LMFDB - Embedded newform 4010.2.a.h.1.4

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 8x^{7} + 16x^{6} + 17x^{5} - 36x^{4} - 4x^{3} + 17x^{2} - 2 $ x^9 - 2x^8 - 8x^7 + 16x^6 + 17x^5 - 36x^4 - 4x^3 + 17*x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.07126$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.922780 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.922780 q^{6} -2.45091 q^{7} +1.00000 q^{8} -2.14848 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.922780 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.922780 q^{6} -2.45091 q^{7} +1.00000 q^{8} -2.14848 q^{9} +1.00000 q^{10} -2.04640 q^{11} -0.922780 q^{12} +2.73473 q^{13} -2.45091 q^{14} -0.922780 q^{15} +1.00000 q^{16} -1.97140 q^{17} -2.14848 q^{18} +2.65749 q^{19} +1.00000 q^{20} +2.26165 q^{21} -2.04640 q^{22} +3.70905 q^{23} -0.922780 q^{24} +1.00000 q^{25} +2.73473 q^{26} +4.75091 q^{27} -2.45091 q^{28} -4.65180 q^{29} -0.922780 q^{30} +5.51086 q^{31} +1.00000 q^{32} +1.88838 q^{33} -1.97140 q^{34} -2.45091 q^{35} -2.14848 q^{36} -0.227375 q^{37} +2.65749 q^{38} -2.52355 q^{39} +1.00000 q^{40} +0.00373133 q^{41} +2.26165 q^{42} -7.62879 q^{43} -2.04640 q^{44} -2.14848 q^{45} +3.70905 q^{46} -7.35091 q^{47} -0.922780 q^{48} -0.993037 q^{49} +1.00000 q^{50} +1.81917 q^{51} +2.73473 q^{52} -4.94341 q^{53} +4.75091 q^{54} -2.04640 q^{55} -2.45091 q^{56} -2.45228 q^{57} -4.65180 q^{58} +0.966468 q^{59} -0.922780 q^{60} -11.6911 q^{61} +5.51086 q^{62} +5.26572 q^{63} +1.00000 q^{64} +2.73473 q^{65} +1.88838 q^{66} -2.64188 q^{67} -1.97140 q^{68} -3.42263 q^{69} -2.45091 q^{70} -0.355281 q^{71} -2.14848 q^{72} -5.79466 q^{73} -0.227375 q^{74} -0.922780 q^{75} +2.65749 q^{76} +5.01554 q^{77} -2.52355 q^{78} -15.2199 q^{79} +1.00000 q^{80} +2.06138 q^{81} +0.00373133 q^{82} -3.67210 q^{83} +2.26165 q^{84} -1.97140 q^{85} -7.62879 q^{86} +4.29259 q^{87} -2.04640 q^{88} -17.8319 q^{89} -2.14848 q^{90} -6.70258 q^{91} +3.70905 q^{92} -5.08531 q^{93} -7.35091 q^{94} +2.65749 q^{95} -0.922780 q^{96} -12.0305 q^{97} -0.993037 q^{98} +4.39664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * 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
$3$	−0.922780	−0.532767	−0.266384	−	0.963867i	$-0.585829\pi$
$3$	−0.922780	−0.532767	−0.266384	+	0.963867i	$0.585829\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.922780	−0.376723
$7$	−2.45091	−0.926357	−0.463179	−	0.886265i	$-0.653291\pi$
$7$	−2.45091	−0.926357	−0.463179	+	0.886265i	$0.653291\pi$
$8$	1.00000	0.353553
$9$	−2.14848	−0.716159
$10$	1.00000	0.316228
$11$	−2.04640	−0.617013	−0.308506	−	0.951222i	$-0.599829\pi$
$11$	−2.04640	−0.617013	−0.308506	+	0.951222i	$0.599829\pi$
$12$	−0.922780	−0.266384
$13$	2.73473	0.758478	0.379239	−	0.925299i	$-0.376186\pi$
$13$	2.73473	0.758478	0.379239	+	0.925299i	$0.376186\pi$
$14$	−2.45091	−0.655033
$15$	−0.922780	−0.238261
$16$	1.00000	0.250000
$17$	−1.97140	−0.478135	−0.239067	−	0.971003i	$-0.576842\pi$
$17$	−1.97140	−0.478135	−0.239067	+	0.971003i	$0.576842\pi$
$18$	−2.14848	−0.506401
$19$	2.65749	0.609669	0.304835	−	0.952405i	$-0.401399\pi$
$19$	2.65749	0.609669	0.304835	+	0.952405i	$0.401399\pi$
$20$	1.00000	0.223607
$21$	2.26165	0.493533
$22$	−2.04640	−0.436294
$23$	3.70905	0.773390	0.386695	−	0.922208i	$-0.373617\pi$
$23$	3.70905	0.773390	0.386695	+	0.922208i	$0.373617\pi$
$24$	−0.922780	−0.188362
$25$	1.00000	0.200000
$26$	2.73473	0.536325
$27$	4.75091	0.914313
$28$	−2.45091	−0.463179
$29$	−4.65180	−0.863817	−0.431909	−	0.901917i	$-0.642160\pi$
$29$	−4.65180	−0.863817	−0.431909	+	0.901917i	$0.642160\pi$
$30$	−0.922780	−0.168476
$31$	5.51086	0.989779	0.494890	−	0.868956i	$-0.335209\pi$
$31$	5.51086	0.989779	0.494890	+	0.868956i	$0.335209\pi$
$32$	1.00000	0.176777
$33$	1.88838	0.328724
$34$	−1.97140	−0.338092
$35$	−2.45091	−0.414279
$36$	−2.14848	−0.358079
$37$	−0.227375	−0.0373803	−0.0186901	−	0.999825i	$-0.505950\pi$
$37$	−0.227375	−0.0373803	−0.0186901	+	0.999825i	$0.505950\pi$
$38$	2.65749	0.431101
$39$	−2.52355	−0.404092
$40$	1.00000	0.158114
$41$	0.00373133	0.000582736 0	0.000291368	−	1.00000i	$-0.499907\pi$
$41$	0.00373133	0.000582736 0	0.000291368		1.00000i	$0.499907\pi$
$42$	2.26165	0.348980
$43$	−7.62879	−1.16338	−0.581690	−	0.813411i	$-0.697608\pi$
$43$	−7.62879	−1.16338	−0.581690	+	0.813411i	$0.697608\pi$
$44$	−2.04640	−0.308506
$45$	−2.14848	−0.320276
$46$	3.70905	0.546869
$47$	−7.35091	−1.07224	−0.536120	−	0.844142i	$-0.680111\pi$
$47$	−7.35091	−1.07224	−0.536120	+	0.844142i	$0.680111\pi$
$48$	−0.922780	−0.133192
$49$	−0.993037	−0.141862
$50$	1.00000	0.141421
$51$	1.81917	0.254735
$52$	2.73473	0.379239
$53$	−4.94341	−0.679030	−0.339515	−	0.940601i	$-0.610263\pi$
$53$	−4.94341	−0.679030	−0.339515	+	0.940601i	$0.610263\pi$
$54$	4.75091	0.646517
$55$	−2.04640	−0.275937
$56$	−2.45091	−0.327517
$57$	−2.45228	−0.324812
$58$	−4.65180	−0.610811
$59$	0.966468	0.125823	0.0629117	−	0.998019i	$-0.479961\pi$
$59$	0.966468	0.125823	0.0629117	+	0.998019i	$0.479961\pi$
$60$	−0.922780	−0.119130
$61$	−11.6911	−1.49690	−0.748448	−	0.663194i	$-0.769201\pi$
$61$	−11.6911	−1.49690	−0.748448	+	0.663194i	$0.769201\pi$
$62$	5.51086	0.699879
$63$	5.26572	0.663419
$64$	1.00000	0.125000
$65$	2.73473	0.339202
$66$	1.88838	0.232443
$67$	−2.64188	−0.322757	−0.161379	−	0.986893i	$-0.551594\pi$
$67$	−2.64188	−0.322757	−0.161379	+	0.986893i	$0.551594\pi$
$68$	−1.97140	−0.239067
$69$	−3.42263	−0.412037
$70$	−2.45091	−0.292940
$71$	−0.355281	−0.0421641	−0.0210820	−	0.999778i	$-0.506711\pi$
$71$	−0.355281	−0.0421641	−0.0210820	+	0.999778i	$0.506711\pi$
$72$	−2.14848	−0.253200
