LMFDB - Embedded newform 8043.2.a.s.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.16078 q^{2} -1.00000 q^{3} +2.66897 q^{4} -0.263100 q^{5} +2.16078 q^{6} -1.00000 q^{7} -1.44551 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16078 q^{2} -1.00000 q^{3} +2.66897 q^{4} -0.263100 q^{5} +2.16078 q^{6} -1.00000 q^{7} -1.44551 q^{8} +1.00000 q^{9} +0.568501 q^{10} -5.05377 q^{11} -2.66897 q^{12} +7.02504 q^{13} +2.16078 q^{14} +0.263100 q^{15} -2.21452 q^{16} -5.39759 q^{17} -2.16078 q^{18} +7.02336 q^{19} -0.702206 q^{20} +1.00000 q^{21} +10.9201 q^{22} -2.66242 q^{23} +1.44551 q^{24} -4.93078 q^{25} -15.1796 q^{26} -1.00000 q^{27} -2.66897 q^{28} -5.62436 q^{29} -0.568501 q^{30} +3.03915 q^{31} +7.67612 q^{32} +5.05377 q^{33} +11.6630 q^{34} +0.263100 q^{35} +2.66897 q^{36} +10.4790 q^{37} -15.1760 q^{38} -7.02504 q^{39} +0.380312 q^{40} -9.03528 q^{41} -2.16078 q^{42} -12.2036 q^{43} -13.4884 q^{44} -0.263100 q^{45} +5.75291 q^{46} -0.191468 q^{47} +2.21452 q^{48} +1.00000 q^{49} +10.6543 q^{50} +5.39759 q^{51} +18.7497 q^{52} +9.86243 q^{53} +2.16078 q^{54} +1.32965 q^{55} +1.44551 q^{56} -7.02336 q^{57} +12.1530 q^{58} +6.60622 q^{59} +0.702206 q^{60} +2.60003 q^{61} -6.56693 q^{62} -1.00000 q^{63} -12.1574 q^{64} -1.84829 q^{65} -10.9201 q^{66} -4.26445 q^{67} -14.4060 q^{68} +2.66242 q^{69} -0.568501 q^{70} +11.1626 q^{71} -1.44551 q^{72} -14.4709 q^{73} -22.6429 q^{74} +4.93078 q^{75} +18.7452 q^{76} +5.05377 q^{77} +15.1796 q^{78} +10.7610 q^{79} +0.582641 q^{80} +1.00000 q^{81} +19.5233 q^{82} -11.1508 q^{83} +2.66897 q^{84} +1.42010 q^{85} +26.3694 q^{86} +5.62436 q^{87} +7.30526 q^{88} -6.49933 q^{89} +0.568501 q^{90} -7.02504 q^{91} -7.10594 q^{92} -3.03915 q^{93} +0.413721 q^{94} -1.84784 q^{95} -7.67612 q^{96} +11.3475 q^{97} -2.16078 q^{98} -5.05377 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16078	−1.52790	−0.763951	−	0.645274i	$-0.776743\pi$
$2$	−2.16078	−1.52790	−0.763951	+	0.645274i	$0.776743\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.66897	1.33449
$5$	−0.263100	−0.117662	−0.0588309	−	0.998268i	$-0.518737\pi$
$5$	−0.263100	−0.117662	−0.0588309	+	0.998268i	$0.518737\pi$
$6$	2.16078	0.882135
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.44551	−0.511064
$9$	1.00000	0.333333
$10$	0.568501	0.179776
$11$	−5.05377	−1.52377	−0.761884	−	0.647713i	$-0.775726\pi$
$11$	−5.05377	−1.52377	−0.761884	+	0.647713i	$0.775726\pi$
$12$	−2.66897	−0.770467
$13$	7.02504	1.94840	0.974198	−	0.225696i	$-0.0724656\pi$
$13$	7.02504	1.94840	0.974198	+	0.225696i	$0.0724656\pi$
$14$	2.16078	0.577493
$15$	0.263100	0.0679320
$16$	−2.21452	−0.553631
$17$	−5.39759	−1.30911	−0.654554	−	0.756015i	$-0.727144\pi$
$17$	−5.39759	−1.30911	−0.654554	+	0.756015i	$0.727144\pi$
$18$	−2.16078	−0.509301
$19$	7.02336	1.61127	0.805635	−	0.592412i	$-0.201824\pi$
$19$	7.02336	1.61127	0.805635	+	0.592412i	$0.201824\pi$
$20$	−0.702206	−0.157018
$21$	1.00000	0.218218
$22$	10.9201	2.32817
$23$	−2.66242	−0.555154	−0.277577	−	0.960703i	$-0.589531\pi$
$23$	−2.66242	−0.555154	−0.277577	+	0.960703i	$0.589531\pi$
$24$	1.44551	0.295063
$25$	−4.93078	−0.986156
$26$	−15.1796	−2.97696
$27$	−1.00000	−0.192450
$28$	−2.66897	−0.504389
$29$	−5.62436	−1.04442	−0.522209	−	0.852818i	$-0.674892\pi$
$29$	−5.62436	−1.04442	−0.522209	+	0.852818i	$0.674892\pi$
$30$	−0.568501	−0.103794
$31$	3.03915	0.545847	0.272923	−	0.962036i	$-0.412009\pi$
$31$	3.03915	0.545847	0.272923	+	0.962036i	$0.412009\pi$
$32$	7.67612	1.35696
$33$	5.05377	0.879748
$34$	11.6630	2.00019
$35$	0.263100	0.0444720
$36$	2.66897	0.444829
$37$	10.4790	1.72274	0.861370	−	0.507978i	$-0.169607\pi$
$37$	10.4790	1.72274	0.861370	+	0.507978i	$0.169607\pi$
$38$	−15.1760	−2.46186
$39$	−7.02504	−1.12491
$40$	0.380312	0.0601327
$41$	−9.03528	−1.41107	−0.705537	−	0.708674i	$-0.749294\pi$
$41$	−9.03528	−1.41107	−0.705537	+	0.708674i	$0.749294\pi$
$42$	−2.16078	−0.333416
$43$	−12.2036	−1.86104	−0.930518	−	0.366247i	$-0.880642\pi$
$43$	−12.2036	−1.86104	−0.930518	+	0.366247i	$0.880642\pi$
$44$	−13.4884	−2.03345
$45$	−0.263100	−0.0392206
$46$	5.75291	0.848221
$47$	−0.191468	−0.0279285	−0.0139643	−	0.999902i	$-0.504445\pi$
$47$	−0.191468	−0.0279285	−0.0139643	+	0.999902i	$0.504445\pi$
$48$	2.21452	0.319639
$49$	1.00000	0.142857
$50$	10.6543	1.50675
$51$	5.39759	0.755814
$52$	18.7497	2.60011
$53$	9.86243	1.35471	0.677355	−	0.735657i	$-0.263126\pi$
$53$	9.86243	1.35471	0.677355	+	0.735657i	$0.263126\pi$
$54$	2.16078	0.294045
$55$	1.32965	0.179289
$56$	1.44551	0.193164
$57$	−7.02336	−0.930267
$58$	12.1530	1.59577
$59$	6.60622	0.860057	0.430028	−	0.902815i	$-0.358504\pi$
$59$	6.60622	0.860057	0.430028	+	0.902815i	$0.358504\pi$
$60$	0.702206	0.0906544
$61$	2.60003	0.332900	0.166450	−	0.986050i	$-0.446770\pi$
$61$	2.60003	0.332900	0.166450	+	0.986050i	$0.446770\pi$
$62$	−6.56693	−0.834001
$63$	−1.00000	−0.125988
$64$	−12.1574	−1.51967
$65$	−1.84829	−0.229252
$66$	−10.9201	−1.34417
$67$	−4.26445	−0.520986	−0.260493	−	0.965476i	$-0.583885\pi$
$67$	−4.26445	−0.520986	−0.260493	+	0.965476i	$0.583885\pi$
$68$	−14.4060	−1.74699
$69$	2.66242	0.320518
$70$	−0.568501	−0.0679488
$71$	11.1626	1.32475	0.662377	−	0.749171i	$-0.269548\pi$
$71$	11.1626	1.32475	0.662377	+	0.749171i	$0.269548\pi$
$72$	−1.44551	−0.170355
$73$	−14.4709	−1.69369	−0.846843	−	0.531844i	$-0.821499\pi$
$73$	−14.4709	−1.69369	−0.846843	+	0.531844i	$0.821499\pi$
$74$	−22.6429	−2.63218
$75$	4.93078	0.569357
$76$	18.7452	2.15022
$77$	5.05377	0.575931
