LMFDB - Embedded newform 4010.2.a.m.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 $ x^20 - 4x^19 - 35x^18 + 154x^17 + 460x^16 - 2392x^15 - 2591x^14 + 19157x^13 + 2776x^12 - 83577x^11 + 34362x^10 + 190617x^9 - 150697x^8 - 189098x^7 + 211360x^6 + 37365x^5 - 68876x^4 - 8984x^3 + 7920x^2 + 1972*x + 104
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.02602$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.02602 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.02602 q^{6} -3.81201 q^{7} -1.00000 q^{8} -1.94728 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.02602 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.02602 q^{6} -3.81201 q^{7} -1.00000 q^{8} -1.94728 q^{9} -1.00000 q^{10} -2.83918 q^{11} +1.02602 q^{12} -0.0600620 q^{13} +3.81201 q^{14} +1.02602 q^{15} +1.00000 q^{16} -5.05914 q^{17} +1.94728 q^{18} -4.22523 q^{19} +1.00000 q^{20} -3.91121 q^{21} +2.83918 q^{22} +8.19324 q^{23} -1.02602 q^{24} +1.00000 q^{25} +0.0600620 q^{26} -5.07602 q^{27} -3.81201 q^{28} -4.58061 q^{29} -1.02602 q^{30} +9.54004 q^{31} -1.00000 q^{32} -2.91306 q^{33} +5.05914 q^{34} -3.81201 q^{35} -1.94728 q^{36} +7.17604 q^{37} +4.22523 q^{38} -0.0616249 q^{39} -1.00000 q^{40} -2.87566 q^{41} +3.91121 q^{42} +0.707096 q^{43} -2.83918 q^{44} -1.94728 q^{45} -8.19324 q^{46} -0.230248 q^{47} +1.02602 q^{48} +7.53145 q^{49} -1.00000 q^{50} -5.19079 q^{51} -0.0600620 q^{52} +2.37088 q^{53} +5.07602 q^{54} -2.83918 q^{55} +3.81201 q^{56} -4.33518 q^{57} +4.58061 q^{58} +8.52669 q^{59} +1.02602 q^{60} +6.74990 q^{61} -9.54004 q^{62} +7.42306 q^{63} +1.00000 q^{64} -0.0600620 q^{65} +2.91306 q^{66} -11.8218 q^{67} -5.05914 q^{68} +8.40644 q^{69} +3.81201 q^{70} +10.1208 q^{71} +1.94728 q^{72} +3.63271 q^{73} -7.17604 q^{74} +1.02602 q^{75} -4.22523 q^{76} +10.8230 q^{77} +0.0616249 q^{78} -4.99070 q^{79} +1.00000 q^{80} +0.633735 q^{81} +2.87566 q^{82} +7.41435 q^{83} -3.91121 q^{84} -5.05914 q^{85} -0.707096 q^{86} -4.69981 q^{87} +2.83918 q^{88} -3.81665 q^{89} +1.94728 q^{90} +0.228957 q^{91} +8.19324 q^{92} +9.78829 q^{93} +0.230248 q^{94} -4.22523 q^{95} -1.02602 q^{96} +15.1842 q^{97} -7.53145 q^{98} +5.52868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * 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
$3$	1.02602	0.592374	0.296187	−	0.955130i	$-0.404285\pi$
$3$	1.02602	0.592374	0.296187	+	0.955130i	$0.404285\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.02602	−0.418872
$7$	−3.81201	−1.44081	−0.720403	−	0.693556i	$-0.756043\pi$
$7$	−3.81201	−1.44081	−0.720403	+	0.693556i	$0.756043\pi$
$8$	−1.00000	−0.353553
$9$	−1.94728	−0.649093
$10$	−1.00000	−0.316228
$11$	−2.83918	−0.856046	−0.428023	−	0.903768i	$-0.640790\pi$
$11$	−2.83918	−0.856046	−0.428023	+	0.903768i	$0.640790\pi$
$12$	1.02602	0.296187
$13$	−0.0600620	−0.0166582	−0.00832909	−	0.999965i	$-0.502651\pi$
$13$	−0.0600620	−0.0166582	−0.00832909	+	0.999965i	$0.502651\pi$
$14$	3.81201	1.01880
$15$	1.02602	0.264918
$16$	1.00000	0.250000
$17$	−5.05914	−1.22702	−0.613511	−	0.789686i	$-0.710244\pi$
$17$	−5.05914	−1.22702	−0.613511	+	0.789686i	$0.710244\pi$
$18$	1.94728	0.458978
$19$	−4.22523	−0.969334	−0.484667	−	0.874699i	$-0.661059\pi$
$19$	−4.22523	−0.969334	−0.484667	+	0.874699i	$0.661059\pi$
$20$	1.00000	0.223607
$21$	−3.91121	−0.853496
$22$	2.83918	0.605316
$23$	8.19324	1.70841	0.854204	−	0.519938i	$-0.174045\pi$
$23$	8.19324	1.70841	0.854204	+	0.519938i	$0.174045\pi$
$24$	−1.02602	−0.209436
$25$	1.00000	0.200000
$26$	0.0600620	0.0117791
$27$	−5.07602	−0.976880
$28$	−3.81201	−0.720403
$29$	−4.58061	−0.850599	−0.425299	−	0.905053i	$-0.639831\pi$
$29$	−4.58061	−0.850599	−0.425299	+	0.905053i	$0.639831\pi$
$30$	−1.02602	−0.187325
$31$	9.54004	1.71344	0.856721	−	0.515780i	$-0.172498\pi$
$31$	9.54004	1.71344	0.856721	+	0.515780i	$0.172498\pi$
$32$	−1.00000	−0.176777
$33$	−2.91306	−0.507099
$34$	5.05914	0.867636
$35$	−3.81201	−0.644348
$36$	−1.94728	−0.324547
$37$	7.17604	1.17973	0.589867	−	0.807501i	$-0.299180\pi$
$37$	7.17604	1.17973	0.589867	+	0.807501i	$0.299180\pi$
$38$	4.22523	0.685422
$39$	−0.0616249	−0.00986788
$40$	−1.00000	−0.158114
$41$	−2.87566	−0.449102	−0.224551	−	0.974462i	$-0.572092\pi$
$41$	−2.87566	−0.449102	−0.224551	+	0.974462i	$0.572092\pi$
$42$	3.91121	0.603513
$43$	0.707096	0.107831	0.0539156	−	0.998545i	$-0.482830\pi$
$43$	0.707096	0.107831	0.0539156	+	0.998545i	$0.482830\pi$
$44$	−2.83918	−0.428023
$45$	−1.94728	−0.290283
$46$	−8.19324	−1.20803
$47$	−0.230248	−0.0335851	−0.0167925	−	0.999859i	$-0.505345\pi$
$47$	−0.230248	−0.0335851	−0.0167925	+	0.999859i	$0.505345\pi$
$48$	1.02602	0.148093
$49$	7.53145	1.07592
$50$	−1.00000	−0.141421
$51$	−5.19079	−0.726856
$52$	−0.0600620	−0.00832909
$53$	2.37088	0.325666	0.162833	−	0.986654i	$-0.447937\pi$
$53$	2.37088	0.325666	0.162833	+	0.986654i	$0.447937\pi$
$54$	5.07602	0.690758
$55$	−2.83918	−0.382835
$56$	3.81201	0.509402
$57$	−4.33518	−0.574208
$58$	4.58061	0.601464
$59$	8.52669	1.11008	0.555040	−	0.831824i	$-0.312703\pi$
$59$	8.52669	1.11008	0.555040	+	0.831824i	$0.312703\pi$
$60$	1.02602	0.132459
$61$	6.74990	0.864236	0.432118	−	0.901817i	$-0.357766\pi$
$61$	6.74990	0.864236	0.432118	+	0.901817i	$0.357766\pi$
$62$	−9.54004	−1.21159
$63$	7.42306	0.935217
$64$	1.00000	0.125000
$65$	−0.0600620	−0.00744977
$66$	2.91306	0.358573
$67$	−11.8218	−1.44427	−0.722134	−	0.691753i	$-0.756839\pi$
$67$	−11.8218	−1.44427	−0.722134	+	0.691753i	$0.756839\pi$
$68$	−5.05914	−0.613511
$69$	8.40644	1.01202
$70$	3.81201	0.455623
$71$	10.1208	1.20112	0.600560	−	0.799580i	$-0.294945\pi$