$73$	−5.79466	−0.678214	−0.339107	−	0.940748i	$-0.610125\pi$
$73$	−5.79466	−0.678214	−0.339107	+	0.940748i	$0.610125\pi$
$74$	−0.227375	−0.0264318
$75$	−0.922780	−0.106553
$76$	2.65749	0.304835
$77$	5.01554	0.571574
$78$	−2.52355	−0.285736
$79$	−15.2199	−1.71238	−0.856189	−	0.516663i	$-0.827174\pi$
$79$	−15.2199	−1.71238	−0.856189	+	0.516663i	$0.827174\pi$
$80$	1.00000	0.111803
$81$	2.06138	0.229043
$82$	0.00373133	0.000412056 0
$83$	−3.67210	−0.403065	−0.201533	−	0.979482i	$-0.564592\pi$
$83$	−3.67210	−0.403065	−0.201533	+	0.979482i	$0.564592\pi$
$84$	2.26165	0.246766
$85$	−1.97140	−0.213828
$86$	−7.62879	−0.822634
$87$	4.29259	0.460214
$88$	−2.04640	−0.218147
$89$	−17.8319	−1.89018	−0.945090	−	0.326810i	$-0.894026\pi$
$89$	−17.8319	−1.89018	−0.945090	+	0.326810i	$0.894026\pi$
$90$	−2.14848	−0.226469
$91$	−6.70258	−0.702621
$92$	3.70905	0.386695
$93$	−5.08531	−0.527322
$94$	−7.35091	−0.758189
$95$	2.65749	0.272652
$96$	−0.922780	−0.0941808
$97$	−12.0305	−1.22152	−0.610758	−	0.791818i	$-0.709135\pi$
$97$	−12.0305	−1.22152	−0.610758	+	0.791818i	$0.709135\pi$
$98$	−0.993037	−0.100312
$99$	4.39664	0.441879
$100$	1.00000	0.100000
$101$	1.54435	0.153668	0.0768341	−	0.997044i	$-0.475519\pi$
$101$	1.54435	0.153668	0.0768341	+	0.997044i	$0.475519\pi$
$102$	1.81917	0.180125
$103$	−16.6311	−1.63871	−0.819357	−	0.573283i	$-0.805670\pi$
$103$	−16.6311	−1.63871	−0.819357	+	0.573283i	$0.805670\pi$
$104$	2.73473	0.268162
$105$	2.26165	0.220715
$106$	−4.94341	−0.480147
$107$	0.161903	0.0156518	0.00782590	−	0.999969i	$-0.497509\pi$
$107$	0.161903	0.0156518	0.00782590	+	0.999969i	$0.497509\pi$
$108$	4.75091	0.457157
$109$	5.27502	0.505255	0.252628	−	0.967564i	$-0.418705\pi$
$109$	5.27502	0.505255	0.252628	+	0.967564i	$0.418705\pi$
$110$	−2.04640	−0.195117
$111$	0.209817	0.0199150
$112$	−2.45091	−0.231589
$113$	12.3870	1.16527	0.582637	−	0.812732i	$-0.302021\pi$
$113$	12.3870	1.16527	0.582637	+	0.812732i	$0.302021\pi$
$114$	−2.45228	−0.229677
$115$	3.70905	0.345870
$116$	−4.65180	−0.431909
$117$	−5.87550	−0.543191
$118$	0.966468	0.0889706
$119$	4.83173	0.442924
$120$	−0.922780	−0.0842379
$121$	−6.81225	−0.619295
$122$	−11.6911	−1.05847
$123$	−0.00344320	−0.000310463 0
$124$	5.51086	0.494890
$125$	1.00000	0.0894427
$126$	5.26572	0.469108
$127$	−5.41403	−0.480418	−0.240209	−	0.970721i	$-0.577216\pi$
$127$	−5.41403	−0.480418	−0.240209	+	0.970721i	$0.577216\pi$
$128$	1.00000	0.0883883
$129$	7.03970	0.619811
$130$	2.73473	0.239852
$131$	0.511531	0.0446927	0.0223464	−	0.999750i	$-0.492886\pi$
$131$	0.511531	0.0446927	0.0223464	+	0.999750i	$0.492886\pi$
$132$	1.88838	0.164362
$133$	−6.51326	−0.564771
$134$	−2.64188	−0.228224
$135$	4.75091	0.408893
$136$	−1.97140	−0.169046
$137$	3.20873	0.274141	0.137070	−	0.990561i	$-0.456231\pi$
$137$	3.20873	0.274141	0.137070	+	0.990561i	$0.456231\pi$
$138$	−3.42263	−0.291354
$139$	2.41193	0.204577	0.102288	−	0.994755i	$-0.467384\pi$
$139$	2.41193	0.204577	0.102288	+	0.994755i	$0.467384\pi$
$140$	−2.45091	−0.207140
$141$	6.78328	0.571255
$142$	−0.355281	−0.0298145
$143$	−5.59635	−0.467990
$144$	−2.14848	−0.179040
$145$	−4.65180	−0.386311
$146$	−5.79466	−0.479570
$147$	0.916355	0.0755797
$148$	−0.227375	−0.0186901
$149$	−2.90623	−0.238088	−0.119044	−	0.992889i	$-0.537983\pi$
$149$	−2.90623	−0.238088	−0.119044	+	0.992889i	$0.537983\pi$
$150$	−0.922780	−0.0753447
$151$	18.4713	1.50318	0.751588	−	0.659633i	$-0.229288\pi$
$151$	18.4713	1.50318	0.751588	+	0.659633i	$0.229288\pi$
$152$	2.65749	0.215551
$153$	4.23551	0.342421
$154$	5.01554	0.404164
$155$	5.51086	0.442643
$156$	−2.52355	−0.202046
$157$	−6.74723	−0.538488	−0.269244	−	0.963072i	$-0.586774\pi$
$157$	−6.74723	−0.538488	−0.269244	+	0.963072i	$0.586774\pi$
$158$	−15.2199	−1.21083
$159$	4.56168	0.361765
$160$	1.00000	0.0790569
$161$	−9.09054	−0.716435
$162$	2.06138	0.161958
$163$	17.0914	1.33870	0.669351	−	0.742947i	$-0.266572\pi$
$163$	17.0914	1.33870	0.669351	+	0.742947i	$0.266572\pi$
$164$	0.00373133	0.000291368 0
$165$	1.88838	0.147010
$166$	−3.67210	−0.285010
$167$	13.5257	1.04665	0.523324	−	0.852134i	$-0.324692\pi$
$167$	13.5257	1.04665	0.523324	+	0.852134i	$0.324692\pi$
$168$	2.26165	0.174490
$169$	−5.52125	−0.424712
$170$	−1.97140	−0.151200
$171$	−5.70955	−0.436620
$172$	−7.62879	−0.581690
$173$	−7.92359	−0.602419	−0.301210	−	0.953558i	$-0.597390\pi$
$173$	−7.92359	−0.602419	−0.301210	+	0.953558i	$0.597390\pi$
$174$	4.29259	0.325420
$175$	−2.45091	−0.185271
$176$	−2.04640	−0.154253
$177$	−0.891837	−0.0670346
$178$	−17.8319	−1.33656
$179$	4.44801	0.332460	0.166230	−	0.986087i	$-0.446841\pi$
$179$	4.44801	0.332460	0.166230	+	0.986087i	$0.446841\pi$
$180$	−2.14848	−0.160138
$181$	−21.6964	−1.61268	−0.806341	−	0.591450i	$-0.798556\pi$
$181$	−21.6964	−1.61268	−0.806341	+	0.591450i	$0.798556\pi$
$182$	−6.70258	−0.496828
$183$	10.7883	0.797497
$184$	3.70905	0.273435
$185$	−0.227375	−0.0167170
$186$	−5.08531	−0.372873
$187$	4.03427	0.295015
$188$	−7.35091	−0.536120
$189$	−11.6441	−0.846981
$190$	2.65749	0.192794
$191$	9.99092	0.722918	0.361459	−	0.932388i	$-0.382279\pi$
$191$	9.99092	0.722918	0.361459	+	0.932388i	$0.382279\pi$
$192$	−0.922780	−0.0665959
$193$	24.4753	1.76177	0.880885	−	0.473330i	$-0.156948\pi$
$193$	24.4753	1.76177	0.880885	+	0.473330i	$0.156948\pi$
$194$	−12.0305	−0.863742
$195$	−2.52355	−0.180715
$196$	−0.993037	−0.0709312
$197$	10.8160	0.770606	0.385303	−	0.922790i	$-0.374097\pi$
$197$	10.8160	0.770606	0.385303	+	0.922790i	$0.374097\pi$
$198$	4.39664	0.312456
$199$	2.11533	0.149952	0.0749758	−	0.997185i	$-0.476112\pi$
