LMFDB - Embedded newform 4010.2.a.m.1.15

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			1.15
Root			$1.96074$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.96074 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.96074 q^{6} -2.08760 q^{7} -1.00000 q^{8} +0.844520 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.96074 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.96074 q^{6} -2.08760 q^{7} -1.00000 q^{8} +0.844520 q^{9} -1.00000 q^{10} +6.37671 q^{11} +1.96074 q^{12} +3.76920 q^{13} +2.08760 q^{14} +1.96074 q^{15} +1.00000 q^{16} -2.53050 q^{17} -0.844520 q^{18} -2.10308 q^{19} +1.00000 q^{20} -4.09325 q^{21} -6.37671 q^{22} -5.05066 q^{23} -1.96074 q^{24} +1.00000 q^{25} -3.76920 q^{26} -4.22635 q^{27} -2.08760 q^{28} +8.31872 q^{29} -1.96074 q^{30} +9.80342 q^{31} -1.00000 q^{32} +12.5031 q^{33} +2.53050 q^{34} -2.08760 q^{35} +0.844520 q^{36} -3.30541 q^{37} +2.10308 q^{38} +7.39043 q^{39} -1.00000 q^{40} +4.53210 q^{41} +4.09325 q^{42} +1.36056 q^{43} +6.37671 q^{44} +0.844520 q^{45} +5.05066 q^{46} -6.07536 q^{47} +1.96074 q^{48} -2.64193 q^{49} -1.00000 q^{50} -4.96167 q^{51} +3.76920 q^{52} +7.29952 q^{53} +4.22635 q^{54} +6.37671 q^{55} +2.08760 q^{56} -4.12361 q^{57} -8.31872 q^{58} +11.8854 q^{59} +1.96074 q^{60} +2.90124 q^{61} -9.80342 q^{62} -1.76302 q^{63} +1.00000 q^{64} +3.76920 q^{65} -12.5031 q^{66} +10.8269 q^{67} -2.53050 q^{68} -9.90306 q^{69} +2.08760 q^{70} +0.945111 q^{71} -0.844520 q^{72} -5.84916 q^{73} +3.30541 q^{74} +1.96074 q^{75} -2.10308 q^{76} -13.3120 q^{77} -7.39043 q^{78} -2.88214 q^{79} +1.00000 q^{80} -10.8203 q^{81} -4.53210 q^{82} +3.70172 q^{83} -4.09325 q^{84} -2.53050 q^{85} -1.36056 q^{86} +16.3109 q^{87} -6.37671 q^{88} -11.1225 q^{89} -0.844520 q^{90} -7.86857 q^{91} -5.05066 q^{92} +19.2220 q^{93} +6.07536 q^{94} -2.10308 q^{95} -1.96074 q^{96} +2.51227 q^{97} +2.64193 q^{98} +5.38526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.96074	1.13204	0.566018	−	0.824393i	$-0.308483\pi$
$3$	1.96074	1.13204	0.566018	+	0.824393i	$0.308483\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.96074	−0.800471
$7$	−2.08760	−0.789038	−0.394519	−	0.918888i	$-0.629089\pi$
$7$	−2.08760	−0.789038	−0.394519	+	0.918888i	$0.629089\pi$
$8$	−1.00000	−0.353553
$9$	0.844520	0.281507
$10$	−1.00000	−0.316228
$11$	6.37671	1.92265	0.961325	−	0.275416i	$-0.0888156\pi$
$11$	6.37671	1.92265	0.961325	+	0.275416i	$0.0888156\pi$
$12$	1.96074	0.566018
$13$	3.76920	1.04539	0.522694	−	0.852521i	$-0.324927\pi$
$13$	3.76920	1.04539	0.522694	+	0.852521i	$0.324927\pi$
$14$	2.08760	0.557934
$15$	1.96074	0.506262
$16$	1.00000	0.250000
$17$	−2.53050	−0.613737	−0.306869	−	0.951752i	$-0.599281\pi$
$17$	−2.53050	−0.613737	−0.306869	+	0.951752i	$0.599281\pi$
$18$	−0.844520	−0.199055
$19$	−2.10308	−0.482480	−0.241240	−	0.970465i	$-0.577554\pi$
$19$	−2.10308	−0.482480	−0.241240	+	0.970465i	$0.577554\pi$
$20$	1.00000	0.223607
$21$	−4.09325	−0.893220
$22$	−6.37671	−1.35952
$23$	−5.05066	−1.05314	−0.526568	−	0.850133i	$-0.676521\pi$
$23$	−5.05066	−1.05314	−0.526568	+	0.850133i	$0.676521\pi$
$24$	−1.96074	−0.400235
$25$	1.00000	0.200000
$26$	−3.76920	−0.739200
$27$	−4.22635	−0.813361
$28$	−2.08760	−0.394519
$29$	8.31872	1.54475	0.772373	−	0.635169i	$-0.219069\pi$
$29$	8.31872	1.54475	0.772373	+	0.635169i	$0.219069\pi$
$30$	−1.96074	−0.357981
$31$	9.80342	1.76075	0.880373	−	0.474282i	$-0.157292\pi$
$31$	9.80342	1.76075	0.880373	+	0.474282i	$0.157292\pi$
$32$	−1.00000	−0.176777
$33$	12.5031	2.17651
$34$	2.53050	0.433978
$35$	−2.08760	−0.352868
$36$	0.844520	0.140753
$37$	−3.30541	−0.543406	−0.271703	−	0.962381i	$-0.587587\pi$
$37$	−3.30541	−0.543406	−0.271703	+	0.962381i	$0.587587\pi$
$38$	2.10308	0.341165
$39$	7.39043	1.18342
$40$	−1.00000	−0.158114
$41$	4.53210	0.707795	0.353898	−	0.935284i	$-0.384856\pi$
$41$	4.53210	0.707795	0.353898	+	0.935284i	$0.384856\pi$
$42$	4.09325	0.631602
$43$	1.36056	0.207483	0.103742	−	0.994604i	$-0.466919\pi$
$43$	1.36056	0.207483	0.103742	+	0.994604i	$0.466919\pi$
$44$	6.37671	0.961325
$45$	0.844520	0.125894
$46$	5.05066	0.744680
$47$	−6.07536	−0.886183	−0.443091	−	0.896476i	$-0.646118\pi$
$47$	−6.07536	−0.886183	−0.443091	+	0.896476i	$0.646118\pi$
$48$	1.96074	0.283009
$49$	−2.64193	−0.377419
$50$	−1.00000	−0.141421
$51$	−4.96167	−0.694773
$52$	3.76920	0.522694
$53$	7.29952	1.00267	0.501333	−	0.865254i	$-0.332843\pi$
$53$	7.29952	1.00267	0.501333	+	0.865254i	$0.332843\pi$
$54$	4.22635	0.575133
$55$	6.37671	0.859835
$56$	2.08760	0.278967
$57$	−4.12361	−0.546185
$58$	−8.31872	−1.09230
$59$	11.8854	1.54734	0.773671	−	0.633588i	$-0.218418\pi$
$59$	11.8854	1.54734	0.773671	+	0.633588i	$0.218418\pi$
$60$	1.96074	0.253131
$61$	2.90124	0.371466	0.185733	−	0.982600i	$-0.440534\pi$
$61$	2.90124	0.371466	0.185733	+	0.982600i	$0.440534\pi$
$62$	−9.80342	−1.24504
$63$	−1.76302	−0.222119
$64$	1.00000	0.125000
$65$	3.76920	0.467511
$66$	−12.5031	−1.53903
$67$	10.8269	1.32271	0.661357	−	0.750071i	$-0.269981\pi$
$67$	10.8269	1.32271	0.661357	+	0.750071i	$0.269981\pi$
$68$	−2.53050	−0.306869
$69$	−9.90306	−1.19219
$70$	2.08760	0.249516
$71$	0.945111	0.112164	0.0560820	−	0.998426i	$-0.482139\pi$
$71$	0.945111	0.112164	0.0560820	+	0.998426i	$0.482139\pi$
$72$	−0.844520	−0.0995276
$73$	−5.84916	−0.684592	−0.342296	−	0.939592i	$-0.611205\pi$
$73$	−5.84916	−0.684592	−0.342296	+	0.939592i	$0.611205\pi$
$74$	3.30541	0.384246
$75$	1.96074	0.226407
$76$	−2.10308	−0.241240
$77$	−13.3120	−1.51704
$78$	−7.39043	−0.836802
