LMFDB - Embedded newform 8026.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.39342 q^{3} +1.00000 q^{4} +1.94313 q^{5} +2.39342 q^{6} +4.16913 q^{7} -1.00000 q^{8} +2.72848 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.39342 q^{3} +1.00000 q^{4} +1.94313 q^{5} +2.39342 q^{6} +4.16913 q^{7} -1.00000 q^{8} +2.72848 q^{9} -1.94313 q^{10} -4.33125 q^{11} -2.39342 q^{12} +2.71319 q^{13} -4.16913 q^{14} -4.65073 q^{15} +1.00000 q^{16} +5.68203 q^{17} -2.72848 q^{18} -2.95964 q^{19} +1.94313 q^{20} -9.97851 q^{21} +4.33125 q^{22} -7.44769 q^{23} +2.39342 q^{24} -1.22426 q^{25} -2.71319 q^{26} +0.649863 q^{27} +4.16913 q^{28} +6.89202 q^{29} +4.65073 q^{30} -1.08928 q^{31} -1.00000 q^{32} +10.3665 q^{33} -5.68203 q^{34} +8.10116 q^{35} +2.72848 q^{36} +5.48734 q^{37} +2.95964 q^{38} -6.49381 q^{39} -1.94313 q^{40} -5.76373 q^{41} +9.97851 q^{42} -4.99002 q^{43} -4.33125 q^{44} +5.30178 q^{45} +7.44769 q^{46} -11.4557 q^{47} -2.39342 q^{48} +10.3817 q^{49} +1.22426 q^{50} -13.5995 q^{51} +2.71319 q^{52} -2.97190 q^{53} -0.649863 q^{54} -8.41616 q^{55} -4.16913 q^{56} +7.08367 q^{57} -6.89202 q^{58} -0.0542823 q^{59} -4.65073 q^{60} +9.99674 q^{61} +1.08928 q^{62} +11.3754 q^{63} +1.00000 q^{64} +5.27207 q^{65} -10.3665 q^{66} -14.2464 q^{67} +5.68203 q^{68} +17.8255 q^{69} -8.10116 q^{70} -6.90714 q^{71} -2.72848 q^{72} -4.68009 q^{73} -5.48734 q^{74} +2.93017 q^{75} -2.95964 q^{76} -18.0575 q^{77} +6.49381 q^{78} +8.28729 q^{79} +1.94313 q^{80} -9.74084 q^{81} +5.76373 q^{82} +10.5633 q^{83} -9.97851 q^{84} +11.0409 q^{85} +4.99002 q^{86} -16.4955 q^{87} +4.33125 q^{88} +1.92493 q^{89} -5.30178 q^{90} +11.3116 q^{91} -7.44769 q^{92} +2.60711 q^{93} +11.4557 q^{94} -5.75095 q^{95} +2.39342 q^{96} -3.23525 q^{97} -10.3817 q^{98} -11.8177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.39342	−1.38184	−0.690922	−	0.722929i	$-0.742795\pi$
$3$	−2.39342	−1.38184	−0.690922	+	0.722929i	$0.742795\pi$
$4$	1.00000	0.500000
$5$	1.94313	0.868993	0.434496	−	0.900674i	$-0.356926\pi$
$5$	1.94313	0.868993	0.434496	+	0.900674i	$0.356926\pi$
$6$	2.39342	0.977111
$7$	4.16913	1.57578	0.787892	−	0.615813i	$-0.211172\pi$
$7$	4.16913	1.57578	0.787892	+	0.615813i	$0.211172\pi$
$8$	−1.00000	−0.353553
$9$	2.72848	0.909493
$10$	−1.94313	−0.614471
$11$	−4.33125	−1.30592	−0.652960	−	0.757393i	$-0.726473\pi$
$11$	−4.33125	−1.30592	−0.652960	+	0.757393i	$0.726473\pi$
$12$	−2.39342	−0.690922
$13$	2.71319	0.752503	0.376251	−	0.926518i	$-0.377213\pi$
$13$	2.71319	0.752503	0.376251	+	0.926518i	$0.377213\pi$
$14$	−4.16913	−1.11425
$15$	−4.65073	−1.20081
$16$	1.00000	0.250000
$17$	5.68203	1.37809	0.689047	−	0.724717i	$-0.258029\pi$
$17$	5.68203	1.37809	0.689047	+	0.724717i	$0.258029\pi$
$18$	−2.72848	−0.643109
$19$	−2.95964	−0.678987	−0.339494	−	0.940608i	$-0.610256\pi$
$19$	−2.95964	−0.678987	−0.339494	+	0.940608i	$0.610256\pi$
$20$	1.94313	0.434496
$21$	−9.97851	−2.17749
$22$	4.33125	0.923425
$23$	−7.44769	−1.55295	−0.776476	−	0.630147i	$-0.782994\pi$
$23$	−7.44769	−1.55295	−0.776476	+	0.630147i	$0.782994\pi$
$24$	2.39342	0.488556
$25$	−1.22426	−0.244851
$26$	−2.71319	−0.532100
$27$	0.649863	0.125066
$28$	4.16913	0.787892
$29$	6.89202	1.27982	0.639908	−	0.768452i	$-0.278973\pi$
$29$	6.89202	1.27982	0.639908	+	0.768452i	$0.278973\pi$
$30$	4.65073	0.849103
$31$	−1.08928	−0.195641	−0.0978203	−	0.995204i	$-0.531187\pi$
$31$	−1.08928	−0.195641	−0.0978203	+	0.995204i	$0.531187\pi$
$32$	−1.00000	−0.176777
$33$	10.3665	1.80458
$34$	−5.68203	−0.974459
$35$	8.10116	1.36935
$36$	2.72848	0.454747
$37$	5.48734	0.902113	0.451056	−	0.892496i	$-0.351047\pi$
$37$	5.48734	0.902113	0.451056	+	0.892496i	$0.351047\pi$
$38$	2.95964	0.480117
$39$	−6.49381	−1.03984
$40$	−1.94313	−0.307235
$41$	−5.76373	−0.900143	−0.450072	−	0.892993i	$-0.648602\pi$
$41$	−5.76373	−0.900143	−0.450072	+	0.892993i	$0.648602\pi$
$42$	9.97851	1.53972
$43$	−4.99002	−0.760972	−0.380486	−	0.924787i	$-0.624243\pi$
$43$	−4.99002	−0.760972	−0.380486	+	0.924787i	$0.624243\pi$
$44$	−4.33125	−0.652960
$45$	5.30178	0.790343
$46$	7.44769	1.09810
$47$	−11.4557	−1.67098	−0.835490	−	0.549506i	$-0.814816\pi$
$47$	−11.4557	−1.67098	−0.835490	+	0.549506i	$0.814816\pi$
$48$	−2.39342	−0.345461
$49$	10.3817	1.48310
$50$	1.22426	0.173136
$51$	−13.5995	−1.90431
$52$	2.71319	0.376251
$53$	−2.97190	−0.408222	−0.204111	−	0.978948i	$-0.565430\pi$
$53$	−2.97190	−0.408222	−0.204111	+	0.978948i	$0.565430\pi$
$54$	−0.649863	−0.0884352
$55$	−8.41616	−1.13483
$56$	−4.16913	−0.557124
$57$	7.08367	0.938255
$58$	−6.89202	−0.904966
$59$	−0.0542823	−0.00706696	−0.00353348	−	0.999994i	$-0.501125\pi$
$59$	−0.0542823	−0.00706696	−0.00353348	+	0.999994i	$0.501125\pi$
$60$	−4.65073	−0.600406
$61$	9.99674	1.27995	0.639975	−	0.768395i	$-0.278945\pi$
$61$	9.99674	1.27995	0.639975	+	0.768395i	$0.278945\pi$
$62$	1.08928	0.138339
$63$	11.3754	1.43317
$64$	1.00000	0.125000
$65$	5.27207	0.653919
$66$	−10.3665	−1.27603
$67$	−14.2464	−1.74048	−0.870240	−	0.492628i	$-0.836036\pi$
$67$	−14.2464	−1.74048	−0.870240	+	0.492628i	$0.836036\pi$
$68$	5.68203	0.689047
$69$	17.8255	2.14594
$70$	−8.10116	−0.968274
$71$	−6.90714	−0.819726	−0.409863	−	0.912147i	$-0.634424\pi$
$71$	−6.90714	−0.819726	−0.409863	+	0.912147i	$0.634424\pi$
$72$	−2.72848	−0.321554
$73$	−4.68009	−0.547763	−0.273882	−	0.961763i	$-0.588308\pi$
$73$	−4.68009	−0.547763	−0.273882	+	0.961763i	$0.588308\pi$
$74$	−5.48734	−0.637890
$75$	2.93017	0.338346
$76$	−2.95964	−0.339494
$77$	−18.0575	−2.05785
