LMFDB - Embedded newform 4010.2.a.m.1.18

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			1.18
Root			$2.72853$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.72853 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.72853 q^{6} +0.894798 q^{7} -1.00000 q^{8} +4.44487 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.72853 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.72853 q^{6} +0.894798 q^{7} -1.00000 q^{8} +4.44487 q^{9} -1.00000 q^{10} -5.03131 q^{11} +2.72853 q^{12} -5.35803 q^{13} -0.894798 q^{14} +2.72853 q^{15} +1.00000 q^{16} +5.62630 q^{17} -4.44487 q^{18} -0.243411 q^{19} +1.00000 q^{20} +2.44148 q^{21} +5.03131 q^{22} +4.21762 q^{23} -2.72853 q^{24} +1.00000 q^{25} +5.35803 q^{26} +3.94236 q^{27} +0.894798 q^{28} +7.69759 q^{29} -2.72853 q^{30} +1.55876 q^{31} -1.00000 q^{32} -13.7281 q^{33} -5.62630 q^{34} +0.894798 q^{35} +4.44487 q^{36} +10.0042 q^{37} +0.243411 q^{38} -14.6195 q^{39} -1.00000 q^{40} +3.18356 q^{41} -2.44148 q^{42} -3.19538 q^{43} -5.03131 q^{44} +4.44487 q^{45} -4.21762 q^{46} +4.78751 q^{47} +2.72853 q^{48} -6.19934 q^{49} -1.00000 q^{50} +15.3515 q^{51} -5.35803 q^{52} -5.76361 q^{53} -3.94236 q^{54} -5.03131 q^{55} -0.894798 q^{56} -0.664153 q^{57} -7.69759 q^{58} +7.35635 q^{59} +2.72853 q^{60} +2.11101 q^{61} -1.55876 q^{62} +3.97726 q^{63} +1.00000 q^{64} -5.35803 q^{65} +13.7281 q^{66} +14.7072 q^{67} +5.62630 q^{68} +11.5079 q^{69} -0.894798 q^{70} -2.41472 q^{71} -4.44487 q^{72} +10.4349 q^{73} -10.0042 q^{74} +2.72853 q^{75} -0.243411 q^{76} -4.50201 q^{77} +14.6195 q^{78} +8.03826 q^{79} +1.00000 q^{80} -2.57776 q^{81} -3.18356 q^{82} +17.4940 q^{83} +2.44148 q^{84} +5.62630 q^{85} +3.19538 q^{86} +21.0031 q^{87} +5.03131 q^{88} +12.8682 q^{89} -4.44487 q^{90} -4.79436 q^{91} +4.21762 q^{92} +4.25313 q^{93} -4.78751 q^{94} -0.243411 q^{95} -2.72853 q^{96} -1.78912 q^{97} +6.19934 q^{98} -22.3635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.72853	1.57532	0.787658	−	0.616112i	$-0.211293\pi$
$3$	2.72853	1.57532	0.787658	+	0.616112i	$0.211293\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.72853	−1.11392
$7$	0.894798	0.338202	0.169101	−	0.985599i	$-0.445914\pi$
$7$	0.894798	0.338202	0.169101	+	0.985599i	$0.445914\pi$
$8$	−1.00000	−0.353553
$9$	4.44487	1.48162
$10$	−1.00000	−0.316228
$11$	−5.03131	−1.51700	−0.758499	−	0.651674i	$-0.774067\pi$
$11$	−5.03131	−1.51700	−0.758499	+	0.651674i	$0.774067\pi$
$12$	2.72853	0.787658
$13$	−5.35803	−1.48605	−0.743026	−	0.669263i	$-0.766610\pi$
$13$	−5.35803	−1.48605	−0.743026	+	0.669263i	$0.766610\pi$
$14$	−0.894798	−0.239145
$15$	2.72853	0.704503
$16$	1.00000	0.250000
$17$	5.62630	1.36458	0.682289	−	0.731083i	$-0.260985\pi$
$17$	5.62630	1.36458	0.682289	+	0.731083i	$0.260985\pi$
$18$	−4.44487	−1.04767
$19$	−0.243411	−0.0558423	−0.0279211	−	0.999610i	$-0.508889\pi$
$19$	−0.243411	−0.0558423	−0.0279211	+	0.999610i	$0.508889\pi$
$20$	1.00000	0.223607
$21$	2.44148	0.532775
$22$	5.03131	1.07268
$23$	4.21762	0.879434	0.439717	−	0.898136i	$-0.355079\pi$
$23$	4.21762	0.879434	0.439717	+	0.898136i	$0.355079\pi$
$24$	−2.72853	−0.556958
$25$	1.00000	0.200000
$26$	5.35803	1.05080
$27$	3.94236	0.758707
$28$	0.894798	0.169101
$29$	7.69759	1.42941	0.714703	−	0.699428i	$-0.246562\pi$
$29$	7.69759	1.42941	0.714703	+	0.699428i	$0.246562\pi$
$30$	−2.72853	−0.498159
$31$	1.55876	0.279962	0.139981	−	0.990154i	$-0.455296\pi$
$31$	1.55876	0.279962	0.139981	+	0.990154i	$0.455296\pi$
$32$	−1.00000	−0.176777
$33$	−13.7281	−2.38975
$34$	−5.62630	−0.964902
$35$	0.894798	0.151248
$36$	4.44487	0.740811
$37$	10.0042	1.64468	0.822342	−	0.568994i	$-0.192667\pi$
$37$	10.0042	1.64468	0.822342	+	0.568994i	$0.192667\pi$
$38$	0.243411	0.0394864
$39$	−14.6195	−2.34100
$40$	−1.00000	−0.158114
$41$	3.18356	0.497188	0.248594	−	0.968608i	$-0.420032\pi$
$41$	3.18356	0.497188	0.248594	+	0.968608i	$0.420032\pi$
$42$	−2.44148	−0.376729
$43$	−3.19538	−0.487290	−0.243645	−	0.969864i	$-0.578343\pi$
$43$	−3.19538	−0.487290	−0.243645	+	0.969864i	$0.578343\pi$
$44$	−5.03131	−0.758499
$45$	4.44487	0.662602
$46$	−4.21762	−0.621854
$47$	4.78751	0.698329	0.349165	−	0.937061i	$-0.386465\pi$
$47$	4.78751	0.698329	0.349165	+	0.937061i	$0.386465\pi$
$48$	2.72853	0.393829
$49$	−6.19934	−0.885620
$50$	−1.00000	−0.141421
$51$	15.3515	2.14964
$52$	−5.35803	−0.743026
$53$	−5.76361	−0.791693	−0.395847	−	0.918317i	$-0.629549\pi$
$53$	−5.76361	−0.791693	−0.395847	+	0.918317i	$0.629549\pi$
$54$	−3.94236	−0.536487
$55$	−5.03131	−0.678422
$56$	−0.894798	−0.119572
$57$	−0.664153	−0.0879692
$58$	−7.69759	−1.01074
$59$	7.35635	0.957715	0.478857	−	0.877893i	$-0.341051\pi$
$59$	7.35635	0.957715	0.478857	+	0.877893i	$0.341051\pi$
$60$	2.72853	0.352251
$61$	2.11101	0.270287	0.135143	−	0.990826i	$-0.456851\pi$
$61$	2.11101	0.270287	0.135143	+	0.990826i	$0.456851\pi$
$62$	−1.55876	−0.197963
$63$	3.97726	0.501087
$64$	1.00000	0.125000
$65$	−5.35803	−0.664582
$66$	13.7281	1.68981
$67$	14.7072	1.79677	0.898386	−	0.439207i	$-0.144740\pi$
$67$	14.7072	1.79677	0.898386	+	0.439207i	$0.144740\pi$
$68$	5.62630	0.682289
$69$	11.5079	1.38539
$70$	−0.894798	−0.106949
$71$	−2.41472	−0.286574	−0.143287	−	0.989681i	$-0.545767\pi$
$71$	−2.41472	−0.286574	−0.143287	+	0.989681i	$0.545767\pi$
$72$	−4.44487	−0.523833
$73$	10.4349	1.22131	0.610654	−	0.791898i	$-0.290907\pi$
$73$	10.4349	1.22131	0.610654	+	0.791898i	$0.290907\pi$
$74$	−10.0042	−1.16297
$75$	2.72853	0.315063
$76$	−0.243411	−0.0279211
$77$	−4.50201	−0.513052