$79$	−2.88214	−0.324267	−0.162133	−	0.986769i	$-0.551837\pi$
$79$	−2.88214	−0.324267	−0.162133	+	0.986769i	$0.551837\pi$
$80$	1.00000	0.111803
$81$	−10.8203	−1.20226
$82$	−4.53210	−0.500487
$83$	3.70172	0.406316	0.203158	−	0.979146i	$-0.434879\pi$
$83$	3.70172	0.406316	0.203158	+	0.979146i	$0.434879\pi$
$84$	−4.09325	−0.446610
$85$	−2.53050	−0.274472
$86$	−1.36056	−0.146713
$87$	16.3109	1.74871
$88$	−6.37671	−0.679760
$89$	−11.1225	−1.17898	−0.589492	−	0.807774i	$-0.700672\pi$
$89$	−11.1225	−1.17898	−0.589492	+	0.807774i	$0.700672\pi$
$90$	−0.844520	−0.0890202
$91$	−7.86857	−0.824850
$92$	−5.05066	−0.526568
$93$	19.2220	1.99323
$94$	6.07536	0.626626
$95$	−2.10308	−0.215772
$96$	−1.96074	−0.200118
$97$	2.51227	0.255082	0.127541	−	0.991833i	$-0.459292\pi$
$97$	2.51227	0.255082	0.127541	+	0.991833i	$0.459292\pi$
$98$	2.64193	0.266876
$99$	5.38526	0.541239
$100$	1.00000	0.100000
$101$	−1.40803	−0.140104	−0.0700519	−	0.997543i	$-0.522317\pi$
$101$	−1.40803	−0.140104	−0.0700519	+	0.997543i	$0.522317\pi$
$102$	4.96167	0.491279
$103$	−0.220448	−0.0217214	−0.0108607	−	0.999941i	$-0.503457\pi$
$103$	−0.220448	−0.0217214	−0.0108607	+	0.999941i	$0.503457\pi$
$104$	−3.76920	−0.369600
$105$	−4.09325	−0.399460
$106$	−7.29952	−0.708992
$107$	2.80255	0.270933	0.135466	−	0.990782i	$-0.456747\pi$
$107$	2.80255	0.270933	0.135466	+	0.990782i	$0.456747\pi$
$108$	−4.22635	−0.406680
$109$	−7.07737	−0.677889	−0.338945	−	0.940806i	$-0.610070\pi$
$109$	−7.07737	−0.677889	−0.338945	+	0.940806i	$0.610070\pi$
$110$	−6.37671	−0.607995
$111$	−6.48107	−0.615156
$112$	−2.08760	−0.197259
$113$	−1.21371	−0.114176	−0.0570881	−	0.998369i	$-0.518182\pi$
$113$	−1.21371	−0.114176	−0.0570881	+	0.998369i	$0.518182\pi$
$114$	4.12361	0.386211
$115$	−5.05066	−0.470977
$116$	8.31872	0.772373
$117$	3.18316	0.294283
$118$	−11.8854	−1.09414
$119$	5.28268	0.484262
$120$	−1.96074	−0.178991
$121$	29.6624	2.69658
$122$	−2.90124	−0.262666
$123$	8.88629	0.801250
$124$	9.80342	0.880373
$125$	1.00000	0.0894427
$126$	1.76302	0.157062
$127$	−7.76353	−0.688902	−0.344451	−	0.938804i	$-0.611935\pi$
$127$	−7.76353	−0.688902	−0.344451	+	0.938804i	$0.611935\pi$
$128$	−1.00000	−0.0883883
$129$	2.66771	0.234879
$130$	−3.76920	−0.330580
$131$	13.4526	1.17536	0.587680	−	0.809093i	$-0.300041\pi$
$131$	13.4526	1.17536	0.587680	+	0.809093i	$0.300041\pi$
$132$	12.5031	1.08826
$133$	4.39039	0.380695
$134$	−10.8269	−0.935300
$135$	−4.22635	−0.363746
$136$	2.53050	0.216989
$137$	16.2463	1.38801	0.694006	−	0.719969i	$-0.255844\pi$
$137$	16.2463	1.38801	0.694006	+	0.719969i	$0.255844\pi$
$138$	9.90306	0.843005
$139$	13.3185	1.12966	0.564828	−	0.825208i	$-0.308942\pi$
$139$	13.3185	1.12966	0.564828	+	0.825208i	$0.308942\pi$
$140$	−2.08760	−0.176434
$141$	−11.9122	−1.00319
$142$	−0.945111	−0.0793119
$143$	24.0351	2.00991
$144$	0.844520	0.0703766
$145$	8.31872	0.690832
$146$	5.84916	0.484080
$147$	−5.18016	−0.427252
$148$	−3.30541	−0.271703
$149$	−9.03559	−0.740224	−0.370112	−	0.928987i	$-0.620681\pi$
$149$	−9.03559	−0.740224	−0.370112	+	0.928987i	$0.620681\pi$
$150$	−1.96074	−0.160094
$151$	−11.6047	−0.944373	−0.472187	−	0.881499i	$-0.656535\pi$
$151$	−11.6047	−0.944373	−0.472187	+	0.881499i	$0.656535\pi$
$152$	2.10308	0.170582
$153$	−2.13706	−0.172771
$154$	13.3120	1.07271
$155$	9.80342	0.787430
$156$	7.39043	0.591708
$157$	−1.10934	−0.0885348	−0.0442674	−	0.999020i	$-0.514095\pi$
$157$	−1.10934	−0.0885348	−0.0442674	+	0.999020i	$0.514095\pi$
$158$	2.88214	0.229291
$159$	14.3125	1.13505
$160$	−1.00000	−0.0790569
$161$	10.5438	0.830964
$162$	10.8203	0.850127
$163$	−10.3189	−0.808236	−0.404118	−	0.914707i	$-0.632421\pi$
$163$	−10.3189	−0.808236	−0.404118	+	0.914707i	$0.632421\pi$
$164$	4.53210	0.353898
$165$	12.5031	0.973365
$166$	−3.70172	−0.287309
$167$	−11.4003	−0.882181	−0.441090	−	0.897463i	$-0.645408\pi$
$167$	−11.4003	−0.882181	−0.441090	+	0.897463i	$0.645408\pi$
$168$	4.09325	0.315801
$169$	1.20685	0.0928343
$170$	2.53050	0.194081
$171$	−1.77609	−0.135821
$172$	1.36056	0.103742
$173$	25.7158	1.95514	0.977569	−	0.210614i	$-0.0675462\pi$
$173$	25.7158	1.95514	0.977569	+	0.210614i	$0.0675462\pi$
$174$	−16.3109	−1.23652
$175$	−2.08760	−0.157808
$176$	6.37671	0.480663
$177$	23.3041	1.75165
$178$	11.1225	0.833668
$179$	3.12582	0.233635	0.116817	−	0.993153i	$-0.462731\pi$
$179$	3.12582	0.233635	0.116817	+	0.993153i	$0.462731\pi$
$180$	0.844520	0.0629468
$181$	3.52525	0.262030	0.131015	−	0.991380i	$-0.458176\pi$
$181$	3.52525	0.262030	0.131015	+	0.991380i	$0.458176\pi$
$182$	7.86857	0.583257
$183$	5.68859	0.420513
$184$	5.05066	0.372340
$185$	−3.30541	−0.243019
$186$	−19.2220	−1.40943
$187$	−16.1363	−1.18000
$188$	−6.07536	−0.443091
$189$	8.82291	0.641772
$190$	2.10308	0.152574
$191$	−0.0668831	−0.00483949	−0.00241975	−	0.999997i	$-0.500770\pi$
$191$	−0.0668831	−0.00483949	−0.00241975	+	0.999997i	$0.500770\pi$
$192$	1.96074	0.141505
$193$	2.40887	0.173394	0.0866971	−	0.996235i	$-0.472369\pi$
$193$	2.40887	0.173394	0.0866971	+	0.996235i	$0.472369\pi$
$194$	−2.51227	−0.180370
$195$	7.39043	0.529240
$196$	−2.64193	−0.188710
$197$	−2.41153	−0.171814	−0.0859071	−	0.996303i	$-0.527379\pi$
$197$	−2.41153	−0.171814	−0.0859071	+	0.996303i	$0.527379\pi$
$198$	−5.38526	−0.382714
$199$	21.0173	1.48988	0.744938	−	0.667134i	$-0.232479\pi$
$199$	21.0173	1.48988	0.744938	+	0.667134i	$0.232479\pi$
$200$	−1.00000	−0.0707107
$201$	21.2287	1.49736
$202$	1.40803	0.0990684
$203$	−17.3661	−1.21886
$204$	−4.96167	−0.347387
$205$	4.53210	0.316536
