LMFDB - Embedded newform 8043.2.a.s.1.14

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:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.46567 q^{2} -1.00000 q^{3} +0.148201 q^{4} +0.335135 q^{5} +1.46567 q^{6} -1.00000 q^{7} +2.71413 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46567 q^{2} -1.00000 q^{3} +0.148201 q^{4} +0.335135 q^{5} +1.46567 q^{6} -1.00000 q^{7} +2.71413 q^{8} +1.00000 q^{9} -0.491199 q^{10} +1.33792 q^{11} -0.148201 q^{12} +1.84424 q^{13} +1.46567 q^{14} -0.335135 q^{15} -4.27444 q^{16} -0.996756 q^{17} -1.46567 q^{18} +3.33095 q^{19} +0.0496673 q^{20} +1.00000 q^{21} -1.96096 q^{22} +4.13212 q^{23} -2.71413 q^{24} -4.88768 q^{25} -2.70305 q^{26} -1.00000 q^{27} -0.148201 q^{28} +6.10548 q^{29} +0.491199 q^{30} -6.72273 q^{31} +0.836665 q^{32} -1.33792 q^{33} +1.46092 q^{34} -0.335135 q^{35} +0.148201 q^{36} +6.92572 q^{37} -4.88208 q^{38} -1.84424 q^{39} +0.909601 q^{40} +9.98044 q^{41} -1.46567 q^{42} +4.08326 q^{43} +0.198281 q^{44} +0.335135 q^{45} -6.05634 q^{46} -4.33568 q^{47} +4.27444 q^{48} +1.00000 q^{49} +7.16375 q^{50} +0.996756 q^{51} +0.273317 q^{52} +5.52590 q^{53} +1.46567 q^{54} +0.448384 q^{55} -2.71413 q^{56} -3.33095 q^{57} -8.94864 q^{58} -5.94373 q^{59} -0.0496673 q^{60} +5.96095 q^{61} +9.85334 q^{62} -1.00000 q^{63} +7.32260 q^{64} +0.618068 q^{65} +1.96096 q^{66} -13.4219 q^{67} -0.147720 q^{68} -4.13212 q^{69} +0.491199 q^{70} +6.45917 q^{71} +2.71413 q^{72} +4.22994 q^{73} -10.1508 q^{74} +4.88768 q^{75} +0.493649 q^{76} -1.33792 q^{77} +2.70305 q^{78} +4.35651 q^{79} -1.43251 q^{80} +1.00000 q^{81} -14.6281 q^{82} +2.11443 q^{83} +0.148201 q^{84} -0.334048 q^{85} -5.98473 q^{86} -6.10548 q^{87} +3.63130 q^{88} -11.3825 q^{89} -0.491199 q^{90} -1.84424 q^{91} +0.612383 q^{92} +6.72273 q^{93} +6.35469 q^{94} +1.11632 q^{95} -0.836665 q^{96} +17.0870 q^{97} -1.46567 q^{98} +1.33792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.46567	−1.03639	−0.518194	−	0.855263i	$-0.673396\pi$
$2$	−1.46567	−1.03639	−0.518194	+	0.855263i	$0.673396\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.148201	0.0741004
$5$	0.335135	0.149877	0.0749384	−	0.997188i	$-0.476124\pi$
$5$	0.335135	0.149877	0.0749384	+	0.997188i	$0.476124\pi$
$6$	1.46567	0.598359
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.71413	0.959591
$9$	1.00000	0.333333
$10$	−0.491199	−0.155331
$11$	1.33792	0.403398	0.201699	−	0.979448i	$-0.435354\pi$
$11$	1.33792	0.403398	0.201699	+	0.979448i	$0.435354\pi$
$12$	−0.148201	−0.0427819
$13$	1.84424	0.511499	0.255750	−	0.966743i	$-0.417678\pi$
$13$	1.84424	0.511499	0.255750	+	0.966743i	$0.417678\pi$
$14$	1.46567	0.391718
$15$	−0.335135	−0.0865315
$16$	−4.27444	−1.06861
$17$	−0.996756	−0.241749	−0.120874	−	0.992668i	$-0.538570\pi$
$17$	−0.996756	−0.241749	−0.120874	+	0.992668i	$0.538570\pi$
$18$	−1.46567	−0.345463
$19$	3.33095	0.764171	0.382086	−	0.924127i	$-0.375206\pi$
$19$	3.33095	0.764171	0.382086	+	0.924127i	$0.375206\pi$
$20$	0.0496673	0.0111059
$21$	1.00000	0.218218
$22$	−1.96096	−0.418077
$23$	4.13212	0.861606	0.430803	−	0.902446i	$-0.358230\pi$
$23$	4.13212	0.861606	0.430803	+	0.902446i	$0.358230\pi$
$24$	−2.71413	−0.554020
$25$	−4.88768	−0.977537
$26$	−2.70305	−0.530112
$27$	−1.00000	−0.192450
$28$	−0.148201	−0.0280073
$29$	6.10548	1.13376	0.566880	−	0.823801i	$-0.308150\pi$
$29$	6.10548	1.13376	0.566880	+	0.823801i	$0.308150\pi$
$30$	0.491199	0.0896802
$31$	−6.72273	−1.20744	−0.603719	−	0.797197i	$-0.706315\pi$
$31$	−6.72273	−1.20744	−0.603719	+	0.797197i	$0.706315\pi$
$32$	0.836665	0.147903
$33$	−1.33792	−0.232902
$34$	1.46092	0.250546
$35$	−0.335135	−0.0566481
$36$	0.148201	0.0247001
$37$	6.92572	1.13858	0.569291	−	0.822136i	$-0.307218\pi$
$37$	6.92572	1.13858	0.569291	+	0.822136i	$0.307218\pi$
$38$	−4.88208	−0.791978
$39$	−1.84424	−0.295314
$40$	0.909601	0.143821
$41$	9.98044	1.55868	0.779342	−	0.626599i	$-0.215554\pi$
$41$	9.98044	1.55868	0.779342	+	0.626599i	$0.215554\pi$
$42$	−1.46567	−0.226158
$43$	4.08326	0.622691	0.311345	−	0.950297i	$-0.399220\pi$
$43$	4.08326	0.622691	0.311345	+	0.950297i	$0.399220\pi$
$44$	0.198281	0.0298920
$45$	0.335135	0.0499590
$46$	−6.05634	−0.892958
$47$	−4.33568	−0.632424	−0.316212	−	0.948689i	$-0.602411\pi$
$47$	−4.33568	−0.632424	−0.316212	+	0.948689i	$0.602411\pi$
$48$	4.27444	0.616962
$49$	1.00000	0.142857
$50$	7.16375	1.01311
$51$	0.996756	0.139574
$52$	0.273317	0.0379023
$53$	5.52590	0.759041	0.379521	−	0.925183i	$-0.376089\pi$
$53$	5.52590	0.759041	0.379521	+	0.925183i	$0.376089\pi$
$54$	1.46567	0.199453
$55$	0.448384	0.0604601
$56$	−2.71413	−0.362691
$57$	−3.33095	−0.441195
$58$	−8.94864	−1.17501
$59$	−5.94373	−0.773807	−0.386904	−	0.922120i	$-0.626455\pi$
$59$	−5.94373	−0.773807	−0.386904	+	0.922120i	$0.626455\pi$
$60$	−0.0496673	−0.00641202
$61$	5.96095	0.763221	0.381611	−	0.924323i	$-0.375370\pi$
$61$	5.96095	0.763221	0.381611	+	0.924323i	$0.375370\pi$
$62$	9.85334	1.25137
$63$	−1.00000	−0.125988
$64$	7.32260	0.915325
$65$	0.618068	0.0766619
$66$	1.96096	0.241377
$67$	−13.4219	−1.63975	−0.819876	−	0.572542i	$-0.805958\pi$
$67$	−13.4219	−1.63975	−0.819876	+	0.572542i	$0.805958\pi$
$68$	−0.147720	−0.0179137
$69$	−4.13212	−0.497448
$70$	0.491199	0.0587095
$71$	6.45917	0.766562	0.383281	−	0.923632i	$-0.374794\pi$
$71$	6.45917	0.766562	0.383281	+	0.923632i	$0.374794\pi$
$72$	2.71413	0.319864
$73$	4.22994	0.495077	0.247538	−	0.968878i	$-0.420378\pi$
$73$	4.22994	0.495077	0.247538	+	0.968878i	$0.420378\pi$
$74$	−10.1508	−1.18001
$75$	4.88768	0.564381
$76$	0.493649	0.0566254
