32.0309	−1.42819	−0.714093	+	0.700051i	$0.753160\pi$
$504$	16.1925	0.721273
$505$	−14.0534	−0.625367
$506$	2.79283	0.124157
$507$	35.2124	1.56384
$508$	−11.6263	−0.515832
$509$	−34.0106	−1.50749	−0.753746	−	0.657166i	$-0.771755\pi$
$509$	−34.0106	−1.50749	−0.753746	+	0.657166i	$0.771755\pi$
$510$	−5.74752	−0.254504
$511$	−52.6358	−2.32847
$512$	−1.00000	−0.0441942
$513$	25.8445	1.14106
$514$	−29.1843	−1.28726
$515$	28.4384	1.25315
$516$	11.8143	0.520096
$517$	−22.1830	−0.975606
$518$	15.0081	0.659417
$519$	13.0192	0.571479
$520$	0.111543	0.00489150
$521$	9.36887	0.410458	0.205229	−	0.978714i	$-0.434206\pi$
$521$	9.36887	0.410458	0.205229	+	0.978714i	$0.434206\pi$
$522$	−23.3469	−1.02187
$523$	−0.180855	−0.00790824	−0.00395412	−	0.999992i	$-0.501259\pi$
$523$	−0.180855	−0.00790824	−0.00395412	+	0.999992i	$0.501259\pi$
$524$	16.0122	0.699494
$525$	−10.4964	−0.458102
$526$	−13.3144	−0.580537
$527$	2.31284	0.100749
$528$	5.68908	0.247586
$529$	−21.2310	−0.923088
$530$	−4.79723	−0.208378
$531$	−27.2210	−1.18129
$532$	26.5523	1.15119
$533$	−0.662732	−0.0287061
$534$	−7.30010	−0.315906
$535$	−8.15299	−0.352484
$536$	3.64226	0.157322
$537$	32.6692	1.40978
$538$	22.7223	0.979630
$539$	−14.5275	−0.625743
$540$	−7.22760	−0.311026
$541$	24.6418	1.05943	0.529717	−	0.848175i	$-0.322298\pi$
$541$	24.6418	1.05943	0.529717	+	0.848175i	$0.322298\pi$
$542$	1.17923	0.0506521
$543$	39.2201	1.68309
$544$	1.06584	0.0456974
$545$	−16.8598	−0.722194
$546$	0.566452	0.0242419
$547$	−33.6679	−1.43954	−0.719768	−	0.694214i	$-0.755752\pi$
$547$	−33.6679	−1.43954	−0.719768	+	0.694214i	$0.755752\pi$
$548$	5.45669	0.233098
$549$	−47.9695	−2.04729
$550$	−2.18060	−0.0929810
$551$	−38.2839	−1.63095
$552$	3.60344	0.153372
$553$	10.4263	0.443373
$554$	−21.5260	−0.914554
$555$	−21.6930	−0.920816
$556$	−5.45191	−0.231212
$557$	27.1141	1.14886	0.574430	−	0.818554i	$-0.305224\pi$
$557$	27.1141	1.14886	0.574430	+	0.818554i	$0.305224\pi$
$558$	9.41834	0.398710
$559$	0.244378	0.0103361
$560$	−7.42551	−0.313785
$561$	−6.06364	−0.256007
$562$	−27.0524	−1.14114
$563$	39.9110	1.68205	0.841024	−	0.540998i	$-0.181954\pi$
$563$	39.9110	1.68205	0.841024	+	0.540998i	$0.181954\pi$
$564$	−28.6214	−1.20518
$565$	1.16894	0.0491775
$566$	−4.66465	−0.196070
$567$	11.8736	0.498645
$568$	−5.93777	−0.249143
$569$	28.5674	1.19761	0.598805	−	0.800895i	$-0.295643\pi$
$569$	28.5674	1.19761	0.598805	+	0.800895i	$0.295643\pi$
$570$	−38.3792	−1.60753
$571$	8.62958	0.361137	0.180568	−	0.983562i	$-0.442206\pi$
$571$	8.62958	0.361137	0.180568	+	0.983562i	$0.442206\pi$
$572$	0.117678	0.00492038
$573$	40.0841	1.67454
$574$	44.1185	1.84147