$206$	0.220448	0.0153593
$207$	−4.26538	−0.296465
$208$	3.76920	0.261347
$209$	−13.4107	−0.927640
$210$	4.09325	0.282461
$211$	26.5948	1.83086	0.915431	−	0.402475i	$-0.131850\pi$
$211$	26.5948	1.83086	0.915431	+	0.402475i	$0.131850\pi$
$212$	7.29952	0.501333
$213$	1.85312	0.126974
$214$	−2.80255	−0.191578
$215$	1.36056	0.0927893
$216$	4.22635	0.287566
$217$	−20.4656	−1.38930
$218$	7.07737	0.479340
$219$	−11.4687	−0.774983
$220$	6.37671	0.429918
$221$	−9.53797	−0.641593
$222$	6.48107	0.434981
$223$	7.85609	0.526083	0.263041	−	0.964785i	$-0.415274\pi$
$223$	7.85609	0.526083	0.263041	+	0.964785i	$0.415274\pi$
$224$	2.08760	0.139484
$225$	0.844520	0.0563013
$226$	1.21371	0.0807347
$227$	−27.5494	−1.82852	−0.914261	−	0.405127i	$-0.867227\pi$
$227$	−27.5494	−1.82852	−0.914261	+	0.405127i	$0.867227\pi$
$228$	−4.12361	−0.273093
$229$	25.4339	1.68072	0.840359	−	0.542030i	$-0.182344\pi$
$229$	25.4339	1.68072	0.840359	+	0.542030i	$0.182344\pi$
$230$	5.05066	0.333031
$231$	−26.1014	−1.71735
$232$	−8.31872	−0.546151
$233$	5.39329	0.353326	0.176663	−	0.984271i	$-0.443470\pi$
$233$	5.39329	0.353326	0.176663	+	0.984271i	$0.443470\pi$
$234$	−3.18316	−0.208090
$235$	−6.07536	−0.396313
$236$	11.8854	0.773671
$237$	−5.65115	−0.367082
$238$	−5.28268	−0.342425
$239$	−8.08622	−0.523054	−0.261527	−	0.965196i	$-0.584226\pi$
$239$	−8.08622	−0.523054	−0.261527	+	0.965196i	$0.584226\pi$
$240$	1.96074	0.126566
$241$	−7.69430	−0.495633	−0.247817	−	0.968807i	$-0.579713\pi$
$241$	−7.69430	−0.495633	−0.247817	+	0.968807i	$0.579713\pi$
$242$	−29.6624	−1.90677
$243$	−8.53690	−0.547642
$244$	2.90124	0.185733
$245$	−2.64193	−0.168787
$246$	−8.88629	−0.566569
$247$	−7.92693	−0.504379
$248$	−9.80342	−0.622518
$249$	7.25812	0.459965
$250$	−1.00000	−0.0632456
$251$	−14.6443	−0.924339	−0.462170	−	0.886792i	$-0.652929\pi$
$251$	−14.6443	−0.924339	−0.462170	+	0.886792i	$0.652929\pi$
$252$	−1.76302	−0.111060
$253$	−32.2066	−2.02481
$254$	7.76353	0.487127
$255$	−4.96167	−0.310712
$256$	1.00000	0.0625000
$257$	−11.9210	−0.743611	−0.371806	−	0.928311i	$-0.621261\pi$
$257$	−11.9210	−0.743611	−0.371806	+	0.928311i	$0.621261\pi$
$258$	−2.66771	−0.166084
$259$	6.90037	0.428768
$260$	3.76920	0.233756
$261$	7.02532	0.434856
$262$	−13.4526	−0.831106
$263$	20.0700	1.23757	0.618785	−	0.785560i	$-0.287625\pi$
$263$	20.0700	1.23757	0.618785	+	0.785560i	$0.287625\pi$
$264$	−12.5031	−0.769513
$265$	7.29952	0.448406
$266$	−4.39039	−0.269192
$267$	−21.8084	−1.33465
$268$	10.8269	0.661357
$269$	−25.7662	−1.57099	−0.785495	−	0.618868i	$-0.787592\pi$
$269$	−25.7662	−1.57099	−0.785495	+	0.618868i	$0.787592\pi$
$270$	4.22635	0.257207
$271$	−30.6438	−1.86148	−0.930738	−	0.365687i	$-0.880834\pi$
$271$	−30.6438	−1.86148	−0.930738	+	0.365687i	$0.880834\pi$
$272$	−2.53050	−0.153434
$273$	−15.4283	−0.933760
$274$	−16.2463	−0.981473
$275$	6.37671	0.384530
$276$	−9.90306	−0.596094
$277$	24.0523	1.44516	0.722580	−	0.691287i	$-0.242956\pi$
$277$	24.0523	1.44516	0.722580	+	0.691287i	$0.242956\pi$
$278$	−13.3185	−0.798788
$279$	8.27918	0.495662
$280$	2.08760	0.124758
$281$	−26.5712	−1.58510	−0.792552	−	0.609804i	$-0.791248\pi$
$281$	−26.5712	−1.58510	−0.792552	+	0.609804i	$0.791248\pi$
$282$	11.9122	0.709363
$283$	−18.1387	−1.07823	−0.539116	−	0.842231i	$-0.681242\pi$
$283$	−18.1387	−1.07823	−0.539116	+	0.842231i	$0.681242\pi$
$284$	0.945111	0.0560820
$285$	−4.12361	−0.244261
$286$	−24.0351	−1.42122
$287$	−9.46121	−0.558477
$288$	−0.844520	−0.0497638
$289$	−10.5965	−0.623326
$290$	−8.31872	−0.488492
$291$	4.92591	0.288762
$292$	−5.84916	−0.342296
$293$	14.6801	0.857623	0.428811	−	0.903394i	$-0.358932\pi$
$293$	14.6801	0.857623	0.428811	+	0.903394i	$0.358932\pi$
$294$	5.18016	0.302113
$295$	11.8854	0.691992
$296$	3.30541	0.192123
$297$	−26.9502	−1.56381
$298$	9.03559	0.523417
$299$	−19.0369	−1.10093
$300$	1.96074	0.113204
$301$	−2.84030	−0.163712
$302$	11.6047	0.667773
$303$	−2.76078	−0.158603
$304$	−2.10308	−0.120620
$305$	2.90124	0.166125
$306$	2.13706	0.122168
$307$	−12.4405	−0.710017	−0.355008	−	0.934863i	$-0.615522\pi$
$307$	−12.4405	−0.710017	−0.355008	+	0.934863i	$0.615522\pi$
$308$	−13.3120	−0.758522
$309$	−0.432242	−0.0245894
$310$	−9.80342	−0.556797
$311$	−7.32753	−0.415506	−0.207753	−	0.978181i	$-0.566615\pi$
$311$	−7.32753	−0.415506	−0.207753	+	0.978181i	$0.566615\pi$
$312$	−7.39043	−0.418401
$313$	29.6916	1.67827	0.839134	−	0.543924i	$-0.183062\pi$
$313$	29.6916	1.67827	0.839134	+	0.543924i	$0.183062\pi$
$314$	1.10934	0.0626036
$315$	−1.76302	−0.0993348
$316$	−2.88214	−0.162133
$317$	13.3816	0.751584	0.375792	−	0.926704i	$-0.377371\pi$
$317$	13.3816	0.751584	0.375792	+	0.926704i	$0.377371\pi$
$318$	−14.3125	−0.802605
$319$	53.0460	2.97001
$320$	1.00000	0.0559017
$321$	5.49508	0.306705
$322$	−10.5438	−0.587580
$323$	5.32186	0.296116
$324$	−10.8203	−0.601130
$325$	3.76920	0.209077
$326$	10.3189	0.571509
$327$	−13.8769	−0.767395
$328$	−4.53210	−0.250243
$329$	12.6829	0.699232
$330$	−12.5031	−0.688273
$331$	28.2587	1.55324	0.776621	−	0.629969i	$-0.216932\pi$
$331$	28.2587	1.55324	0.776621	+	0.629969i	$0.216932\pi$
$332$	3.70172	0.203158
$333$	−2.79149	−0.152972
$334$	11.4003	0.623796
$335$	10.8269	0.591536
$336$	−4.09325	−0.223305
$337$	−18.7128	−1.01935	−0.509676	−	0.860366i	$-0.670235\pi$
$337$	−18.7128	−1.01935	−0.509676	+	0.860366i	$0.670235\pi$
$338$	−1.20685	−0.0656438
$339$	−2.37977	−0.129252
$340$	−2.53050	−0.137236
$341$	62.5136	3.38530
$342$	1.77609	0.0960402
$343$	20.1285	1.08684
$344$	−1.36056	−0.0733564
