LMFDB - Embedded newform 8031.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60983 q^{2} -1.00000 q^{3} +4.81123 q^{4} +0.810523 q^{5} +2.60983 q^{6} -4.83270 q^{7} -7.33685 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60983 q^{2} -1.00000 q^{3} +4.81123 q^{4} +0.810523 q^{5} +2.60983 q^{6} -4.83270 q^{7} -7.33685 q^{8} +1.00000 q^{9} -2.11533 q^{10} -2.92790 q^{11} -4.81123 q^{12} -0.542382 q^{13} +12.6125 q^{14} -0.810523 q^{15} +9.52548 q^{16} +0.917176 q^{17} -2.60983 q^{18} -1.28090 q^{19} +3.89961 q^{20} +4.83270 q^{21} +7.64134 q^{22} -7.46683 q^{23} +7.33685 q^{24} -4.34305 q^{25} +1.41553 q^{26} -1.00000 q^{27} -23.2512 q^{28} +2.29043 q^{29} +2.11533 q^{30} +4.30000 q^{31} -10.1862 q^{32} +2.92790 q^{33} -2.39368 q^{34} -3.91701 q^{35} +4.81123 q^{36} -9.18446 q^{37} +3.34295 q^{38} +0.542382 q^{39} -5.94668 q^{40} +7.44482 q^{41} -12.6125 q^{42} -0.776898 q^{43} -14.0868 q^{44} +0.810523 q^{45} +19.4872 q^{46} -7.44886 q^{47} -9.52548 q^{48} +16.3549 q^{49} +11.3346 q^{50} -0.917176 q^{51} -2.60952 q^{52} +4.63674 q^{53} +2.60983 q^{54} -2.37313 q^{55} +35.4567 q^{56} +1.28090 q^{57} -5.97763 q^{58} -8.70149 q^{59} -3.89961 q^{60} +0.400818 q^{61} -11.2223 q^{62} -4.83270 q^{63} +7.53341 q^{64} -0.439613 q^{65} -7.64134 q^{66} -1.58936 q^{67} +4.41275 q^{68} +7.46683 q^{69} +10.2227 q^{70} -9.82604 q^{71} -7.33685 q^{72} -16.3779 q^{73} +23.9699 q^{74} +4.34305 q^{75} -6.16273 q^{76} +14.1497 q^{77} -1.41553 q^{78} -13.2868 q^{79} +7.72062 q^{80} +1.00000 q^{81} -19.4297 q^{82} +3.38240 q^{83} +23.2512 q^{84} +0.743392 q^{85} +2.02757 q^{86} -2.29043 q^{87} +21.4816 q^{88} -2.56431 q^{89} -2.11533 q^{90} +2.62117 q^{91} -35.9246 q^{92} -4.30000 q^{93} +19.4403 q^{94} -1.03820 q^{95} +10.1862 q^{96} -5.38004 q^{97} -42.6837 q^{98} -2.92790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.60983	−1.84543	−0.922716	−	0.385482i	$-0.874035\pi$
$2$	−2.60983	−1.84543	−0.922716	+	0.385482i	$0.874035\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.81123	2.40562
$5$	0.810523	0.362477	0.181238	−	0.983439i	$-0.441989\pi$
$5$	0.810523	0.362477	0.181238	+	0.983439i	$0.441989\pi$
$6$	2.60983	1.06546
$7$	−4.83270	−1.82659	−0.913294	−	0.407302i	$-0.866470\pi$
$7$	−4.83270	−1.82659	−0.913294	+	0.407302i	$0.866470\pi$
$8$	−7.33685	−2.59397
$9$	1.00000	0.333333
$10$	−2.11533	−0.668926
$11$	−2.92790	−0.882796	−0.441398	−	0.897311i	$-0.645517\pi$
$11$	−2.92790	−0.882796	−0.441398	+	0.897311i	$0.645517\pi$
$12$	−4.81123	−1.38888
$13$	−0.542382	−0.150430	−0.0752148	−	0.997167i	$-0.523964\pi$
$13$	−0.542382	−0.150430	−0.0752148	+	0.997167i	$0.523964\pi$
$14$	12.6125	3.37084
$15$	−0.810523	−0.209276
$16$	9.52548	2.38137
$17$	0.917176	0.222448	0.111224	−	0.993795i	$-0.464523\pi$
$17$	0.917176	0.222448	0.111224	+	0.993795i	$0.464523\pi$
$18$	−2.60983	−0.615144
$19$	−1.28090	−0.293860	−0.146930	−	0.989147i	$-0.546939\pi$
$19$	−1.28090	−0.293860	−0.146930	+	0.989147i	$0.546939\pi$
$20$	3.89961	0.871980
$21$	4.83270	1.05458
$22$	7.64134	1.62914
$23$	−7.46683	−1.55694	−0.778471	−	0.627681i	$-0.784004\pi$
$23$	−7.46683	−1.55694	−0.778471	+	0.627681i	$0.784004\pi$
$24$	7.33685	1.49763
$25$	−4.34305	−0.868611
$26$	1.41553	0.277607
$27$	−1.00000	−0.192450
$28$	−23.2512	−4.39407
$29$	2.29043	0.425321	0.212661	−	0.977126i	$-0.431787\pi$
$29$	2.29043	0.425321	0.212661	+	0.977126i	$0.431787\pi$
$30$	2.11533	0.386204
$31$	4.30000	0.772302	0.386151	−	0.922436i	$-0.373804\pi$
$31$	4.30000	0.772302	0.386151	+	0.922436i	$0.373804\pi$
$32$	−10.1862	−1.80069
$33$	2.92790	0.509682
$34$	−2.39368	−0.410512
$35$	−3.91701	−0.662095
$36$	4.81123	0.801872
$37$	−9.18446	−1.50992	−0.754958	−	0.655773i	$-0.772343\pi$
$37$	−9.18446	−1.50992	−0.754958	+	0.655773i	$0.772343\pi$
$38$	3.34295	0.542298
$39$	0.542382	0.0868506
$40$	−5.94668	−0.940253
$41$	7.44482	1.16269	0.581343	−	0.813659i	$-0.302528\pi$
$41$	7.44482	1.16269	0.581343	+	0.813659i	$0.302528\pi$
$42$	−12.6125	−1.94616
$43$	−0.776898	−0.118476	−0.0592379	−	0.998244i	$-0.518867\pi$
$43$	−0.776898	−0.118476	−0.0592379	+	0.998244i	$0.518867\pi$
$44$	−14.0868	−2.12367
$45$	0.810523	0.120826
$46$	19.4872	2.87323
$47$	−7.44886	−1.08653	−0.543264	−	0.839562i	$-0.682812\pi$
$47$	−7.44886	−1.08653	−0.543264	+	0.839562i	$0.682812\pi$
$48$	−9.52548	−1.37489
$49$	16.3549	2.33642
$50$	11.3346	1.60296
$51$	−0.917176	−0.128430
$52$	−2.60952	−0.361876
$53$	4.63674	0.636905	0.318452	−	0.947939i	$-0.396837\pi$
$53$	4.63674	0.636905	0.318452	+	0.947939i	$0.396837\pi$
$54$	2.60983	0.355153
$55$	−2.37313	−0.319993
$56$	35.4567	4.73811
$57$	1.28090	0.169660
$58$	−5.97763	−0.784901
$59$	−8.70149	−1.13284	−0.566419	−	0.824118i	$-0.691672\pi$
$59$	−8.70149	−1.13284	−0.566419	+	0.824118i	$0.691672\pi$
$60$	−3.89961	−0.503438
$61$	0.400818	0.0513195	0.0256598	−	0.999671i	$-0.491831\pi$
$61$	0.400818	0.0513195	0.0256598	+	0.999671i	$0.491831\pi$
$62$	−11.2223	−1.42523
$63$	−4.83270	−0.608862
$64$	7.53341	0.941677
$65$	−0.439613	−0.0545272
$66$	−7.64134	−0.940584
$67$	−1.58936	−0.194171	−0.0970856	−	0.995276i	$-0.530952\pi$
$67$	−1.58936	−0.194171	−0.0970856	+	0.995276i	$0.530952\pi$
$68$	4.41275	0.535124
$69$	7.46683	0.898901
$70$	10.2227	1.22185
$71$	−9.82604	−1.16614	−0.583068	−	0.812423i	$-0.698148\pi$
$71$	−9.82604	−1.16614	−0.583068	+	0.812423i	$0.698148\pi$
$72$	−7.33685	−0.864656
$73$	−16.3779	−1.91688	−0.958442	−	0.285289i	$-0.907910\pi$
$73$	−16.3779	−1.91688	−0.958442	+	0.285289i	$0.907910\pi$
$74$	23.9699	2.78645
