LMFDB - Embedded newform 6046.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.42034 q^{3} +1.00000 q^{4} +1.09471 q^{5} +1.42034 q^{6} +4.85520 q^{7} -1.00000 q^{8} -0.982644 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.42034 q^{3} +1.00000 q^{4} +1.09471 q^{5} +1.42034 q^{6} +4.85520 q^{7} -1.00000 q^{8} -0.982644 q^{9} -1.09471 q^{10} -1.78556 q^{11} -1.42034 q^{12} +4.96019 q^{13} -4.85520 q^{14} -1.55486 q^{15} +1.00000 q^{16} +0.225886 q^{17} +0.982644 q^{18} -0.946136 q^{19} +1.09471 q^{20} -6.89601 q^{21} +1.78556 q^{22} -1.02983 q^{23} +1.42034 q^{24} -3.80160 q^{25} -4.96019 q^{26} +5.65669 q^{27} +4.85520 q^{28} -10.0994 q^{29} +1.55486 q^{30} +6.20387 q^{31} -1.00000 q^{32} +2.53609 q^{33} -0.225886 q^{34} +5.31505 q^{35} -0.982644 q^{36} +2.76943 q^{37} +0.946136 q^{38} -7.04514 q^{39} -1.09471 q^{40} -10.1357 q^{41} +6.89601 q^{42} -12.3363 q^{43} -1.78556 q^{44} -1.07571 q^{45} +1.02983 q^{46} -8.21869 q^{47} -1.42034 q^{48} +16.5729 q^{49} +3.80160 q^{50} -0.320834 q^{51} +4.96019 q^{52} -5.33549 q^{53} -5.65669 q^{54} -1.95468 q^{55} -4.85520 q^{56} +1.34383 q^{57} +10.0994 q^{58} -1.85141 q^{59} -1.55486 q^{60} +13.5501 q^{61} -6.20387 q^{62} -4.77093 q^{63} +1.00000 q^{64} +5.42999 q^{65} -2.53609 q^{66} -10.2740 q^{67} +0.225886 q^{68} +1.46271 q^{69} -5.31505 q^{70} -4.04411 q^{71} +0.982644 q^{72} -11.9758 q^{73} -2.76943 q^{74} +5.39955 q^{75} -0.946136 q^{76} -8.66924 q^{77} +7.04514 q^{78} -14.6993 q^{79} +1.09471 q^{80} -5.08648 q^{81} +10.1357 q^{82} -8.71114 q^{83} -6.89601 q^{84} +0.247281 q^{85} +12.3363 q^{86} +14.3445 q^{87} +1.78556 q^{88} -9.61708 q^{89} +1.07571 q^{90} +24.0827 q^{91} -1.02983 q^{92} -8.81159 q^{93} +8.21869 q^{94} -1.03575 q^{95} +1.42034 q^{96} -6.03148 q^{97} -16.5729 q^{98} +1.75457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.42034	−0.820032	−0.410016	−	0.912078i	$-0.634477\pi$
$3$	−1.42034	−0.820032	−0.410016	+	0.912078i	$0.634477\pi$
$4$	1.00000	0.500000
$5$	1.09471	0.489571	0.244785	−	0.969577i	$-0.421282\pi$
$5$	1.09471	0.489571	0.244785	+	0.969577i	$0.421282\pi$
$6$	1.42034	0.579850
$7$	4.85520	1.83509	0.917546	−	0.397630i	$-0.130167\pi$
$7$	4.85520	1.83509	0.917546	+	0.397630i	$0.130167\pi$
$8$	−1.00000	−0.353553
$9$	−0.982644	−0.327548
$10$	−1.09471	−0.346179
$11$	−1.78556	−0.538366	−0.269183	−	0.963089i	$-0.586754\pi$
$11$	−1.78556	−0.538366	−0.269183	+	0.963089i	$0.586754\pi$
$12$	−1.42034	−0.410016
$13$	4.96019	1.37571	0.687855	−	0.725848i	$-0.258552\pi$
$13$	4.96019	1.37571	0.687855	+	0.725848i	$0.258552\pi$
$14$	−4.85520	−1.29761
$15$	−1.55486	−0.401464
$16$	1.00000	0.250000
$17$	0.225886	0.0547854	0.0273927	−	0.999625i	$-0.491280\pi$
$17$	0.225886	0.0547854	0.0273927	+	0.999625i	$0.491280\pi$
$18$	0.982644	0.231611
$19$	−0.946136	−0.217058	−0.108529	−	0.994093i	$-0.534614\pi$
$19$	−0.946136	−0.217058	−0.108529	+	0.994093i	$0.534614\pi$
$20$	1.09471	0.244785
$21$	−6.89601	−1.50483
$22$	1.78556	0.380682
$23$	−1.02983	−0.214735	−0.107368	−	0.994219i	$-0.534242\pi$
$23$	−1.02983	−0.214735	−0.107368	+	0.994219i	$0.534242\pi$
$24$	1.42034	0.289925
$25$	−3.80160	−0.760320
$26$	−4.96019	−0.972774
$27$	5.65669	1.08863
$28$	4.85520	0.917546
$29$	−10.0994	−1.87541	−0.937703	−	0.347437i	$-0.887052\pi$
$29$	−10.0994	−1.87541	−0.937703	+	0.347437i	$0.887052\pi$
$30$	1.55486	0.283878
$31$	6.20387	1.11425	0.557124	−	0.830429i	$-0.311905\pi$
$31$	6.20387	1.11425	0.557124	+	0.830429i	$0.311905\pi$
$32$	−1.00000	−0.176777
$33$	2.53609	0.441477
$34$	−0.225886	−0.0387392
$35$	5.31505	0.898408
$36$	−0.982644	−0.163774
$37$	2.76943	0.455292	0.227646	−	0.973744i	$-0.426897\pi$
$37$	2.76943	0.455292	0.227646	+	0.973744i	$0.426897\pi$
$38$	0.946136	0.153483
$39$	−7.04514	−1.12813
$40$	−1.09471	−0.173089
$41$	−10.1357	−1.58293	−0.791464	−	0.611216i	$-0.790681\pi$
$41$	−10.1357	−1.58293	−0.791464	+	0.611216i	$0.790681\pi$
$42$	6.89601	1.06408
$43$	−12.3363	−1.88127	−0.940634	−	0.339422i	$-0.889768\pi$
$43$	−12.3363	−1.88127	−0.940634	+	0.339422i	$0.889768\pi$
$44$	−1.78556	−0.269183
$45$	−1.07571	−0.160358
$46$	1.02983	0.151841
$47$	−8.21869	−1.19882	−0.599409	−	0.800443i	$-0.704598\pi$
$47$	−8.21869	−1.19882	−0.599409	+	0.800443i	$0.704598\pi$
$48$	−1.42034	−0.205008
$49$	16.5729	2.36756
$50$	3.80160	0.537628
$51$	−0.320834	−0.0449258
$52$	4.96019	0.687855
$53$	−5.33549	−0.732886	−0.366443	−	0.930440i	$-0.619425\pi$
$53$	−5.33549	−0.732886	−0.366443	+	0.930440i	$0.619425\pi$
$54$	−5.65669	−0.769779
$55$	−1.95468	−0.263568
$56$	−4.85520	−0.648803
$57$	1.34383	0.177995
$58$	10.0994	1.32611
$59$	−1.85141	−0.241034	−0.120517	−	0.992711i	$-0.538455\pi$
$59$	−1.85141	−0.241034	−0.120517	+	0.992711i	$0.538455\pi$
$60$	−1.55486	−0.200732
$61$	13.5501	1.73491	0.867457	−	0.497512i	$-0.165753\pi$
$61$	13.5501	1.73491	0.867457	+	0.497512i	$0.165753\pi$
$62$	−6.20387	−0.787893
$63$	−4.77093	−0.601081
$64$	1.00000	0.125000
$65$	5.42999	0.673508
$66$	−2.53609	−0.312171
$67$	−10.2740	−1.25516	−0.627582	−	0.778551i	$-0.715955\pi$
$67$	−10.2740	−1.25516	−0.627582	+	0.778551i	$0.715955\pi$
$68$	0.225886	0.0273927
$69$	1.46271	0.176090
$70$	−5.31505	−0.635270
$71$	−4.04411	−0.479948	−0.239974	−	0.970779i	$-0.577139\pi$
$71$	−4.04411	−0.479948	−0.239974	+	0.970779i	$0.577139\pi$
$72$	0.982644	0.115806
$73$	−11.9758	−1.40166	−0.700831	−	0.713327i	$-0.747187\pi$
$73$	−11.9758	−1.40166	−0.700831	+	0.713327i	$0.747187\pi$
$74$	−2.76943	−0.321940
$75$	5.39955	0.623487
$76$	−0.946136	−0.108529
$77$	−8.66924	−0.987951
