LMFDB - Embedded newform 2013.2.a.c.1.11

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 $ x^12 - 5x^11 - 5x^10 + 48x^9 - 173x^7 + 29x^6 + 281x^5 - 41x^4 - 201x^3 + 8x^2 + 49x + 8
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			1.11
Root			$2.66112$ 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)

$f(q)$	$=$	$q+1.66112 q^{2} +1.00000 q^{3} +0.759316 q^{4} -1.47319 q^{5} +1.66112 q^{6} -2.81455 q^{7} -2.06092 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.66112 q^{2} +1.00000 q^{3} +0.759316 q^{4} -1.47319 q^{5} +1.66112 q^{6} -2.81455 q^{7} -2.06092 q^{8} +1.00000 q^{9} -2.44715 q^{10} +1.00000 q^{11} +0.759316 q^{12} +4.11864 q^{13} -4.67530 q^{14} -1.47319 q^{15} -4.94207 q^{16} -4.46728 q^{17} +1.66112 q^{18} +2.28705 q^{19} -1.11862 q^{20} -2.81455 q^{21} +1.66112 q^{22} -7.49465 q^{23} -2.06092 q^{24} -2.82970 q^{25} +6.84155 q^{26} +1.00000 q^{27} -2.13713 q^{28} -10.0128 q^{29} -2.44715 q^{30} +4.99425 q^{31} -4.08752 q^{32} +1.00000 q^{33} -7.42068 q^{34} +4.14637 q^{35} +0.759316 q^{36} -0.685924 q^{37} +3.79906 q^{38} +4.11864 q^{39} +3.03614 q^{40} -9.33901 q^{41} -4.67530 q^{42} -6.98858 q^{43} +0.759316 q^{44} -1.47319 q^{45} -12.4495 q^{46} +1.45467 q^{47} -4.94207 q^{48} +0.921685 q^{49} -4.70047 q^{50} -4.46728 q^{51} +3.12735 q^{52} -4.15316 q^{53} +1.66112 q^{54} -1.47319 q^{55} +5.80057 q^{56} +2.28705 q^{57} -16.6324 q^{58} +13.8976 q^{59} -1.11862 q^{60} -1.00000 q^{61} +8.29605 q^{62} -2.81455 q^{63} +3.09428 q^{64} -6.06756 q^{65} +1.66112 q^{66} -2.34866 q^{67} -3.39208 q^{68} -7.49465 q^{69} +6.88762 q^{70} +1.88712 q^{71} -2.06092 q^{72} +11.5870 q^{73} -1.13940 q^{74} -2.82970 q^{75} +1.73659 q^{76} -2.81455 q^{77} +6.84155 q^{78} -11.0173 q^{79} +7.28063 q^{80} +1.00000 q^{81} -15.5132 q^{82} +1.63500 q^{83} -2.13713 q^{84} +6.58117 q^{85} -11.6089 q^{86} -10.0128 q^{87} -2.06092 q^{88} -11.4605 q^{89} -2.44715 q^{90} -11.5921 q^{91} -5.69081 q^{92} +4.99425 q^{93} +2.41639 q^{94} -3.36927 q^{95} -4.08752 q^{96} -11.9390 q^{97} +1.53103 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * 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 $

$2$	1.66112	1.17459	0.587294	−	0.809374i	$-0.300193\pi$
$2$	1.66112	1.17459	0.587294	+	0.809374i	$0.300193\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.759316	0.379658
$5$	−1.47319	−0.658832	−0.329416	−	0.944185i	$-0.606852\pi$
$5$	−1.47319	−0.658832	−0.329416	+	0.944185i	$0.606852\pi$
$6$	1.66112	0.678149
$7$	−2.81455	−1.06380	−0.531900	−	0.846807i	$-0.678522\pi$
$7$	−2.81455	−1.06380	−0.531900	+	0.846807i	$0.678522\pi$
$8$	−2.06092	−0.728647
$9$	1.00000	0.333333
$10$	−2.44715	−0.773857
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.759316	0.219196
$13$	4.11864	1.14231	0.571153	−	0.820844i	$-0.306496\pi$
$13$	4.11864	1.14231	0.571153	+	0.820844i	$0.306496\pi$
$14$	−4.67530	−1.24953
$15$	−1.47319	−0.380377
$16$	−4.94207	−1.23552
$17$	−4.46728	−1.08347	−0.541737	−	0.840548i	$-0.682233\pi$
$17$	−4.46728	−1.08347	−0.541737	+	0.840548i	$0.682233\pi$
$18$	1.66112	0.391529
$19$	2.28705	0.524685	0.262343	−	0.964975i	$-0.415505\pi$
$19$	2.28705	0.524685	0.262343	+	0.964975i	$0.415505\pi$
$20$	−1.11862	−0.250131
$21$	−2.81455	−0.614185
$22$	1.66112	0.354152
$23$	−7.49465	−1.56274	−0.781372	−	0.624066i	$-0.785480\pi$
$23$	−7.49465	−1.56274	−0.781372	+	0.624066i	$0.785480\pi$
$24$	−2.06092	−0.420684
$25$	−2.82970	−0.565940
$26$	6.84155	1.34174
$27$	1.00000	0.192450
$28$	−2.13713	−0.403880
$29$	−10.0128	−1.85933	−0.929664	−	0.368407i	$-0.879903\pi$
$29$	−10.0128	−1.85933	−0.929664	+	0.368407i	$0.879903\pi$
$30$	−2.44715	−0.446786
$31$	4.99425	0.896995	0.448497	−	0.893784i	$-0.351959\pi$
$31$	4.99425	0.896995	0.448497	+	0.893784i	$0.351959\pi$
$32$	−4.08752	−0.722578
$33$	1.00000	0.174078
$34$	−7.42068	−1.27264
$35$	4.14637	0.700865
$36$	0.759316	0.126553
$37$	−0.685924	−0.112765	−0.0563826	−	0.998409i	$-0.517957\pi$
$37$	−0.685924	−0.112765	−0.0563826	+	0.998409i	$0.517957\pi$
$38$	3.79906	0.616289
$39$	4.11864	0.659511
$40$	3.03614	0.480056
$41$	−9.33901	−1.45851	−0.729254	−	0.684243i	$-0.760133\pi$
$41$	−9.33901	−1.45851	−0.729254	+	0.684243i	$0.760133\pi$
$42$	−4.67530	−0.721414
$43$	−6.98858	−1.06575	−0.532874	−	0.846194i	$-0.678888\pi$
$43$	−6.98858	−1.06575	−0.532874	+	0.846194i	$0.678888\pi$
$44$	0.759316	0.114471
$45$	−1.47319	−0.219611
$46$	−12.4495	−1.83558
$47$	1.45467	0.212186	0.106093	−	0.994356i	$-0.466166\pi$
$47$	1.45467	0.212186	0.106093	+	0.994356i	$0.466166\pi$
$48$	−4.94207	−0.713327
$49$	0.921685	0.131669
$50$	−4.70047	−0.664747
$51$	−4.46728	−0.625544
$52$	3.12735	0.433686
$53$	−4.15316	−0.570480	−0.285240	−	0.958456i	$-0.592073\pi$
$53$	−4.15316	−0.570480	−0.285240	+	0.958456i	$0.592073\pi$
$54$	1.66112	0.226050
$55$	−1.47319	−0.198645
$56$	5.80057	0.775134
$57$	2.28705	0.302927
$58$	−16.6324	−2.18395
$59$	13.8976	1.80932	0.904659	−	0.426136i	$-0.140125\pi$
$59$	13.8976	1.80932	0.904659	+	0.426136i	$0.140125\pi$
$60$	−1.11862	−0.144413
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	8.29605	1.05360
$63$	−2.81455	−0.354600
$64$	3.09428	0.386786
$65$	−6.06756	−0.752588
$66$	1.66112	0.204470
$67$	−2.34866	−0.286934	−0.143467	−	0.989655i	$-0.545825\pi$
$67$	−2.34866	−0.286934	−0.143467	+	0.989655i	$0.545825\pi$
$68$	−3.39208	−0.411350
$69$	−7.49465	−0.902250
$70$	6.88762	0.823228
$71$	1.88712	0.223960	0.111980	−	0.993710i	$-0.464281\pi$
$71$	1.88712	0.223960	0.111980	+	0.993710i	$0.464281\pi$
$72$	−2.06092	−0.242882
$73$	11.5870	1.35615	0.678075	−	0.734992i	$-0.262814\pi$