$75$	4.34305	0.501493
$76$	−6.16273	−0.706913
$77$	14.1497	1.61250
$78$	−1.41553	−0.160277
$79$	−13.2868	−1.49488	−0.747441	−	0.664328i	$-0.768718\pi$
$79$	−13.2868	−1.49488	−0.747441	+	0.664328i	$0.768718\pi$
$80$	7.72062	0.863192
$81$	1.00000	0.111111
$82$	−19.4297	−2.14566
$83$	3.38240	0.371267	0.185633	−	0.982619i	$-0.440566\pi$
$83$	3.38240	0.371267	0.185633	+	0.982619i	$0.440566\pi$
$84$	23.2512	2.53692
$85$	0.743392	0.0806322
$86$	2.02757	0.218639
$87$	−2.29043	−0.245559
$88$	21.4816	2.28994
$89$	−2.56431	−0.271816	−0.135908	−	0.990721i	$-0.543395\pi$
$89$	−2.56431	−0.271816	−0.135908	+	0.990721i	$0.543395\pi$
$90$	−2.11533	−0.222975
$91$	2.62117	0.274773
$92$	−35.9246	−3.74540
$93$	−4.30000	−0.445889
$94$	19.4403	2.00511
$95$	−1.03820	−0.106517
$96$	10.1862	1.03963
$97$	−5.38004	−0.546260	−0.273130	−	0.961977i	$-0.588059\pi$
$97$	−5.38004	−0.546260	−0.273130	+	0.961977i	$0.588059\pi$
$98$	−42.6837	−4.31170
$99$	−2.92790	−0.294265
$100$	−20.8954	−2.08954
$101$	1.29234	0.128593	0.0642964	−	0.997931i	$-0.479520\pi$
$101$	1.29234	0.128593	0.0642964	+	0.997931i	$0.479520\pi$
$102$	2.39368	0.237009
$103$	−13.1087	−1.29164	−0.645819	−	0.763490i	$-0.723484\pi$
$103$	−13.1087	−1.29164	−0.645819	+	0.763490i	$0.723484\pi$
$104$	3.97937	0.390209
$105$	3.91701	0.382261
$106$	−12.1011	−1.17536
$107$	−18.2652	−1.76576	−0.882882	−	0.469596i	$-0.844400\pi$
$107$	−18.2652	−1.76576	−0.882882	+	0.469596i	$0.844400\pi$
$108$	−4.81123	−0.462961
$109$	0.766231	0.0733916	0.0366958	−	0.999326i	$-0.488317\pi$
$109$	0.766231	0.0733916	0.0366958	+	0.999326i	$0.488317\pi$
$110$	6.19348	0.590525
$111$	9.18446	0.871751
$112$	−46.0338	−4.34978
$113$	18.8075	1.76926	0.884631	−	0.466292i	$-0.154410\pi$
$113$	18.8075	1.76926	0.884631	+	0.466292i	$0.154410\pi$
$114$	−3.34295	−0.313096
$115$	−6.05203	−0.564355
$116$	11.0198	1.02316
$117$	−0.542382	−0.0501432
$118$	22.7094	2.09057
$119$	−4.43243	−0.406320
$120$	5.94668	0.542855
$121$	−2.42739	−0.220671
$122$	−1.04607	−0.0947067
$123$	−7.44482	−0.671277
$124$	20.6883	1.85786
$125$	−7.57276	−0.677328
$126$	12.6125	1.12361
$127$	−8.74601	−0.776083	−0.388041	−	0.921642i	$-0.626848\pi$
$127$	−8.74601	−0.776083	−0.388041	+	0.921642i	$0.626848\pi$
$128$	0.711519	0.0628900
$129$	0.776898	0.0684021
$130$	1.14732	0.100626
$131$	−19.8767	−1.73664	−0.868319	−	0.496007i	$-0.834799\pi$
$131$	−19.8767	−1.73664	−0.868319	+	0.496007i	$0.834799\pi$
$132$	14.0868	1.22610
$133$	6.19022	0.536760
$134$	4.14796	0.358330
$135$	−0.810523	−0.0697587
$136$	−6.72918	−0.577022
$137$	14.4176	1.23178	0.615891	−	0.787831i	$-0.288796\pi$
$137$	14.4176	1.23178	0.615891	+	0.787831i	$0.288796\pi$
$138$	−19.4872	−1.65886
$139$	−11.2145	−0.951205	−0.475602	−	0.879660i	$-0.657770\pi$
$139$	−11.2145	−0.951205	−0.475602	+	0.879660i	$0.657770\pi$
$140$	−18.8456	−1.59275
$141$	7.44886	0.627307
$142$	25.6443	2.15202
$143$	1.58804	0.132799
$144$	9.52548	0.793790
$145$	1.85644	0.154169
$146$	42.7435	3.53748
$147$	−16.3549	−1.34893
$148$	−44.1886	−3.63228
$149$	−18.9119	−1.54932	−0.774660	−	0.632378i	$-0.782079\pi$
$149$	−18.9119	−1.54932	−0.774660	+	0.632378i	$0.782079\pi$
$150$	−11.3346	−0.925470
$151$	−6.55304	−0.533279	−0.266639	−	0.963796i	$-0.585913\pi$
$151$	−6.55304	−0.533279	−0.266639	+	0.963796i	$0.585913\pi$
$152$	9.39780	0.762262
$153$	0.917176	0.0741493
$154$	−36.9283	−2.97576
$155$	3.48524	0.279941
$156$	2.60952	0.208929
$157$	−1.15206	−0.0919445	−0.0459723	−	0.998943i	$-0.514639\pi$
$157$	−1.15206	−0.0919445	−0.0459723	+	0.998943i	$0.514639\pi$
$158$	34.6764	2.75870
$159$	−4.63674	−0.367717
$160$	−8.25617	−0.652708
$161$	36.0849	2.84389
$162$	−2.60983	−0.205048
$163$	−7.88492	−0.617595	−0.308797	−	0.951128i	$-0.599926\pi$
$163$	−7.88492	−0.617595	−0.308797	+	0.951128i	$0.599926\pi$
$164$	35.8188	2.79697
$165$	2.37313	0.184748
$166$	−8.82750	−0.685147
$167$	4.31574	0.333962	0.166981	−	0.985960i	$-0.446598\pi$
$167$	4.31574	0.333962	0.166981	+	0.985960i	$0.446598\pi$
$168$	−35.4567	−2.73555
$169$	−12.7058	−0.977371
$170$	−1.94013	−0.148801
$171$	−1.28090	−0.0979532
$172$	−3.73784	−0.285007
$173$	14.8523	1.12920	0.564601	−	0.825364i	$-0.309030\pi$
$173$	14.8523	1.12920	0.564601	+	0.825364i	$0.309030\pi$
$174$	5.97763	0.453163
$175$	20.9887	1.58659
$176$	−27.8897	−2.10226
$177$	8.70149	0.654044
$178$	6.69241	0.501617
$179$	9.50719	0.710601	0.355300	−	0.934752i	$-0.384379\pi$
$179$	9.50719	0.710601	0.355300	+	0.934752i	$0.384379\pi$
$180$	3.89961	0.290660
$181$	14.1876	1.05455	0.527276	−	0.849694i	$-0.323213\pi$
$181$	14.1876	1.05455	0.527276	+	0.849694i	$0.323213\pi$
$182$	−6.84080	−0.507074
$183$	−0.400818	−0.0296294
$184$	54.7830	4.03865
$185$	−7.44422	−0.547310
$186$	11.2223	0.822857
$187$	−2.68540	−0.196376
$188$	−35.8382	−2.61377
$189$	4.83270	0.351527
$190$	2.70953	0.196570
$191$	12.3084	0.890608	0.445304	−	0.895379i	$-0.353096\pi$
$191$	12.3084	0.890608	0.445304	+	0.895379i	$0.353096\pi$
$192$	−7.53341	−0.543677
$193$	−23.0761	−1.66106	−0.830528	−	0.556977i	$-0.811961\pi$
$193$	−23.0761	−1.66106	−0.830528	+	0.556977i	$0.811961\pi$
$194$	14.0410	1.00809
$195$	0.439613	0.0314813
$196$	78.6874	5.62053
$197$	3.45286	0.246006	0.123003	−	0.992406i	$-0.460748\pi$
$197$	3.45286	0.246006	0.123003	+	0.992406i	$0.460748\pi$
$198$	7.64134	0.543046
$199$	12.8114	0.908174	0.454087	−	0.890957i	$-0.349965\pi$
$199$	12.8114	0.908174	0.454087	+	0.890957i	$0.349965\pi$
$200$	31.8643	2.25315
$201$	1.58936	0.112105
$202$	−3.37280	−0.237309
$203$	−11.0689	−0.776887
