LMFDB - Embedded newform 4010.2.a.m.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.a (trivial)

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.17
Root			$2.35112$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.35112 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.35112 q^{6} +2.99774 q^{7} -1.00000 q^{8} +2.52776 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.35112 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.35112 q^{6} +2.99774 q^{7} -1.00000 q^{8} +2.52776 q^{9} -1.00000 q^{10} +3.68623 q^{11} +2.35112 q^{12} +4.94979 q^{13} -2.99774 q^{14} +2.35112 q^{15} +1.00000 q^{16} -3.29792 q^{17} -2.52776 q^{18} -5.50280 q^{19} +1.00000 q^{20} +7.04804 q^{21} -3.68623 q^{22} +9.13143 q^{23} -2.35112 q^{24} +1.00000 q^{25} -4.94979 q^{26} -1.11029 q^{27} +2.99774 q^{28} -2.21912 q^{29} -2.35112 q^{30} -6.71372 q^{31} -1.00000 q^{32} +8.66676 q^{33} +3.29792 q^{34} +2.99774 q^{35} +2.52776 q^{36} +8.15919 q^{37} +5.50280 q^{38} +11.6375 q^{39} -1.00000 q^{40} -3.33511 q^{41} -7.04804 q^{42} +5.63248 q^{43} +3.68623 q^{44} +2.52776 q^{45} -9.13143 q^{46} +4.31143 q^{47} +2.35112 q^{48} +1.98643 q^{49} -1.00000 q^{50} -7.75380 q^{51} +4.94979 q^{52} -4.26798 q^{53} +1.11029 q^{54} +3.68623 q^{55} -2.99774 q^{56} -12.9377 q^{57} +2.21912 q^{58} -2.85194 q^{59} +2.35112 q^{60} +5.94370 q^{61} +6.71372 q^{62} +7.57756 q^{63} +1.00000 q^{64} +4.94979 q^{65} -8.66676 q^{66} +3.25039 q^{67} -3.29792 q^{68} +21.4691 q^{69} -2.99774 q^{70} +4.25016 q^{71} -2.52776 q^{72} -3.45548 q^{73} -8.15919 q^{74} +2.35112 q^{75} -5.50280 q^{76} +11.0503 q^{77} -11.6375 q^{78} -6.67692 q^{79} +1.00000 q^{80} -10.1937 q^{81} +3.33511 q^{82} -7.84142 q^{83} +7.04804 q^{84} -3.29792 q^{85} -5.63248 q^{86} -5.21740 q^{87} -3.68623 q^{88} +6.24116 q^{89} -2.52776 q^{90} +14.8382 q^{91} +9.13143 q^{92} -15.7847 q^{93} -4.31143 q^{94} -5.50280 q^{95} -2.35112 q^{96} -14.5141 q^{97} -1.98643 q^{98} +9.31790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.35112	1.35742	0.678710	−	0.734407i	$-0.262540\pi$
$3$	2.35112	1.35742	0.678710	+	0.734407i	$0.262540\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.35112	−0.959840
$7$	2.99774	1.13304	0.566519	−	0.824049i	$-0.308290\pi$
$7$	2.99774	1.13304	0.566519	+	0.824049i	$0.308290\pi$
$8$	−1.00000	−0.353553
$9$	2.52776	0.842587
$10$	−1.00000	−0.316228
$11$	3.68623	1.11144	0.555720	−	0.831370i	$-0.312443\pi$
$11$	3.68623	1.11144	0.555720	+	0.831370i	$0.312443\pi$
$12$	2.35112	0.678710
$13$	4.94979	1.37282	0.686412	−	0.727213i	$-0.259185\pi$
$13$	4.94979	1.37282	0.686412	+	0.727213i	$0.259185\pi$
$14$	−2.99774	−0.801179
$15$	2.35112	0.607056
$16$	1.00000	0.250000
$17$	−3.29792	−0.799863	−0.399932	−	0.916545i	$-0.630966\pi$
$17$	−3.29792	−0.799863	−0.399932	+	0.916545i	$0.630966\pi$
$18$	−2.52776	−0.595799
$19$	−5.50280	−1.26243	−0.631215	−	0.775608i	$-0.717443\pi$
$19$	−5.50280	−1.26243	−0.631215	+	0.775608i	$0.717443\pi$
$20$	1.00000	0.223607
$21$	7.04804	1.53801
$22$	−3.68623	−0.785906
$23$	9.13143	1.90403	0.952017	−	0.306045i	$-0.0990059\pi$
$23$	9.13143	1.90403	0.952017	+	0.306045i	$0.0990059\pi$
$24$	−2.35112	−0.479920
$25$	1.00000	0.200000
$26$	−4.94979	−0.970733
$27$	−1.11029	−0.213676
$28$	2.99774	0.566519
$29$	−2.21912	−0.412079	−0.206040	−	0.978544i	$-0.566058\pi$
$29$	−2.21912	−0.412079	−0.206040	+	0.978544i	$0.566058\pi$
$30$	−2.35112	−0.429254
$31$	−6.71372	−1.20582	−0.602910	−	0.797810i	$-0.705992\pi$
$31$	−6.71372	−1.20582	−0.602910	+	0.797810i	$0.705992\pi$
$32$	−1.00000	−0.176777
$33$	8.66676	1.50869
$34$	3.29792	0.565589
$35$	2.99774	0.506710
$36$	2.52776	0.421293
$37$	8.15919	1.34136	0.670681	−	0.741746i	$-0.266002\pi$
$37$	8.15919	1.34136	0.670681	+	0.741746i	$0.266002\pi$
$38$	5.50280	0.892673
$39$	11.6375	1.86350
$40$	−1.00000	−0.158114
$41$	−3.33511	−0.520856	−0.260428	−	0.965493i	$-0.583864\pi$
$41$	−3.33511	−0.520856	−0.260428	+	0.965493i	$0.583864\pi$
$42$	−7.04804	−1.08754
$43$	5.63248	0.858945	0.429473	−	0.903080i	$-0.358699\pi$
$43$	5.63248	0.858945	0.429473	+	0.903080i	$0.358699\pi$
$44$	3.68623	0.555720
$45$	2.52776	0.376816
$46$	−9.13143	−1.34636
$47$	4.31143	0.628886	0.314443	−	0.949276i	$-0.398182\pi$
$47$	4.31143	0.628886	0.314443	+	0.949276i	$0.398182\pi$
$48$	2.35112	0.339355
$49$	1.98643	0.283775
$50$	−1.00000	−0.141421
$51$	−7.75380	−1.08575
$52$	4.94979	0.686412
$53$	−4.26798	−0.586252	−0.293126	−	0.956074i	$-0.594696\pi$
$53$	−4.26798	−0.586252	−0.293126	+	0.956074i	$0.594696\pi$
$54$	1.11029	0.151091
$55$	3.68623	0.497051
$56$	−2.99774	−0.400589
$57$	−12.9377	−1.71365
$58$	2.21912	0.291384
$59$	−2.85194	−0.371292	−0.185646	−	0.982617i	$-0.559438\pi$
$59$	−2.85194	−0.371292	−0.185646	+	0.982617i	$0.559438\pi$
$60$	2.35112	0.303528
$61$	5.94370	0.761013	0.380507	−	0.924778i	$-0.375750\pi$
$61$	5.94370	0.761013	0.380507	+	0.924778i	$0.375750\pi$
$62$	6.71372	0.852643
$63$	7.57756	0.954683
$64$	1.00000	0.125000
$65$	4.94979	0.613946
$66$	−8.66676	−1.06680
$67$	3.25039	0.397099	0.198549	−	0.980091i	$-0.436377\pi$
$67$	3.25039	0.397099	0.198549	+	0.980091i	$0.436377\pi$
$68$	−3.29792	−0.399932
$69$	21.4691	2.58457
$70$	−2.99774	−0.358298
$71$	4.25016	0.504401	0.252201	−	0.967675i	$-0.418846\pi$
$71$	4.25016	0.504401	0.252201	+	0.967675i	$0.418846\pi$
$72$	−2.52776	−0.297899
$73$	−3.45548	−0.404434	−0.202217	−	0.979341i	$-0.564815\pi$
$73$	−3.45548	−0.404434	−0.202217	+	0.979341i	$0.564815\pi$
$74$	−8.15919	−0.948487
$75$	2.35112	0.271484
