LMFDB - Embedded newform 6001.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39289 q^{2} -2.96659 q^{3} +3.72594 q^{4} +3.31044 q^{5} +7.09873 q^{6} +0.664206 q^{7} -4.12999 q^{8} +5.80065 q^{9} +O(q^{10})$	\(q-2.39289 q^{2} -2.96659 q^{3} +3.72594 q^{4} +3.31044 q^{5} +7.09873 q^{6} +0.664206 q^{7} -4.12999 q^{8} +5.80065 q^{9} -7.92153 q^{10} +1.52127 q^{11} -11.0533 q^{12} -4.57960 q^{13} -1.58938 q^{14} -9.82071 q^{15} +2.43075 q^{16} +1.00000 q^{17} -13.8803 q^{18} -7.18664 q^{19} +12.3345 q^{20} -1.97043 q^{21} -3.64025 q^{22} +7.41494 q^{23} +12.2520 q^{24} +5.95900 q^{25} +10.9585 q^{26} -8.30836 q^{27} +2.47479 q^{28} +0.513282 q^{29} +23.4999 q^{30} -6.03318 q^{31} +2.44345 q^{32} -4.51299 q^{33} -2.39289 q^{34} +2.19881 q^{35} +21.6129 q^{36} +0.496483 q^{37} +17.1969 q^{38} +13.5858 q^{39} -13.6721 q^{40} -1.38303 q^{41} +4.71502 q^{42} +10.6191 q^{43} +5.66818 q^{44} +19.2027 q^{45} -17.7432 q^{46} +3.44692 q^{47} -7.21104 q^{48} -6.55883 q^{49} -14.2593 q^{50} -2.96659 q^{51} -17.0633 q^{52} +7.55815 q^{53} +19.8810 q^{54} +5.03608 q^{55} -2.74317 q^{56} +21.3198 q^{57} -1.22823 q^{58} -10.6847 q^{59} -36.5914 q^{60} +5.41605 q^{61} +14.4367 q^{62} +3.85283 q^{63} -10.7084 q^{64} -15.1605 q^{65} +10.7991 q^{66} -12.4063 q^{67} +3.72594 q^{68} -21.9971 q^{69} -5.26153 q^{70} +3.25374 q^{71} -23.9566 q^{72} -2.96888 q^{73} -1.18803 q^{74} -17.6779 q^{75} -26.7770 q^{76} +1.01044 q^{77} -32.5094 q^{78} -9.14033 q^{79} +8.04686 q^{80} +7.24556 q^{81} +3.30944 q^{82} -6.20141 q^{83} -7.34170 q^{84} +3.31044 q^{85} -25.4103 q^{86} -1.52270 q^{87} -6.28285 q^{88} +8.10180 q^{89} -45.9500 q^{90} -3.04180 q^{91} +27.6276 q^{92} +17.8979 q^{93} -8.24812 q^{94} -23.7909 q^{95} -7.24872 q^{96} +7.46187 q^{97} +15.6946 q^{98} +8.82437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.39289	−1.69203	−0.846016	−	0.533158i	$-0.821005\pi$
$2$	−2.39289	−1.69203	−0.846016	+	0.533158i	$0.821005\pi$
$3$	−2.96659	−1.71276	−0.856380	−	0.516346i	$-0.827292\pi$
$3$	−2.96659	−1.71276	−0.856380	+	0.516346i	$0.827292\pi$
$4$	3.72594	1.86297
$5$	3.31044	1.48047	0.740236	−	0.672347i	$-0.234714\pi$
$5$	3.31044	1.48047	0.740236	+	0.672347i	$0.234714\pi$
$6$	7.09873	2.89804
$7$	0.664206	0.251046	0.125523	−	0.992091i	$-0.459939\pi$
$7$	0.664206	0.251046	0.125523	+	0.992091i	$0.459939\pi$
$8$	−4.12999	−1.46017
$9$	5.80065	1.93355
$10$	−7.92153	−2.50501
$11$	1.52127	0.458681	0.229341	−	0.973346i	$-0.426343\pi$
$11$	1.52127	0.458681	0.229341	+	0.973346i	$0.426343\pi$
$12$	−11.0533	−3.19082
$13$	−4.57960	−1.27015	−0.635077	−	0.772449i	$-0.719031\pi$
$13$	−4.57960	−1.27015	−0.635077	+	0.772449i	$0.719031\pi$
$14$	−1.58938	−0.424778
$15$	−9.82071	−2.53570
$16$	2.43075	0.607688
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−13.8803	−3.27163
$19$	−7.18664	−1.64873	−0.824364	−	0.566060i	$-0.808467\pi$
$19$	−7.18664	−1.64873	−0.824364	+	0.566060i	$0.808467\pi$
$20$	12.3345	2.75808
$21$	−1.97043	−0.429982
$22$	−3.64025	−0.776103
$23$	7.41494	1.54612	0.773061	−	0.634332i	$-0.218725\pi$
$23$	7.41494	1.54612	0.773061	+	0.634332i	$0.218725\pi$
$24$	12.2520	2.50093
$25$	5.95900	1.19180
$26$	10.9585	2.14914
$27$	−8.30836	−1.59895
$28$	2.47479	0.467692
$29$	0.513282	0.0953141	0.0476571	−	0.998864i	$-0.484825\pi$
$29$	0.513282	0.0953141	0.0476571	+	0.998864i	$0.484825\pi$
$30$	23.4999	4.29048
$31$	−6.03318	−1.08359	−0.541795	−	0.840511i	$-0.682255\pi$
$31$	−6.03318	−1.08359	−0.541795	+	0.840511i	$0.682255\pi$
$32$	2.44345	0.431945
$33$	−4.51299	−0.785611
$34$	−2.39289	−0.410378
$35$	2.19881	0.371667
$36$	21.6129	3.60214
$37$	0.496483	0.0816214	0.0408107	−	0.999167i	$-0.487006\pi$
$37$	0.496483	0.0816214	0.0408107	+	0.999167i	$0.487006\pi$
$38$	17.1969	2.78970
$39$	13.5858	2.17547
$40$	−13.6721	−2.16175
$41$	−1.38303	−0.215993	−0.107996	−	0.994151i	$-0.534443\pi$
$41$	−1.38303	−0.215993	−0.107996	+	0.994151i	$0.534443\pi$
$42$	4.71502	0.727544
$43$	10.6191	1.61939	0.809695	−	0.586851i	$-0.199633\pi$
$43$	10.6191	1.61939	0.809695	+	0.586851i	$0.199633\pi$
$44$	5.66818	0.854510
$45$	19.2027	2.86257
$46$	−17.7432	−2.61609
$47$	3.44692	0.502786	0.251393	−	0.967885i	$-0.419111\pi$
$47$	3.44692	0.502786	0.251393	+	0.967885i	$0.419111\pi$
$48$	−7.21104	−1.04082
$49$	−6.55883	−0.936976
$50$	−14.2593	−2.01656
$51$	−2.96659	−0.415405
$52$	−17.0633	−2.36626
$53$	7.55815	1.03819	0.519096	−	0.854716i	$-0.326269\pi$
$53$	7.55815	1.03819	0.519096	+	0.854716i	$0.326269\pi$
$54$	19.8810	2.70547
$55$	5.03608	0.679065
$56$	−2.74317	−0.366571
$57$	21.3198	2.82388
$58$	−1.22823	−0.161274
$59$	−10.6847	−1.39102	−0.695512	−	0.718514i	$-0.744822\pi$
$59$	−10.6847	−1.39102	−0.695512	+	0.718514i	$0.744822\pi$
$60$	−36.5914	−4.72393
$61$	5.41605	0.693455	0.346727	−	0.937966i	$-0.387293\pi$
$61$	5.41605	0.693455	0.346727	+	0.937966i	$0.387293\pi$
$62$	14.4367	1.83347
$63$	3.85283	0.485411
$64$	−10.7084	−1.33855
$65$	−15.1605	−1.88043
$66$	10.7991	1.32928
$67$	−12.4063	−1.51567	−0.757834	−	0.652447i	$-0.773742\pi$
$67$	−12.4063	−1.51567	−0.757834	+	0.652447i	$0.773742\pi$
$68$	3.72594	0.451837
$69$	−21.9971	−2.64814
$70$	−5.26153	−0.628873
$71$	3.25374	0.386148	0.193074	−	0.981184i	$-0.438154\pi$
$71$	3.25374	0.386148	0.193074	+	0.981184i	$0.438154\pi$
$72$	−23.9566	−2.82332
$73$	−2.96888	−0.347482	−0.173741	−	0.984791i	$-0.555585\pi$
$73$	−2.96888	−0.347482	−0.173741	+	0.984791i	$0.555585\pi$
$74$	−1.18803	−0.138106
$75$	−17.6779	−2.04127