$71$	10.1208	1.20112	0.600560	+	0.799580i	$0.294945\pi$
$72$	1.94728	0.229489
$73$	3.63271	0.425177	0.212588	−	0.977142i	$-0.431811\pi$
$73$	3.63271	0.425177	0.212588	+	0.977142i	$0.431811\pi$
$74$	−7.17604	−0.834197
$75$	1.02602	0.118475
$76$	−4.22523	−0.484667
$77$	10.8230	1.23340
$78$	0.0616249	0.00697764
$79$	−4.99070	−0.561498	−0.280749	−	0.959781i	$-0.590583\pi$
$79$	−4.99070	−0.561498	−0.280749	+	0.959781i	$0.590583\pi$
$80$	1.00000	0.111803
$81$	0.633735	0.0704149
$82$	2.87566	0.317563
$83$	7.41435	0.813830	0.406915	−	0.913466i	$-0.366604\pi$
$83$	7.41435	0.813830	0.406915	+	0.913466i	$0.366604\pi$
$84$	−3.91121	−0.426748
$85$	−5.05914	−0.548741
$86$	−0.707096	−0.0762482
$87$	−4.69981	−0.503872
$88$	2.83918	0.302658
$89$	−3.81665	−0.404564	−0.202282	−	0.979327i	$-0.564836\pi$
$89$	−3.81665	−0.404564	−0.202282	+	0.979327i	$0.564836\pi$
$90$	1.94728	0.205261
$91$	0.228957	0.0240012
$92$	8.19324	0.854204
$93$	9.78829	1.01500
$94$	0.230248	0.0237482
$95$	−4.22523	−0.433499
$96$	−1.02602	−0.104718
$97$	15.1842	1.54172	0.770862	−	0.637003i	$-0.219826\pi$
$97$	15.1842	1.54172	0.770862	+	0.637003i	$0.219826\pi$
$98$	−7.53145	−0.760791
$99$	5.52868	0.555653
$100$	1.00000	0.100000
$101$	13.8094	1.37409	0.687044	−	0.726616i	$-0.258908\pi$
$101$	13.8094	1.37409	0.687044	+	0.726616i	$0.258908\pi$
$102$	5.19079	0.513965
$103$	1.91094	0.188290	0.0941452	−	0.995558i	$-0.469988\pi$
$103$	1.91094	0.188290	0.0941452	+	0.995558i	$0.469988\pi$
$104$	0.0600620	0.00588956
$105$	−3.91121	−0.381695
$106$	−2.37088	−0.230281
$107$	−12.7904	−1.23650	−0.618249	−	0.785982i	$-0.712158\pi$
$107$	−12.7904	−1.23650	−0.618249	+	0.785982i	$0.712158\pi$
$108$	−5.07602	−0.488440
$109$	13.5187	1.29485	0.647427	−	0.762128i	$-0.275845\pi$
$109$	13.5187	1.29485	0.647427	+	0.762128i	$0.275845\pi$
$110$	2.83918	0.270705
$111$	7.36277	0.698843
$112$	−3.81201	−0.360201
$113$	7.59117	0.714118	0.357059	−	0.934082i	$-0.383780\pi$
$113$	7.59117	0.714118	0.357059	+	0.934082i	$0.383780\pi$
$114$	4.33518	0.406026
$115$	8.19324	0.764023
$116$	−4.58061	−0.425299
$117$	0.116957	0.0108127
$118$	−8.52669	−0.784945
$119$	19.2855	1.76790
$120$	−1.02602	−0.0936625
$121$	−2.93905	−0.267186
$122$	−6.74990	−0.611107
$123$	−2.95049	−0.266036
$124$	9.54004	0.856721
$125$	1.00000	0.0894427
$126$	−7.42306	−0.661298
$127$	−7.71307	−0.684424	−0.342212	−	0.939623i	$-0.611176\pi$
$127$	−7.71307	−0.684424	−0.342212	+	0.939623i	$0.611176\pi$
$128$	−1.00000	−0.0883883
$129$	0.725496	0.0638764
$130$	0.0600620	0.00526778
$131$	14.9284	1.30430	0.652148	−	0.758092i	$-0.273868\pi$
$131$	14.9284	1.30430	0.652148	+	0.758092i	$0.273868\pi$
$132$	−2.91306	−0.253550
$133$	16.1066	1.39662
$134$	11.8218	1.02125
$135$	−5.07602	−0.436874
$136$	5.05914	0.433818
$137$	−15.8192	−1.35152	−0.675762	−	0.737120i	$-0.736185\pi$
$137$	−15.8192	−1.35152	−0.675762	+	0.737120i	$0.736185\pi$
$138$	−8.40644	−0.715604
$139$	−5.17609	−0.439030	−0.219515	−	0.975609i	$-0.570448\pi$
$139$	−5.17609	−0.439030	−0.219515	+	0.975609i	$0.570448\pi$
$140$	−3.81201	−0.322174
$141$	−0.236239	−0.0198949
$142$	−10.1208	−0.849319
$143$	0.170527	0.0142602
$144$	−1.94728	−0.162273
$145$	−4.58061	−0.380399
$146$	−3.63271	−0.300645
$147$	7.72743	0.637348
$148$	7.17604	0.589867
$149$	6.58195	0.539214	0.269607	−	0.962970i	$-0.413106\pi$
$149$	6.58195	0.539214	0.269607	+	0.962970i	$0.413106\pi$
$150$	−1.02602	−0.0837743
$151$	19.1521	1.55857	0.779287	−	0.626667i	$-0.215581\pi$
$151$	19.1521	1.55857	0.779287	+	0.626667i	$0.215581\pi$
$152$	4.22523	0.342711
$153$	9.85157	0.796452
$154$	−10.8230	−0.872142
$155$	9.54004	0.766275
$156$	−0.0616249	−0.00493394
$157$	1.25197	0.0999181	0.0499590	−	0.998751i	$-0.484091\pi$
$157$	1.25197	0.0999181	0.0499590	+	0.998751i	$0.484091\pi$
$158$	4.99070	0.397039
$159$	2.43258	0.192916
$160$	−1.00000	−0.0790569
$161$	−31.2327	−2.46148
$162$	−0.633735	−0.0497909
$163$	1.40366	0.109943	0.0549715	−	0.998488i	$-0.482493\pi$
$163$	1.40366	0.109943	0.0549715	+	0.998488i	$0.482493\pi$
$164$	−2.87566	−0.224551
$165$	−2.91306	−0.226782
$166$	−7.41435	−0.575465
$167$	8.87085	0.686447	0.343224	−	0.939254i	$-0.388481\pi$
$167$	8.87085	0.686447	0.343224	+	0.939254i	$0.388481\pi$
$168$	3.91121	0.301756
$169$	−12.9964	−0.999723
$170$	5.05914	0.388019
$171$	8.22770	0.629188
$172$	0.707096	0.0539156
$173$	−10.2824	−0.781756	−0.390878	−	0.920442i	$-0.627829\pi$
$173$	−10.2824	−0.781756	−0.390878	+	0.920442i	$0.627829\pi$
$174$	4.69981	0.356292
$175$	−3.81201	−0.288161
$176$	−2.83918	−0.214011
$177$	8.74857	0.657583
$178$	3.81665	0.286070
$179$	3.08332	0.230458	0.115229	−	0.993339i	$-0.463240\pi$
$179$	3.08332	0.230458	0.115229	+	0.993339i	$0.463240\pi$
$180$	−1.94728	−0.145142
$181$	10.7889	0.801929	0.400965	−	0.916094i	$-0.368675\pi$
$181$	10.7889	0.801929	0.400965	+	0.916094i	$0.368675\pi$
$182$	−0.228957	−0.0169714
$183$	6.92555	0.511951
$184$	−8.19324	−0.604013
$185$	7.17604	0.527593
$186$	−9.78829	−0.717712
$187$	14.3638	1.05039
$188$	−0.230248	−0.0167925
$189$	19.3498	1.40749
$190$	4.22523	0.306530
$191$	22.1217	1.60067	0.800337	−	0.599551i	$-0.204654\pi$
$191$	22.1217	1.60067	0.800337	+	0.599551i	$0.204654\pi$
$192$	1.02602	0.0740467
$193$	−16.6942	−1.20167	−0.600836	−	0.799372i	$-0.705166\pi$
$193$	−16.6942	−1.20167	−0.600836	+	0.799372i	$0.705166\pi$
$194$	−15.1842	−1.09016
$195$	−0.0616249	−0.00441305
$196$	7.53145	0.537961
$197$	−21.6286	−1.54097	−0.770486	−	0.637457i	$-0.779986\pi$
$197$	−21.6286	−1.54097	−0.770486	+	0.637457i	$0.779986\pi$
$198$	−5.52868	−0.392906
$199$	−5.08690	−0.360601	−0.180300	−	0.983612i	$-0.557707\pi$