$78$	15.1796	1.71875
$79$	10.7610	1.21071	0.605356	−	0.795955i	$-0.293031\pi$
$79$	10.7610	1.21071	0.605356	+	0.795955i	$0.293031\pi$
$80$	0.582641	0.0651412
$81$	1.00000	0.111111
$82$	19.5233	2.15598
$83$	−11.1508	−1.22396	−0.611978	−	0.790875i	$-0.709626\pi$
$83$	−11.1508	−1.22396	−0.611978	+	0.790875i	$0.709626\pi$
$84$	2.66897	0.291209
$85$	1.42010	0.154032
$86$	26.3694	2.84348
$87$	5.62436	0.602995
$88$	7.30526	0.778743
$89$	−6.49933	−0.688927	−0.344464	−	0.938800i	$-0.611939\pi$
$89$	−6.49933	−0.688927	−0.344464	+	0.938800i	$0.611939\pi$
$90$	0.568501	0.0599252
$91$	−7.02504	−0.736424
$92$	−7.10594	−0.740845
$93$	−3.03915	−0.315145
$94$	0.413721	0.0426721
$95$	−1.84784	−0.189585
$96$	−7.67612	−0.783440
$97$	11.3475	1.15217	0.576083	−	0.817391i	$-0.304580\pi$
$97$	11.3475	1.15217	0.576083	+	0.817391i	$0.304580\pi$
$98$	−2.16078	−0.218272
$99$	−5.05377	−0.507923
$100$	−13.1601	−1.31601
$101$	−2.87765	−0.286337	−0.143168	−	0.989698i	$-0.545729\pi$
$101$	−2.87765	−0.286337	−0.143168	+	0.989698i	$0.545729\pi$
$102$	−11.6630	−1.15481
$103$	−10.0021	−0.985535	−0.492768	−	0.870161i	$-0.664015\pi$
$103$	−10.0021	−0.985535	−0.492768	+	0.870161i	$0.664015\pi$
$104$	−10.1547	−0.995754
$105$	−0.263100	−0.0256759
$106$	−21.3106	−2.06986
$107$	−8.53938	−0.825533	−0.412767	−	0.910837i	$-0.635437\pi$
$107$	−8.53938	−0.825533	−0.412767	+	0.910837i	$0.635437\pi$
$108$	−2.66897	−0.256822
$109$	−6.13488	−0.587615	−0.293808	−	0.955865i	$-0.594923\pi$
$109$	−6.13488	−0.587615	−0.293808	+	0.955865i	$0.594923\pi$
$110$	−2.87307	−0.273937
$111$	−10.4790	−0.994625
$112$	2.21452	0.209253
$113$	18.9526	1.78291	0.891457	−	0.453106i	$-0.149684\pi$
$113$	18.9526	1.78291	0.891457	+	0.453106i	$0.149684\pi$
$114$	15.1760	1.42136
$115$	0.700483	0.0653203
$116$	−15.0113	−1.39376
$117$	7.02504	0.649465
$118$	−14.2746	−1.31408
$119$	5.39759	0.494796
$120$	−0.380312	−0.0347176
$121$	14.5406	1.32187
$122$	−5.61810	−0.508639
$123$	9.03528	0.814683
$124$	8.11140	0.728426
$125$	2.61278	0.233695
$126$	2.16078	0.192498
$127$	−20.0241	−1.77685	−0.888424	−	0.459024i	$-0.848199\pi$
$127$	−20.0241	−1.77685	−0.888424	+	0.459024i	$0.848199\pi$
$128$	10.9172	0.964949
$129$	12.2036	1.07447
$130$	3.99374	0.350274
$131$	4.71317	0.411792	0.205896	−	0.978574i	$-0.433989\pi$
$131$	4.71317	0.411792	0.205896	+	0.978574i	$0.433989\pi$
$132$	13.4884	1.17401
$133$	−7.02336	−0.609003
$134$	9.21455	0.796016
$135$	0.263100	0.0226440
$136$	7.80225	0.669038
$137$	21.1640	1.80817	0.904083	−	0.427357i	$-0.140555\pi$
$137$	21.1640	1.80817	0.904083	+	0.427357i	$0.140555\pi$
$138$	−5.75291	−0.489721
$139$	−4.36165	−0.369950	−0.184975	−	0.982743i	$-0.559220\pi$
$139$	−4.36165	−0.369950	−0.184975	+	0.982743i	$0.559220\pi$
$140$	0.702206	0.0593473
$141$	0.191468	0.0161245
$142$	−24.1199	−2.02410
$143$	−35.5029	−2.96890
$144$	−2.21452	−0.184544
$145$	1.47977	0.122888
$146$	31.2683	2.58779
$147$	−1.00000	−0.0824786
$148$	27.9682	2.29897
$149$	−6.57145	−0.538354	−0.269177	−	0.963091i	$-0.586752\pi$
$149$	−6.57145	−0.538354	−0.269177	+	0.963091i	$0.586752\pi$
$150$	−10.6543	−0.869923
$151$	5.39237	0.438825	0.219412	−	0.975632i	$-0.429586\pi$
$151$	5.39237	0.438825	0.219412	+	0.975632i	$0.429586\pi$
$152$	−10.1523	−0.823462
$153$	−5.39759	−0.436369
$154$	−10.9201	−0.879966
$155$	−0.799598	−0.0642253
$156$	−18.7497	−1.50117
$157$	−17.6226	−1.40644	−0.703220	−	0.710972i	$-0.748255\pi$
$157$	−17.6226	−1.40644	−0.703220	+	0.710972i	$0.748255\pi$
$158$	−23.2523	−1.84985
$159$	−9.86243	−0.782142
$160$	−2.01958	−0.159662
$161$	2.66242	0.209828
$162$	−2.16078	−0.169767
$163$	14.3050	1.12045	0.560227	−	0.828339i	$-0.310714\pi$
$163$	14.3050	1.12045	0.560227	+	0.828339i	$0.310714\pi$
$164$	−24.1149	−1.88306
$165$	−1.32965	−0.103513
$166$	24.0944	1.87009
$167$	14.8232	1.14705	0.573527	−	0.819187i	$-0.305575\pi$
$167$	14.8232	1.14705	0.573527	+	0.819187i	$0.305575\pi$
$168$	−1.44551	−0.111523
$169$	36.3512	2.79625
$170$	−3.06853	−0.235346
$171$	7.02336	0.537090
$172$	−32.5712	−2.48353
$173$	3.04925	0.231830	0.115915	−	0.993259i	$-0.463020\pi$
$173$	3.04925	0.231830	0.115915	+	0.993259i	$0.463020\pi$
$174$	−12.1530	−0.921318
$175$	4.93078	0.372732
$176$	11.1917	0.843606
$177$	−6.60622	−0.496554
$178$	14.0436	1.05261
$179$	−10.7489	−0.803408	−0.401704	−	0.915770i	$-0.631582\pi$
$179$	−10.7489	−0.803408	−0.401704	+	0.915770i	$0.631582\pi$
$180$	−0.702206	−0.0523394
$181$	−7.45232	−0.553926	−0.276963	−	0.960881i	$-0.589328\pi$
$181$	−7.45232	−0.553926	−0.276963	+	0.960881i	$0.589328\pi$
$182$	15.1796	1.12518
$183$	−2.60003	−0.192200
$184$	3.84855	0.283719
$185$	−2.75703	−0.202701
$186$	6.56693	0.481511
$187$	27.2782	1.99478
$188$	−0.511024	−0.0372702
$189$	1.00000	0.0727393
$190$	3.99279	0.289667
$191$	1.46702	0.106150	0.0530748	−	0.998591i	$-0.483098\pi$
$191$	1.46702	0.106150	0.0530748	+	0.998591i	$0.483098\pi$
$192$	12.1574	0.877382
$193$	−7.82483	−0.563244	−0.281622	−	0.959525i	$-0.590872\pi$
$193$	−7.82483	−0.563244	−0.281622	+	0.959525i	$0.590872\pi$
$194$	−24.5195	−1.76040
$195$	1.84829	0.132358
$196$	2.66897	0.190641
$197$	11.9893	0.854204	0.427102	−	0.904203i	$-0.359535\pi$
$197$	11.9893	0.854204	0.427102	+	0.904203i	$0.359535\pi$
$198$	10.9201	0.776057
$199$	−2.40146	−0.170235	−0.0851173	−	0.996371i	$-0.527127\pi$
$199$	−2.40146	−0.170235	−0.0851173	+	0.996371i	$0.527127\pi$
$200$	7.12747	0.503989
$201$	4.26445	0.300791
$202$	6.21797	0.437495
$203$	5.62436	0.394753
$204$	14.4060	1.00862
$205$	2.37718	0.166029
