LMFDB - Embedded newform 8043.2.a.q.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.01632 q^{2} +1.00000 q^{3} +2.06555 q^{4} +2.51738 q^{5} -2.01632 q^{6} -1.00000 q^{7} -0.132166 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.01632 q^{2} +1.00000 q^{3} +2.06555 q^{4} +2.51738 q^{5} -2.01632 q^{6} -1.00000 q^{7} -0.132166 q^{8} +1.00000 q^{9} -5.07585 q^{10} +2.22076 q^{11} +2.06555 q^{12} -2.17809 q^{13} +2.01632 q^{14} +2.51738 q^{15} -3.86461 q^{16} +6.87612 q^{17} -2.01632 q^{18} -7.75260 q^{19} +5.19977 q^{20} -1.00000 q^{21} -4.47776 q^{22} -2.52495 q^{23} -0.132166 q^{24} +1.33721 q^{25} +4.39173 q^{26} +1.00000 q^{27} -2.06555 q^{28} -4.44605 q^{29} -5.07585 q^{30} -7.77121 q^{31} +8.05662 q^{32} +2.22076 q^{33} -13.8645 q^{34} -2.51738 q^{35} +2.06555 q^{36} +0.386135 q^{37} +15.6317 q^{38} -2.17809 q^{39} -0.332711 q^{40} +10.0609 q^{41} +2.01632 q^{42} -0.278777 q^{43} +4.58708 q^{44} +2.51738 q^{45} +5.09111 q^{46} +8.79353 q^{47} -3.86461 q^{48} +1.00000 q^{49} -2.69624 q^{50} +6.87612 q^{51} -4.49895 q^{52} -14.0287 q^{53} -2.01632 q^{54} +5.59050 q^{55} +0.132166 q^{56} -7.75260 q^{57} +8.96467 q^{58} -13.0768 q^{59} +5.19977 q^{60} -11.1768 q^{61} +15.6693 q^{62} -1.00000 q^{63} -8.51551 q^{64} -5.48308 q^{65} -4.47776 q^{66} +11.4252 q^{67} +14.2030 q^{68} -2.52495 q^{69} +5.07585 q^{70} +3.12631 q^{71} -0.132166 q^{72} -13.6655 q^{73} -0.778572 q^{74} +1.33721 q^{75} -16.0134 q^{76} -2.22076 q^{77} +4.39173 q^{78} -13.5376 q^{79} -9.72869 q^{80} +1.00000 q^{81} -20.2860 q^{82} +5.53562 q^{83} -2.06555 q^{84} +17.3098 q^{85} +0.562104 q^{86} -4.44605 q^{87} -0.293508 q^{88} +0.809204 q^{89} -5.07585 q^{90} +2.17809 q^{91} -5.21541 q^{92} -7.77121 q^{93} -17.7306 q^{94} -19.5163 q^{95} +8.05662 q^{96} +2.77543 q^{97} -2.01632 q^{98} +2.22076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * 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 $

$2$	−2.01632	−1.42575	−0.712877	−	0.701289i	$-0.752608\pi$
$2$	−2.01632	−1.42575	−0.712877	+	0.701289i	$0.752608\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.06555	1.03277
$5$	2.51738	1.12581	0.562904	−	0.826523i	$-0.309684\pi$
$5$	2.51738	1.12581	0.562904	+	0.826523i	$0.309684\pi$
$6$	−2.01632	−0.823159
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.132166	−0.0467276
$9$	1.00000	0.333333
$10$	−5.07585	−1.60512
$11$	2.22076	0.669584	0.334792	−	0.942292i	$-0.391334\pi$
$11$	2.22076	0.669584	0.334792	+	0.942292i	$0.391334\pi$
$12$	2.06555	0.596272
$13$	−2.17809	−0.604093	−0.302047	−	0.953293i	$-0.597670\pi$
$13$	−2.17809	−0.604093	−0.302047	+	0.953293i	$0.597670\pi$
$14$	2.01632	0.538884
$15$	2.51738	0.649985
$16$	−3.86461	−0.966152
$17$	6.87612	1.66771	0.833853	−	0.551987i	$-0.186130\pi$
$17$	6.87612	1.66771	0.833853	+	0.551987i	$0.186130\pi$
$18$	−2.01632	−0.475251
$19$	−7.75260	−1.77857	−0.889285	−	0.457354i	$-0.848797\pi$
$19$	−7.75260	−1.77857	−0.889285	+	0.457354i	$0.848797\pi$
$20$	5.19977	1.16270
$21$	−1.00000	−0.218218
$22$	−4.47776	−0.954662
$23$	−2.52495	−0.526489	−0.263244	−	0.964729i	$-0.584793\pi$
$23$	−2.52495	−0.526489	−0.263244	+	0.964729i	$0.584793\pi$
$24$	−0.132166	−0.0269782
$25$	1.33721	0.267442
$26$	4.39173	0.861288
$27$	1.00000	0.192450
$28$	−2.06555	−0.390352
$29$	−4.44605	−0.825612	−0.412806	−	0.910819i	$-0.635451\pi$
$29$	−4.44605	−0.825612	−0.412806	+	0.910819i	$0.635451\pi$
$30$	−5.07585	−0.926719
$31$	−7.77121	−1.39575	−0.697875	−	0.716219i	$-0.745871\pi$
$31$	−7.77121	−1.39575	−0.697875	+	0.716219i	$0.745871\pi$
$32$	8.05662	1.42422
$33$	2.22076	0.386584
$34$	−13.8645	−2.37774
$35$	−2.51738	−0.425515
$36$	2.06555	0.344258
$37$	0.386135	0.0634802	0.0317401	−	0.999496i	$-0.489895\pi$
$37$	0.386135	0.0634802	0.0317401	+	0.999496i	$0.489895\pi$
$38$	15.6317	2.53580
$39$	−2.17809	−0.348773
$40$	−0.332711	−0.0526062
$41$	10.0609	1.57125	0.785623	−	0.618706i	$-0.212343\pi$
$41$	10.0609	1.57125	0.785623	+	0.618706i	$0.212343\pi$
$42$	2.01632	0.311125
$43$	−0.278777	−0.0425131	−0.0212566	−	0.999774i	$-0.506767\pi$
$43$	−0.278777	−0.0425131	−0.0212566	+	0.999774i	$0.506767\pi$
$44$	4.58708	0.691529
$45$	2.51738	0.375269
$46$	5.09111	0.750644
$47$	8.79353	1.28267	0.641334	−	0.767262i	$-0.278381\pi$
$47$	8.79353	1.28267	0.641334	+	0.767262i	$0.278381\pi$
$48$	−3.86461	−0.557808
$49$	1.00000	0.142857
$50$	−2.69624	−0.381306
$51$	6.87612	0.962850
$52$	−4.49895	−0.623892
$53$	−14.0287	−1.92699	−0.963496	−	0.267724i	$-0.913728\pi$
$53$	−14.0287	−1.92699	−0.963496	+	0.267724i	$0.913728\pi$
$54$	−2.01632	−0.274386
$55$	5.59050	0.753822
$56$	0.132166	0.0176614
$57$	−7.75260	−1.02686
$58$	8.96467	1.17712
$59$	−13.0768	−1.70246	−0.851228	−	0.524796i	$-0.824142\pi$
$59$	−13.0768	−1.70246	−0.851228	+	0.524796i	$0.824142\pi$
$60$	5.19977	0.671288
$61$	−11.1768	−1.43105	−0.715523	−	0.698589i	$-0.753812\pi$
$61$	−11.1768	−1.43105	−0.715523	+	0.698589i	$0.753812\pi$
$62$	15.6693	1.99000
$63$	−1.00000	−0.125988
$64$	−8.51551	−1.06444
$65$	−5.48308	−0.680093
$66$	−4.47776	−0.551174
$67$	11.4252	1.39581	0.697905	−	0.716191i	$-0.254116\pi$
$67$	11.4252	1.39581	0.697905	+	0.716191i	$0.254116\pi$
$68$	14.2030	1.72236
$69$	−2.52495	−0.303969
$70$	5.07585	0.606680
$71$	3.12631	0.371024	0.185512	−	0.982642i	$-0.440606\pi$
$71$	3.12631	0.371024	0.185512	+	0.982642i	$0.440606\pi$
$72$	−0.132166	−0.0155759
$73$	−13.6655	−1.59943	−0.799716	−	0.600379i	$-0.795016\pi$
$73$	−13.6655	−1.59943	−0.799716	+	0.600379i	$0.795016\pi$
$74$	−0.778572	−0.0905072
$75$	1.33721	0.154408
