LMFDB - Embedded newform 8043.2.a.s.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.63224 q^{2} -1.00000 q^{3} +4.92870 q^{4} +3.86633 q^{5} +2.63224 q^{6} -1.00000 q^{7} -7.70903 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63224 q^{2} -1.00000 q^{3} +4.92870 q^{4} +3.86633 q^{5} +2.63224 q^{6} -1.00000 q^{7} -7.70903 q^{8} +1.00000 q^{9} -10.1771 q^{10} -3.94955 q^{11} -4.92870 q^{12} +0.666715 q^{13} +2.63224 q^{14} -3.86633 q^{15} +10.4346 q^{16} -4.28337 q^{17} -2.63224 q^{18} +0.176483 q^{19} +19.0560 q^{20} +1.00000 q^{21} +10.3962 q^{22} -5.36716 q^{23} +7.70903 q^{24} +9.94849 q^{25} -1.75495 q^{26} -1.00000 q^{27} -4.92870 q^{28} -2.72687 q^{29} +10.1771 q^{30} -7.79297 q^{31} -12.0484 q^{32} +3.94955 q^{33} +11.2749 q^{34} -3.86633 q^{35} +4.92870 q^{36} +9.69422 q^{37} -0.464545 q^{38} -0.666715 q^{39} -29.8056 q^{40} +6.28096 q^{41} -2.63224 q^{42} +3.37422 q^{43} -19.4661 q^{44} +3.86633 q^{45} +14.1277 q^{46} +13.0088 q^{47} -10.4346 q^{48} +1.00000 q^{49} -26.1868 q^{50} +4.28337 q^{51} +3.28603 q^{52} -5.03862 q^{53} +2.63224 q^{54} -15.2703 q^{55} +7.70903 q^{56} -0.176483 q^{57} +7.17778 q^{58} -4.21767 q^{59} -19.0560 q^{60} -6.76710 q^{61} +20.5130 q^{62} -1.00000 q^{63} +10.8451 q^{64} +2.57774 q^{65} -10.3962 q^{66} -11.2998 q^{67} -21.1114 q^{68} +5.36716 q^{69} +10.1771 q^{70} -3.54238 q^{71} -7.70903 q^{72} +1.67029 q^{73} -25.5175 q^{74} -9.94849 q^{75} +0.869830 q^{76} +3.94955 q^{77} +1.75495 q^{78} -5.00173 q^{79} +40.3438 q^{80} +1.00000 q^{81} -16.5330 q^{82} -2.95616 q^{83} +4.92870 q^{84} -16.5609 q^{85} -8.88177 q^{86} +2.72687 q^{87} +30.4472 q^{88} +4.67991 q^{89} -10.1771 q^{90} -0.666715 q^{91} -26.4531 q^{92} +7.79297 q^{93} -34.2423 q^{94} +0.682340 q^{95} +12.0484 q^{96} +10.6954 q^{97} -2.63224 q^{98} -3.94955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63224	−1.86128	−0.930638	−	0.365941i	$-0.880747\pi$
$2$	−2.63224	−1.86128	−0.930638	+	0.365941i	$0.880747\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.92870	2.46435
$5$	3.86633	1.72907	0.864537	−	0.502569i	$-0.167612\pi$
$5$	3.86633	1.72907	0.864537	+	0.502569i	$0.167612\pi$
$6$	2.63224	1.07461
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.70903	−2.72555
$9$	1.00000	0.333333
$10$	−10.1771	−3.21828
$11$	−3.94955	−1.19083	−0.595417	−	0.803417i	$-0.703013\pi$
$11$	−3.94955	−1.19083	−0.595417	+	0.803417i	$0.703013\pi$
$12$	−4.92870	−1.42279
$13$	0.666715	0.184913	0.0924567	−	0.995717i	$-0.470528\pi$
$13$	0.666715	0.184913	0.0924567	+	0.995717i	$0.470528\pi$
$14$	2.63224	0.703496
$15$	−3.86633	−0.998282
$16$	10.4346	2.60866
$17$	−4.28337	−1.03887	−0.519435	−	0.854510i	$-0.673857\pi$
$17$	−4.28337	−1.03887	−0.519435	+	0.854510i	$0.673857\pi$
$18$	−2.63224	−0.620425
$19$	0.176483	0.0404879	0.0202440	−	0.999795i	$-0.493556\pi$
$19$	0.176483	0.0404879	0.0202440	+	0.999795i	$0.493556\pi$
$20$	19.0560	4.26104
$21$	1.00000	0.218218
$22$	10.3962	2.21647
$23$	−5.36716	−1.11913	−0.559566	−	0.828786i	$-0.689032\pi$
$23$	−5.36716	−1.11913	−0.559566	+	0.828786i	$0.689032\pi$
$24$	7.70903	1.57360
$25$	9.94849	1.98970
$26$	−1.75495	−0.344175
$27$	−1.00000	−0.192450
$28$	−4.92870	−0.931436
$29$	−2.72687	−0.506367	−0.253184	−	0.967418i	$-0.581478\pi$
$29$	−2.72687	−0.506367	−0.253184	+	0.967418i	$0.581478\pi$
$30$	10.1771	1.85808
$31$	−7.79297	−1.39966	−0.699830	−	0.714310i	$-0.746741\pi$
$31$	−7.79297	−1.39966	−0.699830	+	0.714310i	$0.746741\pi$
$32$	−12.0484	−2.12988
$33$	3.94955	0.687528
$34$	11.2749	1.93362
$35$	−3.86633	−0.653529
$36$	4.92870	0.821449
$37$	9.69422	1.59372	0.796860	−	0.604164i	$-0.206493\pi$
$37$	9.69422	1.59372	0.796860	+	0.604164i	$0.206493\pi$
$38$	−0.464545	−0.0753592
$39$	−0.666715	−0.106760
$40$	−29.8056	−4.71269
$41$	6.28096	0.980920	0.490460	−	0.871464i	$-0.336829\pi$
$41$	6.28096	0.980920	0.490460	+	0.871464i	$0.336829\pi$
$42$	−2.63224	−0.406164
$43$	3.37422	0.514564	0.257282	−	0.966336i	$-0.417173\pi$
$43$	3.37422	0.514564	0.257282	+	0.966336i	$0.417173\pi$
$44$	−19.4661	−2.93463
$45$	3.86633	0.576358
$46$	14.1277	2.08301
$47$	13.0088	1.89753	0.948764	−	0.315985i	$-0.102335\pi$
$47$	13.0088	1.89753	0.948764	+	0.315985i	$0.102335\pi$
$48$	−10.4346	−1.50611
$49$	1.00000	0.142857
$50$	−26.1868	−3.70338
$51$	4.28337	0.599791
$52$	3.28603	0.455691
$53$	−5.03862	−0.692107	−0.346054	−	0.938215i	$-0.612479\pi$
$53$	−5.03862	−0.692107	−0.346054	+	0.938215i	$0.612479\pi$
$54$	2.63224	0.358203
$55$	−15.2703	−2.05904
$56$	7.70903	1.03016
$57$	−0.176483	−0.0233757
$58$	7.17778	0.942489
$59$	−4.21767	−0.549094	−0.274547	−	0.961574i	$-0.588528\pi$
$59$	−4.21767	−0.549094	−0.274547	+	0.961574i	$0.588528\pi$
$60$	−19.0560	−2.46011
$61$	−6.76710	−0.866438	−0.433219	−	0.901289i	$-0.642622\pi$
$61$	−6.76710	−0.866438	−0.433219	+	0.901289i	$0.642622\pi$
$62$	20.5130	2.60515
$63$	−1.00000	−0.125988
$64$	10.8451	1.35564
$65$	2.57774	0.319729
$66$	−10.3962	−1.27968
$67$	−11.2998	−1.38049	−0.690244	−	0.723577i	$-0.742497\pi$
$67$	−11.2998	−1.38049	−0.690244	+	0.723577i	$0.742497\pi$
$68$	−21.1114	−2.56013
$69$	5.36716	0.646131
$70$	10.1771	1.21640
$71$	−3.54238	−0.420403	−0.210202	−	0.977658i	$-0.567412\pi$
$71$	−3.54238	−0.420403	−0.210202	+	0.977658i	$0.567412\pi$
$72$	−7.70903	−0.908518
$73$	1.67029	0.195493	0.0977466	−	0.995211i	$-0.468837\pi$
$73$	1.67029	0.195493	0.0977466	+	0.995211i	$0.468837\pi$
$74$	−25.5175	−2.96635
$75$	−9.94849	−1.14875
$76$	0.869830	0.0997763
$77$	3.94955	0.450093
