LMFDB - Embedded newform 4334.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.57237 q^{3} +1.00000 q^{4} -0.555853 q^{5} -1.57237 q^{6} -2.43578 q^{7} +1.00000 q^{8} -0.527653 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.57237 q^{3} +1.00000 q^{4} -0.555853 q^{5} -1.57237 q^{6} -2.43578 q^{7} +1.00000 q^{8} -0.527653 q^{9} -0.555853 q^{10} -1.00000 q^{11} -1.57237 q^{12} -6.97963 q^{13} -2.43578 q^{14} +0.874006 q^{15} +1.00000 q^{16} -1.73931 q^{17} -0.527653 q^{18} -1.59903 q^{19} -0.555853 q^{20} +3.82995 q^{21} -1.00000 q^{22} -5.45619 q^{23} -1.57237 q^{24} -4.69103 q^{25} -6.97963 q^{26} +5.54678 q^{27} -2.43578 q^{28} +7.42002 q^{29} +0.874006 q^{30} +3.70979 q^{31} +1.00000 q^{32} +1.57237 q^{33} -1.73931 q^{34} +1.35394 q^{35} -0.527653 q^{36} +1.28352 q^{37} -1.59903 q^{38} +10.9746 q^{39} -0.555853 q^{40} +8.56901 q^{41} +3.82995 q^{42} -3.18985 q^{43} -1.00000 q^{44} +0.293297 q^{45} -5.45619 q^{46} +6.73258 q^{47} -1.57237 q^{48} -1.06696 q^{49} -4.69103 q^{50} +2.73483 q^{51} -6.97963 q^{52} +7.77956 q^{53} +5.54678 q^{54} +0.555853 q^{55} -2.43578 q^{56} +2.51427 q^{57} +7.42002 q^{58} -13.9973 q^{59} +0.874006 q^{60} -7.27665 q^{61} +3.70979 q^{62} +1.28525 q^{63} +1.00000 q^{64} +3.87965 q^{65} +1.57237 q^{66} +10.0912 q^{67} -1.73931 q^{68} +8.57914 q^{69} +1.35394 q^{70} +5.22643 q^{71} -0.527653 q^{72} +11.4627 q^{73} +1.28352 q^{74} +7.37603 q^{75} -1.59903 q^{76} +2.43578 q^{77} +10.9746 q^{78} -1.14072 q^{79} -0.555853 q^{80} -7.13862 q^{81} +8.56901 q^{82} +9.12481 q^{83} +3.82995 q^{84} +0.966797 q^{85} -3.18985 q^{86} -11.6670 q^{87} -1.00000 q^{88} +3.21217 q^{89} +0.293297 q^{90} +17.0009 q^{91} -5.45619 q^{92} -5.83316 q^{93} +6.73258 q^{94} +0.888827 q^{95} -1.57237 q^{96} -18.6631 q^{97} -1.06696 q^{98} +0.527653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	−1.57237	−0.907808	−0.453904	−	0.891051i	$-0.649969\pi$
$3$	−1.57237	−0.907808	−0.453904	+	0.891051i	$0.649969\pi$
$4$	1.00000	0.500000
$5$	−0.555853	−0.248585	−0.124292	−	0.992246i	$-0.539666\pi$
$5$	−0.555853	−0.248585	−0.124292	+	0.992246i	$0.539666\pi$
$6$	−1.57237	−0.641917
$7$	−2.43578	−0.920640	−0.460320	−	0.887753i	$-0.652265\pi$
$7$	−2.43578	−0.920640	−0.460320	+	0.887753i	$0.652265\pi$
$8$	1.00000	0.353553
$9$	−0.527653	−0.175884
$10$	−0.555853	−0.175776
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.57237	−0.453904
$13$	−6.97963	−1.93580	−0.967901	−	0.251333i	$-0.919131\pi$
$13$	−6.97963	−1.93580	−0.967901	+	0.251333i	$0.919131\pi$
$14$	−2.43578	−0.650991
$15$	0.874006	0.225667
$16$	1.00000	0.250000
$17$	−1.73931	−0.421843	−0.210922	−	0.977503i	$-0.567647\pi$
$17$	−1.73931	−0.421843	−0.210922	+	0.977503i	$0.567647\pi$
$18$	−0.527653	−0.124369
$19$	−1.59903	−0.366844	−0.183422	−	0.983034i	$-0.558717\pi$
$19$	−1.59903	−0.366844	−0.183422	+	0.983034i	$0.558717\pi$
$20$	−0.555853	−0.124292
$21$	3.82995	0.835764
$22$	−1.00000	−0.213201
$23$	−5.45619	−1.13769	−0.568847	−	0.822444i	$-0.692610\pi$
$23$	−5.45619	−1.13769	−0.568847	+	0.822444i	$0.692610\pi$
$24$	−1.57237	−0.320959
$25$	−4.69103	−0.938206
$26$	−6.97963	−1.36882
$27$	5.54678	1.06748
$28$	−2.43578	−0.460320
$29$	7.42002	1.37786	0.688931	−	0.724827i	$-0.258080\pi$
$29$	7.42002	1.37786	0.688931	+	0.724827i	$0.258080\pi$
$30$	0.874006	0.159571
$31$	3.70979	0.666297	0.333149	−	0.942874i	$-0.391889\pi$
$31$	3.70979	0.666297	0.333149	+	0.942874i	$0.391889\pi$
$32$	1.00000	0.176777
$33$	1.57237	0.273714
$34$	−1.73931	−0.298288
$35$	1.35394	0.228857
$36$	−0.527653	−0.0879422
$37$	1.28352	0.211009	0.105504	−	0.994419i	$-0.466354\pi$
$37$	1.28352	0.211009	0.105504	+	0.994419i	$0.466354\pi$
$38$	−1.59903	−0.259398
$39$	10.9746	1.75734
$40$	−0.555853	−0.0878880
$41$	8.56901	1.33826	0.669128	−	0.743148i	$-0.266668\pi$
$41$	8.56901	1.33826	0.669128	+	0.743148i	$0.266668\pi$
$42$	3.82995	0.590975
$43$	−3.18985	−0.486448	−0.243224	−	0.969970i	$-0.578205\pi$
$43$	−3.18985	−0.486448	−0.243224	+	0.969970i	$0.578205\pi$
$44$	−1.00000	−0.150756
$45$	0.293297	0.0437222
$46$	−5.45619	−0.804471
$47$	6.73258	0.982048	0.491024	−	0.871146i	$-0.336623\pi$
$47$	6.73258	0.982048	0.491024	+	0.871146i	$0.336623\pi$
$48$	−1.57237	−0.226952
$49$	−1.06696	−0.152423
$50$	−4.69103	−0.663412
$51$	2.73483	0.382953
$52$	−6.97963	−0.967901
$53$	7.77956	1.06860	0.534302	−	0.845294i	$-0.320574\pi$
$53$	7.77956	1.06860	0.534302	+	0.845294i	$0.320574\pi$
$54$	5.54678	0.754821
$55$	0.555853	0.0749512
$56$	−2.43578	−0.325495
$57$	2.51427	0.333024
$58$	7.42002	0.974296
$59$	−13.9973	−1.82230	−0.911149	−	0.412076i	$-0.864804\pi$
$59$	−13.9973	−1.82230	−0.911149	+	0.412076i	$0.864804\pi$
$60$	0.874006	0.112834
$61$	−7.27665	−0.931679	−0.465839	−	0.884869i	$-0.654248\pi$
$61$	−7.27665	−0.931679	−0.465839	+	0.884869i	$0.654248\pi$
$62$	3.70979	0.471143
$63$	1.28525	0.161926
$64$	1.00000	0.125000
$65$	3.87965	0.481211
$66$	1.57237	0.193545
$67$	10.0912	1.23283	0.616415	−	0.787421i	$-0.288584\pi$
$67$	10.0912	1.23283	0.616415	+	0.787421i	$0.288584\pi$
$68$	−1.73931	−0.210922
$69$	8.57914	1.03281
$70$	1.35394	0.161826
$71$	5.22643	0.620263	0.310131	−	0.950694i	$-0.399627\pi$
$71$	5.22643	0.620263	0.310131	+	0.950694i	$0.399627\pi$
$72$	−0.527653	−0.0621845
$73$	11.4627	1.34160	0.670802	−	0.741637i	$-0.265950\pi$
$73$	11.4627	1.34160	0.670802	+	0.741637i	$0.265950\pi$
$74$	1.28352	0.149206
$75$	7.37603	0.851711
$76$	−1.59903	−0.183422
$77$	2.43578	0.277583
$78$	10.9746	1.24262
$79$	−1.14072	−0.128341	−0.0641703	−	0.997939i	$-0.520440\pi$
