LMFDB - Embedded newform 6010.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.23485$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.23485 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.23485 q^{6} -0.971978 q^{7} +1.00000 q^{8} +1.99454 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.23485 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.23485 q^{6} -0.971978 q^{7} +1.00000 q^{8} +1.99454 q^{9} +1.00000 q^{10} -2.26985 q^{11} -2.23485 q^{12} +4.74974 q^{13} -0.971978 q^{14} -2.23485 q^{15} +1.00000 q^{16} -5.16829 q^{17} +1.99454 q^{18} -2.10519 q^{19} +1.00000 q^{20} +2.17222 q^{21} -2.26985 q^{22} +3.32666 q^{23} -2.23485 q^{24} +1.00000 q^{25} +4.74974 q^{26} +2.24706 q^{27} -0.971978 q^{28} -7.06139 q^{29} -2.23485 q^{30} +5.27710 q^{31} +1.00000 q^{32} +5.07276 q^{33} -5.16829 q^{34} -0.971978 q^{35} +1.99454 q^{36} -6.88894 q^{37} -2.10519 q^{38} -10.6149 q^{39} +1.00000 q^{40} +11.4261 q^{41} +2.17222 q^{42} +5.15210 q^{43} -2.26985 q^{44} +1.99454 q^{45} +3.32666 q^{46} -2.01855 q^{47} -2.23485 q^{48} -6.05526 q^{49} +1.00000 q^{50} +11.5503 q^{51} +4.74974 q^{52} -9.34168 q^{53} +2.24706 q^{54} -2.26985 q^{55} -0.971978 q^{56} +4.70478 q^{57} -7.06139 q^{58} +8.51427 q^{59} -2.23485 q^{60} -3.05215 q^{61} +5.27710 q^{62} -1.93865 q^{63} +1.00000 q^{64} +4.74974 q^{65} +5.07276 q^{66} -4.20281 q^{67} -5.16829 q^{68} -7.43458 q^{69} -0.971978 q^{70} -3.81103 q^{71} +1.99454 q^{72} -13.6788 q^{73} -6.88894 q^{74} -2.23485 q^{75} -2.10519 q^{76} +2.20624 q^{77} -10.6149 q^{78} -14.8942 q^{79} +1.00000 q^{80} -11.0054 q^{81} +11.4261 q^{82} +11.4562 q^{83} +2.17222 q^{84} -5.16829 q^{85} +5.15210 q^{86} +15.7811 q^{87} -2.26985 q^{88} +2.24524 q^{89} +1.99454 q^{90} -4.61665 q^{91} +3.32666 q^{92} -11.7935 q^{93} -2.01855 q^{94} -2.10519 q^{95} -2.23485 q^{96} -8.88856 q^{97} -6.05526 q^{98} -4.52730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.23485	−1.29029	−0.645144	−	0.764061i	$-0.723203\pi$
$3$	−2.23485	−1.29029	−0.645144	+	0.764061i	$0.723203\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.23485	−0.912372
$7$	−0.971978	−0.367373	−0.183687	−	0.982985i	$-0.558803\pi$
$7$	−0.971978	−0.367373	−0.183687	+	0.982985i	$0.558803\pi$
$8$	1.00000	0.353553
$9$	1.99454	0.664845
$10$	1.00000	0.316228
$11$	−2.26985	−0.684386	−0.342193	−	0.939630i	$-0.611170\pi$
$11$	−2.26985	−0.684386	−0.342193	+	0.939630i	$0.611170\pi$
$12$	−2.23485	−0.645144
$13$	4.74974	1.31734	0.658671	−	0.752431i	$-0.271119\pi$
$13$	4.74974	1.31734	0.658671	+	0.752431i	$0.271119\pi$
$14$	−0.971978	−0.259772
$15$	−2.23485	−0.577035
$16$	1.00000	0.250000
$17$	−5.16829	−1.25349	−0.626747	−	0.779223i	$-0.715614\pi$
$17$	−5.16829	−1.25349	−0.626747	+	0.779223i	$0.715614\pi$
$18$	1.99454	0.470117
$19$	−2.10519	−0.482964	−0.241482	−	0.970405i	$-0.577634\pi$
$19$	−2.10519	−0.482964	−0.241482	+	0.970405i	$0.577634\pi$
$20$	1.00000	0.223607
$21$	2.17222	0.474018
$22$	−2.26985	−0.483934
$23$	3.32666	0.693658	0.346829	−	0.937928i	$-0.387258\pi$
$23$	3.32666	0.693658	0.346829	+	0.937928i	$0.387258\pi$
$24$	−2.23485	−0.456186
$25$	1.00000	0.200000
$26$	4.74974	0.931501
$27$	2.24706	0.432446
$28$	−0.971978	−0.183687
$29$	−7.06139	−1.31127	−0.655633	−	0.755079i	$-0.727598\pi$
$29$	−7.06139	−1.31127	−0.655633	+	0.755079i	$0.727598\pi$
$30$	−2.23485	−0.408025
$31$	5.27710	0.947794	0.473897	−	0.880580i	$-0.342847\pi$
$31$	5.27710	0.947794	0.473897	+	0.880580i	$0.342847\pi$
$32$	1.00000	0.176777
$33$	5.07276	0.883055
$34$	−5.16829	−0.886355
$35$	−0.971978	−0.164294
$36$	1.99454	0.332423
$37$	−6.88894	−1.13253	−0.566267	−	0.824222i	$-0.691613\pi$
$37$	−6.88894	−1.13253	−0.566267	+	0.824222i	$0.691613\pi$
$38$	−2.10519	−0.341507
$39$	−10.6149	−1.69975
$40$	1.00000	0.158114
$41$	11.4261	1.78446	0.892230	−	0.451582i	$-0.149140\pi$
$41$	11.4261	1.78446	0.892230	+	0.451582i	$0.149140\pi$
$42$	2.17222	0.335181
$43$	5.15210	0.785688	0.392844	−	0.919605i	$-0.371491\pi$
$43$	5.15210	0.785688	0.392844	+	0.919605i	$0.371491\pi$
$44$	−2.26985	−0.342193
$45$	1.99454	0.297328
$46$	3.32666	0.490490
$47$	−2.01855	−0.294436	−0.147218	−	0.989104i	$-0.547032\pi$
$47$	−2.01855	−0.294436	−0.147218	+	0.989104i	$0.547032\pi$
$48$	−2.23485	−0.322572
$49$	−6.05526	−0.865037
$50$	1.00000	0.141421
$51$	11.5503	1.61737
$52$	4.74974	0.658671
$53$	−9.34168	−1.28318	−0.641589	−	0.767048i	$-0.721725\pi$
$53$	−9.34168	−1.28318	−0.641589	+	0.767048i	$0.721725\pi$
$54$	2.24706	0.305786
$55$	−2.26985	−0.306067
$56$	−0.971978	−0.129886
$57$	4.70478	0.623163
$58$	−7.06139	−0.927206
$59$	8.51427	1.10846	0.554232	−	0.832362i	$-0.313012\pi$
$59$	8.51427	1.10846	0.554232	+	0.832362i	$0.313012\pi$
$60$	−2.23485	−0.288517
$61$	−3.05215	−0.390788	−0.195394	−	0.980725i	$-0.562599\pi$
$61$	−3.05215	−0.390788	−0.195394	+	0.980725i	$0.562599\pi$
$62$	5.27710	0.670192
$63$	−1.93865	−0.244246
$64$	1.00000	0.125000
$65$	4.74974	0.589133
$66$	5.07276	0.624414
$67$	−4.20281	−0.513455	−0.256728	−	0.966484i	$-0.582644\pi$
$67$	−4.20281	−0.513455	−0.256728	+	0.966484i	$0.582644\pi$
$68$	−5.16829	−0.626747
$69$	−7.43458	−0.895019
$70$	−0.971978	−0.116174
$71$	−3.81103	−0.452286	−0.226143	−	0.974094i	$-0.572612\pi$
$71$	−3.81103	−0.452286	−0.226143	+	0.974094i	$0.572612\pi$
$72$	1.99454	0.235058
$73$	−13.6788	−1.60098	−0.800491	−	0.599345i	$-0.795428\pi$
$73$	−13.6788	−1.60098	−0.800491	+	0.599345i	$0.795428\pi$
$74$	−6.88894	−0.800823
$75$	−2.23485	−0.258058
$76$	−2.10519	−0.241482
$77$	2.20624	0.251425