$76$	−5.50280	−0.631215
$77$	11.0503	1.25930
$78$	−11.6375	−1.31769
$79$	−6.67692	−0.751212	−0.375606	−	0.926779i	$-0.622565\pi$
$79$	−6.67692	−0.751212	−0.375606	+	0.926779i	$0.622565\pi$
$80$	1.00000	0.111803
$81$	−10.1937	−1.13263
$82$	3.33511	0.368301
$83$	−7.84142	−0.860707	−0.430354	−	0.902660i	$-0.641611\pi$
$83$	−7.84142	−0.860707	−0.430354	+	0.902660i	$0.641611\pi$
$84$	7.04804	0.769004
$85$	−3.29792	−0.357710
$86$	−5.63248	−0.607366
$87$	−5.21740	−0.559364
$88$	−3.68623	−0.392953
$89$	6.24116	0.661562	0.330781	−	0.943708i	$-0.392688\pi$
$89$	6.24116	0.661562	0.330781	+	0.943708i	$0.392688\pi$
$90$	−2.52776	−0.266449
$91$	14.8382	1.55546
$92$	9.13143	0.952017
$93$	−15.7847	−1.63680
$94$	−4.31143	−0.444690
$95$	−5.50280	−0.564576
$96$	−2.35112	−0.239960
$97$	−14.5141	−1.47368	−0.736841	−	0.676066i	$-0.763683\pi$
$97$	−14.5141	−1.47368	−0.736841	+	0.676066i	$0.763683\pi$
$98$	−1.98643	−0.200659
$99$	9.31790	0.936484
$100$	1.00000	0.100000
$101$	−4.40983	−0.438795	−0.219397	−	0.975636i	$-0.570409\pi$
$101$	−4.40983	−0.438795	−0.219397	+	0.975636i	$0.570409\pi$
$102$	7.75380	0.767741
$103$	7.25740	0.715093	0.357546	−	0.933895i	$-0.383613\pi$
$103$	7.25740	0.715093	0.357546	+	0.933895i	$0.383613\pi$
$104$	−4.94979	−0.485367
$105$	7.04804	0.687818
$106$	4.26798	0.414543
$107$	−19.6580	−1.90041	−0.950206	−	0.311623i	$-0.899128\pi$
$107$	−19.6580	−1.90041	−0.950206	+	0.311623i	$0.899128\pi$
$108$	−1.11029	−0.106838
$109$	−3.13998	−0.300755	−0.150378	−	0.988629i	$-0.548049\pi$
$109$	−3.13998	−0.300755	−0.150378	+	0.988629i	$0.548049\pi$
$110$	−3.68623	−0.351468
$111$	19.1832	1.82079
$112$	2.99774	0.283259
$113$	7.64125	0.718829	0.359414	−	0.933178i	$-0.382977\pi$
$113$	7.64125	0.718829	0.359414	+	0.933178i	$0.382977\pi$
$114$	12.9377	1.21173
$115$	9.13143	0.851510
$116$	−2.21912	−0.206040
$117$	12.5119	1.15672
$118$	2.85194	0.262543
$119$	−9.88630	−0.906275
$120$	−2.35112	−0.214627
$121$	2.58827	0.235297
$122$	−5.94370	−0.538118
$123$	−7.84123	−0.707020
$124$	−6.71372	−0.602910
$125$	1.00000	0.0894427
$126$	−7.57756	−0.675063
$127$	2.43288	0.215883	0.107941	−	0.994157i	$-0.465574\pi$
$127$	2.43288	0.215883	0.107941	+	0.994157i	$0.465574\pi$
$128$	−1.00000	−0.0883883
$129$	13.2426	1.16595
$130$	−4.94979	−0.434125
$131$	−8.40316	−0.734188	−0.367094	−	0.930184i	$-0.619647\pi$
$131$	−8.40316	−0.734188	−0.367094	+	0.930184i	$0.619647\pi$
$132$	8.66676	0.754344
$133$	−16.4960	−1.43038
$134$	−3.25039	−0.280791
$135$	−1.11029	−0.0955587
$136$	3.29792	0.282794
$137$	−12.0121	−1.02626	−0.513131	−	0.858310i	$-0.671515\pi$
$137$	−12.0121	−1.02626	−0.513131	+	0.858310i	$0.671515\pi$
$138$	−21.4691	−1.82757
$139$	1.76400	0.149620	0.0748101	−	0.997198i	$-0.476165\pi$
$139$	1.76400	0.149620	0.0748101	+	0.997198i	$0.476165\pi$
$140$	2.99774	0.253355
$141$	10.1367	0.853662
$142$	−4.25016	−0.356665
$143$	18.2460	1.52581
$144$	2.52776	0.210647
$145$	−2.21912	−0.184287
$146$	3.45548	0.285978
$147$	4.67032	0.385202
$148$	8.15919	0.670681
$149$	−11.9614	−0.979915	−0.489958	−	0.871746i	$-0.662988\pi$
$149$	−11.9614	−0.979915	−0.489958	+	0.871746i	$0.662988\pi$
$150$	−2.35112	−0.191968
$151$	1.78072	0.144913	0.0724563	−	0.997372i	$-0.476916\pi$
$151$	1.78072	0.144913	0.0724563	+	0.997372i	$0.476916\pi$
$152$	5.50280	0.446336
$153$	−8.33635	−0.673954
$154$	−11.0503	−0.890462
$155$	−6.71372	−0.539259
$156$	11.6375	0.931749
$157$	15.8133	1.26204	0.631018	−	0.775768i	$-0.282637\pi$
$157$	15.8133	1.26204	0.631018	+	0.775768i	$0.282637\pi$
$158$	6.67692	0.531187
$159$	−10.0345	−0.795790
$160$	−1.00000	−0.0790569
$161$	27.3736	2.15734
$162$	10.1937	0.800893
$163$	15.0464	1.17852	0.589261	−	0.807943i	$-0.299419\pi$
$163$	15.0464	1.17852	0.589261	+	0.807943i	$0.299419\pi$
$164$	−3.33511	−0.260428
$165$	8.66676	0.674706
$166$	7.84142	0.608612
$167$	5.44620	0.421439	0.210720	−	0.977547i	$-0.432419\pi$
$167$	5.44620	0.421439	0.210720	+	0.977547i	$0.432419\pi$
$168$	−7.04804	−0.543768
$169$	11.5004	0.884647
$170$	3.29792	0.252939
$171$	−13.9098	−1.06371
$172$	5.63248	0.429473
$173$	13.0125	0.989324	0.494662	−	0.869085i	$-0.335292\pi$
$173$	13.0125	0.989324	0.494662	+	0.869085i	$0.335292\pi$
$174$	5.21740	0.395530
$175$	2.99774	0.226608
$176$	3.68623	0.277860
$177$	−6.70526	−0.503998
$178$	−6.24116	−0.467795
$179$	3.51248	0.262535	0.131267	−	0.991347i	$-0.458095\pi$
$179$	3.51248	0.262535	0.131267	+	0.991347i	$0.458095\pi$
$180$	2.52776	0.188408
$181$	13.4280	0.998098	0.499049	−	0.866574i	$-0.333683\pi$
$181$	13.4280	0.998098	0.499049	+	0.866574i	$0.333683\pi$
$182$	−14.8382	−1.09988
$183$	13.9744	1.03301
$184$	−9.13143	−0.673178
$185$	8.15919	0.599876
$186$	15.7847	1.15739
$187$	−12.1569	−0.888999
$188$	4.31143	0.314443
$189$	−3.32836	−0.242103
$190$	5.50280	0.399215
$191$	−12.9657	−0.938162	−0.469081	−	0.883155i	$-0.655415\pi$
$191$	−12.9657	−0.938162	−0.469081	+	0.883155i	$0.655415\pi$
$192$	2.35112	0.169677
$193$	17.5975	1.26670	0.633349	−	0.773866i	$-0.281680\pi$
$193$	17.5975	1.26670	0.633349	+	0.773866i	$0.281680\pi$
$194$	14.5141	1.04205
$195$	11.6375	0.833382
$196$	1.98643	0.141888
$197$	−3.52793	−0.251355	−0.125677	−	0.992071i	$-0.540110\pi$
$197$	−3.52793	−0.251355	−0.125677	+	0.992071i	$0.540110\pi$
$198$	−9.31790	−0.662194
$199$	−13.2448	−0.938896	−0.469448	−	0.882960i	$-0.655547\pi$
$199$	−13.2448	−0.938896	−0.469448	+	0.882960i	$0.655547\pi$
$200$	−1.00000	−0.0707107
$201$	7.64206	0.539029
$202$	4.40983	0.310275
$203$	−6.65232	−0.466902
$204$	−7.75380	−0.542875
