LMFDB - Embedded newform 4010.2.a.i.1.2

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.47143$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} -1.00000 q^{10} -5.34303 q^{11} -2.70072 q^{12} +4.99519 q^{13} +1.21166 q^{14} -2.70072 q^{15} +1.00000 q^{16} +1.52346 q^{17} -4.29386 q^{18} -5.54062 q^{19} +1.00000 q^{20} +3.27234 q^{21} +5.34303 q^{22} -2.17276 q^{23} +2.70072 q^{24} +1.00000 q^{25} -4.99519 q^{26} -3.49436 q^{27} -1.21166 q^{28} +5.67740 q^{29} +2.70072 q^{30} +7.09841 q^{31} -1.00000 q^{32} +14.4300 q^{33} -1.52346 q^{34} -1.21166 q^{35} +4.29386 q^{36} +1.20281 q^{37} +5.54062 q^{38} -13.4906 q^{39} -1.00000 q^{40} -10.3503 q^{41} -3.27234 q^{42} -12.2971 q^{43} -5.34303 q^{44} +4.29386 q^{45} +2.17276 q^{46} +12.4866 q^{47} -2.70072 q^{48} -5.53188 q^{49} -1.00000 q^{50} -4.11443 q^{51} +4.99519 q^{52} +10.8717 q^{53} +3.49436 q^{54} -5.34303 q^{55} +1.21166 q^{56} +14.9636 q^{57} -5.67740 q^{58} +3.79149 q^{59} -2.70072 q^{60} -6.62515 q^{61} -7.09841 q^{62} -5.20270 q^{63} +1.00000 q^{64} +4.99519 q^{65} -14.4300 q^{66} -7.49485 q^{67} +1.52346 q^{68} +5.86800 q^{69} +1.21166 q^{70} -0.842329 q^{71} -4.29386 q^{72} +8.60525 q^{73} -1.20281 q^{74} -2.70072 q^{75} -5.54062 q^{76} +6.47392 q^{77} +13.4906 q^{78} +4.99850 q^{79} +1.00000 q^{80} -3.44432 q^{81} +10.3503 q^{82} -1.39402 q^{83} +3.27234 q^{84} +1.52346 q^{85} +12.2971 q^{86} -15.3330 q^{87} +5.34303 q^{88} +1.31290 q^{89} -4.29386 q^{90} -6.05247 q^{91} -2.17276 q^{92} -19.1708 q^{93} -12.4866 q^{94} -5.54062 q^{95} +2.70072 q^{96} -9.84430 q^{97} +5.53188 q^{98} -22.9422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.70072	−1.55926	−0.779629	−	0.626241i	$-0.784593\pi$
$3$	−2.70072	−1.55926	−0.779629	+	0.626241i	$0.784593\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.70072	1.10256
$7$	−1.21166	−0.457964	−0.228982	−	0.973431i	$-0.573540\pi$
$7$	−1.21166	−0.457964	−0.228982	+	0.973431i	$0.573540\pi$
$8$	−1.00000	−0.353553
$9$	4.29386	1.43129
$10$	−1.00000	−0.316228
$11$	−5.34303	−1.61098	−0.805492	−	0.592607i	$-0.798099\pi$
$11$	−5.34303	−1.61098	−0.805492	+	0.592607i	$0.798099\pi$
$12$	−2.70072	−0.779629
$13$	4.99519	1.38542	0.692709	−	0.721218i	$-0.256417\pi$
$13$	4.99519	1.38542	0.692709	+	0.721218i	$0.256417\pi$
$14$	1.21166	0.323829
$15$	−2.70072	−0.697322
$16$	1.00000	0.250000
$17$	1.52346	0.369493	0.184746	−	0.982786i	$-0.440854\pi$
$17$	1.52346	0.369493	0.184746	+	0.982786i	$0.440854\pi$
$18$	−4.29386	−1.01207
$19$	−5.54062	−1.27111	−0.635553	−	0.772057i	$-0.719228\pi$
$19$	−5.54062	−1.27111	−0.635553	+	0.772057i	$0.719228\pi$
$20$	1.00000	0.223607
$21$	3.27234	0.714084
$22$	5.34303	1.13914
$23$	−2.17276	−0.453051	−0.226526	−	0.974005i	$-0.572737\pi$
$23$	−2.17276	−0.453051	−0.226526	+	0.974005i	$0.572737\pi$
$24$	2.70072	0.551281
$25$	1.00000	0.200000
$26$	−4.99519	−0.979638
$27$	−3.49436	−0.672490
$28$	−1.21166	−0.228982
$29$	5.67740	1.05427	0.527133	−	0.849783i	$-0.323267\pi$
$29$	5.67740	1.05427	0.527133	+	0.849783i	$0.323267\pi$
$30$	2.70072	0.493081
$31$	7.09841	1.27491	0.637456	−	0.770487i	$-0.279987\pi$
$31$	7.09841	1.27491	0.637456	+	0.770487i	$0.279987\pi$
$32$	−1.00000	−0.176777
$33$	14.4300	2.51194
$34$	−1.52346	−0.261271
$35$	−1.21166	−0.204808
$36$	4.29386	0.715644
$37$	1.20281	0.197740	0.0988701	−	0.995100i	$-0.468477\pi$
$37$	1.20281	0.197740	0.0988701	+	0.995100i	$0.468477\pi$
$38$	5.54062	0.898807
$39$	−13.4906	−2.16022
$40$	−1.00000	−0.158114
$41$	−10.3503	−1.61644	−0.808220	−	0.588880i	$-0.799569\pi$
$41$	−10.3503	−1.61644	−0.808220	+	0.588880i	$0.799569\pi$
$42$	−3.27234	−0.504934
$43$	−12.2971	−1.87530	−0.937649	−	0.347585i	$-0.887002\pi$
$43$	−12.2971	−1.87530	−0.937649	+	0.347585i	$0.887002\pi$
$44$	−5.34303	−0.805492
$45$	4.29386	0.640091
$46$	2.17276	0.320356
$47$	12.4866	1.82136	0.910682	−	0.413108i	$-0.135557\pi$
$47$	12.4866	1.82136	0.910682	+	0.413108i	$0.135557\pi$
$48$	−2.70072	−0.389815
$49$	−5.53188	−0.790269
$50$	−1.00000	−0.141421
$51$	−4.11443	−0.576135
$52$	4.99519	0.692709
$53$	10.8717	1.49334	0.746668	−	0.665197i	$-0.231652\pi$
$53$	10.8717	1.49334	0.746668	+	0.665197i	$0.231652\pi$
$54$	3.49436	0.475522
$55$	−5.34303	−0.720454
$56$	1.21166	0.161915
$57$	14.9636	1.98198
$58$	−5.67740	−0.745479
$59$	3.79149	0.493611	0.246805	−	0.969065i	$-0.420619\pi$
$59$	3.79149	0.493611	0.246805	+	0.969065i	$0.420619\pi$
$60$	−2.70072	−0.348661
$61$	−6.62515	−0.848263	−0.424132	−	0.905601i	$-0.639421\pi$
$61$	−6.62515	−0.848263	−0.424132	+	0.905601i	$0.639421\pi$
$62$	−7.09841	−0.901499
$63$	−5.20270	−0.655478
$64$	1.00000	0.125000
$65$	4.99519	0.619577
$66$	−14.4300	−1.77621
$67$	−7.49485	−0.915641	−0.457821	−	0.889045i	$-0.651370\pi$
$67$	−7.49485	−0.915641	−0.457821	+	0.889045i	$0.651370\pi$
$68$	1.52346	0.184746
$69$	5.86800	0.706424
$70$	1.21166	0.144821
$71$	−0.842329	−0.0999661	−0.0499830	−	0.998750i	$-0.515917\pi$
$71$	−0.842329	−0.0999661	−0.0499830	+	0.998750i	$0.515917\pi$
$72$	−4.29386	−0.506037
$73$	8.60525	1.00717	0.503584	−	0.863946i	$-0.332014\pi$
$73$	8.60525	1.00717	0.503584	+	0.863946i	$0.332014\pi$
$74$	−1.20281	−0.139823
$75$	−2.70072	−0.311852
$76$	−5.54062	−0.635553
$77$	6.47392	0.737772
$78$	13.4906	1.52751
$79$	4.99850	0.562376	0.281188	−	0.959653i	$-0.409272\pi$
$79$	4.99850	0.562376	0.281188	+	0.959653i	$0.409272\pi$
$80$	1.00000	0.111803
$81$	−3.44432	−0.382703
$82$	10.3503	1.14300
