LMFDB - Embedded newform 8026.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.00113 q^{3} +1.00000 q^{4} +2.08729 q^{5} -3.00113 q^{6} +1.33710 q^{7} +1.00000 q^{8} +6.00675 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.00113 q^{3} +1.00000 q^{4} +2.08729 q^{5} -3.00113 q^{6} +1.33710 q^{7} +1.00000 q^{8} +6.00675 q^{9} +2.08729 q^{10} +3.16858 q^{11} -3.00113 q^{12} -1.84415 q^{13} +1.33710 q^{14} -6.26421 q^{15} +1.00000 q^{16} -1.63329 q^{17} +6.00675 q^{18} -3.60617 q^{19} +2.08729 q^{20} -4.01281 q^{21} +3.16858 q^{22} +3.80005 q^{23} -3.00113 q^{24} -0.643236 q^{25} -1.84415 q^{26} -9.02364 q^{27} +1.33710 q^{28} +0.413145 q^{29} -6.26421 q^{30} -5.87702 q^{31} +1.00000 q^{32} -9.50931 q^{33} -1.63329 q^{34} +2.79091 q^{35} +6.00675 q^{36} +1.77461 q^{37} -3.60617 q^{38} +5.53452 q^{39} +2.08729 q^{40} -11.0005 q^{41} -4.01281 q^{42} -5.24811 q^{43} +3.16858 q^{44} +12.5378 q^{45} +3.80005 q^{46} -10.8485 q^{47} -3.00113 q^{48} -5.21216 q^{49} -0.643236 q^{50} +4.90170 q^{51} -1.84415 q^{52} -9.21034 q^{53} -9.02364 q^{54} +6.61374 q^{55} +1.33710 q^{56} +10.8226 q^{57} +0.413145 q^{58} +7.12833 q^{59} -6.26421 q^{60} -5.66067 q^{61} -5.87702 q^{62} +8.03164 q^{63} +1.00000 q^{64} -3.84927 q^{65} -9.50931 q^{66} -5.50242 q^{67} -1.63329 q^{68} -11.4044 q^{69} +2.79091 q^{70} +5.08460 q^{71} +6.00675 q^{72} -14.3286 q^{73} +1.77461 q^{74} +1.93043 q^{75} -3.60617 q^{76} +4.23672 q^{77} +5.53452 q^{78} +1.29969 q^{79} +2.08729 q^{80} +9.06083 q^{81} -11.0005 q^{82} -6.03854 q^{83} -4.01281 q^{84} -3.40914 q^{85} -5.24811 q^{86} -1.23990 q^{87} +3.16858 q^{88} +2.58386 q^{89} +12.5378 q^{90} -2.46581 q^{91} +3.80005 q^{92} +17.6377 q^{93} -10.8485 q^{94} -7.52710 q^{95} -3.00113 q^{96} +6.62642 q^{97} -5.21216 q^{98} +19.0329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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
$3$	−3.00113	−1.73270	−0.866350	−	0.499437i	$-0.833540\pi$
$3$	−3.00113	−1.73270	−0.866350	+	0.499437i	$0.833540\pi$
$4$	1.00000	0.500000
$5$	2.08729	0.933463	0.466731	−	0.884399i	$-0.345431\pi$
$5$	2.08729	0.933463	0.466731	+	0.884399i	$0.345431\pi$
$6$	−3.00113	−1.22520
$7$	1.33710	0.505377	0.252689	−	0.967548i	$-0.418685\pi$
$7$	1.33710	0.505377	0.252689	+	0.967548i	$0.418685\pi$
$8$	1.00000	0.353553
$9$	6.00675	2.00225
$10$	2.08729	0.660058
$11$	3.16858	0.955363	0.477682	−	0.878533i	$-0.341477\pi$
$11$	3.16858	0.955363	0.477682	+	0.878533i	$0.341477\pi$
$12$	−3.00113	−0.866350
$13$	−1.84415	−0.511475	−0.255737	−	0.966746i	$-0.582318\pi$
$13$	−1.84415	−0.511475	−0.255737	+	0.966746i	$0.582318\pi$
$14$	1.33710	0.357356
$15$	−6.26421	−1.61741
$16$	1.00000	0.250000
$17$	−1.63329	−0.396130	−0.198065	−	0.980189i	$-0.563466\pi$
$17$	−1.63329	−0.396130	−0.198065	+	0.980189i	$0.563466\pi$
$18$	6.00675	1.41581
$19$	−3.60617	−0.827312	−0.413656	−	0.910433i	$-0.635748\pi$
$19$	−3.60617	−0.827312	−0.413656	+	0.910433i	$0.635748\pi$
$20$	2.08729	0.466731
$21$	−4.01281	−0.875667
$22$	3.16858	0.675544
$23$	3.80005	0.792364	0.396182	−	0.918172i	$-0.370335\pi$
$23$	3.80005	0.792364	0.396182	+	0.918172i	$0.370335\pi$
$24$	−3.00113	−0.612602
$25$	−0.643236	−0.128647
$26$	−1.84415	−0.361667
$27$	−9.02364	−1.73660
$28$	1.33710	0.252689
$29$	0.413145	0.0767192	0.0383596	−	0.999264i	$-0.487787\pi$
$29$	0.413145	0.0767192	0.0383596	+	0.999264i	$0.487787\pi$
$30$	−6.26421	−1.14368
$31$	−5.87702	−1.05554	−0.527772	−	0.849386i	$-0.676973\pi$
$31$	−5.87702	−1.05554	−0.527772	+	0.849386i	$0.676973\pi$
$32$	1.00000	0.176777
$33$	−9.50931	−1.65536
$34$	−1.63329	−0.280107
$35$	2.79091	0.471751
$36$	6.00675	1.00113
$37$	1.77461	0.291745	0.145872	−	0.989303i	$-0.453401\pi$
$37$	1.77461	0.291745	0.145872	+	0.989303i	$0.453401\pi$
$38$	−3.60617	−0.584998
$39$	5.53452	0.886233
$40$	2.08729	0.330029
$41$	−11.0005	−1.71799	−0.858995	−	0.511985i	$-0.828910\pi$
$41$	−11.0005	−1.71799	−0.858995	+	0.511985i	$0.828910\pi$
$42$	−4.01281	−0.619190
$43$	−5.24811	−0.800329	−0.400165	−	0.916443i	$-0.631047\pi$
$43$	−5.24811	−0.800329	−0.400165	+	0.916443i	$0.631047\pi$
$44$	3.16858	0.477682
$45$	12.5378	1.86903
$46$	3.80005	0.560286
$47$	−10.8485	−1.58242	−0.791209	−	0.611546i	$-0.790548\pi$
$47$	−10.8485	−1.58242	−0.791209	+	0.611546i	$0.790548\pi$
$48$	−3.00113	−0.433175
$49$	−5.21216	−0.744594
$50$	−0.643236	−0.0909673
$51$	4.90170	0.686375
$52$	−1.84415	−0.255737
$53$	−9.21034	−1.26514	−0.632569	−	0.774504i	$-0.718000\pi$
$53$	−9.21034	−1.26514	−0.632569	+	0.774504i	$0.718000\pi$
$54$	−9.02364	−1.22796
$55$	6.61374	0.891796
$56$	1.33710	0.178678
$57$	10.8226	1.43348
$58$	0.413145	0.0542486
$59$	7.12833	0.928030	0.464015	−	0.885827i	$-0.346408\pi$
$59$	7.12833	0.928030	0.464015	+	0.885827i	$0.346408\pi$
$60$	−6.26421	−0.808706
$61$	−5.66067	−0.724775	−0.362387	−	0.932028i	$-0.618038\pi$
$61$	−5.66067	−0.724775	−0.362387	+	0.932028i	$0.618038\pi$
$62$	−5.87702	−0.746383
$63$	8.03164	1.01189
$64$	1.00000	0.125000
$65$	−3.84927	−0.477443
$66$	−9.50931	−1.17052
$67$	−5.50242	−0.672227	−0.336114	−	0.941821i	$-0.609113\pi$
$67$	−5.50242	−0.672227	−0.336114	+	0.941821i	$0.609113\pi$
$68$	−1.63329	−0.198065
$69$	−11.4044	−1.37293
$70$	2.79091	0.333578
$71$	5.08460	0.603431	0.301715	−	0.953398i	$-0.402441\pi$
$71$	5.08460	0.603431	0.301715	+	0.953398i	$0.402441\pi$
$72$	6.00675	0.707903
$73$	−14.3286	−1.67704	−0.838518	−	0.544874i	$-0.816578\pi$
$73$	−14.3286	−1.67704	−0.838518	+	0.544874i	$0.816578\pi$
$74$	1.77461	0.206295
$75$	1.93043	0.222907
$76$	−3.60617	−0.413656