$204$	−4.41275	−0.308954
$205$	6.03420	0.421447
$206$	34.2115	2.38363
$207$	−7.46683	−0.518981
$208$	−5.16645	−0.358229
$209$	3.75036	0.259418
$210$	−10.2227	−0.705436
$211$	18.2426	1.25587	0.627936	−	0.778265i	$-0.283900\pi$
$211$	18.2426	1.25587	0.627936	+	0.778265i	$0.283900\pi$
$212$	22.3084	1.53215
$213$	9.82604	0.673269
$214$	47.6691	3.25859
$215$	−0.629694	−0.0429447
$216$	7.33685	0.499209
$217$	−20.7806	−1.41068
$218$	−1.99973	−0.135439
$219$	16.3779	1.10671
$220$	−11.4177	−0.769780
$221$	−0.497459	−0.0334627
$222$	−23.9699	−1.60876
$223$	−9.87094	−0.661007	−0.330504	−	0.943805i	$-0.607219\pi$
$223$	−9.87094	−0.661007	−0.330504	+	0.943805i	$0.607219\pi$
$224$	49.2270	3.28912
$225$	−4.34305	−0.289537
$226$	−49.0845	−3.26505
$227$	13.8020	0.916073	0.458036	−	0.888933i	$-0.348553\pi$
$227$	13.8020	0.916073	0.458036	+	0.888933i	$0.348553\pi$
$228$	6.16273	0.408137
$229$	−16.7456	−1.10658	−0.553290	−	0.832989i	$-0.686628\pi$
$229$	−16.7456	−1.10658	−0.553290	+	0.832989i	$0.686628\pi$
$230$	15.7948	1.04148
$231$	−14.1497	−0.930979
$232$	−16.8045	−1.10327
$233$	−10.4993	−0.687831	−0.343915	−	0.939001i	$-0.611753\pi$
$233$	−10.4993	−0.687831	−0.343915	+	0.939001i	$0.611753\pi$
$234$	1.41553	0.0925358
$235$	−6.03747	−0.393841
$236$	−41.8649	−2.72517
$237$	13.2868	0.863071
$238$	11.5679	0.749836
$239$	26.2628	1.69880	0.849399	−	0.527751i	$-0.176965\pi$
$239$	26.2628	1.69880	0.849399	+	0.527751i	$0.176965\pi$
$240$	−7.72062	−0.498364
$241$	−19.9536	−1.28532	−0.642661	−	0.766150i	$-0.722170\pi$
$241$	−19.9536	−1.28532	−0.642661	+	0.766150i	$0.722170\pi$
$242$	6.33507	0.407234
$243$	−1.00000	−0.0641500
$244$	1.92843	0.123455
$245$	13.2561	0.846898
$246$	19.4297	1.23880
$247$	0.694739	0.0442052
$248$	−31.5484	−2.00333
$249$	−3.38240	−0.214351
$250$	19.7636	1.24996
$251$	−27.6826	−1.74731	−0.873656	−	0.486544i	$-0.838257\pi$
$251$	−27.6826	−1.74731	−0.873656	+	0.486544i	$0.838257\pi$
$252$	−23.2512	−1.46469
$253$	21.8622	1.37446
$254$	22.8256	1.43221
$255$	−0.743392	−0.0465530
$256$	−16.9238	−1.05774
$257$	13.7086	0.855118	0.427559	−	0.903987i	$-0.359374\pi$
$257$	13.7086	0.855118	0.427559	+	0.903987i	$0.359374\pi$
$258$	−2.02757	−0.126231
$259$	44.3857	2.75799
$260$	−2.11508	−0.131172
$261$	2.29043	0.141774
$262$	51.8749	3.20484
$263$	14.2064	0.876002	0.438001	−	0.898974i	$-0.355687\pi$
$263$	14.2064	0.876002	0.438001	+	0.898974i	$0.355687\pi$
$264$	−21.4816	−1.32210
$265$	3.75818	0.230863
$266$	−16.1555	−0.990554
$267$	2.56431	0.156933
$268$	−7.64678	−0.467101
$269$	−18.6251	−1.13559	−0.567796	−	0.823169i	$-0.692204\pi$
$269$	−18.6251	−1.13559	−0.567796	+	0.823169i	$0.692204\pi$
$270$	2.11533	0.128735
$271$	7.87297	0.478249	0.239124	−	0.970989i	$-0.423140\pi$
$271$	7.87297	0.478249	0.239124	+	0.970989i	$0.423140\pi$
$272$	8.73654	0.529731
$273$	−2.62117	−0.158640
$274$	−37.6277	−2.27317
$275$	12.7160	0.766806
$276$	35.9246	2.16241
$277$	−7.03087	−0.422444	−0.211222	−	0.977438i	$-0.567744\pi$
$277$	−7.03087	−0.422444	−0.211222	+	0.977438i	$0.567744\pi$
$278$	29.2681	1.75538
$279$	4.30000	0.257434
$280$	28.7385	1.71745
$281$	2.53967	0.151504	0.0757519	−	0.997127i	$-0.475864\pi$
$281$	2.53967	0.151504	0.0757519	+	0.997127i	$0.475864\pi$
$282$	−19.4403	−1.15765
$283$	14.7458	0.876545	0.438272	−	0.898842i	$-0.355591\pi$
$283$	14.7458	0.876545	0.438272	+	0.898842i	$0.355591\pi$
$284$	−47.2754	−2.80528
$285$	1.03820	0.0614978
$286$	−4.14452	−0.245071
$287$	−35.9786	−2.12375
$288$	−10.1862	−0.600230
$289$	−16.1588	−0.950517
$290$	−4.84500	−0.284508
$291$	5.38004	0.315383
$292$	−78.7977	−4.61128
$293$	4.91819	0.287324	0.143662	−	0.989627i	$-0.454112\pi$
$293$	4.91819	0.287324	0.143662	+	0.989627i	$0.454112\pi$
$294$	42.6837	2.48936
$295$	−7.05275	−0.410627
$296$	67.3850	3.91667
$297$	2.92790	0.169894
$298$	49.3568	2.85916
$299$	4.04987	0.234210
$300$	20.8954	1.20640
$301$	3.75451	0.216406
$302$	17.1023	0.984129
$303$	−1.29234	−0.0742431
$304$	−12.2012	−0.699789
$305$	0.324872	0.0186021
$306$	−2.39368	−0.136837
$307$	26.4259	1.50821	0.754104	−	0.656755i	$-0.228071\pi$
$307$	26.4259	1.50821	0.754104	+	0.656755i	$0.228071\pi$
$308$	68.0773	3.87906
$309$	13.1087	0.745728
$310$	−9.09590	−0.516613
$311$	23.2233	1.31687	0.658437	−	0.752636i	$-0.271218\pi$
$311$	23.2233	1.31687	0.658437	+	0.752636i	$0.271218\pi$
$312$	−3.97937	−0.225287
$313$	−12.2559	−0.692743	−0.346372	−	0.938097i	$-0.612586\pi$
$313$	−12.2559	−0.692743	−0.346372	+	0.938097i	$0.612586\pi$
$314$	3.00669	0.169677
$315$	−3.91701	−0.220698
$316$	−63.9259	−3.59611
$317$	−26.1194	−1.46701	−0.733505	−	0.679684i	$-0.762117\pi$
$317$	−26.1194	−1.46701	−0.733505	+	0.679684i	$0.762117\pi$
$318$	12.1011	0.678596
$319$	−6.70614	−0.375472
$320$	6.10600	0.341336
$321$	18.2652	1.01946
$322$	−94.1756	−5.24820
$323$	−1.17481	−0.0653684
$324$	4.81123	0.267291
$325$	2.35559	0.130665
$326$	20.5783	1.13973
$327$	−0.766231	−0.0423726
$328$	−54.6215	−3.01597
$329$	35.9981	1.98464
$330$	−6.19348	−0.340940
$331$	−9.27031	−0.509542	−0.254771	−	0.967001i	$-0.582000\pi$
$331$	−9.27031	−0.509542	−0.254771	+	0.967001i	$0.582000\pi$
$332$	16.2735	0.893125
$333$	−9.18446	−0.503306
$334$	−11.2634	−0.616304
$335$	−1.28821	−0.0703825
$336$	46.0338	2.51135
$337$	−15.0367	−0.819099	−0.409550	−	0.912288i	$-0.634314\pi$
$337$	−15.0367	−0.819099	−0.409550	+	0.912288i	$0.634314\pi$
$338$	33.1601	1.80367
$339$	−18.8075	−1.02148
$340$	3.57663	0.193970
$341$	−12.5900	−0.681785
$342$	3.34295	0.180766
$343$	−45.2096	−2.44109