$78$	−10.6149	−1.20191
$79$	−14.8942	−1.67573	−0.837864	−	0.545879i	$-0.816196\pi$
$79$	−14.8942	−1.67573	−0.837864	+	0.545879i	$0.816196\pi$
$80$	1.00000	0.111803
$81$	−11.0054	−1.22283
$82$	11.4261	1.26180
$83$	11.4562	1.25748	0.628742	−	0.777614i	$-0.283570\pi$
$83$	11.4562	1.25748	0.628742	+	0.777614i	$0.283570\pi$
$84$	2.17222	0.237009
$85$	−5.16829	−0.560580
$86$	5.15210	0.555565
$87$	15.7811	1.69191
$88$	−2.26985	−0.241967
$89$	2.24524	0.237995	0.118997	−	0.992895i	$-0.462032\pi$
$89$	2.24524	0.237995	0.118997	+	0.992895i	$0.462032\pi$
$90$	1.99454	0.210243
$91$	−4.61665	−0.483956
$92$	3.32666	0.346829
$93$	−11.7935	−1.22293
$94$	−2.01855	−0.208198
$95$	−2.10519	−0.215988
$96$	−2.23485	−0.228093
$97$	−8.88856	−0.902497	−0.451248	−	0.892398i	$-0.649021\pi$
$97$	−8.88856	−0.902497	−0.451248	+	0.892398i	$0.649021\pi$
$98$	−6.05526	−0.611673
$99$	−4.52730	−0.455010
$100$	1.00000	0.100000
$101$	−10.5587	−1.05063	−0.525314	−	0.850909i	$-0.676052\pi$
$101$	−10.5587	−1.05063	−0.525314	+	0.850909i	$0.676052\pi$
$102$	11.5503	1.14365
$103$	5.85412	0.576823	0.288412	−	0.957506i	$-0.406873\pi$
$103$	5.85412	0.576823	0.288412	+	0.957506i	$0.406873\pi$
$104$	4.74974	0.465751
$105$	2.17222	0.211987
$106$	−9.34168	−0.907344
$107$	−3.31588	−0.320558	−0.160279	−	0.987072i	$-0.551239\pi$
$107$	−3.31588	−0.320558	−0.160279	+	0.987072i	$0.551239\pi$
$108$	2.24706	0.216223
$109$	18.9440	1.81450	0.907252	−	0.420587i	$-0.138176\pi$
$109$	18.9440	1.81450	0.907252	+	0.420587i	$0.138176\pi$
$110$	−2.26985	−0.216422
$111$	15.3957	1.46130
$112$	−0.971978	−0.0918433
$113$	13.9917	1.31623	0.658113	−	0.752919i	$-0.271355\pi$
$113$	13.9917	1.31623	0.658113	+	0.752919i	$0.271355\pi$
$114$	4.70478	0.440643
$115$	3.32666	0.310213
$116$	−7.06139	−0.655633
$117$	9.47353	0.875828
$118$	8.51427	0.783802
$119$	5.02347	0.460500
$120$	−2.23485	−0.204013
$121$	−5.84778	−0.531616
$122$	−3.05215	−0.276329
$123$	−25.5356	−2.30247
$124$	5.27710	0.473897
$125$	1.00000	0.0894427
$126$	−1.93865	−0.172708
$127$	10.9412	0.970871	0.485435	−	0.874273i	$-0.338661\pi$
$127$	10.9412	0.970871	0.485435	+	0.874273i	$0.338661\pi$
$128$	1.00000	0.0883883
$129$	−11.5142	−1.01376
$130$	4.74974	0.416580
$131$	−10.7917	−0.942879	−0.471440	−	0.881898i	$-0.656265\pi$
$131$	−10.7917	−0.942879	−0.471440	+	0.881898i	$0.656265\pi$
$132$	5.07276	0.441528
$133$	2.04620	0.177428
$134$	−4.20281	−0.363068
$135$	2.24706	0.193396
$136$	−5.16829	−0.443177
$137$	−9.17558	−0.783923	−0.391961	−	0.919982i	$-0.628203\pi$
$137$	−9.17558	−0.783923	−0.391961	+	0.919982i	$0.628203\pi$
$138$	−7.43458	−0.632874
$139$	20.1877	1.71230	0.856149	−	0.516728i	$-0.172850\pi$
$139$	20.1877	1.71230	0.856149	+	0.516728i	$0.172850\pi$
$140$	−0.971978	−0.0821471
$141$	4.51116	0.379908
$142$	−3.81103	−0.319814
$143$	−10.7812	−0.901570
$144$	1.99454	0.166211
$145$	−7.06139	−0.586416
$146$	−13.6788	−1.13207
$147$	13.5326	1.11615
$148$	−6.88894	−0.566267
$149$	−12.3242	−1.00964	−0.504820	−	0.863225i	$-0.668441\pi$
$149$	−12.3242	−1.00964	−0.504820	+	0.863225i	$0.668441\pi$
$150$	−2.23485	−0.182474
$151$	−3.50054	−0.284870	−0.142435	−	0.989804i	$-0.545493\pi$
$151$	−3.50054	−0.284870	−0.142435	+	0.989804i	$0.545493\pi$
$152$	−2.10519	−0.170754
$153$	−10.3083	−0.833380
$154$	2.20624	0.177784
$155$	5.27710	0.423866
$156$	−10.6149	−0.849876
$157$	−8.93461	−0.713059	−0.356530	−	0.934284i	$-0.616040\pi$
$157$	−8.93461	−0.713059	−0.356530	+	0.934284i	$0.616040\pi$
$158$	−14.8942	−1.18492
$159$	20.8772	1.65567
$160$	1.00000	0.0790569
$161$	−3.23345	−0.254831
$162$	−11.0054	−0.864669
$163$	16.2048	1.26926	0.634629	−	0.772817i	$-0.281153\pi$
$163$	16.2048	1.26926	0.634629	+	0.772817i	$0.281153\pi$
$164$	11.4261	0.892230
$165$	5.07276	0.394914
$166$	11.4562	0.889176
$167$	−17.0541	−1.31968	−0.659842	−	0.751404i	$-0.729377\pi$
$167$	−17.0541	−1.31968	−0.659842	+	0.751404i	$0.729377\pi$
$168$	2.17222	0.167591
$169$	9.56006	0.735389
$170$	−5.16829	−0.396390
$171$	−4.19888	−0.321096
$172$	5.15210	0.392844
$173$	−19.1959	−1.45944	−0.729719	−	0.683747i	$-0.760349\pi$
$173$	−19.1959	−1.45944	−0.729719	+	0.683747i	$0.760349\pi$
$174$	15.7811	1.19636
$175$	−0.971978	−0.0734746
$176$	−2.26985	−0.171096
$177$	−19.0281	−1.43024
$178$	2.24524	0.168288
$179$	−4.48302	−0.335076	−0.167538	−	0.985866i	$-0.553582\pi$
$179$	−4.48302	−0.335076	−0.167538	+	0.985866i	$0.553582\pi$
$180$	1.99454	0.148664
$181$	−2.13871	−0.158969	−0.0794847	−	0.996836i	$-0.525327\pi$
$181$	−2.13871	−0.158969	−0.0794847	+	0.996836i	$0.525327\pi$
$182$	−4.61665	−0.342209
$183$	6.82109	0.504230
$184$	3.32666	0.245245
$185$	−6.88894	−0.506485
$186$	−11.7935	−0.864741
$187$	11.7312	0.857874
$188$	−2.01855	−0.147218
$189$	−2.18409	−0.158869
$190$	−2.10519	−0.152727
$191$	−23.9579	−1.73353	−0.866767	−	0.498713i	$-0.833806\pi$
$191$	−23.9579	−1.73353	−0.866767	+	0.498713i	$0.833806\pi$
$192$	−2.23485	−0.161286
$193$	8.02182	0.577423	0.288712	−	0.957416i	$-0.406773\pi$
$193$	8.02182	0.577423	0.288712	+	0.957416i	$0.406773\pi$
$194$	−8.88856	−0.638162
$195$	−10.6149	−0.760152
$196$	−6.05526	−0.432518
$197$	−21.4228	−1.52631	−0.763155	−	0.646215i	$-0.776351\pi$
$197$	−21.4228	−1.52631	−0.763155	+	0.646215i	$0.776351\pi$
$198$	−4.52730	−0.321741
$199$	0.485772	0.0344354	0.0172177	−	0.999852i	$-0.494519\pi$
$199$	0.485772	0.0344354	0.0172177	+	0.999852i	$0.494519\pi$
$200$	1.00000	0.0707107
$201$	9.39264	0.662506
$202$	−10.5587	−0.742906
$203$	6.86352	0.481724
$204$	11.5503	0.808685
