LMFDB - Embedded newform 2013.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
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} - 4 x^{12} - 11 x^{11} + 55 x^{10} + 32 x^{9} - 266 x^{8} + 13 x^{7} + 534 x^{6} - 141 x^{5} + \cdots - 11 $ x^13 - 4x^12 - 11x^11 + 55x^10 + 32x^9 - 266x^8 + 13x^7 + 534x^6 - 141x^5 - 404x^4 + 98x^3 + 118x^2 - 16x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.03857$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.03857 q^{2} +1.00000 q^{3} -0.921370 q^{4} +2.59019 q^{5} +1.03857 q^{6} +2.45800 q^{7} -3.03405 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.03857 q^{2} +1.00000 q^{3} -0.921370 q^{4} +2.59019 q^{5} +1.03857 q^{6} +2.45800 q^{7} -3.03405 q^{8} +1.00000 q^{9} +2.69009 q^{10} -1.00000 q^{11} -0.921370 q^{12} -0.671691 q^{13} +2.55280 q^{14} +2.59019 q^{15} -1.30834 q^{16} +6.21727 q^{17} +1.03857 q^{18} +1.35515 q^{19} -2.38652 q^{20} +2.45800 q^{21} -1.03857 q^{22} -4.68937 q^{23} -3.03405 q^{24} +1.70907 q^{25} -0.697599 q^{26} +1.00000 q^{27} -2.26473 q^{28} +3.75473 q^{29} +2.69009 q^{30} +10.9645 q^{31} +4.70930 q^{32} -1.00000 q^{33} +6.45707 q^{34} +6.36668 q^{35} -0.921370 q^{36} -4.57027 q^{37} +1.40742 q^{38} -0.671691 q^{39} -7.85876 q^{40} +7.00531 q^{41} +2.55280 q^{42} -3.15367 q^{43} +0.921370 q^{44} +2.59019 q^{45} -4.87024 q^{46} +0.129852 q^{47} -1.30834 q^{48} -0.958250 q^{49} +1.77500 q^{50} +6.21727 q^{51} +0.618876 q^{52} -5.96418 q^{53} +1.03857 q^{54} -2.59019 q^{55} -7.45769 q^{56} +1.35515 q^{57} +3.89956 q^{58} -5.85500 q^{59} -2.38652 q^{60} -1.00000 q^{61} +11.3874 q^{62} +2.45800 q^{63} +7.50762 q^{64} -1.73981 q^{65} -1.03857 q^{66} +10.8909 q^{67} -5.72840 q^{68} -4.68937 q^{69} +6.61224 q^{70} +7.40554 q^{71} -3.03405 q^{72} -1.18684 q^{73} -4.74655 q^{74} +1.70907 q^{75} -1.24860 q^{76} -2.45800 q^{77} -0.697599 q^{78} -9.52820 q^{79} -3.38884 q^{80} +1.00000 q^{81} +7.27551 q^{82} +8.87131 q^{83} -2.26473 q^{84} +16.1039 q^{85} -3.27531 q^{86} +3.75473 q^{87} +3.03405 q^{88} -14.7152 q^{89} +2.69009 q^{90} -1.65101 q^{91} +4.32064 q^{92} +10.9645 q^{93} +0.134861 q^{94} +3.51010 q^{95} +4.70930 q^{96} +9.17940 q^{97} -0.995210 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * 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 $

$2$	1.03857	0.734381	0.367190	−	0.930146i	$-0.380320\pi$
$2$	1.03857	0.734381	0.367190	+	0.930146i	$0.380320\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.921370	−0.460685
$5$	2.59019	1.15837	0.579184	−	0.815197i	$-0.303371\pi$
$5$	2.59019	1.15837	0.579184	+	0.815197i	$0.303371\pi$
$6$	1.03857	0.423995
$7$	2.45800	0.929036	0.464518	−	0.885564i	$-0.346228\pi$
$7$	2.45800	0.929036	0.464518	+	0.885564i	$0.346228\pi$
$8$	−3.03405	−1.07270
$9$	1.00000	0.333333
$10$	2.69009	0.850683
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.921370	−0.265977
$13$	−0.671691	−0.186294	−0.0931468	−	0.995652i	$-0.529693\pi$
$13$	−0.671691	−0.186294	−0.0931468	+	0.995652i	$0.529693\pi$
$14$	2.55280	0.682266
$15$	2.59019	0.668784
$16$	−1.30834	−0.327084
$17$	6.21727	1.50791	0.753954	−	0.656927i	$-0.228144\pi$
$17$	6.21727	1.50791	0.753954	+	0.656927i	$0.228144\pi$
$18$	1.03857	0.244794
$19$	1.35515	0.310894	0.155447	−	0.987844i	$-0.450318\pi$
$19$	1.35515	0.310894	0.155447	+	0.987844i	$0.450318\pi$
$20$	−2.38652	−0.533643
$21$	2.45800	0.536379
$22$	−1.03857	−0.221424
$23$	−4.68937	−0.977801	−0.488900	−	0.872340i	$-0.662602\pi$
$23$	−4.68937	−0.977801	−0.488900	+	0.872340i	$0.662602\pi$
$24$	−3.03405	−0.619323
$25$	1.70907	0.341815
$26$	−0.697599	−0.136810
$27$	1.00000	0.192450
$28$	−2.26473	−0.427993
$29$	3.75473	0.697237	0.348618	−	0.937265i	$-0.386651\pi$
$29$	3.75473	0.697237	0.348618	+	0.937265i	$0.386651\pi$
$30$	2.69009	0.491142
$31$	10.9645	1.96928	0.984642	−	0.174583i	$-0.0558578\pi$
$31$	10.9645	1.96928	0.984642	+	0.174583i	$0.0558578\pi$
$32$	4.70930	0.832495
$33$	−1.00000	−0.174078
$34$	6.45707	1.10738
$35$	6.36668	1.07616
$36$	−0.921370	−0.153562
$37$	−4.57027	−0.751347	−0.375674	−	0.926752i	$-0.622589\pi$
$37$	−4.57027	−0.751347	−0.375674	+	0.926752i	$0.622589\pi$
$38$	1.40742	0.228314
$39$	−0.671691	−0.107557
$40$	−7.85876	−1.24258
$41$	7.00531	1.09404	0.547022	−	0.837118i	$-0.315761\pi$
$41$	7.00531	1.09404	0.547022	+	0.837118i	$0.315761\pi$
$42$	2.55280	0.393906
$43$	−3.15367	−0.480930	−0.240465	−	0.970658i	$-0.577300\pi$
$43$	−3.15367	−0.480930	−0.240465	+	0.970658i	$0.577300\pi$
$44$	0.921370	0.138902
$45$	2.59019	0.386122
$46$	−4.87024	−0.718078
$47$	0.129852	0.0189409	0.00947046	−	0.999955i	$-0.496985\pi$
$47$	0.129852	0.0189409	0.00947046	+	0.999955i	$0.496985\pi$
$48$	−1.30834	−0.188842
$49$	−0.958250	−0.136893
$50$	1.77500	0.251022
$51$	6.21727	0.870591
$52$	0.618876	0.0858227
$53$	−5.96418	−0.819243	−0.409622	−	0.912255i	$-0.634339\pi$
$53$	−5.96418	−0.819243	−0.409622	+	0.912255i	$0.634339\pi$
$54$	1.03857	0.141332
$55$	−2.59019	−0.349261
$56$	−7.45769	−0.996575
$57$	1.35515	0.179494
$58$	3.89956	0.512037
$59$	−5.85500	−0.762256	−0.381128	−	0.924522i	$-0.624464\pi$
$59$	−5.85500	−0.762256	−0.381128	+	0.924522i	$0.624464\pi$
$60$	−2.38652	−0.308099
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	11.3874	1.44620
$63$	2.45800	0.309679
$64$	7.50762	0.938452
$65$	−1.73981	−0.215796
$66$	−1.03857	−0.127839
$67$	10.8909	1.33054	0.665269	−	0.746604i	$-0.268317\pi$
$67$	10.8909	1.33054	0.665269	+	0.746604i	$0.268317\pi$
$68$	−5.72840	−0.694671
$69$	−4.68937	−0.564534
$70$	6.61224	0.790314
$71$	7.40554	0.878876	0.439438	−	0.898273i	$-0.355178\pi$
$71$	7.40554	0.878876	0.439438	+	0.898273i	$0.355178\pi$
