LMFDB - Embedded newform 4010.2.a.l.1.3

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.24738$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.24738 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24738 q^{6} +2.64455 q^{7} -1.00000 q^{8} +2.05073 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.24738 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24738 q^{6} +2.64455 q^{7} -1.00000 q^{8} +2.05073 q^{9} +1.00000 q^{10} -3.63995 q^{11} -2.24738 q^{12} +4.23279 q^{13} -2.64455 q^{14} +2.24738 q^{15} +1.00000 q^{16} -2.56021 q^{17} -2.05073 q^{18} +2.14346 q^{19} -1.00000 q^{20} -5.94331 q^{21} +3.63995 q^{22} -3.69511 q^{23} +2.24738 q^{24} +1.00000 q^{25} -4.23279 q^{26} +2.13336 q^{27} +2.64455 q^{28} +8.15103 q^{29} -2.24738 q^{30} -1.65648 q^{31} -1.00000 q^{32} +8.18037 q^{33} +2.56021 q^{34} -2.64455 q^{35} +2.05073 q^{36} -8.82225 q^{37} -2.14346 q^{38} -9.51270 q^{39} +1.00000 q^{40} +0.492801 q^{41} +5.94331 q^{42} +3.75914 q^{43} -3.63995 q^{44} -2.05073 q^{45} +3.69511 q^{46} +10.8528 q^{47} -2.24738 q^{48} -0.00636926 q^{49} -1.00000 q^{50} +5.75377 q^{51} +4.23279 q^{52} -9.30244 q^{53} -2.13336 q^{54} +3.63995 q^{55} -2.64455 q^{56} -4.81718 q^{57} -8.15103 q^{58} +5.31155 q^{59} +2.24738 q^{60} -2.57543 q^{61} +1.65648 q^{62} +5.42327 q^{63} +1.00000 q^{64} -4.23279 q^{65} -8.18037 q^{66} +12.1152 q^{67} -2.56021 q^{68} +8.30432 q^{69} +2.64455 q^{70} -11.6438 q^{71} -2.05073 q^{72} +7.12350 q^{73} +8.82225 q^{74} -2.24738 q^{75} +2.14346 q^{76} -9.62603 q^{77} +9.51270 q^{78} -9.66661 q^{79} -1.00000 q^{80} -10.9467 q^{81} -0.492801 q^{82} -2.87890 q^{83} -5.94331 q^{84} +2.56021 q^{85} -3.75914 q^{86} -18.3185 q^{87} +3.63995 q^{88} +7.00615 q^{89} +2.05073 q^{90} +11.1938 q^{91} -3.69511 q^{92} +3.72275 q^{93} -10.8528 q^{94} -2.14346 q^{95} +2.24738 q^{96} +6.50997 q^{97} +0.00636926 q^{98} -7.46458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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
$3$	−2.24738	−1.29753	−0.648764	−	0.760990i	$-0.724714\pi$
$3$	−2.24738	−1.29753	−0.648764	+	0.760990i	$0.724714\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.24738	0.917491
$7$	2.64455	0.999545	0.499772	−	0.866157i	$-0.333417\pi$
$7$	2.64455	0.999545	0.499772	+	0.866157i	$0.333417\pi$
$8$	−1.00000	−0.353553
$9$	2.05073	0.683578
$10$	1.00000	0.316228
$11$	−3.63995	−1.09749	−0.548743	−	0.835991i	$-0.684894\pi$
$11$	−3.63995	−1.09749	−0.548743	+	0.835991i	$0.684894\pi$
$12$	−2.24738	−0.648764
$13$	4.23279	1.17396	0.586982	−	0.809600i	$-0.300316\pi$
$13$	4.23279	1.17396	0.586982	+	0.809600i	$0.300316\pi$
$14$	−2.64455	−0.706785
$15$	2.24738	0.580272
$16$	1.00000	0.250000
$17$	−2.56021	−0.620941	−0.310471	−	0.950583i	$-0.600487\pi$
$17$	−2.56021	−0.620941	−0.310471	+	0.950583i	$0.600487\pi$
$18$	−2.05073	−0.483363
$19$	2.14346	0.491743	0.245872	−	0.969302i	$-0.420926\pi$
$19$	2.14346	0.491743	0.245872	+	0.969302i	$0.420926\pi$
$20$	−1.00000	−0.223607
$21$	−5.94331	−1.29694
$22$	3.63995	0.776040
$23$	−3.69511	−0.770483	−0.385242	−	0.922816i	$-0.625882\pi$
$23$	−3.69511	−0.770483	−0.385242	+	0.922816i	$0.625882\pi$
$24$	2.24738	0.458745
$25$	1.00000	0.200000
$26$	−4.23279	−0.830118
$27$	2.13336	0.410566
$28$	2.64455	0.499772
$29$	8.15103	1.51361	0.756804	−	0.653642i	$-0.226760\pi$
$29$	8.15103	1.51361	0.756804	+	0.653642i	$0.226760\pi$
$30$	−2.24738	−0.410314
$31$	−1.65648	−0.297513	−0.148757	−	0.988874i	$-0.547527\pi$
$31$	−1.65648	−0.297513	−0.148757	+	0.988874i	$0.547527\pi$
$32$	−1.00000	−0.176777
$33$	8.18037	1.42402
$34$	2.56021	0.439072
$35$	−2.64455	−0.447010
$36$	2.05073	0.341789
$37$	−8.82225	−1.45037	−0.725185	−	0.688554i	$-0.758246\pi$
$37$	−8.82225	−1.45037	−0.725185	+	0.688554i	$0.758246\pi$
$38$	−2.14346	−0.347715
$39$	−9.51270	−1.52325
$40$	1.00000	0.158114
$41$	0.492801	0.0769626	0.0384813	−	0.999259i	$-0.487748\pi$
$41$	0.492801	0.0769626	0.0384813	+	0.999259i	$0.487748\pi$
$42$	5.94331	0.917073
$43$	3.75914	0.573264	0.286632	−	0.958041i	$-0.407464\pi$
$43$	3.75914	0.573264	0.286632	+	0.958041i	$0.407464\pi$
$44$	−3.63995	−0.548743
$45$	−2.05073	−0.305706
$46$	3.69511	0.544814
$47$	10.8528	1.58304	0.791522	−	0.611141i	$-0.209289\pi$
$47$	10.8528	1.58304	0.791522	+	0.611141i	$0.209289\pi$
$48$	−2.24738	−0.324382
$49$	−0.00636926	−0.000909894 0
$50$	−1.00000	−0.141421
$51$	5.75377	0.805688
$52$	4.23279	0.586982
$53$	−9.30244	−1.27779	−0.638894	−	0.769295i	$-0.720608\pi$
$53$	−9.30244	−1.27779	−0.638894	+	0.769295i	$0.720608\pi$
$54$	−2.13336	−0.290314
$55$	3.63995	0.490811
$56$	−2.64455	−0.353393
$57$	−4.81718	−0.638051
$58$	−8.15103	−1.07028
$59$	5.31155	0.691504	0.345752	−	0.938326i	$-0.387624\pi$
$59$	5.31155	0.691504	0.345752	+	0.938326i	$0.387624\pi$
$60$	2.24738	0.290136
$61$	−2.57543	−0.329750	−0.164875	−	0.986314i	$-0.552722\pi$
$61$	−2.57543	−0.329750	−0.164875	+	0.986314i	$0.552722\pi$
$62$	1.65648	0.210374
$63$	5.42327	0.683267
$64$	1.00000	0.125000
$65$	−4.23279	−0.525013
$66$	−8.18037	−1.00693
$67$	12.1152	1.48010	0.740052	−	0.672550i	$-0.234801\pi$
$67$	12.1152	1.48010	0.740052	+	0.672550i	$0.234801\pi$
$68$	−2.56021	−0.310471
$69$	8.30432	0.999723
$70$	2.64455	0.316084
$71$	−11.6438	−1.38187	−0.690933	−	0.722919i	$-0.742800\pi$
$71$	−11.6438	−1.38187	−0.690933	+	0.722919i	$0.742800\pi$
$72$	−2.05073	−0.241681
$73$	7.12350	0.833743	0.416872	−	0.908965i	$-0.363127\pi$
$73$	7.12350	0.833743	0.416872	+	0.908965i	$0.363127\pi$
$74$	8.82225	1.02557
$75$	−2.24738	−0.259506