$73$	11.5870	1.35615	0.678075	+	0.734992i	$0.262814\pi$
$74$	−1.13940	−0.132453
$75$	−2.82970	−0.326746
$76$	1.73659	0.199201
$77$	−2.81455	−0.320748
$78$	6.84155	0.774653
$79$	−11.0173	−1.23954	−0.619771	−	0.784783i	$-0.712774\pi$
$79$	−11.0173	−1.23954	−0.619771	+	0.784783i	$0.712774\pi$
$80$	7.28063	0.813999
$81$	1.00000	0.111111
$82$	−15.5132	−1.71315
$83$	1.63500	0.179464	0.0897322	−	0.995966i	$-0.471399\pi$
$83$	1.63500	0.179464	0.0897322	+	0.995966i	$0.471399\pi$
$84$	−2.13713	−0.233180
$85$	6.58117	0.713828
$86$	−11.6089	−1.25182
$87$	−10.0128	−1.07348
$88$	−2.06092	−0.219695
$89$	−11.4605	−1.21481	−0.607404	−	0.794393i	$-0.707789\pi$
$89$	−11.4605	−1.21481	−0.607404	+	0.794393i	$0.707789\pi$
$90$	−2.44715	−0.257952
$91$	−11.5921	−1.21518
$92$	−5.69081	−0.593308
$93$	4.99425	0.517880
$94$	2.41639	0.249231
$95$	−3.36927	−0.345680
$96$	−4.08752	−0.417181
$97$	−11.9390	−1.21222	−0.606109	−	0.795382i	$-0.707270\pi$
$97$	−11.9390	−1.21222	−0.606109	+	0.795382i	$0.707270\pi$
$98$	1.53103	0.154657
$99$	1.00000	0.100504
$100$	−2.14864	−0.214864
$101$	13.8985	1.38295	0.691477	−	0.722398i	$-0.256960\pi$
$101$	13.8985	1.38295	0.691477	+	0.722398i	$0.256960\pi$
$102$	−7.42068	−0.734757
$103$	17.8872	1.76248	0.881240	−	0.472668i	$-0.156709\pi$
$103$	17.8872	1.76248	0.881240	+	0.472668i	$0.156709\pi$
$104$	−8.48821	−0.832337
$105$	4.14637	0.404645
$106$	−6.89889	−0.670080
$107$	5.91853	0.572166	0.286083	−	0.958205i	$-0.407647\pi$
$107$	5.91853	0.572166	0.286083	+	0.958205i	$0.407647\pi$
$108$	0.759316	0.0730652
$109$	12.2248	1.17092	0.585459	−	0.810702i	$-0.300914\pi$
$109$	12.2248	1.17092	0.585459	+	0.810702i	$0.300914\pi$
$110$	−2.44715	−0.233327
$111$	−0.685924	−0.0651050
$112$	13.9097	1.31434
$113$	−12.9974	−1.22270	−0.611348	−	0.791362i	$-0.709372\pi$
$113$	−12.9974	−1.22270	−0.611348	+	0.791362i	$0.709372\pi$
$114$	3.79906	0.355815
$115$	11.0411	1.02959
$116$	−7.60287	−0.705909
$117$	4.11864	0.380769
$118$	23.0856	2.12520
$119$	12.5734	1.15260
$120$	3.03614	0.277160
$121$	1.00000	0.0909091
$122$	−1.66112	−0.150391
$123$	−9.33901	−0.842070
$124$	3.79222	0.340551
$125$	11.5347	1.03169
$126$	−4.67530	−0.416509
$127$	−17.1093	−1.51821	−0.759104	−	0.650969i	$-0.774363\pi$
$127$	−17.1093	−1.51821	−0.759104	+	0.650969i	$0.774363\pi$
$128$	13.3150	1.17689
$129$	−6.98858	−0.615310
$130$	−10.0789	−0.883981
$131$	0.913423	0.0798061	0.0399031	−	0.999204i	$-0.487295\pi$
$131$	0.913423	0.0798061	0.0399031	+	0.999204i	$0.487295\pi$
$132$	0.759316	0.0660900
$133$	−6.43701	−0.558160
$134$	−3.90140	−0.337029
$135$	−1.47319	−0.126792
$136$	9.20672	0.789470
$137$	−0.476568	−0.0407159	−0.0203580	−	0.999793i	$-0.506481\pi$
$137$	−0.476568	−0.0407159	−0.0203580	+	0.999793i	$0.506481\pi$
$138$	−12.4495	−1.05977
$139$	−20.4643	−1.73576	−0.867881	−	0.496772i	$-0.834519\pi$
$139$	−20.4643	−1.73576	−0.867881	+	0.496772i	$0.834519\pi$
$140$	3.14841	0.266089
$141$	1.45467	0.122506
$142$	3.13474	0.263061
$143$	4.11864	0.344418
$144$	−4.94207	−0.411839
$145$	14.7508	1.22499
$146$	19.2473	1.59292
$147$	0.921685	0.0760193
$148$	−0.520833	−0.0428122
$149$	9.95783	0.815777	0.407888	−	0.913032i	$-0.366265\pi$
$149$	9.95783	0.815777	0.407888	+	0.913032i	$0.366265\pi$
$150$	−4.70047	−0.383792
$151$	19.7514	1.60735	0.803673	−	0.595071i	$-0.202876\pi$
$151$	19.7514	1.60735	0.803673	+	0.595071i	$0.202876\pi$
$152$	−4.71344	−0.382310
$153$	−4.46728	−0.361158
$154$	−4.67530	−0.376746
$155$	−7.35750	−0.590969
$156$	3.12735	0.250388
$157$	19.9385	1.59127	0.795633	−	0.605779i	$-0.207139\pi$
$157$	19.9385	1.59127	0.795633	+	0.605779i	$0.207139\pi$
$158$	−18.3010	−1.45595
$159$	−4.15316	−0.329367
$160$	6.02171	0.476058
$161$	21.0941	1.66245
$162$	1.66112	0.130510
$163$	9.22975	0.722930	0.361465	−	0.932386i	$-0.382277\pi$
$163$	9.22975	0.722930	0.361465	+	0.932386i	$0.382277\pi$
$164$	−7.09126	−0.553734
$165$	−1.47319	−0.114688
$166$	2.71593	0.210797
$167$	2.23571	0.173004	0.0865022	−	0.996252i	$-0.472431\pi$
$167$	2.23571	0.173004	0.0865022	+	0.996252i	$0.472431\pi$
$168$	5.80057	0.447524
$169$	3.96321	0.304862
$170$	10.9321	0.838454
$171$	2.28705	0.174895
$172$	−5.30654	−0.404620
$173$	−1.61105	−0.122486	−0.0612431	−	0.998123i	$-0.519506\pi$
$173$	−1.61105	−0.122486	−0.0612431	+	0.998123i	$0.519506\pi$
$174$	−16.6324	−1.26090
$175$	7.96433	0.602047
$176$	−4.94207	−0.372523
$177$	13.8976	1.04461
$178$	−19.0372	−1.42690
$179$	−11.9794	−0.895385	−0.447692	−	0.894188i	$-0.647754\pi$
$179$	−11.9794	−0.895385	−0.447692	+	0.894188i	$0.647754\pi$
$180$	−1.11862	−0.0833770
$181$	14.4236	1.07210	0.536050	−	0.844187i	$-0.319916\pi$
$181$	14.4236	1.07210	0.536050	+	0.844187i	$0.319916\pi$
$182$	−19.2559	−1.42734
$183$	−1.00000	−0.0739221
$184$	15.4459	1.13869
$185$	1.01050	0.0742933
$186$	8.29605	0.608296
$187$	−4.46728	−0.326680
$188$	1.10456	0.0805581
$189$	−2.81455	−0.204728
$190$	−5.59675	−0.406031
$191$	−3.99785	−0.289274	−0.144637	−	0.989485i	$-0.546201\pi$
$191$	−3.99785	−0.289274	−0.144637	+	0.989485i	$0.546201\pi$
$192$	3.09428	0.223311
$193$	3.35056	0.241178	0.120589	−	0.992702i	$-0.461522\pi$
$193$	3.35056	0.241178	0.120589	+	0.992702i	$0.461522\pi$
$194$	−19.8320	−1.42386
$195$	−6.06756	−0.434507
$196$	0.699850	0.0499893
$197$	18.5321	1.32036	0.660178	−	0.751109i	$-0.270481\pi$
$197$	18.5321	1.32036	0.660178	+	0.751109i	$0.270481\pi$
$198$	1.66112	0.118051
$199$	−5.45817	−0.386920	−0.193460	−	0.981108i	$-0.561971\pi$
$199$	−5.45817	−0.386920	−0.193460	+	0.981108i	$0.561971\pi$
$200$	5.83180	0.412370
$201$	−2.34866	−0.165661