$72$	−3.03405	−0.357566
$73$	−1.18684	−0.138909	−0.0694546	−	0.997585i	$-0.522126\pi$
$73$	−1.18684	−0.138909	−0.0694546	+	0.997585i	$0.522126\pi$
$74$	−4.74655	−0.551775
$75$	1.70907	0.197347
$76$	−1.24860	−0.143224
$77$	−2.45800	−0.280115
$78$	−0.697599	−0.0789875
$79$	−9.52820	−1.07201	−0.536003	−	0.844216i	$-0.680067\pi$
$79$	−9.52820	−1.07201	−0.536003	+	0.844216i	$0.680067\pi$
$80$	−3.38884	−0.378884
$81$	1.00000	0.111111
$82$	7.27551	0.803445
$83$	8.87131	0.973753	0.486877	−	0.873471i	$-0.338136\pi$
$83$	8.87131	0.973753	0.486877	+	0.873471i	$0.338136\pi$
$84$	−2.26473	−0.247102
$85$	16.1039	1.74671
$86$	−3.27531	−0.353186
$87$	3.75473	0.402550
$88$	3.03405	0.323431
$89$	−14.7152	−1.55981	−0.779903	−	0.625901i	$-0.784731\pi$
$89$	−14.7152	−1.55981	−0.779903	+	0.625901i	$0.784731\pi$
$90$	2.69009	0.283561
$91$	−1.65101	−0.173073
$92$	4.32064	0.450458
$93$	10.9645	1.13697
$94$	0.134861	0.0139099
$95$	3.51010	0.360129
$96$	4.70930	0.480641
$97$	9.17940	0.932027	0.466013	−	0.884778i	$-0.345690\pi$
$97$	9.17940	0.932027	0.466013	+	0.884778i	$0.345690\pi$
$98$	−0.995210	−0.100531
$99$	−1.00000	−0.100504
$100$	−1.57469	−0.157469
$101$	−3.54731	−0.352970	−0.176485	−	0.984303i	$-0.556473\pi$
$101$	−3.54731	−0.352970	−0.176485	+	0.984303i	$0.556473\pi$
$102$	6.45707	0.639345
$103$	−5.05960	−0.498537	−0.249269	−	0.968434i	$-0.580190\pi$
$103$	−5.05960	−0.498537	−0.249269	+	0.968434i	$0.580190\pi$
$104$	2.03794	0.199837
$105$	6.36668	0.621324
$106$	−6.19423	−0.601636
$107$	6.78621	0.656048	0.328024	−	0.944669i	$-0.393617\pi$
$107$	6.78621	0.656048	0.328024	+	0.944669i	$0.393617\pi$
$108$	−0.921370	−0.0886589
$109$	−7.18006	−0.687725	−0.343863	−	0.939020i	$-0.611735\pi$
$109$	−7.18006	−0.687725	−0.343863	+	0.939020i	$0.611735\pi$
$110$	−2.69009	−0.256490
$111$	−4.57027	−0.433791
$112$	−3.21589	−0.303873
$113$	−2.65973	−0.250206	−0.125103	−	0.992144i	$-0.539926\pi$
$113$	−2.65973	−0.250206	−0.125103	+	0.992144i	$0.539926\pi$
$114$	1.40742	0.131817
$115$	−12.1463	−1.13265
$116$	−3.45950	−0.321207
$117$	−0.671691	−0.0620979
$118$	−6.08083	−0.559786
$119$	15.2820	1.40090
$120$	−7.85876	−0.717403
$121$	1.00000	0.0909091
$122$	−1.03857	−0.0940278
$123$	7.00531	0.631647
$124$	−10.1024	−0.907220
$125$	−8.52412	−0.762420
$126$	2.55280	0.227422
$127$	−4.04154	−0.358629	−0.179315	−	0.983792i	$-0.557388\pi$
$127$	−4.04154	−0.358629	−0.179315	+	0.983792i	$0.557388\pi$
$128$	−1.62141	−0.143314
$129$	−3.15367	−0.277665
$130$	−1.80691	−0.158477
$131$	−10.1752	−0.889011	−0.444506	−	0.895776i	$-0.646621\pi$
$131$	−10.1752	−0.889011	−0.444506	+	0.895776i	$0.646621\pi$
$132$	0.921370	0.0801950
$133$	3.33096	0.288831
$134$	11.3110	0.977122
$135$	2.59019	0.222928
$136$	−18.8635	−1.61753
$137$	−5.22639	−0.446521	−0.223261	−	0.974759i	$-0.571670\pi$
$137$	−5.22639	−0.446521	−0.223261	+	0.974759i	$0.571670\pi$
$138$	−4.87024	−0.414583
$139$	−7.07190	−0.599831	−0.299915	−	0.953966i	$-0.596958\pi$
$139$	−7.07190	−0.599831	−0.299915	+	0.953966i	$0.596958\pi$
$140$	−5.86606	−0.495773
$141$	0.129852	0.0109356
$142$	7.69118	0.645430
$143$	0.671691	0.0561696
$144$	−1.30834	−0.109028
$145$	9.72547	0.807656
$146$	−1.23262	−0.102012
$147$	−0.958250	−0.0790351
$148$	4.21091	0.346135
$149$	−6.34530	−0.519828	−0.259914	−	0.965632i	$-0.583694\pi$
$149$	−6.34530	−0.519828	−0.259914	+	0.965632i	$0.583694\pi$
$150$	1.77500	0.144928
$151$	4.14272	0.337129	0.168565	−	0.985691i	$-0.446087\pi$
$151$	4.14272	0.337129	0.168565	+	0.985691i	$0.446087\pi$
$152$	−4.11160	−0.333495
$153$	6.21727	0.502636
$154$	−2.55280	−0.205711
$155$	28.4002	2.28116
$156$	0.618876	0.0495497
$157$	9.02403	0.720196	0.360098	−	0.932914i	$-0.382743\pi$
$157$	9.02403	0.720196	0.360098	+	0.932914i	$0.382743\pi$
$158$	−9.89572	−0.787261
$159$	−5.96418	−0.472990
$160$	12.1980	0.964335
$161$	−11.5265	−0.908412
$162$	1.03857	0.0815978
$163$	20.8366	1.63205	0.816026	−	0.578015i	$-0.196173\pi$
$163$	20.8366	1.63205	0.816026	+	0.578015i	$0.196173\pi$
$164$	−6.45448	−0.504010
$165$	−2.59019	−0.201646
$166$	9.21349	0.715105
$167$	1.99490	0.154370	0.0771848	−	0.997017i	$-0.475407\pi$
$167$	1.99490	0.154370	0.0771848	+	0.997017i	$0.475407\pi$
$168$	−7.45769	−0.575373
$169$	−12.5488	−0.965295
$170$	16.7250	1.28275
$171$	1.35515	0.103631
$172$	2.90570	0.221557
$173$	3.07200	0.233560	0.116780	−	0.993158i	$-0.462743\pi$
$173$	3.07200	0.233560	0.116780	+	0.993158i	$0.462743\pi$
$174$	3.89956	0.295625
$175$	4.20090	0.317558
$176$	1.30834	0.0986196
$177$	−5.85500	−0.440088
$178$	−15.2828	−1.14549
$179$	16.8408	1.25874	0.629371	−	0.777105i	$-0.283312\pi$
$179$	16.8408	1.25874	0.629371	+	0.777105i	$0.283312\pi$
$180$	−2.38652	−0.177881
$181$	24.7265	1.83791	0.918954	−	0.394365i	$-0.129035\pi$
$181$	24.7265	1.83791	0.918954	+	0.394365i	$0.129035\pi$
$182$	−1.71470	−0.127102
$183$	−1.00000	−0.0739221
$184$	14.2278	1.04889
$185$	−11.8379	−0.870336
$186$	11.3874	0.834967
$187$	−6.21727	−0.454651
$188$	−0.119642	−0.00872580
$189$	2.45800	0.178793
$190$	3.64549	0.264472
$191$	14.6759	1.06191	0.530955	−	0.847400i	$-0.321833\pi$
$191$	14.6759	1.06191	0.530955	+	0.847400i	$0.321833\pi$
$192$	7.50762	0.541816
$193$	−15.2086	−1.09474	−0.547368	−	0.836892i	$-0.684370\pi$
$193$	−15.2086	−1.09474	−0.547368	+	0.836892i	$0.684370\pi$
$194$	9.53346	0.684462
$195$	−1.73981	−0.124590
$196$	0.882903	0.0630645
$197$	−22.2855	−1.58778	−0.793889	−	0.608063i	$-0.791947\pi$
$197$	−22.2855	−1.58778	−0.793889	+	0.608063i	$0.791947\pi$
$198$	−1.03857	−0.0738080
$199$	−22.3623	−1.58522	−0.792612	−	0.609727i	$-0.791279\pi$