$76$	2.14346	0.245872
$77$	−9.62603	−1.09699
$78$	9.51270	1.07710
$79$	−9.66661	−1.08758	−0.543789	−	0.839222i	$-0.683011\pi$
$79$	−9.66661	−1.08758	−0.543789	+	0.839222i	$0.683011\pi$
$80$	−1.00000	−0.111803
$81$	−10.9467	−1.21630
$82$	−0.492801	−0.0544208
$83$	−2.87890	−0.316000	−0.158000	−	0.987439i	$-0.550505\pi$
$83$	−2.87890	−0.316000	−0.158000	+	0.987439i	$0.550505\pi$
$84$	−5.94331	−0.648469
$85$	2.56021	0.277693
$86$	−3.75914	−0.405359
$87$	−18.3185	−1.96395
$88$	3.63995	0.388020
$89$	7.00615	0.742650	0.371325	−	0.928503i	$-0.378904\pi$
$89$	7.00615	0.742650	0.371325	+	0.928503i	$0.378904\pi$
$90$	2.05073	0.216166
$91$	11.1938	1.17343
$92$	−3.69511	−0.385242
$93$	3.72275	0.386032
$94$	−10.8528	−1.11938
$95$	−2.14346	−0.219914
$96$	2.24738	0.229373
$97$	6.50997	0.660987	0.330494	−	0.943808i	$-0.392785\pi$
$97$	6.50997	0.660987	0.330494	+	0.943808i	$0.392785\pi$
$98$	0.00636926	0.000643392 0
$99$	−7.46458	−0.750218
$100$	1.00000	0.100000
$101$	−16.0595	−1.59798	−0.798991	−	0.601343i	$-0.794633\pi$
$101$	−16.0595	−1.59798	−0.798991	+	0.601343i	$0.794633\pi$
$102$	−5.75377	−0.569708
$103$	12.6612	1.24755	0.623774	−	0.781605i	$-0.285599\pi$
$103$	12.6612	1.24755	0.623774	+	0.781605i	$0.285599\pi$
$104$	−4.23279	−0.415059
$105$	5.94331	0.580008
$106$	9.30244	0.903533
$107$	5.69611	0.550664	0.275332	−	0.961349i	$-0.411212\pi$
$107$	5.69611	0.550664	0.275332	+	0.961349i	$0.411212\pi$
$108$	2.13336	0.205283
$109$	−16.3994	−1.57078	−0.785390	−	0.619001i	$-0.787538\pi$
$109$	−16.3994	−1.57078	−0.785390	+	0.619001i	$0.787538\pi$
$110$	−3.63995	−0.347056
$111$	19.8270	1.88189
$112$	2.64455	0.249886
$113$	−5.97011	−0.561621	−0.280810	−	0.959763i	$-0.590603\pi$
$113$	−5.97011	−0.561621	−0.280810	+	0.959763i	$0.590603\pi$
$114$	4.81718	0.451170
$115$	3.69511	0.344570
$116$	8.15103	0.756804
$117$	8.68032	0.802496
$118$	−5.31155	−0.488967
$119$	−6.77059	−0.620659
$120$	−2.24738	−0.205157
$121$	2.24925	0.204477
$122$	2.57543	0.233169
$123$	−1.10751	−0.0998611
$124$	−1.65648	−0.148757
$125$	−1.00000	−0.0894427
$126$	−5.42327	−0.483143
$127$	−14.3666	−1.27483	−0.637415	−	0.770521i	$-0.719996\pi$
$127$	−14.3666	−1.27483	−0.637415	+	0.770521i	$0.719996\pi$
$128$	−1.00000	−0.0883883
$129$	−8.44823	−0.743825
$130$	4.23279	0.371240
$131$	−7.21853	−0.630686	−0.315343	−	0.948978i	$-0.602120\pi$
$131$	−7.21853	−0.630686	−0.315343	+	0.948978i	$0.602120\pi$
$132$	8.18037	0.712010
$133$	5.66848	0.491520
$134$	−12.1152	−1.04659
$135$	−2.13336	−0.183611
$136$	2.56021	0.219536
$137$	6.54622	0.559281	0.279641	−	0.960105i	$-0.409785\pi$
$137$	6.54622	0.559281	0.279641	+	0.960105i	$0.409785\pi$
$138$	−8.30432	−0.706911
$139$	5.72920	0.485945	0.242972	−	0.970033i	$-0.421878\pi$
$139$	5.72920	0.485945	0.242972	+	0.970033i	$0.421878\pi$
$140$	−2.64455	−0.223505
$141$	−24.3904	−2.05404
$142$	11.6438	0.977127
$143$	−15.4071	−1.28841
$144$	2.05073	0.170895
$145$	−8.15103	−0.676906
$146$	−7.12350	−0.589545
$147$	0.0143142	0.00118061
$148$	−8.82225	−0.725185
$149$	−15.7466	−1.29001	−0.645007	−	0.764177i	$-0.723146\pi$
$149$	−15.7466	−1.29001	−0.645007	+	0.764177i	$0.723146\pi$
$150$	2.24738	0.183498
$151$	8.51416	0.692872	0.346436	−	0.938074i	$-0.387392\pi$
$151$	8.51416	0.692872	0.346436	+	0.938074i	$0.387392\pi$
$152$	−2.14346	−0.173858
$153$	−5.25030	−0.424462
$154$	9.62603	0.775687
$155$	1.65648	0.133052
$156$	−9.51270	−0.761625
$157$	13.8003	1.10139	0.550693	−	0.834708i	$-0.314363\pi$
$157$	13.8003	1.10139	0.550693	+	0.834708i	$0.314363\pi$
$158$	9.66661	0.769034
$159$	20.9062	1.65797
$160$	1.00000	0.0790569
$161$	−9.77189	−0.770132
$162$	10.9467	0.860053
$163$	19.8361	1.55368	0.776841	−	0.629697i	$-0.216821\pi$
$163$	19.8361	1.55368	0.776841	+	0.629697i	$0.216821\pi$
$164$	0.492801	0.0384813
$165$	−8.18037	−0.636841
$166$	2.87890	0.223446
$167$	−19.0725	−1.47587	−0.737936	−	0.674871i	$-0.764199\pi$
$167$	−19.0725	−1.47587	−0.737936	+	0.674871i	$0.764199\pi$
$168$	5.94331	0.458537
$169$	4.91649	0.378191
$170$	−2.56021	−0.196359
$171$	4.39567	0.336145
$172$	3.75914	0.286632
$173$	25.4482	1.93479	0.967397	−	0.253264i	$-0.0815040\pi$
$173$	25.4482	1.93479	0.967397	+	0.253264i	$0.0815040\pi$
$174$	18.3185	1.38872
$175$	2.64455	0.199909
$176$	−3.63995	−0.274372
$177$	−11.9371	−0.897246
$178$	−7.00615	−0.525133
$179$	−10.0953	−0.754562	−0.377281	−	0.926099i	$-0.623141\pi$
$179$	−10.0953	−0.754562	−0.377281	+	0.926099i	$0.623141\pi$
$180$	−2.05073	−0.152853
$181$	1.90872	0.141874	0.0709372	−	0.997481i	$-0.477401\pi$
$181$	1.90872	0.141874	0.0709372	+	0.997481i	$0.477401\pi$
$182$	−11.1938	−0.829740
$183$	5.78798	0.427860
$184$	3.69511	0.272407
$185$	8.82225	0.648625
$186$	−3.72275	−0.272966
$187$	9.31903	0.681475
$188$	10.8528	0.791522
$189$	5.64178	0.410379
$190$	2.14346	0.155503
$191$	17.9529	1.29903	0.649513	−	0.760351i	$-0.274973\pi$
$191$	17.9529	1.29903	0.649513	+	0.760351i	$0.274973\pi$
$192$	−2.24738	−0.162191
$193$	6.75068	0.485924	0.242962	−	0.970036i	$-0.421881\pi$
$193$	6.75068	0.485924	0.242962	+	0.970036i	$0.421881\pi$
$194$	−6.50997	−0.467389
$195$	9.51270	0.681218
$196$	−0.00636926	−0.000454947 0
$197$	2.21121	0.157542	0.0787710	−	0.996893i	$-0.474900\pi$
$197$	2.21121	0.157542	0.0787710	+	0.996893i	$0.474900\pi$
$198$	7.46458	0.530484
$199$	−16.9056	−1.19841	−0.599204	−	0.800597i	$-0.704516\pi$
$199$	−16.9056	−1.19841	−0.599204	+	0.800597i	$0.704516\pi$
$200$	−1.00000	−0.0707107
$201$	−27.2274	−1.92048
$202$	16.0595	1.12994
$203$	21.5558	1.51292
$204$	5.75377	0.402844