$77$	−1.33792	−0.152470
$78$	2.70305	0.306060
$79$	4.35651	0.490146	0.245073	−	0.969505i	$-0.421188\pi$
$79$	4.35651	0.490146	0.245073	+	0.969505i	$0.421188\pi$
$80$	−1.43251	−0.160160
$81$	1.00000	0.111111
$82$	−14.6281	−1.61540
$83$	2.11443	0.232089	0.116044	−	0.993244i	$-0.462978\pi$
$83$	2.11443	0.232089	0.116044	+	0.993244i	$0.462978\pi$
$84$	0.148201	0.0161700
$85$	−0.334048	−0.0362326
$86$	−5.98473	−0.645350
$87$	−6.10548	−0.654576
$88$	3.63130	0.387098
$89$	−11.3825	−1.20654	−0.603271	−	0.797537i	$-0.706136\pi$
$89$	−11.3825	−1.20654	−0.603271	+	0.797537i	$0.706136\pi$
$90$	−0.491199	−0.0517769
$91$	−1.84424	−0.193329
$92$	0.612383	0.0638454
$93$	6.72273	0.697115
$94$	6.35469	0.655436
$95$	1.11632	0.114532
$96$	−0.836665	−0.0853918
$97$	17.0870	1.73492	0.867459	−	0.497509i	$-0.165752\pi$
$97$	17.0870	1.73492	0.867459	+	0.497509i	$0.165752\pi$
$98$	−1.46567	−0.148055
$99$	1.33792	0.134466
$100$	−0.724359	−0.0724359
$101$	17.5981	1.75107	0.875536	−	0.483153i	$-0.160508\pi$
$101$	17.5981	1.75107	0.875536	+	0.483153i	$0.160508\pi$
$102$	−1.46092	−0.144653
$103$	19.1092	1.88288	0.941441	−	0.337178i	$-0.109473\pi$
$103$	19.1092	1.88288	0.941441	+	0.337178i	$0.109473\pi$
$104$	5.00551	0.490830
$105$	0.335135	0.0327058
$106$	−8.09917	−0.786661
$107$	−1.69078	−0.163454	−0.0817268	−	0.996655i	$-0.526044\pi$
$107$	−1.69078	−0.163454	−0.0817268	+	0.996655i	$0.526044\pi$
$108$	−0.148201	−0.0142606
$109$	−12.2817	−1.17637	−0.588187	−	0.808725i	$-0.700158\pi$
$109$	−12.2817	−1.17637	−0.588187	+	0.808725i	$0.700158\pi$
$110$	−0.657185	−0.0626601
$111$	−6.92572	−0.657360
$112$	4.27444	0.403896
$113$	3.08758	0.290455	0.145227	−	0.989398i	$-0.453609\pi$
$113$	3.08758	0.290455	0.145227	+	0.989398i	$0.453609\pi$
$114$	4.88208	0.457249
$115$	1.38482	0.129135
$116$	0.904837	0.0840120
$117$	1.84424	0.170500
$118$	8.71157	0.801965
$119$	0.996756	0.0913725
$120$	−0.909601	−0.0830348
$121$	−9.20997	−0.837270
$122$	−8.73681	−0.790993
$123$	−9.98044	−0.899906
$124$	−0.996315	−0.0894717
$125$	−3.31371	−0.296387
$126$	1.46567	0.130573
$127$	−17.5638	−1.55854	−0.779269	−	0.626690i	$-0.784409\pi$
$127$	−17.5638	−1.55854	−0.779269	+	0.626690i	$0.784409\pi$
$128$	−12.4059	−1.09653
$129$	−4.08326	−0.359511
$130$	−0.905886	−0.0794515
$131$	−3.22385	−0.281669	−0.140835	−	0.990033i	$-0.544979\pi$
$131$	−3.22385	−0.281669	−0.140835	+	0.990033i	$0.544979\pi$
$132$	−0.198281	−0.0172581
$133$	−3.33095	−0.288830
$134$	19.6722	1.69942
$135$	−0.335135	−0.0288438
$136$	−2.70533	−0.231980
$137$	−4.52794	−0.386848	−0.193424	−	0.981115i	$-0.561959\pi$
$137$	−4.52794	−0.386848	−0.193424	+	0.981115i	$0.561959\pi$
$138$	6.05634	0.515550
$139$	−4.51941	−0.383331	−0.191666	−	0.981460i	$-0.561389\pi$
$139$	−4.51941	−0.383331	−0.191666	+	0.981460i	$0.561389\pi$
$140$	−0.0496673	−0.00419765
$141$	4.33568	0.365130
$142$	−9.46703	−0.794456
$143$	2.46744	0.206338
$144$	−4.27444	−0.356203
$145$	2.04616	0.169924
$146$	−6.19971	−0.513092
$147$	−1.00000	−0.0824786
$148$	1.02640	0.0843694
$149$	−0.507434	−0.0415706	−0.0207853	−	0.999784i	$-0.506617\pi$
$149$	−0.507434	−0.0415706	−0.0207853	+	0.999784i	$0.506617\pi$
$150$	−7.16375	−0.584918
$151$	11.1832	0.910080	0.455040	−	0.890471i	$-0.349625\pi$
$151$	11.1832	0.910080	0.455040	+	0.890471i	$0.349625\pi$
$152$	9.04063	0.733292
$153$	−0.996756	−0.0805830
$154$	1.96096	0.158018
$155$	−2.25302	−0.180967
$156$	−0.273317	−0.0218829
$157$	10.2976	0.821836	0.410918	−	0.911672i	$-0.365208\pi$
$157$	10.2976	0.821836	0.410918	+	0.911672i	$0.365208\pi$
$158$	−6.38522	−0.507981
$159$	−5.52590	−0.438233
$160$	0.280396	0.0221672
$161$	−4.13212	−0.325656
$162$	−1.46567	−0.115154
$163$	−4.36588	−0.341962	−0.170981	−	0.985274i	$-0.554694\pi$
$163$	−4.36588	−0.341962	−0.170981	+	0.985274i	$0.554694\pi$
$164$	1.47911	0.115499
$165$	−0.448384	−0.0349066
$166$	−3.09907	−0.240534
$167$	−15.1660	−1.17358	−0.586790	−	0.809739i	$-0.699609\pi$
$167$	−15.1660	−1.17358	−0.586790	+	0.809739i	$0.699609\pi$
$168$	2.71413	0.209400
$169$	−9.59879	−0.738369
$170$	0.489605	0.0375510
$171$	3.33095	0.254724
$172$	0.605142	0.0461417
$173$	−5.11159	−0.388627	−0.194313	−	0.980939i	$-0.562248\pi$
$173$	−5.11159	−0.388627	−0.194313	+	0.980939i	$0.562248\pi$
$174$	8.94864	0.678395
$175$	4.88768	0.369474
$176$	−5.71886	−0.431075
$177$	5.94373	0.446758
$178$	16.6830	1.25044
$179$	−6.44031	−0.481371	−0.240686	−	0.970603i	$-0.577372\pi$
$179$	−6.44031	−0.481371	−0.240686	+	0.970603i	$0.577372\pi$
$180$	0.0496673	0.00370198
$181$	−17.6907	−1.31494	−0.657470	−	0.753481i	$-0.728373\pi$
$181$	−17.6907	−1.31494	−0.657470	+	0.753481i	$0.728373\pi$
$182$	2.70305	0.200363
$183$	−5.96095	−0.440646
$184$	11.2151	0.826790
$185$	2.32105	0.170647
$186$	−9.85334	−0.722482
$187$	−1.33358	−0.0975211
$188$	−0.642551	−0.0468629
$189$	1.00000	0.0727393
$190$	−1.63616	−0.118699
$191$	−14.1655	−1.02498	−0.512491	−	0.858692i	$-0.671277\pi$
$191$	−14.1655	−1.02498	−0.512491	+	0.858692i	$0.671277\pi$
$192$	−7.32260	−0.528463
$193$	10.3657	0.746142	0.373071	−	0.927803i	$-0.378305\pi$
$193$	10.3657	0.746142	0.373071	+	0.927803i	$0.378305\pi$
$194$	−25.0439	−1.79805
$195$	−0.618068	−0.0442608
$196$	0.148201	0.0105858
$197$	−14.8897	−1.06085	−0.530423	−	0.847733i	$-0.677967\pi$
$197$	−14.8897	−1.06085	−0.530423	+	0.847733i	$0.677967\pi$
$198$	−1.96096	−0.139359
$199$	8.17477	0.579494	0.289747	−	0.957103i	$-0.406429\pi$
$199$	8.17477	0.579494	0.289747	+	0.957103i	$0.406429\pi$
$200$	−13.2658	−0.938036
$201$	13.4219	0.946711
$202$	−25.7930	−1.81479
$203$	−6.10548	−0.428521
