LMFDB - Embedded newform 4001.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27915 q^{2} +2.08452 q^{3} +3.19451 q^{4} -0.864719 q^{5} -4.75093 q^{6} +2.39591 q^{7} -2.72247 q^{8} +1.34523 q^{9} +O(q^{10})$	\(q-2.27915 q^{2} +2.08452 q^{3} +3.19451 q^{4} -0.864719 q^{5} -4.75093 q^{6} +2.39591 q^{7} -2.72247 q^{8} +1.34523 q^{9} +1.97082 q^{10} -1.00256 q^{11} +6.65904 q^{12} -0.461631 q^{13} -5.46064 q^{14} -1.80253 q^{15} -0.184108 q^{16} -2.54531 q^{17} -3.06598 q^{18} -1.75433 q^{19} -2.76236 q^{20} +4.99433 q^{21} +2.28498 q^{22} +4.84039 q^{23} -5.67506 q^{24} -4.25226 q^{25} +1.05213 q^{26} -3.44940 q^{27} +7.65378 q^{28} +0.626880 q^{29} +4.10822 q^{30} -1.90094 q^{31} +5.86456 q^{32} -2.08986 q^{33} +5.80115 q^{34} -2.07179 q^{35} +4.29736 q^{36} -5.25472 q^{37} +3.99838 q^{38} -0.962280 q^{39} +2.35417 q^{40} +6.02802 q^{41} -11.3828 q^{42} -1.40334 q^{43} -3.20269 q^{44} -1.16325 q^{45} -11.0320 q^{46} -9.81584 q^{47} -0.383776 q^{48} -1.25960 q^{49} +9.69153 q^{50} -5.30576 q^{51} -1.47469 q^{52} +12.1213 q^{53} +7.86169 q^{54} +0.866932 q^{55} -6.52281 q^{56} -3.65694 q^{57} -1.42875 q^{58} +2.75664 q^{59} -5.75819 q^{60} -12.3862 q^{61} +4.33253 q^{62} +3.22306 q^{63} -12.9980 q^{64} +0.399181 q^{65} +4.76309 q^{66} -6.05336 q^{67} -8.13104 q^{68} +10.0899 q^{69} +4.72192 q^{70} -0.808647 q^{71} -3.66236 q^{72} -4.44931 q^{73} +11.9763 q^{74} -8.86393 q^{75} -5.60423 q^{76} -2.40205 q^{77} +2.19318 q^{78} -12.4318 q^{79} +0.159201 q^{80} -11.2260 q^{81} -13.7388 q^{82} -15.6966 q^{83} +15.9545 q^{84} +2.20098 q^{85} +3.19842 q^{86} +1.30675 q^{87} +2.72944 q^{88} +11.5248 q^{89} +2.65121 q^{90} -1.10603 q^{91} +15.4627 q^{92} -3.96255 q^{93} +22.3718 q^{94} +1.51700 q^{95} +12.2248 q^{96} +1.26083 q^{97} +2.87082 q^{98} -1.34868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * 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 $

$2$	−2.27915	−1.61160	−0.805800	−	0.592187i	$-0.798265\pi$
$2$	−2.27915	−1.61160	−0.805800	+	0.592187i	$0.798265\pi$
$3$	2.08452	1.20350	0.601750	−	0.798685i	$-0.294470\pi$
$3$	2.08452	1.20350	0.601750	+	0.798685i	$0.294470\pi$
$4$	3.19451	1.59726
$5$	−0.864719	−0.386714	−0.193357	−	0.981128i	$-0.561938\pi$
$5$	−0.864719	−0.386714	−0.193357	+	0.981128i	$0.561938\pi$
$6$	−4.75093	−1.93956
$7$	2.39591	0.905570	0.452785	−	0.891620i	$-0.350431\pi$
$7$	2.39591	0.905570	0.452785	+	0.891620i	$0.350431\pi$
$8$	−2.72247	−0.962540
$9$	1.34523	0.448411
$10$	1.97082	0.623229
$11$	−1.00256	−0.302283	−0.151142	−	0.988512i	$-0.548295\pi$
$11$	−1.00256	−0.302283	−0.151142	+	0.988512i	$0.548295\pi$
$12$	6.65904	1.92230
$13$	−0.461631	−0.128033	−0.0640167	−	0.997949i	$-0.520391\pi$
$13$	−0.461631	−0.128033	−0.0640167	+	0.997949i	$0.520391\pi$
$14$	−5.46064	−1.45942
$15$	−1.80253	−0.465410
$16$	−0.184108	−0.0460269
$17$	−2.54531	−0.617330	−0.308665	−	0.951171i	$-0.599882\pi$
$17$	−2.54531	−0.617330	−0.308665	+	0.951171i	$0.599882\pi$
$18$	−3.06598	−0.722659
$19$	−1.75433	−0.402471	−0.201235	−	0.979543i	$-0.564496\pi$
$19$	−1.75433	−0.402471	−0.201235	+	0.979543i	$0.564496\pi$
$20$	−2.76236	−0.617682
$21$	4.99433	1.08985
$22$	2.28498	0.487160
$23$	4.84039	1.00929	0.504645	−	0.863327i	$-0.331623\pi$
$23$	4.84039	1.00929	0.504645	+	0.863327i	$0.331623\pi$
$24$	−5.67506	−1.15842
$25$	−4.25226	−0.850452
$26$	1.05213	0.206339
$27$	−3.44940	−0.663837
$28$	7.65378	1.44643
$29$	0.626880	0.116409	0.0582044	−	0.998305i	$-0.481462\pi$
$29$	0.626880	0.116409	0.0582044	+	0.998305i	$0.481462\pi$
$30$	4.10822	0.750055
$31$	−1.90094	−0.341419	−0.170710	−	0.985321i	$-0.554606\pi$
$31$	−1.90094	−0.341419	−0.170710	+	0.985321i	$0.554606\pi$
$32$	5.86456	1.03672
$33$	−2.08986	−0.363797
$34$	5.80115	0.994889
$35$	−2.07179	−0.350197
$36$	4.29736	0.716227
$37$	−5.25472	−0.863871	−0.431935	−	0.901905i	$-0.642169\pi$
$37$	−5.25472	−0.863871	−0.431935	+	0.901905i	$0.642169\pi$
$38$	3.99838	0.648622
$39$	−0.962280	−0.154088
$40$	2.35417	0.372228
$41$	6.02802	0.941419	0.470709	−	0.882288i	$-0.343998\pi$
$41$	6.02802	0.941419	0.470709	+	0.882288i	$0.343998\pi$
$42$	−11.3828	−1.75641
$43$	−1.40334	−0.214007	−0.107004	−	0.994259i	$-0.534126\pi$
$43$	−1.40334	−0.214007	−0.107004	+	0.994259i	$0.534126\pi$
$44$	−3.20269	−0.482824
$45$	−1.16325	−0.173407
$46$	−11.0320	−1.62657
$47$	−9.81584	−1.43179	−0.715894	−	0.698209i	$-0.753981\pi$
$47$	−9.81584	−1.43179	−0.715894	+	0.698209i	$0.753981\pi$
$48$	−0.383776	−0.0553933
$49$	−1.25960	−0.179943
$50$	9.69153	1.37059
$51$	−5.30576	−0.742956
$52$	−1.47469	−0.204502
$53$	12.1213	1.66499	0.832494	−	0.554034i	$-0.186912\pi$
$53$	12.1213	1.66499	0.832494	+	0.554034i	$0.186912\pi$
$54$	7.86169	1.06984
$55$	0.866932	0.116897
$56$	−6.52281	−0.871647
$57$	−3.65694	−0.484373
$58$	−1.42875	−0.187604
$59$	2.75664	0.358884	0.179442	−	0.983769i	$-0.442571\pi$
$59$	2.75664	0.358884	0.179442	+	0.983769i	$0.442571\pi$
$60$	−5.75819	−0.743379
$61$	−12.3862	−1.58589	−0.792944	−	0.609295i	$-0.791453\pi$
$61$	−12.3862	−1.58589	−0.792944	+	0.609295i	$0.791453\pi$
$62$	4.33253	0.550231
$63$	3.22306	0.406067
$64$	−12.9980	−1.62475
$65$	0.399181	0.0495123
$66$	4.76309	0.586296
$67$	−6.05336	−0.739536	−0.369768	−	0.929124i	$-0.620563\pi$
$67$	−6.05336	−0.739536	−0.369768	+	0.929124i	$0.620563\pi$
$68$	−8.13104	−0.986034
$69$	10.0899	1.21468
$70$	4.72192	0.564377
$71$	−0.808647	−0.0959687	−0.0479844	−	0.998848i	$-0.515280\pi$
$71$	−0.808647	−0.0959687	−0.0479844	+	0.998848i	$0.515280\pi$
$72$	−3.66236	−0.431613