$77$	4.23672	0.482819
$78$	5.53452	0.626661
$79$	1.29969	0.146227	0.0731133	−	0.997324i	$-0.476707\pi$
$79$	1.29969	0.146227	0.0731133	+	0.997324i	$0.476707\pi$
$80$	2.08729	0.233366
$81$	9.06083	1.00676
$82$	−11.0005	−1.21480
$83$	−6.03854	−0.662816	−0.331408	−	0.943488i	$-0.607524\pi$
$83$	−6.03854	−0.662816	−0.331408	+	0.943488i	$0.607524\pi$
$84$	−4.01281	−0.437834
$85$	−3.40914	−0.369773
$86$	−5.24811	−0.565918
$87$	−1.23990	−0.132931
$88$	3.16858	0.337772
$89$	2.58386	0.273888	0.136944	−	0.990579i	$-0.456272\pi$
$89$	2.58386	0.273888	0.136944	+	0.990579i	$0.456272\pi$
$90$	12.5378	1.32160
$91$	−2.46581	−0.258488
$92$	3.80005	0.396182
$93$	17.6377	1.82894
$94$	−10.8485	−1.11894
$95$	−7.52710	−0.772265
$96$	−3.00113	−0.306301
$97$	6.62642	0.672812	0.336406	−	0.941717i	$-0.390789\pi$
$97$	6.62642	0.672812	0.336406	+	0.941717i	$0.390789\pi$
$98$	−5.21216	−0.526507
$99$	19.0329	1.91288
$100$	−0.643236	−0.0643236
$101$	−3.55004	−0.353242	−0.176621	−	0.984279i	$-0.556517\pi$
$101$	−3.55004	−0.353242	−0.176621	+	0.984279i	$0.556517\pi$
$102$	4.90170	0.485341
$103$	−5.96472	−0.587721	−0.293861	−	0.955848i	$-0.594940\pi$
$103$	−5.96472	−0.587721	−0.293861	+	0.955848i	$0.594940\pi$
$104$	−1.84415	−0.180834
$105$	−8.37589	−0.817403
$106$	−9.21034	−0.894588
$107$	−3.96223	−0.383043	−0.191522	−	0.981488i	$-0.561342\pi$
$107$	−3.96223	−0.383043	−0.191522	+	0.981488i	$0.561342\pi$
$108$	−9.02364	−0.868301
$109$	−8.39501	−0.804096	−0.402048	−	0.915619i	$-0.631702\pi$
$109$	−8.39501	−0.804096	−0.402048	+	0.915619i	$0.631702\pi$
$110$	6.61374	0.630595
$111$	−5.32584	−0.505506
$112$	1.33710	0.126344
$113$	14.8955	1.40125	0.700627	−	0.713528i	$-0.252904\pi$
$113$	14.8955	1.40125	0.700627	+	0.713528i	$0.252904\pi$
$114$	10.8226	1.01363
$115$	7.93178	0.739643
$116$	0.413145	0.0383596
$117$	−11.0773	−1.02410
$118$	7.12833	0.656216
$119$	−2.18387	−0.200195
$120$	−6.26421	−0.571841
$121$	−0.960087	−0.0872806
$122$	−5.66067	−0.512493
$123$	33.0139	2.97676
$124$	−5.87702	−0.527772
$125$	−11.7790	−1.05355
$126$	8.03164	0.715516
$127$	7.98612	0.708654	0.354327	−	0.935122i	$-0.384710\pi$
$127$	7.98612	0.708654	0.354327	+	0.935122i	$0.384710\pi$
$128$	1.00000	0.0883883
$129$	15.7502	1.38673
$130$	−3.84927	−0.337603
$131$	5.92992	0.518100	0.259050	−	0.965864i	$-0.416591\pi$
$131$	5.92992	0.518100	0.259050	+	0.965864i	$0.416591\pi$
$132$	−9.50931	−0.827679
$133$	−4.82181	−0.418104
$134$	−5.50242	−0.475336
$135$	−18.8349	−1.62105
$136$	−1.63329	−0.140053
$137$	8.89562	0.760004	0.380002	−	0.924986i	$-0.375923\pi$
$137$	8.89562	0.760004	0.380002	+	0.924986i	$0.375923\pi$
$138$	−11.4044	−0.970808
$139$	−20.7908	−1.76345	−0.881726	−	0.471762i	$-0.843618\pi$
$139$	−20.7908	−1.76345	−0.881726	+	0.471762i	$0.843618\pi$
$140$	2.79091	0.235875
$141$	32.5577	2.74186
$142$	5.08460	0.426690
$143$	−5.84334	−0.488644
$144$	6.00675	0.500563
$145$	0.862353	0.0716145
$146$	−14.3286	−1.18584
$147$	15.6423	1.29016
$148$	1.77461	0.145872
$149$	−4.27724	−0.350405	−0.175202	−	0.984532i	$-0.556058\pi$
$149$	−4.27724	−0.350405	−0.175202	+	0.984532i	$0.556058\pi$
$150$	1.93043	0.157619
$151$	5.14371	0.418589	0.209295	−	0.977853i	$-0.432883\pi$
$151$	5.14371	0.418589	0.209295	+	0.977853i	$0.432883\pi$
$152$	−3.60617	−0.292499
$153$	−9.81076	−0.793153
$154$	4.23672	0.341404
$155$	−12.2670	−0.985311
$156$	5.53452	0.443116
$157$	23.6449	1.88707	0.943535	−	0.331272i	$-0.107478\pi$
$157$	23.6449	1.88707	0.943535	+	0.331272i	$0.107478\pi$
$158$	1.29969	0.103398
$159$	27.6414	2.19211
$160$	2.08729	0.165014
$161$	5.08105	0.400443
$162$	9.06083	0.711886
$163$	13.9994	1.09652	0.548258	−	0.836309i	$-0.315291\pi$
$163$	13.9994	1.09652	0.548258	+	0.836309i	$0.315291\pi$
$164$	−11.0005	−0.858995
$165$	−19.8487	−1.54522
$166$	−6.03854	−0.468682
$167$	11.1363	0.861754	0.430877	−	0.902411i	$-0.358204\pi$
$167$	11.1363	0.861754	0.430877	+	0.902411i	$0.358204\pi$
$168$	−4.01281	−0.309595
$169$	−9.59912	−0.738394
$170$	−3.40914	−0.261469
$171$	−21.6614	−1.65649
$172$	−5.24811	−0.400165
$173$	15.4097	1.17158	0.585789	−	0.810464i	$-0.300785\pi$
$173$	15.4097	1.17158	0.585789	+	0.810464i	$0.300785\pi$
$174$	−1.23990	−0.0939966
$175$	−0.860073	−0.0650154
$176$	3.16858	0.238841
$177$	−21.3930	−1.60800
$178$	2.58386	0.193668
$179$	7.49591	0.560271	0.280135	−	0.959961i	$-0.409621\pi$
$179$	7.49591	0.560271	0.280135	+	0.959961i	$0.409621\pi$
$180$	12.5378	0.934513
$181$	−6.77170	−0.503336	−0.251668	−	0.967814i	$-0.580979\pi$
$181$	−6.77170	−0.503336	−0.251668	+	0.967814i	$0.580979\pi$
$182$	−2.46581	−0.182778
$183$	16.9884	1.25582
$184$	3.80005	0.280143
$185$	3.70413	0.272333
$186$	17.6377	1.29326
$187$	−5.17521	−0.378449
$188$	−10.8485	−0.791209
$189$	−12.0655	−0.877638
$190$	−7.52710	−0.546074
$191$	9.31068	0.673697	0.336849	−	0.941559i	$-0.390639\pi$
$191$	9.31068	0.673697	0.336849	+	0.941559i	$0.390639\pi$
$192$	−3.00113	−0.216588
$193$	26.8202	1.93056	0.965280	−	0.261217i	$-0.0841237\pi$
$193$	26.8202	1.93056	0.965280	+	0.261217i	$0.0841237\pi$
$194$	6.62642	0.475750
$195$	11.5521	0.827265
$196$	−5.21216	−0.372297
$197$	−5.55262	−0.395608	−0.197804	−	0.980242i	$-0.563381\pi$
$197$	−5.55262	−0.395608	−0.197804	+	0.980242i	$0.563381\pi$
$198$	19.0329	1.35261
$199$	−2.96161	−0.209943	−0.104972	−	0.994475i	$-0.533475\pi$
$199$	−2.96161	−0.209943	−0.104972	+	0.994475i	$0.533475\pi$
$200$	−0.643236	−0.0454837
$201$	16.5134	1.16477
$202$	−3.55004	−0.249780
$203$	0.552418	0.0387721
$204$	4.90170	0.343188
$205$	−22.9612	−1.60368