$199$	2.11533	0.149952	0.0749758	+	0.997185i	$0.476112\pi$
$200$	1.00000	0.0707107
$201$	2.43788	0.171955
$202$	1.54435	0.108660
$203$	11.4011	0.800203
$204$	1.81917	0.127367
$205$	0.00373133	0.000260607 0
$206$	−16.6311	−1.15875
$207$	−7.96880	−0.553870
$208$	2.73473	0.189619
$209$	−5.43828	−0.376174
$210$	2.26165	0.156069
$211$	−14.3892	−0.990591	−0.495296	−	0.868724i	$-0.664940\pi$
$211$	−14.3892	−0.990591	−0.495296	+	0.868724i	$0.664940\pi$
$212$	−4.94341	−0.339515
$213$	0.327846	0.0224637
$214$	0.161903	0.0110675
$215$	−7.62879	−0.520279
$216$	4.75091	0.323259
$217$	−13.5066	−0.916889
$218$	5.27502	0.357270
$219$	5.34720	0.361330
$220$	−2.04640	−0.137968
$221$	−5.39125	−0.362655
$222$	0.209817	0.0140820
$223$	19.8764	1.33102	0.665511	−	0.746388i	$-0.268214\pi$
$223$	19.8764	1.33102	0.665511	+	0.746388i	$0.268214\pi$
$224$	−2.45091	−0.163758
$225$	−2.14848	−0.143232
$226$	12.3870	0.823973
$227$	5.45753	0.362229	0.181114	−	0.983462i	$-0.442030\pi$
$227$	5.45753	0.362229	0.181114	+	0.983462i	$0.442030\pi$
$228$	−2.45228	−0.162406
$229$	23.1167	1.52759	0.763796	−	0.645457i	$-0.223333\pi$
$229$	23.1167	1.52759	0.763796	+	0.645457i	$0.223333\pi$
$230$	3.70905	0.244567
$231$	−4.62824	−0.304516
$232$	−4.65180	−0.305406
$233$	−9.64058	−0.631575	−0.315788	−	0.948830i	$-0.602269\pi$
$233$	−9.64058	−0.631575	−0.315788	+	0.948830i	$0.602269\pi$
$234$	−5.87550	−0.384094
$235$	−7.35091	−0.479521
$236$	0.966468	0.0629117
$237$	14.0447	0.912299
$238$	4.83173	0.313194
$239$	4.52761	0.292867	0.146433	−	0.989221i	$-0.453221\pi$
$239$	4.52761	0.292867	0.146433	+	0.989221i	$0.453221\pi$
$240$	−0.922780	−0.0595652
$241$	−5.06713	−0.326403	−0.163201	−	0.986593i	$-0.552182\pi$
$241$	−5.06713	−0.326403	−0.163201	+	0.986593i	$0.552182\pi$
$242$	−6.81225	−0.437908
$243$	−16.1549	−1.03634
$244$	−11.6911	−0.748448
$245$	−0.993037	−0.0634428
$246$	−0.00344320	−0.000219530 0
$247$	7.26751	0.462421
$248$	5.51086	0.349940
$249$	3.38854	0.214740
$250$	1.00000	0.0632456
$251$	−6.61496	−0.417533	−0.208766	−	0.977966i	$-0.566945\pi$
$251$	−6.61496	−0.417533	−0.208766	+	0.977966i	$0.566945\pi$
$252$	5.26572	0.331709
$253$	−7.59019	−0.477191
$254$	−5.41403	−0.339707
$255$	1.81917	0.113921
$256$	1.00000	0.0625000
$257$	−11.8660	−0.740181	−0.370090	−	0.928996i	$-0.620673\pi$
$257$	−11.8660	−0.740181	−0.370090	+	0.928996i	$0.620673\pi$
$258$	7.03970	0.438272
$259$	0.557276	0.0346275
$260$	2.73473	0.169601
$261$	9.99428	0.618631
$262$	0.511531	0.0316025
$263$	13.5335	0.834509	0.417254	−	0.908790i	$-0.362992\pi$
$263$	13.5335	0.834509	0.417254	+	0.908790i	$0.362992\pi$
$264$	1.88838	0.116222
$265$	−4.94341	−0.303672
$266$	−6.51326	−0.399354
$267$	16.4549	1.00703
$268$	−2.64188	−0.161379
$269$	−28.9433	−1.76470	−0.882351	−	0.470591i	$-0.844041\pi$
$269$	−28.9433	−1.76470	−0.882351	+	0.470591i	$0.844041\pi$
$270$	4.75091	0.289131
$271$	6.45783	0.392285	0.196143	−	0.980575i	$-0.437158\pi$
$271$	6.45783	0.392285	0.196143	+	0.980575i	$0.437158\pi$
$272$	−1.97140	−0.119534
$273$	6.18501	0.374334
$274$	3.20873	0.193847
$275$	−2.04640	−0.123403
$276$	−3.42263	−0.206018
$277$	−7.57506	−0.455141	−0.227571	−	0.973762i	$-0.573078\pi$
$277$	−7.57506	−0.455141	−0.227571	+	0.973762i	$0.573078\pi$
$278$	2.41193	0.144658
$279$	−11.8399	−0.708839
$280$	−2.45091	−0.146470
$281$	−16.3778	−0.977017	−0.488509	−	0.872559i	$-0.662459\pi$
$281$	−16.3778	−0.977017	−0.488509	+	0.872559i	$0.662459\pi$
$282$	6.78328	0.403938
$283$	−13.4541	−0.799762	−0.399881	−	0.916567i	$-0.630949\pi$
$283$	−13.4541	−0.799762	−0.399881	+	0.916567i	$0.630949\pi$
$284$	−0.355281	−0.0210820
$285$	−2.45228	−0.145260
$286$	−5.59635	−0.330919
$287$	−0.00914515	−0.000539821 0
$288$	−2.14848	−0.126600
$289$	−13.1136	−0.771387
$290$	−4.65180	−0.273163
$291$	11.1015	0.650783
$292$	−5.79466	−0.339107
$293$	19.4961	1.13897	0.569487	−	0.822000i	$-0.307142\pi$
$293$	19.4961	1.13897	0.569487	+	0.822000i	$0.307142\pi$
$294$	0.916355	0.0534429
$295$	0.966468	0.0562699
$296$	−0.227375	−0.0132159
$297$	−9.72227	−0.564143
$298$	−2.90623	−0.168354
$299$	10.1432	0.586599
$300$	−0.922780	−0.0532767
$301$	18.6975	1.07771
$302$	18.4713	1.06291
$303$	−1.42509	−0.0818694
$304$	2.65749	0.152417
$305$	−11.6911	−0.669432
$306$	4.23551	0.242128
$307$	−9.90561	−0.565343	−0.282671	−	0.959217i	$-0.591221\pi$
$307$	−9.90561	−0.565343	−0.282671	+	0.959217i	$0.591221\pi$
$308$	5.01554	0.285787
$309$	15.3469	0.873054
$310$	5.51086	0.312996
$311$	0.113124	0.00641468	0.00320734	−	0.999995i	$-0.498979\pi$
$311$	0.113124	0.00641468	0.00320734	+	0.999995i	$0.498979\pi$
$312$	−2.52355	−0.142868
$313$	11.1183	0.628443	0.314221	−	0.949350i	$-0.398257\pi$
$313$	11.1183	0.628443	0.314221	+	0.949350i	$0.398257\pi$
$314$	−6.74723	−0.380768
$315$	5.26572	0.296690
$316$	−15.2199	−0.856189
$317$	1.08426	0.0608983	0.0304492	−	0.999536i	$-0.490306\pi$
$317$	1.08426	0.0608983	0.0304492	+	0.999536i	$0.490306\pi$
$318$	4.56168	0.255807
$319$	9.51944	0.532986
$320$	1.00000	0.0559017
$321$	−0.149401	−0.00833877
$322$	−9.09054	−0.506596
$323$	−5.23897	−0.291504
$324$	2.06138	0.114521
$325$	2.73473	0.151696
$326$	17.0914	0.946605
$327$	−4.86769	−0.269184
$328$	0.00373133	0.000206028 0
$329$	18.0164	0.993278
$330$	1.88838	0.103952
$331$	31.7890	1.74728	0.873640	−	0.486573i	$-0.161753\pi$
$331$	31.7890	1.74728	0.873640	+	0.486573i	$0.161753\pi$
$332$	−3.67210	−0.201533
$333$	0.488510	0.0267702
$334$	13.5257	0.740092
$335$	−2.64188	−0.144341
$336$	2.26165	0.123383
$337$	−23.9491	−1.30459	−0.652295	−	0.757965i	$-0.726194\pi$
$337$	−23.9491	−1.30459	−0.652295	+	0.757965i	$0.726194\pi$
$338$	−5.52125	−0.300316