$78$	7.04514	0.797705
$79$	−14.6993	−1.65380	−0.826898	−	0.562352i	$-0.809897\pi$
$79$	−14.6993	−1.65380	−0.826898	+	0.562352i	$0.809897\pi$
$80$	1.09471	0.122393
$81$	−5.08648	−0.565164
$82$	10.1357	1.11930
$83$	−8.71114	−0.956172	−0.478086	−	0.878313i	$-0.658669\pi$
$83$	−8.71114	−0.956172	−0.478086	+	0.878313i	$0.658669\pi$
$84$	−6.89601	−0.752417
$85$	0.247281	0.0268214
$86$	12.3363	1.33026
$87$	14.3445	1.53789
$88$	1.78556	0.190341
$89$	−9.61708	−1.01941	−0.509704	−	0.860350i	$-0.670245\pi$
$89$	−9.61708	−1.01941	−0.509704	+	0.860350i	$0.670245\pi$
$90$	1.07571	0.113390
$91$	24.0827	2.52455
$92$	−1.02983	−0.107368
$93$	−8.81159	−0.913719
$94$	8.21869	0.847693
$95$	−1.03575	−0.106265
$96$	1.42034	0.144962
$97$	−6.03148	−0.612404	−0.306202	−	0.951967i	$-0.599058\pi$
$97$	−6.03148	−0.612404	−0.306202	+	0.951967i	$0.599058\pi$
$98$	−16.5729	−1.67412
$99$	1.75457	0.176341
$100$	−3.80160	−0.380160
$101$	3.79614	0.377730	0.188865	−	0.982003i	$-0.439519\pi$
$101$	3.79614	0.377730	0.188865	+	0.982003i	$0.439519\pi$
$102$	0.320834	0.0317673
$103$	−1.13713	−0.112044	−0.0560221	−	0.998430i	$-0.517842\pi$
$103$	−1.13713	−0.112044	−0.0560221	+	0.998430i	$0.517842\pi$
$104$	−4.96019	−0.486387
$105$	−7.54916	−0.736723
$106$	5.33549	0.518229
$107$	−5.45762	−0.527608	−0.263804	−	0.964576i	$-0.584977\pi$
$107$	−5.45762	−0.527608	−0.263804	+	0.964576i	$0.584977\pi$
$108$	5.65669	0.544316
$109$	4.37826	0.419362	0.209681	−	0.977770i	$-0.432758\pi$
$109$	4.37826	0.419362	0.209681	+	0.977770i	$0.432758\pi$
$110$	1.95468	0.186371
$111$	−3.93353	−0.373354
$112$	4.85520	0.458773
$113$	15.9099	1.49668	0.748341	−	0.663315i	$-0.230851\pi$
$113$	15.9099	1.49668	0.748341	+	0.663315i	$0.230851\pi$
$114$	−1.34383	−0.125861
$115$	−1.12737	−0.105128
$116$	−10.0994	−0.937703
$117$	−4.87411	−0.450611
$118$	1.85141	0.170436
$119$	1.09672	0.100536
$120$	1.55486	0.141939
$121$	−7.81178	−0.710162
$122$	−13.5501	−1.22677
$123$	14.3961	1.29805
$124$	6.20387	0.557124
$125$	−9.63524	−0.861802
$126$	4.77093	0.425028
$127$	−1.57260	−0.139546	−0.0697730	−	0.997563i	$-0.522228\pi$
$127$	−1.57260	−0.139546	−0.0697730	+	0.997563i	$0.522228\pi$
$128$	−1.00000	−0.0883883
$129$	17.5217	1.54270
$130$	−5.42999	−0.476242
$131$	2.25024	0.196604	0.0983022	−	0.995157i	$-0.468659\pi$
$131$	2.25024	0.196604	0.0983022	+	0.995157i	$0.468659\pi$
$132$	2.53609	0.220739
$133$	−4.59368	−0.398322
$134$	10.2740	0.887535
$135$	6.19246	0.532962
$136$	−0.225886	−0.0193696
$137$	−15.6651	−1.33836	−0.669178	−	0.743102i	$-0.733354\pi$
$137$	−15.6651	−1.33836	−0.669178	+	0.743102i	$0.733354\pi$
$138$	−1.46271	−0.124514
$139$	−14.3718	−1.21900	−0.609499	−	0.792787i	$-0.708629\pi$
$139$	−14.3718	−1.21900	−0.609499	+	0.792787i	$0.708629\pi$
$140$	5.31505	0.449204
$141$	11.6733	0.983069
$142$	4.04411	0.339374
$143$	−8.85671	−0.740636
$144$	−0.982644	−0.0818870
$145$	−11.0559	−0.918145
$146$	11.9758	0.991125
$147$	−23.5392	−1.94148
$148$	2.76943	0.227646
$149$	11.0253	0.903228	0.451614	−	0.892214i	$-0.350848\pi$
$149$	11.0253	0.903228	0.451614	+	0.892214i	$0.350848\pi$
$150$	−5.39955	−0.440872
$151$	22.3096	1.81553	0.907764	−	0.419482i	$-0.137788\pi$
$151$	22.3096	1.81553	0.907764	+	0.419482i	$0.137788\pi$
$152$	0.946136	0.0767417
$153$	−0.221966	−0.0179449
$154$	8.66924	0.698587
$155$	6.79147	0.545504
$156$	−7.04514	−0.564063
$157$	14.7441	1.17671	0.588354	−	0.808604i	$-0.299776\pi$
$157$	14.7441	1.17671	0.588354	+	0.808604i	$0.299776\pi$
$158$	14.6993	1.16941
$159$	7.57820	0.600990
$160$	−1.09471	−0.0865447
$161$	−5.00005	−0.394059
$162$	5.08648	0.399631
$163$	−3.92240	−0.307226	−0.153613	−	0.988131i	$-0.549091\pi$
$163$	−3.92240	−0.307226	−0.153613	+	0.988131i	$0.549091\pi$
$164$	−10.1357	−0.791464
$165$	2.77630	0.216134
$166$	8.71114	0.676116
$167$	7.86633	0.608715	0.304357	−	0.952558i	$-0.401558\pi$
$167$	7.86633	0.608715	0.304357	+	0.952558i	$0.401558\pi$
$168$	6.89601	0.532039
$169$	11.6035	0.892579
$170$	−0.247281	−0.0189656
$171$	0.929715	0.0710971
$172$	−12.3363	−0.940634
$173$	−16.2659	−1.23667	−0.618337	−	0.785913i	$-0.712193\pi$
$173$	−16.2659	−1.23667	−0.618337	+	0.785913i	$0.712193\pi$
$174$	−14.3445	−1.08745
$175$	−18.4575	−1.39526
$176$	−1.78556	−0.134591
$177$	2.62963	0.197655
$178$	9.61708	0.720831
$179$	12.9235	0.965947	0.482974	−	0.875635i	$-0.339557\pi$
$179$	12.9235	0.965947	0.482974	+	0.875635i	$0.339557\pi$
$180$	−1.07571	−0.0801790
$181$	−13.0464	−0.969731	−0.484865	−	0.874589i	$-0.661131\pi$
$181$	−13.0464	−0.969731	−0.484865	+	0.874589i	$0.661131\pi$
$182$	−24.0827	−1.78513
$183$	−19.2457	−1.42268
$184$	1.02983	0.0759204
$185$	3.03174	0.222898
$186$	8.81159	0.646097
$187$	−0.403333	−0.0294946
$188$	−8.21869	−0.599409
$189$	27.4644	1.99774
$190$	1.03575	0.0751411
$191$	23.4408	1.69612	0.848059	−	0.529902i	$-0.177771\pi$
$191$	23.4408	1.69612	0.848059	+	0.529902i	$0.177771\pi$
$192$	−1.42034	−0.102504
$193$	2.31783	0.166841	0.0834207	−	0.996514i	$-0.473415\pi$
$193$	2.31783	0.166841	0.0834207	+	0.996514i	$0.473415\pi$
$194$	6.03148	0.433035
$195$	−7.71242	−0.552298
$196$	16.5729	1.18378
$197$	17.4755	1.24508	0.622540	−	0.782588i	$-0.286101\pi$
$197$	17.4755	1.24508	0.622540	+	0.782588i	$0.286101\pi$
$198$	−1.75457	−0.124692
$199$	7.40139	0.524671	0.262335	−	0.964977i	$-0.415507\pi$
$199$	7.40139	0.524671	0.262335	+	0.964977i	$0.415507\pi$
$200$	3.80160	0.268814
$201$	14.5925	1.02927
$202$	−3.79614	−0.267096
$203$	−49.0345	−3.44154
$204$	−0.320834	−0.0224629
$205$	−11.0957	−0.774956
$206$	1.13713	0.0792273
