LMFDB - Embedded newform 8018.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.78985 q^{3} +1.00000 q^{4} -2.51493 q^{5} -2.78985 q^{6} -0.381461 q^{7} +1.00000 q^{8} +4.78329 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.78985 q^{3} +1.00000 q^{4} -2.51493 q^{5} -2.78985 q^{6} -0.381461 q^{7} +1.00000 q^{8} +4.78329 q^{9} -2.51493 q^{10} +1.85275 q^{11} -2.78985 q^{12} -1.51269 q^{13} -0.381461 q^{14} +7.01629 q^{15} +1.00000 q^{16} -3.53252 q^{17} +4.78329 q^{18} -1.00000 q^{19} -2.51493 q^{20} +1.06422 q^{21} +1.85275 q^{22} +9.05456 q^{23} -2.78985 q^{24} +1.32487 q^{25} -1.51269 q^{26} -4.97512 q^{27} -0.381461 q^{28} +5.58964 q^{29} +7.01629 q^{30} -6.76333 q^{31} +1.00000 q^{32} -5.16890 q^{33} -3.53252 q^{34} +0.959349 q^{35} +4.78329 q^{36} -10.9012 q^{37} -1.00000 q^{38} +4.22017 q^{39} -2.51493 q^{40} +0.614977 q^{41} +1.06422 q^{42} -5.81105 q^{43} +1.85275 q^{44} -12.0296 q^{45} +9.05456 q^{46} +10.1131 q^{47} -2.78985 q^{48} -6.85449 q^{49} +1.32487 q^{50} +9.85523 q^{51} -1.51269 q^{52} +6.61551 q^{53} -4.97512 q^{54} -4.65954 q^{55} -0.381461 q^{56} +2.78985 q^{57} +5.58964 q^{58} -7.56646 q^{59} +7.01629 q^{60} +10.3001 q^{61} -6.76333 q^{62} -1.82464 q^{63} +1.00000 q^{64} +3.80430 q^{65} -5.16890 q^{66} +7.71648 q^{67} -3.53252 q^{68} -25.2609 q^{69} +0.959349 q^{70} -13.5607 q^{71} +4.78329 q^{72} -11.6082 q^{73} -10.9012 q^{74} -3.69620 q^{75} -1.00000 q^{76} -0.706753 q^{77} +4.22017 q^{78} +3.95164 q^{79} -2.51493 q^{80} -0.470015 q^{81} +0.614977 q^{82} -10.0906 q^{83} +1.06422 q^{84} +8.88405 q^{85} -5.81105 q^{86} -15.5943 q^{87} +1.85275 q^{88} -4.88917 q^{89} -12.0296 q^{90} +0.577031 q^{91} +9.05456 q^{92} +18.8687 q^{93} +10.1131 q^{94} +2.51493 q^{95} -2.78985 q^{96} -4.24563 q^{97} -6.85449 q^{98} +8.86224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	−2.78985	−1.61072	−0.805362	−	0.592784i	$-0.798029\pi$
$3$	−2.78985	−1.61072	−0.805362	+	0.592784i	$0.798029\pi$
$4$	1.00000	0.500000
$5$	−2.51493	−1.12471	−0.562355	−	0.826896i	$-0.690105\pi$
$5$	−2.51493	−1.12471	−0.562355	+	0.826896i	$0.690105\pi$
$6$	−2.78985	−1.13895
$7$	−0.381461	−0.144179	−0.0720894	−	0.997398i	$-0.522967\pi$
$7$	−0.381461	−0.144179	−0.0720894	+	0.997398i	$0.522967\pi$
$8$	1.00000	0.353553
$9$	4.78329	1.59443
$10$	−2.51493	−0.795291
$11$	1.85275	0.558625	0.279313	−	0.960200i	$-0.409893\pi$
$11$	1.85275	0.558625	0.279313	+	0.960200i	$0.409893\pi$
$12$	−2.78985	−0.805362
$13$	−1.51269	−0.419544	−0.209772	−	0.977750i	$-0.567272\pi$
$13$	−1.51269	−0.419544	−0.209772	+	0.977750i	$0.567272\pi$
$14$	−0.381461	−0.101950
$15$	7.01629	1.81160
$16$	1.00000	0.250000
$17$	−3.53252	−0.856763	−0.428382	−	0.903598i	$-0.640916\pi$
$17$	−3.53252	−0.856763	−0.428382	+	0.903598i	$0.640916\pi$
$18$	4.78329	1.12743
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.51493	−0.562355
$21$	1.06422	0.232232
$22$	1.85275	0.395008
$23$	9.05456	1.88801	0.944003	−	0.329937i	$-0.107028\pi$
$23$	9.05456	1.88801	0.944003	+	0.329937i	$0.107028\pi$
$24$	−2.78985	−0.569477
$25$	1.32487	0.264975
$26$	−1.51269	−0.296662
$27$	−4.97512	−0.957462
$28$	−0.381461	−0.0720894
$29$	5.58964	1.03797	0.518985	−	0.854783i	$-0.326310\pi$
$29$	5.58964	1.03797	0.518985	+	0.854783i	$0.326310\pi$
$30$	7.01629	1.28099
$31$	−6.76333	−1.21473	−0.607365	−	0.794423i	$-0.707774\pi$
$31$	−6.76333	−1.21473	−0.607365	+	0.794423i	$0.707774\pi$
$32$	1.00000	0.176777
$33$	−5.16890	−0.899791
$34$	−3.53252	−0.605823
$35$	0.959349	0.162160
$36$	4.78329	0.797215
$37$	−10.9012	−1.79214	−0.896071	−	0.443911i	$-0.853591\pi$
$37$	−10.9012	−1.79214	−0.896071	+	0.443911i	$0.853591\pi$
$38$	−1.00000	−0.162221
$39$	4.22017	0.675769
$40$	−2.51493	−0.397645
$41$	0.614977	0.0960433	0.0480216	−	0.998846i	$-0.484708\pi$
$41$	0.614977	0.0960433	0.0480216	+	0.998846i	$0.484708\pi$
$42$	1.06422	0.164213
$43$	−5.81105	−0.886177	−0.443089	−	0.896478i	$-0.646117\pi$
$43$	−5.81105	−0.886177	−0.443089	+	0.896478i	$0.646117\pi$
$44$	1.85275	0.279313
$45$	−12.0296	−1.79327
$46$	9.05456	1.33502
$47$	10.1131	1.47515	0.737573	−	0.675268i	$-0.235972\pi$
$47$	10.1131	1.47515	0.737573	+	0.675268i	$0.235972\pi$
$48$	−2.78985	−0.402681
$49$	−6.85449	−0.979212
$50$	1.32487	0.187365
$51$	9.85523	1.38001
$52$	−1.51269	−0.209772
$53$	6.61551	0.908711	0.454355	−	0.890821i	$-0.349870\pi$
$53$	6.61551	0.908711	0.454355	+	0.890821i	$0.349870\pi$
$54$	−4.97512	−0.677028
$55$	−4.65954	−0.628292
$56$	−0.381461	−0.0509749
$57$	2.78985	0.369525
$58$	5.58964	0.733956
$59$	−7.56646	−0.985069	−0.492535	−	0.870293i	$-0.663929\pi$
$59$	−7.56646	−0.985069	−0.492535	+	0.870293i	$0.663929\pi$
$60$	7.01629	0.905799
$61$	10.3001	1.31880	0.659398	−	0.751794i	$-0.270811\pi$
$61$	10.3001	1.31880	0.659398	+	0.751794i	$0.270811\pi$
$62$	−6.76333	−0.858944
$63$	−1.82464	−0.229883
$64$	1.00000	0.125000
$65$	3.80430	0.471865
$66$	−5.16890	−0.636248
$67$	7.71648	0.942718	0.471359	−	0.881941i	$-0.343764\pi$
$67$	7.71648	0.942718	0.471359	+	0.881941i	$0.343764\pi$
$68$	−3.53252	−0.428382
$69$	−25.2609	−3.04105
$70$	0.959349	0.114664
$71$	−13.5607	−1.60936	−0.804681	−	0.593707i	$-0.797664\pi$
$71$	−13.5607	−1.60936	−0.804681	+	0.593707i	$0.797664\pi$
$72$	4.78329	0.563716
$73$	−11.6082	−1.35864	−0.679320	−	0.733842i	$-0.737725\pi$
$73$	−11.6082	−1.35864	−0.679320	+	0.733842i	$0.737725\pi$
$74$	−10.9012	−1.26724
$75$	−3.69620	−0.426801
$76$	−1.00000	−0.114708
$77$	−0.706753	−0.0805420
$78$	4.22017	0.477841