$76$	−26.7770	−3.07153
$77$	1.01044	0.115150
$78$	−32.5094	−3.68096
$79$	−9.14033	−1.02837	−0.514184	−	0.857680i	$-0.671905\pi$
$79$	−9.14033	−1.02837	−0.514184	+	0.857680i	$0.671905\pi$
$80$	8.04686	0.899666
$81$	7.24556	0.805062
$82$	3.30944	0.365466
$83$	−6.20141	−0.680694	−0.340347	−	0.940300i	$-0.610544\pi$
$83$	−6.20141	−0.680694	−0.340347	+	0.940300i	$0.610544\pi$
$84$	−7.34170	−0.801045
$85$	3.31044	0.359067
$86$	−25.4103	−2.74006
$87$	−1.52270	−0.163250
$88$	−6.28285	−0.669754
$89$	8.10180	0.858789	0.429394	−	0.903117i	$-0.358727\pi$
$89$	8.10180	0.858789	0.429394	+	0.903117i	$0.358727\pi$
$90$	−45.9500	−4.84355
$91$	−3.04180	−0.318867
$92$	27.6276	2.88038
$93$	17.8979	1.85593
$94$	−8.24812	−0.850729
$95$	−23.7909	−2.44090
$96$	−7.24872	−0.739819
$97$	7.46187	0.757638	0.378819	−	0.925471i	$-0.376330\pi$
$97$	7.46187	0.757638	0.378819	+	0.925471i	$0.376330\pi$
$98$	15.6946	1.58539
$99$	8.82437	0.886883
$100$	22.2029	2.22029
$101$	−8.55186	−0.850942	−0.425471	−	0.904972i	$-0.639891\pi$
$101$	−8.55186	−0.850942	−0.425471	+	0.904972i	$0.639891\pi$
$102$	7.09873	0.702879
$103$	−12.4538	−1.22711	−0.613553	−	0.789654i	$-0.710260\pi$
$103$	−12.4538	−1.22711	−0.613553	+	0.789654i	$0.710260\pi$
$104$	18.9137	1.85464
$105$	−6.52298	−0.636577
$106$	−18.0859	−1.75665
$107$	14.0075	1.35415	0.677077	−	0.735912i	$-0.263246\pi$
$107$	14.0075	1.35415	0.677077	+	0.735912i	$0.263246\pi$
$108$	−30.9565	−2.97879
$109$	19.0845	1.82797	0.913983	−	0.405752i	$-0.132990\pi$
$109$	19.0845	1.82797	0.913983	+	0.405752i	$0.132990\pi$
$110$	−12.0508	−1.14900
$111$	−1.47286	−0.139798
$112$	1.61452	0.152558
$113$	−6.46803	−0.608461	−0.304231	−	0.952598i	$-0.598399\pi$
$113$	−6.46803	−0.608461	−0.304231	+	0.952598i	$0.598399\pi$
$114$	−51.0160	−4.77809
$115$	24.5467	2.28899
$116$	1.91246	0.177567
$117$	−26.5647	−2.45590
$118$	25.5673	2.35366
$119$	0.664206	0.0608877
$120$	40.5594	3.70255
$121$	−8.68573	−0.789612
$122$	−12.9600	−1.17335
$123$	4.10287	0.369944
$124$	−22.4793	−2.01870
$125$	3.17471	0.283955
$126$	−9.21941	−0.821330
$127$	−14.8891	−1.32119	−0.660597	−	0.750741i	$-0.729697\pi$
$127$	−14.8891	−1.32119	−0.660597	+	0.750741i	$0.729697\pi$
$128$	20.7372	1.83293
$129$	−31.5024	−2.77363
$130$	36.2774	3.18174
$131$	−7.57558	−0.661881	−0.330941	−	0.943652i	$-0.607366\pi$
$131$	−7.57558	−0.661881	−0.330941	+	0.943652i	$0.607366\pi$
$132$	−16.8151	−1.46357
$133$	−4.77341	−0.413907
$134$	29.6869	2.56456
$135$	−27.5043	−2.36720
$136$	−4.12999	−0.354144
$137$	3.84937	0.328874	0.164437	−	0.986388i	$-0.447419\pi$
$137$	3.84937	0.328874	0.164437	+	0.986388i	$0.447419\pi$
$138$	52.6366	4.48073
$139$	7.24027	0.614111	0.307056	−	0.951692i	$-0.400656\pi$
$139$	7.24027	0.614111	0.307056	+	0.951692i	$0.400656\pi$
$140$	8.19265	0.692405
$141$	−10.2256	−0.861151
$142$	−7.78585	−0.653374
$143$	−6.96683	−0.582595
$144$	14.0999	1.17499
$145$	1.69919	0.141110
$146$	7.10422	0.587950
$147$	19.4573	1.60482
$148$	1.84987	0.152058
$149$	1.30583	0.106978	0.0534889	−	0.998568i	$-0.482966\pi$
$149$	1.30583	0.106978	0.0534889	+	0.998568i	$0.482966\pi$
$150$	42.3013	3.45389
$151$	12.9743	1.05584	0.527918	−	0.849295i	$-0.322973\pi$
$151$	12.9743	1.05584	0.527918	+	0.849295i	$0.322973\pi$
$152$	29.6808	2.40743
$153$	5.80065	0.468954
$154$	−2.41788	−0.194838
$155$	−19.9725	−1.60423
$156$	50.6199	4.05283
$157$	−10.5795	−0.844336	−0.422168	−	0.906518i	$-0.638731\pi$
$157$	−10.5795	−0.844336	−0.422168	+	0.906518i	$0.638731\pi$
$158$	21.8718	1.74003
$159$	−22.4219	−1.77817
$160$	8.08890	0.639483
$161$	4.92505	0.388148
$162$	−17.3379	−1.36219
$163$	−12.2255	−0.957574	−0.478787	−	0.877931i	$-0.658923\pi$
$163$	−12.2255	−0.957574	−0.478787	+	0.877931i	$0.658923\pi$
$164$	−5.15308	−0.402388
$165$	−14.9400	−1.16308
$166$	14.8393	1.15176
$167$	−13.6663	−1.05753	−0.528765	−	0.848768i	$-0.677345\pi$
$167$	−13.6663	−1.05753	−0.528765	+	0.848768i	$0.677345\pi$
$168$	8.13785	0.627849
$169$	7.97275	0.613289
$170$	−7.92153	−0.607553
$171$	−41.6872	−3.18790
$172$	39.5660	3.01688
$173$	−2.07228	−0.157553	−0.0787764	−	0.996892i	$-0.525101\pi$
$173$	−2.07228	−0.157553	−0.0787764	+	0.996892i	$0.525101\pi$
$174$	3.64365	0.276225
$175$	3.95801	0.299197
$176$	3.69784	0.278735
$177$	31.6970	2.38249
$178$	−19.3867	−1.45310
$179$	−11.3940	−0.851627	−0.425813	−	0.904811i	$-0.640012\pi$
$179$	−11.3940	−0.851627	−0.425813	+	0.904811i	$0.640012\pi$
$180$	71.5480	5.33288
$181$	14.6896	1.09187	0.545934	−	0.837828i	$-0.316175\pi$
$181$	14.6896	1.09187	0.545934	+	0.837828i	$0.316175\pi$
$182$	7.27871	0.539534
$183$	−16.0672	−1.18772
$184$	−30.6236	−2.25760
$185$	1.64358	0.120838
$186$	−42.8279	−3.14029
$187$	1.52127	0.111247
$188$	12.8430	0.936675
$189$	−5.51847	−0.401410
$190$	56.9292	4.13008
$191$	−23.3121	−1.68681	−0.843404	−	0.537280i	$-0.819452\pi$
$191$	−23.3121	−1.68681	−0.843404	+	0.537280i	$0.819452\pi$
$192$	31.7675	2.29262
$193$	0.0943234	0.00678955	0.00339477	−	0.999994i	$-0.498919\pi$
$193$	0.0943234	0.00678955	0.00339477	+	0.999994i	$0.498919\pi$
$194$	−17.8555	−1.28195
$195$	44.9749	3.22072
$196$	−24.4378	−1.74556
$197$	11.9398	0.850676	0.425338	−	0.905035i	$-0.360155\pi$
$197$	11.9398	0.850676	0.425338	+	0.905035i	$0.360155\pi$
$198$	−21.1158	−1.50063
$199$	−3.25428	−0.230689	−0.115345	−	0.993326i	$-0.536797\pi$
$199$	−3.25428	−0.230689	−0.115345	+	0.993326i	$0.536797\pi$
$200$	−24.6106	−1.74023
$201$	36.8043	2.59598
$202$	20.4637	1.43982
$203$	0.340925	0.0239283
$204$	−11.0533	−0.773888
