LMFDB - Embedded newform 2006.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.14219$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.14219 q^{3} +1.00000 q^{4} +1.20202 q^{5} -3.14219 q^{6} +2.33770 q^{7} +1.00000 q^{8} +6.87337 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.14219 q^{3} +1.00000 q^{4} +1.20202 q^{5} -3.14219 q^{6} +2.33770 q^{7} +1.00000 q^{8} +6.87337 q^{9} +1.20202 q^{10} +4.27634 q^{11} -3.14219 q^{12} -0.756476 q^{13} +2.33770 q^{14} -3.77697 q^{15} +1.00000 q^{16} +1.00000 q^{17} +6.87337 q^{18} +5.47508 q^{19} +1.20202 q^{20} -7.34549 q^{21} +4.27634 q^{22} -3.78348 q^{23} -3.14219 q^{24} -3.55515 q^{25} -0.756476 q^{26} -12.1709 q^{27} +2.33770 q^{28} -0.842372 q^{29} -3.77697 q^{30} +5.55160 q^{31} +1.00000 q^{32} -13.4371 q^{33} +1.00000 q^{34} +2.80995 q^{35} +6.87337 q^{36} -5.63686 q^{37} +5.47508 q^{38} +2.37699 q^{39} +1.20202 q^{40} +8.63269 q^{41} -7.34549 q^{42} -1.95188 q^{43} +4.27634 q^{44} +8.26191 q^{45} -3.78348 q^{46} -6.43366 q^{47} -3.14219 q^{48} -1.53517 q^{49} -3.55515 q^{50} -3.14219 q^{51} -0.756476 q^{52} -5.24595 q^{53} -12.1709 q^{54} +5.14024 q^{55} +2.33770 q^{56} -17.2038 q^{57} -0.842372 q^{58} +1.00000 q^{59} -3.77697 q^{60} +11.4346 q^{61} +5.55160 q^{62} +16.0679 q^{63} +1.00000 q^{64} -0.909297 q^{65} -13.4371 q^{66} +9.00105 q^{67} +1.00000 q^{68} +11.8884 q^{69} +2.80995 q^{70} +13.4408 q^{71} +6.87337 q^{72} -5.75403 q^{73} -5.63686 q^{74} +11.1710 q^{75} +5.47508 q^{76} +9.99680 q^{77} +2.37699 q^{78} -3.62517 q^{79} +1.20202 q^{80} +17.6231 q^{81} +8.63269 q^{82} -5.15281 q^{83} -7.34549 q^{84} +1.20202 q^{85} -1.95188 q^{86} +2.64689 q^{87} +4.27634 q^{88} +3.09960 q^{89} +8.26191 q^{90} -1.76841 q^{91} -3.78348 q^{92} -17.4442 q^{93} -6.43366 q^{94} +6.58115 q^{95} -3.14219 q^{96} +15.2125 q^{97} -1.53517 q^{98} +29.3929 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * 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
$3$	−3.14219	−1.81415	−0.907073	−	0.420974i	$-0.861688\pi$
$3$	−3.14219	−1.81415	−0.907073	+	0.420974i	$0.861688\pi$
$4$	1.00000	0.500000
$5$	1.20202	0.537559	0.268779	−	0.963202i	$-0.413380\pi$
$5$	1.20202	0.537559	0.268779	+	0.963202i	$0.413380\pi$
$6$	−3.14219	−1.28279
$7$	2.33770	0.883567	0.441783	−	0.897122i	$-0.354346\pi$
$7$	2.33770	0.883567	0.441783	+	0.897122i	$0.354346\pi$
$8$	1.00000	0.353553
$9$	6.87337	2.29112
$10$	1.20202	0.380111
$11$	4.27634	1.28937	0.644683	−	0.764450i	$-0.276989\pi$
$11$	4.27634	1.28937	0.644683	+	0.764450i	$0.276989\pi$
$12$	−3.14219	−0.907073
$13$	−0.756476	−0.209809	−0.104904	−	0.994482i	$-0.533454\pi$
$13$	−0.756476	−0.209809	−0.104904	+	0.994482i	$0.533454\pi$
$14$	2.33770	0.624776
$15$	−3.77697	−0.975209
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.87337	1.62007
$19$	5.47508	1.25607	0.628035	−	0.778185i	$-0.283859\pi$
$19$	5.47508	1.25607	0.628035	+	0.778185i	$0.283859\pi$
$20$	1.20202	0.268779
$21$	−7.34549	−1.60292
$22$	4.27634	0.911719
$23$	−3.78348	−0.788909	−0.394455	−	0.918915i	$-0.629066\pi$
$23$	−3.78348	−0.788909	−0.394455	+	0.918915i	$0.629066\pi$
$24$	−3.14219	−0.641397
$25$	−3.55515	−0.711031
$26$	−0.756476	−0.148357
$27$	−12.1709	−2.34228
$28$	2.33770	0.441783
$29$	−0.842372	−0.156425	−0.0782123	−	0.996937i	$-0.524921\pi$
$29$	−0.842372	−0.156425	−0.0782123	+	0.996937i	$0.524921\pi$
$30$	−3.77697	−0.689577
$31$	5.55160	0.997097	0.498549	−	0.866862i	$-0.333866\pi$
$31$	5.55160	0.997097	0.498549	+	0.866862i	$0.333866\pi$
$32$	1.00000	0.176777
$33$	−13.4371	−2.33910
$34$	1.00000	0.171499
$35$	2.80995	0.474969
$36$	6.87337	1.14556
$37$	−5.63686	−0.926695	−0.463347	−	0.886177i	$-0.653352\pi$
$37$	−5.63686	−0.926695	−0.463347	+	0.886177i	$0.653352\pi$
$38$	5.47508	0.888176
$39$	2.37699	0.380623
$40$	1.20202	0.190056
$41$	8.63269	1.34820	0.674100	−	0.738640i	$-0.264532\pi$
$41$	8.63269	1.34820	0.674100	+	0.738640i	$0.264532\pi$
$42$	−7.34549	−1.13343
$43$	−1.95188	−0.297658	−0.148829	−	0.988863i	$-0.547550\pi$
$43$	−1.95188	−0.297658	−0.148829	+	0.988863i	$0.547550\pi$
$44$	4.27634	0.644683
$45$	8.26191	1.23161
$46$	−3.78348	−0.557843
$47$	−6.43366	−0.938445	−0.469223	−	0.883080i	$-0.655466\pi$
$47$	−6.43366	−0.938445	−0.469223	+	0.883080i	$0.655466\pi$
$48$	−3.14219	−0.453536
$49$	−1.53517	−0.219310
$50$	−3.55515	−0.502775
$51$	−3.14219	−0.439995
$52$	−0.756476	−0.104904
$53$	−5.24595	−0.720586	−0.360293	−	0.932839i	$-0.617323\pi$
$53$	−5.24595	−0.720586	−0.360293	+	0.932839i	$0.617323\pi$
$54$	−12.1709	−1.65624
$55$	5.14024	0.693110
$56$	2.33770	0.312388
$57$	−17.2038	−2.27869
$58$	−0.842372	−0.110609
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.77697	−0.487605
$61$	11.4346	1.46405	0.732024	−	0.681279i	$-0.238576\pi$
$61$	11.4346	1.46405	0.732024	+	0.681279i	$0.238576\pi$
$62$	5.55160	0.705054
$63$	16.0679	2.02436
$64$	1.00000	0.125000
$65$	−0.909297	−0.112784
$66$	−13.4371	−1.65399
$67$	9.00105	1.09965	0.549827	−	0.835279i	$-0.314694\pi$
$67$	9.00105	1.09965	0.549827	+	0.835279i	$0.314694\pi$
$68$	1.00000	0.121268
$69$	11.8884	1.43120
$70$	2.80995	0.335854
$71$	13.4408	1.59513	0.797564	−	0.603234i	$-0.206121\pi$
$71$	13.4408	1.59513	0.797564	+	0.603234i	$0.206121\pi$
$72$	6.87337	0.810034
$73$	−5.75403	−0.673458	−0.336729	−	0.941602i	$-0.609321\pi$
$73$	−5.75403	−0.673458	−0.336729	+	0.941602i	$0.609321\pi$
$74$	−5.63686	−0.655272
$75$	11.1710	1.28991
$76$	5.47508	0.628035
$77$	9.99680	1.13924
$78$	2.37699	0.269141
$79$	−3.62517	−0.407864	−0.203932	−	0.978985i	$-0.565372\pi$
