LMFDB - Embedded newform 3311.2.a.k.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,2,Mod(1,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3311.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3311.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:	$26.4384681092$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	3311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.603435 q^{2} +2.40207 q^{3} -1.63587 q^{4} +0.408332 q^{5} +1.44949 q^{6} +1.00000 q^{7} -2.19401 q^{8} +2.76995 q^{9} +O(q^{10})$	\(q+0.603435 q^{2} +2.40207 q^{3} -1.63587 q^{4} +0.408332 q^{5} +1.44949 q^{6} +1.00000 q^{7} -2.19401 q^{8} +2.76995 q^{9} +0.246401 q^{10} +1.00000 q^{11} -3.92947 q^{12} +4.04357 q^{13} +0.603435 q^{14} +0.980842 q^{15} +1.94779 q^{16} +1.62021 q^{17} +1.67148 q^{18} +1.34027 q^{19} -0.667976 q^{20} +2.40207 q^{21} +0.603435 q^{22} -2.61433 q^{23} -5.27016 q^{24} -4.83327 q^{25} +2.44003 q^{26} -0.552607 q^{27} -1.63587 q^{28} +4.82749 q^{29} +0.591874 q^{30} -2.31215 q^{31} +5.56338 q^{32} +2.40207 q^{33} +0.977691 q^{34} +0.408332 q^{35} -4.53126 q^{36} +4.42168 q^{37} +0.808767 q^{38} +9.71295 q^{39} -0.895883 q^{40} +7.96916 q^{41} +1.44949 q^{42} +1.00000 q^{43} -1.63587 q^{44} +1.13106 q^{45} -1.57758 q^{46} +9.56759 q^{47} +4.67874 q^{48} +1.00000 q^{49} -2.91656 q^{50} +3.89186 q^{51} -6.61474 q^{52} +10.3466 q^{53} -0.333462 q^{54} +0.408332 q^{55} -2.19401 q^{56} +3.21943 q^{57} +2.91308 q^{58} -13.9395 q^{59} -1.60453 q^{60} +2.87863 q^{61} -1.39523 q^{62} +2.76995 q^{63} -0.538448 q^{64} +1.65112 q^{65} +1.44949 q^{66} -3.16273 q^{67} -2.65045 q^{68} -6.27981 q^{69} +0.246401 q^{70} -12.6918 q^{71} -6.07728 q^{72} +12.4975 q^{73} +2.66819 q^{74} -11.6098 q^{75} -2.19251 q^{76} +1.00000 q^{77} +5.86113 q^{78} -11.2707 q^{79} +0.795345 q^{80} -9.63724 q^{81} +4.80887 q^{82} +6.60453 q^{83} -3.92947 q^{84} +0.661583 q^{85} +0.603435 q^{86} +11.5960 q^{87} -2.19401 q^{88} +18.2262 q^{89} +0.682519 q^{90} +4.04357 q^{91} +4.27670 q^{92} -5.55395 q^{93} +5.77341 q^{94} +0.547276 q^{95} +13.3636 q^{96} -1.58260 q^{97} +0.603435 q^{98} +2.76995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9}+O(q^{10}) $ 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9} + 2 q^{10} + 38 q^{11} + 2 q^{12} + 8 q^{13} + 6 q^{14} + 26 q^{15} + 70 q^{16} + 3 q^{17} + 27 q^{18} + 10 q^{19} + 9 q^{20} + 7 q^{21} + 6 q^{22} + 22 q^{23} - 16 q^{24} + 82 q^{25} + 5 q^{26} + 28 q^{27} + 50 q^{28} + 24 q^{29} + 4 q^{30} + 13 q^{31} + 42 q^{32} + 7 q^{33} + 10 q^{34} + 8 q^{35} + 74 q^{36} + 45 q^{37} - 14 q^{38} + 14 q^{39} - 27 q^{40} - 13 q^{41} + 38 q^{43} + 50 q^{44} - 2 q^{45} + 3 q^{46} - 4 q^{47} - 7 q^{48} + 38 q^{49} - 5 q^{50} + 16 q^{51} + 22 q^{52} + 14 q^{53} - 55 q^{54} + 8 q^{55} + 18 q^{56} + 18 q^{57} + 47 q^{58} + 35 q^{59} + 61 q^{60} + 30 q^{61} + 4 q^{62} + 61 q^{63} + 96 q^{64} + 17 q^{65} + 50 q^{67} - 67 q^{68} + 42 q^{69} + 2 q^{70} + 41 q^{71} + 26 q^{72} + 29 q^{73} - 23 q^{74} + 32 q^{75} + 35 q^{76} + 38 q^{77} - 8 q^{78} + 51 q^{79} + 9 q^{80} + 98 q^{81} - 2 q^{82} - 51 q^{83} + 2 q^{84} + 22 q^{85} + 6 q^{86} - 39 q^{87} + 18 q^{88} + 50 q^{89} - 95 q^{90} + 8 q^{91} + q^{92} + 56 q^{93} + 3 q^{94} + 17 q^{95} - 105 q^{96} + 8 q^{97} + 6 q^{98} + 61 q^{99}+O(q^{100}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9 + 2 * q^10 + 38 * q^11 + 2 * q^12 + 8 * q^13 + 6 * q^14 + 26 * q^15 + 70 * q^16 + 3 * q^17 + 27 * q^18 + 10 * q^19 + 9 * q^20 + 7 * q^21 + 6 * q^22 + 22 * q^23 - 16 * q^24 + 82 * q^25 + 5 * q^26 + 28 * q^27 + 50 * q^28 + 24 * q^29 + 4 * q^30 + 13 * q^31 + 42 * q^32 + 7 * q^33 + 10 * q^34 + 8 * q^35 + 74 * q^36 + 45 * q^37 - 14 * q^38 + 14 * q^39 - 27 * q^40 - 13 * q^41 + 38 * q^43 + 50 * q^44 - 2 * q^45 + 3 * q^46 - 4 * q^47 - 7 * q^48 + 38 * q^49 - 5 * q^50 + 16 * q^51 + 22 * q^52 + 14 * q^53 - 55 * q^54 + 8 * q^55 + 18 * q^56 + 18 * q^57 + 47 * q^58 + 35 * q^59 + 61 * q^60 + 30 * q^61 + 4 * q^62 + 61 * q^63 + 96 * q^64 + 17 * q^65 + 50 * q^67 - 67 * q^68 + 42 * q^69 + 2 * q^70 + 41 * q^71 + 26 * q^72 + 29 * q^73 - 23 * q^74 + 32 * q^75 + 35 * q^76 + 38 * q^77 - 8 * q^78 + 51 * q^79 + 9 * q^80 + 98 * q^81 - 2 * q^82 - 51 * q^83 + 2 * q^84 + 22 * q^85 + 6 * q^86 - 39 * q^87 + 18 * q^88 + 50 * q^89 - 95 * q^90 + 8 * q^91 + q^92 + 56 * q^93 + 3 * q^94 + 17 * q^95 - 105 * q^96 + 8 * q^97 + 6 * q^98 + 61 * 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 $

$2$	0.603435	0.426693	0.213346	−	0.976977i	$-0.431564\pi$
$2$	0.603435	0.426693	0.213346	+	0.976977i	$0.431564\pi$
$3$	2.40207	1.38684	0.693418	−	0.720535i	$-0.256104\pi$
$3$	2.40207	1.38684	0.693418	+	0.720535i	$0.256104\pi$
$4$	−1.63587	−0.817933
$5$	0.408332	0.182611	0.0913057	−	0.995823i	$-0.470896\pi$
$5$	0.408332	0.182611	0.0913057	+	0.995823i	$0.470896\pi$
$6$	1.44949	0.591753
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.19401	−0.775699
$9$	2.76995	0.923315
$10$	0.246401	0.0779190
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.92947	−1.13434
$13$	4.04357	1.12148	0.560742	−	0.827990i	$-0.310516\pi$
$13$	4.04357	1.12148	0.560742	+	0.827990i	$0.310516\pi$
$14$	0.603435	0.161275
$15$	0.980842	0.253252
$16$	1.94779	0.486948
$17$	1.62021	0.392959	0.196479	−	0.980508i	$-0.437049\pi$
$17$	1.62021	0.392959	0.196479	+	0.980508i	$0.437049\pi$
$18$	1.67148	0.393972
$19$	1.34027	0.307480	0.153740	−	0.988111i	$-0.450868\pi$
$19$	1.34027	0.307480	0.153740	+	0.988111i	$0.450868\pi$
$20$	−0.667976	−0.149364
$21$	2.40207	0.524175
$22$	0.603435	0.128653
$23$	−2.61433	−0.545126	−0.272563	−	0.962138i	$-0.587871\pi$
$23$	−2.61433	−0.545126	−0.272563	+	0.962138i	$0.587871\pi$
$24$	−5.27016	−1.07577
$25$	−4.83327	−0.966653
$26$	2.44003	0.478529
$27$	−0.552607	−0.106349
$28$	−1.63587	−0.309150
$29$	4.82749	0.896443	0.448221	−	0.893923i	$-0.352058\pi$
$29$	4.82749	0.896443	0.448221	+	0.893923i	$0.352058\pi$
$30$	0.591874	0.108061
$31$	−2.31215	−0.415275	−0.207637	−	0.978206i	$-0.566577\pi$
$31$	−2.31215	−0.415275	−0.207637	+	0.978206i	$0.566577\pi$
$32$	5.56338	0.983476
$33$	2.40207	0.418147
$34$	0.977691	0.167673
$35$	0.408332	0.0690206