$78$	14.6195	1.65534
$79$	8.03826	0.904375	0.452187	−	0.891923i	$-0.350644\pi$
$79$	8.03826	0.904375	0.452187	+	0.891923i	$0.350644\pi$
$80$	1.00000	0.111803
$81$	−2.57776	−0.286418
$82$	−3.18356	−0.351565
$83$	17.4940	1.92022	0.960110	−	0.279623i	$-0.0902095\pi$
$83$	17.4940	1.92022	0.960110	+	0.279623i	$0.0902095\pi$
$84$	2.44148	0.266387
$85$	5.62630	0.610257
$86$	3.19538	0.344566
$87$	21.0031	2.25177
$88$	5.03131	0.536340
$89$	12.8682	1.36402	0.682011	−	0.731342i	$-0.261106\pi$
$89$	12.8682	1.36402	0.682011	+	0.731342i	$0.261106\pi$
$90$	−4.44487	−0.468530
$91$	−4.79436	−0.502585
$92$	4.21762	0.439717
$93$	4.25313	0.441029
$94$	−4.78751	−0.493793
$95$	−0.243411	−0.0249734
$96$	−2.72853	−0.278479
$97$	−1.78912	−0.181657	−0.0908287	−	0.995867i	$-0.528952\pi$
$97$	−1.78912	−0.181657	−0.0908287	+	0.995867i	$0.528952\pi$
$98$	6.19934	0.626228
$99$	−22.3635	−2.24762
$100$	1.00000	0.100000
$101$	−1.23617	−0.123003	−0.0615016	−	0.998107i	$-0.519589\pi$
$101$	−1.23617	−0.123003	−0.0615016	+	0.998107i	$0.519589\pi$
$102$	−15.3515	−1.52003
$103$	8.59261	0.846655	0.423327	−	0.905977i	$-0.360862\pi$
$103$	8.59261	0.846655	0.423327	+	0.905977i	$0.360862\pi$
$104$	5.35803	0.525398
$105$	2.44148	0.238264
$106$	5.76361	0.559812
$107$	−12.3939	−1.19816	−0.599080	−	0.800689i	$-0.704467\pi$
$107$	−12.3939	−1.19816	−0.599080	+	0.800689i	$0.704467\pi$
$108$	3.94236	0.379354
$109$	−5.77545	−0.553188	−0.276594	−	0.960987i	$-0.589206\pi$
$109$	−5.77545	−0.553188	−0.276594	+	0.960987i	$0.589206\pi$
$110$	5.03131	0.479717
$111$	27.2968	2.59090
$112$	0.894798	0.0845505
$113$	−15.1123	−1.42164	−0.710821	−	0.703373i	$-0.751676\pi$
$113$	−15.1123	−1.42164	−0.710821	+	0.703373i	$0.751676\pi$
$114$	0.664153	0.0622036
$115$	4.21762	0.393295
$116$	7.69759	0.714703
$117$	−23.8157	−2.20177
$118$	−7.35635	−0.677207
$119$	5.03440	0.461502
$120$	−2.72853	−0.249079
$121$	14.3141	1.30128
$122$	−2.11101	−0.191122
$123$	8.68642	0.783228
$124$	1.55876	0.139981
$125$	1.00000	0.0894427
$126$	−3.97726	−0.354322
$127$	−10.4837	−0.930280	−0.465140	−	0.885237i	$-0.653996\pi$
$127$	−10.4837	−0.930280	−0.465140	+	0.885237i	$0.653996\pi$
$128$	−1.00000	−0.0883883
$129$	−8.71868	−0.767637
$130$	5.35803	0.469931
$131$	2.62399	0.229259	0.114629	−	0.993408i	$-0.463432\pi$
$131$	2.62399	0.229259	0.114629	+	0.993408i	$0.463432\pi$
$132$	−13.7281	−1.19488
$133$	−0.217803	−0.0188860
$134$	−14.7072	−1.27051
$135$	3.94236	0.339304
$136$	−5.62630	−0.482451
$137$	−4.80349	−0.410390	−0.205195	−	0.978721i	$-0.565783\pi$
$137$	−4.80349	−0.410390	−0.205195	+	0.978721i	$0.565783\pi$
$138$	−11.5079	−0.979616
$139$	2.95063	0.250269	0.125135	−	0.992140i	$-0.460064\pi$
$139$	2.95063	0.250269	0.125135	+	0.992140i	$0.460064\pi$
$140$	0.894798	0.0756242
$141$	13.0628	1.10009
$142$	2.41472	0.202638
$143$	26.9579	2.25434
$144$	4.44487	0.370406
$145$	7.69759	0.639250
$146$	−10.4349	−0.863595
$147$	−16.9151	−1.39513
$148$	10.0042	0.822342
$149$	−19.6552	−1.61022	−0.805108	−	0.593129i	$-0.797892\pi$
$149$	−19.6552	−1.61022	−0.805108	+	0.593129i	$0.797892\pi$
$150$	−2.72853	−0.222783
$151$	0.0952463	0.00775103	0.00387552	−	0.999992i	$-0.498766\pi$
$151$	0.0952463	0.00775103	0.00387552	+	0.999992i	$0.498766\pi$
$152$	0.243411	0.0197432
$153$	25.0081	2.02179
$154$	4.50201	0.362782
$155$	1.55876	0.125203
$156$	−14.6195	−1.17050
$157$	15.2271	1.21526	0.607628	−	0.794222i	$-0.292121\pi$
$157$	15.2271	1.21526	0.607628	+	0.794222i	$0.292121\pi$
$158$	−8.03826	−0.639490
$159$	−15.7262	−1.24717
$160$	−1.00000	−0.0790569
$161$	3.77391	0.297426
$162$	2.57776	0.202528
$163$	5.79346	0.453779	0.226889	−	0.973921i	$-0.427144\pi$
$163$	5.79346	0.453779	0.226889	+	0.973921i	$0.427144\pi$
$164$	3.18356	0.248594
$165$	−13.7281	−1.06873
$166$	−17.4940	−1.35780
$167$	−6.61990	−0.512263	−0.256132	−	0.966642i	$-0.582448\pi$
$167$	−6.61990	−0.512263	−0.256132	+	0.966642i	$0.582448\pi$
$168$	−2.44148	−0.188364
$169$	15.7085	1.20835
$170$	−5.62630	−0.431517
$171$	−1.08193	−0.0827371
$172$	−3.19538	−0.243645
$173$	16.5171	1.25578	0.627888	−	0.778304i	$-0.283920\pi$
$173$	16.5171	1.25578	0.627888	+	0.778304i	$0.283920\pi$
$174$	−21.0031	−1.59224
$175$	0.894798	0.0676404
$176$	−5.03131	−0.379250
$177$	20.0720	1.50870
$178$	−12.8682	−0.964509
$179$	−24.8250	−1.85551	−0.927753	−	0.373195i	$-0.878262\pi$
$179$	−24.8250	−1.85551	−0.927753	+	0.373195i	$0.878262\pi$
$180$	4.44487	0.331301
$181$	−3.80676	−0.282954	−0.141477	−	0.989942i	$-0.545185\pi$
$181$	−3.80676	−0.282954	−0.141477	+	0.989942i	$0.545185\pi$
$182$	4.79436	0.355381
$183$	5.75994	0.425787
$184$	−4.21762	−0.310927
$185$	10.0042	0.735525
$186$	−4.25313	−0.311854
$187$	−28.3077	−2.07006
$188$	4.78751	0.349165
$189$	3.52761	0.256596
$190$	0.243411	0.0176589
$191$	−25.9989	−1.88121	−0.940606	−	0.339499i	$-0.889742\pi$
$191$	−25.9989	−1.88121	−0.940606	+	0.339499i	$0.889742\pi$
$192$	2.72853	0.196915
$193$	−22.5354	−1.62213	−0.811067	−	0.584953i	$-0.801113\pi$
$193$	−22.5354	−1.62213	−0.811067	+	0.584953i	$0.801113\pi$
$194$	1.78912	0.128451
$195$	−14.6195	−1.04693
$196$	−6.19934	−0.442810
$197$	−10.0738	−0.717731	−0.358865	−	0.933389i	$-0.616836\pi$
$197$	−10.0738	−0.717731	−0.358865	+	0.933389i	$0.616836\pi$
$198$	22.3635	1.58931
$199$	20.8793	1.48009	0.740047	−	0.672555i	$-0.234803\pi$
$199$	20.8793	1.48009	0.740047	+	0.672555i	$0.234803\pi$
$200$	−1.00000	−0.0707107
$201$	40.1290	2.83048
$202$	1.23617	0.0869764
$203$	6.88778	0.483428
$204$	15.3515	1.07482
$205$	3.18356	0.222349