$205$	11.4261	0.798034
$206$	5.85412	0.407876
$207$	6.63515	0.461175
$208$	4.74974	0.329335
$209$	4.77847	0.330534
$210$	2.17222	0.149898
$211$	−20.6922	−1.42451	−0.712256	−	0.701920i	$-0.752326\pi$
$211$	−20.6922	−1.42451	−0.712256	+	0.701920i	$0.752326\pi$
$212$	−9.34168	−0.641589
$213$	8.51706	0.583579
$214$	−3.31588	−0.226669
$215$	5.15210	0.351370
$216$	2.24706	0.152893
$217$	−5.12922	−0.348194
$218$	18.9440	1.28305
$219$	30.5700	2.06573
$220$	−2.26985	−0.153033
$221$	−24.5481	−1.65128
$222$	15.3957	1.03329
$223$	3.28186	0.219770	0.109885	−	0.993944i	$-0.464952\pi$
$223$	3.28186	0.219770	0.109885	+	0.993944i	$0.464952\pi$
$224$	−0.971978	−0.0649430
$225$	1.99454	0.132969
$226$	13.9917	0.930712
$227$	20.8167	1.38166	0.690828	−	0.723020i	$-0.257246\pi$
$227$	20.8167	1.38166	0.690828	+	0.723020i	$0.257246\pi$
$228$	4.70478	0.311582
$229$	−11.5039	−0.760201	−0.380101	−	0.924945i	$-0.624111\pi$
$229$	−11.5039	−0.760201	−0.380101	+	0.924945i	$0.624111\pi$
$230$	3.32666	0.219354
$231$	−4.93062	−0.324411
$232$	−7.06139	−0.463603
$233$	−15.6360	−1.02435	−0.512175	−	0.858881i	$-0.671160\pi$
$233$	−15.6360	−1.02435	−0.512175	+	0.858881i	$0.671160\pi$
$234$	9.47353	0.619304
$235$	−2.01855	−0.131676
$236$	8.51427	0.554232
$237$	33.2862	2.16217
$238$	5.02347	0.325623
$239$	−24.3679	−1.57623	−0.788114	−	0.615529i	$-0.788942\pi$
$239$	−24.3679	−1.57623	−0.788114	+	0.615529i	$0.788942\pi$
$240$	−2.23485	−0.144259
$241$	1.23492	0.0795480	0.0397740	−	0.999209i	$-0.487336\pi$
$241$	1.23492	0.0795480	0.0397740	+	0.999209i	$0.487336\pi$
$242$	−5.84778	−0.375910
$243$	17.8543	1.14535
$244$	−3.05215	−0.195394
$245$	−6.05526	−0.386856
$246$	−25.5356	−1.62809
$247$	−9.99912	−0.636229
$248$	5.27710	0.335096
$249$	−25.6029	−1.62252
$250$	1.00000	0.0632456
$251$	−2.98498	−0.188410	−0.0942050	−	0.995553i	$-0.530031\pi$
$251$	−2.98498	−0.188410	−0.0942050	+	0.995553i	$0.530031\pi$
$252$	−1.93865	−0.122123
$253$	−7.55103	−0.474729
$254$	10.9412	0.686509
$255$	11.5503	0.723310
$256$	1.00000	0.0625000
$257$	7.22097	0.450432	0.225216	−	0.974309i	$-0.427691\pi$
$257$	7.22097	0.450432	0.225216	+	0.974309i	$0.427691\pi$
$258$	−11.5142	−0.716840
$259$	6.69590	0.416063
$260$	4.74974	0.294567
$261$	−14.0842	−0.871790
$262$	−10.7917	−0.666716
$263$	25.9333	1.59911	0.799557	−	0.600590i	$-0.205068\pi$
$263$	25.9333	1.59911	0.799557	+	0.600590i	$0.205068\pi$
$264$	5.07276	0.312207
$265$	−9.34168	−0.573855
$266$	2.04620	0.125461
$267$	−5.01776	−0.307082
$268$	−4.20281	−0.256728
$269$	−20.2849	−1.23679	−0.618395	−	0.785868i	$-0.712217\pi$
$269$	−20.2849	−1.23679	−0.618395	+	0.785868i	$0.712217\pi$
$270$	2.24706	0.136752
$271$	−12.3933	−0.752841	−0.376421	−	0.926449i	$-0.622845\pi$
$271$	−12.3933	−0.752841	−0.376421	+	0.926449i	$0.622845\pi$
$272$	−5.16829	−0.313374
$273$	10.3175	0.624443
$274$	−9.17558	−0.554317
$275$	−2.26985	−0.136877
$276$	−7.43458	−0.447509
$277$	−0.498628	−0.0299596	−0.0149798	−	0.999888i	$-0.504768\pi$
$277$	−0.498628	−0.0299596	−0.0149798	+	0.999888i	$0.504768\pi$
$278$	20.1877	1.21078
$279$	10.5254	0.630137
$280$	−0.971978	−0.0580868
$281$	−26.5416	−1.58334	−0.791668	−	0.610951i	$-0.790787\pi$
$281$	−26.5416	−1.58334	−0.791668	+	0.610951i	$0.790787\pi$
$282$	4.51116	0.268636
$283$	−22.7403	−1.35177	−0.675885	−	0.737007i	$-0.736238\pi$
$283$	−22.7403	−1.35177	−0.675885	+	0.737007i	$0.736238\pi$
$284$	−3.81103	−0.226143
$285$	4.70478	0.278687
$286$	−10.7812	−0.637506
$287$	−11.1059	−0.655563
$288$	1.99454	0.117529
$289$	9.71123	0.571249
$290$	−7.06139	−0.414659
$291$	19.8646	1.16448
$292$	−13.6788	−0.800491
$293$	−9.05231	−0.528842	−0.264421	−	0.964407i	$-0.585181\pi$
$293$	−9.05231	−0.528842	−0.264421	+	0.964407i	$0.585181\pi$
$294$	13.5326	0.789235
$295$	8.51427	0.495720
$296$	−6.88894	−0.400411
$297$	−5.10048	−0.295960
$298$	−12.3242	−0.713923
$299$	15.8008	0.913784
$300$	−2.23485	−0.129029
$301$	−5.00773	−0.288641
$302$	−3.50054	−0.201434
$303$	23.5970	1.35561
$304$	−2.10519	−0.120741
$305$	−3.05215	−0.174766
$306$	−10.3083	−0.589289
$307$	−15.4543	−0.882021	−0.441011	−	0.897502i	$-0.645380\pi$
$307$	−15.4543	−0.882021	−0.441011	+	0.897502i	$0.645380\pi$
$308$	2.20624	0.125712
$309$	−13.0831	−0.744269
$310$	5.27710	0.299719
$311$	−26.0874	−1.47928	−0.739640	−	0.673003i	$-0.765004\pi$
$311$	−26.0874	−1.47928	−0.739640	+	0.673003i	$0.765004\pi$
$312$	−10.6149	−0.600953
$313$	9.66909	0.546529	0.273265	−	0.961939i	$-0.411896\pi$
$313$	9.66909	0.546529	0.273265	+	0.961939i	$0.411896\pi$
$314$	−8.93461	−0.504209
$315$	−1.93865	−0.109230
$316$	−14.8942	−0.837864
$317$	22.1831	1.24593	0.622963	−	0.782251i	$-0.285929\pi$
$317$	22.1831	1.24593	0.622963	+	0.782251i	$0.285929\pi$
$318$	20.8772	1.17074
$319$	16.0283	0.897412
$320$	1.00000	0.0559017
$321$	7.41048	0.413613
$322$	−3.23345	−0.180193
$323$	10.8802	0.605393
$324$	−11.0054	−0.611413
$325$	4.74974	0.263468
$326$	16.2048	0.897501
$327$	−42.3369	−2.34123
$328$	11.4261	0.630902
$329$	1.96199	0.108168
$330$	5.07276	0.279247
$331$	−3.43067	−0.188567	−0.0942833	−	0.995545i	$-0.530056\pi$
$331$	−3.43067	−0.188567	−0.0942833	+	0.995545i	$0.530056\pi$
$332$	11.4562	0.628742
$333$	−13.7402	−0.752960
$334$	−17.0541	−0.933158
$335$	−4.20281	−0.229624
$336$	2.17222	0.118504
$337$	19.2095	1.04641	0.523204	−	0.852208i	$-0.324737\pi$
$337$	19.2095	1.04641	0.523204	+	0.852208i	$0.324737\pi$
$338$	9.56006	0.519999
$339$	−31.2692	−1.69831
$340$	−5.16829	−0.280290
$341$	−11.9782	−0.648657
$342$	−4.19888	−0.227049