$79$	−3.62517	−0.407864	−0.203932	+	0.978985i	$0.565372\pi$
$80$	1.20202	0.134390
$81$	17.6231	1.95812
$82$	8.63269	0.953321
$83$	−5.15281	−0.565594	−0.282797	−	0.959180i	$-0.591262\pi$
$83$	−5.15281	−0.565594	−0.282797	+	0.959180i	$0.591262\pi$
$84$	−7.34549	−0.801459
$85$	1.20202	0.130377
$86$	−1.95188	−0.210476
$87$	2.64689	0.283777
$88$	4.27634	0.455860
$89$	3.09960	0.328557	0.164278	−	0.986414i	$-0.447470\pi$
$89$	3.09960	0.328557	0.164278	+	0.986414i	$0.447470\pi$
$90$	8.26191	0.870882
$91$	−1.76841	−0.185380
$92$	−3.78348	−0.394455
$93$	−17.4442	−1.80888
$94$	−6.43366	−0.663581
$95$	6.58115	0.675212
$96$	−3.14219	−0.320699
$97$	15.2125	1.54459	0.772297	−	0.635262i	$-0.219108\pi$
$97$	15.2125	1.54459	0.772297	+	0.635262i	$0.219108\pi$
$98$	−1.53517	−0.155076
$99$	29.3929	2.95409
$100$	−3.55515	−0.355515
$101$	−2.35447	−0.234278	−0.117139	−	0.993116i	$-0.537372\pi$
$101$	−2.35447	−0.234278	−0.117139	+	0.993116i	$0.537372\pi$
$102$	−3.14219	−0.311123
$103$	9.64753	0.950600	0.475300	−	0.879824i	$-0.342340\pi$
$103$	9.64753	0.950600	0.475300	+	0.879824i	$0.342340\pi$
$104$	−0.756476	−0.0741785
$105$	−8.82941	−0.861662
$106$	−5.24595	−0.509532
$107$	1.37297	0.132730	0.0663651	−	0.997795i	$-0.478860\pi$
$107$	1.37297	0.132730	0.0663651	+	0.997795i	$0.478860\pi$
$108$	−12.1709	−1.17114
$109$	−17.0916	−1.63707	−0.818537	−	0.574454i	$-0.805214\pi$
$109$	−17.0916	−1.63707	−0.818537	+	0.574454i	$0.805214\pi$
$110$	5.14024	0.490103
$111$	17.7121	1.68116
$112$	2.33770	0.220892
$113$	−2.61056	−0.245581	−0.122790	−	0.992433i	$-0.539184\pi$
$113$	−2.61056	−0.245581	−0.122790	+	0.992433i	$0.539184\pi$
$114$	−17.2038	−1.61128
$115$	−4.54781	−0.424085
$116$	−0.842372	−0.0782123
$117$	−5.19953	−0.480697
$118$	1.00000	0.0920575
$119$	2.33770	0.214296
$120$	−3.77697	−0.344789
$121$	7.28711	0.662464
$122$	11.4346	1.03524
$123$	−27.1256	−2.44583
$124$	5.55160	0.498549
$125$	−10.2834	−0.919779
$126$	16.0679	1.43144
$127$	13.1031	1.16271	0.581354	−	0.813650i	$-0.302523\pi$
$127$	13.1031	1.16271	0.581354	+	0.813650i	$0.302523\pi$
$128$	1.00000	0.0883883
$129$	6.13317	0.539995
$130$	−0.909297	−0.0797506
$131$	15.1870	1.32689	0.663447	−	0.748223i	$-0.269093\pi$
$131$	15.1870	1.32689	0.663447	+	0.748223i	$0.269093\pi$
$132$	−13.4371	−1.16955
$133$	12.7991	1.10982
$134$	9.00105	0.777572
$135$	−14.6296	−1.25911
$136$	1.00000	0.0857493
$137$	9.04733	0.772965	0.386483	−	0.922297i	$-0.373690\pi$
$137$	9.04733	0.772965	0.386483	+	0.922297i	$0.373690\pi$
$138$	11.8884	1.01201
$139$	11.2483	0.954069	0.477034	−	0.878885i	$-0.341712\pi$
$139$	11.2483	0.954069	0.477034	+	0.878885i	$0.341712\pi$
$140$	2.80995	0.237484
$141$	20.2158	1.70248
$142$	13.4408	1.12793
$143$	−3.23495	−0.270520
$144$	6.87337	0.572781
$145$	−1.01255	−0.0840874
$146$	−5.75403	−0.476207
$147$	4.82380	0.397860
$148$	−5.63686	−0.463347
$149$	1.42710	0.116913	0.0584563	−	0.998290i	$-0.481382\pi$
$149$	1.42710	0.116913	0.0584563	+	0.998290i	$0.481382\pi$
$150$	11.1710	0.912106
$151$	−0.672936	−0.0547628	−0.0273814	−	0.999625i	$-0.508717\pi$
$151$	−0.672936	−0.0547628	−0.0273814	+	0.999625i	$0.508717\pi$
$152$	5.47508	0.444088
$153$	6.87337	0.555679
$154$	9.99680	0.805565
$155$	6.67313	0.535998
$156$	2.37699	0.190312
$157$	−15.1477	−1.20892	−0.604459	−	0.796636i	$-0.706611\pi$
$157$	−15.1477	−1.20892	−0.604459	+	0.796636i	$0.706611\pi$
$158$	−3.62517	−0.288403
$159$	16.4838	1.30725
$160$	1.20202	0.0950278
$161$	−8.84462	−0.697054
$162$	17.6231	1.38460
$163$	8.85133	0.693289	0.346645	−	0.937997i	$-0.387321\pi$
$163$	8.85133	0.693289	0.346645	+	0.937997i	$0.387321\pi$
$164$	8.63269	0.674100
$165$	−16.1516	−1.25740
$166$	−5.15281	−0.399936
$167$	4.33704	0.335610	0.167805	−	0.985820i	$-0.446332\pi$
$167$	4.33704	0.335610	0.167805	+	0.985820i	$0.446332\pi$
$168$	−7.34549	−0.566717
$169$	−12.4277	−0.955980
$170$	1.20202	0.0921905
$171$	37.6323	2.87781
$172$	−1.95188	−0.148829
$173$	8.87646	0.674865	0.337432	−	0.941350i	$-0.390442\pi$
$173$	8.87646	0.674865	0.337432	+	0.941350i	$0.390442\pi$
$174$	2.64689	0.200661
$175$	−8.31087	−0.628243
$176$	4.27634	0.322341
$177$	−3.14219	−0.236182
$178$	3.09960	0.232325
$179$	−24.0605	−1.79837	−0.899185	−	0.437570i	$-0.855839\pi$
$179$	−24.0605	−1.79837	−0.899185	+	0.437570i	$0.855839\pi$
$180$	8.26191	0.615806
$181$	−20.7872	−1.54510	−0.772550	−	0.634953i	$-0.781019\pi$
$181$	−20.7872	−1.54510	−0.772550	+	0.634953i	$0.781019\pi$
$182$	−1.76841	−0.131083
$183$	−35.9296	−2.65600
$184$	−3.78348	−0.278922
$185$	−6.77561	−0.498153
$186$	−17.4442	−1.27907
$187$	4.27634	0.312717
$188$	−6.43366	−0.469223
$189$	−28.4518	−2.06956
$190$	6.58115	0.477447
$191$	13.0363	0.943274	0.471637	−	0.881793i	$-0.343663\pi$
$191$	13.0363	0.943274	0.471637	+	0.881793i	$0.343663\pi$
$192$	−3.14219	−0.226768
$193$	−11.4535	−0.824444	−0.412222	−	0.911083i	$-0.635247\pi$
$193$	−11.4535	−0.824444	−0.412222	+	0.911083i	$0.635247\pi$
$194$	15.2125	1.09219
$195$	2.85719	0.204607
$196$	−1.53517	−0.109655
$197$	−19.3319	−1.37734	−0.688670	−	0.725075i	$-0.741805\pi$
$197$	−19.3319	−1.37734	−0.688670	+	0.725075i	$0.741805\pi$
$198$	29.3929	2.08886
$199$	10.4663	0.741938	0.370969	−	0.928645i	$-0.379026\pi$
$199$	10.4663	0.741938	0.370969	+	0.928645i	$0.379026\pi$
$200$	−3.55515	−0.251387
$201$	−28.2830	−1.99493
$202$	−2.35447	−0.165660
$203$	−1.96921	−0.138212
$204$	−3.14219	−0.219997
$205$	10.3766	0.724736
$206$	9.64753	0.672176
$207$	−26.0052	−1.80749
$208$	−0.756476	−0.0524521