$76$	−16.0134	−1.83686
$77$	−2.22076	−0.253079
$78$	4.39173	0.497265
$79$	−13.5376	−1.52310	−0.761548	−	0.648108i	$-0.775560\pi$
$79$	−13.5376	−1.52310	−0.761548	+	0.648108i	$0.775560\pi$
$80$	−9.72869	−1.08770
$81$	1.00000	0.111111
$82$	−20.2860	−2.24021
$83$	5.53562	0.607614	0.303807	−	0.952734i	$-0.401742\pi$
$83$	5.53562	0.607614	0.303807	+	0.952734i	$0.401742\pi$
$84$	−2.06555	−0.225370
$85$	17.3098	1.87751
$86$	0.562104	0.0606133
$87$	−4.44605	−0.476667
$88$	−0.293508	−0.0312880
$89$	0.809204	0.0857754	0.0428877	−	0.999080i	$-0.486344\pi$
$89$	0.809204	0.0857754	0.0428877	+	0.999080i	$0.486344\pi$
$90$	−5.07585	−0.535041
$91$	2.17809	0.228326
$92$	−5.21541	−0.543744
$93$	−7.77121	−0.805837
$94$	−17.7306	−1.82877
$95$	−19.5163	−2.00233
$96$	8.05662	0.822275
$97$	2.77543	0.281802	0.140901	−	0.990024i	$-0.455000\pi$
$97$	2.77543	0.281802	0.140901	+	0.990024i	$0.455000\pi$
$98$	−2.01632	−0.203679
$99$	2.22076	0.223195
$100$	2.76207	0.276207
$101$	−4.54797	−0.452540	−0.226270	−	0.974065i	$-0.572653\pi$
$101$	−4.54797	−0.452540	−0.226270	+	0.974065i	$0.572653\pi$
$102$	−13.8645	−1.37279
$103$	−6.92978	−0.682811	−0.341406	−	0.939916i	$-0.610903\pi$
$103$	−6.92978	−0.682811	−0.341406	+	0.939916i	$0.610903\pi$
$104$	0.287868	0.0282278
$105$	−2.51738	−0.245671
$106$	28.2864	2.74742
$107$	5.25189	0.507719	0.253860	−	0.967241i	$-0.418300\pi$
$107$	5.25189	0.507719	0.253860	+	0.967241i	$0.418300\pi$
$108$	2.06555	0.198757
$109$	−3.94906	−0.378252	−0.189126	−	0.981953i	$-0.560565\pi$
$109$	−3.94906	−0.378252	−0.189126	+	0.981953i	$0.560565\pi$
$110$	−11.2722	−1.07477
$111$	0.386135	0.0366503
$112$	3.86461	0.365171
$113$	−5.70572	−0.536749	−0.268375	−	0.963315i	$-0.586487\pi$
$113$	−5.70572	−0.536749	−0.268375	+	0.963315i	$0.586487\pi$
$114$	15.6317	1.46405
$115$	−6.35627	−0.592725
$116$	−9.18354	−0.852670
$117$	−2.17809	−0.201364
$118$	26.3670	2.42728
$119$	−6.87612	−0.630333
$120$	−0.332711	−0.0303722
$121$	−6.06823	−0.551657
$122$	22.5361	2.04032
$123$	10.0609	0.907159
$124$	−16.0518	−1.44150
$125$	−9.22064	−0.824719
$126$	2.01632	0.179628
$127$	−6.73068	−0.597251	−0.298626	−	0.954370i	$-0.596528\pi$
$127$	−6.73068	−0.597251	−0.298626	+	0.954370i	$0.596528\pi$
$128$	1.05676	0.0934049
$129$	−0.278777	−0.0245450
$130$	11.0557	0.969645
$131$	13.4616	1.17615	0.588073	−	0.808808i	$-0.299887\pi$
$131$	13.4616	1.17615	0.588073	+	0.808808i	$0.299887\pi$
$132$	4.58708	0.399254
$133$	7.75260	0.672236
$134$	−23.0369	−1.99008
$135$	2.51738	0.216662
$136$	−0.908787	−0.0779278
$137$	−8.98515	−0.767653	−0.383827	−	0.923405i	$-0.625394\pi$
$137$	−8.98515	−0.767653	−0.383827	+	0.923405i	$0.625394\pi$
$138$	5.09111	0.433384
$139$	22.8274	1.93619	0.968096	−	0.250581i	$-0.0806217\pi$
$139$	22.8274	1.93619	0.968096	+	0.250581i	$0.0806217\pi$
$140$	−5.19977	−0.439461
$141$	8.79353	0.740549
$142$	−6.30363	−0.528989
$143$	−4.83701	−0.404491
$144$	−3.86461	−0.322051
$145$	−11.1924	−0.929480
$146$	27.5541	2.28040
$147$	1.00000	0.0824786
$148$	0.797581	0.0655607
$149$	−3.14143	−0.257356	−0.128678	−	0.991686i	$-0.541073\pi$
$149$	−3.14143	−0.257356	−0.128678	+	0.991686i	$0.541073\pi$
$150$	−2.69624	−0.220147
$151$	−13.3253	−1.08440	−0.542198	−	0.840251i	$-0.682408\pi$
$151$	−13.3253	−1.08440	−0.542198	+	0.840251i	$0.682408\pi$
$152$	1.02463	0.0831082
$153$	6.87612	0.555902
$154$	4.47776	0.360828
$155$	−19.5631	−1.57135
$156$	−4.49895	−0.360204
$157$	15.9153	1.27018	0.635091	−	0.772437i	$-0.280963\pi$
$157$	15.9153	1.27018	0.635091	+	0.772437i	$0.280963\pi$
$158$	27.2961	2.17156
$159$	−14.0287	−1.11255
$160$	20.2816	1.60340
$161$	2.52495	0.198994
$162$	−2.01632	−0.158417
$163$	17.5511	1.37471	0.687355	−	0.726322i	$-0.258772\pi$
$163$	17.5511	1.37471	0.687355	+	0.726322i	$0.258772\pi$
$164$	20.7812	1.62274
$165$	5.59050	0.435220
$166$	−11.1616	−0.866307
$167$	−10.1388	−0.784562	−0.392281	−	0.919845i	$-0.628314\pi$
$167$	−10.1388	−0.784562	−0.392281	+	0.919845i	$0.628314\pi$
$168$	0.132166	0.0101968
$169$	−8.25593	−0.635071
$170$	−34.9022	−2.67687
$171$	−7.75260	−0.592856
$172$	−0.575828	−0.0439065
$173$	16.3533	1.24332	0.621661	−	0.783287i	$-0.286458\pi$
$173$	16.3533	1.24332	0.621661	+	0.783287i	$0.286458\pi$
$174$	8.96467	0.679610
$175$	−1.33721	−0.101084
$176$	−8.58236	−0.646920
$177$	−13.0768	−0.982913
$178$	−1.63161	−0.122295
$179$	7.05336	0.527193	0.263597	−	0.964633i	$-0.415091\pi$
$179$	7.05336	0.527193	0.263597	+	0.964633i	$0.415091\pi$
$180$	5.19977	0.387568
$181$	−9.48522	−0.705031	−0.352515	−	0.935806i	$-0.614674\pi$
$181$	−9.48522	−0.705031	−0.352515	+	0.935806i	$0.614674\pi$
$182$	−4.39173	−0.325536
$183$	−11.1768	−0.826215
$184$	0.333712	0.0246015
$185$	0.972049	0.0714665
$186$	15.6693	1.14893
$187$	15.2702	1.11667
$188$	18.1635	1.32471
$189$	−1.00000	−0.0727393
$190$	39.3510	2.85482
$191$	−20.4996	−1.48330	−0.741649	−	0.670788i	$-0.765956\pi$
$191$	−20.4996	−1.48330	−0.741649	+	0.670788i	$0.765956\pi$
$192$	−8.51551	−0.614554
$193$	−23.0827	−1.66153	−0.830766	−	0.556622i	$-0.812097\pi$
$193$	−23.0827	−1.66153	−0.830766	+	0.556622i	$0.812097\pi$
$194$	−5.59615	−0.401780
$195$	−5.48308	−0.392652
$196$	2.06555	0.147539
$197$	−20.4186	−1.45477	−0.727383	−	0.686232i	$-0.759264\pi$
$197$	−20.4186	−1.45477	−0.727383	+	0.686232i	$0.759264\pi$
$198$	−4.47776	−0.318221
$199$	−11.6660	−0.826980	−0.413490	−	0.910509i	$-0.635690\pi$
$199$	−11.6660	−0.826980	−0.413490	+	0.910509i	$0.635690\pi$
$200$	−0.176733	−0.0124969
$201$	11.4252	0.805871
$202$	9.17017	0.645211
$203$	4.44605	0.312052