$343$	12.6894	0.685165
$344$	5.15210	0.277783
$345$	−7.43458	−0.400264
$346$	−19.1959	−1.03198
$347$	28.0513	1.50587	0.752937	−	0.658093i	$-0.228637\pi$
$347$	28.0513	1.50587	0.752937	+	0.658093i	$0.228637\pi$
$348$	15.7811	0.845957
$349$	−18.7428	−1.00328	−0.501640	−	0.865076i	$-0.667270\pi$
$349$	−18.7428	−1.00328	−0.501640	+	0.865076i	$0.667270\pi$
$350$	−0.971978	−0.0519544
$351$	10.6729	0.569680
$352$	−2.26985	−0.120983
$353$	−2.39277	−0.127354	−0.0636772	−	0.997971i	$-0.520283\pi$
$353$	−2.39277	−0.127354	−0.0636772	+	0.997971i	$0.520283\pi$
$354$	−19.0281	−1.01133
$355$	−3.81103	−0.202268
$356$	2.24524	0.118997
$357$	−11.2267	−0.594178
$358$	−4.48302	−0.236935
$359$	−24.3064	−1.28284	−0.641421	−	0.767189i	$-0.721655\pi$
$359$	−24.3064	−1.28284	−0.641421	+	0.767189i	$0.721655\pi$
$360$	1.99454	0.105121
$361$	−14.5682	−0.766746
$362$	−2.13871	−0.112408
$363$	13.0689	0.685939
$364$	−4.61665	−0.241978
$365$	−13.6788	−0.715981
$366$	6.82109	0.356544
$367$	0.508134	0.0265244	0.0132622	−	0.999912i	$-0.495778\pi$
$367$	0.508134	0.0265244	0.0132622	+	0.999912i	$0.495778\pi$
$368$	3.32666	0.173414
$369$	22.7898	1.18639
$370$	−6.88894	−0.358139
$371$	9.07991	0.471405
$372$	−11.7935	−0.611464
$373$	−20.4909	−1.06098	−0.530490	−	0.847691i	$-0.677992\pi$
$373$	−20.4909	−1.06098	−0.530490	+	0.847691i	$0.677992\pi$
$374$	11.7312	0.606608
$375$	−2.23485	−0.115407
$376$	−2.01855	−0.104099
$377$	−33.5398	−1.72739
$378$	−2.18409	−0.112338
$379$	21.5832	1.10865	0.554326	−	0.832299i	$-0.312976\pi$
$379$	21.5832	1.10865	0.554326	+	0.832299i	$0.312976\pi$
$380$	−2.10519	−0.107994
$381$	−24.4518	−1.25270
$382$	−23.9579	−1.22579
$383$	−30.7891	−1.57325	−0.786625	−	0.617431i	$-0.788174\pi$
$383$	−30.7891	−1.57325	−0.786625	+	0.617431i	$0.788174\pi$
$384$	−2.23485	−0.114046
$385$	2.20624	0.112441
$386$	8.02182	0.408300
$387$	10.2761	0.522361
$388$	−8.88856	−0.451248
$389$	11.3147	0.573680	0.286840	−	0.957979i	$-0.407395\pi$
$389$	11.3147	0.573680	0.286840	+	0.957979i	$0.407395\pi$
$390$	−10.6149	−0.537509
$391$	−17.1932	−0.869496
$392$	−6.05526	−0.305837
$393$	24.1179	1.21659
$394$	−21.4228	−1.07926
$395$	−14.8942	−0.749408
$396$	−4.52730	−0.227505
$397$	−25.7552	−1.29261	−0.646307	−	0.763077i	$-0.723688\pi$
$397$	−25.7552	−1.29261	−0.646307	+	0.763077i	$0.723688\pi$
$398$	0.485772	0.0243495
$399$	−4.57294	−0.228934
$400$	1.00000	0.0500000
$401$	36.4590	1.82068	0.910338	−	0.413866i	$-0.135822\pi$
$401$	36.4590	1.82068	0.910338	+	0.413866i	$0.135822\pi$
$402$	9.39264	0.468462
$403$	25.0648	1.24857
$404$	−10.5587	−0.525314
$405$	−11.0054	−0.546864
$406$	6.86352	0.340631
$407$	15.6369	0.775090
$408$	11.5503	0.571827
$409$	−15.2347	−0.753307	−0.376654	−	0.926354i	$-0.622925\pi$
$409$	−15.2347	−0.753307	−0.376654	+	0.926354i	$0.622925\pi$
$410$	11.4261	0.564296
$411$	20.5060	1.01149
$412$	5.85412	0.288412
$413$	−8.27568	−0.407220
$414$	6.63515	0.326100
$415$	11.4562	0.562364
$416$	4.74974	0.232875
$417$	−45.1164	−2.20936
$418$	4.77847	0.233723
$419$	−4.27469	−0.208832	−0.104416	−	0.994534i	$-0.533297\pi$
$419$	−4.27469	−0.208832	−0.104416	+	0.994534i	$0.533297\pi$
$420$	2.17222	0.105994
$421$	28.7923	1.40325	0.701625	−	0.712546i	$-0.252458\pi$
$421$	28.7923	1.40325	0.701625	+	0.712546i	$0.252458\pi$
$422$	−20.6922	−1.00728
$423$	−4.02608	−0.195755
$424$	−9.34168	−0.453672
$425$	−5.16829	−0.250699
$426$	8.51706	0.412653
$427$	2.96663	0.143565
$428$	−3.31588	−0.160279
$429$	24.0943	1.16329
$430$	5.15210	0.248456
$431$	17.5168	0.843755	0.421878	−	0.906653i	$-0.361371\pi$
$431$	17.5168	0.843755	0.421878	+	0.906653i	$0.361371\pi$
$432$	2.24706	0.108112
$433$	10.8362	0.520755	0.260377	−	0.965507i	$-0.416153\pi$
$433$	10.8362	0.520755	0.260377	+	0.965507i	$0.416153\pi$
$434$	−5.12922	−0.246210
$435$	15.7811	0.756647
$436$	18.9440	0.907252
$437$	−7.00327	−0.335012
$438$	30.5700	1.46069
$439$	−23.8707	−1.13929	−0.569643	−	0.821893i	$-0.692918\pi$
$439$	−23.8707	−1.13929	−0.569643	+	0.821893i	$0.692918\pi$
$440$	−2.26985	−0.108211
$441$	−12.0774	−0.575116
$442$	−24.5481	−1.16763
$443$	−27.9217	−1.32660	−0.663299	−	0.748355i	$-0.730844\pi$
$443$	−27.9217	−1.32660	−0.663299	+	0.748355i	$0.730844\pi$
$444$	15.3957	0.730648
$445$	2.24524	0.106434
$446$	3.28186	0.155401
$447$	27.5427	1.30273
$448$	−0.971978	−0.0459217
$449$	32.8472	1.55015	0.775077	−	0.631867i	$-0.217711\pi$
$449$	32.8472	1.55015	0.775077	+	0.631867i	$0.217711\pi$
$450$	1.99454	0.0940233
$451$	−25.9356	−1.22126
$452$	13.9917	0.658113
$453$	7.82317	0.367565
$454$	20.8167	0.976978
$455$	−4.61665	−0.216432
$456$	4.70478	0.220322
$457$	21.6199	1.01133	0.505667	−	0.862729i	$-0.331246\pi$
$457$	21.6199	1.01133	0.505667	+	0.862729i	$0.331246\pi$
$458$	−11.5039	−0.537543
$459$	−11.6134	−0.542069
$460$	3.32666	0.155107
$461$	4.00324	0.186449	0.0932247	−	0.995645i	$-0.470283\pi$
$461$	4.00324	0.186449	0.0932247	+	0.995645i	$0.470283\pi$
$462$	−4.93062	−0.229393
$463$	8.14567	0.378561	0.189281	−	0.981923i	$-0.439384\pi$
$463$	8.14567	0.378561	0.189281	+	0.981923i	$0.439384\pi$
$464$	−7.06139	−0.327817
$465$	−11.7935	−0.546910
$466$	−15.6360	−0.724324
$467$	12.1779	0.563528	0.281764	−	0.959484i	$-0.409081\pi$
$467$	12.1779	0.563528	0.281764	+	0.959484i	$0.409081\pi$
$468$	9.47353	0.437914
$469$	4.08504	0.188630
$470$	−2.01855	−0.0931090
$471$	19.9675	0.920052
$472$	8.51427	0.391901
$473$	−11.6945	−0.537714
$474$	33.2862	1.52889
$475$	−2.10519	−0.0965928
$476$	5.02347	0.230250
$477$	−18.6323	−0.853115
$478$	−24.3679	−1.11456