$209$	23.4133	1.61953
$210$	−8.82941	−0.609287
$211$	12.6631	0.871767	0.435883	−	0.900003i	$-0.356436\pi$
$211$	12.6631	0.871767	0.435883	+	0.900003i	$0.356436\pi$
$212$	−5.24595	−0.360293
$213$	−42.2336	−2.89380
$214$	1.37297	0.0938545
$215$	−2.34619	−0.160009
$216$	−12.1709	−0.828122
$217$	12.9780	0.881002
$218$	−17.0916	−1.15759
$219$	18.0803	1.22175
$220$	5.14024	0.346555
$221$	−0.756476	−0.0508861
$222$	17.7121	1.18876
$223$	−2.73389	−0.183075	−0.0915375	−	0.995802i	$-0.529178\pi$
$223$	−2.73389	−0.183075	−0.0915375	+	0.995802i	$0.529178\pi$
$224$	2.33770	0.156194
$225$	−24.4359	−1.62906
$226$	−2.61056	−0.173652
$227$	21.5818	1.43243	0.716216	−	0.697879i	$-0.245873\pi$
$227$	21.5818	1.43243	0.716216	+	0.697879i	$0.245873\pi$
$228$	−17.2038	−1.13935
$229$	−21.6213	−1.42877	−0.714387	−	0.699751i	$-0.753294\pi$
$229$	−21.6213	−1.42877	−0.714387	+	0.699751i	$0.753294\pi$
$230$	−4.54781	−0.299873
$231$	−31.4118	−2.06675
$232$	−0.842372	−0.0553044
$233$	16.6924	1.09356	0.546779	−	0.837277i	$-0.315854\pi$
$233$	16.6924	1.09356	0.546779	+	0.837277i	$0.315854\pi$
$234$	−5.19953	−0.339904
$235$	−7.73337	−0.504469
$236$	1.00000	0.0650945
$237$	11.3910	0.739924
$238$	2.33770	0.151530
$239$	−19.9062	−1.28762	−0.643812	−	0.765183i	$-0.722648\pi$
$239$	−19.9062	−1.28762	−0.643812	+	0.765183i	$0.722648\pi$
$240$	−3.77697	−0.243802
$241$	4.59163	0.295773	0.147886	−	0.989004i	$-0.452753\pi$
$241$	4.59163	0.295773	0.147886	+	0.989004i	$0.452753\pi$
$242$	7.28711	0.468433
$243$	−18.8625	−1.21003
$244$	11.4346	0.732024
$245$	−1.84530	−0.117892
$246$	−27.1256	−1.72946
$247$	−4.14177	−0.263534
$248$	5.55160	0.352527
$249$	16.1911	1.02607
$250$	−10.2834	−0.650382
$251$	−29.8039	−1.88121	−0.940603	−	0.339507i	$-0.889740\pi$
$251$	−29.8039	−1.88121	−0.940603	+	0.339507i	$0.889740\pi$
$252$	16.0679	1.01218
$253$	−16.1794	−1.01719
$254$	13.1031	0.822159
$255$	−3.77697	−0.236523
$256$	1.00000	0.0625000
$257$	13.5931	0.847913	0.423956	−	0.905683i	$-0.360641\pi$
$257$	13.5931	0.847913	0.423956	+	0.905683i	$0.360641\pi$
$258$	6.13317	0.381834
$259$	−13.1773	−0.818796
$260$	−0.909297	−0.0563922
$261$	−5.78993	−0.358388
$262$	15.1870	0.938256
$263$	−15.4734	−0.954131	−0.477066	−	0.878868i	$-0.658300\pi$
$263$	−15.4734	−0.954131	−0.477066	+	0.878868i	$0.658300\pi$
$264$	−13.4371	−0.826996
$265$	−6.30572	−0.387357
$266$	12.7991	0.784763
$267$	−9.73953	−0.596050
$268$	9.00105	0.549827
$269$	−4.71596	−0.287537	−0.143768	−	0.989611i	$-0.545922\pi$
$269$	−4.71596	−0.287537	−0.143768	+	0.989611i	$0.545922\pi$
$270$	−14.6296	−0.890328
$271$	18.5652	1.12776	0.563878	−	0.825858i	$-0.309309\pi$
$271$	18.5652	1.12776	0.563878	+	0.825858i	$0.309309\pi$
$272$	1.00000	0.0606339
$273$	5.55669	0.336306
$274$	9.04733	0.546569
$275$	−15.2031	−0.916779
$276$	11.8884	0.715598
$277$	6.44490	0.387236	0.193618	−	0.981077i	$-0.437978\pi$
$277$	6.44490	0.387236	0.193618	+	0.981077i	$0.437978\pi$
$278$	11.2483	0.674628
$279$	38.1582	2.28447
$280$	2.80995	0.167927
$281$	−8.32548	−0.496656	−0.248328	−	0.968676i	$-0.579881\pi$
$281$	−8.32548	−0.496656	−0.248328	+	0.968676i	$0.579881\pi$
$282$	20.2158	1.20383
$283$	−8.28610	−0.492557	−0.246279	−	0.969199i	$-0.579208\pi$
$283$	−8.28610	−0.492557	−0.246279	+	0.969199i	$0.579208\pi$
$284$	13.4408	0.797564
$285$	−20.6792	−1.22493
$286$	−3.23495	−0.191287
$287$	20.1806	1.19122
$288$	6.87337	0.405017
$289$	1.00000	0.0588235
$290$	−1.01255	−0.0594588
$291$	−47.8005	−2.80212
$292$	−5.75403	−0.336729
$293$	−11.8859	−0.694383	−0.347191	−	0.937794i	$-0.612865\pi$
$293$	−11.8859	−0.694383	−0.347191	+	0.937794i	$0.612865\pi$
$294$	4.82380	0.281330
$295$	1.20202	0.0699842
$296$	−5.63686	−0.327636
$297$	−52.0468	−3.02006
$298$	1.42710	0.0826697
$299$	2.86211	0.165520
$300$	11.1710	0.644956
$301$	−4.56290	−0.263001
$302$	−0.672936	−0.0387231
$303$	7.39819	0.425015
$304$	5.47508	0.314018
$305$	13.7446	0.787012
$306$	6.87337	0.392924
$307$	14.8505	0.847561	0.423780	−	0.905765i	$-0.360703\pi$
$307$	14.8505	0.847561	0.423780	+	0.905765i	$0.360703\pi$
$308$	9.99680	0.569620
$309$	−30.3144	−1.72453
$310$	6.67313	0.379008
$311$	4.48808	0.254496	0.127248	−	0.991871i	$-0.459386\pi$
$311$	4.48808	0.254496	0.127248	+	0.991871i	$0.459386\pi$
$312$	2.37699	0.134571
$313$	17.5553	0.992286	0.496143	−	0.868241i	$-0.334749\pi$
$313$	17.5553	0.992286	0.496143	+	0.868241i	$0.334749\pi$
$314$	−15.1477	−0.854834
$315$	19.3138	1.08821
$316$	−3.62517	−0.203932
$317$	−11.1304	−0.625147	−0.312574	−	0.949894i	$-0.601191\pi$
$317$	−11.1304	−0.625147	−0.312574	+	0.949894i	$0.601191\pi$
$318$	16.4838	0.924364
$319$	−3.60227	−0.201689
$320$	1.20202	0.0671948
$321$	−4.31414	−0.240792
$322$	−8.84462	−0.492892
$323$	5.47508	0.304642
$324$	17.6231	0.979059
$325$	2.68939	0.149180
$326$	8.85133	0.490230
$327$	53.7049	2.96989
$328$	8.63269	0.476661
$329$	−15.0399	−0.829179
$330$	−16.1516	−0.889117
$331$	−1.96709	−0.108121	−0.0540604	−	0.998538i	$-0.517216\pi$
$331$	−1.96709	−0.108121	−0.0540604	+	0.998538i	$0.517216\pi$
$332$	−5.15281	−0.282797
$333$	−38.7442	−2.12317
$334$	4.33704	0.237312
$335$	10.8194	0.591128
$336$	−7.34549	−0.400730
$337$	22.4089	1.22069	0.610347	−	0.792134i	$-0.291030\pi$
$337$	22.4089	1.22069	0.610347	+	0.792134i	$0.291030\pi$
$338$	−12.4277	−0.675980
$339$	8.20287	0.445519
$340$	1.20202	0.0651886
$341$	23.7406	1.28562
$342$	37.6323	2.03492
$343$	−19.9526	−1.07734
$344$	−1.95188	−0.105238
$345$	14.2901	0.769352
$346$	8.87646	0.477202
$347$	−2.33494	−0.125346	−0.0626730	−	0.998034i	$-0.519963\pi$