$78$	6.49381	0.735279
$79$	8.28729	0.932393	0.466196	−	0.884681i	$-0.345624\pi$
$79$	8.28729	0.932393	0.466196	+	0.884681i	$0.345624\pi$
$80$	1.94313	0.217248
$81$	−9.74084	−1.08232
$82$	5.76373	0.636497
$83$	10.5633	1.15947	0.579737	−	0.814804i	$-0.303155\pi$
$83$	10.5633	1.15947	0.579737	+	0.814804i	$0.303155\pi$
$84$	−9.97851	−1.08874
$85$	11.0409	1.19755
$86$	4.99002	0.538088
$87$	−16.4955	−1.76851
$88$	4.33125	0.461712
$89$	1.92493	0.204042	0.102021	−	0.994782i	$-0.467469\pi$
$89$	1.92493	0.204042	0.102021	+	0.994782i	$0.467469\pi$
$90$	−5.30178	−0.558857
$91$	11.3116	1.18578
$92$	−7.44769	−0.776476
$93$	2.60711	0.270345
$94$	11.4557	1.18156
$95$	−5.75095	−0.590035
$96$	2.39342	0.244278
$97$	−3.23525	−0.328489	−0.164245	−	0.986420i	$-0.552519\pi$
$97$	−3.23525	−0.328489	−0.164245	+	0.986420i	$0.552519\pi$
$98$	−10.3817	−1.04871
$99$	−11.8177	−1.18772
$100$	−1.22426	−0.122426
$101$	−16.3914	−1.63101	−0.815504	−	0.578751i	$-0.803540\pi$
$101$	−16.3914	−1.63101	−0.815504	+	0.578751i	$0.803540\pi$
$102$	13.5995	1.34655
$103$	−0.0361654	−0.00356348	−0.00178174	−	0.999998i	$-0.500567\pi$
$103$	−0.0361654	−0.00356348	−0.00178174	+	0.999998i	$0.500567\pi$
$104$	−2.71319	−0.266050
$105$	−19.3895	−1.89222
$106$	2.97190	0.288657
$107$	−19.0988	−1.84635	−0.923174	−	0.384383i	$-0.874414\pi$
$107$	−19.0988	−1.84635	−0.923174	+	0.384383i	$0.874414\pi$
$108$	0.649863	0.0625331
$109$	−19.7760	−1.89419	−0.947097	−	0.320947i	$-0.895999\pi$
$109$	−19.7760	−1.89419	−0.947097	+	0.320947i	$0.895999\pi$
$110$	8.41616	0.802449
$111$	−13.1335	−1.24658
$112$	4.16913	0.393946
$113$	2.28462	0.214919	0.107460	−	0.994209i	$-0.465728\pi$
$113$	2.28462	0.214919	0.107460	+	0.994209i	$0.465728\pi$
$114$	−7.08367	−0.663446
$115$	−14.4718	−1.34950
$116$	6.89202	0.639908
$117$	7.40287	0.684396
$118$	0.0542823	0.00499709
$119$	23.6891	2.17158
$120$	4.65073	0.424551
$121$	7.75968	0.705426
$122$	−9.99674	−0.905062
$123$	13.7950	1.24386
$124$	−1.08928	−0.0978203
$125$	−12.0945	−1.08177
$126$	−11.3754	−1.01340
$127$	−14.1060	−1.25170	−0.625852	−	0.779942i	$-0.715249\pi$
$127$	−14.1060	−1.25170	−0.625852	+	0.779942i	$0.715249\pi$
$128$	−1.00000	−0.0883883
$129$	11.9432	1.05154
$130$	−5.27207	−0.462391
$131$	6.78064	0.592428	0.296214	−	0.955122i	$-0.404276\pi$
$131$	6.78064	0.592428	0.296214	+	0.955122i	$0.404276\pi$
$132$	10.3665	0.902289
$133$	−12.3391	−1.06994
$134$	14.2464	1.23071
$135$	1.26277	0.108682
$136$	−5.68203	−0.487230
$137$	−11.7616	−1.00486	−0.502429	−	0.864618i	$-0.667560\pi$
$137$	−11.7616	−1.00486	−0.502429	+	0.864618i	$0.667560\pi$
$138$	−17.8255	−1.51741
$139$	−17.5545	−1.48895	−0.744475	−	0.667650i	$-0.767300\pi$
$139$	−17.5545	−1.48895	−0.744475	+	0.667650i	$0.767300\pi$
$140$	8.10116	0.684673
$141$	27.4182	2.30903
$142$	6.90714	0.579634
$143$	−11.7515	−0.982708
$144$	2.72848	0.227373
$145$	13.3921	1.11215
$146$	4.68009	0.387327
$147$	−24.8478	−2.04941
$148$	5.48734	0.451056
$149$	13.0283	1.06732	0.533659	−	0.845700i	$-0.320817\pi$
$149$	13.0283	1.06732	0.533659	+	0.845700i	$0.320817\pi$
$150$	−2.93017	−0.239247
$151$	−2.92373	−0.237930	−0.118965	−	0.992898i	$-0.537958\pi$
$151$	−2.92373	−0.237930	−0.118965	+	0.992898i	$0.537958\pi$
$152$	2.95964	0.240058
$153$	15.5033	1.25337
$154$	18.0575	1.45512
$155$	−2.11661	−0.170010
$156$	−6.49381	−0.519921
$157$	4.91322	0.392118	0.196059	−	0.980592i	$-0.437186\pi$
$157$	4.91322	0.392118	0.196059	+	0.980592i	$0.437186\pi$
$158$	−8.28729	−0.659301
$159$	7.11303	0.564100
$160$	−1.94313	−0.153618
$161$	−31.0504	−2.44712
$162$	9.74084	0.765312
$163$	6.54567	0.512696	0.256348	−	0.966585i	$-0.417481\pi$
$163$	6.54567	0.512696	0.256348	+	0.966585i	$0.417481\pi$
$164$	−5.76373	−0.450072
$165$	20.1434	1.56816
$166$	−10.5633	−0.819872
$167$	−5.09402	−0.394187	−0.197093	−	0.980385i	$-0.563150\pi$
$167$	−5.09402	−0.394187	−0.197093	+	0.980385i	$0.563150\pi$
$168$	9.97851	0.769858
$169$	−5.63862	−0.433740
$170$	−11.0409	−0.846798
$171$	−8.07531	−0.617534
$172$	−4.99002	−0.380486
$173$	−17.0495	−1.29625	−0.648124	−	0.761535i	$-0.724446\pi$
$173$	−17.0495	−1.29625	−0.648124	+	0.761535i	$0.724446\pi$
$174$	16.4955	1.25052
$175$	−5.10409	−0.385833
$176$	−4.33125	−0.326480
$177$	0.129921	0.00976543
$178$	−1.92493	−0.144280
$179$	−25.3592	−1.89543	−0.947717	−	0.319112i	$-0.896616\pi$
$179$	−25.3592	−1.89543	−0.947717	+	0.319112i	$0.896616\pi$
$180$	5.30178	0.395172
$181$	11.1103	0.825820	0.412910	−	0.910772i	$-0.364512\pi$
$181$	11.1103	0.825820	0.412910	+	0.910772i	$0.364512\pi$
$182$	−11.3116	−0.838474
$183$	−23.9264	−1.76869
$184$	7.44769	0.549051
$185$	10.6626	0.783929
$186$	−2.60711	−0.191163
$187$	−24.6102	−1.79968
$188$	−11.4557	−0.835490
$189$	2.70937	0.197078
$190$	5.75095	0.417218
$191$	18.4000	1.33138	0.665689	−	0.746229i	$-0.268138\pi$
$191$	18.4000	1.33138	0.665689	+	0.746229i	$0.268138\pi$
$192$	−2.39342	−0.172731
$193$	10.4867	0.754851	0.377426	−	0.926040i	$-0.376809\pi$
$193$	10.4867	0.754851	0.377426	+	0.926040i	$0.376809\pi$
$194$	3.23525	0.232277
$195$	−12.6183	−0.903615
$196$	10.3817	0.741548
$197$	12.6056	0.898111	0.449056	−	0.893504i	$-0.351761\pi$
$197$	12.6056	0.898111	0.449056	+	0.893504i	$0.351761\pi$
$198$	11.8177	0.839848
$199$	14.7240	1.04376	0.521879	−	0.853020i	$-0.325231\pi$
$199$	14.7240	1.04376	0.521879	+	0.853020i	$0.325231\pi$
$200$	1.22426	0.0865680
$201$	34.0978	2.40507
$202$	16.3914	1.15330
$203$	28.7337	2.01671
$204$	−13.5995	−0.952155
$205$	−11.1997	−0.782218
$206$	0.0361654	0.00251976