$205$	−3.33511	−0.232934
$206$	−7.25740	−0.505647
$207$	23.0821	1.60431
$208$	4.94979	0.343206
$209$	−20.2846	−1.40311
$210$	−7.04804	−0.486361
$211$	−24.7946	−1.70693	−0.853465	−	0.521151i	$-0.825503\pi$
$211$	−24.7946	−1.70693	−0.853465	+	0.521151i	$0.825503\pi$
$212$	−4.26798	−0.293126
$213$	9.99263	0.684684
$214$	19.6580	1.34379
$215$	5.63248	0.384132
$216$	1.11029	0.0755457
$217$	−20.1260	−1.36624
$218$	3.13998	0.212666
$219$	−8.12425	−0.548986
$220$	3.68623	0.248525
$221$	−16.3240	−1.09807
$222$	−19.1832	−1.28749
$223$	6.19236	0.414671	0.207335	−	0.978270i	$-0.433521\pi$
$223$	6.19236	0.414671	0.207335	+	0.978270i	$0.433521\pi$
$224$	−2.99774	−0.200295
$225$	2.52776	0.168517
$226$	−7.64125	−0.508289
$227$	−3.74292	−0.248426	−0.124213	−	0.992256i	$-0.539641\pi$
$227$	−3.74292	−0.248426	−0.124213	+	0.992256i	$0.539641\pi$
$228$	−12.9377	−0.856823
$229$	4.49519	0.297051	0.148525	−	0.988909i	$-0.452547\pi$
$229$	4.49519	0.297051	0.148525	+	0.988909i	$0.452547\pi$
$230$	−9.13143	−0.602108
$231$	25.9807	1.70940
$232$	2.21912	0.145692
$233$	−25.3781	−1.66258	−0.831288	−	0.555841i	$-0.812396\pi$
$233$	−25.3781	−1.66258	−0.831288	+	0.555841i	$0.812396\pi$
$234$	−12.5119	−0.817927
$235$	4.31143	0.281246
$236$	−2.85194	−0.185646
$237$	−15.6982	−1.01971
$238$	9.88630	0.640833
$239$	−11.4918	−0.743345	−0.371673	−	0.928364i	$-0.621216\pi$
$239$	−11.4918	−0.743345	−0.371673	+	0.928364i	$0.621216\pi$
$240$	2.35112	0.151764
$241$	15.4478	0.995081	0.497541	−	0.867441i	$-0.334237\pi$
$241$	15.4478	0.995081	0.497541	+	0.867441i	$0.334237\pi$
$242$	−2.58827	−0.166380
$243$	−20.6357	−1.32378
$244$	5.94370	0.380507
$245$	1.98643	0.126908
$246$	7.84123	0.499939
$247$	−27.2377	−1.73309
$248$	6.71372	0.426321
$249$	−18.4361	−1.16834
$250$	−1.00000	−0.0632456
$251$	−25.1275	−1.58603	−0.793017	−	0.609199i	$-0.791491\pi$
$251$	−25.1275	−1.58603	−0.793017	+	0.609199i	$0.791491\pi$
$252$	7.57756	0.477341
$253$	33.6605	2.11622
$254$	−2.43288	−0.152652
$255$	−7.75380	−0.485562
$256$	1.00000	0.0625000
$257$	−4.94420	−0.308411	−0.154205	−	0.988039i	$-0.549282\pi$
$257$	−4.94420	−0.308411	−0.154205	+	0.988039i	$0.549282\pi$
$258$	−13.2426	−0.824450
$259$	24.4591	1.51982
$260$	4.94979	0.306973
$261$	−5.60939	−0.347213
$262$	8.40316	0.519149
$263$	21.4350	1.32174	0.660868	−	0.750502i	$-0.270188\pi$
$263$	21.4350	1.32174	0.660868	+	0.750502i	$0.270188\pi$
$264$	−8.66676	−0.533402
$265$	−4.26798	−0.262180
$266$	16.4960	1.01143
$267$	14.6737	0.898017
$268$	3.25039	0.198549
$269$	−24.4060	−1.48806	−0.744031	−	0.668145i	$-0.767089\pi$
$269$	−24.4060	−1.48806	−0.744031	+	0.668145i	$0.767089\pi$
$270$	1.11029	0.0675702
$271$	28.2516	1.71616	0.858082	−	0.513512i	$-0.171656\pi$
$271$	28.2516	1.71616	0.858082	+	0.513512i	$0.171656\pi$
$272$	−3.29792	−0.199966
$273$	34.8863	2.11141
$274$	12.0121	0.725677
$275$	3.68623	0.222288
$276$	21.4691	1.29229
$277$	2.58921	0.155570	0.0777852	−	0.996970i	$-0.475215\pi$
$277$	2.58921	0.155570	0.0777852	+	0.996970i	$0.475215\pi$
$278$	−1.76400	−0.105798
$279$	−16.9707	−1.01601
$280$	−2.99774	−0.179149
$281$	12.8437	0.766192	0.383096	−	0.923709i	$-0.374858\pi$
$281$	12.8437	0.766192	0.383096	+	0.923709i	$0.374858\pi$
$282$	−10.1367	−0.603630
$283$	−16.7005	−0.992742	−0.496371	−	0.868110i	$-0.665334\pi$
$283$	−16.7005	−0.992742	−0.496371	+	0.868110i	$0.665334\pi$
$284$	4.25016	0.252201
$285$	−12.9377	−0.766366
$286$	−18.2460	−1.07891
$287$	−9.99777	−0.590150
$288$	−2.52776	−0.148950
$289$	−6.12372	−0.360219
$290$	2.21912	0.130311
$291$	−34.1243	−2.00040
$292$	−3.45548	−0.202217
$293$	24.3858	1.42463	0.712316	−	0.701859i	$-0.247646\pi$
$293$	24.3858	1.42463	0.712316	+	0.701859i	$0.247646\pi$
$294$	−4.67032	−0.272379
$295$	−2.85194	−0.166047
$296$	−8.15919	−0.474243
$297$	−4.09279	−0.237487
$298$	11.9614	0.692905
$299$	45.1986	2.61390
$300$	2.35112	0.135742
$301$	16.8847	0.973218
$302$	−1.78072	−0.102469
$303$	−10.3680	−0.595628
$304$	−5.50280	−0.315607
$305$	5.94370	0.340335
$306$	8.33635	0.476557
$307$	−20.7455	−1.18401	−0.592004	−	0.805935i	$-0.701663\pi$
$307$	−20.7455	−1.18401	−0.592004	+	0.805935i	$0.701663\pi$
$308$	11.0503	0.629651
$309$	17.0630	0.970681
$310$	6.71372	0.381313
$311$	22.6276	1.28309	0.641547	−	0.767084i	$-0.278293\pi$
$311$	22.6276	1.28309	0.641547	+	0.767084i	$0.278293\pi$
$312$	−11.6375	−0.658846
$313$	−12.3424	−0.697636	−0.348818	−	0.937190i	$-0.613417\pi$
$313$	−12.3424	−0.697636	−0.348818	+	0.937190i	$0.613417\pi$
$314$	−15.8133	−0.892394
$315$	7.57756	0.426947
$316$	−6.67692	−0.375606
$317$	10.8344	0.608518	0.304259	−	0.952589i	$-0.401591\pi$
$317$	10.8344	0.608518	0.304259	+	0.952589i	$0.401591\pi$
$318$	10.0345	0.562709
$319$	−8.18016	−0.458001
$320$	1.00000	0.0559017
$321$	−46.2183	−2.57966
$322$	−27.3736	−1.52547
$323$	18.1478	1.00977
$324$	−10.1937	−0.566317
$325$	4.94979	0.274565
$326$	−15.0464	−0.833341
$327$	−7.38246	−0.408251
$328$	3.33511	0.184150
$329$	12.9245	0.712552
$330$	−8.66676	−0.477089
$331$	33.5489	1.84401	0.922007	−	0.387173i	$-0.126548\pi$
$331$	33.5489	1.84401	0.922007	+	0.387173i	$0.126548\pi$
$332$	−7.84142	−0.430354
$333$	20.6245	1.13021
$334$	−5.44620	−0.298003
$335$	3.25039	0.177588
$336$	7.04804	0.384502
$337$	15.9388	0.868243	0.434122	−	0.900854i	$-0.357059\pi$
$337$	15.9388	0.868243	0.434122	+	0.900854i	$0.357059\pi$
$338$	−11.5004	−0.625540
$339$	17.9655	0.975752
$340$	−3.29792	−0.178855
$341$	−24.7483	−1.34019
$342$	13.9098	0.752154
$343$	−15.0294	−0.811510
$344$	−5.63248	−0.303683