$205$	−4.57843	−0.319771
$206$	29.8005	2.07630
$207$	43.0114	2.98950
$208$	−11.1319	−0.771857
$209$	−10.9328	−0.756241
$210$	15.6088	1.07711
$211$	−15.9941	−1.10108	−0.550539	−	0.834810i	$-0.685578\pi$
$211$	−15.9941	−1.10108	−0.550539	+	0.834810i	$0.685578\pi$
$212$	28.1612	1.93412
$213$	−9.65250	−0.661378
$214$	−33.5184	−2.29127
$215$	35.1537	2.39746
$216$	34.3135	2.33474
$217$	−4.00727	−0.272032
$218$	−45.6673	−3.09298
$219$	8.80746	0.595153
$220$	18.7641	1.26508
$221$	−4.57960	−0.308057
$222$	3.52440	0.236542
$223$	23.2597	1.55759	0.778793	−	0.627281i	$-0.215832\pi$
$223$	23.2597	1.55759	0.778793	+	0.627281i	$0.215832\pi$
$224$	1.62296	0.108438
$225$	34.5661	2.30440
$226$	15.4773	1.02954
$227$	12.5582	0.833517	0.416759	−	0.909017i	$-0.363166\pi$
$227$	12.5582	0.833517	0.416759	+	0.909017i	$0.363166\pi$
$228$	79.4363	5.26080
$229$	−5.46352	−0.361039	−0.180520	−	0.983571i	$-0.557778\pi$
$229$	−5.46352	−0.361039	−0.180520	+	0.983571i	$0.557778\pi$
$230$	−58.7376	−3.87304
$231$	−2.99756	−0.197225
$232$	−2.11985	−0.139175
$233$	16.0949	1.05441	0.527207	−	0.849737i	$-0.323239\pi$
$233$	16.0949	1.05441	0.527207	+	0.849737i	$0.323239\pi$
$234$	63.5664	4.15546
$235$	11.4108	0.744360
$236$	−39.8104	−2.59144
$237$	27.1156	1.76135
$238$	−1.58938	−0.103024
$239$	11.4399	0.739982	0.369991	−	0.929035i	$-0.379361\pi$
$239$	11.4399	0.739982	0.369991	+	0.929035i	$0.379361\pi$
$240$	−23.8717	−1.54091
$241$	−1.91523	−0.123371	−0.0616853	−	0.998096i	$-0.519648\pi$
$241$	−1.91523	−0.123371	−0.0616853	+	0.998096i	$0.519648\pi$
$242$	20.7840	1.33605
$243$	3.43050	0.220067
$244$	20.1799	1.29189
$245$	−21.7126	−1.38717
$246$	−9.81774	−0.625956
$247$	32.9120	2.09414
$248$	24.9170	1.58223
$249$	18.3970	1.16587
$250$	−7.59674	−0.480460
$251$	−29.0417	−1.83310	−0.916548	−	0.399924i	$-0.869037\pi$
$251$	−29.0417	−1.83310	−0.916548	+	0.399924i	$0.869037\pi$
$252$	14.3554	0.904306
$253$	11.2801	0.709177
$254$	35.6280	2.23550
$255$	−9.82071	−0.614997
$256$	−28.2051	−1.76282
$257$	−25.4618	−1.58826	−0.794132	−	0.607746i	$-0.792074\pi$
$257$	−25.4618	−1.58826	−0.794132	+	0.607746i	$0.792074\pi$
$258$	75.3818	4.69306
$259$	0.329768	0.0204908
$260$	−56.4871	−3.50318
$261$	2.97737	0.184295
$262$	18.1275	1.11992
$263$	10.3690	0.639382	0.319691	−	0.947522i	$-0.396421\pi$
$263$	10.3690	0.639382	0.319691	+	0.947522i	$0.396421\pi$
$264$	18.6386	1.14713
$265$	25.0208	1.53702
$266$	11.4223	0.700344
$267$	−24.0347	−1.47090
$268$	−46.2251	−2.82364
$269$	26.9442	1.64282	0.821409	−	0.570339i	$-0.193188\pi$
$269$	26.9442	1.64282	0.821409	+	0.570339i	$0.193188\pi$
$270$	65.8149	4.00537
$271$	−14.9819	−0.910085	−0.455043	−	0.890470i	$-0.650376\pi$
$271$	−14.9819	−0.910085	−0.455043	+	0.890470i	$0.650376\pi$
$272$	2.43075	0.147386
$273$	9.02377	0.546144
$274$	−9.21114	−0.556466
$275$	9.06527	0.546656
$276$	−81.9598	−4.93340
$277$	28.3994	1.70635	0.853176	−	0.521623i	$-0.174673\pi$
$277$	28.3994	1.70635	0.853176	+	0.521623i	$0.174673\pi$
$278$	−17.3252	−1.03910
$279$	−34.9963	−2.09517
$280$	−9.08109	−0.542699
$281$	−31.3888	−1.87250	−0.936250	−	0.351334i	$-0.885728\pi$
$281$	−31.3888	−1.87250	−0.936250	+	0.351334i	$0.885728\pi$
$282$	24.4688	1.45710
$283$	14.5001	0.861944	0.430972	−	0.902365i	$-0.358171\pi$
$283$	14.5001	0.861944	0.430972	+	0.902365i	$0.358171\pi$
$284$	12.1232	0.719381
$285$	70.5779	4.18067
$286$	16.6709	0.985770
$287$	−0.918616	−0.0542242
$288$	14.1736	0.835188
$289$	1.00000	0.0588235
$290$	−4.06598	−0.238763
$291$	−22.1363	−1.29765
$292$	−11.0619	−0.647348
$293$	−4.82214	−0.281712	−0.140856	−	0.990030i	$-0.544986\pi$
$293$	−4.82214	−0.281712	−0.140856	+	0.990030i	$0.544986\pi$
$294$	−46.5594	−2.71540
$295$	−35.3709	−2.05937
$296$	−2.05047	−0.119181
$297$	−12.6393	−0.733406
$298$	−3.12471	−0.181010
$299$	−33.9575	−1.96381
$300$	−65.8668	−3.80282
$301$	7.05324	0.406542
$302$	−31.0462	−1.78651
$303$	25.3698	1.45746
$304$	−17.4689	−1.00191
$305$	17.9295	1.02664
$306$	−13.8803	−0.793486
$307$	−19.6934	−1.12396	−0.561980	−	0.827151i	$-0.689960\pi$
$307$	−19.6934	−1.12396	−0.561980	+	0.827151i	$0.689960\pi$
$308$	3.76484	0.214522
$309$	36.9452	2.10174
$310$	47.7920	2.71440
$311$	−2.09304	−0.118685	−0.0593427	−	0.998238i	$-0.518900\pi$
$311$	−2.09304	−0.118685	−0.0593427	+	0.998238i	$0.518900\pi$
$312$	−56.1092	−3.17656
$313$	−32.5181	−1.83803	−0.919017	−	0.394219i	$-0.871015\pi$
$313$	−32.5181	−1.83803	−0.919017	+	0.394219i	$0.871015\pi$
$314$	25.3156	1.42864
$315$	12.7545	0.718637
$316$	−34.0563	−1.91582
$317$	18.0121	1.01166	0.505831	−	0.862632i	$-0.331186\pi$
$317$	18.0121	1.01166	0.505831	+	0.862632i	$0.331186\pi$
$318$	53.6533	3.00873
$319$	0.780843	0.0437188
$320$	−35.4496	−1.98169
$321$	−41.5544	−2.31934
$322$	−11.7851	−0.656759
$323$	−7.18664	−0.399875
$324$	26.9965	1.49981
$325$	−27.2898	−1.51377
$326$	29.2543	1.62025
$327$	−56.6159	−3.13087
$328$	5.71189	0.315387
$329$	2.28947	0.126223
$330$	35.7498	1.96796
$331$	0.686909	0.0377560	0.0188780	−	0.999822i	$-0.493991\pi$
$331$	0.686909	0.0377560	0.0188780	+	0.999822i	$0.493991\pi$
$332$	−23.1061	−1.26811
$333$	2.87993	0.157819
$334$	32.7020	1.78937
$335$	−41.0702	−2.24391
$336$	−4.78962	−0.261295
$337$	−22.2664	−1.21293	−0.606465	−	0.795110i	$-0.707413\pi$
$337$	−22.2664	−1.21293	−0.606465	+	0.795110i	$0.707413\pi$
$338$	−19.0780	−1.03770
$339$	19.1880	1.04215
$340$	12.3345	0.668932
$341$	−9.17811	−0.497023
$342$	99.7530	5.39402
$343$	−9.00586	−0.486271