$575$	−1.38118	−0.0575991
$576$	4.34031	0.180846
$577$	4.17076	0.173631	0.0868154	−	0.996224i	$-0.472331\pi$
$577$	4.17076	0.173631	0.0868154	+	0.996224i	$0.472331\pi$
$578$	15.8640	0.659855
$579$	25.2484	1.04929
$580$	10.7063	0.444557
$581$	−56.5819	−2.34741
$582$	11.4416	0.474272
$583$	−5.06109	−0.209609
$584$	−14.1087	−0.583821
$585$	−0.484132	−0.0200164
$586$	22.2070	0.917365
$587$	−20.4020	−0.842081	−0.421040	−	0.907042i	$-0.638335\pi$
$587$	−20.4020	−0.842081	−0.421040	+	0.907042i	$0.638335\pi$
$588$	−18.7440	−0.772990
$589$	15.4440	0.636360
$590$	12.4829	0.513914
$591$	−8.45518	−0.347800
$592$	4.02282	0.165337
$593$	−41.9433	−1.72241	−0.861203	−	0.508261i	$-0.830288\pi$
$593$	−41.9433	−1.72241	−0.861203	+	0.508261i	$0.830288\pi$
$594$	−7.62513	−0.312863
$595$	7.91439	0.324458
$596$	17.2939	0.708385
$597$	−23.2357	−0.950974
$598$	0.0745368	0.00304804
$599$	−13.8389	−0.565441	−0.282720	−	0.959202i	$-0.591237\pi$
$599$	−13.8389	−0.565441	−0.282720	+	0.959202i	$0.591237\pi$
$600$	−2.81350	−0.114861
$601$	−12.4694	−0.508638	−0.254319	−	0.967120i	$-0.581851\pi$
$601$	−12.4694	−0.508638	−0.254319	+	0.967120i	$0.581851\pi$
$602$	−16.2684	−0.663052
$603$	−15.8086	−0.643774
$604$	−3.62836	−0.147636
$605$	−13.1179	−0.533317
$606$	−19.1296	−0.777086
$607$	6.29860	0.255652	0.127826	−	0.991797i	$-0.459200\pi$
$607$	6.29860	0.255652	0.127826	+	0.991797i	$0.459200\pi$
$608$	7.11716	0.288639
$609$	54.3702	2.20319
$610$	21.9977	0.890659
$611$	−0.592033	−0.0239511
$612$	−4.62606	−0.186998
$613$	−37.9353	−1.53219	−0.766096	−	0.642726i	$-0.777803\pi$
$613$	−37.9353	−1.53219	−0.766096	+	0.642726i	$0.777803\pi$
$614$	−18.0904	−0.730068
$615$	−63.7699	−2.57145
$616$	−7.83393	−0.315638
$617$	−17.2405	−0.694078	−0.347039	−	0.937851i	$-0.612813\pi$
$617$	−17.2405	−0.694078	−0.347039	+	0.937851i	$0.612813\pi$
$618$	38.7107	1.55717
$619$	−11.5171	−0.462910	−0.231455	−	0.972846i	$-0.574349\pi$
$619$	−11.5171	−0.462910	−0.231455	+	0.972846i	$0.574349\pi$
$620$	−4.31903	−0.173456
$621$	−4.82972	−0.193810
$622$	7.92331	0.317696
$623$	10.0523	0.402738
$624$	0.151834	0.00607822
$625$	−18.7293	−0.749172
$626$	31.2483	1.24893
$627$	−40.4901	−1.61702
$628$	20.8857	0.833432
$629$	−4.28767	−0.170961
$630$	32.2290	1.28404
$631$	16.8138	0.669348	0.334674	−	0.942334i	$-0.391374\pi$
$631$	16.8138	0.669348	0.334674	+	0.942334i	$0.391374\pi$
$632$	2.79471	0.111168
$633$	−0.931052	−0.0370060
$634$	6.46094	0.256597
$635$	−23.1405	−0.918302
$636$	−6.53004	−0.258933
$637$	−0.387719	−0.0153620
$638$	11.2952	0.447182
$639$	25.7718	1.01952
$640$	−1.99036	−0.0786759
$641$	3.88946	0.153625	0.0768123	−	0.997046i	$-0.475526\pi$