$205$	−0.492801	−0.0344187
$206$	−12.6612	−0.882149
$207$	−7.57768	−0.526686
$208$	4.23279	0.293491
$209$	−7.80209	−0.539682
$210$	−5.94331	−0.410128
$211$	26.5778	1.82969	0.914844	−	0.403807i	$-0.132313\pi$
$211$	26.5778	1.82969	0.914844	+	0.403807i	$0.132313\pi$
$212$	−9.30244	−0.638894
$213$	26.1681	1.79301
$214$	−5.69611	−0.389378
$215$	−3.75914	−0.256371
$216$	−2.13336	−0.145157
$217$	−4.38065	−0.297378
$218$	16.3994	1.11071
$219$	−16.0092	−1.08180
$220$	3.63995	0.245406
$221$	−10.8368	−0.728962
$222$	−19.8270	−1.33070
$223$	16.7606	1.12237	0.561187	−	0.827689i	$-0.310345\pi$
$223$	16.7606	1.12237	0.561187	+	0.827689i	$0.310345\pi$
$224$	−2.64455	−0.176696
$225$	2.05073	0.136716
$226$	5.97011	0.397126
$227$	−22.5024	−1.49354	−0.746769	−	0.665084i	$-0.768396\pi$
$227$	−22.5024	−1.49354	−0.746769	+	0.665084i	$0.768396\pi$
$228$	−4.81718	−0.319025
$229$	8.15516	0.538908	0.269454	−	0.963013i	$-0.413157\pi$
$229$	8.15516	0.538908	0.269454	+	0.963013i	$0.413157\pi$
$230$	−3.69511	−0.243648
$231$	21.6334	1.42337
$232$	−8.15103	−0.535141
$233$	13.1091	0.858807	0.429403	−	0.903113i	$-0.358724\pi$
$233$	13.1091	0.858807	0.429403	+	0.903113i	$0.358724\pi$
$234$	−8.68032	−0.567451
$235$	−10.8528	−0.707958
$236$	5.31155	0.345752
$237$	21.7246	1.41116
$238$	6.77059	0.438872
$239$	20.0607	1.29762	0.648811	−	0.760950i	$-0.275267\pi$
$239$	20.0607	1.29762	0.648811	+	0.760950i	$0.275267\pi$
$240$	2.24738	0.145068
$241$	−9.55890	−0.615743	−0.307871	−	0.951428i	$-0.599617\pi$
$241$	−9.55890	−0.615743	−0.307871	+	0.951428i	$0.599617\pi$
$242$	−2.24925	−0.144587
$243$	18.2013	1.16762
$244$	−2.57543	−0.164875
$245$	0.00636926	0.000406917 0
$246$	1.10751	0.0706125
$247$	9.07281	0.577289
$248$	1.65648	0.105187
$249$	6.46999	0.410019
$250$	1.00000	0.0632456
$251$	25.2475	1.59361	0.796805	−	0.604236i	$-0.206522\pi$
$251$	25.2475	1.59361	0.796805	+	0.604236i	$0.206522\pi$
$252$	5.42327	0.341634
$253$	13.4500	0.845595
$254$	14.3666	0.901441
$255$	−5.75377	−0.360315
$256$	1.00000	0.0625000
$257$	11.9655	0.746389	0.373194	−	0.927753i	$-0.378262\pi$
$257$	11.9655	0.746389	0.373194	+	0.927753i	$0.378262\pi$
$258$	8.44823	0.525964
$259$	−23.3309	−1.44971
$260$	−4.23279	−0.262506
$261$	16.7156	1.03467
$262$	7.21853	0.445962
$263$	−19.8387	−1.22331	−0.611654	−	0.791125i	$-0.709496\pi$
$263$	−19.8387	−1.22331	−0.611654	+	0.791125i	$0.709496\pi$
$264$	−8.18037	−0.503467
$265$	9.30244	0.571444
$266$	−5.66848	−0.347557
$267$	−15.7455	−0.963609
$268$	12.1152	0.740052
$269$	−5.28011	−0.321934	−0.160967	−	0.986960i	$-0.551461\pi$
$269$	−5.28011	−0.321934	−0.160967	+	0.986960i	$0.551461\pi$
$270$	2.13336	0.129832
$271$	1.73009	0.105095	0.0525477	−	0.998618i	$-0.483266\pi$
$271$	1.73009	0.105095	0.0525477	+	0.998618i	$0.483266\pi$
$272$	−2.56021	−0.155235
$273$	−25.1568	−1.52256
$274$	−6.54622	−0.395472
$275$	−3.63995	−0.219497
$276$	8.30432	0.499862
$277$	20.7529	1.24692	0.623461	−	0.781855i	$-0.285726\pi$
$277$	20.7529	1.24692	0.623461	+	0.781855i	$0.285726\pi$
$278$	−5.72920	−0.343615
$279$	−3.39701	−0.203374
$280$	2.64455	0.158042
$281$	12.1586	0.725323	0.362661	−	0.931921i	$-0.381868\pi$
$281$	12.1586	0.725323	0.362661	+	0.931921i	$0.381868\pi$
$282$	24.3904	1.45243
$283$	25.9092	1.54014	0.770072	−	0.637957i	$-0.220220\pi$
$283$	25.9092	1.54014	0.770072	+	0.637957i	$0.220220\pi$
$284$	−11.6438	−0.690933
$285$	4.81718	0.285345
$286$	15.4071	0.911043
$287$	1.30324	0.0769276
$288$	−2.05073	−0.120841
$289$	−10.4453	−0.614432
$290$	8.15103	0.478645
$291$	−14.6304	−0.857649
$292$	7.12350	0.416872
$293$	21.7445	1.27033	0.635164	−	0.772377i	$-0.280933\pi$
$293$	21.7445	1.27033	0.635164	+	0.772377i	$0.280933\pi$
$294$	−0.0143142	−0.000834820 0
$295$	−5.31155	−0.309250
$296$	8.82225	0.512783
$297$	−7.76534	−0.450591
$298$	15.7466	0.912178
$299$	−15.6406	−0.904519
$300$	−2.24738	−0.129753
$301$	9.94123	0.573003
$302$	−8.51416	−0.489935
$303$	36.0919	2.07343
$304$	2.14346	0.122936
$305$	2.57543	0.147469
$306$	5.25030	0.300140
$307$	−18.3234	−1.04577	−0.522887	−	0.852402i	$-0.675145\pi$
$307$	−18.3234	−1.04577	−0.522887	+	0.852402i	$0.675145\pi$
$308$	−9.62603	−0.548494
$309$	−28.4546	−1.61873
$310$	−1.65648	−0.0940819
$311$	26.0232	1.47564	0.737820	−	0.674997i	$-0.235855\pi$
$311$	26.0232	1.47564	0.737820	+	0.674997i	$0.235855\pi$
$312$	9.51270	0.538550
$313$	2.46277	0.139204	0.0696021	−	0.997575i	$-0.477827\pi$
$313$	2.46277	0.139204	0.0696021	+	0.997575i	$0.477827\pi$
$314$	−13.8003	−0.778798
$315$	−5.42327	−0.305566
$316$	−9.66661	−0.543789
$317$	−9.97922	−0.560489	−0.280244	−	0.959929i	$-0.590416\pi$
$317$	−9.97922	−0.560489	−0.280244	+	0.959929i	$0.590416\pi$
$318$	−20.9062	−1.17236
$319$	−29.6693	−1.66116
$320$	−1.00000	−0.0559017
$321$	−12.8014	−0.714502
$322$	9.77189	0.544566
$323$	−5.48770	−0.305344
$324$	−10.9467	−0.608149
$325$	4.23279	0.234793
$326$	−19.8361	−1.09862
$327$	36.8558	2.03813
$328$	−0.492801	−0.0272104
$329$	28.7007	1.58232
$330$	8.18037	0.450315
$331$	26.5932	1.46170	0.730848	−	0.682540i	$-0.239125\pi$
$331$	26.5932	1.46170	0.730848	+	0.682540i	$0.239125\pi$
$332$	−2.87890	−0.158000
$333$	−18.0921	−0.991441
$334$	19.0725	1.04360
$335$	−12.1152	−0.661923
$336$	−5.94331	−0.324234
$337$	30.2375	1.64714	0.823571	−	0.567213i	$-0.191978\pi$
$337$	30.2375	1.64714	0.823571	+	0.567213i	$0.191978\pi$
$338$	−4.91649	−0.267422
$339$	13.4171	0.728719
$340$	2.56021	0.138847
$341$	6.02952	0.326517
$342$	−4.39567	−0.237691
$343$	−18.5287	−1.00045
$344$	−3.75914	−0.202679