$204$	0.147720	0.0103425
$205$	3.34480	0.233611
$206$	−28.0078	−1.95140
$207$	4.13212	0.287202
$208$	−7.88308	−0.546593
$209$	4.45654	0.308265
$210$	−0.491199	−0.0338959
$211$	10.5633	0.727208	0.363604	−	0.931554i	$-0.381546\pi$
$211$	10.5633	0.727208	0.363604	+	0.931554i	$0.381546\pi$
$212$	0.818944	0.0562453
$213$	−6.45917	−0.442575
$214$	2.47813	0.169401
$215$	1.36844	0.0933270
$216$	−2.71413	−0.184673
$217$	6.72273	0.456369
$218$	18.0010	1.21918
$219$	−4.22994	−0.285833
$220$	0.0664509	0.00448012
$221$	−1.83825	−0.123654
$222$	10.1508	0.681280
$223$	−9.37508	−0.627802	−0.313901	−	0.949456i	$-0.601636\pi$
$223$	−9.37508	−0.627802	−0.313901	+	0.949456i	$0.601636\pi$
$224$	−0.836665	−0.0559021
$225$	−4.88768	−0.325846
$226$	−4.52538	−0.301024
$227$	17.4572	1.15867	0.579337	−	0.815088i	$-0.303312\pi$
$227$	17.4572	1.15867	0.579337	+	0.815088i	$0.303312\pi$
$228$	−0.493649	−0.0326927
$229$	7.17812	0.474344	0.237172	−	0.971468i	$-0.423780\pi$
$229$	7.17812	0.474344	0.237172	+	0.971468i	$0.423780\pi$
$230$	−2.02969	−0.133834
$231$	1.33792	0.0880287
$232$	16.5711	1.08795
$233$	20.8703	1.36726	0.683629	−	0.729830i	$-0.260401\pi$
$233$	20.8703	1.36726	0.683629	+	0.729830i	$0.260401\pi$
$234$	−2.70305	−0.176704
$235$	−1.45304	−0.0947857
$236$	−0.880865	−0.0573395
$237$	−4.35651	−0.282986
$238$	−1.46092	−0.0946974
$239$	−3.40119	−0.220005	−0.110002	−	0.993931i	$-0.535086\pi$
$239$	−3.40119	−0.220005	−0.110002	+	0.993931i	$0.535086\pi$
$240$	1.43251	0.0924683
$241$	16.6595	1.07313	0.536567	−	0.843858i	$-0.319721\pi$
$241$	16.6595	1.07313	0.536567	+	0.843858i	$0.319721\pi$
$242$	13.4988	0.867737
$243$	−1.00000	−0.0641500
$244$	0.883418	0.0565550
$245$	0.335135	0.0214110
$246$	14.6281	0.932652
$247$	6.14305	0.390873
$248$	−18.2464	−1.15865
$249$	−2.11443	−0.133997
$250$	4.85682	0.307172
$251$	16.3378	1.03123	0.515615	−	0.856820i	$-0.327563\pi$
$251$	16.3378	1.03123	0.515615	+	0.856820i	$0.327563\pi$
$252$	−0.148201	−0.00933578
$253$	5.52844	0.347570
$254$	25.7429	1.61525
$255$	0.334048	0.0209189
$256$	3.53777	0.221111
$257$	−14.5452	−0.907307	−0.453654	−	0.891178i	$-0.649880\pi$
$257$	−14.5452	−0.907307	−0.453654	+	0.891178i	$0.649880\pi$
$258$	5.98473	0.372593
$259$	−6.92572	−0.430343
$260$	0.0915982	0.00568068
$261$	6.10548	0.377920
$262$	4.72512	0.291919
$263$	12.4391	0.767031	0.383515	−	0.923535i	$-0.374713\pi$
$263$	12.4391	0.767031	0.383515	+	0.923535i	$0.374713\pi$
$264$	−3.63130	−0.223491
$265$	1.85192	0.113763
$266$	4.88208	0.299340
$267$	11.3825	0.696597
$268$	−1.98914	−0.121506
$269$	2.87530	0.175310	0.0876549	−	0.996151i	$-0.472063\pi$
$269$	2.87530	0.175310	0.0876549	+	0.996151i	$0.472063\pi$
$270$	0.491199	0.0298934
$271$	−20.1522	−1.22416	−0.612080	−	0.790796i	$-0.709667\pi$
$271$	−20.1522	−1.22416	−0.612080	+	0.790796i	$0.709667\pi$
$272$	4.26057	0.258335
$273$	1.84424	0.111618
$274$	6.63648	0.400925
$275$	−6.53934	−0.394337
$276$	−0.612383	−0.0368611
$277$	−21.7630	−1.30761	−0.653807	−	0.756661i	$-0.726829\pi$
$277$	−21.7630	−1.30761	−0.653807	+	0.756661i	$0.726829\pi$
$278$	6.62398	0.397280
$279$	−6.72273	−0.402479
$280$	−0.909601	−0.0543591
$281$	7.71631	0.460317	0.230158	−	0.973153i	$-0.426076\pi$
$281$	7.71631	0.460317	0.230158	+	0.973153i	$0.426076\pi$
$282$	−6.35469	−0.378416
$283$	−1.94204	−0.115442	−0.0577210	−	0.998333i	$-0.518383\pi$
$283$	−1.94204	−0.115442	−0.0577210	+	0.998333i	$0.518383\pi$
$284$	0.957254	0.0568026
$285$	−1.11632	−0.0661249
$286$	−3.61647	−0.213846
$287$	−9.98044	−0.589127
$288$	0.836665	0.0493010
$289$	−16.0065	−0.941557
$290$	−2.99900	−0.176108
$291$	−17.0870	−1.00165
$292$	0.626880	0.0366854
$293$	−27.0159	−1.57828	−0.789142	−	0.614211i	$-0.789475\pi$
$293$	−27.0159	−1.57828	−0.789142	+	0.614211i	$0.789475\pi$
$294$	1.46567	0.0854799
$295$	−1.99195	−0.115976
$296$	18.7973	1.09257
$297$	−1.33792	−0.0776340
$298$	0.743732	0.0430833
$299$	7.62060	0.440711
$300$	0.724359	0.0418209
$301$	−4.08326	−0.235355
$302$	−16.3910	−0.943196
$303$	−17.5981	−1.01098
$304$	−14.2379	−0.816601
$305$	1.99772	0.114389
$306$	1.46092	0.0835152
$307$	−13.0805	−0.746542	−0.373271	−	0.927722i	$-0.621764\pi$
$307$	−13.0805	−0.746542	−0.373271	+	0.927722i	$0.621764\pi$
$308$	−0.198281	−0.0112981
$309$	−19.1092	−1.08708
$310$	3.30220	0.187552
$311$	−0.285883	−0.0162109	−0.00810546	−	0.999967i	$-0.502580\pi$
$311$	−0.285883	−0.0162109	−0.00810546	+	0.999967i	$0.502580\pi$
$312$	−5.00551	−0.283381
$313$	31.0980	1.75776	0.878882	−	0.477039i	$-0.158290\pi$
$313$	31.0980	1.75776	0.878882	+	0.477039i	$0.158290\pi$
$314$	−15.0929	−0.851741
$315$	−0.335135	−0.0188827
$316$	0.645638	0.0363200
$317$	−7.37400	−0.414165	−0.207082	−	0.978323i	$-0.566397\pi$
$317$	−7.37400	−0.414165	−0.207082	+	0.978323i	$0.566397\pi$
$318$	8.09917	0.454179
$319$	8.16865	0.457356
$320$	2.45406	0.137186
$321$	1.69078	0.0943700
$322$	6.05634	0.337506
$323$	−3.32014	−0.184738
$324$	0.148201	0.00823338
$325$	−9.01405	−0.500009
$326$	6.39896	0.354406
$327$	12.2817	0.679180
$328$	27.0883	1.49570
$329$	4.33568	0.239034
$330$	0.657185	0.0361768
$331$	19.8111	1.08892	0.544459	−	0.838788i	$-0.316735\pi$
$331$	19.8111	1.08892	0.544459	+	0.838788i	$0.316735\pi$
$332$	0.313360	0.0171979
$333$	6.92572	0.379527
$334$	22.2284	1.21629
$335$	−4.49816	−0.245761
$336$	−4.27444	−0.233190
$337$	20.9895	1.14337	0.571686	−	0.820473i	$-0.306290\pi$
$337$	20.9895	1.14337	0.571686	+	0.820473i	$0.306290\pi$
$338$	14.0687	0.765236
$339$	−3.08758	−0.167694
$340$	−0.0495062	−0.00268485
$341$	−8.99448	−0.487079
$342$	−4.88208	−0.263993