$199$	−5.08690	−0.360601	−0.180300	+	0.983612i	$0.557707\pi$
$200$	−1.00000	−0.0707107
$201$	−12.1295	−0.855547
$202$	−13.8094	−0.971627
$203$	17.4614	1.22555
$204$	−5.19079	−0.363428
$205$	−2.87566	−0.200845
$206$	−1.91094	−0.133141
$207$	−15.9545	−1.10892
$208$	−0.0600620	−0.00416455
$209$	11.9962	0.829794
$210$	3.91121	0.269899
$211$	10.6499	0.733167	0.366583	−	0.930385i	$-0.380527\pi$
$211$	10.6499	0.733167	0.366583	+	0.930385i	$0.380527\pi$
$212$	2.37088	0.162833
$213$	10.3842	0.711512
$214$	12.7904	0.874336
$215$	0.707096	0.0482236
$216$	5.07602	0.345379
$217$	−36.3668	−2.46874
$218$	−13.5187	−0.915600
$219$	3.72724	0.251864
$220$	−2.83918	−0.191418
$221$	0.303862	0.0204400
$222$	−7.36277	−0.494157
$223$	−0.372245	−0.0249274	−0.0124637	−	0.999922i	$-0.503967\pi$
$223$	−0.372245	−0.0249274	−0.0124637	+	0.999922i	$0.503967\pi$
$224$	3.81201	0.254701
$225$	−1.94728	−0.129819
$226$	−7.59117	−0.504957
$227$	−4.26913	−0.283352	−0.141676	−	0.989913i	$-0.545249\pi$
$227$	−4.26913	−0.283352	−0.141676	+	0.989913i	$0.545249\pi$
$228$	−4.33518	−0.287104
$229$	−11.1730	−0.738332	−0.369166	−	0.929363i	$-0.620357\pi$
$229$	−11.1730	−0.738332	−0.369166	+	0.929363i	$0.620357\pi$
$230$	−8.19324	−0.540246
$231$	11.1046	0.730631
$232$	4.58061	0.300732
$233$	2.91303	0.190839	0.0954194	−	0.995437i	$-0.469581\pi$
$233$	2.91303	0.190839	0.0954194	+	0.995437i	$0.469581\pi$
$234$	−0.116957	−0.00764574
$235$	−0.230248	−0.0150197
$236$	8.52669	0.555040
$237$	−5.12057	−0.332617
$238$	−19.2855	−1.25010
$239$	−18.7629	−1.21367	−0.606834	−	0.794828i	$-0.707561\pi$
$239$	−18.7629	−1.21367	−0.606834	+	0.794828i	$0.707561\pi$
$240$	1.02602	0.0662294
$241$	5.17217	0.333169	0.166584	−	0.986027i	$-0.446726\pi$
$241$	5.17217	0.333169	0.166584	+	0.986027i	$0.446726\pi$
$242$	2.93905	0.188929
$243$	15.8783	1.01859
$244$	6.74990	0.432118
$245$	7.53145	0.481167
$246$	2.95049	0.188116
$247$	0.253775	0.0161473
$248$	−9.54004	−0.605793
$249$	7.60728	0.482092
$250$	−1.00000	−0.0632456
$251$	−1.37020	−0.0864865	−0.0432433	−	0.999065i	$-0.513769\pi$
$251$	−1.37020	−0.0864865	−0.0432433	+	0.999065i	$0.513769\pi$
$252$	7.42306	0.467609
$253$	−23.2621	−1.46247
$254$	7.71307	0.483961
$255$	−5.19079	−0.325060
$256$	1.00000	0.0625000
$257$	−26.3103	−1.64119	−0.820595	−	0.571510i	$-0.806358\pi$
$257$	−26.3103	−1.64119	−0.820595	+	0.571510i	$0.806358\pi$
$258$	−0.725496	−0.0451674
$259$	−27.3552	−1.69977
$260$	−0.0600620	−0.00372488
$261$	8.91973	0.552118
$262$	−14.9284	−0.922277
$263$	−7.70166	−0.474905	−0.237452	−	0.971399i	$-0.576312\pi$
$263$	−7.70166	−0.474905	−0.237452	+	0.971399i	$0.576312\pi$
$264$	2.91306	0.179287
$265$	2.37088	0.145642
$266$	−16.1066	−0.987561
$267$	−3.91597	−0.239653
$268$	−11.8218	−0.722134
$269$	11.2857	0.688103	0.344052	−	0.938951i	$-0.388201\pi$
$269$	11.2857	0.688103	0.344052	+	0.938951i	$0.388201\pi$
$270$	5.07602	0.308917
$271$	−23.5557	−1.43091	−0.715453	−	0.698661i	$-0.753780\pi$
$271$	−23.5557	−1.43091	−0.715453	+	0.698661i	$0.753780\pi$
$272$	−5.05914	−0.306756
$273$	0.234915	0.0142177
$274$	15.8192	0.955671
$275$	−2.83918	−0.171209
$276$	8.40644	0.506008
$277$	21.2834	1.27880	0.639399	−	0.768875i	$-0.279183\pi$
$277$	21.2834	1.27880	0.639399	+	0.768875i	$0.279183\pi$
$278$	5.17609	0.310441
$279$	−18.5771	−1.11218
$280$	3.81201	0.227811
$281$	7.77606	0.463881	0.231941	−	0.972730i	$-0.425493\pi$
$281$	7.77606	0.463881	0.231941	+	0.972730i	$0.425493\pi$
$282$	0.236239	0.0140678
$283$	−4.40338	−0.261754	−0.130877	−	0.991399i	$-0.541779\pi$
$283$	−4.40338	−0.261754	−0.130877	+	0.991399i	$0.541779\pi$
$284$	10.1208	0.600560
$285$	−4.33518	−0.256794
$286$	−0.170527	−0.0100835
$287$	10.9620	0.647069
$288$	1.94728	0.114745
$289$	8.59495	0.505585
$290$	4.58061	0.268983
$291$	15.5793	0.913277
$292$	3.63271	0.212588
$293$	−22.7215	−1.32740	−0.663702	−	0.747997i	$-0.731016\pi$
$293$	−22.7215	−1.32740	−0.663702	+	0.747997i	$0.731016\pi$
$294$	−7.72743	−0.450673
$295$	8.52669	0.496443
$296$	−7.17604	−0.417099
$297$	14.4117	0.836254
$298$	−6.58195	−0.381282
$299$	−0.492102	−0.0284590
$300$	1.02602	0.0592374
$301$	−2.69546	−0.155364
$302$	−19.1521	−1.10208
$303$	14.1688	0.813974
$304$	−4.22523	−0.242333
$305$	6.74990	0.386498
$306$	−9.85157	−0.563177
$307$	13.1709	0.751705	0.375852	−	0.926680i	$-0.377350\pi$
$307$	13.1709	0.751705	0.375852	+	0.926680i	$0.377350\pi$
$308$	10.8230	0.616698
$309$	1.96067	0.111538
$310$	−9.54004	−0.541838
$311$	2.88029	0.163327	0.0816633	−	0.996660i	$-0.473977\pi$
$311$	2.88029	0.163327	0.0816633	+	0.996660i	$0.473977\pi$
$312$	0.0616249	0.00348882
$313$	−9.85746	−0.557177	−0.278588	−	0.960411i	$-0.589866\pi$
$313$	−9.85746	−0.557177	−0.278588	+	0.960411i	$0.589866\pi$
$314$	−1.25197	−0.0706528
$315$	7.42306	0.418242
$316$	−4.99070	−0.280749
$317$	−16.8840	−0.948297	−0.474149	−	0.880445i	$-0.657244\pi$
$317$	−16.8840	−0.948297	−0.474149	+	0.880445i	$0.657244\pi$
$318$	−2.43258	−0.136412
$319$	13.0052	0.728151
$320$	1.00000	0.0559017
$321$	−13.1233	−0.732469
$322$	31.2327	1.74053
$323$	21.3760	1.18939
$324$	0.633735	0.0352075
$325$	−0.0600620	−0.00333164
$326$	−1.40366	−0.0777415
$327$	13.8704	0.767038
$328$	2.87566	0.158782
$329$	0.877708	0.0483896
$330$	2.91306	0.160359
$331$	−20.8767	−1.14749	−0.573743	−	0.819035i	$-0.694509\pi$
$331$	−20.8767	−1.14749	−0.573743	+	0.819035i	$0.694509\pi$
$332$	7.41435	0.406915
$333$	−13.9737	−0.765757
$334$	−8.87085	−0.485391
$335$	−11.8218	−0.645896
$336$	−3.91121	−0.213374
$337$	25.3229	1.37943	0.689714	−	0.724082i	$-0.257736\pi$