$79$	−1.14072	−0.128341	−0.0641703	+	0.997939i	$0.520440\pi$
$80$	−0.555853	−0.0621462
$81$	−7.13862	−0.793180
$82$	8.56901	0.946289
$83$	9.12481	1.00158	0.500789	−	0.865569i	$-0.333043\pi$
$83$	9.12481	1.00158	0.500789	+	0.865569i	$0.333043\pi$
$84$	3.82995	0.417882
$85$	0.966797	0.104864
$86$	−3.18985	−0.343971
$87$	−11.6670	−1.25083
$88$	−1.00000	−0.106600
$89$	3.21217	0.340490	0.170245	−	0.985402i	$-0.445544\pi$
$89$	3.21217	0.340490	0.170245	+	0.985402i	$0.445544\pi$
$90$	0.293297	0.0309163
$91$	17.0009	1.78218
$92$	−5.45619	−0.568847
$93$	−5.83316	−0.604870
$94$	6.73258	0.694413
$95$	0.888827	0.0911918
$96$	−1.57237	−0.160479
$97$	−18.6631	−1.89495	−0.947473	−	0.319836i	$-0.896372\pi$
$97$	−18.6631	−1.89495	−0.947473	+	0.319836i	$0.896372\pi$
$98$	−1.06696	−0.107779
$99$	0.527653	0.0530311
$100$	−4.69103	−0.469103
$101$	11.3104	1.12543	0.562714	−	0.826652i	$-0.309757\pi$
$101$	11.3104	1.12543	0.562714	+	0.826652i	$0.309757\pi$
$102$	2.73483	0.270789
$103$	13.1151	1.29227	0.646137	−	0.763222i	$-0.276384\pi$
$103$	13.1151	1.29227	0.646137	+	0.763222i	$0.276384\pi$
$104$	−6.97963	−0.684409
$105$	−2.12889	−0.207758
$106$	7.77956	0.755617
$107$	−7.72454	−0.746760	−0.373380	−	0.927679i	$-0.621801\pi$
$107$	−7.72454	−0.746760	−0.373380	+	0.927679i	$0.621801\pi$
$108$	5.54678	0.533739
$109$	−14.1061	−1.35112	−0.675559	−	0.737306i	$-0.736098\pi$
$109$	−14.1061	−1.35112	−0.675559	+	0.737306i	$0.736098\pi$
$110$	0.555853	0.0529985
$111$	−2.01816	−0.191556
$112$	−2.43578	−0.230160
$113$	3.36640	0.316684	0.158342	−	0.987384i	$-0.449385\pi$
$113$	3.36640	0.316684	0.158342	+	0.987384i	$0.449385\pi$
$114$	2.51427	0.235483
$115$	3.03284	0.282813
$116$	7.42002	0.688931
$117$	3.68282	0.340477
$118$	−13.9973	−1.28856
$119$	4.23657	0.388366
$120$	0.874006	0.0797855
$121$	1.00000	0.0909091
$122$	−7.27665	−0.658797
$123$	−13.4737	−1.21488
$124$	3.70979	0.333149
$125$	5.38678	0.481809
$126$	1.28525	0.114499
$127$	−17.1800	−1.52447	−0.762237	−	0.647298i	$-0.775899\pi$
$127$	−17.1800	−1.52447	−0.762237	+	0.647298i	$0.775899\pi$
$128$	1.00000	0.0883883
$129$	5.01563	0.441601
$130$	3.87965	0.340268
$131$	12.8193	1.12002	0.560012	−	0.828484i	$-0.310796\pi$
$131$	12.8193	1.12002	0.560012	+	0.828484i	$0.310796\pi$
$132$	1.57237	0.136857
$133$	3.89490	0.337731
$134$	10.0912	0.871743
$135$	−3.08319	−0.265359
$136$	−1.73931	−0.149144
$137$	−16.0182	−1.36853	−0.684265	−	0.729233i	$-0.739877\pi$
$137$	−16.0182	−1.36853	−0.684265	+	0.729233i	$0.739877\pi$
$138$	8.57914	0.730305
$139$	3.71991	0.315519	0.157760	−	0.987478i	$-0.449573\pi$
$139$	3.71991	0.315519	0.157760	+	0.987478i	$0.449573\pi$
$140$	1.35394	0.114429
$141$	−10.5861	−0.891511
$142$	5.22643	0.438592
$143$	6.97963	0.583666
$144$	−0.527653	−0.0439711
$145$	−4.12444	−0.342516
$146$	11.4627	0.948657
$147$	1.67765	0.138370
$148$	1.28352	0.105504
$149$	−8.50130	−0.696454	−0.348227	−	0.937410i	$-0.613216\pi$
$149$	−8.50130	−0.696454	−0.348227	+	0.937410i	$0.613216\pi$
$150$	7.37603	0.602250
$151$	−21.5314	−1.75220	−0.876101	−	0.482127i	$-0.839864\pi$
$151$	−21.5314	−1.75220	−0.876101	+	0.482127i	$0.839864\pi$
$152$	−1.59903	−0.129699
$153$	0.917750	0.0741957
$154$	2.43578	0.196281
$155$	−2.06209	−0.165631
$156$	10.9746	0.878668
$157$	−11.1835	−0.892542	−0.446271	−	0.894898i	$-0.647248\pi$
$157$	−11.1835	−0.892542	−0.446271	+	0.894898i	$0.647248\pi$
$158$	−1.14072	−0.0907505
$159$	−12.2323	−0.970088
$160$	−0.555853	−0.0439440
$161$	13.2901	1.04741
$162$	−7.13862	−0.560863
$163$	−1.25486	−0.0982882	−0.0491441	−	0.998792i	$-0.515649\pi$
$163$	−1.25486	−0.0982882	−0.0491441	+	0.998792i	$0.515649\pi$
$164$	8.56901	0.669128
$165$	−0.874006	−0.0680413
$166$	9.12481	0.708223
$167$	19.5945	1.51627	0.758136	−	0.652097i	$-0.226110\pi$
$167$	19.5945	1.51627	0.758136	+	0.652097i	$0.226110\pi$
$168$	3.82995	0.295487
$169$	35.7153	2.74733
$170$	0.966797	0.0741500
$171$	0.843735	0.0645220
$172$	−3.18985	−0.243224
$173$	5.06502	0.385086	0.192543	−	0.981289i	$-0.438326\pi$
$173$	5.06502	0.385086	0.192543	+	0.981289i	$0.438326\pi$
$174$	−11.6670	−0.884474
$175$	11.4263	0.863749
$176$	−1.00000	−0.0753778
$177$	22.0090	1.65430
$178$	3.21217	0.240762
$179$	3.15943	0.236147	0.118073	−	0.993005i	$-0.462328\pi$
$179$	3.15943	0.236147	0.118073	+	0.993005i	$0.462328\pi$
$180$	0.293297	0.0218611
$181$	13.8252	1.02762	0.513810	−	0.857904i	$-0.328234\pi$
$181$	13.8252	1.02762	0.513810	+	0.857904i	$0.328234\pi$
$182$	17.0009	1.26019
$183$	11.4416	0.845786
$184$	−5.45619	−0.402235
$185$	−0.713446	−0.0524536
$186$	−5.83316	−0.427708
$187$	1.73931	0.127191
$188$	6.73258	0.491024
$189$	−13.5107	−0.982762
$190$	0.888827	0.0644823
$191$	−8.52129	−0.616579	−0.308289	−	0.951293i	$-0.599757\pi$
$191$	−8.52129	−0.616579	−0.308289	+	0.951293i	$0.599757\pi$
$192$	−1.57237	−0.113476
$193$	10.1604	0.731362	0.365681	−	0.930740i	$-0.380836\pi$
$193$	10.1604	0.731362	0.365681	+	0.930740i	$0.380836\pi$
$194$	−18.6631	−1.33993
$195$	−6.10024	−0.436847
$196$	−1.06696	−0.0762113
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	0.527653	0.0374987
$199$	16.6434	1.17982	0.589911	−	0.807468i	$-0.299163\pi$
$199$	16.6434	1.17982	0.589911	+	0.807468i	$0.299163\pi$
$200$	−4.69103	−0.331706
$201$	−15.8670	−1.11917
$202$	11.3104	0.795797
$203$	−18.0736	−1.26851
$204$	2.73483	0.191476
$205$	−4.76311	−0.332670
$206$	13.1151	0.913775
$207$	2.87897	0.200102
$208$	−6.97963	−0.483950
$209$	1.59903	0.110607
$210$	−2.12889	−0.146907