$73$	−4.44931	−0.520753	−0.260376	−	0.965507i	$-0.583847\pi$
$73$	−4.44931	−0.520753	−0.260376	+	0.965507i	$0.583847\pi$
$74$	11.9763	1.39221
$75$	−8.86393	−1.02352
$76$	−5.60423	−0.642849
$77$	−2.40205	−0.273738
$78$	2.19318	0.248328
$79$	−12.4318	−1.39869	−0.699345	−	0.714784i	$-0.746525\pi$
$79$	−12.4318	−1.39869	−0.699345	+	0.714784i	$0.746525\pi$
$80$	0.159201	0.0177992
$81$	−11.2260	−1.24734
$82$	−13.7388	−1.51719
$83$	−15.6966	−1.72293	−0.861466	−	0.507816i	$-0.830453\pi$
$83$	−15.6966	−1.72293	−0.861466	+	0.507816i	$0.830453\pi$
$84$	15.9545	1.74077
$85$	2.20098	0.238730
$86$	3.19842	0.344894
$87$	1.30675	0.140098
$88$	2.72944	0.290960
$89$	11.5248	1.22162	0.610811	−	0.791776i	$-0.290843\pi$
$89$	11.5248	1.22162	0.610811	+	0.791776i	$0.290843\pi$
$90$	2.65121	0.279462
$91$	−1.10603	−0.115943
$92$	15.4627	1.61210
$93$	−3.96255	−0.410898
$94$	22.3718	2.30747
$95$	1.51700	0.155641
$96$	12.2248	1.24769
$97$	1.26083	0.128018	0.0640091	−	0.997949i	$-0.479611\pi$
$97$	1.26083	0.128018	0.0640091	+	0.997949i	$0.479611\pi$
$98$	2.87082	0.289997
$99$	−1.34868	−0.135547
$100$	−13.5839	−1.35839
$101$	12.7022	1.26392	0.631958	−	0.775003i	$-0.282252\pi$
$101$	12.7022	1.26392	0.631958	+	0.775003i	$0.282252\pi$
$102$	12.0926	1.19735
$103$	16.2907	1.60517	0.802584	−	0.596540i	$-0.203458\pi$
$103$	16.2907	1.60517	0.802584	+	0.596540i	$0.203458\pi$
$104$	1.25678	0.123237
$105$	−4.31869	−0.421461
$106$	−27.6262	−2.68330
$107$	−0.583321	−0.0563917	−0.0281959	−	0.999602i	$-0.508976\pi$
$107$	−0.583321	−0.0563917	−0.0281959	+	0.999602i	$0.508976\pi$
$108$	−11.0192	−1.06032
$109$	−9.70037	−0.929127	−0.464563	−	0.885540i	$-0.653789\pi$
$109$	−9.70037	−0.929127	−0.464563	+	0.885540i	$0.653789\pi$
$110$	−1.97587	−0.188391
$111$	−10.9536	−1.03967
$112$	−0.441105	−0.0416806
$113$	4.27070	0.401754	0.200877	−	0.979617i	$-0.435621\pi$
$113$	4.27070	0.401754	0.200877	+	0.979617i	$0.435621\pi$
$114$	8.33470	0.780616
$115$	−4.18557	−0.390307
$116$	2.00258	0.185935
$117$	−0.621001	−0.0574115
$118$	−6.28280	−0.578378
$119$	−6.09835	−0.559035
$120$	4.90733	0.447976
$121$	−9.99487	−0.908625
$122$	28.2299	2.55582
$123$	12.5655	1.13300
$124$	−6.07258	−0.545334
$125$	8.00060	0.715596
$126$	−7.34583	−0.654418
$127$	−11.3928	−1.01094	−0.505472	−	0.862843i	$-0.668681\pi$
$127$	−11.3928	−1.01094	−0.505472	+	0.862843i	$0.668681\pi$
$128$	17.8952	1.58173
$129$	−2.92529	−0.257557
$130$	−0.909792	−0.0797941
$131$	9.34708	0.816658	0.408329	−	0.912835i	$-0.366112\pi$
$131$	9.34708	0.816658	0.408329	+	0.912835i	$0.366112\pi$
$132$	−6.67608	−0.581078
$133$	−4.20322	−0.364465
$134$	13.7965	1.19184
$135$	2.98276	0.256715
$136$	6.92955	0.594204
$137$	−22.0620	−1.88489	−0.942444	−	0.334365i	$-0.891478\pi$
$137$	−22.0620	−1.88489	−0.942444	+	0.334365i	$0.891478\pi$
$138$	−22.9964	−1.95758
$139$	−2.60250	−0.220741	−0.110371	−	0.993891i	$-0.535204\pi$
$139$	−2.60250	−0.220741	−0.110371	+	0.993891i	$0.535204\pi$
$140$	−6.61836	−0.559354
$141$	−20.4613	−1.72316
$142$	1.84303	0.154663
$143$	0.462812	0.0387023
$144$	−0.247667	−0.0206389
$145$	−0.542075	−0.0450169
$146$	10.1406	0.839246
$147$	−2.62567	−0.216562
$148$	−16.7863	−1.37982
$149$	−5.37507	−0.440343	−0.220171	−	0.975461i	$-0.570662\pi$
$149$	−5.37507	−0.440343	−0.220171	+	0.975461i	$0.570662\pi$
$150$	20.2022	1.64950
$151$	11.6858	0.950976	0.475488	−	0.879722i	$-0.342271\pi$
$151$	11.6858	0.950976	0.475488	+	0.879722i	$0.342271\pi$
$152$	4.77612	0.387394
$153$	−3.42404	−0.276817
$154$	5.47462	0.441157
$155$	1.64378	0.132032
$156$	−3.07402	−0.246118
$157$	−17.6611	−1.40951	−0.704755	−	0.709451i	$-0.748943\pi$
$157$	−17.6611	−1.40951	−0.704755	+	0.709451i	$0.748943\pi$
$158$	28.3340	2.25413
$159$	25.2671	2.00381
$160$	−5.07119	−0.400913
$161$	11.5971	0.913983
$162$	25.5858	2.01021
$163$	10.9159	0.854997	0.427499	−	0.904016i	$-0.359395\pi$
$163$	10.9159	0.854997	0.427499	+	0.904016i	$0.359395\pi$
$164$	19.2566	1.50369
$165$	1.80714	0.140686
$166$	35.7750	2.77668
$167$	−4.60523	−0.356363	−0.178182	−	0.983998i	$-0.557021\pi$
$167$	−4.60523	−0.356363	−0.178182	+	0.983998i	$0.557021\pi$
$168$	−13.5969	−1.04903
$169$	−12.7869	−0.983607
$170$	−5.01636	−0.384737
$171$	−2.35998	−0.180472
$172$	−4.48299	−0.341824
$173$	−14.5153	−1.10358	−0.551790	−	0.833983i	$-0.686055\pi$
$173$	−14.5153	−1.10358	−0.551790	+	0.833983i	$0.686055\pi$
$174$	−2.97827	−0.225782
$175$	−10.1880	−0.770144
$176$	0.184579	0.0139131
$177$	5.74628	0.431917
$178$	−26.2666	−1.96877
$179$	−21.0574	−1.57390	−0.786950	−	0.617017i	$-0.788341\pi$
$179$	−21.0574	−1.57390	−0.786950	+	0.617017i	$0.788341\pi$
$180$	−3.71601	−0.276975
$181$	24.0995	1.79131	0.895653	−	0.444754i	$-0.146709\pi$
$181$	24.0995	1.79131	0.895653	+	0.444754i	$0.146709\pi$
$182$	2.52080	0.186854
$183$	−25.8193	−1.90861
$184$	−13.1778	−0.971483
$185$	4.54385	0.334071
$186$	9.03125	0.662203
$187$	2.55183	0.186608
$188$	−31.3568	−2.28693
$189$	−8.26446	−0.601151
$190$	−3.45747	−0.250831
$191$	−26.4943	−1.91706	−0.958529	−	0.284995i	$-0.908008\pi$
$191$	−26.4943	−1.91706	−0.958529	+	0.284995i	$0.908008\pi$
$192$	−27.0946	−1.95538
$193$	−12.2393	−0.881007	−0.440504	−	0.897751i	$-0.645200\pi$
$193$	−12.2393	−0.881007	−0.440504	+	0.897751i	$0.645200\pi$
$194$	−2.87362	−0.206314
$195$	0.832101	0.0595880
$196$	−4.02382	−0.287416
$197$	13.4877	0.960956	0.480478	−	0.877007i	$-0.340463\pi$
$197$	13.4877	0.960956	0.480478	+	0.877007i	$0.340463\pi$
$198$	3.07383	0.218448
$199$	9.43346	0.668720	0.334360	−	0.942445i	$-0.391480\pi$
$199$	9.43346	0.668720	0.334360	+	0.942445i	$0.391480\pi$