$78$	1.75495	0.198709
$79$	−5.00173	−0.562739	−0.281369	−	0.959600i	$-0.590789\pi$
$79$	−5.00173	−0.562739	−0.281369	+	0.959600i	$0.590789\pi$
$80$	40.3438	4.51057
$81$	1.00000	0.111111
$82$	−16.5330	−1.82576
$83$	−2.95616	−0.324480	−0.162240	−	0.986751i	$-0.551872\pi$
$83$	−2.95616	−0.324480	−0.162240	+	0.986751i	$0.551872\pi$
$84$	4.92870	0.537765
$85$	−16.5609	−1.79628
$86$	−8.88177	−0.957746
$87$	2.72687	0.292351
$88$	30.4472	3.24568
$89$	4.67991	0.496070	0.248035	−	0.968751i	$-0.420215\pi$
$89$	4.67991	0.496070	0.248035	+	0.968751i	$0.420215\pi$
$90$	−10.1771	−1.07276
$91$	−0.666715	−0.0698907
$92$	−26.4531	−2.75793
$93$	7.79297	0.808094
$94$	−34.2423	−3.53182
$95$	0.682340	0.0700066
$96$	12.0484	1.22969
$97$	10.6954	1.08595	0.542976	−	0.839748i	$-0.317297\pi$
$97$	10.6954	1.08595	0.542976	+	0.839748i	$0.317297\pi$
$98$	−2.63224	−0.265897
$99$	−3.94955	−0.396945
$100$	49.0331	4.90331
$101$	−16.9439	−1.68598	−0.842989	−	0.537930i	$-0.819206\pi$
$101$	−16.9439	−1.68598	−0.842989	+	0.537930i	$0.819206\pi$
$102$	−11.2749	−1.11638
$103$	3.87998	0.382306	0.191153	−	0.981560i	$-0.438777\pi$
$103$	3.87998	0.382306	0.191153	+	0.981560i	$0.438777\pi$
$104$	−5.13973	−0.503992
$105$	3.86633	0.377315
$106$	13.2629	1.28820
$107$	−0.943279	−0.0911902	−0.0455951	−	0.998960i	$-0.514518\pi$
$107$	−0.943279	−0.0911902	−0.0455951	+	0.998960i	$0.514518\pi$
$108$	−4.92870	−0.474264
$109$	6.46672	0.619399	0.309700	−	0.950834i	$-0.399772\pi$
$109$	6.46672	0.619399	0.309700	+	0.950834i	$0.399772\pi$
$110$	40.1950	3.83244
$111$	−9.69422	−0.920135
$112$	−10.4346	−0.985981
$113$	16.1795	1.52204	0.761020	−	0.648728i	$-0.224699\pi$
$113$	16.1795	1.52204	0.761020	+	0.648728i	$0.224699\pi$
$114$	0.464545	0.0435087
$115$	−20.7512	−1.93506
$116$	−13.4399	−1.24787
$117$	0.666715	0.0616378
$118$	11.1019	1.02202
$119$	4.28337	0.392656
$120$	29.8056	2.72087
$121$	4.59894	0.418086
$122$	17.8126	1.61268
$123$	−6.28096	−0.566335
$124$	−38.4092	−3.44925
$125$	19.1325	1.71126
$126$	2.63224	0.234499
$127$	14.6315	1.29833	0.649166	−	0.760647i	$-0.275118\pi$
$127$	14.6315	1.29833	0.649166	+	0.760647i	$0.275118\pi$
$128$	−4.45008	−0.393336
$129$	−3.37422	−0.297084
$130$	−6.78523	−0.595104
$131$	−14.1269	−1.23427	−0.617135	−	0.786858i	$-0.711707\pi$
$131$	−14.1269	−1.23427	−0.617135	+	0.786858i	$0.711707\pi$
$132$	19.4661	1.69431
$133$	−0.176483	−0.0153030
$134$	29.7438	2.56947
$135$	−3.86633	−0.332761
$136$	33.0206	2.83149
$137$	−8.36703	−0.714844	−0.357422	−	0.933943i	$-0.616344\pi$
$137$	−8.36703	−0.714844	−0.357422	+	0.933943i	$0.616344\pi$
$138$	−14.1277	−1.20263
$139$	19.6508	1.66676	0.833380	−	0.552700i	$-0.186403\pi$
$139$	19.6508	1.66676	0.833380	+	0.552700i	$0.186403\pi$
$140$	−19.0560	−1.61052
$141$	−13.0088	−1.09554
$142$	9.32440	0.782486
$143$	−2.63322	−0.220201
$144$	10.4346	0.869554
$145$	−10.5430	−0.875547
$146$	−4.39662	−0.363867
$147$	−1.00000	−0.0824786
$148$	47.7799	3.92748
$149$	17.7764	1.45630	0.728149	−	0.685419i	$-0.240381\pi$
$149$	17.7764	1.45630	0.728149	+	0.685419i	$0.240381\pi$
$150$	26.1868	2.13815
$151$	−16.9037	−1.37560	−0.687800	−	0.725900i	$-0.741423\pi$
$151$	−16.9037	−1.37560	−0.687800	+	0.725900i	$0.741423\pi$
$152$	−1.36051	−0.110352
$153$	−4.28337	−0.346290
$154$	−10.3962	−0.837747
$155$	−30.1302	−2.42012
$156$	−3.28603	−0.263093
$157$	22.6283	1.80594	0.902968	−	0.429708i	$-0.141384\pi$
$157$	22.6283	1.80594	0.902968	+	0.429708i	$0.141384\pi$
$158$	13.1658	1.04741
$159$	5.03862	0.399588
$160$	−46.5832	−3.68273
$161$	5.36716	0.422992
$162$	−2.63224	−0.206808
$163$	8.38183	0.656516	0.328258	−	0.944588i	$-0.393538\pi$
$163$	8.38183	0.656516	0.328258	+	0.944588i	$0.393538\pi$
$164$	30.9569	2.41733
$165$	15.2703	1.18879
$166$	7.78131	0.603947
$167$	4.36978	0.338144	0.169072	−	0.985604i	$-0.445923\pi$
$167$	4.36978	0.338144	0.169072	+	0.985604i	$0.445923\pi$
$168$	−7.70903	−0.594765
$169$	−12.5555	−0.965807
$170$	43.5923	3.34338
$171$	0.176483	0.0134960
$172$	16.6305	1.26807
$173$	−23.2721	−1.76934	−0.884671	−	0.466215i	$-0.845617\pi$
$173$	−23.2721	−1.76934	−0.884671	+	0.466215i	$0.845617\pi$
$174$	−7.17778	−0.544146
$175$	−9.94849	−0.752035
$176$	−41.2122	−3.10648
$177$	4.21767	0.317020
$178$	−12.3187	−0.923323
$179$	12.5286	0.936429	0.468215	−	0.883615i	$-0.344897\pi$
$179$	12.5286	0.936429	0.468215	+	0.883615i	$0.344897\pi$
$180$	19.0560	1.42035
$181$	17.5228	1.30246	0.651228	−	0.758882i	$-0.274254\pi$
$181$	17.5228	1.30246	0.651228	+	0.758882i	$0.274254\pi$
$182$	1.75495	0.130086
$183$	6.76710	0.500238
$184$	41.3756	3.05025
$185$	37.4810	2.75566
$186$	−20.5130	−1.50409
$187$	16.9174	1.23712
$188$	64.1164	4.67617
$189$	1.00000	0.0727393
$190$	−1.79608	−0.130302
$191$	−6.05464	−0.438098	−0.219049	−	0.975714i	$-0.570296\pi$
$191$	−6.05464	−0.438098	−0.219049	+	0.975714i	$0.570296\pi$
$192$	−10.8451	−0.782679
$193$	2.29469	0.165175	0.0825876	−	0.996584i	$-0.473682\pi$
$193$	2.29469	0.165175	0.0825876	+	0.996584i	$0.473682\pi$
$194$	−28.1528	−2.02126
$195$	−2.57774	−0.184596
$196$	4.92870	0.352050
$197$	8.17623	0.582532	0.291266	−	0.956642i	$-0.405923\pi$
$197$	8.17623	0.582532	0.291266	+	0.956642i	$0.405923\pi$
$198$	10.3962	0.738824
$199$	7.67703	0.544210	0.272105	−	0.962268i	$-0.412280\pi$
$199$	7.67703	0.544210	0.272105	+	0.962268i	$0.412280\pi$
$200$	−76.6932	−5.42303
$201$	11.2998	0.797025
$202$	44.6004	3.13807
$203$	2.72687	0.191389
$204$	21.1114	1.47809
$205$	24.2842	1.69608
$206$	−10.2130	−0.711576