$641$	3.88946	0.153625	0.0768123	+	0.997046i	$0.475526\pi$
$642$	−11.0979	−0.438000
$643$	−49.5549	−1.95425	−0.977127	−	0.212657i	$-0.931788\pi$
$643$	−49.5549	−1.95425	−0.977127	+	0.212657i	$0.931788\pi$
$644$	−4.96197	−0.195529
$645$	23.5148	0.925893
$646$	−7.58574	−0.298457
$647$	−31.2530	−1.22868	−0.614342	−	0.789040i	$-0.710578\pi$
$647$	−31.2530	−1.22868	−0.614342	+	0.789040i	$0.710578\pi$
$648$	3.18265	0.125026
$649$	13.1695	0.516948
$650$	−0.0581971	−0.00228268
$651$	−21.9334	−0.859637
$652$	−8.99841	−0.352405
$653$	−9.50177	−0.371833	−0.185916	−	0.982566i	$-0.559525\pi$
$653$	−9.50177	−0.371833	−0.185916	+	0.982566i	$0.559525\pi$
$654$	−22.9497	−0.897405
$655$	31.8700	1.24526
$656$	11.8257	0.461716
$657$	61.2360	2.38904
$658$	39.4120	1.53644
$659$	44.6576	1.73961	0.869806	−	0.493393i	$-0.164244\pi$
$659$	44.6576	1.73961	0.869806	+	0.493393i	$0.164244\pi$
$660$	11.3233	0.440760
$661$	−45.2960	−1.76181	−0.880905	−	0.473293i	$-0.843065\pi$
$661$	−45.2960	−1.76181	−0.880905	+	0.473293i	$0.843065\pi$
$662$	8.62997	0.335413
$663$	−0.161830	−0.00628496
$664$	−15.1664	−0.588571
$665$	52.8486	2.04938
$666$	−17.4603	−0.676571
$667$	7.15433	0.277017
$668$	25.2738	0.977873
$669$	27.1831	1.05096
$670$	7.24942	0.280070
$671$	23.2076	0.895919
$672$	−10.1077	−0.389912
$673$	37.1965	1.43382	0.716909	−	0.697167i	$-0.245556\pi$
$673$	37.1965	1.43382	0.716909	+	0.697167i	$0.245556\pi$
$674$	−19.5269	−0.752149
$675$	3.77096	0.145144
$676$	−12.9969	−0.499879
$677$	−40.7037	−1.56437	−0.782185	−	0.623046i	$-0.785895\pi$
$677$	−40.7037	−1.56437	−0.782185	+	0.623046i	$0.785895\pi$
$678$	1.59117	0.0611084
$679$	−15.7553	−0.604632
$680$	2.12140	0.0813521
$681$	70.7124	2.70971
$682$	−4.55658	−0.174480
$683$	−29.6069	−1.13288	−0.566438	−	0.824105i	$-0.691679\pi$
$683$	−29.6069	−1.13288	−0.566438	+	0.824105i	$0.691679\pi$
$684$	−30.8907	−1.18113
$685$	10.8608	0.414969
$686$	−0.304442	−0.0116237
$687$	−28.8867	−1.10210
$688$	−4.36065	−0.166248
$689$	−0.135073	−0.00514589
$690$	7.17214	0.273039
$691$	−21.1378	−0.804119	−0.402059	−	0.915614i	$-0.631705\pi$
$691$	−21.1378	−0.804119	−0.402059	+	0.915614i	$0.631705\pi$
$692$	−4.80537	−0.182673
$693$	34.0017	1.29162
$694$	−30.5519	−1.15973
$695$	−10.8513	−0.411612
$696$	14.5736	0.552410
$697$	−12.6043	−0.477421
$698$	1.57622	0.0596607
$699$	42.0701	1.59124
$700$	3.87422	0.146432
$701$	42.6539	1.61102	0.805508	−	0.592585i	$-0.201893\pi$
$701$	42.6539	1.61102	0.805508	+	0.592585i	$0.201893\pi$
$702$	−0.203504	−0.00768077
$703$	−28.6310	−1.07984
$704$	−2.09984	−0.0791405
$705$	−56.9670	−2.14550
$706$	−12.1035	−0.455522