$207$	−20.3209	−1.41240
$208$	2.71319	0.188126
$209$	12.8189	0.886703
$210$	19.3895	1.33800
$211$	14.6438	1.00812	0.504061	−	0.863668i	$-0.331839\pi$
$211$	14.6438	1.00812	0.504061	+	0.863668i	$0.331839\pi$
$212$	−2.97190	−0.204111
$213$	16.5317	1.13273
$214$	19.0988	1.30556
$215$	−9.69625	−0.661279
$216$	−0.649863	−0.0442176
$217$	−4.54136	−0.308287
$218$	19.7760	1.33940
$219$	11.2014	0.756923
$220$	−8.41616	−0.567417
$221$	15.4164	1.03702
$222$	13.1335	0.881464
$223$	20.2733	1.35760	0.678800	−	0.734323i	$-0.262500\pi$
$223$	20.2733	1.35760	0.678800	+	0.734323i	$0.262500\pi$
$224$	−4.16913	−0.278562
$225$	−3.34036	−0.222691
$226$	−2.28462	−0.151971
$227$	27.3365	1.81439	0.907193	−	0.420715i	$-0.138221\pi$
$227$	27.3365	1.81439	0.907193	+	0.420715i	$0.138221\pi$
$228$	7.08367	0.469127
$229$	−11.1327	−0.735669	−0.367834	−	0.929891i	$-0.619901\pi$
$229$	−11.1327	−0.735669	−0.367834	+	0.929891i	$0.619901\pi$
$230$	14.4718	0.954243
$231$	43.2194	2.84362
$232$	−6.89202	−0.452483
$233$	0.215687	0.0141301	0.00706505	−	0.999975i	$-0.497751\pi$
$233$	0.215687	0.0141301	0.00706505	+	0.999975i	$0.497751\pi$
$234$	−7.40287	−0.483941
$235$	−22.2598	−1.45207
$236$	−0.0542823	−0.00353348
$237$	−19.8350	−1.28842
$238$	−23.6891	−1.53554
$239$	16.5435	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$239$	16.5435	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$240$	−4.65073	−0.300203
$241$	27.1229	1.74714	0.873569	−	0.486700i	$-0.161799\pi$
$241$	27.1229	1.74714	0.873569	+	0.486700i	$0.161799\pi$
$242$	−7.75968	−0.498811
$243$	21.3644	1.37052
$244$	9.99674	0.639975
$245$	20.1729	1.28880
$246$	−13.7950	−0.879540
$247$	−8.03005	−0.510940
$248$	1.08928	0.0691694
$249$	−25.2825	−1.60221
$250$	12.0945	0.764925
$251$	−1.72214	−0.108700	−0.0543502	−	0.998522i	$-0.517309\pi$
$251$	−1.72214	−0.108700	−0.0543502	+	0.998522i	$0.517309\pi$
$252$	11.3754	0.716583
$253$	32.2578	2.02803
$254$	14.1060	0.885088
$255$	−26.4256	−1.65483
$256$	1.00000	0.0625000
$257$	−4.47780	−0.279318	−0.139659	−	0.990200i	$-0.544601\pi$
$257$	−4.47780	−0.279318	−0.139659	+	0.990200i	$0.544601\pi$
$258$	−11.9432	−0.743554
$259$	22.8774	1.42153
$260$	5.27207	0.326960
$261$	18.8047	1.16398
$262$	−6.78064	−0.418910
$263$	−15.5812	−0.960780	−0.480390	−	0.877055i	$-0.659505\pi$
$263$	−15.5812	−0.960780	−0.480390	+	0.877055i	$0.659505\pi$
$264$	−10.3665	−0.638014
$265$	−5.77479	−0.354742
$266$	12.3391	0.756560
$267$	−4.60718	−0.281955
$268$	−14.2464	−0.870240
$269$	1.15183	0.0702281	0.0351140	−	0.999383i	$-0.488821\pi$
$269$	1.15183	0.0702281	0.0351140	+	0.999383i	$0.488821\pi$
$270$	−1.26277	−0.0768496
$271$	23.5103	1.42815	0.714075	−	0.700069i	$-0.246848\pi$
$271$	23.5103	1.42815	0.714075	+	0.700069i	$0.246848\pi$
$272$	5.68203	0.344523
$273$	−27.0735	−1.63857
$274$	11.7616	0.710542
$275$	5.30255	0.319756
$276$	17.8255	1.07297
$277$	−11.7967	−0.708796	−0.354398	−	0.935095i	$-0.615314\pi$
$277$	−11.7967	−0.708796	−0.354398	+	0.935095i	$0.615314\pi$
$278$	17.5545	1.05285
$279$	−2.97208	−0.177934
$280$	−8.10116	−0.484137
$281$	−20.0725	−1.19742	−0.598712	−	0.800964i	$-0.704321\pi$
$281$	−20.0725	−1.19742	−0.598712	+	0.800964i	$0.704321\pi$
$282$	−27.4182	−1.63273
$283$	7.09054	0.421489	0.210744	−	0.977541i	$-0.432411\pi$
$283$	7.09054	0.421489	0.210744	+	0.977541i	$0.432411\pi$
$284$	−6.90714	−0.409863
$285$	13.7645	0.815337
$286$	11.7515	0.694879
$287$	−24.0298	−1.41843
$288$	−2.72848	−0.160777
$289$	15.2854	0.899142
$290$	−13.3921	−0.786409
$291$	7.74331	0.453921
$292$	−4.68009	−0.273882
$293$	−7.50039	−0.438177	−0.219089	−	0.975705i	$-0.570308\pi$
$293$	−7.50039	−0.438177	−0.219089	+	0.975705i	$0.570308\pi$
$294$	24.8478	1.44915
$295$	−0.105477	−0.00614113
$296$	−5.48734	−0.318945
$297$	−2.81472	−0.163326
$298$	−13.0283	−0.754708
$299$	−20.2070	−1.16860
$300$	2.93017	0.169173
$301$	−20.8041	−1.19913
$302$	2.92373	0.168242
$303$	39.2317	2.25380
$304$	−2.95964	−0.169747
$305$	19.4249	1.11227
$306$	−15.5033	−0.886264
$307$	11.2203	0.640374	0.320187	−	0.947354i	$-0.396254\pi$
$307$	11.2203	0.640374	0.320187	+	0.947354i	$0.396254\pi$
$308$	−18.0575	−1.02892
$309$	0.0865592	0.00492418
$310$	2.11661	0.120215
$311$	1.87274	0.106193	0.0530966	−	0.998589i	$-0.483091\pi$
$311$	1.87274	0.106193	0.0530966	+	0.998589i	$0.483091\pi$
$312$	6.49381	0.367639
$313$	−26.8274	−1.51637	−0.758187	−	0.652037i	$-0.773915\pi$
$313$	−26.8274	−1.51637	−0.758187	+	0.652037i	$0.773915\pi$
$314$	−4.91322	−0.277269
$315$	22.1038	1.24541
$316$	8.28729	0.466196
$317$	−34.2630	−1.92440	−0.962200	−	0.272345i	$-0.912201\pi$
$317$	−34.2630	−1.92440	−0.962200	+	0.272345i	$0.912201\pi$
$318$	−7.11303	−0.398879
$319$	−29.8510	−1.67134
$320$	1.94313	0.108624
$321$	45.7114	2.55136
$322$	31.0504	1.73037
$323$	−16.8167	−0.935708
$324$	−9.74084	−0.541158
$325$	−3.32164	−0.184251
$326$	−6.54567	−0.362531
$327$	47.3323	2.61748
$328$	5.76373	0.318249
$329$	−47.7602	−2.63310
$330$	−20.1434	−1.10886
$331$	3.34434	0.183821	0.0919107	−	0.995767i	$-0.470703\pi$
$331$	3.34434	0.183821	0.0919107	+	0.995767i	$0.470703\pi$
$332$	10.5633	0.579737
$333$	14.9721	0.820465
$334$	5.09402	0.278732
$335$	−27.6826	−1.51246
$336$	−9.97851	−0.544372
$337$	26.9648	1.46887	0.734433	−	0.678682i	$-0.237448\pi$
$337$	26.9648	1.46887	0.734433	+	0.678682i	$0.237448\pi$
$338$	5.63862	0.306700
$339$	−5.46807	−0.296985
$340$	11.0409	0.598777
$341$	4.71794	0.255491
$342$	8.07531	0.436663
$343$	14.0987	0.761257
$344$	4.99002	0.269044
$345$	34.6372	1.86480