$207$	1.01196	0.0703361
$208$	4.96019	0.343928
$209$	1.68938	0.116857
$210$	7.54916	0.520942
$211$	−0.372716	−0.0256588	−0.0128294	−	0.999918i	$-0.504084\pi$
$211$	−0.372716	−0.0256588	−0.0128294	+	0.999918i	$0.504084\pi$
$212$	−5.33549	−0.366443
$213$	5.74400	0.393572
$214$	5.45762	0.373075
$215$	−13.5047	−0.921014
$216$	−5.65669	−0.384889
$217$	30.1210	2.04475
$218$	−4.37826	−0.296533
$219$	17.0097	1.14941
$220$	−1.95468	−0.131784
$221$	1.12044	0.0753689
$222$	3.93353	0.264001
$223$	19.4232	1.30067	0.650336	−	0.759647i	$-0.274628\pi$
$223$	19.4232	1.30067	0.650336	+	0.759647i	$0.274628\pi$
$224$	−4.85520	−0.324402
$225$	3.73562	0.249041
$226$	−15.9099	−1.05831
$227$	6.45205	0.428238	0.214119	−	0.976808i	$-0.431312\pi$
$227$	6.45205	0.428238	0.214119	+	0.976808i	$0.431312\pi$
$228$	1.34383	0.0889974
$229$	−24.8694	−1.64342	−0.821709	−	0.569907i	$-0.806979\pi$
$229$	−24.8694	−1.64342	−0.821709	+	0.569907i	$0.806979\pi$
$230$	1.12737	0.0743369
$231$	12.3132	0.810151
$232$	10.0994	0.663057
$233$	−2.71325	−0.177751	−0.0888754	−	0.996043i	$-0.528327\pi$
$233$	−2.71325	−0.177751	−0.0888754	+	0.996043i	$0.528327\pi$
$234$	4.87411	0.318630
$235$	−8.99711	−0.586907
$236$	−1.85141	−0.120517
$237$	20.8779	1.35617
$238$	−1.09672	−0.0710899
$239$	−12.4960	−0.808296	−0.404148	−	0.914694i	$-0.632432\pi$
$239$	−12.4960	−0.808296	−0.404148	+	0.914694i	$0.632432\pi$
$240$	−1.55486	−0.100366
$241$	−5.19482	−0.334628	−0.167314	−	0.985904i	$-0.553509\pi$
$241$	−5.19482	−0.334628	−0.167314	+	0.985904i	$0.553509\pi$
$242$	7.81178	0.502160
$243$	−9.74558	−0.625179
$244$	13.5501	0.867457
$245$	18.1426	1.15909
$246$	−14.3961	−0.917861
$247$	−4.69302	−0.298609
$248$	−6.20387	−0.393946
$249$	12.3728	0.784091
$250$	9.63524	0.609386
$251$	5.49425	0.346794	0.173397	−	0.984852i	$-0.444526\pi$
$251$	5.49425	0.346794	0.173397	+	0.984852i	$0.444526\pi$
$252$	−4.77093	−0.300540
$253$	1.83883	0.115606
$254$	1.57260	0.0986740
$255$	−0.351222	−0.0219944
$256$	1.00000	0.0625000
$257$	−0.845246	−0.0527250	−0.0263625	−	0.999652i	$-0.508392\pi$
$257$	−0.845246	−0.0527250	−0.0263625	+	0.999652i	$0.508392\pi$
$258$	−17.5217	−1.09085
$259$	13.4462	0.835503
$260$	5.42999	0.336754
$261$	9.92409	0.614286
$262$	−2.25024	−0.139020
$263$	−2.00080	−0.123375	−0.0616874	−	0.998096i	$-0.519648\pi$
$263$	−2.00080	−0.123375	−0.0616874	+	0.998096i	$0.519648\pi$
$264$	−2.53609	−0.156086
$265$	−5.84084	−0.358800
$266$	4.59368	0.281656
$267$	13.6595	0.835948
$268$	−10.2740	−0.627582
$269$	−26.2397	−1.59986	−0.799930	−	0.600093i	$-0.795130\pi$
$269$	−26.2397	−1.59986	−0.799930	+	0.600093i	$0.795130\pi$
$270$	−6.19246	−0.376861
$271$	29.9342	1.81837	0.909186	−	0.416391i	$-0.136705\pi$
$271$	29.9342	1.81837	0.909186	+	0.416391i	$0.136705\pi$
$272$	0.225886	0.0136964
$273$	−34.2056	−2.07021
$274$	15.6651	0.946361
$275$	6.78798	0.409331
$276$	1.46271	0.0880449
$277$	−7.42683	−0.446235	−0.223118	−	0.974792i	$-0.571623\pi$
$277$	−7.42683	−0.446235	−0.223118	+	0.974792i	$0.571623\pi$
$278$	14.3718	0.861962
$279$	−6.09620	−0.364970
$280$	−5.31505	−0.317635
$281$	30.5424	1.82201	0.911003	−	0.412399i	$-0.135309\pi$
$281$	30.5424	1.82201	0.911003	+	0.412399i	$0.135309\pi$
$282$	−11.6733	−0.695135
$283$	26.9330	1.60100	0.800500	−	0.599333i	$-0.204567\pi$
$283$	26.9330	1.60100	0.800500	+	0.599333i	$0.204567\pi$
$284$	−4.04411	−0.239974
$285$	1.47111	0.0871411
$286$	8.85671	0.523708
$287$	−49.2108	−2.90482
$288$	0.982644	0.0579029
$289$	−16.9490	−0.996999
$290$	11.0559	0.649226
$291$	8.56673	0.502191
$292$	−11.9758	−0.700831
$293$	27.4953	1.60629	0.803147	−	0.595781i	$-0.203157\pi$
$293$	27.4953	1.60629	0.803147	+	0.595781i	$0.203157\pi$
$294$	23.5392	1.37283
$295$	−2.02677	−0.118003
$296$	−2.76943	−0.160970
$297$	−10.1004	−0.586082
$298$	−11.0253	−0.638678
$299$	−5.10818	−0.295414
$300$	5.39955	0.311743
$301$	−59.8952	−3.45230
$302$	−22.3096	−1.28377
$303$	−5.39180	−0.309751
$304$	−0.946136	−0.0542646
$305$	14.8335	0.849364
$306$	0.221966	0.0126889
$307$	−34.4471	−1.96600	−0.983001	−	0.183602i	$-0.941224\pi$
$307$	−34.4471	−1.96600	−0.983001	+	0.183602i	$0.941224\pi$
$308$	−8.66924	−0.493976
$309$	1.61510	0.0918799
$310$	−6.79147	−0.385729
$311$	−13.0236	−0.738503	−0.369251	−	0.929330i	$-0.620386\pi$
$311$	−13.0236	−0.738503	−0.369251	+	0.929330i	$0.620386\pi$
$312$	7.04514	0.398853
$313$	−10.3528	−0.585174	−0.292587	−	0.956239i	$-0.594516\pi$
$313$	−10.3528	−0.585174	−0.292587	+	0.956239i	$0.594516\pi$
$314$	−14.7441	−0.832058
$315$	−5.22281	−0.294272
$316$	−14.6993	−0.826898
$317$	25.6306	1.43956	0.719779	−	0.694203i	$-0.244243\pi$
$317$	25.6306	1.43956	0.719779	+	0.694203i	$0.244243\pi$
$318$	−7.57820	−0.424964
$319$	18.0330	1.00966
$320$	1.09471	0.0611964
$321$	7.75165	0.432655
$322$	5.00005	0.278642
$323$	−0.213719	−0.0118916
$324$	−5.08648	−0.282582
$325$	−18.8567	−1.04598
$326$	3.92240	0.217242
$327$	−6.21861	−0.343890
$328$	10.1357	0.559650
$329$	−39.9034	−2.19994
$330$	−2.77630	−0.152830
$331$	31.1780	1.71370	0.856848	−	0.515570i	$-0.172420\pi$
$331$	31.1780	1.71370	0.856848	+	0.515570i	$0.172420\pi$
$332$	−8.71114	−0.478086
$333$	−2.72137	−0.149130
$334$	−7.86633	−0.430426
$335$	−11.2470	−0.614492
$336$	−6.89601	−0.376208
$337$	−21.3453	−1.16275	−0.581375	−	0.813635i	$-0.697485\pi$
$337$	−21.3453	−1.16275	−0.581375	+	0.813635i	$0.697485\pi$
$338$	−11.6035	−0.631148
$339$	−22.5975	−1.22733
$340$	0.247281	0.0134107
$341$	−11.0774	−0.599873
$342$	−0.929715	−0.0502732
$343$	46.4785	2.50960
$344$	12.3363	0.665129
$345$	1.60125	0.0862084