$206$	21.6123	1.50580
$207$	−2.66242	−0.185051
$208$	−15.5571	−1.07869
$209$	−35.4945	−2.45520
$210$	0.568501	0.0392303
$211$	−16.2298	−1.11730	−0.558652	−	0.829402i	$-0.688681\pi$
$211$	−16.2298	−1.11730	−0.558652	+	0.829402i	$0.688681\pi$
$212$	26.3226	1.80784
$213$	−11.1626	−0.764847
$214$	18.4517	1.26133
$215$	3.21077	0.218973
$216$	1.44551	0.0983543
$217$	−3.03915	−0.206311
$218$	13.2561	0.897819
$219$	14.4709	0.977850
$220$	3.54879	0.239259
$221$	−37.9183	−2.55066
$222$	22.6429	1.51969
$223$	9.09232	0.608867	0.304433	−	0.952534i	$-0.401533\pi$
$223$	9.09232	0.608867	0.304433	+	0.952534i	$0.401533\pi$
$224$	−7.67612	−0.512882
$225$	−4.93078	−0.328719
$226$	−40.9525	−2.72412
$227$	9.94532	0.660094	0.330047	−	0.943964i	$-0.392935\pi$
$227$	9.94532	0.660094	0.330047	+	0.943964i	$0.392935\pi$
$228$	−18.7452	−1.24143
$229$	8.11140	0.536016	0.268008	−	0.963417i	$-0.413635\pi$
$229$	8.11140	0.536016	0.268008	+	0.963417i	$0.413635\pi$
$230$	−1.51359	−0.0998031
$231$	−5.05377	−0.332514
$232$	8.13005	0.533764
$233$	−3.44573	−0.225737	−0.112869	−	0.993610i	$-0.536004\pi$
$233$	−3.44573	−0.225737	−0.112869	+	0.993610i	$0.536004\pi$
$234$	−15.1796	−0.992320
$235$	0.0503752	0.00328612
$236$	17.6318	1.14773
$237$	−10.7610	−0.699005
$238$	−11.6630	−0.756001
$239$	−10.1661	−0.657589	−0.328794	−	0.944402i	$-0.606642\pi$
$239$	−10.1661	−0.657589	−0.328794	+	0.944402i	$0.606642\pi$
$240$	−0.582641	−0.0376093
$241$	−11.1907	−0.720856	−0.360428	−	0.932787i	$-0.617369\pi$
$241$	−11.1907	−0.720856	−0.360428	+	0.932787i	$0.617369\pi$
$242$	−31.4190	−2.01969
$243$	−1.00000	−0.0641500
$244$	6.93942	0.444251
$245$	−0.263100	−0.0168088
$246$	−19.5233	−1.24476
$247$	49.3394	3.13939
$248$	−4.39311	−0.278963
$249$	11.1508	0.706651
$250$	−5.64565	−0.357063
$251$	−26.5405	−1.67522	−0.837612	−	0.546266i	$-0.816049\pi$
$251$	−26.5405	−1.67522	−0.837612	+	0.546266i	$0.816049\pi$
$252$	−2.66897	−0.168130
$253$	13.4553	0.845926
$254$	43.2676	2.71485
$255$	−1.42010	−0.0889304
$256$	0.725141	0.0453213
$257$	−14.1802	−0.884538	−0.442269	−	0.896882i	$-0.645826\pi$
$257$	−14.1802	−0.884538	−0.442269	+	0.896882i	$0.645826\pi$
$258$	−26.3694	−1.64168
$259$	−10.4790	−0.651135
$260$	−4.93303	−0.305933
$261$	−5.62436	−0.348139
$262$	−10.1841	−0.629178
$263$	−12.3025	−0.758606	−0.379303	−	0.925273i	$-0.623836\pi$
$263$	−12.3025	−0.758606	−0.379303	+	0.925273i	$0.623836\pi$
$264$	−7.30526	−0.449608
$265$	−2.59480	−0.159397
$266$	15.1760	0.930497
$267$	6.49933	0.397752
$268$	−11.3817	−0.695249
$269$	0.237480	0.0144794	0.00723972	−	0.999974i	$-0.497696\pi$
$269$	0.237480	0.0144794	0.00723972	+	0.999974i	$0.497696\pi$
$270$	−0.568501	−0.0345979
$271$	2.58317	0.156917	0.0784583	−	0.996917i	$-0.475000\pi$
$271$	2.58317	0.156917	0.0784583	+	0.996917i	$0.475000\pi$
$272$	11.9531	0.724763
$273$	7.02504	0.425175
$274$	−45.7309	−2.76270
$275$	24.9190	1.50267
$276$	7.10594	0.427727
$277$	−14.0791	−0.845930	−0.422965	−	0.906146i	$-0.639011\pi$
$277$	−14.0791	−0.845930	−0.422965	+	0.906146i	$0.639011\pi$
$278$	9.42456	0.565248
$279$	3.03915	0.181949
$280$	−0.380312	−0.0227280
$281$	12.0891	0.721174	0.360587	−	0.932726i	$-0.382576\pi$
$281$	12.0891	0.721174	0.360587	+	0.932726i	$0.382576\pi$
$282$	−0.413721	−0.0246367
$283$	23.4871	1.39617	0.698083	−	0.716017i	$-0.254037\pi$
$283$	23.4871	1.39617	0.698083	+	0.716017i	$0.254037\pi$
$284$	29.7926	1.76787
$285$	1.84784	0.109457
$286$	76.7141	4.53620
$287$	9.03528	0.533336
$288$	7.67612	0.452320
$289$	12.1340	0.713763
$290$	−3.19745	−0.187761
$291$	−11.3475	−0.665204
$292$	−38.6223	−2.26020
$293$	23.8479	1.39321	0.696604	−	0.717456i	$-0.254694\pi$
$293$	23.8479	1.39321	0.696604	+	0.717456i	$0.254694\pi$
$294$	2.16078	0.126019
$295$	−1.73809	−0.101196
$296$	−15.1475	−0.880430
$297$	5.05377	0.293249
$298$	14.1995	0.822552
$299$	−18.7036	−1.08166
$300$	13.1601	0.759800
$301$	12.2036	0.703405
$302$	−11.6517	−0.670481
$303$	2.87765	0.165317
$304$	−15.5534	−0.892050
$305$	−0.684067	−0.0391696
$306$	11.6630	0.666730
$307$	−24.1250	−1.37689	−0.688444	−	0.725290i	$-0.741706\pi$
$307$	−24.1250	−1.37689	−0.688444	+	0.725290i	$0.741706\pi$
$308$	13.4884	0.768572
$309$	10.0021	0.568999
$310$	1.72776	0.0981300
$311$	−4.02966	−0.228501	−0.114250	−	0.993452i	$-0.536447\pi$
$311$	−4.02966	−0.228501	−0.114250	+	0.993452i	$0.536447\pi$
$312$	10.1547	0.574899
$313$	−12.4110	−0.701513	−0.350756	−	0.936467i	$-0.614075\pi$
$313$	−12.4110	−0.701513	−0.350756	+	0.936467i	$0.614075\pi$
$314$	38.0787	2.14890
$315$	0.263100	0.0148240
$316$	28.7210	1.61568
$317$	14.6526	0.822974	0.411487	−	0.911416i	$-0.365010\pi$
$317$	14.6526	0.822974	0.411487	+	0.911416i	$0.365010\pi$
$318$	21.3106	1.19504
$319$	28.4242	1.59145
$320$	3.19860	0.178807
$321$	8.53938	0.476622
$322$	−5.75291	−0.320597
$323$	−37.9092	−2.10933
$324$	2.66897	0.148276
$325$	−34.6389	−1.92142
$326$	−30.9100	−1.71194
$327$	6.13488	0.339260
$328$	13.0606	0.721148
$329$	0.191468	0.0105560
$330$	2.87307	0.158157
$331$	17.2603	0.948710	0.474355	−	0.880334i	$-0.342681\pi$
$331$	17.2603	0.948710	0.474355	+	0.880334i	$0.342681\pi$
$332$	−29.7611	−1.63335
$333$	10.4790	0.574247
$334$	−32.0297	−1.75259
$335$	1.12198	0.0613001
$336$	−2.21452	−0.120812
$337$	−14.0128	−0.763324	−0.381662	−	0.924302i	$-0.624648\pi$
$337$	−14.0128	−0.763324	−0.381662	+	0.924302i	$0.624648\pi$
$338$	−78.5470	−4.27239
$339$	−18.9526	−1.02937
$340$	3.79022	0.205554
$341$	−15.3591	−0.831744
$342$	−15.1760	−0.820621
$343$	−1.00000	−0.0539949