$200$	11.5767	0.818594
$201$	−12.6184	−0.890031
$202$	−28.9502	−2.03693
$203$	1.50195	0.105416
$204$	−16.9493	−1.18669
$205$	−5.21254	−0.364060
$206$	−37.1288	−2.58689
$207$	6.51144	0.452577
$208$	0.0849897	0.00589298
$209$	1.75882	0.121660
$210$	9.84294	0.679227
$211$	8.50456	0.585478	0.292739	−	0.956192i	$-0.405433\pi$
$211$	8.50456	0.585478	0.292739	+	0.956192i	$0.405433\pi$
$212$	38.7217	2.65941
$213$	−1.68564	−0.115498
$214$	1.32947	0.0908810
$215$	1.21349	0.0827596
$216$	9.39090	0.638970
$217$	−4.55449	−0.309179
$218$	22.1086	1.49738
$219$	−9.27469	−0.626726
$220$	2.76943	0.186715
$221$	1.17500	0.0790388
$222$	24.9648	1.67553
$223$	26.0187	1.74234	0.871169	−	0.490983i	$-0.163362\pi$
$223$	26.0187	1.74234	0.871169	+	0.490983i	$0.163362\pi$
$224$	14.0510	0.938820
$225$	−5.72028	−0.381352
$226$	−9.73355	−0.647466
$227$	−13.8687	−0.920496	−0.460248	−	0.887790i	$-0.652239\pi$
$227$	−13.8687	−0.920496	−0.460248	+	0.887790i	$0.652239\pi$
$228$	−11.6821	−0.773669
$229$	−7.88026	−0.520742	−0.260371	−	0.965509i	$-0.583845\pi$
$229$	−7.88026	−0.520742	−0.260371	+	0.965509i	$0.583845\pi$
$230$	9.53954	0.629019
$231$	−5.00712	−0.329444
$232$	−1.70667	−0.112048
$233$	5.63885	0.369413	0.184707	−	0.982794i	$-0.440866\pi$
$233$	5.63885	0.369413	0.184707	+	0.982794i	$0.440866\pi$
$234$	1.41535	0.0925245
$235$	8.48794	0.553692
$236$	8.80614	0.573231
$237$	−25.9144	−1.68332
$238$	13.8990	0.900941
$239$	−4.53844	−0.293567	−0.146784	−	0.989169i	$-0.546892\pi$
$239$	−4.53844	−0.293567	−0.146784	+	0.989169i	$0.546892\pi$
$240$	0.331858	0.0214214
$241$	23.4315	1.50936	0.754679	−	0.656094i	$-0.227793\pi$
$241$	23.4315	1.50936	0.754679	+	0.656094i	$0.227793\pi$
$242$	22.7798	1.46434
$243$	−13.0527	−0.837334
$244$	−39.5678	−2.53307
$245$	1.08920	0.0695866
$246$	−28.6387	−1.82594
$247$	0.809853	0.0515297
$248$	5.17526	0.328630
$249$	−32.7200	−2.07355
$250$	−18.2346	−1.15325
$251$	14.4037	0.909156	0.454578	−	0.890707i	$-0.349790\pi$
$251$	14.4037	0.909156	0.454578	+	0.890707i	$0.349790\pi$
$252$	10.2961	0.648594
$253$	−4.85278	−0.305091
$254$	25.9658	1.62924
$255$	4.58799	0.287311
$256$	−14.7898	−0.924365
$257$	5.87660	0.366572	0.183286	−	0.983060i	$-0.441327\pi$
$257$	5.87660	0.366572	0.183286	+	0.983060i	$0.441327\pi$
$258$	6.66717	0.415080
$259$	−12.5898	−0.782295
$260$	1.27519	0.0790839
$261$	0.843299	0.0521989
$262$	−21.3034	−1.31613
$263$	−10.4208	−0.642575	−0.321288	−	0.946982i	$-0.604116\pi$
$263$	−10.4208	−0.642575	−0.321288	+	0.946982i	$0.604116\pi$
$264$	5.68958	0.350170
$265$	−10.4815	−0.643874
$266$	9.57976	0.587373
$267$	24.0236	1.47022
$268$	−19.3376	−1.18123
$269$	3.48078	0.212227	0.106113	−	0.994354i	$-0.466159\pi$
$269$	3.48078	0.212227	0.106113	+	0.994354i	$0.466159\pi$
$270$	−6.79815	−0.413722
$271$	31.2996	1.90132	0.950658	−	0.310241i	$-0.100410\pi$
$271$	31.2996	1.90132	0.950658	+	0.310241i	$0.100410\pi$
$272$	0.468612	0.0284137
$273$	−2.30554	−0.139538
$274$	50.2827	3.03769
$275$	4.26315	0.257077
$276$	32.2323	1.94016
$277$	−11.2046	−0.673217	−0.336609	−	0.941645i	$-0.609280\pi$
$277$	−11.2046	−0.673217	−0.336609	+	0.941645i	$0.609280\pi$
$278$	5.93148	0.355747
$279$	−2.55721	−0.153096
$280$	5.64040	0.337078
$281$	19.2976	1.15120	0.575598	−	0.817732i	$-0.304769\pi$
$281$	19.2976	1.15120	0.575598	+	0.817732i	$0.304769\pi$
$282$	46.6344	2.77704
$283$	8.17085	0.485707	0.242853	−	0.970063i	$-0.421917\pi$
$283$	8.17085	0.485707	0.242853	+	0.970063i	$0.421917\pi$
$284$	−2.58323	−0.153287
$285$	3.16222	0.187314
$286$	−1.05482	−0.0623727
$287$	14.4426	0.852520
$288$	7.88919	0.464875
$289$	−10.5214	−0.618904
$290$	1.23547	0.0725493
$291$	2.62823	0.154070
$292$	−14.2134	−0.831776
$293$	17.8246	1.04132	0.520661	−	0.853764i	$-0.325686\pi$
$293$	17.8246	1.04132	0.520661	+	0.853764i	$0.325686\pi$
$294$	5.98429	0.349011
$295$	−2.38372	−0.138786
$296$	14.3058	0.831510
$297$	3.45823	0.200667
$298$	12.2506	0.709657
$299$	−2.23447	−0.129223
$300$	−28.3160	−1.63482
$301$	−3.36228	−0.193798
$302$	−26.6336	−1.53259
$303$	26.4780	1.52112
$304$	0.322985	0.0185245
$305$	10.7106	0.613285
$306$	7.80389	0.446119
$307$	0.242524	0.0138416	0.00692078	−	0.999976i	$-0.497797\pi$
$307$	0.242524	0.0138416	0.00692078	+	0.999976i	$0.497797\pi$
$308$	−7.67337	−0.437231
$309$	33.9583	1.93182
$310$	−3.74642	−0.212782
$311$	11.6347	0.659742	0.329871	−	0.944026i	$-0.392995\pi$
$311$	11.6347	0.659742	0.329871	+	0.944026i	$0.392995\pi$
$312$	2.61978	0.148316
$313$	−20.6511	−1.16727	−0.583634	−	0.812017i	$-0.698370\pi$
$313$	−20.6511	−1.16727	−0.583634	+	0.812017i	$0.698370\pi$
$314$	40.2523	2.27157
$315$	−2.78704	−0.157032
$316$	−39.7137	−2.23407
$317$	17.9416	1.00770	0.503849	−	0.863792i	$-0.331917\pi$
$317$	17.9416	1.00770	0.503849	+	0.863792i	$0.331917\pi$
$318$	−57.5875	−3.22935
$319$	−0.628485	−0.0351884
$320$	11.2396	0.628312
$321$	−1.21594	−0.0678674
$322$	−26.4316	−1.47298
$323$	4.46532	0.248457
$324$	−35.8618	−1.99232
$325$	1.96298	0.108886
$326$	−24.8789	−1.37791
$327$	−20.2206	−1.11820
$328$	−16.4111	−0.906153
$329$	−23.5179	−1.29658
$330$	−4.11874	−0.226729
$331$	3.83033	0.210534	0.105267	−	0.994444i	$-0.466430\pi$
$331$	3.83033	0.210534	0.105267	+	0.994444i	$0.466430\pi$
$332$	−50.1432	−2.75196
$333$	−7.06882	−0.387369
$334$	10.4960	0.574315
$335$	5.23446	0.285989
$336$	−0.919494	−0.0501625
$337$	−4.64463	−0.253009	−0.126504	−	0.991966i	$-0.540376\pi$
$337$	−4.64463	−0.253009	−0.126504	+	0.991966i	$0.540376\pi$
$338$	29.1432	1.58518
$339$	8.90237	0.483510