$36$	−4.53126	−0.755210
$37$	4.42168	0.726919	0.363460	−	0.931610i	$-0.381596\pi$
$37$	4.42168	0.726919	0.363460	+	0.931610i	$0.381596\pi$
$38$	0.808767	0.131199
$39$	9.71295	1.55532
$40$	−0.895883	−0.141652
$41$	7.96916	1.24457	0.622287	−	0.782789i	$-0.286204\pi$
$41$	7.96916	1.24457	0.622287	+	0.782789i	$0.286204\pi$
$42$	1.44949	0.223662
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.63587	−0.246616
$45$	1.13106	0.168608
$46$	−1.57758	−0.232601
$47$	9.56759	1.39558	0.697788	−	0.716304i	$-0.254168\pi$
$47$	9.56759	1.39558	0.697788	+	0.716304i	$0.254168\pi$
$48$	4.67874	0.675317
$49$	1.00000	0.142857
$50$	−2.91656	−0.412464
$51$	3.89186	0.544969
$52$	−6.61474	−0.917300
$53$	10.3466	1.42122	0.710608	−	0.703588i	$-0.248420\pi$
$53$	10.3466	1.42122	0.710608	+	0.703588i	$0.248420\pi$
$54$	−0.333462	−0.0453785
$55$	0.408332	0.0550594
$56$	−2.19401	−0.293187
$57$	3.21943	0.426424
$58$	2.91308	0.382506
$59$	−13.9395	−1.81476	−0.907382	−	0.420307i	$-0.861922\pi$
$59$	−13.9395	−1.81476	−0.907382	+	0.420307i	$0.861922\pi$
$60$	−1.60453	−0.207143
$61$	2.87863	0.368571	0.184285	−	0.982873i	$-0.441003\pi$
$61$	2.87863	0.368571	0.184285	+	0.982873i	$0.441003\pi$
$62$	−1.39523	−0.177195
$63$	2.76995	0.348980
$64$	−0.538448	−0.0673060
$65$	1.65112	0.204796
$66$	1.44949	0.178420
$67$	−3.16273	−0.386390	−0.193195	−	0.981160i	$-0.561885\pi$
$67$	−3.16273	−0.386390	−0.193195	+	0.981160i	$0.561885\pi$
$68$	−2.65045	−0.321414
$69$	−6.27981	−0.756000
$70$	0.246401	0.0294506
$71$	−12.6918	−1.50624	−0.753121	−	0.657882i	$-0.771453\pi$
$71$	−12.6918	−1.50624	−0.753121	+	0.657882i	$0.771453\pi$
$72$	−6.07728	−0.716215
$73$	12.4975	1.46272	0.731362	−	0.681990i	$-0.238885\pi$
$73$	12.4975	1.46272	0.731362	+	0.681990i	$0.238885\pi$
$74$	2.66819	0.310171
$75$	−11.6098	−1.34059
$76$	−2.19251	−0.251498
$77$	1.00000	0.113961
$78$	5.86113	0.663642
$79$	−11.2707	−1.26805	−0.634027	−	0.773311i	$-0.718599\pi$
$79$	−11.2707	−1.26805	−0.634027	+	0.773311i	$0.718599\pi$
$80$	0.795345	0.0889223
$81$	−9.63724	−1.07080
$82$	4.80887	0.531050
$83$	6.60453	0.724942	0.362471	−	0.931995i	$-0.381933\pi$
$83$	6.60453	0.724942	0.362471	+	0.931995i	$0.381933\pi$
$84$	−3.92947	−0.428740
$85$	0.661583	0.0717587
$86$	0.603435	0.0650700
$87$	11.5960	1.24322
$88$	−2.19401	−0.233882
$89$	18.2262	1.93198	0.965989	−	0.258582i	$-0.0832552\pi$
$89$	18.2262	1.93198	0.965989	+	0.258582i	$0.0832552\pi$
$90$	0.682519	0.0719438
$91$	4.04357	0.423881
$92$	4.27670	0.445876
$93$	−5.55395	−0.575918
$94$	5.77341	0.595482
$95$	0.547276	0.0561493
$96$	13.3636	1.36392
$97$	−1.58260	−0.160688	−0.0803441	−	0.996767i	$-0.525602\pi$
$97$	−1.58260	−0.160688	−0.0803441	+	0.996767i	$0.525602\pi$
$98$	0.603435	0.0609561
$99$	2.76995	0.278390
$100$	7.90658	0.790658
$101$	−14.3987	−1.43273	−0.716364	−	0.697726i	$-0.754195\pi$
$101$	−14.3987	−1.43273	−0.716364	+	0.697726i	$0.754195\pi$
$102$	2.34848	0.232534
$103$	7.62874	0.751682	0.375841	−	0.926684i	$-0.377354\pi$
$103$	7.62874	0.751682	0.375841	+	0.926684i	$0.377354\pi$
$104$	−8.87163	−0.869935
$105$	0.980842	0.0957203
$106$	6.24350	0.606423
$107$	8.12735	0.785700	0.392850	−	0.919602i	$-0.371489\pi$
$107$	8.12735	0.785700	0.392850	+	0.919602i	$0.371489\pi$
$108$	0.903992	0.0869866
$109$	12.0075	1.15011	0.575054	−	0.818115i	$-0.304981\pi$
$109$	12.0075	1.15011	0.575054	+	0.818115i	$0.304981\pi$
$110$	0.246401	0.0234935
$111$	10.6212	1.00812
$112$	1.94779	0.184049
$113$	7.61661	0.716511	0.358255	−	0.933624i	$-0.383372\pi$
$113$	7.61661	0.716511	0.358255	+	0.933624i	$0.383372\pi$
$114$	1.94272	0.181952
$115$	−1.06751	−0.0995462
$116$	−7.89713	−0.733230
$117$	11.2005	1.03548
$118$	−8.41156	−0.774347
$119$	1.62021	0.148524
$120$	−2.15197	−0.196447
$121$	1.00000	0.0909091
$122$	1.73706	0.157266
$123$	19.1425	1.72602
$124$	3.78237	0.339667
$125$	−4.01523	−0.359133
$126$	1.67148	0.148907
$127$	−3.97815	−0.353004	−0.176502	−	0.984300i	$-0.556478\pi$
$127$	−3.97815	−0.353004	−0.176502	+	0.984300i	$0.556478\pi$
$128$	−11.4517	−1.01220
$129$	2.40207	0.211491
$130$	0.996342	0.0873850
$131$	−4.14751	−0.362369	−0.181185	−	0.983449i	$-0.557993\pi$
$131$	−4.14751	−0.362369	−0.181185	+	0.983449i	$0.557993\pi$
$132$	−3.92947	−0.342016
$133$	1.34027	0.116216
$134$	−1.90850	−0.164870
$135$	−0.225647	−0.0194206
$136$	−3.55475	−0.304818
$137$	8.06494	0.689035	0.344517	−	0.938780i	$-0.388043\pi$
$137$	8.06494	0.689035	0.344517	+	0.938780i	$0.388043\pi$
$138$	−3.78945	−0.322580
$139$	−4.23740	−0.359411	−0.179706	−	0.983720i	$-0.557515\pi$
$139$	−4.23740	−0.359411	−0.179706	+	0.983720i	$0.557515\pi$
$140$	−0.667976	−0.0564543
$141$	22.9820	1.93544
$142$	−7.65868	−0.642702
$143$	4.04357	0.338140
$144$	5.39528	0.449607
$145$	1.97122	0.163701
$146$	7.54144	0.624134
$147$	2.40207	0.198119
$148$	−7.23327	−0.594571
$149$	−18.5503	−1.51970	−0.759849	−	0.650100i	$-0.774727\pi$
$149$	−18.5503	−1.51970	−0.759849	+	0.650100i	$0.774727\pi$
$150$	−7.00578	−0.572020
$151$	10.0258	0.815890	0.407945	−	0.913006i	$-0.366245\pi$
$151$	10.0258	0.815890	0.407945	+	0.913006i	$0.366245\pi$
$152$	−2.94057	−0.238512
$153$	4.48789	0.362825
$154$	0.603435	0.0486262
$155$	−0.944125	−0.0758339
$156$	−15.8891	−1.27214
$157$	1.26936	0.101306	0.0506529	−	0.998716i	$-0.483870\pi$
$157$	1.26936	0.101306	0.0506529	+	0.998716i	$0.483870\pi$
$158$	−6.80114	−0.541070
$159$	24.8533	1.97099
$160$	2.27170	0.179594
$161$	−2.61433	−0.206038
$162$	−5.81544	−0.456904
$163$	−2.31928	−0.181660	−0.0908298	−	0.995866i	$-0.528952\pi$
$163$	−2.31928	−0.181660	−0.0908298	+	0.995866i	$0.528952\pi$
$164$	−13.0365	−1.01798
$165$	0.980842	0.0763584
$166$	3.98540	0.309327
$167$	7.29813	0.564746	0.282373	−	0.959305i	$-0.408878\pi$
$167$	7.29813	0.564746	0.282373	+	0.959305i	$0.408878\pi$
$168$	−5.27016	−0.406602
$169$	3.35047	0.257728
$170$	0.399222	0.0306189
$171$	3.71248	0.283901
$172$	−1.63587	−0.124734
$173$	7.43037	0.564920	0.282460	−	0.959279i	$-0.408850\pi$
$173$	7.43037	0.564920	0.282460	+	0.959279i	$0.408850\pi$
$174$	6.99742	0.530473
$175$	−4.83327	−0.365361
$176$	1.94779	0.146820
$177$	−33.4836	−2.51678
$178$	10.9984	0.824361