$343$	−1.00000	−0.0539949
$344$	11.0825	0.597529
$345$	−1.38482	−0.0745560
$346$	7.49193	0.402768
$347$	1.33348	0.0715850	0.0357925	−	0.999359i	$-0.488604\pi$
$347$	1.33348	0.0715850	0.0357925	+	0.999359i	$0.488604\pi$
$348$	−0.904837	−0.0485044
$349$	20.7447	1.11044	0.555219	−	0.831704i	$-0.312634\pi$
$349$	20.7447	1.11044	0.555219	+	0.831704i	$0.312634\pi$
$350$	−7.16375	−0.382919
$351$	−1.84424	−0.0984381
$352$	1.11939	0.0596638
$353$	−32.3238	−1.72042	−0.860211	−	0.509938i	$-0.829668\pi$
$353$	−32.3238	−1.72042	−0.860211	+	0.509938i	$0.829668\pi$
$354$	−8.71157	−0.463015
$355$	2.16469	0.114890
$356$	−1.68689	−0.0894052
$357$	−0.996756	−0.0527539
$358$	9.43939	0.498888
$359$	−21.3629	−1.12749	−0.563746	−	0.825949i	$-0.690640\pi$
$359$	−21.3629	−1.12749	−0.563746	+	0.825949i	$0.690640\pi$
$360$	0.909601	0.0479402
$361$	−7.90480	−0.416042
$362$	25.9288	1.36279
$363$	9.20997	0.483398
$364$	−0.273317	−0.0143257
$365$	1.41760	0.0742005
$366$	8.73681	0.456680
$367$	27.1262	1.41597	0.707987	−	0.706226i	$-0.249604\pi$
$367$	27.1262	1.41597	0.707987	+	0.706226i	$0.249604\pi$
$368$	−17.6625	−0.920720
$369$	9.98044	0.519561
$370$	−3.40190	−0.176857
$371$	−5.52590	−0.286891
$372$	0.996315	0.0516565
$373$	11.6512	0.603277	0.301638	−	0.953422i	$-0.402467\pi$
$373$	11.6512	0.603277	0.301638	+	0.953422i	$0.402467\pi$
$374$	1.95460	0.101070
$375$	3.31371	0.171119
$376$	−11.7676	−0.606868
$377$	11.2599	0.579917
$378$	−1.46567	−0.0753861
$379$	−8.21988	−0.422227	−0.211114	−	0.977462i	$-0.567709\pi$
$379$	−8.21988	−0.422227	−0.211114	+	0.977462i	$0.567709\pi$
$380$	0.165439	0.00848684
$381$	17.5638	0.899822
$382$	20.7621	1.06228
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	12.4059	0.633085
$385$	−0.448384	−0.0228518
$386$	−15.1928	−0.773293
$387$	4.08326	0.207564
$388$	2.53230	0.128558
$389$	−23.9619	−1.21492	−0.607459	−	0.794351i	$-0.707811\pi$
$389$	−23.9619	−1.21492	−0.607459	+	0.794351i	$0.707811\pi$
$390$	0.905886	0.0458713
$391$	−4.11871	−0.208292
$392$	2.71413	0.137084
$393$	3.22385	0.162622
$394$	21.8234	1.09945
$395$	1.46002	0.0734615
$396$	0.198281	0.00996400
$397$	12.0671	0.605629	0.302814	−	0.953050i	$-0.402074\pi$
$397$	12.0671	0.605629	0.302814	+	0.953050i	$0.402074\pi$
$398$	−11.9815	−0.600581
$399$	3.33095	0.166756
$400$	20.8921	1.04461
$401$	3.60936	0.180243	0.0901215	−	0.995931i	$-0.471274\pi$
$401$	3.60936	0.180243	0.0901215	+	0.995931i	$0.471274\pi$
$402$	−19.6722	−0.981160
$403$	−12.3983	−0.617604
$404$	2.60805	0.129755
$405$	0.335135	0.0166530
$406$	8.94864	0.444114
$407$	9.26607	0.459302
$408$	2.70533	0.133934
$409$	−4.07952	−0.201719	−0.100860	−	0.994901i	$-0.532159\pi$
$409$	−4.07952	−0.201719	−0.100860	+	0.994901i	$0.532159\pi$
$410$	−4.90238	−0.242111
$411$	4.52794	0.223347
$412$	2.83199	0.139522
$413$	5.94373	0.292472
$414$	−6.05634	−0.297653
$415$	0.708619	0.0347848
$416$	1.54301	0.0756522
$417$	4.51941	0.221316
$418$	−6.53184	−0.319483
$419$	−2.85833	−0.139639	−0.0698194	−	0.997560i	$-0.522242\pi$
$419$	−2.85833	−0.139639	−0.0698194	+	0.997560i	$0.522242\pi$
$420$	0.0496673	0.00242351
$421$	−22.3883	−1.09114	−0.545569	−	0.838066i	$-0.683686\pi$
$421$	−22.3883	−1.09114	−0.545569	+	0.838066i	$0.683686\pi$
$422$	−15.4824	−0.753670
$423$	−4.33568	−0.210808
$424$	14.9980	0.728369
$425$	4.87183	0.236318
$426$	9.46703	0.458679
$427$	−5.96095	−0.288471
$428$	−0.250575	−0.0121120
$429$	−2.46744	−0.119129
$430$	−2.00569	−0.0967230
$431$	34.2822	1.65132	0.825658	−	0.564172i	$-0.190804\pi$
$431$	34.2822	1.65132	0.825658	+	0.564172i	$0.190804\pi$
$432$	4.27444	0.205654
$433$	3.31948	0.159524	0.0797620	−	0.996814i	$-0.474584\pi$
$433$	3.31948	0.159524	0.0797620	+	0.996814i	$0.474584\pi$
$434$	−9.85334	−0.472975
$435$	−2.04616	−0.0981058
$436$	−1.82016	−0.0871698
$437$	13.7639	0.658415
$438$	6.19971	0.296234
$439$	18.6403	0.889651	0.444825	−	0.895617i	$-0.353266\pi$
$439$	18.6403	0.889651	0.444825	+	0.895617i	$0.353266\pi$
$440$	1.21697	0.0580170
$441$	1.00000	0.0476190
$442$	2.69428	0.128154
$443$	18.2432	0.866758	0.433379	−	0.901212i	$-0.357321\pi$
$443$	18.2432	0.866758	0.433379	+	0.901212i	$0.357321\pi$
$444$	−1.02640	−0.0487107
$445$	−3.81467	−0.180833
$446$	13.7408	0.650646
$447$	0.507434	0.0240008
$448$	−7.32260	−0.345960
$449$	−9.33790	−0.440683	−0.220341	−	0.975423i	$-0.570717\pi$
$449$	−9.33790	−0.440683	−0.220341	+	0.975423i	$0.570717\pi$
$450$	7.16375	0.337703
$451$	13.3530	0.628770
$452$	0.457582	0.0215228
$453$	−11.1832	−0.525435
$454$	−25.5865	−1.20084
$455$	−0.618068	−0.0289755
$456$	−9.04063	−0.423366
$457$	26.5229	1.24069	0.620344	−	0.784330i	$-0.286993\pi$
$457$	26.5229	1.24069	0.620344	+	0.784330i	$0.286993\pi$
$458$	−10.5208	−0.491604
$459$	0.996756	0.0465246
$460$	0.205231	0.00956894
$461$	11.3500	0.528622	0.264311	−	0.964437i	$-0.414855\pi$
$461$	11.3500	0.528622	0.264311	+	0.964437i	$0.414855\pi$
$462$	−1.96096	−0.0912319
$463$	39.5340	1.83730	0.918649	−	0.395074i	$-0.129281\pi$
$463$	39.5340	1.83730	0.918649	+	0.395074i	$0.129281\pi$
$464$	−26.0975	−1.21155
$465$	2.25302	0.104481
$466$	−30.5890	−1.41701
$467$	−23.9734	−1.10936	−0.554679	−	0.832064i	$-0.687159\pi$
$467$	−23.9734	−1.10936	−0.554679	+	0.832064i	$0.687159\pi$
$468$	0.273317	0.0126341
$469$	13.4219	0.619768
$470$	2.12968	0.0982347
$471$	−10.2976	−0.474487
$472$	−16.1321	−0.742539
$473$	5.46308	0.251192
$474$	6.38522	0.293283
$475$	−16.2806	−0.747006
$476$	0.147720	0.00677074
$477$	5.52590	0.253014
$478$	4.98504	0.228011
$479$	−20.9539	−0.957409	−0.478704	−	0.877976i	$-0.658893\pi$