$206$	−5.96472	−0.415582
$207$	22.8259	1.58651
$208$	−1.84415	−0.127869
$209$	−11.4264	−0.790383
$210$	−8.37589	−0.577991
$211$	−21.8064	−1.50122	−0.750608	−	0.660748i	$-0.770239\pi$
$211$	−21.8064	−1.50122	−0.750608	+	0.660748i	$0.770239\pi$
$212$	−9.21034	−0.632569
$213$	−15.2595	−1.04557
$214$	−3.96223	−0.270852
$215$	−10.9543	−0.747077
$216$	−9.02364	−0.613981
$217$	−7.85818	−0.533448
$218$	−8.39501	−0.568582
$219$	43.0019	2.90580
$220$	6.61374	0.445898
$221$	3.01202	0.202611
$222$	−5.32584	−0.357447
$223$	12.0859	0.809331	0.404666	−	0.914465i	$-0.367388\pi$
$223$	12.0859	0.809331	0.404666	+	0.914465i	$0.367388\pi$
$224$	1.33710	0.0893389
$225$	−3.86376	−0.257584
$226$	14.8955	0.990836
$227$	18.8844	1.25340	0.626701	−	0.779260i	$-0.284405\pi$
$227$	18.8844	1.25340	0.626701	+	0.779260i	$0.284405\pi$
$228$	10.8226	0.716742
$229$	−6.63267	−0.438299	−0.219150	−	0.975691i	$-0.570328\pi$
$229$	−6.63267	−0.438299	−0.219150	+	0.975691i	$0.570328\pi$
$230$	7.93178	0.523006
$231$	−12.7149	−0.836580
$232$	0.413145	0.0271243
$233$	−24.9792	−1.63644	−0.818220	−	0.574905i	$-0.805039\pi$
$233$	−24.9792	−1.63644	−0.818220	+	0.574905i	$0.805039\pi$
$234$	−11.0773	−0.724149
$235$	−22.6439	−1.47713
$236$	7.12833	0.464015
$237$	−3.90054	−0.253367
$238$	−2.18387	−0.141559
$239$	0.258223	0.0167030	0.00835152	−	0.999965i	$-0.497342\pi$
$239$	0.258223	0.0167030	0.00835152	+	0.999965i	$0.497342\pi$
$240$	−6.26421	−0.404353
$241$	−29.4015	−1.89392	−0.946960	−	0.321351i	$-0.895863\pi$
$241$	−29.4015	−1.89392	−0.946960	+	0.321351i	$0.895863\pi$
$242$	−0.960087	−0.0617167
$243$	−0.121747	−0.00781005
$244$	−5.66067	−0.362387
$245$	−10.8793	−0.695051
$246$	33.0139	2.10489
$247$	6.65031	0.423149
$248$	−5.87702	−0.373191
$249$	18.1224	1.14846
$250$	−11.7790	−0.744972
$251$	0.720691	0.0454896	0.0227448	−	0.999741i	$-0.492759\pi$
$251$	0.720691	0.0454896	0.0227448	+	0.999741i	$0.492759\pi$
$252$	8.03164	0.505946
$253$	12.0408	0.756996
$254$	7.98612	0.501094
$255$	10.2313	0.640706
$256$	1.00000	0.0625000
$257$	−7.31232	−0.456130	−0.228065	−	0.973646i	$-0.573240\pi$
$257$	−7.31232	−0.456130	−0.228065	+	0.973646i	$0.573240\pi$
$258$	15.7502	0.980567
$259$	2.37284	0.147441
$260$	−3.84927	−0.238721
$261$	2.48166	0.153611
$262$	5.92992	0.366352
$263$	11.8954	0.733504	0.366752	−	0.930319i	$-0.380470\pi$
$263$	11.8954	0.733504	0.366752	+	0.930319i	$0.380470\pi$
$264$	−9.50931	−0.585258
$265$	−19.2246	−1.18096
$266$	−4.82181	−0.295644
$267$	−7.75448	−0.474566
$268$	−5.50242	−0.336114
$269$	−13.0795	−0.797469	−0.398735	−	0.917066i	$-0.630551\pi$
$269$	−13.0795	−0.797469	−0.398735	+	0.917066i	$0.630551\pi$
$270$	−18.8349	−1.14626
$271$	−0.868616	−0.0527647	−0.0263823	−	0.999652i	$-0.508399\pi$
$271$	−0.868616	−0.0527647	−0.0263823	+	0.999652i	$0.508399\pi$
$272$	−1.63329	−0.0990326
$273$	7.40022	0.447882
$274$	8.89562	0.537404
$275$	−2.03815	−0.122905
$276$	−11.4044	−0.686465
$277$	−22.6843	−1.36297	−0.681484	−	0.731833i	$-0.738665\pi$
$277$	−22.6843	−1.36297	−0.681484	+	0.731833i	$0.738665\pi$
$278$	−20.7908	−1.24695
$279$	−35.3018	−2.11347
$280$	2.79091	0.166789
$281$	18.1213	1.08103	0.540513	−	0.841336i	$-0.318230\pi$
$281$	18.1213	1.08103	0.540513	+	0.841336i	$0.318230\pi$
$282$	32.5577	1.93878
$283$	12.5709	0.747264	0.373632	−	0.927577i	$-0.378112\pi$
$283$	12.5709	0.747264	0.373632	+	0.927577i	$0.378112\pi$
$284$	5.08460	0.301715
$285$	22.5898	1.33810
$286$	−5.84334	−0.345524
$287$	−14.7088	−0.868232
$288$	6.00675	0.353951
$289$	−14.3324	−0.843081
$290$	0.862353	0.0506391
$291$	−19.8867	−1.16578
$292$	−14.3286	−0.838518
$293$	−16.5601	−0.967449	−0.483725	−	0.875220i	$-0.660716\pi$
$293$	−16.5601	−0.967449	−0.483725	+	0.875220i	$0.660716\pi$
$294$	15.6423	0.912280
$295$	14.8789	0.866281
$296$	1.77461	0.103147
$297$	−28.5922	−1.65909
$298$	−4.27724	−0.247774
$299$	−7.00785	−0.405274
$300$	1.93043	0.111454
$301$	−7.01726	−0.404468
$302$	5.14371	0.295987
$303$	10.6541	0.612063
$304$	−3.60617	−0.206828
$305$	−11.8154	−0.676550
$306$	−9.81076	−0.560844
$307$	7.40053	0.422371	0.211185	−	0.977446i	$-0.432268\pi$
$307$	7.40053	0.422371	0.211185	+	0.977446i	$0.432268\pi$
$308$	4.23672	0.241409
$309$	17.9009	1.01834
$310$	−12.2670	−0.696720
$311$	−6.29254	−0.356817	−0.178409	−	0.983956i	$-0.557095\pi$
$311$	−6.29254	−0.356817	−0.178409	+	0.983956i	$0.557095\pi$
$312$	5.53452	0.313331
$313$	−9.22700	−0.521541	−0.260770	−	0.965401i	$-0.583977\pi$
$313$	−9.22700	−0.521541	−0.260770	+	0.965401i	$0.583977\pi$
$314$	23.6449	1.33436
$315$	16.7643	0.944563
$316$	1.29969	0.0731133
$317$	−7.40794	−0.416071	−0.208036	−	0.978121i	$-0.566707\pi$
$317$	−7.40794	−0.416071	−0.208036	+	0.978121i	$0.566707\pi$
$318$	27.6414	1.55005
$319$	1.30908	0.0732947
$320$	2.08729	0.116683
$321$	11.8911	0.663699
$322$	5.08105	0.283156
$323$	5.88991	0.327723
$324$	9.06083	0.503379
$325$	1.18622	0.0657998
$326$	13.9994	0.775354
$327$	25.1945	1.39326
$328$	−11.0005	−0.607401
$329$	−14.5056	−0.799718
$330$	−19.8487	−1.09263
$331$	−0.669893	−0.0368206	−0.0184103	−	0.999831i	$-0.505861\pi$
$331$	−0.669893	−0.0368206	−0.0184103	+	0.999831i	$0.505861\pi$
$332$	−6.03854	−0.331408
$333$	10.6597	0.584146
$334$	11.1363	0.609352
$335$	−11.4851	−0.627499
$336$	−4.01281	−0.218917
$337$	−27.4448	−1.49502	−0.747508	−	0.664253i	$-0.768750\pi$
$337$	−27.4448	−1.49502	−0.747508	+	0.664253i	$0.768750\pi$
$338$	−9.59912	−0.522123
$339$	−44.7033	−2.42795
$340$	−3.40914	−0.184887
$341$	−18.6218	−1.00843
$342$	−21.6614	−1.17131
$343$	−16.3289	−0.881678