$347$	−2.33494	−0.125346	−0.0626730	+	0.998034i	$0.519963\pi$
$348$	2.64689	0.141888
$349$	−16.7266	−0.895354	−0.447677	−	0.894195i	$-0.647749\pi$
$349$	−16.7266	−0.895354	−0.447677	+	0.894195i	$0.647749\pi$
$350$	−8.31087	−0.444235
$351$	9.20696	0.491431
$352$	4.27634	0.227930
$353$	2.08540	0.110994	0.0554972	−	0.998459i	$-0.482326\pi$
$353$	2.08540	0.110994	0.0554972	+	0.998459i	$0.482326\pi$
$354$	−3.14219	−0.167006
$355$	16.1561	0.857475
$356$	3.09960	0.164278
$357$	−7.34549	−0.388765
$358$	−24.0605	−1.27164
$359$	−31.1421	−1.64362	−0.821809	−	0.569763i	$-0.807035\pi$
$359$	−31.1421	−1.64362	−0.821809	+	0.569763i	$0.807035\pi$
$360$	8.26191	0.435441
$361$	10.9766	0.577713
$362$	−20.7872	−1.09255
$363$	−22.8975	−1.20181
$364$	−1.76841	−0.0926899
$365$	−6.91645	−0.362023
$366$	−35.9296	−1.87807
$367$	11.6950	0.610474	0.305237	−	0.952276i	$-0.401264\pi$
$367$	11.6950	0.610474	0.305237	+	0.952276i	$0.401264\pi$
$368$	−3.78348	−0.197227
$369$	59.3356	3.08889
$370$	−6.77561	−0.352247
$371$	−12.2634	−0.636686
$372$	−17.4442	−0.904440
$373$	−3.30893	−0.171330	−0.0856650	−	0.996324i	$-0.527301\pi$
$373$	−3.30893	−0.171330	−0.0856650	+	0.996324i	$0.527301\pi$
$374$	4.27634	0.221124
$375$	32.3126	1.66861
$376$	−6.43366	−0.331790
$377$	0.637234	0.0328192
$378$	−28.4518	−1.46340
$379$	22.3122	1.14610	0.573051	−	0.819520i	$-0.305760\pi$
$379$	22.3122	1.14610	0.573051	+	0.819520i	$0.305760\pi$
$380$	6.58115	0.337606
$381$	−41.1723	−2.10932
$382$	13.0363	0.666996
$383$	−6.73839	−0.344316	−0.172158	−	0.985069i	$-0.555074\pi$
$383$	−6.73839	−0.344316	−0.172158	+	0.985069i	$0.555074\pi$
$384$	−3.14219	−0.160349
$385$	12.0163	0.612409
$386$	−11.4535	−0.582970
$387$	−13.4160	−0.681972
$388$	15.2125	0.772297
$389$	20.0724	1.01771	0.508856	−	0.860852i	$-0.330069\pi$
$389$	20.0724	1.01771	0.508856	+	0.860852i	$0.330069\pi$
$390$	2.85719	0.144679
$391$	−3.78348	−0.191339
$392$	−1.53517	−0.0775378
$393$	−47.7205	−2.40718
$394$	−19.3319	−0.973927
$395$	−4.35752	−0.219251
$396$	29.3929	1.47705
$397$	−7.99662	−0.401339	−0.200670	−	0.979659i	$-0.564312\pi$
$397$	−7.99662	−0.401339	−0.200670	+	0.979659i	$0.564312\pi$
$398$	10.4663	0.524630
$399$	−40.2172	−2.01338
$400$	−3.55515	−0.177758
$401$	−38.0667	−1.90096	−0.950479	−	0.310788i	$-0.899407\pi$
$401$	−38.0667	−1.90096	−0.950479	+	0.310788i	$0.899407\pi$
$402$	−28.2830	−1.41063
$403$	−4.19965	−0.209200
$404$	−2.35447	−0.117139
$405$	21.1832	1.05260
$406$	−1.96921	−0.0977303
$407$	−24.1052	−1.19485
$408$	−3.14219	−0.155562
$409$	21.4308	1.05968	0.529842	−	0.848097i	$-0.322251\pi$
$409$	21.4308	1.05968	0.529842	+	0.848097i	$0.322251\pi$
$410$	10.3766	0.512466
$411$	−28.4284	−1.40227
$412$	9.64753	0.475300
$413$	2.33770	0.115031
$414$	−26.0052	−1.27809
$415$	−6.19377	−0.304040
$416$	−0.756476	−0.0370893
$417$	−35.3443	−1.73082
$418$	23.4133	1.14518
$419$	−36.9093	−1.80314	−0.901569	−	0.432634i	$-0.857584\pi$
$419$	−36.9093	−1.80314	−0.901569	+	0.432634i	$0.857584\pi$
$420$	−8.82941	−0.430831
$421$	−7.01451	−0.341866	−0.170933	−	0.985283i	$-0.554678\pi$
$421$	−7.01451	−0.341866	−0.170933	+	0.985283i	$0.554678\pi$
$422$	12.6631	0.616432
$423$	−44.2209	−2.15009
$424$	−5.24595	−0.254766
$425$	−3.55515	−0.172450
$426$	−42.2336	−2.04622
$427$	26.7306	1.29358
$428$	1.37297	0.0663651
$429$	10.1648	0.490763
$430$	−2.34619	−0.113143
$431$	32.2301	1.55247	0.776236	−	0.630443i	$-0.217127\pi$
$431$	32.2301	1.55247	0.776236	+	0.630443i	$0.217127\pi$
$432$	−12.1709	−0.585571
$433$	21.9773	1.05616	0.528081	−	0.849194i	$-0.322912\pi$
$433$	21.9773	1.05616	0.528081	+	0.849194i	$0.322912\pi$
$434$	12.9780	0.622963
$435$	3.18161	0.152547
$436$	−17.0916	−0.818537
$437$	−20.7149	−0.990926
$438$	18.0803	0.863908
$439$	−26.5549	−1.26739	−0.633697	−	0.773581i	$-0.718463\pi$
$439$	−26.5549	−1.26739	−0.633697	+	0.773581i	$0.718463\pi$
$440$	5.14024	0.245051
$441$	−10.5518	−0.502466
$442$	−0.756476	−0.0359819
$443$	−19.7994	−0.940700	−0.470350	−	0.882480i	$-0.655872\pi$
$443$	−19.7994	−0.940700	−0.470350	+	0.882480i	$0.655872\pi$
$444$	17.7121	0.840579
$445$	3.72577	0.176619
$446$	−2.73389	−0.129454
$447$	−4.48422	−0.212096
$448$	2.33770	0.110446
$449$	14.5410	0.686233	0.343117	−	0.939293i	$-0.388517\pi$
$449$	14.5410	0.686233	0.343117	+	0.939293i	$0.388517\pi$
$450$	−24.4359	−1.15192
$451$	36.9163	1.73832
$452$	−2.61056	−0.122790
$453$	2.11449	0.0993476
$454$	21.5818	1.01288
$455$	−2.12566	−0.0996525
$456$	−17.2038	−0.805640
$457$	−21.8184	−1.02062	−0.510311	−	0.859990i	$-0.670470\pi$
$457$	−21.8184	−1.02062	−0.510311	+	0.859990i	$0.670470\pi$
$458$	−21.6213	−1.01030
$459$	−12.1709	−0.568087
$460$	−4.54781	−0.212043
$461$	25.0600	1.16716	0.583580	−	0.812056i	$-0.301652\pi$
$461$	25.0600	1.16716	0.583580	+	0.812056i	$0.301652\pi$
$462$	−31.4118	−1.46141
$463$	26.4488	1.22918	0.614589	−	0.788847i	$-0.289322\pi$
$463$	26.4488	1.22918	0.614589	+	0.788847i	$0.289322\pi$
$464$	−0.842372	−0.0391061
$465$	−20.9682	−0.972379
$466$	16.6924	0.773263
$467$	−2.03689	−0.0942559	−0.0471279	−	0.998889i	$-0.515007\pi$
$467$	−2.03689	−0.0942559	−0.0471279	+	0.998889i	$0.515007\pi$
$468$	−5.19953	−0.240349
$469$	21.0417	0.971617
$470$	−7.73337	−0.356714
$471$	47.5970	2.19315
$472$	1.00000	0.0460287
$473$	−8.34689	−0.383790
$474$	11.3910	0.523206
$475$	−19.4648	−0.893105
$476$	2.33770	0.107148
$477$	−36.0573	−1.65095
$478$	−19.9062	−0.910488
$479$	−36.8880	−1.68546	−0.842728	−	0.538340i	$-0.819052\pi$
$479$	−36.8880	−1.68546	−0.842728	+	0.538340i	$0.819052\pi$