$479$	−20.9539	−0.957409	−0.478704	+	0.877976i	$0.658893\pi$
$480$	−0.280396	−0.0127983
$481$	12.7727	0.582383
$482$	−24.4174	−1.11218
$483$	4.13212	0.188018
$484$	−1.36492	−0.0620420
$485$	5.72643	0.260024
$486$	1.46567	0.0664843
$487$	−15.1623	−0.687071	−0.343536	−	0.939140i	$-0.611625\pi$
$487$	−15.1623	−0.687071	−0.343536	+	0.939140i	$0.611625\pi$
$488$	16.1788	0.732380
$489$	4.36588	0.197432
$490$	−0.491199	−0.0221901
$491$	15.0963	0.681286	0.340643	−	0.940193i	$-0.389355\pi$
$491$	15.0963	0.681286	0.340643	+	0.940193i	$0.389355\pi$
$492$	−1.47911	−0.0666834
$493$	−6.08567	−0.274085
$494$	−9.00371	−0.405096
$495$	0.448384	0.0201534
$496$	28.7359	1.29028
$497$	−6.45917	−0.289733
$498$	3.09907	0.138872
$499$	6.63045	0.296820	0.148410	−	0.988926i	$-0.452585\pi$
$499$	6.63045	0.296820	0.148410	+	0.988926i	$0.452585\pi$
$500$	−0.491094	−0.0219624
$501$	15.1660	0.677567
$502$	−23.9458	−1.06876
$503$	−4.13126	−0.184204	−0.0921019	−	0.995750i	$-0.529359\pi$
$503$	−4.13126	−0.184204	−0.0921019	+	0.995750i	$0.529359\pi$
$504$	−2.71413	−0.120897
$505$	5.89772	0.262445
$506$	−8.10290	−0.360218
$507$	9.59879	0.426297
$508$	−2.60297	−0.115488
$509$	−14.9974	−0.664746	−0.332373	−	0.943148i	$-0.607849\pi$
$509$	−14.9974	−0.664746	−0.332373	+	0.943148i	$0.607849\pi$
$510$	−0.489605	−0.0216801
$511$	−4.22994	−0.187121
$512$	19.6265	0.867378
$513$	−3.33095	−0.147065
$514$	21.3186	0.940322
$515$	6.40415	0.282200
$516$	−0.605142	−0.0266399
$517$	−5.80079	−0.255119
$518$	10.1508	0.446003
$519$	5.11159	0.224374
$520$	1.67752	0.0735641
$521$	7.40734	0.324521	0.162261	−	0.986748i	$-0.448121\pi$
$521$	7.40734	0.324521	0.162261	+	0.986748i	$0.448121\pi$
$522$	−8.94864	−0.391671
$523$	41.1584	1.79973	0.899866	−	0.436167i	$-0.143664\pi$
$523$	41.1584	1.79973	0.899866	+	0.436167i	$0.143664\pi$
$524$	−0.477778	−0.0208718
$525$	−4.88768	−0.213316
$526$	−18.2317	−0.794941
$527$	6.70092	0.291897
$528$	5.71886	0.248881
$529$	−5.92561	−0.257635
$530$	−2.71432	−0.117902
$531$	−5.94373	−0.257936
$532$	−0.493649	−0.0214024
$533$	18.4063	0.797265
$534$	−16.6830	−0.721945
$535$	−0.566639	−0.0244979
$536$	−36.4290	−1.57349
$537$	6.44031	0.277920
$538$	−4.21425	−0.181689
$539$	1.33792	0.0576283
$540$	−0.0496673	−0.00213734
$541$	15.2985	0.657732	0.328866	−	0.944377i	$-0.393333\pi$
$541$	15.2985	0.657732	0.328866	+	0.944377i	$0.393333\pi$
$542$	29.5366	1.26871
$543$	17.6907	0.759180
$544$	−0.833951	−0.0357554
$545$	−4.11603	−0.176311
$546$	−2.70305	−0.115680
$547$	33.8638	1.44791	0.723957	−	0.689845i	$-0.242321\pi$
$547$	33.8638	1.44791	0.723957	+	0.689845i	$0.242321\pi$
$548$	−0.671044	−0.0286656
$549$	5.96095	0.254407
$550$	9.58453	0.408686
$551$	20.3370	0.866386
$552$	−11.2151	−0.477347
$553$	−4.35651	−0.185258
$554$	31.8975	1.35520
$555$	−2.32105	−0.0985231
$556$	−0.669780	−0.0284050
$557$	−26.8565	−1.13795	−0.568974	−	0.822356i	$-0.692659\pi$
$557$	−26.8565	−1.13795	−0.568974	+	0.822356i	$0.692659\pi$
$558$	9.85334	0.417125
$559$	7.53049	0.318506
$560$	1.43251	0.0605347
$561$	1.33358	0.0563038
$562$	−11.3096	−0.477067
$563$	6.88757	0.290277	0.145138	−	0.989411i	$-0.453637\pi$
$563$	6.88757	0.290277	0.145138	+	0.989411i	$0.453637\pi$
$564$	0.642551	0.0270563
$565$	1.03476	0.0435325
$566$	2.84639	0.119643
$567$	−1.00000	−0.0419961
$568$	17.5310	0.735586
$569$	30.0349	1.25913	0.629565	−	0.776948i	$-0.283233\pi$
$569$	30.0349	1.25913	0.629565	+	0.776948i	$0.283233\pi$
$570$	1.63616	0.0685310
$571$	41.3202	1.72920	0.864599	−	0.502462i	$-0.167572\pi$
$571$	41.3202	1.72920	0.864599	+	0.502462i	$0.167572\pi$
$572$	0.365677	0.0152897
$573$	14.1655	0.591774
$574$	14.6281	0.610564
$575$	−20.1965	−0.842252
$576$	7.32260	0.305108
$577$	−29.1400	−1.21311	−0.606557	−	0.795040i	$-0.707450\pi$
$577$	−29.1400	−1.21311	−0.606557	+	0.795040i	$0.707450\pi$
$578$	23.4603	0.975819
$579$	−10.3657	−0.430785
$580$	0.303243	0.0125915
$581$	−2.11443	−0.0877214
$582$	25.0439	1.03810
$583$	7.39322	0.306196
$584$	11.4806	0.475071
$585$	0.618068	0.0255540
$586$	39.5965	1.63572
$587$	−29.5187	−1.21837	−0.609185	−	0.793028i	$-0.708503\pi$
$587$	−29.5187	−1.21837	−0.609185	+	0.793028i	$0.708503\pi$
$588$	−0.148201	−0.00611170
$589$	−22.3931	−0.922690
$590$	2.91955	0.120196
$591$	14.8897	0.612480
$592$	−29.6036	−1.21670
$593$	29.2525	1.20126	0.600628	−	0.799528i	$-0.294917\pi$
$593$	29.2525	1.20126	0.600628	+	0.799528i	$0.294917\pi$
$594$	1.96096	0.0804590
$595$	0.334048	0.0136946
$596$	−0.0752021	−0.00308040
$597$	−8.17477	−0.334571
$598$	−11.1693	−0.456747
$599$	−46.3827	−1.89514	−0.947572	−	0.319542i	$-0.896471\pi$
$599$	−46.3827	−1.89514	−0.947572	+	0.319542i	$0.896471\pi$
$600$	13.2658	0.541575
$601$	44.5450	1.81703	0.908514	−	0.417855i	$-0.137218\pi$
$601$	44.5450	1.81703	0.908514	+	0.417855i	$0.137218\pi$
$602$	5.98473	0.243919
$603$	−13.4219	−0.546584
$604$	1.65737	0.0674373
$605$	−3.08658	−0.125487
$606$	25.7930	1.04777
$607$	8.74250	0.354847	0.177423	−	0.984135i	$-0.443224\pi$
$607$	8.74250	0.354847	0.177423	+	0.984135i	$0.443224\pi$
$608$	2.78689	0.113023
$609$	6.10548	0.247407
$610$	−2.92801	−0.118552
$611$	−7.99602	−0.323484
$612$	−0.147720	−0.00597123
$613$	−36.4837	−1.47356	−0.736782	−	0.676131i	$-0.763655\pi$
$613$	−36.4837	−1.47356	−0.736782	+	0.676131i	$0.763655\pi$
$614$	19.1717	0.773708
$615$	−3.34480	−0.134875
$616$	−3.63130	−0.146309
$617$	37.3379	1.50317	0.751583	−	0.659639i	$-0.229291\pi$
$617$	37.3379	1.50317	0.751583	+	0.659639i	$0.229291\pi$
$618$	28.0078	1.12664
$619$	8.09532	0.325379	0.162689	−	0.986677i	$-0.447983\pi$