$202$	23.0871	1.62440
$203$	28.1815	1.97795
$204$	−3.39208	−0.237493
$205$	13.7582	0.960912
$206$	29.7128	2.07019
$207$	−7.49465	−0.520915
$208$	−20.3546	−1.41134
$209$	2.28705	0.158199
$210$	6.88762	0.475291
$211$	−3.49774	−0.240794	−0.120397	−	0.992726i	$-0.538417\pi$
$211$	−3.49774	−0.240794	−0.120397	+	0.992726i	$0.538417\pi$
$212$	−3.15356	−0.216587
$213$	1.88712	0.129304
$214$	9.83139	0.672060
$215$	10.2955	0.702149
$216$	−2.06092	−0.140228
$217$	−14.0566	−0.954222
$218$	20.3068	1.37535
$219$	11.5870	0.782974
$220$	−1.11862	−0.0754173
$221$	−18.3991	−1.23766
$222$	−1.13940	−0.0764716
$223$	−0.888363	−0.0594892	−0.0297446	−	0.999558i	$-0.509469\pi$
$223$	−0.888363	−0.0594892	−0.0297446	+	0.999558i	$0.509469\pi$
$224$	11.5045	0.768679
$225$	−2.82970	−0.188647
$226$	−21.5903	−1.43616
$227$	−23.7868	−1.57878	−0.789392	−	0.613890i	$-0.789604\pi$
$227$	−23.7868	−1.57878	−0.789392	+	0.613890i	$0.789604\pi$
$228$	1.73659	0.115009
$229$	0.175995	0.0116301	0.00581505	−	0.999983i	$-0.498149\pi$
$229$	0.175995	0.0116301	0.00581505	+	0.999983i	$0.498149\pi$
$230$	18.3405	1.20934
$231$	−2.81455	−0.185184
$232$	20.6356	1.35479
$233$	−17.5376	−1.14892	−0.574462	−	0.818531i	$-0.694789\pi$
$233$	−17.5376	−1.14892	−0.574462	+	0.818531i	$0.694789\pi$
$234$	6.84155	0.447246
$235$	−2.14302	−0.139795
$236$	10.5527	0.686922
$237$	−11.0173	−0.715649
$238$	20.8859	1.35383
$239$	−7.95670	−0.514676	−0.257338	−	0.966321i	$-0.582845\pi$
$239$	−7.95670	−0.514676	−0.257338	+	0.966321i	$0.582845\pi$
$240$	7.28063	0.469962
$241$	−10.8700	−0.700200	−0.350100	−	0.936712i	$-0.613852\pi$
$241$	−10.8700	−0.700200	−0.350100	+	0.936712i	$0.613852\pi$
$242$	1.66112	0.106781
$243$	1.00000	0.0641500
$244$	−0.759316	−0.0486102
$245$	−1.35782	−0.0867480
$246$	−15.5132	−0.989085
$247$	9.41954	0.599351
$248$	−10.2928	−0.653592
$249$	1.63500	0.103614
$250$	19.1604	1.21181
$251$	4.89538	0.308994	0.154497	−	0.987993i	$-0.450624\pi$
$251$	4.89538	0.308994	0.154497	+	0.987993i	$0.450624\pi$
$252$	−2.13713	−0.134627
$253$	−7.49465	−0.471185
$254$	−28.4207	−1.78327
$255$	6.58117	0.412129
$256$	15.9293	0.995579
$257$	0.151447	0.00944702	0.00472351	−	0.999989i	$-0.498496\pi$
$257$	0.151447	0.00944702	0.00472351	+	0.999989i	$0.498496\pi$
$258$	−11.6089	−0.722736
$259$	1.93057	0.119960
$260$	−4.60719	−0.285726
$261$	−10.0128	−0.619776
$262$	1.51730	0.0937394
$263$	−25.8581	−1.59448	−0.797240	−	0.603663i	$-0.793707\pi$
$263$	−25.8581	−1.59448	−0.797240	+	0.603663i	$0.793707\pi$
$264$	−2.06092	−0.126841
$265$	6.11841	0.375851
$266$	−10.6926	−0.655608
$267$	−11.4605	−0.701369
$268$	−1.78337	−0.108937
$269$	−8.79991	−0.536540	−0.268270	−	0.963344i	$-0.586452\pi$
$269$	−8.79991	−0.536540	−0.268270	+	0.963344i	$0.586452\pi$
$270$	−2.44715	−0.148929
$271$	−4.84554	−0.294346	−0.147173	−	0.989111i	$-0.547017\pi$
$271$	−4.84554	−0.294346	−0.147173	+	0.989111i	$0.547017\pi$
$272$	22.0776	1.33865
$273$	−11.5921	−0.701587
$274$	−0.791636	−0.0478245
$275$	−2.82970	−0.170637
$276$	−5.69081	−0.342547
$277$	−4.29485	−0.258053	−0.129026	−	0.991641i	$-0.541185\pi$
$277$	−4.29485	−0.258053	−0.129026	+	0.991641i	$0.541185\pi$
$278$	−33.9937	−2.03881
$279$	4.99425	0.298998
$280$	−8.54536	−0.510683
$281$	19.1622	1.14312	0.571561	−	0.820560i	$-0.306338\pi$
$281$	19.1622	1.14312	0.571561	+	0.820560i	$0.306338\pi$
$282$	2.41639	0.143894
$283$	−19.4385	−1.15550	−0.577751	−	0.816213i	$-0.696069\pi$
$283$	−19.4385	−1.15550	−0.577751	+	0.816213i	$0.696069\pi$
$284$	1.43292	0.0850283
$285$	−3.36927	−0.199578
$286$	6.84155	0.404550
$287$	26.2851	1.55156
$288$	−4.08752	−0.240859
$289$	2.95658	0.173917
$290$	24.5028	1.43885
$291$	−11.9390	−0.699874
$292$	8.79816	0.514873
$293$	17.2668	1.00874	0.504369	−	0.863488i	$-0.331725\pi$
$293$	17.2668	1.00874	0.504369	+	0.863488i	$0.331725\pi$
$294$	1.53103	0.0892914
$295$	−20.4739	−1.19204
$296$	1.41364	0.0821660
$297$	1.00000	0.0580259
$298$	16.5411	0.958202
$299$	−30.8678	−1.78513
$300$	−2.14864	−0.124052
$301$	19.6697	1.13374
$302$	32.8094	1.88797
$303$	13.8985	0.798449
$304$	−11.3028	−0.648258
$305$	1.47319	0.0843548
$306$	−7.42068	−0.424212
$307$	−31.2925	−1.78596	−0.892979	−	0.450099i	$-0.851389\pi$
$307$	−31.2925	−1.78596	−0.892979	+	0.450099i	$0.851389\pi$
$308$	−2.13713	−0.121774
$309$	17.8872	1.01757
$310$	−12.2217	−0.694145
$311$	−31.4841	−1.78530	−0.892650	−	0.450750i	$-0.851157\pi$
$311$	−31.4841	−1.78530	−0.892650	+	0.450750i	$0.851157\pi$
$312$	−8.48821	−0.480550
$313$	8.86327	0.500982	0.250491	−	0.968119i	$-0.419408\pi$
$313$	8.86327	0.500982	0.250491	+	0.968119i	$0.419408\pi$
$314$	33.1202	1.86908
$315$	4.14637	0.233622
$316$	−8.36560	−0.470602
$317$	28.8880	1.62251	0.811255	−	0.584693i	$-0.198785\pi$
$317$	28.8880	1.62251	0.811255	+	0.584693i	$0.198785\pi$
$318$	−6.89889	−0.386871
$319$	−10.0128	−0.560609
$320$	−4.55848	−0.254827
$321$	5.91853	0.330340
$322$	35.0398	1.95269
$323$	−10.2169	−0.568483
$324$	0.759316	0.0421842
$325$	−11.6545	−0.646477
$326$	15.3317	0.849145
$327$	12.2248	0.676030
$328$	19.2470	1.06274
$329$	−4.09425	−0.225723
$330$	−2.44715	−0.134711
$331$	13.1372	0.722086	0.361043	−	0.932549i	$-0.382421\pi$
$331$	13.1372	0.722086	0.361043	+	0.932549i	$0.382421\pi$
$332$	1.24148	0.0681351
$333$	−0.685924	−0.0375884
$334$	3.71378	0.203209
$335$	3.46002	0.189041
$336$	13.9097	0.758836
$337$	−25.2216	−1.37391	−0.686953	−	0.726702i	$-0.741052\pi$
$337$	−25.2216	−1.37391	−0.686953	+	0.726702i	$0.741052\pi$
$338$	6.58337	0.358088
$339$	−12.9974	−0.705923
$340$	4.99718	0.271010
$341$	4.99425	0.270454