$199$	−22.3623	−1.58522	−0.792612	+	0.609727i	$0.791279\pi$
$200$	−5.18542	−0.366664
$201$	10.8909	0.768187
$202$	−3.68413	−0.259214
$203$	9.22913	0.647758
$204$	−5.72840	−0.401068
$205$	18.1451	1.26731
$206$	−5.25475	−0.366116
$207$	−4.68937	−0.325934
$208$	0.878798	0.0609337
$209$	−1.35515	−0.0937379
$210$	6.61224	0.456288
$211$	4.90432	0.337627	0.168814	−	0.985648i	$-0.446006\pi$
$211$	4.90432	0.337627	0.168814	+	0.985648i	$0.446006\pi$
$212$	5.49522	0.377413
$213$	7.40554	0.507420
$214$	7.04796	0.481789
$215$	−8.16860	−0.557094
$216$	−3.03405	−0.206441
$217$	26.9507	1.82954
$218$	−7.45700	−0.505052
$219$	−1.18684	−0.0801993
$220$	2.38652	0.160899
$221$	−4.17608	−0.280914
$222$	−4.74655	−0.318567
$223$	−8.32480	−0.557470	−0.278735	−	0.960368i	$-0.589915\pi$
$223$	−8.32480	−0.557470	−0.278735	+	0.960368i	$0.589915\pi$
$224$	11.5754	0.773417
$225$	1.70907	0.113938
$226$	−2.76232	−0.183747
$227$	9.03289	0.599534	0.299767	−	0.954012i	$-0.403091\pi$
$227$	9.03289	0.599534	0.299767	+	0.954012i	$0.403091\pi$
$228$	−1.24860	−0.0826904
$229$	−23.6862	−1.56523	−0.782614	−	0.622507i	$-0.786114\pi$
$229$	−23.6862	−1.56523	−0.782614	+	0.622507i	$0.786114\pi$
$230$	−12.6148	−0.831798
$231$	−2.45800	−0.161724
$232$	−11.3921	−0.747925
$233$	−19.6906	−1.28997	−0.644987	−	0.764193i	$-0.723137\pi$
$233$	−19.6906	−1.28997	−0.644987	+	0.764193i	$0.723137\pi$
$234$	−0.697599	−0.0456035
$235$	0.336342	0.0219406
$236$	5.39462	0.351160
$237$	−9.52820	−0.618923
$238$	15.8715	1.02879
$239$	−1.46270	−0.0946140	−0.0473070	−	0.998880i	$-0.515064\pi$
$239$	−1.46270	−0.0946140	−0.0473070	+	0.998880i	$0.515064\pi$
$240$	−3.38884	−0.218749
$241$	−1.51296	−0.0974584	−0.0487292	−	0.998812i	$-0.515517\pi$
$241$	−1.51296	−0.0974584	−0.0487292	+	0.998812i	$0.515517\pi$
$242$	1.03857	0.0667619
$243$	1.00000	0.0641500
$244$	0.921370	0.0589847
$245$	−2.48205	−0.158572
$246$	7.27551	0.463869
$247$	−0.910245	−0.0579175
$248$	−33.2669	−2.11245
$249$	8.87131	0.562197
$250$	−8.85290	−0.559907
$251$	−25.5694	−1.61393	−0.806965	−	0.590600i	$-0.798891\pi$
$251$	−25.5694	−1.61393	−0.806965	+	0.590600i	$0.798891\pi$
$252$	−2.26473	−0.142664
$253$	4.68937	0.294818
$254$	−4.19743	−0.263370
$255$	16.1039	1.00846
$256$	−16.6992	−1.04370
$257$	2.56557	0.160036	0.0800178	−	0.996793i	$-0.474502\pi$
$257$	2.56557	0.160036	0.0800178	+	0.996793i	$0.474502\pi$
$258$	−3.27531	−0.203912
$259$	−11.2337	−0.698028
$260$	1.60301	0.0994142
$261$	3.75473	0.232412
$262$	−10.5677	−0.652873
$263$	−13.6690	−0.842868	−0.421434	−	0.906859i	$-0.638473\pi$
$263$	−13.6690	−0.842868	−0.421434	+	0.906859i	$0.638473\pi$
$264$	3.03405	0.186733
$265$	−15.4484	−0.948985
$266$	3.45944	0.212112
$267$	−14.7152	−0.900554
$268$	−10.0346	−0.612959
$269$	16.7194	1.01940	0.509699	−	0.860353i	$-0.329757\pi$
$269$	16.7194	1.01940	0.509699	+	0.860353i	$0.329757\pi$
$270$	2.69009	0.163714
$271$	−22.4580	−1.36423	−0.682113	−	0.731246i	$-0.738939\pi$
$271$	−22.4580	−1.36423	−0.682113	+	0.731246i	$0.738939\pi$
$272$	−8.13428	−0.493213
$273$	−1.65101	−0.0999240
$274$	−5.42798	−0.327916
$275$	−1.70907	−0.103061
$276$	4.32064	0.260072
$277$	−30.6375	−1.84083	−0.920415	−	0.390944i	$-0.872149\pi$
$277$	−30.6375	−1.84083	−0.920415	+	0.390944i	$0.872149\pi$
$278$	−7.34467	−0.440504
$279$	10.9645	0.656428
$280$	−19.3168	−1.15440
$281$	3.33065	0.198690	0.0993448	−	0.995053i	$-0.468325\pi$
$281$	3.33065	0.198690	0.0993448	+	0.995053i	$0.468325\pi$
$282$	0.134861	0.00803086
$283$	−13.4522	−0.799648	−0.399824	−	0.916592i	$-0.630929\pi$
$283$	−13.4522	−0.799648	−0.399824	+	0.916592i	$0.630929\pi$
$284$	−6.82325	−0.404885
$285$	3.51010	0.207921
$286$	0.697599	0.0412499
$287$	17.2190	1.01641
$288$	4.70930	0.277498
$289$	21.6544	1.27379
$290$	10.1006	0.593127
$291$	9.17940	0.538106
$292$	1.09352	0.0639934
$293$	18.6240	1.08802	0.544012	−	0.839077i	$-0.316904\pi$
$293$	18.6240	1.08802	0.544012	+	0.839077i	$0.316904\pi$
$294$	−0.995210	−0.0580418
$295$	−15.1655	−0.882972
$296$	13.8664	0.805969
$297$	−1.00000	−0.0580259
$298$	−6.59005	−0.381751
$299$	3.14981	0.182158
$300$	−1.57469	−0.0909148
$301$	−7.75171	−0.446801
$302$	4.30251	0.247581
$303$	−3.54731	−0.203787
$304$	−1.77300	−0.101688
$305$	−2.59019	−0.148314
$306$	6.45707	0.369126
$307$	−23.5213	−1.34243	−0.671216	−	0.741262i	$-0.734228\pi$
$307$	−23.5213	−1.34243	−0.671216	+	0.741262i	$0.734228\pi$
$308$	2.26473	0.129045
$309$	−5.05960	−0.287831
$310$	29.4956	1.67524
$311$	4.96547	0.281566	0.140783	−	0.990040i	$-0.455038\pi$
$311$	4.96547	0.281566	0.140783	+	0.990040i	$0.455038\pi$
$312$	2.03794	0.115376
$313$	−9.52784	−0.538545	−0.269273	−	0.963064i	$-0.586783\pi$
$313$	−9.52784	−0.538545	−0.269273	+	0.963064i	$0.586783\pi$
$314$	9.37210	0.528898
$315$	6.36668	0.358722
$316$	8.77900	0.493858
$317$	24.6012	1.38174	0.690870	−	0.722979i	$-0.257227\pi$
$317$	24.6012	1.38174	0.690870	+	0.722979i	$0.257227\pi$
$318$	−6.19423	−0.347355
$319$	−3.75473	−0.210225
$320$	19.4461	1.08707
$321$	6.78621	0.378769
$322$	−11.9710	−0.667120
$323$	8.42535	0.468799
$324$	−0.921370	−0.0511872
$325$	−1.14797	−0.0636779
$326$	21.6403	1.19855
$327$	−7.18006	−0.397058
$328$	−21.2545	−1.17358
$329$	0.319177	0.0175968
$330$	−2.69009	−0.148085
$331$	5.12173	0.281516	0.140758	−	0.990044i	$-0.455046\pi$
$331$	5.12173	0.281516	0.140758	+	0.990044i	$0.455046\pi$
$332$	−8.17376	−0.448594
$333$	−4.57027	−0.250449
$334$	2.07184	0.113366
$335$	28.2095	1.54125
$336$	−3.21589	−0.175441
$337$	−9.23806	−0.503229	−0.251615	−	0.967828i	$-0.580962\pi$
$337$	−9.23806	−0.503229	−0.251615	+	0.967828i	$0.580962\pi$
$338$	−13.0329	−0.708894