$340$	7.03107	0.381313
$341$	1.90581	0.103205
$342$	5.37874	0.290849
$343$	−19.7893	−1.06852
$344$	3.82055	0.205990
$345$	−8.72492	−0.469734
$346$	33.0826	1.77853
$347$	13.0647	0.701351	0.350676	−	0.936497i	$-0.385952\pi$
$347$	13.0647	0.701351	0.350676	+	0.936497i	$0.385952\pi$
$348$	4.17442	0.223772
$349$	15.5092	0.830187	0.415093	−	0.909779i	$-0.363749\pi$
$349$	15.5092	0.830187	0.415093	+	0.909779i	$0.363749\pi$
$350$	23.2201	1.24116
$351$	1.59235	0.0849933
$352$	−5.87957	−0.313382
$353$	−26.4266	−1.40655	−0.703273	−	0.710920i	$-0.748279\pi$
$353$	−26.4266	−1.40655	−0.703273	+	0.710920i	$0.748279\pi$
$354$	−13.0966	−0.696078
$355$	0.699252	0.0371125
$356$	36.8160	1.95124
$357$	−12.7121	−0.672798
$358$	47.9928	2.53650
$359$	−15.1726	−0.800777	−0.400389	−	0.916345i	$-0.631125\pi$
$359$	−15.1726	−0.800777	−0.400389	+	0.916345i	$0.631125\pi$
$360$	3.16691	0.166911
$361$	−15.9223	−0.838017
$362$	−54.9264	−2.88687
$363$	−20.8345	−1.09353
$364$	−3.53322	−0.185191
$365$	3.84741	0.201382
$366$	58.8459	3.07592
$367$	11.3494	0.592436	0.296218	−	0.955120i	$-0.404275\pi$
$367$	11.3494	0.592436	0.296218	+	0.955120i	$0.404275\pi$
$368$	−0.891152	−0.0464545
$369$	8.10909	0.422142
$370$	−10.3561	−0.538389
$371$	29.0416	1.50776
$372$	−12.6584	−0.656309
$373$	−19.1285	−0.990438	−0.495219	−	0.868768i	$-0.664912\pi$
$373$	−19.1285	−0.990438	−0.495219	+	0.868768i	$0.664912\pi$
$374$	−5.81600	−0.300738
$375$	16.6774	0.861219
$376$	26.7234	1.37815
$377$	−0.289387	−0.0149042
$378$	18.8359	0.968816
$379$	−28.4354	−1.46063	−0.730314	−	0.683112i	$-0.760626\pi$
$379$	−28.4354	−1.46063	−0.730314	+	0.683112i	$0.760626\pi$
$380$	4.84608	0.248599
$381$	−23.7484	−1.21667
$382$	60.3843	3.08953
$383$	−9.93952	−0.507886	−0.253943	−	0.967219i	$-0.581728\pi$
$383$	−9.93952	−0.507886	−0.253943	+	0.967219i	$0.581728\pi$
$384$	37.3029	1.90361
$385$	2.07709	0.105858
$386$	27.8953	1.41983
$387$	−1.88782	−0.0959631
$388$	4.02775	0.204478
$389$	−11.7541	−0.595955	−0.297977	−	0.954573i	$-0.596312\pi$
$389$	−11.7541	−0.595955	−0.297977	+	0.954573i	$0.596312\pi$
$390$	−1.89648	−0.0960321
$391$	−12.3203	−0.623065
$392$	3.42924	0.173203
$393$	19.4842	0.982848
$394$	−30.7404	−1.54868
$395$	10.7500	0.540893
$396$	−4.30836	−0.216503
$397$	10.4550	0.524722	0.262361	−	0.964970i	$-0.415499\pi$
$397$	10.4550	0.524722	0.262361	+	0.964970i	$0.415499\pi$
$398$	−21.5002	−1.07771
$399$	−8.76170	−0.438634
$400$	0.782873	0.0391437
$401$	−16.8576	−0.841829	−0.420914	−	0.907100i	$-0.638291\pi$
$401$	−16.8576	−0.841829	−0.420914	+	0.907100i	$0.638291\pi$
$402$	28.7591	1.43437
$403$	0.877533	0.0437130
$404$	40.5773	2.01880
$405$	9.70737	0.482363
$406$	−3.42317	−0.169889
$407$	5.26817	0.261133
$408$	14.4448	0.715125
$409$	−36.4053	−1.80012	−0.900062	−	0.435761i	$-0.856479\pi$
$409$	−36.4053	−1.80012	−0.900062	+	0.435761i	$0.856479\pi$
$410$	11.8802	0.586719
$411$	−45.9888	−2.26846
$412$	52.0408	2.56386
$413$	6.60468	0.324995
$414$	−14.8405	−0.729373
$415$	13.5732	0.666282
$416$	−2.70726	−0.132734
$417$	−5.42497	−0.265662
$418$	−4.00861	−0.196067
$419$	−36.2447	−1.77067	−0.885336	−	0.464953i	$-0.846071\pi$
$419$	−36.2447	−1.77067	−0.885336	+	0.464953i	$0.846071\pi$
$420$	−13.7961	−0.673182
$421$	31.1150	1.51645	0.758227	−	0.651990i	$-0.226066\pi$
$421$	31.1150	1.51645	0.758227	+	0.651990i	$0.226066\pi$
$422$	−19.3832	−0.943557
$423$	−13.2046	−0.642029
$424$	−32.9999	−1.60262
$425$	10.8233	0.525009
$426$	3.84183	0.186137
$427$	−29.6762	−1.43613
$428$	−1.86343	−0.0900721
$429$	0.964743	0.0465782
$430$	−2.76573	−0.133375
$431$	6.62242	0.318991	0.159495	−	0.987199i	$-0.449013\pi$
$431$	6.62242	0.318991	0.159495	+	0.987199i	$0.449013\pi$
$432$	0.635060	0.0305544
$433$	24.2453	1.16516	0.582578	−	0.812775i	$-0.302044\pi$
$433$	24.2453	1.16516	0.582578	+	0.812775i	$0.302044\pi$
$434$	10.3804	0.498273
$435$	−1.12997	−0.0541778
$436$	−30.9880	−1.48405
$437$	−8.49163	−0.406210
$438$	21.1384	1.01003
$439$	−37.4378	−1.78681	−0.893405	−	0.449253i	$-0.851690\pi$
$439$	−37.4378	−1.78681	−0.893405	+	0.449253i	$0.851690\pi$
$440$	−2.36020	−0.112518
$441$	−1.69446	−0.0806885
$442$	−2.67799	−0.127379
$443$	−40.5123	−1.92480	−0.962398	−	0.271645i	$-0.912432\pi$
$443$	−40.5123	−1.92480	−0.962398	+	0.271645i	$0.912432\pi$
$444$	−34.9914	−1.66062
$445$	−9.96568	−0.472418
$446$	−59.3004	−2.80795
$447$	−11.2044	−0.529952
$448$	−31.1420	−1.47132
$449$	6.11612	0.288637	0.144319	−	0.989531i	$-0.453901\pi$
$449$	6.11612	0.288637	0.144319	+	0.989531i	$0.453901\pi$
$450$	13.0374	0.614587
$451$	−6.04345	−0.284575
$452$	13.6428	0.641704
$453$	24.3593	1.14450
$454$	31.6087	1.48347
$455$	0.956403	0.0448368
$456$	9.95592	0.466229
$457$	−22.1251	−1.03497	−0.517483	−	0.855693i	$-0.673131\pi$
$457$	−22.1251	−1.03497	−0.517483	+	0.855693i	$0.673131\pi$
$458$	17.9603	0.839228
$459$	8.77981	0.409806
$460$	−13.3709	−0.623420
$461$	−37.1092	−1.72835	−0.864174	−	0.503193i	$-0.832159\pi$
$461$	−37.1092	−1.72835	−0.864174	+	0.503193i	$0.832159\pi$
$462$	11.4120	0.530932
$463$	25.2294	1.17251	0.586254	−	0.810127i	$-0.300602\pi$
$463$	25.2294	1.17251	0.586254	+	0.810127i	$0.300602\pi$
$464$	−0.115413	−0.00535793
$465$	3.42649	0.158900
$466$	−12.8518	−0.595347
$467$	−16.6631	−0.771077	−0.385539	−	0.922692i	$-0.625984\pi$
$467$	−16.6631	−0.771077	−0.385539	+	0.922692i	$0.625984\pi$
$468$	−1.98380	−0.0917010
$469$	−14.5033	−0.669701
$470$	−19.3453	−0.892331
$471$	−36.8150	−1.69634
$472$	−7.50489	−0.345441
$473$	1.40693	0.0646907
$474$	59.0628	2.71285
$475$	7.45987	0.342282