$707$	26.3416	0.990680
$708$	16.9919	0.638594
$709$	27.6680	1.03909	0.519547	−	0.854442i	$-0.326101\pi$
$709$	27.6680	1.03909	0.519547	+	0.854442i	$0.326101\pi$
$710$	−11.8183	−0.443533
$711$	−12.1299	−0.454907
$712$	2.69446	0.100979
$713$	−2.88611	−0.108086
$714$	10.7732	0.403175
$715$	0.234222	0.00875942
$716$	−12.0582	−0.450635
$717$	−69.1898	−2.58394
$718$	−22.1772	−0.827644
$719$	−3.26111	−0.121619	−0.0608094	−	0.998149i	$-0.519368\pi$
$719$	−3.26111	−0.121619	−0.0608094	+	0.998149i	$0.519368\pi$
$720$	8.63878	0.321948
$721$	−53.3050	−1.98518
$722$	−31.6540	−1.17804
$723$	6.73526	0.250487
$724$	−14.4761	−0.538000
$725$	−5.58598	−0.207458
$726$	−17.8562	−0.662704
$727$	−9.50656	−0.352579	−0.176289	−	0.984338i	$-0.556409\pi$
$727$	−9.50656	−0.352579	−0.176289	+	0.984338i	$0.556409\pi$
$728$	−0.209077	−0.00774890
$729$	−43.3285	−1.60476
$730$	−28.0814	−1.03934
$731$	4.64775	0.171903
$732$	29.9434	1.10674
$733$	33.8095	1.24878	0.624390	−	0.781113i	$-0.285347\pi$
$733$	33.8095	1.24878	0.624390	+	0.781113i	$0.285347\pi$
$734$	14.3109	0.528226
$735$	−37.3074	−1.37610
$736$	−1.33002	−0.0490254
$737$	7.64816	0.281723
$738$	−51.3271	−1.88938
$739$	−20.8082	−0.765442	−0.382721	−	0.923864i	$-0.625013\pi$
$739$	−20.8082	−0.765442	−0.382721	+	0.923864i	$0.625013\pi$
$740$	8.00686	0.294338
$741$	−1.08063	−0.0396978
$742$	8.99194	0.330104
$743$	44.8497	1.64538	0.822689	−	0.568492i	$-0.192473\pi$
$743$	44.8497	1.64538	0.822689	+	0.568492i	$0.192473\pi$
$744$	−5.87910	−0.215538
$745$	34.4211	1.26109
$746$	−13.6950	−0.501410
$747$	65.8269	2.40848
$748$	2.23808	0.0818324
$749$	15.2820	0.558391
$750$	−32.5623	−1.18901
$751$	−44.4015	−1.62023	−0.810117	−	0.586268i	$-0.800596\pi$
$751$	−44.4015	−1.62023	−0.810117	+	0.586268i	$0.800596\pi$
$752$	10.5641	0.385235
$753$	−43.6202	−1.58961
$754$	0.301454	0.0109783
$755$	−7.22175	−0.262826
$756$	13.5474	0.492715
$757$	0.994772	0.0361556	0.0180778	−	0.999837i	$-0.494245\pi$
$757$	0.994772	0.0361556	0.0180778	+	0.999837i	$0.494245\pi$
$758$	−19.8792	−0.722045
$759$	7.56662	0.274651
$760$	14.1657	0.513845
$761$	12.4239	0.450365	0.225183	−	0.974317i	$-0.427702\pi$
$761$	12.4239	0.450365	0.225183	+	0.974317i	$0.427702\pi$
$762$	−31.4991	−1.14109
$763$	31.6020	1.14407
$764$	−14.7950	−0.535264
$765$	−9.20754	−0.332899
$766$	−35.6083	−1.28658
$767$	0.351476	0.0126911
$768$	−2.70930	−0.0977635
$769$	−8.44718	−0.304613	−0.152307	−	0.988333i	$-0.548670\pi$
$769$	−8.44718	−0.304613	−0.152307	+	0.988333i	$0.548670\pi$
$770$	−15.5924	−0.561910
$771$	−79.0689	−2.84760
$772$	−9.31915	−0.335403
$773$	−5.94807	−0.213937	−0.106969	−	0.994262i	$-0.534114\pi$