$344$	−5.24811	−0.282959
$345$	−23.8043	−1.28158
$346$	15.4097	0.828430
$347$	12.4615	0.668968	0.334484	−	0.942401i	$-0.391438\pi$
$347$	12.4615	0.668968	0.334484	+	0.942401i	$0.391438\pi$
$348$	−1.23990	−0.0664657
$349$	0.999752	0.0535155	0.0267577	−	0.999642i	$-0.491482\pi$
$349$	0.999752	0.0535155	0.0267577	+	0.999642i	$0.491482\pi$
$350$	−0.860073	−0.0459728
$351$	16.6409	0.888228
$352$	3.16858	0.168886
$353$	32.5365	1.73174	0.865871	−	0.500268i	$-0.166765\pi$
$353$	32.5365	1.73174	0.865871	+	0.500268i	$0.166765\pi$
$354$	−21.3930	−1.13703
$355$	10.6130	0.563280
$356$	2.58386	0.136944
$357$	6.55407	0.346878
$358$	7.49591	0.396171
$359$	16.5610	0.874056	0.437028	−	0.899448i	$-0.356031\pi$
$359$	16.5610	0.874056	0.437028	+	0.899448i	$0.356031\pi$
$360$	12.5378	0.660801
$361$	−5.99555	−0.315555
$362$	−6.77170	−0.355912
$363$	2.88134	0.151231
$364$	−2.46581	−0.129244
$365$	−29.9079	−1.56545
$366$	16.9884	0.887997
$367$	3.88205	0.202641	0.101321	−	0.994854i	$-0.467693\pi$
$367$	3.88205	0.202641	0.101321	+	0.994854i	$0.467693\pi$
$368$	3.80005	0.198091
$369$	−66.0773	−3.43985
$370$	3.70413	0.192568
$371$	−12.3152	−0.639372
$372$	17.6377	0.914471
$373$	16.9330	0.876759	0.438379	−	0.898790i	$-0.355553\pi$
$373$	16.9330	0.876759	0.438379	+	0.898790i	$0.355553\pi$
$374$	−5.17521	−0.267604
$375$	35.3504	1.82549
$376$	−10.8485	−0.559469
$377$	−0.761901	−0.0392399
$378$	−12.0655	−0.620584
$379$	2.64876	0.136058	0.0680289	−	0.997683i	$-0.478329\pi$
$379$	2.64876	0.136058	0.0680289	+	0.997683i	$0.478329\pi$
$380$	−7.52710	−0.386132
$381$	−23.9673	−1.22788
$382$	9.31068	0.476376
$383$	15.3603	0.784877	0.392438	−	0.919778i	$-0.371632\pi$
$383$	15.3603	0.784877	0.392438	+	0.919778i	$0.371632\pi$
$384$	−3.00113	−0.153151
$385$	8.84324	0.450693
$386$	26.8202	1.36511
$387$	−31.5241	−1.60246
$388$	6.62642	0.336406
$389$	17.3415	0.879250	0.439625	−	0.898181i	$-0.355111\pi$
$389$	17.3415	0.879250	0.439625	+	0.898181i	$0.355111\pi$
$390$	11.5521	0.584965
$391$	−6.20657	−0.313880
$392$	−5.21216	−0.263254
$393$	−17.7964	−0.897711
$394$	−5.55262	−0.279737
$395$	2.71283	0.136497
$396$	19.0329	0.956439
$397$	−7.93761	−0.398377	−0.199189	−	0.979961i	$-0.563831\pi$
$397$	−7.93761	−0.398377	−0.199189	+	0.979961i	$0.563831\pi$
$398$	−2.96161	−0.148452
$399$	14.4709	0.724450
$400$	−0.643236	−0.0321618
$401$	−8.26152	−0.412561	−0.206280	−	0.978493i	$-0.566136\pi$
$401$	−8.26152	−0.412561	−0.206280	+	0.978493i	$0.566136\pi$
$402$	16.5134	0.823615
$403$	10.8381	0.539884
$404$	−3.55004	−0.176621
$405$	18.9125	0.939772
$406$	0.552418	0.0274160
$407$	5.62301	0.278722
$408$	4.90170	0.242670
$409$	−18.2640	−0.903097	−0.451548	−	0.892247i	$-0.649128\pi$
$409$	−18.2640	−0.903097	−0.451548	+	0.892247i	$0.649128\pi$
$410$	−22.9612	−1.13397
$411$	−26.6969	−1.31686
$412$	−5.96472	−0.293861
$413$	9.53131	0.469005
$414$	22.8259	1.12183
$415$	−12.6042	−0.618714
$416$	−1.84415	−0.0904168
$417$	62.3958	3.05553
$418$	−11.4264	−0.558885
$419$	11.4125	0.557535	0.278768	−	0.960359i	$-0.410074\pi$
$419$	11.4125	0.557535	0.278768	+	0.960359i	$0.410074\pi$
$420$	−8.37589	−0.408701
$421$	−31.9024	−1.55483	−0.777413	−	0.628991i	$-0.783468\pi$
$421$	−31.9024	−1.55483	−0.777413	+	0.628991i	$0.783468\pi$
$422$	−21.8064	−1.06152
$423$	−65.1643	−3.16840
$424$	−9.21034	−0.447294
$425$	1.05059	0.0509611
$426$	−15.2595	−0.739326
$427$	−7.56890	−0.366285
$428$	−3.96223	−0.191522
$429$	17.5366	0.846674
$430$	−10.9543	−0.528264
$431$	−10.1697	−0.489859	−0.244929	−	0.969541i	$-0.578765\pi$
$431$	−10.1697	−0.489859	−0.244929	+	0.969541i	$0.578765\pi$
$432$	−9.02364	−0.434150
$433$	−29.4817	−1.41680	−0.708399	−	0.705812i	$-0.750582\pi$
$433$	−29.4817	−1.41680	−0.708399	+	0.705812i	$0.750582\pi$
$434$	−7.85818	−0.377205
$435$	−2.58803	−0.124086
$436$	−8.39501	−0.402048
$437$	−13.7036	−0.655532
$438$	43.0019	2.05471
$439$	9.05927	0.432376	0.216188	−	0.976352i	$-0.430638\pi$
$439$	9.05927	0.432376	0.216188	+	0.976352i	$0.430638\pi$
$440$	6.61374	0.315298
$441$	−31.3081	−1.49086
$442$	3.01202	0.143267
$443$	−5.53493	−0.262973	−0.131486	−	0.991318i	$-0.541975\pi$
$443$	−5.53493	−0.262973	−0.131486	+	0.991318i	$0.541975\pi$
$444$	−5.32584	−0.252753
$445$	5.39325	0.255665
$446$	12.0859	0.572283
$447$	12.8365	0.607147
$448$	1.33710	0.0631721
$449$	33.2763	1.57041	0.785204	−	0.619238i	$-0.212558\pi$
$449$	33.2763	1.57041	0.785204	+	0.619238i	$0.212558\pi$
$450$	−3.86376	−0.182139
$451$	−34.8560	−1.64130
$452$	14.8955	0.700627
$453$	−15.4369	−0.725290
$454$	18.8844	0.886289
$455$	−5.14686	−0.241289
$456$	10.8226	0.506813
$457$	−22.0121	−1.02968	−0.514841	−	0.857286i	$-0.672149\pi$
$457$	−22.0121	−1.02968	−0.514841	+	0.857286i	$0.672149\pi$
$458$	−6.63267	−0.309924
$459$	14.7382	0.687921
$460$	7.93178	0.369821
$461$	28.7783	1.34034	0.670168	−	0.742209i	$-0.266222\pi$
$461$	28.7783	1.34034	0.670168	+	0.742209i	$0.266222\pi$
$462$	−12.7149	−0.591552
$463$	−20.6196	−0.958273	−0.479136	−	0.877740i	$-0.659050\pi$
$463$	−20.6196	−0.958273	−0.479136	+	0.877740i	$0.659050\pi$
$464$	0.413145	0.0191798
$465$	36.8149	1.70725
$466$	−24.9792	−1.15714
$467$	13.3626	0.618347	0.309174	−	0.951006i	$-0.399948\pi$
$467$	13.3626	0.618347	0.309174	+	0.951006i	$0.399948\pi$
$468$	−11.0773	−0.512050
$469$	−7.35729	−0.339728
$470$	−22.6439	−1.04449
$471$	−70.9614	−3.26973
$472$	7.12833	0.328108
$473$	−16.6291	−0.764605
$474$	−3.90054	−0.179158
$475$	2.31962	0.106431
$476$	−2.18387	−0.100098
$477$	−55.3243	−2.53312
$478$	0.258223	0.0118108