$344$	−43.8566	−2.36459
$345$	−72.8199	−3.92049
$346$	4.95875	0.266584
$347$	32.1424	1.72549	0.862747	−	0.505635i	$-0.168742\pi$
$347$	32.1424	1.72549	0.862747	+	0.505635i	$0.168742\pi$
$348$	−5.67348	−0.304130
$349$	34.4468	1.84389	0.921947	−	0.387317i	$-0.126598\pi$
$349$	34.4468	1.84389	0.921947	+	0.387317i	$0.126598\pi$
$350$	−9.47109	−0.506251
$351$	38.0490	2.03091
$352$	3.71716	0.198125
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−75.8475	−4.03125
$355$	10.7713	0.571681
$356$	30.1868	1.59990
$357$	−1.97043	−0.104286
$358$	27.2646	1.44098
$359$	−24.2077	−1.27763	−0.638816	−	0.769359i	$-0.720576\pi$
$359$	−24.2077	−1.27763	−0.638816	+	0.769359i	$0.720576\pi$
$360$	−79.3069	−4.17984
$361$	32.6478	1.71831
$362$	−35.1506	−1.84747
$363$	25.7670	1.35242
$364$	−11.3336	−0.594041
$365$	−9.82831	−0.514437
$366$	38.4471	2.00966
$367$	7.67252	0.400502	0.200251	−	0.979745i	$-0.435824\pi$
$367$	7.67252	0.400502	0.200251	+	0.979745i	$0.435824\pi$
$368$	18.0239	0.939560
$369$	−8.02245	−0.417632
$370$	−3.93291	−0.204462
$371$	5.02017	0.260634
$372$	66.6867	3.45754
$373$	−4.16614	−0.215715	−0.107857	−	0.994166i	$-0.534399\pi$
$373$	−4.16614	−0.215715	−0.107857	+	0.994166i	$0.534399\pi$
$374$	−3.64025	−0.188233
$375$	−9.41806	−0.486346
$376$	−14.2358	−0.734154
$377$	−2.35063	−0.121064
$378$	13.2051	0.679198
$379$	−9.94519	−0.510850	−0.255425	−	0.966829i	$-0.582215\pi$
$379$	−9.94519	−0.510850	−0.255425	+	0.966829i	$0.582215\pi$
$380$	−88.6436	−4.54732
$381$	44.1698	2.26289
$382$	55.7835	2.85413
$383$	29.7105	1.51814	0.759068	−	0.651012i	$-0.225655\pi$
$383$	29.7105	1.51814	0.759068	+	0.651012i	$0.225655\pi$
$384$	−61.5188	−3.13937
$385$	3.34500	0.170477
$386$	−0.225706	−0.0114881
$387$	61.5974	3.13117
$388$	27.8025	1.41146
$389$	−28.5712	−1.44862	−0.724309	−	0.689476i	$-0.757841\pi$
$389$	−28.5712	−1.44862	−0.724309	+	0.689476i	$0.757841\pi$
$390$	−107.620	−5.44956
$391$	7.41494	0.374990
$392$	27.0879	1.36815
$393$	22.4736	1.13364
$394$	−28.5707	−1.43937
$395$	−30.2585	−1.52247
$396$	32.8791	1.65224
$397$	−35.7002	−1.79174	−0.895870	−	0.444317i	$-0.853446\pi$
$397$	−35.7002	−1.79174	−0.895870	+	0.444317i	$0.853446\pi$
$398$	7.78713	0.390334
$399$	14.1608	0.708924
$400$	14.4849	0.724243
$401$	−28.2692	−1.41170	−0.705848	−	0.708363i	$-0.749434\pi$
$401$	−28.2692	−1.41170	−0.705848	+	0.708363i	$0.749434\pi$
$402$	−88.0688	−4.39247
$403$	27.6295	1.37633
$404$	−31.8637	−1.58528
$405$	23.9860	1.19187
$406$	−0.815798	−0.0404874
$407$	0.755287	0.0374382
$408$	12.2520	0.606564
$409$	−2.06218	−0.101968	−0.0509841	−	0.998699i	$-0.516236\pi$
$409$	−2.06218	−0.101968	−0.0509841	+	0.998699i	$0.516236\pi$
$410$	10.9557	0.541063
$411$	−11.4195	−0.563283
$412$	−46.4020	−2.28606
$413$	−7.09682	−0.349212
$414$	−102.922	−5.05833
$415$	−20.5294	−1.00775
$416$	−11.1900	−0.548637
$417$	−21.4789	−1.05183
$418$	26.1611	1.27958
$419$	−2.11486	−0.103318	−0.0516588	−	0.998665i	$-0.516451\pi$
$419$	−2.11486	−0.103318	−0.0516588	+	0.998665i	$0.516451\pi$
$420$	−24.3042	−1.18592
$421$	23.6134	1.15085	0.575424	−	0.817855i	$-0.304837\pi$
$421$	23.6134	1.15085	0.575424	+	0.817855i	$0.304837\pi$
$422$	38.2721	1.86306
$423$	19.9944	0.972161
$424$	−31.2151	−1.51594
$425$	5.95900	0.289054
$426$	23.0974	1.11907
$427$	3.59738	0.174089
$428$	52.1910	2.52275
$429$	20.6677	0.997846
$430$	−84.1191	−4.05658
$431$	−10.0667	−0.484894	−0.242447	−	0.970165i	$-0.577950\pi$
$431$	−10.0667	−0.484894	−0.242447	+	0.970165i	$0.577950\pi$
$432$	−20.1956	−0.971660
$433$	−20.2518	−0.973238	−0.486619	−	0.873614i	$-0.661770\pi$
$433$	−20.2518	−0.973238	−0.486619	+	0.873614i	$0.661770\pi$
$434$	9.58898	0.460286
$435$	−5.04079	−0.241688
$436$	71.1078	3.40545
$437$	−53.2885	−2.54913
$438$	−21.0753	−1.00702
$439$	1.13571	0.0542044	0.0271022	−	0.999633i	$-0.491372\pi$
$439$	1.13571	0.0542044	0.0271022	+	0.999633i	$0.491372\pi$
$440$	−20.7990	−0.991553
$441$	−38.0455	−1.81169
$442$	10.9585	0.521243
$443$	11.4368	0.543381	0.271690	−	0.962385i	$-0.412417\pi$
$443$	11.4368	0.543381	0.271690	+	0.962385i	$0.412417\pi$
$444$	−5.48780	−0.260439
$445$	26.8205	1.27141
$446$	−55.6580	−2.63548
$447$	−3.87386	−0.183227
$448$	−7.11261	−0.336039
$449$	−0.799392	−0.0377257	−0.0188628	−	0.999822i	$-0.506005\pi$
$449$	−0.799392	−0.0377257	−0.0188628	+	0.999822i	$0.506005\pi$
$450$	−82.7129	−3.89912
$451$	−2.10396	−0.0990718
$452$	−24.0995	−1.13355
$453$	−38.4895	−1.80839
$454$	−30.0505	−1.41034
$455$	−10.0697	−0.472075
$456$	−88.0506	−4.12335
$457$	13.0399	0.609983	0.304992	−	0.952355i	$-0.401346\pi$
$457$	13.0399	0.609983	0.304992	+	0.952355i	$0.401346\pi$
$458$	13.0736	0.610890
$459$	−8.30836	−0.387801
$460$	91.4595	4.26432
$461$	36.6927	1.70895	0.854475	−	0.519492i	$-0.173879\pi$
$461$	36.6927	1.70895	0.854475	+	0.519492i	$0.173879\pi$
$462$	7.17284	0.333711
$463$	−32.4335	−1.50731	−0.753656	−	0.657270i	$-0.771711\pi$
$463$	−32.4335	−1.50731	−0.753656	+	0.657270i	$0.771711\pi$
$464$	1.24766	0.0579213
$465$	59.2500	2.74766
$466$	−38.5134	−1.78410
$467$	−12.6535	−0.585532	−0.292766	−	0.956184i	$-0.594576\pi$
$467$	−12.6535	−0.585532	−0.292766	+	0.956184i	$0.594576\pi$
$468$	−98.9783	−4.57527
$469$	−8.24033	−0.380503
$470$	−27.3049	−1.25948
$471$	31.3850	1.44615
$472$	44.1276	2.03114
$473$	16.1545	0.742784
$474$	−64.8847	−2.98025
$475$	−42.8252	−1.96495
$476$	2.47479	0.113432
$477$	43.8422	2.00740
$478$	−27.3743	−1.25207
$479$	−17.3201	−0.791375	−0.395687	−	0.918385i	$-0.629494\pi$