$345$	21.4691	1.15586
$346$	−13.0125	−0.699558
$347$	−2.46957	−0.132573	−0.0662867	−	0.997801i	$-0.521115\pi$
$347$	−2.46957	−0.132573	−0.0662867	+	0.997801i	$0.521115\pi$
$348$	−5.21740	−0.279682
$349$	19.9313	1.06690	0.533450	−	0.845832i	$-0.320895\pi$
$349$	19.9313	1.06690	0.533450	+	0.845832i	$0.320895\pi$
$350$	−2.99774	−0.160236
$351$	−5.49571	−0.293339
$352$	−3.68623	−0.196477
$353$	−34.1233	−1.81620	−0.908099	−	0.418756i	$-0.862466\pi$
$353$	−34.1233	−1.81620	−0.908099	+	0.418756i	$0.862466\pi$
$354$	6.70526	0.356381
$355$	4.25016	0.225575
$356$	6.24116	0.330781
$357$	−23.2439	−1.23020
$358$	−3.51248	−0.185640
$359$	−16.7422	−0.883619	−0.441810	−	0.897109i	$-0.645663\pi$
$359$	−16.7422	−0.883619	−0.441810	+	0.897109i	$0.645663\pi$
$360$	−2.52776	−0.133225
$361$	11.2809	0.593729
$362$	−13.4280	−0.705762
$363$	6.08533	0.319397
$364$	14.8382	0.777731
$365$	−3.45548	−0.180868
$366$	−13.9744	−0.730451
$367$	30.2053	1.57670	0.788351	−	0.615226i	$-0.210935\pi$
$367$	30.2053	1.57670	0.788351	+	0.615226i	$0.210935\pi$
$368$	9.13143	0.476008
$369$	−8.43035	−0.438867
$370$	−8.15919	−0.424176
$371$	−12.7943	−0.664246
$372$	−15.7847	−0.818401
$373$	35.6200	1.84433	0.922167	−	0.386793i	$-0.126417\pi$
$373$	35.6200	1.84433	0.922167	+	0.386793i	$0.126417\pi$
$374$	12.1569	0.628617
$375$	2.35112	0.121411
$376$	−4.31143	−0.222345
$377$	−10.9842	−0.565713
$378$	3.32836	0.171192
$379$	−21.0459	−1.08106	−0.540528	−	0.841326i	$-0.681775\pi$
$379$	−21.0459	−1.08106	−0.540528	+	0.841326i	$0.681775\pi$
$380$	−5.50280	−0.282288
$381$	5.71998	0.293044
$382$	12.9657	0.663381
$383$	−33.1871	−1.69578	−0.847892	−	0.530169i	$-0.822128\pi$
$383$	−33.1871	−1.69578	−0.847892	+	0.530169i	$0.822128\pi$
$384$	−2.35112	−0.119980
$385$	11.0503	0.563177
$386$	−17.5975	−0.895691
$387$	14.2376	0.723736
$388$	−14.5141	−0.736841
$389$	20.7101	1.05004	0.525022	−	0.851088i	$-0.324057\pi$
$389$	20.7101	1.05004	0.525022	+	0.851088i	$0.324057\pi$
$390$	−11.6375	−0.589290
$391$	−30.1147	−1.52297
$392$	−1.98643	−0.100330
$393$	−19.7568	−0.996601
$394$	3.52793	0.177735
$395$	−6.67692	−0.335952
$396$	9.31790	0.468242
$397$	−29.8335	−1.49730	−0.748650	−	0.662965i	$-0.769298\pi$
$397$	−29.8335	−1.49730	−0.748650	+	0.662965i	$0.769298\pi$
$398$	13.2448	0.663900
$399$	−38.7840	−1.94163
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−7.64206	−0.381151
$403$	−33.2315	−1.65538
$404$	−4.40983	−0.219397
$405$	−10.1937	−0.506529
$406$	6.65232	0.330149
$407$	30.0766	1.49084
$408$	7.75380	0.383870
$409$	10.6247	0.525360	0.262680	−	0.964883i	$-0.415394\pi$
$409$	10.6247	0.525360	0.262680	+	0.964883i	$0.415394\pi$
$410$	3.33511	0.164709
$411$	−28.2419	−1.39307
$412$	7.25740	0.357546
$413$	−8.54938	−0.420687
$414$	−23.0821	−1.13442
$415$	−7.84142	−0.384920
$416$	−4.94979	−0.242683
$417$	4.14737	0.203097
$418$	20.2846	0.992152
$419$	38.7783	1.89445	0.947223	−	0.320576i	$-0.103876\pi$
$419$	38.7783	1.89445	0.947223	+	0.320576i	$0.103876\pi$
$420$	7.04804	0.343909
$421$	16.2911	0.793980	0.396990	−	0.917823i	$-0.370055\pi$
$421$	16.2911	0.793980	0.396990	+	0.917823i	$0.370055\pi$
$422$	24.7946	1.20698
$423$	10.8983	0.529891
$424$	4.26798	0.207272
$425$	−3.29792	−0.159973
$426$	−9.99263	−0.484144
$427$	17.8177	0.862257
$428$	−19.6580	−0.950206
$429$	42.8986	2.07116
$430$	−5.63248	−0.271622
$431$	−30.3455	−1.46169	−0.730846	−	0.682542i	$-0.760874\pi$
$431$	−30.3455	−1.46169	−0.730846	+	0.682542i	$0.760874\pi$
$432$	−1.11029	−0.0534189
$433$	2.06320	0.0991508	0.0495754	−	0.998770i	$-0.484213\pi$
$433$	2.06320	0.0991508	0.0495754	+	0.998770i	$0.484213\pi$
$434$	20.1260	0.966077
$435$	−5.21740	−0.250155
$436$	−3.13998	−0.150378
$437$	−50.2485	−2.40371
$438$	8.12425	0.388192
$439$	11.9990	0.572679	0.286339	−	0.958128i	$-0.407562\pi$
$439$	11.9990	0.572679	0.286339	+	0.958128i	$0.407562\pi$
$440$	−3.68623	−0.175734
$441$	5.02121	0.239105
$442$	16.3240	0.776454
$443$	−13.6497	−0.648516	−0.324258	−	0.945969i	$-0.605115\pi$
$443$	−13.6497	−0.648516	−0.324258	+	0.945969i	$0.605115\pi$
$444$	19.1832	0.910396
$445$	6.24116	0.295860
$446$	−6.19236	−0.293217
$447$	−28.1227	−1.33016
$448$	2.99774	0.141630
$449$	−1.71601	−0.0809835	−0.0404918	−	0.999180i	$-0.512892\pi$
$449$	−1.71601	−0.0809835	−0.0404918	+	0.999180i	$0.512892\pi$
$450$	−2.52776	−0.119160
$451$	−12.2940	−0.578900
$452$	7.64125	0.359414
$453$	4.18668	0.196707
$454$	3.74292	0.175664
$455$	14.8382	0.695624
$456$	12.9377	0.605866
$457$	2.10521	0.0984776	0.0492388	−	0.998787i	$-0.484320\pi$
$457$	2.10521	0.0984776	0.0492388	+	0.998787i	$0.484320\pi$
$458$	−4.49519	−0.210047
$459$	3.66165	0.170911
$460$	9.13143	0.425755
$461$	−11.7972	−0.549449	−0.274725	−	0.961523i	$-0.588587\pi$
$461$	−11.7972	−0.549449	−0.274725	+	0.961523i	$0.588587\pi$
$462$	−25.9807	−1.20873
$463$	7.57470	0.352026	0.176013	−	0.984388i	$-0.443680\pi$
$463$	7.57470	0.352026	0.176013	+	0.984388i	$0.443680\pi$
$464$	−2.21912	−0.103020
$465$	−15.7847	−0.732000
$466$	25.3781	1.17562
$467$	9.50843	0.439998	0.219999	−	0.975500i	$-0.429395\pi$
$467$	9.50843	0.439998	0.219999	+	0.975500i	$0.429395\pi$
$468$	12.5119	0.578362
$469$	9.74382	0.449928
$470$	−4.31143	−0.198871
$471$	37.1789	1.71311
$472$	2.85194	0.131271
$473$	20.7626	0.954666
$474$	15.6982	0.721044
$475$	−5.50280	−0.252486
$476$	−9.88630	−0.453138
$477$	−10.7884	−0.493969
$478$	11.4918	0.525625
$479$	−3.52335	−0.160986	−0.0804929	−	0.996755i	$-0.525649\pi$
$479$	−3.52335	−0.160986	−0.0804929	+	0.996755i	$0.525649\pi$