$206$	−8.59261	−0.598675
$207$	18.7467	1.30299
$208$	−5.35803	−0.371513
$209$	1.22468	0.0847126
$210$	−2.44148	−0.168478
$211$	4.03377	0.277696	0.138848	−	0.990314i	$-0.455660\pi$
$211$	4.03377	0.277696	0.138848	+	0.990314i	$0.455660\pi$
$212$	−5.76361	−0.395847
$213$	−6.58862	−0.451445
$214$	12.3939	0.847227
$215$	−3.19538	−0.217923
$216$	−3.94236	−0.268244
$217$	1.39478	0.0946836
$218$	5.77545	0.391163
$219$	28.4718	1.92395
$220$	−5.03131	−0.339211
$221$	−30.1459	−2.02783
$222$	−27.2968	−1.83204
$223$	16.9664	1.13616	0.568078	−	0.822974i	$-0.307687\pi$
$223$	16.9664	1.13616	0.568078	+	0.822974i	$0.307687\pi$
$224$	−0.894798	−0.0597862
$225$	4.44487	0.296324
$226$	15.1123	1.00525
$227$	−20.1180	−1.33528	−0.667638	−	0.744486i	$-0.732695\pi$
$227$	−20.1180	−1.33528	−0.667638	+	0.744486i	$0.732695\pi$
$228$	−0.664153	−0.0439846
$229$	−20.4312	−1.35013	−0.675066	−	0.737758i	$-0.735885\pi$
$229$	−20.4312	−1.35013	−0.675066	+	0.737758i	$0.735885\pi$
$230$	−4.21762	−0.278101
$231$	−12.2839	−0.808219
$232$	−7.69759	−0.505371
$233$	−22.8310	−1.49571	−0.747853	−	0.663864i	$-0.768915\pi$
$233$	−22.8310	−1.49571	−0.747853	+	0.663864i	$0.768915\pi$
$234$	23.8157	1.55688
$235$	4.78751	0.312302
$236$	7.35635	0.478857
$237$	21.9326	1.42468
$238$	−5.03440	−0.326332
$239$	−1.62500	−0.105113	−0.0525563	−	0.998618i	$-0.516737\pi$
$239$	−1.62500	−0.105113	−0.0525563	+	0.998618i	$0.516737\pi$
$240$	2.72853	0.176126
$241$	0.464813	0.0299412	0.0149706	−	0.999888i	$-0.495235\pi$
$241$	0.464813	0.0299412	0.0149706	+	0.999888i	$0.495235\pi$
$242$	−14.3141	−0.920147
$243$	−18.8606	−1.20991
$244$	2.11101	0.135143
$245$	−6.19934	−0.396061
$246$	−8.68642	−0.553826
$247$	1.30420	0.0829844
$248$	−1.55876	−0.0989815
$249$	47.7330	3.02495
$250$	−1.00000	−0.0632456
$251$	19.7893	1.24909	0.624546	−	0.780988i	$-0.285284\pi$
$251$	19.7893	1.24909	0.624546	+	0.780988i	$0.285284\pi$
$252$	3.97726	0.250544
$253$	−21.2202	−1.33410
$254$	10.4837	0.657807
$255$	15.3515	0.961349
$256$	1.00000	0.0625000
$257$	−26.0631	−1.62577	−0.812887	−	0.582422i	$-0.802105\pi$
$257$	−26.0631	−1.62577	−0.812887	+	0.582422i	$0.802105\pi$
$258$	8.71868	0.542801
$259$	8.95175	0.556235
$260$	−5.35803	−0.332291
$261$	34.2147	2.11784
$262$	−2.62399	−0.162110
$263$	4.82161	0.297313	0.148657	−	0.988889i	$-0.452505\pi$
$263$	4.82161	0.297313	0.148657	+	0.988889i	$0.452505\pi$
$264$	13.7281	0.844905
$265$	−5.76361	−0.354056
$266$	0.217803	0.0133544
$267$	35.1111	2.14877
$268$	14.7072	0.898386
$269$	14.3547	0.875223	0.437611	−	0.899164i	$-0.355825\pi$
$269$	14.3547	0.875223	0.437611	+	0.899164i	$0.355825\pi$
$270$	−3.94236	−0.239924
$271$	−24.0039	−1.45813	−0.729066	−	0.684444i	$-0.760045\pi$
$271$	−24.0039	−1.45813	−0.729066	+	0.684444i	$0.760045\pi$
$272$	5.62630	0.341144
$273$	−13.0815	−0.791731
$274$	4.80349	0.290190
$275$	−5.03131	−0.303400
$276$	11.5079	0.692693
$277$	−18.3925	−1.10510	−0.552549	−	0.833481i	$-0.686345\pi$
$277$	−18.3925	−1.10510	−0.552549	+	0.833481i	$0.686345\pi$
$278$	−2.95063	−0.176967
$279$	6.92849	0.414798
$280$	−0.894798	−0.0534744
$281$	−12.0348	−0.717937	−0.358969	−	0.933350i	$-0.616872\pi$
$281$	−12.0348	−0.717937	−0.358969	+	0.933350i	$0.616872\pi$
$282$	−13.0628	−0.777881
$283$	29.3428	1.74425	0.872124	−	0.489284i	$-0.162742\pi$
$283$	29.3428	1.74425	0.872124	+	0.489284i	$0.162742\pi$
$284$	−2.41472	−0.143287
$285$	−0.664153	−0.0393410
$286$	−26.9579	−1.59406
$287$	2.84864	0.168150
$288$	−4.44487	−0.261916
$289$	14.6552	0.862071
$290$	−7.69759	−0.452018
$291$	−4.88166	−0.286168
$292$	10.4349	0.610654
$293$	3.78143	0.220913	0.110457	−	0.993881i	$-0.464769\pi$
$293$	3.78143	0.220913	0.110457	+	0.993881i	$0.464769\pi$
$294$	16.9151	0.986507
$295$	7.35635	0.428303
$296$	−10.0042	−0.581483
$297$	−19.8352	−1.15096
$298$	19.6552	1.13859
$299$	−22.5981	−1.30688
$300$	2.72853	0.157532
$301$	−2.85922	−0.164803
$302$	−0.0952463	−0.00548081
$303$	−3.37292	−0.193769
$304$	−0.243411	−0.0139606
$305$	2.11101	0.120876
$306$	−25.0081	−1.42962
$307$	15.5960	0.890113	0.445056	−	0.895503i	$-0.353184\pi$
$307$	15.5960	0.890113	0.445056	+	0.895503i	$0.353184\pi$
$308$	−4.50201	−0.256526
$309$	23.4452	1.33375
$310$	−1.55876	−0.0885317
$311$	−19.6206	−1.11258	−0.556292	−	0.830987i	$-0.687776\pi$
$311$	−19.6206	−1.11258	−0.556292	+	0.830987i	$0.687776\pi$
$312$	14.6195	0.827669
$313$	−22.3404	−1.26276	−0.631378	−	0.775475i	$-0.717510\pi$
$313$	−22.3404	−1.26276	−0.631378	+	0.775475i	$0.717510\pi$
$314$	−15.2271	−0.859316
$315$	3.97726	0.224093
$316$	8.03826	0.452187
$317$	−21.4639	−1.20553	−0.602765	−	0.797919i	$-0.705934\pi$
$317$	−21.4639	−1.20553	−0.602765	+	0.797919i	$0.705934\pi$
$318$	15.7262	0.881880
$319$	−38.7290	−2.16841
$320$	1.00000	0.0559017
$321$	−33.8170	−1.88748
$322$	−3.77391	−0.210312
$323$	−1.36950	−0.0762011
$324$	−2.57776	−0.143209
$325$	−5.35803	−0.297210
$326$	−5.79346	−0.320870
$327$	−15.7585	−0.871447
$328$	−3.18356	−0.175783
$329$	4.28385	0.236176
$330$	13.7281	0.755706
$331$	34.7309	1.90898	0.954492	−	0.298238i	$-0.0963988\pi$
$331$	34.7309	1.90898	0.954492	+	0.298238i	$0.0963988\pi$
$332$	17.4940	0.960110
$333$	44.4674	2.43680
$334$	6.61990	0.362225
$335$	14.7072	0.803541
$336$	2.44148	0.133194
$337$	3.67354	0.200111	0.100055	−	0.994982i	$-0.468098\pi$
$337$	3.67354	0.200111	0.100055	+	0.994982i	$0.468098\pi$
$338$	−15.7085	−0.854431
$339$	−41.2342	−2.23954
$340$	5.62630	0.305129
$341$	−7.84262	−0.424702
$342$	1.08193	0.0585040
$343$	−11.8107	−0.637720
$344$	3.19538	0.172283