$83$	−1.39402	−0.153013	−0.0765066	−	0.997069i	$-0.524377\pi$
$83$	−1.39402	−0.153013	−0.0765066	+	0.997069i	$0.524377\pi$
$84$	3.27234	0.357042
$85$	1.52346	0.165242
$86$	12.2971	1.32604
$87$	−15.3330	−1.64387
$88$	5.34303	0.569569
$89$	1.31290	0.139168	0.0695838	−	0.997576i	$-0.477833\pi$
$89$	1.31290	0.139168	0.0695838	+	0.997576i	$0.477833\pi$
$90$	−4.29386	−0.452613
$91$	−6.05247	−0.634471
$92$	−2.17276	−0.226526
$93$	−19.1708	−1.98792
$94$	−12.4866	−1.28790
$95$	−5.54062	−0.568456
$96$	2.70072	0.275641
$97$	−9.84430	−0.999537	−0.499769	−	0.866159i	$-0.666582\pi$
$97$	−9.84430	−0.999537	−0.499769	+	0.866159i	$0.666582\pi$
$98$	5.53188	0.558805
$99$	−22.9422	−2.30578
$100$	1.00000	0.100000
$101$	−0.695446	−0.0691994	−0.0345997	−	0.999401i	$-0.511016\pi$
$101$	−0.695446	−0.0691994	−0.0345997	+	0.999401i	$0.511016\pi$
$102$	4.11443	0.407389
$103$	5.37457	0.529572	0.264786	−	0.964307i	$-0.414699\pi$
$103$	5.37457	0.529572	0.264786	+	0.964307i	$0.414699\pi$
$104$	−4.99519	−0.489819
$105$	3.27234	0.319348
$106$	−10.8717	−1.05595
$107$	16.0568	1.55227	0.776135	−	0.630567i	$-0.217178\pi$
$107$	16.0568	1.55227	0.776135	+	0.630567i	$0.217178\pi$
$108$	−3.49436	−0.336245
$109$	3.85240	0.368993	0.184496	−	0.982833i	$-0.440935\pi$
$109$	3.85240	0.368993	0.184496	+	0.982833i	$0.440935\pi$
$110$	5.34303	0.509438
$111$	−3.24844	−0.308328
$112$	−1.21166	−0.114491
$113$	15.5965	1.46719	0.733597	−	0.679585i	$-0.237840\pi$
$113$	15.5965	1.46719	0.733597	+	0.679585i	$0.237840\pi$
$114$	−14.9636	−1.40147
$115$	−2.17276	−0.202611
$116$	5.67740	0.527133
$117$	21.4487	1.98293
$118$	−3.79149	−0.349035
$119$	−1.84591	−0.169214
$120$	2.70072	0.246540
$121$	17.5479	1.59527
$122$	6.62515	0.599813
$123$	27.9531	2.52045
$124$	7.09841	0.637456
$125$	1.00000	0.0894427
$126$	5.20270	0.463493
$127$	9.13270	0.810396	0.405198	−	0.914229i	$-0.367203\pi$
$127$	9.13270	0.810396	0.405198	+	0.914229i	$0.367203\pi$
$128$	−1.00000	−0.0883883
$129$	33.2111	2.92407
$130$	−4.99519	−0.438107
$131$	4.16835	0.364190	0.182095	−	0.983281i	$-0.441712\pi$
$131$	4.16835	0.364190	0.182095	+	0.983281i	$0.441712\pi$
$132$	14.4300	1.25597
$133$	6.71334	0.582120
$134$	7.49485	0.647456
$135$	−3.49436	−0.300746
$136$	−1.52346	−0.130635
$137$	7.64930	0.653524	0.326762	−	0.945107i	$-0.394042\pi$
$137$	7.64930	0.653524	0.326762	+	0.945107i	$0.394042\pi$
$138$	−5.86800	−0.499517
$139$	−19.2278	−1.63088	−0.815441	−	0.578840i	$-0.803506\pi$
$139$	−19.2278	−1.63088	−0.815441	+	0.578840i	$0.803506\pi$
$140$	−1.21166	−0.102404
$141$	−33.7229	−2.83998
$142$	0.842329	0.0706867
$143$	−26.6895	−2.23188
$144$	4.29386	0.357822
$145$	5.67740	0.471482
$146$	−8.60525	−0.712175
$147$	14.9400	1.23223
$148$	1.20281	0.0988701
$149$	−0.566681	−0.0464243	−0.0232122	−	0.999731i	$-0.507389\pi$
$149$	−0.566681	−0.0464243	−0.0232122	+	0.999731i	$0.507389\pi$
$150$	2.70072	0.220512
$151$	−8.98225	−0.730965	−0.365483	−	0.930818i	$-0.619096\pi$
$151$	−8.98225	−0.730965	−0.365483	+	0.930818i	$0.619096\pi$
$152$	5.54062	0.449404
$153$	6.54152	0.528851
$154$	−6.47392	−0.521684
$155$	7.09841	0.570158
$156$	−13.4906	−1.08011
$157$	−21.7627	−1.73685	−0.868426	−	0.495819i	$-0.834868\pi$
$157$	−21.7627	−1.73685	−0.868426	+	0.495819i	$0.834868\pi$
$158$	−4.99850	−0.397660
$159$	−29.3612	−2.32850
$160$	−1.00000	−0.0790569
$161$	2.63264	0.207481
$162$	3.44432	0.270612
$163$	12.0025	0.940110	0.470055	−	0.882637i	$-0.344234\pi$
$163$	12.0025	0.940110	0.470055	+	0.882637i	$0.344234\pi$
$164$	−10.3503	−0.808220
$165$	14.4300	1.12337
$166$	1.39402	0.108197
$167$	17.3770	1.34467	0.672337	−	0.740245i	$-0.265290\pi$
$167$	17.3770	1.34467	0.672337	+	0.740245i	$0.265290\pi$
$168$	−3.27234	−0.252467
$169$	11.9520	0.919381
$170$	−1.52346	−0.116844
$171$	−23.7907	−1.81932
$172$	−12.2971	−0.937649
$173$	−5.25782	−0.399745	−0.199872	−	0.979822i	$-0.564053\pi$
$173$	−5.25782	−0.399745	−0.199872	+	0.979822i	$0.564053\pi$
$174$	15.3330	1.16239
$175$	−1.21166	−0.0915928
$176$	−5.34303	−0.402746
$177$	−10.2397	−0.769667
$178$	−1.31290	−0.0984063
$179$	7.13480	0.533280	0.266640	−	0.963796i	$-0.414087\pi$
$179$	7.13480	0.533280	0.266640	+	0.963796i	$0.414087\pi$
$180$	4.29386	0.320046
$181$	−14.3555	−1.06704	−0.533520	−	0.845788i	$-0.679131\pi$
$181$	−14.3555	−1.06704	−0.533520	+	0.845788i	$0.679131\pi$
$182$	6.05247	0.448639
$183$	17.8926	1.32266
$184$	2.17276	0.160178
$185$	1.20281	0.0884321
$186$	19.1708	1.40567
$187$	−8.13988	−0.595247
$188$	12.4866	0.910682
$189$	4.23397	0.307976
$190$	5.54062	0.401959
$191$	−21.8421	−1.58044	−0.790220	−	0.612823i	$-0.790034\pi$
$191$	−21.8421	−1.58044	−0.790220	+	0.612823i	$0.790034\pi$
$192$	−2.70072	−0.194907
$193$	−23.8668	−1.71797	−0.858986	−	0.511999i	$-0.828905\pi$
$193$	−23.8668	−1.71797	−0.858986	+	0.511999i	$0.828905\pi$
$194$	9.84430	0.706780
$195$	−13.4906	−0.966082
$196$	−5.53188	−0.395135
$197$	−15.7907	−1.12504	−0.562519	−	0.826784i	$-0.690168\pi$
$197$	−15.7907	−1.12504	−0.562519	+	0.826784i	$0.690168\pi$
$198$	22.9422	1.63043
$199$	−5.88423	−0.417122	−0.208561	−	0.978009i	$-0.566878\pi$
$199$	−5.88423	−0.417122	−0.208561	+	0.978009i	$0.566878\pi$
$200$	−1.00000	−0.0707107
$201$	20.2414	1.42772
$202$	0.695446	0.0489314
$203$	−6.87907	−0.482816
$204$	−4.11443	−0.288068
$205$	−10.3503	−0.722894
$206$	−5.37457	−0.374464
$207$	−9.32953	−0.648447
$208$	4.99519	0.346354
$209$	29.6037	2.04773
$210$	−3.27234	−0.225813
$211$	21.9315	1.50983	0.754914	−	0.655823i	$-0.227678\pi$