$480$	−2.35112	−0.107313
$481$	40.3863	1.84146
$482$	−15.4478	−0.703629
$483$	64.3586	2.92842
$484$	2.58827	0.117649
$485$	−14.5141	−0.659051
$486$	20.6357	0.936057
$487$	−15.3389	−0.695071	−0.347536	−	0.937667i	$-0.612981\pi$
$487$	−15.3389	−0.695071	−0.347536	+	0.937667i	$0.612981\pi$
$488$	−5.94370	−0.269059
$489$	35.3758	1.59975
$490$	−1.98643	−0.0897376
$491$	−23.9914	−1.08272	−0.541358	−	0.840792i	$-0.682089\pi$
$491$	−23.9914	−1.08272	−0.541358	+	0.840792i	$0.682089\pi$
$492$	−7.84123	−0.353510
$493$	7.31846	0.329607
$494$	27.2377	1.22548
$495$	9.31790	0.418808
$496$	−6.71372	−0.301455
$497$	12.7409	0.571505
$498$	18.4361	0.826141
$499$	6.09523	0.272860	0.136430	−	0.990650i	$-0.456437\pi$
$499$	6.09523	0.272860	0.136430	+	0.990650i	$0.456437\pi$
$500$	1.00000	0.0447214
$501$	12.8047	0.572070
$502$	25.1275	1.12150
$503$	6.75372	0.301134	0.150567	−	0.988600i	$-0.451890\pi$
$503$	6.75372	0.301134	0.150567	+	0.988600i	$0.451890\pi$
$504$	−7.57756	−0.337531
$505$	−4.40983	−0.196235
$506$	−33.6605	−1.49639
$507$	27.0388	1.20084
$508$	2.43288	0.107941
$509$	7.02781	0.311502	0.155751	−	0.987796i	$-0.450220\pi$
$509$	7.02781	0.311502	0.155751	+	0.987796i	$0.450220\pi$
$510$	7.75380	0.343344
$511$	−10.3586	−0.458239
$512$	−1.00000	−0.0441942
$513$	6.10972	0.269751
$514$	4.94420	0.218079
$515$	7.25740	0.319799
$516$	13.2426	0.582975
$517$	15.8929	0.698969
$518$	−24.4591	−1.07467
$519$	30.5940	1.34293
$520$	−4.94979	−0.217063
$521$	−29.5769	−1.29579	−0.647894	−	0.761730i	$-0.724350\pi$
$521$	−29.5769	−1.29579	−0.647894	+	0.761730i	$0.724350\pi$
$522$	5.60939	0.245516
$523$	−37.5964	−1.64397	−0.821987	−	0.569506i	$-0.807134\pi$
$523$	−37.5964	−1.64397	−0.821987	+	0.569506i	$0.807134\pi$
$524$	−8.40316	−0.367094
$525$	7.04804	0.307601
$526$	−21.4350	−0.934609
$527$	22.1413	0.964490
$528$	8.66676	0.377172
$529$	60.3829	2.62535
$530$	4.26798	0.185389
$531$	−7.20903	−0.312845
$532$	−16.4960	−0.715191
$533$	−16.5081	−0.715044
$534$	−14.6737	−0.634994
$535$	−19.6580	−0.849890
$536$	−3.25039	−0.140396
$537$	8.25825	0.356370
$538$	24.4060	1.05222
$539$	7.32241	0.315399
$540$	−1.11029	−0.0477793
$541$	6.87485	0.295573	0.147787	−	0.989019i	$-0.452785\pi$
$541$	6.87485	0.295573	0.147787	+	0.989019i	$0.452785\pi$
$542$	−28.2516	−1.21351
$543$	31.5709	1.35484
$544$	3.29792	0.141397
$545$	−3.13998	−0.134502
$546$	−34.8863	−1.49300
$547$	29.4395	1.25874	0.629370	−	0.777106i	$-0.283313\pi$
$547$	29.4395	1.25874	0.629370	+	0.777106i	$0.283313\pi$
$548$	−12.0121	−0.513131
$549$	15.0243	0.641220
$550$	−3.68623	−0.157181
$551$	12.2114	0.520221
$552$	−21.4691	−0.913784
$553$	−20.0157	−0.851152
$554$	−2.58921	−0.110005
$555$	19.1832	0.814283
$556$	1.76400	0.0748101
$557$	−28.3216	−1.20002	−0.600012	−	0.799991i	$-0.704837\pi$
$557$	−28.3216	−1.20002	−0.600012	+	0.799991i	$0.704837\pi$
$558$	16.9707	0.718426
$559$	27.8796	1.17918
$560$	2.99774	0.126677
$561$	−28.5823	−1.20674
$562$	−12.8437	−0.541780
$563$	46.2817	1.95054	0.975271	−	0.221014i	$-0.0709367\pi$
$563$	46.2817	1.95054	0.975271	+	0.221014i	$0.0709367\pi$
$564$	10.1367	0.426831
$565$	7.64125	0.321470
$566$	16.7005	0.701975
$567$	−30.5581	−1.28332
$568$	−4.25016	−0.178333
$569$	19.0887	0.800241	0.400120	−	0.916463i	$-0.368968\pi$
$569$	19.0887	0.800241	0.400120	+	0.916463i	$0.368968\pi$
$570$	12.9377	0.541903
$571$	−13.5320	−0.566296	−0.283148	−	0.959076i	$-0.591379\pi$
$571$	−13.5320	−0.566296	−0.283148	+	0.959076i	$0.591379\pi$
$572$	18.2460	0.762905
$573$	−30.4838	−1.27348
$574$	9.99777	0.417299
$575$	9.13143	0.380807
$576$	2.52776	0.105323
$577$	−3.39489	−0.141331	−0.0706656	−	0.997500i	$-0.522512\pi$
$577$	−3.39489	−0.141331	−0.0706656	+	0.997500i	$0.522512\pi$
$578$	6.12372	0.254713
$579$	41.3739	1.71944
$580$	−2.21912	−0.0921437
$581$	−23.5065	−0.975214
$582$	34.1243	1.41450
$583$	−15.7328	−0.651584
$584$	3.45548	0.142989
$585$	12.5119	0.517303
$586$	−24.3858	−1.00737
$587$	0.510185	0.0210576	0.0105288	−	0.999945i	$-0.496649\pi$
$587$	0.510185	0.0210576	0.0105288	+	0.999945i	$0.496649\pi$
$588$	4.67032	0.192601
$589$	36.9443	1.52226
$590$	2.85194	0.117413
$591$	−8.29459	−0.341194
$592$	8.15919	0.335341
$593$	30.8665	1.26753	0.633767	−	0.773524i	$-0.281508\pi$
$593$	30.8665	1.26753	0.633767	+	0.773524i	$0.281508\pi$
$594$	4.09279	0.167929
$595$	−9.88630	−0.405299
$596$	−11.9614	−0.489958
$597$	−31.1400	−1.27448
$598$	−45.1986	−1.84831
$599$	37.5524	1.53435	0.767176	−	0.641437i	$-0.221662\pi$
$599$	37.5524	1.53435	0.767176	+	0.641437i	$0.221662\pi$
$600$	−2.35112	−0.0959840
$601$	21.8234	0.890193	0.445097	−	0.895483i	$-0.353169\pi$
$601$	21.8234	0.890193	0.445097	+	0.895483i	$0.353169\pi$
$602$	−16.8847	−0.688169
$603$	8.21621	0.334590
$604$	1.78072	0.0724563
$605$	2.58827	0.105228
$606$	10.3680	0.421173
$607$	−9.55411	−0.387789	−0.193895	−	0.981022i	$-0.562112\pi$
$607$	−9.55411	−0.387789	−0.193895	+	0.981022i	$0.562112\pi$
$608$	5.50280	0.223168
$609$	−15.6404	−0.633781
$610$	−5.94370	−0.240653
$611$	21.3406	0.863350
$612$	−8.33635	−0.336977
$613$	−40.4923	−1.63547	−0.817735	−	0.575595i	$-0.804770\pi$
$613$	−40.4923	−1.63547	−0.817735	+	0.575595i	$0.804770\pi$
$614$	20.7455	0.837220
$615$	−7.84123	−0.316189
$616$	−11.0503	−0.445231
$617$	29.8812	1.20297	0.601485	−	0.798884i	$-0.294576\pi$
$617$	29.8812	1.20297	0.601485	+	0.798884i	$0.294576\pi$
$618$	−17.0630	−0.686375
$619$	4.30208	0.172915	0.0864575	−	0.996256i	$-0.472445\pi$
$619$	4.30208	0.172915	0.0864575	+	0.996256i	$0.472445\pi$
