LMFDB - Embedded newform 4010.2.a.m.1.9

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			1.9
Root			$-0.241588$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.241588 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.241588 q^{6} +0.516163 q^{7} -1.00000 q^{8} -2.94164 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.241588 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.241588 q^{6} +0.516163 q^{7} -1.00000 q^{8} -2.94164 q^{9} -1.00000 q^{10} -3.81581 q^{11} -0.241588 q^{12} +6.85447 q^{13} -0.516163 q^{14} -0.241588 q^{15} +1.00000 q^{16} -4.49943 q^{17} +2.94164 q^{18} +3.22522 q^{19} +1.00000 q^{20} -0.124699 q^{21} +3.81581 q^{22} +4.08755 q^{23} +0.241588 q^{24} +1.00000 q^{25} -6.85447 q^{26} +1.43543 q^{27} +0.516163 q^{28} -3.45861 q^{29} +0.241588 q^{30} -2.62808 q^{31} -1.00000 q^{32} +0.921853 q^{33} +4.49943 q^{34} +0.516163 q^{35} -2.94164 q^{36} -4.03902 q^{37} -3.22522 q^{38} -1.65595 q^{39} -1.00000 q^{40} +8.53139 q^{41} +0.124699 q^{42} +8.17552 q^{43} -3.81581 q^{44} -2.94164 q^{45} -4.08755 q^{46} -5.90540 q^{47} -0.241588 q^{48} -6.73358 q^{49} -1.00000 q^{50} +1.08701 q^{51} +6.85447 q^{52} -0.290204 q^{53} -1.43543 q^{54} -3.81581 q^{55} -0.516163 q^{56} -0.779174 q^{57} +3.45861 q^{58} -0.592529 q^{59} -0.241588 q^{60} +4.32804 q^{61} +2.62808 q^{62} -1.51836 q^{63} +1.00000 q^{64} +6.85447 q^{65} -0.921853 q^{66} +7.07758 q^{67} -4.49943 q^{68} -0.987501 q^{69} -0.516163 q^{70} -6.96475 q^{71} +2.94164 q^{72} +10.2404 q^{73} +4.03902 q^{74} -0.241588 q^{75} +3.22522 q^{76} -1.96958 q^{77} +1.65595 q^{78} +8.54212 q^{79} +1.00000 q^{80} +8.47813 q^{81} -8.53139 q^{82} -8.86332 q^{83} -0.124699 q^{84} -4.49943 q^{85} -8.17552 q^{86} +0.835558 q^{87} +3.81581 q^{88} +5.25047 q^{89} +2.94164 q^{90} +3.53802 q^{91} +4.08755 q^{92} +0.634913 q^{93} +5.90540 q^{94} +3.22522 q^{95} +0.241588 q^{96} -14.8257 q^{97} +6.73358 q^{98} +11.2247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.241588	−0.139481	−0.0697403	−	0.997565i	$-0.522217\pi$
$3$	−0.241588	−0.139481	−0.0697403	+	0.997565i	$0.522217\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.241588	0.0986277
$7$	0.516163	0.195091	0.0975456	−	0.995231i	$-0.468901\pi$
$7$	0.516163	0.195091	0.0975456	+	0.995231i	$0.468901\pi$
$8$	−1.00000	−0.353553
$9$	−2.94164	−0.980545
$10$	−1.00000	−0.316228
$11$	−3.81581	−1.15051	−0.575255	−	0.817974i	$-0.695097\pi$
$11$	−3.81581	−1.15051	−0.575255	+	0.817974i	$0.695097\pi$
$12$	−0.241588	−0.0697403
$13$	6.85447	1.90109	0.950544	−	0.310591i	$-0.100527\pi$
$13$	6.85447	1.90109	0.950544	+	0.310591i	$0.100527\pi$
$14$	−0.516163	−0.137950
$15$	−0.241588	−0.0623776
$16$	1.00000	0.250000
$17$	−4.49943	−1.09127	−0.545637	−	0.838022i	$-0.683712\pi$
$17$	−4.49943	−1.09127	−0.545637	+	0.838022i	$0.683712\pi$
$18$	2.94164	0.693350
$19$	3.22522	0.739917	0.369959	−	0.929048i	$-0.379372\pi$
$19$	3.22522	0.739917	0.369959	+	0.929048i	$0.379372\pi$
$20$	1.00000	0.223607
$21$	−0.124699	−0.0272115
$22$	3.81581	0.813534
$23$	4.08755	0.852313	0.426157	−	0.904649i	$-0.359867\pi$
$23$	4.08755	0.852313	0.426157	+	0.904649i	$0.359867\pi$
$24$	0.241588	0.0493139
$25$	1.00000	0.200000
$26$	−6.85447	−1.34427
$27$	1.43543	0.276248
$28$	0.516163	0.0975456
$29$	−3.45861	−0.642248	−0.321124	−	0.947037i	$-0.604061\pi$
$29$	−3.45861	−0.642248	−0.321124	+	0.947037i	$0.604061\pi$
$30$	0.241588	0.0441077
$31$	−2.62808	−0.472018	−0.236009	−	0.971751i	$-0.575839\pi$
$31$	−2.62808	−0.472018	−0.236009	+	0.971751i	$0.575839\pi$
$32$	−1.00000	−0.176777
$33$	0.921853	0.160474
$34$	4.49943	0.771647
$35$	0.516163	0.0872475
$36$	−2.94164	−0.490273
$37$	−4.03902	−0.664010	−0.332005	−	0.943278i	$-0.607725\pi$
$37$	−4.03902	−0.664010	−0.332005	+	0.943278i	$0.607725\pi$
$38$	−3.22522	−0.523200
$39$	−1.65595	−0.265165
$40$	−1.00000	−0.158114
$41$	8.53139	1.33238	0.666190	−	0.745782i	$-0.267924\pi$
$41$	8.53139	1.33238	0.666190	+	0.745782i	$0.267924\pi$
$42$	0.124699	0.0192414
$43$	8.17552	1.24675	0.623377	−	0.781921i	$-0.285760\pi$
$43$	8.17552	1.24675	0.623377	+	0.781921i	$0.285760\pi$
$44$	−3.81581	−0.575255
$45$	−2.94164	−0.438513
$46$	−4.08755	−0.602676
$47$	−5.90540	−0.861391	−0.430695	−	0.902497i	$-0.641732\pi$
$47$	−5.90540	−0.861391	−0.430695	+	0.902497i	$0.641732\pi$
$48$	−0.241588	−0.0348702
$49$	−6.73358	−0.961939
$50$	−1.00000	−0.141421
$51$	1.08701	0.152211
$52$	6.85447	0.950544
$53$	−0.290204	−0.0398626	−0.0199313	−	0.999801i	$-0.506345\pi$
$53$	−0.290204	−0.0398626	−0.0199313	+	0.999801i	$0.506345\pi$
$54$	−1.43543	−0.195337
$55$	−3.81581	−0.514524
$56$	−0.516163	−0.0689752
$57$	−0.779174	−0.103204
$58$	3.45861	0.454138
$59$	−0.592529	−0.0771408	−0.0385704	−	0.999256i	$-0.512280\pi$
$59$	−0.592529	−0.0771408	−0.0385704	+	0.999256i	$0.512280\pi$
$60$	−0.241588	−0.0311888
$61$	4.32804	0.554149	0.277074	−	0.960849i	$-0.410635\pi$
$61$	4.32804	0.554149	0.277074	+	0.960849i	$0.410635\pi$
$62$	2.62808	0.333767
$63$	−1.51836	−0.191296
$64$	1.00000	0.125000
$65$	6.85447	0.850192
$66$	−0.921853	−0.113472
$67$	7.07758	0.864664	0.432332	−	0.901714i	$-0.357691\pi$
$67$	7.07758	0.864664	0.432332	+	0.901714i	$0.357691\pi$
$68$	−4.49943	−0.545637
$69$	−0.987501	−0.118881
$70$	−0.516163	−0.0616933
$71$	−6.96475	−0.826564	−0.413282	−	0.910603i	$-0.635618\pi$
$71$	−6.96475	−0.826564	−0.413282	+	0.910603i	$0.635618\pi$
$72$	2.94164	0.346675
$73$	10.2404	1.19855	0.599276	−	0.800543i	$-0.295455\pi$
$73$	10.2404	1.19855	0.599276	+	0.800543i	$0.295455\pi$
$74$	4.03902	0.469526
$75$	−0.241588	−0.0278961