$619$	8.09532	0.325379	0.162689	+	0.986677i	$0.447983\pi$
$620$	−0.333900	−0.0134097
$621$	−4.13212	−0.165816
$622$	0.419011	0.0168008
$623$	11.3825	0.456030
$624$	7.88308	0.315576
$625$	23.3279	0.933115
$626$	−45.5796	−1.82173
$627$	−4.45654	−0.177977
$628$	1.52611	0.0608984
$629$	−6.90325	−0.275251
$630$	0.491199	0.0195698
$631$	−9.30237	−0.370322	−0.185161	−	0.982708i	$-0.559281\pi$
$631$	−9.30237	−0.370322	−0.185161	+	0.982708i	$0.559281\pi$
$632$	11.8242	0.470340
$633$	−10.5633	−0.419854
$634$	10.8079	0.429236
$635$	−5.88625	−0.233589
$636$	−0.818944	−0.0324732
$637$	1.84424	0.0730713
$638$	−11.9726	−0.473999
$639$	6.45917	0.255521
$640$	−4.15764	−0.164345
$641$	−10.6209	−0.419500	−0.209750	−	0.977755i	$-0.567265\pi$
$641$	−10.6209	−0.419500	−0.209750	+	0.977755i	$0.567265\pi$
$642$	−2.47813	−0.0978040
$643$	26.5213	1.04590	0.522950	−	0.852363i	$-0.324831\pi$
$643$	26.5213	1.04590	0.522950	+	0.852363i	$0.324831\pi$
$644$	−0.612383	−0.0241313
$645$	−1.36844	−0.0538824
$646$	4.86624	0.191460
$647$	48.0151	1.88767	0.943835	−	0.330417i	$-0.107189\pi$
$647$	48.0151	1.88767	0.943835	+	0.330417i	$0.107189\pi$
$648$	2.71413	0.106621
$649$	−7.95224	−0.312153
$650$	13.2117	0.518204
$651$	−6.72273	−0.263485
$652$	−0.647027	−0.0253396
$653$	−4.90446	−0.191926	−0.0959631	−	0.995385i	$-0.530593\pi$
$653$	−4.90446	−0.191926	−0.0959631	+	0.995385i	$0.530593\pi$
$654$	−18.0010	−0.703894
$655$	−1.08043	−0.0422157
$656$	−42.6608	−1.66562
$657$	4.22994	0.165026
$658$	−6.35469	−0.247732
$659$	19.9076	0.775491	0.387746	−	0.921766i	$-0.373254\pi$
$659$	19.9076	0.775491	0.387746	+	0.921766i	$0.373254\pi$
$660$	−0.0664509	−0.00258660
$661$	4.17536	0.162403	0.0812014	−	0.996698i	$-0.474124\pi$
$661$	4.17536	0.162403	0.0812014	+	0.996698i	$0.474124\pi$
$662$	−29.0366	−1.12854
$663$	1.83825	0.0713919
$664$	5.73885	0.222711
$665$	−1.11632	−0.0432889
$666$	−10.1508	−0.393337
$667$	25.2286	0.976853
$668$	−2.24761	−0.0869628
$669$	9.37508	0.362461
$670$	6.59284	0.254704
$671$	7.97528	0.307882
$672$	0.836665	0.0322751
$673$	29.0273	1.11892	0.559460	−	0.828858i	$-0.311009\pi$
$673$	29.0273	1.11892	0.559460	+	0.828858i	$0.311009\pi$
$674$	−30.7638	−1.18498
$675$	4.88768	0.188127
$676$	−1.42255	−0.0547134
$677$	44.7003	1.71797	0.858985	−	0.512000i	$-0.171095\pi$
$677$	44.7003	1.71797	0.858985	+	0.512000i	$0.171095\pi$
$678$	4.52538	0.173796
$679$	−17.0870	−0.655737
$680$	−0.906650	−0.0347685
$681$	−17.4572	−0.668960
$682$	13.1830	0.504803
$683$	−39.4922	−1.51113	−0.755564	−	0.655075i	$-0.772637\pi$
$683$	−39.4922	−1.51113	−0.755564	+	0.655075i	$0.772637\pi$
$684$	0.493649	0.0188751
$685$	−1.51747	−0.0579796
$686$	1.46567	0.0559597
$687$	−7.17812	−0.273863
$688$	−17.4536	−0.665413
$689$	10.1911	0.388249
$690$	2.02969	0.0772690
$691$	−17.5752	−0.668594	−0.334297	−	0.942468i	$-0.608499\pi$
$691$	−17.5752	−0.668594	−0.334297	+	0.942468i	$0.608499\pi$
$692$	−0.757542	−0.0287974
$693$	−1.33792	−0.0508234
$694$	−1.95445	−0.0741898
$695$	−1.51461	−0.0574525
$696$	−16.5711	−0.628126
$697$	−9.94807	−0.376810
$698$	−30.4050	−1.15084
$699$	−20.8703	−0.789387
$700$	0.724359	0.0273782
$701$	13.3369	0.503728	0.251864	−	0.967763i	$-0.418956\pi$
$701$	13.3369	0.503728	0.251864	+	0.967763i	$0.418956\pi$
$702$	2.70305	0.102020
$703$	23.0692	0.870071
$704$	9.79706	0.369240
$705$	1.45304	0.0547245
$706$	47.3761	1.78302
$707$	−17.5981	−0.661843
$708$	0.880865	0.0331050
$709$	17.6767	0.663863	0.331931	−	0.943304i	$-0.392300\pi$
$709$	17.6767	0.663863	0.331931	+	0.943304i	$0.392300\pi$
$710$	−3.17273	−0.119071
$711$	4.35651	0.163382
$712$	−30.8936	−1.15779
$713$	−27.7791	−1.04034
$714$	1.46092	0.0546735
$715$	0.826926	0.0309253
$716$	−0.954459	−0.0356698
$717$	3.40119	0.127020
$718$	31.3111	1.16852
$719$	8.60371	0.320864	0.160432	−	0.987047i	$-0.448711\pi$
$719$	8.60371	0.320864	0.160432	+	0.987047i	$0.448711\pi$
$720$	−1.43251	−0.0533866
$721$	−19.1092	−0.711662
$722$	11.5859	0.431181
$723$	−16.6595	−0.619574
$724$	−2.62178	−0.0974375
$725$	−29.8417	−1.10829
$726$	−13.4988	−0.500988
$727$	25.1483	0.932698	0.466349	−	0.884601i	$-0.345569\pi$
$727$	25.1483	0.932698	0.466349	+	0.884601i	$0.345569\pi$
$728$	−5.00551	−0.185516
$729$	1.00000	0.0370370
$730$	−2.07774	−0.0769006
$731$	−4.07001	−0.150535
$732$	−0.883418	−0.0326521
$733$	32.3961	1.19658	0.598288	−	0.801281i	$-0.295848\pi$
$733$	32.3961	1.19658	0.598288	+	0.801281i	$0.295848\pi$
$734$	−39.7581	−1.46750
$735$	−0.335135	−0.0123616
$736$	3.45720	0.127434
$737$	−17.9575	−0.661473
$738$	−14.6281	−0.538467
$739$	−8.99211	−0.330780	−0.165390	−	0.986228i	$-0.552888\pi$
$739$	−8.99211	−0.330780	−0.165390	+	0.986228i	$0.552888\pi$
$740$	0.343982	0.0126450
$741$	−6.14305	−0.225671
$742$	8.09917	0.297330
$743$	22.9554	0.842152	0.421076	−	0.907025i	$-0.361652\pi$
$743$	22.9554	0.842152	0.421076	+	0.907025i	$0.361652\pi$
$744$	18.2464	0.668945
$745$	−0.170059	−0.00623047
$746$	−17.0769	−0.625229
$747$	2.11443	0.0773630
$748$	−0.197638	−0.00722635
$749$	1.69078	0.0617797
$750$	−4.85682	−0.177346
$751$	−11.9270	−0.435223	−0.217611	−	0.976036i	$-0.569827\pi$
$751$	−11.9270	−0.435223	−0.217611	+	0.976036i	$0.569827\pi$
$752$	18.5326	0.675814
$753$	−16.3378	−0.595381
$754$	−16.5034	−0.601019
$755$	3.74790	0.136400
$756$	0.148201	0.00539001
$757$	−45.5014	−1.65378	−0.826889	−	0.562365i	$-0.809892\pi$
$757$	−45.5014	−1.65378	−0.826889	+	0.562365i	$0.809892\pi$
$758$	12.0477	0.437591
$759$	−5.52844	−0.200670
$760$	3.02983	0.109904
$761$	2.56798	0.0930892	0.0465446	−	0.998916i	$-0.485179\pi$
$761$	2.56798	0.0930892	0.0465446	+	0.998916i	$0.485179\pi$