$620$	−6.71372	−0.269629
$621$	−10.1385	−0.406846
$622$	−22.6276	−0.907284
$623$	18.7094	0.749575
$624$	11.6375	0.465875
$625$	1.00000	0.0400000
$626$	12.3424	0.493303
$627$	−47.6915	−1.90461
$628$	15.8133	0.631018
$629$	−26.9084	−1.07291
$630$	−7.57756	−0.301897
$631$	7.43676	0.296053	0.148026	−	0.988983i	$-0.452708\pi$
$631$	7.43676	0.296053	0.148026	+	0.988983i	$0.452708\pi$
$632$	6.67692	0.265594
$633$	−58.2950	−2.31702
$634$	−10.8344	−0.430287
$635$	2.43288	0.0965458
$636$	−10.0345	−0.397895
$637$	9.83239	0.389573
$638$	8.18016	0.323856
$639$	10.7434	0.425002
$640$	−1.00000	−0.0395285
$641$	29.1784	1.15248	0.576238	−	0.817282i	$-0.304520\pi$
$641$	29.1784	1.15248	0.576238	+	0.817282i	$0.304520\pi$
$642$	46.2183	1.82409
$643$	1.50900	0.0595091	0.0297545	−	0.999557i	$-0.490527\pi$
$643$	1.50900	0.0595091	0.0297545	+	0.999557i	$0.490527\pi$
$644$	27.3736	1.07867
$645$	13.2426	0.521428
$646$	−18.1478	−0.714016
$647$	25.1302	0.987970	0.493985	−	0.869470i	$-0.335540\pi$
$647$	25.1302	0.987970	0.493985	+	0.869470i	$0.335540\pi$
$648$	10.1937	0.400447
$649$	−10.5129	−0.412668
$650$	−4.94979	−0.194147
$651$	−47.3185	−1.85456
$652$	15.0464	0.589261
$653$	15.8848	0.621621	0.310811	−	0.950472i	$-0.399400\pi$
$653$	15.8848	0.621621	0.310811	+	0.950472i	$0.399400\pi$
$654$	7.38246	0.288677
$655$	−8.40316	−0.328339
$656$	−3.33511	−0.130214
$657$	−8.73463	−0.340771
$658$	−12.9245	−0.503850
$659$	30.7260	1.19691	0.598457	−	0.801155i	$-0.295781\pi$
$659$	30.7260	1.19691	0.598457	+	0.801155i	$0.295781\pi$
$660$	8.66676	0.337353
$661$	5.59143	0.217481	0.108741	−	0.994070i	$-0.465318\pi$
$661$	5.59143	0.217481	0.108741	+	0.994070i	$0.465318\pi$
$662$	−33.5489	−1.30391
$663$	−38.3797	−1.49054
$664$	7.84142	0.304306
$665$	−16.4960	−0.639686
$666$	−20.6245	−0.799182
$667$	−20.2637	−0.784613
$668$	5.44620	0.210720
$669$	14.5590	0.562882
$670$	−3.25039	−0.125574
$671$	21.9098	0.845820
$672$	−7.04804	−0.271884
$673$	−19.4920	−0.751361	−0.375680	−	0.926749i	$-0.622591\pi$
$673$	−19.4920	−0.751361	−0.375680	+	0.926749i	$0.622591\pi$
$674$	−15.9388	−0.613941
$675$	−1.11029	−0.0427351
$676$	11.5004	0.442323
$677$	−40.6984	−1.56417	−0.782083	−	0.623174i	$-0.785843\pi$
$677$	−40.6984	−1.56417	−0.782083	+	0.623174i	$0.785843\pi$
$678$	−17.9655	−0.689961
$679$	−43.5094	−1.66974
$680$	3.29792	0.126469
$681$	−8.80004	−0.337218
$682$	24.7483	0.947661
$683$	−12.8568	−0.491953	−0.245977	−	0.969276i	$-0.579109\pi$
$683$	−12.8568	−0.491953	−0.245977	+	0.969276i	$0.579109\pi$
$684$	−13.9098	−0.531853
$685$	−12.0121	−0.458958
$686$	15.0294	0.573824
$687$	10.5687	0.403222
$688$	5.63248	0.214736
$689$	−21.1256	−0.804822
$690$	−21.4691	−0.817314
$691$	11.2202	0.426835	0.213417	−	0.976961i	$-0.431541\pi$
$691$	11.2202	0.426835	0.213417	+	0.976961i	$0.431541\pi$
$692$	13.0125	0.494662
$693$	27.9326	1.06107
$694$	2.46957	0.0937436
$695$	1.76400	0.0669122
$696$	5.21740	0.197765
$697$	10.9989	0.416614
$698$	−19.9313	−0.754412
$699$	−59.6670	−2.25681
$700$	2.99774	0.113304
$701$	−37.1968	−1.40490	−0.702452	−	0.711731i	$-0.747911\pi$
$701$	−37.1968	−1.40490	−0.702452	+	0.711731i	$0.747911\pi$
$702$	5.49571	0.207422
$703$	−44.8984	−1.69338
$704$	3.68623	0.138930
$705$	10.1367	0.381769
$706$	34.1233	1.28425
$707$	−13.2195	−0.497171
$708$	−6.70526	−0.251999
$709$	13.2458	0.497458	0.248729	−	0.968573i	$-0.419987\pi$
$709$	13.2458	0.497458	0.248729	+	0.968573i	$0.419987\pi$
$710$	−4.25016	−0.159506
$711$	−16.8777	−0.632962
$712$	−6.24116	−0.233898
$713$	−61.3058	−2.29592
$714$	23.2439	0.869879
$715$	18.2460	0.682363
$716$	3.51248	0.131267
$717$	−27.0187	−1.00903
$718$	16.7422	0.624813
$719$	−44.2138	−1.64890	−0.824448	−	0.565938i	$-0.808514\pi$
$719$	−44.2138	−1.64890	−0.824448	+	0.565938i	$0.808514\pi$
$720$	2.52776	0.0942041
$721$	21.7558	0.810227
$722$	−11.2809	−0.419830
$723$	36.3196	1.35074
$724$	13.4280	0.499049
$725$	−2.21912	−0.0824159
$726$	−6.08533	−0.225848
$727$	−29.6791	−1.10074	−0.550369	−	0.834922i	$-0.685513\pi$
$727$	−29.6791	−1.10074	−0.550369	+	0.834922i	$0.685513\pi$
$728$	−14.8382	−0.549939
$729$	−17.9360	−0.664295
$730$	3.45548	0.127893
$731$	−18.5755	−0.687039
$732$	13.9744	0.516507
$733$	−22.1985	−0.819922	−0.409961	−	0.912103i	$-0.634458\pi$
$733$	−22.1985	−0.819922	−0.409961	+	0.912103i	$0.634458\pi$
$734$	−30.2053	−1.11490
$735$	4.67032	0.172267
$736$	−9.13143	−0.336589
$737$	11.9817	0.441351
$738$	8.43035	0.310326
$739$	23.1849	0.852870	0.426435	−	0.904518i	$-0.359769\pi$
$739$	23.1849	0.852870	0.426435	+	0.904518i	$0.359769\pi$
$740$	8.15919	0.299938
$741$	−64.0391	−2.35254
$742$	12.7943	0.469693
$743$	−1.14366	−0.0419570	−0.0209785	−	0.999780i	$-0.506678\pi$
$743$	−1.14366	−0.0419570	−0.0209785	+	0.999780i	$0.506678\pi$
$744$	15.7847	0.578697
$745$	−11.9614	−0.438231
$746$	−35.6200	−1.30414
$747$	−19.8212	−0.725221
$748$	−12.1569	−0.444500
$749$	−58.9295	−2.15324
$750$	−2.35112	−0.0858507
$751$	−7.46727	−0.272485	−0.136242	−	0.990676i	$-0.543503\pi$
$751$	−7.46727	−0.272485	−0.136242	+	0.990676i	$0.543503\pi$
$752$	4.31143	0.157222
$753$	−59.0778	−2.15291
$754$	10.9842	0.400019
$755$	1.78072	0.0648069
$756$	−3.32836	−0.121051
$757$	−5.26036	−0.191191	−0.0955954	−	0.995420i	$-0.530476\pi$
$757$	−5.26036	−0.191191	−0.0955954	+	0.995420i	$0.530476\pi$
$758$	21.0459	0.764422
$759$	79.1399	2.87260
$760$	5.50280	0.199608
$761$	34.6686	1.25673	0.628367	−	0.777917i	$-0.283723\pi$
$761$	34.6686	1.25673	0.628367	+	0.777917i	$0.283723\pi$
$762$	−5.71998	−0.207213