$345$	−8.30432	−0.447090
$346$	−25.4482	−1.36811
$347$	19.3462	1.03856	0.519281	−	0.854604i	$-0.326200\pi$
$347$	19.3462	1.03856	0.519281	+	0.854604i	$0.326200\pi$
$348$	−18.3185	−0.981974
$349$	16.9751	0.908654	0.454327	−	0.890835i	$-0.349880\pi$
$349$	16.9751	0.908654	0.454327	+	0.890835i	$0.349880\pi$
$350$	−2.64455	−0.141357
$351$	9.03007	0.481990
$352$	3.63995	0.194010
$353$	−9.96295	−0.530274	−0.265137	−	0.964211i	$-0.585417\pi$
$353$	−9.96295	−0.530274	−0.265137	+	0.964211i	$0.585417\pi$
$354$	11.9371	0.634449
$355$	11.6438	0.617990
$356$	7.00615	0.371325
$357$	15.2161	0.805322
$358$	10.0953	0.533556
$359$	16.2723	0.858817	0.429409	−	0.903110i	$-0.358722\pi$
$359$	16.2723	0.858817	0.429409	+	0.903110i	$0.358722\pi$
$360$	2.05073	0.108083
$361$	−14.4056	−0.758188
$362$	−1.90872	−0.100320
$363$	−5.05493	−0.265315
$364$	11.1938	0.586715
$365$	−7.12350	−0.372861
$366$	−5.78798	−0.302543
$367$	7.06728	0.368909	0.184454	−	0.982841i	$-0.440948\pi$
$367$	7.06728	0.368909	0.184454	+	0.982841i	$0.440948\pi$
$368$	−3.69511	−0.192621
$369$	1.01060	0.0526100
$370$	−8.82225	−0.458647
$371$	−24.6007	−1.27721
$372$	3.72275	0.193016
$373$	20.9790	1.08625	0.543125	−	0.839652i	$-0.317241\pi$
$373$	20.9790	1.08625	0.543125	+	0.839652i	$0.317241\pi$
$374$	−9.31903	−0.481875
$375$	2.24738	0.116054
$376$	−10.8528	−0.559690
$377$	34.5016	1.77692
$378$	−5.64178	−0.290182
$379$	26.9851	1.38613	0.693065	−	0.720875i	$-0.256260\pi$
$379$	26.9851	1.38613	0.693065	+	0.720875i	$0.256260\pi$
$380$	−2.14346	−0.109957
$381$	32.2873	1.65413
$382$	−17.9529	−0.918550
$383$	13.1837	0.673657	0.336829	−	0.941566i	$-0.390646\pi$
$383$	13.1837	0.673657	0.336829	+	0.941566i	$0.390646\pi$
$384$	2.24738	0.114686
$385$	9.62603	0.490588
$386$	−6.75068	−0.343600
$387$	7.70900	0.391871
$388$	6.50997	0.330494
$389$	4.09900	0.207828	0.103914	−	0.994586i	$-0.466863\pi$
$389$	4.09900	0.207828	0.103914	+	0.994586i	$0.466863\pi$
$390$	−9.51270	−0.481694
$391$	9.46023	0.478425
$392$	0.00636926	0.000321696 0
$393$	16.2228	0.818333
$394$	−2.21121	−0.111399
$395$	9.66661	0.486380
$396$	−7.46458	−0.375109
$397$	−9.40802	−0.472175	−0.236088	−	0.971732i	$-0.575865\pi$
$397$	−9.40802	−0.472175	−0.236088	+	0.971732i	$0.575865\pi$
$398$	16.9056	0.847402
$399$	−12.7393	−0.637761
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	27.2274	1.35798
$403$	−7.01154	−0.349270
$404$	−16.0595	−0.798991
$405$	10.9467	0.543945
$406$	−21.5558	−1.06979
$407$	32.1126	1.59176
$408$	−5.75377	−0.284854
$409$	−30.9061	−1.52821	−0.764104	−	0.645093i	$-0.776819\pi$
$409$	−30.9061	−1.52821	−0.764104	+	0.645093i	$0.776819\pi$
$410$	0.492801	0.0243377
$411$	−14.7119	−0.725683
$412$	12.6612	0.623774
$413$	14.0466	0.691190
$414$	7.57768	0.372423
$415$	2.87890	0.141320
$416$	−4.23279	−0.207529
$417$	−12.8757	−0.630527
$418$	7.80209	0.381613
$419$	11.9442	0.583513	0.291757	−	0.956493i	$-0.405760\pi$
$419$	11.9442	0.583513	0.291757	+	0.956493i	$0.405760\pi$
$420$	5.94331	0.290004
$421$	−17.7020	−0.862744	−0.431372	−	0.902174i	$-0.641970\pi$
$421$	−17.7020	−0.862744	−0.431372	+	0.902174i	$0.641970\pi$
$422$	−26.5778	−1.29379
$423$	22.2562	1.08213
$424$	9.30244	0.451766
$425$	−2.56021	−0.124188
$426$	−26.1681	−1.26785
$427$	−6.81085	−0.329600
$428$	5.69611	0.275332
$429$	34.6258	1.67175
$430$	3.75914	0.181282
$431$	11.4989	0.553883	0.276941	−	0.960887i	$-0.410679\pi$
$431$	11.4989	0.553883	0.276941	+	0.960887i	$0.410679\pi$
$432$	2.13336	0.102641
$433$	−5.48287	−0.263490	−0.131745	−	0.991284i	$-0.542058\pi$
$433$	−5.48287	−0.263490	−0.131745	+	0.991284i	$0.542058\pi$
$434$	4.38065	0.210278
$435$	18.3185	0.878304
$436$	−16.3994	−0.785390
$437$	−7.92031	−0.378880
$438$	16.0092	0.764951
$439$	15.1822	0.724608	0.362304	−	0.932060i	$-0.381990\pi$
$439$	15.1822	0.724608	0.362304	+	0.932060i	$0.381990\pi$
$440$	−3.63995	−0.173528
$441$	−0.0130617	−0.000621984 0
$442$	10.8368	0.515454
$443$	28.2058	1.34010	0.670048	−	0.742318i	$-0.266274\pi$
$443$	28.2058	1.34010	0.670048	+	0.742318i	$0.266274\pi$
$444$	19.8270	0.940947
$445$	−7.00615	−0.332123
$446$	−16.7606	−0.793638
$447$	35.3887	1.67383
$448$	2.64455	0.124943
$449$	29.0535	1.37112	0.685560	−	0.728016i	$-0.259557\pi$
$449$	29.0535	1.37112	0.685560	+	0.728016i	$0.259557\pi$
$450$	−2.05073	−0.0966726
$451$	−1.79377	−0.0844654
$452$	−5.97011	−0.280810
$453$	−19.1346	−0.899021
$454$	22.5024	1.05609
$455$	−11.1938	−0.524774
$456$	4.81718	0.225585
$457$	2.42057	0.113230	0.0566148	−	0.998396i	$-0.481969\pi$
$457$	2.42057	0.113230	0.0566148	+	0.998396i	$0.481969\pi$
$458$	−8.15516	−0.381066
$459$	−5.46185	−0.254937
$460$	3.69511	0.172285
$461$	25.7434	1.19899	0.599496	−	0.800378i	$-0.295368\pi$
$461$	25.7434	1.19899	0.599496	+	0.800378i	$0.295368\pi$
$462$	−21.6334	−1.00648
$463$	−6.11273	−0.284083	−0.142041	−	0.989861i	$-0.545367\pi$
$463$	−6.11273	−0.284083	−0.142041	+	0.989861i	$0.545367\pi$
$464$	8.15103	0.378402
$465$	−3.72275	−0.172639
$466$	−13.1091	−0.607268
$467$	28.5787	1.32246	0.661231	−	0.750182i	$-0.270034\pi$
$467$	28.5787	1.32246	0.661231	+	0.750182i	$0.270034\pi$
$468$	8.68032	0.401248
$469$	32.0391	1.47943
$470$	10.8528	0.500602
$471$	−31.0147	−1.42908
$472$	−5.31155	−0.244484
$473$	−13.6831	−0.629149
$474$	−21.7246	−0.997843
$475$	2.14346	0.0983487
$476$	−6.77059	−0.310329
$477$	−19.0768	−0.873468
$478$	−20.0607	−0.917557
$479$	−19.7841	−0.903957	−0.451978	−	0.892029i	$-0.649282\pi$
$479$	−19.7841	−0.903957	−0.451978	+	0.892029i	$0.649282\pi$
$480$	−2.24738	−0.102579
$481$	−37.3427	−1.70268