$207$	−5.36716	−0.373044
$208$	6.95693	0.482376
$209$	−0.697028	−0.0482144
$210$	−10.1771	−0.702287
$211$	26.3071	1.81106	0.905528	−	0.424287i	$-0.139475\pi$
$211$	26.3071	1.81106	0.905528	+	0.424287i	$0.139475\pi$
$212$	−24.8338	−1.70559
$213$	3.54238	0.242720
$214$	2.48294	0.169730
$215$	13.0459	0.889720
$216$	7.70903	0.524533
$217$	7.79297	0.529022
$218$	−17.0220	−1.15287
$219$	−1.67029	−0.112868
$220$	−75.2624	−5.07419
$221$	−2.85578	−0.192101
$222$	25.5175	1.71262
$223$	5.55368	0.371902	0.185951	−	0.982559i	$-0.440463\pi$
$223$	5.55368	0.371902	0.185951	+	0.982559i	$0.440463\pi$
$224$	12.0484	0.805020
$225$	9.94849	0.663233
$226$	−42.5884	−2.83294
$227$	11.8103	0.783879	0.391940	−	0.919991i	$-0.371804\pi$
$227$	11.8103	0.783879	0.391940	+	0.919991i	$0.371804\pi$
$228$	−0.869830	−0.0576059
$229$	10.8487	0.716900	0.358450	−	0.933549i	$-0.383305\pi$
$229$	10.8487	0.716900	0.358450	+	0.933549i	$0.383305\pi$
$230$	54.6222	3.60168
$231$	−3.94955	−0.259861
$232$	21.0215	1.38013
$233$	23.5182	1.54073	0.770364	−	0.637605i	$-0.220075\pi$
$233$	23.5182	1.54073	0.770364	+	0.637605i	$0.220075\pi$
$234$	−1.75495	−0.114725
$235$	50.2963	3.28097
$236$	−20.7876	−1.35316
$237$	5.00173	0.324897
$238$	−11.2749	−0.730840
$239$	−26.3356	−1.70351	−0.851755	−	0.523941i	$-0.824461\pi$
$239$	−26.3356	−1.70351	−0.851755	+	0.523941i	$0.824461\pi$
$240$	−40.3438	−2.60418
$241$	−8.03504	−0.517582	−0.258791	−	0.965933i	$-0.583324\pi$
$241$	−8.03504	−0.517582	−0.258791	+	0.965933i	$0.583324\pi$
$242$	−12.1055	−0.778173
$243$	−1.00000	−0.0641500
$244$	−33.3529	−2.13520
$245$	3.86633	0.247011
$246$	16.5330	1.05411
$247$	0.117664	0.00748676
$248$	60.0763	3.81485
$249$	2.95616	0.187339
$250$	−50.3613	−3.18513
$251$	20.9598	1.32297	0.661486	−	0.749957i	$-0.269926\pi$
$251$	20.9598	1.32297	0.661486	+	0.749957i	$0.269926\pi$
$252$	−4.92870	−0.310479
$253$	21.1979	1.33270
$254$	−38.5135	−2.41655
$255$	16.5609	1.03708
$256$	−9.97654	−0.623534
$257$	−0.394153	−0.0245866	−0.0122933	−	0.999924i	$-0.503913\pi$
$257$	−0.394153	−0.0245866	−0.0122933	+	0.999924i	$0.503913\pi$
$258$	8.88177	0.552955
$259$	−9.69422	−0.602370
$260$	12.7049	0.787923
$261$	−2.72687	−0.168789
$262$	37.1853	2.29732
$263$	10.9986	0.678206	0.339103	−	0.940749i	$-0.389877\pi$
$263$	10.9986	0.678206	0.339103	+	0.940749i	$0.389877\pi$
$264$	−30.4472	−1.87390
$265$	−19.4809	−1.19671
$266$	0.464545	0.0284831
$267$	−4.67991	−0.286406
$268$	−55.6932	−3.40200
$269$	8.27868	0.504760	0.252380	−	0.967628i	$-0.418787\pi$
$269$	8.27868	0.504760	0.252380	+	0.967628i	$0.418787\pi$
$270$	10.1771	0.619359
$271$	−4.70752	−0.285961	−0.142981	−	0.989725i	$-0.545669\pi$
$271$	−4.70752	−0.285961	−0.142981	+	0.989725i	$0.545669\pi$
$272$	−44.6954	−2.71006
$273$	0.666715	0.0403514
$274$	22.0240	1.33052
$275$	−39.2921	−2.36940
$276$	26.4531	1.59229
$277$	27.9629	1.68013	0.840064	−	0.542487i	$-0.182517\pi$
$277$	27.9629	1.68013	0.840064	+	0.542487i	$0.182517\pi$
$278$	−51.7257	−3.10230
$279$	−7.79297	−0.466553
$280$	29.8056	1.78123
$281$	−25.2794	−1.50804	−0.754022	−	0.656849i	$-0.771889\pi$
$281$	−25.2794	−1.50804	−0.754022	+	0.656849i	$0.771889\pi$
$282$	34.2423	2.03910
$283$	−18.2811	−1.08670	−0.543351	−	0.839506i	$-0.682845\pi$
$283$	−18.2811	−1.08670	−0.543351	+	0.839506i	$0.682845\pi$
$284$	−17.4593	−1.03602
$285$	−0.682340	−0.0404184
$286$	6.93128	0.409855
$287$	−6.28096	−0.370753
$288$	−12.0484	−0.709961
$289$	1.34724	0.0792492
$290$	27.7517	1.62963
$291$	−10.6954	−0.626975
$292$	8.23237	0.481763
$293$	−28.4042	−1.65939	−0.829696	−	0.558215i	$-0.811486\pi$
$293$	−28.4042	−1.65939	−0.829696	+	0.558215i	$0.811486\pi$
$294$	2.63224	0.153515
$295$	−16.3069	−0.949425
$296$	−74.7331	−4.34377
$297$	3.94955	0.229176
$298$	−46.7917	−2.71057
$299$	−3.57837	−0.206942
$300$	−49.0331	−2.83093
$301$	−3.37422	−0.194487
$302$	44.4945	2.56037
$303$	16.9439	0.973400
$304$	1.84154	0.105619
$305$	−26.1638	−1.49814
$306$	11.2749	0.644541
$307$	28.0680	1.60192	0.800962	−	0.598715i	$-0.204322\pi$
$307$	28.0680	1.60192	0.800962	+	0.598715i	$0.204322\pi$
$308$	19.4661	1.10919
$309$	−3.87998	−0.220724
$310$	79.3099	4.50450
$311$	−19.3118	−1.09507	−0.547537	−	0.836782i	$-0.684434\pi$
$311$	−19.3118	−1.09507	−0.547537	+	0.836782i	$0.684434\pi$
$312$	5.13973	0.290980
$313$	−22.7937	−1.28838	−0.644188	−	0.764867i	$-0.722805\pi$
$313$	−22.7937	−1.28838	−0.644188	+	0.764867i	$0.722805\pi$
$314$	−59.5632	−3.36134
$315$	−3.86633	−0.217843
$316$	−24.6520	−1.38678
$317$	3.41287	0.191686	0.0958429	−	0.995396i	$-0.469445\pi$
$317$	3.41287	0.191686	0.0958429	+	0.995396i	$0.469445\pi$
$318$	−13.2629	−0.743744
$319$	10.7699	0.602999
$320$	41.9308	2.34400
$321$	0.943279	0.0526487
$322$	−14.1277	−0.787304
$323$	−0.755941	−0.0420617
$324$	4.92870	0.273816
$325$	6.63280	0.367922
$326$	−22.0630	−1.22196
$327$	−6.46672	−0.357610
$328$	−48.4201	−2.67355
$329$	−13.0088	−0.717198
$330$	−40.1950	−2.21266
$331$	15.7570	0.866084	0.433042	−	0.901374i	$-0.357440\pi$
$331$	15.7570	0.866084	0.433042	+	0.901374i	$0.357440\pi$
$332$	−14.5700	−0.799632
$333$	9.69422	0.531240
$334$	−11.5023	−0.629379
$335$	−43.6887	−2.38697
$336$	10.4346	0.569257
$337$	−14.9115	−0.812282	−0.406141	−	0.913810i	$-0.633126\pi$
$337$	−14.9115	−0.812282	−0.406141	+	0.913810i	$0.633126\pi$
$338$	33.0491	1.79763
$339$	−16.1795	−0.878751
$340$	−81.6236	−4.42666
$341$	30.7787	1.66676
$342$	−0.464545	−0.0251197
$343$	−1.00000	−0.0539949
$344$	−26.0120	−1.40247