$345$	−9.90306	−0.533163
$346$	−25.7158	−1.38249
$347$	21.1557	1.13570	0.567848	−	0.823133i	$-0.307776\pi$
$347$	21.1557	1.13570	0.567848	+	0.823133i	$0.307776\pi$
$348$	16.3109	0.874355
$349$	−23.8453	−1.27641	−0.638204	−	0.769867i	$-0.720322\pi$
$349$	−23.8453	−1.27641	−0.638204	+	0.769867i	$0.720322\pi$
$350$	2.08760	0.111587
$351$	−15.9299	−0.850277
$352$	−6.37671	−0.339880
$353$	3.28356	0.174766	0.0873832	−	0.996175i	$-0.472150\pi$
$353$	3.28356	0.174766	0.0873832	+	0.996175i	$0.472150\pi$
$354$	−23.3041	−1.23860
$355$	0.945111	0.0501613
$356$	−11.1225	−0.589492
$357$	10.3580	0.548202
$358$	−3.12582	−0.165205
$359$	−21.8636	−1.15392	−0.576958	−	0.816774i	$-0.695760\pi$
$359$	−21.8636	−1.15392	−0.576958	+	0.816774i	$0.695760\pi$
$360$	−0.844520	−0.0445101
$361$	−14.5770	−0.767213
$362$	−3.52525	−0.185283
$363$	58.1604	3.05263
$364$	−7.86857	−0.412425
$365$	−5.84916	−0.306159
$366$	−5.68859	−0.297348
$367$	3.19453	0.166753	0.0833766	−	0.996518i	$-0.473430\pi$
$367$	3.19453	0.166753	0.0833766	+	0.996518i	$0.473430\pi$
$368$	−5.05066	−0.263284
$369$	3.82745	0.199249
$370$	3.30541	0.171840
$371$	−15.2385	−0.791141
$372$	19.2220	0.996614
$373$	−30.8379	−1.59673	−0.798363	−	0.602177i	$-0.794300\pi$
$373$	−30.8379	−1.59673	−0.798363	+	0.602177i	$0.794300\pi$
$374$	16.1363	0.834388
$375$	1.96074	0.101252
$376$	6.07536	0.313313
$377$	31.3549	1.61486
$378$	−8.82291	−0.453802
$379$	−3.49294	−0.179420	−0.0897100	−	0.995968i	$-0.528594\pi$
$379$	−3.49294	−0.179420	−0.0897100	+	0.995968i	$0.528594\pi$
$380$	−2.10308	−0.107886
$381$	−15.2223	−0.779862
$382$	0.0668831	0.00342204
$383$	23.8942	1.22093	0.610467	−	0.792041i	$-0.290982\pi$
$383$	23.8942	1.22093	0.610467	+	0.792041i	$0.290982\pi$
$384$	−1.96074	−0.100059
$385$	−13.3120	−0.678443
$386$	−2.40887	−0.122608
$387$	1.14902	0.0584079
$388$	2.51227	0.127541
$389$	−26.8170	−1.35967	−0.679837	−	0.733364i	$-0.737949\pi$
$389$	−26.8170	−1.35967	−0.679837	+	0.733364i	$0.737949\pi$
$390$	−7.39043	−0.374229
$391$	12.7807	0.646349
$392$	2.64193	0.133438
$393$	26.3772	1.33055
$394$	2.41153	0.121491
$395$	−2.88214	−0.145016
$396$	5.38526	0.270619
$397$	−4.08273	−0.204906	−0.102453	−	0.994738i	$-0.532669\pi$
$397$	−4.08273	−0.204906	−0.102453	+	0.994738i	$0.532669\pi$
$398$	−21.0173	−1.05350
$399$	8.60843	0.430961
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−21.2287	−1.05879
$403$	36.9510	1.84066
$404$	−1.40803	−0.0700519
$405$	−10.8203	−0.537667
$406$	17.3661	0.861867
$407$	−21.0777	−1.04478
$408$	4.96167	0.245639
$409$	36.4259	1.80114	0.900572	−	0.434706i	$-0.143148\pi$
$409$	36.4259	1.80114	0.900572	+	0.434706i	$0.143148\pi$
$410$	−4.53210	−0.223825
$411$	31.8548	1.57128
$412$	−0.220448	−0.0108607
$413$	−24.8118	−1.22091
$414$	4.26538	0.209632
$415$	3.70172	0.181710
$416$	−3.76920	−0.184800
$417$	26.1141	1.27881
$418$	13.4107	0.655941
$419$	39.5795	1.93359	0.966793	−	0.255560i	$-0.0822597\pi$
$419$	39.5795	1.93359	0.966793	+	0.255560i	$0.0822597\pi$
$420$	−4.09325	−0.199730
$421$	17.9742	0.876007	0.438004	−	0.898973i	$-0.355686\pi$
$421$	17.9742	0.876007	0.438004	+	0.898973i	$0.355686\pi$
$422$	−26.5948	−1.29461
$423$	−5.13076	−0.249466
$424$	−7.29952	−0.354496
$425$	−2.53050	−0.122747
$426$	−1.85312	−0.0897840
$427$	−6.05663	−0.293101
$428$	2.80255	0.135466
$429$	47.1266	2.27530
$430$	−1.36056	−0.0656120
$431$	27.2142	1.31086	0.655431	−	0.755255i	$-0.272487\pi$
$431$	27.2142	1.31086	0.655431	+	0.755255i	$0.272487\pi$
$432$	−4.22635	−0.203340
$433$	25.3012	1.21590	0.607948	−	0.793977i	$-0.291993\pi$
$433$	25.3012	1.21590	0.607948	+	0.793977i	$0.291993\pi$
$434$	20.4656	0.982380
$435$	16.3109	0.782047
$436$	−7.07737	−0.338945
$437$	10.6220	0.508117
$438$	11.4687	0.547996
$439$	10.0471	0.479522	0.239761	−	0.970832i	$-0.422931\pi$
$439$	10.0471	0.479522	0.239761	+	0.970832i	$0.422931\pi$
$440$	−6.37671	−0.303998
$441$	−2.23117	−0.106246
$442$	9.53797	0.453675
$443$	−20.5646	−0.977054	−0.488527	−	0.872549i	$-0.662466\pi$
$443$	−20.5646	−0.977054	−0.488527	+	0.872549i	$0.662466\pi$
$444$	−6.48107	−0.307578
$445$	−11.1225	−0.527258
$446$	−7.85609	−0.371997
$447$	−17.7165	−0.837961
$448$	−2.08760	−0.0986297
$449$	−11.0855	−0.523155	−0.261578	−	0.965182i	$-0.584243\pi$
$449$	−11.0855	−0.523155	−0.261578	+	0.965182i	$0.584243\pi$
$450$	−0.844520	−0.0398110
$451$	28.8999	1.36084
$452$	−1.21371	−0.0570881
$453$	−22.7538	−1.06906
$454$	27.5494	1.29296
$455$	−7.86857	−0.368884
$456$	4.12361	0.193106
$457$	24.1657	1.13042	0.565212	−	0.824946i	$-0.308794\pi$
$457$	24.1657	1.13042	0.565212	+	0.824946i	$0.308794\pi$
$458$	−25.4339	−1.18845
$459$	10.6948	0.499190
$460$	−5.05066	−0.235488
$461$	−30.5704	−1.42380	−0.711902	−	0.702279i	$-0.752166\pi$
$461$	−30.5704	−1.42380	−0.711902	+	0.702279i	$0.752166\pi$
$462$	26.1014	1.21435
$463$	−5.06916	−0.235584	−0.117792	−	0.993038i	$-0.537582\pi$
$463$	−5.06916	−0.235584	−0.117792	+	0.993038i	$0.537582\pi$
$464$	8.31872	0.386187
$465$	19.2220	0.891399
$466$	−5.39329	−0.249839
$467$	3.30339	0.152863	0.0764314	−	0.997075i	$-0.475647\pi$
$467$	3.30339	0.152863	0.0764314	+	0.997075i	$0.475647\pi$
$468$	3.18316	0.147142
$469$	−22.6022	−1.04367
$470$	6.07536	0.280236
$471$	−2.17513	−0.100225
$472$	−11.8854	−0.547068
$473$	8.67589	0.398918
$474$	5.65115	0.259566
$475$	−2.10308	−0.0964960
$476$	5.28268	0.242131
$477$	6.16459	0.282257
$478$	8.08622	0.369855
$479$	−0.672986	−0.0307495	−0.0153748	−	0.999882i	$-0.504894\pi$
$479$	−0.672986	−0.0307495	−0.0153748	+	0.999882i	$0.504894\pi$
$480$	−1.96074	−0.0894953