$346$	16.2659	0.874460
$347$	0.453339	0.0243365	0.0121683	−	0.999926i	$-0.496127\pi$
$347$	0.453339	0.0243365	0.0121683	+	0.999926i	$0.496127\pi$
$348$	14.3445	0.768947
$349$	2.05156	0.109817	0.0549087	−	0.998491i	$-0.482513\pi$
$349$	2.05156	0.109817	0.0549087	+	0.998491i	$0.482513\pi$
$350$	18.4575	0.986596
$351$	28.0583	1.49764
$352$	1.78556	0.0951706
$353$	25.3304	1.34820	0.674100	−	0.738640i	$-0.264531\pi$
$353$	25.3304	1.34820	0.674100	+	0.738640i	$0.264531\pi$
$354$	−2.62963	−0.139763
$355$	−4.42715	−0.234969
$356$	−9.61708	−0.509704
$357$	−1.55771	−0.0824430
$358$	−12.9235	−0.683028
$359$	1.53711	0.0811255	0.0405628	−	0.999177i	$-0.487085\pi$
$359$	1.53711	0.0811255	0.0405628	+	0.999177i	$0.487085\pi$
$360$	1.07571	0.0566951
$361$	−18.1048	−0.952886
$362$	13.0464	0.685703
$363$	11.0954	0.582355
$364$	24.0827	1.26228
$365$	−13.1101	−0.686213
$366$	19.2457	1.00599
$367$	−26.9525	−1.40691	−0.703456	−	0.710739i	$-0.748361\pi$
$367$	−26.9525	−1.40691	−0.703456	+	0.710739i	$0.748361\pi$
$368$	−1.02983	−0.0536838
$369$	9.95977	0.518485
$370$	−3.03174	−0.157613
$371$	−25.9049	−1.34491
$372$	−8.81159	−0.456859
$373$	0.234556	0.0121448	0.00607241	−	0.999982i	$-0.498067\pi$
$373$	0.234556	0.0121448	0.00607241	+	0.999982i	$0.498067\pi$
$374$	0.403333	0.0208558
$375$	13.6853	0.706705
$376$	8.21869	0.423847
$377$	−50.0949	−2.58002
$378$	−27.4644	−1.41261
$379$	25.2428	1.29664	0.648319	−	0.761369i	$-0.275472\pi$
$379$	25.2428	1.29664	0.648319	+	0.761369i	$0.275472\pi$
$380$	−1.03575	−0.0531327
$381$	2.23363	0.114432
$382$	−23.4408	−1.19934
$383$	−5.11135	−0.261178	−0.130589	−	0.991437i	$-0.541687\pi$
$383$	−5.11135	−0.261178	−0.130589	+	0.991437i	$0.541687\pi$
$384$	1.42034	0.0724812
$385$	−9.49033	−0.483672
$386$	−2.31783	−0.117975
$387$	12.1222	0.616206
$388$	−6.03148	−0.306202
$389$	9.81262	0.497519	0.248760	−	0.968565i	$-0.419977\pi$
$389$	9.81262	0.497519	0.248760	+	0.968565i	$0.419977\pi$
$390$	7.71242	0.390533
$391$	−0.232625	−0.0117644
$392$	−16.5729	−0.837060
$393$	−3.19610	−0.161222
$394$	−17.4755	−0.880404
$395$	−16.0915	−0.809651
$396$	1.75457	0.0881704
$397$	7.89448	0.396212	0.198106	−	0.980181i	$-0.436521\pi$
$397$	7.89448	0.396212	0.198106	+	0.980181i	$0.436521\pi$
$398$	−7.40139	−0.370998
$399$	6.52456	0.326637
$400$	−3.80160	−0.190080
$401$	−37.8075	−1.88802	−0.944009	−	0.329920i	$-0.892978\pi$
$401$	−37.8075	−1.88802	−0.944009	+	0.329920i	$0.892978\pi$
$402$	−14.5925	−0.727807
$403$	30.7724	1.53288
$404$	3.79614	0.188865
$405$	−5.56824	−0.276688
$406$	49.0345	2.43354
$407$	−4.94499	−0.245114
$408$	0.320834	0.0158837
$409$	−4.56232	−0.225592	−0.112796	−	0.993618i	$-0.535981\pi$
$409$	−4.56232	−0.225592	−0.112796	+	0.993618i	$0.535981\pi$
$410$	11.0957	0.547976
$411$	22.2497	1.09749
$412$	−1.13713	−0.0560221
$413$	−8.98898	−0.442319
$414$	−1.01196	−0.0497352
$415$	−9.53621	−0.468114
$416$	−4.96019	−0.243194
$417$	20.4128	0.999617
$418$	−1.68938	−0.0826303
$419$	−14.3499	−0.701040	−0.350520	−	0.936555i	$-0.613995\pi$
$419$	−14.3499	−0.701040	−0.350520	+	0.936555i	$0.613995\pi$
$420$	−7.54916	−0.368361
$421$	6.73647	0.328315	0.164158	−	0.986434i	$-0.447509\pi$
$421$	6.73647	0.328315	0.164158	+	0.986434i	$0.447509\pi$
$422$	0.372716	0.0181435
$423$	8.07605	0.392671
$424$	5.33549	0.259114
$425$	−0.858729	−0.0416545
$426$	−5.74400	−0.278298
$427$	65.7885	3.18373
$428$	−5.45762	−0.263804
$429$	12.5795	0.607345
$430$	13.5047	0.651255
$431$	15.5684	0.749905	0.374953	−	0.927044i	$-0.377659\pi$
$431$	15.5684	0.749905	0.374953	+	0.927044i	$0.377659\pi$
$432$	5.65669	0.272158
$433$	−25.4277	−1.22198	−0.610989	−	0.791639i	$-0.709228\pi$
$433$	−25.4277	−1.22198	−0.610989	+	0.791639i	$0.709228\pi$
$434$	−30.1210	−1.44586
$435$	15.7031	0.752908
$436$	4.37826	0.209681
$437$	0.974363	0.0466101
$438$	−17.0097	−0.812754
$439$	15.3340	0.731852	0.365926	−	0.930644i	$-0.380752\pi$
$439$	15.3340	0.731852	0.365926	+	0.930644i	$0.380752\pi$
$440$	1.95468	0.0931855
$441$	−16.2853	−0.775491
$442$	−1.12044	−0.0532939
$443$	11.4627	0.544610	0.272305	−	0.962211i	$-0.412214\pi$
$443$	11.4627	0.544610	0.272305	+	0.962211i	$0.412214\pi$
$444$	−3.93353	−0.186677
$445$	−10.5280	−0.499073
$446$	−19.4232	−0.919713
$447$	−15.6596	−0.740675
$448$	4.85520	0.229387
$449$	16.5470	0.780901	0.390451	−	0.920624i	$-0.372319\pi$
$449$	16.5470	0.780901	0.390451	+	0.920624i	$0.372319\pi$
$450$	−3.73562	−0.176099
$451$	18.0979	0.852195
$452$	15.9099	0.748341
$453$	−31.6871	−1.48879
$454$	−6.45205	−0.302810
$455$	26.3637	1.23595
$456$	−1.34383	−0.0629306
$457$	−28.3119	−1.32438	−0.662189	−	0.749337i	$-0.730372\pi$
$457$	−28.3119	−1.32438	−0.662189	+	0.749337i	$0.730372\pi$
$458$	24.8694	1.16207
$459$	1.27777	0.0596412
$460$	−1.12737	−0.0525641
$461$	−21.9280	−1.02129	−0.510645	−	0.859792i	$-0.670593\pi$
$461$	−21.9280	−1.02129	−0.510645	+	0.859792i	$0.670593\pi$
$462$	−12.3132	−0.572863
$463$	−18.5294	−0.861133	−0.430566	−	0.902559i	$-0.641686\pi$
$463$	−18.5294	−0.861133	−0.430566	+	0.902559i	$0.641686\pi$
$464$	−10.0994	−0.468852
$465$	−9.64617	−0.447330
$466$	2.71325	0.125689
$467$	14.5070	0.671305	0.335653	−	0.941986i	$-0.391043\pi$
$467$	14.5070	0.671305	0.335653	+	0.941986i	$0.391043\pi$
$468$	−4.87411	−0.225306
$469$	−49.8821	−2.30334
$470$	8.99711	0.415006
$471$	−20.9416	−0.964937
$472$	1.85141	0.0852182
$473$	22.0272	1.01281
$474$	−20.8779	−0.958954
$475$	3.59683	0.165034
$476$	1.09672	0.0502682
$477$	5.24289	0.240056
$478$	12.4960	0.571552
$479$	−22.8685	−1.04489	−0.522444	−	0.852674i	$-0.674980\pi$