$482$	9.55890	0.435396
$483$	21.9612	0.999268
$484$	2.24925	0.102239
$485$	−6.50997	−0.295603
$486$	−18.2013	−0.825629
$487$	−4.44801	−0.201559	−0.100779	−	0.994909i	$-0.532134\pi$
$487$	−4.44801	−0.201559	−0.100779	+	0.994909i	$0.532134\pi$
$488$	2.57543	0.116584
$489$	−44.5793	−2.01595
$490$	−0.00636926	−0.000287734 0
$491$	32.7380	1.47745	0.738723	−	0.674009i	$-0.235429\pi$
$491$	32.7380	1.47745	0.738723	+	0.674009i	$0.235429\pi$
$492$	−1.10751	−0.0499305
$493$	−20.8683	−0.939861
$494$	−9.07281	−0.408205
$495$	7.46458	0.335508
$496$	−1.65648	−0.0743783
$497$	−30.7926	−1.38124
$498$	−6.46999	−0.289927
$499$	−33.3590	−1.49336	−0.746678	−	0.665186i	$-0.768352\pi$
$499$	−33.3590	−1.49336	−0.746678	+	0.665186i	$0.768352\pi$
$500$	−1.00000	−0.0447214
$501$	42.8632	1.91498
$502$	−25.2475	−1.12685
$503$	−19.6160	−0.874634	−0.437317	−	0.899307i	$-0.644071\pi$
$503$	−19.6160	−0.874634	−0.437317	+	0.899307i	$0.644071\pi$
$504$	−5.42327	−0.241571
$505$	16.0595	0.714639
$506$	−13.4500	−0.597926
$507$	−11.0492	−0.490714
$508$	−14.3666	−0.637415
$509$	−35.9119	−1.59177	−0.795885	−	0.605448i	$-0.792994\pi$
$509$	−35.9119	−1.59177	−0.795885	+	0.605448i	$0.792994\pi$
$510$	5.75377	0.254781
$511$	18.8384	0.833364
$512$	−1.00000	−0.0441942
$513$	4.57278	0.201893
$514$	−11.9655	−0.527776
$515$	−12.6612	−0.557920
$516$	−8.44823	−0.371913
$517$	−39.5037	−1.73737
$518$	23.3309	1.02510
$519$	−57.1920	−2.51045
$520$	4.23279	0.185620
$521$	−27.8298	−1.21925	−0.609624	−	0.792691i	$-0.708680\pi$
$521$	−27.8298	−1.21925	−0.609624	+	0.792691i	$0.708680\pi$
$522$	−16.7156	−0.731622
$523$	24.3758	1.06588	0.532940	−	0.846153i	$-0.321087\pi$
$523$	24.3758	1.06588	0.532940	+	0.846153i	$0.321087\pi$
$524$	−7.21853	−0.315343
$525$	−5.94331	−0.259387
$526$	19.8387	0.865010
$527$	4.24094	0.184738
$528$	8.18037	0.356005
$529$	−9.34619	−0.406356
$530$	−9.30244	−0.404072
$531$	10.8926	0.472697
$532$	5.66848	0.245760
$533$	2.08592	0.0903513
$534$	15.7455	0.681375
$535$	−5.69611	−0.246264
$536$	−12.1152	−0.523296
$537$	22.6881	0.979065
$538$	5.28011	0.227642
$539$	0.0231838	0.000998597 0
$540$	−2.13336	−0.0918053
$541$	−4.03656	−0.173545	−0.0867726	−	0.996228i	$-0.527655\pi$
$541$	−4.03656	−0.173545	−0.0867726	+	0.996228i	$0.527655\pi$
$542$	−1.73009	−0.0743136
$543$	−4.28964	−0.184086
$544$	2.56021	0.109768
$545$	16.3994	0.702474
$546$	25.1568	1.07661
$547$	−34.1299	−1.45929	−0.729644	−	0.683827i	$-0.760314\pi$
$547$	−34.1299	−1.45929	−0.729644	+	0.683827i	$0.760314\pi$
$548$	6.54622	0.279641
$549$	−5.28153	−0.225410
$550$	3.63995	0.155208
$551$	17.4714	0.744307
$552$	−8.30432	−0.353456
$553$	−25.5638	−1.08708
$554$	−20.7529	−0.881707
$555$	−19.8270	−0.841609
$556$	5.72920	0.242972
$557$	17.3035	0.733174	0.366587	−	0.930384i	$-0.380526\pi$
$557$	17.3035	0.733174	0.366587	+	0.930384i	$0.380526\pi$
$558$	3.39701	0.143807
$559$	15.9116	0.672991
$560$	−2.64455	−0.111753
$561$	−20.9434	−0.884232
$562$	−12.1586	−0.512881
$563$	37.8047	1.59328	0.796638	−	0.604457i	$-0.206610\pi$
$563$	37.8047	1.59328	0.796638	+	0.604457i	$0.206610\pi$
$564$	−24.3904	−1.02702
$565$	5.97011	0.251164
$566$	−25.9092	−1.08905
$567$	−28.9490	−1.21575
$568$	11.6438	0.488564
$569$	−2.56225	−0.107415	−0.0537076	−	0.998557i	$-0.517104\pi$
$569$	−2.56225	−0.107415	−0.0537076	+	0.998557i	$0.517104\pi$
$570$	−4.81718	−0.201769
$571$	13.8184	0.578280	0.289140	−	0.957287i	$-0.406631\pi$
$571$	13.8184	0.578280	0.289140	+	0.957287i	$0.406631\pi$
$572$	−15.4071	−0.644205
$573$	−40.3470	−1.68552
$574$	−1.30324	−0.0543960
$575$	−3.69511	−0.154097
$576$	2.05073	0.0854473
$577$	−32.3766	−1.34786	−0.673928	−	0.738797i	$-0.735394\pi$
$577$	−32.3766	−1.34786	−0.673928	+	0.738797i	$0.735394\pi$
$578$	10.4453	0.434469
$579$	−15.1714	−0.630500
$580$	−8.15103	−0.338453
$581$	−7.61339	−0.315857
$582$	14.6304	0.606450
$583$	33.8604	1.40236
$584$	−7.12350	−0.294773
$585$	−8.68032	−0.358887
$586$	−21.7445	−0.898258
$587$	1.41582	0.0584372	0.0292186	−	0.999573i	$-0.490698\pi$
$587$	1.41582	0.0584372	0.0292186	+	0.999573i	$0.490698\pi$
$588$	0.0143142	0.000590307 0
$589$	−3.55061	−0.146300
$590$	5.31155	0.218673
$591$	−4.96943	−0.204415
$592$	−8.82225	−0.362592
$593$	−33.3084	−1.36781	−0.683906	−	0.729570i	$-0.739720\pi$
$593$	−33.3084	−1.36781	−0.683906	+	0.729570i	$0.739720\pi$
$594$	7.76534	0.318616
$595$	6.77059	0.277567
$596$	−15.7466	−0.645007
$597$	37.9934	1.55497
$598$	15.6406	0.639592
$599$	−25.0294	−1.02267	−0.511337	−	0.859380i	$-0.670850\pi$
$599$	−25.0294	−1.02267	−0.511337	+	0.859380i	$0.670850\pi$
$600$	2.24738	0.0917491
$601$	−42.0536	−1.71540	−0.857701	−	0.514149i	$-0.828108\pi$
$601$	−42.0536	−1.71540	−0.857701	+	0.514149i	$0.828108\pi$
$602$	−9.94123	−0.405174
$603$	24.8450	1.01177
$604$	8.51416	0.346436
$605$	−2.24925	−0.0914451
$606$	−36.0919	−1.46613
$607$	35.6597	1.44738	0.723691	−	0.690125i	$-0.242444\pi$
$607$	35.6597	1.44738	0.723691	+	0.690125i	$0.242444\pi$
$608$	−2.14346	−0.0869288
$609$	−48.4441	−1.96305
$610$	−2.57543	−0.104276
$611$	45.9376	1.85844
$612$	−5.25030	−0.212231
$613$	23.9140	0.965878	0.482939	−	0.875654i	$-0.339569\pi$
$613$	23.9140	0.965878	0.482939	+	0.875654i	$0.339569\pi$
$614$	18.3234	0.739473
$615$	1.10751	0.0446592
$616$	9.62603	0.387844
$617$	13.0895	0.526963	0.263482	−	0.964664i	$-0.415129\pi$
$617$	13.0895	0.526963	0.263482	+	0.964664i	$0.415129\pi$
$618$	28.4546	1.14461
$619$	39.7102	1.59609	0.798043	−	0.602600i	$-0.205869\pi$
$619$	39.7102	1.59609	0.798043	+	0.602600i	$0.205869\pi$