$76$	3.22522	0.369959
$77$	−1.96958	−0.224455
$78$	1.65595	0.187500
$79$	8.54212	0.961064	0.480532	−	0.876977i	$-0.340444\pi$
$79$	8.54212	0.961064	0.480532	+	0.876977i	$0.340444\pi$
$80$	1.00000	0.111803
$81$	8.47813	0.942014
$82$	−8.53139	−0.942135
$83$	−8.86332	−0.972876	−0.486438	−	0.873715i	$-0.661704\pi$
$83$	−8.86332	−0.972876	−0.486438	+	0.873715i	$0.661704\pi$
$84$	−0.124699	−0.0136057
$85$	−4.49943	−0.488032
$86$	−8.17552	−0.881589
$87$	0.835558	0.0895812
$88$	3.81581	0.406767
$89$	5.25047	0.556548	0.278274	−	0.960502i	$-0.410238\pi$
$89$	5.25047	0.556548	0.278274	+	0.960502i	$0.410238\pi$
$90$	2.94164	0.310076
$91$	3.53802	0.370886
$92$	4.08755	0.426157
$93$	0.634913	0.0658374
$94$	5.90540	0.609095
$95$	3.22522	0.330901
$96$	0.241588	0.0246569
$97$	−14.8257	−1.50533	−0.752663	−	0.658406i	$-0.771231\pi$
$97$	−14.8257	−1.50533	−0.752663	+	0.658406i	$0.771231\pi$
$98$	6.73358	0.680194
$99$	11.2247	1.12813
$100$	1.00000	0.100000
$101$	0.460958	0.0458670	0.0229335	−	0.999737i	$-0.492699\pi$
$101$	0.460958	0.0458670	0.0229335	+	0.999737i	$0.492699\pi$
$102$	−1.08701	−0.107630
$103$	18.0921	1.78267	0.891334	−	0.453347i	$-0.149770\pi$
$103$	18.0921	1.78267	0.891334	+	0.453347i	$0.149770\pi$
$104$	−6.85447	−0.672136
$105$	−0.124699	−0.0121693
$106$	0.290204	0.0281871
$107$	1.18223	0.114290	0.0571452	−	0.998366i	$-0.481800\pi$
$107$	1.18223	0.114290	0.0571452	+	0.998366i	$0.481800\pi$
$108$	1.43543	0.138124
$109$	18.5387	1.77569	0.887844	−	0.460145i	$-0.152203\pi$
$109$	18.5387	1.77569	0.887844	+	0.460145i	$0.152203\pi$
$110$	3.81581	0.363823
$111$	0.975776	0.0926166
$112$	0.516163	0.0487728
$113$	−3.90052	−0.366930	−0.183465	−	0.983026i	$-0.558731\pi$
$113$	−3.90052	−0.366930	−0.183465	+	0.983026i	$0.558731\pi$
$114$	0.779174	0.0729763
$115$	4.08755	0.381166
$116$	−3.45861	−0.321124
$117$	−20.1633	−1.86410
$118$	0.592529	0.0545467
$119$	−2.32244	−0.212898
$120$	0.241588	0.0220538
$121$	3.56042	0.323675
$122$	−4.32804	−0.391842
$123$	−2.06108	−0.185841
$124$	−2.62808	−0.236009
$125$	1.00000	0.0894427
$126$	1.51836	0.135267
$127$	19.0065	1.68655	0.843275	−	0.537482i	$-0.180625\pi$
$127$	19.0065	1.68655	0.843275	+	0.537482i	$0.180625\pi$
$128$	−1.00000	−0.0883883
$129$	−1.97510	−0.173898
$130$	−6.85447	−0.601177
$131$	17.3081	1.51222	0.756110	−	0.654445i	$-0.227097\pi$
$131$	17.3081	1.51222	0.756110	+	0.654445i	$0.227097\pi$
$132$	0.921853	0.0802370
$133$	1.66474	0.144351
$134$	−7.07758	−0.611410
$135$	1.43543	0.123542
$136$	4.49943	0.385823
$137$	12.8467	1.09757	0.548784	−	0.835965i	$-0.315091\pi$
$137$	12.8467	1.09757	0.548784	+	0.835965i	$0.315091\pi$
$138$	0.987501	0.0840617
$139$	−12.8590	−1.09068	−0.545342	−	0.838214i	$-0.683600\pi$
$139$	−12.8590	−1.09068	−0.545342	+	0.838214i	$0.683600\pi$
$140$	0.516163	0.0436237
$141$	1.42667	0.120147
$142$	6.96475	0.584469
$143$	−26.1554	−2.18722
$144$	−2.94164	−0.245136
$145$	−3.45861	−0.287222
$146$	−10.2404	−0.847504
$147$	1.62675	0.134172
$148$	−4.03902	−0.332005
$149$	−2.75968	−0.226082	−0.113041	−	0.993590i	$-0.536059\pi$
$149$	−2.75968	−0.226082	−0.113041	+	0.993590i	$0.536059\pi$
$150$	0.241588	0.0197255
$151$	11.3931	0.927155	0.463577	−	0.886056i	$-0.346566\pi$
$151$	11.3931	0.927155	0.463577	+	0.886056i	$0.346566\pi$
$152$	−3.22522	−0.261600
$153$	13.2357	1.07004
$154$	1.96958	0.158713
$155$	−2.62808	−0.211093
$156$	−1.65595	−0.132582
$157$	−21.1622	−1.68893	−0.844464	−	0.535613i	$-0.820081\pi$
$157$	−21.1622	−1.68893	−0.844464	+	0.535613i	$0.820081\pi$
$158$	−8.54212	−0.679575
$159$	0.0701097	0.00556006
$160$	−1.00000	−0.0790569
$161$	2.10984	0.166279
$162$	−8.47813	−0.666104
$163$	−14.9937	−1.17440	−0.587199	−	0.809443i	$-0.699769\pi$
$163$	−14.9937	−1.17440	−0.587199	+	0.809443i	$0.699769\pi$
$164$	8.53139	0.666190
$165$	0.921853	0.0717661
$166$	8.86332	0.687927
$167$	13.4157	1.03814	0.519068	−	0.854733i	$-0.326279\pi$
$167$	13.4157	1.03814	0.519068	+	0.854733i	$0.326279\pi$
$168$	0.124699	0.00962070
$169$	33.9837	2.61413
$170$	4.49943	0.345091
$171$	−9.48743	−0.725522
$172$	8.17552	0.623377
$173$	17.3087	1.31595	0.657977	−	0.753038i	$-0.271412\pi$
$173$	17.3087	1.31595	0.657977	+	0.753038i	$0.271412\pi$
$174$	−0.835558	−0.0633435
$175$	0.516163	0.0390183
$176$	−3.81581	−0.287628
$177$	0.143148	0.0107596
$178$	−5.25047	−0.393539
$179$	−18.3311	−1.37013	−0.685064	−	0.728482i	$-0.740226\pi$
$179$	−18.3311	−1.37013	−0.685064	+	0.728482i	$0.740226\pi$
$180$	−2.94164	−0.219257
$181$	−12.1916	−0.906193	−0.453097	−	0.891461i	$-0.649681\pi$
$181$	−12.1916	−0.906193	−0.453097	+	0.891461i	$0.649681\pi$
$182$	−3.53802	−0.262256
$183$	−1.04560	−0.0772930
$184$	−4.08755	−0.301338
$185$	−4.03902	−0.296954
$186$	−0.634913	−0.0465541
$187$	17.1690	1.25552
$188$	−5.90540	−0.430695
$189$	0.740913	0.0538935
$190$	−3.22522	−0.233982
$191$	−2.02598	−0.146595	−0.0732975	−	0.997310i	$-0.523352\pi$
$191$	−2.02598	−0.146595	−0.0732975	+	0.997310i	$0.523352\pi$
$192$	−0.241588	−0.0174351
$193$	−23.9792	−1.72606	−0.863030	−	0.505152i	$-0.831436\pi$
$193$	−23.9792	−1.72606	−0.863030	+	0.505152i	$0.831436\pi$
$194$	14.8257	1.06443
$195$	−1.65595	−0.118585
$196$	−6.73358	−0.480970
$197$	11.9781	0.853404	0.426702	−	0.904392i	$-0.359675\pi$
$197$	11.9781	0.853404	0.426702	+	0.904392i	$0.359675\pi$
$198$	−11.2247	−0.797707
$199$	16.2076	1.14893	0.574464	−	0.818530i	$-0.305211\pi$
$199$	16.2076	1.14893	0.574464	+	0.818530i	$0.305211\pi$
$200$	−1.00000	−0.0707107
$201$	−1.70986	−0.120604
$202$	−0.460958	−0.0324329
$203$	−1.78521	−0.125297