$346$	17.0495	0.916586
$347$	−12.2128	−0.655618	−0.327809	−	0.944744i	$-0.606310\pi$
$347$	−12.2128	−0.655618	−0.327809	+	0.944744i	$0.606310\pi$
$348$	−16.4955	−0.884253
$349$	2.33229	0.124844	0.0624222	−	0.998050i	$-0.480117\pi$
$349$	2.33229	0.124844	0.0624222	+	0.998050i	$0.480117\pi$
$350$	5.10409	0.272825
$351$	1.76320	0.0941127
$352$	4.33125	0.230856
$353$	−13.9573	−0.742872	−0.371436	−	0.928458i	$-0.621135\pi$
$353$	−13.9573	−0.742872	−0.371436	+	0.928458i	$0.621135\pi$
$354$	−0.129921	−0.00690520
$355$	−13.4214	−0.712336
$356$	1.92493	0.102021
$357$	−56.6981	−3.00078
$358$	25.3592	1.34027
$359$	21.0099	1.10886	0.554430	−	0.832230i	$-0.312936\pi$
$359$	21.0099	1.10886	0.554430	+	0.832230i	$0.312936\pi$
$360$	−5.30178	−0.279429
$361$	−10.2405	−0.538976
$362$	−11.1103	−0.583943
$363$	−18.5722	−0.974789
$364$	11.3116	0.592891
$365$	−9.09401	−0.476002
$366$	23.9264	1.25065
$367$	17.9655	0.937793	0.468897	−	0.883253i	$-0.344652\pi$
$367$	17.9655	0.937793	0.468897	+	0.883253i	$0.344652\pi$
$368$	−7.44769	−0.388238
$369$	−15.7262	−0.818674
$370$	−10.6626	−0.554322
$371$	−12.3903	−0.643270
$372$	2.60711	0.135172
$373$	−9.07032	−0.469643	−0.234822	−	0.972038i	$-0.575451\pi$
$373$	−9.07032	−0.469643	−0.234822	+	0.972038i	$0.575451\pi$
$374$	24.6102	1.27257
$375$	28.9473	1.49483
$376$	11.4557	0.590780
$377$	18.6993	0.963064
$378$	−2.70937	−0.139355
$379$	−28.4905	−1.46346	−0.731730	−	0.681595i	$-0.761287\pi$
$379$	−28.4905	−1.46346	−0.731730	+	0.681595i	$0.761287\pi$
$380$	−5.75095	−0.295018
$381$	33.7616	1.72966
$382$	−18.4000	−0.941426
$383$	29.1766	1.49086	0.745428	−	0.666586i	$-0.232245\pi$
$383$	29.1766	1.49086	0.745428	+	0.666586i	$0.232245\pi$
$384$	2.39342	0.122139
$385$	−35.0881	−1.78826
$386$	−10.4867	−0.533760
$387$	−13.6152	−0.692098
$388$	−3.23525	−0.164245
$389$	−16.6747	−0.845442	−0.422721	−	0.906260i	$-0.638925\pi$
$389$	−16.6747	−0.845442	−0.422721	+	0.906260i	$0.638925\pi$
$390$	12.6183	0.638952
$391$	−42.3180	−2.14011
$392$	−10.3817	−0.524354
$393$	−16.2290	−0.818642
$394$	−12.6056	−0.635060
$395$	16.1033	0.810243
$396$	−11.8177	−0.593862
$397$	10.0850	0.506150	0.253075	−	0.967447i	$-0.418558\pi$
$397$	10.0850	0.506150	0.253075	+	0.967447i	$0.418558\pi$
$398$	−14.7240	−0.738048
$399$	29.5328	1.47849
$400$	−1.22426	−0.0612128
$401$	−9.05638	−0.452254	−0.226127	−	0.974098i	$-0.572606\pi$
$401$	−9.05638	−0.452254	−0.226127	+	0.974098i	$0.572606\pi$
$402$	−34.0978	−1.70064
$403$	−2.95542	−0.147220
$404$	−16.3914	−0.815504
$405$	−18.9277	−0.940524
$406$	−28.7337	−1.42603
$407$	−23.7670	−1.17809
$408$	13.5995	0.673276
$409$	−28.8539	−1.42674	−0.713368	−	0.700790i	$-0.752831\pi$
$409$	−28.8539	−1.42674	−0.713368	+	0.700790i	$0.752831\pi$
$410$	11.1997	0.553112
$411$	28.1504	1.38856
$412$	−0.0361654	−0.00178174
$413$	−0.226310	−0.0111360
$414$	20.3209	0.998717
$415$	20.5259	1.00758
$416$	−2.71319	−0.133025
$417$	42.0153	2.05750
$418$	−12.8189	−0.626994
$419$	−36.0868	−1.76295	−0.881477	−	0.472227i	$-0.843450\pi$
$419$	−36.0868	−1.76295	−0.881477	+	0.472227i	$0.843450\pi$
$420$	−19.3895	−0.946111
$421$	23.2510	1.13318	0.566592	−	0.823999i	$-0.308262\pi$
$421$	23.2510	1.13318	0.566592	+	0.823999i	$0.308262\pi$
$422$	−14.6438	−0.712850
$423$	−31.2565	−1.51974
$424$	2.97190	0.144328
$425$	−6.95626	−0.337428
$426$	−16.5317	−0.800964
$427$	41.6777	2.01693
$428$	−19.0988	−0.923174
$429$	28.1263	1.35795
$430$	9.69625	0.467595
$431$	27.2496	1.31257	0.656283	−	0.754515i	$-0.272128\pi$
$431$	27.2496	1.31257	0.656283	+	0.754515i	$0.272128\pi$
$432$	0.649863	0.0312666
$433$	25.0898	1.20574	0.602868	−	0.797841i	$-0.294024\pi$
$433$	25.0898	1.20574	0.602868	+	0.797841i	$0.294024\pi$
$434$	4.54136	0.217992
$435$	−32.0529	−1.53682
$436$	−19.7760	−0.947097
$437$	22.0425	1.05443
$438$	−11.2014	−0.535226
$439$	−15.7084	−0.749721	−0.374861	−	0.927081i	$-0.622309\pi$
$439$	−15.7084	−0.749721	−0.374861	+	0.927081i	$0.622309\pi$
$440$	8.41616	0.401225
$441$	28.3262	1.34887
$442$	−15.4164	−0.733283
$443$	−35.2775	−1.67609	−0.838043	−	0.545604i	$-0.816300\pi$
$443$	−35.2775	−1.67609	−0.838043	+	0.545604i	$0.816300\pi$
$444$	−13.1335	−0.623289
$445$	3.74039	0.177311
$446$	−20.2733	−0.959968
$447$	−31.1822	−1.47487
$448$	4.16913	0.196973
$449$	−31.7244	−1.49717	−0.748583	−	0.663041i	$-0.769265\pi$
$449$	−31.7244	−1.49717	−0.748583	+	0.663041i	$0.769265\pi$
$450$	3.34036	0.157466
$451$	24.9641	1.17551
$452$	2.28462	0.107460
$453$	6.99773	0.328782
$454$	−27.3365	−1.28296
$455$	21.9800	1.03044
$456$	−7.08367	−0.331723
$457$	12.6934	0.593771	0.296886	−	0.954913i	$-0.404052\pi$
$457$	12.6934	0.593771	0.296886	+	0.954913i	$0.404052\pi$
$458$	11.1327	0.520197
$459$	3.69254	0.172353
$460$	−14.4718	−0.674752
$461$	10.0120	0.466304	0.233152	−	0.972440i	$-0.425096\pi$
$461$	10.0120	0.466304	0.233152	+	0.972440i	$0.425096\pi$
$462$	−43.2194	−2.01075
$463$	39.4617	1.83394	0.916970	−	0.398956i	$-0.130628\pi$
$463$	39.4617	1.83394	0.916970	+	0.398956i	$0.130628\pi$
$464$	6.89202	0.319954
$465$	5.06595	0.234928
$466$	−0.215687	−0.00999149
$467$	35.1410	1.62613	0.813066	−	0.582172i	$-0.197797\pi$
$467$	35.1410	1.62613	0.813066	+	0.582172i	$0.197797\pi$
$468$	7.40287	0.342198
$469$	−59.3953	−2.74262
$470$	22.2598	1.02677
$471$	−11.7594	−0.541846
$472$	0.0542823	0.00249855
$473$	21.6130	0.993768
$474$	19.8350	0.911052
$475$	3.62336	0.166251
$476$	23.6891	1.08579
$477$	−8.10878	−0.371275
$478$	−16.5435	−0.756681
$479$	18.8847	0.862863	0.431432	−	0.902146i	$-0.358009\pi$