$345$	20.7512	1.11721
$346$	61.2577	3.29323
$347$	−1.76998	−0.0950177	−0.0475088	−	0.998871i	$-0.515128\pi$
$347$	−1.76998	−0.0950177	−0.0475088	+	0.998871i	$0.515128\pi$
$348$	13.4399	0.720455
$349$	6.92509	0.370691	0.185346	−	0.982673i	$-0.440660\pi$
$349$	6.92509	0.370691	0.185346	+	0.982673i	$0.440660\pi$
$350$	26.1868	1.39974
$351$	−0.666715	−0.0355866
$352$	47.5859	2.53634
$353$	2.25271	0.119900	0.0599498	−	0.998201i	$-0.480906\pi$
$353$	2.25271	0.119900	0.0599498	+	0.998201i	$0.480906\pi$
$354$	−11.1019	−0.590061
$355$	−13.6960	−0.726908
$356$	23.0659	1.22249
$357$	−4.28337	−0.226700
$358$	−32.9782	−1.74295
$359$	4.90316	0.258779	0.129389	−	0.991594i	$-0.458698\pi$
$359$	4.90316	0.258779	0.129389	+	0.991594i	$0.458698\pi$
$360$	−29.8056	−1.57090
$361$	−18.9689	−0.998361
$362$	−46.1241	−2.42423
$363$	−4.59894	−0.241382
$364$	−3.28603	−0.172235
$365$	6.45790	0.338022
$366$	−17.8126	−0.931081
$367$	26.5141	1.38403	0.692013	−	0.721885i	$-0.256724\pi$
$367$	26.5141	1.38403	0.692013	+	0.721885i	$0.256724\pi$
$368$	−56.0045	−2.91943
$369$	6.28096	0.326973
$370$	−98.6591	−5.12904
$371$	5.03862	0.261592
$372$	38.4092	1.99142
$373$	1.63684	0.0847525	0.0423762	−	0.999102i	$-0.486507\pi$
$373$	1.63684	0.0847525	0.0423762	+	0.999102i	$0.486507\pi$
$374$	−44.5306	−2.30262
$375$	−19.1325	−0.987997
$376$	−100.285	−5.17182
$377$	−1.81805	−0.0936341
$378$	−2.63224	−0.135388
$379$	−11.5065	−0.591050	−0.295525	−	0.955335i	$-0.595495\pi$
$379$	−11.5065	−0.591050	−0.295525	+	0.955335i	$0.595495\pi$
$380$	3.36305	0.172521
$381$	−14.6315	−0.749593
$382$	15.9373	0.815422
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	4.45008	0.227092
$385$	15.2703	0.778244
$386$	−6.04017	−0.307437
$387$	3.37422	0.171521
$388$	52.7143	2.67616
$389$	−1.38743	−0.0703455	−0.0351727	−	0.999381i	$-0.511198\pi$
$389$	−1.38743	−0.0703455	−0.0351727	+	0.999381i	$0.511198\pi$
$390$	6.78523	0.343583
$391$	22.9895	1.16263
$392$	−7.70903	−0.389365
$393$	14.1269	0.712606
$394$	−21.5218	−1.08425
$395$	−19.3383	−0.973017
$396$	−19.4661	−0.978210
$397$	14.3893	0.722180	0.361090	−	0.932531i	$-0.382405\pi$
$397$	14.3893	0.722180	0.361090	+	0.932531i	$0.382405\pi$
$398$	−20.2078	−1.01292
$399$	0.176483	0.00883519
$400$	103.809	5.19045
$401$	27.9566	1.39609	0.698044	−	0.716055i	$-0.254054\pi$
$401$	27.9566	1.39609	0.698044	+	0.716055i	$0.254054\pi$
$402$	−29.7438	−1.48348
$403$	−5.19569	−0.258816
$404$	−83.5112	−4.15484
$405$	3.86633	0.192119
$406$	−7.17778	−0.356227
$407$	−38.2878	−1.89786
$408$	−33.0206	−1.63476
$409$	5.04556	0.249487	0.124744	−	0.992189i	$-0.460189\pi$
$409$	5.04556	0.249487	0.124744	+	0.992189i	$0.460189\pi$
$410$	−63.9220	−3.15688
$411$	8.36703	0.412715
$412$	19.1232	0.942134
$413$	4.21767	0.207538
$414$	14.1277	0.694337
$415$	−11.4295	−0.561050
$416$	−8.03287	−0.393844
$417$	−19.6508	−0.962304
$418$	1.83474	0.0897403
$419$	−27.8679	−1.36144	−0.680719	−	0.732544i	$-0.738333\pi$
$419$	−27.8679	−1.36144	−0.680719	+	0.732544i	$0.738333\pi$
$420$	19.0560	0.929835
$421$	12.6543	0.616732	0.308366	−	0.951268i	$-0.400218\pi$
$421$	12.6543	0.616732	0.308366	+	0.951268i	$0.400218\pi$
$422$	−69.2466	−3.37087
$423$	13.0088	0.632509
$424$	38.8429	1.88638
$425$	−42.6130	−2.06704
$426$	−9.32440	−0.451769
$427$	6.76710	0.327483
$428$	−4.64914	−0.224724
$429$	2.63322	0.127133
$430$	−34.3398	−1.65601
$431$	32.0464	1.54362	0.771811	−	0.635853i	$-0.219351\pi$
$431$	32.0464	1.54362	0.771811	+	0.635853i	$0.219351\pi$
$432$	−10.4346	−0.502037
$433$	34.9609	1.68011	0.840056	−	0.542500i	$-0.182522\pi$
$433$	34.9609	1.68011	0.840056	+	0.542500i	$0.182522\pi$
$434$	−20.5130	−0.984655
$435$	10.5430	0.505497
$436$	31.8725	1.52641
$437$	−0.947212	−0.0453113
$438$	4.39662	0.210079
$439$	6.88854	0.328772	0.164386	−	0.986396i	$-0.447436\pi$
$439$	6.88854	0.328772	0.164386	+	0.986396i	$0.447436\pi$
$440$	117.719	5.61203
$441$	1.00000	0.0476190
$442$	7.51711	0.357553
$443$	−30.9414	−1.47007	−0.735035	−	0.678029i	$-0.762834\pi$
$443$	−30.9414	−1.47007	−0.735035	+	0.678029i	$0.762834\pi$
$444$	−47.7799	−2.26753
$445$	18.0941	0.857742
$446$	−14.6186	−0.692211
$447$	−17.7764	−0.840794
$448$	−10.8451	−0.512384
$449$	20.2572	0.955995	0.477997	−	0.878361i	$-0.341363\pi$
$449$	20.2572	0.955995	0.477997	+	0.878361i	$0.341363\pi$
$450$	−26.1868	−1.23446
$451$	−24.8069	−1.16811
$452$	79.7439	3.75084
$453$	16.9037	0.794203
$454$	−31.0876	−1.45902
$455$	−2.57774	−0.120846
$456$	1.36051	0.0637118
$457$	17.8905	0.836880	0.418440	−	0.908244i	$-0.362577\pi$
$457$	17.8905	0.836880	0.418440	+	0.908244i	$0.362577\pi$
$458$	−28.5563	−1.33435
$459$	4.28337	0.199930
$460$	−102.276	−4.76866
$461$	11.9886	0.558364	0.279182	−	0.960238i	$-0.409937\pi$
$461$	11.9886	0.558364	0.279182	+	0.960238i	$0.409937\pi$
$462$	10.3962	0.483674
$463$	21.1581	0.983299	0.491649	−	0.870793i	$-0.336394\pi$
$463$	21.1581	0.983299	0.491649	+	0.870793i	$0.336394\pi$
$464$	−28.4539	−1.32094
$465$	30.1302	1.39725
$466$	−61.9055	−2.86772
$467$	29.7910	1.37856	0.689281	−	0.724494i	$-0.257926\pi$
$467$	29.7910	1.37856	0.689281	+	0.724494i	$0.257926\pi$
$468$	3.28603	0.151897
$469$	11.2998	0.521775
$470$	−132.392	−6.10678
$471$	−22.6283	−1.04266
$472$	32.5142	1.49659
$473$	−13.3267	−0.612761
$474$	−13.1658	−0.604723
$475$	1.75574	0.0805588
$476$	21.1114	0.967640
$477$	−5.03862	−0.230702
$478$	69.3217	3.17070
$479$	20.4078	0.932455	0.466228	−	0.884665i	$-0.345613\pi$
$479$	20.4078	0.932455	0.466228	+	0.884665i	$0.345613\pi$