$479$	−17.3201	−0.791375	−0.395687	+	0.918385i	$0.629494\pi$
$480$	−23.9964	−1.09528
$481$	−2.27370	−0.103672
$482$	4.58293	0.208747
$483$	−14.6106	−0.664805
$484$	−32.3625	−1.47102
$485$	24.7021	1.12166
$486$	−8.20883	−0.372360
$487$	11.0941	0.502723	0.251361	−	0.967893i	$-0.419122\pi$
$487$	11.0941	0.502723	0.251361	+	0.967893i	$0.419122\pi$
$488$	−22.3683	−1.01256
$489$	36.2680	1.64010
$490$	51.9559	2.34713
$491$	23.2433	1.04895	0.524477	−	0.851425i	$-0.324261\pi$
$491$	23.2433	1.04895	0.524477	+	0.851425i	$0.324261\pi$
$492$	15.2871	0.689194
$493$	0.513282	0.0231171
$494$	−78.7548	−3.54335
$495$	29.2125	1.31301
$496$	−14.6652	−0.658485
$497$	2.16115	0.0969410
$498$	−44.0222	−1.97268
$499$	−40.4438	−1.81051	−0.905256	−	0.424867i	$-0.860321\pi$
$499$	−40.4438	−1.81051	−0.905256	+	0.424867i	$0.860321\pi$
$500$	11.8288	0.528999
$501$	40.5423	1.81130
$502$	69.4937	3.10166
$503$	−6.49672	−0.289674	−0.144837	−	0.989456i	$-0.546266\pi$
$503$	−6.49672	−0.289674	−0.144837	+	0.989456i	$0.546266\pi$
$504$	−15.9121	−0.708783
$505$	−28.3104	−1.25980
$506$	−26.9922	−1.19995
$507$	−23.6519	−1.05042
$508$	−55.4759	−2.46135
$509$	−7.85252	−0.348057	−0.174028	−	0.984741i	$-0.555678\pi$
$509$	−7.85252	−0.348057	−0.174028	+	0.984741i	$0.555678\pi$
$510$	23.4999	1.04059
$511$	−1.97195	−0.0872340
$512$	26.0174	1.14982
$513$	59.7092	2.63623
$514$	60.9274	2.68739
$515$	−41.2274	−1.81670
$516$	−117.376	−5.16719
$517$	5.24372	0.230618
$518$	−0.789099	−0.0346710
$519$	6.14761	0.269850
$520$	62.6127	2.74575
$521$	24.5419	1.07520	0.537600	−	0.843200i	$-0.319331\pi$
$521$	24.5419	1.07520	0.537600	+	0.843200i	$0.319331\pi$
$522$	−7.12453	−0.311832
$523$	−5.67476	−0.248140	−0.124070	−	0.992273i	$-0.539595\pi$
$523$	−5.67476	−0.248140	−0.124070	+	0.992273i	$0.539595\pi$
$524$	−28.2261	−1.23306
$525$	−11.7418	−0.512453
$526$	−24.8120	−1.08185
$527$	−6.03318	−0.262809
$528$	−10.9700	−0.477407
$529$	31.9813	1.39049
$530$	−59.8721	−2.60068
$531$	−61.9779	−2.68961
$532$	−17.7855	−0.771097
$533$	6.33371	0.274344
$534$	57.5125	2.48881
$535$	46.3709	2.00479
$536$	51.2378	2.21314
$537$	33.8013	1.45863
$538$	−64.4747	−2.77970
$539$	−9.97777	−0.429773
$540$	−102.479	−4.41002
$541$	9.12384	0.392265	0.196132	−	0.980577i	$-0.437162\pi$
$541$	9.12384	0.392265	0.196132	+	0.980577i	$0.437162\pi$
$542$	35.8501	1.53989
$543$	−43.5779	−1.87011
$544$	2.44345	0.104762
$545$	63.1782	2.70625
$546$	−21.5929	−0.924092
$547$	45.4620	1.94381	0.971907	−	0.235365i	$-0.0756285\pi$
$547$	45.4620	1.94381	0.971907	+	0.235365i	$0.0756285\pi$
$548$	14.3425	0.612683
$549$	31.4166	1.34083
$550$	−21.6922	−0.924960
$551$	−3.68878	−0.157147
$552$	90.8477	3.86674
$553$	−6.07107	−0.258168
$554$	−67.9566	−2.88720
$555$	−4.87582	−0.206967
$556$	26.9768	1.14407
$557$	−8.19119	−0.347072	−0.173536	−	0.984828i	$-0.555519\pi$
$557$	−8.19119	−0.347072	−0.173536	+	0.984828i	$0.555519\pi$
$558$	83.7425	3.54510
$559$	−48.6310	−2.05687
$560$	5.34477	0.225858
$561$	−4.51299	−0.190539
$562$	75.1101	3.16833
$563$	−25.0413	−1.05536	−0.527682	−	0.849442i	$-0.676939\pi$
$563$	−25.0413	−1.05536	−0.527682	+	0.849442i	$0.676939\pi$
$564$	−38.1000	−1.60430
$565$	−21.4120	−0.900811
$566$	−34.6973	−1.45844
$567$	4.81255	0.202108
$568$	−13.4379	−0.563842
$569$	2.12544	0.0891032	0.0445516	−	0.999007i	$-0.485814\pi$
$569$	2.12544	0.0891032	0.0445516	+	0.999007i	$0.485814\pi$
$570$	−168.885	−7.07383
$571$	−12.3339	−0.516157	−0.258078	−	0.966124i	$-0.583089\pi$
$571$	−12.3339	−0.516157	−0.258078	+	0.966124i	$0.583089\pi$
$572$	−25.9580	−1.08536
$573$	69.1575	2.88910
$574$	2.19815	0.0917490
$575$	44.1856	1.84267
$576$	−62.1158	−2.58816
$577$	−40.0784	−1.66849	−0.834243	−	0.551397i	$-0.814095\pi$
$577$	−40.0784	−1.66849	−0.834243	+	0.551397i	$0.814095\pi$
$578$	−2.39289	−0.0995313
$579$	−0.279819	−0.0116289
$580$	6.33108	0.262884
$581$	−4.11902	−0.170886
$582$	52.9698	2.19567
$583$	11.4980	0.476199
$584$	12.2615	0.507383
$585$	−87.9406	−3.63590
$586$	11.5389	0.476666
$587$	4.83871	0.199715	0.0998575	−	0.995002i	$-0.468161\pi$
$587$	4.83871	0.199715	0.0998575	+	0.995002i	$0.468161\pi$
$588$	72.4969	2.98972
$589$	43.3583	1.78655
$590$	84.6388	3.48453
$591$	−35.4205	−1.45700
$592$	1.20683	0.0496004
$593$	−16.1196	−0.661953	−0.330976	−	0.943639i	$-0.607378\pi$
$593$	−16.1196	−0.661953	−0.330976	+	0.943639i	$0.607378\pi$
$594$	30.2445	1.24095
$595$	2.19881	0.0901426
$596$	4.86544	0.199296
$597$	9.65409	0.395116
$598$	81.2566	3.32283
$599$	−39.1231	−1.59853	−0.799264	−	0.600980i	$-0.794777\pi$
$599$	−39.1231	−1.59853	−0.799264	+	0.600980i	$0.794777\pi$
$600$	73.0096	2.98060
$601$	−4.43535	−0.180922	−0.0904608	−	0.995900i	$-0.528834\pi$
$601$	−4.43535	−0.180922	−0.0904608	+	0.995900i	$0.528834\pi$
$602$	−16.8777	−0.687882
$603$	−71.9644	−2.93062
$604$	48.3416	1.96699
$605$	−28.7536	−1.16900
$606$	−60.7073	−2.46607
$607$	12.5813	0.510660	0.255330	−	0.966854i	$-0.417816\pi$
$607$	12.5813	0.510660	0.255330	+	0.966854i	$0.417816\pi$
$608$	−17.5602	−0.712161
$609$	−1.01139	−0.0409834
$610$	−42.9034	−1.73711
$611$	−15.7855	−0.638615
$612$	21.6129	0.873648
$613$	−16.6562	−0.672736	−0.336368	−	0.941731i	$-0.609199\pi$
$613$	−16.6562	−0.672736	−0.336368	+	0.941731i	$0.609199\pi$
$614$	47.1242	1.90178
$615$	13.5823	0.547691
$616$	−4.17311	−0.168139
$617$	38.4925	1.54965	0.774824	−	0.632177i	$-0.217838\pi$
$617$	38.4925	1.54965	0.774824	+	0.632177i	$0.217838\pi$
$618$	−88.4059	−3.55621
$619$	−11.9418	−0.479980	−0.239990	−	0.970775i	$-0.577144\pi$