$204$	1.08701	0.0761057
$205$	8.53139	0.595858
$206$	−18.0921	−1.26054
$207$	−12.0241	−0.835731
$208$	6.85447	0.475272
$209$	−12.3068	−0.851282
$210$	0.124699	0.00860502
$211$	24.7940	1.70689	0.853443	−	0.521186i	$-0.174510\pi$
$211$	24.7940	1.70689	0.853443	+	0.521186i	$0.174510\pi$
$212$	−0.290204	−0.0199313
$213$	1.68260	0.115290
$214$	−1.18223	−0.0808154
$215$	8.17552	0.557566
$216$	−1.43543	−0.0976683
$217$	−1.35652	−0.0920866
$218$	−18.5387	−1.25560
$219$	−2.47396	−0.167175
$220$	−3.81581	−0.257262
$221$	−30.8412	−2.07461
$222$	−0.975776	−0.0654898
$223$	−17.5914	−1.17801	−0.589004	−	0.808130i	$-0.700480\pi$
$223$	−17.5914	−1.17801	−0.589004	+	0.808130i	$0.700480\pi$
$224$	−0.516163	−0.0344876
$225$	−2.94164	−0.196109
$226$	3.90052	0.259459
$227$	3.24251	0.215213	0.107607	−	0.994194i	$-0.465681\pi$
$227$	3.24251	0.215213	0.107607	+	0.994194i	$0.465681\pi$
$228$	−0.779174	−0.0516021
$229$	17.5573	1.16022	0.580111	−	0.814538i	$-0.303009\pi$
$229$	17.5573	1.16022	0.580111	+	0.814538i	$0.303009\pi$
$230$	−4.08755	−0.269525
$231$	0.475826	0.0313071
$232$	3.45861	0.227069
$233$	−11.9604	−0.783551	−0.391776	−	0.920061i	$-0.628139\pi$
$233$	−11.9604	−0.783551	−0.391776	+	0.920061i	$0.628139\pi$
$234$	20.1633	1.31812
$235$	−5.90540	−0.385226
$236$	−0.592529	−0.0385704
$237$	−2.06367	−0.134050
$238$	2.32244	0.150542
$239$	26.3747	1.70604	0.853020	−	0.521879i	$-0.174769\pi$
$239$	26.3747	1.70604	0.853020	+	0.521879i	$0.174769\pi$
$240$	−0.241588	−0.0155944
$241$	−13.9559	−0.898977	−0.449489	−	0.893286i	$-0.648394\pi$
$241$	−13.9559	−0.898977	−0.449489	+	0.893286i	$0.648394\pi$
$242$	−3.56042	−0.228873
$243$	−6.35449	−0.407640
$244$	4.32804	0.277074
$245$	−6.73358	−0.430192
$246$	2.06108	0.131410
$247$	22.1072	1.40665
$248$	2.62808	0.166884
$249$	2.14127	0.135697
$250$	−1.00000	−0.0632456
$251$	1.05587	0.0666460	0.0333230	−	0.999445i	$-0.489391\pi$
$251$	1.05587	0.0666460	0.0333230	+	0.999445i	$0.489391\pi$
$252$	−1.51836	−0.0956479
$253$	−15.5973	−0.980595
$254$	−19.0065	−1.19257
$255$	1.08701	0.0680710
$256$	1.00000	0.0625000
$257$	−3.44508	−0.214898	−0.107449	−	0.994211i	$-0.534268\pi$
$257$	−3.44508	−0.214898	−0.107449	+	0.994211i	$0.534268\pi$
$258$	1.97510	0.122965
$259$	−2.08479	−0.129543
$260$	6.85447	0.425096
$261$	10.1740	0.629753
$262$	−17.3081	−1.06930
$263$	18.6255	1.14850	0.574249	−	0.818681i	$-0.305294\pi$
$263$	18.6255	1.14850	0.574249	+	0.818681i	$0.305294\pi$
$264$	−0.921853	−0.0567361
$265$	−0.290204	−0.0178271
$266$	−1.66474	−0.102072
$267$	−1.26845	−0.0776277
$268$	7.07758	0.432332
$269$	1.64855	0.100514	0.0502570	−	0.998736i	$-0.483996\pi$
$269$	1.64855	0.100514	0.0502570	+	0.998736i	$0.483996\pi$
$270$	−1.43543	−0.0873572
$271$	18.3965	1.11751	0.558755	−	0.829333i	$-0.311279\pi$
$271$	18.3965	1.11751	0.558755	+	0.829333i	$0.311279\pi$
$272$	−4.49943	−0.272818
$273$	−0.854742	−0.0517313
$274$	−12.8467	−0.776097
$275$	−3.81581	−0.230102
$276$	−0.987501	−0.0594406
$277$	−21.2112	−1.27445	−0.637227	−	0.770676i	$-0.719919\pi$
$277$	−21.2112	−1.27445	−0.637227	+	0.770676i	$0.719919\pi$
$278$	12.8590	0.771230
$279$	7.73087	0.462835
$280$	−0.516163	−0.0308466
$281$	11.3129	0.674870	0.337435	−	0.941349i	$-0.390441\pi$
$281$	11.3129	0.674870	0.337435	+	0.941349i	$0.390441\pi$
$282$	−1.42667	−0.0849570
$283$	−6.06011	−0.360236	−0.180118	−	0.983645i	$-0.557648\pi$
$283$	−6.06011	−0.360236	−0.180118	+	0.983645i	$0.557648\pi$
$284$	−6.96475	−0.413282
$285$	−0.779174	−0.0461543
$286$	26.1554	1.54660
$287$	4.40359	0.259936
$288$	2.94164	0.173338
$289$	3.24491	0.190877
$290$	3.45861	0.203097
$291$	3.58172	0.209964
$292$	10.2404	0.599276
$293$	6.19065	0.361662	0.180831	−	0.983514i	$-0.442121\pi$
$293$	6.19065	0.361662	0.180831	+	0.983514i	$0.442121\pi$
$294$	−1.62675	−0.0948739
$295$	−0.592529	−0.0344984
$296$	4.03902	0.234763
$297$	−5.47731	−0.317826
$298$	2.75968	0.159864
$299$	28.0180	1.62032
$300$	−0.241588	−0.0139481
$301$	4.21990	0.243231
$302$	−11.3931	−0.655598
$303$	−0.111362	−0.00639756
$304$	3.22522	0.184979
$305$	4.32804	0.247823
$306$	−13.2357	−0.756634
$307$	22.3695	1.27670	0.638349	−	0.769747i	$-0.279618\pi$
$307$	22.3695	1.27670	0.638349	+	0.769747i	$0.279618\pi$
$308$	−1.96958	−0.112227
$309$	−4.37083	−0.248648
$310$	2.62808	0.149265
$311$	20.5078	1.16289	0.581445	−	0.813586i	$-0.302488\pi$
$311$	20.5078	1.16289	0.581445	+	0.813586i	$0.302488\pi$
$312$	1.65595	0.0937499
$313$	15.8651	0.896750	0.448375	−	0.893846i	$-0.352003\pi$
$313$	15.8651	0.896750	0.448375	+	0.893846i	$0.352003\pi$
$314$	21.1622	1.19425
$315$	−1.51836	−0.0855501
$316$	8.54212	0.480532
$317$	−5.95150	−0.334270	−0.167135	−	0.985934i	$-0.553452\pi$
$317$	−5.95150	−0.334270	−0.167135	+	0.985934i	$0.553452\pi$
$318$	−0.0701097	−0.00393156
$319$	13.1974	0.738913
$320$	1.00000	0.0559017
$321$	−0.285612	−0.0159413
$322$	−2.10984	−0.117577
$323$	−14.5117	−0.807452
$324$	8.47813	0.471007
$325$	6.85447	0.380217
$326$	14.9937	0.830425
$327$	−4.47872	−0.247674
$328$	−8.53139	−0.471067
$329$	−3.04815	−0.168050
$330$	−0.921853	−0.0507463
$331$	23.9842	1.31829	0.659146	−	0.752015i	$-0.270918\pi$
$331$	23.9842	1.31829	0.659146	+	0.752015i	$0.270918\pi$
$332$	−8.86332	−0.486438
$333$	11.8813	0.651092
$334$	−13.4157	−0.734073
$335$	7.07758	0.386690
$336$	−0.124699	−0.00680286
$337$	−22.1557	−1.20690	−0.603450	−	0.797401i	$-0.706208\pi$
$337$	−22.1557	−1.20690	−0.603450	+	0.797401i	$0.706208\pi$
$338$	−33.9837	−1.84847
$339$	0.942317	0.0511796
$340$	−4.49943	−0.244016
$341$	10.0283	0.543062
$342$	9.48743	0.513022