$479$	−28.2514	−1.29084	−0.645420	−	0.763828i	$-0.723318\pi$
$479$	−28.2514	−1.29084	−0.645420	+	0.763828i	$0.723318\pi$
$480$	−2.23485	−0.102006
$481$	−32.7207	−1.49193
$482$	1.23492	0.0562489
$483$	7.22625	0.328806
$484$	−5.84778	−0.265808
$485$	−8.88856	−0.403609
$486$	17.8543	0.809886
$487$	41.3590	1.87416	0.937078	−	0.349119i	$-0.113519\pi$
$487$	41.3590	1.87416	0.937078	+	0.349119i	$0.113519\pi$
$488$	−3.05215	−0.138164
$489$	−36.2152	−1.63771
$490$	−6.05526	−0.273549
$491$	−18.1492	−0.819061	−0.409530	−	0.912296i	$-0.634307\pi$
$491$	−18.1492	−0.819061	−0.409530	+	0.912296i	$0.634307\pi$
$492$	−25.5356	−1.15123
$493$	36.4953	1.64367
$494$	−9.99912	−0.449882
$495$	−4.52730	−0.203487
$496$	5.27710	0.236949
$497$	3.70424	0.166158
$498$	−25.6029	−1.14729
$499$	−18.0488	−0.807973	−0.403987	−	0.914765i	$-0.632376\pi$
$499$	−18.0488	−0.807973	−0.403987	+	0.914765i	$0.632376\pi$
$500$	1.00000	0.0447214
$501$	38.1132	1.70277
$502$	−2.98498	−0.133226
$503$	39.2573	1.75040	0.875199	−	0.483764i	$-0.160731\pi$
$503$	39.2573	1.75040	0.875199	+	0.483764i	$0.160731\pi$
$504$	−1.93865	−0.0863541
$505$	−10.5587	−0.469855
$506$	−7.55103	−0.335684
$507$	−21.3653	−0.948865
$508$	10.9412	0.485435
$509$	−36.6908	−1.62629	−0.813145	−	0.582061i	$-0.802247\pi$
$509$	−36.6908	−1.62629	−0.813145	+	0.582061i	$0.802247\pi$
$510$	11.5503	0.511457
$511$	13.2955	0.588158
$512$	1.00000	0.0441942
$513$	−4.73049	−0.208856
$514$	7.22097	0.318503
$515$	5.85412	0.257963
$516$	−11.5142	−0.506882
$517$	4.58182	0.201508
$518$	6.69590	0.294201
$519$	42.8999	1.88310
$520$	4.74974	0.208290
$521$	−35.2070	−1.54245	−0.771224	−	0.636564i	$-0.780355\pi$
$521$	−35.2070	−1.54245	−0.771224	+	0.636564i	$0.780355\pi$
$522$	−14.0842	−0.616448
$523$	−5.54557	−0.242491	−0.121245	−	0.992623i	$-0.538689\pi$
$523$	−5.54557	−0.242491	−0.121245	+	0.992623i	$0.538689\pi$
$524$	−10.7917	−0.471440
$525$	2.17222	0.0948035
$526$	25.9333	1.13074
$527$	−27.2736	−1.18806
$528$	5.07276	0.220764
$529$	−11.9333	−0.518839
$530$	−9.34168	−0.405777
$531$	16.9820	0.736957
$532$	2.04620	0.0887141
$533$	54.2711	2.35074
$534$	−5.01776	−0.217140
$535$	−3.31588	−0.143358
$536$	−4.20281	−0.181534
$537$	10.0189	0.432345
$538$	−20.2849	−0.874542
$539$	13.7445	0.592019
$540$	2.24706	0.0966980
$541$	−20.4403	−0.878798	−0.439399	−	0.898292i	$-0.644809\pi$
$541$	−20.4403	−0.878798	−0.439399	+	0.898292i	$0.644809\pi$
$542$	−12.3933	−0.532339
$543$	4.77970	0.205116
$544$	−5.16829	−0.221589
$545$	18.9440	0.811471
$546$	10.3175	0.441548
$547$	−18.5405	−0.792735	−0.396367	−	0.918092i	$-0.629729\pi$
$547$	−18.5405	−0.792735	−0.396367	+	0.918092i	$0.629729\pi$
$548$	−9.17558	−0.391961
$549$	−6.08763	−0.259814
$550$	−2.26985	−0.0967867
$551$	14.8656	0.633295
$552$	−7.43458	−0.316437
$553$	14.4768	0.615617
$554$	−0.498628	−0.0211847
$555$	15.3957	0.653512
$556$	20.1877	0.856149
$557$	−7.03593	−0.298122	−0.149061	−	0.988828i	$-0.547625\pi$
$557$	−7.03593	−0.298122	−0.149061	+	0.988828i	$0.547625\pi$
$558$	10.5254	0.445574
$559$	24.4712	1.03502
$560$	−0.971978	−0.0410736
$561$	−26.2175	−1.10690
$562$	−26.5416	−1.11959
$563$	−4.69898	−0.198039	−0.0990193	−	0.995086i	$-0.531571\pi$
$563$	−4.69898	−0.198039	−0.0990193	+	0.995086i	$0.531571\pi$
$564$	4.51116	0.189954
$565$	13.9917	0.588634
$566$	−22.7403	−0.955845
$567$	10.6970	0.449234
$568$	−3.81103	−0.159907
$569$	21.3855	0.896528	0.448264	−	0.893901i	$-0.352042\pi$
$569$	21.3855	0.896528	0.448264	+	0.893901i	$0.352042\pi$
$570$	4.70478	0.197062
$571$	−12.3691	−0.517629	−0.258814	−	0.965927i	$-0.583332\pi$
$571$	−12.3691	−0.517629	−0.258814	+	0.965927i	$0.583332\pi$
$572$	−10.7812	−0.450785
$573$	53.5423	2.23676
$574$	−11.1059	−0.463553
$575$	3.32666	0.138732
$576$	1.99454	0.0831057
$577$	6.83425	0.284513	0.142257	−	0.989830i	$-0.454564\pi$
$577$	6.83425	0.284513	0.142257	+	0.989830i	$0.454564\pi$
$578$	9.71123	0.403934
$579$	−17.9275	−0.745043
$580$	−7.06139	−0.293208
$581$	−11.1352	−0.461966
$582$	19.8646	0.823413
$583$	21.2042	0.878189
$584$	−13.6788	−0.566033
$585$	9.47353	0.391682
$586$	−9.05231	−0.373948
$587$	29.0110	1.19741	0.598706	−	0.800969i	$-0.295682\pi$
$587$	29.0110	1.19741	0.598706	+	0.800969i	$0.295682\pi$
$588$	13.5326	0.558074
$589$	−11.1093	−0.457751
$590$	8.51427	0.350527
$591$	47.8766	1.96938
$592$	−6.88894	−0.283134
$593$	−25.3143	−1.03953	−0.519767	−	0.854308i	$-0.673981\pi$
$593$	−25.3143	−1.03953	−0.519767	+	0.854308i	$0.673981\pi$
$594$	−5.10048	−0.209275
$595$	5.02347	0.205942
$596$	−12.3242	−0.504820
$597$	−1.08562	−0.0444317
$598$	15.8008	0.646143
$599$	21.0656	0.860719	0.430359	−	0.902658i	$-0.358387\pi$
$599$	21.0656	0.860719	0.430359	+	0.902658i	$0.358387\pi$
$600$	−2.23485	−0.0912372
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−5.00773	−0.204100
$603$	−8.38266	−0.341368
$604$	−3.50054	−0.142435
$605$	−5.84778	−0.237746
$606$	23.5970	0.958563
$607$	38.1811	1.54972	0.774861	−	0.632132i	$-0.217820\pi$
$607$	38.1811	1.54972	0.774861	+	0.632132i	$0.217820\pi$
$608$	−2.10519	−0.0853768
$609$	−15.3389	−0.621564
$610$	−3.05215	−0.123578
$611$	−9.58762	−0.387873
$612$	−10.3083	−0.416690
$613$	13.1729	0.532050	0.266025	−	0.963966i	$-0.414290\pi$
$613$	13.1729	0.532050	0.266025	+	0.963966i	$0.414290\pi$
$614$	−15.4543	−0.623683
$615$	−25.5356	−1.02969
$616$	2.20624	0.0888921
$617$	−35.6371	−1.43470	−0.717348	−	0.696715i	$-0.754644\pi$
$617$	−35.6371	−1.43470	−0.717348	+	0.696715i	$0.754644\pi$
$618$	−13.0831	−0.526277