$344$	17.6404	0.951108
$345$	−0.700483	−0.0377127
$346$	−6.58876	−0.354214
$347$	7.46837	0.400923	0.200462	−	0.979702i	$-0.435756\pi$
$347$	7.46837	0.400923	0.200462	+	0.979702i	$0.435756\pi$
$348$	15.0113	0.804689
$349$	−27.7314	−1.48443	−0.742215	−	0.670162i	$-0.766225\pi$
$349$	−27.7314	−1.48443	−0.742215	+	0.670162i	$0.766225\pi$
$350$	−10.6543	−0.569498
$351$	−7.02504	−0.374969
$352$	−38.7933	−2.06769
$353$	15.6205	0.831396	0.415698	−	0.909503i	$-0.363537\pi$
$353$	15.6205	0.831396	0.415698	+	0.909503i	$0.363537\pi$
$354$	14.2746	0.758686
$355$	−2.93687	−0.155873
$356$	−17.3465	−0.919365
$357$	−5.39759	−0.285671
$358$	23.2259	1.22753
$359$	−18.4725	−0.974943	−0.487472	−	0.873139i	$-0.662081\pi$
$359$	−18.4725	−0.974943	−0.487472	+	0.873139i	$0.662081\pi$
$360$	0.380312	0.0200442
$361$	30.3276	1.59619
$362$	16.1028	0.846346
$363$	−14.5406	−0.763183
$364$	−18.7497	−0.982749
$365$	3.80728	0.199282
$366$	5.61810	0.293663
$367$	23.9268	1.24897	0.624484	−	0.781037i	$-0.285309\pi$
$367$	23.9268	1.24897	0.624484	+	0.781037i	$0.285309\pi$
$368$	5.89600	0.307350
$369$	−9.03528	−0.470358
$370$	5.95733	0.309707
$371$	−9.86243	−0.512032
$372$	−8.11140	−0.420557
$373$	6.61444	0.342483	0.171241	−	0.985229i	$-0.445222\pi$
$373$	6.61444	0.342483	0.171241	+	0.985229i	$0.445222\pi$
$374$	−58.9422	−3.04783
$375$	−2.61278	−0.134924
$376$	0.276769	0.0142733
$377$	−39.5114	−2.03494
$378$	−2.16078	−0.111139
$379$	2.90357	0.149147	0.0745733	−	0.997216i	$-0.476241\pi$
$379$	2.90357	0.149147	0.0745733	+	0.997216i	$0.476241\pi$
$380$	−4.93185	−0.252999
$381$	20.0241	1.02586
$382$	−3.16990	−0.162186
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−10.9172	−0.557114
$385$	−1.32965	−0.0677650
$386$	16.9077	0.860582
$387$	−12.2036	−0.620345
$388$	30.2863	1.53755
$389$	−15.4811	−0.784925	−0.392463	−	0.919768i	$-0.628377\pi$
$389$	−15.4811	−0.784925	−0.392463	+	0.919768i	$0.628377\pi$
$390$	−3.99374	−0.202231
$391$	14.3707	0.726756
$392$	−1.44551	−0.0730091
$393$	−4.71317	−0.237748
$394$	−25.9063	−1.30514
$395$	−2.83123	−0.142455
$396$	−13.4884	−0.677817
$397$	−27.0972	−1.35997	−0.679985	−	0.733226i	$-0.738014\pi$
$397$	−27.0972	−1.35997	−0.679985	+	0.733226i	$0.738014\pi$
$398$	5.18902	0.260102
$399$	7.02336	0.351608
$400$	10.9193	0.545967
$401$	13.0865	0.653508	0.326754	−	0.945109i	$-0.394045\pi$
$401$	13.0865	0.653508	0.326754	+	0.945109i	$0.394045\pi$
$402$	−9.21455	−0.459580
$403$	21.3501	1.06353
$404$	−7.68037	−0.382113
$405$	−0.263100	−0.0130735
$406$	−12.1530	−0.603144
$407$	−52.9586	−2.62506
$408$	−7.80225	−0.386269
$409$	27.4791	1.35875	0.679376	−	0.733790i	$-0.262251\pi$
$409$	27.4791	1.35875	0.679376	+	0.733790i	$0.262251\pi$
$410$	−5.13656	−0.253677
$411$	−21.1640	−1.04395
$412$	−26.6953	−1.31518
$413$	−6.60622	−0.325071
$414$	5.75291	0.282740
$415$	2.93376	0.144013
$416$	53.9250	2.64389
$417$	4.36165	0.213591
$418$	76.6958	3.75131
$419$	−15.7177	−0.767862	−0.383931	−	0.923362i	$-0.625430\pi$
$419$	−15.7177	−0.767862	−0.383931	+	0.923362i	$0.625430\pi$
$420$	−0.702206	−0.0342642
$421$	−13.8141	−0.673260	−0.336630	−	0.941637i	$-0.609287\pi$
$421$	−13.8141	−0.673260	−0.336630	+	0.941637i	$0.609287\pi$
$422$	35.0690	1.70713
$423$	−0.191468	−0.00930950
$424$	−14.2562	−0.692343
$425$	26.6143	1.29098
$426$	24.1199	1.16861
$427$	−2.60003	−0.125824
$428$	−22.7914	−1.10166
$429$	35.5029	1.71410
$430$	−6.93777	−0.334569
$431$	−2.67445	−0.128824	−0.0644118	−	0.997923i	$-0.520517\pi$
$431$	−2.67445	−0.128824	−0.0644118	+	0.997923i	$0.520517\pi$
$432$	2.21452	0.106546
$433$	18.3156	0.880193	0.440097	−	0.897950i	$-0.354944\pi$
$433$	18.3156	0.880193	0.440097	+	0.897950i	$0.354944\pi$
$434$	6.56693	0.315223
$435$	−1.47977	−0.0709494
$436$	−16.3738	−0.784165
$437$	−18.6992	−0.894503
$438$	−31.2683	−1.49406
$439$	−25.6090	−1.22225	−0.611126	−	0.791534i	$-0.709283\pi$
$439$	−25.6090	−1.22225	−0.611126	+	0.791534i	$0.709283\pi$
$440$	−1.92201	−0.0916283
$441$	1.00000	0.0476190
$442$	81.9331	3.89716
$443$	−23.5228	−1.11760	−0.558801	−	0.829302i	$-0.688738\pi$
$443$	−23.5228	−1.11760	−0.558801	+	0.829302i	$0.688738\pi$
$444$	−27.9682	−1.32731
$445$	1.70997	0.0810604
$446$	−19.6465	−0.930289
$447$	6.57145	0.310819
$448$	12.1574	0.574381
$449$	15.8924	0.750011	0.375005	−	0.927023i	$-0.377641\pi$
$449$	15.8924	0.750011	0.375005	+	0.927023i	$0.377641\pi$
$450$	10.6543	0.502250
$451$	45.6622	2.15015
$452$	50.5841	2.37927
$453$	−5.39237	−0.253355
$454$	−21.4897	−1.00856
$455$	1.84829	0.0866490
$456$	10.1523	0.475426
$457$	14.5379	0.680055	0.340027	−	0.940416i	$-0.389564\pi$
$457$	14.5379	0.680055	0.340027	+	0.940416i	$0.389564\pi$
$458$	−17.5270	−0.818981
$459$	5.39759	0.251938
$460$	1.86957	0.0871692
$461$	16.7996	0.782437	0.391219	−	0.920298i	$-0.372054\pi$
$461$	16.7996	0.782437	0.391219	+	0.920298i	$0.372054\pi$
$462$	10.9201	0.508049
$463$	10.2941	0.478408	0.239204	−	0.970969i	$-0.423114\pi$
$463$	10.2941	0.478408	0.239204	+	0.970969i	$0.423114\pi$
$464$	12.4553	0.578222
$465$	0.799598	0.0370805
$466$	7.44547	0.344905
$467$	42.5325	1.96817	0.984084	−	0.177702i	$-0.0568662\pi$
$467$	42.5325	1.96817	0.984084	+	0.177702i	$0.0568662\pi$
$468$	18.7497	0.866703
$469$	4.26445	0.196914
$470$	−0.108850	−0.00502087
$471$	17.6226	0.812008
$472$	−9.54934	−0.439544
$473$	61.6743	2.83579
$474$	23.2523	1.06801
$475$	−34.6307	−1.58896
$476$	14.4060	0.660299
$477$	9.86243	0.451570
$478$	21.9667	1.00473
$479$	−26.1884	−1.19658	−0.598290	−	0.801280i	$-0.704153\pi$