$344$	5.69998	0.307322
$345$	6.05203	0.325831
$346$	−38.7621	−2.08387
$347$	12.1819	0.653960	0.326980	−	0.945031i	$-0.393969\pi$
$347$	12.1819	0.653960	0.326980	+	0.945031i	$0.393969\pi$
$348$	−11.0198	−0.590722
$349$	−11.6517	−0.623699	−0.311849	−	0.950132i	$-0.600948\pi$
$349$	−11.6517	−0.623699	−0.311849	+	0.950132i	$0.600948\pi$
$350$	−54.7769	−2.92795
$351$	0.542382	0.0289502
$352$	29.8243	1.58964
$353$	−17.1466	−0.912621	−0.456311	−	0.889821i	$-0.650829\pi$
$353$	−17.1466	−0.912621	−0.456311	+	0.889821i	$0.650829\pi$
$354$	−22.7094	−1.20699
$355$	−7.96423	−0.422697
$356$	−12.3375	−0.653885
$357$	4.43243	0.234589
$358$	−24.8122	−1.31136
$359$	−6.35571	−0.335442	−0.167721	−	0.985835i	$-0.553641\pi$
$359$	−6.35571	−0.335442	−0.167721	+	0.985835i	$0.553641\pi$
$360$	−5.94668	−0.313418
$361$	−17.3593	−0.913646
$362$	−37.0272	−1.94610
$363$	2.42739	0.127405
$364$	12.6110	0.660998
$365$	−13.2746	−0.694826
$366$	1.04607	0.0546789
$367$	−25.2494	−1.31801	−0.659003	−	0.752140i	$-0.729022\pi$
$367$	−25.2494	−1.31801	−0.659003	+	0.752140i	$0.729022\pi$
$368$	−71.1252	−3.70766
$369$	7.44482	0.387562
$370$	19.4282	1.01002
$371$	−22.4079	−1.16336
$372$	−20.6883	−1.07264
$373$	0.656999	0.0340181	0.0170090	−	0.999855i	$-0.494586\pi$
$373$	0.656999	0.0340181	0.0170090	+	0.999855i	$0.494586\pi$
$374$	7.00845	0.362398
$375$	7.57276	0.391055
$376$	54.6511	2.81842
$377$	−1.24228	−0.0639809
$378$	−12.6125	−0.648719
$379$	22.7680	1.16951	0.584756	−	0.811209i	$-0.301190\pi$
$379$	22.7680	1.16951	0.584756	+	0.811209i	$0.301190\pi$
$380$	−4.99503	−0.256240
$381$	8.74601	0.448072
$382$	−32.1230	−1.64356
$383$	−21.4978	−1.09849	−0.549244	−	0.835662i	$-0.685084\pi$
$383$	−21.4978	−1.09849	−0.549244	+	0.835662i	$0.685084\pi$
$384$	−0.711519	−0.0363096
$385$	11.4686	0.584495
$386$	60.2248	3.06536
$387$	−0.776898	−0.0394920
$388$	−25.8846	−1.31409
$389$	−4.14307	−0.210062	−0.105031	−	0.994469i	$-0.533494\pi$
$389$	−4.14307	−0.210062	−0.105031	+	0.994469i	$0.533494\pi$
$390$	−1.14732	−0.0580966
$391$	−6.84840	−0.346338
$392$	−119.994	−6.06060
$393$	19.8767	1.00265
$394$	−9.01139	−0.453987
$395$	−10.7693	−0.541860
$396$	−14.0868	−0.707889
$397$	1.72022	0.0863354	0.0431677	−	0.999068i	$-0.486255\pi$
$397$	1.72022	0.0863354	0.0431677	+	0.999068i	$0.486255\pi$
$398$	−33.4356	−1.67597
$399$	−6.19022	−0.309899
$400$	−41.3697	−2.06848
$401$	15.2326	0.760680	0.380340	−	0.924847i	$-0.375807\pi$
$401$	15.2326	0.760680	0.380340	+	0.924847i	$0.375807\pi$
$402$	−4.14796	−0.206882
$403$	−2.33224	−0.116177
$404$	6.21776	0.309345
$405$	0.810523	0.0402752
$406$	28.8881	1.43369
$407$	26.8912	1.33295
$408$	6.72918	0.333144
$409$	33.9596	1.67919	0.839597	−	0.543210i	$-0.182791\pi$
$409$	33.9596	1.67919	0.839597	+	0.543210i	$0.182791\pi$
$410$	−15.7482	−0.777750
$411$	−14.4176	−0.711170
$412$	−63.0690	−3.10718
$413$	42.0517	2.06923
$414$	19.4872	0.957743
$415$	2.74151	0.134576
$416$	5.52483	0.270877
$417$	11.2145	0.549178
$418$	−9.78783	−0.478738
$419$	−9.94096	−0.485648	−0.242824	−	0.970070i	$-0.578074\pi$
$419$	−9.94096	−0.485648	−0.242824	+	0.970070i	$0.578074\pi$
$420$	18.8456	0.919573
$421$	−12.5675	−0.612502	−0.306251	−	0.951951i	$-0.599075\pi$
$421$	−12.5675	−0.612502	−0.306251	+	0.951951i	$0.599075\pi$
$422$	−47.6101	−2.31762
$423$	−7.44886	−0.362176
$424$	−34.0190	−1.65211
$425$	−3.98334	−0.193221
$426$	−25.6443	−1.24247
$427$	−1.93703	−0.0937396
$428$	−87.8781	−4.24775
$429$	−1.58804	−0.0766713
$430$	1.64340	0.0792516
$431$	16.6171	0.800419	0.400210	−	0.916424i	$-0.368937\pi$
$431$	16.6171	0.800419	0.400210	+	0.916424i	$0.368937\pi$
$432$	−9.52548	−0.458295
$433$	−7.84784	−0.377143	−0.188572	−	0.982059i	$-0.560386\pi$
$433$	−7.84784	−0.377143	−0.188572	+	0.982059i	$0.560386\pi$
$434$	54.2338	2.60331
$435$	−1.85644	−0.0890096
$436$	3.68651	0.176552
$437$	9.56430	0.457522
$438$	−42.7435	−2.04236
$439$	4.33365	0.206834	0.103417	−	0.994638i	$-0.467022\pi$
$439$	4.33365	0.206834	0.103417	+	0.994638i	$0.467022\pi$
$440$	17.4113	0.830051
$441$	16.3549	0.778807
$442$	1.29829	0.0617532
$443$	20.2349	0.961389	0.480694	−	0.876888i	$-0.340385\pi$
$443$	20.2349	0.961389	0.480694	+	0.876888i	$0.340385\pi$
$444$	44.1886	2.09710
$445$	−2.07843	−0.0985269
$446$	25.7615	1.21984
$447$	18.9119	0.894500
$448$	−36.4067	−1.72005
$449$	−23.5681	−1.11225	−0.556123	−	0.831100i	$-0.687712\pi$
$449$	−23.5681	−1.11225	−0.556123	+	0.831100i	$0.687712\pi$
$450$	11.3346	0.534320
$451$	−21.7977	−1.02641
$452$	90.4873	4.25616
$453$	6.55304	0.307889
$454$	−36.0210	−1.69055
$455$	2.12451	0.0995987
$456$	−9.39780	−0.440092
$457$	24.6287	1.15208	0.576042	−	0.817420i	$-0.304597\pi$
$457$	24.6287	1.15208	0.576042	+	0.817420i	$0.304597\pi$
$458$	43.7032	2.04212
$459$	−0.917176	−0.0428101
$460$	−29.1177	−1.35762
$461$	−28.5532	−1.32986	−0.664928	−	0.746907i	$-0.731538\pi$
$461$	−28.5532	−1.32986	−0.664928	+	0.746907i	$0.731538\pi$
$462$	36.9283	1.71806
$463$	−37.2612	−1.73168	−0.865838	−	0.500324i	$-0.833214\pi$
$463$	−37.2612	−1.73168	−0.865838	+	0.500324i	$0.833214\pi$
$464$	21.8174	1.01285
$465$	−3.48524	−0.161624
$466$	27.4014	1.26934
$467$	−40.5445	−1.87617	−0.938087	−	0.346399i	$-0.887404\pi$
$467$	−40.5445	−1.87617	−0.938087	+	0.346399i	$0.887404\pi$
$468$	−2.60952	−0.120625
$469$	7.68089	0.354671
$470$	15.7568	0.726806
$471$	1.15206	0.0530842
$472$	63.8415	2.93854
$473$	2.27468	0.104590
$474$	−34.6764	−1.59274
$475$	5.56304	0.255250
$476$	−21.3255	−0.977451
$477$	4.63674	0.212302
$478$	−68.5415	−3.13501