$211$	21.9315	1.50983	0.754914	+	0.655823i	$0.227678\pi$
$212$	10.8717	0.746668
$213$	2.27489	0.155873
$214$	−16.0568	−1.09762
$215$	−12.2971	−0.838658
$216$	3.49436	0.237761
$217$	−8.60085	−0.583864
$218$	−3.85240	−0.260917
$219$	−23.2403	−1.57044
$220$	−5.34303	−0.360227
$221$	7.60997	0.511902
$222$	3.24844	0.218021
$223$	−5.44147	−0.364388	−0.182194	−	0.983263i	$-0.558320\pi$
$223$	−5.44147	−0.364388	−0.182194	+	0.983263i	$0.558320\pi$
$224$	1.21166	0.0809573
$225$	4.29386	0.286258
$226$	−15.5965	−1.03746
$227$	1.13806	0.0755356	0.0377678	−	0.999287i	$-0.487975\pi$
$227$	1.13806	0.0755356	0.0377678	+	0.999287i	$0.487975\pi$
$228$	14.9636	0.990991
$229$	−3.68354	−0.243415	−0.121708	−	0.992566i	$-0.538837\pi$
$229$	−3.68354	−0.243415	−0.121708	+	0.992566i	$0.538837\pi$
$230$	2.17276	0.143267
$231$	−17.4842	−1.15038
$232$	−5.67740	−0.372739
$233$	−6.60386	−0.432633	−0.216317	−	0.976323i	$-0.569404\pi$
$233$	−6.60386	−0.432633	−0.216317	+	0.976323i	$0.569404\pi$
$234$	−21.4487	−1.40214
$235$	12.4866	0.814539
$236$	3.79149	0.246805
$237$	−13.4995	−0.876889
$238$	1.84591	0.119653
$239$	−20.7947	−1.34510	−0.672550	−	0.740052i	$-0.734801\pi$
$239$	−20.7947	−1.34510	−0.672550	+	0.740052i	$0.734801\pi$
$240$	−2.70072	−0.174330
$241$	−1.42726	−0.0919379	−0.0459689	−	0.998943i	$-0.514638\pi$
$241$	−1.42726	−0.0919379	−0.0459689	+	0.998943i	$0.514638\pi$
$242$	−17.5479	−1.12802
$243$	19.7852	1.26922
$244$	−6.62515	−0.424132
$245$	−5.53188	−0.353419
$246$	−27.9531	−1.78223
$247$	−27.6765	−1.76101
$248$	−7.09841	−0.450749
$249$	3.76484	0.238587
$250$	−1.00000	−0.0632456
$251$	−18.9136	−1.19382	−0.596909	−	0.802309i	$-0.703605\pi$
$251$	−18.9136	−1.19382	−0.596909	+	0.802309i	$0.703605\pi$
$252$	−5.20270	−0.327739
$253$	11.6091	0.729858
$254$	−9.13270	−0.573036
$255$	−4.11443	−0.257655
$256$	1.00000	0.0625000
$257$	−14.9072	−0.929887	−0.464944	−	0.885340i	$-0.653925\pi$
$257$	−14.9072	−0.929887	−0.464944	+	0.885340i	$0.653925\pi$
$258$	−33.2111	−2.06763
$259$	−1.45739	−0.0905578
$260$	4.99519	0.309789
$261$	24.3780	1.50896
$262$	−4.16835	−0.257521
$263$	12.2108	0.752948	0.376474	−	0.926427i	$-0.377136\pi$
$263$	12.2108	0.752948	0.376474	+	0.926427i	$0.377136\pi$
$264$	−14.4300	−0.888105
$265$	10.8717	0.667840
$266$	−6.71334	−0.411621
$267$	−3.54578	−0.216998
$268$	−7.49485	−0.457821
$269$	−27.5270	−1.67835	−0.839177	−	0.543859i	$-0.816963\pi$
$269$	−27.5270	−1.67835	−0.839177	+	0.543859i	$0.816963\pi$
$270$	3.49436	0.212660
$271$	13.4256	0.815548	0.407774	−	0.913083i	$-0.366305\pi$
$271$	13.4256	0.815548	0.407774	+	0.913083i	$0.366305\pi$
$272$	1.52346	0.0923732
$273$	16.3460	0.989304
$274$	−7.64930	−0.462111
$275$	−5.34303	−0.322197
$276$	5.86800	0.353212
$277$	10.3268	0.620477	0.310238	−	0.950659i	$-0.399591\pi$
$277$	10.3268	0.620477	0.310238	+	0.950659i	$0.399591\pi$
$278$	19.2278	1.15321
$279$	30.4796	1.82477
$280$	1.21166	0.0724104
$281$	21.9607	1.31006	0.655032	−	0.755601i	$-0.272655\pi$
$281$	21.9607	1.31006	0.655032	+	0.755601i	$0.272655\pi$
$282$	33.7229	2.00817
$283$	17.6226	1.04755	0.523777	−	0.851856i	$-0.324523\pi$
$283$	17.6226	1.04755	0.523777	+	0.851856i	$0.324523\pi$
$284$	−0.842329	−0.0499830
$285$	14.9636	0.886369
$286$	26.6895	1.57818
$287$	12.5410	0.740271
$288$	−4.29386	−0.253018
$289$	−14.6791	−0.863475
$290$	−5.67740	−0.333388
$291$	26.5867	1.55854
$292$	8.60525	0.503584
$293$	0.289555	0.0169160	0.00845800	−	0.999964i	$-0.497308\pi$
$293$	0.289555	0.0169160	0.00845800	+	0.999964i	$0.497308\pi$
$294$	−14.9400	−0.871321
$295$	3.79149	0.220749
$296$	−1.20281	−0.0699117
$297$	18.6705	1.08337
$298$	0.566681	0.0328270
$299$	−10.8533	−0.627665
$300$	−2.70072	−0.155926
$301$	14.8999	0.858818
$302$	8.98225	0.516870
$303$	1.87820	0.107900
$304$	−5.54062	−0.317776
$305$	−6.62515	−0.379355
$306$	−6.54152	−0.373954
$307$	−27.4609	−1.56728	−0.783639	−	0.621216i	$-0.786639\pi$
$307$	−27.4609	−1.56728	−0.783639	+	0.621216i	$0.786639\pi$
$308$	6.47392	0.368886
$309$	−14.5152	−0.825740
$310$	−7.09841	−0.403163
$311$	0.821358	0.0465749	0.0232875	−	0.999729i	$-0.492587\pi$
$311$	0.821358	0.0465749	0.0232875	+	0.999729i	$0.492587\pi$
$312$	13.4906	0.763755
$313$	−7.59705	−0.429411	−0.214705	−	0.976679i	$-0.568879\pi$
$313$	−7.59705	−0.429411	−0.214705	+	0.976679i	$0.568879\pi$
$314$	21.7627	1.22814
$315$	−5.20270	−0.293139
$316$	4.99850	0.281188
$317$	−21.7001	−1.21880	−0.609400	−	0.792863i	$-0.708590\pi$
$317$	−21.7001	−1.21880	−0.609400	+	0.792863i	$0.708590\pi$
$318$	29.3612	1.64650
$319$	−30.3345	−1.69841
$320$	1.00000	0.0559017
$321$	−43.3649	−2.42039
$322$	−2.63264	−0.146711
$323$	−8.44090	−0.469664
$324$	−3.44432	−0.191351
$325$	4.99519	0.277083
$326$	−12.0025	−0.664758
$327$	−10.4042	−0.575355
$328$	10.3503	0.571498
$329$	−15.1295	−0.834119
$330$	−14.4300	−0.794345
$331$	16.9939	0.934070	0.467035	−	0.884239i	$-0.345322\pi$
$331$	16.9939	0.934070	0.467035	+	0.884239i	$0.345322\pi$
$332$	−1.39402	−0.0765066
$333$	5.16469	0.283023
$334$	−17.3770	−0.950828
$335$	−7.49485	−0.409487
$336$	3.27234	0.178521
$337$	−23.2625	−1.26719	−0.633595	−	0.773665i	$-0.718422\pi$
$337$	−23.2625	−1.26719	−0.633595	+	0.773665i	$0.718422\pi$
$338$	−11.9520	−0.650101
$339$	−42.1217	−2.28774
$340$	1.52346	0.0826211
$341$	−37.9270	−2.05386
$342$	23.7907	1.28645
$343$	15.1844	0.819878
$344$	12.2971	0.663018
$345$	5.86800	0.315922
$346$	5.25782	0.282662
$347$	8.73692	0.469022	0.234511	−	0.972113i	$-0.424651\pi$