$79$	3.95164	0.444595	0.222297	−	0.974979i	$-0.428644\pi$
$79$	3.95164	0.444595	0.222297	+	0.974979i	$0.428644\pi$
$80$	−2.51493	−0.281178
$81$	−0.470015	−0.0522239
$82$	0.614977	0.0679128
$83$	−10.0906	−1.10759	−0.553796	−	0.832653i	$-0.686821\pi$
$83$	−10.0906	−1.10759	−0.553796	+	0.832653i	$0.686821\pi$
$84$	1.06422	0.116116
$85$	8.88405	0.963611
$86$	−5.81105	−0.626622
$87$	−15.5943	−1.67188
$88$	1.85275	0.197504
$89$	−4.88917	−0.518251	−0.259126	−	0.965844i	$-0.583434\pi$
$89$	−4.88917	−0.518251	−0.259126	+	0.965844i	$0.583434\pi$
$90$	−12.0296	−1.26804
$91$	0.577031	0.0604893
$92$	9.05456	0.944003
$93$	18.8687	1.95660
$94$	10.1131	1.04309
$95$	2.51493	0.258026
$96$	−2.78985	−0.284738
$97$	−4.24563	−0.431078	−0.215539	−	0.976495i	$-0.569151\pi$
$97$	−4.24563	−0.431078	−0.215539	+	0.976495i	$0.569151\pi$
$98$	−6.85449	−0.692408
$99$	8.86224	0.890689
$100$	1.32487	0.132487
$101$	−4.66938	−0.464621	−0.232310	−	0.972642i	$-0.574629\pi$
$101$	−4.66938	−0.464621	−0.232310	+	0.972642i	$0.574629\pi$
$102$	9.85523	0.975813
$103$	−0.552150	−0.0544050	−0.0272025	−	0.999630i	$-0.508660\pi$
$103$	−0.552150	−0.0544050	−0.0272025	+	0.999630i	$0.508660\pi$
$104$	−1.51269	−0.148331
$105$	−2.67644	−0.261194
$106$	6.61551	0.642556
$107$	11.7963	1.14040	0.570198	−	0.821507i	$-0.306867\pi$
$107$	11.7963	1.14040	0.570198	+	0.821507i	$0.306867\pi$
$108$	−4.97512	−0.478731
$109$	12.5577	1.20281	0.601407	−	0.798943i	$-0.294607\pi$
$109$	12.5577	1.20281	0.601407	+	0.798943i	$0.294607\pi$
$110$	−4.65954	−0.444270
$111$	30.4127	2.88664
$112$	−0.381461	−0.0360447
$113$	−2.72236	−0.256098	−0.128049	−	0.991768i	$-0.540871\pi$
$113$	−2.72236	−0.256098	−0.128049	+	0.991768i	$0.540871\pi$
$114$	2.78985	0.261294
$115$	−22.7716	−2.12346
$116$	5.58964	0.518985
$117$	−7.23562	−0.668933
$118$	−7.56646	−0.696549
$119$	1.34752	0.123527
$120$	7.01629	0.640497
$121$	−7.56732	−0.687938
$122$	10.3001	0.932530
$123$	−1.71570	−0.154699
$124$	−6.76333	−0.607365
$125$	9.24269	0.826691
$126$	−1.82464	−0.162552
$127$	12.9012	1.14479	0.572397	−	0.819977i	$-0.306014\pi$
$127$	12.9012	1.14479	0.572397	+	0.819977i	$0.306014\pi$
$128$	1.00000	0.0883883
$129$	16.2120	1.42739
$130$	3.80430	0.333659
$131$	−16.1220	−1.40859	−0.704294	−	0.709908i	$-0.748736\pi$
$131$	−16.1220	−1.40859	−0.704294	+	0.709908i	$0.748736\pi$
$132$	−5.16890	−0.449895
$133$	0.381461	0.0330769
$134$	7.71648	0.666603
$135$	12.5121	1.07687
$136$	−3.53252	−0.302911
$137$	−6.62859	−0.566319	−0.283159	−	0.959073i	$-0.591383\pi$
$137$	−6.62859	−0.566319	−0.283159	+	0.959073i	$0.591383\pi$
$138$	−25.2609	−2.15035
$139$	−8.67522	−0.735823	−0.367911	−	0.929861i	$-0.619927\pi$
$139$	−8.67522	−0.735823	−0.367911	+	0.929861i	$0.619927\pi$
$140$	0.959349	0.0810798
$141$	−28.2141	−2.37605
$142$	−13.5607	−1.13799
$143$	−2.80263	−0.234368
$144$	4.78329	0.398607
$145$	−14.0576	−1.16742
$146$	−11.6082	−0.960704
$147$	19.1230	1.57724
$148$	−10.9012	−0.896071
$149$	18.0044	1.47498	0.737490	−	0.675358i	$-0.236011\pi$
$149$	18.0044	1.47498	0.737490	+	0.675358i	$0.236011\pi$
$150$	−3.69620	−0.301794
$151$	−8.47133	−0.689387	−0.344694	−	0.938715i	$-0.612017\pi$
$151$	−8.47133	−0.689387	−0.344694	+	0.938715i	$0.612017\pi$
$152$	−1.00000	−0.0811107
$153$	−16.8971	−1.36605
$154$	−0.706753	−0.0569518
$155$	17.0093	1.36622
$156$	4.22017	0.337884
$157$	−4.14046	−0.330444	−0.165222	−	0.986256i	$-0.552834\pi$
$157$	−4.14046	−0.330444	−0.165222	+	0.986256i	$0.552834\pi$
$158$	3.95164	0.314376
$159$	−18.4563	−1.46368
$160$	−2.51493	−0.198823
$161$	−3.45396	−0.272210
$162$	−0.470015	−0.0369279
$163$	16.0818	1.25962	0.629812	−	0.776748i	$-0.283132\pi$
$163$	16.0818	1.25962	0.629812	+	0.776748i	$0.283132\pi$
$164$	0.614977	0.0480216
$165$	12.9994	1.01200
$166$	−10.0906	−0.783186
$167$	3.67821	0.284628	0.142314	−	0.989822i	$-0.454546\pi$
$167$	3.67821	0.284628	0.142314	+	0.989822i	$0.454546\pi$
$168$	1.06422	0.0821065
$169$	−10.7118	−0.823983
$170$	8.88405	0.681376
$171$	−4.78329	−0.365787
$172$	−5.81105	−0.443089
$173$	17.1404	1.30316	0.651582	−	0.758578i	$-0.274106\pi$
$173$	17.1404	1.30316	0.651582	+	0.758578i	$0.274106\pi$
$174$	−15.5943	−1.18220
$175$	−0.505388	−0.0382037
$176$	1.85275	0.139656
$177$	21.1093	1.58667
$178$	−4.88917	−0.366459
$179$	17.0170	1.27191	0.635954	−	0.771727i	$-0.280607\pi$
$179$	17.0170	1.27191	0.635954	+	0.771727i	$0.280607\pi$
$180$	−12.0296	−0.896636
$181$	11.4998	0.854774	0.427387	−	0.904069i	$-0.359434\pi$
$181$	11.4998	0.854774	0.427387	+	0.904069i	$0.359434\pi$
$182$	0.577031	0.0427724
$183$	−28.7359	−2.12422
$184$	9.05456	0.667511
$185$	27.4157	2.01564
$186$	18.8687	1.38352
$187$	−6.54489	−0.478610
$188$	10.1131	0.737573
$189$	1.89781	0.138046
$190$	2.51493	0.182452
$191$	7.79323	0.563898	0.281949	−	0.959429i	$-0.409019\pi$
$191$	7.79323	0.563898	0.281949	+	0.959429i	$0.409019\pi$
$192$	−2.78985	−0.201340
$193$	10.5128	0.756731	0.378365	−	0.925656i	$-0.376486\pi$
$193$	10.5128	0.756731	0.378365	+	0.925656i	$0.376486\pi$
$194$	−4.24563	−0.304818
$195$	−10.6134	−0.760045
$196$	−6.85449	−0.489606
$197$	−24.5742	−1.75084	−0.875420	−	0.483364i	$-0.839415\pi$
$197$	−24.5742	−1.75084	−0.875420	+	0.483364i	$0.839415\pi$
$198$	8.86224	0.629812
$199$	−14.5695	−1.03280	−0.516401	−	0.856347i	$-0.672729\pi$
$199$	−14.5695	−1.03280	−0.516401	+	0.856347i	$0.672729\pi$
$200$	1.32487	0.0936827
$201$	−21.5279	−1.51846
$202$	−4.66938	−0.328537
$203$	−2.13223	−0.149653
$204$	9.85523	0.690004
$205$	−1.54662	−0.108021
$206$	−0.552150	−0.0384701