$476$	−19.4813	−0.892923
$477$	16.3060	0.746598
$478$	10.3438	0.473113
$479$	30.6802	1.40182	0.700908	−	0.713252i	$-0.252778\pi$
$479$	30.6802	1.40182	0.700908	+	0.713252i	$0.252778\pi$
$480$	−10.5710	−0.482498
$481$	2.42574	0.110604
$482$	−53.4039	−2.43248
$483$	24.1745	1.09998
$484$	−31.9288	−1.45131
$485$	−1.09027	−0.0495064
$486$	29.7491	1.34945
$487$	−22.2307	−1.00737	−0.503685	−	0.863888i	$-0.668023\pi$
$487$	−22.2307	−1.00737	−0.503685	+	0.863888i	$0.668023\pi$
$488$	33.7210	1.52648
$489$	22.7544	1.02899
$490$	−2.48245	−0.112146
$491$	−6.25379	−0.282230	−0.141115	−	0.989993i	$-0.545069\pi$
$491$	−6.25379	−0.282230	−0.141115	+	0.989993i	$0.545069\pi$
$492$	40.1408	1.80969
$493$	−1.59561	−0.0718626
$494$	−1.84577	−0.0830453
$495$	1.16622	0.0524179
$496$	0.349978	0.0157145
$497$	−1.93745	−0.0869064
$498$	74.5737	3.34173
$499$	25.5754	1.14491	0.572457	−	0.819935i	$-0.305990\pi$
$499$	25.5754	1.14491	0.572457	+	0.819935i	$0.305990\pi$
$500$	25.5580	1.14299
$501$	−9.59970	−0.428883
$502$	−32.8283	−1.46520
$503$	−0.714683	−0.0318661	−0.0159331	−	0.999873i	$-0.505072\pi$
$503$	−0.714683	−0.0318661	−0.0159331	+	0.999873i	$0.505072\pi$
$504$	−8.77469	−0.390856
$505$	−10.9838	−0.488774
$506$	11.0602	0.491686
$507$	−26.6546	−1.18377
$508$	−36.3943	−1.61474
$509$	−26.5952	−1.17881	−0.589406	−	0.807837i	$-0.700638\pi$
$509$	−26.5952	−1.17881	−0.589406	+	0.807837i	$0.700638\pi$
$510$	−10.4567	−0.463031
$511$	−10.6602	−0.471578
$512$	−2.08216	−0.0920196
$513$	6.05138	0.267175
$514$	−13.3936	−0.590768
$515$	−14.0868	−0.620741
$516$	−9.34488	−0.411385
$517$	9.84097	0.432805
$518$	28.6941	1.26075
$519$	−30.2575	−1.32816
$520$	−1.08676	−0.0476576
$521$	42.4786	1.86102	0.930510	−	0.366266i	$-0.119364\pi$
$521$	42.4786	1.86102	0.930510	+	0.366266i	$0.119364\pi$
$522$	−1.92200	−0.0841238
$523$	−32.7575	−1.43238	−0.716192	−	0.697903i	$-0.754117\pi$
$523$	−32.7575	−1.43238	−0.716192	+	0.697903i	$0.754117\pi$
$524$	29.8594	1.30441
$525$	−21.2372	−0.926868
$526$	23.7506	1.03557
$527$	4.83849	0.210768
$528$	0.384758	0.0167445
$529$	0.429354	0.0186676
$530$	23.8889	1.03767
$531$	3.70833	0.160928
$532$	−13.4272	−0.582145
$533$	−2.78272	−0.120533
$534$	−54.7534	−2.36941
$535$	0.504408	0.0218075
$536$	16.4801	0.711833
$537$	−43.8945	−1.89419
$538$	−7.93321	−0.342025
$539$	1.26283	0.0543938
$540$	9.52847	0.410040
$541$	10.7199	0.460885	0.230442	−	0.973086i	$-0.425983\pi$
$541$	10.7199	0.460885	0.230442	+	0.973086i	$0.425983\pi$
$542$	−71.3364	−3.06416
$543$	50.2360	2.15583
$544$	−14.9271	−0.639996
$545$	8.38809	0.359306
$546$	5.25466	0.224879
$547$	25.9883	1.11118	0.555591	−	0.831456i	$-0.312492\pi$
$547$	25.9883	1.11118	0.555591	+	0.831456i	$0.312492\pi$
$548$	−70.4775	−3.01065
$549$	−16.6623	−0.711129
$550$	−9.71634	−0.414306
$551$	−1.09975	−0.0468511
$552$	−27.4695	−1.16918
$553$	−29.7856	−1.26661
$554$	25.5369	1.08496
$555$	9.47176	0.402054
$556$	−8.31372	−0.352580
$557$	−35.5723	−1.50725	−0.753623	−	0.657307i	$-0.771695\pi$
$557$	−35.5723	−1.50725	−0.753623	+	0.657307i	$0.771695\pi$
$558$	5.82825	0.246730
$559$	0.647825	0.0274001
$560$	0.381432	0.0161185
$561$	5.31935	0.224583
$562$	−43.9820	−1.85527
$563$	34.9006	1.47088	0.735442	−	0.677588i	$-0.236975\pi$
$563$	34.9006	1.47088	0.735442	+	0.677588i	$0.236975\pi$
$564$	−65.3640	−2.75232
$565$	−3.69295	−0.155364
$566$	−18.6226	−0.782765
$567$	−26.8966	−1.12955
$568$	2.20152	0.0923737
$569$	17.1629	0.719506	0.359753	−	0.933048i	$-0.382861\pi$
$569$	17.1629	0.719506	0.359753	+	0.933048i	$0.382861\pi$
$570$	−7.20717	−0.301875
$571$	−35.5658	−1.48838	−0.744190	−	0.667968i	$-0.767165\pi$
$571$	−35.5658	−1.48838	−0.744190	+	0.667968i	$0.767165\pi$
$572$	1.47846	0.0618176
$573$	−55.2279	−2.30718
$574$	−32.9168	−1.37392
$575$	−20.5826	−0.858354
$576$	−17.4853	−0.728554
$577$	−32.4388	−1.35044	−0.675222	−	0.737615i	$-0.735952\pi$
$577$	−32.4388	−1.35044	−0.675222	+	0.737615i	$0.735952\pi$
$578$	23.9798	0.997427
$579$	−25.5132	−1.06029
$580$	−1.73167	−0.0719035
$581$	−37.6078	−1.56023
$582$	−5.99013	−0.248299
$583$	−12.1523	−0.503298
$584$	12.1131	0.501245
$585$	0.536991	0.0222018
$586$	−40.6248	−1.67819
$587$	−26.9481	−1.11227	−0.556133	−	0.831093i	$-0.687716\pi$
$587$	−26.9481	−1.11227	−0.556133	+	0.831093i	$0.687716\pi$
$588$	−8.38774	−0.345905
$589$	3.33488	0.137411
$590$	5.43285	0.223667
$591$	28.1153	1.15651
$592$	0.967433	0.0397613
$593$	−41.5472	−1.70614	−0.853069	−	0.521798i	$-0.825261\pi$
$593$	−41.5472	−1.70614	−0.853069	+	0.521798i	$0.825261\pi$
$594$	−7.88182	−0.323395
$595$	5.27336	0.216187
$596$	−17.1707	−0.703341
$597$	19.6642	0.804804
$598$	5.09269	0.208256
$599$	−10.7945	−0.441052	−0.220526	−	0.975381i	$-0.570777\pi$
$599$	−10.7945	−0.441052	−0.220526	+	0.975381i	$0.570777\pi$
$600$	24.1318	0.985178
$601$	33.7565	1.37696	0.688478	−	0.725257i	$-0.258279\pi$
$601$	33.7565	1.37696	0.688478	+	0.725257i	$0.258279\pi$
$602$	7.66313	0.312326
$603$	−8.14318	−0.331616
$604$	37.3304	1.51895
$605$	8.64276	0.351378
$606$	−60.3473	−2.45144
$607$	27.0535	1.09807	0.549035	−	0.835799i	$-0.314995\pi$
$607$	27.0535	1.09807	0.549035	+	0.835799i	$0.314995\pi$
$608$	−10.2884	−0.417248
$609$	3.13085	0.126868
$610$	−24.4109	−0.988370
$611$	4.53130	0.183317
$612$	−10.9381	−0.442148
$613$	45.0437	1.81930	0.909648	−	0.415379i	$-0.136351\pi$
$613$	45.0437	1.81930	0.909648	+	0.415379i	$0.136351\pi$
$614$	−0.552748	−0.0223071
$615$	−10.8657	−0.438146
$616$	6.53951	0.263484
$617$	−18.0257	−0.725686	−0.362843	−	0.931850i	$-0.618194\pi$