$479$	18.8847	0.862863	0.431432	+	0.902146i	$0.358009\pi$
$480$	4.65073	0.212276
$481$	14.8882	0.678842
$482$	−27.1229	−1.23541
$483$	74.3168	3.38153
$484$	7.75968	0.352713
$485$	−6.28649	−0.285455
$486$	−21.3644	−0.969107
$487$	−5.29030	−0.239726	−0.119863	−	0.992790i	$-0.538246\pi$
$487$	−5.29030	−0.239726	−0.119863	+	0.992790i	$0.538246\pi$
$488$	−9.99674	−0.452531
$489$	−15.6666	−0.708466
$490$	−20.1729	−0.911320
$491$	−24.3784	−1.10018	−0.550090	−	0.835105i	$-0.685407\pi$
$491$	−24.3784	−1.10018	−0.550090	+	0.835105i	$0.685407\pi$
$492$	13.7950	0.621929
$493$	39.1606	1.76371
$494$	8.03005	0.361289
$495$	−22.9633	−1.03212
$496$	−1.08928	−0.0489101
$497$	−28.7968	−1.29171
$498$	25.2825	1.13294
$499$	−37.5239	−1.67980	−0.839901	−	0.542740i	$-0.817387\pi$
$499$	−37.5239	−1.67980	−0.839901	+	0.542740i	$0.817387\pi$
$500$	−12.0945	−0.540883
$501$	12.1921	0.544705
$502$	1.72214	0.0768628
$503$	−31.2489	−1.39332	−0.696660	−	0.717402i	$-0.745331\pi$
$503$	−31.2489	−1.39332	−0.696660	+	0.717402i	$0.745331\pi$
$504$	−11.3754	−0.506700
$505$	−31.8506	−1.41734
$506$	−32.2578	−1.43403
$507$	13.4956	0.599361
$508$	−14.1060	−0.625852
$509$	−19.1345	−0.848120	−0.424060	−	0.905634i	$-0.639395\pi$
$509$	−19.1345	−0.848120	−0.424060	+	0.905634i	$0.639395\pi$
$510$	26.4256	1.17014
$511$	−19.5119	−0.863157
$512$	−1.00000	−0.0441942
$513$	−1.92336	−0.0849184
$514$	4.47780	0.197507
$515$	−0.0702740	−0.00309664
$516$	11.9432	0.525772
$517$	49.6173	2.18216
$518$	−22.8774	−1.00518
$519$	40.8067	1.79121
$520$	−5.27207	−0.231195
$521$	3.10270	0.135932	0.0679659	−	0.997688i	$-0.478349\pi$
$521$	3.10270	0.135932	0.0679659	+	0.997688i	$0.478349\pi$
$522$	−18.8047	−0.823061
$523$	−19.0531	−0.833132	−0.416566	−	0.909105i	$-0.636767\pi$
$523$	−19.0531	−0.833132	−0.416566	+	0.909105i	$0.636767\pi$
$524$	6.78064	0.296214
$525$	12.2163	0.533161
$526$	15.5812	0.679374
$527$	−6.18932	−0.269611
$528$	10.3665	0.451144
$529$	32.4681	1.41166
$530$	5.77479	0.250841
$531$	−0.148108	−0.00642735
$532$	−12.3391	−0.534969
$533$	−15.6381	−0.677360
$534$	4.60718	0.199372
$535$	−37.1113	−1.60446
$536$	14.2464	0.615353
$537$	60.6953	2.61919
$538$	−1.15183	−0.0496588
$539$	−44.9656	−1.93681
$540$	1.26277	0.0543409
$541$	−42.7976	−1.84001	−0.920006	−	0.391904i	$-0.871816\pi$
$541$	−42.7976	−1.84001	−0.920006	+	0.391904i	$0.871816\pi$
$542$	−23.5103	−1.00985
$543$	−26.5916	−1.14115
$544$	−5.68203	−0.243615
$545$	−38.4272	−1.64604
$546$	27.0735	1.15864
$547$	−18.9667	−0.810956	−0.405478	−	0.914105i	$-0.632895\pi$
$547$	−18.9667	−0.810956	−0.405478	+	0.914105i	$0.632895\pi$
$548$	−11.7616	−0.502429
$549$	27.2759	1.16411
$550$	−5.30255	−0.226102
$551$	−20.3979	−0.868979
$552$	−17.8255	−0.758703
$553$	34.5508	1.46925
$554$	11.7967	0.501195
$555$	−25.5201	−1.08327
$556$	−17.5545	−0.744475
$557$	−22.6603	−0.960149	−0.480074	−	0.877228i	$-0.659390\pi$
$557$	−22.6603	−0.960149	−0.480074	+	0.877228i	$0.659390\pi$
$558$	2.97208	0.125818
$559$	−13.5389	−0.572633
$560$	8.10116	0.342336
$561$	58.9028	2.48688
$562$	20.0725	0.846707
$563$	2.52568	0.106445	0.0532223	−	0.998583i	$-0.483051\pi$
$563$	2.52568	0.106445	0.0532223	+	0.998583i	$0.483051\pi$
$564$	27.4182	1.15452
$565$	4.43931	0.186763
$566$	−7.09054	−0.298038
$567$	−40.6109	−1.70550
$568$	6.90714	0.289817
$569$	34.2535	1.43598	0.717991	−	0.696052i	$-0.245062\pi$
$569$	34.2535	1.43598	0.717991	+	0.696052i	$0.245062\pi$
$570$	−13.7645	−0.576530
$571$	−43.4271	−1.81737	−0.908683	−	0.417486i	$-0.862911\pi$
$571$	−43.4271	−1.81737	−0.908683	+	0.417486i	$0.862911\pi$
$572$	−11.7515	−0.491354
$573$	−44.0390	−1.83976
$574$	24.0298	1.00298
$575$	9.11789	0.380242
$576$	2.72848	0.113687
$577$	−0.861400	−0.0358605	−0.0179303	−	0.999839i	$-0.505708\pi$
$577$	−0.861400	−0.0358605	−0.0179303	+	0.999839i	$0.505708\pi$
$578$	−15.2854	−0.635790
$579$	−25.0992	−1.04309
$580$	13.3921	0.556075
$581$	44.0399	1.82708
$582$	−7.74331	−0.320971
$583$	12.8720	0.533106
$584$	4.68009	0.193664
$585$	14.3847	0.594735
$586$	7.50039	0.309838
$587$	15.8166	0.652819	0.326410	−	0.945228i	$-0.394161\pi$
$587$	15.8166	0.652819	0.326410	+	0.945228i	$0.394161\pi$
$588$	−24.8478	−1.02470
$589$	3.22388	0.132837
$590$	0.105477	0.00434244
$591$	−30.1705	−1.24105
$592$	5.48734	0.225528
$593$	3.26147	0.133933	0.0669663	−	0.997755i	$-0.478668\pi$
$593$	3.26147	0.133933	0.0669663	+	0.997755i	$0.478668\pi$
$594$	2.81472	0.115489
$595$	46.0310	1.88709
$596$	13.0283	0.533659
$597$	−35.2408	−1.44231
$598$	20.2070	0.826325
$599$	−11.3760	−0.464811	−0.232405	−	0.972619i	$-0.574660\pi$
$599$	−11.3760	−0.464811	−0.232405	+	0.972619i	$0.574660\pi$
$600$	−2.93017	−0.119623
$601$	40.6685	1.65890	0.829450	−	0.558580i	$-0.188654\pi$
$601$	40.6685	1.65890	0.829450	+	0.558580i	$0.188654\pi$
$602$	20.8041	0.847911
$603$	−38.8711	−1.58295
$604$	−2.92373	−0.118965
$605$	15.0781	0.613010
$606$	−39.2317	−1.59368
$607$	8.86610	0.359864	0.179932	−	0.983679i	$-0.442412\pi$
$607$	8.86610	0.359864	0.179932	+	0.983679i	$0.442412\pi$
$608$	2.95964	0.120029
$609$	−68.7720	−2.78678
$610$	−19.4249	−0.786492
$611$	−31.0813	−1.25742
$612$	15.5033	0.626683
$613$	30.3652	1.22644	0.613219	−	0.789913i	$-0.289874\pi$
$613$	30.3652	1.22644	0.613219	+	0.789913i	$0.289874\pi$
$614$	−11.2203	−0.452813
$615$	26.8055	1.08090
$616$	18.0575	0.727559
$617$	−38.5220	−1.55084	−0.775419	−	0.631447i	$-0.782462\pi$
$617$	−38.5220	−1.55084	−0.775419	+	0.631447i	$0.782462\pi$
$618$	−0.0865592	−0.00348192