$479$	−24.7565	−1.13115	−0.565576	−	0.824696i	$-0.691346\pi$
$479$	−24.7565	−1.13115	−0.565576	+	0.824696i	$0.691346\pi$
$480$	8.25617	0.376841
$481$	4.98148	0.227136
$482$	52.0755	2.37197
$483$	−36.0849	−1.64192
$484$	−11.6787	−0.530851
$485$	−4.36064	−0.198007
$486$	2.60983	0.118384
$487$	−1.15315	−0.0522543	−0.0261271	−	0.999659i	$-0.508317\pi$
$487$	−1.15315	−0.0522543	−0.0261271	+	0.999659i	$0.508317\pi$
$488$	−2.94074	−0.133121
$489$	7.88492	0.356568
$490$	−34.5961	−1.56289
$491$	−5.41040	−0.244168	−0.122084	−	0.992520i	$-0.538958\pi$
$491$	−5.41040	−0.244168	−0.122084	+	0.992520i	$0.538958\pi$
$492$	−35.8188	−1.61483
$493$	2.10072	0.0946118
$494$	−1.81315	−0.0815776
$495$	−2.37313	−0.106664
$496$	40.9595	1.83914
$497$	47.4863	2.13005
$498$	8.82750	0.395570
$499$	19.1789	0.858564	0.429282	−	0.903171i	$-0.358767\pi$
$499$	19.1789	0.858564	0.429282	+	0.903171i	$0.358767\pi$
$500$	−36.4343	−1.62939
$501$	−4.31574	−0.192813
$502$	72.2471	3.22454
$503$	−6.30112	−0.280953	−0.140476	−	0.990084i	$-0.544863\pi$
$503$	−6.30112	−0.280953	−0.140476	+	0.990084i	$0.544863\pi$
$504$	35.4567	1.57937
$505$	1.04747	0.0466119
$506$	−57.0566	−2.53647
$507$	12.7058	0.564285
$508$	−42.0791	−1.86696
$509$	36.4615	1.61613	0.808064	−	0.589095i	$-0.200515\pi$
$509$	36.4615	1.61613	0.808064	+	0.589095i	$0.200515\pi$
$510$	1.94013	0.0859103
$511$	79.1492	3.50135
$512$	42.7452	1.88909
$513$	1.28090	0.0565533
$514$	−35.7771	−1.57806
$515$	−10.6249	−0.468189
$516$	3.73784	0.164549
$517$	21.8095	0.959182
$518$	−115.839	−5.08969
$519$	−14.8523	−0.651946
$520$	3.22537	0.141442
$521$	14.6272	0.640831	0.320415	−	0.947277i	$-0.396177\pi$
$521$	14.6272	0.640831	0.320415	+	0.947277i	$0.396177\pi$
$522$	−5.97763	−0.261634
$523$	1.95466	0.0854715	0.0427357	−	0.999086i	$-0.486393\pi$
$523$	1.95466	0.0854715	0.0427357	+	0.999086i	$0.486393\pi$
$524$	−95.6315	−4.17768
$525$	−20.9887	−0.916020
$526$	−37.0762	−1.61660
$527$	3.94385	0.171797
$528$	27.8897	1.21374
$529$	32.7536	1.42407
$530$	−9.80822	−0.426042
$531$	−8.70149	−0.377613
$532$	29.7826	1.29124
$533$	−4.03793	−0.174902
$534$	−6.69241	−0.289609
$535$	−14.8044	−0.640048
$536$	11.6609	0.503674
$537$	−9.50719	−0.410266
$538$	48.6084	2.09566
$539$	−47.8857	−2.06258
$540$	−3.89961	−0.167813
$541$	−4.21895	−0.181387	−0.0906933	−	0.995879i	$-0.528908\pi$
$541$	−4.21895	−0.181387	−0.0906933	+	0.995879i	$0.528908\pi$
$542$	−20.5471	−0.882575
$543$	−14.1876	−0.608846
$544$	−9.34257	−0.400559
$545$	0.621047	0.0266027
$546$	6.84080	0.292759
$547$	42.6075	1.82176	0.910882	−	0.412666i	$-0.135402\pi$
$547$	42.6075	1.82176	0.910882	+	0.412666i	$0.135402\pi$
$548$	69.3666	2.96320
$549$	0.400818	0.0171065
$550$	−33.1867	−1.41509
$551$	−2.93382	−0.124985
$552$	−54.7830	−2.33172
$553$	64.2111	2.73053
$554$	18.3494	0.779592
$555$	7.44422	0.315989
$556$	−53.9557	−2.28823
$557$	9.65967	0.409293	0.204647	−	0.978836i	$-0.434395\pi$
$557$	9.65967	0.409293	0.204647	+	0.978836i	$0.434395\pi$
$558$	−11.2223	−0.475077
$559$	0.421375	0.0178223
$560$	−37.3114	−1.57669
$561$	2.68540	0.113378
$562$	−6.62811	−0.279590
$563$	−11.7193	−0.493910	−0.246955	−	0.969027i	$-0.579430\pi$
$563$	−11.7193	−0.493910	−0.246955	+	0.969027i	$0.579430\pi$
$564$	35.8382	1.50906
$565$	15.2439	0.641316
$566$	−38.4840	−1.61760
$567$	−4.83270	−0.202954
$568$	72.0922	3.02492
$569$	−3.00926	−0.126155	−0.0630774	−	0.998009i	$-0.520091\pi$
$569$	−3.00926	−0.126155	−0.0630774	+	0.998009i	$0.520091\pi$
$570$	−2.70953	−0.113490
$571$	−37.5288	−1.57053	−0.785265	−	0.619160i	$-0.787473\pi$
$571$	−37.5288	−1.57053	−0.785265	+	0.619160i	$0.787473\pi$
$572$	7.64043	0.319462
$573$	−12.3084	−0.514193
$574$	93.8980	3.91923
$575$	32.4288	1.35238
$576$	7.53341	0.313892
$577$	−37.8181	−1.57439	−0.787195	−	0.616704i	$-0.788467\pi$
$577$	−37.8181	−1.57439	−0.787195	+	0.616704i	$0.788467\pi$
$578$	42.1717	1.75411
$579$	23.0761	0.959011
$580$	8.93177	0.370872
$581$	−16.3461	−0.678151
$582$	−14.0410	−0.582018
$583$	−13.5759	−0.562257
$584$	120.162	4.97233
$585$	−0.439613	−0.0181757
$586$	−12.8357	−0.530236
$587$	7.80230	0.322035	0.161018	−	0.986952i	$-0.448522\pi$
$587$	7.80230	0.322035	0.161018	+	0.986952i	$0.448522\pi$
$588$	−78.6874	−3.24501
$589$	−5.50788	−0.226948
$590$	18.4065	0.757784
$591$	−3.45286	−0.142032
$592$	−87.4865	−3.59567
$593$	13.3572	0.548515	0.274257	−	0.961656i	$-0.411568\pi$
$593$	13.3572	0.548515	0.274257	+	0.961656i	$0.411568\pi$
$594$	−7.64134	−0.313528
$595$	−3.59259	−0.147282
$596$	−90.9893	−3.72707
$597$	−12.8114	−0.524335
$598$	−10.5695	−0.432219
$599$	−8.37322	−0.342121	−0.171060	−	0.985261i	$-0.554719\pi$
$599$	−8.37322	−0.342121	−0.171060	+	0.985261i	$0.554719\pi$
$600$	−31.8643	−1.30086
$601$	−12.3425	−0.503460	−0.251730	−	0.967798i	$-0.580999\pi$
$601$	−12.3425	−0.503460	−0.251730	+	0.967798i	$0.580999\pi$
$602$	−9.79865	−0.399363
$603$	−1.58936	−0.0647237
$604$	−31.5282	−1.28286
$605$	−1.96745	−0.0799882
$606$	3.37280	0.137011
$607$	38.6889	1.57033	0.785166	−	0.619285i	$-0.212577\pi$
$607$	38.6889	1.57033	0.785166	+	0.619285i	$0.212577\pi$
$608$	13.0476	0.529150
$609$	11.0689	0.448536
$610$	−0.847863	−0.0343290
$611$	4.04012	0.163446
$612$	4.41275	0.178375
$613$	15.3113	0.618418	0.309209	−	0.950994i	$-0.399936\pi$
$613$	15.3113	0.618418	0.309209	+	0.950994i	$0.399936\pi$
$614$	−68.9673	−2.78329
$615$	−6.03420	−0.243322
$616$	−103.814	−4.18278
$617$	22.9618	0.924407	0.462203	−	0.886774i	$-0.347059\pi$
$617$	22.9618	0.924407	0.462203	+	0.886774i	$0.347059\pi$