$479$	−22.8685	−1.04489	−0.522444	+	0.852674i	$0.674980\pi$
$480$	1.55486	0.0709694
$481$	13.7369	0.626350
$482$	5.19482	0.236618
$483$	7.10175	0.323141
$484$	−7.81178	−0.355081
$485$	−6.60275	−0.299815
$486$	9.74558	0.442068
$487$	−25.5425	−1.15744	−0.578720	−	0.815526i	$-0.696448\pi$
$487$	−25.5425	−1.15744	−0.578720	+	0.815526i	$0.696448\pi$
$488$	−13.5501	−0.613385
$489$	5.57113	0.251935
$490$	−18.1426	−0.819600
$491$	−13.5069	−0.609559	−0.304780	−	0.952423i	$-0.598583\pi$
$491$	−13.5069	−0.609559	−0.304780	+	0.952423i	$0.598583\pi$
$492$	14.3961	0.649026
$493$	−2.28131	−0.102745
$494$	4.69302	0.211149
$495$	1.92075	0.0863313
$496$	6.20387	0.278562
$497$	−19.6350	−0.880748
$498$	−12.3728	−0.554436
$499$	−23.6076	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$499$	−23.6076	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$500$	−9.63524	−0.430901
$501$	−11.1728	−0.499165
$502$	−5.49425	−0.245220
$503$	5.46740	0.243780	0.121890	−	0.992544i	$-0.461105\pi$
$503$	5.46740	0.243780	0.121890	+	0.992544i	$0.461105\pi$
$504$	4.77093	0.212514
$505$	4.15569	0.184926
$506$	−1.83883	−0.0817459
$507$	−16.4809	−0.731943
$508$	−1.57260	−0.0697730
$509$	−16.2118	−0.718574	−0.359287	−	0.933227i	$-0.616980\pi$
$509$	−16.2118	−0.718574	−0.359287	+	0.933227i	$0.616980\pi$
$510$	0.351222	0.0155524
$511$	−58.1449	−2.57218
$512$	−1.00000	−0.0441942
$513$	−5.35200	−0.236297
$514$	0.845246	0.0372822
$515$	−1.24483	−0.0548536
$516$	17.5217	0.771350
$517$	14.6749	0.645403
$518$	−13.4462	−0.590790
$519$	23.1031	1.01411
$520$	−5.42999	−0.238121
$521$	−30.8723	−1.35254	−0.676269	−	0.736655i	$-0.736404\pi$
$521$	−30.8723	−1.35254	−0.676269	+	0.736655i	$0.736404\pi$
$522$	−9.92409	−0.434366
$523$	−36.8540	−1.61151	−0.805756	−	0.592248i	$-0.798241\pi$
$523$	−36.8540	−1.61151	−0.805756	+	0.592248i	$0.798241\pi$
$524$	2.25024	0.0983022
$525$	26.2159	1.14416
$526$	2.00080	0.0872392
$527$	1.40137	0.0610446
$528$	2.53609	0.110369
$529$	−21.9394	−0.953889
$530$	5.84084	0.253710
$531$	1.81928	0.0789501
$532$	−4.59368	−0.199161
$533$	−50.2750	−2.17765
$534$	−13.6595	−0.591104
$535$	−5.97453	−0.258301
$536$	10.2740	0.443767
$537$	−18.3557	−0.792107
$538$	26.2397	1.13127
$539$	−29.5919	−1.27462
$540$	6.19246	0.266481
$541$	−25.0053	−1.07506	−0.537530	−	0.843244i	$-0.680643\pi$
$541$	−25.0053	−1.07506	−0.537530	+	0.843244i	$0.680643\pi$
$542$	−29.9342	−1.28578
$543$	18.5303	0.795210
$544$	−0.225886	−0.00968479
$545$	4.79295	0.205307
$546$	34.2056	1.46386
$547$	10.7754	0.460723	0.230362	−	0.973105i	$-0.426009\pi$
$547$	10.7754	0.460723	0.230362	+	0.973105i	$0.426009\pi$
$548$	−15.6651	−0.669178
$549$	−13.3149	−0.568268
$550$	−6.78798	−0.289440
$551$	9.55538	0.407073
$552$	−1.46271	−0.0622571
$553$	−71.3678	−3.03487
$554$	7.42683	0.315536
$555$	−4.30609	−0.182783
$556$	−14.3718	−0.609499
$557$	39.7230	1.68312	0.841559	−	0.540165i	$-0.181638\pi$
$557$	39.7230	1.68312	0.841559	+	0.540165i	$0.181638\pi$
$558$	6.09620	0.258073
$559$	−61.1904	−2.58808
$560$	5.31505	0.224602
$561$	0.572868	0.0241865
$562$	−30.5424	−1.28835
$563$	−9.71319	−0.409362	−0.204681	−	0.978829i	$-0.565616\pi$
$563$	−9.71319	−0.409362	−0.204681	+	0.978829i	$0.565616\pi$
$564$	11.6733	0.491535
$565$	17.4168	0.732732
$566$	−26.9330	−1.13208
$567$	−24.6959	−1.03713
$568$	4.04411	0.169687
$569$	−18.8454	−0.790039	−0.395019	−	0.918673i	$-0.629262\pi$
$569$	−18.8454	−0.790039	−0.395019	+	0.918673i	$0.629262\pi$
$570$	−1.47111	−0.0616180
$571$	41.4970	1.73660	0.868299	−	0.496042i	$-0.165214\pi$
$571$	41.4970	1.73660	0.868299	+	0.496042i	$0.165214\pi$
$572$	−8.85671	−0.370318
$573$	−33.2938	−1.39087
$574$	49.2108	2.05402
$575$	3.91502	0.163268
$576$	−0.982644	−0.0409435
$577$	−35.0077	−1.45739	−0.728695	−	0.684839i	$-0.759873\pi$
$577$	−35.0077	−1.45739	−0.728695	+	0.684839i	$0.759873\pi$
$578$	16.9490	0.704984
$579$	−3.29211	−0.136815
$580$	−11.0559	−0.459072
$581$	−42.2943	−1.75466
$582$	−8.56673	−0.355102
$583$	9.52683	0.394561
$584$	11.9758	0.495563
$585$	−5.33575	−0.220606
$586$	−27.4953	−1.13582
$587$	38.7580	1.59971	0.799857	−	0.600191i	$-0.204909\pi$
$587$	38.7580	1.59971	0.799857	+	0.600191i	$0.204909\pi$
$588$	−23.5392	−0.970738
$589$	−5.86970	−0.241857
$590$	2.02677	0.0834407
$591$	−24.8211	−1.02100
$592$	2.76943	0.113823
$593$	−26.7682	−1.09924	−0.549619	−	0.835415i	$-0.685227\pi$
$593$	−26.7682	−1.09924	−0.549619	+	0.835415i	$0.685227\pi$
$594$	10.1004	0.414423
$595$	1.20060	0.0492197
$596$	11.0253	0.451614
$597$	−10.5125	−0.430247
$598$	5.10818	0.208889
$599$	38.9893	1.59306	0.796530	−	0.604599i	$-0.206667\pi$
$599$	38.9893	1.59306	0.796530	+	0.604599i	$0.206667\pi$
$600$	−5.39955	−0.220436
$601$	41.0676	1.67518	0.837591	−	0.546298i	$-0.183964\pi$
$601$	41.0676	1.67518	0.837591	+	0.546298i	$0.183964\pi$
$602$	59.8952	2.44114
$603$	10.0956	0.411126
$604$	22.3096	0.907764
$605$	−8.55167	−0.347675
$606$	5.39180	0.219027
$607$	−31.3128	−1.27095	−0.635474	−	0.772122i	$-0.719195\pi$
$607$	−31.3128	−1.27095	−0.635474	+	0.772122i	$0.719195\pi$
$608$	0.946136	0.0383709
$609$	69.6454	2.82218
$610$	−14.8335	−0.600591
$611$	−40.7663	−1.64923
$612$	−0.221966	−0.00897243
$613$	−3.83636	−0.154949	−0.0774746	−	0.996994i	$-0.524686\pi$
$613$	−3.83636	−0.154949	−0.0774746	+	0.996994i	$0.524686\pi$
$614$	34.4471	1.39017
$615$	15.7596	0.635488
$616$	8.66924	0.349293
$617$	−6.50156	−0.261743	−0.130871	−	0.991399i	$-0.541778\pi$
$617$	−6.50156	−0.261743	−0.130871	+	0.991399i	$0.541778\pi$
$618$	−1.61510	−0.0649689