$343$	−7.08876	−0.382757
$344$	−8.17552	−0.440794
$345$	−0.987501	−0.0531653
$346$	−17.3087	−0.930520
$347$	−6.49293	−0.348559	−0.174279	−	0.984696i	$-0.555760\pi$
$347$	−6.49293	−0.348559	−0.174279	+	0.984696i	$0.555760\pi$
$348$	0.835558	0.0447906
$349$	27.6384	1.47945	0.739726	−	0.672908i	$-0.234955\pi$
$349$	27.6384	1.47945	0.739726	+	0.672908i	$0.234955\pi$
$350$	−0.516163	−0.0275901
$351$	9.83907	0.525171
$352$	3.81581	0.203383
$353$	31.0471	1.65247	0.826236	−	0.563324i	$-0.190478\pi$
$353$	31.0471	1.65247	0.826236	+	0.563324i	$0.190478\pi$
$354$	−0.143148	−0.00760822
$355$	−6.96475	−0.369651
$356$	5.25047	0.278274
$357$	0.561073	0.0296951
$358$	18.3311	0.968827
$359$	16.7660	0.884875	0.442438	−	0.896799i	$-0.354114\pi$
$359$	16.7660	0.884875	0.442438	+	0.896799i	$0.354114\pi$
$360$	2.94164	0.155038
$361$	−8.59793	−0.452523
$362$	12.1916	0.640776
$363$	−0.860153	−0.0451463
$364$	3.53802	0.185443
$365$	10.2404	0.536008
$366$	1.04560	0.0546544
$367$	−10.1368	−0.529135	−0.264567	−	0.964367i	$-0.585229\pi$
$367$	−10.1368	−0.529135	−0.264567	+	0.964367i	$0.585229\pi$
$368$	4.08755	0.213078
$369$	−25.0962	−1.30646
$370$	4.03902	0.209979
$371$	−0.149793	−0.00777685
$372$	0.634913	0.0329187
$373$	−36.5306	−1.89149	−0.945743	−	0.324917i	$-0.894664\pi$
$373$	−36.5306	−1.89149	−0.945743	+	0.324917i	$0.894664\pi$
$374$	−17.1690	−0.887788
$375$	−0.241588	−0.0124755
$376$	5.90540	0.304548
$377$	−23.7069	−1.22097
$378$	−0.740913	−0.0381085
$379$	4.32940	0.222386	0.111193	−	0.993799i	$-0.464533\pi$
$379$	4.32940	0.222386	0.111193	+	0.993799i	$0.464533\pi$
$380$	3.22522	0.165450
$381$	−4.59172	−0.235241
$382$	2.02598	0.103658
$383$	35.9374	1.83632	0.918158	−	0.396215i	$-0.129677\pi$
$383$	35.9374	1.83632	0.918158	+	0.396215i	$0.129677\pi$
$384$	0.241588	0.0123285
$385$	−1.96958	−0.100379
$386$	23.9792	1.22051
$387$	−24.0494	−1.22250
$388$	−14.8257	−0.752663
$389$	12.4327	0.630365	0.315182	−	0.949031i	$-0.397934\pi$
$389$	12.4327	0.630365	0.315182	+	0.949031i	$0.397934\pi$
$390$	1.65595	0.0838525
$391$	−18.3917	−0.930106
$392$	6.73358	0.340097
$393$	−4.18143	−0.210925
$394$	−11.9781	−0.603448
$395$	8.54212	0.429801
$396$	11.2247	0.564064
$397$	27.2938	1.36984	0.684918	−	0.728620i	$-0.259838\pi$
$397$	27.2938	1.36984	0.684918	+	0.728620i	$0.259838\pi$
$398$	−16.2076	−0.812415
$399$	−0.402181	−0.0201342
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	1.70986	0.0852798
$403$	−18.0141	−0.897347
$404$	0.460958	0.0229335
$405$	8.47813	0.421281
$406$	1.78521	0.0885984
$407$	15.4121	0.763951
$408$	−1.08701	−0.0538149
$409$	13.9416	0.689368	0.344684	−	0.938719i	$-0.387986\pi$
$409$	13.9416	0.689368	0.344684	+	0.938719i	$0.387986\pi$
$410$	−8.53139	−0.421335
$411$	−3.10360	−0.153089
$412$	18.0921	0.891334
$413$	−0.305842	−0.0150495
$414$	12.0241	0.590951
$415$	−8.86332	−0.435083
$416$	−6.85447	−0.336068
$417$	3.10657	0.152129
$418$	12.3068	0.601948
$419$	17.1648	0.838555	0.419278	−	0.907858i	$-0.362283\pi$
$419$	17.1648	0.838555	0.419278	+	0.907858i	$0.362283\pi$
$420$	−0.124699	−0.00608467
$421$	32.1970	1.56919	0.784594	−	0.620010i	$-0.212871\pi$
$421$	32.1970	1.56919	0.784594	+	0.620010i	$0.212871\pi$
$422$	−24.7940	−1.20695
$423$	17.3715	0.844632
$424$	0.290204	0.0140936
$425$	−4.49943	−0.218255
$426$	−1.68260	−0.0815221
$427$	2.23397	0.108110
$428$	1.18223	0.0571452
$429$	6.31881	0.305075
$430$	−8.17552	−0.394259
$431$	−18.6957	−0.900542	−0.450271	−	0.892892i	$-0.648673\pi$
$431$	−18.6957	−0.900542	−0.450271	+	0.892892i	$0.648673\pi$
$432$	1.43543	0.0690619
$433$	26.2301	1.26054	0.630269	−	0.776377i	$-0.282945\pi$
$433$	26.2301	1.26054	0.630269	+	0.776377i	$0.282945\pi$
$434$	1.35652	0.0651151
$435$	0.835558	0.0400619
$436$	18.5387	0.887844
$437$	13.1833	0.630641
$438$	2.47396	0.118210
$439$	−14.2669	−0.680920	−0.340460	−	0.940259i	$-0.610583\pi$
$439$	−14.2669	−0.680920	−0.340460	+	0.940259i	$0.610583\pi$
$440$	3.81581	0.181912
$441$	19.8077	0.943225
$442$	30.8412	1.46697
$443$	−26.6741	−1.26732	−0.633662	−	0.773610i	$-0.718449\pi$
$443$	−26.6741	−1.26732	−0.633662	+	0.773610i	$0.718449\pi$
$444$	0.975776	0.0463083
$445$	5.25047	0.248896
$446$	17.5914	0.832978
$447$	0.666705	0.0315341
$448$	0.516163	0.0243864
$449$	15.4245	0.727926	0.363963	−	0.931413i	$-0.381423\pi$
$449$	15.4245	0.727926	0.363963	+	0.931413i	$0.381423\pi$
$450$	2.94164	0.138670
$451$	−32.5542	−1.53292
$452$	−3.90052	−0.183465
$453$	−2.75242	−0.129320
$454$	−3.24251	−0.152179
$455$	3.53802	0.165865
$456$	0.779174	0.0364882
$457$	13.9856	0.654221	0.327111	−	0.944986i	$-0.393925\pi$
$457$	13.9856	0.654221	0.327111	+	0.944986i	$0.393925\pi$
$458$	−17.5573	−0.820400
$459$	−6.45860	−0.301462
$460$	4.08755	0.190583
$461$	19.3169	0.899677	0.449839	−	0.893110i	$-0.351481\pi$
$461$	19.3169	0.899677	0.449839	+	0.893110i	$0.351481\pi$
$462$	−0.475826	−0.0221374
$463$	−25.6024	−1.18984	−0.594922	−	0.803784i	$-0.702817\pi$
$463$	−25.6024	−1.18984	−0.594922	+	0.803784i	$0.702817\pi$
$464$	−3.45861	−0.160562
$465$	0.634913	0.0294434
$466$	11.9604	0.554054
$467$	−9.92229	−0.459149	−0.229574	−	0.973291i	$-0.573733\pi$
$467$	−9.92229	−0.459149	−0.229574	+	0.973291i	$0.573733\pi$
$468$	−20.1633	−0.932051
$469$	3.65319	0.168688
$470$	5.90540	0.272396
$471$	5.11253	0.235573
$472$	0.592529	0.0272734
$473$	−31.1962	−1.43440
$474$	2.06367	0.0947876
$475$	3.22522	0.147983
$476$	−2.32244	−0.106449
$477$	0.853675	0.0390871
$478$	−26.3747	−1.20635
$479$	33.2677	1.52004	0.760019	−	0.649900i	$-0.225189\pi$
$479$	33.2677	1.52004	0.760019	+	0.649900i	$0.225189\pi$