$620$	1.65648	0.0665260
$621$	−7.88300	−0.316334
$622$	−26.0232	−1.04344
$623$	18.5281	0.742312
$624$	−9.51270	−0.380813
$625$	1.00000	0.0400000
$626$	−2.46277	−0.0984322
$627$	17.5343	0.700252
$628$	13.8003	0.550693
$629$	22.5868	0.900594
$630$	5.42327	0.216068
$631$	−14.9622	−0.595635	−0.297818	−	0.954623i	$-0.596259\pi$
$631$	−14.9622	−0.595635	−0.297818	+	0.954623i	$0.596259\pi$
$632$	9.66661	0.384517
$633$	−59.7304	−2.37407
$634$	9.97922	0.396325
$635$	14.3666	0.570121
$636$	20.9062	0.828983
$637$	−0.0269597	−0.00106818
$638$	29.6693	1.17462
$639$	−23.8784	−0.944614
$640$	1.00000	0.0395285
$641$	12.1796	0.481066	0.240533	−	0.970641i	$-0.422678\pi$
$641$	12.1796	0.481066	0.240533	+	0.970641i	$0.422678\pi$
$642$	12.8014	0.505229
$643$	−35.9622	−1.41821	−0.709106	−	0.705102i	$-0.750901\pi$
$643$	−35.9622	−1.41821	−0.709106	+	0.705102i	$0.750901\pi$
$644$	−9.77189	−0.385066
$645$	8.44823	0.332649
$646$	5.48770	0.215911
$647$	3.02867	0.119069	0.0595346	−	0.998226i	$-0.481038\pi$
$647$	3.02867	0.119069	0.0595346	+	0.998226i	$0.481038\pi$
$648$	10.9467	0.430027
$649$	−19.3338	−0.758917
$650$	−4.23279	−0.166024
$651$	9.84500	0.385856
$652$	19.8361	0.776841
$653$	−47.6835	−1.86600	−0.933000	−	0.359877i	$-0.882819\pi$
$653$	−47.6835	−1.86600	−0.933000	+	0.359877i	$0.882819\pi$
$654$	−36.8558	−1.44118
$655$	7.21853	0.282051
$656$	0.492801	0.0192406
$657$	14.6084	0.569929
$658$	−28.7007	−1.11887
$659$	−5.83074	−0.227133	−0.113567	−	0.993530i	$-0.536228\pi$
$659$	−5.83074	−0.227133	−0.113567	+	0.993530i	$0.536228\pi$
$660$	−8.18037	−0.318420
$661$	26.5689	1.03341	0.516705	−	0.856163i	$-0.327158\pi$
$661$	26.5689	1.03341	0.516705	+	0.856163i	$0.327158\pi$
$662$	−26.5932	−1.03358
$663$	24.3545	0.945849
$664$	2.87890	0.111723
$665$	−5.66848	−0.219814
$666$	18.0921	0.701055
$667$	−30.1189	−1.16621
$668$	−19.0725	−0.737936
$669$	−37.6675	−1.45631
$670$	12.1152	0.468050
$671$	9.37445	0.361896
$672$	5.94331	0.229268
$673$	6.76895	0.260924	0.130462	−	0.991453i	$-0.458354\pi$
$673$	6.76895	0.260924	0.130462	+	0.991453i	$0.458354\pi$
$674$	−30.2375	−1.16471
$675$	2.13336	0.0821132
$676$	4.91649	0.189096
$677$	27.0777	1.04068	0.520339	−	0.853960i	$-0.325805\pi$
$677$	27.0777	1.04068	0.520339	+	0.853960i	$0.325805\pi$
$678$	−13.4171	−0.515282
$679$	17.2159	0.660687
$680$	−2.56021	−0.0981794
$681$	50.5716	1.93791
$682$	−6.02952	−0.230882
$683$	−11.6449	−0.445578	−0.222789	−	0.974867i	$-0.571516\pi$
$683$	−11.6449	−0.445578	−0.222789	+	0.974867i	$0.571516\pi$
$684$	4.39567	0.168073
$685$	−6.54622	−0.250118
$686$	18.5287	0.707428
$687$	−18.3278	−0.699249
$688$	3.75914	0.143316
$689$	−39.3752	−1.50008
$690$	8.30432	0.316140
$691$	18.4079	0.700271	0.350135	−	0.936699i	$-0.386136\pi$
$691$	18.4079	0.700271	0.350135	+	0.936699i	$0.386136\pi$
$692$	25.4482	0.967397
$693$	−19.7404	−0.749877
$694$	−19.3462	−0.734374
$695$	−5.72920	−0.217321
$696$	18.3185	0.694360
$697$	−1.26167	−0.0477892
$698$	−16.9751	−0.642515
$699$	−29.4612	−1.11433
$700$	2.64455	0.0999545
$701$	41.6674	1.57376	0.786879	−	0.617108i	$-0.211696\pi$
$701$	41.6674	1.57376	0.786879	+	0.617108i	$0.211696\pi$
$702$	−9.03007	−0.340818
$703$	−18.9101	−0.713210
$704$	−3.63995	−0.137186
$705$	24.3904	0.918596
$706$	9.96295	0.374960
$707$	−42.4702	−1.59725
$708$	−11.9371	−0.448623
$709$	6.39902	0.240320	0.120160	−	0.992755i	$-0.461659\pi$
$709$	6.39902	0.240320	0.120160	+	0.992755i	$0.461659\pi$
$710$	−11.6438	−0.436985
$711$	−19.8236	−0.743445
$712$	−7.00615	−0.262566
$713$	6.12088	0.229229
$714$	−15.2161	−0.569448
$715$	15.4071	0.576194
$716$	−10.0953	−0.377281
$717$	−45.0842	−1.68370
$718$	−16.2723	−0.607276
$719$	1.15175	0.0429529	0.0214764	−	0.999769i	$-0.493163\pi$
$719$	1.15175	0.0429529	0.0214764	+	0.999769i	$0.493163\pi$
$720$	−2.05073	−0.0764264
$721$	33.4832	1.24698
$722$	14.4056	0.536120
$723$	21.4825	0.798943
$724$	1.90872	0.0709372
$725$	8.15103	0.302721
$726$	5.05493	0.187606
$727$	22.5219	0.835290	0.417645	−	0.908610i	$-0.362856\pi$
$727$	22.5219	0.835290	0.417645	+	0.908610i	$0.362856\pi$
$728$	−11.1938	−0.414870
$729$	−8.06530	−0.298715
$730$	7.12350	0.263653
$731$	−9.62417	−0.355963
$732$	5.78798	0.213930
$733$	−14.1577	−0.522928	−0.261464	−	0.965213i	$-0.584205\pi$
$733$	−14.1577	−0.522928	−0.261464	+	0.965213i	$0.584205\pi$
$734$	−7.06728	−0.260858
$735$	−0.0143142	−0.000527986 0
$736$	3.69511	0.136203
$737$	−44.0986	−1.62439
$738$	−1.01060	−0.0372009
$739$	13.9682	0.513830	0.256915	−	0.966434i	$-0.417294\pi$
$739$	13.9682	0.513830	0.256915	+	0.966434i	$0.417294\pi$
$740$	8.82225	0.324312
$741$	−20.3901	−0.749049
$742$	24.6007	0.903121
$743$	−20.0697	−0.736286	−0.368143	−	0.929769i	$-0.620006\pi$
$743$	−20.0697	−0.736286	−0.368143	+	0.929769i	$0.620006\pi$
$744$	−3.72275	−0.136483
$745$	15.7466	0.576912
$746$	−20.9790	−0.768095
$747$	−5.90386	−0.216011
$748$	9.31903	0.340737
$749$	15.0636	0.550413
$750$	−2.24738	−0.0820629
$751$	−0.144520	−0.00527362	−0.00263681	−	0.999997i	$-0.500839\pi$
$751$	−0.144520	−0.00527362	−0.00263681	+	0.999997i	$0.500839\pi$
$752$	10.8528	0.395761
$753$	−56.7409	−2.06775
$754$	−34.5016	−1.25647
$755$	−8.51416	−0.309862
$756$	5.64178	0.205190
$757$	−9.76780	−0.355017	−0.177508	−	0.984119i	$-0.556804\pi$
$757$	−9.76780	−0.355017	−0.177508	+	0.984119i	$0.556804\pi$
$758$	−26.9851	−0.980142
$759$	−30.2273	−1.09718
$760$	2.14346	0.0777515
$761$	27.4102	0.993618	0.496809	−	0.867860i	$-0.334505\pi$
$761$	27.4102	0.993618	0.496809	+	0.867860i	$0.334505\pi$
$762$	−32.2873	−1.16964