$179$	−16.9157	−1.26434	−0.632169	−	0.774830i	$-0.717835\pi$
$179$	−16.9157	−1.26434	−0.632169	+	0.774830i	$0.717835\pi$
$180$	−1.85026	−0.137910
$181$	16.3133	1.21256	0.606279	−	0.795252i	$-0.292661\pi$
$181$	16.3133	1.21256	0.606279	+	0.795252i	$0.292661\pi$
$182$	2.44003	0.180867
$183$	6.91467	0.511147
$184$	5.73586	0.422853
$185$	1.80551	0.132744
$186$	−3.35145	−0.245740
$187$	1.62021	0.118481
$188$	−15.6513	−1.14149
$189$	−0.552607	−0.0401963
$190$	0.330245	0.0239585
$191$	2.17463	0.157351	0.0786753	−	0.996900i	$-0.474931\pi$
$191$	2.17463	0.157351	0.0786753	+	0.996900i	$0.474931\pi$
$192$	−1.29339	−0.0933424
$193$	−6.65024	−0.478695	−0.239347	−	0.970934i	$-0.576933\pi$
$193$	−6.65024	−0.478695	−0.239347	+	0.970934i	$0.576933\pi$
$194$	−0.954993	−0.0685645
$195$	3.96610	0.284019
$196$	−1.63587	−0.116848
$197$	−5.60861	−0.399597	−0.199799	−	0.979837i	$-0.564029\pi$
$197$	−5.60861	−0.399597	−0.199799	+	0.979837i	$0.564029\pi$
$198$	1.67148	0.118787
$199$	12.4580	0.883121	0.441560	−	0.897232i	$-0.354425\pi$
$199$	12.4580	0.883121	0.441560	+	0.897232i	$0.354425\pi$
$200$	10.6042	0.749832
$201$	−7.59711	−0.535859
$202$	−8.68870	−0.611335
$203$	4.82749	0.338824
$204$	−6.36656	−0.445748
$205$	3.25406	0.227273
$206$	4.60345	0.320737
$207$	−7.24155	−0.503323
$208$	7.87604	0.546105
$209$	1.34027	0.0927086
$210$	0.591874	0.0408432
$211$	−27.7149	−1.90797	−0.953985	−	0.299853i	$-0.903062\pi$
$211$	−27.7149	−1.90797	−0.953985	+	0.299853i	$0.903062\pi$
$212$	−16.9257	−1.16246
$213$	−30.4867	−2.08891
$214$	4.90432	0.335253
$215$	0.408332	0.0278480
$216$	1.21242	0.0824950
$217$	−2.31215	−0.156959
$218$	7.24573	0.490743
$219$	30.0199	2.02856
$220$	−0.667976	−0.0450349
$221$	6.55143	0.440697
$222$	6.40919	0.430157
$223$	−13.3629	−0.894844	−0.447422	−	0.894323i	$-0.647658\pi$
$223$	−13.3629	−0.894844	−0.447422	+	0.894323i	$0.647658\pi$
$224$	5.56338	0.371719
$225$	−13.3879	−0.892525
$226$	4.59613	0.305730
$227$	−13.8790	−0.921180	−0.460590	−	0.887613i	$-0.652362\pi$
$227$	−13.8790	−0.921180	−0.460590	+	0.887613i	$0.652362\pi$
$228$	−5.26656	−0.348786
$229$	26.6076	1.75828	0.879141	−	0.476562i	$-0.158117\pi$
$229$	26.6076	1.75828	0.879141	+	0.476562i	$0.158117\pi$
$230$	−0.644175	−0.0424756
$231$	2.40207	0.158045
$232$	−10.5916	−0.695370
$233$	−0.405702	−0.0265784	−0.0132892	−	0.999912i	$-0.504230\pi$
$233$	−0.405702	−0.0265784	−0.0132892	+	0.999912i	$0.504230\pi$
$234$	6.75875	0.441834
$235$	3.90675	0.254848
$236$	22.8031	1.48436
$237$	−27.0731	−1.75858
$238$	0.977691	0.0633743
$239$	−19.6685	−1.27225	−0.636124	−	0.771587i	$-0.719463\pi$
$239$	−19.6685	−1.27225	−0.636124	+	0.771587i	$0.719463\pi$
$240$	1.91048	0.123321
$241$	11.4349	0.736586	0.368293	−	0.929710i	$-0.379942\pi$
$241$	11.4349	0.736586	0.368293	+	0.929710i	$0.379942\pi$
$242$	0.603435	0.0387903
$243$	−21.4915	−1.37868
$244$	−4.70905	−0.301466
$245$	0.408332	0.0260874
$246$	11.5512	0.736480
$247$	5.41949	0.344834
$248$	5.07288	0.322128
$249$	15.8646	1.00538
$250$	−2.42293	−0.153240
$251$	11.4539	0.722965	0.361483	−	0.932379i	$-0.382271\pi$
$251$	11.4539	0.722965	0.361483	+	0.932379i	$0.382271\pi$
$252$	−4.53126	−0.285443
$253$	−2.61433	−0.164362
$254$	−2.40055	−0.150624
$255$	1.58917	0.0995176
$256$	−5.83345	−0.364590
$257$	−20.8603	−1.30123	−0.650614	−	0.759409i	$-0.725488\pi$
$257$	−20.8603	−1.30123	−0.650614	+	0.759409i	$0.725488\pi$
$258$	1.44949	0.0902415
$259$	4.42168	0.274750
$260$	−2.70101	−0.167509
$261$	13.3719	0.827699
$262$	−2.50275	−0.154620
$263$	0.548505	0.0338223	0.0169111	−	0.999857i	$-0.494617\pi$
$263$	0.548505	0.0338223	0.0169111	+	0.999857i	$0.494617\pi$
$264$	−5.27016	−0.324356
$265$	4.22485	0.259530
$266$	0.808767	0.0495887
$267$	43.7807	2.67934
$268$	5.17381	0.316041
$269$	−30.4151	−1.85444	−0.927220	−	0.374517i	$-0.877808\pi$
$269$	−30.4151	−1.85444	−0.927220	+	0.374517i	$0.877808\pi$
$270$	−0.136163	−0.00828663
$271$	−19.9254	−1.21038	−0.605190	−	0.796081i	$-0.706903\pi$
$271$	−19.9254	−1.21038	−0.605190	+	0.796081i	$0.706903\pi$
$272$	3.15583	0.191350
$273$	9.71295	0.587854
$274$	4.86667	0.294006
$275$	−4.83327	−0.291457
$276$	10.2729	0.618358
$277$	8.48376	0.509740	0.254870	−	0.966975i	$-0.417967\pi$
$277$	8.48376	0.509740	0.254870	+	0.966975i	$0.417967\pi$
$278$	−2.55699	−0.153358
$279$	−6.40453	−0.383429
$280$	−0.895883	−0.0535392
$281$	−10.6963	−0.638087	−0.319044	−	0.947740i	$-0.603362\pi$
$281$	−10.6963	−0.638087	−0.319044	+	0.947740i	$0.603362\pi$
$282$	13.8681	0.825836
$283$	16.2390	0.965311	0.482655	−	0.875810i	$-0.339672\pi$
$283$	16.2390	0.965311	0.482655	+	0.875810i	$0.339672\pi$
$284$	20.7621	1.23201
$285$	1.31459	0.0778699
$286$	2.44003	0.144282
$287$	7.96916	0.470404
$288$	15.4103	0.908059
$289$	−14.3749	−0.845584
$290$	1.18950	0.0698499
$291$	−3.80151	−0.222848
$292$	−20.4443	−1.19641
$293$	25.9266	1.51465	0.757325	−	0.653039i	$-0.226506\pi$
$293$	25.9266	1.51465	0.757325	+	0.653039i	$0.226506\pi$
$294$	1.44949	0.0845361
$295$	−5.69193	−0.331397
$296$	−9.70119	−0.563870
$297$	−0.552607	−0.0320655
$298$	−11.1939	−0.648444
$299$	−10.5712	−0.611350
$300$	18.9922	1.09651
$301$	1.00000	0.0576390
$302$	6.04993	0.348135
$303$	−34.5868	−1.98696
$304$	2.61057	0.149727
$305$	1.17543	0.0673052
$306$	2.70815	0.154815
$307$	−14.4039	−0.822073	−0.411036	−	0.911619i	$-0.634833\pi$
$307$	−14.4039	−0.822073	−0.411036	+	0.911619i	$0.634833\pi$
$308$	−1.63587	−0.0932121
$309$	18.3248	1.04246
$310$	−0.569718	−0.0323578
$311$	−18.1421	−1.02875	−0.514373	−	0.857567i	$-0.671975\pi$
$311$	−18.1421	−1.02875	−0.514373	+	0.857567i	$0.671975\pi$
$312$	−21.3103	−1.20646
$313$	−1.34633	−0.0760991	−0.0380495	−	0.999276i	$-0.512114\pi$
$313$	−1.34633	−0.0760991	−0.0380495	+	0.999276i	$0.512114\pi$
$314$	0.765975	0.0432264
$315$	1.13106	0.0637278
$316$	18.4374	1.03718
$317$	−6.77815	−0.380699	−0.190349	−	0.981716i	$-0.560962\pi$
$317$	−6.77815	−0.380699	−0.190349	+	0.981716i	$0.560962\pi$
$318$	14.9973	0.841009
$319$	4.82749	0.270288
$320$	−0.219865	−0.0122908
$321$	19.5225	1.08964
$322$	−1.57758	−0.0879150
$323$	2.17152	0.120827
$324$	15.7652	0.875846
$325$	−19.5437	−1.08409
$326$	−1.39953	−0.0775129