$617$	−18.0257	−0.725686	−0.362843	+	0.931850i	$0.618194\pi$
$618$	−77.3959	−3.11332
$619$	45.3391	1.82233	0.911167	−	0.412037i	$-0.135183\pi$
$619$	45.3391	1.82233	0.911167	+	0.412037i	$0.135183\pi$
$620$	5.25108	0.210888
$621$	−16.6964	−0.670005
$622$	−26.5171	−1.06324
$623$	27.6123	1.10626
$624$	0.177163	0.00709219
$625$	14.3430	0.573721
$626$	47.0669	1.88117
$627$	3.66630	0.146418
$628$	−56.4187	−2.25135
$629$	13.3749	0.533293
$630$	6.35207	0.253073
$631$	−39.0046	−1.55275	−0.776373	−	0.630273i	$-0.782943\pi$
$631$	−39.0046	−1.55275	−0.776373	+	0.630273i	$0.782943\pi$
$632$	33.8454	1.34630
$633$	17.7279	0.704623
$634$	−40.8915	−1.62401
$635$	9.85153	0.390946
$636$	80.7161	3.20060
$637$	0.581472	0.0230387
$638$	1.43241	0.0567096
$639$	−1.08782	−0.0430334
$640$	−15.4743	−0.611676
$641$	8.14932	0.321879	0.160939	−	0.986964i	$-0.448548\pi$
$641$	8.14932	0.321879	0.160939	+	0.986964i	$0.448548\pi$
$642$	2.77132	0.109375
$643$	−9.86971	−0.389223	−0.194612	−	0.980880i	$-0.562345\pi$
$643$	−9.86971	−0.389223	−0.194612	+	0.980880i	$0.562345\pi$
$644$	37.0472	1.45987
$645$	2.52955	0.0996011
$646$	−10.1771	−0.400414
$647$	9.02351	0.354751	0.177375	−	0.984143i	$-0.443239\pi$
$647$	9.02351	0.354751	0.177375	+	0.984143i	$0.443239\pi$
$648$	30.5626	1.20061
$649$	−2.76370	−0.108485
$650$	−4.47391	−0.175481
$651$	−9.49393	−0.372097
$652$	34.8709	1.36565
$653$	16.5660	0.648277	0.324138	−	0.946010i	$-0.394926\pi$
$653$	16.5660	0.648277	0.324138	+	0.946010i	$0.394926\pi$
$654$	46.0858	1.80210
$655$	−8.08260	−0.315813
$656$	−1.10980	−0.0433306
$657$	−5.98536	−0.233511
$658$	53.6008	2.08958
$659$	30.2697	1.17914	0.589571	−	0.807717i	$-0.299297\pi$
$659$	30.2697	1.17914	0.589571	+	0.807717i	$0.299297\pi$
$660$	5.77293	0.224711
$661$	−48.6026	−1.89042	−0.945211	−	0.326460i	$-0.894144\pi$
$661$	−48.6026	−1.89042	−0.945211	+	0.326460i	$0.894144\pi$
$662$	−8.72989	−0.339297
$663$	2.44931	0.0951231
$664$	42.7337	1.65839
$665$	3.63460	0.140944
$666$	16.1109	0.624284
$667$	3.03434	0.117490
$668$	−14.7115	−0.569204
$669$	54.2365	2.09690
$670$	−11.9301	−0.460900
$671$	12.4179	0.479387
$672$	29.2895	1.12987
$673$	−26.0038	−1.00237	−0.501187	−	0.865339i	$-0.667103\pi$
$673$	−26.0038	−1.00237	−0.501187	+	0.865339i	$0.667103\pi$
$674$	10.5858	0.407749
$675$	14.6678	0.564562
$676$	−40.8479	−1.57107
$677$	−10.1517	−0.390163	−0.195082	−	0.980787i	$-0.562497\pi$
$677$	−10.1517	−0.390163	−0.195082	+	0.980787i	$0.562497\pi$
$678$	−20.2898	−0.779225
$679$	3.02085	0.115929
$680$	−5.99212	−0.229787
$681$	−28.9095	−1.10782
$682$	−4.34362	−0.166326
$683$	43.2316	1.65421	0.827105	−	0.562047i	$-0.189986\pi$
$683$	43.2316	1.65421	0.827105	+	0.562047i	$0.189986\pi$
$684$	−7.53899	−0.288260
$685$	19.0775	0.728912
$686$	45.1027	1.72203
$687$	−16.4266	−0.626713
$688$	0.258365	0.00985008
$689$	−5.59557	−0.213174
$690$	19.8854	0.757024
$691$	8.29640	0.315610	0.157805	−	0.987470i	$-0.449558\pi$
$691$	8.29640	0.315610	0.157805	+	0.987470i	$0.449558\pi$
$692$	−46.3694	−1.76270
$693$	−3.23131	−0.122747
$694$	−29.7764	−1.13030
$695$	2.25043	0.0853637
$696$	−3.55758	−0.134850
$697$	−15.3432	−0.581166
$698$	−35.3477	−1.33793
$699$	11.7543	0.444589
$700$	−32.5459	−1.23012
$701$	−11.6840	−0.441299	−0.220650	−	0.975353i	$-0.570818\pi$
$701$	−11.6840	−0.441299	−0.220650	+	0.975353i	$0.570818\pi$
$702$	−3.62920	−0.136975
$703$	9.21851	0.347683
$704$	13.0312	0.491134
$705$	17.6933	0.666368
$706$	60.2301	2.26679
$707$	30.4333	1.14456
$708$	18.3566	0.689883
$709$	−8.15888	−0.306413	−0.153207	−	0.988194i	$-0.548960\pi$
$709$	−8.15888	−0.306413	−0.153207	+	0.988194i	$0.548960\pi$
$710$	−1.59370	−0.0598105
$711$	−16.7237	−0.627188
$712$	−31.3759	−1.17586
$713$	−9.20129	−0.344591
$714$	28.9729	1.08428
$715$	−0.400203	−0.0149667
$716$	−67.2680	−2.51392
$717$	−9.46048	−0.353308
$718$	34.5805	1.29053
$719$	−26.5610	−0.990558	−0.495279	−	0.868734i	$-0.664934\pi$
$719$	−26.5610	−0.990558	−0.495279	+	0.868734i	$0.664934\pi$
$720$	0.214163	0.00798137
$721$	39.0310	1.45359
$722$	36.2893	1.35055
$723$	48.8436	1.81651
$724$	76.9863	2.86118
$725$	−2.66566	−0.0990001
$726$	47.4850	1.76233
$727$	−15.7925	−0.585711	−0.292855	−	0.956157i	$-0.594605\pi$
$727$	−15.7925	−0.585711	−0.292855	+	0.956157i	$0.594605\pi$
$728$	3.01113	0.111600
$729$	6.46942	0.239608
$730$	−8.76881	−0.324548
$731$	3.57194	0.132113
$732$	−82.4800	−3.04855
$733$	18.4741	0.682357	0.341179	−	0.939998i	$-0.389174\pi$
$733$	18.4741	0.682357	0.341179	+	0.939998i	$0.389174\pi$
$734$	−25.8670	−0.954770
$735$	2.27047	0.0837474
$736$	28.3867	1.04635
$737$	6.06886	0.223549
$738$	−18.4818	−0.680325
$739$	5.59242	0.205720	0.102860	−	0.994696i	$-0.467201\pi$
$739$	5.59242	0.205720	0.102860	+	0.994696i	$0.467201\pi$
$740$	14.5154	0.533597
$741$	1.68816	0.0620159
$742$	−66.1900	−2.42991
$743$	51.9706	1.90662	0.953309	−	0.301996i	$-0.0976531\pi$
$743$	51.9706	1.90662	0.953309	+	0.301996i	$0.0976531\pi$
$744$	10.7880	0.395505
$745$	4.64792	0.170287
$746$	43.5968	1.59619
$747$	−21.1156	−0.772581
$748$	8.15186	0.298061
$749$	−1.39759	−0.0510666
$750$	−38.0103	−1.38794
$751$	12.9682	0.473215	0.236608	−	0.971605i	$-0.423964\pi$
$751$	12.9682	0.473215	0.236608	+	0.971605i	$0.423964\pi$
$752$	1.80717	0.0659007
$753$	30.0249	1.09417
$754$	0.659556	0.0240196
$755$	−10.1049	−0.367756
$756$	−26.4009	−0.960193
$757$	20.4321	0.742617	0.371309	−	0.928510i	$-0.378909\pi$
$757$	20.4321	0.742617	0.371309	+	0.928510i	$0.378909\pi$
$758$	64.8084	2.35395
$759$	−10.1157	−0.367177
$760$	−4.13000	−0.149811