$339$	−2.65973	−0.144457
$340$	−14.8376	−0.804684
$341$	−10.9645	−0.593762
$342$	1.40742	0.0761047
$343$	−19.5614	−1.05621
$344$	9.56840	0.515893
$345$	−12.1463	−0.653937
$346$	3.19049	0.171522
$347$	7.92938	0.425671	0.212836	−	0.977088i	$-0.431730\pi$
$347$	7.92938	0.425671	0.212836	+	0.977088i	$0.431730\pi$
$348$	−3.45950	−0.185449
$349$	−25.8578	−1.38413	−0.692067	−	0.721833i	$-0.743300\pi$
$349$	−25.8578	−1.38413	−0.692067	+	0.721833i	$0.743300\pi$
$350$	4.36293	0.233209
$351$	−0.671691	−0.0358522
$352$	−4.70930	−0.251007
$353$	12.1228	0.645231	0.322615	−	0.946530i	$-0.395438\pi$
$353$	12.1228	0.645231	0.322615	+	0.946530i	$0.395438\pi$
$354$	−6.08083	−0.323192
$355$	19.1818	1.01806
$356$	13.5581	0.718579
$357$	15.2820	0.808810
$358$	17.4904	0.924396
$359$	3.56989	0.188411	0.0942057	−	0.995553i	$-0.469969\pi$
$359$	3.56989	0.188411	0.0942057	+	0.995553i	$0.469969\pi$
$360$	−7.85876	−0.414193
$361$	−17.1636	−0.903345
$362$	25.6803	1.34972
$363$	1.00000	0.0524864
$364$	1.52120	0.0797323
$365$	−3.07414	−0.160908
$366$	−1.03857	−0.0542870
$367$	−14.5433	−0.759155	−0.379578	−	0.925160i	$-0.623931\pi$
$367$	−14.5433	−0.759155	−0.379578	+	0.925160i	$0.623931\pi$
$368$	6.13527	0.319823
$369$	7.00531	0.364682
$370$	−12.2945	−0.639158
$371$	−14.6599	−0.761106
$372$	−10.1024	−0.523784
$373$	−6.64201	−0.343910	−0.171955	−	0.985105i	$-0.555008\pi$
$373$	−6.64201	−0.343910	−0.171955	+	0.985105i	$0.555008\pi$
$374$	−6.45707	−0.333887
$375$	−8.52412	−0.440183
$376$	−0.393979	−0.0203179
$377$	−2.52202	−0.129891
$378$	2.55280	0.131302
$379$	−3.64651	−0.187309	−0.0936544	−	0.995605i	$-0.529855\pi$
$379$	−3.64651	−0.187309	−0.0936544	+	0.995605i	$0.529855\pi$
$380$	−3.23410	−0.165906
$381$	−4.04154	−0.207055
$382$	15.2420	0.779846
$383$	−21.4030	−1.09364	−0.546821	−	0.837249i	$-0.684162\pi$
$383$	−21.4030	−1.09364	−0.546821	+	0.837249i	$0.684162\pi$
$384$	−1.62141	−0.0827421
$385$	−6.36668	−0.324476
$386$	−15.7952	−0.803952
$387$	−3.15367	−0.160310
$388$	−8.45763	−0.429371
$389$	32.8746	1.66681	0.833405	−	0.552663i	$-0.186388\pi$
$389$	32.8746	1.66681	0.833405	+	0.552663i	$0.186388\pi$
$390$	−1.80691	−0.0914966
$391$	−29.1550	−1.47443
$392$	2.90738	0.146845
$393$	−10.1752	−0.513271
$394$	−23.1451	−1.16603
$395$	−24.6798	−1.24178
$396$	0.921370	0.0463006
$397$	11.2498	0.564610	0.282305	−	0.959325i	$-0.408901\pi$
$397$	11.2498	0.564610	0.282305	+	0.959325i	$0.408901\pi$
$398$	−23.2249	−1.16416
$399$	3.33096	0.166757
$400$	−2.23604	−0.111802
$401$	−18.8968	−0.943659	−0.471829	−	0.881690i	$-0.656406\pi$
$401$	−18.8968	−0.943659	−0.471829	+	0.881690i	$0.656406\pi$
$402$	11.3110	0.564141
$403$	−7.36477	−0.366865
$404$	3.26838	0.162608
$405$	2.59019	0.128707
$406$	9.58510	0.475701
$407$	4.57027	0.226540
$408$	−18.8635	−0.933882
$409$	0.316467	0.0156483	0.00782414	−	0.999969i	$-0.497509\pi$
$409$	0.316467	0.0156483	0.00782414	+	0.999969i	$0.497509\pi$
$410$	18.8449	0.930685
$411$	−5.22639	−0.257799
$412$	4.66176	0.229669
$413$	−14.3916	−0.708163
$414$	−4.87024	−0.239359
$415$	22.9784	1.12796
$416$	−3.16319	−0.155088
$417$	−7.07190	−0.346313
$418$	−1.40742	−0.0688393
$419$	28.2842	1.38177	0.690886	−	0.722964i	$-0.257221\pi$
$419$	28.2842	1.38177	0.690886	+	0.722964i	$0.257221\pi$
$420$	−5.86606	−0.286235
$421$	−11.1862	−0.545181	−0.272590	−	0.962130i	$-0.587880\pi$
$421$	−11.1862	−0.545181	−0.272590	+	0.962130i	$0.587880\pi$
$422$	5.09348	0.247947
$423$	0.129852	0.00631364
$424$	18.0956	0.878801
$425$	10.6258	0.515425
$426$	7.69118	0.372639
$427$	−2.45800	−0.118951
$428$	−6.25261	−0.302231
$429$	0.671691	0.0324295
$430$	−8.48367	−0.409119
$431$	31.2880	1.50709	0.753544	−	0.657397i	$-0.228343\pi$
$431$	31.2880	1.50709	0.753544	+	0.657397i	$0.228343\pi$
$432$	−1.30834	−0.0629474
$433$	1.44868	0.0696192	0.0348096	−	0.999394i	$-0.488918\pi$
$433$	1.44868	0.0696192	0.0348096	+	0.999394i	$0.488918\pi$
$434$	27.9903	1.34358
$435$	9.72547	0.466300
$436$	6.61549	0.316825
$437$	−6.35481	−0.303992
$438$	−1.23262	−0.0588968
$439$	2.81659	0.134428	0.0672142	−	0.997739i	$-0.478589\pi$
$439$	2.81659	0.134428	0.0672142	+	0.997739i	$0.478589\pi$
$440$	7.85876	0.374652
$441$	−0.958250	−0.0456309
$442$	−4.33716	−0.206298
$443$	17.6857	0.840271	0.420136	−	0.907461i	$-0.361983\pi$
$443$	17.6857	0.840271	0.420136	+	0.907461i	$0.361983\pi$
$444$	4.21091	0.199841
$445$	−38.1151	−1.80683
$446$	−8.64590	−0.409395
$447$	−6.34530	−0.300123
$448$	18.4537	0.871855
$449$	−32.9561	−1.55529	−0.777647	−	0.628701i	$-0.783587\pi$
$449$	−32.9561	−1.55529	−0.777647	+	0.628701i	$0.783587\pi$
$450$	1.77500	0.0836741
$451$	−7.00531	−0.329867
$452$	2.45060	0.115266
$453$	4.14272	0.194642
$454$	9.38130	0.440286
$455$	−4.27644	−0.200483
$456$	−4.11160	−0.192544
$457$	−26.4589	−1.23770	−0.618848	−	0.785511i	$-0.712400\pi$
$457$	−26.4589	−1.23770	−0.618848	+	0.785511i	$0.712400\pi$
$458$	−24.5998	−1.14947
$459$	6.21727	0.290197
$460$	11.1913	0.521796
$461$	−20.0346	−0.933106	−0.466553	−	0.884493i	$-0.654504\pi$
$461$	−20.0346	−0.933106	−0.466553	+	0.884493i	$0.654504\pi$
$462$	−2.55280	−0.118767
$463$	16.6984	0.776041	0.388021	−	0.921651i	$-0.373159\pi$
$463$	16.6984	0.776041	0.388021	+	0.921651i	$0.373159\pi$
$464$	−4.91246	−0.228055
$465$	28.4002	1.31703
$466$	−20.4501	−0.947332
$467$	12.0423	0.557250	0.278625	−	0.960400i	$-0.410121\pi$
$467$	12.0423	0.557250	0.278625	+	0.960400i	$0.410121\pi$
$468$	0.618876	0.0286076
$469$	26.7699	1.23612
$470$	0.349315	0.0161127
$471$	9.02403	0.415806
$472$	17.7644	0.817671
$473$	3.15367	0.145006
$474$	−9.89572	−0.454525
$475$	2.31606	0.106268
$476$	−14.0804	−0.645374