$481$	−12.4587	−0.568070
$482$	7.69430	0.350466
$483$	20.6736	0.940682
$484$	29.6624	1.34829
$485$	2.51227	0.114076
$486$	8.53690	0.387241
$487$	−13.9174	−0.630657	−0.315329	−	0.948983i	$-0.602115\pi$
$487$	−13.9174	−0.630657	−0.315329	+	0.948983i	$0.602115\pi$
$488$	−2.90124	−0.131333
$489$	−20.2327	−0.914953
$490$	2.64193	0.119350
$491$	19.3862	0.874887	0.437443	−	0.899246i	$-0.355884\pi$
$491$	19.3862	0.874887	0.437443	+	0.899246i	$0.355884\pi$
$492$	8.88629	0.400625
$493$	−21.0505	−0.948069
$494$	7.92693	0.356649
$495$	5.38526	0.242049
$496$	9.80342	0.440187
$497$	−1.97301	−0.0885016
$498$	−7.25812	−0.325244
$499$	−13.0867	−0.585843	−0.292921	−	0.956137i	$-0.594627\pi$
$499$	−13.0867	−0.585843	−0.292921	+	0.956137i	$0.594627\pi$
$500$	1.00000	0.0447214
$501$	−22.3531	−0.998661
$502$	14.6443	0.653607
$503$	−39.2095	−1.74826	−0.874132	−	0.485689i	$-0.838569\pi$
$503$	−39.2095	−1.74826	−0.874132	+	0.485689i	$0.838569\pi$
$504$	1.76302	0.0785310
$505$	−1.40803	−0.0626564
$506$	32.2066	1.43176
$507$	2.36632	0.105092
$508$	−7.76353	−0.344451
$509$	−28.1475	−1.24762	−0.623809	−	0.781577i	$-0.714416\pi$
$509$	−28.1475	−1.24762	−0.623809	+	0.781577i	$0.714416\pi$
$510$	4.96167	0.219707
$511$	12.2107	0.540169
$512$	−1.00000	−0.0441942
$513$	8.88835	0.392430
$514$	11.9210	0.525813
$515$	−0.220448	−0.00971410
$516$	2.66771	0.117439
$517$	−38.7408	−1.70382
$518$	−6.90037	−0.303185
$519$	50.4222	2.21329
$520$	−3.76920	−0.165290
$521$	−2.48351	−0.108805	−0.0544024	−	0.998519i	$-0.517325\pi$
$521$	−2.48351	−0.108805	−0.0544024	+	0.998519i	$0.517325\pi$
$522$	−7.02532	−0.307490
$523$	−14.2264	−0.622079	−0.311039	−	0.950397i	$-0.600677\pi$
$523$	−14.2264	−0.622079	−0.311039	+	0.950397i	$0.600677\pi$
$524$	13.4526	0.587680
$525$	−4.09325	−0.178644
$526$	−20.0700	−0.875095
$527$	−24.8076	−1.08064
$528$	12.5031	0.544128
$529$	2.50920	0.109096
$530$	−7.29952	−0.317071
$531$	10.0374	0.435587
$532$	4.39039	0.190348
$533$	17.0824	0.739920
$534$	21.8084	0.943743
$535$	2.80255	0.121165
$536$	−10.8269	−0.467650
$537$	6.12894	0.264483
$538$	25.7662	1.11086
$539$	−16.8469	−0.725645
$540$	−4.22635	−0.181873
$541$	0.416109	0.0178899	0.00894496	−	0.999960i	$-0.497153\pi$
$541$	0.416109	0.0178899	0.00894496	+	0.999960i	$0.497153\pi$
$542$	30.6438	1.31626
$543$	6.91212	0.296627
$544$	2.53050	0.108494
$545$	−7.07737	−0.303161
$546$	15.4283	0.660268
$547$	−10.1036	−0.431999	−0.215999	−	0.976393i	$-0.569301\pi$
$547$	−10.1036	−0.431999	−0.215999	+	0.976393i	$0.569301\pi$
$548$	16.2463	0.694006
$549$	2.45016	0.104570
$550$	−6.37671	−0.271904
$551$	−17.4949	−0.745310
$552$	9.90306	0.421502
$553$	6.01676	0.255859
$554$	−24.0523	−1.02188
$555$	−6.48107	−0.275106
$556$	13.3185	0.564828
$557$	−24.6223	−1.04328	−0.521640	−	0.853166i	$-0.674680\pi$
$557$	−24.6223	−1.04328	−0.521640	+	0.853166i	$0.674680\pi$
$558$	−8.27918	−0.350486
$559$	5.12821	0.216900
$560$	−2.08760	−0.0882171
$561$	−31.6391	−1.33581
$562$	26.5712	1.12084
$563$	−20.6298	−0.869442	−0.434721	−	0.900565i	$-0.643153\pi$
$563$	−20.6298	−0.869442	−0.434721	+	0.900565i	$0.643153\pi$
$564$	−11.9122	−0.501596
$565$	−1.21371	−0.0510611
$566$	18.1387	0.762425
$567$	22.5885	0.948629
$568$	−0.945111	−0.0396560
$569$	7.39097	0.309846	0.154923	−	0.987927i	$-0.450487\pi$
$569$	7.39097	0.309846	0.154923	+	0.987927i	$0.450487\pi$
$570$	4.12361	0.172719
$571$	9.39376	0.393117	0.196558	−	0.980492i	$-0.437023\pi$
$571$	9.39376	0.393117	0.196558	+	0.980492i	$0.437023\pi$
$572$	24.0351	1.00496
$573$	−0.131141	−0.00547848
$574$	9.46121	0.394903
$575$	−5.05066	−0.210627
$576$	0.844520	0.0351883
$577$	40.3712	1.68067	0.840337	−	0.542064i	$-0.182357\pi$
$577$	40.3712	1.68067	0.840337	+	0.542064i	$0.182357\pi$
$578$	10.5965	0.440758
$579$	4.72318	0.196289
$580$	8.31872	0.345416
$581$	−7.72770	−0.320599
$582$	−4.92591	−0.204186
$583$	46.5469	1.92778
$584$	5.84916	0.242040
$585$	3.18316	0.131608
$586$	−14.6801	−0.606431
$587$	0.847454	0.0349782	0.0174891	−	0.999847i	$-0.494433\pi$
$587$	0.847454	0.0349782	0.0174891	+	0.999847i	$0.494433\pi$
$588$	−5.18016	−0.213626
$589$	−20.6174	−0.849525
$590$	−11.8854	−0.489312
$591$	−4.72839	−0.194500
$592$	−3.30541	−0.135852
$593$	−41.1358	−1.68925	−0.844623	−	0.535361i	$-0.820175\pi$
$593$	−41.1358	−1.68925	−0.844623	+	0.535361i	$0.820175\pi$
$594$	26.9502	1.10578
$595$	5.28268	0.216569
$596$	−9.03559	−0.370112
$597$	41.2095	1.68659
$598$	19.0369	0.778479
$599$	−16.8822	−0.689789	−0.344894	−	0.938641i	$-0.612085\pi$
$599$	−16.8822	−0.689789	−0.344894	+	0.938641i	$0.612085\pi$
$600$	−1.96074	−0.0800471
$601$	−9.73699	−0.397180	−0.198590	−	0.980083i	$-0.563636\pi$
$601$	−9.73699	−0.397180	−0.198590	+	0.980083i	$0.563636\pi$
$602$	2.84030	0.115762
$603$	9.14351	0.372353
$604$	−11.6047	−0.472187
$605$	29.6624	1.20595
$606$	2.76078	0.112149
$607$	−22.2383	−0.902626	−0.451313	−	0.892366i	$-0.649044\pi$
$607$	−22.2383	−0.902626	−0.451313	+	0.892366i	$0.649044\pi$
$608$	2.10308	0.0852912
$609$	−34.0506	−1.37980
$610$	−2.90124	−0.117468
$611$	−22.8992	−0.926404
$612$	−2.13706	−0.0863856
$613$	−22.8743	−0.923885	−0.461943	−	0.886910i	$-0.652847\pi$
$613$	−22.8743	−0.923885	−0.461943	+	0.886910i	$0.652847\pi$
$614$	12.4405	0.502058
$615$	8.88629	0.358330
$616$	13.3120	0.536356
$617$	9.33912	0.375979	0.187989	−	0.982171i	$-0.439803\pi$
$617$	9.33912	0.375979	0.187989	+	0.982171i	$0.439803\pi$
$618$	0.432242	0.0173873
$619$	−4.46943	−0.179642	−0.0898208	−	0.995958i	$-0.528629\pi$
$619$	−4.46943	−0.179642	−0.0898208	+	0.995958i	$0.528629\pi$