$619$	20.2223	0.812804	0.406402	−	0.913694i	$-0.366783\pi$
$619$	20.2223	0.812804	0.406402	+	0.913694i	$0.366783\pi$
$620$	5.27710	0.211933
$621$	7.47521	0.299970
$622$	−26.0874	−1.04601
$623$	−2.18232	−0.0874328
$624$	−10.6149	−0.424938
$625$	1.00000	0.0400000
$626$	9.66909	0.386455
$627$	−10.6791	−0.426484
$628$	−8.93461	−0.356530
$629$	35.6040	1.41963
$630$	−1.93865	−0.0772375
$631$	−38.0512	−1.51479	−0.757397	−	0.652954i	$-0.773529\pi$
$631$	−38.0512	−1.51479	−0.757397	+	0.652954i	$0.773529\pi$
$632$	−14.8942	−0.592459
$633$	46.2439	1.83803
$634$	22.1831	0.881003
$635$	10.9412	0.434187
$636$	20.8772	0.827835
$637$	−28.7609	−1.13955
$638$	16.0283	0.634566
$639$	−7.60123	−0.300700
$640$	1.00000	0.0395285
$641$	38.2182	1.50953	0.754764	−	0.655997i	$-0.227751\pi$
$641$	38.2182	1.50953	0.754764	+	0.655997i	$0.227751\pi$
$642$	7.41048	0.292468
$643$	30.5939	1.20650	0.603252	−	0.797550i	$-0.293871\pi$
$643$	30.5939	1.20650	0.603252	+	0.797550i	$0.293871\pi$
$644$	−3.23345	−0.127416
$645$	−11.5142	−0.453369
$646$	10.8802	0.428078
$647$	−42.3448	−1.66474	−0.832372	−	0.554217i	$-0.813018\pi$
$647$	−42.3448	−1.66474	−0.832372	+	0.554217i	$0.813018\pi$
$648$	−11.0054	−0.432334
$649$	−19.3261	−0.758616
$650$	4.74974	0.186300
$651$	11.4630	0.449271
$652$	16.2048	0.634629
$653$	28.5492	1.11722	0.558608	−	0.829432i	$-0.311336\pi$
$653$	28.5492	1.11722	0.558608	+	0.829432i	$0.311336\pi$
$654$	−42.3369	−1.65550
$655$	−10.7917	−0.421668
$656$	11.4261	0.446115
$657$	−27.2828	−1.06441
$658$	1.96199	0.0764864
$659$	46.7842	1.82245	0.911227	−	0.411904i	$-0.135136\pi$
$659$	46.7842	1.82245	0.911227	+	0.411904i	$0.135136\pi$
$660$	5.07276	0.197457
$661$	17.4629	0.679230	0.339615	−	0.940565i	$-0.389703\pi$
$661$	17.4629	0.679230	0.339615	+	0.940565i	$0.389703\pi$
$662$	−3.43067	−0.133337
$663$	54.8611	2.13063
$664$	11.4562	0.444588
$665$	2.04620	0.0793483
$666$	−13.7402	−0.532423
$667$	−23.4909	−0.909570
$668$	−17.0541	−0.659842
$669$	−7.33445	−0.283566
$670$	−4.20281	−0.162369
$671$	6.92793	0.267450
$672$	2.17222	0.0837953
$673$	36.7696	1.41736	0.708682	−	0.705528i	$-0.249290\pi$
$673$	36.7696	1.41736	0.708682	+	0.705528i	$0.249290\pi$
$674$	19.2095	0.739922
$675$	2.24706	0.0864893
$676$	9.56006	0.367695
$677$	3.22116	0.123799	0.0618996	−	0.998082i	$-0.480284\pi$
$677$	3.22116	0.123799	0.0618996	+	0.998082i	$0.480284\pi$
$678$	−31.2692	−1.20089
$679$	8.63949	0.331553
$680$	−5.16829	−0.198195
$681$	−46.5222	−1.78273
$682$	−11.9782	−0.458670
$683$	−8.36421	−0.320047	−0.160024	−	0.987113i	$-0.551157\pi$
$683$	−8.36421	−0.320047	−0.160024	+	0.987113i	$0.551157\pi$
$684$	−4.19888	−0.160548
$685$	−9.17558	−0.350581
$686$	12.6894	0.484485
$687$	25.7095	0.980879
$688$	5.15210	0.196422
$689$	−44.3706	−1.69038
$690$	−7.43458	−0.283030
$691$	−32.9538	−1.25362	−0.626811	−	0.779171i	$-0.715640\pi$
$691$	−32.9538	−1.25362	−0.626811	+	0.779171i	$0.715640\pi$
$692$	−19.1959	−0.729719
$693$	4.40043	0.167159
$694$	28.0513	1.06481
$695$	20.1877	0.765763
$696$	15.7811	0.598182
$697$	−59.0535	−2.23681
$698$	−18.7428	−0.709426
$699$	34.9441	1.32171
$700$	−0.971978	−0.0367373
$701$	−4.58362	−0.173121	−0.0865605	−	0.996247i	$-0.527588\pi$
$701$	−4.58362	−0.173121	−0.0865605	+	0.996247i	$0.527588\pi$
$702$	10.6729	0.402824
$703$	14.5025	0.546974
$704$	−2.26985	−0.0855482
$705$	4.51116	0.169900
$706$	−2.39277	−0.0900531
$707$	10.2628	0.385972
$708$	−19.0281	−0.715119
$709$	−12.1221	−0.455255	−0.227628	−	0.973748i	$-0.573097\pi$
$709$	−12.1221	−0.455255	−0.227628	+	0.973748i	$0.573097\pi$
$710$	−3.81103	−0.143025
$711$	−29.7070	−1.11410
$712$	2.24524	0.0841438
$713$	17.5551	0.657445
$714$	−11.2267	−0.420148
$715$	−10.7812	−0.403194
$716$	−4.48302	−0.167538
$717$	54.4585	2.03379
$718$	−24.3064	−0.907107
$719$	−5.44915	−0.203219	−0.101610	−	0.994824i	$-0.532399\pi$
$719$	−5.44915	−0.203219	−0.101610	+	0.994824i	$0.532399\pi$
$720$	1.99454	0.0743320
$721$	−5.69007	−0.211909
$722$	−14.5682	−0.542171
$723$	−2.75985	−0.102640
$724$	−2.13871	−0.0794847
$725$	−7.06139	−0.262253
$726$	13.0689	0.485032
$727$	31.6468	1.17371	0.586857	−	0.809690i	$-0.300365\pi$
$727$	31.6468	1.17371	0.586857	+	0.809690i	$0.300365\pi$
$728$	−4.61665	−0.171104
$729$	−6.88525	−0.255009
$730$	−13.6788	−0.506275
$731$	−26.6276	−0.984856
$732$	6.82109	0.252115
$733$	−31.2485	−1.15419	−0.577094	−	0.816677i	$-0.695814\pi$
$733$	−31.2485	−1.15419	−0.577094	+	0.816677i	$0.695814\pi$
$734$	0.508134	0.0187556
$735$	13.5326	0.499156
$736$	3.32666	0.122622
$737$	9.53976	0.351401
$738$	22.7898	0.838904
$739$	−26.4086	−0.971457	−0.485729	−	0.874110i	$-0.661446\pi$
$739$	−26.4086	−0.971457	−0.485729	+	0.874110i	$0.661446\pi$
$740$	−6.88894	−0.253242
$741$	22.3465	0.820919
$742$	9.07991	0.333334
$743$	−6.88970	−0.252758	−0.126379	−	0.991982i	$-0.540336\pi$
$743$	−6.88970	−0.252758	−0.126379	+	0.991982i	$0.540336\pi$
$744$	−11.7935	−0.432370
$745$	−12.3242	−0.451524
$746$	−20.4909	−0.750226
$747$	22.8499	0.836032
$748$	11.7312	0.428937
$749$	3.22296	0.117765
$750$	−2.23485	−0.0816050
$751$	−31.6083	−1.15340	−0.576702	−	0.816955i	$-0.695661\pi$
$751$	−31.6083	−1.15340	−0.576702	+	0.816955i	$0.695661\pi$
$752$	−2.01855	−0.0736091
$753$	6.67096	0.243103
$754$	−33.5398	−1.22145
$755$	−3.50054	−0.127398
$756$	−2.18409	−0.0794346
$757$	−35.2565	−1.28142	−0.640709	−	0.767784i	$-0.721360\pi$
$757$	−35.2565	−1.28142	−0.640709	+	0.767784i	$0.721360\pi$
$758$	21.5832	0.783936
$759$	16.8754	0.612538
$760$	−2.10519	−0.0763633
$761$	−10.1589	−0.368259	−0.184129	−	0.982902i	$-0.558947\pi$