$619$	−11.9418	−0.479980	−0.239990	+	0.970775i	$0.577144\pi$
$620$	−74.4162	−2.98863
$621$	−61.6060	−2.47216
$622$	5.00842	0.200819
$623$	5.38127	0.215596
$624$	33.0237	1.32201
$625$	−19.2853	−0.771413
$626$	77.8124	3.11001
$627$	32.4333	1.29526
$628$	−39.4186	−1.57297
$629$	0.496483	0.0197961
$630$	−30.5203	−1.21596
$631$	2.20919	0.0879466	0.0439733	−	0.999033i	$-0.485998\pi$
$631$	2.20919	0.0879466	0.0439733	+	0.999033i	$0.485998\pi$
$632$	37.7495	1.50159
$633$	47.4478	1.88588
$634$	−43.1011	−1.71177
$635$	−49.2894	−1.95599
$636$	−83.5428	−3.31269
$637$	30.0368	1.19010
$638$	−1.86847	−0.0739736
$639$	18.8738	0.746635
$640$	68.6493	2.71360
$641$	26.7565	1.05682	0.528410	−	0.848989i	$-0.322788\pi$
$641$	26.7565	1.05682	0.528410	+	0.848989i	$0.322788\pi$
$642$	99.4353	3.92440
$643$	5.95750	0.234941	0.117470	−	0.993076i	$-0.462521\pi$
$643$	5.95750	0.234941	0.117470	+	0.993076i	$0.462521\pi$
$644$	18.3504	0.723109
$645$	−104.287	−4.10628
$646$	17.1969	0.676602
$647$	−18.0701	−0.710408	−0.355204	−	0.934789i	$-0.615589\pi$
$647$	−18.0701	−0.710408	−0.355204	+	0.934789i	$0.615589\pi$
$648$	−29.9241	−1.17553
$649$	−16.2543	−0.638037
$650$	65.3017	2.56134
$651$	11.8879	0.465925
$652$	−45.5514	−1.78393
$653$	32.9171	1.28815	0.644073	−	0.764964i	$-0.277243\pi$
$653$	32.9171	1.28815	0.644073	+	0.764964i	$0.277243\pi$
$654$	135.476	5.29753
$655$	−25.0785	−0.979897
$656$	−3.36180	−0.131256
$657$	−17.2214	−0.671873
$658$	−5.47846	−0.213573
$659$	−44.0159	−1.71462	−0.857309	−	0.514802i	$-0.827865\pi$
$659$	−44.0159	−1.71462	−0.857309	+	0.514802i	$0.827865\pi$
$660$	−55.6655	−2.16678
$661$	38.3417	1.49132	0.745660	−	0.666326i	$-0.232134\pi$
$661$	38.3417	1.49132	0.745660	+	0.666326i	$0.232134\pi$
$662$	−1.64370	−0.0638843
$663$	13.5858	0.527628
$664$	25.6118	0.993931
$665$	−15.8021	−0.612779
$666$	−6.89135	−0.267035
$667$	3.80596	0.147367
$668$	−50.9198	−1.97015
$669$	−69.0020	−2.66777
$670$	98.2767	3.79676
$671$	8.23930	0.318075
$672$	−4.81464	−0.185729
$673$	0.394697	0.0152145	0.00760723	−	0.999971i	$-0.497579\pi$
$673$	0.394697	0.0152145	0.00760723	+	0.999971i	$0.497579\pi$
$674$	53.2812	2.05232
$675$	−49.5095	−1.90562
$676$	29.7060	1.14254
$677$	27.3401	1.05077	0.525383	−	0.850866i	$-0.323922\pi$
$677$	27.3401	1.05077	0.525383	+	0.850866i	$0.323922\pi$
$678$	−45.9148	−1.76335
$679$	4.95622	0.190202
$680$	−13.6721	−0.524301
$681$	−37.2550	−1.42762
$682$	21.9622	0.840978
$683$	−24.9374	−0.954203	−0.477101	−	0.878848i	$-0.658313\pi$
$683$	−24.9374	−0.954203	−0.477101	+	0.878848i	$0.658313\pi$
$684$	−155.324	−5.93896
$685$	12.7431	0.486889
$686$	21.5501	0.822786
$687$	16.2080	0.618374
$688$	25.8123	0.984084
$689$	−34.6133	−1.31866
$690$	174.250	6.63360
$691$	12.2531	0.466131	0.233066	−	0.972461i	$-0.425124\pi$
$691$	12.2531	0.466131	0.233066	+	0.972461i	$0.425124\pi$
$692$	−7.72121	−0.293516
$693$	5.86120	0.222649
$694$	−76.9134	−2.91959
$695$	23.9685	0.909175
$696$	6.28873	0.238374
$697$	−1.38303	−0.0523859
$698$	−82.4275	−3.11993
$699$	−47.7470	−1.80596
$700$	14.7473	0.557395
$701$	25.8486	0.976289	0.488144	−	0.872763i	$-0.337674\pi$
$701$	25.8486	0.976289	0.488144	+	0.872763i	$0.337674\pi$
$702$	−91.0472	−3.43636
$703$	−3.56805	−0.134571
$704$	−16.2904	−0.613969
$705$	−33.8512	−1.27491
$706$	−2.39289	−0.0900577
$707$	−5.68020	−0.213626
$708$	118.101	4.43851
$709$	−2.08673	−0.0783688	−0.0391844	−	0.999232i	$-0.512476\pi$
$709$	−2.08673	−0.0783688	−0.0391844	+	0.999232i	$0.512476\pi$
$710$	−25.7746	−0.967302
$711$	−53.0198	−1.98840
$712$	−33.4604	−1.25398
$713$	−44.7356	−1.67536
$714$	4.71502	0.176455
$715$	−23.0633	−0.862517
$716$	−42.4533	−1.58656
$717$	−33.9373	−1.26741
$718$	57.9264	2.16179
$719$	−10.2721	−0.383086	−0.191543	−	0.981484i	$-0.561349\pi$
$719$	−10.2721	−0.383086	−0.191543	+	0.981484i	$0.561349\pi$
$720$	46.6770	1.73955
$721$	−8.27187	−0.308060
$722$	−78.1227	−2.90743
$723$	5.68169	0.211304
$724$	54.7325	2.03412
$725$	3.05865	0.113595
$726$	−61.6576	−2.28833
$727$	−10.3579	−0.384152	−0.192076	−	0.981380i	$-0.561522\pi$
$727$	−10.3579	−0.384152	−0.192076	+	0.981380i	$0.561522\pi$
$728$	12.5626	0.465602
$729$	−31.9136	−1.18198
$730$	23.5181	0.870444
$731$	10.6191	0.392760
$732$	−59.8654	−2.21269
$733$	−6.60155	−0.243834	−0.121917	−	0.992540i	$-0.538904\pi$
$733$	−6.60155	−0.243834	−0.121917	+	0.992540i	$0.538904\pi$
$734$	−18.3595	−0.677662
$735$	64.4123	2.37589
$736$	18.1180	0.667840
$737$	−18.8733	−0.695209
$738$	19.1969	0.706647
$739$	−23.1340	−0.850996	−0.425498	−	0.904959i	$-0.639901\pi$
$739$	−23.1340	−0.850996	−0.425498	+	0.904959i	$0.639901\pi$
$740$	6.12387	0.225118
$741$	−97.6362	−3.58676
$742$	−12.0127	−0.441002
$743$	−14.5616	−0.534212	−0.267106	−	0.963667i	$-0.586067\pi$
$743$	−14.5616	−0.534212	−0.267106	+	0.963667i	$0.586067\pi$
$744$	−73.9184	−2.70998
$745$	4.32287	0.158378
$746$	9.96913	0.364996
$747$	−35.9722	−1.31615
$748$	5.66818	0.207249
$749$	9.30385	0.339955
$750$	22.5364	0.822913
$751$	−14.0225	−0.511689	−0.255844	−	0.966718i	$-0.582353\pi$
$751$	−14.0225	−0.511689	−0.255844	+	0.966718i	$0.582353\pi$
$752$	8.37862	0.305537
$753$	86.1548	3.13966
$754$	5.62480	0.204843
$755$	42.9507	1.56314
$756$	−20.5615	−0.747814
$757$	19.2348	0.699102	0.349551	−	0.936917i	$-0.386334\pi$
$757$	19.2348	0.699102	0.349551	+	0.936917i	$0.386334\pi$
$758$	23.7978	0.864374
$759$	−33.4636	−1.21465
$760$	98.2564	3.56413
$761$	−50.9408	−1.84660	−0.923301	−	0.384078i	$-0.874519\pi$