$763$	−43.3691	−1.57007
$764$	17.9529	0.649513
$765$	5.25030	0.189825
$766$	−13.1837	−0.476348
$767$	22.4826	0.811801
$768$	−2.24738	−0.0810955
$769$	−7.46809	−0.269306	−0.134653	−	0.990893i	$-0.542992\pi$
$769$	−7.46809	−0.269306	−0.134653	+	0.990893i	$0.542992\pi$
$770$	−9.62603	−0.346898
$771$	−26.8911	−0.968460
$772$	6.75068	0.242962
$773$	38.9756	1.40186	0.700928	−	0.713232i	$-0.252769\pi$
$773$	38.9756	1.40186	0.700928	+	0.713232i	$0.252769\pi$
$774$	−7.70900	−0.277094
$775$	−1.65648	−0.0595026
$776$	−6.50997	−0.233694
$777$	52.4334	1.88104
$778$	−4.09900	−0.146956
$779$	1.05630	0.0378459
$780$	9.51270	0.340609
$781$	42.3829	1.51658
$782$	−9.46023	−0.338297
$783$	17.3891	0.621436
$784$	−0.00636926	−0.000227474 0
$785$	−13.8003	−0.492555
$786$	−16.2228	−0.578649
$787$	24.4377	0.871111	0.435555	−	0.900162i	$-0.356552\pi$
$787$	24.4377	0.871111	0.435555	+	0.900162i	$0.356552\pi$
$788$	2.21121	0.0787710
$789$	44.5853	1.58728
$790$	−9.66661	−0.343922
$791$	−15.7882	−0.561365
$792$	7.46458	0.265242
$793$	−10.9013	−0.387115
$794$	9.40802	0.333878
$795$	−20.9062	−0.741465
$796$	−16.9056	−0.599204
$797$	−32.5269	−1.15216	−0.576081	−	0.817393i	$-0.695419\pi$
$797$	−32.5269	−1.15216	−0.576081	+	0.817393i	$0.695419\pi$
$798$	12.7393	0.450965
$799$	−27.7854	−0.982977
$800$	−1.00000	−0.0353553
$801$	14.3678	0.507659
$802$	−1.00000	−0.0353112
$803$	−25.9292	−0.915022
$804$	−27.2274	−0.960238
$805$	9.77189	0.344414
$806$	7.01154	0.246971
$807$	11.8664	0.417718
$808$	16.0595	0.564972
$809$	−20.9475	−0.736474	−0.368237	−	0.929732i	$-0.620038\pi$
$809$	−20.9475	−0.736474	−0.368237	+	0.929732i	$0.620038\pi$
$810$	−10.9467	−0.384628
$811$	−4.40294	−0.154608	−0.0773041	−	0.997008i	$-0.524631\pi$
$811$	−4.40294	−0.154608	−0.0773041	+	0.997008i	$0.524631\pi$
$812$	21.5558	0.756459
$813$	−3.88817	−0.136364
$814$	−32.1126	−1.12555
$815$	−19.8361	−0.694828
$816$	5.75377	0.201422
$817$	8.05757	0.281899
$818$	30.9061	1.08061
$819$	22.9555	0.802131
$820$	−0.492801	−0.0172094
$821$	24.4861	0.854571	0.427286	−	0.904117i	$-0.359470\pi$
$821$	24.4861	0.854571	0.427286	+	0.904117i	$0.359470\pi$
$822$	14.7119	0.513135
$823$	36.6232	1.27661	0.638303	−	0.769786i	$-0.279637\pi$
$823$	36.6232	1.27661	0.638303	+	0.769786i	$0.279637\pi$
$824$	−12.6612	−0.441075
$825$	8.18037	0.284804
$826$	−14.0466	−0.488745
$827$	21.0412	0.731674	0.365837	−	0.930679i	$-0.380783\pi$
$827$	21.0412	0.731674	0.365837	+	0.930679i	$0.380783\pi$
$828$	−7.57768	−0.263343
$829$	32.3549	1.12373	0.561867	−	0.827228i	$-0.310083\pi$
$829$	32.3549	1.12373	0.561867	+	0.827228i	$0.310083\pi$
$830$	−2.87890	−0.0999281
$831$	−46.6398	−1.61792
$832$	4.23279	0.146745
$833$	0.0163066	0.000564991 0
$834$	12.8757	0.445850
$835$	19.0725	0.660030
$836$	−7.80209	−0.269841
$837$	−3.53388	−0.122149
$838$	−11.9442	−0.412606
$839$	39.5482	1.36536	0.682678	−	0.730719i	$-0.260815\pi$
$839$	39.5482	1.36536	0.682678	+	0.730719i	$0.260815\pi$
$840$	−5.94331	−0.205064
$841$	37.4392	1.29101
$842$	17.7020	0.610052
$843$	−27.3251	−0.941127
$844$	26.5778	0.914844
$845$	−4.91649	−0.169132
$846$	−22.2562	−0.765184
$847$	5.94825	0.204384
$848$	−9.30244	−0.319447
$849$	−58.2280	−1.99838
$850$	2.56021	0.0878143
$851$	32.5992	1.11748
$852$	26.1681	0.896505
$853$	−4.47754	−0.153308	−0.0766540	−	0.997058i	$-0.524424\pi$
$853$	−4.47754	−0.153308	−0.0766540	+	0.997058i	$0.524424\pi$
$854$	6.81085	0.233062
$855$	−4.39567	−0.150329
$856$	−5.69611	−0.194689
$857$	−29.8856	−1.02087	−0.510436	−	0.859916i	$-0.670516\pi$
$857$	−29.8856	−1.02087	−0.510436	+	0.859916i	$0.670516\pi$
$858$	−34.6258	−1.18210
$859$	−46.5935	−1.58975	−0.794875	−	0.606773i	$-0.792464\pi$
$859$	−46.5935	−1.58975	−0.794875	+	0.606773i	$0.792464\pi$
$860$	−3.75914	−0.128186
$861$	−2.92887	−0.0998157
$862$	−11.4989	−0.391654
$863$	−37.0533	−1.26131	−0.630654	−	0.776064i	$-0.717213\pi$
$863$	−37.0533	−1.26131	−0.630654	+	0.776064i	$0.717213\pi$
$864$	−2.13336	−0.0725785
$865$	−25.4482	−0.865266
$866$	5.48287	0.186315
$867$	23.4747	0.797243
$868$	−4.38065	−0.148689
$869$	35.1860	1.19360
$870$	−18.3185	−0.621055
$871$	51.2809	1.73759
$872$	16.3994	0.555355
$873$	13.3502	0.451837
$874$	7.92031	0.267909
$875$	−2.64455	−0.0894020
$876$	−16.0092	−0.540902
$877$	−13.9198	−0.470038	−0.235019	−	0.971991i	$-0.575515\pi$
$877$	−13.9198	−0.470038	−0.235019	+	0.971991i	$0.575515\pi$
$878$	−15.1822	−0.512375
$879$	−48.8683	−1.64829
$880$	3.63995	0.122703
$881$	−21.3258	−0.718483	−0.359242	−	0.933245i	$-0.616965\pi$
$881$	−21.3258	−0.718483	−0.359242	+	0.933245i	$0.616965\pi$
$882$	0.0130617	0.000439809 0
$883$	−8.85142	−0.297874	−0.148937	−	0.988847i	$-0.547585\pi$
$883$	−8.85142	−0.297874	−0.148937	+	0.988847i	$0.547585\pi$
$884$	−10.8368	−0.364481
$885$	11.9371	0.401261
$886$	−28.2058	−0.947591
$887$	−26.4880	−0.889379	−0.444689	−	0.895685i	$-0.646686\pi$
$887$	−26.4880	−0.889379	−0.444689	+	0.895685i	$0.646686\pi$
$888$	−19.8270	−0.665350
$889$	−37.9932	−1.27425
$890$	7.00615	0.234847
$891$	39.8454	1.33487
$892$	16.7606	0.561187
$893$	23.2625	0.778451
$894$	−35.3887	−1.18358
$895$	10.0953	0.337450
$896$	−2.64455	−0.0883481
$897$	35.1504	1.17364
$898$	−29.0535	−0.969528
$899$	−13.5020	−0.450318
$900$	2.05073	0.0683578
$901$	23.8162	0.793431
$902$	1.79377	0.0597261
$903$	−22.3418	−0.743487
$904$	5.97011	0.198563
$905$	−1.90872	−0.0634481
$906$	19.1346	0.635704
$907$	24.3462	0.808403	0.404202	−	0.914670i	$-0.367549\pi$
$907$	24.3462	0.808403	0.404202	+	0.914670i	$0.367549\pi$