$207$	43.3106	3.01029
$208$	−1.51269	−0.104886
$209$	−1.85275	−0.128157
$210$	−2.67644	−0.184692
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.61551	0.454355
$213$	37.8325	2.59224
$214$	11.7963	0.806382
$215$	14.6144	0.996693
$216$	−4.97512	−0.338514
$217$	2.57995	0.175138
$218$	12.5577	0.850517
$219$	32.3853	2.18839
$220$	−4.65954	−0.314146
$221$	5.34360	0.359450
$222$	30.4127	2.04117
$223$	16.5493	1.10823	0.554113	−	0.832442i	$-0.313058\pi$
$223$	16.5493	1.10823	0.554113	+	0.832442i	$0.313058\pi$
$224$	−0.381461	−0.0254875
$225$	6.33725	0.422483
$226$	−2.72236	−0.181089
$227$	7.46037	0.495162	0.247581	−	0.968867i	$-0.420364\pi$
$227$	7.46037	0.495162	0.247581	+	0.968867i	$0.420364\pi$
$228$	2.78985	0.184763
$229$	27.3715	1.80876	0.904381	−	0.426725i	$-0.140333\pi$
$229$	27.3715	1.80876	0.904381	+	0.426725i	$0.140333\pi$
$230$	−22.7716	−1.50151
$231$	1.97174	0.129731
$232$	5.58964	0.366978
$233$	−3.38922	−0.222035	−0.111017	−	0.993818i	$-0.535411\pi$
$233$	−3.38922	−0.222035	−0.111017	+	0.993818i	$0.535411\pi$
$234$	−7.23562	−0.473007
$235$	−25.4337	−1.65911
$236$	−7.56646	−0.492535
$237$	−11.0245	−0.716119
$238$	1.34752	0.0873469
$239$	−2.24183	−0.145012	−0.0725060	−	0.997368i	$-0.523100\pi$
$239$	−2.24183	−0.145012	−0.0725060	+	0.997368i	$0.523100\pi$
$240$	7.01629	0.452900
$241$	−25.2142	−1.62419	−0.812094	−	0.583527i	$-0.801672\pi$
$241$	−25.2142	−1.62419	−0.812094	+	0.583527i	$0.801672\pi$
$242$	−7.56732	−0.486445
$243$	16.2366	1.04158
$244$	10.3001	0.659398
$245$	17.2386	1.10133
$246$	−1.71570	−0.109389
$247$	1.51269	0.0962499
$248$	−6.76333	−0.429472
$249$	28.1514	1.78402
$250$	9.24269	0.584559
$251$	25.9381	1.63720	0.818598	−	0.574367i	$-0.194752\pi$
$251$	25.9381	1.63720	0.818598	+	0.574367i	$0.194752\pi$
$252$	−1.82464	−0.114942
$253$	16.7758	1.05469
$254$	12.9012	0.809491
$255$	−24.7852	−1.55211
$256$	1.00000	0.0625000
$257$	24.0627	1.50099	0.750494	−	0.660878i	$-0.229816\pi$
$257$	24.0627	1.50099	0.750494	+	0.660878i	$0.229816\pi$
$258$	16.2120	1.00931
$259$	4.15838	0.258389
$260$	3.80430	0.235933
$261$	26.7369	1.65497
$262$	−16.1220	−0.996022
$263$	3.75304	0.231423	0.115711	−	0.993283i	$-0.463085\pi$
$263$	3.75304	0.231423	0.115711	+	0.993283i	$0.463085\pi$
$264$	−5.16890	−0.318124
$265$	−16.6376	−1.02204
$266$	0.381461	0.0233889
$267$	13.6401	0.834759
$268$	7.71648	0.471359
$269$	24.9123	1.51893	0.759465	−	0.650548i	$-0.225461\pi$
$269$	24.9123	1.51893	0.759465	+	0.650548i	$0.225461\pi$
$270$	12.5121	0.761460
$271$	−3.64088	−0.221168	−0.110584	−	0.993867i	$-0.535272\pi$
$271$	−3.64088	−0.221168	−0.110584	+	0.993867i	$0.535272\pi$
$272$	−3.53252	−0.214191
$273$	−1.60983	−0.0974316
$274$	−6.62859	−0.400448
$275$	2.45466	0.148022
$276$	−25.2609	−1.52053
$277$	−16.0293	−0.963108	−0.481554	−	0.876417i	$-0.659927\pi$
$277$	−16.0293	−0.963108	−0.481554	+	0.876417i	$0.659927\pi$
$278$	−8.67522	−0.520305
$279$	−32.3510	−1.93680
$280$	0.959349	0.0573320
$281$	−11.4881	−0.685322	−0.342661	−	0.939459i	$-0.611328\pi$
$281$	−11.4881	−0.685322	−0.342661	+	0.939459i	$0.611328\pi$
$282$	−28.2141	−1.68012
$283$	−20.9876	−1.24759	−0.623793	−	0.781590i	$-0.714409\pi$
$283$	−20.9876	−1.24759	−0.623793	+	0.781590i	$0.714409\pi$
$284$	−13.5607	−0.804681
$285$	−7.01629	−0.415609
$286$	−2.80263	−0.165723
$287$	−0.234590	−0.0138474
$288$	4.78329	0.281858
$289$	−4.52127	−0.265957
$290$	−14.0576	−0.825488
$291$	11.8447	0.694348
$292$	−11.6082	−0.679320
$293$	14.2041	0.829812	0.414906	−	0.909864i	$-0.363814\pi$
$293$	14.2041	0.829812	0.414906	+	0.909864i	$0.363814\pi$
$294$	19.1230	1.11528
$295$	19.0291	1.10792
$296$	−10.9012	−0.633618
$297$	−9.21765	−0.534862
$298$	18.0044	1.04297
$299$	−13.6967	−0.792101
$300$	−3.69620	−0.213400
$301$	2.21669	0.127768
$302$	−8.47133	−0.487471
$303$	13.0269	0.748376
$304$	−1.00000	−0.0573539
$305$	−25.9041	−1.48326
$306$	−16.8971	−0.965942
$307$	11.4576	0.653922	0.326961	−	0.945038i	$-0.393975\pi$
$307$	11.4576	0.653922	0.326961	+	0.945038i	$0.393975\pi$
$308$	−0.706753	−0.0402710
$309$	1.54042	0.0876314
$310$	17.0093	0.966064
$311$	32.6557	1.85173	0.925866	−	0.377851i	$-0.123337\pi$
$311$	32.6557	1.85173	0.925866	+	0.377851i	$0.123337\pi$
$312$	4.22017	0.238920
$313$	16.7725	0.948039	0.474019	−	0.880514i	$-0.342803\pi$
$313$	16.7725	0.948039	0.474019	+	0.880514i	$0.342803\pi$
$314$	−4.14046	−0.233659
$315$	4.58884	0.258552
$316$	3.95164	0.222297
$317$	20.6606	1.16041	0.580207	−	0.814469i	$-0.302972\pi$
$317$	20.6606	1.16041	0.580207	+	0.814469i	$0.302972\pi$
$318$	−18.4563	−1.03498
$319$	10.3562	0.579836
$320$	−2.51493	−0.140589
$321$	−32.9101	−1.83686
$322$	−3.45396	−0.192482
$323$	3.53252	0.196555
$324$	−0.470015	−0.0261119
$325$	−2.00412	−0.111168
$326$	16.0818	0.890688
$327$	−35.0343	−1.93740
$328$	0.614977	0.0339564
$329$	−3.85775	−0.212685
$330$	12.9994	0.715595
$331$	20.0656	1.10291	0.551453	−	0.834206i	$-0.314074\pi$
$331$	20.0656	1.10291	0.551453	+	0.834206i	$0.314074\pi$
$332$	−10.0906	−0.553796
$333$	−52.1434	−2.85744
$334$	3.67821	0.201263
$335$	−19.4064	−1.06029
$336$	1.06422	0.0580581
$337$	18.5215	1.00893	0.504465	−	0.863432i	$-0.331690\pi$
$337$	18.5215	1.00893	0.504465	+	0.863432i	$0.331690\pi$
$338$	−10.7118	−0.582644
$339$	7.59498	0.412503
$340$	8.88405	0.481805
$341$	−12.5308	−0.678579
$342$	−4.78329	−0.258651
$343$	5.28495	0.285361
$344$	−5.81105	−0.313311
$345$	63.5294	3.42031
$346$	17.1404	0.921476
$347$	−19.1719	−1.02920	−0.514602	−	0.857429i	$-0.672060\pi$