$761$	−50.9408	−1.84660	−0.923301	+	0.384078i	$0.874519\pi$
$762$	−105.694	−3.82888
$763$	12.6761	0.458904
$764$	−86.8597	−3.14247
$765$	19.2027	0.694274
$766$	−71.0941	−2.56873
$767$	48.9315	1.76681
$768$	83.6730	3.01929
$769$	8.70472	0.313900	0.156950	−	0.987607i	$-0.449834\pi$
$769$	8.70472	0.313900	0.156950	+	0.987607i	$0.449834\pi$
$770$	−8.00423	−0.288452
$771$	75.5347	2.72031
$772$	0.351443	0.0126487
$773$	−12.6343	−0.454424	−0.227212	−	0.973845i	$-0.572961\pi$
$773$	−12.6343	−0.454424	−0.227212	+	0.973845i	$0.572961\pi$
$774$	−147.396	−5.29804
$775$	−35.9517	−1.29142
$776$	−30.8175	−1.10628
$777$	−0.978285	−0.0350958
$778$	68.3678	2.45111
$779$	9.93932	0.356113
$780$	167.574	6.00011
$781$	4.94982	0.177119
$782$	−17.7432	−0.634494
$783$	−4.26454	−0.152402
$784$	−15.9429	−0.569389
$785$	−35.0228	−1.25002
$786$	−53.7770	−1.91816
$787$	3.44042	0.122638	0.0613188	−	0.998118i	$-0.480469\pi$
$787$	3.44042	0.122638	0.0613188	+	0.998118i	$0.480469\pi$
$788$	44.4870	1.58478
$789$	−30.7606	−1.09511
$790$	72.4053	2.57607
$791$	−4.29611	−0.152752
$792$	−36.4446	−1.29500
$793$	−24.8034	−0.880793
$794$	85.4267	3.03168
$795$	−74.2264	−2.63254
$796$	−12.1252	−0.429768
$797$	41.1756	1.45851	0.729256	−	0.684240i	$-0.239866\pi$
$797$	41.1756	1.45851	0.729256	+	0.684240i	$0.239866\pi$
$798$	−33.8852	−1.19952
$799$	3.44692	0.121943
$800$	14.5605	0.514793
$801$	46.9957	1.66051
$802$	67.6452	2.38863
$803$	−4.51649	−0.159383
$804$	137.131	4.83623
$805$	16.3041	0.574643
$806$	−66.1146	−2.32879
$807$	−79.9324	−2.81375
$808$	35.3191	1.24252
$809$	6.91375	0.243075	0.121537	−	0.992587i	$-0.461218\pi$
$809$	6.91375	0.243075	0.121537	+	0.992587i	$0.461218\pi$
$810$	−57.3959	−2.01669
$811$	2.15880	0.0758056	0.0379028	−	0.999281i	$-0.487932\pi$
$811$	2.15880	0.0758056	0.0379028	+	0.999281i	$0.487932\pi$
$812$	1.27027	0.0445777
$813$	44.4451	1.55876
$814$	−1.80732	−0.0633466
$815$	−40.4717	−1.41766
$816$	−7.21104	−0.252437
$817$	−76.3153	−2.66993
$818$	4.93457	0.172533
$819$	−17.6444	−0.616546
$820$	−17.0589	−0.595724
$821$	6.86394	0.239553	0.119777	−	0.992801i	$-0.461782\pi$
$821$	6.86394	0.239553	0.119777	+	0.992801i	$0.461782\pi$
$822$	27.3257	0.953092
$823$	3.42194	0.119281	0.0596406	−	0.998220i	$-0.481005\pi$
$823$	3.42194	0.119281	0.0596406	+	0.998220i	$0.481005\pi$
$824$	51.4339	1.79179
$825$	−26.8929	−0.936291
$826$	16.9819	0.590877
$827$	5.66646	0.197042	0.0985210	−	0.995135i	$-0.468589\pi$
$827$	5.66646	0.197042	0.0985210	+	0.995135i	$0.468589\pi$
$828$	160.258	5.56935
$829$	45.1402	1.56778	0.783892	−	0.620897i	$-0.213231\pi$
$829$	45.1402	1.56778	0.783892	+	0.620897i	$0.213231\pi$
$830$	49.1247	1.70514
$831$	−84.2492	−2.92257
$832$	49.0403	1.70017
$833$	−6.55883	−0.227250
$834$	51.3967	1.77972
$835$	−45.2414	−1.56564
$836$	−40.7351	−1.40885
$837$	50.1258	1.73260
$838$	5.06063	0.174817
$839$	−25.5119	−0.880768	−0.440384	−	0.897809i	$-0.645158\pi$
$839$	−25.5119	−0.880768	−0.440384	+	0.897809i	$0.645158\pi$
$840$	26.9398	0.929513
$841$	−28.7365	−0.990915
$842$	−56.5045	−1.94727
$843$	93.1177	3.20715
$844$	−59.5930	−2.05127
$845$	26.3933	0.907957
$846$	−47.8445	−1.64493
$847$	−5.76912	−0.198229
$848$	18.3720	0.630897
$849$	−43.0160	−1.47630
$850$	−14.2593	−0.489088
$851$	3.68139	0.126197
$852$	−35.9646	−1.23213
$853$	−42.9552	−1.47076	−0.735378	−	0.677657i	$-0.762995\pi$
$853$	−42.9552	−1.47076	−0.735378	+	0.677657i	$0.762995\pi$
$854$	−8.60814	−0.294565
$855$	−138.003	−4.71960
$856$	−57.8508	−1.97730
$857$	−38.7699	−1.32435	−0.662177	−	0.749347i	$-0.730367\pi$
$857$	−38.7699	−1.32435	−0.662177	+	0.749347i	$0.730367\pi$
$858$	−49.4556	−1.68839
$859$	9.42261	0.321495	0.160748	−	0.986996i	$-0.448609\pi$
$859$	9.42261	0.321495	0.160748	+	0.986996i	$0.448609\pi$
$860$	130.981	4.46640
$861$	2.72515	0.0928730
$862$	24.0885	0.820457
$863$	−10.0989	−0.343771	−0.171885	−	0.985117i	$-0.554986\pi$
$863$	−10.0989	−0.343771	−0.171885	+	0.985117i	$0.554986\pi$
$864$	−20.3011	−0.690657
$865$	−6.86017	−0.233253
$866$	48.4603	1.64675
$867$	−2.96659	−0.100751
$868$	−14.9309	−0.506787
$869$	−13.9049	−0.471693
$870$	12.0621	0.408943
$871$	56.8158	1.92513
$872$	−78.8190	−2.66915
$873$	43.2837	1.46493
$874$	127.514	4.31322
$875$	2.10866	0.0712858
$876$	32.8161	1.10875
$877$	10.0707	0.340064	0.170032	−	0.985438i	$-0.445613\pi$
$877$	10.0707	0.340064	0.170032	+	0.985438i	$0.445613\pi$
$878$	−2.71763	−0.0917156
$879$	14.3053	0.482506
$880$	12.2415	0.412660
$881$	17.7225	0.597086	0.298543	−	0.954396i	$-0.403499\pi$
$881$	17.7225	0.597086	0.298543	+	0.954396i	$0.403499\pi$
$882$	91.0387	3.06543
$883$	−12.4113	−0.417672	−0.208836	−	0.977951i	$-0.566967\pi$
$883$	−12.4113	−0.417672	−0.208836	+	0.977951i	$0.566967\pi$
$884$	−17.0633	−0.573902
$885$	104.931	3.52721
$886$	−27.3671	−0.919417
$887$	−19.6307	−0.659134	−0.329567	−	0.944132i	$-0.606903\pi$
$887$	−19.6307	−0.659134	−0.329567	+	0.944132i	$0.606903\pi$
$888$	6.08291	0.204129
$889$	−9.88944	−0.331681
$890$	−64.1786	−2.15127
$891$	11.0225	0.369267
$892$	86.6643	2.90174
$893$	−24.7718	−0.828957
$894$	9.26973	0.310026
$895$	−37.7191	−1.26081
$896$	13.7738	0.460150
$897$	100.738	3.36354
$898$	1.91286	0.0638330
$899$	−3.09672	−0.103281
$900$	128.791	4.29304
$901$	7.55815	0.251799
$902$	5.03456	0.167633
$903$	−20.9241	−0.696309
$904$	26.7129	0.888459
$905$	48.6289	1.61648
$906$	92.1013	3.05986
$907$	−52.0106	−1.72698	−0.863492	−	0.504363i	$-0.831727\pi$
$907$	−52.0106	−1.72698	−0.863492	+	0.504363i	$0.831727\pi$