$480$	0.241588	0.0110269
$481$	−27.6853	−1.26234
$482$	13.9559	0.635673
$483$	−0.509712	−0.0231927
$484$	3.56042	0.161837
$485$	−14.8257	−0.673202
$486$	6.35449	0.288245
$487$	−17.5974	−0.797417	−0.398708	−	0.917078i	$-0.630541\pi$
$487$	−17.5974	−0.797417	−0.398708	+	0.917078i	$0.630541\pi$
$488$	−4.32804	−0.195921
$489$	3.62229	0.163806
$490$	6.73358	0.304192
$491$	−4.30157	−0.194127	−0.0970635	−	0.995278i	$-0.530945\pi$
$491$	−4.30157	−0.194127	−0.0970635	+	0.995278i	$0.530945\pi$
$492$	−2.06108	−0.0929206
$493$	15.5618	0.700868
$494$	−22.1072	−0.994649
$495$	11.2247	0.504514
$496$	−2.62808	−0.118004
$497$	−3.59495	−0.161255
$498$	−2.14127	−0.0959525
$499$	−4.78584	−0.214244	−0.107122	−	0.994246i	$-0.534163\pi$
$499$	−4.78584	−0.214244	−0.107122	+	0.994246i	$0.534163\pi$
$500$	1.00000	0.0447214
$501$	−3.24106	−0.144800
$502$	−1.05587	−0.0471258
$503$	33.5981	1.49807	0.749033	−	0.662532i	$-0.230518\pi$
$503$	33.5981	1.49807	0.749033	+	0.662532i	$0.230518\pi$
$504$	1.51836	0.0676333
$505$	0.460958	0.0205124
$506$	15.5973	0.693386
$507$	−8.21004	−0.364621
$508$	19.0065	0.843275
$509$	−15.8437	−0.702261	−0.351131	−	0.936326i	$-0.614203\pi$
$509$	−15.8437	−0.702261	−0.351131	+	0.936326i	$0.614203\pi$
$510$	−1.08701	−0.0481335
$511$	5.28573	0.233827
$512$	−1.00000	−0.0441942
$513$	4.62957	0.204400
$514$	3.44508	0.151956
$515$	18.0921	0.797233
$516$	−1.97510	−0.0869491
$517$	22.5339	0.991039
$518$	2.08479	0.0916005
$519$	−4.18156	−0.183550
$520$	−6.85447	−0.300588
$521$	−21.2698	−0.931845	−0.465922	−	0.884826i	$-0.654277\pi$
$521$	−21.2698	−0.931845	−0.465922	+	0.884826i	$0.654277\pi$
$522$	−10.1740	−0.445303
$523$	32.9099	1.43905	0.719525	−	0.694467i	$-0.244360\pi$
$523$	32.9099	1.43905	0.719525	+	0.694467i	$0.244360\pi$
$524$	17.3081	0.756110
$525$	−0.124699	−0.00544229
$526$	−18.6255	−0.812111
$527$	11.8249	0.515101
$528$	0.921853	0.0401185
$529$	−6.29194	−0.273562
$530$	0.290204	0.0126057
$531$	1.74301	0.0756400
$532$	1.66474	0.0721757
$533$	58.4781	2.53297
$534$	1.26845	0.0548911
$535$	1.18223	0.0511122
$536$	−7.07758	−0.305705
$537$	4.42856	0.191106
$538$	−1.64855	−0.0710741
$539$	25.6941	1.10672
$540$	1.43543	0.0617709
$541$	−25.4354	−1.09355	−0.546776	−	0.837279i	$-0.684145\pi$
$541$	−25.4354	−1.09355	−0.546776	+	0.837279i	$0.684145\pi$
$542$	−18.3965	−0.790199
$543$	2.94534	0.126396
$544$	4.49943	0.192912
$545$	18.5387	0.794112
$546$	0.854742	0.0365796
$547$	−9.91277	−0.423840	−0.211920	−	0.977287i	$-0.567972\pi$
$547$	−9.91277	−0.423840	−0.211920	+	0.977287i	$0.567972\pi$
$548$	12.8467	0.548784
$549$	−12.7315	−0.543368
$550$	3.81581	0.162707
$551$	−11.1548	−0.475210
$552$	0.987501	0.0420308
$553$	4.40913	0.187495
$554$	21.2112	0.901176
$555$	0.975776	0.0414194
$556$	−12.8590	−0.545342
$557$	−26.1499	−1.10801	−0.554003	−	0.832515i	$-0.686900\pi$
$557$	−26.1499	−1.10801	−0.554003	+	0.832515i	$0.686900\pi$
$558$	−7.73087	−0.327274
$559$	56.0388	2.37019
$560$	0.516163	0.0218119
$561$	−4.14782	−0.175121
$562$	−11.3129	−0.477205
$563$	−11.5076	−0.484986	−0.242493	−	0.970153i	$-0.577965\pi$
$563$	−11.5076	−0.484986	−0.242493	+	0.970153i	$0.577965\pi$
$564$	1.42667	0.0600737
$565$	−3.90052	−0.164096
$566$	6.06011	0.254726
$567$	4.37609	0.183779
$568$	6.96475	0.292234
$569$	10.6106	0.444820	0.222410	−	0.974953i	$-0.428608\pi$
$569$	10.6106	0.444820	0.222410	+	0.974953i	$0.428608\pi$
$570$	0.779174	0.0326360
$571$	8.06845	0.337654	0.168827	−	0.985646i	$-0.446002\pi$
$571$	8.06845	0.337654	0.168827	+	0.985646i	$0.446002\pi$
$572$	−26.1554	−1.09361
$573$	0.489453	0.0204472
$574$	−4.40359	−0.183802
$575$	4.08755	0.170463
$576$	−2.94164	−0.122568
$577$	−25.1104	−1.04536	−0.522679	−	0.852530i	$-0.675067\pi$
$577$	−25.1104	−1.04536	−0.522679	+	0.852530i	$0.675067\pi$
$578$	−3.24491	−0.134970
$579$	5.79308	0.240752
$580$	−3.45861	−0.143611
$581$	−4.57492	−0.189800
$582$	−3.58172	−0.148467
$583$	1.10737	0.0458624
$584$	−10.2404	−0.423752
$585$	−20.1633	−0.833652
$586$	−6.19065	−0.255733
$587$	−21.9035	−0.904053	−0.452026	−	0.892005i	$-0.649299\pi$
$587$	−21.9035	−0.904053	−0.452026	+	0.892005i	$0.649299\pi$
$588$	1.62675	0.0670860
$589$	−8.47616	−0.349254
$590$	0.592529	0.0243940
$591$	−2.89376	−0.119033
$592$	−4.03902	−0.166003
$593$	−33.8509	−1.39009	−0.695044	−	0.718967i	$-0.744615\pi$
$593$	−33.8509	−1.39009	−0.695044	+	0.718967i	$0.744615\pi$
$594$	5.47731	0.224737
$595$	−2.32244	−0.0952108
$596$	−2.75968	−0.113041
$597$	−3.91556	−0.160253
$598$	−28.0180	−1.14574
$599$	−16.6180	−0.678991	−0.339496	−	0.940608i	$-0.610256\pi$
$599$	−16.6180	−0.678991	−0.339496	+	0.940608i	$0.610256\pi$
$600$	0.241588	0.00986277
$601$	35.3538	1.44211	0.721055	−	0.692878i	$-0.243657\pi$
$601$	35.3538	1.44211	0.721055	+	0.692878i	$0.243657\pi$
$602$	−4.21990	−0.171990
$603$	−20.8197	−0.847842
$604$	11.3931	0.463577
$605$	3.56042	0.144752
$606$	0.111362	0.00452376
$607$	7.65318	0.310633	0.155316	−	0.987865i	$-0.450360\pi$
$607$	7.65318	0.310633	0.155316	+	0.987865i	$0.450360\pi$
$608$	−3.22522	−0.130800
$609$	0.431284	0.0174765
$610$	−4.32804	−0.175237
$611$	−40.4783	−1.63758
$612$	13.2357	0.535021
$613$	14.0492	0.567443	0.283721	−	0.958907i	$-0.408431\pi$
$613$	14.0492	0.567443	0.283721	+	0.958907i	$0.408431\pi$
$614$	−22.3695	−0.902761
$615$	−2.06108	−0.0831107
$616$	1.96958	0.0793567
$617$	−35.6213	−1.43406	−0.717029	−	0.697043i	$-0.754499\pi$
$617$	−35.6213	−1.43406	−0.717029	+	0.697043i	$0.754499\pi$
$618$	4.37083	0.175820
$619$	−34.2803	−1.37784	−0.688920	−	0.724837i	$-0.741915\pi$