$347$	−19.1719	−1.02920	−0.514602	+	0.857429i	$0.672060\pi$
$348$	−15.5943	−0.835941
$349$	14.6746	0.785513	0.392757	−	0.919642i	$-0.371521\pi$
$349$	14.6746	0.785513	0.392757	+	0.919642i	$0.371521\pi$
$350$	−0.505388	−0.0270141
$351$	7.52579	0.401697
$352$	1.85275	0.0987519
$353$	24.3574	1.29641	0.648206	−	0.761465i	$-0.275519\pi$
$353$	24.3574	1.29641	0.648206	+	0.761465i	$0.275519\pi$
$354$	21.1093	1.12195
$355$	34.1043	1.81007
$356$	−4.88917	−0.259126
$357$	−3.75939	−0.198968
$358$	17.0170	0.899374
$359$	−28.7641	−1.51811	−0.759057	−	0.651024i	$-0.774340\pi$
$359$	−28.7641	−1.51811	−0.759057	+	0.651024i	$0.774340\pi$
$360$	−12.0296	−0.634018
$361$	1.00000	0.0526316
$362$	11.4998	0.604417
$363$	21.1117	1.10808
$364$	0.577031	0.0302447
$365$	29.1939	1.52808
$366$	−28.7359	−1.50205
$367$	23.2429	1.21327	0.606634	−	0.794981i	$-0.292519\pi$
$367$	23.2429	1.21327	0.606634	+	0.794981i	$0.292519\pi$
$368$	9.05456	0.472001
$369$	2.94161	0.153134
$370$	27.4157	1.42527
$371$	−2.52356	−0.131017
$372$	18.8687	0.978298
$373$	18.0135	0.932705	0.466352	−	0.884599i	$-0.345568\pi$
$373$	18.0135	0.932705	0.466352	+	0.884599i	$0.345568\pi$
$374$	−6.54489	−0.338428
$375$	−25.7858	−1.33157
$376$	10.1131	0.521543
$377$	−8.45537	−0.435474
$378$	1.89781	0.0976130
$379$	−0.852570	−0.0437936	−0.0218968	−	0.999760i	$-0.506971\pi$
$379$	−0.852570	−0.0437936	−0.0218968	+	0.999760i	$0.506971\pi$
$380$	2.51493	0.129013
$381$	−35.9924	−1.84395
$382$	7.79323	0.398736
$383$	−30.7968	−1.57364	−0.786822	−	0.617180i	$-0.788275\pi$
$383$	−30.7968	−1.57364	−0.786822	+	0.617180i	$0.788275\pi$
$384$	−2.78985	−0.142369
$385$	1.77743	0.0905864
$386$	10.5128	0.535089
$387$	−27.7959	−1.41295
$388$	−4.24563	−0.215539
$389$	5.99114	0.303763	0.151882	−	0.988399i	$-0.451467\pi$
$389$	5.99114	0.303763	0.151882	+	0.988399i	$0.451467\pi$
$390$	−10.6134	−0.537433
$391$	−31.9854	−1.61757
$392$	−6.85449	−0.346204
$393$	44.9781	2.26885
$394$	−24.5742	−1.23803
$395$	−9.93811	−0.500040
$396$	8.86224	0.445344
$397$	25.0779	1.25862	0.629312	−	0.777153i	$-0.283337\pi$
$397$	25.0779	1.25862	0.629312	+	0.777153i	$0.283337\pi$
$398$	−14.5695	−0.730302
$399$	−1.06422	−0.0532777
$400$	1.32487	0.0662437
$401$	27.9765	1.39708	0.698540	−	0.715571i	$-0.253833\pi$
$401$	27.9765	1.39708	0.698540	+	0.715571i	$0.253833\pi$
$402$	−21.5279	−1.07371
$403$	10.2308	0.509633
$404$	−4.66938	−0.232310
$405$	1.18205	0.0587368
$406$	−2.13223	−0.105821
$407$	−20.1972	−1.00114
$408$	9.85523	0.487907
$409$	−15.1309	−0.748175	−0.374087	−	0.927393i	$-0.622044\pi$
$409$	−15.1309	−0.748175	−0.374087	+	0.927393i	$0.622044\pi$
$410$	−1.54662	−0.0763823
$411$	18.4928	0.912183
$412$	−0.552150	−0.0272025
$413$	2.88631	0.142026
$414$	43.3106	2.12860
$415$	25.3773	1.24572
$416$	−1.51269	−0.0741655
$417$	24.2026	1.18521
$418$	−1.85275	−0.0906210
$419$	14.2414	0.695737	0.347869	−	0.937543i	$-0.386906\pi$
$419$	14.2414	0.695737	0.347869	+	0.937543i	$0.386906\pi$
$420$	−2.67644	−0.130597
$421$	1.99964	0.0974566	0.0487283	−	0.998812i	$-0.484483\pi$
$421$	1.99964	0.0974566	0.0487283	+	0.998812i	$0.484483\pi$
$422$	−1.00000	−0.0486792
$423$	48.3738	2.35202
$424$	6.61551	0.321278
$425$	−4.68015	−0.227020
$426$	37.8325	1.83299
$427$	−3.92910	−0.190142
$428$	11.7963	0.570198
$429$	7.81893	0.377502
$430$	14.6144	0.704768
$431$	−32.2995	−1.55581	−0.777907	−	0.628379i	$-0.783719\pi$
$431$	−32.2995	−1.55581	−0.777907	+	0.628379i	$0.783719\pi$
$432$	−4.97512	−0.239365
$433$	9.51355	0.457192	0.228596	−	0.973521i	$-0.426587\pi$
$433$	9.51355	0.457192	0.228596	+	0.973521i	$0.426587\pi$
$434$	2.57995	0.123842
$435$	39.2185	1.88038
$436$	12.5577	0.601407
$437$	−9.05456	−0.433138
$438$	32.3853	1.54743
$439$	−39.7801	−1.89860	−0.949300	−	0.314370i	$-0.898207\pi$
$439$	−39.7801	−1.89860	−0.949300	+	0.314370i	$0.898207\pi$
$440$	−4.65954	−0.222135
$441$	−32.7870	−1.56129
$442$	5.34360	0.254169
$443$	−24.3353	−1.15621	−0.578103	−	0.815964i	$-0.696207\pi$
$443$	−24.3353	−1.15621	−0.578103	+	0.815964i	$0.696207\pi$
$444$	30.4127	1.44332
$445$	12.2959	0.582883
$446$	16.5493	0.783634
$447$	−50.2297	−2.37579
$448$	−0.381461	−0.0180224
$449$	−13.8915	−0.655580	−0.327790	−	0.944751i	$-0.606304\pi$
$449$	−13.8915	−0.655580	−0.327790	+	0.944751i	$0.606304\pi$
$450$	6.33725	0.298741
$451$	1.13940	0.0536522
$452$	−2.72236	−0.128049
$453$	23.6338	1.11041
$454$	7.46037	0.350133
$455$	−1.45119	−0.0680330
$456$	2.78985	0.130647
$457$	41.1067	1.92289	0.961445	−	0.274996i	$-0.0886767\pi$
$457$	41.1067	1.92289	0.961445	+	0.274996i	$0.0886767\pi$
$458$	27.3715	1.27899
$459$	17.5747	0.820318
$460$	−22.7716	−1.06173
$461$	−7.92899	−0.369290	−0.184645	−	0.982805i	$-0.559114\pi$
$461$	−7.92899	−0.369290	−0.184645	+	0.982805i	$0.559114\pi$
$462$	1.97174	0.0917335
$463$	7.25597	0.337213	0.168607	−	0.985683i	$-0.446073\pi$
$463$	7.25597	0.337213	0.168607	+	0.985683i	$0.446073\pi$
$464$	5.58964	0.259493
$465$	−47.4535	−2.20060
$466$	−3.38922	−0.157002
$467$	−26.2984	−1.21694	−0.608471	−	0.793576i	$-0.708217\pi$
$467$	−26.2984	−1.21694	−0.608471	+	0.793576i	$0.708217\pi$
$468$	−7.23562	−0.334466
$469$	−2.94354	−0.135920
$470$	−25.4337	−1.17317
$471$	11.5513	0.532254
$472$	−7.56646	−0.348274
$473$	−10.7664	−0.495041
$474$	−11.0245	−0.506372
$475$	−1.32487	−0.0607893
$476$	1.34752	0.0617636
$477$	31.6439	1.44888
$478$	−2.24183	−0.102539
$479$	30.9834	1.41567	0.707834	−	0.706378i	$-0.249672\pi$
$479$	30.9834	1.41567	0.707834	+	0.706378i	$0.249672\pi$
$480$	7.01629	0.320248