$339$	−11.4305	−0.620820
$340$	−1.97140	−0.106914
$341$	−11.2774	−0.610706
$342$	−5.70955	−0.308737
$343$	19.5902	1.05777
$344$	−7.62879	−0.411317
$345$	−3.42263	−0.184268
$346$	−7.92359	−0.425975
$347$	−18.6597	−1.00171	−0.500853	−	0.865532i	$-0.666980\pi$
$347$	−18.6597	−1.00171	−0.500853	+	0.865532i	$0.666980\pi$
$348$	4.29259	0.230107
$349$	−12.9162	−0.691390	−0.345695	−	0.938347i	$-0.612357\pi$
$349$	−12.9162	−0.691390	−0.345695	+	0.938347i	$0.612357\pi$
$350$	−2.45091	−0.131007
$351$	12.9925	0.693486
$352$	−2.04640	−0.109073
$353$	31.3587	1.66905	0.834527	−	0.550968i	$-0.185741\pi$
$353$	31.3587	1.66905	0.834527	+	0.550968i	$0.185741\pi$
$354$	−0.891837	−0.0474006
$355$	−0.355281	−0.0188564
$356$	−17.8319	−0.945090
$357$	−4.45862	−0.235975
$358$	4.44801	0.235085
$359$	11.6583	0.615301	0.307650	−	0.951499i	$-0.400457\pi$
$359$	11.6583	0.615301	0.307650	+	0.951499i	$0.400457\pi$
$360$	−2.14848	−0.113235
$361$	−11.9378	−0.628303
$362$	−21.6964	−1.14034
$363$	6.28621	0.329940
$364$	−6.70258	−0.351311
$365$	−5.79466	−0.303307
$366$	10.7883	0.563916
$367$	−4.75497	−0.248208	−0.124104	−	0.992269i	$-0.539606\pi$
$367$	−4.75497	−0.248208	−0.124104	+	0.992269i	$0.539606\pi$
$368$	3.70905	0.193347
$369$	−0.00801667	−0.000417331 0
$370$	−0.227375	−0.0118207
$371$	12.1159	0.629025
$372$	−5.08531	−0.263661
$373$	27.4122	1.41935	0.709675	−	0.704529i	$-0.248842\pi$
$373$	27.4122	1.41935	0.709675	+	0.704529i	$0.248842\pi$
$374$	4.03427	0.208607
$375$	−0.922780	−0.0476522
$376$	−7.35091	−0.379094
$377$	−12.7214	−0.655186
$378$	−11.6441	−0.598906
$379$	−17.4550	−0.896605	−0.448302	−	0.893882i	$-0.647971\pi$
$379$	−17.4550	−0.896605	−0.448302	+	0.893882i	$0.647971\pi$
$380$	2.65749	0.136326
$381$	4.99596	0.255951
$382$	9.99092	0.511180
$383$	28.3119	1.44667	0.723335	−	0.690497i	$-0.242608\pi$
$383$	28.3119	1.44667	0.723335	+	0.690497i	$0.242608\pi$
$384$	−0.922780	−0.0470904
$385$	5.01554	0.255616
$386$	24.4753	1.24576
$387$	16.3903	0.833165
$388$	−12.0305	−0.610758
$389$	−37.1661	−1.88440	−0.942198	−	0.335056i	$-0.891245\pi$
$389$	−37.1661	−1.88440	−0.942198	+	0.335056i	$0.891245\pi$
$390$	−2.52355	−0.127785
$391$	−7.31202	−0.369785
$392$	−0.993037	−0.0501560
$393$	−0.472031	−0.0238108
$394$	10.8160	0.544901
$395$	−15.2199	−0.765799
$396$	4.39664	0.220940
$397$	−13.9940	−0.702341	−0.351171	−	0.936311i	$-0.614216\pi$
$397$	−13.9940	−0.702341	−0.351171	+	0.936311i	$0.614216\pi$
$398$	2.11533	0.106032
$399$	6.01031	0.300892
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	2.43788	0.121590
$403$	15.0707	0.750725
$404$	1.54435	0.0768341
$405$	2.06138	0.102431
$406$	11.4011	0.565829
$407$	0.465301	0.0230641
$408$	1.81917	0.0900623
$409$	10.4249	0.515477	0.257739	−	0.966215i	$-0.417023\pi$
$409$	10.4249	0.515477	0.257739	+	0.966215i	$0.417023\pi$
$410$	0.00373133	0.000184277 0
$411$	−2.96096	−0.146053
$412$	−16.6311	−0.819357
$413$	−2.36873	−0.116557
$414$	−7.96880	−0.391645
$415$	−3.67210	−0.180256
$416$	2.73473	0.134081
$417$	−2.22568	−0.108992
$418$	−5.43828	−0.265995
$419$	13.3108	0.650277	0.325139	−	0.945666i	$-0.394589\pi$
$419$	13.3108	0.650277	0.325139	+	0.945666i	$0.394589\pi$
$420$	2.26165	0.110357
$421$	−19.2465	−0.938015	−0.469007	−	0.883194i	$-0.655388\pi$
$421$	−19.2465	−0.938015	−0.469007	+	0.883194i	$0.655388\pi$
$422$	−14.3892	−0.700454
$423$	15.7933	0.767895
$424$	−4.94341	−0.240073
$425$	−1.97140	−0.0956270
$426$	0.327846	0.0158842
$427$	28.6539	1.38666
$428$	0.161903	0.00782590
$429$	5.16420	0.249330
$430$	−7.62879	−0.367893
$431$	−22.7421	−1.09545	−0.547724	−	0.836659i	$-0.684505\pi$
$431$	−22.7421	−1.09545	−0.547724	+	0.836659i	$0.684505\pi$
$432$	4.75091	0.228578
$433$	3.78758	0.182020	0.0910098	−	0.995850i	$-0.470991\pi$
$433$	3.78758	0.182020	0.0910098	+	0.995850i	$0.470991\pi$
$434$	−13.5066	−0.648338
$435$	4.29259	0.205814
$436$	5.27502	0.252628
$437$	9.85674	0.471512
$438$	5.34720	0.255499
$439$	6.53287	0.311797	0.155898	−	0.987773i	$-0.450173\pi$
$439$	6.53287	0.311797	0.155898	+	0.987773i	$0.450173\pi$
$440$	−2.04640	−0.0975583
$441$	2.13352	0.101596
$442$	−5.39125	−0.256436
$443$	32.2961	1.53444	0.767218	−	0.641387i	$-0.221641\pi$
$443$	32.2961	1.53444	0.767218	+	0.641387i	$0.221641\pi$
$444$	0.209817	0.00995749
$445$	−17.8319	−0.845314
$446$	19.8764	0.941175
$447$	2.68181	0.126845
$448$	−2.45091	−0.115795
$449$	−4.44737	−0.209884	−0.104942	−	0.994478i	$-0.533466\pi$
$449$	−4.44737	−0.209884	−0.104942	+	0.994478i	$0.533466\pi$
$450$	−2.14848	−0.101280
$451$	−0.00763579	−0.000359555 0
$452$	12.3870	0.582637
$453$	−17.0450	−0.800843
$454$	5.45753	0.256134
$455$	−6.70258	−0.314222
$456$	−2.45228	−0.114838
$457$	0.243377	0.0113847	0.00569234	−	0.999984i	$-0.498188\pi$
$457$	0.243377	0.0113847	0.00569234	+	0.999984i	$0.498188\pi$
$458$	23.1167	1.08017
$459$	−9.36595	−0.437165
$460$	3.70905	0.172935
$461$	−27.2016	−1.26690	−0.633452	−	0.773782i	$-0.718363\pi$
$461$	−27.2016	−1.26690	−0.633452	+	0.773782i	$0.718363\pi$
$462$	−4.62824	−0.215325
$463$	−31.0283	−1.44201	−0.721004	−	0.692931i	$-0.756319\pi$
$463$	−31.0283	−1.44201	−0.721004	+	0.692931i	$0.756319\pi$
$464$	−4.65180	−0.215954
$465$	−5.08531	−0.235826
$466$	−9.64058	−0.446591
$467$	16.5367	0.765227	0.382614	−	0.923908i	$-0.375024\pi$
$467$	16.5367	0.765227	0.382614	+	0.923908i	$0.375024\pi$
$468$	−5.87550	−0.271595
$469$	6.47502	0.298989
$470$	−7.35091	−0.339072
$471$	6.22621	0.286889
$472$	0.966468	0.0444853
$473$	15.6116	0.717820
$474$	14.0447	0.645093
$475$	2.65749	0.121934
$476$	4.83173	0.221462
$477$	10.6208	0.486294
$478$	4.52761	0.207088