$619$	−30.2580	−1.21617	−0.608087	−	0.793871i	$-0.708063\pi$
$619$	−30.2580	−1.21617	−0.608087	+	0.793871i	$0.708063\pi$
$620$	−2.11661	−0.0850051
$621$	−4.83998	−0.194222
$622$	−1.87274	−0.0750900
$623$	8.02530	0.321527
$624$	−6.49381	−0.259960
$625$	−17.3799	−0.695197
$626$	26.8274	1.07224
$627$	−30.6811	−1.22529
$628$	4.91322	0.196059
$629$	31.1792	1.24320
$630$	−22.1038	−0.880638
$631$	−35.7124	−1.42169	−0.710844	−	0.703350i	$-0.751687\pi$
$631$	−35.7124	−1.42169	−0.710844	+	0.703350i	$0.751687\pi$
$632$	−8.28729	−0.329651
$633$	−35.0489	−1.39307
$634$	34.2630	1.36076
$635$	−27.4097	−1.08772
$636$	7.11303	0.282050
$637$	28.1674	1.11603
$638$	29.8510	1.18181
$639$	−18.8460	−0.745535
$640$	−1.94313	−0.0768088
$641$	−36.0350	−1.42330	−0.711649	−	0.702535i	$-0.752051\pi$
$641$	−36.0350	−1.42330	−0.711649	+	0.702535i	$0.752051\pi$
$642$	−45.7114	−1.80409
$643$	25.2333	0.995106	0.497553	−	0.867434i	$-0.334232\pi$
$643$	25.2333	0.995106	0.497553	+	0.867434i	$0.334232\pi$
$644$	−31.0504	−1.22356
$645$	23.2072	0.913784
$646$	16.8167	0.661646
$647$	−23.1262	−0.909184	−0.454592	−	0.890700i	$-0.650215\pi$
$647$	−23.1262	−0.909184	−0.454592	+	0.890700i	$0.650215\pi$
$648$	9.74084	0.382656
$649$	0.235110	0.00922888
$650$	3.32164	0.130285
$651$	10.8694	0.426005
$652$	6.54567	0.256348
$653$	17.4034	0.681048	0.340524	−	0.940236i	$-0.389396\pi$
$653$	17.4034	0.681048	0.340524	+	0.940236i	$0.389396\pi$
$654$	−47.3323	−1.85084
$655$	13.1757	0.514815
$656$	−5.76373	−0.225036
$657$	−12.7695	−0.498187
$658$	47.7602	1.86189
$659$	−12.7356	−0.496108	−0.248054	−	0.968746i	$-0.579791\pi$
$659$	−12.7356	−0.496108	−0.248054	+	0.968746i	$0.579791\pi$
$660$	20.1434	0.784082
$661$	25.7885	1.00306	0.501528	−	0.865141i	$-0.332771\pi$
$661$	25.7885	1.00306	0.501528	+	0.865141i	$0.332771\pi$
$662$	−3.34434	−0.129981
$663$	−36.8980	−1.43300
$664$	−10.5633	−0.409936
$665$	−23.9765	−0.929768
$666$	−14.9721	−0.580157
$667$	−51.3296	−1.98749
$668$	−5.09402	−0.197093
$669$	−48.5226	−1.87599
$670$	27.6826	1.06947
$671$	−43.2983	−1.67151
$672$	9.97851	0.384929
$673$	−39.5163	−1.52324	−0.761621	−	0.648023i	$-0.775596\pi$
$673$	−39.5163	−1.52324	−0.761621	+	0.648023i	$0.775596\pi$
$674$	−26.9648	−1.03864
$675$	−0.795600	−0.0306226
$676$	−5.63862	−0.216870
$677$	4.46518	0.171611	0.0858054	−	0.996312i	$-0.472654\pi$
$677$	4.46518	0.171611	0.0858054	+	0.996312i	$0.472654\pi$
$678$	5.46807	0.210000
$679$	−13.4882	−0.517628
$680$	−11.0409	−0.423399
$681$	−65.4278	−2.50720
$682$	−4.71794	−0.180659
$683$	28.1324	1.07646	0.538228	−	0.842799i	$-0.319094\pi$
$683$	28.1324	1.07646	0.538228	+	0.842799i	$0.319094\pi$
$684$	−8.07531	−0.308767
$685$	−22.8542	−0.873215
$686$	−14.0987	−0.538290
$687$	26.6453	1.01658
$688$	−4.99002	−0.190243
$689$	−8.06333	−0.307188
$690$	−34.6372	−1.31862
$691$	18.5205	0.704555	0.352277	−	0.935896i	$-0.385407\pi$
$691$	18.5205	0.704555	0.352277	+	0.935896i	$0.385407\pi$
$692$	−17.0495	−0.648124
$693$	−49.2696	−1.87160
$694$	12.2128	0.463592
$695$	−34.1106	−1.29389
$696$	16.4955	0.625261
$697$	−32.7497	−1.24048
$698$	−2.33229	−0.0882784
$699$	−0.516230	−0.0195256
$700$	−5.10409	−0.192916
$701$	16.8389	0.635997	0.317999	−	0.948091i	$-0.396989\pi$
$701$	16.8389	0.635997	0.317999	+	0.948091i	$0.396989\pi$
$702$	−1.76320	−0.0665477
$703$	−16.2405	−0.612523
$704$	−4.33125	−0.163240
$705$	53.2771	2.00653
$706$	13.9573	0.525290
$707$	−68.3381	−2.57012
$708$	0.129921	0.00488272
$709$	−39.9157	−1.49907	−0.749533	−	0.661967i	$-0.769722\pi$
$709$	−39.9157	−1.49907	−0.749533	+	0.661967i	$0.769722\pi$
$710$	13.4214	0.503698
$711$	22.6117	0.848005
$712$	−1.92493	−0.0721398
$713$	8.11263	0.303820
$714$	56.6981	2.12187
$715$	−22.8346	−0.853966
$716$	−25.3592	−0.947717
$717$	−39.5956	−1.47872
$718$	−21.0099	−0.784083
$719$	10.6302	0.396440	0.198220	−	0.980158i	$-0.436484\pi$
$719$	10.6302	0.396440	0.198220	+	0.980158i	$0.436484\pi$
$720$	5.30178	0.197586
$721$	−0.150778	−0.00561528
$722$	10.2405	0.381114
$723$	−64.9166	−2.41427
$724$	11.1103	0.412910
$725$	−8.43760	−0.313364
$726$	18.5722	0.689280
$727$	30.8953	1.14584	0.572921	−	0.819611i	$-0.305810\pi$
$727$	30.8953	1.14584	0.572921	+	0.819611i	$0.305810\pi$
$728$	−11.3116	−0.419237
$729$	−21.9115	−0.811536
$730$	9.09401	0.336585
$731$	−28.3534	−1.04869
$732$	−23.9264	−0.884346
$733$	−45.0743	−1.66486	−0.832428	−	0.554133i	$-0.813050\pi$
$733$	−45.0743	−1.66486	−0.832428	+	0.554133i	$0.813050\pi$
$734$	−17.9655	−0.663120
$735$	−48.2824	−1.78092
$736$	7.44769	0.274526
$737$	61.7048	2.27293
$738$	15.7262	0.578890
$739$	19.5871	0.720522	0.360261	−	0.932852i	$-0.382688\pi$
$739$	19.5871	0.720522	0.360261	+	0.932852i	$0.382688\pi$
$740$	10.6626	0.391965
$741$	19.2193	0.706039
$742$	12.3903	0.454861
$743$	19.6090	0.719384	0.359692	−	0.933071i	$-0.382882\pi$
$743$	19.6090	0.719384	0.359692	+	0.933071i	$0.382882\pi$
$744$	−2.60711	−0.0955813
$745$	25.3156	0.927492
$746$	9.07032	0.332088
$747$	28.8218	1.05453
$748$	−24.6102	−0.899840
$749$	−79.6253	−2.90945
$750$	−28.9473	−1.05701
$751$	27.4195	1.00055	0.500276	−	0.865866i	$-0.333232\pi$
$751$	27.4195	1.00055	0.500276	+	0.865866i	$0.333232\pi$
$752$	−11.4557	−0.417745
$753$	4.12181	0.150207
$754$	−18.6993	−0.680989
$755$	−5.68119	−0.206760
$756$	2.70937	0.0985388
$757$	−16.9437	−0.615829	−0.307915	−	0.951414i	$-0.599631\pi$
$757$	−16.9437	−0.615829	−0.307915	+	0.951414i	$0.599631\pi$
$758$	28.4905	1.03482
$759$	−77.2066	−2.80242
$760$	5.75095	0.208609
$761$	−22.6779	−0.822073	−0.411037	−	0.911619i	$-0.634833\pi$