$342$	3.79906	0.205430
$343$	17.1077	0.923730
$344$	14.4029	0.776554
$345$	11.0411	0.594432
$346$	−2.67615	−0.143871
$347$	3.68914	0.198043	0.0990217	−	0.995085i	$-0.468429\pi$
$347$	3.68914	0.198043	0.0990217	+	0.995085i	$0.468429\pi$
$348$	−7.60287	−0.407557
$349$	24.2145	1.29617	0.648087	−	0.761567i	$-0.275569\pi$
$349$	24.2145	1.29617	0.648087	+	0.761567i	$0.275569\pi$
$350$	13.2297	0.707157
$351$	4.11864	0.219837
$352$	−4.08752	−0.217866
$353$	−35.5517	−1.89222	−0.946112	−	0.323839i	$-0.895026\pi$
$353$	−35.5517	−1.89222	−0.946112	+	0.323839i	$0.895026\pi$
$354$	23.0856	1.22699
$355$	−2.78010	−0.147552
$356$	−8.70212	−0.461211
$357$	12.5734	0.665454
$358$	−19.8993	−1.05171
$359$	−8.51892	−0.449611	−0.224806	−	0.974404i	$-0.572175\pi$
$359$	−8.51892	−0.449611	−0.224806	+	0.974404i	$0.572175\pi$
$360$	3.03614	0.160019
$361$	−13.7694	−0.724705
$362$	23.9593	1.25928
$363$	1.00000	0.0524864
$364$	−8.80208	−0.461354
$365$	−17.0698	−0.893475
$366$	−1.66112	−0.0868281
$367$	2.27453	0.118729	0.0593646	−	0.998236i	$-0.481093\pi$
$367$	2.27453	0.118729	0.0593646	+	0.998236i	$0.481093\pi$
$368$	37.0391	1.93080
$369$	−9.33901	−0.486169
$370$	1.67856	0.0872641
$371$	11.6893	0.606877
$372$	3.79222	0.196617
$373$	−19.0163	−0.984629	−0.492314	−	0.870418i	$-0.663849\pi$
$373$	−19.0163	−0.984629	−0.492314	+	0.870418i	$0.663849\pi$
$374$	−7.42068	−0.383714
$375$	11.5347	0.595647
$376$	−2.99797	−0.154609
$377$	−41.2391	−2.12392
$378$	−4.67530	−0.240471
$379$	2.07661	0.106668	0.0533341	−	0.998577i	$-0.483015\pi$
$379$	2.07661	0.106668	0.0533341	+	0.998577i	$0.483015\pi$
$380$	−2.55834	−0.131240
$381$	−17.1093	−0.876538
$382$	−6.64090	−0.339778
$383$	−18.3744	−0.938889	−0.469445	−	0.882962i	$-0.655546\pi$
$383$	−18.3744	−0.938889	−0.469445	+	0.882962i	$0.655546\pi$
$384$	13.3150	0.679479
$385$	4.14637	0.211319
$386$	5.56567	0.283285
$387$	−6.98858	−0.355250
$388$	−9.06544	−0.460228
$389$	−0.191275	−0.00969801	−0.00484901	−	0.999988i	$-0.501543\pi$
$389$	−0.191275	−0.00969801	−0.00484901	+	0.999988i	$0.501543\pi$
$390$	−10.0789	−0.510367
$391$	33.4807	1.69319
$392$	−1.89952	−0.0959404
$393$	0.913423	0.0460761
$394$	30.7840	1.55087
$395$	16.2306	0.816649
$396$	0.759316	0.0381571
$397$	−19.4396	−0.975646	−0.487823	−	0.872942i	$-0.662209\pi$
$397$	−19.4396	−0.975646	−0.487823	+	0.872942i	$0.662209\pi$
$398$	−9.06667	−0.454471
$399$	−6.43701	−0.322254
$400$	13.9846	0.699229
$401$	−8.50930	−0.424934	−0.212467	−	0.977168i	$-0.568150\pi$
$401$	−8.50930	−0.424934	−0.212467	+	0.977168i	$0.568150\pi$
$402$	−3.90140	−0.194584
$403$	20.5695	1.02464
$404$	10.5534	0.525050
$405$	−1.47319	−0.0732036
$406$	46.8128	2.32328
$407$	−0.685924	−0.0340000
$408$	9.20672	0.455801
$409$	9.98566	0.493759	0.246880	−	0.969046i	$-0.420595\pi$
$409$	9.98566	0.493759	0.246880	+	0.969046i	$0.420595\pi$
$410$	22.8539	1.12868
$411$	−0.476568	−0.0235073
$412$	13.5821	0.669140
$413$	−39.1156	−1.92475
$414$	−12.4495	−0.611860
$415$	−2.40867	−0.118237
$416$	−16.8350	−0.825406
$417$	−20.4643	−1.00214
$418$	3.79906	0.185818
$419$	38.1216	1.86236	0.931181	−	0.364557i	$-0.118780\pi$
$419$	38.1216	1.86236	0.931181	+	0.364557i	$0.118780\pi$
$420$	3.14841	0.153627
$421$	−22.7144	−1.10703	−0.553516	−	0.832839i	$-0.686714\pi$
$421$	−22.7144	−1.10703	−0.553516	+	0.832839i	$0.686714\pi$
$422$	−5.81017	−0.282834
$423$	1.45467	0.0707286
$424$	8.55935	0.415679
$425$	12.6411	0.613182
$426$	3.13474	0.151878
$427$	2.81455	0.136206
$428$	4.49404	0.217228
$429$	4.11864	0.198850
$430$	17.1021	0.824737
$431$	−19.4262	−0.935727	−0.467863	−	0.883801i	$-0.654976\pi$
$431$	−19.4262	−0.935727	−0.467863	+	0.883801i	$0.654976\pi$
$432$	−4.94207	−0.237776
$433$	24.0574	1.15612	0.578062	−	0.815993i	$-0.303809\pi$
$433$	24.0574	1.15612	0.578062	+	0.815993i	$0.303809\pi$
$434$	−23.3496	−1.12082
$435$	14.7508	0.707246
$436$	9.28245	0.444549
$437$	−17.1407	−0.819949
$438$	19.2473	0.919672
$439$	−16.3119	−0.778523	−0.389262	−	0.921127i	$-0.627270\pi$
$439$	−16.3119	−0.778523	−0.389262	+	0.921127i	$0.627270\pi$
$440$	3.03614	0.144742
$441$	0.921685	0.0438898
$442$	−30.5631	−1.45374
$443$	11.8617	0.563567	0.281783	−	0.959478i	$-0.409074\pi$
$443$	11.8617	0.563567	0.281783	+	0.959478i	$0.409074\pi$
$444$	−0.520833	−0.0247176
$445$	16.8835	0.800354
$446$	−1.47568	−0.0698753
$447$	9.95783	0.470989
$448$	−8.70901	−0.411462
$449$	−14.9882	−0.707335	−0.353668	−	0.935371i	$-0.615066\pi$
$449$	−14.9882	−0.707335	−0.353668	+	0.935371i	$0.615066\pi$
$450$	−4.70047	−0.221582
$451$	−9.33901	−0.439757
$452$	−9.86916	−0.464206
$453$	19.7514	0.928002
$454$	−39.5127	−1.85442
$455$	17.0774	0.800602
$456$	−4.71344	−0.220727
$457$	−22.3763	−1.04672	−0.523358	−	0.852113i	$-0.675321\pi$
$457$	−22.3763	−1.04672	−0.523358	+	0.852113i	$0.675321\pi$
$458$	0.292349	0.0136606
$459$	−4.46728	−0.208515
$460$	8.38367	0.390890
$461$	19.8786	0.925837	0.462919	−	0.886401i	$-0.346802\pi$
$461$	19.8786	0.925837	0.462919	+	0.886401i	$0.346802\pi$
$462$	−4.67530	−0.217515
$463$	29.0105	1.34823	0.674116	−	0.738626i	$-0.264525\pi$
$463$	29.0105	1.34823	0.674116	+	0.738626i	$0.264525\pi$
$464$	49.4839	2.29723
$465$	−7.35750	−0.341196
$466$	−29.1320	−1.34951
$467$	−36.6315	−1.69510	−0.847552	−	0.530712i	$-0.821924\pi$
$467$	−36.6315	−1.69510	−0.847552	+	0.530712i	$0.821924\pi$
$468$	3.12735	0.144562
$469$	6.61041	0.305240
$470$	−3.55980	−0.164201
$471$	19.9385	0.918718
$472$	−28.6420	−1.31835
$473$	−6.98858	−0.321335
$474$	−18.3010	−0.840594
$475$	−6.47167	−0.296941
$476$	9.54717	0.437594
$477$	−4.15316	−0.190160
$478$	−13.2170	−0.604533