$481$	16.4901	0.751882
$482$	−25.2142	−1.14847
$483$	9.63606	0.438456
$484$	−7.56732	−0.343969
$485$	10.6775	0.484838
$486$	16.2366	0.736508
$487$	11.5194	0.521992	0.260996	−	0.965340i	$-0.415949\pi$
$487$	11.5194	0.521992	0.260996	+	0.965340i	$0.415949\pi$
$488$	10.3001	0.466265
$489$	−44.8659	−2.02891
$490$	17.2386	0.778759
$491$	−11.0127	−0.496997	−0.248499	−	0.968632i	$-0.579937\pi$
$491$	−11.0127	−0.496997	−0.248499	+	0.968632i	$0.579937\pi$
$492$	−1.71570	−0.0773496
$493$	−19.7455	−0.889294
$494$	1.51269	0.0680590
$495$	−22.2879	−1.00177
$496$	−6.76333	−0.303683
$497$	5.17289	0.232036
$498$	28.1514	1.26150
$499$	7.53530	0.337326	0.168663	−	0.985674i	$-0.446055\pi$
$499$	7.53530	0.337326	0.168663	+	0.985674i	$0.446055\pi$
$500$	9.24269	0.413346
$501$	−10.2617	−0.458458
$502$	25.9381	1.15767
$503$	30.0720	1.34085	0.670423	−	0.741979i	$-0.266113\pi$
$503$	30.0720	1.34085	0.670423	+	0.741979i	$0.266113\pi$
$504$	−1.82464	−0.0812759
$505$	11.7432	0.522564
$506$	16.7758	0.745777
$507$	29.8843	1.32721
$508$	12.9012	0.572397
$509$	19.9165	0.882782	0.441391	−	0.897315i	$-0.354485\pi$
$509$	19.9165	0.882782	0.441391	+	0.897315i	$0.354485\pi$
$510$	−24.7852	−1.09751
$511$	4.42809	0.195887
$512$	1.00000	0.0441942
$513$	4.97512	0.219657
$514$	24.0627	1.06136
$515$	1.38862	0.0611899
$516$	16.2120	0.713693
$517$	18.7370	0.824054
$518$	4.15838	0.182709
$519$	−47.8194	−2.09904
$520$	3.80430	0.166830
$521$	39.1365	1.71460	0.857301	−	0.514816i	$-0.172140\pi$
$521$	39.1365	1.71460	0.857301	+	0.514816i	$0.172140\pi$
$522$	26.7369	1.17024
$523$	−16.3609	−0.715413	−0.357707	−	0.933834i	$-0.616441\pi$
$523$	−16.3609	−0.715413	−0.357707	+	0.933834i	$0.616441\pi$
$524$	−16.1220	−0.704294
$525$	1.40996	0.0615356
$526$	3.75304	0.163640
$527$	23.8916	1.04074
$528$	−5.16890	−0.224948
$529$	58.9850	2.56457
$530$	−16.6376	−0.722689
$531$	−36.1926	−1.57062
$532$	0.381461	0.0165384
$533$	−0.930267	−0.0402943
$534$	13.6401	0.590264
$535$	−29.6670	−1.28262
$536$	7.71648	0.333301
$537$	−47.4748	−2.04869
$538$	24.9123	1.07405
$539$	−12.6997	−0.547013
$540$	12.5121	0.538434
$541$	−3.90353	−0.167826	−0.0839130	−	0.996473i	$-0.526742\pi$
$541$	−3.90353	−0.167826	−0.0839130	+	0.996473i	$0.526742\pi$
$542$	−3.64088	−0.156389
$543$	−32.0828	−1.37681
$544$	−3.53252	−0.151456
$545$	−31.5818	−1.35282
$546$	−1.60983	−0.0688945
$547$	16.5851	0.709126	0.354563	−	0.935032i	$-0.384630\pi$
$547$	16.5851	0.709126	0.354563	+	0.935032i	$0.384630\pi$
$548$	−6.62859	−0.283159
$549$	49.2685	2.10273
$550$	2.45466	0.104667
$551$	−5.58964	−0.238127
$552$	−25.2609	−1.07518
$553$	−1.50740	−0.0641011
$554$	−16.0293	−0.681020
$555$	−76.4858	−3.24664
$556$	−8.67522	−0.367911
$557$	−29.7482	−1.26047	−0.630235	−	0.776404i	$-0.717042\pi$
$557$	−29.7482	−1.26047	−0.630235	+	0.776404i	$0.717042\pi$
$558$	−32.3510	−1.36953
$559$	8.79030	0.371790
$560$	0.959349	0.0405399
$561$	18.2593	0.770908
$562$	−11.4881	−0.484596
$563$	15.6976	0.661574	0.330787	−	0.943705i	$-0.392686\pi$
$563$	15.6976	0.661574	0.330787	+	0.943705i	$0.392686\pi$
$564$	−28.2141	−1.18803
$565$	6.84654	0.288036
$566$	−20.9876	−0.882176
$567$	0.179293	0.00752958
$568$	−13.5607	−0.568996
$569$	−21.5637	−0.903997	−0.451998	−	0.892019i	$-0.649289\pi$
$569$	−21.5637	−0.903997	−0.451998	+	0.892019i	$0.649289\pi$
$570$	−7.01629	−0.293880
$571$	43.8490	1.83502	0.917512	−	0.397708i	$-0.130194\pi$
$571$	43.8490	1.83502	0.917512	+	0.397708i	$0.130194\pi$
$572$	−2.80263	−0.117184
$573$	−21.7420	−0.908284
$574$	−0.234590	−0.00979159
$575$	11.9961	0.500274
$576$	4.78329	0.199304
$577$	44.6223	1.85765	0.928826	−	0.370516i	$-0.120819\pi$
$577$	44.6223	1.85765	0.928826	+	0.370516i	$0.120819\pi$
$578$	−4.52127	−0.188060
$579$	−29.3293	−1.21888
$580$	−14.0576	−0.583708
$581$	3.84919	0.159691
$582$	11.8447	0.490978
$583$	12.2569	0.507629
$584$	−11.6082	−0.480352
$585$	18.1971	0.752356
$586$	14.2041	0.586766
$587$	−45.3034	−1.86987	−0.934936	−	0.354815i	$-0.884544\pi$
$587$	−45.3034	−1.86987	−0.934936	+	0.354815i	$0.884544\pi$
$588$	19.1230	0.788620
$589$	6.76333	0.278678
$590$	19.0291	0.783416
$591$	68.5584	2.82012
$592$	−10.9012	−0.448035
$593$	−38.9167	−1.59812	−0.799059	−	0.601252i	$-0.794669\pi$
$593$	−38.9167	−1.59812	−0.799059	+	0.601252i	$0.794669\pi$
$594$	−9.21765	−0.378205
$595$	−3.38892	−0.138932
$596$	18.0044	0.737490
$597$	40.6467	1.66356
$598$	−13.6967	−0.560100
$599$	−32.3158	−1.32039	−0.660194	−	0.751095i	$-0.729526\pi$
$599$	−32.3158	−1.32039	−0.660194	+	0.751095i	$0.729526\pi$
$600$	−3.69620	−0.150897
$601$	−9.53104	−0.388779	−0.194390	−	0.980924i	$-0.562273\pi$
$601$	−9.53104	−0.388779	−0.194390	+	0.980924i	$0.562273\pi$
$602$	2.21669	0.0903456
$603$	36.9102	1.50310
$604$	−8.47133	−0.344694
$605$	19.0313	0.773731
$606$	13.0269	0.529182
$607$	9.16268	0.371902	0.185951	−	0.982559i	$-0.440464\pi$
$607$	9.16268	0.371902	0.185951	+	0.982559i	$0.440464\pi$
$608$	−1.00000	−0.0405554
$609$	5.94862	0.241050
$610$	−25.9041	−1.04883
$611$	−15.2979	−0.618888
$612$	−16.8971	−0.683024
$613$	31.7215	1.28122	0.640611	−	0.767866i	$-0.278681\pi$
$613$	31.7215	1.28122	0.640611	+	0.767866i	$0.278681\pi$
$614$	11.4576	0.462393
$615$	4.31486	0.173992
$616$	−0.706753	−0.0284759
$617$	−27.0219	−1.08786	−0.543931	−	0.839130i	$-0.683065\pi$
$617$	−27.0219	−1.08786	−0.543931	+	0.839130i	$0.683065\pi$
$618$	1.54042	0.0619647
$619$	−22.9196	−0.921217	−0.460608	−	0.887603i	$-0.652369\pi$
$619$	−22.9196	−0.921217	−0.460608	+	0.887603i	$0.652369\pi$