$479$	−5.68828	−0.259904	−0.129952	−	0.991520i	$-0.541482\pi$
$479$	−5.68828	−0.259904	−0.129952	+	0.991520i	$0.541482\pi$
$480$	−0.922780	−0.0421190
$481$	−0.621810	−0.0283521
$482$	−5.06713	−0.230802
$483$	8.38857	0.381693
$484$	−6.81225	−0.309648
$485$	−12.0305	−0.546278
$486$	−16.1549	−0.732803
$487$	33.2964	1.50880	0.754402	−	0.656413i	$-0.227927\pi$
$487$	33.2964	1.50880	0.754402	+	0.656413i	$0.227927\pi$
$488$	−11.6911	−0.529233
$489$	−15.7716	−0.713216
$490$	−0.993037	−0.0448609
$491$	−15.3136	−0.691094	−0.345547	−	0.938401i	$-0.612307\pi$
$491$	−15.3136	−0.691094	−0.345547	+	0.938401i	$0.612307\pi$
$492$	−0.00344320	−0.000155231 0
$493$	9.17056	0.413021
$494$	7.26751	0.326981
$495$	4.39664	0.197614
$496$	5.51086	0.247445
$497$	0.870762	0.0390590
$498$	3.38854	0.151844
$499$	−12.0608	−0.539915	−0.269957	−	0.962872i	$-0.587010\pi$
$499$	−12.0608	−0.539915	−0.269957	+	0.962872i	$0.587010\pi$
$500$	1.00000	0.0447214
$501$	−12.4812	−0.557620
$502$	−6.61496	−0.295240
$503$	2.14248	0.0955284	0.0477642	−	0.998859i	$-0.484790\pi$
$503$	2.14248	0.0955284	0.0477642	+	0.998859i	$0.484790\pi$
$504$	5.26572	0.234554
$505$	1.54435	0.0687225
$506$	−7.59019	−0.337425
$507$	5.09490	0.226272
$508$	−5.41403	−0.240209
$509$	7.41304	0.328577	0.164289	−	0.986412i	$-0.447467\pi$
$509$	7.41304	0.328577	0.164289	+	0.986412i	$0.447467\pi$
$510$	1.81917	0.0805542
$511$	14.2022	0.628268
$512$	1.00000	0.0441942
$513$	12.6255	0.557429
$514$	−11.8660	−0.523387
$515$	−16.6311	−0.732856
$516$	7.03970	0.309905
$517$	15.0429	0.661586
$518$	0.557276	0.0244853
$519$	7.31173	0.320949
$520$	2.73473	0.119926
$521$	−13.8021	−0.604679	−0.302340	−	0.953200i	$-0.597768\pi$
$521$	−13.8021	−0.604679	−0.302340	+	0.953200i	$0.597768\pi$
$522$	9.99428	0.437438
$523$	−8.40757	−0.367637	−0.183819	−	0.982960i	$-0.558846\pi$
$523$	−8.40757	−0.367637	−0.183819	+	0.982960i	$0.558846\pi$
$524$	0.511531	0.0223464
$525$	2.26165	0.0987066
$526$	13.5335	0.590087
$527$	−10.8641	−0.473248
$528$	1.88838	0.0821811
$529$	−9.24297	−0.401868
$530$	−4.94341	−0.214728
$531$	−2.07643	−0.0901096
$532$	−6.51326	−0.282386
$533$	0.0102042	0.000441992 0
$534$	16.4549	0.712075
$535$	0.161903	0.00699970
$536$	−2.64188	−0.114112
$537$	−4.10454	−0.177124
$538$	−28.9433	−1.24783
$539$	2.03215	0.0875310
$540$	4.75091	0.204447
$541$	−2.68937	−0.115625	−0.0578125	−	0.998327i	$-0.518413\pi$
$541$	−2.68937	−0.115625	−0.0578125	+	0.998327i	$0.518413\pi$
$542$	6.45783	0.277387
$543$	20.0210	0.859185
$544$	−1.97140	−0.0845231
$545$	5.27502	0.225957
$546$	6.18501	0.264694
$547$	−14.8940	−0.636821	−0.318411	−	0.947953i	$-0.603149\pi$
$547$	−14.8940	−0.636821	−0.318411	+	0.947953i	$0.603149\pi$
$548$	3.20873	0.137070
$549$	25.1181	1.07202
$550$	−2.04640	−0.0872588
$551$	−12.3621	−0.526643
$552$	−3.42263	−0.145677
$553$	37.3027	1.58627
$554$	−7.57506	−0.321833
$555$	0.209817	0.00890625
$556$	2.41193	0.102288
$557$	−3.30756	−0.140146	−0.0700730	−	0.997542i	$-0.522323\pi$
$557$	−3.30756	−0.140146	−0.0700730	+	0.997542i	$0.522323\pi$
$558$	−11.8399	−0.501225
$559$	−20.8627	−0.882398
$560$	−2.45091	−0.103570
$561$	−3.72275	−0.157175
$562$	−16.3778	−0.690855
$563$	−13.2024	−0.556413	−0.278207	−	0.960521i	$-0.589740\pi$
$563$	−13.2024	−0.556413	−0.278207	+	0.960521i	$0.589740\pi$
$564$	6.78328	0.285627
$565$	12.3870	0.521127
$566$	−13.4541	−0.565517
$567$	−5.05227	−0.212175
$568$	−0.355281	−0.0149073
$569$	6.64575	0.278605	0.139302	−	0.990250i	$-0.455514\pi$
$569$	6.64575	0.278605	0.139302	+	0.990250i	$0.455514\pi$
$570$	−2.45228	−0.102715
$571$	−16.4542	−0.688586	−0.344293	−	0.938862i	$-0.611881\pi$
$571$	−16.4542	−0.688586	−0.344293	+	0.938862i	$0.611881\pi$
$572$	−5.59635	−0.233995
$573$	−9.21942	−0.385147
$574$	−0.00914515	−0.000381711 0
$575$	3.70905	0.154678
$576$	−2.14848	−0.0895199
$577$	9.68167	0.403053	0.201526	−	0.979483i	$-0.435410\pi$
$577$	9.68167	0.403053	0.201526	+	0.979483i	$0.435410\pi$
$578$	−13.1136	−0.545453
$579$	−22.5853	−0.938614
$580$	−4.65180	−0.193155
$581$	8.99999	0.373383
$582$	11.1015	0.460173
$583$	10.1162	0.418970
$584$	−5.79466	−0.239785
$585$	−5.87550	−0.242922
$586$	19.4961	0.805376
$587$	0.312361	0.0128925	0.00644626	−	0.999979i	$-0.497948\pi$
$587$	0.312361	0.0128925	0.00644626	+	0.999979i	$0.497948\pi$
$588$	0.916355	0.0377899
$589$	14.6450	0.603438
$590$	0.966468	0.0397889
$591$	−9.98076	−0.410554
$592$	−0.227375	−0.00934507
$593$	22.2507	0.913727	0.456864	−	0.889537i	$-0.348973\pi$
$593$	22.2507	0.913727	0.456864	+	0.889537i	$0.348973\pi$
$594$	−9.72227	−0.398909
$595$	4.83173	0.198081
$596$	−2.90623	−0.119044
$597$	−1.95198	−0.0798893
$598$	10.1432	0.414788
$599$	8.30189	0.339206	0.169603	−	0.985512i	$-0.445751\pi$
$599$	8.30189	0.339206	0.169603	+	0.985512i	$0.445751\pi$
$600$	−0.922780	−0.0376723
$601$	23.5068	0.958861	0.479431	−	0.877580i	$-0.340843\pi$
$601$	23.5068	0.958861	0.479431	+	0.877580i	$0.340843\pi$
$602$	18.6975	0.762053
$603$	5.67602	0.231146
$604$	18.4713	0.751588
$605$	−6.81225	−0.276957
$606$	−1.42509	−0.0578904
$607$	36.5286	1.48265	0.741325	−	0.671146i	$-0.234198\pi$
$607$	36.5286	1.48265	0.741325	+	0.671146i	$0.234198\pi$
$608$	2.65749	0.107775
$609$	−10.5207	−0.426322
$610$	−11.6911	−0.473360
$611$	−20.1028	−0.813271
$612$	4.23551	0.171210
$613$	4.32587	0.174720	0.0873601	−	0.996177i	$-0.472157\pi$
$613$	4.32587	0.174720	0.0873601	+	0.996177i	$0.472157\pi$
$614$	−9.90561	−0.399758
$615$	−0.00344320	−0.000138843 0
$616$	5.01554	0.202082
$617$	−32.7264	−1.31752	−0.658758	−	0.752355i	$-0.728918\pi$
$617$	−32.7264	−1.31752	−0.658758	+	0.752355i	$0.728918\pi$
$618$	15.3469	0.617342