$762$	−25.7429	−0.932565
$763$	12.2817	0.444627
$764$	−2.09935	−0.0759517
$765$	−0.334048	−0.0120775
$766$	−1.46567	−0.0529570
$767$	−10.9616	−0.395802
$768$	−3.53777	−0.127658
$769$	55.1665	1.98936	0.994678	−	0.103032i	$-0.0328543\pi$
$769$	55.1665	1.98936	0.994678	+	0.103032i	$0.0328543\pi$
$770$	0.657185	0.0236833
$771$	14.5452	0.523834
$772$	1.53621	0.0552894
$773$	−39.2540	−1.41187	−0.705934	−	0.708278i	$-0.749473\pi$
$773$	−39.2540	−1.41187	−0.705934	+	0.708278i	$0.749473\pi$
$774$	−5.98473	−0.215117
$775$	32.8586	1.18032
$776$	46.3763	1.66481
$777$	6.92572	0.248459
$778$	35.1204	1.25913
$779$	33.2443	1.19110
$780$	−0.0915982	−0.00327974
$781$	8.64185	0.309230
$782$	6.03669	0.215872
$783$	−6.10548	−0.218192
$784$	−4.27444	−0.152659
$785$	3.45108	0.123174
$786$	−4.72512	−0.168539
$787$	3.16768	0.112916	0.0564578	−	0.998405i	$-0.482019\pi$
$787$	3.16768	0.112916	0.0564578	+	0.998405i	$0.482019\pi$
$788$	−2.20666	−0.0786092
$789$	−12.4391	−0.442845
$790$	−2.13991	−0.0761346
$791$	−3.08758	−0.109782
$792$	3.63130	0.129033
$793$	10.9934	0.390387
$794$	−17.6864	−0.627667
$795$	−1.85192	−0.0656809
$796$	1.21151	0.0429407
$797$	0.767840	0.0271983	0.0135991	−	0.999908i	$-0.495671\pi$
$797$	0.767840	0.0271983	0.0135991	+	0.999908i	$0.495671\pi$
$798$	−4.88208	−0.172824
$799$	4.32161	0.152888
$800$	−4.08936	−0.144581
$801$	−11.3825	−0.402180
$802$	−5.29015	−0.186802
$803$	5.65932	0.199713
$804$	1.98914	0.0701517
$805$	−1.38482	−0.0488084
$806$	18.1719	0.640077
$807$	−2.87530	−0.101215
$808$	47.7635	1.68031
$809$	6.97126	0.245096	0.122548	−	0.992463i	$-0.460893\pi$
$809$	6.97126	0.245096	0.122548	+	0.992463i	$0.460893\pi$
$810$	−0.491199	−0.0172590
$811$	32.0155	1.12422	0.562109	−	0.827063i	$-0.309990\pi$
$811$	32.0155	1.12422	0.562109	+	0.827063i	$0.309990\pi$
$812$	−0.904837	−0.0317536
$813$	20.1522	0.706770
$814$	−13.5810	−0.476015
$815$	−1.46316	−0.0512522
$816$	−4.26057	−0.149150
$817$	13.6011	0.475843
$818$	5.97924	0.209059
$819$	−1.84424	−0.0644428
$820$	0.495702	0.0173106
$821$	−8.82758	−0.308085	−0.154042	−	0.988064i	$-0.549229\pi$
$821$	−8.82758	−0.308085	−0.154042	+	0.988064i	$0.549229\pi$
$822$	−6.63648	−0.231474
$823$	33.8566	1.18017	0.590084	−	0.807342i	$-0.299095\pi$
$823$	33.8566	1.18017	0.590084	+	0.807342i	$0.299095\pi$
$824$	51.8648	1.80680
$825$	6.53934	0.227670
$826$	−8.71157	−0.303114
$827$	−30.7877	−1.07059	−0.535297	−	0.844664i	$-0.679800\pi$
$827$	−30.7877	−1.07059	−0.535297	+	0.844664i	$0.679800\pi$
$828$	0.612383	0.0212818
$829$	27.8437	0.967050	0.483525	−	0.875330i	$-0.339356\pi$
$829$	27.8437	0.967050	0.483525	+	0.875330i	$0.339356\pi$
$830$	−1.03861	−0.0360505
$831$	21.7630	0.754951
$832$	13.5046	0.468188
$833$	−0.996756	−0.0345356
$834$	−6.62398	−0.229370
$835$	−5.08266	−0.175893
$836$	0.660463	0.0228426
$837$	6.72273	0.232372
$838$	4.18939	0.144720
$839$	−46.0476	−1.58974	−0.794869	−	0.606781i	$-0.792461\pi$
$839$	−46.0476	−1.58974	−0.794869	+	0.606781i	$0.792461\pi$
$840$	0.909601	0.0313842
$841$	8.27688	0.285410
$842$	32.8139	1.13084
$843$	−7.71631	−0.265764
$844$	1.56549	0.0538864
$845$	−3.21689	−0.110664
$846$	6.35469	0.218479
$847$	9.20997	0.316458
$848$	−23.6201	−0.811119
$849$	1.94204	0.0666505
$850$	−7.14051	−0.244918
$851$	28.6179	0.981008
$852$	−0.957254	−0.0327950
$853$	7.42419	0.254200	0.127100	−	0.991890i	$-0.459433\pi$
$853$	7.42419	0.254200	0.127100	+	0.991890i	$0.459433\pi$
$854$	8.73681	0.298967
$855$	1.11632	0.0381772
$856$	−4.58900	−0.156849
$857$	26.1326	0.892674	0.446337	−	0.894865i	$-0.352728\pi$
$857$	26.1326	0.892674	0.446337	+	0.894865i	$0.352728\pi$
$858$	3.61647	0.123464
$859$	−40.9194	−1.39615	−0.698076	−	0.716024i	$-0.745960\pi$
$859$	−40.9194	−1.39615	−0.698076	+	0.716024i	$0.745960\pi$
$860$	0.202804	0.00691557
$861$	9.98044	0.340133
$862$	−50.2465	−1.71140
$863$	−23.8606	−0.812225	−0.406112	−	0.913823i	$-0.633116\pi$
$863$	−23.8606	−0.812225	−0.406112	+	0.913823i	$0.633116\pi$
$864$	−0.836665	−0.0284639
$865$	−1.71307	−0.0582462
$866$	−4.86527	−0.165329
$867$	16.0065	0.543608
$868$	0.996315	0.0338171
$869$	5.82867	0.197724
$870$	2.99900	0.101676
$871$	−24.7532	−0.838732
$872$	−33.3342	−1.12884
$873$	17.0870	0.578306
$874$	−20.1733	−0.682373
$875$	3.31371	0.112024
$876$	−0.626880	−0.0211803
$877$	22.1556	0.748142	0.374071	−	0.927400i	$-0.377962\pi$
$877$	22.1556	0.748142	0.374071	+	0.927400i	$0.377962\pi$
$878$	−27.3205	−0.922023
$879$	27.0159	0.911223
$880$	−1.91659	−0.0646082
$881$	−24.5833	−0.828233	−0.414116	−	0.910224i	$-0.635909\pi$
$881$	−24.5833	−0.828233	−0.414116	+	0.910224i	$0.635909\pi$
$882$	−1.46567	−0.0493518
$883$	24.4878	0.824081	0.412040	−	0.911166i	$-0.364816\pi$
$883$	24.4878	0.824081	0.412040	+	0.911166i	$0.364816\pi$
$884$	−0.272431	−0.00916284
$885$	1.99195	0.0669587
$886$	−26.7385	−0.898298
$887$	−40.3077	−1.35340	−0.676700	−	0.736259i	$-0.736591\pi$
$887$	−40.3077	−1.35340	−0.676700	+	0.736259i	$0.736591\pi$
$888$	−18.7973	−0.630797
$889$	17.5638	0.589072
$890$	5.59106	0.187413
$891$	1.33792	0.0448220
$892$	−1.38939	−0.0465204
$893$	−14.4419	−0.483280
$894$	−0.743732	−0.0248741
$895$	−2.15837	−0.0721464
$896$	12.4059	0.414451
$897$	−7.62060	−0.254444
$898$	13.6863	0.456718
$899$	−41.0455	−1.36894
$900$	−0.724359	−0.0241453
$901$	−5.50798	−0.183497
$902$	−19.5712	−0.651650
$903$	4.08326	0.135882
$904$	8.38010	0.278718
$905$	−5.92877	−0.197079
$906$	16.3910	0.544554
$907$	2.06861	0.0686870	0.0343435	−	0.999410i	$-0.489066\pi$
$907$	2.06861	0.0686870	0.0343435	+	0.999410i	$0.489066\pi$
$908$	2.58717	0.0858582