$345$	11.5079	0.619564
$346$	−16.5171	−0.887967
$347$	2.85432	0.153228	0.0766141	−	0.997061i	$-0.475589\pi$
$347$	2.85432	0.153228	0.0766141	+	0.997061i	$0.475589\pi$
$348$	21.0031	1.12588
$349$	29.4690	1.57744	0.788720	−	0.614753i	$-0.210744\pi$
$349$	29.4690	1.57744	0.788720	+	0.614753i	$0.210744\pi$
$350$	−0.894798	−0.0478290
$351$	−21.1233	−1.12748
$352$	5.03131	0.268170
$353$	10.0491	0.534861	0.267430	−	0.963577i	$-0.413825\pi$
$353$	10.0491	0.534861	0.267430	+	0.963577i	$0.413825\pi$
$354$	−20.0720	−1.06681
$355$	−2.41472	−0.128160
$356$	12.8682	0.682011
$357$	13.7365	0.727012
$358$	24.8250	1.31204
$359$	−20.8179	−1.09872	−0.549362	−	0.835584i	$-0.685129\pi$
$359$	−20.8179	−1.09872	−0.549362	+	0.835584i	$0.685129\pi$
$360$	−4.44487	−0.234265
$361$	−18.9408	−0.996882
$362$	3.80676	0.200079
$363$	39.0565	2.04993
$364$	−4.79436	−0.251293
$365$	10.4349	0.546185
$366$	−5.75994	−0.301077
$367$	−31.4818	−1.64334	−0.821668	−	0.569966i	$-0.806956\pi$
$367$	−31.4818	−1.64334	−0.821668	+	0.569966i	$0.806956\pi$
$368$	4.21762	0.219858
$369$	14.1505	0.736645
$370$	−10.0042	−0.520095
$371$	−5.15727	−0.267752
$372$	4.25313	0.220514
$373$	−18.8122	−0.974058	−0.487029	−	0.873386i	$-0.661919\pi$
$373$	−18.8122	−0.974058	−0.487029	+	0.873386i	$0.661919\pi$
$374$	28.3077	1.46375
$375$	2.72853	0.140901
$376$	−4.78751	−0.246897
$377$	−41.2439	−2.12417
$378$	−3.52761	−0.181441
$379$	3.02315	0.155289	0.0776444	−	0.996981i	$-0.475260\pi$
$379$	3.02315	0.155289	0.0776444	+	0.996981i	$0.475260\pi$
$380$	−0.243411	−0.0124867
$381$	−28.6051	−1.46548
$382$	25.9989	1.33022
$383$	−7.86592	−0.401930	−0.200965	−	0.979598i	$-0.564408\pi$
$383$	−7.86592	−0.401930	−0.200965	+	0.979598i	$0.564408\pi$
$384$	−2.72853	−0.139240
$385$	−4.50201	−0.229444
$386$	22.5354	1.14702
$387$	−14.2030	−0.721980
$388$	−1.78912	−0.0908287
$389$	−26.1360	−1.32515	−0.662575	−	0.748996i	$-0.730536\pi$
$389$	−26.1360	−1.32515	−0.662575	+	0.748996i	$0.730536\pi$
$390$	14.6195	0.740289
$391$	23.7296	1.20006
$392$	6.19934	0.313114
$393$	7.15962	0.361155
$394$	10.0738	0.507512
$395$	8.03826	0.404449
$396$	−22.3635	−1.12381
$397$	23.8038	1.19468	0.597340	−	0.801988i	$-0.296224\pi$
$397$	23.8038	1.19468	0.597340	+	0.801988i	$0.296224\pi$
$398$	−20.8793	−1.04658
$399$	−0.594283	−0.0297514
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−40.1290	−2.00146
$403$	−8.35190	−0.416038
$404$	−1.23617	−0.0615016
$405$	−2.57776	−0.128090
$406$	−6.88778	−0.341835
$407$	−50.3344	−2.49498
$408$	−15.3515	−0.760013
$409$	−16.5119	−0.816462	−0.408231	−	0.912879i	$-0.633854\pi$
$409$	−16.5119	−0.816462	−0.408231	+	0.912879i	$0.633854\pi$
$410$	−3.18356	−0.157225
$411$	−13.1065	−0.646494
$412$	8.59261	0.423327
$413$	6.58244	0.323901
$414$	−18.7467	−0.921352
$415$	17.4940	0.858748
$416$	5.35803	0.262699
$417$	8.05088	0.394253
$418$	−1.22468	−0.0599009
$419$	24.3281	1.18850	0.594252	−	0.804279i	$-0.297448\pi$
$419$	24.3281	1.18850	0.594252	+	0.804279i	$0.297448\pi$
$420$	2.44148	0.119132
$421$	23.2449	1.13289	0.566443	−	0.824101i	$-0.308319\pi$
$421$	23.2449	1.13289	0.566443	+	0.824101i	$0.308319\pi$
$422$	−4.03377	−0.196361
$423$	21.2798	1.03466
$424$	5.76361	0.279906
$425$	5.62630	0.272915
$426$	6.58862	0.319220
$427$	1.88892	0.0914115
$428$	−12.3939	−0.599080
$429$	73.5555	3.55129
$430$	3.19538	0.154095
$431$	−10.0840	−0.485728	−0.242864	−	0.970060i	$-0.578087\pi$
$431$	−10.0840	−0.485728	−0.242864	+	0.970060i	$0.578087\pi$
$432$	3.94236	0.189677
$433$	8.81685	0.423711	0.211855	−	0.977301i	$-0.432049\pi$
$433$	8.81685	0.423711	0.211855	+	0.977301i	$0.432049\pi$
$434$	−1.39478	−0.0669514
$435$	21.0031	1.00702
$436$	−5.77545	−0.276594
$437$	−1.02661	−0.0491096
$438$	−28.4718	−1.36044
$439$	−25.9384	−1.23797	−0.618985	−	0.785403i	$-0.712456\pi$
$439$	−25.9384	−1.23797	−0.618985	+	0.785403i	$0.712456\pi$
$440$	5.03131	0.239858
$441$	−27.5552	−1.31215
$442$	30.1459	1.43389
$443$	18.3380	0.871266	0.435633	−	0.900124i	$-0.356524\pi$
$443$	18.3380	0.871266	0.435633	+	0.900124i	$0.356524\pi$
$444$	27.2968	1.29545
$445$	12.8682	0.610009
$446$	−16.9664	−0.803384
$447$	−53.6297	−2.53660
$448$	0.894798	0.0422752
$449$	20.7522	0.979358	0.489679	−	0.871903i	$-0.337114\pi$
$449$	20.7522	0.979358	0.489679	+	0.871903i	$0.337114\pi$
$450$	−4.44487	−0.209533
$451$	−16.0175	−0.754233
$452$	−15.1123	−0.710821
$453$	0.259882	0.0122103
$454$	20.1180	0.944183
$455$	−4.79436	−0.224763
$456$	0.664153	0.0311018
$457$	−19.5612	−0.915034	−0.457517	−	0.889201i	$-0.651261\pi$
$457$	−19.5612	−0.915034	−0.457517	+	0.889201i	$0.651261\pi$
$458$	20.4312	0.954687
$459$	22.1809	1.03531
$460$	4.21762	0.196647
$461$	3.79984	0.176976	0.0884880	−	0.996077i	$-0.471796\pi$
$461$	3.79984	0.176976	0.0884880	+	0.996077i	$0.471796\pi$
$462$	12.2839	0.571497
$463$	2.45295	0.113998	0.0569990	−	0.998374i	$-0.481847\pi$
$463$	2.45295	0.113998	0.0569990	+	0.998374i	$0.481847\pi$
$464$	7.69759	0.357352
$465$	4.25313	0.197234
$466$	22.8310	1.05762
$467$	15.9542	0.738271	0.369135	−	0.929376i	$-0.379654\pi$
$467$	15.9542	0.738271	0.369135	+	0.929376i	$0.379654\pi$
$468$	−23.8157	−1.10088
$469$	13.1600	0.607672
$470$	−4.78751	−0.220831
$471$	41.5476	1.91441
$472$	−7.35635	−0.338603
$473$	16.0769	0.739219
$474$	−21.9326	−1.00740
$475$	−0.243411	−0.0111685
$476$	5.03440	0.230751
$477$	−25.6185	−1.17299
$478$	1.62500	0.0743258
$479$	−19.3798	−0.885485	−0.442743	−	0.896649i	$-0.645994\pi$
$479$	−19.3798	−0.885485	−0.442743	+	0.896649i	$0.645994\pi$
$480$	−2.72853	−0.124540