$618$	−34.2115	−1.37619
$619$	28.3114	1.13793	0.568965	−	0.822362i	$-0.307344\pi$
$619$	28.3114	1.13793	0.568965	+	0.822362i	$0.307344\pi$
$620$	16.7683	0.673432
$621$	7.46683	0.299634
$622$	−60.6090	−2.43020
$623$	12.3925	0.496495
$624$	5.16645	0.206823
$625$	15.5774	0.623095
$626$	31.9858	1.27841
$627$	−3.75036	−0.149775
$628$	−5.54284	−0.221183
$629$	−8.42377	−0.335878
$630$	10.2227	0.407284
$631$	−20.5309	−0.817322	−0.408661	−	0.912686i	$-0.634004\pi$
$631$	−20.5309	−0.817322	−0.408661	+	0.912686i	$0.634004\pi$
$632$	97.4833	3.87768
$633$	−18.2426	−0.725078
$634$	68.1672	2.70727
$635$	−7.08884	−0.281312
$636$	−22.3084	−0.884586
$637$	−8.87062	−0.351467
$638$	17.5019	0.692908
$639$	−9.82604	−0.388712
$640$	0.576702	0.0227962
$641$	12.4641	0.492303	0.246151	−	0.969231i	$-0.420834\pi$
$641$	12.4641	0.492303	0.246151	+	0.969231i	$0.420834\pi$
$642$	−47.6691	−1.88135
$643$	3.81758	0.150551	0.0752753	−	0.997163i	$-0.476016\pi$
$643$	3.81758	0.150551	0.0752753	+	0.997163i	$0.476016\pi$
$644$	173.613	6.84131
$645$	0.629694	0.0247942
$646$	3.06607	0.120633
$647$	21.8964	0.860838	0.430419	−	0.902629i	$-0.358366\pi$
$647$	21.8964	0.860838	0.430419	+	0.902629i	$0.358366\pi$
$648$	−7.33685	−0.288219
$649$	25.4771	1.00006
$650$	−6.14770	−0.241133
$651$	20.7806	0.814455
$652$	−37.9362	−1.48570
$653$	−4.10259	−0.160547	−0.0802733	−	0.996773i	$-0.525579\pi$
$653$	−4.10259	−0.160547	−0.0802733	+	0.996773i	$0.525579\pi$
$654$	1.99973	0.0781958
$655$	−16.1105	−0.629491
$656$	70.9155	2.76879
$657$	−16.3779	−0.638961
$658$	−93.9490	−3.66251
$659$	47.1083	1.83508	0.917540	−	0.397643i	$-0.130172\pi$
$659$	47.1083	1.83508	0.917540	+	0.397643i	$0.130172\pi$
$660$	11.4177	0.444433
$661$	−39.9123	−1.55241	−0.776205	−	0.630481i	$-0.782858\pi$
$661$	−39.9123	−1.55241	−0.776205	+	0.630481i	$0.782858\pi$
$662$	24.1940	0.940325
$663$	0.497459	0.0193197
$664$	−24.8161	−0.963053
$665$	5.01732	0.194563
$666$	23.9699	0.928816
$667$	−17.1022	−0.662201
$668$	20.7640	0.803384
$669$	9.87094	0.381633
$670$	3.36202	0.129886
$671$	−1.17356	−0.0453047
$672$	−49.2270	−1.89897
$673$	48.3565	1.86401	0.932003	−	0.362450i	$-0.118060\pi$
$673$	48.3565	1.86401	0.932003	+	0.362450i	$0.118060\pi$
$674$	39.2432	1.51159
$675$	4.34305	0.167164
$676$	−61.1306	−2.35118
$677$	46.0825	1.77109	0.885547	−	0.464550i	$-0.153784\pi$
$677$	46.0825	1.77109	0.885547	+	0.464550i	$0.153784\pi$
$678$	49.0845	1.88508
$679$	26.0001	0.997792
$680$	−5.45415	−0.209157
$681$	−13.8020	−0.528895
$682$	32.8577	1.25819
$683$	−43.6100	−1.66869	−0.834345	−	0.551243i	$-0.814154\pi$
$683$	−43.6100	−1.66869	−0.834345	+	0.551243i	$0.814154\pi$
$684$	−6.16273	−0.235638
$685$	11.6858	0.446492
$686$	117.990	4.50486
$687$	16.7456	0.638884
$688$	−7.40033	−0.282135
$689$	−2.51488	−0.0958093
$690$	−15.7948	−0.601298
$691$	31.7020	1.20600	0.603001	−	0.797740i	$-0.293971\pi$
$691$	31.7020	1.20600	0.603001	+	0.797740i	$0.293971\pi$
$692$	71.4581	2.71643
$693$	14.1497	0.537501
$694$	−31.7928	−1.20684
$695$	−9.08964	−0.344790
$696$	16.8045	0.636973
$697$	6.82821	0.258637
$698$	30.4089	1.15099
$699$	10.4993	0.397119
$700$	100.981	3.81673
$701$	−26.9382	−1.01744	−0.508722	−	0.860931i	$-0.669882\pi$
$701$	−26.9382	−1.01744	−0.508722	+	0.860931i	$0.669882\pi$
$702$	−1.41553	−0.0534256
$703$	11.7644	0.443704
$704$	−22.0571	−0.831308
$705$	6.03747	0.227384
$706$	44.7498	1.68418
$707$	−6.24549	−0.234886
$708$	41.8649	1.57338
$709$	−2.82817	−0.106214	−0.0531071	−	0.998589i	$-0.516912\pi$
$709$	−2.82817	−0.106214	−0.0531071	+	0.998589i	$0.516912\pi$
$710$	20.7853	0.780059
$711$	−13.2868	−0.498294
$712$	18.8139	0.705081
$713$	−32.1073	−1.20243
$714$	−11.5679	−0.432918
$715$	1.28714	0.0481364
$716$	45.7413	1.70943
$717$	−26.2628	−0.980802
$718$	16.5874	0.619034
$719$	32.7184	1.22019	0.610095	−	0.792328i	$-0.291131\pi$
$719$	32.7184	1.22019	0.610095	+	0.792328i	$0.291131\pi$
$720$	7.72062	0.287731
$721$	63.3503	2.35929
$722$	45.3048	1.68607
$723$	19.9536	0.742082
$724$	68.2596	2.53685
$725$	−9.94744	−0.369439
$726$	−6.33507	−0.235117
$727$	−18.9975	−0.704577	−0.352288	−	0.935892i	$-0.614596\pi$
$727$	−18.9975	−0.704577	−0.352288	+	0.935892i	$0.614596\pi$
$728$	−19.2311	−0.712751
$729$	1.00000	0.0370370
$730$	34.6446	1.28225
$731$	−0.712552	−0.0263547
$732$	−1.92843	−0.0712768
$733$	−15.4251	−0.569741	−0.284870	−	0.958566i	$-0.591951\pi$
$733$	−15.4251	−0.569741	−0.284870	+	0.958566i	$0.591951\pi$
$734$	65.8966	2.43229
$735$	−13.2561	−0.488957
$736$	76.0589	2.80357
$737$	4.65349	0.171414
$738$	−19.4297	−0.715219
$739$	−31.6677	−1.16492	−0.582458	−	0.812861i	$-0.697909\pi$
$739$	−31.6677	−1.16492	−0.582458	+	0.812861i	$0.697909\pi$
$740$	−35.8158	−1.31662
$741$	−0.694739	−0.0255219
$742$	58.4810	2.14690
$743$	−46.2397	−1.69637	−0.848185	−	0.529700i	$-0.822304\pi$
$743$	−46.2397	−1.69637	−0.848185	+	0.529700i	$0.822304\pi$
$744$	31.5484	1.15662
$745$	−15.3285	−0.561592
$746$	−1.71466	−0.0627780
$747$	3.38240	0.123756
$748$	−12.9201	−0.472405
$749$	88.2701	3.22532
$750$	−19.7636	−0.721666
$751$	24.7070	0.901573	0.450786	−	0.892632i	$-0.351144\pi$
$751$	24.7070	0.901573	0.450786	+	0.892632i	$0.351144\pi$
$752$	−70.9540	−2.58743
$753$	27.6826	1.00881
$754$	3.24216	0.118072
$755$	−5.31138	−0.193301
$756$	23.2512	0.845639
$757$	−6.67985	−0.242783	−0.121392	−	0.992605i	$-0.538736\pi$
$757$	−6.67985	−0.242783	−0.121392	+	0.992605i	$0.538736\pi$
$758$	−59.4206	−2.15825
$759$	−21.8622	−0.793546
$760$	7.61713	0.276302
$761$	−11.3534	−0.411561	−0.205781	−	0.978598i	$-0.565973\pi$