$761$	−10.1589	−0.368259	−0.184129	+	0.982902i	$0.558947\pi$
$762$	−24.4518	−0.885795
$763$	−18.4131	−0.666600
$764$	−23.9579	−0.866767
$765$	−10.3083	−0.372699
$766$	−30.7891	−1.11246
$767$	40.4406	1.46023
$768$	−2.23485	−0.0806431
$769$	39.7266	1.43258	0.716289	−	0.697804i	$-0.245839\pi$
$769$	39.7266	1.43258	0.716289	+	0.697804i	$0.245839\pi$
$770$	2.20624	0.0795075
$771$	−16.1378	−0.581187
$772$	8.02182	0.288712
$773$	33.8580	1.21779	0.608893	−	0.793252i	$-0.291614\pi$
$773$	33.8580	1.21779	0.608893	+	0.793252i	$0.291614\pi$
$774$	10.2761	0.369365
$775$	5.27710	0.189559
$776$	−8.88856	−0.319081
$777$	−14.9643	−0.536841
$778$	11.3147	0.405653
$779$	−24.0542	−0.861830
$780$	−10.6149	−0.380076
$781$	8.65046	0.309538
$782$	−17.1932	−0.614827
$783$	−15.8673	−0.567053
$784$	−6.05526	−0.216259
$785$	−8.93461	−0.318890
$786$	24.1179	0.860257
$787$	44.0259	1.56935	0.784677	−	0.619905i	$-0.212829\pi$
$787$	44.0259	1.56935	0.784677	+	0.619905i	$0.212829\pi$
$788$	−21.4228	−0.763155
$789$	−57.9569	−2.06332
$790$	−14.8942	−0.529912
$791$	−13.5996	−0.483546
$792$	−4.52730	−0.160870
$793$	−14.4969	−0.514802
$794$	−25.7552	−0.914017
$795$	20.8772	0.740439
$796$	0.485772	0.0172177
$797$	28.6875	1.01616	0.508081	−	0.861309i	$-0.330355\pi$
$797$	28.6875	1.01616	0.508081	+	0.861309i	$0.330355\pi$
$798$	−4.57294	−0.161880
$799$	10.4325	0.369074
$800$	1.00000	0.0353553
$801$	4.47820	0.158230
$802$	36.4590	1.28741
$803$	31.0488	1.09569
$804$	9.39264	0.331253
$805$	−3.23345	−0.113964
$806$	25.0648	0.882872
$807$	45.3335	1.59582
$808$	−10.5587	−0.371453
$809$	13.3210	0.468343	0.234172	−	0.972195i	$-0.424762\pi$
$809$	13.3210	0.468343	0.234172	+	0.972195i	$0.424762\pi$
$810$	−11.0054	−0.386692
$811$	−12.2378	−0.429729	−0.214864	−	0.976644i	$-0.568931\pi$
$811$	−12.2378	−0.429729	−0.214864	+	0.976644i	$0.568931\pi$
$812$	6.86352	0.240862
$813$	27.6972	0.971382
$814$	15.6369	0.548072
$815$	16.2048	0.567629
$816$	11.5503	0.404343
$817$	−10.8462	−0.379459
$818$	−15.2347	−0.532669
$819$	−9.20807	−0.321756
$820$	11.4261	0.399017
$821$	30.5918	1.06766	0.533831	−	0.845591i	$-0.320752\pi$
$821$	30.5918	1.06766	0.533831	+	0.845591i	$0.320752\pi$
$822$	20.5060	0.715229
$823$	22.8423	0.796232	0.398116	−	0.917335i	$-0.369664\pi$
$823$	22.8423	0.796232	0.398116	+	0.917335i	$0.369664\pi$
$824$	5.85412	0.203938
$825$	5.07276	0.176611
$826$	−8.27568	−0.287948
$827$	6.71335	0.233446	0.116723	−	0.993165i	$-0.462761\pi$
$827$	6.71335	0.233446	0.116723	+	0.993165i	$0.462761\pi$
$828$	6.63515	0.230587
$829$	0.256997	0.00892587	0.00446293	−	0.999990i	$-0.498579\pi$
$829$	0.256997	0.00892587	0.00446293	+	0.999990i	$0.498579\pi$
$830$	11.4562	0.397651
$831$	1.11436	0.0386566
$832$	4.74974	0.164668
$833$	31.2953	1.08432
$834$	−45.1164	−1.56225
$835$	−17.0541	−0.590181
$836$	4.77847	0.165267
$837$	11.8579	0.409870
$838$	−4.27469	−0.147667
$839$	6.09546	0.210439	0.105219	−	0.994449i	$-0.466446\pi$
$839$	6.09546	0.210439	0.105219	+	0.994449i	$0.466446\pi$
$840$	2.17222	0.0749488
$841$	20.8632	0.719421
$842$	28.7923	0.992248
$843$	59.3163	2.04296
$844$	−20.6922	−0.712256
$845$	9.56006	0.328876
$846$	−4.02608	−0.138419
$847$	5.68392	0.195302
$848$	−9.34168	−0.320795
$849$	50.8210	1.74417
$850$	−5.16829	−0.177271
$851$	−22.9172	−0.785591
$852$	8.51706	0.291790
$853$	46.8459	1.60397	0.801986	−	0.597342i	$-0.203777\pi$
$853$	46.8459	1.60397	0.801986	+	0.597342i	$0.203777\pi$
$854$	2.96663	0.101516
$855$	−4.19888	−0.143599
$856$	−3.31588	−0.113334
$857$	−21.3035	−0.727715	−0.363857	−	0.931455i	$-0.618540\pi$
$857$	−21.3035	−0.727715	−0.363857	+	0.931455i	$0.618540\pi$
$858$	24.0943	0.822567
$859$	19.3737	0.661023	0.330511	−	0.943802i	$-0.392779\pi$
$859$	19.3737	0.661023	0.330511	+	0.943802i	$0.392779\pi$
$860$	5.15210	0.175685
$861$	24.8200	0.845865
$862$	17.5168	0.596625
$863$	−53.0306	−1.80518	−0.902591	−	0.430498i	$-0.858338\pi$
$863$	−53.0306	−1.80518	−0.902591	+	0.430498i	$0.858338\pi$
$864$	2.24706	0.0764464
$865$	−19.1959	−0.652680
$866$	10.8362	0.368229
$867$	−21.7031	−0.737076
$868$	−5.12922	−0.174097
$869$	33.8076	1.14684
$870$	15.7811	0.535030
$871$	−19.9623	−0.676396
$872$	18.9440	0.641524
$873$	−17.7286	−0.600021
$874$	−7.00327	−0.236889
$875$	−0.971978	−0.0328589
$876$	30.5700	1.03286
$877$	52.1085	1.75958	0.879789	−	0.475364i	$-0.157683\pi$
$877$	52.1085	1.75958	0.879789	+	0.475364i	$0.157683\pi$
$878$	−23.8707	−0.805596
$879$	20.2305	0.682358
$880$	−2.26985	−0.0765166
$881$	28.5352	0.961376	0.480688	−	0.876892i	$-0.340387\pi$
$881$	28.5352	0.961376	0.480688	+	0.876892i	$0.340387\pi$
$882$	−12.0774	−0.406668
$883$	15.2947	0.514707	0.257354	−	0.966317i	$-0.417150\pi$
$883$	15.2947	0.514707	0.257354	+	0.966317i	$0.417150\pi$
$884$	−24.5481	−0.825640
$885$	−19.0281	−0.639622
$886$	−27.9217	−0.938046
$887$	−3.30869	−0.111095	−0.0555475	−	0.998456i	$-0.517690\pi$
$887$	−3.30869	−0.111095	−0.0555475	+	0.998456i	$0.517690\pi$
$888$	15.3957	0.516646
$889$	−10.6346	−0.356672
$890$	2.24524	0.0752605
$891$	24.9807	0.836884
$892$	3.28186	0.109885
$893$	4.24945	0.142202
$894$	27.5427	0.921166
$895$	−4.48302	−0.149851
$896$	−0.971978	−0.0324715
$897$	−35.3124	−1.17905
$898$	32.8472	1.09612
$899$	−37.2636	−1.24281
$900$	1.99454	0.0664845
$901$	48.2805	1.60846
$902$	−25.9356	−0.863560
$903$	11.1915	0.372430
$904$	13.9917	0.465356
$905$	−2.13871	−0.0710933
$906$	7.82317	0.259908
$907$	−47.9859	−1.59334	−0.796672	−	0.604412i	$-0.793408\pi$