$477$	−5.96418	−0.273081
$478$	−1.51911	−0.0694827
$479$	−27.7699	−1.26884	−0.634419	−	0.772989i	$-0.718761\pi$
$479$	−27.7699	−1.26884	−0.634419	+	0.772989i	$0.718761\pi$
$480$	12.1980	0.556759
$481$	3.06981	0.139971
$482$	−1.57132	−0.0715715
$483$	−11.5265	−0.524472
$484$	−0.921370	−0.0418805
$485$	23.7764	1.07963
$486$	1.03857	0.0471105
$487$	−20.4003	−0.924426	−0.462213	−	0.886769i	$-0.652944\pi$
$487$	−20.4003	−0.924426	−0.462213	+	0.886769i	$0.652944\pi$
$488$	3.03405	0.137345
$489$	20.8366	0.942266
$490$	−2.57778	−0.116452
$491$	9.35479	0.422176	0.211088	−	0.977467i	$-0.432299\pi$
$491$	9.35479	0.422176	0.211088	+	0.977467i	$0.432299\pi$
$492$	−6.45448	−0.290990
$493$	23.3442	1.05137
$494$	−0.945354	−0.0425335
$495$	−2.59019	−0.116420
$496$	−14.3453	−0.644122
$497$	18.2028	0.816507
$498$	9.21349	0.412866
$499$	−5.49067	−0.245796	−0.122898	−	0.992419i	$-0.539219\pi$
$499$	−5.49067	−0.245796	−0.122898	+	0.992419i	$0.539219\pi$
$500$	7.85387	0.351236
$501$	1.99490	0.0891253
$502$	−26.5557	−1.18524
$503$	11.4997	0.512746	0.256373	−	0.966578i	$-0.417472\pi$
$503$	11.4997	0.512746	0.256373	+	0.966578i	$0.417472\pi$
$504$	−7.45769	−0.332192
$505$	−9.18819	−0.408869
$506$	4.87024	0.216509
$507$	−12.5488	−0.557313
$508$	3.72376	0.165215
$509$	−28.7730	−1.27534	−0.637670	−	0.770310i	$-0.720102\pi$
$509$	−28.7730	−1.27534	−0.637670	+	0.770310i	$0.720102\pi$
$510$	16.7250	0.740597
$511$	−2.91725	−0.129052
$512$	−14.1005	−0.623159
$513$	1.35515	0.0598315
$514$	2.66452	0.117527
$515$	−13.1053	−0.577489
$516$	2.90570	0.127916
$517$	−0.129852	−0.00571091
$518$	−11.6670	−0.512619
$519$	3.07200	0.134846
$520$	5.27866	0.231485
$521$	45.2160	1.98095	0.990475	−	0.137695i	$-0.0439694\pi$
$521$	45.2160	1.98095	0.990475	+	0.137695i	$0.0439694\pi$
$522$	3.89956	0.170679
$523$	−15.7158	−0.687202	−0.343601	−	0.939116i	$-0.611647\pi$
$523$	−15.7158	−0.687202	−0.343601	+	0.939116i	$0.611647\pi$
$524$	9.37512	0.409554
$525$	4.20090	0.183342
$526$	−14.1963	−0.618986
$527$	68.1693	2.96950
$528$	1.30834	0.0569380
$529$	−1.00983	−0.0439055
$530$	−16.0442	−0.696916
$531$	−5.85500	−0.254085
$532$	−3.06905	−0.133060
$533$	−4.70540	−0.203814
$534$	−15.2828	−0.661349
$535$	17.5776	0.759944
$536$	−33.0436	−1.42727
$537$	16.8408	0.726736
$538$	17.3643	0.748627
$539$	0.958250	0.0412747
$540$	−2.38652	−0.102700
$541$	18.6208	0.800571	0.400286	−	0.916390i	$-0.368911\pi$
$541$	18.6208	0.800571	0.400286	+	0.916390i	$0.368911\pi$
$542$	−23.3242	−1.00186
$543$	24.7265	1.06112
$544$	29.2790	1.25533
$545$	−18.5977	−0.796638
$546$	−1.71470	−0.0733822
$547$	25.0612	1.07154	0.535770	−	0.844364i	$-0.320021\pi$
$547$	25.0612	1.07154	0.535770	+	0.844364i	$0.320021\pi$
$548$	4.81544	0.205706
$549$	−1.00000	−0.0426790
$550$	−1.77500	−0.0756860
$551$	5.08824	0.216766
$552$	14.2278	0.605575
$553$	−23.4203	−0.995932
$554$	−31.8192	−1.35187
$555$	−11.8379	−0.502489
$556$	6.51584	0.276333
$557$	16.3942	0.694643	0.347322	−	0.937746i	$-0.387091\pi$
$557$	16.3942	0.694643	0.347322	+	0.937746i	$0.387091\pi$
$558$	11.3874	0.482068
$559$	2.11829	0.0895942
$560$	−8.32975	−0.351996
$561$	−6.21727	−0.262493
$562$	3.45911	0.145914
$563$	−2.17322	−0.0915901	−0.0457951	−	0.998951i	$-0.514582\pi$
$563$	−2.17322	−0.0915901	−0.0457951	+	0.998951i	$0.514582\pi$
$564$	−0.119642	−0.00503785
$565$	−6.88920	−0.289831
$566$	−13.9710	−0.587246
$567$	2.45800	0.103226
$568$	−22.4688	−0.942770
$569$	23.5470	0.987141	0.493570	−	0.869706i	$-0.335692\pi$
$569$	23.5470	0.987141	0.493570	+	0.869706i	$0.335692\pi$
$570$	3.64549	0.152693
$571$	6.13515	0.256748	0.128374	−	0.991726i	$-0.459024\pi$
$571$	6.13515	0.256748	0.128374	+	0.991726i	$0.459024\pi$
$572$	−0.618876	−0.0258765
$573$	14.6759	0.613094
$574$	17.8832	0.746429
$575$	−8.01448	−0.334227
$576$	7.50762	0.312817
$577$	−22.3118	−0.928851	−0.464425	−	0.885612i	$-0.653739\pi$
$577$	−22.3118	−0.928851	−0.464425	+	0.885612i	$0.653739\pi$
$578$	22.4896	0.935445
$579$	−15.2086	−0.632046
$580$	−8.96076	−0.372075
$581$	21.8057	0.904651
$582$	9.53346	0.395175
$583$	5.96418	0.247011
$584$	3.60094	0.149008
$585$	−1.73981	−0.0719321
$586$	19.3423	0.799024
$587$	−27.1712	−1.12147	−0.560737	−	0.827994i	$-0.689482\pi$
$587$	−27.1712	−1.12147	−0.560737	+	0.827994i	$0.689482\pi$
$588$	0.882903	0.0364103
$589$	14.8586	0.612238
$590$	−15.7505	−0.648437
$591$	−22.2855	−0.916704
$592$	5.97945	0.245754
$593$	0.0478401	0.00196456	0.000982278	−	1.00000i	$-0.499687\pi$
$593$	0.0478401	0.00196456	0.000982278		1.00000i	$0.499687\pi$
$594$	−1.03857	−0.0426131
$595$	39.5833	1.62276
$596$	5.84637	0.239477
$597$	−22.3623	−0.915229
$598$	3.27130	0.133773
$599$	−22.1568	−0.905302	−0.452651	−	0.891688i	$-0.649522\pi$
$599$	−22.1568	−0.905302	−0.452651	+	0.891688i	$0.649522\pi$
$600$	−5.18542	−0.211694
$601$	−7.49957	−0.305914	−0.152957	−	0.988233i	$-0.548880\pi$
$601$	−7.49957	−0.305914	−0.152957	+	0.988233i	$0.548880\pi$
$602$	−8.05071	−0.328122
$603$	10.8909	0.443513
$604$	−3.81698	−0.155311
$605$	2.59019	0.105306
$606$	−3.68413	−0.149658
$607$	−14.4002	−0.584486	−0.292243	−	0.956344i	$-0.594402\pi$
$607$	−14.4002	−0.584486	−0.292243	+	0.956344i	$0.594402\pi$
$608$	6.38183	0.258817
$609$	9.22913	0.373983
$610$	−2.69009	−0.108919
$611$	−0.0872207	−0.00352857
$612$	−5.72840	−0.231557
$613$	38.5814	1.55829	0.779143	−	0.626846i	$-0.215655\pi$
$613$	38.5814	1.55829	0.779143	+	0.626846i	$0.215655\pi$
$614$	−24.4285	−0.985856
$615$	18.1451	0.731679
$616$	7.45769	0.300479
$617$	−8.04565	−0.323905	−0.161953	−	0.986799i	$-0.551779\pi$
$617$	−8.04565	−0.323905	−0.161953	+	0.986799i	$0.551779\pi$