$619$	23.1423	0.930169	0.465084	−	0.885266i	$-0.346024\pi$
$619$	23.1423	0.930169	0.465084	+	0.885266i	$0.346024\pi$
$620$	6.79147	0.272752
$621$	−5.82546	−0.233768
$622$	13.0236	0.522200
$623$	−46.6928	−1.87071
$624$	−7.04514	−0.282031
$625$	8.46018	0.338407
$626$	10.3528	0.413781
$627$	−2.39949	−0.0958263
$628$	14.7441	0.588354
$629$	0.625577	0.0249434
$630$	5.22281	0.208082
$631$	−12.6332	−0.502920	−0.251460	−	0.967868i	$-0.580911\pi$
$631$	−12.6332	−0.502920	−0.251460	+	0.967868i	$0.580911\pi$
$632$	14.6993	0.584705
$633$	0.529382	0.0210411
$634$	−25.6306	−1.01792
$635$	−1.72155	−0.0683177
$636$	7.57820	0.300495
$637$	82.2050	3.25708
$638$	−18.0330	−0.713934
$639$	3.97392	0.157206
$640$	−1.09471	−0.0432724
$641$	−20.8616	−0.823982	−0.411991	−	0.911188i	$-0.635167\pi$
$641$	−20.8616	−0.823982	−0.411991	+	0.911188i	$0.635167\pi$
$642$	−7.75165	−0.305933
$643$	8.29880	0.327273	0.163636	−	0.986521i	$-0.447678\pi$
$643$	8.29880	0.327273	0.163636	+	0.986521i	$0.447678\pi$
$644$	−5.00005	−0.197030
$645$	19.1812	0.755261
$646$	0.213719	0.00840866
$647$	−46.4215	−1.82502	−0.912508	−	0.409059i	$-0.865857\pi$
$647$	−46.4215	−1.82502	−0.912508	+	0.409059i	$0.865857\pi$
$648$	5.08648	0.199816
$649$	3.30581	0.129764
$650$	18.8567	0.739620
$651$	−42.7820	−1.67676
$652$	−3.92240	−0.153613
$653$	−15.3587	−0.601032	−0.300516	−	0.953777i	$-0.597159\pi$
$653$	−15.3587	−0.601032	−0.300516	+	0.953777i	$0.597159\pi$
$654$	6.21861	0.243167
$655$	2.46337	0.0962518
$656$	−10.1357	−0.395732
$657$	11.7680	0.459112
$658$	39.9034	1.55559
$659$	−16.7879	−0.653964	−0.326982	−	0.945031i	$-0.606032\pi$
$659$	−16.7879	−0.653964	−0.326982	+	0.945031i	$0.606032\pi$
$660$	2.77630	0.108067
$661$	−24.1395	−0.938919	−0.469459	−	0.882954i	$-0.655551\pi$
$661$	−24.1395	−0.938919	−0.469459	+	0.882954i	$0.655551\pi$
$662$	−31.1780	−1.21177
$663$	−1.59140	−0.0618049
$664$	8.71114	0.338058
$665$	−5.02876	−0.195007
$666$	2.72137	0.105451
$667$	10.4007	0.402716
$668$	7.86633	0.304357
$669$	−27.5874	−1.06659
$670$	11.2470	0.434511
$671$	−24.1945	−0.934019
$672$	6.89601	0.266020
$673$	39.9656	1.54056	0.770279	−	0.637706i	$-0.220117\pi$
$673$	39.9656	1.54056	0.770279	+	0.637706i	$0.220117\pi$
$674$	21.3453	0.822189
$675$	−21.5045	−0.827709
$676$	11.6035	0.446289
$677$	−34.1673	−1.31316	−0.656579	−	0.754257i	$-0.727997\pi$
$677$	−34.1673	−1.31316	−0.656579	+	0.754257i	$0.727997\pi$
$678$	22.5975	0.867851
$679$	−29.2840	−1.12382
$680$	−0.247281	−0.00948278
$681$	−9.16408	−0.351168
$682$	11.0774	0.424175
$683$	47.7647	1.82766	0.913832	−	0.406093i	$-0.133109\pi$
$683$	47.7647	1.82766	0.913832	+	0.406093i	$0.133109\pi$
$684$	0.929715	0.0355485
$685$	−17.1488	−0.655221
$686$	−46.4785	−1.77456
$687$	35.3230	1.34766
$688$	−12.3363	−0.470317
$689$	−26.4651	−1.00824
$690$	−1.60125	−0.0609586
$691$	38.3623	1.45937	0.729686	−	0.683783i	$-0.239666\pi$
$691$	38.3623	1.45937	0.729686	+	0.683783i	$0.239666\pi$
$692$	−16.2659	−0.618337
$693$	8.51878	0.323602
$694$	−0.453339	−0.0172085
$695$	−15.7330	−0.596786
$696$	−14.3445	−0.543727
$697$	−2.28951	−0.0867214
$698$	−2.05156	−0.0776526
$699$	3.85373	0.145761
$700$	−18.4575	−0.697629
$701$	−7.03039	−0.265534	−0.132767	−	0.991147i	$-0.542386\pi$
$701$	−7.03039	−0.265534	−0.132767	+	0.991147i	$0.542386\pi$
$702$	−28.0583	−1.05899
$703$	−2.62026	−0.0988250
$704$	−1.78556	−0.0672957
$705$	12.7789	0.481282
$706$	−25.3304	−0.953322
$707$	18.4310	0.693170
$708$	2.62963	0.0988276
$709$	−5.24181	−0.196860	−0.0984301	−	0.995144i	$-0.531382\pi$
$709$	−5.24181	−0.196860	−0.0984301	+	0.995144i	$0.531382\pi$
$710$	4.42715	0.166148
$711$	14.4441	0.541698
$712$	9.61708	0.360415
$713$	−6.38896	−0.239268
$714$	1.55771	0.0582960
$715$	−9.69557	−0.362594
$716$	12.9235	0.482974
$717$	17.7485	0.662829
$718$	−1.53711	−0.0573644
$719$	33.5007	1.24937	0.624683	−	0.780879i	$-0.285228\pi$
$719$	33.5007	1.24937	0.624683	+	0.780879i	$0.285228\pi$
$720$	−1.07571	−0.0400895
$721$	−5.52097	−0.205612
$722$	18.1048	0.673792
$723$	7.37840	0.274406
$724$	−13.0464	−0.484865
$725$	38.3938	1.42591
$726$	−11.0954	−0.411787
$727$	30.2248	1.12098	0.560488	−	0.828163i	$-0.310614\pi$
$727$	30.2248	1.12098	0.560488	+	0.828163i	$0.310614\pi$
$728$	−24.0827	−0.892565
$729$	29.1014	1.07783
$730$	13.1101	0.485226
$731$	−2.78660	−0.103066
$732$	−19.2457	−0.711342
$733$	10.7711	0.397840	0.198920	−	0.980016i	$-0.436257\pi$
$733$	10.7711	0.397840	0.198920	+	0.980016i	$0.436257\pi$
$734$	26.9525	0.994836
$735$	−25.7686	−0.950491
$736$	1.02983	0.0379602
$737$	18.3447	0.675737
$738$	−9.95977	−0.366624
$739$	−46.5853	−1.71367	−0.856833	−	0.515594i	$-0.827571\pi$
$739$	−46.5853	−1.71367	−0.856833	+	0.515594i	$0.827571\pi$
$740$	3.03174	0.111449
$741$	6.66566	0.244869
$742$	25.9049	0.950998
$743$	1.90538	0.0699015	0.0349508	−	0.999389i	$-0.488873\pi$
$743$	1.90538	0.0699015	0.0349508	+	0.999389i	$0.488873\pi$
$744$	8.81159	0.323048
$745$	12.0695	0.442194
$746$	−0.234556	−0.00858769
$747$	8.55996	0.313192
$748$	−0.403333	−0.0147473
$749$	−26.4978	−0.968209
$750$	−13.6853	−0.499716
$751$	−37.3386	−1.36251	−0.681253	−	0.732048i	$-0.738565\pi$
$751$	−37.3386	−1.36251	−0.681253	+	0.732048i	$0.738565\pi$
$752$	−8.21869	−0.299705
$753$	−7.80369	−0.284382
$754$	50.0949	1.82435
$755$	24.4226	0.888829
$756$	27.4644	0.998869
$757$	36.8300	1.33861	0.669304	−	0.742989i	$-0.266592\pi$
$757$	36.8300	1.33861	0.669304	+	0.742989i	$0.266592\pi$
$758$	−25.2428	−0.916861
$759$	−2.61176	−0.0948007
$760$	1.03575	0.0375705
$761$	4.18019	0.151532	0.0757658	−	0.997126i	$-0.475860\pi$