$479$	−37.5446	−1.71546	−0.857729	−	0.514101i	$-0.828125\pi$
$479$	−37.5446	−1.71546	−0.857729	+	0.514101i	$0.828125\pi$
$480$	6.02171	0.274852
$481$	−2.82508	−0.128812
$482$	−18.0564	−0.822447
$483$	21.0941	0.959814
$484$	0.759316	0.0345144
$485$	17.5884	0.798647
$486$	1.66112	0.0753499
$487$	14.4607	0.655275	0.327638	−	0.944803i	$-0.393747\pi$
$487$	14.4607	0.655275	0.327638	+	0.944803i	$0.393747\pi$
$488$	2.06092	0.0932936
$489$	9.22975	0.417384
$490$	−2.25550	−0.101893
$491$	23.7449	1.07159	0.535797	−	0.844347i	$-0.320011\pi$
$491$	23.7449	1.07159	0.535797	+	0.844347i	$0.320011\pi$
$492$	−7.09126	−0.319699
$493$	44.7299	2.01454
$494$	15.6470	0.703991
$495$	−1.47319	−0.0662151
$496$	−24.6820	−1.10825
$497$	−5.31140	−0.238249
$498$	2.71593	0.121704
$499$	15.8268	0.708504	0.354252	−	0.935150i	$-0.384736\pi$
$499$	15.8268	0.708504	0.354252	+	0.935150i	$0.384736\pi$
$500$	8.75846	0.391690
$501$	2.23571	0.0998841
$502$	8.13180	0.362940
$503$	−29.6249	−1.32091	−0.660455	−	0.750865i	$-0.729637\pi$
$503$	−29.6249	−1.32091	−0.660455	+	0.750865i	$0.729637\pi$
$504$	5.80057	0.258378
$505$	−20.4752	−0.911135
$506$	−12.4495	−0.553448
$507$	3.96321	0.176012
$508$	−12.9914	−0.576400
$509$	20.3765	0.903171	0.451585	−	0.892228i	$-0.350859\pi$
$509$	20.3765	0.903171	0.451585	+	0.892228i	$0.350859\pi$
$510$	10.9321	0.484081
$511$	−32.6121	−1.44267
$512$	−0.169642	−0.00749719
$513$	2.28705	0.100976
$514$	0.251572	0.0110964
$515$	−26.3513	−1.16118
$516$	−5.30654	−0.233607
$517$	1.45467	0.0639765
$518$	3.20690	0.140903
$519$	−1.61105	−0.0707174
$520$	12.5048	0.548370
$521$	6.10030	0.267259	0.133630	−	0.991031i	$-0.457337\pi$
$521$	6.10030	0.267259	0.133630	+	0.991031i	$0.457337\pi$
$522$	−16.6324	−0.727982
$523$	−5.29661	−0.231605	−0.115802	−	0.993272i	$-0.536944\pi$
$523$	−5.29661	−0.231605	−0.115802	+	0.993272i	$0.536944\pi$
$524$	0.693577	0.0302990
$525$	7.96433	0.347592
$526$	−42.9534	−1.87286
$527$	−22.3107	−0.971871
$528$	−4.94207	−0.215076
$529$	33.1699	1.44217
$530$	10.1634	0.441470
$531$	13.8976	0.603106
$532$	−4.88773	−0.211910
$533$	−38.4640	−1.66606
$534$	−19.0372	−0.823820
$535$	−8.71914	−0.376961
$536$	4.84040	0.209073
$537$	−11.9794	−0.516951
$538$	−14.6177	−0.630214
$539$	0.921685	0.0396998
$540$	−1.11862	−0.0481377
$541$	24.7253	1.06303	0.531513	−	0.847050i	$-0.321624\pi$
$541$	24.7253	1.06303	0.531513	+	0.847050i	$0.321624\pi$
$542$	−8.04902	−0.345735
$543$	14.4236	0.618977
$544$	18.2601	0.782895
$545$	−18.0094	−0.771439
$546$	−19.2559	−0.824076
$547$	11.4147	0.488057	0.244028	−	0.969768i	$-0.421531\pi$
$547$	11.4147	0.488057	0.244028	+	0.969768i	$0.421531\pi$
$548$	−0.361865	−0.0154581
$549$	−1.00000	−0.0426790
$550$	−4.70047	−0.200429
$551$	−22.8998	−0.975563
$552$	15.4459	0.657422
$553$	31.0087	1.31862
$554$	−7.13426	−0.303106
$555$	1.01050	0.0428933
$556$	−15.5389	−0.658996
$557$	−42.5738	−1.80391	−0.901954	−	0.431831i	$-0.857868\pi$
$557$	−42.5738	−1.80391	−0.901954	+	0.431831i	$0.857868\pi$
$558$	8.29605	0.351200
$559$	−28.7835	−1.21741
$560$	−20.4917	−0.865931
$561$	−4.46728	−0.188609
$562$	31.8307	1.34270
$563$	24.4660	1.03112	0.515560	−	0.856854i	$-0.327584\pi$
$563$	24.4660	1.03112	0.515560	+	0.856854i	$0.327584\pi$
$564$	1.10456	0.0465102
$565$	19.1477	0.805551
$566$	−32.2897	−1.35724
$567$	−2.81455	−0.118200
$568$	−3.88922	−0.163188
$569$	−4.26207	−0.178675	−0.0893376	−	0.996001i	$-0.528475\pi$
$569$	−4.26207	−0.178675	−0.0893376	+	0.996001i	$0.528475\pi$
$570$	−5.59675	−0.234422
$571$	−11.3495	−0.474962	−0.237481	−	0.971392i	$-0.576322\pi$
$571$	−11.3495	−0.474962	−0.237481	+	0.971392i	$0.576322\pi$
$572$	3.12735	0.130761
$573$	−3.99785	−0.167013
$574$	43.6627	1.82244
$575$	21.2076	0.884420
$576$	3.09428	0.128929
$577$	−29.5215	−1.22900	−0.614498	−	0.788918i	$-0.710642\pi$
$577$	−29.5215	−1.22900	−0.614498	+	0.788918i	$0.710642\pi$
$578$	4.91124	0.204280
$579$	3.35056	0.139244
$580$	11.2005	0.465076
$581$	−4.60179	−0.190914
$582$	−19.8320	−0.822064
$583$	−4.15316	−0.172006
$584$	−23.8798	−0.988154
$585$	−6.06756	−0.250863
$586$	28.6822	1.18485
$587$	−18.6594	−0.770156	−0.385078	−	0.922884i	$-0.625825\pi$
$587$	−18.6594	−0.770156	−0.385078	+	0.922884i	$0.625825\pi$
$588$	0.699850	0.0288613
$589$	11.4221	0.470640
$590$	−34.0096	−1.40015
$591$	18.5321	0.762308
$592$	3.38989	0.139323
$593$	26.6484	1.09432	0.547159	−	0.837028i	$-0.315709\pi$
$593$	26.6484	1.09432	0.547159	+	0.837028i	$0.315709\pi$
$594$	1.66112	0.0681565
$595$	−18.5230	−0.759369
$596$	7.56114	0.309716
$597$	−5.45817	−0.223388
$598$	−51.2751	−2.09679
$599$	1.09807	0.0448660	0.0224330	−	0.999748i	$-0.492859\pi$
$599$	1.09807	0.0448660	0.0224330	+	0.999748i	$0.492859\pi$
$600$	5.83180	0.238082
$601$	40.6922	1.65987	0.829934	−	0.557862i	$-0.188378\pi$
$601$	40.6922	1.65987	0.829934	+	0.557862i	$0.188378\pi$
$602$	32.6737	1.33168
$603$	−2.34866	−0.0956447
$604$	14.9976	0.610242
$605$	−1.47319	−0.0598938
$606$	23.0871	0.937849
$607$	27.3651	1.11071	0.555357	−	0.831612i	$-0.312582\pi$
$607$	27.3651	1.11071	0.555357	+	0.831612i	$0.312582\pi$
$608$	−9.34837	−0.379126
$609$	28.1815	1.14197
$610$	2.44715	0.0990822
$611$	5.99128	0.242381
$612$	−3.39208	−0.137117
$613$	−2.10876	−0.0851720	−0.0425860	−	0.999093i	$-0.513560\pi$
$613$	−2.10876	−0.0851720	−0.0425860	+	0.999093i	$0.513560\pi$
$614$	−51.9806	−2.09777
$615$	13.7582	0.554783
$616$	5.80057	0.233712
$617$	−4.11409	−0.165627	−0.0828136	−	0.996565i	$-0.526391\pi$
$617$	−4.11409	−0.165627	−0.0828136	+	0.996565i	$0.526391\pi$
$618$	29.7128	1.19522