$347$	8.73692	0.469022	0.234511	+	0.972113i	$0.424651\pi$
$348$	−15.3330	−0.821937
$349$	−24.1059	−1.29036	−0.645180	−	0.764031i	$-0.723217\pi$
$349$	−24.1059	−1.29036	−0.645180	+	0.764031i	$0.723217\pi$
$350$	1.21166	0.0647659
$351$	−17.4550	−0.931679
$352$	5.34303	0.284784
$353$	−14.6510	−0.779793	−0.389896	−	0.920859i	$-0.627489\pi$
$353$	−14.6510	−0.779793	−0.389896	+	0.920859i	$0.627489\pi$
$354$	10.2397	0.544236
$355$	−0.842329	−0.0447062
$356$	1.31290	0.0695838
$357$	4.98528	0.263849
$358$	−7.13480	−0.377086
$359$	−3.20140	−0.168963	−0.0844816	−	0.996425i	$-0.526923\pi$
$359$	−3.20140	−0.168963	−0.0844816	+	0.996425i	$0.526923\pi$
$360$	−4.29386	−0.226307
$361$	11.6985	0.615709
$362$	14.3555	0.754511
$363$	−47.3920	−2.48743
$364$	−6.05247	−0.317235
$365$	8.60525	0.450419
$366$	−17.8926	−0.935263
$367$	−34.4463	−1.79808	−0.899042	−	0.437862i	$-0.855736\pi$
$367$	−34.4463	−1.79808	−0.899042	+	0.437862i	$0.855736\pi$
$368$	−2.17276	−0.113263
$369$	−44.4427	−2.31359
$370$	−1.20281	−0.0625309
$371$	−13.1727	−0.683894
$372$	−19.1708	−0.993959
$373$	9.02476	0.467284	0.233642	−	0.972323i	$-0.424936\pi$
$373$	9.02476	0.467284	0.233642	+	0.972323i	$0.424936\pi$
$374$	8.13988	0.420903
$375$	−2.70072	−0.139464
$376$	−12.4866	−0.643950
$377$	28.3597	1.46060
$378$	−4.23397	−0.217772
$379$	−36.0474	−1.85163	−0.925815	−	0.377977i	$-0.876620\pi$
$379$	−36.0474	−1.85163	−0.925815	+	0.377977i	$0.876620\pi$
$380$	−5.54062	−0.284228
$381$	−24.6648	−1.26362
$382$	21.8421	1.11754
$383$	−9.20022	−0.470109	−0.235055	−	0.971982i	$-0.575527\pi$
$383$	−9.20022	−0.470109	−0.235055	+	0.971982i	$0.575527\pi$
$384$	2.70072	0.137820
$385$	6.47392	0.329942
$386$	23.8668	1.21479
$387$	−52.8023	−2.68409
$388$	−9.84430	−0.499769
$389$	−18.2536	−0.925494	−0.462747	−	0.886490i	$-0.653136\pi$
$389$	−18.2536	−0.925494	−0.462747	+	0.886490i	$0.653136\pi$
$390$	13.4906	0.683123
$391$	−3.31011	−0.167399
$392$	5.53188	0.279402
$393$	−11.2575	−0.567867
$394$	15.7907	0.795522
$395$	4.99850	0.251502
$396$	−22.9422	−1.15289
$397$	−10.5197	−0.527970	−0.263985	−	0.964527i	$-0.585037\pi$
$397$	−10.5197	−0.527970	−0.263985	+	0.964527i	$0.585037\pi$
$398$	5.88423	0.294950
$399$	−18.1308	−0.907676
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−20.2414	−1.00955
$403$	35.4579	1.76629
$404$	−0.695446	−0.0345997
$405$	−3.44432	−0.171150
$406$	6.87907	0.341402
$407$	−6.42663	−0.318556
$408$	4.11443	0.203694
$409$	−2.94928	−0.145833	−0.0729163	−	0.997338i	$-0.523231\pi$
$409$	−2.94928	−0.145833	−0.0729163	+	0.997338i	$0.523231\pi$
$410$	10.3503	0.511163
$411$	−20.6586	−1.01901
$412$	5.37457	0.264786
$413$	−4.59400	−0.226056
$414$	9.32953	0.458521
$415$	−1.39402	−0.0684296
$416$	−4.99519	−0.244909
$417$	51.9289	2.54297
$418$	−29.6037	−1.44796
$419$	−0.557921	−0.0272562	−0.0136281	−	0.999907i	$-0.504338\pi$
$419$	−0.557921	−0.0272562	−0.0136281	+	0.999907i	$0.504338\pi$
$420$	3.27234	0.159674
$421$	−37.7997	−1.84225	−0.921123	−	0.389271i	$-0.872727\pi$
$421$	−37.7997	−1.84225	−0.921123	+	0.389271i	$0.872727\pi$
$422$	−21.9315	−1.06761
$423$	53.6160	2.60690
$424$	−10.8717	−0.527974
$425$	1.52346	0.0738986
$426$	−2.27489	−0.110219
$427$	8.02742	0.388474
$428$	16.0568	0.776135
$429$	72.0806	3.48008
$430$	12.2971	0.593021
$431$	4.48691	0.216127	0.108063	−	0.994144i	$-0.465535\pi$
$431$	4.48691	0.216127	0.108063	+	0.994144i	$0.465535\pi$
$432$	−3.49436	−0.168122
$433$	−5.08697	−0.244464	−0.122232	−	0.992502i	$-0.539005\pi$
$433$	−5.08697	−0.244464	−0.122232	+	0.992502i	$0.539005\pi$
$434$	8.60085	0.412854
$435$	−15.3330	−0.735163
$436$	3.85240	0.184496
$437$	12.0384	0.575876
$438$	23.2403	1.11047
$439$	14.0287	0.669555	0.334777	−	0.942297i	$-0.391339\pi$
$439$	14.0287	0.669555	0.334777	+	0.942297i	$0.391339\pi$
$440$	5.34303	0.254719
$441$	−23.7532	−1.13110
$442$	−7.60997	−0.361969
$443$	−38.4453	−1.82659	−0.913296	−	0.407297i	$-0.866471\pi$
$443$	−38.4453	−1.82659	−0.913296	+	0.407297i	$0.866471\pi$
$444$	−3.24844	−0.154164
$445$	1.31290	0.0622376
$446$	5.44147	0.257661
$447$	1.53044	0.0723875
$448$	−1.21166	−0.0572455
$449$	−26.4681	−1.24911	−0.624554	−	0.780981i	$-0.714719\pi$
$449$	−26.4681	−1.24911	−0.624554	+	0.780981i	$0.714719\pi$
$450$	−4.29386	−0.202415
$451$	55.3018	2.60406
$452$	15.5965	0.733597
$453$	24.2585	1.13976
$454$	−1.13806	−0.0534117
$455$	−6.05247	−0.283744
$456$	−14.9636	−0.700737
$457$	−37.0750	−1.73429	−0.867147	−	0.498052i	$-0.834049\pi$
$457$	−37.0750	−1.73429	−0.867147	+	0.498052i	$0.834049\pi$
$458$	3.68354	0.172121
$459$	−5.32351	−0.248480
$460$	−2.17276	−0.101305
$461$	−20.4921	−0.954413	−0.477207	−	0.878791i	$-0.658351\pi$
$461$	−20.4921	−0.954413	−0.477207	+	0.878791i	$0.658351\pi$
$462$	17.4842	0.813440
$463$	−8.88342	−0.412847	−0.206424	−	0.978463i	$-0.566183\pi$
$463$	−8.88342	−0.412847	−0.206424	+	0.978463i	$0.566183\pi$
$464$	5.67740	0.263567
$465$	−19.1708	−0.889024
$466$	6.60386	0.305918
$467$	−8.47376	−0.392119	−0.196059	−	0.980592i	$-0.562815\pi$
$467$	−8.47376	−0.392119	−0.196059	+	0.980592i	$0.562815\pi$
$468$	21.4487	0.991466
$469$	9.08119	0.419331
$470$	−12.4866	−0.575966
$471$	58.7748	2.70820
$472$	−3.79149	−0.174518
$473$	65.7040	3.02107
$474$	13.4995	0.620054
$475$	−5.54062	−0.254221
$476$	−1.84591	−0.0846072
$477$	46.6814	2.13739
$478$	20.7947	0.951130
$479$	−0.931984	−0.0425834	−0.0212917	−	0.999773i	$-0.506778\pi$
$479$	−0.931984	−0.0425834	−0.0212917	+	0.999773i	$0.506778\pi$