$481$	−53.6029	−2.44408
$482$	−0.464813	−0.0211716
$483$	10.2972	0.468540
$484$	14.3141	0.650642
$485$	−1.78912	−0.0812397
$486$	18.8606	0.855533
$487$	37.3488	1.69244	0.846219	−	0.532836i	$-0.178874\pi$
$487$	37.3488	1.69244	0.846219	+	0.532836i	$0.178874\pi$
$488$	−2.11101	−0.0955608
$489$	15.8076	0.714845
$490$	6.19934	0.280057
$491$	4.55930	0.205759	0.102879	−	0.994694i	$-0.467194\pi$
$491$	4.55930	0.205759	0.102879	+	0.994694i	$0.467194\pi$
$492$	8.68642	0.391614
$493$	43.3089	1.95054
$494$	−1.30420	−0.0586789
$495$	−22.3635	−1.00517
$496$	1.55876	0.0699905
$497$	−2.16068	−0.0969199
$498$	−47.7330	−2.13897
$499$	22.5876	1.01116	0.505579	−	0.862780i	$-0.331279\pi$
$499$	22.5876	1.01116	0.505579	+	0.862780i	$0.331279\pi$
$500$	1.00000	0.0447214
$501$	−18.0626	−0.806976
$502$	−19.7893	−0.883241
$503$	−32.2685	−1.43878	−0.719390	−	0.694606i	$-0.755579\pi$
$503$	−32.2685	−1.43878	−0.719390	+	0.694606i	$0.755579\pi$
$504$	−3.97726	−0.177161
$505$	−1.23617	−0.0550087
$506$	21.2202	0.943351
$507$	42.8611	1.90353
$508$	−10.4837	−0.465140
$509$	35.8416	1.58865	0.794326	−	0.607492i	$-0.207824\pi$
$509$	35.8416	1.58865	0.794326	+	0.607492i	$0.207824\pi$
$510$	−15.3515	−0.679776
$511$	9.33709	0.413049
$512$	−1.00000	−0.0441942
$513$	−0.959612	−0.0423679
$514$	26.0631	1.14960
$515$	8.59261	0.378635
$516$	−8.71868	−0.383818
$517$	−24.0874	−1.05936
$518$	−8.95175	−0.393317
$519$	45.0675	1.97824
$520$	5.35803	0.234965
$521$	37.3168	1.63488	0.817440	−	0.576014i	$-0.195393\pi$
$521$	37.3168	1.63488	0.817440	+	0.576014i	$0.195393\pi$
$522$	−34.2147	−1.49754
$523$	−19.1717	−0.838321	−0.419161	−	0.907912i	$-0.637676\pi$
$523$	−19.1717	−0.838321	−0.419161	+	0.907912i	$0.637676\pi$
$524$	2.62399	0.114629
$525$	2.44148	0.106555
$526$	−4.82161	−0.210232
$527$	8.77006	0.382030
$528$	−13.7281	−0.597438
$529$	−5.21171	−0.226596
$530$	5.76361	0.250355
$531$	32.6980	1.41897
$532$	−0.217803	−0.00944298
$533$	−17.0576	−0.738847
$534$	−35.1111	−1.51941
$535$	−12.3939	−0.535834
$536$	−14.7072	−0.635255
$537$	−67.7357	−2.92301
$538$	−14.3547	−0.618876
$539$	31.1908	1.34348
$540$	3.94236	0.169652
$541$	−25.4853	−1.09570	−0.547849	−	0.836577i	$-0.684553\pi$
$541$	−25.4853	−1.09570	−0.547849	+	0.836577i	$0.684553\pi$
$542$	24.0039	1.03105
$543$	−10.3868	−0.445742
$544$	−5.62630	−0.241225
$545$	−5.77545	−0.247393
$546$	13.0815	0.559838
$547$	8.37489	0.358084	0.179042	−	0.983841i	$-0.442700\pi$
$547$	8.37489	0.358084	0.179042	+	0.983841i	$0.442700\pi$
$548$	−4.80349	−0.205195
$549$	9.38314	0.400463
$550$	5.03131	0.214536
$551$	−1.87368	−0.0798213
$552$	−11.5079	−0.489808
$553$	7.19262	0.305861
$554$	18.3925	0.781422
$555$	27.2968	1.15868
$556$	2.95063	0.125135
$557$	−10.0136	−0.424291	−0.212145	−	0.977238i	$-0.568045\pi$
$557$	−10.0136	−0.424291	−0.212145	+	0.977238i	$0.568045\pi$
$558$	−6.92849	−0.293306
$559$	17.1209	0.724139
$560$	0.894798	0.0378121
$561$	−77.2383	−3.26100
$562$	12.0348	0.507658
$563$	−29.9016	−1.26020	−0.630101	−	0.776513i	$-0.716987\pi$
$563$	−29.9016	−1.26020	−0.630101	+	0.776513i	$0.716987\pi$
$564$	13.0628	0.550045
$565$	−15.1123	−0.635777
$566$	−29.3428	−1.23337
$567$	−2.30658	−0.0968671
$568$	2.41472	0.101319
$569$	31.2502	1.31008	0.655039	−	0.755595i	$-0.272652\pi$
$569$	31.2502	1.31008	0.655039	+	0.755595i	$0.272652\pi$
$570$	0.664153	0.0278183
$571$	−36.6838	−1.53517	−0.767585	−	0.640948i	$-0.778542\pi$
$571$	−36.6838	−1.53517	−0.767585	+	0.640948i	$0.778542\pi$
$572$	26.9579	1.12717
$573$	−70.9387	−2.96351
$574$	−2.84864	−0.118900
$575$	4.21762	0.175887
$576$	4.44487	0.185203
$577$	28.8918	1.20278	0.601391	−	0.798955i	$-0.294613\pi$
$577$	28.8918	1.20278	0.601391	+	0.798955i	$0.294613\pi$
$578$	−14.6552	−0.609576
$579$	−61.4885	−2.55537
$580$	7.69759	0.319625
$581$	15.6536	0.649422
$582$	4.88166	0.202351
$583$	28.9985	1.20100
$584$	−10.4349	−0.431798
$585$	−23.8157	−0.984660
$586$	−3.78143	−0.156209
$587$	−16.4456	−0.678784	−0.339392	−	0.940645i	$-0.610221\pi$
$587$	−16.4456	−0.678784	−0.339392	+	0.940645i	$0.610221\pi$
$588$	−16.9151	−0.697566
$589$	−0.379419	−0.0156337
$590$	−7.35635	−0.302856
$591$	−27.4867	−1.13065
$592$	10.0042	0.411171
$593$	21.2403	0.872234	0.436117	−	0.899890i	$-0.356353\pi$
$593$	21.2403	0.872234	0.436117	+	0.899890i	$0.356353\pi$
$594$	19.8352	0.813850
$595$	5.03440	0.206390
$596$	−19.6552	−0.805108
$597$	56.9698	2.33162
$598$	22.5981	0.924106
$599$	−0.763881	−0.0312113	−0.0156057	−	0.999878i	$-0.504968\pi$
$599$	−0.763881	−0.0312113	−0.0156057	+	0.999878i	$0.504968\pi$
$600$	−2.72853	−0.111392
$601$	16.2508	0.662884	0.331442	−	0.943476i	$-0.392465\pi$
$601$	16.2508	0.662884	0.331442	+	0.943476i	$0.392465\pi$
$602$	2.85922	0.116533
$603$	65.3716	2.66214
$604$	0.0952463	0.00387552
$605$	14.3141	0.581952
$606$	3.37292	0.137015
$607$	−15.1357	−0.614340	−0.307170	−	0.951655i	$-0.599382\pi$
$607$	−15.1357	−0.614340	−0.307170	+	0.951655i	$0.599382\pi$
$608$	0.243411	0.00987161
$609$	18.7935	0.761552
$610$	−2.11101	−0.0854722
$611$	−25.6516	−1.03775
$612$	25.0081	1.01089
$613$	−3.72696	−0.150530	−0.0752652	−	0.997164i	$-0.523980\pi$
$613$	−3.72696	−0.150530	−0.0752652	+	0.997164i	$0.523980\pi$
$614$	−15.5960	−0.629405
$615$	8.68642	0.350270
$616$	4.50201	0.181391
$617$	−0.00373384	−0.000150319 0	−7.51593e−5	−	1.00000i	$-0.500024\pi$
$617$	−0.00373384	−0.000150319 0	−7.51593e−5		1.00000i	$0.500024\pi$
$618$	−23.4452	−0.943103
$619$	−1.15230	−0.0463147	−0.0231573	−	0.999732i	$-0.507372\pi$
$619$	−1.15230	−0.0463147	−0.0231573	+	0.999732i	$0.507372\pi$