$479$	−26.1884	−1.19658	−0.598290	+	0.801280i	$0.704153\pi$
$480$	2.01958	0.0921810
$481$	73.6155	3.35658
$482$	24.1806	1.10140
$483$	−2.66242	−0.121144
$484$	38.8085	1.76402
$485$	−2.98553	−0.135566
$486$	2.16078	0.0980150
$487$	−31.1075	−1.40962	−0.704808	−	0.709398i	$-0.748967\pi$
$487$	−31.1075	−1.40962	−0.704808	+	0.709398i	$0.748967\pi$
$488$	−3.75836	−0.170133
$489$	−14.3050	−0.646894
$490$	0.568501	0.0256822
$491$	1.05946	0.0478127	0.0239064	−	0.999714i	$-0.492390\pi$
$491$	1.05946	0.0478127	0.0239064	+	0.999714i	$0.492390\pi$
$492$	24.1149	1.08718
$493$	30.3580	1.36726
$494$	−106.612	−4.79669
$495$	1.32965	0.0597631
$496$	−6.73027	−0.302198
$497$	−11.1626	−0.500710
$498$	−24.0944	−1.07969
$499$	40.4493	1.81076	0.905380	−	0.424603i	$-0.139586\pi$
$499$	40.4493	1.81076	0.905380	+	0.424603i	$0.139586\pi$
$500$	6.97345	0.311862
$501$	−14.8232	−0.662251
$502$	57.3483	2.55958
$503$	−15.0416	−0.670672	−0.335336	−	0.942099i	$-0.608850\pi$
$503$	−15.0416	−0.670672	−0.335336	+	0.942099i	$0.608850\pi$
$504$	1.44551	0.0643880
$505$	0.757109	0.0336909
$506$	−29.0739	−1.29249
$507$	−36.3512	−1.61441
$508$	−53.4437	−2.37118
$509$	−41.7905	−1.85233	−0.926166	−	0.377117i	$-0.876915\pi$
$509$	−41.7905	−1.85233	−0.926166	+	0.377117i	$0.876915\pi$
$510$	3.06853	0.135877
$511$	14.4709	0.640153
$512$	−23.4012	−1.03420
$513$	−7.02336	−0.310089
$514$	30.6404	1.35149
$515$	2.63155	0.115960
$516$	32.5712	1.43387
$517$	0.967636	0.0425566
$518$	22.6429	0.994870
$519$	−3.04925	−0.133847
$520$	2.67171	0.117162
$521$	11.7346	0.514103	0.257052	−	0.966398i	$-0.417249\pi$
$521$	11.7346	0.514103	0.257052	+	0.966398i	$0.417249\pi$
$522$	12.1530	0.531923
$523$	−23.2485	−1.01658	−0.508292	−	0.861185i	$-0.669723\pi$
$523$	−23.2485	−1.01658	−0.508292	+	0.861185i	$0.669723\pi$
$524$	12.5793	0.549531
$525$	−4.93078	−0.215197
$526$	26.5830	1.15908
$527$	−16.4041	−0.714572
$528$	−11.1917	−0.487056
$529$	−15.9115	−0.691804
$530$	5.60680	0.243544
$531$	6.60622	0.286686
$532$	−18.7452	−0.812707
$533$	−63.4732	−2.74933
$534$	−14.0436	−0.607727
$535$	2.24671	0.0971337
$536$	6.16430	0.266257
$537$	10.7489	0.463848
$538$	−0.513143	−0.0221232
$539$	−5.05377	−0.217681
$540$	0.702206	0.0302181
$541$	35.4292	1.52322	0.761609	−	0.648036i	$-0.224409\pi$
$541$	35.4292	1.52322	0.761609	+	0.648036i	$0.224409\pi$
$542$	−5.58167	−0.239753
$543$	7.45232	0.319810
$544$	−41.4325	−1.77641
$545$	1.61409	0.0691398
$546$	−15.1796	−0.649626
$547$	−42.3203	−1.80949	−0.904743	−	0.425958i	$-0.859937\pi$
$547$	−42.3203	−1.80949	−0.904743	+	0.425958i	$0.859937\pi$
$548$	56.4863	2.41297
$549$	2.60003	0.110967
$550$	−53.8445	−2.29594
$551$	−39.5019	−1.68284
$552$	−3.84855	−0.163805
$553$	−10.7610	−0.457606
$554$	30.4218	1.29250
$555$	2.75703	0.117029
$556$	−11.6411	−0.493693
$557$	5.09890	0.216047	0.108024	−	0.994148i	$-0.465548\pi$
$557$	5.09890	0.216047	0.108024	+	0.994148i	$0.465548\pi$
$558$	−6.56693	−0.278000
$559$	−85.7309	−3.62603
$560$	−0.582641	−0.0246211
$561$	−27.2782	−1.15169
$562$	−26.1219	−1.10188
$563$	14.4883	0.610610	0.305305	−	0.952255i	$-0.401242\pi$
$563$	14.4883	0.610610	0.305305	+	0.952255i	$0.401242\pi$
$564$	0.511024	0.0215180
$565$	−4.98643	−0.209781
$566$	−50.7505	−2.13320
$567$	−1.00000	−0.0419961
$568$	−16.1356	−0.677034
$569$	45.7581	1.91828	0.959139	−	0.282936i	$-0.0913084\pi$
$569$	45.7581	1.91828	0.959139	+	0.282936i	$0.0913084\pi$
$570$	−3.99279	−0.167239
$571$	−14.4083	−0.602969	−0.301484	−	0.953471i	$-0.597482\pi$
$571$	−14.4083	−0.602969	−0.301484	+	0.953471i	$0.597482\pi$
$572$	−94.7564	−3.96196
$573$	−1.46702	−0.0612856
$574$	−19.5233	−0.814885
$575$	13.1278	0.547468
$576$	−12.1574	−0.506557
$577$	32.7013	1.36137	0.680686	−	0.732575i	$-0.261682\pi$
$577$	32.7013	1.36137	0.680686	+	0.732575i	$0.261682\pi$
$578$	−26.2189	−1.09056
$579$	7.82483	0.325189
$580$	3.94946	0.163992
$581$	11.1508	0.462612
$582$	24.5195	1.01637
$583$	−49.8425	−2.06426
$584$	20.9177	0.865581
$585$	−1.84829	−0.0764172
$586$	−51.5300	−2.12869
$587$	30.3319	1.25193	0.625966	−	0.779850i	$-0.284705\pi$
$587$	30.3319	1.25193	0.625966	+	0.779850i	$0.284705\pi$
$588$	−2.66897	−0.110067
$589$	21.3450	0.879507
$590$	3.75564	0.154617
$591$	−11.9893	−0.493175
$592$	−23.2061	−0.953763
$593$	20.6304	0.847188	0.423594	−	0.905852i	$-0.360768\pi$
$593$	20.6304	0.847188	0.423594	+	0.905852i	$0.360768\pi$
$594$	−10.9201	−0.448057
$595$	−1.42010	−0.0582186
$596$	−17.5390	−0.718426
$597$	2.40146	0.0982850
$598$	40.4144	1.65267
$599$	8.04973	0.328903	0.164452	−	0.986385i	$-0.447415\pi$
$599$	8.04973	0.328903	0.164452	+	0.986385i	$0.447415\pi$
$600$	−7.12747	−0.290978
$601$	1.10313	0.0449977	0.0224988	−	0.999747i	$-0.492838\pi$
$601$	1.10313	0.0449977	0.0224988	+	0.999747i	$0.492838\pi$
$602$	−26.3694	−1.07473
$603$	−4.26445	−0.173662
$604$	14.3921	0.585606
$605$	−3.82562	−0.155534
$606$	−6.21797	−0.252588
$607$	37.0956	1.50566	0.752832	−	0.658213i	$-0.228687\pi$
$607$	37.0956	1.50566	0.752832	+	0.658213i	$0.228687\pi$
$608$	53.9122	2.18643
$609$	−5.62436	−0.227911
$610$	1.47812	0.0598473
$611$	−1.34507	−0.0544158
$612$	−14.4060	−0.582329
$613$	21.7943	0.880263	0.440132	−	0.897933i	$-0.354932\pi$
$613$	21.7943	0.880263	0.440132	+	0.897933i	$0.354932\pi$
$614$	52.1289	2.10375
$615$	−2.37718	−0.0958571
$616$	−7.30526	−0.294337
$617$	5.26138	0.211815	0.105908	−	0.994376i	$-0.466225\pi$
$617$	5.26138	0.211815	0.105908	+	0.994376i	$0.466225\pi$
$618$	−21.6123	−0.869375
$619$	2.61709	0.105190	0.0525949	−	0.998616i	$-0.483251\pi$