$480$	−3.77697	−0.172394
$481$	4.26415	0.194428
$482$	4.59163	0.209143
$483$	27.7915	1.26456
$484$	7.28711	0.331232
$485$	18.2857	0.830310
$486$	−18.8625	−0.855619
$487$	−0.676975	−0.0306766	−0.0153383	−	0.999882i	$-0.504883\pi$
$487$	−0.676975	−0.0306766	−0.0153383	+	0.999882i	$0.504883\pi$
$488$	11.4346	0.517619
$489$	−27.8126	−1.25773
$490$	−1.84530	−0.0833622
$491$	−25.7054	−1.16007	−0.580035	−	0.814592i	$-0.696961\pi$
$491$	−25.7054	−1.16007	−0.580035	+	0.814592i	$0.696961\pi$
$492$	−27.1256	−1.22291
$493$	−0.842372	−0.0379385
$494$	−4.14177	−0.186347
$495$	35.3307	1.58800
$496$	5.55160	0.249274
$497$	31.4205	1.40940
$498$	16.1911	0.725541
$499$	4.19620	0.187848	0.0939238	−	0.995579i	$-0.470059\pi$
$499$	4.19620	0.187848	0.0939238	+	0.995579i	$0.470059\pi$
$500$	−10.2834	−0.459890
$501$	−13.6278	−0.608846
$502$	−29.8039	−1.33021
$503$	−15.3949	−0.686423	−0.343212	−	0.939258i	$-0.611515\pi$
$503$	−15.3949	−0.686423	−0.343212	+	0.939258i	$0.611515\pi$
$504$	16.0679	0.715719
$505$	−2.83011	−0.125938
$506$	−16.1794	−0.719264
$507$	39.0504	1.73429
$508$	13.1031	0.581354
$509$	4.43815	0.196718	0.0983588	−	0.995151i	$-0.468641\pi$
$509$	4.43815	0.196718	0.0983588	+	0.995151i	$0.468641\pi$
$510$	−3.77697	−0.167247
$511$	−13.4512	−0.595045
$512$	1.00000	0.0441942
$513$	−66.6365	−2.94207
$514$	13.5931	0.599565
$515$	11.5965	0.511003
$516$	6.13317	0.269998
$517$	−27.5125	−1.21000
$518$	−13.1773	−0.578977
$519$	−27.8915	−1.22430
$520$	−0.909297	−0.0398753
$521$	39.3368	1.72338	0.861688	−	0.507438i	$-0.169407\pi$
$521$	39.3368	1.72338	0.861688	+	0.507438i	$0.169407\pi$
$522$	−5.78993	−0.253418
$523$	26.5131	1.15934	0.579669	−	0.814852i	$-0.303182\pi$
$523$	26.5131	1.15934	0.579669	+	0.814852i	$0.303182\pi$
$524$	15.1870	0.663447
$525$	26.1144	1.13972
$526$	−15.4734	−0.674673
$527$	5.55160	0.241832
$528$	−13.4371	−0.584774
$529$	−8.68531	−0.377622
$530$	−6.30572	−0.273903
$531$	6.87337	0.298279
$532$	12.7991	0.554911
$533$	−6.53042	−0.282864
$534$	−9.73953	−0.421471
$535$	1.65034	0.0713503
$536$	9.00105	0.388786
$537$	75.6028	3.26250
$538$	−4.71596	−0.203319
$539$	−6.56491	−0.282771
$540$	−14.6296	−0.629557
$541$	1.10066	0.0473212	0.0236606	−	0.999720i	$-0.492468\pi$
$541$	1.10066	0.0473212	0.0236606	+	0.999720i	$0.492468\pi$
$542$	18.5652	0.797443
$543$	65.3174	2.80304
$544$	1.00000	0.0428746
$545$	−20.5443	−0.880023
$546$	5.55669	0.237804
$547$	−12.8010	−0.547331	−0.273666	−	0.961825i	$-0.588236\pi$
$547$	−12.8010	−0.547331	−0.273666	+	0.961825i	$0.588236\pi$
$548$	9.04733	0.386483
$549$	78.5941	3.35431
$550$	−15.2031	−0.648260
$551$	−4.61206	−0.196480
$552$	11.8884	0.506004
$553$	−8.47456	−0.360375
$554$	6.44490	0.273817
$555$	21.2903	0.903721
$556$	11.2483	0.477034
$557$	−30.1199	−1.27622	−0.638110	−	0.769946i	$-0.720283\pi$
$557$	−30.1199	−1.27622	−0.638110	+	0.769946i	$0.720283\pi$
$558$	38.1582	1.61537
$559$	1.47655	0.0624513
$560$	2.80995	0.118742
$561$	−13.4371	−0.567314
$562$	−8.32548	−0.351189
$563$	−2.52012	−0.106211	−0.0531053	−	0.998589i	$-0.516912\pi$
$563$	−2.52012	−0.106211	−0.0531053	+	0.998589i	$0.516912\pi$
$564$	20.2158	0.851238
$565$	−3.13794	−0.132014
$566$	−8.28610	−0.348291
$567$	41.1974	1.73013
$568$	13.4408	0.563963
$569$	−30.3875	−1.27391	−0.636954	−	0.770902i	$-0.719806\pi$
$569$	−30.3875	−1.27391	−0.636954	+	0.770902i	$0.719806\pi$
$570$	−20.6792	−0.866158
$571$	−28.5123	−1.19320	−0.596602	−	0.802537i	$-0.703483\pi$
$571$	−28.5123	−1.19320	−0.596602	+	0.802537i	$0.703483\pi$
$572$	−3.23495	−0.135260
$573$	−40.9626	−1.71124
$574$	20.1806	0.842323
$575$	13.4508	0.560939
$576$	6.87337	0.286390
$577$	2.84462	0.118423	0.0592115	−	0.998245i	$-0.481141\pi$
$577$	2.84462	0.118423	0.0592115	+	0.998245i	$0.481141\pi$
$578$	1.00000	0.0415945
$579$	35.9892	1.49566
$580$	−1.01255	−0.0420437
$581$	−12.0457	−0.499740
$582$	−47.8005	−1.98140
$583$	−22.4335	−0.929100
$584$	−5.75403	−0.238103
$585$	−6.24993	−0.258403
$586$	−11.8859	−0.491003
$587$	31.9012	1.31670	0.658352	−	0.752710i	$-0.271254\pi$
$587$	31.9012	1.31670	0.658352	+	0.752710i	$0.271254\pi$
$588$	4.82380	0.198930
$589$	30.3955	1.25242
$590$	1.20202	0.0494863
$591$	60.7445	2.49870
$592$	−5.63686	−0.231674
$593$	−18.9311	−0.777408	−0.388704	−	0.921363i	$-0.627077\pi$
$593$	−18.9311	−0.777408	−0.388704	+	0.921363i	$0.627077\pi$
$594$	−52.0468	−2.13550
$595$	2.80995	0.115197
$596$	1.42710	0.0584563
$597$	−32.8872	−1.34598
$598$	2.86211	0.117040
$599$	42.7873	1.74824	0.874121	−	0.485708i	$-0.161438\pi$
$599$	42.7873	1.74824	0.874121	+	0.485708i	$0.161438\pi$
$600$	11.1710	0.456053
$601$	34.4275	1.40433	0.702164	−	0.712015i	$-0.252217\pi$
$601$	34.4275	1.40433	0.702164	+	0.712015i	$0.252217\pi$
$602$	−4.56290	−0.185970
$603$	61.8675	2.51944
$604$	−0.672936	−0.0273814
$605$	8.75923	0.356113
$606$	7.39819	0.300531
$607$	−19.3868	−0.786886	−0.393443	−	0.919349i	$-0.628716\pi$
$607$	−19.3868	−0.786886	−0.393443	+	0.919349i	$0.628716\pi$
$608$	5.47508	0.222044
$609$	6.18764	0.250736
$610$	13.7446	0.556501
$611$	4.86690	0.196894
$612$	6.87337	0.277839
$613$	−11.8114	−0.477057	−0.238529	−	0.971135i	$-0.576665\pi$
$613$	−11.8114	−0.477057	−0.238529	+	0.971135i	$0.576665\pi$
$614$	14.8505	0.599316
$615$	−32.6054	−1.31478
$616$	9.99680	0.402782
$617$	40.0188	1.61110	0.805548	−	0.592530i	$-0.201871\pi$
$617$	40.0188	1.61110	0.805548	+	0.592530i	$0.201871\pi$
$618$	−30.3144	−1.21942
$619$	−16.4430	−0.660900	−0.330450	−	0.943823i	$-0.607201\pi$