$618$	−5.25475	−0.211377
$619$	−11.6528	−0.468367	−0.234184	−	0.972192i	$-0.575242\pi$
$619$	−11.6528	−0.468367	−0.234184	+	0.972192i	$0.575242\pi$
$620$	−26.1671	−1.05089
$621$	−4.68937	−0.188178
$622$	5.15699	0.206777
$623$	−36.1699	−1.44911
$624$	0.878798	0.0351801
$625$	−30.6244	−1.22498
$626$	−9.89534	−0.395497
$627$	−1.35515	−0.0541196
$628$	−8.31448	−0.331784
$629$	−28.4146	−1.13296
$630$	6.61224	0.263438
$631$	40.3337	1.60566	0.802830	−	0.596209i	$-0.203327\pi$
$631$	40.3337	1.60566	0.802830	+	0.596209i	$0.203327\pi$
$632$	28.9091	1.14994
$633$	4.90432	0.194929
$634$	25.5501	1.01472
$635$	−10.4684	−0.415424
$636$	5.49522	0.217900
$637$	0.643648	0.0255022
$638$	−3.89956	−0.154385
$639$	7.40554	0.292959
$640$	−4.19975	−0.166010
$641$	6.04109	0.238609	0.119304	−	0.992858i	$-0.461934\pi$
$641$	6.04109	0.238609	0.119304	+	0.992858i	$0.461934\pi$
$642$	7.04796	0.278161
$643$	47.4680	1.87196	0.935979	−	0.352057i	$-0.114518\pi$
$643$	47.4680	1.87196	0.935979	+	0.352057i	$0.114518\pi$
$644$	10.6201	0.418492
$645$	−8.16860	−0.321638
$646$	8.75032	0.344277
$647$	33.1249	1.30228	0.651138	−	0.758960i	$-0.274292\pi$
$647$	33.1249	1.30228	0.651138	+	0.758960i	$0.274292\pi$
$648$	−3.03405	−0.119189
$649$	5.85500	0.229829
$650$	−1.19225	−0.0467638
$651$	26.9507	1.05628
$652$	−19.1983	−0.751862
$653$	13.9703	0.546700	0.273350	−	0.961915i	$-0.411868\pi$
$653$	13.9703	0.546700	0.273350	+	0.961915i	$0.411868\pi$
$654$	−7.45700	−0.291592
$655$	−26.3557	−1.02980
$656$	−9.16530	−0.357845
$657$	−1.18684	−0.0463031
$658$	0.331488	0.0129227
$659$	42.4909	1.65521	0.827605	−	0.561312i	$-0.189703\pi$
$659$	42.4909	1.65521	0.827605	+	0.561312i	$0.189703\pi$
$660$	2.38652	0.0928952
$661$	−15.2591	−0.593509	−0.296754	−	0.954954i	$-0.595904\pi$
$661$	−15.2591	−0.593509	−0.296754	+	0.954954i	$0.595904\pi$
$662$	5.31929	0.206740
$663$	−4.17608	−0.162186
$664$	−26.9160	−1.04454
$665$	8.62782	0.334573
$666$	−4.74655	−0.183925
$667$	−17.6073	−0.681759
$668$	−1.83804	−0.0711158
$669$	−8.32480	−0.321855
$670$	29.2976	1.13187
$671$	1.00000	0.0386046
$672$	11.5754	0.446533
$673$	−23.6405	−0.911275	−0.455637	−	0.890165i	$-0.650589\pi$
$673$	−23.6405	−0.911275	−0.455637	+	0.890165i	$0.650589\pi$
$674$	−9.59438	−0.369562
$675$	1.70907	0.0657823
$676$	11.5621	0.444697
$677$	31.3736	1.20578	0.602892	−	0.797823i	$-0.294015\pi$
$677$	31.3736	1.20578	0.602892	+	0.797823i	$0.294015\pi$
$678$	−2.76232	−0.106086
$679$	22.5629	0.865886
$680$	−48.8600	−1.87370
$681$	9.03289	0.346141
$682$	−11.3874	−0.436047
$683$	4.92411	0.188416	0.0942079	−	0.995553i	$-0.469968\pi$
$683$	4.92411	0.188416	0.0942079	+	0.995553i	$0.469968\pi$
$684$	−1.24860	−0.0477413
$685$	−13.5373	−0.517235
$686$	−20.3159	−0.775663
$687$	−23.6862	−0.903685
$688$	4.12606	0.157305
$689$	4.00609	0.152620
$690$	−12.6148	−0.480239
$691$	−13.9837	−0.531965	−0.265983	−	0.963978i	$-0.585696\pi$
$691$	−13.9837	−0.531965	−0.265983	+	0.963978i	$0.585696\pi$
$692$	−2.83045	−0.107598
$693$	−2.45800	−0.0933716
$694$	8.23522	0.312605
$695$	−18.3176	−0.694825
$696$	−11.3921	−0.431815
$697$	43.5538	1.64972
$698$	−26.8551	−1.01648
$699$	−19.6906	−0.744767
$700$	−3.87058	−0.146294
$701$	17.3421	0.655002	0.327501	−	0.944851i	$-0.393794\pi$
$701$	17.3421	0.655002	0.327501	+	0.944851i	$0.393794\pi$
$702$	−0.697599	−0.0263292
$703$	−6.19342	−0.233589
$704$	−7.50762	−0.282954
$705$	0.336342	0.0126674
$706$	12.5904	0.473845
$707$	−8.71927	−0.327922
$708$	5.39462	0.202742
$709$	26.7158	1.00333	0.501666	−	0.865062i	$-0.332721\pi$
$709$	26.7158	1.00333	0.501666	+	0.865062i	$0.332721\pi$
$710$	19.9216	0.747645
$711$	−9.52820	−0.357336
$712$	44.6466	1.67320
$713$	−51.4166	−1.92557
$714$	15.8715	0.593975
$715$	1.73981	0.0650651
$716$	−15.5166	−0.579884
$717$	−1.46270	−0.0546254
$718$	3.70758	0.138366
$719$	35.7153	1.33196	0.665979	−	0.745971i	$-0.268014\pi$
$719$	35.7153	1.33196	0.665979	+	0.745971i	$0.268014\pi$
$720$	−3.38884	−0.126295
$721$	−12.4365	−0.463159
$722$	−17.8256	−0.663399
$723$	−1.51296	−0.0562676
$724$	−22.7823	−0.846697
$725$	6.41712	0.238326
$726$	1.03857	0.0385450
$727$	16.2124	0.601283	0.300642	−	0.953737i	$-0.402799\pi$
$727$	16.2124	0.601283	0.300642	+	0.953737i	$0.402799\pi$
$728$	5.00926	0.185656
$729$	1.00000	0.0370370
$730$	−3.19272	−0.118168
$731$	−19.6072	−0.725199
$732$	0.921370	0.0340548
$733$	−9.43198	−0.348378	−0.174189	−	0.984712i	$-0.555730\pi$
$733$	−9.43198	−0.348378	−0.174189	+	0.984712i	$0.555730\pi$
$734$	−15.1043	−0.557509
$735$	−2.48205	−0.0915517
$736$	−22.0836	−0.814014
$737$	−10.8909	−0.401172
$738$	7.27551	0.267815
$739$	46.3708	1.70578	0.852889	−	0.522093i	$-0.174848\pi$
$739$	46.3708	1.70578	0.852889	+	0.522093i	$0.174848\pi$
$740$	10.9070	0.400951
$741$	−0.910245	−0.0334387
$742$	−15.2254	−0.558942
$743$	−26.6293	−0.976934	−0.488467	−	0.872582i	$-0.662444\pi$
$743$	−26.6293	−0.976934	−0.488467	+	0.872582i	$0.662444\pi$
$744$	−33.2669	−1.21962
$745$	−16.4355	−0.602151
$746$	−6.89820	−0.252561
$747$	8.87131	0.324584
$748$	5.72840	0.209451
$749$	16.6805	0.609492
$750$	−8.85290	−0.323262
$751$	−53.0091	−1.93433	−0.967165	−	0.254150i	$-0.918204\pi$
$751$	−53.0091	−1.93433	−0.967165	+	0.254150i	$0.918204\pi$
$752$	−0.169891	−0.00619528
$753$	−25.5694	−0.931802
$754$	−2.61930	−0.0953892
$755$	10.7304	0.390520
$756$	−2.26473	−0.0823673
$757$	25.4000	0.923179	0.461589	−	0.887094i	$-0.347279\pi$
$757$	25.4000	0.923179	0.461589	+	0.887094i	$0.347279\pi$
$758$	−3.78716	−0.137556
$759$	4.68937	0.170213
$760$	−10.6498	−0.386310
$761$	−36.7039	−1.33052	−0.665258	−	0.746614i	$-0.731678\pi$