$337$	25.3229	1.37943	0.689714	+	0.724082i	$0.257736\pi$
$338$	12.9964	0.706911
$339$	7.78871	0.423025
$340$	−5.05914	−0.274371
$341$	−27.0859	−1.46678
$342$	−8.22770	−0.444903
$343$	−2.02590	−0.109388
$344$	−0.707096	−0.0381241
$345$	8.40644	0.452587
$346$	10.2824	0.552785
$347$	−1.92580	−0.103382	−0.0516911	−	0.998663i	$-0.516461\pi$
$347$	−1.92580	−0.103382	−0.0516911	+	0.998663i	$0.516461\pi$
$348$	−4.69981	−0.251936
$349$	6.70738	0.359038	0.179519	−	0.983755i	$-0.442546\pi$
$349$	6.70738	0.359038	0.179519	+	0.983755i	$0.442546\pi$
$350$	3.81201	0.203761
$351$	0.304875	0.0162730
$352$	2.83918	0.151329
$353$	−30.5721	−1.62719	−0.813595	−	0.581432i	$-0.802493\pi$
$353$	−30.5721	−1.62719	−0.813595	+	0.581432i	$0.802493\pi$
$354$	−8.74857	−0.464981
$355$	10.1208	0.537157
$356$	−3.81665	−0.202282
$357$	19.7874	1.04726
$358$	−3.08332	−0.162959
$359$	21.5773	1.13880	0.569402	−	0.822059i	$-0.307175\pi$
$359$	21.5773	1.13880	0.569402	+	0.822059i	$0.307175\pi$
$360$	1.94728	0.102631
$361$	−1.14745	−0.0603922
$362$	−10.7889	−0.567050
$363$	−3.01553	−0.158274
$364$	0.228957	0.0120006
$365$	3.63271	0.190145
$366$	−6.92555	−0.362004
$367$	37.3989	1.95221	0.976105	−	0.217301i	$-0.0697254\pi$
$367$	37.3989	1.95221	0.976105	+	0.217301i	$0.0697254\pi$
$368$	8.19324	0.427102
$369$	5.59971	0.291509
$370$	−7.17604	−0.373064
$371$	−9.03785	−0.469222
$372$	9.78829	0.507499
$373$	−6.26345	−0.324309	−0.162155	−	0.986765i	$-0.551844\pi$
$373$	−6.26345	−0.324309	−0.162155	+	0.986765i	$0.551844\pi$
$374$	−14.3638	−0.742736
$375$	1.02602	0.0529835
$376$	0.230248	0.0118741
$377$	0.275121	0.0141694
$378$	−19.3498	−0.995249
$379$	20.6983	1.06320	0.531600	−	0.846996i	$-0.321591\pi$
$379$	20.6983	1.06320	0.531600	+	0.846996i	$0.321591\pi$
$380$	−4.22523	−0.216750
$381$	−7.91377	−0.405435
$382$	−22.1217	−1.13185
$383$	33.2733	1.70019	0.850093	−	0.526633i	$-0.176546\pi$
$383$	33.2733	1.70019	0.850093	+	0.526633i	$0.176546\pi$
$384$	−1.02602	−0.0523590
$385$	10.8230	0.551591
$386$	16.6942	0.849711
$387$	−1.37691	−0.0699925
$388$	15.1842	0.770862
$389$	6.30931	0.319895	0.159947	−	0.987126i	$-0.448868\pi$
$389$	6.30931	0.319895	0.159947	+	0.987126i	$0.448868\pi$
$390$	0.0616249	0.00312050
$391$	−41.4508	−2.09626
$392$	−7.53145	−0.380396
$393$	15.3168	0.772631
$394$	21.6286	1.08963
$395$	−4.99070	−0.251110
$396$	5.52868	0.277827
$397$	32.9865	1.65555	0.827773	−	0.561063i	$-0.189607\pi$
$397$	32.9865	1.65555	0.827773	+	0.561063i	$0.189607\pi$
$398$	5.08690	0.254983
$399$	16.5258	0.827322
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	12.1295	0.604963
$403$	−0.572994	−0.0285428
$404$	13.8094	0.687044
$405$	0.633735	0.0314905
$406$	−17.4614	−0.866593
$407$	−20.3741	−1.00991
$408$	5.19079	0.256983
$409$	−11.5782	−0.572506	−0.286253	−	0.958154i	$-0.592410\pi$
$409$	−11.5782	−0.572506	−0.286253	+	0.958154i	$0.592410\pi$
$410$	2.87566	0.142019
$411$	−16.2308	−0.800607
$412$	1.91094	0.0941452
$413$	−32.5039	−1.59941
$414$	15.9545	0.784122
$415$	7.41435	0.363956
$416$	0.0600620	0.00294478
$417$	−5.31078	−0.260070
$418$	−11.9962	−0.586753
$419$	12.1502	0.593575	0.296787	−	0.954944i	$-0.404085\pi$
$419$	12.1502	0.593575	0.296787	+	0.954944i	$0.404085\pi$
$420$	−3.91121	−0.190847
$421$	14.7818	0.720422	0.360211	−	0.932871i	$-0.382705\pi$
$421$	14.7818	0.720422	0.360211	+	0.932871i	$0.382705\pi$
$422$	−10.6499	−0.518427
$423$	0.448357	0.0217998
$424$	−2.37088	−0.115140
$425$	−5.05914	−0.245405
$426$	−10.3842	−0.503115
$427$	−25.7307	−1.24520
$428$	−12.7904	−0.618249
$429$	0.174964	0.00844735
$430$	−0.707096	−0.0340992
$431$	11.2478	0.541786	0.270893	−	0.962610i	$-0.412681\pi$
$431$	11.2478	0.541786	0.270893	+	0.962610i	$0.412681\pi$
$432$	−5.07602	−0.244220
$433$	26.4507	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$433$	26.4507	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$434$	36.3668	1.74566
$435$	−4.69981	−0.225339
$436$	13.5187	0.647427
$437$	−34.6183	−1.65602
$438$	−3.72724	−0.178095
$439$	31.2270	1.49039	0.745193	−	0.666849i	$-0.232357\pi$
$439$	31.2270	1.49039	0.745193	+	0.666849i	$0.232357\pi$
$440$	2.83918	0.135353
$441$	−14.6658	−0.698373
$442$	−0.303862	−0.0144532
$443$	10.1216	0.480892	0.240446	−	0.970663i	$-0.422706\pi$
$443$	10.1216	0.480892	0.240446	+	0.970663i	$0.422706\pi$
$444$	7.36277	0.349422
$445$	−3.81665	−0.180927
$446$	0.372245	0.0176263
$447$	6.75322	0.319416
$448$	−3.81201	−0.180101
$449$	−18.1971	−0.858776	−0.429388	−	0.903120i	$-0.641271\pi$
$449$	−18.1971	−0.858776	−0.429388	+	0.903120i	$0.641271\pi$
$450$	1.94728	0.0917956
$451$	8.16451	0.384452
$452$	7.59117	0.357059
$453$	19.6505	0.923259
$454$	4.26913	0.200360
$455$	0.228957	0.0107337
$456$	4.33518	0.203013
$457$	−42.1368	−1.97108	−0.985539	−	0.169450i	$-0.945801\pi$
$457$	−42.1368	−1.97108	−0.985539	+	0.169450i	$0.945801\pi$
$458$	11.1730	0.522080
$459$	25.6803	1.19865
$460$	8.19324	0.382012
$461$	14.6396	0.681833	0.340917	−	0.940094i	$-0.389263\pi$
$461$	14.6396	0.681833	0.340917	+	0.940094i	$0.389263\pi$
$462$	−11.1046	−0.516634
$463$	30.1478	1.40109	0.700543	−	0.713610i	$-0.252941\pi$
$463$	30.1478	1.40109	0.700543	+	0.713610i	$0.252941\pi$
$464$	−4.58061	−0.212650
$465$	9.78829	0.453921
$466$	−2.91303	−0.134943
$467$	−12.6979	−0.587590	−0.293795	−	0.955869i	$-0.594918\pi$
$467$	−12.6979	−0.587590	−0.293795	+	0.955869i	$0.594918\pi$
$468$	0.116957	0.00540636
$469$	45.0650	2.08091
$470$	0.230248	0.0106205
$471$	1.28455	0.0591889
$472$	−8.52669	−0.392473
$473$	−2.00757	−0.0923084
$474$	5.12057	0.235196
$475$	−4.22523	−0.193867
$476$	19.2855	0.883951