$620$	9.80342	0.393715
$621$	21.3459	0.856580
$622$	7.32753	0.293807
$623$	23.2193	0.930263
$624$	7.39043	0.295854
$625$	1.00000	0.0400000
$626$	−29.6916	−1.18672
$627$	−26.2950	−1.05012
$628$	−1.10934	−0.0442674
$629$	8.36436	0.333509
$630$	1.76302	0.0702403
$631$	−15.4302	−0.614268	−0.307134	−	0.951666i	$-0.599370\pi$
$631$	−15.4302	−0.614268	−0.307134	+	0.951666i	$0.599370\pi$
$632$	2.88214	0.114646
$633$	52.1456	2.07260
$634$	−13.3816	−0.531450
$635$	−7.76353	−0.308086
$636$	14.3125	0.567527
$637$	−9.95797	−0.394549
$638$	−53.0460	−2.10011
$639$	0.798165	0.0315749
$640$	−1.00000	−0.0395285
$641$	29.3220	1.15815	0.579076	−	0.815274i	$-0.303414\pi$
$641$	29.3220	1.15815	0.579076	+	0.815274i	$0.303414\pi$
$642$	−5.49508	−0.216874
$643$	46.3366	1.82734	0.913669	−	0.406459i	$-0.133237\pi$
$643$	46.3366	1.82734	0.913669	+	0.406459i	$0.133237\pi$
$644$	10.5438	0.415482
$645$	2.66771	0.105041
$646$	−5.32186	−0.209386
$647$	−25.0156	−0.983465	−0.491733	−	0.870746i	$-0.663636\pi$
$647$	−25.0156	−0.983465	−0.491733	+	0.870746i	$0.663636\pi$
$648$	10.8203	0.425063
$649$	75.7895	2.97500
$650$	−3.76920	−0.147840
$651$	−40.1278	−1.57273
$652$	−10.3189	−0.404118
$653$	−41.4320	−1.62136	−0.810679	−	0.585491i	$-0.800902\pi$
$653$	−41.4320	−1.62136	−0.810679	+	0.585491i	$0.800902\pi$
$654$	13.8769	0.542630
$655$	13.4526	0.525637
$656$	4.53210	0.176949
$657$	−4.93973	−0.192717
$658$	−12.6829	−0.494431
$659$	−36.4339	−1.41927	−0.709633	−	0.704572i	$-0.751139\pi$
$659$	−36.4339	−1.41927	−0.709633	+	0.704572i	$0.751139\pi$
$660$	12.5031	0.486682
$661$	34.0399	1.32400	0.662000	−	0.749504i	$-0.269708\pi$
$661$	34.0399	1.32400	0.662000	+	0.749504i	$0.269708\pi$
$662$	−28.2587	−1.09831
$663$	−18.7015	−0.726307
$664$	−3.70172	−0.143655
$665$	4.39039	0.170252
$666$	2.79149	0.108168
$667$	−42.0150	−1.62683
$668$	−11.4003	−0.441090
$669$	15.4038	0.595545
$670$	−10.8269	−0.418279
$671$	18.5004	0.714199
$672$	4.09325	0.157900
$673$	−0.362295	−0.0139655	−0.00698273	−	0.999976i	$-0.502223\pi$
$673$	−0.362295	−0.0139655	−0.00698273	+	0.999976i	$0.502223\pi$
$674$	18.7128	0.720791
$675$	−4.22635	−0.162672
$676$	1.20685	0.0464172
$677$	−33.7837	−1.29841	−0.649207	−	0.760612i	$-0.724899\pi$
$677$	−33.7837	−1.29841	−0.649207	+	0.760612i	$0.724899\pi$
$678$	2.37977	0.0913946
$679$	−5.24460	−0.201269
$680$	2.53050	0.0970404
$681$	−54.0174	−2.06995
$682$	−62.5136	−2.39377
$683$	−14.8676	−0.568891	−0.284446	−	0.958692i	$-0.591809\pi$
$683$	−14.8676	−0.568891	−0.284446	+	0.958692i	$0.591809\pi$
$684$	−1.77609	−0.0679107
$685$	16.2463	0.620738
$686$	−20.1285	−0.768509
$687$	49.8693	1.90263
$688$	1.36056	0.0518708
$689$	27.5133	1.04817
$690$	9.90306	0.377003
$691$	−7.20618	−0.274136	−0.137068	−	0.990562i	$-0.543768\pi$
$691$	−7.20618	−0.274136	−0.137068	+	0.990562i	$0.543768\pi$
$692$	25.7158	0.977569
$693$	−11.2423	−0.427058
$694$	−21.1557	−0.803059
$695$	13.3185	0.505198
$696$	−16.3109	−0.618262
$697$	−11.4685	−0.434401
$698$	23.8453	0.902557
$699$	10.5749	0.399978
$700$	−2.08760	−0.0789038
$701$	−41.0984	−1.55226	−0.776132	−	0.630571i	$-0.782821\pi$
$701$	−41.0984	−1.55226	−0.776132	+	0.630571i	$0.782821\pi$
$702$	15.9299	0.601237
$703$	6.95155	0.262183
$704$	6.37671	0.240331
$705$	−11.9122	−0.448641
$706$	−3.28356	−0.123579
$707$	2.93939	0.110547
$708$	23.3041	0.875824
$709$	30.1696	1.13304	0.566522	−	0.824047i	$-0.308289\pi$
$709$	30.1696	1.13304	0.566522	+	0.824047i	$0.308289\pi$
$710$	−0.945111	−0.0354694
$711$	−2.43403	−0.0912832
$712$	11.1225	0.416834
$713$	−49.5138	−1.85431
$714$	−10.3580	−0.387638
$715$	24.0351	0.898861
$716$	3.12582	0.116817
$717$	−15.8550	−0.592116
$718$	21.8636	0.815942
$719$	25.1301	0.937196	0.468598	−	0.883412i	$-0.344759\pi$
$719$	25.1301	0.937196	0.468598	+	0.883412i	$0.344759\pi$
$720$	0.844520	0.0314734
$721$	0.460207	0.0171390
$722$	14.5770	0.542501
$723$	−15.0866	−0.561075
$724$	3.52525	0.131015
$725$	8.31872	0.308949
$726$	−58.1604	−2.15854
$727$	33.1459	1.22931	0.614656	−	0.788795i	$-0.289295\pi$
$727$	33.1459	1.22931	0.614656	+	0.788795i	$0.289295\pi$
$728$	7.86857	0.291629
$729$	15.7224	0.582310
$730$	5.84916	0.216487
$731$	−3.44290	−0.127340
$732$	5.68859	0.210256
$733$	−13.8067	−0.509963	−0.254981	−	0.966946i	$-0.582069\pi$
$733$	−13.8067	−0.509963	−0.254981	+	0.966946i	$0.582069\pi$
$734$	−3.19453	−0.117912
$735$	−5.18016	−0.191073
$736$	5.05066	0.186170
$737$	69.0399	2.54312
$738$	−3.82745	−0.140890
$739$	−21.0725	−0.775163	−0.387581	−	0.921835i	$-0.626689\pi$
$739$	−21.0725	−0.775163	−0.387581	+	0.921835i	$0.626689\pi$
$740$	−3.30541	−0.121509
$741$	−15.5427	−0.570975
$742$	15.2385	0.559422
$743$	−16.6808	−0.611960	−0.305980	−	0.952038i	$-0.598984\pi$
$743$	−16.6808	−0.611960	−0.305980	+	0.952038i	$0.598984\pi$
$744$	−19.2220	−0.704713
$745$	−9.03559	−0.331038
$746$	30.8379	1.12906
$747$	3.12617	0.114381
$748$	−16.1363	−0.590001
$749$	−5.85059	−0.213776
$750$	−1.96074	−0.0715963
$751$	−22.7609	−0.830558	−0.415279	−	0.909694i	$-0.636316\pi$
$751$	−22.7609	−0.830558	−0.415279	+	0.909694i	$0.636316\pi$
$752$	−6.07536	−0.221546
$753$	−28.7137	−1.04639
$754$	−31.3549	−1.14188
$755$	−11.6047	−0.422337
$756$	8.82291	0.320886
$757$	−43.9138	−1.59607	−0.798037	−	0.602608i	$-0.794128\pi$
$757$	−43.9138	−1.59607	−0.798037	+	0.602608i	$0.794128\pi$
$758$	3.49294	0.126869
$759$	−63.1489	−2.29216
$760$	2.10308	0.0762868
$761$	−28.4504	−1.03133	−0.515663	−	0.856792i	$-0.672454\pi$
$761$	−28.4504	−1.03133	−0.515663	+	0.856792i	$0.672454\pi$