$619$	−16.4430	−0.660900	−0.330450	+	0.943823i	$0.607201\pi$
$620$	6.67313	0.267999
$621$	46.0482	1.84785
$622$	4.48808	0.179956
$623$	7.24592	0.290302
$624$	2.37699	0.0951558
$625$	5.41488	0.216595
$626$	17.5553	0.701652
$627$	−73.5692	−2.93807
$628$	−15.1477	−0.604459
$629$	−5.63686	−0.224756
$630$	19.3138	0.769482
$631$	8.19824	0.326367	0.163183	−	0.986596i	$-0.447824\pi$
$631$	8.19824	0.326367	0.163183	+	0.986596i	$0.447824\pi$
$632$	−3.62517	−0.144202
$633$	−39.7900	−1.58151
$634$	−11.1304	−0.442046
$635$	15.7501	0.625024
$636$	16.4838	0.653624
$637$	1.16132	0.0460131
$638$	−3.60227	−0.142615
$639$	92.3835	3.65464
$640$	1.20202	0.0475139
$641$	−32.9248	−1.30045	−0.650227	−	0.759740i	$-0.725326\pi$
$641$	−32.9248	−1.30045	−0.650227	+	0.759740i	$0.725326\pi$
$642$	−4.31414	−0.170266
$643$	−37.9377	−1.49612	−0.748058	−	0.663633i	$-0.769014\pi$
$643$	−37.9377	−1.49612	−0.748058	+	0.663633i	$0.769014\pi$
$644$	−8.84462	−0.348527
$645$	7.37218	0.290279
$646$	5.47508	0.215414
$647$	−37.4029	−1.47046	−0.735230	−	0.677817i	$-0.762926\pi$
$647$	−37.4029	−1.47046	−0.735230	+	0.677817i	$0.762926\pi$
$648$	17.6231	0.692300
$649$	4.27634	0.167861
$650$	2.68939	0.105486
$651$	−40.7793	−1.59827
$652$	8.85133	0.346645
$653$	−10.1081	−0.395559	−0.197780	−	0.980247i	$-0.563373\pi$
$653$	−10.1081	−0.395559	−0.197780	+	0.980247i	$0.563373\pi$
$654$	53.7049	2.10003
$655$	18.2551	0.713284
$656$	8.63269	0.337050
$657$	−39.5496	−1.54298
$658$	−15.0399	−0.586318
$659$	1.46428	0.0570404	0.0285202	−	0.999593i	$-0.490921\pi$
$659$	1.46428	0.0570404	0.0285202	+	0.999593i	$0.490921\pi$
$660$	−16.1516	−0.628701
$661$	24.1469	0.939206	0.469603	−	0.882878i	$-0.344397\pi$
$661$	24.1469	0.939206	0.469603	+	0.882878i	$0.344397\pi$
$662$	−1.96709	−0.0764530
$663$	2.37699	0.0923147
$664$	−5.15281	−0.199968
$665$	15.3847	0.596594
$666$	−38.7442	−1.50131
$667$	3.18710	0.123405
$668$	4.33704	0.167805
$669$	8.59042	0.332125
$670$	10.8194	0.417991
$671$	48.8982	1.88769
$672$	−7.34549	−0.283359
$673$	−4.98071	−0.191992	−0.0959962	−	0.995382i	$-0.530604\pi$
$673$	−4.98071	−0.191992	−0.0959962	+	0.995382i	$0.530604\pi$
$674$	22.4089	0.863160
$675$	43.2693	1.66544
$676$	−12.4277	−0.477990
$677$	45.9679	1.76669	0.883345	−	0.468724i	$-0.155286\pi$
$677$	45.9679	1.76669	0.883345	+	0.468724i	$0.155286\pi$
$678$	8.20287	0.315029
$679$	35.5622	1.36475
$680$	1.20202	0.0460953
$681$	−67.8140	−2.59864
$682$	23.7406	0.909073
$683$	−16.4275	−0.628582	−0.314291	−	0.949327i	$-0.601767\pi$
$683$	−16.4275	−0.628582	−0.314291	+	0.949327i	$0.601767\pi$
$684$	37.6323	1.43891
$685$	10.8750	0.415514
$686$	−19.9526	−0.761796
$687$	67.9382	2.59200
$688$	−1.95188	−0.0744146
$689$	3.96843	0.151185
$690$	14.2901	0.544014
$691$	−30.5646	−1.16273	−0.581366	−	0.813642i	$-0.697481\pi$
$691$	−30.5646	−1.16273	−0.581366	+	0.813642i	$0.697481\pi$
$692$	8.87646	0.337432
$693$	68.7116	2.61014
$694$	−2.33494	−0.0886330
$695$	13.5207	0.512868
$696$	2.64689	0.100330
$697$	8.63269	0.326986
$698$	−16.7266	−0.633111
$699$	−52.4509	−1.98387
$700$	−8.31087	−0.314121
$701$	−39.2999	−1.48434	−0.742169	−	0.670213i	$-0.766203\pi$
$701$	−39.2999	−1.48434	−0.742169	+	0.670213i	$0.766203\pi$
$702$	9.20696	0.347494
$703$	−30.8623	−1.16399
$704$	4.27634	0.161171
$705$	24.2997	0.915180
$706$	2.08540	0.0784849
$707$	−5.50403	−0.207000
$708$	−3.14219	−0.118091
$709$	25.7242	0.966091	0.483045	−	0.875595i	$-0.339531\pi$
$709$	25.7242	0.966091	0.483045	+	0.875595i	$0.339531\pi$
$710$	16.1561	0.606327
$711$	−24.9172	−0.934466
$712$	3.09960	0.116162
$713$	−21.0044	−0.786620
$714$	−7.34549	−0.274898
$715$	−3.88847	−0.145420
$716$	−24.0605	−0.899185
$717$	62.5491	2.33594
$718$	−31.1421	−1.16221
$719$	53.0400	1.97806	0.989029	−	0.147724i	$-0.0471947\pi$
$719$	53.0400	1.97806	0.989029	+	0.147724i	$0.0471947\pi$
$720$	8.26191	0.307903
$721$	22.5530	0.839918
$722$	10.9766	0.408505
$723$	−14.4278	−0.536575
$724$	−20.7872	−0.772550
$725$	2.99476	0.111223
$726$	−22.8975	−0.849805
$727$	−42.5702	−1.57884	−0.789420	−	0.613853i	$-0.789619\pi$
$727$	−42.5702	−1.57884	−0.789420	+	0.613853i	$0.789619\pi$
$728$	−1.76841	−0.0655417
$729$	6.40031	0.237048
$730$	−6.91645	−0.255989
$731$	−1.95188	−0.0721927
$732$	−35.9296	−1.32800
$733$	42.2175	1.55934	0.779670	−	0.626191i	$-0.215387\pi$
$733$	42.2175	1.55934	0.779670	+	0.626191i	$0.215387\pi$
$734$	11.6950	0.431670
$735$	5.79829	0.213873
$736$	−3.78348	−0.139461
$737$	38.4916	1.41786
$738$	59.3356	2.18418
$739$	−10.6049	−0.390107	−0.195053	−	0.980793i	$-0.562488\pi$
$739$	−10.6049	−0.390107	−0.195053	+	0.980793i	$0.562488\pi$
$740$	−6.77561	−0.249076
$741$	13.0142	0.478090
$742$	−12.2634	−0.450205
$743$	−41.4503	−1.52066	−0.760331	−	0.649535i	$-0.774963\pi$
$743$	−41.4503	−1.52066	−0.760331	+	0.649535i	$0.774963\pi$
$744$	−17.4442	−0.639535
$745$	1.71540	0.0628474
$746$	−3.30893	−0.121149
$747$	−35.4171	−1.29585
$748$	4.27634	0.156359
$749$	3.20959	0.117276
$750$	32.3126	1.17989
$751$	9.76140	0.356199	0.178099	−	0.984013i	$-0.443005\pi$
$751$	9.76140	0.356199	0.178099	+	0.984013i	$0.443005\pi$
$752$	−6.43366	−0.234611
$753$	93.6496	3.41278
$754$	0.637234	0.0232067
$755$	−0.808881	−0.0294382
$756$	−28.4518	−1.03478
$757$	−27.8663	−1.01282	−0.506409	−	0.862293i	$-0.669027\pi$
$757$	−27.8663	−1.01282	−0.506409	+	0.862293i	$0.669027\pi$
$758$	22.3122	0.810417
$759$	50.8389	1.84534
$760$	6.58115	0.238723
$761$	32.0892	1.16323	0.581615	−	0.813464i	$-0.302421\pi$
$761$	32.0892	1.16323	0.581615	+	0.813464i	$0.302421\pi$