$763$	−9.41282	−0.340767
$764$	−12.9657	−0.469081
$765$	−8.33635	−0.301401
$766$	33.1871	1.19910
$767$	−14.1165	−0.509718
$768$	2.35112	0.0848387
$769$	−21.2550	−0.766476	−0.383238	−	0.923650i	$-0.625191\pi$
$769$	−21.2550	−0.766476	−0.383238	+	0.923650i	$0.625191\pi$
$770$	−11.0503	−0.398227
$771$	−11.6244	−0.418643
$772$	17.5975	0.633349
$773$	−19.4219	−0.698556	−0.349278	−	0.937019i	$-0.613573\pi$
$773$	−19.4219	−0.698556	−0.349278	+	0.937019i	$0.613573\pi$
$774$	−14.2376	−0.511759
$775$	−6.71372	−0.241164
$776$	14.5141	0.521025
$777$	57.5063	2.06303
$778$	−20.7101	−0.742494
$779$	18.3524	0.657544
$780$	11.6375	0.416691
$781$	15.6670	0.560611
$782$	30.1147	1.07690
$783$	2.46386	0.0880513
$784$	1.98643	0.0709438
$785$	15.8133	0.564400
$786$	19.7568	0.704703
$787$	−20.8511	−0.743263	−0.371632	−	0.928380i	$-0.621202\pi$
$787$	−20.8511	−0.743263	−0.371632	+	0.928380i	$0.621202\pi$
$788$	−3.52793	−0.125677
$789$	50.3961	1.79415
$790$	6.67692	0.237554
$791$	22.9065	0.814460
$792$	−9.31790	−0.331097
$793$	29.4201	1.04474
$794$	29.8335	1.05875
$795$	−10.0345	−0.355888
$796$	−13.2448	−0.469448
$797$	6.31392	0.223650	0.111825	−	0.993728i	$-0.464330\pi$
$797$	6.31392	0.223650	0.111825	+	0.993728i	$0.464330\pi$
$798$	38.7840	1.37294
$799$	−14.2187	−0.503023
$800$	−1.00000	−0.0353553
$801$	15.7762	0.557423
$802$	1.00000	0.0353112
$803$	−12.7377	−0.449504
$804$	7.64206	0.269515
$805$	27.3736	0.964793
$806$	33.2315	1.17053
$807$	−57.3815	−2.01992
$808$	4.40983	0.155137
$809$	11.7734	0.413931	0.206965	−	0.978348i	$-0.433641\pi$
$809$	11.7734	0.413931	0.206965	+	0.978348i	$0.433641\pi$
$810$	10.1937	0.358170
$811$	−19.7408	−0.693195	−0.346597	−	0.938014i	$-0.612663\pi$
$811$	−19.7408	−0.693195	−0.346597	+	0.938014i	$0.612663\pi$
$812$	−6.65232	−0.233451
$813$	66.4230	2.32955
$814$	−30.0766	−1.05419
$815$	15.0464	0.527051
$816$	−7.75380	−0.271437
$817$	−30.9944	−1.08436
$818$	−10.6247	−0.371485
$819$	37.5073	1.31061
$820$	−3.33511	−0.116467
$821$	−10.7199	−0.374127	−0.187064	−	0.982348i	$-0.559897\pi$
$821$	−10.7199	−0.374127	−0.187064	+	0.982348i	$0.559897\pi$
$822$	28.2419	0.985048
$823$	6.35721	0.221598	0.110799	−	0.993843i	$-0.464659\pi$
$823$	6.35721	0.221598	0.110799	+	0.993843i	$0.464659\pi$
$824$	−7.25740	−0.252823
$825$	8.66676	0.301738
$826$	8.54938	0.297471
$827$	−6.27225	−0.218107	−0.109054	−	0.994036i	$-0.534782\pi$
$827$	−6.27225	−0.218107	−0.109054	+	0.994036i	$0.534782\pi$
$828$	23.0821	0.802157
$829$	−28.1630	−0.978143	−0.489071	−	0.872244i	$-0.662664\pi$
$829$	−28.1630	−0.978143	−0.489071	+	0.872244i	$0.662664\pi$
$830$	7.84142	0.272180
$831$	6.08754	0.211174
$832$	4.94979	0.171603
$833$	−6.55107	−0.226981
$834$	−4.14737	−0.143612
$835$	5.44620	0.188473
$836$	−20.2846	−0.701557
$837$	7.45418	0.257654
$838$	−38.7783	−1.33958
$839$	51.7688	1.78726	0.893629	−	0.448806i	$-0.148151\pi$
$839$	51.7688	1.78726	0.893629	+	0.448806i	$0.148151\pi$
$840$	−7.04804	−0.243180
$841$	−24.0755	−0.830191
$842$	−16.2911	−0.561429
$843$	30.1971	1.04004
$844$	−24.7946	−0.853465
$845$	11.5004	0.395626
$846$	−10.8983	−0.374690
$847$	7.75895	0.266601
$848$	−4.26798	−0.146563
$849$	−39.2649	−1.34757
$850$	3.29792	0.113118
$851$	74.5051	2.55400
$852$	9.99263	0.342342
$853$	−50.0009	−1.71200	−0.855998	−	0.516978i	$-0.827057\pi$
$853$	−50.0009	−1.71200	−0.855998	+	0.516978i	$0.827057\pi$
$854$	−17.8177	−0.609708
$855$	−13.9098	−0.475704
$856$	19.6580	0.671897
$857$	−22.9613	−0.784342	−0.392171	−	0.919892i	$-0.628276\pi$
$857$	−22.9613	−0.784342	−0.392171	+	0.919892i	$0.628276\pi$
$858$	−42.8986	−1.46453
$859$	−27.5890	−0.941324	−0.470662	−	0.882314i	$-0.655985\pi$
$859$	−27.5890	−0.941324	−0.470662	+	0.882314i	$0.655985\pi$
$860$	5.63248	0.192066
$861$	−23.5060	−0.801081
$862$	30.3455	1.03357
$863$	9.05930	0.308382	0.154191	−	0.988041i	$-0.450723\pi$
$863$	9.05930	0.308382	0.154191	+	0.988041i	$0.450723\pi$
$864$	1.11029	0.0377729
$865$	13.0125	0.442439
$866$	−2.06320	−0.0701102
$867$	−14.3976	−0.488968
$868$	−20.1260	−0.683119
$869$	−24.6126	−0.834927
$870$	5.21740	0.176887
$871$	16.0888	0.545147
$872$	3.13998	0.106333
$873$	−36.6881	−1.24170
$874$	50.2485	1.69968
$875$	2.99774	0.101342
$876$	−8.12425	−0.274493
$877$	34.5357	1.16619	0.583093	−	0.812405i	$-0.301842\pi$
$877$	34.5357	1.16619	0.583093	+	0.812405i	$0.301842\pi$
$878$	−11.9990	−0.404945
$879$	57.3338	1.93382
$880$	3.68623	0.124263
$881$	−40.4892	−1.36411	−0.682057	−	0.731299i	$-0.738914\pi$
$881$	−40.4892	−1.36411	−0.682057	+	0.731299i	$0.738914\pi$
$882$	−5.02121	−0.169073
$883$	56.9375	1.91610	0.958050	−	0.286602i	$-0.0925257\pi$
$883$	56.9375	1.91610	0.958050	+	0.286602i	$0.0925257\pi$
$884$	−16.3240	−0.549036
$885$	−6.70526	−0.225395
$886$	13.6497	0.458570
$887$	−40.5215	−1.36058	−0.680290	−	0.732943i	$-0.738146\pi$
$887$	−40.5215	−1.36058	−0.680290	+	0.732943i	$0.738146\pi$
$888$	−19.1832	−0.643747
$889$	7.29313	0.244604
$890$	−6.24116	−0.209204
$891$	−37.5763	−1.25885
$892$	6.19236	0.207335
$893$	−23.7249	−0.793925
$894$	28.1227	0.940562
$895$	3.51248	0.117409
$896$	−2.99774	−0.100147
$897$	106.267	3.54816
$898$	1.71601	0.0572640
$899$	14.8985	0.496893
$900$	2.52776	0.0842587
$901$	14.0755	0.468922
$902$	12.2940	0.409344
$903$	39.6979	1.32106
$904$	−7.64125	−0.254144
$905$	13.4280	0.446363
$906$	−4.18668	−0.139093
$907$	−41.5800	−1.38064	−0.690321	−	0.723503i	$-0.742531\pi$
$907$	−41.5800	−1.38064	−0.690321	+	0.723503i	$0.742531\pi$
$908$	−3.74292	−0.124213
$909$	−11.1470	−0.369723