$619$	35.1725	1.41370	0.706850	−	0.707363i	$-0.250115\pi$
$619$	35.1725	1.41370	0.706850	+	0.707363i	$0.250115\pi$
$620$	−5.58667	−0.224366
$621$	−7.49465	−0.300750
$622$	−52.2989	−2.09699
$623$	32.2560	1.29231
$624$	−20.3546	−0.814837
$625$	−2.84428	−0.113771
$626$	14.7230	0.588448
$627$	2.28705	0.0913360
$628$	15.1396	0.604137
$629$	3.06421	0.122178
$630$	6.88762	0.274409
$631$	5.37797	0.214093	0.107047	−	0.994254i	$-0.465861\pi$
$631$	5.37797	0.214093	0.107047	+	0.994254i	$0.465861\pi$
$632$	22.7058	0.903187
$633$	−3.49774	−0.139023
$634$	47.9863	1.90578
$635$	25.2054	1.00024
$636$	−3.15356	−0.125047
$637$	3.79609	0.150407
$638$	−16.6324	−0.658485
$639$	1.88712	0.0746534
$640$	−19.6156	−0.775374
$641$	−18.7103	−0.739013	−0.369506	−	0.929228i	$-0.620473\pi$
$641$	−18.7103	−0.739013	−0.369506	+	0.929228i	$0.620473\pi$
$642$	9.83139	0.388014
$643$	−15.4398	−0.608885	−0.304442	−	0.952531i	$-0.598470\pi$
$643$	−15.4398	−0.608885	−0.304442	+	0.952531i	$0.598470\pi$
$644$	16.0171	0.631161
$645$	10.2955	0.405386
$646$	−16.9715	−0.667734
$647$	−17.3725	−0.682984	−0.341492	−	0.939885i	$-0.610932\pi$
$647$	−17.3725	−0.682984	−0.341492	+	0.939885i	$0.610932\pi$
$648$	−2.06092	−0.0809607
$649$	13.8976	0.545530
$650$	−19.3596	−0.759344
$651$	−14.0566	−0.550921
$652$	7.00830	0.274466
$653$	−25.2136	−0.986683	−0.493341	−	0.869836i	$-0.664225\pi$
$653$	−25.2136	−0.986683	−0.493341	+	0.869836i	$0.664225\pi$
$654$	20.3068	0.794057
$655$	−1.34565	−0.0525788
$656$	46.1540	1.80201
$657$	11.5870	0.452050
$658$	−6.80104	−0.265132
$659$	18.5187	0.721387	0.360694	−	0.932684i	$-0.382540\pi$
$659$	18.5187	0.721387	0.360694	+	0.932684i	$0.382540\pi$
$660$	−1.11862	−0.0435422
$661$	12.9891	0.505219	0.252609	−	0.967568i	$-0.418711\pi$
$661$	12.9891	0.505219	0.252609	+	0.967568i	$0.418711\pi$
$662$	21.8225	0.848154
$663$	−18.3991	−0.714563
$664$	−3.36961	−0.130766
$665$	9.48297	0.367734
$666$	−1.13940	−0.0441509
$667$	75.0424	2.90565
$668$	1.69761	0.0656825
$669$	−0.888363	−0.0343461
$670$	5.74751	0.222046
$671$	−1.00000	−0.0386046
$672$	11.5045	0.443797
$673$	−13.7463	−0.529881	−0.264941	−	0.964265i	$-0.585352\pi$
$673$	−13.7463	−0.529881	−0.264941	+	0.964265i	$0.585352\pi$
$674$	−41.8960	−1.61377
$675$	−2.82970	−0.108915
$676$	3.00933	0.115743
$677$	−1.82406	−0.0701044	−0.0350522	−	0.999385i	$-0.511160\pi$
$677$	−1.82406	−0.0701044	−0.0350522	+	0.999385i	$0.511160\pi$
$678$	−21.5903	−0.829169
$679$	33.6028	1.28956
$680$	−13.5633	−0.520128
$681$	−23.7868	−0.911511
$682$	8.29605	0.317672
$683$	32.9064	1.25913	0.629565	−	0.776948i	$-0.283233\pi$
$683$	32.9064	1.25913	0.629565	+	0.776948i	$0.283233\pi$
$684$	1.73659	0.0664003
$685$	0.702076	0.0268250
$686$	28.4179	1.08500
$687$	0.175995	0.00671464
$688$	34.5381	1.31675
$689$	−17.1054	−0.651663
$690$	18.3405	0.698212
$691$	−24.5172	−0.932677	−0.466338	−	0.884606i	$-0.654427\pi$
$691$	−24.5172	−0.932677	−0.466338	+	0.884606i	$0.654427\pi$
$692$	−1.22330	−0.0465029
$693$	−2.81455	−0.106916
$694$	6.12810	0.232620
$695$	30.1479	1.14358
$696$	20.6356	0.782190
$697$	41.7199	1.58026
$698$	40.2232	1.52247
$699$	−17.5376	−0.663332
$700$	6.04745	0.228572
$701$	−31.3871	−1.18548	−0.592738	−	0.805395i	$-0.701953\pi$
$701$	−31.3871	−1.18548	−0.592738	+	0.805395i	$0.701953\pi$
$702$	6.84155	0.258218
$703$	−1.56874	−0.0591663
$704$	3.09428	0.116620
$705$	−2.14302	−0.0807106
$706$	−59.0556	−2.22259
$707$	−39.1181	−1.47119
$708$	10.5527	0.396595
$709$	36.3497	1.36514	0.682570	−	0.730820i	$-0.260862\pi$
$709$	36.3497	1.36514	0.682570	+	0.730820i	$0.260862\pi$
$710$	−4.61807	−0.173313
$711$	−11.0173	−0.413180
$712$	23.6191	0.885165
$713$	−37.4302	−1.40177
$714$	20.8859	0.781634
$715$	−6.06756	−0.226914
$716$	−9.09618	−0.339940
$717$	−7.95670	−0.297148
$718$	−14.1509	−0.528108
$719$	−44.5308	−1.66072	−0.830358	−	0.557230i	$-0.811864\pi$
$719$	−44.5308	−1.66072	−0.830358	+	0.557230i	$0.811864\pi$
$720$	7.28063	0.271333
$721$	−50.3445	−1.87493
$722$	−22.8726	−0.851230
$723$	−10.8700	−0.404261
$724$	10.9521	0.407031
$725$	28.3332	1.05227
$726$	1.66112	0.0616499
$727$	−41.6665	−1.54532	−0.772662	−	0.634818i	$-0.781075\pi$
$727$	−41.6665	−1.54532	−0.772662	+	0.634818i	$0.781075\pi$
$728$	23.8905	0.885440
$729$	1.00000	0.0370370
$730$	−28.3550	−1.04947
$731$	31.2199	1.15471
$732$	−0.759316	−0.0280651
$733$	38.5219	1.42284	0.711420	−	0.702767i	$-0.248052\pi$
$733$	38.5219	1.42284	0.711420	+	0.702767i	$0.248052\pi$
$734$	3.77826	0.139458
$735$	−1.35782	−0.0500840
$736$	30.6346	1.12920
$737$	−2.34866	−0.0865139
$738$	−15.5132	−0.571049
$739$	4.61423	0.169737	0.0848686	−	0.996392i	$-0.472953\pi$
$739$	4.61423	0.169737	0.0848686	+	0.996392i	$0.472953\pi$
$740$	0.767288	0.0282061
$741$	9.41954	0.346036
$742$	19.4173	0.712830
$743$	−50.4021	−1.84907	−0.924537	−	0.381093i	$-0.875548\pi$
$743$	−50.4021	−1.84907	−0.924537	+	0.381093i	$0.875548\pi$
$744$	−10.2928	−0.377352
$745$	−14.6698	−0.537460
$746$	−31.5884	−1.15653
$747$	1.63500	0.0598215
$748$	−3.39208	−0.124027
$749$	−16.6580	−0.608670
$750$	19.1604	0.699641
$751$	26.2161	0.956639	0.478319	−	0.878186i	$-0.341246\pi$
$751$	26.2161	0.956639	0.478319	+	0.878186i	$0.341246\pi$
$752$	−7.18910	−0.262160
$753$	4.89538	0.178397
$754$	−68.5031	−2.49473
$755$	−29.0976	−1.05897
$756$	−2.13713	−0.0777267
$757$	16.1801	0.588075	0.294037	−	0.955794i	$-0.405001\pi$
$757$	16.1801	0.588075	0.294037	+	0.955794i	$0.405001\pi$
$758$	3.44949	0.125291
$759$	−7.49465	−0.272039
$760$	6.94380	0.251878
$761$	−23.9432	−0.867941	−0.433970	−	0.900927i	$-0.642888\pi$