$762$	−41.1723	−1.49152
$763$	−39.9549	−1.44646
$764$	13.0363	0.471637
$765$	8.26191	0.298710
$766$	−6.73839	−0.243468
$767$	−0.756476	−0.0273148
$768$	−3.14219	−0.113384
$769$	−25.0972	−0.905030	−0.452515	−	0.891757i	$-0.649473\pi$
$769$	−25.0972	−0.905030	−0.452515	+	0.891757i	$0.649473\pi$
$770$	12.0163	0.433038
$771$	−42.7120	−1.53824
$772$	−11.4535	−0.412222
$773$	11.7765	0.423572	0.211786	−	0.977316i	$-0.432072\pi$
$773$	11.7765	0.423572	0.211786	+	0.977316i	$0.432072\pi$
$774$	−13.4160	−0.482227
$775$	−19.7368	−0.708967
$776$	15.2125	0.546096
$777$	41.4055	1.48542
$778$	20.0724	0.719631
$779$	47.2647	1.69343
$780$	2.85719	0.102304
$781$	57.4774	2.05670
$782$	−3.78348	−0.135297
$783$	10.2524	0.366391
$784$	−1.53517	−0.0548275
$785$	−18.2078	−0.649864
$786$	−47.7205	−1.70213
$787$	−19.2632	−0.686657	−0.343329	−	0.939215i	$-0.611554\pi$
$787$	−19.2632	−0.686657	−0.343329	+	0.939215i	$0.611554\pi$
$788$	−19.3319	−0.688670
$789$	48.6204	1.73093
$790$	−4.35752	−0.155034
$791$	−6.10270	−0.216987
$792$	29.3929	1.04443
$793$	−8.64998	−0.307170
$794$	−7.99662	−0.283790
$795$	19.8138	0.702723
$796$	10.4663	0.370969
$797$	−3.99441	−0.141489	−0.0707446	−	0.997494i	$-0.522538\pi$
$797$	−3.99441	−0.141489	−0.0707446	+	0.997494i	$0.522538\pi$
$798$	−40.2172	−1.42367
$799$	−6.43366	−0.227606
$800$	−3.55515	−0.125694
$801$	21.3047	0.752764
$802$	−38.0667	−1.34418
$803$	−24.6062	−0.868334
$804$	−28.2830	−0.997465
$805$	−10.6314	−0.374707
$806$	−4.19965	−0.147926
$807$	14.8184	0.521634
$808$	−2.35447	−0.0828299
$809$	29.9083	1.05152	0.525760	−	0.850633i	$-0.323781\pi$
$809$	29.9083	1.05152	0.525760	+	0.850633i	$0.323781\pi$
$810$	21.1832	0.744303
$811$	43.0586	1.51199	0.755996	−	0.654576i	$-0.227153\pi$
$811$	43.0586	1.51199	0.755996	+	0.654576i	$0.227153\pi$
$812$	−1.96921	−0.0691058
$813$	−58.3354	−2.04591
$814$	−24.1052	−0.844885
$815$	10.6395	0.372684
$816$	−3.14219	−0.109999
$817$	−10.6867	−0.373880
$818$	21.4308	0.749309
$819$	−12.1549	−0.424728
$820$	10.3766	0.362368
$821$	5.68989	0.198579	0.0992893	−	0.995059i	$-0.468343\pi$
$821$	5.68989	0.198579	0.0992893	+	0.995059i	$0.468343\pi$
$822$	−28.4284	−0.991556
$823$	40.0792	1.39707	0.698537	−	0.715574i	$-0.253835\pi$
$823$	40.0792	1.39707	0.698537	+	0.715574i	$0.253835\pi$
$824$	9.64753	0.336088
$825$	47.7709	1.66317
$826$	2.33770	0.0813389
$827$	−33.3773	−1.16064	−0.580322	−	0.814387i	$-0.697073\pi$
$827$	−33.3773	−1.16064	−0.580322	+	0.814387i	$0.697073\pi$
$828$	−26.0052	−0.903744
$829$	−20.5673	−0.714331	−0.357165	−	0.934041i	$-0.616257\pi$
$829$	−20.5673	−0.714331	−0.357165	+	0.934041i	$0.616257\pi$
$830$	−6.19377	−0.214989
$831$	−20.2511	−0.702503
$832$	−0.756476	−0.0262261
$833$	−1.53517	−0.0531905
$834$	−35.3443	−1.22387
$835$	5.21320	0.180410
$836$	23.4133	0.809767
$837$	−67.5678	−2.33548
$838$	−36.9093	−1.27501
$839$	−7.45248	−0.257288	−0.128644	−	0.991691i	$-0.541063\pi$
$839$	−7.45248	−0.257288	−0.128644	+	0.991691i	$0.541063\pi$
$840$	−8.82941	−0.304644
$841$	−28.2904	−0.975531
$842$	−7.01451	−0.241736
$843$	26.1602	0.901007
$844$	12.6631	0.435883
$845$	−14.9384	−0.513896
$846$	−44.2209	−1.52034
$847$	17.0350	0.585331
$848$	−5.24595	−0.180147
$849$	26.0365	0.893570
$850$	−3.55515	−0.121941
$851$	21.3269	0.731078
$852$	−42.2336	−1.44690
$853$	−28.2328	−0.966674	−0.483337	−	0.875434i	$-0.660575\pi$
$853$	−28.2328	−0.966674	−0.483337	+	0.875434i	$0.660575\pi$
$854$	26.7306	0.914702
$855$	45.2346	1.54699
$856$	1.37297	0.0469272
$857$	−5.54003	−0.189244	−0.0946218	−	0.995513i	$-0.530164\pi$
$857$	−5.54003	−0.189244	−0.0946218	+	0.995513i	$0.530164\pi$
$858$	10.1648	0.347022
$859$	21.1952	0.723171	0.361585	−	0.932339i	$-0.382236\pi$
$859$	21.1952	0.723171	0.361585	+	0.932339i	$0.382236\pi$
$860$	−2.34619	−0.0800044
$861$	−63.4114	−2.16105
$862$	32.2301	1.09776
$863$	3.90694	0.132994	0.0664969	−	0.997787i	$-0.478818\pi$
$863$	3.90694	0.132994	0.0664969	+	0.997787i	$0.478818\pi$
$864$	−12.1709	−0.414061
$865$	10.6697	0.362779
$866$	21.9773	0.746820
$867$	−3.14219	−0.106714
$868$	12.9780	0.440501
$869$	−15.5025	−0.525886
$870$	3.18161	0.107867
$871$	−6.80907	−0.230717
$872$	−17.0916	−0.578793
$873$	104.561	3.53885
$874$	−20.7149	−0.700690
$875$	−24.0396	−0.812686
$876$	18.0803	0.610875
$877$	12.8337	0.433364	0.216682	−	0.976242i	$-0.430477\pi$
$877$	12.8337	0.433364	0.216682	+	0.976242i	$0.430477\pi$
$878$	−26.5549	−0.896183
$879$	37.3478	1.25971
$880$	5.14024	0.173277
$881$	−46.6739	−1.57248	−0.786242	−	0.617919i	$-0.787976\pi$
$881$	−46.6739	−1.57248	−0.786242	+	0.617919i	$0.787976\pi$
$882$	−10.5518	−0.355297
$883$	−0.670310	−0.0225577	−0.0112789	−	0.999936i	$-0.503590\pi$
$883$	−0.670310	−0.0225577	−0.0112789	+	0.999936i	$0.503590\pi$
$884$	−0.756476	−0.0254430
$885$	−3.77697	−0.126961
$886$	−19.7994	−0.665175
$887$	−53.8403	−1.80778	−0.903890	−	0.427766i	$-0.859301\pi$
$887$	−53.8403	−1.80778	−0.903890	+	0.427766i	$0.859301\pi$
$888$	17.7121	0.594379
$889$	30.6310	1.02733
$890$	3.72577	0.124888
$891$	75.3623	2.52473
$892$	−2.73389	−0.0915375
$893$	−35.2248	−1.17875
$894$	−4.48422	−0.149975
$895$	−28.9212	−0.966729
$896$	2.33770	0.0780970
$897$	−8.99329	−0.300277
$898$	14.5410	0.485240
$899$	−4.67652	−0.155971
$900$	−24.4359	−0.814529
$901$	−5.24595	−0.174768
$902$	36.9163	1.22918
$903$	14.3375	0.477122
$904$	−2.61056	−0.0868259
$905$	−24.9866	−0.830582
$906$	2.11449	0.0702494
$907$	47.5284	1.57815	0.789077	−	0.614295i	$-0.210559\pi$
$907$	47.5284	1.57815	0.789077	+	0.614295i	$0.210559\pi$