$477$	−4.61677	−0.211388
$478$	18.7629	0.858193
$479$	23.6094	1.07874	0.539371	−	0.842068i	$-0.318662\pi$
$479$	23.6094	1.07874	0.539371	+	0.842068i	$0.318662\pi$
$480$	−1.02602	−0.0468313
$481$	−0.431007	−0.0196522
$482$	−5.17217	−0.235586
$483$	−32.0455	−1.45812
$484$	−2.93905	−0.133593
$485$	15.1842	0.689480
$486$	−15.8783	−0.720253
$487$	32.6718	1.48050	0.740250	−	0.672332i	$-0.234707\pi$
$487$	32.6718	1.48050	0.740250	+	0.672332i	$0.234707\pi$
$488$	−6.74990	−0.305554
$489$	1.44018	0.0651274
$490$	−7.53145	−0.340236
$491$	15.6896	0.708061	0.354031	−	0.935234i	$-0.384811\pi$
$491$	15.6896	0.708061	0.354031	+	0.935234i	$0.384811\pi$
$492$	−2.95049	−0.133018
$493$	23.1740	1.04370
$494$	−0.253775	−0.0114179
$495$	5.52868	0.248496
$496$	9.54004	0.428361
$497$	−38.5807	−1.73058
$498$	−7.60728	−0.340890
$499$	17.9501	0.803559	0.401779	−	0.915736i	$-0.368392\pi$
$499$	17.9501	0.803559	0.401779	+	0.915736i	$0.368392\pi$
$500$	1.00000	0.0447214
$501$	9.10169	0.406633
$502$	1.37020	0.0611552
$503$	−23.0559	−1.02801	−0.514006	−	0.857786i	$-0.671839\pi$
$503$	−23.0559	−1.02801	−0.514006	+	0.857786i	$0.671839\pi$
$504$	−7.42306	−0.330649
$505$	13.8094	0.614511
$506$	23.2621	1.03413
$507$	−13.3346	−0.592210
$508$	−7.71307	−0.342212
$509$	−13.0484	−0.578361	−0.289181	−	0.957275i	$-0.593383\pi$
$509$	−13.0484	−0.578361	−0.289181	+	0.957275i	$0.593383\pi$
$510$	5.19079	0.229852
$511$	−13.8480	−0.612597
$512$	−1.00000	−0.0441942
$513$	21.4473	0.946923
$514$	26.3103	1.16050
$515$	1.91094	0.0842061
$516$	0.725496	0.0319382
$517$	0.653715	0.0287504
$518$	27.3552	1.20192
$519$	−10.5500	−0.463092
$520$	0.0600620	0.00263389
$521$	9.36957	0.410488	0.205244	−	0.978711i	$-0.434201\pi$
$521$	9.36957	0.410488	0.205244	+	0.978711i	$0.434201\pi$
$522$	−8.91973	−0.390406
$523$	15.6961	0.686343	0.343172	−	0.939273i	$-0.388499\pi$
$523$	15.6961	0.686343	0.343172	+	0.939273i	$0.388499\pi$
$524$	14.9284	0.652148
$525$	−3.91121	−0.170699
$526$	7.70166	0.335808
$527$	−48.2645	−2.10243
$528$	−2.91306	−0.126775
$529$	44.1291	1.91866
$530$	−2.37088	−0.102985
$531$	−16.6038	−0.720545
$532$	16.1066	0.698311
$533$	0.172718	0.00748123
$534$	3.91597	0.169460
$535$	−12.7904	−0.552979
$536$	11.8218	0.510626
$537$	3.16355	0.136517
$538$	−11.2857	−0.486562
$539$	−21.3832	−0.921038
$540$	−5.07602	−0.218437
$541$	3.97637	0.170957	0.0854786	−	0.996340i	$-0.472758\pi$
$541$	3.97637	0.170957	0.0854786	+	0.996340i	$0.472758\pi$
$542$	23.5557	1.01180
$543$	11.0696	0.475042
$544$	5.05914	0.216909
$545$	13.5187	0.579076
$546$	−0.234915	−0.0100534
$547$	12.2263	0.522760	0.261380	−	0.965236i	$-0.415822\pi$
$547$	12.2263	0.522760	0.261380	+	0.965236i	$0.415822\pi$
$548$	−15.8192	−0.675762
$549$	−13.1439	−0.560970
$550$	2.83918	0.121063
$551$	19.3541	0.824514
$552$	−8.40644	−0.357802
$553$	19.0246	0.809010
$554$	−21.2834	−0.904246
$555$	7.36277	0.312532
$556$	−5.17609	−0.219515
$557$	37.1608	1.57455	0.787276	−	0.616601i	$-0.211491\pi$
$557$	37.1608	1.57455	0.787276	+	0.616601i	$0.211491\pi$
$558$	18.5771	0.786433
$559$	−0.0424696	−0.00179627
$560$	−3.81201	−0.161087
$561$	14.7376	0.622222
$562$	−7.77606	−0.328013
$563$	−28.5033	−1.20127	−0.600635	−	0.799523i	$-0.705086\pi$
$563$	−28.5033	−1.20127	−0.600635	+	0.799523i	$0.705086\pi$
$564$	−0.236239	−0.00994747
$565$	7.59117	0.319363
$566$	4.40338	0.185088
$567$	−2.41580	−0.101454
$568$	−10.1208	−0.424660
$569$	7.96596	0.333950	0.166975	−	0.985961i	$-0.446600\pi$
$569$	7.96596	0.333950	0.166975	+	0.985961i	$0.446600\pi$
$570$	4.33518	0.181581
$571$	32.7160	1.36912	0.684560	−	0.728956i	$-0.259994\pi$
$571$	32.7160	1.36912	0.684560	+	0.728956i	$0.259994\pi$
$572$	0.170527	0.00713008
$573$	22.6974	0.948197
$574$	−10.9620	−0.457547
$575$	8.19324	0.341682
$576$	−1.94728	−0.0811366
$577$	10.7239	0.446441	0.223220	−	0.974768i	$-0.428343\pi$
$577$	10.7239	0.446441	0.223220	+	0.974768i	$0.428343\pi$
$578$	−8.59495	−0.357503
$579$	−17.1286	−0.711839
$580$	−4.58061	−0.190200
$581$	−28.2636	−1.17257
$582$	−15.5793	−0.645784
$583$	−6.73137	−0.278785
$584$	−3.63271	−0.150323
$585$	0.116957	0.00483559
$586$	22.7215	0.938617
$587$	43.9953	1.81588	0.907940	−	0.419101i	$-0.137655\pi$
$587$	43.9953	1.81588	0.907940	+	0.419101i	$0.137655\pi$
$588$	7.72743	0.318674
$589$	−40.3089	−1.66090
$590$	−8.52669	−0.351038
$591$	−22.1914	−0.912831
$592$	7.17604	0.294933
$593$	−5.95594	−0.244581	−0.122291	−	0.992494i	$-0.539024\pi$
$593$	−5.95594	−0.244581	−0.122291	+	0.992494i	$0.539024\pi$
$594$	−14.4117	−0.591321
$595$	19.2855	0.790630
$596$	6.58195	0.269607
$597$	−5.21927	−0.213611
$598$	0.492102	0.0201235
$599$	−38.3330	−1.56624	−0.783122	−	0.621868i	$-0.786374\pi$
$599$	−38.3330	−1.56624	−0.783122	+	0.621868i	$0.786374\pi$
$600$	−1.02602	−0.0418872
$601$	−11.9060	−0.485655	−0.242828	−	0.970069i	$-0.578075\pi$
$601$	−11.9060	−0.485655	−0.242828	+	0.970069i	$0.578075\pi$
$602$	2.69546	0.109859
$603$	23.0204	0.937464
$604$	19.1521	0.779287
$605$	−2.93905	−0.119489
$606$	−14.1688	−0.575567
$607$	20.0404	0.813417	0.406708	−	0.913558i	$-0.366677\pi$
$607$	20.0404	0.813417	0.406708	+	0.913558i	$0.366677\pi$
$608$	4.22523	0.171356
$609$	17.9157	0.725982
$610$	−6.74990	−0.273296
$611$	0.0138291	0.000559467 0
$612$	9.85157	0.398226
$613$	−34.0665	−1.37593	−0.687966	−	0.725743i	$-0.741496\pi$
$613$	−34.0665	−1.37593	−0.687966	+	0.725743i	$0.741496\pi$
$614$	−13.1709	−0.531536
$615$	−2.95049	−0.118975
$616$	−10.8230	−0.436071
$617$	−20.1106	−0.809621	−0.404811	−	0.914401i	$-0.632663\pi$
$617$	−20.1106	−0.809621	−0.404811	+	0.914401i	$0.632663\pi$
$618$	−1.96067	−0.0788695