$620$	17.0093	0.683110
$621$	−45.0475	−1.80769
$622$	32.6557	1.30937
$623$	1.86503	0.0747208
$624$	4.22017	0.168942
$625$	−29.8691	−1.19476
$626$	16.7725	0.670365
$627$	5.16890	0.206426
$628$	−4.14046	−0.165222
$629$	38.5087	1.53544
$630$	4.58884	0.182824
$631$	32.1996	1.28184	0.640922	−	0.767606i	$-0.278552\pi$
$631$	32.1996	1.28184	0.640922	+	0.767606i	$0.278552\pi$
$632$	3.95164	0.157188
$633$	2.78985	0.110887
$634$	20.6606	0.820537
$635$	−32.4455	−1.28756
$636$	−18.4563	−0.731841
$637$	10.3687	0.410822
$638$	10.3562	0.410006
$639$	−64.8649	−2.56602
$640$	−2.51493	−0.0994113
$641$	16.2029	0.639978	0.319989	−	0.947421i	$-0.396321\pi$
$641$	16.2029	0.639978	0.319989	+	0.947421i	$0.396321\pi$
$642$	−32.9101	−1.29886
$643$	44.7222	1.76367	0.881835	−	0.471557i	$-0.156308\pi$
$643$	44.7222	1.76367	0.881835	+	0.471557i	$0.156308\pi$
$644$	−3.45396	−0.136105
$645$	−40.7720	−1.60540
$646$	3.53252	0.138985
$647$	44.0424	1.73149	0.865743	−	0.500490i	$-0.166847\pi$
$647$	44.0424	1.73149	0.865743	+	0.500490i	$0.166847\pi$
$648$	−0.470015	−0.0184639
$649$	−14.0188	−0.550285
$650$	−2.00412	−0.0786079
$651$	−7.19769	−0.282100
$652$	16.0818	0.629812
$653$	21.2712	0.832407	0.416204	−	0.909271i	$-0.363360\pi$
$653$	21.2712	0.832407	0.416204	+	0.909271i	$0.363360\pi$
$654$	−35.0343	−1.36995
$655$	40.5458	1.58425
$656$	0.614977	0.0240108
$657$	−55.5255	−2.16626
$658$	−3.85775	−0.150391
$659$	3.92847	0.153031	0.0765157	−	0.997068i	$-0.475620\pi$
$659$	3.92847	0.153031	0.0765157	+	0.997068i	$0.475620\pi$
$660$	12.9994	0.506002
$661$	42.5418	1.65468	0.827342	−	0.561699i	$-0.189852\pi$
$661$	42.5418	1.65468	0.827342	+	0.561699i	$0.189852\pi$
$662$	20.0656	0.779873
$663$	−14.9079	−0.578974
$664$	−10.0906	−0.391593
$665$	−0.959349	−0.0372019
$666$	−52.1434	−2.02052
$667$	50.6117	1.95969
$668$	3.67821	0.142314
$669$	−46.1702	−1.78504
$670$	−19.4064	−0.749735
$671$	19.0836	0.736713
$672$	1.06422	0.0410532
$673$	32.8997	1.26819	0.634095	−	0.773255i	$-0.281373\pi$
$673$	32.8997	1.26819	0.634095	+	0.773255i	$0.281373\pi$
$674$	18.5215	0.713421
$675$	−6.59140	−0.253703
$676$	−10.7118	−0.411992
$677$	−3.01893	−0.116027	−0.0580134	−	0.998316i	$-0.518477\pi$
$677$	−3.01893	−0.116027	−0.0580134	+	0.998316i	$0.518477\pi$
$678$	7.59498	0.291684
$679$	1.61954	0.0621524
$680$	8.88405	0.340688
$681$	−20.8134	−0.797569
$682$	−12.5308	−0.479828
$683$	11.0354	0.422259	0.211130	−	0.977458i	$-0.432286\pi$
$683$	11.0354	0.422259	0.211130	+	0.977458i	$0.432286\pi$
$684$	−4.78329	−0.182894
$685$	16.6704	0.636945
$686$	5.28495	0.201780
$687$	−76.3626	−2.91342
$688$	−5.81105	−0.221544
$689$	−10.0072	−0.381244
$690$	63.5294	2.41852
$691$	−37.7357	−1.43553	−0.717767	−	0.696283i	$-0.754836\pi$
$691$	−37.7357	−1.43553	−0.717767	+	0.696283i	$0.754836\pi$
$692$	17.1404	0.651582
$693$	−3.38060	−0.128418
$694$	−19.1719	−0.727757
$695$	21.8176	0.827588
$696$	−15.5943	−0.591100
$697$	−2.17242	−0.0822863
$698$	14.6746	0.555442
$699$	9.45542	0.357637
$700$	−0.505388	−0.0191019
$701$	−9.85042	−0.372045	−0.186023	−	0.982545i	$-0.559560\pi$
$701$	−9.85042	−0.372045	−0.186023	+	0.982545i	$0.559560\pi$
$702$	7.52579	0.284043
$703$	10.9012	0.411145
$704$	1.85275	0.0698282
$705$	70.9564	2.67237
$706$	24.3574	0.916702
$707$	1.78119	0.0669885
$708$	21.1093	0.793337
$709$	−17.8571	−0.670637	−0.335318	−	0.942105i	$-0.608844\pi$
$709$	−17.8571	−0.670637	−0.335318	+	0.942105i	$0.608844\pi$
$710$	34.1043	1.27991
$711$	18.9018	0.708875
$712$	−4.88917	−0.183229
$713$	−61.2390	−2.29342
$714$	−3.75939	−0.140692
$715$	7.04842	0.263596
$716$	17.0170	0.635954
$717$	6.25438	0.233574
$718$	−28.7641	−1.07347
$719$	−1.13320	−0.0422613	−0.0211306	−	0.999777i	$-0.506727\pi$
$719$	−1.13320	−0.0422613	−0.0211306	+	0.999777i	$0.506727\pi$
$720$	−12.0296	−0.448318
$721$	0.210624	0.00784405
$722$	1.00000	0.0372161
$723$	70.3439	2.61612
$724$	11.4998	0.427387
$725$	7.40556	0.275036
$726$	21.1117	0.783529
$727$	−22.6380	−0.839598	−0.419799	−	0.907617i	$-0.637899\pi$
$727$	−22.6380	−0.839598	−0.419799	+	0.907617i	$0.637899\pi$
$728$	0.577031	0.0213862
$729$	−43.8878	−1.62547
$730$	29.1939	1.08051
$731$	20.5277	0.759244
$732$	−28.7359	−1.06211
$733$	−1.61203	−0.0595415	−0.0297708	−	0.999557i	$-0.509478\pi$
$733$	−1.61203	−0.0595415	−0.0297708	+	0.999557i	$0.509478\pi$
$734$	23.2429	0.857910
$735$	−48.0931	−1.77394
$736$	9.05456	0.333755
$737$	14.2967	0.526626
$738$	2.94161	0.108282
$739$	−17.5972	−0.647323	−0.323661	−	0.946173i	$-0.604914\pi$
$739$	−17.5972	−0.647323	−0.323661	+	0.946173i	$0.604914\pi$
$740$	27.4157	1.00782
$741$	−4.22017	−0.155032
$742$	−2.52356	−0.0926429
$743$	−21.2998	−0.781412	−0.390706	−	0.920515i	$-0.627769\pi$
$743$	−21.2998	−0.781412	−0.390706	+	0.920515i	$0.627769\pi$
$744$	18.8687	0.691761
$745$	−45.2799	−1.65893
$746$	18.0135	0.659522
$747$	−48.2664	−1.76598
$748$	−6.54489	−0.239305
$749$	−4.49985	−0.164421
$750$	−25.7858	−0.941563
$751$	6.74135	0.245995	0.122998	−	0.992407i	$-0.460749\pi$
$751$	6.74135	0.245995	0.122998	+	0.992407i	$0.460749\pi$
$752$	10.1131	0.368786
$753$	−72.3634	−2.63707
$754$	−8.45537	−0.307926
$755$	21.3048	0.775362
$756$	1.89781	0.0690228
$757$	−49.8042	−1.81017	−0.905083	−	0.425236i	$-0.860191\pi$
$757$	−49.8042	−1.81017	−0.905083	+	0.425236i	$0.860191\pi$
$758$	−0.852570	−0.0309667
$759$	−46.8021	−1.69881
$760$	2.51493	0.0912261
$761$	31.3263	1.13558	0.567789	−	0.823174i	$-0.307799\pi$
$761$	31.3263	1.13558	0.567789	+	0.823174i	$0.307799\pi$
$762$	−35.9924	−1.30387