$619$	−34.2803	−1.37784	−0.688920	+	0.724837i	$0.741915\pi$
$620$	−2.62808	−0.105546
$621$	5.86737	0.235450
$622$	−20.5078	−0.822287
$623$	2.71010	0.108578
$624$	−1.65595	−0.0662912
$625$	1.00000	0.0400000
$626$	−15.8651	−0.634098
$627$	2.97318	0.118737
$628$	−21.1622	−0.844464
$629$	18.1733	0.724617
$630$	1.51836	0.0604930
$631$	−19.1872	−0.763829	−0.381915	−	0.924198i	$-0.624735\pi$
$631$	−19.1872	−0.763829	−0.381915	+	0.924198i	$0.624735\pi$
$632$	−8.54212	−0.339787
$633$	−5.98991	−0.238078
$634$	5.95150	0.236364
$635$	19.0065	0.754248
$636$	0.0701097	0.00278003
$637$	−46.1551	−1.82873
$638$	−13.1974	−0.522491
$639$	20.4878	0.810483
$640$	−1.00000	−0.0395285
$641$	−11.2440	−0.444110	−0.222055	−	0.975034i	$-0.571276\pi$
$641$	−11.2440	−0.444110	−0.222055	+	0.975034i	$0.571276\pi$
$642$	0.285612	0.0112722
$643$	10.3775	0.409247	0.204623	−	0.978841i	$-0.434403\pi$
$643$	10.3775	0.409247	0.204623	+	0.978841i	$0.434403\pi$
$644$	2.10984	0.0831394
$645$	−1.97510	−0.0777696
$646$	14.5117	0.570954
$647$	6.78731	0.266837	0.133418	−	0.991060i	$-0.457405\pi$
$647$	6.78731	0.266837	0.133418	+	0.991060i	$0.457405\pi$
$648$	−8.47813	−0.333052
$649$	2.26098	0.0887513
$650$	−6.85447	−0.268854
$651$	0.327718	0.0128443
$652$	−14.9937	−0.587199
$653$	32.1745	1.25909	0.629543	−	0.776966i	$-0.283242\pi$
$653$	32.1745	1.25909	0.629543	+	0.776966i	$0.283242\pi$
$654$	4.47872	0.175132
$655$	17.3081	0.676285
$656$	8.53139	0.333095
$657$	−30.1236	−1.17523
$658$	3.04815	0.118829
$659$	14.9181	0.581125	0.290563	−	0.956856i	$-0.406158\pi$
$659$	14.9181	0.581125	0.290563	+	0.956856i	$0.406158\pi$
$660$	0.921853	0.0358831
$661$	−25.4998	−0.991828	−0.495914	−	0.868372i	$-0.665167\pi$
$661$	−25.4998	−0.991828	−0.495914	+	0.868372i	$0.665167\pi$
$662$	−23.9842	−0.932174
$663$	7.45086	0.289367
$664$	8.86332	0.343963
$665$	1.66474	0.0645559
$666$	−11.8813	−0.460392
$667$	−14.1373	−0.547397
$668$	13.4157	0.519068
$669$	4.24987	0.164309
$670$	−7.07758	−0.273431
$671$	−16.5150	−0.637554
$672$	0.124699	0.00481035
$673$	−10.6627	−0.411018	−0.205509	−	0.978655i	$-0.565885\pi$
$673$	−10.6627	−0.411018	−0.205509	+	0.978655i	$0.565885\pi$
$674$	22.1557	0.853408
$675$	1.43543	0.0552495
$676$	33.9837	1.30707
$677$	24.1367	0.927647	0.463824	−	0.885928i	$-0.346477\pi$
$677$	24.1367	0.927647	0.463824	+	0.885928i	$0.346477\pi$
$678$	−0.942317	−0.0361895
$679$	−7.65250	−0.293676
$680$	4.49943	0.172545
$681$	−0.783351	−0.0300181
$682$	−10.0283	−0.384003
$683$	−25.2150	−0.964826	−0.482413	−	0.875944i	$-0.660240\pi$
$683$	−25.2150	−0.964826	−0.482413	+	0.875944i	$0.660240\pi$
$684$	−9.48743	−0.362761
$685$	12.8467	0.490847
$686$	7.08876	0.270650
$687$	−4.24163	−0.161828
$688$	8.17552	0.311689
$689$	−1.98920	−0.0757823
$690$	0.987501	0.0375935
$691$	−14.3717	−0.546727	−0.273364	−	0.961911i	$-0.588136\pi$
$691$	−14.3717	−0.546727	−0.273364	+	0.961911i	$0.588136\pi$
$692$	17.3087	0.657977
$693$	5.79379	0.220088
$694$	6.49293	0.246468
$695$	−12.8590	−0.487769
$696$	−0.835558	−0.0316717
$697$	−38.3864	−1.45399
$698$	−27.6384	−1.04613
$699$	2.88948	0.109290
$700$	0.516163	0.0195091
$701$	−22.5149	−0.850375	−0.425187	−	0.905105i	$-0.639792\pi$
$701$	−22.5149	−0.850375	−0.425187	+	0.905105i	$0.639792\pi$
$702$	−9.83907	−0.371352
$703$	−13.0267	−0.491313
$704$	−3.81581	−0.143814
$705$	1.42667	0.0537315
$706$	−31.0471	−1.16847
$707$	0.237929	0.00894826
$708$	0.143148	0.00537982
$709$	9.44356	0.354660	0.177330	−	0.984151i	$-0.443254\pi$
$709$	9.44356	0.354660	0.177330	+	0.984151i	$0.443254\pi$
$710$	6.96475	0.261382
$711$	−25.1278	−0.942367
$712$	−5.25047	−0.196770
$713$	−10.7424	−0.402307
$714$	−0.561073	−0.0209976
$715$	−26.1554	−0.978155
$716$	−18.3311	−0.685064
$717$	−6.37181	−0.237959
$718$	−16.7660	−0.625701
$719$	13.9425	0.519967	0.259984	−	0.965613i	$-0.416283\pi$
$719$	13.9425	0.519967	0.259984	+	0.965613i	$0.416283\pi$
$720$	−2.94164	−0.109628
$721$	9.33847	0.347783
$722$	8.59793	0.319982
$723$	3.37157	0.125390
$724$	−12.1916	−0.453097
$725$	−3.45861	−0.128450
$726$	0.860153	0.0319233
$727$	31.9379	1.18451	0.592255	−	0.805750i	$-0.298238\pi$
$727$	31.9379	1.18451	0.592255	+	0.805750i	$0.298238\pi$
$728$	−3.53802	−0.131128
$729$	−23.8992	−0.885156
$730$	−10.2404	−0.379015
$731$	−36.7852	−1.36055
$732$	−1.04560	−0.0386465
$733$	−47.3691	−1.74962	−0.874810	−	0.484467i	$-0.839014\pi$
$733$	−47.3691	−1.74962	−0.874810	+	0.484467i	$0.839014\pi$
$734$	10.1368	0.374155
$735$	1.62675	0.0600035
$736$	−4.08755	−0.150669
$737$	−27.0067	−0.994805
$738$	25.0962	0.923805
$739$	24.1837	0.889613	0.444807	−	0.895627i	$-0.353272\pi$
$739$	24.1837	0.889613	0.444807	+	0.895627i	$0.353272\pi$
$740$	−4.03902	−0.148477
$741$	−5.34082	−0.196200
$742$	0.149793	0.00549906
$743$	−18.2345	−0.668960	−0.334480	−	0.942403i	$-0.608561\pi$
$743$	−18.2345	−0.668960	−0.334480	+	0.942403i	$0.608561\pi$
$744$	−0.634913	−0.0232770
$745$	−2.75968	−0.101107
$746$	36.5306	1.33748
$747$	26.0727	0.953948
$748$	17.1690	0.627761
$749$	0.610222	0.0222970
$750$	0.241588	0.00882153
$751$	−45.7160	−1.66820	−0.834101	−	0.551612i	$-0.814013\pi$
$751$	−45.7160	−1.66820	−0.834101	+	0.551612i	$0.814013\pi$
$752$	−5.90540	−0.215348
$753$	−0.255085	−0.00929583
$754$	23.7069	0.863356
$755$	11.3931	0.414636
$756$	0.740913	0.0269468
$757$	49.2202	1.78894	0.894469	−	0.447129i	$-0.147554\pi$
$757$	49.2202	1.78894	0.894469	+	0.447129i	$0.147554\pi$
$758$	−4.32940	−0.157251
$759$	3.76812	0.136774
$760$	−3.22522	−0.116991
$761$	−38.7167	−1.40348	−0.701739	−	0.712434i	$-0.747593\pi$