$619$	24.4724	0.983629	0.491815	−	0.870700i	$-0.336334\pi$
$619$	24.4724	0.983629	0.491815	+	0.870700i	$0.336334\pi$
$620$	5.51086	0.221321
$621$	17.6214	0.707121
$622$	0.113124	0.00453586
$623$	43.7045	1.75098
$624$	−2.52355	−0.101023
$625$	1.00000	0.0400000
$626$	11.1183	0.444376
$627$	5.01834	0.200413
$628$	−6.74723	−0.269244
$629$	0.448248	0.0178728
$630$	5.26572	0.209791
$631$	−19.4909	−0.775919	−0.387959	−	0.921676i	$-0.626820\pi$
$631$	−19.4909	−0.775919	−0.387959	+	0.921676i	$0.626820\pi$
$632$	−15.2199	−0.605417
$633$	13.2780	0.527755
$634$	1.08426	0.0430616
$635$	−5.41403	−0.214849
$636$	4.56168	0.180883
$637$	−2.71569	−0.107600
$638$	9.51944	0.376878
$639$	0.763313	0.0301962
$640$	1.00000	0.0395285
$641$	−18.2070	−0.719134	−0.359567	−	0.933119i	$-0.617076\pi$
$641$	−18.2070	−0.719134	−0.359567	+	0.933119i	$0.617076\pi$
$642$	−0.149401	−0.00589640
$643$	−18.6447	−0.735274	−0.367637	−	0.929969i	$-0.619833\pi$
$643$	−18.6447	−0.735274	−0.367637	+	0.929969i	$0.619833\pi$
$644$	−9.09054	−0.358218
$645$	7.03970	0.277188
$646$	−5.23897	−0.206125
$647$	−3.11585	−0.122497	−0.0612483	−	0.998123i	$-0.519508\pi$
$647$	−3.11585	−0.122497	−0.0612483	+	0.998123i	$0.519508\pi$
$648$	2.06138	0.0809788
$649$	−1.97778	−0.0776347
$650$	2.73473	0.107265
$651$	12.4636	0.488488
$652$	17.0914	0.669351
$653$	50.2257	1.96548	0.982742	−	0.184981i	$-0.0592223\pi$
$653$	50.2257	1.96548	0.982742	+	0.184981i	$0.0592223\pi$
$654$	−4.86769	−0.190342
$655$	0.511531	0.0199872
$656$	0.00373133	0.000145684 0
$657$	12.4497	0.485709
$658$	18.0164	0.702354
$659$	−11.4529	−0.446142	−0.223071	−	0.974802i	$-0.571608\pi$
$659$	−11.4529	−0.446142	−0.223071	+	0.974802i	$0.571608\pi$
$660$	1.88838	0.0735050
$661$	−34.0381	−1.32393	−0.661963	−	0.749536i	$-0.730277\pi$
$661$	−34.0381	−1.32393	−0.661963	+	0.749536i	$0.730277\pi$
$662$	31.7890	1.23551
$663$	4.97494	0.193211
$664$	−3.67210	−0.142505
$665$	−6.51326	−0.252573
$666$	0.488510	0.0189294
$667$	−17.2537	−0.668067
$668$	13.5257	0.523324
$669$	−18.3415	−0.709125
$670$	−2.64188	−0.102065
$671$	23.9247	0.923604
$672$	2.26165	0.0872451
$673$	36.0807	1.39081	0.695404	−	0.718619i	$-0.255225\pi$
$673$	36.0807	1.39081	0.695404	+	0.718619i	$0.255225\pi$
$674$	−23.9491	−0.922484
$675$	4.75091	0.182863
$676$	−5.52125	−0.212356
$677$	−6.48407	−0.249203	−0.124602	−	0.992207i	$-0.539765\pi$
$677$	−6.48407	−0.249203	−0.124602	+	0.992207i	$0.539765\pi$
$678$	−11.4305	−0.438986
$679$	29.4858	1.13156
$680$	−1.97140	−0.0755998
$681$	−5.03610	−0.192984
$682$	−11.2774	−0.431835
$683$	−42.1316	−1.61212	−0.806061	−	0.591833i	$-0.798405\pi$
$683$	−42.1316	−1.61212	−0.806061	+	0.591833i	$0.798405\pi$
$684$	−5.70955	−0.218310
$685$	3.20873	0.122599
$686$	19.5902	0.747958
$687$	−21.3316	−0.813852
$688$	−7.62879	−0.290845
$689$	−13.5189	−0.515029
$690$	−3.42263	−0.130297
$691$	−10.4025	−0.395729	−0.197864	−	0.980229i	$-0.563401\pi$
$691$	−10.4025	−0.395729	−0.197864	+	0.980229i	$0.563401\pi$
$692$	−7.92359	−0.301210
$693$	−10.7758	−0.409338
$694$	−18.6597	−0.708313
$695$	2.41193	0.0914896
$696$	4.29259	0.162710
$697$	−0.00735595	−0.000278626 0
$698$	−12.9162	−0.488887
$699$	8.89614	0.336483
$700$	−2.45091	−0.0926357
$701$	7.60802	0.287351	0.143675	−	0.989625i	$-0.454108\pi$
$701$	7.60802	0.287351	0.143675	+	0.989625i	$0.454108\pi$
$702$	12.9925	0.490369
$703$	−0.604247	−0.0227896
$704$	−2.04640	−0.0771266
$705$	6.78328	0.255473
$706$	31.3587	1.18020
$707$	−3.78506	−0.142352
$708$	−0.891837	−0.0335173
$709$	19.7996	0.743588	0.371794	−	0.928315i	$-0.378743\pi$
$709$	19.7996	0.743588	0.371794	+	0.928315i	$0.378743\pi$
$710$	−0.355281	−0.0133335
$711$	32.6997	1.22633
$712$	−17.8319	−0.668280
$713$	20.4400	0.765485
$714$	−4.45862	−0.166860
$715$	−5.59635	−0.209292
$716$	4.44801	0.166230
$717$	−4.17799	−0.156030
$718$	11.6583	0.435083
$719$	47.7753	1.78172	0.890859	−	0.454280i	$-0.150103\pi$
$719$	47.7753	1.78172	0.890859	+	0.454280i	$0.150103\pi$
$720$	−2.14848	−0.0800690
$721$	40.7614	1.51804
$722$	−11.9378	−0.444278
$723$	4.67585	0.173897
$724$	−21.6964	−0.806341
$725$	−4.65180	−0.172763
$726$	6.28621	0.233303
$727$	−2.78307	−0.103218	−0.0516092	−	0.998667i	$-0.516435\pi$
$727$	−2.78307	−0.103218	−0.0516092	+	0.998667i	$0.516435\pi$
$728$	−6.70258	−0.248414
$729$	8.72330	0.323085
$730$	−5.79466	−0.214470
$731$	15.0394	0.556253
$732$	10.7883	0.398749
$733$	48.4360	1.78902	0.894512	−	0.447043i	$-0.147523\pi$
$733$	48.4360	1.78902	0.894512	+	0.447043i	$0.147523\pi$
$734$	−4.75497	−0.175509
$735$	0.916355	0.0338003
$736$	3.70905	0.136717
$737$	5.40635	0.199145
$738$	−0.00801667	−0.000295098 0
$739$	−7.85014	−0.288772	−0.144386	−	0.989521i	$-0.546121\pi$
$739$	−7.85014	−0.288772	−0.144386	+	0.989521i	$0.546121\pi$
$740$	−0.227375	−0.00835848
$741$	−6.70631	−0.246363
$742$	12.1159	0.444787
$743$	43.8662	1.60929	0.804647	−	0.593753i	$-0.202354\pi$
$743$	43.8662	1.60929	0.804647	+	0.593753i	$0.202354\pi$
$744$	−5.08531	−0.186436
$745$	−2.90623	−0.106476
$746$	27.4122	1.00363
$747$	7.88942	0.288659
$748$	4.03427	0.147508
$749$	−0.396811	−0.0144992
$750$	−0.922780	−0.0336952
$751$	36.7947	1.34266	0.671329	−	0.741159i	$-0.265724\pi$
$751$	36.7947	1.34266	0.671329	+	0.741159i	$0.265724\pi$
$752$	−7.35091	−0.268060
$753$	6.10416	0.222448
$754$	−12.7214	−0.463287
$755$	18.4713	0.672241
$756$	−11.6441	−0.423490
$757$	−26.6341	−0.968033	−0.484016	−	0.875059i	$-0.660823\pi$
$757$	−26.6341	−0.968033	−0.484016	+	0.875059i	$0.660823\pi$
$758$	−17.4550	−0.633995
$759$	7.00408	0.254232
$760$	2.65749	0.0963972
$761$	38.3806	1.39129	0.695647	−	0.718384i	$-0.255118\pi$