$619$	2.61709	0.105190	0.0525949	+	0.998616i	$0.483251\pi$
$620$	−2.13411	−0.0857078
$621$	2.66242	0.106839
$622$	8.70721	0.349127
$623$	6.49933	0.260390
$624$	15.5571	0.622783
$625$	23.9665	0.958659
$626$	26.8175	1.07184
$627$	35.4945	1.41751
$628$	−47.0344	−1.87688
$629$	−56.5615	−2.25525
$630$	−0.568501	−0.0226496
$631$	23.6800	0.942687	0.471344	−	0.881950i	$-0.343769\pi$
$631$	23.6800	0.942687	0.471344	+	0.881950i	$0.343769\pi$
$632$	−15.5552	−0.618751
$633$	16.2298	0.645076
$634$	−31.6611	−1.25742
$635$	5.26832	0.209067
$636$	−26.3226	−1.04376
$637$	7.02504	0.278342
$638$	−61.4185	−2.43158
$639$	11.1626	0.441585
$640$	−2.87230	−0.113538
$641$	6.25193	0.246937	0.123468	−	0.992349i	$-0.460598\pi$
$641$	6.25193	0.246937	0.123468	+	0.992349i	$0.460598\pi$
$642$	−18.4517	−0.728232
$643$	−11.2840	−0.444998	−0.222499	−	0.974933i	$-0.571421\pi$
$643$	−11.2840	−0.444998	−0.222499	+	0.974933i	$0.571421\pi$
$644$	7.10594	0.280013
$645$	−3.21077	−0.126424
$646$	81.9136	3.22285
$647$	−26.0847	−1.02549	−0.512747	−	0.858540i	$-0.671372\pi$
$647$	−26.0847	−1.02549	−0.512747	+	0.858540i	$0.671372\pi$
$648$	−1.44551	−0.0567849
$649$	−33.3863	−1.31053
$650$	74.8471	2.93575
$651$	3.03915	0.119114
$652$	38.1797	1.49523
$653$	28.8780	1.13009	0.565043	−	0.825062i	$-0.308860\pi$
$653$	28.8780	1.13009	0.565043	+	0.825062i	$0.308860\pi$
$654$	−13.2561	−0.518356
$655$	−1.24003	−0.0484522
$656$	20.0088	0.781214
$657$	−14.4709	−0.564562
$658$	−0.413721	−0.0161285
$659$	−25.0449	−0.975610	−0.487805	−	0.872953i	$-0.662202\pi$
$659$	−25.0449	−0.975610	−0.487805	+	0.872953i	$0.662202\pi$
$660$	−3.54879	−0.138136
$661$	22.6502	0.880992	0.440496	−	0.897755i	$-0.354803\pi$
$661$	22.6502	0.880992	0.440496	+	0.897755i	$0.354803\pi$
$662$	−37.2957	−1.44954
$663$	37.9183	1.47262
$664$	16.1185	0.625519
$665$	1.84784	0.0716563
$666$	−22.6429	−0.877393
$667$	14.9744	0.579812
$668$	39.5627	1.53073
$669$	−9.09232	−0.351529
$670$	−2.42434	−0.0936606
$671$	−13.1400	−0.507263
$672$	7.67612	0.296113
$673$	29.2387	1.12707	0.563535	−	0.826092i	$-0.309441\pi$
$673$	29.2387	1.12707	0.563535	+	0.826092i	$0.309441\pi$
$674$	30.2785	1.16628
$675$	4.93078	0.189786
$676$	97.0204	3.73155
$677$	34.7944	1.33726	0.668629	−	0.743596i	$-0.266881\pi$
$677$	34.7944	1.33726	0.668629	+	0.743596i	$0.266881\pi$
$678$	40.9525	1.57277
$679$	−11.3475	−0.435478
$680$	−2.05277	−0.0787201
$681$	−9.94532	−0.381106
$682$	33.1878	1.27082
$683$	−11.4391	−0.437703	−0.218852	−	0.975758i	$-0.570231\pi$
$683$	−11.4391	−0.437703	−0.218852	+	0.975758i	$0.570231\pi$
$684$	18.7452	0.716740
$685$	−5.56825	−0.212752
$686$	2.16078	0.0824990
$687$	−8.11140	−0.309469
$688$	27.0252	1.03033
$689$	69.2840	2.63951
$690$	1.51359	0.0576214
$691$	32.8594	1.25003	0.625015	−	0.780613i	$-0.285093\pi$
$691$	32.8594	1.25003	0.625015	+	0.780613i	$0.285093\pi$
$692$	8.13837	0.309374
$693$	5.05377	0.191977
$694$	−16.1375	−0.612572
$695$	1.14755	0.0435290
$696$	−8.13005	−0.308169
$697$	48.7687	1.84725
$698$	59.9216	2.26807
$699$	3.44573	0.130330
$700$	13.1601	0.497406
$701$	30.9550	1.16915	0.584577	−	0.811338i	$-0.301260\pi$
$701$	30.9550	1.16915	0.584577	+	0.811338i	$0.301260\pi$
$702$	15.1796	0.572916
$703$	73.5980	2.77580
$704$	61.4405	2.31563
$705$	−0.0503752	−0.00189724
$706$	−33.7525	−1.27029
$707$	2.87765	0.108225
$708$	−17.6318	−0.662645
$709$	0.762355	0.0286308	0.0143154	−	0.999898i	$-0.495443\pi$
$709$	0.762355	0.0286308	0.0143154	+	0.999898i	$0.495443\pi$
$710$	6.34593	0.238159
$711$	10.7610	0.403571
$712$	9.39482	0.352086
$713$	−8.09150	−0.303029
$714$	11.6630	0.436477
$715$	9.34081	0.349326
$716$	−28.6884	−1.07214
$717$	10.1661	0.379659
$718$	39.9151	1.48962
$719$	−23.7330	−0.885092	−0.442546	−	0.896746i	$-0.645925\pi$
$719$	−23.7330	−0.885092	−0.442546	+	0.896746i	$0.645925\pi$
$720$	0.582641	0.0217137
$721$	10.0021	0.372497
$722$	−65.5314	−2.43883
$723$	11.1907	0.416186
$724$	−19.8900	−0.739208
$725$	27.7325	1.02996
$726$	31.4190	1.16607
$727$	28.9645	1.07423	0.537117	−	0.843508i	$-0.319513\pi$
$727$	28.9645	1.07423	0.537117	+	0.843508i	$0.319513\pi$
$728$	10.1547	0.376360
$729$	1.00000	0.0370370
$730$	−8.22669	−0.304483
$731$	65.8702	2.43630
$732$	−6.93942	−0.256488
$733$	21.0341	0.776913	0.388457	−	0.921467i	$-0.373008\pi$
$733$	21.0341	0.776913	0.388457	+	0.921467i	$0.373008\pi$
$734$	−51.7006	−1.90830
$735$	0.263100	0.00970458
$736$	−20.4371	−0.753321
$737$	21.5516	0.793862
$738$	19.5233	0.718661
$739$	0.498596	0.0183412	0.00917058	−	0.999958i	$-0.497081\pi$
$739$	0.498596	0.0183412	0.00917058	+	0.999958i	$0.497081\pi$
$740$	−7.35843	−0.270501
$741$	−49.3394	−1.81253
$742$	21.3106	0.782335
$743$	2.74403	0.100669	0.0503343	−	0.998732i	$-0.483971\pi$
$743$	2.74403	0.100669	0.0503343	+	0.998732i	$0.483971\pi$
$744$	4.39311	0.161059
$745$	1.72895	0.0633436
$746$	−14.2924	−0.523280
$747$	−11.1508	−0.407985
$748$	72.8048	2.66201
$749$	8.53938	0.312022
$750$	5.64565	0.206150
$751$	6.25828	0.228368	0.114184	−	0.993460i	$-0.463575\pi$
$751$	6.25828	0.228368	0.114184	+	0.993460i	$0.463575\pi$
$752$	0.424011	0.0154621
$753$	26.5405	0.967191
$754$	85.3754	3.10919
$755$	−1.41873	−0.0516329
$756$	2.66897	0.0970697
$757$	50.2488	1.82632	0.913161	−	0.407598i	$-0.133634\pi$
$757$	50.2488	1.82632	0.913161	+	0.407598i	$0.133634\pi$
$758$	−6.27399	−0.227881
$759$	−13.4553	−0.488396
$760$	2.67107	0.0968900
$761$	49.6054	1.79819	0.899097	−	0.437749i	$-0.144224\pi$
$761$	49.6054	1.79819	0.899097	+	0.437749i	$0.144224\pi$