$761$	−36.7039	−1.33052	−0.665258	+	0.746614i	$0.731678\pi$
$762$	−4.19743	−0.152057
$763$	−17.6486	−0.638921
$764$	−13.5219	−0.489206
$765$	16.1039	0.582237
$766$	−22.2285	−0.803150
$767$	3.93275	0.142003
$768$	−16.6992	−0.602580
$769$	−11.5276	−0.415697	−0.207848	−	0.978161i	$-0.566646\pi$
$769$	−11.5276	−0.415697	−0.207848	+	0.978161i	$0.566646\pi$
$770$	−6.61224	−0.238289
$771$	2.56557	0.0923966
$772$	14.0127	0.504328
$773$	22.9949	0.827068	0.413534	−	0.910489i	$-0.364294\pi$
$773$	22.9949	0.827068	0.413534	+	0.910489i	$0.364294\pi$
$774$	−3.27531	−0.117729
$775$	18.7392	0.673131
$776$	−27.8508	−0.999784
$777$	−11.2337	−0.403007
$778$	34.1426	1.22407
$779$	9.49327	0.340132
$780$	1.60301	0.0573968
$781$	−7.40554	−0.264991
$782$	−30.2796	−1.08280
$783$	3.75473	0.134183
$784$	1.25371	0.0447755
$785$	23.3739	0.834252
$786$	−10.5677	−0.376936
$787$	16.8410	0.600317	0.300158	−	0.953889i	$-0.402960\pi$
$787$	16.8410	0.600317	0.300158	+	0.953889i	$0.402960\pi$
$788$	20.5332	0.731466
$789$	−13.6690	−0.486630
$790$	−25.6318	−0.911937
$791$	−6.53761	−0.232451
$792$	3.03405	0.107810
$793$	0.671691	0.0238524
$794$	11.6837	0.414639
$795$	−15.4484	−0.547897
$796$	20.6040	0.730289
$797$	−4.19473	−0.148585	−0.0742924	−	0.997236i	$-0.523670\pi$
$797$	−4.19473	−0.148585	−0.0742924	+	0.997236i	$0.523670\pi$
$798$	3.45944	0.122463
$799$	0.807327	0.0285612
$800$	8.04854	0.284559
$801$	−14.7152	−0.519935
$802$	−19.6256	−0.693005
$803$	1.18684	0.0418827
$804$	−10.0346	−0.353892
$805$	−29.8557	−1.05227
$806$	−7.64883	−0.269419
$807$	16.7194	0.588550
$808$	10.7627	0.378631
$809$	54.1413	1.90351	0.951753	−	0.306865i	$-0.0992800\pi$
$809$	54.1413	1.90351	0.951753	+	0.306865i	$0.0992800\pi$
$810$	2.69009	0.0945203
$811$	13.9146	0.488609	0.244305	−	0.969699i	$-0.421440\pi$
$811$	13.9146	0.488609	0.244305	+	0.969699i	$0.421440\pi$
$812$	−8.50344	−0.298412
$813$	−22.4580	−0.787637
$814$	4.74655	0.166366
$815$	53.9708	1.89052
$816$	−8.13428	−0.284757
$817$	−4.27371	−0.149518
$818$	0.328673	0.0114918
$819$	−1.65101	−0.0576911
$820$	−16.7183	−0.583829
$821$	−50.8155	−1.77347	−0.886737	−	0.462274i	$-0.847033\pi$
$821$	−50.8155	−1.77347	−0.886737	+	0.462274i	$0.847033\pi$
$822$	−5.42798	−0.189323
$823$	12.9220	0.450434	0.225217	−	0.974309i	$-0.427691\pi$
$823$	12.9220	0.450434	0.225217	+	0.974309i	$0.427691\pi$
$824$	15.3511	0.534780
$825$	−1.70907	−0.0595023
$826$	−14.9467	−0.520061
$827$	−39.2293	−1.36414	−0.682068	−	0.731289i	$-0.738919\pi$
$827$	−39.2293	−1.36414	−0.682068	+	0.731289i	$0.738919\pi$
$828$	4.32064	0.150153
$829$	53.5611	1.86026	0.930128	−	0.367236i	$-0.119696\pi$
$829$	53.5611	1.86026	0.930128	+	0.367236i	$0.119696\pi$
$830$	23.8647	0.828355
$831$	−30.6375	−1.06280
$832$	−5.04280	−0.174828
$833$	−5.95769	−0.206422
$834$	−7.34467	−0.254325
$835$	5.16715	0.178817
$836$	1.24860	0.0431837
$837$	10.9645	0.378989
$838$	29.3751	1.01475
$839$	−5.70039	−0.196799	−0.0983997	−	0.995147i	$-0.531372\pi$
$839$	−5.70039	−0.196799	−0.0983997	+	0.995147i	$0.531372\pi$
$840$	−19.3168	−0.666493
$841$	−14.9020	−0.513861
$842$	−11.6176	−0.400370
$843$	3.33065	0.114714
$844$	−4.51869	−0.155540
$845$	−32.5038	−1.11817
$846$	0.134861	0.00463662
$847$	2.45800	0.0844578
$848$	7.80316	0.267961
$849$	−13.4522	−0.461677
$850$	11.0356	0.378518
$851$	21.4317	0.734668
$852$	−6.82325	−0.233761
$853$	−49.7719	−1.70416	−0.852079	−	0.523413i	$-0.824658\pi$
$853$	−49.7719	−1.70416	−0.852079	+	0.523413i	$0.824658\pi$
$854$	−2.55280	−0.0873552
$855$	3.51010	0.120043
$856$	−20.5897	−0.703741
$857$	21.5289	0.735412	0.367706	−	0.929942i	$-0.380143\pi$
$857$	21.5289	0.735412	0.367706	+	0.929942i	$0.380143\pi$
$858$	0.697599	0.0238156
$859$	−5.73933	−0.195823	−0.0979117	−	0.995195i	$-0.531216\pi$
$859$	−5.73933	−0.195823	−0.0979117	+	0.995195i	$0.531216\pi$
$860$	7.52630	0.256645
$861$	17.2190	0.586823
$862$	32.4948	1.10678
$863$	48.7710	1.66018	0.830092	−	0.557626i	$-0.188288\pi$
$863$	48.7710	1.66018	0.830092	+	0.557626i	$0.188288\pi$
$864$	4.70930	0.160214
$865$	7.95706	0.270548
$866$	1.50456	0.0511270
$867$	21.6544	0.735422
$868$	−24.8316	−0.842840
$869$	9.52820	0.323222
$870$	10.1006	0.342442
$871$	−7.31534	−0.247871
$872$	21.7847	0.737722
$873$	9.17940	0.310676
$874$	−6.59993	−0.223246
$875$	−20.9523	−0.708315
$876$	1.09352	0.0369466
$877$	25.9331	0.875699	0.437849	−	0.899048i	$-0.355740\pi$
$877$	25.9331	0.875699	0.437849	+	0.899048i	$0.355740\pi$
$878$	2.92523	0.0987217
$879$	18.6240	0.628171
$880$	3.38884	0.114238
$881$	−34.0725	−1.14793	−0.573966	−	0.818879i	$-0.694596\pi$
$881$	−34.0725	−1.14793	−0.573966	+	0.818879i	$0.694596\pi$
$882$	−0.995210	−0.0335105
$883$	14.9438	0.502897	0.251449	−	0.967871i	$-0.419093\pi$
$883$	14.9438	0.502897	0.251449	+	0.967871i	$0.419093\pi$
$884$	3.84772	0.129413
$885$	−15.1655	−0.509784
$886$	18.3678	0.617079
$887$	45.2177	1.51826	0.759130	−	0.650939i	$-0.225625\pi$
$887$	45.2177	1.51826	0.759130	+	0.650939i	$0.225625\pi$
$888$	13.8664	0.465327
$889$	−9.93411	−0.333179
$890$	−39.5852	−1.32690
$891$	−1.00000	−0.0335013
$892$	7.67022	0.256818
$893$	0.175970	0.00588861
$894$	−6.59005	−0.220404
$895$	43.6209	1.45809
$896$	−3.98542	−0.133143
$897$	3.14981	0.105169
$898$	−34.2272	−1.14218
$899$	41.1688	1.37306
$900$	−1.57469	−0.0524897
$901$	−37.0809	−1.23534
$902$	−7.27551	−0.242248
$903$	−7.75171	−0.257961
$904$	8.06976	0.268396
$905$	64.0463	2.12897
$906$	4.30251	0.142941
$907$	−25.5067	−0.846937	−0.423469	−	0.905911i	$-0.639188\pi$
$907$	−25.5067	−0.846937	−0.423469	+	0.905911i	$0.639188\pi$
$908$	−8.32263	−0.276196
$909$	−3.54731	−0.117657