$761$	−38.7167	−1.40348	−0.701739	+	0.712434i	$0.747593\pi$
$762$	4.59172	0.166341
$763$	9.56900	0.346421
$764$	−2.02598	−0.0732975
$765$	13.2357	0.478538
$766$	−35.9374	−1.29847
$767$	−4.06147	−0.146651
$768$	−0.241588	−0.00871754
$769$	17.5498	0.632863	0.316431	−	0.948615i	$-0.397515\pi$
$769$	17.5498	0.632863	0.316431	+	0.948615i	$0.397515\pi$
$770$	1.96958	0.0709788
$771$	0.832289	0.0299741
$772$	−23.9792	−0.863030
$773$	−35.0922	−1.26218	−0.631089	−	0.775710i	$-0.717392\pi$
$773$	−35.0922	−1.26218	−0.631089	+	0.775710i	$0.717392\pi$
$774$	24.0494	0.864438
$775$	−2.62808	−0.0944036
$776$	14.8257	0.532213
$777$	0.503660	0.0180687
$778$	−12.4327	−0.445735
$779$	27.5156	0.985850
$780$	−1.65595	−0.0592927
$781$	26.5762	0.950970
$782$	18.3917	0.657685
$783$	−4.96458	−0.177420
$784$	−6.73358	−0.240485
$785$	−21.1622	−0.755311
$786$	4.18143	0.149147
$787$	−11.2837	−0.402221	−0.201110	−	0.979569i	$-0.564455\pi$
$787$	−11.2837	−0.402221	−0.201110	+	0.979569i	$0.564455\pi$
$788$	11.9781	0.426702
$789$	−4.49969	−0.160193
$790$	−8.54212	−0.303915
$791$	−2.01330	−0.0715848
$792$	−11.2247	−0.398853
$793$	29.6664	1.05348
$794$	−27.2938	−0.968620
$795$	0.0701097	0.00248654
$796$	16.2076	0.574464
$797$	−42.2264	−1.49574	−0.747868	−	0.663847i	$-0.768923\pi$
$797$	−42.2264	−1.49574	−0.747868	+	0.663847i	$0.768923\pi$
$798$	0.402181	0.0142370
$799$	26.5709	0.940012
$800$	−1.00000	−0.0353553
$801$	−15.4450	−0.545721
$802$	1.00000	0.0353112
$803$	−39.0755	−1.37895
$804$	−1.70986	−0.0603019
$805$	2.10984	0.0743622
$806$	18.0141	0.634520
$807$	−0.398269	−0.0140197
$808$	−0.460958	−0.0162164
$809$	−23.3762	−0.821862	−0.410931	−	0.911666i	$-0.634796\pi$
$809$	−23.3762	−0.821862	−0.410931	+	0.911666i	$0.634796\pi$
$810$	−8.47813	−0.297891
$811$	−38.0678	−1.33674	−0.668371	−	0.743828i	$-0.733008\pi$
$811$	−38.0678	−1.33674	−0.668371	+	0.743828i	$0.733008\pi$
$812$	−1.78521	−0.0626485
$813$	−4.44437	−0.155871
$814$	−15.4121	−0.540195
$815$	−14.9937	−0.525207
$816$	1.08701	0.0380529
$817$	26.3679	0.922495
$818$	−13.9416	−0.487457
$819$	−10.4076	−0.363670
$820$	8.53139	0.297929
$821$	23.3511	0.814959	0.407479	−	0.913214i	$-0.366408\pi$
$821$	23.3511	0.814959	0.407479	+	0.913214i	$0.366408\pi$
$822$	3.10360	0.108251
$823$	39.6043	1.38052	0.690259	−	0.723562i	$-0.257496\pi$
$823$	39.6043	1.38052	0.690259	+	0.723562i	$0.257496\pi$
$824$	−18.0921	−0.630268
$825$	0.921853	0.0320948
$826$	0.305842	0.0106416
$827$	−55.2596	−1.92156	−0.960782	−	0.277305i	$-0.910559\pi$
$827$	−55.2596	−1.92156	−0.960782	+	0.277305i	$0.910559\pi$
$828$	−12.0241	−0.417866
$829$	−6.06745	−0.210731	−0.105366	−	0.994434i	$-0.533601\pi$
$829$	−6.06745	−0.210731	−0.105366	+	0.994434i	$0.533601\pi$
$830$	8.86332	0.307650
$831$	5.12435	0.177762
$832$	6.85447	0.237636
$833$	30.2973	1.04974
$834$	−3.10657	−0.107572
$835$	13.4157	0.464269
$836$	−12.3068	−0.425641
$837$	−3.77242	−0.130394
$838$	−17.1648	−0.592948
$839$	−7.30427	−0.252171	−0.126086	−	0.992019i	$-0.540241\pi$
$839$	−7.30427	−0.252171	−0.126086	+	0.992019i	$0.540241\pi$
$840$	0.124699	0.00430251
$841$	−17.0380	−0.587517
$842$	−32.1970	−1.10958
$843$	−2.73305	−0.0941312
$844$	24.7940	0.853443
$845$	33.9837	1.16908
$846$	−17.3715	−0.597245
$847$	1.83776	0.0631461
$848$	−0.290204	−0.00996566
$849$	1.46405	0.0502460
$850$	4.49943	0.154329
$851$	−16.5097	−0.565945
$852$	1.68260	0.0576448
$853$	46.7327	1.60010	0.800049	−	0.599935i	$-0.204807\pi$
$853$	46.7327	1.60010	0.800049	+	0.599935i	$0.204807\pi$
$854$	−2.23397	−0.0764450
$855$	−9.48743	−0.324463
$856$	−1.18223	−0.0404077
$857$	−12.8692	−0.439605	−0.219803	−	0.975544i	$-0.570541\pi$
$857$	−12.8692	−0.439605	−0.219803	+	0.975544i	$0.570541\pi$
$858$	−6.31881	−0.215721
$859$	31.0281	1.05866	0.529332	−	0.848415i	$-0.322443\pi$
$859$	31.0281	1.05866	0.529332	+	0.848415i	$0.322443\pi$
$860$	8.17552	0.278783
$861$	−1.06385	−0.0362560
$862$	18.6957	0.636780
$863$	−9.35428	−0.318423	−0.159212	−	0.987244i	$-0.550895\pi$
$863$	−9.35428	−0.318423	−0.159212	+	0.987244i	$0.550895\pi$
$864$	−1.43543	−0.0488342
$865$	17.3087	0.588513
$866$	−26.2301	−0.891335
$867$	−0.783930	−0.0266237
$868$	−1.35652	−0.0460433
$869$	−32.5951	−1.10571
$870$	−0.835558	−0.0283281
$871$	48.5130	1.64380
$872$	−18.5387	−0.627800
$873$	43.6119	1.47604
$874$	−13.1833	−0.445930
$875$	0.516163	0.0174495
$876$	−2.47396	−0.0835873
$877$	14.1281	0.477073	0.238536	−	0.971134i	$-0.423332\pi$
$877$	14.1281	0.477073	0.238536	+	0.971134i	$0.423332\pi$
$878$	14.2669	0.481483
$879$	−1.49558	−0.0504448
$880$	−3.81581	−0.128631
$881$	15.9899	0.538714	0.269357	−	0.963040i	$-0.413189\pi$
$881$	15.9899	0.538714	0.269357	+	0.963040i	$0.413189\pi$
$882$	−19.8077	−0.666961
$883$	−13.7689	−0.463359	−0.231679	−	0.972792i	$-0.574422\pi$
$883$	−13.7689	−0.463359	−0.231679	+	0.972792i	$0.574422\pi$
$884$	−30.8412	−1.03730
$885$	0.143148	0.00481186
$886$	26.6741	0.896134
$887$	54.2852	1.82272	0.911359	−	0.411613i	$-0.135034\pi$
$887$	54.2852	1.82272	0.911359	+	0.411613i	$0.135034\pi$
$888$	−0.975776	−0.0327449
$889$	9.81043	0.329031
$890$	−5.25047	−0.175996
$891$	−32.3509	−1.08380
$892$	−17.5914	−0.589004
$893$	−19.0462	−0.637358
$894$	−0.666705	−0.0222980
$895$	−18.3311	−0.612740
$896$	−0.516163	−0.0172438
$897$	−6.76879	−0.226003
$898$	−15.4245	−0.514721
$899$	9.08953	0.303153
$900$	−2.94164	−0.0980545
$901$	1.30576	0.0435010
$902$	32.5542	1.08394
$903$	−1.01948	−0.0339260
$904$	3.90052	0.129729
$905$	−12.1916	−0.405262
$906$	2.75242	0.0914432
$907$	34.7168	1.15275	0.576376	−	0.817185i	$-0.304466\pi$