$909$	17.5981	0.583691
$910$	0.905886	0.0300298
$911$	−17.6189	−0.583742	−0.291871	−	0.956458i	$-0.594278\pi$
$911$	−17.6189	−0.583742	−0.291871	+	0.956458i	$0.594278\pi$
$912$	14.2379	0.471465
$913$	2.82894	0.0936243
$914$	−38.8739	−1.28583
$915$	−1.99772	−0.0660426
$916$	1.06380	0.0351491
$917$	3.22385	0.106461
$918$	−1.46092	−0.0482175
$919$	−33.9019	−1.11832	−0.559161	−	0.829059i	$-0.688877\pi$
$919$	−33.9019	−1.11832	−0.559161	+	0.829059i	$0.688877\pi$
$920$	3.75858	0.123917
$921$	13.0805	0.431016
$922$	−16.6354	−0.547858
$923$	11.9122	0.392096
$924$	0.198281	0.00652297
$925$	−33.8507	−1.11301
$926$	−57.9439	−1.90415
$927$	19.1092	0.627627
$928$	5.10824	0.167686
$929$	−33.0691	−1.08496	−0.542481	−	0.840068i	$-0.682515\pi$
$929$	−33.0691	−1.08496	−0.542481	+	0.840068i	$0.682515\pi$
$930$	−3.30220	−0.108283
$931$	3.33095	0.109167
$932$	3.09299	0.101314
$933$	0.285883	0.00935938
$934$	35.1372	1.14973
$935$	−0.446929	−0.0146162
$936$	5.00551	0.163610
$937$	15.8323	0.517217	0.258609	−	0.965982i	$-0.416736\pi$
$937$	15.8323	0.517217	0.258609	+	0.965982i	$0.416736\pi$
$938$	−19.6722	−0.642320
$939$	−31.0980	−1.01485
$940$	−0.215341	−0.00702366
$941$	56.7624	1.85040	0.925201	−	0.379477i	$-0.123896\pi$
$941$	56.7624	1.85040	0.925201	+	0.379477i	$0.123896\pi$
$942$	15.0929	0.491753
$943$	41.2404	1.34297
$944$	25.4061	0.826898
$945$	0.335135	0.0109019
$946$	−8.00709	−0.260333
$947$	12.7907	0.415643	0.207822	−	0.978167i	$-0.433363\pi$
$947$	12.7907	0.415643	0.207822	+	0.978167i	$0.433363\pi$
$948$	−0.645638	−0.0209694
$949$	7.80100	0.253231
$950$	23.8621	0.774188
$951$	7.37400	0.239118
$952$	2.70533	0.0876802
$953$	0.324016	0.0104959	0.00524795	−	0.999986i	$-0.498330\pi$
$953$	0.324016	0.0104959	0.00524795	+	0.999986i	$0.498330\pi$
$954$	−8.09917	−0.262220
$955$	−4.74737	−0.153621
$956$	−0.504060	−0.0163025
$957$	−8.16865	−0.264055
$958$	30.7116	0.992247
$959$	4.52794	0.146215
$960$	−2.45406	−0.0792044
$961$	14.1951	0.457908
$962$	−18.7206	−0.603575
$963$	−1.69078	−0.0544846
$964$	2.46895	0.0795197
$965$	3.47392	0.111829
$966$	−6.05634	−0.194859
$967$	0.899802	0.0289357	0.0144678	−	0.999895i	$-0.495395\pi$
$967$	0.899802	0.0289357	0.0144678	+	0.999895i	$0.495395\pi$
$968$	−24.9971	−0.803437
$969$	3.32014	0.106658
$970$	−8.39309	−0.269486
$971$	22.7211	0.729154	0.364577	−	0.931173i	$-0.381214\pi$
$971$	22.7211	0.729154	0.364577	+	0.931173i	$0.381214\pi$
$972$	−0.148201	−0.00475354
$973$	4.51941	0.144886
$974$	22.2230	0.712072
$975$	9.01405	0.288681
$976$	−25.4797	−0.815585
$977$	5.99893	0.191923	0.0959613	−	0.995385i	$-0.469407\pi$
$977$	5.99893	0.191923	0.0959613	+	0.995385i	$0.469407\pi$
$978$	−6.39896	−0.204616
$979$	−15.2289	−0.486717
$980$	0.0496673	0.00158656
$981$	−12.2817	−0.392124
$982$	−22.1262	−0.706077
$983$	5.21495	0.166331	0.0831656	−	0.996536i	$-0.473497\pi$
$983$	5.21495	0.166331	0.0831656	+	0.996536i	$0.473497\pi$
$984$	−27.0883	−0.863542
$985$	−4.99006	−0.158996
$986$	8.91962	0.284058
$987$	−4.33568	−0.138006
$988$	0.910406	0.0289639
$989$	16.8725	0.536514
$990$	−0.657185	−0.0208867
$991$	43.9638	1.39655	0.698277	−	0.715827i	$-0.253950\pi$
$991$	43.9638	1.39655	0.698277	+	0.715827i	$0.253950\pi$
$992$	−5.62468	−0.178584
$993$	−19.8111	−0.628687
$994$	9.46703	0.300276
$995$	2.73965	0.0868527
$996$	−0.313360	−0.00992920
$997$	34.4302	1.09041	0.545207	−	0.838301i	$-0.316451\pi$
$997$	34.4302	1.09041	0.545207	+	0.838301i	$0.316451\pi$
$998$	−9.71808	−0.307620
$999$	−6.92572	−0.219120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.14	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.14	✓	50	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)

\(f(q)\)	\(=\)	\(q-1.46567 q^{2} -1.00000 q^{3} +0.148201 q^{4} +0.335135 q^{5} +1.46567 q^{6} -1.00000 q^{7} +2.71413 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46567 q^{2} -1.00000 q^{3} +0.148201 q^{4} +0.335135 q^{5} +1.46567 q^{6} -1.00000 q^{7} +2.71413 q^{8} +1.00000 q^{9} -0.491199 q^{10} +1.33792 q^{11} -0.148201 q^{12} +1.84424 q^{13} +1.46567 q^{14} -0.335135 q^{15} -4.27444 q^{16} -0.996756 q^{17} -1.46567 q^{18} +3.33095 q^{19} +0.0496673 q^{20} +1.00000 q^{21} -1.96096 q^{22} +4.13212 q^{23} -2.71413 q^{24} -4.88768 q^{25} -2.70305 q^{26} -1.00000 q^{27} -0.148201 q^{28} +6.10548 q^{29} +0.491199 q^{30} -6.72273 q^{31} +0.836665 q^{32} -1.33792 q^{33} +1.46092 q^{34} -0.335135 q^{35} +0.148201 q^{36} +6.92572 q^{37} -4.88208 q^{38} -1.84424 q^{39} +0.909601 q^{40} +9.98044 q^{41} -1.46567 q^{42} +4.08326 q^{43} +0.198281 q^{44} +0.335135 q^{45} -6.05634 q^{46} -4.33568 q^{47} +4.27444 q^{48} +1.00000 q^{49} +7.16375 q^{50} +0.996756 q^{51} +0.273317 q^{52} +5.52590 q^{53} +1.46567 q^{54} +0.448384 q^{55} -2.71413 q^{56} -3.33095 q^{57} -8.94864 q^{58} -5.94373 q^{59} -0.0496673 q^{60} +5.96095 q^{61} +9.85334 q^{62} -1.00000 q^{63} +7.32260 q^{64} +0.618068 q^{65} +1.96096 q^{66} -13.4219 q^{67} -0.147720 q^{68} -4.13212 q^{69} +0.491199 q^{70} +6.45917 q^{71} +2.71413 q^{72} +4.22994 q^{73} -10.1508 q^{74} +4.88768 q^{75} +0.493649 q^{76} -1.33792 q^{77} +2.70305 q^{78} +4.35651 q^{79} -1.43251 q^{80} +1.00000 q^{81} -14.6281 q^{82} +2.11443 q^{83} +0.148201 q^{84} -0.334048 q^{85} -5.98473 q^{86} -6.10548 q^{87} +3.63130 q^{88} -11.3825 q^{89} -0.491199 q^{90} -1.84424 q^{91} +0.612383 q^{92} +6.72273 q^{93} +6.35469 q^{94} +1.11632 q^{95} -0.836665 q^{96} +17.0870 q^{97} -1.46567 q^{98} +1.33792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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