$761$	38.3806	1.39129	0.695647	+	0.718384i	$0.255118\pi$
$762$	4.99596	0.180985
$763$	−12.9286	−0.468047
$764$	9.99092	0.361459
$765$	4.23551	0.153135
$766$	28.3119	1.02295
$767$	2.64303	0.0954342
$768$	−0.922780	−0.0332980
$769$	−18.0998	−0.652695	−0.326348	−	0.945250i	$-0.605818\pi$
$769$	−18.0998	−0.652695	−0.326348	+	0.945250i	$0.605818\pi$
$770$	5.01554	0.180748
$771$	10.9497	0.394344
$772$	24.4753	0.880885
$773$	12.9229	0.464805	0.232403	−	0.972620i	$-0.425341\pi$
$773$	12.9229	0.464805	0.232403	+	0.972620i	$0.425341\pi$
$774$	16.3903	0.589137
$775$	5.51086	0.197956
$776$	−12.0305	−0.431871
$777$	−0.514244	−0.0184484
$778$	−37.1661	−1.33247
$779$	0.00991596	0.000355276 0
$780$	−2.52355	−0.0903577
$781$	0.727047	0.0260158
$782$	−7.31202	−0.261477
$783$	−22.1003	−0.789800
$784$	−0.993037	−0.0354656
$785$	−6.74723	−0.240819
$786$	−0.472031	−0.0168368
$787$	−27.3918	−0.976412	−0.488206	−	0.872728i	$-0.662348\pi$
$787$	−27.3918	−0.976412	−0.488206	+	0.872728i	$0.662348\pi$
$788$	10.8160	0.385303
$789$	−12.4884	−0.444599
$790$	−15.2199	−0.541502
$791$	−30.3595	−1.07946
$792$	4.39664	0.156228
$793$	−31.9721	−1.13536
$794$	−13.9940	−0.496630
$795$	4.56168	0.161786
$796$	2.11533	0.0749758
$797$	−22.5919	−0.800245	−0.400123	−	0.916462i	$-0.631032\pi$
$797$	−22.5919	−0.800245	−0.400123	+	0.916462i	$0.631032\pi$
$798$	6.01031	0.212763
$799$	14.4916	0.512676
$800$	1.00000	0.0353553
$801$	38.3115	1.35367
$802$	−1.00000	−0.0353112
$803$	11.8582	0.418467
$804$	2.43788	0.0859773
$805$	−9.09054	−0.320400
$806$	15.0707	0.530843
$807$	26.7083	0.940176
$808$	1.54435	0.0543299
$809$	−19.7015	−0.692669	−0.346334	−	0.938111i	$-0.612574\pi$
$809$	−19.7015	−0.692669	−0.346334	+	0.938111i	$0.612574\pi$
$810$	2.06138	0.0724296
$811$	8.03457	0.282132	0.141066	−	0.990000i	$-0.454947\pi$
$811$	8.03457	0.282132	0.141066	+	0.990000i	$0.454947\pi$
$812$	11.4011	0.400102
$813$	−5.95915	−0.208997
$814$	0.465301	0.0163088
$815$	17.0914	0.598685
$816$	1.81917	0.0636837
$817$	−20.2734	−0.709277
$818$	10.4249	0.364498
$819$	14.4003	0.503188
$820$	0.00373133	0.000130304 0
$821$	−40.9195	−1.42810	−0.714051	−	0.700094i	$-0.753141\pi$
$821$	−40.9195	−1.42810	−0.714051	+	0.700094i	$0.753141\pi$
$822$	−2.96096	−0.103275
$823$	−38.2432	−1.33308	−0.666538	−	0.745471i	$-0.732224\pi$
$823$	−38.2432	−1.33308	−0.666538	+	0.745471i	$0.732224\pi$
$824$	−16.6311	−0.579373
$825$	1.88838	0.0657449
$826$	−2.36873	−0.0824185
$827$	−0.507986	−0.0176644	−0.00883219	−	0.999961i	$-0.502811\pi$
$827$	−0.507986	−0.0176644	−0.00883219	+	0.999961i	$0.502811\pi$
$828$	−7.96880	−0.276935
$829$	38.4468	1.33531	0.667656	−	0.744470i	$-0.267298\pi$
$829$	38.4468	1.33531	0.667656	+	0.744470i	$0.267298\pi$
$830$	−3.67210	−0.127460
$831$	6.99011	0.242484
$832$	2.73473	0.0948097
$833$	1.95767	0.0678294
$834$	−2.22568	−0.0770689
$835$	13.5257	0.468075
$836$	−5.43828	−0.188087
$837$	26.1816	0.904968
$838$	13.3108	0.459815
$839$	−30.1127	−1.03961	−0.519803	−	0.854286i	$-0.673995\pi$
$839$	−30.1127	−1.03961	−0.519803	+	0.854286i	$0.673995\pi$
$840$	2.26165	0.0780344
$841$	−7.36077	−0.253820
$842$	−19.2465	−0.663277
$843$	15.1131	0.520523
$844$	−14.3892	−0.495296
$845$	−5.52125	−0.189937
$846$	15.7933	0.542984
$847$	16.6962	0.573688
$848$	−4.94341	−0.169758
$849$	12.4152	0.426087
$850$	−1.97140	−0.0676185
$851$	−0.843345	−0.0289095
$852$	0.327846	0.0112318
$853$	3.94574	0.135099	0.0675497	−	0.997716i	$-0.478482\pi$
$853$	3.94574	0.135099	0.0675497	+	0.997716i	$0.478482\pi$
$854$	28.6539	0.980517
$855$	−5.70955	−0.195262
$856$	0.161903	0.00553375
$857$	−2.29015	−0.0782300	−0.0391150	−	0.999235i	$-0.512454\pi$
$857$	−2.29015	−0.0782300	−0.0391150	+	0.999235i	$0.512454\pi$
$858$	5.16420	0.176303
$859$	−6.59854	−0.225139	−0.112570	−	0.993644i	$-0.535908\pi$
$859$	−6.59854	−0.225139	−0.112570	+	0.993644i	$0.535908\pi$
$860$	−7.62879	−0.260140
$861$	0.00843897	0.000287599 0
$862$	−22.7421	−0.774598
$863$	9.21364	0.313636	0.156818	−	0.987628i	$-0.449876\pi$
$863$	9.21364	0.313636	0.156818	+	0.987628i	$0.449876\pi$
$864$	4.75091	0.161629
$865$	−7.92359	−0.269410
$866$	3.78758	0.128707
$867$	12.1009	0.410970
$868$	−13.5066	−0.458444
$869$	31.1461	1.05656
$870$	4.29259	0.145532
$871$	−7.22484	−0.244804
$872$	5.27502	0.178635
$873$	25.8473	0.874799
$874$	9.85674	0.333409
$875$	−2.45091	−0.0828559
$876$	5.34720	0.180665
$877$	15.4131	0.520462	0.260231	−	0.965546i	$-0.416201\pi$
$877$	15.4131	0.520462	0.260231	+	0.965546i	$0.416201\pi$
$878$	6.53287	0.220474
$879$	−17.9906	−0.606808
$880$	−2.04640	−0.0689841
$881$	37.9884	1.27986	0.639932	−	0.768432i	$-0.278963\pi$
$881$	37.9884	1.27986	0.639932	+	0.768432i	$0.278963\pi$
$882$	2.13352	0.0718393
$883$	7.46660	0.251271	0.125636	−	0.992076i	$-0.459903\pi$
$883$	7.46660	0.251271	0.125636	+	0.992076i	$0.459903\pi$
$884$	−5.39125	−0.181327
$885$	−0.891837	−0.0299788
$886$	32.2961	1.08501
$887$	17.3832	0.583672	0.291836	−	0.956468i	$-0.405734\pi$
$887$	17.3832	0.583672	0.291836	+	0.956468i	$0.405734\pi$
$888$	0.209817	0.00704101
$889$	13.2693	0.445038
$890$	−17.8319	−0.597727
$891$	−4.21842	−0.141322
$892$	19.8764	0.665511
$893$	−19.5350	−0.653712
$894$	2.68181	0.0896933
$895$	4.44801	0.148681
$896$	−2.45091	−0.0818792
$897$	−9.35998	−0.312521
$898$	−4.44737	−0.148411
$899$	−25.6354	−0.854988
$900$	−2.14848	−0.0716159
$901$	9.74545	0.324668
$902$	−0.00763579	−0.000254244 0
$903$	−17.2537	−0.574166
$904$	12.3870	0.411987
$905$	−21.6964	−0.721214
$906$	−17.0450	−0.566282
$907$	−0.626009	−0.0207863	−0.0103931	−	0.999946i	$-0.503308\pi$
$907$	−0.626009	−0.0207863	−0.0103931	+	0.999946i	$0.503308\pi$