$908$	46.7911	1.55282
$909$	−49.6063	−1.64534
$910$	24.0957	0.798765
$911$	0.973267	0.0322458	0.0161229	−	0.999870i	$-0.494868\pi$
$911$	0.973267	0.0322458	0.0161229	+	0.999870i	$0.494868\pi$
$912$	51.8232	1.71604
$913$	−9.43405	−0.312221
$914$	−31.2032	−1.03211
$915$	−53.1895	−1.75839
$916$	−20.3567	−0.672605
$917$	−5.03175	−0.166163
$918$	19.8810	0.656172
$919$	−3.05292	−0.100707	−0.0503533	−	0.998731i	$-0.516035\pi$
$919$	−3.05292	−0.100707	−0.0503533	+	0.998731i	$0.516035\pi$
$920$	−101.378	−3.34232
$921$	58.4222	1.92508
$922$	−87.8018	−2.89160
$923$	−14.9008	−0.490466
$924$	−11.1687	−0.367424
$925$	2.95854	0.0972764
$926$	77.6098	2.55042
$927$	−72.2398	−2.37267
$928$	1.25418	0.0411705
$929$	5.72496	0.187830	0.0939150	−	0.995580i	$-0.470062\pi$
$929$	5.72496	0.187830	0.0939150	+	0.995580i	$0.470062\pi$
$930$	−141.779	−4.64912
$931$	47.1360	1.54482
$932$	59.9687	1.96434
$933$	6.20918	0.203280
$934$	30.2784	0.990739
$935$	5.03608	0.164697
$936$	109.712	3.58604
$937$	−5.60332	−0.183053	−0.0915263	−	0.995803i	$-0.529175\pi$
$937$	−5.60332	−0.183053	−0.0915263	+	0.995803i	$0.529175\pi$
$938$	19.7182	0.643823
$939$	96.4679	3.14811
$940$	42.5161	1.38672
$941$	29.0085	0.945649	0.472824	−	0.881157i	$-0.343234\pi$
$941$	29.0085	0.945649	0.472824	+	0.881157i	$0.343234\pi$
$942$	−75.1010	−2.44692
$943$	−10.2551	−0.333951
$944$	−25.9718	−0.845309
$945$	−18.2686	−0.594276
$946$	−38.6560	−1.25681
$947$	53.1651	1.72763	0.863817	−	0.503806i	$-0.168067\pi$
$947$	53.1651	1.72763	0.863817	+	0.503806i	$0.168067\pi$
$948$	101.031	3.28134
$949$	13.5963	0.441355
$950$	102.476	3.32476
$951$	−53.4346	−1.73274
$952$	−2.74317	−0.0889066
$953$	−56.1998	−1.82049	−0.910245	−	0.414070i	$-0.864107\pi$
$953$	−56.1998	−1.82049	−0.910245	+	0.414070i	$0.864107\pi$
$954$	−104.910	−3.39658
$955$	−77.1734	−2.49727
$956$	42.6242	1.37857
$957$	−2.31644	−0.0748798
$958$	41.4451	1.33903
$959$	2.55678	0.0825627
$960$	105.164	3.39416
$961$	5.39921	0.174168
$962$	5.44071	0.175416
$963$	81.2524	2.61832
$964$	−7.13602	−0.229836
$965$	0.312252	0.0100517
$966$	34.9616	1.12487
$967$	28.2464	0.908342	0.454171	−	0.890915i	$-0.349936\pi$
$967$	28.2464	0.908342	0.454171	+	0.890915i	$0.349936\pi$
$968$	35.8720	1.15297
$969$	21.3198	0.684891
$970$	−59.1094	−1.89789
$971$	9.23425	0.296341	0.148171	−	0.988962i	$-0.452662\pi$
$971$	9.23425	0.296341	0.148171	+	0.988962i	$0.452662\pi$
$972$	12.7818	0.409978
$973$	4.80903	0.154170
$974$	−26.5471	−0.850623
$975$	80.9577	2.59272
$976$	13.1651	0.421404
$977$	7.32781	0.234438	0.117219	−	0.993106i	$-0.462602\pi$
$977$	7.32781	0.234438	0.117219	+	0.993106i	$0.462602\pi$
$978$	−86.7855	−2.77509
$979$	12.3251	0.393910
$980$	−80.8999	−2.58425
$981$	110.703	3.53446
$982$	−55.6186	−1.77486
$983$	−13.1255	−0.418638	−0.209319	−	0.977847i	$-0.567125\pi$
$983$	−13.1255	−0.418638	−0.209319	+	0.977847i	$0.567125\pi$
$984$	−16.9448	−0.540182
$985$	39.5260	1.25940
$986$	−1.22823	−0.0391148
$987$	−6.79191	−0.216189
$988$	122.628	3.90132
$989$	78.7396	2.50377
$990$	−69.9025	−2.22165
$991$	46.8070	1.48687	0.743437	−	0.668806i	$-0.233194\pi$
$991$	46.8070	1.48687	0.743437	+	0.668806i	$0.233194\pi$
$992$	−14.7418	−0.468052
$993$	−2.03778	−0.0646669
$994$	−5.17141	−0.164027
$995$	−10.7731	−0.341529
$996$	68.5463	2.17197
$997$	15.9560	0.505333	0.252666	−	0.967553i	$-0.418693\pi$
$997$	15.9560	0.505333	0.252666	+	0.967553i	$0.418693\pi$
$998$	96.7777	3.06344
$999$	−4.12497	−0.130508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.10	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.10	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39289 q^{2} -2.96659 q^{3} +3.72594 q^{4} +3.31044 q^{5} +7.09873 q^{6} +0.664206 q^{7} -4.12999 q^{8} +5.80065 q^{9} +O(q^{10})\)	\(q-2.39289 q^{2} -2.96659 q^{3} +3.72594 q^{4} +3.31044 q^{5} +7.09873 q^{6} +0.664206 q^{7} -4.12999 q^{8} +5.80065 q^{9} -7.92153 q^{10} +1.52127 q^{11} -11.0533 q^{12} -4.57960 q^{13} -1.58938 q^{14} -9.82071 q^{15} +2.43075 q^{16} +1.00000 q^{17} -13.8803 q^{18} -7.18664 q^{19} +12.3345 q^{20} -1.97043 q^{21} -3.64025 q^{22} +7.41494 q^{23} +12.2520 q^{24} +5.95900 q^{25} +10.9585 q^{26} -8.30836 q^{27} +2.47479 q^{28} +0.513282 q^{29} +23.4999 q^{30} -6.03318 q^{31} +2.44345 q^{32} -4.51299 q^{33} -2.39289 q^{34} +2.19881 q^{35} +21.6129 q^{36} +0.496483 q^{37} +17.1969 q^{38} +13.5858 q^{39} -13.6721 q^{40} -1.38303 q^{41} +4.71502 q^{42} +10.6191 q^{43} +5.66818 q^{44} +19.2027 q^{45} -17.7432 q^{46} +3.44692 q^{47} -7.21104 q^{48} -6.55883 q^{49} -14.2593 q^{50} -2.96659 q^{51} -17.0633 q^{52} +7.55815 q^{53} +19.8810 q^{54} +5.03608 q^{55} -2.74317 q^{56} +21.3198 q^{57} -1.22823 q^{58} -10.6847 q^{59} -36.5914 q^{60} +5.41605 q^{61} +14.4367 q^{62} +3.85283 q^{63} -10.7084 q^{64} -15.1605 q^{65} +10.7991 q^{66} -12.4063 q^{67} +3.72594 q^{68} -21.9971 q^{69} -5.26153 q^{70} +3.25374 q^{71} -23.9566 q^{72} -2.96888 q^{73} -1.18803 q^{74} -17.6779 q^{75} -26.7770 q^{76} +1.01044 q^{77} -32.5094 q^{78} -9.14033 q^{79} +8.04686 q^{80} +7.24556 q^{81} +3.30944 q^{82} -6.20141 q^{83} -7.34170 q^{84} +3.31044 q^{85} -25.4103 q^{86} -1.52270 q^{87} -6.28285 q^{88} +8.10180 q^{89} -45.9500 q^{90} -3.04180 q^{91} +27.6276 q^{92} +17.8979 q^{93} -8.24812 q^{94} -23.7909 q^{95} -7.24872 q^{96} +7.46187 q^{97} +15.6946 q^{98} +8.82437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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