$763$	−4.79029	−0.173420
$764$	7.79323	0.281949
$765$	42.4950	1.53641
$766$	−30.7968	−1.11273
$767$	11.4457	0.413279
$768$	−2.78985	−0.100670
$769$	−26.5863	−0.958726	−0.479363	−	0.877617i	$-0.659132\pi$
$769$	−26.5863	−0.958726	−0.479363	+	0.877617i	$0.659132\pi$
$770$	1.77743	0.0640543
$771$	−67.1313	−2.41768
$772$	10.5128	0.378365
$773$	30.2003	1.08623	0.543115	−	0.839659i	$-0.317245\pi$
$773$	30.2003	1.08623	0.543115	+	0.839659i	$0.317245\pi$
$774$	−27.7959	−0.999104
$775$	−8.96056	−0.321873
$776$	−4.24563	−0.152409
$777$	−11.6013	−0.416193
$778$	5.99114	0.214793
$779$	−0.614977	−0.0220338
$780$	−10.6134	−0.380022
$781$	−25.1247	−0.899031
$782$	−31.9854	−1.14380
$783$	−27.8091	−0.993816
$784$	−6.85449	−0.244803
$785$	10.4130	0.371654
$786$	44.9781	1.60432
$787$	−14.6882	−0.523576	−0.261788	−	0.965125i	$-0.584312\pi$
$787$	−14.6882	−0.523576	−0.261788	+	0.965125i	$0.584312\pi$
$788$	−24.5742	−0.875420
$789$	−10.4704	−0.372758
$790$	−9.93811	−0.353582
$791$	1.03847	0.0369239
$792$	8.86224	0.314906
$793$	−15.5809	−0.553293
$794$	25.0779	0.889981
$795$	46.4164	1.64622
$796$	−14.5695	−0.516401
$797$	40.3293	1.42854	0.714268	−	0.699872i	$-0.246760\pi$
$797$	40.3293	1.42854	0.714268	+	0.699872i	$0.246760\pi$
$798$	−1.06422	−0.0376730
$799$	−35.7247	−1.26385
$800$	1.32487	0.0468413
$801$	−23.3863	−0.826315
$802$	27.9765	0.987885
$803$	−21.5072	−0.758971
$804$	−21.5279	−0.759229
$805$	8.68648	0.306158
$806$	10.2308	0.360365
$807$	−69.5017	−2.44658
$808$	−4.66938	−0.164268
$809$	23.2684	0.818075	0.409038	−	0.912518i	$-0.365865\pi$
$809$	23.2684	0.818075	0.409038	+	0.912518i	$0.365865\pi$
$810$	1.18205	0.0415332
$811$	−14.6454	−0.514269	−0.257135	−	0.966376i	$-0.582778\pi$
$811$	−14.6454	−0.514269	−0.257135	+	0.966376i	$0.582778\pi$
$812$	−2.13223	−0.0748267
$813$	10.1575	0.356240
$814$	−20.1972	−0.707910
$815$	−40.4446	−1.41671
$816$	9.85523	0.345002
$817$	5.81105	0.203303
$818$	−15.1309	−0.529039
$819$	2.76011	0.0964460
$820$	−1.54662	−0.0540105
$821$	−28.5448	−0.996221	−0.498111	−	0.867114i	$-0.665973\pi$
$821$	−28.5448	−0.996221	−0.498111	+	0.867114i	$0.665973\pi$
$822$	18.4928	0.645011
$823$	35.8240	1.24875	0.624373	−	0.781126i	$-0.285355\pi$
$823$	35.8240	1.24875	0.624373	+	0.781126i	$0.285355\pi$
$824$	−0.552150	−0.0192351
$825$	−6.84814	−0.238422
$826$	2.88631	0.100428
$827$	−3.00602	−0.104529	−0.0522647	−	0.998633i	$-0.516644\pi$
$827$	−3.00602	−0.104529	−0.0522647	+	0.998633i	$0.516644\pi$
$828$	43.3106	1.50515
$829$	−3.99999	−0.138925	−0.0694627	−	0.997585i	$-0.522128\pi$
$829$	−3.99999	−0.138925	−0.0694627	+	0.997585i	$0.522128\pi$
$830$	25.3773	0.880857
$831$	44.7194	1.55130
$832$	−1.51269	−0.0524430
$833$	24.2136	0.838953
$834$	24.2026	0.838068
$835$	−9.25044	−0.320125
$836$	−1.85275	−0.0640787
$837$	33.6484	1.16306
$838$	14.2414	0.491961
$839$	−9.79810	−0.338268	−0.169134	−	0.985593i	$-0.554097\pi$
$839$	−9.79810	−0.338268	−0.169134	+	0.985593i	$0.554097\pi$
$840$	−2.67644	−0.0923461
$841$	2.24407	0.0773819
$842$	1.99964	0.0689122
$843$	32.0501	1.10386
$844$	−1.00000	−0.0344214
$845$	26.9394	0.926743
$846$	48.3738	1.66313
$847$	2.88664	0.0991861
$848$	6.61551	0.227178
$849$	58.5525	2.00952
$850$	−4.68015	−0.160528
$851$	−98.7053	−3.38357
$852$	37.8325	1.29612
$853$	29.3378	1.00451	0.502253	−	0.864721i	$-0.332505\pi$
$853$	29.3378	1.00451	0.502253	+	0.864721i	$0.332505\pi$
$854$	−3.92910	−0.134451
$855$	12.0296	0.411405
$856$	11.7963	0.403191
$857$	−6.83964	−0.233638	−0.116819	−	0.993153i	$-0.537270\pi$
$857$	−6.83964	−0.233638	−0.116819	+	0.993153i	$0.537270\pi$
$858$	7.81893	0.266934
$859$	−19.6782	−0.671412	−0.335706	−	0.941967i	$-0.608975\pi$
$859$	−19.6782	−0.671412	−0.335706	+	0.941967i	$0.608975\pi$
$860$	14.6144	0.498347
$861$	0.654472	0.0223043
$862$	−32.2995	−1.10013
$863$	−21.5803	−0.734600	−0.367300	−	0.930102i	$-0.619718\pi$
$863$	−21.5803	−0.734600	−0.367300	+	0.930102i	$0.619718\pi$
$864$	−4.97512	−0.169257
$865$	−43.1070	−1.46568
$866$	9.51355	0.323284
$867$	12.6137	0.428383
$868$	2.57995	0.0875692
$869$	7.32141	0.248362
$870$	39.2185	1.32963
$871$	−11.6726	−0.395512
$872$	12.5577	0.425259
$873$	−20.3081	−0.687324
$874$	−9.05456	−0.306275
$875$	−3.52573	−0.119191
$876$	32.3853	1.09420
$877$	30.2120	1.02019	0.510093	−	0.860119i	$-0.329611\pi$
$877$	30.2120	1.02019	0.510093	+	0.860119i	$0.329611\pi$
$878$	−39.7801	−1.34251
$879$	−39.6274	−1.33660
$880$	−4.65954	−0.157073
$881$	9.50022	0.320070	0.160035	−	0.987111i	$-0.448839\pi$
$881$	9.50022	0.320070	0.160035	+	0.987111i	$0.448839\pi$
$882$	−32.7870	−1.10400
$883$	−13.4375	−0.452207	−0.226104	−	0.974103i	$-0.572599\pi$
$883$	−13.4375	−0.452207	−0.226104	+	0.974103i	$0.572599\pi$
$884$	5.34360	0.179725
$885$	−53.0885	−1.78455
$886$	−24.3353	−0.817561
$887$	18.9522	0.636351	0.318176	−	0.948032i	$-0.396930\pi$
$887$	18.9522	0.636351	0.318176	+	0.948032i	$0.396930\pi$
$888$	30.4127	1.02058
$889$	−4.92130	−0.165055
$890$	12.2959	0.412160
$891$	−0.870821	−0.0291736
$892$	16.5493	0.554113
$893$	−10.1131	−0.338422
$894$	−50.2297	−1.67993
$895$	−42.7965	−1.43053
$896$	−0.381461	−0.0127437
$897$	38.2118	1.27586
$898$	−13.8915	−0.463565
$899$	−37.8046	−1.26085
$900$	6.33725	0.211242
$901$	−23.3695	−0.778550
$902$	1.13940	0.0379378
$903$	−6.18425	−0.205799
$904$	−2.72236	−0.0905443
$905$	−28.9212	−0.961374
$906$	23.6338	0.785180
$907$	10.3122	0.342411	0.171205	−	0.985235i	$-0.445234\pi$
$907$	10.3122	0.342411	0.171205	+	0.985235i	$0.445234\pi$