$211$	27.1783	1.87103	0.935517	−	0.353282i	$-0.114934\pi$
$211$	27.1783	1.87103	0.935517	+	0.353282i	$0.114934\pi$
$212$	7.77956	0.534302
$213$	−8.21788	−0.563080
$214$	−7.72454	−0.528039
$215$	1.77309	0.120924
$216$	5.54678	0.377410
$217$	−9.03624	−0.613420
$218$	−14.1061	−0.955384
$219$	−18.0236	−1.21792
$220$	0.555853	0.0374756
$221$	12.1397	0.816605
$222$	−2.01816	−0.135450
$223$	−4.30048	−0.287982	−0.143991	−	0.989579i	$-0.545994\pi$
$223$	−4.30048	−0.287982	−0.143991	+	0.989579i	$0.545994\pi$
$224$	−2.43578	−0.162748
$225$	2.47524	0.165016
$226$	3.36640	0.223930
$227$	−4.67278	−0.310143	−0.155072	−	0.987903i	$-0.549561\pi$
$227$	−4.67278	−0.310143	−0.155072	+	0.987903i	$0.549561\pi$
$228$	2.51427	0.166512
$229$	−11.4160	−0.754394	−0.377197	−	0.926133i	$-0.623112\pi$
$229$	−11.4160	−0.754394	−0.377197	+	0.926133i	$0.623112\pi$
$230$	3.03284	0.199979
$231$	−3.82995	−0.251992
$232$	7.42002	0.487148
$233$	−1.12068	−0.0734179	−0.0367089	−	0.999326i	$-0.511687\pi$
$233$	−1.12068	−0.0734179	−0.0367089	+	0.999326i	$0.511687\pi$
$234$	3.68282	0.240754
$235$	−3.74232	−0.244122
$236$	−13.9973	−0.911149
$237$	1.79363	0.116509
$238$	4.23657	0.274616
$239$	−13.5119	−0.874009	−0.437005	−	0.899459i	$-0.643961\pi$
$239$	−13.5119	−0.874009	−0.437005	+	0.899459i	$0.643961\pi$
$240$	0.874006	0.0564168
$241$	11.4682	0.738729	0.369365	−	0.929285i	$-0.379575\pi$
$241$	11.4682	0.738729	0.369365	+	0.929285i	$0.379575\pi$
$242$	1.00000	0.0642824
$243$	−5.41577	−0.347422
$244$	−7.27665	−0.465839
$245$	0.593072	0.0378900
$246$	−13.4737	−0.859049
$247$	11.1607	0.710136
$248$	3.70979	0.235572
$249$	−14.3476	−0.909241
$250$	5.38678	0.340690
$251$	12.4558	0.786204	0.393102	−	0.919495i	$-0.371402\pi$
$251$	12.4558	0.786204	0.393102	+	0.919495i	$0.371402\pi$
$252$	1.28525	0.0809631
$253$	5.45619	0.343027
$254$	−17.1800	−1.07797
$255$	−1.52016	−0.0951963
$256$	1.00000	0.0625000
$257$	−7.73794	−0.482679	−0.241340	−	0.970441i	$-0.577587\pi$
$257$	−7.73794	−0.482679	−0.241340	+	0.970441i	$0.577587\pi$
$258$	5.01563	0.312259
$259$	−3.12637	−0.194263
$260$	3.87965	0.240605
$261$	−3.91520	−0.242345
$262$	12.8193	0.791977
$263$	21.1152	1.30202	0.651010	−	0.759069i	$-0.274345\pi$
$263$	21.1152	1.30202	0.651010	+	0.759069i	$0.274345\pi$
$264$	1.57237	0.0967727
$265$	−4.32429	−0.265639
$266$	3.89490	0.238812
$267$	−5.05072	−0.309099
$268$	10.0912	0.616415
$269$	18.1474	1.10647	0.553233	−	0.833027i	$-0.313394\pi$
$269$	18.1474	1.10647	0.553233	+	0.833027i	$0.313394\pi$
$270$	−3.08319	−0.187637
$271$	10.5830	0.642872	0.321436	−	0.946931i	$-0.395834\pi$
$271$	10.5830	0.642872	0.321436	+	0.946931i	$0.395834\pi$
$272$	−1.73931	−0.105461
$273$	−26.7317	−1.61787
$274$	−16.0182	−0.967697
$275$	4.69103	0.282880
$276$	8.57914	0.516404
$277$	−25.4813	−1.53102	−0.765512	−	0.643421i	$-0.777514\pi$
$277$	−25.4813	−1.53102	−0.765512	+	0.643421i	$0.777514\pi$
$278$	3.71991	0.223106
$279$	−1.95748	−0.117191
$280$	1.35394	0.0809132
$281$	22.7003	1.35419	0.677093	−	0.735897i	$-0.263239\pi$
$281$	22.7003	1.35419	0.677093	+	0.735897i	$0.263239\pi$
$282$	−10.5861	−0.630394
$283$	25.7915	1.53315	0.766573	−	0.642157i	$-0.221960\pi$
$283$	25.7915	1.53315	0.766573	+	0.642157i	$0.221960\pi$
$284$	5.22643	0.310131
$285$	−1.39757	−0.0827846
$286$	6.97963	0.412714
$287$	−20.8723	−1.23205
$288$	−0.527653	−0.0310923
$289$	−13.9748	−0.822048
$290$	−4.12444	−0.242195
$291$	29.3452	1.72025
$292$	11.4627	0.670802
$293$	14.8305	0.866406	0.433203	−	0.901296i	$-0.357383\pi$
$293$	14.8305	0.866406	0.433203	+	0.901296i	$0.357383\pi$
$294$	1.67765	0.0978427
$295$	7.78046	0.452996
$296$	1.28352	0.0746029
$297$	−5.54678	−0.321857
$298$	−8.50130	−0.492467
$299$	38.0822	2.20235
$300$	7.37603	0.425855
$301$	7.76979	0.447843
$302$	−21.5314	−1.23899
$303$	−17.7841	−1.02167
$304$	−1.59903	−0.0917109
$305$	4.04474	0.231601
$306$	0.917750	0.0524643
$307$	−3.86391	−0.220525	−0.110262	−	0.993903i	$-0.535169\pi$
$307$	−3.86391	−0.220525	−0.110262	+	0.993903i	$0.535169\pi$
$308$	2.43578	0.138792
$309$	−20.6219	−1.17314
$310$	−2.06209	−0.117119
$311$	−14.2591	−0.808562	−0.404281	−	0.914635i	$-0.632478\pi$
$311$	−14.2591	−0.808562	−0.404281	+	0.914635i	$0.632478\pi$
$312$	10.9746	0.621312
$313$	−22.4119	−1.26679	−0.633396	−	0.773828i	$-0.718340\pi$
$313$	−22.4119	−1.26679	−0.633396	+	0.773828i	$0.718340\pi$
$314$	−11.1835	−0.631123
$315$	−0.714409	−0.0402524
$316$	−1.14072	−0.0641703
$317$	−31.0887	−1.74611	−0.873057	−	0.487618i	$-0.837866\pi$
$317$	−31.0887	−1.74611	−0.873057	+	0.487618i	$0.837866\pi$
$318$	−12.2323	−0.685956
$319$	−7.42002	−0.415441
$320$	−0.555853	−0.0310731
$321$	12.1458	0.677915
$322$	13.2901	0.740628
$323$	2.78121	0.154751
$324$	−7.13862	−0.396590
$325$	32.7416	1.81618
$326$	−1.25486	−0.0695003
$327$	22.1800	1.22656
$328$	8.56901	0.473145
$329$	−16.3991	−0.904113
$330$	−0.874006	−0.0481124
$331$	33.3741	1.83440	0.917202	−	0.398422i	$-0.130442\pi$
$331$	33.3741	1.83440	0.917202	+	0.398422i	$0.130442\pi$
$332$	9.12481	0.500789
$333$	−0.677252	−0.0371132
$334$	19.5945	1.07217
$335$	−5.60919	−0.306463
$336$	3.82995	0.208941
$337$	11.2321	0.611853	0.305927	−	0.952055i	$-0.401034\pi$
$337$	11.2321	0.611853	0.305927	+	0.952055i	$0.401034\pi$
$338$	35.7153	1.94265
$339$	−5.29323	−0.287489
$340$	0.966797	0.0524319
$341$	−3.70979	−0.200896
$342$	0.843735	0.0456240
$343$	19.6494	1.06097
$344$	−3.18985	−0.171985
$345$	−4.76874	−0.256740
$346$	5.06502	0.272297
$347$	−27.4964	−1.47608	−0.738041	−	0.674755i	$-0.764249\pi$