$479$	21.2647	0.971609	0.485805	−	0.874067i	$-0.338527\pi$
$479$	21.2647	0.971609	0.485805	+	0.874067i	$0.338527\pi$
$480$	−6.26421	−0.285921
$481$	−3.27265	−0.149220
$482$	−29.4015	−1.33920
$483$	−15.2489	−0.693848
$484$	−0.960087	−0.0436403
$485$	13.8312	0.628044
$486$	−0.121747	−0.00552254
$487$	35.9627	1.62963	0.814813	−	0.579723i	$-0.196839\pi$
$487$	35.9627	1.62963	0.814813	+	0.579723i	$0.196839\pi$
$488$	−5.66067	−0.256247
$489$	−42.0139	−1.89993
$490$	−10.8793	−0.491475
$491$	−11.2003	−0.505461	−0.252731	−	0.967537i	$-0.581329\pi$
$491$	−11.2003	−0.505461	−0.252731	+	0.967537i	$0.581329\pi$
$492$	33.0139	1.48838
$493$	−0.674785	−0.0303908
$494$	6.65031	0.299212
$495$	39.7271	1.78560
$496$	−5.87702	−0.263886
$497$	6.79863	0.304960
$498$	18.1224	0.812085
$499$	−15.4138	−0.690017	−0.345008	−	0.938600i	$-0.612124\pi$
$499$	−15.4138	−0.690017	−0.345008	+	0.938600i	$0.612124\pi$
$500$	−11.7790	−0.526775
$501$	−33.4215	−1.49316
$502$	0.720691	0.0321660
$503$	−10.4323	−0.465153	−0.232576	−	0.972578i	$-0.574716\pi$
$503$	−10.4323	−0.465153	−0.232576	+	0.972578i	$0.574716\pi$
$504$	8.03164	0.357758
$505$	−7.40995	−0.329739
$506$	12.0408	0.535277
$507$	28.8082	1.27942
$508$	7.98612	0.354327
$509$	26.2538	1.16368	0.581840	−	0.813303i	$-0.302333\pi$
$509$	26.2538	1.16368	0.581840	+	0.813303i	$0.302333\pi$
$510$	10.2313	0.453047
$511$	−19.1588	−0.847536
$512$	1.00000	0.0441942
$513$	32.5408	1.43671
$514$	−7.31232	−0.322533
$515$	−12.4501	−0.548616
$516$	15.7502	0.693365
$517$	−34.3744	−1.51178
$518$	2.37284	0.104257
$519$	−46.2464	−2.02999
$520$	−3.84927	−0.168801
$521$	−34.5538	−1.51383	−0.756914	−	0.653514i	$-0.773294\pi$
$521$	−34.5538	−1.51383	−0.756914	+	0.653514i	$0.773294\pi$
$522$	2.48166	0.108619
$523$	10.6774	0.466891	0.233446	−	0.972370i	$-0.425000\pi$
$523$	10.6774	0.466891	0.233446	+	0.972370i	$0.425000\pi$
$524$	5.92992	0.259050
$525$	2.58119	0.112652
$526$	11.8954	0.518666
$527$	9.59887	0.418133
$528$	−9.50931	−0.413840
$529$	−8.55965	−0.372159
$530$	−19.2246	−0.835064
$531$	42.8181	1.85815
$532$	−4.82181	−0.209052
$533$	20.2865	0.878708
$534$	−7.75448	−0.335569
$535$	−8.27030	−0.357556
$536$	−5.50242	−0.237668
$537$	−22.4962	−0.970781
$538$	−13.0795	−0.563896
$539$	−16.5152	−0.711358
$540$	−18.8349	−0.810526
$541$	37.9733	1.63260	0.816300	−	0.577628i	$-0.196021\pi$
$541$	37.9733	1.63260	0.816300	+	0.577628i	$0.196021\pi$
$542$	−0.868616	−0.0373103
$543$	20.3227	0.872131
$544$	−1.63329	−0.0700266
$545$	−17.5228	−0.750594
$546$	7.40022	0.316700
$547$	0.602101	0.0257440	0.0128720	−	0.999917i	$-0.495903\pi$
$547$	0.602101	0.0257440	0.0128720	+	0.999917i	$0.495903\pi$
$548$	8.89562	0.380002
$549$	−34.0023	−1.45118
$550$	−2.03815	−0.0869069
$551$	−1.48987	−0.0634707
$552$	−11.4044	−0.485404
$553$	1.73782	0.0738996
$554$	−22.6843	−0.963764
$555$	−11.1165	−0.471871
$556$	−20.7908	−0.881726
$557$	−4.29612	−0.182032	−0.0910161	−	0.995849i	$-0.529011\pi$
$557$	−4.29612	−0.182032	−0.0910161	+	0.995849i	$0.529011\pi$
$558$	−35.3018	−1.49445
$559$	9.67829	0.409348
$560$	2.79091	0.117938
$561$	15.5314	0.655738
$562$	18.1213	0.764400
$563$	−7.30892	−0.308034	−0.154017	−	0.988068i	$-0.549221\pi$
$563$	−7.30892	−0.308034	−0.154017	+	0.988068i	$0.549221\pi$
$564$	32.5577	1.37093
$565$	31.0912	1.30802
$566$	12.5709	0.528395
$567$	12.1153	0.508793
$568$	5.08460	0.213345
$569$	−4.95641	−0.207783	−0.103892	−	0.994589i	$-0.533130\pi$
$569$	−4.95641	−0.207783	−0.103892	+	0.994589i	$0.533130\pi$
$570$	22.5898	0.946182
$571$	10.5446	0.441277	0.220638	−	0.975356i	$-0.429186\pi$
$571$	10.5446	0.441277	0.220638	+	0.975356i	$0.429186\pi$
$572$	−5.84334	−0.244322
$573$	−27.9425	−1.16732
$574$	−14.7088	−0.613933
$575$	−2.44433	−0.101936
$576$	6.00675	0.250281
$577$	−36.5470	−1.52147	−0.760736	−	0.649061i	$-0.775162\pi$
$577$	−36.5470	−1.52147	−0.760736	+	0.649061i	$0.775162\pi$
$578$	−14.3324	−0.596148
$579$	−80.4908	−3.34508
$580$	0.862353	0.0358072
$581$	−8.07415	−0.334972
$582$	−19.8867	−0.824332
$583$	−29.1837	−1.20867
$584$	−14.3286	−0.592922
$585$	−23.1216	−0.955960
$586$	−16.5601	−0.684090
$587$	−43.9690	−1.81479	−0.907397	−	0.420275i	$-0.861934\pi$
$587$	−43.9690	−1.81479	−0.907397	+	0.420275i	$0.861934\pi$
$588$	15.6423	0.645079
$589$	21.1935	0.873264
$590$	14.8789	0.612553
$591$	16.6641	0.685470
$592$	1.77461	0.0729361
$593$	29.5047	1.21161	0.605806	−	0.795613i	$-0.292851\pi$
$593$	29.5047	1.21161	0.605806	+	0.795613i	$0.292851\pi$
$594$	−28.5922	−1.17315
$595$	−4.55837	−0.186875
$596$	−4.27724	−0.175202
$597$	8.88818	0.363769
$598$	−7.00785	−0.286572
$599$	−27.3311	−1.11672	−0.558359	−	0.829599i	$-0.688569\pi$
$599$	−27.3311	−1.11672	−0.558359	+	0.829599i	$0.688569\pi$
$600$	1.93043	0.0788096
$601$	0.190471	0.00776948	0.00388474	−	0.999992i	$-0.498763\pi$
$601$	0.190471	0.00776948	0.00388474	+	0.999992i	$0.498763\pi$
$602$	−7.01726	−0.286002
$603$	−33.0517	−1.34597
$604$	5.14371	0.209295
$605$	−2.00398	−0.0814732
$606$	10.6541	0.432794
$607$	−15.7796	−0.640473	−0.320236	−	0.947338i	$-0.603762\pi$
$607$	−15.7796	−0.640473	−0.320236	+	0.947338i	$0.603762\pi$
$608$	−3.60617	−0.146249
$609$	−1.65787	−0.0671805
$610$	−11.8154	−0.478393
$611$	20.0063	0.809367
$612$	−9.81076	−0.396576
$613$	24.6963	0.997473	0.498736	−	0.866754i	$-0.333798\pi$
$613$	24.6963	0.997473	0.498736	+	0.866754i	$0.333798\pi$
$614$	7.40053	0.298661
$615$	68.9094	2.77870
$616$	4.23672	0.170702
$617$	−13.2054	−0.531629	−0.265814	−	0.964024i	$-0.585641\pi$
$617$	−13.2054	−0.531629	−0.265814	+	0.964024i	$0.585641\pi$