$620$	1.55876	0.0626014
$621$	16.6274	0.667233
$622$	19.6206	0.786715
$623$	11.5144	0.461315
$624$	−14.6195	−0.585250
$625$	1.00000	0.0400000
$626$	22.3404	0.892903
$627$	3.34156	0.133449
$628$	15.2271	0.607628
$629$	56.2867	2.24430
$630$	−3.97726	−0.158458
$631$	44.5712	1.77435	0.887176	−	0.461431i	$-0.152664\pi$
$631$	44.5712	1.77435	0.887176	+	0.461431i	$0.152664\pi$
$632$	−8.03826	−0.319745
$633$	11.0062	0.437459
$634$	21.4639	0.852438
$635$	−10.4837	−0.416034
$636$	−15.7262	−0.623584
$637$	33.2163	1.31608
$638$	38.7290	1.53329
$639$	−10.7331	−0.424594
$640$	−1.00000	−0.0395285
$641$	−7.59158	−0.299849	−0.149925	−	0.988697i	$-0.547903\pi$
$641$	−7.59158	−0.299849	−0.149925	+	0.988697i	$0.547903\pi$
$642$	33.8170	1.33465
$643$	35.9825	1.41901	0.709506	−	0.704699i	$-0.248918\pi$
$643$	35.9825	1.41901	0.709506	+	0.704699i	$0.248918\pi$
$644$	3.77391	0.148713
$645$	−8.71868	−0.343298
$646$	1.36950	0.0538823
$647$	−22.9325	−0.901570	−0.450785	−	0.892633i	$-0.648856\pi$
$647$	−22.9325	−0.901570	−0.450785	+	0.892633i	$0.648856\pi$
$648$	2.57776	0.101264
$649$	−37.0121	−1.45285
$650$	5.35803	0.210159
$651$	3.80569	0.149157
$652$	5.79346	0.226889
$653$	3.88956	0.152210	0.0761051	−	0.997100i	$-0.475752\pi$
$653$	3.88956	0.152210	0.0761051	+	0.997100i	$0.475752\pi$
$654$	15.7585	0.616206
$655$	2.62399	0.102528
$656$	3.18356	0.124297
$657$	46.3815	1.80952
$658$	−4.28385	−0.167002
$659$	17.5907	0.685238	0.342619	−	0.939474i	$-0.388686\pi$
$659$	17.5907	0.685238	0.342619	+	0.939474i	$0.388686\pi$
$660$	−13.7281	−0.534365
$661$	29.5701	1.15015	0.575073	−	0.818102i	$-0.304974\pi$
$661$	29.5701	1.15015	0.575073	+	0.818102i	$0.304974\pi$
$662$	−34.7309	−1.34986
$663$	−82.2539	−3.19448
$664$	−17.4940	−0.678900
$665$	−0.217803	−0.00844605
$666$	−44.4674	−1.72308
$667$	32.4655	1.25707
$668$	−6.61990	−0.256132
$669$	46.2934	1.78981
$670$	−14.7072	−0.568189
$671$	−10.6211	−0.410024
$672$	−2.44148	−0.0941822
$673$	−9.96166	−0.383994	−0.191997	−	0.981396i	$-0.561496\pi$
$673$	−9.96166	−0.383994	−0.191997	+	0.981396i	$0.561496\pi$
$674$	−3.67354	−0.141500
$675$	3.94236	0.151741
$676$	15.7085	0.604174
$677$	16.1733	0.621589	0.310794	−	0.950477i	$-0.399405\pi$
$677$	16.1733	0.621589	0.310794	+	0.950477i	$0.399405\pi$
$678$	41.2342	1.58359
$679$	−1.60090	−0.0614369
$680$	−5.62630	−0.215759
$681$	−54.8924	−2.10348
$682$	7.84262	0.300309
$683$	28.4972	1.09042	0.545208	−	0.838301i	$-0.316451\pi$
$683$	28.4972	1.09042	0.545208	+	0.838301i	$0.316451\pi$
$684$	−1.08193	−0.0413686
$685$	−4.80349	−0.183532
$686$	11.8107	0.450936
$687$	−55.7471	−2.12688
$688$	−3.19538	−0.121823
$689$	30.8816	1.17650
$690$	−11.5079	−0.438098
$691$	9.68828	0.368560	0.184280	−	0.982874i	$-0.441005\pi$
$691$	9.68828	0.368560	0.184280	+	0.982874i	$0.441005\pi$
$692$	16.5171	0.627888
$693$	−20.0108	−0.760149
$694$	−2.85432	−0.108349
$695$	2.95063	0.111924
$696$	−21.0031	−0.796120
$697$	17.9116	0.678451
$698$	−29.4690	−1.11542
$699$	−62.2949	−2.35621
$700$	0.894798	0.0338202
$701$	25.8560	0.976568	0.488284	−	0.872685i	$-0.337623\pi$
$701$	25.8560	0.976568	0.488284	+	0.872685i	$0.337623\pi$
$702$	21.1233	0.797247
$703$	−2.43513	−0.0918428
$704$	−5.03131	−0.189625
$705$	13.0628	0.491975
$706$	−10.0491	−0.378204
$707$	−1.10612	−0.0415999
$708$	20.0720	0.754352
$709$	−1.29263	−0.0485458	−0.0242729	−	0.999705i	$-0.507727\pi$
$709$	−1.29263	−0.0485458	−0.0242729	+	0.999705i	$0.507727\pi$
$710$	2.41472	0.0906227
$711$	35.7290	1.33994
$712$	−12.8682	−0.482254
$713$	6.57426	0.246208
$714$	−13.7365	−0.514075
$715$	26.9579	1.00817
$716$	−24.8250	−0.927753
$717$	−4.43386	−0.165586
$718$	20.8179	0.776916
$719$	23.0518	0.859688	0.429844	−	0.902903i	$-0.358568\pi$
$719$	23.0518	0.859688	0.429844	+	0.902903i	$0.358568\pi$
$720$	4.44487	0.165650
$721$	7.68865	0.286340
$722$	18.9408	0.704902
$723$	1.26825	0.0471669
$724$	−3.80676	−0.141477
$725$	7.69759	0.285881
$726$	−39.0565	−1.44952
$727$	−27.2377	−1.01019	−0.505094	−	0.863064i	$-0.668542\pi$
$727$	−27.2377	−1.01019	−0.505094	+	0.863064i	$0.668542\pi$
$728$	4.79436	0.177691
$729$	−43.7283	−1.61957
$730$	−10.4349	−0.386211
$731$	−17.9781	−0.664946
$732$	5.75994	0.212894
$733$	6.86877	0.253704	0.126852	−	0.991922i	$-0.459513\pi$
$733$	6.86877	0.253704	0.126852	+	0.991922i	$0.459513\pi$
$734$	31.4818	1.16201
$735$	−16.9151	−0.623922
$736$	−4.21762	−0.155463
$737$	−73.9966	−2.72570
$738$	−14.1505	−0.520886
$739$	25.7942	0.948854	0.474427	−	0.880295i	$-0.342655\pi$
$739$	25.7942	0.948854	0.474427	+	0.880295i	$0.342655\pi$
$740$	10.0042	0.367762
$741$	3.55855	0.130727
$742$	5.15727	0.189329
$743$	−6.59485	−0.241942	−0.120971	−	0.992656i	$-0.538601\pi$
$743$	−6.59485	−0.241942	−0.120971	+	0.992656i	$0.538601\pi$
$744$	−4.25313	−0.155927
$745$	−19.6552	−0.720110
$746$	18.8122	0.688763
$747$	77.7586	2.84504
$748$	−28.3077	−1.03503
$749$	−11.0900	−0.405220
$750$	−2.72853	−0.0996318
$751$	−21.0220	−0.767103	−0.383552	−	0.923519i	$-0.625299\pi$
$751$	−21.0220	−0.767103	−0.383552	+	0.923519i	$0.625299\pi$
$752$	4.78751	0.174582
$753$	53.9958	1.96772
$754$	41.2439	1.50202
$755$	0.0952463	0.00346637
$756$	3.52761	0.128298
$757$	−9.18875	−0.333971	−0.166985	−	0.985959i	$-0.553403\pi$
$757$	−9.18875	−0.333971	−0.166985	+	0.985959i	$0.553403\pi$
$758$	−3.02315	−0.109806
$759$	−57.8998	−2.10163
$760$	0.243411	0.00882944
$761$	29.3852	1.06521	0.532606	−	0.846363i	$-0.321213\pi$
$761$	29.3852	1.06521	0.532606	+	0.846363i	$0.321213\pi$
$762$	28.6051	1.03625