$762$	−43.2676	−1.56742
$763$	6.13488	0.222098
$764$	3.91543	0.141655
$765$	1.42010	0.0513440
$766$	−2.16078	−0.0780722
$767$	46.4090	1.67573
$768$	−0.725141	−0.0261663
$769$	9.16052	0.330337	0.165168	−	0.986265i	$-0.447183\pi$
$769$	9.16052	0.330337	0.165168	+	0.986265i	$0.447183\pi$
$770$	2.87307	0.103538
$771$	14.1802	0.510688
$772$	−20.8843	−0.751642
$773$	44.9574	1.61700	0.808502	−	0.588493i	$-0.200279\pi$
$773$	44.9574	1.61700	0.808502	+	0.588493i	$0.200279\pi$
$774$	26.3694	0.947827
$775$	−14.9854	−0.538290
$776$	−16.4029	−0.588831
$777$	10.4790	0.375933
$778$	33.4514	1.19929
$779$	−63.4580	−2.27362
$780$	4.93303	0.176631
$781$	−56.4131	−2.01862
$782$	−31.0519	−1.11041
$783$	5.62436	0.200998
$784$	−2.21452	−0.0790902
$785$	4.63651	0.165484
$786$	10.1841	0.363256
$787$	−20.0640	−0.715205	−0.357603	−	0.933874i	$-0.616406\pi$
$787$	−20.0640	−0.715205	−0.357603	+	0.933874i	$0.616406\pi$
$788$	31.9992	1.13992
$789$	12.3025	0.437981
$790$	6.11766	0.217657
$791$	−18.9526	−0.673878
$792$	7.30526	0.259581
$793$	18.2653	0.648621
$794$	58.5512	2.07790
$795$	2.59480	0.0920282
$796$	−6.40942	−0.227176
$797$	−20.4608	−0.724757	−0.362379	−	0.932031i	$-0.618035\pi$
$797$	−20.4608	−0.724757	−0.362379	+	0.932031i	$0.618035\pi$
$798$	−15.1760	−0.537223
$799$	1.03347	0.0365614
$800$	−37.8492	−1.33817
$801$	−6.49933	−0.229642
$802$	−28.2770	−0.998497
$803$	73.1324	2.58078
$804$	11.3817	0.401402
$805$	−0.700483	−0.0246888
$806$	−46.1329	−1.62496
$807$	−0.237480	−0.00835971
$808$	4.15966	0.146336
$809$	−34.3751	−1.20856	−0.604282	−	0.796770i	$-0.706540\pi$
$809$	−34.3751	−1.20856	−0.604282	+	0.796770i	$0.706540\pi$
$810$	0.568501	0.0199751
$811$	21.9025	0.769102	0.384551	−	0.923104i	$-0.374356\pi$
$811$	21.9025	0.769102	0.384551	+	0.923104i	$0.374356\pi$
$812$	15.0113	0.526793
$813$	−2.58317	−0.0905958
$814$	114.432	4.01083
$815$	−3.76364	−0.131835
$816$	−11.9531	−0.418442
$817$	−85.7105	−2.99863
$818$	−59.3762	−2.07604
$819$	−7.02504	−0.245475
$820$	6.34463	0.221564
$821$	−19.0450	−0.664675	−0.332337	−	0.943161i	$-0.607837\pi$
$821$	−19.0450	−0.664675	−0.332337	+	0.943161i	$0.607837\pi$
$822$	45.7309	1.59505
$823$	12.6360	0.440463	0.220232	−	0.975448i	$-0.429319\pi$
$823$	12.6360	0.440463	0.220232	+	0.975448i	$0.429319\pi$
$824$	14.4581	0.503671
$825$	−24.9190	−0.867569
$826$	14.2746	0.496677
$827$	44.2088	1.53729	0.768645	−	0.639676i	$-0.220931\pi$
$827$	44.2088	1.53729	0.768645	+	0.639676i	$0.220931\pi$
$828$	−7.10594	−0.246948
$829$	23.1231	0.803098	0.401549	−	0.915838i	$-0.368472\pi$
$829$	23.1231	0.803098	0.401549	+	0.915838i	$0.368472\pi$
$830$	−6.33922	−0.220037
$831$	14.0791	0.488398
$832$	−85.4059	−2.96092
$833$	−5.39759	−0.187015
$834$	−9.42456	−0.326346
$835$	−3.89998	−0.134964
$836$	−94.7338	−3.27644
$837$	−3.03915	−0.105048
$838$	33.9626	1.17322
$839$	34.1555	1.17918	0.589589	−	0.807704i	$-0.299290\pi$
$839$	34.1555	1.17918	0.589589	+	0.807704i	$0.299290\pi$
$840$	0.380312	0.0131220
$841$	2.63344	0.0908083
$842$	29.8493	1.02868
$843$	−12.0891	−0.416370
$844$	−43.3168	−1.49103
$845$	−9.56398	−0.329011
$846$	0.413721	0.0142240
$847$	−14.5406	−0.499621
$848$	−21.8406	−0.750009
$849$	−23.4871	−0.806076
$850$	−57.5077	−1.97250
$851$	−27.8996	−0.956386
$852$	−29.7926	−1.02068
$853$	−5.96220	−0.204142	−0.102071	−	0.994777i	$-0.532547\pi$
$853$	−5.96220	−0.204142	−0.102071	+	0.994777i	$0.532547\pi$
$854$	5.61810	0.192247
$855$	−1.84784	−0.0631949
$856$	12.3437	0.421900
$857$	19.8748	0.678911	0.339455	−	0.940622i	$-0.389757\pi$
$857$	19.8748	0.678911	0.339455	+	0.940622i	$0.389757\pi$
$858$	−76.7141	−2.61898
$859$	18.6203	0.635315	0.317657	−	0.948206i	$-0.397104\pi$
$859$	18.6203	0.635315	0.317657	+	0.948206i	$0.397104\pi$
$860$	8.56946	0.292216
$861$	−9.03528	−0.307921
$862$	5.77890	0.196830
$863$	38.8098	1.32110	0.660551	−	0.750781i	$-0.270323\pi$
$863$	38.8098	1.32110	0.660551	+	0.750781i	$0.270323\pi$
$864$	−7.67612	−0.261147
$865$	−0.802257	−0.0272775
$866$	−39.5761	−1.34485
$867$	−12.1340	−0.412091
$868$	−8.11140	−0.275319
$869$	−54.3839	−1.84485
$870$	3.19745	0.108404
$871$	−29.9580	−1.01509
$872$	8.86802	0.300309
$873$	11.3475	0.384056
$874$	40.4048	1.36671
$875$	−2.61278	−0.0883282
$876$	38.6223	1.30493
$877$	40.8024	1.37780	0.688899	−	0.724857i	$-0.258094\pi$
$877$	40.8024	1.37780	0.688899	+	0.724857i	$0.258094\pi$
$878$	55.3355	1.86748
$879$	−23.8479	−0.804369
$880$	−2.94453	−0.0992602
$881$	−37.9916	−1.27997	−0.639984	−	0.768388i	$-0.721059\pi$
$881$	−37.9916	−1.27997	−0.639984	+	0.768388i	$0.721059\pi$
$882$	−2.16078	−0.0727573
$883$	20.7258	0.697480	0.348740	−	0.937220i	$-0.386610\pi$
$883$	20.7258	0.697480	0.348740	+	0.937220i	$0.386610\pi$
$884$	−101.203	−3.40382
$885$	1.73809	0.0584254
$886$	50.8276	1.70759
$887$	−8.90787	−0.299097	−0.149548	−	0.988754i	$-0.547782\pi$
$887$	−8.90787	−0.299097	−0.149548	+	0.988754i	$0.547782\pi$
$888$	15.1475	0.508317
$889$	20.0241	0.671585
$890$	−3.69487	−0.123852
$891$	−5.05377	−0.169308
$892$	24.2672	0.812525
$893$	−1.34475	−0.0450004
$894$	−14.1995	−0.474901
$895$	2.82802	0.0945304
$896$	−10.9172	−0.364716
$897$	18.7036	0.624496
$898$	−34.3401	−1.14594
$899$	−17.0933	−0.570092
$900$	−13.1601	−0.438671
$901$	−53.2334	−1.77346
$902$	−98.6660	−3.28522
$903$	−12.2036	−0.406111
$904$	−27.3962	−0.911183
$905$	1.96070	0.0651759
$906$	11.6517	0.387103
$907$	36.3897	1.20830	0.604149	−	0.796871i	$-0.293513\pi$
$907$	36.3897	1.20830	0.604149	+	0.796871i	$0.293513\pi$
$908$	26.5438	0.880887