$347$	−27.4964	−1.47608	−0.738041	+	0.674755i	$0.764249\pi$
$348$	−11.6670	−0.625417
$349$	7.18445	0.384575	0.192287	−	0.981339i	$-0.438409\pi$
$349$	7.18445	0.384575	0.192287	+	0.981339i	$0.438409\pi$
$350$	11.4263	0.610763
$351$	−38.7144	−2.06642
$352$	−1.00000	−0.0533002
$353$	11.3402	0.603579	0.301790	−	0.953375i	$-0.402416\pi$
$353$	11.3402	0.603579	0.301790	+	0.953375i	$0.402416\pi$
$354$	22.0090	1.16977
$355$	−2.90512	−0.154188
$356$	3.21217	0.170245
$357$	−6.66146	−0.352562
$358$	3.15943	0.166981
$359$	30.8915	1.63039	0.815196	−	0.579185i	$-0.196629\pi$
$359$	30.8915	1.63039	0.815196	+	0.579185i	$0.196629\pi$
$360$	0.293297	0.0154581
$361$	−16.4431	−0.865426
$362$	13.8252	0.726637
$363$	−1.57237	−0.0825280
$364$	17.0009	0.891088
$365$	−6.37155	−0.333502
$366$	11.4416	0.598061
$367$	−1.05473	−0.0550566	−0.0275283	−	0.999621i	$-0.508764\pi$
$367$	−1.05473	−0.0550566	−0.0275283	+	0.999621i	$0.508764\pi$
$368$	−5.45619	−0.284423
$369$	−4.52147	−0.235378
$370$	−0.713446	−0.0370903
$371$	−18.9493	−0.983800
$372$	−5.83316	−0.302435
$373$	−14.9993	−0.776633	−0.388317	−	0.921526i	$-0.626943\pi$
$373$	−14.9993	−0.776633	−0.388317	+	0.921526i	$0.626943\pi$
$374$	1.73931	0.0899373
$375$	−8.47002	−0.437390
$376$	6.73258	0.347206
$377$	−51.7890	−2.66727
$378$	−13.5107	−0.694918
$379$	1.16255	0.0597161	0.0298581	−	0.999554i	$-0.490494\pi$
$379$	1.16255	0.0597161	0.0298581	+	0.999554i	$0.490494\pi$
$380$	0.888827	0.0455959
$381$	27.0132	1.38393
$382$	−8.52129	−0.435987
$383$	4.37742	0.223676	0.111838	−	0.993726i	$-0.464326\pi$
$383$	4.37742	0.223676	0.111838	+	0.993726i	$0.464326\pi$
$384$	−1.57237	−0.0802397
$385$	−1.35394	−0.0690030
$386$	10.1604	0.517151
$387$	1.68314	0.0855586
$388$	−18.6631	−0.947473
$389$	24.8469	1.25979	0.629894	−	0.776681i	$-0.283098\pi$
$389$	24.8469	1.25979	0.629894	+	0.776681i	$0.283098\pi$
$390$	−6.10024	−0.308898
$391$	9.48997	0.479928
$392$	−1.06696	−0.0538895
$393$	−20.1566	−1.01677
$394$	−1.00000	−0.0503793
$395$	0.634070	0.0319035
$396$	0.527653	0.0265156
$397$	−31.3019	−1.57100	−0.785498	−	0.618864i	$-0.787593\pi$
$397$	−31.3019	−1.57100	−0.785498	+	0.618864i	$0.787593\pi$
$398$	16.6434	0.834260
$399$	−6.12422	−0.306595
$400$	−4.69103	−0.234551
$401$	23.4039	1.16873	0.584367	−	0.811489i	$-0.301343\pi$
$401$	23.4039	1.16873	0.584367	+	0.811489i	$0.301343\pi$
$402$	−15.8670	−0.791375
$403$	−25.8929	−1.28982
$404$	11.3104	0.562714
$405$	3.96802	0.197173
$406$	−18.0736	−0.896976
$407$	−1.28352	−0.0636216
$408$	2.73483	0.135394
$409$	−14.0078	−0.692641	−0.346321	−	0.938116i	$-0.612569\pi$
$409$	−14.0078	−0.692641	−0.346321	+	0.938116i	$0.612569\pi$
$410$	−4.76311	−0.235233
$411$	25.1866	1.24236
$412$	13.1151	0.646137
$413$	34.0945	1.67768
$414$	2.87897	0.141494
$415$	−5.07205	−0.248977
$416$	−6.97963	−0.342205
$417$	−5.84908	−0.286431
$418$	1.59903	0.0782113
$419$	12.2243	0.597195	0.298598	−	0.954379i	$-0.403481\pi$
$419$	12.2243	0.597195	0.298598	+	0.954379i	$0.403481\pi$
$420$	−2.12889	−0.103879
$421$	−17.4150	−0.848756	−0.424378	−	0.905485i	$-0.639507\pi$
$421$	−17.4150	−0.848756	−0.424378	+	0.905485i	$0.639507\pi$
$422$	27.1783	1.32302
$423$	−3.55247	−0.172727
$424$	7.77956	0.377809
$425$	8.15913	0.395776
$426$	−8.21788	−0.398158
$427$	17.7243	0.857741
$428$	−7.72454	−0.373380
$429$	−10.9746	−0.529857
$430$	1.77309	0.0855059
$431$	15.7223	0.757314	0.378657	−	0.925537i	$-0.376386\pi$
$431$	15.7223	0.757314	0.378657	+	0.925537i	$0.376386\pi$
$432$	5.54678	0.266869
$433$	−26.5707	−1.27691	−0.638453	−	0.769661i	$-0.720425\pi$
$433$	−26.5707	−1.27691	−0.638453	+	0.769661i	$0.720425\pi$
$434$	−9.03624	−0.433753
$435$	6.48514	0.310939
$436$	−14.1061	−0.675559
$437$	8.72462	0.417355
$438$	−18.0236	−0.861199
$439$	31.5571	1.50614	0.753070	−	0.657940i	$-0.228572\pi$
$439$	31.5571	1.50614	0.753070	+	0.657940i	$0.228572\pi$
$440$	0.555853	0.0264992
$441$	0.562984	0.0268088
$442$	12.1397	0.577427
$443$	−6.38606	−0.303411	−0.151706	−	0.988426i	$-0.548477\pi$
$443$	−6.38606	−0.303411	−0.151706	+	0.988426i	$0.548477\pi$
$444$	−2.01816	−0.0957778
$445$	−1.78549	−0.0846406
$446$	−4.30048	−0.203634
$447$	13.3672	0.632246
$448$	−2.43578	−0.115080
$449$	15.9926	0.754735	0.377368	−	0.926064i	$-0.376829\pi$
$449$	15.9926	0.754735	0.377368	+	0.926064i	$0.376829\pi$
$450$	2.47524	0.116684
$451$	−8.56901	−0.403499
$452$	3.36640	0.158342
$453$	33.8554	1.59066
$454$	−4.67278	−0.219305
$455$	−9.44998	−0.443022
$456$	2.51427	0.117742
$457$	−26.5483	−1.24188	−0.620938	−	0.783860i	$-0.713248\pi$
$457$	−26.5483	−1.24188	−0.620938	+	0.783860i	$0.713248\pi$
$458$	−11.4160	−0.533437
$459$	−9.64753	−0.450308
$460$	3.03284	0.141407
$461$	−16.0157	−0.745925	−0.372962	−	0.927846i	$-0.621658\pi$
$461$	−16.0157	−0.745925	−0.372962	+	0.927846i	$0.621658\pi$
$462$	−3.82995	−0.178186
$463$	−22.3607	−1.03919	−0.519594	−	0.854413i	$-0.673917\pi$
$463$	−22.3607	−1.03919	−0.519594	+	0.854413i	$0.673917\pi$
$464$	7.42002	0.344466
$465$	3.24238	0.150362
$466$	−1.12068	−0.0519143
$467$	9.65353	0.446712	0.223356	−	0.974737i	$-0.428299\pi$
$467$	9.65353	0.446712	0.223356	+	0.974737i	$0.428299\pi$
$468$	3.68282	0.170239
$469$	−24.5799	−1.13499
$470$	−3.74232	−0.172621
$471$	17.5846	0.810257
$472$	−13.9973	−0.644280
$473$	3.18985	0.146670
$474$	1.79363	0.0823841
$475$	7.50111	0.344175
$476$	4.23657	0.194183
$477$	−4.10491	−0.187951
$478$	−13.5119	−0.618018
$479$	3.71754	0.169859	0.0849293	−	0.996387i	$-0.472934\pi$
$479$	3.71754	0.169859	0.0849293	+	0.996387i	$0.472934\pi$
$480$	0.874006	0.0398927