$763$	−5.16786	−0.187089
$764$	−25.9989	−0.940606
$765$	25.0081	0.904171
$766$	7.86592	0.284207
$767$	−39.4156	−1.42321
$768$	2.72853	0.0984573
$769$	32.8609	1.18499	0.592497	−	0.805572i	$-0.298142\pi$
$769$	32.8609	1.18499	0.592497	+	0.805572i	$0.298142\pi$
$770$	4.50201	0.162241
$771$	−71.1140	−2.56111
$772$	−22.5354	−0.811067
$773$	−29.4283	−1.05846	−0.529231	−	0.848478i	$-0.677519\pi$
$773$	−29.4283	−1.05846	−0.529231	+	0.848478i	$0.677519\pi$
$774$	14.2030	0.510517
$775$	1.55876	0.0559924
$776$	1.78912	0.0642256
$777$	24.4251	0.876246
$778$	26.1360	0.937022
$779$	−0.774912	−0.0277641
$780$	−14.6195	−0.523464
$781$	12.1492	0.434732
$782$	−23.7296	−0.848567
$783$	30.3466	1.08450
$784$	−6.19934	−0.221405
$785$	15.2271	0.543479
$786$	−7.15962	−0.255375
$787$	3.57112	0.127297	0.0636484	−	0.997972i	$-0.479726\pi$
$787$	3.57112	0.127297	0.0636484	+	0.997972i	$0.479726\pi$
$788$	−10.0738	−0.358865
$789$	13.1559	0.468363
$790$	−8.03826	−0.285988
$791$	−13.5224	−0.480802
$792$	22.3635	0.794653
$793$	−11.3108	−0.401660
$794$	−23.8038	−0.844766
$795$	−15.7262	−0.557750
$796$	20.8793	0.740047
$797$	17.8650	0.632810	0.316405	−	0.948624i	$-0.397524\pi$
$797$	17.8650	0.632810	0.316405	+	0.948624i	$0.397524\pi$
$798$	0.594283	0.0210374
$799$	26.9359	0.952924
$800$	−1.00000	−0.0353553
$801$	57.1972	2.02096
$802$	1.00000	0.0353112
$803$	−52.5010	−1.85272
$804$	40.1290	1.41524
$805$	3.77391	0.133013
$806$	8.35190	0.294183
$807$	39.1673	1.37875
$808$	1.23617	0.0434882
$809$	11.4972	0.404222	0.202111	−	0.979363i	$-0.435220\pi$
$809$	11.4972	0.404222	0.202111	+	0.979363i	$0.435220\pi$
$810$	2.57776	0.0905733
$811$	47.1499	1.65566	0.827829	−	0.560981i	$-0.189576\pi$
$811$	47.1499	1.65566	0.827829	+	0.560981i	$0.189576\pi$
$812$	6.88778	0.241714
$813$	−65.4952	−2.29702
$814$	50.3344	1.76422
$815$	5.79346	0.202936
$816$	15.3515	0.537410
$817$	0.777789	0.0272114
$818$	16.5119	0.577326
$819$	−21.3103	−0.744641
$820$	3.18356	0.111175
$821$	43.4740	1.51725	0.758627	−	0.651525i	$-0.225871\pi$
$821$	43.4740	1.51725	0.758627	+	0.651525i	$0.225871\pi$
$822$	13.1065	0.457140
$823$	−34.8654	−1.21533	−0.607666	−	0.794193i	$-0.707894\pi$
$823$	−34.8654	−1.21533	−0.607666	+	0.794193i	$0.707894\pi$
$824$	−8.59261	−0.299338
$825$	−13.7281	−0.477950
$826$	−6.58244	−0.229033
$827$	−46.6846	−1.62338	−0.811692	−	0.584086i	$-0.801453\pi$
$827$	−46.6846	−1.62338	−0.811692	+	0.584086i	$0.801453\pi$
$828$	18.7467	0.651494
$829$	−5.34913	−0.185783	−0.0928915	−	0.995676i	$-0.529611\pi$
$829$	−5.34913	−0.185783	−0.0928915	+	0.995676i	$0.529611\pi$
$830$	−17.4940	−0.607227
$831$	−50.1844	−1.74088
$832$	−5.35803	−0.185756
$833$	−34.8793	−1.20850
$834$	−8.05088	−0.278779
$835$	−6.61990	−0.229091
$836$	1.22468	0.0423563
$837$	6.14520	0.212409
$838$	−24.3281	−0.840399
$839$	−37.2921	−1.28747	−0.643733	−	0.765250i	$-0.722615\pi$
$839$	−37.2921	−1.28747	−0.643733	+	0.765250i	$0.722615\pi$
$840$	−2.44148	−0.0842391
$841$	30.2529	1.04320
$842$	−23.2449	−0.801072
$843$	−32.8374	−1.13098
$844$	4.03377	0.138848
$845$	15.7085	0.540390
$846$	−21.2798	−0.731615
$847$	12.8082	0.440097
$848$	−5.76361	−0.197923
$849$	80.0627	2.74774
$850$	−5.62630	−0.192980
$851$	42.1940	1.44639
$852$	−6.58862	−0.225722
$853$	4.77536	0.163505	0.0817526	−	0.996653i	$-0.473948\pi$
$853$	4.77536	0.163505	0.0817526	+	0.996653i	$0.473948\pi$
$854$	−1.88892	−0.0646377
$855$	−1.08193	−0.0370012
$856$	12.3939	0.423614
$857$	−48.4486	−1.65497	−0.827486	−	0.561486i	$-0.810230\pi$
$857$	−48.4486	−1.65497	−0.827486	+	0.561486i	$0.810230\pi$
$858$	−73.5555	−2.51114
$859$	51.4333	1.75488	0.877441	−	0.479684i	$-0.159249\pi$
$859$	51.4333	1.75488	0.877441	+	0.479684i	$0.159249\pi$
$860$	−3.19538	−0.108961
$861$	7.77259	0.264889
$862$	10.0840	0.343462
$863$	−2.60248	−0.0885896	−0.0442948	−	0.999019i	$-0.514104\pi$
$863$	−2.60248	−0.0885896	−0.0442948	+	0.999019i	$0.514104\pi$
$864$	−3.94236	−0.134122
$865$	16.5171	0.561600
$866$	−8.81685	−0.299609
$867$	39.9871	1.35803
$868$	1.39478	0.0473418
$869$	−40.4430	−1.37194
$870$	−21.0031	−0.712071
$871$	−78.8017	−2.67010
$872$	5.77545	0.195582
$873$	−7.95239	−0.269148
$874$	1.02661	0.0347257
$875$	0.894798	0.0302497
$876$	28.4718	0.961973
$877$	−39.3222	−1.32782	−0.663908	−	0.747814i	$-0.731103\pi$
$877$	−39.3222	−1.32782	−0.663908	+	0.747814i	$0.731103\pi$
$878$	25.9384	0.875377
$879$	10.3177	0.348008
$880$	−5.03131	−0.169606
$881$	29.4359	0.991722	0.495861	−	0.868402i	$-0.334853\pi$
$881$	29.4359	0.991722	0.495861	+	0.868402i	$0.334853\pi$
$882$	27.5552	0.927833
$883$	43.6761	1.46982	0.734909	−	0.678166i	$-0.237225\pi$
$883$	43.6761	1.46982	0.734909	+	0.678166i	$0.237225\pi$
$884$	−30.1459	−1.01392
$885$	20.0720	0.674713
$886$	−18.3380	−0.616078
$887$	14.1872	0.476359	0.238180	−	0.971221i	$-0.423449\pi$
$887$	14.1872	0.476359	0.238180	+	0.971221i	$0.423449\pi$
$888$	−27.2968	−0.916020
$889$	−9.38081	−0.314622
$890$	−12.8682	−0.431342
$891$	12.9695	0.434496
$892$	16.9664	0.568078
$893$	−1.16533	−0.0389963
$894$	53.6297	1.79365
$895$	−24.8250	−0.829808
$896$	−0.894798	−0.0298931
$897$	−61.6596	−2.05876
$898$	−20.7522	−0.692511
$899$	11.9987	0.400179
$900$	4.44487	0.148162
$901$	−32.4278	−1.08033
$902$	16.0175	0.533324
$903$	−7.80145	−0.259616
$904$	15.1123	0.502626
$905$	−3.80676	−0.126541
$906$	−0.259882	−0.00863401
$907$	−12.5778	−0.417639	−0.208820	−	0.977954i	$-0.566962\pi$
$907$	−12.5778	−0.417639	−0.208820	+	0.977954i	$0.566962\pi$
$908$	−20.1180	−0.667638
$909$	−5.49460	−0.182244