$910$	−14.8382	−0.491880
$911$	17.7217	0.587147	0.293573	−	0.955937i	$-0.405155\pi$
$911$	17.7217	0.587147	0.293573	+	0.955937i	$0.405155\pi$
$912$	−12.9377	−0.428412
$913$	−28.9052	−0.956624
$914$	−2.10521	−0.0696342
$915$	13.9744	0.461978
$916$	4.49519	0.148525
$917$	−25.1905	−0.831863
$918$	−3.66165	−0.120853
$919$	3.95679	0.130522	0.0652612	−	0.997868i	$-0.479212\pi$
$919$	3.95679	0.130522	0.0652612	+	0.997868i	$0.479212\pi$
$920$	−9.13143	−0.301054
$921$	−48.7751	−1.60719
$922$	11.7972	0.388519
$923$	21.0374	0.692454
$924$	25.9807	0.854701
$925$	8.15919	0.268273
$926$	−7.57470	−0.248920
$927$	18.3450	0.602528
$928$	2.21912	0.0728460
$929$	16.9992	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$929$	16.9992	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$930$	15.7847	0.517602
$931$	−10.9309	−0.358246
$932$	−25.3781	−0.831288
$933$	53.2002	1.74170
$934$	−9.50843	−0.311125
$935$	−12.1569	−0.397573
$936$	−12.5119	−0.408964
$937$	−21.4671	−0.701299	−0.350649	−	0.936507i	$-0.614039\pi$
$937$	−21.4671	−0.701299	−0.350649	+	0.936507i	$0.614039\pi$
$938$	−9.74382	−0.318147
$939$	−29.0186	−0.946985
$940$	4.31143	0.140623
$941$	4.32304	0.140927	0.0704635	−	0.997514i	$-0.477552\pi$
$941$	4.32304	0.140927	0.0704635	+	0.997514i	$0.477552\pi$
$942$	−37.1789	−1.21135
$943$	−30.4543	−0.991728
$944$	−2.85194	−0.0928229
$945$	−3.32836	−0.108272
$946$	−20.7626	−0.675051
$947$	−18.2237	−0.592192	−0.296096	−	0.955158i	$-0.595685\pi$
$947$	−18.2237	−0.592192	−0.296096	+	0.955158i	$0.595685\pi$
$948$	−15.6982	−0.509855
$949$	−17.1039	−0.555216
$950$	5.50280	0.178535
$951$	25.4729	0.826014
$952$	9.88630	0.320417
$953$	1.30223	0.0421834	0.0210917	−	0.999778i	$-0.493286\pi$
$953$	1.30223	0.0421834	0.0210917	+	0.999778i	$0.493286\pi$
$954$	10.7884	0.349289
$955$	−12.9657	−0.419559
$956$	−11.4918	−0.371673
$957$	−19.2325	−0.621700
$958$	3.52335	0.113834
$959$	−36.0091	−1.16279
$960$	2.35112	0.0758820
$961$	14.0740	0.454000
$962$	−40.3863	−1.30211
$963$	−49.6908	−1.60126
$964$	15.4478	0.497541
$965$	17.5975	0.566485
$966$	−64.3586	−2.07070
$967$	−34.2424	−1.10116	−0.550580	−	0.834782i	$-0.685593\pi$
$967$	−34.2424	−1.10116	−0.550580	+	0.834782i	$0.685593\pi$
$968$	−2.58827	−0.0831901
$969$	42.6677	1.37068
$970$	14.5141	0.466019
$971$	−60.3465	−1.93661	−0.968306	−	0.249767i	$-0.919646\pi$
$971$	−60.3465	−1.93661	−0.968306	+	0.249767i	$0.919646\pi$
$972$	−20.6357	−0.661892
$973$	5.28800	0.169525
$974$	15.3389	0.491490
$975$	11.6375	0.372700
$976$	5.94370	0.190253
$977$	−6.24579	−0.199821	−0.0999103	−	0.994996i	$-0.531856\pi$
$977$	−6.24579	−0.199821	−0.0999103	+	0.994996i	$0.531856\pi$
$978$	−35.3758	−1.13119
$979$	23.0063	0.735286
$980$	1.98643	0.0634540
$981$	−7.93711	−0.253412
$982$	23.9914	0.765595
$983$	−6.12249	−0.195277	−0.0976386	−	0.995222i	$-0.531129\pi$
$983$	−6.12249	−0.195277	−0.0976386	+	0.995222i	$0.531129\pi$
$984$	7.84123	0.249969
$985$	−3.52793	−0.112409
$986$	−7.31846	−0.233067
$987$	30.3871	0.967231
$988$	−27.2377	−0.866547
$989$	51.4326	1.63546
$990$	−9.31790	−0.296142
$991$	−62.4483	−1.98374	−0.991868	−	0.127270i	$-0.959378\pi$
$991$	−62.4483	−1.98374	−0.991868	+	0.127270i	$0.959378\pi$
$992$	6.71372	0.213161
$993$	78.8774	2.50310
$994$	−12.7409	−0.404115
$995$	−13.2448	−0.419887
$996$	−18.4361	−0.584170
$997$	−25.3476	−0.802768	−0.401384	−	0.915910i	$-0.631471\pi$
$997$	−25.3476	−0.802768	−0.401384	+	0.915910i	$0.631471\pi$
$998$	−6.09523	−0.192941
$999$	−9.05908	−0.286617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.17	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.17	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.35112 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.35112 q^{6} +2.99774 q^{7} -1.00000 q^{8} +2.52776 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.35112 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.35112 q^{6} +2.99774 q^{7} -1.00000 q^{8} +2.52776 q^{9} -1.00000 q^{10} +3.68623 q^{11} +2.35112 q^{12} +4.94979 q^{13} -2.99774 q^{14} +2.35112 q^{15} +1.00000 q^{16} -3.29792 q^{17} -2.52776 q^{18} -5.50280 q^{19} +1.00000 q^{20} +7.04804 q^{21} -3.68623 q^{22} +9.13143 q^{23} -2.35112 q^{24} +1.00000 q^{25} -4.94979 q^{26} -1.11029 q^{27} +2.99774 q^{28} -2.21912 q^{29} -2.35112 q^{30} -6.71372 q^{31} -1.00000 q^{32} +8.66676 q^{33} +3.29792 q^{34} +2.99774 q^{35} +2.52776 q^{36} +8.15919 q^{37} +5.50280 q^{38} +11.6375 q^{39} -1.00000 q^{40} -3.33511 q^{41} -7.04804 q^{42} +5.63248 q^{43} +3.68623 q^{44} +2.52776 q^{45} -9.13143 q^{46} +4.31143 q^{47} +2.35112 q^{48} +1.98643 q^{49} -1.00000 q^{50} -7.75380 q^{51} +4.94979 q^{52} -4.26798 q^{53} +1.11029 q^{54} +3.68623 q^{55} -2.99774 q^{56} -12.9377 q^{57} +2.21912 q^{58} -2.85194 q^{59} +2.35112 q^{60} +5.94370 q^{61} +6.71372 q^{62} +7.57756 q^{63} +1.00000 q^{64} +4.94979 q^{65} -8.66676 q^{66} +3.25039 q^{67} -3.29792 q^{68} +21.4691 q^{69} -2.99774 q^{70} +4.25016 q^{71} -2.52776 q^{72} -3.45548 q^{73} -8.15919 q^{74} +2.35112 q^{75} -5.50280 q^{76} +11.0503 q^{77} -11.6375 q^{78} -6.67692 q^{79} +1.00000 q^{80} -10.1937 q^{81} +3.33511 q^{82} -7.84142 q^{83} +7.04804 q^{84} -3.29792 q^{85} -5.63248 q^{86} -5.21740 q^{87} -3.68623 q^{88} +6.24116 q^{89} -2.52776 q^{90} +14.8382 q^{91} +9.13143 q^{92} -15.7847 q^{93} -4.31143 q^{94} -5.50280 q^{95} -2.35112 q^{96} -14.5141 q^{97} -1.98643 q^{98} +9.31790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

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