$481$	−8.95848	−0.408471
$482$	11.4682	0.522360
$483$	−20.8969	−0.950843
$484$	1.00000	0.0454545
$485$	10.3739	0.471055
$486$	−5.41577	−0.245664
$487$	−11.7142	−0.530819	−0.265409	−	0.964136i	$-0.585507\pi$
$487$	−11.7142	−0.530819	−0.265409	+	0.964136i	$0.585507\pi$
$488$	−7.27665	−0.329398
$489$	1.97310	0.0892269
$490$	0.593072	0.0267922
$491$	−13.7803	−0.621896	−0.310948	−	0.950427i	$-0.600647\pi$
$491$	−13.7803	−0.621896	−0.310948	+	0.950427i	$0.600647\pi$
$492$	−13.4737	−0.607439
$493$	−12.9057	−0.581242
$494$	11.1607	0.502142
$495$	−0.293297	−0.0131827
$496$	3.70979	0.166574
$497$	−12.7304	−0.571039
$498$	−14.3476	−0.642930
$499$	40.7554	1.82446	0.912232	−	0.409675i	$-0.134358\pi$
$499$	40.7554	1.82446	0.912232	+	0.409675i	$0.134358\pi$
$500$	5.38678	0.240904
$501$	−30.8099	−1.37648
$502$	12.4558	0.555930
$503$	−29.4260	−1.31204	−0.656019	−	0.754744i	$-0.727761\pi$
$503$	−29.4260	−1.31204	−0.656019	+	0.754744i	$0.727761\pi$
$504$	1.28525	0.0572495
$505$	−6.28692	−0.279764
$506$	5.45619	0.242557
$507$	−56.1576	−2.49405
$508$	−17.1800	−0.762237
$509$	24.6104	1.09084	0.545419	−	0.838164i	$-0.316371\pi$
$509$	24.6104	1.09084	0.545419	+	0.838164i	$0.316371\pi$
$510$	−1.52016	−0.0673139
$511$	−27.9206	−1.23513
$512$	1.00000	0.0441942
$513$	−8.86948	−0.391597
$514$	−7.73794	−0.341306
$515$	−7.29009	−0.321240
$516$	5.01563	0.220801
$517$	−6.73258	−0.296099
$518$	−3.12637	−0.137365
$519$	−7.96408	−0.349584
$520$	3.87965	0.170134
$521$	−32.8216	−1.43794	−0.718970	−	0.695041i	$-0.755386\pi$
$521$	−32.8216	−1.43794	−0.718970	+	0.695041i	$0.755386\pi$
$522$	−3.91520	−0.171363
$523$	3.96227	0.173258	0.0866291	−	0.996241i	$-0.472391\pi$
$523$	3.96227	0.173258	0.0866291	+	0.996241i	$0.472391\pi$
$524$	12.8193	0.560012
$525$	−17.9664	−0.784119
$526$	21.1152	0.920668
$527$	−6.45245	−0.281073
$528$	1.57237	0.0684286
$529$	6.76996	0.294346
$530$	−4.32429	−0.187835
$531$	7.38574	0.320514
$532$	3.89490	0.168865
$533$	−59.8086	−2.59060
$534$	−5.05072	−0.218566
$535$	4.29371	0.185633
$536$	10.0912	0.435871
$537$	−4.96779	−0.214376
$538$	18.1474	0.782389
$539$	1.06696	0.0459571
$540$	−3.08319	−0.132679
$541$	36.0690	1.55073	0.775364	−	0.631514i	$-0.217566\pi$
$541$	36.0690	1.55073	0.775364	+	0.631514i	$0.217566\pi$
$542$	10.5830	0.454579
$543$	−21.7383	−0.932881
$544$	−1.73931	−0.0745721
$545$	7.84090	0.335867
$546$	−26.7317	−1.14401
$547$	0.395078	0.0168923	0.00844615	−	0.999964i	$-0.497311\pi$
$547$	0.395078	0.0168923	0.00844615	+	0.999964i	$0.497311\pi$
$548$	−16.0182	−0.684265
$549$	3.83954	0.163868
$550$	4.69103	0.200026
$551$	−11.8649	−0.505460
$552$	8.57914	0.365152
$553$	2.77854	0.118155
$554$	−25.4813	−1.08260
$555$	1.12180	0.0476178
$556$	3.71991	0.157760
$557$	13.3932	0.567487	0.283743	−	0.958900i	$-0.408424\pi$
$557$	13.3932	0.567487	0.283743	+	0.958900i	$0.408424\pi$
$558$	−1.95748	−0.0828667
$559$	22.2640	0.941667
$560$	1.35394	0.0572143
$561$	−2.73483	−0.115465
$562$	22.7003	0.957554
$563$	22.1885	0.935135	0.467568	−	0.883957i	$-0.345130\pi$
$563$	22.1885	0.935135	0.467568	+	0.883957i	$0.345130\pi$
$564$	−10.5861	−0.445756
$565$	−1.87122	−0.0787230
$566$	25.7915	1.08410
$567$	17.3881	0.730233
$568$	5.22643	0.219296
$569$	−10.0407	−0.420930	−0.210465	−	0.977601i	$-0.567498\pi$
$569$	−10.0407	−0.420930	−0.210465	+	0.977601i	$0.567498\pi$
$570$	−1.39757	−0.0585376
$571$	−6.17541	−0.258433	−0.129216	−	0.991616i	$-0.541246\pi$
$571$	−6.17541	−0.258433	−0.129216	+	0.991616i	$0.541246\pi$
$572$	6.97963	0.291833
$573$	13.3986	0.559735
$574$	−20.8723	−0.871191
$575$	25.5951	1.06739
$576$	−0.527653	−0.0219855
$577$	−19.0284	−0.792162	−0.396081	−	0.918216i	$-0.629630\pi$
$577$	−19.0284	−0.792162	−0.396081	+	0.918216i	$0.629630\pi$
$578$	−13.9748	−0.581276
$579$	−15.9759	−0.663936
$580$	−4.12444	−0.171258
$581$	−22.2261	−0.922092
$582$	29.3452	1.21640
$583$	−7.77956	−0.322196
$584$	11.4627	0.474329
$585$	−2.04711	−0.0846375
$586$	14.8305	0.612642
$587$	−30.3860	−1.25417	−0.627083	−	0.778953i	$-0.715751\pi$
$587$	−30.3860	−1.25417	−0.627083	+	0.778953i	$0.715751\pi$
$588$	1.67765	0.0691852
$589$	−5.93207	−0.244427
$590$	7.78046	0.320317
$591$	1.57237	0.0646787
$592$	1.28352	0.0527522
$593$	−14.0748	−0.577981	−0.288991	−	0.957332i	$-0.593320\pi$
$593$	−14.0748	−0.577981	−0.288991	+	0.957332i	$0.593320\pi$
$594$	−5.54678	−0.227587
$595$	−2.35491	−0.0965419
$596$	−8.50130	−0.348227
$597$	−26.1696	−1.07105
$598$	38.0822	1.55730
$599$	20.1810	0.824574	0.412287	−	0.911054i	$-0.364730\pi$
$599$	20.1810	0.824574	0.412287	+	0.911054i	$0.364730\pi$
$600$	7.37603	0.301125
$601$	29.1048	1.18721	0.593604	−	0.804757i	$-0.297704\pi$
$601$	29.1048	1.18721	0.593604	+	0.804757i	$0.297704\pi$
$602$	7.76979	0.316673
$603$	−5.32463	−0.216836
$604$	−21.5314	−0.876101
$605$	−0.555853	−0.0225986
$606$	−17.7841	−0.722431
$607$	35.9682	1.45990	0.729952	−	0.683499i	$-0.239542\pi$
$607$	35.9682	1.45990	0.729952	+	0.683499i	$0.239542\pi$
$608$	−1.59903	−0.0648494
$609$	28.4183	1.15157
$610$	4.04474	0.163767
$611$	−46.9910	−1.90105
$612$	0.917750	0.0370978
$613$	−4.00930	−0.161934	−0.0809671	−	0.996717i	$-0.525801\pi$
$613$	−4.00930	−0.161934	−0.0809671	+	0.996717i	$0.525801\pi$
$614$	−3.86391	−0.155935
$615$	7.48937	0.302001
$616$	2.43578	0.0981405
$617$	16.1163	0.648817	0.324408	−	0.945917i	$-0.394835\pi$
$617$	16.1163	0.648817	0.324408	+	0.945917i	$0.394835\pi$
$618$	−20.6219	−0.829533
$619$	−19.2428	−0.773435	−0.386718	−	0.922198i	$-0.626391\pi$