$480$	2.70072	0.123270
$481$	6.00825	0.273953
$482$	1.42726	0.0650099
$483$	−7.11001	−0.323517
$484$	17.5479	0.797634
$485$	−9.84430	−0.447007
$486$	−19.7852	−0.897476
$487$	16.4234	0.744215	0.372108	−	0.928190i	$-0.378635\pi$
$487$	16.4234	0.744215	0.372108	+	0.928190i	$0.378635\pi$
$488$	6.62515	0.299906
$489$	−32.4154	−1.46588
$490$	5.53188	0.249905
$491$	10.0951	0.455586	0.227793	−	0.973710i	$-0.426849\pi$
$491$	10.0951	0.455586	0.227793	+	0.973710i	$0.426849\pi$
$492$	27.9531	1.26022
$493$	8.64928	0.389544
$494$	27.6765	1.24522
$495$	−22.9422	−1.03118
$496$	7.09841	0.318728
$497$	1.02062	0.0457809
$498$	−3.76484	−0.168707
$499$	−22.6531	−1.01409	−0.507045	−	0.861920i	$-0.669262\pi$
$499$	−22.6531	−1.01409	−0.507045	+	0.861920i	$0.669262\pi$
$500$	1.00000	0.0447214
$501$	−46.9304	−2.09670
$502$	18.9136	0.844157
$503$	−4.00867	−0.178738	−0.0893688	−	0.995999i	$-0.528485\pi$
$503$	−4.00867	−0.178738	−0.0893688	+	0.995999i	$0.528485\pi$
$504$	5.20270	0.231747
$505$	−0.695446	−0.0309469
$506$	−11.6091	−0.516088
$507$	−32.2788	−1.43355
$508$	9.13270	0.405198
$509$	10.3818	0.460164	0.230082	−	0.973171i	$-0.426101\pi$
$509$	10.3818	0.460164	0.230082	+	0.973171i	$0.426101\pi$
$510$	4.11443	0.182190
$511$	−10.4266	−0.461247
$512$	−1.00000	−0.0441942
$513$	19.3609	0.854805
$514$	14.9072	0.657529
$515$	5.37457	0.236832
$516$	33.2111	1.46204
$517$	−66.7165	−2.93419
$518$	1.45739	0.0640341
$519$	14.1999	0.623305
$520$	−4.99519	−0.219054
$521$	14.6708	0.642740	0.321370	−	0.946954i	$-0.395857\pi$
$521$	14.6708	0.642740	0.321370	+	0.946954i	$0.395857\pi$
$522$	−24.3780	−1.06699
$523$	4.56784	0.199738	0.0998688	−	0.995001i	$-0.468158\pi$
$523$	4.56784	0.199738	0.0998688	+	0.995001i	$0.468158\pi$
$524$	4.16835	0.182095
$525$	3.27234	0.142817
$526$	−12.2108	−0.532415
$527$	10.8141	0.471071
$528$	14.4300	0.627985
$529$	−18.2791	−0.794745
$530$	−10.8717	−0.472234
$531$	16.2802	0.706499
$532$	6.71334	0.291060
$533$	−51.7016	−2.23944
$534$	3.54578	0.153441
$535$	16.0568	0.694196
$536$	7.49485	0.323728
$537$	−19.2691	−0.831521
$538$	27.5270	1.18677
$539$	29.5570	1.27311
$540$	−3.49436	−0.150373
$541$	28.5670	1.22819	0.614096	−	0.789231i	$-0.289521\pi$
$541$	28.5670	1.22819	0.614096	+	0.789231i	$0.289521\pi$
$542$	−13.4256	−0.576680
$543$	38.7702	1.66379
$544$	−1.52346	−0.0653177
$545$	3.85240	0.165019
$546$	−16.3460	−0.699544
$547$	31.6764	1.35439	0.677193	−	0.735805i	$-0.263196\pi$
$547$	31.6764	1.35439	0.677193	+	0.735805i	$0.263196\pi$
$548$	7.64930	0.326762
$549$	−28.4475	−1.21411
$550$	5.34303	0.227827
$551$	−31.4563	−1.34008
$552$	−5.86800	−0.249759
$553$	−6.05648	−0.257548
$554$	−10.3268	−0.438743
$555$	−3.24844	−0.137889
$556$	−19.2278	−0.815441
$557$	−42.9003	−1.81775	−0.908873	−	0.417073i	$-0.863056\pi$
$557$	−42.9003	−1.81775	−0.908873	+	0.417073i	$0.863056\pi$
$558$	−30.4796	−1.29030
$559$	−61.4266	−2.59807
$560$	−1.21166	−0.0512019
$561$	21.9835	0.928144
$562$	−21.9607	−0.926355
$563$	−1.50822	−0.0635640	−0.0317820	−	0.999495i	$-0.510118\pi$
$563$	−1.50822	−0.0635640	−0.0317820	+	0.999495i	$0.510118\pi$
$564$	−33.7229	−1.41999
$565$	15.5965	0.656149
$566$	−17.6226	−0.740732
$567$	4.17334	0.175264
$568$	0.842329	0.0353434
$569$	20.0853	0.842019	0.421009	−	0.907056i	$-0.361676\pi$
$569$	20.0853	0.842019	0.421009	+	0.907056i	$0.361676\pi$
$570$	−14.9636	−0.626758
$571$	−11.2142	−0.469298	−0.234649	−	0.972080i	$-0.575394\pi$
$571$	−11.2142	−0.469298	−0.234649	+	0.972080i	$0.575394\pi$
$572$	−26.6895	−1.11594
$573$	58.9894	2.46432
$574$	−12.5410	−0.523451
$575$	−2.17276	−0.0906103
$576$	4.29386	0.178911
$577$	31.6646	1.31821	0.659107	−	0.752049i	$-0.270934\pi$
$577$	31.6646	1.31821	0.659107	+	0.752049i	$0.270934\pi$
$578$	14.6791	0.610569
$579$	64.4575	2.67876
$580$	5.67740	0.235741
$581$	1.68907	0.0700745
$582$	−26.5867	−1.10205
$583$	−58.0875	−2.40574
$584$	−8.60525	−0.356088
$585$	21.4487	0.886794
$586$	−0.289555	−0.0119614
$587$	−18.3157	−0.755971	−0.377986	−	0.925811i	$-0.623383\pi$
$587$	−18.3157	−0.755971	−0.377986	+	0.925811i	$0.623383\pi$
$588$	14.9400	0.616117
$589$	−39.3296	−1.62055
$590$	−3.79149	−0.156093
$591$	42.6461	1.75423
$592$	1.20281	0.0494350
$593$	31.9549	1.31223	0.656115	−	0.754661i	$-0.272199\pi$
$593$	31.9549	1.31223	0.656115	+	0.754661i	$0.272199\pi$
$594$	−18.6705	−0.766058
$595$	−1.84591	−0.0756750
$596$	−0.566681	−0.0232122
$597$	15.8916	0.650401
$598$	10.8533	0.443826
$599$	27.3376	1.11698	0.558491	−	0.829510i	$-0.311380\pi$
$599$	27.3376	1.11698	0.558491	+	0.829510i	$0.311380\pi$
$600$	2.70072	0.110256
$601$	19.3201	0.788083	0.394041	−	0.919093i	$-0.371077\pi$
$601$	19.3201	0.788083	0.394041	+	0.919093i	$0.371077\pi$
$602$	−14.8999	−0.607276
$603$	−32.1819	−1.31055
$604$	−8.98225	−0.365483
$605$	17.5479	0.713425
$606$	−1.87820	−0.0762967
$607$	0.428965	0.0174112	0.00870558	−	0.999962i	$-0.497229\pi$
$607$	0.428965	0.0174112	0.00870558	+	0.999962i	$0.497229\pi$
$608$	5.54062	0.224702
$609$	18.5784	0.752835
$610$	6.62515	0.268244
$611$	62.3732	2.52335
$612$	6.54152	0.264425
$613$	16.8503	0.680579	0.340289	−	0.940321i	$-0.389475\pi$
$613$	16.8503	0.680579	0.340289	+	0.940321i	$0.389475\pi$
$614$	27.4609	1.10823
$615$	27.9531	1.12718
$616$	−6.47392	−0.260842
$617$	−12.1060	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$617$	−12.1060	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$618$	14.5152	0.583886