$761$	4.18019	0.151532	0.0757658	+	0.997126i	$0.475860\pi$
$762$	−2.23363	−0.0809158
$763$	21.2573	0.769567
$764$	23.4408	0.848059
$765$	−0.242989	−0.00878529
$766$	5.11135	0.184681
$767$	−9.18337	−0.331592
$768$	−1.42034	−0.0512520
$769$	32.0213	1.15472	0.577358	−	0.816491i	$-0.304084\pi$
$769$	32.0213	1.15472	0.577358	+	0.816491i	$0.304084\pi$
$770$	9.49033	0.342008
$771$	1.20053	0.0432362
$772$	2.31783	0.0834207
$773$	−31.4755	−1.13210	−0.566048	−	0.824372i	$-0.691528\pi$
$773$	−31.4755	−1.13210	−0.566048	+	0.824372i	$0.691528\pi$
$774$	−12.1222	−0.435723
$775$	−23.5846	−0.847186
$776$	6.03148	0.216518
$777$	−19.0981	−0.685139
$778$	−9.81262	−0.351799
$779$	9.58973	0.343588
$780$	−7.71242	−0.276149
$781$	7.22100	0.258388
$782$	0.232625	0.00831867
$783$	−57.1291	−2.04163
$784$	16.5729	0.591891
$785$	16.1406	0.576082
$786$	3.19610	0.114001
$787$	−2.56266	−0.0913490	−0.0456745	−	0.998956i	$-0.514544\pi$
$787$	−2.56266	−0.0913490	−0.0456745	+	0.998956i	$0.514544\pi$
$788$	17.4755	0.622540
$789$	2.84182	0.101171
$790$	16.0915	0.572509
$791$	77.2459	2.74655
$792$	−1.75457	−0.0623459
$793$	67.2112	2.38674
$794$	−7.89448	−0.280165
$795$	8.29596	0.294227
$796$	7.40139	0.262335
$797$	50.4375	1.78659	0.893294	−	0.449473i	$-0.148388\pi$
$797$	50.4375	1.78659	0.893294	+	0.449473i	$0.148388\pi$
$798$	−6.52456	−0.230967
$799$	−1.85649	−0.0656778
$800$	3.80160	0.134407
$801$	9.45017	0.333905
$802$	37.8075	1.33503
$803$	21.3835	0.754608
$804$	14.5925	0.514637
$805$	−5.47362	−0.192920
$806$	−30.7724	−1.08391
$807$	37.2692	1.31194
$808$	−3.79614	−0.133548
$809$	19.3744	0.681166	0.340583	−	0.940214i	$-0.389376\pi$
$809$	19.3744	0.681166	0.340583	+	0.940214i	$0.389376\pi$
$810$	5.56824	0.195648
$811$	10.3112	0.362076	0.181038	−	0.983476i	$-0.442054\pi$
$811$	10.3112	0.362076	0.181038	+	0.983476i	$0.442054\pi$
$812$	−49.0345	−1.72077
$813$	−42.5166	−1.49112
$814$	4.94499	0.173322
$815$	−4.29390	−0.150409
$816$	−0.320834	−0.0112314
$817$	11.6718	0.408345
$818$	4.56232	0.159518
$819$	−23.6647	−0.826913
$820$	−11.0957	−0.387478
$821$	7.70624	0.268950	0.134475	−	0.990917i	$-0.457065\pi$
$821$	7.70624	0.268950	0.134475	+	0.990917i	$0.457065\pi$
$822$	−22.2497	−0.776046
$823$	−33.4374	−1.16555	−0.582776	−	0.812633i	$-0.698034\pi$
$823$	−33.4374	−1.16555	−0.582776	+	0.812633i	$0.698034\pi$
$824$	1.13713	0.0396136
$825$	−9.64121	−0.335664
$826$	8.98898	0.312767
$827$	30.6821	1.06692	0.533461	−	0.845825i	$-0.320891\pi$
$827$	30.6821	1.06692	0.533461	+	0.845825i	$0.320891\pi$
$828$	1.01196	0.0351681
$829$	−33.5587	−1.16554	−0.582771	−	0.812637i	$-0.698031\pi$
$829$	−33.5587	−1.16554	−0.582771	+	0.812637i	$0.698031\pi$
$830$	9.53621	0.331007
$831$	10.5486	0.365927
$832$	4.96019	0.171964
$833$	3.74360	0.129708
$834$	−20.4128	−0.706836
$835$	8.61138	0.298009
$836$	1.68938	0.0584284
$837$	35.0934	1.21301
$838$	14.3499	0.495710
$839$	14.7991	0.510922	0.255461	−	0.966819i	$-0.417773\pi$
$839$	14.7991	0.510922	0.255461	+	0.966819i	$0.417773\pi$
$840$	7.54916	0.260471
$841$	72.9974	2.51715
$842$	−6.73647	−0.232154
$843$	−43.3805	−1.49410
$844$	−0.372716	−0.0128294
$845$	12.7025	0.436981
$846$	−8.07605	−0.277660
$847$	−37.9277	−1.30321
$848$	−5.33549	−0.183222
$849$	−38.2539	−1.31287
$850$	0.858729	0.0294542
$851$	−2.85206	−0.0977673
$852$	5.74400	0.196786
$853$	2.68882	0.0920635	0.0460317	−	0.998940i	$-0.485342\pi$
$853$	2.68882	0.0920635	0.0460317	+	0.998940i	$0.485342\pi$
$854$	−65.7885	−2.25124
$855$	1.01777	0.0348071
$856$	5.45762	0.186537
$857$	19.9438	0.681268	0.340634	−	0.940196i	$-0.389358\pi$
$857$	19.9438	0.681268	0.340634	+	0.940196i	$0.389358\pi$
$858$	−12.5795	−0.429457
$859$	4.36002	0.148762	0.0743810	−	0.997230i	$-0.476302\pi$
$859$	4.36002	0.148762	0.0743810	+	0.997230i	$0.476302\pi$
$860$	−13.5047	−0.460507
$861$	69.8958	2.38204
$862$	−15.5684	−0.530263
$863$	−20.4497	−0.696115	−0.348058	−	0.937473i	$-0.613159\pi$
$863$	−20.4497	−0.696115	−0.348058	+	0.937473i	$0.613159\pi$
$864$	−5.65669	−0.192445
$865$	−17.8065	−0.605440
$866$	25.4277	0.864069
$867$	24.0732	0.817570
$868$	30.1210	1.02237
$869$	26.2464	0.890348
$870$	−15.7031	−0.532386
$871$	−50.9608	−1.72674
$872$	−4.37826	−0.148267
$873$	5.92680	0.200592
$874$	−0.974363	−0.0329583
$875$	−46.7810	−1.58149
$876$	17.0097	0.574704
$877$	−3.70637	−0.125155	−0.0625777	−	0.998040i	$-0.519932\pi$
$877$	−3.70637	−0.125155	−0.0625777	+	0.998040i	$0.519932\pi$
$878$	−15.3340	−0.517498
$879$	−39.0526	−1.31721
$880$	−1.95468	−0.0658921
$881$	47.1684	1.58914	0.794571	−	0.607171i	$-0.207696\pi$
$881$	47.1684	1.58914	0.794571	+	0.607171i	$0.207696\pi$
$882$	16.2853	0.548355
$883$	11.4385	0.384938	0.192469	−	0.981303i	$-0.438351\pi$
$883$	11.4385	0.384938	0.192469	+	0.981303i	$0.438351\pi$
$884$	1.12044	0.0376844
$885$	2.87869	0.0967662
$886$	−11.4627	−0.385097
$887$	−14.9896	−0.503303	−0.251652	−	0.967818i	$-0.580974\pi$
$887$	−14.9896	−0.503303	−0.251652	+	0.967818i	$0.580974\pi$
$888$	3.93353	0.132001
$889$	−7.63530	−0.256080
$890$	10.5280	0.352898
$891$	9.08220	0.304265
$892$	19.4232	0.650336
$893$	7.77599	0.260214
$894$	15.6596	0.523737
$895$	14.1475	0.472900
$896$	−4.85520	−0.162201
$897$	7.25533	0.242248
$898$	−16.5470	−0.552181
$899$	−62.6552	−2.08967
$900$	3.73562	0.124521
$901$	−1.20521	−0.0401515
$902$	−18.0979	−0.602593
$903$	85.0713	2.83100
$904$	−15.9099	−0.529157
$905$	−14.2821	−0.474752
$906$	31.6871	1.05273
$907$	−10.7434	−0.356727	−0.178364	−	0.983965i	$-0.557080\pi$
$907$	−10.7434	−0.356727	−0.178364	+	0.983965i	$0.557080\pi$