$480$	46.5832	2.12622
$481$	6.46328	0.294700
$482$	21.1502	0.963363
$483$	−5.36716	−0.244214
$484$	22.6668	1.03031
$485$	41.3519	1.87769
$486$	2.63224	0.119401
$487$	3.69399	0.167391	0.0836954	−	0.996491i	$-0.473328\pi$
$487$	3.69399	0.167391	0.0836954	+	0.996491i	$0.473328\pi$
$488$	52.1678	2.36152
$489$	−8.38183	−0.379040
$490$	−10.1771	−0.459755
$491$	−14.7016	−0.663472	−0.331736	−	0.943372i	$-0.607634\pi$
$491$	−14.7016	−0.663472	−0.331736	+	0.943372i	$0.607634\pi$
$492$	−30.9569	−1.39565
$493$	11.6802	0.526049
$494$	−0.309719	−0.0139349
$495$	−15.2703	−0.686347
$496$	−81.3169	−3.65124
$497$	3.54238	0.158897
$498$	−7.78131	−0.348689
$499$	22.7557	1.01869	0.509343	−	0.860564i	$-0.329889\pi$
$499$	22.7557	1.01869	0.509343	+	0.860564i	$0.329889\pi$
$500$	94.2982	4.21714
$501$	−4.36978	−0.195227
$502$	−55.1713	−2.46242
$503$	−40.9223	−1.82463	−0.912317	−	0.409484i	$-0.865709\pi$
$503$	−40.9223	−1.82463	−0.912317	+	0.409484i	$0.865709\pi$
$504$	7.70903	0.343388
$505$	−65.5106	−2.91518
$506$	−55.7979	−2.48052
$507$	12.5555	0.557609
$508$	72.1140	3.19954
$509$	20.4399	0.905984	0.452992	−	0.891515i	$-0.350357\pi$
$509$	20.4399	0.905984	0.452992	+	0.891515i	$0.350357\pi$
$510$	−43.5923	−1.93030
$511$	−1.67029	−0.0738895
$512$	35.1608	1.55390
$513$	−0.176483	−0.00779191
$514$	1.03751	0.0457625
$515$	15.0013	0.661035
$516$	−16.6305	−0.732118
$517$	−51.3789	−2.25964
$518$	25.5175	1.12118
$519$	23.2721	1.02153
$520$	−19.8719	−0.871439
$521$	−30.3007	−1.32750	−0.663750	−	0.747955i	$-0.731036\pi$
$521$	−30.3007	−1.32750	−0.663750	+	0.747955i	$0.731036\pi$
$522$	7.17778	0.314163
$523$	2.41888	0.105770	0.0528851	−	0.998601i	$-0.483158\pi$
$523$	2.41888	0.105770	0.0528851	+	0.998601i	$0.483158\pi$
$524$	−69.6270	−3.04167
$525$	9.94849	0.434188
$526$	−28.9511	−1.26233
$527$	33.3802	1.45406
$528$	41.2122	1.79353
$529$	5.80645	0.252454
$530$	51.2786	2.22740
$531$	−4.21767	−0.183031
$532$	−0.869830	−0.0377119
$533$	4.18761	0.181385
$534$	12.3187	0.533081
$535$	−3.64703	−0.157675
$536$	87.1104	3.76260
$537$	−12.5286	−0.540648
$538$	−21.7915	−0.939498
$539$	−3.94955	−0.170119
$540$	−19.0560	−0.820038
$541$	−6.44495	−0.277090	−0.138545	−	0.990356i	$-0.544243\pi$
$541$	−6.44495	−0.277090	−0.138545	+	0.990356i	$0.544243\pi$
$542$	12.3913	0.532253
$543$	−17.5228	−0.751973
$544$	51.6079	2.21267
$545$	25.0024	1.07099
$546$	−1.75495	−0.0751051
$547$	−20.2807	−0.867138	−0.433569	−	0.901120i	$-0.642746\pi$
$547$	−20.2807	−0.867138	−0.433569	+	0.901120i	$0.642746\pi$
$548$	−41.2385	−1.76162
$549$	−6.76710	−0.288813
$550$	103.426	4.41011
$551$	−0.481246	−0.0205018
$552$	−41.3756	−1.76106
$553$	5.00173	0.212695
$554$	−73.6051	−3.12718
$555$	−37.4810	−1.59098
$556$	96.8529	4.10748
$557$	2.40730	0.102000	0.0510002	−	0.998699i	$-0.483759\pi$
$557$	2.40730	0.102000	0.0510002	+	0.998699i	$0.483759\pi$
$558$	20.5130	0.868384
$559$	2.24964	0.0951498
$560$	−40.3438	−1.70484
$561$	−16.9174	−0.714252
$562$	66.5415	2.80688
$563$	−9.70373	−0.408963	−0.204482	−	0.978870i	$-0.565551\pi$
$563$	−9.70373	−0.408963	−0.204482	+	0.978870i	$0.565551\pi$
$564$	−64.1164	−2.69979
$565$	62.5553	2.63172
$566$	48.1204	2.02265
$567$	−1.00000	−0.0419961
$568$	27.3083	1.14583
$569$	21.6908	0.909326	0.454663	−	0.890663i	$-0.349760\pi$
$569$	21.6908	0.909326	0.454663	+	0.890663i	$0.349760\pi$
$570$	1.79608	0.0752297
$571$	−17.6964	−0.740571	−0.370286	−	0.928918i	$-0.620740\pi$
$571$	−17.6964	−0.740571	−0.370286	+	0.928918i	$0.620740\pi$
$572$	−12.9784	−0.542652
$573$	6.05464	0.252936
$574$	16.5330	0.690074
$575$	−53.3952	−2.22673
$576$	10.8451	0.451880
$577$	−9.89506	−0.411937	−0.205968	−	0.978559i	$-0.566034\pi$
$577$	−9.89506	−0.411937	−0.205968	+	0.978559i	$0.566034\pi$
$578$	−3.54625	−0.147505
$579$	−2.29469	−0.0953640
$580$	−51.9631	−2.15765
$581$	2.95616	0.122642
$582$	28.1528	1.16697
$583$	19.9003	0.824185
$584$	−12.8764	−0.532827
$585$	2.57774	0.106576
$586$	74.7668	3.08859
$587$	−13.5376	−0.558758	−0.279379	−	0.960181i	$-0.590129\pi$
$587$	−13.5376	−0.558758	−0.279379	+	0.960181i	$0.590129\pi$
$588$	−4.92870	−0.203256
$589$	−1.37533	−0.0566693
$590$	42.9237	1.76714
$591$	−8.17623	−0.336325
$592$	101.156	4.15748
$593$	21.2673	0.873342	0.436671	−	0.899621i	$-0.356157\pi$
$593$	21.2673	0.873342	0.436671	+	0.899621i	$0.356157\pi$
$594$	−10.3962	−0.426560
$595$	16.5609	0.678931
$596$	87.6144	3.58882
$597$	−7.67703	−0.314200
$598$	9.41913	0.385177
$599$	14.0614	0.574534	0.287267	−	0.957851i	$-0.407253\pi$
$599$	14.0614	0.574534	0.287267	+	0.957851i	$0.407253\pi$
$600$	76.6932	3.13099
$601$	−6.04380	−0.246532	−0.123266	−	0.992374i	$-0.539337\pi$
$601$	−6.04380	−0.246532	−0.123266	+	0.992374i	$0.539337\pi$
$602$	8.88177	0.361994
$603$	−11.2998	−0.460163
$604$	−83.3130	−3.38996
$605$	17.7810	0.722901
$606$	−44.6004	−1.81177
$607$	−13.8956	−0.564007	−0.282003	−	0.959413i	$-0.590999\pi$
$607$	−13.8956	−0.564007	−0.282003	+	0.959413i	$0.590999\pi$
$608$	−2.12634	−0.0862346
$609$	−2.72687	−0.110498
$610$	68.8695	2.78844
$611$	8.67316	0.350878
$612$	−21.1114	−0.853378
$613$	−4.66681	−0.188491	−0.0942454	−	0.995549i	$-0.530044\pi$
$613$	−4.66681	−0.188491	−0.0942454	+	0.995549i	$0.530044\pi$
$614$	−73.8817	−2.98162
$615$	−24.2842	−0.979235
$616$	−30.4472	−1.22675
$617$	21.1660	0.852110	0.426055	−	0.904697i	$-0.359903\pi$
$617$	21.1660	0.852110	0.426055	+	0.904697i	$0.359903\pi$
$618$	10.2130	0.410829
$619$	10.3794	0.417183	0.208591	−	0.978003i	$-0.433112\pi$