$761$	−52.8401	−1.91545	−0.957727	−	0.287680i	$-0.907116\pi$
$761$	−52.8401	−1.91545	−0.957727	+	0.287680i	$0.907116\pi$
$762$	54.1262	1.96079
$763$	−23.2412	−0.841389
$764$	−84.6363	−3.06203
$765$	2.96083	0.107049
$766$	22.6536	0.818509
$767$	−1.27255	−0.0459492
$768$	−30.8297	−1.11247
$769$	4.47674	0.161436	0.0807178	−	0.996737i	$-0.474279\pi$
$769$	4.47674	0.161436	0.0807178	+	0.996737i	$0.474279\pi$
$770$	−4.73400	−0.170602
$771$	12.2499	0.441169
$772$	−39.0988	−1.40720
$773$	18.6990	0.672557	0.336278	−	0.941763i	$-0.390832\pi$
$773$	18.6990	0.672557	0.336278	+	0.941763i	$0.390832\pi$
$774$	4.30261	0.154654
$775$	8.08330	0.290361
$776$	−3.43259	−0.123223
$777$	−26.2438	−0.941492
$778$	26.7892	0.960441
$779$	−10.5751	−0.378894
$780$	2.65816	0.0951774
$781$	0.810717	0.0290097
$782$	28.0798	1.00413
$783$	−2.16236	−0.0772765
$784$	0.231902	0.00828223
$785$	15.2719	0.545077
$786$	−44.4074	−1.58396
$787$	44.1325	1.57315	0.786577	−	0.617492i	$-0.211851\pi$
$787$	44.1325	1.57315	0.786577	+	0.617492i	$0.211851\pi$
$788$	43.0865	1.53489
$789$	−21.7224	−0.773339
$790$	−24.5009	−0.871704
$791$	10.2322	0.363816
$792$	3.67173	0.130469
$793$	5.71784	0.203047
$794$	−23.8285	−0.845643
$795$	−21.8489	−0.774902
$796$	30.1353	1.06812
$797$	−21.8244	−0.773061	−0.386531	−	0.922277i	$-0.626327\pi$
$797$	−21.8244	−0.773061	−0.386531	+	0.922277i	$0.626327\pi$
$798$	19.9692	0.706903
$799$	24.9844	0.883885
$800$	−24.9376	−0.881678
$801$	15.5035	0.547788
$802$	38.4210	1.35669
$803$	4.46070	0.157415
$804$	−40.3096	−1.42161
$805$	−10.0283	−0.353450
$806$	−2.00003	−0.0704480
$807$	7.25576	0.255415
$808$	−34.5814	−1.21657
$809$	−13.8990	−0.488662	−0.244331	−	0.969692i	$-0.578568\pi$
$809$	−13.8990	−0.488662	−0.244331	+	0.969692i	$0.578568\pi$
$810$	−22.1245	−0.777377
$811$	36.8152	1.29276	0.646379	−	0.763017i	$-0.276283\pi$
$811$	36.8152	1.29276	0.646379	+	0.763017i	$0.276283\pi$
$812$	4.79800	0.168377
$813$	65.2447	2.28823
$814$	−12.0069	−0.420843
$815$	−9.43916	−0.330639
$816$	0.976831	0.0341959
$817$	2.46192	0.0861316
$818$	82.9730	2.90108
$819$	−1.48786	−0.0519902
$820$	−16.6515	−0.581497
$821$	25.2949	0.882797	0.441399	−	0.897311i	$-0.354482\pi$
$821$	25.2949	0.882797	0.441399	+	0.897311i	$0.354482\pi$
$822$	104.815	3.65585
$823$	−33.8067	−1.17843	−0.589214	−	0.807977i	$-0.700562\pi$
$823$	−33.8067	−1.17843	−0.589214	+	0.807977i	$0.700562\pi$
$824$	−44.3509	−1.54504
$825$	8.88662	0.309392
$826$	−15.0530	−0.523762
$827$	40.4394	1.40621	0.703107	−	0.711084i	$-0.251795\pi$
$827$	40.4394	1.40621	0.703107	+	0.711084i	$0.251795\pi$
$828$	20.8009	0.722881
$829$	−33.1953	−1.15292	−0.576460	−	0.817126i	$-0.695566\pi$
$829$	−33.1953	−1.15292	−0.576460	+	0.817126i	$0.695566\pi$
$830$	−30.9353	−1.07378
$831$	−23.3562	−0.810217
$832$	6.00027	0.208022
$833$	3.20609	0.111084
$834$	12.3643	0.428141
$835$	3.98223	0.137811
$836$	5.61857	0.194322
$837$	6.55711	0.226647
$838$	82.6071	2.85362
$839$	−8.69388	−0.300146	−0.150073	−	0.988675i	$-0.547951\pi$
$839$	−8.69388	−0.300146	−0.150073	+	0.988675i	$0.547951\pi$
$840$	11.7575	0.405673
$841$	−28.6070	−0.986449
$842$	−70.9158	−2.44392
$843$	40.2262	1.38546
$844$	27.1679	0.935159
$845$	11.0571	0.380375
$846$	30.0952	1.03469
$847$	−23.9468	−0.822823
$848$	−2.23162	−0.0766342
$849$	17.0323	0.584548
$850$	−24.6680	−0.846105
$851$	−25.4349	−0.871896
$852$	−5.38481	−0.184480
$853$	−55.7539	−1.90898	−0.954488	−	0.298249i	$-0.903597\pi$
$853$	−55.7539	−1.90898	−0.954488	+	0.298249i	$0.903597\pi$
$854$	67.6364	2.31447
$855$	2.04072	0.0697911
$856$	1.58808	0.0542793
$857$	35.7705	1.22190	0.610949	−	0.791670i	$-0.290788\pi$
$857$	35.7705	1.22190	0.610949	+	0.791670i	$0.290788\pi$
$858$	−2.19879	−0.0750655
$859$	35.7233	1.21886	0.609431	−	0.792839i	$-0.291398\pi$
$859$	35.7233	1.21886	0.609431	+	0.792839i	$0.291398\pi$
$860$	3.87652	0.132188
$861$	30.1059	1.02601
$862$	−15.0935	−0.514086
$863$	−9.55894	−0.325390	−0.162695	−	0.986676i	$-0.552019\pi$
$863$	−9.55894	−0.325390	−0.162695	+	0.986676i	$0.552019\pi$
$864$	−20.2292	−0.688211
$865$	12.5517	0.426770
$866$	−55.2587	−1.87777
$867$	−21.9320	−0.744851
$868$	−14.5494	−0.493838
$869$	12.4637	0.422801
$870$	2.57536	0.0873130
$871$	2.79442	0.0946853
$872$	26.4090	0.894321
$873$	1.69611	0.0574047
$874$	19.3537	0.654648
$875$	19.1687	0.648022
$876$	−29.6281	−1.00104
$877$	12.8141	0.432702	0.216351	−	0.976316i	$-0.430584\pi$
$877$	12.8141	0.432702	0.216351	+	0.976316i	$0.430584\pi$
$878$	85.3263	2.87962
$879$	37.1557	1.25323
$880$	−0.159609	−0.00538041
$881$	−23.1246	−0.779088	−0.389544	−	0.921008i	$-0.627367\pi$
$881$	−23.1246	−0.779088	−0.389544	+	0.921008i	$0.627367\pi$
$882$	3.86192	0.130038
$883$	−10.7221	−0.360829	−0.180414	−	0.983591i	$-0.557744\pi$
$883$	−10.7221	−0.360829	−0.180414	+	0.983591i	$0.557744\pi$
$884$	3.75354	0.126245
$885$	−4.96892	−0.167028
$886$	92.3334	3.10200
$887$	21.4983	0.721843	0.360922	−	0.932596i	$-0.382462\pi$
$887$	21.4983	0.721843	0.360922	+	0.932596i	$0.382462\pi$
$888$	29.8208	1.00072
$889$	−27.2960	−0.915480
$890$	22.7133	0.761350
$891$	11.2548	0.377049
$892$	83.1170	2.78296
$893$	17.2202	0.576253
$894$	25.5366	0.854071
$895$	18.2087	0.608649
$896$	42.8753	1.43236
$897$	−4.65781	−0.155520
$898$	−13.9395	−0.465168
$899$	−1.19166	−0.0397442
$900$	−18.2735	−0.609117
$901$	−30.8525	−1.02785
$902$	13.7739	0.458621
$903$	−7.00874	−0.233236
$904$	−11.6269	−0.386704
$905$	−20.8393	−0.692723
$906$	−55.5184	−1.84448
$907$	−16.1028	−0.534683	−0.267342	−	0.963602i	$-0.586145\pi$