$908$	6.45205	0.214119
$909$	−3.73026	−0.123725
$910$	−26.3637	−0.873948
$911$	−24.0436	−0.796601	−0.398300	−	0.917255i	$-0.630400\pi$
$911$	−24.0436	−0.796601	−0.398300	+	0.917255i	$0.630400\pi$
$912$	1.34383	0.0444987
$913$	15.5543	0.514771
$914$	28.3119	0.936476
$915$	−21.0686	−0.696505
$916$	−24.8694	−0.821709
$917$	10.9254	0.360787
$918$	−1.27777	−0.0421727
$919$	40.2300	1.32707	0.663533	−	0.748147i	$-0.269056\pi$
$919$	40.2300	1.32707	0.663533	+	0.748147i	$0.269056\pi$
$920$	1.12737	0.0371684
$921$	48.9265	1.61218
$922$	21.9280	0.722161
$923$	−20.0596	−0.660269
$924$	12.3132	0.405076
$925$	−10.5283	−0.346168
$926$	18.5294	0.608913
$927$	1.11739	0.0366999
$928$	10.0994	0.331528
$929$	9.77703	0.320774	0.160387	−	0.987054i	$-0.448726\pi$
$929$	9.77703	0.320774	0.160387	+	0.987054i	$0.448726\pi$
$930$	9.64617	0.316310
$931$	−15.6802	−0.513899
$932$	−2.71325	−0.0888754
$933$	18.4979	0.605595
$934$	−14.5070	−0.474684
$935$	−0.441534	−0.0144397
$936$	4.87411	0.159315
$937$	17.5552	0.573504	0.286752	−	0.958005i	$-0.407424\pi$
$937$	17.5552	0.573504	0.286752	+	0.958005i	$0.407424\pi$
$938$	49.8821	1.62871
$939$	14.7044	0.479861
$940$	−8.99711	−0.293453
$941$	29.7003	0.968203	0.484102	−	0.875012i	$-0.339147\pi$
$941$	29.7003	0.968203	0.484102	+	0.875012i	$0.339147\pi$
$942$	20.9416	0.682314
$943$	10.4381	0.339911
$944$	−1.85141	−0.0602584
$945$	30.0656	0.978035
$946$	−22.0272	−0.716165
$947$	−9.40792	−0.305716	−0.152858	−	0.988248i	$-0.548848\pi$
$947$	−9.40792	−0.305716	−0.152858	+	0.988248i	$0.548848\pi$
$948$	20.8779	0.678083
$949$	−59.4023	−1.92828
$950$	−3.59683	−0.116697
$951$	−36.4041	−1.18048
$952$	−1.09672	−0.0355450
$953$	−11.2092	−0.363101	−0.181551	−	0.983382i	$-0.558112\pi$
$953$	−11.2092	−0.363101	−0.181551	+	0.983382i	$0.558112\pi$
$954$	−5.24289	−0.169745
$955$	25.6610	0.830370
$956$	−12.4960	−0.404148
$957$	−25.6130	−0.827949
$958$	22.8685	0.738847
$959$	−76.0570	−2.45601
$960$	−1.55486	−0.0501830
$961$	7.48803	0.241549
$962$	−13.7369	−0.442896
$963$	5.36289	0.172817
$964$	−5.19482	−0.167314
$965$	2.53737	0.0816807
$966$	−7.10175	−0.228495
$967$	8.15915	0.262380	0.131190	−	0.991357i	$-0.458120\pi$
$967$	8.15915	0.262380	0.131190	+	0.991357i	$0.458120\pi$
$968$	7.81178	0.251080
$969$	0.303553	0.00975152
$970$	6.60275	0.212001
$971$	19.3090	0.619656	0.309828	−	0.950793i	$-0.399728\pi$
$971$	19.3090	0.619656	0.309828	+	0.950793i	$0.399728\pi$
$972$	−9.74558	−0.312589
$973$	−69.7778	−2.23697
$974$	25.5425	0.818434
$975$	26.7828	0.857737
$976$	13.5501	0.433729
$977$	4.50905	0.144257	0.0721286	−	0.997395i	$-0.477021\pi$
$977$	4.50905	0.144257	0.0721286	+	0.997395i	$0.477021\pi$
$978$	−5.57113	−0.178145
$979$	17.1719	0.548815
$980$	18.1426	0.579545
$981$	−4.30228	−0.137361
$982$	13.5069	0.431023
$983$	−1.61321	−0.0514535	−0.0257268	−	0.999669i	$-0.508190\pi$
$983$	−1.61321	−0.0514535	−0.0257268	+	0.999669i	$0.508190\pi$
$984$	−14.3961	−0.458930
$985$	19.1307	0.609555
$986$	2.28131	0.0726517
$987$	56.6762	1.80402
$988$	−4.69302	−0.149305
$989$	12.7043	0.403975
$990$	−1.92075	−0.0610455
$991$	−5.45377	−0.173245	−0.0866223	−	0.996241i	$-0.527607\pi$
$991$	−5.45377	−0.173245	−0.0866223	+	0.996241i	$0.527607\pi$
$992$	−6.20387	−0.196973
$993$	−44.2832	−1.40528
$994$	19.6350	0.622783
$995$	8.10241	0.256864
$996$	12.3728	0.392046
$997$	−1.27528	−0.0403885	−0.0201943	−	0.999796i	$-0.506428\pi$
$997$	−1.27528	−0.0403885	−0.0201943	+	0.999796i	$0.506428\pi$
$998$	23.6076	0.747287
$999$	15.6658	0.495645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.17	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.17	✓	55	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.42034 q^{3} +1.00000 q^{4} +1.09471 q^{5} +1.42034 q^{6} +4.85520 q^{7} -1.00000 q^{8} -0.982644 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.42034 q^{3} +1.00000 q^{4} +1.09471 q^{5} +1.42034 q^{6} +4.85520 q^{7} -1.00000 q^{8} -0.982644 q^{9} -1.09471 q^{10} -1.78556 q^{11} -1.42034 q^{12} +4.96019 q^{13} -4.85520 q^{14} -1.55486 q^{15} +1.00000 q^{16} +0.225886 q^{17} +0.982644 q^{18} -0.946136 q^{19} +1.09471 q^{20} -6.89601 q^{21} +1.78556 q^{22} -1.02983 q^{23} +1.42034 q^{24} -3.80160 q^{25} -4.96019 q^{26} +5.65669 q^{27} +4.85520 q^{28} -10.0994 q^{29} +1.55486 q^{30} +6.20387 q^{31} -1.00000 q^{32} +2.53609 q^{33} -0.225886 q^{34} +5.31505 q^{35} -0.982644 q^{36} +2.76943 q^{37} +0.946136 q^{38} -7.04514 q^{39} -1.09471 q^{40} -10.1357 q^{41} +6.89601 q^{42} -12.3363 q^{43} -1.78556 q^{44} -1.07571 q^{45} +1.02983 q^{46} -8.21869 q^{47} -1.42034 q^{48} +16.5729 q^{49} +3.80160 q^{50} -0.320834 q^{51} +4.96019 q^{52} -5.33549 q^{53} -5.65669 q^{54} -1.95468 q^{55} -4.85520 q^{56} +1.34383 q^{57} +10.0994 q^{58} -1.85141 q^{59} -1.55486 q^{60} +13.5501 q^{61} -6.20387 q^{62} -4.77093 q^{63} +1.00000 q^{64} +5.42999 q^{65} -2.53609 q^{66} -10.2740 q^{67} +0.225886 q^{68} +1.46271 q^{69} -5.31505 q^{70} -4.04411 q^{71} +0.982644 q^{72} -11.9758 q^{73} -2.76943 q^{74} +5.39955 q^{75} -0.946136 q^{76} -8.66924 q^{77} +7.04514 q^{78} -14.6993 q^{79} +1.09471 q^{80} -5.08648 q^{81} +10.1357 q^{82} -8.71114 q^{83} -6.89601 q^{84} +0.247281 q^{85} +12.3363 q^{86} +14.3445 q^{87} +1.78556 q^{88} -9.61708 q^{89} +1.07571 q^{90} +24.0827 q^{91} -1.02983 q^{92} -8.81159 q^{93} +8.21869 q^{94} -1.03575 q^{95} +1.42034 q^{96} -6.03148 q^{97} -16.5729 q^{98} +1.75457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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