$619$	40.3475	1.62170	0.810852	−	0.585251i	$-0.199004\pi$
$619$	40.3475	1.62170	0.810852	+	0.585251i	$0.199004\pi$
$620$	9.54004	0.383137
$621$	−41.5890	−1.66891
$622$	−2.88029	−0.115489
$623$	14.5491	0.582898
$624$	−0.0616249	−0.00246697
$625$	1.00000	0.0400000
$626$	9.85746	0.393983
$627$	12.3084	0.491548
$628$	1.25197	0.0499590
$629$	−36.3046	−1.44756
$630$	−7.42306	−0.295742
$631$	18.2878	0.728024	0.364012	−	0.931394i	$-0.381407\pi$
$631$	18.2878	0.728024	0.364012	+	0.931394i	$0.381407\pi$
$632$	4.99070	0.198520
$633$	10.9270	0.434309
$634$	16.8840	0.670548
$635$	−7.71307	−0.306084
$636$	2.43258	0.0964580
$637$	−0.452354	−0.0179229
$638$	−13.0052	−0.514881
$639$	−19.7080	−0.779638
$640$	−1.00000	−0.0395285
$641$	−45.6341	−1.80244	−0.901218	−	0.433365i	$-0.857326\pi$
$641$	−45.6341	−1.80244	−0.901218	+	0.433365i	$0.857326\pi$
$642$	13.1233	0.517934
$643$	−38.6173	−1.52292	−0.761458	−	0.648214i	$-0.775516\pi$
$643$	−38.6173	−1.52292	−0.761458	+	0.648214i	$0.775516\pi$
$644$	−31.2327	−1.23074
$645$	0.725496	0.0285664
$646$	−21.3760	−0.841029
$647$	−43.8955	−1.72571	−0.862855	−	0.505451i	$-0.831326\pi$
$647$	−43.8955	−1.72571	−0.862855	+	0.505451i	$0.831326\pi$
$648$	−0.633735	−0.0248954
$649$	−24.2088	−0.950279
$650$	0.0600620	0.00235582
$651$	−37.3131	−1.46242
$652$	1.40366	0.0549715
$653$	−3.12228	−0.122184	−0.0610922	−	0.998132i	$-0.519458\pi$
$653$	−3.12228	−0.122184	−0.0610922	+	0.998132i	$0.519458\pi$
$654$	−13.8704	−0.542377
$655$	14.9284	0.583299
$656$	−2.87566	−0.112275
$657$	−7.07391	−0.275979
$658$	−0.877708	−0.0342166
$659$	25.4076	0.989738	0.494869	−	0.868968i	$-0.335216\pi$
$659$	25.4076	0.989738	0.494869	+	0.868968i	$0.335216\pi$
$660$	−2.91306	−0.113391
$661$	−26.9407	−1.04787	−0.523936	−	0.851758i	$-0.675537\pi$
$661$	−26.9407	−1.04787	−0.523936	+	0.851758i	$0.675537\pi$
$662$	20.8767	0.811395
$663$	0.311769	0.0121081
$664$	−7.41435	−0.287732
$665$	16.1066	0.624588
$666$	13.9737	0.541472
$667$	−37.5301	−1.45317
$668$	8.87085	0.343224
$669$	−0.381932	−0.0147663
$670$	11.8218	0.456718
$671$	−19.1642	−0.739826
$672$	3.91121	0.150878
$673$	16.0826	0.619939	0.309970	−	0.950746i	$-0.399681\pi$
$673$	16.0826	0.619939	0.309970	+	0.950746i	$0.399681\pi$
$674$	−25.3229	−0.975403
$675$	−5.07602	−0.195376
$676$	−12.9964	−0.499861
$677$	11.3254	0.435269	0.217635	−	0.976030i	$-0.430166\pi$
$677$	11.3254	0.435269	0.217635	+	0.976030i	$0.430166\pi$
$678$	−7.78871	−0.299124
$679$	−57.8824	−2.22132
$680$	5.05914	0.194009
$681$	−4.38022	−0.167850
$682$	27.0859	1.03717
$683$	−25.3062	−0.968314	−0.484157	−	0.874981i	$-0.660874\pi$
$683$	−25.3062	−0.968314	−0.484157	+	0.874981i	$0.660874\pi$
$684$	8.22770	0.314594
$685$	−15.8192	−0.604420
$686$	2.02590	0.0773492
$687$	−11.4637	−0.437369
$688$	0.707096	0.0269578
$689$	−0.142400	−0.00542501
$690$	−8.40644	−0.320028
$691$	−41.2801	−1.57037	−0.785185	−	0.619262i	$-0.787432\pi$
$691$	−41.2801	−1.57037	−0.785185	+	0.619262i	$0.787432\pi$
$692$	−10.2824	−0.390878
$693$	−21.0754	−0.800588
$694$	1.92580	0.0731023
$695$	−5.17609	−0.196340
$696$	4.69981	0.178146
$697$	14.5484	0.551058
$698$	−6.70738	−0.253878
$699$	2.98883	0.113048
$700$	−3.81201	−0.144081
$701$	10.8088	0.408242	0.204121	−	0.978946i	$-0.434566\pi$
$701$	10.8088	0.408242	0.204121	+	0.978946i	$0.434566\pi$
$702$	−0.304875	−0.0115068
$703$	−30.3204	−1.14356
$704$	−2.83918	−0.107006
$705$	−0.236239	−0.00889728
$706$	30.5721	1.15060
$707$	−52.6417	−1.97979
$708$	8.74857	0.328791
$709$	37.1722	1.39603	0.698016	−	0.716082i	$-0.254066\pi$
$709$	37.1722	1.39603	0.698016	+	0.716082i	$0.254066\pi$
$710$	−10.1208	−0.379827
$711$	9.71829	0.364465
$712$	3.81665	0.143035
$713$	78.1638	2.92726
$714$	−19.7874	−0.740524
$715$	0.170527	0.00637734
$716$	3.08332	0.115229
$717$	−19.2511	−0.718946
$718$	−21.5773	−0.805256
$719$	−22.8945	−0.853820	−0.426910	−	0.904294i	$-0.640398\pi$
$719$	−22.8945	−0.853820	−0.426910	+	0.904294i	$0.640398\pi$
$720$	−1.94728	−0.0725708
$721$	−7.28453	−0.271290
$722$	1.14745	0.0427037
$723$	5.30676	0.197360
$724$	10.7889	0.400965
$725$	−4.58061	−0.170120
$726$	3.01553	0.111917
$727$	30.7558	1.14067	0.570334	−	0.821413i	$-0.306814\pi$
$727$	30.7558	1.14067	0.570334	+	0.821413i	$0.306814\pi$
$728$	−0.228957	−0.00848571
$729$	14.3903	0.532972
$730$	−3.63271	−0.134453
$731$	−3.57730	−0.132311
$732$	6.92555	0.255976
$733$	8.99157	0.332111	0.166056	−	0.986116i	$-0.446897\pi$
$733$	8.99157	0.332111	0.166056	+	0.986116i	$0.446897\pi$
$734$	−37.3989	−1.38042
$735$	7.72743	0.285031
$736$	−8.19324	−0.302007
$737$	33.5644	1.23636
$738$	−5.59971	−0.206128
$739$	10.2220	0.376023	0.188012	−	0.982167i	$-0.439796\pi$
$739$	10.2220	0.376023	0.188012	+	0.982167i	$0.439796\pi$
$740$	7.17604	0.263796
$741$	0.260379	0.00956527
$742$	9.03785	0.331790
$743$	−24.5826	−0.901849	−0.450924	−	0.892562i	$-0.648906\pi$
$743$	−24.5826	−0.901849	−0.450924	+	0.892562i	$0.648906\pi$
$744$	−9.78829	−0.358856
$745$	6.58195	0.241144
$746$	6.26345	0.229321
$747$	−14.4378	−0.528252
$748$	14.3638	0.525194
$749$	48.7573	1.78155
$750$	−1.02602	−0.0374650
$751$	43.0736	1.57178	0.785888	−	0.618369i	$-0.212206\pi$
$751$	43.0736	1.57178	0.785888	+	0.618369i	$0.212206\pi$
$752$	−0.230248	−0.00839627
$753$	−1.40586	−0.0512324
$754$	−0.275121	−0.0100193
$755$	19.1521	0.697016
$756$	19.3498	0.703747
$757$	−3.24488	−0.117937	−0.0589685	−	0.998260i	$-0.518781\pi$
$757$	−3.24488	−0.117937	−0.0589685	+	0.998260i	$0.518781\pi$
$758$	−20.6983	−0.751795
$759$	−23.8674	−0.866332
$760$	4.22523	0.153265
$761$	13.6532	0.494927	0.247464	−	0.968897i	$-0.420403\pi$