$761$	−11.3534	−0.411561	−0.205781	+	0.978598i	$0.565973\pi$
$762$	−22.8256	−0.826885
$763$	−3.70296	−0.134056
$764$	59.2188	2.14246
$765$	0.743392	0.0268774
$766$	56.1058	2.02718
$767$	4.71953	0.170412
$768$	16.9238	0.610684
$769$	−28.0668	−1.01212	−0.506058	−	0.862500i	$-0.668898\pi$
$769$	−28.0668	−1.01212	−0.506058	+	0.862500i	$0.668898\pi$
$770$	−29.9312	−1.07865
$771$	−13.7086	−0.493703
$772$	−111.025	−3.99586
$773$	−8.39982	−0.302121	−0.151060	−	0.988525i	$-0.548269\pi$
$773$	−8.39982	−0.302121	−0.151060	+	0.988525i	$0.548269\pi$
$774$	2.02757	0.0728797
$775$	−18.6751	−0.670830
$776$	39.4725	1.41698
$777$	−44.3857	−1.59233
$778$	10.8127	0.387655
$779$	−9.53611	−0.341666
$780$	2.11508	0.0757319
$781$	28.7697	1.02946
$782$	17.8732	0.639143
$783$	−2.29043	−0.0818531
$784$	155.789	5.56388
$785$	−0.933772	−0.0333278
$786$	−51.8749	−1.85032
$787$	39.1231	1.39459	0.697294	−	0.716785i	$-0.254387\pi$
$787$	39.1231	1.39459	0.697294	+	0.716785i	$0.254387\pi$
$788$	16.6125	0.591796
$789$	−14.2064	−0.505760
$790$	28.1060	0.999966
$791$	−90.8910	−3.23171
$792$	21.4816	0.763314
$793$	−0.217397	−0.00771998
$794$	−4.48949	−0.159326
$795$	−3.75818	−0.133289
$796$	61.6385	2.18472
$797$	−19.0415	−0.674485	−0.337243	−	0.941418i	$-0.609494\pi$
$797$	−19.0415	−0.674485	−0.337243	+	0.941418i	$0.609494\pi$
$798$	16.1555	0.571897
$799$	−6.83191	−0.241696
$800$	44.2394	1.56410
$801$	−2.56431	−0.0906053
$802$	−39.7546	−1.40378
$803$	47.9528	1.69222
$804$	7.64678	0.269681
$805$	29.2476	1.03084
$806$	6.08675	0.214397
$807$	18.6251	0.655635
$808$	−9.48171	−0.333565
$809$	−26.5307	−0.932770	−0.466385	−	0.884582i	$-0.654444\pi$
$809$	−26.5307	−0.932770	−0.466385	+	0.884582i	$0.654444\pi$
$810$	−2.11533	−0.0743251
$811$	48.2999	1.69604	0.848019	−	0.529966i	$-0.177796\pi$
$811$	48.2999	1.69604	0.848019	+	0.529966i	$0.177796\pi$
$812$	−53.2552	−1.86889
$813$	−7.87297	−0.276117
$814$	−70.1816	−2.45986
$815$	−6.39090	−0.223864
$816$	−8.73654	−0.305840
$817$	0.995133	0.0348153
$818$	−88.6289	−3.09884
$819$	2.62117	0.0915909
$820$	29.0319	1.01384
$821$	25.7749	0.899552	0.449776	−	0.893141i	$-0.351504\pi$
$821$	25.7749	0.899552	0.449776	+	0.893141i	$0.351504\pi$
$822$	37.6277	1.31242
$823$	18.6463	0.649969	0.324984	−	0.945719i	$-0.394641\pi$
$823$	18.6463	0.649969	0.324984	+	0.945719i	$0.394641\pi$
$824$	96.1765	3.35047
$825$	−12.7160	−0.442716
$826$	−109.748	−3.81861
$827$	28.1105	0.977499	0.488750	−	0.872424i	$-0.337453\pi$
$827$	28.1105	0.977499	0.488750	+	0.872424i	$0.337453\pi$
$828$	−35.9246	−1.24847
$829$	14.6020	0.507147	0.253574	−	0.967316i	$-0.418394\pi$
$829$	14.6020	0.507147	0.253574	+	0.967316i	$0.418394\pi$
$830$	−7.15489	−0.248350
$831$	7.03087	0.243898
$832$	−4.08598	−0.141656
$833$	15.0004	0.519732
$834$	−29.2681	−1.01347
$835$	3.49800	0.121053
$836$	18.0439	0.624060
$837$	−4.30000	−0.148630
$838$	25.9442	0.896229
$839$	−36.2628	−1.25193	−0.625966	−	0.779851i	$-0.715295\pi$
$839$	−36.2628	−1.25193	−0.625966	+	0.779851i	$0.715295\pi$
$840$	−28.7385	−0.991572
$841$	−23.7540	−0.819102
$842$	32.7990	1.13033
$843$	−2.53967	−0.0874708
$844$	87.7693	3.02114
$845$	−10.2984	−0.354274
$846$	19.4403	0.668371
$847$	11.7308	0.403076
$848$	44.1672	1.51671
$849$	−14.7458	−0.506073
$850$	10.3959	0.356575
$851$	68.5788	2.35085
$852$	47.2754	1.61963
$853$	−14.2072	−0.486446	−0.243223	−	0.969970i	$-0.578205\pi$
$853$	−14.2072	−0.486446	−0.243223	+	0.969970i	$0.578205\pi$
$854$	5.05533	0.172990
$855$	−1.03820	−0.0355058
$856$	134.009	4.58033
$857$	51.4231	1.75658	0.878289	−	0.478130i	$-0.158685\pi$
$857$	51.4231	1.75658	0.878289	+	0.478130i	$0.158685\pi$
$858$	4.14452	0.141492
$859$	31.8374	1.08628	0.543139	−	0.839643i	$-0.317236\pi$
$859$	31.8374	1.08628	0.543139	+	0.839643i	$0.317236\pi$
$860$	−3.02960	−0.103309
$861$	35.9786	1.22615
$862$	−43.3680	−1.47712
$863$	−12.7690	−0.434663	−0.217331	−	0.976098i	$-0.569735\pi$
$863$	−12.7690	−0.434663	−0.217331	+	0.976098i	$0.569735\pi$
$864$	10.1862	0.346543
$865$	12.0382	0.409310
$866$	20.4816	0.695991
$867$	16.1588	0.548781
$868$	−99.9801	−3.39355
$869$	38.9025	1.31968
$870$	4.84500	0.164261
$871$	0.862040	0.0292091
$872$	−5.62172	−0.190375
$873$	−5.38004	−0.182087
$874$	−24.9612	−0.844326
$875$	36.5968	1.23720
$876$	78.7977	2.66233
$877$	−34.7946	−1.17493	−0.587466	−	0.809249i	$-0.699874\pi$
$877$	−34.7946	−1.17493	−0.587466	+	0.809249i	$0.699874\pi$
$878$	−11.3101	−0.381698
$879$	−4.91819	−0.165886
$880$	−22.6052	−0.762022
$881$	4.03089	0.135804	0.0679020	−	0.997692i	$-0.478369\pi$
$881$	4.03089	0.135804	0.0679020	+	0.997692i	$0.478369\pi$
$882$	−42.6837	−1.43723
$883$	0.0614527	0.00206805	0.00103402	−	0.999999i	$-0.499671\pi$
$883$	0.0614527	0.00206805	0.00103402	+	0.999999i	$0.499671\pi$
$884$	−2.39339	−0.0804985
$885$	7.05275	0.237076
$886$	−52.8097	−1.77418
$887$	28.5598	0.958944	0.479472	−	0.877557i	$-0.340828\pi$
$887$	28.5598	0.958944	0.479472	+	0.877557i	$0.340828\pi$
$888$	−67.3850	−2.26129
$889$	42.2668	1.41758
$890$	5.42435	0.181825
$891$	−2.92790	−0.0980884
$892$	−47.4914	−1.59013
$893$	9.54128	0.319287
$894$	−49.3568	−1.65074
$895$	7.70579	0.257576
$896$	−3.43856	−0.114874
$897$	−4.04987	−0.135221
$898$	61.5088	2.05257
$899$	9.84882	0.328476
$900$	−20.8954	−0.696514
$901$	4.25270	0.141678
$902$	56.8884	1.89418
$903$	−3.75451	−0.124942
$904$	−137.988	−4.58941
$905$	11.4993	0.382251
$906$	−17.1023	−0.568187
$907$	11.9599	0.397122	0.198561	−	0.980089i	$-0.436373\pi$
$907$	11.9599	0.397122	0.198561	+	0.980089i	$0.436373\pi$