$327$	28.8428	1.59501
$328$	−17.4844	−0.965414
$329$	9.56759	0.527478
$330$	0.591874	0.0325816
$331$	−17.0899	−0.939345	−0.469673	−	0.882841i	$-0.655628\pi$
$331$	−17.0899	−0.939345	−0.469673	+	0.882841i	$0.655628\pi$
$332$	−10.8041	−0.592954
$333$	12.2478	0.671175
$334$	4.40395	0.240973
$335$	−1.29144	−0.0705592
$336$	4.67874	0.255246
$337$	−9.15884	−0.498914	−0.249457	−	0.968386i	$-0.580252\pi$
$337$	−9.15884	−0.498914	−0.249457	+	0.968386i	$0.580252\pi$
$338$	2.02179	0.109971
$339$	18.2956	0.993683
$340$	−1.08226	−0.0586939
$341$	−2.31215	−0.125210
$342$	2.24024	0.121138
$343$	1.00000	0.0539949
$344$	−2.19401	−0.118293
$345$	−2.56424	−0.138054
$346$	4.48374	0.241047
$347$	−28.4212	−1.52573	−0.762865	−	0.646558i	$-0.776208\pi$
$347$	−28.4212	−1.52573	−0.762865	+	0.646558i	$0.776208\pi$
$348$	−18.9695	−1.01687
$349$	−23.0398	−1.23329	−0.616647	−	0.787240i	$-0.711509\pi$
$349$	−23.0398	−1.23329	−0.616647	+	0.787240i	$0.711509\pi$
$350$	−2.91656	−0.155897
$351$	−2.23451	−0.119269
$352$	5.56338	0.296529
$353$	16.6564	0.886533	0.443267	−	0.896390i	$-0.353820\pi$
$353$	16.6564	0.886533	0.443267	+	0.896390i	$0.353820\pi$
$354$	−20.2052	−1.07389
$355$	−5.18247	−0.275057
$356$	−29.8157	−1.58023
$357$	3.89186	0.205979
$358$	−10.2075	−0.539484
$359$	−22.6944	−1.19776	−0.598881	−	0.800838i	$-0.704388\pi$
$359$	−22.6944	−1.19776	−0.598881	+	0.800838i	$0.704388\pi$
$360$	−2.48155	−0.130789
$361$	−17.2037	−0.905456
$362$	9.84401	0.517390
$363$	2.40207	0.126076
$364$	−6.61474	−0.346707
$365$	5.10313	0.267110
$366$	4.17255	0.218103
$367$	10.7506	0.561175	0.280588	−	0.959828i	$-0.409471\pi$
$367$	10.7506	0.561175	0.280588	+	0.959828i	$0.409471\pi$
$368$	−5.09217	−0.265448
$369$	22.0741	1.14913
$370$	1.08951	0.0566408
$371$	10.3466	0.537169
$372$	9.08553	0.471063
$373$	−11.8449	−0.613307	−0.306653	−	0.951821i	$-0.599209\pi$
$373$	−11.8449	−0.613307	−0.306653	+	0.951821i	$0.599209\pi$
$374$	0.977691	0.0505552
$375$	−9.64488	−0.498059
$376$	−20.9914	−1.08255
$377$	19.5203	1.00535
$378$	−0.333462	−0.0171515
$379$	26.5701	1.36481	0.682407	−	0.730972i	$-0.260933\pi$
$379$	26.5701	1.36481	0.682407	+	0.730972i	$0.260933\pi$
$380$	−0.895270	−0.0459264
$381$	−9.55580	−0.489559
$382$	1.31225	0.0671404
$383$	33.4559	1.70952	0.854759	−	0.519025i	$-0.173705\pi$
$383$	33.4559	1.70952	0.854759	+	0.519025i	$0.173705\pi$
$384$	−27.5078	−1.40375
$385$	0.408332	0.0208105
$386$	−4.01298	−0.204256
$387$	2.76995	0.140804
$388$	2.58892	0.131432
$389$	−17.6609	−0.895444	−0.447722	−	0.894173i	$-0.647765\pi$
$389$	−17.6609	−0.895444	−0.447722	+	0.894173i	$0.647765\pi$
$390$	2.39328	0.121189
$391$	−4.23576	−0.214212
$392$	−2.19401	−0.110814
$393$	−9.96260	−0.502547
$394$	−3.38443	−0.170505
$395$	−4.60219	−0.231561
$396$	−4.53126	−0.227704
$397$	15.5472	0.780292	0.390146	−	0.920753i	$-0.372424\pi$
$397$	15.5472	0.780292	0.390146	+	0.920753i	$0.372424\pi$
$398$	7.51756	0.376821
$399$	3.21943	0.161173
$400$	−9.41420	−0.470710
$401$	8.36309	0.417633	0.208816	−	0.977955i	$-0.433039\pi$
$401$	8.36309	0.417633	0.208816	+	0.977955i	$0.433039\pi$
$402$	−4.58436	−0.228647
$403$	−9.34935	−0.465724
$404$	23.5544	1.17188
$405$	−3.93519	−0.195541
$406$	2.91308	0.144574
$407$	4.42168	0.219174
$408$	−8.53877	−0.422732
$409$	−11.3670	−0.562061	−0.281031	−	0.959699i	$-0.590676\pi$
$409$	−11.3670	−0.562061	−0.281031	+	0.959699i	$0.590676\pi$
$410$	1.96361	0.0969759
$411$	19.3726	0.955578
$412$	−12.4796	−0.614826
$413$	−13.9395	−0.685916
$414$	−4.36980	−0.214764
$415$	2.69684	0.132383
$416$	22.4959	1.10295
$417$	−10.1785	−0.498445
$418$	0.808767	0.0395581
$419$	−4.96967	−0.242784	−0.121392	−	0.992605i	$-0.538736\pi$
$419$	−4.96967	−0.242784	−0.121392	+	0.992605i	$0.538736\pi$
$420$	−1.60453	−0.0782929
$421$	−24.3955	−1.18897	−0.594483	−	0.804108i	$-0.702643\pi$
$421$	−24.3955	−1.18897	−0.594483	+	0.804108i	$0.702643\pi$
$422$	−16.7241	−0.814117
$423$	26.5017	1.28856
$424$	−22.7005	−1.10244
$425$	−7.83090	−0.379855
$426$	−18.3967	−0.891323
$427$	2.87863	0.139307
$428$	−13.2953	−0.642651
$429$	9.71295	0.468945
$430$	0.246401	0.0118825
$431$	−21.5260	−1.03687	−0.518435	−	0.855117i	$-0.673485\pi$
$431$	−21.5260	−1.03687	−0.518435	+	0.855117i	$0.673485\pi$
$432$	−1.07636	−0.0517866
$433$	−20.0319	−0.962673	−0.481336	−	0.876536i	$-0.659848\pi$
$433$	−20.0319	−0.962673	−0.481336	+	0.876536i	$0.659848\pi$
$434$	−1.39523	−0.0669733
$435$	4.73500	0.227026
$436$	−19.6426	−0.940712
$437$	−3.50392	−0.167615
$438$	18.1151	0.865571
$439$	1.65175	0.0788337	0.0394168	−	0.999223i	$-0.487450\pi$
$439$	1.65175	0.0788337	0.0394168	+	0.999223i	$0.487450\pi$
$440$	−0.895883	−0.0427095
$441$	2.76995	0.131902
$442$	3.95336	0.188042
$443$	9.60132	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$443$	9.60132	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$444$	−17.3748	−0.824573
$445$	7.44235	0.352801
$446$	−8.06362	−0.381823
$447$	−44.5591	−2.10757
$448$	−0.538448	−0.0254393
$449$	25.6669	1.21129	0.605647	−	0.795733i	$-0.292914\pi$
$449$	25.6669	1.21129	0.605647	+	0.795733i	$0.292914\pi$
$450$	−8.07871	−0.380834
$451$	7.96916	0.375253
$452$	−12.4598	−0.586058
$453$	24.0828	1.13151
$454$	−8.37506	−0.393061
$455$	1.65112	0.0774056
$456$	−7.06345	−0.330777
$457$	−11.1410	−0.521156	−0.260578	−	0.965453i	$-0.583913\pi$
$457$	−11.1410	−0.521156	−0.260578	+	0.965453i	$0.583913\pi$
$458$	16.0560	0.750246
$459$	−0.895339	−0.0417909
$460$	1.74631	0.0814221
$461$	12.0543	0.561425	0.280712	−	0.959792i	$-0.409429\pi$
$461$	12.0543	0.561425	0.280712	+	0.959792i	$0.409429\pi$
$462$	1.44949	0.0674365
$463$	−10.5727	−0.491355	−0.245677	−	0.969352i	$-0.579010\pi$
$463$	−10.5727	−0.491355	−0.245677	+	0.969352i	$0.579010\pi$
$464$	9.40295	0.436521
$465$	−2.26785	−0.105169
$466$	−0.244815	−0.0113408
$467$	−8.78994	−0.406750	−0.203375	−	0.979101i	$-0.565191\pi$
$467$	−8.78994	−0.406750	−0.203375	+	0.979101i	$0.565191\pi$
$468$	−18.3225	−0.846957
$469$	−3.16273	−0.146042
$470$	2.35747	0.108742
$471$	3.04909	0.140495
$472$	30.5833	1.40771
$473$	1.00000	0.0459800
$474$	−16.3368	−0.750375
$475$	−6.47789	−0.297226
$476$	−2.65045	−0.121483