$907$	−47.9859	−1.59334	−0.796672	+	0.604412i	$0.793408\pi$
$908$	20.8167	0.690828
$909$	−21.0597	−0.698505
$910$	−4.61665	−0.153040
$911$	−40.8483	−1.35336	−0.676682	−	0.736275i	$-0.736583\pi$
$911$	−40.8483	−1.35336	−0.676682	+	0.736275i	$0.736583\pi$
$912$	4.70478	0.155791
$913$	−26.0039	−0.860604
$914$	21.6199	0.715121
$915$	6.82109	0.225498
$916$	−11.5039	−0.380101
$917$	10.4893	0.346389
$918$	−11.6134	−0.383301
$919$	22.7650	0.750949	0.375474	−	0.926833i	$-0.377480\pi$
$919$	22.7650	0.750949	0.375474	+	0.926833i	$0.377480\pi$
$920$	3.32666	0.109677
$921$	34.5379	1.13806
$922$	4.00324	0.131840
$923$	−18.1014	−0.595815
$924$	−4.93062	−0.162205
$925$	−6.88894	−0.226507
$926$	8.14567	0.267683
$927$	11.6762	0.383498
$928$	−7.06139	−0.231801
$929$	−8.25807	−0.270938	−0.135469	−	0.990782i	$-0.543254\pi$
$929$	−8.25807	−0.270938	−0.135469	+	0.990782i	$0.543254\pi$
$930$	−11.7935	−0.386724
$931$	12.7475	0.417782
$932$	−15.6360	−0.512175
$933$	58.3013	1.90870
$934$	12.1779	0.398474
$935$	11.7312	0.383653
$936$	9.47353	0.309652
$937$	−27.7469	−0.906453	−0.453227	−	0.891395i	$-0.649727\pi$
$937$	−27.7469	−0.906453	−0.453227	+	0.891395i	$0.649727\pi$
$938$	4.08504	0.133381
$939$	−21.6089	−0.705181
$940$	−2.01855	−0.0658380
$941$	6.47070	0.210939	0.105469	−	0.994423i	$-0.466365\pi$
$941$	6.47070	0.210939	0.105469	+	0.994423i	$0.466365\pi$
$942$	19.9675	0.650575
$943$	38.0109	1.23780
$944$	8.51427	0.277116
$945$	−2.18409	−0.0710485
$946$	−11.6945	−0.380221
$947$	18.3903	0.597604	0.298802	−	0.954315i	$-0.403413\pi$
$947$	18.3903	0.597604	0.298802	+	0.954315i	$0.403413\pi$
$948$	33.2862	1.08109
$949$	−64.9708	−2.10904
$950$	−2.10519	−0.0683015
$951$	−49.5758	−1.60761
$952$	5.02347	0.162811
$953$	26.8309	0.869137	0.434568	−	0.900639i	$-0.356901\pi$
$953$	26.8309	0.869137	0.434568	+	0.900639i	$0.356901\pi$
$954$	−18.6323	−0.603244
$955$	−23.9579	−0.775260
$956$	−24.3679	−0.788114
$957$	−35.8208	−1.15792
$958$	−28.2514	−0.912762
$959$	8.91846	0.287992
$960$	−2.23485	−0.0721293
$961$	−3.15227	−0.101686
$962$	−32.7207	−1.05496
$963$	−6.61364	−0.213122
$964$	1.23492	0.0397740
$965$	8.02182	0.258231
$966$	7.22625	0.232501
$967$	−45.4897	−1.46285	−0.731425	−	0.681921i	$-0.761145\pi$
$967$	−45.4897	−1.46285	−0.731425	+	0.681921i	$0.761145\pi$
$968$	−5.84778	−0.187955
$969$	−24.3157	−0.781132
$970$	−8.88856	−0.285395
$971$	−53.3021	−1.71055	−0.855273	−	0.518177i	$-0.826611\pi$
$971$	−53.3021	−1.71055	−0.855273	+	0.518177i	$0.826611\pi$
$972$	17.8543	0.572676
$973$	−19.6220	−0.629053
$974$	41.3590	1.32523
$975$	−10.6149	−0.339950
$976$	−3.05215	−0.0976970
$977$	−5.36889	−0.171766	−0.0858829	−	0.996305i	$-0.527371\pi$
$977$	−5.36889	−0.171766	−0.0858829	+	0.996305i	$0.527371\pi$
$978$	−36.2152	−1.15804
$979$	−5.09635	−0.162880
$980$	−6.05526	−0.193428
$981$	37.7844	1.20636
$982$	−18.1492	−0.579164
$983$	−38.4174	−1.22532	−0.612662	−	0.790345i	$-0.709901\pi$
$983$	−38.4174	−1.22532	−0.612662	+	0.790345i	$0.709901\pi$
$984$	−25.5356	−0.814045
$985$	−21.4228	−0.682587
$986$	36.4953	1.16225
$987$	−4.38475	−0.139568
$988$	−9.99912	−0.318114
$989$	17.1393	0.544999
$990$	−4.52730	−0.143887
$991$	38.7074	1.22958	0.614790	−	0.788691i	$-0.289241\pi$
$991$	38.7074	1.22958	0.614790	+	0.788691i	$0.289241\pi$
$992$	5.27710	0.167548
$993$	7.66701	0.243305
$994$	3.70424	0.117491
$995$	0.485772	0.0154000
$996$	−25.6029	−0.811259
$997$	41.9316	1.32799	0.663993	−	0.747739i	$-0.268860\pi$
$997$	41.9316	1.32799	0.663993	+	0.747739i	$0.268860\pi$
$998$	−18.0488	−0.571323
$999$	−15.4798	−0.489760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.4	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.23485 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.23485 q^{6} -0.971978 q^{7} +1.00000 q^{8} +1.99454 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.23485 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.23485 q^{6} -0.971978 q^{7} +1.00000 q^{8} +1.99454 q^{9} +1.00000 q^{10} -2.26985 q^{11} -2.23485 q^{12} +4.74974 q^{13} -0.971978 q^{14} -2.23485 q^{15} +1.00000 q^{16} -5.16829 q^{17} +1.99454 q^{18} -2.10519 q^{19} +1.00000 q^{20} +2.17222 q^{21} -2.26985 q^{22} +3.32666 q^{23} -2.23485 q^{24} +1.00000 q^{25} +4.74974 q^{26} +2.24706 q^{27} -0.971978 q^{28} -7.06139 q^{29} -2.23485 q^{30} +5.27710 q^{31} +1.00000 q^{32} +5.07276 q^{33} -5.16829 q^{34} -0.971978 q^{35} +1.99454 q^{36} -6.88894 q^{37} -2.10519 q^{38} -10.6149 q^{39} +1.00000 q^{40} +11.4261 q^{41} +2.17222 q^{42} +5.15210 q^{43} -2.26985 q^{44} +1.99454 q^{45} +3.32666 q^{46} -2.01855 q^{47} -2.23485 q^{48} -6.05526 q^{49} +1.00000 q^{50} +11.5503 q^{51} +4.74974 q^{52} -9.34168 q^{53} +2.24706 q^{54} -2.26985 q^{55} -0.971978 q^{56} +4.70478 q^{57} -7.06139 q^{58} +8.51427 q^{59} -2.23485 q^{60} -3.05215 q^{61} +5.27710 q^{62} -1.93865 q^{63} +1.00000 q^{64} +4.74974 q^{65} +5.07276 q^{66} -4.20281 q^{67} -5.16829 q^{68} -7.43458 q^{69} -0.971978 q^{70} -3.81103 q^{71} +1.99454 q^{72} -13.6788 q^{73} -6.88894 q^{74} -2.23485 q^{75} -2.10519 q^{76} +2.20624 q^{77} -10.6149 q^{78} -14.8942 q^{79} +1.00000 q^{80} -11.0054 q^{81} +11.4261 q^{82} +11.4562 q^{83} +2.17222 q^{84} -5.16829 q^{85} +5.15210 q^{86} +15.7811 q^{87} -2.26985 q^{88} +2.24524 q^{89} +1.99454 q^{90} -4.61665 q^{91} +3.32666 q^{92} -11.7935 q^{93} -2.01855 q^{94} -2.10519 q^{95} -2.23485 q^{96} -8.88856 q^{97} -6.05526 q^{98} -4.52730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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