$204$	14.2030	0.994406
$205$	25.3271	1.76892
$206$	13.9727	0.973521
$207$	−2.52495	−0.175496
$208$	8.41746	0.583646
$209$	−17.2167	−1.19090
$210$	5.07585	0.350267
$211$	−13.9726	−0.961916	−0.480958	−	0.876744i	$-0.659711\pi$
$211$	−13.9726	−0.961916	−0.480958	+	0.876744i	$0.659711\pi$
$212$	−28.9770	−1.99015
$213$	3.12631	0.214211
$214$	−10.5895	−0.723882
$215$	−0.701789	−0.0478616
$216$	−0.132166	−0.00899272
$217$	7.77121	0.527544
$218$	7.96258	0.539294
$219$	−13.6655	−0.923432
$220$	11.5474	0.778528
$221$	−14.9768	−1.00745
$222$	−0.778572	−0.0522543
$223$	8.16065	0.546478	0.273239	−	0.961946i	$-0.411905\pi$
$223$	8.16065	0.546478	0.273239	+	0.961946i	$0.411905\pi$
$224$	−8.05662	−0.538305
$225$	1.33721	0.0891473
$226$	11.5046	0.765272
$227$	−27.1961	−1.80507	−0.902536	−	0.430615i	$-0.858297\pi$
$227$	−27.1961	−1.80507	−0.902536	+	0.430615i	$0.858297\pi$
$228$	−16.0134	−1.06051
$229$	−22.0658	−1.45815	−0.729074	−	0.684435i	$-0.760049\pi$
$229$	−22.0658	−1.45815	−0.729074	+	0.684435i	$0.760049\pi$
$230$	12.8163	0.845080
$231$	−2.22076	−0.146115
$232$	0.587615	0.0385788
$233$	−5.02117	−0.328948	−0.164474	−	0.986381i	$-0.552593\pi$
$233$	−5.02117	−0.328948	−0.164474	+	0.986381i	$0.552593\pi$
$234$	4.39173	0.287096
$235$	22.1367	1.44404
$236$	−27.0108	−1.75825
$237$	−13.5376	−0.879360
$238$	13.8645	0.898700
$239$	23.1049	1.49453	0.747265	−	0.664526i	$-0.231367\pi$
$239$	23.1049	1.49453	0.747265	+	0.664526i	$0.231367\pi$
$240$	−9.72869	−0.627984
$241$	−15.6852	−1.01037	−0.505187	−	0.863010i	$-0.668576\pi$
$241$	−15.6852	−1.01037	−0.505187	+	0.863010i	$0.668576\pi$
$242$	12.2355	0.786528
$243$	1.00000	0.0641500
$244$	−23.0863	−1.47795
$245$	2.51738	0.160830
$246$	−20.2860	−1.29339
$247$	16.8859	1.07442
$248$	1.02709	0.0652200
$249$	5.53562	0.350806
$250$	18.5918	1.17585
$251$	25.2216	1.59198	0.795988	−	0.605313i	$-0.206952\pi$
$251$	25.2216	1.59198	0.795988	+	0.605313i	$0.206952\pi$
$252$	−2.06555	−0.130117
$253$	−5.60731	−0.352528
$254$	13.5712	0.851533
$255$	17.3098	1.08398
$256$	14.9003	0.931266
$257$	−8.88095	−0.553979	−0.276989	−	0.960873i	$-0.589337\pi$
$257$	−8.88095	−0.553979	−0.276989	+	0.960873i	$0.589337\pi$
$258$	0.562104	0.0349951
$259$	−0.386135	−0.0239933
$260$	−11.3256	−0.702382
$261$	−4.44605	−0.275204
$262$	−27.1429	−1.67689
$263$	11.5132	0.709937	0.354969	−	0.934878i	$-0.384492\pi$
$263$	11.5132	0.709937	0.354969	+	0.934878i	$0.384492\pi$
$264$	−0.293508	−0.0180641
$265$	−35.3156	−2.16942
$266$	−15.6317	−0.958443
$267$	0.809204	0.0495225
$268$	23.5993	1.44156
$269$	−12.0201	−0.732876	−0.366438	−	0.930442i	$-0.619423\pi$
$269$	−12.0201	−0.732876	−0.366438	+	0.930442i	$0.619423\pi$
$270$	−5.07585	−0.308906
$271$	16.4543	0.999530	0.499765	−	0.866161i	$-0.333420\pi$
$271$	16.4543	0.999530	0.499765	+	0.866161i	$0.333420\pi$
$272$	−26.5735	−1.61126
$273$	2.17809	0.131824
$274$	18.1169	1.09448
$275$	2.96962	0.179075
$276$	−5.21541	−0.313931
$277$	12.1307	0.728863	0.364432	−	0.931230i	$-0.381263\pi$
$277$	12.1307	0.728863	0.364432	+	0.931230i	$0.381263\pi$
$278$	−46.0273	−2.76053
$279$	−7.77121	−0.465250
$280$	0.332711	0.0198833
$281$	24.4137	1.45640	0.728199	−	0.685366i	$-0.240358\pi$
$281$	24.4137	1.45640	0.728199	+	0.685366i	$0.240358\pi$
$282$	−17.7306	−1.05584
$283$	16.6608	0.990384	0.495192	−	0.868784i	$-0.335098\pi$
$283$	16.6608	0.990384	0.495192	+	0.868784i	$0.335098\pi$
$284$	6.45753	0.383184
$285$	−19.5163	−1.15604
$286$	9.75296	0.576705
$287$	−10.0609	−0.593875
$288$	8.05662	0.474741
$289$	30.2811	1.78124
$290$	22.5675	1.32521
$291$	2.77543	0.162698
$292$	−28.2268	−1.65185
$293$	6.83003	0.399014	0.199507	−	0.979896i	$-0.436066\pi$
$293$	6.83003	0.399014	0.199507	+	0.979896i	$0.436066\pi$
$294$	−2.01632	−0.117594
$295$	−32.9193	−1.91664
$296$	−0.0510337	−0.00296628
$297$	2.22076	0.128861
$298$	6.33412	0.366926
$299$	5.49957	0.318048
$300$	2.76207	0.159468
$301$	0.278777	0.0160685
$302$	26.8680	1.54608
$303$	−4.54797	−0.261274
$304$	29.9608	1.71837
$305$	−28.1363	−1.61108
$306$	−13.8645	−0.792579
$307$	14.8281	0.846283	0.423141	−	0.906064i	$-0.360927\pi$
$307$	14.8281	0.846283	0.423141	+	0.906064i	$0.360927\pi$
$308$	−4.58708	−0.261373
$309$	−6.92978	−0.394221
$310$	39.4455	2.24035
$311$	−25.0572	−1.42086	−0.710432	−	0.703766i	$-0.751500\pi$
$311$	−25.0572	−1.42086	−0.710432	+	0.703766i	$0.751500\pi$
$312$	0.287868	0.0162973
$313$	4.98857	0.281971	0.140985	−	0.990012i	$-0.454973\pi$
$313$	4.98857	0.281971	0.140985	+	0.990012i	$0.454973\pi$
$314$	−32.0904	−1.81097
$315$	−2.51738	−0.141838
$316$	−27.9625	−1.57301
$317$	−11.1882	−0.628391	−0.314196	−	0.949358i	$-0.601735\pi$
$317$	−11.1882	−0.628391	−0.314196	+	0.949358i	$0.601735\pi$
$318$	28.2864	1.58622
$319$	−9.87361	−0.552816
$320$	−21.4368	−1.19835
$321$	5.25189	0.293132
$322$	−5.09111	−0.283717
$323$	−53.3079	−2.96613
$324$	2.06555	0.114753
$325$	−2.91256	−0.161560
$326$	−35.3887	−1.96000
$327$	−3.94906	−0.218384
$328$	−1.32970	−0.0734205
$329$	−8.79353	−0.484803
$330$	−11.2722	−0.620516
$331$	−10.0548	−0.552663	−0.276331	−	0.961062i	$-0.589119\pi$
$331$	−10.0548	−0.552663	−0.276331	+	0.961062i	$0.589119\pi$
$332$	11.4341	0.627528
$333$	0.386135	0.0211601
$334$	20.4430	1.11859
$335$	28.7616	1.57141
$336$	3.86461	0.210832
$337$	11.3053	0.615836	0.307918	−	0.951413i	$-0.400368\pi$
$337$	11.3053	0.615836	0.307918	+	0.951413i	$0.400368\pi$
$338$	16.6466	0.905455
$339$	−5.70572	−0.309892
$340$	35.7543	1.93905
$341$	−17.2580	−0.934572
$342$	15.6317	0.845267
$343$	−1.00000	−0.0539949