$773$	−5.94807	−0.213937	−0.106969	+	0.994262i	$0.534114\pi$
$774$	18.9266	0.680302
$775$	2.25343	0.0809456
$776$	−4.22310	−0.151600
$777$	40.6614	1.45872
$778$	12.6316	0.452865
$779$	−84.1654	−3.01554
$780$	0.302204	0.0108206
$781$	−12.4683	−0.446153
$782$	1.41759	0.0506929
$783$	−19.5331	−0.698056
$784$	6.91840	0.247086
$785$	41.5702	1.48370
$786$	43.3817	1.54738
$787$	−4.24358	−0.151267	−0.0756337	−	0.997136i	$-0.524098\pi$
$787$	−4.24358	−0.151267	−0.0756337	+	0.997136i	$0.524098\pi$
$788$	3.12080	0.111174
$789$	−36.0728	−1.28423
$790$	5.56248	0.197904
$791$	−2.19106	−0.0779050
$792$	9.11393	0.323850
$793$	0.619378	0.0219948
$794$	26.0023	0.922786
$795$	−12.9971	−0.460961
$796$	8.57627	0.303978
$797$	−4.45645	−0.157856	−0.0789278	−	0.996880i	$-0.525150\pi$
$797$	−4.45645	−0.157856	−0.0789278	+	0.996880i	$0.525150\pi$
$798$	71.9380	2.54658
$799$	−11.2597	−0.398338
$800$	1.03846	0.0367151
$801$	−11.6948	−0.413215
$802$	18.3997	0.649715
$803$	−29.6259	−1.04548
$804$	9.86799	0.348017
$805$	−9.87612	−0.348087
$806$	−0.121609	−0.00428349
$807$	61.5617	2.16707
$808$	7.06071	0.248395
$809$	4.16661	0.146490	0.0732451	−	0.997314i	$-0.476664\pi$
$809$	4.16661	0.146490	0.0732451	+	0.997314i	$0.476664\pi$
$810$	6.33462	0.222576
$811$	−4.17995	−0.146778	−0.0733890	−	0.997303i	$-0.523381\pi$
$811$	−4.17995	−0.146778	−0.0733890	+	0.997303i	$0.523381\pi$
$812$	−20.0680	−0.704248
$813$	3.19488	0.112049
$814$	8.44725	0.296076
$815$	−17.9101	−0.627363
$816$	2.88767	0.101089
$817$	31.0355	1.08579
$818$	11.5467	0.403721
$819$	0.907458	0.0317091
$820$	23.5374	0.821962
$821$	10.9914	0.383603	0.191802	−	0.981434i	$-0.438567\pi$
$821$	10.9914	0.383603	0.191802	+	0.981434i	$0.438567\pi$
$822$	14.7838	0.515645
$823$	12.7357	0.443937	0.221968	−	0.975054i	$-0.428752\pi$
$823$	12.7357	0.443937	0.221968	+	0.975054i	$0.428752\pi$
$824$	−14.2881	−0.497748
$825$	−5.90789	−0.205686
$826$	−23.3980	−0.814121
$827$	33.7748	1.17447	0.587233	−	0.809418i	$-0.300217\pi$
$827$	33.7748	1.17447	0.587233	+	0.809418i	$0.300217\pi$
$828$	5.77272	0.200616
$829$	−36.9334	−1.28275	−0.641374	−	0.767228i	$-0.721635\pi$
$829$	−36.9334	−1.28275	−0.641374	+	0.767228i	$0.721635\pi$
$830$	−30.1866	−1.04779
$831$	−58.3205	−2.02312
$832$	−0.0560417	−0.00194290
$833$	−7.37389	−0.255490
$834$	−14.7709	−0.511473
$835$	50.3040	1.74084
$836$	14.9449	0.516879
$837$	7.87981	0.272366
$838$	−8.44652	−0.291780
$839$	−26.8241	−0.926070	−0.463035	−	0.886340i	$-0.653240\pi$
$839$	−26.8241	−0.926070	−0.463035	+	0.886340i	$0.653240\pi$
$840$	−20.1179	−0.694135
$841$	−0.0653326	−0.00225285
$842$	7.29503	0.251403
$843$	−73.2931	−2.52435