$619$	15.9974	0.642991	0.321495	−	0.946911i	$-0.395815\pi$
$619$	15.9974	0.642991	0.321495	+	0.946911i	$0.395815\pi$
$620$	7.09841	0.285079
$621$	7.59239	0.304672
$622$	−0.821358	−0.0329335
$623$	−1.59079	−0.0637337
$624$	−13.4906	−0.540056
$625$	1.00000	0.0400000
$626$	7.59705	0.303639
$627$	−79.9511	−3.19294
$628$	−21.7627	−0.868426
$629$	1.83243	0.0730636
$630$	5.20270	0.207280
$631$	23.0677	0.918312	0.459156	−	0.888356i	$-0.348152\pi$
$631$	23.0677	0.918312	0.459156	+	0.888356i	$0.348152\pi$
$632$	−4.99850	−0.198830
$633$	−59.2308	−2.35421
$634$	21.7001	0.861822
$635$	9.13270	0.362420
$636$	−29.3612	−1.16425
$637$	−27.6328	−1.09485
$638$	30.3345	1.20095
$639$	−3.61685	−0.143080
$640$	−1.00000	−0.0395285
$641$	15.9870	0.631449	0.315725	−	0.948851i	$-0.397752\pi$
$641$	15.9870	0.631449	0.315725	+	0.948851i	$0.397752\pi$
$642$	43.3649	1.71147
$643$	−13.2518	−0.522598	−0.261299	−	0.965258i	$-0.584151\pi$
$643$	−13.2518	−0.522598	−0.261299	+	0.965258i	$0.584151\pi$
$644$	2.63264	0.103741
$645$	33.2111	1.30769
$646$	8.44090	0.332103
$647$	18.5071	0.727589	0.363794	−	0.931479i	$-0.381481\pi$
$647$	18.5071	0.727589	0.363794	+	0.931479i	$0.381481\pi$
$648$	3.44432	0.135306
$649$	−20.2581	−0.795198
$650$	−4.99519	−0.195928
$651$	23.2284	0.910394
$652$	12.0025	0.470055
$653$	28.5627	1.11775	0.558873	−	0.829253i	$-0.311234\pi$
$653$	28.5627	1.11775	0.558873	+	0.829253i	$0.311234\pi$
$654$	10.4042	0.406838
$655$	4.16835	0.162871
$656$	−10.3503	−0.404110
$657$	36.9498	1.44155
$658$	15.1295	0.589811
$659$	−33.8891	−1.32013	−0.660066	−	0.751208i	$-0.729472\pi$
$659$	−33.8891	−1.32013	−0.660066	+	0.751208i	$0.729472\pi$
$660$	14.4300	0.561687
$661$	40.1703	1.56244	0.781222	−	0.624253i	$-0.214596\pi$
$661$	40.1703	1.56244	0.781222	+	0.624253i	$0.214596\pi$
$662$	−16.9939	−0.660487
$663$	−20.5524	−0.798187
$664$	1.39402	0.0540983
$665$	6.71334	0.260332
$666$	−5.16469	−0.200128
$667$	−12.3356	−0.477637
$668$	17.3770	0.672337
$669$	14.6959	0.568175
$670$	7.49485	0.289551
$671$	35.3984	1.36654
$672$	−3.27234	−0.126233
$673$	−31.7673	−1.22454	−0.612271	−	0.790648i	$-0.709744\pi$
$673$	−31.7673	−1.22454	−0.612271	+	0.790648i	$0.709744\pi$
$674$	23.2625	0.896039
$675$	−3.49436	−0.134498
$676$	11.9520	0.459691
$677$	−30.9474	−1.18941	−0.594703	−	0.803945i	$-0.702731\pi$
$677$	−30.9474	−1.18941	−0.594703	+	0.803945i	$0.702731\pi$
$678$	42.1217	1.61767
$679$	11.9279	0.457752
$680$	−1.52346	−0.0584220
$681$	−3.07357	−0.117780
$682$	37.9270	1.45230
$683$	28.9294	1.10695	0.553477	−	0.832865i	$-0.313301\pi$
$683$	28.9294	1.10695	0.553477	+	0.832865i	$0.313301\pi$
$684$	−23.7907	−0.909659
$685$	7.64930	0.292265
$686$	−15.1844	−0.579742
$687$	9.94820	0.379548
$688$	−12.2971	−0.468824
$689$	54.3060	2.06889
$690$	−5.86800	−0.223391
$691$	−35.4006	−1.34670	−0.673352	−	0.739322i	$-0.735146\pi$
$691$	−35.4006	−1.34670	−0.673352	+	0.739322i	$0.735146\pi$
$692$	−5.25782	−0.199872
$693$	27.7981	1.05596
$694$	−8.73692	−0.331649
$695$	−19.2278	−0.729353
$696$	15.3330	0.581197
$697$	−15.7682	−0.597263
$698$	24.1059	0.912422
$699$	17.8352	0.674588
$700$	−1.21166	−0.0457964
$701$	6.80979	0.257202	0.128601	−	0.991696i	$-0.458951\pi$
$701$	6.80979	0.257202	0.128601	+	0.991696i	$0.458951\pi$
$702$	17.4550	0.658796
$703$	−6.66429	−0.251349
$704$	−5.34303	−0.201373
$705$	−33.7229	−1.27008
$706$	14.6510	0.551397
$707$	0.842642	0.0316908
$708$	−10.2397	−0.384833
$709$	1.45240	0.0545460	0.0272730	−	0.999628i	$-0.491318\pi$
$709$	1.45240	0.0545460	0.0272730	+	0.999628i	$0.491318\pi$
$710$	0.842329	0.0316121
$711$	21.4629	0.804922
$712$	−1.31290	−0.0492031
$713$	−15.4231	−0.577601
$714$	−4.98528	−0.186569
$715$	−26.6895	−0.998129
$716$	7.13480	0.266640
$717$	56.1607	2.09736
$718$	3.20140	0.119475
$719$	−21.0938	−0.786667	−0.393334	−	0.919396i	$-0.628678\pi$
$719$	−21.0938	−0.786667	−0.393334	+	0.919396i	$0.628678\pi$
$720$	4.29386	0.160023
$721$	−6.51214	−0.242525
$722$	−11.6985	−0.435372
$723$	3.85462	0.143355
$724$	−14.3555	−0.533520
$725$	5.67740	0.210853
$726$	47.3920	1.75888
$727$	−24.9938	−0.926970	−0.463485	−	0.886105i	$-0.653401\pi$
$727$	−24.9938	−0.926970	−0.463485	+	0.886105i	$0.653401\pi$
$728$	6.05247	0.224319
$729$	−43.1013	−1.59634
$730$	−8.60525	−0.318495
$731$	−18.7342	−0.692909
$732$	17.8926	0.661331
$733$	−40.5866	−1.49910	−0.749550	−	0.661947i	$-0.769730\pi$
$733$	−40.5866	−1.49910	−0.749550	+	0.661947i	$0.769730\pi$
$734$	34.4463	1.27144
$735$	14.9400	0.551072
$736$	2.17276	0.0800889
$737$	40.0452	1.47508
$738$	44.4427	1.63596
$739$	16.9594	0.623862	0.311931	−	0.950105i	$-0.399024\pi$
$739$	16.9594	0.623862	0.311931	+	0.950105i	$0.399024\pi$
$740$	1.20281	0.0442160
$741$	74.7463	2.74587
$742$	13.1727	0.483586
$743$	37.3868	1.37159	0.685794	−	0.727795i	$-0.259455\pi$
$743$	37.3868	1.37159	0.685794	+	0.727795i	$0.259455\pi$
$744$	19.1708	0.702835
$745$	−0.566681	−0.0207616
$746$	−9.02476	−0.330420
$747$	−5.98572	−0.219006
$748$	−8.13988	−0.297623
$749$	−19.4554	−0.710883
$750$	2.70072	0.0986162
$751$	−34.9924	−1.27689	−0.638445	−	0.769667i	$-0.720422\pi$
$751$	−34.9924	−1.27689	−0.638445	+	0.769667i	$0.720422\pi$
$752$	12.4866	0.455341
$753$	51.0804	1.86147
$754$	−28.3597	−1.03280
$755$	−8.98225	−0.326898
$756$	4.23397	0.153988
$757$	−4.30523	−0.156476	−0.0782381	−	0.996935i	$-0.524929\pi$
$757$	−4.30523	−0.156476	−0.0782381	+	0.996935i	$0.524929\pi$
$758$	36.0474	1.30930
$759$	−31.3529	−1.13804
$760$	5.54062	0.200979