$344$	0.0368447	0.00198654
$345$	−6.35627	−0.342210
$346$	−32.9736	−1.77267
$347$	31.7819	1.70614	0.853070	−	0.521796i	$-0.174738\pi$
$347$	31.7819	1.70614	0.853070	+	0.521796i	$0.174738\pi$
$348$	−9.18354	−0.492289
$349$	−21.6620	−1.15954	−0.579771	−	0.814780i	$-0.696858\pi$
$349$	−21.6620	−1.15954	−0.579771	+	0.814780i	$0.696858\pi$
$350$	2.69624	0.144120
$351$	−2.17809	−0.116258
$352$	17.8918	0.953636
$353$	−11.7623	−0.626042	−0.313021	−	0.949746i	$-0.601341\pi$
$353$	−11.7623	−0.626042	−0.313021	+	0.949746i	$0.601341\pi$
$354$	26.3670	1.40139
$355$	7.87010	0.417702
$356$	1.67145	0.0885866
$357$	−6.87612	−0.363923
$358$	−14.2218	−0.751647
$359$	32.9909	1.74120	0.870598	−	0.491996i	$-0.163732\pi$
$359$	32.9909	1.74120	0.870598	+	0.491996i	$0.163732\pi$
$360$	−0.332711	−0.0175354
$361$	41.1029	2.16331
$362$	19.1252	1.00520
$363$	−6.06823	−0.318500
$364$	4.49895	0.235809
$365$	−34.4014	−1.80065
$366$	22.5361	1.17798
$367$	10.6442	0.555624	0.277812	−	0.960635i	$-0.410391\pi$
$367$	10.6442	0.555624	0.277812	+	0.960635i	$0.410391\pi$
$368$	9.75795	0.508668
$369$	10.0609	0.523749
$370$	−1.95996	−0.101894
$371$	14.0287	0.728334
$372$	−16.0518	−0.832248
$373$	−2.24024	−0.115995	−0.0579976	−	0.998317i	$-0.518472\pi$
$373$	−2.24024	−0.115995	−0.0579976	+	0.998317i	$0.518472\pi$
$374$	−30.7896	−1.59209
$375$	−9.22064	−0.476152
$376$	−1.16220	−0.0599360
$377$	9.68391	0.498747
$378$	2.01632	0.103708
$379$	−13.7487	−0.706223	−0.353111	−	0.935581i	$-0.614876\pi$
$379$	−13.7487	−0.706223	−0.353111	+	0.935581i	$0.614876\pi$
$380$	−40.3118	−2.06795
$381$	−6.73068	−0.344823
$382$	41.3337	2.11482
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	1.05676	0.0539274
$385$	−5.59050	−0.284918
$386$	46.5422	2.36894
$387$	−0.278777	−0.0141710
$388$	5.73278	0.291038
$389$	5.75286	0.291682	0.145841	−	0.989308i	$-0.453411\pi$
$389$	5.75286	0.291682	0.145841	+	0.989308i	$0.453411\pi$
$390$	11.0557	0.559825
$391$	−17.3619	−0.878028
$392$	−0.132166	−0.00667537
$393$	13.4616	0.679048
$394$	41.1705	2.07414
$395$	−34.0792	−1.71471
$396$	4.58708	0.230510
$397$	−19.1413	−0.960672	−0.480336	−	0.877085i	$-0.659485\pi$
$397$	−19.1413	−0.960672	−0.480336	+	0.877085i	$0.659485\pi$
$398$	23.5224	1.17907
$399$	7.75260	0.388116
$400$	−5.16779	−0.258390
$401$	−7.69091	−0.384066	−0.192033	−	0.981389i	$-0.561508\pi$
$401$	−7.69091	−0.384066	−0.192033	+	0.981389i	$0.561508\pi$
$402$	−23.0369	−1.14897
$403$	16.9264	0.843164
$404$	−9.39406	−0.467372
$405$	2.51738	0.125090
$406$	−8.96467	−0.444909
$407$	0.857513	0.0425053
$408$	−0.908787	−0.0449916
$409$	−12.8104	−0.633435	−0.316717	−	0.948520i	$-0.602581\pi$
$409$	−12.8104	−0.633435	−0.316717	+	0.948520i	$0.602581\pi$
$410$	−51.0675	−2.52204
$411$	−8.98515	−0.443205
$412$	−14.3138	−0.705190
$413$	13.0768	0.643468
$414$	5.09111	0.250215
$415$	13.9353	0.684056
$416$	−17.5480	−0.860363
$417$	22.8274	1.11786
$418$	34.7143	1.69793
$419$	9.04216	0.441739	0.220869	−	0.975303i	$-0.429111\pi$
$419$	9.04216	0.441739	0.220869	+	0.975303i	$0.429111\pi$
$420$	−5.19977	−0.253723
$421$	−6.82474	−0.332618	−0.166309	−	0.986074i	$-0.553185\pi$
$421$	−6.82474	−0.332618	−0.166309	+	0.986074i	$0.553185\pi$
$422$	28.1733	1.37146
$423$	8.79353	0.427556
$424$	1.85411	0.0900436
$425$	9.19482	0.446014
$426$	−6.30363	−0.305412
$427$	11.1768	0.540885
$428$	10.8480	0.524359
$429$	−4.83701	−0.233533
$430$	1.41503	0.0682389
$431$	36.7788	1.77157	0.885786	−	0.464094i	$-0.153620\pi$
$431$	36.7788	1.77157	0.885786	+	0.464094i	$0.153620\pi$
$432$	−3.86461	−0.185936
$433$	−2.31088	−0.111054	−0.0555269	−	0.998457i	$-0.517684\pi$
$433$	−2.31088	−0.111054	−0.0555269	+	0.998457i	$0.517684\pi$
$434$	−15.6693	−0.752148
$435$	−11.1924	−0.536635
$436$	−8.15698	−0.390649
$437$	19.5750	0.936397
$438$	27.5541	1.31659
$439$	14.1286	0.674323	0.337161	−	0.941447i	$-0.390533\pi$
$439$	14.1286	0.674323	0.337161	+	0.941447i	$0.390533\pi$
$440$	−0.738871	−0.0352243
$441$	1.00000	0.0476190
$442$	30.1981	1.43638
$443$	30.2829	1.43878	0.719392	−	0.694604i	$-0.244421\pi$
$443$	30.2829	1.43878	0.719392	+	0.694604i	$0.244421\pi$
$444$	0.797581	0.0378515
$445$	2.03707	0.0965666
$446$	−16.4545	−0.779143
$447$	−3.14143	−0.148584
$448$	8.51551	0.402320
$449$	5.64152	0.266240	0.133120	−	0.991100i	$-0.457500\pi$
$449$	5.64152	0.266240	0.133120	+	0.991100i	$0.457500\pi$
$450$	−2.69624	−0.127102
$451$	22.3428	1.05208
$452$	−11.7854	−0.554341
$453$	−13.3253	−0.626076
$454$	54.8361	2.57359
$455$	5.48308	0.257051
$456$	1.02463	0.0479825
$457$	−26.6394	−1.24614	−0.623070	−	0.782166i	$-0.714115\pi$
$457$	−26.6394	−1.24614	−0.623070	+	0.782166i	$0.714115\pi$
$458$	44.4917	2.07896
$459$	6.87612	0.320950
$460$	−13.1292	−0.612151
$461$	21.5019	1.00144	0.500721	−	0.865609i	$-0.333068\pi$
$461$	21.5019	1.00144	0.500721	+	0.865609i	$0.333068\pi$
$462$	4.47776	0.208324
$463$	−9.48174	−0.440654	−0.220327	−	0.975426i	$-0.570712\pi$
$463$	−9.48174	−0.440654	−0.220327	+	0.975426i	$0.570712\pi$
$464$	17.1823	0.797666
$465$	−19.5631	−0.907217
$466$	10.1243	0.468998
$467$	18.4493	0.853732	0.426866	−	0.904315i	$-0.359618\pi$
$467$	18.4493	0.853732	0.426866	+	0.904315i	$0.359618\pi$
$468$	−4.49895	−0.207964
$469$	−11.4252	−0.527566
$470$	−44.6346	−2.05884
$471$	15.9153	0.733340
$472$	1.72830	0.0795516
$473$	−0.619097	−0.0284661
$474$	27.2961	1.25375
$475$	−10.3669	−0.475664
$476$	−14.2030	−0.650992
$477$	−14.0287	−0.642330
$478$	−46.5868	−2.13083
$479$	−30.6813	−1.40186	−0.700932	−	0.713228i	$-0.747232\pi$
$479$	−30.6813	−1.40186	−0.700932	+	0.713228i	$0.747232\pi$