$908$	−22.5024	−0.746769
$909$	−32.9338	−1.09235
$910$	11.1938	0.371071
$911$	−5.34248	−0.177004	−0.0885021	−	0.996076i	$-0.528208\pi$
$911$	−5.34248	−0.177004	−0.0885021	+	0.996076i	$0.528208\pi$
$912$	−4.81718	−0.159513
$913$	10.4791	0.346806
$914$	−2.42057	−0.0800655
$915$	−5.78798	−0.191345
$916$	8.15516	0.269454
$917$	−19.0897	−0.630399
$918$	5.46185	0.180268
$919$	30.1191	0.993537	0.496768	−	0.867883i	$-0.334520\pi$
$919$	30.1191	0.993537	0.496768	+	0.867883i	$0.334520\pi$
$920$	−3.69511	−0.121824
$921$	41.1798	1.35692
$922$	−25.7434	−0.847815
$923$	−49.2858	−1.62226
$924$	21.6334	0.711686
$925$	−8.82225	−0.290074
$926$	6.11273	0.200877
$927$	25.9648	0.852796
$928$	−8.15103	−0.267571
$929$	38.5146	1.26362	0.631812	−	0.775122i	$-0.282311\pi$
$929$	38.5146	1.26362	0.631812	+	0.775122i	$0.282311\pi$
$930$	3.72275	0.122074
$931$	−0.0136523	−0.000447435 0
$932$	13.1091	0.429403
$933$	−58.4841	−1.91468
$934$	−28.5787	−0.935122
$935$	−9.31903	−0.304765
$936$	−8.68032	−0.283725
$937$	5.34984	0.174772	0.0873858	−	0.996175i	$-0.472149\pi$
$937$	5.34984	0.174772	0.0873858	+	0.996175i	$0.472149\pi$
$938$	−32.0391	−1.04612
$939$	−5.53480	−0.180621
$940$	−10.8528	−0.353979
$941$	−4.09505	−0.133495	−0.0667474	−	0.997770i	$-0.521262\pi$
$941$	−4.09505	−0.133495	−0.0667474	+	0.997770i	$0.521262\pi$
$942$	31.0147	1.01051
$943$	−1.82095	−0.0592984
$944$	5.31155	0.172876
$945$	−5.64178	−0.183527
$946$	13.6831	0.444876
$947$	−49.5429	−1.60993	−0.804964	−	0.593324i	$-0.797815\pi$
$947$	−49.5429	−1.60993	−0.804964	+	0.593324i	$0.797815\pi$
$948$	21.7246	0.705581
$949$	30.1523	0.978784
$950$	−2.14346	−0.0695430
$951$	22.4271	0.727250
$952$	6.77059	0.219436
$953$	41.4007	1.34110	0.670551	−	0.741864i	$-0.266058\pi$
$953$	41.4007	1.34110	0.670551	+	0.741864i	$0.266058\pi$
$954$	19.0768	0.617635
$955$	−17.9529	−0.580942
$956$	20.0607	0.648811
$957$	66.6784	2.15541
$958$	19.7841	0.639194
$959$	17.3118	0.559027
$960$	2.24738	0.0725340
$961$	−28.2561	−0.911486
$962$	37.3427	1.20398
$963$	11.6812	0.376422
$964$	−9.55890	−0.307871
$965$	−6.75068	−0.217312
$966$	−21.9612	−0.706589
$967$	31.6390	1.01744	0.508720	−	0.860932i	$-0.330119\pi$
$967$	31.6390	1.01744	0.508720	+	0.860932i	$0.330119\pi$
$968$	−2.24925	−0.0722937
$969$	12.3330	0.396192
$970$	6.50997	0.209023
$971$	−1.51187	−0.0485182	−0.0242591	−	0.999706i	$-0.507723\pi$
$971$	−1.51187	−0.0485182	−0.0242591	+	0.999706i	$0.507723\pi$
$972$	18.2013	0.583808
$973$	15.1512	0.485724
$974$	4.44801	0.142523
$975$	−9.51270	−0.304650
$976$	−2.57543	−0.0824375
$977$	37.9954	1.21558	0.607791	−	0.794097i	$-0.292056\pi$
$977$	37.9954	1.21558	0.607791	+	0.794097i	$0.292056\pi$
$978$	44.5793	1.42549
$979$	−25.5020	−0.815049
$980$	0.00636926	0.000203459 0
$981$	−33.6309	−1.07375
$982$	−32.7380	−1.04471
$983$	−39.8909	−1.27232	−0.636160	−	0.771557i	$-0.719478\pi$
$983$	−39.8909	−1.27232	−0.636160	+	0.771557i	$0.719478\pi$
$984$	1.10751	0.0353062
$985$	−2.21121	−0.0704550
$986$	20.8683	0.664582
$987$	−64.5016	−2.05311
$988$	9.07281	0.288645
$989$	−13.8904	−0.441690
$990$	−7.46458	−0.237240
$991$	19.2149	0.610380	0.305190	−	0.952291i	$-0.401280\pi$
$991$	19.2149	0.610380	0.305190	+	0.952291i	$0.401280\pi$
$992$	1.65648	0.0525934
$993$	−59.7652	−1.89659
$994$	30.7926	0.976683
$995$	16.9056	0.535944
$996$	6.46999	0.205010
$997$	−9.66377	−0.306055	−0.153027	−	0.988222i	$-0.548902\pi$
$997$	−9.66377	−0.306055	−0.153027	+	0.988222i	$0.548902\pi$
$998$	33.3590	1.05596
$999$	−18.8211	−0.595472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.3	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.3	✓	17	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.24738 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24738 q^{6} +2.64455 q^{7} -1.00000 q^{8} +2.05073 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.24738 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24738 q^{6} +2.64455 q^{7} -1.00000 q^{8} +2.05073 q^{9} +1.00000 q^{10} -3.63995 q^{11} -2.24738 q^{12} +4.23279 q^{13} -2.64455 q^{14} +2.24738 q^{15} +1.00000 q^{16} -2.56021 q^{17} -2.05073 q^{18} +2.14346 q^{19} -1.00000 q^{20} -5.94331 q^{21} +3.63995 q^{22} -3.69511 q^{23} +2.24738 q^{24} +1.00000 q^{25} -4.23279 q^{26} +2.13336 q^{27} +2.64455 q^{28} +8.15103 q^{29} -2.24738 q^{30} -1.65648 q^{31} -1.00000 q^{32} +8.18037 q^{33} +2.56021 q^{34} -2.64455 q^{35} +2.05073 q^{36} -8.82225 q^{37} -2.14346 q^{38} -9.51270 q^{39} +1.00000 q^{40} +0.492801 q^{41} +5.94331 q^{42} +3.75914 q^{43} -3.63995 q^{44} -2.05073 q^{45} +3.69511 q^{46} +10.8528 q^{47} -2.24738 q^{48} -0.00636926 q^{49} -1.00000 q^{50} +5.75377 q^{51} +4.23279 q^{52} -9.30244 q^{53} -2.13336 q^{54} +3.63995 q^{55} -2.64455 q^{56} -4.81718 q^{57} -8.15103 q^{58} +5.31155 q^{59} +2.24738 q^{60} -2.57543 q^{61} +1.65648 q^{62} +5.42327 q^{63} +1.00000 q^{64} -4.23279 q^{65} -8.18037 q^{66} +12.1152 q^{67} -2.56021 q^{68} +8.30432 q^{69} +2.64455 q^{70} -11.6438 q^{71} -2.05073 q^{72} +7.12350 q^{73} +8.82225 q^{74} -2.24738 q^{75} +2.14346 q^{76} -9.62603 q^{77} +9.51270 q^{78} -9.66661 q^{79} -1.00000 q^{80} -10.9467 q^{81} -0.492801 q^{82} -2.87890 q^{83} -5.94331 q^{84} +2.56021 q^{85} -3.75914 q^{86} -18.3185 q^{87} +3.63995 q^{88} +7.00615 q^{89} +2.05073 q^{90} +11.1938 q^{91} -3.69511 q^{92} +3.72275 q^{93} -10.8528 q^{94} -2.14346 q^{95} +2.24738 q^{96} +6.50997 q^{97} +0.00636926 q^{98} -7.46458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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