$477$	28.6595	1.31223
$478$	−11.8686	−0.542859
$479$	−31.4769	−1.43822	−0.719108	−	0.694898i	$-0.755450\pi$
$479$	−31.4769	−1.43822	−0.719108	+	0.694898i	$0.755450\pi$
$480$	5.45680	0.249068
$481$	17.8794	0.815229
$482$	6.90021	0.314296
$483$	−6.27981	−0.285741
$484$	−1.63587	−0.0743576
$485$	−0.646224	−0.0293435
$486$	−12.9687	−0.588273
$487$	−33.2900	−1.50851	−0.754256	−	0.656581i	$-0.772002\pi$
$487$	−33.2900	−1.50851	−0.754256	+	0.656581i	$0.772002\pi$
$488$	−6.31573	−0.285900
$489$	−5.57106	−0.251932
$490$	0.246401	0.0111313
$491$	15.2939	0.690202	0.345101	−	0.938565i	$-0.387845\pi$
$491$	15.2939	0.690202	0.345101	+	0.938565i	$0.387845\pi$
$492$	−31.3145	−1.41177
$493$	7.82155	0.352265
$494$	3.27031	0.147138
$495$	1.13106	0.0508372
$496$	−4.50359	−0.202217
$497$	−12.6918	−0.569306
$498$	9.57322	0.428986
$499$	33.5920	1.50379	0.751893	−	0.659285i	$-0.229141\pi$
$499$	33.5920	1.50379	0.751893	+	0.659285i	$0.229141\pi$
$500$	6.56839	0.293747
$501$	17.5306	0.783211
$502$	6.91169	0.308484
$503$	−0.223835	−0.00998032	−0.00499016	−	0.999988i	$-0.501588\pi$
$503$	−0.223835	−0.00998032	−0.00499016	+	0.999988i	$0.501588\pi$
$504$	−6.07728	−0.270704
$505$	−5.87946	−0.261633
$506$	−1.57758	−0.0701319
$507$	8.04806	0.357427
$508$	6.50772	0.288734
$509$	−10.0511	−0.445509	−0.222755	−	0.974875i	$-0.571505\pi$
$509$	−10.0511	−0.445509	−0.222755	+	0.974875i	$0.571505\pi$
$510$	0.958960	0.0424634
$511$	12.4975	0.552858
$512$	19.3833	0.856627
$513$	−0.740644	−0.0327002
$514$	−12.5878	−0.555224
$515$	3.11506	0.137266
$516$	−3.92947	−0.172985
$517$	9.56759	0.420782
$518$	2.66819	0.117234
$519$	17.8483	0.783452
$520$	−3.62257	−0.158860
$521$	42.1850	1.84816	0.924079	−	0.382200i	$-0.124834\pi$
$521$	42.1850	1.84816	0.924079	+	0.382200i	$0.124834\pi$
$522$	8.06906	0.353173
$523$	14.9318	0.652923	0.326461	−	0.945211i	$-0.394144\pi$
$523$	14.9318	0.652923	0.326461	+	0.945211i	$0.394144\pi$
$524$	6.78477	0.296394
$525$	−11.6098	−0.506695
$526$	0.330987	0.0144317
$527$	−3.74617	−0.163186
$528$	4.67874	0.203616
$529$	−16.1653	−0.702838
$530$	2.54942	0.110740
$531$	−38.6116	−1.67560
$532$	−2.19251	−0.0950572
$533$	32.2239	1.39577
$534$	26.4188	1.14325
$535$	3.31865	0.143478
$536$	6.93907	0.299722
$537$	−40.6327	−1.75343
$538$	−18.3535	−0.791276
$539$	1.00000	0.0430730
$540$	0.369128	0.0158848
$541$	29.1065	1.25139	0.625694	−	0.780069i	$-0.284816\pi$
$541$	29.1065	1.25139	0.625694	+	0.780069i	$0.284816\pi$
$542$	−12.0237	−0.516461
$543$	39.1857	1.68162
$544$	9.01384	0.386465
$545$	4.90304	0.210023
$546$	5.86113	0.250833
$547$	−20.8064	−0.889619	−0.444809	−	0.895625i	$-0.646729\pi$
$547$	−20.8064	−0.889619	−0.444809	+	0.895625i	$0.646729\pi$
$548$	−13.1932	−0.563584
$549$	7.97364	0.340307
$550$	−2.91656	−0.124363
$551$	6.47015	0.275638
$552$	13.7779	0.586428
$553$	−11.2707	−0.479280
$554$	5.11940	0.217502
$555$	4.33696	0.184094
$556$	6.93182	0.293975
$557$	32.0551	1.35822	0.679109	−	0.734038i	$-0.262366\pi$
$557$	32.0551	1.35822	0.679109	+	0.734038i	$0.262366\pi$
$558$	−3.86472	−0.163607
$559$	4.04357	0.171025
$560$	0.795345	0.0336095
$561$	3.89186	0.164314
$562$	−6.45451	−0.272267
$563$	1.93236	0.0814393	0.0407196	−	0.999171i	$-0.487035\pi$
$563$	1.93236	0.0814393	0.0407196	+	0.999171i	$0.487035\pi$
$564$	−37.5955	−1.58306
$565$	3.11010	0.130843
$566$	9.79920	0.411891
$567$	−9.63724	−0.404726
$568$	27.8460	1.16839
$569$	−27.5919	−1.15671	−0.578356	−	0.815784i	$-0.696306\pi$
$569$	−27.5919	−1.15671	−0.578356	+	0.815784i	$0.696306\pi$
$570$	0.793272	0.0332265
$571$	−19.5884	−0.819751	−0.409876	−	0.912141i	$-0.634428\pi$
$571$	−19.5884	−0.819751	−0.409876	+	0.912141i	$0.634428\pi$
$572$	−6.61474	−0.276576
$573$	5.22362	0.218220
$574$	4.80887	0.200718
$575$	12.6358	0.526947
$576$	−1.49147	−0.0621446
$577$	−29.1100	−1.21187	−0.605934	−	0.795515i	$-0.707200\pi$
$577$	−29.1100	−1.21187	−0.605934	+	0.795515i	$0.707200\pi$
$578$	−8.67433	−0.360804
$579$	−15.9743	−0.663871
$580$	−3.22465	−0.133896
$581$	6.60453	0.274002
$582$	−2.29396	−0.0950877
$583$	10.3466	0.428513
$584$	−27.4197	−1.13463
$585$	4.57351	0.189091
$586$	15.6450	0.646290
$587$	−33.5252	−1.38373	−0.691867	−	0.722025i	$-0.743212\pi$
$587$	−33.5252	−1.38373	−0.691867	+	0.722025i	$0.743212\pi$
$588$	−3.92947	−0.162049
$589$	−3.09891	−0.127688
$590$	−3.43471	−0.141405
$591$	−13.4723	−0.554176
$592$	8.61251	0.353972
$593$	−25.5082	−1.04750	−0.523749	−	0.851873i	$-0.675467\pi$
$593$	−25.5082	−1.04750	−0.523749	+	0.851873i	$0.675467\pi$
$594$	−0.333462	−0.0136821
$595$	0.661583	0.0271223
$596$	30.3458	1.24301
$597$	29.9249	1.22474
$598$	−6.37905	−0.260859
$599$	0.754499	0.0308280	0.0154140	−	0.999881i	$-0.495093\pi$
$599$	0.754499	0.0308280	0.0154140	+	0.999881i	$0.495093\pi$
$600$	25.4721	1.03989
$601$	−30.1997	−1.23187	−0.615935	−	0.787797i	$-0.711222\pi$
$601$	−30.1997	−1.23187	−0.615935	+	0.787797i	$0.711222\pi$
$602$	0.603435	0.0245942
$603$	−8.76060	−0.356759
$604$	−16.4009	−0.667344
$605$	0.408332	0.0166010
$606$	−20.8709	−0.847822
$607$	40.4354	1.64122	0.820612	−	0.571486i	$-0.193633\pi$
$607$	40.4354	1.64122	0.820612	+	0.571486i	$0.193633\pi$
$608$	7.45645	0.302399
$609$	11.5960	0.469893
$610$	0.709298	0.0287186
$611$	38.6872	1.56512
$612$	−7.34159	−0.296766
$613$	9.67157	0.390631	0.195316	−	0.980740i	$-0.437427\pi$
$613$	9.67157	0.390631	0.195316	+	0.980740i	$0.437427\pi$
$614$	−8.69180	−0.350772
$615$	7.81648	0.315191
$616$	−2.19401	−0.0883991
$617$	−40.4345	−1.62783	−0.813916	−	0.580983i	$-0.802668\pi$
$617$	−40.4345	−1.62783	−0.813916	+	0.580983i	$0.802668\pi$
$618$	11.0578	0.444810
$619$	11.8511	0.476336	0.238168	−	0.971224i	$-0.423453\pi$
$619$	11.8511	0.476336	0.238168	+	0.971224i	$0.423453\pi$
$620$	1.54446	0.0620271
$621$	1.44470	0.0579737
$622$	−10.9476	−0.438958
$623$	18.2262	0.730219
$624$	18.9188	0.757358
$625$	22.5268	0.901071
$626$	−0.812422	−0.0324709
$627$	3.21943	0.128572
$628$	−2.07650	−0.0828614
$629$	7.16404	0.285649
$630$	0.682519	0.0271922
$631$	0.176834	0.00703967	0.00351983	−	0.999994i	$-0.498880\pi$
$631$	0.176834	0.00703967	0.00351983	+	0.999994i	$0.498880\pi$
$632$	24.7280	0.983629
$633$	−66.5731	−2.64604