$910$	4.79436	0.158931
$911$	−21.2296	−0.703368	−0.351684	−	0.936119i	$-0.614391\pi$
$911$	−21.2296	−0.703368	−0.351684	+	0.936119i	$0.614391\pi$
$912$	−0.664153	−0.0219923
$913$	−88.0180	−2.91297
$914$	19.5612	0.647027
$915$	5.75994	0.190418
$916$	−20.4312	−0.675066
$917$	2.34794	0.0775357
$918$	−22.1809	−0.732078
$919$	−27.0226	−0.891394	−0.445697	−	0.895184i	$-0.647044\pi$
$919$	−27.0226	−0.891394	−0.445697	+	0.895184i	$0.647044\pi$
$920$	−4.21762	−0.139051
$921$	42.5542	1.40221
$922$	−3.79984	−0.125141
$923$	12.9381	0.425864
$924$	−12.2839	−0.404109
$925$	10.0042	0.328937
$926$	−2.45295	−0.0806088
$927$	38.1930	1.25442
$928$	−7.69759	−0.252686
$929$	−52.2035	−1.71274	−0.856370	−	0.516363i	$-0.827286\pi$
$929$	−52.2035	−1.71274	−0.856370	+	0.516363i	$0.827286\pi$
$930$	−4.25313	−0.139465
$931$	1.50899	0.0494550
$932$	−22.8310	−0.747853
$933$	−53.5354	−1.75267
$934$	−15.9542	−0.522036
$935$	−28.3077	−0.925760
$936$	23.8157	0.778442
$937$	−32.6730	−1.06738	−0.533690	−	0.845680i	$-0.679195\pi$
$937$	−32.6730	−1.06738	−0.533690	+	0.845680i	$0.679195\pi$
$938$	−13.1600	−0.429689
$939$	−60.9565	−1.98924
$940$	4.78751	0.156151
$941$	24.2253	0.789723	0.394862	−	0.918741i	$-0.370793\pi$
$941$	24.2253	0.789723	0.394862	+	0.918741i	$0.370793\pi$
$942$	−41.5476	−1.35369
$943$	13.4270	0.437244
$944$	7.35635	0.239429
$945$	3.52761	0.114753
$946$	−16.0769	−0.522707
$947$	1.20884	0.0392820	0.0196410	−	0.999807i	$-0.493748\pi$
$947$	1.20884	0.0392820	0.0196410	+	0.999807i	$0.493748\pi$
$948$	21.9326	0.712338
$949$	−55.9103	−1.81493
$950$	0.243411	0.00789729
$951$	−58.5647	−1.89909
$952$	−5.03440	−0.163166
$953$	−32.3480	−1.04785	−0.523927	−	0.851763i	$-0.675533\pi$
$953$	−32.3480	−1.04785	−0.523927	+	0.851763i	$0.675533\pi$
$954$	25.6185	0.829429
$955$	−25.9989	−0.841304
$956$	−1.62500	−0.0525563
$957$	−105.673	−3.41593
$958$	19.3798	0.626133
$959$	−4.29815	−0.138795
$960$	2.72853	0.0880629
$961$	−28.5703	−0.921621
$962$	53.6029	1.72823
$963$	−55.0891	−1.77522
$964$	0.464813	0.0149706
$965$	−22.5354	−0.725440
$966$	−10.2972	−0.331308
$967$	−35.7776	−1.15053	−0.575265	−	0.817967i	$-0.695101\pi$
$967$	−35.7776	−1.15053	−0.575265	+	0.817967i	$0.695101\pi$
$968$	−14.3141	−0.460073
$969$	−3.73672	−0.120041
$970$	1.78912	0.0574451
$971$	−4.46037	−0.143140	−0.0715700	−	0.997436i	$-0.522801\pi$
$971$	−4.46037	−0.143140	−0.0715700	+	0.997436i	$0.522801\pi$
$972$	−18.8606	−0.604953
$973$	2.64022	0.0846415
$974$	−37.3488	−1.19673
$975$	−14.6195	−0.468200
$976$	2.11101	0.0675717
$977$	−40.5221	−1.29642	−0.648208	−	0.761463i	$-0.724481\pi$
$977$	−40.5221	−1.29642	−0.648208	+	0.761463i	$0.724481\pi$
$978$	−15.8076	−0.505472
$979$	−64.7437	−2.06922
$980$	−6.19934	−0.198031
$981$	−25.6711	−0.819616
$982$	−4.55930	−0.145493
$983$	−20.0733	−0.640238	−0.320119	−	0.947377i	$-0.603723\pi$
$983$	−20.0733	−0.640238	−0.320119	+	0.947377i	$0.603723\pi$
$984$	−8.68642	−0.276913
$985$	−10.0738	−0.320979
$986$	−43.3089	−1.37924
$987$	11.6886	0.372052
$988$	1.30420	0.0414922
$989$	−13.4769	−0.428540
$990$	22.3635	0.710759
$991$	54.2591	1.72360	0.861799	−	0.507251i	$-0.169338\pi$
$991$	54.2591	1.72360	0.861799	+	0.507251i	$0.169338\pi$
$992$	−1.55876	−0.0494907
$993$	94.7643	3.00725
$994$	2.16068	0.0685327
$995$	20.8793	0.661918
$996$	47.7330	1.51248
$997$	−3.22505	−0.102138	−0.0510692	−	0.998695i	$-0.516263\pi$
$997$	−3.22505	−0.102138	−0.0510692	+	0.998695i	$0.516263\pi$
$998$	−22.5876	−0.714997
$999$	39.4402	1.24783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.18	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.72853 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.72853 q^{6} +0.894798 q^{7} -1.00000 q^{8} +4.44487 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.72853 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.72853 q^{6} +0.894798 q^{7} -1.00000 q^{8} +4.44487 q^{9} -1.00000 q^{10} -5.03131 q^{11} +2.72853 q^{12} -5.35803 q^{13} -0.894798 q^{14} +2.72853 q^{15} +1.00000 q^{16} +5.62630 q^{17} -4.44487 q^{18} -0.243411 q^{19} +1.00000 q^{20} +2.44148 q^{21} +5.03131 q^{22} +4.21762 q^{23} -2.72853 q^{24} +1.00000 q^{25} +5.35803 q^{26} +3.94236 q^{27} +0.894798 q^{28} +7.69759 q^{29} -2.72853 q^{30} +1.55876 q^{31} -1.00000 q^{32} -13.7281 q^{33} -5.62630 q^{34} +0.894798 q^{35} +4.44487 q^{36} +10.0042 q^{37} +0.243411 q^{38} -14.6195 q^{39} -1.00000 q^{40} +3.18356 q^{41} -2.44148 q^{42} -3.19538 q^{43} -5.03131 q^{44} +4.44487 q^{45} -4.21762 q^{46} +4.78751 q^{47} +2.72853 q^{48} -6.19934 q^{49} -1.00000 q^{50} +15.3515 q^{51} -5.35803 q^{52} -5.76361 q^{53} -3.94236 q^{54} -5.03131 q^{55} -0.894798 q^{56} -0.664153 q^{57} -7.69759 q^{58} +7.35635 q^{59} +2.72853 q^{60} +2.11101 q^{61} -1.55876 q^{62} +3.97726 q^{63} +1.00000 q^{64} -5.35803 q^{65} +13.7281 q^{66} +14.7072 q^{67} +5.62630 q^{68} +11.5079 q^{69} -0.894798 q^{70} -2.41472 q^{71} -4.44487 q^{72} +10.4349 q^{73} -10.0042 q^{74} +2.72853 q^{75} -0.243411 q^{76} -4.50201 q^{77} +14.6195 q^{78} +8.03826 q^{79} +1.00000 q^{80} -2.57776 q^{81} -3.18356 q^{82} +17.4940 q^{83} +2.44148 q^{84} +5.62630 q^{85} +3.19538 q^{86} +21.0031 q^{87} +5.03131 q^{88} +12.8682 q^{89} -4.44487 q^{90} -4.79436 q^{91} +4.21762 q^{92} +4.25313 q^{93} -4.78751 q^{94} -0.243411 q^{95} -2.72853 q^{96} -1.78912 q^{97} +6.19934 q^{98} -22.3635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 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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