$618$	17.9009	0.720079
$619$	30.0480	1.20773	0.603865	−	0.797086i	$-0.293627\pi$
$619$	30.0480	1.20773	0.603865	+	0.797086i	$0.293627\pi$
$620$	−12.2670	−0.492656
$621$	−34.2903	−1.37602
$622$	−6.29254	−0.252308
$623$	3.45488	0.138417
$624$	5.53452	0.221558
$625$	−21.3701	−0.854803
$626$	−9.22700	−0.368785
$627$	34.2922	1.36950
$628$	23.6449	0.943535
$629$	−2.89845	−0.115569
$630$	16.7643	0.667907
$631$	5.03355	0.200383	0.100191	−	0.994968i	$-0.468055\pi$
$631$	5.03355	0.200383	0.100191	+	0.994968i	$0.468055\pi$
$632$	1.29969	0.0516989
$633$	65.4438	2.60116
$634$	−7.40794	−0.294207
$635$	16.6693	0.661502
$636$	27.6414	1.09605
$637$	9.61199	0.380841
$638$	1.30908	0.0518272
$639$	30.5419	1.20822
$640$	2.08729	0.0825072
$641$	−30.5043	−1.20485	−0.602423	−	0.798177i	$-0.705798\pi$
$641$	−30.5043	−1.20485	−0.602423	+	0.798177i	$0.705798\pi$
$642$	11.8911	0.469306
$643$	−15.9261	−0.628065	−0.314033	−	0.949412i	$-0.601680\pi$
$643$	−15.9261	−0.628065	−0.314033	+	0.949412i	$0.601680\pi$
$644$	5.08105	0.200221
$645$	32.8752	1.29446
$646$	5.88991	0.231735
$647$	−43.0629	−1.69298	−0.846490	−	0.532405i	$-0.821288\pi$
$647$	−43.0629	−1.69298	−0.846490	+	0.532405i	$0.821288\pi$
$648$	9.06083	0.355943
$649$	22.5867	0.886606
$650$	1.18622	0.0465275
$651$	23.5834	0.924306
$652$	13.9994	0.548258
$653$	−3.19883	−0.125180	−0.0625899	−	0.998039i	$-0.519936\pi$
$653$	−3.19883	−0.125180	−0.0625899	+	0.998039i	$0.519936\pi$
$654$	25.1945	0.985182
$655$	12.3774	0.483627
$656$	−11.0005	−0.429497
$657$	−86.0684	−3.35785
$658$	−14.5056	−0.565486
$659$	15.1532	0.590284	0.295142	−	0.955453i	$-0.404633\pi$
$659$	15.1532	0.590284	0.295142	+	0.955453i	$0.404633\pi$
$660$	−19.8487	−0.772608
$661$	−25.2186	−0.980891	−0.490445	−	0.871472i	$-0.663166\pi$
$661$	−25.2186	−0.980891	−0.490445	+	0.871472i	$0.663166\pi$
$662$	−0.669893	−0.0260361
$663$	−9.03946	−0.351064
$664$	−6.03854	−0.234341
$665$	−10.0645	−0.390285
$666$	10.6597	0.413054
$667$	1.56997	0.0607895
$668$	11.1363	0.430877
$669$	−36.2713	−1.40233
$670$	−11.4851	−0.443709
$671$	−17.9363	−0.692423
$672$	−4.01281	−0.154798
$673$	−20.5719	−0.792987	−0.396493	−	0.918038i	$-0.629773\pi$
$673$	−20.5719	−0.792987	−0.396493	+	0.918038i	$0.629773\pi$
$674$	−27.4448	−1.05714
$675$	5.80433	0.223409
$676$	−9.59912	−0.369197
$677$	−44.9422	−1.72727	−0.863635	−	0.504117i	$-0.831818\pi$
$677$	−44.9422	−1.72727	−0.863635	+	0.504117i	$0.831818\pi$
$678$	−44.7033	−1.71682
$679$	8.86021	0.340024
$680$	−3.40914	−0.130735
$681$	−56.6744	−2.17177
$682$	−18.6218	−0.713067
$683$	6.81950	0.260941	0.130471	−	0.991452i	$-0.458351\pi$
$683$	6.81950	0.260941	0.130471	+	0.991452i	$0.458351\pi$
$684$	−21.6614	−0.828243
$685$	18.5677	0.709435
$686$	−16.3289	−0.623440
$687$	19.9055	0.759442
$688$	−5.24811	−0.200082
$689$	16.9852	0.647086
$690$	−23.8043	−0.906213
$691$	−27.9055	−1.06158	−0.530788	−	0.847505i	$-0.678104\pi$
$691$	−27.9055	−1.06158	−0.530788	+	0.847505i	$0.678104\pi$
$692$	15.4097	0.585789
$693$	25.4489	0.966725
$694$	12.4615	0.473032
$695$	−43.3963	−1.64612
$696$	−1.23990	−0.0469983
$697$	17.9670	0.680548
$698$	0.999752	0.0378412
$699$	74.9657	2.83546
$700$	−0.860073	−0.0325077
$701$	−4.04718	−0.152860	−0.0764300	−	0.997075i	$-0.524352\pi$
$701$	−4.04718	−0.152860	−0.0764300	+	0.997075i	$0.524352\pi$
$702$	16.6409	0.628072
$703$	−6.39955	−0.241364
$704$	3.16858	0.119420
$705$	67.9573	2.55942
$706$	32.5365	1.22453
$707$	−4.74677	−0.178521
$708$	−21.3930	−0.803999
$709$	−14.1153	−0.530110	−0.265055	−	0.964233i	$-0.585390\pi$
$709$	−14.1153	−0.530110	−0.265055	+	0.964233i	$0.585390\pi$
$710$	10.6130	0.398299
$711$	7.80693	0.292783
$712$	2.58386	0.0968341
$713$	−22.3330	−0.836376
$714$	6.55407	0.245280
$715$	−12.1967	−0.456131
$716$	7.49591	0.280135
$717$	−0.774959	−0.0289414
$718$	16.5610	0.618051
$719$	−31.3214	−1.16809	−0.584046	−	0.811721i	$-0.698531\pi$
$719$	−31.3214	−1.16809	−0.584046	+	0.811721i	$0.698531\pi$
$720$	12.5378	0.467257
$721$	−7.97544	−0.297021
$722$	−5.99555	−0.223131
$723$	88.2377	3.28160
$724$	−6.77170	−0.251668
$725$	−0.265750	−0.00986971
$726$	2.88134	0.106937
$727$	9.41861	0.349317	0.174658	−	0.984629i	$-0.444118\pi$
$727$	9.41861	0.349317	0.174658	+	0.984629i	$0.444118\pi$
$728$	−2.46581	−0.0913892
$729$	−26.8171	−0.993226
$730$	−29.9079	−1.10694
$731$	8.57167	0.317035
$732$	16.9884	0.627909
$733$	30.8714	1.14026	0.570131	−	0.821554i	$-0.306892\pi$
$733$	30.8714	1.14026	0.570131	+	0.821554i	$0.306892\pi$
$734$	3.88205	0.143289
$735$	32.6500	1.20431
$736$	3.80005	0.140072
$737$	−17.4349	−0.642221
$738$	−66.0773	−2.43234
$739$	34.7989	1.28010	0.640050	−	0.768333i	$-0.278914\pi$
$739$	34.7989	1.28010	0.640050	+	0.768333i	$0.278914\pi$
$740$	3.70413	0.136166
$741$	−19.9584	−0.733190
$742$	−12.3152	−0.452104
$743$	2.03662	0.0747162	0.0373581	−	0.999302i	$-0.488106\pi$
$743$	2.03662	0.0747162	0.0373581	+	0.999302i	$0.488106\pi$
$744$	17.6377	0.646629
$745$	−8.92782	−0.327090
$746$	16.9330	0.619962
$747$	−36.2720	−1.32712
$748$	−5.17521	−0.189224
$749$	−5.29790	−0.193581
$750$	35.3504	1.29081
$751$	−1.92978	−0.0704187	−0.0352093	−	0.999380i	$-0.511210\pi$
$751$	−1.92978	−0.0704187	−0.0352093	+	0.999380i	$0.511210\pi$
$752$	−10.8485	−0.395604
$753$	−2.16288	−0.0788199
$754$	−0.761901	−0.0277468
$755$	10.7364	0.390737
$756$	−12.0655	−0.438819
$757$	35.0344	1.27335	0.636673	−	0.771134i	$-0.280310\pi$
$757$	35.0344	1.27335	0.636673	+	0.771134i	$0.280310\pi$
$758$	2.64876	0.0962073
$759$	−36.1358	−1.31165
$760$	−7.52710	−0.273037