$634$	−4.09017	−0.162442
$635$	−1.62441	−0.0644625
$636$	−40.6567	−1.61214
$637$	4.04357	0.160212
$638$	2.91308	0.115330
$639$	−35.1556	−1.39074
$640$	−4.67608	−0.184838
$641$	−34.3671	−1.35742	−0.678709	−	0.734407i	$-0.737460\pi$
$641$	−34.3671	−1.35742	−0.678709	+	0.734407i	$0.737460\pi$
$642$	11.7805	0.464941
$643$	−7.74519	−0.305441	−0.152720	−	0.988269i	$-0.548803\pi$
$643$	−7.74519	−0.305441	−0.152720	+	0.988269i	$0.548803\pi$
$644$	4.27670	0.168525
$645$	0.980842	0.0386206
$646$	1.31037	0.0515559
$647$	12.1723	0.478542	0.239271	−	0.970953i	$-0.423092\pi$
$647$	12.1723	0.478542	0.239271	+	0.970953i	$0.423092\pi$
$648$	21.1442	0.830622
$649$	−13.9395	−0.547172
$650$	−11.7933	−0.462572
$651$	−5.55395	−0.217677
$652$	3.79402	0.148585
$653$	34.2471	1.34019	0.670096	−	0.742275i	$-0.266253\pi$
$653$	34.2471	1.34019	0.670096	+	0.742275i	$0.266253\pi$
$654$	17.4048	0.680580
$655$	−1.69356	−0.0661728
$656$	15.5223	0.606043
$657$	34.6174	1.35056
$658$	5.77341	0.225071
$659$	10.8357	0.422098	0.211049	−	0.977475i	$-0.432312\pi$
$659$	10.8357	0.422098	0.211049	+	0.977475i	$0.432312\pi$
$660$	−1.60453	−0.0624561
$661$	15.7952	0.614362	0.307181	−	0.951651i	$-0.400614\pi$
$661$	15.7952	0.614362	0.307181	+	0.951651i	$0.400614\pi$
$662$	−10.3126	−0.400812
$663$	15.7370	0.611175
$664$	−14.4904	−0.562336
$665$	0.547276	0.0212224
$666$	7.39075	0.286386
$667$	−12.6207	−0.488674
$668$	−11.9388	−0.461925
$669$	−32.0986	−1.24100
$670$	−0.779303	−0.0301071
$671$	2.87863	0.111128
$672$	13.3636	0.515514
$673$	18.6791	0.720027	0.360014	−	0.932947i	$-0.382772\pi$
$673$	18.6791	0.720027	0.360014	+	0.932947i	$0.382772\pi$
$674$	−5.52676	−0.212883
$675$	2.67090	0.102803
$676$	−5.48092	−0.210805
$677$	−33.5317	−1.28873	−0.644364	−	0.764719i	$-0.722878\pi$
$677$	−33.5317	−1.28873	−0.644364	+	0.764719i	$0.722878\pi$
$678$	11.0402	0.423997
$679$	−1.58260	−0.0607344
$680$	−1.45152	−0.0556632
$681$	−33.3383	−1.27753
$682$	−1.39523	−0.0534262
$683$	8.52168	0.326073	0.163037	−	0.986620i	$-0.447871\pi$
$683$	8.52168	0.326073	0.163037	+	0.986620i	$0.447871\pi$
$684$	−6.07312	−0.232212
$685$	3.29317	0.125826
$686$	0.603435	0.0230392
$687$	63.9134	2.43845
$688$	1.94779	0.0742589
$689$	41.8373	1.59387
$690$	−1.54735	−0.0589068
$691$	44.2236	1.68235	0.841173	−	0.540766i	$-0.181866\pi$
$691$	44.2236	1.68235	0.841173	+	0.540766i	$0.181866\pi$
$692$	−12.1551	−0.462067
$693$	2.76995	0.105222
$694$	−17.1503	−0.651018
$695$	−1.73026	−0.0656326
$696$	−25.4417	−0.964364
$697$	12.9117	0.489066
$698$	−13.9030	−0.526238
$699$	−0.974525	−0.0368599
$700$	7.90658	0.298841
$701$	−48.4089	−1.82838	−0.914190	−	0.405285i	$-0.867172\pi$
$701$	−48.4089	−1.82838	−0.914190	+	0.405285i	$0.867172\pi$
$702$	−1.34838	−0.0508913
$703$	5.92625	0.223513
$704$	−0.538448	−0.0202935
$705$	9.38429	0.353433
$706$	10.0511	0.378277
$707$	−14.3987	−0.541521
$708$	54.7747	2.05856
$709$	−37.0208	−1.39035	−0.695173	−	0.718843i	$-0.744672\pi$
$709$	−37.0208	−1.39035	−0.695173	+	0.718843i	$0.744672\pi$
$710$	−3.12728	−0.117365
$711$	−31.2193	−1.17081
$712$	−39.9885	−1.49863
$713$	6.04473	0.226377
$714$	2.34848	0.0878897
$715$	1.65112	0.0617483
$716$	27.6718	1.03414
$717$	−47.2451	−1.76440
$718$	−13.6946	−0.511077
$719$	−33.0306	−1.23184	−0.615918	−	0.787811i	$-0.711215\pi$
$719$	−33.0306	−1.23184	−0.615918	+	0.787811i	$0.711215\pi$
$720$	2.20306	0.0821033
$721$	7.62874	0.284109
$722$	−10.3813	−0.386352
$723$	27.4674	1.02152
$724$	−26.6864	−0.991792
$725$	−23.3325	−0.866549
$726$	1.44949	0.0537957
$727$	−21.3078	−0.790264	−0.395132	−	0.918624i	$-0.629301\pi$
$727$	−21.3078	−0.790264	−0.395132	+	0.918624i	$0.629301\pi$
$728$	−8.87163	−0.328804
$729$	−22.7124	−0.841201
$730$	3.07941	0.113974
$731$	1.62021	0.0599256
$732$	−11.3115	−0.418084
$733$	−28.9005	−1.06746	−0.533732	−	0.845654i	$-0.679211\pi$
$733$	−28.9005	−1.06746	−0.533732	+	0.845654i	$0.679211\pi$
$734$	6.48727	0.239449
$735$	0.980842	0.0361789
$736$	−14.5445	−0.536118
$737$	−3.16273	−0.116501
$738$	13.3203	0.490327
$739$	28.7421	1.05729	0.528647	−	0.848842i	$-0.322699\pi$
$739$	28.7421	1.05729	0.528647	+	0.848842i	$0.322699\pi$
$740$	−2.95357	−0.108576
$741$	13.0180	0.478228
$742$	6.24350	0.229206
$743$	−21.4826	−0.788121	−0.394060	−	0.919085i	$-0.628930\pi$
$743$	−21.4826	−0.788121	−0.394060	+	0.919085i	$0.628930\pi$
$744$	12.1854	0.446739
$745$	−7.57466	−0.277514
$746$	−7.14764	−0.261694
$747$	18.2942	0.669350
$748$	−2.65045	−0.0969099
$749$	8.12735	0.296967
$750$	−5.82005	−0.212518
$751$	15.7063	0.573132	0.286566	−	0.958061i	$-0.407486\pi$
$751$	15.7063	0.573132	0.286566	+	0.958061i	$0.407486\pi$
$752$	18.6357	0.679573
$753$	27.5131	1.00263
$754$	11.7792	0.428974
$755$	4.09386	0.148991
$756$	0.903992	0.0328779
$757$	32.5390	1.18265	0.591325	−	0.806434i	$-0.298605\pi$
$757$	32.5390	1.18265	0.591325	+	0.806434i	$0.298605\pi$
$758$	16.0333	0.582356
$759$	−6.27981	−0.227943
$760$	−1.20073	−0.0435549
$761$	37.6442	1.36460	0.682300	−	0.731072i	$-0.260980\pi$
$761$	37.6442	1.36460	0.682300	+	0.731072i	$0.260980\pi$
$762$	−5.76630	−0.208891
$763$	12.0075	0.434700
$764$	−3.55740	−0.128702
$765$	1.83255	0.0662559
$766$	20.1885	0.729439
$767$	−56.3652	−2.03523
$768$	−14.0124	−0.505627
$769$	−8.87070	−0.319886	−0.159943	−	0.987126i	$-0.551131\pi$
$769$	−8.87070	−0.319886	−0.159943	+	0.987126i	$0.551131\pi$
$770$	0.246401	0.00887969
$771$	−50.1078	−1.80459
$772$	10.8789	0.391540
$773$	25.6293	0.921822	0.460911	−	0.887446i	$-0.347523\pi$
$773$	25.6293	0.921822	0.460911	+	0.887446i	$0.347523\pi$
$774$	1.67148	0.0600802
$775$	11.1752	0.401427
$776$	3.47223	0.124646
$777$	10.6212	0.381033
$778$	−10.6572	−0.382080
$779$	10.6808	0.382681
$780$	−6.48802	−0.232308
$781$	−12.6918	−0.454149
$782$	−2.55601	−0.0914026
$783$	−2.66771	−0.0953361
$784$	1.94779	0.0695640
$785$	0.518319	0.0184996
$786$	−6.01178	−0.214433
$787$	21.6246	0.770834	0.385417	−	0.922743i	$-0.374058\pi$
$787$	21.6246	0.770834	0.385417	+	0.922743i	$0.374058\pi$
$788$	9.17494	0.326844
$789$	1.31755	0.0469059
$790$	−2.77712	−0.0988056
$791$	7.61661	0.270816
$792$	−6.07728	−0.215947
$793$	11.6399	0.413346