$909$	−2.87765	−0.0954456
$910$	−3.99374	−0.132391
$911$	9.70497	0.321540	0.160770	−	0.986992i	$-0.448602\pi$
$911$	9.70497	0.321540	0.160770	+	0.986992i	$0.448602\pi$
$912$	15.5534	0.515025
$913$	56.3534	1.86503
$914$	−31.4132	−1.03906
$915$	0.684067	0.0226146
$916$	21.6491	0.715307
$917$	−4.71317	−0.155643
$918$	−11.6630	−0.384937
$919$	−30.7792	−1.01531	−0.507656	−	0.861560i	$-0.669488\pi$
$919$	−30.7792	−1.01531	−0.507656	+	0.861560i	$0.669488\pi$
$920$	−1.01255	−0.0333829
$921$	24.1250	0.794946
$922$	−36.3003	−1.19549
$923$	78.4176	2.58115
$924$	−13.4884	−0.443735
$925$	−51.6697	−1.69889
$926$	−22.2433	−0.730960
$927$	−10.0021	−0.328512
$928$	−43.1733	−1.41723
$929$	47.2238	1.54936	0.774681	−	0.632352i	$-0.217910\pi$
$929$	47.2238	1.54936	0.774681	+	0.632352i	$0.217910\pi$
$930$	−1.72776	−0.0566554
$931$	7.02336	0.230181
$932$	−9.19657	−0.301244
$933$	4.02966	0.131925
$934$	−91.9034	−3.00717
$935$	−7.17688	−0.234709
$936$	−10.1547	−0.331918
$937$	51.5502	1.68407	0.842035	−	0.539422i	$-0.181357\pi$
$937$	51.5502	1.68407	0.842035	+	0.539422i	$0.181357\pi$
$938$	−9.21455	−0.300866
$939$	12.4110	0.405019
$940$	0.134450	0.00438528
$941$	−0.486624	−0.0158635	−0.00793175	−	0.999969i	$-0.502525\pi$
$941$	−0.486624	−0.0158635	−0.00793175	+	0.999969i	$0.502525\pi$
$942$	−38.0787	−1.24067
$943$	24.0557	0.783362
$944$	−14.6296	−0.476154
$945$	−0.263100	−0.00855863
$946$	−133.265	−4.33281
$947$	−4.08503	−0.132746	−0.0663728	−	0.997795i	$-0.521143\pi$
$947$	−4.08503	−0.132746	−0.0663728	+	0.997795i	$0.521143\pi$
$948$	−28.7210	−0.932813
$949$	−101.658	−3.29997
$950$	74.8293	2.42778
$951$	−14.6526	−0.475144
$952$	−7.80225	−0.252872
$953$	38.9993	1.26331	0.631655	−	0.775249i	$-0.282376\pi$
$953$	38.9993	1.26331	0.631655	+	0.775249i	$0.282376\pi$
$954$	−21.3106	−0.689955
$955$	−0.385972	−0.0124898
$956$	−27.1330	−0.877544
$957$	−28.4242	−0.918825
$958$	56.5875	1.82826
$959$	−21.1640	−0.683423
$960$	−3.19860	−0.103234
$961$	−21.7636	−0.702051
$962$	−159.067	−5.12853
$963$	−8.53938	−0.275178
$964$	−29.8677	−0.961973
$965$	2.05871	0.0662722
$966$	5.75291	0.185097
$967$	−14.2384	−0.457875	−0.228938	−	0.973441i	$-0.573525\pi$
$967$	−14.2384	−0.457875	−0.228938	+	0.973441i	$0.573525\pi$
$968$	−21.0185	−0.675561
$969$	37.9092	1.21782
$970$	6.45108	0.207132
$971$	14.4765	0.464574	0.232287	−	0.972647i	$-0.425379\pi$
$971$	14.4765	0.464574	0.232287	+	0.972647i	$0.425379\pi$
$972$	−2.66897	−0.0856074
$973$	4.36165	0.139828
$974$	67.2165	2.15376
$975$	34.6389	1.10933
$976$	−5.75783	−0.184304
$977$	16.3976	0.524606	0.262303	−	0.964986i	$-0.415518\pi$
$977$	16.3976	0.524606	0.262303	+	0.964986i	$0.415518\pi$
$978$	30.9100	0.988392
$979$	32.8461	1.04977
$980$	−0.702206	−0.0224312
$981$	−6.13488	−0.195872
$982$	−2.28926	−0.0730532
$983$	30.2302	0.964194	0.482097	−	0.876118i	$-0.339875\pi$
$983$	30.2302	0.964194	0.482097	+	0.876118i	$0.339875\pi$
$984$	−13.0606	−0.416355
$985$	−3.15439	−0.100507
$986$	−65.5970	−2.08903
$987$	−0.191468	−0.00609450
$988$	131.686	4.18948
$989$	32.4912	1.03316
$990$	−2.87307	−0.0913122
$991$	−23.1234	−0.734538	−0.367269	−	0.930115i	$-0.619707\pi$
$991$	−23.1234	−0.734538	−0.367269	+	0.930115i	$0.619707\pi$
$992$	23.3288	0.740692
$993$	−17.2603	−0.547738
$994$	24.1199	0.765036
$995$	0.631822	0.0200301
$996$	29.7611	0.943017
$997$	−44.9672	−1.42413	−0.712063	−	0.702116i	$-0.752239\pi$
$997$	−44.9672	−1.42413	−0.712063	+	0.702116i	$0.752239\pi$
$998$	−87.4021	−2.76666
$999$	−10.4790	−0.331542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.9	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.16078 q^{2} -1.00000 q^{3} +2.66897 q^{4} -0.263100 q^{5} +2.16078 q^{6} -1.00000 q^{7} -1.44551 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16078 q^{2} -1.00000 q^{3} +2.66897 q^{4} -0.263100 q^{5} +2.16078 q^{6} -1.00000 q^{7} -1.44551 q^{8} +1.00000 q^{9} +0.568501 q^{10} -5.05377 q^{11} -2.66897 q^{12} +7.02504 q^{13} +2.16078 q^{14} +0.263100 q^{15} -2.21452 q^{16} -5.39759 q^{17} -2.16078 q^{18} +7.02336 q^{19} -0.702206 q^{20} +1.00000 q^{21} +10.9201 q^{22} -2.66242 q^{23} +1.44551 q^{24} -4.93078 q^{25} -15.1796 q^{26} -1.00000 q^{27} -2.66897 q^{28} -5.62436 q^{29} -0.568501 q^{30} +3.03915 q^{31} +7.67612 q^{32} +5.05377 q^{33} +11.6630 q^{34} +0.263100 q^{35} +2.66897 q^{36} +10.4790 q^{37} -15.1760 q^{38} -7.02504 q^{39} +0.380312 q^{40} -9.03528 q^{41} -2.16078 q^{42} -12.2036 q^{43} -13.4884 q^{44} -0.263100 q^{45} +5.75291 q^{46} -0.191468 q^{47} +2.21452 q^{48} +1.00000 q^{49} +10.6543 q^{50} +5.39759 q^{51} +18.7497 q^{52} +9.86243 q^{53} +2.16078 q^{54} +1.32965 q^{55} +1.44551 q^{56} -7.02336 q^{57} +12.1530 q^{58} +6.60622 q^{59} +0.702206 q^{60} +2.60003 q^{61} -6.56693 q^{62} -1.00000 q^{63} -12.1574 q^{64} -1.84829 q^{65} -10.9201 q^{66} -4.26445 q^{67} -14.4060 q^{68} +2.66242 q^{69} -0.568501 q^{70} +11.1626 q^{71} -1.44551 q^{72} -14.4709 q^{73} -22.6429 q^{74} +4.93078 q^{75} +18.7452 q^{76} +5.05377 q^{77} +15.1796 q^{78} +10.7610 q^{79} +0.582641 q^{80} +1.00000 q^{81} +19.5233 q^{82} -11.1508 q^{83} +2.66897 q^{84} +1.42010 q^{85} +26.3694 q^{86} +5.62436 q^{87} +7.30526 q^{88} -6.49933 q^{89} +0.568501 q^{90} -7.02504 q^{91} -7.10594 q^{92} -3.03915 q^{93} +0.413721 q^{94} -1.84784 q^{95} -7.67612 q^{96} +11.3475 q^{97} -2.16078 q^{98} -5.05377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 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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