$761$	−23.9432	−0.867941	−0.433970	+	0.900927i	$0.642888\pi$
$762$	−28.4207	−1.02957
$763$	−34.4072	−1.24562
$764$	−3.03563	−0.109825
$765$	6.58117	0.237943
$766$	−30.5221	−1.10281
$767$	57.2394	2.06679
$768$	15.9293	0.574798
$769$	−11.4165	−0.411690	−0.205845	−	0.978585i	$-0.565994\pi$
$769$	−11.4165	−0.411690	−0.205845	+	0.978585i	$0.565994\pi$
$770$	6.88762	0.248213
$771$	0.151447	0.00545424
$772$	2.54413	0.0915653
$773$	10.0161	0.360253	0.180126	−	0.983643i	$-0.442349\pi$
$773$	10.0161	0.360253	0.180126	+	0.983643i	$0.442349\pi$
$774$	−11.6089	−0.417272
$775$	−14.1323	−0.507645
$776$	24.6053	0.883278
$777$	1.93057	0.0692587
$778$	−0.317730	−0.0113912
$779$	−21.3588	−0.765258
$780$	−4.60719	−0.164964
$781$	1.88712	0.0675266
$782$	55.6154	1.98880
$783$	−10.0128	−0.357828
$784$	−4.55503	−0.162680
$785$	−29.3733	−1.04838
$786$	1.51730	0.0541204
$787$	−0.994185	−0.0354389	−0.0177194	−	0.999843i	$-0.505641\pi$
$787$	−0.994185	−0.0354389	−0.0177194	+	0.999843i	$0.505641\pi$
$788$	14.0717	0.501284
$789$	−25.8581	−0.920573
$790$	26.9609	0.959227
$791$	36.5819	1.30070
$792$	−2.06092	−0.0732317
$793$	−4.11864	−0.146257
$794$	−32.2915	−1.14598
$795$	6.11841	0.216998
$796$	−4.14448	−0.146897
$797$	−14.5631	−0.515850	−0.257925	−	0.966165i	$-0.583039\pi$
$797$	−14.5631	−0.515850	−0.257925	+	0.966165i	$0.583039\pi$
$798$	−10.6926	−0.378516
$799$	−6.49843	−0.229898
$800$	11.5665	0.408936
$801$	−11.4605	−0.404936
$802$	−14.1350	−0.499123
$803$	11.5870	0.408895
$804$	−1.78337	−0.0628947
$805$	−31.0756	−1.09527
$806$	34.1685	1.20353
$807$	−8.79991	−0.309772
$808$	−28.6438	−1.00768
$809$	−19.4621	−0.684251	−0.342125	−	0.939654i	$-0.611147\pi$
$809$	−19.4621	−0.684251	−0.342125	+	0.939654i	$0.611147\pi$
$810$	−2.44715	−0.0859841
$811$	3.09086	0.108535	0.0542674	−	0.998526i	$-0.482718\pi$
$811$	3.09086	0.108535	0.0542674	+	0.998526i	$0.482718\pi$
$812$	21.3987	0.750946
$813$	−4.84554	−0.169941
$814$	−1.13940	−0.0399360
$815$	−13.5972	−0.476290
$816$	22.0776	0.772871
$817$	−15.9832	−0.559183
$818$	16.5874	0.579964
$819$	−11.5921	−0.405061
$820$	10.4468	0.364818
$821$	45.1084	1.57429	0.787147	−	0.616766i	$-0.211557\pi$
$821$	45.1084	1.57429	0.787147	+	0.616766i	$0.211557\pi$
$822$	−0.791636	−0.0276115
$823$	−46.9386	−1.63618	−0.818088	−	0.575093i	$-0.804966\pi$
$823$	−46.9386	−1.63618	−0.818088	+	0.575093i	$0.804966\pi$
$824$	−36.8642	−1.28423
$825$	−2.82970	−0.0985176
$826$	−64.9756	−2.26079
$827$	11.4404	0.397820	0.198910	−	0.980018i	$-0.436260\pi$
$827$	11.4404	0.397820	0.198910	+	0.980018i	$0.436260\pi$
$828$	−5.69081	−0.197769
$829$	41.5722	1.44386	0.721931	−	0.691965i	$-0.243255\pi$
$829$	41.5722	1.44386	0.721931	+	0.691965i	$0.243255\pi$
$830$	−4.00109	−0.138880
$831$	−4.29485	−0.148987
$832$	12.7442	0.441827
$833$	−4.11742	−0.142660
$834$	−33.9937	−1.17711
$835$	−3.29363	−0.113981
$836$	1.73659	0.0600614
$837$	4.99425	0.172627
$838$	63.3245	2.18751
$839$	−18.1912	−0.628029	−0.314015	−	0.949418i	$-0.601674\pi$
$839$	−18.1912	−0.628029	−0.314015	+	0.949418i	$0.601674\pi$
$840$	−8.54536	−0.294843
$841$	71.2560	2.45710
$842$	−37.7313	−1.30031
$843$	19.1622	0.659982
$844$	−2.65589	−0.0914196
$845$	−5.83858	−0.200853
$846$	2.41639	0.0830771
$847$	−2.81455	−0.0967090
$848$	20.5252	0.704839
$849$	−19.4385	−0.667129
$850$	20.9983	0.720236
$851$	5.14076	0.176223
$852$	1.43292	0.0490911
$853$	40.3960	1.38313	0.691567	−	0.722313i	$-0.256921\pi$
$853$	40.3960	1.38313	0.691567	+	0.722313i	$0.256921\pi$
$854$	4.67530	0.159985
$855$	−3.36927	−0.115227
$856$	−12.1976	−0.416907
$857$	−43.5580	−1.48791	−0.743957	−	0.668228i	$-0.767053\pi$
$857$	−43.5580	−1.48791	−0.743957	+	0.668228i	$0.767053\pi$
$858$	6.84155	0.233567
$859$	−30.7316	−1.04855	−0.524275	−	0.851549i	$-0.675664\pi$
$859$	−30.7316	−1.04855	−0.524275	+	0.851549i	$0.675664\pi$
$860$	7.81756	0.266577
$861$	26.2851	0.895793
$862$	−32.2692	−1.09909
$863$	53.2458	1.81251	0.906255	−	0.422732i	$-0.138929\pi$
$863$	53.2458	1.81251	0.906255	+	0.422732i	$0.138929\pi$
$864$	−4.08752	−0.139060
$865$	2.37339	0.0806978
$866$	39.9622	1.35797
$867$	2.95658	0.100411
$868$	−10.6734	−0.362278
$869$	−11.0173	−0.373736
$870$	24.5028	0.830723
$871$	−9.67327	−0.327766
$872$	−25.1943	−0.853186
$873$	−11.9390	−0.404072
$874$	−28.4727	−0.963102
$875$	−32.4649	−1.09751
$876$	8.79816	0.297262
$877$	−30.5194	−1.03057	−0.515283	−	0.857020i	$-0.672313\pi$
$877$	−30.5194	−1.03057	−0.515283	+	0.857020i	$0.672313\pi$
$878$	−27.0960	−0.914444
$879$	17.2668	0.582395
$880$	7.28063	0.245430
$881$	38.7833	1.30664	0.653320	−	0.757081i	$-0.273375\pi$
$881$	38.7833	1.30664	0.653320	+	0.757081i	$0.273375\pi$
$882$	1.53103	0.0515524
$883$	10.0742	0.339025	0.169513	−	0.985528i	$-0.445781\pi$
$883$	10.0742	0.339025	0.169513	+	0.985528i	$0.445781\pi$
$884$	−13.9708	−0.469887
$885$	−20.4739	−0.688223
$886$	19.7037	0.661959
$887$	20.8428	0.699834	0.349917	−	0.936781i	$-0.386210\pi$
$887$	20.8428	0.699834	0.349917	+	0.936781i	$0.386210\pi$
$888$	1.41364	0.0474386
$889$	48.1551	1.61507
$890$	28.0455	0.940086
$891$	1.00000	0.0335013
$892$	−0.674549	−0.0225856
$893$	3.32691	0.111331
$894$	16.5411	0.553218
$895$	17.6480	0.589908
$896$	−37.4758	−1.25198
$897$	−30.8678	−1.03065
$898$	−24.8971	−0.830828
$899$	−50.0064	−1.66781
$900$	−2.14864	−0.0716213
$901$	18.5533	0.618101
$902$	−15.5132	−0.516533
$903$	19.6697	0.654567
$904$	26.7867	0.890913
$905$	−21.2488	−0.706333
$906$	32.8094	1.09002
$907$	35.8755	1.19122	0.595612	−	0.803272i	$-0.296909\pi$
$907$	35.8755	1.19122	0.595612	+	0.803272i	$0.296909\pi$
$908$	−18.0617	−0.599398