$794$	9.38173	0.332945
$795$	10.1484	0.359926
$796$	−20.3795	−0.722334
$797$	−46.8314	−1.65885	−0.829427	−	0.558615i	$-0.811333\pi$
$797$	−46.8314	−1.65885	−0.829427	+	0.558615i	$0.811333\pi$
$798$	1.94272	0.0687714
$799$	15.5015	0.548403
$800$	−26.8893	−0.950680
$801$	50.4857	1.78383
$802$	5.04658	0.178201
$803$	12.4975	0.441028
$804$	12.4279	0.438297
$805$	−1.06751	−0.0376249
$806$	−5.64172	−0.198721
$807$	−73.0592	−2.57180
$808$	31.5910	1.11137
$809$	4.06567	0.142941	0.0714706	−	0.997443i	$-0.477231\pi$
$809$	4.06567	0.142941	0.0714706	+	0.997443i	$0.477231\pi$
$810$	−2.37463	−0.0834360
$811$	28.3918	0.996972	0.498486	−	0.866898i	$-0.333890\pi$
$811$	28.3918	0.996972	0.498486	+	0.866898i	$0.333890\pi$
$812$	−7.89713	−0.277135
$813$	−47.8622	−1.67860
$814$	2.66819	0.0935201
$815$	−0.947033	−0.0331731
$816$	7.58053	0.265372
$817$	1.34027	0.0468902
$818$	−6.85923	−0.239828
$819$	11.2005	0.391376
$820$	−5.32321	−0.185894
$821$	8.86868	0.309519	0.154760	−	0.987952i	$-0.450540\pi$
$821$	8.86868	0.309519	0.154760	+	0.987952i	$0.450540\pi$
$822$	11.6901	0.407738
$823$	50.0345	1.74409	0.872046	−	0.489424i	$-0.162793\pi$
$823$	50.0345	1.74409	0.872046	+	0.489424i	$0.162793\pi$
$824$	−16.7375	−0.583079
$825$	−11.6098	−0.404203
$826$	−8.41156	−0.292676
$827$	25.4106	0.883612	0.441806	−	0.897111i	$-0.354338\pi$
$827$	25.4106	0.883612	0.441806	+	0.897111i	$0.354338\pi$
$828$	11.8462	0.411684
$829$	−51.3302	−1.78277	−0.891386	−	0.453246i	$-0.850266\pi$
$829$	−51.3302	−1.78277	−0.891386	+	0.453246i	$0.850266\pi$
$830$	1.62737	0.0564867
$831$	20.3786	0.706926
$832$	−2.17725	−0.0754827
$833$	1.62021	0.0561369
$834$	−6.14208	−0.212683
$835$	2.98006	0.103129
$836$	−2.19251	−0.0758294
$837$	1.27771	0.0441642
$838$	−2.99887	−0.103594
$839$	−42.3775	−1.46303	−0.731516	−	0.681824i	$-0.761187\pi$
$839$	−42.3775	−1.46303	−0.731516	+	0.681824i	$0.761187\pi$
$840$	−2.15197	−0.0742502
$841$	−5.69532	−0.196390
$842$	−14.7211	−0.507323
$843$	−25.6932	−0.884922
$844$	45.3378	1.56059
$845$	1.36810	0.0470641
$846$	15.9920	0.549818
$847$	1.00000	0.0343604
$848$	20.1531	0.692059
$849$	39.0073	1.33873
$850$	−4.72544	−0.162081
$851$	−11.5597	−0.396262
$852$	49.8721	1.70859
$853$	8.35755	0.286157	0.143079	−	0.989711i	$-0.454300\pi$
$853$	8.35755	0.286157	0.143079	+	0.989711i	$0.454300\pi$
$854$	1.73706	0.0594411
$855$	1.51592	0.0518435
$856$	−17.8315	−0.609467
$857$	−46.4027	−1.58508	−0.792542	−	0.609817i	$-0.791243\pi$
$857$	−46.4027	−1.58508	−0.792542	+	0.609817i	$0.791243\pi$
$858$	5.86113	0.200096
$859$	12.6595	0.431938	0.215969	−	0.976400i	$-0.430709\pi$
$859$	12.6595	0.431938	0.215969	+	0.976400i	$0.430709\pi$
$860$	−0.667976	−0.0227778
$861$	19.1425	0.652374
$862$	−12.9895	−0.442425
$863$	31.0496	1.05694	0.528470	−	0.848952i	$-0.322766\pi$
$863$	31.0496	1.05694	0.528470	+	0.848952i	$0.322766\pi$
$864$	−3.07436	−0.104592
$865$	3.03405	0.103161
$866$	−12.0880	−0.410766
$867$	−34.5296	−1.17269
$868$	3.78237	0.128382
$869$	−11.2707	−0.382333
$870$	2.85727	0.0968704
$871$	−12.7887	−0.433330
$872$	−26.3445	−0.892138
$873$	−4.38370	−0.148366
$874$	−2.11438	−0.0715201
$875$	−4.01523	−0.135740
$876$	−49.1086	−1.65923
$877$	43.6362	1.47349	0.736746	−	0.676170i	$-0.236362\pi$
$877$	43.6362	1.47349	0.736746	+	0.676170i	$0.236362\pi$
$878$	0.996723	0.0336378
$879$	62.2776	2.10057
$880$	0.795345	0.0268111
$881$	18.8242	0.634205	0.317102	−	0.948391i	$-0.397290\pi$
$881$	18.8242	0.634205	0.317102	+	0.948391i	$0.397290\pi$
$882$	1.67148	0.0562817
$883$	38.0731	1.28126	0.640632	−	0.767848i	$-0.278673\pi$
$883$	38.0731	1.28126	0.640632	+	0.767848i	$0.278673\pi$
$884$	−10.7173	−0.360461
$885$	−13.6724	−0.459593
$886$	5.79377	0.194645
$887$	36.7886	1.23524	0.617620	−	0.786477i	$-0.288097\pi$
$887$	36.7886	1.23524	0.617620	+	0.786477i	$0.288097\pi$
$888$	−23.3030	−0.781996
$889$	−3.97815	−0.133423
$890$	4.49097	0.150538
$891$	−9.63724	−0.322860
$892$	21.8599	0.731923
$893$	12.8232	0.429111
$894$	−26.8885	−0.899286
$895$	−6.90722	−0.230883
$896$	−11.4517	−0.382574
$897$	−25.3929	−0.847843
$898$	15.4883	0.516850
$899$	−11.1619	−0.372270
$900$	21.9008	0.730026
$901$	16.7637	0.558479
$902$	4.80887	0.160118
$903$	2.40207	0.0799359
$904$	−16.7109	−0.555796
$905$	6.66124	0.221427
$906$	14.5324	0.482806
$907$	53.0065	1.76005	0.880026	−	0.474925i	$-0.157525\pi$
$907$	53.0065	1.76005	0.880026	+	0.474925i	$0.157525\pi$
$908$	22.7042	0.753464
$909$	−39.8837	−1.32286
$910$	0.996342	0.0330284
$911$	−20.9647	−0.694592	−0.347296	−	0.937756i	$-0.612900\pi$
$911$	−20.9647	−0.694592	−0.347296	+	0.937756i	$0.612900\pi$
$912$	6.27078	0.207646
$913$	6.60453	0.218578
$914$	−6.72289	−0.222374
$915$	2.82348	0.0933413
$916$	−43.5265	−1.43816
$917$	−4.14751	−0.136963
$918$	−0.540279	−0.0178319
$919$	−9.40929	−0.310384	−0.155192	−	0.987884i	$-0.549600\pi$
$919$	−9.40929	−0.310384	−0.155192	+	0.987884i	$0.549600\pi$
$920$	2.34213	0.0772179
$921$	−34.5991	−1.14008
$922$	7.27398	0.239556
$923$	−51.3203	−1.68923
$924$	−3.92947	−0.129270
$925$	−21.3711	−0.702678
$926$	−6.37993	−0.209657
$927$	21.1312	0.694040
$928$	26.8572	0.881630
$929$	44.4757	1.45920	0.729601	−	0.683873i	$-0.239706\pi$
$929$	44.4757	1.45920	0.729601	+	0.683873i	$0.239706\pi$
$930$	−1.36850	−0.0448750
$931$	1.34027	0.0439257
$932$	0.663674	0.0217394
$933$	−43.5787	−1.42670
$934$	−5.30416	−0.173557
$935$	0.661583	0.0216361
$936$	−24.5739	−0.803224
$937$	−25.4802	−0.832401	−0.416201	−	0.909273i	$-0.636639\pi$
$937$	−25.4802	−0.832401	−0.416201	+	0.909273i	$0.636639\pi$
$938$	−1.90850	−0.0623149
$939$	−3.23398	−0.105537
$940$	−6.39092	−0.208449
$941$	−58.7888	−1.91646	−0.958230	−	0.285999i	$-0.907675\pi$
$941$	−58.7888	−1.91646	−0.958230	+	0.285999i	$0.907675\pi$
$942$	1.83993	0.0599480
$943$	−20.8340	−0.678449
$944$	−27.1512	−0.883696
$945$	−0.225647	−0.00734030
$946$	0.603435	0.0196194
$947$	−8.76518	−0.284830	−0.142415	−	0.989807i	$-0.545487\pi$
$947$	−8.76518	−0.284830	−0.142415	+	0.989807i	$0.545487\pi$
$948$	44.2879	1.43840
$949$	50.5346	1.64042
$950$	−3.90898	−0.126824
$951$	−16.2816	−0.527967
$952$	−3.55475	−0.115210
$953$	54.0869	1.75205	0.876024	−	0.482268i	$-0.160187\pi$