$619$	−19.2428	−0.773435	−0.386718	+	0.922198i	$0.626391\pi$
$620$	−2.06209	−0.0828157
$621$	−30.2642	−1.21446
$622$	−14.2591	−0.571740
$623$	−7.82416	−0.313468
$624$	10.9746	0.439334
$625$	20.4609	0.818435
$626$	−22.4119	−0.895758
$627$	−2.51427	−0.100410
$628$	−11.1835	−0.446271
$629$	−2.23243	−0.0890127
$630$	−0.714409	−0.0284627
$631$	26.2131	1.04353	0.521763	−	0.853090i	$-0.325275\pi$
$631$	26.2131	1.04353	0.521763	+	0.853090i	$0.325275\pi$
$632$	−1.14072	−0.0453753
$633$	−42.7344	−1.69854
$634$	−31.0887	−1.23469
$635$	9.54952	0.378961
$636$	−12.2323	−0.485044
$637$	7.44697	0.295060
$638$	−7.42002	−0.293761
$639$	−2.75774	−0.109095
$640$	−0.555853	−0.0219720
$641$	−22.7926	−0.900254	−0.450127	−	0.892965i	$-0.648621\pi$
$641$	−22.7926	−0.900254	−0.450127	+	0.892965i	$0.648621\pi$
$642$	12.1458	0.479358
$643$	10.2388	0.403779	0.201889	−	0.979408i	$-0.435292\pi$
$643$	10.2388	0.403779	0.201889	+	0.979408i	$0.435292\pi$
$644$	13.2901	0.523703
$645$	−2.78795	−0.109775
$646$	2.78121	0.109425
$647$	−5.78184	−0.227308	−0.113654	−	0.993520i	$-0.536255\pi$
$647$	−5.78184	−0.227308	−0.113654	+	0.993520i	$0.536255\pi$
$648$	−7.13862	−0.280432
$649$	13.9973	0.549444
$650$	32.7416	1.28423
$651$	14.2083	0.556867
$652$	−1.25486	−0.0491441
$653$	−7.11975	−0.278617	−0.139309	−	0.990249i	$-0.544488\pi$
$653$	−7.11975	−0.278617	−0.139309	+	0.990249i	$0.544488\pi$
$654$	22.1800	0.867306
$655$	−7.12562	−0.278421
$656$	8.56901	0.334564
$657$	−6.04831	−0.235967
$658$	−16.3991	−0.639304
$659$	−18.7447	−0.730188	−0.365094	−	0.930971i	$-0.618963\pi$
$659$	−18.7447	−0.730188	−0.365094	+	0.930971i	$0.618963\pi$
$660$	−0.874006	−0.0340206
$661$	27.3118	1.06231	0.531153	−	0.847276i	$-0.321759\pi$
$661$	27.3118	1.06231	0.531153	+	0.847276i	$0.321759\pi$
$662$	33.3741	1.29712
$663$	−19.0881	−0.741321
$664$	9.12481	0.354111
$665$	−2.16499	−0.0839547
$666$	−0.677252	−0.0262430
$667$	−40.4850	−1.56758
$668$	19.5945	0.758136
$669$	6.76195	0.261432
$670$	−5.60919	−0.216702
$671$	7.27665	0.280912
$672$	3.82995	0.147744
$673$	23.3017	0.898214	0.449107	−	0.893478i	$-0.351742\pi$
$673$	23.3017	0.898214	0.449107	+	0.893478i	$0.351742\pi$
$674$	11.2321	0.432646
$675$	−26.0201	−1.00151
$676$	35.7153	1.37366
$677$	38.7765	1.49030	0.745150	−	0.666896i	$-0.232378\pi$
$677$	38.7765	1.49030	0.745150	+	0.666896i	$0.232378\pi$
$678$	−5.29323	−0.203285
$679$	45.4592	1.74456
$680$	0.966797	0.0370750
$681$	7.34734	0.281551
$682$	−3.70979	−0.142055
$683$	47.6844	1.82459	0.912296	−	0.409532i	$-0.134308\pi$
$683$	47.6844	1.82459	0.912296	+	0.409532i	$0.134308\pi$
$684$	0.843735	0.0322610
$685$	8.90378	0.340196
$686$	19.6494	0.750216
$687$	17.9503	0.684845
$688$	−3.18985	−0.121612
$689$	−54.2984	−2.06861
$690$	−4.76874	−0.181543
$691$	47.8046	1.81857	0.909286	−	0.416172i	$-0.136629\pi$
$691$	47.8046	1.81857	0.909286	+	0.416172i	$0.136629\pi$
$692$	5.06502	0.192543
$693$	−1.28525	−0.0488226
$694$	−27.4964	−1.04375
$695$	−2.06772	−0.0784333
$696$	−11.6670	−0.442237
$697$	−14.9041	−0.564534
$698$	7.18445	0.271935
$699$	1.76212	0.0666494
$700$	11.4263	0.431875
$701$	−20.8957	−0.789222	−0.394611	−	0.918848i	$-0.629121\pi$
$701$	−20.8957	−0.789222	−0.394611	+	0.918848i	$0.629121\pi$
$702$	−38.7144	−1.46118
$703$	−2.05239	−0.0774072
$704$	−1.00000	−0.0376889
$705$	5.88432	0.221616
$706$	11.3402	0.426795
$707$	−27.5497	−1.03611
$708$	22.0090	0.827149
$709$	−28.0755	−1.05440	−0.527198	−	0.849742i	$-0.676758\pi$
$709$	−28.0755	−1.05440	−0.527198	+	0.849742i	$0.676758\pi$
$710$	−2.90512	−0.109027
$711$	0.601903	0.0225731
$712$	3.21217	0.120381
$713$	−20.2413	−0.758042
$714$	−6.66146	−0.249299
$715$	−3.87965	−0.145091
$716$	3.15943	0.118073
$717$	21.2456	0.793433
$718$	30.8915	1.15286
$719$	13.3536	0.498007	0.249003	−	0.968503i	$-0.419897\pi$
$719$	13.3536	0.498007	0.249003	+	0.968503i	$0.419897\pi$
$720$	0.293297	0.0109305
$721$	−31.9457	−1.18972
$722$	−16.4431	−0.611948
$723$	−18.0322	−0.670624
$724$	13.8252	0.513810
$725$	−34.8075	−1.29272
$726$	−1.57237	−0.0583561
$727$	31.5300	1.16938	0.584691	−	0.811256i	$-0.301216\pi$
$727$	31.5300	1.16938	0.584691	+	0.811256i	$0.301216\pi$
$728$	17.0009	0.630094
$729$	29.9315	1.10857
$730$	−6.37155	−0.235822
$731$	5.54813	0.205205
$732$	11.4416	0.422893
$733$	−8.34073	−0.308072	−0.154036	−	0.988065i	$-0.549227\pi$
$733$	−8.34073	−0.308072	−0.154036	+	0.988065i	$0.549227\pi$
$734$	−1.05473	−0.0389309
$735$	−0.932528	−0.0343968
$736$	−5.45619	−0.201118
$737$	−10.0912	−0.371712
$738$	−4.52147	−0.166438
$739$	26.5328	0.976025	0.488013	−	0.872837i	$-0.337722\pi$
$739$	26.5328	0.976025	0.488013	+	0.872837i	$0.337722\pi$
$740$	−0.713446	−0.0262268
$741$	−17.5487	−0.644667
$742$	−18.9493	−0.695651
$743$	25.5488	0.937294	0.468647	−	0.883386i	$-0.344742\pi$
$743$	25.5488	0.937294	0.468647	+	0.883386i	$0.344742\pi$
$744$	−5.83316	−0.213854
$745$	4.72547	0.173128
$746$	−14.9993	−0.549163
$747$	−4.81473	−0.176162
$748$	1.73931	0.0635953
$749$	18.8153	0.687497
$750$	−8.47002	−0.309281
$751$	−43.1390	−1.57416	−0.787082	−	0.616849i	$-0.788409\pi$
$751$	−43.1390	−1.57416	−0.787082	+	0.616849i	$0.788409\pi$
$752$	6.73258	0.245512
$753$	−19.5851	−0.713723
$754$	−51.7890	−1.88604
$755$	11.9683	0.435571
$756$	−13.5107	−0.491381
$757$	−21.0190	−0.763949	−0.381974	−	0.924173i	$-0.624756\pi$
$757$	−21.0190	−0.763949	−0.381974	+	0.924173i	$0.624756\pi$
$758$	1.16255	0.0422257
$759$	−8.57914	−0.311403
$760$	0.888827	0.0322412
$761$	−9.13320	−0.331078	−0.165539	−	0.986203i	$-0.552936\pi$