$480$	20.2816	0.925723
$481$	−0.841037	−0.0383480
$482$	31.6264	1.44054
$483$	2.52495	0.114889
$484$	−12.5342	−0.569737
$485$	6.98681	0.317255
$486$	−2.01632	−0.0914621
$487$	18.5126	0.838885	0.419443	−	0.907782i	$-0.362226\pi$
$487$	18.5126	0.838885	0.419443	+	0.907782i	$0.362226\pi$
$488$	1.47719	0.0668693
$489$	17.5511	0.793689
$490$	−5.07585	−0.229303
$491$	40.7557	1.83928	0.919639	−	0.392765i	$-0.128481\pi$
$491$	40.7557	1.83928	0.919639	+	0.392765i	$0.128481\pi$
$492$	20.7812	0.936890
$493$	−30.5716	−1.37688
$494$	−34.0473	−1.53186
$495$	5.59050	0.251274
$496$	30.0327	1.34851
$497$	−3.12631	−0.140234
$498$	−11.1616	−0.500163
$499$	−5.28798	−0.236722	−0.118361	−	0.992971i	$-0.537764\pi$
$499$	−5.28798	−0.236722	−0.118361	+	0.992971i	$0.537764\pi$
$500$	−19.0457	−0.851748
$501$	−10.1388	−0.452967
$502$	−50.8549	−2.26976
$503$	4.20795	0.187623	0.0938116	−	0.995590i	$-0.470095\pi$
$503$	4.20795	0.187623	0.0938116	+	0.995590i	$0.470095\pi$
$504$	0.132166	0.00588712
$505$	−11.4490	−0.509473
$506$	11.3061	0.502619
$507$	−8.25593	−0.366659
$508$	−13.9025	−0.616825
$509$	6.57919	0.291618	0.145809	−	0.989313i	$-0.453422\pi$
$509$	6.57919	0.291618	0.145809	+	0.989313i	$0.453422\pi$
$510$	−34.9022	−1.54549
$511$	13.6655	0.604528
$512$	−32.1572	−1.42116
$513$	−7.75260	−0.342286
$514$	17.9068	0.789837
$515$	−17.4449	−0.768714
$516$	−0.575828	−0.0253494
$517$	19.5283	0.858854
$518$	0.778572	0.0342085
$519$	16.3533	0.717832
$520$	0.724674	0.0317791
$521$	−13.9228	−0.609969	−0.304984	−	0.952357i	$-0.598651\pi$
$521$	−13.9228	−0.609969	−0.304984	+	0.952357i	$0.598651\pi$
$522$	8.96467	0.392373
$523$	15.6954	0.686312	0.343156	−	0.939278i	$-0.388504\pi$
$523$	15.6954	0.686312	0.343156	+	0.939278i	$0.388504\pi$
$524$	27.8056	1.21469
$525$	−1.33721	−0.0583606
$526$	−23.2144	−1.01220
$527$	−53.4358	−2.32770
$528$	−8.58236	−0.373499
$529$	−16.6246	−0.722809
$530$	71.2076	3.09306
$531$	−13.0768	−0.567485
$532$	16.0134	0.694268
$533$	−21.9135	−0.949179
$534$	−1.63161	−0.0706068
$535$	13.2210	0.571594
$536$	−1.51002	−0.0652228
$537$	7.05336	0.304375
$538$	24.2363	1.04490
$539$	2.22076	0.0956548
$540$	5.19977	0.223763
$541$	−15.2246	−0.654559	−0.327279	−	0.944928i	$-0.606132\pi$
$541$	−15.2246	−0.654559	−0.327279	+	0.944928i	$0.606132\pi$
$542$	−33.1772	−1.42508
$543$	−9.48522	−0.407050
$544$	55.3983	2.37518
$545$	−9.94130	−0.425839
$546$	−4.39173	−0.187949
$547$	13.8663	0.592880	0.296440	−	0.955051i	$-0.404200\pi$
$547$	13.8663	0.592880	0.296440	+	0.955051i	$0.404200\pi$
$548$	−18.5593	−0.792812
$549$	−11.1768	−0.477015
$550$	−5.98771	−0.255317
$551$	34.4685	1.46841
$552$	0.333712	0.0142037
$553$	13.5376	0.575676
$554$	−24.4594	−1.03918
$555$	0.972049	0.0412612
$556$	47.1510	1.99965
$557$	−37.3740	−1.58359	−0.791793	−	0.610790i	$-0.790852\pi$
$557$	−37.3740	−1.58359	−0.791793	+	0.610790i	$0.790852\pi$
$558$	15.6693	0.663332
$559$	0.607202	0.0256819
$560$	9.72869	0.411112
$561$	15.2702	0.644709
$562$	−49.2258	−2.07646
$563$	−25.4904	−1.07429	−0.537147	−	0.843489i	$-0.680498\pi$
$563$	−25.4904	−1.07429	−0.537147	+	0.843489i	$0.680498\pi$
$564$	18.1635	0.764819
$565$	−14.3635	−0.604276
$566$	−33.5936	−1.41204
$567$	−1.00000	−0.0419961
$568$	−0.413190	−0.0173371
$569$	−23.5222	−0.986102	−0.493051	−	0.870000i	$-0.664118\pi$
$569$	−23.5222	−0.986102	−0.493051	+	0.870000i	$0.664118\pi$
$570$	39.3510	1.64823
$571$	0.824951	0.0345231	0.0172616	−	0.999851i	$-0.494505\pi$
$571$	0.824951	0.0345231	0.0172616	+	0.999851i	$0.494505\pi$
$572$	−9.99108	−0.417748
$573$	−20.4996	−0.856382
$574$	20.2860	0.846720
$575$	−3.37639	−0.140805
$576$	−8.51551	−0.354813
$577$	−19.0298	−0.792221	−0.396110	−	0.918203i	$-0.629640\pi$
$577$	−19.0298	−0.792221	−0.396110	+	0.918203i	$0.629640\pi$
$578$	−61.0564	−2.53961
$579$	−23.0827	−0.959286
$580$	−23.1185	−0.959942
$581$	−5.53562	−0.229656
$582$	−5.59615	−0.231968
$583$	−31.1544	−1.29028
$584$	1.80611	0.0747375
$585$	−5.48308	−0.226698
$586$	−13.7715	−0.568896
$587$	14.5599	0.600950	0.300475	−	0.953790i	$-0.402855\pi$
$587$	14.5599	0.600950	0.300475	+	0.953790i	$0.402855\pi$
$588$	2.06555	0.0851818
$589$	60.2471	2.48244
$590$	66.3759	2.73265
$591$	−20.4186	−0.839910
$592$	−1.49226	−0.0613315
$593$	−14.8911	−0.611505	−0.305753	−	0.952111i	$-0.598908\pi$
$593$	−14.8911	−0.611505	−0.305753	+	0.952111i	$0.598908\pi$
$594$	−4.47776	−0.183725
$595$	−17.3098	−0.709634
$596$	−6.48877	−0.265790
$597$	−11.6660	−0.477457
$598$	−11.0889	−0.453459
$599$	−30.7671	−1.25711	−0.628555	−	0.777765i	$-0.716353\pi$
$599$	−30.7671	−1.25711	−0.628555	+	0.777765i	$0.716353\pi$
$600$	−0.176733	−0.00721510
$601$	−4.36496	−0.178050	−0.0890252	−	0.996029i	$-0.528375\pi$
$601$	−4.36496	−0.178050	−0.0890252	+	0.996029i	$0.528375\pi$
$602$	−0.562104	−0.0229097
$603$	11.4252	0.465270
$604$	−27.5240	−1.11994
$605$	−15.2761	−0.621060
$606$	9.17017	0.372513
$607$	4.58070	0.185925	0.0929625	−	0.995670i	$-0.470366\pi$
$607$	4.58070	0.185925	0.0929625	+	0.995670i	$0.470366\pi$
$608$	−62.4598	−2.53308
$609$	4.44605	0.180163
$610$	56.7319	2.29701
$611$	−19.1531	−0.774851
$612$	14.2030	0.574121
$613$	−17.4060	−0.703024	−0.351512	−	0.936183i	$-0.614332\pi$
$613$	−17.4060	−0.703024	−0.351512	+	0.936183i	$0.614332\pi$
$614$	−29.8981	−1.20659
$615$	25.3271	1.02129
$616$	0.293508	0.0118258
$617$	36.4227	1.46632	0.733161	−	0.680055i	$-0.238044\pi$
$617$	36.4227	1.46632	0.733161	+	0.680055i	$0.238044\pi$
$618$	13.9727	0.562062
$619$	13.7535	0.552802	0.276401	−	0.961042i	$-0.410858\pi$