$761$	24.4534	0.886434	0.443217	−	0.896414i	$-0.353837\pi$
$761$	24.4534	0.886434	0.443217	+	0.896414i	$0.353837\pi$
$762$	−23.9673	−0.868245
$763$	−11.2250	−0.406372
$764$	9.31068	0.336849
$765$	−20.4779	−0.740378
$766$	15.3603	0.554992
$767$	−13.1457	−0.474664
$768$	−3.00113	−0.108294
$769$	29.6971	1.07090	0.535452	−	0.844566i	$-0.320141\pi$
$769$	29.6971	1.07090	0.535452	+	0.844566i	$0.320141\pi$
$770$	8.84324	0.318688
$771$	21.9452	0.790337
$772$	26.8202	0.965280
$773$	43.6701	1.57070	0.785351	−	0.619050i	$-0.212482\pi$
$773$	43.6701	1.57070	0.785351	+	0.619050i	$0.212482\pi$
$774$	−31.5241	−1.13311
$775$	3.78031	0.135793
$776$	6.62642	0.237875
$777$	−7.12119	−0.255471
$778$	17.3415	0.621724
$779$	39.6696	1.42131
$780$	11.5521	0.413633
$781$	16.1110	0.576496
$782$	−6.20657	−0.221946
$783$	−3.72808	−0.133231
$784$	−5.21216	−0.186148
$785$	49.3537	1.76151
$786$	−17.7964	−0.634778
$787$	44.9139	1.60101	0.800505	−	0.599327i	$-0.204565\pi$
$787$	44.9139	1.60101	0.800505	+	0.599327i	$0.204565\pi$
$788$	−5.55262	−0.197804
$789$	−35.6997	−1.27094
$790$	2.71283	0.0965181
$791$	19.9168	0.708161
$792$	19.0329	0.676304
$793$	10.4391	0.370704
$794$	−7.93761	−0.281695
$795$	57.6955	2.04625
$796$	−2.96161	−0.104972
$797$	8.75276	0.310039	0.155019	−	0.987911i	$-0.450456\pi$
$797$	8.75276	0.310039	0.155019	+	0.987911i	$0.450456\pi$
$798$	14.4709	0.512263
$799$	17.7187	0.626844
$800$	−0.643236	−0.0227418
$801$	15.5206	0.548393
$802$	−8.26152	−0.291724
$803$	−45.4014	−1.60218
$804$	16.5134	0.582384
$805$	10.6056	0.373799
$806$	10.8381	0.381756
$807$	39.2531	1.38178
$808$	−3.55004	−0.124890
$809$	50.7400	1.78392	0.891962	−	0.452111i	$-0.149329\pi$
$809$	50.7400	1.78392	0.891962	+	0.452111i	$0.149329\pi$
$810$	18.9125	0.664519
$811$	51.9880	1.82554	0.912772	−	0.408469i	$-0.133937\pi$
$811$	51.9880	1.82554	0.912772	+	0.408469i	$0.133937\pi$
$812$	0.552418	0.0193861
$813$	2.60683	0.0914254
$814$	5.62301	0.197086
$815$	29.2207	1.02356
$816$	4.90170	0.171594
$817$	18.9256	0.662122
$818$	−18.2640	−0.638586
$819$	−14.8115	−0.517557
$820$	−22.9612	−0.801839
$821$	−41.3773	−1.44408	−0.722038	−	0.691853i	$-0.756795\pi$
$821$	−41.3773	−1.44408	−0.722038	+	0.691853i	$0.756795\pi$
$822$	−26.6969	−0.931160
$823$	2.03680	0.0709985	0.0354992	−	0.999370i	$-0.488698\pi$
$823$	2.03680	0.0709985	0.0354992	+	0.999370i	$0.488698\pi$
$824$	−5.96472	−0.207791
$825$	6.11673	0.212957
$826$	9.53131	0.331637
$827$	41.4815	1.44245	0.721227	−	0.692699i	$-0.243579\pi$
$827$	41.4815	1.44245	0.721227	+	0.692699i	$0.243579\pi$
$828$	22.8259	0.793256
$829$	25.3777	0.881403	0.440702	−	0.897654i	$-0.354730\pi$
$829$	25.3777	0.881403	0.440702	+	0.897654i	$0.354730\pi$
$830$	−12.6042	−0.437497
$831$	68.0784	2.36161
$832$	−1.84415	−0.0639343
$833$	8.51295	0.294956
$834$	62.3958	2.16059
$835$	23.2447	0.804416
$836$	−11.4264	−0.395192
$837$	53.0322	1.83306
$838$	11.4125	0.394237
$839$	31.8217	1.09861	0.549303	−	0.835623i	$-0.314893\pi$
$839$	31.8217	1.09861	0.549303	+	0.835623i	$0.314893\pi$
$840$	−8.37589	−0.288996
$841$	−28.8293	−0.994114
$842$	−31.9024	−1.09943
$843$	−54.3842	−1.87309
$844$	−21.8064	−0.750608
$845$	−20.0361	−0.689263
$846$	−65.1643	−2.24040
$847$	−1.28373	−0.0441096
$848$	−9.21034	−0.316285
$849$	−37.7269	−1.29478
$850$	1.05059	0.0360349
$851$	6.74361	0.231168
$852$	−15.2595	−0.522783
$853$	10.5041	0.359652	0.179826	−	0.983698i	$-0.442447\pi$
$853$	10.5041	0.359652	0.179826	+	0.983698i	$0.442447\pi$
$854$	−7.56890	−0.259002
$855$	−45.2135	−1.54627
$856$	−3.96223	−0.135426
$857$	11.2361	0.383819	0.191909	−	0.981413i	$-0.438532\pi$
$857$	11.2361	0.383819	0.191909	+	0.981413i	$0.438532\pi$
$858$	17.5366	0.598689
$859$	−39.6188	−1.35178	−0.675889	−	0.737004i	$-0.736240\pi$
$859$	−39.6188	−1.35178	−0.675889	+	0.737004i	$0.736240\pi$
$860$	−10.9543	−0.373539
$861$	44.1429	1.50439
$862$	−10.1697	−0.346382
$863$	53.2847	1.81383	0.906916	−	0.421312i	$-0.138430\pi$
$863$	53.2847	1.81383	0.906916	+	0.421312i	$0.138430\pi$
$864$	−9.02364	−0.306991
$865$	32.1644	1.09362
$866$	−29.4817	−1.00183
$867$	43.0132	1.46081
$868$	−7.85818	−0.266724
$869$	4.11818	0.139700
$870$	−2.58803	−0.0877424
$871$	10.1473	0.343827
$872$	−8.39501	−0.284291
$873$	39.8033	1.34714
$874$	−13.7036	−0.463531
$875$	−15.7498	−0.532440
$876$	43.0019	1.45290
$877$	30.4711	1.02894	0.514468	−	0.857510i	$-0.327990\pi$
$877$	30.4711	1.02894	0.514468	+	0.857510i	$0.327990\pi$
$878$	9.05927	0.305736
$879$	49.6988	1.67630
$880$	6.61374	0.222949
$881$	−17.7469	−0.597909	−0.298955	−	0.954267i	$-0.596638\pi$
$881$	−17.7469	−0.597909	−0.298955	+	0.954267i	$0.596638\pi$
$882$	−31.3081	−1.05420
$883$	−2.01809	−0.0679143	−0.0339571	−	0.999423i	$-0.510811\pi$
$883$	−2.01809	−0.0679143	−0.0339571	+	0.999423i	$0.510811\pi$
$884$	3.01202	0.101305
$885$	−44.6533	−1.50101
$886$	−5.53493	−0.185950
$887$	21.2063	0.712037	0.356019	−	0.934479i	$-0.384134\pi$
$887$	21.2063	0.712037	0.356019	+	0.934479i	$0.384134\pi$
$888$	−5.32584	−0.178723
$889$	10.6783	0.358137
$890$	5.39325	0.180782
$891$	28.7100	0.961820
$892$	12.0859	0.404666
$893$	39.1215	1.30915
$894$	12.8365	0.429318
$895$	15.6461	0.522992
$896$	1.33710	0.0446694
$897$	21.0314	0.702219
$898$	33.2763	1.11045
$899$	−2.42806	−0.0809805
$900$	−3.86376	−0.128792
$901$	15.0431	0.501160
$902$	−34.8560	−1.16058
$903$	21.0597	0.700822
$904$	14.8955	0.495418
$905$	−14.1345	−0.469846
$906$	−15.4369	−0.512857
$907$	7.10653	0.235968	0.117984	−	0.993015i	$-0.462357\pi$
$907$	7.10653	0.235968	0.117984	+	0.993015i	$0.462357\pi$