$953$	54.0869	1.75205	0.876024	+	0.482268i	$0.160187\pi$
$954$	17.2942	0.559919
$955$	0.887970	0.0287340
$956$	32.1750	1.04061
$957$	11.5960	0.374845
$958$	−18.9943	−0.613677
$959$	8.06494	0.260431
$960$	−0.528132	−0.0170454
$961$	−25.6540	−0.827547
$962$	10.7890	0.347852
$963$	22.5123	0.725449
$964$	−18.7060	−0.602478
$965$	−2.71550	−0.0874151
$966$	−3.78945	−0.121924
$967$	−60.0556	−1.93126	−0.965629	−	0.259923i	$-0.916303\pi$
$967$	−60.0556	−1.93126	−0.965629	+	0.259923i	$0.916303\pi$
$968$	−2.19401	−0.0705181
$969$	5.21615	0.167567
$970$	−0.389954	−0.0125207
$971$	−5.31992	−0.170724	−0.0853622	−	0.996350i	$-0.527205\pi$
$971$	−5.31992	−0.170724	−0.0853622	+	0.996350i	$0.527205\pi$
$972$	35.1572	1.12767
$973$	−4.23740	−0.135845
$974$	−20.0883	−0.643671
$975$	−46.9452	−1.50345
$976$	5.60697	0.179475
$977$	−3.16258	−0.101180	−0.0505899	−	0.998720i	$-0.516110\pi$
$977$	−3.16258	−0.101180	−0.0505899	+	0.998720i	$0.516110\pi$
$978$	−3.36177	−0.107498
$979$	18.2262	0.582513
$980$	−0.667976	−0.0213377
$981$	33.2601	1.06191
$982$	9.22885	0.294504
$983$	−8.91826	−0.284448	−0.142224	−	0.989834i	$-0.545425\pi$
$983$	−8.91826	−0.284448	−0.142224	+	0.989834i	$0.545425\pi$
$984$	−41.9988	−1.33887
$985$	−2.29017	−0.0729710
$986$	4.71979	0.150309
$987$	22.9820	0.731526
$988$	−8.86556	−0.282051
$989$	−2.61433	−0.0831309
$990$	0.682519	0.0216919
$991$	−32.6198	−1.03620	−0.518101	−	0.855319i	$-0.673361\pi$
$991$	−32.6198	−1.03620	−0.518101	+	0.855319i	$0.673361\pi$
$992$	−12.8634	−0.408413
$993$	−41.0511	−1.30272
$994$	−7.65868	−0.242919
$995$	5.08698	0.161268
$996$	−25.9523	−0.822330
$997$	−34.6052	−1.09596	−0.547979	−	0.836492i	$-0.684603\pi$
$997$	−34.6052	−1.09596	−0.547979	+	0.836492i	$0.684603\pi$
$998$	20.2706	0.641655
$999$	−2.44345	−0.0773073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.2.a.k.1.21	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.2.a.k.1.21	✓	38	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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3311.a (trivial)

\(f(q)\)	\(=\)	\(q+0.603435 q^{2} +2.40207 q^{3} -1.63587 q^{4} +0.408332 q^{5} +1.44949 q^{6} +1.00000 q^{7} -2.19401 q^{8} +2.76995 q^{9} +O(q^{10})\)	\(q+0.603435 q^{2} +2.40207 q^{3} -1.63587 q^{4} +0.408332 q^{5} +1.44949 q^{6} +1.00000 q^{7} -2.19401 q^{8} +2.76995 q^{9} +0.246401 q^{10} +1.00000 q^{11} -3.92947 q^{12} +4.04357 q^{13} +0.603435 q^{14} +0.980842 q^{15} +1.94779 q^{16} +1.62021 q^{17} +1.67148 q^{18} +1.34027 q^{19} -0.667976 q^{20} +2.40207 q^{21} +0.603435 q^{22} -2.61433 q^{23} -5.27016 q^{24} -4.83327 q^{25} +2.44003 q^{26} -0.552607 q^{27} -1.63587 q^{28} +4.82749 q^{29} +0.591874 q^{30} -2.31215 q^{31} +5.56338 q^{32} +2.40207 q^{33} +0.977691 q^{34} +0.408332 q^{35} -4.53126 q^{36} +4.42168 q^{37} +0.808767 q^{38} +9.71295 q^{39} -0.895883 q^{40} +7.96916 q^{41} +1.44949 q^{42} +1.00000 q^{43} -1.63587 q^{44} +1.13106 q^{45} -1.57758 q^{46} +9.56759 q^{47} +4.67874 q^{48} +1.00000 q^{49} -2.91656 q^{50} +3.89186 q^{51} -6.61474 q^{52} +10.3466 q^{53} -0.333462 q^{54} +0.408332 q^{55} -2.19401 q^{56} +3.21943 q^{57} +2.91308 q^{58} -13.9395 q^{59} -1.60453 q^{60} +2.87863 q^{61} -1.39523 q^{62} +2.76995 q^{63} -0.538448 q^{64} +1.65112 q^{65} +1.44949 q^{66} -3.16273 q^{67} -2.65045 q^{68} -6.27981 q^{69} +0.246401 q^{70} -12.6918 q^{71} -6.07728 q^{72} +12.4975 q^{73} +2.66819 q^{74} -11.6098 q^{75} -2.19251 q^{76} +1.00000 q^{77} +5.86113 q^{78} -11.2707 q^{79} +0.795345 q^{80} -9.63724 q^{81} +4.80887 q^{82} +6.60453 q^{83} -3.92947 q^{84} +0.661583 q^{85} +0.603435 q^{86} +11.5960 q^{87} -2.19401 q^{88} +18.2262 q^{89} +0.682519 q^{90} +4.04357 q^{91} +4.27670 q^{92} -5.55395 q^{93} +5.77341 q^{94} +0.547276 q^{95} +13.3636 q^{96} -1.58260 q^{97} +0.603435 q^{98} +2.76995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9}+O(q^{10}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9} + 2 q^{10} + 38 q^{11} + 2 q^{12} + 8 q^{13} + 6 q^{14} + 26 q^{15} + 70 q^{16} + 3 q^{17} + 27 q^{18} + 10 q^{19} + 9 q^{20} + 7 q^{21} + 6 q^{22} + 22 q^{23} - 16 q^{24} + 82 q^{25} + 5 q^{26} + 28 q^{27} + 50 q^{28} + 24 q^{29} + 4 q^{30} + 13 q^{31} + 42 q^{32} + 7 q^{33} + 10 q^{34} + 8 q^{35} + 74 q^{36} + 45 q^{37} - 14 q^{38} + 14 q^{39} - 27 q^{40} - 13 q^{41} + 38 q^{43} + 50 q^{44} - 2 q^{45} + 3 q^{46} - 4 q^{47} - 7 q^{48} + 38 q^{49} - 5 q^{50} + 16 q^{51} + 22 q^{52} + 14 q^{53} - 55 q^{54} + 8 q^{55} + 18 q^{56} + 18 q^{57} + 47 q^{58} + 35 q^{59} + 61 q^{60} + 30 q^{61} + 4 q^{62} + 61 q^{63} + 96 q^{64} + 17 q^{65} + 50 q^{67} - 67 q^{68} + 42 q^{69} + 2 q^{70} + 41 q^{71} + 26 q^{72} + 29 q^{73} - 23 q^{74} + 32 q^{75} + 35 q^{76} + 38 q^{77} - 8 q^{78} + 51 q^{79} + 9 q^{80} + 98 q^{81} - 2 q^{82} - 51 q^{83} + 2 q^{84} + 22 q^{85} + 6 q^{86} - 39 q^{87} + 18 q^{88} + 50 q^{89} - 95 q^{90} + 8 q^{91} + q^{92} + 56 q^{93} + 3 q^{94} + 17 q^{95} - 105 q^{96} + 8 q^{97} + 6 q^{98} + 61 q^{99}+O(q^{100}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9 + 2 * q^10 + 38 * q^11 + 2 * q^12 + 8 * q^13 + 6 * q^14 + 26 * q^15 + 70 * q^16 + 3 * q^17 + 27 * q^18 + 10 * q^19 + 9 * q^20 + 7 * q^21 + 6 * q^22 + 22 * q^23 - 16 * q^24 + 82 * q^25 + 5 * q^26 + 28 * q^27 + 50 * q^28 + 24 * q^29 + 4 * q^30 + 13 * q^31 + 42 * q^32 + 7 * q^33 + 10 * q^34 + 8 * q^35 + 74 * q^36 + 45 * q^37 - 14 * q^38 + 14 * q^39 - 27 * q^40 - 13 * q^41 + 38 * q^43 + 50 * q^44 - 2 * q^45 + 3 * q^46 - 4 * q^47 - 7 * q^48 + 38 * q^49 - 5 * q^50 + 16 * q^51 + 22 * q^52 + 14 * q^53 - 55 * q^54 + 8 * q^55 + 18 * q^56 + 18 * q^57 + 47 * q^58 + 35 * q^59 + 61 * q^60 + 30 * q^61 + 4 * q^62 + 61 * q^63 + 96 * q^64 + 17 * q^65 + 50 * q^67 - 67 * q^68 + 42 * q^69 + 2 * q^70 + 41 * q^71 + 26 * q^72 + 29 * q^73 - 23 * q^74 + 32 * q^75 + 35 * q^76 + 38 * q^77 - 8 * q^78 + 51 * q^79 + 9 * q^80 + 98 * q^81 - 2 * q^82 - 51 * q^83 + 2 * q^84 + 22 * q^85 + 6 * q^86 - 39 * q^87 + 18 * q^88 + 50 * q^89 - 95 * q^90 + 8 * q^91 + q^92 + 56 * q^93 + 3 * q^94 + 17 * q^95 - 105 * q^96 + 8 * q^97 + 6 * q^98 + 61 * q^99

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