$844$	0.343650	0.0118289
$845$	−25.8684	−0.889902
$846$	−45.8516	−1.57641
$847$	24.5881	0.844858
$848$	2.41023	0.0827677
$849$	−12.6379	−0.433733
$850$	−1.10683	−0.0379640
$851$	5.35044	0.183411
$852$	−16.0872	−0.551139
$853$	−5.21924	−0.178703	−0.0893516	−	0.996000i	$-0.528479\pi$
$853$	−5.21924	−0.178703	−0.0893516	+	0.996000i	$0.528479\pi$
$854$	−41.2325	−1.41095
$855$	−61.4836	−2.10270
$856$	4.09624	0.140006
$857$	−51.5993	−1.76260	−0.881300	−	0.472558i	$-0.843331\pi$
$857$	−51.5993	−1.76260	−0.881300	+	0.472558i	$0.843331\pi$
$858$	0.318826	0.0108845
$859$	−38.5838	−1.31646	−0.658232	−	0.752815i	$-0.728695\pi$
$859$	−38.5838	−1.31646	−0.658232	+	0.752815i	$0.728695\pi$
$860$	−8.67927	−0.295961
$861$	119.530	4.07358
$862$	22.5907	0.769442
$863$	−37.9173	−1.29072	−0.645359	−	0.763879i	$-0.723292\pi$
$863$	−37.9173	−1.29072	−0.645359	+	0.763879i	$0.723292\pi$
$864$	3.63130	0.123539
$865$	−9.56442	−0.325200
$866$	15.5705	0.529107
$867$	42.9803	1.45969
$868$	8.09559	0.274782
$869$	5.86843	0.199073
$870$	29.0067	0.983419
$871$	0.204119	0.00691630
$872$	8.47072	0.286855
$873$	18.3296	0.620362
$874$	9.46600	0.320192
$875$	44.8387	1.51582
$876$	−38.2246	−1.29149
$877$	−16.6850	−0.563411	−0.281706	−	0.959501i	$-0.590900\pi$
$877$	−16.6850	−0.563411	−0.281706	+	0.959501i	$0.590900\pi$
$878$	28.9085	0.975614
$879$	60.1656	2.02933
$880$	−4.17943	−0.140889
$881$	34.2479	1.15384	0.576920	−	0.816800i	$-0.304254\pi$
$881$	34.2479	1.15384	0.576920	+	0.816800i	$0.304254\pi$
$882$	−30.0280	−1.01109
$883$	−11.5168	−0.387573	−0.193786	−	0.981044i	$-0.562077\pi$
$883$	−11.5168	−0.387573	−0.193786	+	0.981044i	$0.562077\pi$
$884$	0.0597314	0.00200898
$885$	33.8200	1.13685
$886$	35.2291	1.18354
$887$	−33.5441	−1.12630	−0.563151	−	0.826354i	$-0.690411\pi$
$887$	−33.5441	−1.12630	−0.563151	+	0.826354i	$0.690411\pi$
$888$	10.8990	0.365747
$889$	43.3746	1.45474
$890$	5.36295	0.179766
$891$	6.68304	0.223890
$892$	−10.0333	−0.335939
$893$	−75.1867	−2.51603
$894$	46.8543	1.56704
$895$	−24.0001	−0.802236
$896$	3.73074	0.124635
$897$	0.201943	0.00674267
$898$	17.0986	0.570588
$899$	−11.6725	−0.389299
$900$	−4.50724	−0.150241
$901$	−2.56891	−0.0855829
$902$	24.8320	0.826815
$903$	−44.0761	−1.46676
$904$	−0.587298	−0.0195332
$905$	−28.8126	−0.957765
$906$	−9.83032	−0.326590
$907$	−12.1776	−0.404349	−0.202174	−	0.979350i	$-0.564801\pi$
$907$	−12.1776	−0.404349	−0.202174	+	0.979350i	$0.564801\pi$
$908$	−26.0999	−0.866155
$909$	−30.6457	−1.01645
$910$	−0.416138	−0.0137949
$911$	8.33538	0.276163	0.138082	−	0.990421i	$-0.455906\pi$
$911$	8.33538	0.276163	0.138082	+	0.990421i	$0.455906\pi$
$912$	19.2825	0.638508