$908$	66.4048	2.20372
$909$	1.29234	0.0428643
$910$	−5.54463	−0.183803
$911$	34.1331	1.13088	0.565440	−	0.824789i	$-0.308706\pi$
$911$	34.1331	1.13088	0.565440	+	0.824789i	$0.308706\pi$
$912$	12.2012	0.404023
$913$	−9.90334	−0.327753
$914$	−64.2769	−2.12609
$915$	−0.324872	−0.0107399
$916$	−80.5669	−2.66200
$917$	96.0581	3.17212
$918$	2.39368	0.0790031
$919$	−37.1794	−1.22644	−0.613218	−	0.789914i	$-0.710125\pi$
$919$	−37.1794	−1.22644	−0.613218	+	0.789914i	$0.710125\pi$
$920$	44.4028	1.46392
$921$	−26.4259	−0.870764
$922$	74.5192	2.45416
$923$	5.32947	0.175421
$924$	−68.0773	−2.23958
$925$	39.8886	1.31153
$926$	97.2456	3.19569
$927$	−13.1087	−0.430546
$928$	−23.3308	−0.765871
$929$	−12.0080	−0.393970	−0.196985	−	0.980407i	$-0.563115\pi$
$929$	−12.0080	−0.393970	−0.196985	+	0.980407i	$0.563115\pi$
$930$	9.09590	0.298266
$931$	−20.9491	−0.686580
$932$	−50.5144	−1.65466
$933$	−23.2233	−0.760297
$934$	105.814	3.46235
$935$	−2.17658	−0.0711817
$936$	3.97937	0.130070
$937$	−22.7586	−0.743490	−0.371745	−	0.928335i	$-0.621240\pi$
$937$	−22.7586	−0.743490	−0.371745	+	0.928335i	$0.621240\pi$
$938$	−20.0458	−0.654520
$939$	12.2559	0.399955
$940$	−29.0477	−0.947430
$941$	13.1268	0.427923	0.213961	−	0.976842i	$-0.431363\pi$
$941$	13.1268	0.427923	0.213961	+	0.976842i	$0.431363\pi$
$942$	−3.00669	−0.0979632
$943$	−55.5892	−1.81023
$944$	−82.8859	−2.69771
$945$	3.91701	0.127420
$946$	−5.93654	−0.193014
$947$	−22.3295	−0.725610	−0.362805	−	0.931865i	$-0.618181\pi$
$947$	−22.3295	−0.725610	−0.362805	+	0.931865i	$0.618181\pi$
$948$	63.9259	2.07622
$949$	8.88305	0.288356
$950$	−14.5186	−0.471046
$951$	26.1194	0.846979
$952$	32.5201	1.05398
$953$	29.4689	0.954590	0.477295	−	0.878743i	$-0.341617\pi$
$953$	29.4689	0.954590	0.477295	+	0.878743i	$0.341617\pi$
$954$	−12.1011	−0.391788
$955$	9.97627	0.322825
$956$	126.356	4.08666
$957$	6.70614	0.216779
$958$	64.6103	2.08746
$959$	−69.6761	−2.24996
$960$	−6.10600	−0.197070
$961$	−12.5100	−0.403550
$962$	−13.0008	−0.419164
$963$	−18.2652	−0.588588
$964$	−96.0013	−3.09199
$965$	−18.7037	−0.602094
$966$	94.1756	3.03005
$967$	39.1800	1.25994	0.629971	−	0.776618i	$-0.283067\pi$
$967$	39.1800	1.25994	0.629971	+	0.776618i	$0.283067\pi$
$968$	17.8094	0.572414
$969$	1.17481	0.0377405
$970$	11.3805	0.365407
$971$	−5.19398	−0.166683	−0.0833413	−	0.996521i	$-0.526559\pi$
$971$	−5.19398	−0.166683	−0.0833413	+	0.996521i	$0.526559\pi$
$972$	−4.81123	−0.154320
$973$	54.1964	1.73746
$974$	3.00953	0.0964317
$975$	−2.35559	−0.0754393
$976$	3.81799	0.122211
$977$	26.2994	0.841392	0.420696	−	0.907202i	$-0.361786\pi$
$977$	26.2994	0.841392	0.420696	+	0.907202i	$0.361786\pi$
$978$	−20.5783	−0.658022
$979$	7.50804	0.239958
$980$	63.7779	2.03731
$981$	0.766231	0.0244639
$982$	14.1203	0.450595
$983$	0.865170	0.0275946	0.0137973	−	0.999905i	$-0.495608\pi$
$983$	0.865170	0.0275946	0.0137973	+	0.999905i	$0.495608\pi$
$984$	54.6215	1.74127
$985$	2.79862	0.0891715
$986$	−5.48254	−0.174600
$987$	−35.9981	−1.14583
$988$	3.34255	0.106341
$989$	5.80097	0.184460
$990$	6.19348	0.196842
$991$	31.3598	0.996177	0.498089	−	0.867126i	$-0.334035\pi$
$991$	31.3598	0.996177	0.498089	+	0.867126i	$0.334035\pi$
$992$	−43.8008	−1.39068
$993$	9.27031	0.294184
$994$	−123.931	−3.93086
$995$	10.3839	0.329192
$996$	−16.2735	−0.515646
$997$	9.23258	0.292399	0.146199	−	0.989255i	$-0.453296\pi$
$997$	9.23258	0.292399	0.146199	+	0.989255i	$0.453296\pi$
$998$	−50.0536	−1.58442
$999$	9.18446	0.290584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.6	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.6	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60983 q^{2} -1.00000 q^{3} +4.81123 q^{4} +0.810523 q^{5} +2.60983 q^{6} -4.83270 q^{7} -7.33685 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60983 q^{2} -1.00000 q^{3} +4.81123 q^{4} +0.810523 q^{5} +2.60983 q^{6} -4.83270 q^{7} -7.33685 q^{8} +1.00000 q^{9} -2.11533 q^{10} -2.92790 q^{11} -4.81123 q^{12} -0.542382 q^{13} +12.6125 q^{14} -0.810523 q^{15} +9.52548 q^{16} +0.917176 q^{17} -2.60983 q^{18} -1.28090 q^{19} +3.89961 q^{20} +4.83270 q^{21} +7.64134 q^{22} -7.46683 q^{23} +7.33685 q^{24} -4.34305 q^{25} +1.41553 q^{26} -1.00000 q^{27} -23.2512 q^{28} +2.29043 q^{29} +2.11533 q^{30} +4.30000 q^{31} -10.1862 q^{32} +2.92790 q^{33} -2.39368 q^{34} -3.91701 q^{35} +4.81123 q^{36} -9.18446 q^{37} +3.34295 q^{38} +0.542382 q^{39} -5.94668 q^{40} +7.44482 q^{41} -12.6125 q^{42} -0.776898 q^{43} -14.0868 q^{44} +0.810523 q^{45} +19.4872 q^{46} -7.44886 q^{47} -9.52548 q^{48} +16.3549 q^{49} +11.3346 q^{50} -0.917176 q^{51} -2.60952 q^{52} +4.63674 q^{53} +2.60983 q^{54} -2.37313 q^{55} +35.4567 q^{56} +1.28090 q^{57} -5.97763 q^{58} -8.70149 q^{59} -3.89961 q^{60} +0.400818 q^{61} -11.2223 q^{62} -4.83270 q^{63} +7.53341 q^{64} -0.439613 q^{65} -7.64134 q^{66} -1.58936 q^{67} +4.41275 q^{68} +7.46683 q^{69} +10.2227 q^{70} -9.82604 q^{71} -7.33685 q^{72} -16.3779 q^{73} +23.9699 q^{74} +4.34305 q^{75} -6.16273 q^{76} +14.1497 q^{77} -1.41553 q^{78} -13.2868 q^{79} +7.72062 q^{80} +1.00000 q^{81} -19.4297 q^{82} +3.38240 q^{83} +23.2512 q^{84} +0.743392 q^{85} +2.02757 q^{86} -2.29043 q^{87} +21.4816 q^{88} -2.56431 q^{89} -2.11533 q^{90} +2.62117 q^{91} -35.9246 q^{92} -4.30000 q^{93} +19.4403 q^{94} -1.03820 q^{95} +10.1862 q^{96} -5.38004 q^{97} -42.6837 q^{98} -2.92790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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