$907$	34.7168	1.15275	0.576376	+	0.817185i	$0.304466\pi$
$908$	3.24251	0.107607
$909$	−1.35597	−0.0449747
$910$	−3.53802	−0.117284
$911$	56.6511	1.87694	0.938468	−	0.345366i	$-0.112245\pi$
$911$	56.6511	1.87694	0.938468	+	0.345366i	$0.112245\pi$
$912$	−0.779174	−0.0258010
$913$	33.8208	1.11930
$914$	−13.9856	−0.462604
$915$	−1.04560	−0.0345665
$916$	17.5573	0.580111
$917$	8.93383	0.295021
$918$	6.45860	0.213166
$919$	−12.1292	−0.400105	−0.200052	−	0.979785i	$-0.564111\pi$
$919$	−12.1292	−0.400105	−0.200052	+	0.979785i	$0.564111\pi$
$920$	−4.08755	−0.134763
$921$	−5.40420	−0.178075
$922$	−19.3169	−0.636168
$923$	−47.7396	−1.57137
$924$	0.475826	0.0156535
$925$	−4.03902	−0.132802
$926$	25.6024	0.841346
$927$	−53.2204	−1.74799
$928$	3.45861	0.113535
$929$	−8.44092	−0.276937	−0.138469	−	0.990367i	$-0.544218\pi$
$929$	−8.44092	−0.276937	−0.138469	+	0.990367i	$0.544218\pi$
$930$	−0.634913	−0.0208196
$931$	−21.7173	−0.711755
$932$	−11.9604	−0.391776
$933$	−4.95443	−0.162201
$934$	9.92229	0.324667
$935$	17.1690	0.561486
$936$	20.1633	0.659059
$937$	−16.0511	−0.524368	−0.262184	−	0.965018i	$-0.584443\pi$
$937$	−16.0511	−0.524368	−0.262184	+	0.965018i	$0.584443\pi$
$938$	−3.65319	−0.119281
$939$	−3.83282	−0.125079
$940$	−5.90540	−0.192613
$941$	−34.8623	−1.13648	−0.568239	−	0.822864i	$-0.692375\pi$
$941$	−34.8623	−1.13648	−0.568239	+	0.822864i	$0.692375\pi$
$942$	−5.11253	−0.166575
$943$	34.8725	1.13560
$944$	−0.592529	−0.0192852
$945$	0.740913	0.0241019
$946$	31.1962	1.01428
$947$	51.1469	1.66205	0.831026	−	0.556234i	$-0.187754\pi$
$947$	51.1469	1.66205	0.831026	+	0.556234i	$0.187754\pi$
$948$	−2.06367	−0.0670249
$949$	70.1927	2.27855
$950$	−3.22522	−0.104640
$951$	1.43781	0.0466241
$952$	2.32244	0.0752708
$953$	23.0830	0.747733	0.373866	−	0.927483i	$-0.378032\pi$
$953$	23.0830	0.747733	0.373866	+	0.927483i	$0.378032\pi$
$954$	−0.853675	−0.0276388
$955$	−2.02598	−0.0655593
$956$	26.3747	0.853020
$957$	−3.18833	−0.103064
$958$	−33.2677	−1.07483
$959$	6.63099	0.214126
$960$	−0.241588	−0.00779720
$961$	−24.0932	−0.777199
$962$	27.6853	0.892610
$963$	−3.47768	−0.112067
$964$	−13.9559	−0.449489
$965$	−23.9792	−0.771918
$966$	0.509712	0.0163997
$967$	−25.6649	−0.825326	−0.412663	−	0.910884i	$-0.635401\pi$
$967$	−25.6649	−0.825326	−0.412663	+	0.910884i	$0.635401\pi$
$968$	−3.56042	−0.114436
$969$	3.50584	0.112624
$970$	14.8257	0.476026
$971$	35.1332	1.12748	0.563740	−	0.825952i	$-0.309362\pi$
$971$	35.1332	1.12748	0.563740	+	0.825952i	$0.309362\pi$
$972$	−6.35449	−0.203820
$973$	−6.63733	−0.212783
$974$	17.5974	0.563859
$975$	−1.65595	−0.0530330
$976$	4.32804	0.138537
$977$	−12.5701	−0.402154	−0.201077	−	0.979575i	$-0.564444\pi$
$977$	−12.5701	−0.402154	−0.201077	+	0.979575i	$0.564444\pi$
$978$	−3.62229	−0.115828
$979$	−20.0348	−0.640315
$980$	−6.73358	−0.215096
$981$	−54.5342	−1.74114
$982$	4.30157	0.137269
$983$	49.2035	1.56935	0.784674	−	0.619909i	$-0.212830\pi$
$983$	49.2035	1.56935	0.784674	+	0.619909i	$0.212830\pi$
$984$	2.06108	0.0657048
$985$	11.9781	0.381654
$986$	−15.5618	−0.495589
$987$	0.736394	0.0234397
$988$	22.1072	0.703323
$989$	33.4178	1.06263
$990$	−11.2247	−0.356745
$991$	−26.5195	−0.842419	−0.421209	−	0.906963i	$-0.638394\pi$
$991$	−26.5195	−0.842419	−0.421209	+	0.906963i	$0.638394\pi$
$992$	2.62808	0.0834418
$993$	−5.79429	−0.183876
$994$	3.59495	0.114025
$995$	16.2076	0.513816
$996$	2.14127	0.0678487
$997$	40.8600	1.29405	0.647025	−	0.762469i	$-0.276013\pi$
$997$	40.8600	1.29405	0.647025	+	0.762469i	$0.276013\pi$
$998$	4.78584	0.151493
$999$	−5.79771	−0.183431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.241588 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.241588 q^{6} +0.516163 q^{7} -1.00000 q^{8} -2.94164 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.241588 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.241588 q^{6} +0.516163 q^{7} -1.00000 q^{8} -2.94164 q^{9} -1.00000 q^{10} -3.81581 q^{11} -0.241588 q^{12} +6.85447 q^{13} -0.516163 q^{14} -0.241588 q^{15} +1.00000 q^{16} -4.49943 q^{17} +2.94164 q^{18} +3.22522 q^{19} +1.00000 q^{20} -0.124699 q^{21} +3.81581 q^{22} +4.08755 q^{23} +0.241588 q^{24} +1.00000 q^{25} -6.85447 q^{26} +1.43543 q^{27} +0.516163 q^{28} -3.45861 q^{29} +0.241588 q^{30} -2.62808 q^{31} -1.00000 q^{32} +0.921853 q^{33} +4.49943 q^{34} +0.516163 q^{35} -2.94164 q^{36} -4.03902 q^{37} -3.22522 q^{38} -1.65595 q^{39} -1.00000 q^{40} +8.53139 q^{41} +0.124699 q^{42} +8.17552 q^{43} -3.81581 q^{44} -2.94164 q^{45} -4.08755 q^{46} -5.90540 q^{47} -0.241588 q^{48} -6.73358 q^{49} -1.00000 q^{50} +1.08701 q^{51} +6.85447 q^{52} -0.290204 q^{53} -1.43543 q^{54} -3.81581 q^{55} -0.516163 q^{56} -0.779174 q^{57} +3.45861 q^{58} -0.592529 q^{59} -0.241588 q^{60} +4.32804 q^{61} +2.62808 q^{62} -1.51836 q^{63} +1.00000 q^{64} +6.85447 q^{65} -0.921853 q^{66} +7.07758 q^{67} -4.49943 q^{68} -0.987501 q^{69} -0.516163 q^{70} -6.96475 q^{71} +2.94164 q^{72} +10.2404 q^{73} +4.03902 q^{74} -0.241588 q^{75} +3.22522 q^{76} -1.96958 q^{77} +1.65595 q^{78} +8.54212 q^{79} +1.00000 q^{80} +8.47813 q^{81} -8.53139 q^{82} -8.86332 q^{83} -0.124699 q^{84} -4.49943 q^{85} -8.17552 q^{86} +0.835558 q^{87} +3.81581 q^{88} +5.25047 q^{89} +2.94164 q^{90} +3.53802 q^{91} +4.08755 q^{92} +0.634913 q^{93} +5.90540 q^{94} +3.22522 q^{95} +0.241588 q^{96} -14.8257 q^{97} +6.73358 q^{98} +11.2247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 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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