$619$	13.7535	0.552802	0.276401	+	0.961042i	$0.410858\pi$
$620$	−40.4085	−1.62285
$621$	−2.52495	−0.101323
$622$	50.5234	2.02580
$623$	−0.809204	−0.0324201
$624$	8.41746	0.336968
$625$	−29.8979	−1.19592
$626$	−10.0586	−0.402021
$627$	−17.2167	−0.687567
$628$	32.8739	1.31181
$629$	2.65511	0.105866
$630$	5.07585	0.202227
$631$	−1.12159	−0.0446497	−0.0223248	−	0.999751i	$-0.507107\pi$
$631$	−1.12159	−0.0446497	−0.0223248	+	0.999751i	$0.507107\pi$
$632$	1.78920	0.0711706
$633$	−13.9726	−0.555363
$634$	22.5590	0.895931
$635$	−16.9437	−0.672390
$636$	−28.9770	−1.14901
$637$	−2.17809	−0.0862991
$638$	19.9084	0.788180
$639$	3.12631	0.123675
$640$	2.66026	0.105156
$641$	19.3960	0.766098	0.383049	−	0.923728i	$-0.374874\pi$
$641$	19.3960	0.766098	0.383049	+	0.923728i	$0.374874\pi$
$642$	−10.5895	−0.417934
$643$	12.5580	0.495238	0.247619	−	0.968857i	$-0.420352\pi$
$643$	12.5580	0.495238	0.247619	+	0.968857i	$0.420352\pi$
$644$	5.21541	0.205516
$645$	−0.701789	−0.0276329
$646$	107.486	4.22897
$647$	20.9376	0.823142	0.411571	−	0.911378i	$-0.364980\pi$
$647$	20.9376	0.823142	0.411571	+	0.911378i	$0.364980\pi$
$648$	−0.132166	−0.00519195
$649$	−29.0404	−1.13994
$650$	5.87266	0.230345
$651$	7.77121	0.304578
$652$	36.2527	1.41976
$653$	−29.3424	−1.14826	−0.574129	−	0.818765i	$-0.694659\pi$
$653$	−29.3424	−1.14826	−0.574129	+	0.818765i	$0.694659\pi$
$654$	7.96258	0.311362
$655$	33.8880	1.32411
$656$	−38.8814	−1.51806
$657$	−13.6655	−0.533144
$658$	17.7306	0.691210
$659$	−9.09693	−0.354366	−0.177183	−	0.984178i	$-0.556698\pi$
$659$	−9.09693	−0.354366	−0.177183	+	0.984178i	$0.556698\pi$
$660$	11.5474	0.449483
$661$	−28.8073	−1.12047	−0.560236	−	0.828333i	$-0.689290\pi$
$661$	−28.8073	−1.12047	−0.560236	+	0.828333i	$0.689290\pi$
$662$	20.2737	0.787961
$663$	−14.9768	−0.581651
$664$	−0.731619	−0.0283923
$665$	19.5163	0.756808
$666$	−0.778572	−0.0301691
$667$	11.2261	0.434675
$668$	−20.9421	−0.810275
$669$	8.16065	0.315509
$670$	−57.9925	−2.24045
$671$	−24.8210	−0.958205
$672$	−8.05662	−0.310791
$673$	7.57614	0.292039	0.146019	−	0.989282i	$-0.453354\pi$
$673$	7.57614	0.292039	0.146019	+	0.989282i	$0.453354\pi$
$674$	−22.7950	−0.878031
$675$	1.33721	0.0514692
$676$	−17.0530	−0.655885
$677$	7.01979	0.269793	0.134896	−	0.990860i	$-0.456930\pi$
$677$	7.01979	0.269793	0.134896	+	0.990860i	$0.456930\pi$
$678$	11.5046	0.441830
$679$	−2.77543	−0.106511
$680$	−2.28776	−0.0877317
$681$	−27.1961	−1.04216
$682$	34.7976	1.33247
$683$	−17.0192	−0.651220	−0.325610	−	0.945504i	$-0.605570\pi$
$683$	−17.0192	−0.651220	−0.325610	+	0.945504i	$0.605570\pi$
$684$	−16.0134	−0.612287
$685$	−22.6190	−0.864229
$686$	2.01632	0.0769835
$687$	−22.0658	−0.841862
$688$	1.07736	0.0410742
$689$	30.5558	1.16408
$690$	12.8163	0.487907
$691$	11.1367	0.423661	0.211830	−	0.977306i	$-0.432058\pi$
$691$	11.1367	0.423661	0.211830	+	0.977306i	$0.432058\pi$
$692$	33.7786	1.28407
$693$	−2.22076	−0.0843596
$694$	−64.0824	−2.43254
$695$	57.4652	2.17978
$696$	0.587615	0.0222735
$697$	69.1799	2.62037
$698$	43.6776	1.65322
$699$	−5.02117	−0.189918
$700$	−2.76207	−0.104396
$701$	3.13627	0.118455	0.0592277	−	0.998244i	$-0.481136\pi$
$701$	3.13627	0.118455	0.0592277	+	0.998244i	$0.481136\pi$
$702$	4.39173	0.165755
$703$	−2.99355	−0.112904
$704$	−18.9109	−0.712731
$705$	22.1367	0.833715
$706$	23.7165	0.892582
$707$	4.54797	0.171044
$708$	−27.0108	−1.01513
$709$	46.9385	1.76281	0.881406	−	0.472359i	$-0.156597\pi$
$709$	46.9385	1.76281	0.881406	+	0.472359i	$0.156597\pi$
$710$	−15.8686	−0.595540
$711$	−13.5376	−0.507699
$712$	−0.106949	−0.00400808
$713$	19.6219	0.734847
$714$	13.8645	0.518865
$715$	−12.1766	−0.455379
$716$	14.5691	0.544471
$717$	23.1049	0.862867
$718$	−66.5203	−2.48252
$719$	−42.8800	−1.59916	−0.799578	−	0.600562i	$-0.794943\pi$
$719$	−42.8800	−1.59916	−0.799578	+	0.600562i	$0.794943\pi$
$720$	−9.72869	−0.362567
$721$	6.92978	0.258078
$722$	−82.8765	−3.08435
$723$	−15.6852	−0.583339
$724$	−19.5922	−0.728137
$725$	−5.94531	−0.220803
$726$	12.2355	0.454102
$727$	−16.5946	−0.615459	−0.307729	−	0.951474i	$-0.599569\pi$
$727$	−16.5946	−0.615459	−0.307729	+	0.951474i	$0.599569\pi$
$728$	−0.287868	−0.0106691
$729$	1.00000	0.0370370
$730$	69.3642	2.56729
$731$	−1.91691	−0.0708994
$732$	−23.0863	−0.853293
$733$	−29.1103	−1.07522	−0.537608	−	0.843195i	$-0.680672\pi$
$733$	−29.1103	−1.07522	−0.537608	+	0.843195i	$0.680672\pi$
$734$	−21.4622	−0.792184
$735$	2.51738	0.0928550
$736$	−20.3426	−0.749837
$737$	25.3726	0.934612
$738$	−20.2860	−0.746737
$739$	23.5908	0.867802	0.433901	−	0.900961i	$-0.357137\pi$
$739$	23.5908	0.867802	0.433901	+	0.900961i	$0.357137\pi$
$740$	2.00781	0.0738087
$741$	16.8859	0.620318
$742$	−28.2864	−1.03843
$743$	24.8187	0.910511	0.455256	−	0.890361i	$-0.349548\pi$
$743$	24.8187	0.910511	0.455256	+	0.890361i	$0.349548\pi$
$744$	1.02709	0.0376548
$745$	−7.90817	−0.289733
$746$	4.51704	0.165381
$747$	5.53562	0.202538
$748$	31.5414	1.15327
$749$	−5.25189	−0.191900
$750$	18.5918	0.678875
$751$	−8.32607	−0.303823	−0.151911	−	0.988394i	$-0.548543\pi$
$751$	−8.32607	−0.303823	−0.151911	+	0.988394i	$0.548543\pi$
$752$	−33.9835	−1.23925
$753$	25.2216	0.919127
$754$	−19.5259	−0.711090
$755$	−33.5448	−1.22082
$756$	−2.06555	−0.0751232
$757$	−46.9073	−1.70487	−0.852437	−	0.522830i	$-0.824876\pi$
$757$	−46.9073	−1.70487	−0.852437	+	0.522830i	$0.824876\pi$
$758$	27.7218	1.00690
$759$	−5.60731	−0.203532
$760$	2.57938	0.0935638
$761$	34.7395	1.25930	0.629652	−	0.776877i	$-0.283197\pi$