$908$	21.5818	0.716216
$909$	−16.1831	−0.536760
$910$	−2.12566	−0.0704650
$911$	−31.2230	−1.03446	−0.517232	−	0.855845i	$-0.673038\pi$
$911$	−31.2230	−1.03446	−0.517232	+	0.855845i	$0.673038\pi$
$912$	−17.2038	−0.569674
$913$	−22.0352	−0.729258
$914$	−21.8184	−0.721689
$915$	−43.1881	−1.42775
$916$	−21.6213	−0.714387
$917$	35.5026	1.17240
$918$	−12.1709	−0.401698
$919$	47.3684	1.56254	0.781270	−	0.624193i	$-0.214572\pi$
$919$	47.3684	1.56254	0.781270	+	0.624193i	$0.214572\pi$
$920$	−4.54781	−0.149937
$921$	−46.6630	−1.53760
$922$	25.0600	0.825306
$923$	−10.1676	−0.334672
$924$	−31.4118	−1.03337
$925$	20.0399	0.658908
$926$	26.4488	0.869161
$927$	66.3110	2.17794
$928$	−0.842372	−0.0276522
$929$	−29.5824	−0.970567	−0.485283	−	0.874357i	$-0.661284\pi$
$929$	−29.5824	−0.970567	−0.485283	+	0.874357i	$0.661284\pi$
$930$	−20.9682	−0.687576
$931$	−8.40519	−0.275469
$932$	16.6924	0.546779
$933$	−14.1024	−0.461692
$934$	−2.03689	−0.0666490
$935$	5.14024	0.168104
$936$	−5.19953	−0.169952
$937$	20.8883	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$937$	20.8883	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$938$	21.0417	0.687037
$939$	−55.1622	−1.80015
$940$	−7.73337	−0.252235
$941$	−33.9779	−1.10765	−0.553823	−	0.832634i	$-0.686832\pi$
$941$	−33.9779	−1.10765	−0.553823	+	0.832634i	$0.686832\pi$
$942$	47.5970	1.55079
$943$	−32.6616	−1.06361
$944$	1.00000	0.0325472
$945$	−34.1996	−1.11251
$946$	−8.34689	−0.271381
$947$	−33.0940	−1.07541	−0.537705	−	0.843133i	$-0.680709\pi$
$947$	−33.0940	−1.07541	−0.537705	+	0.843133i	$0.680709\pi$
$948$	11.3910	0.369962
$949$	4.35278	0.141297
$950$	−19.4648	−0.631520
$951$	34.9739	1.13411
$952$	2.33770	0.0757652
$953$	−17.5385	−0.568127	−0.284063	−	0.958806i	$-0.591683\pi$
$953$	−17.5385	−0.568127	−0.284063	+	0.958806i	$0.591683\pi$
$954$	−36.0573	−1.16740
$955$	15.6699	0.507065
$956$	−19.9062	−0.643812
$957$	11.3190	0.365892
$958$	−36.8880	−1.19180
$959$	21.1499	0.682966
$960$	−3.77697	−0.121901
$961$	−0.179698	−0.00579671
$962$	4.26415	0.137482
$963$	9.43694	0.304101
$964$	4.59163	0.147886
$965$	−13.7674	−0.443187
$966$	27.7915	0.894177
$967$	11.6111	0.373388	0.186694	−	0.982418i	$-0.440223\pi$
$967$	11.6111	0.373388	0.186694	+	0.982418i	$0.440223\pi$
$968$	7.28711	0.234216
$969$	−17.2038	−0.552665
$970$	18.2857	0.587118
$971$	−59.3528	−1.90472	−0.952361	−	0.304974i	$-0.901352\pi$
$971$	−59.3528	−1.90472	−0.952361	+	0.304974i	$0.901352\pi$
$972$	−18.8625	−0.605014
$973$	26.2951	0.842983
$974$	−0.676975	−0.0216917
$975$	−8.45057	−0.270635
$976$	11.4346	0.366012
$977$	4.48879	0.143609	0.0718045	−	0.997419i	$-0.477124\pi$
$977$	4.48879	0.143609	0.0718045	+	0.997419i	$0.477124\pi$
$978$	−27.8126	−0.889348
$979$	13.2549	0.423630
$980$	−1.84530	−0.0589460
$981$	−117.477	−3.75074
$982$	−25.7054	−0.820293
$983$	33.1632	1.05774	0.528871	−	0.848702i	$-0.322616\pi$
$983$	33.1632	1.05774	0.528871	+	0.848702i	$0.322616\pi$
$984$	−27.1256	−0.864731
$985$	−23.2373	−0.740401
$986$	−0.842372	−0.0268266
$987$	47.2584	1.50425
$988$	−4.14177	−0.131767
$989$	7.38488	0.234825
$990$	35.3307	1.12288
$991$	14.0275	0.445598	0.222799	−	0.974864i	$-0.428481\pi$
$991$	14.0275	0.445598	0.222799	+	0.974864i	$0.428481\pi$
$992$	5.55160	0.176264
$993$	6.18096	0.196147
$994$	31.4205	0.996598
$995$	12.5807	0.398835
$996$	16.1911	0.513035
$997$	−18.3703	−0.581795	−0.290897	−	0.956754i	$-0.593954\pi$
$997$	−18.3703	−0.581795	−0.290897	+	0.956754i	$0.593954\pi$
$998$	4.19620	0.132828
$999$	68.6055	2.17058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.1	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.1	✓	13	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.14219 q^{3} +1.00000 q^{4} +1.20202 q^{5} -3.14219 q^{6} +2.33770 q^{7} +1.00000 q^{8} +6.87337 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.14219 q^{3} +1.00000 q^{4} +1.20202 q^{5} -3.14219 q^{6} +2.33770 q^{7} +1.00000 q^{8} +6.87337 q^{9} +1.20202 q^{10} +4.27634 q^{11} -3.14219 q^{12} -0.756476 q^{13} +2.33770 q^{14} -3.77697 q^{15} +1.00000 q^{16} +1.00000 q^{17} +6.87337 q^{18} +5.47508 q^{19} +1.20202 q^{20} -7.34549 q^{21} +4.27634 q^{22} -3.78348 q^{23} -3.14219 q^{24} -3.55515 q^{25} -0.756476 q^{26} -12.1709 q^{27} +2.33770 q^{28} -0.842372 q^{29} -3.77697 q^{30} +5.55160 q^{31} +1.00000 q^{32} -13.4371 q^{33} +1.00000 q^{34} +2.80995 q^{35} +6.87337 q^{36} -5.63686 q^{37} +5.47508 q^{38} +2.37699 q^{39} +1.20202 q^{40} +8.63269 q^{41} -7.34549 q^{42} -1.95188 q^{43} +4.27634 q^{44} +8.26191 q^{45} -3.78348 q^{46} -6.43366 q^{47} -3.14219 q^{48} -1.53517 q^{49} -3.55515 q^{50} -3.14219 q^{51} -0.756476 q^{52} -5.24595 q^{53} -12.1709 q^{54} +5.14024 q^{55} +2.33770 q^{56} -17.2038 q^{57} -0.842372 q^{58} +1.00000 q^{59} -3.77697 q^{60} +11.4346 q^{61} +5.55160 q^{62} +16.0679 q^{63} +1.00000 q^{64} -0.909297 q^{65} -13.4371 q^{66} +9.00105 q^{67} +1.00000 q^{68} +11.8884 q^{69} +2.80995 q^{70} +13.4408 q^{71} +6.87337 q^{72} -5.75403 q^{73} -5.63686 q^{74} +11.1710 q^{75} +5.47508 q^{76} +9.99680 q^{77} +2.37699 q^{78} -3.62517 q^{79} +1.20202 q^{80} +17.6231 q^{81} +8.63269 q^{82} -5.15281 q^{83} -7.34549 q^{84} +1.20202 q^{85} -1.95188 q^{86} +2.64689 q^{87} +4.27634 q^{88} +3.09960 q^{89} +8.26191 q^{90} -1.76841 q^{91} -3.78348 q^{92} -17.4442 q^{93} -6.43366 q^{94} +6.58115 q^{95} -3.14219 q^{96} +15.2125 q^{97} -1.53517 q^{98} +29.3929 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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