$761$	−9.13320	−0.331078	−0.165539	+	0.986203i	$0.552936\pi$
$762$	27.0132	0.978586
$763$	34.3594	1.24389
$764$	−8.52129	−0.308289
$765$	−0.510134	−0.0184439
$766$	4.37742	0.158163
$767$	97.6963	3.52761
$768$	−1.57237	−0.0567380
$769$	−15.8117	−0.570185	−0.285093	−	0.958500i	$-0.592024\pi$
$769$	−15.8117	−0.570185	−0.285093	+	0.958500i	$0.592024\pi$
$770$	−1.35394	−0.0487925
$771$	12.1669	0.438180
$772$	10.1604	0.365681
$773$	2.94452	0.105907	0.0529535	−	0.998597i	$-0.483136\pi$
$773$	2.94452	0.105907	0.0529535	+	0.998597i	$0.483136\pi$
$774$	1.68314	0.0604991
$775$	−17.4027	−0.625124
$776$	−18.6631	−0.669965
$777$	4.91581	0.176354
$778$	24.8469	0.890804
$779$	−13.7021	−0.490930
$780$	−6.10024	−0.218424
$781$	−5.22643	−0.187016
$782$	9.48997	0.339361
$783$	41.1572	1.47084
$784$	−1.06696	−0.0381056
$785$	6.21639	0.221872
$786$	−20.1566	−0.718963
$787$	32.5203	1.15922	0.579612	−	0.814892i	$-0.303204\pi$
$787$	32.5203	1.15922	0.579612	+	0.814892i	$0.303204\pi$
$788$	−1.00000	−0.0356235
$789$	−33.2009	−1.18198
$790$	0.634070	0.0225592
$791$	−8.19983	−0.291552
$792$	0.527653	0.0187493
$793$	50.7883	1.80355
$794$	−31.3019	−1.11086
$795$	6.79938	0.241149
$796$	16.6434	0.589911
$797$	−5.08540	−0.180134	−0.0900670	−	0.995936i	$-0.528708\pi$
$797$	−5.08540	−0.180134	−0.0900670	+	0.995936i	$0.528708\pi$
$798$	−6.12422	−0.216795
$799$	−11.7100	−0.414271
$800$	−4.69103	−0.165853
$801$	−1.69491	−0.0598868
$802$	23.4039	0.826420
$803$	−11.4627	−0.404509
$804$	−15.8670	−0.559587
$805$	−7.38733	−0.260369
$806$	−25.8929	−0.912040
$807$	−28.5344	−1.00446
$808$	11.3104	0.397899
$809$	−29.6899	−1.04384	−0.521921	−	0.852994i	$-0.674784\pi$
$809$	−29.6899	−1.04384	−0.521921	+	0.852994i	$0.674784\pi$
$810$	3.96802	0.139422
$811$	−29.1441	−1.02339	−0.511694	−	0.859168i	$-0.670982\pi$
$811$	−29.1441	−1.02339	−0.511694	+	0.859168i	$0.670982\pi$
$812$	−18.0736	−0.634257
$813$	−16.6404	−0.583605
$814$	−1.28352	−0.0449872
$815$	0.697517	0.0244330
$816$	2.73483	0.0957382
$817$	5.10068	0.178450
$818$	−14.0078	−0.489771
$819$	−8.97056	−0.313457
$820$	−4.76311	−0.166335
$821$	24.0105	0.837971	0.418985	−	0.907993i	$-0.362386\pi$
$821$	24.0105	0.837971	0.418985	+	0.907993i	$0.362386\pi$
$822$	25.1866	0.878483
$823$	16.2676	0.567052	0.283526	−	0.958965i	$-0.408496\pi$
$823$	16.2676	0.567052	0.283526	+	0.958965i	$0.408496\pi$
$824$	13.1151	0.456888
$825$	−7.37603	−0.256800
$826$	34.0945	1.18630
$827$	−35.4540	−1.23286	−0.616429	−	0.787411i	$-0.711421\pi$
$827$	−35.4540	−1.23286	−0.616429	+	0.787411i	$0.711421\pi$
$828$	2.87897	0.100051
$829$	44.2302	1.53618	0.768088	−	0.640344i	$-0.221208\pi$
$829$	44.2302	1.53618	0.768088	+	0.640344i	$0.221208\pi$
$830$	−5.07205	−0.176053
$831$	40.0661	1.38988
$832$	−6.97963	−0.241975
$833$	1.85577	0.0642985
$834$	−5.84908	−0.202537
$835$	−10.8917	−0.376922
$836$	1.59903	0.0553037
$837$	20.5773	0.711257
$838$	12.2243	0.422281
$839$	−43.8078	−1.51241	−0.756207	−	0.654332i	$-0.772950\pi$
$839$	−43.8078	−1.51241	−0.756207	+	0.654332i	$0.772950\pi$
$840$	−2.12889	−0.0734537
$841$	26.0567	0.898505
$842$	−17.4150	−0.600161
$843$	−35.6933	−1.22934
$844$	27.1783	0.935517
$845$	−19.8524	−0.682944
$846$	−3.55247	−0.122136
$847$	−2.43578	−0.0836945
$848$	7.77956	0.267151
$849$	−40.5538	−1.39180
$850$	8.15913	0.279856
$851$	−7.00311	−0.240063
$852$	−8.21788	−0.281540
$853$	−5.37841	−0.184153	−0.0920766	−	0.995752i	$-0.529350\pi$
$853$	−5.37841	−0.184153	−0.0920766	+	0.995752i	$0.529350\pi$
$854$	17.7243	0.606514
$855$	−0.468993	−0.0160392
$856$	−7.72454	−0.264019
$857$	−41.4167	−1.41477	−0.707384	−	0.706829i	$-0.750125\pi$
$857$	−41.4167	−1.41477	−0.707384	+	0.706829i	$0.750125\pi$
$858$	−10.9746	−0.374665
$859$	−1.22743	−0.0418795	−0.0209398	−	0.999781i	$-0.506666\pi$
$859$	−1.22743	−0.0418795	−0.0209398	+	0.999781i	$0.506666\pi$
$860$	1.77309	0.0604618
$861$	32.8189	1.11847
$862$	15.7223	0.535502
$863$	−24.5686	−0.836323	−0.418162	−	0.908373i	$-0.637325\pi$
$863$	−24.5686	−0.836323	−0.418162	+	0.908373i	$0.637325\pi$
$864$	5.54678	0.188705
$865$	−2.81540	−0.0957266
$866$	−26.5707	−0.902908
$867$	21.9736	0.746262
$868$	−9.03624	−0.306710
$869$	1.14072	0.0386961
$870$	6.48514	0.219867
$871$	−70.4325	−2.38651
$872$	−14.1061	−0.477692
$873$	9.84762	0.333291
$874$	8.72462	0.295115
$875$	−13.1210	−0.443572
$876$	−18.0236	−0.608959
$877$	−37.9608	−1.28185	−0.640923	−	0.767605i	$-0.721448\pi$
$877$	−37.9608	−1.28185	−0.640923	+	0.767605i	$0.721448\pi$
$878$	31.5571	1.06500
$879$	−23.3190	−0.786531
$880$	0.555853	0.0187378
$881$	−15.3064	−0.515684	−0.257842	−	0.966187i	$-0.583011\pi$
$881$	−15.3064	−0.515684	−0.257842	+	0.966187i	$0.583011\pi$
$882$	0.562984	0.0189567
$883$	43.9403	1.47871	0.739354	−	0.673317i	$-0.235131\pi$
$883$	43.9403	1.47871	0.739354	+	0.673317i	$0.235131\pi$
$884$	12.1397	0.408303
$885$	−12.2338	−0.411233
$886$	−6.38606	−0.214544
$887$	49.2443	1.65346	0.826730	−	0.562598i	$-0.190198\pi$
$887$	49.2443	1.65346	0.826730	+	0.562598i	$0.190198\pi$
$888$	−2.01816	−0.0677251
$889$	41.8466	1.40349
$890$	−1.78549	−0.0598499
$891$	7.13862	0.239153
$892$	−4.30048	−0.143991
$893$	−10.7656	−0.360258
$894$	13.3672	0.447066
$895$	−1.75618	−0.0587025
$896$	−2.43578	−0.0813738
$897$	−59.8792	−1.99931
$898$	15.9926	0.533678
$899$	27.5267	0.918066
$900$	2.47524	0.0825079
$901$	−13.5310	−0.450784
$902$	−8.56901	−0.285317
$903$	−12.2170	−0.406556
$904$	3.36640	0.111965
$905$	−7.68478	−0.255451
$906$	33.8554	1.12477
$907$	−55.7833	−1.85226	−0.926128	−	0.377211i	$-0.876883\pi$