$908$	5.45753	0.181114
$909$	−3.31799	−0.110051
$910$	−6.70258	−0.222188
$911$	−41.5123	−1.37536	−0.687682	−	0.726012i	$-0.741372\pi$
$911$	−41.5123	−1.37536	−0.687682	+	0.726012i	$0.741372\pi$
$912$	−2.45228	−0.0812030
$913$	7.51459	0.248697
$914$	0.243377	0.00805018
$915$	10.7883	0.356652
$916$	23.1167	0.763796
$917$	−1.25372	−0.0414014
$918$	−9.36595	−0.309122
$919$	−36.1870	−1.19370	−0.596849	−	0.802353i	$-0.703581\pi$
$919$	−36.1870	−1.19370	−0.596849	+	0.802353i	$0.703581\pi$
$920$	3.70905	0.122284
$921$	9.14070	0.301196
$922$	−27.2016	−0.895837
$923$	−0.971598	−0.0319805
$924$	−4.62824	−0.152258
$925$	−0.227375	−0.00747605
$926$	−31.0283	−1.01965
$927$	35.7316	1.17358
$928$	−4.65180	−0.152703
$929$	44.0799	1.44621	0.723107	−	0.690736i	$-0.242714\pi$
$929$	44.0799	1.44621	0.723107	+	0.690736i	$0.242714\pi$
$930$	−5.08531	−0.166754
$931$	−2.63898	−0.0864892
$932$	−9.64058	−0.315788
$933$	−0.104389	−0.00341753
$934$	16.5367	0.541098
$935$	4.03427	0.131935
$936$	−5.87550	−0.192047
$937$	−34.5337	−1.12817	−0.564084	−	0.825718i	$-0.690771\pi$
$937$	−34.5337	−1.12817	−0.564084	+	0.825718i	$0.690771\pi$
$938$	6.47502	0.211417
$939$	−10.2597	−0.334814
$940$	−7.35091	−0.239760
$941$	41.9608	1.36788	0.683942	−	0.729537i	$-0.260264\pi$
$941$	41.9608	1.36788	0.683942	+	0.729537i	$0.260264\pi$
$942$	6.22621	0.202861
$943$	0.0138397	0.000450682 0
$944$	0.966468	0.0314559
$945$	−11.6441	−0.378781
$946$	15.6116	0.507576
$947$	−1.14779	−0.0372980	−0.0186490	−	0.999826i	$-0.505937\pi$
$947$	−1.14779	−0.0372980	−0.0186490	+	0.999826i	$0.505937\pi$
$948$	14.0447	0.456150
$949$	−15.8468	−0.514410
$950$	2.65749	0.0862203
$951$	−1.00054	−0.0324446
$952$	4.83173	0.156597
$953$	31.0553	1.00598	0.502990	−	0.864292i	$-0.332233\pi$
$953$	31.0553	1.00598	0.502990	+	0.864292i	$0.332233\pi$
$954$	10.6208	0.343862
$955$	9.99092	0.323299
$956$	4.52761	0.146433
$957$	−8.78435	−0.283958
$958$	−5.68828	−0.183780
$959$	−7.86432	−0.253952
$960$	−0.922780	−0.0297826
$961$	−0.630461	−0.0203375
$962$	−0.621810	−0.0200480
$963$	−0.347846	−0.0112092
$964$	−5.06713	−0.163201
$965$	24.4753	0.787888
$966$	8.38857	0.269898
$967$	36.4909	1.17347	0.586734	−	0.809779i	$-0.300413\pi$
$967$	36.4909	1.17347	0.586734	+	0.809779i	$0.300413\pi$
$968$	−6.81225	−0.218954
$969$	4.83442	0.155304
$970$	−12.0305	−0.386277
$971$	27.2658	0.875000	0.437500	−	0.899218i	$-0.355864\pi$
$971$	27.2658	0.875000	0.437500	+	0.899218i	$0.355864\pi$
$972$	−16.1549	−0.518170
$973$	−5.91141	−0.189511
$974$	33.2964	1.06688
$975$	−2.52355	−0.0808184
$976$	−11.6911	−0.374224
$977$	1.57450	0.0503728	0.0251864	−	0.999683i	$-0.491982\pi$
$977$	1.57450	0.0503728	0.0251864	+	0.999683i	$0.491982\pi$
$978$	−15.7716	−0.504320
$979$	36.4913	1.16627
$980$	−0.993037	−0.0317214
$981$	−11.3333	−0.361843
$982$	−15.3136	−0.488677
$983$	5.84083	0.186294	0.0931468	−	0.995652i	$-0.470307\pi$
$983$	5.84083	0.186294	0.0931468	+	0.995652i	$0.470307\pi$
$984$	−0.00344320	−0.000109765 0
$985$	10.8160	0.344625
$986$	9.17056	0.292050
$987$	−16.6252	−0.529186
$988$	7.26751	0.231210
$989$	−28.2955	−0.899746
$990$	4.39664	0.139735
$991$	59.4355	1.88803	0.944015	−	0.329903i	$-0.107016\pi$
$991$	59.4355	1.88803	0.944015	+	0.329903i	$0.107016\pi$
$992$	5.51086	0.174970
$993$	−29.3342	−0.930894
$994$	0.870762	0.0276189
$995$	2.11533	0.0670604
$996$	3.38854	0.107370
$997$	41.5433	1.31569	0.657844	−	0.753154i	$-0.271469\pi$
$997$	41.5433	1.31569	0.657844	+	0.753154i	$0.271469\pi$
$998$	−12.0608	−0.381777
$999$	−1.08024	−0.0341773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.h.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.h.1.4	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.922780 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.922780 q^{6} -2.45091 q^{7} +1.00000 q^{8} -2.14848 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.922780 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.922780 q^{6} -2.45091 q^{7} +1.00000 q^{8} -2.14848 q^{9} +1.00000 q^{10} -2.04640 q^{11} -0.922780 q^{12} +2.73473 q^{13} -2.45091 q^{14} -0.922780 q^{15} +1.00000 q^{16} -1.97140 q^{17} -2.14848 q^{18} +2.65749 q^{19} +1.00000 q^{20} +2.26165 q^{21} -2.04640 q^{22} +3.70905 q^{23} -0.922780 q^{24} +1.00000 q^{25} +2.73473 q^{26} +4.75091 q^{27} -2.45091 q^{28} -4.65180 q^{29} -0.922780 q^{30} +5.51086 q^{31} +1.00000 q^{32} +1.88838 q^{33} -1.97140 q^{34} -2.45091 q^{35} -2.14848 q^{36} -0.227375 q^{37} +2.65749 q^{38} -2.52355 q^{39} +1.00000 q^{40} +0.00373133 q^{41} +2.26165 q^{42} -7.62879 q^{43} -2.04640 q^{44} -2.14848 q^{45} +3.70905 q^{46} -7.35091 q^{47} -0.922780 q^{48} -0.993037 q^{49} +1.00000 q^{50} +1.81917 q^{51} +2.73473 q^{52} -4.94341 q^{53} +4.75091 q^{54} -2.04640 q^{55} -2.45091 q^{56} -2.45228 q^{57} -4.65180 q^{58} +0.966468 q^{59} -0.922780 q^{60} -11.6911 q^{61} +5.51086 q^{62} +5.26572 q^{63} +1.00000 q^{64} +2.73473 q^{65} +1.88838 q^{66} -2.64188 q^{67} -1.97140 q^{68} -3.42263 q^{69} -2.45091 q^{70} -0.355281 q^{71} -2.14848 q^{72} -5.79466 q^{73} -0.227375 q^{74} -0.922780 q^{75} +2.65749 q^{76} +5.01554 q^{77} -2.52355 q^{78} -15.2199 q^{79} +1.00000 q^{80} +2.06138 q^{81} +0.00373133 q^{82} -3.67210 q^{83} +2.26165 q^{84} -1.97140 q^{85} -7.62879 q^{86} +4.29259 q^{87} -2.04640 q^{88} -17.8319 q^{89} -2.14848 q^{90} -6.70258 q^{91} +3.70905 q^{92} -5.08531 q^{93} -7.35091 q^{94} +2.65749 q^{95} -0.922780 q^{96} -12.0305 q^{97} -0.993037 q^{98} +4.39664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * q^99

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