$762$	15.2223	0.551446
$763$	14.7747	0.534880
$764$	−0.0668831	−0.00241975
$765$	−2.13706	−0.0772656
$766$	−23.8942	−0.863331
$767$	44.7983	1.61757
$768$	1.96074	0.0707523
$769$	29.1989	1.05294	0.526469	−	0.850194i	$-0.323516\pi$
$769$	29.1989	1.05294	0.526469	+	0.850194i	$0.323516\pi$
$770$	13.3120	0.479731
$771$	−23.3740	−0.841795
$772$	2.40887	0.0866971
$773$	−32.3731	−1.16438	−0.582190	−	0.813053i	$-0.697804\pi$
$773$	−32.3731	−1.16438	−0.582190	+	0.813053i	$0.697804\pi$
$774$	−1.14902	−0.0413006
$775$	9.80342	0.352149
$776$	−2.51227	−0.0901851
$777$	13.5299	0.485381
$778$	26.8170	0.961434
$779$	−9.53138	−0.341497
$780$	7.39043	0.264620
$781$	6.02670	0.215652
$782$	−12.7807	−0.457038
$783$	−35.1578	−1.25644
$784$	−2.64193	−0.0943548
$785$	−1.10934	−0.0395940
$786$	−26.3772	−0.940842
$787$	31.2800	1.11501	0.557506	−	0.830173i	$-0.311758\pi$
$787$	31.2800	1.11501	0.557506	+	0.830173i	$0.311758\pi$
$788$	−2.41153	−0.0859071
$789$	39.3522	1.40098
$790$	2.88214	0.102542
$791$	2.53374	0.0900893
$792$	−5.38526	−0.191357
$793$	10.9354	0.388326
$794$	4.08273	0.144891
$795$	14.3125	0.507612
$796$	21.0173	0.744938
$797$	−54.7402	−1.93900	−0.969499	−	0.245097i	$-0.921180\pi$
$797$	−54.7402	−1.93900	−0.969499	+	0.245097i	$0.921180\pi$
$798$	−8.60843	−0.304735
$799$	15.3737	0.543883
$800$	−1.00000	−0.0353553
$801$	−9.39319	−0.331892
$802$	1.00000	0.0353112
$803$	−37.2984	−1.31623
$804$	21.2287	0.748680
$805$	10.5438	0.371619
$806$	−36.9510	−1.30154
$807$	−50.5208	−1.77842
$808$	1.40803	0.0495342
$809$	26.1553	0.919570	0.459785	−	0.888030i	$-0.347926\pi$
$809$	26.1553	0.919570	0.459785	+	0.888030i	$0.347926\pi$
$810$	10.8203	0.380188
$811$	−56.9087	−1.99834	−0.999168	−	0.0407803i	$-0.987016\pi$
$811$	−56.9087	−1.99834	−0.999168	+	0.0407803i	$0.987016\pi$
$812$	−17.3661	−0.609432
$813$	−60.0846	−2.10726
$814$	21.0777	0.738771
$815$	−10.3189	−0.361454
$816$	−4.96167	−0.173693
$817$	−2.86137	−0.100107
$818$	−36.4259	−1.27360
$819$	−6.64516	−0.232201
$820$	4.53210	0.158268
$821$	−16.9610	−0.591944	−0.295972	−	0.955197i	$-0.595643\pi$
$821$	−16.9610	−0.591944	−0.295972	+	0.955197i	$0.595643\pi$
$822$	−31.8548	−1.11106
$823$	3.84790	0.134129	0.0670647	−	0.997749i	$-0.478637\pi$
$823$	3.84790	0.134129	0.0670647	+	0.997749i	$0.478637\pi$
$824$	0.220448	0.00767967
$825$	12.5031	0.435302
$826$	24.8118	0.863315
$827$	26.4692	0.920425	0.460213	−	0.887809i	$-0.347773\pi$
$827$	26.4692	0.920425	0.460213	+	0.887809i	$0.347773\pi$
$828$	−4.26538	−0.148232
$829$	−8.76753	−0.304509	−0.152254	−	0.988341i	$-0.548653\pi$
$829$	−8.76753	−0.304509	−0.152254	+	0.988341i	$0.548653\pi$
$830$	−3.70172	−0.128488
$831$	47.1603	1.63597
$832$	3.76920	0.130673
$833$	6.68543	0.231636
$834$	−26.1141	−0.904257
$835$	−11.4003	−0.394523
$836$	−13.4107	−0.463820
$837$	−41.4326	−1.43212
$838$	−39.5795	−1.36725
$839$	−4.10144	−0.141597	−0.0707987	−	0.997491i	$-0.522555\pi$
$839$	−4.10144	−0.141597	−0.0707987	+	0.997491i	$0.522555\pi$
$840$	4.09325	0.141230
$841$	40.2010	1.38624
$842$	−17.9742	−0.619431
$843$	−52.0993	−1.79440
$844$	26.5948	0.915431
$845$	1.20685	0.0415168
$846$	5.13076	0.176399
$847$	−61.9232	−2.12771
$848$	7.29952	0.250667
$849$	−35.5653	−1.22060
$850$	2.53050	0.0867956
$851$	16.6945	0.572281
$852$	1.85312	0.0634869
$853$	4.04613	0.138537	0.0692684	−	0.997598i	$-0.477934\pi$
$853$	4.04613	0.138537	0.0692684	+	0.997598i	$0.477934\pi$
$854$	6.05663	0.207253
$855$	−1.77609	−0.0607411
$856$	−2.80255	−0.0957891
$857$	−34.0441	−1.16292	−0.581462	−	0.813574i	$-0.697519\pi$
$857$	−34.0441	−1.16292	−0.581462	+	0.813574i	$0.697519\pi$
$858$	−47.1266	−1.60888
$859$	56.5349	1.92895	0.964473	−	0.264182i	$-0.0851018\pi$
$859$	56.5349	1.92895	0.964473	+	0.264182i	$0.0851018\pi$
$860$	1.36056	0.0463947
$861$	−18.5510	−0.632217
$862$	−27.2142	−0.926919
$863$	−26.1160	−0.888999	−0.444499	−	0.895779i	$-0.646618\pi$
$863$	−26.1160	−0.888999	−0.444499	+	0.895779i	$0.646618\pi$
$864$	4.22635	0.143783
$865$	25.7158	0.874365
$866$	−25.3012	−0.859769
$867$	−20.7771	−0.705628
$868$	−20.4656	−0.694648
$869$	−18.3786	−0.623451
$870$	−16.3109	−0.552991
$871$	40.8086	1.38275
$872$	7.07737	0.239670
$873$	2.12166	0.0718073
$874$	−10.6220	−0.359293
$875$	−2.08760	−0.0705737
$876$	−11.4687	−0.387491
$877$	−2.25784	−0.0762419	−0.0381209	−	0.999273i	$-0.512137\pi$
$877$	−2.25784	−0.0762419	−0.0381209	+	0.999273i	$0.512137\pi$
$878$	−10.0471	−0.339073
$879$	28.7840	0.970860
$880$	6.37671	0.214959
$881$	−42.2900	−1.42479	−0.712393	−	0.701781i	$-0.752388\pi$
$881$	−42.2900	−1.42479	−0.712393	+	0.701781i	$0.752388\pi$
$882$	2.23117	0.0751273
$883$	5.63602	0.189667	0.0948336	−	0.995493i	$-0.469768\pi$
$883$	5.63602	0.189667	0.0948336	+	0.995493i	$0.469768\pi$
$884$	−9.53797	−0.320797
$885$	23.3041	0.783360
$886$	20.5646	0.690882
$887$	11.0520	0.371091	0.185545	−	0.982636i	$-0.440595\pi$
$887$	11.0520	0.371091	0.185545	+	0.982636i	$0.440595\pi$
$888$	6.48107	0.217490
$889$	16.2071	0.543570
$890$	11.1225	0.372828
$891$	−68.9982	−2.31153
$892$	7.85609	0.263041
$893$	12.7770	0.427565
$894$	17.7165	0.592528
$895$	3.12582	0.104485
$896$	2.08760	0.0697418
$897$	−37.3266	−1.24630
$898$	11.0855	0.369927
$899$	81.5519	2.71991
$900$	0.844520	0.0281507
$901$	−18.4715	−0.615374
$902$	−28.8999	−0.962261
$903$	−5.56910	−0.185328
$904$	1.21371	0.0403674
$905$	3.52525	0.117183
$906$	22.7538	0.755943
$907$	39.2778	1.30420	0.652100	−	0.758133i	$-0.273888\pi$
$907$	39.2778	1.30420	0.652100	+	0.758133i	$0.273888\pi$
$908$	−27.5494	−0.914261