$619$	10.3794	0.417183	0.208591	+	0.978003i	$0.433112\pi$
$620$	−148.503	−5.96401
$621$	5.36716	0.215377
$622$	50.8334	2.03823
$623$	−4.67991	−0.187497
$624$	−6.95693	−0.278500
$625$	24.2300	0.969200
$626$	59.9985	2.39802
$627$	0.697028	0.0278366
$628$	111.528	4.45045
$629$	−41.5239	−1.65567
$630$	10.1771	0.405466
$631$	38.9154	1.54920	0.774598	−	0.632454i	$-0.217952\pi$
$631$	38.9154	1.54920	0.774598	+	0.632454i	$0.217952\pi$
$632$	38.5585	1.53377
$633$	−26.3071	−1.04561
$634$	−8.98350	−0.356780
$635$	56.5700	2.24491
$636$	24.8338	0.984725
$637$	0.666715	0.0264162
$638$	−28.3490	−1.12235
$639$	−3.54238	−0.140134
$640$	−17.2055	−0.680106
$641$	29.9437	1.18271	0.591353	−	0.806413i	$-0.298594\pi$
$641$	29.9437	1.18271	0.591353	+	0.806413i	$0.298594\pi$
$642$	−2.48294	−0.0979938
$643$	18.9275	0.746427	0.373214	−	0.927745i	$-0.378256\pi$
$643$	18.9275	0.746427	0.373214	+	0.927745i	$0.378256\pi$
$644$	26.4531	1.04240
$645$	−13.0459	−0.513680
$646$	1.98982	0.0782884
$647$	−35.7508	−1.40551	−0.702755	−	0.711432i	$-0.748047\pi$
$647$	−35.7508	−1.40551	−0.702755	+	0.711432i	$0.748047\pi$
$648$	−7.70903	−0.302839
$649$	16.6579	0.653880
$650$	−17.4591	−0.684804
$651$	−7.79297	−0.305431
$652$	41.3115	1.61788
$653$	1.81891	0.0711794	0.0355897	−	0.999366i	$-0.488669\pi$
$653$	1.81891	0.0711794	0.0355897	+	0.999366i	$0.488669\pi$
$654$	17.0220	0.665611
$655$	−54.6191	−2.13414
$656$	65.5395	2.55889
$657$	1.67029	0.0651644
$658$	34.2423	1.33490
$659$	10.2583	0.399606	0.199803	−	0.979836i	$-0.435970\pi$
$659$	10.2583	0.399606	0.199803	+	0.979836i	$0.435970\pi$
$660$	75.2624	2.92959
$661$	0.799759	0.0311070	0.0155535	−	0.999879i	$-0.495049\pi$
$661$	0.799759	0.0311070	0.0155535	+	0.999879i	$0.495049\pi$
$662$	−41.4763	−1.61202
$663$	2.85578	0.110909
$664$	22.7891	0.884389
$665$	−0.682340	−0.0264600
$666$	−25.5175	−0.988784
$667$	14.6356	0.566691
$668$	21.5373	0.833303
$669$	−5.55368	−0.214717
$670$	114.999	4.44280
$671$	26.7270	1.03178
$672$	−12.0484	−0.464779
$673$	20.6600	0.796384	0.398192	−	0.917302i	$-0.369638\pi$
$673$	20.6600	0.796384	0.398192	+	0.917302i	$0.369638\pi$
$674$	39.2507	1.51188
$675$	−9.94849	−0.382918
$676$	−61.8822	−2.38008
$677$	−11.0619	−0.425145	−0.212573	−	0.977145i	$-0.568184\pi$
$677$	−11.0619	−0.425145	−0.212573	+	0.977145i	$0.568184\pi$
$678$	42.5884	1.63560
$679$	−10.6954	−0.410451
$680$	127.669	4.89587
$681$	−11.8103	−0.452573
$682$	−81.0171	−3.10230
$683$	4.15426	0.158958	0.0794791	−	0.996837i	$-0.474674\pi$
$683$	4.15426	0.158958	0.0794791	+	0.996837i	$0.474674\pi$
$684$	0.869830	0.0332588
$685$	−32.3497	−1.23602
$686$	2.63224	0.100499
$687$	−10.8487	−0.413902
$688$	35.2088	1.34232
$689$	−3.35932	−0.127980
$690$	−54.6222	−2.07943
$691$	25.5928	0.973597	0.486799	−	0.873514i	$-0.338165\pi$
$691$	25.5928	0.973597	0.486799	+	0.873514i	$0.338165\pi$
$692$	−114.701	−4.36028
$693$	3.94955	0.150031
$694$	4.65902	0.176854
$695$	75.9765	2.88195
$696$	−21.0215	−0.796820
$697$	−26.9036	−1.01905
$698$	−18.2285	−0.689959
$699$	−23.5182	−0.889539
$700$	−49.0331	−1.85328
$701$	−13.2617	−0.500886	−0.250443	−	0.968131i	$-0.580576\pi$
$701$	−13.2617	−0.500886	−0.250443	+	0.968131i	$0.580576\pi$
$702$	1.75495	0.0662365
$703$	1.71086	0.0645264
$704$	−42.8333	−1.61434
$705$	−50.2963	−1.89427
$706$	−5.92967	−0.223166
$707$	16.9439	0.637240
$708$	20.7876	0.781247
$709$	−8.39250	−0.315187	−0.157593	−	0.987504i	$-0.550374\pi$
$709$	−8.39250	−0.315187	−0.157593	+	0.987504i	$0.550374\pi$
$710$	36.0512	1.35298
$711$	−5.00173	−0.187580
$712$	−36.0776	−1.35207
$713$	41.8262	1.56640
$714$	11.2749	0.421951
$715$	−10.1809	−0.380744
$716$	61.7495	2.30769
$717$	26.3356	0.983522
$718$	−12.9063	−0.481659
$719$	3.55060	0.132415	0.0662075	−	0.997806i	$-0.478910\pi$
$719$	3.55060	0.132415	0.0662075	+	0.997806i	$0.478910\pi$
$720$	40.3438	1.50352
$721$	−3.87998	−0.144498
$722$	49.9306	1.85822
$723$	8.03504	0.298826
$724$	86.3643	3.20970
$725$	−27.1283	−1.00752
$726$	12.1055	0.449278
$727$	43.6733	1.61975	0.809877	−	0.586599i	$-0.199534\pi$
$727$	43.6733	1.61975	0.809877	+	0.586599i	$0.199534\pi$
$728$	5.13973	0.190491
$729$	1.00000	0.0370370
$730$	−16.9988	−0.629152
$731$	−14.4530	−0.534565
$732$	33.3529	1.23276
$733$	−31.9478	−1.18002	−0.590010	−	0.807396i	$-0.700876\pi$
$733$	−31.9478	−1.18002	−0.590010	+	0.807396i	$0.700876\pi$
$734$	−69.7916	−2.57606
$735$	−3.86633	−0.142612
$736$	64.6660	2.38362
$737$	44.6290	1.64393
$738$	−16.5330	−0.608588
$739$	51.6325	1.89933	0.949666	−	0.313265i	$-0.101423\pi$
$739$	51.6325	1.89933	0.949666	+	0.313265i	$0.101423\pi$
$740$	184.733	6.79090
$741$	−0.117664	−0.00432248
$742$	−13.2629	−0.486895
$743$	34.2545	1.25667	0.628337	−	0.777941i	$-0.283736\pi$
$743$	34.2545	1.25667	0.628337	+	0.777941i	$0.283736\pi$
$744$	−60.0763	−2.20250
$745$	68.7293	2.51805
$746$	−4.30856	−0.157748
$747$	−2.95616	−0.108160
$748$	83.3806	3.04870
$749$	0.943279	0.0344667
$750$	50.3613	1.83894
$751$	−34.8550	−1.27188	−0.635938	−	0.771740i	$-0.719387\pi$
$751$	−34.8550	−1.27188	−0.635938	+	0.771740i	$0.719387\pi$
$752$	135.742	4.95001
$753$	−20.9598	−0.763818
$754$	4.78553	0.174279
$755$	−65.3551	−2.37851
$756$	4.92870	0.179255
$757$	9.08748	0.330290	0.165145	−	0.986269i	$-0.447191\pi$
$757$	9.08748	0.330290	0.165145	+	0.986269i	$0.447191\pi$
$758$	30.2879	1.10011
$759$	−21.1979	−0.769434
$760$	−5.26018	−0.190807
$761$	33.6896	1.22125	0.610624	−	0.791921i	$-0.290919\pi$
$761$	33.6896	1.22125	0.610624	+	0.791921i	$0.290919\pi$