$907$	−16.1028	−0.534683	−0.267342	+	0.963602i	$0.586145\pi$
$908$	−44.3036	−1.47027
$909$	17.0874	0.566753
$910$	−2.17978	−0.0722591
$911$	0.117779	0.00390220	0.00195110	−	0.999998i	$-0.499379\pi$
$911$	0.117779	0.00390220	0.00195110	+	0.999998i	$0.499379\pi$
$912$	0.673270	0.0222942
$913$	15.7368	0.520813
$914$	50.4263	1.66795
$915$	22.3264	0.738088
$916$	−25.1736	−0.831759
$917$	22.3948	0.739541
$918$	−20.0105	−0.660444
$919$	16.7297	0.551861	0.275930	−	0.961178i	$-0.411014\pi$
$919$	16.7297	0.551861	0.275930	+	0.961178i	$0.411014\pi$
$920$	11.3951	0.375686
$921$	0.505546	0.0166583
$922$	84.5774	2.78541
$923$	0.373296	0.0122872
$924$	−15.9953	−0.526207
$925$	22.3444	0.734681
$926$	−57.5015	−1.88962
$927$	21.9147	0.719774
$928$	3.67637	0.120683
$929$	14.1523	0.464322	0.232161	−	0.972677i	$-0.425420\pi$
$929$	14.1523	0.464322	0.232161	+	0.972677i	$0.425420\pi$
$930$	−7.80949	−0.256083
$931$	2.20976	0.0724219
$932$	18.0134	0.590048
$933$	24.2527	0.793999
$934$	37.9777	1.24267
$935$	−2.20662	−0.0721640
$936$	1.69066	0.0552609
$937$	52.4526	1.71355	0.856776	−	0.515688i	$-0.172464\pi$
$937$	52.4526	1.71355	0.856776	+	0.515688i	$0.172464\pi$
$938$	33.0552	1.07929
$939$	−43.0476	−1.40481
$940$	27.1149	0.884389
$941$	−51.4102	−1.67592	−0.837962	−	0.545728i	$-0.816253\pi$
$941$	−51.4102	−1.67592	−0.837962	+	0.545728i	$0.816253\pi$
$942$	83.9067	2.73383
$943$	29.1780	0.950165
$944$	−0.507519	−0.0165183
$945$	7.14644	0.232474
$946$	−3.20660	−0.104256
$947$	43.6848	1.41957	0.709783	−	0.704420i	$-0.248793\pi$
$947$	43.6848	1.41957	0.709783	+	0.704420i	$0.248793\pi$
$948$	−82.7840	−2.68870
$949$	2.05394	0.0666738
$950$	−17.0021	−0.551622
$951$	37.3996	1.21276
$952$	16.6026	0.538094
$953$	38.6534	1.25211	0.626053	−	0.779780i	$-0.284669\pi$
$953$	38.6534	1.25211	0.626053	+	0.779780i	$0.284669\pi$
$954$	−37.1637	−1.20322
$955$	22.9101	0.741353
$956$	−14.4981	−0.468902
$957$	−1.31009	−0.0423492
$958$	−69.9248	−2.25917
$959$	−52.8587	−1.70690
$960$	23.4292	0.756174
$961$	−27.3864	−0.883433
$962$	−5.52862	−0.178250
$963$	−0.784701	−0.0252867
$964$	74.8524	2.41083
$965$	10.5836	0.340698
$966$	−55.0973	−1.77273
$967$	−19.5985	−0.630246	−0.315123	−	0.949051i	$-0.602046\pi$
$967$	−19.5985	−0.630246	−0.315123	+	0.949051i	$0.602046\pi$
$968$	27.2108	0.874588
$969$	9.30806	0.299018
$970$	2.48488	0.0797846
$971$	−48.5718	−1.55874	−0.779372	−	0.626561i	$-0.784462\pi$
$971$	−48.5718	−1.55874	−0.779372	+	0.626561i	$0.784462\pi$
$972$	−41.6972	−1.33744
$973$	−6.23536	−0.199897
$974$	50.6671	1.62348
$975$	4.09187	0.131045
$976$	2.28039	0.0729934
$977$	47.5548	1.52141	0.760707	−	0.649096i	$-0.224853\pi$
$977$	47.5548	1.52141	0.760707	+	0.649096i	$0.224853\pi$
$978$	−51.8606	−1.65832
$979$	−11.5543	−0.369276
$980$	3.47947	0.111148
$981$	−13.0492	−0.416630
$982$	14.2533	0.454841
$983$	45.1476	1.43998	0.719992	−	0.693983i	$-0.244146\pi$
$983$	45.1476	1.43998	0.719992	+	0.693983i	$0.244146\pi$
$984$	−34.2094	−1.09055
$985$	−11.6630	−0.371615
$986$	3.63663	0.115814
$987$	−49.0236	−1.56044
$988$	2.58709	0.0823062
$989$	−6.79270	−0.215995
$990$	−2.65800	−0.0844767
$991$	−57.0791	−1.81318	−0.906589	−	0.422016i	$-0.861323\pi$
$991$	−57.0791	−1.81318	−0.906589	+	0.422016i	$0.861323\pi$
$992$	−11.1482	−0.353955
$993$	7.98441	0.253377
$994$	4.41573	0.140058
$995$	−8.15729	−0.258603
$996$	−104.525	−3.31199
$997$	−1.79545	−0.0568626	−0.0284313	−	0.999596i	$-0.509051\pi$
$997$	−1.79545	−0.0568626	−0.0284313	+	0.999596i	$0.509051\pi$
$998$	−58.2902	−1.84514
$999$	18.1256	0.573470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.15	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.15	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27915 q^{2} +2.08452 q^{3} +3.19451 q^{4} -0.864719 q^{5} -4.75093 q^{6} +2.39591 q^{7} -2.72247 q^{8} +1.34523 q^{9} +O(q^{10})\)	\(q-2.27915 q^{2} +2.08452 q^{3} +3.19451 q^{4} -0.864719 q^{5} -4.75093 q^{6} +2.39591 q^{7} -2.72247 q^{8} +1.34523 q^{9} +1.97082 q^{10} -1.00256 q^{11} +6.65904 q^{12} -0.461631 q^{13} -5.46064 q^{14} -1.80253 q^{15} -0.184108 q^{16} -2.54531 q^{17} -3.06598 q^{18} -1.75433 q^{19} -2.76236 q^{20} +4.99433 q^{21} +2.28498 q^{22} +4.84039 q^{23} -5.67506 q^{24} -4.25226 q^{25} +1.05213 q^{26} -3.44940 q^{27} +7.65378 q^{28} +0.626880 q^{29} +4.10822 q^{30} -1.90094 q^{31} +5.86456 q^{32} -2.08986 q^{33} +5.80115 q^{34} -2.07179 q^{35} +4.29736 q^{36} -5.25472 q^{37} +3.99838 q^{38} -0.962280 q^{39} +2.35417 q^{40} +6.02802 q^{41} -11.3828 q^{42} -1.40334 q^{43} -3.20269 q^{44} -1.16325 q^{45} -11.0320 q^{46} -9.81584 q^{47} -0.383776 q^{48} -1.25960 q^{49} +9.69153 q^{50} -5.30576 q^{51} -1.47469 q^{52} +12.1213 q^{53} +7.86169 q^{54} +0.866932 q^{55} -6.52281 q^{56} -3.65694 q^{57} -1.42875 q^{58} +2.75664 q^{59} -5.75819 q^{60} -12.3862 q^{61} +4.33253 q^{62} +3.22306 q^{63} -12.9980 q^{64} +0.399181 q^{65} +4.76309 q^{66} -6.05336 q^{67} -8.13104 q^{68} +10.0899 q^{69} +4.72192 q^{70} -0.808647 q^{71} -3.66236 q^{72} -4.44931 q^{73} +11.9763 q^{74} -8.86393 q^{75} -5.60423 q^{76} -2.40205 q^{77} +2.19318 q^{78} -12.4318 q^{79} +0.159201 q^{80} -11.2260 q^{81} -13.7388 q^{82} -15.6966 q^{83} +15.9545 q^{84} +2.20098 q^{85} +3.19842 q^{86} +1.30675 q^{87} +2.72944 q^{88} +11.5248 q^{89} +2.65121 q^{90} -1.10603 q^{91} +15.4627 q^{92} -3.96255 q^{93} +22.3718 q^{94} +1.51700 q^{95} +12.2248 q^{96} +1.26083 q^{97} +2.87082 q^{98} -1.34868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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