$909$	13.8985	0.460985
$910$	28.3676	0.940378
$911$	5.46997	0.181228	0.0906140	−	0.995886i	$-0.471117\pi$
$911$	5.46997	0.181228	0.0906140	+	0.995886i	$0.471117\pi$
$912$	−11.3028	−0.374272
$913$	1.63500	0.0541106
$914$	−37.1696	−1.22946
$915$	1.47319	0.0487023
$916$	0.133636	0.00441546
$917$	−2.57087	−0.0848977
$918$	−7.42068	−0.244919
$919$	−24.8018	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$919$	−24.8018	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$920$	−22.7548	−0.750204
$921$	−31.2925	−1.03112
$922$	33.0207	1.08748
$923$	7.77238	0.255831
$924$	−2.13713	−0.0703065
$925$	1.94096	0.0638184
$926$	48.1899	1.58362
$927$	17.8872	0.587494
$928$	40.9275	1.34351
$929$	22.3547	0.733434	0.366717	−	0.930332i	$-0.380482\pi$
$929$	22.3547	0.733434	0.366717	+	0.930332i	$0.380482\pi$
$930$	−12.2217	−0.400765
$931$	2.10794	0.0690849
$932$	−13.3166	−0.436198
$933$	−31.4841	−1.03074
$934$	−60.8493	−1.99105
$935$	6.58117	0.215227
$936$	−8.48821	−0.277446
$937$	−52.9976	−1.73136	−0.865678	−	0.500601i	$-0.833112\pi$
$937$	−52.9976	−1.73136	−0.865678	+	0.500601i	$0.833112\pi$
$938$	10.9807	0.358532
$939$	8.86327	0.289242
$940$	−1.62723	−0.0530743
$941$	−19.0962	−0.622517	−0.311259	−	0.950325i	$-0.600751\pi$
$941$	−19.0962	−0.622517	−0.311259	+	0.950325i	$0.600751\pi$
$942$	33.1202	1.07912
$943$	69.9926	2.27927
$944$	−68.6831	−2.23544
$945$	4.14637	0.134882
$946$	−11.6089	−0.377437
$947$	−3.98469	−0.129485	−0.0647425	−	0.997902i	$-0.520623\pi$
$947$	−3.98469	−0.129485	−0.0647425	+	0.997902i	$0.520623\pi$
$948$	−8.36560	−0.271702
$949$	47.7225	1.54914
$950$	−10.7502	−0.348783
$951$	28.8880	0.936756
$952$	−25.9128	−0.839838
$953$	53.9687	1.74822	0.874109	−	0.485730i	$-0.161446\pi$
$953$	53.9687	1.74822	0.874109	+	0.485730i	$0.161446\pi$
$954$	−6.89889	−0.223360
$955$	5.88960	0.190583
$956$	−6.04165	−0.195401
$957$	−10.0128	−0.323668
$958$	−62.3661	−2.01496
$959$	1.34132	0.0433136
$960$	−4.55848	−0.147124
$961$	−6.05742	−0.195401
$962$	−4.69279	−0.151302
$963$	5.91853	0.190722
$964$	−8.25378	−0.265836
$965$	−4.93602	−0.158896
$966$	35.0398	1.12739
$967$	−44.4105	−1.42815	−0.714073	−	0.700071i	$-0.753152\pi$
$967$	−44.4105	−1.42815	−0.714073	+	0.700071i	$0.753152\pi$
$968$	−2.06092	−0.0662406
$969$	−10.2169	−0.328214
$970$	29.2164	0.938082
$971$	36.8254	1.18178	0.590891	−	0.806751i	$-0.298776\pi$
$971$	36.8254	1.18178	0.590891	+	0.806751i	$0.298776\pi$
$972$	0.759316	0.0243551
$973$	57.5979	1.84650
$974$	24.0209	0.769679
$975$	−11.6545	−0.373244
$976$	4.94207	0.158192
$977$	16.0019	0.511947	0.255974	−	0.966684i	$-0.417604\pi$
$977$	16.0019	0.511947	0.255974	+	0.966684i	$0.417604\pi$
$978$	15.3317	0.490254
$979$	−11.4605	−0.366278
$980$	−1.03101	−0.0329346
$981$	12.2248	0.390306
$982$	39.4431	1.25868
$983$	10.0083	0.319216	0.159608	−	0.987180i	$-0.448977\pi$
$983$	10.0083	0.319216	0.159608	+	0.987180i	$0.448977\pi$
$984$	19.2470	0.613571
$985$	−27.3013	−0.869893
$986$	74.3017	2.36625
$987$	−4.09425	−0.130321
$988$	7.15241	0.227548
$989$	52.3770	1.66549
$990$	−2.44715	−0.0777755
$991$	10.3552	0.328944	0.164472	−	0.986382i	$-0.447408\pi$
$991$	10.3552	0.328944	0.164472	+	0.986382i	$0.447408\pi$
$992$	−20.4141	−0.648149
$993$	13.1372	0.416897
$994$	−8.82287	−0.279844
$995$	8.04094	0.254915
$996$	1.24148	0.0393378
$997$	−28.3712	−0.898525	−0.449263	−	0.893400i	$-0.648313\pi$
$997$	−28.3712	−0.898525	−0.449263	+	0.893400i	$0.648313\pi$
$998$	26.2901	0.832200
$999$	−0.685924	−0.0217017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.11	✓	12
3.2	odd	2		6039.2.a.f.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.11	✓	12	1.1	even	1	trivial
6039.2.a.f.1.2		12	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)

\(f(q)\)	\(=\)	\(q+1.66112 q^{2} +1.00000 q^{3} +0.759316 q^{4} -1.47319 q^{5} +1.66112 q^{6} -2.81455 q^{7} -2.06092 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.66112 q^{2} +1.00000 q^{3} +0.759316 q^{4} -1.47319 q^{5} +1.66112 q^{6} -2.81455 q^{7} -2.06092 q^{8} +1.00000 q^{9} -2.44715 q^{10} +1.00000 q^{11} +0.759316 q^{12} +4.11864 q^{13} -4.67530 q^{14} -1.47319 q^{15} -4.94207 q^{16} -4.46728 q^{17} +1.66112 q^{18} +2.28705 q^{19} -1.11862 q^{20} -2.81455 q^{21} +1.66112 q^{22} -7.49465 q^{23} -2.06092 q^{24} -2.82970 q^{25} +6.84155 q^{26} +1.00000 q^{27} -2.13713 q^{28} -10.0128 q^{29} -2.44715 q^{30} +4.99425 q^{31} -4.08752 q^{32} +1.00000 q^{33} -7.42068 q^{34} +4.14637 q^{35} +0.759316 q^{36} -0.685924 q^{37} +3.79906 q^{38} +4.11864 q^{39} +3.03614 q^{40} -9.33901 q^{41} -4.67530 q^{42} -6.98858 q^{43} +0.759316 q^{44} -1.47319 q^{45} -12.4495 q^{46} +1.45467 q^{47} -4.94207 q^{48} +0.921685 q^{49} -4.70047 q^{50} -4.46728 q^{51} +3.12735 q^{52} -4.15316 q^{53} +1.66112 q^{54} -1.47319 q^{55} +5.80057 q^{56} +2.28705 q^{57} -16.6324 q^{58} +13.8976 q^{59} -1.11862 q^{60} -1.00000 q^{61} +8.29605 q^{62} -2.81455 q^{63} +3.09428 q^{64} -6.06756 q^{65} +1.66112 q^{66} -2.34866 q^{67} -3.39208 q^{68} -7.49465 q^{69} +6.88762 q^{70} +1.88712 q^{71} -2.06092 q^{72} +11.5870 q^{73} -1.13940 q^{74} -2.82970 q^{75} +1.73659 q^{76} -2.81455 q^{77} +6.84155 q^{78} -11.0173 q^{79} +7.28063 q^{80} +1.00000 q^{81} -15.5132 q^{82} +1.63500 q^{83} -2.13713 q^{84} +6.58117 q^{85} -11.6089 q^{86} -10.0128 q^{87} -2.06092 q^{88} -11.4605 q^{89} -2.44715 q^{90} -11.5921 q^{91} -5.69081 q^{92} +4.99425 q^{93} +2.41639 q^{94} -3.36927 q^{95} -4.08752 q^{96} -11.9390 q^{97} +1.53103 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

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