$761$	14.2365	0.516072	0.258036	−	0.966135i	$-0.416925\pi$
$761$	14.2365	0.516072	0.258036	+	0.966135i	$0.416925\pi$
$762$	24.6648	0.893512
$763$	−4.66779	−0.168985
$764$	−21.8421	−0.790220
$765$	6.54152	0.236509
$766$	9.20022	0.332418
$767$	18.9392	0.683857
$768$	−2.70072	−0.0974537
$769$	50.5184	1.82174	0.910871	−	0.412692i	$-0.135411\pi$
$769$	50.5184	1.82174	0.910871	+	0.412692i	$0.135411\pi$
$770$	−6.47392	−0.233304
$771$	40.2602	1.44993
$772$	−23.8668	−0.858986
$773$	−33.9247	−1.22019	−0.610093	−	0.792330i	$-0.708868\pi$
$773$	−33.9247	−1.22019	−0.610093	+	0.792330i	$0.708868\pi$
$774$	52.8023	1.89794
$775$	7.09841	0.254982
$776$	9.84430	0.353390
$777$	3.93600	0.141203
$778$	18.2536	0.654423
$779$	57.3469	2.05467
$780$	−13.4906	−0.483041
$781$	4.50059	0.161044
$782$	3.31011	0.118369
$783$	−19.8389	−0.708983
$784$	−5.53188	−0.197567
$785$	−21.7627	−0.776744
$786$	11.2575	0.401542
$787$	27.1358	0.967287	0.483643	−	0.875265i	$-0.339313\pi$
$787$	27.1358	0.967287	0.483643	+	0.875265i	$0.339313\pi$
$788$	−15.7907	−0.562519
$789$	−32.9778	−1.17404
$790$	−4.99850	−0.177839
$791$	−18.8976	−0.671922
$792$	22.9422	0.815217
$793$	−33.0939	−1.17520
$794$	10.5197	0.373331
$795$	−29.3612	−1.04134
$796$	−5.88423	−0.208561
$797$	2.13348	0.0755717	0.0377859	−	0.999286i	$-0.487970\pi$
$797$	2.13348	0.0755717	0.0377859	+	0.999286i	$0.487970\pi$
$798$	18.1308	0.641824
$799$	19.0229	0.672981
$800$	−1.00000	−0.0353553
$801$	5.63743	0.199189
$802$	−1.00000	−0.0353112
$803$	−45.9781	−1.62253
$804$	20.2414	0.713861
$805$	2.63264	0.0927884
$806$	−35.4579	−1.24895
$807$	74.3427	2.61699
$808$	0.695446	0.0244657
$809$	18.6538	0.655833	0.327917	−	0.944707i	$-0.393653\pi$
$809$	18.6538	0.655833	0.327917	+	0.944707i	$0.393653\pi$
$810$	3.44432	0.121021
$811$	39.7943	1.39737	0.698684	−	0.715430i	$-0.253769\pi$
$811$	39.7943	1.39737	0.698684	+	0.715430i	$0.253769\pi$
$812$	−6.87907	−0.241408
$813$	−36.2588	−1.27165
$814$	6.42663	0.225253
$815$	12.0025	0.420430
$816$	−4.11443	−0.144034
$817$	68.1338	2.38370
$818$	2.94928	0.103119
$819$	−25.9885	−0.908111
$820$	−10.3503	−0.361447
$821$	41.7529	1.45719	0.728593	−	0.684946i	$-0.240174\pi$
$821$	41.7529	1.45719	0.728593	+	0.684946i	$0.240174\pi$
$822$	20.6586	0.720551
$823$	−33.6256	−1.17211	−0.586057	−	0.810270i	$-0.699320\pi$
$823$	−33.6256	−1.17211	−0.586057	+	0.810270i	$0.699320\pi$
$824$	−5.37457	−0.187232
$825$	14.4300	0.502388
$826$	4.59400	0.159846
$827$	−26.1355	−0.908822	−0.454411	−	0.890792i	$-0.650150\pi$
$827$	−26.1355	−0.908822	−0.454411	+	0.890792i	$0.650150\pi$
$828$	−9.32953	−0.324223
$829$	−14.0631	−0.488433	−0.244217	−	0.969721i	$-0.578531\pi$
$829$	−14.0631	−0.488433	−0.244217	+	0.969721i	$0.578531\pi$
$830$	1.39402	0.0483870
$831$	−27.8897	−0.967484
$832$	4.99519	0.173177
$833$	−8.42759	−0.291999
$834$	−51.9289	−1.79815
$835$	17.3770	0.601357
$836$	29.6037	1.02386
$837$	−24.8044	−0.857365
$838$	0.557921	0.0192730
$839$	41.9824	1.44939	0.724697	−	0.689067i	$-0.241980\pi$
$839$	41.9824	1.44939	0.724697	+	0.689067i	$0.241980\pi$
$840$	−3.27234	−0.112907
$841$	3.23284	0.111477
$842$	37.7997	1.30266
$843$	−59.3095	−2.04273
$844$	21.9315	0.754914
$845$	11.9520	0.411160
$846$	−53.6160	−1.84335
$847$	−21.2621	−0.730575
$848$	10.8717	0.373334
$849$	−47.5936	−1.63341
$850$	−1.52346	−0.0522542
$851$	−2.61341	−0.0895864
$852$	2.27489	0.0779365
$853$	−16.1430	−0.552726	−0.276363	−	0.961053i	$-0.589129\pi$
$853$	−16.1430	−0.552726	−0.276363	+	0.961053i	$0.589129\pi$
$854$	−8.02742	−0.274693
$855$	−23.7907	−0.813624
$856$	−16.0568	−0.548810
$857$	47.3125	1.61616	0.808082	−	0.589069i	$-0.200506\pi$
$857$	47.3125	1.61616	0.808082	+	0.589069i	$0.200506\pi$
$858$	−72.0806	−2.46079
$859$	−12.6657	−0.432150	−0.216075	−	0.976377i	$-0.569325\pi$
$859$	−12.6657	−0.432150	−0.216075	+	0.976377i	$0.569325\pi$
$860$	−12.2971	−0.419329
$861$	−33.8696	−1.15427
$862$	−4.48691	−0.152825
$863$	−38.7489	−1.31903	−0.659514	−	0.751692i	$-0.729238\pi$
$863$	−38.7489	−1.31903	−0.659514	+	0.751692i	$0.729238\pi$
$864$	3.49436	0.118880
$865$	−5.25782	−0.178771
$866$	5.08697	0.172862
$867$	39.6440	1.34638
$868$	−8.60085	−0.291932
$869$	−26.7071	−0.905978
$870$	15.3330	0.519839
$871$	−37.4382	−1.26855
$872$	−3.85240	−0.130459
$873$	−42.2701	−1.43063
$874$	−12.0384	−0.407206
$875$	−1.21166	−0.0409615
$876$	−23.2403	−0.785218
$877$	−2.43898	−0.0823585	−0.0411792	−	0.999152i	$-0.513111\pi$
$877$	−2.43898	−0.0823585	−0.0411792	+	0.999152i	$0.513111\pi$
$878$	−14.0287	−0.473447
$879$	−0.782006	−0.0263764
$880$	−5.34303	−0.180113
$881$	9.18259	0.309369	0.154685	−	0.987964i	$-0.450564\pi$
$881$	9.18259	0.309369	0.154685	+	0.987964i	$0.450564\pi$
$882$	23.7532	0.799810
$883$	5.39833	0.181668	0.0908342	−	0.995866i	$-0.471047\pi$
$883$	5.39833	0.181668	0.0908342	+	0.995866i	$0.471047\pi$
$884$	7.60997	0.255951
$885$	−10.2397	−0.344205
$886$	38.4453	1.29160
$887$	6.61687	0.222173	0.111086	−	0.993811i	$-0.464567\pi$
$887$	6.61687	0.222173	0.111086	+	0.993811i	$0.464567\pi$
$888$	3.24844	0.109010
$889$	−11.0657	−0.371132
$890$	−1.31290	−0.0440086
$891$	18.4031	0.616528
$892$	−5.44147	−0.182194
$893$	−69.1838	−2.31515
$894$	−1.53044	−0.0511857
$895$	7.13480	0.238490
$896$	1.21166	0.0404787
$897$	29.3118	0.978692
$898$	26.4681	0.883253
$899$	40.3005	1.34410
$900$	4.29386	0.143129
$901$	16.5625	0.551777
$902$	−55.3018	−1.84135
$903$	−40.2405	−1.33912
$904$	−15.5965	−0.518732