$761$	34.7395	1.25930	0.629652	+	0.776877i	$0.283197\pi$
$762$	13.5712	0.491633
$763$	3.94906	0.142966
$764$	−42.3429	−1.53191
$765$	17.3098	0.625838
$766$	−2.01632	−0.0728526
$767$	28.4825	1.02844
$768$	14.9003	0.537667
$769$	42.6938	1.53958	0.769789	−	0.638298i	$-0.220361\pi$
$769$	42.6938	1.53958	0.769789	+	0.638298i	$0.220361\pi$
$770$	11.2722	0.406223
$771$	−8.88095	−0.319840
$772$	−47.6785	−1.71599
$773$	−18.6932	−0.672349	−0.336174	−	0.941800i	$-0.609133\pi$
$773$	−18.6932	−0.672349	−0.336174	+	0.941800i	$0.609133\pi$
$774$	0.562104	0.0202044
$775$	−10.3917	−0.373282
$776$	−0.366816	−0.0131679
$777$	−0.386135	−0.0138525
$778$	−11.5996	−0.415866
$779$	−77.9980	−2.79457
$780$	−11.3256	−0.405520
$781$	6.94277	0.248432
$782$	35.0071	1.25185
$783$	−4.44605	−0.158889
$784$	−3.86461	−0.138022
$785$	40.0650	1.42998
$786$	−27.1429	−0.968156
$787$	24.3195	0.866898	0.433449	−	0.901178i	$-0.357296\pi$
$787$	24.3195	0.866898	0.433449	+	0.901178i	$0.357296\pi$
$788$	−42.1756	−1.50244
$789$	11.5132	0.409882
$790$	68.7147	2.44476
$791$	5.70572	0.202872
$792$	−0.293508	−0.0104293
$793$	24.3441	0.864485
$794$	38.5949	1.36968
$795$	−35.3156	−1.25252
$796$	−24.0967	−0.854083
$797$	−20.7783	−0.736003	−0.368002	−	0.929825i	$-0.619958\pi$
$797$	−20.7783	−0.736003	−0.368002	+	0.929825i	$0.619958\pi$
$798$	−15.6317	−0.553357
$799$	60.4654	2.13911
$800$	10.7734	0.380897
$801$	0.809204	0.0285918
$802$	15.5073	0.547583
$803$	−30.3479	−1.07095
$804$	23.5993	0.832283
$805$	6.35627	0.224029
$806$	−34.1290	−1.20214
$807$	−12.0201	−0.423126
$808$	0.601085	0.0211461
$809$	43.3741	1.52495	0.762476	−	0.647017i	$-0.223984\pi$
$809$	43.3741	1.52495	0.762476	+	0.647017i	$0.223984\pi$
$810$	−5.07585	−0.178347
$811$	−16.9710	−0.595932	−0.297966	−	0.954577i	$-0.596308\pi$
$811$	−16.9710	−0.595932	−0.297966	+	0.954577i	$0.596308\pi$
$812$	9.18354	0.322279
$813$	16.4543	0.577079
$814$	−1.72902	−0.0606021
$815$	44.1828	1.54766
$816$	−26.5735	−0.930259
$817$	2.16125	0.0756126
$818$	25.8299	0.903122
$819$	2.17809	0.0761086
$820$	52.3143	1.82689
$821$	−1.12508	−0.0392655	−0.0196327	−	0.999807i	$-0.506250\pi$
$821$	−1.12508	−0.0392655	−0.0196327	+	0.999807i	$0.506250\pi$
$822$	18.1169	0.631901
$823$	−34.6168	−1.20667	−0.603333	−	0.797489i	$-0.706161\pi$
$823$	−34.6168	−1.20667	−0.603333	+	0.797489i	$0.706161\pi$
$824$	0.915878	0.0319061
$825$	2.96962	0.103389
$826$	−26.3670	−0.917427
$827$	−51.1645	−1.77916	−0.889581	−	0.456777i	$-0.849004\pi$
$827$	−51.1645	−1.77916	−0.889581	+	0.456777i	$0.849004\pi$
$828$	−5.21541	−0.181248
$829$	20.4909	0.711679	0.355840	−	0.934547i	$-0.384195\pi$
$829$	20.4909	0.711679	0.355840	+	0.934547i	$0.384195\pi$
$830$	−28.0980	−0.975295
$831$	12.1307	0.420809
$832$	18.5475	0.643020
$833$	6.87612	0.238244
$834$	−46.0273	−1.59379
$835$	−25.5232	−0.883265
$836$	−35.5618	−1.22993
$837$	−7.77121	−0.268612
$838$	−18.2319	−0.629810
$839$	33.7776	1.16613	0.583066	−	0.812425i	$-0.301853\pi$
$839$	33.7776	1.16613	0.583066	+	0.812425i	$0.301853\pi$
$840$	0.332711	0.0114796
$841$	−9.23260	−0.318365
$842$	13.7609	0.474231
$843$	24.4137	0.840852
$844$	−28.8612	−0.993442
$845$	−20.7833	−0.714968
$846$	−17.7306	−0.609590
$847$	6.06823	0.208507
$848$	54.2155	1.86177
$849$	16.6608	0.571799
$850$	−18.5397	−0.635907
$851$	−0.974973	−0.0334216
$852$	6.45753	0.221231
$853$	−1.80663	−0.0618578	−0.0309289	−	0.999522i	$-0.509847\pi$
$853$	−1.80663	−0.0618578	−0.0309289	+	0.999522i	$0.509847\pi$
$854$	−22.5361	−0.771168
$855$	−19.5163	−0.667442
$856$	−0.694118	−0.0237245
$857$	−47.5989	−1.62595	−0.812974	−	0.582299i	$-0.802153\pi$
$857$	−47.5989	−1.62595	−0.812974	+	0.582299i	$0.802153\pi$
$858$	9.75296	0.332961
$859$	−15.3238	−0.522842	−0.261421	−	0.965225i	$-0.584191\pi$
$859$	−15.3238	−0.522842	−0.261421	+	0.965225i	$0.584191\pi$
$860$	−1.44958	−0.0494302
$861$	−10.0609	−0.342874
$862$	−74.1578	−2.52582
$863$	18.7329	0.637675	0.318838	−	0.947809i	$-0.396708\pi$
$863$	18.7329	0.637675	0.318838	+	0.947809i	$0.396708\pi$
$864$	8.05662	0.274092
$865$	41.1676	1.39974
$866$	4.65948	0.158335
$867$	30.2811	1.02840
$868$	16.0518	0.544834
$869$	−30.0637	−1.01984
$870$	22.5675	0.765110
$871$	−24.8851	−0.843199
$872$	0.521930	0.0176748
$873$	2.77543	0.0939339
$874$	−39.4694	−1.33507
$875$	9.22064	0.311715
$876$	−28.2268	−0.953697
$877$	−24.1072	−0.814042	−0.407021	−	0.913419i	$-0.633432\pi$
$877$	−24.1072	−0.814042	−0.407021	+	0.913419i	$0.633432\pi$
$878$	−28.4879	−0.961418
$879$	6.83003	0.230371
$880$	−21.6051	−0.728307
$881$	−32.7856	−1.10457	−0.552287	−	0.833654i	$-0.686245\pi$
$881$	−32.7856	−1.10457	−0.552287	+	0.833654i	$0.686245\pi$
$882$	−2.01632	−0.0678930
$883$	−41.6750	−1.40248	−0.701238	−	0.712927i	$-0.747369\pi$
$883$	−41.6750	−1.40248	−0.701238	+	0.712927i	$0.747369\pi$
$884$	−30.9353	−1.04047
$885$	−32.9193	−1.10657
$886$	−61.0600	−2.05135
$887$	3.28513	0.110304	0.0551519	−	0.998478i	$-0.482436\pi$
$887$	3.28513	0.110304	0.0551519	+	0.998478i	$0.482436\pi$
$888$	−0.0510337	−0.00171258
$889$	6.73068	0.225740
$890$	−4.10740	−0.137680
$891$	2.22076	0.0743982
$892$	16.8562	0.564388
$893$	−68.1727	−2.28131
$894$	6.33412	0.211845
$895$	17.7560	0.593518
$896$	−1.05676	−0.0353037
$897$	5.49957	0.183625
$898$	−11.3751	−0.379592
$899$	34.5512	1.15235
$900$	2.76207	0.0920690
$901$	−96.4631	−3.21365
$902$	−45.0502	−1.50001
$903$	0.278777	0.00927713
$904$	0.754100	0.0250810
$905$	−23.8779	−0.793729
$906$	26.8680	0.892630
$907$	−35.6378	−1.18333	−0.591667	−	0.806183i	$-0.701530\pi$
$907$	−35.6378	−1.18333	−0.591667	+	0.806183i	$0.701530\pi$