$761$	13.6532	0.494927	0.247464	+	0.968897i	$0.420403\pi$
$762$	7.91377	0.286686
$763$	−51.5334	−1.86563
$764$	22.1217	0.800337
$765$	9.85157	0.356184
$766$	−33.2733	−1.20221
$767$	−0.512129	−0.0184919
$768$	1.02602	0.0370234
$769$	38.8276	1.40016	0.700080	−	0.714064i	$-0.253147\pi$
$769$	38.8276	1.40016	0.700080	+	0.714064i	$0.253147\pi$
$770$	−10.8230	−0.390034
$771$	−26.9949	−0.972198
$772$	−16.6942	−0.600836
$773$	−48.6195	−1.74872	−0.874362	−	0.485275i	$-0.838720\pi$
$773$	−48.6195	−1.74872	−0.874362	+	0.485275i	$0.838720\pi$
$774$	1.37691	0.0494922
$775$	9.54004	0.342688
$776$	−15.1842	−0.545081
$777$	−28.0670	−1.00690
$778$	−6.30931	−0.226200
$779$	12.1503	0.435330
$780$	−0.0616249	−0.00220652
$781$	−28.7348	−1.02821
$782$	41.4508	1.48228
$783$	23.2513	0.830933
$784$	7.53145	0.268980
$785$	1.25197	0.0446847
$786$	−15.3168	−0.546333
$787$	−12.4110	−0.442404	−0.221202	−	0.975228i	$-0.570998\pi$
$787$	−12.4110	−0.442404	−0.221202	+	0.975228i	$0.570998\pi$
$788$	−21.6286	−0.770486
$789$	−7.90207	−0.281321
$790$	4.99070	0.177561
$791$	−28.9377	−1.02890
$792$	−5.52868	−0.196453
$793$	−0.405412	−0.0143966
$794$	−32.9865	−1.17065
$795$	2.43258	0.0862747
$796$	−5.08690	−0.180300
$797$	−16.8737	−0.597695	−0.298848	−	0.954301i	$-0.596602\pi$
$797$	−16.8737	−0.597695	−0.298848	+	0.954301i	$0.596602\pi$
$798$	−16.5258	−0.585005
$799$	1.16486	0.0412097
$800$	−1.00000	−0.0353553
$801$	7.43209	0.262600
$802$	1.00000	0.0353112
$803$	−10.3139	−0.363971
$804$	−12.1295	−0.427773
$805$	−31.2327	−1.10081
$806$	0.572994	0.0201828
$807$	11.5794	0.407614
$808$	−13.8094	−0.485814
$809$	−3.13494	−0.110219	−0.0551093	−	0.998480i	$-0.517551\pi$
$809$	−3.13494	−0.110219	−0.0551093	+	0.998480i	$0.517551\pi$
$810$	−0.633735	−0.0222672
$811$	40.7686	1.43158	0.715790	−	0.698315i	$-0.246067\pi$
$811$	40.7686	1.43158	0.715790	+	0.698315i	$0.246067\pi$
$812$	17.4614	0.612774
$813$	−24.1687	−0.847632
$814$	20.3741	0.714111
$815$	1.40366	0.0491680
$816$	−5.19079	−0.181714
$817$	−2.98764	−0.104524
$818$	11.5782	0.404823
$819$	−0.445843	−0.0155790
$820$	−2.87566	−0.100422
$821$	11.8701	0.414268	0.207134	−	0.978313i	$-0.433586\pi$
$821$	11.8701	0.414268	0.207134	+	0.978313i	$0.433586\pi$
$822$	16.2308	0.566115
$823$	−5.66292	−0.197397	−0.0986986	−	0.995117i	$-0.531468\pi$
$823$	−5.66292	−0.197397	−0.0986986	+	0.995117i	$0.531468\pi$
$824$	−1.91094	−0.0665707
$825$	−2.91306	−0.101420
$826$	32.5039	1.13095
$827$	26.7734	0.931004	0.465502	−	0.885047i	$-0.345874\pi$
$827$	26.7734	0.931004	0.465502	+	0.885047i	$0.345874\pi$
$828$	−15.9545	−0.554458
$829$	−19.4425	−0.675266	−0.337633	−	0.941278i	$-0.609626\pi$
$829$	−19.4425	−0.675266	−0.337633	+	0.941278i	$0.609626\pi$
$830$	−7.41435	−0.257356
$831$	21.8373	0.757526
$832$	−0.0600620	−0.00208227
$833$	−38.1027	−1.32018
$834$	5.31078	0.183897
$835$	8.87085	0.306989
$836$	11.9962	0.414897
$837$	−48.4254	−1.67383
$838$	−12.1502	−0.419721
$839$	31.7180	1.09503	0.547513	−	0.836797i	$-0.315575\pi$
$839$	31.7180	1.09503	0.547513	+	0.836797i	$0.315575\pi$
$840$	3.91121	0.134950
$841$	−8.01798	−0.276482
$842$	−14.7818	−0.509415
$843$	7.97841	0.274791
$844$	10.6499	0.366583
$845$	−12.9964	−0.447089
$846$	−0.448357	−0.0154148
$847$	11.2037	0.384963
$848$	2.37088	0.0814165
$849$	−4.51796	−0.155056
$850$	5.05914	0.173527
$851$	58.7950	2.01547
$852$	10.3842	0.355756
$853$	50.8955	1.74263	0.871314	−	0.490726i	$-0.163268\pi$
$853$	50.8955	1.74263	0.871314	+	0.490726i	$0.163268\pi$
$854$	25.7307	0.880487
$855$	8.22770	0.281381
$856$	12.7904	0.437168
$857$	1.65949	0.0566872	0.0283436	−	0.999598i	$-0.490977\pi$
$857$	1.65949	0.0566872	0.0283436	+	0.999598i	$0.490977\pi$
$858$	−0.174964	−0.00597318
$859$	−30.3290	−1.03481	−0.517405	−	0.855740i	$-0.673102\pi$
$859$	−30.3290	−1.03481	−0.517405	+	0.855740i	$0.673102\pi$
$860$	0.707096	0.0241118
$861$	11.2473	0.383307
$862$	−11.2478	−0.383100
$863$	45.8012	1.55909	0.779545	−	0.626346i	$-0.215450\pi$
$863$	45.8012	1.55909	0.779545	+	0.626346i	$0.215450\pi$
$864$	5.07602	0.172690
$865$	−10.2824	−0.349612
$866$	−26.4507	−0.898832
$867$	8.81860	0.299495
$868$	−36.3668	−1.23437
$869$	14.1695	0.480668
$870$	4.69981	0.159338
$871$	0.710043	0.0240589
$872$	−13.5187	−0.457800
$873$	−29.5679	−1.00072
$874$	34.6183	1.17098
$875$	−3.81201	−0.128870
$876$	3.72724	0.125932
$877$	41.1733	1.39032	0.695161	−	0.718854i	$-0.255333\pi$
$877$	41.1733	1.39032	0.695161	+	0.718854i	$0.255333\pi$
$878$	−31.2270	−1.05386
$879$	−23.3128	−0.786320
$880$	−2.83918	−0.0957088
$881$	29.8656	1.00620	0.503099	−	0.864229i	$-0.332193\pi$
$881$	29.8656	1.00620	0.503099	+	0.864229i	$0.332193\pi$
$882$	14.6658	0.493824
$883$	−51.6300	−1.73749	−0.868744	−	0.495261i	$-0.835072\pi$
$883$	−51.6300	−1.73749	−0.868744	+	0.495261i	$0.835072\pi$
$884$	0.303862	0.0102200
$885$	8.74857	0.294080
$886$	−10.1216	−0.340042
$887$	−17.2285	−0.578475	−0.289238	−	0.957257i	$-0.593402\pi$
$887$	−17.2285	−0.578475	−0.289238	+	0.957257i	$0.593402\pi$
$888$	−7.36277	−0.247078
$889$	29.4023	0.986122
$890$	3.81665	0.127934
$891$	−1.79929	−0.0602784
$892$	−0.372245	−0.0124637
$893$	0.972849	0.0325552
$894$	−6.75322	−0.225862
$895$	3.08332	0.103064
$896$	3.81201	0.127350
$897$	−0.504907	−0.0168584
$898$	18.1971	0.607246
$899$	−43.6993	−1.45745
$900$	−1.94728	−0.0649093
$901$	−11.9946	−0.399600
$902$	−8.16451	−0.271848
$903$	−2.76560	−0.0920335
$904$	−7.59117	−0.252479
$905$	10.7889	0.358634
$906$	−19.6505	−0.652843
$907$	19.1681	0.636466	0.318233	−	0.948013i	$-0.396911\pi$
$907$	19.1681	0.636466	0.318233	+	0.948013i	$0.396911\pi$