$761$	−22.6779	−0.822073	−0.411037	+	0.911619i	$0.634833\pi$
$762$	−33.7616	−1.22305
$763$	−82.4487	−2.98484
$764$	18.4000	0.665689
$765$	30.1249	1.08917
$766$	−29.1766	−1.05419
$767$	−0.147278	−0.00531790
$768$	−2.39342	−0.0863653
$769$	54.4430	1.96327	0.981633	−	0.190779i	$-0.0611013\pi$
$769$	54.4430	1.96327	0.981633	+	0.190779i	$0.0611013\pi$
$770$	35.0881	1.26449
$771$	10.7173	0.385973
$772$	10.4867	0.377426
$773$	23.7275	0.853421	0.426710	−	0.904388i	$-0.359672\pi$
$773$	23.7275	0.853421	0.426710	+	0.904388i	$0.359672\pi$
$774$	13.6152	0.489388
$775$	1.33356	0.0479028
$776$	3.23525	0.116139
$777$	−54.7554	−1.96434
$778$	16.6747	0.597818
$779$	17.0585	0.611186
$780$	−12.6183	−0.451807
$781$	29.9165	1.07050
$782$	42.3180	1.51329
$783$	4.47887	0.160062
$784$	10.3817	0.370774
$785$	9.54702	0.340748
$786$	16.2290	0.578868
$787$	11.2934	0.402567	0.201283	−	0.979533i	$-0.435489\pi$
$787$	11.2934	0.402567	0.201283	+	0.979533i	$0.435489\pi$
$788$	12.6056	0.449056
$789$	37.2925	1.32765
$790$	−16.1033	−0.572928
$791$	9.52490	0.338666
$792$	11.8177	0.419924
$793$	27.1230	0.963166
$794$	−10.0850	−0.357902
$795$	13.8215	0.490199
$796$	14.7240	0.521879
$797$	−4.59914	−0.162910	−0.0814550	−	0.996677i	$-0.525957\pi$
$797$	−4.59914	−0.162910	−0.0814550	+	0.996677i	$0.525957\pi$
$798$	−29.5328	−1.04545
$799$	−65.0913	−2.30277
$800$	1.22426	0.0432840
$801$	5.25213	0.185575
$802$	9.05638	0.319792
$803$	20.2706	0.715335
$804$	34.0978	1.20254
$805$	−60.3349	−2.12653
$806$	2.95542	0.104100
$807$	−2.75681	−0.0970443
$808$	16.3914	0.576649
$809$	26.1697	0.920078	0.460039	−	0.887899i	$-0.347835\pi$
$809$	26.1697	0.920078	0.460039	+	0.887899i	$0.347835\pi$
$810$	18.9277	0.665051
$811$	−6.27402	−0.220310	−0.110155	−	0.993914i	$-0.535135\pi$
$811$	−6.27402	−0.220310	−0.110155	+	0.993914i	$0.535135\pi$
$812$	28.7337	1.00836
$813$	−56.2701	−1.97348
$814$	23.7670	0.833033
$815$	12.7191	0.445529
$816$	−13.5995	−0.476078
$817$	14.7687	0.516690
$818$	28.8539	1.00885
$819$	30.8636	1.07846
$820$	−11.1997	−0.391109
$821$	−30.9781	−1.08114	−0.540572	−	0.841298i	$-0.681792\pi$
$821$	−30.9781	−1.08114	−0.540572	+	0.841298i	$0.681792\pi$
$822$	−28.1504	−0.981859
$823$	30.8907	1.07678	0.538391	−	0.842695i	$-0.319032\pi$
$823$	30.8907	1.07678	0.538391	+	0.842695i	$0.319032\pi$
$824$	0.0361654	0.00125988
$825$	−12.6913	−0.441853
$826$	0.226310	0.00787434
$827$	−13.7984	−0.479818	−0.239909	−	0.970795i	$-0.577118\pi$
$827$	−13.7984	−0.479818	−0.239909	+	0.970795i	$0.577118\pi$
$828$	−20.3209	−0.706199
$829$	−26.6331	−0.925005	−0.462502	−	0.886618i	$-0.653048\pi$
$829$	−26.6331	−0.925005	−0.462502	+	0.886618i	$0.653048\pi$
$830$	−20.5259	−0.712463
$831$	28.2346	0.979446
$832$	2.71319	0.0940628
$833$	58.9890	2.04385
$834$	−42.0153	−1.45487
$835$	−9.89832	−0.342545
$836$	12.8189	0.443351
$837$	−0.707884	−0.0244680
$838$	36.0868	1.24660
$839$	−20.2614	−0.699500	−0.349750	−	0.936843i	$-0.613734\pi$
$839$	−20.2614	−0.699500	−0.349750	+	0.936843i	$0.613734\pi$
$840$	19.3895	0.669002
$841$	18.4999	0.637927
$842$	−23.2510	−0.801282
$843$	48.0420	1.65465
$844$	14.6438	0.504061
$845$	−10.9566	−0.376917
$846$	31.2565	1.07462
$847$	32.3512	1.11160
$848$	−2.97190	−0.102056
$849$	−16.9707	−0.582432
$850$	6.95626	0.238598
$851$	−40.8680	−1.40094
$852$	16.5317	0.566367
$853$	−21.0615	−0.721132	−0.360566	−	0.932734i	$-0.617416\pi$
$853$	−21.0615	−0.721132	−0.360566	+	0.932734i	$0.617416\pi$
$854$	−41.6777	−1.42618
$855$	−15.6914	−0.536633
$856$	19.0988	0.652782
$857$	−21.3145	−0.728088	−0.364044	−	0.931382i	$-0.618604\pi$
$857$	−21.3145	−0.728088	−0.364044	+	0.931382i	$0.618604\pi$
$858$	−28.1263	−0.960215
$859$	3.90743	0.133320	0.0666599	−	0.997776i	$-0.478766\pi$
$859$	3.90743	0.133320	0.0666599	+	0.997776i	$0.478766\pi$
$860$	−9.69625	−0.330639
$861$	57.5134	1.96005
$862$	−27.2496	−0.928124
$863$	2.42849	0.0826666	0.0413333	−	0.999145i	$-0.486839\pi$
$863$	2.42849	0.0826666	0.0413333	+	0.999145i	$0.486839\pi$
$864$	−0.649863	−0.0221088
$865$	−33.1293	−1.12643
$866$	−25.0898	−0.852585
$867$	−36.5845	−1.24247
$868$	−4.54136	−0.154144
$869$	−35.8943	−1.21763
$870$	32.0529	1.08669
$871$	−38.6533	−1.30972
$872$	19.7760	0.669699
$873$	−8.82730	−0.298759
$874$	−22.0425	−0.745598
$875$	−50.4237	−1.70463
$876$	11.2014	0.378462
$877$	−36.3404	−1.22713	−0.613563	−	0.789646i	$-0.710264\pi$
$877$	−36.3404	−1.22713	−0.613563	+	0.789646i	$0.710264\pi$
$878$	15.7084	0.530133
$879$	17.9516	0.605493
$880$	−8.41616	−0.283709
$881$	56.7582	1.91223	0.956117	−	0.292985i	$-0.0946487\pi$
$881$	56.7582	1.91223	0.956117	+	0.292985i	$0.0946487\pi$
$882$	−28.3262	−0.953793
$883$	−9.34946	−0.314634	−0.157317	−	0.987548i	$-0.550284\pi$
$883$	−9.34946	−0.314634	−0.157317	+	0.987548i	$0.550284\pi$
$884$	15.4164	0.518510
$885$	0.252452	0.00848609
$886$	35.2775	1.18517
$887$	45.0943	1.51412	0.757059	−	0.653346i	$-0.226635\pi$
$887$	45.0943	1.51412	0.757059	+	0.653346i	$0.226635\pi$
$888$	13.1335	0.440732
$889$	−58.8098	−1.97242
$890$	−3.74039	−0.125378
$891$	42.1900	1.41342
$892$	20.2733	0.678800
$893$	33.9046	1.13457
$894$	31.1822	1.04289
$895$	−49.2761	−1.64712
$896$	−4.16913	−0.139281
$897$	48.3639	1.61482
$898$	31.7244	1.05866
$899$	−7.50734	−0.250384
$900$	−3.34036	−0.111345
$901$	−16.8864	−0.562569
$902$	−24.9641	−0.831214
$903$	49.7930	1.65701
$904$	−2.28462	−0.0759854
$905$	21.5887	0.717631
$906$	−6.99773	−0.232484
$907$	−19.1081	−0.634474	−0.317237	−	0.948346i	$-0.602755\pi$
$907$	−19.1081	−0.634474	−0.317237	+	0.948346i	$0.602755\pi$