$908$	−56.1749	−1.86423
$909$	−4.54797	−0.150847
$910$	−11.0557	−0.366491
$911$	31.6360	1.04815	0.524074	−	0.851672i	$-0.324411\pi$
$911$	31.6360	1.04815	0.524074	+	0.851672i	$0.324411\pi$
$912$	29.9608	0.992100
$913$	12.2933	0.406848
$914$	53.7136	1.77669
$915$	−28.1363	−0.930159
$916$	−45.5779	−1.50594
$917$	−13.4616	−0.444541
$918$	−13.8645	−0.457596
$919$	−12.3123	−0.406145	−0.203072	−	0.979164i	$-0.565093\pi$
$919$	−12.3123	−0.406145	−0.203072	+	0.979164i	$0.565093\pi$
$920$	0.840079	0.0276966
$921$	14.8281	0.488602
$922$	−43.3547	−1.42781
$923$	−6.80937	−0.224133
$924$	−4.58708	−0.150904
$925$	0.516344	0.0169773
$926$	19.1182	0.628264
$927$	−6.92978	−0.227604
$928$	−35.8202	−1.17585
$929$	−18.0998	−0.593835	−0.296918	−	0.954903i	$-0.595959\pi$
$929$	−18.0998	−0.593835	−0.296918	+	0.954903i	$0.595959\pi$
$930$	39.4455	1.29347
$931$	−7.75260	−0.254081
$932$	−10.3715	−0.339729
$933$	−25.0572	−0.820336
$934$	−37.1997	−1.21721
$935$	38.4409	1.25715
$936$	0.287868	0.00940927
$937$	−4.07121	−0.133000	−0.0665002	−	0.997786i	$-0.521183\pi$
$937$	−4.07121	−0.133000	−0.0665002	+	0.997786i	$0.521183\pi$
$938$	23.0369	0.752180
$939$	4.98857	0.162796
$940$	45.7243	1.49136
$941$	29.7710	0.970508	0.485254	−	0.874373i	$-0.338727\pi$
$941$	29.7710	0.970508	0.485254	+	0.874373i	$0.338727\pi$
$942$	−32.0904	−1.04556
$943$	−25.4032	−0.827244
$944$	50.5368	1.64483
$945$	−2.51738	−0.0818904
$946$	1.24830	0.0405857
$947$	−44.4272	−1.44369	−0.721845	−	0.692055i	$-0.756705\pi$
$947$	−44.4272	−1.44369	−0.721845	+	0.692055i	$0.756705\pi$
$948$	−27.9625	−0.908180
$949$	29.7648	0.966206
$950$	20.9029	0.678180
$951$	−11.1882	−0.362802
$952$	0.908787	0.0294539
$953$	13.9193	0.450889	0.225445	−	0.974256i	$-0.427617\pi$
$953$	13.9193	0.450889	0.225445	+	0.974256i	$0.427617\pi$
$954$	28.2864	0.915805
$955$	−51.6053	−1.66991
$956$	47.7242	1.54351
$957$	−9.87361	−0.319169
$958$	61.8633	1.99871
$959$	8.98515	0.290146
$960$	−21.4368	−0.691869
$961$	29.3917	0.948121
$962$	1.69580	0.0546748
$963$	5.25189	0.169240
$964$	−32.3986	−1.04349
$965$	−58.1081	−1.87056
$966$	−5.09111	−0.163804
$967$	−17.0131	−0.547104	−0.273552	−	0.961857i	$-0.588199\pi$
$967$	−17.0131	−0.547104	−0.273552	+	0.961857i	$0.588199\pi$
$968$	0.802011	0.0257776
$969$	−53.3079	−1.71250
$970$	−14.0876	−0.452327
$971$	−44.3958	−1.42473	−0.712365	−	0.701810i	$-0.752376\pi$
$971$	−44.3958	−1.42473	−0.712365	+	0.701810i	$0.752376\pi$
$972$	2.06555	0.0662525
$973$	−22.8274	−0.731811
$974$	−37.3273	−1.19604
$975$	−2.91256	−0.0932767
$976$	43.1940	1.38261
$977$	32.3540	1.03510	0.517548	−	0.855654i	$-0.326845\pi$
$977$	32.3540	1.03510	0.517548	+	0.855654i	$0.326845\pi$
$978$	−35.3887	−1.13160
$979$	1.79705	0.0574338
$980$	5.19977	0.166101
$981$	−3.94906	−0.126084
$982$	−82.1765	−2.62236
$983$	49.0295	1.56380	0.781899	−	0.623405i	$-0.214251\pi$
$983$	49.0295	1.56380	0.781899	+	0.623405i	$0.214251\pi$
$984$	−1.32970	−0.0423893
$985$	−51.4015	−1.63779
$986$	61.6422	1.96309
$987$	−8.79353	−0.279901
$988$	34.8786	1.10963
$989$	0.703899	0.0223827
$990$	−11.2722	−0.358255
$991$	−25.6901	−0.816072	−0.408036	−	0.912966i	$-0.633786\pi$
$991$	−25.6901	−0.816072	−0.408036	+	0.912966i	$0.633786\pi$
$992$	−62.6097	−1.98786
$993$	−10.0548	−0.319080
$994$	6.30363	0.199939
$995$	−29.3677	−0.931020
$996$	11.4341	0.362303
$997$	51.5005	1.63104	0.815519	−	0.578731i	$-0.196452\pi$
$997$	51.5005	1.63104	0.815519	+	0.578731i	$0.196452\pi$
$998$	10.6623	0.337508
$999$	0.386135	0.0122168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.10	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.10	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01632 q^{2} +1.00000 q^{3} +2.06555 q^{4} +2.51738 q^{5} -2.01632 q^{6} -1.00000 q^{7} -0.132166 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.01632 q^{2} +1.00000 q^{3} +2.06555 q^{4} +2.51738 q^{5} -2.01632 q^{6} -1.00000 q^{7} -0.132166 q^{8} +1.00000 q^{9} -5.07585 q^{10} +2.22076 q^{11} +2.06555 q^{12} -2.17809 q^{13} +2.01632 q^{14} +2.51738 q^{15} -3.86461 q^{16} +6.87612 q^{17} -2.01632 q^{18} -7.75260 q^{19} +5.19977 q^{20} -1.00000 q^{21} -4.47776 q^{22} -2.52495 q^{23} -0.132166 q^{24} +1.33721 q^{25} +4.39173 q^{26} +1.00000 q^{27} -2.06555 q^{28} -4.44605 q^{29} -5.07585 q^{30} -7.77121 q^{31} +8.05662 q^{32} +2.22076 q^{33} -13.8645 q^{34} -2.51738 q^{35} +2.06555 q^{36} +0.386135 q^{37} +15.6317 q^{38} -2.17809 q^{39} -0.332711 q^{40} +10.0609 q^{41} +2.01632 q^{42} -0.278777 q^{43} +4.58708 q^{44} +2.51738 q^{45} +5.09111 q^{46} +8.79353 q^{47} -3.86461 q^{48} +1.00000 q^{49} -2.69624 q^{50} +6.87612 q^{51} -4.49895 q^{52} -14.0287 q^{53} -2.01632 q^{54} +5.59050 q^{55} +0.132166 q^{56} -7.75260 q^{57} +8.96467 q^{58} -13.0768 q^{59} +5.19977 q^{60} -11.1768 q^{61} +15.6693 q^{62} -1.00000 q^{63} -8.51551 q^{64} -5.48308 q^{65} -4.47776 q^{66} +11.4252 q^{67} +14.2030 q^{68} -2.52495 q^{69} +5.07585 q^{70} +3.12631 q^{71} -0.132166 q^{72} -13.6655 q^{73} -0.778572 q^{74} +1.33721 q^{75} -16.0134 q^{76} -2.22076 q^{77} +4.39173 q^{78} -13.5376 q^{79} -9.72869 q^{80} +1.00000 q^{81} -20.2860 q^{82} +5.53562 q^{83} -2.06555 q^{84} +17.3098 q^{85} +0.562104 q^{86} -4.44605 q^{87} -0.293508 q^{88} +0.809204 q^{89} -5.07585 q^{90} +2.17809 q^{91} -5.21541 q^{92} -7.77121 q^{93} -17.7306 q^{94} -19.5163 q^{95} +8.05662 q^{96} +2.77543 q^{97} -2.01632 q^{98} +2.22076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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