$908$	−4.26913	−0.141676
$909$	−26.8908	−0.891911
$910$	−0.228957	−0.00758985
$911$	−32.6092	−1.08039	−0.540195	−	0.841540i	$-0.681650\pi$
$911$	−32.6092	−1.08039	−0.540195	+	0.841540i	$0.681650\pi$
$912$	−4.33518	−0.143552
$913$	−21.0507	−0.696676
$914$	42.1368	1.39376
$915$	6.92555	0.228951
$916$	−11.1730	−0.369166
$917$	−56.9071	−1.87924
$918$	−25.6803	−0.847576
$919$	9.02246	0.297624	0.148812	−	0.988866i	$-0.452455\pi$
$919$	9.02246	0.297624	0.148812	+	0.988866i	$0.452455\pi$
$920$	−8.19324	−0.270123
$921$	13.5137	0.445290
$922$	−14.6396	−0.482129
$923$	−0.607876	−0.0200085
$924$	11.1046	0.365316
$925$	7.17604	0.235947
$926$	−30.1478	−0.990717
$927$	−3.72113	−0.122218
$928$	4.58061	0.150366
$929$	27.0139	0.886296	0.443148	−	0.896448i	$-0.353862\pi$
$929$	27.0139	0.886296	0.443148	+	0.896448i	$0.353862\pi$
$930$	−9.78829	−0.320971
$931$	−31.8221	−1.04293
$932$	2.91303	0.0954194
$933$	2.95525	0.0967504
$934$	12.6979	0.415489
$935$	14.3638	0.469748
$936$	−0.116957	−0.00382287
$937$	−22.8518	−0.746537	−0.373269	−	0.927723i	$-0.621763\pi$
$937$	−22.8518	−0.746537	−0.373269	+	0.927723i	$0.621763\pi$
$938$	−45.0650	−1.47143
$939$	−10.1140	−0.330057
$940$	−0.230248	−0.00750985
$941$	−13.8813	−0.452516	−0.226258	−	0.974067i	$-0.572649\pi$
$941$	−13.8813	−0.452516	−0.226258	+	0.974067i	$0.572649\pi$
$942$	−1.28455	−0.0418529
$943$	−23.5609	−0.767249
$944$	8.52669	0.277520
$945$	19.3498	0.629451
$946$	2.00757	0.0652719
$947$	−13.2755	−0.431395	−0.215698	−	0.976460i	$-0.569203\pi$
$947$	−13.2755	−0.431395	−0.215698	+	0.976460i	$0.569203\pi$
$948$	−5.12057	−0.166308
$949$	−0.218188	−0.00708268
$950$	4.22523	0.137084
$951$	−17.3233	−0.561747
$952$	−19.2855	−0.625048
$953$	−21.0095	−0.680565	−0.340283	−	0.940323i	$-0.610523\pi$
$953$	−21.0095	−0.680565	−0.340283	+	0.940323i	$0.610523\pi$
$954$	4.61677	0.149474
$955$	22.1217	0.715843
$956$	−18.7629	−0.606834
$957$	13.3436	0.431338
$958$	−23.6094	−0.762786
$959$	60.3029	1.94728
$960$	1.02602	0.0331147
$961$	60.0124	1.93588
$962$	0.431007	0.0138962
$963$	24.9066	0.802602
$964$	5.17217	0.166584
$965$	−16.6942	−0.537404
$966$	32.0455	1.03105
$967$	2.28773	0.0735683	0.0367842	−	0.999323i	$-0.488289\pi$
$967$	2.28773	0.0735683	0.0367842	+	0.999323i	$0.488289\pi$
$968$	2.93905	0.0944645
$969$	21.9323	0.704566
$970$	−15.1842	−0.487536
$971$	24.3149	0.780302	0.390151	−	0.920751i	$-0.372423\pi$
$971$	24.3149	0.780302	0.390151	+	0.920751i	$0.372423\pi$
$972$	15.8783	0.509296
$973$	19.7313	0.632557
$974$	−32.6718	−1.04687
$975$	−0.0616249	−0.00197358
$976$	6.74990	0.216059
$977$	42.1664	1.34902	0.674511	−	0.738265i	$-0.264355\pi$
$977$	42.1664	1.34902	0.674511	+	0.738265i	$0.264355\pi$
$978$	−1.44018	−0.0460520
$979$	10.8362	0.346325
$980$	7.53145	0.240583
$981$	−26.3246	−0.840481
$982$	−15.6896	−0.500675
$983$	16.1592	0.515397	0.257699	−	0.966225i	$-0.417036\pi$
$983$	16.1592	0.515397	0.257699	+	0.966225i	$0.417036\pi$
$984$	2.95049	0.0940580
$985$	−21.6286	−0.689143
$986$	−23.1740	−0.738010
$987$	0.900547	0.0286647
$988$	0.253775	0.00807367
$989$	5.79341	0.184220
$990$	−5.52868	−0.175713
$991$	−5.51896	−0.175316	−0.0876578	−	0.996151i	$-0.527938\pi$
$991$	−5.51896	−0.175316	−0.0876578	+	0.996151i	$0.527938\pi$
$992$	−9.54004	−0.302897
$993$	−21.4199	−0.679741
$994$	38.5807	1.22370
$995$	−5.08690	−0.161266
$996$	7.60728	0.241046
$997$	−39.8092	−1.26077	−0.630384	−	0.776283i	$-0.717103\pi$
$997$	−39.8092	−1.26077	−0.630384	+	0.776283i	$0.717103\pi$
$998$	−17.9501	−0.568202
$999$	−36.4257	−1.15246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.12	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.12	✓	20	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.02602 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.02602 q^{6} -3.81201 q^{7} -1.00000 q^{8} -1.94728 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.02602 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.02602 q^{6} -3.81201 q^{7} -1.00000 q^{8} -1.94728 q^{9} -1.00000 q^{10} -2.83918 q^{11} +1.02602 q^{12} -0.0600620 q^{13} +3.81201 q^{14} +1.02602 q^{15} +1.00000 q^{16} -5.05914 q^{17} +1.94728 q^{18} -4.22523 q^{19} +1.00000 q^{20} -3.91121 q^{21} +2.83918 q^{22} +8.19324 q^{23} -1.02602 q^{24} +1.00000 q^{25} +0.0600620 q^{26} -5.07602 q^{27} -3.81201 q^{28} -4.58061 q^{29} -1.02602 q^{30} +9.54004 q^{31} -1.00000 q^{32} -2.91306 q^{33} +5.05914 q^{34} -3.81201 q^{35} -1.94728 q^{36} +7.17604 q^{37} +4.22523 q^{38} -0.0616249 q^{39} -1.00000 q^{40} -2.87566 q^{41} +3.91121 q^{42} +0.707096 q^{43} -2.83918 q^{44} -1.94728 q^{45} -8.19324 q^{46} -0.230248 q^{47} +1.02602 q^{48} +7.53145 q^{49} -1.00000 q^{50} -5.19079 q^{51} -0.0600620 q^{52} +2.37088 q^{53} +5.07602 q^{54} -2.83918 q^{55} +3.81201 q^{56} -4.33518 q^{57} +4.58061 q^{58} +8.52669 q^{59} +1.02602 q^{60} +6.74990 q^{61} -9.54004 q^{62} +7.42306 q^{63} +1.00000 q^{64} -0.0600620 q^{65} +2.91306 q^{66} -11.8218 q^{67} -5.05914 q^{68} +8.40644 q^{69} +3.81201 q^{70} +10.1208 q^{71} +1.94728 q^{72} +3.63271 q^{73} -7.17604 q^{74} +1.02602 q^{75} -4.22523 q^{76} +10.8230 q^{77} +0.0616249 q^{78} -4.99070 q^{79} +1.00000 q^{80} +0.633735 q^{81} +2.87566 q^{82} +7.41435 q^{83} -3.91121 q^{84} -5.05914 q^{85} -0.707096 q^{86} -4.69981 q^{87} +2.83918 q^{88} -3.81665 q^{89} +1.94728 q^{90} +0.228957 q^{91} +8.19324 q^{92} +9.78829 q^{93} +0.230248 q^{94} -4.22523 q^{95} -1.02602 q^{96} +15.1842 q^{97} -7.53145 q^{98} +5.52868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

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