$908$	7.46037	0.247581
$909$	−22.3350	−0.740805
$910$	−1.45119	−0.0481066
$911$	−58.1985	−1.92820	−0.964101	−	0.265535i	$-0.914452\pi$
$911$	−58.1985	−1.92820	−0.964101	+	0.265535i	$0.914452\pi$
$912$	2.78985	0.0923813
$913$	−18.6954	−0.618729
$914$	41.1067	1.35969
$915$	72.2687	2.38913
$916$	27.3715	0.904381
$917$	6.14993	0.203089
$918$	17.5747	0.580052
$919$	−58.8412	−1.94099	−0.970495	−	0.241120i	$-0.922485\pi$
$919$	−58.8412	−1.94099	−0.970495	+	0.241120i	$0.922485\pi$
$920$	−22.7716	−0.750757
$921$	−31.9652	−1.05329
$922$	−7.92899	−0.261127
$923$	20.5131	0.675198
$924$	1.97174	0.0648654
$925$	−14.4427	−0.474872
$926$	7.25597	0.238446
$927$	−2.64109	−0.0867449
$928$	5.58964	0.183489
$929$	−14.6133	−0.479445	−0.239723	−	0.970841i	$-0.577056\pi$
$929$	−14.6133	−0.479445	−0.239723	+	0.970841i	$0.577056\pi$
$930$	−47.4535	−1.55606
$931$	6.85449	0.224647
$932$	−3.38922	−0.111017
$933$	−91.1045	−2.98263
$934$	−26.2984	−0.860508
$935$	16.4599	0.538297
$936$	−7.23562	−0.236503
$937$	−2.83842	−0.0927270	−0.0463635	−	0.998925i	$-0.514763\pi$
$937$	−2.83842	−0.0927270	−0.0463635	+	0.998925i	$0.514763\pi$
$938$	−2.94354	−0.0961100
$939$	−46.7929	−1.52703
$940$	−25.4337	−0.829556
$941$	−55.5845	−1.81200	−0.906001	−	0.423275i	$-0.860880\pi$
$941$	−55.5845	−1.81200	−0.906001	+	0.423275i	$0.860880\pi$
$942$	11.5513	0.376361
$943$	5.56834	0.181330
$944$	−7.56646	−0.246267
$945$	−4.77287	−0.155262
$946$	−10.7664	−0.350047
$947$	10.4270	0.338832	0.169416	−	0.985545i	$-0.445812\pi$
$947$	10.4270	0.338832	0.169416	+	0.985545i	$0.445812\pi$
$948$	−11.0245	−0.358059
$949$	17.5596	0.570009
$950$	−1.32487	−0.0429846
$951$	−57.6401	−1.86911
$952$	1.34752	0.0436734
$953$	8.04135	0.260485	0.130242	−	0.991482i	$-0.458424\pi$
$953$	8.04135	0.260485	0.130242	+	0.991482i	$0.458424\pi$
$954$	31.6439	1.02451
$955$	−19.5994	−0.634223
$956$	−2.24183	−0.0725060
$957$	−28.8923	−0.933956
$958$	30.9834	1.00103
$959$	2.52855	0.0816512
$960$	7.01629	0.226450
$961$	14.7427	0.475571
$962$	16.4901	0.531661
$963$	56.4253	1.81828
$964$	−25.2142	−0.812094
$965$	−26.4391	−0.851103
$966$	9.63606	0.310035
$967$	−14.9287	−0.480075	−0.240038	−	0.970764i	$-0.577160\pi$
$967$	−14.9287	−0.480075	−0.240038	+	0.970764i	$0.577160\pi$
$968$	−7.56732	−0.243223
$969$	−9.85523	−0.316596
$970$	10.6775	0.342833
$971$	−11.6150	−0.372742	−0.186371	−	0.982479i	$-0.559673\pi$
$971$	−11.6150	−0.372742	−0.186371	+	0.982479i	$0.559673\pi$
$972$	16.2366	0.520790
$973$	3.30926	0.106090
$974$	11.5194	0.369104
$975$	5.59120	0.179062
$976$	10.3001	0.329699
$977$	28.9508	0.926218	0.463109	−	0.886301i	$-0.346734\pi$
$977$	28.9508	0.926218	0.463109	+	0.886301i	$0.346734\pi$
$978$	−44.8659	−1.43465
$979$	−9.05841	−0.289508
$980$	17.2386	0.550665
$981$	60.0673	1.91780
$982$	−11.0127	−0.351430
$983$	−50.4130	−1.60792	−0.803962	−	0.594681i	$-0.797279\pi$
$983$	−50.4130	−1.60792	−0.803962	+	0.594681i	$0.797279\pi$
$984$	−1.71570	−0.0546944
$985$	61.8024	1.96919
$986$	−19.7455	−0.628826
$987$	10.7626	0.342576
$988$	1.51269	0.0481250
$989$	−52.6165	−1.67311
$990$	−22.2879	−0.708356
$991$	−6.48746	−0.206081	−0.103041	−	0.994677i	$-0.532857\pi$
$991$	−6.48746	−0.206081	−0.103041	+	0.994677i	$0.532857\pi$
$992$	−6.76333	−0.214736
$993$	−55.9802	−1.77648
$994$	5.17289	0.164074
$995$	36.6412	1.16160
$996$	28.1514	0.892012
$997$	0.807451	0.0255722	0.0127861	−	0.999918i	$-0.495930\pi$
$997$	0.807451	0.0255722	0.0127861	+	0.999918i	$0.495930\pi$
$998$	7.53530	0.238526
$999$	54.2346	1.71591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.6	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.6	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.78985 q^{3} +1.00000 q^{4} -2.51493 q^{5} -2.78985 q^{6} -0.381461 q^{7} +1.00000 q^{8} +4.78329 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.78985 q^{3} +1.00000 q^{4} -2.51493 q^{5} -2.78985 q^{6} -0.381461 q^{7} +1.00000 q^{8} +4.78329 q^{9} -2.51493 q^{10} +1.85275 q^{11} -2.78985 q^{12} -1.51269 q^{13} -0.381461 q^{14} +7.01629 q^{15} +1.00000 q^{16} -3.53252 q^{17} +4.78329 q^{18} -1.00000 q^{19} -2.51493 q^{20} +1.06422 q^{21} +1.85275 q^{22} +9.05456 q^{23} -2.78985 q^{24} +1.32487 q^{25} -1.51269 q^{26} -4.97512 q^{27} -0.381461 q^{28} +5.58964 q^{29} +7.01629 q^{30} -6.76333 q^{31} +1.00000 q^{32} -5.16890 q^{33} -3.53252 q^{34} +0.959349 q^{35} +4.78329 q^{36} -10.9012 q^{37} -1.00000 q^{38} +4.22017 q^{39} -2.51493 q^{40} +0.614977 q^{41} +1.06422 q^{42} -5.81105 q^{43} +1.85275 q^{44} -12.0296 q^{45} +9.05456 q^{46} +10.1131 q^{47} -2.78985 q^{48} -6.85449 q^{49} +1.32487 q^{50} +9.85523 q^{51} -1.51269 q^{52} +6.61551 q^{53} -4.97512 q^{54} -4.65954 q^{55} -0.381461 q^{56} +2.78985 q^{57} +5.58964 q^{58} -7.56646 q^{59} +7.01629 q^{60} +10.3001 q^{61} -6.76333 q^{62} -1.82464 q^{63} +1.00000 q^{64} +3.80430 q^{65} -5.16890 q^{66} +7.71648 q^{67} -3.53252 q^{68} -25.2609 q^{69} +0.959349 q^{70} -13.5607 q^{71} +4.78329 q^{72} -11.6082 q^{73} -10.9012 q^{74} -3.69620 q^{75} -1.00000 q^{76} -0.706753 q^{77} +4.22017 q^{78} +3.95164 q^{79} -2.51493 q^{80} -0.470015 q^{81} +0.614977 q^{82} -10.0906 q^{83} +1.06422 q^{84} +8.88405 q^{85} -5.81105 q^{86} -15.5943 q^{87} +1.85275 q^{88} -4.88917 q^{89} -12.0296 q^{90} +0.577031 q^{91} +9.05456 q^{92} +18.8687 q^{93} +10.1131 q^{94} +2.51493 q^{95} -2.78985 q^{96} -4.24563 q^{97} -6.85449 q^{98} +8.86224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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