$762$	38.5135	1.39520
$763$	−6.46672	−0.234111
$764$	−29.8415	−1.07963
$765$	−16.5609	−0.598761
$766$	−2.63224	−0.0951068
$767$	−2.81199	−0.101535
$768$	9.97654	0.359997
$769$	−29.3529	−1.05849	−0.529246	−	0.848469i	$-0.677525\pi$
$769$	−29.3529	−1.05849	−0.529246	+	0.848469i	$0.677525\pi$
$770$	−40.1950	−1.44853
$771$	0.394153	0.0141951
$772$	11.3098	0.407049
$773$	37.3234	1.34243	0.671214	−	0.741264i	$-0.265773\pi$
$773$	37.3234	1.34243	0.671214	+	0.741264i	$0.265773\pi$
$774$	−8.88177	−0.319249
$775$	−77.5283	−2.78490
$776$	−82.4511	−2.95982
$777$	9.69422	0.347778
$778$	3.65205	0.130932
$779$	1.10848	0.0397154
$780$	−12.7049	−0.454908
$781$	13.9908	0.500630
$782$	−60.5140	−2.16398
$783$	2.72687	0.0974504
$784$	10.4346	0.372666
$785$	87.4885	3.12260
$786$	−37.1853	−1.32636
$787$	−5.71479	−0.203710	−0.101855	−	0.994799i	$-0.532478\pi$
$787$	−5.71479	−0.203710	−0.101855	+	0.994799i	$0.532478\pi$
$788$	40.2981	1.43556
$789$	−10.9986	−0.391562
$790$	50.9031	1.81105
$791$	−16.1795	−0.575277
$792$	30.4472	1.08189
$793$	−4.51172	−0.160216
$794$	−37.8762	−1.34418
$795$	19.4809	0.690918
$796$	37.8377	1.34112
$797$	4.80861	0.170330	0.0851649	−	0.996367i	$-0.472858\pi$
$797$	4.80861	0.170330	0.0851649	+	0.996367i	$0.472858\pi$
$798$	−0.464545	−0.0164447
$799$	−55.7215	−1.97128
$800$	−119.864	−4.23783
$801$	4.67991	0.165357
$802$	−73.5886	−2.59850
$803$	−6.59691	−0.232800
$804$	55.6932	1.96415
$805$	20.7512	0.731384
$806$	13.6763	0.481727
$807$	−8.27868	−0.291423
$808$	130.621	4.59523
$809$	−24.0899	−0.846957	−0.423479	−	0.905906i	$-0.639191\pi$
$809$	−24.0899	−0.846957	−0.423479	+	0.905906i	$0.639191\pi$
$810$	−10.1771	−0.357587
$811$	−39.1445	−1.37455	−0.687274	−	0.726398i	$-0.741193\pi$
$811$	−39.1445	−1.37455	−0.687274	+	0.726398i	$0.741193\pi$
$812$	13.4399	0.471649
$813$	4.70752	0.165100
$814$	100.783	3.53243
$815$	32.4069	1.13516
$816$	44.6954	1.56465
$817$	0.595492	0.0208336
$818$	−13.2811	−0.464364
$819$	−0.666715	−0.0232969
$820$	119.690	4.17974
$821$	−46.4994	−1.62284	−0.811420	−	0.584464i	$-0.801305\pi$
$821$	−46.4994	−1.62284	−0.811420	+	0.584464i	$0.801305\pi$
$822$	−22.0240	−0.768177
$823$	51.1841	1.78417	0.892083	−	0.451871i	$-0.149243\pi$
$823$	51.1841	1.78417	0.892083	+	0.451871i	$0.149243\pi$
$824$	−29.9109	−1.04199
$825$	39.2921	1.36797
$826$	−11.1019	−0.386286
$827$	20.5583	0.714884	0.357442	−	0.933935i	$-0.383649\pi$
$827$	20.5583	0.714884	0.357442	+	0.933935i	$0.383649\pi$
$828$	−26.4531	−0.919309
$829$	−18.7428	−0.650963	−0.325482	−	0.945548i	$-0.605526\pi$
$829$	−18.7428	−0.650963	−0.325482	+	0.945548i	$0.605526\pi$
$830$	30.0851	1.04427
$831$	−27.9629	−0.970022
$832$	7.23060	0.250676
$833$	−4.28337	−0.148410
$834$	51.7257	1.79111
$835$	16.8950	0.584675
$836$	−3.43544	−0.118817
$837$	7.79297	0.269365
$838$	73.3552	2.53401
$839$	16.1626	0.557996	0.278998	−	0.960292i	$-0.409998\pi$
$839$	16.1626	0.557996	0.278998	+	0.960292i	$0.409998\pi$
$840$	−29.8056	−1.02839
$841$	−21.5642	−0.743592
$842$	−33.3091	−1.14791
$843$	25.2794	0.870669
$844$	129.660	4.46307
$845$	−48.5436	−1.66995
$846$	−34.2423	−1.17727
$847$	−4.59894	−0.158022
$848$	−52.5762	−1.80547
$849$	18.2811	0.627407
$850$	112.168	3.84732
$851$	−52.0305	−1.78358
$852$	17.4593	0.598146
$853$	−54.0201	−1.84961	−0.924807	−	0.380437i	$-0.875774\pi$
$853$	−54.0201	−1.84961	−0.924807	+	0.380437i	$0.875774\pi$
$854$	−17.8126	−0.609536
$855$	0.682340	0.0233355
$856$	7.27177	0.248544
$857$	−6.78512	−0.231775	−0.115888	−	0.993262i	$-0.536971\pi$
$857$	−6.78512	−0.231775	−0.115888	+	0.993262i	$0.536971\pi$
$858$	−6.93128	−0.236630
$859$	−55.7660	−1.90271	−0.951356	−	0.308094i	$-0.900309\pi$
$859$	−55.7660	−1.90271	−0.951356	+	0.308094i	$0.900309\pi$
$860$	64.2990	2.19258
$861$	6.28096	0.214054
$862$	−84.3539	−2.87310
$863$	−0.624497	−0.0212581	−0.0106291	−	0.999944i	$-0.503383\pi$
$863$	−0.624497	−0.0212581	−0.0106291	+	0.999944i	$0.503383\pi$
$864$	12.0484	0.409896
$865$	−89.9774	−3.05933
$866$	−92.0254	−3.12715
$867$	−1.34724	−0.0457545
$868$	38.4092	1.30369
$869$	19.7546	0.670128
$870$	−27.7517	−0.940870
$871$	−7.53373	−0.255271
$872$	−49.8521	−1.68821
$873$	10.6954	0.361984
$874$	2.49329	0.0843368
$875$	−19.1325	−0.646796
$876$	−8.23237	−0.278146
$877$	−4.26994	−0.144186	−0.0720929	−	0.997398i	$-0.522968\pi$
$877$	−4.26994	−0.144186	−0.0720929	+	0.997398i	$0.522968\pi$
$878$	−18.1323	−0.611936
$879$	28.4042	0.958051
$880$	−159.340	−5.37134
$881$	−12.5768	−0.423725	−0.211862	−	0.977300i	$-0.567953\pi$
$881$	−12.5768	−0.423725	−0.211862	+	0.977300i	$0.567953\pi$
$882$	−2.63224	−0.0886322
$883$	−50.3970	−1.69599	−0.847997	−	0.530001i	$-0.822192\pi$
$883$	−50.3970	−1.69599	−0.847997	+	0.530001i	$0.822192\pi$
$884$	−14.0753	−0.473403
$885$	16.3069	0.548151
$886$	81.4452	2.73621
$887$	24.5216	0.823356	0.411678	−	0.911329i	$-0.364943\pi$
$887$	24.5216	0.823356	0.411678	+	0.911329i	$0.364943\pi$
$888$	74.7331	2.50788
$889$	−14.6315	−0.490723
$890$	−47.6280	−1.59649
$891$	−3.94955	−0.132315
$892$	27.3724	0.916495
$893$	2.29583	0.0768270
$894$	46.7917	1.56495
$895$	48.4395	1.61916
$896$	4.45008	0.148667
$897$	3.57837	0.119478
$898$	−53.3217	−1.77937
$899$	21.2504	0.708742
$900$	49.0331	1.63444
$901$	21.5823	0.719009
$902$	65.2979	2.17418
$903$	3.37422	0.112287
$904$	−124.728	−4.14841
$905$	67.7487	2.25204
$906$	−44.4945	−1.47823
$907$	−13.8610	−0.460245	−0.230123	−	0.973162i	$-0.573913\pi$
$907$	−13.8610	−0.460245	−0.230123	+	0.973162i	$0.573913\pi$