$908$	18.8844	0.626701
$909$	−21.3242	−0.707280
$910$	−5.14686	−0.170617
$911$	−36.3459	−1.20419	−0.602097	−	0.798423i	$-0.705668\pi$
$911$	−36.3459	−1.20419	−0.602097	+	0.798423i	$0.705668\pi$
$912$	10.8226	0.358371
$913$	−19.1336	−0.633230
$914$	−22.0121	−0.728095
$915$	35.4596	1.17226
$916$	−6.63267	−0.219150
$917$	7.92891	0.261836
$918$	14.7382	0.486433
$919$	−25.9421	−0.855752	−0.427876	−	0.903837i	$-0.640738\pi$
$919$	−25.9421	−0.855752	−0.427876	+	0.903837i	$0.640738\pi$
$920$	7.93178	0.261503
$921$	−22.2099	−0.731842
$922$	28.7783	0.947761
$923$	−9.37676	−0.308640
$924$	−12.7149	−0.418290
$925$	−1.14150	−0.0375321
$926$	−20.6196	−0.677601
$927$	−35.8286	−1.17677
$928$	0.413145	0.0135622
$929$	8.08687	0.265322	0.132661	−	0.991161i	$-0.457648\pi$
$929$	8.08687	0.265322	0.132661	+	0.991161i	$0.457648\pi$
$930$	36.8149	1.20721
$931$	18.7959	0.616011
$932$	−24.9792	−0.818220
$933$	18.8847	0.618258
$934$	13.3626	0.437238
$935$	−10.8021	−0.353268
$936$	−11.0773	−0.362074
$937$	39.5557	1.29223	0.646114	−	0.763241i	$-0.276393\pi$
$937$	39.5557	1.29223	0.646114	+	0.763241i	$0.276393\pi$
$938$	−7.35729	−0.240224
$939$	27.6914	0.903674
$940$	−22.6439	−0.738564
$941$	37.6272	1.22661	0.613305	−	0.789846i	$-0.289839\pi$
$941$	37.6272	1.22661	0.613305	+	0.789846i	$0.289839\pi$
$942$	−70.9614	−2.31205
$943$	−41.8024	−1.36127
$944$	7.12833	0.232007
$945$	−25.1842	−0.819243
$946$	−16.6291	−0.540658
$947$	−38.1407	−1.23941	−0.619703	−	0.784836i	$-0.712747\pi$
$947$	−38.1407	−1.23941	−0.619703	+	0.784836i	$0.712747\pi$
$948$	−3.90054	−0.126684
$949$	26.4241	0.857762
$950$	2.31962	0.0752583
$951$	22.2322	0.720927
$952$	−2.18387	−0.0707797
$953$	−17.8739	−0.578993	−0.289497	−	0.957179i	$-0.593488\pi$
$953$	−17.8739	−0.578993	−0.289497	+	0.957179i	$0.593488\pi$
$954$	−55.3243	−1.79119
$955$	19.4341	0.628871
$956$	0.258223	0.00835152
$957$	−3.92873	−0.126998
$958$	21.2647	0.687031
$959$	11.8944	0.384089
$960$	−6.26421	−0.202176
$961$	3.53940	0.114174
$962$	−3.27265	−0.105514
$963$	−23.8001	−0.766948
$964$	−29.4015	−0.946960
$965$	55.9814	1.80211
$966$	−15.2489	−0.490624
$967$	−13.4392	−0.432175	−0.216087	−	0.976374i	$-0.569330\pi$
$967$	−13.4392	−0.432175	−0.216087	+	0.976374i	$0.569330\pi$
$968$	−0.960087	−0.0308584
$969$	−17.6764	−0.567846
$970$	13.8312	0.444095
$971$	19.5554	0.627564	0.313782	−	0.949495i	$-0.398404\pi$
$971$	19.5554	0.627564	0.313782	+	0.949495i	$0.398404\pi$
$972$	−0.121747	−0.00390502
$973$	−27.7994	−0.891208
$974$	35.9627	1.15232
$975$	−3.56000	−0.114011
$976$	−5.66067	−0.181194
$977$	−12.9560	−0.414501	−0.207250	−	0.978288i	$-0.566451\pi$
$977$	−12.9560	−0.414501	−0.207250	+	0.978288i	$0.566451\pi$
$978$	−42.0139	−1.34346
$979$	8.18716	0.261663
$980$	−10.8793	−0.347525
$981$	−50.4268	−1.61000
$982$	−11.2003	−0.357415
$983$	−41.1898	−1.31375	−0.656875	−	0.754000i	$-0.728122\pi$
$983$	−41.1898	−1.31375	−0.656875	+	0.754000i	$0.728122\pi$
$984$	33.0139	1.05244
$985$	−11.5899	−0.369285
$986$	−0.674785	−0.0214895
$987$	43.5330	1.38567
$988$	6.65031	0.211574
$989$	−19.9431	−0.634152
$990$	39.7271	1.26261
$991$	−13.8071	−0.438597	−0.219298	−	0.975658i	$-0.570377\pi$
$991$	−13.8071	−0.438597	−0.219298	+	0.975658i	$0.570377\pi$
$992$	−5.87702	−0.186596
$993$	2.01043	0.0637991
$994$	6.79863	0.215639
$995$	−6.18174	−0.195974
$996$	18.1224	0.574231
$997$	−55.7105	−1.76437	−0.882184	−	0.470904i	$-0.843928\pi$
$997$	−55.7105	−1.76437	−0.882184	+	0.470904i	$0.843928\pi$
$998$	−15.4138	−0.487915
$999$	−16.0135	−0.506644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.4	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.4	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.00113 q^{3} +1.00000 q^{4} +2.08729 q^{5} -3.00113 q^{6} +1.33710 q^{7} +1.00000 q^{8} +6.00675 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.00113 q^{3} +1.00000 q^{4} +2.08729 q^{5} -3.00113 q^{6} +1.33710 q^{7} +1.00000 q^{8} +6.00675 q^{9} +2.08729 q^{10} +3.16858 q^{11} -3.00113 q^{12} -1.84415 q^{13} +1.33710 q^{14} -6.26421 q^{15} +1.00000 q^{16} -1.63329 q^{17} +6.00675 q^{18} -3.60617 q^{19} +2.08729 q^{20} -4.01281 q^{21} +3.16858 q^{22} +3.80005 q^{23} -3.00113 q^{24} -0.643236 q^{25} -1.84415 q^{26} -9.02364 q^{27} +1.33710 q^{28} +0.413145 q^{29} -6.26421 q^{30} -5.87702 q^{31} +1.00000 q^{32} -9.50931 q^{33} -1.63329 q^{34} +2.79091 q^{35} +6.00675 q^{36} +1.77461 q^{37} -3.60617 q^{38} +5.53452 q^{39} +2.08729 q^{40} -11.0005 q^{41} -4.01281 q^{42} -5.24811 q^{43} +3.16858 q^{44} +12.5378 q^{45} +3.80005 q^{46} -10.8485 q^{47} -3.00113 q^{48} -5.21216 q^{49} -0.643236 q^{50} +4.90170 q^{51} -1.84415 q^{52} -9.21034 q^{53} -9.02364 q^{54} +6.61374 q^{55} +1.33710 q^{56} +10.8226 q^{57} +0.413145 q^{58} +7.12833 q^{59} -6.26421 q^{60} -5.66067 q^{61} -5.87702 q^{62} +8.03164 q^{63} +1.00000 q^{64} -3.84927 q^{65} -9.50931 q^{66} -5.50242 q^{67} -1.63329 q^{68} -11.4044 q^{69} +2.79091 q^{70} +5.08460 q^{71} +6.00675 q^{72} -14.3286 q^{73} +1.77461 q^{74} +1.93043 q^{75} -3.60617 q^{76} +4.23672 q^{77} +5.53452 q^{78} +1.29969 q^{79} +2.08729 q^{80} +9.06083 q^{81} -11.0005 q^{82} -6.03854 q^{83} -4.01281 q^{84} -3.40914 q^{85} -5.24811 q^{86} -1.23990 q^{87} +3.16858 q^{88} +2.58386 q^{89} +12.5378 q^{90} -2.46581 q^{91} +3.80005 q^{92} +17.6377 q^{93} -10.8485 q^{94} -7.52710 q^{95} -3.00113 q^{96} +6.62642 q^{97} -5.21216 q^{98} +19.0329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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