$905$	−14.3555	−0.477194
$906$	−24.2585	−0.805935
$907$	−13.8899	−0.461207	−0.230604	−	0.973048i	$-0.574070\pi$
$907$	−13.8899	−0.461207	−0.230604	+	0.973048i	$0.574070\pi$
$908$	1.13806	0.0377678
$909$	−2.98615	−0.0990443
$910$	6.05247	0.200637
$911$	58.3015	1.93162	0.965808	−	0.259258i	$-0.0834780\pi$
$911$	58.3015	1.93162	0.965808	+	0.259258i	$0.0834780\pi$
$912$	14.9636	0.495496
$913$	7.44827	0.246502
$914$	37.0750	1.22633
$915$	17.8926	0.591513
$916$	−3.68354	−0.121708
$917$	−5.05061	−0.166786
$918$	5.32351	0.175702
$919$	10.0652	0.332020	0.166010	−	0.986124i	$-0.446912\pi$
$919$	10.0652	0.332020	0.166010	+	0.986124i	$0.446912\pi$
$920$	2.17276	0.0716337
$921$	74.1642	2.44379
$922$	20.4921	0.674872
$923$	−4.20760	−0.138495
$924$	−17.4842	−0.575189
$925$	1.20281	0.0395480
$926$	8.88342	0.291927
$927$	23.0777	0.757970
$928$	−5.67740	−0.186370
$929$	−12.3800	−0.406174	−0.203087	−	0.979161i	$-0.565098\pi$
$929$	−12.3800	−0.406174	−0.203087	+	0.979161i	$0.565098\pi$
$930$	19.1708	0.628635
$931$	30.6501	1.00452
$932$	−6.60386	−0.216317
$933$	−2.21825	−0.0726224
$934$	8.47376	0.277270
$935$	−8.13988	−0.266202
$936$	−21.4487	−0.701072
$937$	48.3051	1.57806	0.789030	−	0.614355i	$-0.210584\pi$
$937$	48.3051	1.57806	0.789030	+	0.614355i	$0.210584\pi$
$938$	−9.08119	−0.296512
$939$	20.5175	0.669562
$940$	12.4866	0.407269
$941$	47.5709	1.55077	0.775384	−	0.631490i	$-0.217556\pi$
$941$	47.5709	1.55077	0.775384	+	0.631490i	$0.217556\pi$
$942$	−58.7748	−1.91499
$943$	22.4886	0.732330
$944$	3.79149	0.123403
$945$	4.23397	0.137731
$946$	−65.7040	−2.13622
$947$	−49.4700	−1.60756	−0.803780	−	0.594926i	$-0.797181\pi$
$947$	−49.4700	−1.60756	−0.803780	+	0.594926i	$0.797181\pi$
$948$	−13.4995	−0.438445
$949$	42.9849	1.39535
$950$	5.54062	0.179761
$951$	58.6059	1.90043
$952$	1.84591	0.0598263
$953$	−22.5320	−0.729884	−0.364942	−	0.931030i	$-0.618911\pi$
$953$	−22.5320	−0.729884	−0.364942	+	0.931030i	$0.618911\pi$
$954$	−46.6814	−1.51137
$955$	−21.8421	−0.706794
$956$	−20.7947	−0.672550
$957$	81.9248	2.64825
$958$	0.931984	0.0301110
$959$	−9.26834	−0.299290
$960$	−2.70072	−0.0871652
$961$	19.3874	0.625401
$962$	−6.00825	−0.193714
$963$	68.9457	2.22175
$964$	−1.42726	−0.0459689
$965$	−23.8668	−0.768301
$966$	7.11001	0.228761
$967$	−23.2547	−0.747820	−0.373910	−	0.927465i	$-0.621983\pi$
$967$	−23.2547	−0.747820	−0.373910	+	0.927465i	$0.621983\pi$
$968$	−17.5479	−0.564012
$969$	22.7965	0.732328
$970$	9.84430	0.316081
$971$	−35.7342	−1.14677	−0.573383	−	0.819287i	$-0.694369\pi$
$971$	−35.7342	−1.14677	−0.573383	+	0.819287i	$0.694369\pi$
$972$	19.7852	0.634611
$973$	23.2976	0.746885
$974$	−16.4234	−0.526240
$975$	−13.4906	−0.432045
$976$	−6.62515	−0.212066
$977$	−38.7290	−1.23905	−0.619525	−	0.784977i	$-0.712675\pi$
$977$	−38.7290	−1.23905	−0.619525	+	0.784977i	$0.712675\pi$
$978$	32.4154	1.03653
$979$	−7.01488	−0.224197
$980$	−5.53188	−0.176710
$981$	16.5417	0.528135
$982$	−10.0951	−0.322148
$983$	53.3366	1.70117	0.850587	−	0.525835i	$-0.176247\pi$
$983$	53.3366	1.70117	0.850587	+	0.525835i	$0.176247\pi$
$984$	−27.9531	−0.891113
$985$	−15.7907	−0.503132
$986$	−8.64928	−0.275449
$987$	40.8606	1.30061
$988$	−27.6765	−0.880506
$989$	26.7187	0.849606
$990$	22.9422	0.729152
$991$	−41.5338	−1.31936	−0.659682	−	0.751545i	$-0.729309\pi$
$991$	−41.5338	−1.31936	−0.659682	+	0.751545i	$0.729309\pi$
$992$	−7.09841	−0.225375
$993$	−45.8957	−1.45646
$994$	−1.02062	−0.0323720
$995$	−5.88423	−0.186543
$996$	3.76484	0.119294
$997$	6.15493	0.194928	0.0974642	−	0.995239i	$-0.468927\pi$
$997$	6.15493	0.194928	0.0974642	+	0.995239i	$0.468927\pi$
$998$	22.6531	0.717070
$999$	−4.20304	−0.132978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.2	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.70072 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.70072 q^{6} -1.21166 q^{7} -1.00000 q^{8} +4.29386 q^{9} -1.00000 q^{10} -5.34303 q^{11} -2.70072 q^{12} +4.99519 q^{13} +1.21166 q^{14} -2.70072 q^{15} +1.00000 q^{16} +1.52346 q^{17} -4.29386 q^{18} -5.54062 q^{19} +1.00000 q^{20} +3.27234 q^{21} +5.34303 q^{22} -2.17276 q^{23} +2.70072 q^{24} +1.00000 q^{25} -4.99519 q^{26} -3.49436 q^{27} -1.21166 q^{28} +5.67740 q^{29} +2.70072 q^{30} +7.09841 q^{31} -1.00000 q^{32} +14.4300 q^{33} -1.52346 q^{34} -1.21166 q^{35} +4.29386 q^{36} +1.20281 q^{37} +5.54062 q^{38} -13.4906 q^{39} -1.00000 q^{40} -10.3503 q^{41} -3.27234 q^{42} -12.2971 q^{43} -5.34303 q^{44} +4.29386 q^{45} +2.17276 q^{46} +12.4866 q^{47} -2.70072 q^{48} -5.53188 q^{49} -1.00000 q^{50} -4.11443 q^{51} +4.99519 q^{52} +10.8717 q^{53} +3.49436 q^{54} -5.34303 q^{55} +1.21166 q^{56} +14.9636 q^{57} -5.67740 q^{58} +3.79149 q^{59} -2.70072 q^{60} -6.62515 q^{61} -7.09841 q^{62} -5.20270 q^{63} +1.00000 q^{64} +4.99519 q^{65} -14.4300 q^{66} -7.49485 q^{67} +1.52346 q^{68} +5.86800 q^{69} +1.21166 q^{70} -0.842329 q^{71} -4.29386 q^{72} +8.60525 q^{73} -1.20281 q^{74} -2.70072 q^{75} -5.54062 q^{76} +6.47392 q^{77} +13.4906 q^{78} +4.99850 q^{79} +1.00000 q^{80} -3.44432 q^{81} +10.3503 q^{82} -1.39402 q^{83} +3.27234 q^{84} +1.52346 q^{85} +12.2971 q^{86} -15.3330 q^{87} +5.34303 q^{88} +1.31290 q^{89} -4.29386 q^{90} -6.05247 q^{91} -2.17276 q^{92} -19.1708 q^{93} -12.4866 q^{94} -5.54062 q^{95} +2.70072 q^{96} -9.84430 q^{97} +5.53188 q^{98} -22.9422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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