$907$	−55.7833	−1.85226	−0.926128	+	0.377211i	$0.876883\pi$
$908$	−4.67278	−0.155072
$909$	−5.96797	−0.197945
$910$	−9.44998	−0.313264
$911$	12.4608	0.412844	0.206422	−	0.978463i	$-0.433818\pi$
$911$	12.4608	0.412844	0.206422	+	0.978463i	$0.433818\pi$
$912$	2.51427	0.0832559
$913$	−9.12481	−0.301987
$914$	−26.5483	−0.878139
$915$	−6.35983	−0.210250
$916$	−11.4160	−0.377197
$917$	−31.2250	−1.03114
$918$	−9.64753	−0.318416
$919$	6.18741	0.204104	0.102052	−	0.994779i	$-0.467459\pi$
$919$	6.18741	0.204104	0.102052	+	0.994779i	$0.467459\pi$
$920$	3.03284	0.0999896
$921$	6.07549	0.200194
$922$	−16.0157	−0.527449
$923$	−36.4785	−1.20071
$924$	−3.82995	−0.125996
$925$	−6.02101	−0.197970
$926$	−22.3607	−0.734817
$927$	−6.92025	−0.227291
$928$	7.42002	0.243574
$929$	−59.8343	−1.96310	−0.981549	−	0.191210i	$-0.938759\pi$
$929$	−59.8343	−1.96310	−0.981549	+	0.191210i	$0.938759\pi$
$930$	3.24238	0.106322
$931$	1.70610	0.0559152
$932$	−1.12068	−0.0367089
$933$	22.4207	0.734019
$934$	9.65353	0.315873
$935$	−0.966797	−0.0316177
$936$	3.68282	0.120377
$937$	−60.0677	−1.96233	−0.981163	−	0.193182i	$-0.938119\pi$
$937$	−60.0677	−1.96233	−0.981163	+	0.193182i	$0.938119\pi$
$938$	−24.5799	−0.802561
$939$	35.2397	1.15000
$940$	−3.74232	−0.122061
$941$	−50.8162	−1.65656	−0.828280	−	0.560314i	$-0.810680\pi$
$941$	−50.8162	−1.65656	−0.828280	+	0.560314i	$0.810680\pi$
$942$	17.5846	0.572938
$943$	−46.7541	−1.52252
$944$	−13.9973	−0.455575
$945$	7.50998	0.244300
$946$	3.18985	0.103711
$947$	−45.2005	−1.46882	−0.734409	−	0.678707i	$-0.762541\pi$
$947$	−45.2005	−1.46882	−0.734409	+	0.678707i	$0.762541\pi$
$948$	1.79363	0.0582543
$949$	−80.0052	−2.59708
$950$	7.50111	0.243368
$951$	48.8829	1.58514
$952$	4.23657	0.137308
$953$	6.91715	0.224069	0.112034	−	0.993704i	$-0.464263\pi$
$953$	6.91715	0.224069	0.112034	+	0.993704i	$0.464263\pi$
$954$	−4.10491	−0.132901
$955$	4.73658	0.153272
$956$	−13.5119	−0.437005
$957$	11.6670	0.377141
$958$	3.71754	0.120108
$959$	39.0170	1.25992
$960$	0.874006	0.0282084
$961$	−17.2375	−0.556048
$962$	−8.95848	−0.288833
$963$	4.07588	0.131343
$964$	11.4682	0.369365
$965$	−5.64769	−0.181806
$966$	−20.8969	−0.672348
$967$	25.3937	0.816606	0.408303	−	0.912846i	$-0.366121\pi$
$967$	25.3937	0.816606	0.408303	+	0.912846i	$0.366121\pi$
$968$	1.00000	0.0321412
$969$	−4.37309	−0.140484
$970$	10.3739	0.333086
$971$	−13.0399	−0.418469	−0.209235	−	0.977865i	$-0.567097\pi$
$971$	−13.0399	−0.418469	−0.209235	+	0.977865i	$0.567097\pi$
$972$	−5.41577	−0.173711
$973$	−9.06091	−0.290479
$974$	−11.7142	−0.375346
$975$	−51.4820	−1.64874
$976$	−7.27665	−0.232920
$977$	60.3991	1.93234	0.966170	−	0.257907i	$-0.0830330\pi$
$977$	60.3991	1.93234	0.966170	+	0.257907i	$0.0830330\pi$
$978$	1.97310	0.0630929
$979$	−3.21217	−0.102661
$980$	0.593072	0.0189450
$981$	7.44312	0.237641
$982$	−13.7803	−0.439747
$983$	−13.4538	−0.429109	−0.214554	−	0.976712i	$-0.568830\pi$
$983$	−13.4538	−0.429109	−0.214554	+	0.976712i	$0.568830\pi$
$984$	−13.4737	−0.429525
$985$	0.555853	0.0177109
$986$	−12.9057	−0.411000
$987$	25.7855	0.820761
$988$	11.1607	0.355068
$989$	17.4044	0.553429
$990$	−0.293297	−0.00932160
$991$	0.184197	0.00585122	0.00292561	−	0.999996i	$-0.499069\pi$
$991$	0.184197	0.00585122	0.00292561	+	0.999996i	$0.499069\pi$
$992$	3.70979	0.117786
$993$	−52.4764	−1.66529
$994$	−12.7304	−0.403785
$995$	−9.25130	−0.293286
$996$	−14.3476	−0.454620
$997$	46.2359	1.46431	0.732153	−	0.681140i	$-0.238516\pi$
$997$	46.2359	1.46431	0.732153	+	0.681140i	$0.238516\pi$
$998$	40.7554	1.29009
$999$	7.11938	0.225247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.7	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.57237 q^{3} +1.00000 q^{4} -0.555853 q^{5} -1.57237 q^{6} -2.43578 q^{7} +1.00000 q^{8} -0.527653 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.57237 q^{3} +1.00000 q^{4} -0.555853 q^{5} -1.57237 q^{6} -2.43578 q^{7} +1.00000 q^{8} -0.527653 q^{9} -0.555853 q^{10} -1.00000 q^{11} -1.57237 q^{12} -6.97963 q^{13} -2.43578 q^{14} +0.874006 q^{15} +1.00000 q^{16} -1.73931 q^{17} -0.527653 q^{18} -1.59903 q^{19} -0.555853 q^{20} +3.82995 q^{21} -1.00000 q^{22} -5.45619 q^{23} -1.57237 q^{24} -4.69103 q^{25} -6.97963 q^{26} +5.54678 q^{27} -2.43578 q^{28} +7.42002 q^{29} +0.874006 q^{30} +3.70979 q^{31} +1.00000 q^{32} +1.57237 q^{33} -1.73931 q^{34} +1.35394 q^{35} -0.527653 q^{36} +1.28352 q^{37} -1.59903 q^{38} +10.9746 q^{39} -0.555853 q^{40} +8.56901 q^{41} +3.82995 q^{42} -3.18985 q^{43} -1.00000 q^{44} +0.293297 q^{45} -5.45619 q^{46} +6.73258 q^{47} -1.57237 q^{48} -1.06696 q^{49} -4.69103 q^{50} +2.73483 q^{51} -6.97963 q^{52} +7.77956 q^{53} +5.54678 q^{54} +0.555853 q^{55} -2.43578 q^{56} +2.51427 q^{57} +7.42002 q^{58} -13.9973 q^{59} +0.874006 q^{60} -7.27665 q^{61} +3.70979 q^{62} +1.28525 q^{63} +1.00000 q^{64} +3.87965 q^{65} +1.57237 q^{66} +10.0912 q^{67} -1.73931 q^{68} +8.57914 q^{69} +1.35394 q^{70} +5.22643 q^{71} -0.527653 q^{72} +11.4627 q^{73} +1.28352 q^{74} +7.37603 q^{75} -1.59903 q^{76} +2.43578 q^{77} +10.9746 q^{78} -1.14072 q^{79} -0.555853 q^{80} -7.13862 q^{81} +8.56901 q^{82} +9.12481 q^{83} +3.82995 q^{84} +0.966797 q^{85} -3.18985 q^{86} -11.6670 q^{87} -1.00000 q^{88} +3.21217 q^{89} +0.293297 q^{90} +17.0009 q^{91} -5.45619 q^{92} -5.83316 q^{93} +6.73258 q^{94} +0.888827 q^{95} -1.57237 q^{96} -18.6631 q^{97} -1.06696 q^{98} +0.527653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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