$910$	−4.44139	−0.147230
$911$	11.9557	0.396109	0.198055	−	0.980191i	$-0.436538\pi$
$911$	11.9557	0.396109	0.198055	+	0.980191i	$0.436538\pi$
$912$	−1.77300	−0.0587098
$913$	−8.87131	−0.293598
$914$	−27.4795	−0.908940
$915$	−2.59019	−0.0856290
$916$	21.8238	0.721077
$917$	−25.0106	−0.825923
$918$	6.45707	0.213115
$919$	2.74429	0.0905258	0.0452629	−	0.998975i	$-0.485587\pi$
$919$	2.74429	0.0905258	0.0452629	+	0.998975i	$0.485587\pi$
$920$	36.8526	1.21500
$921$	−23.5213	−0.775053
$922$	−20.8074	−0.685255
$923$	−4.97424	−0.163729
$924$	2.26473	0.0745040
$925$	−7.81093	−0.256822
$926$	17.3425	0.569910
$927$	−5.05960	−0.166179
$928$	17.6822	0.580446
$929$	38.8561	1.27483	0.637414	−	0.770521i	$-0.280004\pi$
$929$	38.8561	1.27483	0.637414	+	0.770521i	$0.280004\pi$
$930$	29.4956	0.967198
$931$	−1.29858	−0.0425591
$932$	18.1423	0.594272
$933$	4.96547	0.162562
$934$	12.5068	0.409233
$935$	−16.1039	−0.526653
$936$	2.03794	0.0666123
$937$	−22.2001	−0.725247	−0.362623	−	0.931936i	$-0.618119\pi$
$937$	−22.2001	−0.725247	−0.362623	+	0.931936i	$0.618119\pi$
$938$	27.8024	0.907781
$939$	−9.52784	−0.310929
$940$	−0.309896	−0.0101077
$941$	−10.2012	−0.332549	−0.166274	−	0.986080i	$-0.553174\pi$
$941$	−10.2012	−0.332549	−0.166274	+	0.986080i	$0.553174\pi$
$942$	9.37210	0.305360
$943$	−32.8505	−1.06976
$944$	7.66030	0.249322
$945$	6.36668	0.207108
$946$	3.27531	0.106490
$947$	25.5054	0.828813	0.414406	−	0.910092i	$-0.363989\pi$
$947$	25.5054	0.828813	0.414406	+	0.910092i	$0.363989\pi$
$948$	8.77900	0.285129
$949$	0.797191	0.0258779
$950$	2.40539	0.0780412
$951$	24.6012	0.797748
$952$	−46.3664	−1.50274
$953$	−29.9188	−0.969166	−0.484583	−	0.874745i	$-0.661029\pi$
$953$	−29.9188	−0.969166	−0.484583	+	0.874745i	$0.661029\pi$
$954$	−6.19423	−0.200545
$955$	38.0133	1.23008
$956$	1.34769	0.0435873
$957$	−3.75473	−0.121373
$958$	−28.8410	−0.931811
$959$	−12.8465	−0.414834
$960$	19.4461	0.627621
$961$	89.2206	2.87808
$962$	3.18821	0.102792
$963$	6.78621	0.218683
$964$	1.39400	0.0448976
$965$	−39.3930	−1.26811
$966$	−11.9710	−0.385162
$967$	−22.5668	−0.725698	−0.362849	−	0.931848i	$-0.618196\pi$
$967$	−22.5668	−0.725698	−0.362849	+	0.931848i	$0.618196\pi$
$968$	−3.03405	−0.0975181
$969$	8.42535	0.270661
$970$	24.6935	0.792859
$971$	−7.77906	−0.249642	−0.124821	−	0.992179i	$-0.539836\pi$
$971$	−7.77906	−0.249642	−0.124821	+	0.992179i	$0.539836\pi$
$972$	−0.921370	−0.0295530
$973$	−17.3827	−0.557264
$974$	−21.1872	−0.678880
$975$	−1.14797	−0.0367645
$976$	1.30834	0.0418788
$977$	−9.18882	−0.293976	−0.146988	−	0.989138i	$-0.546958\pi$
$977$	−9.18882	−0.293976	−0.146988	+	0.989138i	$0.546958\pi$
$978$	21.6403	0.691982
$979$	14.7152	0.470299
$980$	2.28688	0.0730518
$981$	−7.18006	−0.229242
$982$	9.71561	0.310038
$983$	25.6226	0.817233	0.408617	−	0.912706i	$-0.366011\pi$
$983$	25.6226	0.817233	0.408617	+	0.912706i	$0.366011\pi$
$984$	−21.2545	−0.677567
$985$	−57.7237	−1.83923
$986$	24.2446	0.772105
$987$	0.319177	0.0101595
$988$	0.838672	0.0266817
$989$	14.7887	0.470254
$990$	−2.69009	−0.0854968
$991$	−4.13304	−0.131290	−0.0656451	−	0.997843i	$-0.520911\pi$
$991$	−4.13304	−0.131290	−0.0656451	+	0.997843i	$0.520911\pi$
$992$	51.6352	1.63942
$993$	5.12173	0.162533
$994$	18.9049	0.599627
$995$	−57.9226	−1.83627
$996$	−8.17376	−0.258996
$997$	37.2645	1.18018	0.590089	−	0.807338i	$-0.299093\pi$
$997$	37.2645	1.18018	0.590089	+	0.807338i	$0.299093\pi$
$998$	−5.70245	−0.180508
$999$	−4.57027	−0.144597

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.9	✓	13
3.2	odd	2		6039.2.a.g.1.5		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.9	✓	13	1.1	even	1	trivial
6039.2.a.g.1.5		13	3.2	odd	2

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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+1.03857 q^{2} +1.00000 q^{3} -0.921370 q^{4} +2.59019 q^{5} +1.03857 q^{6} +2.45800 q^{7} -3.03405 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.03857 q^{2} +1.00000 q^{3} -0.921370 q^{4} +2.59019 q^{5} +1.03857 q^{6} +2.45800 q^{7} -3.03405 q^{8} +1.00000 q^{9} +2.69009 q^{10} -1.00000 q^{11} -0.921370 q^{12} -0.671691 q^{13} +2.55280 q^{14} +2.59019 q^{15} -1.30834 q^{16} +6.21727 q^{17} +1.03857 q^{18} +1.35515 q^{19} -2.38652 q^{20} +2.45800 q^{21} -1.03857 q^{22} -4.68937 q^{23} -3.03405 q^{24} +1.70907 q^{25} -0.697599 q^{26} +1.00000 q^{27} -2.26473 q^{28} +3.75473 q^{29} +2.69009 q^{30} +10.9645 q^{31} +4.70930 q^{32} -1.00000 q^{33} +6.45707 q^{34} +6.36668 q^{35} -0.921370 q^{36} -4.57027 q^{37} +1.40742 q^{38} -0.671691 q^{39} -7.85876 q^{40} +7.00531 q^{41} +2.55280 q^{42} -3.15367 q^{43} +0.921370 q^{44} +2.59019 q^{45} -4.87024 q^{46} +0.129852 q^{47} -1.30834 q^{48} -0.958250 q^{49} +1.77500 q^{50} +6.21727 q^{51} +0.618876 q^{52} -5.96418 q^{53} +1.03857 q^{54} -2.59019 q^{55} -7.45769 q^{56} +1.35515 q^{57} +3.89956 q^{58} -5.85500 q^{59} -2.38652 q^{60} -1.00000 q^{61} +11.3874 q^{62} +2.45800 q^{63} +7.50762 q^{64} -1.73981 q^{65} -1.03857 q^{66} +10.8909 q^{67} -5.72840 q^{68} -4.68937 q^{69} +6.61224 q^{70} +7.40554 q^{71} -3.03405 q^{72} -1.18684 q^{73} -4.74655 q^{74} +1.70907 q^{75} -1.24860 q^{76} -2.45800 q^{77} -0.697599 q^{78} -9.52820 q^{79} -3.38884 q^{80} +1.00000 q^{81} +7.27551 q^{82} +8.87131 q^{83} -2.26473 q^{84} +16.1039 q^{85} -3.27531 q^{86} +3.75473 q^{87} +3.03405 q^{88} -14.7152 q^{89} +2.69009 q^{90} -1.65101 q^{91} +4.32064 q^{92} +10.9645 q^{93} +0.134861 q^{94} +3.51010 q^{95} +4.70930 q^{96} +9.17940 q^{97} -0.995210 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

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