$913$	−31.8470	−1.05398
$914$	8.18456	0.270721
$915$	59.5983	1.97026
$916$	10.6621	0.352285
$917$	−59.7371	−1.97269
$918$	−3.87037	−0.127741
$919$	−10.9489	−0.361170	−0.180585	−	0.983559i	$-0.557799\pi$
$919$	−10.9489	−0.361170	−0.180585	+	0.983559i	$0.557799\pi$
$920$	−2.64723	−0.0872766
$921$	−49.0123	−1.61501
$922$	35.9486	1.18390
$923$	−0.332763	−0.0109530
$924$	−21.2245	−0.698234
$925$	−4.17754	−0.137357
$926$	30.7560	1.01070
$927$	62.0146	2.03683
$928$	−5.37910	−0.176577
$929$	29.1502	0.956389	0.478194	−	0.878254i	$-0.341291\pi$
$929$	29.1502	0.956389	0.478194	+	0.878254i	$0.341291\pi$
$930$	−11.7015	−0.383709
$931$	−49.2393	−1.61375
$932$	−15.5280	−0.508638
$933$	21.4666	0.702786
$934$	3.33174	0.109018
$935$	4.45460	0.145681
$936$	0.243238	0.00795049
$937$	9.44886	0.308681	0.154340	−	0.988018i	$-0.450675\pi$
$937$	9.44886	0.308681	0.154340	+	0.988018i	$0.450675\pi$
$938$	−13.5883	−0.443675
$939$	84.6611	2.76281
$940$	21.0265	0.685808
$941$	−1.62711	−0.0530421	−0.0265211	−	0.999648i	$-0.508443\pi$
$941$	−1.62711	−0.0530421	−0.0265211	+	0.999648i	$0.508443\pi$
$942$	56.5858	1.84366
$943$	15.7285	0.512189
$944$	−6.27169	−0.204126
$945$	26.9643	0.877147
$946$	−9.15665	−0.297708
$947$	3.09770	0.100662	0.0503308	−	0.998733i	$-0.483972\pi$
$947$	3.09770	0.100662	0.0503308	+	0.998733i	$0.483972\pi$
$948$	7.57171	0.245918
$949$	−0.790674	−0.0256664
$950$	−7.39090	−0.239792
$951$	17.5046	0.567626
$952$	−3.97636	−0.128875
$953$	22.7583	0.737213	0.368606	−	0.929586i	$-0.379835\pi$
$953$	22.7583	0.737213	0.368606	+	0.929586i	$0.379835\pi$
$954$	−10.4611	−0.338692
$955$	−29.4474	−0.952895
$956$	25.5379	0.825955
$957$	30.6021	0.989226
$958$	23.7113	0.766077
$959$	−20.3575	−0.657377
$960$	−5.39249	−0.174042
$961$	−26.2912	−0.848104
$962$	0.225445	0.00726865
$963$	−17.7789	−0.572918
$964$	−2.48598	−0.0800679
$965$	−18.5485	−0.597096
$966$	−13.4435	−0.432537
$967$	15.6253	0.502475	0.251238	−	0.967925i	$-0.419162\pi$
$967$	15.6253	0.502475	0.251238	+	0.967925i	$0.419162\pi$
$968$	6.59069	0.211833
$969$	−20.5520	−0.660227
$970$	−8.40550	−0.269884
$971$	−42.4970	−1.36379	−0.681897	−	0.731448i	$-0.738845\pi$
$971$	−42.4970	−1.36379	−0.681897	+	0.731448i	$0.738845\pi$
$972$	19.5166	0.625997
$973$	20.3396	0.652059
$974$	−3.27314	−0.104878
$975$	−0.157673	−0.00504959
$976$	−11.0521	−0.353769
$977$	−41.8391	−1.33855	−0.669275	−	0.743015i	$-0.733395\pi$
$977$	−41.8391	−1.33855	−0.669275	+	0.743015i	$0.733395\pi$
$978$	−24.3794	−0.779567
$979$	5.65792	0.180828
$980$	13.7701	0.439870
$981$	−36.7655	−1.17383
$982$	−8.04876	−0.256846
$983$	−54.0942	−1.72534	−0.862668	−	0.505770i	$-0.831208\pi$