$908$	58.2095	1.93175
$909$	−16.9439	−0.561993
$910$	6.78523	0.224928
$911$	25.8502	0.856456	0.428228	−	0.903671i	$-0.359138\pi$
$911$	25.8502	0.856456	0.428228	+	0.903671i	$0.359138\pi$
$912$	−1.84154	−0.0609793
$913$	11.6755	0.386402
$914$	−47.0920	−1.55766
$915$	26.1638	0.864949
$916$	53.4698	1.76669
$917$	14.1269	0.466510
$918$	−11.2749	−0.372126
$919$	19.6521	0.648264	0.324132	−	0.946012i	$-0.394928\pi$
$919$	19.6521	0.648264	0.324132	+	0.946012i	$0.394928\pi$
$920$	159.972	5.27411
$921$	−28.0680	−0.924872
$922$	−31.5568	−1.03927
$923$	−2.36176	−0.0777382
$924$	−19.4661	−0.640389
$925$	96.4428	3.17102
$926$	−55.6931	−1.83019
$927$	3.87998	0.127435
$928$	32.8546	1.07850
$929$	−9.75732	−0.320127	−0.160064	−	0.987107i	$-0.551170\pi$
$929$	−9.75732	−0.320127	−0.160064	+	0.987107i	$0.551170\pi$
$930$	−79.3099	−2.60068
$931$	0.176483	0.00578399
$932$	115.914	3.79689
$933$	19.3118	0.632241
$934$	−78.4171	−2.56589
$935$	65.4081	2.13907
$936$	−5.13973	−0.167997
$937$	−37.5499	−1.22670	−0.613351	−	0.789811i	$-0.710179\pi$
$937$	−37.5499	−1.22670	−0.613351	+	0.789811i	$0.710179\pi$
$938$	−29.7438	−0.971168
$939$	22.7937	0.743844
$940$	247.895	8.08544
$941$	−7.93812	−0.258775	−0.129388	−	0.991594i	$-0.541301\pi$
$941$	−7.93812	−0.258775	−0.129388	+	0.991594i	$0.541301\pi$
$942$	59.5632	1.94067
$943$	−33.7109	−1.09778
$944$	−44.0099	−1.43240
$945$	3.86633	0.125772
$946$	35.0790	1.14052
$947$	−18.4299	−0.598891	−0.299446	−	0.954113i	$-0.596802\pi$
$947$	−18.4299	−0.598891	−0.299446	+	0.954113i	$0.596802\pi$
$948$	24.6520	0.800660
$949$	1.11361	0.0361493
$950$	−4.62152	−0.149942
$951$	−3.41287	−0.110670
$952$	−33.0206	−1.07020
$953$	26.6089	0.861947	0.430973	−	0.902365i	$-0.358170\pi$
$953$	26.6089	0.861947	0.430973	+	0.902365i	$0.358170\pi$
$954$	13.2629	0.429401
$955$	−23.4092	−0.757505
$956$	−129.800	−4.19804
$957$	−10.7699	−0.348142
$958$	−53.7182	−1.73556
$959$	8.36703	0.270186
$960$	−41.9308	−1.35331
$961$	29.7304	0.959047
$962$	−17.0129	−0.548518
$963$	−0.943279	−0.0303967
$964$	−39.6022	−1.27550
$965$	8.87202	0.285600
$966$	14.1277	0.454550
$967$	53.2422	1.71215	0.856077	−	0.516849i	$-0.172895\pi$
$967$	53.2422	1.71215	0.856077	+	0.516849i	$0.172895\pi$
$968$	−35.4534	−1.13952
$969$	0.755941	0.0242843
$970$	−108.848	−3.49490
$971$	55.6755	1.78671	0.893357	−	0.449348i	$-0.148344\pi$
$971$	55.6755	1.78671	0.893357	+	0.449348i	$0.148344\pi$
$972$	−4.92870	−0.158088
$973$	−19.6508	−0.629976
$974$	−9.72348	−0.311560
$975$	−6.63280	−0.212420
$976$	−70.6122	−2.26024
$977$	−28.2024	−0.902273	−0.451137	−	0.892455i	$-0.648981\pi$
$977$	−28.2024	−0.902273	−0.451137	+	0.892455i	$0.648981\pi$
$978$	22.0630	0.705497
$979$	−18.4836	−0.590737
$980$	19.0560	0.608720
$981$	6.46672	0.206466
$982$	38.6980	1.23490
$983$	−44.6311	−1.42351	−0.711756	−	0.702427i	$-0.752100\pi$
$983$	−44.6311	−1.42351	−0.711756	+	0.702427i	$0.752100\pi$
$984$	48.4201	1.54358
$985$	31.6120	1.00724
$986$	−30.7451	−0.979123
$987$	13.0088	0.414075
$988$	0.579928	0.0184500
$989$	−18.1100	−0.575865
$990$	40.1950	1.27748
$991$	41.2610	1.31070	0.655350	−	0.755325i	$-0.272521\pi$
$991$	41.2610	1.31070	0.655350	+	0.755325i	$0.272521\pi$
$992$	93.8932	2.98111
$993$	−15.7570	−0.500034
$994$	−9.32440	−0.295752
$995$	29.6819	0.940980
$996$	14.5700	0.461668
$997$	51.0344	1.61628	0.808138	−	0.588993i	$-0.200475\pi$
$997$	51.0344	1.61628	0.808138	+	0.588993i	$0.200475\pi$
$998$	−59.8985	−1.89605
$999$	−9.69422	−0.306712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.2	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.63224 q^{2} -1.00000 q^{3} +4.92870 q^{4} +3.86633 q^{5} +2.63224 q^{6} -1.00000 q^{7} -7.70903 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63224 q^{2} -1.00000 q^{3} +4.92870 q^{4} +3.86633 q^{5} +2.63224 q^{6} -1.00000 q^{7} -7.70903 q^{8} +1.00000 q^{9} -10.1771 q^{10} -3.94955 q^{11} -4.92870 q^{12} +0.666715 q^{13} +2.63224 q^{14} -3.86633 q^{15} +10.4346 q^{16} -4.28337 q^{17} -2.63224 q^{18} +0.176483 q^{19} +19.0560 q^{20} +1.00000 q^{21} +10.3962 q^{22} -5.36716 q^{23} +7.70903 q^{24} +9.94849 q^{25} -1.75495 q^{26} -1.00000 q^{27} -4.92870 q^{28} -2.72687 q^{29} +10.1771 q^{30} -7.79297 q^{31} -12.0484 q^{32} +3.94955 q^{33} +11.2749 q^{34} -3.86633 q^{35} +4.92870 q^{36} +9.69422 q^{37} -0.464545 q^{38} -0.666715 q^{39} -29.8056 q^{40} +6.28096 q^{41} -2.63224 q^{42} +3.37422 q^{43} -19.4661 q^{44} +3.86633 q^{45} +14.1277 q^{46} +13.0088 q^{47} -10.4346 q^{48} +1.00000 q^{49} -26.1868 q^{50} +4.28337 q^{51} +3.28603 q^{52} -5.03862 q^{53} +2.63224 q^{54} -15.2703 q^{55} +7.70903 q^{56} -0.176483 q^{57} +7.17778 q^{58} -4.21767 q^{59} -19.0560 q^{60} -6.76710 q^{61} +20.5130 q^{62} -1.00000 q^{63} +10.8451 q^{64} +2.57774 q^{65} -10.3962 q^{66} -11.2998 q^{67} -21.1114 q^{68} +5.36716 q^{69} +10.1771 q^{70} -3.54238 q^{71} -7.70903 q^{72} +1.67029 q^{73} -25.5175 q^{74} -9.94849 q^{75} +0.869830 q^{76} +3.94955 q^{77} +1.75495 q^{78} -5.00173 q^{79} +40.3438 q^{80} +1.00000 q^{81} -16.5330 q^{82} -2.95616 q^{83} +4.92870 q^{84} -16.5609 q^{85} -8.88177 q^{86} +2.72687 q^{87} +30.4472 q^{88} +4.67991 q^{89} -10.1771 q^{90} -0.666715 q^{91} -26.4531 q^{92} +7.79297 q^{93} -34.2423 q^{94} +0.682340 q^{95} +12.0484 q^{96} +10.6954 q^{97} -2.63224 q^{98} -3.94955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 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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