$909$	−1.18911	−0.0394402
$910$	7.86857	0.260840
$911$	20.0109	0.662990	0.331495	−	0.943457i	$-0.392447\pi$
$911$	20.0109	0.662990	0.331495	+	0.943457i	$0.392447\pi$
$912$	−4.12361	−0.136546
$913$	23.6048	0.781204
$914$	−24.1657	−0.799331
$915$	5.68859	0.188059
$916$	25.4339	0.840359
$917$	−28.0837	−0.927404
$918$	−10.6948	−0.352981
$919$	5.65249	0.186458	0.0932292	−	0.995645i	$-0.470281\pi$
$919$	5.65249	0.186458	0.0932292	+	0.995645i	$0.470281\pi$
$920$	5.05066	0.166515
$921$	−24.3926	−0.803765
$922$	30.5704	1.00678
$923$	3.56231	0.117255
$924$	−26.1014	−0.858674
$925$	−3.30541	−0.108681
$926$	5.06916	0.166583
$927$	−0.186173	−0.00611472
$928$	−8.31872	−0.273075
$929$	−40.1245	−1.31644	−0.658221	−	0.752825i	$-0.728691\pi$
$929$	−40.1245	−1.31644	−0.658221	+	0.752825i	$0.728691\pi$
$930$	−19.2220	−0.630314
$931$	5.55621	0.182097
$932$	5.39329	0.176663
$933$	−14.3674	−0.470368
$934$	−3.30339	−0.108090
$935$	−16.1363	−0.527713
$936$	−3.18316	−0.104045
$937$	18.3764	0.600331	0.300166	−	0.953887i	$-0.402958\pi$
$937$	18.3764	0.600331	0.300166	+	0.953887i	$0.402958\pi$
$938$	22.6022	0.737987
$939$	58.2177	1.89986
$940$	−6.07536	−0.198156
$941$	−4.10282	−0.133748	−0.0668741	−	0.997761i	$-0.521303\pi$
$941$	−4.10282	−0.133748	−0.0668741	+	0.997761i	$0.521303\pi$
$942$	2.17513	0.0708695
$943$	−22.8901	−0.745405
$944$	11.8854	0.386835
$945$	8.82291	0.287009
$946$	−8.67589	−0.282077
$947$	−6.23324	−0.202553	−0.101277	−	0.994858i	$-0.532293\pi$
$947$	−6.23324	−0.202553	−0.101277	+	0.994858i	$0.532293\pi$
$948$	−5.65115	−0.183541
$949$	−22.0466	−0.715663
$950$	2.10308	0.0682330
$951$	26.2378	0.850820
$952$	−5.28268	−0.171213
$953$	−9.62250	−0.311703	−0.155852	−	0.987780i	$-0.549812\pi$
$953$	−9.62250	−0.311703	−0.155852	+	0.987780i	$0.549812\pi$
$954$	−6.16459	−0.199586
$955$	−0.0668831	−0.00216429
$956$	−8.08622	−0.261527
$957$	104.010	3.36216
$958$	0.672986	0.0217432
$959$	−33.9157	−1.09519
$960$	1.96074	0.0632828
$961$	65.1070	2.10023
$962$	12.4587	0.401686
$963$	2.36681	0.0762693
$964$	−7.69430	−0.247817
$965$	2.40887	0.0775442
$966$	−20.6736	−0.665162
$967$	31.7306	1.02039	0.510194	−	0.860059i	$-0.329573\pi$
$967$	31.7306	1.02039	0.510194	+	0.860059i	$0.329573\pi$
$968$	−29.6624	−0.953386
$969$	10.4348	0.335214
$970$	−2.51227	−0.0806640
$971$	−48.7642	−1.56492	−0.782458	−	0.622703i	$-0.786035\pi$
$971$	−48.7642	−1.56492	−0.782458	+	0.622703i	$0.786035\pi$
$972$	−8.53690	−0.273821
$973$	−27.8036	−0.891342
$974$	13.9174	0.445942
$975$	7.39043	0.236683
$976$	2.90124	0.0928665
$977$	33.1489	1.06053	0.530263	−	0.847833i	$-0.322093\pi$
$977$	33.1489	1.06053	0.530263	+	0.847833i	$0.322093\pi$
$978$	20.2327	0.646969
$979$	−70.9251	−2.26677
$980$	−2.64193	−0.0843935
$981$	−5.97698	−0.190830
$982$	−19.3862	−0.618639
$983$	−3.40573	−0.108626	−0.0543130	−	0.998524i	$-0.517297\pi$
$983$	−3.40573	−0.108626	−0.0543130	+	0.998524i	$0.517297\pi$
$984$	−8.88629	−0.283285
$985$	−2.41153	−0.0768377
$986$	21.0505	0.670386
$987$	24.8680	0.791556
$988$	−7.92693	−0.252189
$989$	−6.87172	−0.218508
$990$	−5.38526	−0.171155
$991$	−30.8612	−0.980339	−0.490169	−	0.871627i	$-0.663065\pi$
$991$	−30.8612	−0.980339	−0.490169	+	0.871627i	$0.663065\pi$
$992$	−9.80342	−0.311259
$993$	55.4082	1.75833
$994$	1.97301	0.0625801
$995$	21.0173	0.666293
$996$	7.25812	0.229982
$997$	−49.6449	−1.57227	−0.786134	−	0.618056i	$-0.787921\pi$
$997$	−49.6449	−1.57227	−0.786134	+	0.618056i	$0.787921\pi$
$998$	13.0867	0.414253
$999$	13.9698	0.441985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.15	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.96074 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.96074 q^{6} -2.08760 q^{7} -1.00000 q^{8} +0.844520 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.96074 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.96074 q^{6} -2.08760 q^{7} -1.00000 q^{8} +0.844520 q^{9} -1.00000 q^{10} +6.37671 q^{11} +1.96074 q^{12} +3.76920 q^{13} +2.08760 q^{14} +1.96074 q^{15} +1.00000 q^{16} -2.53050 q^{17} -0.844520 q^{18} -2.10308 q^{19} +1.00000 q^{20} -4.09325 q^{21} -6.37671 q^{22} -5.05066 q^{23} -1.96074 q^{24} +1.00000 q^{25} -3.76920 q^{26} -4.22635 q^{27} -2.08760 q^{28} +8.31872 q^{29} -1.96074 q^{30} +9.80342 q^{31} -1.00000 q^{32} +12.5031 q^{33} +2.53050 q^{34} -2.08760 q^{35} +0.844520 q^{36} -3.30541 q^{37} +2.10308 q^{38} +7.39043 q^{39} -1.00000 q^{40} +4.53210 q^{41} +4.09325 q^{42} +1.36056 q^{43} +6.37671 q^{44} +0.844520 q^{45} +5.05066 q^{46} -6.07536 q^{47} +1.96074 q^{48} -2.64193 q^{49} -1.00000 q^{50} -4.96167 q^{51} +3.76920 q^{52} +7.29952 q^{53} +4.22635 q^{54} +6.37671 q^{55} +2.08760 q^{56} -4.12361 q^{57} -8.31872 q^{58} +11.8854 q^{59} +1.96074 q^{60} +2.90124 q^{61} -9.80342 q^{62} -1.76302 q^{63} +1.00000 q^{64} +3.76920 q^{65} -12.5031 q^{66} +10.8269 q^{67} -2.53050 q^{68} -9.90306 q^{69} +2.08760 q^{70} +0.945111 q^{71} -0.844520 q^{72} -5.84916 q^{73} +3.30541 q^{74} +1.96074 q^{75} -2.10308 q^{76} -13.3120 q^{77} -7.39043 q^{78} -2.88214 q^{79} +1.00000 q^{80} -10.8203 q^{81} -4.53210 q^{82} +3.70172 q^{83} -4.09325 q^{84} -2.53050 q^{85} -1.36056 q^{86} +16.3109 q^{87} -6.37671 q^{88} -11.1225 q^{89} -0.844520 q^{90} -7.86857 q^{91} -5.05066 q^{92} +19.2220 q^{93} +6.07536 q^{94} -2.10308 q^{95} -1.96074 q^{96} +2.51227 q^{97} +2.64193 q^{98} +5.38526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 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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