$983$	−54.0942	−1.72534	−0.862668	+	0.505770i	$0.831208\pi$
$984$	32.0394	1.02138
$985$	6.21152	0.197915
$986$	5.73324	0.182584
$987$	106.779	3.39882
$988$	0.398858	0.0126894
$989$	−5.79978	−0.184422
$990$	18.1400	0.576528
$991$	37.0784	1.17784	0.588918	−	0.808193i	$-0.299554\pi$
$991$	37.0784	1.17784	0.588918	+	0.808193i	$0.299554\pi$
$992$	2.16997	0.0688966
$993$	23.3812	0.741979
$994$	22.1523	0.702627
$995$	17.0699	0.541152
$996$	−41.0904	−1.30200
$997$	−32.0605	−1.01536	−0.507682	−	0.861544i	$-0.669498\pi$
$997$	−32.0605	−1.01536	−0.507682	+	0.861544i	$0.669498\pi$
$998$	−34.7193	−1.09902
$999$	−14.6080	−0.462178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.9	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.9	✓	81	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.70930 q^{3} +1.00000 q^{4} +1.99036 q^{5} +2.70930 q^{6} -3.73074 q^{7} -1.00000 q^{8} +4.34031 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.70930 q^{3} +1.00000 q^{4} +1.99036 q^{5} +2.70930 q^{6} -3.73074 q^{7} -1.00000 q^{8} +4.34031 q^{9} -1.99036 q^{10} -2.09984 q^{11} -2.70930 q^{12} -0.0560417 q^{13} +3.73074 q^{14} -5.39249 q^{15} +1.00000 q^{16} -1.06584 q^{17} -4.34031 q^{18} -7.11716 q^{19} +1.99036 q^{20} +10.1077 q^{21} +2.09984 q^{22} +1.33002 q^{23} +2.70930 q^{24} -1.03846 q^{25} +0.0560417 q^{26} -3.63130 q^{27} -3.73074 q^{28} +5.37910 q^{29} +5.39249 q^{30} -2.16997 q^{31} -1.00000 q^{32} +5.68908 q^{33} +1.06584 q^{34} -7.42551 q^{35} +4.34031 q^{36} +4.02282 q^{37} +7.11716 q^{38} +0.151834 q^{39} -1.99036 q^{40} +11.8257 q^{41} -10.1077 q^{42} -4.36065 q^{43} -2.09984 q^{44} +8.63878 q^{45} -1.33002 q^{46} +10.5641 q^{47} -2.70930 q^{48} +6.91840 q^{49} +1.03846 q^{50} +2.88767 q^{51} -0.0560417 q^{52} +2.41023 q^{53} +3.63130 q^{54} -4.17943 q^{55} +3.73074 q^{56} +19.2825 q^{57} -5.37910 q^{58} -6.27169 q^{59} -5.39249 q^{60} -11.0521 q^{61} +2.16997 q^{62} -16.1925 q^{63} +1.00000 q^{64} -0.111543 q^{65} -5.68908 q^{66} -3.64226 q^{67} -1.06584 q^{68} -3.60344 q^{69} +7.42551 q^{70} +5.93777 q^{71} -4.34031 q^{72} +14.1087 q^{73} -4.02282 q^{74} +2.81350 q^{75} -7.11716 q^{76} +7.83393 q^{77} -0.151834 q^{78} -2.79471 q^{79} +1.99036 q^{80} -3.18265 q^{81} -11.8257 q^{82} +15.1664 q^{83} +10.1077 q^{84} -2.12140 q^{85} +4.36065 q^{86} -14.5736 q^{87} +2.09984 q^{88} -2.69446 q^{89} -8.63878 q^{90} +0.209077 q^{91} +1.33002 q^{92} +5.87910 q^{93} -10.5641 q^{94} -14.1657 q^{95} +2.70930 q^{96} +4.22310 q^{97} -6.91840 q^{98} -9.11393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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