$908$	27.3365	0.907193
$909$	−44.7237	−1.48339
$910$	−21.9800	−0.728628
$911$	−30.4724	−1.00960	−0.504799	−	0.863237i	$-0.668433\pi$
$911$	−30.4724	−1.00960	−0.504799	+	0.863237i	$0.668433\pi$
$912$	7.08367	0.234564
$913$	−45.7523	−1.51418
$914$	−12.6934	−0.419860
$915$	−46.4921	−1.53698
$916$	−11.1327	−0.367834
$917$	28.2694	0.933538
$918$	−3.69254	−0.121872
$919$	8.68114	0.286364	0.143182	−	0.989696i	$-0.454267\pi$
$919$	8.68114	0.286364	0.143182	+	0.989696i	$0.454267\pi$
$920$	14.4718	0.477122
$921$	−26.8548	−0.884897
$922$	−10.0120	−0.329727
$923$	−18.7403	−0.616846
$924$	43.2194	1.42181
$925$	−6.71791	−0.220883
$926$	−39.4617	−1.29679
$927$	−0.0986766	−0.00324097
$928$	−6.89202	−0.226242
$929$	−7.89059	−0.258882	−0.129441	−	0.991587i	$-0.541318\pi$
$929$	−7.89059	−0.258882	−0.129441	+	0.991587i	$0.541318\pi$
$930$	−5.06595	−0.166119
$931$	−30.7260	−1.00700
$932$	0.215687	0.00706505
$933$	−4.48226	−0.146743
$934$	−35.1410	−1.14985
$935$	−47.8208	−1.56391
$936$	−7.40287	−0.241970
$937$	4.17264	0.136314	0.0681570	−	0.997675i	$-0.478288\pi$
$937$	4.17264	0.136314	0.0681570	+	0.997675i	$0.478288\pi$
$938$	59.3953	1.93933
$939$	64.2094	2.09539
$940$	−22.2598	−0.726035
$941$	−20.2127	−0.658916	−0.329458	−	0.944170i	$-0.606866\pi$
$941$	−20.2127	−0.658916	−0.329458	+	0.944170i	$0.606866\pi$
$942$	11.7594	0.383143
$943$	42.9265	1.39788
$944$	−0.0542823	−0.00176674
$945$	5.26465	0.171259
$946$	−21.6130	−0.702700
$947$	30.0721	0.977213	0.488607	−	0.872504i	$-0.337505\pi$
$947$	30.0721	0.977213	0.488607	+	0.872504i	$0.337505\pi$
$948$	−19.8350	−0.644211
$949$	−12.6980	−0.412193
$950$	−3.62336	−0.117557
$951$	82.0058	2.65922
$952$	−23.6891	−0.767769
$953$	32.3158	1.04681	0.523406	−	0.852083i	$-0.324661\pi$
$953$	32.3158	1.04681	0.523406	+	0.852083i	$0.324661\pi$
$954$	8.10878	0.262531
$955$	35.7536	1.15696
$956$	16.5435	0.535054
$957$	71.4461	2.30953
$958$	−18.8847	−0.610136
$959$	−49.0355	−1.58344
$960$	−4.65073	−0.150102
$961$	−29.8135	−0.961725
$962$	−14.8882	−0.480014
$963$	−52.1106	−1.67924
$964$	27.1229	0.873569
$965$	20.3770	0.655960
$966$	−74.3168	−2.39111
$967$	−16.6079	−0.534074	−0.267037	−	0.963686i	$-0.586045\pi$
$967$	−16.6079	−0.534074	−0.267037	+	0.963686i	$0.586045\pi$
$968$	−7.75968	−0.249406
$969$	40.2496	1.29300
$970$	6.28649	0.201847
$971$	−11.3801	−0.365203	−0.182602	−	0.983187i	$-0.558452\pi$
$971$	−11.3801	−0.365203	−0.182602	+	0.983187i	$0.558452\pi$
$972$	21.3644	0.685262
$973$	−73.1870	−2.34627
$974$	5.29030	0.169512
$975$	7.95008	0.254606
$976$	9.99674	0.319988
$977$	−34.7575	−1.11199	−0.555995	−	0.831186i	$-0.687663\pi$
$977$	−34.7575	−1.11199	−0.555995	+	0.831186i	$0.687663\pi$
$978$	15.6666	0.500961
$979$	−8.33735	−0.266463
$980$	20.1729	0.644400
$981$	−53.9583	−1.72276
$982$	24.3784	0.777945
$983$	51.2355	1.63416	0.817079	−	0.576526i	$-0.195592\pi$
$983$	51.2355	1.63416	0.817079	+	0.576526i	$0.195592\pi$
$984$	−13.7950	−0.439770
$985$	24.4943	0.780452
$986$	−39.1606	−1.24713
$987$	114.310	3.63854
$988$	−8.03005	−0.255470
$989$	37.1642	1.18175
$990$	22.9633	0.729822
$991$	55.2451	1.75492	0.877460	−	0.479650i	$-0.159237\pi$
$991$	55.2451	1.75492	0.877460	+	0.479650i	$0.159237\pi$
$992$	1.08928	0.0345847
$993$	−8.00442	−0.254013
$994$	28.7968	0.913378
$995$	28.6106	0.907018
$996$	−25.2825	−0.801106
$997$	−32.2517	−1.02142	−0.510711	−	0.859753i	$-0.670618\pi$
$997$	−32.2517	−1.02142	−0.510711	+	0.859753i	$0.670618\pi$
$998$	37.5239	1.18780
$999$	3.56602	0.112824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.15	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.39342 q^{3} +1.00000 q^{4} +1.94313 q^{5} +2.39342 q^{6} +4.16913 q^{7} -1.00000 q^{8} +2.72848 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.39342 q^{3} +1.00000 q^{4} +1.94313 q^{5} +2.39342 q^{6} +4.16913 q^{7} -1.00000 q^{8} +2.72848 q^{9} -1.94313 q^{10} -4.33125 q^{11} -2.39342 q^{12} +2.71319 q^{13} -4.16913 q^{14} -4.65073 q^{15} +1.00000 q^{16} +5.68203 q^{17} -2.72848 q^{18} -2.95964 q^{19} +1.94313 q^{20} -9.97851 q^{21} +4.33125 q^{22} -7.44769 q^{23} +2.39342 q^{24} -1.22426 q^{25} -2.71319 q^{26} +0.649863 q^{27} +4.16913 q^{28} +6.89202 q^{29} +4.65073 q^{30} -1.08928 q^{31} -1.00000 q^{32} +10.3665 q^{33} -5.68203 q^{34} +8.10116 q^{35} +2.72848 q^{36} +5.48734 q^{37} +2.95964 q^{38} -6.49381 q^{39} -1.94313 q^{40} -5.76373 q^{41} +9.97851 q^{42} -4.99002 q^{43} -4.33125 q^{44} +5.30178 q^{45} +7.44769 q^{46} -11.4557 q^{47} -2.39342 q^{48} +10.3817 q^{49} +1.22426 q^{50} -13.5995 q^{51} +2.71319 q^{52} -2.97190 q^{53} -0.649863 q^{54} -8.41616 q^{55} -4.16913 q^{56} +7.08367 q^{57} -6.89202 q^{58} -0.0542823 q^{59} -4.65073 q^{60} +9.99674 q^{61} +1.08928 q^{62} +11.3754 q^{63} +1.00000 q^{64} +5.27207 q^{65} -10.3665 q^{66} -14.2464 q^{67} +5.68203 q^{68} +17.8255 q^{69} -8.10116 q^{70} -6.90714 q^{71} -2.72848 q^{72} -4.68009 q^{73} -5.48734 q^{74} +2.93017 q^{75} -2.95964 q^{76} -18.0575 q^{77} +6.49381 q^{78} +8.28729 q^{79} +1.94313 q^{80} -9.74084 q^{81} +5.76373 q^{82} +10.5633 q^{83} -9.97851 q^{84} +11.0409 q^{85} +4.99002 q^{86} -16.4955 q^{87} +4.33125 q^{88} +1.92493 q^{89} -5.30178 q^{90} +11.3116 q^{91} -7.44769 q^{92} +2.60711 q^{93} +11.4557 q^{94} -5.75095 q^{95} +2.39342 q^{96} -3.23525 q^{97} -10.3817 q^{98} -11.8177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 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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